LMFDB - Embedded newform 43.6.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,6,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, 6, names="a")

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

chi := DirichletCharacter("43.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 6 $
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:	$6.89650425196$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 173x^{6} + 462x^{5} + 9118x^{4} - 14192x^{3} - 167688x^{2} + 106368x + 681984 $ x^8 - 4x^7 - 173x^6 + 462x^5 + 9118x^4 - 14192x^3 - 167688x^2 + 106368*x + 681984
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-9.16809$ 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)

$f(q)$	$=$	$q-11.1681 q^{2} -28.1764 q^{3} +92.7262 q^{4} -10.1483 q^{5} +314.677 q^{6} +135.849 q^{7} -678.196 q^{8} +550.912 q^{9} +O(q^{10})$	\(q-11.1681 q^{2} -28.1764 q^{3} +92.7262 q^{4} -10.1483 q^{5} +314.677 q^{6} +135.849 q^{7} -678.196 q^{8} +550.912 q^{9} +113.337 q^{10} -74.1258 q^{11} -2612.70 q^{12} -252.408 q^{13} -1517.17 q^{14} +285.942 q^{15} +4606.91 q^{16} +233.541 q^{17} -6152.64 q^{18} +550.209 q^{19} -941.010 q^{20} -3827.74 q^{21} +827.844 q^{22} +1951.63 q^{23} +19109.1 q^{24} -3022.01 q^{25} +2818.92 q^{26} -8675.87 q^{27} +12596.8 q^{28} -4679.01 q^{29} -3193.42 q^{30} +3331.10 q^{31} -29748.1 q^{32} +2088.60 q^{33} -2608.21 q^{34} -1378.63 q^{35} +51084.0 q^{36} -13497.0 q^{37} -6144.79 q^{38} +7111.96 q^{39} +6882.51 q^{40} +8205.81 q^{41} +42748.5 q^{42} -1849.00 q^{43} -6873.41 q^{44} -5590.80 q^{45} -21796.0 q^{46} -22043.6 q^{47} -129806. q^{48} +1647.91 q^{49} +33750.1 q^{50} -6580.36 q^{51} -23404.8 q^{52} +6348.62 q^{53} +96892.9 q^{54} +752.248 q^{55} -92132.1 q^{56} -15502.9 q^{57} +52255.6 q^{58} -14937.7 q^{59} +26514.3 q^{60} -23854.4 q^{61} -37202.0 q^{62} +74840.8 q^{63} +184809. q^{64} +2561.50 q^{65} -23325.7 q^{66} +38603.2 q^{67} +21655.4 q^{68} -54990.0 q^{69} +15396.7 q^{70} +4917.85 q^{71} -373626. q^{72} +5260.97 q^{73} +150736. q^{74} +85149.6 q^{75} +51018.8 q^{76} -10069.9 q^{77} -79427.0 q^{78} -26865.7 q^{79} -46752.1 q^{80} +110584. q^{81} -91643.2 q^{82} +48430.7 q^{83} -354932. q^{84} -2370.04 q^{85} +20649.8 q^{86} +131838. q^{87} +50271.8 q^{88} -117672. q^{89} +62438.5 q^{90} -34289.3 q^{91} +180967. q^{92} -93858.5 q^{93} +246185. q^{94} -5583.67 q^{95} +838197. q^{96} -62399.7 q^{97} -18404.1 q^{98} -40836.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{2} - 26 q^{3} + 122 q^{4} - 212 q^{5} - 69 q^{6} - 136 q^{7} - 666 q^{8} + 546 q^{9}+O(q^{10}) $ 8 * q - 12 * q^2 - 26 * q^3 + 122 * q^4 - 212 * q^5 - 69 * q^6 - 136 * q^7 - 666 * q^8 + 546 * q^9	\( 8 q - 12 q^{2} - 26 q^{3} + 122 q^{4} - 212 q^{5} - 69 q^{6} - 136 q^{7} - 666 q^{8} + 546 q^{9} - 617 q^{10} - 532 q^{11} - 4195 q^{12} - 2492 q^{13} - 4240 q^{14} - 1780 q^{15} + 1882 q^{16} - 2534 q^{17} - 3711 q^{18} - 1678 q^{19} - 2607 q^{20} - 2256 q^{21} + 11502 q^{22} - 2488 q^{23} + 19953 q^{24} + 4378 q^{25} + 4586 q^{26} - 8960 q^{27} + 18640 q^{28} - 4360 q^{29} + 25092 q^{30} + 5704 q^{31} - 18294 q^{32} - 12852 q^{33} + 30007 q^{34} + 5640 q^{35} + 67969 q^{36} - 3772 q^{37} - 6559 q^{38} + 11120 q^{39} + 14869 q^{40} - 10698 q^{41} + 78698 q^{42} - 14792 q^{43} - 356 q^{44} - 44912 q^{45} - 19389 q^{46} - 77864 q^{47} - 118727 q^{48} + 7188 q^{49} + 26877 q^{50} - 80246 q^{51} - 60736 q^{52} - 62352 q^{53} + 61026 q^{54} - 49552 q^{55} - 144528 q^{56} - 808 q^{57} + 52951 q^{58} - 26224 q^{59} + 101500 q^{60} - 82540 q^{61} - 9023 q^{62} - 61768 q^{63} + 153858 q^{64} - 5000 q^{65} - 48516 q^{66} + 27784 q^{67} + 40507 q^{68} - 93776 q^{69} + 185910 q^{70} - 9504 q^{71} - 186687 q^{72} + 14260 q^{73} - 15239 q^{74} + 167420 q^{75} + 1279 q^{76} - 218140 q^{77} + 264170 q^{78} + 160248 q^{79} - 1291 q^{80} + 161076 q^{81} - 47781 q^{82} - 77176 q^{83} + 16382 q^{84} + 141096 q^{85} + 22188 q^{86} + 268136 q^{87} + 129544 q^{88} - 265692 q^{89} + 48990 q^{90} + 401148 q^{91} + 190391 q^{92} - 123860 q^{93} + 248737 q^{94} + 135884 q^{95} + 950817 q^{96} + 144742 q^{97} - 292244 q^{98} + 239516 q^{99}+O(q^{100}) \) 8 * q - 12 * q^2 - 26 * q^3 + 122 * q^4 - 212 * q^5 - 69 * q^6 - 136 * q^7 - 666 * q^8 + 546 * q^9 - 617 * q^10 - 532 * q^11 - 4195 * q^12 - 2492 * q^13 - 4240 * q^14 - 1780 * q^15 + 1882 * q^16 - 2534 * q^17 - 3711 * q^18 - 1678 * q^19 - 2607 * q^20 - 2256 * q^21 + 11502 * q^22 - 2488 * q^23 + 19953 * q^24 + 4378 * q^25 + 4586 * q^26 - 8960 * q^27 + 18640 * q^28 - 4360 * q^29 + 25092 * q^30 + 5704 * q^31 - 18294 * q^32 - 12852 * q^33 + 30007 * q^34 + 5640 * q^35 + 67969 * q^36 - 3772 * q^37 - 6559 * q^38 + 11120 * q^39 + 14869 * q^40 - 10698 * q^41 + 78698 * q^42 - 14792 * q^43 - 356 * q^44 - 44912 * q^45 - 19389 * q^46 - 77864 * q^47 - 118727 * q^48 + 7188 * q^49 + 26877 * q^50 - 80246 * q^51 - 60736 * q^52 - 62352 * q^53 + 61026 * q^54 - 49552 * q^55 - 144528 * q^56 - 808 * q^57 + 52951 * q^58 - 26224 * q^59 + 101500 * q^60 - 82540 * q^61 - 9023 * q^62 - 61768 * q^63 + 153858 * q^64 - 5000 * q^65 - 48516 * q^66 + 27784 * q^67 + 40507 * q^68 - 93776 * q^69 + 185910 * q^70 - 9504 * q^71 - 186687 * q^72 + 14260 * q^73 - 15239 * q^74 + 167420 * q^75 + 1279 * q^76 - 218140 * q^77 + 264170 * q^78 + 160248 * q^79 - 1291 * q^80 + 161076 * q^81 - 47781 * q^82 - 77176 * q^83 + 16382 * q^84 + 141096 * q^85 + 22188 * q^86 + 268136 * q^87 + 129544 * q^88 - 265692 * q^89 + 48990 * q^90 + 401148 * q^91 + 190391 * q^92 - 123860 * q^93 + 248737 * q^94 + 135884 * q^95 + 950817 * q^96 + 144742 * q^97 - 292244 * q^98 + 239516 * 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 $

$2$	−11.1681	−1.97426	−0.987129	−	0.159926i	$-0.948874\pi$
$2$	−11.1681	−1.97426	−0.987129	+	0.159926i	$0.948874\pi$
$3$	−28.1764	−1.80752	−0.903760	−	0.428040i	$-0.859204\pi$
$3$	−28.1764	−1.80752	−0.903760	+	0.428040i	$0.859204\pi$
$4$	92.7262	2.89769
$5$	−10.1483	−0.181538	−0.0907688	−	0.995872i	$-0.528932\pi$
$5$	−10.1483	−0.181538	−0.0907688	+	0.995872i	$0.528932\pi$
$6$	314.677	3.56851
$7$	135.849	1.04788	0.523939	−	0.851756i	$-0.324462\pi$
$7$	135.849	1.04788	0.523939	+	0.851756i	$0.324462\pi$
$8$	−678.196	−3.74654
$9$	550.912	2.26713
$10$	113.337	0.358402
$11$	−74.1258	−0.184709	−0.0923544	−	0.995726i	$-0.529439\pi$
$11$	−74.1258	−0.184709	−0.0923544	+	0.995726i	$0.529439\pi$
$12$	−2612.70	−5.23764
$13$	−252.408	−0.414233	−0.207117	−	0.978316i	$-0.566408\pi$
$13$	−252.408	−0.414233	−0.207117	+	0.978316i	$0.566408\pi$
$14$	−1517.17	−2.06878
$15$	285.942	0.328133
$16$	4606.91	4.49894
