LMFDB - Embedded newform 43.8.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,8,Mod(1,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, 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("43.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	43.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:	$13.4325560958$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 3 x^{12} - 1279 x^{11} + 3765 x^{10} + 598742 x^{9} - 1518614 x^{8} - 124677082 x^{7} + \cdots + 1551032970660 $ x^13 - 3x^12 - 1279x^11 + 3765x^10 + 598742x^9 - 1518614x^8 - 124677082x^7 + 193428526x^6 + 11160446785x^5 + 1754605765x^4 - 349352939351x^3 - 481872751923x^2 + 2098464001560x + 1551032970660
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$16.3440$ of defining polynomial
Character	$\chi$	$=$	43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+17.3440 q^{2} +73.8355 q^{3} +172.814 q^{4} -122.945 q^{5} +1280.60 q^{6} +247.011 q^{7} +777.246 q^{8} +3264.69 q^{9} +O(q^{10})$	\(q+17.3440 q^{2} +73.8355 q^{3} +172.814 q^{4} -122.945 q^{5} +1280.60 q^{6} +247.011 q^{7} +777.246 q^{8} +3264.69 q^{9} -2132.35 q^{10} +2503.52 q^{11} +12759.8 q^{12} +1376.69 q^{13} +4284.15 q^{14} -9077.68 q^{15} -8639.60 q^{16} -32082.0 q^{17} +56622.6 q^{18} +10245.1 q^{19} -21246.5 q^{20} +18238.2 q^{21} +43421.0 q^{22} -21850.6 q^{23} +57388.4 q^{24} -63009.6 q^{25} +23877.3 q^{26} +79571.5 q^{27} +42686.8 q^{28} +173813. q^{29} -157443. q^{30} +16044.0 q^{31} -249333. q^{32} +184849. q^{33} -556429. q^{34} -30368.6 q^{35} +564182. q^{36} -75677.9 q^{37} +177691. q^{38} +101649. q^{39} -95558.2 q^{40} +452656. q^{41} +316323. q^{42} -79507.0 q^{43} +432643. q^{44} -401375. q^{45} -378977. q^{46} +113517. q^{47} -637910. q^{48} -762529. q^{49} -1.09284e6 q^{50} -2.36879e6 q^{51} +237911. q^{52} -1.42412e6 q^{53} +1.38009e6 q^{54} -307794. q^{55} +191988. q^{56} +756453. q^{57} +3.01460e6 q^{58} +1.48283e6 q^{59} -1.56875e6 q^{60} -2.69078e6 q^{61} +278267. q^{62} +806413. q^{63} -3.21855e6 q^{64} -169257. q^{65} +3.20601e6 q^{66} +2.19036e6 q^{67} -5.54420e6 q^{68} -1.61335e6 q^{69} -526713. q^{70} +4.77162e6 q^{71} +2.53746e6 q^{72} +4.98637e6 q^{73} -1.31256e6 q^{74} -4.65235e6 q^{75} +1.77049e6 q^{76} +618397. q^{77} +1.76299e6 q^{78} +3.39256e6 q^{79} +1.06219e6 q^{80} -1.26466e6 q^{81} +7.85086e6 q^{82} +8.35875e6 q^{83} +3.15180e6 q^{84} +3.94431e6 q^{85} -1.37897e6 q^{86} +1.28336e7 q^{87} +1.94585e6 q^{88} -7.83169e6 q^{89} -6.96145e6 q^{90} +340058. q^{91} -3.77608e6 q^{92} +1.18462e6 q^{93} +1.96883e6 q^{94} -1.25958e6 q^{95} -1.84096e7 q^{96} +6.12777e6 q^{97} -1.32253e7 q^{98} +8.17321e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 16 q^{2} + 94 q^{3} + 922 q^{4} + 998 q^{5} + 183 q^{6} + 1360 q^{7} + 3870 q^{8} + 10011 q^{9}+O(q^{10}) $ 13 * q + 16 * q^2 + 94 * q^3 + 922 * q^4 + 998 * q^5 + 183 * q^6 + 1360 * q^7 + 3870 * q^8 + 10011 * q^9	\( 13 q + 16 q^{2} + 94 q^{3} + 922 q^{4} + 998 q^{5} + 183 q^{6} + 1360 q^{7} + 3870 q^{8} + 10011 q^{9} + 4667 q^{10} + 1620 q^{11} - 19681 q^{12} + 13550 q^{13} + 44160 q^{14} + 31412 q^{15} + 114026 q^{16} + 110880 q^{17} + 159267 q^{18} + 105058 q^{19} + 167251 q^{20} + 129840 q^{21} + 201504 q^{22} + 160184 q^{23} + 161289 q^{24} + 270149 q^{25} + 272104 q^{26} + 252544 q^{27} + 208172 q^{28} + 285546 q^{29} + 107580 q^{30} - 99616 q^{31} + 200126 q^{32} + 531468 q^{33} - 80941 q^{34} - 187104 q^{35} - 608975 q^{36} + 176038 q^{37} + 652165 q^{38} - 794680 q^{39} - 895387 q^{40} - 410260 q^{41} - 3413218 q^{42} - 1033591 q^{43} - 2177076 q^{44} - 1051178 q^{45} - 3975765 q^{46} - 424556 q^{47} - 2360477 q^{48} - 1561359 q^{49} - 4063801 q^{50} - 2375738 q^{51} - 4172312 q^{52} + 3992458 q^{53} - 10438626 q^{54} + 406960 q^{55} + 1559556 q^{56} - 3116152 q^{57} - 4052005 q^{58} + 2248836 q^{59} - 2911436 q^{60} + 6210394 q^{61} + 885317 q^{62} + 11622368 q^{63} - 3096318 q^{64} + 5600420 q^{65} - 2174604 q^{66} - 1993648 q^{67} + 9327135 q^{68} + 13366240 q^{69} - 1105098 q^{70} + 4978064 q^{71} + 11370663 q^{72} + 8224814 q^{73} - 3613563 q^{74} + 27115592 q^{75} + 10687121 q^{76} + 17261892 q^{77} - 15226630 q^{78} + 6945708 q^{79} + 15822799 q^{80} + 35113185 q^{81} - 508449 q^{82} + 22937328 q^{83} - 14010106 q^{84} - 575532 q^{85} - 1272112 q^{86} + 9081380 q^{87} + 11202656 q^{88} + 9291302 q^{89} + 2841402 q^{90} + 25581108 q^{91} - 14388137 q^{92} + 25930480 q^{93} - 24645805 q^{94} + 30750464 q^{95} - 22461255 q^{96} + 10001852 q^{97} - 32304856 q^{98} + 5055452 q^{99}+O(q^{100}) \) 13 * q + 16 * q^2 + 94 * q^3 + 922 * q^4 + 998 * q^5 + 183 * q^6 + 1360 * q^7 + 3870 * q^8 + 10011 * q^9 + 4667 * q^10 + 1620 * q^11 - 19681 * q^12 + 13550 * q^13 + 44160 * q^14 + 31412 * q^15 + 114026 * q^16 + 110880 * q^17 + 159267 * q^18 + 105058 * q^19 + 167251 * q^20 + 129840 * q^21 + 201504 * q^22 + 160184 * q^23 + 161289 * q^24 + 270149 * q^25 + 272104 * q^26 + 252544 * q^27 + 208172 * q^28 + 285546 * q^29 + 107580 * q^30 - 99616 * q^31 + 200126 * q^32 + 531468 * q^33 - 80941 * q^34 - 187104 * q^35 - 608975 * q^36 + 176038 * q^37 + 652165 * q^38 - 794680 * q^39 - 895387 * q^40 - 410260 * q^41 - 3413218 * q^42 - 1033591 * q^43 - 2177076 * q^44 - 1051178 * q^45 - 3975765 * q^46 - 424556 * q^47 - 2360477 * q^48 - 1561359 * q^49 - 4063801 * q^50 - 2375738 * q^51 - 4172312 * q^52 + 3992458 * q^53 - 10438626 * q^54 + 406960 * q^55 + 1559556 * q^56 - 3116152 * q^57 - 4052005 * q^58 + 2248836 * q^59 - 2911436 * q^60 + 6210394 * q^61 + 885317 * q^62 + 11622368 * q^63 - 3096318 * q^64 + 5600420 * q^65 - 2174604 * q^66 - 1993648 * q^67 + 9327135 * q^68 + 13366240 * q^69 - 1105098 * q^70 + 4978064 * q^71 + 11370663 * q^72 + 8224814 * q^73 - 3613563 * q^74 + 27115592 * q^75 + 10687121 * q^76 + 17261892 * q^77 - 15226630 * q^78 + 6945708 * q^79 + 15822799 * q^80 + 35113185 * q^81 - 508449 * q^82 + 22937328 * q^83 - 14010106 * q^84 - 575532 * q^85 - 1272112 * q^86 + 9081380 * q^87 + 11202656 * q^88 + 9291302 * q^89 + 2841402 * q^90 + 25581108 * q^91 - 14388137 * q^92 + 25930480 * q^93 - 24645805 * q^94 + 30750464 * q^95 - 22461255 * q^96 + 10001852 * q^97 - 32304856 * q^98 + 5055452 * 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 $

$2$	17.3440	1.53301	0.766503	−	0.642241i	$-0.221995\pi$
$2$	17.3440	1.53301	0.766503	+	0.642241i	$0.221995\pi$
$3$	73.8355	1.57885	0.789425	−	0.613847i	$-0.210379\pi$
$3$	73.8355	1.57885	0.789425	+	0.613847i	$0.210379\pi$
$4$	172.814	1.35011
$5$	−122.945	−0.439860	−0.219930	−	0.975516i	$-0.570583\pi$
$5$	−122.945	−0.439860	−0.219930	+	0.975516i	$0.570583\pi$
$6$	1280.60	2.42039
$7$	247.011	0.272190	0.136095	−	0.990696i	$-0.456545\pi$
$7$	247.011	0.272190	0.136095	+	0.990696i	$0.456545\pi$
$8$	777.246	0.536715
$9$	3264.69	1.49277
$10$	−2132.35	−0.674308
