LMFDB - Embedded newform 538.8.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,8,Mod(1,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("538.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 538 = 2 \cdot 269 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	538.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:	$168.063143710$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	538.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-8.00000 q^{2} -88.0215 q^{3} +64.0000 q^{4} -492.867 q^{5} +704.172 q^{6} +1216.54 q^{7} -512.000 q^{8} +5560.79 q^{9} +3942.93 q^{10} -1443.80 q^{11} -5633.38 q^{12} -7376.30 q^{13} -9732.32 q^{14} +43382.9 q^{15} +4096.00 q^{16} -20695.8 q^{17} -44486.3 q^{18} +12989.6 q^{19} -31543.5 q^{20} -107082. q^{21} +11550.4 q^{22} +35916.4 q^{23} +45067.0 q^{24} +164792. q^{25} +59010.4 q^{26} -296966. q^{27} +77858.6 q^{28} -191838. q^{29} -347063. q^{30} -127665. q^{31} -32768.0 q^{32} +127086. q^{33} +165567. q^{34} -599592. q^{35} +355891. q^{36} -545515. q^{37} -103917. q^{38} +649273. q^{39} +252348. q^{40} +133610. q^{41} +856654. q^{42} -148832. q^{43} -92403.4 q^{44} -2.74073e6 q^{45} -287331. q^{46} +1.15121e6 q^{47} -360536. q^{48} +656426. q^{49} -1.31834e6 q^{50} +1.82168e6 q^{51} -472083. q^{52} -2.07007e6 q^{53} +2.37573e6 q^{54} +711602. q^{55} -622868. q^{56} -1.14336e6 q^{57} +1.53470e6 q^{58} -463944. q^{59} +2.77650e6 q^{60} +3.41230e6 q^{61} +1.02132e6 q^{62} +6.76492e6 q^{63} +262144. q^{64} +3.63553e6 q^{65} -1.01669e6 q^{66} +3.73995e6 q^{67} -1.32453e6 q^{68} -3.16142e6 q^{69} +4.79673e6 q^{70} -1.42078e6 q^{71} -2.84713e6 q^{72} +440582. q^{73} +4.36412e6 q^{74} -1.45053e7 q^{75} +831333. q^{76} -1.75644e6 q^{77} -5.19418e6 q^{78} +2.30629e6 q^{79} -2.01878e6 q^{80} +1.39780e7 q^{81} -1.06888e6 q^{82} +8.55941e6 q^{83} -6.85323e6 q^{84} +1.02003e7 q^{85} +1.19065e6 q^{86} +1.68859e7 q^{87} +739227. q^{88} +5.33157e6 q^{89} +2.19258e7 q^{90} -8.97356e6 q^{91} +2.29865e6 q^{92} +1.12373e7 q^{93} -9.20967e6 q^{94} -6.40213e6 q^{95} +2.88429e6 q^{96} -359524. q^{97} -5.25141e6 q^{98} -8.02869e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 320 q^{2} - 109 q^{3} + 2560 q^{4} - 751 q^{5} + 872 q^{6} - 233 q^{7} - 20480 q^{8} + 29623 q^{9} + 6008 q^{10} - 12977 q^{11} - 6976 q^{12} - 4870 q^{13} + 1864 q^{14} - 9068 q^{15} + 163840 q^{16}+ \cdots + 9909340 q^{99}+O(q^{100}) $ 40 * q - 320 * q^2 - 109 * q^3 + 2560 * q^4 - 751 * q^5 + 872 * q^6 - 233 * q^7 - 20480 * q^8 + 29623 * q^9 + 6008 * q^10 - 12977 * q^11 - 6976 * q^12 - 4870 * q^13 + 1864 * q^14 - 9068 * q^15 + 163840 * q^16 - 37896 * q^17 - 236984 * q^18 + 36270 * q^19 - 48064 * q^20 - 39351 * q^21 + 103816 * q^22 - 254388 * q^23 + 55808 * q^24 + 621875 * q^25 + 38960 * q^26 - 314650 * q^27 - 14912 * q^28 - 77138 * q^29 + 72544 * q^30 - 170617 * q^31 - 1310720 * q^32 - 338481 * q^33 + 303168 * q^34 - 498065 * q^35 + 1895872 * q^36 - 432250 * q^37 - 290160 * q^38 - 237233 * q^39 + 384512 * q^40 - 739673 * q^41 + 314808 * q^42 - 949447 * q^43 - 830528 * q^44 - 889534 * q^45 + 2035104 * q^46 - 1712951 * q^47 - 446464 * q^48 + 5466815 * q^49 - 4975000 * q^50 - 1611137 * q^51 - 311680 * q^52 - 3150530 * q^53 + 2517200 * q^54 - 466659 * q^55 + 119296 * q^56 - 3495794 * q^57 + 617104 * q^58 - 4357669 * q^59 - 580352 * q^60 + 4667204 * q^61 + 1364936 * q^62 + 1730648 * q^63 + 10485760 * q^64 - 1915803 * q^65 + 2707848 * q^66 - 6921617 * q^67 - 2425344 * q^68 - 10298459 * q^69 + 3984520 * q^70 - 18615993 * q^71 - 15166976 * q^72 - 6531063 * q^73 + 3458000 * q^74 - 22172708 * q^75 + 2321280 * q^76 - 20594134 * q^77 + 1897864 * q^78 + 1641715 * q^79 - 3076096 * q^80 + 21032872 * q^81 + 5917384 * q^82 - 16336922 * q^83 - 2518464 * q^84 + 13126141 * q^85 + 7595576 * q^86 + 11928706 * q^87 + 6644224 * q^88 + 9041896 * q^89 + 7116272 * q^90 + 9867502 * q^91 - 16280832 * q^92 + 10660597 * q^93 + 13703608 * q^94 + 8580994 * q^95 + 3571712 * q^96 + 10979403 * q^97 - 43734520 * q^98 + 9909340 * q^99

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 $

$2$	−8.00000	−0.707107
$2$	−8.00000	−0.707107
$3$	−88.0215	−1.88219	−0.941097	−	0.338136i	$-0.890204\pi$
$3$	−88.0215	−1.88219	−0.941097	+	0.338136i	$0.890204\pi$
$4$	64.0000	0.500000
$5$	−492.867	−1.76333	−0.881666	−	0.471873i	$-0.843578\pi$
$5$	−492.867	−1.76333	−0.881666	+	0.471873i	$0.843578\pi$
$6$	704.172	1.33091
$7$	1216.54	1.34055	0.670275	−	0.742113i	$-0.266176\pi$
$7$	1216.54	1.34055	0.670275	+	0.742113i	$0.266176\pi$
$8$	−512.000	−0.353553
$9$	5560.79	2.54266
$10$	3942.93	1.24686
$11$	−1443.80	−0.327065	−0.163532	−	0.986538i	$-0.552289\pi$
$11$	−1443.80	−0.327065	−0.163532	+	0.986538i	$0.552289\pi$
$12$	−5633.38	−0.941097
$13$	−7376.30	−0.931186	−0.465593	−	0.884999i	$-0.654159\pi$
$13$	−7376.30	−0.931186	−0.465593	+	0.884999i	$0.654159\pi$
$14$	−9732.32	−0.947912
$15$	43382.9	3.31894
$16$	4096.00	0.250000
$17$	−20695.8	−1.02167	−0.510836	−	0.859678i	$-0.670664\pi$
$17$	−20695.8	−1.02167	−0.510836	+	0.859678i	$0.670664\pi$
$18$	−44486.3	−1.79793
$19$	12989.6	0.434468	0.217234	−	0.976120i	$-0.430297\pi$
$19$	12989.6	0.434468	0.217234	+	0.976120i	$0.430297\pi$
$20$	−31543.5	−0.881666
$21$	−107082.	−2.52318
$22$	11550.4	0.231270
$23$	35916.4	0.615525	0.307763	−	0.951463i	$-0.400420\pi$
$23$	35916.4	0.615525	0.307763	+	0.951463i	$0.400420\pi$
$24$	45067.0	0.665456
$25$	164792.	2.10934
$26$	59010.4	0.658448
$27$	−296966.	−2.90358
$28$	77858.6	0.670275
$29$	−191838.	−1.46063	−0.730317	−	0.683108i	$-0.760628\pi$
$29$	−191838.	−1.46063	−0.730317	+	0.683108i	$0.760628\pi$
$30$	−347063.	−2.34684
$31$	−127665.	−0.769673	−0.384836	−	0.922985i	$-0.625742\pi$
$31$	−127665.	−0.769673	−0.384836	+	0.922985i	$0.625742\pi$
$32$	−32768.0	−0.176777
$33$	127086.	0.615599
$34$	165567.	0.722431
$35$	−599592.	−2.36384
$36$	355891.	1.27133
$37$	−545515.	−1.77052	−0.885259	−	0.465098i	$-0.846019\pi$
$37$	−545515.	−1.77052	−0.885259	+	0.465098i	$0.846019\pi$
$38$	−103917.	−0.307215
$39$	649273.	1.75267
$40$	252348.	0.623432
$41$	133610.	0.302757	0.151379	−	0.988476i	$-0.451629\pi$
$41$	133610.	0.302757	0.151379	+	0.988476i	$0.451629\pi$
$42$	856654.	1.78416
$43$	−148832.	−0.285467	−0.142733	−	0.989761i	$-0.545589\pi$
$43$	−148832.	−0.285467	−0.142733	+	0.989761i	$0.545589\pi$
