LMFDB - Embedded newform 138.8.a.h.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,8,Mod(1,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("138.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	138.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$43.1091335168$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 8367x^{2} - 89140x + 11077220 $ x^4 - 2x^3 - 8367x^2 - 89140*x + 11077220
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-56.1267$ of defining polynomial
Character	$\chi$	$=$	138.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +366.876 q^{5} +216.000 q^{6} -561.721 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +366.876 q^{5} +216.000 q^{6} -561.721 q^{7} +512.000 q^{8} +729.000 q^{9} +2935.00 q^{10} -1096.20 q^{11} +1728.00 q^{12} +6925.11 q^{13} -4493.77 q^{14} +9905.64 q^{15} +4096.00 q^{16} +13654.6 q^{17} +5832.00 q^{18} +29540.8 q^{19} +23480.0 q^{20} -15166.5 q^{21} -8769.58 q^{22} -12167.0 q^{23} +13824.0 q^{24} +56472.7 q^{25} +55400.9 q^{26} +19683.0 q^{27} -35950.1 q^{28} +150266. q^{29} +79245.1 q^{30} -204841. q^{31} +32768.0 q^{32} -29597.3 q^{33} +109237. q^{34} -206082. q^{35} +46656.0 q^{36} -492163. q^{37} +236327. q^{38} +186978. q^{39} +187840. q^{40} +416521. q^{41} -121332. q^{42} +371500. q^{43} -70156.6 q^{44} +267452. q^{45} -97336.0 q^{46} +930660. q^{47} +110592. q^{48} -508013. q^{49} +451782. q^{50} +368675. q^{51} +443207. q^{52} +1.01318e6 q^{53} +157464. q^{54} -402168. q^{55} -287601. q^{56} +797602. q^{57} +1.20213e6 q^{58} -2.28957e6 q^{59} +633961. q^{60} +2.95586e6 q^{61} -1.63873e6 q^{62} -409495. q^{63} +262144. q^{64} +2.54066e6 q^{65} -236779. q^{66} -1.46138e6 q^{67} +873896. q^{68} -328509. q^{69} -1.64865e6 q^{70} -1.82588e6 q^{71} +373248. q^{72} -40352.1 q^{73} -3.93731e6 q^{74} +1.52476e6 q^{75} +1.89061e6 q^{76} +615757. q^{77} +1.49582e6 q^{78} -2.36229e6 q^{79} +1.50272e6 q^{80} +531441. q^{81} +3.33217e6 q^{82} +1.27885e6 q^{83} -970654. q^{84} +5.00955e6 q^{85} +2.97200e6 q^{86} +4.05718e6 q^{87} -561253. q^{88} +3.88462e6 q^{89} +2.13962e6 q^{90} -3.88998e6 q^{91} -778688. q^{92} -5.53072e6 q^{93} +7.44528e6 q^{94} +1.08378e7 q^{95} +884736. q^{96} -8.46502e6 q^{97} -4.06410e6 q^{98} -799128. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 32 q^{2} + 108 q^{3} + 256 q^{4} + 270 q^{5} + 864 q^{6} + 2022 q^{7} + 2048 q^{8} + 2916 q^{9}+O(q^{10}) $ 4 * q + 32 * q^2 + 108 * q^3 + 256 * q^4 + 270 * q^5 + 864 * q^6 + 2022 * q^7 + 2048 * q^8 + 2916 * q^9	\( 4 q + 32 q^{2} + 108 q^{3} + 256 q^{4} + 270 q^{5} + 864 q^{6} + 2022 q^{7} + 2048 q^{8} + 2916 q^{9} + 2160 q^{10} + 4120 q^{11} + 6912 q^{12} + 8036 q^{13} + 16176 q^{14} + 7290 q^{15} + 16384 q^{16} + 37182 q^{17} + 23328 q^{18} + 5702 q^{19} + 17280 q^{20} + 54594 q^{21} + 32960 q^{22} - 48668 q^{23} + 55296 q^{24} + 121480 q^{25} + 64288 q^{26} + 78732 q^{27} + 129408 q^{28} + 217716 q^{29} + 58320 q^{30} + 222852 q^{31} + 131072 q^{32} + 111240 q^{33} + 297456 q^{34} + 68440 q^{35} + 186624 q^{36} + 486428 q^{37} + 45616 q^{38} + 216972 q^{39} + 138240 q^{40} + 338336 q^{41} + 436752 q^{42} + 730974 q^{43} + 263680 q^{44} + 196830 q^{45} - 389344 q^{46} + 338248 q^{47} + 442368 q^{48} - 310552 q^{49} + 971840 q^{50} + 1003914 q^{51} + 514304 q^{52} - 375502 q^{53} + 629856 q^{54} + 424840 q^{55} + 1035264 q^{56} + 153954 q^{57} + 1741728 q^{58} + 71392 q^{59} + 466560 q^{60} + 2101164 q^{61} + 1782816 q^{62} + 1474038 q^{63} + 1048576 q^{64} + 1578780 q^{65} + 889920 q^{66} + 4337162 q^{67} + 2379648 q^{68} - 1314036 q^{69} + 547520 q^{70} + 2288016 q^{71} + 1492992 q^{72} - 1107328 q^{73} + 3891424 q^{74} + 3279960 q^{75} + 364928 q^{76} + 5826200 q^{77} + 1735776 q^{78} + 60610 q^{79} + 1105920 q^{80} + 2125764 q^{81} + 2706688 q^{82} + 1485464 q^{83} + 3494016 q^{84} - 8843820 q^{85} + 5847792 q^{86} + 5878332 q^{87} + 2109440 q^{88} + 1485090 q^{89} + 1574640 q^{90} - 2898412 q^{91} - 3114752 q^{92} + 6017004 q^{93} + 2705984 q^{94} + 8545200 q^{95} + 3538944 q^{96} + 1935444 q^{97} - 2484416 q^{98} + 3003480 q^{99}+O(q^{100}) \) 4 * q + 32 * q^2 + 108 * q^3 + 256 * q^4 + 270 * q^5 + 864 * q^6 + 2022 * q^7 + 2048 * q^8 + 2916 * q^9 + 2160 * q^10 + 4120 * q^11 + 6912 * q^12 + 8036 * q^13 + 16176 * q^14 + 7290 * q^15 + 16384 * q^16 + 37182 * q^17 + 23328 * q^18 + 5702 * q^19 + 17280 * q^20 + 54594 * q^21 + 32960 * q^22 - 48668 * q^23 + 55296 * q^24 + 121480 * q^25 + 64288 * q^26 + 78732 * q^27 + 129408 * q^28 + 217716 * q^29 + 58320 * q^30 + 222852 * q^31 + 131072 * q^32 + 111240 * q^33 + 297456 * q^34 + 68440 * q^35 + 186624 * q^36 + 486428 * q^37 + 45616 * q^38 + 216972 * q^39 + 138240 * q^40 + 338336 * q^41 + 436752 * q^42 + 730974 * q^43 + 263680 * q^44 + 196830 * q^45 - 389344 * q^46 + 338248 * q^47 + 442368 * q^48 - 310552 * q^49 + 971840 * q^50 + 1003914 * q^51 + 514304 * q^52 - 375502 * q^53 + 629856 * q^54 + 424840 * q^55 + 1035264 * q^56 + 153954 * q^57 + 1741728 * q^58 + 71392 * q^59 + 466560 * q^60 + 2101164 * q^61 + 1782816 * q^62 + 1474038 * q^63 + 1048576 * q^64 + 1578780 * q^65 + 889920 * q^66 + 4337162 * q^67 + 2379648 * q^68 - 1314036 * q^69 + 547520 * q^70 + 2288016 * q^71 + 1492992 * q^72 - 1107328 * q^73 + 3891424 * q^74 + 3279960 * q^75 + 364928 * q^76 + 5826200 * q^77 + 1735776 * q^78 + 60610 * q^79 + 1105920 * q^80 + 2125764 * q^81 + 2706688 * q^82 + 1485464 * q^83 + 3494016 * q^84 - 8843820 * q^85 + 5847792 * q^86 + 5878332 * q^87 + 2109440 * q^88 + 1485090 * q^89 + 1574640 * q^90 - 2898412 * q^91 - 3114752 * q^92 + 6017004 * q^93 + 2705984 * q^94 + 8545200 * q^95 + 3538944 * q^96 + 1935444 * q^97 - 2484416 * q^98 + 3003480 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	8.00000	0.707107
$2$	8.00000	0.707107
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	64.0000	0.500000
$5$	366.876	1.31257	0.656287	−	0.754511i	$-0.272126\pi$
$5$	366.876	1.31257	0.656287	+	0.754511i	$0.272126\pi$
$6$	216.000	0.408248
$7$	−561.721	−0.618981	−0.309491	−	0.950903i	$-0.600159\pi$
$7$	−561.721	−0.618981	−0.309491	+	0.950903i	$0.600159\pi$
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	2935.00	0.928130
$11$	−1096.20	−0.248322	−0.124161	−	0.992262i	$-0.539624\pi$
$11$	−1096.20	−0.248322	−0.124161	+	0.992262i	$0.539624\pi$
$12$	1728.00	0.288675
$13$	6925.11	0.874229	0.437115	−	0.899406i	$-0.356000\pi$
$13$	6925.11	0.874229	0.437115	+	0.899406i	$0.356000\pi$
$14$	−4493.77	−0.437686
$15$	9905.64	0.757815
$16$	4096.00	0.250000
$17$	13654.6	0.674075	0.337038	−	0.941491i	$-0.390575\pi$
$17$	13654.6	0.674075	0.337038	+	0.941491i	$0.390575\pi$
$18$	5832.00	0.235702
$19$	29540.8	0.988064	0.494032	−	0.869444i	$-0.335523\pi$
$19$	29540.8	0.988064	0.494032	+	0.869444i	$0.335523\pi$
