LMFDB - Embedded newform 182.8.a.b.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [182,8,Mod(1,182)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(182, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("182.1"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 182 = 2 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	182.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,32,-29,256,315] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$56.8540746381$
Analytic rank:	$1$
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} - x^{3} - 4737x^{2} + 19603x + 4029734 $ x^4 - x^3 - 4737x^2 + 19603x + 4029734
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-30.0795$ of defining polynomial
Character	$\chi$	$=$	182.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+8.00000 q^{2} +23.0795 q^{3} +64.0000 q^{4} +183.620 q^{5} +184.636 q^{6} -343.000 q^{7} +512.000 q^{8} -1654.34 q^{9} +1468.96 q^{10} -4070.34 q^{11} +1477.09 q^{12} -2197.00 q^{13} -2744.00 q^{14} +4237.86 q^{15} +4096.00 q^{16} -17340.4 q^{17} -13234.7 q^{18} -24058.7 q^{19} +11751.7 q^{20} -7916.26 q^{21} -32562.7 q^{22} -52264.6 q^{23} +11816.7 q^{24} -44408.6 q^{25} -17576.0 q^{26} -88656.1 q^{27} -21952.0 q^{28} +68165.8 q^{29} +33902.9 q^{30} +62020.9 q^{31} +32768.0 q^{32} -93941.3 q^{33} -138723. q^{34} -62981.7 q^{35} -105878. q^{36} -68534.9 q^{37} -192469. q^{38} -50705.6 q^{39} +94013.6 q^{40} +227262. q^{41} -63330.1 q^{42} +660998. q^{43} -260502. q^{44} -303770. q^{45} -418117. q^{46} -653712. q^{47} +94533.5 q^{48} +117649. q^{49} -355269. q^{50} -400208. q^{51} -140608. q^{52} +581219. q^{53} -709249. q^{54} -747397. q^{55} -175616. q^{56} -555262. q^{57} +545326. q^{58} +1.59440e6 q^{59} +271223. q^{60} -1.67570e6 q^{61} +496167. q^{62} +567438. q^{63} +262144. q^{64} -403414. q^{65} -751531. q^{66} -4.07217e6 q^{67} -1.10979e6 q^{68} -1.20624e6 q^{69} -503854. q^{70} +1.01076e6 q^{71} -847021. q^{72} -2.75028e6 q^{73} -548279. q^{74} -1.02493e6 q^{75} -1.53976e6 q^{76} +1.39613e6 q^{77} -405645. q^{78} +4.25906e6 q^{79} +752109. q^{80} +1.57190e6 q^{81} +1.81810e6 q^{82} -7.80046e6 q^{83} -506641. q^{84} -3.18405e6 q^{85} +5.28798e6 q^{86} +1.57323e6 q^{87} -2.08401e6 q^{88} -1.51987e6 q^{89} -2.43016e6 q^{90} +753571. q^{91} -3.34494e6 q^{92} +1.43141e6 q^{93} -5.22970e6 q^{94} -4.41766e6 q^{95} +756268. q^{96} +1.40671e7 q^{97} +941192. q^{98} +6.73372e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 32 q^{2} - 29 q^{3} + 256 q^{4} + 315 q^{5} - 232 q^{6} - 1372 q^{7} + 2048 q^{8} + 937 q^{9} + 2520 q^{10} - 2799 q^{11} - 1856 q^{12} - 8788 q^{13} - 10976 q^{14} - 38960 q^{15} + 16384 q^{16} - 47156 q^{17}+ \cdots - 4859772 q^{99}+O(q^{100}) $ 4 * q + 32 * q^2 - 29 * q^3 + 256 * q^4 + 315 * q^5 - 232 * q^6 - 1372 * q^7 + 2048 * q^8 + 937 * q^9 + 2520 * q^10 - 2799 * q^11 - 1856 * q^12 - 8788 * q^13 - 10976 * q^14 - 38960 * q^15 + 16384 * q^16 - 47156 * q^17 + 7496 * q^18 + 21167 * q^19 + 20160 * q^20 + 9947 * q^21 - 22392 * q^22 + 17508 * q^23 - 14848 * q^24 + 18907 * q^25 - 70304 * q^26 - 29051 * q^27 - 87808 * q^28 - 291911 * q^29 - 311680 * q^30 - 223770 * q^31 + 131072 * q^32 - 175251 * q^33 - 377248 * q^34 - 108045 * q^35 + 59968 * q^36 - 607537 * q^37 + 169336 * q^38 + 63713 * q^39 + 161280 * q^40 - 240123 * q^41 + 79576 * q^42 - 1268985 * q^43 - 179136 * q^44 + 281035 * q^45 + 140064 * q^46 - 465948 * q^47 - 118784 * q^48 + 470596 * q^49 + 151256 * q^50 + 59912 * q^51 - 562432 * q^52 + 29873 * q^53 - 232408 * q^54 - 3067466 * q^55 - 702464 * q^56 - 1981802 * q^57 - 2335288 * q^58 - 418226 * q^59 - 2493440 * q^60 - 1574237 * q^61 - 1790160 * q^62 - 321391 * q^63 + 1048576 * q^64 - 692055 * q^65 - 1402008 * q^66 - 6741503 * q^67 - 3017984 * q^68 - 3087009 * q^69 - 864360 * q^70 - 8260728 * q^71 + 479744 * q^72 - 4307556 * q^73 - 4860296 * q^74 - 6095923 * q^75 + 1354688 * q^76 + 960057 * q^77 + 509704 * q^78 - 2673678 * q^79 + 1290240 * q^80 - 14163560 * q^81 - 1920984 * q^82 - 10767561 * q^83 + 636608 * q^84 - 3422836 * q^85 - 10151880 * q^86 - 249448 * q^87 - 1433088 * q^88 - 2068133 * q^89 + 2248280 * q^90 + 3014284 * q^91 + 1120512 * q^92 + 9940639 * q^93 - 3727584 * q^94 - 7373999 * q^95 - 950272 * q^96 + 11642054 * q^97 + 3764768 * q^98 - 4859772 * q^99

Coefficient data

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

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

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

$2$	8.00000	0.707107
$2$	8.00000	0.707107
$3$	23.0795	0.493516	0.246758	−	0.969077i	$-0.420635\pi$
$3$	23.0795	0.493516	0.246758	+	0.969077i	$0.420635\pi$
$4$	64.0000	0.500000
$5$	183.620	0.656940	0.328470	−	0.944514i	$-0.393467\pi$
$5$	183.620	0.656940	0.328470	+	0.944514i	$0.393467\pi$
$6$	184.636	0.348969
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	512.000	0.353553
$9$	−1654.34	−0.756442
$10$	1468.96	0.464527
$11$	−4070.34	−0.922054	−0.461027	−	0.887386i	$-0.652519\pi$
$11$	−4070.34	−0.922054	−0.461027	+	0.887386i	$0.652519\pi$
$12$	1477.09	0.246758
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	−2744.00	−0.267261
$15$	4237.86	0.324211
$16$	4096.00	0.250000
$17$	−17340.4	−0.856028	−0.428014	−	0.903772i	$-0.640787\pi$
$17$	−17340.4	−0.856028	−0.428014	+	0.903772i	$0.640787\pi$
$18$	−13234.7	−0.534885
$19$	−24058.7	−0.804701	−0.402350	−	0.915486i	$-0.631807\pi$
$19$	−24058.7	−0.804701	−0.402350	+	0.915486i	$0.631807\pi$
$20$	11751.7	0.328470
$21$	−7916.26	−0.186532
$22$	−32562.7	−0.651991
$23$	−52264.6	−0.895695	−0.447848	−	0.894110i	$-0.647809\pi$
$23$	−52264.6	−0.895695	−0.447848	+	0.894110i	$0.647809\pi$
$24$	11816.7	0.174484
$25$	−44408.6	−0.568430
$26$	−17576.0	−0.196116
$27$	−88656.1	−0.866833
$28$	−21952.0	−0.188982
$29$	68165.8	0.519007	0.259504	−	0.965742i	$-0.416441\pi$
$29$	68165.8	0.519007	0.259504	+	0.965742i	$0.416441\pi$
$30$	33902.9	0.229251
$31$	62020.9	0.373915	0.186957	−	0.982368i	$-0.440137\pi$
$31$	62020.9	0.373915	0.186957	+	0.982368i	$0.440137\pi$
$32$	32768.0	0.176777
$33$	−93941.3	−0.455049
$34$	−138723.	−0.605303
$35$	−62981.7	−0.248300
$36$	−105878.	−0.378221
$37$	−68534.9	−0.222436	−0.111218	−	0.993796i	$-0.535475\pi$
$37$	−68534.9	−0.222436	−0.111218	+	0.993796i	$0.535475\pi$
$38$	−192469.	−0.569009
$39$	−50705.6	−0.136877
$40$	94013.6	0.232263
$41$	227262.	0.514971	0.257486	−	0.966282i	$-0.417106\pi$
