LMFDB - Embedded newform 25.34.b.a.24.1

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:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1178101x^{2} + 346979902500 $ x^4 + 1178101*x^2 + 346979902500
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{4}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 1)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.1
Root			$-767.996i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.34.b.a.24.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-171359. i q^{2} -5.34420e7i q^{3} -2.07741e10 q^{4} -9.15779e12 q^{6} +5.50153e13i q^{7} +2.08788e15i q^{8} +2.70301e15 q^{9} +O(q^{10})$	\(q-171359. i q^{2} -5.34420e7i q^{3} -2.07741e10 q^{4} -9.15779e12 q^{6} +5.50153e13i q^{7} +2.08788e15i q^{8} +2.70301e15 q^{9} -8.18909e16 q^{11} +1.11021e18i q^{12} +1.90399e18i q^{13} +9.42739e18 q^{14} +1.79329e20 q^{16} -3.33893e20i q^{17} -4.63187e20i q^{18} +1.40494e20 q^{19} +2.94013e21 q^{21} +1.40328e22i q^{22} -3.12767e22i q^{23} +1.11580e23 q^{24} +3.26267e23 q^{26} -4.41542e23i q^{27} -1.14289e24i q^{28} +1.50979e24 q^{29} +5.18762e23 q^{31} -1.27950e25i q^{32} +4.37641e24i q^{33} -5.72158e25 q^{34} -5.61527e25 q^{36} -3.01507e25i q^{37} -2.40749e25i q^{38} +1.01753e26 q^{39} -2.18887e26 q^{41} -5.03818e26i q^{42} -1.76701e27i q^{43} +1.70121e27 q^{44} -5.35955e27 q^{46} +3.25654e27i q^{47} -9.58369e27i q^{48} +4.70431e27 q^{49} -1.78439e28 q^{51} -3.95538e28i q^{52} -9.17652e27i q^{53} -7.56623e28 q^{54} -1.14865e29 q^{56} -7.50826e27i q^{57} -2.58716e29i q^{58} +1.18267e29 q^{59} -9.92930e27 q^{61} -8.88948e28i q^{62} +1.48707e29i q^{63} -6.52116e29 q^{64} +7.49940e29 q^{66} +1.11293e30i q^{67} +6.93634e30i q^{68} -1.67149e30 q^{69} +7.58425e29 q^{71} +5.64355e30i q^{72} +6.06835e30i q^{73} -5.16661e30 q^{74} -2.91863e30 q^{76} -4.50525e30i q^{77} -1.74364e31i q^{78} +5.57890e30 q^{79} -8.57067e30 q^{81} +3.75083e31i q^{82} -4.13746e31i q^{83} -6.10785e31 q^{84} -3.02793e32 q^{86} -8.06860e31i q^{87} -1.70978e32i q^{88} -6.21572e31 q^{89} -1.04749e32 q^{91} +6.49745e32i q^{92} -2.77237e31i q^{93} +5.58039e32 q^{94} -6.83789e32 q^{96} +4.04003e32i q^{97} -8.06129e32i q^{98} -2.21352e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 29304467968 q^{4} - 19857844386432 q^{6} + 16\!\cdots\!08 q^{9}+O(q^{10}) $ 4 * q - 29304467968 * q^4 - 19857844386432 * q^6 + 16042273909941708 * q^9	$ 4 q - 29304467968 q^{4} - 19857844386432 q^{6} + 16\!\cdots\!08 q^{9}+ \cdots + 18\!\cdots\!56 q^{99}+O(q^{100}) $ 4 * q - 29304467968 * q^4 - 19857844386432 * q^6 + 16042273909941708 * q^9 + 267743630883828528 * q^11 + 30993282524936680704 * q^14 + 391211958223788703744 * q^16 + 2721392886083394343600 * q^19 + 9672877686165602283648 * q^21 + 200471037176639420006400 * q^24 + 545463367269284185420608 * q^26 + 3349039943260799858219400 * q^29 - 12476602451447264674191232 * q^31 - 139721581072333832146151616 * q^34 - 47191510192394271217153536 * q^36 + 170052544876039337673566496 * q^39 + 555133226044004365464376488 * q^41 + 6044171828775532171616692224 * q^44 - 11227101269526771362941738752 * q^46 - 4979598731777777866889702628 * q^49 - 43589619182878870777337248992 * q^51 - 168100149856471058168032147200 * q^54 - 51150475590343517519644262400 * q^56 + 611572819270596866053327990800 * q^59 - 11491787966826529718134724872 * q^61 - 1728730644720761719947419189248 * q^64 + 1167116717113660076116539326976 * q^66 - 3501697060634855952551484887424 * q^69 - 5339523875912209431473620169952 * q^71 - 2915873996160038988422692385856 * q^74 + 9102629314941605097126324070400 * q^76 + 17070399945531272939460212382400 * q^79 + 36744800901410202817388860698084 * q^81 - 98939068122295455684135817199616 * q^84 - 625393771475157003834429652812672 * q^86 - 265438935311208632529877195453800 * q^89 + 53804204294904716821097774423488 * q^91 + 901012867777735797670099123060224 * q^94 - 1587582565113120422998050185674752 * q^96 + 1852201390665529560061313880141456 * 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 $

$2$	− 171359.i	− 1.84890i	−0.381305	−	0.924449i	$-0.624525\pi$
$2$	− 171359.i	− 1.84890i	0.381305	−	0.924449i	$-0.375475\pi$
$3$	− 5.34420e7i	− 0.716774i	−0.933573	−	0.358387i	$-0.883327\pi$
$3$	− 5.34420e7i	− 0.716774i	0.933573	−	0.358387i	$-0.116673\pi$
$4$	−2.07741e10	−2.41843
$5$	0	0
$5$	0	0
$6$	−9.15779e12	−1.32524
$7$	5.50153e13i	0.625699i	0.949803	+	0.312850i	$0.101284\pi$
$7$	5.50153e13i	0.625699i	−0.949803	+	0.312850i	$0.898716\pi$
$8$	2.08788e15i	2.62253i
$9$	2.70301e15	0.486236
$10$	0	0
$11$	−8.18909e16	−0.537349	−0.268674	−	0.963231i	$-0.586586\pi$
