LMFDB - Embedded newform 37.8.a.a.1.2

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			1.2
Root			$16.8983$ 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)

$f(q)$	$=$	$q-18.8983 q^{2} +75.2961 q^{3} +229.145 q^{4} -439.542 q^{5} -1422.97 q^{6} +380.249 q^{7} -1911.48 q^{8} +3482.50 q^{9} +O(q^{10})$	\(q-18.8983 q^{2} +75.2961 q^{3} +229.145 q^{4} -439.542 q^{5} -1422.97 q^{6} +380.249 q^{7} -1911.48 q^{8} +3482.50 q^{9} +8306.59 q^{10} -6423.60 q^{11} +17253.8 q^{12} +6848.72 q^{13} -7186.05 q^{14} -33095.8 q^{15} +6793.01 q^{16} +7862.62 q^{17} -65813.3 q^{18} -45716.7 q^{19} -100719. q^{20} +28631.2 q^{21} +121395. q^{22} -84113.5 q^{23} -143927. q^{24} +115072. q^{25} -129429. q^{26} +97546.1 q^{27} +87132.3 q^{28} -119332. q^{29} +625454. q^{30} -235484. q^{31} +116293. q^{32} -483672. q^{33} -148590. q^{34} -167135. q^{35} +797999. q^{36} +50653.0 q^{37} +863968. q^{38} +515682. q^{39} +840173. q^{40} -53726.9 q^{41} -541082. q^{42} -590637. q^{43} -1.47194e6 q^{44} -1.53070e6 q^{45} +1.58960e6 q^{46} -146884. q^{47} +511487. q^{48} -678954. q^{49} -2.17467e6 q^{50} +592024. q^{51} +1.56935e6 q^{52} +2.05564e6 q^{53} -1.84345e6 q^{54} +2.82344e6 q^{55} -726836. q^{56} -3.44229e6 q^{57} +2.25516e6 q^{58} +307062. q^{59} -7.58375e6 q^{60} +2.77124e6 q^{61} +4.45024e6 q^{62} +1.32422e6 q^{63} -3.06724e6 q^{64} -3.01030e6 q^{65} +9.14057e6 q^{66} +1.50678e6 q^{67} +1.80168e6 q^{68} -6.33342e6 q^{69} +3.15857e6 q^{70} -1.10072e6 q^{71} -6.65671e6 q^{72} +875893. q^{73} -957255. q^{74} +8.66448e6 q^{75} -1.04758e7 q^{76} -2.44257e6 q^{77} -9.74550e6 q^{78} +5050.86 q^{79} -2.98581e6 q^{80} -271389. q^{81} +1.01535e6 q^{82} -6.62463e6 q^{83} +6.56072e6 q^{84} -3.45595e6 q^{85} +1.11620e7 q^{86} -8.98521e6 q^{87} +1.22786e7 q^{88} +2.63830e6 q^{89} +2.89277e7 q^{90} +2.60422e6 q^{91} -1.92742e7 q^{92} -1.77310e7 q^{93} +2.77586e6 q^{94} +2.00944e7 q^{95} +8.75638e6 q^{96} +3.79133e6 q^{97} +1.28311e7 q^{98} -2.23702e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−18.8983	−1.67039	−0.835194	−	0.549955i	$-0.814645\pi$
$2$	−18.8983	−1.67039	−0.835194	+	0.549955i	$0.814645\pi$
$3$	75.2961	1.61008	0.805041	−	0.593219i	$-0.202143\pi$
$3$	75.2961	1.61008	0.805041	+	0.593219i	$0.202143\pi$
$4$	229.145	1.79020
$5$	−439.542	−1.57255	−0.786276	−	0.617875i	$-0.787994\pi$
$5$	−439.542	−1.57255	−0.786276	+	0.617875i	$0.787994\pi$
$6$	−1422.97	−2.68946
$7$	380.249	0.419010	0.209505	−	0.977808i	$-0.432815\pi$
$7$	380.249	0.419010	0.209505	+	0.977808i	$0.432815\pi$
$8$	−1911.48	−1.31994
$9$	3482.50	1.59236
$10$	8306.59	2.62677
$11$	−6423.60	−1.45514	−0.727569	−	0.686035i	$-0.759350\pi$
$11$	−6423.60	−1.45514	−0.727569	+	0.686035i	$0.759350\pi$
$12$	17253.8	2.88237
$13$	6848.72	0.864585	0.432292	−	0.901733i	$-0.357705\pi$
$13$	6848.72	0.864585	0.432292	+	0.901733i	$0.357705\pi$
$14$	−7186.05	−0.699910
$15$	−33095.8	−2.53194
$16$	6793.01	0.414612
$17$	7862.62	0.388147	0.194073	−	0.980987i	$-0.437830\pi$
$17$	7862.62	0.388147	0.194073	+	0.980987i	$0.437830\pi$
$18$	−65813.3	−2.65987
$19$	−45716.7	−1.52911	−0.764553	−	0.644561i	$-0.777040\pi$
$19$	−45716.7	−1.52911	−0.764553	+	0.644561i	$0.777040\pi$
$20$	−100719.	−2.81518
$21$	28631.2	0.674641
$22$	121395.	2.43065
$23$	−84113.5	−1.44151	−0.720756	−	0.693189i	$-0.756205\pi$
$23$	−84113.5	−1.44151	−0.720756	+	0.693189i	$0.756205\pi$
$24$	−143927.	−2.12521
$25$	115072.	1.47292
$26$	−129429.	−1.44419
$27$	97546.1	0.953755
$28$	87132.3	0.750112
$29$	−119332.	−0.908579	−0.454290	−	0.890854i	$-0.650107\pi$
$29$	−119332.	−0.908579	−0.454290	+	0.890854i	$0.650107\pi$
$30$	625454.	4.22932
$31$	−235484.	−1.41969	−0.709847	−	0.704356i	$-0.751236\pi$
$31$	−235484.	−1.41969	−0.709847	+	0.704356i	$0.751236\pi$
$32$	116293.	0.627375
$33$	−483672.	−2.34289
$34$	−148590.	−0.648356
$35$	−167135.	−0.658916
$36$	797999.	2.85065
$37$	50653.0	0.164399
$37$	50653.0	0.164399
$38$	863968.	2.55420
$39$	515682.	1.39205
$40$	840173.	2.07567
$41$	−53726.9	−0.121744	−0.0608721	−	0.998146i	$-0.519388\pi$
$41$	−53726.9	−0.121744	−0.0608721	+	0.998146i	$0.519388\pi$
$42$	−541082.	−1.12691
$43$	−590637.	−1.13287	−0.566436	−	0.824106i	$-0.691678\pi$
$43$	−590637.	−1.13287	−0.566436	+	0.824106i	$0.691678\pi$
$44$	−1.47194e6	−2.60499
$45$	−1.53070e6	−2.50408
$46$	1.58960e6	2.40789
$47$	−146884.	−0.206363	−0.103182	−	0.994663i	$-0.532902\pi$
$47$	−146884.	−0.206363	−0.103182	+	0.994663i	$0.532902\pi$
$48$	511487.	0.667560
$49$	−678954.	−0.824430
$50$	−2.17467e6	−2.46035
$51$	592024.	0.624948
$52$	1.56935e6	1.54778
$53$	2.05564e6	1.89662	0.948311	−	0.317341i	$-0.102790\pi$
$53$	2.05564e6	1.89662	0.948311	+	0.317341i	$0.102790\pi$
$54$	−1.84345e6	−1.59314
$55$	2.82344e6	2.28828
$56$	−726836.	−0.553068
$57$	−3.44229e6	−2.46199
$58$	2.25516e6	1.51768
$59$	307062.	0.194645	0.0973226	−	0.995253i	$-0.468972\pi$
$59$	307062.	0.194645	0.0973226	+	0.995253i	$0.468972\pi$
$60$	−7.58375e6	−4.53267
$61$	2.77124e6	1.56322	0.781608	−	0.623770i	$-0.214400\pi$
$61$	2.77124e6	1.56322	0.781608	+	0.623770i	$0.214400\pi$
$62$	4.45024e6	2.37144
$63$	1.32422e6	0.667217
$64$	−3.06724e6	−1.46257
$65$	−3.01030e6	−1.35961
$66$	9.14057e6	3.91354
$67$	1.50678e6	0.612051	0.306025	−	0.952023i	$-0.401001\pi$
$67$	1.50678e6	0.612051	0.306025	+	0.952023i	$0.401001\pi$
$68$	1.80168e6	0.694860
$69$	−6.33342e6	−2.32095
$70$	3.15857e6	1.10065
$71$	−1.10072e6	−0.364982	−0.182491	−	0.983208i	$-0.558416\pi$
$71$	−1.10072e6	−0.364982	−0.182491	+	0.983208i	$0.558416\pi$
$72$	−6.65671e6	−2.10182
$73$	875893.	0.263525	0.131762	−	0.991281i	$-0.457936\pi$
$73$	875893.	0.263525	0.131762	+	0.991281i	$0.457936\pi$
$74$	−957255.	−0.274610
$75$	8.66448e6	2.37153
$76$	−1.04758e7	−2.73740
$77$	−2.44257e6	−0.609718
$78$	−9.74550e6	−2.32527
$79$	5050.86	0.00115258	0.000576289	−	1.00000i	$-0.499817\pi$
