LMFDB - Embedded newform 43.8.a.b.1.4

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			1.4
Root			$-8.80627$ 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)

$f(q)$	$=$	$q-7.80627 q^{2} -2.71381 q^{3} -67.0621 q^{4} -402.005 q^{5} +21.1847 q^{6} -356.766 q^{7} +1522.71 q^{8} -2179.64 q^{9} +O(q^{10})$	\(q-7.80627 q^{2} -2.71381 q^{3} -67.0621 q^{4} -402.005 q^{5} +21.1847 q^{6} -356.766 q^{7} +1522.71 q^{8} -2179.64 q^{9} +3138.16 q^{10} +338.626 q^{11} +181.994 q^{12} -1901.99 q^{13} +2785.01 q^{14} +1090.96 q^{15} -3302.71 q^{16} -13710.6 q^{17} +17014.8 q^{18} +32375.1 q^{19} +26959.3 q^{20} +968.193 q^{21} -2643.41 q^{22} +103235. q^{23} -4132.34 q^{24} +83482.7 q^{25} +14847.4 q^{26} +11850.2 q^{27} +23925.5 q^{28} +97.3595 q^{29} -8516.35 q^{30} -2919.43 q^{31} -169125. q^{32} -918.966 q^{33} +107029. q^{34} +143421. q^{35} +146171. q^{36} -280235. q^{37} -252729. q^{38} +5161.63 q^{39} -612136. q^{40} -68080.9 q^{41} -7557.98 q^{42} -79507.0 q^{43} -22709.0 q^{44} +876223. q^{45} -805883. q^{46} +145265. q^{47} +8962.93 q^{48} -696261. q^{49} -651689. q^{50} +37208.1 q^{51} +127551. q^{52} -450286. q^{53} -92505.9 q^{54} -136129. q^{55} -543250. q^{56} -87859.8 q^{57} -760.015 q^{58} +2.16940e6 q^{59} -73162.3 q^{60} -240945. q^{61} +22789.9 q^{62} +777619. q^{63} +1.74298e6 q^{64} +764608. q^{65} +7173.70 q^{66} +763129. q^{67} +919465. q^{68} -280161. q^{69} -1.11959e6 q^{70} +256406. q^{71} -3.31895e6 q^{72} -4.25607e6 q^{73} +2.18759e6 q^{74} -226556. q^{75} -2.17114e6 q^{76} -120810. q^{77} -40293.1 q^{78} +6.60338e6 q^{79} +1.32771e6 q^{80} +4.73470e6 q^{81} +531458. q^{82} +1.57834e6 q^{83} -64929.1 q^{84} +5.51174e6 q^{85} +620653. q^{86} -264.215 q^{87} +515629. q^{88} +1.01079e7 q^{89} -6.84004e6 q^{90} +678564. q^{91} -6.92319e6 q^{92} +7922.77 q^{93} -1.13398e6 q^{94} -1.30149e7 q^{95} +458972. q^{96} -1.90764e6 q^{97} +5.43520e6 q^{98} -738081. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−7.80627	−0.689983	−0.344992	−	0.938606i	$-0.612118\pi$
$2$	−7.80627	−0.689983	−0.344992	+	0.938606i	$0.612118\pi$
$3$	−2.71381	−0.0580303	−0.0290151	−	0.999579i	$-0.509237\pi$
$3$	−2.71381	−0.0580303	−0.0290151	+	0.999579i	$0.509237\pi$
$4$	−67.0621	−0.523923
$5$	−402.005	−1.43826	−0.719128	−	0.694878i	$-0.755458\pi$
$5$	−402.005	−1.43826	−0.719128	+	0.694878i	$0.755458\pi$
$6$	21.1847	0.0400399
$7$	−356.766	−0.393133	−0.196567	−	0.980490i	$-0.562979\pi$
$7$	−356.766	−0.393133	−0.196567	+	0.980490i	$0.562979\pi$
$8$	1522.71	1.05148
$9$	−2179.64	−0.996632
$10$	3138.16	0.992372
$11$	338.626	0.0767090	0.0383545	−	0.999264i	$-0.487788\pi$
$11$	338.626	0.0767090	0.0383545	+	0.999264i	$0.487788\pi$
$12$	181.994	0.0304034
$13$	−1901.99	−0.240108	−0.120054	−	0.992767i	$-0.538307\pi$
$13$	−1901.99	−0.240108	−0.120054	+	0.992767i	$0.538307\pi$
$14$	2785.01	0.271255
$15$	1090.96	0.0834624
$16$	−3302.71	−0.201582
$17$	−13710.6	−0.676841	−0.338421	−	0.940995i	$-0.609893\pi$
$17$	−13710.6	−0.676841	−0.338421	+	0.940995i	$0.609893\pi$
$18$	17014.8	0.687660
$19$	32375.1	1.08286	0.541431	−	0.840745i	$-0.317883\pi$
$19$	32375.1	1.08286	0.541431	+	0.840745i	$0.317883\pi$
$20$	26959.3	0.753535
$21$	968.193	0.0228136
$22$	−2643.41	−0.0529279
$23$	103235.	1.76922	0.884609	−	0.466334i	$-0.154426\pi$
$23$	103235.	1.76922	0.884609	+	0.466334i	$0.154426\pi$
$24$	−4132.34	−0.0610178
$25$	83482.7	1.06858
$26$	14847.4	0.165670
$27$	11850.2	0.115865
$28$	23925.5	0.205972
$29$	97.3595	0.000741285 0	0.000370643	−	1.00000i	$-0.499882\pi$
$29$	97.3595	0.000741285 0	0.000370643		1.00000i	$0.499882\pi$
$30$	−8516.35	−0.0575876
$31$	−2919.43	−0.0176008	−0.00880039	−	0.999961i	$-0.502801\pi$
$31$	−2919.43	−0.0176008	−0.00880039	+	0.999961i	$0.502801\pi$
$32$	−169125.	−0.912394
$33$	−918.966	−0.00445144
$34$	107029.	0.467009
$35$	143421.	0.565426
$36$	146171.	0.522159
$37$	−280235.	−0.909529	−0.454764	−	0.890612i	$-0.650277\pi$
$37$	−280235.	−0.909529	−0.454764	+	0.890612i	$0.650277\pi$
$38$	−252729.	−0.747157
$39$	5161.63	0.0139335
$40$	−612136.	−1.51230
$41$	−68080.9	−0.154270	−0.0771350	−	0.997021i	$-0.524577\pi$
$41$	−68080.9	−0.154270	−0.0771350	+	0.997021i	$0.524577\pi$
$42$	−7557.98	−0.0157410
$43$	−79507.0	−0.152499
$43$	−79507.0	−0.152499
$44$	−22709.0	−0.0401896
$45$	876223.	1.43341
$46$	−805883.	−1.22073
$47$	145265.	0.204089	0.102044	−	0.994780i	$-0.467462\pi$
$47$	145265.	0.204089	0.102044	+	0.994780i	$0.467462\pi$
$48$	8962.93	0.0116978
$49$	−696261.	−0.845446
$50$	−651689.	−0.737301
$51$	37208.1	0.0392773
$52$	127551.	0.125798
$53$	−450286.	−0.415454	−0.207727	−	0.978187i	$-0.566607\pi$
$53$	−450286.	−0.415454	−0.207727	+	0.978187i	$0.566607\pi$
$54$	−92505.9	−0.0799450
$55$	−136129.	−0.110327
$56$	−543250.	−0.413372
$57$	−87859.8	−0.0628388
$58$	−760.015	−0.000511474 0
$59$	2.16940e6	1.37518	0.687588	−	0.726101i	$-0.258670\pi$
$59$	2.16940e6	1.37518	0.687588	+	0.726101i	$0.258670\pi$
$60$	−73162.3	−0.0437279
$61$	−240945.	−0.135914	−0.0679570	−	0.997688i	$-0.521648\pi$
$61$	−240945.	−0.135914	−0.0679570	+	0.997688i	$0.521648\pi$
$62$	22789.9	0.0121442
$63$	777619.	0.391809
$64$	1.74298e6	0.831118
$65$	764608.	0.345336
$66$	7173.70	0.00307142
$67$	763129.	0.309982	0.154991	−	0.987916i	$-0.450465\pi$
$67$	763129.	0.309982	0.154991	+	0.987916i	$0.450465\pi$
$68$	919465.	0.354613
$69$	−280161.	−0.102668
$70$	−1.11959e6	−0.390135
$71$	256406.	0.0850206	0.0425103	−	0.999096i	$-0.486464\pi$
$71$	256406.	0.0850206	0.0425103	+	0.999096i	$0.486464\pi$
$72$	−3.31895e6	−1.04794
$73$	−4.25607e6	−1.28050	−0.640249	−	0.768168i	$-0.721169\pi$
$73$	−4.25607e6	−1.28050	−0.640249	+	0.768168i	$0.721169\pi$
$74$	2.18759e6	0.627560
$75$	−226556.	−0.0620099
$76$	−2.17114e6	−0.567337
$77$	−120810.	−0.0301568
$78$	−40293.1	−0.00961390
$79$	6.60338e6	1.50686	0.753428	−	0.657531i	$-0.228399\pi$
$79$	6.60338e6	1.50686	0.753428	+	0.657531i	$0.228399\pi$
