LMFDB - Embedded newform 138.8.a.h.1.1

Newspace parameters

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	138.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$43.1091335168$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
Defining polynomial:	$ x^{4} - 2x^{3} - 8367x^{2} - 89140x + 11077220 $ x^4 - 2x^3 - 8367x^2 - 89140*x + 11077220
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$33.2734$ of defining polynomial
Character	$\chi$	$=$	138.1

$q$-expansion

$f(q)$	$=$	$q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -427.795 q^{5} +216.000 q^{6} +345.429 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -427.795 q^{5} +216.000 q^{6} +345.429 q^{7} +512.000 q^{8} +729.000 q^{9} -3422.36 q^{10} +2181.54 q^{11} +1728.00 q^{12} -2610.39 q^{13} +2763.43 q^{14} -11550.5 q^{15} +4096.00 q^{16} +37979.0 q^{17} +5832.00 q^{18} -26348.1 q^{19} -27378.9 q^{20} +9326.57 q^{21} +17452.3 q^{22} -12167.0 q^{23} +13824.0 q^{24} +104884. q^{25} -20883.1 q^{26} +19683.0 q^{27} +22107.4 q^{28} +250851. q^{29} -92403.8 q^{30} +179145. q^{31} +32768.0 q^{32} +58901.7 q^{33} +303832. q^{34} -147773. q^{35} +46656.0 q^{36} +434281. q^{37} -210785. q^{38} -70480.6 q^{39} -219031. q^{40} -200429. q^{41} +74612.6 q^{42} +841346. q^{43} +139619. q^{44} -311863. q^{45} -97336.0 q^{46} -200025. q^{47} +110592. q^{48} -704222. q^{49} +839072. q^{50} +1.02543e6 q^{51} -167065. q^{52} -1.62417e6 q^{53} +157464. q^{54} -933254. q^{55} +176859. q^{56} -711399. q^{57} +2.00681e6 q^{58} -2.18662e6 q^{59} -739231. q^{60} +2.54771e6 q^{61} +1.43316e6 q^{62} +251817. q^{63} +262144. q^{64} +1.11671e6 q^{65} +471213. q^{66} +4.66306e6 q^{67} +2.43066e6 q^{68} -328509. q^{69} -1.18218e6 q^{70} +4.02892e6 q^{71} +373248. q^{72} -2.58030e6 q^{73} +3.47425e6 q^{74} +2.83187e6 q^{75} -1.68628e6 q^{76} +753568. q^{77} -563845. q^{78} +1.22032e6 q^{79} -1.75225e6 q^{80} +531441. q^{81} -1.60343e6 q^{82} -2.16585e6 q^{83} +596901. q^{84} -1.62473e7 q^{85} +6.73077e6 q^{86} +6.77298e6 q^{87} +1.11695e6 q^{88} +1.19998e6 q^{89} -2.49490e6 q^{90} -901704. q^{91} -778688. q^{92} +4.83690e6 q^{93} -1.60020e6 q^{94} +1.12716e7 q^{95} +884736. q^{96} +8.97814e6 q^{97} -5.63378e6 q^{98} +1.59035e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 32 q^{2} + 108 q^{3} + 256 q^{4} + 270 q^{5} + 864 q^{6} + 2022 q^{7} + 2048 q^{8} + 2916 q^{9}+O(q^{10}) $ 4 * q + 32 * q^2 + 108 * q^3 + 256 * q^4 + 270 * q^5 + 864 * q^6 + 2022 * q^7 + 2048 * q^8 + 2916 * q^9	\( 4 q + 32 q^{2} + 108 q^{3} + 256 q^{4} + 270 q^{5} + 864 q^{6} + 2022 q^{7} + 2048 q^{8} + 2916 q^{9} + 2160 q^{10} + 4120 q^{11} + 6912 q^{12} + 8036 q^{13} + 16176 q^{14} + 7290 q^{15} + 16384 q^{16} + 37182 q^{17} + 23328 q^{18} + 5702 q^{19} + 17280 q^{20} + 54594 q^{21} + 32960 q^{22} - 48668 q^{23} + 55296 q^{24} + 121480 q^{25} + 64288 q^{26} + 78732 q^{27} + 129408 q^{28} + 217716 q^{29} + 58320 q^{30} + 222852 q^{31} + 131072 q^{32} + 111240 q^{33} + 297456 q^{34} + 68440 q^{35} + 186624 q^{36} + 486428 q^{37} + 45616 q^{38} + 216972 q^{39} + 138240 q^{40} + 338336 q^{41} + 436752 q^{42} + 730974 q^{43} + 263680 q^{44} + 196830 q^{45} - 389344 q^{46} + 338248 q^{47} + 442368 q^{48} - 310552 q^{49} + 971840 q^{50} + 1003914 q^{51} + 514304 q^{52} - 375502 q^{53} + 629856 q^{54} + 424840 q^{55} + 1035264 q^{56} + 153954 q^{57} + 1741728 q^{58} + 71392 q^{59} + 466560 q^{60} + 2101164 q^{61} + 1782816 q^{62} + 1474038 q^{63} + 1048576 q^{64} + 1578780 q^{65} + 889920 q^{66} + 4337162 q^{67} + 2379648 q^{68} - 1314036 q^{69} + 547520 q^{70} + 2288016 q^{71} + 1492992 q^{72} - 1107328 q^{73} + 3891424 q^{74} + 3279960 q^{75} + 364928 q^{76} + 5826200 q^{77} + 1735776 q^{78} + 60610 q^{79} + 1105920 q^{80} + 2125764 q^{81} + 2706688 q^{82} + 1485464 q^{83} + 3494016 q^{84} - 8843820 q^{85} + 5847792 q^{86} + 5878332 q^{87} + 2109440 q^{88} + 1485090 q^{89} + 1574640 q^{90} - 2898412 q^{91} - 3114752 q^{92} + 6017004 q^{93} + 2705984 q^{94} + 8545200 q^{95} + 3538944 q^{96} + 1935444 q^{97} - 2484416 q^{98} + 3003480 q^{99}+O(q^{100}) \) 4 * q + 32 * q^2 + 108 * q^3 + 256 * q^4 + 270 * q^5 + 864 * q^6 + 2022 * q^7 + 2048 * q^8 + 2916 * q^9 + 2160 * q^10 + 4120 * q^11 + 6912 * q^12 + 8036 * q^13 + 16176 * q^14 + 7290 * q^15 + 16384 * q^16 + 37182 * q^17 + 23328 * q^18 + 5702 * q^19 + 17280 * q^20 + 54594 * q^21 + 32960 * q^22 - 48668 * q^23 + 55296 * q^24 + 121480 * q^25 + 64288 * q^26 + 78732 * q^27 + 129408 * q^28 + 217716 * q^29 + 58320 * q^30 + 222852 * q^31 + 131072 * q^32 + 111240 * q^33 + 297456 * q^34 + 68440 * q^35 + 186624 * q^36 + 486428 * q^37 + 45616 * q^38 + 216972 * q^39 + 138240 * q^40 + 338336 * q^41 + 436752 * q^42 + 730974 * q^43 + 263680 * q^44 + 196830 * q^45 - 389344 * q^46 + 338248 * q^47 + 442368 * q^48 - 310552 * q^49 + 971840 * q^50 + 1003914 * q^51 + 514304 * q^52 - 375502 * q^53 + 629856 * q^54 + 424840 * q^55 + 1035264 * q^56 + 153954 * q^57 + 1741728 * q^58 + 71392 * q^59 + 466560 * q^60 + 2101164 * q^61 + 1782816 * q^62 + 1474038 * q^63 + 1048576 * q^64 + 1578780 * q^65 + 889920 * q^66 + 4337162 * q^67 + 2379648 * q^68 - 1314036 * q^69 + 547520 * q^70 + 2288016 * q^71 + 1492992 * q^72 - 1107328 * q^73 + 3891424 * q^74 + 3279960 * q^75 + 364928 * q^76 + 5826200 * q^77 + 1735776 * q^78 + 60610 * q^79 + 1105920 * q^80 + 2125764 * q^81 + 2706688 * q^82 + 1485464 * q^83 + 3494016 * q^84 - 8843820 * q^85 + 5847792 * q^86 + 5878332 * q^87 + 2109440 * q^88 + 1485090 * q^89 + 1574640 * q^90 - 2898412 * q^91 - 3114752 * q^92 + 6017004 * q^93 + 2705984 * q^94 + 8545200 * q^95 + 3538944 * q^96 + 1935444 * q^97 - 2484416 * q^98 + 3003480 * 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 $

$2$	8.00000	0.707107
$2$	8.00000	0.707107
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	64.0000	0.500000
$5$	−427.795	−1.53053	−0.765264	−	0.643717i	$-0.777391\pi$
$5$	−427.795	−1.53053	−0.765264	+	0.643717i	$0.777391\pi$
$6$	216.000	0.408248
$7$	345.429	0.380641	0.190320	−	0.981722i	$-0.439047\pi$
$7$	345.429	0.380641	0.190320	+	0.981722i	$0.439047\pi$
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	−3422.36	−1.08225
$11$	2181.54	0.494185	0.247092	−	0.968992i	$-0.420525\pi$
$11$	2181.54	0.494185	0.247092	+	0.968992i	$0.420525\pi$
$12$	1728.00	0.288675
$13$	−2610.39	−0.329537	−0.164768	−	0.986332i	$-0.552688\pi$
$13$	−2610.39	−0.329537	−0.164768	+	0.986332i	$0.552688\pi$
$14$	2763.43	0.269154
$15$	−11550.5	−0.883651
$16$	4096.00	0.250000
$17$	37979.0	1.87488	0.937438	−	0.348152i	$-0.113191\pi$
$17$	37979.0	1.87488	0.937438	+	0.348152i	$0.113191\pi$
$18$	5832.00	0.235702
$19$	−26348.1	−0.881276	−0.440638	−	0.897685i	$-0.645248\pi$
$19$	−26348.1	−0.881276	−0.440638	+	0.897685i	$0.645248\pi$