$11$	2503.52	0.567123	0.283561	−	0.958954i	$-0.408484\pi$
$11$	2503.52	0.567123	0.283561	+	0.958954i	$0.408484\pi$
$12$	12759.8	2.13162
$13$	1376.69	0.173794	0.0868970	−	0.996217i	$-0.472305\pi$
$13$	1376.69	0.173794	0.0868970	+	0.996217i	$0.472305\pi$
$14$	4284.15	0.417269
$15$	−9077.68	−0.694473
$16$	−8639.60	−0.527320
$17$	−32082.0	−1.58376	−0.791881	−	0.610675i	$-0.790898\pi$
$17$	−32082.0	−1.58376	−0.791881	+	0.610675i	$0.790898\pi$
$18$	56622.6	2.28842
$19$	10245.1	0.342672	0.171336	−	0.985213i	$-0.445192\pi$
$19$	10245.1	0.342672	0.171336	+	0.985213i	$0.445192\pi$
$20$	−21246.5	−0.593858
$21$	18238.2	0.429748
$22$	43421.0	0.869402
$23$	−21850.6	−0.374469	−0.187235	−	0.982315i	$-0.559952\pi$
$23$	−21850.6	−0.374469	−0.187235	+	0.982315i	$0.559952\pi$
$24$	57388.4	0.847392
$25$	−63009.6	−0.806523
$26$	23877.3	0.266427
$27$	79571.5	0.778009
$28$	42686.8	0.367486
$29$	173813.	1.32339	0.661696	−	0.749772i	$-0.269837\pi$
$29$	173813.	1.32339	0.661696	+	0.749772i	$0.269837\pi$
$30$	−157443.	−1.06463
$31$	16044.0	0.0967270	0.0483635	−	0.998830i	$-0.484599\pi$
$31$	16044.0	0.0967270	0.0483635	+	0.998830i	$0.484599\pi$
$32$	−249333.	−1.34510
$33$	184849.	0.895402
$34$	−556429.	−2.42792
$35$	−30368.6	−0.119726
$36$	564182.	2.01540
$37$	−75677.9	−0.245620	−0.122810	−	0.992430i	$-0.539191\pi$
$37$	−75677.9	−0.245620	−0.122810	+	0.992430i	$0.539191\pi$
$38$	177691.	0.525318
$39$	101649.	0.274395
$40$	−95558.2	−0.236079
$41$	452656.	1.02571	0.512855	−	0.858475i	$-0.328588\pi$
$41$	452656.	1.02571	0.512855	+	0.858475i	$0.328588\pi$
$42$	316323.	0.658806
$43$	−79507.0	−0.152499
$43$	−79507.0	−0.152499
$44$	432643.	0.765676
$45$	−401375.	−0.656609
$46$	−378977.	−0.574063
$47$	113517.	0.159484	0.0797420	−	0.996816i	$-0.474590\pi$
$47$	113517.	0.159484	0.0797420	+	0.996816i	$0.474590\pi$
$48$	−637910.	−0.832559
$49$	−762529.	−0.925912
$50$	−1.09284e6	−1.23640
$51$	−2.36879e6	−2.50052
$52$	237911.	0.234640
$53$	−1.42412e6	−1.31395	−0.656976	−	0.753911i	$-0.728165\pi$
$53$	−1.42412e6	−1.31395	−0.656976	+	0.753911i	$0.728165\pi$
$54$	1.38009e6	1.19269
$55$	−307794.	−0.249455
$56$	191988.	0.146089
$57$	756453.	0.541028
$58$	3.01460e6	2.02877
$59$	1.48283e6	0.939960	0.469980	−	0.882677i	$-0.344261\pi$
$59$	1.48283e6	0.939960	0.469980	+	0.882677i	$0.344261\pi$
$60$	−1.56875e6	−0.937612
$61$	−2.69078e6	−1.51784	−0.758918	−	0.651187i	$-0.774271\pi$
$61$	−2.69078e6	−1.51784	−0.758918	+	0.651187i	$0.774271\pi$
$62$	278267.	0.148283
$63$	806413.	0.406318
$64$	−3.21855e6	−1.53472
$65$	−169257.	−0.0764450
$66$	3.20601e6	1.37266
$67$	2.19036e6	0.889722	0.444861	−	0.895600i	$-0.353253\pi$
$67$	2.19036e6	0.889722	0.444861	+	0.895600i	$0.353253\pi$
$68$	−5.54420e6	−2.13825
$69$	−1.61335e6	−0.591231
$70$	−526713.	−0.183540
$71$	4.77162e6	1.58220	0.791101	−	0.611685i	$-0.209508\pi$
$71$	4.77162e6	1.58220	0.791101	+	0.611685i	$0.209508\pi$
$72$	2.53746e6	0.801191
$73$	4.98637e6	1.50022	0.750109	−	0.661314i	$-0.230001\pi$
$73$	4.98637e6	1.50022	0.750109	+	0.661314i	$0.230001\pi$
$74$	−1.31256e6	−0.376536
$75$	−4.65235e6	−1.27338
$76$	1.77049e6	0.462644
$77$	618397.	0.154365
$78$	1.76299e6	0.420649
$79$	3.39256e6	0.774163	0.387081	−	0.922046i	$-0.373483\pi$
$79$	3.39256e6	0.774163	0.387081	+	0.922046i	$0.373483\pi$
$80$	1.06219e6	0.231947
$81$	−1.26466e6	−0.264409
$82$	7.85086e6	1.57242
$83$	8.35875e6	1.60460	0.802302	−	0.596918i	$-0.203608\pi$
$83$	8.35875e6	1.60460	0.802302	+	0.596918i	$0.203608\pi$
$84$	3.15180e6	0.580205
$85$	3.94431e6	0.696634
$86$	−1.37897e6	−0.233781
$87$	1.28336e7	2.08944
$88$	1.94585e6	0.304383
$89$	−7.83169e6	−1.17758	−0.588790	−	0.808286i	$-0.700396\pi$
$89$	−7.83169e6	−1.17758	−0.588790	+	0.808286i	$0.700396\pi$
$90$	−6.96145e6	−1.00659
$91$	340058.	0.0473051
$92$	−3.77608e6	−0.505573
$93$	1.18462e6	0.152717
$94$	1.96883e6	0.244490
$95$	−1.25958e6	−0.150728
$96$	−1.84096e7	−2.12371
$97$	6.12777e6	0.681712	0.340856	−	0.940115i	$-0.389283\pi$
$97$	6.12777e6	0.681712	0.340856	+	0.940115i	$0.389283\pi$
$98$	−1.32253e7	−1.41943
$99$	8.17321e6	0.846583
$100$	−1.08889e7	−1.08889
$101$	−1.48954e7	−1.43856	−0.719279	−	0.694721i	$-0.755528\pi$
$101$	−1.48954e7	−1.43856	−0.719279	+	0.694721i	$0.755528\pi$
$102$	−4.10843e7	−3.83332
$103$	8.96048e6	0.807981	0.403990	−	0.914763i	$-0.367623\pi$
$103$	8.96048e6	0.807981	0.403990	+	0.914763i	$0.367623\pi$
$104$	1.07003e6	0.0932778
$105$	−2.24229e6	−0.189029
$106$	−2.46998e7	−2.01430
$107$	−2.20290e6	−0.173841	−0.0869204	−	0.996215i	$-0.527703\pi$
$107$	−2.20290e6	−0.173841	−0.0869204	+	0.996215i	$0.527703\pi$
$108$	1.37510e7	1.05039
$109$	1.43255e7	1.05954	0.529770	−	0.848141i	$-0.322278\pi$
$109$	1.43255e7	1.05954	0.529770	+	0.848141i	$0.322278\pi$
$110$	−5.33838e6	−0.382415
$111$	−5.58772e6	−0.387797
$112$	−2.13408e6	−0.143531
$113$	5.69345e6	0.371194	0.185597	−	0.982626i	$-0.440578\pi$
$113$	5.69345e6	0.371194	0.185597	+	0.982626i	$0.440578\pi$
$114$	1.31199e7	0.829399
$115$	2.68641e6	0.164714
$116$	3.00372e7	1.78672
$117$	4.49447e6	0.259434
$118$	2.57182e7	1.44096
$119$	−7.92460e6	−0.431085
$120$	−7.05559e6	−0.372734
$121$	−1.32196e7	−0.678372
$122$	−4.66689e7	−2.32685
$123$	3.34221e7	1.61944
$124$	2.77263e6	0.130592
$125$	1.73517e7	0.794617
$126$	1.39864e7	0.622887
$127$	2.89632e7	1.25468	0.627342	−	0.778744i	$-0.284143\pi$
$127$	2.89632e7	1.25468	0.627342	+	0.778744i	$0.284143\pi$
$128$	−2.39079e7	−1.00764
$129$	−5.87044e6	−0.240772
$130$	−2.93559e6	−0.117191
$131$	1.30359e7	0.506632	0.253316	−	0.967384i	$-0.418479\pi$
$131$	1.30359e7	0.506632	0.253316	+	0.967384i	$0.418479\pi$
$132$	3.19444e7	1.20889
$133$	2.53065e6	0.0932721
$134$	3.79896e7	1.36395
$135$	−9.78289e6	−0.342215
$136$	−2.49356e7	−0.850029
$137$	−3.16388e7	−1.05123	−0.525615	−	0.850723i	$-0.676165\pi$
$137$	−3.16388e7	−1.05123	−0.525615	+	0.850723i	$0.676165\pi$
$138$	−2.79819e7	−0.906360
$139$	−4.62889e7	−1.46193	−0.730963	−	0.682418i	$-0.760929\pi$
$139$	−4.62889e7	−1.46193	−0.730963	+	0.682418i	$0.760929\pi$
$140$	−5.24811e6	−0.161642
$141$	8.38156e6	0.251801
$142$	8.27589e7	2.42552
$143$	3.44658e6	0.0985625
$144$	−2.82056e7	−0.787166
$145$	−2.13693e7	−0.582107
$146$	8.64835e7	2.29984
$147$	−5.63017e7	−1.46188
$148$	−1.30782e7	−0.331613
$149$	3.21433e7	0.796048	0.398024	−	0.917375i	$-0.369696\pi$
$149$	3.21433e7	0.796048	0.398024	+	0.917375i	$0.369696\pi$
$150$	−8.06903e7	−1.95210
$151$	2.05927e7	0.486737	0.243369	−	0.969934i	$-0.421748\pi$
$151$	2.05927e7	0.486737	0.243369	+	0.969934i	$0.421748\pi$
$152$	7.96296e6	0.183917
$153$	−1.04738e8	−2.36419
$154$	1.07255e7	0.236643
$155$	−1.97253e6	−0.0425463
$156$	1.75663e7	0.370462
$157$	−2.11067e7	−0.435283	−0.217641	−	0.976029i	$-0.569836\pi$
$157$	−2.11067e7	−0.435283	−0.217641	+	0.976029i	$0.569836\pi$
$158$	5.88404e7	1.18680
$159$	−1.05150e8	−2.07453