$79$	5050.86	0.00115258	0.000576289		1.00000i	$0.499817\pi$
$80$	−2.98581e6	−0.651999
$81$	−271389.	−0.0567406
$82$	1.01535e6	0.203360
$83$	−6.62463e6	−1.27171	−0.635855	−	0.771808i	$-0.719352\pi$
$83$	−6.62463e6	−1.27171	−0.635855	+	0.771808i	$0.719352\pi$
$84$	6.56072e6	1.20774
$85$	−3.45595e6	−0.610381
$86$	1.11620e7	1.89234
$87$	−8.98521e6	−1.46289
$88$	1.22786e7	1.92069
$89$	2.63830e6	0.396698	0.198349	−	0.980131i	$-0.436442\pi$
$89$	2.63830e6	0.396698	0.198349	+	0.980131i	$0.436442\pi$
$90$	2.89277e7	4.18278
$91$	2.60422e6	0.362270
$92$	−1.92742e7	−2.58059
$93$	−1.77310e7	−2.28582
$94$	2.77586e6	0.344707
$95$	2.00944e7	2.40460
$96$	8.75638e6	1.01013
$97$	3.79133e6	0.421784	0.210892	−	0.977509i	$-0.432363\pi$
$97$	3.79133e6	0.421784	0.210892	+	0.977509i	$0.432363\pi$
$98$	1.28311e7	1.37712
$99$	−2.23702e7	−2.31711
$100$	2.63682e7	2.63682
$101$	1.54544e7	1.49254	0.746270	−	0.665643i	$-0.231843\pi$
$101$	1.54544e7	1.49254	0.746270	+	0.665643i	$0.231843\pi$
$102$	−1.11882e7	−1.04391
$103$	7.09169e6	0.639469	0.319735	−	0.947507i	$-0.396406\pi$
$103$	7.09169e6	0.639469	0.319735	+	0.947507i	$0.396406\pi$
$104$	−1.30912e7	−1.14120
$105$	−1.25846e7	−1.06091
$106$	−3.88480e7	−3.16810
$107$	−8.82351e6	−0.696302	−0.348151	−	0.937438i	$-0.613190\pi$
$107$	−8.82351e6	−0.696302	−0.348151	+	0.937438i	$0.613190\pi$
$108$	2.23522e7	1.70741
$109$	−1.10760e7	−0.819202	−0.409601	−	0.912265i	$-0.634332\pi$
$109$	−1.10760e7	−0.819202	−0.409601	+	0.912265i	$0.634332\pi$
$110$	−5.33582e7	−3.82232
$111$	3.81397e6	0.264696
$112$	2.58303e6	0.173727
$113$	1.87589e7	1.22302	0.611508	−	0.791239i	$-0.290563\pi$
$113$	1.87589e7	1.22302	0.611508	+	0.791239i	$0.290563\pi$
$114$	6.50534e7	4.11247
$115$	3.69714e7	2.26685
$116$	−2.73443e7	−1.62654
$117$	2.38507e7	1.37673
$118$	−5.80294e6	−0.325133
$119$	2.98975e6	0.162637
$120$	6.32618e7	3.34200
$121$	2.17755e7	1.11743
$122$	−5.23716e7	−2.61118
$123$	−4.04543e6	−0.196018
$124$	−5.39600e7	−2.54153
$125$	−1.62398e7	−0.743696
$126$	−2.50254e7	−1.11451
$127$	1.60424e7	0.694954	0.347477	−	0.937688i	$-0.387038\pi$
$127$	1.60424e7	0.694954	0.347477	+	0.937688i	$0.387038\pi$
$128$	4.30801e7	1.81569
$129$	−4.44726e7	−1.82402
$130$	5.68895e7	2.27107
$131$	−4.60125e7	−1.78824	−0.894121	−	0.447825i	$-0.852199\pi$
$131$	−4.60125e7	−1.78824	−0.894121	+	0.447825i	$0.852199\pi$
$132$	−1.10831e8	−4.19424
$133$	−1.73837e7	−0.640711
$134$	−2.84755e7	−1.02236
$135$	−4.28756e7	−1.49983
$136$	−1.50292e7	−0.512330
$137$	3.81452e6	0.126741	0.0633707	−	0.997990i	$-0.479815\pi$
$137$	3.81452e6	0.126741	0.0633707	+	0.997990i	$0.479815\pi$
$138$	1.19691e8	3.87689
$139$	−3.47077e6	−0.109616	−0.0548080	−	0.998497i	$-0.517455\pi$
$139$	−3.47077e6	−0.109616	−0.0548080	+	0.998497i	$0.517455\pi$
$140$	−3.82983e7	−1.17959
$141$	−1.10598e7	−0.332262
$142$	2.08017e7	0.609662
$143$	−4.39934e7	−1.25809
$144$	2.36566e7	0.660213
$145$	5.24513e7	1.42879
$146$	−1.65529e7	−0.440188
$147$	−5.11226e7	−1.32740
$148$	1.16069e7	0.294307
$149$	1.87036e6	0.0463205	0.0231603	−	0.999732i	$-0.492627\pi$
$149$	1.87036e6	0.0463205	0.0231603	+	0.999732i	$0.492627\pi$
$150$	−1.63744e8	−3.96137
$151$	−1.09313e7	−0.258375	−0.129188	−	0.991620i	$-0.541237\pi$
$151$	−1.09313e7	−0.258375	−0.129188	+	0.991620i	$0.541237\pi$
$152$	8.73864e7	2.01833
$153$	2.73816e7	0.618071
$154$	4.61603e7	1.01847
$155$	1.03505e8	2.23254
$156$	1.18166e8	2.49205
$157$	−4.72126e7	−0.973665	−0.486832	−	0.873495i	$-0.661848\pi$
$157$	−4.72126e7	−0.973665	−0.486832	+	0.873495i	$0.661848\pi$
$158$	−95452.7	−0.00192525
$159$	1.54781e8	3.05372
$160$	−5.11155e7	−0.986581
$161$	−3.19841e7	−0.604009
$162$	5.12878e6	0.0947789
$163$	−3.34005e7	−0.604083	−0.302042	−	0.953295i	$-0.597668\pi$
$163$	−3.34005e7	−0.604083	−0.302042	+	0.953295i	$0.597668\pi$
$164$	−1.23113e7	−0.217946
$165$	2.12594e8	3.68432
$166$	1.25194e8	2.12425
$167$	3.10031e7	0.515108	0.257554	−	0.966264i	$-0.417084\pi$
$167$	3.10031e7	0.515108	0.257554	+	0.966264i	$0.417084\pi$
$168$	−5.47279e7	−0.890485
$169$	−1.58436e7	−0.252493
$170$	6.53115e7	1.01957
$171$	−1.59209e8	−2.43489
$172$	−1.35342e8	−2.02807
$173$	−9.38196e7	−1.37763	−0.688814	−	0.724938i	$-0.741868\pi$
$173$	−9.38196e7	−1.37763	−0.688814	+	0.724938i	$0.741868\pi$
$174$	1.69805e8	2.44359
$175$	4.37560e7	0.617170
$176$	−4.36355e7	−0.603318
$177$	2.31206e7	0.313395
$178$	−4.98594e7	−0.662639
$179$	−1.67015e7	−0.217655	−0.108828	−	0.994061i	$-0.534710\pi$
$179$	−1.67015e7	−0.217655	−0.108828	+	0.994061i	$0.534710\pi$
$180$	−3.50754e8	−4.48279
$181$	7.68067e7	0.962774	0.481387	−	0.876508i	$-0.340133\pi$
$181$	7.68067e7	0.962774	0.481387	+	0.876508i	$0.340133\pi$
$182$	−4.92153e7	−0.605132
$183$	2.08663e8	2.51691
$184$	1.60781e8	1.90271
$185$	−2.22641e7	−0.258526
$186$	3.35085e8	3.81821
$187$	−5.05063e7	−0.564807
$188$	−3.36579e7	−0.369432
$189$	3.70918e7	0.399633
$190$	−3.79750e8	−4.01662
$191$	3.02212e7	0.313830	0.156915	−	0.987612i	$-0.449845\pi$
$191$	3.02212e7	0.313830	0.156915	+	0.987612i	$0.449845\pi$
$192$	−2.30951e8	−2.35486
$193$	−2.35969e7	−0.236267	−0.118134	−	0.992998i	$-0.537691\pi$
$193$	−2.35969e7	−0.236267	−0.118134	+	0.992998i	$0.537691\pi$
$194$	−7.16496e7	−0.704543
$195$	−2.26664e8	−2.18908
$196$	−1.55579e8	−1.47589
$197$	−1.18554e8	−1.10481	−0.552403	−	0.833577i	$-0.686289\pi$
$197$	−1.18554e8	−1.10481	−0.552403	+	0.833577i	$0.686289\pi$
$198$	4.22758e8	3.87047
$199$	1.62388e8	1.46072	0.730360	−	0.683063i	$-0.239352\pi$
$199$	1.62388e8	1.46072	0.730360	+	0.683063i	$0.239352\pi$
$200$	−2.19957e8	−1.94417
$201$	1.13454e8	0.985452
$202$	−2.92061e8	−2.49312
$203$	−4.53757e7	−0.380704
$204$	1.35660e8	1.11878
$205$	2.36152e7	0.191449
$206$	−1.34021e8	−1.06816
$207$	−2.92925e8	−2.29541
$208$	4.65234e7	0.358467
$209$	2.93666e8	2.22506
$210$	2.37828e8	1.77213
$211$	−1.63231e8	−1.19623	−0.598113	−	0.801412i	$-0.704083\pi$
