LMFDB - Embedded newform 21.30.a.d.1.4

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			1.4
Root			$-1200.71$ 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)

$f(q)$	$=$	$q-3633.71 q^{2} +4.78297e6 q^{3} -5.23667e8 q^{4} -8.87892e9 q^{5} -1.73799e10 q^{6} -6.78223e11 q^{7} +3.85369e12 q^{8} +2.28768e13 q^{9} +O(q^{10})$	\(q-3633.71 q^{2} +4.78297e6 q^{3} -5.23667e8 q^{4} -8.87892e9 q^{5} -1.73799e10 q^{6} -6.78223e11 q^{7} +3.85369e12 q^{8} +2.28768e13 q^{9} +3.22634e13 q^{10} +3.80677e14 q^{11} -2.50468e15 q^{12} +8.47845e15 q^{13} +2.46447e15 q^{14} -4.24676e16 q^{15} +2.67138e17 q^{16} -9.60505e16 q^{17} -8.31277e16 q^{18} -4.81076e18 q^{19} +4.64960e18 q^{20} -3.24392e18 q^{21} -1.38327e18 q^{22} -6.45279e19 q^{23} +1.84321e19 q^{24} -1.07429e20 q^{25} -3.08082e19 q^{26} +1.09419e20 q^{27} +3.55163e20 q^{28} -2.39423e21 q^{29} +1.54315e20 q^{30} -2.42170e21 q^{31} -3.03964e21 q^{32} +1.82077e21 q^{33} +3.49020e20 q^{34} +6.02189e21 q^{35} -1.19798e22 q^{36} -4.74114e22 q^{37} +1.74809e22 q^{38} +4.05521e22 q^{39} -3.42166e22 q^{40} +3.02869e23 q^{41} +1.17875e22 q^{42} +5.89266e23 q^{43} -1.99348e23 q^{44} -2.03121e23 q^{45} +2.34476e23 q^{46} -7.09088e22 q^{47} +1.27771e24 q^{48} +4.59987e23 q^{49} +3.90367e23 q^{50} -4.59407e23 q^{51} -4.43988e24 q^{52} +1.71244e25 q^{53} -3.97597e23 q^{54} -3.38000e24 q^{55} -2.61366e24 q^{56} -2.30097e25 q^{57} +8.69994e24 q^{58} -6.77447e25 q^{59} +2.22389e25 q^{60} +9.92211e24 q^{61} +8.79977e24 q^{62} -1.55156e25 q^{63} -1.32374e26 q^{64} -7.52794e25 q^{65} -6.61615e24 q^{66} -1.22810e26 q^{67} +5.02985e25 q^{68} -3.08635e26 q^{69} -2.18818e25 q^{70} +4.09491e26 q^{71} +8.81601e25 q^{72} +8.87864e26 q^{73} +1.72279e26 q^{74} -5.13831e26 q^{75} +2.51924e27 q^{76} -2.58184e26 q^{77} -1.47355e26 q^{78} -3.62572e25 q^{79} -2.37190e27 q^{80} +5.23348e26 q^{81} -1.10054e27 q^{82} +4.08914e27 q^{83} +1.69873e27 q^{84} +8.52825e26 q^{85} -2.14122e27 q^{86} -1.14515e28 q^{87} +1.46701e27 q^{88} -2.81544e27 q^{89} +7.38084e26 q^{90} -5.75028e27 q^{91} +3.37911e28 q^{92} -1.15829e28 q^{93} +2.57662e26 q^{94} +4.27144e28 q^{95} -1.45385e28 q^{96} -6.19333e28 q^{97} -1.67146e27 q^{98} +8.70867e27 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3633.71	−0.156825	−0.0784126	−	0.996921i	$-0.524985\pi$
$2$	−3633.71	−0.156825	−0.0784126	+	0.996921i	$0.524985\pi$
$3$	4.78297e6	0.577350
$3$	4.78297e6	0.577350
$4$	−5.23667e8	−0.975406
$5$	−8.87892e9	−0.650571	−0.325286	−	0.945616i	$-0.605460\pi$
$5$	−8.87892e9	−0.650571	−0.325286	+	0.945616i	$0.605460\pi$
$6$	−1.73799e10	−0.0905431
$7$	−6.78223e11	−0.377964
$7$	−6.78223e11	−0.377964
$8$	3.85369e12	0.309793
$9$	2.28768e13	0.333333
$10$	3.22634e13	0.102026
$11$	3.80677e14	0.302248	0.151124	−	0.988515i	$-0.451711\pi$
$11$	3.80677e14	0.302248	0.151124	+	0.988515i	$0.451711\pi$
$12$	−2.50468e15	−0.563151
$13$	8.47845e15	0.597225	0.298612	−	0.954375i	$-0.403476\pi$
$13$	8.47845e15	0.597225	0.298612	+	0.954375i	$0.403476\pi$
$14$	2.46447e15	0.0592743
$15$	−4.24676e16	−0.375608
$16$	2.67138e17	0.926822
$17$	−9.60505e16	−0.138354	−0.0691768	−	0.997604i	$-0.522037\pi$
$17$	−9.60505e16	−0.138354	−0.0691768	+	0.997604i	$0.522037\pi$
$18$	−8.31277e16	−0.0522751
$19$	−4.81076e18	−1.38130	−0.690648	−	0.723191i	$-0.742675\pi$
$19$	−4.81076e18	−1.38130	−0.690648	+	0.723191i	$0.742675\pi$
$20$	4.64960e18	0.634571
$21$	−3.24392e18	−0.218218
$22$	−1.38327e18	−0.0474000
$23$	−6.45279e19	−1.16063	−0.580315	−	0.814392i	$-0.697071\pi$
$23$	−6.45279e19	−1.16063	−0.580315	+	0.814392i	$0.697071\pi$
$24$	1.84321e19	0.178859
$25$	−1.07429e20	−0.576757
$26$	−3.08082e19	−0.0936599
$27$	1.09419e20	0.192450
$28$	3.55163e20	0.368669
$29$	−2.39423e21	−1.49415	−0.747075	−	0.664740i	$-0.768543\pi$
$29$	−2.39423e21	−1.49415	−0.747075	+	0.664740i	$0.768543\pi$
$30$	1.54315e20	0.0589047
$31$	−2.42170e21	−0.574614	−0.287307	−	0.957839i	$-0.592760\pi$
$31$	−2.42170e21	−0.574614	−0.287307	+	0.957839i	$0.592760\pi$
$32$	−3.03964e21	−0.455142
$33$	1.82077e21	0.174503
$34$	3.49020e20	0.0216973
$35$	6.02189e21	0.245893
$36$	−1.19798e22	−0.325135
$37$	−4.74114e22	−0.864883	−0.432442	−	0.901662i	$-0.642348\pi$
$37$	−4.74114e22	−0.864883	−0.432442	+	0.901662i	$0.642348\pi$
$38$	1.74809e22	0.216622
$39$	4.05521e22	0.344808
$40$	−3.42166e22	−0.201543
$41$	3.02869e23	1.24706	0.623531	−	0.781798i	$-0.285697\pi$
$41$	3.02869e23	1.24706	0.623531	+	0.781798i	$0.285697\pi$
$42$	1.17875e22	0.0342221
$43$	5.89266e23	1.21624	0.608119	−	0.793846i	$-0.291924\pi$
$43$	5.89266e23	1.21624	0.608119	+	0.793846i	$0.291924\pi$
$44$	−1.99348e23	−0.294814
$45$	−2.03121e23	−0.216857
$46$	2.34476e23	0.182016
$47$	−7.09088e22	−0.0402978	−0.0201489	−	0.999797i	$-0.506414\pi$
$47$	−7.09088e22	−0.0402978	−0.0201489	+	0.999797i	$0.506414\pi$
$48$	1.27771e24	0.535101
$49$	4.59987e23	0.142857
$50$	3.90367e23	0.0904500
$51$	−4.59407e23	−0.0798785
$52$	−4.43988e24	−0.582536
$53$	1.71244e25	1.70458	0.852288	−	0.523073i	$-0.175215\pi$
$53$	1.71244e25	1.70458	0.852288	+	0.523073i	$0.175215\pi$
$54$	−3.97597e23	−0.0301810
$55$	−3.38000e24	−0.196634
$56$	−2.61366e24	−0.117091
$57$	−2.30097e25	−0.797492
$58$	8.69994e24	0.234320
$59$	−6.77447e25	−1.42404	−0.712018	−	0.702161i	$-0.752219\pi$
$59$	−6.77447e25	−1.42404	−0.712018	+	0.702161i	$0.752219\pi$
$60$	2.22389e25	0.366370
$61$	9.92211e24	0.128624	0.0643119	−	0.997930i	$-0.479515\pi$
$61$	9.92211e24	0.128624	0.0643119	+	0.997930i	$0.479515\pi$
$62$	8.79977e24	0.0901140
$63$	−1.55156e25	−0.125988
$64$	−1.32374e26	−0.855445
$65$	−7.52794e25	−0.388537
$66$	−6.61615e24	−0.0273664
$67$	−1.22810e26	−0.408459	−0.204229	−	0.978923i	$-0.565469\pi$
$67$	−1.22810e26	−0.408459	−0.204229	+	0.978923i	$0.565469\pi$
$68$	5.02985e25	0.134951
$69$	−3.08635e26	−0.670091
$70$	−2.18818e25	−0.0385622
$71$	4.09491e26	0.587487	0.293743	−	0.955884i	$-0.405099\pi$
$71$	4.09491e26	0.587487	0.293743	+	0.955884i	$0.405099\pi$
$72$	8.81601e25	0.103264
$73$	8.87864e26	0.851461	0.425731	−	0.904850i	$-0.360017\pi$
$73$	8.87864e26	0.851461	0.425731	+	0.904850i	$0.360017\pi$
$74$	1.72279e26	0.135635