$17$	233.541	0.195993	0.0979967	−	0.995187i	$-0.468757\pi$
$17$	233.541	0.195993	0.0979967	+	0.995187i	$0.468757\pi$
$18$	−6152.64	−4.47590
$19$	550.209	0.349658	0.174829	−	0.984599i	$-0.444063\pi$
$19$	550.209	0.349658	0.174829	+	0.984599i	$0.444063\pi$
$20$	−941.010	−0.526040
$21$	−3827.74	−1.89406
$22$	827.844	0.364663
$23$	1951.63	0.769269	0.384634	−	0.923069i	$-0.374328\pi$
$23$	1951.63	0.769269	0.384634	+	0.923069i	$0.374328\pi$
$24$	19109.1	6.77194
$25$	−3022.01	−0.967044
$26$	2818.92	0.817803
$27$	−8675.87	−2.29036
$28$	12596.8	3.03643
$29$	−4679.01	−1.03314	−0.516570	−	0.856245i	$-0.672791\pi$
$29$	−4679.01	−1.03314	−0.516570	+	0.856245i	$0.672791\pi$
$30$	−3193.42	−0.647819
$31$	3331.10	0.622563	0.311281	−	0.950318i	$-0.399242\pi$
$31$	3331.10	0.622563	0.311281	+	0.950318i	$0.399242\pi$
$32$	−29748.1	−5.13553
$33$	2088.60	0.333865
$34$	−2608.21	−0.386942
$35$	−1378.63	−0.190229
$36$	51084.0	6.56944
$37$	−13497.0	−1.62081	−0.810407	−	0.585867i	$-0.800754\pi$
$37$	−13497.0	−1.62081	−0.810407	+	0.585867i	$0.800754\pi$
$38$	−6144.79	−0.690316
$39$	7111.96	0.748735
$40$	6882.51	0.680137
$41$	8205.81	0.762363	0.381181	−	0.924500i	$-0.375517\pi$
$41$	8205.81	0.762363	0.381181	+	0.924500i	$0.375517\pi$
$42$	42748.5	3.73937
$43$	−1849.00	−0.152499
$43$	−1849.00	−0.152499
$44$	−6873.41	−0.535230
$45$	−5590.80	−0.411569
$46$	−21796.0	−1.51873
$47$	−22043.6	−1.45559	−0.727793	−	0.685797i	$-0.759454\pi$
$47$	−22043.6	−1.45559	−0.727793	+	0.685797i	$0.759454\pi$
$48$	−129806.	−8.13192
$49$	1647.91	0.0980493
$50$	33750.1	1.90919
$51$	−6580.36	−0.354262
$52$	−23404.8	−1.20032
$53$	6348.62	0.310449	0.155224	−	0.987879i	$-0.450390\pi$
$53$	6348.62	0.310449	0.155224	+	0.987879i	$0.450390\pi$
$54$	96892.9	4.52176
$55$	752.248	0.0335316
$56$	−92132.1	−3.92592
$57$	−15502.9	−0.632015
$58$	52255.6	2.03968
$59$	−14937.7	−0.558669	−0.279334	−	0.960194i	$-0.590114\pi$
$59$	−14937.7	−0.558669	−0.279334	+	0.960194i	$0.590114\pi$
$60$	26514.3	0.950829
$61$	−23854.4	−0.820812	−0.410406	−	0.911903i	$-0.634613\pi$
$61$	−23854.4	−0.820812	−0.410406	+	0.911903i	$0.634613\pi$
$62$	−37202.0	−1.22910
$63$	74840.8	2.37567
$64$	184809.	5.63992
$65$	2561.50	0.0751989
$66$	−23325.7	−0.659136
$67$	38603.2	1.05060	0.525299	−	0.850918i	$-0.323953\pi$
$67$	38603.2	1.05060	0.525299	+	0.850918i	$0.323953\pi$
$68$	21655.4	0.567929
$69$	−54990.0	−1.39047
$70$	15396.7	0.375562
$71$	4917.85	0.115779	0.0578894	−	0.998323i	$-0.481563\pi$
$71$	4917.85	0.115779	0.0578894	+	0.998323i	$0.481563\pi$
$72$	−373626.	−8.49388
$73$	5260.97	0.115547	0.0577735	−	0.998330i	$-0.481600\pi$
$73$	5260.97	0.115547	0.0577735	+	0.998330i	$0.481600\pi$
$74$	150736.	3.19991
$75$	85149.6	1.74795
$76$	51018.8	1.01320
$77$	−10069.9	−0.193552
$78$	−79427.0	−1.47820
$79$	−26865.7	−0.484318	−0.242159	−	0.970237i	$-0.577856\pi$
$79$	−26865.7	−0.484318	−0.242159	+	0.970237i	$0.577856\pi$
$80$	−46752.1	−0.816726
$81$	110584.	1.87274
$82$	−91643.2	−1.50510
$83$	48430.7	0.771659	0.385830	−	0.922570i	$-0.373915\pi$
$83$	48430.7	0.771659	0.385830	+	0.922570i	$0.373915\pi$
$84$	−354932.	−5.48841
$85$	−2370.04	−0.0355802
$86$	20649.8	0.301072
$87$	131838.	1.86742
$88$	50271.8	0.692019
$89$	−117672.	−1.57470	−0.787352	−	0.616504i	$-0.788549\pi$
$89$	−117672.	−1.57470	−0.787352	+	0.616504i	$0.788549\pi$
$90$	62438.5	0.812543
$91$	−34289.3	−0.434066
$92$	180967.	2.22911
$93$	−93858.5	−1.12529
$94$	246185.	2.87370
$95$	−5583.67	−0.0634762
$96$	838197.	9.28257
$97$	−62399.7	−0.673369	−0.336684	−	0.941618i	$-0.609306\pi$
$97$	−62399.7	−0.673369	−0.336684	+	0.941618i	$0.609306\pi$
$98$	−18404.1	−0.193575
$99$	−40836.8	−0.418759
$100$	−280220.	−2.80220
$101$	−184829.	−1.80288	−0.901441	−	0.432902i	$-0.857490\pi$
$101$	−184829.	−1.80288	−0.901441	+	0.432902i	$0.857490\pi$
$102$	73490.1	0.699405
$103$	−131556.	−1.22185	−0.610924	−	0.791689i	$-0.709202\pi$
$103$	−131556.	−1.22185	−0.610924	+	0.791689i	$0.709202\pi$
$104$	171182.	1.55194
$105$	38844.9	0.343843
$106$	−70902.0	−0.612906
$107$	−26372.2	−0.222683	−0.111341	−	0.993782i	$-0.535515\pi$
$107$	−26372.2	−0.222683	−0.111341	+	0.993782i	$0.535515\pi$
$108$	−804481.	−6.63676
$109$	−171471.	−1.38237	−0.691183	−	0.722680i	$-0.742910\pi$
$109$	−171471.	−1.38237	−0.691183	+	0.722680i	$0.742910\pi$
$110$	−8401.17	−0.0662000
$111$	380298.	2.92965
$112$	625844.	4.71434
$113$	108442.	0.798917	0.399459	−	0.916751i	$-0.369198\pi$
$113$	108442.	0.798917	0.399459	+	0.916751i	$0.369198\pi$
$114$	173138.	1.24776
$115$	−19805.7	−0.139651
$116$	−433867.	−2.99372
$117$	−139055.	−0.939120
$118$	166826.	1.10296
$119$	31726.3	0.205377
$120$	−193925.	−1.22936
$121$	−155556.	−0.965883
$122$	266408.	1.62049
$123$	−231211.	−1.37799
$124$	308880.	1.80400
$125$	62381.5	0.357092
$126$	−835829.	−4.69019
$127$	162713.	0.895186	0.447593	−	0.894237i	$-0.352281\pi$
$127$	162713.	0.895186	0.447593	+	0.894237i	$0.352281\pi$
$128$	−1.11202e6	−5.99912
$129$	52098.3	0.275644
$130$	−28607.1	−0.148462
$131$	−128326.	−0.653335	−0.326667	−	0.945139i	$-0.605926\pi$
$131$	−128326.	−0.653335	−0.326667	+	0.945139i	$0.605926\pi$
$132$	193668.	0.967439
$133$	74745.3	0.366400
$134$	−431125.	−2.07415
$135$	88045.0	0.415786
$136$	−158387.	−0.734297
$137$	192870.	0.877937	0.438968	−	0.898503i	$-0.355344\pi$
$137$	192870.	0.877937	0.438968	+	0.898503i	$0.355344\pi$
$138$	614133.	2.74514
$139$	−276084.	−1.21200	−0.606002	−	0.795463i	$-0.707228\pi$
$139$	−276084.	−1.21200	−0.606002	+	0.795463i	$0.707228\pi$
$140$	−127835.	−0.551226
$141$	621110.	2.63100
$142$	−54923.0	−0.228577
$143$	18709.9	0.0765125
$144$	2.53800e6	10.1997
$145$	47483.8	0.187554
$146$	−58755.0	−0.228120
$147$	−46432.4	−0.177226
$148$	−1.25153e6	−4.69662
$149$	217182.	0.801414	0.400707	−	0.916206i	$-0.368764\pi$
$149$	217182.	0.801414	0.400707	+	0.916206i	$0.368764\pi$
$150$	−950958.	−3.45091
$151$	404181.	1.44256	0.721279	−	0.692644i	$-0.243554\pi$
$151$	404181.	1.44256	0.721279	+	0.692644i	$0.243554\pi$
$152$	−373150.	−1.31001
$153$	128661.	0.444342
$154$	112462.	0.382122
$155$	−33804.8	−0.113019
$156$	659465.	2.16960
$157$	44527.8	0.144173	0.0720863	−	0.997398i	$-0.477034\pi$
$157$	44527.8	0.144173	0.0720863	+	0.997398i	$0.477034\pi$
$158$	300038.	0.956168
$159$	−178882.	−0.561142
$160$	301892.	0.932291
$161$	265127.	0.806100
$162$	−1.23501e6	−3.69728
$163$	−214840.	−0.633354	−0.316677	−	0.948533i	$-0.602567\pi$
$163$	−214840.	−0.633354	−0.316677	+	0.948533i	$0.602567\pi$
$164$	760894.	2.20909
$165$	−21195.7	−0.0606090
$166$	−540879.	−1.52345
$167$	−249849.	−0.693245	−0.346623	−	0.938005i	$-0.612672\pi$
