LMFDB - Embedded newform 105.10.a.f.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [105,10,Mod(1,105)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("105.1"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(105, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	105.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$54.0787627972$
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} - 307x^{2} - 270x + 8836 $ x^4 - 307x^2 - 270x + 8836
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$5.15226$ of defining polynomial
Character	$\chi$	$=$	105.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-8.30453 q^{2} +81.0000 q^{3} -443.035 q^{4} -625.000 q^{5} -672.667 q^{6} -2401.00 q^{7} +7931.11 q^{8} +6561.00 q^{9} +5190.33 q^{10} +14902.2 q^{11} -35885.8 q^{12} -85007.1 q^{13} +19939.2 q^{14} -50625.0 q^{15} +160970. q^{16} -582410. q^{17} -54486.0 q^{18} -264118. q^{19} +276897. q^{20} -194481. q^{21} -123756. q^{22} -768571. q^{23} +642420. q^{24} +390625. q^{25} +705944. q^{26} +531441. q^{27} +1.06373e6 q^{28} +188493. q^{29} +420417. q^{30} +6.59032e6 q^{31} -5.39751e6 q^{32} +1.20708e6 q^{33} +4.83664e6 q^{34} +1.50062e6 q^{35} -2.90675e6 q^{36} -1.94757e6 q^{37} +2.19338e6 q^{38} -6.88557e6 q^{39} -4.95695e6 q^{40} +1.41517e7 q^{41} +1.61507e6 q^{42} -9.39531e6 q^{43} -6.60218e6 q^{44} -4.10062e6 q^{45} +6.38262e6 q^{46} +2.23972e7 q^{47} +1.30385e7 q^{48} +5.76480e6 q^{49} -3.24396e6 q^{50} -4.71752e7 q^{51} +3.76611e7 q^{52} +3.32886e7 q^{53} -4.41337e6 q^{54} -9.31386e6 q^{55} -1.90426e7 q^{56} -2.13936e7 q^{57} -1.56534e6 q^{58} -9.10729e7 q^{59} +2.24286e7 q^{60} +9.84479e7 q^{61} -5.47295e7 q^{62} -1.57530e7 q^{63} -3.75927e7 q^{64} +5.31294e7 q^{65} -1.00242e7 q^{66} +1.15591e8 q^{67} +2.58028e8 q^{68} -6.22542e7 q^{69} -1.24620e7 q^{70} +1.86826e8 q^{71} +5.20360e7 q^{72} +1.59090e8 q^{73} +1.61737e7 q^{74} +3.16406e7 q^{75} +1.17013e8 q^{76} -3.57801e7 q^{77} +5.71814e7 q^{78} +2.05688e8 q^{79} -1.00606e8 q^{80} +4.30467e7 q^{81} -1.17524e8 q^{82} +5.94838e8 q^{83} +8.61619e7 q^{84} +3.64006e8 q^{85} +7.80236e7 q^{86} +1.52679e7 q^{87} +1.18191e8 q^{88} +1.02347e9 q^{89} +3.40538e7 q^{90} +2.04102e8 q^{91} +3.40504e8 q^{92} +5.33816e8 q^{93} -1.85998e8 q^{94} +1.65074e8 q^{95} -4.37198e8 q^{96} +1.35649e9 q^{97} -4.78740e7 q^{98} +9.77732e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} + 324 q^{3} + 424 q^{4} - 2500 q^{5} + 648 q^{6} - 9604 q^{7} + 96 q^{8} + 26244 q^{9} - 5000 q^{10} + 9832 q^{11} + 34344 q^{12} - 68264 q^{13} - 19208 q^{14} - 202500 q^{15} - 290784 q^{16}+ \cdots + 64507752 q^{99}+O(q^{100}) $ 4 * q + 8 * q^2 + 324 * q^3 + 424 * q^4 - 2500 * q^5 + 648 * q^6 - 9604 * q^7 + 96 * q^8 + 26244 * q^9 - 5000 * q^10 + 9832 * q^11 + 34344 * q^12 - 68264 * q^13 - 19208 * q^14 - 202500 * q^15 - 290784 * q^16 + 86272 * q^17 + 52488 * q^18 + 807672 * q^19 - 265000 * q^20 - 777924 * q^21 + 4293352 * q^22 + 683032 * q^23 + 7776 * q^24 + 1562500 * q^25 + 4583544 * q^26 + 2125764 * q^27 - 1018024 * q^28 + 5029312 * q^29 - 405000 * q^30 + 9802992 * q^31 + 497280 * q^32 + 796392 * q^33 + 429792 * q^34 + 6002500 * q^35 + 2781864 * q^36 - 4536432 * q^37 + 21534872 * q^38 - 5529384 * q^39 - 60000 * q^40 + 11081000 * q^41 - 1555848 * q^42 - 34442248 * q^43 + 35679024 * q^44 - 16402500 * q^45 + 67652080 * q^46 - 39230168 * q^47 - 23553504 * q^48 + 23059204 * q^49 + 3125000 * q^50 + 6988032 * q^51 - 14778976 * q^52 + 76012528 * q^53 + 4251528 * q^54 - 6145000 * q^55 - 230496 * q^56 + 65421432 * q^57 + 57813344 * q^58 + 74595424 * q^59 - 21465000 * q^60 + 101246592 * q^61 + 392291880 * q^62 - 63011844 * q^63 - 276909952 * q^64 + 42665000 * q^65 + 347761512 * q^66 - 45694264 * q^67 + 345896144 * q^68 + 55325592 * q^69 + 12005000 * q^70 + 447187600 * q^71 + 629856 * q^72 + 141527624 * q^73 + 480388368 * q^74 + 126562500 * q^75 + 1081835504 * q^76 - 23606632 * q^77 + 371267064 * q^78 + 789659136 * q^79 + 181740000 * q^80 + 172186884 * q^81 + 937199856 * q^82 + 586282352 * q^83 - 82459944 * q^84 - 53920000 * q^85 + 132711648 * q^86 + 407374272 * q^87 + 1042925024 * q^88 + 1050230088 * q^89 - 32805000 * q^90 + 163901864 * q^91 + 44316096 * q^92 + 794042352 * q^93 - 1211140960 * q^94 - 504795000 * q^95 + 40279680 * q^96 + 788061288 * q^97 + 46118408 * q^98 + 64507752 * q^99

Coefficient data

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

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

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

$2$	−8.30453	−0.367012	−0.183506	−	0.983019i	$-0.558745\pi$
$2$	−8.30453	−0.367012	−0.183506	+	0.983019i	$0.558745\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	−443.035	−0.865302
$5$	−625.000	−0.447214
$5$	−625.000	−0.447214
$6$	−672.667	−0.211894
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	7931.11	0.684588
$9$	6561.00	0.333333
$10$	5190.33	0.164133
$11$	14902.2	0.306890	0.153445	−	0.988157i	$-0.450963\pi$
$11$	14902.2	0.306890	0.153445	+	0.988157i	$0.450963\pi$
$12$	−35885.8	−0.499583
$13$	−85007.1	−0.825487	−0.412743	−	0.910847i	$-0.635429\pi$
$13$	−85007.1	−0.825487	−0.412743	+	0.910847i	$0.635429\pi$
$14$	19939.2	0.138717
$15$	−50625.0	−0.258199
$16$	160970.	0.614050
$17$	−582410.	−1.69125	−0.845626	−	0.533775i	$-0.820773\pi$
$17$	−582410.	−1.69125	−0.845626	+	0.533775i	$0.820773\pi$
$18$	−54486.0	−0.122337
$19$	−264118.	−0.464951	−0.232475	−	0.972602i	$-0.574682\pi$
$19$	−264118.	−0.464951	−0.232475	+	0.972602i	$0.574682\pi$
$20$	276897.	0.386975
$21$	−194481.	−0.218218
$22$	−123756.	−0.112632
$23$	−768571.	−0.572675	−0.286338	−	0.958129i	$-0.592438\pi$
$23$	−768571.	−0.572675	−0.286338	+	0.958129i	$0.592438\pi$
$24$	642420.	0.395247
$25$	390625.	0.200000
$26$	705944.	0.302963
$27$	531441.	0.192450
$28$	1.06373e6	0.327054
$29$	188493.	0.0494884	0.0247442	−	0.999694i	$-0.492123\pi$
$29$	188493.	0.0494884	0.0247442	+	0.999694i	$0.492123\pi$
$30$	420417.	0.0947620
$31$	6.59032e6	1.28168	0.640839	−	0.767675i	$-0.278587\pi$
$31$	6.59032e6	1.28168	0.640839	+	0.767675i	$0.278587\pi$
$32$	−5.39751e6	−0.909952
$33$	1.20708e6	0.177183
$34$	4.83664e6	0.620710
$35$	1.50062e6	0.169031
$36$	−2.90675e6	−0.288434
$37$	−1.94757e6	−0.170839	−0.0854193	−	0.996345i	$-0.527223\pi$
$37$	−1.94757e6	−0.170839	−0.0854193	+	0.996345i	$0.527223\pi$
$38$	2.19338e6	0.170642
$39$	−6.88557e6	−0.476595
$40$	−4.95695e6	−0.306157
$41$	1.41517e7	0.782137	0.391068	−	0.920362i	$-0.372106\pi$
$41$	1.41517e7	0.782137	0.391068	+	0.920362i	$0.372106\pi$