$20$	−27378.9	−0.765264
$21$	9326.57	0.219763
$22$	17452.3	0.349442
$23$	−12167.0	−0.208514
$23$	−12167.0	−0.208514
$24$	13824.0	0.204124
$25$	104884.	1.34251
$26$	−20883.1	−0.233018
$27$	19683.0	0.192450
$28$	22107.4	0.190320
$29$	250851.	1.90995	0.954977	−	0.296679i	$-0.0958793\pi$
$29$	250851.	1.90995	0.954977	+	0.296679i	$0.0958793\pi$
$30$	−92403.8	−0.624835
$31$	179145.	1.08003	0.540017	−	0.841654i	$-0.318418\pi$
$31$	179145.	1.08003	0.540017	+	0.841654i	$0.318418\pi$
$32$	32768.0	0.176777
$33$	58901.7	0.285318
$34$	303832.	1.32574
$35$	−147773.	−0.582581
$36$	46656.0	0.166667
$37$	434281.	1.40950	0.704749	−	0.709456i	$-0.251059\pi$
$37$	434281.	1.40950	0.704749	+	0.709456i	$0.251059\pi$
$38$	−210785.	−0.623157
$39$	−70480.6	−0.190258
$40$	−219031.	−0.541123
$41$	−200429.	−0.454168	−0.227084	−	0.973875i	$-0.572919\pi$
$41$	−200429.	−0.454168	−0.227084	+	0.973875i	$0.572919\pi$
$42$	74612.6	0.155396
$43$	841346.	1.61375	0.806873	−	0.590725i	$-0.201158\pi$
$43$	841346.	1.61375	0.806873	+	0.590725i	$0.201158\pi$
$44$	139619.	0.247092
$45$	−311863.	−0.510176
$46$	−97336.0	−0.147442
$47$	−200025.	−0.281024	−0.140512	−	0.990079i	$-0.544875\pi$
$47$	−200025.	−0.281024	−0.140512	+	0.990079i	$0.544875\pi$
$48$	110592.	0.144338
$49$	−704222.	−0.855113
$50$	839072.	0.949301
$51$	1.02543e6	1.08246
$52$	−167065.	−0.164768
$53$	−1.62417e6	−1.49853	−0.749266	−	0.662269i	$-0.769593\pi$
$53$	−1.62417e6	−1.49853	−0.749266	+	0.662269i	$0.769593\pi$
$54$	157464.	0.136083
$55$	−933254.	−0.756364
$56$	176859.	0.134577
$57$	−711399.	−0.508805
$58$	2.00681e6	1.35054
$59$	−2.18662e6	−1.38609	−0.693044	−	0.720895i	$-0.743731\pi$
$59$	−2.18662e6	−1.38609	−0.693044	+	0.720895i	$0.743731\pi$
$60$	−739231.	−0.441825
$61$	2.54771e6	1.43713	0.718564	−	0.695460i	$-0.244800\pi$
$61$	2.54771e6	1.43713	0.718564	+	0.695460i	$0.244800\pi$
$62$	1.43316e6	0.763700
$63$	251817.	0.126880
$64$	262144.	0.125000
$65$	1.11671e6	0.504365
$66$	471213.	0.201750
$67$	4.66306e6	1.89413	0.947063	−	0.321048i	$-0.104035\pi$
$67$	4.66306e6	1.89413	0.947063	+	0.321048i	$0.104035\pi$
$68$	2.43066e6	0.937438
$69$	−328509.	−0.120386
$70$	−1.18218e6	−0.411947
$71$	4.02892e6	1.33593	0.667966	−	0.744192i	$-0.267165\pi$
$71$	4.02892e6	1.33593	0.667966	+	0.744192i	$0.267165\pi$
$72$	373248.	0.117851
$73$	−2.58030e6	−0.776319	−0.388160	−	0.921592i	$-0.626889\pi$
$73$	−2.58030e6	−0.776319	−0.388160	+	0.921592i	$0.626889\pi$
$74$	3.47425e6	0.996666
$75$	2.83187e6	0.775101
$76$	−1.68628e6	−0.440638
$77$	753568.	0.188107
$78$	−563845.	−0.134533
$79$	1.22032e6	0.278471	0.139236	−	0.990259i	$-0.455535\pi$
$79$	1.22032e6	0.278471	0.139236	+	0.990259i	$0.455535\pi$
$80$	−1.75225e6	−0.382632
$81$	531441.	0.111111
$82$	−1.60343e6	−0.321145
$83$	−2.16585e6	−0.415771	−0.207886	−	0.978153i	$-0.566658\pi$
$83$	−2.16585e6	−0.415771	−0.207886	+	0.978153i	$0.566658\pi$
$84$	596901.	0.109881
$85$	−1.62473e7	−2.86955
$86$	6.73077e6	1.14109
$87$	6.77298e6	1.10271
$88$	1.11695e6	0.174721
$89$	1.19998e6	0.180430	0.0902148	−	0.995922i	$-0.471245\pi$
$89$	1.19998e6	0.180430	0.0902148	+	0.995922i	$0.471245\pi$
$90$	−2.49490e6	−0.360749
$91$	−901704.	−0.125435
$92$	−778688.	−0.104257
$93$	4.83690e6	0.623558
$94$	−1.60020e6	−0.198714
$95$	1.12716e7	1.34882
$96$	884736.	0.102062
$97$	8.97814e6	0.998815	0.499408	−	0.866367i	$-0.333551\pi$
$97$	8.97814e6	0.998815	0.499408	+	0.866367i	$0.333551\pi$
$98$	−5.63378e6	−0.604656
$99$	1.59035e6	0.164728
$100$	6.71257e6	0.671257
$101$	−9.74940e6	−0.941571	−0.470785	−	0.882248i	$-0.656029\pi$
$101$	−9.74940e6	−0.941571	−0.470785	+	0.882248i	$0.656029\pi$
$102$	8.20347e6	0.765415
$103$	−1.50223e7	−1.35459	−0.677294	−	0.735713i	$-0.736847\pi$
$103$	−1.50223e7	−1.35459	−0.677294	+	0.735713i	$0.736847\pi$
$104$	−1.33652e6	−0.116509
$105$	−3.98987e6	−0.336353
$106$	−1.29934e7	−1.05962
$107$	−1.75798e7	−1.38730	−0.693650	−	0.720312i	$-0.743999\pi$
$107$	−1.75798e7	−1.38730	−0.693650	+	0.720312i	$0.743999\pi$
$108$	1.25971e6	0.0962250
$109$	1.64602e7	1.21742	0.608711	−	0.793392i	$-0.291687\pi$
$109$	1.64602e7	1.21742	0.608711	+	0.793392i	$0.291687\pi$
$110$	−7.46604e6	−0.534830
$111$	1.17256e7	0.813775
$112$	1.41488e6	0.0951602
$113$	1.70487e6	0.111152	0.0555761	−	0.998454i	$-0.482300\pi$
$113$	1.70487e6	0.111152	0.0555761	+	0.998454i	$0.482300\pi$
$114$	−5.69120e6	−0.359780
$115$	5.20499e6	0.319137
$116$	1.60545e7	0.954977
$117$	−1.90298e6	−0.109846
$118$	−1.74929e7	−0.980112
$119$	1.31190e7	0.713654
$120$	−5.91384e6	−0.312418
$121$	−1.47280e7	−0.755781
$122$	2.03817e7	1.01620
$123$	−5.41157e6	−0.262214
$124$	1.14653e7	0.540017
$125$	−1.14474e7	−0.524228
$126$	2.01454e6	0.0897179
$127$	1.90880e7	0.826889	0.413444	−	0.910529i	$-0.364326\pi$
$127$	1.90880e7	0.826889	0.413444	+	0.910529i	$0.364326\pi$
$128$	2.09715e6	0.0883883
$129$	2.27163e7	0.931696
$130$	8.93371e6	0.356640
$131$	3.31709e6	0.128916	0.0644582	−	0.997920i	$-0.479468\pi$
$131$	3.31709e6	0.128916	0.0644582	+	0.997920i	$0.479468\pi$
$132$	3.76971e6	0.142659
$133$	−9.10140e6	−0.335450
$134$	3.73045e7	1.33935
$135$	−8.42030e6	−0.294550
$136$	1.94453e7	0.662869
$137$	−5.17700e7	−1.72011	−0.860055	−	0.510202i	$-0.829571\pi$
$137$	−5.17700e7	−1.72011	−0.860055	+	0.510202i	$0.829571\pi$
$138$	−2.62807e6	−0.0851257
$139$	−1.27587e7	−0.402954	−0.201477	−	0.979493i	$-0.564574\pi$
$139$	−1.27587e7	−0.402954	−0.201477	+	0.979493i	$0.564574\pi$
$140$	−9.45746e6	−0.291291
$141$	−5.40069e6	−0.162249
$142$	3.22314e7	0.944647
$143$	−5.69468e6	−0.162852
$144$	2.98598e6	0.0833333
$145$	−1.07313e8	−2.92324
$146$	−2.06424e7	−0.548941
$147$	−1.90140e7	−0.493700
$148$	2.77940e7	0.704749
$149$	−4.76667e7	−1.18049	−0.590246	−	0.807223i	$-0.700969\pi$
$149$	−4.76667e7	−1.18049	−0.590246	+	0.807223i	$0.700969\pi$
$150$	2.26549e7	0.548079
$151$	4.87918e7	1.15326	0.576631	−	0.817005i	$-0.304367\pi$
$151$	4.87918e7	1.15326	0.576631	+	0.817005i	$0.304367\pi$
$152$	−1.34902e7	−0.311578
$153$	2.76867e7	0.624959
$154$	6.02854e6	0.133012
$155$	−7.66372e7	−1.65302
$156$	−4.51076e6	−0.0951291
$157$	1.52646e7	0.314801	0.157401	−	0.987535i	$-0.449689\pi$
$157$	1.52646e7	0.314801	0.157401	+	0.987535i	$0.449689\pi$
$158$	9.76259e6	0.196909
$159$	−4.38526e7	−0.865178
$160$	−1.40180e7	−0.270562
$161$	−4.20283e6	−0.0793691
$162$	4.25153e6	0.0785674
$163$	−7.21694e7	−1.30526	−0.652629	−	0.757678i	$-0.726334\pi$
$163$	−7.21694e7	−1.30526	−0.652629	+	0.757678i	$0.726334\pi$
$164$	−1.28274e7	−0.227084
$165$	−2.51979e7	−0.436687
$166$	−1.73268e7	−0.293995
$167$	3.34621e7	0.555962	0.277981	−	0.960587i	$-0.410335\pi$
$167$	3.34621e7	0.555962	0.277981	+	0.960587i	$0.410335\pi$
$168$	4.77521e6	0.0776979
$169$	−5.59344e7	−0.891405
