LMFDB - Embedded newform 138.6.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,6,Mod(1,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("138.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	138.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:	$22.1329671342$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{154}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 154 $ x^2 - 154
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-12.4097$ of defining polynomial
Character	$\chi$	$=$	138.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -39.2290 q^{5} -36.0000 q^{6} +42.0484 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -39.2290 q^{5} -36.0000 q^{6} +42.0484 q^{7} -64.0000 q^{8} +81.0000 q^{9} +156.916 q^{10} +168.193 q^{11} +144.000 q^{12} -876.916 q^{13} -168.193 q^{14} -353.061 q^{15} +256.000 q^{16} +1457.31 q^{17} -324.000 q^{18} -2420.51 q^{19} -627.664 q^{20} +378.435 q^{21} -672.774 q^{22} +529.000 q^{23} -576.000 q^{24} -1586.08 q^{25} +3507.66 q^{26} +729.000 q^{27} +672.774 q^{28} -317.528 q^{29} +1412.24 q^{30} +5843.88 q^{31} -1024.00 q^{32} +1513.74 q^{33} -5829.22 q^{34} -1649.52 q^{35} +1296.00 q^{36} -14682.7 q^{37} +9682.05 q^{38} -7892.24 q^{39} +2510.66 q^{40} -19857.1 q^{41} -1513.74 q^{42} -5563.48 q^{43} +2691.10 q^{44} -3177.55 q^{45} -2116.00 q^{46} -6052.81 q^{47} +2304.00 q^{48} -15038.9 q^{49} +6344.34 q^{50} +13115.8 q^{51} -14030.7 q^{52} -10716.1 q^{53} -2916.00 q^{54} -6598.07 q^{55} -2691.10 q^{56} -21784.6 q^{57} +1270.11 q^{58} -23573.4 q^{59} -5648.98 q^{60} -38395.5 q^{61} -23375.5 q^{62} +3405.92 q^{63} +4096.00 q^{64} +34400.6 q^{65} -6054.97 q^{66} -47054.8 q^{67} +23316.9 q^{68} +4761.00 q^{69} +6598.07 q^{70} +62279.3 q^{71} -5184.00 q^{72} +75900.2 q^{73} +58730.8 q^{74} -14274.8 q^{75} -38728.2 q^{76} +7072.26 q^{77} +31569.0 q^{78} +40034.8 q^{79} -10042.6 q^{80} +6561.00 q^{81} +79428.3 q^{82} -48605.9 q^{83} +6054.97 q^{84} -57168.7 q^{85} +22253.9 q^{86} -2857.75 q^{87} -10764.4 q^{88} +48840.7 q^{89} +12710.2 q^{90} -36872.9 q^{91} +8464.00 q^{92} +52594.9 q^{93} +24211.2 q^{94} +94954.3 q^{95} -9216.00 q^{96} -100275. q^{97} +60155.7 q^{98} +13623.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{2} + 18 q^{3} + 32 q^{4} - 4 q^{5} - 72 q^{6} - 40 q^{7} - 128 q^{8} + 162 q^{9}+O(q^{10}) $ 2 * q - 8 * q^2 + 18 * q^3 + 32 * q^4 - 4 * q^5 - 72 * q^6 - 40 * q^7 - 128 * q^8 + 162 * q^9	\( 2 q - 8 q^{2} + 18 q^{3} + 32 q^{4} - 4 q^{5} - 72 q^{6} - 40 q^{7} - 128 q^{8} + 162 q^{9} + 16 q^{10} - 160 q^{11} + 288 q^{12} - 1456 q^{13} + 160 q^{14} - 36 q^{15} + 512 q^{16} - 436 q^{17} - 648 q^{18} - 448 q^{19} - 64 q^{20} - 360 q^{21} + 640 q^{22} + 1058 q^{23} - 1152 q^{24} - 3470 q^{25} + 5824 q^{26} + 1458 q^{27} - 640 q^{28} + 6364 q^{29} + 144 q^{30} - 2360 q^{31} - 2048 q^{32} - 1440 q^{33} + 1744 q^{34} - 4540 q^{35} + 2592 q^{36} - 19388 q^{37} + 1792 q^{38} - 13104 q^{39} + 256 q^{40} - 17476 q^{41} + 1440 q^{42} - 23760 q^{43} - 2560 q^{44} - 324 q^{45} - 4232 q^{46} - 35684 q^{47} + 4608 q^{48} - 25114 q^{49} + 13880 q^{50} - 3924 q^{51} - 23296 q^{52} + 1476 q^{53} - 5832 q^{54} - 18160 q^{55} + 2560 q^{56} - 4032 q^{57} - 25456 q^{58} + 23092 q^{59} - 576 q^{60} - 70884 q^{61} + 9440 q^{62} - 3240 q^{63} + 8192 q^{64} + 14000 q^{65} + 5760 q^{66} - 81824 q^{67} - 6976 q^{68} + 9522 q^{69} + 18160 q^{70} + 15552 q^{71} - 10368 q^{72} + 49644 q^{73} + 77552 q^{74} - 31230 q^{75} - 7168 q^{76} + 34000 q^{77} + 52416 q^{78} + 102680 q^{79} - 1024 q^{80} + 13122 q^{81} + 69904 q^{82} + 39096 q^{83} - 5760 q^{84} - 123868 q^{85} + 95040 q^{86} + 57276 q^{87} + 10240 q^{88} - 21228 q^{89} + 1296 q^{90} + 10640 q^{91} + 16928 q^{92} - 21240 q^{93} + 142736 q^{94} + 164444 q^{95} - 18432 q^{96} - 25772 q^{97} + 100456 q^{98} - 12960 q^{99}+O(q^{100}) \) 2 * q - 8 * q^2 + 18 * q^3 + 32 * q^4 - 4 * q^5 - 72 * q^6 - 40 * q^7 - 128 * q^8 + 162 * q^9 + 16 * q^10 - 160 * q^11 + 288 * q^12 - 1456 * q^13 + 160 * q^14 - 36 * q^15 + 512 * q^16 - 436 * q^17 - 648 * q^18 - 448 * q^19 - 64 * q^20 - 360 * q^21 + 640 * q^22 + 1058 * q^23 - 1152 * q^24 - 3470 * q^25 + 5824 * q^26 + 1458 * q^27 - 640 * q^28 + 6364 * q^29 + 144 * q^30 - 2360 * q^31 - 2048 * q^32 - 1440 * q^33 + 1744 * q^34 - 4540 * q^35 + 2592 * q^36 - 19388 * q^37 + 1792 * q^38 - 13104 * q^39 + 256 * q^40 - 17476 * q^41 + 1440 * q^42 - 23760 * q^43 - 2560 * q^44 - 324 * q^45 - 4232 * q^46 - 35684 * q^47 + 4608 * q^48 - 25114 * q^49 + 13880 * q^50 - 3924 * q^51 - 23296 * q^52 + 1476 * q^53 - 5832 * q^54 - 18160 * q^55 + 2560 * q^56 - 4032 * q^57 - 25456 * q^58 + 23092 * q^59 - 576 * q^60 - 70884 * q^61 + 9440 * q^62 - 3240 * q^63 + 8192 * q^64 + 14000 * q^65 + 5760 * q^66 - 81824 * q^67 - 6976 * q^68 + 9522 * q^69 + 18160 * q^70 + 15552 * q^71 - 10368 * q^72 + 49644 * q^73 + 77552 * q^74 - 31230 * q^75 - 7168 * q^76 + 34000 * q^77 + 52416 * q^78 + 102680 * q^79 - 1024 * q^80 + 13122 * q^81 + 69904 * q^82 + 39096 * q^83 - 5760 * q^84 - 123868 * q^85 + 95040 * q^86 + 57276 * q^87 + 10240 * q^88 - 21228 * q^89 + 1296 * q^90 + 10640 * q^91 + 16928 * q^92 - 21240 * q^93 + 142736 * q^94 + 164444 * q^95 - 18432 * q^96 - 25772 * q^97 + 100456 * q^98 - 12960 * 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 $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	16.0000	0.500000
$5$	−39.2290	−0.701750	−0.350875	−	0.936422i	$-0.614116\pi$
$5$	−39.2290	−0.701750	−0.350875	+	0.936422i	$0.614116\pi$
$6$	−36.0000	−0.408248
$7$	42.0484	0.324343	0.162171	−	0.986763i	$-0.448150\pi$
$7$	42.0484	0.324343	0.162171	+	0.986763i	$0.448150\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	156.916	0.496212
$11$	168.193	0.419109	0.209555	−	0.977797i	$-0.432799\pi$
$11$	168.193	0.419109	0.209555	+	0.977797i	$0.432799\pi$
$12$	144.000	0.288675
$13$	−876.916	−1.43913	−0.719564	−	0.694426i	$-0.755658\pi$
$13$	−876.916	−1.43913	−0.719564	+	0.694426i	$0.755658\pi$
$14$	−168.193	−0.229345
$15$	−353.061	−0.405156
$16$	256.000	0.250000
$17$	1457.31	1.22301	0.611503	−	0.791242i	$-0.290565\pi$
$17$	1457.31	1.22301	0.611503	+	0.791242i	$0.290565\pi$
$18$	−324.000	−0.235702
$19$	−2420.51	−1.53824	−0.769119	−	0.639106i	$-0.779304\pi$
$19$	−2420.51	−1.53824	−0.769119	+	0.639106i	$0.779304\pi$
$20$	−627.664	−0.350875
$21$	378.435	0.187259
$22$	−672.774	−0.296355
$23$	529.000	0.208514
$23$	529.000	0.208514
$24$	−576.000	−0.204124
$25$	−1586.08	−0.507547
$26$	3507.66	1.01762
$27$	729.000	0.192450