$42$	1.61507e6	0.0800885
$43$	−9.39531e6	−0.419086	−0.209543	−	0.977799i	$-0.567198\pi$
$43$	−9.39531e6	−0.419086	−0.209543	+	0.977799i	$0.567198\pi$
$44$	−6.60218e6	−0.265552
$45$	−4.10062e6	−0.149071
$46$	6.38262e6	0.210179
$47$	2.23972e7	0.669505	0.334753	−	0.942306i	$-0.391347\pi$
$47$	2.23972e7	0.669505	0.334753	+	0.942306i	$0.391347\pi$
$48$	1.30385e7	0.354522
$49$	5.76480e6	0.142857
$50$	−3.24396e6	−0.0734024
$51$	−4.71752e7	−0.976445
$52$	3.76611e7	0.714295
$53$	3.32886e7	0.579501	0.289750	−	0.957102i	$-0.406428\pi$
$53$	3.32886e7	0.579501	0.289750	+	0.957102i	$0.406428\pi$
$54$	−4.41337e6	−0.0706315
$55$	−9.31386e6	−0.137245
$56$	−1.90426e7	−0.258750
$57$	−2.13936e7	−0.268439
$58$	−1.56534e6	−0.0181628
$59$	−9.10729e7	−0.978487	−0.489244	−	0.872147i	$-0.662727\pi$
$59$	−9.10729e7	−0.978487	−0.489244	+	0.872147i	$0.662727\pi$
$60$	2.24286e7	0.223420
$61$	9.84479e7	0.910379	0.455190	−	0.890395i	$-0.349571\pi$
$61$	9.84479e7	0.910379	0.455190	+	0.890395i	$0.349571\pi$
$62$	−5.47295e7	−0.470391
$63$	−1.57530e7	−0.125988
$64$	−3.75927e7	−0.280087
$65$	5.31294e7	0.369169
$66$	−1.00242e7	−0.0650282
$67$	1.15591e8	0.700788	0.350394	−	0.936602i	$-0.386048\pi$
$67$	1.15591e8	0.700788	0.350394	+	0.936602i	$0.386048\pi$
$68$	2.58028e8	1.46344
$69$	−6.22542e7	−0.330634
$70$	−1.24620e7	−0.0620363
$71$	1.86826e8	0.872519	0.436260	−	0.899821i	$-0.356303\pi$
$71$	1.86826e8	0.872519	0.436260	+	0.899821i	$0.356303\pi$
$72$	5.20360e7	0.228196
$73$	1.59090e8	0.655677	0.327838	−	0.944734i	$-0.393680\pi$
$73$	1.59090e8	0.655677	0.327838	+	0.944734i	$0.393680\pi$
$74$	1.61737e7	0.0626998
$75$	3.16406e7	0.115470
$76$	1.17013e8	0.402323
$77$	−3.57801e7	−0.115993
$78$	5.71814e7	0.174916
$79$	2.05688e8	0.594138	0.297069	−	0.954856i	$-0.403991\pi$
$79$	2.05688e8	0.594138	0.297069	+	0.954856i	$0.403991\pi$
$80$	−1.00606e8	−0.274612
$81$	4.30467e7	0.111111
$82$	−1.17524e8	−0.287053
$83$	5.94838e8	1.37577	0.687887	−	0.725818i	$-0.258538\pi$
$83$	5.94838e8	1.37577	0.687887	+	0.725818i	$0.258538\pi$
$84$	8.61619e7	0.188824
$85$	3.64006e8	0.756351
$86$	7.80236e7	0.153809
$87$	1.52679e7	0.0285721
$88$	1.18191e8	0.210093
$89$	1.02347e9	1.72910	0.864552	−	0.502543i	$-0.167602\pi$
$89$	1.02347e9	1.72910	0.864552	+	0.502543i	$0.167602\pi$
$90$	3.40538e7	0.0547109
$91$	2.04102e8	0.312005
$92$	3.40504e8	0.495537
$93$	5.33816e8	0.739977
$94$	−1.85998e8	−0.245716
$95$	1.65074e8	0.207932
$96$	−4.37198e8	−0.525361
$97$	1.35649e9	1.55577	0.777883	−	0.628409i	$-0.216294\pi$
$97$	1.35649e9	1.55577	0.777883	+	0.628409i	$0.216294\pi$
$98$	−4.78740e7	−0.0524303
$99$	9.77732e7	0.102297
$100$	−1.73060e8	−0.173060
$101$	−6.05703e8	−0.579180	−0.289590	−	0.957151i	$-0.593519\pi$
$101$	−6.05703e8	−0.579180	−0.289590	+	0.957151i	$0.593519\pi$
$102$	3.91768e8	0.358367
$103$	−3.74165e8	−0.327564	−0.163782	−	0.986497i	$-0.552369\pi$
$103$	−3.74165e8	−0.327564	−0.163782	+	0.986497i	$0.552369\pi$
$104$	−6.74201e8	−0.565118
$105$	1.21551e8	0.0975900
$106$	−2.76446e8	−0.212684
$107$	−1.76404e9	−1.30101	−0.650507	−	0.759500i	$-0.725444\pi$
$107$	−1.76404e9	−1.30101	−0.650507	+	0.759500i	$0.725444\pi$
$108$	−2.35447e8	−0.166528
$109$	−2.43042e8	−0.164916	−0.0824580	−	0.996595i	$-0.526277\pi$
$109$	−2.43042e8	−0.164916	−0.0824580	+	0.996595i	$0.526277\pi$
$110$	7.73472e7	0.0503706
$111$	−1.57753e8	−0.0986338
$112$	−3.86488e8	−0.232089
$113$	1.06491e9	0.614411	0.307206	−	0.951643i	$-0.400606\pi$
$113$	1.06491e9	0.614411	0.307206	+	0.951643i	$0.400606\pi$
$114$	1.77663e8	0.0985204
$115$	4.80357e8	0.256108
$116$	−8.35088e7	−0.0428224
$117$	−5.57731e8	−0.275162
$118$	7.56317e8	0.359116
$119$	1.39837e9	0.639233
$120$	−4.01513e8	−0.176760
$121$	−2.13587e9	−0.905819
$122$	−8.17564e8	−0.334120
$123$	1.14629e9	0.451567
$124$	−2.91974e9	−1.10904
$125$	−2.44141e8	−0.0894427
$126$	1.30821e8	0.0462391
$127$	−3.31480e9	−1.13068	−0.565341	−	0.824857i	$-0.691256\pi$
$127$	−3.31480e9	−1.13068	−0.565341	+	0.824857i	$0.691256\pi$
$128$	3.07571e9	1.01275
$129$	−7.61020e8	−0.241959
$130$	−4.41215e8	−0.135489
$131$	5.40328e9	1.60301	0.801506	−	0.597986i	$-0.204032\pi$
$131$	5.40328e9	1.60301	0.801506	+	0.597986i	$0.204032\pi$
$132$	−5.34777e8	−0.153317
$133$	6.34147e8	0.175735
$134$	−9.59928e8	−0.257198
$135$	−3.32151e8	−0.0860663
$136$	−4.61916e9	−1.15781
$137$	4.08237e9	0.990078	0.495039	−	0.868871i	$-0.335154\pi$
$137$	4.08237e9	0.990078	0.495039	+	0.868871i	$0.335154\pi$
$138$	5.16992e8	0.121347
$139$	−7.54578e9	−1.71450	−0.857250	−	0.514900i	$-0.827829\pi$
$139$	−7.54578e9	−1.71450	−0.857250	+	0.514900i	$0.827829\pi$
$140$	−6.64829e8	−0.146263
$141$	1.81418e9	0.386539
$142$	−1.55150e9	−0.320225
$143$	−1.26679e9	−0.253333
$144$	1.05612e9	0.204683
$145$	−1.17808e8	−0.0221319
$146$	−1.32117e9	−0.240641
$147$	4.66949e8	0.0824786
$148$	8.62843e8	0.147827
$149$	4.86426e8	0.0808498	0.0404249	−	0.999183i	$-0.487129\pi$
$149$	4.86426e8	0.0808498	0.0404249	+	0.999183i	$0.487129\pi$
$150$	−2.62760e8	−0.0423789
$151$	6.20733e9	0.971647	0.485824	−	0.874057i	$-0.338520\pi$
$151$	6.20733e9	0.971647	0.485824	+	0.874057i	$0.338520\pi$
$152$	−2.09475e9	−0.318300
$153$	−3.82119e9	−0.563751
$154$	2.97137e8	0.0425710
$155$	−4.11895e9	−0.573184
$156$	3.05055e9	0.412399
$157$	−9.71573e9	−1.27622	−0.638112	−	0.769943i	$-0.720285\pi$
$157$	−9.71573e9	−1.27622	−0.638112	+	0.769943i	$0.720285\pi$
$158$	−1.70814e9	−0.218056
$159$	2.69638e9	0.334575
$160$	3.37344e9	0.406943
$161$	1.84534e9	0.216451
$162$	−3.57483e8	−0.0407791
$163$	3.98507e9	0.442173	0.221086	−	0.975254i	$-0.429040\pi$
$163$	3.98507e9	0.442173	0.221086	+	0.975254i	$0.429040\pi$
$164$	−6.26971e9	−0.676785
$165$	−7.54422e8	−0.0792386
$166$	−4.93985e9	−0.504925
$167$	7.63594e9	0.759694	0.379847	−	0.925049i	$-0.375977\pi$
$167$	7.63594e9	0.759694	0.379847	+	0.925049i	$0.375977\pi$
$168$	−1.54245e9	−0.149389
$169$	−3.37830e9	−0.318572
$170$	−3.02290e9	−0.277590
$171$	−1.73288e9	−0.154984
$172$	4.16245e9	0.362636
$173$	1.39108e9	0.118071	0.0590355	−	0.998256i	$-0.481197\pi$
$173$	1.39108e9	0.118071	0.0590355	+	0.998256i	$0.481197\pi$
$174$	−1.26793e8	−0.0104863
$175$	−9.37891e8	−0.0755929
$176$	2.39880e9	0.188446
$177$	−7.37690e9	−0.564930
$178$	−8.49946e9	−0.634602
$179$	−1.87616e9	−0.136594	−0.0682969	−	0.997665i	$-0.521757\pi$
$179$	−1.87616e9	−0.136594	−0.0682969	+	0.997665i	$0.521757\pi$
$180$	1.81672e9	0.128992
$181$	−2.42614e9	−0.168021	−0.0840104	−	0.996465i	$-0.526773\pi$
$181$	−2.42614e9	−0.168021	−0.0840104	+	0.996465i	$0.526773\pi$
$182$	−1.69497e9	−0.114509
