LMFDB - Embedded newform 25.34.b.d.24.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,34,Mod(24,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 34, names="a")

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

chi := DirichletCharacter("25.24");

S:= CuspForms(chi, 34);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 34 $
Character orbit:	$[\chi]$	$=$	25.b (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$172.457072203$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.5
Character	$\chi$	$=$	25.24
Dual form			25.34.b.d.24.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-109239. i q^{2} -1.96178e7i q^{3} -3.34318e9 q^{4} -2.14302e12 q^{6} -7.24227e12i q^{7} -5.73150e14i q^{8} +5.17420e15 q^{9} +O(q^{10})$	\(q-109239. i q^{2} -1.96178e7i q^{3} -3.34318e9 q^{4} -2.14302e12 q^{6} -7.24227e12i q^{7} -5.73150e14i q^{8} +5.17420e15 q^{9} +1.80998e17 q^{11} +6.55856e16i q^{12} +1.38383e18i q^{13} -7.91136e17 q^{14} -9.13278e19 q^{16} +6.46344e19i q^{17} -5.65224e20i q^{18} -1.46370e21 q^{19} -1.42077e20 q^{21} -1.97720e22i q^{22} +7.51392e21i q^{23} -1.12439e22 q^{24} +1.51168e23 q^{26} -2.10563e23i q^{27} +2.42122e22i q^{28} +3.42626e23 q^{29} +1.13942e24 q^{31} +5.05322e24i q^{32} -3.55077e24i q^{33} +7.06058e24 q^{34} -1.72983e25 q^{36} -2.61955e25i q^{37} +1.59893e26i q^{38} +2.71476e25 q^{39} +1.74813e26 q^{41} +1.55203e25i q^{42} -1.37416e27i q^{43} -6.05108e26 q^{44} +8.20811e26 q^{46} +3.57221e27i q^{47} +1.79165e27i q^{48} +7.67854e27 q^{49} +1.26798e27 q^{51} -4.62639e27i q^{52} -3.47129e27i q^{53} -2.30016e28 q^{54} -4.15090e27 q^{56} +2.87146e28i q^{57} -3.74280e28i q^{58} +1.06805e29 q^{59} +3.27030e29 q^{61} -1.24468e29i q^{62} -3.74730e28i q^{63} -2.32492e29 q^{64} -3.87882e29 q^{66} -5.06936e29i q^{67} -2.16084e29i q^{68} +1.47406e29 q^{69} -2.35556e30 q^{71} -2.96559e30i q^{72} -2.40851e30i q^{73} -2.86157e30 q^{74} +4.89342e30 q^{76} -1.31083e30i q^{77} -2.96557e30i q^{78} +2.85259e31 q^{79} +2.46330e31 q^{81} -1.90963e31i q^{82} -1.04315e31i q^{83} +4.74988e29 q^{84} -1.50111e32 q^{86} -6.72154e30i q^{87} -1.03739e32i q^{88} +2.05429e32 q^{89} +1.00221e31 q^{91} -2.51204e31i q^{92} -2.23528e31i q^{93} +3.90224e32 q^{94} +9.91329e31 q^{96} -7.08500e32i q^{97} -8.38795e32i q^{98} +9.36520e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 98676413354 q^{4} - 35567955353446 q^{6} - 48\!\cdots\!16 q^{9}+O(q^{10}) $ 22 * q - 98676413354 * q^4 - 35567955353446 * q^6 - 48599275949251316 * q^9	$ 22 q - 98676413354 q^{4} - 35567955353446 q^{6} - 48\!\cdots\!16 q^{9}+ \cdots - 26\!\cdots\!12 q^{99}+O(q^{100}) $ 22 * q - 98676413354 * q^4 - 35567955353446 * q^6 - 48599275949251316 * q^9 - 388975069134227046 * q^11 - 19390008595334902068 * q^14 + 575591759119330759202 * q^16 + 4608842794243084808630 * q^19 + 7903359076848510896124 * q^21 + 404192556148581428871090 * q^24 + 464682665356996878920184 * q^26 - 3351264573191459117593680 * q^29 - 3759368993361156279858876 * q^31 + 89746721762579763434900102 * q^34 + 387355373506331566119004012 * q^36 + 718345493252093200854565688 * q^39 + 1099039609507795057059146334 * q^41 + 5953087248173453754548821422 * q^44 + 3376724462669734942026715164 * q^46 + 5003317848948805057160966146 * q^49 + 132635930632492996145333201114 * q^51 + 426786304479392249563776060130 * q^54 + 679074245273936256251630129820 * q^56 + 135413981096960311593168243840 * q^59 - 689538516943594572498942901796 * q^61 - 2840052535921821128029255801474 * q^64 - 320033315173213395102299074022 * q^66 - 14437009323987384127917423522852 * q^69 - 11051811216899923387221184379736 * q^71 - 16966204054892971302102433594308 * q^74 - 7588775596602318790343300932510 * q^76 - 56833627147150708379517479188380 * q^79 - 9022895406968638344517956762058 * q^81 + 599893154314490734522302146543532 * q^84 + 911820864247632195182318378176824 * q^86 + 48061740522903759998741201101110 * q^89 - 693375717774307216790074646600496 * q^91 - 465076424153121919006535311120888 * q^94 - 3684220565182840604743827051904706 * q^96 - 2601899095573470033938075107273612 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$	− 109239.i	− 1.17864i	−0.807899	−	0.589321i	$-0.799395\pi$
$2$	− 109239.i	− 1.17864i	0.807899	−	0.589321i	$-0.200605\pi$
$3$	− 1.96178e7i	− 0.263117i	−0.991308	−	0.131558i	$-0.958002\pi$
$3$	− 1.96178e7i	− 0.263117i	0.991308	−	0.131558i	$-0.0419981\pi$
$4$	−3.34318e9	−0.389197
$5$	0	0
$5$	0	0
$6$	−2.14302e12	−0.310120
$7$	− 7.24227e12i	− 0.0823677i	−0.999152	−	0.0411838i	$-0.986887\pi$
$7$	− 7.24227e12i	− 0.0823677i	0.999152	−	0.0411838i	$-0.0131129\pi$
$8$	− 5.73150e14i	− 0.719918i
$9$	5.17420e15	0.930770
$10$	0	0
$11$	1.80998e17	1.18767	0.593833	−	0.804589i	$-0.297614\pi$
$11$	1.80998e17	1.18767	0.593833	+	0.804589i	$0.297614\pi$
$12$	6.55856e16i	0.102404i
$13$	1.38383e18i	0.576790i	0.957512	+	0.288395i	$0.0931216\pi$
$13$	1.38383e18i	0.576790i	−0.957512	+	0.288395i	$0.906878\pi$
$14$	−7.91136e17	−0.0970820
$15$	0	0
$16$	−9.13278e19	−1.23772
$17$	6.46344e19i	0.322149i	0.986942	+	0.161074i	$0.0514959\pi$
$17$	6.46344e19i	0.322149i	−0.986942	+	0.161074i	$0.948504\pi$
$18$	− 5.65224e20i	− 1.09704i
$19$	−1.46370e21	−1.16418	−0.582088	−	0.813126i	$-0.697764\pi$
$19$	−1.46370e21	−1.16418	−0.582088	+	0.813126i	$0.697764\pi$
$20$	0	0
$21$	−1.42077e20	−0.0216723
$22$	− 1.97720e22i	− 1.39983i
$23$	7.51392e21i	0.255480i	0.991808	+	0.127740i	$0.0407723\pi$
$23$	7.51392e21i	0.255480i	−0.991808	+	0.127740i	$0.959228\pi$
$24$	−1.12439e22	−0.189423
$25$	0	0
$26$	1.51168e23	0.679829
$27$	− 2.10563e23i	− 0.508018i
$28$	2.42122e22i	0.0320572i
$29$	3.42626e23	0.254245	0.127123	−	0.991887i	$-0.459426\pi$
$29$	3.42626e23	0.254245	0.127123	+	0.991887i	$0.459426\pi$
$30$	0	0
$31$	1.13942e24	0.281329	0.140665	−	0.990057i	$-0.455076\pi$
$31$	1.13942e24	0.281329	0.140665	+	0.990057i	$0.455076\pi$
$32$	5.05322e24i	0.738914i
$33$	− 3.55077e24i	− 0.312495i
$34$	7.06058e24	0.379698
$35$	0	0
$36$	−1.72983e25	−0.362253
$37$	− 2.61955e25i	− 0.349059i	−0.984652	−	0.174529i	$-0.944160\pi$
$37$	− 2.61955e25i	− 0.349059i	0.984652	−	0.174529i	$-0.0558404\pi$
$38$	1.59893e26i	1.37215i
$39$	2.71476e25	0.151763
$40$	0	0
$41$	1.74813e26	0.428193	0.214096	−	0.976813i	$-0.431319\pi$