$80$	1.32771e6	0.289926
$81$	4.73470e6	0.989909
$82$	531458.	0.106444
$83$	1.57834e6	0.302989	0.151495	−	0.988458i	$-0.451591\pi$
$83$	1.57834e6	0.302989	0.151495	+	0.988458i	$0.451591\pi$
$84$	−64929.1	−0.0119526
$85$	5.51174e6	0.973470
$86$	620653.	0.105221
$87$	−264.215	−4.30170e−5 0
$88$	515629.	0.0806580
$89$	1.01079e7	1.51983	0.759914	−	0.650024i	$-0.225241\pi$
$89$	1.01079e7	1.51983	0.759914	+	0.650024i	$0.225241\pi$
$90$	−6.84004e6	−0.989030
$91$	678564.	0.0943944
$92$	−6.92319e6	−0.926934
$93$	7922.77	0.00102138
$94$	−1.13398e6	−0.140818
$95$	−1.30149e7	−1.55743
$96$	458972.	0.0529465
$97$	−1.90764e6	−0.212224	−0.106112	−	0.994354i	$-0.533840\pi$
$97$	−1.90764e6	−0.212224	−0.106112	+	0.994354i	$0.533840\pi$
$98$	5.43520e6	0.583344
$99$	−738081.	−0.0764506
$100$	−5.59853e6	−0.559853
$101$	−8.79838e6	−0.849724	−0.424862	−	0.905258i	$-0.639677\pi$
$101$	−8.79838e6	−0.849724	−0.424862	+	0.905258i	$0.639677\pi$
$102$	−290456.	−0.0271007
$103$	1.98046e7	1.78581	0.892907	−	0.450242i	$-0.148662\pi$
$103$	1.98046e7	1.78581	0.892907	+	0.450242i	$0.148662\pi$
$104$	−2.89617e6	−0.252469
$105$	−389218.	−0.0328118
$106$	3.51506e6	0.286657
$107$	1.19023e7	0.939264	0.469632	−	0.882862i	$-0.344387\pi$
$107$	1.19023e7	0.939264	0.469632	+	0.882862i	$0.344387\pi$
$108$	−794700.	−0.0607044
$109$	−1.61101e7	−1.19153	−0.595766	−	0.803158i	$-0.703151\pi$
$109$	−1.61101e7	−1.19153	−0.595766	+	0.803158i	$0.703151\pi$
$110$	1.06266e6	0.0761238
$111$	760504.	0.0527802
$112$	1.17829e6	0.0792484
$113$	7.15228e6	0.466305	0.233153	−	0.972440i	$-0.425096\pi$
$113$	7.15228e6	0.466305	0.233153	+	0.972440i	$0.425096\pi$
$114$	685857.	0.0433577
$115$	−4.15011e7	−2.54459
$116$	−6529.14	−0.000388376 0
$117$	4.14564e6	0.239299
$118$	−1.69349e7	−0.948849
$119$	4.89149e6	0.266089
$120$	1.66122e6	0.0877591
$121$	−1.93725e7	−0.994116
$122$	1.88088e6	0.0937784
$123$	184758.	0.00895234
$124$	195783.	0.00922146
$125$	−2.15382e6	−0.0986336
$126$	−6.07030e6	−0.270342
$127$	−1.95885e7	−0.848569	−0.424284	−	0.905529i	$-0.639474\pi$
$127$	−1.95885e7	−0.848569	−0.424284	+	0.905529i	$0.639474\pi$
$128$	8.04179e6	0.338936
$129$	215767.	0.00884953
$130$	−5.96874e6	−0.238276
$131$	3.84474e7	1.49423	0.747115	−	0.664695i	$-0.231438\pi$
$131$	3.84474e7	1.49423	0.747115	+	0.664695i	$0.231438\pi$
$132$	61627.8	0.00233221
$133$	−1.15503e7	−0.425709
$134$	−5.95719e6	−0.213882
$135$	−4.76384e6	−0.166644
$136$	−2.08773e7	−0.711686
$137$	5.35857e7	1.78044	0.890219	−	0.455533i	$-0.150551\pi$
$137$	5.35857e7	1.78044	0.890219	+	0.455533i	$0.150551\pi$
$138$	2.18701e6	0.0708393
$139$	−2.44467e7	−0.772091	−0.386046	−	0.922480i	$-0.626159\pi$
$139$	−2.44467e7	−0.772091	−0.386046	+	0.922480i	$0.626159\pi$
$140$	−9.61815e6	−0.296240
$141$	−394222.	−0.0118433
$142$	−2.00158e6	−0.0586628
$143$	−644063.	−0.0184184
$144$	7.19871e6	0.200903
$145$	−39139.0	−0.00106616
$146$	3.32240e7	0.883522
$147$	1.88952e6	0.0490615
$148$	1.87932e7	0.476523
$149$	6.83645e7	1.69308	0.846542	−	0.532321i	$-0.178680\pi$
$149$	6.83645e7	1.69308	0.846542	+	0.532321i	$0.178680\pi$
$150$	1.76856e6	0.0427858
$151$	4.48140e7	1.05924	0.529620	−	0.848235i	$-0.322335\pi$
$151$	4.48140e7	1.05924	0.529620	+	0.848235i	$0.322335\pi$
$152$	4.92978e7	1.13861
$153$	2.98842e7	0.674562
$154$	943077.	0.0208077
$155$	1.17362e6	0.0253144
$156$	−346150.	−0.00730009
$157$	4.45418e7	0.918585	0.459293	−	0.888285i	$-0.348103\pi$
$157$	4.45418e7	0.918585	0.459293	+	0.888285i	$0.348103\pi$
$158$	−5.15478e7	−1.03970
$159$	1.22199e6	0.0241089
$160$	6.79889e7	1.31225
$161$	−3.68308e7	−0.695538
$162$	−3.69604e7	−0.683021
$163$	−2.04717e7	−0.370251	−0.185126	−	0.982715i	$-0.559269\pi$
$163$	−2.04717e7	−0.370251	−0.185126	+	0.982715i	$0.559269\pi$
$164$	4.56565e6	0.0808256
$165$	369429.	0.00640231
$166$	−1.23209e7	−0.209057
$167$	9.99656e6	0.166090	0.0830449	−	0.996546i	$-0.473536\pi$
$167$	9.99656e6	0.166090	0.0830449	+	0.996546i	$0.473536\pi$
$168$	1.47428e6	0.0239881
$169$	−5.91310e7	−0.942348
$170$	−4.30262e7	−0.671678
$171$	−7.05659e7	−1.07922
$172$	5.33191e6	0.0798975
$173$	9.15039e7	1.34363	0.671813	−	0.740721i	$-0.265516\pi$
$173$	9.15039e7	1.34363	0.671813	+	0.740721i	$0.265516\pi$
$174$	2062.53	2.96810e−5 0
$175$	−2.97838e7	−0.420094
$176$	−1.11838e6	−0.0154631
$177$	−5.88734e6	−0.0798019
$178$	−7.89047e7	−1.04866
$179$	−7.48516e7	−0.975474	−0.487737	−	0.872991i	$-0.662177\pi$
$179$	−7.48516e7	−0.975474	−0.487737	+	0.872991i	$0.662177\pi$
$180$	−5.87614e7	−0.750998
$181$	−1.08411e7	−0.135894	−0.0679470	−	0.997689i	$-0.521645\pi$
$181$	−1.08411e7	−0.135894	−0.0679470	+	0.997689i	$0.521645\pi$
$182$	−5.29706e6	−0.0651305
$183$	653879.	0.00788712
$184$	1.57197e8	1.86030
$185$	1.12656e8	1.30813
$186$	−61847.3	−0.000704734 0
$187$	−4.64278e6	−0.0519198
$188$	−9.74179e6	−0.106927
$189$	−4.22775e6	−0.0455504
$190$	1.01598e8	1.07460
$191$	−1.37400e8	−1.42682	−0.713410	−	0.700747i	$-0.752850\pi$
$191$	−1.37400e8	−1.42682	−0.713410	+	0.700747i	$0.752850\pi$
$192$	−4.73011e6	−0.0482300
$193$	−1.16548e8	−1.16695	−0.583477	−	0.812129i	$-0.698308\pi$
$193$	−1.16548e8	−1.16695	−0.583477	+	0.812129i	$0.698308\pi$
$194$	1.48915e7	0.146431
$195$	−2.07500e6	−0.0200400
$196$	4.66928e7	0.442949
$197$	−1.79080e8	−1.66884	−0.834422	−	0.551126i	$-0.814198\pi$
$197$	−1.79080e8	−1.66884	−0.834422	+	0.551126i	$0.814198\pi$
$198$	5.76166e6	0.0527497
$199$	−1.30708e8	−1.17575	−0.587875	−	0.808952i	$-0.700035\pi$
$199$	−1.30708e8	−1.17575	−0.587875	+	0.808952i	$0.700035\pi$
$200$	1.27120e8	1.12359
$201$	−2.07099e6	−0.0179883
$202$	6.86825e7	0.586295
$203$	−34734.5	−0.000291424 0
$204$	−2.49525e6	−0.0205783
$205$	2.73688e7	0.221880
$206$	−1.54600e8	−1.23218
$207$	−2.25015e8	−1.76326
$208$	6.28172e6	0.0484013
$209$	1.09631e7	0.0830653
$210$	3.03834e6	0.0226396
$211$	3.03753e7	0.222604	0.111302	−	0.993787i	$-0.464498\pi$
$211$	3.03753e7	0.222604	0.111302	+	0.993787i	$0.464498\pi$