$211$	−1.63231e8	−1.19623	−0.598113	+	0.801412i	$0.704083\pi$
$212$	4.71040e8	3.39533
$213$	−8.28797e7	−0.587651
$214$	1.66749e8	1.16310
$215$	2.59609e8	1.78150
$216$	−1.86457e8	−1.25890
$217$	−8.95423e7	−0.594866
$218$	2.09318e8	1.36839
$219$	6.59513e7	0.424296
$220$	6.46979e8	4.09648
$221$	5.38489e7	0.335586
$222$	−7.20776e7	−0.442145
$223$	−3.17911e8	−1.91972	−0.959860	−	0.280480i	$-0.909506\pi$
$223$	−3.17911e8	−1.91972	−0.959860	+	0.280480i	$0.909506\pi$
$224$	4.42201e7	0.262877
$225$	4.00739e8	2.34543
$226$	−3.54510e8	−2.04291
$227$	1.01028e8	0.573259	0.286629	−	0.958042i	$-0.407465\pi$
$227$	1.01028e8	0.573259	0.286629	+	0.958042i	$0.407465\pi$
$228$	−7.88785e8	−4.40744
$229$	2.04620e8	1.12596	0.562981	−	0.826470i	$-0.309654\pi$
$229$	2.04620e8	1.12596	0.562981	+	0.826470i	$0.309654\pi$
$230$	−6.98697e8	−3.78653
$231$	−1.83916e8	−0.981696
$232$	2.28100e8	1.19927
$233$	8.79214e7	0.455354	0.227677	−	0.973737i	$-0.426887\pi$
$233$	8.79214e7	0.455354	0.227677	+	0.973737i	$0.426887\pi$
$234$	−4.50737e8	−2.29968
$235$	6.45618e7	0.324517
$236$	7.03618e7	0.348454
$237$	380310.	0.00185575
$238$	−5.65012e7	−0.271668
$239$	−4.10394e7	−0.194450	−0.0972251	−	0.995262i	$-0.530997\pi$
$239$	−4.10394e7	−0.194450	−0.0972251	+	0.995262i	$0.530997\pi$
$240$	−2.24820e8	−1.04977
$241$	−9.31831e7	−0.428822	−0.214411	−	0.976743i	$-0.568783\pi$
$241$	−9.31831e7	−0.428822	−0.214411	+	0.976743i	$0.568783\pi$
$242$	−4.11519e8	−1.86654
$243$	−2.33768e8	−1.04511
$244$	6.35016e8	2.79847
$245$	2.98429e8	1.29646
$246$	7.64516e7	0.327426
$247$	−3.13101e8	−1.32204
$248$	4.50121e8	1.87391
$249$	−4.98809e8	−2.04756
$250$	3.06904e8	1.24226
$251$	1.73589e8	0.692888	0.346444	−	0.938071i	$-0.387389\pi$
$251$	1.73589e8	0.692888	0.346444	+	0.938071i	$0.387389\pi$
$252$	3.03438e8	1.19445
$253$	5.40312e8	2.09760
$254$	−3.03174e8	−1.16084
$255$	−2.60219e8	−0.982764
$256$	−4.21534e8	−1.57033
$257$	3.71729e7	0.136603	0.0683015	−	0.997665i	$-0.478242\pi$
$257$	3.71729e7	0.136603	0.0683015	+	0.997665i	$0.478242\pi$
$258$	8.40456e8	3.04682
$259$	1.92607e7	0.0688849
$260$	−6.89796e8	−2.43396
$261$	−4.15573e8	−1.44679
$262$	8.69558e8	2.98706
$263$	−5.81220e7	−0.197013	−0.0985066	−	0.995136i	$-0.531407\pi$
$263$	−5.81220e7	−0.197013	−0.0985066	+	0.995136i	$0.531407\pi$
$264$	9.24527e8	3.09247
$265$	−9.03539e8	−2.98254
$266$	3.28523e8	1.07024
$267$	1.98654e8	0.638716
$268$	3.45271e8	1.09569
$269$	−2.19731e6	−0.00688271	−0.00344135	−	0.999994i	$-0.501095\pi$
$269$	−2.19731e6	−0.00688271	−0.00344135	+	0.999994i	$0.501095\pi$
$270$	8.10276e8	2.50530
$271$	4.08769e8	1.24763	0.623814	−	0.781573i	$-0.285582\pi$
$271$	4.08769e8	1.24763	0.623814	+	0.781573i	$0.285582\pi$
$272$	5.34108e7	0.160930
$273$	1.96087e8	0.583284
$274$	−7.20880e7	−0.211707
$275$	−7.39177e8	−2.14331
$276$	−1.45127e9	−4.15497
$277$	−4.36571e7	−0.123417	−0.0617086	−	0.998094i	$-0.519655\pi$
$277$	−4.36571e7	−0.123417	−0.0617086	+	0.998094i	$0.519655\pi$
$278$	6.55916e7	0.183101
$279$	−8.20072e8	−2.26067
$280$	3.19475e8	0.869729
$281$	2.03390e8	0.546837	0.273418	−	0.961895i	$-0.411846\pi$
$281$	2.03390e8	0.546837	0.273418	+	0.961895i	$0.411846\pi$
$282$	2.09012e8	0.555007
$283$	−7.25327e8	−1.90231	−0.951155	−	0.308714i	$-0.900101\pi$
$283$	−7.25327e8	−1.90231	−0.951155	+	0.308714i	$0.900101\pi$
$284$	−2.52224e8	−0.653391
$285$	1.51303e9	3.87160
$286$	8.31401e8	2.10150
$287$	−2.04296e7	−0.0510121
$288$	4.04989e8	0.999010
$289$	−3.48518e8	−0.849342
$290$	−9.91239e8	−2.38663
$291$	2.85472e8	0.679107
$292$	2.00707e8	0.471761
$293$	−2.30651e6	−0.00535695	−0.00267848	−	0.999996i	$-0.500853\pi$
$293$	−2.30651e6	−0.00535695	−0.00267848	+	0.999996i	$0.500853\pi$
$294$	9.66129e8	2.21727
$295$	−1.34967e8	−0.306090
$296$	−9.68220e7	−0.216997
$297$	−6.26597e8	−1.38784
$298$	−3.53466e7	−0.0773733
$299$	−5.76070e8	−1.24631
$300$	1.98542e9	4.24550
$301$	−2.24589e8	−0.474685
$302$	2.06582e8	0.431587
$303$	1.16365e9	2.40311
$304$	−3.10554e8	−0.633986
$305$	−1.21807e9	−2.45824
$306$	−5.17465e8	−1.03242
$307$	−5.82200e8	−1.14839	−0.574193	−	0.818720i	$-0.694684\pi$
$307$	−5.82200e8	−1.14839	−0.574193	+	0.818720i	$0.694684\pi$
$308$	−5.59703e8	−1.09152
$309$	5.33977e8	1.02960
$310$	−1.95607e9	−3.72922
$311$	5.89135e8	1.11059	0.555294	−	0.831654i	$-0.312606\pi$
$311$	5.89135e8	1.11059	0.555294	+	0.831654i	$0.312606\pi$
$312$	−9.85713e8	−1.83742
$313$	4.99421e8	0.920579	0.460290	−	0.887769i	$-0.347746\pi$
$313$	4.99421e8	0.920579	0.460290	+	0.887769i	$0.347746\pi$
$314$	8.92238e8	1.62640
$315$	−5.82049e8	−1.04923
$316$	1.15738e6	0.00206335
$317$	4.42985e8	0.781055	0.390528	−	0.920591i	$-0.372293\pi$
$317$	4.42985e8	0.781055	0.390528	+	0.920591i	$0.372293\pi$
$318$	−2.92510e9	−5.10090
$319$	7.66539e8	1.32211
$320$	1.34818e9	2.29997
$321$	−6.64375e8	−1.12110
$322$	6.04444e8	1.00893
$323$	−3.59453e8	−0.593517
$324$	−6.21875e7	−0.101577
$325$	7.88096e8	1.27347
$326$	6.31213e8	1.00905
$327$	−8.33981e8	−1.31898
$328$	1.02698e8	0.160695
$329$	−5.58526e7	−0.0864684
$330$	−4.01766e9	−6.15425
$331$	−3.93875e7	−0.0596981	−0.0298491	−	0.999554i	$-0.509503\pi$
$331$	−3.93875e7	−0.0596981	−0.0298491	+	0.999554i	$0.509503\pi$
$332$	−1.51800e9	−2.27661
$333$	1.76399e8	0.261783
$334$	−5.85906e8	−0.860430
$335$	−6.62292e8	−0.962482
$336$	1.94492e8	0.279714
$337$	−6.28279e8	−0.894227	−0.447114	−	0.894477i	$-0.647548\pi$
$337$	−6.28279e8	−0.894227	−0.447114	+	0.894477i	$0.647548\pi$
$338$	2.99416e8	0.421761
$339$	1.41247e9	1.96915
$340$	−7.91915e8	−1.09270
$341$	1.51265e9	2.06585
$342$	3.00877e9	4.06722
$343$	−5.71323e8	−0.764455
$344$	1.12899e9	1.49532
$345$	2.78380e9	3.64982
$346$	1.77303e9	2.30118
$347$	9.17755e8	1.17916	0.589581	−	0.807709i	$-0.299293\pi$
$347$	9.17755e8	1.17916	0.589581	+	0.807709i	$0.299293\pi$
$348$	−2.05892e9	−2.61886
$349$	−3.44578e8	−0.433909	−0.216954	−	0.976182i	$-0.569612\pi$
$349$	−3.44578e8	−0.433909	−0.216954	+	0.976182i	$0.569612\pi$
