LMFDB - Embedded newform 37.8.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,8,Mod(1,37)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("37.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	37.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$11.5582459429$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4 x^{9} - 905 x^{8} + 4018 x^{7} + 291290 x^{6} - 1367036 x^{5} - 39566544 x^{4} + \cdots - 45399525376 $ x^10 - 4x^9 - 905x^8 + 4018x^7 + 291290x^6 - 1367036x^5 - 39566544x^4 + 175732512x^3 + 2143908736x^2 - 5929608704*x - 45399525376
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$10.4614$ of defining polynomial
Character	$\chi$	$=$	37.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-12.4614 q^{2} +49.0521 q^{3} +27.2868 q^{4} -16.1140 q^{5} -611.258 q^{6} -704.986 q^{7} +1255.03 q^{8} +219.106 q^{9} +O(q^{10})$	\(q-12.4614 q^{2} +49.0521 q^{3} +27.2868 q^{4} -16.1140 q^{5} -611.258 q^{6} -704.986 q^{7} +1255.03 q^{8} +219.106 q^{9} +200.803 q^{10} +6425.66 q^{11} +1338.48 q^{12} -9639.47 q^{13} +8785.12 q^{14} -790.425 q^{15} -19132.1 q^{16} -33123.9 q^{17} -2730.37 q^{18} -4521.07 q^{19} -439.700 q^{20} -34581.0 q^{21} -80072.8 q^{22} -50212.0 q^{23} +61561.7 q^{24} -77865.3 q^{25} +120121. q^{26} -96529.3 q^{27} -19236.8 q^{28} -170108. q^{29} +9849.81 q^{30} +301806. q^{31} +77769.9 q^{32} +315192. q^{33} +412771. q^{34} +11360.1 q^{35} +5978.70 q^{36} +50653.0 q^{37} +56339.0 q^{38} -472836. q^{39} -20223.5 q^{40} -209106. q^{41} +430928. q^{42} -43153.5 q^{43} +175336. q^{44} -3530.67 q^{45} +625713. q^{46} -117766. q^{47} -938471. q^{48} -326538. q^{49} +970312. q^{50} -1.62480e6 q^{51} -263031. q^{52} +336845. q^{53} +1.20289e6 q^{54} -103543. q^{55} -884777. q^{56} -221768. q^{57} +2.11978e6 q^{58} +141086. q^{59} -21568.2 q^{60} +1.61439e6 q^{61} -3.76093e6 q^{62} -154466. q^{63} +1.47979e6 q^{64} +155330. q^{65} -3.92774e6 q^{66} +2.71548e6 q^{67} -903847. q^{68} -2.46300e6 q^{69} -141563. q^{70} +3.12792e6 q^{71} +274984. q^{72} -2.19209e6 q^{73} -631208. q^{74} -3.81946e6 q^{75} -123366. q^{76} -4.53000e6 q^{77} +5.89221e6 q^{78} -2.76709e6 q^{79} +308295. q^{80} -5.21415e6 q^{81} +2.60576e6 q^{82} +7.31499e6 q^{83} -943606. q^{84} +533759. q^{85} +537754. q^{86} -8.34413e6 q^{87} +8.06439e6 q^{88} -6.30446e6 q^{89} +43997.1 q^{90} +6.79569e6 q^{91} -1.37013e6 q^{92} +1.48042e7 q^{93} +1.46753e6 q^{94} +72852.6 q^{95} +3.81477e6 q^{96} -1.27419e7 q^{97} +4.06913e6 q^{98} +1.40790e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 24 q^{2} - 95 q^{3} + 602 q^{4} - 624 q^{5} - 777 q^{6} - 501 q^{7} - 3810 q^{8} + 6181 q^{9}+O(q^{10}) $ 10 * q - 24 * q^2 - 95 * q^3 + 602 * q^4 - 624 * q^5 - 777 * q^6 - 501 * q^7 - 3810 * q^8 + 6181 * q^9	\( 10 q - 24 q^{2} - 95 q^{3} + 602 q^{4} - 624 q^{5} - 777 q^{6} - 501 q^{7} - 3810 q^{8} + 6181 q^{9} + 8595 q^{10} - 8325 q^{11} - 19645 q^{12} - 17108 q^{13} - 65418 q^{14} - 55756 q^{15} - 56998 q^{16} - 72924 q^{17} - 156165 q^{18} - 47786 q^{19} - 226209 q^{20} - 65313 q^{21} - 138973 q^{22} - 148086 q^{23} - 68031 q^{24} + 108736 q^{25} - 60237 q^{26} - 87329 q^{27} + 219974 q^{28} - 164154 q^{29} + 78864 q^{30} - 189560 q^{31} - 30114 q^{32} - 179737 q^{33} + 532624 q^{34} - 705156 q^{35} + 1923693 q^{36} + 506530 q^{37} + 1256412 q^{38} + 1322800 q^{39} + 2936777 q^{40} + 814263 q^{41} + 3415826 q^{42} - 590572 q^{43} + 610311 q^{44} - 250574 q^{45} + 2903897 q^{46} - 1534185 q^{47} + 2082419 q^{48} - 214337 q^{49} - 2313525 q^{50} + 722138 q^{51} + 149159 q^{52} - 2518209 q^{53} + 1095990 q^{54} - 3482468 q^{55} - 3645834 q^{56} - 9225638 q^{57} + 5626023 q^{58} - 5894748 q^{59} - 1289832 q^{60} - 2569480 q^{61} - 863697 q^{62} - 2836574 q^{63} - 4093742 q^{64} - 6774600 q^{65} + 17251556 q^{66} - 6983232 q^{67} - 8114412 q^{68} - 11557564 q^{69} + 8982748 q^{70} - 5013963 q^{71} - 7567137 q^{72} - 11678449 q^{73} - 1215672 q^{74} - 6586901 q^{75} + 4912252 q^{76} + 1333113 q^{77} - 7352119 q^{78} - 3853378 q^{79} - 11975661 q^{80} - 7381718 q^{81} + 564093 q^{82} - 15677895 q^{83} + 4781738 q^{84} + 11909320 q^{85} + 34274010 q^{86} - 12611710 q^{87} + 14448317 q^{88} - 25836 q^{89} + 64591590 q^{90} + 12335744 q^{91} + 7579845 q^{92} + 4592632 q^{93} + 26251718 q^{94} + 11723664 q^{95} + 42299113 q^{96} + 4648834 q^{97} + 15230184 q^{98} - 16904018 q^{99}+O(q^{100}) \) 10 * q - 24 * q^2 - 95 * q^3 + 602 * q^4 - 624 * q^5 - 777 * q^6 - 501 * q^7 - 3810 * q^8 + 6181 * q^9 + 8595 * q^10 - 8325 * q^11 - 19645 * q^12 - 17108 * q^13 - 65418 * q^14 - 55756 * q^15 - 56998 * q^16 - 72924 * q^17 - 156165 * q^18 - 47786 * q^19 - 226209 * q^20 - 65313 * q^21 - 138973 * q^22 - 148086 * q^23 - 68031 * q^24 + 108736 * q^25 - 60237 * q^26 - 87329 * q^27 + 219974 * q^28 - 164154 * q^29 + 78864 * q^30 - 189560 * q^31 - 30114 * q^32 - 179737 * q^33 + 532624 * q^34 - 705156 * q^35 + 1923693 * q^36 + 506530 * q^37 + 1256412 * q^38 + 1322800 * q^39 + 2936777 * q^40 + 814263 * q^41 + 3415826 * q^42 - 590572 * q^43 + 610311 * q^44 - 250574 * q^45 + 2903897 * q^46 - 1534185 * q^47 + 2082419 * q^48 - 214337 * q^49 - 2313525 * q^50 + 722138 * q^51 + 149159 * q^52 - 2518209 * q^53 + 1095990 * q^54 - 3482468 * q^55 - 3645834 * q^56 - 9225638 * q^57 + 5626023 * q^58 - 5894748 * q^59 - 1289832 * q^60 - 2569480 * q^61 - 863697 * q^62 - 2836574 * q^63 - 4093742 * q^64 - 6774600 * q^65 + 17251556 * q^66 - 6983232 * q^67 - 8114412 * q^68 - 11557564 * q^69 + 8982748 * q^70 - 5013963 * q^71 - 7567137 * q^72 - 11678449 * q^73 - 1215672 * q^74 - 6586901 * q^75 + 4912252 * q^76 + 1333113 * q^77 - 7352119 * q^78 - 3853378 * q^79 - 11975661 * q^80 - 7381718 * q^81 + 564093 * q^82 - 15677895 * q^83 + 4781738 * q^84 + 11909320 * q^85 + 34274010 * q^86 - 12611710 * q^87 + 14448317 * q^88 - 25836 * q^89 + 64591590 * q^90 + 12335744 * q^91 + 7579845 * q^92 + 4592632 * q^93 + 26251718 * q^94 + 11723664 * q^95 + 42299113 * q^96 + 4648834 * q^97 + 15230184 * q^98 - 16904018 * 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 $

$2$	−12.4614	−1.10144	−0.550722	−	0.834689i	$-0.685648\pi$
$2$	−12.4614	−1.10144	−0.550722	+	0.834689i	$0.685648\pi$
$3$	49.0521	1.04890	0.524449	−	0.851442i	$-0.324271\pi$
$3$	49.0521	1.04890	0.524449	+	0.851442i	$0.324271\pi$
$4$	27.2868	0.213178
$5$	−16.1140	−0.0576512	−0.0288256	−	0.999584i	$-0.509177\pi$
$5$	−16.1140	−0.0576512	−0.0288256	+	0.999584i	$0.509177\pi$
$6$	−611.258	−1.15530
$7$	−704.986	−0.776850	−0.388425	−	0.921480i	$-0.626981\pi$
$7$	−704.986	−0.776850	−0.388425	+	0.921480i	$0.626981\pi$
$8$	1255.03	0.866640
$9$	219.106	0.100186
$10$	200.803	0.0634995
$11$	6425.66	1.45560	0.727802	−	0.685787i	$-0.240542\pi$
$11$	6425.66	1.45560	0.727802	+	0.685787i	$0.240542\pi$
$12$	1338.48	0.223602
$13$	−9639.47	−1.21689	−0.608445	−	0.793596i	$-0.708207\pi$