$20$	23480.0	0.656287
$21$	−15166.5	−0.357369
$22$	−8769.58	−0.175590
$23$	−12167.0	−0.208514
$23$	−12167.0	−0.208514
$24$	13824.0	0.204124
$25$	56472.7	0.722851
$26$	55400.9	0.618173
$27$	19683.0	0.192450
$28$	−35950.1	−0.309491
$29$	150266.	1.14411	0.572054	−	0.820216i	$-0.306147\pi$
$29$	150266.	1.14411	0.572054	+	0.820216i	$0.306147\pi$
$30$	79245.1	0.535856
$31$	−204841.	−1.23496	−0.617479	−	0.786588i	$-0.711846\pi$
$31$	−204841.	−1.23496	−0.617479	+	0.786588i	$0.711846\pi$
$32$	32768.0	0.176777
$33$	−29597.3	−0.143368
$34$	109237.	0.476643
$35$	−206082.	−0.812459
$36$	46656.0	0.166667
$37$	−492163.	−1.59736	−0.798681	−	0.601755i	$-0.794468\pi$
$37$	−492163.	−1.59736	−0.798681	+	0.601755i	$0.794468\pi$
$38$	236327.	0.698667
$39$	186978.	0.504736
$40$	187840.	0.464065
$41$	416521.	0.943829	0.471915	−	0.881644i	$-0.343563\pi$
$41$	416521.	0.943829	0.471915	+	0.881644i	$0.343563\pi$
$42$	−121332.	−0.252698
$43$	371500.	0.712557	0.356279	−	0.934380i	$-0.384045\pi$
$43$	371500.	0.712557	0.356279	+	0.934380i	$0.384045\pi$
$44$	−70156.6	−0.124161
$45$	267452.	0.437525
$46$	−97336.0	−0.147442
$47$	930660.	1.30752	0.653760	−	0.756702i	$-0.273191\pi$
$47$	930660.	1.30752	0.653760	+	0.756702i	$0.273191\pi$
$48$	110592.	0.144338
$49$	−508013.	−0.616862
$50$	451782.	0.511133
$51$	368675.	0.389177
$52$	443207.	0.437115
$53$	1.01318e6	0.934804	0.467402	−	0.884045i	$-0.345190\pi$
$53$	1.01318e6	0.934804	0.467402	+	0.884045i	$0.345190\pi$
$54$	157464.	0.136083
$55$	−402168.	−0.325940
$56$	−287601.	−0.218843
$57$	797602.	0.570459
$58$	1.20213e6	0.809007
$59$	−2.28957e6	−1.45135	−0.725676	−	0.688036i	$-0.758473\pi$
$59$	−2.28957e6	−1.45135	−0.725676	+	0.688036i	$0.758473\pi$
$60$	633961.	0.378908
$61$	2.95586e6	1.66736	0.833681	−	0.552246i	$-0.186229\pi$
$61$	2.95586e6	1.66736	0.833681	+	0.552246i	$0.186229\pi$
$62$	−1.63873e6	−0.873246
$63$	−409495.	−0.206327
$64$	262144.	0.125000
$65$	2.54066e6	1.14749
$66$	−236779.	−0.101377
$67$	−1.46138e6	−0.593609	−0.296804	−	0.954938i	$-0.595921\pi$
$67$	−1.46138e6	−0.593609	−0.296804	+	0.954938i	$0.595921\pi$
$68$	873896.	0.337038
$69$	−328509.	−0.120386
$70$	−1.64865e6	−0.574495
$71$	−1.82588e6	−0.605437	−0.302718	−	0.953080i	$-0.597894\pi$
$71$	−1.82588e6	−0.605437	−0.302718	+	0.953080i	$0.597894\pi$
$72$	373248.	0.117851
$73$	−40352.1	−0.0121405	−0.00607024	−	0.999982i	$-0.501932\pi$
$73$	−40352.1	−0.0121405	−0.00607024	+	0.999982i	$0.501932\pi$
$74$	−3.93731e6	−1.12951
$75$	1.52476e6	0.417338
$76$	1.89061e6	0.494032
$77$	615757.	0.153706
$78$	1.49582e6	0.356903
$79$	−2.36229e6	−0.539061	−0.269531	−	0.962992i	$-0.586869\pi$
$79$	−2.36229e6	−0.539061	−0.269531	+	0.962992i	$0.586869\pi$
$80$	1.50272e6	0.328144
$81$	531441.	0.111111
$82$	3.33217e6	0.667388
$83$	1.27885e6	0.245497	0.122749	−	0.992438i	$-0.460829\pi$
$83$	1.27885e6	0.245497	0.122749	+	0.992438i	$0.460829\pi$
$84$	−970654.	−0.178684
$85$	5.00955e6	0.884774
$86$	2.97200e6	0.503854
$87$	4.05718e6	0.660551
$88$	−561253.	−0.0877949
$89$	3.88462e6	0.584095	0.292047	−	0.956404i	$-0.405664\pi$
$89$	3.88462e6	0.584095	0.292047	+	0.956404i	$0.405664\pi$
$90$	2.13962e6	0.309377
$91$	−3.88998e6	−0.541131
$92$	−778688.	−0.104257
$93$	−5.53072e6	−0.713003
$94$	7.44528e6	0.924556
$95$	1.08378e7	1.29691
$96$	884736.	0.102062
$97$	−8.46502e6	−0.941731	−0.470865	−	0.882205i	$-0.656058\pi$
$97$	−8.46502e6	−0.941731	−0.470865	+	0.882205i	$0.656058\pi$
$98$	−4.06410e6	−0.436188
$99$	−799128.	−0.0827738
$100$	3.61425e6	0.361425
$101$	5.79563e6	0.559727	0.279863	−	0.960040i	$-0.409711\pi$
$101$	5.79563e6	0.559727	0.279863	+	0.960040i	$0.409711\pi$
$102$	2.94940e6	0.275190
$103$	1.34033e6	0.120860	0.0604298	−	0.998172i	$-0.480753\pi$
$103$	1.34033e6	0.120860	0.0604298	+	0.998172i	$0.480753\pi$
$104$	3.54566e6	0.309087
$105$	−5.56421e6	−0.469073
$106$	8.10543e6	0.661006
$107$	−1.37815e7	−1.08756	−0.543779	−	0.839229i	$-0.683007\pi$
$107$	−1.37815e7	−1.08756	−0.543779	+	0.839229i	$0.683007\pi$
$108$	1.25971e6	0.0962250
$109$	9.40692e6	0.695752	0.347876	−	0.937541i	$-0.386903\pi$
$109$	9.40692e6	0.695752	0.347876	+	0.937541i	$0.386903\pi$
$110$	−3.21734e6	−0.230475
$111$	−1.32884e7	−0.922237
$112$	−2.30081e6	−0.154745
$113$	−776740.	−0.0506409	−0.0253204	−	0.999679i	$-0.508061\pi$
$113$	−776740.	−0.0506409	−0.0253204	+	0.999679i	$0.508061\pi$
$114$	6.38082e6	0.403375
$115$	−4.46378e6	−0.273691
$116$	9.61701e6	0.572054
$117$	5.04841e6	0.291410
$118$	−1.83166e7	−1.02626
$119$	−7.67008e6	−0.417240
$120$	5.07169e6	0.267928
$121$	−1.82855e7	−0.938336
$122$	2.36469e7	1.17900
$123$	1.12461e7	0.544920
$124$	−1.31099e7	−0.617479
$125$	−7.94369e6	−0.363779
$126$	−3.27596e6	−0.145895
$127$	−2.02779e7	−0.878434	−0.439217	−	0.898381i	$-0.644744\pi$
$127$	−2.02779e7	−0.878434	−0.439217	+	0.898381i	$0.644744\pi$
$128$	2.09715e6	0.0883883
$129$	1.00305e7	0.411395
$130$	2.03252e7	0.811398
$131$	−5.73353e6	−0.222829	−0.111415	−	0.993774i	$-0.535538\pi$
$131$	−5.73353e6	−0.222829	−0.111415	+	0.993774i	$0.535538\pi$
$132$	−1.89423e6	−0.0716842
$133$	−1.65937e7	−0.611593
$134$	−1.16910e7	−0.419745
$135$	7.22121e6	0.252605
$136$	6.99116e6	0.238322
$137$	−2.96971e7	−0.986716	−0.493358	−	0.869826i	$-0.664231\pi$
$137$	−2.96971e7	−0.986716	−0.493358	+	0.869826i	$0.664231\pi$
$138$	−2.62807e6	−0.0851257
$139$	2.70200e7	0.853362	0.426681	−	0.904402i	$-0.359683\pi$
$139$	2.70200e7	0.853362	0.426681	+	0.904402i	$0.359683\pi$
$140$	−1.31892e7	−0.406229
$141$	2.51278e7	0.754897
$142$	−1.46071e7	−0.428108
$143$	−7.59129e6	−0.217090
$144$	2.98598e6	0.0833333
$145$	5.51289e7	1.50173
$146$	−322816.	−0.00858461
$147$	−1.37163e7	−0.356146
$148$	−3.14984e7	−0.798681
$149$	−1.22268e7	−0.302803	−0.151401	−	0.988472i	$-0.548379\pi$
$149$	−1.22268e7	−0.302803	−0.151401	+	0.988472i	$0.548379\pi$
$150$	1.21981e7	0.295103
$151$	−7.91442e7	−1.87068	−0.935341	−	0.353747i	$-0.884907\pi$
$151$	−7.91442e7	−1.87068	−0.935341	+	0.353747i	$0.884907\pi$
$152$	1.51249e7	0.349333
$153$	9.95422e6	0.224692
$154$	4.92606e6	0.108687
$155$	−7.51513e7	−1.62097
$156$	1.19666e7	0.252368
$157$	−6.65855e7	−1.37319	−0.686595	−	0.727040i	$-0.740895\pi$
$157$	−6.65855e7	−1.37319	−0.686595	+	0.727040i	$0.740895\pi$
$158$	−1.88983e7	−0.381174
$159$	2.73558e7	0.539709
$160$	1.20218e7	0.232033
$161$	6.83446e6	0.129066
$162$	4.25153e6	0.0785674
$163$	5.57898e7	1.00902	0.504508	−	0.863407i	$-0.331674\pi$
$163$	5.57898e7	1.00902	0.504508	+	0.863407i	$0.331674\pi$
$164$	2.66573e7	0.471915
$165$	−1.08585e7	−0.188182
$166$	1.02308e7	0.173593
$167$	−2.85952e7	−0.475100	−0.237550	−	0.971375i	$-0.576344\pi$
$167$	−2.85952e7	−0.475100	−0.237550	+	0.971375i	$0.576344\pi$
$168$	−7.76523e6	−0.126349
$169$	−1.47913e7	−0.235724
