LMFDB - Embedded newform 91.8.a.e.1.2

Newspace parameters

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
Defining polynomial:	$ x^{12} - 6 x^{11} - 1243 x^{10} + 5598 x^{9} + 567554 x^{8} - 1739560 x^{7} - 117081910 x^{6} + 186018392 x^{5} + 10752389517 x^{4} + 491049966 x^{3} + \cdots + 59402280000 $ x^12 - 6x^11 - 1243x^10 + 5598x^9 + 567554x^8 - 1739560x^7 - 117081910x^6 + 186018392x^5 + 10752389517x^4 + 491049966x^3 - 344602049215x^2 - 835334324470*x + 59402280000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$19.0596$ of defining polynomial
Character	$\chi$	$=$	91.1

$q$-expansion

$f(q)$	$=$	$q-18.0596 q^{2} -64.0898 q^{3} +198.149 q^{4} +13.5880 q^{5} +1157.44 q^{6} +343.000 q^{7} -1266.87 q^{8} +1920.50 q^{9} +O(q^{10})$	\(q-18.0596 q^{2} -64.0898 q^{3} +198.149 q^{4} +13.5880 q^{5} +1157.44 q^{6} +343.000 q^{7} -1266.87 q^{8} +1920.50 q^{9} -245.394 q^{10} +6489.06 q^{11} -12699.3 q^{12} +2197.00 q^{13} -6194.44 q^{14} -870.853 q^{15} -2484.01 q^{16} -31064.5 q^{17} -34683.4 q^{18} -6937.84 q^{19} +2692.46 q^{20} -21982.8 q^{21} -117190. q^{22} +6153.33 q^{23} +81193.1 q^{24} -77940.4 q^{25} -39676.9 q^{26} +17080.0 q^{27} +67965.2 q^{28} -86998.5 q^{29} +15727.3 q^{30} +282367. q^{31} +207019. q^{32} -415883. q^{33} +561012. q^{34} +4660.69 q^{35} +380545. q^{36} -232493. q^{37} +125295. q^{38} -140805. q^{39} -17214.2 q^{40} +412653. q^{41} +397000. q^{42} -603630. q^{43} +1.28580e6 q^{44} +26095.8 q^{45} -111127. q^{46} -217376. q^{47} +159199. q^{48} +117649. q^{49} +1.40757e6 q^{50} +1.99092e6 q^{51} +435334. q^{52} +1.08757e6 q^{53} -308457. q^{54} +88173.5 q^{55} -434535. q^{56} +444645. q^{57} +1.57116e6 q^{58} -641874. q^{59} -172559. q^{60} -576801. q^{61} -5.09944e6 q^{62} +658731. q^{63} -3.42073e6 q^{64} +29852.9 q^{65} +7.51067e6 q^{66} -3.17002e6 q^{67} -6.15540e6 q^{68} -394366. q^{69} -84170.2 q^{70} +1.13223e6 q^{71} -2.43301e6 q^{72} +4.75764e6 q^{73} +4.19872e6 q^{74} +4.99518e6 q^{75} -1.37473e6 q^{76} +2.22575e6 q^{77} +2.54289e6 q^{78} -5.25839e6 q^{79} -33752.7 q^{80} -5.29478e6 q^{81} -7.45234e6 q^{82} +5.20649e6 q^{83} -4.35587e6 q^{84} -422105. q^{85} +1.09013e7 q^{86} +5.57572e6 q^{87} -8.22077e6 q^{88} +6.22177e6 q^{89} -471279. q^{90} +753571. q^{91} +1.21928e6 q^{92} -1.80969e7 q^{93} +3.92573e6 q^{94} -94271.6 q^{95} -1.32678e7 q^{96} -4.76838e6 q^{97} -2.12469e6 q^{98} +1.24622e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9}+O(q^{10}) $ 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9	\( 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9} + 6668 q^{10} + 12168 q^{11} - 183 q^{12} + 26364 q^{13} + 2058 q^{14} - 28790 q^{15} + 85914 q^{16} + 82710 q^{17} - 44965 q^{18} - 10302 q^{19} + 141318 q^{20} + 28126 q^{21} - 97457 q^{22} + 98376 q^{23} - 519981 q^{24} + 272736 q^{25} + 13182 q^{26} + 306652 q^{27} + 338198 q^{28} + 350592 q^{29} + 231528 q^{30} + 55092 q^{31} + 114420 q^{32} + 609912 q^{33} + 812002 q^{34} + 351918 q^{35} + 1472143 q^{36} + 376310 q^{37} + 2825424 q^{38} + 180154 q^{39} + 2169290 q^{40} + 1387272 q^{41} + 105987 q^{42} + 568708 q^{43} + 3392031 q^{44} + 3556226 q^{45} - 1736829 q^{46} + 1359444 q^{47} + 4151249 q^{48} + 1411788 q^{49} + 3983712 q^{50} + 2709260 q^{51} + 2166242 q^{52} + 2061780 q^{53} + 2196651 q^{54} - 2112846 q^{55} + 78204 q^{56} + 2359902 q^{57} + 670268 q^{58} + 395964 q^{59} - 1052376 q^{60} + 444006 q^{61} + 2854353 q^{62} + 3739386 q^{63} + 12026858 q^{64} + 2254122 q^{65} - 4605681 q^{66} - 3094010 q^{67} + 4668954 q^{68} + 3839892 q^{69} + 2287124 q^{70} + 5694366 q^{71} - 9780585 q^{72} + 7052346 q^{73} - 4436259 q^{74} - 16288696 q^{75} - 3051830 q^{76} + 4173624 q^{77} + 678873 q^{78} + 4304160 q^{79} + 3807018 q^{80} - 6689556 q^{81} - 4733665 q^{82} + 2704554 q^{83} - 62769 q^{84} + 9301878 q^{85} + 1510998 q^{86} + 16231802 q^{87} - 70453923 q^{88} - 10986042 q^{89} - 12851300 q^{90} + 9042852 q^{91} - 16505451 q^{92} - 47230934 q^{93} - 24306151 q^{94} - 21839424 q^{95} - 86512741 q^{96} - 24462382 q^{97} + 705894 q^{98} + 11555078 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9 + 6668 * q^10 + 12168 * q^11 - 183 * q^12 + 26364 * q^13 + 2058 * q^14 - 28790 * q^15 + 85914 * q^16 + 82710 * q^17 - 44965 * q^18 - 10302 * q^19 + 141318 * q^20 + 28126 * q^21 - 97457 * q^22 + 98376 * q^23 - 519981 * q^24 + 272736 * q^25 + 13182 * q^26 + 306652 * q^27 + 338198 * q^28 + 350592 * q^29 + 231528 * q^30 + 55092 * q^31 + 114420 * q^32 + 609912 * q^33 + 812002 * q^34 + 351918 * q^35 + 1472143 * q^36 + 376310 * q^37 + 2825424 * q^38 + 180154 * q^39 + 2169290 * q^40 + 1387272 * q^41 + 105987 * q^42 + 568708 * q^43 + 3392031 * q^44 + 3556226 * q^45 - 1736829 * q^46 + 1359444 * q^47 + 4151249 * q^48 + 1411788 * q^49 + 3983712 * q^50 + 2709260 * q^51 + 2166242 * q^52 + 2061780 * q^53 + 2196651 * q^54 - 2112846 * q^55 + 78204 * q^56 + 2359902 * q^57 + 670268 * q^58 + 395964 * q^59 - 1052376 * q^60 + 444006 * q^61 + 2854353 * q^62 + 3739386 * q^63 + 12026858 * q^64 + 2254122 * q^65 - 4605681 * q^66 - 3094010 * q^67 + 4668954 * q^68 + 3839892 * q^69 + 2287124 * q^70 + 5694366 * q^71 - 9780585 * q^72 + 7052346 * q^73 - 4436259 * q^74 - 16288696 * q^75 - 3051830 * q^76 + 4173624 * q^77 + 678873 * q^78 + 4304160 * q^79 + 3807018 * q^80 - 6689556 * q^81 - 4733665 * q^82 + 2704554 * q^83 - 62769 * q^84 + 9301878 * q^85 + 1510998 * q^86 + 16231802 * q^87 - 70453923 * q^88 - 10986042 * q^89 - 12851300 * q^90 + 9042852 * q^91 - 16505451 * q^92 - 47230934 * q^93 - 24306151 * q^94 - 21839424 * q^95 - 86512741 * q^96 - 24462382 * q^97 + 705894 * q^98 + 11555078 * 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 $

$2$	−18.0596	−1.59626	−0.798129	−	0.602486i	$-0.794177\pi$
$2$	−18.0596	−1.59626	−0.798129	+	0.602486i	$0.794177\pi$
$3$	−64.0898	−1.37045	−0.685227	−	0.728330i	$-0.740297\pi$
$3$	−64.0898	−1.37045	−0.685227	+	0.728330i	$0.740297\pi$
$4$	198.149	1.54804
$5$	13.5880	0.0486140	0.0243070	−	0.999705i	$-0.492262\pi$
$5$	13.5880	0.0486140	0.0243070	+	0.999705i	$0.492262\pi$
$6$	1157.44	2.18760
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	−1266.87	−0.874814
$9$	1920.50	0.878143
$10$	−245.394	−0.0776005
$11$	6489.06	1.46997	0.734983	−	0.678085i	$-0.237190\pi$
$11$	6489.06	1.46997	0.734983	+	0.678085i	$0.237190\pi$
$12$	−12699.3	−2.12152
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	−6194.44	−0.603329
$15$	−870.853	−0.0666232
$16$	−2484.01	−0.151612
$17$	−31064.5	−1.53353	−0.766766	−	0.641926i	$-0.778136\pi$
$17$	−31064.5	−1.53353	−0.766766	+	0.641926i	$0.778136\pi$
$18$	−34683.4	−1.40174
$19$	−6937.84	−0.232053	−0.116026	−	0.993246i	$-0.537016\pi$
