LMFDB - Embedded newform 21.30.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,30,Mod(1,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 30, names="a")

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

chi := DirichletCharacter("21.1");

S:= CuspForms(chi, 30);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 30 $
Character orbit:	$[\chi]$	$=$	21.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$111.883889004$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3 x^{7} - 2857317313 x^{6} - 1405020216555 x^{5} + \cdots - 19\!\cdots\!94 $ x^8 - 3x^7 - 2857317313x^6 - 1405020216555x^5 + 2511494407820476041x^4 + 1309688035004575248975x^3 - 671343000872604695849378947x^2 - 963948141617979543405904380129*x - 192489451427205341333847862033094
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{26}\cdot 3^{16}\cdot 5^{2}\cdot 7^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$25358.2$ of defining polynomial
Character	$\chi$	$=$	21.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+22925.2 q^{2} +4.78297e6 q^{3} -1.13081e7 q^{4} -1.77814e10 q^{5} +1.09650e11 q^{6} -6.78223e11 q^{7} -1.25671e13 q^{8} +2.28768e13 q^{9} +O(q^{10})$	\(q+22925.2 q^{2} +4.78297e6 q^{3} -1.13081e7 q^{4} -1.77814e10 q^{5} +1.09650e11 q^{6} -6.78223e11 q^{7} -1.25671e13 q^{8} +2.28768e13 q^{9} -4.07642e14 q^{10} -2.01756e15 q^{11} -5.40862e13 q^{12} -5.13262e15 q^{13} -1.55484e16 q^{14} -8.50481e16 q^{15} -2.82032e17 q^{16} +4.65799e17 q^{17} +5.24454e17 q^{18} +5.09724e17 q^{19} +2.01074e17 q^{20} -3.24392e18 q^{21} -4.62529e19 q^{22} +3.60381e19 q^{23} -6.01080e19 q^{24} +1.29915e20 q^{25} -1.17666e20 q^{26} +1.09419e20 q^{27} +7.66940e18 q^{28} -9.09379e20 q^{29} -1.94974e21 q^{30} -3.68617e21 q^{31} +2.81288e20 q^{32} -9.64994e21 q^{33} +1.06785e22 q^{34} +1.20598e22 q^{35} -2.58692e20 q^{36} +1.06038e23 q^{37} +1.16855e22 q^{38} -2.45491e22 q^{39} +2.23461e23 q^{40} +2.67064e23 q^{41} -7.43674e22 q^{42} -5.83755e23 q^{43} +2.28147e22 q^{44} -4.06782e23 q^{45} +8.26178e23 q^{46} +1.05421e24 q^{47} -1.34895e24 q^{48} +4.59987e23 q^{49} +2.97832e24 q^{50} +2.22790e24 q^{51} +5.80400e22 q^{52} -1.57377e25 q^{53} +2.50845e24 q^{54} +3.58752e25 q^{55} +8.52329e24 q^{56} +2.43800e24 q^{57} -2.08476e25 q^{58} +7.97516e25 q^{59} +9.61730e23 q^{60} +5.17361e25 q^{61} -8.45059e25 q^{62} -1.55156e25 q^{63} +1.57863e26 q^{64} +9.12653e25 q^{65} -2.21226e26 q^{66} -6.66336e25 q^{67} -5.26729e24 q^{68} +1.72369e26 q^{69} +2.76472e26 q^{70} -8.22026e26 q^{71} -2.87495e26 q^{72} +9.66135e26 q^{73} +2.43094e27 q^{74} +6.21379e26 q^{75} -5.76400e24 q^{76} +1.36836e27 q^{77} -5.62793e26 q^{78} +2.57557e27 q^{79} +5.01493e27 q^{80} +5.23348e26 q^{81} +6.12249e27 q^{82} -9.93933e27 q^{83} +3.66825e25 q^{84} -8.28258e27 q^{85} -1.33827e28 q^{86} -4.34953e27 q^{87} +2.53549e28 q^{88} -2.67960e28 q^{89} -9.32555e27 q^{90} +3.48106e27 q^{91} -4.07521e26 q^{92} -1.76308e28 q^{93} +2.41680e28 q^{94} -9.06363e27 q^{95} +1.34539e27 q^{96} -1.58327e28 q^{97} +1.05453e28 q^{98} -4.61554e28 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 19461 q^{2} + 38263752 q^{3} + 1467008653 q^{4} - 8498112672 q^{5} - 93081359709 q^{6} - 5425784582792 q^{7} - 16689415716987 q^{8} + 183014339639688 q^{9}+O(q^{10}) $ 8 * q - 19461 * q^2 + 38263752 * q^3 + 1467008653 * q^4 - 8498112672 * q^5 - 93081359709 * q^6 - 5425784582792 * q^7 - 16689415716987 * q^8 + 183014339639688 * q^9	$ 8 q - 19461 q^{2} + 38263752 q^{3} + 1467008653 q^{4} - 8498112672 q^{5} - 93081359709 q^{6} - 5425784582792 q^{7} - 16689415716987 q^{8} + 183014339639688 q^{9} + 636942348029770 q^{10} + 395708686257744 q^{11} + 70\!\cdots\!57 q^{12}+ \cdots + 90\!\cdots\!84 q^{99}+O(q^{100}) $ 8 * q - 19461 * q^2 + 38263752 * q^3 + 1467008653 * q^4 - 8498112672 * q^5 - 93081359709 * q^6 - 5425784582792 * q^7 - 16689415716987 * q^8 + 183014339639688 * q^9 + 636942348029770 * q^10 + 395708686257744 * q^11 + 7016656910030757 * q^12 + 22809319742321168 * q^13 + 13198899220714389 * q^14 - 40646209468683168 * q^15 - 529929838419631103 * q^16 - 875764906948588224 * q^17 - 445205257965996021 * q^18 + 1426892827775457824 * q^19 - 28899057412113817626 * q^20 - 25951359460172069448 * q^21 - 5186094623833295684 * q^22 + 31571815389865907376 * q^23 - 79824958002461594403 * q^24 + 484933790864619664792 * q^25 + 871531917323138656458 * q^26 + 875351913052098873672 * q^27 - 994959116533732362397 * q^28 + 403819311812853278064 * q^29 + 3046475505413600987130 * q^30 + 6056711864477051297664 * q^31 + 495732442702744435125 * q^32 + 1892662379401515561936 * q^33 + 27608278255426542993054 * q^34 + 5763616089820866042528 * q^35 + 33560452484312899777533 * q^36 + 249301086380038228224144 * q^37 + 232307666312718559908396 * q^38 + 109096269238610134587792 * q^39 + 222254097261275058064470 * q^40 - 118485395827236320088480 * q^41 + 63129925806801080440941 * q^42 + 955811315548717966687456 * q^43 + 2197776642577416647616228 * q^44 - 194409559856218063365792 * q^45 - 728621547286381001073120 * q^46 + 1724730703353294103329696 * q^47 - 2534637989336104557084807 * q^48 + 3679892292357919687814408 * q^49 + 3315945636459433646107605 * q^50 - 4188756401222982069157056 * q^51 + 7867779844424116360460902 * q^52 + 2121223193154060481519824 * q^53 - 2129402947488362022566349 * q^54 - 7250285279281800197516224 * q^55 + 11319146811629319667785963 * q^56 + 6824784161572353732999456 * q^57 - 14457635242040178152167718 * q^58 + 42196882197868232719878528 * q^59 - 138223295731360614176811594 * q^60 - 101117722940093083661366416 * q^61 + 186299525380851520014926400 * q^62 - 124124547805859742835631112 * q^63 - 578691286566308562959878519 * q^64 - 350548464914993356143283200 * q^65 - 24804929816861314424405796 * q^66 - 76630272082508454921299392 * q^67 - 980499057011951020658835918 * q^68 + 151007014283451549136279344 * q^69 - 431988996508407810330714730 * q^70 - 1078132490609618557101526320 * q^71 - 381800299552075729720122507 * q^72 - 247553894478620130982212048 * q^73 - 75659580621831989514366414 * q^74 + 2319423288757959053490527448 * q^75 + 3177709658750992797170923828 * q^76 - 268378761146767994102392656 * q^77 + 4168510143067135176540263802 * q^78 + 2428644145165587926516228512 * q^79 + 1621802770176465933634958622 * q^80 + 4186781064218884297708092168 * q^81 + 31867674822051710989797094358 * q^82 - 12963768045528470934634770144 * q^83 - 4758858610648229343641616693 * q^84 + 8949893682441356527904874624 * q^85 + 19361425567422560435180442756 * q^86 + 1931455250002211030528492016 * q^87 + 36039744054684227265332026212 * q^88 + 19612047814410613791670511136 * q^89 + 14571197901652585699812188970 * q^90 - 15469806925232423432818767632 * q^91 - 33565399363855362024322385952 * q^92 + 28969065089725937568136684416 * q^93 + 23248231331633687228175413280 * q^94 - 70429226382314318765891409984 * q^95 + 2371072905741502848125386125 * q^96 - 5439618388643531441097237456 * q^97 - 8951797987697184380569524261 * q^98 + 9052545488143687485757467984 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	22925.2	0.989412	0.494706	−	0.869060i	$-0.335276\pi$
