LMFDB - Embedded newform 43.8.a.b.1.6

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			1.6
Root			$-4.71679$ 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)

$f(q)$	$=$	$q-3.71679 q^{2} -24.7485 q^{3} -114.185 q^{4} +385.350 q^{5} +91.9851 q^{6} -1546.77 q^{7} +900.153 q^{8} -1574.51 q^{9} +O(q^{10})$	\(q-3.71679 q^{2} -24.7485 q^{3} -114.185 q^{4} +385.350 q^{5} +91.9851 q^{6} -1546.77 q^{7} +900.153 q^{8} -1574.51 q^{9} -1432.27 q^{10} -1662.15 q^{11} +2825.92 q^{12} +12725.9 q^{13} +5749.00 q^{14} -9536.85 q^{15} +11270.1 q^{16} +23803.1 q^{17} +5852.12 q^{18} +30546.0 q^{19} -44001.4 q^{20} +38280.2 q^{21} +6177.85 q^{22} -63784.8 q^{23} -22277.4 q^{24} +70369.8 q^{25} -47299.5 q^{26} +93091.8 q^{27} +176618. q^{28} +190003. q^{29} +35446.5 q^{30} +143977. q^{31} -157108. q^{32} +41135.6 q^{33} -88471.1 q^{34} -596047. q^{35} +179786. q^{36} -53873.0 q^{37} -113533. q^{38} -314947. q^{39} +346874. q^{40} -355277. q^{41} -142279. q^{42} -79507.0 q^{43} +189793. q^{44} -606738. q^{45} +237075. q^{46} -39435.7 q^{47} -278917. q^{48} +1.56894e6 q^{49} -261550. q^{50} -589091. q^{51} -1.45311e6 q^{52} +1.01320e6 q^{53} -346003. q^{54} -640508. q^{55} -1.39233e6 q^{56} -755970. q^{57} -706202. q^{58} +1.24979e6 q^{59} +1.08897e6 q^{60} -751833. q^{61} -535133. q^{62} +2.43540e6 q^{63} -858631. q^{64} +4.90393e6 q^{65} -152893. q^{66} -3.22613e6 q^{67} -2.71797e6 q^{68} +1.57858e6 q^{69} +2.21538e6 q^{70} +1.10265e6 q^{71} -1.41730e6 q^{72} +4.53962e6 q^{73} +200235. q^{74} -1.74155e6 q^{75} -3.48791e6 q^{76} +2.57095e6 q^{77} +1.17059e6 q^{78} +3.63589e6 q^{79} +4.34292e6 q^{80} +1.13957e6 q^{81} +1.32049e6 q^{82} -149479. q^{83} -4.37104e6 q^{84} +9.17253e6 q^{85} +295511. q^{86} -4.70230e6 q^{87} -1.49618e6 q^{88} -8.46943e6 q^{89} +2.25512e6 q^{90} -1.96840e7 q^{91} +7.28329e6 q^{92} -3.56322e6 q^{93} +146574. q^{94} +1.17709e7 q^{95} +3.88819e6 q^{96} +5.99834e6 q^{97} -5.83143e6 q^{98} +2.61707e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.71679	−0.328521	−0.164260	−	0.986417i	$-0.552524\pi$
$2$	−3.71679	−0.328521	−0.164260	+	0.986417i	$0.552524\pi$
$3$	−24.7485	−0.529206	−0.264603	−	0.964357i	$-0.585241\pi$
$3$	−24.7485	−0.529206	−0.264603	+	0.964357i	$0.585241\pi$
$4$	−114.185	−0.892074
$5$	385.350	1.37867	0.689336	−	0.724442i	$-0.257903\pi$
$5$	385.350	1.37867	0.689336	+	0.724442i	$0.257903\pi$
$6$	91.9851	0.173855
$7$	−1546.77	−1.70444	−0.852219	−	0.523185i	$-0.824744\pi$
$7$	−1546.77	−1.70444	−0.852219	+	0.523185i	$0.824744\pi$
$8$	900.153	0.621586
$9$	−1574.51	−0.719941
$10$	−1432.27	−0.452922
$11$	−1662.15	−0.376526	−0.188263	−	0.982119i	$-0.560286\pi$
$11$	−1662.15	−0.376526	−0.188263	+	0.982119i	$0.560286\pi$
$12$	2825.92	0.472091
$13$	12725.9	1.60652	0.803261	−	0.595628i	$-0.203097\pi$
$13$	12725.9	1.60652	0.803261	+	0.595628i	$0.203097\pi$
$14$	5749.00	0.559944
$15$	−9536.85	−0.729601
$16$	11270.1	0.687870
$17$	23803.1	1.17507	0.587533	−	0.809200i	$-0.300099\pi$
$17$	23803.1	1.17507	0.587533	+	0.809200i	$0.300099\pi$
$18$	5852.12	0.236516
$19$	30546.0	1.02169	0.510843	−	0.859674i	$-0.329333\pi$
$19$	30546.0	1.02169	0.510843	+	0.859674i	$0.329333\pi$
$20$	−44001.4	−1.22988
$21$	38280.2	0.902000
$22$	6177.85	0.123697
$23$	−63784.8	−1.09312	−0.546562	−	0.837419i	$-0.684064\pi$
$23$	−63784.8	−1.09312	−0.546562	+	0.837419i	$0.684064\pi$
$24$	−22277.4	−0.328947
$25$	70369.8	0.900734
$26$	−47299.5	−0.527776
$27$	93091.8	0.910203
$28$	176618.	1.52049
$29$	190003.	1.44666	0.723332	−	0.690500i	$-0.242609\pi$
$29$	190003.	1.44666	0.723332	+	0.690500i	$0.242609\pi$
$30$	35446.5	0.239689
$31$	143977.	0.868015	0.434008	−	0.900909i	$-0.357099\pi$
$31$	143977.	0.868015	0.434008	+	0.900909i	$0.357099\pi$
$32$	−157108.	−0.847566
$33$	41135.6	0.199260
$34$	−88471.1	−0.386034
$35$	−596047.	−2.34986
$36$	179786.	0.642240
$37$	−53873.0	−0.174850	−0.0874249	−	0.996171i	$-0.527864\pi$
$37$	−53873.0	−0.174850	−0.0874249	+	0.996171i	$0.527864\pi$
$38$	−113533.	−0.335645
$39$	−314947.	−0.850181
$40$	346874.	0.856963
$41$	−355277.	−0.805051	−0.402526	−	0.915409i	$-0.631868\pi$
$41$	−355277.	−0.805051	−0.402526	+	0.915409i	$0.631868\pi$
$42$	−142279.	−0.296326
$43$	−79507.0	−0.152499
$43$	−79507.0	−0.152499
$44$	189793.	0.335889
$45$	−606738.	−0.992561
$46$	237075.	0.359114
$47$	−39435.7	−0.0554047	−0.0277024	−	0.999616i	$-0.508819\pi$
$47$	−39435.7	−0.0554047	−0.0277024	+	0.999616i	$0.508819\pi$
$48$	−278917.	−0.364025
$49$	1.56894e6	1.90511
$50$	−261550.	−0.295910
$51$	−589091.	−0.621852
$52$	−1.45311e6	−1.43314
$53$	1.01320e6	0.934823	0.467411	−	0.884040i	$-0.345187\pi$
$53$	1.01320e6	0.934823	0.467411	+	0.884040i	$0.345187\pi$
$54$	−346003.	−0.299021
$55$	−640508.	−0.519105
$56$	−1.39233e6	−1.05946
$57$	−755970.	−0.540682
$58$	−706202.	−0.475260
$59$	1.24979e6	0.792236	0.396118	−	0.918200i	$-0.370357\pi$
$59$	1.24979e6	0.792236	0.396118	+	0.918200i	$0.370357\pi$
$60$	1.08897e6	0.650858
$61$	−751833.	−0.424098	−0.212049	−	0.977259i	$-0.568014\pi$
$61$	−751833.	−0.424098	−0.212049	+	0.977259i	$0.568014\pi$
$62$	−535133.	−0.285161
$63$	2.43540e6	1.22709
$64$	−858631.	−0.409427
$65$	4.90393e6	2.21486
$66$	−152893.	−0.0654610
$67$	−3.22613e6	−1.31045	−0.655224	−	0.755435i	$-0.727426\pi$
$67$	−3.22613e6	−1.31045	−0.655224	+	0.755435i	$0.727426\pi$
$68$	−2.71797e6	−1.04825
$69$	1.57858e6	0.578488
$70$	2.21538e6	0.771978
$71$	1.10265e6	0.365623	0.182811	−	0.983148i	$-0.441480\pi$
$71$	1.10265e6	0.365623	0.182811	+	0.983148i	$0.441480\pi$
$72$	−1.41730e6	−0.447505
$73$	4.53962e6	1.36581	0.682904	−	0.730508i	$-0.260717\pi$
$73$	4.53962e6	1.36581	0.682904	+	0.730508i	$0.260717\pi$
$74$	200235.	0.0574418
$75$	−1.74155e6	−0.476674
$76$	−3.48791e6	−0.911419
$77$	2.57095e6	0.641765
$78$	1.17059e6	0.279302
$79$	3.63589e6	0.829691	0.414846	−	0.909892i	$-0.363836\pi$