$44$	−92403.4	−0.163532
$45$	−2.74073e6	−4.48355
$46$	−287331.	−0.435242
$47$	1.15121e6	1.61738	0.808689	−	0.588237i	$-0.200178\pi$
$47$	1.15121e6	1.61738	0.808689	+	0.588237i	$0.200178\pi$
$48$	−360536.	−0.470549
$49$	656426.	0.797076
$50$	−1.31834e6	−1.49153
$51$	1.82168e6	1.92299
$52$	−472083.	−0.465593
$53$	−2.07007e6	−1.90994	−0.954970	−	0.296703i	$-0.904113\pi$
$53$	−2.07007e6	−1.90994	−0.954970	+	0.296703i	$0.904113\pi$
$54$	2.37573e6	2.05314
$55$	711602.	0.576724
$56$	−622868.	−0.473956
$57$	−1.14336e6	−0.817753
$58$	1.53470e6	1.03282
$59$	−463944.	−0.294092	−0.147046	−	0.989130i	$-0.546977\pi$
$59$	−463944.	−0.294092	−0.147046	+	0.989130i	$0.546977\pi$
$60$	2.77650e6	1.65947
$61$	3.41230e6	1.92483	0.962417	−	0.271575i	$-0.0875447\pi$
$61$	3.41230e6	1.92483	0.962417	+	0.271575i	$0.0875447\pi$
$62$	1.02132e6	0.544241
$63$	6.76492e6	3.40856
$64$	262144.	0.125000
$65$	3.63553e6	1.64199
$66$	−1.01669e6	−0.435294
$67$	3.73995e6	1.51916	0.759580	−	0.650414i	$-0.225404\pi$
$67$	3.73995e6	1.51916	0.759580	+	0.650414i	$0.225404\pi$
$68$	−1.32453e6	−0.510836
$69$	−3.16142e6	−1.15854
$70$	4.79673e6	1.67149
$71$	−1.42078e6	−0.471109	−0.235554	−	0.971861i	$-0.575691\pi$
$71$	−1.42078e6	−0.471109	−0.235554	+	0.971861i	$0.575691\pi$
$72$	−2.84713e6	−0.898965
$73$	440582.	0.132555	0.0662776	−	0.997801i	$-0.478888\pi$
$73$	440582.	0.132555	0.0662776	+	0.997801i	$0.478888\pi$
$74$	4.36412e6	1.25195
$75$	−1.45053e7	−3.97019
$76$	831333.	0.217234
$77$	−1.75644e6	−0.438447
$78$	−5.19418e6	−1.23933
$79$	2.30629e6	0.526283	0.263142	−	0.964757i	$-0.415241\pi$
$79$	2.30629e6	0.526283	0.263142	+	0.964757i	$0.415241\pi$
$80$	−2.01878e6	−0.440833
$81$	1.39780e7	2.92245
$82$	−1.06888e6	−0.214082
$83$	8.55941e6	1.64312	0.821562	−	0.570119i	$-0.193103\pi$
$83$	8.55941e6	1.64312	0.821562	+	0.570119i	$0.193103\pi$
$84$	−6.85323e6	−1.26159
$85$	1.02003e7	1.80155
$86$	1.19065e6	0.201855
$87$	1.68859e7	2.74920
$88$	739227.	0.115635
$89$	5.33157e6	0.801660	0.400830	−	0.916153i	$-0.368722\pi$
$89$	5.33157e6	0.801660	0.400830	+	0.916153i	$0.368722\pi$
$90$	2.19258e7	3.17035
$91$	−8.97356e6	−1.24830
$92$	2.29865e6	0.307763
$93$	1.12373e7	1.44867
$94$	−9.20967e6	−1.14366
$95$	−6.40213e6	−0.766111
$96$	2.88429e6	0.332728
$97$	−359524.	−0.0399970	−0.0199985	−	0.999800i	$-0.506366\pi$
$97$	−359524.	−0.0399970	−0.0199985	+	0.999800i	$0.506366\pi$
$98$	−5.25141e6	−0.563618
$99$	−8.02869e6	−0.831613
$100$	1.05467e7	1.05467
$101$	−1.14253e7	−1.10342	−0.551710	−	0.834036i	$-0.686025\pi$
$101$	−1.14253e7	−1.10342	−0.551710	+	0.834036i	$0.686025\pi$
$102$	−1.45734e7	−1.35976
$103$	−1.77746e6	−0.160276	−0.0801381	−	0.996784i	$-0.525536\pi$
$103$	−1.77746e6	−0.160276	−0.0801381	+	0.996784i	$0.525536\pi$
$104$	3.77666e6	0.329224
$105$	5.27770e7	4.44920
$106$	1.65606e7	1.35053
$107$	1.64869e7	1.30106	0.650529	−	0.759481i	$-0.274547\pi$
$107$	1.64869e7	1.30106	0.650529	+	0.759481i	$0.274547\pi$
$108$	−1.90058e7	−1.45179
$109$	−3.64888e6	−0.269877	−0.134939	−	0.990854i	$-0.543084\pi$
$109$	−3.64888e6	−0.269877	−0.134939	+	0.990854i	$0.543084\pi$
$110$	−5.69282e6	−0.407805
$111$	4.80171e7	3.33246
$112$	4.98295e6	0.335138
$113$	−1.56703e7	−1.02165	−0.510826	−	0.859684i	$-0.670660\pi$
$113$	−1.56703e7	−1.02165	−0.510826	+	0.859684i	$0.670660\pi$
$114$	9.14690e6	0.578239
$115$	−1.77020e7	−1.08538
$116$	−1.22776e7	−0.730317
$117$	−4.10180e7	−2.36769
$118$	3.71155e6	0.207955
$119$	−2.51773e7	−1.36960
$120$	−2.22120e7	−1.17342
$121$	−1.74026e7	−0.893029
$122$	−2.72984e7	−1.36106
$123$	−1.17605e7	−0.569848
$124$	−8.17056e6	−0.384836
$125$	−4.27155e7	−1.95614
$126$	−5.41194e7	−2.41022
$127$	5.52370e6	0.239286	0.119643	−	0.992817i	$-0.461825\pi$
$127$	5.52370e6	0.239286	0.119643	+	0.992817i	$0.461825\pi$
$128$	−2.09715e6	−0.0883883
$129$	1.31004e7	0.537304
$130$	−2.90842e7	−1.16106
$131$	1.34141e7	0.521329	0.260664	−	0.965429i	$-0.416058\pi$
$131$	1.34141e7	0.521329	0.260664	+	0.965429i	$0.416058\pi$
$132$	8.13349e6	0.307800
$133$	1.58023e7	0.582426
$134$	−2.99196e7	−1.07421
$135$	1.46365e8	5.11998
$136$	1.05963e7	0.361216
$137$	−4.37320e7	−1.45304	−0.726520	−	0.687145i	$-0.758864\pi$
$137$	−4.37320e7	−1.45304	−0.726520	+	0.687145i	$0.758864\pi$
$138$	2.52914e7	0.819210
$139$	3.67585e7	1.16093	0.580466	−	0.814285i	$-0.302871\pi$
$139$	3.67585e7	1.16093	0.580466	+	0.814285i	$0.302871\pi$
$140$	−3.83739e7	−1.18192
$141$	−1.01331e8	−3.04422
$142$	1.13662e7	0.333124
$143$	1.06499e7	0.304558
$144$	2.27770e7	0.635664
$145$	9.45505e7	2.57559
$146$	−3.52466e6	−0.0937307
$147$	−5.77797e7	−1.50025
$148$	−3.49129e7	−0.885259
$149$	4.69788e7	1.16346	0.581729	−	0.813383i	$-0.302377\pi$
$149$	4.69788e7	1.16346	0.581729	+	0.813383i	$0.302377\pi$
$150$	1.16042e8	2.80735
$151$	3.19053e7	0.754125	0.377062	−	0.926188i	$-0.376934\pi$
$151$	3.19053e7	0.754125	0.377062	+	0.926188i	$0.376934\pi$
$152$	−6.65067e6	−0.153608
$153$	−1.15085e8	−2.59776
$154$	1.40515e7	0.310029
$155$	6.29218e7	1.35719
$156$	4.15535e7	0.876337
$157$	8.88040e7	1.83140	0.915701	−	0.401860i	$-0.131636\pi$
$157$	8.88040e7	1.83140	0.915701	+	0.401860i	$0.131636\pi$
$158$	−1.84503e7	−0.372139
$159$	1.82211e8	3.59488
$160$	1.61503e7	0.311716
$161$	4.36938e7	0.825143
$162$	−1.11824e8	−2.06648
$163$	−3.92694e6	−0.0710227	−0.0355114	−	0.999369i	$-0.511306\pi$
$163$	−3.92694e6	−0.0710227	−0.0355114	+	0.999369i	$0.511306\pi$
$164$	8.55103e6	0.151379
$165$	−6.26363e7	−1.08551
$166$	−6.84753e7	−1.16186
$167$	5.56321e7	0.924310	0.462155	−	0.886799i	$-0.347076\pi$
$167$	5.56321e7	0.924310	0.462155	+	0.886799i	$0.347076\pi$
$168$	5.48258e7	0.892078
$169$	−8.33878e6	−0.132892
$170$	−8.16022e7	−1.27389
$171$	7.22323e7	1.10470
$172$	−9.52522e6	−0.142733
$173$	−1.05245e8	−1.54540	−0.772700	−	0.634772i	$-0.781094\pi$
$173$	−1.05245e8	−1.54540	−0.772700	+	0.634772i	$0.781094\pi$
$174$	−1.35087e8	−1.94398
$175$	2.00477e8	2.82768
$176$	−5.91382e6	−0.0817661
$177$	4.08371e7	0.553539
$178$	−4.26526e7	−0.566859
$179$	1.05662e8	1.37699	0.688497	−	0.725239i	$-0.258271\pi$
$179$	1.05662e8	1.37699	0.688497	+	0.725239i	$0.258271\pi$
$180$	−1.75407e8	−2.24178
$181$	3.46559e7	0.434412	0.217206	−	0.976126i	$-0.430306\pi$
$181$	3.46559e7	0.434412	0.217206	+	0.976126i	$0.430306\pi$
$182$	7.17885e7	0.882683