$2$	22925.2	0.989412	0.494706	+	0.869060i	$0.335276\pi$
$3$	4.78297e6	0.577350
$3$	4.78297e6	0.577350
$4$	−1.13081e7	−0.0210629
$5$	−1.77814e10	−1.30287	−0.651436	−	0.758704i	$-0.725833\pi$
$5$	−1.77814e10	−1.30287	−0.651436	+	0.758704i	$0.725833\pi$
$6$	1.09650e11	0.571238
$7$	−6.78223e11	−0.377964
$7$	−6.78223e11	−0.377964
$8$	−1.25671e13	−1.01025
$9$	2.28768e13	0.333333
$10$	−4.07642e14	−1.28908
$11$	−2.01756e15	−1.60189	−0.800946	−	0.598737i	$-0.795670\pi$
$11$	−2.01756e15	−1.60189	−0.800946	+	0.598737i	$0.795670\pi$
$12$	−5.40862e13	−0.0121607
$13$	−5.13262e15	−0.361543	−0.180772	−	0.983525i	$-0.557859\pi$
$13$	−5.13262e15	−0.361543	−0.180772	+	0.983525i	$0.557859\pi$
$14$	−1.55484e16	−0.373963
$15$	−8.50481e16	−0.752214
$16$	−2.82032e17	−0.978493
$17$	4.65799e17	0.670949	0.335474	−	0.942049i	$-0.391103\pi$
$17$	4.65799e17	0.670949	0.335474	+	0.942049i	$0.391103\pi$
$18$	5.24454e17	0.329804
$19$	5.09724e17	0.146355	0.0731776	−	0.997319i	$-0.476686\pi$
$19$	5.09724e17	0.146355	0.0731776	+	0.997319i	$0.476686\pi$
$20$	2.01074e17	0.0274423
$21$	−3.24392e18	−0.218218
$22$	−4.62529e19	−1.58493
$23$	3.60381e19	0.648198	0.324099	−	0.946023i	$-0.394939\pi$
$23$	3.60381e19	0.648198	0.324099	+	0.946023i	$0.394939\pi$
$24$	−6.01080e19	−0.583270
$25$	1.29915e20	0.697476
$26$	−1.17666e20	−0.357715
$27$	1.09419e20	0.192450
$28$	7.66940e18	0.00796104
$29$	−9.09379e20	−0.567510	−0.283755	−	0.958897i	$-0.591580\pi$
$29$	−9.09379e20	−0.567510	−0.283755	+	0.958897i	$0.591580\pi$
$30$	−1.94974e21	−0.744250
$31$	−3.68617e21	−0.874642	−0.437321	−	0.899306i	$-0.644073\pi$
$31$	−3.68617e21	−0.874642	−0.437321	+	0.899306i	$0.644073\pi$
$32$	2.81288e20	0.0421188
$33$	−9.64994e21	−0.924853
$34$	1.06785e22	0.663845
$35$	1.20598e22	0.492439
$36$	−2.58692e20	−0.00702098
$37$	1.06038e23	1.93436	0.967181	−	0.254090i	$-0.0817759\pi$
$37$	1.06038e23	1.93436	0.967181	+	0.254090i	$0.0817759\pi$
$38$	1.16855e22	0.144806
$39$	−2.45491e22	−0.208737
$40$	2.23461e23	1.31623
$41$	2.67064e23	1.09964	0.549819	−	0.835284i	$-0.314697\pi$
$41$	2.67064e23	1.09964	0.549819	+	0.835284i	$0.314697\pi$
$42$	−7.43674e22	−0.215908
$43$	−5.83755e23	−1.20486	−0.602432	−	0.798170i	$-0.705802\pi$
$43$	−5.83755e23	−1.20486	−0.602432	+	0.798170i	$0.705802\pi$
$44$	2.28147e22	0.0337405
$45$	−4.06782e23	−0.434291
$46$	8.26178e23	0.641335
$47$	1.05421e24	0.599114	0.299557	−	0.954078i	$-0.403161\pi$
$47$	1.05421e24	0.599114	0.299557	+	0.954078i	$0.403161\pi$
$48$	−1.34895e24	−0.564933
$49$	4.59987e23	0.142857
$50$	2.97832e24	0.690091
$51$	2.22790e24	0.387372
$52$	5.80400e22	0.00761516
$53$	−1.57377e25	−1.56654	−0.783269	−	0.621683i	$-0.786449\pi$
$53$	−1.57377e25	−1.56654	−0.783269	+	0.621683i	$0.786449\pi$
$54$	2.50845e24	0.190413
$55$	3.58752e25	2.08706
$56$	8.52329e24	0.381840
$57$	2.43800e24	0.0844982
$58$	−2.08476e25	−0.561502
$59$	7.97516e25	1.67643	0.838215	−	0.545340i	$-0.183599\pi$
$59$	7.97516e25	1.67643	0.838215	+	0.545340i	$0.183599\pi$
$60$	9.61730e23	0.0158438
$61$	5.17361e25	0.670673	0.335336	−	0.942098i	$-0.391150\pi$
$61$	5.17361e25	0.670673	0.335336	+	0.942098i	$0.391150\pi$
$62$	−8.45059e25	−0.865382
$63$	−1.55156e25	−0.125988
$64$	1.57863e26	1.02017
$65$	9.12653e25	0.471044
$66$	−2.21226e26	−0.915061
$67$	−6.66336e25	−0.221620	−0.110810	−	0.993842i	$-0.535345\pi$
$67$	−6.66336e25	−0.221620	−0.110810	+	0.993842i	$0.535345\pi$
$68$	−5.26729e24	−0.0141321
$69$	1.72369e26	0.374237
$70$	2.76472e26	0.487226
$71$	−8.22026e26	−1.17934	−0.589671	−	0.807644i	$-0.700743\pi$
$71$	−8.22026e26	−1.17934	−0.589671	+	0.807644i	$0.700743\pi$
$72$	−2.87495e26	−0.336751
$73$	9.66135e26	0.926524	0.463262	−	0.886221i	$-0.346679\pi$
$73$	9.66135e26	0.926524	0.463262	+	0.886221i	$0.346679\pi$
$74$	2.43094e27	1.91388
$75$	6.21379e26	0.402688
$76$	−5.76400e24	−0.00308267
$77$	1.36836e27	0.605458
$78$	−5.62793e26	−0.206527
$79$	2.57557e27	0.785744	0.392872	−	0.919593i	$-0.371481\pi$
$79$	2.57557e27	0.785744	0.392872	+	0.919593i	$0.371481\pi$
$80$	5.01493e27	1.27485
$81$	5.23348e26	0.111111
$82$	6.12249e27	1.08800
$83$	−9.93933e27	−1.48158	−0.740789	−	0.671738i	$-0.765548\pi$
$83$	−9.93933e27	−1.48158	−0.740789	+	0.671738i	$0.765548\pi$
$84$	3.66825e25	0.00459631
$85$	−8.28258e27	−0.874160
$86$	−1.33827e28	−1.19211
$87$	−4.34953e27	−0.327652
$88$	2.53549e28	1.61831
$89$	−2.67960e28	−1.45183	−0.725915	−	0.687785i	$-0.758583\pi$
$89$	−2.67960e28	−1.45183	−0.725915	+	0.687785i	$0.758583\pi$
$90$	−9.32555e27	−0.429693
$91$	3.48106e27	0.136650
$92$	−4.07521e26	−0.0136529
$93$	−1.76308e28	−0.504975
$94$	2.41680e28	0.592770
$95$	−9.06363e27	−0.190682
$96$	1.34539e27	0.0243173
$97$	−1.58327e28	−0.246244	−0.123122	−	0.992392i	$-0.539291\pi$
$97$	−1.58327e28	−0.246244	−0.123122	+	0.992392i	$0.539291\pi$
$98$	1.05453e28	0.141345
$99$	−4.61554e28	−0.533964
$100$	−1.46909e27	−0.0146909
$101$	4.68929e27	0.0405926	0.0202963	−	0.999794i	$-0.493539\pi$
$101$	4.68929e27	0.0405926	0.0202963	+	0.999794i	$0.493539\pi$
$102$	5.10750e28	0.383271
$103$	−1.42129e29	−0.925855	−0.462927	−	0.886396i	$-0.653201\pi$
$103$	−1.42129e29	−0.925855	−0.462927	+	0.886396i	$0.653201\pi$
$104$	6.45020e28	0.365250
$105$	5.76816e28	0.284310
$106$	−3.60789e29	−1.54995
$107$	3.75092e29	1.40628	0.703141	−	0.711050i	$-0.251780\pi$
$107$	3.75092e29	1.40628	0.703141	+	0.711050i	$0.251780\pi$
$108$	−1.23732e27	−0.00405356
$109$	1.30619e29	0.374389	0.187195	−	0.982323i	$-0.440060\pi$
$109$	1.30619e29	0.374389	0.187195	+	0.982323i	$0.440060\pi$
$110$	8.22444e29	2.06496
$111$	5.07178e29	1.11680
$112$	1.91280e29	0.369836
$113$	−2.55498e29	−0.434260	−0.217130	−	0.976143i	$-0.569670\pi$
$113$	−2.55498e29	−0.434260	−0.217130	+	0.976143i	$0.569670\pi$
$114$	5.58914e28	0.0836036
$115$	−6.40808e29	−0.844519
$116$	1.02833e28	0.0119534
$117$	−1.17418e29	−0.120514
$118$	1.82832e30	1.65868
$119$	−3.15916e29	−0.253595
$120$	1.06881e30	0.759926
$121$	2.48425e30	1.56606
$122$	1.18606e30	0.663572
$123$	1.27736e30	0.634877
$124$	4.16834e28	0.0184225
$125$	1.00198e30	0.394150
$126$	−3.55697e29	−0.124654
$127$	2.63009e30	0.821896	0.410948	−	0.911659i	$-0.365198\pi$
$127$	2.63009e30	0.821896	0.410948	+	0.911659i	$0.365198\pi$
$128$	3.46802e30	0.967246
$129$	−2.79208e30	−0.695629
$130$	2.09227e30	0.466057
$131$	6.51167e30	1.29795	0.648976	−	0.760809i	$-0.275198\pi$
$131$	6.51167e30	1.29795	0.648976	+	0.760809i	$0.275198\pi$
$132$	1.09122e29	0.0194801
$133$	−3.45707e29	−0.0553171
$134$	−1.52759e30	−0.219274
$135$	−1.94563e30	−0.250738
$136$	−5.85374e30	−0.677827
$137$	−3.89809e30	−0.405885	−0.202943	−	0.979191i	$-0.565050\pi$
$137$	−3.89809e30	−0.405885	−0.202943	+	0.979191i	$0.565050\pi$
$138$	3.95158e30	0.370275
$139$	1.47046e31	1.24090	0.620451	−	0.784245i	$-0.286949\pi$
$139$	1.47046e31	1.24090	0.620451	+	0.784245i	$0.286949\pi$
$140$	−1.36373e29	−0.0103722
$141$	5.04227e30	0.345898
$142$	−1.88451e31	−1.16686
$143$	1.03554e31	0.579153
$144$	−6.45198e30	−0.326164
$145$	1.61701e31	0.739393
$146$	2.21488e31	0.916714
$147$	2.20010e30	0.0824786
$148$	−1.19909e30	−0.0407433
$149$	−3.95465e31	−1.21873	−0.609364	−	0.792891i	$-0.708575\pi$
$149$	−3.95465e31	−1.21873	−0.609364	+	0.792891i	$0.708575\pi$