$13$	−9639.47	−1.21689	−0.608445	+	0.793596i	$0.708207\pi$
$14$	8785.12	0.855657
$15$	−790.425	−0.0604702
$16$	−19132.1	−1.16773
$17$	−33123.9	−1.63520	−0.817599	−	0.575788i	$-0.804696\pi$
$17$	−33123.9	−1.63520	−0.817599	+	0.575788i	$0.804696\pi$
$18$	−2730.37	−0.110349
$19$	−4521.07	−0.151218	−0.0756091	−	0.997138i	$-0.524090\pi$
$19$	−4521.07	−0.151218	−0.0756091	+	0.997138i	$0.524090\pi$
$20$	−439.700	−0.0122900
$21$	−34581.0	−0.814836
$22$	−80072.8	−1.60327
$23$	−50212.0	−0.860519	−0.430260	−	0.902705i	$-0.641578\pi$
$23$	−50212.0	−0.860519	−0.430260	+	0.902705i	$0.641578\pi$
$24$	61561.7	0.909016
$25$	−77865.3	−0.996676
$26$	120121.	1.34034
$27$	−96529.3	−0.943813
$28$	−19236.8	−0.165608
$29$	−170108.	−1.29518	−0.647591	−	0.761988i	$-0.724224\pi$
$29$	−170108.	−1.29518	−0.647591	+	0.761988i	$0.724224\pi$
$30$	9849.81	0.0666045
$31$	301806.	1.81954	0.909770	−	0.415113i	$-0.136258\pi$
$31$	301806.	1.81954	0.909770	+	0.415113i	$0.136258\pi$
$32$	77769.9	0.419553
$33$	315192.	1.52678
$34$	412771.	1.80108
$35$	11360.1	0.0447863
$36$	5978.70	0.0213574
$37$	50653.0	0.164399
$37$	50653.0	0.164399
$38$	56339.0	0.166558
$39$	−472836.	−1.27639
$40$	−20223.5	−0.0499628
$41$	−209106.	−0.473831	−0.236915	−	0.971530i	$-0.576136\pi$
$41$	−209106.	−0.473831	−0.236915	+	0.971530i	$0.576136\pi$
$42$	430928.	0.897496
$43$	−43153.5	−0.0827707	−0.0413853	−	0.999143i	$-0.513177\pi$
$43$	−43153.5	−0.0827707	−0.0413853	+	0.999143i	$0.513177\pi$
$44$	175336.	0.310303
$45$	−3530.67	−0.00577581
$46$	625713.	0.947813
$47$	−117766.	−0.165454	−0.0827271	−	0.996572i	$-0.526363\pi$
$47$	−117766.	−0.165454	−0.0827271	+	0.996572i	$0.526363\pi$
$48$	−938471.	−1.22483
$49$	−326538.	−0.396504
$50$	970312.	1.09778
$51$	−1.62480e6	−1.71516
$52$	−263031.	−0.259415
$53$	336845.	0.310789	0.155394	−	0.987853i	$-0.450335\pi$
$53$	336845.	0.310789	0.155394	+	0.987853i	$0.450335\pi$
$54$	1.20289e6	1.03956
$55$	−103543.	−0.0839173
$56$	−884777.	−0.673249
$57$	−221768.	−0.158612
$58$	2.11978e6	1.42657
$59$	141086.	0.0894341	0.0447170	−	0.999000i	$-0.485761\pi$
$59$	141086.	0.0894341	0.0447170	+	0.999000i	$0.485761\pi$
$60$	−21568.2	−0.0128909
$61$	1.61439e6	0.910656	0.455328	−	0.890324i	$-0.349522\pi$
$61$	1.61439e6	0.910656	0.455328	+	0.890324i	$0.349522\pi$
$62$	−3.76093e6	−2.00412
$63$	−154466.	−0.0778291
$64$	1.47979e6	0.705620
$65$	155330.	0.0701552
$66$	−3.92774e6	−1.68166
$67$	2.71548e6	1.10302	0.551511	−	0.834167i	$-0.314051\pi$
$67$	2.71548e6	1.10302	0.551511	+	0.834167i	$0.314051\pi$
$68$	−903847.	−0.348589
$69$	−2.46300e6	−0.902596
$70$	−141563.	−0.0493296
$71$	3.12792e6	1.03717	0.518587	−	0.855025i	$-0.326458\pi$
$71$	3.12792e6	1.03717	0.518587	+	0.855025i	$0.326458\pi$
$72$	274984.	0.0868248
$73$	−2.19209e6	−0.659520	−0.329760	−	0.944065i	$-0.606968\pi$
$73$	−2.19209e6	−0.659520	−0.329760	+	0.944065i	$0.606968\pi$
$74$	−631208.	−0.181076
$75$	−3.81946e6	−1.04541
$76$	−123366.	−0.0322364
$77$	−4.53000e6	−1.13079
$78$	5.89221e6	1.40588
$79$	−2.76709e6	−0.631434	−0.315717	−	0.948853i	$-0.602245\pi$
$79$	−2.76709e6	−0.631434	−0.315717	+	0.948853i	$0.602245\pi$
$80$	308295.	0.0673212
$81$	−5.21415e6	−1.09015
$82$	2.60576e6	0.521898
$83$	7.31499e6	1.40424	0.702119	−	0.712060i	$-0.252237\pi$
$83$	7.31499e6	1.40424	0.702119	+	0.712060i	$0.252237\pi$
$84$	−943606.	−0.173705
$85$	533759.	0.0942711
$86$	537754.	0.0911673
$87$	−8.34413e6	−1.35851
$88$	8.06439e6	1.26148
$89$	−6.30446e6	−0.947945	−0.473972	−	0.880540i	$-0.657180\pi$
$89$	−6.30446e6	−0.947945	−0.473972	+	0.880540i	$0.657180\pi$
$90$	43997.1	0.00636173
$91$	6.79569e6	0.945342
$92$	−1.37013e6	−0.183444
$93$	1.48042e7	1.90851
$94$	1.46753e6	0.182238
$95$	72852.6	0.00871791
$96$	3.81477e6	0.440068
$97$	−1.27419e7	−1.41753	−0.708764	−	0.705445i	$-0.750747\pi$
$97$	−1.27419e7	−1.41753	−0.708764	+	0.705445i	$0.750747\pi$
$98$	4.06913e6	0.436727
$99$	1.40790e6	0.145831
$100$	−2.12470e6	−0.212470
$101$	506189.	0.0488864	0.0244432	−	0.999701i	$-0.492219\pi$
$101$	506189.	0.0488864	0.0244432	+	0.999701i	$0.492219\pi$
$102$	2.02473e7	1.88915
$103$	2.10862e7	1.90137	0.950686	−	0.310154i	$-0.100381\pi$
$103$	2.10862e7	1.90137	0.950686	+	0.310154i	$0.100381\pi$
$104$	−1.20978e7	−1.05461
$105$	557238.	0.0469762
$106$	−4.19757e6	−0.342316
$107$	−9.16759e6	−0.723456	−0.361728	−	0.932284i	$-0.617813\pi$
$107$	−9.16759e6	−0.723456	−0.361728	+	0.932284i	$0.617813\pi$
$108$	−2.63398e6	−0.201200
$109$	206992.	0.0153095	0.00765476	−	0.999971i	$-0.497563\pi$
$109$	206992.	0.0153095	0.00765476	+	0.999971i	$0.497563\pi$
$110$	1.29029e6	0.0924302
$111$	2.48463e6	0.172438
$112$	1.34879e7	0.907154
$113$	−3.00754e7	−1.96081	−0.980407	−	0.196982i	$-0.936886\pi$
$113$	−3.00754e7	−1.96081	−0.980407	+	0.196982i	$0.936886\pi$
$114$	2.76354e6	0.174703
$115$	809117.	0.0496099
$116$	−4.64170e6	−0.276105
$117$	−2.11206e6	−0.121915
$118$	−1.75814e6	−0.0985066
$119$	2.33519e7	1.27030
$120$	−992006.	−0.0524058
$121$	2.18019e7	1.11878
$122$	−2.01176e7	−1.00304
$123$	−1.02571e7	−0.497000
$124$	8.23532e6	0.387886
$125$	2.51363e6	0.115111
$126$	1.92487e6	0.0857244
$127$	−3.92244e6	−0.169920	−0.0849599	−	0.996384i	$-0.527076\pi$
$127$	−3.92244e6	−0.169920	−0.0849599	+	0.996384i	$0.527076\pi$
$128$	−2.83948e7	−1.19675
$129$	−2.11677e6	−0.0868180
$130$	−1.93564e6	−0.0772720
$131$	−2.38934e7	−0.928598	−0.464299	−	0.885679i	$-0.653694\pi$
$131$	−2.38934e7	−0.928598	−0.464299	+	0.885679i	$0.653694\pi$
$132$	8.60059e6	0.325476
$133$	3.18729e6	0.117474
$134$	−3.38387e7	−1.21492
$135$	1.55547e6	0.0544119
$136$	−4.15715e7	−1.41713
$137$	−5.88642e6	−0.195582	−0.0977910	−	0.995207i	$-0.531178\pi$
$137$	−5.88642e6	−0.195582	−0.0977910	+	0.995207i	$0.531178\pi$
$138$	3.06925e7	0.994159
$139$	−2.70244e7	−0.853501	−0.426750	−	0.904370i	$-0.640342\pi$
$139$	−2.70244e7	−0.853501	−0.426750	+	0.904370i	$0.640342\pi$
$140$	309982.	0.00954747
$141$	−5.77667e6	−0.173544
$142$	−3.89783e7	−1.14239
$143$	−6.19400e7	−1.77131
$144$	−4.19196e6	−0.116990
$145$	2.74111e6	0.0746688
$146$	2.73165e7	0.726424
$147$	−1.60174e7	−0.415892
$148$	1.38216e6	0.0350463
$149$	6.18544e7	1.53186	0.765929	−	0.642925i	$-0.222279\pi$
$149$	6.18544e7	1.53186	0.765929	+	0.642925i	$0.222279\pi$
$150$	4.75958e7	1.15146
$151$	4.82342e7	1.14008	0.570041	−	0.821617i	$-0.306927\pi$
$151$	4.82342e7	1.14008	0.570041	+	0.821617i	$0.306927\pi$
$152$	−5.67408e6	−0.131052
$153$	−7.25764e6	−0.163823
$154$	5.64502e7	1.24550
$155$	−4.86330e6	−0.104899
$156$	−1.29022e7	−0.272099
$157$	7.07200e6	0.145846	0.0729228	−	0.997338i	$-0.476767\pi$
$157$	7.07200e6	0.145846	0.0729228	+	0.997338i	$0.476767\pi$
$158$	3.44818e7	0.695489
$159$	1.65230e7	0.325985
$160$	−1.25318e6	−0.0241877
$161$	3.53988e7	0.668494
$162$	6.49756e7	1.20074
$163$	5.51611e7	0.997646	0.498823	−	0.866704i	$-0.333766\pi$