$19$	−6937.84	−0.232053	−0.116026	+	0.993246i	$0.537016\pi$
$20$	2692.46	0.0752564
$21$	−21982.8	−0.517983
$22$	−117190.	−2.34645
$23$	6153.33	0.105454	0.0527270	−	0.998609i	$-0.483209\pi$
$23$	6153.33	0.105454	0.0527270	+	0.998609i	$0.483209\pi$
$24$	81193.1	1.19889
$25$	−77940.4	−0.997637
$26$	−39676.9	−0.442722
$27$	17080.0	0.166999
$28$	67965.2	0.585104
$29$	−86998.5	−0.662398	−0.331199	−	0.943561i	$-0.607453\pi$
$29$	−86998.5	−0.662398	−0.331199	+	0.943561i	$0.607453\pi$
$30$	15727.3	0.106348
$31$	282367.	1.70235	0.851174	−	0.524883i	$-0.175891\pi$
$31$	282367.	1.70235	0.851174	+	0.524883i	$0.175891\pi$
$32$	207019.	1.11683
$33$	−415883.	−2.01452
$34$	561012.	2.44791
$35$	4660.69	0.0183744
$36$	380545.	1.35940
$37$	−232493.	−0.754576	−0.377288	−	0.926096i	$-0.623143\pi$
$37$	−232493.	−0.754576	−0.377288	+	0.926096i	$0.623143\pi$
$38$	125295.	0.370416
$39$	−140805.	−0.380095
$40$	−17214.2	−0.0425282
$41$	412653.	0.935064	0.467532	−	0.883976i	$-0.345143\pi$
$41$	412653.	0.935064	0.467532	+	0.883976i	$0.345143\pi$
$42$	397000.	0.826834
$43$	−603630.	−1.15779	−0.578897	−	0.815401i	$-0.696517\pi$
$43$	−603630.	−1.15779	−0.578897	+	0.815401i	$0.696517\pi$
$44$	1.28580e6	2.27557
$45$	26095.8	0.0426900
$46$	−111127.	−0.168332
$47$	−217376.	−0.305401	−0.152700	−	0.988273i	$-0.548797\pi$
$47$	−217376.	−0.305401	−0.152700	+	0.988273i	$0.548797\pi$
$48$	159199.	0.207777
$49$	117649.	0.142857
$50$	1.40757e6	1.59249
$51$	1.99092e6	2.10164
$52$	435334.	0.429349
$53$	1.08757e6	1.00344	0.501721	−	0.865029i	$-0.332700\pi$
$53$	1.08757e6	1.00344	0.501721	+	0.865029i	$0.332700\pi$
$54$	−308457.	−0.266574
$55$	88173.5	0.0714610
$56$	−434535.	−0.330648
$57$	444645.	0.318018
$58$	1.57116e6	1.05736
$59$	−641874.	−0.406881	−0.203441	−	0.979087i	$-0.565212\pi$
$59$	−641874.	−0.406881	−0.203441	+	0.979087i	$0.565212\pi$
$60$	−172559.	−0.103135
$61$	−576801.	−0.325366	−0.162683	−	0.986678i	$-0.552015\pi$
$61$	−576801.	−0.325366	−0.162683	+	0.986678i	$0.552015\pi$
$62$	−5.09944e6	−2.71739
$63$	658731.	0.331907
$64$	−3.42073e6	−1.63113
$65$	29852.9	0.0134831
$66$	7.51067e6	3.21570
$67$	−3.17002e6	−1.28766	−0.643828	−	0.765170i	$-0.722655\pi$
$67$	−3.17002e6	−1.28766	−0.643828	+	0.765170i	$0.722655\pi$
$68$	−6.15540e6	−2.37397
$69$	−394366.	−0.144520
$70$	−84170.2	−0.0293302
$71$	1.13223e6	0.375432	0.187716	−	0.982223i	$-0.439891\pi$
$71$	1.13223e6	0.375432	0.187716	+	0.982223i	$0.439891\pi$
$72$	−2.43301e6	−0.768212
$73$	4.75764e6	1.43140	0.715701	−	0.698406i	$-0.246107\pi$
$73$	4.75764e6	1.43140	0.715701	+	0.698406i	$0.246107\pi$
$74$	4.19872e6	1.20450
$75$	4.99518e6	1.36721
$76$	−1.37473e6	−0.359227
$77$	2.22575e6	0.555595
$78$	2.54289e6	0.606730
$79$	−5.25839e6	−1.19994	−0.599968	−	0.800024i	$-0.704820\pi$
$79$	−5.25839e6	−1.19994	−0.599968	+	0.800024i	$0.704820\pi$
$80$	−33752.7	−0.00737045
$81$	−5.29478e6	−1.10701
$82$	−7.45234e6	−1.49260
$83$	5.20649e6	0.999475	0.499737	−	0.866177i	$-0.333430\pi$
$83$	5.20649e6	0.999475	0.499737	+	0.866177i	$0.333430\pi$
$84$	−4.35587e6	−0.801858
$85$	−422105.	−0.0745511
$86$	1.09013e7	1.84814
$87$	5.57572e6	0.907786
$88$	−8.22077e6	−1.28595
$89$	6.22177e6	0.935511	0.467756	−	0.883858i	$-0.345063\pi$
$89$	6.22177e6	0.935511	0.467756	+	0.883858i	$0.345063\pi$
$90$	−471279.	−0.0681443
$91$	753571.	0.104828
$92$	1.21928e6	0.163247
$93$	−1.80969e7	−2.33299
$94$	3.92573e6	0.487498
$95$	−94271.6	−0.0112810
$96$	−1.32678e7	−1.53056
$97$	−4.76838e6	−0.530481	−0.265241	−	0.964182i	$-0.585451\pi$
$97$	−4.76838e6	−0.530481	−0.265241	+	0.964182i	$0.585451\pi$
$98$	−2.12469e6	−0.228037
$99$	1.24622e7	1.29084
$100$	−1.54438e7	−1.54438
$101$	1.50570e7	1.45417	0.727084	−	0.686548i	$-0.240875\pi$
$101$	1.50570e7	1.45417	0.727084	+	0.686548i	$0.240875\pi$
$102$	−3.59552e7	−3.35475
$103$	−1.44181e7	−1.30010	−0.650050	−	0.759891i	$-0.725252\pi$
$103$	−1.44181e7	−1.30010	−0.650050	+	0.759891i	$0.725252\pi$
$104$	−2.78330e6	−0.242630
$105$	−298703.	−0.0251812
$106$	−1.96411e7	−1.60175
$107$	−1.56711e7	−1.23668	−0.618339	−	0.785911i	$-0.712194\pi$
$107$	−1.56711e7	−1.23668	−0.618339	+	0.785911i	$0.712194\pi$
$108$	3.38438e6	0.258521
$109$	1.05853e7	0.782909	0.391454	−	0.920198i	$-0.371972\pi$
$109$	1.05853e7	0.782909	0.391454	+	0.920198i	$0.371972\pi$
$110$	−1.59238e6	−0.114070
$111$	1.49004e7	1.03411
$112$	−852014.	−0.0573038
$113$	1.71706e7	1.11946	0.559732	−	0.828673i	$-0.310904\pi$
$113$	1.71706e7	1.11946	0.559732	+	0.828673i	$0.310904\pi$
$114$	−8.03011e6	−0.507638
$115$	83611.6	0.00512654
$116$	−1.72387e7	−1.02542
$117$	4.21934e6	0.243553
$118$	1.15920e7	0.649487
$119$	−1.06551e7	−0.579621
$120$	1.10325e6	0.0582829
$121$	2.26208e7	1.16080
$122$	1.04168e7	0.519368
$123$	−2.64468e7	−1.28146
$124$	5.59508e7	2.63530
$125$	−2.12062e6	−0.0971131
$126$	−1.18964e7	−0.529809
$127$	1.15826e7	0.501758	0.250879	−	0.968018i	$-0.419280\pi$
$127$	1.15826e7	0.501758	0.250879	+	0.968018i	$0.419280\pi$
$128$	3.52785e7	1.48688
$129$	3.86865e7	1.58670
$130$	−539131.	−0.0215225
$131$	3.85740e7	1.49915	0.749576	−	0.661919i	$-0.230258\pi$
$131$	3.85740e7	1.49915	0.749576	+	0.661919i	$0.230258\pi$
$132$	−8.24068e7	−3.11856
$133$	−2.37968e6	−0.0877077
$134$	5.72492e7	2.05543
$135$	232083.	0.00811849
$136$	3.93545e7	1.34156
$137$	3.91337e7	1.30026	0.650128	−	0.759825i	$-0.274715\pi$
$137$	3.91337e7	1.30026	0.650128	+	0.759825i	$0.274715\pi$
$138$	7.12208e6	0.230691
$139$	2.36964e7	0.748396	0.374198	−	0.927349i	$-0.377918\pi$
$139$	2.36964e7	0.748396	0.374198	+	0.927349i	$0.377918\pi$
$140$	923512.	0.0284442
$141$	1.39316e7	0.418537
$142$	−2.04477e7	−0.599287
$143$	1.42565e7	0.407695
$144$	−4.77053e6	−0.133137
$145$	−1.18214e6	−0.0322018
$146$	−8.59211e7	−2.28489
$147$	−7.54010e6	−0.195779
$148$	−4.60682e7	−1.16811
$149$	4.32940e6	0.107220	0.0536100	−	0.998562i	$-0.482927\pi$
$149$	4.32940e6	0.107220	0.0536100	+	0.998562i	$0.482927\pi$
$150$	−9.02110e7	−2.18243
$151$	4.42889e7	1.04683	0.523415	−	0.852078i	$-0.324658\pi$
$151$	4.42889e7	1.04683	0.523415	+	0.852078i	$0.324658\pi$
$152$	8.78931e6	0.203003
$153$	−5.96593e7	−1.34666
$154$	−4.01961e7	−0.886873
$155$	3.83681e6	0.0827580
$156$	−2.79004e7	−0.588403
$157$	1.88511e7	0.388765	0.194383	−	0.980926i	$-0.437730\pi$
$157$	1.88511e7	0.388765	0.194383	+	0.980926i	$0.437730\pi$
$158$	9.49644e7	1.91541
$159$	−6.97022e7	−1.37517
$160$	2.81298e6	0.0542933
$161$	2.11059e6	0.0398578
$162$	9.56217e7	1.76707
$163$	−1.12952e7	−0.204285	−0.102143	−	0.994770i	$-0.532570\pi$
$163$	−1.12952e7	−0.204285	−0.102143	+	0.994770i	$0.532570\pi$
$164$	8.17668e7	1.44752
$165$	−5.65102e6	−0.0979339
$166$	−9.40272e7	−1.59542
$167$	4.71435e7	0.783274	0.391637	−	0.920120i	$-0.371909\pi$