$183$	7.97428e9	0.525608
$184$	−6.09562e9	−0.392047
$185$	1.21723e9	0.0764014
$186$	−4.43309e9	−0.271580
$187$	−8.67917e9	−0.519028
$188$	−9.92275e9	−0.579324
$189$	−1.27599e9	−0.0727393
$190$	−1.37086e9	−0.0763136
$191$	9.41804e9	0.512048	0.256024	−	0.966670i	$-0.417587\pi$
$191$	9.41804e9	0.512048	0.256024	+	0.966670i	$0.417587\pi$
$192$	−3.04501e9	−0.161709
$193$	−1.49145e10	−0.773749	−0.386874	−	0.922132i	$-0.626445\pi$
$193$	−1.49145e10	−0.773749	−0.386874	+	0.922132i	$0.626445\pi$
$194$	−1.12650e10	−0.570984
$195$	4.30348e9	0.213140
$196$	−2.55401e9	−0.123615
$197$	−1.49680e10	−0.708054	−0.354027	−	0.935235i	$-0.615188\pi$
$197$	−1.49680e10	−0.708054	−0.354027	+	0.935235i	$0.615188\pi$
$198$	−8.11960e8	−0.0375441
$199$	−8.64658e9	−0.390846	−0.195423	−	0.980719i	$-0.562608\pi$
$199$	−8.64658e9	−0.390846	−0.195423	+	0.980719i	$0.562608\pi$
$200$	3.09809e9	0.136918
$201$	9.36286e9	0.404600
$202$	5.03008e9	0.212566
$203$	−4.52571e8	−0.0187048
$204$	2.09003e10	0.844920
$205$	−8.84484e9	−0.349782
$206$	3.10727e9	0.120220
$207$	−5.04259e9	−0.190892
$208$	−1.36836e10	−0.506890
$209$	−3.93593e9	−0.142689
$210$	−1.00942e9	−0.0358167
$211$	4.04960e10	1.40651	0.703253	−	0.710940i	$-0.251730\pi$
$211$	4.04960e10	1.40651	0.703253	+	0.710940i	$0.251730\pi$
$212$	−1.47480e10	−0.501443
$213$	1.51329e10	0.503749
$214$	1.46495e10	0.477487
$215$	5.87207e9	0.187421
$216$	4.21492e9	0.131749
$217$	−1.58234e10	−0.484429
$218$	2.01835e9	0.0605261
$219$	1.28863e10	0.378555
$220$	4.12636e9	0.118759
$221$	4.95090e10	1.39611
$222$	1.31007e9	0.0361998
$223$	−4.98356e10	−1.34948	−0.674742	−	0.738053i	$-0.735745\pi$
$223$	−4.98356e10	−1.34948	−0.674742	+	0.738053i	$0.735745\pi$
$224$	1.29594e10	0.343929
$225$	2.56289e9	0.0666667
$226$	−8.84356e9	−0.225496
$227$	−1.87758e10	−0.469334	−0.234667	−	0.972076i	$-0.575400\pi$
$227$	−1.87758e10	−0.469334	−0.234667	+	0.972076i	$0.575400\pi$
$228$	9.47809e9	0.232281
$229$	7.34599e10	1.76519	0.882594	−	0.470136i	$-0.155795\pi$
$229$	7.34599e10	1.76519	0.882594	+	0.470136i	$0.155795\pi$
$230$	−3.98914e9	−0.0939947
$231$	−2.89819e9	−0.0669689
$232$	1.49496e9	0.0338791
$233$	5.23351e10	1.16330	0.581650	−	0.813439i	$-0.302408\pi$
$233$	5.23351e10	1.16330	0.581650	+	0.813439i	$0.302408\pi$
$234$	4.63170e9	0.100988
$235$	−1.39983e10	−0.299412
$236$	4.03485e10	0.846687
$237$	1.66608e10	0.343026
$238$	−1.16128e10	−0.234606
$239$	6.86346e9	0.136067	0.0680334	−	0.997683i	$-0.478328\pi$
$239$	6.86346e9	0.136067	0.0680334	+	0.997683i	$0.478328\pi$
$240$	−8.14909e9	−0.158547
$241$	−5.02151e10	−0.958865	−0.479433	−	0.877579i	$-0.659157\pi$
$241$	−5.02151e10	−0.958865	−0.479433	+	0.877579i	$0.659157\pi$
$242$	1.77374e10	0.332446
$243$	3.48678e9	0.0641500
$244$	−4.36159e10	−0.787753
$245$	−3.60300e9	−0.0638877
$246$	−9.51941e9	−0.165730
$247$	2.24519e10	0.383811
$248$	5.22686e10	0.877421
$249$	4.81819e10	0.794304
$250$	2.02747e9	0.0328265
$251$	−7.34378e9	−0.116785	−0.0583926	−	0.998294i	$-0.518598\pi$
$251$	−7.34378e9	−0.116785	−0.0583926	+	0.998294i	$0.518598\pi$
$252$	6.97911e9	0.109018
$253$	−1.14534e10	−0.175748
$254$	2.75279e10	0.414974
$255$	2.94845e10	0.436680
$256$	−6.29489e9	−0.0916027
$257$	9.49808e10	1.35812	0.679058	−	0.734085i	$-0.262389\pi$
$257$	9.49808e10	1.35812	0.679058	+	0.734085i	$0.262389\pi$
$258$	6.31991e9	0.0888019
$259$	4.67612e9	0.0645709
$260$	−2.35382e10	−0.319443
$261$	1.23670e9	0.0164961
$262$	−4.48717e10	−0.588325
$263$	−6.93155e10	−0.893366	−0.446683	−	0.894692i	$-0.647395\pi$
$263$	−6.93155e10	−0.893366	−0.446683	+	0.894692i	$0.647395\pi$
$264$	9.57346e9	0.121297
$265$	−2.08054e10	−0.259161
$266$	−5.26630e9	−0.0644968
$267$	8.29013e10	0.998299
$268$	−5.12108e10	−0.606394
$269$	9.53527e10	1.11032	0.555159	−	0.831744i	$-0.312657\pi$
$269$	9.53527e10	1.11032	0.555159	+	0.831744i	$0.312657\pi$
$270$	2.75835e9	0.0315873
$271$	−6.38320e10	−0.718914	−0.359457	−	0.933162i	$-0.617038\pi$
$271$	−6.38320e10	−0.718914	−0.359457	+	0.933162i	$0.617038\pi$
$272$	−9.37503e10	−1.03851
$273$	1.65323e10	0.180136
$274$	−3.39021e10	−0.363370
$275$	5.82116e9	0.0613780
$276$	2.75808e10	0.286099
$277$	−1.77106e11	−1.80748	−0.903742	−	0.428078i	$-0.859191\pi$
$277$	−1.77106e11	−1.80748	−0.903742	+	0.428078i	$0.859191\pi$
$278$	6.26642e10	0.629242
$279$	4.32391e10	0.427226
$280$	1.19016e10	0.115716
$281$	1.61938e10	0.154942	0.0774710	−	0.996995i	$-0.475315\pi$
$281$	1.61938e10	0.154942	0.0774710	+	0.996995i	$0.475315\pi$
$282$	−1.50659e10	−0.141864
$283$	1.05574e11	0.978404	0.489202	−	0.872170i	$-0.337288\pi$
$283$	1.05574e11	0.978404	0.489202	+	0.872170i	$0.337288\pi$
$284$	−8.27705e10	−0.754993
$285$	1.33710e10	0.120050
$286$	1.05201e10	0.0929764
$287$	−3.39783e10	−0.295620
$288$	−3.54130e10	−0.303317
$289$	2.20613e11	1.86034
$290$	9.78339e8	0.00812266
$291$	1.09876e11	0.898222
$292$	−7.04824e10	−0.567359
$293$	1.71735e11	1.36131	0.680653	−	0.732606i	$-0.261696\pi$
$293$	1.71735e11	1.36131	0.680653	+	0.732606i	$0.261696\pi$
$294$	−3.87779e9	−0.0302706
$295$	5.69206e10	0.437593
$296$	−1.54464e10	−0.116954
$297$	7.91963e9	0.0590610
$298$	−4.03954e9	−0.0296728
$299$	6.53339e10	0.472736
$300$	−1.40179e10	−0.0999165
$301$	2.25581e10	0.158400
$302$	−5.15489e10	−0.356606
$303$	−4.90619e10	−0.334390
$304$	−4.25150e10	−0.285503
$305$	−6.15300e10	−0.407134
$306$	3.17332e10	0.206903
$307$	−2.84858e11	−1.83023	−0.915114	−	0.403194i	$-0.867900\pi$
$307$	−2.84858e11	−1.83023	−0.915114	+	0.403194i	$0.867900\pi$
$308$	1.58518e10	0.100369
$309$	−3.03074e10	−0.189119
$310$	3.42059e10	0.210365
$311$	7.98673e10	0.484113	0.242057	−	0.970262i	$-0.422178\pi$
$311$	7.98673e10	0.484113	0.242057	+	0.970262i	$0.422178\pi$
$312$	−5.46103e10	−0.326271
$313$	−1.43657e10	−0.0846016	−0.0423008	−	0.999105i	$-0.513469\pi$
$313$	−1.43657e10	−0.0846016	−0.0423008	+	0.999105i	$0.513469\pi$
$314$	8.06846e10	0.468390
$315$	9.84560e9	0.0563436
$316$	−9.11271e10	−0.514109
$317$	4.97249e9	0.0276572	0.0138286	−	0.999904i	$-0.495598\pi$
$317$	4.97249e9	0.0276572	0.0138286	+	0.999904i	$0.495598\pi$
$318$	−2.23921e10	−0.122793
$319$	2.80895e9	0.0151875
$320$	2.34954e10	0.125259
$321$	−1.42887e11	−0.751141
$322$	−1.53247e10	−0.0794401
$323$	1.53825e11	0.786349
$324$	−1.90712e10	−0.0961447
$325$	−3.32059e10	−0.165097
$326$	−3.30942e10	−0.162283
$327$	−1.96864e10	−0.0952143
$328$	1.12239e11	0.535441
$329$	−5.37757e10	−0.253049
$330$	6.26512e9	0.0290815
$331$	−1.22488e11	−0.560879	−0.280439	−	0.959872i	$-0.590480\pi$
$331$	−1.22488e11	−0.560879	−0.280439	+	0.959872i	$0.590480\pi$