$163$	5.51611e7	0.997646	0.498823	+	0.866704i	$0.333766\pi$
$164$	−5.70584e6	−0.101010
$165$	−5.07900e6	−0.0880206
$166$	−9.11552e7	−1.54669
$167$	−1.37888e7	−0.229097	−0.114549	−	0.993418i	$-0.536542\pi$
$167$	−1.37888e7	−0.229097	−0.114549	+	0.993418i	$0.536542\pi$
$168$	−4.34001e7	−0.706169
$169$	3.01709e7	0.480823
$170$	−6.65139e6	−0.103834
$171$	−990594.	−0.0151499
$172$	−1.17752e6	−0.0176449
$173$	3.92470e7	0.576296	0.288148	−	0.957586i	$-0.406960\pi$
$173$	3.92470e7	0.576296	0.288148	+	0.957586i	$0.406960\pi$
$174$	1.03980e8	1.49633
$175$	5.48939e7	0.774268
$176$	−1.22937e8	−1.69976
$177$	6.92058e6	0.0938071
$178$	7.85625e7	1.04411
$179$	1.12025e8	1.45992	0.729959	−	0.683491i	$-0.239539\pi$
$179$	1.12025e8	1.45992	0.729959	+	0.683491i	$0.239539\pi$
$180$	−96340.7	−0.00123128
$181$	5.67686e7	0.711595	0.355798	−	0.934563i	$-0.384209\pi$
$181$	5.67686e7	0.711595	0.355798	+	0.934563i	$0.384209\pi$
$182$	−8.46839e7	−1.04124
$183$	7.91892e7	0.955184
$184$	−6.30175e7	−0.745760
$185$	−816222.	−0.00947779
$186$	−1.84481e8	−2.10212
$187$	−2.12843e8	−2.38020
$188$	−3.21346e6	−0.0352712
$189$	6.80518e7	0.733201
$190$	−907846.	−0.00960228
$191$	−1.52494e8	−1.58357	−0.791783	−	0.610803i	$-0.790847\pi$
$191$	−1.52494e8	−1.58357	−0.791783	+	0.610803i	$0.790847\pi$
$192$	7.25868e7	0.740122
$193$	−9.69210e7	−0.970437	−0.485218	−	0.874393i	$-0.661260\pi$
$193$	−9.69210e7	−0.970437	−0.485218	+	0.874393i	$0.661260\pi$
$194$	1.58782e8	1.56133
$195$	7.61928e6	0.0735856
$196$	−8.91019e6	−0.0845261
$197$	−6.31856e7	−0.588825	−0.294412	−	0.955678i	$-0.595124\pi$
$197$	−6.31856e7	−0.588825	−0.294412	+	0.955678i	$0.595124\pi$
$198$	−1.75444e7	−0.160624
$199$	−1.55705e8	−1.40061	−0.700303	−	0.713846i	$-0.746952\pi$
$199$	−1.55705e8	−1.40061	−0.700303	+	0.713846i	$0.746952\pi$
$200$	−9.77232e7	−0.863759
$201$	1.33200e8	1.15696
$202$	−6.30784e6	−0.0538456
$203$	1.19923e8	1.00616
$204$	−4.43356e7	−0.365634
$205$	3.36953e6	0.0273169
$206$	−2.62763e8	−2.09425
$207$	−1.10017e7	−0.0862116
$208$	1.84424e8	1.42100
$209$	−2.90509e7	−0.220114
$210$	−6.94397e6	−0.0517417
$211$	2.18443e8	1.60084	0.800422	−	0.599436i	$-0.204609\pi$
$211$	2.18443e8	1.60084	0.800422	+	0.599436i	$0.204609\pi$
$212$	9.19144e6	0.0662534
$213$	1.53431e8	1.08789
$214$	1.14241e8	0.796846
$215$	695375.	0.00477183
$216$	−1.21147e8	−0.817946
$217$	−2.12769e8	−1.41351
$218$	−2.57942e6	−0.0168626
$219$	−1.07526e8	−0.691769
$220$	−2.82536e6	−0.0178894
$221$	3.19297e8	1.98986
$222$	−3.09621e7	−0.189930
$223$	−5.05279e6	−0.0305115	−0.0152558	−	0.999884i	$-0.504856\pi$
$223$	−5.05279e6	−0.0305115	−0.0152558	+	0.999884i	$0.504856\pi$
$224$	−5.48267e7	−0.325930
$225$	−1.70607e7	−0.0998526
$226$	3.74782e8	2.15973
$227$	−2.46513e8	−1.39878	−0.699389	−	0.714742i	$-0.746544\pi$
$227$	−2.46513e8	−1.39878	−0.699389	+	0.714742i	$0.746544\pi$
$228$	−6.05135e6	−0.0338127
$229$	2.70083e8	1.48619	0.743094	−	0.669187i	$-0.233358\pi$
$229$	2.70083e8	1.48619	0.743094	+	0.669187i	$0.233358\pi$
$230$	−1.00827e7	−0.0546426
$231$	−2.22206e8	−1.18608
$232$	−2.13490e8	−1.12246
$233$	1.12269e8	0.581452	0.290726	−	0.956806i	$-0.406103\pi$
$233$	1.12269e8	0.581452	0.290726	+	0.956806i	$0.406103\pi$
$234$	2.63193e7	0.134282
$235$	1.89768e6	0.00953862
$236$	3.84980e6	0.0190654
$237$	−1.35731e8	−0.662310
$238$	−2.90998e8	−1.39917
$239$	−2.31450e8	−1.09664	−0.548321	−	0.836268i	$-0.684733\pi$
$239$	−2.31450e8	−1.09664	−0.548321	+	0.836268i	$0.684733\pi$
$240$	1.51225e7	0.0706130
$241$	−2.11480e8	−0.973218	−0.486609	−	0.873620i	$-0.661766\pi$
$241$	−2.11480e8	−0.973218	−0.486609	+	0.873620i	$0.661766\pi$
$242$	−2.71683e8	−1.23228
$243$	−4.46551e7	−0.199641
$244$	4.40516e7	0.194132
$245$	5.26183e6	0.0228589
$246$	1.27818e8	0.547417
$247$	4.35808e7	0.184016
$248$	3.78775e8	1.57689
$249$	3.58816e8	1.47290
$250$	−3.13233e7	−0.126788
$251$	−2.56034e7	−0.102197	−0.0510986	−	0.998694i	$-0.516272\pi$
$251$	−2.56034e7	−0.102197	−0.0510986	+	0.998694i	$0.516272\pi$
$252$	−4.21490e6	−0.0165915
$253$	−3.22646e8	−1.25258
$254$	4.88792e7	0.187157
$255$	2.61820e7	0.0988807
$256$	1.64427e8	0.612537
$257$	4.77526e8	1.75482	0.877408	−	0.479745i	$-0.159271\pi$
$257$	4.77526e8	1.75482	0.877408	+	0.479745i	$0.159271\pi$
$258$	2.63779e7	0.0956251
$259$	−3.57096e7	−0.127713
$260$	4.23847e6	0.0149556
$261$	−3.72716e7	−0.129759
$262$	2.97745e8	1.02280
$263$	−3.13115e8	−1.06135	−0.530676	−	0.847575i	$-0.678062\pi$
$263$	−3.13115e8	−1.06135	−0.530676	+	0.847575i	$0.678062\pi$
$264$	3.95575e8	1.32317
$265$	−5.42792e6	−0.0179173
$266$	−3.97182e7	−0.129391
$267$	−3.09247e8	−0.994297
$268$	7.40968e7	0.235141
$269$	−1.88856e8	−0.591557	−0.295779	−	0.955257i	$-0.595579\pi$
$269$	−1.88856e8	−0.591557	−0.295779	+	0.955257i	$0.595579\pi$
$270$	−1.93834e7	−0.0599317
$271$	−5.37066e7	−0.163921	−0.0819607	−	0.996636i	$-0.526118\pi$
$271$	−5.37066e7	−0.163921	−0.0819607	+	0.996636i	$0.526118\pi$
$272$	6.33732e8	1.90948
$273$	3.33343e8	0.991566
$274$	7.33531e7	0.215423
$275$	−5.00336e8	−1.45077
$276$	−6.72076e7	−0.192414
$277$	4.91624e7	0.138980	0.0694902	−	0.997583i	$-0.477863\pi$
$277$	4.91624e7	0.138980	0.0694902	+	0.997583i	$0.477863\pi$
$278$	3.36762e8	0.940083
$279$	6.61274e7	0.182292
$280$	1.42573e7	0.0388136
$281$	−1.87276e8	−0.503513	−0.251756	−	0.967791i	$-0.581008\pi$
$281$	−1.87276e8	−0.503513	−0.251756	+	0.967791i	$0.581008\pi$
$282$	7.19854e7	0.191149
$283$	3.62969e7	0.0951956	0.0475978	−	0.998867i	$-0.484843\pi$
$283$	3.62969e7	0.0951956	0.0475978	+	0.998867i	$0.484843\pi$
$284$	8.53510e7	0.221103
$285$	3.57357e6	0.00914419
$286$	7.71860e8	1.95100
$287$	1.47417e8	0.368095
$288$	1.70398e7	0.0420331
$289$	6.86855e8	1.67387
$290$	−3.41582e7	−0.0822435
$291$	−6.25015e8	−1.48684
$292$	−5.98151e7	−0.140595
$293$	−8.05307e8	−1.87036	−0.935179	−	0.354176i	$-0.884761\pi$
$293$	−8.05307e8	−1.87036	−0.935179	+	0.354176i	$0.884761\pi$
$294$	1.99599e8	0.458082
$295$	−2.27346e6	−0.00515598
$296$	6.35710e7	0.142475
$297$	−6.20264e8	−1.37382
$298$	−7.70793e8	−1.68726
$299$	4.84018e8	1.04716
$300$	−1.04221e8	−0.222859
$301$	3.04226e7	0.0643004
$302$	−6.01066e8	−1.25574
$303$	2.48296e7	0.0512768
$304$	8.64979e7	0.176583
$305$	−2.60143e7	−0.0525004
$306$	9.04405e7	0.180442
$307$	2.11955e8	0.418079	0.209039	−	0.977907i	$-0.432966\pi$
$307$	2.11955e8	0.418079	0.209039	+	0.977907i	$0.432966\pi$
$308$	−1.23609e8	−0.241059
$309$	1.03432e9	1.99434
$310$	6.06035e7	0.115540
$311$	−9.92149e7	−0.187032	−0.0935159	−	0.995618i	$-0.529811\pi$
$311$	−9.92149e7	−0.187032	−0.0935159	+	0.995618i	$0.529811\pi$
$312$	−5.93423e8	−1.10617
$313$	−7.64132e8	−1.40852	−0.704261	−	0.709941i	$-0.748721\pi$
$313$	−7.64132e8	−1.40852	−0.704261	+	0.709941i	$0.748721\pi$
$314$	−8.81271e7	−0.160641
$315$	2.48907e6	0.00448694
$316$	−7.55051e7	−0.134608
$317$	−3.46329e8	−0.610634	−0.305317	−	0.952251i	$-0.598762\pi$