$11$	−8.18909e16	−0.537349	−0.268674	+	0.963231i	$0.586586\pi$
$12$	1.11021e18i	1.73346i
$13$	1.90399e18i	0.793597i	0.917906	+	0.396798i	$0.129879\pi$
$13$	1.90399e18i	0.793597i	−0.917906	+	0.396798i	$0.870121\pi$
$14$	9.42739e18	1.15685
$15$	0	0
$16$	1.79329e20	2.43036
$17$	− 3.33893e20i	− 1.66418i	−0.554640	−	0.832090i	$-0.687144\pi$
$17$	− 3.33893e20i	− 1.66418i	0.554640	−	0.832090i	$-0.312856\pi$
$18$	− 4.63187e20i	− 0.899000i
$19$	1.40494e20	0.111743	0.0558717	−	0.998438i	$-0.482206\pi$
$19$	1.40494e20	0.111743	0.0558717	+	0.998438i	$0.482206\pi$
$20$	0	0
$21$	2.94013e21	0.448485
$22$	1.40328e22i	0.993503i
$23$	− 3.12767e22i	− 1.06344i	−0.846922	−	0.531718i	$-0.821547\pi$
$23$	− 3.12767e22i	− 1.06344i	0.846922	−	0.531718i	$-0.178453\pi$
$24$	1.11580e23	1.87976
$25$	0	0
$26$	3.26267e23	1.46728
$27$	− 4.41542e23i	− 1.06529i
$28$	− 1.14289e24i	− 1.51321i
$29$	1.50979e24	1.12034	0.560168	−	0.828379i	$-0.310736\pi$
$29$	1.50979e24	1.12034	0.560168	+	0.828379i	$0.310736\pi$
$30$	0	0
$31$	5.18762e23	0.128086	0.0640428	−	0.997947i	$-0.479601\pi$
$31$	5.18762e23	0.128086	0.0640428	+	0.997947i	$0.479601\pi$
$32$	− 1.27950e25i	− 1.87096i
$33$	4.37641e24i	0.385157i
$34$	−5.72158e25	−3.07690
$35$	0	0
$36$	−5.61527e25	−1.17592
$37$	− 3.01507e25i	− 0.401762i	−0.979616	−	0.200881i	$-0.935620\pi$
$37$	− 3.01507e25i	− 0.401762i	0.979616	−	0.200881i	$-0.0643805\pi$
$38$	− 2.40749e25i	− 0.206602i
$39$	1.01753e26	0.568829
$40$	0	0
$41$	−2.18887e26	−0.536149	−0.268075	−	0.963398i	$-0.586387\pi$
$41$	−2.18887e26	−0.536149	−0.268075	+	0.963398i	$0.586387\pi$
$42$	− 5.03818e26i	− 0.829203i
$43$	− 1.76701e27i	− 1.97246i	−0.165369	−	0.986232i	$-0.552882\pi$
$43$	− 1.76701e27i	− 1.97246i	0.165369	−	0.986232i	$-0.447118\pi$
$44$	1.70121e27	1.29954
$45$	0	0
$46$	−5.35955e27	−1.96618
$47$	3.25654e27i	0.837802i	0.908032	+	0.418901i	$0.137585\pi$
$47$	3.25654e27i	0.837802i	−0.908032	+	0.418901i	$0.862415\pi$
$48$	− 9.58369e27i	− 1.74202i
$49$	4.70431e27	0.608500
$50$	0	0
$51$	−1.78439e28	−1.19284
$52$	− 3.95538e28i	− 1.91926i
$53$	− 9.17652e27i	− 0.325182i	−0.986694	−	0.162591i	$-0.948015\pi$
$53$	− 9.17652e27i	− 0.325182i	0.986694	−	0.162591i	$-0.0519850\pi$
$54$	−7.56623e28	−1.96962
$55$	0	0
$56$	−1.14865e29	−1.64091
$57$	− 7.50826e27i	− 0.0800948i
$58$	− 2.58716e29i	− 2.07139i
$59$	1.18267e29	0.714174	0.357087	−	0.934071i	$-0.383770\pi$
$59$	1.18267e29	0.714174	0.357087	+	0.934071i	$0.383770\pi$
$60$	0	0
$61$	−9.92930e27	−0.0345920	−0.0172960	−	0.999850i	$-0.505506\pi$
$61$	−9.92930e27	−0.0345920	−0.0172960	+	0.999850i	$0.505506\pi$
$62$	− 8.88948e28i	− 0.236817i
$63$	1.48707e29i	0.304237i
$64$	−6.52116e29	−1.02886
$65$	0	0
$66$	7.49940e29	0.712117
$67$	1.11293e30i	0.824583i	0.911052	+	0.412291i	$0.135271\pi$
$67$	1.11293e30i	0.824583i	−0.911052	+	0.412291i	$0.864729\pi$
$68$	6.93634e30i	4.02470i
$69$	−1.67149e30	−0.762242
$70$	0	0
$71$	7.58425e29	0.215849	0.107924	−	0.994159i	$-0.465580\pi$
$71$	7.58425e29	0.215849	0.107924	+	0.994159i	$0.465580\pi$
$72$	5.64355e30i	1.27517i
$73$	6.06835e30i	1.09205i	0.837768	+	0.546026i	$0.183860\pi$
$73$	6.06835e30i	1.09205i	−0.837768	+	0.546026i	$0.816140\pi$
$74$	−5.16661e30	−0.742818
$75$	0	0
$76$	−2.91863e30	−0.270243
$77$	− 4.50525e30i	− 0.336219i
$78$	− 1.74364e31i	− 1.05171i
$79$	5.57890e30	0.272711	0.136355	−	0.990660i	$-0.456461\pi$
$79$	5.57890e30	0.272711	0.136355	+	0.990660i	$0.456461\pi$
$80$	0	0
$81$	−8.57067e30	−0.277339
$82$	3.75083e31i	0.991286i
$83$	− 4.13746e31i	− 0.895252i	−0.894221	−	0.447626i	$-0.852270\pi$
$83$	− 4.13746e31i	− 0.895252i	0.894221	−	0.447626i	$-0.147730\pi$
$84$	−6.10785e31	−1.08463
$85$	0	0
$86$	−3.02793e32	−3.64688
$87$	− 8.06860e31i	− 0.803028i
$88$	− 1.70978e32i	− 1.40921i
$89$	−6.21572e31	−0.425164	−0.212582	−	0.977143i	$-0.568187\pi$
$89$	−6.21572e31	−0.425164	−0.212582	+	0.977143i	$0.568187\pi$
$90$	0	0
$91$	−1.04749e32	−0.496553
$92$	6.49745e32i	2.57184i
$93$	− 2.77237e31i	− 0.0918084i
$94$	5.58039e32	1.54901
$95$	0	0
$96$	−6.83789e32	−1.34106
$97$	4.04003e32i	0.667808i	0.942607	+	0.333904i	$0.108366\pi$
$97$	4.04003e32i	0.667808i	−0.942607	+	0.333904i	$0.891634\pi$
$98$	− 8.06129e32i	− 1.12506i
$99$	−2.21352e32	−0.261278
$100$	0	0
$101$	−1.20576e33	−1.02319	−0.511596	−	0.859226i	$-0.670946\pi$
$101$	−1.20576e33	−1.02319	−0.511596	+	0.859226i	$0.670946\pi$
$102$	3.05773e33i	2.20544i
$103$	1.69378e33i	1.04002i	0.854159	+	0.520011i	$0.174072\pi$
$103$	1.69378e33i	1.04002i	−0.854159	+	0.520011i	$0.825928\pi$
$104$	−3.97530e33	−2.08123
$105$	0	0
$106$	−1.57248e33	−0.601228
$107$	7.07121e32i	0.231559i	0.993275	+	0.115780i	$0.0369366\pi$
$107$	7.07121e32i	0.231559i	−0.993275	+	0.115780i	$0.963063\pi$