$183$	−3.00356e8	−3.62291
$184$	−1.83892e7	−0.217621
$185$	2.68866e8	3.12201
$186$	−8.98982e7	−1.02437
$187$	2.98807e7	0.334153
$188$	7.36773e7	0.808689
$189$	−3.61271e8	−3.89240
$190$	5.12170e7	0.541722
$191$	−2.41672e7	−0.250963	−0.125482	−	0.992096i	$-0.540048\pi$
$191$	−2.41672e7	−0.250963	−0.125482	+	0.992096i	$0.540048\pi$
$192$	−2.30743e7	−0.235274
$193$	−1.14144e8	−1.14288	−0.571441	−	0.820643i	$-0.693615\pi$
$193$	−1.14144e8	−1.14288	−0.571441	+	0.820643i	$0.693615\pi$
$194$	2.87619e6	0.0282821
$195$	−3.20005e8	−3.09055
$196$	4.20113e7	0.398538
$197$	−1.35146e8	−1.25943	−0.629714	−	0.776827i	$-0.716828\pi$
$197$	−1.35146e8	−1.25943	−0.629714	+	0.776827i	$0.716828\pi$
$198$	6.42295e7	0.588039
$199$	8.99524e7	0.809146	0.404573	−	0.914506i	$-0.367420\pi$
$199$	8.99524e7	0.809146	0.404573	+	0.914506i	$0.367420\pi$
$200$	−8.43737e7	−0.745765
$201$	−3.29196e8	−2.85936
$202$	9.14020e7	0.780236
$203$	−2.33379e8	−1.95805
$204$	1.16587e8	0.961493
$205$	−6.58518e7	−0.533862
$206$	1.42197e7	0.113332
$207$	1.99724e8	1.56507
$208$	−3.02133e7	−0.232797
$209$	−1.87544e7	−0.142099
$210$	−4.22216e8	−3.14606
$211$	−1.44727e8	−1.06063	−0.530313	−	0.847802i	$-0.677926\pi$
$211$	−1.44727e8	−1.06063	−0.530313	+	0.847802i	$0.677926\pi$
$212$	−1.32485e8	−0.954970
$213$	1.25059e8	0.886719
$214$	−1.31895e8	−0.919987
$215$	7.33541e7	0.503373
$216$	1.52047e8	1.02657
$217$	−1.55310e8	−1.03179
$218$	2.91910e7	0.190832
$219$	−3.87807e7	−0.249495
$220$	4.55425e7	0.288362
$221$	1.52658e8	0.951367
$222$	−3.84136e8	−2.35641
$223$	−8.28565e7	−0.500333	−0.250167	−	0.968203i	$-0.580485\pi$
$223$	−8.28565e7	−0.500333	−0.250167	+	0.968203i	$0.580485\pi$
$224$	−3.98636e7	−0.236978
$225$	9.16376e8	5.36334
$226$	1.25362e8	0.722417
$227$	−9.69944e7	−0.550372	−0.275186	−	0.961391i	$-0.588739\pi$
$227$	−9.69944e7	−0.550372	−0.275186	+	0.961391i	$0.588739\pi$
$228$	−7.31752e7	−0.408876
$229$	3.39457e8	1.86793	0.933965	−	0.357365i	$-0.116325\pi$
$229$	3.39457e8	1.86793	0.933965	+	0.357365i	$0.116325\pi$
$230$	1.41616e8	0.767476
$231$	1.54605e8	0.825242
$232$	9.82210e7	0.516412
$233$	−1.51498e8	−0.784625	−0.392313	−	0.919832i	$-0.628325\pi$
$233$	−1.51498e8	−0.784625	−0.392313	+	0.919832i	$0.628325\pi$
$234$	3.28144e8	1.67421
$235$	−5.67392e8	−2.85197
$236$	−2.96924e7	−0.147046
$237$	−2.03003e8	−0.990568
$238$	2.01418e8	0.968455
$239$	1.82150e8	0.863051	0.431526	−	0.902101i	$-0.357975\pi$
$239$	1.82150e8	0.863051	0.431526	+	0.902101i	$0.357975\pi$
$240$	1.77696e8	0.829734
$241$	3.25479e8	1.49783	0.748916	−	0.662664i	$-0.230574\pi$
$241$	3.25479e8	1.49783	0.748916	+	0.662664i	$0.230574\pi$
$242$	1.39221e8	0.631467
$243$	−5.80898e8	−2.59704
$244$	2.18387e8	0.962417
$245$	−3.23531e8	−1.40551
$246$	9.40843e7	0.402944
$247$	−9.58150e7	−0.404570
$248$	6.53645e7	0.272120
$249$	−7.53412e8	−3.09268
$250$	3.41724e8	1.38320
$251$	−6.16485e7	−0.246073	−0.123037	−	0.992402i	$-0.539263\pi$
$251$	−6.16485e7	−0.246073	−0.123037	+	0.992402i	$0.539263\pi$
$252$	4.32955e8	1.70428
$253$	−5.18562e7	−0.201316
$254$	−4.41896e7	−0.169201
$255$	−8.97844e8	−3.39086
$256$	1.67772e7	0.0625000
$257$	1.87245e8	0.688088	0.344044	−	0.938953i	$-0.388203\pi$
$257$	1.87245e8	0.688088	0.344044	+	0.938953i	$0.388203\pi$
$258$	−1.04803e8	−0.379931
$259$	−6.63641e8	−2.37347
$260$	2.32674e8	0.820996
$261$	−1.06677e9	−3.71389
$262$	−1.07313e8	−0.368635
$263$	7.30178e7	0.247505	0.123752	−	0.992313i	$-0.460507\pi$
$263$	7.30178e7	0.247505	0.123752	+	0.992313i	$0.460507\pi$
$264$	−6.50679e7	−0.217647
$265$	1.02027e9	3.36786
$266$	−1.26419e8	−0.411837
$267$	−4.69293e8	−1.50888
$268$	2.39357e8	0.759580
$269$	1.94651e7	0.0609711
$269$	1.94651e7	0.0609711
$270$	−1.17092e9	−3.62037
$271$	5.46529e8	1.66809	0.834047	−	0.551694i	$-0.186018\pi$
$271$	5.46529e8	1.66809	0.834047	+	0.551694i	$0.186018\pi$
$272$	−8.47701e7	−0.255418
$273$	7.89866e8	2.34955
$274$	3.49856e8	1.02745
$275$	−2.37928e8	−0.689891
$276$	−2.02331e8	−0.579269
$277$	−4.40412e7	−0.124503	−0.0622515	−	0.998060i	$-0.519828\pi$
$277$	−4.40412e7	−0.124503	−0.0622515	+	0.998060i	$0.519828\pi$
$278$	−2.94068e8	−0.820902
$279$	−7.09919e8	−1.95701
$280$	3.06991e8	0.835743
$281$	−3.22684e8	−0.867573	−0.433786	−	0.901016i	$-0.642823\pi$
$281$	−3.22684e8	−0.867573	−0.433786	+	0.901016i	$0.642823\pi$
$282$	8.10649e8	2.15259
$283$	−2.16450e8	−0.567681	−0.283840	−	0.958872i	$-0.591609\pi$
$283$	−2.16450e8	−0.567681	−0.283840	+	0.958872i	$0.591609\pi$
$284$	−9.09296e7	−0.235554
$285$	5.63525e8	1.44197
$286$	−8.51993e7	−0.215355
$287$	1.62542e8	0.405862
$288$	−1.82216e8	−0.449483
$289$	1.79783e7	0.0438133
$290$	−7.56404e8	−1.82121
$291$	3.16459e7	0.0752821
$292$	2.81973e7	0.0662776
$293$	1.39158e8	0.323199	0.161600	−	0.986856i	$-0.448335\pi$
$293$	1.39158e8	0.323199	0.161600	+	0.986856i	$0.448335\pi$
$294$	4.62237e8	1.06084
$295$	2.28663e8	0.518583
$296$	2.79304e8	0.625973
$297$	4.28761e8	0.949659
$298$	−3.75831e8	−0.822688
$299$	−2.64930e8	−0.573168
$300$	−9.28338e8	−1.98510
$301$	−1.81060e8	−0.382683
$302$	−2.55242e8	−0.533247
$303$	1.00567e9	2.07685
$304$	5.32053e7	0.108617
$305$	−1.68181e9	−3.39412
$306$	9.20681e8	1.83689
$307$	−2.16245e8	−0.426543	−0.213271	−	0.976993i	$-0.568412\pi$
$307$	−2.16245e8	−0.426543	−0.213271	+	0.976993i	$0.568412\pi$
$308$	−1.12412e8	−0.219223
$309$	1.56455e8	0.301671
$310$	−5.03375e8	−0.959677
$311$	6.87655e7	0.129631	0.0648156	−	0.997897i	$-0.479354\pi$
$311$	6.87655e7	0.129631	0.0648156	+	0.997897i	$0.479354\pi$
$312$	−3.32428e8	−0.619664
$313$	6.39677e8	1.17911	0.589557	−	0.807727i	$-0.299302\pi$
$313$	6.39677e8	1.17911	0.589557	+	0.807727i	$0.299302\pi$
$314$	−7.10432e8	−1.29500
$315$	−3.33421e9	−6.01043
$316$	1.47603e8	0.263142
$317$	6.34709e8	1.11910	0.559548	−	0.828798i	$-0.310975\pi$
$317$	6.34709e8	1.11910	0.559548	+	0.828798i	$0.310975\pi$
$318$	−1.45769e9	−2.54196
$319$	2.76976e8	0.477722
$320$	−1.29202e8	−0.220417
$321$	−1.45121e9	−2.44884
$322$	−3.49550e8	−0.583464
$323$	−2.68830e8	−0.443883
$324$	8.94591e8	1.46122
$325$	−1.21556e9	−1.96419
$326$	3.14155e7	0.0502207
$327$	3.21180e8	0.507962
$328$	−6.84082e7	−0.107041
$329$	1.40049e9	2.16818
$330$	5.01090e8	0.767569
$331$	7.05974e8	1.07002	0.535009	−	0.844847i	$-0.320308\pi$
$331$	7.05974e8	1.07002	0.535009	+	0.844847i	$0.320308\pi$
$332$	5.47802e8	0.821562