$150$	1.42452e31	0.398424
$151$	4.19893e31	1.06653	0.533264	−	0.845949i	$-0.320965\pi$
$151$	4.19893e31	1.06653	0.533264	+	0.845949i	$0.320965\pi$
$152$	−6.40575e30	−0.147856
$153$	1.06560e31	0.223650
$154$	3.13698e31	0.599048
$155$	6.55453e31	1.13955
$156$	2.77603e29	0.00439661
$157$	2.18317e31	0.315169	0.157584	−	0.987506i	$-0.449629\pi$
$157$	2.18317e31	0.315169	0.157584	+	0.987506i	$0.449629\pi$
$158$	5.90454e31	0.777425
$159$	−7.52729e31	−0.904441
$160$	−5.00170e30	−0.0548754
$161$	−2.44418e31	−0.244996
$162$	1.19978e31	0.109935
$163$	−2.65374e31	−0.222401	−0.111201	−	0.993798i	$-0.535470\pi$
$163$	−2.65374e31	−0.222401	−0.111201	+	0.993798i	$0.535470\pi$
$164$	−3.01998e30	−0.0231616
$165$	1.71590e32	1.20496
$166$	−2.27861e32	−1.46589
$167$	7.85102e31	0.462954	0.231477	−	0.972840i	$-0.425644\pi$
$167$	7.85102e31	0.462954	0.231477	+	0.972840i	$0.425644\pi$
$168$	4.07666e31	0.220455
$169$	−1.75194e32	−0.869287
$170$	−1.89879e32	−0.864905
$171$	1.16609e31	0.0487851
$172$	6.60115e30	0.0253780
$173$	−2.83207e31	−0.100100	−0.0500502	−	0.998747i	$-0.515938\pi$
$173$	−2.83207e31	−0.100100	−0.0500502	+	0.998747i	$0.515938\pi$
$174$	−9.97136e31	−0.324183
$175$	−8.81113e31	−0.263621
$176$	5.69016e32	1.56744
$177$	3.81450e32	0.967887
$178$	−6.14304e32	−1.43646
$179$	7.14861e32	1.54118	0.770588	−	0.637333i	$-0.219963\pi$
$179$	7.14861e32	1.54118	0.770588	+	0.637333i	$0.219963\pi$
$180$	4.59992e30	0.00914743
$181$	2.39459e32	0.439433	0.219716	−	0.975564i	$-0.429487\pi$
$181$	2.39459e32	0.439433	0.219716	+	0.975564i	$0.429487\pi$
$182$	7.98038e31	0.135204
$183$	2.47452e32	0.387213
$184$	−4.52893e32	−0.654844
$185$	−1.88551e33	−2.52023
$186$	−4.04189e32	−0.499628
$187$	−9.39779e32	−1.07479
$188$	−1.19211e31	−0.0126191
$189$	−7.42105e31	−0.0727393
$190$	−2.07785e32	−0.188663
$191$	−6.34810e32	−0.534146	−0.267073	−	0.963676i	$-0.586057\pi$
$191$	−6.34810e32	−0.534146	−0.267073	+	0.963676i	$0.586057\pi$
$192$	7.55054e32	0.588993
$193$	−1.53934e33	−1.11367	−0.556833	−	0.830625i	$-0.687984\pi$
$193$	−1.53934e33	−1.11367	−0.556833	+	0.830625i	$0.687984\pi$
$194$	−3.62968e32	−0.243637
$195$	4.36519e32	0.271958
$196$	−5.20156e30	−0.00300899
$197$	1.21772e33	0.654318	0.327159	−	0.944969i	$-0.393909\pi$
$197$	1.21772e33	0.654318	0.327159	+	0.944969i	$0.393909\pi$
$198$	−1.05812e33	−0.528311
$199$	−3.25090e33	−1.50881	−0.754405	−	0.656410i	$-0.772074\pi$
$199$	−3.25090e33	−1.50881	−0.754405	+	0.656410i	$0.772074\pi$
$200$	−1.63265e33	−0.704627
$201$	−3.18707e32	−0.127952
$202$	1.07503e32	0.0401629
$203$	6.16762e32	0.214499
$204$	−2.51933e31	−0.00815920
$205$	−4.74879e33	−1.43269
$206$	−3.25833e33	−0.916052
$207$	8.24435e32	0.216066
$208$	1.44756e33	0.353768
$209$	−1.02840e33	−0.234445
$210$	1.32236e33	0.281300
$211$	−6.03397e33	−1.19814	−0.599070	−	0.800697i	$-0.704463\pi$
$211$	−6.03397e33	−1.19814	−0.599070	+	0.800697i	$0.704463\pi$
$212$	1.77963e32	0.0329959
$213$	−3.93173e33	−0.680893
$214$	8.59904e33	1.39139
$215$	1.03800e34	1.56978
$216$	−1.37508e33	−0.194423
$217$	2.50004e33	0.330584
$218$	2.99447e33	0.370426
$219$	4.62100e33	0.534929
$220$	−4.05679e32	−0.0439596
$221$	−2.39077e33	−0.242577
$222$	1.16271e34	1.10498
$223$	1.26095e34	1.12274	0.561369	−	0.827565i	$-0.310275\pi$
$223$	1.26095e34	1.12274	0.561369	+	0.827565i	$0.310275\pi$
$224$	−1.90776e32	−0.0159194
$225$	2.97204e33	0.232492
$226$	−5.85733e33	−0.429662
$227$	1.72793e34	1.18892	0.594459	−	0.804126i	$-0.297366\pi$
$227$	1.72793e34	1.18892	0.594459	+	0.804126i	$0.297366\pi$
$228$	−2.75690e31	−0.00177978
$229$	−1.70169e34	−1.03102	−0.515510	−	0.856884i	$-0.672397\pi$
$229$	−1.70169e34	−1.03102	−0.515510	+	0.856884i	$0.672397\pi$
$230$	−1.46906e34	−0.835578
$231$	6.54481e33	0.349561
$232$	1.14282e34	0.573329
$233$	1.73570e34	0.818116	0.409058	−	0.912508i	$-0.365857\pi$
$233$	1.73570e34	0.818116	0.409058	+	0.912508i	$0.365857\pi$
$234$	−2.69182e33	−0.119238
$235$	−1.87454e34	−0.780568
$236$	−9.01837e32	−0.0353105
$237$	1.23189e34	0.453650
$238$	−7.24242e33	−0.250910
$239$	3.69518e34	1.20466	0.602332	−	0.798246i	$-0.294238\pi$
$239$	3.69518e34	1.20466	0.602332	+	0.798246i	$0.294238\pi$
$240$	2.39862e34	0.736036
$241$	1.86771e34	0.539588	0.269794	−	0.962918i	$-0.413044\pi$
$241$	1.86771e34	0.539588	0.269794	+	0.962918i	$0.413044\pi$
$242$	5.69518e34	1.54948
$243$	2.50316e33	0.0641500
$244$	−5.85035e32	−0.0141263
$245$	−8.17922e33	−0.186125
$246$	2.92837e34	0.628155
$247$	−2.61622e33	−0.0529137
$248$	4.63244e34	0.883609
$249$	−4.75395e34	−0.855390
$250$	2.29704e34	0.389977
$251$	−6.56467e34	−1.05183	−0.525913	−	0.850538i	$-0.676276\pi$
$251$	−6.56467e34	−1.05183	−0.525913	+	0.850538i	$0.676276\pi$
$252$	1.75451e32	0.00265368
$253$	−7.27090e34	−1.03834
$254$	6.02953e34	0.813194
$255$	−3.96153e34	−0.504697
$256$	−5.24717e33	−0.0631606
$257$	−1.62704e35	−1.85084	−0.925420	−	0.378944i	$-0.876287\pi$
$257$	−1.62704e35	−1.85084	−0.925420	+	0.378944i	$0.876287\pi$
$258$	−6.40090e34	−0.688264
$259$	−7.19176e34	−0.731120
$260$	−1.03203e33	−0.00992158
$261$	−2.08037e34	−0.189170
$262$	1.49281e35	1.28421
$263$	−1.67817e35	−1.36608	−0.683042	−	0.730379i	$-0.739343\pi$
$263$	−1.67817e35	−1.36608	−0.683042	+	0.730379i	$0.739343\pi$
$264$	1.21272e35	0.934335
$265$	2.79839e35	2.04100
$266$	−7.92538e33	−0.0547314
$267$	−1.28165e35	−0.838214
$268$	7.53498e32	0.00466797
$269$	−1.38248e35	−0.811428	−0.405714	−	0.914000i	$-0.632977\pi$
$269$	−1.38248e35	−0.811428	−0.405714	+	0.914000i	$0.632977\pi$
$270$	−4.46038e34	−0.248083
$271$	3.60560e35	1.90074	0.950369	−	0.311124i	$-0.100705\pi$
$271$	3.60560e35	1.90074	0.950369	+	0.311124i	$0.100705\pi$
$272$	−1.31370e35	−0.656519
$273$	1.66498e34	0.0788952
$274$	−8.93642e34	−0.401588
$275$	−2.62112e35	−1.11728
$276$	−1.94916e33	−0.00788253
$277$	1.48466e35	0.569733	0.284867	−	0.958567i	$-0.408051\pi$
$277$	1.48466e35	0.569733	0.284867	+	0.958567i	$0.408051\pi$
$278$	3.37105e35	1.22776
$279$	−8.43276e34	−0.291547
$280$	−1.51556e35	−0.497488
$281$	2.82153e35	0.879515	0.439757	−	0.898117i	$-0.355064\pi$
$281$	2.82153e35	0.879515	0.439757	+	0.898117i	$0.355064\pi$
$282$	1.15595e35	0.342236
$283$	2.45191e35	0.689606	0.344803	−	0.938675i	$-0.387946\pi$
$283$	2.45191e35	0.689606	0.344803	+	0.938675i	$0.387946\pi$
$284$	9.29554e33	0.0248404
$285$	−4.33511e34	−0.110090
$286$	2.37399e35	0.573021
$287$	−1.81129e35	−0.415624
$288$	6.43496e33	0.0140396
$289$	−2.65000e35	−0.549828
$290$	3.70701e35	0.731565
$291$	−7.57274e34	−0.142169
$292$	−1.09251e34	−0.0195153
$293$	−7.61444e35	−1.29437	−0.647183	−	0.762334i	$-0.724053\pi$
$293$	−7.61444e35	−1.29437	−0.647183	+	0.762334i	$0.724053\pi$
$294$	5.04377e34	0.0816054
$295$	−1.41810e36	−2.18417
$296$	−1.33259e36	−1.95419
$297$	−2.20760e35	−0.308284
$298$	−9.06609e35	−1.20582
$299$	−1.84969e35	−0.234352
$300$	−7.02660e33	−0.00848179
$301$	3.95916e35	0.455396
$302$	9.62611e35	1.05524
$303$	2.24287e34	0.0234362
$304$	−1.43758e35	−0.143208
$305$	−9.19941e35	−0.873801
$306$	2.44290e35	0.221282
$307$	9.65902e35	0.834501	0.417250	−	0.908792i	$-0.362994\pi$
$307$	9.65902e35	0.834501	0.417250	+	0.908792i	$0.362994\pi$