$75$	−5.13831e26	−0.332991
$76$	2.51924e27	1.34732
$77$	−2.58184e26	−0.114239
$78$	−1.47355e26	−0.0540745
$79$	−3.62572e25	−0.0110612	−0.00553060	−	0.999985i	$-0.501760\pi$
$79$	−3.62572e25	−0.0110612	−0.00553060	+	0.999985i	$0.501760\pi$
$80$	−2.37190e27	−0.602964
$81$	5.23348e26	0.111111
$82$	−1.10054e27	−0.195571
$83$	4.08914e27	0.609536	0.304768	−	0.952427i	$-0.401421\pi$
$83$	4.08914e27	0.609536	0.304768	+	0.952427i	$0.401421\pi$
$84$	1.69873e27	0.212851
$85$	8.52825e26	0.0900089
$86$	−2.14122e27	−0.190737
$87$	−1.14515e28	−0.862648
$88$	1.46701e27	0.0936343
$89$	−2.81544e27	−0.152542	−0.0762712	−	0.997087i	$-0.524301\pi$
$89$	−2.81544e27	−0.152542	−0.0762712	+	0.997087i	$0.524301\pi$
$90$	7.38084e26	0.0340087
$91$	−5.75028e27	−0.225730
$92$	3.37911e28	1.13209
$93$	−1.15829e28	−0.331754
$94$	2.57662e26	0.00631971
$95$	4.27144e28	0.898632
$96$	−1.45385e28	−0.262777
$97$	−6.19333e28	−0.963239	−0.481619	−	0.876381i	$-0.659951\pi$
$97$	−6.19333e28	−0.963239	−0.481619	+	0.876381i	$0.659951\pi$
$98$	−1.67146e27	−0.0224036
$99$	8.70867e27	0.100749
$100$	5.62572e28	0.562572
$101$	8.99346e28	0.778515	0.389258	−	0.921129i	$-0.372732\pi$
$101$	8.99346e28	0.778515	0.389258	+	0.921129i	$0.372732\pi$
$102$	1.66935e27	0.0125270
$103$	1.95749e29	1.27514	0.637572	−	0.770391i	$-0.279939\pi$
$103$	1.95749e29	1.27514	0.637572	+	0.770391i	$0.279939\pi$
$104$	3.26733e28	0.185016
$105$	2.88025e28	0.141966
$106$	−6.22253e28	−0.267320
$107$	3.17126e29	1.18896	0.594479	−	0.804111i	$-0.297358\pi$
$107$	3.17126e29	1.18896	0.594479	+	0.804111i	$0.297358\pi$
$108$	−5.72991e28	−0.187717
$109$	−2.86612e29	−0.821506	−0.410753	−	0.911747i	$-0.634734\pi$
$109$	−2.86612e29	−0.821506	−0.410753	+	0.911747i	$0.634734\pi$
$110$	1.22820e28	0.0308371
$111$	−2.26767e29	−0.499340
$112$	−1.81179e29	−0.350306
$113$	8.34583e28	0.141851	0.0709254	−	0.997482i	$-0.477405\pi$
$113$	8.34583e28	0.141851	0.0709254	+	0.997482i	$0.477405\pi$
$114$	8.36108e28	0.125067
$115$	5.72938e29	0.755073
$116$	1.25378e30	1.45740
$117$	1.93960e29	0.199075
$118$	2.46165e29	0.223325
$119$	6.51437e28	0.0522927
$120$	−1.63657e29	−0.116361
$121$	−1.44139e30	−0.908646
$122$	−3.60541e28	−0.0201715
$123$	1.44861e30	0.719992
$124$	1.26817e30	0.560482
$125$	2.60768e30	1.02579
$126$	5.63791e28	0.0197581
$127$	5.74152e30	1.79421	0.897105	−	0.441817i	$-0.145666\pi$
$127$	5.74152e30	1.79421	0.897105	+	0.441817i	$0.145666\pi$
$128$	2.11290e30	0.589298
$129$	2.81844e30	0.702195
$130$	2.73544e29	0.0609324
$131$	−2.97790e30	−0.593576	−0.296788	−	0.954943i	$-0.595915\pi$
$131$	−2.97790e30	−0.593576	−0.296788	+	0.954943i	$0.595915\pi$
$132$	−9.53476e29	−0.170211
$133$	3.26277e30	0.522081
$134$	4.46256e29	0.0640566
$135$	−9.71522e29	−0.125203
$136$	−3.70149e29	−0.0428610
$137$	−1.31955e30	−0.137398	−0.0686988	−	0.997637i	$-0.521885\pi$
$137$	−1.31955e30	−0.137398	−0.0686988	+	0.997637i	$0.521885\pi$
$138$	1.12149e30	0.105087
$139$	1.06535e31	0.899038	0.449519	−	0.893271i	$-0.351595\pi$
$139$	1.06535e31	0.899038	0.449519	+	0.893271i	$0.351595\pi$
$140$	−3.15346e30	−0.239845
$141$	−3.39155e29	−0.0232659
$142$	−1.48797e30	−0.0921327
$143$	3.22755e30	0.180510
$144$	6.11127e30	0.308941
$145$	2.12581e31	0.972051
$146$	−3.22624e30	−0.133531
$147$	2.20010e30	0.0824786
$148$	2.48278e31	0.843612
$149$	5.02080e31	1.54729	0.773645	−	0.633619i	$-0.218431\pi$
$149$	5.02080e31	1.54729	0.773645	+	0.633619i	$0.218431\pi$
$150$	1.86712e30	0.0522213
$151$	4.38414e31	1.11357	0.556786	−	0.830656i	$-0.312034\pi$
$151$	4.38414e31	1.11357	0.556786	+	0.830656i	$0.312034\pi$
$152$	−1.85392e31	−0.427916
$153$	−2.19733e30	−0.0461179
$154$	9.38167e29	0.0179155
$155$	2.15021e31	0.373827
$156$	−2.12358e31	−0.336328
$157$	2.93853e31	0.424214	0.212107	−	0.977246i	$-0.431967\pi$
$157$	2.93853e31	0.424214	0.212107	+	0.977246i	$0.431967\pi$
$158$	1.31748e29	0.00173467
$159$	8.19057e31	0.984137
$160$	2.69887e31	0.296103
$161$	4.37643e31	0.438677
$162$	−1.90170e30	−0.0174250
$163$	−8.60271e31	−0.720967	−0.360483	−	0.932766i	$-0.617388\pi$
$163$	−8.60271e31	−0.720967	−0.360483	+	0.932766i	$0.617388\pi$
$164$	−1.58602e32	−1.21639
$165$	−1.61664e31	−0.113526
$166$	−1.48588e31	−0.0955906
$167$	4.82822e31	0.284707	0.142353	−	0.989816i	$-0.454533\pi$
$167$	4.82822e31	0.284707	0.142353	+	0.989816i	$0.454533\pi$
$168$	−1.25011e31	−0.0676025
$169$	−1.29654e32	−0.643323
$170$	−3.09892e30	−0.0141157
$171$	−1.10055e32	−0.460432
$172$	−3.08579e32	−1.18633
$173$	−2.22694e32	−0.787119	−0.393559	−	0.919299i	$-0.628756\pi$
$173$	−2.22694e32	−0.787119	−0.393559	+	0.919299i	$0.628756\pi$
$174$	4.16115e31	0.135285
$175$	7.28611e31	0.217994
$176$	1.01693e32	0.280130
$177$	−3.24021e32	−0.822168
$178$	1.02305e31	0.0239225
$179$	2.42555e32	0.522927	0.261463	−	0.965213i	$-0.415795\pi$
$179$	2.42555e32	0.522927	0.261463	+	0.965213i	$0.415795\pi$
$180$	1.06368e32	0.211524
$181$	−6.08529e32	−1.11671	−0.558357	−	0.829601i	$-0.688568\pi$
$181$	−6.08529e32	−1.11671	−0.558357	+	0.829601i	$0.688568\pi$
$182$	2.08949e31	0.0354001
$183$	4.74571e31	0.0742610
$184$	−2.48671e32	−0.359556
$185$	4.20962e32	0.562668
$186$	4.20890e31	0.0520273
$187$	−3.65643e31	−0.0418170
$188$	3.71326e31	0.0393067
$189$	−7.42105e31	−0.0727393
$190$	−1.55212e32	−0.140928
$191$	−1.47264e33	−1.23912	−0.619559	−	0.784950i	$-0.712688\pi$
$191$	−1.47264e33	−1.23912	−0.619559	+	0.784950i	$0.712688\pi$
$192$	−6.33139e32	−0.493891
$193$	2.36621e33	1.71188	0.855939	−	0.517076i	$-0.172980\pi$
$193$	2.36621e33	1.71188	0.855939	+	0.517076i	$0.172980\pi$
$194$	2.25048e32	0.151060
$195$	−3.60059e32	−0.224322
$196$	−2.40880e32	−0.139344
$197$	−1.59183e33	−0.855337	−0.427668	−	0.903936i	$-0.640665\pi$
$197$	−1.59183e33	−0.855337	−0.427668	+	0.903936i	$0.640665\pi$
$198$	−3.16448e31	−0.0158000
$199$	−3.40279e33	−1.57931	−0.789653	−	0.613554i	$-0.789739\pi$
$199$	−3.40279e33	−1.57931	−0.789653	+	0.613554i	$0.789739\pi$
$200$	−4.14000e32	−0.178675
$201$	−5.87395e32	−0.235824
$202$	−3.26797e32	−0.122091
$203$	1.62382e33	0.564736
$204$	2.40576e32	0.0779140
$205$	−2.68914e33	−0.811303
$206$	−7.11295e32	−0.199975
