LMFDB - Embedded newform 10.16.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,16,Mod(1,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	10.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:	$14.2693505100$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{239569}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 59892 $ x^2 - x - 59892
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-244.229$ of defining polynomial
Character	$\chi$	$=$	10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+128.000 q^{2} +3972.58 q^{3} +16384.0 q^{4} +78125.0 q^{5} +508490. q^{6} +1.57794e6 q^{7} +2.09715e6 q^{8} +1.43247e6 q^{9} +1.00000e7 q^{10} -2.98824e6 q^{11} +6.50867e7 q^{12} +4.92637e6 q^{13} +2.01976e8 q^{14} +3.10358e8 q^{15} +2.68435e8 q^{16} +6.45145e8 q^{17} +1.83357e8 q^{18} +2.41911e9 q^{19} +1.28000e9 q^{20} +6.26849e9 q^{21} -3.82495e8 q^{22} +2.33075e10 q^{23} +8.33110e9 q^{24} +6.10352e9 q^{25} +6.30575e8 q^{26} -5.13115e10 q^{27} +2.58530e10 q^{28} -1.80269e11 q^{29} +3.97258e10 q^{30} -2.85505e11 q^{31} +3.43597e10 q^{32} -1.18710e10 q^{33} +8.25786e10 q^{34} +1.23277e11 q^{35} +2.34697e10 q^{36} +1.04185e11 q^{37} +3.09646e11 q^{38} +1.95704e10 q^{39} +1.63840e11 q^{40} -1.28393e12 q^{41} +8.02367e11 q^{42} -5.11969e11 q^{43} -4.89593e10 q^{44} +1.11912e11 q^{45} +2.98336e12 q^{46} +5.22662e12 q^{47} +1.06638e12 q^{48} -2.25766e12 q^{49} +7.81250e11 q^{50} +2.56289e12 q^{51} +8.07136e10 q^{52} -1.39001e13 q^{53} -6.56788e12 q^{54} -2.33456e11 q^{55} +3.30918e12 q^{56} +9.61011e12 q^{57} -2.30744e13 q^{58} +9.11699e12 q^{59} +5.08490e12 q^{60} -1.50270e13 q^{61} -3.65446e13 q^{62} +2.26036e12 q^{63} +4.39805e12 q^{64} +3.84872e11 q^{65} -1.51949e12 q^{66} +2.18097e13 q^{67} +1.05701e13 q^{68} +9.25908e13 q^{69} +1.57794e13 q^{70} -6.45213e13 q^{71} +3.00412e12 q^{72} +9.76233e13 q^{73} +1.33356e13 q^{74} +2.42467e13 q^{75} +3.96347e13 q^{76} -4.71526e12 q^{77} +2.50501e12 q^{78} +2.35831e14 q^{79} +2.09715e13 q^{80} -2.24394e14 q^{81} -1.64343e14 q^{82} -4.13505e14 q^{83} +1.02703e14 q^{84} +5.04020e13 q^{85} -6.55320e13 q^{86} -7.16133e14 q^{87} -6.26679e12 q^{88} +5.45429e14 q^{89} +1.43247e13 q^{90} +7.77352e12 q^{91} +3.81870e14 q^{92} -1.13419e15 q^{93} +6.69007e14 q^{94} +1.88993e14 q^{95} +1.36497e14 q^{96} +4.71267e14 q^{97} -2.88981e14 q^{98} -4.28057e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 256 q^{2} - 1844 q^{3} + 32768 q^{4} + 156250 q^{5} - 236032 q^{6} - 984932 q^{7} + 4194304 q^{8} + 20916154 q^{9} + 20000000 q^{10} + 111552144 q^{11} - 30212096 q^{12} + 289313596 q^{13} - 126071296 q^{14}+ \cdots + 22\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q + 256 * q^2 - 1844 * q^3 + 32768 * q^4 + 156250 * q^5 - 236032 * q^6 - 984932 * q^7 + 4194304 * q^8 + 20916154 * q^9 + 20000000 * q^10 + 111552144 * q^11 - 30212096 * q^12 + 289313596 * q^13 - 126071296 * q^14 - 144062500 * q^15 + 536870912 * q^16 + 1421739348 * q^17 + 2677267712 * q^18 + 6159406120 * q^19 + 2560000000 * q^20 + 21175644704 * q^21 + 14278674432 * q^22 - 4330165884 * q^23 - 3867148288 * q^24 + 12207031250 * q^25 + 37032140288 * q^26 - 81178356680 * q^27 - 16137125888 * q^28 - 164295941940 * q^29 - 18440000000 * q^30 - 282710965016 * q^31 + 68719476736 * q^32 - 678104159568 * q^33 + 181982636544 * q^34 - 76947812500 * q^35 + 342690267136 * q^36 + 790105159228 * q^37 + 788403983360 * q^38 - 1634590297912 * q^39 + 327680000000 * q^40 - 374717265276 * q^41 + 2710482522112 * q^42 - 923824433204 * q^43 + 1827670327296 * q^44 + 1634074531250 * q^45 - 554261233152 * q^46 + 4796717212428 * q^47 - 494994980864 * q^48 - 436909177374 * q^49 + 1562500000000 * q^50 - 1954230185256 * q^51 + 4740113956864 * q^52 - 2768921292084 * q^53 - 10390829655040 * q^54 + 8715011250000 * q^55 - 2065552113664 * q^56 - 12145610545840 * q^57 - 21029880568320 * q^58 - 20737233989880 * q^59 - 2360320000000 * q^60 + 577887725164 * q^61 - 36187003522048 * q^62 - 47673833661364 * q^63 + 8796093022208 * q^64 + 22602624687500 * q^65 - 86797332424704 * q^66 + 86553258077668 * q^67 + 23293777477632 * q^68 + 253347375370848 * q^69 - 9849320000000 * q^70 + 73838906689464 * q^71 + 43864354193408 * q^72 + 39973727021476 * q^73 + 101133460381184 * q^74 - 11254882812500 * q^75 + 100915709870080 * q^76 - 298267692171504 * q^77 - 209227558132736 * q^78 + 421665304874800 * q^79 + 41943040000000 * q^80 - 330240444620318 * q^81 - 47963809955328 * q^82 - 721146660038964 * q^83 + 346941762830336 * q^84 + 111073386562500 * q^85 - 118249527450112 * q^86 - 809041723785720 * q^87 + 233941801893888 * q^88 + 363712836623220 * q^89 + 209161540000000 * q^90 - 721074767062936 * q^91 - 70945437843456 * q^92 - 1150443201950848 * q^93 + 613979803190784 * q^94 + 481203603125000 * q^95 - 63359357550592 * q^96 + 289030099396948 * q^97 - 55924374703872 * q^98 + 2227387596150288 * 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 $

$2$	128.000	0.707107
$2$	128.000	0.707107
$3$	3972.58	1.04873	0.524364	−	0.851494i	$-0.324303\pi$
$3$	3972.58	1.04873	0.524364	+	0.851494i	$0.324303\pi$
$4$	16384.0	0.500000
$5$	78125.0	0.447214
$5$	78125.0	0.447214
$6$	508490.	0.741563
$7$	1.57794e6	0.724195	0.362097	−	0.932140i	$-0.382061\pi$
$7$	1.57794e6	0.724195	0.362097	+	0.932140i	$0.382061\pi$
$8$	2.09715e6	0.353553
$9$	1.43247e6	0.0998316
$10$	1.00000e7	0.316228
$11$	−2.98824e6	−0.0462349	−0.0231175	−	0.999733i	$-0.507359\pi$
$11$	−2.98824e6	−0.0462349	−0.0231175	+	0.999733i	$0.507359\pi$
$12$	6.50867e7	0.524364
$13$	4.92637e6	0.0217747	0.0108873	−	0.999941i	$-0.496534\pi$
$13$	4.92637e6	0.0217747	0.0108873	+	0.999941i	$0.496534\pi$
$14$	2.01976e8	0.512083
$15$	3.10358e8	0.469006
$16$	2.68435e8	0.250000
$17$	6.45145e8	0.381321	0.190660	−	0.981656i	$-0.438937\pi$
$17$	6.45145e8	0.381321	0.190660	+	0.981656i	$0.438937\pi$
$18$	1.83357e8	0.0705916
$19$	2.41911e9	0.620874	0.310437	−	0.950594i	$-0.399525\pi$
$19$	2.41911e9	0.620874	0.310437	+	0.950594i	$0.399525\pi$
$20$	1.28000e9	0.223607
$21$	6.26849e9	0.759484
$22$	−3.82495e8	−0.0326930
$23$	2.33075e10	1.42737	0.713685	−	0.700467i	$-0.247025\pi$
$23$	2.33075e10	1.42737	0.713685	+	0.700467i	$0.247025\pi$
$24$	8.33110e9	0.370782
$25$	6.10352e9	0.200000
$26$	6.30575e8	0.0153970
$27$	−5.13115e10	−0.944032
$28$	2.58530e10	0.362097
$29$	−1.80269e11	−1.94060	−0.970300	−	0.241904i	$-0.922228\pi$
$29$	−1.80269e11	−1.94060	−0.970300	+	0.241904i	$0.922228\pi$
$30$	3.97258e10	0.331637
$31$	−2.85505e11	−1.86381	−0.931904	−	0.362706i	$-0.881853\pi$
$31$	−2.85505e11	−1.86381	−0.931904	+	0.362706i	$0.881853\pi$
$32$	3.43597e10	0.176777
$33$	−1.18710e10	−0.0484879
$34$	8.25786e10	0.269635
$35$	1.23277e11	0.323870