$332$	−2.63534e11	−1.19046
$333$	−1.27780e10	−0.0569462
$334$	−6.34129e10	−0.278817
$335$	−7.22443e10	−0.313402
$336$	−3.13055e10	−0.133997
$337$	−3.27544e10	−0.138336	−0.0691680	−	0.997605i	$-0.522034\pi$
$337$	−3.27544e10	−0.138336	−0.0691680	+	0.997605i	$0.522034\pi$
$338$	2.80552e10	0.116920
$339$	8.62576e10	0.354730
$340$	−1.61267e11	−0.654472
$341$	9.82101e10	0.393334
$342$	1.43907e10	0.0568808
$343$	−1.38413e10	−0.0539949
$344$	−7.45153e10	−0.286901
$345$	3.89089e10	0.147864
$346$	−1.15522e10	−0.0433335
$347$	−1.96183e11	−0.726405	−0.363203	−	0.931710i	$-0.618317\pi$
$347$	−1.96183e11	−0.726405	−0.363203	+	0.931710i	$0.618317\pi$
$348$	−6.76421e9	−0.0247235
$349$	4.28405e11	1.54575	0.772876	−	0.634557i	$-0.218818\pi$
$349$	4.28405e11	1.54575	0.772876	+	0.634557i	$0.218818\pi$
$350$	7.78874e9	0.0277435
$351$	−4.51762e10	−0.158865
$352$	−8.04346e10	−0.279255
$353$	2.10417e11	0.721264	0.360632	−	0.932708i	$-0.382561\pi$
$353$	2.10417e11	0.721264	0.360632	+	0.932708i	$0.382561\pi$
$354$	6.12617e10	0.207336
$355$	−1.16766e11	−0.390203
$356$	−4.53434e11	−1.49620
$357$	1.13268e11	0.369062
$358$	1.55806e10	0.0501315
$359$	−2.64740e11	−0.841190	−0.420595	−	0.907248i	$-0.638179\pi$
$359$	−2.64740e11	−0.841190	−0.420595	+	0.907248i	$0.638179\pi$
$360$	−3.25225e10	−0.102052
$361$	−2.52929e11	−0.783821
$362$	2.01480e10	0.0616656
$363$	−1.73006e11	−0.522975
$364$	−9.04243e10	−0.269978
$365$	−9.94312e10	−0.293228
$366$	−6.62227e10	−0.192904
$367$	−3.85439e11	−1.10907	−0.554534	−	0.832161i	$-0.687103\pi$
$367$	−3.85439e11	−1.10907	−0.554534	+	0.832161i	$0.687103\pi$
$368$	−1.23717e11	−0.351652
$369$	9.28496e10	0.260712
$370$	−1.01086e10	−0.0280402
$371$	−7.99259e10	−0.219031
$372$	−2.36499e11	−0.640304
$373$	−6.14857e10	−0.164469	−0.0822346	−	0.996613i	$-0.526206\pi$
$373$	−6.14857e10	−0.164469	−0.0822346	+	0.996613i	$0.526206\pi$
$374$	7.20764e10	0.190489
$375$	−1.97754e10	−0.0516398
$376$	1.77635e11	0.458335
$377$	−1.60232e10	−0.0408520
$378$	1.05965e10	0.0266962
$379$	3.85377e11	0.959421	0.479710	−	0.877427i	$-0.340742\pi$
$379$	3.85377e11	0.959421	0.479710	+	0.877427i	$0.340742\pi$
$380$	−7.31334e10	−0.179924
$381$	−2.68499e11	−0.652800
$382$	−7.82124e10	−0.187928
$383$	2.30751e11	0.547961	0.273981	−	0.961735i	$-0.411660\pi$
$383$	2.30751e11	0.547961	0.273981	+	0.961735i	$0.411660\pi$
$384$	2.49133e11	0.584710
$385$	2.23626e10	0.0518739
$386$	1.23858e11	0.283975
$387$	−6.16426e10	−0.139695
$388$	−6.00973e11	−1.34621
$389$	−1.36395e11	−0.302014	−0.151007	−	0.988533i	$-0.548252\pi$
$389$	−1.36395e11	−0.302014	−0.151007	+	0.988533i	$0.548252\pi$
$390$	−3.57384e10	−0.0782248
$391$	4.47623e11	0.968539
$392$	4.57213e10	0.0977983
$393$	4.37666e11	0.925500
$394$	1.24302e11	0.259864
$395$	−1.28555e11	−0.265707
$396$	−4.33169e10	−0.0885175
$397$	5.45803e11	1.10275	0.551377	−	0.834256i	$-0.314102\pi$
$397$	5.45803e11	1.10275	0.551377	+	0.834256i	$0.314102\pi$
$398$	7.18058e10	0.143445
$399$	5.13659e10	0.101461
$400$	6.28788e10	0.122810
$401$	−2.89087e11	−0.558315	−0.279157	−	0.960245i	$-0.590055\pi$
$401$	−2.89087e11	−0.558315	−0.279157	+	0.960245i	$0.590055\pi$
$402$	−7.77541e10	−0.148493
$403$	−5.60224e11	−1.05801
$404$	2.68347e11	0.501166
$405$	−2.69042e10	−0.0496904
$406$	3.75839e9	0.00686490
$407$	−2.90231e10	−0.0524287
$408$	−3.74152e11	−0.668463
$409$	−1.92007e11	−0.339282	−0.169641	−	0.985506i	$-0.554261\pi$
$409$	−1.92007e11	−0.339282	−0.169641	+	0.985506i	$0.554261\pi$
$410$	7.34522e10	0.128374
$411$	3.30672e11	0.571622
$412$	1.65768e11	0.283442
$413$	2.18666e11	0.369833
$414$	4.18764e10	0.0700595
$415$	−3.71774e11	−0.615265
$416$	4.58826e11	0.751153
$417$	−6.11208e11	−0.989867
$418$	3.26861e10	0.0523684
$419$	1.41343e11	0.224033	0.112017	−	0.993706i	$-0.464269\pi$
$419$	1.41343e11	0.224033	0.112017	+	0.993706i	$0.464269\pi$
$420$	−5.38512e10	−0.0844449
$421$	8.37353e11	1.29909	0.649545	−	0.760323i	$-0.274959\pi$
$421$	8.37353e11	1.29909	0.649545	+	0.760323i	$0.274959\pi$
$422$	−3.36301e11	−0.516204
$423$	1.46948e11	0.223168
$424$	2.64016e11	0.396719
$425$	−2.27504e11	−0.338251
$426$	−1.25672e11	−0.184882
$427$	−2.36373e11	−0.344091
$428$	7.81532e11	1.12577
$429$	−1.02610e11	−0.146262
$430$	−4.87648e10	−0.0687857
$431$	6.27369e11	0.875740	0.437870	−	0.899038i	$-0.355733\pi$
$431$	6.27369e11	0.875740	0.437870	+	0.899038i	$0.355733\pi$
$432$	8.55459e10	0.118174
$433$	1.32269e12	1.80827	0.904133	−	0.427251i	$-0.140518\pi$
$433$	1.32269e12	1.80827	0.904133	+	0.427251i	$0.140518\pi$
$434$	1.31406e11	0.177791
$435$	−9.54244e9	−0.0127778
$436$	1.07676e11	0.142702
$437$	2.02993e11	0.266266
$438$	−1.07015e11	−0.138934
$439$	9.03428e11	1.16092	0.580461	−	0.814288i	$-0.302872\pi$
$439$	9.03428e11	1.16092	0.580461	+	0.814288i	$0.302872\pi$
$440$	−7.38693e10	−0.0939565
$441$	3.78229e10	0.0476190
$442$	−4.11149e11	−0.512388
$443$	2.06273e11	0.254464	0.127232	−	0.991873i	$-0.459391\pi$
$443$	2.06273e11	0.254464	0.127232	+	0.991873i	$0.459391\pi$
$444$	6.98903e10	0.0853480
$445$	−6.39670e11	−0.773279
$446$	4.13861e11	0.495277
$447$	3.94005e10	0.0466786
$448$	9.02601e10	0.105863
$449$	4.66846e11	0.542082	0.271041	−	0.962568i	$-0.412632\pi$
$449$	4.66846e11	0.542082	0.271041	+	0.962568i	$0.412632\pi$
$450$	−2.12836e10	−0.0244675
$451$	2.10892e11	0.240030
$452$	−4.71791e11	−0.531651
$453$	5.02794e11	0.560981
$454$	1.55924e11	0.172251
$455$	−1.27564e11	−0.139533
$456$	−1.69675e11	−0.183770
$457$	8.24857e11	0.884618	0.442309	−	0.896863i	$-0.354159\pi$
$457$	8.24857e11	0.884618	0.442309	+	0.896863i	$0.354159\pi$
$458$	−6.10050e11	−0.647845
$459$	−3.09516e11	−0.325482
$460$	−2.12815e11	−0.221611
$461$	8.87190e10	0.0914876	0.0457438	−	0.998953i	$-0.485434\pi$
$461$	8.87190e10	0.0914876	0.0457438	+	0.998953i	$0.485434\pi$
$462$	2.40681e10	0.0245784
$463$	1.10664e12	1.11916	0.559581	−	0.828776i	$-0.310962\pi$
$463$	1.10664e12	1.11916	0.559581	+	0.828776i	$0.310962\pi$
$464$	3.03416e10	0.0303884
$465$	−3.33635e11	−0.330928
$466$	−4.34618e11	−0.426944
$467$	−1.11998e12	−1.08964	−0.544821	−	0.838552i	$-0.683403\pi$
$467$	−1.11998e12	−1.08964	−0.544821	+	0.838552i	$0.683403\pi$
$468$	2.47094e11	0.238098
$469$	−2.77534e11	−0.264873
$470$	1.16249e11	0.109888
$471$	−7.86974e11	−0.736829
$472$	−7.22310e11	−0.669860
$473$	−1.40010e11	−0.128613
$474$	−1.38360e11	−0.125895
$475$	−1.03171e11	−0.0929901
$476$	−6.19525e11	−0.553130
$477$	2.18406e11	0.193167
$478$	−5.69978e10	−0.0499381
$479$	6.71179e11	0.582544	0.291272	−	0.956640i	$-0.405922\pi$