$317$	−3.46329e8	−0.610634	−0.305317	+	0.952251i	$0.598762\pi$
$318$	−2.05899e8	−0.359054
$319$	−1.09305e9	−1.88527
$320$	−2.38453e7	−0.0406798
$321$	−4.49689e8	−0.758831
$322$	−4.41119e8	−0.736309
$323$	1.49756e8	0.247272
$324$	−1.42277e8	−0.232396
$325$	7.50581e8	1.21285
$326$	−6.87386e8	−1.09885
$327$	1.01534e7	0.0160581
$328$	−2.62434e8	−0.410641
$329$	8.30234e7	0.128533
$330$	6.32915e7	0.0969498
$331$	4.03683e8	0.611847	0.305923	−	0.952056i	$-0.401035\pi$
$331$	4.03683e8	0.611847	0.305923	+	0.952056i	$0.401035\pi$
$332$	1.99603e8	0.299353
$333$	1.10984e7	0.0164704
$334$	1.71828e8	0.252338
$335$	−4.37572e7	−0.0635906
$336$	6.61609e8	0.951511
$337$	8.51714e7	0.121224	0.0606120	−	0.998161i	$-0.480695\pi$
$337$	8.51714e7	0.121224	0.0606120	+	0.998161i	$0.480695\pi$
$338$	−3.75973e8	−0.529600
$339$	−1.47526e9	−2.05669
$340$	1.45646e7	0.0200966
$341$	1.93930e9	2.64853
$342$	1.23442e7	0.0166867
$343$	8.10791e8	1.08487
$344$	−5.41589e7	−0.0717324
$345$	3.96888e7	0.0520357
$346$	−4.89074e8	−0.634758
$347$	1.52540e8	0.195988	0.0979942	−	0.995187i	$-0.468757\pi$
$347$	1.52540e8	0.195988	0.0979942	+	0.995187i	$0.468757\pi$
$348$	−2.27685e8	−0.289606
$349$	1.08157e9	1.36196	0.680980	−	0.732302i	$-0.261554\pi$
$349$	1.08157e9	1.36196	0.680980	+	0.732302i	$0.261554\pi$
$350$	−6.84056e8	−0.852813
$351$	9.30492e8	1.14852
$352$	4.99723e8	0.610703
$353$	4.29956e8	0.520251	0.260125	−	0.965575i	$-0.416236\pi$
$353$	4.29956e8	0.520251	0.260125	+	0.965575i	$0.416236\pi$
$354$	−8.62402e7	−0.103323
$355$	−5.04033e7	−0.0597943
$356$	−1.72029e8	−0.202081
$357$	1.14546e9	1.33242
$358$	−1.39599e9	−1.60802
$359$	1.18874e9	1.35599	0.677996	−	0.735066i	$-0.262849\pi$
$359$	1.18874e9	1.35599	0.677996	+	0.735066i	$0.262849\pi$
$360$	−4.43109e6	−0.00500555
$361$	−8.73432e8	−0.977133
$362$	−7.07417e8	−0.783782
$363$	1.06943e9	1.17349
$364$	1.85433e8	0.201526
$365$	3.53233e7	0.0380221
$366$	−9.86809e8	−1.05208
$367$	−1.08954e9	−1.15057	−0.575286	−	0.817952i	$-0.695109\pi$
$367$	−1.08954e9	−1.15057	−0.575286	+	0.817952i	$0.695109\pi$
$368$	9.60664e8	1.00486
$369$	−4.58164e7	−0.0474710
$370$	1.01713e7	0.0104393
$371$	−2.37471e8	−0.241436
$372$	4.03960e8	0.406853
$373$	−1.68837e9	−1.68456	−0.842280	−	0.539040i	$-0.818787\pi$
$373$	−1.68837e9	−1.68456	−0.842280	+	0.539040i	$0.818787\pi$
$374$	2.65233e9	2.62166
$375$	1.23299e8	0.120739
$376$	−1.47800e8	−0.143389
$377$	1.63975e9	1.57610
$378$	−8.48021e8	−0.807580
$379$	3.13125e8	0.295447	0.147724	−	0.989029i	$-0.452805\pi$
$379$	3.13125e8	0.295447	0.147724	+	0.989029i	$0.452805\pi$
$380$	1.98792e6	0.00185847
$381$	−1.92404e8	−0.178228
$382$	1.90029e9	1.74421
$383$	−2.98967e8	−0.271911	−0.135956	−	0.990715i	$-0.543410\pi$
$383$	−2.98967e8	−0.271911	−0.135956	+	0.990715i	$0.543410\pi$
$384$	−1.39283e9	−1.25527
$385$	7.29964e7	0.0651912
$386$	1.20777e9	1.06888
$387$	−9.45518e6	−0.00829243
$388$	−3.47685e8	−0.302186
$389$	2.97708e8	0.256429	0.128215	−	0.991746i	$-0.459075\pi$
$389$	2.97708e8	0.256429	0.128215	+	0.991746i	$0.459075\pi$
$390$	−9.49470e7	−0.0810504
$391$	1.66322e9	1.40712
$392$	−4.09815e8	−0.343626
$393$	−1.17202e9	−0.974004
$394$	7.87381e8	0.648557
$395$	4.45888e7	0.0364029
$396$	3.84171e7	0.0310879
$397$	9.85091e8	0.790150	0.395075	−	0.918649i	$-0.370719\pi$
$397$	9.85091e8	0.790150	0.395075	+	0.918649i	$0.370719\pi$
$398$	1.94030e9	1.54269
$399$	1.56343e8	0.123218
$400$	1.48973e9	1.16385
$401$	−1.01120e9	−0.783126	−0.391563	−	0.920151i	$-0.628065\pi$
$401$	−1.01120e9	−0.783126	−0.391563	+	0.920151i	$0.628065\pi$
$402$	−1.65986e9	−1.27432
$403$	−2.90925e9	−2.21418
$404$	1.38123e7	0.0104215
$405$	8.40207e7	0.0628483
$406$	−1.49442e9	−1.10823
$407$	3.25479e8	0.239300
$408$	−2.03917e9	−1.48642
$409$	−2.51969e9	−1.82102	−0.910511	−	0.413484i	$-0.864312\pi$
$409$	−2.51969e9	−1.82102	−0.910511	+	0.413484i	$0.864312\pi$
$410$	−4.19892e7	−0.0300880
$411$	−2.88741e8	−0.205145
$412$	5.75374e8	0.405331
$413$	−9.94638e7	−0.0694768
$414$	1.37097e8	0.0949572
$415$	−1.17874e8	−0.0809560
$416$	−7.49661e8	−0.510550
$417$	−1.32560e9	−0.895234
$418$	3.62015e8	0.242443
$419$	1.96274e9	1.30351	0.651753	−	0.758431i	$-0.274034\pi$
$419$	1.96274e9	1.30351	0.651753	+	0.758431i	$0.274034\pi$
$420$	1.52053e7	0.0100143
$421$	2.92864e9	1.91284	0.956419	−	0.291998i	$-0.0943200\pi$
$421$	2.92864e9	1.91284	0.956419	+	0.291998i	$0.0943200\pi$
$422$	−2.72211e9	−1.76324
$423$	−2.58032e7	−0.0165761
$424$	4.22750e8	0.269342
$425$	2.57921e9	1.62976
$426$	−1.91197e9	−1.19825
$427$	−1.13812e9	−0.707443
$428$	−2.50154e8	−0.154225
$429$	−3.03828e9	−1.85792
$430$	−8.66536e6	−0.00525590
$431$	−5.37412e8	−0.323323	−0.161662	−	0.986846i	$-0.551685\pi$
$431$	−5.37412e8	−0.323323	−0.161662	+	0.986846i	$0.551685\pi$
$432$	1.84681e9	1.10212
$433$	−1.30965e9	−0.775262	−0.387631	−	0.921815i	$-0.626707\pi$
$433$	−1.30965e9	−0.775262	−0.387631	+	0.921815i	$0.626707\pi$
$434$	2.65140e9	1.55690
$435$	1.34457e8	0.0783199
$436$	5.64816e6	0.00326366
$437$	2.27012e8	0.130126
$438$	1.33993e9	0.761944
$439$	−1.75361e9	−0.989250	−0.494625	−	0.869107i	$-0.664695\pi$
$439$	−1.75361e9	−0.989250	−0.494625	+	0.869107i	$0.664695\pi$
$440$	−1.29949e8	−0.0727261
$441$	−7.15464e7	−0.0397240
$442$	−3.97889e9	−2.19172
$443$	−3.58264e9	−1.95790	−0.978949	−	0.204104i	$-0.934572\pi$
$443$	−3.58264e9	−1.95790	−0.978949	+	0.204104i	$0.934572\pi$
$444$	6.77978e7	0.0367600
$445$	1.01590e8	0.0546501
$446$	6.29649e7	0.0336068
$447$	3.03409e9	1.60676
$448$	−1.04323e9	−0.548161
$449$	2.23605e9	1.16579	0.582893	−	0.812549i	$-0.301920\pi$
$449$	2.23605e9	1.16579	0.582893	+	0.812549i	$0.301920\pi$
$450$	2.12601e8	0.109982
$451$	−1.34364e9	−0.689710
$452$	−8.20661e8	−0.418003
$453$	2.36599e9	1.19583
$454$	3.07190e9	1.54067
$455$	−1.09506e8	−0.0545001
$456$	−2.78325e8	−0.137460
$457$	7.13049e8	0.349472	0.174736	−	0.984615i	$-0.444093\pi$
$457$	7.13049e8	0.349472	0.174736	+	0.984615i	$0.444093\pi$
$458$	−3.36562e9	−1.63695
$459$	3.19743e9	1.54332
$460$	2.20782e7	0.0105758
$461$	−1.78269e9	−0.847465	−0.423732	−	0.905787i	$-0.639280\pi$
$461$	−1.78269e9	−0.847465	−0.423732	+	0.905787i	$0.639280\pi$
$462$	2.76900e9	1.30640
$463$	−2.77841e9	−1.30095	−0.650477	−	0.759526i	$-0.725431\pi$
$463$	−2.77841e9	−1.30095	−0.650477	+	0.759526i	$0.725431\pi$
$464$	3.25452e9	1.51243
$465$	−2.38555e8	−0.110028
$466$	−1.39903e9	−0.640437
$467$	8.95146e8	0.406710	0.203355	−	0.979105i	$-0.434815\pi$
$467$	8.95146e8	0.406710	0.203355	+	0.979105i	$0.434815\pi$
$468$	−5.76315e7	−0.0259896
$469$	−1.91437e9	−0.856883
$470$	−2.36478e7	−0.0105063
$471$	3.46896e8	0.152977
$472$	1.77067e8	0.0775071
$473$	−2.77290e8	−0.120481
$474$	1.69141e9	0.729497
$475$	3.52035e8	0.150716
$476$	6.37199e8	0.270801
$477$	7.38048e7	0.0311365
$478$	2.88420e9	1.20789
$479$	−2.27186e9	−0.944513	−0.472257	−	0.881461i	$-0.656560\pi$