$160$	3.06541e7	0.591655
$161$	−5.39734e6	−0.101927
$162$	−2.19343e7	−0.405341
$163$	983833.	0.0177936	0.00889682	−	0.999960i	$-0.497168\pi$
$163$	983833.	0.0177936	0.00889682	+	0.999960i	$0.497168\pi$
$164$	7.82251e7	1.38482
$165$	−2.27262e7	−0.393851
$166$	1.44974e8	2.45987
$167$	9.39137e7	1.56035	0.780174	−	0.625563i	$-0.215131\pi$
$167$	9.39137e7	1.56035	0.780174	+	0.625563i	$0.215131\pi$
$168$	1.41755e7	0.230652
$169$	−6.08532e7	−0.969796
$170$	6.84100e7	1.06794
$171$	3.34470e7	0.511530
$172$	−1.37399e7	−0.205889
$173$	1.05361e8	1.54710	0.773551	−	0.633734i	$-0.218478\pi$
$173$	1.05361e8	1.54710	0.773551	+	0.633734i	$0.218478\pi$
$174$	2.22585e8	3.20312
$175$	−1.55641e7	−0.219528
$176$	−2.16294e7	−0.299055
$177$	1.09486e8	1.48406
$178$	−1.35833e8	−1.80524
$179$	−7.52808e7	−0.981067	−0.490533	−	0.871422i	$-0.663198\pi$
$179$	−7.52808e7	−0.981067	−0.490533	+	0.871422i	$0.663198\pi$
$180$	−6.93631e7	−0.886492
$181$	−2.35542e7	−0.295253	−0.147626	−	0.989043i	$-0.547163\pi$
$181$	−2.35542e7	−0.295253	−0.147626	+	0.989043i	$0.547163\pi$
$182$	5.89795e6	0.0725189
$183$	−1.98676e8	−2.39643
$184$	−1.69833e7	−0.200983
$185$	9.30419e6	0.108038
$186$	2.05460e7	0.234117
$187$	−8.03180e7	−0.898188
$188$	1.96172e7	0.215320
$189$	1.96550e7	0.211767
$190$	−2.18461e7	−0.231066
$191$	1.11671e8	1.15964	0.579820	−	0.814745i	$-0.303123\pi$
$191$	1.11671e8	1.15964	0.579820	+	0.814745i	$0.303123\pi$
$192$	−2.37643e8	−2.42310
$193$	−1.17636e8	−1.17785	−0.588926	−	0.808187i	$-0.700449\pi$
$193$	−1.17636e8	−1.17785	−0.588926	+	0.808187i	$0.700449\pi$
$194$	1.06280e8	1.04507
$195$	−1.24972e7	−0.120695
$196$	−1.31775e8	−1.25008
$197$	−5.42883e7	−0.505912	−0.252956	−	0.967478i	$-0.581403\pi$
$197$	−5.42883e7	−0.505912	−0.252956	+	0.967478i	$0.581403\pi$
$198$	1.41756e8	1.29782
$199$	8.13364e7	0.731643	0.365822	−	0.930685i	$-0.380788\pi$
$199$	8.13364e7	0.731643	0.365822	+	0.930685i	$0.380788\pi$
$200$	−4.89740e7	−0.432873
$201$	1.61727e8	1.40474
$202$	−2.58346e8	−2.20532
$203$	4.29336e7	0.360215
$204$	−4.09359e8	−3.37597
$205$	−5.56516e7	−0.451169
$206$	1.55410e8	1.23864
$207$	−7.13354e7	−0.558996
$208$	−1.18941e7	−0.0916450
$209$	2.56488e7	0.194337
$210$	−3.88901e7	−0.289782
$211$	7.38401e7	0.541132	0.270566	−	0.962701i	$-0.412789\pi$
$211$	7.38401e7	0.541132	0.270566	+	0.962701i	$0.412789\pi$
$212$	−2.46106e8	−1.77397
$213$	3.52315e8	2.49806
$214$	−3.82071e7	−0.266499
$215$	9.77496e6	0.0670780
$216$	6.18466e7	0.417569
$217$	3.96305e6	0.0263282
$218$	2.48461e8	1.62428
$219$	3.68171e8	2.36862
$220$	−5.31911e7	−0.336790
$221$	−4.41670e7	−0.275248
$222$	−9.69133e7	−0.594495
$223$	−1.01645e8	−0.613790	−0.306895	−	0.951743i	$-0.599290\pi$
$223$	−1.01645e8	−0.613790	−0.306895	+	0.951743i	$0.599290\pi$
$224$	−6.15878e7	−0.366123
$225$	−2.05707e8	−1.20395
$226$	9.87471e7	0.569043
$227$	−1.95225e8	−1.10776	−0.553880	−	0.832596i	$-0.686854\pi$
$227$	−1.95225e8	−1.10776	−0.553880	+	0.832596i	$0.686854\pi$
$228$	1.30725e8	0.730445
$229$	−1.38246e8	−0.760727	−0.380363	−	0.924837i	$-0.624201\pi$
$229$	−1.38246e8	−0.760727	−0.380363	+	0.924837i	$0.624201\pi$
$230$	4.65931e7	0.252507
$231$	4.56597e7	0.243720
$232$	1.35095e8	0.710284
$233$	−7.52341e7	−0.389645	−0.194822	−	0.980839i	$-0.562413\pi$
$233$	−7.52341e7	−0.389645	−0.194822	+	0.980839i	$0.562413\pi$
$234$	7.79519e7	0.397714
$235$	−1.39563e7	−0.0701506
$236$	2.56253e8	1.26905
$237$	2.50491e8	1.22229
$238$	−1.37444e8	−0.660856
$239$	−5.37584e7	−0.254715	−0.127357	−	0.991857i	$-0.540649\pi$
$239$	−5.37584e7	−0.254715	−0.127357	+	0.991857i	$0.540649\pi$
$240$	7.84276e7	0.366209
$241$	−4.33242e8	−1.99375	−0.996876	−	0.0789843i	$-0.974832\pi$
$241$	−4.33242e8	−1.99375	−0.996876	+	0.0789843i	$0.974832\pi$
$242$	−2.29280e8	−1.03995
$243$	−2.67400e8	−1.19547
$244$	−4.65004e8	−2.04924
$245$	9.37488e7	0.407272
$246$	5.79672e8	2.48262
$247$	1.41043e7	0.0595544
$248$	1.24702e7	0.0519148
$249$	6.17173e8	2.53343
$250$	3.00948e8	1.21815
$251$	−3.50742e8	−1.40001	−0.700003	−	0.714140i	$-0.746818\pi$
$251$	−3.50742e8	−1.40001	−0.700003	+	0.714140i	$0.746818\pi$
$252$	1.39359e8	0.548572
$253$	−5.47035e7	−0.212370
$254$	5.02338e8	1.92344
$255$	2.91230e8	1.09988
$256$	−2.68346e6	−0.00999666
$257$	3.82436e8	1.40538	0.702689	−	0.711497i	$-0.251983\pi$
$257$	3.82436e8	1.40538	0.702689	+	0.711497i	$0.251983\pi$
$258$	−1.01817e8	−0.369106
$259$	−1.86933e7	−0.0668554
$260$	−2.92499e7	−0.103209
$261$	5.67444e8	1.97552
$262$	2.26095e8	0.776670
$263$	−4.76819e8	−1.61625	−0.808125	−	0.589011i	$-0.799517\pi$
$263$	−4.76819e8	−1.61625	−0.808125	+	0.589011i	$0.799517\pi$
$264$	1.43673e8	0.480575
$265$	1.75087e8	0.577955
$266$	4.38916e7	0.142987
$267$	−5.78257e8	−1.85922
$268$	3.78524e8	1.20122
$269$	4.56754e8	1.43070	0.715352	−	0.698765i	$-0.246267\pi$
$269$	4.56754e8	1.43070	0.715352	+	0.698765i	$0.246267\pi$
$270$	−1.69674e8	−0.524617
$271$	−3.80308e8	−1.16076	−0.580381	−	0.814345i	$-0.697096\pi$
$271$	−3.80308e8	−1.16076	−0.580381	+	0.814345i	$0.697096\pi$
$272$	2.77176e8	0.835149
$273$	2.51083e7	0.0746876
$274$	−5.48742e8	−1.61154
$275$	−1.57746e8	−0.457398
$276$	−2.78809e8	−0.798225
$277$	−1.74969e8	−0.494632	−0.247316	−	0.968935i	$-0.579549\pi$
$277$	−1.74969e8	−0.494632	−0.247316	+	0.968935i	$0.579549\pi$
$278$	−8.02834e8	−2.24114
$279$	5.23787e7	0.144391
$280$	−2.36039e7	−0.0642585
$281$	−9.23019e7	−0.248164	−0.124082	−	0.992272i	$-0.539599\pi$
$281$	−9.23019e7	−0.248164	−0.124082	+	0.992272i	$0.539599\pi$
$282$	1.45370e8	0.386013
$283$	−6.07622e8	−1.59361	−0.796803	−	0.604239i	$-0.793477\pi$
$283$	−6.07622e8	−1.59361	−0.796803	+	0.604239i	$0.793477\pi$
$284$	8.24601e8	2.13614
$285$	−9.30018e7	−0.237977
$286$	5.97773e7	0.151097
$287$	1.11811e8	0.279189
$288$	−8.13993e8	−2.00792
$289$	6.18915e8	1.50830
$290$	−3.70629e8	−0.892373
$291$	4.52447e8	1.07632
$292$	8.61712e8	2.02545
$293$	−4.12823e8	−0.958798	−0.479399	−	0.877597i	$-0.659145\pi$
$293$	−4.12823e8	−0.958798	−0.479399	+	0.877597i	$0.659145\pi$
$294$	−9.76496e8	−2.24107
$295$	−1.82306e8	−0.413451
$296$	−5.88204e7	−0.131828
$297$	1.99209e8	0.441226
$298$	5.57493e8	1.22035
$299$	−3.00815e7	−0.0650805
$300$	−8.03989e8	−1.71920
$301$	−1.96391e7	−0.0415087
$302$	3.57160e8	0.746171
$303$	−1.09981e9	−2.27127
$304$	−8.85136e7	−0.180698
$305$	3.30817e8	0.667635
$306$	−1.81657e9	−3.62432
$307$	3.39020e8	0.668715	0.334358	−	0.942446i	$-0.391481\pi$
$307$	3.39020e8	0.668715	0.334358	+	0.942446i	$0.391481\pi$
$308$	1.06867e8	0.208410
$309$	6.61602e8	1.27568
$310$	−3.42115e7	−0.0652237
$311$	3.14861e8	0.593550	0.296775	−	0.954947i	$-0.404089\pi$
$311$	3.14861e8	0.593550	0.296775	+	0.954947i	$0.404089\pi$
$312$	7.90061e7	0.147272
$313$	−7.61170e7	−0.140306	−0.0701531	−	0.997536i	$-0.522349\pi$
$313$	−7.61170e7	−0.140306	−0.0701531	+	0.997536i	$0.522349\pi$
$314$	−3.66074e8	−0.667291