$308$	−1.54735e34	−0.0127527
$309$	−6.79799e35	−0.534543
$310$	1.50264e36	1.12748
$311$	−2.35009e36	−1.68290	−0.841452	−	0.540331i	$-0.818299\pi$
$311$	−2.35009e36	−1.68290	−0.841452	+	0.540331i	$0.818299\pi$
$312$	3.08511e35	0.210877
$313$	1.02407e36	0.668246	0.334123	−	0.942529i	$-0.391560\pi$
$313$	1.02407e36	0.668246	0.334123	+	0.942529i	$0.391560\pi$
$314$	5.00496e35	0.311832
$315$	2.75889e35	0.164146
$316$	−2.91248e34	−0.0165501
$317$	1.35733e36	0.736762	0.368381	−	0.929675i	$-0.379912\pi$
$317$	1.35733e36	0.736762	0.368381	+	0.929675i	$0.379912\pi$
$318$	−1.72564e36	−0.894866
$319$	1.83473e36	0.909090
$320$	−2.80703e36	−1.32915
$321$	1.79405e36	0.811918
$322$	−5.60333e35	−0.242402
$323$	2.37429e35	0.0981968
$324$	−5.91805e33	−0.00234033
$325$	−6.66804e35	−0.252168
$326$	−6.08373e35	−0.220047
$327$	6.24749e35	0.216154
$328$	−3.35622e36	−1.11091
$329$	−7.14991e35	−0.226444
$330$	3.93372e36	1.19221
$331$	1.88471e36	0.546688	0.273344	−	0.961916i	$-0.411870\pi$
$331$	1.88471e36	0.546688	0.273344	+	0.961916i	$0.411870\pi$
$332$	1.12395e35	0.0312064
$333$	2.42582e36	0.644787
$334$	1.79986e36	0.458052
$335$	1.18484e36	0.288743
$336$	9.14888e35	0.213525
$337$	5.93119e36	1.32589	0.662946	−	0.748667i	$-0.269306\pi$
$337$	5.93119e36	1.32589	0.662946	+	0.748667i	$0.269306\pi$
$338$	−4.01636e36	−0.860083
$339$	−1.22204e36	−0.250720
$340$	9.36600e34	0.0184124
$341$	7.43707e36	1.40108
$342$	2.67327e35	0.0482685
$343$	−3.11973e35	−0.0539949
$344$	7.33611e36	1.21722
$345$	−3.06497e36	−0.487583
$346$	−6.49257e35	−0.0990405
$347$	9.62787e36	1.40849	0.704244	−	0.709958i	$-0.251286\pi$
$347$	9.62787e36	1.40849	0.704244	+	0.709958i	$0.251286\pi$
$348$	4.91848e34	0.00690131
$349$	2.15637e35	0.0290238	0.0145119	−	0.999895i	$-0.495381\pi$
$349$	2.15637e35	0.0290238	0.0145119	+	0.999895i	$0.495381\pi$
$350$	−2.01997e36	−0.260830
$351$	−5.61606e35	−0.0695790
$352$	−5.67515e35	−0.0674697
$353$	−9.79999e36	−1.11813	−0.559065	−	0.829124i	$-0.688840\pi$
$353$	−9.79999e36	−1.11813	−0.559065	+	0.829124i	$0.688840\pi$
$354$	8.74479e36	0.957640
$355$	1.46168e37	1.53653
$356$	3.03012e35	0.0305798
$357$	−1.51101e36	−0.146413
$358$	1.63883e37	1.52486
$359$	−1.72861e37	−1.54464	−0.772321	−	0.635233i	$-0.780904\pi$
$359$	−1.72861e37	−1.54464	−0.772321	+	0.635233i	$0.780904\pi$
$360$	5.11207e36	0.438743
$361$	−1.18700e37	−0.978580
$362$	5.48964e36	0.434780
$363$	1.18821e37	0.904163
$364$	−3.93641e34	−0.00287826
$365$	−1.71793e37	−1.20714
$366$	5.67287e36	0.383113
$367$	9.23579e36	0.599537	0.299769	−	0.954012i	$-0.403090\pi$
$367$	9.23579e36	0.599537	0.299769	+	0.954012i	$0.403090\pi$
$368$	−1.01639e37	−0.634258
$369$	6.10957e36	0.366546
$370$	−4.32257e37	−2.49354
$371$	1.06737e37	0.592096
$372$	1.99371e35	0.0106362
$373$	1.30379e37	0.669005	0.334502	−	0.942395i	$-0.391432\pi$
$373$	1.30379e37	0.669005	0.334502	+	0.942395i	$0.391432\pi$
$374$	−2.15446e37	−1.06341
$375$	4.79242e36	0.227563
$376$	−1.32484e37	−0.605256
$377$	4.66749e36	0.205179
$378$	−1.70129e36	−0.0719692
$379$	−4.15949e37	−1.69345	−0.846723	−	0.532033i	$-0.821428\pi$
$379$	−4.15949e37	−1.69345	−0.846723	+	0.532033i	$0.821428\pi$
$380$	1.02492e35	0.00401632
$381$	1.25796e37	0.474522
$382$	−1.45531e37	−0.528491
$383$	−4.35239e37	−1.52176	−0.760880	−	0.648893i	$-0.775232\pi$
$383$	−4.35239e37	−1.52176	−0.760880	+	0.648893i	$0.775232\pi$
$384$	1.65874e37	0.558440
$385$	−2.43314e37	−0.788835
$386$	−3.52897e37	−1.10187
$387$	−1.33545e37	−0.401622
$388$	1.79038e35	0.00518662
$389$	6.16319e37	1.72003	0.860016	−	0.510267i	$-0.170454\pi$
$389$	6.16319e37	1.72003	0.860016	+	0.510267i	$0.170454\pi$
$390$	1.00073e37	0.269078
$391$	1.67865e37	0.434908
$392$	−5.78069e36	−0.144322
$393$	3.11451e37	0.749372
$394$	2.79165e37	0.647390
$395$	−4.57974e37	−1.02372
$396$	5.21928e35	0.0112468
$397$	3.51053e37	0.729308	0.364654	−	0.931143i	$-0.381187\pi$
$397$	3.51053e37	0.729308	0.364654	+	0.931143i	$0.381187\pi$
$398$	−7.45275e37	−1.49283
$399$	−1.65350e36	−0.0319373
$400$	−3.66401e37	−0.682476
$401$	6.34278e37	1.13943	0.569713	−	0.821843i	$-0.307054\pi$
$401$	6.34278e37	1.13943	0.569713	+	0.821843i	$0.307054\pi$
$402$	−7.30640e36	−0.126598
$403$	1.89197e37	0.316221
$404$	−5.30268e34	−0.000855000 0
$405$	−9.30587e36	−0.144764
$406$	1.41394e37	0.212228
$407$	−2.13939e38	−3.09864
$408$	−2.79982e37	−0.391344
$409$	4.43562e37	0.598365	0.299183	−	0.954196i	$-0.403286\pi$
$409$	4.43562e37	0.598365	0.299183	+	0.954196i	$0.403286\pi$
$410$	−1.08867e38	−1.41752
$411$	−1.86444e37	−0.234338
$412$	1.60720e36	0.0195012
$413$	−5.40894e37	−0.633631
$414$	1.89003e37	0.213778
$415$	1.76736e38	1.93031
$416$	−1.44374e36	−0.0152278
$417$	7.03315e37	0.716435
$418$	−2.35762e37	−0.231963
$419$	6.85053e37	0.651060	0.325530	−	0.945532i	$-0.394457\pi$
$419$	6.85053e37	0.651060	0.325530	+	0.945532i	$0.394457\pi$
$420$	−6.52267e35	−0.00598840
$421$	1.20241e38	1.06651	0.533253	−	0.845956i	$-0.320969\pi$
$421$	1.20241e38	1.06651	0.533253	+	0.845956i	$0.320969\pi$
$422$	−1.38330e38	−1.18545
$423$	2.41170e37	0.199705
$424$	1.97777e38	1.58260
$425$	6.05143e37	0.467970
$426$	−9.01355e37	−0.673684
$427$	−3.50886e37	−0.253490
$428$	−4.24156e36	−0.0296204
$429$	4.95294e37	0.334374
$430$	2.37963e38	1.55316
$431$	7.06433e37	0.445811	0.222905	−	0.974840i	$-0.428446\pi$
$431$	7.06433e37	0.445811	0.222905	+	0.974840i	$0.428446\pi$
$432$	−3.08596e37	−0.188311
$433$	−2.69350e37	−0.158944	−0.0794718	−	0.996837i	$-0.525323\pi$
$433$	−2.69350e37	−0.158944	−0.0794718	+	0.996837i	$0.525323\pi$
$434$	5.73139e37	0.327083
$435$	7.73409e37	0.426889
$436$	−1.47705e36	−0.00788574
$437$	1.83695e37	0.0948671
$438$	1.05937e38	0.529265
$439$	4.13142e37	0.199693	0.0998466	−	0.995003i	$-0.468165\pi$
$439$	4.13142e37	0.199693	0.0998466	+	0.995003i	$0.468165\pi$
$440$	−4.50846e38	−2.10846
$441$	1.05230e37	0.0476190
$442$	−5.48087e37	−0.240009
$443$	−1.02172e38	−0.432989	−0.216495	−	0.976284i	$-0.569462\pi$
$443$	−1.02172e38	−0.432989	−0.216495	+	0.976284i	$0.569462\pi$
$444$	−5.73520e36	−0.0235232
$445$	4.76472e38	1.89155
$446$	2.89076e38	1.11085
$447$	−1.89149e38	−0.703633
$448$	−1.07066e38	−0.385587
$449$	1.73220e38	0.603985	0.301993	−	0.953310i	$-0.402348\pi$
$449$	1.73220e38	0.603985	0.301993	+	0.953310i	$0.402348\pi$
$450$	6.81344e37	0.230030
$451$	−5.38819e38	−1.76150
$452$	2.88919e36	0.00914679
$453$	2.00833e38	0.615761
$454$	3.96131e38	1.17633
$455$	−6.18982e37	−0.178038
$456$	−3.06385e37	−0.0853645
$457$	−1.74195e36	−0.00470165	−0.00235083	−	0.999997i	$-0.500748\pi$
$457$	−1.74195e36	−0.00470165	−0.00235083	+	0.999997i	$0.500748\pi$
$458$	−3.90116e38	−1.02010
$459$	5.09673e37	0.129124
$460$	7.24631e36	0.0177880
$461$	−7.11796e38	−1.69314	−0.846569	−	0.532279i	$-0.821336\pi$
$461$	−7.11796e38	−1.69314	−0.846569	+	0.532279i	$0.821336\pi$
$462$	1.50041e38	0.345860
$463$	2.40727e37	0.0537776	0.0268888	−	0.999638i	$-0.491440\pi$
$463$	2.40727e37	0.0537776	0.0268888	+	0.999638i	$0.491440\pi$
$464$	2.56473e38	0.555305
$465$	3.13501e38	0.657917
$466$	3.97913e38	0.809454
$467$	−3.78745e38	−0.746882	−0.373441	−	0.927654i	$-0.621822\pi$
$467$	−3.78745e38	−0.746882	−0.373441	+	0.927654i	$0.621822\pi$