$207$	−1.47619e33	−0.386877
$208$	2.26492e33	0.553521
$209$	−1.83135e33	−0.417493
$210$	−1.04660e32	−0.0222639
$211$	6.20183e33	1.23147	0.615736	−	0.787953i	$-0.288859\pi$
$211$	6.20183e33	1.23147	0.615736	+	0.787953i	$0.288859\pi$
$212$	−8.96751e33	−1.66265
$213$	1.95858e33	0.339186
$214$	−1.15234e33	−0.186459
$215$	−5.23204e33	−0.791249
$216$	4.21667e32	0.0596198
$217$	1.64245e33	0.217184
$218$	1.04147e33	0.128833
$219$	4.24662e33	0.491591
$220$	1.77000e33	0.191798
$221$	−8.14359e32	−0.0826282
$222$	8.24007e32	0.0783092
$223$	1.14849e33	0.102260	0.0511301	−	0.998692i	$-0.483718\pi$
$223$	1.14849e33	0.102260	0.0511301	+	0.998692i	$0.483718\pi$
$224$	2.06155e33	0.172028
$225$	−2.45764e33	−0.192252
$226$	−3.03263e32	−0.0222458
$227$	2.32471e34	1.59954	0.799768	−	0.600310i	$-0.204956\pi$
$227$	2.32471e34	1.59954	0.799768	+	0.600310i	$0.204956\pi$
$228$	1.20494e34	0.777878
$229$	2.06085e34	1.24863	0.624313	−	0.781174i	$-0.285379\pi$
$229$	2.06085e34	1.24863	0.624313	+	0.781174i	$0.285379\pi$
$230$	−2.08189e33	−0.118414
$231$	−1.23489e33	−0.0659558
$232$	−9.22661e33	−0.462878
$233$	−1.05272e34	−0.496195	−0.248097	−	0.968735i	$-0.579805\pi$
$233$	−1.05272e34	−0.496195	−0.248097	+	0.968735i	$0.579805\pi$
$234$	−7.04794e32	−0.0312200
$235$	6.29594e32	0.0262166
$236$	3.54756e34	1.38901
$237$	−1.73417e32	−0.00638618
$238$	−2.36714e32	−0.00820082
$239$	7.72336e33	0.251789	0.125894	−	0.992044i	$-0.459820\pi$
$239$	7.72336e33	0.251789	0.125894	+	0.992044i	$0.459820\pi$
$240$	−1.13447e34	−0.348122
$241$	4.96898e34	1.43555	0.717777	−	0.696273i	$-0.245160\pi$
$241$	4.96898e34	1.43555	0.717777	+	0.696273i	$0.245160\pi$
$242$	5.23761e33	0.142499
$243$	2.50316e33	0.0641500
$244$	−5.19588e33	−0.125460
$245$	−4.08418e33	−0.0929388
$246$	−5.26384e33	−0.112913
$247$	−4.07878e34	−0.824944
$248$	−9.33249e33	−0.178012
$249$	1.95582e34	0.351916
$250$	−9.47558e33	−0.160870
$251$	4.29941e34	0.688874	0.344437	−	0.938809i	$-0.388070\pi$
$251$	4.29941e34	0.688874	0.344437	+	0.938809i	$0.388070\pi$
$252$	8.12499e33	0.122890
$253$	−2.45643e34	−0.350798
$254$	−2.08631e34	−0.281377
$255$	4.07903e33	0.0519667
$256$	6.33899e34	0.763028
$257$	1.18587e35	1.34898	0.674490	−	0.738284i	$-0.264363\pi$
$257$	1.18587e35	1.34898	0.674490	+	0.738284i	$0.264363\pi$
$258$	−1.02414e34	−0.110122
$259$	3.21555e34	0.326895
$260$	3.94214e34	0.378981
$261$	−5.47722e34	−0.498050
$262$	1.08208e34	0.0930877
$263$	−8.75529e34	−0.712709	−0.356354	−	0.934351i	$-0.615980\pi$
$263$	−8.75529e34	−0.712709	−0.356354	+	0.934351i	$0.615980\pi$
$264$	7.01667e33	0.0540598
$265$	−1.52046e35	−1.10895
$266$	−1.18560e34	−0.0818754
$267$	−1.34661e34	−0.0880704
$268$	6.43114e34	0.398413
$269$	−2.94831e34	−0.173047	−0.0865236	−	0.996250i	$-0.527576\pi$
$269$	−2.94831e34	−0.173047	−0.0865236	+	0.996250i	$0.527576\pi$
$270$	3.53023e33	0.0196349
$271$	1.93462e35	1.01986	0.509931	−	0.860215i	$-0.329671\pi$
$271$	1.93462e35	1.01986	0.509931	+	0.860215i	$0.329671\pi$
$272$	−2.56588e34	−0.128229
$273$	−2.75034e34	−0.130325
$274$	4.79488e33	0.0215474
$275$	−4.08959e34	−0.174323
$276$	1.61622e35	0.653610
$277$	−2.35465e35	−0.903585	−0.451793	−	0.892123i	$-0.649215\pi$
$277$	−2.35465e35	−0.903585	−0.451793	+	0.892123i	$0.649215\pi$
$278$	−3.87118e34	−0.140992
$279$	−5.54008e34	−0.191538
$280$	2.32065e34	0.0761760
$281$	−3.55057e35	−1.10677	−0.553384	−	0.832926i	$-0.686664\pi$
$281$	−3.55057e35	−1.10677	−0.553384	+	0.832926i	$0.686664\pi$
$282$	1.23239e33	0.00364869
$283$	6.82513e34	0.191959	0.0959793	−	0.995383i	$-0.469402\pi$
$283$	6.82513e34	0.191959	0.0959793	+	0.995383i	$0.469402\pi$
$284$	−2.14437e35	−0.573038
$285$	2.04301e35	0.518825
$286$	−1.17280e34	−0.0283085
$287$	−2.05412e35	−0.471345
$288$	−6.95372e34	−0.151714
$289$	−4.72743e35	−0.980858
$290$	−7.72460e34	−0.152442
$291$	−2.96225e35	−0.556126
$292$	−4.64945e35	−0.830520
$293$	−4.04610e35	−0.687791	−0.343895	−	0.939008i	$-0.611747\pi$
$293$	−4.04610e35	−0.687791	−0.343895	+	0.939008i	$0.611747\pi$
$294$	−7.99454e33	−0.0129347
$295$	6.01499e35	0.926437
$296$	−1.82709e35	−0.267935
$297$	4.16533e34	0.0581676
$298$	−1.82441e35	−0.242654
$299$	−5.47097e35	−0.693157
$300$	2.69076e35	0.324801
$301$	−3.99654e35	−0.459695
$302$	−1.59307e35	−0.174636
$303$	4.30155e35	0.449476
$304$	−1.28514e36	−1.28022
$305$	−8.80976e34	−0.0836790
$306$	7.98446e33	0.00723244
$307$	8.86071e35	0.765530	0.382765	−	0.923846i	$-0.374972\pi$
$307$	8.86071e35	0.765530	0.382765	+	0.923846i	$0.374972\pi$
$308$	1.35202e35	0.111429
$309$	9.36260e35	0.736205
$310$	−7.81325e34	−0.0586256
$311$	−3.47598e35	−0.248915	−0.124458	−	0.992225i	$-0.539719\pi$
$311$	−3.47598e35	−0.248915	−0.124458	+	0.992225i	$0.539719\pi$
$312$	1.56275e35	0.106819
$313$	2.22318e36	1.45072	0.725358	−	0.688372i	$-0.241674\pi$
$313$	2.22318e36	1.45072	0.725358	+	0.688372i	$0.241674\pi$
$314$	−1.06778e35	−0.0665275
$315$	1.37761e35	0.0819643
$316$	1.89867e34	0.0107892
$317$	−5.66780e35	−0.307649	−0.153825	−	0.988098i	$-0.549159\pi$
$317$	−5.66780e35	−0.307649	−0.153825	+	0.988098i	$0.549159\pi$
$318$	−2.97622e35	−0.154337
$319$	−9.11427e35	−0.451603
$320$	1.17533e36	0.556528
$321$	1.51680e36	0.686445
$322$	−1.59027e35	−0.0687956
$323$	4.62076e35	0.191107
$324$	−2.74060e35	−0.108378
$325$	−9.10834e35	−0.344453
$326$	3.12598e35	0.113066
$327$	−1.37086e36	−0.474297
$328$	1.16716e36	0.386332
$329$	4.80920e34	0.0152311
$330$	5.87442e34	0.0178038
$331$	3.97553e36	1.15316	0.576579	−	0.817042i	$-0.304387\pi$
$331$	3.97553e36	1.15316	0.576579	+	0.817042i	$0.304387\pi$
$332$	−2.14135e36	−0.594545
$333$	−1.08462e36	−0.288294
$334$	−1.75444e35	−0.0446492
$335$	1.09042e36	0.265732
$336$	−8.66576e35	−0.202249
$337$	6.94812e36	1.55322	0.776611	−	0.629980i	$-0.216937\pi$
$337$	6.94812e36	1.55322	0.776611	+	0.629980i	$0.216937\pi$
$338$	4.71126e35	0.100889
$339$	3.99178e35	0.0818976
$340$	−4.46596e35	−0.0877952
$341$	−9.21887e35	−0.173676
$342$	3.99908e35	0.0722073
$343$	−3.11973e35	−0.0539949
$344$	2.27085e36	0.376782
$345$	2.74035e36	0.435942
$346$	8.09207e35	0.123440
$347$	−1.83435e36	−0.268351	−0.134176	−	0.990958i	$-0.542839\pi$