$315$	−9.91441e7	−0.178723
$316$	5.86280e8	1.04520
$317$	3.04947e6	0.00537671	0.00268835	−	0.999996i	$-0.499144\pi$
$317$	3.04947e6	0.00537671	0.00268835	+	0.999996i	$0.499144\pi$
$318$	−1.82372e9	−3.18027
$319$	4.35144e8	0.750525
$320$	3.95703e8	0.675064
$321$	−1.62652e8	−0.274469
$322$	−9.36113e7	−0.156255
$323$	−3.28683e8	−0.542711
$324$	−2.18551e8	−0.356981
$325$	−8.67448e7	−0.140169
$326$	1.70636e7	0.0272777
$327$	1.05773e9	1.67286
$328$	3.51825e8	0.550514
$329$	2.80398e7	0.0434100
$330$	−3.94162e8	−0.603776
$331$	−6.34097e8	−0.961076	−0.480538	−	0.876974i	$-0.659559\pi$
$331$	−6.34097e8	−0.961076	−0.480538	+	0.876974i	$0.659559\pi$
$332$	1.44450e9	2.16639
$333$	−2.47065e8	−0.366654
$334$	1.62884e9	2.39202
$335$	−2.69293e8	−0.391353
$336$	−1.57571e8	−0.226615
$337$	2.48720e8	0.354003	0.177001	−	0.984211i	$-0.443360\pi$
$337$	2.48720e8	0.354003	0.177001	+	0.984211i	$0.443360\pi$
$338$	−1.05544e9	−1.48670
$339$	4.20379e8	0.586060
$340$	6.81630e8	0.940529
$341$	4.01666e7	0.0548560
$342$	5.80105e8	0.784179
$343$	−3.91777e8	−0.524215
$344$	−6.17965e7	−0.0818482
$345$	1.98353e8	0.260059
$346$	1.82738e9	2.37172
$347$	7.91060e8	1.01638	0.508190	−	0.861245i	$-0.330315\pi$
$347$	7.91060e8	1.01638	0.508190	+	0.861245i	$0.330315\pi$
$348$	2.21781e9	2.82096
$349$	−5.53018e8	−0.696386	−0.348193	−	0.937423i	$-0.613205\pi$
$349$	−5.53018e8	−0.696386	−0.348193	+	0.937423i	$0.613205\pi$
$350$	−2.69943e8	−0.336538
$351$	1.09545e8	0.135213
$352$	−6.24209e8	−0.762836
$353$	1.06776e9	1.29200	0.645999	−	0.763338i	$-0.276441\pi$
$353$	1.06776e9	1.29200	0.645999	+	0.763338i	$0.276441\pi$
$354$	1.89891e9	2.27507
$355$	−5.86645e8	−0.695947
$356$	−1.35342e9	−1.58986
$357$	−5.85117e8	−0.680619
$358$	−1.30567e9	−1.50398
$359$	1.46087e9	1.66641	0.833203	−	0.552967i	$-0.186504\pi$
$359$	1.46087e9	1.66641	0.833203	+	0.552967i	$0.186504\pi$
$360$	−3.11967e8	−0.352412
$361$	−7.88910e8	−0.882576
$362$	−4.08524e8	−0.452624
$363$	−9.76073e8	−1.07105
$364$	5.87666e7	0.0638669
$365$	−6.13047e8	−0.659886
$366$	−3.44582e9	−3.67375
$367$	1.28374e9	1.35564	0.677822	−	0.735226i	$-0.262924\pi$
$367$	1.28374e9	1.35564	0.677822	+	0.735226i	$0.262924\pi$
$368$	1.88781e8	0.197465
$369$	1.47778e9	1.53115
$370$	1.61372e8	0.165623
$371$	−3.51772e8	−0.357645
$372$	2.04718e8	0.206185
$373$	−4.86215e8	−0.485118	−0.242559	−	0.970137i	$-0.577987\pi$
$373$	−4.86215e8	−0.485118	−0.242559	+	0.970137i	$0.577987\pi$
$374$	−1.39303e9	−1.37693
$375$	1.28117e9	1.25458
$376$	8.82303e7	0.0855974
$377$	2.39286e8	0.229998
$378$	3.40896e8	0.324639
$379$	−1.35199e9	−1.27567	−0.637834	−	0.770174i	$-0.720169\pi$
$379$	−1.35199e9	−1.27567	−0.637834	+	0.770174i	$0.720169\pi$
$380$	−2.17673e8	−0.203498
$381$	2.13852e9	1.98096
$382$	1.93682e9	1.77773
$383$	−6.26582e8	−0.569878	−0.284939	−	0.958546i	$-0.591973\pi$
$383$	−6.26582e8	−0.569878	−0.284939	+	0.958546i	$0.591973\pi$
$384$	−1.76525e9	−1.59092
$385$	−7.60286e7	−0.0678991
$386$	−2.04028e9	−1.80565
$387$	−2.59565e8	−0.227645
$388$	1.05896e9	0.920384
$389$	−1.29391e9	−1.11450	−0.557250	−	0.830345i	$-0.688144\pi$
$389$	−1.29391e9	−1.11450	−0.557250	+	0.830345i	$0.688144\pi$
$390$	−2.16751e8	−0.185027
$391$	7.01011e8	0.593070
$392$	−5.92672e8	−0.496951
$393$	9.62515e8	0.799896
$394$	−9.41575e8	−0.775565
$395$	−4.17096e8	−0.340523
$396$	1.41244e9	1.14298
$397$	2.44753e9	1.96319	0.981594	−	0.190981i	$-0.0611669\pi$
$397$	2.44753e9	1.96319	0.981594	+	0.190981i	$0.0611669\pi$
$398$	1.41070e9	1.12161
$399$	1.86852e8	0.147263
$400$	5.44378e8	0.425296
$401$	−8.46869e8	−0.655860	−0.327930	−	0.944702i	$-0.606351\pi$
$401$	−8.46869e8	−0.655860	−0.327930	+	0.944702i	$0.606351\pi$
$402$	2.80498e9	2.15347
$403$	2.20877e7	0.0168106
$404$	−2.57413e9	−1.94221
$405$	1.55483e8	0.116303
$406$	7.44640e8	0.552211
$407$	−1.89461e8	−0.139297
$408$	−1.84113e9	−1.34207
$409$	−1.06925e9	−0.772763	−0.386381	−	0.922339i	$-0.626275\pi$
$409$	−1.06925e9	−0.772763	−0.386381	+	0.922339i	$0.626275\pi$
$410$	−9.65221e8	−0.691645
$411$	−2.33606e9	−1.65973
$412$	1.54849e9	1.09086
$413$	3.66275e8	0.255848
$414$	−1.23724e9	−0.856944
$415$	−1.02766e9	−0.705801
$416$	−3.43254e8	−0.233770
$417$	−3.41777e9	−2.30816
$418$	4.44853e8	0.297920
$419$	8.44198e8	0.560654	0.280327	−	0.959905i	$-0.409557\pi$
$419$	8.44198e8	0.560654	0.280327	+	0.959905i	$0.409557\pi$
$420$	−3.87497e8	−0.255209
$421$	−8.77632e8	−0.573225	−0.286612	−	0.958047i	$-0.592529\pi$
$421$	−8.77632e8	−0.573225	−0.286612	+	0.958047i	$0.592529\pi$
$422$	1.28068e9	0.829559
$423$	3.70596e8	0.238073
$424$	−1.10689e9	−0.705217
$425$	2.02147e9	1.27734
$426$	6.11055e9	3.82954
$427$	−6.64653e8	−0.413140
$428$	−3.80691e8	−0.234704
$429$	2.54480e8	0.155615
$430$	1.69537e8	0.102831
$431$	−4.03075e7	−0.0242502	−0.0121251	−	0.999926i	$-0.503860\pi$
$431$	−4.03075e7	−0.0242502	−0.0121251	+	0.999926i	$0.503860\pi$
$432$	−6.87467e8	−0.410259
$433$	1.00411e9	0.594391	0.297196	−	0.954817i	$-0.403949\pi$
$433$	1.00411e9	0.594391	0.297196	+	0.954817i	$0.403949\pi$
$434$	6.87351e7	0.0403612
$435$	−1.57782e9	−0.919060
$436$	2.47564e9	1.43049
$437$	−2.23862e8	−0.128320
$438$	6.38555e9	3.63111
$439$	6.13553e8	0.346120	0.173060	−	0.984911i	$-0.444635\pi$
$439$	6.13553e8	0.346120	0.173060	+	0.984911i	$0.444635\pi$
$440$	−2.39232e8	−0.133886
$441$	−2.48942e9	−1.38217
$442$	−7.66031e8	−0.421957
$443$	−1.76951e9	−0.967028	−0.483514	−	0.875337i	$-0.660640\pi$
$443$	−1.76951e9	−0.967028	−0.483514	+	0.875337i	$0.660640\pi$
$444$	−9.65634e8	−0.523567
$445$	9.62864e8	0.517970
$446$	−1.76293e9	−0.940944
$447$	2.37332e9	1.25684
$448$	−7.95017e8	−0.417737
$449$	−2.28688e9	−1.19229	−0.596145	−	0.802877i	$-0.703302\pi$
$449$	−2.28688e9	−1.19229	−0.596145	+	0.802877i	$0.703302\pi$
$450$	−3.56777e9	−1.84567
$451$	1.13323e9	0.581704
$452$	9.83906e8	0.501152
$453$	1.52047e9	0.768485
$454$	−3.38599e9	−1.69820
$455$	−4.18083e7	−0.0208076
$456$	5.87950e8	0.290378
$457$	8.79369e8	0.430987	0.215494	−	0.976505i	$-0.430864\pi$
$457$	8.79369e8	0.430987	0.215494	+	0.976505i	$0.430864\pi$
$458$	−2.39774e9	−1.16620
$459$	−2.55281e9	−1.23218
$460$	4.64249e8	0.222381
$461$	1.43825e9	0.683724	0.341862	−	0.939750i	$-0.388942\pi$
$461$	1.43825e9	0.683724	0.341862	+	0.939750i	$0.388942\pi$
$462$	7.91920e8	0.373624
$463$	−3.40869e9	−1.59608	−0.798040	−	0.602605i	$-0.794130\pi$
$463$	−3.40869e9	−1.59608	−0.798040	+	0.602605i	$0.794130\pi$
$464$	−1.50167e9	−0.697850
$465$	−1.45643e8	−0.0671743
$466$	−1.30486e9	−0.597327
$467$	3.01086e9	1.36798	0.683992	−	0.729490i	$-0.260242\pi$
$467$	3.01086e9	1.36798	0.683992	+	0.729490i	$0.260242\pi$
$468$	7.76705e8	0.350264
$469$	5.41043e8	0.242174
$470$	−2.42057e8	−0.107541
$471$	−1.55842e9	−0.687247
$472$	1.15252e9	0.504490
$473$	−1.99047e8	−0.0864854
$474$	4.34451e9	1.87377
$475$	−6.45540e8	−0.276373
$476$	−1.36948e9	−0.582011