$468$	1.32777e36	0.00253839
$469$	4.51925e37	0.0837645
$470$	−4.29742e38	−0.772304
$471$	1.04421e38	0.181963
$472$	−1.00225e39	−1.69362
$473$	1.17776e39	1.93006
$474$	2.82413e38	0.448847
$475$	6.62208e37	0.102079
$476$	3.57240e36	0.00534145
$477$	−3.60028e38	−0.522180
$478$	8.47126e38	1.19191
$479$	−3.47499e38	−0.474338	−0.237169	−	0.971468i	$-0.576220\pi$
$479$	−3.47499e38	−0.474338	−0.237169	+	0.971468i	$0.576220\pi$
$480$	−2.39230e37	−0.0316823
$481$	−5.44254e38	−0.699355
$482$	4.28175e38	0.533875
$483$	−1.16905e38	−0.141448
$484$	−2.80921e37	−0.0329857
$485$	2.81529e38	0.320824
$486$	5.73852e37	0.0634708
$487$	8.36238e38	0.897760	0.448880	−	0.893592i	$-0.351823\pi$
$487$	8.36238e38	0.897760	0.448880	+	0.893592i	$0.351823\pi$
$488$	−6.50172e38	−0.677549
$489$	−1.26927e38	−0.128403
$490$	−1.87510e38	−0.184154
$491$	1.30990e39	1.24898	0.624491	−	0.781032i	$-0.285307\pi$
$491$	1.30990e39	1.24898	0.624491	+	0.781032i	$0.285307\pi$
$492$	−1.44445e37	−0.0133724
$493$	−4.23588e38	−0.380770
$494$	−5.99772e37	−0.0523535
$495$	8.20709e38	0.695687
$496$	1.03961e39	0.855831
$497$	5.57517e38	0.445749
$498$	−1.08985e39	−0.846333
$499$	4.91650e38	0.370850	0.185425	−	0.982658i	$-0.440634\pi$
$499$	4.91650e38	0.370850	0.185425	+	0.982658i	$0.440634\pi$
$500$	−1.13304e37	−0.00830196
$501$	3.75512e38	0.267286
$502$	−1.50496e39	−1.04069
$503$	−1.73535e39	−1.16587	−0.582937	−	0.812517i	$-0.698097\pi$
$503$	−1.73535e39	−1.16587	−0.582937	+	0.812517i	$0.698097\pi$
$504$	1.94986e38	0.127280
$505$	−8.33823e37	−0.0528870
$506$	−1.66687e39	−1.02735
$507$	−8.37949e38	−0.501883
$508$	−2.97413e37	−0.0173115
$509$	5.65466e38	0.319889	0.159944	−	0.987126i	$-0.448869\pi$
$509$	5.65466e38	0.319889	0.159944	+	0.987126i	$0.448869\pi$
$510$	−9.08187e38	−0.499353
$511$	−6.55255e38	−0.350193
$512$	−1.98217e39	−1.02974
$513$	5.57735e37	0.0281661
$514$	−3.73002e39	−1.83124
$515$	2.52726e39	1.20627
$516$	3.15731e37	0.0146520
$517$	−2.12694e39	−0.959715
$518$	−1.64872e39	−0.723379
$519$	−1.35457e38	−0.0577930
$520$	−1.14694e39	−0.475874
$521$	1.50324e39	0.606569	0.303284	−	0.952900i	$-0.401917\pi$
$521$	1.50324e39	0.606569	0.303284	+	0.952900i	$0.401917\pi$
$522$	−4.76927e38	−0.187167
$523$	1.90914e39	0.728725	0.364362	−	0.931257i	$-0.381287\pi$
$523$	1.90914e39	0.728725	0.364362	+	0.931257i	$0.381287\pi$
$524$	−7.36344e37	−0.0273387
$525$	−4.21434e38	−0.152202
$526$	−3.84723e39	−1.35162
$527$	−1.71701e39	−0.586840
$528$	2.72159e39	0.904962
$529$	−1.79232e39	−0.579839
$530$	6.41535e39	2.01939
$531$	1.82446e39	0.558810
$532$	3.90928e36	0.00116514
$533$	−1.37074e39	−0.397567
$534$	−2.93819e39	−0.829340
$535$	−6.66967e39	−1.83221
$536$	8.37391e38	0.223892
$537$	3.41916e39	0.889799
$538$	−3.16935e39	−0.802837
$539$	−9.28052e38	−0.228842
$540$	2.20013e37	0.00528127
$541$	4.80418e39	1.12269	0.561343	−	0.827583i	$-0.310285\pi$
$541$	4.80418e39	1.12269	0.561343	+	0.827583i	$0.310285\pi$
$542$	8.26589e39	1.88061
$543$	1.14533e39	0.253707
$544$	1.31024e38	0.0282595
$545$	−2.32260e39	−0.487781
$546$	3.81699e38	0.0780599
$547$	7.37917e39	1.46957	0.734787	−	0.678298i	$-0.237282\pi$
$547$	7.37917e39	1.46957	0.734787	+	0.678298i	$0.237282\pi$
$548$	4.40798e37	0.00854913
$549$	1.18355e39	0.223558
$550$	−6.00895e39	−1.10545
$551$	−4.63532e38	−0.0830581
$552$	−2.16618e39	−0.378074
$553$	−1.74681e39	−0.296983
$554$	3.40362e39	0.563701
$555$	−9.01835e39	−1.45505
$556$	−1.66280e38	−0.0261370
$557$	9.54010e39	1.46101	0.730504	−	0.682909i	$-0.239285\pi$
$557$	9.54010e39	1.46101	0.730504	+	0.682909i	$0.239285\pi$
$558$	−1.93322e39	−0.288461
$559$	2.99619e39	0.435611
$560$	−3.40124e39	−0.481849
$561$	−4.49493e39	−0.620529
$562$	6.46840e39	0.870203
$563$	1.21915e40	1.59839	0.799197	−	0.601070i	$-0.205259\pi$
$563$	1.21915e40	1.59839	0.799197	+	0.601070i	$0.205259\pi$
$564$	−5.70183e37	−0.00728563
$565$	4.54312e39	0.565785
$566$	5.62104e39	0.682304
$567$	−3.54946e38	−0.0419961
$568$	1.03305e40	1.19143
$569$	1.59342e40	1.79144	0.895720	−	0.444618i	$-0.146660\pi$
$569$	1.59342e40	1.79144	0.895720	+	0.444618i	$0.146660\pi$
$570$	−9.93830e38	−0.108925
$571$	6.51267e39	0.695882	0.347941	−	0.937516i	$-0.386881\pi$
$571$	6.51267e39	0.695882	0.347941	+	0.937516i	$0.386881\pi$
$572$	−1.17099e38	−0.0121987
$573$	−3.03628e39	−0.308389
$574$	−4.15241e39	−0.411224
$575$	4.68188e39	0.452102
$576$	3.61140e39	0.340055
$577$	6.50356e39	0.597175	0.298588	−	0.954382i	$-0.403484\pi$
$577$	6.50356e39	0.597175	0.298588	+	0.954382i	$0.403484\pi$
$578$	−6.07516e39	−0.544007
$579$	−7.36263e39	−0.642975
$580$	−1.82852e38	−0.0155738
$581$	6.74108e39	0.559984
$582$	−1.73606e39	−0.140664
$583$	3.17518e40	2.50942
$584$	−1.21415e40	−0.936023
$585$	2.08786e39	0.157015
$586$	−1.74562e40	−1.28066
$587$	4.99604e39	0.357580	0.178790	−	0.983887i	$-0.442782\pi$
$587$	4.99604e39	0.357580	0.178790	+	0.983887i	$0.442782\pi$
$588$	−2.48789e37	−0.00173724
$589$	−1.87893e39	−0.128008
$590$	−3.25101e40	−2.16105
$591$	5.82434e39	0.377771
$592$	−2.99061e40	−1.89276
$593$	2.90426e40	1.79367	0.896835	−	0.442365i	$-0.145860\pi$
$593$	2.90426e40	1.79367	0.896835	+	0.442365i	$0.145860\pi$
$594$	−5.06095e39	−0.305020
$595$	5.61743e39	0.330402
$596$	4.47194e38	0.0256700
$597$	−1.55490e40	−0.871111
$598$	−4.24045e39	−0.231870
$599$	−3.96140e39	−0.211427	−0.105713	−	0.994397i	$-0.533713\pi$
$599$	−3.96140e39	−0.211427	−0.105713	+	0.994397i	$0.533713\pi$
$600$	−7.80893e39	−0.406816
$601$	2.09013e40	1.06290	0.531450	−	0.847090i	$-0.321647\pi$
$601$	2.09013e40	1.06290	0.531450	+	0.847090i	$0.321647\pi$
$602$	9.07645e39	0.450575
$603$	−1.52436e39	−0.0738733
$604$	−4.74818e38	−0.0224642
$605$	−4.41735e40	−2.04037
$606$	5.14182e38	0.0231880
$607$	−9.26737e39	−0.408057	−0.204028	−	0.978965i	$-0.565403\pi$
$607$	−9.26737e39	−0.408057	−0.204028	+	0.978965i	$0.565403\pi$
$608$	1.43379e38	0.00616430
$609$	2.94995e39	0.123841
$610$	−2.10898e40	−0.864550
$611$	−5.41087e39	−0.216605
$612$	−1.20499e38	−0.00471071
$613$	−2.48482e39	−0.0948675	−0.0474337	−	0.998874i	$-0.515104\pi$
$613$	−2.48482e39	−0.0948675	−0.0474337	+	0.998874i	$0.515104\pi$
$614$	2.21435e40	0.825665
$615$	−2.27133e40	−0.827163
$616$	−1.71963e40	−0.611666
$617$	−1.58925e40	−0.552149	−0.276075	−	0.961136i	$-0.589034\pi$
$617$	−1.58925e40	−0.552149	−0.276075	+	0.961136i	$0.589034\pi$
$618$	−1.55845e40	−0.528883
$619$	1.93387e40	0.641083	0.320541	−	0.947235i	$-0.396135\pi$
$619$	1.93387e40	0.641083	0.320541	+	0.947235i	$0.396135\pi$
$620$	−7.41191e38	−0.0240022
$621$	3.94325e39	0.124746
$622$	−5.38763e40	−1.66509
$623$	1.81737e40	0.548740
$624$	6.92363e39	0.204248
$625$	−4.20151e40	−1.21100
$626$	2.34770e40	0.661171
$627$	−4.91881e39	−0.135357
$628$	−2.46875e38	−0.00663838
$629$	4.93925e40	1.29786
$630$	6.32480e39	0.162409
$631$	6.55693e40	1.64541	0.822706	−	0.568467i	$-0.192463\pi$
$631$	6.55693e40	1.64541	0.822706	+	0.568467i	$0.192463\pi$
$632$	−3.23675e40	−0.793800
$633$	−2.88603e40	−0.691746
$634$	3.11171e40	0.728961
$635$	−4.67668e40	−1.07083
$636$	8.51192e38	0.0190502
$637$	−2.36093e39	−0.0516490
$638$	4.20614e40	0.899465
$639$	−1.88053e40	−0.393114
$640$	−6.16664e40	−1.26020