$108$	9.17264e33i	2.57634i
$109$	−4.42814e33	−1.06828	−0.534139	−	0.845397i	$-0.679364\pi$
$109$	−4.42814e33	−1.06828	−0.534139	+	0.845397i	$0.679364\pi$
$110$	0	0
$111$	−1.61131e33	−0.287973
$112$	9.86582e33i	1.52067i
$113$	− 1.36496e34i	− 1.81687i	−0.418023	−	0.908437i	$-0.637277\pi$
$113$	− 1.36496e34i	− 1.81687i	0.418023	−	0.908437i	$-0.362723\pi$
$114$	−1.28661e33	−0.148087
$115$	0	0
$116$	−3.13645e34	−2.70945
$117$	5.14652e33i	0.385875i
$118$	− 2.02661e34i	− 1.32043i
$119$	1.83692e34	1.04128
$120$	0	0
$121$	−1.65190e34	−0.711256
$122$	1.70148e33i	0.0639572i
$123$	1.16977e34i	0.384298i
$124$	−1.07768e34	−0.309766
$125$	0	0
$126$	2.54823e34	0.562504
$127$	− 7.12185e34i	− 1.37985i	−0.723881	−	0.689925i	$-0.757644\pi$
$127$	− 7.12185e34i	− 1.37985i	0.723881	−	0.689925i	$-0.242356\pi$
$128$	1.83832e33i	0.0312936i
$129$	−9.44324e34	−1.41381
$130$	0	0
$131$	−2.95217e34	−0.342898	−0.171449	−	0.985193i	$-0.554845\pi$
$131$	−2.95217e34	−0.342898	−0.171449	+	0.985193i	$0.554845\pi$
$132$	− 9.09161e34i	− 0.931475i
$133$	7.72929e33i	0.0699178i
$134$	1.90711e35	1.52457
$135$	0	0
$136$	6.97128e35	4.36436
$137$	8.90834e34i	0.494205i	0.968989	+	0.247103i	$0.0794785\pi$
$137$	8.90834e34i	0.494205i	−0.968989	+	0.247103i	$0.920521\pi$
$138$	2.86425e35i	1.40931i
$139$	3.61707e35	1.57984	0.789920	−	0.613210i	$-0.210122\pi$
$139$	3.61707e35	1.57984	0.789920	+	0.613210i	$0.210122\pi$
$140$	0	0
$141$	1.74036e35	0.600515
$142$	− 1.29963e35i	− 0.399083i
$143$	− 1.55920e35i	− 0.426438i
$144$	4.84728e35	1.18173
$145$	0	0
$146$	1.03987e36	2.01909
$147$	− 2.51408e35i	− 0.436157i
$148$	6.26354e35i	0.971632i
$149$	−1.73500e35	−0.240839	−0.120419	−	0.992723i	$-0.538424\pi$
$149$	−1.73500e35	−0.240839	−0.120419	+	0.992723i	$0.538424\pi$
$150$	0	0
$151$	−1.35744e36	−1.51217	−0.756085	−	0.654473i	$-0.772891\pi$
$151$	−1.35744e36	−1.51217	−0.756085	+	0.654473i	$0.772891\pi$
$152$	2.93333e35i	0.293050i
$153$	− 9.02518e35i	− 0.809184i
$154$	−7.72017e35	−0.621634
$155$	0	0
$156$	−2.11383e36	−1.37567
$157$	− 2.78049e36i	− 1.62846i	−0.580543	−	0.814229i	$-0.697160\pi$
$157$	− 2.78049e36i	− 1.62846i	0.580543	−	0.814229i	$-0.302840\pi$
$158$	− 9.55998e35i	− 0.504214i
$159$	−4.90411e35	−0.233082
$160$	0	0
$161$	1.72069e36	0.665390
$162$	1.46866e36i	0.512773i
$163$	− 2.81381e36i	− 0.887565i	−0.896135	−	0.443782i	$-0.853636\pi$
$163$	− 2.81381e36i	− 0.887565i	0.896135	−	0.443782i	$-0.146364\pi$
$164$	4.54718e36	1.29664
$165$	0	0
$166$	−7.08993e36	−1.65523
$167$	6.77893e36i	1.43331i	0.697430	+	0.716653i	$0.254327\pi$
$167$	6.77893e36i	1.43331i	−0.697430	+	0.716653i	$0.745673\pi$
$168$	6.13862e36i	1.17616i
$169$	2.13094e36	0.370204
$170$	0	0
$171$	3.79756e35	0.0543336
$172$	3.67080e37i	4.77026i
$173$	1.42570e37i	1.68370i	0.539708	+	0.841852i	$0.318535\pi$
$173$	1.42570e37i	1.68370i	−0.539708	+	0.841852i	$0.681465\pi$
$174$	−1.38263e37	−1.48472
$175$	0	0
$176$	−1.46854e37	−1.30595
$177$	− 6.32040e36i	− 0.511901i
$178$	1.06512e37i	0.786085i
$179$	−7.37934e36	−0.496527	−0.248263	−	0.968693i	$-0.579860\pi$
$179$	−7.37934e36	−0.496527	−0.248263	+	0.968693i	$0.579860\pi$
$180$	0	0
$181$	2.39313e36	0.134051	0.0670254	−	0.997751i	$-0.478649\pi$
$181$	2.39313e36	0.134051	0.0670254	+	0.997751i	$0.478649\pi$
$182$	1.79497e37i	0.918076i
$183$	5.30642e35i	0.0247947i
$184$	6.53018e37	2.78889
$185$	0	0
$186$	−4.75072e36	−0.169744
$187$	2.73428e37i	0.894245i
$188$	− 6.76517e37i	− 2.02616i
$189$	2.42915e37	0.666554
$190$	0	0
$191$	−6.98026e35	−0.0160998	−0.00804991	−	0.999968i	$-0.502562\pi$
$191$	−6.98026e35	−0.0160998	−0.00804991	+	0.999968i	$0.502562\pi$
$192$	3.48504e37i	0.737458i
$193$	− 6.67098e36i	− 0.129567i	−0.997899	−	0.0647835i	$-0.979364\pi$
$193$	− 6.67098e36i	− 0.129567i	0.997899	−	0.0647835i	$-0.0206357\pi$
$194$	6.92298e37	1.23471
$195$	0	0
$196$	−9.77280e37	−1.47161
$197$	− 8.89563e37i	− 1.23164i	−0.787886	−	0.615821i	$-0.788825\pi$
$197$	− 8.89563e37i	− 1.23164i	0.787886	−	0.615821i	$-0.211175\pi$
$198$	3.79308e37i	0.483077i
$199$	−1.05106e38	−1.23183	−0.615916	−	0.787812i	$-0.711214\pi$
$199$	−1.05106e38	−1.23183	−0.615916	+	0.787812i	$0.711214\pi$
$200$	0	0
$201$	5.94773e37	0.591039
$202$	2.06618e38i	1.89178i
$203$	8.30613e37i	0.700994i
$204$	3.70692e38	2.88480
$205$	0	0
$206$	2.90245e38	1.92290
$207$	− 8.45412e37i	− 0.517080i
$208$	3.41441e38i	1.92873i
$209$	−1.15051e37	−0.0600452
$210$	0	0
$211$	−5.59870e37	−0.249705	−0.124852	−	0.992175i	$-0.539846\pi$
$211$	−5.59870e37	−0.249705	−0.124852	+	0.992175i	$0.539846\pi$
$212$	1.90634e38i	0.786428i
$213$	− 4.05318e37i	− 0.154715i
$214$	1.21172e38	0.428129
$215$	0	0
$216$	9.21884e38	2.79376
$217$	2.85398e37i	0.0801431i