$36$	2.34697e10	0.0499158
$37$	1.04185e11	0.180422	0.0902112	−	0.995923i	$-0.471246\pi$
$37$	1.04185e11	0.180422	0.0902112	+	0.995923i	$0.471246\pi$
$38$	3.09646e11	0.439025
$39$	1.95704e10	0.0228357
$40$	1.63840e11	0.158114
$41$	−1.28393e12	−1.02958	−0.514792	−	0.857315i	$-0.672131\pi$
$41$	−1.28393e12	−1.02958	−0.514792	+	0.857315i	$0.672131\pi$
$42$	8.02367e11	0.537036
$43$	−5.11969e11	−0.287230	−0.143615	−	0.989634i	$-0.545873\pi$
$43$	−5.11969e11	−0.287230	−0.143615	+	0.989634i	$0.545873\pi$
$44$	−4.89593e10	−0.0231175
$45$	1.11912e11	0.0446460
$46$	2.98336e12	1.00930
$47$	5.22662e12	1.50483	0.752414	−	0.658690i	$-0.228889\pi$
$47$	5.22662e12	1.50483	0.752414	+	0.658690i	$0.228889\pi$
$48$	1.06638e12	0.262182
$49$	−2.25766e12	−0.475542
$50$	7.81250e11	0.141421
$51$	2.56289e12	0.399902
$52$	8.07136e10	0.0108873
$53$	−1.39001e13	−1.62536	−0.812680	−	0.582710i	$-0.801992\pi$
$53$	−1.39001e13	−1.62536	−0.812680	+	0.582710i	$0.801992\pi$
$54$	−6.56788e12	−0.667532
$55$	−2.33456e11	−0.0206769
$56$	3.30918e12	0.256042
$57$	9.61011e12	0.651129
$58$	−2.30744e13	−1.37221
$59$	9.11699e12	0.476938	0.238469	−	0.971150i	$-0.423355\pi$
$59$	9.11699e12	0.476938	0.238469	+	0.971150i	$0.423355\pi$
$60$	5.08490e12	0.234503
$61$	−1.50270e13	−0.612206	−0.306103	−	0.951998i	$-0.599025\pi$
$61$	−1.50270e13	−0.612206	−0.306103	+	0.951998i	$0.599025\pi$
$62$	−3.65446e13	−1.31791
$63$	2.26036e12	0.0722975
$64$	4.39805e12	0.125000
$65$	3.84872e11	0.00973793
$66$	−1.51949e12	−0.0342861
$67$	2.18097e13	0.439631	0.219816	−	0.975541i	$-0.429454\pi$
$67$	2.18097e13	0.439631	0.219816	+	0.975541i	$0.429454\pi$
$68$	1.05701e13	0.190660
$69$	9.25908e13	1.49692
$70$	1.57794e13	0.229011
$71$	−6.45213e13	−0.841909	−0.420955	−	0.907082i	$-0.638305\pi$
$71$	−6.45213e13	−0.841909	−0.420955	+	0.907082i	$0.638305\pi$
$72$	3.00412e12	0.0352958
$73$	9.76233e13	1.03427	0.517133	−	0.855905i	$-0.326999\pi$
$73$	9.76233e13	1.03427	0.517133	+	0.855905i	$0.326999\pi$
$74$	1.33356e13	0.127578
$75$	2.42467e13	0.209746
$76$	3.96347e13	0.310437
$77$	−4.71526e12	−0.0334831
$78$	2.50501e12	0.0161473
$79$	2.35831e14	1.38165	0.690823	−	0.723024i	$-0.257248\pi$
$79$	2.35831e14	1.38165	0.690823	+	0.723024i	$0.257248\pi$
$80$	2.09715e13	0.111803
$81$	−2.24394e14	−1.08987
$82$	−1.64343e14	−0.728026
$83$	−4.13505e14	−1.67261	−0.836305	−	0.548264i	$-0.815289\pi$
$83$	−4.13505e14	−1.67261	−0.836305	+	0.548264i	$0.815289\pi$
$84$	1.02703e14	0.379742
$85$	5.04020e13	0.170532
$86$	−6.55320e13	−0.203102
$87$	−7.16133e14	−2.03516
$88$	−6.26679e12	−0.0163465
$89$	5.45429e14	1.30711	0.653556	−	0.756878i	$-0.273276\pi$
$89$	5.45429e14	1.30711	0.653556	+	0.756878i	$0.273276\pi$
$90$	1.43247e13	0.0315695
$91$	7.77352e12	0.0157691
$92$	3.81870e14	0.713685
$93$	−1.13419e15	−1.95463
$94$	6.69007e14	1.06407
$95$	1.88993e14	0.277664
$96$	1.36497e14	0.185391
$97$	4.71267e14	0.592214	0.296107	−	0.955155i	$-0.404311\pi$
$97$	4.71267e14	0.592214	0.296107	+	0.955155i	$0.404311\pi$
$98$	−2.88981e14	−0.336259
$99$	−4.28057e12	−0.00461571
$100$	1.00000e14	0.100000
$101$	8.62387e14	0.800372	0.400186	−	0.916434i	$-0.368945\pi$
$101$	8.62387e14	0.800372	0.400186	+	0.916434i	$0.368945\pi$
$102$	3.28050e14	0.282773
$103$	−1.08890e15	−0.872385	−0.436192	−	0.899853i	$-0.643673\pi$
$103$	−1.08890e15	−0.872385	−0.436192	+	0.899853i	$0.643673\pi$
$104$	1.03313e13	0.00769851
$105$	4.89726e14	0.339651
$106$	−1.77922e15	−1.14930
$107$	1.24168e15	0.747536	0.373768	−	0.927522i	$-0.378066\pi$
$107$	1.24168e15	0.747536	0.373768	+	0.927522i	$0.378066\pi$
$108$	−8.40688e14	−0.472016
$109$	2.12985e15	1.11596	0.557982	−	0.829853i	$-0.311576\pi$
$109$	2.12985e15	1.11596	0.557982	+	0.829853i	$0.311576\pi$
$110$	−2.98824e13	−0.0146208
$111$	4.13881e14	0.189214
$112$	4.23575e14	0.181049
$113$	6.89269e14	0.275613	0.137807	−	0.990459i	$-0.455995\pi$
$113$	6.89269e14	0.275613	0.137807	+	0.990459i	$0.455995\pi$
$114$	1.23009e15	0.460418
$115$	1.82090e15	0.638339
$116$	−2.95353e15	−0.970300
$117$	7.05689e12	0.00217380
$118$	1.16698e15	0.337246
$119$	1.01800e15	0.276151
$120$	6.50867e14	0.165819
$121$	−4.16832e15	−0.997862
$122$	−1.92345e15	−0.432895
$123$	−5.10050e15	−1.07975
$124$	−4.67771e15	−0.931904
$125$	4.76837e14	0.0894427
$126$	2.89326e14	0.0511221
$127$	−6.43459e15	−1.07150	−0.535751	−	0.844376i	$-0.679971\pi$
$127$	−6.43459e15	−1.07150	−0.535751	+	0.844376i	$0.679971\pi$
$128$	5.62950e14	0.0883883
$129$	−2.03384e15	−0.301226
$130$	4.92637e13	0.00688576
$131$	2.77378e15	0.366047	0.183023	−	0.983109i	$-0.441412\pi$
$131$	2.77378e15	0.366047	0.183023	+	0.983109i	$0.441412\pi$
$132$	−1.94495e14	−0.0242439
$133$	3.81721e15	0.449634
$134$	2.79164e15	0.310866
$135$	−4.00871e15	−0.422184
$136$	1.35297e15	0.134817
$137$	1.42960e16	1.34837	0.674185	−	0.738563i	$-0.264495\pi$
$137$	1.42960e16	1.34837	0.674185	+	0.738563i	$0.264495\pi$
$138$	1.18516e16	1.05849
$139$	−4.57651e15	−0.387189	−0.193595	−	0.981082i	$-0.562015\pi$
$139$	−4.57651e15	−0.387189	−0.193595	+	0.981082i	$0.562015\pi$
$140$	2.01976e15	0.161935
$141$	2.07632e16	1.57816
$142$	−8.25872e15	−0.595320
$143$	−1.47212e13	−0.00100675
$144$	3.84527e14	0.0249579
$145$	−1.40835e16	−0.867863
$146$	1.24958e16	0.731336
$147$	−8.96875e15	−0.498714
$148$	1.70696e15	0.0902112
$149$	1.32935e16	0.667947	0.333974	−	0.942582i	$-0.391610\pi$
$149$	1.32935e16	0.667947	0.333974	+	0.942582i	$0.391610\pi$
$150$	3.10358e15	0.148313
$151$	−1.93100e16	−0.877922	−0.438961	−	0.898506i	$-0.644653\pi$
$151$	−1.93100e16	−0.877922	−0.438961	+	0.898506i	$0.644653\pi$
$152$	5.07324e15	0.219512
$153$	9.24154e14	0.0380679
$154$	−6.03554e14	−0.0236761
$155$	−2.23051e16	−0.833520
$156$	3.20641e14	0.0114179
$157$	1.06880e16	0.362784	0.181392	−	0.983411i	$-0.441940\pi$
$157$	1.06880e16	0.362784	0.181392	+	0.983411i	$0.441940\pi$
$158$	3.01863e16	0.976971
$159$	−5.52193e16	−1.70456
$160$	2.68435e15	0.0790569
$161$	3.67778e16	1.03369
$162$	−2.87224e16	−0.770651
$163$	−3.29026e16	−0.842991	−0.421496	−	0.906830i	$-0.638495\pi$
$163$	−3.29026e16	−0.842991	−0.421496	+	0.906830i	$0.638495\pi$
$164$	−2.10359e16	−0.514792
$165$	−9.27423e14	−0.0216844
$166$	−5.29286e16	−1.18271
$167$	3.14439e16	0.671681	0.335841	−	0.941919i	$-0.390980\pi$
$167$	3.14439e16	0.671681	0.335841	+	0.941919i	$0.390980\pi$
$168$	1.31460e16	0.268518
$169$	−5.11616e16	−0.999526
$170$	6.45145e15	0.120584
$171$	3.46531e15	0.0619829
$172$	−8.38809e15	−0.143615
$173$	1.19867e17	1.96496	0.982482	−	0.186359i	$-0.0596686\pi$
$173$	1.19867e17	1.96496	0.982482	+	0.186359i	$0.0596686\pi$
$174$	−9.16650e16	−1.43908
$175$	9.63099e15	0.144839
$176$	−8.02149e14	−0.0115587
$177$	3.62180e16	0.500178
$178$	6.98149e16	0.924268
$179$	4.18778e16	0.531602	0.265801	−	0.964028i	$-0.414364\pi$