$347$	−1.83435e36	−0.268351	−0.134176	+	0.990958i	$0.542839\pi$
$348$	5.99678e36	0.841432
$349$	1.17430e37	1.58056	0.790279	−	0.612747i	$-0.209936\pi$
$349$	1.17430e37	1.58056	0.790279	+	0.612747i	$0.209936\pi$
$350$	−2.64756e35	−0.0341869
$351$	9.27703e35	0.114936
$352$	−1.15712e36	−0.137566
$353$	−9.12832e36	−1.04150	−0.520748	−	0.853710i	$-0.674347\pi$
$353$	−9.12832e36	−1.04150	−0.520748	+	0.853710i	$0.674347\pi$
$354$	1.17740e36	0.128937
$355$	−3.63583e36	−0.382202
$356$	1.47435e36	0.148791
$357$	3.11580e35	0.0301912
$358$	−8.81375e35	−0.0820081
$359$	5.08774e36	0.454627	0.227314	−	0.973822i	$-0.427006\pi$
$359$	5.08774e36	0.454627	0.227314	+	0.973822i	$0.427006\pi$
$360$	−7.82766e35	−0.0671809
$361$	1.10136e37	0.907978
$362$	2.21122e36	0.175129
$363$	−6.89414e36	−0.524607
$364$	3.01123e36	0.220178
$365$	−7.88327e36	−0.553936
$366$	−1.72446e35	−0.0116460
$367$	−1.24361e37	−0.807283	−0.403641	−	0.914917i	$-0.632256\pi$
$367$	−1.24361e37	−0.807283	−0.403641	+	0.914917i	$0.632256\pi$
$368$	−1.72379e37	−1.07570
$369$	6.92866e36	0.415688
$370$	−1.52965e36	−0.0882405
$371$	−1.16142e37	−0.644269
$372$	6.06560e36	0.323594
$373$	−9.33484e34	−0.00478993	−0.00239496	−	0.999997i	$-0.500762\pi$
$373$	−9.33484e34	−0.00478993	−0.00239496	+	0.999997i	$0.500762\pi$
$374$	1.32864e35	0.00655797
$375$	1.24725e37	0.592242
$376$	−2.73261e35	−0.0124840
$377$	−2.02993e37	−0.892343
$378$	2.69660e35	0.0114074
$379$	3.92350e36	0.159737	0.0798684	−	0.996805i	$-0.474550\pi$
$379$	3.92350e36	0.159737	0.0798684	+	0.996805i	$0.474550\pi$
$380$	−2.23681e37	−0.876531
$381$	2.74615e37	1.03589
$382$	5.35115e36	0.194325
$383$	−2.56741e37	−0.897663	−0.448831	−	0.893616i	$-0.648160\pi$
$383$	−2.56741e37	−0.897663	−0.448831	+	0.893616i	$0.648160\pi$
$384$	1.01059e37	0.340231
$385$	2.29239e36	0.0743205
$386$	−8.59814e36	−0.268466
$387$	1.34805e37	0.405413
$388$	3.24324e37	0.939549
$389$	−6.74557e37	−1.88256	−0.941282	−	0.337622i	$-0.890377\pi$
$389$	−6.74557e37	−1.88256	−0.941282	+	0.337622i	$0.890377\pi$
$390$	1.30835e36	0.0351793
$391$	6.19794e36	0.160577
$392$	1.77265e36	0.0442562
$393$	−1.42432e37	−0.342701
$394$	5.78426e36	0.134138
$395$	3.21925e35	0.00719609
$396$	−4.56044e36	−0.0982714
$397$	2.72864e37	0.566872	0.283436	−	0.958991i	$-0.408526\pi$
$397$	2.72864e37	0.566872	0.283436	+	0.958991i	$0.408526\pi$
$398$	1.23648e37	0.247675
$399$	1.56057e37	0.301423
$400$	−2.86985e37	−0.534551
$401$	−8.27230e37	−1.48605	−0.743024	−	0.669264i	$-0.766609\pi$
$401$	−8.27230e37	−1.48605	−0.743024	+	0.669264i	$0.766609\pi$
$402$	2.13443e36	0.0369831
$403$	−2.05323e37	−0.343174
$404$	−4.70958e37	−0.759368
$405$	−4.64676e36	−0.0722857
$406$	−5.90050e36	−0.0885648
$407$	−1.80484e37	−0.261409
$408$	−1.77041e36	−0.0247458
$409$	3.09831e37	0.417962	0.208981	−	0.977920i	$-0.432985\pi$
$409$	3.09831e37	0.417962	0.208981	+	0.977920i	$0.432985\pi$
$410$	9.77158e36	0.127233
$411$	−6.31138e36	−0.0793265
$412$	−1.02507e38	−1.24378
$413$	4.59460e37	0.538235
$414$	5.36406e36	0.0606720
$415$	−3.63071e37	−0.396547
$416$	−2.57714e37	−0.271822
$417$	5.09554e37	0.519060
$418$	6.65459e36	0.0654735
$419$	−1.68094e38	−1.59753	−0.798766	−	0.601641i	$-0.794514\pi$
$419$	−1.68094e38	−1.59753	−0.798766	+	0.601641i	$0.794514\pi$
$420$	−1.50829e37	−0.138475
$421$	6.43544e37	0.570805	0.285403	−	0.958408i	$-0.407873\pi$
$421$	6.43544e37	0.570805	0.285403	+	0.958408i	$0.407873\pi$
$422$	−2.25357e37	−0.193126
$423$	−1.62217e36	−0.0134326
$424$	6.59923e37	0.528066
$425$	1.03186e37	0.0797964
$426$	−7.11692e36	−0.0531928
$427$	−6.72940e36	−0.0486152
$428$	−1.66068e38	−1.15972
$429$	1.54373e37	0.104217
$430$	1.90117e37	0.124088
$431$	1.49591e38	0.944029	0.472015	−	0.881591i	$-0.343527\pi$
$431$	1.49591e38	0.944029	0.472015	+	0.881591i	$0.343527\pi$
$432$	2.92300e37	0.178367
$433$	2.29503e38	1.35430	0.677148	−	0.735847i	$-0.263216\pi$
$433$	2.29503e38	1.35430	0.677148	+	0.735847i	$0.263216\pi$
$434$	−5.96821e36	−0.0340599
$435$	1.01677e38	0.561214
$436$	1.50089e38	0.801302
$437$	3.10429e38	1.60317
$438$	−1.54310e37	−0.0770939
$439$	3.59590e37	0.173809	0.0869044	−	0.996217i	$-0.472303\pi$
$439$	3.59590e37	0.173809	0.0869044	+	0.996217i	$0.472303\pi$
$440$	−1.30255e37	−0.0609158
$441$	1.05230e37	0.0476190
$442$	2.95915e36	0.0129582
$443$	4.62689e37	0.196081	0.0980403	−	0.995182i	$-0.468743\pi$
$443$	4.62689e37	0.196081	0.0980403	+	0.995182i	$0.468743\pi$
$444$	1.18750e38	0.487060
$445$	2.49980e37	0.0992397
$446$	−4.17328e36	−0.0160370
$447$	2.40143e38	0.893329
$448$	8.97789e37	0.323328
$449$	−1.74073e38	−0.606961	−0.303480	−	0.952838i	$-0.598149\pi$
$449$	−1.74073e38	−0.606961	−0.303480	+	0.952838i	$0.598149\pi$
$450$	8.93036e36	0.0301500
$451$	1.15295e38	0.376922
$452$	−4.37043e37	−0.138362
$453$	2.09692e38	0.642921
$454$	−8.44733e37	−0.250847
$455$	5.10562e37	0.146853
$456$	−8.86724e37	−0.247058
$457$	2.93269e38	0.791554	0.395777	−	0.918347i	$-0.370475\pi$
$457$	2.93269e38	0.791554	0.395777	+	0.918347i	$0.370475\pi$
$458$	−7.48855e37	−0.195816
$459$	−1.05098e37	−0.0266262
$460$	−3.00029e38	−0.736503
$461$	1.16268e38	0.276566	0.138283	−	0.990393i	$-0.455842\pi$
$461$	1.16268e38	0.276566	0.138283	+	0.990393i	$0.455842\pi$
$462$	4.48722e36	0.0103435
$463$	8.05997e37	0.180057	0.0900283	−	0.995939i	$-0.471304\pi$
$463$	8.05997e37	0.180057	0.0900283	+	0.995939i	$0.471304\pi$
$464$	−6.39590e38	−1.38481
$465$	1.02844e38	0.215829
$466$	3.82529e37	0.0778159
$467$	−6.21316e38	−1.22523	−0.612615	−	0.790381i	$-0.709882\pi$
$467$	−6.21316e38	−1.22523	−0.612615	+	0.790381i	$0.709882\pi$
$468$	−1.01570e38	−0.194179
$469$	8.32924e37	0.154383
$470$	−2.28776e36	−0.00411142
$471$	1.40549e38	0.244920
$472$	−2.61067e38	−0.441157
$473$	2.24320e38	0.367605
$474$	6.30149e35	0.00100151
$475$	5.16817e38	0.796672
$476$	−3.41136e37	−0.0510067
$477$	3.91752e38	0.568192
$478$	−2.80645e37	−0.0394868
$479$	−9.33228e38	−1.27386	−0.636932	−	0.770920i	$-0.719797\pi$
$479$	−9.33228e38	−1.27386	−0.636932	+	0.770920i	$0.719797\pi$
$480$	1.29086e38	0.170955
$481$	−4.01975e38	−0.516529
$482$	−1.80558e38	−0.225131