$350$	−8.26914e8	−1.03091
$351$	6.68066e8	0.824602
$352$	−7.47017e8	−0.912917
$353$	3.54713e8	0.429206	0.214603	−	0.976701i	$-0.431154\pi$
$353$	3.54713e8	0.429206	0.214603	+	0.976701i	$0.431154\pi$
$354$	−4.36939e8	−0.523491
$355$	4.83811e8	0.573954
$356$	6.04555e8	0.710167
$357$	2.25116e8	0.261860
$358$	3.15629e8	0.363569
$359$	6.24453e8	0.712310	0.356155	−	0.934427i	$-0.384088\pi$
$359$	6.24453e8	0.712310	0.356155	+	0.934427i	$0.384088\pi$
$360$	2.92590e9	3.30523
$361$	1.19615e9	1.33817
$362$	−1.45152e9	−1.60821
$363$	1.63961e9	1.79915
$364$	5.96744e8	0.648535
$365$	−3.84992e8	−0.414406
$366$	−3.94338e9	−4.20421
$367$	−3.47657e8	−0.367130	−0.183565	−	0.983008i	$-0.558764\pi$
$367$	−3.47657e8	−0.367130	−0.183565	+	0.983008i	$0.558764\pi$
$368$	−5.71384e8	−0.597669
$369$	−1.87104e8	−0.193861
$370$	4.20754e8	0.431839
$371$	7.81654e8	0.794705
$372$	−4.06297e9	−4.09208
$373$	−1.50299e9	−1.49960	−0.749800	−	0.661664i	$-0.769850\pi$
$373$	−1.50299e9	−1.49960	−0.749800	+	0.661664i	$0.769850\pi$
$374$	9.54483e8	0.943447
$375$	−1.22279e9	−1.19741
$376$	2.80766e8	0.272387
$377$	−8.17269e8	−0.785544
$378$	−7.00971e8	−0.667543
$379$	−1.17412e8	−0.110783	−0.0553916	−	0.998465i	$-0.517641\pi$
$379$	−1.17412e8	−0.110783	−0.0553916	+	0.998465i	$0.517641\pi$
$380$	4.60454e9	4.30471
$381$	1.20793e9	1.11893
$382$	−5.71129e8	−0.524218
$383$	4.89762e8	0.445440	0.222720	−	0.974882i	$-0.428506\pi$
$383$	4.89762e8	0.445440	0.222720	+	0.974882i	$0.428506\pi$
$384$	3.24376e9	2.92341
$385$	1.07361e9	0.958813
$386$	4.45940e8	0.394658
$387$	−2.05689e9	−1.80394
$388$	8.68765e8	0.755077
$389$	−1.12043e9	−0.965076	−0.482538	−	0.875875i	$-0.660285\pi$
$389$	−1.12043e9	−0.965076	−0.482538	+	0.875875i	$0.660285\pi$
$390$	4.28356e9	3.65661
$391$	−6.61352e8	−0.559518
$392$	1.29780e9	1.08820
$393$	−3.46456e9	−2.87922
$394$	2.24048e9	1.84546
$395$	−2.22007e6	−0.00181249
$396$	−5.12603e9	−4.14809
$397$	1.30106e9	1.04359	0.521796	−	0.853070i	$-0.325262\pi$
$397$	1.30106e9	1.04359	0.521796	+	0.853070i	$0.325262\pi$
$398$	−3.06885e9	−2.43997
$399$	−1.30893e9	−1.03160
$400$	7.81685e8	0.610692
$401$	5.00395e8	0.387532	0.193766	−	0.981048i	$-0.437930\pi$
$401$	5.00395e8	0.387532	0.193766	+	0.981048i	$0.437930\pi$
$402$	−2.14410e9	−1.64609
$403$	−1.61276e9	−1.22745
$404$	3.54129e9	2.67194
$405$	1.19287e8	0.0892276
$406$	8.57524e8	0.635924
$407$	−3.25375e8	−0.239223
$408$	−1.13164e9	−0.824893
$409$	−2.35192e9	−1.69977	−0.849885	−	0.526968i	$-0.823329\pi$
$409$	−2.35192e9	−1.69977	−0.849885	+	0.526968i	$0.823329\pi$
$410$	−4.46287e8	−0.319795
$411$	2.87219e8	0.204064
$412$	1.62503e9	1.14478
$413$	1.16760e8	0.0815584
$414$	5.53579e9	3.83423
$415$	2.91180e9	1.99983
$416$	7.96456e8	0.542419
$417$	−2.61335e8	−0.176491
$418$	−5.54979e9	−3.71672
$419$	−2.75330e8	−0.182854	−0.0914268	−	0.995812i	$-0.529143\pi$
$419$	−2.75330e8	−0.182854	−0.0914268	+	0.995812i	$0.529143\pi$
$420$	−2.88371e9	−1.89924
$421$	−1.36910e9	−0.894226	−0.447113	−	0.894477i	$-0.647548\pi$
$421$	−1.36910e9	−0.894226	−0.447113	+	0.894477i	$0.647548\pi$
$422$	3.08478e9	1.99816
$423$	−5.11525e8	−0.328606
$424$	−3.92930e9	−2.50343
$425$	9.04767e8	0.571710
$426$	1.56629e9	0.981606
$427$	1.05376e9	0.655004
$428$	−2.02187e9	−1.24652
$429$	−3.31253e9	−2.02563
$430$	−4.90618e9	−2.97580
$431$	2.06650e9	1.24327	0.621633	−	0.783308i	$-0.286469\pi$
$431$	2.06650e9	1.24327	0.621633	+	0.783308i	$0.286469\pi$
$432$	6.62631e8	0.395438
$433$	1.98684e9	1.17613	0.588065	−	0.808814i	$-0.299890\pi$
$433$	1.98684e9	1.17613	0.588065	+	0.808814i	$0.299890\pi$
$434$	1.69220e9	0.993658
$435$	3.94938e9	2.30047
$436$	−2.53802e9	−1.46653
$437$	3.84540e9	2.20423
$438$	−1.24637e9	−0.708740
$439$	−1.85817e9	−1.04823	−0.524117	−	0.851646i	$-0.675605\pi$
$439$	−1.85817e9	−1.04823	−0.524117	+	0.851646i	$0.675605\pi$
$440$	−5.39694e9	−3.02039
$441$	−2.36446e9	−1.31279
$442$	−1.01765e9	−0.560559
$443$	−9.85556e8	−0.538603	−0.269301	−	0.963056i	$-0.586793\pi$
$443$	−9.85556e8	−0.538603	−0.269301	+	0.963056i	$0.586793\pi$
$444$	8.73954e8	0.473858
$445$	−1.15964e9	−0.623828
$446$	6.00797e9	3.20668
$447$	1.40831e8	0.0745799
$448$	−1.16631e9	−0.612833
$449$	−1.56851e9	−0.817761	−0.408881	−	0.912588i	$-0.634081\pi$
$449$	−1.56851e9	−0.817761	−0.408881	+	0.912588i	$0.634081\pi$
$450$	−7.57327e9	−3.91778
$451$	3.45120e8	0.177155
$452$	4.29851e9	2.18944
$453$	−8.23081e8	−0.416006
$454$	−1.90925e9	−0.957565
$455$	−1.14466e9	−0.569689
$456$	6.57985e9	3.24967
$457$	−2.03948e9	−0.999569	−0.499784	−	0.866150i	$-0.666587\pi$
$457$	−2.03948e9	−0.999569	−0.499784	+	0.866150i	$0.666587\pi$
$458$	−3.86697e9	−1.88079
$459$	7.66968e8	0.370197
$460$	8.47183e9	4.05812
$461$	−1.38283e9	−0.657379	−0.328690	−	0.944438i	$-0.606607\pi$
$461$	−1.38283e9	−0.657379	−0.328690	+	0.944438i	$0.606607\pi$
$462$	3.47569e9	1.63981
$463$	3.33530e9	1.56171	0.780857	−	0.624710i	$-0.214783\pi$
$463$	3.33530e9	1.56171	0.780857	+	0.624710i	$0.214783\pi$
$464$	−8.10621e8	−0.376708
$465$	7.79351e9	3.59458
$466$	−1.66156e9	−0.760618
$467$	−2.60700e9	−1.18449	−0.592245	−	0.805758i	$-0.701758\pi$
$467$	−2.60700e9	−1.18449	−0.592245	+	0.805758i	$0.701758\pi$
$468$	5.46527e9	2.46463
$469$	5.72950e8	0.256456
$470$	−1.22011e9	−0.542070
$471$	−3.55493e9	−1.56768
$472$	−5.86941e8	−0.256920
$473$	3.79401e9	1.64848
$474$	−7.18721e6	−0.00309982
$475$	−5.26072e9	−2.25225
$476$	6.85088e8	0.291153
$477$	7.15876e9	3.02011
$478$	7.75574e8	0.324807
$479$	−3.53388e9	−1.46919	−0.734594	−	0.678507i	$-0.762627\pi$
$479$	−3.53388e9	−1.46919	−0.734594	+	0.678507i	$0.762627\pi$
$480$	−3.84880e9	−1.58848
$481$	3.46908e8	0.142137
$482$	1.76100e9	0.716300
$483$	−2.40827e9	−0.972503
$484$	4.98975e9	2.00041
$485$	−1.66645e9	−0.663278
$486$	4.41781e9	1.74574
$487$	4.04436e8	0.158671	0.0793357	−	0.996848i	$-0.474720\pi$