$28$	672.774	0.162171
$29$	−317.528	−0.0701111	−0.0350556	−	0.999385i	$-0.511161\pi$
$29$	−317.528	−0.0701111	−0.0350556	+	0.999385i	$0.511161\pi$
$30$	1412.24	0.286488
$31$	5843.88	1.09219	0.546093	−	0.837724i	$-0.316114\pi$
$31$	5843.88	1.09219	0.546093	+	0.837724i	$0.316114\pi$
$32$	−1024.00	−0.176777
$33$	1513.74	0.241973
$34$	−5829.22	−0.864796
$35$	−1649.52	−0.227607
$36$	1296.00	0.166667
$37$	−14682.7	−1.76320	−0.881599	−	0.471998i	$-0.843533\pi$
$37$	−14682.7	−1.76320	−0.881599	+	0.471998i	$0.843533\pi$
$38$	9682.05	1.08770
$39$	−7892.24	−0.830881
$40$	2510.66	0.248106
$41$	−19857.1	−1.84483	−0.922413	−	0.386205i	$-0.873786\pi$
$41$	−19857.1	−1.84483	−0.922413	+	0.386205i	$0.873786\pi$
$42$	−1513.74	−0.132412
$43$	−5563.48	−0.458855	−0.229427	−	0.973326i	$-0.573685\pi$
$43$	−5563.48	−0.458855	−0.229427	+	0.973326i	$0.573685\pi$
$44$	2691.10	0.209555
$45$	−3177.55	−0.233917
$46$	−2116.00	−0.147442
$47$	−6052.81	−0.399680	−0.199840	−	0.979829i	$-0.564042\pi$
$47$	−6052.81	−0.399680	−0.199840	+	0.979829i	$0.564042\pi$
$48$	2304.00	0.144338
$49$	−15038.9	−0.894802
$50$	6344.34	0.358890
$51$	13115.8	0.706103
$52$	−14030.7	−0.719564
$53$	−10716.1	−0.524020	−0.262010	−	0.965065i	$-0.584385\pi$
$53$	−10716.1	−0.524020	−0.262010	+	0.965065i	$0.584385\pi$
$54$	−2916.00	−0.136083
$55$	−6598.07	−0.294110
$56$	−2691.10	−0.114672
$57$	−21784.6	−0.888102
$58$	1270.11	0.0495761
$59$	−23573.4	−0.881641	−0.440820	−	0.897595i	$-0.645312\pi$
$59$	−23573.4	−0.881641	−0.440820	+	0.897595i	$0.645312\pi$
$60$	−5648.98	−0.202578
$61$	−38395.5	−1.32116	−0.660581	−	0.750755i	$-0.729690\pi$
$61$	−38395.5	−1.32116	−0.660581	+	0.750755i	$0.729690\pi$
$62$	−23375.5	−0.772292
$63$	3405.92	0.108114
$64$	4096.00	0.125000
$65$	34400.6	1.00991
$66$	−6054.97	−0.171101
$67$	−47054.8	−1.28061	−0.640305	−	0.768121i	$-0.721192\pi$
$67$	−47054.8	−1.28061	−0.640305	+	0.768121i	$0.721192\pi$
$68$	23316.9	0.611503
$69$	4761.00	0.120386
$70$	6598.07	0.160943
$71$	62279.3	1.46622	0.733108	−	0.680113i	$-0.238069\pi$
$71$	62279.3	1.46622	0.733108	+	0.680113i	$0.238069\pi$
$72$	−5184.00	−0.117851
$73$	75900.2	1.66700	0.833501	−	0.552519i	$-0.186333\pi$
$73$	75900.2	1.66700	0.833501	+	0.552519i	$0.186333\pi$
$74$	58730.8	1.24677
$75$	−14274.8	−0.293032
$76$	−38728.2	−0.769119
$77$	7072.26	0.135935
$78$	31569.0	0.587522
$79$	40034.8	0.721722	0.360861	−	0.932620i	$-0.382483\pi$
$79$	40034.8	0.721722	0.360861	+	0.932620i	$0.382483\pi$
$80$	−10042.6	−0.175438
$81$	6561.00	0.111111
$82$	79428.3	1.30449
$83$	−48605.9	−0.774451	−0.387226	−	0.921985i	$-0.626567\pi$
$83$	−48605.9	−0.774451	−0.387226	+	0.921985i	$0.626567\pi$
$84$	6054.97	0.0936297
$85$	−57168.7	−0.858244
$86$	22253.9	0.324459
$87$	−2857.75	−0.0404787
$88$	−10764.4	−0.148178
$89$	48840.7	0.653593	0.326796	−	0.945095i	$-0.394031\pi$
$89$	48840.7	0.653593	0.326796	+	0.945095i	$0.394031\pi$
$90$	12710.2	0.165404
$91$	−36872.9	−0.466771
$92$	8464.00	0.104257
$93$	52594.9	0.630574
$94$	24211.2	0.282616
$95$	94954.3	1.07946
$96$	−9216.00	−0.102062
$97$	−100275.	−1.08209	−0.541045	−	0.840994i	$-0.681971\pi$
$97$	−100275.	−1.08209	−0.541045	+	0.840994i	$0.681971\pi$
$98$	60155.7	0.632720
$99$	13623.7	0.139703
$100$	−25377.3	−0.253773
$101$	48116.5	0.469343	0.234672	−	0.972075i	$-0.424599\pi$
$101$	48116.5	0.469343	0.234672	+	0.972075i	$0.424599\pi$
$102$	−52463.0	−0.499290
$103$	130127.	1.20858	0.604289	−	0.796765i	$-0.293457\pi$
$103$	130127.	1.20858	0.604289	+	0.796765i	$0.293457\pi$
$104$	56122.6	0.508809
$105$	−14845.6	−0.131409
$106$	42864.5	0.370538
$107$	130482.	1.10177	0.550886	−	0.834581i	$-0.314290\pi$
$107$	130482.	1.10177	0.550886	+	0.834581i	$0.314290\pi$
$108$	11664.0	0.0962250
$109$	7513.51	0.0605727	0.0302863	−	0.999541i	$-0.490358\pi$
$109$	7513.51	0.0605727	0.0302863	+	0.999541i	$0.490358\pi$
$110$	26392.3	0.207967
$111$	−132144.	−1.01798
$112$	10764.4	0.0810857
$113$	−169099.	−1.24579	−0.622895	−	0.782305i	$-0.714044\pi$
$113$	−169099.	−1.24579	−0.622895	+	0.782305i	$0.714044\pi$
$114$	87138.4	0.627983
$115$	−20752.2	−0.146325
$116$	−5080.45	−0.0350556
$117$	−71030.2	−0.479710
$118$	94293.5	0.623414
$119$	61277.3	0.396673
$120$	22595.9	0.143244
$121$	−132762.	−0.824347
$122$	153582.	0.934202
$123$	−178714.	−1.06511
$124$	93502.0	0.546093
$125$	184811.	1.05792
$126$	−13623.7	−0.0764483
$127$	70541.1	0.388090	0.194045	−	0.980993i	$-0.437839\pi$
$127$	70541.1	0.388090	0.194045	+	0.980993i	$0.437839\pi$
$128$	−16384.0	−0.0883883
$129$	−50071.3	−0.264920
$130$	−137602.	−0.714113
$131$	283941.	1.44561	0.722803	−	0.691055i	$-0.242854\pi$
$131$	283941.	1.44561	0.722803	+	0.691055i	$0.242854\pi$
$132$	24219.9	0.120986
$133$	−101779.	−0.498916
$134$	188219.	0.905528
$135$	−28598.0	−0.135052
$136$	−93267.6	−0.432398
$137$	−19715.0	−0.0897417	−0.0448709	−	0.998993i	$-0.514288\pi$
$137$	−19715.0	−0.0897417	−0.0448709	+	0.998993i	$0.514288\pi$
$138$	−19044.0	−0.0851257
$139$	−224701.	−0.986435	−0.493218	−	0.869906i	$-0.664179\pi$
$139$	−224701.	−0.986435	−0.493218	+	0.869906i	$0.664179\pi$
$140$	−26392.3	−0.113804
$141$	−54475.3	−0.230755
$142$	−249117.	−1.03677
$143$	−147492.	−0.603152
$144$	20736.0	0.0833333
$145$	12456.3	0.0492005
$146$	−303601.	−1.17875
$147$	−135350.	−0.516614
$148$	−234923.	−0.881599
$149$	−33712.3	−0.124401	−0.0622003	−	0.998064i	$-0.519812\pi$
$149$	−33712.3	−0.124401	−0.0622003	+	0.998064i	$0.519812\pi$
$150$	57099.0	0.207205
$151$	414861.	1.48068	0.740338	−	0.672234i	$-0.234665\pi$
$151$	414861.	1.48068	0.740338	+	0.672234i	$0.234665\pi$
$152$	154913.	0.543849
$153$	118042.	0.407669
$154$	−28289.0	−0.0961206
$155$	−229250.	−0.766442
$156$	−126276.	−0.415441
$157$	477252.	1.54525	0.772625	−	0.634863i	$-0.218943\pi$
$157$	477252.	1.54525	0.772625	+	0.634863i	$0.218943\pi$
$158$	−160139.	−0.510334
$159$	−96445.2	−0.302543
$160$	40170.5	0.124053
$161$	22243.6	0.0676301
$162$	−26244.0	−0.0785674
$163$	−527003.	−1.55362	−0.776809	−	0.629736i	$-0.783163\pi$
$163$	−527003.	−1.55362	−0.776809	+	0.629736i	$0.783163\pi$
$164$	−317713.	−0.922413
$165$	−59382.6	−0.169805
$166$	194424.	0.547620
$167$	−254254.	−0.705467	−0.352733	−	0.935724i	$-0.614748\pi$
$167$	−254254.	−0.705467	−0.352733	+	0.935724i	$0.614748\pi$
$168$	−24219.9	−0.0662062
$169$	397689.	1.07109
$170$	228675.	0.606870
$171$	−196061.	−0.512746
$172$	−89015.6	−0.229427
$173$	310108.	0.787767	0.393883	−	0.919160i	$-0.371131\pi$
$173$	310108.	0.787767	0.393883	+	0.919160i	$0.371131\pi$