$212$	3.01972e7	0.217666
$213$	−695837.	−0.00493377
$214$	−9.29126e7	−0.648076
$215$	3.19622e7	0.219332
$216$	1.80444e7	0.121830
$217$	1.04155e6	0.00691945
$218$	1.25760e8	0.822137
$219$	1.15502e7	0.0743076
$220$	9.12912e6	0.0578029
$221$	2.60775e7	0.162515
$222$	−5.93670e6	−0.0364175
$223$	8.68403e7	0.524390	0.262195	−	0.965015i	$-0.415554\pi$
$223$	8.68403e7	0.524390	0.262195	+	0.965015i	$0.415554\pi$
$224$	6.03379e7	0.358692
$225$	−1.81962e8	−1.06498
$226$	−5.58326e7	−0.321743
$227$	1.67604e8	0.951028	0.475514	−	0.879708i	$-0.342262\pi$
$227$	1.67604e8	0.951028	0.475514	+	0.879708i	$0.342262\pi$
$228$	5.89206e6	0.0329227
$229$	1.15619e8	0.636218	0.318109	−	0.948054i	$-0.396952\pi$
$229$	1.15619e8	0.636218	0.318109	+	0.948054i	$0.396952\pi$
$230$	3.23969e8	1.75572
$231$	327855.	0.00175001
$232$	148250.	0.000779448 0
$233$	1.02835e8	0.532592	0.266296	−	0.963891i	$-0.414200\pi$
$233$	1.02835e8	0.532592	0.266296	+	0.963891i	$0.414200\pi$
$234$	−3.23620e7	−0.165112
$235$	−5.83973e7	−0.293532
$236$	−1.45485e8	−0.720486
$237$	−1.79203e7	−0.0874432
$238$	−3.81843e7	−0.183597
$239$	2.55890e8	1.21244	0.606221	−	0.795296i	$-0.292685\pi$
$239$	2.55890e8	1.21244	0.606221	+	0.795296i	$0.292685\pi$
$240$	−3.60314e6	−0.0168245
$241$	−1.95565e6	−0.00899976	−0.00449988	−	0.999990i	$-0.501432\pi$
$241$	−1.95565e6	−0.00899976	−0.00449988	+	0.999990i	$0.501432\pi$
$242$	1.51227e8	0.685923
$243$	−3.87655e7	−0.173310
$244$	1.61583e7	0.0712085
$245$	2.79900e8	1.21597
$246$	−1.44227e6	−0.00617696
$247$	−6.15771e7	−0.260004
$248$	−4.44544e6	−0.0185069
$249$	−4.28331e6	−0.0175825
$250$	1.68133e7	0.0680556
$251$	−2.99606e8	−1.19589	−0.597946	−	0.801536i	$-0.704016\pi$
$251$	−2.99606e8	−1.19589	−0.597946	+	0.801536i	$0.704016\pi$
$252$	−5.21488e7	−0.205278
$253$	3.49582e7	0.135715
$254$	1.52913e8	0.585498
$255$	−1.49578e7	−0.0564908
$256$	−2.85878e8	−1.06498
$257$	−3.65657e8	−1.34372	−0.671859	−	0.740679i	$-0.734504\pi$
$257$	−3.65657e8	−1.34372	−0.671859	+	0.740679i	$0.734504\pi$
$258$	−1.68433e6	−0.00610603
$259$	9.99782e7	0.357566
$260$	−5.12763e7	−0.180930
$261$	−212208.	−0.000738789 0
$262$	−3.00131e8	−1.03099
$263$	4.38062e8	1.48488	0.742438	−	0.669914i	$-0.233669\pi$
$263$	4.38062e8	1.48488	0.742438	+	0.669914i	$0.233669\pi$
$264$	−1.39932e6	−0.00468061
$265$	1.81017e8	0.597529
$266$	9.01649e7	0.293732
$267$	−2.74308e7	−0.0881960
$268$	−5.11771e7	−0.162407
$269$	−6.37770e7	−0.199771	−0.0998853	−	0.994999i	$-0.531848\pi$
$269$	−6.37770e7	−0.199771	−0.0998853	+	0.994999i	$0.531848\pi$
$270$	3.71878e7	0.114981
$271$	3.49200e8	1.06582	0.532908	−	0.846173i	$-0.321099\pi$
$271$	3.49200e8	1.06582	0.532908	+	0.846173i	$0.321099\pi$
$272$	4.52823e7	0.136439
$273$	−1.84149e6	−0.00547773
$274$	−4.18304e8	−1.22847
$275$	2.82694e7	0.0819695
$276$	1.87882e7	0.0537902
$277$	2.62910e8	0.743238	0.371619	−	0.928385i	$-0.378803\pi$
$277$	2.62910e8	0.743238	0.371619	+	0.928385i	$0.378803\pi$
$278$	1.90838e8	0.532730
$279$	6.36329e6	0.0175415
$280$	2.18389e8	0.594535
$281$	−3.13673e8	−0.843345	−0.421673	−	0.906748i	$-0.638557\pi$
$281$	−3.13673e8	−0.843345	−0.421673	+	0.906748i	$0.638557\pi$
$282$	3.07740e6	0.00817170
$283$	3.05065e7	0.0800093	0.0400046	−	0.999199i	$-0.487263\pi$
$283$	3.05065e7	0.0800093	0.0400046	+	0.999199i	$0.487263\pi$
$284$	−1.71951e7	−0.0445442
$285$	3.53200e7	0.0903783
$286$	5.02773e6	0.0127084
$287$	2.42889e7	0.0606487
$288$	3.68630e8	0.909321
$289$	−2.22357e8	−0.541886
$290$	305529.	0.000735631 0
$291$	5.17696e6	0.0123154
$292$	2.85421e8	0.670882
$293$	6.50794e8	1.51149	0.755747	−	0.654863i	$-0.227274\pi$
$293$	6.50794e8	1.51149	0.755747	+	0.654863i	$0.227274\pi$
$294$	−1.47501e7	−0.0338516
$295$	−8.72110e8	−1.97785
$296$	−4.26716e8	−0.956353
$297$	4.01279e6	0.00888789
$298$	−5.33672e8	−1.16820
$299$	−1.96353e8	−0.424803
$300$	1.51933e7	0.0324884
$301$	2.83654e7	0.0599523
$302$	−3.49830e8	−0.730858
$303$	2.38771e7	0.0493097
$304$	−1.06926e8	−0.218285
$305$	9.68611e7	0.195479
$306$	−2.33284e8	−0.465436
$307$	−1.64397e8	−0.324273	−0.162136	−	0.986768i	$-0.551838\pi$
$307$	−1.64397e8	−0.324273	−0.162136	+	0.986768i	$0.551838\pi$
$308$	8.10179e6	0.0157999
$309$	−5.37459e7	−0.103631
$310$	−9.16163e6	−0.0174665
$311$	6.67878e7	0.125903	0.0629515	−	0.998017i	$-0.479949\pi$
$311$	6.67878e7	0.125903	0.0629515	+	0.998017i	$0.479949\pi$
$312$	7.85966e6	0.0146508
$313$	3.66247e8	0.675101	0.337550	−	0.941307i	$-0.390402\pi$
$313$	3.66247e8	0.675101	0.337550	+	0.941307i	$0.390402\pi$
$314$	−3.47706e8	−0.633808
$315$	−3.12606e8	−0.563522
$316$	−4.42837e8	−0.789476
$317$	8.45942e8	1.49153	0.745767	−	0.666206i	$-0.232083\pi$
$317$	8.45942e8	1.49153	0.745767	+	0.666206i	$0.232083\pi$
$318$	−9.53919e6	−0.0166348
$319$	32968.5	5.68632e−5 0
$320$	−7.00686e8	−1.19536
$321$	−3.23006e7	−0.0545058
$322$	2.87511e8	0.479910
$323$	−4.43883e8	−0.732926
$324$	−3.17519e8	−0.518636
$325$	−1.58783e8	−0.256574
$326$	1.59807e8	0.255467
$327$	4.37197e7	0.0691449
$328$	−1.03667e8	−0.162212
$329$	−5.18256e7	−0.0802341
$330$	−2.88386e6	−0.00441749
$331$	−1.56474e8	−0.237162	−0.118581	−	0.992944i	$-0.537835\pi$
$331$	−1.56474e8	−0.237162	−0.118581	+	0.992944i	$0.537835\pi$
$332$	−1.05847e8	−0.158743
$333$	6.10810e8	0.906466
$334$	−7.80358e7	−0.114599
$335$	−3.06781e8	−0.445833
$336$	−3.19766e6	−0.00459881
$337$	1.10367e9	1.57085	0.785424	−	0.618958i	$-0.212445\pi$
$337$	1.10367e9	1.57085	0.785424	+	0.618958i	$0.212445\pi$
$338$	4.61592e8	0.650205
$339$	−1.94099e7	−0.0270598
$340$	−3.69629e8	−0.510024
$341$	−988595.	−0.00135014
$342$	5.50856e8	0.744641
$343$	5.42214e8	0.725506
$344$	−1.21066e8	−0.160349
$345$	1.12626e8	0.147663
$346$	−7.14304e8	−0.927079
$347$	−7.51448e7	−0.0965485	−0.0482743	−	0.998834i	$-0.515372\pi$
$347$	−7.51448e7	−0.0965485	−0.0482743	+	0.998834i	$0.515372\pi$
$348$	17718.8	2.25376e−5 0
$349$	4.40370e8	0.554534	0.277267	−	0.960793i	$-0.410571\pi$