$487$	4.04436e8	0.158671	0.0793357	+	0.996848i	$0.474720\pi$
$488$	−5.29715e9	−2.06335
$489$	−2.51493e9	−0.972624
$490$	−5.63979e9	−2.16559
$491$	−3.98191e9	−1.51812	−0.759060	−	0.651020i	$-0.774341\pi$
$491$	−3.98191e9	−1.51812	−0.759060	+	0.651020i	$0.774341\pi$
$492$	−9.26991e8	−0.350911
$493$	−9.38259e8	−0.352662
$494$	5.91708e9	2.20832
$495$	9.83264e9	3.64378
$496$	−1.59964e9	−0.588622
$497$	−4.18547e8	−0.152931
$498$	9.42663e9	3.42022
$499$	2.31017e9	0.832325	0.416162	−	0.909290i	$-0.363375\pi$
$499$	2.31017e9	0.832325	0.416162	+	0.909290i	$0.363375\pi$
$500$	−3.72127e9	−1.33136
$501$	2.33441e9	0.829366
$502$	−3.28053e9	−1.15739
$503$	6.72502e8	0.235616	0.117808	−	0.993036i	$-0.462413\pi$
$503$	6.72502e8	0.235616	0.117808	+	0.993036i	$0.462413\pi$
$504$	−2.53121e9	−0.880685
$505$	−6.79284e9	−2.34710
$506$	−1.02110e10	−3.50381
$507$	−1.19296e9	−0.406534
$508$	3.67604e9	1.24411
$509$	6.95262e8	0.233688	0.116844	−	0.993150i	$-0.462722\pi$
$509$	6.95262e8	0.233688	0.116844	+	0.993150i	$0.462722\pi$
$510$	4.91770e9	1.64160
$511$	3.33057e8	0.110420
$512$	2.45201e9	0.807380
$513$	−4.45949e9	−1.45839
$514$	−7.02503e8	−0.228180
$515$	−3.11710e9	−1.00560
$516$	−1.01907e10	−3.26535
$517$	9.43526e8	0.300287
$518$	−3.63995e8	−0.115065
$519$	−7.06425e9	−2.21810
$520$	5.75411e9	1.79460
$521$	−3.58117e9	−1.10941	−0.554706	−	0.832046i	$-0.687169\pi$
$521$	−3.58117e9	−1.10941	−0.554706	+	0.832046i	$0.687169\pi$
$522$	7.85361e9	2.41670
$523$	3.51864e9	1.07552	0.537761	−	0.843097i	$-0.319270\pi$
$523$	3.51864e9	1.07552	0.537761	+	0.843097i	$0.319270\pi$
$524$	−1.05436e10	−3.20131
$525$	3.29466e9	0.993694
$526$	1.09841e9	0.329089
$527$	−1.85152e9	−0.551049
$528$	−3.28559e9	−0.971391
$529$	3.67026e9	1.07796
$530$	1.70753e10	4.98200
$531$	1.06934e9	0.309946
$532$	−3.98340e9	−1.14700
$533$	−3.67960e8	−0.105258
$534$	−3.75422e9	−1.06690
$535$	3.87830e9	1.09497
$536$	−2.88017e9	−0.807869
$537$	−1.25756e9	−0.350443
$538$	4.15255e7	0.0114968
$539$	4.36133e9	1.19966
$540$	−9.82475e9	−2.68499
$541$	4.69337e9	1.27437	0.637184	−	0.770712i	$-0.280099\pi$
$541$	4.69337e9	1.27437	0.637184	+	0.770712i	$0.280099\pi$
$542$	−7.72503e9	−2.08402
$543$	5.78324e9	1.55014
$544$	9.14364e8	0.243514
$545$	4.86837e9	1.28824
$546$	−3.70572e9	−0.974312
$547$	−1.79897e9	−0.469969	−0.234985	−	0.971999i	$-0.575504\pi$
$547$	−1.79897e9	−0.469969	−0.234985	+	0.971999i	$0.575504\pi$
$548$	8.74080e8	0.226892
$549$	9.65083e9	2.48921
$550$	1.39692e10	3.58015
$551$	5.45545e9	1.38931
$552$	1.21062e10	3.06352
$553$	1.92058e6	0.000482942 0
$554$	8.25045e8	0.206155
$555$	−1.67640e9	−0.416248
$556$	−7.95311e8	−0.196234
$557$	2.61614e9	0.641457	0.320729	−	0.947171i	$-0.396072\pi$
$557$	2.61614e9	0.641457	0.320729	+	0.947171i	$0.396072\pi$
$558$	1.54980e10	3.77620
$559$	−4.04510e9	−0.979464
$560$	−1.13535e9	−0.273195
$561$	−3.80293e9	−0.909385
$562$	−3.84373e9	−0.913430
$563$	1.78124e9	0.420671	0.210336	−	0.977629i	$-0.432544\pi$
$563$	1.78124e9	0.420671	0.210336	+	0.977629i	$0.432544\pi$
$564$	−2.53430e9	−0.594815
$565$	−8.24530e9	−1.92326
$566$	1.37074e10	3.17760
$567$	−1.03195e8	−0.0237749
$568$	2.10399e9	0.481754
$569$	−6.87913e9	−1.56546	−0.782728	−	0.622364i	$-0.786172\pi$
$569$	−6.87913e9	−1.56546	−0.782728	+	0.622364i	$0.786172\pi$
$570$	−2.85937e10	−6.46708
$571$	6.36024e8	0.142971	0.0714854	−	0.997442i	$-0.477226\pi$
$571$	6.36024e8	0.142971	0.0714854	+	0.997442i	$0.477226\pi$
$572$	−1.00809e10	−2.25223
$573$	2.27554e9	0.505292
$574$	3.86084e8	0.0852100
$575$	−9.67912e9	−2.12324
$576$	−1.06817e10	−2.32895
$577$	4.23162e8	0.0917047	0.0458523	−	0.998948i	$-0.485400\pi$
$577$	4.23162e8	0.0917047	0.0458523	+	0.998948i	$0.485400\pi$
$578$	6.58639e9	1.41873
$579$	−1.77675e9	−0.380410
$580$	1.20190e10	2.55782
$581$	−2.51901e9	−0.532860
$582$	−5.39493e9	−1.13437
$583$	−1.32046e10	−2.75985
$584$	−1.67425e9	−0.347836
$585$	−1.04834e10	−2.16499
$586$	4.35890e7	0.00894819
$587$	−6.97185e9	−1.42270	−0.711352	−	0.702836i	$-0.751917\pi$
$587$	−6.97185e9	−1.42270	−0.711352	+	0.702836i	$0.751917\pi$
$588$	−1.17145e10	−2.37631
$589$	1.07655e10	2.17086
$590$	2.55064e9	0.511289
$591$	−8.92668e9	−1.77883
$592$	3.44086e8	0.0681618
$593$	4.34879e9	0.856400	0.428200	−	0.903684i	$-0.359148\pi$
$593$	4.34879e9	0.856400	0.428200	+	0.903684i	$0.359148\pi$
$594$	1.18416e10	2.31824
$595$	−1.31412e9	−0.255756
$596$	4.28585e8	0.0829230
$597$	1.22271e10	2.35188
$598$	1.08867e10	2.08182
$599$	−6.49652e9	−1.23506	−0.617528	−	0.786549i	$-0.711866\pi$
$599$	−6.49652e9	−1.23506	−0.617528	+	0.786549i	$0.711866\pi$
$600$	−1.65619e10	−3.13027
$601$	−3.10778e9	−0.583969	−0.291984	−	0.956423i	$-0.594316\pi$
$601$	−3.10778e9	−0.583969	−0.291984	+	0.956423i	$0.594316\pi$
$602$	4.24435e9	0.792908
$603$	5.24735e9	0.974608
$604$	−2.50485e9	−0.462543
$605$	−9.57123e9	−1.75721
$606$	−2.19910e10	−4.01413
$607$	8.20401e9	1.48890	0.744451	−	0.667677i	$-0.232711\pi$
$607$	8.20401e9	1.48890	0.744451	+	0.667677i	$0.232711\pi$
$608$	−5.31652e9	−0.959323
$609$	−3.41661e9	−0.612965
$610$	2.30195e10	4.10622
$611$	−1.00597e9	−0.178419
$612$	6.27436e9	1.10647
$613$	7.80271e8	0.136815	0.0684075	−	0.997657i	$-0.478208\pi$
$613$	7.80271e8	0.136815	0.0684075	+	0.997657i	$0.478208\pi$
$614$	1.10026e10	1.91825
$615$	1.77813e9	0.308249
$616$	4.66891e9	0.804790
$617$	5.61544e9	0.962467	0.481233	−	0.876593i	$-0.340189\pi$
$617$	5.61544e9	0.962467	0.481233	+	0.876593i	$0.340189\pi$
$618$	−1.00912e10	−1.71983
$619$	3.76207e9	0.637544	0.318772	−	0.947831i	$-0.396730\pi$
$619$	3.76207e9	0.637544	0.318772	+	0.947831i	$0.396730\pi$
$620$	2.37177e10	3.99670
$621$	−8.20495e9	−1.37485
$622$	−1.11336e10	−1.85511
$623$	1.00321e9	0.166220
$624$	3.50303e9	0.577162
$625$	−1.85194e9	−0.303422
$626$	−9.43820e9	−1.53773
$627$	2.21119e10	3.58253
$628$	−1.08186e10	−1.74305
$629$	3.98265e8	0.0638109
$630$	1.09997e10	1.75263