$41$	1.74813e26	0.428193	0.214096	+	0.976813i	$0.431319\pi$
$42$	1.55203e25i	0.0255439i
$43$	− 1.37416e27i	− 1.53393i	−0.641687	−	0.766966i	$-0.721765\pi$
$43$	− 1.37416e27i	− 1.53393i	0.641687	−	0.766966i	$-0.278235\pi$
$44$	−6.05108e26	−0.462236
$45$	0	0
$46$	8.20811e26	0.301120
$47$	3.57221e27i	0.919015i	0.888174	+	0.459508i	$0.151974\pi$
$47$	3.57221e27i	0.919015i	−0.888174	+	0.459508i	$0.848026\pi$
$48$	1.79165e27i	0.325666i
$49$	7.67854e27	0.993216
$50$	0	0
$51$	1.26798e27	0.0847627
$52$	− 4.62639e27i	− 0.224485i
$53$	− 3.47129e27i	− 0.123010i	−0.998107	−	0.0615049i	$-0.980410\pi$
$53$	− 3.47129e27i	− 0.123010i	0.998107	−	0.0615049i	$-0.0195900\pi$
$54$	−2.30016e28	−0.598771
$55$	0	0
$56$	−4.15090e27	−0.0592980
$57$	2.87146e28i	0.306314i
$58$	− 3.74280e28i	− 0.299664i
$59$	1.06805e29	0.644958	0.322479	−	0.946577i	$-0.395484\pi$
$59$	1.06805e29	0.644958	0.322479	+	0.946577i	$0.395484\pi$
$60$	0	0
$61$	3.27030e29	1.13932	0.569660	−	0.821880i	$-0.307075\pi$
$61$	3.27030e29	1.13932	0.569660	+	0.821880i	$0.307075\pi$
$62$	− 1.24468e29i	− 0.331586i
$63$	− 3.74730e28i	− 0.0766653i
$64$	−2.32492e29	−0.366808
$65$	0	0
$66$	−3.87882e29	−0.368319
$67$	− 5.06936e29i	− 0.375594i	−0.982208	−	0.187797i	$-0.939865\pi$
$67$	− 5.06936e29i	− 0.375594i	0.982208	−	0.187797i	$-0.0601347\pi$
$68$	− 2.16084e29i	− 0.125379i
$69$	1.47406e29	0.0672211
$70$	0	0
$71$	−2.35556e30	−0.670396	−0.335198	−	0.942148i	$-0.608803\pi$
$71$	−2.35556e30	−0.670396	−0.335198	+	0.942148i	$0.608803\pi$
$72$	− 2.96559e30i	− 0.670078i
$73$	− 2.40851e30i	− 0.433432i	−0.976235	−	0.216716i	$-0.930465\pi$
$73$	− 2.40851e30i	− 0.433432i	0.976235	−	0.216716i	$-0.0695346\pi$
$74$	−2.86157e30	−0.411415
$75$	0	0
$76$	4.89342e30	0.453094
$77$	− 1.31083e30i	− 0.0978252i
$78$	− 2.96557e30i	− 0.178874i
$79$	2.85259e31	1.39441	0.697207	−	0.716870i	$-0.254426\pi$
$79$	2.85259e31	1.39441	0.697207	+	0.716870i	$0.254426\pi$
$80$	0	0
$81$	2.46330e31	0.797102
$82$	− 1.90963e31i	− 0.504686i
$83$	− 1.04315e31i	− 0.225715i	−0.993611	−	0.112857i	$-0.964000\pi$
$83$	− 1.04315e31i	− 0.225715i	0.993611	−	0.112857i	$-0.0360003\pi$
$84$	4.74988e29	0.00843480
$85$	0	0
$86$	−1.50111e32	−1.80796
$87$	− 6.72154e30i	− 0.0668962i
$88$	− 1.03739e32i	− 0.855022i
$89$	2.05429e32	1.40516	0.702581	−	0.711603i	$-0.252031\pi$
$89$	2.05429e32	1.40516	0.702581	+	0.711603i	$0.252031\pi$
$90$	0	0
$91$	1.00221e31	0.0475088
$92$	− 2.51204e31i	− 0.0994321i
$93$	− 2.23528e31i	− 0.0740224i
$94$	3.90224e32	1.08319
$95$	0	0
$96$	9.91329e31	0.194421
$97$	− 7.08500e32i	− 1.17113i	−0.810624	−	0.585566i	$-0.800872\pi$
$97$	− 7.08500e32i	− 1.17113i	0.810624	−	0.585566i	$-0.199128\pi$
$98$	− 8.38795e32i	− 1.17065i
$99$	9.36520e32	1.10544
$100$	0	0
$101$	−1.86281e33	−1.58076	−0.790380	−	0.612617i	$-0.790117\pi$
$101$	−1.86281e33	−1.58076	−0.790380	+	0.612617i	$0.790117\pi$
$102$	− 1.38513e32i	− 0.0999049i
$103$	− 7.41307e32i	− 0.455181i	−0.973757	−	0.227590i	$-0.926915\pi$
$103$	− 7.41307e32i	− 0.455181i	0.973757	−	0.227590i	$-0.0730847\pi$
$104$	7.93142e32	0.415241
$105$	0	0
$106$	−3.79200e32	−0.144984
$107$	− 5.76499e33i	− 1.88785i	−0.330166	−	0.943923i	$-0.607105\pi$
$107$	− 5.76499e33i	− 1.88785i	0.330166	−	0.943923i	$-0.392895\pi$
$108$	7.03948e32i	0.197719i
$109$	6.57177e33	1.58542	0.792711	−	0.609598i	$-0.208669\pi$
$109$	6.57177e33	1.58542	0.792711	+	0.609598i	$0.208669\pi$
$110$	0	0
$111$	−5.13897e32	−0.0918432
$112$	6.61420e32i	0.101948i
$113$	− 8.95137e33i	− 1.19150i	−0.803169	−	0.595751i	$-0.796854\pi$
$113$	− 8.95137e33i	− 1.19150i	0.803169	−	0.595751i	$-0.203146\pi$
$114$	3.13675e33	0.361035
$115$	0	0
$116$	−1.14546e33	−0.0989515
$117$	7.16022e33i	0.536858i
$118$	− 1.16672e34i	− 0.760175i
$119$	4.68099e32	0.0265346
$120$	0	0
$121$	9.53505e33	0.410549
$122$	− 3.57244e34i	− 1.34285i
$123$	− 3.42943e33i	− 0.112665i
$124$	−3.80927e33	−0.109492
$125$	0	0
$126$	−4.09350e33	−0.0903610
$127$	7.07774e34i	1.37130i	0.727930	+	0.685651i	$0.240482\pi$
$127$	7.07774e34i	1.37130i	−0.727930	+	0.685651i	$0.759518\pi$
$128$	6.88040e34i	1.17125i
$129$	−2.69578e34	−0.403603
$130$	0	0
$131$	−1.14692e34	−0.133216	−0.0666079	−	0.997779i	$-0.521218\pi$
$131$	−1.14692e34	−0.133216	−0.0666079	+	0.997779i	$0.521218\pi$
$132$	1.18708e34i	0.121622i
$133$	1.06005e34i	0.0958905i
$134$	−5.53770e34	−0.442691
$135$	0	0
$136$	3.70452e34	0.231921
$137$	8.29417e34i	0.460133i	0.973175	+	0.230067i	$0.0738944\pi$
$137$	8.29417e34i	0.460133i	−0.973175	+	0.230067i	$0.926106\pi$
$138$	− 1.61025e34i	− 0.0792296i
$139$	−3.40975e35	−1.48929	−0.744643	−	0.667463i	$-0.767380\pi$
$139$	−3.40975e35	−1.48929	−0.744643	+	0.667463i	$0.767380\pi$
$140$	0	0
$141$	7.00788e34	0.241808
$142$	2.57319e35i	0.790157i
$143$	2.50470e35i	0.685033i
$144$	−4.72549e35	−1.15203
$145$	0	0
$146$	−2.63103e35	−0.510861
$147$	− 1.50636e35i	− 0.261332i
$148$	8.75762e34i	0.135853i
$149$	−1.79313e35	−0.248908	−0.124454	−	0.992225i	$-0.539718\pi$
$149$	−1.79313e35	−0.248908	−0.124454	+	0.992225i	$0.539718\pi$
$150$	0	0
$151$	2.78845e35	0.310630	0.155315	−	0.987865i	$-0.450361\pi$
$151$	2.78845e35	0.310630	0.155315	+	0.987865i	$0.450361\pi$
$152$	8.38921e35i	0.838112i
$153$	3.34431e35i	0.299846i
$154$	−1.43194e35	−0.115301
$155$	0	0
$156$	−9.07593e34	−0.0590657
$157$	1.75653e36i	1.02875i	0.857565	+	0.514376i	$0.171976\pi$
$157$	1.75653e36i	1.02875i	−0.857565	+	0.514376i	$0.828024\pi$
$158$	− 3.11613e36i	− 1.64352i
$159$	−6.80990e34	−0.0323659
$160$	0	0
$161$	5.44178e34	0.0210433
$162$	− 2.69087e36i	− 0.939497i
$163$	− 2.40082e36i	− 0.757295i	−0.925541	−	0.378647i	$-0.876389\pi$
$163$	− 2.40082e36i	− 0.757295i	0.925541	−	0.378647i	$-0.123611\pi$
$164$	−5.84430e35	−0.166651
$165$	0	0
$166$	−1.13953e36	−0.266037
$167$	− 4.72050e36i	− 0.998081i	−0.866579	−	0.499041i	$-0.833686\pi$
$167$	− 4.72050e36i	− 0.998081i	0.866579	−	0.499041i	$-0.166314\pi$
$168$	8.14314e34i	0.0156023i
$169$	3.84114e36	0.667314
$170$	0	0
$171$	−7.57350e36	−1.08358
$172$	4.59404e36i	0.597002i
$173$	− 1.39436e37i	− 1.64670i	−0.567534	−	0.823350i	$-0.692102\pi$
$173$	− 1.39436e37i	− 1.64670i	0.567534	−	0.823350i	$-0.307898\pi$
$174$	−7.34253e35	−0.0788467
$175$	0	0
$176$	−1.65301e37	−1.47000
$177$	− 2.09526e36i	− 0.169699i
$178$	− 2.24408e37i	− 1.65618i