$179$	4.18778e16	0.531602	0.265801	+	0.964028i	$0.414364\pi$
$180$	1.83357e15	0.0223230
$181$	1.25193e17	1.46214	0.731071	−	0.682301i	$-0.239021\pi$
$181$	1.25193e17	1.46214	0.731071	+	0.682301i	$0.239021\pi$
$182$	9.95010e14	0.0111504
$183$	−5.96959e16	−0.642038
$184$	4.88793e16	0.504652
$185$	8.13942e15	0.0806874
$186$	−1.45176e17	−1.38213
$187$	−1.92785e15	−0.0176303
$188$	8.56330e16	0.752414
$189$	−8.09666e16	−0.683663
$190$	2.41911e16	0.196338
$191$	7.75948e16	0.605456	0.302728	−	0.953077i	$-0.402103\pi$
$191$	7.75948e16	0.605456	0.302728	+	0.953077i	$0.402103\pi$
$192$	1.74716e16	0.131091
$193$	−2.25828e17	−1.62967	−0.814834	−	0.579695i	$-0.803172\pi$
$193$	−2.25828e17	−1.62967	−0.814834	+	0.579695i	$0.803172\pi$
$194$	6.03221e16	0.418759
$195$	1.52894e15	0.0102124
$196$	−3.69896e16	−0.237771
$197$	5.36977e16	0.332246	0.166123	−	0.986105i	$-0.446875\pi$
$197$	5.36977e16	0.332246	0.166123	+	0.986105i	$0.446875\pi$
$198$	−5.47914e14	−0.00326380
$199$	1.41350e17	0.810771	0.405386	−	0.914146i	$-0.367137\pi$
$199$	1.41350e17	0.810771	0.405386	+	0.914146i	$0.367137\pi$
$200$	1.28000e16	0.0707107
$201$	8.66407e16	0.461054
$202$	1.10386e17	0.565949
$203$	−2.84454e17	−1.40537
$204$	4.19904e16	0.199951
$205$	−1.00307e17	−0.460444
$206$	−1.39379e17	−0.616869
$207$	3.33874e16	0.142497
$208$	1.32241e15	0.00544367
$209$	−7.22888e15	−0.0287061
$210$	6.26849e16	0.240170
$211$	−4.41718e16	−0.163315	−0.0816577	−	0.996660i	$-0.526021\pi$
$211$	−4.41718e16	−0.163315	−0.0816577	+	0.996660i	$0.526021\pi$
$212$	−2.27740e17	−0.812680
$213$	−2.56316e17	−0.882934
$214$	1.58935e17	0.528587
$215$	−3.99975e16	−0.128453
$216$	−1.07608e17	−0.333766
$217$	−4.50510e17	−1.34976
$218$	2.72621e17	0.789105
$219$	3.87816e17	1.08466
$220$	−3.82495e15	−0.0103384
$221$	3.17822e15	0.00830314
$222$	5.29768e16	0.133795
$223$	−5.00066e17	−1.22107	−0.610535	−	0.791989i	$-0.709046\pi$
$223$	−5.00066e17	−1.22107	−0.610535	+	0.791989i	$0.709046\pi$
$224$	5.42176e16	0.128021
$225$	8.74313e15	0.0199663
$226$	8.82264e16	0.194888
$227$	−1.16741e17	−0.249477	−0.124738	−	0.992190i	$-0.539809\pi$
$227$	−1.16741e17	−0.249477	−0.124738	+	0.992190i	$0.539809\pi$
$228$	1.57452e17	0.325564
$229$	6.72239e17	1.34511	0.672555	−	0.740047i	$-0.265197\pi$
$229$	6.72239e17	1.34511	0.672555	+	0.740047i	$0.265197\pi$
$230$	2.33075e17	0.451374
$231$	−1.87318e16	−0.0351147
$232$	−3.78052e17	−0.686106
$233$	4.08177e17	0.717265	0.358632	−	0.933479i	$-0.383243\pi$
$233$	4.08177e17	0.717265	0.358632	+	0.933479i	$0.383243\pi$
$234$	9.03282e14	0.00153711
$235$	4.08330e17	0.672980
$236$	1.49373e17	0.238469
$237$	9.36855e17	1.44897
$238$	1.30304e17	0.195268
$239$	1.27317e18	1.84885	0.924424	−	0.381366i	$-0.124546\pi$
$239$	1.27317e18	1.84885	0.924424	+	0.381366i	$0.124546\pi$
$240$	8.33110e16	0.117251
$241$	−4.00654e17	−0.546565	−0.273282	−	0.961934i	$-0.588109\pi$
$241$	−4.00654e17	−0.546565	−0.273282	+	0.961934i	$0.588109\pi$
$242$	−5.33545e17	−0.705595
$243$	−1.55157e17	−0.198940
$244$	−2.46202e17	−0.306103
$245$	−1.76380e17	−0.212669
$246$	−6.52864e17	−0.763501
$247$	1.19174e16	0.0135193
$248$	−5.98747e17	−0.658955
$249$	−1.64268e18	−1.75411
$250$	6.10352e16	0.0632456
$251$	−3.69701e17	−0.371790	−0.185895	−	0.982570i	$-0.559518\pi$
$251$	−3.69701e17	−0.371790	−0.185895	+	0.982570i	$0.559518\pi$
$252$	3.70337e16	0.0361488
$253$	−6.96483e16	−0.0659944
$254$	−8.23628e17	−0.757666
$255$	2.00226e17	0.178842
$256$	7.20576e16	0.0625000
$257$	−5.68963e16	−0.0479276	−0.0239638	−	0.999713i	$-0.507629\pi$
$257$	−5.68963e16	−0.0479276	−0.0239638	+	0.999713i	$0.507629\pi$
$258$	−2.60331e17	−0.212999
$259$	1.64397e17	0.130661
$260$	6.30575e15	0.00486896
$261$	−2.58231e17	−0.193733
$262$	3.55043e17	0.258834
$263$	4.31202e16	0.0305501	0.0152751	−	0.999883i	$-0.495138\pi$
$263$	4.31202e16	0.0305501	0.0152751	+	0.999883i	$0.495138\pi$
$264$	−2.48953e16	−0.0171431
$265$	−1.08595e18	−0.726883
$266$	4.88603e17	0.317939
$267$	2.16676e18	1.37081
$268$	3.57330e17	0.219816
$269$	−2.57678e18	−1.54147	−0.770737	−	0.637154i	$-0.780112\pi$
$269$	−2.57678e18	−1.54147	−0.770737	+	0.637154i	$0.780112\pi$
$270$	−5.13115e17	−0.298529
$271$	1.81142e18	1.02506	0.512530	−	0.858669i	$-0.328708\pi$
$271$	1.81142e18	1.02506	0.512530	+	0.858669i	$0.328708\pi$
$272$	1.73180e17	0.0953302
$273$	3.08809e16	0.0165375
$274$	1.82988e18	0.953442
$275$	−1.82388e16	−0.00924699
$276$	1.51701e18	0.748462
$277$	−1.36071e18	−0.653381	−0.326690	−	0.945131i	$-0.605933\pi$
$277$	−1.36071e18	−0.653381	−0.326690	+	0.945131i	$0.605933\pi$
$278$	−5.85793e17	−0.273784
$279$	−4.08979e17	−0.186067
$280$	2.58530e17	0.114505
$281$	2.12909e17	0.0918115	0.0459057	−	0.998946i	$-0.485383\pi$
$281$	2.12909e17	0.0918115	0.0459057	+	0.998946i	$0.485383\pi$
$282$	2.65768e18	1.11593
$283$	1.23798e18	0.506193	0.253096	−	0.967441i	$-0.418551\pi$
$283$	1.23798e18	0.506193	0.253096	+	0.967441i	$0.418551\pi$
$284$	−1.05712e18	−0.420955
$285$	7.50790e17	0.291194
$286$	−1.88431e15	−0.000711880 0
$287$	−2.02596e18	−0.745619
$288$	4.92194e16	0.0176479
$289$	−2.44621e18	−0.854594
$290$	−1.80269e18	−0.613672
$291$	1.87214e18	0.621072
$292$	1.59946e18	0.517133
$293$	3.88932e18	1.22565	0.612825	−	0.790219i	$-0.290033\pi$
$293$	3.88932e18	1.22565	0.612825	+	0.790219i	$0.290033\pi$
$294$	−1.14800e18	−0.352644
$295$	7.12265e17	0.213293
$296$	2.18491e17	0.0637890
$297$	1.53331e17	0.0436473
$298$	1.70157e18	0.472310
$299$	1.14821e17	0.0310805
$300$	3.97258e17	0.104873
$301$	−8.07856e17	−0.208011
$302$	−2.47169e18	−0.620785
$303$	3.42590e18	0.839373
$304$	6.49375e17	0.155219
$305$	−1.17398e18	−0.273787
$306$	1.18292e17	0.0269180
$307$	−7.12129e18	−1.58132	−0.790662	−	0.612253i	$-0.790263\pi$
$307$	−7.12129e18	−1.58132	−0.790662	+	0.612253i	$0.790263\pi$
$308$	−7.72549e16	−0.0167415
$309$	−4.32573e18	−0.914895
$310$	−2.85505e18	−0.589388
$311$	−8.62738e18	−1.73851	−0.869253	−	0.494367i	$-0.835400\pi$
$311$	−8.62738e18	−1.73851	−0.869253	+	0.494367i	$0.835400\pi$
$312$	4.10421e16	0.00807365
$313$	8.40829e18	1.61482	0.807411	−	0.589989i	$-0.200868\pi$
$313$	8.40829e18	1.61482	0.807411	+	0.589989i	$0.200868\pi$
$314$	1.36806e18	0.256527
$315$	1.76591e17	0.0323324
$316$	3.86385e18	0.690823
$317$	−5.66897e18	−0.989828	−0.494914	−	0.868942i	$-0.664801\pi$
$317$	−5.66897e18	−0.989828	−0.494914	+	0.868942i	$0.664801\pi$
$318$	−7.06807e18	−1.20531
$319$	5.38687e17	0.0897235
$320$	3.43597e17	0.0559017
$321$	4.93268e18	0.783962
$322$	4.70756e18	0.730932
$323$	1.56068e18	0.236752
$324$	−3.67646e18	−0.544933
$325$	3.00682e16	0.00435493
$326$	−4.21153e18	−0.596085
$327$	8.46099e18	1.17034
$328$	−2.69259e18	−0.364013
$329$	8.24730e18	1.08979