$218$	7.58804e38i	1.97514i
$219$	3.24305e38	0.782755
$220$	0	0
$221$	6.35730e38	1.32069
$222$	2.76114e38i	0.532432i
$223$	− 4.65676e38i	− 0.833784i	−0.908956	−	0.416892i	$-0.863119\pi$
$223$	− 4.65676e38i	− 0.833784i	0.908956	−	0.416892i	$-0.136881\pi$
$224$	7.03919e38	1.17066
$225$	0	0
$226$	−2.33898e39	−3.35921
$227$	− 2.61802e38i	− 0.349580i	−0.984606	−	0.174790i	$-0.944075\pi$
$227$	− 2.61802e38i	− 0.349580i	0.984606	−	0.174790i	$-0.0559246\pi$
$228$	1.55977e38i	0.193703i
$229$	−9.20963e38	−1.06404	−0.532018	−	0.846733i	$-0.678566\pi$
$229$	−9.20963e38	−1.06404	−0.532018	+	0.846733i	$0.678566\pi$
$230$	0	0
$231$	−2.40770e38	−0.240993
$232$	3.15225e39i	2.93811i
$233$	− 7.13755e37i	− 0.0619693i	−0.999520	−	0.0309847i	$-0.990136\pi$
$233$	− 7.13755e37i	− 0.0619693i	0.999520	−	0.0309847i	$-0.00986430\pi$
$234$	8.81904e38	0.713444
$235$	0	0
$236$	−2.45688e39	−1.72718
$237$	− 2.98148e38i	− 0.195472i
$238$	− 3.14774e39i	− 1.92522i
$239$	1.83178e39	1.04546	0.522731	−	0.852498i	$-0.324913\pi$
$239$	1.83178e39	1.04546	0.522731	+	0.852498i	$0.324913\pi$
$240$	0	0
$241$	−3.05313e39	−1.51867	−0.759336	−	0.650698i	$-0.774476\pi$
$241$	−3.05313e39	−1.51867	−0.759336	+	0.650698i	$0.774476\pi$
$242$	2.83069e39i	1.31504i
$243$	− 1.99652e39i	− 0.866505i
$244$	2.06272e38	0.0836583
$245$	0	0
$246$	2.00452e39	0.710527
$247$	2.67499e38i	0.0886793i
$248$	1.08311e39i	0.335908i
$249$	−2.21114e39	−0.641693
$250$	0	0
$251$	3.03407e39	0.771631	0.385815	−	0.922576i	$-0.373920\pi$
$251$	3.03407e39	0.771631	0.385815	+	0.922576i	$0.373920\pi$
$252$	− 3.08926e39i	− 0.735775i
$253$	2.56127e39i	0.571435i
$254$	−1.22040e40	−2.55120
$255$	0	0
$256$	−5.28662e39	−0.970999
$257$	− 2.91186e39i	− 0.501503i	−0.968051	−	0.250752i	$-0.919322\pi$
$257$	− 2.91186e39i	− 0.501503i	0.968051	−	0.250752i	$-0.0806778\pi$
$258$	1.61819e40i	2.61399i
$259$	1.65875e39	0.251382
$260$	0	0
$261$	4.08097e39	0.544748
$262$	5.05883e39i	0.633984i
$263$	5.62907e39i	0.662471i	0.943548	+	0.331236i	$0.107466\pi$
$263$	5.62907e39i	0.662471i	−0.943548	+	0.331236i	$0.892534\pi$
$264$	−9.13740e39	−1.01009
$265$	0	0
$266$	1.32449e39	0.129271
$267$	3.32180e39i	0.304746i
$268$	− 2.31202e40i	− 1.99419i
$269$	9.77080e39	0.792533	0.396266	−	0.918136i	$-0.370306\pi$
$269$	9.77080e39	0.792533	0.396266	+	0.918136i	$0.370306\pi$
$270$	0	0
$271$	2.38779e40	1.71397	0.856985	−	0.515342i	$-0.172335\pi$
$271$	2.38779e40	1.71397	0.856985	+	0.515342i	$0.172335\pi$
$272$	− 5.98767e40i	− 4.04456i
$273$	5.59798e39i	0.355916i
$274$	1.52653e40	0.913736
$275$	0	0
$276$	3.47237e40	1.84343
$277$	− 1.39835e40i	− 0.699358i	−0.936870	−	0.349679i	$-0.886291\pi$
$277$	− 1.39835e40i	− 0.699358i	0.936870	−	0.349679i	$-0.113709\pi$
$278$	− 6.19820e40i	− 2.92096i
$279$	1.40222e39	0.0622798
$280$	0	0
$281$	−2.89927e40	−1.14455	−0.572274	−	0.820062i	$-0.693939\pi$
$281$	−2.89927e40	−1.14455	−0.572274	+	0.820062i	$0.693939\pi$
$282$	− 2.98227e40i	− 1.11029i
$283$	1.50945e40i	0.530081i	0.964237	+	0.265040i	$0.0853853\pi$
$283$	1.50945e40i	0.530081i	−0.964237	+	0.265040i	$0.914615\pi$
$284$	−1.57556e40	−0.522015
$285$	0	0
$286$	−2.67183e40	−0.788441
$287$	− 1.20421e40i	− 0.335468i
$288$	− 3.45850e40i	− 0.909728i
$289$	−7.12303e40	−1.76950
$290$	0	0
$291$	2.15907e40	0.478667
$292$	− 1.26065e41i	− 2.64105i
$293$	1.40305e40i	0.277816i	0.990305	+	0.138908i	$0.0443593\pi$
$293$	1.40305e40i	0.277816i	−0.990305	+	0.138908i	$0.955641\pi$
$294$	−4.30811e40	−0.806410
$295$	0	0
$296$	6.29509e40	1.05363
$297$	3.61582e40i	0.572435i
$298$	2.97309e40i	0.445286i
$299$	5.95505e40	0.843939
$300$	0	0
$301$	9.72124e40	1.23417
$302$	2.32610e41i	2.79585i
$303$	6.44381e40i	0.733398i
$304$	2.51945e40	0.271577
$305$	0	0
$306$	−1.54655e41	−1.49610
$307$	− 2.92194e40i	− 0.267848i	−0.990992	−	0.133924i	$-0.957242\pi$
$307$	− 2.92194e40i	− 0.267848i	0.990992	−	0.133924i	$-0.0427578\pi$
$308$	9.35926e40i	0.813120i
$309$	9.05190e40	0.745461
$310$	0	0
$311$	−2.24927e41	−1.66531	−0.832653	−	0.553794i	$-0.813179\pi$
$311$	−2.24927e41	−1.66531	−0.832653	+	0.553794i	$0.813179\pi$
$312$	2.12448e41i	1.49177i
$313$	− 1.17836e41i	− 0.784868i	−0.919780	−	0.392434i	$-0.871633\pi$
$313$	− 1.17836e41i	− 0.784868i	0.919780	−	0.392434i	$-0.128367\pi$
$314$	−4.76463e41	−3.01086
$315$	0	0
$316$	−1.15897e41	−0.659530
$317$	− 9.02704e40i	− 0.487604i	−0.969825	−	0.243802i	$-0.921605\pi$
$317$	− 9.02704e40i	− 0.487604i	0.969825	−	0.243802i	$-0.0783947\pi$
$318$	8.40366e40i	0.430944i
$319$	−1.23638e41	−0.602012
$320$	0	0
$321$	3.77900e40	0.165975
$322$	− 2.94857e41i	− 1.23024i
$323$	− 4.69099e40i	− 0.185961i
$324$	1.78048e41	0.670725
$325$	0	0
$326$	−4.82174e41	−1.64102