$479$	−2.27186e9	−0.944513	−0.472257	+	0.881461i	$0.656560\pi$
$480$	−6.14713e7	−0.0253704
$481$	−4.88268e8	−0.200056
$482$	2.63534e9	1.07195
$483$	1.73638e9	0.701182
$484$	5.94906e8	0.238501
$485$	2.05322e8	0.0817222
$486$	5.56466e8	0.219893
$487$	−8.11508e8	−0.318377	−0.159188	−	0.987248i	$-0.550888\pi$
$487$	−8.11508e8	−0.318377	−0.159188	+	0.987248i	$0.550888\pi$
$488$	2.02611e9	0.789210
$489$	2.70577e9	1.04643
$490$	−6.55699e7	−0.0251778
$491$	−2.13174e9	−0.812737	−0.406368	−	0.913709i	$-0.633205\pi$
$491$	−2.13174e9	−0.812737	−0.406368	+	0.913709i	$0.633205\pi$
$492$	−2.79883e8	−0.105950
$493$	5.63463e9	2.11788
$494$	−5.43078e8	−0.202683
$495$	−2.26869e7	−0.00840730
$496$	−5.77419e9	−2.12474
$497$	−2.20514e9	−0.805728
$498$	−4.47135e9	−1.62232
$499$	9.08651e8	0.327375	0.163687	−	0.986512i	$-0.447661\pi$
$499$	9.08651e8	0.327375	0.163687	+	0.986512i	$0.447661\pi$
$500$	6.85889e7	0.0245391
$501$	−6.76370e8	−0.240299
$502$	3.19054e8	0.112564
$503$	−3.47815e9	−1.21860	−0.609299	−	0.792940i	$-0.708549\pi$
$503$	−3.47815e9	−1.21860	−0.609299	+	0.792940i	$0.708549\pi$
$504$	−1.93860e8	−0.0674498
$505$	−8.15673e6	−0.00281836
$506$	4.02062e9	1.37964
$507$	1.47995e9	0.504334
$508$	−1.07031e8	−0.0362232
$509$	−9.85942e8	−0.331390	−0.165695	−	0.986177i	$-0.552987\pi$
$509$	−9.85942e8	−0.331390	−0.165695	+	0.986177i	$0.552987\pi$
$510$	−3.26264e8	−0.108912
$511$	1.54539e9	0.512348
$512$	1.58555e9	0.522078
$513$	4.36416e8	0.142722
$514$	−5.95065e9	−1.93283
$515$	−3.39782e8	−0.109616
$516$	−5.77599e7	−0.0185077
$517$	−7.56725e8	−0.240836
$518$	4.44993e8	0.140669
$519$	1.92515e9	0.604475
$520$	1.94944e8	0.0607993
$521$	−4.02097e8	−0.124566	−0.0622829	−	0.998059i	$-0.519838\pi$
$521$	−4.02097e8	−0.124566	−0.0622829	+	0.998059i	$0.519838\pi$
$522$	4.64457e8	0.142922
$523$	3.88898e9	1.18872	0.594360	−	0.804199i	$-0.297405\pi$
$523$	3.88898e9	1.18872	0.594360	+	0.804199i	$0.297405\pi$
$524$	−6.51974e8	−0.197957
$525$	2.69266e9	0.812128
$526$	3.90186e9	1.16902
$527$	−9.99699e9	−2.97531
$528$	−6.03030e9	−1.78287
$529$	−8.83576e8	−0.259507
$530$	6.76396e7	0.0197349
$531$	3.09128e7	0.00896000
$532$	8.69711e7	0.0250429
$533$	2.01567e9	0.576600
$534$	3.85365e9	1.09516
$535$	1.47726e8	0.0417081
$536$	3.40800e9	0.955923
$537$	5.49505e9	1.53130
$538$	2.35341e9	0.651567
$539$	−2.09822e9	−0.577153
$540$	4.24439e7	0.0115994
$541$	−1.82807e9	−0.496366	−0.248183	−	0.968713i	$-0.579833\pi$
$541$	−1.82807e9	−0.496366	−0.248183	+	0.968713i	$0.579833\pi$
$542$	6.69261e8	0.180550
$543$	2.78462e9	0.746390
$544$	−2.57604e9	−0.686052
$545$	−3.33547e6	−0.000882612 0
$546$	−4.15392e9	−1.09215
$547$	5.49936e9	1.43667	0.718335	−	0.695698i	$-0.244905\pi$
$547$	5.49936e9	1.43667	0.718335	+	0.695698i	$0.244905\pi$
$548$	−1.60622e8	−0.0416939
$549$	3.53722e8	0.0912345
$550$	6.23490e9	1.59794
$551$	7.69070e8	0.195855
$552$	−3.09114e9	−0.782226
$553$	1.95076e9	0.490530
$554$	−6.12633e8	−0.153079
$555$	−4.00374e7	−0.00994123
$556$	−7.37409e8	−0.181948
$557$	6.28158e9	1.54019	0.770097	−	0.637926i	$-0.220208\pi$
$557$	6.28158e9	1.54019	0.770097	+	0.637926i	$0.220208\pi$
$558$	−8.24041e8	−0.200784
$559$	4.15977e8	0.100723
$560$	−2.17344e8	−0.0522985
$561$	−1.04404e10	−2.49659
$562$	2.33373e9	0.554591
$563$	−3.02329e9	−0.714003	−0.357002	−	0.934104i	$-0.616201\pi$
$563$	−3.02329e9	−0.714003	−0.357002	+	0.934104i	$0.616201\pi$
$564$	−1.57627e8	−0.0369959
$565$	4.84634e8	0.113043
$566$	−4.52310e8	−0.104853
$567$	3.67590e9	0.846882
$568$	3.92563e9	0.898856
$569$	−7.57257e9	−1.72326	−0.861629	−	0.507539i	$-0.830555\pi$
$569$	−7.57257e9	−1.72326	−0.861629	+	0.507539i	$0.830555\pi$
$570$	−4.45317e7	−0.0100718
$571$	−6.53357e8	−0.146867	−0.0734335	−	0.997300i	$-0.523396\pi$
$571$	−6.53357e8	−0.146867	−0.0734335	+	0.997300i	$0.523396\pi$
$572$	−1.69015e9	−0.377605
$573$	−7.48015e9	−1.66100
$574$	−1.83702e9	−0.405436
$575$	3.90978e9	0.857659
$576$	3.24231e8	0.0706929
$577$	1.23788e8	0.0268264	0.0134132	−	0.999910i	$-0.495730\pi$
$577$	1.23788e8	0.0268264	0.0134132	+	0.999910i	$0.495730\pi$
$578$	−8.55919e9	−1.84368
$579$	−4.75418e9	−1.01789
$580$	7.47963e7	0.0159178
$581$	−5.15697e9	−1.09088
$582$	7.78857e9	1.63767
$583$	2.16445e9	0.452385
$584$	−2.75113e9	−0.571566
$585$	3.40338e7	0.00702853
$586$	1.00353e10	2.06009
$587$	−2.76551e9	−0.564340	−0.282170	−	0.959364i	$-0.591054\pi$
$587$	−2.76551e9	−0.564340	−0.282170	+	0.959364i	$0.591054\pi$
$588$	−4.37063e8	−0.0886592
$589$	−1.36449e9	−0.275148
$590$	2.83306e7	0.00567902
$591$	−3.09938e9	−0.617617
$592$	−9.69100e8	−0.191974
$593$	−7.98446e9	−1.57237	−0.786184	−	0.617992i	$-0.787946\pi$
$593$	−7.98446e9	−1.57237	−0.786184	+	0.617992i	$0.787946\pi$
$594$	7.72937e9	1.51318
$595$	−3.76292e8	−0.0732345
$596$	1.68781e9	0.326559
$597$	−7.63764e9	−1.46909
$598$	−6.03154e9	−1.15339
$599$	1.59263e9	0.302776	0.151388	−	0.988474i	$-0.451626\pi$
$599$	1.59263e9	0.302776	0.151388	+	0.988474i	$0.451626\pi$
$600$	−4.79353e9	−0.905995
$601$	−8.28849e9	−1.55745	−0.778726	−	0.627364i	$-0.784134\pi$
$601$	−8.28849e9	−1.55745	−0.778726	+	0.627364i	$0.784134\pi$
$602$	−3.79109e8	−0.0708233
$603$	5.94977e8	0.110507
$604$	1.31616e9	0.243041
$605$	−3.51316e8	−0.0644992
$606$	−3.09412e8	−0.0564786
$607$	−3.32819e9	−0.604015	−0.302007	−	0.953306i	$-0.597657\pi$
$607$	−3.32819e9	−0.604015	−0.302007	+	0.953306i	$0.597657\pi$
$608$	−3.51604e8	−0.0634440
$609$	5.88250e9	1.05536
$610$	3.24175e8	0.0578262
$611$	1.13520e9	0.201340
$612$	−1.98038e8	−0.0349236
$613$	6.45385e9	1.13164	0.565818	−	0.824530i	$-0.308560\pi$
$613$	6.45385e9	1.13164	0.565818	+	0.824530i	$0.308560\pi$
$614$	−2.64125e9	−0.460490
$615$	1.65283e8	0.0286526
$616$	−5.68528e9	−0.979984
$617$	4.48371e9	0.768492	0.384246	−	0.923231i	$-0.374461\pi$
$617$	4.48371e9	0.768492	0.384246	+	0.923231i	$0.374461\pi$
$618$	−1.28891e10	−2.19666
$619$	−4.65876e9	−0.789501	−0.394751	−	0.918788i	$-0.629169\pi$
$619$	−4.65876e9	−0.789501	−0.394751	+	0.918788i	$0.629169\pi$
$620$	−1.32704e8	−0.0223621
$621$	4.84693e9	0.812169
$622$	1.23636e9	0.206005
$623$	4.44456e9	0.736411
$624$	9.04637e9	1.49049
$625$	6.04273e9	0.990040
$626$	9.52217e9	1.55141
$627$	−1.42501e9	−0.230877
$628$	1.92972e8	0.0310911
$629$	−1.67783e9	−0.268825
$630$	−3.10173e7	−0.00494211
$631$	1.00255e10	1.58855	0.794277	−	0.607555i	$-0.207850\pi$
$631$	1.00255e10	1.58855	0.794277	+	0.607555i	$0.207850\pi$
$632$	−3.47278e9	−0.547226
$633$	1.07151e10	1.67912
$634$	4.31575e9	0.672579
$635$	6.32062e7	0.00979607
$636$	4.50859e8	0.0694930
$637$	3.14766e9	0.482502
$638$	1.36210e10	2.07652
$639$	6.85345e8	0.103910
$640$	4.57554e8	0.0689942
$641$	−9.33061e9	−1.39929	−0.699644	−	0.714492i	$-0.746658\pi$
$641$	−9.33061e9	−1.39929	−0.699644	+	0.714492i	$0.746658\pi$
$642$	5.60376e9	0.835809
$643$	4.64752e9	0.689418	0.344709	−	0.938710i	$-0.387978\pi$