$330$	−1.18710e17	−0.0153332
$331$	−6.94615e18	−0.877070	−0.438535	−	0.898714i	$-0.644502\pi$
$331$	−6.94615e18	−0.877070	−0.438535	+	0.898714i	$0.644502\pi$
$332$	−6.77486e18	−0.836305
$333$	1.49242e17	0.0180119
$334$	4.02482e18	0.474950
$335$	1.70388e18	0.196609
$336$	1.68269e18	0.189871
$337$	1.06418e19	1.17433	0.587166	−	0.809466i	$-0.300244\pi$
$337$	1.06418e19	1.17433	0.587166	+	0.809466i	$0.300244\pi$
$338$	−6.54869e18	−0.706772
$339$	2.73817e18	0.289044
$340$	8.25786e17	0.0852659
$341$	8.53157e17	0.0861730
$342$	4.43560e17	0.0438285
$343$	−1.10538e19	−1.06858
$344$	−1.07368e18	−0.101551
$345$	7.23366e18	0.669445
$346$	1.53430e19	1.38944
$347$	1.32412e18	0.117342	0.0586712	−	0.998277i	$-0.481314\pi$
$347$	1.32412e18	0.117342	0.0586712	+	0.998277i	$0.481314\pi$
$348$	−1.17331e19	−1.01758
$349$	7.66248e18	0.650397	0.325198	−	0.945646i	$-0.394569\pi$
$349$	7.66248e18	0.650397	0.325198	+	0.945646i	$0.394569\pi$
$350$	1.23277e18	0.102417
$351$	−2.52780e17	−0.0205560
$352$	−1.02675e17	−0.00817326
$353$	2.74207e18	0.213682	0.106841	−	0.994276i	$-0.465926\pi$
$353$	2.74207e18	0.213682	0.106841	+	0.994276i	$0.465926\pi$
$354$	4.63590e18	0.353679
$355$	−5.04072e18	−0.376513
$356$	8.93630e18	0.653556
$357$	4.04409e18	0.289607
$358$	5.36036e18	0.375899
$359$	2.87954e18	0.197749	0.0988746	−	0.995100i	$-0.468476\pi$
$359$	2.87954e18	0.197749	0.0988746	+	0.995100i	$0.468476\pi$
$360$	2.34697e17	0.0157848
$361$	−9.32903e18	−0.614515
$362$	1.60247e19	1.03389
$363$	−1.65590e19	−1.04649
$364$	1.27361e17	0.00788455
$365$	7.62682e18	0.462538
$366$	−7.64107e18	−0.453990
$367$	−2.01936e19	−1.17549	−0.587744	−	0.809047i	$-0.699984\pi$
$367$	−2.01936e19	−1.17549	−0.587744	+	0.809047i	$0.699984\pi$
$368$	6.25656e18	0.356843
$369$	−1.83919e18	−0.102785
$370$	1.04185e18	0.0570546
$371$	−2.19336e19	−1.17708
$372$	−1.85826e19	−0.977314
$373$	−3.62151e19	−1.86670	−0.933348	−	0.358972i	$-0.883127\pi$
$373$	−3.62151e19	−1.86670	−0.933348	+	0.358972i	$0.883127\pi$
$374$	−2.46765e17	−0.0124665
$375$	1.89427e18	0.0938011
$376$	1.09610e19	0.532037
$377$	−8.88071e17	−0.0422559
$378$	−1.03637e19	−0.483423
$379$	−1.59928e19	−0.731359	−0.365679	−	0.930741i	$-0.619163\pi$
$379$	−1.59928e19	−0.731359	−0.365679	+	0.930741i	$0.619163\pi$
$380$	3.09646e18	0.138832
$381$	−2.55619e19	−1.12371
$382$	9.93214e18	0.428122
$383$	3.56761e19	1.50795	0.753975	−	0.656903i	$-0.228134\pi$
$383$	3.56761e19	1.50795	0.753975	+	0.656903i	$0.228134\pi$
$384$	2.23636e18	0.0926954
$385$	−3.68380e17	−0.0149741
$386$	−2.89060e19	−1.15235
$387$	−7.33382e17	−0.0286746
$388$	7.72123e18	0.296107
$389$	4.67525e19	1.75866	0.879331	−	0.476211i	$-0.157990\pi$
$389$	4.67525e19	1.75866	0.879331	+	0.476211i	$0.157990\pi$
$390$	1.95704e17	0.00722129
$391$	1.50367e19	0.544286
$392$	−4.73467e18	−0.168129
$393$	1.10190e19	0.383884
$394$	6.87331e18	0.234933
$395$	1.84243e19	0.617891
$396$	−7.01329e16	−0.00230785
$397$	1.61556e18	0.0521668	0.0260834	−	0.999660i	$-0.491696\pi$
$397$	1.61556e18	0.0521668	0.0260834	+	0.999660i	$0.491696\pi$
$398$	1.80928e19	0.573302
$399$	1.51642e19	0.471544
$400$	1.63840e18	0.0500000
$401$	3.22657e19	0.966402	0.483201	−	0.875509i	$-0.339474\pi$
$401$	3.22657e19	0.966402	0.483201	+	0.875509i	$0.339474\pi$
$402$	1.10900e19	0.326014
$403$	−1.40650e18	−0.0405838
$404$	1.41294e19	0.400186
$405$	−1.75307e19	−0.487403
$406$	−3.64101e19	−0.993749
$407$	−3.11328e17	−0.00834182
$408$	5.37477e18	0.141387
$409$	−2.09116e19	−0.540084	−0.270042	−	0.962849i	$-0.587038\pi$
$409$	−2.09116e19	−0.540084	−0.270042	+	0.962849i	$0.587038\pi$
$410$	−1.28393e19	−0.325583
$411$	5.67918e19	1.41407
$412$	−1.78405e19	−0.436192
$413$	1.43861e19	0.345396
$414$	4.27358e18	0.100760
$415$	−3.23051e19	−0.748014
$416$	1.69269e17	0.00384925
$417$	−1.81805e19	−0.406057
$418$	−9.25297e17	−0.0202983
$419$	−4.31574e19	−0.929930	−0.464965	−	0.885329i	$-0.653933\pi$
$419$	−4.31574e19	−0.929930	−0.464965	+	0.885329i	$0.653933\pi$
$420$	8.02367e18	0.169826
$421$	3.44152e19	0.715541	0.357770	−	0.933810i	$-0.383537\pi$
$421$	3.44152e19	0.715541	0.357770	+	0.933810i	$0.383537\pi$
$422$	−5.65399e18	−0.115481
$423$	7.48700e18	0.150229
$424$	−2.91507e19	−0.574652
$425$	3.93765e18	0.0762642
$426$	−3.28084e19	−0.624329
$427$	−2.37117e19	−0.443357
$428$	2.03437e19	0.373768
$429$	−5.84810e16	−0.00105581
$430$	−5.11969e18	−0.0908301
$431$	7.95134e19	1.38631	0.693156	−	0.720788i	$-0.256220\pi$
$431$	7.95134e19	1.38631	0.693156	+	0.720788i	$0.256220\pi$
$432$	−1.37738e19	−0.236008
$433$	−6.99185e19	−1.17742	−0.588712	−	0.808343i	$-0.700365\pi$
$433$	−6.99185e19	−1.17742	−0.588712	+	0.808343i	$0.700365\pi$
$434$	−5.76653e19	−0.954424
$435$	−5.59479e19	−0.910153
$436$	3.48954e19	0.557982
$437$	5.63834e19	0.886218
$438$	4.96405e19	0.766973
$439$	−5.37736e19	−0.816743	−0.408372	−	0.912816i	$-0.633903\pi$
$439$	−5.37736e19	−0.816743	−0.408372	+	0.912816i	$0.633903\pi$
$440$	−4.89593e17	−0.00731038
$441$	−3.23405e18	−0.0474741
$442$	4.06812e17	0.00587121
$443$	1.46107e19	0.207321	0.103660	−	0.994613i	$-0.466945\pi$
$443$	1.46107e19	0.207321	0.103660	+	0.994613i	$0.466945\pi$
$444$	6.78103e18	0.0946071
$445$	4.26116e19	0.584558
$446$	−6.40084e19	−0.863427
$447$	5.28094e19	0.700495
$448$	6.93986e18	0.0905243
$449$	−7.03318e19	−0.902203	−0.451101	−	0.892473i	$-0.648969\pi$
$449$	−7.03318e19	−0.902203	−0.451101	+	0.892473i	$0.648969\pi$
$450$	1.11912e18	0.0141183
$451$	3.83668e18	0.0476027
$452$	1.12930e19	0.137807
$453$	−7.67107e19	−0.920702
$454$	−1.49429e19	−0.176407
$455$	6.07306e17	0.00705216
$456$	2.01539e19	0.230209
$457$	4.35839e19	0.489728	0.244864	−	0.969557i	$-0.421257\pi$
$457$	4.35839e19	0.489728	0.244864	+	0.969557i	$0.421257\pi$
$458$	8.60466e19	0.951136
$459$	−3.31034e19	−0.359979
$460$	2.98336e19	0.319170
$461$	−1.24140e20	−1.30663	−0.653317	−	0.757084i	$-0.726623\pi$
$461$	−1.24140e20	−1.30663	−0.653317	+	0.757084i	$0.726623\pi$
$462$	−2.39767e18	−0.0248298
$463$	6.58546e19	0.671009	0.335505	−	0.942039i	$-0.391093\pi$
$463$	6.58546e19	0.671009	0.335505	+	0.942039i	$0.391093\pi$
$464$	−4.83906e19	−0.485150
$465$	−8.86087e19	−0.874136
$466$	5.22467e19	0.507183
$467$	1.28108e19	0.122377	0.0611886	−	0.998126i	$-0.480511\pi$
$467$	1.28108e19	0.122377	0.0611886	+	0.998126i	$0.480511\pi$
$468$	1.15620e17	0.00108690
$469$	3.44144e19	0.318379
$470$	5.22662e19	0.475869
$471$	4.24589e19	0.380462
$472$	1.91197e19	0.168623
$473$	1.52988e18	0.0132801
$474$	1.19917e20	1.02458
$475$	1.47651e19	0.124175
$476$	1.66789e19	0.138075
$477$	−1.99116e19	−0.162262
$478$	1.62965e20	1.30733
$479$	2.89091e19	0.228307	0.114153	−	0.993463i	$-0.463584\pi$
$479$	2.89091e19	0.228307	0.114153	+	0.993463i	$0.463584\pi$
$480$	1.06638e19	0.0829093