$327$	2.36649e41i	0.765714i
$328$	− 4.57008e41i	− 1.40607i
$329$	−1.79159e41	−0.524212
$330$	0	0
$331$	−2.91394e41	−0.771469	−0.385734	−	0.922610i	$-0.626052\pi$
$331$	−2.91394e41	−0.771469	−0.385734	+	0.922610i	$0.626052\pi$
$332$	8.59521e41i	2.16510i
$333$	− 8.14977e40i	− 0.195351i
$334$	1.16163e42	2.65004
$335$	0	0
$336$	5.27249e41	1.08998
$337$	− 5.69474e41i	− 1.12094i	−0.828176	−	0.560468i	$-0.810621\pi$
$337$	− 5.69474e41i	− 1.12094i	0.828176	−	0.560468i	$-0.189379\pi$
$338$	− 3.65157e41i	− 0.684470i
$339$	−7.29460e41	−1.30229
$340$	0	0
$341$	−4.24819e40	−0.0688266
$342$	− 6.50748e40i	− 0.100457i
$343$	6.84132e41i	1.00644i
$344$	3.68929e42	5.17284
$345$	0	0
$346$	2.44306e42	3.11300
$347$	4.85020e41i	0.589283i	0.955608	+	0.294641i	$0.0952002\pi$
$347$	4.85020e41i	0.589283i	−0.955608	+	0.294641i	$0.904800\pi$
$348$	1.67618e42i	1.94206i
$349$	−5.38533e41	−0.595104	−0.297552	−	0.954706i	$-0.596170\pi$
$349$	−5.38533e41	−0.595104	−0.297552	+	0.954706i	$0.596170\pi$
$350$	0	0
$351$	8.40692e41	0.845414
$352$	1.04779e42i	1.00536i
$353$	9.77578e41i	0.895094i	0.894260	+	0.447547i	$0.147702\pi$
$353$	9.77578e41i	0.895094i	−0.894260	+	0.447547i	$0.852298\pi$
$354$	−1.08306e42	−0.946453
$355$	0	0
$356$	1.29126e42	1.02823
$357$	− 9.81689e41i	− 0.746360i
$358$	1.26452e42i	0.918027i
$359$	−1.18143e42	−0.819124	−0.409562	−	0.912282i	$-0.634318\pi$
$359$	−1.18143e42	−0.819124	−0.409562	+	0.912282i	$0.634318\pi$
$360$	0	0
$361$	−1.56103e42	−0.987513
$362$	− 4.10085e41i	− 0.247846i
$363$	8.82811e41i	0.509810i
$364$	2.17606e42	1.20088
$365$	0	0
$366$	9.09304e40	0.0458428
$367$	7.16875e41i	0.345504i	0.984965	+	0.172752i	$0.0552659\pi$
$367$	7.16875e41i	0.345504i	−0.984965	+	0.172752i	$0.944734\pi$
$368$	− 5.60881e42i	− 2.58453i
$369$	−5.91654e41	−0.260695
$370$	0	0
$371$	5.04849e41	0.203466
$372$	5.75935e41i	0.222032i
$373$	6.80691e41i	0.251047i	0.992091	+	0.125523i	$0.0400610\pi$
$373$	6.80691e41i	0.251047i	−0.992091	+	0.125523i	$0.959939\pi$
$374$	4.68545e42	1.65337
$375$	0	0
$376$	−6.79925e42	−2.19716
$377$	2.87462e42i	0.889096i
$378$	− 4.16258e42i	− 1.23239i
$379$	−5.14200e42	−1.45742	−0.728711	−	0.684821i	$-0.759880\pi$
$379$	−5.14200e42	−1.45742	−0.728711	+	0.684821i	$0.759880\pi$
$380$	0	0
$381$	−3.80606e42	−0.989040
$382$	1.19613e41i	0.0297669i
$383$	6.82496e42i	1.62675i	0.581740	+	0.813375i	$0.302372\pi$
$383$	6.82496e42i	1.62675i	−0.581740	+	0.813375i	$0.697628\pi$
$384$	9.82434e40	0.0224305
$385$	0	0
$386$	−1.14314e42	−0.239556
$387$	− 4.77624e42i	− 0.959082i
$388$	− 8.39281e42i	− 1.61504i
$389$	−3.03602e42	−0.559933	−0.279966	−	0.960010i	$-0.590323\pi$
$389$	−3.03602e42	−0.559933	−0.279966	+	0.960010i	$0.590323\pi$
$390$	0	0
$391$	−1.04431e43	−1.76975
$392$	9.82202e42i	1.59581i
$393$	1.57770e42i	0.245781i
$394$	−1.52435e43	−2.27718
$395$	0	0
$396$	4.59839e42	0.631882
$397$	8.54761e42i	1.12668i	0.826225	+	0.563341i	$0.190484\pi$
$397$	8.54761e42i	1.12668i	−0.826225	+	0.563341i	$0.809516\pi$
$398$	1.80109e43i	2.27753i
$399$	4.13069e41	0.0501152
$400$	0	0
$401$	4.64638e42	0.519078	0.259539	−	0.965733i	$-0.416429\pi$
$401$	4.64638e42	0.519078	0.259539	+	0.965733i	$0.416429\pi$
$402$	− 1.01920e43i	− 1.09277i
$403$	9.87719e41i	0.101648i
$404$	2.50486e43	2.47452
$405$	0	0
$406$	1.42333e43	1.29607
$407$	2.46907e42i	0.215886i
$408$	− 3.72559e43i	− 3.12826i
$409$	−1.73477e43	−1.39897	−0.699483	−	0.714649i	$-0.746586\pi$
$409$	−1.73477e43	−1.39897	−0.699483	+	0.714649i	$0.746586\pi$
$410$	0	0
$411$	4.76080e42	0.354233
$412$	− 3.51868e43i	− 2.51522i
$413$	6.50647e42i	0.446858i
$414$	−1.44869e43	−0.956028
$415$	0	0
$416$	2.43615e43	1.48479
$417$	− 1.93304e43i	− 1.13239i
$418$	1.97151e42i	0.111017i
$419$	−1.59552e43	−0.863717	−0.431858	−	0.901941i	$-0.642142\pi$
$419$	−1.59552e43	−0.863717	−0.431858	+	0.901941i	$0.642142\pi$
$420$	0	0
$421$	−2.07154e43	−1.03667	−0.518333	−	0.855179i	$-0.673447\pi$
$421$	−2.07154e43	−1.03667	−0.518333	+	0.855179i	$0.673447\pi$
$422$	9.59390e42i	0.461679i
$423$	8.80247e42i	0.407369i
$424$	1.91594e43	0.852797
$425$	0	0
$426$	−6.94550e42	−0.286052
$427$	− 5.46263e41i	− 0.0216442i
$428$	− 1.46898e43i	− 0.560008i
$429$	−8.33266e42	−0.305660
$430$	0	0
$431$	−2.15255e43	−0.731272	−0.365636	−	0.930758i	$-0.619149\pi$
$431$	−2.15255e43	−0.731272	−0.365636	+	0.930758i	$0.619149\pi$
$432$	− 7.91812e43i	− 2.58905i
$433$	2.62411e43i	0.825908i	0.910752	+	0.412954i	$0.135503\pi$
$433$	2.62411e43i	0.825908i	−0.910752	+	0.412954i	$0.864497\pi$
$434$	4.89057e42	0.148176
$435$	0	0
$436$	9.19908e43	2.58355
$437$	− 4.39417e42i	− 0.118832i
$438$	− 5.55727e43i	− 1.44723i
$439$	−1.50091e43	−0.376434	−0.188217	−	0.982127i	$-0.560271\pi$