$333$	−3.03349e9	−4.50182
$334$	−4.45057e8	−0.653586
$335$	−1.84329e9	−2.67879
$336$	−4.38607e8	−0.630794
$337$	1.21373e9	1.72750	0.863752	−	0.503918i	$-0.168108\pi$
$337$	1.21373e9	1.72750	0.863752	+	0.503918i	$0.168108\pi$
$338$	6.67103e7	0.0939689
$339$	1.37932e9	1.92295
$340$	6.52818e8	0.900774
$341$	1.84323e8	0.251733
$342$	−5.77859e8	−0.781143
$343$	−2.03304e8	−0.272030
$344$	7.62018e7	0.100928
$345$	1.55816e9	2.04289
$346$	8.41961e8	1.09276
$347$	3.64471e8	0.468285	0.234142	−	0.972202i	$-0.424772\pi$
$347$	3.64471e8	0.468285	0.234142	+	0.972202i	$0.424772\pi$
$348$	1.08070e9	1.37460
$349$	6.64302e8	0.836521	0.418261	−	0.908327i	$-0.362640\pi$
$349$	6.64302e8	0.836521	0.418261	+	0.908327i	$0.362640\pi$
$350$	−1.60381e9	−1.99947
$351$	2.19051e9	2.70378
$352$	4.73105e7	0.0578174
$353$	−9.17247e8	−1.10988	−0.554938	−	0.831892i	$-0.687258\pi$
$353$	−9.17247e8	−1.10988	−0.554938	+	0.831892i	$0.687258\pi$
$354$	−3.26697e8	−0.391411
$355$	7.00253e8	0.830722
$356$	3.41220e8	0.400830
$357$	2.21614e9	2.57786
$358$	−8.45294e8	−0.973682
$359$	2.74949e8	0.313633	0.156817	−	0.987628i	$-0.449877\pi$
$359$	2.74949e8	0.313633	0.156817	+	0.987628i	$0.449877\pi$
$360$	1.40325e9	1.58517
$361$	−7.25143e8	−0.811238
$362$	−2.77247e8	−0.307176
$363$	1.53180e9	1.68085
$364$	−5.74308e8	−0.624151
$365$	−2.17148e8	−0.233739
$366$	2.40285e9	2.56179
$367$	4.28831e8	0.452850	0.226425	−	0.974029i	$-0.427296\pi$
$367$	4.28831e8	0.452850	0.226425	+	0.974029i	$0.427296\pi$
$368$	1.47114e8	0.153881
$369$	7.42976e8	0.769808
$370$	−2.15093e9	−2.20760
$371$	−2.51832e9	−2.56037
$372$	7.19185e8	0.724337
$373$	−5.59787e8	−0.558524	−0.279262	−	0.960215i	$-0.590090\pi$
$373$	−5.59787e8	−0.558524	−0.279262	+	0.960215i	$0.590090\pi$
$374$	−2.39045e8	−0.236282
$375$	3.75988e9	3.68184
$376$	−5.89419e8	−0.571829
$377$	1.41505e9	1.36012
$378$	2.89017e9	2.75234
$379$	1.03619e9	0.977690	0.488845	−	0.872371i	$-0.337418\pi$
$379$	1.03619e9	0.977690	0.488845	+	0.872371i	$0.337418\pi$
$380$	−4.09736e8	−0.383056
$381$	−4.86205e8	−0.450383
$382$	1.93338e8	0.177458
$383$	1.72413e8	0.156810	0.0784051	−	0.996922i	$-0.475017\pi$
$383$	1.72413e8	0.156810	0.0784051	+	0.996922i	$0.475017\pi$
$384$	1.84595e8	0.166364
$385$	8.65692e8	0.773127
$386$	9.13149e8	0.808139
$387$	−8.27621e8	−0.725844
$388$	−2.30096e7	−0.0199985
$389$	4.90152e8	0.422189	0.211095	−	0.977466i	$-0.432297\pi$
$389$	4.90152e8	0.422189	0.211095	+	0.977466i	$0.432297\pi$
$390$	2.56004e9	2.18535
$391$	−7.43320e8	−0.628865
$392$	−3.36090e8	−0.281809
$393$	−1.18073e9	−0.981242
$394$	1.08117e9	0.890549
$395$	−1.13669e9	−0.928013
$396$	−5.13836e8	−0.415807
$397$	−5.29097e8	−0.424394	−0.212197	−	0.977227i	$-0.568062\pi$
$397$	−5.29097e8	−0.424394	−0.212197	+	0.977227i	$0.568062\pi$
$398$	−7.19619e8	−0.572153
$399$	−1.39095e9	−1.09624
$400$	6.74990e8	0.527336
$401$	−6.62533e8	−0.513100	−0.256550	−	0.966531i	$-0.582586\pi$
$401$	−6.62533e8	−0.513100	−0.256550	+	0.966531i	$0.582586\pi$
$402$	2.63357e9	2.02187
$403$	9.41695e8	0.716709
$404$	−7.31216e8	−0.551710
$405$	−6.88928e9	−5.15325
$406$	1.86703e9	1.38455
$407$	7.87616e8	0.579074
$408$	−9.32699e8	−0.679878
$409$	9.25060e8	0.668557	0.334278	−	0.942474i	$-0.391507\pi$
$409$	9.25060e8	0.668557	0.334278	+	0.942474i	$0.391507\pi$
$410$	5.26814e8	0.377497
$411$	3.84936e9	2.73490
$412$	−1.13757e8	−0.0801381
$413$	−5.64407e8	−0.394246
$414$	−1.59779e9	−1.10667
$415$	−4.21865e9	−2.89737
$416$	2.41706e8	0.164612
$417$	−3.23554e9	−2.18510
$418$	1.50035e8	0.100479
$419$	−2.16950e9	−1.44082	−0.720411	−	0.693547i	$-0.756047\pi$
$419$	−2.16950e9	−1.44082	−0.720411	+	0.693547i	$0.756047\pi$
$420$	3.37773e9	2.22460
$421$	−2.53024e9	−1.65263	−0.826314	−	0.563210i	$-0.809566\pi$
$421$	−2.53024e9	−1.65263	−0.826314	+	0.563210i	$0.809566\pi$
$422$	1.15782e9	0.749976
$423$	6.40163e9	4.11244
$424$	1.05988e9	0.675266
$425$	−3.41051e9	−2.15506
$426$	−1.00047e9	−0.627005
$427$	4.15120e9	2.58034
$428$	1.05516e9	0.650529
$429$	−9.37422e8	−0.573238
$430$	−5.86833e8	−0.355938
$431$	−2.79567e9	−1.68196	−0.840979	−	0.541068i	$-0.818020\pi$
$431$	−2.79567e9	−1.68196	−0.840979	+	0.541068i	$0.818020\pi$
$432$	−1.21637e9	−0.725895
$433$	2.94375e9	1.74258	0.871291	−	0.490767i	$-0.163283\pi$
$433$	2.94375e9	1.74258	0.871291	+	0.490767i	$0.163283\pi$
$434$	1.24248e9	0.729582
$435$	−8.32248e9	−4.84775
$436$	−2.33528e8	−0.134939
$437$	4.66539e8	0.267426
$438$	3.10246e8	0.176419
$439$	8.37467e8	0.472435	0.236217	−	0.971700i	$-0.424092\pi$
$439$	8.37467e8	0.472435	0.236217	+	0.971700i	$0.424092\pi$
$440$	−3.64340e8	−0.203903
$441$	3.65025e9	2.02669
$442$	−1.22127e9	−0.672718
$443$	1.57930e9	0.863079	0.431539	−	0.902094i	$-0.357971\pi$
$443$	1.57930e9	0.863079	0.431539	+	0.902094i	$0.357971\pi$
$444$	3.07309e9	1.66623
$445$	−2.62775e9	−1.41359
$446$	6.62852e8	0.353789
$447$	−4.13515e9	−2.18985
$448$	3.18909e8	0.167569
$449$	6.12101e8	0.319125	0.159562	−	0.987188i	$-0.448992\pi$
$449$	6.12101e8	0.319125	0.159562	+	0.987188i	$0.448992\pi$
$450$	−7.33101e9	−3.79245
$451$	−1.92906e8	−0.0990212
$452$	−1.00290e9	−0.510826
$453$	−2.80835e9	−1.41941
$454$	7.75955e8	0.389171
$455$	4.42277e9	2.20117
$456$	5.85402e8	0.289119
$457$	−2.47564e8	−0.121334	−0.0606669	−	0.998158i	$-0.519323\pi$
$457$	−2.47564e8	−0.121334	−0.0606669	+	0.998158i	$0.519323\pi$
$458$	−2.71566e9	−1.32083
$459$	6.14596e9	2.96651
$460$	−1.13293e9	−0.542688
$461$	2.56202e9	1.21795	0.608975	−	0.793190i	$-0.291581\pi$
$461$	2.56202e9	1.21795	0.608975	+	0.793190i	$0.291581\pi$
$462$	−1.23684e9	−0.583534
$463$	7.67205e8	0.359235	0.179617	−	0.983737i	$-0.442514\pi$
$463$	7.67205e8	0.359235	0.179617	+	0.983737i	$0.442514\pi$
$464$	−7.85768e8	−0.365159
$465$	−5.53848e9	−2.55449
$466$	1.21199e9	0.554814
$467$	−2.76961e9	−1.25837	−0.629186	−	0.777255i	$-0.716612\pi$
$467$	−2.76961e9	−1.25837	−0.629186	+	0.777255i	$0.716612\pi$
$468$	−2.62515e9	−1.18384
$469$	4.54979e9	2.03651
$470$	4.53914e9	2.01665
$471$	−7.81666e9	−3.44706
$472$	2.37539e8	0.103977
$473$	2.14883e8	0.0933660
$474$	1.62403e9	0.700437
$475$	2.14058e9	0.916441
$476$	−1.61135e9	−0.684801
$477$	−1.15112e10	−4.85632
$478$	−1.45720e9	−0.610269
$479$	−5.87045e8	−0.244060	−0.122030	−	0.992526i	$-0.538940\pi$
$479$	−5.87045e8	−0.244060	−0.122030	+	0.992526i	$0.538940\pi$