$481$	5.13251e17	0.00392864
$482$	−5.12837e19	−0.386480
$483$	1.46103e20	1.08406
$484$	−6.82937e19	−0.498931
$485$	3.68177e19	0.264846
$486$	−1.98600e19	−0.140672
$487$	1.96397e20	1.36983	0.684916	−	0.728622i	$-0.259839\pi$
$487$	1.96397e20	1.36983	0.684916	+	0.728622i	$0.259839\pi$
$488$	−3.15139e19	−0.216448
$489$	−1.30708e20	−0.884069
$490$	−2.25766e19	−0.150380
$491$	−1.38375e20	−0.907707	−0.453854	−	0.891076i	$-0.649951\pi$
$491$	−1.38375e20	−0.907707	−0.453854	+	0.891076i	$0.649951\pi$
$492$	−8.35666e19	−0.539877
$493$	−1.16300e20	−0.739992
$494$	1.52543e18	0.00955962
$495$	−3.34420e17	−0.00206421
$496$	−7.66397e19	−0.465952
$497$	−1.01811e20	−0.609706
$498$	−2.10263e20	−1.24035
$499$	1.95546e20	1.13630	0.568152	−	0.822924i	$-0.307659\pi$
$499$	1.95546e20	1.13630	0.568152	+	0.822924i	$0.307659\pi$
$500$	7.81250e18	0.0447214
$501$	1.24913e20	0.704411
$502$	−4.73218e19	−0.262895
$503$	−1.06861e20	−0.584869	−0.292434	−	0.956286i	$-0.594465\pi$
$503$	−1.06861e20	−0.584869	−0.292434	+	0.956286i	$0.594465\pi$
$504$	4.74032e18	0.0255610
$505$	6.73740e19	0.357937
$506$	−8.91499e18	−0.0466651
$507$	−2.03244e20	−1.04823
$508$	−1.05424e20	−0.535751
$509$	1.52058e19	0.0761424	0.0380712	−	0.999275i	$-0.487879\pi$
$509$	1.52058e19	0.0761424	0.0380712	+	0.999275i	$0.487879\pi$
$510$	2.56289e19	0.126460
$511$	1.54044e20	0.749010
$512$	9.22337e18	0.0441942
$513$	−1.24128e20	−0.586126
$514$	−7.28272e18	−0.0338899
$515$	−8.50702e19	−0.390142
$516$	−3.33224e19	−0.150613
$517$	−1.56184e19	−0.0695756
$518$	2.10428e19	0.0923913
$519$	4.76182e20	2.06071
$520$	8.07136e17	0.00344288
$521$	−1.96345e20	−0.825536	−0.412768	−	0.910836i	$-0.635438\pi$
$521$	−1.96345e20	−0.825536	−0.412768	+	0.910836i	$0.635438\pi$
$522$	−3.30535e19	−0.136990
$523$	−4.20870e20	−1.71943	−0.859716	−	0.510773i	$-0.829359\pi$
$523$	−4.20870e20	−1.71943	−0.859716	+	0.510773i	$0.829359\pi$
$524$	4.54455e19	0.183023
$525$	3.82598e19	0.151897
$526$	5.51939e18	0.0216022
$527$	−1.84192e20	−0.710709
$528$	−3.18660e18	−0.0121220
$529$	2.76604e20	1.03739
$530$	−1.39001e20	−0.513984
$531$	1.30599e19	0.0476134
$532$	6.25412e19	0.224817
$533$	−6.32510e18	−0.0224188
$534$	2.77345e20	0.969306
$535$	9.70064e19	0.334308
$536$	4.57382e19	0.155433
$537$	1.66363e20	0.557506
$538$	−3.29828e20	−1.08999
$539$	6.74644e18	0.0219866
$540$	−6.56788e19	−0.211092
$541$	3.30654e20	1.04808	0.524040	−	0.851694i	$-0.324424\pi$
$541$	3.30654e20	1.04808	0.524040	+	0.851694i	$0.324424\pi$
$542$	2.31862e20	0.724827
$543$	4.97338e20	1.53339
$544$	2.21670e19	0.0674086
$545$	1.66394e20	0.499074
$546$	3.95276e18	0.0116938
$547$	−3.44218e20	−1.00445	−0.502225	−	0.864737i	$-0.667485\pi$
$547$	−3.44218e20	−1.00445	−0.502225	+	0.864737i	$0.667485\pi$
$548$	2.34225e20	0.674185
$549$	−2.15258e19	−0.0611175
$550$	−2.33456e18	−0.00653861
$551$	−4.36091e20	−1.20487
$552$	1.94177e20	0.529243
$553$	3.72127e20	1.00058
$554$	−1.74170e20	−0.462010
$555$	3.23345e19	0.0846191
$556$	−7.49816e19	−0.193595
$557$	4.03852e20	1.02875	0.514374	−	0.857566i	$-0.328024\pi$
$557$	4.03852e20	1.02875	0.514374	+	0.857566i	$0.328024\pi$
$558$	−5.23493e19	−0.131569
$559$	−2.52215e18	−0.00625434
$560$	3.30918e19	0.0809674
$561$	−7.65853e18	−0.0184894
$562$	2.72524e19	0.0649205
$563$	−3.78722e20	−0.890240	−0.445120	−	0.895471i	$-0.646839\pi$
$563$	−3.78722e20	−0.890240	−0.445120	+	0.895471i	$0.646839\pi$
$564$	3.40184e20	0.789078
$565$	5.38491e19	0.123258
$566$	1.58462e20	0.357932
$567$	−3.54080e20	−0.789275
$568$	−1.35311e20	−0.297660
$569$	−5.32798e20	−1.15670	−0.578350	−	0.815789i	$-0.696303\pi$
$569$	−5.32798e20	−1.15670	−0.578350	+	0.815789i	$0.696303\pi$
$570$	9.61011e19	0.205905
$571$	−6.45129e20	−1.36419	−0.682097	−	0.731262i	$-0.738932\pi$
$571$	−6.45129e20	−1.36419	−0.682097	+	0.731262i	$0.738932\pi$
$572$	−2.41192e17	−0.000503375 0
$573$	3.08251e20	0.634959
$574$	−2.59323e20	−0.527232
$575$	1.42258e20	0.285474
$576$	6.30009e18	0.0124789
$577$	5.38124e18	0.0105212	0.00526058	−	0.999986i	$-0.498325\pi$
$577$	5.38124e18	0.0105212	0.00526058	+	0.999986i	$0.498325\pi$
$578$	−3.13115e20	−0.604289
$579$	−8.97121e20	−1.70908
$580$	−2.30744e20	−0.433931
$581$	−6.52486e20	−1.21130
$582$	2.39634e20	0.439164
$583$	4.15369e19	0.0751484
$584$	2.04731e20	0.365668
$585$	5.51320e17	0.000972153 0
$586$	4.97833e20	0.866665
$587$	−6.26245e20	−1.07636	−0.538181	−	0.842829i	$-0.680888\pi$
$587$	−6.26245e20	−1.07636	−0.538181	+	0.842829i	$0.680888\pi$
$588$	−1.46944e20	−0.249357
$589$	−6.90668e20	−1.15719
$590$	9.11699e19	0.150821
$591$	2.13318e20	0.348435
$592$	2.79668e19	0.0451056
$593$	6.78491e20	1.08052	0.540262	−	0.841497i	$-0.318325\pi$
$593$	6.78491e20	1.08052	0.540262	+	0.841497i	$0.318325\pi$
$594$	1.96264e19	0.0308633
$595$	7.95313e19	0.123498
$596$	2.17801e20	0.333974
$597$	5.61525e20	0.850279
$598$	1.46971e19	0.0219772
$599$	1.26446e21	1.86725	0.933625	−	0.358251i	$-0.116627\pi$
$599$	1.26446e21	1.86725	0.933625	+	0.358251i	$0.116627\pi$
$600$	5.08490e19	0.0741563
$601$	9.57115e20	1.37850	0.689248	−	0.724526i	$-0.257941\pi$
$601$	9.57115e20	1.37850	0.689248	+	0.724526i	$0.257941\pi$
$602$	−1.03406e20	−0.147086
$603$	3.12418e19	0.0438891
$604$	−3.16376e20	−0.438961
$605$	−3.25650e20	−0.446258
$606$	4.38515e20	0.593526
$607$	1.00033e20	0.133730	0.0668650	−	0.997762i	$-0.478700\pi$
$607$	1.00033e20	0.133730	0.0668650	+	0.997762i	$0.478700\pi$
$608$	8.31200e19	0.109756
$609$	−1.13002e21	−1.47385
$610$	−1.50270e20	−0.193597
$611$	2.57483e19	0.0327672
$612$	1.51413e19	0.0190339
$613$	7.36761e20	0.914898	0.457449	−	0.889236i	$-0.348763\pi$
$613$	7.36761e20	0.914898	0.457449	+	0.889236i	$0.348763\pi$
$614$	−9.11525e20	−1.11816
$615$	−3.98477e20	−0.482881
$616$	−9.88863e18	−0.0118381
$617$	1.36626e21	1.61582	0.807910	−	0.589305i	$-0.200599\pi$
$617$	1.36626e21	1.61582	0.807910	+	0.589305i	$0.200599\pi$
$618$	−5.53694e20	−0.646928
$619$	4.69623e20	0.542087	0.271044	−	0.962567i	$-0.412631\pi$
$619$	4.69623e20	0.542087	0.271044	+	0.962567i	$0.412631\pi$
$620$	−3.65446e20	−0.416760
$621$	−1.19594e21	−1.34748
$622$	−1.10431e21	−1.22931
$623$	8.60654e20	0.946604
$624$	5.25338e18	0.00570893
$625$	3.72529e19	0.0400000
$626$	1.07626e21	1.14185
$627$	−2.87173e19	−0.0301049
$628$	1.75112e20	0.181392
$629$	6.72142e19	0.0687988
$630$	2.26036e19	0.0228625
$631$	1.56542e21	1.56463	0.782315	−	0.622882i	$-0.214039\pi$
$631$	1.56542e21	1.56463	0.782315	+	0.622882i	$0.214039\pi$
$632$	4.94572e20	0.488486
$633$	−1.75476e20	−0.171273
$634$	−7.25629e20	−0.699914
$635$	−5.02702e20	−0.479190
$636$	−9.04713e20	−0.852281
$637$	−1.11221e19	−0.0103548
$638$	6.89519e19	0.0634441
$639$	−9.24250e19	−0.0840491
$640$	4.39805e19	0.0395285