$179$	1.33795e35	0.00900255	0.00450128	−	0.999990i	$-0.498567\pi$
$179$	1.33795e35	0.00900255	0.00450128	+	0.999990i	$0.498567\pi$
$180$	0	0
$181$	−6.42440e36	−0.359862	−0.179931	−	0.983679i	$-0.557587\pi$
$181$	−6.42440e36	−0.359862	−0.179931	+	0.983679i	$0.557587\pi$
$182$	− 1.09480e36i	− 0.0559959i
$183$	− 6.41560e36i	− 0.299774i
$184$	4.30660e36	0.183925
$185$	0	0
$186$	−2.44179e36	−0.0872459
$187$	1.16987e37i	0.382605i
$188$	− 1.19425e37i	− 0.357678i
$189$	−1.52495e36	−0.0418443
$190$	0	0
$191$	−4.06643e37	−0.937914	−0.468957	−	0.883221i	$-0.655370\pi$
$191$	−4.06643e37	−0.937914	−0.468957	+	0.883221i	$0.655370\pi$
$192$	4.56097e36i	0.0965133i
$193$	− 6.26368e37i	− 1.21656i	−0.793722	−	0.608281i	$-0.791859\pi$
$193$	− 6.26368e37i	− 1.21656i	0.793722	−	0.608281i	$-0.208141\pi$
$194$	−7.73957e37	−1.38035
$195$	0	0
$196$	−2.56707e37	−0.386556
$197$	5.72700e37i	0.792930i	0.918050	+	0.396465i	$0.129763\pi$
$197$	5.72700e37i	0.792930i	−0.918050	+	0.396465i	$0.870237\pi$
$198$	− 1.02304e38i	− 1.30292i
$199$	−1.51928e38	−1.78058	−0.890289	−	0.455396i	$-0.849498\pi$
$199$	−1.51928e38	−1.78058	−0.890289	+	0.455396i	$0.849498\pi$
$200$	0	0
$201$	−9.94494e36	−0.0988250
$202$	2.03491e38i	1.86315i
$203$	− 2.48139e36i	− 0.0209416i
$204$	−4.23908e36	−0.0329894
$205$	0	0
$206$	−8.09795e37	−0.536495
$207$	3.88786e37i	0.237793i
$208$	− 1.26382e38i	− 0.713906i
$209$	−2.64927e38	−1.38265
$210$	0	0
$211$	7.89682e36	0.0352202	0.0176101	−	0.999845i	$-0.494394\pi$
$211$	7.89682e36	0.0352202	0.0176101	+	0.999845i	$0.494394\pi$
$212$	1.16051e37i	0.0478750i
$213$	4.62108e37i	0.176392i
$214$	−6.29761e38	−2.22509
$215$	0	0
$216$	−1.20684e38	−0.365731
$217$	− 8.25196e36i	− 0.0231724i
$218$	− 7.17892e38i	− 1.86864i
$219$	−4.72495e37	−0.114043
$220$	0	0
$221$	−8.94430e37	−0.185812
$222$	5.61375e37i	0.108250i
$223$	5.86319e36i	0.0104979i	0.999986	+	0.00524896i	$0.00167081\pi$
$223$	5.86319e36i	0.0104979i	−0.999986	+	0.00524896i	$0.998329\pi$
$224$	3.65968e37	0.0608626
$225$	0	0
$226$	−9.77836e38	−1.40436
$227$	9.99903e38i	1.33515i	0.744541	+	0.667577i	$0.232669\pi$
$227$	9.99903e38i	1.33515i	−0.744541	+	0.667577i	$0.767331\pi$
$228$	− 9.59979e37i	− 0.119217i
$229$	−1.69123e38	−0.195396	−0.0976982	−	0.995216i	$-0.531148\pi$
$229$	−1.69123e38	−0.195396	−0.0976982	+	0.995216i	$0.531148\pi$
$230$	0	0
$231$	−2.57156e37	−0.0257395
$232$	− 1.96376e38i	− 0.183036i
$233$	− 1.96054e39i	− 1.70217i	−0.525026	−	0.851086i	$-0.675944\pi$
$233$	− 1.96054e39i	− 1.70217i	0.525026	−	0.851086i	$-0.324056\pi$
$234$	7.82174e38	0.632764
$235$	0	0
$236$	−3.57066e38	−0.251016
$237$	− 5.59613e38i	− 0.366894i
$238$	− 5.11346e37i	− 0.0312748i
$239$	2.20476e39	1.25833	0.629166	−	0.777271i	$-0.283396\pi$
$239$	2.20476e39	1.25833	0.629166	+	0.777271i	$0.283396\pi$
$240$	0	0
$241$	−9.40073e38	−0.467606	−0.233803	−	0.972284i	$-0.575117\pi$
$241$	−9.40073e38	−0.467606	−0.233803	+	0.972284i	$0.575117\pi$
$242$	− 1.04160e39i	− 0.483890i
$243$	− 1.65377e39i	− 0.717749i
$244$	−1.09332e39	−0.443420
$245$	0	0
$246$	−3.74627e38	−0.132791
$247$	− 2.02552e39i	− 0.671485i
$248$	− 6.53056e38i	− 0.202534i
$249$	−2.04643e38	−0.0593894
$250$	0	0
$251$	−1.27323e39	−0.323810	−0.161905	−	0.986806i	$-0.551764\pi$
$251$	−1.27323e39	−0.323810	−0.161905	+	0.986806i	$0.551764\pi$
$252$	1.25279e38i	0.0298379i
$253$	1.36000e39i	0.303425i
$254$	7.73164e39	1.61627
$255$	0	0
$256$	5.51897e39	1.01368
$257$	− 1.83336e39i	− 0.315755i	−0.987459	−	0.157878i	$-0.949535\pi$
$257$	− 1.83336e39i	− 0.315755i	0.987459	−	0.157878i	$-0.0504652\pi$
$258$	2.94484e39i	0.475704i
$259$	−1.89715e38	−0.0287512
$260$	0	0
$261$	1.77281e39	0.236644
$262$	1.25288e39i	0.157014i
$263$	1.40189e40i	1.64984i	0.565247	+	0.824922i	$0.308781\pi$
$263$	1.40189e40i	1.64984i	−0.565247	+	0.824922i	$0.691219\pi$
$264$	−2.03512e39	−0.224971
$265$	0	0
$266$	1.15799e39	0.113021
$267$	− 4.03006e39i	− 0.369722i
$268$	1.69477e39i	0.146180i
$269$	−1.72452e40	−1.39880	−0.699399	−	0.714732i	$-0.746549\pi$
$269$	−1.72452e40	−1.39880	−0.699399	+	0.714732i	$0.746549\pi$
$270$	0	0
$271$	1.59037e40	1.14158	0.570788	−	0.821098i	$-0.306638\pi$
$271$	1.59037e40	1.14158	0.570788	+	0.821098i	$0.306638\pi$
$272$	− 5.90291e39i	− 0.398731i
$273$	− 1.96610e38i	− 0.0125004i
$274$	9.06045e39	0.542332
$275$	0	0
$276$	−4.92805e38	−0.0261623
$277$	2.65726e40i	1.32898i	0.747298	+	0.664489i	$0.231351\pi$
$277$	2.65726e40i	1.32898i	−0.747298	+	0.664489i	$0.768649\pi$
$278$	3.72477e40i	1.75533i
$279$	5.89557e39	0.261853
$280$	0	0
$281$	3.55370e40	1.40290	0.701450	−	0.712719i	$-0.252537\pi$
$281$	3.55370e40	1.40290	0.701450	+	0.712719i	$0.252537\pi$
$282$	− 7.65532e39i	− 0.285005i
$283$	5.38426e40i	1.89082i	0.325884	+	0.945410i	$0.394338\pi$
$283$	5.38426e40i	1.89082i	−0.325884	+	0.945410i	$0.605662\pi$
$284$	7.87505e39	0.260916
$285$	0	0
$286$	2.73611e40	0.807409
$287$	− 1.26604e39i	− 0.0352693i
$288$	2.61464e40i	0.687758i
$289$	3.60769e40	0.896220
$290$	0	0
$291$	−1.38992e40	−0.308145
$292$	8.05207e39i	0.168690i
$293$	− 1.19080e40i	− 0.235789i	−0.993026	−	0.117895i	$-0.962385\pi$
$293$	− 1.19080e40i	− 0.235789i	0.993026	−	0.117895i	$-0.0376145\pi$
$294$	−1.64553e40	−0.308016
$295$	0	0
$296$	−1.50140e40	−0.251294
$297$	− 3.81114e40i	− 0.603355i
$298$	1.95880e40i	0.293374i
$299$	−1.03980e40	−0.147358
$300$	0	0
$301$	−9.95200e39	−0.126346
$302$	− 3.04607e40i	− 0.366122i
$303$	3.65442e40i	0.415925i
$304$	1.33677e41	1.44093
$305$	0	0
$306$	3.65329e40	0.353411
$307$	− 1.92332e41i	− 1.76307i	−0.472123	−	0.881533i	$-0.656512\pi$
$307$	− 1.92332e41i	− 1.76307i	0.472123	−	0.881533i	$-0.343488\pi$
$308$	4.38235e39i	0.0380733i
$309$	−1.45428e40	−0.119766
$310$	0	0
$311$	7.59201e40	0.562096	0.281048	−	0.959694i	$-0.409318\pi$
$311$	7.59201e40	0.562096	0.281048	+	0.959694i	$0.409318\pi$
$312$	− 1.55597e40i	− 0.109257i
$313$	− 2.38953e41i	− 1.59159i	−0.605566	−	0.795795i	$-0.707053\pi$
$313$	− 2.38953e41i	− 1.59159i	0.605566	−	0.795795i	$-0.292947\pi$
$314$	1.91881e41	1.21253
$315$	0	0
$316$	−9.53670e40	−0.542702
$317$	1.87224e41i	1.01131i	0.862736	+	0.505655i	$0.168749\pi$
$317$	1.87224e41i	1.01131i	−0.862736	+	0.505655i	$0.831251\pi$
$318$	7.43905e39i	0.0381478i
$319$	6.20145e40	0.301958
$320$	0	0
$321$	−1.13096e41	−0.496724
$322$	− 5.94453e39i	− 0.0248025i