$641$	−3.72650e40	−0.744491	−0.372245	−	0.928134i	$-0.621412\pi$
$641$	−3.72650e40	−0.744491	−0.372245	+	0.928134i	$0.621412\pi$
$642$	4.11289e40	0.803322
$643$	7.95138e40	1.51839	0.759195	−	0.650863i	$-0.225593\pi$
$643$	7.95138e40	1.51839	0.759195	+	0.650863i	$0.225593\pi$
$644$	2.76390e38	0.00516033
$645$	4.96473e40	0.906316
$646$	5.44310e39	0.0971571
$647$	7.96018e40	1.38935	0.694674	−	0.719325i	$-0.255549\pi$
$647$	7.96018e40	1.38935	0.694674	+	0.719325i	$0.255549\pi$
$648$	−6.57696e39	−0.112250
$649$	−1.60904e41	−2.68546
$650$	−1.52866e40	−0.249498
$651$	1.19576e40	0.190862
$652$	3.00086e38	0.00468442
$653$	4.50038e39	0.0687081	0.0343541	−	0.999410i	$-0.489063\pi$
$653$	4.50038e39	0.0687081	0.0343541	+	0.999410i	$0.489063\pi$
$654$	1.43225e40	0.213865
$655$	−1.15787e41	−1.69106
$656$	−7.53206e40	−1.07599
$657$	2.21021e40	0.308841
$658$	−1.63913e40	−0.224046
$659$	−1.63629e40	−0.218788	−0.109394	−	0.993998i	$-0.534891\pi$
$659$	−1.63629e40	−0.218788	−0.109394	+	0.993998i	$0.534891\pi$
$660$	−1.94035e39	−0.0253801
$661$	7.00754e40	0.896694	0.448347	−	0.893860i	$-0.352013\pi$
$661$	7.00754e40	0.896694	0.448347	+	0.893860i	$0.352013\pi$
$662$	4.32074e40	0.540900
$663$	−1.14350e40	−0.140052
$664$	1.24908e41	1.49677
$665$	6.14716e39	0.0720711
$666$	5.56122e40	0.637960
$667$	−3.27722e40	−0.367859
$668$	−8.87799e38	−0.00975116
$669$	6.03110e40	0.648213
$670$	2.71627e40	0.285685
$671$	−1.04381e41	−1.07435
$672$	−9.12475e38	−0.00919107
$673$	−1.23231e41	−1.21479	−0.607397	−	0.794398i	$-0.707786\pi$
$673$	−1.23231e41	−1.21479	−0.607397	+	0.794398i	$0.707786\pi$
$674$	1.35973e41	1.31185
$675$	1.42152e40	0.134229
$676$	1.98111e39	0.0183097
$677$	−1.34433e41	−1.21611	−0.608053	−	0.793897i	$-0.708049\pi$
$677$	−1.34433e41	−1.21611	−0.608053	+	0.793897i	$0.708049\pi$
$678$	−2.80154e40	−0.248066
$679$	1.07381e40	0.0930714
$680$	1.04088e41	0.883122
$681$	8.26465e40	0.686422
$682$	1.70496e41	1.38625
$683$	1.74375e40	0.138798	0.0693990	−	0.997589i	$-0.477892\pi$
$683$	1.74375e40	0.138798	0.0693990	+	0.997589i	$0.477892\pi$
$684$	−1.31862e38	−0.00102756
$685$	6.93136e40	0.528817
$686$	−7.15204e39	−0.0534233
$687$	−8.13915e40	−0.595259
$688$	1.64637e41	1.17895
$689$	8.07756e40	0.566371
$690$	−7.02648e40	−0.482421
$691$	−1.54766e41	−1.04051	−0.520253	−	0.854012i	$-0.674162\pi$
$691$	−1.54766e41	−1.04051	−0.520253	+	0.854012i	$0.674162\pi$
$692$	3.20253e38	0.00210841
$693$	3.13036e40	0.201819
$694$	2.20720e41	1.39357
$695$	−2.61468e41	−1.61674
$696$	5.46609e40	0.331011
$697$	1.24398e41	0.737801
$698$	4.94350e39	0.0287165
$699$	8.30182e40	0.472340
$700$	9.96370e38	0.00555263
$701$	1.41187e41	0.770699	0.385349	−	0.922771i	$-0.374081\pi$
$701$	1.41187e41	0.770699	0.385349	+	0.922771i	$0.374081\pi$
$702$	−1.28749e40	−0.0688423
$703$	5.40503e40	0.283104
$704$	−3.18499e41	−1.63420
$705$	−8.96587e40	−0.450661
$706$	−2.24666e41	−1.10629
$707$	−3.18038e39	−0.0153426
$708$	−4.31346e39	−0.0203865
$709$	8.67698e40	0.401789	0.200895	−	0.979613i	$-0.435615\pi$
$709$	8.67698e40	0.401789	0.200895	+	0.979613i	$0.435615\pi$
$710$	3.35093e41	1.52026
$711$	5.89209e40	0.261915
$712$	3.36748e41	1.46671
$713$	−1.32842e41	−0.566941
$714$	−3.46403e40	−0.144863
$715$	−1.84133e41	−0.754562
$716$	−8.08370e39	−0.0324617
$717$	1.76739e41	0.695513
$718$	−3.96287e41	−1.52829
$719$	−2.82012e41	−1.06586	−0.532929	−	0.846160i	$-0.678909\pi$
$719$	−2.82012e41	−1.06586	−0.532929	+	0.846160i	$0.678909\pi$
$720$	1.14725e41	0.424951
$721$	9.63952e40	0.349940
$722$	−2.72122e41	−0.968219
$723$	8.93319e40	0.311531
$724$	−2.70782e39	−0.00925574
$725$	−1.18142e41	−0.395825
$726$	2.72399e41	0.894590
$727$	−1.15837e41	−0.372905	−0.186452	−	0.982464i	$-0.559699\pi$
$727$	−1.15837e41	−0.372905	−0.186452	+	0.982464i	$0.559699\pi$
$728$	−4.37468e40	−0.138051
$729$	1.19725e40	0.0370370
$730$	−3.93838e41	−1.19436
$731$	−2.71913e41	−0.808402
$732$	−2.79820e39	−0.00815584
$733$	1.37397e41	0.392618	0.196309	−	0.980542i	$-0.437104\pi$
$733$	1.37397e41	0.392618	0.196309	+	0.980542i	$0.437104\pi$
$734$	2.11732e41	0.593190
$735$	−3.91210e40	−0.107459
$736$	1.01371e40	0.0273013
$737$	1.34438e41	0.355011
$738$	1.40063e41	0.362665
$739$	1.70692e41	0.433381	0.216690	−	0.976240i	$-0.430474\pi$
$739$	1.70692e41	0.433381	0.216690	+	0.976240i	$0.430474\pi$
$740$	2.13215e40	0.0530833
$741$	−1.25133e40	−0.0305497
$742$	2.44696e41	0.585827
$743$	5.49247e41	1.28952	0.644762	−	0.764383i	$-0.276956\pi$
$743$	5.49247e41	1.28952	0.644762	+	0.764383i	$0.276956\pi$
$744$	2.21568e41	0.510152
$745$	7.03193e41	1.58785
$746$	2.98896e41	0.661922
$747$	−2.27380e41	−0.493859
$748$	1.06271e40	0.0226382
$749$	−2.54396e41	−0.531525
$750$	1.09867e41	0.225153
$751$	−1.43221e41	−0.287891	−0.143946	−	0.989586i	$-0.545979\pi$
$751$	−1.43221e41	−0.287891	−0.143946	+	0.989586i	$0.545979\pi$
$752$	−2.97321e41	−0.586229
$753$	−3.13986e41	−0.607272
$754$	1.07003e41	0.203007
$755$	−7.46630e41	−1.38955
$756$	8.39178e38	0.00153210
$757$	1.06729e42	1.91157	0.955786	−	0.294064i	$-0.0950080\pi$
$757$	1.06729e42	1.91157	0.955786	+	0.294064i	$0.0950080\pi$
$758$	−9.53570e41	−1.67552
$759$	−3.47765e41	−0.599488
$760$	1.13903e41	0.192637
$761$	−4.38311e41	−0.727285	−0.363643	−	0.931538i	$-0.618467\pi$
$761$	−4.38311e41	−0.727285	−0.363643	+	0.931538i	$0.618467\pi$
$762$	2.88390e41	0.469498
$763$	−8.85891e40	−0.141506
$764$	7.17848e39	0.0112507
$765$	−1.89479e41	−0.291387
$766$	−9.97793e41	−1.50565
$767$	−4.09334e41	−0.606102
$768$	−2.50971e40	−0.0364658
$769$	−6.98506e41	−0.995952	−0.497976	−	0.867191i	$-0.665923\pi$
$769$	−6.98506e41	−0.995952	−0.497976	+	0.867191i	$0.665923\pi$
$770$	−5.57800e41	−0.780483
$771$	−7.78210e41	−1.06858
$772$	1.74070e40	0.0234570
$773$	−7.24450e41	−0.958089	−0.479044	−	0.877791i	$-0.659017\pi$
$773$	−7.24450e41	−0.958089	−0.479044	+	0.877791i	$0.659017\pi$
$774$	−3.06153e41	−0.397369
$775$	−4.78888e41	−0.610042
$776$	1.98971e41	0.248768
$777$	−3.43980e41	−0.422112
$778$	1.41292e42	1.70182
$779$	1.36129e41	0.160938
$780$	−4.93619e39	−0.00572822
$781$	1.65849e42	1.88918
$782$	3.84833e41	0.430303
$783$	−9.95033e40	−0.109217
$784$	−1.29731e41	−0.139785
$785$	−3.88200e41	−0.410625
$786$	7.14006e41	0.741438
$787$	−4.37591e41	−0.446102	−0.223051	−	0.974807i	$-0.571602\pi$
$787$	−4.37591e41	−0.446102	−0.223051	+	0.974807i	$0.571602\pi$
$788$	−1.37701e40	−0.0137818
$789$	−8.02663e41	−0.788709
$790$	−1.04991e42	−1.01289
$791$	1.73285e41	0.164135
$792$	5.80039e41	0.539438
$793$	−2.65541e41	−0.242477
$794$	8.04795e41	0.721586
$795$	1.33846e42	1.17837
$796$	3.67614e40	0.0317799
$797$	−4.56823e40	−0.0387795	−0.0193898	−	0.999812i	$-0.506172\pi$
$797$	−4.56823e40	−0.0387795	−0.0193898	+	0.999812i	$0.506172\pi$
$798$	−3.79069e40	−0.0315992
$799$	4.91051e41	0.401974
$800$	3.65435e40	0.0293768
$801$	−6.13008e41	−0.483943
$802$	1.45409e42	1.12736
$803$	−1.94924e42	−1.48419
$804$	3.60396e39	0.00269505
$805$	4.34611e41	0.319198
$806$	4.33736e41	0.312873
$807$	−6.61235e41	−0.468478
$808$	−5.89307e40	−0.0410088
$809$	−3.03868e41	−0.207697	−0.103849	−	0.994593i	$-0.533116\pi$
$809$	−3.03868e41	−0.207697	−0.103849	+	0.994593i	$0.533116\pi$
$810$	−2.13339e41	−0.143231