$349$	4.40370e8	0.554534	0.277267	+	0.960793i	$0.410571\pi$
$350$	2.32500e8	0.289858
$351$	−2.25390e7	−0.0278201
$352$	−5.72701e7	−0.0699888
$353$	−8.89528e7	−0.107634	−0.0538168	−	0.998551i	$-0.517139\pi$
$353$	−8.89528e7	−0.107634	−0.0538168	+	0.998551i	$0.517139\pi$
$354$	4.59582e7	0.0550619
$355$	−1.03076e8	−0.122281
$356$	−6.77855e8	−0.796273
$357$	−1.32746e7	−0.0154412
$358$	5.84312e8	0.673061
$359$	−1.09248e9	−1.24619	−0.623095	−	0.782146i	$-0.714125\pi$
$359$	−1.09248e9	−1.24619	−0.623095	+	0.782146i	$0.714125\pi$
$360$	1.33423e9	1.50721
$361$	1.54275e8	0.172591
$362$	8.46289e7	0.0937645
$363$	5.25732e7	0.0576888
$364$	−4.55060e7	−0.0494554
$365$	1.71096e9	1.84168
$366$	−5.10436e6	−0.00544198
$367$	−5.91559e8	−0.624693	−0.312346	−	0.949968i	$-0.601115\pi$
$367$	−5.91559e8	−0.624693	−0.312346	+	0.949968i	$0.601115\pi$
$368$	−3.40957e8	−0.356642
$369$	1.48391e8	0.153751
$370$	−8.79422e8	−0.902591
$371$	1.60647e8	0.163329
$372$	−531318.	−0.000535124 0
$373$	1.17638e9	1.17373	0.586863	−	0.809686i	$-0.300363\pi$
$373$	1.17638e9	1.17373	0.586863	+	0.809686i	$0.300363\pi$
$374$	3.62428e7	0.0358238
$375$	5.84506e6	0.00572374
$376$	2.21196e8	0.214595
$377$	−185177.	−0.000177988 0
$378$	3.30029e7	0.0314290
$379$	1.58878e9	1.49908	0.749541	−	0.661958i	$-0.230274\pi$
$379$	1.58878e9	1.49908	0.749541	+	0.661958i	$0.230274\pi$
$380$	8.72810e8	0.815975
$381$	5.31593e7	0.0492427
$382$	1.07258e9	0.984482
$383$	−1.52083e9	−1.38320	−0.691599	−	0.722281i	$-0.743094\pi$
$383$	−1.52083e9	−1.38320	−0.691599	+	0.722281i	$0.743094\pi$
$384$	−2.18239e7	−0.0196686
$385$	4.85662e7	0.0433732
$386$	9.09805e8	0.805179
$387$	1.73296e8	0.151985
$388$	1.27930e8	0.111189
$389$	1.81957e9	1.56728	0.783639	−	0.621217i	$-0.213361\pi$
$389$	1.81957e9	1.56728	0.783639	+	0.621217i	$0.213361\pi$
$390$	1.61980e7	0.0138272
$391$	−1.41542e9	−1.19748
$392$	−1.06020e9	−0.888971
$393$	−1.04339e8	−0.0867106
$394$	1.39795e9	1.15147
$395$	−2.65459e9	−2.16724
$396$	4.94973e7	0.0400542
$397$	2.11509e9	1.69653	0.848265	−	0.529571i	$-0.177647\pi$
$397$	2.11509e9	1.69653	0.848265	+	0.529571i	$0.177647\pi$
$398$	1.02034e9	0.811248
$399$	3.13453e7	0.0247040
$400$	−2.75719e8	−0.215406
$401$	−2.18744e9	−1.69407	−0.847034	−	0.531539i	$-0.821614\pi$
$401$	−2.18744e9	−1.69407	−0.847034	+	0.531539i	$0.821614\pi$
$402$	1.61667e7	0.0124116
$403$	5.55272e6	0.00422609
$404$	5.90038e8	0.445190
$405$	−1.90337e9	−1.42374
$406$	271147.	0.000201078 0
$407$	−9.48949e7	−0.0697690
$408$	5.66570e7	0.0412993
$409$	−1.16511e9	−0.842045	−0.421022	−	0.907050i	$-0.638329\pi$
$409$	−1.16511e9	−0.842045	−0.421022	+	0.907050i	$0.638329\pi$
$410$	−2.13648e8	−0.153093
$411$	−1.45421e8	−0.103319
$412$	−1.32814e9	−0.935629
$413$	−7.73968e8	−0.540627
$414$	1.75653e9	1.21662
$415$	−6.34499e8	−0.435776
$416$	3.21673e8	0.219073
$417$	6.63437e7	0.0448047
$418$	−8.55805e7	−0.0573136
$419$	−9.59686e8	−0.637353	−0.318677	−	0.947864i	$-0.603238\pi$
$419$	−9.59686e8	−0.637353	−0.318677	+	0.947864i	$0.603238\pi$
$420$	2.61018e7	0.0171909
$421$	−1.02361e7	−0.00668572	−0.00334286	−	0.999994i	$-0.501064\pi$
$421$	−1.02361e7	−0.00668572	−0.00334286	+	0.999994i	$0.501064\pi$
$422$	−2.37118e8	−0.153593
$423$	−3.16625e8	−0.203401
$424$	−6.85655e8	−0.436843
$425$	−1.14460e9	−0.723258
$426$	5.43189e6	0.00340422
$427$	8.59610e7	0.0534323
$428$	−7.98194e8	−0.492102
$429$	1.74786e6	0.00106883
$430$	−2.49505e8	−0.151335
$431$	−3.14206e9	−1.89036	−0.945179	−	0.326552i	$-0.894113\pi$
$431$	−3.14206e9	−1.89036	−0.945179	+	0.326552i	$0.894113\pi$
$432$	−3.91378e7	−0.0233563
$433$	−2.31364e9	−1.36958	−0.684792	−	0.728739i	$-0.740107\pi$
$433$	−2.31364e9	−1.36958	−0.684792	+	0.728739i	$0.740107\pi$
$434$	−8.13063e6	−0.00477431
$435$	106216.	6.18694e−5 0
$436$	1.08038e9	0.624271
$437$	3.34225e9	1.91582
$438$	−9.01636e7	−0.0512710
$439$	1.64208e9	0.926337	0.463168	−	0.886270i	$-0.346713\pi$
$439$	1.64208e9	0.926337	0.463168	+	0.886270i	$0.346713\pi$
$440$	−2.07285e8	−0.116007
$441$	1.51760e9	0.842599
$442$	−2.03568e8	−0.112133
$443$	7.12250e8	0.389242	0.194621	−	0.980879i	$-0.437652\pi$
$443$	7.12250e8	0.389242	0.194621	+	0.980879i	$0.437652\pi$
$444$	−5.10010e7	−0.0276528
$445$	−4.06341e9	−2.18590
$446$	−6.77899e8	−0.361820
$447$	−1.85528e8	−0.0982502
$448$	−6.21835e8	−0.326740
$449$	2.15899e9	1.12561	0.562805	−	0.826590i	$-0.309722\pi$
$449$	2.15899e9	1.12561	0.562805	+	0.826590i	$0.309722\pi$
$450$	1.42044e9	0.734819
$451$	−2.30540e7	−0.0118339
$452$	−4.79647e8	−0.244308
$453$	−1.21617e8	−0.0614680
$454$	−1.30836e9	−0.656193
$455$	−2.72786e8	−0.135763
$456$	−1.33785e8	−0.0660739
$457$	−1.05753e9	−0.518308	−0.259154	−	0.965836i	$-0.583444\pi$
$457$	−1.05753e9	−0.518308	−0.259154	+	0.965836i	$0.583444\pi$
$458$	−9.02555e8	−0.438980
$459$	−1.62474e8	−0.0784223
$460$	2.78315e9	1.33317
$461$	−2.93548e9	−1.39549	−0.697743	−	0.716348i	$-0.745812\pi$
$461$	−2.93548e9	−1.39549	−0.697743	+	0.716348i	$0.745812\pi$
$462$	−2.55933e6	−0.00120748
$463$	2.80303e9	1.31248	0.656242	−	0.754550i	$-0.272145\pi$
$463$	2.80303e9	1.31248	0.656242	+	0.754550i	$0.272145\pi$
$464$	−321551.	−0.000149429 0
$465$	−3.18499e6	−0.00146900
$466$	−8.02756e8	−0.367479
$467$	1.35420e9	0.615281	0.307640	−	0.951503i	$-0.400461\pi$
$467$	1.35420e9	0.615281	0.307640	+	0.951503i	$0.400461\pi$
$468$	−2.78016e8	−0.125374
$469$	−2.72258e8	−0.121864
$470$	4.55865e8	0.202532
$471$	−1.20878e8	−0.0533058
$472$	3.30337e9	1.44597
$473$	−2.69231e7	−0.0116980
$474$	1.39891e8	0.0603344
$475$	2.70276e9	1.15712
$476$	−3.28034e8	−0.139410
$477$	9.81460e8	0.414055
$478$	−1.99755e9	−0.836565
$479$	1.17660e9	0.489165	0.244583	−	0.969628i	$-0.421349\pi$
$479$	1.17660e9	0.489165	0.244583	+	0.969628i	$0.421349\pi$
$480$	−1.84509e8	−0.0761505
$481$	5.33004e8	0.218385
$482$	1.52663e7	0.00620969
$483$	9.99518e7	0.0403623
$484$	1.29916e9	0.520840
$485$	7.66879e8	0.305233
$486$	3.02614e8	0.119581