$41$	227262.	0.514971	0.257486	+	0.966282i	$0.417106\pi$
$42$	−63330.1	−0.131898
$43$	660998.	1.26783	0.633914	−	0.773404i	$-0.281447\pi$
$43$	660998.	1.26783	0.633914	+	0.773404i	$0.281447\pi$
$44$	−260502.	−0.461027
$45$	−303770.	−0.496937
$46$	−418117.	−0.633352
$47$	−653712.	−0.918426	−0.459213	−	0.888326i	$-0.651868\pi$
$47$	−653712.	−0.918426	−0.459213	+	0.888326i	$0.651868\pi$
$48$	94533.5	0.123379
$49$	117649.	0.142857
$50$	−355269.	−0.401941
$51$	−400208.	−0.422464
$52$	−140608.	−0.138675
$53$	581219.	0.536259	0.268130	−	0.963383i	$-0.413594\pi$
$53$	581219.	0.536259	0.268130	+	0.963383i	$0.413594\pi$
$54$	−709249.	−0.612943
$55$	−747397.	−0.605734
$56$	−175616.	−0.133631
$57$	−555262.	−0.397133
$58$	545326.	0.366994
$59$	1.59440e6	1.01068	0.505342	−	0.862919i	$-0.331366\pi$
$59$	1.59440e6	1.01068	0.505342	+	0.862919i	$0.331366\pi$
$60$	271223.	0.162105
$61$	−1.67570e6	−0.945239	−0.472620	−	0.881267i	$-0.656692\pi$
$61$	−1.67570e6	−0.945239	−0.472620	+	0.881267i	$0.656692\pi$
$62$	496167.	0.264398
$63$	567438.	0.285908
$64$	262144.	0.125000
$65$	−403414.	−0.182202
$66$	−751531.	−0.321768
$67$	−4.07217e6	−1.65411	−0.827055	−	0.562121i	$-0.809985\pi$
$67$	−4.07217e6	−1.65411	−0.827055	+	0.562121i	$0.809985\pi$
$68$	−1.10979e6	−0.428014
$69$	−1.20624e6	−0.442040
$70$	−503854.	−0.175575
$71$	1.01076e6	0.335153	0.167576	−	0.985859i	$-0.446406\pi$
$71$	1.01076e6	0.335153	0.167576	+	0.985859i	$0.446406\pi$
$72$	−847021.	−0.267442
$73$	−2.75028e6	−0.827460	−0.413730	−	0.910400i	$-0.635774\pi$
$73$	−2.75028e6	−0.827460	−0.413730	+	0.910400i	$0.635774\pi$
$74$	−548279.	−0.157286
$75$	−1.02493e6	−0.280530
$76$	−1.53976e6	−0.402350
$77$	1.39613e6	0.348504
$78$	−405645.	−0.0967865
$79$	4.25906e6	0.971895	0.485947	−	0.873988i	$-0.338475\pi$
$79$	4.25906e6	0.971895	0.485947	+	0.873988i	$0.338475\pi$
$80$	752109.	0.164235
$81$	1.57190e6	0.328645
$82$	1.81810e6	0.364140
$83$	−7.80046e6	−1.49743	−0.748715	−	0.662892i	$-0.769329\pi$
$83$	−7.80046e6	−1.49743	−0.748715	+	0.662892i	$0.769329\pi$
$84$	−506641.	−0.0932658
$85$	−3.18405e6	−0.562359
$86$	5.28798e6	0.896490
$87$	1.57323e6	0.256139
$88$	−2.08401e6	−0.325995
$89$	−1.51987e6	−0.228530	−0.114265	−	0.993450i	$-0.536451\pi$
$89$	−1.51987e6	−0.228530	−0.114265	+	0.993450i	$0.536451\pi$
$90$	−2.43016e6	−0.351387
$91$	753571.	0.104828
$92$	−3.34494e6	−0.447848
$93$	1.43141e6	0.184533
$94$	−5.22970e6	−0.649425
$95$	−4.41766e6	−0.528640
$96$	756268.	0.0872422
$97$	1.40671e7	1.56496	0.782482	−	0.622673i	$-0.213953\pi$
$97$	1.40671e7	1.56496	0.782482	+	0.622673i	$0.213953\pi$
$98$	941192.	0.101015
$99$	6.73372e6	0.697480
$100$	−2.84215e6	−0.284215
$101$	−7.11685e6	−0.687327	−0.343663	−	0.939093i	$-0.611668\pi$
$101$	−7.11685e6	−0.687327	−0.343663	+	0.939093i	$0.611668\pi$
$102$	−3.20166e6	−0.298727
$103$	−1.71485e7	−1.54630	−0.773152	−	0.634221i	$-0.781321\pi$
$103$	−1.71485e7	−1.54630	−0.773152	+	0.634221i	$0.781321\pi$
$104$	−1.12486e6	−0.0980581
$105$	−1.45359e6	−0.122540
$106$	4.64976e6	0.379192
$107$	−2.31239e6	−0.182481	−0.0912407	−	0.995829i	$-0.529083\pi$
$107$	−2.31239e6	−0.182481	−0.0912407	+	0.995829i	$0.529083\pi$
$108$	−5.67399e6	−0.433416
$109$	1.03524e7	0.765681	0.382840	−	0.923814i	$-0.374946\pi$
$109$	1.03524e7	0.765681	0.382840	+	0.923814i	$0.374946\pi$
$110$	−5.97918e6	−0.428319
$111$	−1.58175e6	−0.109776
$112$	−1.40493e6	−0.0944911
$113$	−2.58441e6	−0.168495	−0.0842474	−	0.996445i	$-0.526849\pi$
$113$	−2.58441e6	−0.168495	−0.0842474	+	0.996445i	$0.526849\pi$
$114$	−4.44209e6	−0.280815
$115$	−9.59684e6	−0.588418
$116$	4.36261e6	0.259504
$117$	3.63458e6	0.209799
$118$	1.27552e7	0.714662
$119$	5.94776e6	0.323548
$120$	2.16978e6	0.114626
$121$	−2.91950e6	−0.149816
$122$	−1.34056e7	−0.668385
$123$	5.24509e6	0.254147
$124$	3.96934e6	0.186957
$125$	−2.24997e7	−1.03036
$126$	4.53950e6	0.202168
$127$	−3.60313e7	−1.56087	−0.780436	−	0.625236i	$-0.785003\pi$
$127$	−3.60313e7	−1.56087	−0.780436	+	0.625236i	$0.785003\pi$
$128$	2.09715e6	0.0883883
$129$	1.52555e7	0.625694
$130$	−3.22731e6	−0.128836
$131$	3.55927e7	1.38328	0.691642	−	0.722241i	$-0.256888\pi$
$131$	3.55927e7	1.38328	0.691642	+	0.722241i	$0.256888\pi$
$132$	−6.01225e6	−0.227524
$133$	8.25213e6	0.304148
$134$	−3.25774e7	−1.16963
$135$	−1.62790e7	−0.569457
$136$	−8.87829e6	−0.302652
$137$	150722.	0.00500788	0.00250394	−	0.999997i	$-0.499203\pi$
$137$	150722.	0.00500788	0.00250394	+	0.999997i	$0.499203\pi$
$138$	−9.64992e6	−0.312570
$139$	3.00477e7	0.948984	0.474492	−	0.880260i	$-0.342632\pi$
$139$	3.00477e7	0.948984	0.474492	+	0.880260i	$0.342632\pi$
$140$	−4.03083e6	−0.124150
$141$	−1.50873e7	−0.453258
$142$	8.08606e6	0.236989
$143$	8.94254e6	0.255732
$144$	−6.77617e6	−0.189110
$145$	1.25166e7	0.340956
$146$	−2.20023e7	−0.585103
$147$	2.71528e6	0.0705023
$148$	−4.38623e6	−0.111218
$149$	−4.75949e7	−1.17871	−0.589357	−	0.807873i	$-0.700619\pi$
$149$	−4.75949e7	−1.17871	−0.589357	+	0.807873i	$0.700619\pi$
$150$	−8.19942e6	−0.198364
$151$	−1.39410e7	−0.329515	−0.164758	−	0.986334i	$-0.552684\pi$
$151$	−1.39410e7	−0.329515	−0.164758	+	0.986334i	$0.552684\pi$
$152$	−1.23180e7	−0.284505
$153$	2.86869e7	0.647535
$154$	1.11690e7	0.246429
$155$	1.13883e7	0.245639
$156$	−3.24516e6	−0.0684384
$157$	6.28960e7	1.29710	0.648551	−	0.761171i	$-0.275375\pi$
$157$	6.28960e7	1.29710	0.648551	+	0.761171i	$0.275375\pi$
$158$	3.40725e7	0.687233
$159$	1.34142e7	0.264653
$160$	6.01687e6	0.116132
$161$	1.79268e7	0.338541
$162$	1.25752e7	0.232387
$163$	4.08840e7	0.739430	0.369715	−	0.929145i	$-0.379455\pi$
$163$	4.08840e7	0.739430	0.369715	+	0.929145i	$0.379455\pi$
$164$	1.45448e7	0.257486
$165$	−1.72495e7	−0.298940
$166$	−6.24037e7	−1.05884
$167$	−3.92235e7	−0.651687	−0.325843	−	0.945424i	$-0.605648\pi$
$167$	−3.92235e7	−0.651687	−0.325843	+	0.945424i	$0.605648\pi$
$168$	−4.05313e6	−0.0659489
$169$	4.82681e6	0.0769231
$170$	−2.54724e7	−0.397648
$171$	3.98012e7	0.608709
$172$	4.23039e7	0.633914
$173$	2.78247e7	0.408573	0.204286	−	0.978911i	$-0.434513\pi$
$173$	2.78247e7	0.408573	0.204286	+	0.978911i	$0.434513\pi$
$174$	1.25858e7	0.181117
$175$	1.52322e7	0.214846
$176$	−1.66721e7	−0.230513
$177$	3.67979e7	0.498789
$178$	−1.21590e7	−0.161595
$179$	−8.40839e7	−1.09579	−0.547895	−	0.836547i	$-0.684571\pi$
$179$	−8.40839e7	−1.09579	−0.547895	+	0.836547i	$0.684571\pi$