$439$	−1.50091e43	−0.376434	−0.188217	+	0.982127i	$0.560271\pi$
$440$	0	0
$441$	1.27158e43	0.295875
$442$	− 1.08938e44i	− 2.44182i
$443$	− 1.03686e43i	− 0.223902i	−0.993714	−	0.111951i	$-0.964290\pi$
$443$	− 1.03686e43i	− 0.223902i	0.993714	−	0.111951i	$-0.0357099\pi$
$444$	3.34736e43	0.696440
$445$	0	0
$446$	−7.97979e43	−1.54158
$447$	9.27219e42i	0.172627i
$448$	− 3.58764e43i	− 0.643756i
$449$	3.05007e42	0.0527528	0.0263764	−	0.999652i	$-0.491603\pi$
$449$	3.05007e42	0.0527528	0.0263764	+	0.999652i	$0.491603\pi$
$450$	0	0
$451$	1.79248e43	0.288099
$452$	2.83558e44i	4.39397i
$453$	7.25443e43i	1.08388i
$454$	−4.48623e43	−0.646338
$455$	0	0
$456$	1.56763e43	0.210051
$457$	− 8.15124e43i	− 1.05343i	−0.850042	−	0.526716i	$-0.823423\pi$
$457$	− 8.15124e43i	− 1.05343i	0.850042	−	0.526716i	$-0.176577\pi$
$458$	1.57816e44i	1.96730i
$459$	−1.47428e44	−1.77284
$460$	0	0
$461$	9.49311e43	1.06253	0.531267	−	0.847204i	$-0.321716\pi$
$461$	9.49311e43	1.06253	0.531267	+	0.847204i	$0.321716\pi$
$462$	4.12581e43i	0.445571i
$463$	6.84730e43i	0.713564i	0.934188	+	0.356782i	$0.116126\pi$
$463$	6.84730e43i	0.713564i	−0.934188	+	0.356782i	$0.883874\pi$
$464$	2.70748e44	2.72282
$465$	0	0
$466$	−1.22309e43	−0.114575
$467$	1.13867e44i	1.02961i	0.857308	+	0.514803i	$0.172135\pi$
$467$	1.13867e44i	1.02961i	−0.857308	+	0.514803i	$0.827865\pi$
$468$	− 1.06914e44i	− 0.933210i
$469$	−6.12282e43	−0.515941
$470$	0	0
$471$	−1.48595e44	−1.16724
$472$	2.46926e44i	1.87294i
$473$	1.44702e44i	1.05990i
$474$	−5.10904e43	−0.361407
$475$	0	0
$476$	−3.81605e44	−2.51825
$477$	− 2.48042e43i	− 0.158115i
$478$	− 3.13893e44i	− 1.93295i
$479$	2.43710e44	1.44990	0.724948	−	0.688804i	$-0.241864\pi$
$479$	2.43710e44	1.44990	0.724948	+	0.688804i	$0.241864\pi$
$480$	0	0
$481$	5.74067e43	0.318837
$482$	5.23183e44i	2.80787i
$483$	− 9.19573e43i	− 0.476934i
$484$	3.43169e44	1.72012
$485$	0	0
$486$	−3.42123e44	−1.60208
$487$	− 1.55812e44i	− 0.705300i	−0.935755	−	0.352650i	$-0.885281\pi$
$487$	− 1.55812e44i	− 0.705300i	0.935755	−	0.352650i	$-0.114719\pi$
$488$	− 2.07311e43i	− 0.0907185i
$489$	−1.50376e44	−0.636183
$490$	0	0
$491$	−2.64492e43	−0.104609	−0.0523044	−	0.998631i	$-0.516657\pi$
$491$	−2.64492e43	−0.104609	−0.0523044	+	0.998631i	$0.516657\pi$
$492$	− 2.43010e44i	− 0.929396i
$493$	− 5.04108e44i	− 1.86444i
$494$	4.58384e43	0.163959
$495$	0	0
$496$	9.30290e43	0.311294
$497$	4.17250e43i	0.135057i
$498$	3.78900e44i	1.18643i
$499$	−3.31565e44	−1.00441	−0.502203	−	0.864750i	$-0.667477\pi$
$499$	−3.31565e44	−1.00441	−0.502203	+	0.864750i	$0.667477\pi$
$500$	0	0
$501$	3.62279e44	1.02736
$502$	− 5.19917e44i	− 1.42667i
$503$	4.39485e44i	1.16700i	0.812112	+	0.583502i	$0.198318\pi$
$503$	4.39485e44i	1.16700i	−0.812112	+	0.583502i	$0.801682\pi$
$504$	−3.10482e44	−0.797870
$505$	0	0
$506$	4.38898e44	1.05653
$507$	− 1.13882e44i	− 0.265352i
$508$	1.47950e45i	3.33706i
$509$	7.37330e44	1.60997	0.804986	−	0.593294i	$-0.202173\pi$
$509$	7.37330e44	1.60997	0.804986	+	0.593294i	$0.202173\pi$
$510$	0	0
$511$	−3.33852e44	−0.683296
$512$	9.21704e44i	1.82657i
$513$	− 6.20338e43i	− 0.119040i
$514$	−4.98975e44	−0.927229
$515$	0	0
$516$	1.96175e45	3.41919
$517$	− 2.66681e44i	− 0.450192i
$518$	− 2.84242e44i	− 0.464780i
$519$	7.61920e44	1.20684
$520$	0	0
$521$	1.67201e43	0.0248552	0.0124276	−	0.999923i	$-0.496044\pi$
$521$	1.67201e43	0.0248552	0.0124276	+	0.999923i	$0.496044\pi$
$522$	− 6.99313e44i	− 1.00718i
$523$	− 1.06261e45i	− 1.48284i	−0.671041	−	0.741420i	$-0.734153\pi$
$523$	− 1.06261e45i	− 1.48284i	0.671041	−	0.741420i	$-0.265847\pi$
$524$	6.13288e44	0.829275
$525$	0	0
$526$	9.64595e44	1.22484
$527$	− 1.73211e44i	− 0.213158i
$528$	7.84817e44i	0.936071i
$529$	−1.13224e44	−0.130894
$530$	0	0
$531$	3.19676e44	0.347257
$532$	− 1.60569e44i	− 0.169091i
$533$	− 4.16759e44i	− 0.425486i
$534$	5.69223e44	0.563445
$535$	0	0
$536$	−2.32366e45	−2.16249
$537$	3.94367e44i	0.355897i
$538$	− 1.67432e45i	− 1.46531i
$539$	−3.85240e44	−0.326977
$540$	0	0
$541$	−1.73107e45	−1.38217	−0.691084	−	0.722774i	$-0.742867\pi$
$541$	−1.73107e45	−1.38217	−0.691084	+	0.722774i	$0.742867\pi$
$542$	− 4.09171e45i	− 3.16896i
$543$	− 1.27894e44i	− 0.0960841i
$544$	−4.27216e45	−3.11362
$545$	0	0
$546$	9.59267e44	0.658053
$547$	1.88809e45i	1.25670i	0.777931	+	0.628350i	$0.216269\pi$
$547$	1.88809e45i	1.25670i	−0.777931	+	0.628350i	$0.783731\pi$
$548$	− 1.85063e45i	− 1.19520i
$549$	−2.68390e43	−0.0168199
$550$	0	0
$551$	2.12115e44	0.125190
$552$	− 3.48986e45i	− 1.99900i
$553$	3.06925e44i	0.170635i
$554$	−2.39620e45	−1.29304
$555$	0	0
$556$	−7.51415e45	−3.82073
$557$	1.82254e45i	0.899636i	0.893120	+	0.449818i	$0.148511\pi$