$487$	−1.73453e9	−0.680504	−0.340252	−	0.940334i	$-0.610512\pi$
$487$	−1.73453e9	−0.680504	−0.340252	+	0.940334i	$0.610512\pi$
$488$	−3.66889e8	−0.142911
$489$	5.55562e7	0.0214858
$490$	−2.18498e9	−0.838997
$491$	7.94788e8	0.303016	0.151508	−	0.988456i	$-0.451587\pi$
$491$	7.94788e8	0.303016	0.151508	+	0.988456i	$0.451587\pi$
$492$	−1.23903e7	−0.00469033
$493$	−1.33486e6	−0.000501732 0
$494$	4.80687e8	0.179398
$495$	2.96712e8	0.109956
$496$	9.64204e6	0.00354799
$497$	−9.14769e7	−0.0334244
$498$	3.34367e7	0.0121317
$499$	−2.73492e8	−0.0985354	−0.0492677	−	0.998786i	$-0.515689\pi$
$499$	−2.73492e8	−0.0985354	−0.0492677	+	0.998786i	$0.515689\pi$
$500$	1.44440e8	0.0516764
$501$	−2.71287e7	−0.00963824
$502$	2.33880e9	0.825146
$503$	3.20927e9	1.12439	0.562197	−	0.827004i	$-0.309956\pi$
$503$	3.20927e9	1.12439	0.562197	+	0.827004i	$0.309956\pi$
$504$	1.18409e9	0.411980
$505$	3.53699e9	1.22212
$506$	−2.72893e8	−0.0936409
$507$	1.60470e8	0.0546847
$508$	1.31364e9	0.444585
$509$	−2.06801e9	−0.695090	−0.347545	−	0.937663i	$-0.612985\pi$
$509$	−2.06801e9	−0.695090	−0.347545	+	0.937663i	$0.612985\pi$
$510$	1.16765e8	0.0389777
$511$	1.51842e9	0.503406
$512$	1.20229e9	0.395881
$513$	3.83652e8	0.125466
$514$	2.85442e9	0.927143
$515$	−7.96155e9	−2.56846
$516$	−1.44698e7	−0.00463648
$517$	4.91906e7	0.0156554
$518$	−7.80457e8	−0.246715
$519$	−2.48324e8	−0.0779709
$520$	1.16428e9	0.363115
$521$	−3.73056e8	−0.115569	−0.0577846	−	0.998329i	$-0.518404\pi$
$521$	−3.73056e8	−0.115569	−0.0577846	+	0.998329i	$0.518404\pi$
$522$	1.65655e6	0.000509752 0
$523$	3.23366e9	0.988414	0.494207	−	0.869344i	$-0.335459\pi$
$523$	3.23366e9	0.988414	0.494207	+	0.869344i	$0.335459\pi$
$524$	−2.57837e9	−0.782862
$525$	8.08274e7	0.0243782
$526$	−3.41963e9	−1.02454
$527$	4.00273e7	0.0119129
$528$	3.03508e6	0.000897329 0
$529$	7.25272e9	2.13013
$530$	−1.41307e9	−0.412285
$531$	−4.72851e9	−1.37055
$532$	7.74589e8	0.223039
$533$	1.29489e8	0.0370414
$534$	2.14132e8	0.0608538
$535$	−4.78478e9	−1.35090
$536$	1.16202e9	0.325940
$537$	2.03133e8	0.0566070
$538$	4.97861e8	0.137838
$539$	−2.35772e8	−0.0648533
$540$	3.19473e8	0.0873085
$541$	−6.33940e9	−1.72131	−0.860653	−	0.509192i	$-0.829944\pi$
$541$	−6.33940e9	−1.72131	−0.860653	+	0.509192i	$0.829944\pi$
$542$	−2.72595e9	−0.735395
$543$	2.94208e7	0.00788596
$544$	2.31881e9	0.617545
$545$	6.47633e9	1.71373
$546$	1.43752e7	0.00377954
$547$	2.18850e9	0.571731	0.285865	−	0.958270i	$-0.407719\pi$
$547$	2.18850e9	0.571731	0.285865	+	0.958270i	$0.407719\pi$
$548$	−3.59357e9	−0.932812
$549$	5.25173e8	0.135456
$550$	−2.20679e8	−0.0565576
$551$	3.15202e6	0.000802710 0
$552$	−4.26603e8	−0.107954
$553$	−2.35586e9	−0.592395
$554$	−2.05235e9	−0.512822
$555$	−3.05726e8	−0.0759114
$556$	1.63945e9	0.404516
$557$	−2.65106e9	−0.650019	−0.325009	−	0.945711i	$-0.605367\pi$
$557$	−2.65106e9	−0.650019	−0.325009	+	0.945711i	$0.605367\pi$
$558$	−4.96736e7	−0.0121034
$559$	1.51221e8	0.0366161
$560$	−4.73680e8	−0.113979
$561$	1.25996e7	0.00301292
$562$	2.44862e9	0.581894
$563$	−4.33945e9	−1.02484	−0.512419	−	0.858736i	$-0.671251\pi$
$563$	−4.33945e9	−1.02484	−0.512419	+	0.858736i	$0.671251\pi$
$564$	2.64374e7	0.00620499
$565$	−2.87525e9	−0.670666
$566$	−2.38142e8	−0.0552051
$567$	−1.68918e9	−0.389166
$568$	3.90432e8	0.0893976
$569$	6.16980e8	0.140404	0.0702018	−	0.997533i	$-0.477636\pi$
$569$	6.16980e8	0.140404	0.0702018	+	0.997533i	$0.477636\pi$
$570$	−2.75718e8	−0.0623595
$571$	5.73913e9	1.29009	0.645045	−	0.764145i	$-0.276839\pi$
$571$	5.73913e9	1.29009	0.645045	+	0.764145i	$0.276839\pi$
$572$	4.31923e7	0.00964983
$573$	3.72877e8	0.0827988
$574$	−1.89606e8	−0.0418466
$575$	8.61837e9	1.89055
$576$	−3.79906e9	−0.828319
$577$	5.29584e9	1.14768	0.573838	−	0.818969i	$-0.305454\pi$
$577$	5.29584e9	1.14768	0.573838	+	0.818969i	$0.305454\pi$
$578$	1.73578e9	0.373892
$579$	3.16289e8	0.0677187
$580$	2.62474e6	0.000558585 0
$581$	−5.63097e8	−0.119115
$582$	−4.04128e7	−0.00849744
$583$	−1.52479e8	−0.0318691
$584$	−6.48075e9	−1.34642
$585$	−1.66657e9	−0.344173
$586$	−5.08027e9	−1.04291
$587$	4.99464e8	0.101923	0.0509613	−	0.998701i	$-0.483771\pi$
$587$	4.99464e8	0.101923	0.0509613	+	0.998701i	$0.483771\pi$
$588$	−1.26715e8	−0.0257044
$589$	−9.45168e7	−0.0190592
$590$	6.80793e9	1.36469
$591$	4.85989e8	0.0968435
$592$	9.25536e8	0.183344
$593$	−1.20268e9	−0.236842	−0.118421	−	0.992963i	$-0.537783\pi$
$593$	−1.20268e9	−0.236842	−0.118421	+	0.992963i	$0.537783\pi$
$594$	−3.13249e7	−0.00613250
$595$	−1.96640e9	−0.382704
$596$	−4.58467e9	−0.887046
$597$	3.54715e8	0.0682291
$598$	1.53278e9	0.293107
$599$	−5.47286e9	−1.04045	−0.520224	−	0.854030i	$-0.674151\pi$
$599$	−5.47286e9	−1.04045	−0.520224	+	0.854030i	$0.674151\pi$
$600$	−3.44979e8	−0.0652023
$601$	−4.60823e9	−0.865912	−0.432956	−	0.901415i	$-0.642529\pi$
$601$	−4.60823e9	−0.865912	−0.432956	+	0.901415i	$0.642529\pi$
$602$	−2.21428e8	−0.0413661
$603$	−1.66334e9	−0.308938
$604$	−3.00532e9	−0.554960
$605$	7.78784e9	1.42979
$606$	−1.86391e8	−0.0340229
$607$	7.85259e9	1.42512	0.712562	−	0.701610i	$-0.247535\pi$
$607$	7.85259e9	1.42512	0.712562	+	0.701610i	$0.247535\pi$
$608$	−5.47543e9	−0.987997
$609$	94262.8	1.69114e−5 0
$610$	−7.56124e8	−0.134877
$611$	−2.76293e8	−0.0490033
$612$	−2.00410e9	−0.353418
$613$	−1.04035e10	−1.82419	−0.912095	−	0.409980i	$-0.865536\pi$
$613$	−1.04035e10	−1.82419	−0.912095	+	0.409980i	$0.865536\pi$
$614$	1.28333e9	0.223743
$615$	−7.42737e7	−0.0128757
$616$	−1.83959e8	−0.0317094
$617$	2.89619e9	0.496397	0.248198	−	0.968709i	$-0.420162\pi$
$617$	2.89619e9	0.496397	0.248198	+	0.968709i	$0.420162\pi$
$618$	4.19555e8	0.0715038
$619$	−1.69036e9	−0.286458	−0.143229	−	0.989690i	$-0.545749\pi$
$619$	−1.69036e9	−0.286458	−0.143229	+	0.989690i	$0.545749\pi$
$620$	−7.87057e7	−0.0132628
$621$	1.22336e9	0.204991
$622$	−5.21364e8	−0.0868710
$623$	−3.60614e9	−0.597495
$624$	−1.70474e7	−0.00280874
$625$	−5.65624e9	−0.926718