$167$	4.71435e7	0.783274	0.391637	+	0.920120i	$0.371909\pi$
$168$	2.78492e7	0.453138
$169$	4.82681e6	0.0769231
$170$	7.62305e6	0.119003
$171$	−1.33241e7	−0.203776
$172$	−1.19609e8	−1.79231
$173$	−8.73356e7	−1.28242	−0.641210	−	0.767366i	$-0.721567\pi$
$173$	−8.73356e7	−1.28242	−0.641210	+	0.767366i	$0.721567\pi$
$174$	−1.00695e8	−1.44906
$175$	−2.67335e7	−0.377071
$176$	−1.61189e7	−0.222864
$177$	4.11376e7	0.557612
$178$	−1.12363e8	−1.49332
$179$	1.44092e8	1.87782	0.938910	−	0.344164i	$-0.111838\pi$
$179$	1.44092e8	1.87782	0.938910	+	0.344164i	$0.111838\pi$
$180$	5.17086e6	0.0660859
$181$	8.95747e7	1.12282	0.561410	−	0.827538i	$-0.310259\pi$
$181$	8.95747e7	1.12282	0.561410	+	0.827538i	$0.310259\pi$
$182$	−1.36092e7	−0.167333
$183$	3.69671e7	0.445898
$184$	−7.79544e6	−0.0922525
$185$	−3.15911e6	−0.0366830
$186$	3.26822e8	3.72405
$187$	−2.01579e8	−2.25424
$188$	−4.30729e7	−0.472772
$189$	5.85843e6	0.0631197
$190$	1.70251e6	0.0180074
$191$	−1.40233e8	−1.45624	−0.728119	−	0.685450i	$-0.759605\pi$
$191$	−1.40233e8	−1.45624	−0.728119	+	0.685450i	$0.759605\pi$
$192$	2.19234e8	2.23539
$193$	4.24144e7	0.424681	0.212341	−	0.977196i	$-0.431891\pi$
$193$	4.24144e7	0.424681	0.212341	+	0.977196i	$0.431891\pi$
$194$	8.61151e7	0.846785
$195$	−1.91326e6	−0.0184780
$196$	2.33120e7	0.221149
$197$	2.59251e7	0.241595	0.120798	−	0.992677i	$-0.461455\pi$
$197$	2.59251e7	0.241595	0.120798	+	0.992677i	$0.461455\pi$
$198$	−2.25063e8	−2.06052
$199$	1.49127e8	1.34144	0.670721	−	0.741710i	$-0.265985\pi$
$199$	1.49127e8	1.34144	0.670721	+	0.741710i	$0.265985\pi$
$200$	9.87400e7	0.872746
$201$	2.03166e8	1.76467
$202$	−2.71924e8	−2.32123
$203$	−2.98405e7	−0.250363
$204$	3.94498e8	3.25342
$205$	5.60714e6	0.0454572
$206$	2.60385e8	2.07530
$207$	1.18175e7	0.0926037
$208$	−5.45736e6	−0.0420495
$209$	−4.50201e7	−0.341110
$210$	5.39445e6	0.0401957
$211$	−2.18089e8	−1.59825	−0.799127	−	0.601163i	$-0.794704\pi$
$211$	−2.18089e8	−1.59825	−0.799127	+	0.601163i	$0.794704\pi$
$212$	2.15501e8	1.55337
$213$	−7.25646e7	−0.514513
$214$	2.83014e8	1.97406
$215$	−8.20213e6	−0.0562849
$216$	−2.16380e7	−0.146093
$217$	9.68520e7	0.643427
$218$	−1.91167e8	−1.24972
$219$	−3.04916e8	−1.96167
$220$	1.74715e7	0.110624
$221$	−6.82487e7	−0.425325
$222$	−2.69095e8	−1.65071
$223$	−8.12974e7	−0.490919	−0.245459	−	0.969407i	$-0.578939\pi$
$223$	−8.12974e7	−0.490919	−0.245459	+	0.969407i	$0.578939\pi$
$224$	7.10075e7	0.422120
$225$	−1.49684e8	−0.876068
$226$	−3.10094e8	−1.78695
$227$	−1.99361e8	−1.13123	−0.565614	−	0.824670i	$-0.691361\pi$
$227$	−1.99361e8	−1.13123	−0.565614	+	0.824670i	$0.691361\pi$
$228$	8.81060e7	0.492304
$229$	−5.12300e7	−0.281903	−0.140952	−	0.990016i	$-0.545016\pi$
$229$	−5.12300e7	−0.281903	−0.140952	+	0.990016i	$0.545016\pi$
$230$	−1.50999e6	−0.00818328
$231$	−1.42648e8	−0.761418
$232$	1.10215e8	0.579475
$233$	1.32927e8	0.688443	0.344221	−	0.938889i	$-0.388143\pi$
$233$	1.32927e8	0.688443	0.344221	+	0.938889i	$0.388143\pi$
$234$	−7.61995e7	−0.388774
$235$	−2.95371e6	−0.0148467
$236$	−1.27187e8	−0.629869
$237$	3.37009e8	1.64446
$238$	1.92427e8	0.925225
$239$	3.79964e8	1.80032	0.900161	−	0.435558i	$-0.143449\pi$
$239$	3.79964e8	1.80032	0.900161	+	0.435558i	$0.143449\pi$
$240$	2.16320e6	0.0101009
$241$	−2.17702e8	−1.00185	−0.500925	−	0.865491i	$-0.667007\pi$
$241$	−2.17702e8	−1.00185	−0.500925	+	0.865491i	$0.667007\pi$
$242$	−4.08522e8	−1.85294
$243$	3.01988e8	1.35010
$244$	−1.14293e8	−0.503679
$245$	1.59862e6	0.00694486
$246$	4.77619e8	2.04554
$247$	−1.52424e7	−0.0643599
$248$	−3.57721e8	−1.48924
$249$	−3.33683e8	−1.36973
$250$	3.82975e7	0.155018
$251$	2.96487e6	0.0118344	0.00591721	−	0.999982i	$-0.498116\pi$
$251$	2.96487e6	0.0118344	0.00591721	+	0.999982i	$0.498116\pi$
$252$	1.30527e8	0.513805
$253$	3.99293e7	0.155014
$254$	−2.09178e8	−0.800935
$255$	2.70526e7	0.102169
$256$	−1.99263e8	−0.742313
$257$	6.08740e7	0.223700	0.111850	−	0.993725i	$-0.464322\pi$
$257$	6.08740e7	0.223700	0.111850	+	0.993725i	$0.464322\pi$
$258$	−6.98663e8	−2.53279
$259$	−7.97450e7	−0.285203
$260$	5.91532e6	0.0208724
$261$	−1.67081e8	−0.581680
$262$	−6.96632e8	−2.39303
$263$	−2.65978e8	−0.901573	−0.450787	−	0.892632i	$-0.648856\pi$
$263$	−2.65978e8	−0.901573	−0.450787	+	0.892632i	$0.648856\pi$
$264$	5.26867e8	1.76233
$265$	1.47779e7	0.0487813
$266$	4.29761e7	0.140004
$267$	−3.98752e8	−1.28208
$268$	−6.28136e8	−1.99334
$269$	3.71244e8	1.16286	0.581429	−	0.813597i	$-0.302494\pi$
$269$	3.71244e8	1.16286	0.581429	+	0.813597i	$0.302494\pi$
$270$	−4.19133e6	−0.0129592
$271$	−3.00232e7	−0.0916357	−0.0458179	−	0.998950i	$-0.514589\pi$
$271$	−3.00232e7	−0.0916357	−0.0458179	+	0.998950i	$0.514589\pi$
$272$	7.71644e7	0.232502
$273$	−4.82962e7	−0.143663
$274$	−7.06739e8	−2.07554
$275$	−5.05760e8	−1.46649
$276$	−7.81432e7	−0.223722
$277$	2.27552e8	0.643283	0.321642	−	0.946861i	$-0.395765\pi$
$277$	2.27552e8	0.643283	0.321642	+	0.946861i	$0.395765\pi$
$278$	−4.27948e8	−1.19463
$279$	5.42286e8	1.49491
$280$	−5.90447e6	−0.0160741
$281$	2.09229e8	0.562536	0.281268	−	0.959629i	$-0.409245\pi$
$281$	2.09229e8	0.562536	0.281268	+	0.959629i	$0.409245\pi$
$282$	−2.51599e8	−0.668094
$283$	4.77356e8	1.25196	0.625979	−	0.779840i	$-0.284699\pi$
$283$	4.77356e8	1.25196	0.625979	+	0.779840i	$0.284699\pi$
$284$	2.24351e8	0.581184
$285$	6.04184e6	0.0154601
$286$	−2.57466e8	−0.650787
$287$	1.41540e8	0.353421
$288$	3.97580e8	0.980732
$289$	5.54664e8	1.35172
$290$	2.13489e7	0.0514024
$291$	3.05605e8	0.727000
$292$	9.42723e8	2.21587
$293$	7.52718e8	1.74822	0.874109	−	0.485730i	$-0.161446\pi$
$293$	7.52718e8	1.74822	0.874109	+	0.485730i	$0.161446\pi$
$294$	1.36171e8	0.312514
$295$	−8.72180e6	−0.0197801
$296$	2.94537e8	0.660114
$297$	1.10833e8	0.245483
$298$	−7.81873e7	−0.171151
$299$	1.35189e7	0.0292477
$300$	9.89791e8	2.11650
$301$	−2.07045e8	−0.437605
$302$	−7.99840e8	−1.67101
$303$	−9.65002e8	−1.99287
$304$	1.72336e7	0.0351819
$305$	−7.83759e6	−0.0158173
$306$	1.07742e9	2.14962
$307$	1.70871e8	0.337042	0.168521	−	0.985698i	$-0.446101\pi$
$307$	1.70871e8	0.337042	0.168521	+	0.985698i	$0.446101\pi$
$308$	4.41030e8	0.860084
$309$	9.24051e8	1.78173
$310$	−6.92913e7	−0.132103
$311$	3.68376e8	0.694432	0.347216	−	0.937785i	$-0.387127\pi$
$311$	3.68376e8	0.694432	0.347216	+	0.937785i	$0.387127\pi$
$312$	1.78381e8	0.332513
$313$	2.94356e8	0.542586	0.271293	−	0.962497i	$-0.412549\pi$
$313$	2.94356e8	0.542586	0.271293	+	0.962497i	$0.412549\pi$
$314$	−3.40443e8	−0.620570
$315$	8.95086e6	0.0161353
$316$	−1.04195e9	−1.85755
$317$	−2.29062e8	−0.403873	−0.201937	−	0.979399i	$-0.564724\pi$
$317$	−2.29062e8	−0.403873	−0.201937	+	0.979399i	$0.564724\pi$
$318$	1.25879e9	2.19513
$319$	−5.64539e8	−0.973703