$170$	4.00764e7	0.625629
$171$	2.15353e7	0.329355
$172$	2.37760e7	0.356279
$173$	−5.94429e7	−0.872847	−0.436424	−	0.899741i	$-0.643755\pi$
$173$	−5.94429e7	−0.872847	−0.436424	+	0.899741i	$0.643755\pi$
$174$	3.24574e7	0.467080
$175$	−3.17219e7	−0.447431
$176$	−4.49002e6	−0.0620804
$177$	−6.18185e7	−0.837939
$178$	3.10769e7	0.413017
$179$	−1.09127e8	−1.42216	−0.711079	−	0.703112i	$-0.751793\pi$
$179$	−1.09127e8	−1.42216	−0.711079	+	0.703112i	$0.751793\pi$
$180$	1.71169e7	0.218762
$181$	−9.89431e7	−1.24025	−0.620127	−	0.784501i	$-0.712919\pi$
$181$	−9.89431e7	−1.24025	−0.620127	+	0.784501i	$0.712919\pi$
$182$	−3.11199e7	−0.382638
$183$	7.98083e7	0.962652
$184$	−6.22950e6	−0.0737210
$185$	−1.80563e8	−2.09666
$186$	−4.42457e7	−0.504169
$187$	−1.49682e7	−0.167387
$188$	5.95622e7	0.653760
$189$	−1.10564e7	−0.119123
$190$	8.67025e7	0.917052
$191$	−6.19114e7	−0.642916	−0.321458	−	0.946924i	$-0.604173\pi$
$191$	−6.19114e7	−0.642916	−0.321458	+	0.946924i	$0.604173\pi$
$192$	7.07789e6	0.0721688
$193$	1.03484e8	1.03615	0.518076	−	0.855334i	$-0.326648\pi$
$193$	1.03484e8	1.03615	0.518076	+	0.855334i	$0.326648\pi$
$194$	−6.77201e7	−0.665904
$195$	6.85977e7	0.662504
$196$	−3.25128e7	−0.308431
$197$	−1.11986e8	−1.04360	−0.521798	−	0.853069i	$-0.674739\pi$
$197$	−1.11986e8	−1.04360	−0.521798	+	0.853069i	$0.674739\pi$
$198$	−6.39302e6	−0.0585299
$199$	−1.09861e7	−0.0988228	−0.0494114	−	0.998779i	$-0.515735\pi$
$199$	−1.09861e7	−0.0988228	−0.0494114	+	0.998779i	$0.515735\pi$
$200$	2.89140e7	0.255566
$201$	−3.94572e7	−0.342720
$202$	4.63651e7	0.395787
$203$	−8.44074e7	−0.708182
$204$	2.35952e7	0.194589
$205$	1.52811e8	1.23885
$206$	1.07226e7	0.0854606
$207$	−8.86974e6	−0.0695048
$208$	2.83653e7	0.218557
$209$	−3.23826e7	−0.245357
$210$	−4.45136e7	−0.331685
$211$	7.14052e7	0.523289	0.261644	−	0.965164i	$-0.415735\pi$
$211$	7.14052e7	0.523289	0.261644	+	0.965164i	$0.415735\pi$
$212$	6.48434e7	0.467402
$213$	−4.92988e7	−0.349549
$214$	−1.10252e8	−0.769019
$215$	1.36294e8	0.935284
$216$	1.00777e7	0.0680414
$217$	1.15064e8	0.764415
$218$	7.52553e7	0.491971
$219$	−1.08951e6	−0.00700931
$220$	−2.57388e7	−0.162970
$221$	9.45598e7	0.589296
$222$	−1.06307e8	−0.652120
$223$	1.21124e8	0.731415	0.365707	−	0.930730i	$-0.380827\pi$
$223$	1.21124e8	0.731415	0.365707	+	0.930730i	$0.380827\pi$
$224$	−1.84065e7	−0.109421
$225$	4.11686e7	0.240950
$226$	−6.21392e6	−0.0358085
$227$	3.23693e7	0.183672	0.0918360	−	0.995774i	$-0.470726\pi$
$227$	3.23693e7	0.183672	0.0918360	+	0.995774i	$0.470726\pi$
$228$	5.10465e7	0.285229
$229$	2.14673e8	1.18128	0.590642	−	0.806934i	$-0.298875\pi$
$229$	2.14673e8	1.18128	0.590642	+	0.806934i	$0.298875\pi$
$230$	−3.57102e7	−0.193528
$231$	1.66254e7	0.0887424
$232$	7.69361e7	0.404503
$233$	−2.34580e8	−1.21491	−0.607457	−	0.794353i	$-0.707810\pi$
$233$	−2.34580e8	−1.21491	−0.607457	+	0.794353i	$0.707810\pi$
$234$	4.03873e7	0.206058
$235$	3.41436e8	1.71622
$236$	−1.46533e8	−0.725676
$237$	−6.37818e7	−0.311227
$238$	−6.13607e7	−0.295033
$239$	−1.73526e8	−0.822189	−0.411095	−	0.911593i	$-0.634853\pi$
$239$	−1.73526e8	−0.822189	−0.411095	+	0.911593i	$0.634853\pi$
$240$	4.05735e7	0.189454
$241$	1.89649e8	0.872752	0.436376	−	0.899764i	$-0.356262\pi$
$241$	1.89649e8	0.872752	0.436376	+	0.899764i	$0.356262\pi$
$242$	−1.46284e8	−0.663504
$243$	1.43489e7	0.0641500
$244$	1.89175e8	0.833681
$245$	−1.86377e8	−0.809678
$246$	8.99685e7	0.385317
$247$	2.04574e8	0.863794
$248$	−1.04879e8	−0.436623
$249$	3.45290e7	0.141738
$250$	−6.35495e7	−0.257230
$251$	2.71105e8	1.08213	0.541064	−	0.840981i	$-0.318022\pi$
$251$	2.71105e8	1.08213	0.541064	+	0.840981i	$0.318022\pi$
$252$	−2.62076e7	−0.103164
$253$	1.33374e7	0.0517786
$254$	−1.62223e8	−0.621147
$255$	1.35258e8	0.510824
$256$	1.67772e7	0.0625000
$257$	4.36260e8	1.60317	0.801584	−	0.597882i	$-0.203991\pi$
$257$	4.36260e8	1.60317	0.801584	+	0.597882i	$0.203991\pi$
$258$	8.02441e7	0.290900
$259$	2.76458e8	0.988737
$260$	1.62602e8	0.573745
$261$	1.09544e8	0.381369
$262$	−4.58682e7	−0.157564
$263$	1.27332e8	0.431609	0.215805	−	0.976437i	$-0.430763\pi$
$263$	1.27332e8	0.431609	0.215805	+	0.976437i	$0.430763\pi$
$264$	−1.51538e7	−0.0506884
$265$	3.71711e8	1.22700
$266$	−1.32750e8	−0.432461
$267$	1.04885e8	0.337227
$268$	−9.35281e7	−0.296804
$269$	2.50990e8	0.786182	0.393091	−	0.919500i	$-0.371406\pi$
$269$	2.50990e8	0.786182	0.393091	+	0.919500i	$0.371406\pi$
$270$	5.77697e7	0.178619
$271$	1.19209e8	0.363844	0.181922	−	0.983313i	$-0.441768\pi$
$271$	1.19209e8	0.363844	0.181922	+	0.983313i	$0.441768\pi$
$272$	5.59293e7	0.168519
$273$	−1.05029e8	−0.312422
$274$	−2.37577e8	−0.697714
$275$	−6.19052e7	−0.179499
$276$	−2.10246e7	−0.0601929
$277$	−2.70183e8	−0.763799	−0.381899	−	0.924204i	$-0.624730\pi$
$277$	−2.70183e8	−0.763799	−0.381899	+	0.924204i	$0.624730\pi$
$278$	2.16160e8	0.603418
$279$	−1.49329e8	−0.411652
$280$	−1.05514e8	−0.287248
$281$	−6.33010e8	−1.70192	−0.850958	−	0.525233i	$-0.823978\pi$
$281$	−6.33010e8	−1.70192	−0.850958	+	0.525233i	$0.823978\pi$
$282$	2.01022e8	0.533793
$283$	6.68305e8	1.75276	0.876379	−	0.481622i	$-0.159952\pi$
$283$	6.68305e8	1.75276	0.876379	+	0.481622i	$0.159952\pi$
$284$	−1.16857e8	−0.302718
$285$	2.92621e8	0.748770
$286$	−6.07303e7	−0.153506
$287$	−2.33969e8	−0.584213
$288$	2.38879e7	0.0589256
$289$	−2.23890e8	−0.545623
$290$	4.41031e8	1.06188
$291$	−2.28555e8	−0.543709
$292$	−2.58253e6	−0.00607024
$293$	5.36402e8	1.24582	0.622908	−	0.782295i	$-0.285951\pi$
$293$	5.36402e8	1.24582	0.622908	+	0.782295i	$0.285951\pi$
$294$	−1.09731e8	−0.251833
$295$	−8.39989e8	−1.90501
$296$	−2.51988e8	−0.564753
$297$	−2.15765e7	−0.0477895
$298$	−9.78141e7	−0.214114
$299$	−8.42579e7	−0.182289
$300$	9.75849e7	0.208669
$301$	−2.08680e8	−0.441059
$302$	−6.33154e8	−1.32277
$303$	1.56482e8	0.323158
$304$	1.20999e8	0.247016
$305$	1.08443e9	2.18854
$306$	7.96337e7	0.158881
$307$	−1.07221e8	−0.211493	−0.105746	−	0.994393i	$-0.533723\pi$
$307$	−1.07221e8	−0.211493	−0.105746	+	0.994393i	$0.533723\pi$
$308$	3.94084e7	0.0768532
$309$	3.61889e7	0.0697783
$310$	−6.01211e8	−1.14620
$311$	−9.74611e8	−1.83726	−0.918629	−	0.395122i	$-0.870702\pi$
$311$	−9.74611e8	−1.83726	−0.918629	+	0.395122i	$0.870702\pi$
$312$	9.57328e7	0.178451
$313$	−6.47093e8	−1.19278	−0.596392	−	0.802693i	$-0.703400\pi$
$313$	−6.47093e8	−1.19278	−0.596392	+	0.802693i	$0.703400\pi$
$314$	−5.32684e8	−0.970992
$315$	−1.50234e8	−0.270820
$316$	−1.51186e8	−0.269531
$317$	5.22962e8	0.922068	0.461034	−	0.887382i	$-0.347479\pi$
$317$	5.22962e8	0.922068	0.461034	+	0.887382i	$0.347479\pi$
$318$	2.18847e8	0.381632
$319$	−1.64721e8	−0.284107
$320$	9.61742e7	0.164072
$321$	−3.72100e8	−0.627902
$322$	5.46757e7	0.0912638
$323$	4.03369e8	0.666029