$170$	−1.29978e8	−2.02908
$171$	−1.92078e7	−0.293759
$172$	5.38461e7	0.806873
$173$	−4.16573e7	−0.611688	−0.305844	−	0.952082i	$-0.598939\pi$
$173$	−4.16573e7	−0.611688	−0.305844	+	0.952082i	$0.598939\pi$
$174$	5.41838e7	0.779736
$175$	3.62299e7	0.511016
$176$	8.93560e6	0.123546
$177$	−5.90387e7	−0.800258
$178$	9.59982e6	0.127583
$179$	−6.94962e7	−0.905682	−0.452841	−	0.891591i	$-0.649589\pi$
$179$	−6.94962e7	−0.905682	−0.452841	+	0.891591i	$0.649589\pi$
$180$	−1.99592e7	−0.255088
$181$	3.54533e7	0.444408	0.222204	−	0.975000i	$-0.428675\pi$
$181$	3.54533e7	0.444408	0.222204	+	0.975000i	$0.428675\pi$
$182$	−7.21363e6	−0.0886960
$183$	6.87882e7	0.829727
$184$	−6.22950e6	−0.0737210
$185$	−1.85783e8	−2.15728
$186$	3.86952e7	0.440922
$187$	8.28529e7	0.926536
$188$	−1.28016e7	−0.140512
$189$	6.79907e6	0.0732543
$190$	9.01729e7	0.953758
$191$	5.59759e7	0.581279	0.290639	−	0.956833i	$-0.406132\pi$
$191$	5.59759e7	0.581279	0.290639	+	0.956833i	$0.406132\pi$
$192$	7.07789e6	0.0721688
$193$	8.02723e7	0.803740	0.401870	−	0.915697i	$-0.368360\pi$
$193$	8.02723e7	0.803740	0.401870	+	0.915697i	$0.368360\pi$
$194$	7.18251e7	0.706269
$195$	3.01513e7	0.291195
$196$	−4.50702e7	−0.427556
$197$	3.52484e7	0.328479	0.164240	−	0.986420i	$-0.447483\pi$
$197$	3.52484e7	0.328479	0.164240	+	0.986420i	$0.447483\pi$
$198$	1.27228e7	0.116481
$199$	4.36909e7	0.393012	0.196506	−	0.980503i	$-0.437041\pi$
$199$	4.36909e7	0.393012	0.196506	+	0.980503i	$0.437041\pi$
$200$	5.37006e7	0.474651
$201$	1.25903e8	1.09357
$202$	−7.79952e7	−0.665791
$203$	8.66511e7	0.727006
$204$	6.56278e7	0.541230
$205$	8.57425e7	0.695116
$206$	−1.20179e8	−0.957838
$207$	−8.86974e6	−0.0695048
$208$	−1.06922e7	−0.0823842
$209$	−5.74796e7	−0.435514
$210$	−3.19189e7	−0.237838
$211$	−1.86224e8	−1.36473	−0.682365	−	0.731012i	$-0.739048\pi$
$211$	−1.86224e8	−1.36473	−0.682365	+	0.731012i	$0.739048\pi$
$212$	−1.03947e8	−0.749266
$213$	1.08781e8	0.771301
$214$	−1.40638e8	−0.980970
$215$	−3.59924e8	−2.46988
$216$	1.00777e7	0.0680414
$217$	6.18817e7	0.411105
$218$	1.31681e8	0.860848
$219$	−6.96681e7	−0.448208
$220$	−5.97283e7	−0.378182
$221$	−9.91401e7	−0.617841
$222$	9.38047e7	0.575425
$223$	4.97859e7	0.300635	0.150317	−	0.988638i	$-0.451970\pi$
$223$	4.97859e7	0.300635	0.150317	+	0.988638i	$0.451970\pi$
$224$	1.13190e7	0.0672884
$225$	7.64604e7	0.447505
$226$	1.36390e7	0.0785964
$227$	1.75842e8	0.997773	0.498886	−	0.866667i	$-0.333743\pi$
$227$	1.75842e8	0.997773	0.498886	+	0.866667i	$0.333743\pi$
$228$	−4.55296e7	−0.254403
$229$	4.00032e7	0.220125	0.110063	−	0.993925i	$-0.464895\pi$
$229$	4.00032e7	0.220125	0.110063	+	0.993925i	$0.464895\pi$
$230$	4.16399e7	0.225664
$231$	2.03463e7	0.108604
$232$	1.28436e8	0.675271
$233$	1.16608e8	0.603923	0.301962	−	0.953320i	$-0.402359\pi$
$233$	1.16608e8	0.603923	0.301962	+	0.953320i	$0.402359\pi$
$234$	−1.52238e7	−0.0776726
$235$	8.55700e7	0.430114
$236$	−1.39944e8	−0.693044
$237$	3.29487e7	0.160775
$238$	1.04952e8	0.504630
$239$	−7.54954e7	−0.357707	−0.178854	−	0.983876i	$-0.557239\pi$
$239$	−7.54954e7	−0.357707	−0.178854	+	0.983876i	$0.557239\pi$
$240$	−4.73108e7	−0.220913
$241$	4.32182e8	1.98887	0.994436	−	0.105346i	$-0.0335949\pi$
$241$	4.32182e8	1.98887	0.994436	+	0.105346i	$0.0335949\pi$
$242$	−1.17824e8	−0.534418
$243$	1.43489e7	0.0641500
$244$	1.63053e8	0.718564
$245$	3.01263e8	1.30877
$246$	−4.32926e7	−0.185413
$247$	6.87789e7	0.290413
$248$	9.17220e7	0.381850
$249$	−5.84779e7	−0.240046
$250$	−9.15789e7	−0.370685
$251$	−1.77661e8	−0.709141	−0.354571	−	0.935029i	$-0.615373\pi$
$251$	−1.77661e8	−0.709141	−0.354571	+	0.935029i	$0.615373\pi$
$252$	1.61163e7	0.0634401
$253$	−2.65428e7	−0.103045
$254$	1.52704e8	0.584699
$255$	−4.38676e8	−1.65674
$256$	1.67772e7	0.0625000
$257$	−3.32079e8	−1.22033	−0.610163	−	0.792276i	$-0.708896\pi$
$257$	−3.32079e8	−1.22033	−0.610163	+	0.792276i	$0.708896\pi$
$258$	1.81731e8	0.658809
$259$	1.50013e8	0.536513
$260$	7.14697e7	0.252183
$261$	1.82870e8	0.636651
$262$	2.65368e7	0.0911577
$263$	3.55827e8	1.20613	0.603064	−	0.797693i	$-0.293946\pi$
$263$	3.55827e8	1.20613	0.603064	+	0.797693i	$0.293946\pi$
$264$	3.01577e7	0.100875
$265$	6.94812e8	2.29354
$266$	−7.28112e7	−0.237199
$267$	3.23994e7	0.104171
$268$	2.98436e8	0.947063
$269$	2.51996e6	0.00789332	0.00394666	−	0.999992i	$-0.498744\pi$
$269$	2.51996e6	0.00789332	0.00394666	+	0.999992i	$0.498744\pi$
$270$	−6.73624e7	−0.208278
$271$	−4.75682e7	−0.145186	−0.0725929	−	0.997362i	$-0.523127\pi$
$271$	−4.75682e7	−0.145186	−0.0725929	+	0.997362i	$0.523127\pi$
$272$	1.55562e8	0.468719
$273$	−2.43460e7	−0.0724200
$274$	−4.14160e8	−1.21630
$275$	2.28809e8	0.663451
$276$	−2.10246e7	−0.0601929
$277$	−6.57962e7	−0.186004	−0.0930018	−	0.995666i	$-0.529646\pi$
$277$	−6.57962e7	−0.186004	−0.0930018	+	0.995666i	$0.529646\pi$
$278$	−1.02070e8	−0.284932
$279$	1.30596e8	0.360012
$280$	−7.56597e7	−0.205973
$281$	1.33552e8	0.359069	0.179535	−	0.983752i	$-0.442541\pi$
$281$	1.33552e8	0.359069	0.179535	+	0.983752i	$0.442541\pi$
$282$	−4.32055e7	−0.114727
$283$	−1.61478e8	−0.423508	−0.211754	−	0.977323i	$-0.567917\pi$
$283$	−1.61478e8	−0.423508	−0.211754	+	0.977323i	$0.567917\pi$
$284$	2.57851e8	0.667966
$285$	3.04333e8	0.778740
$286$	−4.55575e7	−0.115154
$287$	−6.92338e7	−0.172875
$288$	2.38879e7	0.0589256
$289$	1.03207e9	2.51516
$290$	−8.58504e8	−2.06704
$291$	2.42410e8	0.576666
$292$	−1.65139e8	−0.388160
$293$	−1.53715e8	−0.357009	−0.178505	−	0.983939i	$-0.557126\pi$
$293$	−1.53715e8	−0.357009	−0.178505	+	0.983939i	$0.557126\pi$
$294$	−1.52112e8	−0.349098
$295$	9.35425e8	2.12145
$296$	2.22352e8	0.498333
$297$	4.29393e7	0.0951059
$298$	−3.81333e8	−0.834734
$299$	3.17606e7	0.0687132
$300$	1.81239e8	0.387551
$301$	2.90625e8	0.614257
$302$	3.90335e8	0.815479
$303$	−2.63234e8	−0.543616
$304$	−1.07922e8	−0.220319
$305$	−1.08990e9	−2.19957
$306$	2.21494e8	0.441913
$307$	−4.52238e8	−0.892037	−0.446019	−	0.895024i	$-0.647159\pi$
$307$	−4.52238e8	−0.892037	−0.446019	+	0.895024i	$0.647159\pi$
$308$	4.82283e7	0.0940534
$309$	−4.05603e8	−0.782071
$310$	−6.13098e8	−1.16886
$311$	7.24988e8	1.36669	0.683344	−	0.730096i	$-0.260525\pi$
$311$	7.24988e8	1.36669	0.683344	+	0.730096i	$0.260525\pi$
$312$	−3.60861e7	−0.0672664
$313$	−5.66818e8	−1.04481	−0.522407	−	0.852696i	$-0.674966\pi$
$313$	−5.66818e8	−1.04481	−0.522407	+	0.852696i	$0.674966\pi$
$314$	1.22117e8	0.222598
$315$	−1.07726e8	−0.194194
$316$	7.81007e7	0.139236
$317$	−9.63349e8	−1.69854	−0.849271	−	0.527958i	$-0.822958\pi$
$317$	−9.63349e8	−1.69854	−0.849271	+	0.527958i	$0.822958\pi$
$318$	−3.50821e8	−0.611773
$319$	5.47243e8	0.943871
$320$	−1.12144e8	−0.191316
$321$	−4.74654e8	−0.800958
$322$	−3.36226e7	−0.0561224
$323$	−1.00068e9	−1.65228