$320$	−4.64809e7	−0.0792957
$321$	1.00436e9	1.69481
$322$	−3.81165e7	−0.0636234
$323$	2.15521e8	0.355861
$324$	−1.04916e9	−1.71369
$325$	−1.71235e8	−0.276695
$326$	2.03987e8	0.326092
$327$	−6.78411e8	−1.07294
$328$	−5.22776e8	−0.818007
$329$	−7.45601e7	−0.115431
$330$	1.02055e8	0.156328
$331$	1.31268e9	1.98958	0.994789	−	0.101959i	$-0.0325112\pi$
$331$	1.31268e9	1.98958	0.994789	+	0.101959i	$0.0325112\pi$
$332$	1.03166e9	1.54723
$333$	−4.46502e8	−0.662626
$334$	−8.51392e8	−1.25031
$335$	−4.30743e7	−0.0625981
$336$	5.46054e7	0.0785322
$337$	−4.44497e8	−0.632651	−0.316326	−	0.948651i	$-0.602449\pi$
$337$	−4.44497e8	−0.632651	−0.316326	+	0.948651i	$0.602449\pi$
$338$	−8.71702e7	−0.122789
$339$	−1.10046e9	−1.53417
$340$	−8.36398e7	−0.115408
$341$	1.83230e9	2.50240
$342$	2.40628e8	0.325278
$343$	4.03536e7	0.0539949
$344$	7.64718e8	1.01285
$345$	−5.35865e6	−0.00702568
$346$	1.57725e9	2.04707
$347$	−6.01032e7	−0.0772225	−0.0386113	−	0.999254i	$-0.512293\pi$
$347$	−6.01032e7	−0.0772225	−0.0386113	+	0.999254i	$0.512293\pi$
$348$	1.10482e9	1.40529
$349$	−1.29834e9	−1.63493	−0.817463	−	0.575980i	$-0.804620\pi$
$349$	−1.29834e9	−1.63493	−0.817463	+	0.575980i	$0.804620\pi$
$350$	4.82797e8	0.601903
$351$	3.75247e7	0.0463172
$352$	1.34336e9	1.64170
$353$	−8.17130e7	−0.0988734	−0.0494367	−	0.998777i	$-0.515743\pi$
$353$	−8.17130e7	−0.0988734	−0.0494367	+	0.998777i	$0.515743\pi$
$354$	−7.42928e8	−0.890093
$355$	1.53848e7	0.0182513
$356$	1.23284e9	1.44821
$357$	6.82884e8	0.794344
$358$	−2.60224e9	−2.99748
$359$	7.04389e8	0.803493	0.401747	−	0.915751i	$-0.368403\pi$
$359$	7.04389e8	0.803493	0.401747	+	0.915751i	$0.368403\pi$
$360$	−3.30599e7	−0.0373458
$361$	−8.45738e8	−0.946152
$362$	−1.61768e9	−1.79231
$363$	−1.44976e9	−1.59083
$364$	1.49319e8	0.162279
$365$	6.46470e7	0.0695862
$366$	−6.67610e8	−0.711769
$367$	7.55308e6	0.00797614	0.00398807	−	0.999992i	$-0.498731\pi$
$367$	7.55308e6	0.00797614	0.00398807	+	0.999992i	$0.498731\pi$
$368$	−1.52849e7	−0.0159880
$369$	7.92499e8	0.821120
$370$	5.70523e7	0.0585555
$371$	3.73037e8	0.379265
$372$	−3.58588e9	−3.61156
$373$	−4.06459e8	−0.405542	−0.202771	−	0.979226i	$-0.564995\pi$
$373$	−4.06459e8	−0.405542	−0.202771	+	0.979226i	$0.564995\pi$
$374$	3.64044e9	3.59835
$375$	1.35910e8	0.133089
$376$	2.75387e8	0.267169
$377$	−1.91136e8	−0.183716
$378$	−1.05801e8	−0.100755
$379$	−4.82455e8	−0.455218	−0.227609	−	0.973753i	$-0.573091\pi$
$379$	−4.82455e8	−0.455218	−0.227609	+	0.973753i	$0.573091\pi$
$380$	−1.86798e7	−0.0174635
$381$	−7.42328e8	−0.687636
$382$	2.53255e9	2.32453
$383$	−3.62016e8	−0.329255	−0.164628	−	0.986356i	$-0.552642\pi$
$383$	−3.62016e8	−0.329255	−0.164628	+	0.986356i	$0.552642\pi$
$384$	−2.26099e9	−2.03770
$385$	3.02435e7	0.0270097
$386$	−7.65987e8	−0.677901
$387$	−1.15927e9	−1.01671
$388$	−9.44851e8	−0.821206
$389$	9.51268e8	0.819368	0.409684	−	0.912227i	$-0.365639\pi$
$389$	9.51268e8	0.819368	0.409684	+	0.912227i	$0.365639\pi$
$390$	3.45528e7	0.0294956
$391$	−1.91150e8	−0.161717
$392$	−1.49045e8	−0.124973
$393$	−2.47220e9	−2.05452
$394$	−4.68197e8	−0.385649
$395$	−7.14511e7	−0.0583337
$396$	2.46938e9	1.99827
$397$	1.01269e9	0.812291	0.406145	−	0.913808i	$-0.366873\pi$
$397$	1.01269e9	0.812291	0.406145	+	0.913808i	$0.366873\pi$
$398$	−2.69318e9	−2.14129
$399$	1.52513e8	0.120199
$400$	1.93604e8	0.151253
$401$	6.31867e8	0.489351	0.244676	−	0.969605i	$-0.421319\pi$
$401$	6.31867e8	0.489351	0.244676	+	0.969605i	$0.421319\pi$
$402$	−3.66909e9	−2.81687
$403$	6.20361e8	0.472147
$404$	2.98354e9	2.25111
$405$	−7.19456e7	−0.0538161
$406$	5.38908e8	0.399644
$407$	−1.50866e9	−1.10920
$408$	−2.52222e9	−1.83854
$409$	−1.02626e9	−0.741695	−0.370847	−	0.928694i	$-0.620933\pi$
$409$	−1.02626e9	−0.741695	−0.370847	+	0.928694i	$0.620933\pi$
$410$	−1.01263e8	−0.0725614
$411$	−2.50807e9	−1.78194
$412$	−2.85693e9	−2.01261
$413$	−2.20163e8	−0.153787
$414$	−2.13419e8	−0.147819
$415$	7.07459e7	0.0485885
$416$	4.54821e8	0.309752
$417$	−1.51870e9	−1.02564
$418$	8.13045e8	0.544500
$419$	1.68359e9	1.11811	0.559057	−	0.829129i	$-0.311163\pi$
$419$	1.68359e9	1.11811	0.559057	+	0.829129i	$0.311163\pi$
$420$	−5.91877e7	−0.0389815
$421$	7.56670e8	0.494219	0.247109	−	0.968988i	$-0.420519\pi$
$421$	7.56670e8	0.494219	0.247109	+	0.968988i	$0.420519\pi$
$422$	3.93860e9	2.55122
$423$	−4.17471e8	−0.268185
$424$	−1.37781e9	−0.877825
$425$	2.42118e9	1.52991
$426$	1.31049e9	0.821295
$427$	−1.97843e8	−0.122977
$428$	−3.10522e9	−1.91443
$429$	−9.13694e8	−0.558728
$430$	1.48127e8	0.0898453
$431$	−2.68350e9	−1.61447	−0.807237	−	0.590228i	$-0.799038\pi$
$431$	−2.68350e9	−1.61447	−0.807237	+	0.590228i	$0.799038\pi$
$432$	−4.24267e7	−0.0253190
$433$	1.52805e8	0.0904546	0.0452273	−	0.998977i	$-0.485599\pi$
$433$	1.52805e8	0.0904546	0.0452273	+	0.998977i	$0.485599\pi$
$434$	−1.74911e9	−1.02708
$435$	7.57630e7	0.0441311
$436$	2.09747e9	1.21197
$437$	−4.26908e7	−0.0244709
$438$	5.50667e9	3.13133
$439$	3.28997e9	1.85595	0.927976	−	0.372641i	$-0.121548\pi$
$439$	3.28997e9	1.85595	0.927976	+	0.372641i	$0.121548\pi$
$440$	−1.11704e8	−0.0625150
$441$	2.25945e8	0.125449
$442$	1.23254e9	0.678929
$443$	−1.89428e9	−1.03522	−0.517609	−	0.855617i	$-0.673178\pi$
$443$	−1.89428e9	−1.03522	−0.517609	+	0.855617i	$0.673178\pi$
$444$	2.95250e9	1.60085
$445$	8.45416e7	0.0454789
$446$	1.46820e9	0.783633
$447$	−2.77470e8	−0.146940
$448$	−1.17331e9	−0.616509
$449$	−3.53879e9	−1.84498	−0.922491	−	0.386019i	$-0.873850\pi$
$449$	−3.53879e9	−1.84498	−0.922491	+	0.386019i	$0.873850\pi$
$450$	2.70324e9	1.39843
$451$	2.67773e9	1.37451
$452$	3.40234e9	1.73298
$453$	−2.83847e9	−1.43463
$454$	3.60038e9	1.80573
$455$	1.02395e7	0.00509613
$456$	−5.63305e8	−0.278206
$457$	1.43128e9	0.701485	0.350743	−	0.936472i	$-0.385929\pi$
$457$	1.43128e9	0.701485	0.350743	+	0.936472i	$0.385929\pi$
$458$	9.25194e8	0.449991
$459$	−5.30581e8	−0.256099
$460$	1.65676e7	0.00793608
$461$	−1.19485e9	−0.568018	−0.284009	−	0.958822i	$-0.591664\pi$
$461$	−1.19485e9	−0.568018	−0.284009	+	0.958822i	$0.591664\pi$
$462$	2.57616e9	1.21542
$463$	2.80198e9	1.31199	0.655996	−	0.754765i	$-0.272249\pi$
$463$	2.80198e9	1.31199	0.655996	+	0.754765i	$0.272249\pi$
$464$	2.16105e8	0.100427
$465$	−2.45901e8	−0.113416
$466$	−2.40061e9	−1.09893
$467$	1.71210e9	0.777894	0.388947	−	0.921260i	$-0.372839\pi$
$467$	1.71210e9	0.777894	0.388947	+	0.921260i	$0.372839\pi$
$468$	8.36058e8	0.377030
$469$	−1.08732e9	−0.486688
$470$	5.33429e7	0.0236992
$471$	−1.20816e9	−0.532785
$472$	8.13168e8	0.355945
$473$	−3.91699e9	−1.70192
$474$	−6.08625e9	−2.62498
$475$	5.40738e8	0.231504
$476$	−2.11130e9	−0.897277
$477$	2.08868e9	0.881166
$478$	−6.86200e9	−2.87378