$79$	3.63589e6	0.829691	0.414846	+	0.909892i	$0.363836\pi$
$80$	4.34292e6	0.948347
$81$	1.13957e6	0.238255
$82$	1.32049e6	0.264476
$83$	−149479.	−0.0286951	−0.0143476	−	0.999897i	$-0.504567\pi$
$83$	−149479.	−0.0286951	−0.0143476	+	0.999897i	$0.504567\pi$
$84$	−4.37104e6	−0.804650
$85$	9.17253e6	1.62003
$86$	295511.	0.0500990
$87$	−4.70230e6	−0.765584
$88$	−1.49618e6	−0.234043
$89$	−8.46943e6	−1.27347	−0.636736	−	0.771082i	$-0.719716\pi$
$89$	−8.46943e6	−1.27347	−0.636736	+	0.771082i	$0.719716\pi$
$90$	2.25512e6	0.326077
$91$	−1.96840e7	−2.73822
$92$	7.28329e6	0.975148
$93$	−3.56322e6	−0.459359
$94$	146574.	0.0182016
$95$	1.17709e7	1.40857
$96$	3.88819e6	0.448537
$97$	5.99834e6	0.667313	0.333657	−	0.942695i	$-0.391717\pi$
$97$	5.99834e6	0.667313	0.333657	+	0.942695i	$0.391717\pi$
$98$	−5.83143e6	−0.625869
$99$	2.61707e6	0.271076
$100$	−8.03521e6	−0.803521
$101$	−8.50960e6	−0.821834	−0.410917	−	0.911673i	$-0.634791\pi$
$101$	−8.50960e6	−0.821834	−0.410917	+	0.911673i	$0.634791\pi$
$102$	2.18953e6	0.204291
$103$	1.74827e6	0.157644	0.0788222	−	0.996889i	$-0.474884\pi$
$103$	1.74827e6	0.157644	0.0788222	+	0.996889i	$0.474884\pi$
$104$	1.14552e7	0.998591
$105$	1.47513e7	1.24356
$106$	−3.76585e6	−0.307109
$107$	1.06723e7	0.842196	0.421098	−	0.907015i	$-0.361645\pi$
$107$	1.06723e7	0.842196	0.421098	+	0.907015i	$0.361645\pi$
$108$	−1.06297e7	−0.811969
$109$	5.16184e6	0.381779	0.190889	−	0.981612i	$-0.438863\pi$
$109$	5.16184e6	0.381779	0.190889	+	0.981612i	$0.438863\pi$
$110$	2.38063e6	0.170537
$111$	1.33328e6	0.0925316
$112$	−1.74321e7	−1.17243
$113$	1.76860e7	1.15307	0.576534	−	0.817073i	$-0.304405\pi$
$113$	1.76860e7	1.15307	0.576534	+	0.817073i	$0.304405\pi$
$114$	2.80978e6	0.177626
$115$	−2.45795e7	−1.50706
$116$	−2.16956e7	−1.29053
$117$	−2.00370e7	−1.15660
$118$	−4.64520e6	−0.260266
$119$	−3.68178e7	−2.00283
$120$	−8.58462e6	−0.453510
$121$	−1.67244e7	−0.858228
$122$	2.79440e6	0.139325
$123$	8.79258e6	0.426038
$124$	−1.64401e7	−0.774334
$125$	−2.98845e6	−0.136855
$126$	−9.05187e6	−0.403126
$127$	4.09391e7	1.77347	0.886737	−	0.462274i	$-0.152966\pi$
$127$	4.09391e7	1.77347	0.886737	+	0.462274i	$0.152966\pi$
$128$	2.33012e7	0.982071
$129$	1.96768e6	0.0807032
$130$	−1.82269e7	−0.727629
$131$	4.15303e7	1.61404	0.807021	−	0.590522i	$-0.201078\pi$
$131$	4.15303e7	1.61404	0.807021	+	0.590522i	$0.201078\pi$
$132$	−4.69709e6	−0.177754
$133$	−4.72476e7	−1.74140
$134$	1.19908e7	0.430509
$135$	3.58730e7	1.25487
$136$	2.14264e7	0.730404
$137$	−3.50608e7	−1.16493	−0.582466	−	0.812855i	$-0.697912\pi$
$137$	−3.50608e7	−1.16493	−0.582466	+	0.812855i	$0.697912\pi$
$138$	−5.86725e6	−0.190045
$139$	5.57867e7	1.76189	0.880945	−	0.473219i	$-0.156908\pi$
$139$	5.57867e7	1.76189	0.880945	+	0.473219i	$0.156908\pi$
$140$	6.80599e7	2.09625
$141$	975974.	0.0293205
$142$	−4.09831e6	−0.120115
$143$	−2.11523e7	−0.604897
$144$	−1.77448e7	−0.495226
$145$	7.32178e7	1.99447
$146$	−1.68728e7	−0.448697
$147$	−3.88290e7	−1.00820
$148$	6.15151e6	0.155979
$149$	−1.78918e7	−0.443099	−0.221550	−	0.975149i	$-0.571112\pi$
$149$	−1.78918e7	−0.443099	−0.221550	+	0.975149i	$0.571112\pi$
$150$	6.47298e6	0.156597
$151$	−2.85564e7	−0.674970	−0.337485	−	0.941331i	$-0.609576\pi$
$151$	−2.85564e7	−0.674970	−0.337485	+	0.941331i	$0.609576\pi$
$152$	2.74961e7	0.635065
$153$	−3.74782e7	−0.845978
$154$	−9.55568e6	−0.210833
$155$	5.54816e7	1.19671
$156$	3.59624e7	0.758424
$157$	6.75273e7	1.39261	0.696307	−	0.717744i	$-0.254825\pi$
$157$	6.75273e7	1.39261	0.696307	+	0.717744i	$0.254825\pi$
$158$	−1.35139e7	−0.272571
$159$	−2.50752e7	−0.494714
$160$	−6.05416e7	−1.16851
$161$	9.86601e7	1.86316
$162$	−4.23554e6	−0.0782719
$163$	−7.20769e7	−1.30359	−0.651793	−	0.758397i	$-0.725983\pi$
$163$	−7.20769e7	−1.30359	−0.651793	+	0.758397i	$0.725983\pi$
$164$	4.05675e7	0.718165
$165$	1.58516e7	0.274714
$166$	555583.	0.00942694
$167$	2.87709e7	0.478019	0.239010	−	0.971017i	$-0.423177\pi$
$167$	2.87709e7	0.478019	0.239010	+	0.971017i	$0.423177\pi$
$168$	3.44580e7	0.560670
$169$	9.91998e7	1.58091
$170$	−3.40924e7	−0.532213
$171$	−4.80951e7	−0.735553
$172$	9.07854e6	0.136040
$173$	−1.24594e8	−1.82951	−0.914755	−	0.404010i	$-0.867616\pi$
$173$	−1.24594e8	−1.82951	−0.914755	+	0.404010i	$0.867616\pi$
$174$	1.74775e7	0.251510
$175$	−1.08846e8	−1.53525
$176$	−1.87325e7	−0.259001
$177$	−3.09304e7	−0.419256
$178$	3.14791e7	0.418362
$179$	−1.45448e7	−0.189550	−0.0947749	−	0.995499i	$-0.530213\pi$
$179$	−1.45448e7	−0.189550	−0.0947749	+	0.995499i	$0.530213\pi$
$180$	6.92807e7	0.885438
$181$	−4.71999e7	−0.591651	−0.295826	−	0.955242i	$-0.595595\pi$
$181$	−4.71999e7	−0.591651	−0.295826	+	0.955242i	$0.595595\pi$
$182$	7.31612e7	0.899562
$183$	1.86067e7	0.224436
$184$	−5.74160e7	−0.679471
$185$	−2.07600e7	−0.241060
$186$	1.32437e7	0.150909
$187$	−3.95642e7	−0.442442
$188$	4.50298e6	0.0494251
$189$	−1.43991e8	−1.55139
$190$	−4.37501e7	−0.462744
$191$	−5.66800e6	−0.0588590	−0.0294295	−	0.999567i	$-0.509369\pi$
$191$	−5.66800e6	−0.0588590	−0.0294295	+	0.999567i	$0.509369\pi$
$192$	2.12498e7	0.216671
$193$	1.30205e8	1.30369	0.651847	−	0.758350i	$-0.273994\pi$
$193$	1.30205e8	1.30369	0.651847	+	0.758350i	$0.273994\pi$
$194$	−2.22946e7	−0.219226
$195$	−1.21365e8	−1.17212
$196$	−1.79150e8	−1.69950
$197$	1.88254e8	1.75434	0.877169	−	0.480182i	$-0.159429\pi$
$197$	1.88254e8	1.75434	0.877169	+	0.480182i	$0.159429\pi$
$198$	−9.72708e6	−0.0890542
$199$	1.14630e8	1.03113	0.515564	−	0.856851i	$-0.327583\pi$
$199$	1.14630e8	1.03113	0.515564	+	0.856851i	$0.327583\pi$
$200$	6.33436e7	0.559884
$201$	7.98419e7	0.693497
$202$	3.16284e7	0.269990
$203$	−2.93890e8	−2.46575
$204$	6.72657e7	0.554738
$205$	−1.36906e8	−1.10990
$206$	−6.49796e6	−0.0517895
$207$	1.00430e8	0.786985
$208$	1.43422e8	1.10508
$209$	−5.07720e7	−0.384691
$210$	−5.48274e7	−0.408536
$211$	3.12083e7	0.228708	0.114354	−	0.993440i	$-0.463520\pi$