$174$	11431.0	0.0286228
$175$	−66692.2	−0.164619
$176$	43057.5	0.104777
$177$	−212160.	−0.509016
$178$	−195363.	−0.462160
$179$	−349949.	−0.816342	−0.408171	−	0.912905i	$-0.633833\pi$
$179$	−349949.	−0.816342	−0.408171	+	0.912905i	$0.633833\pi$
$180$	−50840.8	−0.116958
$181$	91264.6	0.207065	0.103532	−	0.994626i	$-0.466985\pi$
$181$	91264.6	0.207065	0.103532	+	0.994626i	$0.466985\pi$
$182$	147492.	0.330057
$183$	−345560.	−0.762773
$184$	−33856.0	−0.0737210
$185$	575988.	1.23732
$186$	−210380.	−0.445883
$187$	245109.	0.512573
$188$	−96845.0	−0.199840
$189$	30653.3	0.0624198
$190$	−379817.	−0.763292
$191$	600180.	1.19041	0.595207	−	0.803572i	$-0.297070\pi$
$191$	600180.	1.19041	0.595207	+	0.803572i	$0.297070\pi$
$192$	36864.0	0.0721688
$193$	585171.	1.13081	0.565405	−	0.824813i	$-0.308720\pi$
$193$	585171.	1.13081	0.565405	+	0.824813i	$0.308720\pi$
$194$	401100.	0.765152
$195$	309605.	0.583071
$196$	−240623.	−0.447401
$197$	−541101.	−0.993374	−0.496687	−	0.867930i	$-0.665450\pi$
$197$	−541101.	−0.993374	−0.496687	+	0.867930i	$0.665450\pi$
$198$	−54494.7	−0.0987850
$199$	−235577.	−0.421697	−0.210848	−	0.977519i	$-0.567623\pi$
$199$	−235577.	−0.421697	−0.210848	+	0.977519i	$0.567623\pi$
$200$	101509.	0.179445
$201$	−423493.	−0.739360
$202$	−192466.	−0.331876
$203$	−13351.5	−0.0227400
$204$	209852.	0.353051
$205$	778973.	1.29461
$206$	−520508.	−0.854594
$207$	42849.0	0.0695048
$208$	−224491.	−0.359782
$209$	−407114.	−0.644690
$210$	59382.6	0.0929204
$211$	−646393.	−0.999517	−0.499759	−	0.866165i	$-0.666578\pi$
$211$	−646393.	−0.999517	−0.499759	+	0.866165i	$0.666578\pi$
$212$	−171458.	−0.262010
$213$	560514.	0.846520
$214$	−521929.	−0.779070
$215$	218250.	0.322001
$216$	−46656.0	−0.0680414
$217$	245725.	0.354243
$218$	−30054.1	−0.0428314
$219$	683102.	0.962443
$220$	−105569.	−0.147055
$221$	−1.27794e6	−1.76006
$222$	528577.	0.719823
$223$	−985822.	−1.32751	−0.663753	−	0.747952i	$-0.731037\pi$
$223$	−985822.	−1.32751	−0.663753	+	0.747952i	$0.731037\pi$
$224$	−43057.5	−0.0573362
$225$	−128473.	−0.169182
$226$	676396.	0.880907
$227$	853893.	1.09986	0.549932	−	0.835209i	$-0.314654\pi$
$227$	853893.	1.09986	0.549932	+	0.835209i	$0.314654\pi$
$228$	−348554.	−0.444051
$229$	65386.0	0.0823941	0.0411971	−	0.999151i	$-0.486883\pi$
$229$	65386.0	0.0823941	0.0411971	+	0.999151i	$0.486883\pi$
$230$	83008.6	0.103467
$231$	63650.3	0.0784821
$232$	20321.8	0.0247880
$233$	180577.	0.217908	0.108954	−	0.994047i	$-0.465250\pi$
$233$	180577.	0.217908	0.108954	+	0.994047i	$0.465250\pi$
$234$	284121.	0.339206
$235$	237446.	0.280475
$236$	−377174.	−0.440820
$237$	360313.	0.416686
$238$	−245109.	−0.280490
$239$	−1.21196e6	−1.37244	−0.686219	−	0.727395i	$-0.740731\pi$
$239$	−1.21196e6	−1.37244	−0.686219	+	0.727395i	$0.740731\pi$
$240$	−90383.7	−0.101289
$241$	315085.	0.349450	0.174725	−	0.984617i	$-0.444096\pi$
$241$	315085.	0.349450	0.174725	+	0.984617i	$0.444096\pi$
$242$	531048.	0.582902
$243$	59049.0	0.0641500
$244$	−614328.	−0.660581
$245$	589963.	0.627927
$246$	714854.	0.753147
$247$	2.12259e6	2.21372
$248$	−374008.	−0.386146
$249$	−437453.	−0.447130
$250$	−739245.	−0.748063
$251$	−45135.2	−0.0452201	−0.0226100	−	0.999744i	$-0.507198\pi$
$251$	−45135.2	−0.0452201	−0.0226100	+	0.999744i	$0.507198\pi$
$252$	54494.7	0.0540571
$253$	88974.3	0.0873904
$254$	−282164.	−0.274421
$255$	−514518.	−0.495508
$256$	65536.0	0.0625000
$257$	−41149.0	−0.0388621	−0.0194310	−	0.999811i	$-0.506185\pi$
$257$	−41149.0	−0.0388621	−0.0194310	+	0.999811i	$0.506185\pi$
$258$	200285.	0.187327
$259$	−617383.	−0.571881
$260$	550409.	0.504954
$261$	−25719.8	−0.0233704
$262$	−1.13576e6	−1.02220
$263$	−998844.	−0.890448	−0.445224	−	0.895419i	$-0.646876\pi$
$263$	−998844.	−0.890448	−0.445224	+	0.895419i	$0.646876\pi$
$264$	−96879.4	−0.0855504
$265$	420383.	0.367731
$266$	407114.	0.352787
$267$	439567.	0.377352
$268$	−752877.	−0.640305
$269$	462351.	0.389575	0.194787	−	0.980845i	$-0.437598\pi$
$269$	462351.	0.389575	0.194787	+	0.980845i	$0.437598\pi$
$270$	114392.	0.0954961
$271$	−1.10409e6	−0.913235	−0.456618	−	0.889663i	$-0.650939\pi$
$271$	−1.10409e6	−0.913235	−0.456618	+	0.889663i	$0.650939\pi$
$272$	373070.	0.305751
$273$	−331856.	−0.269490
$274$	78859.8	0.0634570
$275$	−266769.	−0.212718
$276$	76176.0	0.0601929
$277$	579363.	0.453682	0.226841	−	0.973932i	$-0.427160\pi$
$277$	579363.	0.453682	0.226841	+	0.973932i	$0.427160\pi$
$278$	898805.	0.697515
$279$	473354.	0.364062
$280$	105569.	0.0804714
$281$	2.07604e6	1.56845	0.784223	−	0.620479i	$-0.213062\pi$
$281$	2.07604e6	1.56845	0.784223	+	0.620479i	$0.213062\pi$
$282$	217901.	0.163169
$283$	2.08824e6	1.54994	0.774969	−	0.632000i	$-0.217766\pi$
$283$	2.08824e6	1.54994	0.774969	+	0.632000i	$0.217766\pi$
$284$	996469.	0.733108
$285$	854589.	0.623225
$286$	589966.	0.426493
$287$	−834957.	−0.598356
$288$	−82944.0	−0.0589256
$289$	703884.	0.495743
$290$	−49825.2	−0.0347900
$291$	−902474.	−0.624744
$292$	1.21440e6	0.833501
$293$	398191.	0.270971	0.135485	−	0.990779i	$-0.456741\pi$
$293$	398191.	0.270971	0.135485	+	0.990779i	$0.456741\pi$
$294$	541402.	0.365301
$295$	924760.	0.618692
$296$	939692.	0.623385
$297$	122613.	0.0806576
$298$	134849.	0.0879645
$299$	−463889.	−0.300079
$300$	−228396.	−0.146516
$301$	−233935.	−0.148826
$302$	−1.65944e6	−1.04700
$303$	433048.	0.270975
$304$	−619651.	−0.384559
$305$	1.50622e6	0.927125
$306$	−472167.	−0.288265
$307$	−1.41209e6	−0.855097	−0.427549	−	0.903992i	$-0.640623\pi$
$307$	−1.41209e6	−0.855097	−0.427549	+	0.903992i	$0.640623\pi$
$308$	113156.	0.0679675
$309$	1.17114e6	0.697773
$310$	916998.	0.541956
$311$	−604173.	−0.354210	−0.177105	−	0.984192i	$-0.556673\pi$
$311$	−604173.	−0.354210	−0.177105	+	0.984192i	$0.556673\pi$
$312$	505104.	0.293761
$313$	1.27267e6	0.734271	0.367136	−	0.930167i	$-0.380339\pi$
$313$	1.27267e6	0.734271	0.367136	+	0.930167i	$0.380339\pi$
$314$	−1.90901e6	−1.09266
$315$	−133611.	−0.0758692
$316$	640557.	0.360861
$317$	−2.13283e6	−1.19209	−0.596044	−	0.802952i	$-0.703262\pi$
$317$	−2.13283e6	−1.19209	−0.596044	+	0.802952i	$0.703262\pi$
$318$	385781.	0.213930
$319$	−53406.1	−0.0293842
$320$	−160682.	−0.0877188
$321$	1.17434e6	0.636108
$322$	−88974.3	−0.0478217
$323$	−3.52743e6	−1.88127
$324$	104976.	0.0555556
$325$	1.39086e6	0.730425
$326$	2.10801e6	1.09857
$327$	67621.6	0.0349717
$328$	1.27085e6	0.652245
$329$	−254511.	−0.129633
$330$	237530.	0.120070
$331$	−1.25522e6	−0.629721	−0.314861	−	0.949138i	$-0.601958\pi$