$324$	3.40122e7	0.0555556
$325$	−2.73788e8	−0.442408
$326$	−5.77355e8	−0.922957
$327$	4.44424e8	0.702879
$328$	−1.02619e8	−0.160573
$329$	−6.90945e7	−0.106969
$330$	−2.01583e8	−0.308784
$331$	−4.26221e8	−0.646006	−0.323003	−	0.946398i	$-0.604692\pi$
$331$	−4.26221e8	−0.646006	−0.323003	+	0.946398i	$0.604692\pi$
$332$	−1.38614e8	−0.207886
$333$	3.16591e8	0.469833
$334$	2.67697e8	0.393125
$335$	−1.99483e9	−2.89901
$336$	3.82016e7	0.0549407
$337$	−2.41775e8	−0.344118	−0.172059	−	0.985087i	$-0.555042\pi$
$337$	−2.41775e8	−0.344118	−0.172059	+	0.985087i	$0.555042\pi$
$338$	−4.47475e8	−0.630319
$339$	4.60316e7	0.0641737
$340$	−1.03982e9	−1.43477
$341$	3.90812e8	0.533737
$342$	−1.53662e8	−0.207719
$343$	−5.27734e8	−0.706131
$344$	4.30769e8	0.570545
$345$	1.40535e8	0.184254
$346$	−3.33258e8	−0.432528
$347$	1.34412e9	1.72697	0.863484	−	0.504375i	$-0.168277\pi$
$347$	1.34412e9	1.72697	0.863484	+	0.504375i	$0.168277\pi$
$348$	4.33471e8	0.551356
$349$	3.27029e8	0.411811	0.205905	−	0.978572i	$-0.433986\pi$
$349$	3.27029e8	0.411811	0.205905	+	0.978572i	$0.433986\pi$
$350$	2.89839e8	0.361343
$351$	−5.13803e7	−0.0634194
$352$	7.14848e7	0.0873604
$353$	1.52857e9	1.84958	0.924789	−	0.380480i	$-0.124241\pi$
$353$	1.52857e9	1.84958	0.924789	+	0.380480i	$0.124241\pi$
$354$	−4.72309e8	−0.565868
$355$	−1.72355e9	−2.04468
$356$	7.67985e7	0.0902148
$357$	3.54214e8	0.412028
$358$	−5.55970e8	−0.640414
$359$	−4.65294e7	−0.0530759	−0.0265379	−	0.999648i	$-0.508448\pi$
$359$	−4.65294e7	−0.0530759	−0.0265379	+	0.999648i	$0.508448\pi$
$360$	−1.59674e8	−0.180374
$361$	−1.99648e8	−0.223352
$362$	2.83627e8	0.314244
$363$	−3.97657e8	−0.436351
$364$	−5.77091e7	−0.0627176
$365$	1.10384e9	1.18818
$366$	5.50306e8	0.586705
$367$	4.58322e8	0.483993	0.241997	−	0.970277i	$-0.422198\pi$
$367$	4.58322e8	0.483993	0.241997	+	0.970277i	$0.422198\pi$
$368$	−4.98360e7	−0.0521286
$369$	−1.46112e8	−0.151389
$370$	−1.48627e9	−1.52543
$371$	−5.61035e8	−0.570402
$372$	3.09562e8	0.311779
$373$	7.39771e8	0.738102	0.369051	−	0.929409i	$-0.379683\pi$
$373$	7.39771e8	0.738102	0.369051	+	0.929409i	$0.379683\pi$
$374$	6.62823e8	0.655160
$375$	−3.09079e8	−0.302663
$376$	−1.02413e8	−0.0993568
$377$	−6.54820e8	−0.629400
$378$	5.43926e7	0.0517986
$379$	3.93984e8	0.371742	0.185871	−	0.982574i	$-0.440489\pi$
$379$	3.93984e8	0.371742	0.185871	+	0.982574i	$0.440489\pi$
$380$	7.21383e8	0.674409
$381$	5.15376e8	0.477404
$382$	4.47807e8	0.411026
$383$	1.33816e9	1.21706	0.608530	−	0.793531i	$-0.291760\pi$
$383$	1.33816e9	1.21706	0.608530	+	0.793531i	$0.291760\pi$
$384$	5.66231e7	0.0510310
$385$	−3.22373e8	−0.287903
$386$	6.42179e8	0.568330
$387$	6.13341e8	0.537915
$388$	5.74601e8	0.499408
$389$	−1.71698e9	−1.47891	−0.739455	−	0.673206i	$-0.764917\pi$
$389$	−1.71698e9	−1.47891	−0.739455	+	0.673206i	$0.764917\pi$
$390$	2.41210e8	0.205906
$391$	−4.62091e8	−0.390939
$392$	−3.60562e8	−0.302328
$393$	8.95615e7	0.0744299
$394$	2.81987e8	0.232270
$395$	−5.22049e8	−0.426208
$396$	1.01782e8	0.0823642
$397$	−9.91563e7	−0.0795341	−0.0397671	−	0.999209i	$-0.512662\pi$
$397$	−9.91563e7	−0.0795341	−0.0397671	+	0.999209i	$0.512662\pi$
$398$	3.49528e8	0.277901
$399$	−2.45738e8	−0.193672
$400$	4.29605e8	0.335629
$401$	1.41606e9	1.09667	0.548334	−	0.836259i	$-0.315262\pi$
$401$	1.41606e9	1.09667	0.548334	+	0.836259i	$0.315262\pi$
$402$	1.00722e9	0.773274
$403$	−4.67638e8	−0.355911
$404$	−6.23961e8	−0.470785
$405$	−2.27348e8	−0.170059
$406$	6.93209e8	0.514071
$407$	9.47403e8	0.696553
$408$	5.25022e8	0.382707
$409$	−1.39619e9	−1.00905	−0.504524	−	0.863397i	$-0.668332\pi$
$409$	−1.39619e9	−1.00905	−0.504524	+	0.863397i	$0.668332\pi$
$410$	6.85940e8	0.491521
$411$	−1.39779e9	−0.993106
$412$	−9.61429e8	−0.677294
$413$	−7.55320e8	−0.527601
$414$	−7.09579e7	−0.0491473
$415$	9.26540e8	0.636350
$416$	−8.55373e7	−0.0582544
$417$	−3.44486e8	−0.232646
$418$	−4.59837e8	−0.307955
$419$	−9.81338e8	−0.651733	−0.325866	−	0.945416i	$-0.605656\pi$
$419$	−9.81338e8	−0.651733	−0.325866	+	0.945416i	$0.605656\pi$
$420$	−2.55351e8	−0.168177
$421$	−1.16824e9	−0.763037	−0.381518	−	0.924361i	$-0.624599\pi$
$421$	−1.16824e9	−0.763037	−0.381518	+	0.924361i	$0.624599\pi$
$422$	−1.48979e9	−0.965010
$423$	−1.45819e8	−0.0936745
$424$	−8.31575e8	−0.529811
$425$	3.98339e9	2.51705
$426$	8.70247e8	0.545392
$427$	8.80052e8	0.547030
$428$	−1.12511e9	−0.693650
$429$	−1.53756e8	−0.0940227
$430$	−2.87939e9	−1.74647
$431$	1.91210e9	1.15037	0.575187	−	0.818022i	$-0.304929\pi$
$431$	1.91210e9	1.15037	0.575187	+	0.818022i	$0.304929\pi$
$432$	8.06216e7	0.0481125
$433$	1.67730e9	0.992894	0.496447	−	0.868067i	$-0.334638\pi$
$433$	1.67730e9	0.992894	0.496447	+	0.868067i	$0.334638\pi$
$434$	4.95053e8	0.290695
$435$	−2.89745e9	−1.68773
$436$	1.05345e9	0.608711
$437$	3.20578e8	0.183759
$438$	−5.57345e8	−0.316931
$439$	−1.78469e8	−0.100679	−0.0503393	−	0.998732i	$-0.516030\pi$
$439$	−1.78469e8	−0.100679	−0.0503393	+	0.998732i	$0.516030\pi$
$440$	−4.77826e8	−0.267415
$441$	−5.13378e8	−0.285038
$442$	−7.93121e8	−0.436879
$443$	1.00078e7	0.00546921	0.00273461	−	0.999996i	$-0.499130\pi$
$443$	1.00078e7	0.00546921	0.00273461	+	0.999996i	$0.499130\pi$
$444$	7.50437e8	0.406887
$445$	−5.13345e8	−0.276153
$446$	3.98287e8	0.212581
$447$	−1.28700e9	−0.681557
$448$	9.05520e7	0.0475801
$449$	2.38685e9	1.24441	0.622203	−	0.782856i	$-0.286238\pi$
$449$	2.38685e9	1.24441	0.622203	+	0.782856i	$0.286238\pi$
$450$	6.11683e8	0.316434
$451$	−4.37244e8	−0.224443
$452$	1.09112e8	0.0555761
$453$	1.31738e9	0.665836
$454$	1.40673e9	0.705532
$455$	3.85745e8	0.191982
$456$	−3.64237e8	−0.179890
$457$	1.40659e9	0.689385	0.344692	−	0.938716i	$-0.387983\pi$
$457$	1.40659e9	0.689385	0.344692	+	0.938716i	$0.387983\pi$
$458$	3.20025e8	0.155652
$459$	7.47541e8	0.360820
$460$	3.33119e8	0.159569
$461$	−8.75198e8	−0.416057	−0.208029	−	0.978123i	$-0.566705\pi$
$461$	−8.75198e8	−0.416057	−0.208029	+	0.978123i	$0.566705\pi$
$462$	1.62771e8	0.0767943
$463$	−8.95572e8	−0.419341	−0.209670	−	0.977772i	$-0.567239\pi$
$463$	−8.95572e8	−0.419341	−0.209670	+	0.977772i	$0.567239\pi$
$464$	1.02749e9	0.477489
$465$	−2.06921e9	−0.954373
$466$	9.32862e8	0.427038
$467$	−2.18071e9	−0.990807	−0.495403	−	0.868663i	$-0.664980\pi$
$467$	−2.18071e9	−0.990807	−0.495403	+	0.868663i	$0.664980\pi$
$468$	−1.21790e8	−0.0549228
$469$	1.61075e9	0.720981
$470$	6.84560e8	0.304137
$471$	4.12144e8	0.181751
$472$	−1.11955e9	−0.490056
$473$	1.83543e9	0.797489
$474$	2.63590e8	0.113685
$475$	−2.76350e9	−1.18313
$476$	8.39619e8	0.356827
$477$	−1.18402e9	−0.499510
$478$	−6.03963e8	−0.252937
$479$	1.86608e9	0.775812	0.387906	−	0.921699i	$-0.373199\pi$
$479$	1.86608e9	0.775812	0.387906	+	0.921699i	$0.373199\pi$
$480$	−3.78486e8	−0.156209
$481$	−1.13364e9	−0.464482