$479$	6.71179e11	0.582544	0.291272	+	0.956640i	$0.405922\pi$
$480$	2.73249e11	0.234949
$481$	1.65558e11	0.141025
$482$	4.17013e11	0.351915
$483$	1.49472e11	0.124968
$484$	9.46266e11	0.783807
$485$	−8.47807e11	−0.695760
$486$	−2.89561e10	−0.0235438
$487$	2.01428e12	1.62270	0.811352	−	0.584558i	$-0.198732\pi$
$487$	2.01428e12	1.62270	0.811352	+	0.584558i	$0.198732\pi$
$488$	7.80802e11	0.623235
$489$	3.22791e11	0.255289
$490$	2.99212e10	0.0234475
$491$	1.13665e12	0.882594	0.441297	−	0.897361i	$-0.354519\pi$
$491$	1.13665e12	0.882594	0.441297	+	0.897361i	$0.354519\pi$
$492$	−5.07847e11	−0.390742
$493$	−1.09780e11	−0.0836973
$494$	−1.86452e11	−0.140863
$495$	−6.11082e10	−0.0457484
$496$	1.06084e12	0.787015
$497$	−4.48570e11	−0.329781
$498$	−4.00128e11	−0.291519
$499$	1.82340e12	1.31653	0.658263	−	0.752788i	$-0.271292\pi$
$499$	1.82340e12	1.31653	0.658263	+	0.752788i	$0.271292\pi$
$500$	1.08163e11	0.0773950
$501$	6.18511e11	0.438609
$502$	6.09867e10	0.0428616
$503$	−5.72073e11	−0.398470	−0.199235	−	0.979952i	$-0.563846\pi$
$503$	−5.72073e11	−0.398470	−0.199235	+	0.979952i	$0.563846\pi$
$504$	−1.24939e11	−0.0862500
$505$	3.78564e11	0.259017
$506$	9.51149e10	0.0645017
$507$	−2.73642e11	−0.183928
$508$	1.46857e12	0.978382
$509$	2.95989e12	1.95455	0.977273	−	0.211986i	$-0.0679931\pi$
$509$	2.95989e12	1.95455	0.977273	+	0.211986i	$0.0679931\pi$
$510$	−2.44855e11	−0.160267
$511$	−3.81975e11	−0.247822
$512$	−1.52249e12	−0.979128
$513$	−1.40363e11	−0.0894798
$514$	−7.88771e11	−0.498445
$515$	2.33853e11	0.146491
$516$	3.37158e11	0.209368
$517$	3.33767e11	0.205464
$518$	−3.88330e10	−0.0236983
$519$	1.12677e11	0.0681683
$520$	4.21376e11	0.252729
$521$	−2.85602e12	−1.69821	−0.849107	−	0.528222i	$-0.822859\pi$
$521$	−2.85602e12	−1.69821	−0.849107	+	0.528222i	$0.822859\pi$
$522$	−1.02702e10	−0.00605427
$523$	3.83909e11	0.224373	0.112187	−	0.993687i	$-0.464215\pi$
$523$	3.83909e11	0.224373	0.112187	+	0.993687i	$0.464215\pi$
$524$	−2.39384e12	−1.38709
$525$	−7.59691e10	−0.0436436
$526$	5.75632e11	0.327876
$527$	−3.83827e12	−2.16764
$528$	1.94303e11	0.108799
$529$	−1.21045e12	−0.672043
$530$	1.72779e11	0.0951150
$531$	−5.97529e11	−0.326162
$532$	−2.80949e11	−0.152064
$533$	−1.20300e12	−0.645643
$534$	−6.88456e11	−0.366387
$535$	1.10253e12	0.581831
$536$	9.16764e11	0.479751
$537$	−1.51969e11	−0.0788624
$538$	−7.91859e11	−0.407500
$539$	8.59081e10	0.0438414
$540$	1.47154e11	0.0744734
$541$	−8.49593e11	−0.426406	−0.213203	−	0.977008i	$-0.568390\pi$
$541$	−8.49593e11	−0.426406	−0.213203	+	0.977008i	$0.568390\pi$
$542$	5.30095e11	0.263850
$543$	−1.96518e11	−0.0970068
$544$	3.14356e12	1.53896
$545$	1.51901e11	0.0737526
$546$	−1.37293e11	−0.0661120
$547$	−1.94856e12	−0.930618	−0.465309	−	0.885148i	$-0.654057\pi$
$547$	−1.94856e12	−0.930618	−0.465309	+	0.885148i	$0.654057\pi$
$548$	−1.80863e12	−0.856717
$549$	6.45917e11	0.303460
$550$	−4.83420e10	−0.0225264
$551$	−4.97843e10	−0.0230097
$552$	−4.93745e11	−0.226348
$553$	−4.93858e11	−0.224563
$554$	1.47078e12	0.663368
$555$	9.85959e10	0.0441104
$556$	3.34304e12	1.48356
$557$	−3.99623e12	−1.75915	−0.879574	−	0.475762i	$-0.842172\pi$
$557$	−3.99623e12	−1.75915	−0.879574	+	0.475762i	$0.842172\pi$
$558$	−3.59080e11	−0.156797
$559$	7.98668e11	0.345950
$560$	2.41555e11	0.103793
$561$	−7.03013e11	−0.299661
$562$	−1.34482e11	−0.0568656
$563$	−2.64531e12	−1.10966	−0.554829	−	0.831964i	$-0.687216\pi$
$563$	−2.64531e12	−1.10966	−0.554829	+	0.831964i	$0.687216\pi$
$564$	−8.03743e11	−0.334473
$565$	−6.65568e11	−0.274773
$566$	−8.76743e11	−0.359086
$567$	−1.03355e11	−0.0419961
$568$	1.48174e12	0.597316
$569$	−2.09982e12	−0.839801	−0.419900	−	0.907570i	$-0.637935\pi$
$569$	−2.09982e12	−0.839801	−0.419900	+	0.907570i	$0.637935\pi$
$570$	−1.11040e11	−0.0440597
$571$	−4.39896e12	−1.73176	−0.865881	−	0.500251i	$-0.833241\pi$
$571$	−4.39896e12	−1.73176	−0.865881	+	0.500251i	$0.833241\pi$
$572$	5.61232e11	0.219210
$573$	7.62862e11	0.295631
$574$	2.82174e11	0.108496
$575$	−3.00223e11	−0.114535
$576$	−2.46646e11	−0.0933625
$577$	−3.17807e12	−1.19364	−0.596818	−	0.802377i	$-0.703569\pi$
$577$	−3.17807e12	−1.19364	−0.596818	+	0.802377i	$0.703569\pi$
$578$	−1.83209e12	−0.682765
$579$	−1.20807e12	−0.446724
$580$	5.21930e10	0.0191508
$581$	−1.42821e12	−0.519994
$582$	−9.12467e11	−0.329658
$583$	4.96072e11	0.177843
$584$	1.26176e12	0.448868
$585$	3.48582e11	0.123056
$586$	−1.42618e12	−0.499615
$587$	4.91687e12	1.70930	0.854648	−	0.519207i	$-0.173773\pi$
$587$	4.91687e12	1.70930	0.854648	+	0.519207i	$0.173773\pi$
$588$	−2.06875e11	−0.0713689
$589$	−1.74062e12	−0.595917
$590$	−4.72698e11	−0.160602
$591$	−1.21241e12	−0.408795
$592$	−3.13500e11	−0.104904
$593$	4.74114e12	1.57448	0.787239	−	0.616648i	$-0.211510\pi$
$593$	4.74114e12	1.57448	0.787239	+	0.616648i	$0.211510\pi$
$594$	−6.57688e10	−0.0216761
$595$	−8.73979e11	−0.285874
$596$	−2.15504e11	−0.0699595
$597$	−7.00373e11	−0.225655
$598$	−5.42568e11	−0.173500
$599$	2.19748e12	0.697436	0.348718	−	0.937228i	$-0.386617\pi$
$599$	2.19748e12	0.697436	0.348718	+	0.937228i	$0.386617\pi$
$600$	2.50945e11	0.0790494
$601$	3.12379e12	0.976667	0.488334	−	0.872657i	$-0.337605\pi$
$601$	3.12379e12	0.976667	0.488334	+	0.872657i	$0.337605\pi$
$602$	−1.87335e11	−0.0581345
$603$	7.58392e11	0.233596
$604$	−2.75006e12	−0.840768
$605$	1.33492e12	0.405094
$606$	4.07436e11	0.122725
$607$	5.39395e12	1.61272	0.806358	−	0.591428i	$-0.201436\pi$
$607$	5.39395e12	1.61272	0.806358	+	0.591428i	$0.201436\pi$
$608$	1.42558e12	0.423083
$609$	−3.66582e10	−0.0107992
$610$	5.10977e11	0.149423
$611$	−1.90392e12	−0.552667
$612$	1.69292e12	0.487815
$613$	−3.40302e12	−0.973402	−0.486701	−	0.873569i	$-0.661800\pi$
$613$	−3.40302e12	−0.973402	−0.486701	+	0.873569i	$0.661800\pi$
$614$	2.36561e12	0.671716
$615$	−7.16432e11	−0.201947
$616$	−2.83776e11	−0.0794077
$617$	−1.74671e12	−0.485220	−0.242610	−	0.970124i	$-0.578003\pi$
$617$	−1.74671e12	−0.485220	−0.242610	+	0.970124i	$0.578003\pi$
$618$	2.51689e11	0.0694089
$619$	−1.47701e12	−0.404368	−0.202184	−	0.979348i	$-0.564804\pi$
$619$	−1.47701e12	−0.404368	−0.202184	+	0.979348i	$0.564804\pi$
$620$	1.82484e12	0.495977
$621$	−4.08450e11	−0.110211
$622$	−6.63260e11	−0.177675
$623$	−2.45736e12	−0.653540
$624$	−1.10837e12	−0.292653
$625$	1.52588e11	0.0400000
$626$	1.19301e11	0.0310498
$627$	−3.18811e11	−0.0823813
$628$	4.30441e12	1.10432
$629$	1.13429e12	0.288931
$630$	−8.17631e10	−0.0206788
$631$	5.31333e12	1.33424	0.667121	−	0.744949i	$-0.267526\pi$
$631$	5.31333e12	1.33424	0.667121	+	0.744949i	$0.267526\pi$