$331$	−1.25522e6	−0.629721	−0.314861	+	0.949138i	$0.601958\pi$
$332$	−777695.	−0.387226
$333$	−1.18930e6	−0.587733
$334$	1.01702e6	0.498840
$335$	1.84591e6	0.898668
$336$	96879.4	0.0468148
$337$	−1.28823e6	−0.617903	−0.308951	−	0.951078i	$-0.599978\pi$
$337$	−1.28823e6	−0.617903	−0.308951	+	0.951078i	$0.599978\pi$
$338$	−1.59076e6	−0.757376
$339$	−1.52189e6	−0.719257
$340$	−914699.	−0.429122
$341$	982902.	0.457746
$342$	784246.	0.362566
$343$	−1.33907e6	−0.614565
$344$	356062.	0.162230
$345$	−186769.	−0.0844808
$346$	−1.24043e6	−0.557035
$347$	−1.43576e6	−0.640116	−0.320058	−	0.947398i	$-0.603702\pi$
$347$	−1.43576e6	−0.640116	−0.320058	+	0.947398i	$0.603702\pi$
$348$	−45724.0	−0.0202393
$349$	3.09697e6	1.36105	0.680523	−	0.732727i	$-0.261753\pi$
$349$	3.09697e6	1.36105	0.680523	+	0.732727i	$0.261753\pi$
$350$	266769.	0.116403
$351$	−639272.	−0.276960
$352$	−172230.	−0.0740888
$353$	−4.11210e6	−1.75641	−0.878206	−	0.478283i	$-0.841259\pi$
$353$	−4.11210e6	−1.75641	−0.878206	+	0.478283i	$0.841259\pi$
$354$	848642.	0.359928
$355$	−2.44316e6	−1.02892
$356$	781452.	0.326796
$357$	551496.	0.229019
$358$	1.39980e6	0.577241
$359$	−3.49182e6	−1.42994	−0.714968	−	0.699158i	$-0.753559\pi$
$359$	−3.49182e6	−1.42994	−0.714968	+	0.699158i	$0.753559\pi$
$360$	203363.	0.0827020
$361$	3.38278e6	1.36617
$362$	−365059.	−0.146417
$363$	−1.19486e6	−0.475937
$364$	−589966.	−0.233385
$365$	−2.97749e6	−1.16982
$366$	1.38224e6	0.539362
$367$	2.24683e6	0.870773	0.435387	−	0.900244i	$-0.356612\pi$
$367$	2.24683e6	0.870773	0.435387	+	0.900244i	$0.356612\pi$
$368$	135424.	0.0521286
$369$	−1.60842e6	−0.614942
$370$	−2.30395e6	−0.874921
$371$	−450596.	−0.169962
$372$	841518.	0.315287
$373$	−4.90998e6	−1.82729	−0.913645	−	0.406513i	$-0.866744\pi$
$373$	−4.90998e6	−1.82729	−0.913645	+	0.406513i	$0.866744\pi$
$374$	−980437.	−0.362444
$375$	1.66330e6	0.610791
$376$	387380.	0.141308
$377$	278445.	0.100899
$378$	−122613.	−0.0441374
$379$	1.60147e6	0.572692	0.286346	−	0.958126i	$-0.407559\pi$
$379$	1.60147e6	0.572692	0.286346	+	0.958126i	$0.407559\pi$
$380$	1.51927e6	0.539729
$381$	634870.	0.224064
$382$	−2.40072e6	−0.841750
$383$	2.10866e6	0.734530	0.367265	−	0.930116i	$-0.380294\pi$
$383$	2.10866e6	0.734530	0.367265	+	0.930116i	$0.380294\pi$
$384$	−147456.	−0.0510310
$385$	−277438.	−0.0953924
$386$	−2.34069e6	−0.799604
$387$	−450642.	−0.152952
$388$	−1.60440e6	−0.541045
$389$	4.60883e6	1.54425	0.772123	−	0.635473i	$-0.219195\pi$
$389$	4.60883e6	1.54425	0.772123	+	0.635473i	$0.219195\pi$
$390$	−1.23842e6	−0.412294
$391$	770915.	0.255014
$392$	962492.	0.316360
$393$	2.55547e6	0.834620
$394$	2.16440e6	0.702421
$395$	−1.57053e6	−0.506468
$396$	217979.	0.0698516
$397$	1.37321e6	0.437281	0.218640	−	0.975806i	$-0.429838\pi$
$397$	1.37321e6	0.437281	0.218640	+	0.975806i	$0.429838\pi$
$398$	942308.	0.298185
$399$	−916007.	−0.288049
$400$	−406037.	−0.126887
$401$	−3.79827e6	−1.17957	−0.589787	−	0.807559i	$-0.700788\pi$
$401$	−3.79827e6	−1.17957	−0.589787	+	0.807559i	$0.700788\pi$
$402$	1.69397e6	0.522807
$403$	−5.12459e6	−1.57180
$404$	769864.	0.234672
$405$	−257382.	−0.0779722
$406$	53406.1	0.0160796
$407$	−2.46953e6	−0.738973
$408$	−839408.	−0.249645
$409$	−1.61441e6	−0.477205	−0.238603	−	0.971117i	$-0.576689\pi$
$409$	−1.61441e6	−0.477205	−0.238603	+	0.971117i	$0.576689\pi$
$410$	−3.11589e6	−0.915425
$411$	−177435.	−0.0518124
$412$	2.08203e6	0.604289
$413$	−991222.	−0.285954
$414$	−171396.	−0.0491473
$415$	1.90676e6	0.543471
$416$	897962.	0.254404
$417$	−2.02231e6	−0.569519
$418$	1.62846e6	0.455864
$419$	980150.	0.272746	0.136373	−	0.990658i	$-0.456456\pi$
$419$	980150.	0.272746	0.136373	+	0.990658i	$0.456456\pi$
$420$	−237530.	−0.0657046
$421$	6.29807e6	1.73182	0.865909	−	0.500201i	$-0.166741\pi$
$421$	6.29807e6	1.73182	0.865909	+	0.500201i	$0.166741\pi$
$422$	2.58557e6	0.706765
$423$	−490278.	−0.133227
$424$	685832.	0.185269
$425$	−2.31141e6	−0.620733
$426$	−2.24205e6	−0.598580
$427$	−1.61447e6	−0.428509
$428$	2.08771e6	0.550886
$429$	−1.32742e6	−0.348230
$430$	−872999.	−0.227689
$431$	−2.03779e6	−0.528405	−0.264202	−	0.964467i	$-0.585109\pi$
$431$	−2.03779e6	−0.528405	−0.264202	+	0.964467i	$0.585109\pi$
$432$	186624.	0.0481125
$433$	−4.31185e6	−1.10521	−0.552603	−	0.833444i	$-0.686366\pi$
$433$	−4.31185e6	−1.10521	−0.552603	+	0.833444i	$0.686366\pi$
$434$	−982902.	−0.250487
$435$	112107.	0.0284059
$436$	120216.	0.0302863
$437$	−1.28045e6	−0.320745
$438$	−2.73241e6	−0.680550
$439$	−2.76050e6	−0.683637	−0.341819	−	0.939766i	$-0.611043\pi$
$439$	−2.76050e6	−0.683637	−0.341819	+	0.939766i	$0.611043\pi$
$440$	422276.	0.103984
$441$	−1.21815e6	−0.298267
$442$	5.11174e6	1.24455
$443$	−4.92501e6	−1.19233	−0.596167	−	0.802860i	$-0.703310\pi$
$443$	−4.92501e6	−1.19233	−0.596167	+	0.802860i	$0.703310\pi$
$444$	−2.11431e6	−0.508992
$445$	−1.91597e6	−0.458659
$446$	3.94329e6	0.938688
$447$	−303410.	−0.0718227
$448$	172230.	0.0405428
$449$	−1.32613e6	−0.310434	−0.155217	−	0.987880i	$-0.549608\pi$
$449$	−1.32613e6	−0.310434	−0.155217	+	0.987880i	$0.549608\pi$
$450$	513891.	0.119630
$451$	−3.33983e6	−0.773184
$452$	−2.70558e6	−0.622895
$453$	3.73375e6	0.854869
$454$	−3.41557e6	−0.777721
$455$	1.44649e6	0.327556
$456$	1.39422e6	0.313991
$457$	4.06128e6	0.909646	0.454823	−	0.890582i	$-0.349703\pi$
$457$	4.06128e6	0.909646	0.454823	+	0.890582i	$0.349703\pi$
$458$	−261544.	−0.0582614
$459$	1.06238e6	0.235368
$460$	−332034.	−0.0731625
$461$	7.85711e6	1.72191	0.860955	−	0.508681i	$-0.169867\pi$
$461$	7.85711e6	1.72191	0.860955	+	0.508681i	$0.169867\pi$
$462$	−254601.	−0.0554953
$463$	−6.56180e6	−1.42256	−0.711280	−	0.702909i	$-0.751884\pi$
$463$	−6.56180e6	−1.42256	−0.711280	+	0.702909i	$0.751884\pi$
$464$	−81287.2	−0.0175278
$465$	−2.06325e6	−0.442505
$466$	−722310.	−0.154084
$467$	5.37198e6	1.13983	0.569917	−	0.821702i	$-0.306975\pi$
$467$	5.37198e6	1.13983	0.569917	+	0.821702i	$0.306975\pi$
$468$	−1.13648e6	−0.239855
$469$	−1.97858e6	−0.415356
$470$	−949783.	−0.198326
$471$	4.29527e6	0.892150
$472$	1.50870e6	0.311707
$473$	−935740.	−0.192310
$474$	−1.44125e6	−0.294642
$475$	3.83914e6	0.780727
$476$	980437.	0.198336
$477$	−868006.	−0.174673
$478$	4.84783e6	0.970460
$479$	4.07672e6	0.811844	0.405922	−	0.913908i	$-0.366950\pi$
$479$	4.07672e6	0.811844	0.405922	+	0.913908i	$0.366950\pi$
$480$	361535.	0.0716221
$481$	1.28755e7	2.53747
$482$	−1.26034e6	−0.247098
$483$	200192.	0.0390463
$484$	−2.12419e6	−0.412174
$485$	3.93369e6	0.759356
$486$	−236196.	−0.0453609