$477$	−4.64929e9	−1.96143
$478$	−9.32385e8	−0.390479
$479$	3.75213e7	0.0155992	0.00779961	−	0.999970i	$-0.497517\pi$
$479$	3.75213e7	0.0155992	0.00779961	+	0.999970i	$0.497517\pi$
$480$	2.26336e9	0.934135
$481$	−1.04185e8	−0.0426872
$482$	−7.51414e9	−3.05643
$483$	−3.98515e8	−0.160927
$484$	−2.28452e9	−0.915874
$485$	−7.53376e8	−0.299858
$486$	−4.63778e9	−1.83266
$487$	1.34816e8	0.0528921	0.0264460	−	0.999650i	$-0.491581\pi$
$487$	1.34816e8	0.0528921	0.0264460	+	0.999650i	$0.491581\pi$
$488$	−2.09140e9	−0.814644
$489$	7.26418e7	0.0280935
$490$	1.62598e9	0.624350
$491$	1.26229e9	0.481253	0.240627	−	0.970618i	$-0.422647\pi$
$491$	1.26229e9	0.481253	0.240627	+	0.970618i	$0.422647\pi$
$492$	5.77579e9	2.18642
$493$	−5.57626e9	−2.09594
$494$	2.44625e8	0.0912972
$495$	−1.00485e9	−0.372378
$496$	−1.38614e8	−0.0510060
$497$	1.17864e9	0.430660
$498$	1.07042e10	3.88376
$499$	−1.34095e9	−0.483128	−0.241564	−	0.970385i	$-0.577660\pi$
$499$	−1.34095e9	−0.483128	−0.241564	+	0.970385i	$0.577660\pi$
$500$	2.99862e9	1.07282
$501$	6.93417e9	2.46356
$502$	−6.08326e9	−2.14622
$503$	5.65419e9	1.98099	0.990495	−	0.137546i	$-0.0439215\pi$
$503$	5.65419e9	1.98099	0.990495	+	0.137546i	$0.0439215\pi$
$504$	6.26781e8	0.218077
$505$	1.83131e9	0.632764
$506$	−9.48776e8	−0.325564
$507$	−4.49313e9	−1.53116
$508$	5.00524e9	1.69396
$509$	4.83455e9	1.62497	0.812483	−	0.582985i	$-0.198115\pi$
$509$	4.83455e9	1.62497	0.812483	+	0.582985i	$0.198115\pi$
$510$	5.05109e9	1.68612
$511$	1.23169e9	0.408345
$512$	3.01367e9	0.992317
$513$	8.15218e8	0.266602
$514$	6.63297e9	2.15445
$515$	−1.10164e9	−0.355398
$516$	−1.01449e9	−0.325068
$517$	2.84191e8	0.0904470
$518$	−3.24216e8	−0.102490
$519$	7.77940e9	2.44264
$520$	−1.31554e8	−0.0410292
$521$	1.47590e9	0.457218	0.228609	−	0.973518i	$-0.426582\pi$
$521$	1.47590e9	0.457218	0.228609	+	0.973518i	$0.426582\pi$
$522$	9.84173e9	3.02848
$523$	−3.13778e9	−0.959106	−0.479553	−	0.877513i	$-0.659201\pi$
$523$	−3.13778e9	−0.959106	−0.479553	+	0.877513i	$0.659201\pi$
$524$	2.25279e9	0.684007
$525$	−1.14918e9	−0.346602
$526$	−8.26994e9	−2.47772
$527$	−5.14724e8	−0.153193
$528$	−1.59702e9	−0.472163
$529$	−2.92738e9	−0.859773
$530$	3.03671e9	0.886008
$531$	4.84097e9	1.40314
$532$	4.37331e8	0.125927
$533$	6.23168e8	0.178262
$534$	−1.00293e10	−2.85020
$535$	2.70835e8	0.0764656
$536$	1.70245e9	0.477527
$537$	−5.55840e9	−1.54896
$538$	7.92193e9	2.19328
$539$	−1.90901e9	−0.525106
$540$	−1.69062e9	−0.462026
$541$	−2.43519e9	−0.661214	−0.330607	−	0.943768i	$-0.607254\pi$
$541$	−2.43519e9	−0.661214	−0.330607	+	0.943768i	$0.607254\pi$
$542$	−6.59606e9	−1.77945
$543$	−1.73914e9	−0.466160
$544$	7.99909e9	2.13032
$545$	−1.76124e9	−0.466049
$546$	4.35479e8	0.114497
$547$	−4.11336e9	−1.07458	−0.537292	−	0.843396i	$-0.680553\pi$
$547$	−4.11336e9	−1.07458	−0.537292	+	0.843396i	$0.680553\pi$
$548$	−5.46761e9	−1.41927
$549$	−8.78457e9	−2.26578
$550$	−2.73594e9	−0.701193
$551$	1.78073e9	0.453489
$552$	−1.25397e9	−0.317322
$553$	8.37998e8	0.210720
$554$	−3.03466e9	−0.758274
$555$	6.86980e8	0.170576
$556$	−7.99935e9	−1.97375
$557$	5.89179e9	1.44462	0.722311	−	0.691568i	$-0.243080\pi$
$557$	5.89179e9	1.44462	0.722311	+	0.691568i	$0.243080\pi$
$558$	9.08456e8	0.221352
$559$	−1.09457e8	−0.0265033
$560$	2.62373e8	0.0631337
$561$	−5.93032e9	−1.41810
$562$	−1.60088e9	−0.380437
$563$	−3.72337e9	−0.879341	−0.439671	−	0.898159i	$-0.644905\pi$
$563$	−3.72337e9	−0.879341	−0.439671	+	0.898159i	$0.644905\pi$
$564$	1.44845e9	0.339959
$565$	−6.99979e8	−0.163273
$566$	−1.05386e10	−2.44301
$567$	−3.12385e8	−0.0719697
$568$	3.70872e9	0.849191
$569$	5.89440e9	1.34136	0.670682	−	0.741745i	$-0.266001\pi$
$569$	5.89440e9	1.34136	0.670682	+	0.741745i	$0.266001\pi$
$570$	−1.61302e9	−0.364819
$571$	−4.09269e9	−0.919988	−0.459994	−	0.887922i	$-0.652148\pi$
$571$	−4.09269e9	−0.919988	−0.459994	+	0.887922i	$0.652148\pi$
$572$	5.95615e8	0.133070
$573$	8.24528e9	1.83090
$574$	1.93925e9	0.427998
$575$	1.37680e9	0.302018
$576$	−1.05076e10	−2.29099
$577$	6.73874e9	1.46037	0.730185	−	0.683249i	$-0.239434\pi$
$577$	6.73874e9	1.46037	0.730185	+	0.683249i	$0.239434\pi$
$578$	1.07345e10	2.31224
$579$	−8.68574e9	−1.85965
$580$	−3.69291e9	−0.785906
$581$	2.06470e9	0.436758
$582$	7.84723e9	1.65001
$583$	−3.56530e9	−0.745172
$584$	3.87563e9	0.805189
$585$	−5.52570e8	−0.114115
$586$	−7.15999e9	−1.46984
$587$	6.12315e9	1.24951	0.624757	−	0.780819i	$-0.285198\pi$
$587$	6.12315e9	1.24951	0.624757	+	0.780819i	$0.285198\pi$
$588$	−9.72970e9	−1.97369
$589$	1.64373e8	0.0331456
$590$	−3.16191e9	−0.633822
$591$	−4.00841e9	−0.798759
$592$	6.53827e8	0.129520
$593$	−5.62188e9	−1.10711	−0.553554	−	0.832813i	$-0.686729\pi$
$593$	−5.62188e9	−1.10711	−0.553554	+	0.832813i	$0.686729\pi$
$594$	3.45508e9	0.676403
$595$	9.74287e8	0.189617
$596$	5.55481e9	1.07475
$597$	6.00552e9	1.15516
$598$	−5.21734e8	−0.0997688
$599$	2.62393e9	0.498836	0.249418	−	0.968396i	$-0.419761\pi$
$599$	2.62393e9	0.498836	0.249418	+	0.968396i	$0.419761\pi$
$600$	−3.61602e9	−0.683442
$601$	5.85029e9	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$601$	5.85029e9	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$602$	−3.40620e8	−0.0636330
$603$	7.15085e9	1.32815
$604$	3.55870e9	0.657147
$605$	1.62527e9	0.298389
$606$	−1.90751e10	−3.48187
$607$	3.51051e9	0.637103	0.318552	−	0.947905i	$-0.396804\pi$
$607$	3.51051e9	0.637103	0.318552	+	0.947905i	$0.396804\pi$
$608$	−2.55444e9	−0.460928
$609$	3.17003e9	0.568725
$610$	5.73769e9	1.02349
$611$	1.56277e8	0.0277174
$612$	−1.81001e10	−3.19191
$613$	−6.95815e9	−1.22006	−0.610032	−	0.792377i	$-0.708843\pi$
$613$	−6.95815e9	−1.22006	−0.610032	+	0.792377i	$0.708843\pi$
$614$	5.87996e9	1.02514
$615$	−4.10907e9	−0.712329
$616$	4.80646e8	0.0828501
$617$	−7.18978e8	−0.123230	−0.0616151	−	0.998100i	$-0.519625\pi$
$617$	−7.18978e8	−0.123230	−0.0616151	+	0.998100i	$0.519625\pi$
$618$	1.14748e10	1.95563
$619$	−1.57508e9	−0.266922	−0.133461	−	0.991054i	$-0.542609\pi$
$619$	−1.57508e9	−0.266922	−0.133461	+	0.991054i	$0.542609\pi$
$620$	−3.40879e8	−0.0574420
$621$	−1.73869e9	−0.291340
$622$	5.46094e9	0.909916
$623$	−1.93451e9	−0.320526
$624$	−8.78205e8	−0.144694
$625$	2.78932e9	0.457003
$626$	−1.32017e9	−0.215090
$627$	1.89380e9	0.306829
$628$	−3.64753e9	−0.587678
$629$	2.42790e9	0.389003
$630$	−1.71955e9	−0.273983
$631$	8.53967e9	1.35313	0.676564	−	0.736384i	$-0.263468\pi$
$631$	8.53967e9	1.35313	0.676564	+	0.736384i	$0.263468\pi$
$632$	2.63685e9	0.415504
$633$	5.45202e9	0.854367
$634$	5.28899e7	0.00824252
$635$	−3.56087e9	−0.551885
$636$	−1.81714e10	−2.80084
$637$	−1.04977e9	−0.160918
$638$	7.54712e9	1.15056
$639$	1.55779e10	2.36186
$640$	2.93934e9	0.443221
$641$	−1.19699e9	−0.179509	−0.0897547	−	0.995964i	$-0.528608\pi$
$641$	−1.19699e9	−0.179509	−0.0897547	+	0.995964i	$0.528608\pi$