$626$	−2.85902e9	−0.465808
$627$	−2.97516e7	−0.00482030
$628$	−2.98707e9	−0.481268
$629$	3.84220e9	0.615606
$630$	2.44029e9	0.388821
$631$	−3.25816e9	−0.516261	−0.258131	−	0.966110i	$-0.583106\pi$
$631$	−3.25816e9	−0.516261	−0.258131	+	0.966110i	$0.583106\pi$
$632$	1.00550e10	1.58443
$633$	−8.24328e7	−0.0129178
$634$	−6.60366e9	−1.02913
$635$	7.87465e9	1.22046
$636$	−8.19493e7	−0.0126312
$637$	1.32428e9	0.202998
$638$	−257361.	−3.92347e−5 0
$639$	−5.58872e8	−0.0847343
$640$	−3.23284e9	−0.487477
$641$	1.62115e9	0.243119	0.121560	−	0.992584i	$-0.461210\pi$
$641$	1.62115e9	0.243119	0.121560	+	0.992584i	$0.461210\pi$
$642$	2.52147e8	0.0376081
$643$	−4.87271e8	−0.0722823	−0.0361412	−	0.999347i	$-0.511507\pi$
$643$	−4.87271e8	−0.0722823	−0.0361412	+	0.999347i	$0.511507\pi$
$644$	2.46995e9	0.364408
$645$	−8.67392e7	−0.0127279
$646$	3.46507e9	0.505707
$647$	1.32422e10	1.92219	0.961095	−	0.276219i	$-0.0890817\pi$
$647$	1.32422e10	1.92219	0.961095	+	0.276219i	$0.0890817\pi$
$648$	7.20957e9	1.04087
$649$	7.34617e8	0.105488
$650$	1.23950e9	0.177032
$651$	−2.82657e6	−0.000401538 0
$652$	1.37287e9	0.193983
$653$	1.05133e10	1.47755	0.738774	−	0.673953i	$-0.235405\pi$
$653$	1.05133e10	1.47755	0.738774	+	0.673953i	$0.235405\pi$
$654$	−3.41288e8	−0.0477088
$655$	−1.54560e10	−2.14908
$656$	2.24852e8	0.0310980
$657$	9.27668e9	1.27619
$658$	4.04565e8	0.0553602
$659$	5.82980e9	0.793514	0.396757	−	0.917924i	$-0.370136\pi$
$659$	5.82980e9	0.793514	0.396757	+	0.917924i	$0.370136\pi$
$660$	−2.47747e7	−0.00335432
$661$	4.98936e9	0.671954	0.335977	−	0.941870i	$-0.390934\pi$
$661$	4.98936e9	0.671954	0.335977	+	0.941870i	$0.390934\pi$
$662$	1.22148e9	0.163638
$663$	−7.07693e7	−0.00943078
$664$	2.40335e9	0.318587
$665$	4.64328e9	0.612279
$666$	−4.76815e9	−0.625446
$667$	1.00509e7	0.00131149
$668$	−6.70391e8	−0.0870183
$669$	−2.35668e8	−0.0304305
$670$	2.39482e9	0.307617
$671$	−8.15904e7	−0.0104258
$672$	−1.63745e8	−0.0208150
$673$	−9.45755e9	−1.19599	−0.597993	−	0.801502i	$-0.704035\pi$
$673$	−9.45755e9	−1.19599	−0.597993	+	0.801502i	$0.704035\pi$
$674$	−8.61554e9	−1.08386
$675$	9.89287e8	0.123811
$676$	3.96545e9	0.493718
$677$	−1.17413e10	−1.45431	−0.727155	−	0.686474i	$-0.759158\pi$
$677$	−1.17413e10	−1.45431	−0.727155	+	0.686474i	$0.759158\pi$
$678$	1.51519e8	0.0186708
$679$	6.80579e8	0.0834324
$680$	8.39277e9	1.02359
$681$	−4.54844e8	−0.0551884
$682$	7.71724e6	0.000931572 0
$683$	8.01180e9	0.962183	0.481091	−	0.876670i	$-0.340241\pi$
$683$	8.01180e9	0.962183	0.481091	+	0.876670i	$0.340241\pi$
$684$	4.73230e9	0.565426
$685$	−2.15417e10	−2.56072
$686$	−4.23267e9	−0.500587
$687$	−3.13768e8	−0.0369199
$688$	2.62589e8	0.0307409
$689$	8.56440e8	0.0997538
$690$	−8.79189e8	−0.101885
$691$	9.40691e9	1.08461	0.542305	−	0.840181i	$-0.317552\pi$
$691$	9.40691e9	1.08461	0.542305	+	0.840181i	$0.317552\pi$
$692$	−6.13645e9	−0.703956
$693$	2.63322e8	0.0300553
$694$	5.86600e8	0.0666169
$695$	9.82769e9	1.11046
$696$	−402322.	−4.52316e−5 0
$697$	9.33433e8	0.104416
$698$	−3.43765e9	−0.382619
$699$	−2.79074e8	−0.0309064
$700$	1.99736e9	0.220097
$701$	5.77903e9	0.633639	0.316819	−	0.948486i	$-0.397385\pi$
$701$	5.77903e9	0.633639	0.316819	+	0.948486i	$0.397385\pi$
$702$	1.75945e8	0.0191954
$703$	−9.07264e9	−0.984895
$704$	5.90219e8	0.0637542
$705$	1.58479e8	0.0170337
$706$	6.94389e8	0.0742654
$707$	3.13896e9	0.334055
$708$	3.94818e8	0.0418100
$709$	1.04068e10	1.09662	0.548311	−	0.836274i	$-0.315271\pi$
$709$	1.04068e10	1.09662	0.548311	+	0.836274i	$0.315271\pi$
$710$	8.04642e8	0.0843721
$711$	−1.43930e10	−1.50178
$712$	1.53913e10	1.59807
$713$	−3.01388e8	−0.0311396
$714$	1.03625e8	0.0106542
$715$	2.58916e8	0.0264904
$716$	5.01971e9	0.511073
$717$	−6.94437e8	−0.0703583
$718$	8.52822e9	0.859851
$719$	1.83550e10	1.84164	0.920819	−	0.389991i	$-0.127522\pi$
$719$	1.83550e10	1.84164	0.920819	+	0.389991i	$0.127522\pi$
$720$	−2.89391e9	−0.288949
$721$	−7.06560e9	−0.702063
$722$	−1.20431e9	−0.119085
$723$	5.30725e6	0.000522259 0
$724$	7.27030e8	0.0711980
$725$	8.12784e6	0.000792122 0
$726$	−4.10401e8	−0.0398043
$727$	1.38023e9	0.133223	0.0666116	−	0.997779i	$-0.478781\pi$
$727$	1.38023e9	0.133223	0.0666116	+	0.997779i	$0.478781\pi$
$728$	1.03325e9	0.0992539
$729$	−1.02496e10	−0.979852
$730$	−1.33562e10	−1.27073
$731$	1.09009e9	0.103217
$732$	−4.38505e7	−0.00413225
$733$	2.24467e9	0.210518	0.105259	−	0.994445i	$-0.466433\pi$
$733$	2.24467e9	0.210518	0.105259	+	0.994445i	$0.466433\pi$
$734$	4.61787e9	0.431028
$735$	−7.59595e8	−0.0705629
$736$	−1.74597e10	−1.61422
$737$	2.58415e8	0.0237784
$738$	−1.15838e9	−0.106085
$739$	4.41123e9	0.402072	0.201036	−	0.979584i	$-0.435569\pi$
$739$	4.41123e9	0.402072	0.201036	+	0.979584i	$0.435569\pi$
$740$	−7.55494e9	−0.685362
$741$	1.67108e8	0.0150881
$742$	−1.25405e9	−0.112694
$743$	1.31411e10	1.17536	0.587679	−	0.809094i	$-0.300042\pi$
$743$	1.31411e10	1.17536	0.587679	+	0.809094i	$0.300042\pi$
$744$	1.20641e7	0.00107396
$745$	−2.74828e10	−2.43509
$746$	−9.18315e9	−0.809852
$747$	−3.44020e9	−0.301969
$748$	3.11355e8	0.0272020
$749$	−4.24633e9	−0.369256
$750$	−4.56281e7	−0.00394928
$751$	8.90398e9	0.767087	0.383543	−	0.923523i	$-0.374704\pi$
$751$	8.90398e9	0.767087	0.383543	+	0.923523i	$0.374704\pi$
$752$	−4.79769e8	−0.0411405
$753$	8.13072e8	0.0693980
$754$	1.44554e6	0.000122809 0
$755$	−1.80154e10	−1.52346
$756$	2.83522e8	0.0238649
$757$	−1.98575e10	−1.66375	−0.831877	−	0.554960i	$-0.812734\pi$
$757$	−1.98575e10	−1.66375	−0.831877	+	0.554960i	$0.812734\pi$
$758$	−1.24024e10	−1.03434
$759$	−9.48698e7	−0.00787557
$760$	−1.98179e10	−1.63761
$761$	4.10456e9	0.337614	0.168807	−	0.985649i	$-0.446009\pi$
$761$	4.10456e9	0.337614	0.168807	+	0.985649i	$0.446009\pi$
$762$	−4.14976e8	−0.0339766
$763$	5.74753e9	0.468431
$764$	9.21432e9	0.747544
$765$	−1.20136e10	−0.970192
$766$	1.18720e10	0.954384
$767$	−4.12618e9	−0.330190
$768$	7.75818e8	0.0618010