$180$	−1.94413e7	−0.248468
$181$	−8.32015e7	−1.04293	−0.521466	−	0.853272i	$-0.674615\pi$
$181$	−8.32015e7	−1.04293	−0.521466	+	0.853272i	$0.674615\pi$
$182$	6.02857e6	0.0741249
$183$	−3.86743e7	−0.466491
$184$	−2.67595e7	−0.316676
$185$	−1.25844e7	−0.146127
$186$	1.14513e7	0.130485
$187$	7.05814e7	0.789304
$188$	−4.18376e7	−0.459213
$189$	3.04090e7	0.327632
$190$	−3.53413e7	−0.373805
$191$	1.25390e8	1.30210	0.651051	−	0.759034i	$-0.274328\pi$
$191$	1.25390e8	1.30210	0.651051	+	0.759034i	$0.274328\pi$
$192$	6.05015e6	0.0616895
$193$	1.27244e8	1.27405	0.637024	−	0.770844i	$-0.280165\pi$
$193$	1.27244e8	1.27405	0.637024	+	0.770844i	$0.280165\pi$
$194$	1.12537e8	1.10660
$195$	−9.31058e6	−0.0899198
$196$	7.52954e6	0.0714286
$197$	5.81746e7	0.542127	0.271064	−	0.962561i	$-0.412625\pi$
$197$	5.81746e7	0.542127	0.271064	+	0.962561i	$0.412625\pi$
$198$	5.38697e7	0.493193
$199$	8.24594e7	0.741744	0.370872	−	0.928684i	$-0.379059\pi$
$199$	8.24594e7	0.741744	0.370872	+	0.928684i	$0.379059\pi$
$200$	−2.27372e7	−0.200970
$201$	−9.39836e7	−0.816330
$202$	−5.69348e7	−0.486013
$203$	−2.33809e7	−0.196166
$204$	−2.56133e7	−0.211232
$205$	4.17299e7	0.338305
$206$	−1.37188e8	−1.09340
$207$	8.64633e7	0.677541
$208$	−8.99891e6	−0.0693375
$209$	9.79270e7	0.741977
$210$	−1.16287e7	−0.0866489
$211$	7.07852e7	0.518745	0.259372	−	0.965777i	$-0.416484\pi$
$211$	7.07852e7	0.518745	0.259372	+	0.965777i	$0.416484\pi$
$212$	3.71980e7	0.268130
$213$	2.33278e7	0.165403
$214$	−1.84991e7	−0.129034
$215$	1.21373e8	0.832887
$216$	−4.53919e7	−0.306472
$217$	−2.12732e7	−0.141326
$218$	8.28191e7	0.541418
$219$	−6.34751e7	−0.408365
$220$	−4.78334e7	−0.302867
$221$	3.80969e7	0.237420
$222$	−1.26540e7	−0.0776233
$223$	−1.04103e8	−0.628632	−0.314316	−	0.949318i	$-0.601775\pi$
$223$	−1.04103e8	−0.628632	−0.314316	+	0.949318i	$0.601775\pi$
$224$	−1.12394e7	−0.0668153
$225$	7.34668e7	0.429984
$226$	−2.06753e7	−0.119144
$227$	6.99445e7	0.396884	0.198442	−	0.980113i	$-0.436412\pi$
$227$	6.99445e7	0.396884	0.198442	+	0.980113i	$0.436412\pi$
$228$	−3.55368e7	−0.198566
$229$	1.93775e8	1.06629	0.533143	−	0.846025i	$-0.321011\pi$
$229$	1.93775e8	1.06629	0.533143	+	0.846025i	$0.321011\pi$
$230$	−7.67747e7	−0.416074
$231$	3.22219e7	0.171992
$232$	3.49009e7	0.183497
$233$	3.84808e7	0.199296	0.0996479	−	0.995023i	$-0.468228\pi$
$233$	3.84808e7	0.199296	0.0996479	+	0.995023i	$0.468228\pi$
$234$	2.90766e7	0.148350
$235$	−1.20035e8	−0.603350
$236$	1.02042e8	0.505342
$237$	9.82970e7	0.479646
$238$	4.75821e7	0.228783
$239$	1.47559e8	0.699154	0.349577	−	0.936908i	$-0.386325\pi$
$239$	1.47559e8	0.699154	0.349577	+	0.936908i	$0.386325\pi$
$240$	1.73583e7	0.0810526
$241$	1.95553e8	0.899924	0.449962	−	0.893048i	$-0.351438\pi$
$241$	1.95553e8	0.899924	0.449962	+	0.893048i	$0.351438\pi$
$242$	−2.33560e7	−0.105936
$243$	2.30169e8	1.02902
$244$	−1.07245e8	−0.472620
$245$	2.16027e7	0.0938485
$246$	4.19607e7	0.179709
$247$	5.28569e7	0.223184
$248$	3.17547e7	0.132199
$249$	−1.80030e8	−0.739007
$250$	−1.79997e8	−0.728577
$251$	1.92972e8	0.770257	0.385129	−	0.922863i	$-0.374157\pi$
$251$	1.92972e8	0.770257	0.385129	+	0.922863i	$0.374157\pi$
$252$	3.63160e7	0.142954
$253$	2.12735e8	0.825880
$254$	−2.88251e8	−1.10370
$255$	−7.34862e7	−0.277533
$256$	1.67772e7	0.0625000
$257$	1.42650e8	0.524211	0.262106	−	0.965039i	$-0.415583\pi$
$257$	1.42650e8	0.524211	0.262106	+	0.965039i	$0.415583\pi$
$258$	1.22044e8	0.442432
$259$	2.35075e7	0.0840730
$260$	−2.58185e7	−0.0911012
$261$	−1.12769e8	−0.392599
$262$	2.84741e8	0.978129
$263$	−3.64707e7	−0.123623	−0.0618114	−	0.998088i	$-0.519688\pi$
$263$	−3.64707e7	−0.123623	−0.0618114	+	0.998088i	$0.519688\pi$
$264$	−4.80980e7	−0.160884
$265$	1.06724e8	0.352290
$266$	6.60170e7	0.215065
$267$	−3.50779e7	−0.112783
$268$	−2.60619e8	−0.827055
$269$	−7.68527e7	−0.240728	−0.120364	−	0.992730i	$-0.538406\pi$
$269$	−7.68527e7	−0.240728	−0.120364	+	0.992730i	$0.538406\pi$
$270$	−1.30232e8	−0.402667
$271$	−2.23561e8	−0.682345	−0.341172	−	0.940001i	$-0.610824\pi$
$271$	−2.23561e8	−0.682345	−0.341172	+	0.940001i	$0.610824\pi$
$272$	−7.10263e7	−0.214007
$273$	1.73920e7	0.0517346
$274$	1.20577e6	0.00354110
$275$	1.80758e8	0.524123
$276$	−7.71994e7	−0.221020
$277$	−3.50922e8	−0.992045	−0.496023	−	0.868310i	$-0.665207\pi$
$277$	−3.50922e8	−0.992045	−0.496023	+	0.868310i	$0.665207\pi$
$278$	2.40381e8	0.671033
$279$	−1.02604e8	−0.282845
$280$	−3.22467e7	−0.0877873
$281$	−5.24004e8	−1.40884	−0.704422	−	0.709781i	$-0.748794\pi$
$281$	−5.24004e8	−1.40884	−0.704422	+	0.709781i	$0.748794\pi$
$282$	−1.20699e8	−0.320502
$283$	1.14856e8	0.301232	0.150616	−	0.988592i	$-0.451874\pi$
$283$	1.14856e8	0.301232	0.150616	+	0.988592i	$0.451874\pi$
$284$	6.46885e7	0.167576
$285$	−1.01957e8	−0.260892
$286$	7.15403e7	0.180830
$287$	−7.79508e7	−0.194641
$288$	−5.42093e7	−0.133721
$289$	−1.09649e8	−0.267216
$290$	1.00133e8	0.241093
$291$	3.24662e8	0.772335
$292$	−1.76018e8	−0.413730
$293$	−2.91385e8	−0.676755	−0.338377	−	0.941011i	$-0.609878\pi$
$293$	−2.91385e8	−0.676755	−0.338377	+	0.941011i	$0.609878\pi$
$294$	2.17222e7	0.0498527
$295$	2.92764e8	0.663959
$296$	−3.50899e7	−0.0786431
$297$	3.60860e8	0.799267
$298$	−3.80759e8	−0.833477
$299$	1.14825e8	0.248421
$300$	−6.55954e7	−0.140265
$301$	−2.26722e8	−0.479194
$302$	−1.11528e8	−0.233003
$303$	−1.64253e8	−0.339207
$304$	−9.85444e7	−0.201175
$305$	−3.07692e8	−0.620965
$306$	2.29495e8	0.457877
$307$	−2.99232e8	−0.590233	−0.295117	−	0.955461i	$-0.595359\pi$
$307$	−2.99232e8	−0.590233	−0.295117	+	0.955461i	$0.595359\pi$
$308$	8.93521e7	0.174252
$309$	−3.95777e8	−0.763126
$310$	9.11064e7	0.173693
$311$	−4.80712e8	−0.906199	−0.453100	−	0.891460i	$-0.649682\pi$
$311$	−4.80712e8	−0.906199	−0.453100	+	0.891460i	$0.649682\pi$
$312$	−2.59613e7	−0.0483933
$313$	−2.88969e7	−0.0532656	−0.0266328	−	0.999645i	$-0.508478\pi$
$313$	−2.88969e7	−0.0532656	−0.0266328	+	0.999645i	$0.508478\pi$
$314$	5.03168e8	0.917190
$315$	1.04193e8	0.187824
$316$	2.72580e8	0.485947
$317$	−5.32897e8	−0.939585	−0.469792	−	0.882777i	$-0.655671\pi$
$317$	−5.32897e8	−0.939585	−0.469792	+	0.882777i	$0.655671\pi$
$318$	1.07314e8	0.187138
$319$	−2.77458e8	−0.478553
$320$	4.81349e7	0.0821175
$321$	−5.33688e7	−0.0900575
$322$	1.43414e8	0.239385
$323$	4.17187e8	0.688846
$324$	1.00602e8	0.164323
$325$	9.75657e7	0.157654
$326$	3.27072e8	0.522856
$327$	2.38928e8	0.377876