$480$	−1.42157e9	−0.586711
$481$	4.02388e9	1.64868
$482$	−2.60383e9	−1.05913
$483$	−3.84599e9	−1.55308
$484$	−1.11377e9	−0.446514
$485$	1.77198e8	0.0705280
$486$	4.64718e9	1.83638
$487$	−1.98955e9	−0.780553	−0.390277	−	0.920698i	$-0.627621\pi$
$487$	−1.98955e9	−0.780553	−0.390277	+	0.920698i	$0.627621\pi$
$488$	−1.74710e9	−0.680532
$489$	3.45655e8	0.133679
$490$	2.58825e9	0.993846
$491$	5.36482e8	0.204536	0.102268	−	0.994757i	$-0.467390\pi$
$491$	5.36482e8	0.204536	0.102268	+	0.994757i	$0.467390\pi$
$492$	−7.52674e8	−0.284924
$493$	3.97024e9	1.49229
$494$	7.66520e8	0.286074
$495$	3.95707e9	1.46641
$496$	−5.22916e8	−0.192418
$497$	−1.72843e9	−0.631545
$498$	6.02730e9	2.18685
$499$	4.28919e9	1.54534	0.772669	−	0.634809i	$-0.218921\pi$
$499$	4.28919e9	1.54534	0.772669	+	0.634809i	$0.218921\pi$
$500$	−2.73379e9	−0.978071
$501$	−4.89682e9	−1.73973
$502$	4.93188e8	0.174000
$503$	1.62102e9	0.567936	0.283968	−	0.958834i	$-0.408349\pi$
$503$	1.62102e9	0.567936	0.283968	+	0.958834i	$0.408349\pi$
$504$	−3.46364e9	−1.20511
$505$	5.63112e9	1.94570
$506$	4.14850e8	0.142352
$507$	7.33992e8	0.250129
$508$	3.53517e8	0.119643
$509$	−1.58823e9	−0.533826	−0.266913	−	0.963721i	$-0.586004\pi$
$509$	−1.58823e9	−0.533826	−0.266913	+	0.963721i	$0.586004\pi$
$510$	7.18275e9	2.39770
$511$	5.35986e8	0.177697
$512$	−1.34218e8	−0.0441942
$513$	−3.85747e9	−1.26151
$514$	−1.49796e9	−0.486552
$515$	8.76049e8	0.282620
$516$	8.38424e8	0.268652
$517$	−1.66212e9	−0.528987
$518$	5.30912e9	1.67830
$519$	9.26384e9	2.90874
$520$	−1.86139e9	−0.580532
$521$	−5.79817e9	−1.79622	−0.898109	−	0.439772i	$-0.855059\pi$
$521$	−5.79817e9	−1.79622	−0.898109	+	0.439772i	$0.855059\pi$
$522$	8.53417e9	2.62612
$523$	−3.48456e9	−1.06510	−0.532552	−	0.846397i	$-0.678767\pi$
$523$	−3.48456e9	−1.06510	−0.532552	+	0.846397i	$0.678767\pi$
$524$	8.58502e8	0.260664
$525$	−1.76463e10	−5.32225
$526$	−5.84142e8	−0.175012
$527$	2.64213e9	0.786353
$528$	5.20543e8	0.153900
$529$	−2.11484e9	−0.621129
$530$	−8.16215e9	−2.38144
$531$	−2.57990e9	−0.747776
$532$	1.01135e9	0.291213
$533$	−9.85545e8	−0.281924
$534$	3.75434e9	1.06694
$535$	−8.12586e9	−2.29420
$536$	−1.91485e9	−0.537104
$537$	−9.30051e9	−2.59177
$538$	−1.55721e8	−0.0431131
$539$	−9.47750e8	−0.260695
$540$	9.36734e9	2.55999
$541$	6.98788e9	1.89738	0.948692	−	0.316203i	$-0.102408\pi$
$541$	6.98788e9	1.89738	0.948692	+	0.316203i	$0.102408\pi$
$542$	−4.37223e9	−1.17952
$543$	−3.05046e9	−0.817648
$544$	6.78161e8	0.180608
$545$	1.79841e9	0.475884
$546$	−6.31893e9	−1.66138
$547$	−3.05827e8	−0.0798952	−0.0399476	−	0.999202i	$-0.512719\pi$
$547$	−3.05827e8	−0.0798952	−0.0399476	+	0.999202i	$0.512719\pi$
$548$	−2.79885e9	−0.726520
$549$	1.89751e10	4.89419
$550$	1.90342e9	0.487827
$551$	−2.49189e9	−0.634599
$552$	1.61865e9	0.409605
$553$	2.80570e9	0.705510
$554$	3.52329e8	0.0880369
$555$	−2.36660e10	−5.87624
$556$	2.35255e9	0.580466
$557$	−2.93501e8	−0.0719642	−0.0359821	−	0.999352i	$-0.511456\pi$
$557$	−2.93501e8	−0.0719642	−0.0359821	+	0.999352i	$0.511456\pi$
$558$	5.67935e9	1.38382
$559$	1.09783e9	0.265823
$560$	−2.45593e9	−0.590959
$561$	−2.63014e9	−0.628940
$562$	2.58148e9	0.613467
$563$	−1.69684e9	−0.400739	−0.200370	−	0.979720i	$-0.564214\pi$
$563$	−1.69684e9	−0.400739	−0.200370	+	0.979720i	$0.564214\pi$
$564$	−6.48519e9	−1.52211
$565$	7.72337e9	1.80151
$566$	1.73160e9	0.401411
$567$	1.70048e10	3.91769
$568$	7.27437e8	0.166562
$569$	−6.62911e9	−1.50856	−0.754279	−	0.656553i	$-0.772014\pi$
$569$	−6.62911e9	−1.50856	−0.754279	+	0.656553i	$0.772014\pi$
$570$	−4.50820e9	−1.01963
$571$	8.02130e7	0.0180309	0.00901547	−	0.999959i	$-0.497130\pi$
$571$	8.02130e7	0.0180309	0.00901547	+	0.999959i	$0.497130\pi$
$572$	6.81595e8	0.152279
$573$	2.12724e9	0.472362
$574$	−1.30033e9	−0.286987
$575$	5.91876e9	1.29835
$576$	1.45773e9	0.317832
$577$	−3.17118e9	−0.687235	−0.343617	−	0.939110i	$-0.611652\pi$
$577$	−3.17118e9	−0.687235	−0.343617	+	0.939110i	$0.611652\pi$
$578$	−1.43826e8	−0.0309807
$579$	1.00471e10	2.15113
$580$	6.05123e9	1.28779
$581$	1.04129e10	2.20269
$582$	−2.53167e8	−0.0532325
$583$	2.98877e9	0.624674
$584$	−2.25578e8	−0.0468653
$585$	2.02164e10	4.17502
$586$	−1.11326e9	−0.228536
$587$	6.78270e9	1.38411	0.692053	−	0.721847i	$-0.256707\pi$
$587$	6.78270e9	1.38411	0.692053	+	0.721847i	$0.256707\pi$
$588$	−3.69790e9	−0.750126
$589$	−1.65832e9	−0.334398
$590$	−1.82930e9	−0.366693
$591$	1.18958e10	2.37049
$592$	−2.23443e9	−0.442630
$593$	3.49852e9	0.688958	0.344479	−	0.938794i	$-0.388056\pi$
$593$	3.49852e9	0.688958	0.344479	+	0.938794i	$0.388056\pi$
$594$	−3.43009e9	−0.671510
$595$	1.24090e10	2.41507
$596$	3.00665e9	0.581729
$597$	−7.91775e9	−1.52297
$598$	2.11944e9	0.405291
$599$	1.88586e9	0.358521	0.179261	−	0.983802i	$-0.442630\pi$
$599$	1.88586e9	0.358521	0.179261	+	0.983802i	$0.442630\pi$
$600$	7.42670e9	1.40368
$601$	−8.38929e9	−1.57639	−0.788196	−	0.615424i	$-0.788985\pi$
$601$	−8.38929e9	−1.57639	−0.788196	+	0.615424i	$0.788985\pi$
$602$	1.44848e9	0.270597
$603$	2.07971e10	3.86270
$604$	2.04194e9	0.377062
$605$	8.57716e9	1.57471
$606$	−8.04535e9	−1.46856
$607$	−6.82124e9	−1.23795	−0.618975	−	0.785411i	$-0.712452\pi$
$607$	−6.82124e9	−1.23795	−0.618975	+	0.785411i	$0.712452\pi$
$608$	−4.25643e8	−0.0768038
$609$	2.05423e10	3.68544
$610$	1.34545e10	2.40001
$611$	−8.49165e9	−1.50608
$612$	−7.36545e9	−1.29888
$613$	3.88964e9	0.682021	0.341010	−	0.940059i	$-0.389231\pi$
$613$	3.88964e9	0.682021	0.341010	+	0.940059i	$0.389231\pi$
$614$	1.72996e9	0.301611
$615$	5.79638e9	1.00483
$616$	8.99299e8	0.155014
$617$	−8.84775e9	−1.51647	−0.758237	−	0.651979i	$-0.773939\pi$
$617$	−8.84775e9	−1.51647	−0.758237	+	0.651979i	$0.773939\pi$
$618$	−1.25164e9	−0.213314
$619$	−1.05785e10	−1.79270	−0.896352	−	0.443342i	$-0.853793\pi$
$619$	−1.05785e10	−1.79270	−0.896352	+	0.443342i	$0.853793\pi$
$620$	4.02700e9	0.678594
$621$	−1.06660e10	−1.78723
$622$	−5.50124e8	−0.0916630
$623$	6.48607e9	1.07467
$624$	2.65942e9	0.438168
$625$	8.17862e9	1.33998
$626$	−5.11742e9	−0.833759
$627$	1.65079e9	0.267458
$628$	5.68346e9	0.915701
$629$	1.12899e10	1.80889
$630$	2.66736e10	4.25001
$631$	−6.53588e9	−1.03562	−0.517811	−	0.855495i	$-0.673253\pi$
$631$	−6.53588e9	−1.03562	−0.517811	+	0.855495i	$0.673253\pi$
$632$	−1.18082e9	−0.186069
$633$	1.27391e10	1.99631