$323$	− 9.46056e40i	− 0.375038i
$324$	−8.23523e40	−0.310229
$325$	0	0
$326$	−2.62263e41	−0.892579
$327$	− 1.28923e41i	− 0.417151i
$328$	− 1.00194e41i	− 0.308264i
$329$	2.58709e40	0.0756972
$330$	0	0
$331$	1.81289e41	0.479965	0.239983	−	0.970777i	$-0.422858\pi$
$331$	1.81289e41	0.479965	0.239983	+	0.970777i	$0.422858\pi$
$332$	3.48745e40i	0.0878475i
$333$	− 1.35541e41i	− 0.324893i
$334$	−5.15661e41	−1.17638
$335$	0	0
$336$	1.29756e40	0.0268243
$337$	2.06387e41i	0.406246i	0.979153	+	0.203123i	$0.0651091\pi$
$337$	2.06387e41i	0.406246i	−0.979153	+	0.203123i	$0.934891\pi$
$338$	− 4.19602e41i	− 0.786524i
$339$	−1.75606e41	−0.313504
$340$	0	0
$341$	2.06232e41	0.334125
$342$	8.27320e41i	1.27715i
$343$	− 1.11600e41i	− 0.164177i
$344$	−7.87597e41	−1.10431
$345$	0	0
$346$	−1.52318e42	−1.94087
$347$	2.42023e41i	0.294050i	0.989133	+	0.147025i	$0.0469698\pi$
$347$	2.42023e41i	0.294050i	−0.989133	+	0.147025i	$0.953030\pi$
$348$	2.24713e40i	0.0260358i
$349$	−9.38948e41	−1.03758	−0.518790	−	0.854902i	$-0.673617\pi$
$349$	−9.38948e41	−1.03758	−0.518790	+	0.854902i	$0.673617\pi$
$350$	0	0
$351$	2.91383e41	0.293019
$352$	9.14622e41i	0.877582i
$353$	− 6.44457e41i	− 0.590081i	−0.955485	−	0.295040i	$-0.904667\pi$
$353$	− 6.44457e41i	− 0.590081i	0.955485	−	0.295040i	$-0.0953331\pi$
$354$	−2.28884e41	−0.200015
$355$	0	0
$356$	−6.86785e41	−0.546885
$357$	− 9.18305e39i	− 0.00698171i
$358$	− 1.46156e40i	− 0.0106108i
$359$	−2.55980e42	−1.77479	−0.887397	−	0.461005i	$-0.847489\pi$
$359$	−2.55980e42	−1.77479	−0.887397	+	0.461005i	$0.847489\pi$
$360$	0	0
$361$	5.61659e41	0.355307
$362$	7.01794e41i	0.424149i
$363$	− 1.87056e41i	− 0.108022i
$364$	−3.35055e40	−0.0184903
$365$	0	0
$366$	−7.00832e41	−0.353326
$367$	− 1.65759e42i	− 0.798890i	−0.916757	−	0.399445i	$-0.869203\pi$
$367$	− 1.65759e42i	− 0.798890i	0.916757	−	0.399445i	$-0.130797\pi$
$368$	− 6.86230e41i	− 0.316214i
$369$	9.04517e41	0.398549
$370$	0	0
$371$	−2.51400e40	−0.0101320
$372$	7.47293e40i	0.0288093i
$373$	− 1.60280e42i	− 0.591131i	−0.955322	−	0.295566i	$-0.904492\pi$
$373$	− 1.60280e42i	− 0.591131i	0.955322	−	0.295566i	$-0.0955081\pi$
$374$	1.27795e42	0.450954
$375$	0	0
$376$	2.04741e42	0.661616
$377$	4.74136e41i	0.146646i
$378$	1.66584e41i	0.0493194i
$379$	7.63887e41	0.216512	0.108256	−	0.994123i	$-0.465473\pi$
$379$	7.63887e41	0.216512	0.108256	+	0.994123i	$0.465473\pi$
$380$	0	0
$381$	1.38849e42	0.360813
$382$	4.44212e42i	1.10546i
$383$	− 6.89316e42i	− 1.64300i	−0.570206	−	0.821502i	$-0.693136\pi$
$383$	− 6.89316e42i	− 1.64300i	0.570206	−	0.821502i	$-0.306864\pi$
$384$	1.34978e42	0.308175
$385$	0	0
$386$	−6.84237e42	−1.43389
$387$	− 7.11016e42i	− 1.42774i
$388$	2.36864e42i	0.455801i
$389$	6.00537e42	1.10757	0.553785	−	0.832660i	$-0.313183\pi$
$389$	6.00537e42	1.10757	0.553785	+	0.832660i	$0.313183\pi$
$390$	0	0
$391$	−4.85657e41	−0.0823026
$392$	− 4.40095e42i	− 0.715034i
$393$	2.25000e41i	0.0350513i
$394$	6.25611e42	0.934580
$395$	0	0
$396$	−3.13095e42	−0.430235
$397$	− 6.47973e42i	− 0.854110i	−0.904226	−	0.427055i	$-0.859551\pi$
$397$	− 6.47973e42i	− 0.854110i	0.904226	−	0.427055i	$-0.140449\pi$
$398$	1.65964e43i	2.09866i
$399$	2.07959e41	0.0252304
$400$	0	0
$401$	1.49165e43	1.66642	0.833211	−	0.552956i	$-0.186500\pi$
$401$	1.49165e43	1.66642	0.833211	+	0.552956i	$0.186500\pi$
$402$	1.08637e42i	0.116479i
$403$	1.57676e42i	0.162268i
$404$	6.22770e42	0.615227
$405$	0	0
$406$	−2.71064e41	−0.0246826
$407$	− 4.74133e42i	− 0.414565i
$408$	− 7.26743e41i	− 0.0610222i
$409$	1.52685e42	0.123130	0.0615648	−	0.998103i	$-0.480391\pi$
$409$	1.52685e42	0.123130	0.0615648	+	0.998103i	$0.480391\pi$
$410$	0	0
$411$	1.62713e42	0.121069
$412$	2.47832e42i	0.177155i
$413$	− 7.73507e41i	− 0.0531237i
$414$	4.24705e42	0.280273
$415$	0	0
$416$	−6.99280e42	−0.426198
$417$	6.68916e42i	0.391856i
$418$	2.89403e43i	1.62965i
$419$	−9.92998e42	−0.537547	−0.268774	−	0.963203i	$-0.586618\pi$
$419$	−9.92998e42	−0.537547	−0.268774	+	0.963203i	$0.586618\pi$
$420$	0	0
$421$	3.76712e43	1.88519	0.942596	−	0.333936i	$-0.108377\pi$
$421$	3.76712e43	1.88519	0.942596	+	0.333936i	$0.108377\pi$
$422$	− 8.62639e41i	− 0.0415120i
$423$	1.84834e43i	0.855391i
$424$	−1.98957e42	−0.0885569
$425$	0	0
$426$	5.04801e42	0.207904
$427$	− 2.36844e42i	− 0.0938432i
$428$	1.92734e43i	0.734744i
$429$	4.91366e42	0.180244
$430$	0	0
$431$	1.57215e43	0.534097	0.267048	−	0.963683i	$-0.413952\pi$
$431$	1.57215e43	0.534097	0.267048	+	0.963683i	$0.413952\pi$
$432$	1.92302e43i	0.628785i
$433$	2.48284e43i	0.781446i	0.920508	+	0.390723i	$0.127775\pi$
$433$	2.48284e43i	0.781446i	−0.920508	+	0.390723i	$0.872225\pi$
$434$	−9.01434e41	−0.0273120
$435$	0	0
$436$	−2.19706e43	−0.617041
$437$	− 1.09982e43i	− 0.297424i
$438$	5.16148e42i	0.134416i
$439$	−4.21958e43	−1.05829	−0.529145	−	0.848531i	$-0.677487\pi$
$439$	−4.21958e43	−1.05829	−0.529145	+	0.848531i	$0.677487\pi$
$440$	0	0
$441$	3.97304e43	0.924455
$442$	9.77064e42i	0.219006i
$443$	− 4.28416e43i	− 0.925133i	−0.886585	−	0.462567i	$-0.846929\pi$
$443$	− 4.28416e43i	− 0.925133i	0.886585	−	0.462567i	$-0.153071\pi$
$444$	1.71805e42	0.0357451
$445$	0	0
$446$	6.40488e41	0.0123733
$447$	3.51773e42i	0.0654919i
$448$	1.68377e42i	0.0302131i
$449$	−4.10901e43	−0.710678	−0.355339	−	0.934737i	$-0.615635\pi$
$449$	−4.10901e43	−0.710678	−0.355339	+	0.934737i	$0.615635\pi$
$450$	0	0
$451$	3.16407e43	0.508550
$452$	2.99260e43i	0.463729i
$453$	− 5.47032e42i	− 0.0817321i
$454$	1.09228e44	1.57367
$455$	0	0
$456$	1.64577e43	0.220521
$457$	− 1.07321e44i	− 1.38697i	−0.720471	−	0.693485i	$-0.756075\pi$
$457$	− 1.07321e44i	− 1.38697i	0.720471	−	0.693485i	$-0.243925\pi$
$458$	1.84748e43i	0.230302i
$459$	1.36096e43	0.163657
$460$	0	0
$461$	−1.65449e44	−1.85182	−0.925910	−	0.377744i	$-0.876700\pi$
$461$	−1.65449e44	−1.85182	−0.925910	+	0.377744i	$0.876700\pi$
$462$	2.80914e42i	0.0303376i
$463$	− 7.01897e43i	− 0.731454i	−0.930722	−	0.365727i	$-0.880820\pi$
$463$	− 7.01897e43i	− 0.731454i	0.930722	−	0.365727i	$-0.119180\pi$
$464$	−3.12912e43	−0.314685
$465$	0	0
$466$	−2.14167e44	−2.00625
$467$	6.51752e43i	0.589324i	0.955602	+	0.294662i	$0.0952070\pi$
$467$	6.51752e43i	0.589324i	−0.955602	+	0.294662i	$0.904793\pi$
$468$	− 2.39379e43i	− 0.208944i
$469$	−3.67136e42	−0.0309368
$470$	0	0