$483$	2.09323e38	0.253270
$484$	7.54811e38	0.886299
$485$	5.49900e38	0.626655
$486$	−9.09575e36	−0.0100603
$487$	−1.83599e38	−0.197106	−0.0985530	−	0.995132i	$-0.531421\pi$
$487$	−1.83599e38	−0.197106	−0.0985530	+	0.995132i	$0.531421\pi$
$488$	3.82367e37	0.0398468
$489$	−4.11465e38	−0.416250
$490$	1.48408e37	0.0145751
$491$	7.82501e38	0.746111	0.373055	−	0.927809i	$-0.378310\pi$
$491$	7.82501e38	0.746111	0.373055	+	0.927809i	$0.378310\pi$
$492$	−7.58590e38	−0.702284
$493$	2.29967e38	0.206721
$494$	1.48211e38	0.129372
$495$	−7.73236e37	−0.0655445
$496$	−6.46930e38	−0.532565
$497$	−2.77726e38	−0.222049
$498$	−7.10690e37	−0.0551892
$499$	1.42455e39	1.07453	0.537267	−	0.843412i	$-0.319457\pi$
$499$	1.42455e39	1.07453	0.537267	+	0.843412i	$0.319457\pi$
$500$	−1.36556e39	−1.00056
$501$	2.30932e38	0.164376
$502$	−1.56228e38	−0.108033
$503$	1.06630e39	0.716377	0.358189	−	0.933649i	$-0.383394\pi$
$503$	1.06630e39	0.716377	0.358189	+	0.933649i	$0.383394\pi$
$504$	−5.97922e37	−0.0390303
$505$	−7.98522e38	−0.506480
$506$	8.92597e37	0.0550139
$507$	−6.20131e38	−0.371423
$508$	−3.00665e39	−1.75008
$509$	−8.52959e38	−0.482526	−0.241263	−	0.970460i	$-0.577562\pi$
$509$	−8.52959e38	−0.482526	−0.241263	+	0.970460i	$0.577562\pi$
$510$	−1.48220e37	−0.00814968
$511$	−6.02170e38	−0.321822
$512$	−1.36470e39	−0.708960
$513$	−5.26389e38	−0.265831
$514$	−4.30910e38	−0.211554
$515$	−1.73804e39	−0.829572
$516$	−1.47592e39	−0.684925
$517$	−2.69934e37	−0.0121799
$518$	−1.16844e38	−0.0512654
$519$	−1.06514e39	−0.454443
$520$	−2.90104e38	−0.120366
$521$	3.61771e39	1.45978	0.729888	−	0.683566i	$-0.239572\pi$
$521$	3.61771e39	1.45978	0.729888	+	0.683566i	$0.239572\pi$
$522$	1.99027e38	0.0781068
$523$	−9.29857e38	−0.354929	−0.177465	−	0.984127i	$-0.556790\pi$
$523$	−9.29857e38	−0.354929	−0.177465	+	0.984127i	$0.556790\pi$
$524$	1.55943e39	0.578978
$525$	3.48492e38	0.125859
$526$	3.18142e38	0.111771
$527$	2.32606e38	0.0794999
$528$	4.86397e38	0.161733
$529$	1.07280e39	0.347064
$530$	5.52493e38	0.173911
$531$	−1.54978e39	−0.474679
$532$	−1.70861e39	−0.509241
$533$	2.56785e39	0.744776
$534$	4.89321e37	0.0138117
$535$	−2.81573e39	−0.773502
$536$	−4.73271e38	−0.126538
$537$	1.16013e39	0.301912
$538$	1.07133e38	0.0271381
$539$	1.75106e38	0.0431782
$540$	5.08754e38	0.122123
$541$	3.39435e39	0.793224	0.396612	−	0.917986i	$-0.370186\pi$
$541$	3.39435e39	0.793224	0.396612	+	0.917986i	$0.370186\pi$
$542$	−7.02986e38	−0.159940
$543$	−2.91057e39	−0.644735
$544$	2.91959e38	0.0629706
$545$	2.54481e39	0.534448
$546$	9.99395e37	0.0204383
$547$	−5.36641e38	−0.106873	−0.0534365	−	0.998571i	$-0.517017\pi$
$547$	−5.36641e38	−0.106873	−0.0534365	+	0.998571i	$0.517017\pi$
$548$	6.91007e38	0.134018
$549$	2.26986e38	0.0428746
$550$	1.48604e38	0.0273383
$551$	1.15181e40	2.06386
$552$	−1.18938e39	−0.207590
$553$	2.45905e37	0.00418074
$554$	8.55611e38	0.141705
$555$	2.01345e39	0.324857
$556$	−5.57889e39	−0.876927
$557$	4.80013e39	0.735110	0.367555	−	0.930002i	$-0.380195\pi$
$557$	4.80013e39	0.735110	0.367555	+	0.930002i	$0.380195\pi$
$558$	2.01311e38	0.0300380
$559$	4.99606e39	0.726367
$560$	1.60868e39	0.227899
$561$	−1.74886e38	−0.0241431
$562$	1.29018e39	0.173569
$563$	1.43537e40	1.88188	0.940938	−	0.338580i	$-0.109946\pi$
$563$	1.43537e40	1.88188	0.940938	+	0.338580i	$0.109946\pi$
$564$	1.77604e38	0.0226937
$565$	−7.41019e38	−0.0922841
$566$	−2.48006e38	−0.0301040
$567$	−3.54946e38	−0.0419961
$568$	1.57805e39	0.181999
$569$	−1.50324e40	−1.69006	−0.845028	−	0.534722i	$-0.820416\pi$
$569$	−1.50324e40	−1.69006	−0.845028	+	0.534722i	$0.820416\pi$
$570$	−7.42373e38	−0.0813649
$571$	−3.51983e39	−0.376096	−0.188048	−	0.982160i	$-0.560216\pi$
$571$	−3.51983e39	−0.376096	−0.188048	+	0.982160i	$0.560216\pi$
$572$	−1.69016e39	−0.176070
$573$	−7.04359e39	−0.715405
$574$	7.46410e38	0.0739188
$575$	6.93219e39	0.669402
$576$	−3.02828e39	−0.285148
$577$	9.21808e39	0.846430	0.423215	−	0.906029i	$-0.360902\pi$
$577$	9.21808e39	0.846430	0.423215	+	0.906029i	$0.360902\pi$
$578$	1.71781e39	0.153823
$579$	1.13175e40	0.988354
$580$	−1.11322e40	−0.948145
$581$	−2.77335e39	−0.230383
$582$	1.07640e39	0.0872146
$583$	6.51888e39	0.515204
$584$	3.42155e39	0.263777
$585$	−1.72215e39	−0.129512
$586$	1.47024e39	0.107863
$587$	8.60137e39	0.615623	0.307812	−	0.951447i	$-0.400403\pi$
$587$	8.60137e39	0.615623	0.307812	+	0.951447i	$0.400403\pi$
$588$	−1.15212e39	−0.0804501
$589$	1.16502e40	0.793712
$590$	−2.18568e39	−0.145289
$591$	−7.61368e39	−0.493829
$592$	−1.26654e40	−0.801593
$593$	3.36460e39	0.207797	0.103899	−	0.994588i	$-0.466868\pi$
$593$	3.36460e39	0.207797	0.103899	+	0.994588i	$0.466868\pi$
$594$	−1.51356e38	−0.00912214
$595$	−5.78406e38	−0.0340202
$596$	−2.62923e40	−1.50924
$597$	−1.62755e40	−0.911812
$598$	1.98799e39	0.108705
$599$	3.39065e40	1.80965	0.904825	−	0.425785i	$-0.140002\pi$
$599$	3.39065e40	1.80965	0.904825	+	0.425785i	$0.140002\pi$
$600$	−1.98015e39	−0.103158
$601$	−2.21509e39	−0.112645	−0.0563224	−	0.998413i	$-0.517937\pi$
$601$	−2.21509e39	−0.112645	−0.0563224	+	0.998413i	$0.517937\pi$
$602$	1.45223e39	0.0720917
$603$	−2.80949e39	−0.136153
$604$	−2.29583e40	−1.08618
$605$	1.27980e40	0.591139
$606$	−1.56306e39	−0.0704891
$607$	1.75389e39	0.0772265	0.0386132	−	0.999254i	$-0.487706\pi$
$607$	1.75389e39	0.0772265	0.0386132	+	0.999254i	$0.487706\pi$
$608$	1.46230e40	0.628686
$609$	7.76668e39	0.326050
$610$	3.20121e38	0.0131230
$611$	−6.01197e38	−0.0240668
$612$	1.15067e39	0.0449836
$613$	−7.03638e39	−0.268641	−0.134321	−	0.990938i	$-0.542885\pi$
$613$	−7.03638e39	−0.268641	−0.134321	+	0.990938i	$0.542885\pi$
$614$	−3.21973e39	−0.120054
$615$	−1.28621e40	−0.468406
$616$	−9.94962e38	−0.0353904
$617$	3.03784e40	1.05543	0.527716	−	0.849421i	$-0.323048\pi$
$617$	3.03784e40	1.05543	0.527716	+	0.849421i	$0.323048\pi$
$618$	−3.40210e39	−0.115455
$619$	−4.20073e40	−1.39255	−0.696274	−	0.717776i	$-0.745160\pi$
$619$	−4.20073e40	−1.39255	−0.696274	+	0.717776i	$0.745160\pi$
$620$	−1.12599e40	−0.364634
$621$	−7.06058e39	−0.223364
$622$	1.26307e39	0.0390362
$623$	1.90949e39	0.0576556
$624$	1.08330e40	0.319576