$167$	−249849.	−0.693245	−0.346623	+	0.938005i	$0.612672\pi$
$168$	2.59596e6	7.09617
$169$	−307583.	−0.828411
$170$	26468.8	0.0702444
$171$	303117.	0.792721
$172$	−171451.	−0.441894
$173$	148039.	0.376064	0.188032	−	0.982163i	$-0.439789\pi$
$173$	148039.	0.376064	0.188032	+	0.982163i	$0.439789\pi$
$174$	−1.47238e6	−3.68677
$175$	−410537.	−1.01334
$176$	−341491.	−0.830994
$177$	420892.	1.00980
$178$	1.31417e6	3.10887
$179$	492820.	1.14962	0.574812	−	0.818286i	$-0.305075\pi$
$179$	492820.	1.14962	0.574812	+	0.818286i	$0.305075\pi$
$180$	−518414.	−1.19260
$181$	−379943.	−0.862030	−0.431015	−	0.902345i	$-0.641844\pi$
$181$	−379943.	−0.862030	−0.431015	+	0.902345i	$0.641844\pi$
$182$	382946.	0.856958
$183$	672132.	1.48363
$184$	−1.32359e6	−2.88209
$185$	136971.	0.294239
$186$	1.04822e6	2.22162
$187$	−17311.4	−0.0362017
$188$	−2.04402e6	−4.21784
$189$	−1.17861e6	−2.40002
$190$	62358.9	0.125318
$191$	844630.	1.67526	0.837631	−	0.546236i	$-0.183940\pi$
$191$	844630.	1.67526	0.837631	+	0.546236i	$0.183940\pi$
$192$	−5.20725e6	−10.1943
$193$	−228384.	−0.441339	−0.220669	−	0.975349i	$-0.570824\pi$
$193$	−228384.	−0.441339	−0.220669	+	0.975349i	$0.570824\pi$
$194$	696885.	1.32940
$195$	−72174.0	−0.135923
$196$	152805.	0.284117
$197$	405691.	0.744783	0.372391	−	0.928076i	$-0.378538\pi$
$197$	405691.	0.744783	0.372391	+	0.928076i	$0.378538\pi$
$198$	456069.	0.826738
$199$	−720104.	−1.28903	−0.644514	−	0.764593i	$-0.722940\pi$
$199$	−720104.	−1.28903	−0.644514	+	0.764593i	$0.722940\pi$
$200$	2.04952e6	3.62307
$201$	−1.08770e6	−1.89898
$202$	2.06419e6	3.55935
$203$	−635638.	−1.08260
$204$	−610172.	−1.02654
$205$	−83274.7	−0.138398
$206$	1.46923e6	2.41224
$207$	1.07518e6	1.74403
$208$	−1.16282e6	−1.86361
$209$	−40784.7	−0.0645850
$210$	−433823.	−0.678835
$211$	626107.	0.968149	0.484074	−	0.875027i	$-0.339156\pi$
$211$	626107.	0.968149	0.484074	+	0.875027i	$0.339156\pi$
$212$	588684.	0.899585
$213$	−138567.	−0.209273
$214$	294527.	0.439633
$215$	18764.1	0.0276842
$216$	5.88394e6	8.58092
$217$	452526.	0.652370
$218$	1.91500e6	2.72915
$219$	−148236.	−0.208854
$220$	69753.1	0.0971643
$221$	−58947.7	−0.0811870
$222$	−4.24720e6	−5.78389
$223$	513365.	0.691296	0.345648	−	0.938364i	$-0.387659\pi$
$223$	513365.	0.691296	0.345648	+	0.938364i	$0.387659\pi$
$224$	−4.04125e6	−5.38141
$225$	−1.66486e6	−2.19241
$226$	−1.21109e6	−1.57727
$227$	−1.20833e6	−1.55640	−0.778200	−	0.628017i	$-0.783867\pi$
$227$	−1.20833e6	−1.55640	−0.778200	+	0.628017i	$0.783867\pi$
$228$	−1.43753e6	−1.83139
$229$	−313322.	−0.394822	−0.197411	−	0.980321i	$-0.563253\pi$
$229$	−313322.	−0.394822	−0.197411	+	0.980321i	$0.563253\pi$
$230$	221191.	0.275707
$231$	283734.	0.349850
$232$	3.17328e6	3.87070
$233$	−194052.	−0.234168	−0.117084	−	0.993122i	$-0.537355\pi$
$233$	−194052.	−0.234168	−0.117084	+	0.993122i	$0.537355\pi$
$234$	1.55297e6	1.85406
$235$	223704.	0.264243
$236$	−1.38512e6	−1.61885
$237$	756980.	0.875414
$238$	−354322.	−0.405468
$239$	−349700.	−0.396005	−0.198002	−	0.980202i	$-0.563445\pi$
$239$	−349700.	−0.396005	−0.198002	+	0.980202i	$0.563445\pi$
$240$	1.31731e6	1.47625
$241$	−21340.0	−0.0236675	−0.0118338	−	0.999930i	$-0.503767\pi$
$241$	−21340.0	−0.0236675	−0.0118338	+	0.999930i	$0.503767\pi$
$242$	1.73727e6	1.90690
$243$	−1.00761e6	−1.09466
$244$	−2.21193e6	−2.37846
$245$	−16723.5	−0.0177996
$246$	2.58218e6	2.72050
$247$	−138877.	−0.144840
$248$	−2.25914e6	−2.33245
$249$	−1.36461e6	−1.39479
$250$	−696682.	−0.704993
$251$	−881880.	−0.883538	−0.441769	−	0.897129i	$-0.645649\pi$
$251$	−881880.	−0.883538	−0.441769	+	0.897129i	$0.645649\pi$
$252$	6.93970e6	6.88398
$253$	−144666.	−0.142091
$254$	−1.81719e6	−1.76733
$255$	66779.2	0.0643119
$256$	6.50526e6	6.20390
$257$	−1.90048e6	−1.79486	−0.897428	−	0.441160i	$-0.854567\pi$
$257$	−1.90048e6	−1.79486	−0.897428	+	0.441160i	$0.854567\pi$
$258$	−581838.	−0.544193
$259$	−1.83355e6	−1.69842
$260$	237518.	0.217903
$261$	−2.57772e6	−2.34226
$262$	1.43315e6	1.28985
$263$	−598922.	−0.533925	−0.266963	−	0.963707i	$-0.586020\pi$
$263$	−598922.	−0.533925	−0.266963	+	0.963707i	$0.586020\pi$
$264$	−1.41648e6	−1.25084
$265$	−64427.5	−0.0563581
$266$	−834763.	−0.723367
$267$	3.31559e6	2.84631
$268$	3.57953e6	3.04431
$269$	1.21294e6	1.02202	0.511010	−	0.859575i	$-0.329271\pi$
$269$	1.21294e6	1.02202	0.511010	+	0.859575i	$0.329271\pi$
$270$	−983294.	−0.820869
$271$	215767.	0.178469	0.0892344	−	0.996011i	$-0.471558\pi$
$271$	215767.	0.178469	0.0892344	+	0.996011i	$0.471558\pi$
$272$	1.07590e6	0.881762
$273$	966152.	0.784583
$274$	−2.15399e6	−1.73327
$275$	224009.	0.178622
$276$	−5.09902e6	−4.02915
$277$	235442.	0.184368	0.0921838	−	0.995742i	$-0.470615\pi$
$277$	235442.	0.184368	0.0921838	+	0.995742i	$0.470615\pi$
$278$	3.08333e6	2.39281
$279$	1.83514e6	1.41143
$280$	934981.	0.712701
$281$	1.25852e6	0.950813	0.475407	−	0.879766i	$-0.342301\pi$
$281$	1.25852e6	0.950813	0.475407	+	0.879766i	$0.342301\pi$
$282$	−6.93661e6	−5.19427
$283$	1.12093e6	0.831982	0.415991	−	0.909369i	$-0.363435\pi$
$283$	1.12093e6	0.831982	0.415991	+	0.909369i	$0.363435\pi$
$284$	456013.	0.335492
$285$	157328.	0.114734
$286$	−208954.	−0.151055
$287$	1.11475e6	0.798864
$288$	−1.63886e7	−11.6429
$289$	−1.36532e6	−0.961587
$290$	−530303.	−0.370279
$291$	1.75820e6	1.21713
$292$	487830.	0.334820
$293$	2.44369e6	1.66294	0.831469	−	0.555570i	$-0.187500\pi$
$293$	2.44369e6	1.66294	0.831469	+	0.555570i	$0.187500\pi$
$294$	518561.	0.349890
$295$	151592.	0.101419
$296$	9.15362e6	6.07244
$297$	643106.	0.423050
$298$	−2.42550e6	−1.58220
$299$	−492607.	−0.318657
$300$	7.89560e6	5.06503
$301$	−251185.	−0.159800
$302$	−4.51393e6	−2.84798
$303$	5.20783e6	3.25875
$304$	2.53477e6	1.57309
$305$	242080.	0.149008
$306$	−1.43689e6	−0.877246
$307$	−3.07195e6	−1.86024	−0.930120	−	0.367257i	$-0.880297\pi$
$307$	−3.07195e6	−1.86024	−0.930120	+	0.367257i	$0.880297\pi$
$308$	−933744.	−0.560856
$309$	3.70678e6	2.20852
$310$	377535.	0.223128
$311$	−1.02013e6	−0.598076	−0.299038	−	0.954241i	$-0.596666\pi$
$311$	−1.02013e6	−0.598076	−0.299038	+	0.954241i	$0.596666\pi$
$312$	−4.82330e6	−2.80516
$313$	1.25975e6	0.726814	0.363407	−	0.931630i	$-0.381613\pi$
$313$	1.25975e6	0.726814	0.363407	+	0.931630i	$0.381613\pi$
$314$	−497291.	−0.284634
$315$	−759504.	−0.431274
$316$	−2.49115e6	−1.40340
$317$	−3.42675e6	−1.91529	−0.957644	−	0.287953i	$-0.907025\pi$
$317$	−3.42675e6	−1.91529	−0.957644	+	0.287953i	$0.907025\pi$
$318$	1.99777e6	1.10784
$319$	346835.	0.190830
$320$	−1.87549e6	−1.02386
$321$	743074.	0.402503
$322$	−2.96096e6	−1.59145