$328$	1.16358e8	0.182070
$329$	2.24223e8	0.347132
$330$	−1.37996e8	−0.211382
$331$	−8.20934e8	−1.24426	−0.622129	−	0.782915i	$-0.713732\pi$
$331$	−8.20934e8	−1.24426	−0.622129	+	0.782915i	$0.713732\pi$
$332$	−4.99229e8	−0.748715
$333$	1.13380e8	0.168260
$334$	−3.13788e8	−0.460812
$335$	−7.47733e8	−1.08665
$336$	−3.24250e7	−0.0466329
$337$	−7.25888e8	−1.03315	−0.516577	−	0.856241i	$-0.672794\pi$
$337$	−7.25888e8	−1.03315	−0.516577	+	0.856241i	$0.672794\pi$
$338$	3.86145e7	0.0543928
$339$	−5.96468e7	−0.0831549
$340$	−2.03779e8	−0.281180
$341$	−2.52446e8	−0.344769
$342$	3.18410e8	0.430422
$343$	−4.03536e7	−0.0539949
$344$	3.38431e8	0.448245
$345$	−2.21490e8	−0.290394
$346$	2.22598e8	0.288905
$347$	−1.34610e9	−1.72951	−0.864756	−	0.502193i	$-0.832527\pi$
$347$	−1.34610e9	−1.72951	−0.864756	+	0.502193i	$0.832527\pi$
$348$	1.00687e8	0.128069
$349$	−8.88214e8	−1.11848	−0.559241	−	0.829005i	$-0.688907\pi$
$349$	−8.88214e8	−1.11848	−0.559241	+	0.829005i	$0.688907\pi$
$350$	1.21857e8	0.151919
$351$	1.94777e8	0.240416
$352$	−1.33377e8	−0.162998
$353$	−2.14605e8	−0.259674	−0.129837	−	0.991535i	$-0.541445\pi$
$353$	−2.14605e8	−0.259674	−0.129837	+	0.991535i	$0.541445\pi$
$354$	2.94383e8	0.352697
$355$	1.85596e8	0.220175
$356$	−9.72719e7	−0.114265
$357$	1.37271e8	0.159676
$358$	−6.72672e8	−0.774841
$359$	−9.10135e8	−1.03819	−0.519093	−	0.854718i	$-0.673730\pi$
$359$	−9.10135e8	−1.03819	−0.519093	+	0.854718i	$0.673730\pi$
$360$	−1.55530e8	−0.175694
$361$	−3.15051e8	−0.352457
$362$	−6.65612e8	−0.737464
$363$	−6.73805e7	−0.0739369
$364$	4.82285e7	0.0524142
$365$	−5.05007e8	−0.543592
$366$	−3.09394e8	−0.329859
$367$	1.40174e9	1.48025	0.740125	−	0.672469i	$-0.234766\pi$
$367$	1.40174e9	1.48025	0.740125	+	0.672469i	$0.234766\pi$
$368$	−2.14076e8	−0.223924
$369$	−3.75968e8	−0.389546
$370$	−1.00675e8	−0.103328
$371$	−1.99358e8	−0.202687
$372$	9.16103e7	0.0922665
$373$	−1.11141e9	−1.10890	−0.554450	−	0.832217i	$-0.687071\pi$
$373$	−1.11141e9	−1.10890	−0.554450	+	0.832217i	$0.687071\pi$
$374$	5.64651e8	0.558122
$375$	−5.19280e8	−0.508502
$376$	−3.34701e8	−0.324712
$377$	−1.49760e8	−0.143947
$378$	2.43272e8	0.231671
$379$	5.31109e8	0.501126	0.250563	−	0.968100i	$-0.419384\pi$
$379$	5.31109e8	0.501126	0.250563	+	0.968100i	$0.419384\pi$
$380$	−2.82730e8	−0.264320
$381$	−8.31584e8	−0.770316
$382$	1.00312e9	0.920726
$383$	2.56652e8	0.233425	0.116713	−	0.993166i	$-0.462764\pi$
$383$	2.56652e8	0.233425	0.116713	+	0.993166i	$0.462764\pi$
$384$	4.84012e7	0.0436211
$385$	2.56357e8	0.228946
$386$	1.01795e9	0.900887
$387$	−1.09351e9	−0.959038
$388$	9.00296e8	0.782482
$389$	1.86807e9	1.60905	0.804527	−	0.593916i	$-0.202419\pi$
$389$	1.86807e9	1.60905	0.804527	+	0.593916i	$0.202419\pi$
$390$	−7.44846e7	−0.0635829
$391$	9.06290e8	0.766741
$392$	6.02363e7	0.0505076
$393$	8.21461e8	0.682673
$394$	4.65397e8	0.383342
$395$	7.82050e8	0.638476
$396$	4.30958e8	0.348740
$397$	2.49858e8	0.200413	0.100207	−	0.994967i	$-0.468050\pi$
$397$	2.49858e8	0.200413	0.100207	+	0.994967i	$0.468050\pi$
$398$	6.59675e8	0.524492
$399$	1.90455e8	0.150102
$400$	−1.81898e8	−0.142108
$401$	3.38168e8	0.261895	0.130948	−	0.991389i	$-0.458198\pi$
$401$	3.38168e8	0.261895	0.130948	+	0.991389i	$0.458198\pi$
$402$	−7.51869e8	−0.577233
$403$	−1.36260e8	−0.103705
$404$	−4.55479e8	−0.343663
$405$	2.88633e8	0.215900
$406$	−1.87047e8	−0.138711
$407$	2.78960e8	0.205098
$408$	−2.04906e8	−0.149364
$409$	2.20948e9	1.59683	0.798415	−	0.602108i	$-0.205672\pi$
$409$	2.20948e9	1.59683	0.798415	+	0.602108i	$0.205672\pi$
$410$	3.33839e8	0.239218
$411$	3.47858e6	0.00247147
$412$	−1.09750e9	−0.773152
$413$	−5.46879e8	−0.382003
$414$	6.91707e8	0.479094
$415$	−1.43232e9	−0.983722
$416$	−7.19913e7	−0.0490290
$417$	6.93484e8	0.468339
$418$	7.83416e8	0.524657
$419$	−7.04836e8	−0.468100	−0.234050	−	0.972225i	$-0.575198\pi$
$419$	−7.04836e8	−0.468100	−0.234050	+	0.972225i	$0.575198\pi$
$420$	−9.30295e7	−0.0612700
$421$	1.18814e8	0.0776035	0.0388017	−	0.999247i	$-0.487646\pi$
$421$	1.18814e8	0.0776035	0.0388017	+	0.999247i	$0.487646\pi$
$422$	5.66281e8	0.366808
$423$	1.08146e9	0.694735
$424$	2.97584e8	0.189596
$425$	7.70063e8	0.486592
$426$	1.86622e8	0.116958
$427$	5.74765e8	0.357267
$428$	−1.47993e8	−0.0912407
$429$	2.06389e8	0.126208
$430$	9.70980e8	0.588940
$431$	−1.67908e9	−1.01019	−0.505094	−	0.863064i	$-0.668542\pi$
$431$	−1.67908e9	−1.01019	−0.505094	+	0.863064i	$0.668542\pi$
$432$	−3.63135e8	−0.216708
$433$	2.56536e9	1.51859	0.759295	−	0.650747i	$-0.225544\pi$
$433$	2.56536e9	1.51859	0.759295	+	0.650747i	$0.225544\pi$
$434$	−1.70185e8	−0.0999329
$435$	2.88877e8	0.168268
$436$	6.62553e8	0.382840
$437$	1.25742e9	0.720767
$438$	−5.07800e8	−0.288758
$439$	−1.22677e9	−0.692047	−0.346024	−	0.938226i	$-0.612468\pi$
$439$	−1.22677e9	−0.692047	−0.346024	+	0.938226i	$0.612468\pi$
$440$	−3.82667e8	−0.214159
$441$	−1.94631e8	−0.108063
$442$	3.04775e8	0.167881
$443$	−3.42131e9	−1.86973	−0.934867	−	0.354999i	$-0.884481\pi$
$443$	−3.42131e9	−1.86973	−0.934867	+	0.354999i	$0.884481\pi$
$444$	−1.01232e8	−0.0548880
$445$	−2.79080e8	−0.150130
$446$	−8.32824e8	−0.444510
$447$	−1.09847e9	−0.581715
$448$	−8.99154e7	−0.0472456
$449$	1.79424e9	0.935446	0.467723	−	0.883875i	$-0.345074\pi$
$449$	1.79424e9	0.935446	0.467723	+	0.883875i	$0.345074\pi$
$450$	5.87735e8	0.304045
$451$	−9.25033e8	−0.474831
$452$	−1.65402e8	−0.0842474
$453$	−3.21752e8	−0.162621
$454$	5.59556e8	0.280639
$455$	1.38371e8	0.0688660
$456$	−2.84294e8	−0.140408
$457$	1.95376e9	0.957558	0.478779	−	0.877935i	$-0.341080\pi$
$457$	1.95376e9	0.957558	0.478779	+	0.877935i	$0.341080\pi$
$458$	1.55020e9	0.753978
$459$	1.53733e9	0.742033
$460$	−6.14198e8	−0.294209
$461$	2.30832e9	1.09735	0.548673	−	0.836037i	$-0.315133\pi$
$461$	2.30832e9	1.09735	0.548673	+	0.836037i	$0.315133\pi$
$462$	2.57775e8	0.121617
$463$	5.70818e8	0.267279	0.133639	−	0.991030i	$-0.457334\pi$
$463$	5.70818e8	0.267279	0.133639	+	0.991030i	$0.457334\pi$
$464$	2.79207e8	0.129752
$465$	2.62836e8	0.121227
$466$	3.07846e8	0.140923
$467$	−3.04459e9	−1.38331	−0.691656	−	0.722227i	$-0.743119\pi$
$467$	−3.04459e9	−1.38331	−0.691656	+	0.722227i	$0.743119\pi$
$468$	2.32613e8	0.104900
$469$	1.39676e9	0.625195
$470$	−9.60278e8	−0.426633
$471$	1.45161e9	0.640141
$472$	8.16333e8	0.357331
$473$	−2.69049e9	−1.16901
$474$	7.86376e8	0.339161
$475$	1.06841e9	0.457416