$769$	1.69512e10	1.34418	0.672091	−	0.740468i	$-0.265396\pi$
$769$	1.69512e10	1.34418	0.672091	+	0.740468i	$0.265396\pi$
$770$	−3.79121e8	−0.0299268
$771$	9.92323e8	0.0779763
$772$	7.81595e9	0.611394
$773$	7.71790e8	0.0600995	0.0300498	−	0.999548i	$-0.490433\pi$
$773$	7.71790e8	0.0600995	0.0300498	+	0.999548i	$0.490433\pi$
$774$	−1.35280e9	−0.104867
$775$	−2.43722e8	−0.0188078
$776$	−2.90478e9	−0.223150
$777$	−2.71322e8	−0.0207497
$778$	−1.42041e10	−1.08140
$779$	−2.20412e9	−0.167053
$780$	1.39154e8	0.0104994
$781$	8.68258e7	0.00652184
$782$	1.10492e10	0.826240
$783$	1.15373e6	8.58891e−5 0
$784$	2.29955e9	0.170426
$785$	−1.79060e10	−1.32116
$786$	8.14497e8	0.0598289
$787$	−1.55107e10	−1.13428	−0.567139	−	0.823622i	$-0.691950\pi$
$787$	−1.55107e10	−1.13428	−0.567139	+	0.823622i	$0.691950\pi$
$788$	1.20095e10	0.874346
$789$	−1.18882e9	−0.0861678
$790$	2.07224e10	1.49536
$791$	−2.55169e9	−0.183320
$792$	−1.12388e9	−0.0803864
$793$	4.58275e8	0.0326340
$794$	−1.65110e10	−1.17058
$795$	−4.91246e8	−0.0346748
$796$	8.76553e9	0.616003
$797$	1.44069e10	1.00801	0.504006	−	0.863700i	$-0.331859\pi$
$797$	1.44069e10	1.00801	0.504006	+	0.863700i	$0.331859\pi$
$798$	−2.44690e8	−0.0170454
$799$	−1.99168e9	−0.138136
$800$	−1.41190e10	−0.974964
$801$	−2.20315e10	−1.51471
$802$	1.70757e10	1.16888
$803$	−1.44122e9	−0.0982256
$804$	1.38885e8	0.00942450
$805$	1.48062e10	1.00036
$806$	−4.33460e7	−0.00291593
$807$	1.73079e8	0.0115927
$808$	−1.33974e10	−0.893469
$809$	−1.32032e10	−0.876714	−0.438357	−	0.898801i	$-0.644440\pi$
$809$	−1.32032e10	−0.876714	−0.438357	+	0.898801i	$0.644440\pi$
$810$	1.48582e10	0.982358
$811$	2.59038e10	1.70526	0.852629	−	0.522517i	$-0.175007\pi$
$811$	2.59038e10	1.70526	0.852629	+	0.522517i	$0.175007\pi$
$812$	2.32937e6	0.000152684 0
$813$	−9.47663e8	−0.0618496
$814$	7.40775e8	0.0481394
$815$	8.22971e9	0.532516
$816$	−1.22888e8	−0.00791758
$817$	−2.57405e9	−0.165135
$818$	9.09516e9	0.580997
$819$	−1.47902e9	−0.0940765
$820$	−1.83541e9	−0.116248
$821$	−1.80408e9	−0.113777	−0.0568885	−	0.998381i	$-0.518118\pi$
$821$	−1.80408e9	−0.113777	−0.0568885	+	0.998381i	$0.518118\pi$
$822$	1.13520e9	0.0712886
$823$	2.15004e10	1.34445	0.672227	−	0.740345i	$-0.265338\pi$
$823$	2.15004e10	1.34445	0.672227	+	0.740345i	$0.265338\pi$
$824$	3.01566e10	1.87775
$825$	−7.67178e7	−0.00475672
$826$	6.04181e9	0.373024
$827$	1.95017e10	1.19895	0.599477	−	0.800392i	$-0.295375\pi$
$827$	1.95017e10	1.19895	0.599477	+	0.800392i	$0.295375\pi$
$828$	1.50900e10	0.923812
$829$	1.50758e10	0.919049	0.459524	−	0.888165i	$-0.348020\pi$
$829$	1.50758e10	0.919049	0.459524	+	0.888165i	$0.348020\pi$
$830$	4.95307e9	0.300678
$831$	−7.13487e8	−0.0431303
$832$	−3.31513e9	−0.199558
$833$	9.54619e9	0.572233
$834$	−5.17896e8	−0.0309145
$835$	−4.01866e9	−0.238880
$836$	−7.35206e8	−0.0435198
$837$	−3.45958e7	−0.00203932
$838$	7.49157e9	0.439763
$839$	−3.01700e10	−1.76363	−0.881816	−	0.471594i	$-0.843679\pi$
$839$	−3.01700e10	−1.76363	−0.881816	+	0.471594i	$0.843679\pi$
$840$	−5.92665e8	−0.0345010
$841$	−1.72499e10	−0.999999
$842$	7.99060e7	0.00461304
$843$	8.51249e8	0.0489396
$844$	−2.03703e9	−0.116627
$845$	2.37709e10	1.35534
$846$	2.47166e9	0.140344
$847$	6.91144e9	0.390820
$848$	1.48717e9	0.0837480
$849$	−8.27889e7	−0.00464296
$850$	8.93507e9	0.499036
$851$	−2.89302e10	−1.60915
$852$	4.66643e7	0.00258492
$853$	−1.64145e9	−0.0905534	−0.0452767	−	0.998974i	$-0.514417\pi$
$853$	−1.64145e9	−0.0905534	−0.0452767	+	0.998974i	$0.514417\pi$
$854$	−6.71035e8	−0.0368674
$855$	2.83678e10	1.55219
$856$	1.81237e10	0.987619
$857$	−2.57589e10	−1.39796	−0.698981	−	0.715141i	$-0.746363\pi$
$857$	−2.57589e10	−1.39796	−0.698981	+	0.715141i	$0.746363\pi$
$858$	−1.36443e7	−0.000737472 0
$859$	−2.14742e10	−1.15595	−0.577977	−	0.816053i	$-0.696158\pi$
$859$	−2.14742e10	−1.15595	−0.577977	+	0.816053i	$0.696158\pi$
$860$	−2.14345e9	−0.114913
$861$	−6.59154e7	−0.00351946
$862$	2.45278e10	1.30432
$863$	−3.38483e9	−0.179266	−0.0896332	−	0.995975i	$-0.528569\pi$
$863$	−3.38483e9	−0.179266	−0.0896332	+	0.995975i	$0.528569\pi$
$864$	−2.00416e9	−0.105715
$865$	−3.67850e10	−1.93248
$866$	1.80609e10	0.944990
$867$	6.03434e8	0.0314458
$868$	−6.98487e7	−0.00362526
$869$	2.23608e9	0.115589
$870$	−829148.	−4.26889e−5 0
$871$	−1.45146e9	−0.0744290
$872$	−2.45310e10	−1.25287
$873$	4.15795e9	0.211510
$874$	−2.60905e10	−1.32188
$875$	7.68410e8	0.0387762
$876$	−7.74578e8	−0.0389315
$877$	−2.37382e10	−1.18836	−0.594182	−	0.804331i	$-0.702524\pi$
$877$	−2.37382e10	−1.18836	−0.594182	+	0.804331i	$0.702524\pi$
$878$	−1.28185e10	−0.639157
$879$	−1.76613e9	−0.0877124
$880$	4.49596e8	0.0222399
$881$	−1.49518e10	−0.736678	−0.368339	−	0.929692i	$-0.620073\pi$
$881$	−1.49518e10	−0.736678	−0.368339	+	0.929692i	$0.620073\pi$
$882$	−1.18468e10	−0.581379
$883$	2.73527e10	1.33702	0.668510	−	0.743703i	$-0.266932\pi$
$883$	2.73527e10	1.33702	0.668510	+	0.743703i	$0.266932\pi$
$884$	−1.74881e9	−0.0851453
$885$	2.36674e9	0.114775
$886$	−5.56002e9	−0.268570
$887$	3.74606e10	1.80236	0.901181	−	0.433443i	$-0.142701\pi$
$887$	3.74606e10	1.80236	0.901181	+	0.433443i	$0.142701\pi$
$888$	1.15803e9	0.0554974
$889$	6.98849e9	0.333601
$890$	3.17201e10	1.50823
$891$	1.60329e9	0.0759349
$892$	−5.82370e9	−0.274740
$893$	4.70297e9	0.221000
$894$	1.44828e9	0.0677910
$895$	3.00907e10	1.40298
$896$	−2.86903e9	−0.133247
$897$	5.32863e8	0.0246514
$898$	−1.68536e10	−0.776652
$899$	−284234.	−1.30472e−5 0
$900$	1.22028e10	0.557968
$901$	6.17372e9	0.281197
$902$	1.79965e8	0.00816519
$903$	−7.69781e7	−0.00347905
$904$	1.08908e10	0.490311
$905$	4.35819e9	0.195450
$906$	9.49372e8	0.0424119
$907$	−4.76936e9	−0.212243	−0.106122	−	0.994353i	$-0.533843\pi$
$907$	−4.76936e9	−0.212243	−0.106122	+	0.994353i	$0.533843\pi$
$908$	−1.12399e10	−0.498265
$909$	1.91773e10	0.846863
$910$	2.12944e9	0.0936743
$911$	−4.59972e9	−0.201566	−0.100783	−	0.994908i	$-0.532135\pi$