$482$	3.45745e9	1.40634
$483$	−1.13476e8	−0.0458237
$484$	−9.42594e8	−0.377891
$485$	−3.84081e9	−1.52871
$486$	1.14791e8	0.0453609
$487$	−9.54001e8	−0.374281	−0.187140	−	0.982333i	$-0.559922\pi$
$487$	−9.54001e8	−0.374281	−0.187140	+	0.982333i	$0.559922\pi$
$488$	1.30443e9	0.508102
$489$	−1.94857e9	−0.753591
$490$	2.41010e9	0.925443
$491$	1.21183e9	0.462017	0.231008	−	0.972952i	$-0.425798\pi$
$491$	1.21183e9	0.462017	0.231008	+	0.972952i	$0.425798\pi$
$492$	−3.46341e8	−0.131107
$493$	9.52708e9	3.58093
$494$	5.50232e8	0.205353
$495$	−6.80343e8	−0.252121
$496$	7.33776e8	0.270009
$497$	1.39170e9	0.508510
$498$	−4.67823e8	−0.169738
$499$	−1.17097e9	−0.421884	−0.210942	−	0.977499i	$-0.567653\pi$
$499$	−1.17097e9	−0.421884	−0.210942	+	0.977499i	$0.567653\pi$
$500$	−7.32631e8	−0.262114
$501$	9.03476e8	0.320985
$502$	−1.42128e9	−0.501439
$503$	−3.36243e9	−1.17806	−0.589028	−	0.808113i	$-0.700489\pi$
$503$	−3.36243e9	−1.17806	−0.589028	+	0.808113i	$0.700489\pi$
$504$	1.28931e8	0.0448589
$505$	4.17075e9	1.44110
$506$	−2.12343e8	−0.0728636
$507$	−1.51023e9	−0.514653
$508$	1.22163e9	0.413444
$509$	−3.89948e9	−1.31067	−0.655336	−	0.755337i	$-0.727473\pi$
$509$	−3.89948e9	−1.31067	−0.655336	+	0.755337i	$0.727473\pi$
$510$	−3.50941e9	−1.17149
$511$	−8.91310e8	−0.295499
$512$	1.34218e8	0.0441942
$513$	−5.18610e8	−0.169602
$514$	−2.65663e9	−0.862900
$515$	6.42648e9	2.07323
$516$	1.45385e9	0.465848
$517$	−4.36364e8	−0.138878
$518$	1.20010e9	0.379372
$519$	−1.12475e9	−0.353158
$520$	5.71758e8	0.178320
$521$	−4.08573e9	−1.26572	−0.632860	−	0.774266i	$-0.718119\pi$
$521$	−4.08573e9	−1.26572	−0.632860	+	0.774266i	$0.718119\pi$
$522$	1.46296e9	0.450181
$523$	−6.17299e9	−1.88686	−0.943430	−	0.331571i	$-0.892421\pi$
$523$	−6.17299e9	−1.88686	−0.943430	+	0.331571i	$0.892421\pi$
$524$	2.12294e8	0.0644582
$525$	9.78208e8	0.295035
$526$	2.84661e9	0.852861
$527$	6.80374e9	2.02493
$528$	2.41261e8	0.0713295
$529$	1.48036e8	0.0434783
$530$	5.55850e9	1.62178
$531$	−1.59404e9	−0.462029
$532$	−5.82489e8	−0.167725
$533$	5.23197e8	0.149665
$534$	2.59195e8	0.0736601
$535$	7.52056e9	2.12330
$536$	2.38748e9	0.669675
$537$	−1.87640e9	−0.522896
$538$	2.01596e7	0.00558142
$539$	−1.53629e9	−0.422584
$540$	−5.38899e8	−0.147275
$541$	6.18398e9	1.67910	0.839552	−	0.543280i	$-0.182818\pi$
$541$	6.18398e9	1.67910	0.839552	+	0.543280i	$0.182818\pi$
$542$	−3.80546e8	−0.102662
$543$	9.57240e8	0.256579
$544$	1.24450e9	0.331434
$545$	−7.04158e9	−1.86330
$546$	−1.94768e8	−0.0512087
$547$	−3.11011e9	−0.812494	−0.406247	−	0.913763i	$-0.633163\pi$
$547$	−3.11011e9	−0.812494	−0.406247	+	0.913763i	$0.633163\pi$
$548$	−3.31328e9	−0.860055
$549$	1.85728e9	0.479043
$550$	1.83047e9	0.469130
$551$	−6.60946e9	−1.68320
$552$	−1.68197e8	−0.0425628
$553$	4.21535e8	0.105997
$554$	−5.26369e8	−0.131524
$555$	−5.01615e9	−1.24550
$556$	−8.16559e8	−0.201477
$557$	5.56754e9	1.36512	0.682559	−	0.730831i	$-0.260867\pi$
$557$	5.56754e9	1.36512	0.682559	+	0.730831i	$0.260867\pi$
$558$	1.04477e9	0.254567
$559$	−2.19624e9	−0.531789
$560$	−6.05277e8	−0.145645
$561$	2.23703e9	0.534936
$562$	1.06842e9	0.253900
$563$	−6.88023e9	−1.62489	−0.812445	−	0.583038i	$-0.801864\pi$
$563$	−6.88023e9	−1.62489	−0.812445	+	0.583038i	$0.801864\pi$
$564$	−3.45644e8	−0.0811245
$565$	−7.29337e8	−0.170121
$566$	−1.29182e9	−0.299465
$567$	1.83575e8	0.0422934
$568$	2.06281e9	0.472323
$569$	8.40627e9	1.91298	0.956490	−	0.291765i	$-0.0942425\pi$
$569$	8.40627e9	1.91298	0.956490	+	0.291765i	$0.0942425\pi$
$570$	2.43467e9	0.550653
$571$	−5.25925e8	−0.118222	−0.0591109	−	0.998251i	$-0.518827\pi$
$571$	−5.25925e8	−0.118222	−0.0591109	+	0.998251i	$0.518827\pi$
$572$	−3.64460e8	−0.0814261
$573$	1.51135e9	0.335602
$574$	−5.53870e8	−0.122241
$575$	−1.27612e9	−0.279934
$576$	1.91103e8	0.0416667
$577$	−1.66741e9	−0.361349	−0.180674	−	0.983543i	$-0.557828\pi$
$577$	−1.66741e9	−0.361349	−0.180674	+	0.983543i	$0.557828\pi$
$578$	8.25654e9	1.77849
$579$	2.16735e9	0.464039
$580$	−6.86803e9	−1.46162
$581$	−7.48146e8	−0.158259
$582$	1.93928e9	0.407765
$583$	−3.54320e9	−0.740552
$584$	−1.32111e9	−0.274470
$585$	8.14084e8	0.168122
$586$	−1.22972e9	−0.252444
$587$	−1.24841e9	−0.254756	−0.127378	−	0.991854i	$-0.540656\pi$
$587$	−1.24841e9	−0.254756	−0.127378	+	0.991854i	$0.540656\pi$
$588$	−1.21690e9	−0.246850
$589$	−4.72012e9	−0.951809
$590$	7.48340e9	1.50009
$591$	9.51707e8	0.189648
$592$	1.77881e9	0.352375
$593$	−2.61091e9	−0.514163	−0.257081	−	0.966390i	$-0.582761\pi$
$593$	−2.61091e9	−0.514163	−0.257081	+	0.966390i	$0.582761\pi$
$594$	3.43515e8	0.0672501
$595$	−5.61227e9	−1.09227
$596$	−3.05067e9	−0.590246
$597$	1.17966e9	0.226905
$598$	2.54085e8	0.0485876
$599$	−6.36475e9	−1.21001	−0.605003	−	0.796223i	$-0.706828\pi$
$599$	−6.36475e9	−1.21001	−0.605003	+	0.796223i	$0.706828\pi$
$600$	1.44992e9	0.274040
$601$	−1.44570e9	−0.271656	−0.135828	−	0.990732i	$-0.543369\pi$
$601$	−1.44570e9	−0.271656	−0.135828	+	0.990732i	$0.543369\pi$
$602$	2.32500e9	0.434345
$603$	3.39937e9	0.631375
$604$	3.12268e9	0.576631
$605$	6.30059e9	1.15674
$606$	−2.10587e9	−0.384395
$607$	−4.03112e9	−0.731586	−0.365793	−	0.930696i	$-0.619202\pi$
$607$	−4.03112e9	−0.731586	−0.365793	+	0.930696i	$0.619202\pi$
$608$	−8.63375e8	−0.155789
$609$	2.33958e9	0.419737
$610$	−8.71919e9	−1.55533
$611$	5.22145e8	0.0926076
$612$	1.77195e9	0.312479
$613$	2.16682e9	0.379936	0.189968	−	0.981790i	$-0.439162\pi$
$613$	2.16682e9	0.379936	0.189968	+	0.981790i	$0.439162\pi$
$614$	−3.61791e9	−0.630766
$615$	2.31505e9	0.401325
$616$	3.85827e8	0.0665058
$617$	−3.74148e9	−0.641276	−0.320638	−	0.947202i	$-0.603897\pi$
$617$	−3.74148e9	−0.641276	−0.320638	+	0.947202i	$0.603897\pi$
$618$	−3.24482e9	−0.553008
$619$	1.01384e10	1.71811	0.859054	−	0.511885i	$-0.171053\pi$
$619$	1.01384e10	1.71811	0.859054	+	0.511885i	$0.171053\pi$
$620$	−4.90478e9	−0.826511
$621$	−2.39483e8	−0.0401286
$622$	5.79990e9	0.966394
$623$	4.14506e8	0.0686789
$624$	−2.88688e8	−0.0475645
$625$	−3.29693e9	−0.540169
$626$	−4.53455e9	−0.738795
$627$	−1.55195e9	−0.251444
$628$	9.76934e8	0.157401
$629$	1.64936e10	2.64264
$630$	−8.61811e8	−0.137316
$631$	8.21596e9	1.30183	0.650917	−	0.759149i	$-0.274385\pi$
$631$	8.21596e9	1.30183	0.650917	+	0.759149i	$0.274385\pi$
$632$	6.24806e8	0.0984544
$633$	−5.02804e9	−0.787927
$634$	−7.70679e9	−1.20105
$635$	−8.16575e9	−1.26558
$636$	−2.80657e9	−0.432589
$637$	1.83830e9	0.281791
$638$	4.37794e9	0.667417
$639$	2.93708e9	0.445311
$640$	−8.97152e8	−0.135281
$641$	8.20911e8	0.123110	0.0615549	−	0.998104i	$-0.480394\pi$
$641$	8.20911e8	0.123110	0.0615549	+	0.998104i	$0.480394\pi$
$642$	−3.79724e9	−0.566363
$643$	5.92103e9	0.878333	0.439166	−	0.898406i	$-0.355274\pi$