$641$	1.07910e21	0.958578	0.479289	−	0.877657i	$-0.340895\pi$
$641$	1.07910e21	0.958578	0.479289	+	0.877657i	$0.340895\pi$
$642$	6.31383e20	0.554345
$643$	7.31630e20	0.634906	0.317453	−	0.948274i	$-0.397172\pi$
$643$	7.31630e20	0.634906	0.317453	+	0.948274i	$0.397172\pi$
$644$	6.02568e20	0.516847
$645$	−1.58893e20	−0.134713
$646$	1.99767e20	0.167409
$647$	−3.86121e20	−0.319846	−0.159923	−	0.987129i	$-0.551125\pi$
$647$	−3.86121e20	−0.319846	−0.159923	+	0.987129i	$0.551125\pi$
$648$	−4.70587e20	−0.385326
$649$	−2.72438e19	−0.0220512
$650$	3.84872e18	0.00307940
$651$	−1.78969e21	−1.41553
$652$	−5.39076e20	−0.421496
$653$	−8.04784e20	−0.622057	−0.311029	−	0.950401i	$-0.600674\pi$
$653$	−8.04784e20	−0.622057	−0.311029	+	0.950401i	$0.600674\pi$
$654$	1.08301e21	0.827557
$655$	2.16701e20	0.163701
$656$	−3.44652e20	−0.257396
$657$	1.39843e20	0.103252
$658$	1.05565e21	0.770597
$659$	1.07785e21	0.777889	0.388945	−	0.921261i	$-0.372840\pi$
$659$	1.07785e21	0.777889	0.388945	+	0.921261i	$0.372840\pi$
$660$	−1.51949e19	−0.0108422
$661$	−8.11863e20	−0.572759	−0.286379	−	0.958116i	$-0.592452\pi$
$661$	−8.11863e20	−0.572759	−0.286379	+	0.958116i	$0.592452\pi$
$662$	−8.89107e20	−0.620182
$663$	1.26257e19	0.00870774
$664$	−8.67183e20	−0.591357
$665$	2.98220e20	0.201082
$666$	1.91029e19	0.0127363
$667$	−4.20162e21	−2.76996
$668$	5.15177e20	0.335841
$669$	−1.98655e21	−1.28057
$670$	2.18097e20	0.139024
$671$	4.49042e19	0.0283053
$672$	2.15384e20	0.134259
$673$	−5.57984e20	−0.343961	−0.171980	−	0.985100i	$-0.555017\pi$
$673$	−5.57984e20	−0.343961	−0.171980	+	0.985100i	$0.555017\pi$
$674$	1.36215e21	0.830378
$675$	−3.13181e20	−0.188806
$676$	−8.38232e20	−0.499763
$677$	−1.86877e20	−0.110190	−0.0550948	−	0.998481i	$-0.517546\pi$
$677$	−1.86877e20	−0.110190	−0.0550948	+	0.998481i	$0.517546\pi$
$678$	3.50486e20	0.204385
$679$	7.43631e20	0.428878
$680$	1.05701e20	0.0602921
$681$	−4.63763e20	−0.261633
$682$	1.09204e20	0.0609335
$683$	−1.32462e21	−0.731034	−0.365517	−	0.930805i	$-0.619108\pi$
$683$	−1.32462e21	−0.731034	−0.365517	+	0.930805i	$0.619108\pi$
$684$	5.67757e19	0.0309914
$685$	1.11687e21	0.603009
$686$	−1.41489e21	−0.755600
$687$	2.67052e21	1.41065
$688$	−1.37431e20	−0.0718075
$689$	−6.84771e19	−0.0353917
$690$	9.25908e20	0.473369
$691$	1.97901e21	1.00084	0.500418	−	0.865784i	$-0.333180\pi$
$691$	1.97901e21	1.00084	0.500418	+	0.865784i	$0.333180\pi$
$692$	1.96390e21	0.982482
$693$	−6.75449e18	−0.00334267
$694$	1.69487e20	0.0829736
$695$	−3.57540e20	−0.173156
$696$	−1.50184e21	−0.719539
$697$	−8.28320e20	−0.392602
$698$	9.80797e20	0.459900
$699$	1.62152e21	0.752216
$700$	1.57794e20	0.0724195
$701$	2.58448e21	1.17351	0.586757	−	0.809763i	$-0.300404\pi$
$701$	2.58448e21	1.17351	0.586757	+	0.809763i	$0.300404\pi$
$702$	−3.23558e19	−0.0145353
$703$	2.52034e20	0.112020
$704$	−1.31424e19	−0.00577937
$705$	1.62212e21	0.705773
$706$	3.50985e20	0.151096
$707$	1.36080e21	0.579625
$708$	5.93395e20	0.250089
$709$	−2.35138e21	−0.980562	−0.490281	−	0.871564i	$-0.663106\pi$
$709$	−2.35138e21	−0.980562	−0.490281	+	0.871564i	$0.663106\pi$
$710$	−6.45213e20	−0.266235
$711$	3.37821e20	0.137932
$712$	1.14385e21	0.462134
$713$	−6.65440e21	−2.66034
$714$	5.17643e20	0.204783
$715$	−1.15009e18	−0.000450232 0
$716$	6.86126e20	0.265801
$717$	5.05776e21	1.93894
$718$	3.68581e20	0.139830
$719$	5.01526e21	1.88290	0.941450	−	0.337153i	$-0.109464\pi$
$719$	5.01526e21	1.88290	0.941450	+	0.337153i	$0.109464\pi$
$720$	3.00412e19	0.0111615
$721$	−1.71822e21	−0.631776
$722$	−1.19412e21	−0.434528
$723$	−1.59163e21	−0.573198
$724$	2.05116e21	0.731071
$725$	−1.10027e21	−0.388120
$726$	−2.11955e21	−0.739978
$727$	−2.68041e21	−0.926175	−0.463087	−	0.886313i	$-0.653258\pi$
$727$	−2.68041e21	−0.926175	−0.463087	+	0.886313i	$0.653258\pi$
$728$	1.63022e19	0.00557522
$729$	2.60343e21	0.881231
$730$	9.76233e20	0.327063
$731$	−3.30294e20	−0.109527
$732$	−9.78057e20	−0.321019
$733$	−5.84752e21	−1.89973	−0.949865	−	0.312661i	$-0.898780\pi$
$733$	−5.84752e21	−1.89973	−0.949865	+	0.312661i	$0.898780\pi$
$734$	−2.58478e21	−0.831195
$735$	−7.00684e20	−0.223032
$736$	8.00839e20	0.252326
$737$	−6.51726e19	−0.0203263
$738$	−2.35417e20	−0.0726799
$739$	−2.19735e20	−0.0671530	−0.0335765	−	0.999436i	$-0.510690\pi$
$739$	−2.19735e20	−0.0671530	−0.0335765	+	0.999436i	$0.510690\pi$
$740$	1.33356e20	0.0403437
$741$	4.73429e19	0.0141781
$742$	−2.80750e21	−0.832319
$743$	1.85608e21	0.544730	0.272365	−	0.962194i	$-0.412194\pi$
$743$	1.85608e21	0.544730	0.272365	+	0.962194i	$0.412194\pi$
$744$	−2.37857e21	−0.691065
$745$	1.03855e21	0.298715
$746$	−4.63554e21	−1.31995
$747$	−5.92335e20	−0.166979
$748$	−3.15859e19	−0.00881517
$749$	1.95930e21	0.541361
$750$	2.42467e20	0.0663274
$751$	4.78115e21	1.29489	0.647445	−	0.762112i	$-0.275837\pi$
$751$	4.78115e21	1.29489	0.647445	+	0.762112i	$0.275837\pi$
$752$	1.40301e21	0.376207
$753$	−1.46867e21	−0.389907
$754$	−1.13673e20	−0.0298795
$755$	−1.50860e21	−0.392619
$756$	−1.32656e21	−0.341832
$757$	2.41955e21	0.617326	0.308663	−	0.951171i	$-0.400118\pi$
$757$	2.41955e21	0.617326	0.308663	+	0.951171i	$0.400118\pi$
$758$	−2.04708e21	−0.517149
$759$	−2.76683e20	−0.0692102
$760$	3.96347e20	0.0981689
$761$	−3.48193e21	−0.853955	−0.426978	−	0.904262i	$-0.640422\pi$
$761$	−3.48193e21	−0.853955	−0.426978	+	0.904262i	$0.640422\pi$
$762$	−3.27193e21	−0.794586
$763$	3.36077e21	0.808175
$764$	1.27131e21	0.302728
$765$	7.21995e19	0.0170245
$766$	4.56654e21	1.06628
$767$	4.49137e19	0.0103852
$768$	2.86254e20	0.0655455
$769$	−2.58771e21	−0.586770	−0.293385	−	0.955994i	$-0.594782\pi$
$769$	−2.58771e21	−0.586770	−0.293385	+	0.955994i	$0.594782\pi$
$770$	−4.71526e19	−0.0105883
$771$	−2.26025e20	−0.0502630
$772$	−3.69997e21	−0.814834
$773$	3.07396e21	0.670429	0.335214	−	0.942142i	$-0.391191\pi$
$773$	3.07396e21	0.670429	0.335214	+	0.942142i	$0.391191\pi$
$774$	−9.38729e19	−0.0202760
$775$	−1.74258e21	−0.372762
$776$	9.88318e20	0.209379
$777$	6.53080e20	0.137028
$778$	5.98431e21	1.24356
$779$	−3.10596e21	−0.639242
$780$	2.50501e19	0.00510622
$781$	1.92805e20	0.0389256
$782$	1.92470e21	0.384868
$783$	9.24988e21	1.83199
$784$	−6.06037e20	−0.118885
$785$	8.34999e20	0.162242
$786$	1.41044e21	0.271447
$787$	−5.67154e21	−1.08116	−0.540581	−	0.841292i	$-0.681795\pi$
$787$	−5.67154e21	−1.08116	−0.540581	+	0.841292i	$0.681795\pi$
$788$	8.79784e20	0.166123
$789$	1.71298e20	0.0320388
$790$	2.35831e21	0.436915
$791$	1.08763e21	0.199598
$792$	−8.97702e18	−0.00163190
$793$	−7.40284e19	−0.0133306
$794$	2.06792e20	0.0368875
$795$	−4.31401e21	−0.762303
$796$	2.31588e21	0.405386
$797$	6.99506e21	1.21298	0.606491	−	0.795091i	$-0.292577\pi$
$797$	6.99506e21	1.21298	0.606491	+	0.795091i	$0.292577\pi$
$798$	1.94102e21	0.333432