$324$	3.40122e7	0.0555556
$325$	3.91080e8	0.631937
$326$	4.46319e8	0.713483
$327$	2.53987e8	0.401693
$328$	2.13259e8	0.333694
$329$	−5.22771e8	−0.809330
$330$	−8.68683e7	−0.133065
$331$	−1.00533e8	−0.152373	−0.0761867	−	0.997094i	$-0.524275\pi$
$331$	−1.00533e8	−0.152373	−0.0761867	+	0.997094i	$0.524275\pi$
$332$	8.18465e7	0.122749
$333$	−3.58787e8	−0.532454
$334$	−2.28761e8	−0.335946
$335$	−5.36144e8	−0.779156
$336$	−6.21218e7	−0.0893422
$337$	−4.77653e8	−0.679842	−0.339921	−	0.940454i	$-0.610400\pi$
$337$	−4.77653e8	−0.679842	−0.339921	+	0.940454i	$0.610400\pi$
$338$	−1.18330e8	−0.166682
$339$	−2.09720e7	−0.0292375
$340$	3.20611e8	0.442387
$341$	2.24547e8	0.306666
$342$	1.72282e8	0.232889
$343$	7.47963e8	1.00081
$344$	1.90208e8	0.251927
$345$	−1.20522e8	−0.158015
$346$	−4.75543e8	−0.617196
$347$	−9.37582e8	−1.20464	−0.602318	−	0.798256i	$-0.705756\pi$
$347$	−9.37582e8	−1.20464	−0.602318	+	0.798256i	$0.705756\pi$
$348$	2.59659e8	0.330276
$349$	9.69080e8	1.22031	0.610155	−	0.792282i	$-0.291107\pi$
$349$	9.69080e8	1.22031	0.610155	+	0.792282i	$0.291107\pi$
$350$	−2.53775e8	−0.316382
$351$	1.36307e8	0.168245
$352$	−3.59202e7	−0.0438975
$353$	−4.61929e8	−0.558938	−0.279469	−	0.960155i	$-0.590158\pi$
$353$	−4.61929e8	−0.558938	−0.279469	+	0.960155i	$0.590158\pi$
$354$	−4.94548e8	−0.592512
$355$	−6.69872e8	−0.794680
$356$	2.48616e8	0.292047
$357$	−2.07092e8	−0.240894
$358$	−8.73019e8	−1.00562
$359$	−7.75397e8	−0.884491	−0.442245	−	0.896894i	$-0.645818\pi$
$359$	−7.75397e8	−0.884491	−0.442245	+	0.896894i	$0.645818\pi$
$360$	1.36936e8	0.154688
$361$	−2.12115e7	−0.0237299
$362$	−7.91545e8	−0.876992
$363$	−4.93709e8	−0.541749
$364$	−2.48959e8	−0.270566
$365$	−1.48042e7	−0.0159353
$366$	6.38467e8	0.680698
$367$	−2.89183e8	−0.305381	−0.152690	−	0.988274i	$-0.548794\pi$
$367$	−2.89183e8	−0.305381	−0.152690	+	0.988274i	$0.548794\pi$
$368$	−4.98360e7	−0.0521286
$369$	3.03644e8	0.314610
$370$	−1.44450e9	−1.48256
$371$	−5.69124e8	−0.578626
$372$	−3.53966e8	−0.356501
$373$	6.15666e8	0.614277	0.307138	−	0.951665i	$-0.400629\pi$
$373$	6.15666e8	0.614277	0.307138	+	0.951665i	$0.400629\pi$
$374$	−1.19745e8	−0.118361
$375$	−2.14480e8	−0.210028
$376$	4.76498e8	0.462278
$377$	1.04061e9	1.00021
$378$	−8.84508e7	−0.0842327
$379$	9.95325e8	0.939134	0.469567	−	0.882897i	$-0.344410\pi$
$379$	9.95325e8	0.939134	0.469567	+	0.882897i	$0.344410\pi$
$380$	6.93620e8	0.648453
$381$	−5.47502e8	−0.507164
$382$	−4.95292e8	−0.454610
$383$	−2.09760e8	−0.190777	−0.0953887	−	0.995440i	$-0.530409\pi$
$383$	−2.09760e8	−0.190777	−0.0953887	+	0.995440i	$0.530409\pi$
$384$	5.66231e7	0.0510310
$385$	2.25906e8	0.201751
$386$	8.27874e8	0.732671
$387$	2.70824e8	0.237519
$388$	−5.41761e8	−0.470865
$389$	2.53008e8	0.217927	0.108963	−	0.994046i	$-0.465247\pi$
$389$	2.53008e8	0.217927	0.108963	+	0.994046i	$0.465247\pi$
$390$	5.48782e8	0.468461
$391$	−1.66136e8	−0.140554
$392$	−2.60102e8	−0.218094
$393$	−1.54805e8	−0.128651
$394$	−8.95889e8	−0.737934
$395$	−8.66666e8	−0.707558
$396$	−5.11442e7	−0.0413869
$397$	1.23414e9	0.989914	0.494957	−	0.868917i	$-0.335184\pi$
$397$	1.23414e9	0.989914	0.494957	+	0.868917i	$0.335184\pi$
$398$	−8.78887e7	−0.0698783
$399$	−4.48030e8	−0.353103
$400$	2.31312e8	0.180713
$401$	1.41825e9	1.09837	0.549185	−	0.835701i	$-0.314938\pi$
$401$	1.41825e9	1.09837	0.549185	+	0.835701i	$0.314938\pi$
$402$	−3.15657e8	−0.242340
$403$	−1.41855e9	−1.07964
$404$	3.70921e8	0.279863
$405$	1.94973e8	0.145842
$406$	−6.75260e8	−0.500760
$407$	5.39508e8	0.396659
$408$	1.88761e8	0.137595
$409$	8.33868e8	0.602651	0.301325	−	0.953521i	$-0.402571\pi$
$409$	8.33868e8	0.602651	0.301325	+	0.953521i	$0.402571\pi$
$410$	1.22249e9	0.875996
$411$	−8.01822e8	−0.569681
$412$	8.57810e7	0.0604298
$413$	1.28610e9	0.898360
$414$	−7.09579e7	−0.0491473
$415$	4.69180e8	0.322234
$416$	2.26922e8	0.154543
$417$	7.29540e8	0.492689
$418$	−2.59061e8	−0.173494
$419$	−5.56088e8	−0.369313	−0.184656	−	0.982803i	$-0.559117\pi$
$419$	−5.56088e8	−0.369313	−0.184656	+	0.982803i	$0.559117\pi$
$420$	−3.56109e8	−0.234537
$421$	1.76819e9	1.15489	0.577447	−	0.816428i	$-0.304049\pi$
$421$	1.76819e9	1.15489	0.577447	+	0.816428i	$0.304049\pi$
$422$	5.71242e8	0.370021
$423$	6.78451e8	0.435840
$424$	5.18747e8	0.330503
$425$	7.71113e8	0.487256
$426$	−3.94391e8	−0.247168
$427$	−1.66037e9	−1.03207
$428$	−8.82014e8	−0.543779
$429$	−2.04965e8	−0.125337
$430$	1.09036e9	0.661346
$431$	1.86575e9	1.12249	0.561244	−	0.827650i	$-0.310323\pi$
$431$	1.86575e9	1.12249	0.561244	+	0.827650i	$0.310323\pi$
$432$	8.06216e7	0.0481125
$433$	−8.86037e8	−0.524498	−0.262249	−	0.965000i	$-0.584464\pi$
$433$	−8.86037e8	−0.524498	−0.262249	+	0.965000i	$0.584464\pi$
$434$	9.20510e8	0.540523
$435$	1.48848e9	0.867023
$436$	6.02043e8	0.347876
$437$	−3.59423e8	−0.206026
$438$	−8.71604e6	−0.00495633
$439$	−1.11162e9	−0.627094	−0.313547	−	0.949573i	$-0.601517\pi$
$439$	−1.11162e9	−0.627094	−0.313547	+	0.949573i	$0.601517\pi$
$440$	−2.05910e8	−0.115237
$441$	−3.70341e8	−0.205621
$442$	7.56478e8	0.416695
$443$	3.79851e8	0.207587	0.103794	−	0.994599i	$-0.466902\pi$
$443$	3.79851e8	0.207587	0.103794	+	0.994599i	$0.466902\pi$
$444$	−8.50458e8	−0.461119
$445$	1.42517e9	0.766668
$446$	9.68993e8	0.517188
$447$	−3.30123e8	−0.174823
$448$	−1.47252e8	−0.0773726
$449$	1.04853e9	0.546664	0.273332	−	0.961920i	$-0.411874\pi$
$449$	1.04853e9	0.546664	0.273332	+	0.961920i	$0.411874\pi$
$450$	3.29349e8	0.170378
$451$	−4.56589e8	−0.234373
$452$	−4.97114e7	−0.0253204
$453$	−2.13689e9	−1.08004
$454$	2.58955e8	0.129876
$455$	−1.42714e9	−0.710275
$456$	4.08372e8	0.201688
$457$	−1.49813e9	−0.734250	−0.367125	−	0.930172i	$-0.619658\pi$
$457$	−1.49813e9	−0.734250	−0.367125	+	0.930172i	$0.619658\pi$
$458$	1.71739e9	0.835293
$459$	2.68764e8	0.129726
$460$	−2.85682e8	−0.136845
$461$	1.49236e9	0.709447	0.354723	−	0.934971i	$-0.384575\pi$
$461$	1.49236e9	0.709447	0.354723	+	0.934971i	$0.384575\pi$
$462$	1.33003e8	0.0627503
$463$	−3.06867e9	−1.43687	−0.718433	−	0.695596i	$-0.755140\pi$
$463$	−3.06867e9	−1.43687	−0.718433	+	0.695596i	$0.755140\pi$
$464$	6.15489e8	0.286027
$465$	−2.02909e9	−0.935869
$466$	−1.87664e9	−0.859074
$467$	1.68526e9	0.765698	0.382849	−	0.923811i	$-0.374943\pi$
$467$	1.68526e9	0.765698	0.382849	+	0.923811i	$0.374943\pi$
$468$	3.23098e8	0.145705
$469$	8.20886e8	0.367433
$470$	2.73149e9	1.21355
$471$	−1.79781e9	−0.792812
$472$	−1.17226e9	−0.513131
$473$	−4.07238e8	−0.176943
$474$	−5.10254e8	−0.220071
$475$	1.66825e9	0.714223
$476$	−4.90885e8	−0.208620
$477$	7.38607e8	0.311601
$478$	−1.38821e9	−0.581376
$479$	−2.69509e9	−1.12047	−0.560233	−	0.828335i	$-0.689288\pi$
$479$	−2.69509e9	−1.12047	−0.560233	+	0.828335i	$0.689288\pi$
$480$	3.24588e8	0.133964
$481$	−3.40829e9	−1.39646