$634$	−5.07768e9	−0.791321
$635$	−2.72245e9	−0.421941
$636$	1.16615e10	1.79744
$637$	−4.84200e9	−0.742226
$638$	−2.21581e9	−0.337800
$639$	−7.90064e9	−1.19787
$640$	1.03362e9	0.155858
$641$	8.51251e9	1.27660	0.638299	−	0.769788i	$-0.279638\pi$
$641$	8.51251e9	1.27660	0.638299	+	0.769788i	$0.279638\pi$
$642$	1.16096e10	1.73159
$643$	−2.20248e9	−0.326718	−0.163359	−	0.986567i	$-0.552233\pi$
$643$	−2.20248e9	−0.326718	−0.163359	+	0.986567i	$0.552233\pi$
$644$	2.79640e9	0.412571
$645$	−6.45674e9	−0.947446
$646$	2.15064e9	0.313873
$647$	7.71884e9	1.12044	0.560218	−	0.828345i	$-0.310717\pi$
$647$	7.71884e9	1.12044	0.560218	+	0.828345i	$0.310717\pi$
$648$	−7.15673e9	−1.03324
$649$	6.69844e8	0.0961872
$650$	9.72446e9	1.38889
$651$	1.36706e10	1.94202
$652$	−2.51324e8	−0.0355114
$653$	−3.51568e9	−0.494098	−0.247049	−	0.969003i	$-0.579461\pi$
$653$	−3.51568e9	−0.494098	−0.247049	+	0.969003i	$0.579461\pi$
$654$	−2.56944e9	−0.359183
$655$	−6.61136e9	−0.919276
$656$	5.47266e8	0.0756893
$657$	2.44998e9	0.337042
$658$	−1.12039e10	−1.53313
$659$	−7.26535e8	−0.0988912	−0.0494456	−	0.998777i	$-0.515745\pi$
$659$	−7.26535e8	−0.0988912	−0.0494456	+	0.998777i	$0.515745\pi$
$660$	−4.00872e9	−0.542753
$661$	−2.77604e9	−0.373871	−0.186935	−	0.982372i	$-0.559855\pi$
$661$	−2.77604e9	−0.373871	−0.186935	+	0.982372i	$0.559855\pi$
$662$	−5.64779e9	−0.756617
$663$	−1.34372e10	−1.79066
$664$	−4.38242e9	−0.580932
$665$	−7.78845e9	−1.02701
$666$	2.42680e10	3.18327
$667$	−6.89014e9	−0.899057
$668$	3.56045e9	0.462155
$669$	7.29315e9	0.941725
$670$	1.47464e10	1.89419
$671$	−4.92669e9	−0.629545
$672$	3.50885e9	0.446039
$673$	−1.09520e10	−1.38498	−0.692489	−	0.721429i	$-0.743486\pi$
$673$	−1.09520e10	−1.38498	−0.692489	+	0.721429i	$0.743486\pi$
$674$	−9.70987e9	−1.22153
$675$	−4.89378e10	−6.12465
$676$	−5.33682e8	−0.0664461
$677$	6.24392e9	0.773388	0.386694	−	0.922208i	$-0.373617\pi$
$677$	6.24392e9	0.773388	0.386694	+	0.922208i	$0.373617\pi$
$678$	−1.10346e10	−1.35973
$679$	−4.37376e8	−0.0536180
$680$	−5.22254e9	−0.636943
$681$	8.53759e9	1.03591
$682$	−1.47458e9	−0.178002
$683$	1.04305e10	1.25265	0.626326	−	0.779561i	$-0.284558\pi$
$683$	1.04305e10	1.25265	0.626326	+	0.779561i	$0.284558\pi$
$684$	4.62287e9	0.552351
$685$	2.15540e10	2.56219
$686$	1.62643e9	0.192354
$687$	−2.98795e10	−3.51581
$688$	−6.09614e8	−0.0713667
$689$	1.52695e10	1.77851
$690$	−1.24653e10	−1.44454
$691$	1.19753e9	0.138075	0.0690373	−	0.997614i	$-0.478007\pi$
$691$	1.19753e9	0.138075	0.0690373	+	0.997614i	$0.478007\pi$
$692$	−6.73569e9	−0.772700
$693$	−9.76722e9	−1.11482
$694$	−2.91577e9	−0.331127
$695$	−1.81171e10	−2.04711
$696$	−8.64557e9	−0.971989
$697$	−2.76516e9	−0.309319
$698$	−5.31442e9	−0.591510
$699$	1.33351e10	1.47682
$700$	1.28305e10	1.41384
$701$	6.76271e9	0.741495	0.370747	−	0.928734i	$-0.379102\pi$
$701$	6.76271e9	0.741495	0.370747	+	0.928734i	$0.379102\pi$
$702$	−1.75241e10	−1.91186
$703$	−7.08601e9	−0.769233
$704$	−3.78484e8	−0.0408831
$705$	4.99427e10	5.36797
$706$	7.33797e9	0.784801
$707$	−1.38993e10	−1.47919
$708$	2.61357e9	0.276770
$709$	−1.22972e10	−1.29582	−0.647908	−	0.761718i	$-0.724356\pi$
$709$	−1.22972e10	−1.29582	−0.647908	+	0.761718i	$0.724356\pi$
$710$	−5.60202e9	−0.587409
$711$	1.28248e10	1.33816
$712$	−2.72976e9	−0.283429
$713$	−4.58527e9	−0.473753
$714$	−1.77292e10	−1.82282
$715$	−5.24899e9	−0.537037
$716$	6.76235e9	0.688497
$717$	−1.60331e10	−1.62443
$718$	−2.19959e9	−0.221772
$719$	−1.16208e10	−1.16596	−0.582981	−	0.812486i	$-0.698114\pi$
$719$	−1.16208e10	−1.16596	−0.582981	+	0.812486i	$0.698114\pi$
$720$	−1.12260e10	−1.12089
$721$	−2.16235e9	−0.214858
$722$	5.80114e9	0.573632
$723$	−2.86492e10	−2.81921
$724$	2.21797e9	0.217206
$725$	−3.16134e10	−3.08098
$726$	−1.22544e10	−1.18854
$727$	1.00995e10	0.974834	0.487417	−	0.873169i	$-0.337939\pi$
$727$	1.00995e10	0.974834	0.487417	+	0.873169i	$0.337939\pi$
$728$	4.59446e9	0.441342
$729$	2.05617e10	1.96568
$730$	1.73719e9	0.165278
$731$	3.08019e9	0.291653
$732$	−1.92228e10	−1.81146
$733$	−9.18647e9	−0.861559	−0.430779	−	0.902457i	$-0.641761\pi$
$733$	−9.18647e9	−0.861559	−0.430779	+	0.902457i	$0.641761\pi$
$734$	−3.43065e9	−0.320214
$735$	2.84777e10	2.64544
$736$	−1.17691e9	−0.108810
$737$	−5.39975e9	−0.496864
$738$	−5.94381e9	−0.544337
$739$	1.13863e10	1.03783	0.518917	−	0.854824i	$-0.326335\pi$
$739$	1.13863e10	1.03783	0.518917	+	0.854824i	$0.326335\pi$
$740$	1.72074e10	1.56101
$741$	8.43378e9	0.761480
$742$	2.01466e10	1.81046
$743$	1.25954e10	1.12655	0.563274	−	0.826270i	$-0.309542\pi$
$743$	1.25954e10	1.12655	0.563274	+	0.826270i	$0.309542\pi$
$744$	−5.75348e9	−0.512183
$745$	−2.31543e10	−2.05156
$746$	4.47830e9	0.394936
$747$	4.75971e10	4.17790
$748$	1.91236e9	0.167076
$749$	2.00570e10	1.74413
$750$	−3.00791e10	−2.60345
$751$	8.64358e9	0.744653	0.372327	−	0.928102i	$-0.378560\pi$
$751$	8.64358e9	0.744653	0.372327	+	0.928102i	$0.378560\pi$
$752$	4.71535e9	0.404344
$753$	5.42640e9	0.463158
$754$	−1.13204e10	−0.961752
$755$	−1.57250e10	−1.32977
$756$	−2.31214e10	−1.94620
$757$	1.65823e9	0.138934	0.0694669	−	0.997584i	$-0.477870\pi$
$757$	1.65823e9	0.138934	0.0694669	+	0.997584i	$0.477870\pi$
$758$	−8.28950e9	−0.691331
$759$	4.56447e9	0.378917
$760$	3.27789e9	0.270861
$761$	−7.56528e9	−0.622270	−0.311135	−	0.950366i	$-0.600709\pi$
$761$	−7.56528e9	−0.622270	−0.311135	+	0.950366i	$0.600709\pi$
$762$	3.88964e9	0.318469
$763$	−4.43900e9	−0.361784
$764$	−1.54670e9	−0.125482
$765$	5.67216e10	4.58072
$766$	−1.37930e9	−0.110882
$767$	3.42219e9	0.273855
$768$	−1.47676e9	−0.117637
$769$	−9.38451e9	−0.744165	−0.372083	−	0.928200i	$-0.621356\pi$
$769$	−9.38451e9	−0.744165	−0.372083	+	0.928200i	$0.621356\pi$
$770$	−6.92554e9	−0.546684
$771$	−1.64816e10	−1.29512
$772$	−7.30519e9	−0.571441
$773$	−3.52203e9	−0.274262	−0.137131	−	0.990553i	$-0.543788\pi$
$773$	−3.52203e9	−0.274262	−0.137131	+	0.990553i	$0.543788\pi$
$774$	6.62097e9	0.513249
$775$	−2.10382e10	−1.62350
$776$	1.84076e8	0.0141411
$777$	5.84147e10	4.46733
$778$	−3.92122e9	−0.298533
$779$	1.73553e9	0.131538
$780$	−2.04803e10	−1.54527
$781$	2.05132e9	0.154083
$782$	5.94656e9	0.444674
$783$	5.69694e10	4.24107
$784$	2.68872e9	0.199269
$785$	−4.37685e10	−3.22937
$786$	9.44583e9	0.693843
$787$	−7.56382e8	−0.0553133	−0.0276567	−	0.999617i	$-0.508805\pi$