$625$	−3.14313e39	−0.0905946
$626$	−8.07841e39	−0.227509
$627$	−8.75928e39	−0.241040
$628$	−1.53881e40	−0.413781
$629$	4.55389e39	0.119660
$630$	−5.00586e38	−0.0128541
$631$	−1.93119e40	−0.484618	−0.242309	−	0.970199i	$-0.577905\pi$
$631$	−1.93119e40	−0.484618	−0.242309	+	0.970199i	$0.577905\pi$
$632$	−1.39724e38	−0.00342668
$633$	2.96632e40	0.710990
$634$	2.05952e39	0.0482471
$635$	−5.09785e40	−1.16726
$636$	−4.28913e40	−0.959933
$637$	3.89997e39	0.0853178
$638$	3.31187e39	0.0708228
$639$	9.36783e39	0.195829
$640$	−1.87603e40	−0.383380
$641$	5.76353e40	1.15146	0.575728	−	0.817642i	$-0.304719\pi$
$641$	5.76353e40	1.15146	0.575728	+	0.817642i	$0.304719\pi$
$642$	−5.51162e39	−0.107652
$643$	−6.55423e40	−1.25159	−0.625795	−	0.779987i	$-0.715225\pi$
$643$	−6.55423e40	−1.25159	−0.625795	+	0.779987i	$0.715225\pi$
$644$	−2.29179e40	−0.427888
$645$	−2.50247e40	−0.456828
$646$	−1.67905e39	−0.0299704
$647$	−1.03906e40	−0.181354	−0.0906771	−	0.995880i	$-0.528903\pi$
$647$	−1.03906e40	−0.181354	−0.0906771	+	0.995880i	$0.528903\pi$
$648$	2.01682e39	0.0344215
$649$	−2.57888e40	−0.430411
$650$	3.30971e39	0.0540190
$651$	7.85581e39	0.125391
$652$	4.50496e40	0.703235
$653$	−5.07380e40	−0.774627	−0.387313	−	0.921948i	$-0.626597\pi$
$653$	−5.07380e40	−0.774627	−0.387313	+	0.921948i	$0.626597\pi$
$654$	4.98130e39	0.0743816
$655$	2.64405e40	0.386164
$656$	8.09078e40	1.15581
$657$	2.03115e40	0.283820
$658$	−1.74753e38	−0.00238863
$659$	−9.58058e40	−1.28101	−0.640506	−	0.767953i	$-0.721275\pi$
$659$	−9.58058e40	−1.28101	−0.640506	+	0.767953i	$0.721275\pi$
$660$	8.46583e39	0.110734
$661$	−2.66332e40	−0.340802	−0.170401	−	0.985375i	$-0.554506\pi$
$661$	−2.66332e40	−0.340802	−0.170401	+	0.985375i	$0.554506\pi$
$662$	−1.44459e40	−0.180844
$663$	−3.89506e39	−0.0477054
$664$	1.57583e40	0.188830
$665$	−2.89699e40	−0.339651
$666$	3.94120e39	0.0452118
$667$	1.54495e41	1.73416
$668$	−2.52838e40	−0.277705
$669$	5.49319e39	0.0590399
$670$	−3.96227e39	−0.0416734
$671$	3.77712e39	0.0388762
$672$	9.86035e39	0.0993202
$673$	1.36281e41	1.34344	0.671718	−	0.740807i	$-0.265557\pi$
$673$	1.36281e41	1.34344	0.671718	+	0.740807i	$0.265557\pi$
$674$	−2.52475e40	−0.243584
$675$	−1.17548e40	−0.110997
$676$	6.78956e40	0.627501
$677$	−1.94178e41	−1.75656	−0.878281	−	0.478146i	$-0.841309\pi$
$677$	−1.94178e41	−1.75656	−0.878281	+	0.478146i	$0.841309\pi$
$678$	−1.45050e39	−0.0128436
$679$	4.20046e40	0.364070
$680$	3.28652e39	0.0278842
$681$	1.11190e41	0.923492
$682$	3.34987e39	0.0272367
$683$	8.57315e39	0.0682402	0.0341201	−	0.999418i	$-0.489137\pi$
$683$	8.57315e39	0.0682402	0.0341201	+	0.999418i	$0.489137\pi$
$684$	5.76321e40	0.449108
$685$	1.17162e40	0.0893869
$686$	1.13362e39	0.00846776
$687$	9.85700e40	0.720895
$688$	1.57415e41	1.12724
$689$	1.45189e41	1.01801
$690$	−9.95763e39	−0.0683666
$691$	−6.24494e40	−0.419852	−0.209926	−	0.977717i	$-0.567322\pi$
$691$	−6.24494e40	−0.419852	−0.209926	+	0.977717i	$0.567322\pi$
$692$	1.16618e41	0.767760
$693$	−5.90642e39	−0.0380796
$694$	6.66549e39	0.0420842
$695$	−9.45916e40	−0.584889
$696$	−4.41306e40	−0.267243
$697$	−2.90907e40	−0.172536
$698$	−4.26707e40	−0.247871
$699$	−5.03513e40	−0.286478
$700$	−3.81549e40	−0.212632
$701$	−5.51803e40	−0.301213	−0.150606	−	0.988594i	$-0.548123\pi$
$701$	−5.51803e40	−0.301213	−0.150606	+	0.988594i	$0.548123\pi$
$702$	−3.37101e39	−0.0180248
$703$	2.28085e41	1.19466
$704$	−5.03916e40	−0.258556
$705$	3.01133e39	0.0151362
$706$	3.31697e40	0.163333
$707$	−6.09958e40	−0.294251
$708$	1.69679e41	0.801947
$709$	1.34252e41	0.621657	0.310828	−	0.950466i	$-0.399394\pi$
$709$	1.34252e41	0.621657	0.310828	+	0.950466i	$0.399394\pi$
$710$	1.32116e40	0.0599389
$711$	−8.29449e38	−0.00368706
$712$	−1.08498e40	−0.0472566
$713$	1.56267e41	0.666915
$714$	−1.13219e39	−0.00473475
$715$	−2.86572e40	−0.117434
$716$	−1.27018e41	−0.510066
$717$	3.69406e40	0.145370
$718$	−1.84874e40	−0.0712970
$719$	−2.01339e41	−0.760956	−0.380478	−	0.924790i	$-0.624240\pi$
$719$	−2.01339e41	−0.760956	−0.380478	+	0.924790i	$0.624240\pi$
$720$	−5.42615e40	−0.200988
$721$	−1.32761e41	−0.481959
$722$	−4.00203e40	−0.142394
$723$	2.37665e41	0.828818
$724$	3.18666e41	1.08925
$725$	2.57210e41	0.861762
$726$	2.50513e40	0.0822716
$727$	−5.82850e41	−1.87632	−0.938161	−	0.346198i	$-0.887473\pi$
$727$	−5.82850e41	−1.87632	−0.938161	+	0.346198i	$0.887473\pi$
$728$	−2.21598e40	−0.0699296
$729$	1.19725e40	0.0370370
$730$	2.86455e40	0.0868712
$731$	−5.65993e40	−0.168271
$732$	−2.48517e40	−0.0724346
$733$	1.18247e41	0.337897	0.168948	−	0.985625i	$-0.445963\pi$
$733$	1.18247e41	0.337897	0.168948	+	0.985625i	$0.445963\pi$
$734$	4.51892e40	0.126602
$735$	−1.95345e40	−0.0536582
$736$	1.96142e41	0.528252
$737$	−4.67509e40	−0.123456
$738$	−2.51768e40	−0.0651903
$739$	−1.22673e41	−0.311462	−0.155731	−	0.987800i	$-0.549773\pi$
$739$	−1.22673e41	−0.311462	−0.155731	+	0.987800i	$0.549773\pi$
$740$	−2.20444e41	−0.548830
$741$	−1.95087e41	−0.476282
$742$	4.22026e40	0.101038
$743$	−2.95369e41	−0.693470	−0.346735	−	0.937963i	$-0.612710\pi$
$743$	−2.95369e41	−0.693470	−0.346735	+	0.937963i	$0.612710\pi$
$744$	−4.46370e40	−0.102775
$745$	−4.45793e41	−1.00662
$746$	3.39201e38	0.000751181 0
$747$	9.35463e40	0.203179
$748$	1.91475e40	0.0407886
$749$	−2.15082e41	−0.449384
$750$	−4.53214e40	−0.0928784
$751$	−8.03061e41	−1.61424	−0.807122	−	0.590384i	$-0.798976\pi$
$751$	−8.03061e41	−1.61424	−0.807122	+	0.590384i	$0.798976\pi$
$752$	−1.89425e40	−0.0373489
$753$	2.05639e41	0.397722
$754$	7.37619e40	0.139942
$755$	−3.89264e41	−0.724458
$756$	3.88616e40	0.0709503
$757$	5.39321e41	0.965955	0.482978	−	0.875633i	$-0.339555\pi$
$757$	5.39321e41	0.965955	0.482978	+	0.875633i	$0.339555\pi$
$758$	−1.42569e40	−0.0250507
$759$	−1.17490e41	−0.202533
$760$	1.64608e41	0.278390
$761$	−9.38813e41	−1.55776	−0.778882	−	0.627170i	$-0.784213\pi$
$761$	−9.38813e41	−1.55776	−0.778882	+	0.627170i	$0.784213\pi$
$762$	−9.97874e40	−0.162453
$763$	1.94387e41	0.310500
$764$	7.71173e41	1.20864
$765$	1.95099e40	0.0300030
$766$	9.32924e40	0.140776
$767$	−5.74370e41	−0.850469
$768$	3.03192e41	0.440534