$476$	3.80657e8	0.161774
$477$	−9.61533e8	−0.405649
$478$	1.18047e9	0.494376
$479$	−8.18399e8	−0.340244	−0.170122	−	0.985423i	$-0.554416\pi$
$479$	−8.18399e8	−0.340244	−0.170122	+	0.985423i	$0.554416\pi$
$480$	1.38866e8	0.0573129
$481$	1.50571e8	0.0616927
$482$	1.56443e9	0.636342
$483$	4.13740e8	0.167076
$484$	−1.86848e8	−0.0749082
$485$	2.58301e9	1.02809
$486$	1.84136e9	0.727630
$487$	2.42158e9	0.950051	0.475025	−	0.879972i	$-0.342439\pi$
$487$	2.42158e9	0.950051	0.475025	+	0.879972i	$0.342439\pi$
$488$	−8.57958e8	−0.334193
$489$	9.43582e8	0.364921
$490$	1.72822e8	0.0663609
$491$	1.68633e9	0.642919	0.321460	−	0.946923i	$-0.395827\pi$
$491$	1.68633e9	0.642919	0.321460	+	0.946923i	$0.395827\pi$
$492$	3.35685e8	0.127073
$493$	−1.18202e9	−0.444285
$494$	4.22855e8	0.157815
$495$	1.23645e9	0.458202
$496$	2.54038e8	0.0934786
$497$	−3.46690e8	−0.126676
$498$	−1.44024e9	−0.522557
$499$	−4.20396e9	−1.51463	−0.757315	−	0.653049i	$-0.773489\pi$
$499$	−4.20396e9	−1.51463	−0.757315	+	0.653049i	$0.773489\pi$
$500$	−1.43998e9	−0.515182
$501$	−9.05258e8	−0.321618
$502$	1.54377e9	0.544654
$503$	3.02461e9	1.05970	0.529849	−	0.848092i	$-0.322249\pi$
$503$	3.02461e9	1.05970	0.529849	+	0.848092i	$0.322249\pi$
$504$	2.90528e8	0.101084
$505$	−1.30680e9	−0.451532
$506$	1.70188e9	0.583985
$507$	1.11400e8	0.0379628
$508$	−2.30600e9	−0.780436
$509$	2.45988e8	0.0826803	0.0413402	−	0.999145i	$-0.486837\pi$
$509$	2.45988e8	0.0826803	0.0413402	+	0.999145i	$0.486837\pi$
$510$	−5.87890e8	−0.196246
$511$	9.43347e8	0.312751
$512$	1.34218e8	0.0441942
$513$	2.13295e9	0.697541
$514$	1.14120e9	0.370673
$515$	−3.14880e9	−1.01583
$516$	9.76351e8	0.312847
$517$	2.66083e9	0.846838
$518$	1.88060e8	0.0594486
$519$	6.42180e8	0.201637
$520$	−2.06548e8	−0.0644182
$521$	−1.20695e9	−0.373903	−0.186951	−	0.982369i	$-0.559861\pi$
$521$	−1.20695e9	−0.373903	−0.186951	+	0.982369i	$0.559861\pi$
$522$	−9.02154e8	−0.277609
$523$	−3.59991e9	−1.10036	−0.550182	−	0.835045i	$-0.685442\pi$
$523$	−3.59991e9	−1.10036	−0.550182	+	0.835045i	$0.685442\pi$
$524$	2.27793e9	0.691642
$525$	3.51550e8	0.106030
$526$	−2.91765e8	−0.0874145
$527$	−1.07547e9	−0.320081
$528$	−3.84784e8	−0.113762
$529$	−6.73235e8	−0.197730
$530$	8.53789e8	0.249107
$531$	−2.63768e9	−0.764523
$532$	5.28136e8	0.152074
$533$	−4.99294e8	−0.142827
$534$	−2.80623e8	−0.0797497
$535$	−4.24602e8	−0.119879
$536$	−2.08495e9	−0.584816
$537$	−1.94061e9	−0.540790
$538$	−6.14821e8	−0.170220
$539$	−4.78871e8	−0.131722
$540$	−1.04186e9	−0.284728
$541$	2.85551e8	0.0775341	0.0387670	−	0.999248i	$-0.487657\pi$
$541$	2.85551e8	0.0775341	0.0387670	+	0.999248i	$0.487657\pi$
$542$	−1.78849e9	−0.482491
$543$	−1.92025e9	−0.514704
$544$	−5.68211e8	−0.151326
$545$	1.90091e9	0.503006
$546$	1.39136e8	0.0365819
$547$	−5.26043e9	−1.37425	−0.687125	−	0.726539i	$-0.741128\pi$
$547$	−5.26043e9	−1.37425	−0.687125	+	0.726539i	$0.741128\pi$
$548$	9.64619e6	0.00250394
$549$	2.77217e9	0.715018
$550$	1.44607e9	0.370611
$551$	−1.63998e9	−0.417645
$552$	−6.17595e8	−0.156285
$553$	−1.46086e9	−0.367342
$554$	−2.80738e9	−0.701482
$555$	−2.90441e8	−0.0721162
$556$	1.92305e9	0.474492
$557$	−7.96679e9	−1.95340	−0.976698	−	0.214620i	$-0.931149\pi$
$557$	−7.96679e9	−1.95340	−0.976698	+	0.214620i	$0.931149\pi$
$558$	−8.20829e8	−0.200001
$559$	−1.45221e9	−0.351632
$560$	−2.57973e8	−0.0620750
$561$	1.62898e9	0.389535
$562$	−4.19204e9	−0.996203
$563$	7.42023e9	1.75242	0.876209	−	0.481931i	$-0.160064\pi$
$563$	7.42023e9	1.75242	0.876209	+	0.481931i	$0.160064\pi$
$564$	−9.65589e8	−0.226629
$565$	−4.74550e8	−0.110691
$566$	9.18848e8	0.213003
$567$	−5.39162e8	−0.124216
$568$	5.17508e8	0.118494
$569$	4.55498e8	0.103656	0.0518279	−	0.998656i	$-0.483495\pi$
$569$	4.55498e8	0.103656	0.0518279	+	0.998656i	$0.483495\pi$
$570$	−8.15659e8	−0.184479
$571$	−7.92015e9	−1.78036	−0.890178	−	0.455612i	$-0.849420\pi$
$571$	−7.92015e9	−1.78036	−0.890178	+	0.455612i	$0.849420\pi$
$572$	5.72322e8	0.127866
$573$	2.89393e9	0.642609
$574$	−6.23607e8	−0.137632
$575$	2.32100e9	0.509140
$576$	−4.33675e8	−0.0945552
$577$	−8.24075e8	−0.178588	−0.0892938	−	0.996005i	$-0.528461\pi$
$577$	−8.24075e8	−0.178588	−0.0892938	+	0.996005i	$0.528461\pi$
$578$	−8.77191e8	−0.188950
$579$	2.93672e9	0.628763
$580$	8.01064e8	0.170478
$581$	2.67556e9	0.565976
$582$	2.59730e9	0.546124
$583$	−2.36576e9	−0.494460
$584$	−1.40814e9	−0.292551
$585$	6.67382e8	0.137825
$586$	−2.33108e9	−0.478538
$587$	3.67778e9	0.750502	0.375251	−	0.926923i	$-0.377556\pi$
$587$	3.67778e9	0.750502	0.375251	+	0.926923i	$0.377556\pi$
$588$	1.73778e8	0.0352512
$589$	−1.49214e9	−0.300889
$590$	2.34211e9	0.469490
$591$	1.34264e9	0.267549
$592$	−2.80719e8	−0.0556091
$593$	2.20121e9	0.433481	0.216741	−	0.976229i	$-0.430457\pi$
$593$	2.20121e9	0.433481	0.216741	+	0.976229i	$0.430457\pi$
$594$	2.88688e9	0.565167
$595$	1.09213e9	0.212552
$596$	−3.04607e9	−0.589357
$597$	1.90312e9	0.366063
$598$	9.18603e8	0.175660
$599$	−8.04509e7	−0.0152946	−0.00764728	−	0.999971i	$-0.502434\pi$
$599$	−8.04509e7	−0.0152946	−0.00764728	+	0.999971i	$0.502434\pi$
$600$	−5.24763e8	−0.0991822
$601$	1.03902e10	1.95238	0.976192	−	0.216909i	$-0.0695976\pi$
$601$	1.03902e10	1.95238	0.976192	+	0.216909i	$0.0695976\pi$
$602$	−1.81378e9	−0.338841
$603$	6.73675e9	1.25124
$604$	−8.92226e8	−0.164758
$605$	−5.36079e8	−0.0984204
$606$	−1.31403e9	−0.239856
$607$	−5.98662e9	−1.08648	−0.543239	−	0.839578i	$-0.682802\pi$
$607$	−5.98662e9	−1.08648	−0.543239	+	0.839578i	$0.682802\pi$
$608$	−7.88355e8	−0.142252
$609$	−5.39618e8	−0.0968113
$610$	−2.46154e9	−0.439089
$611$	1.43621e9	0.254725
$612$	1.83596e9	0.323768
$613$	−6.72220e9	−1.17869	−0.589345	−	0.807882i	$-0.700614\pi$
$613$	−6.72220e9	−1.17869	−0.589345	+	0.807882i	$0.700614\pi$
$614$	−2.39386e9	−0.417358
$615$	9.63104e8	0.166959
$616$	7.14817e8	0.123215
$617$	9.94486e9	1.70451	0.852257	−	0.523123i	$-0.175233\pi$
$617$	9.94486e9	1.70451	0.852257	+	0.523123i	$0.175233\pi$
$618$	−3.16622e9	−0.539612
$619$	−1.17899e9	−0.199798	−0.0998992	−	0.994998i	$-0.531852\pi$
$619$	−1.17899e9	−0.199798	−0.0998992	+	0.994998i	$0.531852\pi$
$620$	7.28851e8	0.122820
$621$	4.63358e9	0.776418
$622$	−3.84570e9	−0.640780
$623$	5.21317e8	0.0863761
$624$	−2.07690e8	−0.0342192
$625$	−6.61969e8	−0.108457
$626$	−2.31175e8	−0.0376644
$627$	2.26010e9	0.366178
$628$	4.02534e9	0.648551
$629$	1.18842e9	0.190412