$643$	5.92103e9	0.878333	0.439166	+	0.898406i	$0.355274\pi$
$644$	−2.68981e8	−0.0396845
$645$	−9.71795e9	−1.42599
$646$	−8.00541e9	−1.16834
$647$	−1.09657e10	−1.59174	−0.795870	−	0.605468i	$-0.792986\pi$
$647$	−1.09657e10	−1.59174	−0.795870	+	0.605468i	$0.792986\pi$
$648$	2.72098e8	0.0392837
$649$	−4.77020e9	−0.684984
$650$	−2.19031e9	−0.312830
$651$	1.67080e9	0.237352
$652$	−4.61884e9	−0.652629
$653$	−6.73255e9	−0.946201	−0.473101	−	0.881008i	$-0.656865\pi$
$653$	−6.73255e9	−0.946201	−0.473101	+	0.881008i	$0.656865\pi$
$654$	3.55539e9	0.497011
$655$	−1.41904e9	−0.197310
$656$	−8.20956e8	−0.113542
$657$	−1.88104e9	−0.258773
$658$	−5.52756e8	−0.0756385
$659$	−1.25637e10	−1.71009	−0.855043	−	0.518557i	$-0.826469\pi$
$659$	−1.25637e10	−1.71009	−0.855043	+	0.518557i	$0.826469\pi$
$660$	−1.61266e9	−0.218343
$661$	7.27312e9	0.979526	0.489763	−	0.871856i	$-0.337083\pi$
$661$	7.27312e9	0.979526	0.489763	+	0.871856i	$0.337083\pi$
$662$	−3.40977e9	−0.456796
$663$	−2.67678e9	−0.356711
$664$	−1.10891e9	−0.146997
$665$	3.89354e9	0.513415
$666$	2.53273e9	0.332222
$667$	−3.05210e9	−0.398253
$668$	2.14157e9	0.277981
$669$	1.34422e9	0.173572
$670$	−1.59587e10	−2.04991
$671$	5.55794e9	0.710207
$672$	3.05613e8	0.0388490
$673$	−2.38576e9	−0.301699	−0.150849	−	0.988557i	$-0.548201\pi$
$673$	−2.38576e9	−0.301699	−0.150849	+	0.988557i	$0.548201\pi$
$674$	−1.93420e9	−0.243328
$675$	2.06443e9	0.258367
$676$	−3.57980e9	−0.445703
$677$	−1.25080e10	−1.54928	−0.774639	−	0.632404i	$-0.782068\pi$
$677$	−1.25080e10	−1.54928	−0.774639	+	0.632404i	$0.782068\pi$
$678$	3.68253e8	0.0453777
$679$	3.10131e9	0.380190
$680$	−8.31859e9	−1.01454
$681$	4.74773e9	0.576064
$682$	3.12649e9	0.377409
$683$	−6.33284e9	−0.760548	−0.380274	−	0.924874i	$-0.624170\pi$
$683$	−6.33284e9	−0.760548	−0.380274	+	0.924874i	$0.624170\pi$
$684$	−1.22930e9	−0.146879
$685$	2.21470e10	2.63267
$686$	−4.22187e9	−0.499310
$687$	1.08009e9	0.127089
$688$	3.44615e9	0.403436
$689$	4.23972e9	0.493821
$690$	1.12428e9	0.130287
$691$	−2.30362e9	−0.265606	−0.132803	−	0.991142i	$-0.542398\pi$
$691$	−2.30362e9	−0.265606	−0.132803	+	0.991142i	$0.542398\pi$
$692$	−2.66607e9	−0.305844
$693$	5.49351e8	0.0627023
$694$	1.07530e10	1.22115
$695$	5.45813e9	0.616733
$696$	3.46777e9	0.389868
$697$	−7.61208e9	−0.851508
$698$	2.61624e9	0.291194
$699$	3.14841e9	0.348675
$700$	2.31871e9	0.255508
$701$	−5.07693e9	−0.556657	−0.278329	−	0.960486i	$-0.589780\pi$
$701$	−5.07693e9	−0.556657	−0.278329	+	0.960486i	$0.589780\pi$
$702$	−4.11043e8	−0.0448443
$703$	−1.14425e10	−1.24216
$704$	5.71879e8	0.0617731
$705$	2.31039e9	0.248327
$706$	1.22285e10	1.30785
$707$	−3.36772e9	−0.358400
$708$	−3.77848e9	−0.400129
$709$	8.96481e8	0.0944669	0.0472334	−	0.998884i	$-0.484960\pi$
$709$	8.96481e8	0.0944669	0.0472334	+	0.998884i	$0.484960\pi$
$710$	−1.37884e10	−1.44581
$711$	8.89616e8	0.0928237
$712$	6.14388e8	0.0637915
$713$	−2.17965e9	−0.225203
$714$	2.83371e9	0.291348
$715$	2.43616e9	0.249250
$716$	−4.44776e9	−0.452841
$717$	−2.03838e9	−0.206522
$718$	−3.72235e8	−0.0375303
$719$	−4.13828e9	−0.415210	−0.207605	−	0.978213i	$-0.566567\pi$
$719$	−4.13828e9	−0.415210	−0.207605	+	0.978213i	$0.566567\pi$
$720$	−1.27739e9	−0.127544
$721$	−5.18914e9	−0.515611
$722$	−1.59718e9	−0.157934
$723$	1.16689e10	1.14828
$724$	2.26901e9	0.222204
$725$	2.63103e10	2.56414
$726$	−3.18126e9	−0.308546
$727$	1.34281e10	1.29611	0.648057	−	0.761591i	$-0.275582\pi$
$727$	1.34281e10	1.29611	0.648057	+	0.761591i	$0.275582\pi$
$728$	−4.61672e8	−0.0443480
$729$	3.87420e8	0.0370370
$730$	8.83073e9	0.840169
$731$	3.19535e10	3.02557
$732$	4.40244e9	0.414863
$733$	2.59875e8	0.0243725	0.0121863	−	0.999926i	$-0.496121\pi$
$733$	2.59875e8	0.0243725	0.0121863	+	0.999926i	$0.496121\pi$
$734$	3.66658e9	0.342235
$735$	8.13410e9	0.755621
$736$	−3.98688e8	−0.0368605
$737$	1.01727e10	0.936049
$738$	−1.16890e9	−0.107048
$739$	−1.08950e10	−0.993056	−0.496528	−	0.868021i	$-0.665392\pi$
$739$	−1.08950e10	−0.993056	−0.496528	+	0.868021i	$0.665392\pi$
$740$	−1.18901e10	−1.07864
$741$	1.85703e9	0.167670
$742$	−4.48828e9	−0.403335
$743$	−1.77102e10	−1.58403	−0.792014	−	0.610503i	$-0.790967\pi$
$743$	−1.77102e10	−1.58403	−0.792014	+	0.610503i	$0.790967\pi$
$744$	2.47649e9	0.220461
$745$	2.03916e10	1.80678
$746$	5.91817e9	0.521917
$747$	−1.57890e9	−0.138590
$748$	5.30259e9	0.463268
$749$	−6.07256e9	−0.528063
$750$	−2.47263e9	−0.214015
$751$	−2.21088e10	−1.90470	−0.952348	−	0.305013i	$-0.901339\pi$
$751$	−2.21088e10	−1.90470	−0.952348	+	0.305013i	$0.901339\pi$
$752$	−8.19304e8	−0.0702559
$753$	−4.79683e9	−0.409423
$754$	−5.23856e9	−0.445053
$755$	−2.08729e10	−1.76510
$756$	4.35141e8	0.0366272
$757$	−1.59200e10	−1.33385	−0.666925	−	0.745125i	$-0.732390\pi$
$757$	−1.59200e10	−1.33385	−0.666925	+	0.745125i	$0.732390\pi$
$758$	3.15188e9	0.262861
$759$	−7.16657e8	−0.0594929
$760$	5.77106e9	0.476879
$761$	−6.68228e7	−0.00549640	−0.00274820	−	0.999996i	$-0.500875\pi$
$761$	−6.68228e7	−0.00549640	−0.00274820	+	0.999996i	$0.500875\pi$
$762$	4.12301e9	0.337576
$763$	5.68581e9	0.463400
$764$	3.58246e9	0.290639
$765$	−1.18442e10	−0.956517
$766$	1.07053e10	0.860591
$767$	5.70793e9	0.456767
$768$	4.52985e8	0.0360844
$769$	−6.62635e9	−0.525451	−0.262726	−	0.964871i	$-0.584621\pi$
$769$	−6.62635e9	−0.525451	−0.262726	+	0.964871i	$0.584621\pi$
$770$	−2.57898e9	−0.203578
$771$	−8.96613e9	−0.704555
$772$	5.13743e9	0.401870
$773$	−3.61939e9	−0.281843	−0.140922	−	0.990021i	$-0.545007\pi$
$773$	−3.61939e9	−0.281843	−0.140922	+	0.990021i	$0.545007\pi$
$774$	4.90673e9	0.380363
$775$	1.87894e10	1.44996
$776$	4.59681e9	0.353135
$777$	4.05035e9	0.309756
$778$	−1.37359e10	−1.04575
$779$	5.28092e9	0.400247
$780$	1.92968e9	0.145598
$781$	8.78926e9	0.660197
$782$	−3.69673e9	−0.276435
$783$	4.93750e9	0.367571
$784$	−2.88449e9	−0.213778
$785$	−6.53012e9	−0.481812
$786$	7.16492e8	0.0526299
$787$	1.01537e10	0.742525	0.371263	−	0.928528i	$-0.378925\pi$
$787$	1.01537e10	0.742525	0.371263	+	0.928528i	$0.378925\pi$
$788$	2.25590e9	0.164240
$789$	9.60732e9	0.696358
$790$	−4.17639e9	−0.301374
$791$	5.88912e8	0.0423090
$792$	8.14257e8	0.0582403
$793$	−6.65052e9	−0.473587
$794$	−7.93250e8	−0.0562391
$795$	1.87599e10	1.32418
$796$	2.79622e9	0.196506
$797$	1.25904e10	0.880916	0.440458	−	0.897773i	$-0.354816\pi$
$797$	1.25904e10	0.880916	0.440458	+	0.897773i	$0.354816\pi$
$798$	−1.96590e9	−0.136947
$799$	−7.59677e9	−0.526884
$800$	3.43684e9	0.237325
$801$	8.74783e8	0.0601432
$802$	1.13285e10	0.775461
$803$	−5.62904e9	−0.383645
$804$	8.05776e9	0.546787
$805$	1.79795e9	0.121477
$806$	−3.74110e9	−0.251667
$807$	6.80388e7	0.00455721
$808$	−4.99169e9	−0.332896
$809$	2.20668e10	1.46528	0.732638	−	0.680618i	$-0.238289\pi$
$809$	2.20668e10	1.46528	0.732638	+	0.680618i	$0.238289\pi$