$787$	−7.56382e8	−0.0553133	−0.0276567	+	0.999617i	$0.508805\pi$
$788$	−8.64938e9	−0.629714
$789$	−6.42714e9	−0.465852
$790$	9.09356e9	0.656204
$791$	−1.90636e10	−1.36958
$792$	4.11069e9	0.294020
$793$	−2.51702e10	−1.79238
$794$	4.23278e9	0.300092
$795$	−8.98056e10	−6.33897
$796$	5.75696e9	0.404573
$797$	−1.21549e10	−0.850449	−0.425224	−	0.905088i	$-0.639805\pi$
$797$	−1.21549e10	−0.850449	−0.425224	+	0.905088i	$0.639805\pi$
$798$	1.11276e10	0.775158
$799$	−2.38252e10	−1.65243
$800$	−5.39992e9	−0.372883
$801$	2.96477e10	2.03835
$802$	5.30026e9	0.362817
$803$	−6.36114e8	−0.0433541
$804$	−2.10685e10	−1.42968
$805$	−2.15352e10	−1.45500
$806$	−7.53356e9	−0.506789
$807$	−1.71335e9	−0.114759
$808$	5.84973e9	0.390118
$809$	2.68446e10	1.78253	0.891267	−	0.453479i	$-0.149817\pi$
$809$	2.68446e10	1.78253	0.891267	+	0.453479i	$0.149817\pi$
$810$	5.51142e10	3.64390
$811$	1.04648e9	0.0688904	0.0344452	−	0.999407i	$-0.489034\pi$
$811$	1.04648e9	0.0688904	0.0344452	+	0.999407i	$0.489034\pi$
$812$	−1.49362e10	−0.979027
$813$	−4.81063e10	−3.13968
$814$	−6.30093e9	−0.409467
$815$	1.93546e9	0.125237
$816$	7.46159e9	0.480746
$817$	−1.93326e9	−0.124026
$818$	−7.40048e9	−0.472741
$819$	−4.99001e10	−3.17401
$820$	−4.21451e9	−0.266931
$821$	1.64524e10	1.03759	0.518796	−	0.854898i	$-0.326380\pi$
$821$	1.64524e10	1.03759	0.518796	+	0.854898i	$0.326380\pi$
$822$	−3.07949e10	−1.93387
$823$	8.77217e9	0.548539	0.274270	−	0.961653i	$-0.411564\pi$
$823$	8.77217e9	0.548539	0.274270	+	0.961653i	$0.411564\pi$
$824$	9.10058e8	0.0566662
$825$	2.09428e10	1.29851
$826$	4.51525e9	0.278774
$827$	−2.81393e10	−1.72999	−0.864995	−	0.501780i	$-0.832679\pi$
$827$	−2.81393e10	−1.72999	−0.864995	+	0.501780i	$0.832679\pi$
$828$	1.27823e10	0.782535
$829$	9.74747e9	0.594225	0.297113	−	0.954842i	$-0.403976\pi$
$829$	9.74747e9	0.594225	0.297113	+	0.954842i	$0.403976\pi$
$830$	3.37492e10	2.04875
$831$	3.87657e9	0.234339
$832$	−1.93365e9	−0.116398
$833$	−1.35853e10	−0.814350
$834$	2.58844e10	1.54510
$835$	−2.74192e10	−1.62987
$836$	−1.20028e9	−0.0710495
$837$	3.79122e10	2.23481
$838$	1.73560e10	1.01881
$839$	1.63736e10	0.957147	0.478573	−	0.878048i	$-0.341154\pi$
$839$	1.63736e10	0.957147	0.478573	+	0.878048i	$0.341154\pi$
$840$	−2.70218e10	−1.57303
$841$	1.95519e10	1.13345
$842$	2.02420e10	1.16858
$843$	2.84032e10	1.63294
$844$	−9.26256e9	−0.530313
$845$	4.10991e9	0.234333
$846$	−5.12130e10	−2.90793
$847$	−2.11710e10	−1.19715
$848$	−8.47901e9	−0.477485
$849$	1.90522e10	1.06849
$850$	2.72841e10	1.52385
$851$	−1.95929e10	−1.08980
$852$	8.00377e9	0.443359
$853$	−5.66702e9	−0.312632	−0.156316	−	0.987707i	$-0.549962\pi$
$853$	−5.66702e9	−0.312632	−0.156316	+	0.987707i	$0.549962\pi$
$854$	−3.32096e10	−1.82457
$855$	−3.56009e10	−1.94796
$856$	−8.44131e9	−0.459993
$857$	−1.78522e10	−0.968853	−0.484427	−	0.874832i	$-0.660972\pi$
$857$	−1.78522e10	−0.968853	−0.484427	+	0.874832i	$0.660972\pi$
$858$	7.49938e9	0.405340
$859$	−2.90647e10	−1.56455	−0.782274	−	0.622934i	$-0.785941\pi$
$859$	−2.90647e10	−1.56455	−0.782274	+	0.622934i	$0.785941\pi$
$860$	4.69466e9	0.251686
$861$	−1.43072e10	−0.763911
$862$	2.23653e10	1.18932
$863$	−8.87461e9	−0.470015	−0.235007	−	0.971994i	$-0.575511\pi$
$863$	−8.87461e9	−0.470015	−0.235007	+	0.971994i	$0.575511\pi$
$864$	9.73099e9	0.513286
$865$	5.18718e10	2.72505
$866$	−2.35500e10	−1.23219
$867$	−1.58248e9	−0.0824651
$868$	−9.93981e9	−0.515893
$869$	−3.32983e9	−0.172129
$870$	6.65799e10	3.42788
$871$	−2.75870e10	−1.41462
$872$	1.86822e9	0.0954160
$873$	−1.99924e9	−0.101699
$874$	−3.73231e9	−0.189099
$875$	−5.19651e10	−2.62231
$876$	−2.48197e9	−0.124747
$877$	2.64332e10	1.32328	0.661638	−	0.749823i	$-0.269861\pi$
$877$	2.64332e10	1.32328	0.661638	+	0.749823i	$0.269861\pi$
$878$	−6.69973e9	−0.334062
$879$	−1.22489e10	−0.608324
$880$	2.91472e9	0.144181
$881$	−4.25046e9	−0.209421	−0.104711	−	0.994503i	$-0.533392\pi$
$881$	−4.25046e9	−0.209421	−0.104711	+	0.994503i	$0.533392\pi$
$882$	−2.92020e10	−1.43309
$883$	−3.54534e10	−1.73299	−0.866494	−	0.499188i	$-0.833632\pi$
$883$	−3.54534e10	−1.73299	−0.866494	+	0.499188i	$0.833632\pi$
$884$	9.77014e9	0.475683
$885$	−2.01272e10	−0.976074
$886$	−1.26344e10	−0.610289
$887$	−2.11585e10	−1.01801	−0.509006	−	0.860763i	$-0.669987\pi$
$887$	−2.11585e10	−1.01801	−0.509006	+	0.860763i	$0.669987\pi$
$888$	−2.45847e10	−1.17820
$889$	6.71980e9	0.320775
$890$	2.10220e10	0.999561
$891$	−2.01814e10	−0.955829
$892$	−5.30281e9	−0.250167
$893$	1.49537e10	0.702698
$894$	3.30812e10	1.54846
$895$	−5.20771e10	−2.42810
$896$	−2.55127e9	−0.118489
$897$	2.33196e10	1.07881
$898$	−4.89681e9	−0.225655
$899$	2.44910e10	1.12421
$900$	5.86481e10	2.68167
$901$	4.28418e10	1.95133
$902$	1.54325e9	0.0700186
$903$	1.59371e10	0.720283
$904$	8.02320e9	0.361209
$905$	−1.70807e10	−0.766013
$906$	2.24668e10	1.00367
$907$	−4.33173e10	−1.92768	−0.963842	−	0.266474i	$-0.914141\pi$
$907$	−4.33173e10	−1.92768	−0.963842	+	0.266474i	$0.914141\pi$
$908$	−6.20764e9	−0.275186
$909$	−6.35334e10	−2.80562
$910$	−3.53821e10	−1.55646
$911$	2.50022e10	1.09563	0.547814	−	0.836600i	$-0.315460\pi$
$911$	2.50022e10	1.09563	0.547814	+	0.836600i	$0.315460\pi$
$912$	−4.68321e9	−0.204438
$913$	−1.23581e10	−0.537408
$914$	1.98052e9	0.0857959
$915$	1.48036e11	6.38840
$916$	2.17252e10	0.933965
$917$	1.63188e10	0.698868
$918$	−4.91677e10	−2.09764
$919$	−3.83511e10	−1.62995	−0.814974	−	0.579497i	$-0.803249\pi$
$919$	−3.83511e10	−1.62995	−0.814974	+	0.579497i	$0.803249\pi$
$920$	9.06343e9	0.383738
$921$	1.90343e10	0.802836
$922$	−2.04962e10	−0.861220
$923$	1.04801e10	0.438690
$924$	9.89471e9	0.412621
$925$	−8.98967e10	−3.73463
$926$	−6.13764e9	−0.254017
$927$	−9.88407e9	−0.407527
$928$	6.28615e9	0.258206
$929$	−8.93240e9	−0.365522	−0.182761	−	0.983157i	$-0.558503\pi$
$929$	−8.93240e9	−0.365522	−0.182761	+	0.983157i	$0.558503\pi$
$930$	4.43078e10	1.80630
$931$	8.52670e9	0.346304
$932$	−9.69590e9	−0.392313
$933$	−6.05285e9	−0.243991
$934$	2.21569e10	0.889804
$935$	−1.47272e10	−0.589222
$936$	2.10012e10	0.837104
$937$	2.53768e8	0.0100774	0.00503869	−	0.999987i	$-0.498396\pi$
$937$	2.53768e8	0.0100774	0.00503869	+	0.999987i	$0.498396\pi$
$938$	−3.63984e10	−1.44003
$939$	−5.63054e10	−2.21932
$940$	−3.63131e10	−1.42599
$941$	1.82576e9	0.0714300	0.0357150	−	0.999362i	$-0.488629\pi$