$323$	128497.	0.0685308
$324$	1.02540e7	5.42663
$325$	762780.	0.400582
$326$	2.39935e6	1.25040
$327$	4.83143e6	2.49866
$328$	−5.56515e6	−2.85622
$329$	−2.99460e6	−1.52528
$330$	236715.	0.119658
$331$	−958608.	−0.480918	−0.240459	−	0.970659i	$-0.577298\pi$
$331$	−958608.	−0.480918	−0.240459	+	0.970659i	$0.577298\pi$
$332$	4.49080e6	2.23603
$333$	−7.43567e6	−3.67459
$334$	2.79034e6	1.36865
$335$	−391756.	−0.190723
$336$	−1.76341e7	−8.52126
$337$	2.25932e6	1.08369	0.541843	−	0.840479i	$-0.317727\pi$
$337$	2.25932e6	1.08369	0.541843	+	0.840479i	$0.317727\pi$
$338$	3.43512e6	1.63550
$339$	−3.05551e6	−1.44406
$340$	−219765.	−0.103100
$341$	−246920.	−0.114993
$342$	−3.38524e6	−1.56503
$343$	−2.05934e6	−0.945135
$344$	1.25398e6	0.571342
$345$	558053.	0.252422
$346$	−1.65332e6	−0.742448
$347$	2.66606e6	1.18863	0.594315	−	0.804233i	$-0.297423\pi$
$347$	2.66606e6	1.18863	0.594315	+	0.804233i	$0.297423\pi$
$348$	1.22248e7	5.41121
$349$	−394009.	−0.173158	−0.0865791	−	0.996245i	$-0.527594\pi$
$349$	−394009.	−0.173158	−0.0865791	+	0.996245i	$0.527594\pi$
$350$	4.58491e6	2.00060
$351$	2.18986e6	0.948743
$352$	2.20511e6	0.948577
$353$	−781472.	−0.333793	−0.166896	−	0.985974i	$-0.553375\pi$
$353$	−781472.	−0.333793	−0.166896	+	0.985974i	$0.553375\pi$
$354$	−4.70056e6	−1.99362
$355$	−49907.6	−0.0210182
$356$	−1.09113e7	−4.56301
$357$	−893935.	−0.371223
$358$	−5.50385e6	−2.26965
$359$	−2.39149e6	−0.979338	−0.489669	−	0.871909i	$-0.662882\pi$
$359$	−2.39149e6	−0.979338	−0.489669	+	0.871909i	$0.662882\pi$
$360$	3.79166e6	1.54196
$361$	−2.17337e6	−0.877739
$362$	4.24324e6	1.70187
$363$	4.38303e6	1.74585
$364$	−3.17952e6	−1.25779
$365$	−53389.7	−0.0209761
$366$	−7.50643e6	−2.92908
$367$	3.30667e6	1.28152	0.640761	−	0.767741i	$-0.278619\pi$
$367$	3.30667e6	1.28152	0.640761	+	0.767741i	$0.278619\pi$
$368$	8.99099e6	3.46089
$369$	4.52068e6	1.72837
$370$	−1.52971e6	−0.580903
$371$	862453.	0.325313
$372$	−8.70314e6	−3.26076
$373$	−3.41830e6	−1.27215	−0.636075	−	0.771627i	$-0.719443\pi$
$373$	−3.41830e6	−1.27215	−0.636075	+	0.771627i	$0.719443\pi$
$374$	193336.	0.0714715
$375$	−1.75769e6	−0.645452
$376$	1.49499e7	5.45341
$377$	1.18102e6	0.427960
$378$	1.31628e7	4.73826
$379$	3.68158e6	1.31655	0.658273	−	0.752779i	$-0.271287\pi$
$379$	3.68158e6	1.31655	0.658273	+	0.752779i	$0.271287\pi$
$380$	−517752.	−0.183935
$381$	−4.58468e6	−1.61807
$382$	−9.43290e6	−3.30740
$383$	−1.78008e6	−0.620071	−0.310036	−	0.950725i	$-0.600341\pi$
$383$	−1.78008e6	−0.620071	−0.310036	+	0.950725i	$0.600341\pi$
$384$	3.13328e7	10.8435
$385$	102192.	0.0351370
$386$	2.55061e6	0.871317
$387$	−1.01864e6	−0.345734
$388$	−5.78609e6	−1.95122
$389$	3.35648e6	1.12463	0.562315	−	0.826923i	$-0.309911\pi$
$389$	3.35648e6	1.12463	0.562315	+	0.826923i	$0.309911\pi$
$390$	806046.	0.268348
$391$	455786.	0.150772
$392$	−1.11761e6	−0.367346
$393$	3.61577e6	1.18092
$394$	−4.53079e6	−1.47039
$395$	272640.	0.0879219
$396$	−3.78664e6	−1.21343
$397$	2.81124e6	0.895202	0.447601	−	0.894233i	$-0.352278\pi$
$397$	2.81124e6	0.895202	0.447601	+	0.894233i	$0.352278\pi$
$398$	8.04218e6	2.54487
$399$	−2.10606e6	−0.662275
$400$	−1.39222e7	−4.35067
$401$	−487846.	−0.151503	−0.0757517	−	0.997127i	$-0.524136\pi$
$401$	−487846.	−0.151503	−0.0757517	+	0.997127i	$0.524136\pi$
$402$	1.21476e7	3.74907
$403$	−840796.	−0.257886
$404$	−1.71385e7	−5.22420
$405$	−1.12223e6	−0.339973
$406$	7.09886e6	2.13734
$407$	1.00048e6	0.299379
$408$	4.46278e6	1.32726
$409$	5.28714e6	1.56283	0.781416	−	0.624010i	$-0.214497\pi$
$409$	5.28714e6	1.56283	0.781416	+	0.624010i	$0.214497\pi$
$410$	930019.	0.273232
$411$	−5.43439e6	−1.58689
$412$	−1.21987e7	−3.54054
$413$	−2.02927e6	−0.585417
$414$	−1.20077e7	−3.44317
$415$	−491487.	−0.140085
$416$	7.50867e6	2.12731
$417$	7.77906e6	2.19072
$418$	455487.	0.127507
$419$	−4.56344e6	−1.26986	−0.634932	−	0.772568i	$-0.718972\pi$
$419$	−4.56344e6	−1.26986	−0.634932	+	0.772568i	$0.718972\pi$
$420$	3.60194e6	0.996353
$421$	3.35431e6	0.922356	0.461178	−	0.887308i	$-0.347427\pi$
$421$	3.35431e6	0.922356	0.461178	+	0.887308i	$0.347427\pi$
$422$	−6.99241e6	−1.91138
$423$	−1.21441e7	−3.30000
$424$	−4.30561e6	−1.16311
$425$	−705765.	−0.189534
$426$	1.54753e6	0.413158
$427$	−3.24059e6	−0.860111
$428$	−2.44539e6	−0.645266
$429$	−527180.	−0.138298
$430$	−209559.	−0.0546558
$431$	4.51725e6	1.17133	0.585667	−	0.810552i	$-0.300833\pi$
$431$	4.51725e6	1.17133	0.585667	+	0.810552i	$0.300833\pi$
$432$	−3.99690e7	−10.3042
$433$	−7.39491e6	−1.89545	−0.947727	−	0.319084i	$-0.896625\pi$
$433$	−7.39491e6	−1.89545	−0.947727	+	0.319084i	$0.896625\pi$
$434$	−5.05385e6	−1.28795
$435$	−1.33792e6	−0.339007
$436$	−1.58998e7	−4.00568
$437$	1.07381e6	0.268981
$438$	1.65551e6	0.412331
$439$	4.68334e6	1.15983	0.579915	−	0.814677i	$-0.303086\pi$
$439$	4.68334e6	1.15983	0.579915	+	0.814677i	$0.303086\pi$
$440$	−510171.	−0.125627
$441$	907856.	0.222290
$442$	658333.	0.160284
$443$	−2.43782e6	−0.590190	−0.295095	−	0.955468i	$-0.595351\pi$
$443$	−2.43782e6	−0.590190	−0.295095	+	0.955468i	$0.595351\pi$
$444$	3.52636e7	8.48924
$445$	1.19417e6	0.285868
$446$	−5.73331e6	−1.36480
$447$	−6.11940e6	−1.44857
$448$	2.51061e7	5.90995
$449$	3.20725e6	0.750788	0.375394	−	0.926865i	$-0.377507\pi$
$449$	3.20725e6	0.750788	0.375394	+	0.926865i	$0.377507\pi$
$450$	1.85933e7	4.32839
$451$	−608262.	−0.140815
$452$	1.00554e7	2.31502
$453$	−1.13884e7	−2.60745
$454$	1.34947e7	3.07273
$455$	347977.	0.0787993
$456$	1.05140e7	2.36787
$457$	8.02184e6	1.79673	0.898366	−	0.439247i	$-0.144755\pi$
$457$	8.02184e6	1.79673	0.898366	+	0.439247i	$0.144755\pi$
$458$	3.49920e6	0.779481
$459$	−2.02617e6	−0.448895
$460$	−1.83650e6	−0.404666
$461$	4.78328e6	1.04827	0.524136	−	0.851635i	$-0.324388\pi$
$461$	4.78328e6	1.04827	0.524136	+	0.851635i	$0.324388\pi$
$462$	−3.16877e6	−0.690694
$463$	1.35182e6	0.293066	0.146533	−	0.989206i	$-0.453189\pi$
$463$	1.35182e6	0.293066	0.146533	+	0.989206i	$0.453189\pi$
$464$	−2.15558e7	−4.64803
$465$	952500.	0.204283
$466$	2.16719e6	0.462309
$467$	−6.92509e6	−1.46938	−0.734688	−	0.678405i	$-0.762671\pi$
$467$	−6.92509e6	−1.46938	−0.734688	+	0.678405i	$0.762671\pi$
$468$	−1.28940e7	−2.72128
$469$	5.24421e6	1.10090
$470$	−2.49835e6	−0.521685
$471$	−1.25464e6	−0.260595
$472$	1.01307e7	2.09307
$473$	137059.	0.0281678
$474$	−8.45402e6	−1.72829
$475$	−1.66274e6	−0.338135
$476$	2.94186e6	0.595121
$477$	3.49753e6	0.703827
$478$	3.90548e6	0.781816
$479$	−4.12443e6	−0.821343	−0.410672	−	0.911783i	$-0.634706\pi$
$479$	−4.12443e6	−0.821343	−0.410672	+	0.911783i	$0.634706\pi$
$480$	−8.50624e6	−1.68513