$487$	−1.44093e6	−0.275308	−0.137654	−	0.990480i	$-0.543956\pi$
$487$	−1.44093e6	−0.275308	−0.137654	+	0.990480i	$0.543956\pi$
$488$	2.45731e6	0.467101
$489$	−4.74303e6	−0.896982
$490$	−2.35985e6	−0.444012
$491$	1.03554e7	1.93850	0.969249	−	0.246084i	$-0.0791438\pi$
$491$	1.03554e7	1.93850	0.969249	+	0.246084i	$0.0791438\pi$
$492$	−2.85942e6	−0.532555
$493$	−462735.	−0.0857463
$494$	−8.49034e6	−1.56534
$495$	−534443.	−0.0980367
$496$	1.49603e6	0.273047
$497$	2.61874e6	0.475556
$498$	1.74981e6	0.316168
$499$	5.72788e6	1.02978	0.514888	−	0.857257i	$-0.327833\pi$
$499$	5.72788e6	1.02978	0.514888	+	0.857257i	$0.327833\pi$
$500$	2.95698e6	0.528961
$501$	−2.28829e6	−0.407302
$502$	180541.	0.0319754
$503$	399692.	0.0704378	0.0352189	−	0.999380i	$-0.488787\pi$
$503$	399692.	0.0704378	0.0352189	+	0.999380i	$0.488787\pi$
$504$	−217979.	−0.0382241
$505$	−1.88756e6	−0.329362
$506$	−355897.	−0.0617943
$507$	3.57920e6	0.618395
$508$	1.12866e6	0.194045
$509$	6.04828e6	1.03476	0.517378	−	0.855757i	$-0.326908\pi$
$509$	6.04828e6	1.03476	0.517378	+	0.855757i	$0.326908\pi$
$510$	2.05807e6	0.350377
$511$	3.19148e6	0.540680
$512$	−262144.	−0.0441942
$513$	−1.76455e6	−0.296034
$514$	164596.	0.0274796
$515$	−5.10476e6	−0.848120
$516$	−801141.	−0.132460
$517$	−1.01804e6	−0.167510
$518$	2.46953e6	0.404381
$519$	2.79097e6	0.454817
$520$	−2.20164e6	−0.357057
$521$	−282711.	−0.0456298	−0.0228149	−	0.999740i	$-0.507263\pi$
$521$	−282711.	−0.0456298	−0.0228149	+	0.999740i	$0.507263\pi$
$522$	102879.	0.0165254
$523$	−8.49845e6	−1.35858	−0.679291	−	0.733869i	$-0.737712\pi$
$523$	−8.49845e6	−1.35858	−0.679291	+	0.733869i	$0.737712\pi$
$524$	4.54305e6	0.722803
$525$	−600230.	−0.0950429
$526$	3.99538e6	0.629642
$527$	8.51631e6	1.33575
$528$	387518.	0.0604932
$529$	279841.	0.0434783
$530$	−1.68153e6	−0.260025
$531$	−1.90944e6	−0.293880
$532$	−1.62846e6	−0.249458
$533$	1.74130e7	2.65494
$534$	−1.75827e6	−0.266828
$535$	−5.11869e6	−0.773169
$536$	3.01151e6	0.452764
$537$	−3.14954e6	−0.471315
$538$	−1.84940e6	−0.275471
$539$	−2.52945e6	−0.375020
$540$	−457567.	−0.0675259
$541$	7.82338e6	1.14922	0.574608	−	0.818429i	$-0.305155\pi$
$541$	7.82338e6	1.14922	0.574608	+	0.818429i	$0.305155\pi$
$542$	4.41637e6	0.645755
$543$	821382.	0.119549
$544$	−1.49228e6	−0.216199
$545$	−294748.	−0.0425069
$546$	1.32742e6	0.190558
$547$	1.57758e6	0.225437	0.112718	−	0.993627i	$-0.464044\pi$
$547$	1.57758e6	0.225437	0.112718	+	0.993627i	$0.464044\pi$
$548$	−315439.	−0.0448709
$549$	−3.11004e6	−0.440387
$550$	1.06708e6	0.150414
$551$	768580.	0.107848
$552$	−304704.	−0.0425628
$553$	1.68340e6	0.234085
$554$	−2.31745e6	−0.320802
$555$	5.18389e6	0.714370
$556$	−3.59522e6	−0.493218
$557$	−2.71642e6	−0.370987	−0.185494	−	0.982645i	$-0.559388\pi$
$557$	−2.71642e6	−0.370987	−0.185494	+	0.982645i	$0.559388\pi$
$558$	−1.89342e6	−0.257431
$559$	4.87870e6	0.660351
$560$	−422276.	−0.0569019
$561$	2.20598e6	0.295934
$562$	−8.30416e6	−1.10906
$563$	7.74293e6	1.02952	0.514760	−	0.857334i	$-0.327881\pi$
$563$	7.74293e6	1.02952	0.514760	+	0.857334i	$0.327881\pi$
$564$	−871605.	−0.115378
$565$	6.63359e6	0.874233
$566$	−8.35296e6	−1.09597
$567$	275879.	0.0360381
$568$	−3.98587e6	−0.518385
$569$	5.97315e6	0.773433	0.386717	−	0.922199i	$-0.373609\pi$
$569$	5.97315e6	0.773433	0.386717	+	0.922199i	$0.373609\pi$
$570$	−3.41836e6	−0.440687
$571$	−1.71884e6	−0.220621	−0.110310	−	0.993897i	$-0.535184\pi$
$571$	−1.71884e6	−0.220621	−0.110310	+	0.993897i	$0.535184\pi$
$572$	−2.35986e6	−0.301576
$573$	5.40162e6	0.687286
$574$	3.33983e6	0.423101
$575$	−839038.	−0.105831
$576$	331776.	0.0416667
$577$	−1.09493e7	−1.36914	−0.684571	−	0.728946i	$-0.740011\pi$
$577$	−1.09493e7	−1.36914	−0.684571	+	0.728946i	$0.740011\pi$
$578$	−2.81553e6	−0.350543
$579$	5.26654e6	0.652874
$580$	199301.	0.0246002
$581$	−2.04380e6	−0.251188
$582$	3.60990e6	0.441761
$583$	−1.80238e6	−0.219622
$584$	−4.85761e6	−0.589374
$585$	2.78645e6	0.336636
$586$	−1.59276e6	−0.191605
$587$	3.22606e6	0.386435	0.193218	−	0.981156i	$-0.438108\pi$
$587$	3.22606e6	0.386435	0.193218	+	0.981156i	$0.438108\pi$
$588$	−2.16561e6	−0.258307
$589$	−1.41452e7	−1.68004
$590$	−3.69904e6	−0.437481
$591$	−4.86991e6	−0.573525
$592$	−3.75877e6	−0.440800
$593$	7.66271e6	0.894841	0.447420	−	0.894324i	$-0.352343\pi$
$593$	7.66271e6	0.894841	0.447420	+	0.894324i	$0.352343\pi$
$594$	−490452.	−0.0570336
$595$	−2.40385e6	−0.278365
$596$	−539396.	−0.0622003
$597$	−2.12019e6	−0.243467
$598$	1.85555e6	0.212188
$599$	404249.	0.0460343	0.0230172	−	0.999735i	$-0.492673\pi$
$599$	404249.	0.0460343	0.0230172	+	0.999735i	$0.492673\pi$
$600$	913584.	0.103603
$601$	−1.13706e7	−1.28410	−0.642049	−	0.766664i	$-0.721915\pi$
$601$	−1.13706e7	−1.28410	−0.642049	+	0.766664i	$0.721915\pi$
$602$	935740.	0.105236
$603$	−3.81144e6	−0.426870
$604$	6.63778e6	0.740338
$605$	5.20812e6	0.578486
$606$	−1.73219e6	−0.191609
$607$	−3.01482e6	−0.332115	−0.166058	−	0.986116i	$-0.553104\pi$
$607$	−3.01482e6	−0.332115	−0.166058	+	0.986116i	$0.553104\pi$
$608$	2.47860e6	0.271924
$609$	−120164.	−0.0131290
$610$	−6.02487e6	−0.655576
$611$	5.30781e6	0.575191
$612$	1.88867e6	0.203834
$613$	−1.31504e7	−1.41348	−0.706739	−	0.707475i	$-0.749834\pi$
$613$	−1.31504e7	−1.41348	−0.706739	+	0.707475i	$0.749834\pi$
$614$	5.64835e6	0.604645
$615$	7.01076e6	0.747442
$616$	−452625.	−0.0480603
$617$	−7.07082e6	−0.747751	−0.373875	−	0.927479i	$-0.621971\pi$
$617$	−7.07082e6	−0.747751	−0.373875	+	0.927479i	$0.621971\pi$
$618$	−4.68457e6	−0.493400
$619$	−1.02493e7	−1.07514	−0.537571	−	0.843218i	$-0.680658\pi$
$619$	−1.02493e7	−1.07514	−0.537571	+	0.843218i	$0.680658\pi$
$620$	−3.66799e6	−0.383221
$621$	385641.	0.0401286
$622$	2.41669e6	0.250464
$623$	2.05367e6	0.211988
$624$	−2.02041e6	−0.207720
$625$	−2.29345e6	−0.234849
$626$	−5.09070e6	−0.519208
$627$	−3.66403e6	−0.372212
$628$	7.63603e6	0.772625
$629$	−2.13972e7	−2.15640
$630$	534443.	0.0536476
$631$	−6.24393e6	−0.624287	−0.312144	−	0.950035i	$-0.601047\pi$
$631$	−6.24393e6	−0.624287	−0.312144	+	0.950035i	$0.601047\pi$
$632$	−2.56223e6	−0.255167
$633$	−5.81753e6	−0.577071
$634$	8.53133e6	0.842934
$635$	−2.76726e6	−0.272342
$636$	−1.54312e6	−0.151272
$637$	1.31879e7	1.28774
$638$	213625.	0.0207778
$639$	5.04462e6	0.488738
$640$	642728.	0.0620265
$641$	1.31658e7	1.26561	0.632807	−	0.774310i	$-0.281903\pi$
$641$	1.31658e7	1.26561	0.632807	+	0.774310i	$0.281903\pi$
$642$	−4.69736e6	−0.449797
$643$	−3.93335e6	−0.375176	−0.187588	−	0.982248i	$-0.560067\pi$