$479$	−1.28285e9	−0.533335	−0.266668	−	0.963789i	$-0.585923\pi$
$479$	−1.28285e9	−0.533335	−0.266668	+	0.963789i	$0.585923\pi$
$480$	−1.80283e8	−0.0744065
$481$	−5.10786e8	−0.209282
$482$	3.93161e9	1.59921
$483$	−1.35267e8	−0.0546233
$484$	4.48228e9	1.79697
$485$	−6.47929e7	−0.0257888
$486$	−5.45377e9	−2.15511
$487$	−2.20830e9	−0.866377	−0.433188	−	0.901303i	$-0.642611\pi$
$487$	−2.20830e9	−0.866377	−0.433188	+	0.901303i	$0.642611\pi$
$488$	7.30729e8	0.284634
$489$	7.23906e8	0.279963
$490$	−2.88704e7	−0.0110858
$491$	2.82900e9	1.07857	0.539283	−	0.842124i	$-0.318695\pi$
$491$	2.82900e9	1.07857	0.539283	+	0.842124i	$0.318695\pi$
$492$	−5.24042e9	−1.98375
$493$	2.70257e9	1.01581
$494$	2.75272e8	0.102735
$495$	1.69337e8	0.0627530
$496$	−7.01402e8	−0.258096
$497$	3.88356e8	0.141900
$498$	6.02618e9	2.18645
$499$	−3.18287e9	−1.14675	−0.573373	−	0.819295i	$-0.694365\pi$
$499$	−3.18287e9	−1.14675	−0.573373	+	0.819295i	$0.694365\pi$
$500$	−4.20199e8	−0.150335
$501$	−3.02141e9	−1.07344
$502$	−5.35443e7	−0.0188908
$503$	−5.34031e9	−1.87102	−0.935510	−	0.353301i	$-0.885059\pi$
$503$	−5.34031e9	−1.87102	−0.935510	+	0.353301i	$0.885059\pi$
$504$	−8.34524e8	−0.290357
$505$	2.04595e8	0.0706929
$506$	−7.21108e8	−0.247442
$507$	−3.09349e8	−0.105420
$508$	2.29509e9	0.776741
$509$	1.21801e9	0.409391	0.204696	−	0.978826i	$-0.434380\pi$
$509$	1.21801e9	0.409391	0.204696	+	0.978826i	$0.434380\pi$
$510$	−4.88559e8	−0.163088
$511$	1.63187e9	0.541019
$512$	−9.17040e8	−0.301956
$513$	−1.18498e8	−0.0387526
$514$	−1.09936e9	−0.357083
$515$	−1.95913e8	−0.0632030
$516$	7.66570e9	2.45628
$517$	−1.41057e9	−0.448929
$518$	1.44016e9	0.455258
$519$	5.59732e9	1.75750
$520$	−3.78196e7	−0.0117952
$521$	−4.13286e9	−1.28032	−0.640161	−	0.768241i	$-0.721132\pi$
$521$	−4.13286e9	−1.28032	−0.640161	+	0.768241i	$0.721132\pi$
$522$	3.01741e9	0.928512
$523$	5.27698e9	1.61298	0.806491	−	0.591247i	$-0.201364\pi$
$523$	5.27698e9	1.61298	0.806491	+	0.591247i	$0.201364\pi$
$524$	7.64341e9	2.32075
$525$	1.71335e9	0.516759
$526$	4.80346e9	1.43914
$527$	−8.77160e9	−2.61061
$528$	1.03305e9	0.305425
$529$	−3.36696e9	−0.988879
$530$	−2.66884e8	−0.0778676
$531$	−1.23272e9	−0.357300
$532$	−4.71532e8	−0.135775
$533$	9.06598e8	0.259340
$534$	7.20130e9	2.04652
$535$	−2.12939e8	−0.0601199
$536$	4.01598e9	1.12646
$537$	−9.23481e9	−2.57346
$538$	−6.70453e9	−1.85622
$539$	7.63432e8	0.209995
$540$	4.59871e7	0.0125677
$541$	3.81762e9	1.03658	0.518290	−	0.855205i	$-0.326569\pi$
$541$	3.81762e9	1.03658	0.518290	+	0.855205i	$0.326569\pi$
$542$	5.42207e8	0.146274
$543$	−5.74082e9	−1.53877
$544$	−6.43094e9	−1.71269
$545$	1.43834e8	0.0380603
$546$	8.72210e8	0.229323
$547$	5.52169e9	1.44250	0.721251	−	0.692674i	$-0.243567\pi$
$547$	5.52169e9	1.44250	0.721251	+	0.692674i	$0.243567\pi$
$548$	7.75431e9	2.01285
$549$	−1.10775e9	−0.285718
$550$	9.13382e9	2.34090
$551$	6.03582e8	0.153711
$552$	4.99608e8	0.126428
$553$	−1.80363e9	−0.453533
$554$	−4.10951e9	−1.02685
$555$	2.02467e8	0.0502723
$556$	4.69543e9	1.15855
$557$	1.32102e9	0.323904	0.161952	−	0.986799i	$-0.448221\pi$
$557$	1.32102e9	0.323904	0.161952	+	0.986799i	$0.448221\pi$
$558$	−9.79347e9	−2.38626
$559$	−1.32617e9	−0.321114
$560$	−1.15772e7	−0.00278577
$561$	1.29192e10	3.08933
$562$	−3.77860e9	−0.897953
$563$	5.95845e9	1.40719	0.703597	−	0.710599i	$-0.251576\pi$
$563$	5.95845e9	1.40719	0.703597	+	0.710599i	$0.251576\pi$
$564$	2.76054e9	0.647913
$565$	2.33314e8	0.0544216
$566$	−8.62086e9	−1.99845
$567$	−1.81611e9	−0.418410
$568$	−1.43439e9	−0.328433
$569$	2.49678e9	0.568182	0.284091	−	0.958797i	$-0.408308\pi$
$569$	2.49678e9	0.568182	0.284091	+	0.958797i	$0.408308\pi$
$570$	−1.09113e8	−0.0246783
$571$	−5.66005e8	−0.127231	−0.0636156	−	0.997974i	$-0.520263\pi$
$571$	−5.66005e8	−0.127231	−0.0636156	+	0.997974i	$0.520263\pi$
$572$	2.82491e9	0.631129
$573$	8.98748e9	1.99571
$574$	−2.55615e9	−0.564151
$575$	−4.79593e8	−0.105205
$576$	−6.56950e9	−1.43237
$577$	5.17728e9	1.12198	0.560992	−	0.827821i	$-0.310420\pi$
$577$	5.17728e9	1.12198	0.560992	+	0.827821i	$0.310420\pi$
$578$	−1.00170e10	−2.15770
$579$	−2.71833e9	−0.582006
$580$	−2.34240e8	−0.0498497
$581$	1.78583e9	0.377766
$582$	−5.51910e9	−1.16048
$583$	7.05732e9	1.47503
$584$	−6.02730e9	−1.25221
$585$	5.73324e7	0.0118401
$586$	−1.35938e10	−2.79061
$587$	6.60553e9	1.34795	0.673975	−	0.738754i	$-0.264585\pi$
$587$	6.60553e9	1.34795	0.673975	+	0.738754i	$0.264585\pi$
$588$	−1.49406e9	−0.303074
$589$	−1.95902e9	−0.395035
$590$	1.57512e8	0.0315742
$591$	−1.66153e9	−0.331095
$592$	5.77513e8	0.114403
$593$	9.46379e9	1.86369	0.931845	−	0.362857i	$-0.118199\pi$
$593$	9.46379e9	1.86369	0.931845	+	0.362857i	$0.118199\pi$
$594$	−2.00160e9	−0.391854
$595$	−1.44782e8	−0.0281777
$596$	8.57867e8	0.165981
$597$	−9.55755e9	−1.83838
$598$	−2.44145e8	−0.0466868
$599$	−5.88369e9	−1.11855	−0.559275	−	0.828982i	$-0.688920\pi$
$599$	−5.88369e9	−1.11855	−0.559275	+	0.828982i	$0.688920\pi$
$600$	−6.32822e9	−1.19606
$601$	6.91141e9	1.29869	0.649346	−	0.760493i	$-0.275043\pi$
$601$	6.91141e9	1.29869	0.649346	+	0.760493i	$0.275043\pi$
$602$	3.73915e9	0.698530
$603$	−6.08801e9	−1.13075
$604$	8.77581e9	1.62053
$605$	3.07371e8	0.0564312
$606$	1.74276e10	3.18114
$607$	−1.03483e10	−1.87805	−0.939024	−	0.343852i	$-0.888268\pi$
$607$	−1.03483e10	−1.87805	−0.939024	+	0.343852i	$0.888268\pi$
$608$	−1.43626e9	−0.259162
$609$	1.91247e9	0.343111
$610$	1.41544e8	0.0252485
$611$	−4.77576e8	−0.0847029
$612$	−1.18214e10	−2.08469
$613$	−6.87166e9	−1.20490	−0.602448	−	0.798158i	$-0.705808\pi$
$613$	−6.87166e9	−1.20490	−0.602448	+	0.798158i	$0.705808\pi$
$614$	−3.08586e9	−0.538006
$615$	−3.59360e8	−0.0622970
$616$	−2.81972e9	−0.486042
$617$	2.90376e9	0.497694	0.248847	−	0.968543i	$-0.419948\pi$
$617$	2.90376e9	0.497694	0.248847	+	0.968543i	$0.419948\pi$
$618$	−1.66880e10	−2.84410
$619$	4.97057e9	0.842343	0.421171	−	0.906981i	$-0.361619\pi$
$619$	4.97057e9	0.842343	0.421171	+	0.906981i	$0.361619\pi$
$620$	7.60261e8	0.128113
$621$	1.05099e8	0.0176107
$622$	−6.65272e9	−1.10849
$623$	2.13407e9	0.353590
$624$	3.49761e8	0.0576269
$625$	6.06028e9	0.992916
$626$	−5.31596e9	−0.866107
$627$	2.88533e9	0.467475
$628$	3.73533e9	0.601824
$629$	7.22226e9	1.15717
$630$	−1.61649e8	−0.0257561
$631$	1.15484e10	1.82987	0.914936	−	0.403600i	$-0.132241\pi$
$631$	1.15484e10	1.82987	0.914936	+	0.403600i	$0.132241\pi$
$632$	6.66167e9	1.04972
$633$	1.39773e10	2.19033
$634$	4.13676e9	0.644686
$635$	1.57385e8	0.0243924
$636$	−1.38114e10	−2.12882
$637$	2.58475e8	0.0396214
$638$	1.01953e10	1.55428
$639$	2.17445e9	0.329683
$640$	4.79365e8	0.0722831
$641$	4.99629e9	0.749281	0.374641	−	0.927170i	$-0.377766\pi$
$641$	4.99629e9	0.749281	0.374641	+	0.927170i	$0.377766\pi$