$481$	3.40675e6	0.671395
$482$	238327.	0.0467258
$483$	−7.47033e6	−1.45704
$484$	−1.44242e7	−2.79883
$485$	633248.	0.122242
$486$	1.12531e7	2.16114
$487$	−2.39619e6	−0.457825	−0.228913	−	0.973447i	$-0.573517\pi$
$487$	−2.39619e6	−0.457825	−0.228913	+	0.973447i	$0.573517\pi$
$488$	1.61779e7	3.07520
$489$	6.05343e6	1.14480
$490$	186769.	0.0351411
$491$	−1.38935e6	−0.260081	−0.130041	−	0.991509i	$-0.541511\pi$
$491$	−1.38935e6	−0.260081	−0.130041	+	0.991509i	$0.541511\pi$
$492$	−2.14393e7	−3.99298
$493$	−1.09274e6	−0.202488
$494$	1.55099e6	0.285952
$495$	414423.	0.0760204
$496$	1.53461e7	2.80087
$497$	668084.	0.121322
$498$	1.52400e7	2.75367
$499$	−4.94748e6	−0.889473	−0.444736	−	0.895662i	$-0.646703\pi$
$499$	−4.94748e6	−0.889473	−0.444736	+	0.895662i	$0.646703\pi$
$500$	5.78440e6	1.03474
$501$	7.03987e6	1.25305
$502$	9.84891e6	1.74433
$503$	−143778.	−0.0253381	−0.0126690	−	0.999920i	$-0.504033\pi$
$503$	−143778.	−0.0253381	−0.0126690	+	0.999920i	$0.504033\pi$
$504$	−5.07567e7	−8.90056
$505$	1.87570e6	0.327291
$506$	1.61564e6	0.280524
$507$	8.66660e6	1.49737
$508$	1.50878e7	2.59398
$509$	−804164.	−0.137578	−0.0687892	−	0.997631i	$-0.521914\pi$
$509$	−804164.	−0.137578	−0.0687892	+	0.997631i	$0.521914\pi$
$510$	−745797.	−0.126968
$511$	714697.	0.121079
$512$	−3.70667e7	−6.24897
$513$	−4.77355e6	−0.800844
$514$	2.12247e7	3.54351
$515$	1.33506e6	0.221811
$516$	4.83087e6	0.798733
$517$	1.63400e6	0.268860
$518$	2.04773e7	3.35311
$519$	−4.17123e6	−0.679744
$520$	−1.73720e6	−0.281735
$521$	1.33327e6	0.215191	0.107595	−	0.994195i	$-0.465685\pi$
$521$	1.33327e6	0.215191	0.107595	+	0.994195i	$0.465685\pi$
$522$	2.87882e7	4.62422
$523$	870192.	0.139111	0.0695554	−	0.997578i	$-0.477842\pi$
$523$	870192.	0.139111	0.0695554	+	0.997578i	$0.477842\pi$
$524$	−1.18992e7	−1.89316
$525$	1.15675e7	1.83164
$526$	6.68881e6	1.05411
$527$	777949.	0.122018
$528$	9.62201e6	1.50204
$529$	−2.62748e6	−0.408226
$530$	719532.	0.111265
$531$	−8.22937e6	−1.26657
$532$	6.93085e6	1.06171
$533$	−2.07121e6	−0.315796
$534$	−3.70288e7	−5.61935
$535$	267632.	0.0404253
$536$	−2.61806e7	−3.93611
$537$	−1.38859e7	−2.07797
$538$	−1.35463e7	−2.01773
$539$	−122153.	−0.0181106
$540$	8.16408e6	1.20482
$541$	8.24525e6	1.21119	0.605593	−	0.795774i	$-0.292936\pi$
$541$	8.24525e6	1.21119	0.605593	+	0.795774i	$0.292936\pi$
$542$	−2.40971e6	−0.352344
$543$	1.07054e7	1.55814
$544$	−6.94742e6	−1.00653
$545$	1.74013e6	0.250951
$546$	−1.07901e7	−1.54897
$547$	9.45890e6	1.35168	0.675838	−	0.737050i	$-0.263782\pi$
$547$	9.45890e6	1.35168	0.675838	+	0.737050i	$0.263782\pi$
$548$	1.78841e7	2.54399
$549$	−1.31417e7	−1.86089
$550$	−2.50175e6	−0.352645
$551$	−2.57443e6	−0.361246
$552$	3.72940e7	5.20944
$553$	−3.64967e6	−0.507506
$554$	−2.62944e6	−0.363989
$555$	−3.85936e6	−0.531842
$556$	−2.56002e7	−3.51202
$557$	−1.05787e7	−1.44476	−0.722380	−	0.691497i	$-0.756952\pi$
$557$	−1.05787e7	−1.44476	−0.722380	+	0.691497i	$0.756952\pi$
$558$	−2.04950e7	−2.78653
$559$	466702.	0.0631700
$560$	−6.35123e6	−0.855830
$561$	487775.	0.0654353
$562$	−1.40553e7	−1.87715
$563$	7.11281e6	0.945737	0.472869	−	0.881133i	$-0.343219\pi$
$563$	7.11281e6	0.945737	0.472869	+	0.881133i	$0.343219\pi$
$564$	5.75932e7	7.62383
$565$	−1.10050e6	−0.145033
$566$	−1.25187e7	−1.64255
$567$	1.50226e7	1.96241
$568$	−3.33526e6	−0.433770
$569$	−431278.	−0.0558440	−0.0279220	−	0.999610i	$-0.508889\pi$
$569$	−431278.	−0.0558440	−0.0279220	+	0.999610i	$0.508889\pi$
$570$	−1.75705e6	−0.226515
$571$	−4.96062e6	−0.636716	−0.318358	−	0.947971i	$-0.603131\pi$
$571$	−4.96062e6	−0.636716	−0.318358	+	0.947971i	$0.603131\pi$
$572$	1.73490e6	0.221710
$573$	−2.37987e7	−3.02807
$574$	−1.24496e7	−1.57716
$575$	−5.89785e6	−0.743917
$576$	1.01813e8	12.7864
$577$	1.02637e7	1.28341	0.641705	−	0.766952i	$-0.278228\pi$
$577$	1.02637e7	1.28341	0.641705	+	0.766952i	$0.278228\pi$
$578$	1.52480e7	1.89842
$579$	6.43505e6	0.797729
$580$	4.40299e6	0.543473
$581$	6.57926e6	0.808605
$582$	−1.96357e7	−2.40292
$583$	−470597.	−0.0573426
$584$	−3.56797e6	−0.432901
$585$	1.41116e6	0.170485
$586$	−2.72913e7	−3.28307
$587$	6.47940e6	0.776140	0.388070	−	0.921630i	$-0.373142\pi$
$587$	6.47940e6	0.776140	0.388070	+	0.921630i	$0.373142\pi$
$588$	−4.30550e6	−0.513547
$589$	1.83280e6	0.217684
$590$	−1.69299e6	−0.200228
$591$	−1.14309e7	−1.34621
$592$	−6.21795e7	−7.29194
$593$	−3.51558e6	−0.410545	−0.205272	−	0.978705i	$-0.565808\pi$
$593$	−3.51558e6	−0.410545	−0.205272	+	0.978705i	$0.565808\pi$
$594$	−7.18226e6	−0.835209
$595$	−321967.	−0.0372837
$596$	2.01384e7	2.32225
$597$	2.02900e7	2.32994
$598$	5.50148e6	0.629110
$599$	−993536.	−0.113140	−0.0565701	−	0.998399i	$-0.518016\pi$
$599$	−993536.	−0.113140	−0.0565701	+	0.998399i	$0.518016\pi$
$600$	−5.77481e7	−6.54877
$601$	6.25981e6	0.706928	0.353464	−	0.935448i	$-0.385004\pi$
$601$	6.25981e6	0.706928	0.353464	+	0.935448i	$0.385004\pi$
$602$	2.80525e6	0.315486
$603$	2.12670e7	2.38184
$604$	3.74782e7	4.18009
$605$	1.57863e6	0.175344
$606$	−5.81615e7	−6.43360
$607$	−3.58799e6	−0.395257	−0.197628	−	0.980277i	$-0.563324\pi$
$607$	−3.58799e6	−0.395257	−0.197628	+	0.980277i	$0.563324\pi$
$608$	−1.63677e7	−1.79568
$609$	1.79100e7	1.95683
$610$	−2.70358e6	−0.294181
$611$	5.56398e6	0.602952
$612$	1.19302e7	1.28757
$613$	7.67762e6	0.825231	0.412615	−	0.910905i	$-0.364615\pi$
$613$	7.67762e6	0.825231	0.412615	+	0.910905i	$0.364615\pi$
$614$	3.43079e7	3.67259
$615$	2.34638e6	0.250156
$616$	6.82937e6	0.725152
$617$	−9.88787e6	−1.04566	−0.522829	−	0.852438i	$-0.675123\pi$
$617$	−9.88787e6	−1.04566	−0.522829	+	0.852438i	$0.675123\pi$
$618$	−4.13976e7	−4.36018
$619$	759066.	0.0796256	0.0398128	−	0.999207i	$-0.487324\pi$
$619$	759066.	0.0796256	0.0398128	+	0.999207i	$0.487324\pi$
$620$	−3.13459e6	−0.327493
$621$	−1.69321e7	−1.76190
$622$	1.13930e7	1.18076
$623$	−1.59856e7	−1.65010
$624$	3.27642e7	3.36851
$625$	8.81073e6	0.902218
$626$	−1.40690e7	−1.43492
$627$	1.14917e6	0.116739
$628$	4.12890e6	0.417768
$629$	−3.15211e6	−0.317669
$630$	8.48221e6	0.851447
$631$	−8.94214e6	−0.894063	−0.447031	−	0.894518i	$-0.647519\pi$
$631$	−8.94214e6	−0.894063	−0.447031	+	0.894518i	$0.647519\pi$
$632$	1.82202e7	1.81451
$633$	−1.76415e7	−1.74995
$634$	3.82703e7	3.78127
$635$	−1.65126e6	−0.162510
$636$	−1.65870e7	−1.62602
$637$	−415947.	−0.0406153
$638$	−3.87349e6	−0.376748
$639$	2.70930e6	0.262485
$640$	1.12851e7	1.08907
$641$	−1.38335e6	−0.132981	−0.0664903	−	0.997787i	$-0.521180\pi$
$641$	−1.38335e6	−0.132981	−0.0664903	+	0.997787i	$0.521180\pi$
$642$	−8.29872e6	−0.794646
$643$	1.42540e7	1.35959	0.679797	−	0.733400i	$-0.262068\pi$