$630$	8.33545e8	0.132812
$631$	−4.37167e9	−0.692699	−0.346349	−	0.938106i	$-0.612579\pi$
$631$	−4.37167e9	−0.692699	−0.346349	+	0.938106i	$0.612579\pi$
$632$	2.18064e9	0.343617
$633$	1.63368e9	0.256009
$634$	−4.26318e9	−0.664387
$635$	−6.61608e9	−1.02540
$636$	8.58511e8	0.132326
$637$	−2.58475e8	−0.0396214
$638$	−2.21966e9	−0.338388
$639$	−1.67213e9	−0.253523
$640$	3.85080e8	0.0580658
$641$	−8.34777e8	−0.125189	−0.0625947	−	0.998039i	$-0.519938\pi$
$641$	−8.34777e8	−0.125189	−0.0625947	+	0.998039i	$0.519938\pi$
$642$	−4.26951e8	−0.0636803
$643$	−6.30960e9	−0.935973	−0.467986	−	0.883736i	$-0.655020\pi$
$643$	−6.30960e9	−0.935973	−0.467986	+	0.883736i	$0.655020\pi$
$644$	1.14731e9	0.169271
$645$	2.80122e9	0.411043
$646$	3.33750e9	0.487088
$647$	−6.30563e9	−0.915300	−0.457650	−	0.889132i	$-0.651309\pi$
$647$	−6.30563e9	−0.915300	−0.457650	+	0.889132i	$0.651309\pi$
$648$	8.04813e8	0.116194
$649$	−6.48975e9	−0.931905
$650$	7.80526e8	0.111478
$651$	−4.90974e8	−0.0697469
$652$	2.61658e9	0.369715
$653$	−3.17943e9	−0.446841	−0.223420	−	0.974722i	$-0.571722\pi$
$653$	−3.17943e9	−0.446841	−0.223420	+	0.974722i	$0.571722\pi$
$654$	1.91142e9	0.267199
$655$	6.53554e9	0.908734
$656$	9.30865e8	0.128743
$657$	4.54989e9	0.625925
$658$	1.79379e9	0.245460
$659$	−1.44859e9	−0.197173	−0.0985863	−	0.995129i	$-0.531432\pi$
$659$	−1.44859e9	−0.197173	−0.0985863	+	0.995129i	$0.531432\pi$
$660$	−1.10397e9	−0.149470
$661$	3.27875e9	0.441574	0.220787	−	0.975322i	$-0.429137\pi$
$661$	3.27875e9	0.441574	0.220787	+	0.975322i	$0.429137\pi$
$662$	−6.56747e9	−0.879823
$663$	8.79256e8	0.117170
$664$	−3.99383e9	−0.529422
$665$	1.51526e9	0.199807
$666$	9.07039e8	0.118978
$667$	−3.56266e9	−0.464872
$668$	−2.51030e9	−0.325843
$669$	−2.40264e9	−0.310240
$670$	−5.98187e9	−0.768378
$671$	6.82067e9	0.871562
$672$	−2.59400e8	−0.0329745
$673$	9.58420e9	1.21200	0.606001	−	0.795464i	$-0.292773\pi$
$673$	9.58420e9	1.21200	0.606001	+	0.795464i	$0.292773\pi$
$674$	−5.80711e9	−0.730550
$675$	3.93709e9	0.492734
$676$	3.08916e8	0.0384615
$677$	−1.49888e9	−0.185655	−0.0928277	−	0.995682i	$-0.529591\pi$
$677$	−1.49888e9	−0.185655	−0.0928277	+	0.995682i	$0.529591\pi$
$678$	−4.77174e8	−0.0587994
$679$	−4.82502e9	−0.591501
$680$	−1.63023e9	−0.198824
$681$	1.61428e9	0.195869
$682$	−2.01957e9	−0.243789
$683$	−1.03529e10	−1.24334	−0.621670	−	0.783279i	$-0.713545\pi$
$683$	−1.03529e10	−1.24334	−0.621670	+	0.783279i	$0.713545\pi$
$684$	2.54728e9	0.304354
$685$	2.76756e7	0.00328987
$686$	−3.22829e8	−0.0381802
$687$	4.47223e9	0.526230
$688$	2.70745e9	0.316957
$689$	−1.27694e9	−0.148731
$690$	−1.77192e9	−0.205339
$691$	1.59535e9	0.183943	0.0919717	−	0.995762i	$-0.470683\pi$
$691$	1.59535e9	0.183943	0.0919717	+	0.995762i	$0.470683\pi$
$692$	1.78078e9	0.204286
$693$	−2.30967e9	−0.263623
$694$	−1.07688e10	−1.22295
$695$	5.51736e9	0.623425
$696$	8.05494e8	0.0905587
$697$	−3.94081e9	−0.440830
$698$	−7.10572e9	−0.790886
$699$	8.88116e8	0.0983557
$700$	9.74858e8	0.107423
$701$	8.14619e9	0.893185	0.446592	−	0.894738i	$-0.352637\pi$
$701$	8.14619e9	0.893185	0.446592	+	0.894738i	$0.352637\pi$
$702$	1.55822e9	0.170000
$703$	1.64886e9	0.178995
$704$	−1.06702e9	−0.115257
$705$	−2.77034e9	−0.297763
$706$	−1.71684e9	−0.183617
$707$	2.44108e9	0.259785
$708$	2.35507e9	0.249395
$709$	−6.58404e9	−0.693794	−0.346897	−	0.937903i	$-0.612765\pi$
$709$	−6.58404e9	−0.693794	−0.346897	+	0.937903i	$0.612765\pi$
$710$	1.48476e9	0.155687
$711$	−7.04593e9	−0.735182
$712$	−7.78175e8	−0.0807974
$713$	−3.24150e9	−0.334914
$714$	1.09817e9	0.112908
$715$	1.64203e9	0.168000
$716$	−5.38137e9	−0.547895
$717$	3.40558e9	0.345044
$718$	−7.28108e9	−0.734109
$719$	−4.92336e9	−0.493982	−0.246991	−	0.969018i	$-0.579442\pi$
$719$	−4.92336e9	−0.493982	−0.246991	+	0.969018i	$0.579442\pi$
$720$	−1.24424e9	−0.124234
$721$	5.88192e9	0.584448
$722$	−2.52041e9	−0.249225
$723$	4.51327e9	0.444127
$724$	−5.32489e9	−0.521466
$725$	−3.02715e9	−0.295019
$726$	−5.39044e8	−0.0522813
$727$	−1.79335e9	−0.173099	−0.0865495	−	0.996248i	$-0.527584\pi$
$727$	−1.79335e9	−0.173099	−0.0865495	+	0.996248i	$0.527584\pi$
$728$	3.85828e8	0.0370625
$729$	1.87444e9	0.179195
$730$	−4.04006e9	−0.384377
$731$	−1.14620e10	−1.08530
$732$	−2.47515e9	−0.233246
$733$	9.81470e8	0.0920478	0.0460239	−	0.998940i	$-0.485345\pi$
$733$	9.81470e8	0.0920478	0.0460239	+	0.998940i	$0.485345\pi$
$734$	1.12139e10	1.04670
$735$	4.98580e8	0.0463158
$736$	−1.71261e9	−0.158338
$737$	1.65751e10	1.52518
$738$	−3.00774e9	−0.275450
$739$	−1.86858e10	−1.70316	−0.851581	−	0.524223i	$-0.824356\pi$
$739$	−1.86858e10	−1.70316	−0.851581	+	0.524223i	$0.824356\pi$
$740$	−8.05401e8	−0.0730636
$741$	1.21991e9	0.110145
$742$	−1.59487e9	−0.143321
$743$	−6.58756e9	−0.589201	−0.294601	−	0.955620i	$-0.595187\pi$
$743$	−6.58756e9	−0.589201	−0.294601	+	0.955620i	$0.595187\pi$
$744$	7.32882e8	0.0652423
$745$	−8.73939e9	−0.774344
$746$	−8.89126e9	−0.784111
$747$	1.29046e10	1.13272
$748$	4.51721e9	0.394652
$749$	7.93151e8	0.0689715
$750$	−4.15424e9	−0.359565
$751$	−1.12906e10	−0.972699	−0.486350	−	0.873764i	$-0.661672\pi$
$751$	−1.12906e10	−0.972699	−0.486350	+	0.873764i	$0.661672\pi$
$752$	−2.67760e9	−0.229606
$753$	4.45369e9	0.380135
$754$	−1.19808e9	−0.101786
$755$	−2.55986e9	−0.216472
$756$	1.94618e9	0.163816
$757$	1.88372e10	1.57827	0.789136	−	0.614219i	$-0.210529\pi$
$757$	1.88372e10	1.57827	0.789136	+	0.614219i	$0.210529\pi$
$758$	4.24888e9	0.354349
$759$	4.90981e9	0.407585
$760$	−2.26184e9	−0.186902
$761$	−1.12210e10	−0.922965	−0.461483	−	0.887149i	$-0.652682\pi$
$761$	−1.12210e10	−0.922965	−0.461483	+	0.887149i	$0.652682\pi$
$762$	−6.65267e9	−0.544695
$763$	−3.55087e9	−0.289400
$764$	8.02495e9	0.651051
$765$	5.26749e9	0.425392
$766$	2.05321e9	0.165057
$767$	−3.50290e9	−0.280313
$768$	3.87209e8	0.0308448
$769$	−1.55757e10	−1.23511	−0.617555	−	0.786528i	$-0.711877\pi$
$769$	−1.55757e10	−1.23511	−0.617555	+	0.786528i	$0.711877\pi$
$770$	2.05086e9	0.161889
$771$	3.29229e9	0.258707
$772$	8.14359e9	0.637024
$773$	1.31804e10	1.02636	0.513182	−	0.858280i	$-0.328466\pi$
$773$	1.31804e10	1.02636	0.513182	+	0.858280i	$0.328466\pi$
$774$	−8.74811e9	−0.678142
$775$	−2.75426e9	−0.212544
$776$	7.20237e9	0.553298
$777$	5.42540e8	0.0414914
$778$	1.49446e10	1.13777
$779$	−5.46762e9	−0.414398
$780$	−5.95877e8	−0.0449599
$781$	−4.11413e9	−0.309029
$782$	7.25032e9	0.542168