$211$	3.12083e7	0.228708	0.114354	+	0.993440i	$0.463520\pi$
$212$	−1.15693e8	−0.833931
$213$	−2.72889e7	−0.193490
$214$	−3.96666e7	−0.276679
$215$	−3.06380e7	−0.210245
$216$	8.37969e7	0.565770
$217$	−2.22699e8	−1.47948
$218$	−1.91855e7	−0.125422
$219$	−1.12349e8	−0.722794
$220$	7.31367e7	0.463080
$221$	3.02916e8	1.88777
$222$	−4.95551e6	−0.0303986
$223$	−1.46395e8	−0.884015	−0.442007	−	0.897011i	$-0.645733\pi$
$223$	−1.46395e8	−0.884015	−0.442007	+	0.897011i	$0.645733\pi$
$224$	2.43009e8	1.44462
$225$	−1.10798e8	−0.648475
$226$	−6.57352e7	−0.378807
$227$	−2.31019e7	−0.131086	−0.0655432	−	0.997850i	$-0.520878\pi$
$227$	−2.31019e7	−0.131086	−0.0655432	+	0.997850i	$0.520878\pi$
$228$	8.63207e7	0.482329
$229$	−2.46033e8	−1.35385	−0.676924	−	0.736053i	$-0.736687\pi$
$229$	−2.46033e8	−1.35385	−0.676924	+	0.736053i	$0.736687\pi$
$230$	9.13568e7	0.495100
$231$	−6.36272e7	−0.339626
$232$	1.71032e8	0.899226
$233$	2.56892e8	1.33047	0.665235	−	0.746634i	$-0.268331\pi$
$233$	2.56892e8	1.33047	0.665235	+	0.746634i	$0.268331\pi$
$234$	7.44735e7	0.379967
$235$	−1.51965e7	−0.0763849
$236$	−1.42708e8	−0.706733
$237$	−8.99830e7	−0.439078
$238$	1.36844e8	0.657971
$239$	2.98201e8	1.41292	0.706458	−	0.707755i	$-0.250292\pi$
$239$	2.98201e8	1.41292	0.706458	+	0.707755i	$0.250292\pi$
$240$	−1.07481e8	−0.501871
$241$	−2.29672e8	−1.05694	−0.528468	−	0.848953i	$-0.677233\pi$
$241$	−2.29672e8	−1.05694	−0.528468	+	0.848953i	$0.677233\pi$
$242$	6.21612e7	0.281946
$243$	−2.31794e8	−1.03629
$244$	8.58484e7	0.378327
$245$	6.04592e8	2.62652
$246$	−3.26802e7	−0.139962
$247$	3.88726e8	1.64136
$248$	1.29601e8	0.539546
$249$	3.69939e6	0.0151856
$250$	1.11075e7	0.0449598
$251$	1.54752e8	0.617702	0.308851	−	0.951111i	$-0.400056\pi$
$251$	1.54752e8	0.617702	0.308851	+	0.951111i	$0.400056\pi$
$252$	−2.78087e8	−1.09466
$253$	1.06020e8	0.411589
$254$	−1.52162e8	−0.582623
$255$	−2.27007e8	−0.857329
$256$	2.32992e7	0.0867961
$257$	2.73313e8	1.00437	0.502185	−	0.864760i	$-0.332530\pi$
$257$	2.73313e8	1.00437	0.502185	+	0.864760i	$0.332530\pi$
$258$	−7.31346e6	−0.0265127
$259$	8.33289e7	0.298021
$260$	−5.59957e8	−1.97582
$261$	−2.99162e8	−1.04151
$262$	−1.54359e8	−0.530247
$263$	2.20336e8	0.746863	0.373431	−	0.927658i	$-0.378181\pi$
$263$	2.20336e8	0.746863	0.373431	+	0.927658i	$0.378181\pi$
$264$	3.70284e7	0.123857
$265$	3.90437e8	1.28881
$266$	1.75609e8	0.572087
$267$	2.09606e8	0.673929
$268$	3.68377e8	1.16902
$269$	−1.74740e8	−0.547342	−0.273671	−	0.961823i	$-0.588238\pi$
$269$	−1.74740e8	−0.547342	−0.273671	+	0.961823i	$0.588238\pi$
$270$	−1.33332e8	−0.412251
$271$	−5.89750e8	−1.80001	−0.900005	−	0.435879i	$-0.856438\pi$
$271$	−5.89750e8	−1.80001	−0.900005	+	0.435879i	$0.856438\pi$
$272$	2.68262e8	0.808292
$273$	4.87149e8	1.44908
$274$	1.30314e8	0.382704
$275$	−1.16965e8	−0.339149
$276$	−1.80251e8	−0.516054
$277$	−3.46288e8	−0.978944	−0.489472	−	0.872019i	$-0.662810\pi$
$277$	−3.46288e8	−0.978944	−0.489472	+	0.872019i	$0.662810\pi$
$278$	−2.07347e8	−0.578818
$279$	−2.26693e8	−0.624920
$280$	−5.36533e8	−1.46064
$281$	−2.47819e8	−0.666289	−0.333145	−	0.942876i	$-0.608110\pi$
$281$	−2.47819e8	−0.666289	−0.333145	+	0.942876i	$0.608110\pi$
$282$	−3.62749e6	−0.00963240
$283$	2.38221e8	0.624779	0.312390	−	0.949954i	$-0.398871\pi$
$283$	2.38221e8	0.624779	0.312390	+	0.949954i	$0.398871\pi$
$284$	−1.25906e8	−0.326162
$285$	−2.91313e8	−0.745423
$286$	7.86186e7	0.198721
$287$	5.49530e8	1.37216
$288$	2.47368e8	0.610197
$289$	1.56248e8	0.380779
$290$	−2.72135e8	−0.655227
$291$	−1.48450e8	−0.353146
$292$	−5.18359e8	−1.21840
$293$	6.02688e8	1.39977	0.699884	−	0.714257i	$-0.253235\pi$
$293$	6.02688e8	1.39977	0.699884	+	0.714257i	$0.253235\pi$
$294$	1.44319e8	0.331214
$295$	4.81606e8	1.09223
$296$	−4.84939e7	−0.108684
$297$	−1.54732e8	−0.342715
$298$	6.64999e7	0.145567
$299$	−8.11718e8	−1.75613
$300$	1.98860e8	0.425229
$301$	1.22979e8	0.259924
$302$	1.06138e8	0.221742
$303$	2.10600e8	0.434920
$304$	3.44256e8	0.702787
$305$	−2.89719e8	−0.584692
$306$	1.39299e8	0.277921
$307$	−5.50528e8	−1.08591	−0.542957	−	0.839761i	$-0.682695\pi$
$307$	−5.50528e8	−1.08591	−0.542957	+	0.839761i	$0.682695\pi$
$308$	−2.93565e8	−0.572502
$309$	−4.32672e7	−0.0834264
$310$	−2.06213e8	−0.393143
$311$	−8.54076e8	−1.61003	−0.805017	−	0.593251i	$-0.797844\pi$
$311$	−8.54076e8	−1.61003	−0.805017	+	0.593251i	$0.797844\pi$
$312$	−2.83500e8	−0.528461
$313$	6.27627e8	1.15690	0.578451	−	0.815717i	$-0.303657\pi$
$313$	6.27627e8	1.15690	0.578451	+	0.815717i	$0.303657\pi$
$314$	−2.50985e8	−0.457503
$315$	9.38482e8	1.69176
$316$	−4.15166e8	−0.740146
$317$	−8.96686e7	−0.158100	−0.0790502	−	0.996871i	$-0.525189\pi$
$317$	−8.96686e7	−0.158100	−0.0790502	+	0.996871i	$0.525189\pi$
$318$	9.31992e7	0.162524
$319$	−3.15813e8	−0.544706
$320$	−3.30874e8	−0.564465
$321$	−2.64123e8	−0.445695
$322$	−3.66699e8	−0.612088
$323$	7.27090e8	1.20055
$324$	−1.30122e8	−0.212541
$325$	8.95519e8	1.44705
$326$	2.67895e8	0.428255
$327$	−1.27748e8	−0.202040
$328$	−3.19803e8	−0.500408
$329$	6.09977e7	0.0944339
$330$	−5.89172e7	−0.0902492
$331$	2.00092e8	0.303271	0.151635	−	0.988436i	$-0.451546\pi$
$331$	2.00092e8	0.303271	0.151635	+	0.988436i	$0.451546\pi$
$332$	1.70684e7	0.0255982
$333$	8.48236e7	0.125881
$334$	−1.06935e8	−0.157039
$335$	−1.24319e9	−1.80668
$336$	4.31420e8	0.620459
$337$	4.67534e8	0.665439	0.332719	−	0.943026i	$-0.392034\pi$
$337$	4.67534e8	0.665439	0.332719	+	0.943026i	$0.392034\pi$
$338$	−3.68705e8	−0.519362
$339$	−4.37703e8	−0.610211
$340$	−1.04737e9	−1.44519
$341$	−2.39311e8	−0.326830
$342$	1.78759e8	0.241645
$343$	−1.15296e9	−1.54271
$344$	−7.15684e7	−0.0947910
$345$	6.08306e8	0.797545
$346$	4.63089e8	0.601032
$347$	−1.38116e8	−0.177456	−0.0887279	−	0.996056i	$-0.528280\pi$
$347$	−1.38116e8	−0.177456	−0.0887279	+	0.996056i	$0.528280\pi$
$348$	5.36934e8	0.682958
$349$	−6.09602e7	−0.0767639	−0.0383820	−	0.999263i	$-0.512220\pi$