$642$	−2.82104e9	−0.420762
$643$	1.19758e10	1.77651	0.888254	−	0.459353i	$-0.151919\pi$
$643$	1.19758e10	1.77651	0.888254	+	0.459353i	$0.151919\pi$
$644$	−9.32733e8	−0.137612
$645$	7.21739e8	0.105906
$646$	−5.70068e9	−0.831979
$647$	−2.44410e9	−0.354776	−0.177388	−	0.984141i	$-0.556765\pi$
$647$	−2.44410e9	−0.354776	−0.177388	+	0.984141i	$0.556765\pi$
$648$	−9.82953e8	−0.141912
$649$	3.71230e9	0.533072
$650$	−1.50450e9	−0.214880
$651$	2.92614e8	0.0415682
$652$	1.70020e8	0.0240233
$653$	1.08778e10	1.52878	0.764389	−	0.644755i	$-0.223041\pi$
$653$	1.08778e10	1.52878	0.764389	+	0.644755i	$0.223041\pi$
$654$	1.83453e10	2.56450
$655$	−1.60270e9	−0.222847
$656$	−3.91077e9	−0.540877
$657$	1.62789e10	2.23948
$658$	4.86322e8	0.0665478
$659$	−9.90053e9	−1.34760	−0.673798	−	0.738916i	$-0.735338\pi$
$659$	−9.90053e9	−1.34760	−0.673798	+	0.738916i	$0.735338\pi$
$660$	−3.92739e9	−0.531741
$661$	−1.16773e9	−0.157267	−0.0786337	−	0.996904i	$-0.525056\pi$
$661$	−1.16773e9	−0.157267	−0.0786337	+	0.996904i	$0.525056\pi$
$662$	−1.09978e10	−1.47334
$663$	−3.26109e9	−0.434576
$664$	6.49680e9	0.861214
$665$	−3.11130e8	−0.0410266
$666$	−4.28509e9	−0.562082
$667$	−3.79791e9	−0.495570
$668$	1.62296e10	2.10664
$669$	−7.50503e9	−0.969083
$670$	−4.67062e9	−0.599946
$671$	−6.73644e9	−0.860799
$672$	−4.54737e9	−0.578053
$673$	−3.21526e9	−0.406596	−0.203298	−	0.979117i	$-0.565166\pi$
$673$	−3.21526e9	−0.406596	−0.203298	+	0.979117i	$0.565166\pi$
$674$	4.31380e9	0.542688
$675$	−5.01377e9	−0.627482
$676$	−1.05163e10	−1.30933
$677$	1.11460e10	1.38057	0.690287	−	0.723536i	$-0.257484\pi$
$677$	1.11460e10	1.38057	0.690287	+	0.723536i	$0.257484\pi$
$678$	7.29105e9	0.898434
$679$	1.51362e9	0.185556
$680$	3.06570e9	0.373894
$681$	−1.44146e10	−1.74899
$682$	6.96648e8	0.0840946
$683$	1.36119e10	1.63473	0.817364	−	0.576121i	$-0.195434\pi$
$683$	1.36119e10	1.63473	0.817364	+	0.576121i	$0.195434\pi$
$684$	5.78010e9	0.690620
$685$	3.88981e9	0.462394
$686$	−6.79497e9	−0.803624
$687$	−1.02075e10	−1.20107
$688$	6.86909e8	0.0804155
$689$	−1.96057e9	−0.228357
$690$	3.44023e9	0.398672
$691$	5.11725e9	0.590016	0.295008	−	0.955495i	$-0.404678\pi$
$691$	5.11725e9	0.590016	0.295008	+	0.955495i	$0.404678\pi$
$692$	1.82078e10	2.08875
$693$	2.01887e9	0.230432
$694$	1.37201e10	1.55812
$695$	5.69097e9	0.643042
$696$	9.97482e9	1.12143
$697$	−1.45221e10	−1.62448
$698$	−9.59153e9	−1.06756
$699$	−5.55495e9	−0.615191
$700$	−2.68968e9	−0.296386
$701$	−5.39916e9	−0.591988	−0.295994	−	0.955190i	$-0.595651\pi$
$701$	−5.39916e9	−0.591988	−0.295994	+	0.955190i	$0.595651\pi$
$702$	1.89995e9	0.207283
$703$	−7.75328e8	−0.0841670
$704$	−8.05771e9	−0.870377
$705$	−1.03047e9	−0.110757
$706$	1.85192e10	1.98064
$707$	−3.67933e9	−0.391562
$708$	1.89206e10	2.00363
$709$	−1.04570e9	−0.110191	−0.0550954	−	0.998481i	$-0.517546\pi$
$709$	−1.04570e9	−0.110191	−0.0550954	+	0.998481i	$0.517546\pi$
$710$	−1.01748e10	−1.06689
$711$	1.10756e10	1.15565
$712$	−6.08715e9	−0.632025
$713$	−3.50572e8	−0.0362213
$714$	−1.01483e10	−1.04339
$715$	−4.23738e8	−0.0433537
$716$	−1.30095e10	−1.32454
$717$	−3.96928e9	−0.402156
$718$	2.53373e10	2.55461
$719$	−6.61572e8	−0.0663783	−0.0331892	−	0.999449i	$-0.510566\pi$
$719$	−6.61572e8	−0.0663783	−0.0331892	+	0.999449i	$0.510566\pi$
$720$	3.46773e9	0.346243
$721$	2.21334e9	0.219925
$722$	−1.36828e10	−1.35299
$723$	−3.19887e10	−3.14784
$724$	−4.07049e9	−0.398623
$725$	−1.09519e10	−1.06735
$726$	−1.69290e10	−1.64192
$727$	1.73518e9	0.167484	0.0837421	−	0.996487i	$-0.473313\pi$
$727$	1.73518e9	0.167484	0.0837421	+	0.996487i	$0.473313\pi$
$728$	2.64308e8	0.0253893
$729$	−1.69778e10	−1.62306
$730$	−1.06327e10	−1.01161
$731$	2.55074e9	0.241522
$732$	−3.43338e10	−3.23544
$733$	−6.25015e9	−0.586174	−0.293087	−	0.956086i	$-0.594683\pi$
$733$	−6.25015e9	−0.586174	−0.293087	+	0.956086i	$0.594683\pi$
$734$	2.22651e10	2.07821
$735$	6.92199e9	0.643021
$736$	5.44807e9	0.503698
$737$	5.48362e9	0.504581
$738$	2.56306e10	2.34726
$739$	9.00137e9	0.820452	0.410226	−	0.911984i	$-0.365450\pi$
$739$	9.00137e9	0.820452	0.410226	+	0.911984i	$0.365450\pi$
$740$	1.60789e9	0.145863
$741$	1.04140e9	0.0940274
$742$	−6.10112e9	−0.548272
$743$	−1.37996e10	−1.23426	−0.617129	−	0.786862i	$-0.711704\pi$
$743$	−1.37996e10	−1.23426	−0.617129	+	0.786862i	$0.711704\pi$
$744$	9.20741e8	0.0819657
$745$	−3.95185e9	−0.350149
$746$	−8.43290e9	−0.743689
$747$	2.72887e10	2.39530
$748$	−1.38800e10	−1.21265
$749$	−5.44141e8	−0.0473178
$750$	2.22207e10	1.92328
$751$	2.50869e9	0.216126	0.108063	−	0.994144i	$-0.465535\pi$
$751$	2.50869e9	0.216126	0.108063	+	0.994144i	$0.465535\pi$
$752$	−9.80739e8	−0.0840990
$753$	−2.58972e10	−2.21040
$754$	4.15018e9	0.352588
$755$	−2.53176e9	−0.214096
$756$	3.39666e9	0.285907
$757$	−1.59957e10	−1.34020	−0.670099	−	0.742272i	$-0.733748\pi$
$757$	−1.59957e10	−1.34020	−0.670099	+	0.742272i	$0.733748\pi$
$758$	−2.34490e10	−1.95561
$759$	−4.03906e9	−0.335300
$760$	−9.79003e8	−0.0808978
$761$	−1.66651e10	−1.37076	−0.685378	−	0.728187i	$-0.740363\pi$
$761$	−1.66651e10	−1.37076	−0.685378	+	0.728187i	$0.740363\pi$
$762$	3.70904e10	3.03682
$763$	3.53856e9	0.288397
$764$	1.92982e10	1.56564
$765$	1.28769e10	1.03991
$766$	−1.08674e10	−0.873627
$767$	2.04140e9	0.163359
$768$	−1.98134e8	−0.0157832
$769$	9.23584e9	0.732376	0.366188	−	0.930541i	$-0.380663\pi$
$769$	9.23584e9	0.732376	0.366188	+	0.930541i	$0.380663\pi$
$770$	−1.31864e9	−0.104090
$771$	2.82374e10	2.21888
$772$	−2.03291e10	−1.59022
$773$	−2.96075e9	−0.230554	−0.115277	−	0.993333i	$-0.536776\pi$
$773$	−2.96075e9	−0.230554	−0.115277	+	0.993333i	$0.536776\pi$
$774$	−4.50190e9	−0.348981
$775$	−1.01093e9	−0.0780126
$776$	4.76278e9	0.365885
$777$	−1.38023e9	−0.105555
$778$	−2.24415e10	−1.70854
$779$	4.63751e9	0.351482
$780$	−2.15968e9	−0.162951
$781$	1.19459e10	0.897303
$782$	1.21583e10	0.909180
$783$	1.38305e10	1.02961
$784$	6.58795e9	0.488252
$785$	2.59496e9	0.191464
$786$	1.66938e10	1.22625
$787$	9.32429e9	0.681874	0.340937	−	0.940086i	$-0.389256\pi$
$787$	9.32429e9	0.681874	0.340937	+	0.940086i	$0.389256\pi$
$788$	−9.38176e9	−0.683034
$789$	−3.52062e10	−2.55182
$790$	−7.23411e9	−0.522024
$791$	1.40634e9	0.101036
$792$	6.35260e9	0.454374
$793$	−3.70438e9	−0.263791
$794$	4.24500e10	3.00958
$795$	1.29277e10	0.912504
$796$	1.40560e10	0.987796
$797$	−2.22955e10	−1.55996	−0.779978	−	0.625806i	$-0.784770\pi$
$797$	−2.22955e10	−1.55996	−0.779978	+	0.625806i	$0.784770\pi$
$798$	3.24076e9	0.225754
$799$	−3.64184e9	−0.252585
$800$	1.57104e10	1.08485
$801$	−2.55680e10	−1.75786
$802$	−1.46881e10	−1.00544
$803$	1.24835e10	0.850808
$804$	2.79486e10	1.89654
$805$	6.63573e8	0.0448336
$806$	3.83088e8	0.0257707
$807$	3.37247e10	2.25887
$808$	−1.15774e10	−0.772096
$809$	−5.80413e9	−0.385405	−0.192703	−	0.981257i	$-0.561725\pi$
$809$	−5.80413e9	−0.385405	−0.192703	+	0.981257i	$0.561725\pi$