$482$	1.51719e9	0.617129
$483$	1.84530e8	0.0745166
$484$	−1.17027e9	−0.469168
$485$	−3.10561e9	−1.23609
$486$	1.14791e8	0.0453609
$487$	−2.88969e9	−1.13371	−0.566853	−	0.823819i	$-0.691839\pi$
$487$	−2.88969e9	−1.13371	−0.566853	+	0.823819i	$0.691839\pi$
$488$	1.51340e9	0.589502
$489$	1.50633e9	0.582556
$490$	−1.49102e9	−0.572528
$491$	−2.94886e9	−1.12427	−0.562133	−	0.827047i	$-0.690019\pi$
$491$	−2.94886e9	−1.12427	−0.562133	+	0.827047i	$0.690019\pi$
$492$	7.19748e8	0.272460
$493$	2.05182e9	0.771215
$494$	1.63659e9	0.610795
$495$	−2.93181e8	−0.108647
$496$	−8.39030e8	−0.308739
$497$	1.02564e9	0.374754
$498$	2.76232e8	0.100224
$499$	3.10068e9	1.11713	0.558567	−	0.829459i	$-0.311351\pi$
$499$	3.10068e9	1.11713	0.558567	+	0.829459i	$0.311351\pi$
$500$	−5.08396e8	−0.181889
$501$	−7.72070e8	−0.274299
$502$	2.16884e9	0.765181
$503$	−6.25596e8	−0.219183	−0.109591	−	0.993977i	$-0.534954\pi$
$503$	−6.25596e8	−0.219183	−0.109591	+	0.993977i	$0.534954\pi$
$504$	−2.09661e8	−0.0729476
$505$	2.12628e9	0.734683
$506$	1.06699e8	0.0366130
$507$	−3.99365e8	−0.136095
$508$	−1.29778e9	−0.439217
$509$	4.35887e9	1.46508	0.732541	−	0.680723i	$-0.238334\pi$
$509$	4.35887e9	1.46508	0.732541	+	0.680723i	$0.238334\pi$
$510$	1.08206e9	0.361207
$511$	2.26666e7	0.00751472
$512$	1.34218e8	0.0441942
$513$	5.81452e8	0.190153
$514$	3.49008e9	1.13361
$515$	4.91734e8	0.158637
$516$	6.41953e8	0.205698
$517$	−1.02019e9	−0.324685
$518$	2.21167e9	0.699142
$519$	−1.60496e9	−0.503939
$520$	1.30082e9	0.405699
$521$	1.86006e9	0.576229	0.288115	−	0.957596i	$-0.406972\pi$
$521$	1.86006e9	0.576229	0.288115	+	0.957596i	$0.406972\pi$
$522$	8.76350e8	0.269669
$523$	1.89981e9	0.580703	0.290352	−	0.956920i	$-0.406228\pi$
$523$	1.89981e9	0.580703	0.290352	+	0.956920i	$0.406228\pi$
$524$	−3.66946e8	−0.111415
$525$	−8.56491e8	−0.258324
$526$	1.01865e9	0.305194
$527$	−2.79703e9	−0.832454
$528$	−1.21231e8	−0.0358421
$529$	1.48036e8	0.0434783
$530$	2.97368e9	0.867620
$531$	−1.66910e9	−0.483784
$532$	−1.06200e9	−0.305796
$533$	2.88446e9	0.825123
$534$	8.39077e8	0.238456
$535$	−5.05608e9	−1.42750
$536$	−7.48225e8	−0.209872
$537$	−2.94644e9	−0.821083
$538$	2.00792e9	0.555914
$539$	5.56882e8	0.153180
$540$	4.62158e8	0.126303
$541$	6.17189e9	1.67582	0.837910	−	0.545808i	$-0.183777\pi$
$541$	6.17189e9	1.67582	0.837910	+	0.545808i	$0.183777\pi$
$542$	9.53670e8	0.257277
$543$	−2.67147e9	−0.716061
$544$	4.47435e8	0.119161
$545$	3.45117e9	0.913226
$546$	−8.40236e8	−0.220916
$547$	4.97696e9	1.30020	0.650098	−	0.759851i	$-0.274728\pi$
$547$	4.97696e9	1.30020	0.650098	+	0.759851i	$0.274728\pi$
$548$	−1.90061e9	−0.493358
$549$	2.15483e9	0.555788
$550$	−4.95242e8	−0.126925
$551$	4.43898e9	1.13045
$552$	−1.68197e8	−0.0425628
$553$	1.32695e9	0.333669
$554$	−2.16146e9	−0.540087
$555$	−4.87519e9	−1.21050
$556$	1.72928e9	0.426681
$557$	−2.16771e9	−0.531506	−0.265753	−	0.964041i	$-0.585621\pi$
$557$	−2.16771e9	−0.531506	−0.265753	+	0.964041i	$0.585621\pi$
$558$	−1.19464e9	−0.291082
$559$	2.57268e9	0.622938
$560$	−8.44111e8	−0.203115
$561$	−4.04140e8	−0.0966411
$562$	−5.06408e9	−1.20344
$563$	4.33727e9	1.02432	0.512162	−	0.858889i	$-0.328845\pi$
$563$	4.33727e9	1.02432	0.512162	+	0.858889i	$0.328845\pi$
$564$	1.60818e9	0.377449
$565$	−2.84967e8	−0.0664699
$566$	5.34644e9	1.23939
$567$	−2.98522e8	−0.0687757
$568$	−9.34852e8	−0.214054
$569$	−1.76759e9	−0.402243	−0.201122	−	0.979566i	$-0.564459\pi$
$569$	−1.76759e9	−0.402243	−0.201122	+	0.979566i	$0.564459\pi$
$570$	2.34097e9	0.529460
$571$	4.35096e9	0.978046	0.489023	−	0.872271i	$-0.337353\pi$
$571$	4.35096e9	0.978046	0.489023	+	0.872271i	$0.337353\pi$
$572$	−4.85843e8	−0.108545
$573$	−1.67161e9	−0.371188
$574$	−1.87175e9	−0.413101
$575$	−6.87104e8	−0.150725
$576$	1.91103e8	0.0416667
$577$	7.46172e9	1.61705	0.808525	−	0.588462i	$-0.200266\pi$
$577$	7.46172e9	1.61705	0.808525	+	0.588462i	$0.200266\pi$
$578$	−1.79112e9	−0.385813
$579$	2.79407e9	0.598223
$580$	3.52825e9	0.750864
$581$	−7.18358e8	−0.151958
$582$	−1.82844e9	−0.384460
$583$	−1.11064e9	−0.232132
$584$	−2.06603e7	−0.00429231
$585$	1.85214e9	0.382497
$586$	4.29122e9	0.880925
$587$	−3.27341e9	−0.667985	−0.333992	−	0.942576i	$-0.608396\pi$
$587$	−3.27341e9	−0.667985	−0.333992	+	0.942576i	$0.608396\pi$
$588$	−8.77846e8	−0.178073
$589$	−6.05118e9	−1.22022
$590$	−6.71991e9	−1.34704
$591$	−3.02363e9	−0.602521
$592$	−2.01590e9	−0.399340
$593$	−5.07631e9	−0.999670	−0.499835	−	0.866121i	$-0.666606\pi$
$593$	−5.07631e9	−0.999670	−0.499835	+	0.866121i	$0.666606\pi$
$594$	−1.72612e8	−0.0337923
$595$	−2.81397e9	−0.547658
$596$	−7.82513e8	−0.151401
$597$	−2.96624e8	−0.0570554
$598$	−6.74063e8	−0.128898
$599$	−9.57665e9	−1.82062	−0.910311	−	0.413926i	$-0.864157\pi$
$599$	−9.57665e9	−1.82062	−0.910311	+	0.413926i	$0.864157\pi$
$600$	7.80679e8	0.147551
$601$	−1.02812e9	−0.193189	−0.0965945	−	0.995324i	$-0.530795\pi$
$601$	−1.02812e9	−0.193189	−0.0965945	+	0.995324i	$0.530795\pi$
$602$	−1.66944e9	−0.311876
$603$	−1.06534e9	−0.197870
$604$	−5.06523e9	−0.935341
$605$	−6.70851e9	−1.23164
$606$	1.25186e9	0.228507
$607$	2.45045e9	0.444719	0.222359	−	0.974965i	$-0.428624\pi$
$607$	2.45045e9	0.444719	0.222359	+	0.974965i	$0.428624\pi$
$608$	9.67994e8	0.174667
$609$	−2.27900e9	−0.408869
$610$	8.67548e9	1.54753
$611$	6.44492e9	1.14307
$612$	6.37070e8	0.112346
$613$	8.90460e8	0.156136	0.0780679	−	0.996948i	$-0.475125\pi$
$613$	8.90460e8	0.156136	0.0780679	+	0.996948i	$0.475125\pi$
$614$	−8.57767e8	−0.149548
$615$	4.12591e9	0.715248
$616$	3.15268e8	0.0543434
$617$	3.73214e9	0.639675	0.319838	−	0.947472i	$-0.396372\pi$
$617$	3.73214e9	0.639675	0.319838	+	0.947472i	$0.396372\pi$
$618$	2.89511e8	0.0493407
$619$	−9.73916e9	−1.65046	−0.825228	−	0.564799i	$-0.808954\pi$
$619$	−9.73916e9	−1.65046	−0.825228	+	0.564799i	$0.808954\pi$
$620$	−4.80968e9	−0.810486
$621$	−2.39483e8	−0.0401286
$622$	−7.79689e9	−1.29914
$623$	−2.18207e9	−0.361544
$624$	7.65862e8	0.126184
$625$	−7.32628e9	−1.20034
$626$	−5.17675e9	−0.843426
$627$	−8.74329e8	−0.141657
$628$	−4.26147e9	−0.686595
$629$	−6.72030e9	−1.07674
$630$	−1.20187e9	−0.191498
$631$	−8.10602e8	−0.128441	−0.0642207	−	0.997936i	$-0.520456\pi$
$631$	−8.10602e8	−0.128441	−0.0642207	+	0.997936i	$0.520456\pi$
$632$	−1.20949e9	−0.190587
$633$	1.92794e9	0.302121
$634$	4.18370e9	0.652001
$635$	−7.43946e9	−1.15301
$636$	1.75077e9	0.269855
$637$	−3.51805e9	−0.539279
$638$	−1.31777e9	−0.200894
$639$	−1.33107e9	−0.201812
$640$	7.69394e8	0.116016
$641$	−1.53566e9	−0.230299	−0.115150	−	0.993348i	$-0.536735\pi$
$641$	−1.53566e9	−0.230299	−0.115150	+	0.993348i	$0.536735\pi$
$642$	−2.97680e9	−0.443993
$643$	9.03556e9	1.34035	0.670173	−	0.742205i	$-0.266220\pi$
$643$	9.03556e9	1.34035	0.670173	+	0.742205i	$0.266220\pi$