$632$	1.63134e12	0.406740
$633$	3.28018e12	0.812046
$634$	−4.12942e10	−0.0101505
$635$	2.07175e12	0.505657
$636$	−1.19459e12	−0.289508
$637$	−4.90049e11	−0.117927
$638$	−2.33270e10	−0.00557398
$639$	1.22577e12	0.290840
$640$	−1.92232e12	−0.452914
$641$	1.02026e12	0.238699	0.119349	−	0.992852i	$-0.461919\pi$
$641$	1.02026e12	0.238699	0.119349	+	0.992852i	$0.461919\pi$
$642$	1.18661e12	0.275678
$643$	−6.29061e12	−1.45125	−0.725627	−	0.688088i	$-0.758450\pi$
$643$	−6.29061e12	−1.45125	−0.725627	+	0.688088i	$0.758450\pi$
$644$	−8.17549e11	−0.187296
$645$	4.75637e11	0.108207
$646$	−1.27744e12	−0.288599
$647$	−6.48657e12	−1.45528	−0.727639	−	0.685960i	$-0.759382\pi$
$647$	−6.48657e12	−1.45528	−0.727639	+	0.685960i	$0.759382\pi$
$648$	3.41408e11	0.0760653
$649$	−1.35718e12	−0.300288
$650$	2.75759e11	0.0605927
$651$	−1.28169e12	−0.279685
$652$	−1.76553e12	−0.382613
$653$	6.85042e12	1.47437	0.737187	−	0.675689i	$-0.236154\pi$
$653$	6.85042e12	1.47437	0.737187	+	0.675689i	$0.236154\pi$
$654$	1.63486e11	0.0349448
$655$	−3.37705e12	−0.716889
$656$	2.27800e12	0.480271
$657$	1.04379e12	0.218559
$658$	4.46582e11	0.0928720
$659$	−6.33720e12	−1.30892	−0.654460	−	0.756097i	$-0.727104\pi$
$659$	−6.33720e12	−1.30892	−0.654460	+	0.756097i	$0.727104\pi$
$660$	3.34235e11	0.0685654
$661$	1.13408e12	0.231066	0.115533	−	0.993304i	$-0.463142\pi$
$661$	1.13408e12	0.231066	0.115533	+	0.993304i	$0.463142\pi$
$662$	1.01721e12	0.205849
$663$	4.01023e12	0.806042
$664$	4.71773e12	0.941839
$665$	−3.96342e11	−0.0785910
$666$	1.06116e11	0.0208999
$667$	−1.44870e11	−0.0283408
$668$	−3.38299e12	−0.657365
$669$	−4.03668e12	−0.779125
$670$	5.99955e11	0.115022
$671$	1.46709e12	0.279386
$672$	1.04971e12	0.198568
$673$	−8.81447e12	−1.65626	−0.828129	−	0.560537i	$-0.810595\pi$
$673$	−8.81447e12	−1.65626	−0.828129	+	0.560537i	$0.810595\pi$
$674$	2.72010e11	0.0507709
$675$	2.07594e11	0.0384900
$676$	1.49670e12	0.275661
$677$	7.77532e12	1.42256	0.711278	−	0.702911i	$-0.248117\pi$
$677$	7.77532e12	1.42256	0.711278	+	0.702911i	$0.248117\pi$
$678$	−7.16328e11	−0.130190
$679$	−3.25694e12	−0.588024
$680$	2.88697e12	0.517789
$681$	−1.52084e12	−0.270970
$682$	−8.15588e11	−0.144358
$683$	−1.63173e12	−0.286916	−0.143458	−	0.989656i	$-0.545822\pi$
$683$	−1.63173e12	−0.286916	−0.143458	+	0.989656i	$0.545822\pi$
$684$	7.67725e11	0.134108
$685$	−2.55148e12	−0.442776
$686$	1.14945e11	0.0198168
$687$	5.95025e12	1.01913
$688$	−1.51236e12	−0.257340
$689$	−2.82977e12	−0.478370
$690$	−3.23120e11	−0.0542679
$691$	−4.11023e12	−0.685828	−0.342914	−	0.939367i	$-0.611414\pi$
$691$	−4.11023e12	−0.685828	−0.342914	+	0.939367i	$0.611414\pi$
$692$	−6.16295e11	−0.102167
$693$	−2.34753e11	−0.0386645
$694$	1.62921e12	0.266599
$695$	4.71611e12	0.766748
$696$	1.21091e11	0.0195601
$697$	−8.24211e12	−1.32279
$698$	−3.55770e12	−0.567309
$699$	4.23914e12	0.671631
$700$	4.15518e11	0.0654107
$701$	1.05286e13	1.64680	0.823398	−	0.567464i	$-0.192076\pi$
$701$	1.05286e13	1.64680	0.823398	+	0.567464i	$0.192076\pi$
$702$	3.75167e11	0.0583053
$703$	5.14389e11	0.0794315
$704$	−5.60213e11	−0.0859560
$705$	−1.13386e12	−0.172865
$706$	−1.74741e12	−0.264712
$707$	1.45429e12	0.218909
$708$	3.26823e12	0.488835
$709$	−1.03943e13	−1.54485	−0.772425	−	0.635106i	$-0.780956\pi$
$709$	−1.03943e13	−1.54485	−0.772425	+	0.635106i	$0.780956\pi$
$710$	9.69689e11	0.143209
$711$	1.34952e12	0.198046
$712$	8.11728e12	1.18372
$713$	−5.06513e12	−0.733985
$714$	−9.40634e11	−0.135450
$715$	7.91744e11	0.113294
$716$	8.31203e11	0.118195
$717$	5.55940e11	0.0785582
$718$	2.19854e12	0.308727
$719$	2.48589e11	0.0346898	0.0173449	−	0.999850i	$-0.494479\pi$
$719$	2.48589e11	0.0346898	0.0173449	+	0.999850i	$0.494479\pi$
$720$	−6.60076e11	−0.0915372
$721$	8.98371e11	0.123807
$722$	2.10046e12	0.287672
$723$	−4.06742e12	−0.553601
$724$	1.07487e12	0.145389
$725$	7.36299e10	0.00989767
$726$	1.43673e12	0.191938
$727$	6.33150e12	0.840624	0.420312	−	0.907380i	$-0.361921\pi$
$727$	6.33150e12	0.840624	0.420312	+	0.907380i	$0.361921\pi$
$728$	1.61876e12	0.213595
$729$	2.82430e11	0.0370370
$730$	8.25729e11	0.107618
$731$	5.47192e12	0.708780
$732$	−3.53288e12	−0.454810
$733$	2.64023e10	0.00337812	0.00168906	−	0.999999i	$-0.499462\pi$
$733$	2.64023e10	0.00337812	0.00168906	+	0.999999i	$0.499462\pi$
$734$	3.20089e12	0.407041
$735$	−2.91843e11	−0.0368856
$736$	4.14837e12	0.521107
$737$	1.72256e12	0.215065
$738$	−7.71072e11	−0.0956845
$739$	−2.86810e11	−0.0353748	−0.0176874	−	0.999844i	$-0.505630\pi$
$739$	−2.86810e11	−0.0353748	−0.0176874	+	0.999844i	$0.505630\pi$
$740$	−5.39277e11	−0.0661103
$741$	1.81860e12	0.221593
$742$	6.63747e11	0.0803868
$743$	6.53255e12	0.786381	0.393190	−	0.919457i	$-0.371371\pi$
$743$	6.53255e12	0.786381	0.393190	+	0.919457i	$0.371371\pi$
$744$	4.23375e12	0.506579
$745$	−3.04016e11	−0.0361571
$746$	5.10610e11	0.0603621
$747$	3.90273e12	0.458591
$748$	3.84517e12	0.449116
$749$	4.23547e12	0.491737
$750$	1.64225e11	0.0189524
$751$	−1.25151e13	−1.43567	−0.717833	−	0.696216i	$-0.754866\pi$
$751$	−1.25151e13	−1.43567	−0.717833	+	0.696216i	$0.754866\pi$
$752$	3.60527e12	0.411110
$753$	−5.94846e11	−0.0674260
$754$	1.33065e11	0.0149932
$755$	−3.87958e12	−0.434534
$756$	5.65308e11	0.0629415
$757$	4.70847e12	0.521132	0.260566	−	0.965456i	$-0.416091\pi$
$757$	4.70847e12	0.521132	0.260566	+	0.965456i	$0.416091\pi$
$758$	−3.20037e12	−0.352119
$759$	−9.27723e11	−0.101468
$760$	1.30922e12	0.142348
$761$	−3.14056e12	−0.339450	−0.169725	−	0.985491i	$-0.554288\pi$
$761$	−3.14056e12	−0.339450	−0.169725	+	0.985491i	$0.554288\pi$
$762$	2.22976e12	0.239585
$763$	5.83545e11	0.0623324
$764$	−4.17252e12	−0.443076
$765$	2.38824e12	0.252117
$766$	−1.91628e12	−0.201108
$767$	7.74184e12	0.807728
$768$	−5.09886e11	−0.0528868
$769$	1.54826e12	0.159652	0.0798260	−	0.996809i	$-0.474564\pi$
$769$	1.54826e12	0.159652	0.0798260	+	0.996809i	$0.474564\pi$
$770$	−1.85711e11	−0.0190383
$771$	7.69345e12	0.784109
$772$	6.60763e12	0.669527
$773$	−3.03796e12	−0.306038	−0.153019	−	0.988223i	$-0.548900\pi$
$773$	−3.03796e12	−0.306038	−0.153019	+	0.988223i	$0.548900\pi$
$774$	5.11913e11	0.0512698
$775$	2.57434e12	0.256336
$776$	1.07585e13	1.06506
$777$	3.78766e11	0.0372801
$778$	1.13270e12	0.110843
$779$	−3.73773e12	−0.363655
$780$	−1.90659e12	−0.184430
$781$	2.78412e12	0.267767
$782$	−3.71730e12	−0.355465
$783$	1.00173e11	0.00952404
$784$	9.27958e11	0.0877215
$785$	6.07233e12	0.570745
$786$	−3.63461e12	−0.339669
$787$	1.23112e13	1.14397	0.571983	−	0.820266i	$-0.306174\pi$