$349$	−6.09602e7	−0.0767639	−0.0383820	+	0.999263i	$0.512220\pi$
$350$	4.04556e8	0.504360
$351$	1.18468e9	1.46226
$352$	2.61136e8	0.319130
$353$	−8.21666e7	−0.0994223	−0.0497111	−	0.998764i	$-0.515830\pi$
$353$	−8.21666e7	−0.0994223	−0.0497111	+	0.998764i	$0.515830\pi$
$354$	1.14962e8	0.137734
$355$	4.24906e8	0.504073
$356$	9.67086e8	1.13603
$357$	9.11186e8	1.05991
$358$	5.40601e7	0.0622711
$359$	−1.75626e8	−0.200336	−0.100168	−	0.994971i	$-0.531938\pi$
$359$	−1.75626e8	−0.200336	−0.100168	+	0.994971i	$0.531938\pi$
$360$	−5.46157e8	−0.616962
$361$	3.91890e7	0.0438418
$362$	1.75432e8	0.194370
$363$	4.13905e8	0.454180
$364$	2.24762e9	2.44269
$365$	1.74934e9	1.88300
$366$	−6.91574e7	−0.0737318
$367$	3.51295e7	0.0370972	0.0185486	−	0.999828i	$-0.494095\pi$
$367$	3.51295e7	0.0370972	0.0185486	+	0.999828i	$0.494095\pi$
$368$	−7.18858e8	−0.751927
$369$	5.59387e8	0.579589
$370$	7.71605e7	0.0791934
$371$	−1.56718e9	−1.59335
$372$	4.06868e8	0.409782
$373$	−1.67183e9	−1.66806	−0.834031	−	0.551718i	$-0.813972\pi$
$373$	−1.67183e9	−1.66806	−0.834031	+	0.551718i	$0.813972\pi$
$374$	1.47052e8	0.145352
$375$	7.39598e7	0.0724246
$376$	−3.54981e7	−0.0344388
$377$	2.41796e9	2.32410
$378$	5.35185e8	0.509663
$379$	−1.75757e9	−1.65835	−0.829175	−	0.558989i	$-0.811189\pi$
$379$	−1.75757e9	−1.65835	−0.829175	+	0.558989i	$0.811189\pi$
$380$	−1.34407e9	−1.25655
$381$	−1.01318e9	−0.938534
$382$	2.10668e7	0.0193364
$383$	−2.17759e8	−0.198053	−0.0990263	−	0.995085i	$-0.531573\pi$
$383$	−2.17759e8	−0.198053	−0.0990263	+	0.995085i	$0.531573\pi$
$384$	−5.76670e8	−0.519718
$385$	9.90716e8	0.884783
$386$	−4.83943e8	−0.428291
$387$	1.25185e8	0.109790
$388$	−6.84923e8	−0.595293
$389$	4.98336e8	0.429239	0.214619	−	0.976698i	$-0.431149\pi$
$389$	4.98336e8	0.429239	0.214619	+	0.976698i	$0.431149\pi$
$390$	4.51088e8	0.385066
$391$	−1.51827e9	−1.28449
$392$	1.41229e9	1.18419
$393$	−1.02781e9	−0.854162
$394$	−6.99702e8	−0.576337
$395$	1.40109e9	1.14387
$396$	−2.98831e8	−0.241820
$397$	−9.41907e8	−0.755512	−0.377756	−	0.925905i	$-0.623304\pi$
$397$	−9.41907e8	−0.755512	−0.377756	+	0.925905i	$0.623304\pi$
$398$	−4.26056e8	−0.338747
$399$	1.16931e9	0.921560
$400$	7.93073e8	0.619588
$401$	−1.13370e9	−0.877994	−0.438997	−	0.898488i	$-0.644666\pi$
$401$	−1.13370e9	−0.877994	−0.438997	+	0.898488i	$0.644666\pi$
$402$	−2.96756e8	−0.227828
$403$	1.83224e9	1.39449
$404$	9.71672e8	0.733137
$405$	4.39133e8	0.328476
$406$	1.09233e9	0.810051
$407$	8.95447e7	0.0658354
$408$	−5.30272e8	−0.386534
$409$	2.01366e9	1.45531	0.727653	−	0.685946i	$-0.240611\pi$
$409$	2.01366e9	1.45531	0.727653	+	0.685946i	$0.240611\pi$
$410$	5.08851e8	0.364626
$411$	8.67704e8	0.616489
$412$	−1.99627e8	−0.140631
$413$	−1.93313e9	−1.35032
$414$	−3.73276e8	−0.258541
$415$	−5.76019e7	−0.0395611
$416$	−1.99934e9	−1.36163
$417$	−1.38064e9	−0.932403
$418$	1.88709e8	0.126379
$419$	−2.42088e9	−1.60777	−0.803886	−	0.594784i	$-0.797238\pi$
$419$	−2.42088e9	−1.60777	−0.803886	+	0.594784i	$0.797238\pi$
$420$	−1.68438e9	−1.10935
$421$	6.39130e8	0.417448	0.208724	−	0.977975i	$-0.433069\pi$
$421$	6.39130e8	0.417448	0.208724	+	0.977975i	$0.433069\pi$
$422$	−1.15995e8	−0.0751355
$423$	6.20919e7	0.0398881
$424$	9.12034e8	0.581073
$425$	1.67502e9	1.05842
$426$	1.01427e8	0.0635654
$427$	1.16291e9	0.722850
$428$	−1.21862e9	−0.751301
$429$	5.23488e8	0.320115
$430$	1.13875e8	0.0690700
$431$	−2.22935e9	−1.34125	−0.670623	−	0.741798i	$-0.733973\pi$
$431$	−2.22935e9	−1.34125	−0.670623	+	0.741798i	$0.733973\pi$
$432$	1.04915e9	0.626102
$433$	−6.57831e8	−0.389409	−0.194705	−	0.980862i	$-0.562375\pi$
$433$	−6.57831e8	−0.389409	−0.194705	+	0.980862i	$0.562375\pi$
$434$	8.27725e8	0.486040
$435$	−1.81203e9	−1.05549
$436$	−5.89407e8	−0.340575
$437$	−1.94837e9	−1.11683
$438$	4.17578e8	0.237453
$439$	−1.25699e9	−0.709097	−0.354549	−	0.935038i	$-0.615365\pi$
$439$	−1.25699e9	−0.709097	−0.354549	+	0.935038i	$0.615365\pi$
$440$	−5.76555e8	−0.322668
$441$	−2.47031e9	−1.37157
$442$	−1.12587e9	−0.620171
$443$	6.21522e8	0.339659	0.169830	−	0.985473i	$-0.445678\pi$
$443$	6.21522e8	0.339659	0.169830	+	0.985473i	$0.445678\pi$
$444$	−1.52241e8	−0.0825450
$445$	−3.26370e9	−1.75570
$446$	5.44120e8	0.290417
$447$	4.42795e8	0.234491
$448$	1.32810e9	0.697843
$449$	3.37102e8	0.175752	0.0878758	−	0.996131i	$-0.471992\pi$
$449$	3.37102e8	0.175752	0.0878758	+	0.996131i	$0.471992\pi$
$450$	4.11813e8	0.213038
$451$	5.90522e8	0.303122
$452$	−2.01948e9	−1.02862
$453$	7.06730e8	0.357199
$454$	8.58650e7	0.0430646
$455$	−7.58522e9	−3.77510
$456$	−6.80488e8	−0.336081
$457$	3.14261e9	1.54022	0.770112	−	0.637909i	$-0.220200\pi$
$457$	3.14261e9	1.54022	0.770112	+	0.637909i	$0.220200\pi$
$458$	9.14455e8	0.444767
$459$	2.21587e9	1.06955
$460$	2.80662e9	1.34441
$461$	6.04340e8	0.287295	0.143647	−	0.989629i	$-0.454117\pi$
$461$	6.04340e8	0.287295	0.143647	+	0.989629i	$0.454117\pi$
$462$	2.36489e8	0.111574
$463$	−1.62669e8	−0.0761677	−0.0380839	−	0.999275i	$-0.512125\pi$
$463$	−1.62669e8	−0.0761677	−0.0380839	+	0.999275i	$0.512125\pi$
$464$	2.14135e9	0.995117
$465$	−1.37309e9	−0.633305
$466$	−9.54814e8	−0.437087
$467$	1.96986e9	0.895005	0.447502	−	0.894283i	$-0.352314\pi$
$467$	1.96986e9	0.895005	0.447502	+	0.894283i	$0.352314\pi$
$468$	2.28794e9	1.03177
$469$	4.99006e9	2.23358
$470$	5.64824e7	0.0250940
$471$	−1.67120e9	−0.736980
$472$	1.12500e9	0.492443
$473$	1.32152e8	0.0574196
$474$	3.34448e8	0.144246
$475$	2.14952e9	0.920267
$476$	4.20406e9	1.78667
$477$	−1.59529e9	−0.673017
$478$	−1.10835e9	−0.464173
$479$	−2.56454e9	−1.06619	−0.533097	−	0.846054i	$-0.678972\pi$
$479$	−2.56454e9	−1.06619	−0.533097	+	0.846054i	$0.678972\pi$
$480$	1.49832e9	0.618385
$481$	−6.85582e8	−0.280900
$482$	8.53643e8	0.347225
$483$	−2.44169e9	−0.985998
$484$	1.90969e9	0.765603
$485$	2.31146e9	0.920005
$486$	8.61531e8	0.340443