$799$	3.37193e21	0.573823
$800$	2.09715e20	0.0353553
$801$	7.81313e20	0.130491
$802$	4.13001e21	0.683350
$803$	−2.91722e20	−0.0478192
$804$	1.41952e21	0.230527
$805$	2.87327e21	0.462282
$806$	−1.80032e20	−0.0286971
$807$	−1.02365e22	−1.61659
$808$	1.80856e21	0.282974
$809$	−1.02572e22	−1.59007	−0.795036	−	0.606562i	$-0.792548\pi$
$809$	−1.02572e22	−1.59007	−0.795036	+	0.606562i	$0.792548\pi$
$810$	−2.24394e21	−0.344646
$811$	5.19989e20	0.0791294	0.0395647	−	0.999217i	$-0.487403\pi$
$811$	5.19989e20	0.0791294	0.0395647	+	0.999217i	$0.487403\pi$
$812$	−4.66049e21	−0.702686
$813$	7.19601e21	1.07501
$814$	−3.98500e19	−0.00589856
$815$	−2.57051e21	−0.376997
$816$	6.87971e20	0.0999755
$817$	−1.23851e21	−0.178334
$818$	−2.67668e21	−0.381897
$819$	1.11354e19	0.00157425
$820$	−1.64343e21	−0.230222
$821$	−1.18946e22	−1.65111	−0.825557	−	0.564319i	$-0.809139\pi$
$821$	−1.18946e22	−1.65111	−0.825557	+	0.564319i	$0.809139\pi$
$822$	7.26935e21	0.999901
$823$	−4.67215e21	−0.636822	−0.318411	−	0.947953i	$-0.603149\pi$
$823$	−4.67215e21	−0.636822	−0.318411	+	0.947953i	$0.603149\pi$
$824$	−2.28358e21	−0.308435
$825$	−7.24549e19	−0.00969758
$826$	1.84142e21	0.244232
$827$	−6.43261e19	−0.00845465	−0.00422733	−	0.999991i	$-0.501346\pi$
$827$	−6.43261e19	−0.00845465	−0.00422733	+	0.999991i	$0.501346\pi$
$828$	5.47019e20	0.0712483
$829$	−1.59621e21	−0.206030	−0.103015	−	0.994680i	$-0.532849\pi$
$829$	−1.59621e21	−0.206030	−0.103015	+	0.994680i	$0.532849\pi$
$830$	−4.13505e21	−0.528926
$831$	−5.40551e21	−0.685219
$832$	2.16664e19	0.00272183
$833$	−1.45652e21	−0.181334
$834$	−2.32711e21	−0.287125
$835$	2.45656e21	0.300385
$836$	−1.18438e20	−0.0143530
$837$	1.46497e22	1.75949
$838$	−5.52415e21	−0.657560
$839$	−1.03172e22	−1.21715	−0.608577	−	0.793495i	$-0.708259\pi$
$839$	−1.03172e22	−1.21715	−0.608577	+	0.793495i	$0.708259\pi$
$840$	1.02703e21	0.120085
$841$	2.38677e22	2.76593
$842$	4.40514e21	0.505964
$843$	8.45799e20	0.0962853
$844$	−7.23711e20	−0.0816577
$845$	−3.99700e21	−0.447002
$846$	9.58336e20	0.106228
$847$	−6.57736e21	−0.722647
$848$	−3.73129e21	−0.406340
$849$	4.91798e21	0.530859
$850$	5.04020e20	0.0539269
$851$	2.42828e21	0.257530
$852$	−4.19948e21	−0.441467
$853$	−2.65492e21	−0.276652	−0.138326	−	0.990387i	$-0.544172\pi$
$853$	−2.65492e21	−0.276652	−0.138326	+	0.990387i	$0.544172\pi$
$854$	−3.03510e21	−0.313501
$855$	2.70728e20	0.0277196
$856$	2.60399e21	0.264294
$857$	9.17781e21	0.923385	0.461693	−	0.887040i	$-0.347242\pi$
$857$	9.17781e21	0.923385	0.461693	+	0.887040i	$0.347242\pi$
$858$	−7.48557e18	−0.000746569 0
$859$	−1.85419e22	−1.83318	−0.916592	−	0.399824i	$-0.869071\pi$
$859$	−1.85419e22	−1.83318	−0.916592	+	0.399824i	$0.869071\pi$
$860$	−6.55320e20	−0.0642266
$861$	−8.04829e21	−0.781952
$862$	1.01777e22	0.980270
$863$	3.65598e21	0.349078	0.174539	−	0.984650i	$-0.444156\pi$
$863$	3.65598e21	0.349078	0.174539	+	0.984650i	$0.444156\pi$
$864$	−1.76305e21	−0.166883
$865$	9.36462e21	0.878758
$866$	−8.94957e21	−0.832565
$867$	−9.71776e21	−0.896238
$868$	−7.38116e21	−0.674880
$869$	−7.04718e20	−0.0638803
$870$	−7.16133e21	−0.643575
$871$	1.07443e20	0.00957282
$872$	4.46662e21	0.394553
$873$	6.75077e20	0.0591217
$874$	7.21707e21	0.626651
$875$	7.52421e20	0.0647740
$876$	6.35398e21	0.542332
$877$	−1.66541e21	−0.140937	−0.0704683	−	0.997514i	$-0.522449\pi$
$877$	−1.66541e21	−0.140937	−0.0704683	+	0.997514i	$0.522449\pi$
$878$	−6.88302e21	−0.577525
$879$	1.54506e22	1.28537
$880$	−6.26679e19	−0.00516922
$881$	4.64406e21	0.379821	0.189910	−	0.981801i	$-0.439180\pi$
$881$	4.64406e21	0.379821	0.189910	+	0.981801i	$0.439180\pi$
$882$	−4.13958e20	−0.0335693
$883$	1.60318e22	1.28907	0.644536	−	0.764574i	$-0.277051\pi$
$883$	1.60318e22	1.28907	0.644536	+	0.764574i	$0.277051\pi$
$884$	5.20720e19	0.00415157
$885$	2.82953e21	0.223686
$886$	1.87017e21	0.146598
$887$	−1.91774e21	−0.149061	−0.0745304	−	0.997219i	$-0.523746\pi$
$887$	−1.91774e21	−0.149061	−0.0745304	+	0.997219i	$0.523746\pi$
$888$	8.67972e20	0.0668973
$889$	−1.01534e22	−0.775976
$890$	5.45429e21	0.413345
$891$	6.70542e20	0.0503898
$892$	−8.19308e21	−0.610535
$893$	1.26438e22	0.934310
$894$	6.75961e21	0.495325
$895$	3.27170e21	0.237739
$896$	8.88302e20	0.0640104
$897$	4.56136e20	0.0325950
$898$	−9.00247e21	−0.637954
$899$	5.14677e22	3.61691
$900$	1.43247e20	0.00998316
$901$	−8.96760e21	−0.619784
$902$	4.91095e20	0.0336602
$903$	−3.20927e21	−0.218147
$904$	1.44550e21	0.0974440
$905$	9.78068e21	0.653890
$906$	−9.81896e21	−0.651035
$907$	−1.43639e22	−0.944532	−0.472266	−	0.881456i	$-0.656564\pi$
$907$	−1.43639e22	−0.944532	−0.472266	+	0.881456i	$0.656564\pi$
$908$	−1.91269e21	−0.124738
$909$	1.23535e21	0.0799024
$910$	7.77352e19	0.00498663
$911$	−1.53974e22	−0.979626	−0.489813	−	0.871828i	$-0.662935\pi$
$911$	−1.53974e22	−0.979626	−0.489813	+	0.871828i	$0.662935\pi$
$912$	2.57969e21	0.162782
$913$	1.23565e21	0.0773330
$914$	5.57874e21	0.346290
$915$	−4.66374e21	−0.287128
$916$	1.10140e22	0.672555
$917$	4.37685e21	0.265089
$918$	−4.23724e21	−0.254544
$919$	−9.59237e21	−0.571557	−0.285779	−	0.958296i	$-0.592252\pi$
$919$	−9.59237e21	−0.571557	−0.285779	+	0.958296i	$0.592252\pi$
$920$	3.81870e21	0.225687
$921$	−2.82899e22	−1.65838
$922$	−1.58899e22	−0.923930
$923$	−3.17855e20	−0.0183323
$924$	−3.06901e20	−0.0175573
$925$	6.35892e20	0.0360845
$926$	8.42938e21	0.474475
$927$	−1.55982e21	−0.0870915
$928$	−6.19400e21	−0.343053
$929$	−2.12844e22	−1.16935	−0.584673	−	0.811269i	$-0.698777\pi$
$929$	−2.12844e22	−1.16935	−0.584673	+	0.811269i	$0.698777\pi$
$930$	−1.13419e22	−0.618108
$931$	−5.46154e21	−0.295252
$932$	6.68758e21	0.358632
$933$	−3.42730e22	−1.82322
$934$	1.63979e21	0.0865337
$935$	−1.50613e20	−0.00788453
$936$	1.47994e19	0.000768554 0
$937$	−3.01568e22	−1.55360	−0.776799	−	0.629748i	$-0.783158\pi$
$937$	−3.01568e22	−1.55360	−0.776799	+	0.629748i	$0.783158\pi$
$938$	4.40504e21	0.225128
$939$	3.34026e22	1.69351
$940$	6.69007e21	0.336490
$941$	−1.85558e22	−0.925885	−0.462943	−	0.886388i	$-0.653206\pi$
$941$	−1.85558e22	−0.925885	−0.462943	+	0.886388i	$0.653206\pi$
$942$	5.43473e21	0.269027
$943$	−2.99251e22	−1.46960
$944$	2.44732e21	0.119234
$945$	−6.32551e21	−0.305744
$946$	1.95825e20	0.00939042
$947$	1.73295e22	0.824444	0.412222	−	0.911083i	$-0.364753\pi$
$947$	1.73295e22	0.824444	0.412222	+	0.911083i	$0.364753\pi$
$948$	1.53494e22	0.724486
$949$	4.80928e20	0.0225208
$950$	1.88993e21	0.0878049
$951$	−2.25204e22	−1.03806
$952$	2.13490e21	0.0976340
$953$	2.51658e22	1.14186	0.570931	−	0.820998i	$-0.306583\pi$
$953$	2.51658e22	1.14186	0.570931	+	0.820998i	$0.306583\pi$
$954$	−2.54868e21	−0.114737
$955$	6.06209e21	0.270768
$956$	2.08596e22	0.924424