$631$	1.17529e10	1.86226	0.931130	−	0.364686i	$-0.118824\pi$
$631$	1.17529e10	1.86226	0.931130	+	0.364686i	$0.118824\pi$
$632$	−9.65460e6	−0.00152133
$633$	−1.22906e10	−1.92602
$634$	−8.37166e9	−1.30467
$635$	−7.05130e9	−1.09285
$636$	3.54675e10	5.46676
$637$	−4.64996e9	−0.712790
$638$	−1.44863e10	−2.20843
$639$	−3.83325e9	−0.581185
$640$	−1.89355e10	−2.85527
$641$	−1.02244e10	−1.53333	−0.766663	−	0.642050i	$-0.778084\pi$
$641$	−1.02244e10	−1.53333	−0.766663	+	0.642050i	$0.778084\pi$
$642$	1.25556e10	1.87268
$643$	3.91110e9	0.580177	0.290088	−	0.957000i	$-0.406315\pi$
$643$	3.91110e9	0.580177	0.290088	+	0.957000i	$0.406315\pi$
$644$	−7.32900e9	−1.08130
$645$	1.95476e10	2.86836
$646$	6.79305e9	0.991405
$647$	−2.17392e8	−0.0315558	−0.0157779	−	0.999876i	$-0.505022\pi$
$647$	−2.17392e8	−0.0315558	−0.0157779	+	0.999876i	$0.505022\pi$
$648$	5.18753e8	0.0748942
$649$	−1.97244e9	−0.283236
$650$	−1.48937e10	−2.12718
$651$	−6.74219e9	−0.957784
$652$	−7.65358e9	−1.08143
$653$	−8.14082e9	−1.14412	−0.572060	−	0.820212i	$-0.693856\pi$
$653$	−8.14082e9	−1.14412	−0.572060	+	0.820212i	$0.693856\pi$
$654$	1.57608e10	2.20321
$655$	2.02244e10	2.81211
$656$	−3.64967e8	−0.0504766
$657$	3.05030e9	0.419627
$658$	1.05552e9	0.144436
$659$	1.22173e10	1.66293	0.831467	−	0.555574i	$-0.187501\pi$
$659$	1.22173e10	1.66293	0.831467	+	0.555574i	$0.187501\pi$
$660$	4.87150e10	6.59566
$661$	−1.26260e10	−1.70044	−0.850218	−	0.526431i	$-0.823530\pi$
$661$	−1.26260e10	−1.70044	−0.850218	+	0.526431i	$0.823530\pi$
$662$	7.44357e8	0.0997191
$663$	4.05461e9	0.540321
$664$	1.26628e10	1.67858
$665$	7.64088e9	1.00755
$666$	−3.33364e9	−0.437279
$667$	1.00374e10	1.30973
$668$	7.10423e9	0.922145
$669$	−2.39374e10	−3.09091
$670$	1.25162e10	1.60772
$671$	−1.78013e10	−2.27470
$672$	3.32960e9	0.423253
$673$	−1.59341e9	−0.201499	−0.100750	−	0.994912i	$-0.532124\pi$
$673$	−1.59341e9	−0.201499	−0.100750	+	0.994912i	$0.532124\pi$
$674$	1.18734e10	1.49371
$675$	1.12248e10	1.40481
$676$	−3.63048e9	−0.452012
$677$	−7.67273e9	−0.950363	−0.475182	−	0.879888i	$-0.657618\pi$
$677$	−7.67273e9	−0.950363	−0.475182	+	0.879888i	$0.657618\pi$
$678$	−2.66932e10	−3.28925
$679$	1.44165e9	0.176732
$680$	6.60596e9	0.805666
$681$	7.60700e9	0.922993
$682$	−2.85865e10	−3.45077
$683$	−1.08087e9	−0.129808	−0.0649041	−	0.997892i	$-0.520674\pi$
$683$	−1.08087e9	−0.129808	−0.0649041	+	0.997892i	$0.520674\pi$
$684$	−3.64819e10	−4.35894
$685$	−1.67664e9	−0.199307
$686$	1.07970e10	1.27694
$687$	1.54071e10	1.81289
$688$	−4.01220e9	−0.469702
$689$	1.40785e10	1.63979
$690$	−5.26091e10	−6.09662
$691$	1.14058e10	1.31508	0.657539	−	0.753420i	$-0.271597\pi$
$691$	1.14058e10	1.31508	0.657539	+	0.753420i	$0.271597\pi$
$692$	−2.14983e10	−2.46623
$693$	−8.50624e9	−0.970893
$694$	−1.73440e10	−1.96966
$695$	1.52555e9	0.172377
$696$	1.71750e10	1.93092
$697$	−4.22434e8	−0.0472546
$698$	6.51193e9	0.724796
$699$	6.62014e9	0.733157
$700$	1.00265e10	1.10486
$701$	−8.08912e9	−0.886928	−0.443464	−	0.896292i	$-0.646251\pi$
$701$	−8.08912e9	−0.886928	−0.443464	+	0.896292i	$0.646251\pi$
$702$	−1.26253e10	−1.37741
$703$	−2.31569e9	−0.251383
$704$	1.97027e10	2.12824
$705$	4.86125e9	0.522500
$706$	−6.70347e9	−0.716941
$707$	5.87650e9	0.625390
$708$	5.29797e9	0.561039
$709$	−8.49976e9	−0.895663	−0.447832	−	0.894118i	$-0.647804\pi$
$709$	−8.49976e9	−0.895663	−0.447832	+	0.894118i	$0.647804\pi$
$710$	−9.14321e9	−0.958726
$711$	1.75896e7	0.00183533
$712$	−5.04305e9	−0.523617
$713$	1.98073e10	2.04651
$714$	−4.25432e9	−0.437407
$715$	1.93370e10	1.97841
$716$	−3.82707e9	−0.389646
$717$	−3.09011e9	−0.313081
$718$	−1.18011e10	−1.18983
$719$	−4.11103e9	−0.412477	−0.206238	−	0.978502i	$-0.566122\pi$
$719$	−4.11103e9	−0.412477	−0.206238	+	0.978502i	$0.566122\pi$
$720$	−1.03981e10	−1.03822
$721$	2.69661e9	0.267944
$722$	−2.26052e10	−2.23526
$723$	−7.01632e9	−0.690439
$724$	1.75999e10	1.72356
$725$	−1.37317e10	−1.33827
$726$	−3.09858e10	−3.00528
$727$	2.03895e10	1.96805	0.984023	−	0.178043i	$-0.0569767\pi$
$727$	2.03895e10	1.96805	0.984023	+	0.178043i	$0.0569767\pi$
$728$	−4.97790e9	−0.478174
$729$	−1.70083e10	−1.62598
$730$	7.27569e9	0.692220
$731$	−4.64395e9	−0.439720
$732$	4.78142e10	4.50576
$733$	−4.67011e9	−0.437989	−0.218995	−	0.975726i	$-0.570278\pi$
$733$	−4.67011e9	−0.437989	−0.218995	+	0.975726i	$0.570278\pi$
$734$	6.57013e9	0.613250
$735$	2.24705e10	2.08741
$736$	−9.78178e9	−0.904369
$737$	−9.67894e9	−0.890618
$738$	3.53594e9	0.323823
$739$	−5.72617e9	−0.521925	−0.260963	−	0.965349i	$-0.584040\pi$
$739$	−5.72617e9	−0.521925	−0.260963	+	0.965349i	$0.584040\pi$
$740$	−5.10172e9	−0.462813
$741$	−2.35753e10	−2.12860
$742$	−1.47719e10	−1.32747
$743$	8.98539e9	0.803667	0.401833	−	0.915713i	$-0.368373\pi$
$743$	8.98539e9	0.803667	0.401833	+	0.915713i	$0.368373\pi$
$744$	3.38923e10	3.01715
$745$	−8.22102e8	−0.0728415
$746$	2.84040e10	2.50492
$747$	−2.30703e10	−2.02503
$748$	−1.15733e10	−1.01112
$749$	−3.35513e9	−0.291758
$750$	2.31087e10	2.00014
$751$	−1.31553e10	−1.13334	−0.566670	−	0.823945i	$-0.691769\pi$
$751$	−1.31553e10	−1.13334	−0.566670	+	0.823945i	$0.691769\pi$
$752$	−9.97786e8	−0.0855608
$753$	1.30705e10	1.11561
$754$	1.54450e10	1.31216
$755$	4.80475e9	0.406309
$756$	8.49941e9	0.715423
$757$	−2.14388e8	−0.0179624	−0.00898120	−	0.999960i	$-0.502859\pi$
$757$	−2.14388e8	−0.0179624	−0.00898120	+	0.999960i	$0.502859\pi$
$758$	2.21888e9	0.185051
$759$	4.06833e10	3.37731
$760$	−3.84100e10	−3.17392
$761$	5.73708e9	0.471894	0.235947	−	0.971766i	$-0.424181\pi$
$761$	5.73708e9	0.471894	0.235947	+	0.971766i	$0.424181\pi$
$762$	−2.28278e10	−1.86905
$763$	−4.21164e9	−0.343254
$764$	6.92504e9	0.561818
$765$	−1.20353e10	−0.971949
$766$	−9.25566e9	−0.744058
$767$	2.10298e9	0.168287
$768$	−3.17398e10	−2.52837
$769$	7.34224e9	0.582219	0.291109	−	0.956690i	$-0.405976\pi$
$769$	7.34224e9	0.582219	0.291109	+	0.956690i	$0.405976\pi$