$487$	−2.97468e9	−1.16705	−0.583523	−	0.812096i	$-0.698326\pi$
$487$	−2.97468e9	−1.16705	−0.583523	+	0.812096i	$0.698326\pi$
$488$	−6.76764e8	−0.263614
$489$	1.78380e9	0.689865
$490$	−2.24714e9	−0.862868
$491$	1.23197e9	0.469696	0.234848	−	0.972032i	$-0.424541\pi$
$491$	1.23197e9	0.469696	0.234848	+	0.972032i	$0.424541\pi$
$492$	−1.00398e9	−0.380058
$493$	4.52266e9	1.69993
$494$	−1.44481e9	−0.539221
$495$	1.00849e9	0.373725
$496$	1.62263e9	0.597082
$497$	−1.70554e9	−0.623181
$498$	−1.37499e7	−0.00498880
$499$	2.78394e9	1.00301	0.501507	−	0.865153i	$-0.332779\pi$
$499$	2.78394e9	1.00301	0.501507	+	0.865153i	$0.332779\pi$
$500$	3.41238e8	0.122085
$501$	−7.12037e8	−0.252971
$502$	−5.75181e8	−0.202928
$503$	3.98467e8	0.139606	0.0698030	−	0.997561i	$-0.477763\pi$
$503$	3.98467e8	0.139606	0.0698030	+	0.997561i	$0.477763\pi$
$504$	2.19223e9	0.762745
$505$	−3.27918e9	−1.13304
$506$	−3.94052e8	−0.135216
$507$	−2.45505e9	−0.836628
$508$	−4.67465e9	−1.58207
$509$	2.69989e9	0.907473	0.453736	−	0.891136i	$-0.350091\pi$
$509$	2.69989e9	0.907473	0.453736	+	0.891136i	$0.350091\pi$
$510$	8.43736e8	0.281651
$511$	−7.02173e9	−2.32794
$512$	−3.06915e9	−1.01059
$513$	2.84359e9	0.929942
$514$	−1.01585e9	−0.329956
$515$	6.73697e8	0.217340
$516$	−2.24681e8	−0.0719932
$517$	6.55478e7	0.0208613
$518$	−3.09716e8	−0.0979060
$519$	3.08351e9	0.968188
$520$	4.41428e9	1.37673
$521$	3.82871e8	0.118610	0.0593049	−	0.998240i	$-0.481112\pi$
$521$	3.82871e8	0.118610	0.0593049	+	0.998240i	$0.481112\pi$
$522$	1.11192e9	0.342159
$523$	2.76861e9	0.846264	0.423132	−	0.906068i	$-0.360931\pi$
$523$	2.76861e9	0.846264	0.423132	+	0.906068i	$0.360931\pi$
$524$	−4.74215e9	−1.43985
$525$	2.69377e9	0.812462
$526$	−8.18943e8	−0.245360
$527$	3.42710e9	1.01997
$528$	4.63601e8	0.137065
$529$	6.63671e8	0.194921
$530$	−1.45117e9	−0.423402
$531$	−1.96781e9	−0.570363
$532$	5.39499e9	1.55346
$533$	−4.52122e9	−1.29333
$534$	−7.79062e8	−0.221400
$535$	4.11256e9	1.16111
$536$	−2.90401e9	−0.814556
$537$	3.59963e8	0.100311
$538$	6.49471e8	0.179813
$539$	−2.60781e9	−0.717323
$540$	−4.09617e9	−1.11944
$541$	−3.30164e9	−0.896477	−0.448238	−	0.893914i	$-0.647948\pi$
$541$	−3.30164e9	−0.896477	−0.448238	+	0.893914i	$0.647948\pi$
$542$	2.19198e9	0.591341
$543$	1.16813e9	0.313105
$544$	−3.73966e9	−0.995945
$545$	1.98912e9	0.526347
$546$	−1.81063e9	−0.476054
$547$	6.45168e9	1.68546	0.842728	−	0.538340i	$-0.180948\pi$
$547$	6.45168e9	1.68546	0.842728	+	0.538340i	$0.180948\pi$
$548$	4.00344e9	1.03921
$549$	1.18377e9	0.305326
$550$	4.34734e8	0.111418
$551$	5.80385e9	1.47804
$552$	1.42096e9	0.359580
$553$	−5.62388e9	−1.41416
$554$	1.28708e9	0.321604
$555$	5.13779e8	0.127571
$556$	−6.37003e9	−1.57174
$557$	6.11372e9	1.49904	0.749519	−	0.661983i	$-0.230285\pi$
$557$	6.11372e9	1.49904	0.749519	+	0.661983i	$0.230285\pi$
$558$	8.42572e8	0.205299
$559$	−1.01180e9	−0.244992
$560$	−6.71748e9	−1.61640
$561$	9.79156e8	0.234143
$562$	9.21092e8	0.218890
$563$	−4.59129e9	−1.08432	−0.542158	−	0.840277i	$-0.682392\pi$
$563$	−4.59129e9	−1.08432	−0.542158	+	0.840277i	$0.682392\pi$
$564$	−1.11442e8	−0.0261561
$565$	6.81531e9	1.58970
$566$	−8.85416e8	−0.205253
$567$	−1.76265e9	−0.406092
$568$	9.92552e8	0.227266
$569$	−4.85419e9	−1.10465	−0.552324	−	0.833630i	$-0.686259\pi$
$569$	−4.85419e9	−1.10465	−0.552324	+	0.833630i	$0.686259\pi$
$570$	1.08275e9	0.244887
$571$	−3.97419e9	−0.893351	−0.446675	−	0.894696i	$-0.647392\pi$
$571$	−3.97419e9	−0.893351	−0.446675	+	0.894696i	$0.647392\pi$
$572$	2.41528e9	0.539612
$573$	1.40275e8	0.0311486
$574$	−2.04249e9	−0.450783
$575$	−4.48852e9	−0.984614
$576$	1.35192e9	0.294763
$577$	2.46945e9	0.535161	0.267581	−	0.963535i	$-0.413776\pi$
$577$	2.46945e9	0.535161	0.267581	+	0.963535i	$0.413776\pi$
$578$	−5.80743e8	−0.125094
$579$	−3.22237e9	−0.689923
$580$	−8.36041e9	−1.77922
$581$	2.31209e8	0.0489090
$582$	5.51757e8	0.116016
$583$	−1.68408e9	−0.351985
$584$	4.08635e9	0.848967
$585$	−7.72128e9	−1.59457
$586$	−2.24006e9	−0.459853
$587$	8.02057e9	1.63671	0.818355	−	0.574713i	$-0.194886\pi$
$587$	8.02057e9	1.63671	0.818355	+	0.574713i	$0.194886\pi$
$588$	4.43371e9	0.899386
$589$	4.39793e9	0.886839
$590$	−1.79003e9	−0.358821
$591$	−4.65902e9	−0.928407
$592$	−6.07152e8	−0.120274
$593$	1.99128e9	0.392141	0.196070	−	0.980590i	$-0.437182\pi$
$593$	1.99128e9	0.392141	0.196070	+	0.980590i	$0.437182\pi$
$594$	5.75107e8	0.112589
$595$	−1.41878e10	−2.76124
$596$	2.04298e9	0.395278
$597$	−2.83692e9	−0.545679
$598$	3.01699e9	0.576925
$599$	4.99536e9	0.949670	0.474835	−	0.880075i	$-0.342508\pi$
$599$	4.99536e9	0.949670	0.474835	+	0.880075i	$0.342508\pi$
$600$	−1.56766e9	−0.296294
$601$	−4.19069e9	−0.787454	−0.393727	−	0.919227i	$-0.628814\pi$
$601$	−4.19069e9	−0.787454	−0.393727	+	0.919227i	$0.628814\pi$
$602$	−4.57086e8	−0.0853906
$603$	5.07957e9	0.943445
$604$	3.26073e9	0.602124
$605$	−6.44477e9	−1.18321
$606$	−7.82756e8	−0.142880
$607$	−2.91949e9	−0.529842	−0.264921	−	0.964270i	$-0.585346\pi$
$607$	−2.91949e9	−0.529842	−0.264921	+	0.964270i	$0.585346\pi$
$608$	−4.79903e9	−0.865946
$609$	7.27335e9	1.30489
$610$	1.07682e9	0.192084
$611$	−5.01854e8	−0.0890088
$612$	4.27947e9	0.754675
$613$	−3.83809e9	−0.672983	−0.336491	−	0.941687i	$-0.609240\pi$
$613$	−3.83809e9	−0.672983	−0.336491	+	0.941687i	$0.609240\pi$
$614$	2.04620e9	0.356745
$615$	3.38822e9	0.587366
$616$	2.31425e9	0.398912
$617$	−5.20036e9	−0.891323	−0.445661	−	0.895202i	$-0.647031\pi$
$617$	−5.20036e9	−0.891323	−0.445661	+	0.895202i	$0.647031\pi$
$618$	1.60815e8	0.0274073
$619$	−6.96863e9	−1.18095	−0.590473	−	0.807058i	$-0.701059\pi$
$619$	−6.96863e9	−1.18095	−0.590473	+	0.807058i	$0.701059\pi$
$620$	−6.33519e9	−1.06755
$621$	−5.93784e9	−0.994965
$622$	3.17442e9	0.528930
$623$	1.31002e10	2.17055
$624$	−3.54947e9	−0.584814
$625$	−6.64924e9	−1.08941
$626$	−2.33276e9	−0.380067
$627$	1.25653e9	0.203581
$628$	−7.71064e9	−1.24232