$642$	−1.81383e10	−2.70535
$643$	8.74939e9	1.29789	0.648947	−	0.760833i	$-0.275210\pi$
$643$	8.74939e9	1.29789	0.648947	+	0.760833i	$0.275210\pi$
$644$	4.18212e8	0.0617015
$645$	5.25673e8	0.0771359
$646$	−3.89222e9	−0.568045
$647$	−9.81643e9	−1.42491	−0.712457	−	0.701716i	$-0.752418\pi$
$647$	−9.81643e9	−1.42491	−0.712457	+	0.701716i	$0.752418\pi$
$648$	6.70778e9	0.968425
$649$	−4.16516e9	−0.598102
$650$	3.09244e9	0.441676
$651$	−6.20722e9	−0.881787
$652$	−2.23813e9	−0.316242
$653$	1.05908e10	1.48844	0.744221	−	0.667934i	$-0.232821\pi$
$653$	1.05908e10	1.48844	0.744221	+	0.667934i	$0.232821\pi$
$654$	1.22518e10	1.71269
$655$	5.24145e8	0.0728797
$656$	−1.02503e9	−0.141767
$657$	9.13705e9	1.25698
$658$	1.34653e9	0.184257
$659$	−1.02716e10	−1.39810	−0.699050	−	0.715073i	$-0.746394\pi$
$659$	−1.02716e10	−1.39810	−0.699050	+	0.715073i	$0.746394\pi$
$660$	−1.11975e9	−0.151606
$661$	−2.47221e9	−0.332951	−0.166475	−	0.986046i	$-0.553239\pi$
$661$	−2.47221e9	−0.332951	−0.166475	+	0.986046i	$0.553239\pi$
$662$	−2.37065e10	−3.17588
$663$	4.37404e9	0.582889
$664$	−6.59593e9	−0.874354
$665$	−3.23351e7	−0.00426382
$666$	8.06364e9	1.05772
$667$	−5.35331e8	−0.0698525
$668$	9.34144e9	1.21254
$669$	5.21033e9	0.672781
$670$	7.77904e8	0.0999227
$671$	−3.74290e9	−0.478277
$672$	−4.55085e9	−0.578496
$673$	−8.81539e9	−1.11478	−0.557389	−	0.830251i	$-0.688197\pi$
$673$	−8.81539e9	−1.11478	−0.557389	+	0.830251i	$0.688197\pi$
$674$	8.02744e9	1.00987
$675$	−1.33122e9	−0.166604
$676$	9.56428e8	0.119080
$677$	−1.46015e10	−1.80858	−0.904289	−	0.426921i	$-0.859598\pi$
$677$	−1.46015e10	−1.80858	−0.904289	+	0.426921i	$0.859598\pi$
$678$	1.98738e10	2.44894
$679$	−1.63556e9	−0.200503
$680$	5.34750e8	0.0652184
$681$	1.27770e10	1.55030
$682$	−3.30906e10	−3.99447
$683$	1.09423e10	1.31413	0.657064	−	0.753835i	$-0.271798\pi$
$683$	1.09423e10	1.31413	0.657064	+	0.753835i	$0.271798\pi$
$684$	−2.64016e9	−0.315453
$685$	5.31749e8	0.0632106
$686$	−7.28770e8	−0.0861898
$687$	3.28332e9	0.386336
$688$	1.49942e9	0.175535
$689$	2.38939e9	0.278305
$690$	9.67750e7	0.0112148
$691$	−6.77060e9	−0.780646	−0.390323	−	0.920678i	$-0.627637\pi$
$691$	−6.77060e9	−0.780646	−0.390323	+	0.920678i	$0.627637\pi$
$692$	−1.73055e10	−1.98524
$693$	4.27455e9	0.487892
$694$	1.08544e9	0.123267
$695$	3.21988e8	0.0363825
$696$	−7.06368e9	−0.794143
$697$	−1.28189e10	−1.43395
$698$	2.34474e10	2.60977
$699$	−8.51927e9	−0.943479
$700$	−5.29723e9	−0.583721
$701$	−1.55109e10	−1.70068	−0.850342	−	0.526231i	$-0.823605\pi$
$701$	−1.55109e10	−1.70068	−0.850342	+	0.526231i	$0.823605\pi$
$702$	−6.77681e8	−0.0739342
$703$	1.61300e9	0.175101
$704$	−2.21973e10	−2.39771
$705$	1.89303e8	0.0203468
$706$	1.47570e9	0.157827
$707$	5.16457e9	0.549624
$708$	8.15137e9	0.863206
$709$	−3.96173e9	−0.417468	−0.208734	−	0.977972i	$-0.566934\pi$
$709$	−3.96173e9	−0.417468	−0.208734	+	0.977972i	$0.566934\pi$
$710$	−2.77844e8	−0.0291337
$711$	−1.00987e10	−1.05372
$712$	−7.88215e9	−0.818398
$713$	1.73750e9	0.179519
$714$	−1.23326e10	−1.26798
$715$	1.93717e8	0.0198197
$716$	2.85517e10	2.90694
$717$	−2.43518e10	−2.46726
$718$	−1.27210e10	−1.28258
$719$	1.68875e9	0.169439	0.0847195	−	0.996405i	$-0.473001\pi$
$719$	1.68875e9	0.169439	0.0847195	+	0.996405i	$0.473001\pi$
$720$	−6.48221e7	−0.00647231
$721$	−4.94540e9	−0.491392
$722$	1.52737e10	1.51030
$723$	1.39525e10	1.37299
$724$	1.77491e10	1.73817
$725$	6.78070e9	0.660833
$726$	2.61821e10	2.53937
$727$	−1.12769e10	−1.08848	−0.544240	−	0.838930i	$-0.683182\pi$
$727$	−1.12769e10	−1.08848	−0.544240	+	0.838930i	$0.683182\pi$
$728$	−9.54673e8	−0.0917054
$729$	−7.77462e9	−0.743247
$730$	−1.16750e9	−0.111078
$731$	1.87515e10	1.77551
$732$	7.32499e9	0.690269
$733$	1.62161e10	1.52084	0.760419	−	0.649433i	$-0.224994\pi$
$733$	1.62161e10	1.52084	0.760419	+	0.649433i	$0.224994\pi$
$734$	−1.36406e8	−0.0127320
$735$	−1.02455e8	−0.00951760
$736$	1.27386e9	0.117774
$737$	−2.05704e10	−1.89281
$738$	−1.43122e10	−1.31072
$739$	−1.25803e10	−1.14666	−0.573329	−	0.819325i	$-0.694348\pi$
$739$	−1.25803e10	−1.14666	−0.573329	+	0.819325i	$0.694348\pi$
$740$	−6.25976e8	−0.0567867
$741$	9.76884e8	0.0882022
$742$	−6.73690e9	−0.605406
$743$	−6.47067e9	−0.578747	−0.289373	−	0.957216i	$-0.593447\pi$
$743$	−6.47067e9	−0.578747	−0.289373	+	0.957216i	$0.593447\pi$
$744$	2.29263e10	2.04093
$745$	5.88280e7	0.00521239
$746$	7.34048e9	0.647349
$747$	9.99906e9	0.877682
$748$	−3.99428e10	−3.48966
$749$	−5.37519e9	−0.467420
$750$	−2.45448e9	−0.212444
$751$	−1.46699e10	−1.26383	−0.631913	−	0.775040i	$-0.717730\pi$
$751$	−1.46699e10	−1.26383	−0.631913	+	0.775040i	$0.717730\pi$
$752$	5.39964e8	0.0463023
$753$	−1.90018e8	−0.0162185
$754$	3.45184e9	0.293258
$755$	6.01799e8	0.0508905
$756$	1.16084e9	0.0977118
$757$	1.26419e10	1.05920	0.529598	−	0.848249i	$-0.322343\pi$
$757$	1.26419e10	1.05920	0.529598	+	0.848249i	$0.322343\pi$
$758$	8.71294e9	0.726645
$759$	−2.55906e9	−0.212439
$760$	1.19429e8	0.00986878
$761$	1.64848e8	0.0135593	0.00677964	−	0.999977i	$-0.497842\pi$
$761$	1.64848e8	0.0135593	0.00677964	+	0.999977i	$0.497842\pi$
$762$	1.34061e10	1.09764
$763$	3.63076e9	0.295912
$764$	−2.77870e10	−2.25432
$765$	−8.10652e8	−0.0654666
$766$	6.53787e9	0.525576
$767$	−1.41020e9	−0.112849
$768$	1.27707e10	1.01731
$769$	1.70983e10	1.35585	0.677925	−	0.735131i	$-0.262879\pi$
$769$	1.70983e10	1.35585	0.677925	+	0.735131i	$0.262879\pi$
$770$	−5.46186e8	−0.0431145
$771$	−3.90140e9	−0.306570
$772$	8.40438e9	0.657423
$773$	−5.74494e9	−0.447360	−0.223680	−	0.974663i	$-0.571807\pi$
$773$	−5.74494e9	−0.447360	−0.223680	+	0.974663i	$0.571807\pi$
$774$	2.09360e10	1.62293
$775$	−2.20078e10	−1.69833
$776$	6.04090e9	0.464072
$777$	5.11084e9	0.390857
$778$	−1.71795e10	−1.30792
$779$	−2.86292e9	−0.216984
$780$	−3.79112e8	−0.0286046
$781$	7.34713e9	0.551873
$782$	3.45209e9	0.258142
$783$	−1.48593e9	−0.110620
$784$	−2.92241e8	−0.0216588
$785$	2.56149e8	0.0188994
$786$	4.46470e10	3.27954
$787$	7.62864e9	0.557873	0.278937	−	0.960309i	$-0.410018\pi$
$787$	7.62864e9	0.557873	0.278937	+	0.960309i	$0.410018\pi$
$788$	5.13704e9	0.373999
$789$	1.70465e10	1.23556
$790$	1.29038e9	0.0931156
$791$	5.88951e9	0.423118
$792$	−1.57880e10	−1.12925
$793$	−1.26723e9	−0.0902402
$794$	−1.82889e10	−1.29663
$795$	−9.47115e8	−0.0668525
$796$	2.95495e10	2.07661
$797$	9.18514e9	0.642661	0.321330	−	0.946967i	$-0.395870\pi$
$797$	9.18514e9	0.642661	0.321330	+	0.946967i	$0.395870\pi$
$798$	−2.75433e9	−0.191869
$799$	6.75269e9	0.468342
$800$	−1.61351e10	−1.11419
$801$	1.19489e10	0.821513
$802$	−1.14113e10	−0.781131
$803$	3.08726e10	2.10411
$804$	4.02571e10	2.73178
$805$	2.86788e7	0.00193765
$806$	−1.12035e10	−0.753668