$770$	−2.02894e10	−1.60159
$771$	2.79897e9	0.219942
$772$	−5.40711e9	−0.422966
$773$	2.01302e10	1.56754	0.783771	−	0.621049i	$-0.213293\pi$
$773$	2.01302e10	1.56754	0.783771	+	0.621049i	$0.213293\pi$
$774$	3.88717e10	3.01329
$775$	−2.70976e10	−2.09110
$776$	−7.24703e9	−0.556729
$777$	1.45026e9	0.110910
$778$	2.11742e10	1.61205
$779$	2.45622e9	0.186160
$780$	−5.19390e10	−3.91888
$781$	7.07057e9	0.531099
$782$	1.24984e10	0.934613
$783$	−1.16403e10	−0.866562
$784$	−4.61214e9	−0.341819
$785$	2.07519e10	1.53114
$786$	6.54743e10	4.80941
$787$	−2.49923e10	−1.82766	−0.913830	−	0.406097i	$-0.866890\pi$
$787$	−2.49923e10	−1.82766	−0.913830	+	0.406097i	$0.866890\pi$
$788$	−2.71662e10	−1.97782
$789$	−4.37636e9	−0.317208
$790$	4.19554e7	0.00302757
$791$	7.13303e9	0.512456
$792$	4.27601e10	3.05844
$793$	1.89794e10	1.35153
$794$	−2.45878e10	−1.74320
$795$	−6.80329e10	−4.80213
$796$	3.72104e10	2.61498
$797$	−1.06278e10	−0.743598	−0.371799	−	0.928313i	$-0.621259\pi$
$797$	−1.06278e10	−0.743598	−0.371799	+	0.928313i	$0.621259\pi$
$798$	2.47365e10	1.72317
$799$	−1.15489e9	−0.0800993
$800$	1.33820e10	0.924075
$801$	9.18789e9	0.631687
$802$	−9.45661e9	−0.647329
$803$	−5.62639e9	−0.383465
$804$	2.59976e10	1.76415
$805$	1.40583e10	0.949835
$806$	3.04784e10	2.05031
$807$	−1.65449e8	−0.0110817
$808$	−2.95406e10	−1.97006
$809$	1.19850e10	0.795824	0.397912	−	0.917424i	$-0.369735\pi$
$809$	1.19850e10	0.795824	0.397912	+	0.917424i	$0.369735\pi$
$810$	−2.25431e9	−0.149045
$811$	1.18991e10	0.783323	0.391661	−	0.920109i	$-0.371900\pi$
$811$	1.18991e10	0.783323	0.391661	+	0.920109i	$0.371900\pi$
$812$	−1.03976e10	−0.681536
$813$	3.07787e10	2.00878
$814$	6.14902e9	0.399596
$815$	1.46809e10	0.949953
$816$	4.02162e9	0.259111
$817$	2.70020e10	1.73228
$818$	4.44472e10	2.83928
$819$	9.06919e9	0.576866
$820$	5.41132e9	0.342732
$821$	−2.27166e10	−1.43265	−0.716327	−	0.697765i	$-0.754178\pi$
$821$	−2.27166e10	−1.43265	−0.716327	+	0.697765i	$0.754178\pi$
$822$	−5.42794e9	−0.340866
$823$	3.20813e9	0.200610	0.100305	−	0.994957i	$-0.468018\pi$
$823$	3.20813e9	0.200610	0.100305	+	0.994957i	$0.468018\pi$
$824$	−1.35556e10	−0.844060
$825$	−5.56571e10	−3.45090
$826$	−2.20656e9	−0.136234
$827$	−2.68744e10	−1.65223	−0.826114	−	0.563503i	$-0.809453\pi$
$827$	−2.68744e10	−1.65223	−0.826114	+	0.563503i	$0.809453\pi$
$828$	−6.71225e10	−4.10924
$829$	−2.73199e8	−0.0166548	−0.00832738	−	0.999965i	$-0.502651\pi$
$829$	−2.73199e8	−0.0166548	−0.00832738	+	0.999965i	$0.502651\pi$
$830$	−5.50281e10	−3.34050
$831$	−3.28721e9	−0.198712
$832$	−2.10066e10	−1.26452
$833$	−5.33835e9	−0.320000
$834$	4.93879e9	0.294808
$835$	−1.36272e10	−0.810034
$836$	6.72922e10	3.98330
$837$	−2.29705e10	−1.35404
$838$	5.20326e9	0.305437
$839$	−8.41026e9	−0.491635	−0.245817	−	0.969316i	$-0.579056\pi$
$839$	−8.41026e9	−0.491635	−0.245817	+	0.969316i	$0.579056\pi$
$840$	2.40552e10	1.40033
$841$	−3.00983e9	−0.174484
$842$	2.58736e10	1.49371
$843$	1.53145e10	0.880452
$844$	−3.74036e10	−2.14148
$845$	6.96391e9	0.397058
$846$	9.66694e9	0.548899
$847$	8.28010e9	0.468213
$848$	1.39640e10	0.786363
$849$	−5.46143e10	−3.06287
$850$	−1.70986e10	−0.954978
$851$	−4.26060e9	−0.236983
$852$	−1.89915e10	−1.05201
$853$	−4.35536e9	−0.240271	−0.120136	−	0.992757i	$-0.538333\pi$
$853$	−4.35536e9	−0.240271	−0.120136	+	0.992757i	$0.538333\pi$
$854$	−1.99142e10	−1.09411
$855$	6.99788e10	3.82900
$856$	1.68659e10	0.919077
$857$	3.21686e10	1.74582	0.872909	−	0.487883i	$-0.162231\pi$
$857$	3.21686e10	1.74582	0.872909	+	0.487883i	$0.162231\pi$
$858$	6.26012e10	3.38359
$859$	−3.29618e10	−1.77433	−0.887165	−	0.461452i	$-0.847329\pi$
$859$	−3.29618e10	−1.77433	−0.887165	+	0.461452i	$0.847329\pi$
$860$	5.94883e10	3.18924
$861$	−1.53827e9	−0.0821336
$862$	−3.90533e10	−2.07674
$863$	−1.98592e10	−1.05178	−0.525890	−	0.850553i	$-0.676268\pi$
$863$	−1.98592e10	−1.05178	−0.525890	+	0.850553i	$0.676268\pi$
$864$	1.13439e10	0.598362
$865$	4.12376e10	2.16639
$866$	−3.75479e10	−1.96459
$867$	−2.62420e10	−1.36751
$868$	−2.05182e10	−1.06493
$869$	−3.24447e7	−0.00167716
$870$	−7.46364e10	−3.84267
$871$	1.03195e10	0.529170
$872$	2.11715e10	1.08130
$873$	1.32033e10	0.671634
$874$	−7.26714e10	−3.68191
$875$	−6.17516e9	−0.311616
$876$	1.51124e10	0.759574
$877$	1.60613e9	0.0804047	0.0402023	−	0.999192i	$-0.487200\pi$
$877$	1.60613e9	0.0804047	0.0402023	+	0.999192i	$0.487200\pi$
$878$	3.51161e10	1.75096
$879$	−1.73671e8	−0.00862513
$880$	1.91797e10	0.948749
$881$	1.93364e10	0.952707	0.476354	−	0.879254i	$-0.341958\pi$
$881$	1.93364e10	0.952707	0.476354	+	0.879254i	$0.341958\pi$
$882$	4.46842e10	2.19288
$883$	−5.89448e9	−0.288127	−0.144063	−	0.989568i	$-0.546017\pi$
$883$	−5.89448e9	−0.288127	−0.144063	+	0.989568i	$0.546017\pi$
$884$	1.23392e10	0.600765
$885$	−1.01625e10	−0.492830
$886$	1.86253e10	0.899676
$887$	−2.37041e10	−1.14049	−0.570243	−	0.821476i	$-0.693151\pi$
$887$	−2.37041e10	−1.14049	−0.570243	+	0.821476i	$0.693151\pi$
$888$	−7.29031e9	−0.349382
$889$	6.10010e9	0.291193
$890$	2.19153e10	1.04204
$891$	1.74329e9	0.0825654
$892$	−7.28477e10	−3.43668
$893$	6.71507e9	0.315552
$894$	−2.66146e9	−0.124577
$895$	7.34100e9	0.342275
$896$	1.63811e10	0.760793
$897$	−4.33758e10	−2.00666
$898$	2.96423e10	1.36598
$899$	2.81006e10	1.28990
$900$	9.18274e10	4.19878
$901$	1.61627e10	0.736168
$902$	−6.52218e9	−0.295917
$903$	−1.69107e10	−0.764282
$904$	−3.58571e10	−1.61430
$905$	−3.37598e10	−1.51401
$906$	1.55548e10	0.694891
$907$	−3.77753e10	−1.68106	−0.840529	−	0.541767i	$-0.817755\pi$
$907$	−3.77753e10	−1.68106	−0.840529	+	0.541767i	$0.817755\pi$
$908$	2.31501e10	1.02625
$909$	5.38198e10	2.37667
$910$	2.16322e10	0.951602
$911$	−2.32737e10	−1.01988	−0.509942	−	0.860208i	$-0.670333\pi$
$911$	−2.32737e10	−1.01988	−0.509942	+	0.860208i	$0.670333\pi$
$912$	−2.33835e10	−1.02077
$913$	4.25540e10	1.85051
$914$	3.85427e10	1.66967