$644$	4.37405e8	0.0645332
$645$	3.67995e9	0.539986
$646$	3.22695e9	0.470954
$647$	−6.44225e8	−0.0935132	−0.0467566	−	0.998906i	$-0.514889\pi$
$647$	−6.44225e8	−0.0935132	−0.0467566	+	0.998906i	$0.514889\pi$
$648$	2.72098e8	0.0392837
$649$	2.50983e9	0.360402
$650$	3.12864e9	0.446847
$651$	3.10672e9	0.441335
$652$	3.57055e9	0.504508
$653$	−3.14760e9	−0.442368	−0.221184	−	0.975232i	$-0.570992\pi$
$653$	−3.14760e9	−0.442368	−0.221184	+	0.975232i	$0.570992\pi$
$654$	2.03189e9	0.284040
$655$	−2.10349e9	−0.292480
$656$	1.70607e9	0.235957
$657$	−2.94166e7	−0.00404682
$658$	−4.18217e9	−0.572283
$659$	1.35636e10	1.84619	0.923093	−	0.384577i	$-0.125653\pi$
$659$	1.35636e10	1.84619	0.923093	+	0.384577i	$0.125653\pi$
$660$	−6.94946e8	−0.0940909
$661$	1.38238e10	1.86176	0.930880	−	0.365325i	$-0.119042\pi$
$661$	1.38238e10	1.86176	0.930880	+	0.365325i	$0.119042\pi$
$662$	−8.04261e8	−0.107744
$663$	2.55311e9	0.340230
$664$	6.54772e8	0.0867964
$665$	−6.08782e9	−0.802761
$666$	−2.87030e9	−0.376502
$667$	−1.82828e9	−0.238563
$668$	−1.83009e9	−0.237550
$669$	3.27035e9	0.422283
$670$	−4.28915e9	−0.550946
$671$	−3.24021e9	−0.414042
$672$	−4.96975e8	−0.0631745
$673$	−3.45394e9	−0.436780	−0.218390	−	0.975862i	$-0.570080\pi$
$673$	−3.45394e9	−0.436780	−0.218390	+	0.975862i	$0.570080\pi$
$674$	−3.82123e9	−0.480721
$675$	1.11155e9	0.139113
$676$	−9.46644e8	−0.117862
$677$	6.53708e9	0.809699	0.404849	−	0.914383i	$-0.367324\pi$
$677$	6.53708e9	0.809699	0.404849	+	0.914383i	$0.367324\pi$
$678$	−1.67776e8	−0.0206741
$679$	4.75498e9	0.582914
$680$	2.56489e9	0.312815
$681$	8.73971e8	0.106043
$682$	1.79637e9	0.216846
$683$	−1.53942e10	−1.84877	−0.924386	−	0.381457i	$-0.875422\pi$
$683$	−1.53942e10	−1.84877	−0.924386	+	0.381457i	$0.875422\pi$
$684$	1.37826e9	0.164677
$685$	−1.08951e10	−1.29514
$686$	5.98370e9	0.707678
$687$	5.79618e9	0.682014
$688$	1.52167e9	0.178139
$689$	7.01638e9	0.817233
$690$	−9.64176e8	−0.111734
$691$	−6.43606e9	−0.742074	−0.371037	−	0.928618i	$-0.620998\pi$
$691$	−6.43606e9	−0.742074	−0.371037	+	0.928618i	$0.620998\pi$
$692$	−3.80434e9	−0.436424
$693$	4.48887e8	0.0512354
$694$	−7.50066e9	−0.851807
$695$	9.91297e9	1.12010
$696$	2.07727e9	0.233540
$697$	5.68744e9	0.636212
$698$	7.75264e9	0.862890
$699$	−6.33366e9	−0.701431
$700$	−2.03020e9	−0.223716
$701$	3.29232e9	0.360985	0.180492	−	0.983576i	$-0.442231\pi$
$701$	3.29232e9	0.360985	0.180492	+	0.983576i	$0.442231\pi$
$702$	1.09046e9	0.118968
$703$	−1.45389e10	−1.57829
$704$	−2.87362e8	−0.0310402
$705$	9.21878e9	0.990858
$706$	−3.69543e9	−0.395229
$707$	−3.25553e9	−0.346460
$708$	−3.95639e9	−0.418969
$709$	−1.33790e10	−1.40981	−0.704907	−	0.709300i	$-0.749011\pi$
$709$	−1.33790e10	−1.40981	−0.704907	+	0.709300i	$0.749011\pi$
$710$	−5.35898e9	−0.561924
$711$	−1.72211e9	−0.179687
$712$	1.98892e9	0.206509
$713$	2.49231e9	0.257506
$714$	−1.65674e9	−0.170337
$715$	−2.78506e9	−0.284947
$716$	−6.98415e9	−0.711079
$717$	−4.68520e9	−0.474691
$718$	−6.20317e9	−0.625430
$719$	9.99931e9	1.00327	0.501636	−	0.865079i	$-0.332732\pi$
$719$	9.99931e9	1.00327	0.501636	+	0.865079i	$0.332732\pi$
$720$	1.09548e9	0.109381
$721$	−7.52890e8	−0.0748098
$722$	−1.69692e8	−0.0167796
$723$	5.12052e9	0.503884
$724$	−6.33236e9	−0.620127
$725$	8.48592e9	0.827020
$726$	−3.94967e9	−0.383074
$727$	3.87514e9	0.374039	0.187019	−	0.982356i	$-0.440117\pi$
$727$	3.87514e9	0.374039	0.187019	+	0.982356i	$0.440117\pi$
$728$	−1.99167e9	−0.191319
$729$	3.87420e8	0.0370370
$730$	−1.18433e8	−0.0112679
$731$	5.07270e9	0.480317
$732$	5.10773e9	0.481326
$733$	2.03185e10	1.90559	0.952793	−	0.303620i	$-0.0981954\pi$
$733$	2.03185e10	1.90559	0.952793	+	0.303620i	$0.0981954\pi$
$734$	−2.31346e9	−0.215937
$735$	−5.03219e9	−0.467468
$736$	−3.98688e8	−0.0368605
$737$	1.60196e9	0.147406
$738$	2.42915e9	0.222463
$739$	6.01270e9	0.548042	0.274021	−	0.961724i	$-0.411646\pi$
$739$	6.01270e9	0.548042	0.274021	+	0.961724i	$0.411646\pi$
$740$	−1.15560e10	−1.04833
$741$	5.52349e9	0.498712
$742$	−4.55299e9	−0.409150
$743$	7.10581e9	0.635554	0.317777	−	0.948165i	$-0.397064\pi$
$743$	7.10581e9	0.635554	0.317777	+	0.948165i	$0.397064\pi$
$744$	−2.83173e9	−0.252085
$745$	−4.48570e9	−0.397451
$746$	4.92533e9	0.434359
$747$	9.32283e8	0.0818325
$748$	−9.57962e8	−0.0836937
$749$	7.74134e9	0.673178
$750$	−1.71584e9	−0.148512
$751$	−2.66674e9	−0.229743	−0.114871	−	0.993380i	$-0.536646\pi$
$751$	−2.66674e9	−0.229743	−0.114871	+	0.993380i	$0.536646\pi$
$752$	3.81198e9	0.326880
$753$	7.31983e9	0.624767
$754$	8.32486e9	0.707257
$755$	−2.90361e10	−2.45541
$756$	−7.07607e8	−0.0595615
$757$	1.21053e10	1.01424	0.507119	−	0.861876i	$-0.330711\pi$
$757$	1.21053e10	1.01424	0.507119	+	0.861876i	$0.330711\pi$
$758$	7.96260e9	0.664068
$759$	3.60111e8	0.0298944
$760$	5.54896e9	0.458526
$761$	−2.97000e9	−0.244293	−0.122146	−	0.992512i	$-0.538978\pi$
$761$	−2.97000e9	−0.244293	−0.122146	+	0.992512i	$0.538978\pi$
$762$	−4.38002e9	−0.358619
$763$	−5.28406e9	−0.430657
$764$	−3.96233e9	−0.321458
$765$	3.65196e9	0.294925
$766$	−1.67808e9	−0.134900
$767$	−1.58556e10	−1.26881
$768$	4.52985e8	0.0360844
$769$	1.95706e10	1.55190	0.775948	−	0.630797i	$-0.217272\pi$
$769$	1.95706e10	1.55190	0.775948	+	0.630797i	$0.217272\pi$
$770$	1.80725e9	0.142659
$771$	1.17790e10	0.925589
$772$	6.62299e9	0.518076
$773$	−1.54223e9	−0.120094	−0.0600468	−	0.998196i	$-0.519125\pi$
$773$	−1.54223e9	−0.120094	−0.0600468	+	0.998196i	$0.519125\pi$
$774$	2.16659e9	0.167951
$775$	−1.15680e10	−0.892690
$776$	−4.33409e9	−0.332952
$777$	7.46438e9	0.570847
$778$	2.02406e9	0.154098
$779$	1.23044e10	0.932564
$780$	4.39025e9	0.331252
$781$	2.00153e9	0.150343
$782$	−1.32909e9	−0.0993870
$783$	2.95768e9	0.220184
$784$	−2.08082e9	−0.154216
$785$	−2.44286e10	−1.80241
$786$	−1.23844e9	−0.0909697
$787$	−1.76348e10	−1.28961	−0.644805	−	0.764347i	$-0.723061\pi$
$787$	−1.76348e10	−1.28961	−0.644805	+	0.764347i	$0.723061\pi$
$788$	−7.16712e9	−0.521798
$789$	3.43795e9	0.249190
$790$	−6.93333e9	−0.500319
$791$	4.36311e8	0.0313458
$792$	−4.09153e8	−0.0292650
$793$	2.04697e10	1.45766
$794$	9.87312e9	0.699975
$795$	1.00362e10	0.708408
$796$	−7.03110e8	−0.0494114
$797$	2.10641e10	1.47380	0.736901	−	0.676000i	$-0.236288\pi$
$797$	2.10641e10	1.47380	0.736901	+	0.676000i	$0.236288\pi$
$798$	−3.58424e9	−0.249682
$799$	1.27078e10	0.881367
$800$	1.85050e9	0.127783
$801$	2.83189e9	0.194698
$802$	1.13460e10	0.776664
$803$	4.42338e7	0.00301474
$804$	−2.52526e9	−0.171360
$805$	2.50740e9	0.169409
$806$	−1.13484e10	−0.763417
$807$	6.77672e9	0.453902
$808$	2.96736e9	0.197893
$809$	−2.12308e10	−1.40977	−0.704884	−	0.709323i	$-0.749001\pi$
$809$	−2.12308e10	−1.40977	−0.704884	+	0.709323i	$0.749001\pi$
$810$	1.55978e9	0.103126