$769$	−1.37183e41	−0.195599	−0.0977996	−	0.995206i	$-0.531180\pi$
$769$	−1.37183e41	−0.195599	−0.0977996	+	0.995206i	$0.531180\pi$
$770$	−8.32991e39	−0.0116553
$771$	5.67196e41	0.778834
$772$	−1.23911e42	−1.66978
$773$	−4.30042e40	−0.0568733	−0.0284367	−	0.999596i	$-0.509053\pi$
$773$	−4.30042e40	−0.0568733	−0.0284367	+	0.999596i	$0.509053\pi$
$774$	−4.89843e40	−0.0635789
$775$	2.60162e41	0.331413
$776$	−2.38672e41	−0.298405
$777$	1.53799e41	0.188733
$778$	2.45115e41	0.295233
$779$	−1.45703e42	−1.72256
$780$	1.88551e41	0.218805
$781$	1.55884e41	0.177566
$782$	−2.25216e40	−0.0251826
$783$	−2.61974e41	−0.287549
$784$	1.22880e41	0.132403
$785$	−2.60910e41	−0.275982
$786$	5.17557e40	0.0537442
$787$	8.74476e41	0.891486	0.445743	−	0.895161i	$-0.352940\pi$
$787$	8.74476e41	0.891486	0.445743	+	0.895161i	$0.352940\pi$
$788$	8.33590e41	0.834300
$789$	−4.18763e41	−0.411482
$790$	−1.16978e39	−0.00112853
$791$	−5.66033e40	−0.0536146
$792$	3.35605e40	0.0312114
$793$	8.41241e40	0.0768173
$794$	−9.91512e40	−0.0888997
$795$	−7.27234e41	−0.640252
$796$	1.78193e42	1.54046
$797$	1.71438e42	1.45533	0.727664	−	0.685934i	$-0.240606\pi$
$797$	1.71438e42	1.45533	0.727664	+	0.685934i	$0.240606\pi$
$798$	−5.67068e40	−0.0472708
$799$	6.81083e39	0.00557535
$800$	3.26546e41	0.262507
$801$	−6.44081e40	−0.0508475
$802$	3.00592e41	0.233050
$803$	3.37989e41	0.257352
$804$	3.07600e41	0.230024
$805$	−3.88580e41	−0.285391
$806$	7.46084e40	0.0538183
$807$	−1.41017e41	−0.0999088
$808$	3.46580e41	0.241179
$809$	6.28943e41	0.429890	0.214945	−	0.976626i	$-0.431043\pi$
$809$	6.28943e41	0.429890	0.214945	+	0.976626i	$0.431043\pi$
$810$	1.68850e40	0.0113362
$811$	−2.79839e42	−1.84546	−0.922732	−	0.385442i	$-0.874049\pi$
$811$	−2.79839e42	−1.84546	−0.922732	+	0.385442i	$0.874049\pi$
$812$	−8.50341e41	−0.550847
$813$	9.25324e41	0.588818
$814$	6.55828e40	0.0409955
$815$	7.63828e41	0.469040
$816$	−1.22725e41	−0.0740332
$817$	−2.83482e42	−1.67998
$818$	−1.12584e41	−0.0655470
$819$	−1.31548e41	−0.0752432
$820$	1.40822e42	0.791350
$821$	−2.41390e42	−1.33273	−0.666367	−	0.745624i	$-0.732152\pi$
$821$	−2.41390e42	−1.33273	−0.666367	+	0.745624i	$0.732152\pi$
$822$	2.29338e40	0.0124404
$823$	9.60101e41	0.511705	0.255852	−	0.966716i	$-0.417644\pi$
$823$	9.60101e41	0.511705	0.255852	+	0.966716i	$0.417644\pi$
$824$	7.54355e41	0.395031
$825$	−1.95604e41	−0.100646
$826$	−1.66955e41	−0.0844088
$827$	3.65713e42	1.81681	0.908406	−	0.418088i	$-0.137300\pi$
$827$	3.65713e42	1.81681	0.908406	+	0.418088i	$0.137300\pi$
$828$	7.73033e41	0.377362
$829$	2.25339e42	1.08093	0.540463	−	0.841368i	$-0.318249\pi$
$829$	2.25339e42	1.08093	0.540463	+	0.841368i	$0.318249\pi$
$830$	1.31930e41	0.0621885
$831$	−1.12622e42	−0.521685
$832$	−1.12232e42	−0.510893
$833$	−4.41820e40	−0.0197648
$834$	−1.85157e41	−0.0814017
$835$	−4.28693e41	−0.185222
$836$	9.59016e41	0.407226
$837$	−2.64980e41	−0.110585
$838$	6.10807e41	0.250533
$839$	−5.00036e40	−0.0201582	−0.0100791	−	0.999949i	$-0.503208\pi$
$839$	−5.00036e40	−0.0201582	−0.0100791	+	0.999949i	$0.503208\pi$
$840$	1.10996e41	0.0439802
$841$	3.16464e42	1.23249
$842$	−2.33846e41	−0.0895167
$843$	−1.69823e42	−0.638993
$844$	−3.24769e42	−1.20118
$845$	1.15119e42	0.418527
$846$	5.89449e39	0.00210657
$847$	9.77587e41	0.343436
$848$	4.57460e42	1.57984
$849$	3.26444e41	0.110827
$850$	−3.74950e40	−0.0125141
$851$	3.05936e42	1.00381
$852$	−1.02564e42	−0.330844
$853$	1.60104e42	0.507741	0.253871	−	0.967238i	$-0.418296\pi$
$853$	1.60104e42	0.507741	0.253871	+	0.967238i	$0.418296\pi$
$854$	2.44527e40	0.00762409
$855$	9.77168e41	0.299544
$856$	1.22210e42	0.368331
$857$	4.49709e42	1.33263	0.666316	−	0.745670i	$-0.267870\pi$
$857$	4.49709e42	1.33263	0.666316	+	0.745670i	$0.267870\pi$
$858$	−5.60946e40	−0.0163439
$859$	−5.89486e42	−1.68878	−0.844389	−	0.535730i	$-0.820037\pi$
$859$	−5.89486e42	−1.68878	−0.844389	+	0.535730i	$0.820037\pi$
$860$	2.73985e42	0.771789
$861$	−9.82481e41	−0.272131
$862$	−5.43572e41	−0.148048
$863$	5.72298e42	1.53273	0.766365	−	0.642405i	$-0.222063\pi$
$863$	5.72298e42	1.53273	0.766365	+	0.642405i	$0.222063\pi$
$864$	−3.32594e41	−0.0875922
$865$	1.97728e42	0.512077
$866$	−8.33948e41	−0.212388
$867$	−2.26111e42	−0.566299
$868$	−8.60099e41	−0.211842
$869$	−1.38023e40	−0.00334322
$870$	−3.69465e41	−0.0880125
$871$	−1.04124e42	−0.243942
$872$	−1.10452e42	−0.254497
$873$	−1.41683e42	−0.321080
$874$	−1.12801e42	−0.251418
$875$	−1.76859e42	−0.387713
$876$	−2.22382e42	−0.479501
$877$	−7.82257e42	−1.65903	−0.829517	−	0.558482i	$-0.811384\pi$
$877$	−7.82257e42	−1.65903	−0.829517	+	0.558482i	$0.811384\pi$
$878$	−1.30665e41	−0.0272576
$879$	−1.93524e42	−0.397096
$880$	−9.02928e41	−0.182244
$881$	−9.14774e42	−1.81620	−0.908099	−	0.418757i	$-0.862466\pi$
$881$	−9.14774e42	−1.81620	−0.908099	+	0.418757i	$0.862466\pi$
$882$	−3.82376e40	−0.00746787
$883$	6.80723e42	1.30780	0.653899	−	0.756582i	$-0.273132\pi$
$883$	6.80723e42	1.30780	0.653899	+	0.756582i	$0.273132\pi$
$884$	4.26453e41	0.0805960
$885$	2.87695e42	0.534879
$886$	−1.68128e41	−0.0307504
$887$	−8.60987e42	−1.54919	−0.774594	−	0.632459i	$-0.782046\pi$
$887$	−8.60987e42	−1.54919	−0.774594	+	0.632459i	$0.782046\pi$
$888$	−8.73890e41	−0.154692
$889$	−3.89403e42	−0.678148
$890$	−9.08356e40	−0.0155633
$891$	1.99226e41	0.0335831
$892$	−6.01426e41	−0.0997452
$893$	3.41126e41	0.0556632
$894$	−8.72612e41	−0.140096
$895$	−2.15362e42	−0.340201
$896$	−1.43302e42	−0.222734
$897$	−2.61675e42	−0.400195
$898$	6.32533e41	0.0951867
$899$	5.79811e42	0.858560
$900$	1.28698e42	0.187524
$901$	−1.64481e42	−0.235834
$902$	−4.18950e41	−0.0591108
$903$	−1.91153e42	−0.265405
$904$	3.21622e41	0.0439444
$905$	5.40308e42	0.726502
$906$	−7.61960e41	−0.100826
$907$	−1.20408e42	−0.156802	−0.0784009	−	0.996922i	$-0.524981\pi$
$907$	−1.20408e42	−0.156802	−0.0784009	+	0.996922i	$0.524981\pi$
$908$	−1.21737e43	−1.56020
$909$	2.05742e42	0.259505
$910$	−1.85524e41	−0.0230303
$911$	8.99011e42	1.09837	0.549185	−	0.835701i	$-0.314938\pi$
$911$	8.99011e42	1.09837	0.549185	+	0.835701i	$0.314938\pi$
$912$	−6.14678e42	−0.739133