$471$	3.44591e43	0.270682
$472$	− 6.12150e43i	− 0.464317i
$473$	− 2.48719e44i	− 1.82180i
$474$	−6.11315e43	−0.432436
$475$	0	0
$476$	−1.56494e42	−0.0103272
$477$	− 1.79612e43i	− 0.114494i
$478$	− 2.40845e44i	− 1.48312i
$479$	1.66158e44	0.988519	0.494259	−	0.869314i	$-0.335439\pi$
$479$	1.66158e44	0.988519	0.494259	+	0.869314i	$0.335439\pi$
$480$	0	0
$481$	3.62502e43	0.201334
$482$	1.02692e44i	0.551140i
$483$	− 1.06756e42i	− 0.00553685i
$484$	−3.18774e43	−0.159784
$485$	0	0
$486$	−1.80656e44	−0.845969
$487$	1.12846e44i	0.510809i	0.966834	+	0.255404i	$0.0822086\pi$
$487$	1.12846e44i	0.510809i	−0.966834	+	0.255404i	$0.917791\pi$
$488$	− 1.87437e44i	− 0.820217i
$489$	−4.70988e43	−0.199257
$490$	0	0
$491$	1.02544e44	0.405568	0.202784	−	0.979223i	$-0.435001\pi$
$491$	1.02544e44	0.405568	0.202784	+	0.979223i	$0.435001\pi$
$492$	1.14652e43i	0.0438488i
$493$	2.21454e43i	0.0819048i
$494$	−2.21265e44	−0.791441
$495$	0	0
$496$	−1.04060e44	−0.348207
$497$	1.70596e43i	0.0552190i
$498$	2.23550e43i	0.0699988i
$499$	−7.84092e43	−0.237524	−0.118762	−	0.992923i	$-0.537893\pi$
$499$	−7.84092e43	−0.237524	−0.118762	+	0.992923i	$0.537893\pi$
$500$	0	0
$501$	−9.26055e43	−0.262612
$502$	1.39086e44i	0.381656i
$503$	1.09015e44i	0.289478i	0.989470	+	0.144739i	$0.0462342\pi$
$503$	1.09015e44i	0.289478i	−0.989470	+	0.144739i	$0.953766\pi$
$504$	−2.14776e43	−0.0551928
$505$	0	0
$506$	1.48565e44	0.357629
$507$	− 7.53546e43i	− 0.175581i
$508$	− 2.36621e44i	− 0.533707i
$509$	−8.09488e44	−1.76753	−0.883766	−	0.467930i	$-0.845000\pi$
$509$	−8.09488e44	−1.76753	−0.883766	+	0.467930i	$0.845000\pi$
$510$	0	0
$511$	−1.74431e43	−0.0357008
$512$	− 1.18640e43i	− 0.0235112i
$513$	3.08201e44i	0.591422i
$514$	−2.00274e44	−0.372163
$515$	0	0
$516$	9.01248e43	0.157081
$517$	6.46563e44i	1.09148i
$518$	2.07242e43i	0.0338873i
$519$	−2.73542e44	−0.433274
$520$	0	0
$521$	−6.34148e44	−0.942688	−0.471344	−	0.881950i	$-0.656231\pi$
$521$	−6.34148e44	−0.942688	−0.471344	+	0.881950i	$0.656231\pi$
$522$	− 1.93660e44i	− 0.278918i
$523$	3.63034e44i	0.506605i	0.967387	+	0.253303i	$0.0815168\pi$
$523$	3.63034e44i	0.506605i	−0.967387	+	0.253303i	$0.918483\pi$
$524$	3.83435e43	0.0518472
$525$	0	0
$526$	1.53140e45	1.94457
$527$	7.36455e43i	0.0906298i
$528$	3.24284e44i	0.386782i
$529$	8.08546e44	0.934730
$530$	0	0
$531$	5.52628e44	0.600307
$532$	− 3.54395e43i	− 0.0373203i
$533$	2.41911e44i	0.246977i
$534$	−4.40238e44	−0.435770
$535$	0	0
$536$	−2.90550e44	−0.270397
$537$	− 2.62476e42i	− 0.00236872i
$538$	1.88384e45i	1.64868i
$539$	1.38980e45	1.17961
$540$	0	0
$541$	−4.70277e44	−0.375490	−0.187745	−	0.982218i	$-0.560118\pi$
$541$	−4.70277e44	−0.375490	−0.187745	+	0.982218i	$0.560118\pi$
$542$	− 1.73730e45i	− 1.34551i
$543$	1.26032e44i	0.0946857i
$544$	−3.26612e44	−0.238040
$545$	0	0
$546$	−2.14775e43	−0.0147335
$547$	5.18112e44i	0.344852i	0.985022	+	0.172426i	$0.0551605\pi$
$547$	5.18112e44i	0.344852i	−0.985022	+	0.172426i	$0.944839\pi$
$548$	− 2.77289e44i	− 0.179082i
$549$	1.69212e45	1.06044
$550$	0	0
$551$	−5.01502e44	−0.295986
$552$	− 8.44858e43i	− 0.0483937i
$553$	− 2.06592e44i	− 0.114855i
$554$	2.90276e45	1.56639
$555$	0	0
$556$	1.13994e45	0.579625
$557$	2.37652e44i	0.117309i	0.998278	+	0.0586543i	$0.0186810\pi$
$557$	2.37652e44i	0.117309i	−0.998278	+	0.0586543i	$0.981319\pi$
$558$	− 6.44025e44i	− 0.308630i
$559$	1.90160e45	0.884757
$560$	0	0
$561$	2.29502e44	0.100670
$562$	− 3.88202e45i	− 1.65352i
$563$	1.99820e45i	0.826515i	0.910614	+	0.413258i	$0.135609\pi$
$563$	1.99820e45i	0.826515i	−0.910614	+	0.413258i	$0.864391\pi$
$564$	−2.34286e44	−0.0941110
$565$	0	0
$566$	5.88170e45	2.22860
$567$	− 1.78398e44i	− 0.0656554i
$568$	1.35009e45i	0.482630i
$569$	1.93847e45	0.673143	0.336572	−	0.941658i	$-0.390733\pi$
$569$	1.93847e45	0.673143	0.336572	+	0.941658i	$0.390733\pi$
$570$	0	0
$571$	−3.94735e45	−1.29363	−0.646814	−	0.762648i	$-0.723899\pi$
$571$	−3.94735e45	−1.29363	−0.646814	+	0.762648i	$0.723899\pi$
$572$	− 8.37366e44i	− 0.266613i
$573$	7.97743e44i	0.246781i
$574$	−1.38301e44	−0.0415698
$575$	0	0
$576$	−1.20296e45	−0.341414
$577$	− 3.00897e45i	− 0.829884i	−0.909848	−	0.414942i	$-0.863802\pi$
$577$	− 3.00897e45i	− 0.829884i	0.909848	−	0.414942i	$-0.136198\pi$
$578$	− 3.94100e45i	− 1.05632i
$579$	−1.22879e45	−0.320098
$580$	0	0
$581$	−7.55480e43	−0.0185916
$582$	1.51833e45i	0.363192i
$583$	− 6.28296e44i	− 0.146094i
$584$	−1.38044e45	−0.312036
$585$	0	0
$586$	−1.30082e45	−0.277911
$587$	1.28524e45i	0.266966i	0.991051	+	0.133483i	$0.0426162\pi$
$587$	1.28524e45i	0.266966i	−0.991051	+	0.133483i	$0.957384\pi$
$588$	5.03602e44i	0.101709i
$589$	−1.66777e45	−0.327517
$590$	0	0
$591$	1.12351e45	0.208633
$592$	2.39238e45i	0.432038i
$593$	9.50883e45i	1.67003i	0.550226	+	0.835016i	$0.314542\pi$
$593$	9.50883e45i	1.67003i	−0.550226	+	0.835016i	$0.685458\pi$
$594$	−4.16324e45	−0.711140
$595$	0	0
$596$	5.99476e44	0.0968743
$597$	2.98048e45i	0.468500i
$598$	1.13586e45i	0.173683i
$599$	1.27061e44	0.0189004	0.00945019	−	0.999955i	$-0.496992\pi$
$599$	1.27061e44	0.0189004	0.00945019	+	0.999955i	$0.496992\pi$
$600$	0	0
$601$	1.36330e45	0.191939	0.0959693	−	0.995384i	$-0.469405\pi$
$601$	1.36330e45	0.191939	0.0959693	+	0.995384i	$0.469405\pi$
$602$	1.08714e45i	0.148917i
$603$	− 2.62299e45i	− 0.349591i
$604$	−9.32229e44	−0.120896
$605$	0	0
$606$	3.99204e45	0.490226
$607$	1.10280e46i	1.31790i	0.752187	+	0.658950i	$0.228999\pi$
$607$	1.10280e46i	1.31790i	−0.752187	+	0.658950i	$0.771001\pi$
$608$	− 7.39642e45i	− 0.860226i
$609$	−4.86792e43	−0.00551008
$610$	0	0
$611$	−4.94334e45	−0.530079
$612$	− 1.11806e45i	− 0.116699i
$613$	− 1.31076e46i	− 1.33176i	−0.746061	−	0.665878i	$-0.768057\pi$
$613$	− 1.31076e46i	− 1.33176i	0.746061	−	0.665878i	$-0.231943\pi$
$614$	−2.10101e46	−2.07802
$615$	0	0
$616$	−7.51304e44	−0.0704262
$617$	1.57052e46i	1.43330i	0.697431	+	0.716652i	$0.254326\pi$
$617$	1.57052e46i	1.43330i	−0.697431	+	0.716652i	$0.745674\pi$
$618$	1.58863e45i	0.141161i
$619$	−1.19014e46	−1.02968	−0.514839	−	0.857287i	$-0.672148\pi$
$619$	−1.19014e46	−1.02968	−0.514839	+	0.857287i	$0.672148\pi$
$620$	0	0
$621$	1.58215e45	0.129788
$622$	− 8.29342e45i	− 0.662510i
$623$	− 1.48777e45i	− 0.115740i
$624$	−2.47933e45	−0.187841
$625$	0	0
$626$	−2.61030e46	−1.87592