$957$	2.13998e21	0.0940956
$958$	3.70037e21	0.161437
$959$	2.25582e22	0.976482
$960$	1.36497e21	0.0586257
$961$	5.80479e22	2.47378
$962$	6.56962e19	0.00277797
$963$	1.77868e21	0.0746277
$964$	−6.56432e21	−0.273282
$965$	−1.76429e22	−0.728809
$966$	1.87012e22	0.766549
$967$	−9.74068e21	−0.396178	−0.198089	−	0.980184i	$-0.563474\pi$
$967$	−9.74068e21	−0.396178	−0.198089	+	0.980184i	$0.563474\pi$
$968$	−8.74160e21	−0.352798
$969$	6.19992e21	0.248289
$970$	4.71267e21	0.187275
$971$	−1.21314e22	−0.478373	−0.239187	−	0.970974i	$-0.576881\pi$
$971$	−1.21314e22	−0.478373	−0.239187	+	0.970974i	$0.576881\pi$
$972$	−2.54209e21	−0.0994702
$973$	−7.22146e21	−0.280401
$974$	2.51388e22	0.968618
$975$	1.19448e20	0.00456714
$976$	−4.03377e21	−0.153052
$977$	1.82562e22	0.687388	0.343694	−	0.939082i	$-0.388322\pi$
$977$	1.82562e22	0.687388	0.343694	+	0.939082i	$0.388322\pi$
$978$	−1.67306e22	−0.625131
$979$	−1.62987e21	−0.0604343
$980$	−2.88981e21	−0.106334
$981$	3.05095e21	0.111408
$982$	−1.77120e22	−0.641846
$983$	4.33715e21	0.155974	0.0779872	−	0.996954i	$-0.475151\pi$
$983$	4.33715e21	0.155974	0.0779872	+	0.996954i	$0.475151\pi$
$984$	−1.06965e22	−0.381751
$985$	4.19513e21	0.148585
$986$	−1.48864e22	−0.523253
$987$	3.27630e22	1.14289
$988$	1.95255e20	0.00675967
$989$	−1.19327e22	−0.409984
$990$	−4.28057e19	−0.00145961
$991$	5.10575e22	1.72786	0.863928	−	0.503615i	$-0.167997\pi$
$991$	5.10575e22	1.72786	0.863928	+	0.503615i	$0.167997\pi$
$992$	−9.80988e21	−0.329478
$993$	−2.75941e22	−0.919808
$994$	−1.30318e22	−0.431127
$995$	1.10430e22	0.362588
$996$	−2.69137e22	−0.877057
$997$	3.95869e22	1.28038	0.640188	−	0.768219i	$-0.278857\pi$
$997$	3.95869e22	1.28038	0.640188	+	0.768219i	$0.278857\pi$
$998$	2.50299e22	0.803488
$999$	−5.34587e21	−0.170325

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.16.a.d.1.2	✓	2
3.2	odd	2		90.16.a.j.1.2		2
4.3	odd	2		80.16.a.f.1.1		2
5.2	odd	4		50.16.b.e.49.3		4
5.3	odd	4		50.16.b.e.49.2		4
5.4	even	2		50.16.a.f.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.16.a.d.1.2	✓	2	1.1	even	1	trivial
50.16.a.f.1.1		2	5.4	even	2
50.16.b.e.49.2		4	5.3	odd	4
50.16.b.e.49.3		4	5.2	odd	4
80.16.a.f.1.1		2	4.3	odd	2
90.16.a.j.1.2		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q+128.000 q^{2} +3972.58 q^{3} +16384.0 q^{4} +78125.0 q^{5} +508490. q^{6} +1.57794e6 q^{7} +2.09715e6 q^{8} +1.43247e6 q^{9} +1.00000e7 q^{10} -2.98824e6 q^{11} +6.50867e7 q^{12} +4.92637e6 q^{13} +2.01976e8 q^{14} +3.10358e8 q^{15} +2.68435e8 q^{16} +6.45145e8 q^{17} +1.83357e8 q^{18} +2.41911e9 q^{19} +1.28000e9 q^{20} +6.26849e9 q^{21} -3.82495e8 q^{22} +2.33075e10 q^{23} +8.33110e9 q^{24} +6.10352e9 q^{25} +6.30575e8 q^{26} -5.13115e10 q^{27} +2.58530e10 q^{28} -1.80269e11 q^{29} +3.97258e10 q^{30} -2.85505e11 q^{31} +3.43597e10 q^{32} -1.18710e10 q^{33} +8.25786e10 q^{34} +1.23277e11 q^{35} +2.34697e10 q^{36} +1.04185e11 q^{37} +3.09646e11 q^{38} +1.95704e10 q^{39} +1.63840e11 q^{40} -1.28393e12 q^{41} +8.02367e11 q^{42} -5.11969e11 q^{43} -4.89593e10 q^{44} +1.11912e11 q^{45} +2.98336e12 q^{46} +5.22662e12 q^{47} +1.06638e12 q^{48} -2.25766e12 q^{49} +7.81250e11 q^{50} +2.56289e12 q^{51} +8.07136e10 q^{52} -1.39001e13 q^{53} -6.56788e12 q^{54} -2.33456e11 q^{55} +3.30918e12 q^{56} +9.61011e12 q^{57} -2.30744e13 q^{58} +9.11699e12 q^{59} +5.08490e12 q^{60} -1.50270e13 q^{61} -3.65446e13 q^{62} +2.26036e12 q^{63} +4.39805e12 q^{64} +3.84872e11 q^{65} -1.51949e12 q^{66} +2.18097e13 q^{67} +1.05701e13 q^{68} +9.25908e13 q^{69} +1.57794e13 q^{70} -6.45213e13 q^{71} +3.00412e12 q^{72} +9.76233e13 q^{73} +1.33356e13 q^{74} +2.42467e13 q^{75} +3.96347e13 q^{76} -4.71526e12 q^{77} +2.50501e12 q^{78} +2.35831e14 q^{79} +2.09715e13 q^{80} -2.24394e14 q^{81} -1.64343e14 q^{82} -4.13505e14 q^{83} +1.02703e14 q^{84} +5.04020e13 q^{85} -6.55320e13 q^{86} -7.16133e14 q^{87} -6.26679e12 q^{88} +5.45429e14 q^{89} +1.43247e13 q^{90} +7.77352e12 q^{91} +3.81870e14 q^{92} -1.13419e15 q^{93} +6.69007e14 q^{94} +1.88993e14 q^{95} +1.36497e14 q^{96} +4.71267e14 q^{97} -2.88981e14 q^{98} -4.28057e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 256 q^{2} - 1844 q^{3} + 32768 q^{4} + 156250 q^{5} - 236032 q^{6} - 984932 q^{7} + 4194304 q^{8} + 20916154 q^{9} + 20000000 q^{10} + 111552144 q^{11} - 30212096 q^{12} + 289313596 q^{13} - 126071296 q^{14}+ \cdots + 22\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q + 256 * q^2 - 1844 * q^3 + 32768 * q^4 + 156250 * q^5 - 236032 * q^6 - 984932 * q^7 + 4194304 * q^8 + 20916154 * q^9 + 20000000 * q^10 + 111552144 * q^11 - 30212096 * q^12 + 289313596 * q^13 - 126071296 * q^14 - 144062500 * q^15 + 536870912 * q^16 + 1421739348 * q^17 + 2677267712 * q^18 + 6159406120 * q^19 + 2560000000 * q^20 + 21175644704 * q^21 + 14278674432 * q^22 - 4330165884 * q^23 - 3867148288 * q^24 + 12207031250 * q^25 + 37032140288 * q^26 - 81178356680 * q^27 - 16137125888 * q^28 - 164295941940 * q^29 - 18440000000 * q^30 - 282710965016 * q^31 + 68719476736 * q^32 - 678104159568 * q^33 + 181982636544 * q^34 - 76947812500 * q^35 + 342690267136 * q^36 + 790105159228 * q^37 + 788403983360 * q^38 - 1634590297912 * q^39 + 327680000000 * q^40 - 374717265276 * q^41 + 2710482522112 * q^42 - 923824433204 * q^43 + 1827670327296 * q^44 + 1634074531250 * q^45 - 554261233152 * q^46 + 4796717212428 * q^47 - 494994980864 * q^48 - 436909177374 * q^49 + 1562500000000 * q^50 - 1954230185256 * q^51 + 4740113956864 * q^52 - 2768921292084 * q^53 - 10390829655040 * q^54 + 8715011250000 * q^55 - 2065552113664 * q^56 - 12145610545840 * q^57 - 21029880568320 * q^58 - 20737233989880 * q^59 - 2360320000000 * q^60 + 577887725164 * q^61 - 36187003522048 * q^62 - 47673833661364 * q^63 + 8796093022208 * q^64 + 22602624687500 * q^65 - 86797332424704 * q^66 + 86553258077668 * q^67 + 23293777477632 * q^68 + 253347375370848 * q^69 - 9849320000000 * q^70 + 73838906689464 * q^71 + 43864354193408 * q^72 + 39973727021476 * q^73 + 101133460381184 * q^74 - 11254882812500 * q^75 + 100915709870080 * q^76 - 298267692171504 * q^77 - 209227558132736 * q^78 + 421665304874800 * q^79 + 41943040000000 * q^80 - 330240444620318 * q^81 - 47963809955328 * q^82 - 721146660038964 * q^83 + 346941762830336 * q^84 + 111073386562500 * q^85 - 118249527450112 * q^86 - 809041723785720 * q^87 + 233941801893888 * q^88 + 363712836623220 * q^89 + 209161540000000 * q^90 - 721074767062936 * q^91 - 70945437843456 * q^92 - 1150443201950848 * q^93 + 613979803190784 * q^94 + 481203603125000 * q^95 - 63359357550592 * q^96 + 289030099396948 * q^97 - 55924374703872 * q^98 + 2227387596150288 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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