$807$	−2.37930e10	−1.59364
$808$	−1.90752e10	−1.27213
$809$	6.69362e9	0.444469	0.222234	−	0.974993i	$-0.428665\pi$
$809$	6.69362e9	0.444469	0.222234	+	0.974993i	$0.428665\pi$
$810$	1.29931e9	0.0859043
$811$	9.00116e9	0.592551	0.296275	−	0.955103i	$-0.404255\pi$
$811$	9.00116e9	0.592551	0.296275	+	0.955103i	$0.404255\pi$
$812$	−5.91287e9	−0.387572
$813$	1.92418e9	0.125582
$814$	2.72458e10	1.77057
$815$	−1.53479e8	−0.00993112
$816$	−4.94545e9	−0.318633
$817$	4.18789e9	0.268669
$818$	1.85338e10	1.18394
$819$	1.44723e9	0.0920544
$820$	1.11105e9	0.0703695
$821$	1.60680e10	1.01335	0.506677	−	0.862136i	$-0.330874\pi$
$821$	1.60680e10	1.01335	0.506677	+	0.862136i	$0.330874\pi$
$822$	4.52947e10	2.84444
$823$	2.07361e10	1.29667	0.648333	−	0.761357i	$-0.275467\pi$
$823$	2.07361e10	1.29667	0.648333	+	0.761357i	$0.275467\pi$
$824$	1.82658e10	1.13735
$825$	3.24140e10	2.00976
$826$	3.97605e9	0.245483
$827$	−2.72719e10	−1.67667	−0.838334	−	0.545158i	$-0.816470\pi$
$827$	−2.72719e10	−1.67667	−0.838334	+	0.545158i	$0.816470\pi$
$828$	2.34162e9	0.143354
$829$	8.40379e9	0.512312	0.256156	−	0.966635i	$-0.417544\pi$
$829$	8.40379e9	0.512312	0.256156	+	0.966635i	$0.417544\pi$
$830$	−1.27764e9	−0.0775597
$831$	−1.45838e10	−0.881590
$832$	−7.51534e9	−0.452394
$833$	−3.65471e9	−0.219076
$834$	2.74271e10	1.63719
$835$	6.40586e8	0.0380781
$836$	−8.92069e9	−0.528052
$837$	4.82283e9	0.284291
$838$	−3.04049e10	−1.78480
$839$	3.20862e9	0.187565	0.0937825	−	0.995593i	$-0.470104\pi$
$839$	3.20862e9	0.187565	0.0937825	+	0.995593i	$0.470104\pi$
$840$	3.78416e8	0.0220289
$841$	−9.68113e9	−0.561229
$842$	−1.36652e10	−0.788900
$843$	−1.34095e10	−0.770930
$844$	−4.32142e10	−2.47416
$845$	6.55868e7	0.00373954
$846$	7.53936e9	0.428093
$847$	7.75892e9	0.438742
$848$	−2.70153e9	−0.152134
$849$	−3.05936e10	−1.71575
$850$	−4.37255e10	−2.44213
$851$	−1.43060e9	−0.0795730
$852$	−1.43786e10	−0.796486
$853$	1.92263e10	1.06066	0.530329	−	0.847792i	$-0.322069\pi$
$853$	1.92263e10	1.06066	0.530329	+	0.847792i	$0.322069\pi$
$854$	3.57296e9	0.196302
$855$	−1.81048e8	−0.00990634
$856$	1.98532e10	1.08186
$857$	2.53280e10	1.37457	0.687287	−	0.726386i	$-0.258801\pi$
$857$	2.53280e10	1.37457	0.687287	+	0.726386i	$0.258801\pi$
$858$	1.65009e10	0.891874
$859$	−1.64704e10	−0.886598	−0.443299	−	0.896374i	$-0.646192\pi$
$859$	−1.64704e10	−0.886598	−0.443299	+	0.896374i	$0.646192\pi$
$860$	−1.62525e9	−0.0871314
$861$	−9.07126e9	−0.484347
$862$	4.84629e10	2.57712
$863$	2.95746e10	1.56632	0.783160	−	0.621820i	$-0.213607\pi$
$863$	2.95746e10	1.56632	0.783160	+	0.621820i	$0.213607\pi$
$864$	3.53588e9	0.186509
$865$	−1.18672e9	−0.0623435
$866$	−2.75960e9	−0.144389
$867$	−3.55483e10	−1.85247
$868$	1.91911e10	0.996051
$869$	−3.41220e10	−1.76387
$870$	−1.36825e9	−0.0704446
$871$	−6.96453e9	−0.357131
$872$	−1.34102e10	−0.684899
$873$	−9.15768e9	−0.465839
$874$	7.70979e8	0.0390618
$875$	−7.27373e8	−0.0367053
$876$	−6.04189e10	−3.03675
$877$	1.56818e10	0.785049	0.392524	−	0.919742i	$-0.371602\pi$
$877$	1.56818e10	0.785049	0.392524	+	0.919742i	$0.371602\pi$
$878$	−5.94156e10	−2.96258
$879$	−4.82415e10	−2.39585
$880$	−2.19024e8	−0.0108343
$881$	3.70407e9	0.182500	0.0912501	−	0.995828i	$-0.470914\pi$
$881$	3.70407e9	0.182500	0.0912501	+	0.995828i	$0.470914\pi$
$882$	−4.08047e9	−0.200249
$883$	−3.17603e10	−1.55247	−0.776234	−	0.630445i	$-0.782872\pi$
$883$	−3.17603e10	−1.55247	−0.776234	+	0.630445i	$0.782872\pi$
$884$	−1.35234e10	−0.658421
$885$	5.58978e8	0.0271077
$886$	3.42100e10	1.65247
$887$	−2.88472e10	−1.38794	−0.693970	−	0.720004i	$-0.744140\pi$
$887$	−2.88472e10	−1.38794	−0.693970	+	0.720004i	$0.744140\pi$
$888$	−1.88768e10	−0.904655
$889$	3.97284e9	0.189647
$890$	−1.52679e9	−0.0725961
$891$	−3.43582e10	−1.62726
$892$	−1.61090e10	−0.759962
$893$	1.50812e9	0.0708690
$894$	5.01100e9	0.234554
$895$	1.95792e9	0.0912883
$896$	1.21005e10	0.561987
$897$	−8.66421e8	−0.0400826
$898$	6.39090e10	2.94507
$899$	−2.45655e10	−1.12763
$900$	−2.96598e10	−1.35619
$901$	−3.37849e10	−1.53881
$902$	−4.83587e10	−2.19408
$903$	1.32695e10	0.599717
$904$	−2.17528e10	−0.979323
$905$	1.21714e9	0.0545848
$906$	5.12616e10	2.29004
$907$	−3.44892e10	−1.53482	−0.767409	−	0.641158i	$-0.778454\pi$
$907$	−3.44892e10	−1.53482	−0.767409	+	0.641158i	$0.778454\pi$
$908$	−3.95033e10	−1.75119
$909$	2.89170e10	1.27697
$910$	−1.84922e8	−0.00813474
$911$	−3.96476e10	−1.73741	−0.868705	−	0.495330i	$-0.835047\pi$
$911$	−3.96476e10	−1.73741	−0.868705	+	0.495330i	$0.835047\pi$
$912$	−1.10450e9	−0.0482152
$913$	3.37853e10	1.46920
$914$	−2.58484e10	−1.11975
$915$	5.02309e8	0.0216769
$916$	−1.01512e10	−0.436398
$917$	1.32309e10	0.566626
$918$	9.58207e9	0.408799
$919$	6.76983e9	0.287722	0.143861	−	0.989598i	$-0.454048\pi$
$919$	6.76983e9	0.287722	0.143861	+	0.989598i	$0.454048\pi$
$920$	−1.05925e8	−0.00448476
$921$	−1.09511e10	−0.461901
$922$	2.15786e10	0.906703
$923$	2.48752e9	0.104126
$924$	−2.82655e10	−1.17871
$925$	1.81206e10	0.752793
$926$	−5.06026e10	−2.09428
$927$	−2.76899e10	−1.14167
$928$	−1.80103e10	−0.739783
$929$	−2.26338e10	−0.926195	−0.463097	−	0.886307i	$-0.653262\pi$
$929$	−2.26338e10	−0.926195	−0.463097	+	0.886307i	$0.653262\pi$
$930$	4.44087e9	0.181041
$931$	−8.16230e8	−0.0331504
$932$	2.63394e10	1.06574
$933$	−2.36091e10	−0.951687
$934$	−3.09199e10	−1.24172
$935$	−2.73907e9	−0.109588
$936$	−5.34533e9	−0.213064
$937$	−7.17774e9	−0.285036	−0.142518	−	0.989792i	$-0.545520\pi$
$937$	−7.17774e9	−0.285036	−0.142518	+	0.989792i	$0.545520\pi$
$938$	1.96365e10	0.776880
$939$	−1.88652e10	−0.743589
$940$	−5.85276e8	−0.0229833
$941$	7.71375e9	0.301788	0.150894	−	0.988550i	$-0.451785\pi$
$941$	7.71375e9	0.301788	0.150894	+	0.988550i	$0.451785\pi$
$942$	2.18189e10	0.850462
$943$	2.53919e9	0.0986062
$944$	1.59442e9	0.0616879
$945$	7.96045e7	0.00306850
$946$	7.07393e10	2.71670
$947$	3.60811e10	1.38056	0.690280	−	0.723542i	$-0.257487\pi$
$947$	3.60811e10	1.38056	0.690280	+	0.723542i	$0.257487\pi$
$948$	6.67780e10	2.54568
$949$	1.04525e10	0.397000
$950$	−9.76551e9	−0.369541
$951$	1.46805e10	0.553490
$952$	1.34986e10	0.507060
$953$	2.80356e10	1.04926	0.524632	−	0.851329i	$-0.324203\pi$
$953$	2.80356e10	1.04926	0.524632	+	0.851329i	$0.324203\pi$
$954$	−3.77207e10	−1.40657
$955$	−1.90549e9	−0.0707936
$956$	7.52896e10	2.78697
$957$	3.61812e10	1.33442
$958$	2.31677e10	0.851341
$959$	1.34229e10	0.491450
$960$	2.97895e9	0.108671
$961$	5.22187e10	1.89799
$962$	9.22459e9	0.334068
$963$	−3.00964e10	−1.08598
$964$	−4.31374e10	−1.55090
$965$	5.76328e8	0.0206454
$966$	2.44287e9	0.0871929
$967$	4.53973e10	1.61450	0.807248	−	0.590213i	$-0.200956\pi$
$967$	4.53973e10	1.61450	0.807248	+	0.590213i	$0.200956\pi$