$811$	1.37306e41	0.0905494	0.0452747	−	0.998975i	$-0.485584\pi$
$811$	1.37306e41	0.0905494	0.0452747	+	0.998975i	$0.485584\pi$
$812$	−6.97438e39	−0.00451797
$813$	1.72455e42	1.09739
$814$	−4.90458e42	−3.06583
$815$	4.71872e41	0.289760
$816$	−6.28339e41	−0.379041
$817$	−2.97554e41	−0.176338
$818$	1.01687e42	0.592030
$819$	7.96354e40	0.0455502
$820$	5.36996e40	0.0301766
$821$	2.53189e42	1.39788	0.698940	−	0.715180i	$-0.253656\pi$
$821$	2.53189e42	1.39788	0.698940	+	0.715180i	$0.253656\pi$
$822$	−4.27426e41	−0.231857
$823$	9.69305e41	0.516610	0.258305	−	0.966063i	$-0.416836\pi$
$823$	9.69305e41	0.516610	0.258305	+	0.966063i	$0.416836\pi$
$824$	1.78615e42	0.935347
$825$	−1.25367e42	−0.645062
$826$	−1.24001e42	−0.626922
$827$	2.28966e42	1.13747	0.568737	−	0.822520i	$-0.307432\pi$
$827$	2.28966e42	1.13747	0.568737	+	0.822520i	$0.307432\pi$
$828$	−9.32277e39	−0.00455098
$829$	3.46482e42	1.66203	0.831017	−	0.556246i	$-0.187759\pi$
$829$	3.46482e42	1.66203	0.831017	+	0.556246i	$0.187759\pi$
$830$	4.05169e42	1.90987
$831$	7.10111e41	0.328936
$832$	−8.10251e41	−0.368834
$833$	2.14261e41	0.0958498
$834$	1.61236e42	0.708850
$835$	−1.39602e42	−0.603169
$836$	1.16292e40	0.00493810
$837$	−4.03336e41	−0.168325
$838$	1.57049e42	0.644166
$839$	−1.22795e42	−0.495029	−0.247515	−	0.968884i	$-0.579614\pi$
$839$	−1.22795e42	−0.495029	−0.247515	+	0.968884i	$0.579614\pi$
$840$	−7.24889e41	−0.287225
$841$	−1.74072e42	−0.677932
$842$	2.75655e42	1.05521
$843$	1.34953e42	0.507788
$844$	6.82326e40	0.0252363
$845$	3.11521e42	1.13257
$846$	5.52886e41	0.197590
$847$	−1.68488e42	−0.591914
$848$	4.43853e42	1.53285
$849$	1.17274e42	0.398144
$850$	1.38730e42	0.463016
$851$	3.82141e42	1.25385
$852$	4.44603e40	0.0143416
$853$	−4.03848e42	−1.28073	−0.640364	−	0.768071i	$-0.721217\pi$
$853$	−4.03848e42	−1.28073	−0.640364	+	0.768071i	$0.721217\pi$
$854$	−8.04411e41	−0.250807
$855$	−2.07347e41	−0.0635607
$856$	−4.71381e42	−1.42070
$857$	−2.24849e42	−0.666298	−0.333149	−	0.942874i	$-0.608111\pi$
$857$	−2.24849e42	−0.666298	−0.333149	+	0.942874i	$0.608111\pi$
$858$	1.13547e42	0.330834
$859$	3.52741e42	1.01054	0.505272	−	0.862960i	$-0.331392\pi$
$859$	3.52741e42	1.01054	0.505272	+	0.862960i	$0.331392\pi$
$860$	−1.17378e41	−0.0330643
$861$	−8.66335e41	−0.239961
$862$	1.61951e42	0.441090
$863$	−4.18792e41	−0.112161	−0.0560805	−	0.998426i	$-0.517860\pi$
$863$	−4.18792e41	−0.112161	−0.0560805	+	0.998426i	$0.517860\pi$
$864$	3.07782e40	0.00810577
$865$	5.03583e41	0.130418
$866$	−6.17490e41	−0.157261
$867$	−1.26749e42	−0.317443
$868$	−2.82707e40	−0.00696306
$869$	−5.19638e42	−1.25868
$870$	1.77305e42	0.422369
$871$	3.42005e41	0.0801252
$872$	−1.64151e42	−0.378228
$873$	−3.62202e41	−0.0820813
$874$	4.21123e41	0.0938627
$875$	−6.79563e41	−0.148975
$876$	−5.22546e40	−0.0112672
$877$	7.97498e42	1.69136	0.845679	−	0.533692i	$-0.179196\pi$
$877$	7.97498e42	1.69136	0.845679	+	0.533692i	$0.179196\pi$
$878$	9.47134e41	0.197579
$879$	−3.64196e42	−0.747303
$880$	−1.01179e43	−2.04217
$881$	−2.13736e42	−0.424353	−0.212177	−	0.977231i	$-0.568055\pi$
$881$	−2.13736e42	−0.424353	−0.212177	+	0.977231i	$0.568055\pi$
$882$	2.41242e41	0.0471149
$883$	−9.39442e42	−1.80484	−0.902422	−	0.430852i	$-0.858213\pi$
$883$	−9.39442e42	−1.80484	−0.902422	+	0.430852i	$0.858213\pi$
$884$	2.70350e40	0.00510938
$885$	−6.78272e42	−1.26103
$886$	−2.34231e42	−0.428405
$887$	−3.75410e42	−0.675481	−0.337740	−	0.941239i	$-0.609663\pi$
$887$	−3.75410e42	−0.675481	−0.337740	+	0.941239i	$0.609663\pi$
$888$	−6.37375e42	−1.12825
$889$	−1.78379e42	−0.310647
$890$	1.09232e43	1.87152
$891$	−1.05589e42	−0.177988
$892$	−1.42590e41	−0.0236482
$893$	5.37358e41	0.0876834
$894$	−4.33628e42	−0.696183
$895$	−1.27112e43	−2.00796
$896$	−2.35209e42	−0.365585
$897$	−8.84703e41	−0.135303
$898$	3.97110e42	0.597590
$899$	3.35212e42	0.496368
$900$	−3.36080e40	−0.00489696
$901$	−7.33060e42	−1.05107
$902$	−1.23525e43	−1.74285
$903$	1.89366e42	0.262923
$904$	3.21086e42	0.438712
$905$	−4.25793e42	−0.572525
$906$	4.60414e42	0.609241
$907$	9.98580e42	1.30040	0.650201	−	0.759763i	$-0.274685\pi$
$907$	9.98580e42	1.30040	0.650201	+	0.759763i	$0.274685\pi$
$908$	−1.95396e41	−0.0250421
$909$	1.07276e41	0.0135309
$910$	−1.41903e42	−0.176153
$911$	1.53555e43	1.87607	0.938033	−	0.346546i	$-0.112645\pi$
$911$	1.53555e43	1.87607	0.938033	+	0.346546i	$0.112645\pi$
$912$	−6.87592e41	−0.0826809
$913$	2.00532e43	2.37333
$914$	−3.99345e40	−0.00465187
$915$	−4.40005e42	−0.504489
$916$	1.92429e41	0.0217163
$917$	−4.41636e42	−0.490579
$918$	1.16843e42	0.127757
$919$	−4.09627e42	−0.440873	−0.220437	−	0.975401i	$-0.570748\pi$
$919$	−4.09627e42	−0.440873	−0.220437	+	0.975401i	$0.570748\pi$
$920$	8.05310e42	0.853178
$921$	4.61988e42	0.481799
$922$	−1.63180e43	−1.67521
$923$	4.21915e42	0.426383
$924$	−7.40092e40	−0.00736279
$925$	1.37760e43	1.34917
$926$	5.51872e41	0.0532082
$927$	−3.25146e42	−0.308618
$928$	−2.55797e41	−0.0239029
$929$	−1.85868e43	−1.70993	−0.854964	−	0.518688i	$-0.826421\pi$
$929$	−1.85868e43	−1.70993	−0.854964	+	0.518688i	$0.826421\pi$
$930$	7.18706e42	0.650952
$931$	2.34466e41	0.0209079
$932$	−1.96275e41	−0.0172319
$933$	−1.12404e43	−0.971626
$934$	−8.68279e42	−0.738975
$935$	1.67106e43	1.40031
$936$	1.47560e42	0.121750
$937$	−7.30717e42	−0.593643	−0.296821	−	0.954933i	$-0.595927\pi$
$937$	−7.30717e42	−0.593643	−0.296821	+	0.954933i	$0.595927\pi$
$938$	1.03604e42	0.0828776
$939$	4.89809e42	0.385812
$940$	2.11974e41	0.0164411
$941$	2.00780e43	1.53345	0.766727	−	0.641974i	$-0.221884\pi$
$941$	2.00780e43	1.53345	0.766727	+	0.641974i	$0.221884\pi$
$942$	2.39386e42	0.180036
$943$	9.62448e42	0.712784
$944$	−2.24925e43	−1.64038
$945$	1.31957e42	0.0947700
$946$	2.70004e43	1.90963
$947$	−1.45577e43	−1.01395	−0.506976	−	0.861960i	$-0.669237\pi$
$947$	−1.45577e43	−1.01395	−0.506976	+	0.861960i	$0.669237\pi$
$948$	−1.39303e41	−0.00955519
$949$	−4.95880e42	−0.334978
$950$	1.51812e42	0.100998
$951$	6.49208e42	0.425369
$952$	3.97014e42	0.256195
$953$	3.92888e42	0.249702	0.124851	−	0.992176i	$-0.460155\pi$
$953$	3.92888e42	0.249702	0.124851	+	0.992176i	$0.460155\pi$
$954$	−8.25370e42	−0.516651
$955$	1.12878e43	0.695924
$956$	−4.17854e41	−0.0253738
$957$	8.77545e42	0.524863
$958$	−7.96646e42	−0.469316
$959$	2.64377e42	0.153410
$960$	−1.34259e43	−0.767383
$961$	−4.17407e42	−0.235002
$962$	−1.24771e43	−0.691951
$963$	8.58089e42	0.468761
$964$	−2.11202e41	−0.0113653
$965$	2.73717e43	1.45096
$966$	−2.68006e42	−0.139951
$967$	2.50390e43	1.28805	0.644026	−	0.765004i	$-0.277263\pi$
$967$	2.50390e43	1.28805	0.644026	+	0.765004i	$0.277263\pi$
$968$	−3.12198e43	−1.58211
$969$	1.13562e42	0.0566939
$970$	6.45409e42	0.317428
$971$	−2.48241e43	−1.20280	−0.601401	−	0.798948i	$-0.705390\pi$
$971$	−2.48241e43	−1.20280	−0.601401	+	0.798948i	$0.705390\pi$
$972$	−2.83059e40	−0.00135119
$973$	−9.97298e42	−0.469017
$974$	1.91709e43	0.888255
$975$	−3.18930e42	−0.145589
$976$	−1.45912e43	−0.656249
$977$	−6.12721e42	−0.271514	−0.135757	−	0.990742i	$-0.543347\pi$
$977$	−6.12721e42	−0.271514	−0.135757	+	0.990742i	$0.543347\pi$
$978$	−2.90983e42	−0.127044
$979$	5.40627e43	2.32567
$980$	9.24912e40	0.00392033