$915$	−9.17162e10	−3.95797
$916$	4.68877e10	2.01570
$917$	−1.74962e10	−0.749292
$918$	−1.44944e10	−0.618372
$919$	−1.30152e10	−0.553156	−0.276578	−	0.960991i	$-0.589200\pi$
$919$	−1.30152e10	−0.553156	−0.276578	+	0.960991i	$0.589200\pi$
$920$	−7.06699e10	−2.99211
$921$	−4.38374e10	−1.84900
$922$	2.61331e10	1.09808
$923$	−7.53851e9	−0.315558
$924$	−4.21434e10	−1.75743
$925$	5.82875e9	0.242147
$926$	−6.30315e10	−2.60867
$927$	2.46968e10	1.01827
$928$	−1.38774e10	−0.570020
$929$	−3.01149e10	−1.23233	−0.616165	−	0.787617i	$-0.711315\pi$
$929$	−3.01149e10	−1.23233	−0.616165	+	0.787617i	$0.711315\pi$
$930$	−1.47284e11	−6.00434
$931$	3.10396e10	1.26064
$932$	2.01468e10	0.815173
$933$	4.43595e10	1.78814
$934$	4.92678e10	1.97856
$935$	2.21996e10	0.888189
$936$	−4.55900e10	−1.81720
$937$	5.10220e9	0.202614	0.101307	−	0.994855i	$-0.467698\pi$
$937$	5.10220e9	0.202614	0.101307	+	0.994855i	$0.467698\pi$
$938$	−1.08278e10	−0.428381
$939$	3.76044e10	1.48221
$940$	1.47940e10	0.580951
$941$	−4.18861e9	−0.163873	−0.0819363	−	0.996638i	$-0.526110\pi$
$941$	−4.18861e9	−0.163873	−0.0819363	+	0.996638i	$0.526110\pi$
$942$	6.71820e10	2.61863
$943$	4.51916e9	0.175496
$944$	2.08587e9	0.0807023
$945$	−1.63034e10	−0.628444
$946$	−7.17004e10	−2.75361
$947$	−3.06742e9	−0.117368	−0.0586838	−	0.998277i	$-0.518690\pi$
$947$	−3.06742e9	−0.117368	−0.0586838	+	0.998277i	$0.518690\pi$
$948$	8.71463e7	0.00332215
$949$	5.99875e9	0.227839
$950$	9.94186e10	3.76214
$951$	3.33551e10	1.25756
$952$	−5.71483e9	−0.214671
$953$	−5.54778e9	−0.207632	−0.103816	−	0.994597i	$-0.533105\pi$
$953$	−5.54778e9	−0.207632	−0.103816	+	0.994597i	$0.533105\pi$
$954$	−1.35288e11	−5.04476
$955$	−1.32835e10	−0.493514
$956$	−9.40399e9	−0.348104
$957$	5.77174e10	2.12870
$958$	6.67843e10	2.45411
$959$	1.45047e9	0.0531059
$960$	1.01513e11	3.70314
$961$	2.79399e10	1.01553
$962$	−6.55597e9	−0.237424
$963$	−3.07279e10	−1.10877
$964$	−2.13525e10	−0.767677
$965$	1.03718e10	0.371543
$966$	4.55123e10	1.62446
$967$	−1.11999e10	−0.398310	−0.199155	−	0.979968i	$-0.563820\pi$
$967$	−1.11999e10	−0.398310	−0.199155	+	0.979968i	$0.563820\pi$
$968$	−4.16233e10	−1.47493
$969$	−2.70654e10	−0.955612
$970$	3.14930e10	1.10793
$971$	2.84651e10	0.997803	0.498902	−	0.866659i	$-0.333737\pi$
$971$	2.84651e10	0.997803	0.498902	+	0.866659i	$0.333737\pi$
$972$	−5.35668e10	−1.87096
$973$	−1.31976e9	−0.0459303
$974$	−7.64315e9	−0.265043
$975$	5.93406e10	2.05039
$976$	1.88250e10	0.648128
$977$	1.94143e10	0.666024	0.333012	−	0.942923i	$-0.391935\pi$
$977$	1.94143e10	0.666024	0.333012	+	0.942923i	$0.391935\pi$
$978$	4.75279e10	1.62466
$979$	−1.69474e10	−0.577250
$980$	6.83836e10	2.32092
$981$	−3.85722e10	−1.30447
$982$	7.52513e10	2.53585
$983$	−5.08502e10	−1.70748	−0.853740	−	0.520700i	$-0.825671\pi$
$983$	−5.08502e10	−1.70748	−0.853740	+	0.520700i	$0.825671\pi$
$984$	7.73273e9	0.258732
$985$	5.21096e10	1.73737
$986$	1.77315e10	0.589083
$987$	−4.20548e9	−0.139221
$988$	−7.17457e10	−2.36672
$989$	4.96805e10	1.63305
$990$	−1.85820e11	−6.08652
$991$	4.99002e10	1.62871	0.814356	−	0.580366i	$-0.197090\pi$
$991$	4.99002e10	1.62871	0.814356	+	0.580366i	$0.197090\pi$
$992$	−2.73850e10	−0.890681
$993$	−2.96573e9	−0.0961189
$994$	7.90981e9	0.255455
$995$	−7.13761e10	−2.29706
$996$	−1.14300e11	−3.66554
$997$	−2.66774e10	−0.852532	−0.426266	−	0.904598i	$-0.640171\pi$
$997$	−2.66774e10	−0.852532	−0.426266	+	0.904598i	$0.640171\pi$
$998$	−4.36583e10	−1.39031
$999$	4.94100e9	0.156796

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.8.a.a.1.2	✓	10
3.2	odd	2		333.8.a.c.1.9		10
4.3	odd	2		592.8.a.f.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.8.a.a.1.2	✓	10	1.1	even	1	trivial
333.8.a.c.1.9		10	3.2	odd	2
592.8.a.f.1.1		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)

\(f(q)\)	\(=\)	\(q-18.8983 q^{2} +75.2961 q^{3} +229.145 q^{4} -439.542 q^{5} -1422.97 q^{6} +380.249 q^{7} -1911.48 q^{8} +3482.50 q^{9} +O(q^{10})\)	\(q-18.8983 q^{2} +75.2961 q^{3} +229.145 q^{4} -439.542 q^{5} -1422.97 q^{6} +380.249 q^{7} -1911.48 q^{8} +3482.50 q^{9} +8306.59 q^{10} -6423.60 q^{11} +17253.8 q^{12} +6848.72 q^{13} -7186.05 q^{14} -33095.8 q^{15} +6793.01 q^{16} +7862.62 q^{17} -65813.3 q^{18} -45716.7 q^{19} -100719. q^{20} +28631.2 q^{21} +121395. q^{22} -84113.5 q^{23} -143927. q^{24} +115072. q^{25} -129429. q^{26} +97546.1 q^{27} +87132.3 q^{28} -119332. q^{29} +625454. q^{30} -235484. q^{31} +116293. q^{32} -483672. q^{33} -148590. q^{34} -167135. q^{35} +797999. q^{36} +50653.0 q^{37} +863968. q^{38} +515682. q^{39} +840173. q^{40} -53726.9 q^{41} -541082. q^{42} -590637. q^{43} -1.47194e6 q^{44} -1.53070e6 q^{45} +1.58960e6 q^{46} -146884. q^{47} +511487. q^{48} -678954. q^{49} -2.17467e6 q^{50} +592024. q^{51} +1.56935e6 q^{52} +2.05564e6 q^{53} -1.84345e6 q^{54} +2.82344e6 q^{55} -726836. q^{56} -3.44229e6 q^{57} +2.25516e6 q^{58} +307062. q^{59} -7.58375e6 q^{60} +2.77124e6 q^{61} +4.45024e6 q^{62} +1.32422e6 q^{63} -3.06724e6 q^{64} -3.01030e6 q^{65} +9.14057e6 q^{66} +1.50678e6 q^{67} +1.80168e6 q^{68} -6.33342e6 q^{69} +3.15857e6 q^{70} -1.10072e6 q^{71} -6.65671e6 q^{72} +875893. q^{73} -957255. q^{74} +8.66448e6 q^{75} -1.04758e7 q^{76} -2.44257e6 q^{77} -9.74550e6 q^{78} +5050.86 q^{79} -2.98581e6 q^{80} -271389. q^{81} +1.01535e6 q^{82} -6.62463e6 q^{83} +6.56072e6 q^{84} -3.45595e6 q^{85} +1.11620e7 q^{86} -8.98521e6 q^{87} +1.22786e7 q^{88} +2.63830e6 q^{89} +2.89277e7 q^{90} +2.60422e6 q^{91} -1.92742e7 q^{92} -1.77310e7 q^{93} +2.77586e6 q^{94} +2.00944e7 q^{95} +8.75638e6 q^{96} +3.79133e6 q^{97} +1.28311e7 q^{98} -2.23702e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 24 q^{2} - 95 q^{3} + 602 q^{4} - 624 q^{5} - 777 q^{6} - 501 q^{7} - 3810 q^{8} + 6181 q^{9}+O(q^{10}) \) 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

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