$968$	−2.86575e10	−1.01549
$969$	−1.38127e10	−0.487690
$970$	1.17013e9	0.0411656
$971$	−3.65836e10	−1.28239	−0.641194	−	0.767379i	$-0.721560\pi$
$971$	−3.65836e10	−1.28239	−0.641194	+	0.767379i	$0.721560\pi$
$972$	5.98386e10	2.09001
$973$	8.12788e9	0.282867
$974$	3.98810e10	1.38296
$975$	1.09744e10	0.379197
$976$	1.43278e9	0.0493292
$977$	3.46498e9	0.118869	0.0594347	−	0.998232i	$-0.481070\pi$
$977$	3.46498e9	0.118869	0.0594347	+	0.998232i	$0.481070\pi$
$978$	−1.30735e10	−0.446894
$979$	4.03735e10	1.37517
$980$	3.16765e8	0.0107509
$981$	2.03291e10	0.687506
$982$	−5.10905e10	−1.72167
$983$	−2.52120e10	−0.846583	−0.423291	−	0.905994i	$-0.639125\pi$
$983$	−2.52120e10	−0.846583	−0.423291	+	0.905994i	$0.639125\pi$
$984$	3.35046e10	1.12104
$985$	3.52271e8	0.0117449
$986$	−4.88073e10	−1.62149
$987$	4.77854e9	0.158192
$988$	−3.02028e9	−0.0996317
$989$	−3.71433e9	−0.122094
$990$	−3.05816e9	−0.100170
$991$	−5.79005e10	−1.88984	−0.944919	−	0.327303i	$-0.893860\pi$
$991$	−5.79005e10	−1.88984	−0.944919	+	0.327303i	$0.893860\pi$
$992$	5.84554e10	1.90123
$993$	−8.41293e10	−2.72662
$994$	−7.01355e9	−0.226509
$995$	2.02635e9	0.0652129
$996$	−6.61190e10	−2.12040
$997$	1.71906e10	0.549360	0.274680	−	0.961536i	$-0.411428\pi$
$997$	1.71906e10	0.549360	0.274680	+	0.961536i	$0.411428\pi$
$998$	5.74814e10	1.83050
$999$	−3.97097e9	−0.126013

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.e.1.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.e.1.2	✓	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.a (trivial)

\(f(q)\)	\(=\)	\(q-18.0596 q^{2} -64.0898 q^{3} +198.149 q^{4} +13.5880 q^{5} +1157.44 q^{6} +343.000 q^{7} -1266.87 q^{8} +1920.50 q^{9} +O(q^{10})\)	\(q-18.0596 q^{2} -64.0898 q^{3} +198.149 q^{4} +13.5880 q^{5} +1157.44 q^{6} +343.000 q^{7} -1266.87 q^{8} +1920.50 q^{9} -245.394 q^{10} +6489.06 q^{11} -12699.3 q^{12} +2197.00 q^{13} -6194.44 q^{14} -870.853 q^{15} -2484.01 q^{16} -31064.5 q^{17} -34683.4 q^{18} -6937.84 q^{19} +2692.46 q^{20} -21982.8 q^{21} -117190. q^{22} +6153.33 q^{23} +81193.1 q^{24} -77940.4 q^{25} -39676.9 q^{26} +17080.0 q^{27} +67965.2 q^{28} -86998.5 q^{29} +15727.3 q^{30} +282367. q^{31} +207019. q^{32} -415883. q^{33} +561012. q^{34} +4660.69 q^{35} +380545. q^{36} -232493. q^{37} +125295. q^{38} -140805. q^{39} -17214.2 q^{40} +412653. q^{41} +397000. q^{42} -603630. q^{43} +1.28580e6 q^{44} +26095.8 q^{45} -111127. q^{46} -217376. q^{47} +159199. q^{48} +117649. q^{49} +1.40757e6 q^{50} +1.99092e6 q^{51} +435334. q^{52} +1.08757e6 q^{53} -308457. q^{54} +88173.5 q^{55} -434535. q^{56} +444645. q^{57} +1.57116e6 q^{58} -641874. q^{59} -172559. q^{60} -576801. q^{61} -5.09944e6 q^{62} +658731. q^{63} -3.42073e6 q^{64} +29852.9 q^{65} +7.51067e6 q^{66} -3.17002e6 q^{67} -6.15540e6 q^{68} -394366. q^{69} -84170.2 q^{70} +1.13223e6 q^{71} -2.43301e6 q^{72} +4.75764e6 q^{73} +4.19872e6 q^{74} +4.99518e6 q^{75} -1.37473e6 q^{76} +2.22575e6 q^{77} +2.54289e6 q^{78} -5.25839e6 q^{79} -33752.7 q^{80} -5.29478e6 q^{81} -7.45234e6 q^{82} +5.20649e6 q^{83} -4.35587e6 q^{84} -422105. q^{85} +1.09013e7 q^{86} +5.57572e6 q^{87} -8.22077e6 q^{88} +6.22177e6 q^{89} -471279. q^{90} +753571. q^{91} +1.21928e6 q^{92} -1.80969e7 q^{93} +3.92573e6 q^{94} -94271.6 q^{95} -1.32678e7 q^{96} -4.76838e6 q^{97} -2.12469e6 q^{98} +1.24622e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9}+O(q^{10}) \) 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9	\( 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9} + 6668 q^{10} + 12168 q^{11} - 183 q^{12} + 26364 q^{13} + 2058 q^{14} - 28790 q^{15} + 85914 q^{16} + 82710 q^{17} - 44965 q^{18} - 10302 q^{19} + 141318 q^{20} + 28126 q^{21} - 97457 q^{22} + 98376 q^{23} - 519981 q^{24} + 272736 q^{25} + 13182 q^{26} + 306652 q^{27} + 338198 q^{28} + 350592 q^{29} + 231528 q^{30} + 55092 q^{31} + 114420 q^{32} + 609912 q^{33} + 812002 q^{34} + 351918 q^{35} + 1472143 q^{36} + 376310 q^{37} + 2825424 q^{38} + 180154 q^{39} + 2169290 q^{40} + 1387272 q^{41} + 105987 q^{42} + 568708 q^{43} + 3392031 q^{44} + 3556226 q^{45} - 1736829 q^{46} + 1359444 q^{47} + 4151249 q^{48} + 1411788 q^{49} + 3983712 q^{50} + 2709260 q^{51} + 2166242 q^{52} + 2061780 q^{53} + 2196651 q^{54} - 2112846 q^{55} + 78204 q^{56} + 2359902 q^{57} + 670268 q^{58} + 395964 q^{59} - 1052376 q^{60} + 444006 q^{61} + 2854353 q^{62} + 3739386 q^{63} + 12026858 q^{64} + 2254122 q^{65} - 4605681 q^{66} - 3094010 q^{67} + 4668954 q^{68} + 3839892 q^{69} + 2287124 q^{70} + 5694366 q^{71} - 9780585 q^{72} + 7052346 q^{73} - 4436259 q^{74} - 16288696 q^{75} - 3051830 q^{76} + 4173624 q^{77} + 678873 q^{78} + 4304160 q^{79} + 3807018 q^{80} - 6689556 q^{81} - 4733665 q^{82} + 2704554 q^{83} - 62769 q^{84} + 9301878 q^{85} + 1510998 q^{86} + 16231802 q^{87} - 70453923 q^{88} - 10986042 q^{89} - 12851300 q^{90} + 9042852 q^{91} - 16505451 q^{92} - 47230934 q^{93} - 24306151 q^{94} - 21839424 q^{95} - 86512741 q^{96} - 24462382 q^{97} + 705894 q^{98} + 11555078 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9 + 6668 * q^10 + 12168 * q^11 - 183 * q^12 + 26364 * q^13 + 2058 * q^14 - 28790 * q^15 + 85914 * q^16 + 82710 * q^17 - 44965 * q^18 - 10302 * q^19 + 141318 * q^20 + 28126 * q^21 - 97457 * q^22 + 98376 * q^23 - 519981 * q^24 + 272736 * q^25 + 13182 * q^26 + 306652 * q^27 + 338198 * q^28 + 350592 * q^29 + 231528 * q^30 + 55092 * q^31 + 114420 * q^32 + 609912 * q^33 + 812002 * q^34 + 351918 * q^35 + 1472143 * q^36 + 376310 * q^37 + 2825424 * q^38 + 180154 * q^39 + 2169290 * q^40 + 1387272 * q^41 + 105987 * q^42 + 568708 * q^43 + 3392031 * q^44 + 3556226 * q^45 - 1736829 * q^46 + 1359444 * q^47 + 4151249 * q^48 + 1411788 * q^49 + 3983712 * q^50 + 2709260 * q^51 + 2166242 * q^52 + 2061780 * q^53 + 2196651 * q^54 - 2112846 * q^55 + 78204 * q^56 + 2359902 * q^57 + 670268 * q^58 + 395964 * q^59 - 1052376 * q^60 + 444006 * q^61 + 2854353 * q^62 + 3739386 * q^63 + 12026858 * q^64 + 2254122 * q^65 - 4605681 * q^66 - 3094010 * q^67 + 4668954 * q^68 + 3839892 * q^69 + 2287124 * q^70 + 5694366 * q^71 - 9780585 * q^72 + 7052346 * q^73 - 4436259 * q^74 - 16288696 * q^75 - 3051830 * q^76 + 4173624 * q^77 + 678873 * q^78 + 4304160 * q^79 + 3807018 * q^80 - 6689556 * q^81 - 4733665 * q^82 + 2704554 * q^83 - 62769 * q^84 + 9301878 * q^85 + 1510998 * q^86 + 16231802 * q^87 - 70453923 * q^88 - 10986042 * q^89 - 12851300 * q^90 + 9042852 * q^91 - 16505451 * q^92 - 47230934 * q^93 - 24306151 * q^94 - 21839424 * q^95 - 86512741 * q^96 - 24462382 * q^97 + 705894 * q^98 + 11555078 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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