$810$	−1.81878e9	−0.120250
$811$	7.09047e9	0.466769	0.233384	−	0.972385i	$-0.425020\pi$
$811$	7.09047e9	0.466769	0.233384	+	0.972385i	$0.425020\pi$
$812$	5.54567e9	0.363503
$813$	−1.28434e9	−0.0838231
$814$	7.57922e9	0.492537
$815$	3.08737e10	1.99773
$816$	4.20018e9	0.270615
$817$	−2.21679e10	−1.42216
$818$	−1.11695e10	−0.713505
$819$	−6.57342e8	−0.0418117
$820$	5.48752e9	0.347558
$821$	3.26295e9	0.205783	0.102891	−	0.994693i	$-0.467191\pi$
$821$	3.26295e9	0.205783	0.102891	+	0.994693i	$0.467191\pi$
$822$	−1.11823e10	−0.702232
$823$	4.72161e9	0.295250	0.147625	−	0.989043i	$-0.452837\pi$
$823$	4.72161e9	0.295250	0.147625	+	0.989043i	$0.452837\pi$
$824$	−7.69143e9	−0.478919
$825$	6.17784e9	0.383043
$826$	−6.04256e9	−0.373071
$827$	1.78452e10	1.09712	0.548558	−	0.836112i	$-0.315177\pi$
$827$	1.78452e10	1.09712	0.548558	+	0.836112i	$0.315177\pi$
$828$	−5.67664e8	−0.0347524
$829$	−2.93379e10	−1.78850	−0.894248	−	0.447572i	$-0.852289\pi$
$829$	−2.93379e10	−1.78850	−0.894248	+	0.447572i	$0.852289\pi$
$830$	7.41232e9	0.449967
$831$	−1.77650e9	−0.107389
$832$	−6.84299e8	−0.0411921
$833$	−2.67457e10	−1.60323
$834$	−2.75589e9	−0.164505
$835$	−1.43149e10	−0.850916
$836$	−3.67869e9	−0.217757
$837$	3.52610e9	0.207853
$838$	−7.85070e9	−0.460845
$839$	−1.90554e9	−0.111391	−0.0556957	−	0.998448i	$-0.517738\pi$
$839$	−1.90554e9	−0.111391	−0.0556957	+	0.998448i	$0.517738\pi$
$840$	−2.04281e9	−0.118919
$841$	4.56764e10	2.64793
$842$	−9.34594e9	−0.539549
$843$	3.60590e9	0.207309
$844$	−1.19183e10	−0.682365
$845$	2.39285e10	1.36432
$846$	−1.16655e9	−0.0662379
$847$	−5.08749e9	−0.287681
$848$	−6.65260e9	−0.374633
$849$	−4.35991e9	−0.244512
$850$	3.18671e10	1.77982
$851$	−5.28390e9	−0.293901
$852$	6.96197e9	0.385650
$853$	1.63652e8	0.00902818	0.00451409	−	0.999990i	$-0.498563\pi$
$853$	1.63652e8	0.00902818	0.00451409	+	0.999990i	$0.498563\pi$
$854$	7.04042e9	0.386808
$855$	8.21700e9	0.449606
$856$	−9.00085e9	−0.490485
$857$	−6.70099e9	−0.363669	−0.181834	−	0.983329i	$-0.558203\pi$
$857$	−6.70099e9	−0.363669	−0.181834	+	0.983329i	$0.558203\pi$
$858$	−1.23005e9	−0.0664841
$859$	1.52632e10	0.821620	0.410810	−	0.911721i	$-0.365246\pi$
$859$	1.52632e10	0.821620	0.410810	+	0.911721i	$0.365246\pi$
$860$	−2.30351e10	−1.23494
$861$	−1.86931e9	−0.0998092
$862$	1.52968e10	0.813437
$863$	−1.65285e9	−0.0875376	−0.0437688	−	0.999042i	$-0.513936\pi$
$863$	−1.65285e9	−0.0875376	−0.0437688	+	0.999042i	$0.513936\pi$
$864$	6.44973e8	0.0340207
$865$	1.78208e10	0.936205
$866$	1.34184e10	0.702082
$867$	2.78658e10	1.45213
$868$	3.96043e9	0.205553
$869$	2.66219e9	0.137616
$870$	−2.31796e10	−1.19341
$871$	−1.21724e10	−0.624184
$872$	8.42760e9	0.430424
$873$	6.54506e9	0.332938
$874$	2.56462e9	0.129937
$875$	−3.95425e9	−0.199543
$876$	−4.45876e9	−0.224104
$877$	−1.13923e10	−0.570313	−0.285156	−	0.958481i	$-0.592045\pi$
$877$	−1.13923e10	−0.570313	−0.285156	+	0.958481i	$0.592045\pi$
$878$	−1.42775e9	−0.0711905
$879$	−4.15030e9	−0.206119
$880$	−3.82261e9	−0.189091
$881$	−1.15694e10	−0.570024	−0.285012	−	0.958524i	$-0.591998\pi$
$881$	−1.15694e10	−0.570024	−0.285012	+	0.958524i	$0.591998\pi$
$882$	−4.10702e9	−0.201552
$883$	−2.51966e10	−1.23163	−0.615814	−	0.787892i	$-0.711173\pi$
$883$	−2.51966e10	−1.23163	−0.615814	+	0.787892i	$0.711173\pi$
$884$	−6.34497e9	−0.308920
$885$	2.52565e10	1.22482
$886$	8.00622e7	0.00386732
$887$	−3.78563e10	−1.82140	−0.910700	−	0.413069i	$-0.864457\pi$
$887$	−3.78563e10	−1.82140	−0.910700	+	0.413069i	$0.864457\pi$
$888$	6.00350e9	0.287713
$889$	6.59354e9	0.314747
$890$	−4.10676e9	−0.195269
$891$	1.15936e9	0.0549094
$892$	3.18630e9	0.150317
$893$	5.27030e9	0.247659
$894$	−1.02960e10	−0.481934
$895$	2.97302e10	1.38617
$896$	7.24416e8	0.0336442
$897$	8.57537e8	0.0396716
$898$	1.90948e10	0.879928
$899$	4.49386e10	2.06282
$900$	4.89347e9	0.223752
$901$	−6.16844e10	−2.80956
$902$	−3.49795e9	−0.158705
$903$	7.84687e9	0.354641
$904$	8.72895e8	0.0392982
$905$	−1.51668e10	−0.680179
$906$	1.05390e10	0.470817
$907$	−9.07644e9	−0.403915	−0.201957	−	0.979394i	$-0.564730\pi$
$907$	−9.07644e9	−0.403915	−0.201957	+	0.979394i	$0.564730\pi$
$908$	1.12539e10	0.498886
$909$	−7.10731e9	−0.313857
$910$	3.08596e9	0.135752
$911$	−3.63398e10	−1.59246	−0.796229	−	0.604995i	$-0.793175\pi$
$911$	−3.63398e10	−1.59246	−0.796229	+	0.604995i	$0.793175\pi$
$912$	−2.91389e9	−0.127201
$913$	−4.72489e9	−0.205468
$914$	1.12527e10	0.487469
$915$	−2.94273e10	−1.26992
$916$	2.56020e9	0.110063
$917$	1.14582e9	0.0490708
$918$	5.98033e9	0.255138
$919$	2.16445e10	0.919904	0.459952	−	0.887944i	$-0.347867\pi$
$919$	2.16445e10	0.919904	0.459952	+	0.887944i	$0.347867\pi$
$920$	2.66495e9	0.112832
$921$	−1.22104e10	−0.515018
$922$	−7.00158e9	−0.294197
$923$	−1.05171e10	−0.440239
$924$	1.30216e9	0.0543018
$925$	4.55491e10	1.89227
$926$	−7.16458e9	−0.296519
$927$	−1.09513e10	−0.451529
$928$	8.21989e9	0.337635
$929$	7.00431e9	0.286623	0.143311	−	0.989678i	$-0.454225\pi$
$929$	7.00431e9	0.286623	0.143311	+	0.989678i	$0.454225\pi$
$930$	−1.65536e10	−0.674844
$931$	1.85549e10	0.753591
$932$	7.46289e9	0.301962
$933$	1.95747e10	0.789058
$934$	−1.74457e10	−0.700606
$935$	−3.54441e10	−1.41809
$936$	−9.74324e8	−0.0388363
$937$	−3.16263e10	−1.25591	−0.627957	−	0.778248i	$-0.716109\pi$
$937$	−3.16263e10	−1.25591	−0.627957	+	0.778248i	$0.716109\pi$
$938$	1.28860e10	0.509811
$939$	−1.53041e10	−0.603223
$940$	5.47648e9	0.215057
$941$	−2.31615e10	−0.906155	−0.453077	−	0.891471i	$-0.649674\pi$
$941$	−2.31615e10	−0.906155	−0.453077	+	0.891471i	$0.649674\pi$
$942$	3.29715e9	0.128517
$943$	2.43861e9	0.0947005
$944$	−8.95639e9	−0.346522
$945$	−2.90861e9	−0.112118
$946$	1.46835e10	0.563910
$947$	1.11874e10	0.428060	0.214030	−	0.976827i	$-0.431341\pi$
$947$	1.11874e10	0.428060	0.214030	+	0.976827i	$0.431341\pi$
$948$	2.10872e9	0.0803877
$949$	6.73560e9	0.255826
$950$	−2.21080e10	−0.836597
$951$	−2.60104e10	−0.980653
$952$	6.71695e9	0.252315
$953$	−1.85383e10	−0.693817	−0.346908	−	0.937899i	$-0.612768\pi$
$953$	−1.85383e10	−0.693817	−0.346908	+	0.937899i	$0.612768\pi$
$954$	−9.47216e9	−0.353207
$955$	−2.39463e10	−0.889663
$956$	−4.83170e9	−0.178854
$957$	1.47755e10	0.544944
$958$	1.49287e10	0.548582
$959$	−1.78828e10	−0.654743
$960$	−3.02789e9	−0.110456
$961$	4.58016e9	0.166475
$962$	−9.06915e9	−0.328438
$963$	−1.28157e10	−0.462433
$964$	2.76596e10	0.994436
$965$	−3.43401e10	−1.23015
$966$	−9.07811e8	−0.0324023
$967$	−7.91753e9	−0.281577	−0.140788	−	0.990040i	$-0.544964\pi$
$967$	−7.91753e9	−0.281577	−0.140788	+	0.990040i	$0.544964\pi$
$968$	−7.54076e9	−0.267209
$969$	−2.70183e10	−0.953947
$970$	−3.07265e10	−1.08096
$971$	−3.25866e10	−1.14228	−0.571139	−	0.820853i	$-0.693498\pi$