$627$	5.19728e45i	0.363799i
$628$	− 5.87238e45i	− 0.400387i
$629$	1.69313e45	0.112449
$630$	0	0
$631$	−1.38247e46	−0.871305	−0.435653	−	0.900115i	$-0.643482\pi$
$631$	−1.38247e46	−0.871305	−0.435653	+	0.900115i	$0.643482\pi$
$632$	− 1.63496e46i	− 1.00386i
$633$	− 1.54918e44i	− 0.00926702i
$634$	2.04521e46	1.19197
$635$	0	0
$636$	2.27667e44	0.0125967
$637$	1.06258e46i	0.572877i
$638$	− 6.77439e45i	− 0.355901i
$639$	−1.21882e46	−0.623984
$640$	0	0
$641$	2.51084e46	1.22085	0.610424	−	0.792075i	$-0.290999\pi$
$641$	2.51084e46	1.22085	0.610424	+	0.792075i	$0.290999\pi$
$642$	1.23545e46i	0.585459i
$643$	− 2.27110e46i	− 1.04895i	−0.851426	−	0.524474i	$-0.824262\pi$
$643$	− 2.27110e46i	− 1.04895i	0.851426	−	0.524474i	$-0.175738\pi$
$644$	−1.81928e44	−0.00818999
$645$	0	0
$646$	−1.03346e46	−0.442035
$647$	− 3.85605e46i	− 1.60776i	−0.594788	−	0.803882i	$-0.702764\pi$
$647$	− 3.85605e46i	− 1.60776i	0.594788	−	0.803882i	$-0.297236\pi$
$648$	− 1.41184e46i	− 0.573848i
$649$	1.93314e46	0.765994
$650$	0	0
$651$	−1.61885e44	−0.00609705
$652$	8.02638e45i	0.294737i
$653$	− 2.29880e46i	− 0.823065i	−0.911395	−	0.411533i	$-0.864994\pi$
$653$	− 2.29880e46i	− 0.823065i	0.911395	−	0.411533i	$-0.135006\pi$
$654$	−1.40834e46	−0.491672
$655$	0	0
$656$	−1.59653e46	−0.529984
$657$	− 1.24621e46i	− 0.403425i
$658$	− 2.82611e45i	− 0.0892198i
$659$	4.66885e46	1.43748	0.718738	−	0.695281i	$-0.244720\pi$
$659$	4.66885e46	1.43748	0.718738	+	0.695281i	$0.244720\pi$
$660$	0	0
$661$	−1.75754e46	−0.514731	−0.257366	−	0.966314i	$-0.582854\pi$
$661$	−1.75754e46	−0.514731	−0.257366	+	0.966314i	$0.582854\pi$
$662$	− 1.98038e46i	− 0.565707i
$663$	1.75467e45i	0.0488903i
$664$	−5.97883e45	−0.162496
$665$	0	0
$666$	−1.48063e46	−0.382933
$667$	2.57446e45i	0.0649546i
$668$	1.57814e46i	0.388450i
$669$	1.15023e44	0.00276218
$670$	0	0
$671$	5.91918e46	1.35313
$672$	− 7.17947e44i	− 0.0160140i
$673$	6.04589e45i	0.131587i	0.997833	+	0.0657933i	$0.0209578\pi$
$673$	6.04589e45i	0.131587i	−0.997833	+	0.0657933i	$0.979042\pi$
$674$	2.25454e46	0.478818
$675$	0	0
$676$	−1.28416e46	−0.259716
$677$	3.42156e46i	0.675323i	0.941268	+	0.337662i	$0.109636\pi$
$677$	3.42156e46i	0.675323i	−0.941268	+	0.337662i	$0.890364\pi$
$678$	1.91830e46i	0.369509i
$679$	−5.13114e45	−0.0964635
$680$	0	0
$681$	1.96159e46	0.351301
$682$	− 2.25285e46i	− 0.393813i
$683$	2.32228e46i	0.396253i	0.980176	+	0.198127i	$0.0634857\pi$
$683$	2.32228e46i	0.396253i	−0.980176	+	0.198127i	$0.936514\pi$
$684$	2.53196e46	0.421726
$685$	0	0
$686$	−1.21910e46	−0.193505
$687$	3.31781e45i	0.0514121i
$688$	1.25499e47i	1.89858i
$689$	4.80368e45	0.0709507
$690$	0	0
$691$	8.01402e46	1.12840	0.564199	−	0.825638i	$-0.309185\pi$
$691$	8.01402e46	1.12840	0.564199	+	0.825638i	$0.309185\pi$
$692$	4.66159e46i	0.640890i
$693$	− 6.78253e45i	− 0.0910527i
$694$	2.64383e46	0.346580
$695$	0	0
$696$	−3.85245e45	−0.0481598
$697$	1.12989e46i	0.137942i
$698$	1.02569e47i	1.22294i
$699$	−3.84614e46	−0.447870
$700$	0	0
$701$	1.00753e47	1.11921	0.559605	−	0.828760i	$-0.310953\pi$
$701$	1.00753e47	1.11921	0.559605	+	0.828760i	$0.310953\pi$
$702$	− 3.18303e46i	− 0.345365i
$703$	3.83425e46i	0.406366i
$704$	−4.20806e46	−0.435645
$705$	0	0
$706$	−7.03997e46	−0.695494
$707$	1.34910e46i	0.130204i
$708$	7.00484e45i	0.0660464i
$709$	−1.27253e47	−1.17220	−0.586102	−	0.810237i	$-0.699338\pi$
$709$	−1.27253e47	−1.17220	−0.586102	+	0.810237i	$0.699338\pi$
$710$	0	0
$711$	1.47599e47	1.29788
$712$	− 1.17742e47i	− 1.01160i
$713$	8.56148e45i	0.0718740i
$714$	−1.00315e45	−0.00822893
$715$	0	0
$716$	−4.47301e44	−0.00350377
$717$	− 4.32524e46i	− 0.331088i
$718$	2.79630e47i	2.09185i
$719$	1.16194e47	0.849490	0.424745	−	0.905313i	$-0.360364\pi$
$719$	1.16194e47	0.849490	0.424745	+	0.905313i	$0.360364\pi$
$720$	0	0
$721$	−5.36874e45	−0.0374922
$722$	− 6.13549e46i	− 0.418780i
$723$	1.84421e46i	0.123035i
$724$	2.14779e46	0.140057
$725$	0	0
$726$	−2.04338e46	−0.127319
$727$	2.67321e47i	1.62823i	0.580705	+	0.814114i	$0.302777\pi$
$727$	2.67321e47i	1.62823i	−0.580705	+	0.814114i	$0.697223\pi$
$728$	− 5.74414e45i	− 0.0342025i
$729$	1.04493e47	0.608250
$730$	0	0
$731$	8.88177e46	0.494154
$732$	2.14485e46i	0.116671i
$733$	− 2.06440e47i	− 1.09794i	−0.835843	−	0.548968i	$-0.815021\pi$
$733$	− 2.06440e47i	− 1.09794i	0.835843	−	0.548968i	$-0.184979\pi$
$734$	−1.81073e47	−0.941606
$735$	0	0
$736$	−3.79695e46	−0.188778
$737$	− 9.17542e46i	− 0.446080i
$738$	− 9.88083e46i	− 0.469746i
$739$	3.44156e47	1.60001	0.800004	−	0.599994i	$-0.204831\pi$
$739$	3.44156e47	1.60001	0.800004	+	0.599994i	$0.204831\pi$
$740$	0	0
$741$	−3.97361e46	−0.176679
$742$	2.74627e45i	0.0119420i
$743$	− 3.56403e47i	− 1.51575i	−0.652402	−	0.757873i	$-0.726239\pi$
$743$	− 3.56403e47i	− 1.51575i	0.652402	−	0.757873i	$-0.273761\pi$
$744$	−1.28115e46	−0.0532901
$745$	0	0
$746$	−1.75088e47	−0.696732
$747$	− 5.39749e46i	− 0.210088i
$748$	− 3.91107e46i	− 0.148909i
$749$	−4.17516e46	−0.155497
$750$	0	0
$751$	−3.38219e46	−0.120542	−0.0602710	−	0.998182i	$-0.519196\pi$
$751$	−3.38219e46	−0.120542	−0.0602710	+	0.998182i	$0.519196\pi$
$752$	− 3.26242e47i	− 1.13749i
$753$	2.49779e46i	0.0851999i
$754$	5.17940e46	0.172843
$755$	0	0
$756$	5.09818e45	0.0162857
$757$	1.03676e47i	0.324038i	0.986788	+	0.162019i	$0.0518006\pi$
$757$	1.03676e47i	0.324038i	−0.986788	+	0.162019i	$0.948199\pi$
$758$	− 8.34461e46i	− 0.255190i
$759$	2.66802e46	0.0798362
$760$	0	0
$761$	1.98844e47	0.569726	0.284863	−	0.958568i	$-0.408052\pi$
$761$	1.98844e47	0.569726	0.284863	+	0.958568i	$0.408052\pi$
$762$	− 1.51677e47i	− 0.425269i
$763$	− 4.75945e46i	− 0.130588i
$764$	1.35948e47	0.365033
$765$	0	0
$766$	−7.53000e47	−1.93651
$767$	1.47799e47i	0.372005i
$768$	− 1.08270e47i	− 0.266715i
$769$	4.79063e47	1.15507	0.577534	−	0.816367i	$-0.304015\pi$
$769$	4.79063e47	1.15507	0.577534	+	0.816367i	$0.304015\pi$
$770$	0	0
$771$	−3.59664e46	−0.0830805
$772$	2.09406e47i	0.473482i
$773$	− 3.87609e47i	− 0.857891i	−0.903330	−	0.428946i	$-0.858885\pi$
$773$	− 3.87609e47i	− 0.857891i	0.903330	−	0.428946i	$-0.141115\pi$
$774$	−7.76705e47	−1.68279
$775$	0	0
$776$	−4.06076e47	−0.843120
$777$	3.72178e45i	0.00756491i
$778$	− 6.56019e47i	− 1.30543i
$779$	−2.55874e47	−0.498492
$780$	0	0
$781$	−4.26351e47	−0.796206
$782$	5.30526e46i	0.0970053i