$810$	2.69670e9	0.178293
$811$	−1.62210e10	−1.06783	−0.533917	−	0.845537i	$-0.679280\pi$
$811$	−1.62210e10	−1.06783	−0.533917	+	0.845537i	$0.679280\pi$
$812$	7.41951e9	0.486328
$813$	−2.80803e10	−1.83267
$814$	−3.28601e9	−0.213542
$815$	−1.20957e8	−0.00782671
$816$	2.04654e10	1.31858
$817$	−8.14557e8	−0.0522570
$818$	−1.85450e10	−1.18465
$819$	1.11018e9	0.0706156
$820$	−9.61736e9	−0.609126
$821$	6.33227e9	0.399354	0.199677	−	0.979862i	$-0.436011\pi$
$821$	6.33227e9	0.399354	0.199677	+	0.979862i	$0.436011\pi$
$822$	−4.05166e10	−2.54438
$823$	−2.22297e10	−1.39006	−0.695031	−	0.718980i	$-0.744609\pi$
$823$	−2.22297e10	−1.39006	−0.695031	+	0.718980i	$0.744609\pi$
$824$	6.96450e9	0.433655
$825$	−1.16473e10	−0.722162
$826$	6.35267e9	0.392216
$827$	−4.64860e9	−0.285794	−0.142897	−	0.989738i	$-0.545642\pi$
$827$	−4.64860e9	−0.285794	−0.142897	+	0.989738i	$0.545642\pi$
$828$	−1.23277e10	−0.754704
$829$	−8.14688e9	−0.496650	−0.248325	−	0.968677i	$-0.579880\pi$
$829$	−8.14688e9	−0.496650	−0.248325	+	0.968677i	$0.579880\pi$
$830$	−1.78238e10	−1.08200
$831$	−1.29189e10	−0.780950
$832$	−4.43095e9	−0.266726
$833$	2.44634e10	1.46643
$834$	−5.92777e10	−3.53842
$835$	−1.15462e10	−0.686335
$836$	4.43247e9	0.262376
$837$	1.27665e9	0.0752544
$838$	1.46417e10	0.859486
$839$	1.95604e10	1.14343	0.571715	−	0.820452i	$-0.306278\pi$
$839$	1.95604e10	1.14343	0.571715	+	0.820452i	$0.306278\pi$
$840$	−1.74281e9	−0.101455
$841$	1.29610e10	0.751366
$842$	−1.52216e10	−0.878757
$843$	−6.81516e9	−0.391814
$844$	1.27606e10	0.730586
$845$	7.48158e9	0.426574
$846$	6.42761e9	0.364967
$847$	−3.26537e9	−0.184646
$848$	1.23038e10	0.692873
$849$	−4.48641e10	−2.51607
$850$	3.50604e10	1.95817
$851$	1.65361e9	0.0919770
$852$	6.08849e10	3.37265
$853$	1.58440e10	0.874061	0.437031	−	0.899447i	$-0.356030\pi$
$853$	1.58440e10	0.874061	0.437031	+	0.899447i	$0.356030\pi$
$854$	−1.15277e10	−0.633346
$855$	−4.11213e9	−0.225002
$856$	−1.71220e9	−0.0933029
$857$	2.56284e10	1.39088	0.695438	−	0.718586i	$-0.255210\pi$
$857$	2.56284e10	1.39088	0.695438	+	0.718586i	$0.255210\pi$
$858$	4.41369e9	0.238559
$859$	−3.28663e9	−0.176919	−0.0884596	−	0.996080i	$-0.528194\pi$
$859$	−3.28663e9	−0.176919	−0.0884596	+	0.996080i	$0.528194\pi$
$860$	1.68925e9	0.0905624
$861$	8.25562e9	0.440797
$862$	−6.99092e8	−0.0371757
$863$	1.66288e10	0.880688	0.440344	−	0.897829i	$-0.354857\pi$
$863$	1.66288e10	0.880688	0.440344	+	0.897829i	$0.354857\pi$
$864$	−1.98398e10	−1.04650
$865$	−1.29536e10	−0.680508
$866$	1.74152e10	0.911205
$867$	4.56980e10	2.38139
$868$	6.84869e8	0.0355458
$869$	8.49334e9	0.439045
$870$	−2.73656e10	−1.40892
$871$	3.01545e9	0.154628
$872$	1.11344e10	0.568671
$873$	2.00052e10	1.01764
$874$	−3.88265e9	−0.196715
$875$	4.28607e9	0.216287
$876$	6.36250e10	3.19789
$877$	−6.52780e9	−0.326790	−0.163395	−	0.986561i	$-0.552244\pi$
$877$	−6.52780e9	−0.326790	−0.163395	+	0.986561i	$0.552244\pi$
$878$	1.06415e10	0.530603
$879$	−3.04810e10	−1.51380
$880$	2.65922e9	0.131542
$881$	2.61062e10	1.28626	0.643128	−	0.765759i	$-0.277636\pi$
$881$	2.61062e10	1.28626	0.643128	+	0.765759i	$0.277636\pi$
$882$	−4.31764e10	−2.11888
$883$	9.02672e9	0.441232	0.220616	−	0.975361i	$-0.429193\pi$
$883$	9.02672e9	0.441232	0.220616	+	0.975361i	$0.429193\pi$
$884$	−7.63266e9	−0.371615
$885$	−1.34607e10	−0.652777
$886$	−3.06903e10	−1.48246
$887$	2.03347e9	0.0978372	0.0489186	−	0.998803i	$-0.484423\pi$
$887$	2.03347e9	0.0978372	0.0489186	+	0.998803i	$0.484423\pi$
$888$	−4.34303e9	−0.208136
$889$	7.15423e9	0.341513
$890$	1.66999e10	0.794051
$891$	−3.16611e9	−0.149953
$892$	−1.75657e10	−0.828682
$893$	1.16299e9	0.0546507
$894$	4.11628e10	1.92674
$895$	9.25537e9	0.431532
$896$	−5.90551e9	−0.274270
$897$	−2.22109e9	−0.102752
$898$	−3.96637e10	−1.82779
$899$	2.78866e9	0.128008
$900$	−3.55489e10	−1.62546
$901$	4.56884e10	2.08099
$902$	1.96548e10	0.891755
$903$	−1.45006e9	−0.0655360
$904$	4.42521e9	0.199225
$905$	2.89587e9	0.129870
$906$	2.63711e10	1.17809
$907$	3.47024e10	1.54431	0.772155	−	0.635435i	$-0.219179\pi$
$907$	3.47024e10	1.54431	0.772155	+	0.635435i	$0.219179\pi$
$908$	−3.37376e10	−1.49559
$909$	−4.86288e10	−2.14744
$910$	−7.25121e8	−0.0318982
$911$	−3.83459e10	−1.68037	−0.840183	−	0.542302i	$-0.817553\pi$
$911$	−3.83459e10	−1.68037	−0.840183	+	0.542302i	$0.817553\pi$
$912$	−6.53545e9	−0.285295
$913$	2.09263e10	0.910007
$914$	1.52518e10	0.660706
$915$	2.44261e10	1.05410
$916$	−2.38908e10	−1.02706
$917$	3.22002e9	0.137900
$918$	−4.42759e10	−1.88894
$919$	7.63731e9	0.324591	0.162295	−	0.986742i	$-0.448110\pi$
$919$	7.63731e9	0.324591	0.162295	+	0.986742i	$0.448110\pi$
$920$	2.08800e9	0.0884044
$921$	2.50317e10	1.05580
$922$	2.49450e10	1.04815
$923$	6.56905e9	0.274977
$924$	7.89061e9	0.329048
$925$	4.76844e9	0.198098
$926$	−5.91203e10	−2.44680
$927$	2.92532e10	1.20613
$928$	−4.33372e10	−1.78009
$929$	−1.44540e10	−0.591469	−0.295734	−	0.955270i	$-0.595564\pi$
$929$	−1.44540e10	−0.591469	−0.295734	+	0.955270i	$0.595564\pi$
$930$	−2.52602e9	−0.102979
$931$	−7.81218e9	−0.317284
$932$	−1.30015e10	−0.526062
$933$	2.32479e10	0.937127
$934$	5.22202e10	2.09713
$935$	9.87466e9	0.395077
$936$	3.49330e9	0.139242
$937$	−2.76136e10	−1.09656	−0.548282	−	0.836293i	$-0.684718\pi$
$937$	−2.76136e10	−1.09656	−0.548282	+	0.836293i	$0.684718\pi$
$938$	9.38384e9	0.371254
$939$	−5.62014e9	−0.221522
$940$	−2.41183e9	−0.0947108
$941$	1.88863e10	0.738894	0.369447	−	0.929252i	$-0.379547\pi$
$941$	1.88863e10	0.738894	0.369447	+	0.929252i	$0.379547\pi$
$942$	−2.70293e10	−1.05355
$943$	−9.89081e9	−0.384097
$944$	−1.28111e10	−0.495659
$945$	−2.41648e9	−0.0931476
$946$	−3.45228e9	−0.132583
$947$	−1.55375e10	−0.594506	−0.297253	−	0.954799i	$-0.596070\pi$
$947$	−1.55375e10	−0.594506	−0.297253	+	0.954799i	$0.596070\pi$
$948$	4.32883e10	1.65022
$949$	6.86469e9	0.260729
$950$	−1.11962e10	−0.423681
$951$	2.25159e8	0.00848902
$952$	−6.15936e9	−0.231370
$953$	−1.05814e10	−0.396021	−0.198011	−	0.980200i	$-0.563448\pi$
$953$	−1.05814e10	−0.396021	−0.198011	+	0.980200i	$0.563448\pi$
$954$	−8.06372e10	−3.00688
$955$	−1.37293e10	−0.510079
$956$	−9.29019e9	−0.343892
$957$	3.21291e10	1.18497
$958$	6.50768e8	0.0239137
$959$	−7.81511e9	−0.286134
$960$	2.92170e10	1.06582
$961$	−2.72552e10	−0.990644
$962$	−1.80699e9	−0.0654398
$963$	−7.19178e9	−0.259504
$964$	−7.48701e10	−2.69178
$965$	1.44627e10	0.518090
$966$	−6.91184e9	−0.246703
$967$	−1.98827e9	−0.0707102	−0.0353551	−	0.999375i	$-0.511256\pi$
$967$	−1.98827e9	−0.0707102	−0.0353551	+	0.999375i	$0.511256\pi$
$968$	−1.02748e10	−0.364092
$969$	−2.42685e10	−0.856860
$970$	−1.30665e10	−0.459684
$971$	−1.06982e10	−0.375012	−0.187506	−	0.982263i	$-0.560040\pi$
$971$	−1.06982e10	−0.375012	−0.187506	+	0.982263i	$0.560040\pi$
$972$	−4.62103e10	−1.61401
$973$	−1.14339e10	−0.397922