$787$	1.23112e13	1.14397	0.571983	+	0.820266i	$0.306174\pi$
$788$	6.63136e12	0.612681
$789$	−5.61455e12	−0.515785
$790$	1.06759e12	0.0975175
$791$	−2.55684e12	−0.232226
$792$	7.75450e11	0.0700310
$793$	−8.36877e12	−0.751506
$794$	−4.53264e12	−0.404724
$795$	−1.68523e12	−0.149626
$796$	3.83074e12	0.338200
$797$	3.93564e12	0.345504	0.172752	−	0.984965i	$-0.444734\pi$
$797$	3.93564e12	0.345504	0.172752	+	0.984965i	$0.444734\pi$
$798$	−4.26570e11	−0.0372372
$799$	−1.30444e13	−1.13230
$800$	−2.10840e12	−0.181990
$801$	6.71500e12	0.576368
$802$	2.40073e12	0.204908
$803$	2.37079e12	0.201221
$804$	−4.14807e12	−0.350102
$805$	−1.15334e12	−0.0967998
$806$	4.65239e12	0.388301
$807$	7.72357e12	0.641043
$808$	−4.80390e12	−0.396500
$809$	−1.20730e13	−0.990936	−0.495468	−	0.868626i	$-0.665003\pi$
$809$	−1.20730e13	−0.990936	−0.495468	+	0.868626i	$0.665003\pi$
$810$	2.23427e11	0.0182370
$811$	3.10097e12	0.251712	0.125856	−	0.992049i	$-0.459832\pi$
$811$	3.10097e12	0.251712	0.125856	+	0.992049i	$0.459832\pi$
$812$	2.00505e11	0.0161853
$813$	−5.17039e12	−0.415065
$814$	2.41023e11	0.0192419
$815$	−2.49067e12	−0.197746
$816$	−7.59377e12	−0.599587
$817$	2.48147e12	0.194854
$818$	1.59452e12	0.124521
$819$	1.33911e12	0.104002
$820$	3.91857e12	0.302667
$821$	−2.69315e12	−0.206879	−0.103439	−	0.994636i	$-0.532985\pi$
$821$	−2.69315e12	−0.206879	−0.103439	+	0.994636i	$0.532985\pi$
$822$	−2.74607e12	−0.209792
$823$	−7.54132e12	−0.572992	−0.286496	−	0.958081i	$-0.592490\pi$
$823$	−7.54132e12	−0.572992	−0.286496	+	0.958081i	$0.592490\pi$
$824$	−2.96755e12	−0.224246
$825$	4.71514e11	0.0354366
$826$	−1.81592e12	−0.135733
$827$	3.97671e12	0.295630	0.147815	−	0.989015i	$-0.452776\pi$
$827$	3.97671e12	0.295630	0.147815	+	0.989015i	$0.452776\pi$
$828$	2.23404e12	0.165179
$829$	−2.22856e13	−1.63881	−0.819405	−	0.573215i	$-0.805696\pi$
$829$	−2.22856e13	−1.63881	−0.819405	+	0.573215i	$0.805696\pi$
$830$	3.08741e12	0.225810
$831$	−1.43456e13	−1.04355
$832$	3.19565e12	0.231208
$833$	−3.35748e12	−0.241608
$834$	5.07580e12	0.363293
$835$	−4.77246e12	−0.339745
$836$	1.74376e12	0.123469
$837$	3.50237e12	0.246659
$838$	−1.17379e12	−0.0822229
$839$	−1.40634e13	−0.979857	−0.489929	−	0.871762i	$-0.662977\pi$
$839$	−1.40634e13	−0.979857	−0.489929	+	0.871762i	$0.662977\pi$
$840$	9.64032e11	0.0668089
$841$	−1.44716e13	−0.997551
$842$	−6.95383e12	−0.476782
$843$	1.31169e12	0.0894558
$844$	−1.79412e13	−1.21705
$845$	2.11143e12	0.142470
$846$	−1.22034e12	−0.0819054
$847$	5.12823e12	0.342367
$848$	5.35845e12	0.355843
$849$	8.55150e12	0.564882
$850$	1.88931e12	0.124142
$851$	1.49685e12	0.0978351
$852$	−6.70441e12	−0.435895
$853$	−3.03343e13	−1.96184	−0.980920	−	0.194411i	$-0.937720\pi$
$853$	−3.03343e13	−1.96184	−0.980920	+	0.194411i	$0.937720\pi$
$854$	1.96297e12	0.126285
$855$	1.08305e12	0.0693107
$856$	−1.39908e13	−0.890659
$857$	−2.53281e13	−1.60394	−0.801971	−	0.597363i	$-0.796215\pi$
$857$	−2.53281e13	−1.60394	−0.801971	+	0.597363i	$0.796215\pi$
$858$	8.52128e11	0.0536799
$859$	6.84041e12	0.428660	0.214330	−	0.976761i	$-0.431243\pi$
$859$	6.84041e12	0.428660	0.214330	+	0.976761i	$0.431243\pi$
$860$	−2.60153e12	−0.162176
$861$	−2.75225e12	−0.170676
$862$	−5.21000e12	−0.321407
$863$	1.75856e13	1.07922	0.539608	−	0.841916i	$-0.318572\pi$
$863$	1.75856e13	1.07922	0.539608	+	0.841916i	$0.318572\pi$
$864$	−2.86846e12	−0.175120
$865$	−8.69422e11	−0.0528030
$866$	−1.09843e13	−0.663655
$867$	1.78697e13	1.07407
$868$	7.01030e12	0.419177
$869$	3.06520e12	0.182335
$870$	7.92454e10	0.00468962
$871$	−9.82604e12	−0.578491
$872$	−1.92760e12	−0.112899
$873$	8.89994e12	0.518589
$874$	−1.68576e12	−0.0977227
$875$	5.86182e11	0.0338062
$876$	−5.70907e12	−0.327565
$877$	8.22398e12	0.469444	0.234722	−	0.972063i	$-0.424582\pi$
$877$	8.22398e12	0.469444	0.234722	+	0.972063i	$0.424582\pi$
$878$	−7.50255e12	−0.426072
$879$	1.39106e13	0.785950
$880$	−1.49925e12	−0.0842755
$881$	−6.30199e12	−0.352441	−0.176220	−	0.984351i	$-0.556387\pi$
$881$	−6.30199e12	−0.352441	−0.176220	+	0.984351i	$0.556387\pi$
$882$	−3.14101e11	−0.0174768
$883$	4.44356e12	0.245985	0.122992	−	0.992408i	$-0.460751\pi$
$883$	4.44356e12	0.245985	0.122992	+	0.992408i	$0.460751\pi$
$884$	−2.19342e13	−1.20805
$885$	4.61057e12	0.252644
$886$	−1.71300e12	−0.0933912
$887$	1.23069e13	0.667562	0.333781	−	0.942651i	$-0.391675\pi$
$887$	1.23069e13	0.667562	0.333781	+	0.942651i	$0.391675\pi$
$888$	−1.25116e12	−0.0675235
$889$	7.95884e12	0.427358
$890$	5.31216e12	0.283802
$891$	6.41490e11	0.0340989
$892$	2.20789e13	1.16771
$893$	−5.91551e12	−0.311287
$894$	−3.27203e11	−0.0171316
$895$	1.17260e12	0.0610866
$896$	−7.38479e12	−0.382782
$897$	5.29205e12	0.272934
$898$	−3.87694e12	−0.198951
$899$	1.24223e12	0.0634281
$900$	−1.13545e12	−0.0576868
$901$	−1.93876e13	−0.980082
$902$	−1.75136e12	−0.0880938
$903$	1.82721e12	0.0914520
$904$	8.44591e12	0.420619
$905$	1.51634e12	0.0751412
$906$	−4.17546e12	−0.205887
$907$	−3.62565e12	−0.177891	−0.0889453	−	0.996037i	$-0.528350\pi$
$907$	−3.62565e12	−0.177891	−0.0889453	+	0.996037i	$0.528350\pi$
$908$	8.31834e12	0.406116
$909$	−3.97402e12	−0.193060
$910$	1.05936e12	0.0512101
$911$	9.19296e12	0.442204	0.221102	−	0.975251i	$-0.429035\pi$
$911$	9.19296e12	0.442204	0.221102	+	0.975251i	$0.429035\pi$
$912$	−3.44371e12	−0.164835
$913$	8.86438e12	0.422211
$914$	−6.85005e12	−0.324665
$915$	−4.98393e12	−0.235059
$916$	−3.25453e13	−1.52742
$917$	−1.29733e13	−0.605882
$918$	2.57039e12	0.119456
$919$	5.32373e12	0.246205	0.123102	−	0.992394i	$-0.460716\pi$
$919$	5.32373e12	0.246205	0.123102	+	0.992394i	$0.460716\pi$
$920$	3.80976e12	0.175329
$921$	−2.30735e13	−1.05668
$922$	−7.36769e11	−0.0335770
$923$	−1.58815e13	−0.720253
$924$	1.28400e12	0.0579483
$925$	−7.60771e11	−0.0341677
$926$	−9.19014e12	−0.410745
$927$	−2.45490e12	−0.109188
$928$	−1.01739e12	−0.0450320
$929$	−2.28515e13	−1.00657	−0.503285	−	0.864121i	$-0.667875\pi$
$929$	−2.28515e13	−1.00657	−0.503285	+	0.864121i	$0.667875\pi$
$930$	2.77068e12	0.121454
$931$	−1.52259e12	−0.0664215
$932$	−2.31863e13	−1.00661
$933$	6.46925e12	0.279503
$934$	9.30090e12	0.399912
$935$	5.42448e12	0.232116
$936$	−4.42343e12	−0.188373
$937$	4.49728e13	1.90600	0.952998	−	0.302976i	$-0.0979801\pi$
$937$	4.49728e13	1.90600	0.952998	+	0.302976i	$0.0979801\pi$
$938$	2.30479e12	0.0972116
$939$	−1.16362e12	−0.0488447
$940$	6.20172e12	0.259082
$941$	4.05411e13	1.68555	0.842775	−	0.538265i	$-0.180920\pi$
$941$	4.05411e13	1.68555	0.842775	+	0.538265i	$0.180920\pi$
$942$	6.53545e12	0.270425