$783$	−6.04331e9	−0.449892
$784$	4.81890e8	0.0357143
$785$	1.15490e10	0.852118
$786$	6.57168e9	0.482723
$787$	−4.21715e9	−0.308395	−0.154198	−	0.988040i	$-0.549279\pi$
$787$	−4.21715e9	−0.308395	−0.154198	+	0.988040i	$0.549279\pi$
$788$	3.72317e9	0.271064
$789$	−8.41724e8	−0.0610099
$790$	6.25640e9	0.451471
$791$	8.86452e8	0.0636850
$792$	3.44766e9	0.246596
$793$	3.68151e9	0.262162
$794$	1.99886e9	0.141713
$795$	2.46313e9	0.173861
$796$	5.27740e9	0.370872
$797$	9.34521e9	0.653860	0.326930	−	0.945049i	$-0.393986\pi$
$797$	9.34521e9	0.653860	0.326930	+	0.945049i	$0.393986\pi$
$798$	1.52364e9	0.106138
$799$	1.13356e10	0.786198
$800$	−1.45518e9	−0.100485
$801$	2.51438e9	0.172869
$802$	2.70534e9	0.185188
$803$	1.11946e10	0.762963
$804$	−6.01495e9	−0.408165
$805$	3.29172e9	0.222401
$806$	−1.09008e9	−0.0733307
$807$	−1.77372e9	−0.118803
$808$	−3.64383e9	−0.243007
$809$	2.34554e10	1.55748	0.778741	−	0.627345i	$-0.215859\pi$
$809$	2.34554e10	1.55748	0.778741	+	0.627345i	$0.215859\pi$
$810$	2.30906e9	0.152665
$811$	6.57070e8	0.0432552	0.0216276	−	0.999766i	$-0.493115\pi$
$811$	6.57070e8	0.0432552	0.0216276	+	0.999766i	$0.493115\pi$
$812$	−1.49638e9	−0.0980832
$813$	−5.15968e9	−0.336748
$814$	2.23168e9	0.145026
$815$	7.50713e9	0.485761
$816$	−1.63925e9	−0.105616
$817$	−1.59027e10	−1.02022
$818$	1.76758e10	1.12913
$819$	−1.24666e9	−0.0792966
$820$	2.67071e9	0.169153
$821$	2.19235e10	1.38264	0.691319	−	0.722550i	$-0.257030\pi$
$821$	2.19235e10	1.38264	0.691319	+	0.722550i	$0.257030\pi$
$822$	2.78286e7	0.00174759
$823$	−1.96884e10	−1.23115	−0.615576	−	0.788077i	$-0.711077\pi$
$823$	−1.96884e10	−1.23115	−0.615576	+	0.788077i	$0.711077\pi$
$824$	−8.78001e9	−0.546701
$825$	4.17180e9	0.258663
$826$	−4.37504e9	−0.270117
$827$	2.04793e10	1.25906	0.629530	−	0.776976i	$-0.283248\pi$
$827$	2.04793e10	1.25906	0.629530	+	0.776976i	$0.283248\pi$
$828$	5.53365e9	0.338771
$829$	−8.11646e9	−0.494795	−0.247398	−	0.968914i	$-0.579575\pi$
$829$	−8.11646e9	−0.494795	−0.247398	+	0.968914i	$0.579575\pi$
$830$	−1.14586e10	−0.695596
$831$	−8.09910e9	−0.489591
$832$	−5.75930e8	−0.0346688
$833$	−2.04008e9	−0.122290
$834$	5.54788e9	0.331166
$835$	−7.20223e9	−0.428119
$836$	6.26733e9	0.370989
$837$	−5.49853e9	−0.324121
$838$	−5.63869e9	−0.330997
$839$	2.90478e10	1.69803	0.849017	−	0.528366i	$-0.177195\pi$
$839$	2.90478e10	1.69803	0.849017	+	0.528366i	$0.177195\pi$
$840$	−7.44236e8	−0.0433245
$841$	−1.26033e10	−0.730631
$842$	9.50514e8	0.0548740
$843$	−1.20937e10	−0.695288
$844$	4.53025e9	0.259372
$845$	8.86300e8	0.0505338
$846$	8.65168e9	0.491252
$847$	1.00139e9	0.0566253
$848$	2.38067e9	0.134065
$849$	2.65082e9	0.148663
$850$	6.16051e9	0.344073
$851$	3.58195e9	0.199235
$852$	1.49298e9	0.0827017
$853$	1.60905e10	0.887661	0.443831	−	0.896111i	$-0.353619\pi$
$853$	1.60905e10	0.887661	0.443831	+	0.896111i	$0.353619\pi$
$854$	4.59812e9	0.252626
$855$	7.30830e9	0.399885
$856$	−1.18395e9	−0.0645169
$857$	3.27784e10	1.77891	0.889457	−	0.457019i	$-0.151083\pi$
$857$	3.27784e10	1.77891	0.889457	+	0.457019i	$0.151083\pi$
$858$	1.65111e9	0.0892424
$859$	−3.55834e10	−1.91545	−0.957726	−	0.287682i	$-0.907115\pi$
$859$	−3.55834e10	−1.91545	−0.957726	+	0.287682i	$0.907115\pi$
$860$	7.76784e9	0.416443
$861$	−1.79906e9	−0.0960585
$862$	−1.34327e10	−0.714311
$863$	3.31130e10	1.75372	0.876861	−	0.480744i	$-0.159633\pi$
$863$	3.31130e10	1.75372	0.876861	+	0.480744i	$0.159633\pi$
$864$	−2.90508e9	−0.153236
$865$	5.10918e9	0.268408
$866$	2.05229e10	1.07380
$867$	−2.53064e9	−0.131875
$868$	−1.36148e9	−0.0706632
$869$	−1.73358e10	−0.896140
$870$	2.31102e9	0.118983
$871$	8.94656e9	0.458768
$872$	5.30042e9	0.270709
$873$	−2.32718e10	−1.18380
$874$	1.00593e10	0.509659
$875$	7.71738e9	0.389441
$876$	−4.06240e9	−0.204183
$877$	2.88156e9	0.144254	0.0721272	−	0.997395i	$-0.477021\pi$
$877$	2.88156e9	0.144254	0.0721272	+	0.997395i	$0.477021\pi$
$878$	−9.81412e9	−0.489351
$879$	−6.72502e9	−0.333989
$880$	−3.06134e9	−0.151433
$881$	−2.67484e10	−1.31790	−0.658949	−	0.752188i	$-0.728999\pi$
$881$	−2.67484e10	−1.31790	−0.658949	+	0.752188i	$0.728999\pi$
$882$	−1.55705e9	−0.0764121
$883$	−1.93041e9	−0.0943600	−0.0471800	−	0.998886i	$-0.515023\pi$
$883$	−1.93041e9	−0.0943600	−0.0471800	+	0.998886i	$0.515023\pi$
$884$	2.43820e9	0.118710
$885$	6.75685e9	0.327674
$886$	−2.73705e10	−1.32210
$887$	1.20408e10	0.579326	0.289663	−	0.957129i	$-0.406457\pi$
$887$	1.20408e10	0.579326	0.289663	+	0.957129i	$0.406457\pi$
$888$	−8.09856e8	−0.0388117
$889$	1.23587e10	0.589954
$890$	−2.23264e9	−0.106158
$891$	−6.39817e9	−0.303029
$892$	−6.66259e9	−0.314316
$893$	1.57275e10	0.739058
$894$	−8.78772e9	−0.411334
$895$	−1.54395e10	−0.719868
$896$	−7.19323e8	−0.0334077
$897$	2.65011e9	0.122600
$898$	1.43539e10	0.661460
$899$	4.22771e9	0.194064
$900$	4.70188e9	0.214992
$901$	−1.00786e10	−0.459053
$902$	−7.40027e9	−0.335757
$903$	−5.23263e9	−0.236490
$904$	−1.32322e9	−0.0595719
$905$	−1.52775e10	−0.685143
$906$	−2.57401e9	−0.114991
$907$	−1.58259e10	−0.704275	−0.352137	−	0.935948i	$-0.614545\pi$
$907$	−1.58259e10	−0.704275	−0.352137	+	0.935948i	$0.614545\pi$
$908$	4.47645e9	0.198442
$909$	1.17737e10	0.519922
$910$	1.10697e9	0.0486956
$911$	−1.52002e9	−0.0666092	−0.0333046	−	0.999445i	$-0.510603\pi$
$911$	−1.52002e9	−0.0666092	−0.0333046	+	0.999445i	$0.510603\pi$
$912$	−2.27435e9	−0.0992832
$913$	3.17505e10	1.38071
$914$	1.56301e10	0.677096
$915$	−7.10138e9	−0.306457
$916$	1.24016e10	0.533143
$917$	−1.22083e10	−0.522832
$918$	1.22987e10	0.524697
$919$	−1.82852e10	−0.777133	−0.388567	−	0.921421i	$-0.627030\pi$
$919$	−1.82852e10	−0.777133	−0.388567	+	0.921421i	$0.627030\pi$
$920$	−4.91358e9	−0.208037
$921$	−6.90612e9	−0.291290
$922$	1.84666e10	0.775941
$923$	−2.22063e9	−0.0929547
$924$	2.06220e9	0.0859961
$925$	3.04354e9	0.126440
$926$	4.56655e9	0.188995
$927$	2.83693e10	1.16969
$928$	2.23366e9	0.0917484
$929$	−2.26030e10	−0.924934	−0.462467	−	0.886637i	$-0.653036\pi$
$929$	−2.26030e10	−0.924934	−0.462467	+	0.886637i	$0.653036\pi$
$930$	2.10269e9	0.0857205
$931$	−2.83048e9	−0.114957
$932$	2.46277e9	0.0996479
$933$	−1.10946e10	−0.447224
$934$	−2.43567e10	−0.978149
$935$	1.29602e10	0.518525
$936$	1.86090e9	0.0741752
$937$	−2.42762e10	−0.964033	−0.482016	−	0.876162i	$-0.660095\pi$
$937$	−2.42762e10	−0.964033	−0.482016	+	0.876162i	$0.660095\pi$
$938$	1.11740e10	0.442079
$939$	−6.66926e8	−0.0262874