$629$	−1.28234e9	−0.205460
$630$	−3.48814e9	−0.555779
$631$	1.04787e10	1.66037	0.830183	−	0.557490i	$-0.188236\pi$
$631$	1.04787e10	1.66037	0.830183	+	0.557490i	$0.188236\pi$
$632$	3.27286e9	0.515724
$633$	−7.72361e8	−0.121034
$634$	3.33279e8	0.0519393
$635$	1.57759e10	2.44504
$636$	2.86322e9	0.441322
$637$	1.99662e10	3.06060
$638$	1.17381e9	0.178947
$639$	−1.73613e9	−0.263227
$640$	8.97911e9	1.35395
$641$	−2.92164e9	−0.438151	−0.219076	−	0.975708i	$-0.570304\pi$
$641$	−2.92164e9	−0.438151	−0.219076	+	0.975708i	$0.570304\pi$
$642$	9.81689e8	0.146420
$643$	7.68989e9	1.14073	0.570364	−	0.821392i	$-0.306802\pi$
$643$	7.68989e9	1.14073	0.570364	+	0.821392i	$0.306802\pi$
$644$	−1.12655e10	−1.66208
$645$	7.58246e8	0.111263
$646$	−2.70244e9	−0.394405
$647$	1.38869e8	0.0201577	0.0100789	−	0.999949i	$-0.496792\pi$
$647$	1.38869e8	0.0201577	0.0100789	+	0.999949i	$0.496792\pi$
$648$	1.02579e9	0.148096
$649$	−2.07733e9	−0.298297
$650$	−3.32846e9	−0.475386
$651$	5.51147e9	0.782950
$652$	8.23013e9	1.16289
$653$	4.91204e9	0.690344	0.345172	−	0.938539i	$-0.387821\pi$
$653$	4.91204e9	0.690344	0.345172	+	0.938539i	$0.387821\pi$
$654$	4.74812e8	0.0663742
$655$	1.60037e10	2.22523
$656$	−4.00399e9	−0.553771
$657$	−7.14768e9	−0.983301
$658$	−2.26716e8	−0.0310235
$659$	−1.44098e9	−0.196137	−0.0980686	−	0.995180i	$-0.531266\pi$
$659$	−1.44098e9	−0.196137	−0.0980686	+	0.995180i	$0.531266\pi$
$660$	−1.81003e9	−0.245065
$661$	6.29813e9	0.848216	0.424108	−	0.905612i	$-0.360588\pi$
$661$	6.29813e9	0.848216	0.424108	+	0.905612i	$0.360588\pi$
$662$	−7.43698e8	−0.0996309
$663$	−7.49671e9	−0.999019
$664$	−1.34554e8	−0.0178365
$665$	−1.82069e10	−2.40082
$666$	−3.15271e8	−0.0413547
$667$	−1.21193e10	−1.58138
$668$	−3.28522e9	−0.426429
$669$	3.62306e9	0.467826
$670$	4.62067e9	0.593531
$671$	1.24966e9	0.159684
$672$	−6.01412e9	−0.764504
$673$	−1.12010e10	−1.41646	−0.708229	−	0.705983i	$-0.750505\pi$
$673$	−1.12010e10	−1.41646	−0.708229	+	0.705983i	$0.750505\pi$
$674$	−1.73772e9	−0.218611
$675$	6.55086e9	0.819851
$676$	−1.13272e10	−1.41029
$677$	1.35096e10	1.67333	0.836666	−	0.547714i	$-0.184502\pi$
$677$	1.35096e10	1.67333	0.836666	+	0.547714i	$0.184502\pi$
$678$	1.62685e9	0.200467
$679$	−9.27802e9	−1.13739
$680$	8.25667e9	1.00699
$681$	5.71739e8	0.0693718
$682$	8.89468e8	0.107371
$683$	7.42709e9	0.891962	0.445981	−	0.895042i	$-0.352855\pi$
$683$	7.42709e9	0.891962	0.445981	+	0.895042i	$0.352855\pi$
$684$	5.49176e9	0.656168
$685$	−1.35107e10	−1.60606
$686$	4.28530e9	0.506812
$687$	6.08896e9	0.716465
$688$	−8.96049e8	−0.104899
$689$	1.28939e10	1.50181
$690$	−2.26095e9	−0.262010
$691$	6.66846e9	0.768869	0.384434	−	0.923152i	$-0.374397\pi$
$691$	6.66846e9	0.768869	0.384434	+	0.923152i	$0.374397\pi$
$692$	1.42268e10	1.63206
$693$	−4.04799e9	−0.462033
$694$	5.13347e8	0.0582979
$695$	2.14974e10	2.42907
$696$	−4.23279e9	−0.475876
$697$	−8.45669e9	−0.945988
$698$	2.26576e8	0.0252185
$699$	−6.35770e9	−0.704093
$700$	1.24286e10	1.36955
$701$	−8.02719e9	−0.880137	−0.440069	−	0.897964i	$-0.645046\pi$
$701$	−8.02719e9	−0.880137	−0.440069	+	0.897964i	$0.645046\pi$
$702$	−4.40319e9	−0.480383
$703$	−1.64561e9	−0.178642
$704$	1.42717e9	0.154160
$705$	3.76092e8	0.0404233
$706$	3.05396e8	0.0326623
$707$	1.31624e10	1.40077
$708$	3.53181e9	0.374008
$709$	6.52080e9	0.687130	0.343565	−	0.939129i	$-0.388365\pi$
$709$	6.52080e9	0.687130	0.343565	+	0.939129i	$0.388365\pi$
$710$	−1.57929e9	−0.165599
$711$	−5.72475e9	−0.597328
$712$	−7.62378e9	−0.791572
$713$	−9.18354e9	−0.948849
$714$	−3.38669e9	−0.348202
$715$	−8.15104e9	−0.833953
$716$	1.66081e9	0.169092
$717$	−7.38003e9	−0.747724
$718$	6.52765e8	0.0658145
$719$	1.19598e10	1.19997	0.599986	−	0.800010i	$-0.295173\pi$
$719$	1.19598e10	1.19997	0.599986	+	0.800010i	$0.295173\pi$
$720$	−6.83798e9	−0.682753
$721$	−2.70417e9	−0.268695
$722$	−1.45657e8	−0.0144030
$723$	5.68404e9	0.559337
$724$	5.38954e9	0.527797
$725$	1.33705e10	1.30306
$726$	−1.53840e9	−0.149208
$727$	−3.08388e9	−0.297665	−0.148832	−	0.988862i	$-0.547551\pi$
$727$	−3.08388e9	−0.297665	−0.148832	+	0.988862i	$0.547551\pi$
$728$	−1.77186e10	−1.70204
$729$	3.24434e9	0.310156
$730$	−6.50195e9	−0.618605
$731$	−1.89251e9	−0.179196
$732$	−2.12462e9	−0.200213
$733$	−1.53686e10	−1.44135	−0.720676	−	0.693272i	$-0.756168\pi$
$733$	−1.53686e10	−1.44135	−0.720676	+	0.693272i	$0.756168\pi$
$734$	−1.30569e8	−0.0121872
$735$	−1.49628e10	−1.38997
$736$	1.00211e10	0.926495
$737$	5.36229e9	0.493417
$738$	−2.07912e9	−0.190407
$739$	−8.64423e9	−0.787899	−0.393949	−	0.919132i	$-0.628892\pi$
$739$	−8.64423e9	−0.787899	−0.393949	+	0.919132i	$0.628892\pi$
$740$	2.37049e9	0.215044
$741$	−9.62039e9	−0.868618
$742$	5.82489e9	0.523448
$743$	6.82591e9	0.610520	0.305260	−	0.952269i	$-0.401257\pi$
$743$	6.82591e9	0.610520	0.305260	+	0.952269i	$0.401257\pi$
$744$	−3.20744e9	−0.285531
$745$	−6.89460e9	−0.610888
$746$	6.21385e9	0.547993
$747$	2.35357e8	0.0206588
$748$	4.51766e9	0.394691
$749$	−1.65075e10	−1.43547
$750$	−2.74893e8	−0.0237930
$751$	−1.00999e10	−0.870113	−0.435057	−	0.900403i	$-0.643272\pi$
$751$	−1.00999e10	−0.870113	−0.435057	+	0.900403i	$0.643272\pi$
$752$	−4.44442e8	−0.0381112
$753$	−3.82989e9	−0.326892
$754$	−8.98705e9	−0.763515
$755$	−1.10042e10	−0.930562
$756$	1.64417e10	1.38395
$757$	−1.25390e10	−1.05057	−0.525287	−	0.850925i	$-0.676042\pi$
$757$	−1.25390e10	−1.05057	−0.525287	+	0.850925i	$0.676042\pi$
$758$	6.53253e9	0.544803
$759$	−2.62383e9	−0.217816
$760$	1.05956e10	0.875546
$761$	1.68387e10	1.38504	0.692518	−	0.721400i	$-0.256501\pi$
$761$	1.68387e10	1.38504	0.692518	+	0.721400i	$0.256501\pi$
$762$	3.76578e9	0.308328
$763$	−7.98415e9	−0.650718
$764$	6.47203e8	0.0525066
$765$	−1.44422e10	−1.16632
$766$	8.09365e8	0.0650644
$767$	1.59047e10	1.27274
$768$	−5.76620e8	−0.0459331
$769$	5.50473e9	0.436510	0.218255	−	0.975892i	$-0.429964\pi$