$971$	−3.25866e10	−1.14228	−0.571139	+	0.820853i	$0.693498\pi$
$972$	9.18330e8	0.0320750
$973$	−4.40723e9	−0.153381
$974$	−7.63201e9	−0.264656
$975$	−7.39228e9	−0.255424
$976$	1.04354e10	0.359282
$977$	6.25658e9	0.214638	0.107319	−	0.994225i	$-0.465773\pi$
$977$	6.25658e9	0.214638	0.107319	+	0.994225i	$0.465773\pi$
$978$	−1.55886e10	−0.532869
$979$	2.61780e9	0.0891656
$980$	1.92808e10	0.654387
$981$	1.19995e10	0.405807
$982$	9.69467e9	0.326695
$983$	8.04489e9	0.270136	0.135068	−	0.990836i	$-0.456875\pi$
$983$	8.04489e9	0.270136	0.135068	+	0.990836i	$0.456875\pi$
$984$	−2.77073e9	−0.0927066
$985$	−1.50791e10	−0.502746
$986$	7.62166e10	2.53210
$987$	−1.86555e9	−0.0617586
$988$	4.40185e9	0.145207
$989$	−1.02367e10	−0.336489
$990$	−5.44274e9	−0.178277
$991$	−3.99983e10	−1.30552	−0.652761	−	0.757564i	$-0.726389\pi$
$991$	−3.99983e10	−1.30552	−0.652761	+	0.757564i	$0.726389\pi$
$992$	5.87021e9	0.190925
$993$	−1.15080e10	−0.372972
$994$	1.11336e10	0.359571
$995$	−1.86908e10	−0.601515
$996$	−3.74258e9	−0.120023
$997$	3.00799e10	0.961267	0.480633	−	0.876922i	$-0.340407\pi$
$997$	3.00799e10	0.961267	0.480633	+	0.876922i	$0.340407\pi$
$998$	−9.36774e9	−0.298317
$999$	8.54795e9	0.271258

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.8.a.h.1.1	✓	4
3.2	odd	2		414.8.a.i.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.8.a.h.1.1	✓	4	1.1	even	1	trivial
414.8.a.i.1.4		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	138.a (trivial)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -427.795 q^{5} +216.000 q^{6} +345.429 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} -427.795 q^{5} +216.000 q^{6} +345.429 q^{7} +512.000 q^{8} +729.000 q^{9} -3422.36 q^{10} +2181.54 q^{11} +1728.00 q^{12} -2610.39 q^{13} +2763.43 q^{14} -11550.5 q^{15} +4096.00 q^{16} +37979.0 q^{17} +5832.00 q^{18} -26348.1 q^{19} -27378.9 q^{20} +9326.57 q^{21} +17452.3 q^{22} -12167.0 q^{23} +13824.0 q^{24} +104884. q^{25} -20883.1 q^{26} +19683.0 q^{27} +22107.4 q^{28} +250851. q^{29} -92403.8 q^{30} +179145. q^{31} +32768.0 q^{32} +58901.7 q^{33} +303832. q^{34} -147773. q^{35} +46656.0 q^{36} +434281. q^{37} -210785. q^{38} -70480.6 q^{39} -219031. q^{40} -200429. q^{41} +74612.6 q^{42} +841346. q^{43} +139619. q^{44} -311863. q^{45} -97336.0 q^{46} -200025. q^{47} +110592. q^{48} -704222. q^{49} +839072. q^{50} +1.02543e6 q^{51} -167065. q^{52} -1.62417e6 q^{53} +157464. q^{54} -933254. q^{55} +176859. q^{56} -711399. q^{57} +2.00681e6 q^{58} -2.18662e6 q^{59} -739231. q^{60} +2.54771e6 q^{61} +1.43316e6 q^{62} +251817. q^{63} +262144. q^{64} +1.11671e6 q^{65} +471213. q^{66} +4.66306e6 q^{67} +2.43066e6 q^{68} -328509. q^{69} -1.18218e6 q^{70} +4.02892e6 q^{71} +373248. q^{72} -2.58030e6 q^{73} +3.47425e6 q^{74} +2.83187e6 q^{75} -1.68628e6 q^{76} +753568. q^{77} -563845. q^{78} +1.22032e6 q^{79} -1.75225e6 q^{80} +531441. q^{81} -1.60343e6 q^{82} -2.16585e6 q^{83} +596901. q^{84} -1.62473e7 q^{85} +6.73077e6 q^{86} +6.77298e6 q^{87} +1.11695e6 q^{88} +1.19998e6 q^{89} -2.49490e6 q^{90} -901704. q^{91} -778688. q^{92} +4.83690e6 q^{93} -1.60020e6 q^{94} +1.12716e7 q^{95} +884736. q^{96} +8.97814e6 q^{97} -5.63378e6 q^{98} +1.59035e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32 q^{2} + 108 q^{3} + 256 q^{4} + 270 q^{5} + 864 q^{6} + 2022 q^{7} + 2048 q^{8} + 2916 q^{9}+O(q^{10}) \) 4 * q + 32 * q^2 + 108 * q^3 + 256 * q^4 + 270 * q^5 + 864 * q^6 + 2022 * q^7 + 2048 * q^8 + 2916 * q^9	\( 4 q + 32 q^{2} + 108 q^{3} + 256 q^{4} + 270 q^{5} + 864 q^{6} + 2022 q^{7} + 2048 q^{8} + 2916 q^{9} + 2160 q^{10} + 4120 q^{11} + 6912 q^{12} + 8036 q^{13} + 16176 q^{14} + 7290 q^{15} + 16384 q^{16} + 37182 q^{17} + 23328 q^{18} + 5702 q^{19} + 17280 q^{20} + 54594 q^{21} + 32960 q^{22} - 48668 q^{23} + 55296 q^{24} + 121480 q^{25} + 64288 q^{26} + 78732 q^{27} + 129408 q^{28} + 217716 q^{29} + 58320 q^{30} + 222852 q^{31} + 131072 q^{32} + 111240 q^{33} + 297456 q^{34} + 68440 q^{35} + 186624 q^{36} + 486428 q^{37} + 45616 q^{38} + 216972 q^{39} + 138240 q^{40} + 338336 q^{41} + 436752 q^{42} + 730974 q^{43} + 263680 q^{44} + 196830 q^{45} - 389344 q^{46} + 338248 q^{47} + 442368 q^{48} - 310552 q^{49} + 971840 q^{50} + 1003914 q^{51} + 514304 q^{52} - 375502 q^{53} + 629856 q^{54} + 424840 q^{55} + 1035264 q^{56} + 153954 q^{57} + 1741728 q^{58} + 71392 q^{59} + 466560 q^{60} + 2101164 q^{61} + 1782816 q^{62} + 1474038 q^{63} + 1048576 q^{64} + 1578780 q^{65} + 889920 q^{66} + 4337162 q^{67} + 2379648 q^{68} - 1314036 q^{69} + 547520 q^{70} + 2288016 q^{71} + 1492992 q^{72} - 1107328 q^{73} + 3891424 q^{74} + 3279960 q^{75} + 364928 q^{76} + 5826200 q^{77} + 1735776 q^{78} + 60610 q^{79} + 1105920 q^{80} + 2125764 q^{81} + 2706688 q^{82} + 1485464 q^{83} + 3494016 q^{84} - 8843820 q^{85} + 5847792 q^{86} + 5878332 q^{87} + 2109440 q^{88} + 1485090 q^{89} + 1574640 q^{90} - 2898412 q^{91} - 3114752 q^{92} + 6017004 q^{93} + 2705984 q^{94} + 8545200 q^{95} + 3538944 q^{96} + 1935444 q^{97} - 2484416 q^{98} + 3003480 q^{99}+O(q^{100}) \) 4 * q + 32 * q^2 + 108 * q^3 + 256 * q^4 + 270 * q^5 + 864 * q^6 + 2022 * q^7 + 2048 * q^8 + 2916 * q^9 + 2160 * q^10 + 4120 * q^11 + 6912 * q^12 + 8036 * q^13 + 16176 * q^14 + 7290 * q^15 + 16384 * q^16 + 37182 * q^17 + 23328 * q^18 + 5702 * q^19 + 17280 * q^20 + 54594 * q^21 + 32960 * q^22 - 48668 * q^23 + 55296 * q^24 + 121480 * q^25 + 64288 * q^26 + 78732 * q^27 + 129408 * q^28 + 217716 * q^29 + 58320 * q^30 + 222852 * q^31 + 131072 * q^32 + 111240 * q^33 + 297456 * q^34 + 68440 * q^35 + 186624 * q^36 + 486428 * q^37 + 45616 * q^38 + 216972 * q^39 + 138240 * q^40 + 338336 * q^41 + 436752 * q^42 + 730974 * q^43 + 263680 * q^44 + 196830 * q^45 - 389344 * q^46 + 338248 * q^47 + 442368 * q^48 - 310552 * q^49 + 971840 * q^50 + 1003914 * q^51 + 514304 * q^52 - 375502 * q^53 + 629856 * q^54 + 424840 * q^55 + 1035264 * q^56 + 153954 * q^57 + 1741728 * q^58 + 71392 * q^59 + 466560 * q^60 + 2101164 * q^61 + 1782816 * q^62 + 1474038 * q^63 + 1048576 * q^64 + 1578780 * q^65 + 889920 * q^66 + 4337162 * q^67 + 2379648 * q^68 - 1314036 * q^69 + 547520 * q^70 + 2288016 * q^71 + 1492992 * q^72 - 1107328 * q^73 + 3891424 * q^74 + 3279960 * q^75 + 364928 * q^76 + 5826200 * q^77 + 1735776 * q^78 + 60610 * q^79 + 1105920 * q^80 + 2125764 * q^81 + 2706688 * q^82 + 1485464 * q^83 + 3494016 * q^84 - 8843820 * q^85 + 5847792 * q^86 + 5878332 * q^87 + 2109440 * q^88 + 1485090 * q^89 + 1574640 * q^90 - 2898412 * q^91 - 3114752 * q^92 + 6017004 * q^93 + 2705984 * q^94 + 8545200 * q^95 + 3538944 * q^96 + 1935444 * q^97 - 2484416 * q^98 + 3003480 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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