$643$	−3.93335e6	−0.375176	−0.187588	+	0.982248i	$0.560067\pi$
$644$	355897.	0.0338151
$645$	1.96425e6	0.185908
$646$	1.41097e7	1.33026
$647$	1.11845e7	1.05040	0.525202	−	0.850977i	$-0.323990\pi$
$647$	1.11845e7	1.05040	0.525202	+	0.850977i	$0.323990\pi$
$648$	−419904.	−0.0392837
$649$	−3.96489e6	−0.369504
$650$	−5.56345e6	−0.516489
$651$	2.21153e6	0.204522
$652$	−8.43205e6	−0.776809
$653$	−1.88145e7	−1.72667	−0.863334	−	0.504633i	$-0.831628\pi$
$653$	−1.88145e7	−1.72667	−0.863334	+	0.504633i	$0.831628\pi$
$654$	−270486.	−0.0247287
$655$	−1.11387e7	−1.01445
$656$	−5.08341e6	−0.461207
$657$	6.14792e6	0.555667
$658$	1.01804e6	0.0916646
$659$	2.71666e6	0.243681	0.121841	−	0.992550i	$-0.461120\pi$
$659$	2.71666e6	0.243681	0.121841	+	0.992550i	$0.461120\pi$
$660$	−950121.	−0.0849023
$661$	168992.	0.0150440	0.00752200	−	0.999972i	$-0.497606\pi$
$661$	168992.	0.0150440	0.00752200	+	0.999972i	$0.497606\pi$
$662$	5.02086e6	0.445280
$663$	−1.15014e7	−1.01617
$664$	3.11078e6	0.273810
$665$	3.99267e6	0.350114
$666$	4.75719e6	0.415590
$667$	−167972.	−0.0146192
$668$	−4.06806e6	−0.352733
$669$	−8.87240e6	−0.766436
$670$	−7.38365e6	−0.635454
$671$	−6.45787e6	−0.553711
$672$	−387518.	−0.0331031
$673$	−6.32149e6	−0.537999	−0.269000	−	0.963140i	$-0.586693\pi$
$673$	−6.32149e6	−0.537999	−0.269000	+	0.963140i	$0.586693\pi$
$674$	5.15294e6	0.436923
$675$	−1.15626e6	−0.0976774
$676$	6.36302e6	0.535546
$677$	−1.84240e7	−1.54494	−0.772472	−	0.635049i	$-0.780980\pi$
$677$	−1.84240e7	−1.54494	−0.772472	+	0.635049i	$0.780980\pi$
$678$	6.08756e6	0.508592
$679$	−4.21640e6	−0.350968
$680$	3.65880e6	0.303435
$681$	7.68504e6	0.635007
$682$	−3.93161e6	−0.323675
$683$	−1.68530e7	−1.38237	−0.691187	−	0.722676i	$-0.742912\pi$
$683$	−1.68530e7	−1.38237	−0.691187	+	0.722676i	$0.742912\pi$
$684$	−3.13698e6	−0.256373
$685$	773399.	0.0629763
$686$	5.35628e6	0.434563
$687$	588474.	0.0475703
$688$	−1.42425e6	−0.114714
$689$	9.39715e6	0.754133
$690$	747077.	0.0597369
$691$	1.15358e7	0.919077	0.459538	−	0.888158i	$-0.348015\pi$
$691$	1.15358e7	0.919077	0.459538	+	0.888158i	$0.348015\pi$
$692$	4.96173e6	0.393883
$693$	572853.	0.0453117
$694$	5.74305e6	0.452630
$695$	8.81481e6	0.692231
$696$	182896.	0.0143114
$697$	−2.89378e7	−2.25623
$698$	−1.23879e7	−0.962405
$699$	1.62520e6	0.125809
$700$	−1.06708e6	−0.0823095
$701$	6.01983e6	0.462689	0.231344	−	0.972872i	$-0.425688\pi$
$701$	6.01983e6	0.462689	0.231344	+	0.972872i	$0.425688\pi$
$702$	2.55709e6	0.195841
$703$	3.55396e7	2.71222
$704$	688920.	0.0523887
$705$	2.13701e6	0.161933
$706$	1.64484e7	1.24197
$707$	2.02322e6	0.152228
$708$	−3.39457e6	−0.254508
$709$	3.83210e6	0.286300	0.143150	−	0.989701i	$-0.454277\pi$
$709$	3.83210e6	0.286300	0.143150	+	0.989701i	$0.454277\pi$
$710$	9.77262e6	0.727554
$711$	3.24282e6	0.240574
$712$	−3.12581e6	−0.231080
$713$	3.09141e6	0.227737
$714$	−2.20598e6	−0.161941
$715$	5.78595e6	0.423262
$716$	−5.59919e6	−0.408171
$717$	−1.09076e7	−0.792377
$718$	1.39673e7	1.01112
$719$	−2.30378e7	−1.66195	−0.830975	−	0.556309i	$-0.812217\pi$
$719$	−2.30378e7	−1.66195	−0.830975	+	0.556309i	$0.812217\pi$
$720$	−813453.	−0.0584792
$721$	5.47163e6	0.391993
$722$	−1.35311e7	−0.966030
$723$	2.83576e6	0.201755
$724$	1.46023e6	0.103532
$725$	503626.	0.0355847
$726$	4.77943e6	0.336538
$727$	3.72268e6	0.261228	0.130614	−	0.991433i	$-0.458305\pi$
$727$	3.72268e6	0.261228	0.130614	+	0.991433i	$0.458305\pi$
$728$	2.35986e6	0.165028
$729$	531441.	0.0370370
$730$	1.19100e7	0.827186
$731$	−8.10769e6	−0.561182
$732$	−5.52895e6	−0.381386
$733$	2.39520e6	0.164658	0.0823290	−	0.996605i	$-0.473764\pi$
$733$	2.39520e6	0.164658	0.0823290	+	0.996605i	$0.473764\pi$
$734$	−8.98732e6	−0.615729
$735$	5.30966e6	0.362534
$736$	−541696.	−0.0368605
$737$	−7.91431e6	−0.536716
$738$	6.43369e6	0.434830
$739$	−580301.	−0.0390879	−0.0195440	−	0.999809i	$-0.506221\pi$
$739$	−580301.	−0.0390879	−0.0195440	+	0.999809i	$0.506221\pi$
$740$	9.21580e6	0.618662
$741$	1.91033e7	1.27809
$742$	1.80238e6	0.120181
$743$	4.22216e6	0.280584	0.140292	−	0.990110i	$-0.455196\pi$
$743$	4.22216e6	0.280584	0.140292	+	0.990110i	$0.455196\pi$
$744$	−3.36607e6	−0.222942
$745$	1.32250e6	0.0872981
$746$	1.96399e7	1.29209
$747$	−3.93708e6	−0.258150
$748$	3.92175e6	0.256287
$749$	5.48656e6	0.357352
$750$	−6.65320e6	−0.431894
$751$	−1.54792e7	−1.00149	−0.500747	−	0.865594i	$-0.666941\pi$
$751$	−1.54792e7	−1.00149	−0.500747	+	0.865594i	$0.666941\pi$
$752$	−1.54952e6	−0.0999200
$753$	−406217.	−0.0261078
$754$	−1.11378e6	−0.0713463
$755$	−1.62746e7	−1.03906
$756$	490452.	0.0312099
$757$	2.13538e7	1.35437	0.677183	−	0.735815i	$-0.263201\pi$
$757$	2.13538e7	1.35437	0.677183	+	0.735815i	$0.263201\pi$
$758$	−6.40589e6	−0.404955
$759$	800769.	0.0504548
$760$	−6.07708e6	−0.381646
$761$	6.56676e6	0.411045	0.205523	−	0.978652i	$-0.434111\pi$
$761$	6.56676e6	0.411045	0.205523	+	0.978652i	$0.434111\pi$
$762$	−2.53948e6	−0.158437
$763$	315931.	0.0196463
$764$	9.60288e6	0.595207
$765$	−4.63066e6	−0.286081
$766$	−8.43464e6	−0.519391
$767$	2.06719e7	1.26879
$768$	589824.	0.0360844
$769$	4.02260e6	0.245297	0.122648	−	0.992450i	$-0.460861\pi$
$769$	4.02260e6	0.245297	0.122648	+	0.992450i	$0.460861\pi$
$770$	1.10975e6	0.0674526
$771$	−370341.	−0.0224370
$772$	9.36274e6	0.565405
$773$	−2.60057e7	−1.56538	−0.782690	−	0.622412i	$-0.786153\pi$
$773$	−2.60057e7	−1.56538	−0.782690	+	0.622412i	$0.786153\pi$
$774$	1.80257e6	0.108153
$775$	−9.26888e6	−0.554336
$776$	6.41759e6	0.382576
$777$	−5.55645e6	−0.330175
$778$	−1.84353e7	−1.09195
$779$	4.80643e7	2.83778
$780$	4.95368e6	0.291536
$781$	1.04750e7	0.614505
$782$	−3.08366e6	−0.180322
$783$	−231478.	−0.0134929
$784$	−3.84997e6	−0.223700
$785$	−1.87221e7	−1.08438
$786$	−1.02219e7	−0.590166
$787$	−2.02503e7	−1.16545	−0.582725	−	0.812669i	$-0.698014\pi$
$787$	−2.02503e7	−1.16545	−0.582725	+	0.812669i	$0.698014\pi$
$788$	−8.65761e6	−0.496687
$789$	−8.98960e6	−0.514100
$790$	6.28210e6	0.358127
$791$	−7.11034e6	−0.404063
$792$	−871915.	−0.0493925
$793$	3.36696e7	1.90132
$794$	−5.49284e6	−0.309204
$795$	3.78345e6	0.212310
$796$	−3.76923e6	−0.210848
$797$	−2.61096e7	−1.45598	−0.727988	−	0.685589i	$-0.759545\pi$
$797$	−2.61096e7	−1.45598	−0.727988	+	0.685589i	$0.759545\pi$
$798$	3.66403e6	0.203682
$799$	−8.82080e6	−0.488811
$800$	1.62415e6	0.0897225
$801$	3.95610e6	0.217864
$802$	1.51931e7	0.834085
$803$	1.27659e7	0.698656
$804$	−6.77589e6	−0.369680
$805$	−872594.	−0.0474594
$806$	2.04984e7	1.11143
$807$	4.16116e6	0.224921