$941$	1.82576e9	0.0714300	0.0357150	+	0.999362i	$0.488629\pi$
$942$	6.25333e10	2.43744
$943$	4.79879e9	0.186355
$944$	−1.90032e9	−0.0735231
$945$	1.78059e11	6.86359
$946$	−1.71907e9	−0.0660198
$947$	2.92107e10	1.11768	0.558839	−	0.829276i	$-0.311247\pi$
$947$	2.92107e10	1.11768	0.558839	+	0.829276i	$0.311247\pi$
$948$	−1.29922e10	−0.495284
$949$	−3.24986e9	−0.123434
$950$	−1.71247e10	−0.648022
$951$	−5.58681e10	−2.10636
$952$	1.28908e10	0.484228
$953$	1.67736e8	0.00627772	0.00313886	−	0.999995i	$-0.499001\pi$
$953$	1.67736e8	0.00627772	0.00313886	+	0.999995i	$0.499001\pi$
$954$	9.20899e10	3.43394
$955$	1.19112e10	0.442532
$956$	1.16576e10	0.431526
$957$	−2.43799e10	−0.899166
$958$	4.69636e9	0.172577
$959$	−5.32017e10	−1.94787
$960$	1.13726e10	0.414867
$961$	−1.12143e10	−0.407604
$962$	−3.21910e10	−1.16579
$963$	9.16804e10	3.30814
$964$	2.08307e10	0.748916
$965$	5.62576e10	2.01528
$966$	3.07679e10	1.09819
$967$	1.51863e10	0.540080	0.270040	−	0.962849i	$-0.412963\pi$
$967$	1.51863e10	0.540080	0.270040	+	0.962849i	$0.412963\pi$
$968$	8.91013e9	0.315733
$969$	2.36628e10	0.835475
$970$	−1.41758e9	−0.0498708
$971$	4.65394e10	1.63137	0.815687	−	0.578494i	$-0.196359\pi$
$971$	4.65394e10	1.63137	0.815687	+	0.578494i	$0.196359\pi$
$972$	−3.71775e10	−1.29852
$973$	4.47182e10	1.55629
$974$	1.59164e10	0.551934
$975$	1.06995e11	3.69699
$976$	1.39768e10	0.481209
$977$	−4.67271e10	−1.60302	−0.801508	−	0.597984i	$-0.795969\pi$
$977$	−4.67271e10	−1.60302	−0.801508	+	0.597984i	$0.795969\pi$
$978$	−2.76524e9	−0.0945251
$979$	−7.69773e9	−0.262194
$980$	−2.07060e10	−0.702755
$981$	−2.02906e10	−0.686205
$982$	−4.29186e9	−0.144629
$983$	−4.51065e10	−1.51461	−0.757307	−	0.653059i	$-0.773485\pi$
$983$	−4.51065e10	−1.51461	−0.757307	+	0.653059i	$0.773485\pi$
$984$	6.02140e9	0.201472
$985$	6.66092e10	2.22079
$986$	−3.17620e10	−1.05521
$987$	−1.23273e11	−4.08093
$988$	−6.13216e9	−0.202285
$989$	−5.34550e9	−0.175712
$990$	−3.16566e10	−1.03691
$991$	−2.61054e10	−0.852064	−0.426032	−	0.904708i	$-0.640089\pi$
$991$	−2.61054e10	−0.852064	−0.426032	+	0.904708i	$0.640089\pi$
$992$	4.18333e9	0.136060
$993$	−6.21409e10	−2.01398
$994$	1.38274e10	0.446570
$995$	−4.43345e10	−1.42679
$996$	−4.82184e10	−1.54634
$997$	−4.41959e10	−1.41237	−0.706185	−	0.708027i	$-0.749585\pi$
$997$	−4.41959e10	−1.41237	−0.706185	+	0.708027i	$0.749585\pi$
$998$	−3.43135e10	−1.09272
$999$	1.62000e11	5.14084

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.8.a.c.1.1	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.8.a.c.1.1	✓	40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	538.a (trivial)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} -88.0215 q^{3} +64.0000 q^{4} -492.867 q^{5} +704.172 q^{6} +1216.54 q^{7} -512.000 q^{8} +5560.79 q^{9} +3942.93 q^{10} -1443.80 q^{11} -5633.38 q^{12} -7376.30 q^{13} -9732.32 q^{14} +43382.9 q^{15} +4096.00 q^{16} -20695.8 q^{17} -44486.3 q^{18} +12989.6 q^{19} -31543.5 q^{20} -107082. q^{21} +11550.4 q^{22} +35916.4 q^{23} +45067.0 q^{24} +164792. q^{25} +59010.4 q^{26} -296966. q^{27} +77858.6 q^{28} -191838. q^{29} -347063. q^{30} -127665. q^{31} -32768.0 q^{32} +127086. q^{33} +165567. q^{34} -599592. q^{35} +355891. q^{36} -545515. q^{37} -103917. q^{38} +649273. q^{39} +252348. q^{40} +133610. q^{41} +856654. q^{42} -148832. q^{43} -92403.4 q^{44} -2.74073e6 q^{45} -287331. q^{46} +1.15121e6 q^{47} -360536. q^{48} +656426. q^{49} -1.31834e6 q^{50} +1.82168e6 q^{51} -472083. q^{52} -2.07007e6 q^{53} +2.37573e6 q^{54} +711602. q^{55} -622868. q^{56} -1.14336e6 q^{57} +1.53470e6 q^{58} -463944. q^{59} +2.77650e6 q^{60} +3.41230e6 q^{61} +1.02132e6 q^{62} +6.76492e6 q^{63} +262144. q^{64} +3.63553e6 q^{65} -1.01669e6 q^{66} +3.73995e6 q^{67} -1.32453e6 q^{68} -3.16142e6 q^{69} +4.79673e6 q^{70} -1.42078e6 q^{71} -2.84713e6 q^{72} +440582. q^{73} +4.36412e6 q^{74} -1.45053e7 q^{75} +831333. q^{76} -1.75644e6 q^{77} -5.19418e6 q^{78} +2.30629e6 q^{79} -2.01878e6 q^{80} +1.39780e7 q^{81} -1.06888e6 q^{82} +8.55941e6 q^{83} -6.85323e6 q^{84} +1.02003e7 q^{85} +1.19065e6 q^{86} +1.68859e7 q^{87} +739227. q^{88} +5.33157e6 q^{89} +2.19258e7 q^{90} -8.97356e6 q^{91} +2.29865e6 q^{92} +1.12373e7 q^{93} -9.20967e6 q^{94} -6.40213e6 q^{95} +2.88429e6 q^{96} -359524. q^{97} -5.25141e6 q^{98} -8.02869e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 320 q^{2} - 109 q^{3} + 2560 q^{4} - 751 q^{5} + 872 q^{6} - 233 q^{7} - 20480 q^{8} + 29623 q^{9} + 6008 q^{10} - 12977 q^{11} - 6976 q^{12} - 4870 q^{13} + 1864 q^{14} - 9068 q^{15} + 163840 q^{16}+ \cdots + 9909340 q^{99}+O(q^{100}) \) 40 * q - 320 * q^2 - 109 * q^3 + 2560 * q^4 - 751 * q^5 + 872 * q^6 - 233 * q^7 - 20480 * q^8 + 29623 * q^9 + 6008 * q^10 - 12977 * q^11 - 6976 * q^12 - 4870 * q^13 + 1864 * q^14 - 9068 * q^15 + 163840 * q^16 - 37896 * q^17 - 236984 * q^18 + 36270 * q^19 - 48064 * q^20 - 39351 * q^21 + 103816 * q^22 - 254388 * q^23 + 55808 * q^24 + 621875 * q^25 + 38960 * q^26 - 314650 * q^27 - 14912 * q^28 - 77138 * q^29 + 72544 * q^30 - 170617 * q^31 - 1310720 * q^32 - 338481 * q^33 + 303168 * q^34 - 498065 * q^35 + 1895872 * q^36 - 432250 * q^37 - 290160 * q^38 - 237233 * q^39 + 384512 * q^40 - 739673 * q^41 + 314808 * q^42 - 949447 * q^43 - 830528 * q^44 - 889534 * q^45 + 2035104 * q^46 - 1712951 * q^47 - 446464 * q^48 + 5466815 * q^49 - 4975000 * q^50 - 1611137 * q^51 - 311680 * q^52 - 3150530 * q^53 + 2517200 * q^54 - 466659 * q^55 + 119296 * q^56 - 3495794 * q^57 + 617104 * q^58 - 4357669 * q^59 - 580352 * q^60 + 4667204 * q^61 + 1364936 * q^62 + 1730648 * q^63 + 10485760 * q^64 - 1915803 * q^65 + 2707848 * q^66 - 6921617 * q^67 - 2425344 * q^68 - 10298459 * q^69 + 3984520 * q^70 - 18615993 * q^71 - 15166976 * q^72 - 6531063 * q^73 + 3458000 * q^74 - 22172708 * q^75 + 2321280 * q^76 - 20594134 * q^77 + 1897864 * q^78 + 1641715 * q^79 - 3076096 * q^80 + 21032872 * q^81 + 5917384 * q^82 - 16336922 * q^83 - 2518464 * q^84 + 13126141 * q^85 + 7595576 * q^86 + 11928706 * q^87 + 6644224 * q^88 + 9041896 * q^89 + 7116272 * q^90 + 9867502 * q^91 - 16280832 * q^92 + 10660597 * q^93 + 13703608 * q^94 + 8580994 * q^95 + 3571712 * q^96 + 10979403 * q^97 - 43734520 * q^98 + 9909340 * q^99

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