$643$	1.42540e7	1.35959	0.679797	+	0.733400i	$0.262068\pi$
$644$	2.45842e7	2.33583
$645$	−528707.	−0.0500398
$646$	−1.43506e6	−0.135297
$647$	−9.93069e6	−0.932650	−0.466325	−	0.884613i	$-0.654422\pi$
$647$	−9.93069e6	−0.932650	−0.466325	+	0.884613i	$0.654422\pi$
$648$	−7.49973e7	−7.01630
$649$	1.10727e6	0.103191
$650$	−8.51880e6	−0.790852
$651$	−1.27506e7	−1.17917
$652$	−1.99213e7	−1.83527
$653$	−1.48917e7	−1.36666	−0.683330	−	0.730110i	$-0.739469\pi$
$653$	−1.48917e7	−1.36666	−0.683330	+	0.730110i	$0.739469\pi$
$654$	−5.39578e7	−4.93299
$655$	1.30228e6	0.118605
$656$	3.78035e7	3.42982
$657$	2.89833e6	0.261960
$658$	3.34439e7	3.01129
$659$	−834285.	−0.0748343	−0.0374172	−	0.999300i	$-0.511913\pi$
$659$	−834285.	−0.0748343	−0.0374172	+	0.999300i	$0.511913\pi$
$660$	−1.96539e6	−0.175626
$661$	9.69443e6	0.863016	0.431508	−	0.902109i	$-0.357982\pi$
$661$	9.69443e6	0.863016	0.431508	+	0.902109i	$0.357982\pi$
$662$	1.07058e7	0.949456
$663$	1.66094e6	0.146747
$664$	−3.28455e7	−2.89105
$665$	−758535.	−0.0665153
$666$	8.30422e7	7.25460
$667$	−9.13170e6	−0.794762
$668$	−2.31676e7	−2.00881
$669$	−1.44648e7	−1.24953
$670$	4.37516e6	0.376537
$671$	1.76823e6	0.151611
$672$	1.13868e8	9.72700
$673$	−5.45965e6	−0.464651	−0.232326	−	0.972638i	$-0.574634\pi$
$673$	−5.45965e6	−0.464651	−0.232326	+	0.972638i	$0.574634\pi$
$674$	−2.52323e7	−2.13948
$675$	2.62186e7	2.21488
$676$	−2.85210e7	−2.40048
$677$	503614.	0.0422305	0.0211152	−	0.999777i	$-0.493278\pi$
$677$	503614.	0.0422305	0.0211152	+	0.999777i	$0.493278\pi$
$678$	3.41242e7	2.85094
$679$	−8.47692e6	−0.705609
$680$	1.60735e6	0.133302
$681$	3.40465e7	2.81322
$682$	2.75763e6	0.227026
$683$	−9.08309e6	−0.745044	−0.372522	−	0.928023i	$-0.621507\pi$
$683$	−9.08309e6	−0.745044	−0.372522	+	0.928023i	$0.621507\pi$
$684$	2.81069e7	2.29706
$685$	−1.95729e6	−0.159378
$686$	2.29989e7	1.86594
$687$	8.82829e6	0.713649
$688$	−8.51818e6	−0.686082
$689$	−1.60244e6	−0.128598
$690$	−6.23238e6	−0.498347
$691$	2.14373e7	1.70795	0.853976	−	0.520313i	$-0.174185\pi$
$691$	2.14373e7	1.70795	0.853976	+	0.520313i	$0.174185\pi$
$692$	1.37271e7	1.08972
$693$	−5.54763e6	−0.438808
$694$	−2.97748e7	−2.34666
$695$	2.80177e6	0.220024
$696$	−8.94119e7	−6.99636
$697$	1.91640e6	0.149418
$698$	4.40033e6	0.341859
$699$	5.46770e6	0.423264
$700$	−3.80675e7	−2.93636
$701$	−2.39509e7	−1.84088	−0.920442	−	0.390878i	$-0.872171\pi$
$701$	−2.39509e7	−1.84088	−0.920442	+	0.390878i	$0.872171\pi$
$702$	−2.44565e7	−1.87306
$703$	−7.42618e6	−0.566731
$704$	−1.36991e7	−1.04174
$705$	−6.30319e6	−0.477625
$706$	8.72755e6	0.658993
$707$	−2.51088e7	−1.88920
$708$	3.90277e7	2.92611
$709$	1.01183e7	0.755949	0.377975	−	0.925816i	$-0.376621\pi$
$709$	1.01183e7	0.755949	0.377975	+	0.925816i	$0.376621\pi$
$710$	557372.	0.0414954
$711$	−1.48006e7	−1.09801
$712$	7.98048e7	5.89969
$713$	6.50107e6	0.478918
$714$	9.98355e6	0.732891
$715$	−189873.	−0.0138899
$716$	4.56973e7	3.33126
$717$	9.85329e6	0.715787
$718$	2.67084e7	1.93347
$719$	−1.59945e6	−0.115384	−0.0576922	−	0.998334i	$-0.518374\pi$
$719$	−1.59945e6	−0.115384	−0.0576922	+	0.998334i	$0.518374\pi$
$720$	−2.57563e7	−1.85162
$721$	−1.78717e7	−1.28035
$722$	2.42724e7	1.73288
$723$	601287.	0.0427795
$724$	−3.52307e7	−2.49790
$725$	1.41400e7	0.999091
$726$	−4.89500e7	−3.44676
$727$	−2.36374e7	−1.65868	−0.829340	−	0.558744i	$-0.811284\pi$
$727$	−2.36374e7	−1.65868	−0.829340	+	0.558744i	$0.811284\pi$
$728$	2.32549e7	1.62624
$729$	1.51921e6	0.105876
$730$	596261.	0.0414123
$731$	−431818.	−0.0298887
$732$	6.23242e7	4.29912
$733$	−8.73268e6	−0.600327	−0.300163	−	0.953888i	$-0.597041\pi$
$733$	−8.73268e6	−0.600327	−0.300163	+	0.953888i	$0.597041\pi$
$734$	−3.69292e7	−2.53005
$735$	471208.	0.0321732
$736$	−5.80574e7	−3.95060
$737$	−2.86150e6	−0.194055
$738$	−5.04874e7	−3.41226
$739$	1.45547e7	0.980378	0.490189	−	0.871616i	$-0.336928\pi$
$739$	1.45547e7	0.980378	0.490189	+	0.871616i	$0.336928\pi$
$740$	1.27008e7	0.852614
$741$	3.91307e6	0.261801
$742$	−9.63195e6	−0.642251
$743$	1.04520e7	0.694591	0.347296	−	0.937756i	$-0.387100\pi$
$743$	1.04520e7	0.694591	0.347296	+	0.937756i	$0.387100\pi$
$744$	6.36544e7	4.21596
$745$	−2.20401e6	−0.145487
$746$	3.81759e7	2.51155
$747$	2.66811e7	1.74945
$748$	−1.60522e6	−0.104902
$749$	−3.58263e6	−0.233344
$750$	1.96300e7	1.27429
$751$	−2.90334e6	−0.187844	−0.0939221	−	0.995580i	$-0.529940\pi$
$751$	−2.90334e6	−0.187844	−0.0939221	+	0.995580i	$0.529940\pi$
$752$	−1.01553e8	−6.54859
$753$	2.48482e7	1.59701
$754$	−1.31897e7	−0.844904
$755$	−4.10173e6	−0.261879
$756$	−1.09288e8	−6.95452
$757$	−8.00481e6	−0.507705	−0.253852	−	0.967243i	$-0.581698\pi$
$757$	−8.00481e6	−0.507705	−0.253852	+	0.967243i	$0.581698\pi$
$758$	−4.11162e7	−2.59920
$759$	4.07618e6	0.256832
$760$	3.78682e6	0.237816
$761$	1.58931e7	0.994826	0.497413	−	0.867514i	$-0.334283\pi$
$761$	1.58931e7	0.994826	0.497413	+	0.867514i	$0.334283\pi$
$762$	5.12021e7	3.19448
$763$	−2.32941e7	−1.44855
$764$	7.83193e7	4.85440
$765$	−1.30568e6	−0.0806648
$766$	1.98801e7	1.22418
$767$	3.77040e6	0.231419
$768$	−1.83295e8	−11.2137
$769$	1.55997e7	0.951264	0.475632	−	0.879644i	$-0.342219\pi$
$769$	1.55997e7	0.951264	0.475632	+	0.879644i	$0.342219\pi$
$770$	−1.14129e6	−0.0693696
$771$	5.35487e7	3.24424
$772$	−2.11772e7	−1.27887
$773$	−2.37032e7	−1.42678	−0.713392	−	0.700765i	$-0.752842\pi$
$773$	−2.37032e7	−1.42678	−0.713392	+	0.700765i	$0.752842\pi$
$774$	1.13762e7	0.682568
$775$	−1.00666e7	−0.602046
$776$	4.23192e7	2.52280
$777$	5.16630e7	3.06992
$778$	−3.74855e7	−2.22031
$779$	4.51491e6	0.266567
$780$	−6.69243e6	−0.393865
$781$	−364539.	−0.0213854
$782$	−5.09026e6	−0.297662
$783$	4.05945e7	2.36626
$784$	7.59180e6	0.441118
$785$	−451880.	−0.0261727
$786$	−4.03812e7	−2.33143
$787$	2.03168e7	1.16928	0.584639	−	0.811294i	$-0.301236\pi$
$787$	2.03168e7	1.16928	0.584639	+	0.811294i	$0.301236\pi$
$788$	3.76182e7	2.15815
$789$	1.68755e7	0.965081
$790$	−3.04487e6	−0.173580
$791$	1.47317e7	0.837168
$792$	2.76954e7	1.56890
$793$	6.02104e6	0.340007
$794$	−3.13961e7	−1.76736
$795$	1.81534e6	0.101868
$796$	−6.67725e7	−3.73521
$797$	−9.05526e6	−0.504958	−0.252479	−	0.967602i	$-0.581246\pi$
$797$	−9.05526e6	−0.504958	−0.252479	+	0.967602i	$0.581246\pi$
$798$	2.35206e7	1.30750
$799$	−5.14809e6	−0.285285
$800$	8.98993e7	4.96628
$801$	−6.48271e7	−3.57006
$802$	5.44831e6	0.299107
$803$	−389974.	−0.0213426
$804$	−1.00859e8	−5.50266
$805$	−2.69058e6	−0.146337
$806$	9.39008e6	0.509134
$807$	−3.41764e7	−1.84732
$808$	1.25350e8	6.75457
$809$	−6.37396e6	−0.342403	−0.171202	−	0.985236i	$-0.554765\pi$