$643$	4.64752e9	0.689418	0.344709	+	0.938710i	$0.387978\pi$
$644$	9.65920e8	0.142508
$645$	3.41096e7	0.00500516
$646$	−1.86617e9	−0.272356
$647$	1.13470e10	1.64708	0.823539	−	0.567259i	$-0.191996\pi$
$647$	1.13470e10	1.64708	0.823539	+	0.567259i	$0.191996\pi$
$648$	−6.54390e9	−0.944766
$649$	9.06573e8	0.130181
$650$	−9.35330e9	−1.33588
$651$	−1.04367e10	−1.48263
$652$	1.50517e9	0.212677
$653$	−2.12637e9	−0.298843	−0.149422	−	0.988774i	$-0.547741\pi$
$653$	−2.12637e9	−0.298843	−0.149422	+	0.988774i	$0.547741\pi$
$654$	−1.26526e8	−0.0176871
$655$	3.85017e8	0.0535348
$656$	4.00065e9	0.553308
$657$	−4.80299e8	−0.0660744
$658$	−1.03459e9	−0.141572
$659$	−5.95539e9	−0.810609	−0.405304	−	0.914182i	$-0.632834\pi$
$659$	−5.95539e9	−0.810609	−0.405304	+	0.914182i	$0.632834\pi$
$660$	−1.38590e8	−0.0187641
$661$	6.23963e8	0.0840337	0.0420168	−	0.999117i	$-0.486622\pi$
$661$	6.23963e8	0.0840337	0.0420168	+	0.999117i	$0.486622\pi$
$662$	−5.03046e9	−0.673915
$663$	1.56622e10	2.08716
$664$	9.18053e9	1.21697
$665$	−5.13600e7	−0.00677251
$666$	−1.38301e8	−0.0181412
$667$	8.54145e9	1.11453
$668$	−3.76253e8	−0.0488385
$669$	−2.47850e8	−0.0320035
$670$	5.45277e8	0.0700414
$671$	1.03735e10	1.32555
$672$	−2.68936e9	−0.341867
$673$	−2.48065e9	−0.313699	−0.156849	−	0.987623i	$-0.550134\pi$
$673$	−2.48065e9	−0.313699	−0.156849	+	0.987623i	$0.550134\pi$
$674$	−1.06136e9	−0.133522
$675$	7.51629e9	0.940676
$676$	8.23269e8	0.102501
$677$	−1.53229e10	−1.89793	−0.948967	−	0.315376i	$-0.897869\pi$
$677$	−1.53229e10	−1.89793	−0.948967	+	0.315376i	$0.897869\pi$
$678$	1.83838e10	2.26533
$679$	8.98283e9	1.10121
$680$	6.69882e8	0.0816991
$681$	−1.20920e10	−1.46717
$682$	−2.41664e10	−2.91721
$683$	−1.24122e10	−1.49065	−0.745323	−	0.666703i	$-0.767705\pi$
$683$	−1.24122e10	−1.49065	−0.745323	+	0.666703i	$0.767705\pi$
$684$	−2.70302e7	−0.00322963
$685$	9.48537e7	0.0112755
$686$	−1.01036e10	−1.19493
$687$	1.32481e10	1.55886
$688$	8.25619e8	0.0966541
$689$	−3.24701e9	−0.378196
$690$	−4.94579e8	−0.0573144
$691$	1.18917e10	1.37110	0.685552	−	0.728023i	$-0.259561\pi$
$691$	1.18917e10	1.37110	0.685552	+	0.728023i	$0.259561\pi$
$692$	1.07093e9	0.122854
$693$	−9.92549e8	−0.113288
$694$	−1.90086e9	−0.215870
$695$	4.35471e8	0.0492053
$696$	−1.04721e10	−1.17734
$697$	6.92641e9	0.774807
$698$	−1.34779e10	−1.50012
$699$	5.50702e9	0.609884
$700$	1.49788e9	0.165057
$701$	−7.44309e9	−0.816094	−0.408047	−	0.912961i	$-0.633790\pi$
$701$	−7.44309e9	−0.816094	−0.408047	+	0.912961i	$0.633790\pi$
$702$	−1.15952e10	−1.26503
$703$	−2.29006e8	−0.0248601
$704$	9.50864e9	1.02710
$705$	9.30852e7	0.0100050
$706$	−5.35786e9	−0.573027
$707$	−3.56856e8	−0.0379774
$708$	1.88841e8	0.0199976
$709$	2.66642e9	0.280974	0.140487	−	0.990083i	$-0.455133\pi$
$709$	2.66642e9	0.280974	0.140487	+	0.990083i	$0.455133\pi$
$710$	6.28096e8	0.0658600
$711$	−6.06285e8	−0.0632606
$712$	−7.91228e9	−0.821527
$713$	−1.51543e10	−1.56575
$714$	−1.42740e10	−1.46758
$715$	9.98101e8	0.102118
$716$	3.05680e9	0.311223
$717$	−1.13531e10	−1.15027
$718$	−1.48134e10	−1.49355
$719$	1.02486e10	1.02828	0.514141	−	0.857706i	$-0.328111\pi$
$719$	1.02486e10	1.02828	0.514141	+	0.857706i	$0.328111\pi$
$720$	6.75493e7	0.00674461
$721$	−1.48654e10	−1.47708
$722$	1.08842e10	1.07626
$723$	−1.03735e10	−1.02081
$724$	1.54903e9	0.151697
$725$	1.32455e10	1.29088
$726$	−1.33266e10	−1.29253
$727$	−1.03249e10	−0.996588	−0.498294	−	0.867008i	$-0.666040\pi$
$727$	−1.03249e10	−0.996588	−0.498294	+	0.867008i	$0.666040\pi$
$728$	8.52879e9	0.819271
$729$	9.21291e9	0.880746
$730$	−4.40178e8	−0.0418792
$731$	1.42941e9	0.135347
$732$	2.16082e9	0.203625
$733$	2.40256e9	0.225326	0.112663	−	0.993633i	$-0.464062\pi$
$733$	2.40256e9	0.225326	0.112663	+	0.993633i	$0.464062\pi$
$734$	1.35773e10	1.26729
$735$	2.58104e8	0.0239767
$736$	−3.90499e9	−0.361033
$737$	1.74487e10	1.60556
$738$	5.70937e8	0.0522866
$739$	−3.15560e9	−0.287625	−0.143813	−	0.989605i	$-0.545936\pi$
$739$	−3.15560e9	−0.287625	−0.143813	+	0.989605i	$0.545936\pi$
$740$	−2.22721e7	−0.00202046
$741$	2.13773e9	0.193014
$742$	2.95923e9	0.265928
$743$	−1.35961e10	−1.21606	−0.608029	−	0.793915i	$-0.708040\pi$
$743$	−1.35961e10	−1.21606	−0.608029	+	0.793915i	$0.708040\pi$
$744$	1.85797e10	1.65399
$745$	−9.96722e8	−0.0883135
$746$	2.10395e10	1.85545
$747$	1.60276e9	0.140684
$748$	−5.80781e9	−0.507408
$749$	6.46302e9	0.562016
$750$	−1.53648e9	−0.132988
$751$	−9.70560e9	−0.836147	−0.418074	−	0.908413i	$-0.637295\pi$
$751$	−9.70560e9	−0.836147	−0.418074	+	0.908413i	$0.637295\pi$
$752$	2.25312e9	0.193206
$753$	−1.25590e9	−0.107194
$754$	−2.04336e10	−1.73598
$755$	−7.77245e8	−0.0657270
$756$	1.85692e9	0.156303
$757$	−1.04503e10	−0.875579	−0.437789	−	0.899078i	$-0.644238\pi$
$757$	−1.04503e10	−0.875579	−0.437789	+	0.899078i	$0.644238\pi$
$758$	−3.90197e9	−0.325418
$759$	−1.58264e10	−1.31382
$760$	9.14321e7	0.00755529
$761$	6.33416e9	0.521006	0.260503	−	0.965473i	$-0.416112\pi$
$761$	6.33416e9	0.521006	0.260503	+	0.965473i	$0.416112\pi$
$762$	2.39763e9	0.196308
$763$	−1.45927e8	−0.0118932
$764$	−4.16108e9	−0.337582
$765$	1.16950e8	0.00944460
$766$	3.72555e9	0.299495
$767$	−1.36000e9	−0.108831
$768$	8.06546e9	0.642488
$769$	2.31138e10	1.83286	0.916428	−	0.400200i	$-0.131059\pi$
$769$	2.31138e10	1.83286	0.916428	+	0.400200i	$0.131059\pi$
$770$	−9.09638e8	−0.0718044
$771$	2.34237e10	1.84062
$772$	−2.64467e9	−0.206876
$773$	5.02538e9	0.391328	0.195664	−	0.980671i	$-0.437314\pi$
$773$	5.02538e9	0.391328	0.195664	+	0.980671i	$0.437314\pi$
$774$	1.17825e8	0.00913364
$775$	−2.35002e10	−1.81349
$776$	−1.59914e10	−1.22849
$777$	−1.75163e9	−0.133958
$778$	−3.70987e9	−0.282442
$779$	9.45384e8	0.0716518
$780$	2.07906e8	0.0156869
$781$	2.00989e10	1.50971
$782$	−2.07261e10	−1.54986
$783$	1.64204e10	1.22241
$784$	6.24738e9	0.463011
$785$	−1.13958e8	−0.00840817
$786$	1.46050e10	1.07281
$787$	1.06438e10	0.778367	0.389183	−	0.921160i	$-0.372757\pi$
$787$	1.06438e10	0.778367	0.389183	+	0.921160i	$0.372757\pi$
$788$	−1.72413e9	−0.125525
$789$	−1.53590e10	−1.11325
$790$	−5.55640e8	−0.0400958
$791$	2.12027e10	1.52326
$792$	1.76695e9	0.126383
$793$	−1.55619e10	−1.10817
$794$	−1.22756e10	−0.870306
$795$	−2.66251e8	−0.0187934
$796$	−4.24869e9	−0.298579
$797$	−7.50920e9	−0.525399	−0.262700	−	0.964878i	$-0.584613\pi$
$797$	−7.50920e9	−0.525399	−0.262700	+	0.964878i	$0.584613\pi$
$798$	−1.94826e9	−0.135718
$799$	3.90087e9	0.270550
$800$	−6.05558e9	−0.418158
$801$	−1.38134e9	−0.0949703
$802$	1.26010e10	0.862569
$803$	−1.40856e10	−0.960000
$804$	3.63460e9	0.246638
$805$	−5.70416e8	−0.0385395
$806$	3.62533e10	2.43880
$807$	−9.26376e9	−0.620483
$808$	6.35282e8	0.0423669
$809$	−1.04044e9	−0.0690869	−0.0345435	−	0.999403i	$-0.510998\pi$
$809$	−1.04044e9	−0.0690869	−0.0345435	+	0.999403i	$0.510998\pi$
$810$	−1.04702e9	−0.0692239