$783$	− 7.21441e46i	− 0.129161i
$784$	−7.01265e47	−1.22933
$785$	0	0
$786$	2.45787e46	0.0413130
$787$	1.12069e48i	1.84461i	0.386465	+	0.922304i	$0.373696\pi$
$787$	1.12069e48i	1.84461i	−0.386465	+	0.922304i	$0.626304\pi$
$788$	− 1.91464e47i	− 0.308606i
$789$	2.75018e47	0.434101
$790$	0	0
$791$	−6.48282e46	−0.0981413
$792$	− 5.36766e47i	− 0.795828i
$793$	4.52555e47i	0.657148i
$794$	−7.07838e47	−1.00669
$795$	0	0
$796$	5.07921e47	0.692995
$797$	9.96509e47i	1.33174i	0.746069	+	0.665869i	$0.231939\pi$
$797$	9.96509e47i	1.33174i	−0.746069	+	0.665869i	$0.768061\pi$
$798$	− 2.27171e46i	− 0.0297376i
$799$	−2.30888e47	−0.296059
$800$	0	0
$801$	1.06293e48	1.30788
$802$	− 1.62946e48i	− 1.96411i
$803$	− 4.35935e47i	− 0.514772i
$804$	3.32477e46	0.0384624
$805$	0	0
$806$	1.72243e47	0.191256
$807$	3.38311e47i	0.368047i
$808$	1.06767e48i	1.13802i
$809$	−9.98570e47	−1.04286	−0.521432	−	0.853293i	$-0.674602\pi$
$809$	−9.98570e47	−1.04286	−0.521432	+	0.853293i	$0.674602\pi$
$810$	0	0
$811$	−1.14204e48	−1.14509	−0.572544	−	0.819874i	$-0.694043\pi$
$811$	−1.14204e48	−1.14509	−0.572544	+	0.819874i	$0.694043\pi$
$812$	8.29571e45i	0.00815040i
$813$	− 3.11995e47i	− 0.300368i
$814$	−5.17937e47	−0.488624
$815$	0	0
$816$	−1.15802e47	−0.104913
$817$	2.01136e48i	1.78577i
$818$	− 1.66791e47i	− 0.145126i
$819$	5.18562e46	0.0442198
$820$	0	0
$821$	1.20008e48	0.982989	0.491495	−	0.870881i	$-0.336451\pi$
$821$	1.20008e48	0.982989	0.491495	+	0.870881i	$0.336451\pi$
$822$	− 1.77746e47i	− 0.142697i
$823$	8.31615e47i	0.654372i	0.944960	+	0.327186i	$0.106100\pi$
$823$	8.31615e47i	0.654372i	−0.944960	+	0.327186i	$0.893900\pi$
$824$	−4.24880e47	−0.327693
$825$	0	0
$826$	−8.44969e46	−0.0626138
$827$	7.47488e47i	0.542955i	0.962445	+	0.271477i	$0.0875122\pi$
$827$	7.47488e47i	0.542955i	−0.962445	+	0.271477i	$0.912488\pi$
$828$	− 1.29978e47i	− 0.0925484i
$829$	2.01484e48	1.40634	0.703171	−	0.711020i	$-0.251767\pi$
$829$	2.01484e48	1.40634	0.703171	+	0.711020i	$0.251767\pi$
$830$	0	0
$831$	5.21294e47	0.349676
$832$	− 3.21730e47i	− 0.211571i
$833$	4.96298e47i	0.319963i
$834$	7.30716e47	0.461858
$835$	0	0
$836$	8.85698e47	0.538124
$837$	− 2.39918e47i	− 0.142920i
$838$	1.08474e48i	0.633576i
$839$	6.19222e47	0.354629	0.177314	−	0.984154i	$-0.443259\pi$
$839$	6.19222e47	0.354629	0.177314	+	0.984154i	$0.443259\pi$
$840$	0	0
$841$	−1.69868e48	−0.935359
$842$	− 4.11516e48i	− 2.22197i
$843$	− 6.97156e47i	− 0.369126i
$844$	−2.64005e46	−0.0137076
$845$	0	0
$846$	2.01910e48	1.00820
$847$	− 6.90554e46i	− 0.0338159i
$848$	3.17026e47i	0.152252i
$849$	1.05627e48	0.497506
$850$	0	0
$851$	1.96831e47	0.0891776
$852$	− 1.54491e47i	− 0.0686514i
$853$	3.53602e48i	1.54119i	0.637327	+	0.770594i	$0.280040\pi$
$853$	3.53602e48i	1.54119i	−0.637327	+	0.770594i	$0.719960\pi$
$854$	−2.58726e47	−0.110607
$855$	0	0
$856$	−3.30420e48	−1.35909
$857$	− 9.74863e47i	− 0.393333i	−0.980470	−	0.196666i	$-0.936988\pi$
$857$	− 9.74863e47i	− 0.393333i	0.980470	−	0.196666i	$-0.0630116\pi$
$858$	− 5.36763e47i	− 0.212443i
$859$	4.20702e48	1.63338	0.816690	−	0.577076i	$-0.195806\pi$
$859$	4.20702e48	1.63338	0.816690	+	0.577076i	$0.195806\pi$
$860$	0	0
$861$	−2.48369e46	−0.00927993
$862$	− 1.71740e48i	− 0.629509i
$863$	6.84409e46i	0.0246115i	0.999924	+	0.0123057i	$0.00391714\pi$
$863$	6.84409e46i	0.0246115i	−0.999924	+	0.0123057i	$0.996083\pi$
$864$	1.06402e48	0.375381
$865$	0	0
$866$	2.71223e48	0.921045
$867$	− 7.07748e47i	− 0.235811i
$868$	2.75877e46i	0.00901863i
$869$	5.16312e48	1.65610
$870$	0	0
$871$	7.01513e47	0.216639
$872$	− 3.76660e48i	− 1.14137i
$873$	− 3.66592e48i	− 1.09005i
$874$	−1.20142e48	−0.350556
$875$	0	0
$876$	1.57963e47	0.0443853
$877$	6.44909e48i	1.77830i	0.457615	+	0.889150i	$0.348704\pi$
$877$	6.44909e48i	1.77830i	−0.457615	+	0.889150i	$0.651296\pi$
$878$	4.60942e48i	1.24735i
$879$	−2.33609e47	−0.0620402
$880$	0	0
$881$	3.47493e48	0.888882	0.444441	−	0.895808i	$-0.353402\pi$
$881$	3.47493e48	0.888882	0.444441	+	0.895808i	$0.353402\pi$
$882$	− 4.34010e48i	− 1.08960i
$883$	4.36520e48i	1.07560i	0.843071	+	0.537802i	$0.180745\pi$
$883$	4.36520e48i	1.07560i	−0.843071	+	0.537802i	$0.819255\pi$
$884$	2.99024e47	0.0723175
$885$	0	0
$886$	−4.67996e48	−1.09040
$887$	4.94841e48i	1.13168i	0.824513	+	0.565842i	$0.191449\pi$
$887$	4.94841e48i	1.13168i	−0.824513	+	0.565842i	$0.808551\pi$
$888$	2.94540e47i	0.0661196i
$889$	5.12589e47	0.112951
$890$	0	0
$891$	4.45851e48	0.946690
$892$	− 1.96017e46i	− 0.00408576i
$893$	− 5.22866e48i	− 1.06990i
$894$	3.84272e47	0.0771915
$895$	0	0
$896$	4.98297e47	0.0964731
$897$	2.03985e47i	0.0387725i
$898$	4.48864e48i	0.837635i
$899$	3.90393e47	0.0715266
$900$	0	0
$901$	2.24365e47	0.0396274
$902$	− 3.45639e48i	− 0.599398i
$903$	1.95236e47i	0.0332439i
$904$	−5.13047e48	−0.857785
$905$	0	0
$906$	−5.97571e47	−0.0963328
$907$	3.55400e48i	0.562596i	0.959620	+	0.281298i	$0.0907650\pi$
$907$	3.55400e48i	0.562596i	−0.959620	+	0.281298i	$0.909235\pi$
$908$	− 3.34285e48i	− 0.519638i
$909$	−9.63856e48	−1.47132
$910$	0	0
$911$	4.07509e48	0.599908	0.299954	−	0.953954i	$-0.403029\pi$
$911$	4.07509e48	0.599908	0.299954	+	0.953954i	$0.403029\pi$
$912$	− 2.62244e48i	− 0.379132i
$913$	− 1.88809e48i	− 0.268074i
$914$	−1.17236e49	−1.63474
$915$	0	0
$916$	5.65407e47	0.0760477
$917$	8.30629e46i	0.0109727i
$918$	− 1.48669e48i	− 0.192893i
$919$	−6.75427e47	−0.0860740	−0.0430370	−	0.999073i	$-0.513703\pi$
$919$	−6.75427e47	−0.0860740	−0.0430370	+	0.999073i	$0.513703\pi$
$920$	0	0
$921$	−3.77312e48	−0.463892
$922$	1.80734e49i	2.18263i
$923$	− 3.25970e48i	− 0.386678i
$924$	8.59718e46	0.0100177
$925$	0	0
$926$	−7.66744e48	−0.862122
$927$	− 3.83567e48i	− 0.423668i
$928$	1.73136e48i	0.187865i
$929$	−3.55712e48	−0.379174	−0.189587	−	0.981864i	$-0.560715\pi$
$929$	−3.55712e48	−0.379174	−0.189587	+	0.981864i	$0.560715\pi$
$930$	0	0
$931$	−1.12391e49	−1.15628
$932$	6.55444e48i	0.662480i
$933$	− 1.48938e48i	− 0.147897i
$934$	7.11966e48	0.694602
$935$	0	0
$936$	4.10388e48	0.386494
$937$	5.42233e48i	0.501744i	0.968020	+	0.250872i	$0.0807173\pi$
$937$	5.42233e48i	0.501744i	−0.968020	+	0.250872i	$0.919283\pi$
$938$	4.01055e47i	0.0364634i
$939$	−4.68773e48	−0.418774
$940$	0	0
$941$	1.76662e49	1.52375	0.761877	−	0.647722i	$-0.224278\pi$
$941$	1.76662e49	1.52375	0.761877	+	0.647722i	$0.224278\pi$