$943$	−1.08766e13	−0.447910
$944$	−1.46600e13	−0.600840
$945$	7.97494e11	0.0325300
$946$	1.16272e12	0.0472026
$947$	3.97581e13	1.60639	0.803194	−	0.595718i	$-0.203132\pi$
$947$	3.97581e13	1.60639	0.803194	+	0.595718i	$0.203132\pi$
$948$	−7.38129e12	−0.296821
$949$	−1.35238e13	−0.541252
$950$	8.56787e11	0.0341285
$951$	4.02772e11	0.0159679
$952$	1.10906e13	0.437612
$953$	2.02769e13	0.796311	0.398155	−	0.917318i	$-0.369650\pi$
$953$	2.02769e13	0.796311	0.398155	+	0.917318i	$0.369650\pi$
$954$	−1.81376e12	−0.0708945
$955$	−5.88628e12	−0.228995
$956$	−3.04075e12	−0.117739
$957$	2.27525e11	0.00876850
$958$	−5.57383e12	−0.213801
$959$	−9.80176e12	−0.374214
$960$	1.90313e12	0.0723183
$961$	1.69927e13	0.642698
$962$	−1.37488e12	−0.0517578
$963$	−1.15739e13	−0.433671
$964$	2.22470e13	0.829708
$965$	9.32155e12	0.346031
$966$	−1.24130e12	−0.0458647
$967$	−2.76625e13	−1.01736	−0.508678	−	0.860957i	$-0.669866\pi$
$967$	−2.76625e13	−1.01736	−0.508678	+	0.860957i	$0.669866\pi$
$968$	−1.69399e13	−0.620113
$969$	1.24598e13	0.453999
$970$	7.04064e12	0.255352
$971$	4.14078e13	1.49484	0.747421	−	0.664351i	$-0.231292\pi$
$971$	4.14078e13	1.49484	0.747421	+	0.664351i	$0.231292\pi$
$972$	−1.54477e12	−0.0555092
$973$	1.81174e13	0.648020
$974$	−1.67276e13	−0.595552
$975$	−2.68968e12	−0.0953190
$976$	1.58471e13	0.559019
$977$	1.16278e13	0.408292	0.204146	−	0.978940i	$-0.434558\pi$
$977$	1.16278e13	0.408292	0.204146	+	0.978940i	$0.434558\pi$
$978$	−2.68063e12	−0.0936939
$979$	1.52520e13	0.530644
$980$	1.59625e12	0.0552821
$981$	−1.59460e12	−0.0549720
$982$	−9.43936e12	−0.323922
$983$	−1.24150e12	−0.0424089	−0.0212044	−	0.999775i	$-0.506750\pi$
$983$	−1.24150e12	−0.0424089	−0.0212044	+	0.999775i	$0.506750\pi$
$984$	9.09137e12	0.309137
$985$	9.35502e12	0.316652
$986$	9.11670e11	0.0307179
$987$	−4.35584e12	−0.146098
$988$	−9.94697e12	−0.332112
$989$	7.22096e12	0.240000
$990$	5.07475e11	0.0167902
$991$	4.90415e13	1.61522	0.807611	−	0.589715i	$-0.200760\pi$
$991$	4.90415e13	1.61522	0.807611	+	0.589715i	$0.200760\pi$
$992$	−3.55713e13	−1.16626
$993$	−9.92156e12	−0.323823
$994$	3.72516e12	0.121034
$995$	5.40412e12	0.174792
$996$	−2.13462e13	−0.687313
$997$	9.18652e12	0.294458	0.147229	−	0.989102i	$-0.452965\pi$
$997$	9.18652e12	0.294458	0.147229	+	0.989102i	$0.452965\pi$
$998$	−1.51425e13	−0.483180
$999$	−1.03502e12	−0.0328779

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.10.a.f.1.2	✓	4
3.2	odd	2		315.10.a.c.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.10.a.f.1.2	✓	4	1.1	even	1	trivial
315.10.a.c.1.3		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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	105.a (trivial)

\(f(q)\)	\(=\)	\(q-8.30453 q^{2} +81.0000 q^{3} -443.035 q^{4} -625.000 q^{5} -672.667 q^{6} -2401.00 q^{7} +7931.11 q^{8} +6561.00 q^{9} +5190.33 q^{10} +14902.2 q^{11} -35885.8 q^{12} -85007.1 q^{13} +19939.2 q^{14} -50625.0 q^{15} +160970. q^{16} -582410. q^{17} -54486.0 q^{18} -264118. q^{19} +276897. q^{20} -194481. q^{21} -123756. q^{22} -768571. q^{23} +642420. q^{24} +390625. q^{25} +705944. q^{26} +531441. q^{27} +1.06373e6 q^{28} +188493. q^{29} +420417. q^{30} +6.59032e6 q^{31} -5.39751e6 q^{32} +1.20708e6 q^{33} +4.83664e6 q^{34} +1.50062e6 q^{35} -2.90675e6 q^{36} -1.94757e6 q^{37} +2.19338e6 q^{38} -6.88557e6 q^{39} -4.95695e6 q^{40} +1.41517e7 q^{41} +1.61507e6 q^{42} -9.39531e6 q^{43} -6.60218e6 q^{44} -4.10062e6 q^{45} +6.38262e6 q^{46} +2.23972e7 q^{47} +1.30385e7 q^{48} +5.76480e6 q^{49} -3.24396e6 q^{50} -4.71752e7 q^{51} +3.76611e7 q^{52} +3.32886e7 q^{53} -4.41337e6 q^{54} -9.31386e6 q^{55} -1.90426e7 q^{56} -2.13936e7 q^{57} -1.56534e6 q^{58} -9.10729e7 q^{59} +2.24286e7 q^{60} +9.84479e7 q^{61} -5.47295e7 q^{62} -1.57530e7 q^{63} -3.75927e7 q^{64} +5.31294e7 q^{65} -1.00242e7 q^{66} +1.15591e8 q^{67} +2.58028e8 q^{68} -6.22542e7 q^{69} -1.24620e7 q^{70} +1.86826e8 q^{71} +5.20360e7 q^{72} +1.59090e8 q^{73} +1.61737e7 q^{74} +3.16406e7 q^{75} +1.17013e8 q^{76} -3.57801e7 q^{77} +5.71814e7 q^{78} +2.05688e8 q^{79} -1.00606e8 q^{80} +4.30467e7 q^{81} -1.17524e8 q^{82} +5.94838e8 q^{83} +8.61619e7 q^{84} +3.64006e8 q^{85} +7.80236e7 q^{86} +1.52679e7 q^{87} +1.18191e8 q^{88} +1.02347e9 q^{89} +3.40538e7 q^{90} +2.04102e8 q^{91} +3.40504e8 q^{92} +5.33816e8 q^{93} -1.85998e8 q^{94} +1.65074e8 q^{95} -4.37198e8 q^{96} +1.35649e9 q^{97} -4.78740e7 q^{98} +9.77732e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} + 324 q^{3} + 424 q^{4} - 2500 q^{5} + 648 q^{6} - 9604 q^{7} + 96 q^{8} + 26244 q^{9} - 5000 q^{10} + 9832 q^{11} + 34344 q^{12} - 68264 q^{13} - 19208 q^{14} - 202500 q^{15} - 290784 q^{16}+ \cdots + 64507752 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 + 324 * q^3 + 424 * q^4 - 2500 * q^5 + 648 * q^6 - 9604 * q^7 + 96 * q^8 + 26244 * q^9 - 5000 * q^10 + 9832 * q^11 + 34344 * q^12 - 68264 * q^13 - 19208 * q^14 - 202500 * q^15 - 290784 * q^16 + 86272 * q^17 + 52488 * q^18 + 807672 * q^19 - 265000 * q^20 - 777924 * q^21 + 4293352 * q^22 + 683032 * q^23 + 7776 * q^24 + 1562500 * q^25 + 4583544 * q^26 + 2125764 * q^27 - 1018024 * q^28 + 5029312 * q^29 - 405000 * q^30 + 9802992 * q^31 + 497280 * q^32 + 796392 * q^33 + 429792 * q^34 + 6002500 * q^35 + 2781864 * q^36 - 4536432 * q^37 + 21534872 * q^38 - 5529384 * q^39 - 60000 * q^40 + 11081000 * q^41 - 1555848 * q^42 - 34442248 * q^43 + 35679024 * q^44 - 16402500 * q^45 + 67652080 * q^46 - 39230168 * q^47 - 23553504 * q^48 + 23059204 * q^49 + 3125000 * q^50 + 6988032 * q^51 - 14778976 * q^52 + 76012528 * q^53 + 4251528 * q^54 - 6145000 * q^55 - 230496 * q^56 + 65421432 * q^57 + 57813344 * q^58 + 74595424 * q^59 - 21465000 * q^60 + 101246592 * q^61 + 392291880 * q^62 - 63011844 * q^63 - 276909952 * q^64 + 42665000 * q^65 + 347761512 * q^66 - 45694264 * q^67 + 345896144 * q^68 + 55325592 * q^69 + 12005000 * q^70 + 447187600 * q^71 + 629856 * q^72 + 141527624 * q^73 + 480388368 * q^74 + 126562500 * q^75 + 1081835504 * q^76 - 23606632 * q^77 + 371267064 * q^78 + 789659136 * q^79 + 181740000 * q^80 + 172186884 * q^81 + 937199856 * q^82 + 586282352 * q^83 - 82459944 * q^84 - 53920000 * q^85 + 132711648 * q^86 + 407374272 * q^87 + 1042925024 * q^88 + 1050230088 * q^89 - 32805000 * q^90 + 163901864 * q^91 + 44316096 * q^92 + 794042352 * q^93 - 1211140960 * q^94 - 504795000 * q^95 + 40279680 * q^96 + 788061288 * q^97 + 46118408 * q^98 + 64507752 * q^99

Introduction

L-functions

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