$808$	−3.07946e6	−0.165938
$809$	−1.97774e7	−1.06242	−0.531212	−	0.847239i	$-0.678263\pi$
$809$	−1.97774e7	−1.06242	−0.531212	+	0.847239i	$0.678263\pi$
$810$	1.02953e6	0.0551347
$811$	−1.45964e6	−0.0779279	−0.0389639	−	0.999241i	$-0.512406\pi$
$811$	−1.45964e6	−0.0779279	−0.0389639	+	0.999241i	$0.512406\pi$
$812$	−213625.	−0.0113700
$813$	−9.93684e6	−0.527256
$814$	9.87813e6	0.522533
$815$	2.06738e7	1.09025
$816$	3.35763e6	0.176526
$817$	1.34665e7	0.705827
$818$	6.45763e6	0.337435
$819$	−2.98670e6	−0.155590
$820$	1.24636e7	0.647303
$821$	−9.59134e6	−0.496617	−0.248308	−	0.968681i	$-0.579875\pi$
$821$	−9.59134e6	−0.496617	−0.248308	+	0.968681i	$0.579875\pi$
$822$	709739.	0.0366369
$823$	−3.20554e6	−0.164969	−0.0824843	−	0.996592i	$-0.526285\pi$
$823$	−3.20554e6	−0.164969	−0.0824843	+	0.996592i	$0.526285\pi$
$824$	−8.32813e6	−0.427297
$825$	−2.40092e6	−0.122813
$826$	3.96489e6	0.202200
$827$	−2.00842e7	−1.02116	−0.510578	−	0.859832i	$-0.670568\pi$
$827$	−2.00842e7	−1.02116	−0.510578	+	0.859832i	$0.670568\pi$
$828$	685584.	0.0347524
$829$	2.69371e7	1.36134	0.680668	−	0.732592i	$-0.261690\pi$
$829$	2.69371e7	1.36134	0.680668	+	0.732592i	$0.261690\pi$
$830$	−7.62705e6	−0.384292
$831$	5.21427e6	0.261933
$832$	−3.59185e6	−0.179891
$833$	−2.19163e7	−1.09435
$834$	8.08925e6	0.402711
$835$	9.97414e6	0.495061
$836$	−6.51383e6	−0.322345
$837$	4.26019e6	0.210191
$838$	−3.92060e6	−0.192860
$839$	−1.56962e7	−0.769820	−0.384910	−	0.922954i	$-0.625767\pi$
$839$	−1.56962e7	−0.769820	−0.384910	+	0.922954i	$0.625767\pi$
$840$	950121.	0.0464602
$841$	−2.04103e7	−0.995084
$842$	−2.51923e7	−1.22458
$843$	1.86844e7	0.905543
$844$	−1.03423e7	−0.499759
$845$	−1.56009e7	−0.751639
$846$	1.96111e6	0.0942055
$847$	−5.58242e6	−0.267371
$848$	−2.74333e6	−0.131005
$849$	1.87942e7	0.894857
$850$	9.24564e6	0.438924
$851$	−7.76714e6	−0.367652
$852$	8.96822e6	0.423260
$853$	3.24410e7	1.52659	0.763294	−	0.646051i	$-0.223581\pi$
$853$	3.24410e7	1.52659	0.763294	+	0.646051i	$0.223581\pi$
$854$	6.45787e6	0.303002
$855$	7.69130e6	0.359819
$856$	−8.35086e6	−0.389535
$857$	−4.05659e7	−1.88673	−0.943364	−	0.331758i	$-0.892358\pi$
$857$	−4.05659e7	−1.88673	−0.943364	+	0.331758i	$0.892358\pi$
$858$	5.30970e6	0.246236
$859$	−3.82216e7	−1.76736	−0.883682	−	0.468089i	$-0.844943\pi$
$859$	−3.82216e7	−1.76736	−0.883682	+	0.468089i	$0.844943\pi$
$860$	3.49200e6	0.161001
$861$	−7.51462e6	−0.345461
$862$	8.15117e6	0.373639
$863$	2.19362e7	1.00262	0.501308	−	0.865269i	$-0.332852\pi$
$863$	2.19362e7	1.00262	0.501308	+	0.865269i	$0.332852\pi$
$864$	−746496.	−0.0340207
$865$	−1.21652e7	−0.552815
$866$	1.72474e7	0.781499
$867$	6.33495e6	0.286217
$868$	3.93161e6	0.177121
$869$	6.73359e6	0.302480
$870$	−448427.	−0.0200860
$871$	4.12631e7	1.84296
$872$	−480865.	−0.0214157
$873$	−8.12227e6	−0.360696
$874$	5.12180e6	0.226801
$875$	7.77101e6	0.343129
$876$	1.09296e7	0.481222
$877$	1.01057e7	0.443678	0.221839	−	0.975083i	$-0.428794\pi$
$877$	1.01057e7	0.443678	0.221839	+	0.975083i	$0.428794\pi$
$878$	1.10420e7	0.483405
$879$	3.58372e6	0.156445
$880$	−1.68910e6	−0.0735275
$881$	3.72001e7	1.61475	0.807374	−	0.590040i	$-0.200888\pi$
$881$	3.72001e7	1.61475	0.807374	+	0.590040i	$0.200888\pi$
$882$	4.87261e6	0.210907
$883$	−2.02349e7	−0.873374	−0.436687	−	0.899614i	$-0.643848\pi$
$883$	−2.02349e7	−0.873374	−0.436687	+	0.899614i	$0.643848\pi$
$884$	−2.04470e7	−0.880031
$885$	8.32284e6	0.357202
$886$	1.97001e7	0.843108
$887$	5.55892e6	0.237236	0.118618	−	0.992940i	$-0.462154\pi$
$887$	5.55892e6	0.237236	0.118618	+	0.992940i	$0.462154\pi$
$888$	8.45723e6	0.359911
$889$	2.96614e6	0.125874
$890$	7.66390e6	0.324321
$891$	1.10352e6	0.0465677
$892$	−1.57732e7	−0.663753
$893$	1.46509e7	0.614803
$894$	1.21364e6	0.0507863
$895$	1.37282e7	0.572868
$896$	−688920.	−0.0286681
$897$	−4.17500e6	−0.173251
$898$	5.30450e6	0.219510
$899$	−1.85559e6	−0.0765744
$900$	−2.05556e6	−0.0845911
$901$	−1.56167e7	−0.640880
$902$	1.33593e7	0.546724
$903$	−2.10542e6	−0.0859248
$904$	1.08223e7	0.440453
$905$	−3.58022e6	−0.145308
$906$	−1.49350e7	−0.604484
$907$	−3.50612e7	−1.41517	−0.707585	−	0.706628i	$-0.750216\pi$
$907$	−3.50612e7	−1.41517	−0.707585	+	0.706628i	$0.750216\pi$
$908$	1.36623e7	0.549932
$909$	3.89744e6	0.156448
$910$	−5.78595e6	−0.231617
$911$	3.49042e7	1.39342	0.696710	−	0.717353i	$-0.254646\pi$
$911$	3.49042e7	1.39342	0.696710	+	0.717353i	$0.254646\pi$
$912$	−5.57686e6	−0.222025
$913$	−8.17520e6	−0.324580
$914$	−1.62451e7	−0.643217
$915$	1.35560e7	0.535276
$916$	1.04618e6	0.0411971
$917$	1.19392e7	0.468871
$918$	−4.24950e6	−0.166430
$919$	3.40740e7	1.33087	0.665434	−	0.746457i	$-0.268247\pi$
$919$	3.40740e7	1.33087	0.665434	+	0.746457i	$0.268247\pi$
$920$	1.32814e6	0.0517337
$921$	−1.27088e7	−0.493691
$922$	−3.14284e7	−1.21757
$923$	−5.46137e7	−2.11007
$924$	1.01841e6	0.0392411
$925$	2.32880e7	0.894906
$926$	2.62472e7	1.00590
$927$	1.05403e7	0.402859
$928$	325149.	0.0123940
$929$	−1.04128e7	−0.395849	−0.197924	−	0.980217i	$-0.563420\pi$
$929$	−1.04128e7	−0.395849	−0.197924	+	0.980217i	$0.563420\pi$
$930$	8.25298e6	0.312899
$931$	3.64019e7	1.37642
$932$	2.88924e6	0.108954
$933$	−5.43756e6	−0.204503
$934$	−2.14879e7	−0.805985
$935$	−9.61540e6	−0.359698
$936$	4.54593e6	0.169603
$937$	3.91499e7	1.45674	0.728370	−	0.685184i	$-0.240278\pi$
$937$	3.91499e7	1.45674	0.728370	+	0.685184i	$0.240278\pi$
$938$	7.91431e6	0.293701
$939$	1.14541e7	0.423932
$940$	3.79913e6	0.140238
$941$	−3.05088e7	−1.12319	−0.561593	−	0.827414i	$-0.689811\pi$
$941$	−3.05088e7	−1.12319	−0.561593	+	0.827414i	$0.689811\pi$
$942$	−1.71811e7	−0.630846
$943$	−1.05044e7	−0.384673
$944$	−6.03478e6	−0.220410
$945$	−1.20250e6	−0.0438031
$946$	3.74296e6	0.135984
$947$	1.15386e7	0.418097	0.209048	−	0.977905i	$-0.432963\pi$
$947$	1.15386e7	0.418097	0.209048	+	0.977905i	$0.432963\pi$
$948$	5.76501e6	0.208343
$949$	−6.65581e7	−2.39903
$950$	−1.53565e7	−0.552058
$951$	−1.91955e7	−0.688252
$952$	−3.92175e6	−0.140245
$953$	−494199.	−0.0176266	−0.00881332	−	0.999961i	$-0.502805\pi$
$953$	−494199.	−0.0176266	−0.00881332	+	0.999961i	$0.502805\pi$
$954$	3.47203e6	0.123513
$955$	−2.35445e7	−0.835373
$956$	−1.93913e7	−0.686219
$957$	−480655.	−0.0169650
$958$	−1.63069e7	−0.574060
$959$	−828982.	−0.0291071
$960$	−1.44614e6	−0.0506444
$961$	5.52173e6	0.192871
$962$	−5.15019e7	−1.79426
$963$	1.05691e7	0.367257
$964$	5.04135e6	0.174725
$965$	−2.29557e7	−0.793546
$966$	−800769.	−0.0276099
$967$	1.27795e7	0.439489	0.219744	−	0.975558i	$-0.429478\pi$