$811$	−2.99664e8	−0.0197270	−0.00986350	−	0.999951i	$-0.503140\pi$
$811$	−2.99664e8	−0.0197270	−0.00986350	+	0.999951i	$0.503140\pi$
$812$	3.27233e9	0.214492
$813$	−2.63442e9	−0.171937
$814$	−4.05593e9	−0.263575
$815$	−8.88866e8	−0.0575155
$816$	3.10858e10	2.00284
$817$	1.95100e8	0.0125164
$818$	3.13989e10	2.00575
$819$	1.48898e9	0.0947096
$820$	9.19439e7	0.00582337
$821$	−1.85821e10	−1.17191	−0.585955	−	0.810344i	$-0.699280\pi$
$821$	−1.85821e10	−1.17191	−0.585955	+	0.810344i	$0.699280\pi$
$822$	3.59812e9	0.225956
$823$	1.75756e10	1.09903	0.549515	−	0.835484i	$-0.314813\pi$
$823$	1.75756e10	1.09903	0.549515	+	0.835484i	$0.314813\pi$
$824$	2.64637e10	1.64781
$825$	−2.45425e10	−1.52171
$826$	1.23946e9	0.0765248
$827$	6.35013e9	0.390403	0.195202	−	0.980763i	$-0.437464\pi$
$827$	6.35013e9	0.390403	0.195202	+	0.980763i	$0.437464\pi$
$828$	−3.00203e8	−0.0183784
$829$	1.12188e10	0.683922	0.341961	−	0.939714i	$-0.388909\pi$
$829$	1.12188e10	0.683922	0.341961	+	0.939714i	$0.388909\pi$
$830$	1.46887e9	0.0891684
$831$	2.41152e9	0.145776
$832$	−1.42644e10	−0.858662
$833$	1.08162e10	0.648363
$834$	1.65189e10	0.986050
$835$	2.22193e8	0.0132077
$836$	−7.92707e8	−0.0469235
$837$	−2.91331e10	−1.71731
$838$	−2.44585e10	−1.43574
$839$	4.62067e9	0.270108	0.135054	−	0.990838i	$-0.456879\pi$
$839$	4.62067e9	0.270108	0.135054	+	0.990838i	$0.456879\pi$
$840$	6.99350e8	0.0407115
$841$	1.16867e10	0.677497
$842$	−3.64950e10	−2.10688
$843$	−9.18629e9	−0.528133
$844$	5.96061e9	0.341265
$845$	−4.86174e8	−0.0277200
$846$	3.21545e8	0.0182577
$847$	−1.53701e10	−0.869128
$848$	−6.44457e9	−0.362918
$849$	1.78044e9	0.0998504
$850$	−3.21405e10	−1.79509
$851$	−2.54339e9	−0.141468
$852$	4.18664e9	0.231914
$853$	−1.15504e10	−0.637198	−0.318599	−	0.947890i	$-0.603212\pi$
$853$	−1.15504e10	−0.637198	−0.318599	+	0.947890i	$0.603212\pi$
$854$	1.41826e10	0.779209
$855$	1.59624e7	0.000873408 0
$856$	−1.15056e10	−0.626975
$857$	−1.79416e10	−0.973707	−0.486854	−	0.873484i	$-0.661855\pi$
$857$	−1.79416e10	−0.973707	−0.486854	+	0.873484i	$0.661855\pi$
$858$	3.78613e10	2.04640
$859$	−2.00001e10	−1.07660	−0.538301	−	0.842752i	$-0.680934\pi$
$859$	−2.00001e10	−1.07660	−0.538301	+	0.842752i	$0.680934\pi$
$860$	1.89746e7	0.00101725
$861$	7.23110e9	0.386094
$862$	6.69691e9	0.356122
$863$	2.44732e10	1.29614	0.648071	−	0.761580i	$-0.275576\pi$
$863$	2.44732e10	1.29614	0.648071	+	0.761580i	$0.275576\pi$
$864$	−7.50707e9	−0.395979
$865$	−6.32427e8	−0.0332241
$866$	1.63201e10	0.853908
$867$	3.36917e10	1.75572
$868$	−5.80578e9	−0.301330
$869$	−1.77804e10	−0.919119
$870$	−1.67553e9	−0.0862650
$871$	−2.61758e10	−1.34226
$872$	2.59781e8	0.0132678
$873$	−2.79182e9	−0.142016
$874$	−2.82890e9	−0.143327
$875$	−1.77207e9	−0.0894238
$876$	−2.93406e9	−0.147470
$877$	9.08809e9	0.454961	0.227480	−	0.973783i	$-0.426951\pi$
$877$	9.08809e9	0.454961	0.227480	+	0.973783i	$0.426951\pi$
$878$	2.18524e10	1.08960
$879$	−3.95020e10	−1.96181
$880$	1.98100e9	0.0979930
$881$	1.97789e9	0.0974512	0.0487256	−	0.998812i	$-0.484484\pi$
$881$	1.97789e9	0.0974512	0.0487256	+	0.998812i	$0.484484\pi$
$882$	8.91569e8	0.0437537
$883$	3.59991e10	1.75966	0.879831	−	0.475287i	$-0.157656\pi$
$883$	3.59991e10	1.75966	0.879831	+	0.475287i	$0.157656\pi$
$884$	8.71261e9	0.424195
$885$	−1.11518e8	−0.00540809
$886$	4.46448e10	2.15652
$887$	1.75238e10	0.843132	0.421566	−	0.906798i	$-0.361481\pi$
$887$	1.75238e10	0.843132	0.421566	+	0.906798i	$0.361481\pi$
$888$	3.11829e9	0.149441
$889$	2.76527e9	0.132002
$890$	−1.26596e9	−0.0601940
$891$	−3.35043e10	−1.58682
$892$	−1.37875e8	−0.00650440
$893$	5.32429e8	0.0250197
$894$	−3.78090e10	−1.76976
$895$	−1.80517e9	−0.0841660
$896$	2.00180e10	0.929698
$897$	2.37421e10	1.09836
$898$	−2.78643e10	−1.28405
$899$	−5.13395e10	−2.35664
$900$	−4.65534e8	−0.0212864
$901$	−1.11576e10	−0.508201
$902$	1.67437e10	0.759677
$903$	1.49229e9	0.0674445
$904$	−3.77454e10	−1.69932
$905$	−9.14769e8	−0.0410243
$906$	−2.94835e10	−1.31714
$907$	−2.35715e10	−1.04897	−0.524484	−	0.851420i	$-0.675742\pi$
$907$	−2.35715e10	−1.04897	−0.524484	+	0.851420i	$0.675742\pi$
$908$	−6.72655e9	−0.298189
$909$	1.10909e8	0.00489771
$910$	1.36460e9	0.0600287
$911$	−4.39687e9	−0.192677	−0.0963383	−	0.995349i	$-0.530713\pi$
$911$	−4.39687e9	−0.192677	−0.0963383	+	0.995349i	$0.530713\pi$
$912$	4.24290e9	0.185217
$913$	4.70037e10	2.04401
$914$	−8.88560e9	−0.384924
$915$	−1.27605e9	−0.0550675
$916$	7.36972e9	0.316823
$917$	1.68445e10	0.721381
$918$	−3.98445e10	−1.69988
$919$	2.54432e10	1.08135	0.540677	−	0.841230i	$-0.318168\pi$
$919$	2.54432e10	1.08135	0.540677	+	0.841230i	$0.318168\pi$
$920$	1.01546e9	0.0429939
$921$	1.03968e10	0.438522
$922$	2.22148e10	0.933435
$923$	−3.01515e10	−1.26213
$924$	−6.06329e9	−0.252846
$925$	−3.94411e9	−0.163853
$926$	3.46229e10	1.43293
$927$	4.62010e9	0.190490
$928$	−1.32293e10	−0.543397
$929$	2.12448e10	0.869355	0.434678	−	0.900586i	$-0.356862\pi$
$929$	2.12448e10	0.869355	0.434678	+	0.900586i	$0.356862\pi$
$930$	2.97273e9	0.121190
$931$	1.47630e9	0.0599586
$932$	3.06346e9	0.123953
$933$	−4.86670e9	−0.196177
$934$	−1.11548e10	−0.447968
$935$	3.42975e9	0.137221
$936$	−2.65070e9	−0.105656
$937$	−1.60944e10	−0.639127	−0.319564	−	0.947565i	$-0.603536\pi$
$937$	−1.60944e10	−0.639127	−0.319564	+	0.947565i	$0.603536\pi$
$938$	2.38558e10	0.943809
$939$	−3.74823e10	−1.47739
$940$	5.17817e7	0.00203343
$941$	−1.18234e10	−0.462572	−0.231286	−	0.972886i	$-0.574293\pi$
$941$	−1.18234e10	−0.462572	−0.231286	+	0.972886i	$0.574293\pi$
$942$	−4.32282e9	−0.168496
$943$	1.04996e10	0.407740
$944$	−2.69928e9	−0.104435
$945$	−1.09659e9	−0.0422699
$946$	3.45542e9	0.132703
$947$	−3.70513e10	−1.41768	−0.708841	−	0.705368i	$-0.750782\pi$
$947$	−3.70513e10	−1.41768	−0.708841	+	0.705368i	$0.750782\pi$
$948$	−3.70368e9	−0.141190
$949$	2.11306e10	0.802564
$950$	−4.38685e9	−0.166005
$951$	−1.69881e10	−0.640492
$952$	2.93073e10	1.10090
$953$	4.10840e10	1.53761	0.768807	−	0.639481i	$-0.220851\pi$
$953$	4.10840e10	1.53761	0.768807	+	0.639481i	$0.220851\pi$
$954$	−9.19712e8	−0.0342951
$955$	2.45729e9	0.0912944
$956$	−6.31555e9	−0.233780
$957$	−5.36166e10	−1.97746
$958$	2.83106e10	1.04033
$959$	4.14984e9	0.151938
$960$	−1.16966e9	−0.0426689
$961$	6.35741e10	2.31072
$962$	6.08451e9	0.220350
$963$	−2.00867e9	−0.0724798
$964$	−5.77063e9	−0.207469
$965$	1.56178e9	0.0559468
$966$	−2.16378e10	−0.772312
$967$	1.77583e10	0.631553	0.315776	−	0.948834i	$-0.397735\pi$
$967$	1.77583e10	0.631553	0.315776	+	0.948834i	$0.397735\pi$
$968$	2.73621e10	0.969583
$969$	7.34583e9	0.259363
$970$	−2.55861e9	−0.0900124
$971$	−3.85376e10	−1.35088	−0.675442	−	0.737414i	$-0.736047\pi$
$971$	−3.85376e10	−1.35088	−0.675442	+	0.737414i	$0.736047\pi$
$972$	−1.21850e9	−0.0425591
$973$	1.90518e10	0.663042
$974$	1.01125e10	0.350674
$975$	3.68175e10	1.27215