$557$	1.82254e45i	0.899636i	−0.893120	+	0.449818i	$0.851489\pi$
$558$	− 2.40284e44i	− 0.115149i
$559$	3.36437e45	1.56534
$560$	0	0
$561$	1.46125e45	0.640972
$562$	4.96817e45i	2.11615i
$563$	− 3.54966e45i	− 1.46824i	−0.679018	−	0.734122i	$-0.737594\pi$
$563$	− 3.54966e45i	− 1.46824i	0.679018	−	0.734122i	$-0.262406\pi$
$564$	−3.61544e45	−1.45230
$565$	0	0
$566$	2.58658e45	0.980066
$567$	− 4.71517e44i	− 0.173531i
$568$	1.58350e45i	0.566070i
$569$	3.23817e45	1.12447	0.562234	−	0.826978i	$-0.309942\pi$
$569$	3.23817e45	1.12447	0.562234	+	0.826978i	$0.309942\pi$
$570$	0	0
$571$	1.75221e45	0.574237	0.287118	−	0.957895i	$-0.407303\pi$
$571$	1.75221e45	0.574237	0.287118	+	0.957895i	$0.407303\pi$
$572$	3.23909e45i	1.03131i
$573$	3.73039e43i	0.0115399i
$574$	−2.06353e45	−0.620247
$575$	0	0
$576$	−1.76268e45	−0.500267
$577$	− 2.22828e45i	− 0.614566i	−0.951618	−	0.307283i	$-0.900580\pi$
$577$	− 2.22828e45i	− 0.614566i	0.951618	−	0.307283i	$-0.0994198\pi$
$578$	1.22060e46i	3.27162i
$579$	−3.56511e44	−0.0928702
$580$	0	0
$581$	2.27624e45	0.560159
$582$	− 3.69978e45i	− 0.885006i
$583$	7.51473e44i	0.174736i
$584$	−1.26700e46	−2.86394
$585$	0	0
$586$	2.40426e45	0.513654
$587$	1.91072e45i	0.396889i	0.980112	+	0.198444i	$0.0635889\pi$
$587$	1.91072e45i	0.396889i	−0.980112	+	0.198444i	$0.936411\pi$
$588$	5.22278e45i	1.05481i
$589$	7.28827e43	0.0143127
$590$	0	0
$591$	−4.75400e45	−0.882808
$592$	− 5.40689e45i	− 0.976426i
$593$	− 8.87275e45i	− 1.55832i	−0.626827	−	0.779158i	$-0.715647\pi$
$593$	− 8.87275e45i	− 1.55832i	0.626827	−	0.779158i	$-0.284353\pi$
$594$	6.19606e45	1.05837
$595$	0	0
$596$	3.60431e45	0.582451
$597$	5.61707e45i	0.882945i
$598$	− 1.02045e46i	− 1.56036i
$599$	1.96939e45	0.292947	0.146474	−	0.989215i	$-0.453208\pi$
$599$	1.96939e45	0.292947	0.146474	+	0.989215i	$0.453208\pi$
$600$	0	0
$601$	6.49113e45	0.913885	0.456942	−	0.889496i	$-0.348945\pi$
$601$	6.49113e45	0.913885	0.456942	+	0.889496i	$0.348945\pi$
$602$	− 1.66583e46i	− 2.28185i
$603$	3.00827e45i	0.400941i
$604$	2.81996e46	3.65707
$605$	0	0
$606$	1.10421e46	1.35598
$607$	− 1.08656e46i	− 1.29849i	−0.760577	−	0.649247i	$-0.775084\pi$
$607$	− 1.08656e46i	− 1.29849i	0.760577	−	0.649247i	$-0.224916\pi$
$608$	− 1.79761e45i	− 0.209068i
$609$	4.43896e45	0.502454
$610$	0	0
$611$	−6.20043e45	−0.664877
$612$	1.87490e46i	1.95695i
$613$	− 8.70542e45i	− 0.884488i	−0.896895	−	0.442244i	$-0.854182\pi$
$613$	− 8.70542e45i	− 0.884488i	0.896895	−	0.442244i	$-0.145818\pi$
$614$	−5.00703e45	−0.495224
$615$	0	0
$616$	9.40640e45	0.881742
$617$	− 1.12685e46i	− 1.02840i	−0.857671	−	0.514199i	$-0.828089\pi$
$617$	− 1.12685e46i	− 1.02840i	0.857671	−	0.514199i	$-0.171911\pi$
$618$	− 1.55113e46i	− 1.37828i
$619$	1.07685e46	0.931663	0.465831	−	0.884874i	$-0.345755\pi$
$619$	1.07685e46	0.931663	0.465831	+	0.884874i	$0.345755\pi$
$620$	0	0
$621$	−1.38099e46	−1.13287
$622$	3.85433e46i	3.07898i
$623$	− 3.41959e45i	− 0.266025i
$624$	1.82473e46	1.38246
$625$	0	0
$626$	−2.01923e46	−1.45114
$627$	6.14858e44i	0.0430388i
$628$	5.77622e46i	3.93831i
$629$	−1.00671e46	−0.668605
$630$	0	0
$631$	2.47581e46	1.56039	0.780196	−	0.625535i	$-0.215119\pi$
$631$	2.47581e46	1.56039	0.780196	+	0.625535i	$0.215119\pi$
$632$	1.16481e46i	0.715190i
$633$	2.99206e45i	0.178982i
$634$	−1.54687e46	−0.901531
$635$	0	0
$636$	1.01879e46	0.563691
$637$	8.95698e45i	0.482904i
$638$	2.11865e46i	1.11306i
$639$	2.05003e45	0.104953
$640$	0	0
$641$	−6.66844e45	−0.324240	−0.162120	−	0.986771i	$-0.551833\pi$
$641$	−6.66844e45	−0.324240	−0.162120	+	0.986771i	$0.551833\pi$
$642$	− 6.47567e45i	− 0.306872i
$643$	8.88748e42i	0 0.000410485i	1.00000		0.000205243i	$6.53307e-5\pi$
$643$	8.88748e42i	0 0.000410485i	−1.00000		0.000205243i	$0.999935\pi$
$644$	−3.57459e46	−1.60920
$645$	0	0
$646$	−8.03845e45	−0.343824
$647$	− 1.36920e46i	− 0.570884i	−0.958396	−	0.285442i	$-0.907860\pi$
$647$	− 1.36920e46i	− 0.570884i	0.958396	−	0.285442i	$-0.0921403\pi$
$648$	− 1.78945e46i	− 0.727330i
$649$	−9.68495e45	−0.383760
$650$	0	0
$651$	1.52523e45	0.0574444
$652$	5.84545e46i	2.14651i
$653$	1.32140e46i	0.473115i	0.971618	+	0.236557i	$0.0760191\pi$
$653$	1.32140e46i	0.473115i	−0.971618	+	0.236557i	$0.923981\pi$
$654$	4.05520e46	1.41573
$655$	0	0
$656$	−3.92527e46	−1.30304
$657$	1.64028e46i	0.530995i
$658$	3.07007e46i	0.969215i
$659$	−3.14029e46	−0.966852	−0.483426	−	0.875385i	$-0.660608\pi$
$659$	−3.14029e46	−0.966852	−0.483426	+	0.875385i	$0.660608\pi$
$660$	0	0
$661$	−5.62366e46	−1.64701	−0.823503	−	0.567313i	$-0.807983\pi$
$661$	−5.62366e46	−1.64701	−0.823503	+	0.567313i	$0.807983\pi$
$662$	4.99331e46i	1.42637i
$663$	− 3.39747e46i	− 0.946635i