$974$	2.33825e9	0.0810838
$975$	−6.40485e9	−0.221306
$976$	2.32473e10	0.800384
$977$	−3.25937e10	−1.11816	−0.559078	−	0.829115i	$-0.688845\pi$
$977$	−3.25937e10	−1.11816	−0.559078	+	0.829115i	$0.688845\pi$
$978$	1.25990e9	0.0430675
$979$	−1.96068e10	−0.667832
$980$	1.62011e10	0.549860
$981$	4.67683e10	1.58165
$982$	2.18931e10	0.737764
$983$	−3.26564e10	−1.09656	−0.548278	−	0.836296i	$-0.684716\pi$
$983$	−3.26564e10	−1.09656	−0.548278	+	0.836296i	$0.684716\pi$
$984$	2.59772e10	0.869179
$985$	6.67446e9	0.222530
$986$	−9.67145e10	−3.21309
$987$	2.07034e9	0.0685379
$988$	2.43742e9	0.0804047
$989$	1.73728e9	0.0571060
$990$	−1.74281e10	−0.570858
$991$	1.86068e10	0.607316	0.303658	−	0.952781i	$-0.401792\pi$
$991$	1.86068e10	0.607316	0.303658	+	0.952781i	$0.401792\pi$
$992$	−4.00030e9	−0.130107
$993$	−4.68189e10	−1.51740
$994$	2.04424e10	0.660205
$995$	−9.99987e9	−0.321821
$996$	1.06656e11	3.42040
$997$	5.77600e10	1.84584	0.922920	−	0.384993i	$-0.125796\pi$
$997$	5.77600e10	1.84584	0.922920	+	0.384993i	$0.125796\pi$
$998$	−2.32575e10	−0.740638
$999$	−6.02181e9	−0.191094

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.a.b.1.11	✓	13
3.2	odd	2		387.8.a.d.1.3		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.a.b.1.11	✓	13	1.1	even	1	trivial
387.8.a.d.1.3		13	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	43.a (trivial)

\(f(q)\)	\(=\)	\(q+17.3440 q^{2} +73.8355 q^{3} +172.814 q^{4} -122.945 q^{5} +1280.60 q^{6} +247.011 q^{7} +777.246 q^{8} +3264.69 q^{9} +O(q^{10})\)	\(q+17.3440 q^{2} +73.8355 q^{3} +172.814 q^{4} -122.945 q^{5} +1280.60 q^{6} +247.011 q^{7} +777.246 q^{8} +3264.69 q^{9} -2132.35 q^{10} +2503.52 q^{11} +12759.8 q^{12} +1376.69 q^{13} +4284.15 q^{14} -9077.68 q^{15} -8639.60 q^{16} -32082.0 q^{17} +56622.6 q^{18} +10245.1 q^{19} -21246.5 q^{20} +18238.2 q^{21} +43421.0 q^{22} -21850.6 q^{23} +57388.4 q^{24} -63009.6 q^{25} +23877.3 q^{26} +79571.5 q^{27} +42686.8 q^{28} +173813. q^{29} -157443. q^{30} +16044.0 q^{31} -249333. q^{32} +184849. q^{33} -556429. q^{34} -30368.6 q^{35} +564182. q^{36} -75677.9 q^{37} +177691. q^{38} +101649. q^{39} -95558.2 q^{40} +452656. q^{41} +316323. q^{42} -79507.0 q^{43} +432643. q^{44} -401375. q^{45} -378977. q^{46} +113517. q^{47} -637910. q^{48} -762529. q^{49} -1.09284e6 q^{50} -2.36879e6 q^{51} +237911. q^{52} -1.42412e6 q^{53} +1.38009e6 q^{54} -307794. q^{55} +191988. q^{56} +756453. q^{57} +3.01460e6 q^{58} +1.48283e6 q^{59} -1.56875e6 q^{60} -2.69078e6 q^{61} +278267. q^{62} +806413. q^{63} -3.21855e6 q^{64} -169257. q^{65} +3.20601e6 q^{66} +2.19036e6 q^{67} -5.54420e6 q^{68} -1.61335e6 q^{69} -526713. q^{70} +4.77162e6 q^{71} +2.53746e6 q^{72} +4.98637e6 q^{73} -1.31256e6 q^{74} -4.65235e6 q^{75} +1.77049e6 q^{76} +618397. q^{77} +1.76299e6 q^{78} +3.39256e6 q^{79} +1.06219e6 q^{80} -1.26466e6 q^{81} +7.85086e6 q^{82} +8.35875e6 q^{83} +3.15180e6 q^{84} +3.94431e6 q^{85} -1.37897e6 q^{86} +1.28336e7 q^{87} +1.94585e6 q^{88} -7.83169e6 q^{89} -6.96145e6 q^{90} +340058. q^{91} -3.77608e6 q^{92} +1.18462e6 q^{93} +1.96883e6 q^{94} -1.25958e6 q^{95} -1.84096e7 q^{96} +6.12777e6 q^{97} -1.32253e7 q^{98} +8.17321e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 16 q^{2} + 94 q^{3} + 922 q^{4} + 998 q^{5} + 183 q^{6} + 1360 q^{7} + 3870 q^{8} + 10011 q^{9}+O(q^{10}) \) 13 * q + 16 * q^2 + 94 * q^3 + 922 * q^4 + 998 * q^5 + 183 * q^6 + 1360 * q^7 + 3870 * q^8 + 10011 * q^9	\( 13 q + 16 q^{2} + 94 q^{3} + 922 q^{4} + 998 q^{5} + 183 q^{6} + 1360 q^{7} + 3870 q^{8} + 10011 q^{9} + 4667 q^{10} + 1620 q^{11} - 19681 q^{12} + 13550 q^{13} + 44160 q^{14} + 31412 q^{15} + 114026 q^{16} + 110880 q^{17} + 159267 q^{18} + 105058 q^{19} + 167251 q^{20} + 129840 q^{21} + 201504 q^{22} + 160184 q^{23} + 161289 q^{24} + 270149 q^{25} + 272104 q^{26} + 252544 q^{27} + 208172 q^{28} + 285546 q^{29} + 107580 q^{30} - 99616 q^{31} + 200126 q^{32} + 531468 q^{33} - 80941 q^{34} - 187104 q^{35} - 608975 q^{36} + 176038 q^{37} + 652165 q^{38} - 794680 q^{39} - 895387 q^{40} - 410260 q^{41} - 3413218 q^{42} - 1033591 q^{43} - 2177076 q^{44} - 1051178 q^{45} - 3975765 q^{46} - 424556 q^{47} - 2360477 q^{48} - 1561359 q^{49} - 4063801 q^{50} - 2375738 q^{51} - 4172312 q^{52} + 3992458 q^{53} - 10438626 q^{54} + 406960 q^{55} + 1559556 q^{56} - 3116152 q^{57} - 4052005 q^{58} + 2248836 q^{59} - 2911436 q^{60} + 6210394 q^{61} + 885317 q^{62} + 11622368 q^{63} - 3096318 q^{64} + 5600420 q^{65} - 2174604 q^{66} - 1993648 q^{67} + 9327135 q^{68} + 13366240 q^{69} - 1105098 q^{70} + 4978064 q^{71} + 11370663 q^{72} + 8224814 q^{73} - 3613563 q^{74} + 27115592 q^{75} + 10687121 q^{76} + 17261892 q^{77} - 15226630 q^{78} + 6945708 q^{79} + 15822799 q^{80} + 35113185 q^{81} - 508449 q^{82} + 22937328 q^{83} - 14010106 q^{84} - 575532 q^{85} - 1272112 q^{86} + 9081380 q^{87} + 11202656 q^{88} + 9291302 q^{89} + 2841402 q^{90} + 25581108 q^{91} - 14388137 q^{92} + 25930480 q^{93} - 24645805 q^{94} + 30750464 q^{95} - 22461255 q^{96} + 10001852 q^{97} - 32304856 q^{98} + 5055452 q^{99}+O(q^{100}) \) 13 * q + 16 * q^2 + 94 * q^3 + 922 * q^4 + 998 * q^5 + 183 * q^6 + 1360 * q^7 + 3870 * q^8 + 10011 * q^9 + 4667 * q^10 + 1620 * q^11 - 19681 * q^12 + 13550 * q^13 + 44160 * q^14 + 31412 * q^15 + 114026 * q^16 + 110880 * q^17 + 159267 * q^18 + 105058 * q^19 + 167251 * q^20 + 129840 * q^21 + 201504 * q^22 + 160184 * q^23 + 161289 * q^24 + 270149 * q^25 + 272104 * q^26 + 252544 * q^27 + 208172 * q^28 + 285546 * q^29 + 107580 * q^30 - 99616 * q^31 + 200126 * q^32 + 531468 * q^33 - 80941 * q^34 - 187104 * q^35 - 608975 * q^36 + 176038 * q^37 + 652165 * q^38 - 794680 * q^39 - 895387 * q^40 - 410260 * q^41 - 3413218 * q^42 - 1033591 * q^43 - 2177076 * q^44 - 1051178 * q^45 - 3975765 * q^46 - 424556 * q^47 - 2360477 * q^48 - 1561359 * q^49 - 4063801 * q^50 - 2375738 * q^51 - 4172312 * q^52 + 3992458 * q^53 - 10438626 * q^54 + 406960 * q^55 + 1559556 * q^56 - 3116152 * q^57 - 4052005 * q^58 + 2248836 * q^59 - 2911436 * q^60 + 6210394 * q^61 + 885317 * q^62 + 11622368 * q^63 - 3096318 * q^64 + 5600420 * q^65 - 2174604 * q^66 - 1993648 * q^67 + 9327135 * q^68 + 13366240 * q^69 - 1105098 * q^70 + 4978064 * q^71 + 11370663 * q^72 + 8224814 * q^73 - 3613563 * q^74 + 27115592 * q^75 + 10687121 * q^76 + 17261892 * q^77 - 15226630 * q^78 + 6945708 * q^79 + 15822799 * q^80 + 35113185 * q^81 - 508449 * q^82 + 22937328 * q^83 - 14010106 * q^84 - 575532 * q^85 - 1272112 * q^86 + 9081380 * q^87 + 11202656 * q^88 + 9291302 * q^89 + 2841402 * q^90 + 25581108 * q^91 - 14388137 * q^92 + 25930480 * q^93 - 24645805 * q^94 + 30750464 * q^95 - 22461255 * q^96 + 10001852 * q^97 - 32304856 * q^98 + 5055452 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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