$811$	9.31477e9	0.613196	0.306598	−	0.951839i	$-0.400809\pi$
$811$	9.31477e9	0.613196	0.306598	+	0.951839i	$0.400809\pi$
$812$	−5.40208e9	−0.354091
$813$	3.21864e9	0.210066
$814$	4.31606e9	0.280480
$815$	2.04679e10	1.32441
$816$	1.51009e9	0.0972944
$817$	1.09744e10	0.704052
$818$	6.67094e9	0.426138
$819$	−2.83580e9	−0.180377
$820$	9.77993e9	0.619423
$821$	−1.51846e10	−0.957642	−0.478821	−	0.877913i	$-0.658936\pi$
$821$	−1.51846e10	−0.957642	−0.478821	+	0.877913i	$0.658936\pi$
$822$	−6.41458e9	−0.402825
$823$	−9.38917e9	−0.587121	−0.293561	−	0.955940i	$-0.594840\pi$
$823$	−9.38917e9	−0.587121	−0.293561	+	0.955940i	$0.594840\pi$
$824$	6.86248e8	0.0427303
$825$	−1.67144e9	−0.103634
$826$	1.02888e10	0.635236
$827$	1.40878e10	0.866114	0.433057	−	0.901366i	$-0.357435\pi$
$827$	1.40878e10	0.866114	0.433057	+	0.901366i	$0.357435\pi$
$828$	−5.67664e8	−0.0347524
$829$	1.99910e10	1.21869	0.609345	−	0.792905i	$-0.291432\pi$
$829$	1.99910e10	1.21869	0.609345	+	0.792905i	$0.291432\pi$
$830$	3.75344e9	0.227854
$831$	−7.29494e9	−0.440979
$832$	1.81538e9	0.109279
$833$	−6.93672e9	−0.415812
$834$	5.83632e9	0.348384
$835$	−1.04909e10	−0.623604
$836$	−2.07248e9	−0.122679
$837$	−4.03189e9	−0.237668
$838$	−4.44870e9	−0.261143
$839$	2.49729e10	1.45983	0.729915	−	0.683538i	$-0.239560\pi$
$839$	2.49729e10	1.45983	0.729915	+	0.683538i	$0.239560\pi$
$840$	−2.84887e9	−0.165842
$841$	5.32994e9	0.308984
$842$	1.41455e10	0.816633
$843$	−1.70913e10	−0.982602
$844$	4.56993e9	0.261644
$845$	−5.42657e9	−0.309405
$846$	5.42761e9	0.308185
$847$	1.02714e10	0.580813
$848$	4.14998e9	0.233701
$849$	1.80442e10	1.01196
$850$	6.16891e9	0.344542
$851$	5.98815e9	0.333073
$852$	−3.15513e9	−0.174775
$853$	2.15537e10	1.18905	0.594526	−	0.804077i	$-0.297340\pi$
$853$	2.15537e10	1.18905	0.594526	+	0.804077i	$0.297340\pi$
$854$	−1.32830e10	−0.729781
$855$	7.90076e9	0.432302
$856$	−7.05611e9	−0.384510
$857$	−1.83252e9	−0.0994524	−0.0497262	−	0.998763i	$-0.515835\pi$
$857$	−1.83252e9	−0.0994524	−0.0497262	+	0.998763i	$0.515835\pi$
$858$	−1.63972e9	−0.0886266
$859$	2.88323e10	1.55204	0.776020	−	0.630708i	$-0.217235\pi$
$859$	2.88323e10	1.55204	0.776020	+	0.630708i	$0.217235\pi$
$860$	8.72284e9	0.467642
$861$	−6.31715e9	−0.337295
$862$	1.49260e10	0.793719
$863$	−2.80605e10	−1.48613	−0.743067	−	0.669217i	$-0.766630\pi$
$863$	−2.80605e10	−1.48613	−0.743067	+	0.669217i	$0.766630\pi$
$864$	6.44973e8	0.0340207
$865$	−2.18081e10	−1.14568
$866$	−7.08829e9	−0.370876
$867$	−6.04503e9	−0.315015
$868$	7.36408e9	0.382208
$869$	2.58953e9	0.133860
$870$	1.19078e10	0.613078
$871$	−1.01202e10	−0.518950
$872$	4.81634e9	0.245986
$873$	−6.17100e9	−0.313910
$874$	−2.87539e9	−0.145682
$875$	4.46214e9	0.225172
$876$	−6.97283e7	−0.00350465
$877$	−1.07928e10	−0.540299	−0.270149	−	0.962818i	$-0.587073\pi$
$877$	−1.07928e10	−0.540299	−0.270149	+	0.962818i	$0.587073\pi$
$878$	−8.89300e9	−0.443422
$879$	1.44829e10	0.719272
$880$	−1.64728e9	−0.0814851
$881$	−2.86597e10	−1.41207	−0.706034	−	0.708178i	$-0.749517\pi$
$881$	−2.86597e10	−1.41207	−0.706034	+	0.708178i	$0.749517\pi$
$882$	−2.96273e9	−0.145396
$883$	−3.47774e10	−1.69994	−0.849972	−	0.526828i	$-0.823381\pi$
$883$	−3.47774e10	−1.69994	−0.849972	+	0.526828i	$0.823381\pi$
$884$	6.05183e9	0.294648
$885$	−2.26797e10	−1.09986
$886$	3.03881e9	0.146786
$887$	6.42202e9	0.308986	0.154493	−	0.987994i	$-0.450626\pi$
$887$	6.42202e9	0.308986	0.154493	+	0.987994i	$0.450626\pi$
$888$	−6.80367e9	−0.326060
$889$	1.13905e10	0.543734
$890$	1.14014e10	0.542116
$891$	−5.82564e8	−0.0275913
$892$	7.75195e9	0.365707
$893$	2.74925e10	1.29191
$894$	−2.64098e9	−0.123619
$895$	−4.00362e10	−1.86669
$896$	−1.17801e9	−0.0547107
$897$	−2.27496e9	−0.105245
$898$	8.38827e9	0.386550
$899$	−3.07807e10	−1.41292
$900$	2.63479e9	0.120475
$901$	1.38346e10	0.630128
$902$	−3.65271e9	−0.165727
$903$	−5.63435e9	−0.254646
$904$	−3.97691e8	−0.0179043
$905$	−3.62998e10	−1.62793
$906$	−1.70952e10	−0.763703
$907$	−3.96724e10	−1.76548	−0.882740	−	0.469861i	$-0.844304\pi$
$907$	−3.96724e10	−1.76548	−0.882740	+	0.469861i	$0.844304\pi$
$908$	2.07164e9	0.0918360
$909$	4.22502e9	0.186576
$910$	−1.14171e10	−0.502240
$911$	3.39607e10	1.48820	0.744102	−	0.668066i	$-0.232878\pi$
$911$	3.39607e10	1.48820	0.744102	+	0.668066i	$0.232878\pi$
$912$	3.26698e9	0.142615
$913$	−1.40187e9	−0.0609623
$914$	−1.19851e10	−0.519193
$915$	2.92797e10	1.26355
$916$	1.37391e10	0.590642
$917$	3.22064e9	0.137927
$918$	2.15011e9	0.0917300
$919$	1.98186e10	0.842304	0.421152	−	0.906990i	$-0.361626\pi$
$919$	1.98186e10	0.842304	0.421152	+	0.906990i	$0.361626\pi$
$920$	−2.28545e9	−0.0967642
$921$	−2.89496e9	−0.122105
$922$	1.19389e10	0.501655
$923$	−1.26444e10	−0.529290
$924$	1.06403e9	0.0443712
$925$	−2.77938e10	−1.15465
$926$	−2.45493e10	−1.01602
$927$	9.77099e8	0.0402865
$928$	4.92391e9	0.202252
$929$	−2.08980e10	−0.855164	−0.427582	−	0.903976i	$-0.640635\pi$
$929$	−2.08980e10	−0.855164	−0.427582	+	0.903976i	$0.640635\pi$
$930$	−1.62327e10	−0.661759
$931$	−1.50071e10	−0.609499
$932$	−1.50131e10	−0.607457
$933$	−2.63145e10	−1.06074
$934$	1.34821e10	0.541430
$935$	−5.49145e9	−0.219708
$936$	2.58479e9	0.103029
$937$	−4.61325e9	−0.183197	−0.0915986	−	0.995796i	$-0.529198\pi$
$937$	−4.61325e9	−0.183197	−0.0915986	+	0.995796i	$0.529198\pi$
$938$	6.56709e9	0.259814
$939$	−1.74715e10	−0.688654
$940$	2.18519e10	0.858109
$941$	2.61949e10	1.02483	0.512417	−	0.858737i	$-0.328750\pi$
$941$	2.61949e10	1.02483	0.512417	+	0.858737i	$0.328750\pi$
$942$	−1.43825e10	−0.560603
$943$	−5.06781e9	−0.196802
$944$	−9.37810e9	−0.362838
$945$	−4.05631e9	−0.156358
$946$	−3.25790e9	−0.125118
$947$	−1.01216e10	−0.387278	−0.193639	−	0.981073i	$-0.562029\pi$
$947$	−1.01216e10	−0.387278	−0.193639	+	0.981073i	$0.562029\pi$
$948$	−4.08203e9	−0.155614
$949$	−2.79443e8	−0.0106136
$950$	1.33460e10	0.505032
$951$	1.41200e10	0.532356
$952$	−3.92708e9	−0.147517
$953$	−5.16517e9	−0.193312	−0.0966562	−	0.995318i	$-0.530815\pi$
$953$	−5.16517e9	−0.193312	−0.0966562	+	0.995318i	$0.530815\pi$
$954$	5.90886e9	0.220335
$955$	−2.27138e10	−0.843875
$956$	−1.11057e10	−0.411095
$957$	−4.44747e9	−0.164029
$958$	−2.15607e10	−0.792289
$959$	1.66815e10	0.610759
$960$	2.59670e9	0.0947269
$961$	1.44474e10	0.525119
$962$	−2.72663e10	−0.987446
$963$	−1.00467e10	−0.362519
$964$	1.21375e10	0.436376
$965$	3.79659e10	1.36003
$966$	1.47624e9	0.0526912
$967$	2.33871e10	0.831734	0.415867	−	0.909425i	$-0.363478\pi$
$967$	2.33871e10	0.831734	0.415867	+	0.909425i	$0.363478\pi$
$968$	−9.36219e9	−0.331752
$969$	1.08910e10	0.384532
$970$	−2.48449e10	−0.874049
$971$	−4.05447e9	−0.142124	−0.0710619	−	0.997472i	$-0.522639\pi$
$971$	−4.05447e9	−0.142124	−0.0710619	+	0.997472i	$0.522639\pi$
$972$	9.18330e8	0.0320750