$976$	−3.08868e10	−1.06340
$977$	−1.89012e10	−0.648423	−0.324211	−	0.945985i	$-0.605099\pi$
$977$	−1.89012e10	−0.648423	−0.324211	+	0.945985i	$0.605099\pi$
$978$	−3.37177e10	−1.15258
$979$	−4.05103e10	−1.37983
$980$	1.43579e8	0.00487303
$981$	4.53532e7	0.00153379
$982$	2.65645e10	0.895184
$983$	3.56952e9	0.119860	0.0599298	−	0.998203i	$-0.480912\pi$
$983$	3.56952e9	0.119860	0.0599298	+	0.998203i	$0.480912\pi$
$984$	−1.28729e10	−0.430720
$985$	1.01817e9	0.0339464
$986$	−7.02155e10	−2.33273
$987$	4.07247e9	0.134818
$988$	1.18918e9	0.0392282
$989$	2.16683e9	0.0712258
$990$	2.82711e8	0.00926017
$991$	−2.31794e10	−0.756562	−0.378281	−	0.925691i	$-0.623485\pi$
$991$	−2.31794e10	−0.756562	−0.378281	+	0.925691i	$0.623485\pi$
$992$	2.34714e10	0.763393
$993$	1.98015e10	0.641764
$994$	2.74791e10	0.887464
$995$	2.50902e9	0.0807466
$996$	9.79094e9	0.313991
$997$	−1.26842e10	−0.405351	−0.202676	−	0.979246i	$-0.564964\pi$
$997$	−1.26842e10	−0.405351	−0.202676	+	0.979246i	$0.564964\pi$
$998$	−1.13231e10	−0.360585
$999$	−4.88950e9	−0.155162

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.8.a.a.1.4	✓	10
3.2	odd	2		333.8.a.c.1.7		10
4.3	odd	2		592.8.a.f.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.8.a.a.1.4	✓	10	1.1	even	1	trivial
333.8.a.c.1.7		10	3.2	odd	2
592.8.a.f.1.3		10	4.3	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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	37.a (trivial)

\(f(q)\)	\(=\)	\(q-12.4614 q^{2} +49.0521 q^{3} +27.2868 q^{4} -16.1140 q^{5} -611.258 q^{6} -704.986 q^{7} +1255.03 q^{8} +219.106 q^{9} +O(q^{10})\)	\(q-12.4614 q^{2} +49.0521 q^{3} +27.2868 q^{4} -16.1140 q^{5} -611.258 q^{6} -704.986 q^{7} +1255.03 q^{8} +219.106 q^{9} +200.803 q^{10} +6425.66 q^{11} +1338.48 q^{12} -9639.47 q^{13} +8785.12 q^{14} -790.425 q^{15} -19132.1 q^{16} -33123.9 q^{17} -2730.37 q^{18} -4521.07 q^{19} -439.700 q^{20} -34581.0 q^{21} -80072.8 q^{22} -50212.0 q^{23} +61561.7 q^{24} -77865.3 q^{25} +120121. q^{26} -96529.3 q^{27} -19236.8 q^{28} -170108. q^{29} +9849.81 q^{30} +301806. q^{31} +77769.9 q^{32} +315192. q^{33} +412771. q^{34} +11360.1 q^{35} +5978.70 q^{36} +50653.0 q^{37} +56339.0 q^{38} -472836. q^{39} -20223.5 q^{40} -209106. q^{41} +430928. q^{42} -43153.5 q^{43} +175336. q^{44} -3530.67 q^{45} +625713. q^{46} -117766. q^{47} -938471. q^{48} -326538. q^{49} +970312. q^{50} -1.62480e6 q^{51} -263031. q^{52} +336845. q^{53} +1.20289e6 q^{54} -103543. q^{55} -884777. q^{56} -221768. q^{57} +2.11978e6 q^{58} +141086. q^{59} -21568.2 q^{60} +1.61439e6 q^{61} -3.76093e6 q^{62} -154466. q^{63} +1.47979e6 q^{64} +155330. q^{65} -3.92774e6 q^{66} +2.71548e6 q^{67} -903847. q^{68} -2.46300e6 q^{69} -141563. q^{70} +3.12792e6 q^{71} +274984. q^{72} -2.19209e6 q^{73} -631208. q^{74} -3.81946e6 q^{75} -123366. q^{76} -4.53000e6 q^{77} +5.89221e6 q^{78} -2.76709e6 q^{79} +308295. q^{80} -5.21415e6 q^{81} +2.60576e6 q^{82} +7.31499e6 q^{83} -943606. q^{84} +533759. q^{85} +537754. q^{86} -8.34413e6 q^{87} +8.06439e6 q^{88} -6.30446e6 q^{89} +43997.1 q^{90} +6.79569e6 q^{91} -1.37013e6 q^{92} +1.48042e7 q^{93} +1.46753e6 q^{94} +72852.6 q^{95} +3.81477e6 q^{96} -1.27419e7 q^{97} +4.06913e6 q^{98} +1.40790e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 24 q^{2} - 95 q^{3} + 602 q^{4} - 624 q^{5} - 777 q^{6} - 501 q^{7} - 3810 q^{8} + 6181 q^{9}+O(q^{10}) \) 10 * q - 24 * q^2 - 95 * q^3 + 602 * q^4 - 624 * q^5 - 777 * q^6 - 501 * q^7 - 3810 * q^8 + 6181 * q^9	\( 10 q - 24 q^{2} - 95 q^{3} + 602 q^{4} - 624 q^{5} - 777 q^{6} - 501 q^{7} - 3810 q^{8} + 6181 q^{9} + 8595 q^{10} - 8325 q^{11} - 19645 q^{12} - 17108 q^{13} - 65418 q^{14} - 55756 q^{15} - 56998 q^{16} - 72924 q^{17} - 156165 q^{18} - 47786 q^{19} - 226209 q^{20} - 65313 q^{21} - 138973 q^{22} - 148086 q^{23} - 68031 q^{24} + 108736 q^{25} - 60237 q^{26} - 87329 q^{27} + 219974 q^{28} - 164154 q^{29} + 78864 q^{30} - 189560 q^{31} - 30114 q^{32} - 179737 q^{33} + 532624 q^{34} - 705156 q^{35} + 1923693 q^{36} + 506530 q^{37} + 1256412 q^{38} + 1322800 q^{39} + 2936777 q^{40} + 814263 q^{41} + 3415826 q^{42} - 590572 q^{43} + 610311 q^{44} - 250574 q^{45} + 2903897 q^{46} - 1534185 q^{47} + 2082419 q^{48} - 214337 q^{49} - 2313525 q^{50} + 722138 q^{51} + 149159 q^{52} - 2518209 q^{53} + 1095990 q^{54} - 3482468 q^{55} - 3645834 q^{56} - 9225638 q^{57} + 5626023 q^{58} - 5894748 q^{59} - 1289832 q^{60} - 2569480 q^{61} - 863697 q^{62} - 2836574 q^{63} - 4093742 q^{64} - 6774600 q^{65} + 17251556 q^{66} - 6983232 q^{67} - 8114412 q^{68} - 11557564 q^{69} + 8982748 q^{70} - 5013963 q^{71} - 7567137 q^{72} - 11678449 q^{73} - 1215672 q^{74} - 6586901 q^{75} + 4912252 q^{76} + 1333113 q^{77} - 7352119 q^{78} - 3853378 q^{79} - 11975661 q^{80} - 7381718 q^{81} + 564093 q^{82} - 15677895 q^{83} + 4781738 q^{84} + 11909320 q^{85} + 34274010 q^{86} - 12611710 q^{87} + 14448317 q^{88} - 25836 q^{89} + 64591590 q^{90} + 12335744 q^{91} + 7579845 q^{92} + 4592632 q^{93} + 26251718 q^{94} + 11723664 q^{95} + 42299113 q^{96} + 4648834 q^{97} + 15230184 q^{98} - 16904018 q^{99}+O(q^{100}) \) 10 * q - 24 * q^2 - 95 * q^3 + 602 * q^4 - 624 * q^5 - 777 * q^6 - 501 * q^7 - 3810 * q^8 + 6181 * q^9 + 8595 * q^10 - 8325 * q^11 - 19645 * q^12 - 17108 * q^13 - 65418 * q^14 - 55756 * q^15 - 56998 * q^16 - 72924 * q^17 - 156165 * q^18 - 47786 * q^19 - 226209 * q^20 - 65313 * q^21 - 138973 * q^22 - 148086 * q^23 - 68031 * q^24 + 108736 * q^25 - 60237 * q^26 - 87329 * q^27 + 219974 * q^28 - 164154 * q^29 + 78864 * q^30 - 189560 * q^31 - 30114 * q^32 - 179737 * q^33 + 532624 * q^34 - 705156 * q^35 + 1923693 * q^36 + 506530 * q^37 + 1256412 * q^38 + 1322800 * q^39 + 2936777 * q^40 + 814263 * q^41 + 3415826 * q^42 - 590572 * q^43 + 610311 * q^44 - 250574 * q^45 + 2903897 * q^46 - 1534185 * q^47 + 2082419 * q^48 - 214337 * q^49 - 2313525 * q^50 + 722138 * q^51 + 149159 * q^52 - 2518209 * q^53 + 1095990 * q^54 - 3482468 * q^55 - 3645834 * q^56 - 9225638 * q^57 + 5626023 * q^58 - 5894748 * q^59 - 1289832 * q^60 - 2569480 * q^61 - 863697 * q^62 - 2836574 * q^63 - 4093742 * q^64 - 6774600 * q^65 + 17251556 * q^66 - 6983232 * q^67 - 8114412 * q^68 - 11557564 * q^69 + 8982748 * q^70 - 5013963 * q^71 - 7567137 * q^72 - 11678449 * q^73 - 1215672 * q^74 - 6586901 * q^75 + 4912252 * q^76 + 1333113 * q^77 - 7352119 * q^78 - 3853378 * q^79 - 11975661 * q^80 - 7381718 * q^81 + 564093 * q^82 - 15677895 * q^83 + 4781738 * q^84 + 11909320 * q^85 + 34274010 * q^86 - 12611710 * q^87 + 14448317 * q^88 - 25836 * q^89 + 64591590 * q^90 + 12335744 * q^91 + 7579845 * q^92 + 4592632 * q^93 + 26251718 * q^94 + 11723664 * q^95 + 42299113 * q^96 + 4648834 * q^97 + 15230184 * q^98 - 16904018 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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