$769$	5.50473e9	0.436510	0.218255	+	0.975892i	$0.429964\pi$
$770$	−3.68228e9	−0.290670
$771$	−6.76408e9	−0.531519
$772$	−1.48675e10	−1.16299
$773$	−1.58271e9	−0.123246	−0.0616230	−	0.998099i	$-0.519628\pi$
$773$	−1.58271e9	−0.123246	−0.0616230	+	0.998099i	$0.519628\pi$
$774$	−4.65285e8	−0.0360683
$775$	1.01316e10	0.781851
$776$	5.39942e9	0.414793
$777$	−2.06227e9	−0.157714
$778$	−1.85221e9	−0.141014
$779$	−1.08523e10	−0.822509
$780$	1.38581e10	1.04562
$781$	−1.83276e9	−0.137666
$782$	5.64311e9	0.421983
$783$	1.76877e10	1.31676
$784$	1.76821e10	1.31047
$785$	2.60217e10	1.91996
$786$	3.82016e9	0.280610
$787$	−9.16094e9	−0.669929	−0.334964	−	0.942231i	$-0.608724\pi$
$787$	−9.16094e9	−0.669929	−0.334964	+	0.942231i	$0.608724\pi$
$788$	−2.14959e10	−1.56500
$789$	−5.45300e9	−0.395244
$790$	−5.20757e9	−0.375786
$791$	−2.73561e10	−1.96534
$792$	2.35576e9	0.168497
$793$	−9.56774e9	−0.681323
$794$	3.50087e9	0.248202
$795$	−9.66273e9	−0.682048
$796$	−1.30891e10	−0.919842
$797$	−1.42782e10	−0.999006	−0.499503	−	0.866312i	$-0.666484\pi$
$797$	−1.42782e10	−0.999006	−0.499503	+	0.866312i	$0.666484\pi$
$798$	−4.34607e9	−0.302752
$799$	−9.38691e8	−0.0651042
$800$	−1.10557e10	−0.763431
$801$	1.33352e10	0.916824
$802$	4.21371e9	0.288440
$803$	−7.54551e9	−0.514262
$804$	−9.11678e9	−0.618651
$805$	3.80187e10	2.56869
$806$	−6.81004e9	−0.458118
$807$	4.32455e9	0.289657
$808$	−7.65994e9	−0.510841
$809$	8.21284e9	0.545348	0.272674	−	0.962106i	$-0.412092\pi$
$809$	8.21284e9	0.545348	0.272674	+	0.962106i	$0.412092\pi$
$810$	−1.63217e9	−0.107911
$811$	−1.87787e10	−1.23621	−0.618104	−	0.786096i	$-0.712099\pi$
$811$	−1.87787e10	−1.23621	−0.618104	+	0.786096i	$0.712099\pi$
$812$	3.35580e10	2.19963
$813$	1.45954e10	0.952577
$814$	−3.32819e8	−0.0216283
$815$	−2.77748e10	−1.79721
$816$	−6.63910e9	−0.427753
$817$	−2.42862e9	−0.155806
$818$	−7.48434e9	−0.478098
$819$	3.09926e10	1.97135
$820$	1.56327e10	0.990114
$821$	−1.50345e10	−0.948173	−0.474086	−	0.880478i	$-0.657222\pi$
$821$	−1.50345e10	−0.948173	−0.474086	+	0.880478i	$0.657222\pi$
$822$	−3.22507e9	−0.202530
$823$	9.26651e9	0.579451	0.289726	−	0.957110i	$-0.406436\pi$
$823$	9.26651e9	0.579451	0.289726	+	0.957110i	$0.406436\pi$
$824$	1.57371e9	0.0979896
$825$	2.89471e9	0.179480
$826$	7.18504e9	0.443608
$827$	−2.93861e10	−1.80665	−0.903323	−	0.428962i	$-0.858879\pi$
$827$	−2.93861e10	−1.80665	−0.903323	+	0.428962i	$0.858879\pi$
$828$	−1.14676e10	−0.702049
$829$	3.66600e9	0.223487	0.111743	−	0.993737i	$-0.464357\pi$
$829$	3.66600e9	0.223487	0.111743	+	0.993737i	$0.464357\pi$
$830$	2.14094e8	0.0129967
$831$	8.57011e9	0.518063
$832$	−1.09268e10	−0.657753
$833$	3.73457e10	2.23863
$834$	5.13154e9	0.306314
$835$	1.10869e10	0.659031
$836$	5.79742e9	0.343173
$837$	1.34031e10	0.790070
$838$	8.99791e9	0.528187
$839$	−1.20233e9	−0.0702840	−0.0351420	−	0.999382i	$-0.511188\pi$
$839$	−1.20233e9	−0.0702840	−0.0351420	+	0.999382i	$0.511188\pi$
$840$	1.32784e10	0.772980
$841$	1.88513e10	1.09284
$842$	−2.37551e9	−0.137140
$843$	6.13316e9	0.352604
$844$	−3.56354e9	−0.204025
$845$	3.82267e10	2.17956
$846$	−2.30782e8	−0.0131041
$847$	2.58688e10	1.46280
$848$	1.14188e10	0.643037
$849$	−5.89561e9	−0.330637
$850$	−6.22570e9	−0.347714
$851$	3.43628e9	0.191133
$852$	3.11600e9	0.172607
$853$	2.76893e10	1.52753	0.763767	−	0.645491i	$-0.223347\pi$
$853$	2.76893e10	1.52753	0.763767	+	0.645491i	$0.223347\pi$
$854$	−4.32229e9	−0.237471
$855$	−1.85334e10	−1.01409
$856$	9.60666e9	0.523497
$857$	−3.11448e10	−1.69025	−0.845127	−	0.534565i	$-0.820475\pi$
$857$	−3.11448e10	−1.69025	−0.845127	+	0.534565i	$0.820475\pi$
$858$	−1.94569e9	−0.105164
$859$	1.06707e10	0.574405	0.287202	−	0.957870i	$-0.407275\pi$
$859$	1.06707e10	0.574405	0.287202	+	0.957870i	$0.407275\pi$
$860$	3.49842e9	0.187554
$861$	−1.36001e10	−0.726156
$862$	8.28604e9	0.440627
$863$	2.01685e10	1.06816	0.534079	−	0.845435i	$-0.320659\pi$
$863$	2.01685e10	1.06816	0.534079	+	0.845435i	$0.320659\pi$
$864$	−1.46255e10	−0.771457
$865$	−4.80122e10	−2.52229
$866$	2.44502e9	0.127929
$867$	−3.86692e9	−0.201511
$868$	2.54290e10	1.31980
$869$	−6.04338e9	−0.312400
$870$	6.73494e9	0.346750
$871$	−4.10553e10	−2.10526
$872$	4.64644e9	0.237308
$873$	−9.44444e9	−0.480426
$874$	7.24169e9	0.366902
$875$	4.62244e9	0.233261
$876$	1.28286e10	0.644786
$877$	−8.78810e9	−0.439943	−0.219971	−	0.975506i	$-0.570596\pi$
$877$	−8.78810e9	−0.439943	−0.219971	+	0.975506i	$0.570596\pi$
$878$	4.67197e9	0.232953
$879$	−1.49156e10	−0.740765
$880$	−7.21857e9	−0.357077
$881$	−2.67005e10	−1.31554	−0.657769	−	0.753220i	$-0.728500\pi$
$881$	−2.67005e10	−1.31554	−0.657769	+	0.753220i	$0.728500\pi$
$882$	9.18164e9	0.450589
$883$	2.75848e10	1.34836	0.674181	−	0.738566i	$-0.264497\pi$
$883$	2.75848e10	1.34836	0.674181	+	0.738566i	$0.264497\pi$
$884$	−3.45886e10	−1.68403
$885$	−1.19190e10	−0.578016
$886$	−2.31007e9	−0.111585
$887$	1.57163e10	0.756165	0.378083	−	0.925772i	$-0.376584\pi$
$887$	1.57163e10	0.756165	0.378083	+	0.925772i	$0.376584\pi$
$888$	1.20015e9	0.0575163
$889$	−6.33231e10	−3.02278
$890$	1.21305e10	0.576784
$891$	−1.89413e9	−0.0897093
$892$	1.67162e10	0.788606
$893$	−1.20460e9	−0.0566062
$894$	−1.64578e9	−0.0770352
$895$	−5.60486e9	−0.261327
$896$	−3.60415e10	−1.67388
$897$	2.00888e10	0.929354
$898$	−1.25294e9	−0.0577381
$899$	2.73561e10	1.25573
$900$	1.26515e10	0.578488
$901$	2.41173e10	1.09848
$902$	−2.19485e9	−0.0995821
$903$	−3.04354e9	−0.137554
$904$	1.59201e10	0.716731
$905$	−1.81885e10	−0.815692
$906$	−2.62677e9	−0.117347
$907$	−2.21424e10	−0.985369	−0.492685	−	0.870208i	$-0.663984\pi$
$907$	−2.21424e10	−0.985369	−0.492685	+	0.870208i	$0.663984\pi$
$908$	2.63790e9	0.116939
$909$	1.33984e10	0.591672
$910$	2.81927e10	1.24020
$911$	2.20181e10	0.964862	0.482431	−	0.875934i	$-0.339754\pi$
$911$	2.20181e10	0.964862	0.482431	+	0.875934i	$0.339754\pi$
$912$	−8.51982e9	−0.371919