$973$	−1.51777e10	−0.528215
$974$	−2.31176e10	−0.801651
$975$	1.05592e10	0.364849
$976$	1.21072e10	0.416841
$977$	5.68903e10	1.95167	0.975837	−	0.218499i	$-0.0701160\pi$
$977$	5.68903e10	1.95167	0.975837	+	0.218499i	$0.0701160\pi$
$978$	1.20506e10	0.411929
$979$	−4.25831e9	−0.145043
$980$	−1.19282e10	−0.404839
$981$	6.85764e9	0.231917
$982$	−2.35909e10	−0.794977
$983$	3.74559e10	1.25772	0.628859	−	0.777519i	$-0.283522\pi$
$983$	3.74559e10	1.25772	0.628859	+	0.777519i	$0.283522\pi$
$984$	5.75799e9	0.192658
$985$	−4.10850e10	−1.36980
$986$	1.64146e10	0.545331
$987$	−1.41148e10	−0.467267
$988$	1.30927e10	0.431897
$989$	−4.52004e9	−0.148578
$990$	−2.34544e9	−0.0768249
$991$	1.00112e8	0.00326759	0.00163379	−	0.999999i	$-0.499480\pi$
$991$	1.00112e8	0.00326759	0.00163379	+	0.999999i	$0.499480\pi$
$992$	−6.71224e9	−0.218312
$993$	−2.71438e9	−0.0879729
$994$	8.20509e9	0.264991
$995$	−4.03053e9	−0.129712
$996$	2.20986e9	0.0708690
$997$	−3.72236e10	−1.18956	−0.594779	−	0.803889i	$-0.702760\pi$
$997$	−3.72236e10	−1.18956	−0.594779	+	0.803889i	$0.702760\pi$
$998$	2.48055e10	0.789934
$999$	−9.68725e9	−0.307412

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.8.a.h.1.4	✓	4
3.2	odd	2		414.8.a.i.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.8.a.h.1.4	✓	4	1.1	even	1	trivial
414.8.a.i.1.1		4	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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	138.a (trivial)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +366.876 q^{5} +216.000 q^{6} -561.721 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} +27.0000 q^{3} +64.0000 q^{4} +366.876 q^{5} +216.000 q^{6} -561.721 q^{7} +512.000 q^{8} +729.000 q^{9} +2935.00 q^{10} -1096.20 q^{11} +1728.00 q^{12} +6925.11 q^{13} -4493.77 q^{14} +9905.64 q^{15} +4096.00 q^{16} +13654.6 q^{17} +5832.00 q^{18} +29540.8 q^{19} +23480.0 q^{20} -15166.5 q^{21} -8769.58 q^{22} -12167.0 q^{23} +13824.0 q^{24} +56472.7 q^{25} +55400.9 q^{26} +19683.0 q^{27} -35950.1 q^{28} +150266. q^{29} +79245.1 q^{30} -204841. q^{31} +32768.0 q^{32} -29597.3 q^{33} +109237. q^{34} -206082. q^{35} +46656.0 q^{36} -492163. q^{37} +236327. q^{38} +186978. q^{39} +187840. q^{40} +416521. q^{41} -121332. q^{42} +371500. q^{43} -70156.6 q^{44} +267452. q^{45} -97336.0 q^{46} +930660. q^{47} +110592. q^{48} -508013. q^{49} +451782. q^{50} +368675. q^{51} +443207. q^{52} +1.01318e6 q^{53} +157464. q^{54} -402168. q^{55} -287601. q^{56} +797602. q^{57} +1.20213e6 q^{58} -2.28957e6 q^{59} +633961. q^{60} +2.95586e6 q^{61} -1.63873e6 q^{62} -409495. q^{63} +262144. q^{64} +2.54066e6 q^{65} -236779. q^{66} -1.46138e6 q^{67} +873896. q^{68} -328509. q^{69} -1.64865e6 q^{70} -1.82588e6 q^{71} +373248. q^{72} -40352.1 q^{73} -3.93731e6 q^{74} +1.52476e6 q^{75} +1.89061e6 q^{76} +615757. q^{77} +1.49582e6 q^{78} -2.36229e6 q^{79} +1.50272e6 q^{80} +531441. q^{81} +3.33217e6 q^{82} +1.27885e6 q^{83} -970654. q^{84} +5.00955e6 q^{85} +2.97200e6 q^{86} +4.05718e6 q^{87} -561253. q^{88} +3.88462e6 q^{89} +2.13962e6 q^{90} -3.88998e6 q^{91} -778688. q^{92} -5.53072e6 q^{93} +7.44528e6 q^{94} +1.08378e7 q^{95} +884736. q^{96} -8.46502e6 q^{97} -4.06410e6 q^{98} -799128. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32 q^{2} + 108 q^{3} + 256 q^{4} + 270 q^{5} + 864 q^{6} + 2022 q^{7} + 2048 q^{8} + 2916 q^{9}+O(q^{10}) \) 4 * q + 32 * q^2 + 108 * q^3 + 256 * q^4 + 270 * q^5 + 864 * q^6 + 2022 * q^7 + 2048 * q^8 + 2916 * q^9	\( 4 q + 32 q^{2} + 108 q^{3} + 256 q^{4} + 270 q^{5} + 864 q^{6} + 2022 q^{7} + 2048 q^{8} + 2916 q^{9} + 2160 q^{10} + 4120 q^{11} + 6912 q^{12} + 8036 q^{13} + 16176 q^{14} + 7290 q^{15} + 16384 q^{16} + 37182 q^{17} + 23328 q^{18} + 5702 q^{19} + 17280 q^{20} + 54594 q^{21} + 32960 q^{22} - 48668 q^{23} + 55296 q^{24} + 121480 q^{25} + 64288 q^{26} + 78732 q^{27} + 129408 q^{28} + 217716 q^{29} + 58320 q^{30} + 222852 q^{31} + 131072 q^{32} + 111240 q^{33} + 297456 q^{34} + 68440 q^{35} + 186624 q^{36} + 486428 q^{37} + 45616 q^{38} + 216972 q^{39} + 138240 q^{40} + 338336 q^{41} + 436752 q^{42} + 730974 q^{43} + 263680 q^{44} + 196830 q^{45} - 389344 q^{46} + 338248 q^{47} + 442368 q^{48} - 310552 q^{49} + 971840 q^{50} + 1003914 q^{51} + 514304 q^{52} - 375502 q^{53} + 629856 q^{54} + 424840 q^{55} + 1035264 q^{56} + 153954 q^{57} + 1741728 q^{58} + 71392 q^{59} + 466560 q^{60} + 2101164 q^{61} + 1782816 q^{62} + 1474038 q^{63} + 1048576 q^{64} + 1578780 q^{65} + 889920 q^{66} + 4337162 q^{67} + 2379648 q^{68} - 1314036 q^{69} + 547520 q^{70} + 2288016 q^{71} + 1492992 q^{72} - 1107328 q^{73} + 3891424 q^{74} + 3279960 q^{75} + 364928 q^{76} + 5826200 q^{77} + 1735776 q^{78} + 60610 q^{79} + 1105920 q^{80} + 2125764 q^{81} + 2706688 q^{82} + 1485464 q^{83} + 3494016 q^{84} - 8843820 q^{85} + 5847792 q^{86} + 5878332 q^{87} + 2109440 q^{88} + 1485090 q^{89} + 1574640 q^{90} - 2898412 q^{91} - 3114752 q^{92} + 6017004 q^{93} + 2705984 q^{94} + 8545200 q^{95} + 3538944 q^{96} + 1935444 q^{97} - 2484416 q^{98} + 3003480 q^{99}+O(q^{100}) \) 4 * q + 32 * q^2 + 108 * q^3 + 256 * q^4 + 270 * q^5 + 864 * q^6 + 2022 * q^7 + 2048 * q^8 + 2916 * q^9 + 2160 * q^10 + 4120 * q^11 + 6912 * q^12 + 8036 * q^13 + 16176 * q^14 + 7290 * q^15 + 16384 * q^16 + 37182 * q^17 + 23328 * q^18 + 5702 * q^19 + 17280 * q^20 + 54594 * q^21 + 32960 * q^22 - 48668 * q^23 + 55296 * q^24 + 121480 * q^25 + 64288 * q^26 + 78732 * q^27 + 129408 * q^28 + 217716 * q^29 + 58320 * q^30 + 222852 * q^31 + 131072 * q^32 + 111240 * q^33 + 297456 * q^34 + 68440 * q^35 + 186624 * q^36 + 486428 * q^37 + 45616 * q^38 + 216972 * q^39 + 138240 * q^40 + 338336 * q^41 + 436752 * q^42 + 730974 * q^43 + 263680 * q^44 + 196830 * q^45 - 389344 * q^46 + 338248 * q^47 + 442368 * q^48 - 310552 * q^49 + 971840 * q^50 + 1003914 * q^51 + 514304 * q^52 - 375502 * q^53 + 629856 * q^54 + 424840 * q^55 + 1035264 * q^56 + 153954 * q^57 + 1741728 * q^58 + 71392 * q^59 + 466560 * q^60 + 2101164 * q^61 + 1782816 * q^62 + 1474038 * q^63 + 1048576 * q^64 + 1578780 * q^65 + 889920 * q^66 + 4337162 * q^67 + 2379648 * q^68 - 1314036 * q^69 + 547520 * q^70 + 2288016 * q^71 + 1492992 * q^72 - 1107328 * q^73 + 3891424 * q^74 + 3279960 * q^75 + 364928 * q^76 + 5826200 * q^77 + 1735776 * q^78 + 60610 * q^79 + 1105920 * q^80 + 2125764 * q^81 + 2706688 * q^82 + 1485464 * q^83 + 3494016 * q^84 - 8843820 * q^85 + 5847792 * q^86 + 5878332 * q^87 + 2109440 * q^88 + 1485090 * q^89 + 1574640 * q^90 - 2898412 * q^91 - 3114752 * q^92 + 6017004 * q^93 + 2705984 * q^94 + 8545200 * q^95 + 3538944 * q^96 + 1935444 * q^97 - 2484416 * q^98 + 3003480 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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