$942$	− 3.76427e48i	− 0.319037i
$943$	1.31353e48i	0.109395i
$944$	−9.75422e48	−0.798279
$945$	0	0
$946$	−2.71698e49	−2.14725
$947$	− 9.85410e48i	− 0.765318i	−0.923890	−	0.382659i	$-0.875008\pi$
$947$	− 9.85410e48i	− 0.765318i	0.923890	−	0.382659i	$-0.124992\pi$
$948$	1.87089e48i	0.142794i
$949$	3.33297e48	0.249999
$950$	0	0
$951$	3.67292e48	0.266092
$952$	− 2.68291e47i	− 0.0191028i
$953$	− 1.89853e49i	− 1.32857i	−0.747480	−	0.664284i	$-0.768737\pi$
$953$	− 1.89853e49i	− 1.32857i	0.747480	−	0.664284i	$-0.231263\pi$
$954$	−1.96206e48	−0.134947
$955$	0	0
$956$	−7.37089e48	−0.489739
$957$	− 1.21658e48i	− 0.0794503i
$958$	− 1.81509e49i	− 1.16511i
$959$	6.00686e47	0.0379001
$960$	0	0
$961$	−1.51052e49	−0.920854
$962$	− 3.95992e48i	− 0.237300i
$963$	− 2.98293e49i	− 1.75715i
$964$	3.14283e48	0.181991
$965$	0	0
$966$	−1.16618e47	−0.00652596
$967$	1.65793e49i	0.912070i	0.889962	+	0.456035i	$0.150731\pi$
$967$	1.65793e49i	0.912070i	−0.889962	+	0.456035i	$0.849269\pi$
$968$	− 5.46501e48i	− 0.295561i
$969$	−1.85595e48	−0.0986787
$970$	0	0
$971$	1.44525e49	0.742723	0.371361	−	0.928488i	$-0.378891\pi$
$971$	1.44525e49	0.742723	0.371361	+	0.928488i	$0.378891\pi$
$972$	5.52885e48i	0.279346i
$973$	2.46943e48i	0.122669i
$974$	1.23272e49	0.602061
$975$	0	0
$976$	−2.98670e49	−1.41016
$977$	− 1.83197e49i	− 0.850467i	−0.905084	−	0.425234i	$-0.860192\pi$
$977$	− 1.83197e49i	− 0.850467i	0.905084	−	0.425234i	$-0.139808\pi$
$978$	5.14501e48i	0.234853i
$979$	3.71822e49	1.66886
$980$	0	0
$981$	3.40037e49	1.47566
$982$	− 1.12017e49i	− 0.478020i
$983$	9.70579e48i	0.407285i	0.979045	+	0.203642i	$0.0652780\pi$
$983$	9.70579e48i	0.407285i	−0.979045	+	0.203642i	$0.934722\pi$
$984$	−1.96558e48	−0.0811094
$985$	0	0
$986$	2.41914e48	0.0965364
$987$	− 5.07529e47i	− 0.0199172i
$988$	6.77166e48i	0.261340i
$989$	1.03253e49	0.391889
$990$	0	0
$991$	−1.33593e49	−0.490421	−0.245210	−	0.969470i	$-0.578857\pi$
$991$	−1.33593e49	−0.490421	−0.245210	+	0.969470i	$0.578857\pi$
$992$	5.75772e48i	0.207878i
$993$	− 3.55648e48i	− 0.126287i
$994$	1.86357e48	0.0650834
$995$	0	0
$996$	6.84159e47	0.0231142
$997$	− 3.08053e49i	− 1.02366i	−0.859088	−	0.511829i	$-0.828968\pi$
$997$	− 3.08053e49i	− 1.02366i	0.859088	−	0.511829i	$-0.171032\pi$
$998$	8.56533e48i	0.279956i
$999$	−5.51580e48	−0.177328

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.b.d.24.5		22
5.2	odd	4		25.34.a.d.1.9	✓	11
5.3	odd	4		25.34.a.e.1.3	yes	11
5.4	even	2	inner	25.34.b.d.24.18		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.34.a.d.1.9	✓	11	5.2	odd	4
25.34.a.e.1.3	yes	11	5.3	odd	4
25.34.b.d.24.5		22	1.1	even	1	trivial
25.34.b.d.24.18		22	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-109239. i q^{2} -1.96178e7i q^{3} -3.34318e9 q^{4} -2.14302e12 q^{6} -7.24227e12i q^{7} -5.73150e14i q^{8} +5.17420e15 q^{9} +O(q^{10})\)	\(q-109239. i q^{2} -1.96178e7i q^{3} -3.34318e9 q^{4} -2.14302e12 q^{6} -7.24227e12i q^{7} -5.73150e14i q^{8} +5.17420e15 q^{9} +1.80998e17 q^{11} +6.55856e16i q^{12} +1.38383e18i q^{13} -7.91136e17 q^{14} -9.13278e19 q^{16} +6.46344e19i q^{17} -5.65224e20i q^{18} -1.46370e21 q^{19} -1.42077e20 q^{21} -1.97720e22i q^{22} +7.51392e21i q^{23} -1.12439e22 q^{24} +1.51168e23 q^{26} -2.10563e23i q^{27} +2.42122e22i q^{28} +3.42626e23 q^{29} +1.13942e24 q^{31} +5.05322e24i q^{32} -3.55077e24i q^{33} +7.06058e24 q^{34} -1.72983e25 q^{36} -2.61955e25i q^{37} +1.59893e26i q^{38} +2.71476e25 q^{39} +1.74813e26 q^{41} +1.55203e25i q^{42} -1.37416e27i q^{43} -6.05108e26 q^{44} +8.20811e26 q^{46} +3.57221e27i q^{47} +1.79165e27i q^{48} +7.67854e27 q^{49} +1.26798e27 q^{51} -4.62639e27i q^{52} -3.47129e27i q^{53} -2.30016e28 q^{54} -4.15090e27 q^{56} +2.87146e28i q^{57} -3.74280e28i q^{58} +1.06805e29 q^{59} +3.27030e29 q^{61} -1.24468e29i q^{62} -3.74730e28i q^{63} -2.32492e29 q^{64} -3.87882e29 q^{66} -5.06936e29i q^{67} -2.16084e29i q^{68} +1.47406e29 q^{69} -2.35556e30 q^{71} -2.96559e30i q^{72} -2.40851e30i q^{73} -2.86157e30 q^{74} +4.89342e30 q^{76} -1.31083e30i q^{77} -2.96557e30i q^{78} +2.85259e31 q^{79} +2.46330e31 q^{81} -1.90963e31i q^{82} -1.04315e31i q^{83} +4.74988e29 q^{84} -1.50111e32 q^{86} -6.72154e30i q^{87} -1.03739e32i q^{88} +2.05429e32 q^{89} +1.00221e31 q^{91} -2.51204e31i q^{92} -2.23528e31i q^{93} +3.90224e32 q^{94} +9.91329e31 q^{96} -7.08500e32i q^{97} -8.38795e32i q^{98} +9.36520e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 98676413354 q^{4} - 35567955353446 q^{6} - 48\!\cdots\!16 q^{9}+O(q^{10}) \) 22 * q - 98676413354 * q^4 - 35567955353446 * q^6 - 48599275949251316 * q^9	\( 22 q - 98676413354 q^{4} - 35567955353446 q^{6} - 48\!\cdots\!16 q^{9}+ \cdots - 26\!\cdots\!12 q^{99}+O(q^{100}) \) 22 * q - 98676413354 * q^4 - 35567955353446 * q^6 - 48599275949251316 * q^9 - 388975069134227046 * q^11 - 19390008595334902068 * q^14 + 575591759119330759202 * q^16 + 4608842794243084808630 * q^19 + 7903359076848510896124 * q^21 + 404192556148581428871090 * q^24 + 464682665356996878920184 * q^26 - 3351264573191459117593680 * q^29 - 3759368993361156279858876 * q^31 + 89746721762579763434900102 * q^34 + 387355373506331566119004012 * q^36 + 718345493252093200854565688 * q^39 + 1099039609507795057059146334 * q^41 + 5953087248173453754548821422 * q^44 + 3376724462669734942026715164 * q^46 + 5003317848948805057160966146 * q^49 + 132635930632492996145333201114 * q^51 + 426786304479392249563776060130 * q^54 + 679074245273936256251630129820 * q^56 + 135413981096960311593168243840 * q^59 - 689538516943594572498942901796 * q^61 - 2840052535921821128029255801474 * q^64 - 320033315173213395102299074022 * q^66 - 14437009323987384127917423522852 * q^69 - 11051811216899923387221184379736 * q^71 - 16966204054892971302102433594308 * q^74 - 7588775596602318790343300932510 * q^76 - 56833627147150708379517479188380 * q^79 - 9022895406968638344517956762058 * q^81 + 599893154314490734522302146543532 * q^84 + 911820864247632195182318378176824 * q^86 + 48061740522903759998741201101110 * q^89 - 693375717774307216790074646600496 * q^91 - 465076424153121919006535311120888 * q^94 - 3684220565182840604743827051904706 * q^96 - 2601899095573470033938075107273612 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more