$981$	2.98815e42	0.124796
$982$	3.00296e43	1.23576
$983$	7.69051e42	0.311838	0.155919	−	0.987770i	$-0.450166\pi$
$983$	7.69051e42	0.311838	0.155919	+	0.987770i	$0.450166\pi$
$984$	−1.60527e43	−0.641386
$985$	−2.16529e43	−0.852492
$986$	−9.71081e42	−0.376739
$987$	−3.41978e42	−0.130737
$988$	2.95844e40	0.00111452
$989$	−2.10374e43	−0.780991
$990$	1.88149e43	0.688321
$991$	−3.05338e43	−1.10081	−0.550405	−	0.834898i	$-0.685527\pi$
$991$	−3.05338e43	−1.10081	−0.550405	+	0.834898i	$0.685527\pi$
$992$	−1.03687e42	−0.0368389
$993$	9.01453e42	0.315631
$994$	1.27812e43	0.441030
$995$	5.78057e43	1.96579
$996$	5.37580e41	0.0180170
$997$	−2.55101e43	−0.842622	−0.421311	−	0.906916i	$-0.638430\pi$
$997$	−2.55101e43	−0.842622	−0.421311	+	0.906916i	$0.638430\pi$
$998$	1.12712e43	0.366924
$999$	1.16026e43	0.372268

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.a.d.1.6	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.a.d.1.6	✓	8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 30 \)
Character orbit:	\([\chi]\)	\(=\)	21.a (trivial)

\(f(q)\)	\(=\)	\(q+22925.2 q^{2} +4.78297e6 q^{3} -1.13081e7 q^{4} -1.77814e10 q^{5} +1.09650e11 q^{6} -6.78223e11 q^{7} -1.25671e13 q^{8} +2.28768e13 q^{9} +O(q^{10})\)	\(q+22925.2 q^{2} +4.78297e6 q^{3} -1.13081e7 q^{4} -1.77814e10 q^{5} +1.09650e11 q^{6} -6.78223e11 q^{7} -1.25671e13 q^{8} +2.28768e13 q^{9} -4.07642e14 q^{10} -2.01756e15 q^{11} -5.40862e13 q^{12} -5.13262e15 q^{13} -1.55484e16 q^{14} -8.50481e16 q^{15} -2.82032e17 q^{16} +4.65799e17 q^{17} +5.24454e17 q^{18} +5.09724e17 q^{19} +2.01074e17 q^{20} -3.24392e18 q^{21} -4.62529e19 q^{22} +3.60381e19 q^{23} -6.01080e19 q^{24} +1.29915e20 q^{25} -1.17666e20 q^{26} +1.09419e20 q^{27} +7.66940e18 q^{28} -9.09379e20 q^{29} -1.94974e21 q^{30} -3.68617e21 q^{31} +2.81288e20 q^{32} -9.64994e21 q^{33} +1.06785e22 q^{34} +1.20598e22 q^{35} -2.58692e20 q^{36} +1.06038e23 q^{37} +1.16855e22 q^{38} -2.45491e22 q^{39} +2.23461e23 q^{40} +2.67064e23 q^{41} -7.43674e22 q^{42} -5.83755e23 q^{43} +2.28147e22 q^{44} -4.06782e23 q^{45} +8.26178e23 q^{46} +1.05421e24 q^{47} -1.34895e24 q^{48} +4.59987e23 q^{49} +2.97832e24 q^{50} +2.22790e24 q^{51} +5.80400e22 q^{52} -1.57377e25 q^{53} +2.50845e24 q^{54} +3.58752e25 q^{55} +8.52329e24 q^{56} +2.43800e24 q^{57} -2.08476e25 q^{58} +7.97516e25 q^{59} +9.61730e23 q^{60} +5.17361e25 q^{61} -8.45059e25 q^{62} -1.55156e25 q^{63} +1.57863e26 q^{64} +9.12653e25 q^{65} -2.21226e26 q^{66} -6.66336e25 q^{67} -5.26729e24 q^{68} +1.72369e26 q^{69} +2.76472e26 q^{70} -8.22026e26 q^{71} -2.87495e26 q^{72} +9.66135e26 q^{73} +2.43094e27 q^{74} +6.21379e26 q^{75} -5.76400e24 q^{76} +1.36836e27 q^{77} -5.62793e26 q^{78} +2.57557e27 q^{79} +5.01493e27 q^{80} +5.23348e26 q^{81} +6.12249e27 q^{82} -9.93933e27 q^{83} +3.66825e25 q^{84} -8.28258e27 q^{85} -1.33827e28 q^{86} -4.34953e27 q^{87} +2.53549e28 q^{88} -2.67960e28 q^{89} -9.32555e27 q^{90} +3.48106e27 q^{91} -4.07521e26 q^{92} -1.76308e28 q^{93} +2.41680e28 q^{94} -9.06363e27 q^{95} +1.34539e27 q^{96} -1.58327e28 q^{97} +1.05453e28 q^{98} -4.61554e28 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 19461 q^{2} + 38263752 q^{3} + 1467008653 q^{4} - 8498112672 q^{5} - 93081359709 q^{6} - 5425784582792 q^{7} - 16689415716987 q^{8} + 183014339639688 q^{9}+O(q^{10}) \) 8 * q - 19461 * q^2 + 38263752 * q^3 + 1467008653 * q^4 - 8498112672 * q^5 - 93081359709 * q^6 - 5425784582792 * q^7 - 16689415716987 * q^8 + 183014339639688 * q^9	\( 8 q - 19461 q^{2} + 38263752 q^{3} + 1467008653 q^{4} - 8498112672 q^{5} - 93081359709 q^{6} - 5425784582792 q^{7} - 16689415716987 q^{8} + 183014339639688 q^{9} + 636942348029770 q^{10} + 395708686257744 q^{11} + 70\!\cdots\!57 q^{12}+ \cdots + 90\!\cdots\!84 q^{99}+O(q^{100}) \) 8 * q - 19461 * q^2 + 38263752 * q^3 + 1467008653 * q^4 - 8498112672 * q^5 - 93081359709 * q^6 - 5425784582792 * q^7 - 16689415716987 * q^8 + 183014339639688 * q^9 + 636942348029770 * q^10 + 395708686257744 * q^11 + 7016656910030757 * q^12 + 22809319742321168 * q^13 + 13198899220714389 * q^14 - 40646209468683168 * q^15 - 529929838419631103 * q^16 - 875764906948588224 * q^17 - 445205257965996021 * q^18 + 1426892827775457824 * q^19 - 28899057412113817626 * q^20 - 25951359460172069448 * q^21 - 5186094623833295684 * q^22 + 31571815389865907376 * q^23 - 79824958002461594403 * q^24 + 484933790864619664792 * q^25 + 871531917323138656458 * q^26 + 875351913052098873672 * q^27 - 994959116533732362397 * q^28 + 403819311812853278064 * q^29 + 3046475505413600987130 * q^30 + 6056711864477051297664 * q^31 + 495732442702744435125 * q^32 + 1892662379401515561936 * q^33 + 27608278255426542993054 * q^34 + 5763616089820866042528 * q^35 + 33560452484312899777533 * q^36 + 249301086380038228224144 * q^37 + 232307666312718559908396 * q^38 + 109096269238610134587792 * q^39 + 222254097261275058064470 * q^40 - 118485395827236320088480 * q^41 + 63129925806801080440941 * q^42 + 955811315548717966687456 * q^43 + 2197776642577416647616228 * q^44 - 194409559856218063365792 * q^45 - 728621547286381001073120 * q^46 + 1724730703353294103329696 * q^47 - 2534637989336104557084807 * q^48 + 3679892292357919687814408 * q^49 + 3315945636459433646107605 * q^50 - 4188756401222982069157056 * q^51 + 7867779844424116360460902 * q^52 + 2121223193154060481519824 * q^53 - 2129402947488362022566349 * q^54 - 7250285279281800197516224 * q^55 + 11319146811629319667785963 * q^56 + 6824784161572353732999456 * q^57 - 14457635242040178152167718 * q^58 + 42196882197868232719878528 * q^59 - 138223295731360614176811594 * q^60 - 101117722940093083661366416 * q^61 + 186299525380851520014926400 * q^62 - 124124547805859742835631112 * q^63 - 578691286566308562959878519 * q^64 - 350548464914993356143283200 * q^65 - 24804929816861314424405796 * q^66 - 76630272082508454921299392 * q^67 - 980499057011951020658835918 * q^68 + 151007014283451549136279344 * q^69 - 431988996508407810330714730 * q^70 - 1078132490609618557101526320 * q^71 - 381800299552075729720122507 * q^72 - 247553894478620130982212048 * q^73 - 75659580621831989514366414 * q^74 + 2319423288757959053490527448 * q^75 + 3177709658750992797170923828 * q^76 - 268378761146767994102392656 * q^77 + 4168510143067135176540263802 * q^78 + 2428644145165587926516228512 * q^79 + 1621802770176465933634958622 * q^80 + 4186781064218884297708092168 * q^81 + 31867674822051710989797094358 * q^82 - 12963768045528470934634770144 * q^83 - 4758858610648229343641616693 * q^84 + 8949893682441356527904874624 * q^85 + 19361425567422560435180442756 * q^86 + 1931455250002211030528492016 * q^87 + 36039744054684227265332026212 * q^88 + 19612047814410613791670511136 * q^89 + 14571197901652585699812188970 * q^90 - 15469806925232423432818767632 * q^91 - 33565399363855362024322385952 * q^92 + 28969065089725937568136684416 * q^93 + 23248231331633687228175413280 * q^94 - 70429226382314318765891409984 * q^95 + 2371072905741502848125386125 * q^96 - 5439618388643531441097237456 * q^97 - 8951797987697184380569524261 * q^98 + 9052545488143687485757467984 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more