$913$	1.55664e42	0.184231
$914$	−1.06565e42	−0.124136
$915$	−4.21368e41	−0.0483121
$916$	−1.07920e43	−1.21792
$917$	2.01968e42	0.224351
$918$	3.81894e40	0.00417565
$919$	1.26537e42	0.136190	0.0680948	−	0.997679i	$-0.478308\pi$
$919$	1.26537e42	0.136190	0.0680948	+	0.997679i	$0.478308\pi$
$920$	2.20793e42	0.233917
$921$	4.23805e42	0.441979
$922$	−4.22486e41	−0.0433724
$923$	3.47184e42	0.350861
$924$	6.46669e41	0.0643337
$925$	5.09337e42	0.498827
$926$	−2.92876e41	−0.0282374
$927$	4.47810e42	0.425048
$928$	7.27759e42	0.680051
$929$	−3.38546e42	−0.311451	−0.155725	−	0.987800i	$-0.549771\pi$
$929$	−3.38546e42	−0.311451	−0.155725	+	0.987800i	$0.549771\pi$
$930$	−3.73705e41	−0.0338475
$931$	−2.21289e42	−0.197328
$932$	5.51275e42	0.483991
$933$	−1.66255e42	−0.143711
$934$	2.25768e42	0.192147
$935$	3.24651e41	0.0272050
$936$	7.47461e41	0.0616721
$937$	3.00066e42	0.243777	0.121889	−	0.992544i	$-0.461105\pi$
$937$	3.00066e42	0.243777	0.121889	+	0.992544i	$0.461105\pi$
$938$	−3.02661e41	−0.0242111
$939$	1.06334e43	0.837571
$940$	−3.29697e41	−0.0255718
$941$	−7.51534e42	−0.573983	−0.286991	−	0.957933i	$-0.592655\pi$
$941$	−7.51534e42	−0.573983	−0.286991	+	0.957933i	$0.592655\pi$
$942$	−5.10715e41	−0.0384097
$943$	−1.95435e43	−1.44738
$944$	−1.80972e43	−1.31983
$945$	6.58909e41	0.0473221
$946$	−8.15115e41	−0.0576497
$947$	−3.04978e42	−0.212419	−0.106209	−	0.994344i	$-0.533871\pi$
$947$	−3.04978e42	−0.212419	−0.106209	+	0.994344i	$0.533871\pi$
$948$	9.08129e40	0.00622912
$949$	7.52771e42	0.508514
$950$	−1.87797e42	−0.124938
$951$	−2.71089e42	−0.177621
$952$	2.51044e41	0.0161999
$953$	3.04136e43	1.93295	0.966476	−	0.256759i	$-0.0826545\pi$
$953$	3.04136e43	1.93295	0.966476	+	0.256759i	$0.0826545\pi$
$954$	−1.42352e42	−0.0891068
$955$	1.30754e43	0.806134
$956$	−4.04447e42	−0.245596
$957$	−4.35933e42	−0.260733
$958$	3.39108e42	0.199774
$959$	8.94952e41	0.0519314
$960$	5.62159e42	0.321311
$961$	−1.18972e43	−0.669819
$962$	1.46066e42	0.0810048
$963$	7.25482e42	0.396319
$964$	−2.60209e43	−1.40025
$965$	−2.10094e43	−1.11370
$966$	−7.60621e41	−0.0397192
$967$	1.94987e43	1.00305	0.501524	−	0.865144i	$-0.332773\pi$
$967$	1.94987e43	1.00305	0.501524	+	0.865144i	$0.332773\pi$
$968$	−5.55469e42	−0.281493
$969$	2.21010e42	0.110336
$970$	−1.99818e42	−0.0982753
$971$	2.13422e43	1.03409	0.517047	−	0.855957i	$-0.327031\pi$
$971$	2.13422e43	1.03409	0.517047	+	0.855957i	$0.327031\pi$
$972$	−1.31082e42	−0.0625723
$973$	−7.22546e42	−0.339805
$974$	6.67145e41	0.0309112
$975$	−4.35649e42	−0.198870
$976$	2.65058e42	0.119211
$977$	2.10718e43	0.933752	0.466876	−	0.884323i	$-0.345380\pi$
$977$	2.10718e43	0.933752	0.466876	+	0.884323i	$0.345380\pi$
$978$	1.49515e42	0.0652785
$979$	−1.07177e42	−0.0461056
$980$	2.13875e42	0.0906530
$981$	−6.55677e42	−0.273835
$982$	−2.84338e42	−0.117009
$983$	4.41317e43	1.78947	0.894736	−	0.446596i	$-0.147364\pi$
$983$	4.41317e43	1.78947	0.894736	+	0.446596i	$0.147364\pi$
$984$	5.58250e42	0.223049
$985$	1.41337e43	0.556457
$986$	−8.35634e41	−0.0324191
$987$	2.30023e41	0.00879370
$988$	2.13592e43	0.804655
$989$	−3.80241e43	−1.41160
$990$	2.80972e41	0.0102790
$991$	5.00190e43	1.80330	0.901648	−	0.432471i	$-0.142358\pi$
$991$	5.00190e43	1.80330	0.901648	+	0.432471i	$0.142358\pi$
$992$	7.36110e42	0.261531
$993$	1.90148e43	0.665776
$994$	1.00918e42	0.0348229
$995$	3.02131e43	1.02745
$996$	−1.02420e43	−0.343261
$997$	1.73653e43	0.573591	0.286796	−	0.957992i	$-0.407410\pi$
$997$	1.73653e43	0.573591	0.286796	+	0.957992i	$0.407410\pi$
$998$	−5.17641e42	−0.168514
$999$	−5.18770e42	−0.166447

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.a.d.1.4	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.a.d.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-3633.71 q^{2} +4.78297e6 q^{3} -5.23667e8 q^{4} -8.87892e9 q^{5} -1.73799e10 q^{6} -6.78223e11 q^{7} +3.85369e12 q^{8} +2.28768e13 q^{9} +O(q^{10})\)	\(q-3633.71 q^{2} +4.78297e6 q^{3} -5.23667e8 q^{4} -8.87892e9 q^{5} -1.73799e10 q^{6} -6.78223e11 q^{7} +3.85369e12 q^{8} +2.28768e13 q^{9} +3.22634e13 q^{10} +3.80677e14 q^{11} -2.50468e15 q^{12} +8.47845e15 q^{13} +2.46447e15 q^{14} -4.24676e16 q^{15} +2.67138e17 q^{16} -9.60505e16 q^{17} -8.31277e16 q^{18} -4.81076e18 q^{19} +4.64960e18 q^{20} -3.24392e18 q^{21} -1.38327e18 q^{22} -6.45279e19 q^{23} +1.84321e19 q^{24} -1.07429e20 q^{25} -3.08082e19 q^{26} +1.09419e20 q^{27} +3.55163e20 q^{28} -2.39423e21 q^{29} +1.54315e20 q^{30} -2.42170e21 q^{31} -3.03964e21 q^{32} +1.82077e21 q^{33} +3.49020e20 q^{34} +6.02189e21 q^{35} -1.19798e22 q^{36} -4.74114e22 q^{37} +1.74809e22 q^{38} +4.05521e22 q^{39} -3.42166e22 q^{40} +3.02869e23 q^{41} +1.17875e22 q^{42} +5.89266e23 q^{43} -1.99348e23 q^{44} -2.03121e23 q^{45} +2.34476e23 q^{46} -7.09088e22 q^{47} +1.27771e24 q^{48} +4.59987e23 q^{49} +3.90367e23 q^{50} -4.59407e23 q^{51} -4.43988e24 q^{52} +1.71244e25 q^{53} -3.97597e23 q^{54} -3.38000e24 q^{55} -2.61366e24 q^{56} -2.30097e25 q^{57} +8.69994e24 q^{58} -6.77447e25 q^{59} +2.22389e25 q^{60} +9.92211e24 q^{61} +8.79977e24 q^{62} -1.55156e25 q^{63} -1.32374e26 q^{64} -7.52794e25 q^{65} -6.61615e24 q^{66} -1.22810e26 q^{67} +5.02985e25 q^{68} -3.08635e26 q^{69} -2.18818e25 q^{70} +4.09491e26 q^{71} +8.81601e25 q^{72} +8.87864e26 q^{73} +1.72279e26 q^{74} -5.13831e26 q^{75} +2.51924e27 q^{76} -2.58184e26 q^{77} -1.47355e26 q^{78} -3.62572e25 q^{79} -2.37190e27 q^{80} +5.23348e26 q^{81} -1.10054e27 q^{82} +4.08914e27 q^{83} +1.69873e27 q^{84} +8.52825e26 q^{85} -2.14122e27 q^{86} -1.14515e28 q^{87} +1.46701e27 q^{88} -2.81544e27 q^{89} +7.38084e26 q^{90} -5.75028e27 q^{91} +3.37911e28 q^{92} -1.15829e28 q^{93} +2.57662e26 q^{94} +4.27144e28 q^{95} -1.45385e28 q^{96} -6.19333e28 q^{97} -1.67146e27 q^{98} +8.70867e27 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 19461 q^{2} + 38263752 q^{3} + 1467008653 q^{4} - 8498112672 q^{5} - 93081359709 q^{6} - 5425784582792 q^{7} - 16689415716987 q^{8} + 183014339639688 q^{9}+O(q^{10}) \) 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

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