$967$	1.27795e7	0.439489	0.219744	+	0.975558i	$0.429478\pi$
$968$	8.49677e6	0.291451
$969$	−3.17468e7	−1.08615
$970$	−1.57347e7	−0.536946
$971$	3.52664e7	1.20037	0.600183	−	0.799863i	$-0.295095\pi$
$971$	3.52664e7	1.20037	0.600183	+	0.799863i	$0.295095\pi$
$972$	944784.	0.0320750
$973$	−9.44832e6	−0.319943
$974$	5.76371e6	0.194672
$975$	1.25178e7	0.421711
$976$	−9.82925e6	−0.330290
$977$	2.08907e7	0.700190	0.350095	−	0.936714i	$-0.386149\pi$
$977$	2.08907e7	0.700190	0.350095	+	0.936714i	$0.386149\pi$
$978$	1.89721e7	0.634262
$979$	8.21469e6	0.273927
$980$	9.43940e6	0.313964
$981$	608595.	0.0201909
$982$	−4.14218e7	−1.37072
$983$	8.11583e6	0.267885	0.133943	−	0.990989i	$-0.457236\pi$
$983$	8.11583e6	0.267885	0.133943	+	0.990989i	$0.457236\pi$
$984$	1.14377e7	0.376574
$985$	2.12269e7	0.697100
$986$	1.85094e6	0.0606318
$987$	−2.29060e6	−0.0748438
$988$	3.39614e7	1.10686
$989$	−2.94308e6	−0.0956778
$990$	2.13777e6	0.0693224
$991$	7.26212e6	0.234898	0.117449	−	0.993079i	$-0.462528\pi$
$991$	7.26212e6	0.234898	0.117449	+	0.993079i	$0.462528\pi$
$992$	−5.98413e6	−0.193073
$993$	−1.12969e7	−0.363570
$994$	−1.04750e7	−0.336269
$995$	9.24146e6	0.295926
$996$	−6.99925e6	−0.223565
$997$	−1.55810e7	−0.496428	−0.248214	−	0.968705i	$-0.579844\pi$
$997$	−1.55810e7	−0.496428	−0.248214	+	0.968705i	$0.579844\pi$
$998$	−2.29115e7	−0.728162
$999$	−1.07037e7	−0.339328

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.6.a.e.1.1	✓	2
3.2	odd	2		414.6.a.g.1.2		2
4.3	odd	2		1104.6.a.f.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.6.a.e.1.1	✓	2	1.1	even	1	trivial
414.6.a.g.1.2		2	3.2	odd	2
1104.6.a.f.1.1		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	138.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -39.2290 q^{5} -36.0000 q^{6} +42.0484 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -39.2290 q^{5} -36.0000 q^{6} +42.0484 q^{7} -64.0000 q^{8} +81.0000 q^{9} +156.916 q^{10} +168.193 q^{11} +144.000 q^{12} -876.916 q^{13} -168.193 q^{14} -353.061 q^{15} +256.000 q^{16} +1457.31 q^{17} -324.000 q^{18} -2420.51 q^{19} -627.664 q^{20} +378.435 q^{21} -672.774 q^{22} +529.000 q^{23} -576.000 q^{24} -1586.08 q^{25} +3507.66 q^{26} +729.000 q^{27} +672.774 q^{28} -317.528 q^{29} +1412.24 q^{30} +5843.88 q^{31} -1024.00 q^{32} +1513.74 q^{33} -5829.22 q^{34} -1649.52 q^{35} +1296.00 q^{36} -14682.7 q^{37} +9682.05 q^{38} -7892.24 q^{39} +2510.66 q^{40} -19857.1 q^{41} -1513.74 q^{42} -5563.48 q^{43} +2691.10 q^{44} -3177.55 q^{45} -2116.00 q^{46} -6052.81 q^{47} +2304.00 q^{48} -15038.9 q^{49} +6344.34 q^{50} +13115.8 q^{51} -14030.7 q^{52} -10716.1 q^{53} -2916.00 q^{54} -6598.07 q^{55} -2691.10 q^{56} -21784.6 q^{57} +1270.11 q^{58} -23573.4 q^{59} -5648.98 q^{60} -38395.5 q^{61} -23375.5 q^{62} +3405.92 q^{63} +4096.00 q^{64} +34400.6 q^{65} -6054.97 q^{66} -47054.8 q^{67} +23316.9 q^{68} +4761.00 q^{69} +6598.07 q^{70} +62279.3 q^{71} -5184.00 q^{72} +75900.2 q^{73} +58730.8 q^{74} -14274.8 q^{75} -38728.2 q^{76} +7072.26 q^{77} +31569.0 q^{78} +40034.8 q^{79} -10042.6 q^{80} +6561.00 q^{81} +79428.3 q^{82} -48605.9 q^{83} +6054.97 q^{84} -57168.7 q^{85} +22253.9 q^{86} -2857.75 q^{87} -10764.4 q^{88} +48840.7 q^{89} +12710.2 q^{90} -36872.9 q^{91} +8464.00 q^{92} +52594.9 q^{93} +24211.2 q^{94} +94954.3 q^{95} -9216.00 q^{96} -100275. q^{97} +60155.7 q^{98} +13623.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{2} + 18 q^{3} + 32 q^{4} - 4 q^{5} - 72 q^{6} - 40 q^{7} - 128 q^{8} + 162 q^{9}+O(q^{10}) \) 2 * q - 8 * q^2 + 18 * q^3 + 32 * q^4 - 4 * q^5 - 72 * q^6 - 40 * q^7 - 128 * q^8 + 162 * q^9	\( 2 q - 8 q^{2} + 18 q^{3} + 32 q^{4} - 4 q^{5} - 72 q^{6} - 40 q^{7} - 128 q^{8} + 162 q^{9} + 16 q^{10} - 160 q^{11} + 288 q^{12} - 1456 q^{13} + 160 q^{14} - 36 q^{15} + 512 q^{16} - 436 q^{17} - 648 q^{18} - 448 q^{19} - 64 q^{20} - 360 q^{21} + 640 q^{22} + 1058 q^{23} - 1152 q^{24} - 3470 q^{25} + 5824 q^{26} + 1458 q^{27} - 640 q^{28} + 6364 q^{29} + 144 q^{30} - 2360 q^{31} - 2048 q^{32} - 1440 q^{33} + 1744 q^{34} - 4540 q^{35} + 2592 q^{36} - 19388 q^{37} + 1792 q^{38} - 13104 q^{39} + 256 q^{40} - 17476 q^{41} + 1440 q^{42} - 23760 q^{43} - 2560 q^{44} - 324 q^{45} - 4232 q^{46} - 35684 q^{47} + 4608 q^{48} - 25114 q^{49} + 13880 q^{50} - 3924 q^{51} - 23296 q^{52} + 1476 q^{53} - 5832 q^{54} - 18160 q^{55} + 2560 q^{56} - 4032 q^{57} - 25456 q^{58} + 23092 q^{59} - 576 q^{60} - 70884 q^{61} + 9440 q^{62} - 3240 q^{63} + 8192 q^{64} + 14000 q^{65} + 5760 q^{66} - 81824 q^{67} - 6976 q^{68} + 9522 q^{69} + 18160 q^{70} + 15552 q^{71} - 10368 q^{72} + 49644 q^{73} + 77552 q^{74} - 31230 q^{75} - 7168 q^{76} + 34000 q^{77} + 52416 q^{78} + 102680 q^{79} - 1024 q^{80} + 13122 q^{81} + 69904 q^{82} + 39096 q^{83} - 5760 q^{84} - 123868 q^{85} + 95040 q^{86} + 57276 q^{87} + 10240 q^{88} - 21228 q^{89} + 1296 q^{90} + 10640 q^{91} + 16928 q^{92} - 21240 q^{93} + 142736 q^{94} + 164444 q^{95} - 18432 q^{96} - 25772 q^{97} + 100456 q^{98} - 12960 q^{99}+O(q^{100}) \) 2 * q - 8 * q^2 + 18 * q^3 + 32 * q^4 - 4 * q^5 - 72 * q^6 - 40 * q^7 - 128 * q^8 + 162 * q^9 + 16 * q^10 - 160 * q^11 + 288 * q^12 - 1456 * q^13 + 160 * q^14 - 36 * q^15 + 512 * q^16 - 436 * q^17 - 648 * q^18 - 448 * q^19 - 64 * q^20 - 360 * q^21 + 640 * q^22 + 1058 * q^23 - 1152 * q^24 - 3470 * q^25 + 5824 * q^26 + 1458 * q^27 - 640 * q^28 + 6364 * q^29 + 144 * q^30 - 2360 * q^31 - 2048 * q^32 - 1440 * q^33 + 1744 * q^34 - 4540 * q^35 + 2592 * q^36 - 19388 * q^37 + 1792 * q^38 - 13104 * q^39 + 256 * q^40 - 17476 * q^41 + 1440 * q^42 - 23760 * q^43 - 2560 * q^44 - 324 * q^45 - 4232 * q^46 - 35684 * q^47 + 4608 * q^48 - 25114 * q^49 + 13880 * q^50 - 3924 * q^51 - 23296 * q^52 + 1476 * q^53 - 5832 * q^54 - 18160 * q^55 + 2560 * q^56 - 4032 * q^57 - 25456 * q^58 + 23092 * q^59 - 576 * q^60 - 70884 * q^61 + 9440 * q^62 - 3240 * q^63 + 8192 * q^64 + 14000 * q^65 + 5760 * q^66 - 81824 * q^67 - 6976 * q^68 + 9522 * q^69 + 18160 * q^70 + 15552 * q^71 - 10368 * q^72 + 49644 * q^73 + 77552 * q^74 - 31230 * q^75 - 7168 * q^76 + 34000 * q^77 + 52416 * q^78 + 102680 * q^79 - 1024 * q^80 + 13122 * q^81 + 69904 * q^82 + 39096 * q^83 - 5760 * q^84 - 123868 * q^85 + 95040 * q^86 + 57276 * q^87 + 10240 * q^88 - 21228 * q^89 + 1296 * q^90 + 10640 * q^91 + 16928 * q^92 - 21240 * q^93 + 142736 * q^94 + 164444 * q^95 - 18432 * q^96 - 25772 * q^97 + 100456 * q^98 - 12960 * q^99

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