$809$	−6.37396e6	−0.342403	−0.171202	+	0.985236i	$0.554765\pi$
$810$	1.25332e7	0.671195
$811$	8.10409e6	0.432665	0.216333	−	0.976320i	$-0.430590\pi$
$811$	8.10409e6	0.432665	0.216333	+	0.976320i	$0.430590\pi$
$812$	−5.89403e7	−3.13706
$813$	−6.07956e6	−0.322586
$814$	−1.11734e7	−0.591051
$815$	2.18025e6	0.114977
$816$	−3.03152e7	−1.59380
$817$	−1.01734e6	−0.0533224
$818$	−5.90473e7	−3.08544
$819$	−1.88904e7	−0.984083
$820$	−7.72175e6	−0.401034
$821$	−1.15491e6	−0.0597983	−0.0298992	−	0.999553i	$-0.509519\pi$
$821$	−1.15491e6	−0.0597983	−0.0298992	+	0.999553i	$0.509519\pi$
$822$	6.06917e7	3.13293
$823$	−5.41617e6	−0.278736	−0.139368	−	0.990241i	$-0.544507\pi$
$823$	−5.41617e6	−0.278736	−0.139368	+	0.990241i	$0.544507\pi$
$824$	8.92207e7	4.57770
$825$	−6.31178e6	−0.322862
$826$	2.26631e7	1.15576
$827$	2.73522e7	1.39068	0.695342	−	0.718679i	$-0.255253\pi$
$827$	2.73522e7	1.39068	0.695342	+	0.718679i	$0.255253\pi$
$828$	9.96971e7	5.05367
$829$	−2.13862e7	−1.08081	−0.540403	−	0.841407i	$-0.681728\pi$
$829$	−2.13862e7	−1.08081	−0.540403	+	0.841407i	$0.681728\pi$
$830$	5.48898e6	0.276564
$831$	−6.63392e6	−0.333248
$832$	−4.66472e7	−2.33624
$833$	384856.	0.0192170
$834$	−8.68772e7	−4.32505
$835$	2.53554e6	0.125850
$836$	−3.78181e6	−0.187148
$837$	−2.89002e7	−1.42589
$838$	5.09649e7	2.50704
$839$	−1.45057e7	−0.711432	−0.355716	−	0.934594i	$-0.615763\pi$
$839$	−1.45057e7	−0.711432	−0.355716	+	0.934594i	$0.615763\pi$
$840$	−2.63444e7	−1.28822
$841$	1.38197e6	0.0673766
$842$	−3.74613e7	−1.82097
$843$	−3.54607e7	−1.71861
$844$	5.80565e7	2.80540
$845$	3.12143e6	0.150388
$846$	1.35626e8	6.51505
$847$	−2.11322e7	−1.01213
$848$	2.92476e7	1.39669
$849$	−3.15839e7	−1.50382
$850$	7.88205e6	0.374190
$851$	−2.63412e7	−1.24684
$852$	−1.28488e7	−0.606408
$853$	−1.15298e7	−0.542563	−0.271282	−	0.962500i	$-0.587447\pi$
$853$	−1.15298e7	−0.542563	−0.271282	+	0.962500i	$0.587447\pi$
$854$	3.61912e7	1.69808
$855$	−3.07611e6	−0.143909
$856$	1.78855e7	0.834289
$857$	2.85360e7	1.32722	0.663608	−	0.748080i	$-0.269024\pi$
$857$	2.85360e7	1.32722	0.663608	+	0.748080i	$0.269024\pi$
$858$	5.88759e6	0.273036
$859$	−2.75999e7	−1.27622	−0.638109	−	0.769946i	$-0.720283\pi$
$859$	−2.75999e7	−1.27622	−0.638109	+	0.769946i	$0.720283\pi$
$860$	1.73993e6	0.0802204
$861$	−3.14097e7	−1.44396
$862$	−5.04490e7	−2.31251
$863$	6.90832e6	0.315752	0.157876	−	0.987459i	$-0.449535\pi$
$863$	6.90832e6	0.315752	0.157876	+	0.987459i	$0.449535\pi$
$864$	2.58091e8	11.7622
$865$	−1.50234e6	−0.0682698
$866$	8.25870e7	3.74211
$867$	3.84697e7	1.73809
$868$	4.19610e7	1.89037
$869$	1.99144e6	0.0894578
$870$	1.49421e7	0.669287
$871$	−9.74377e6	−0.435193
$872$	1.16291e8	5.17909
$873$	−3.43767e7	−1.52661
$874$	−1.19924e7	−0.531038
$875$	8.47445e6	0.374189
$876$	−1.37453e7	−0.605194
$877$	1.00172e7	0.439790	0.219895	−	0.975524i	$-0.429429\pi$
$877$	1.00172e7	0.439790	0.219895	+	0.975524i	$0.429429\pi$
$878$	−5.23040e7	−2.28981
$879$	−6.88544e7	−3.00580
$880$	3.46554e6	0.150857
$881$	2.80779e7	1.21878	0.609389	−	0.792871i	$-0.291415\pi$
$881$	2.80779e7	1.21878	0.609389	+	0.792871i	$0.291415\pi$
$882$	−1.01390e7	−0.438859
$883$	2.54617e7	1.09897	0.549485	−	0.835504i	$-0.314824\pi$
$883$	2.54617e7	1.09897	0.549485	+	0.835504i	$0.314824\pi$
$884$	−5.46600e6	−0.235255
$885$	−4.27132e6	−0.183318
$886$	2.72258e7	1.16519
$887$	1.53530e7	0.655216	0.327608	−	0.944814i	$-0.393757\pi$
$887$	1.53530e7	0.655216	0.327608	+	0.944814i	$0.393757\pi$
$888$	−2.57916e8	−10.9761
$889$	2.21044e7	0.938046
$890$	−1.33366e7	−0.564377
$891$	−8.19709e6	−0.345912
$892$	4.76024e7	2.00317
$893$	−1.21286e7	−0.508958
$894$	6.83420e7	2.85986
$895$	−5.00126e6	−0.208700
$896$	−1.51067e8	−6.28635
$897$	1.38799e7	0.575978
$898$	−3.58189e7	−1.48225
$899$	−1.55862e7	−0.643194
$900$	−1.54377e8	−6.35294
$901$	1.48267e6	0.0608459
$902$	6.79313e6	0.278006
$903$	7.07749e6	0.288842
$904$	−7.35450e7	−2.99317
$905$	3.85576e6	0.156491
$906$	1.27186e8	5.14778
$907$	−2.57735e7	−1.04029	−0.520146	−	0.854077i	$-0.674123\pi$
$907$	−2.57735e7	−1.04029	−0.520146	+	0.854077i	$0.674123\pi$
$908$	−1.12044e8	−4.50997
$909$	−1.01825e8	−4.08737
$910$	−3.88624e6	−0.155570
$911$	1.30975e7	0.522869	0.261435	−	0.965221i	$-0.415804\pi$
$911$	1.30975e7	0.522869	0.261435	+	0.965221i	$0.415804\pi$
$912$	−7.14207e7	−2.84340
$913$	−3.58997e6	−0.142532
$914$	−8.95886e7	−3.54721
$915$	−6.82097e6	−0.269335
$916$	−2.90531e7	−1.14407
$917$	−1.74329e7	−0.684616
$918$	2.26285e7	0.886235
$919$	2.00241e7	0.782104	0.391052	−	0.920369i	$-0.372111\pi$
$919$	2.00241e7	0.782104	0.391052	+	0.920369i	$0.372111\pi$
$920$	1.34321e7	0.523208
$921$	8.65568e7	3.36242
$922$	−5.34201e7	−2.06956
$923$	−1.24130e6	−0.0479594
$924$	2.63096e7	1.01376
$925$	4.07881e7	1.56740
$926$	−1.50972e7	−0.578588
$927$	−7.24758e7	−2.77009
$928$	1.39192e8	5.30571
$929$	2.20794e7	0.839361	0.419681	−	0.907672i	$-0.362142\pi$
$929$	2.20794e7	0.839361	0.419681	+	0.907672i	$0.362142\pi$
$930$	−1.06376e7	−0.403308
$931$	906698.	0.0342838
$932$	−1.79937e7	−0.678549
$933$	2.87438e7	1.08103
$934$	7.73400e7	2.90093
$935$	175681.	0.00657197
$936$	9.43063e7	3.51845
$937$	3.08266e7	1.14704	0.573518	−	0.819193i	$-0.305578\pi$
$937$	3.08266e7	1.14704	0.573518	+	0.819193i	$0.305578\pi$
$938$	−5.85678e7	−2.17346
$939$	−3.54953e7	−1.31373
$940$	2.07432e7	0.765697
$941$	2.58954e7	0.953342	0.476671	−	0.879082i	$-0.341843\pi$
$941$	2.58954e7	0.953342	0.476671	+	0.879082i	$0.341843\pi$
$942$	1.40119e7	0.514481
$943$	1.60147e7	0.586462
$944$	−6.88168e7	−2.51342
$945$	1.19608e7	0.435694
$946$	−1.53068e6	−0.0556106
$947$	3.84495e7	1.39321	0.696604	−	0.717456i	$-0.254693\pi$
$947$	3.84495e7	1.39321	0.696604	+	0.717456i	$0.254693\pi$
$948$	7.01919e7	2.53668
$949$	−1.32791e6	−0.0478634
$950$	1.85696e7	0.667566
$951$	9.65536e7	3.46192
$952$	−2.15167e7	−0.769454
$953$	4.30967e7	1.53713	0.768567	−	0.639769i	$-0.220970\pi$
$953$	4.30967e7	1.53713	0.768567	+	0.639769i	$0.220970\pi$
$954$	−3.90608e7	−1.38954
$955$	−8.57152e6	−0.304123
$956$	−3.24263e7	−1.14750
$957$	−9.77259e6	−0.344929
$958$	4.60620e7	1.62154
$959$	2.62012e7	0.919971
$960$	5.28446e7	1.85064
$961$	−1.75329e7	−0.612416
$962$	−3.80469e7	−1.32551
$963$	−1.45288e7	−0.504850
$964$	−1.97878e6	−0.0685812
$965$	2.31770e6	0.0801196
$966$	8.34293e7	2.87658
$967$	1.74442e7	0.599910	0.299955	−	0.953953i	$-0.403028\pi$
$967$	1.74442e7	0.599910	0.299955	+	0.953953i	$0.403028\pi$
$968$	1.05498e8	3.61872
$969$	−3.62058e6	−0.123871
$970$	−7.07217e6	−0.241337
$971$	−1.03144e7	−0.351071	−0.175536	−	0.984473i	$-0.556166\pi$