$911$	−4.59972e9	−0.201566	−0.100783	+	0.994908i	$0.532135\pi$
$912$	2.90176e8	0.0126671
$913$	5.34467e8	0.0232420
$914$	8.25540e9	0.357624
$915$	−2.62862e8	−0.0113437
$916$	−7.75368e9	−0.333329
$917$	−1.37167e10	−0.587432
$918$	1.26832e9	0.0541101
$919$	1.59138e10	0.676348	0.338174	−	0.941084i	$-0.390191\pi$
$919$	1.59138e10	0.676348	0.338174	+	0.941084i	$0.390191\pi$
$920$	−6.31941e10	−2.67559
$921$	4.46143e8	0.0188176
$922$	2.29151e10	0.962862
$923$	−4.87682e8	−0.0204141
$924$	−2.19867e7	−0.000916871 0
$925$	−2.33948e10	−0.971903
$926$	−2.18812e10	−0.905592
$927$	−4.31668e10	−1.77980
$928$	−1.64659e7	−0.000676344 0
$929$	−2.22650e10	−0.911102	−0.455551	−	0.890210i	$-0.650558\pi$
$929$	−2.22650e10	−0.911102	−0.455551	+	0.890210i	$0.650558\pi$
$930$	2.48629e7	0.00101359
$931$	−2.25415e10	−0.915502
$932$	−6.89632e9	−0.279037
$933$	−1.81249e8	−0.00730619
$934$	−1.05712e10	−0.424533
$935$	1.86642e9	0.0746739
$936$	6.31260e9	0.251619
$937$	−2.34525e10	−0.931322	−0.465661	−	0.884963i	$-0.654183\pi$
$937$	−2.34525e10	−0.931322	−0.465661	+	0.884963i	$0.654183\pi$
$938$	2.12532e9	0.0840842
$939$	−9.93923e8	−0.0391763
$940$	3.91625e9	0.153788
$941$	2.99250e10	1.17077	0.585383	−	0.810757i	$-0.300944\pi$
$941$	2.99250e10	1.17077	0.585383	+	0.810757i	$0.300944\pi$
$942$	9.43606e8	0.0367801
$943$	−7.02836e9	−0.272937
$944$	−7.16492e9	−0.277210
$945$	1.69957e9	0.0655132
$946$	2.10169e8	0.00807143
$947$	−2.94339e10	−1.12622	−0.563109	−	0.826383i	$-0.690395\pi$
$947$	−2.94339e10	−1.12622	−0.563109	+	0.826383i	$0.690395\pi$
$948$	1.20177e9	0.0458135
$949$	8.09500e9	0.307457
$950$	−2.10985e10	−0.798396
$951$	−2.29573e9	−0.0865542
$952$	7.44830e9	0.279787
$953$	3.72084e10	1.39257	0.696283	−	0.717767i	$-0.254836\pi$
$953$	3.72084e10	1.39257	0.696283	+	0.717767i	$0.254836\pi$
$954$	−7.66154e9	−0.285691
$955$	5.52353e10	2.05213
$956$	−1.71605e10	−0.635226
$957$	−89470.1	−3.29979e−6 0
$958$	−9.18488e9	−0.337516
$959$	−1.91175e10	−0.699949
$960$	1.90153e9	0.0693671
$961$	−2.75041e10	−0.999690
$962$	−4.16077e9	−0.150682
$963$	−2.59427e10	−0.936101
$964$	1.31150e8	0.00471518
$965$	4.68528e10	1.67838
$966$	−7.80251e8	−0.0278493
$967$	−1.49635e10	−0.532159	−0.266080	−	0.963951i	$-0.585728\pi$
$967$	−1.49635e10	−0.532159	−0.266080	+	0.963951i	$0.585728\pi$
$968$	−2.94987e10	−1.04529
$969$	1.20461e9	0.0425319
$970$	−5.98647e9	−0.210605
$971$	3.15367e10	1.10548	0.552738	−	0.833355i	$-0.313583\pi$
$971$	3.15367e10	1.10548	0.552738	+	0.833355i	$0.313583\pi$
$972$	2.59970e9	0.0908010
$973$	8.72174e9	0.303535
$974$	1.35402e10	0.469536
$975$	4.30907e8	0.0148891
$976$	7.95773e8	0.0273978
$977$	1.36797e10	0.469295	0.234648	−	0.972080i	$-0.424606\pi$
$977$	1.36797e10	0.469295	0.234648	+	0.972080i	$0.424606\pi$
$978$	−4.33687e8	−0.0148248
$979$	3.42279e9	0.116584
$980$	−1.87707e10	−0.637073
$981$	3.51141e10	1.18752
$982$	−6.20433e9	−0.209076
$983$	1.28389e10	0.431112	0.215556	−	0.976491i	$-0.430844\pi$
$983$	1.28389e10	0.431112	0.215556	+	0.976491i	$0.430844\pi$
$984$	2.81333e8	0.00941321
$985$	7.19910e10	2.40022
$986$	1.04203e7	0.000346187 0
$987$	1.40645e8	0.00465601
$988$	4.12949e9	0.136222
$989$	−8.20794e9	−0.269803
$990$	−2.31622e9	−0.0758675
$991$	−5.51139e10	−1.79889	−0.899443	−	0.437038i	$-0.856028\pi$
$991$	−5.51139e10	−1.79889	−0.899443	+	0.437038i	$0.856028\pi$
$992$	4.93748e8	0.0160588
$993$	4.24641e8	0.0137626
$994$	7.14093e8	0.0230623
$995$	5.25451e10	1.69103
$996$	2.87248e8	0.00921190
$997$	5.87820e10	1.87850	0.939250	−	0.343234i	$-0.111522\pi$
$997$	5.87820e10	1.87850	0.939250	+	0.343234i	$0.111522\pi$
$998$	2.13495e9	0.0679878
$999$	−3.32084e9	−0.105383

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.a.b.1.4	✓	13
3.2	odd	2		387.8.a.d.1.10		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.a.b.1.4	✓	13	1.1	even	1	trivial
387.8.a.d.1.10		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)

\(f(q)\)	\(=\)	\(q-7.80627 q^{2} -2.71381 q^{3} -67.0621 q^{4} -402.005 q^{5} +21.1847 q^{6} -356.766 q^{7} +1522.71 q^{8} -2179.64 q^{9} +O(q^{10})\)	\(q-7.80627 q^{2} -2.71381 q^{3} -67.0621 q^{4} -402.005 q^{5} +21.1847 q^{6} -356.766 q^{7} +1522.71 q^{8} -2179.64 q^{9} +3138.16 q^{10} +338.626 q^{11} +181.994 q^{12} -1901.99 q^{13} +2785.01 q^{14} +1090.96 q^{15} -3302.71 q^{16} -13710.6 q^{17} +17014.8 q^{18} +32375.1 q^{19} +26959.3 q^{20} +968.193 q^{21} -2643.41 q^{22} +103235. q^{23} -4132.34 q^{24} +83482.7 q^{25} +14847.4 q^{26} +11850.2 q^{27} +23925.5 q^{28} +97.3595 q^{29} -8516.35 q^{30} -2919.43 q^{31} -169125. q^{32} -918.966 q^{33} +107029. q^{34} +143421. q^{35} +146171. q^{36} -280235. q^{37} -252729. q^{38} +5161.63 q^{39} -612136. q^{40} -68080.9 q^{41} -7557.98 q^{42} -79507.0 q^{43} -22709.0 q^{44} +876223. q^{45} -805883. q^{46} +145265. q^{47} +8962.93 q^{48} -696261. q^{49} -651689. q^{50} +37208.1 q^{51} +127551. q^{52} -450286. q^{53} -92505.9 q^{54} -136129. q^{55} -543250. q^{56} -87859.8 q^{57} -760.015 q^{58} +2.16940e6 q^{59} -73162.3 q^{60} -240945. q^{61} +22789.9 q^{62} +777619. q^{63} +1.74298e6 q^{64} +764608. q^{65} +7173.70 q^{66} +763129. q^{67} +919465. q^{68} -280161. q^{69} -1.11959e6 q^{70} +256406. q^{71} -3.31895e6 q^{72} -4.25607e6 q^{73} +2.18759e6 q^{74} -226556. q^{75} -2.17114e6 q^{76} -120810. q^{77} -40293.1 q^{78} +6.60338e6 q^{79} +1.32771e6 q^{80} +4.73470e6 q^{81} +531458. q^{82} +1.57834e6 q^{83} -64929.1 q^{84} +5.51174e6 q^{85} +620653. q^{86} -264.215 q^{87} +515629. q^{88} +1.01079e7 q^{89} -6.84004e6 q^{90} +678564. q^{91} -6.92319e6 q^{92} +7922.77 q^{93} -1.13398e6 q^{94} -1.30149e7 q^{95} +458972. q^{96} -1.90764e6 q^{97} +5.43520e6 q^{98} -738081. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 16 q^{2} + 94 q^{3} + 922 q^{4} + 998 q^{5} + 183 q^{6} + 1360 q^{7} + 3870 q^{8} + 10011 q^{9}+O(q^{10}) \) 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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