$940$	−7.68222e9	−0.301675
$941$	2.43875e10	0.954121	0.477061	−	0.878870i	$-0.341702\pi$
$941$	2.43875e10	0.954121	0.477061	+	0.878870i	$0.341702\pi$
$942$	1.16129e10	0.452648
$943$	−1.18778e10	−0.461258
$944$	6.53067e9	0.252671
$945$	5.58371e9	0.215234
$946$	−2.15239e10	−0.826612
$947$	8.40577e9	0.321627	0.160813	−	0.986985i	$-0.448588\pi$
$947$	8.40577e9	0.321627	0.160813	+	0.986985i	$0.448588\pi$
$948$	6.29101e9	0.239823
$949$	6.04237e9	0.229496
$950$	8.54730e9	0.323442
$951$	−1.22990e10	−0.463700
$952$	3.04525e9	0.114392
$953$	1.36490e10	0.510827	0.255414	−	0.966832i	$-0.417788\pi$
$953$	1.36490e10	0.510827	0.255414	+	0.966832i	$0.417788\pi$
$954$	−7.69227e9	−0.286837
$955$	2.30241e10	0.855403
$956$	9.44377e9	0.349577
$957$	−6.40358e9	−0.236174
$958$	−6.54720e9	−0.240589
$959$	−5.16975e7	−0.00189280
$960$	1.11093e9	0.0405263
$961$	−2.36660e10	−0.860188
$962$	1.20457e9	0.0436234
$963$	3.82548e9	0.138036
$964$	1.25154e10	0.449962
$965$	2.33645e10	0.836972
$966$	3.30992e9	0.118140
$967$	−3.44474e10	−1.22508	−0.612540	−	0.790440i	$-0.709852\pi$
$967$	−3.44474e10	−1.22508	−0.612540	+	0.790440i	$0.709852\pi$
$968$	−1.49478e9	−0.0529681
$969$	9.62847e9	0.339957
$970$	2.06641e10	0.726967
$971$	−1.08047e10	−0.378743	−0.189372	−	0.981905i	$-0.560645\pi$
$971$	−1.08047e10	−0.378743	−0.189372	+	0.981905i	$0.560645\pi$
$972$	1.47308e10	0.514512
$973$	−1.03064e10	−0.358682
$974$	1.93726e10	0.671787
$975$	2.25177e9	0.0778049
$976$	−6.86367e9	−0.236310
$977$	−1.65062e10	−0.566260	−0.283130	−	0.959082i	$-0.591373\pi$
$977$	−1.65062e10	−0.566260	−0.283130	+	0.959082i	$0.591373\pi$
$978$	7.54866e9	0.258038
$979$	6.18640e9	0.210717
$980$	1.38258e9	0.0469243
$981$	−1.71263e10	−0.579193
$982$	1.34906e10	0.454613
$983$	−6.42525e9	−0.215751	−0.107876	−	0.994164i	$-0.534405\pi$
$983$	−6.42525e9	−0.215751	−0.107876	+	0.994164i	$0.534405\pi$
$984$	2.68548e9	0.0898545
$985$	1.06820e10	0.356145
$986$	−9.45618e9	−0.314157
$987$	5.17495e9	0.171315
$988$	3.38284e9	0.111592
$989$	−3.45468e10	−1.13559
$990$	9.89158e9	0.323998
$991$	−3.70850e10	−1.21043	−0.605215	−	0.796062i	$-0.706913\pi$
$991$	−3.70850e10	−1.21043	−0.605215	+	0.796062i	$0.706913\pi$
$992$	2.03230e9	0.0660994
$993$	−1.89467e10	−0.614062
$994$	−2.77352e9	−0.0895733
$995$	1.51412e10	0.487281
$996$	−1.15220e10	−0.369503
$997$	−1.82218e10	−0.582316	−0.291158	−	0.956675i	$-0.594041\pi$
$997$	−1.82218e10	−0.582316	−0.291158	+	0.956675i	$0.594041\pi$
$998$	−3.36317e10	−1.07101
$999$	6.07603e9	0.192815

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	182.8.a.b.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.8.a.b.1.3	✓	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 182 = 2 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	182.a (trivial)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} +23.0795 q^{3} +64.0000 q^{4} +183.620 q^{5} +184.636 q^{6} -343.000 q^{7} +512.000 q^{8} -1654.34 q^{9} +1468.96 q^{10} -4070.34 q^{11} +1477.09 q^{12} -2197.00 q^{13} -2744.00 q^{14} +4237.86 q^{15} +4096.00 q^{16} -17340.4 q^{17} -13234.7 q^{18} -24058.7 q^{19} +11751.7 q^{20} -7916.26 q^{21} -32562.7 q^{22} -52264.6 q^{23} +11816.7 q^{24} -44408.6 q^{25} -17576.0 q^{26} -88656.1 q^{27} -21952.0 q^{28} +68165.8 q^{29} +33902.9 q^{30} +62020.9 q^{31} +32768.0 q^{32} -93941.3 q^{33} -138723. q^{34} -62981.7 q^{35} -105878. q^{36} -68534.9 q^{37} -192469. q^{38} -50705.6 q^{39} +94013.6 q^{40} +227262. q^{41} -63330.1 q^{42} +660998. q^{43} -260502. q^{44} -303770. q^{45} -418117. q^{46} -653712. q^{47} +94533.5 q^{48} +117649. q^{49} -355269. q^{50} -400208. q^{51} -140608. q^{52} +581219. q^{53} -709249. q^{54} -747397. q^{55} -175616. q^{56} -555262. q^{57} +545326. q^{58} +1.59440e6 q^{59} +271223. q^{60} -1.67570e6 q^{61} +496167. q^{62} +567438. q^{63} +262144. q^{64} -403414. q^{65} -751531. q^{66} -4.07217e6 q^{67} -1.10979e6 q^{68} -1.20624e6 q^{69} -503854. q^{70} +1.01076e6 q^{71} -847021. q^{72} -2.75028e6 q^{73} -548279. q^{74} -1.02493e6 q^{75} -1.53976e6 q^{76} +1.39613e6 q^{77} -405645. q^{78} +4.25906e6 q^{79} +752109. q^{80} +1.57190e6 q^{81} +1.81810e6 q^{82} -7.80046e6 q^{83} -506641. q^{84} -3.18405e6 q^{85} +5.28798e6 q^{86} +1.57323e6 q^{87} -2.08401e6 q^{88} -1.51987e6 q^{89} -2.43016e6 q^{90} +753571. q^{91} -3.34494e6 q^{92} +1.43141e6 q^{93} -5.22970e6 q^{94} -4.41766e6 q^{95} +756268. q^{96} +1.40671e7 q^{97} +941192. q^{98} +6.73372e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32 q^{2} - 29 q^{3} + 256 q^{4} + 315 q^{5} - 232 q^{6} - 1372 q^{7} + 2048 q^{8} + 937 q^{9} + 2520 q^{10} - 2799 q^{11} - 1856 q^{12} - 8788 q^{13} - 10976 q^{14} - 38960 q^{15} + 16384 q^{16} - 47156 q^{17}+ \cdots - 4859772 q^{99}+O(q^{100}) \) 4 * q + 32 * q^2 - 29 * q^3 + 256 * q^4 + 315 * q^5 - 232 * q^6 - 1372 * q^7 + 2048 * q^8 + 937 * q^9 + 2520 * q^10 - 2799 * q^11 - 1856 * q^12 - 8788 * q^13 - 10976 * q^14 - 38960 * q^15 + 16384 * q^16 - 47156 * q^17 + 7496 * q^18 + 21167 * q^19 + 20160 * q^20 + 9947 * q^21 - 22392 * q^22 + 17508 * q^23 - 14848 * q^24 + 18907 * q^25 - 70304 * q^26 - 29051 * q^27 - 87808 * q^28 - 291911 * q^29 - 311680 * q^30 - 223770 * q^31 + 131072 * q^32 - 175251 * q^33 - 377248 * q^34 - 108045 * q^35 + 59968 * q^36 - 607537 * q^37 + 169336 * q^38 + 63713 * q^39 + 161280 * q^40 - 240123 * q^41 + 79576 * q^42 - 1268985 * q^43 - 179136 * q^44 + 281035 * q^45 + 140064 * q^46 - 465948 * q^47 - 118784 * q^48 + 470596 * q^49 + 151256 * q^50 + 59912 * q^51 - 562432 * q^52 + 29873 * q^53 - 232408 * q^54 - 3067466 * q^55 - 702464 * q^56 - 1981802 * q^57 - 2335288 * q^58 - 418226 * q^59 - 2493440 * q^60 - 1574237 * q^61 - 1790160 * q^62 - 321391 * q^63 + 1048576 * q^64 - 692055 * q^65 - 1402008 * q^66 - 6741503 * q^67 - 3017984 * q^68 - 3087009 * q^69 - 864360 * q^70 - 8260728 * q^71 + 479744 * q^72 - 4307556 * q^73 - 4860296 * q^74 - 6095923 * q^75 + 1354688 * q^76 + 960057 * q^77 + 509704 * q^78 - 2673678 * q^79 + 1290240 * q^80 - 14163560 * q^81 - 1920984 * q^82 - 10767561 * q^83 + 636608 * q^84 - 3422836 * q^85 - 10151880 * q^86 - 249448 * q^87 - 1433088 * q^88 - 2068133 * q^89 + 2248280 * q^90 + 3014284 * q^91 + 1120512 * q^92 + 9940639 * q^93 - 3727584 * q^94 - 7373999 * q^95 - 950272 * q^96 + 11642054 * q^97 + 3764768 * q^98 - 4859772 * q^99

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