$971$	−1.03144e7	−0.351071	−0.175536	+	0.984473i	$0.556166\pi$
$972$	−9.34323e7	−3.17199
$973$	−3.75057e7	−1.27003
$974$	2.67609e7	0.903865
$975$	−2.14924e7	−0.724059
$976$	−1.09895e8	−3.69278
$977$	−3.92840e7	−1.31668	−0.658338	−	0.752722i	$-0.728740\pi$
$977$	−3.92840e7	−1.31668	−0.658338	+	0.752722i	$0.728740\pi$
$978$	−6.76052e7	−2.26013
$979$	8.72255e6	0.290862
$980$	−1.55070e6	−0.0515779
$981$	−9.44652e7	−3.13400
$982$	1.55164e7	0.513467
$983$	2.20437e7	0.727613	0.363807	−	0.931474i	$-0.381477\pi$
$983$	2.20437e7	0.727613	0.363807	+	0.931474i	$0.381477\pi$
$984$	1.56806e8	5.16268
$985$	−4.11706e6	−0.135206
$986$	1.22038e7	0.399764
$987$	8.43771e7	2.75697
$988$	−1.28776e7	−0.419702
$989$	−3.60856e6	−0.117312
$990$	−4.62831e6	−0.150084
$991$	−3.97800e7	−1.28671	−0.643356	−	0.765567i	$-0.722458\pi$
$991$	−3.97800e7	−1.28671	−0.643356	+	0.765567i	$0.722458\pi$
$992$	−9.90940e7	−3.19719
$993$	2.70102e7	0.869269
$994$	−7.46122e6	−0.239521
$995$	7.30780e6	0.234007
$996$	−1.26535e8	−4.04167
$997$	−2.94784e7	−0.939218	−0.469609	−	0.882875i	$-0.655605\pi$
$997$	−2.94784e7	−0.939218	−0.469609	+	0.882875i	$0.655605\pi$
$998$	5.52539e7	1.75605
$999$	1.17098e8	3.71225

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.a.a.1.1	✓	8
3.2	odd	2		387.6.a.c.1.8		8
4.3	odd	2		688.6.a.e.1.8		8
5.4	even	2		1075.6.a.a.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.a.a.1.1	✓	8	1.1	even	1	trivial
387.6.a.c.1.8		8	3.2	odd	2
688.6.a.e.1.8		8	4.3	odd	2
1075.6.a.a.1.8		8	5.4	even	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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	43.a (trivial)

\(f(q)\)	\(=\)	\(q-11.1681 q^{2} -28.1764 q^{3} +92.7262 q^{4} -10.1483 q^{5} +314.677 q^{6} +135.849 q^{7} -678.196 q^{8} +550.912 q^{9} +O(q^{10})\)	\(q-11.1681 q^{2} -28.1764 q^{3} +92.7262 q^{4} -10.1483 q^{5} +314.677 q^{6} +135.849 q^{7} -678.196 q^{8} +550.912 q^{9} +113.337 q^{10} -74.1258 q^{11} -2612.70 q^{12} -252.408 q^{13} -1517.17 q^{14} +285.942 q^{15} +4606.91 q^{16} +233.541 q^{17} -6152.64 q^{18} +550.209 q^{19} -941.010 q^{20} -3827.74 q^{21} +827.844 q^{22} +1951.63 q^{23} +19109.1 q^{24} -3022.01 q^{25} +2818.92 q^{26} -8675.87 q^{27} +12596.8 q^{28} -4679.01 q^{29} -3193.42 q^{30} +3331.10 q^{31} -29748.1 q^{32} +2088.60 q^{33} -2608.21 q^{34} -1378.63 q^{35} +51084.0 q^{36} -13497.0 q^{37} -6144.79 q^{38} +7111.96 q^{39} +6882.51 q^{40} +8205.81 q^{41} +42748.5 q^{42} -1849.00 q^{43} -6873.41 q^{44} -5590.80 q^{45} -21796.0 q^{46} -22043.6 q^{47} -129806. q^{48} +1647.91 q^{49} +33750.1 q^{50} -6580.36 q^{51} -23404.8 q^{52} +6348.62 q^{53} +96892.9 q^{54} +752.248 q^{55} -92132.1 q^{56} -15502.9 q^{57} +52255.6 q^{58} -14937.7 q^{59} +26514.3 q^{60} -23854.4 q^{61} -37202.0 q^{62} +74840.8 q^{63} +184809. q^{64} +2561.50 q^{65} -23325.7 q^{66} +38603.2 q^{67} +21655.4 q^{68} -54990.0 q^{69} +15396.7 q^{70} +4917.85 q^{71} -373626. q^{72} +5260.97 q^{73} +150736. q^{74} +85149.6 q^{75} +51018.8 q^{76} -10069.9 q^{77} -79427.0 q^{78} -26865.7 q^{79} -46752.1 q^{80} +110584. q^{81} -91643.2 q^{82} +48430.7 q^{83} -354932. q^{84} -2370.04 q^{85} +20649.8 q^{86} +131838. q^{87} +50271.8 q^{88} -117672. q^{89} +62438.5 q^{90} -34289.3 q^{91} +180967. q^{92} -93858.5 q^{93} +246185. q^{94} -5583.67 q^{95} +838197. q^{96} -62399.7 q^{97} -18404.1 q^{98} -40836.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{2} - 26 q^{3} + 122 q^{4} - 212 q^{5} - 69 q^{6} - 136 q^{7} - 666 q^{8} + 546 q^{9}+O(q^{10}) \) 8 * q - 12 * q^2 - 26 * q^3 + 122 * q^4 - 212 * q^5 - 69 * q^6 - 136 * q^7 - 666 * q^8 + 546 * q^9	\( 8 q - 12 q^{2} - 26 q^{3} + 122 q^{4} - 212 q^{5} - 69 q^{6} - 136 q^{7} - 666 q^{8} + 546 q^{9} - 617 q^{10} - 532 q^{11} - 4195 q^{12} - 2492 q^{13} - 4240 q^{14} - 1780 q^{15} + 1882 q^{16} - 2534 q^{17} - 3711 q^{18} - 1678 q^{19} - 2607 q^{20} - 2256 q^{21} + 11502 q^{22} - 2488 q^{23} + 19953 q^{24} + 4378 q^{25} + 4586 q^{26} - 8960 q^{27} + 18640 q^{28} - 4360 q^{29} + 25092 q^{30} + 5704 q^{31} - 18294 q^{32} - 12852 q^{33} + 30007 q^{34} + 5640 q^{35} + 67969 q^{36} - 3772 q^{37} - 6559 q^{38} + 11120 q^{39} + 14869 q^{40} - 10698 q^{41} + 78698 q^{42} - 14792 q^{43} - 356 q^{44} - 44912 q^{45} - 19389 q^{46} - 77864 q^{47} - 118727 q^{48} + 7188 q^{49} + 26877 q^{50} - 80246 q^{51} - 60736 q^{52} - 62352 q^{53} + 61026 q^{54} - 49552 q^{55} - 144528 q^{56} - 808 q^{57} + 52951 q^{58} - 26224 q^{59} + 101500 q^{60} - 82540 q^{61} - 9023 q^{62} - 61768 q^{63} + 153858 q^{64} - 5000 q^{65} - 48516 q^{66} + 27784 q^{67} + 40507 q^{68} - 93776 q^{69} + 185910 q^{70} - 9504 q^{71} - 186687 q^{72} + 14260 q^{73} - 15239 q^{74} + 167420 q^{75} + 1279 q^{76} - 218140 q^{77} + 264170 q^{78} + 160248 q^{79} - 1291 q^{80} + 161076 q^{81} - 47781 q^{82} - 77176 q^{83} + 16382 q^{84} + 141096 q^{85} + 22188 q^{86} + 268136 q^{87} + 129544 q^{88} - 265692 q^{89} + 48990 q^{90} + 401148 q^{91} + 190391 q^{92} - 123860 q^{93} + 248737 q^{94} + 135884 q^{95} + 950817 q^{96} + 144742 q^{97} - 292244 q^{98} + 239516 q^{99}+O(q^{100}) \) 8 * q - 12 * q^2 - 26 * q^3 + 122 * q^4 - 212 * q^5 - 69 * q^6 - 136 * q^7 - 666 * q^8 + 546 * q^9 - 617 * q^10 - 532 * q^11 - 4195 * q^12 - 2492 * q^13 - 4240 * q^14 - 1780 * q^15 + 1882 * q^16 - 2534 * q^17 - 3711 * q^18 - 1678 * q^19 - 2607 * q^20 - 2256 * q^21 + 11502 * q^22 - 2488 * q^23 + 19953 * q^24 + 4378 * q^25 + 4586 * q^26 - 8960 * q^27 + 18640 * q^28 - 4360 * q^29 + 25092 * q^30 + 5704 * q^31 - 18294 * q^32 - 12852 * q^33 + 30007 * q^34 + 5640 * q^35 + 67969 * q^36 - 3772 * q^37 - 6559 * q^38 + 11120 * q^39 + 14869 * q^40 - 10698 * q^41 + 78698 * q^42 - 14792 * q^43 - 356 * q^44 - 44912 * q^45 - 19389 * q^46 - 77864 * q^47 - 118727 * q^48 + 7188 * q^49 + 26877 * q^50 - 80246 * q^51 - 60736 * q^52 - 62352 * q^53 + 61026 * q^54 - 49552 * q^55 - 144528 * q^56 - 808 * q^57 + 52951 * q^58 - 26224 * q^59 + 101500 * q^60 - 82540 * q^61 - 9023 * q^62 - 61768 * q^63 + 153858 * q^64 - 5000 * q^65 - 48516 * q^66 + 27784 * q^67 + 40507 * q^68 - 93776 * q^69 + 185910 * q^70 - 9504 * q^71 - 186687 * q^72 + 14260 * q^73 - 15239 * q^74 + 167420 * q^75 + 1279 * q^76 - 218140 * q^77 + 264170 * q^78 + 160248 * q^79 - 1291 * q^80 + 161076 * q^81 - 47781 * q^82 - 77176 * q^83 + 16382 * q^84 + 141096 * q^85 + 22188 * q^86 + 268136 * q^87 + 129544 * q^88 - 265692 * q^89 + 48990 * q^90 + 401148 * q^91 + 190391 * q^92 - 123860 * q^93 + 248737 * q^94 + 135884 * q^95 + 950817 * q^96 + 144742 * q^97 - 292244 * q^98 + 239516 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more