$913$	2.48456e8	0.0108044
$914$	−1.16804e10	−0.505996
$915$	7.17012e9	0.309423
$916$	2.80934e10	1.20773
$917$	−6.42376e10	−2.75104
$918$	−8.23594e9	−0.351369
$919$	1.01632e10	0.431943	0.215972	−	0.976400i	$-0.430708\pi$
$919$	1.01632e10	0.431943	0.215972	+	0.976400i	$0.430708\pi$
$920$	−2.21253e10	−0.936766
$921$	1.36248e10	0.574672
$922$	−2.24620e9	−0.0943824
$923$	1.40322e10	0.587381
$924$	7.26530e9	0.302972
$925$	−3.79103e9	−0.157493
$926$	6.04606e8	0.0250227
$927$	−2.75267e9	−0.113495
$928$	−2.98510e10	−1.22614
$929$	−8.04262e9	−0.329111	−0.164556	−	0.986368i	$-0.552619\pi$
$929$	−8.04262e9	−0.329111	−0.164556	+	0.986368i	$0.552619\pi$
$930$	5.10348e9	0.208054
$931$	4.79249e10	1.94643
$932$	−2.93333e10	−1.18688
$933$	2.11371e10	0.852040
$934$	−7.32154e9	−0.294028
$935$	−1.52461e10	−0.609983
$936$	−1.80364e10	−0.718926
$937$	−3.08374e10	−1.22459	−0.612293	−	0.790631i	$-0.709753\pi$
$937$	−3.08374e10	−1.22459	−0.612293	+	0.790631i	$0.709753\pi$
$938$	−1.85470e10	−0.733777
$939$	−1.55329e10	−0.612240
$940$	1.73522e9	0.0681409
$941$	8.87704e8	0.0347300	0.0173650	−	0.999849i	$-0.494472\pi$
$941$	8.87704e8	0.0347300	0.0173650	+	0.999849i	$0.494472\pi$
$942$	6.21151e9	0.242113
$943$	2.26613e10	0.880021
$944$	1.40852e10	0.544955
$945$	−5.54871e10	−2.13885
$946$	−4.91182e8	−0.0188635
$947$	−8.02900e9	−0.307211	−0.153605	−	0.988132i	$-0.549088\pi$
$947$	−8.02900e9	−0.307211	−0.153605	+	0.988132i	$0.549088\pi$
$948$	1.02748e10	0.391690
$949$	5.77707e10	2.19420
$950$	−7.98931e9	−0.302327
$951$	2.21917e9	0.0836678
$952$	−3.31416e10	−1.24493
$953$	−6.27853e9	−0.234981	−0.117491	−	0.993074i	$-0.537485\pi$
$953$	−6.27853e9	−0.234981	−0.117491	+	0.993074i	$0.537485\pi$
$954$	5.92937e9	0.221100
$955$	−2.18417e9	−0.0811472
$956$	−3.40502e10	−1.26043
$957$	7.81590e9	0.288262
$958$	9.53187e9	0.350267
$959$	5.42309e10	1.98555
$960$	8.18863e9	0.298718
$961$	−6.78322e9	−0.246549
$962$	2.54816e9	0.0922815
$963$	−1.68036e10	−0.606331
$964$	2.62252e10	0.942865
$965$	5.01744e10	1.79737
$966$	9.07526e9	0.323921
$967$	−1.81180e10	−0.644343	−0.322172	−	0.946681i	$-0.604413\pi$
$967$	−1.81180e10	−0.644343	−0.322172	+	0.946681i	$0.604413\pi$
$968$	−1.50546e10	−0.533463
$969$	−1.79944e10	−0.635337
$970$	−8.59121e9	−0.302241
$971$	−2.56716e10	−0.899883	−0.449942	−	0.893058i	$-0.648555\pi$
$971$	−2.56716e10	−0.899883	−0.449942	+	0.893058i	$0.648555\pi$
$972$	2.64676e10	0.924447
$973$	−8.62889e10	−3.00303
$974$	1.10562e10	0.383399
$975$	−2.21628e10	−0.765787
$976$	−8.47320e9	−0.291725
$977$	2.60682e10	0.894295	0.447148	−	0.894460i	$-0.352440\pi$
$977$	2.60682e10	0.894295	0.447148	+	0.894460i	$0.352440\pi$
$978$	−6.63000e9	−0.226635
$979$	1.40774e10	0.479495
$980$	−6.90356e10	−2.34305
$981$	−8.12737e9	−0.274858
$982$	−4.57899e9	−0.154305
$983$	1.74429e10	0.585708	0.292854	−	0.956157i	$-0.405395\pi$
$983$	1.74429e10	0.585708	0.292854	+	0.956157i	$0.405395\pi$
$984$	7.91466e9	0.264819
$985$	7.25439e10	2.41866
$986$	−1.68098e10	−0.558461
$987$	−1.50960e9	−0.0499750
$988$	−4.43868e10	−1.46421
$989$	5.07134e9	0.166700
$990$	−3.74833e9	−0.122776
$991$	1.57746e10	0.514874	0.257437	−	0.966295i	$-0.417122\pi$
$991$	1.57746e10	0.514874	0.257437	+	0.966295i	$0.417122\pi$
$992$	−2.26199e10	−0.735700
$993$	−4.95197e9	−0.160493
$994$	6.33913e9	0.204728
$995$	4.41727e10	1.42159
$996$	−4.22417e8	−0.0135467
$997$	2.18743e9	0.0699040	0.0349520	−	0.999389i	$-0.488872\pi$
$997$	2.18743e9	0.0699040	0.0349520	+	0.999389i	$0.488872\pi$
$998$	−1.03473e10	−0.329511
$999$	−5.01514e9	−0.159149

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.a.b.1.6	✓	13
3.2	odd	2		387.8.a.d.1.8		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.a.b.1.6	✓	13	1.1	even	1	trivial
387.8.a.d.1.8		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)

\(f(q)\)	\(=\)	\(q-3.71679 q^{2} -24.7485 q^{3} -114.185 q^{4} +385.350 q^{5} +91.9851 q^{6} -1546.77 q^{7} +900.153 q^{8} -1574.51 q^{9} +O(q^{10})\)	\(q-3.71679 q^{2} -24.7485 q^{3} -114.185 q^{4} +385.350 q^{5} +91.9851 q^{6} -1546.77 q^{7} +900.153 q^{8} -1574.51 q^{9} -1432.27 q^{10} -1662.15 q^{11} +2825.92 q^{12} +12725.9 q^{13} +5749.00 q^{14} -9536.85 q^{15} +11270.1 q^{16} +23803.1 q^{17} +5852.12 q^{18} +30546.0 q^{19} -44001.4 q^{20} +38280.2 q^{21} +6177.85 q^{22} -63784.8 q^{23} -22277.4 q^{24} +70369.8 q^{25} -47299.5 q^{26} +93091.8 q^{27} +176618. q^{28} +190003. q^{29} +35446.5 q^{30} +143977. q^{31} -157108. q^{32} +41135.6 q^{33} -88471.1 q^{34} -596047. q^{35} +179786. q^{36} -53873.0 q^{37} -113533. q^{38} -314947. q^{39} +346874. q^{40} -355277. q^{41} -142279. q^{42} -79507.0 q^{43} +189793. q^{44} -606738. q^{45} +237075. q^{46} -39435.7 q^{47} -278917. q^{48} +1.56894e6 q^{49} -261550. q^{50} -589091. q^{51} -1.45311e6 q^{52} +1.01320e6 q^{53} -346003. q^{54} -640508. q^{55} -1.39233e6 q^{56} -755970. q^{57} -706202. q^{58} +1.24979e6 q^{59} +1.08897e6 q^{60} -751833. q^{61} -535133. q^{62} +2.43540e6 q^{63} -858631. q^{64} +4.90393e6 q^{65} -152893. q^{66} -3.22613e6 q^{67} -2.71797e6 q^{68} +1.57858e6 q^{69} +2.21538e6 q^{70} +1.10265e6 q^{71} -1.41730e6 q^{72} +4.53962e6 q^{73} +200235. q^{74} -1.74155e6 q^{75} -3.48791e6 q^{76} +2.57095e6 q^{77} +1.17059e6 q^{78} +3.63589e6 q^{79} +4.34292e6 q^{80} +1.13957e6 q^{81} +1.32049e6 q^{82} -149479. q^{83} -4.37104e6 q^{84} +9.17253e6 q^{85} +295511. q^{86} -4.70230e6 q^{87} -1.49618e6 q^{88} -8.46943e6 q^{89} +2.25512e6 q^{90} -1.96840e7 q^{91} +7.28329e6 q^{92} -3.56322e6 q^{93} +146574. q^{94} +1.17709e7 q^{95} +3.88819e6 q^{96} +5.99834e6 q^{97} -5.83143e6 q^{98} +2.61707e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 16 q^{2} + 94 q^{3} + 922 q^{4} + 998 q^{5} + 183 q^{6} + 1360 q^{7} + 3870 q^{8} + 10011 q^{9}+O(q^{10}) \) 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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