$664$	8.63851e46	2.34782
$665$	0	0
$666$	−1.39654e46	−0.361184
$667$	− 4.72211e46i	− 1.19141i
$668$	− 1.40826e47i	− 3.46635i
$669$	−2.48866e46	−0.597634
$670$	0	0
$671$	8.13119e44	0.0185880
$672$	− 3.76188e46i	− 0.839097i
$673$	− 1.86687e45i	− 0.0406317i	−0.999794	−	0.0203159i	$-0.993533\pi$
$673$	− 1.86687e45i	− 0.0406317i	0.999794	−	0.0203159i	$-0.00646719\pi$
$674$	−9.75848e46	−2.07250
$675$	0	0
$676$	−4.42685e46	−0.895311
$677$	− 3.19535e46i	− 0.630674i	−0.948980	−	0.315337i	$-0.897882\pi$
$677$	− 3.19535e46i	− 0.630674i	0.948980	−	0.315337i	$-0.102118\pi$
$678$	1.25000e47i	2.40780i
$679$	−2.22264e46	−0.417847
$680$	0	0
$681$	−1.39912e46	−0.250570
$682$	7.27967e45i	0.127253i
$683$	9.67204e46i	1.65035i	0.564876	+	0.825176i	$0.308924\pi$
$683$	9.67204e46i	1.65035i	−0.564876	+	0.825176i	$0.691076\pi$
$684$	−7.88910e45	−0.131402
$685$	0	0
$686$	1.17232e47	1.86080
$687$	4.92181e46i	0.762673i
$688$	− 3.16875e47i	− 4.79379i
$689$	1.74720e46	0.258063
$690$	0	0
$691$	−4.21417e46	−0.593368	−0.296684	−	0.954976i	$-0.595881\pi$
$691$	−4.21417e46	−0.593368	−0.296684	+	0.954976i	$0.595881\pi$
$692$	− 2.96176e47i	− 4.07192i
$693$	− 1.21777e46i	− 0.163481i
$694$	8.31128e46	1.08952
$695$	0	0
$696$	1.68462e47	2.10596
$697$	7.30848e46i	0.892249i
$698$	9.22827e46i	1.10029i
$699$	−3.81445e45	−0.0444180
$700$	0	0
$701$	1.07382e47	1.19284	0.596422	−	0.802671i	$-0.296589\pi$
$701$	1.07382e47	1.19284	0.596422	+	0.802671i	$0.296589\pi$
$702$	− 1.44061e47i	− 1.56309i
$703$	− 4.23598e45i	− 0.0448943i
$704$	5.34024e46	0.552856
$705$	0	0
$706$	1.67517e47	1.65494
$707$	− 6.63351e46i	− 0.640211i
$708$	1.31301e47i	1.23799i
$709$	−9.99645e46	−0.920837	−0.460419	−	0.887702i	$-0.652301\pi$
$709$	−9.99645e46	−0.920837	−0.460419	+	0.887702i	$0.652301\pi$
$710$	0	0
$711$	1.50798e46	0.132602
$712$	− 1.29776e47i	− 1.11500i
$713$	− 1.62251e46i	− 0.136211i
$714$	−1.68222e47	−1.37994
$715$	0	0
$716$	1.53299e47	1.20081
$717$	− 9.78940e46i	− 0.749359i
$718$	2.02449e47i	1.51448i
$719$	7.93598e46	0.580195	0.290097	−	0.956997i	$-0.406312\pi$
$719$	7.93598e46	0.580195	0.290097	+	0.956997i	$0.406312\pi$
$720$	0	0
$721$	−9.31838e46	−0.650741
$722$	2.67498e47i	1.82581i
$723$	1.63165e47i	1.08854i
$724$	−4.97151e46	−0.324192
$725$	0	0
$726$	1.51278e47	0.942587
$727$	1.33485e47i	0.813046i	0.913641	+	0.406523i	$0.133259\pi$
$727$	1.33485e47i	0.813046i	−0.913641	+	0.406523i	$0.866741\pi$
$728$	− 2.18702e47i	− 1.30222i
$729$	−1.54343e47	−0.898427
$730$	0	0
$731$	−5.89992e47	−3.28254
$732$	− 1.10236e46i	− 0.0599641i
$733$	− 8.41792e46i	− 0.447702i	−0.974623	−	0.223851i	$-0.928137\pi$
$733$	− 8.41792e46i	− 0.447702i	0.974623	−	0.223851i	$-0.0718629\pi$
$734$	1.22843e47	0.638802
$735$	0	0
$736$	−4.00184e47	−1.98965
$737$	− 9.11389e46i	− 0.443088i
$738$	1.01385e47i	0.481998i
$739$	−2.39720e47	−1.11448	−0.557239	−	0.830352i	$-0.688139\pi$
$739$	−2.39720e47	−1.11448	−0.557239	+	0.830352i	$0.688139\pi$
$740$	0	0
$741$	1.42957e46	0.0635630
$742$	− 8.65106e46i	− 0.376188i
$743$	− 4.51636e47i	− 1.92076i	−0.278695	−	0.960380i	$-0.589902\pi$
$743$	− 4.51636e47i	− 1.92076i	0.278695	−	0.960380i	$-0.410098\pi$
$744$	5.78836e46	0.240770
$745$	0	0
$746$	1.16643e47	0.464160
$747$	− 1.11836e47i	− 0.435304i
$748$	− 5.68023e47i	− 2.16267i
$749$	−3.89025e46	−0.144886
$750$	0	0
$751$	−2.31769e46	−0.0826030	−0.0413015	−	0.999147i	$-0.513150\pi$
$751$	−2.31769e46	−0.0826030	−0.0413015	+	0.999147i	$0.513150\pi$
$752$	5.83991e47i	2.03616i
$753$	− 1.62147e47i	− 0.553085i
$754$	4.92594e47	1.64385
$755$	0	0
$756$	−5.04635e47	−1.61201
$757$	− 6.14297e46i	− 0.191998i	−0.995381	−	0.0959989i	$-0.969395\pi$
$757$	− 6.14297e46i	− 0.191998i	0.995381	−	0.0959989i	$-0.0306045\pi$
$758$	8.81131e47i	2.69463i
$759$	1.36880e47	0.409590
$760$	0	0
$761$	−4.18126e47	−1.19801	−0.599004	−	0.800746i	$-0.704437\pi$
$761$	−4.18126e47	−1.19801	−0.599004	+	0.800746i	$0.704437\pi$
$762$	6.52205e47i	1.82863i
$763$	− 2.43616e47i	− 0.668421i
$764$	1.45009e46	0.0389362
$765$	0	0
$766$	1.16952e48	3.00769
$767$	2.25179e47i	0.566766i
$768$	2.82528e47i	0.695987i
$769$	2.07493e47	0.500286	0.250143	−	0.968209i	$-0.419522\pi$
$769$	2.07493e47	0.500286	0.250143	+	0.968209i	$0.419522\pi$
$770$	0	0
$771$	−1.55616e47	−0.359464
$772$	1.38584e47i	0.313348i
$773$	3.82656e47i	0.846930i	0.905912	+	0.423465i	$0.139186\pi$
$773$	3.82656e47i	0.846930i	−0.905912	+	0.423465i	$0.860814\pi$
$774$	−8.18455e47	−1.77324
$775$	0	0
$776$	−8.43509e47	−1.75134
$777$	− 8.86469e46i	− 0.180184i
$778$	5.20250e47i	1.03526i
$779$	−3.07522e46	−0.0599112
$780$	0	0
$781$	−6.21081e46	−0.115986
$782$	1.78952e48i	3.27209i
$783$	− 6.66634e47i	− 1.19349i
$784$	8.43619e47	1.47887
$785$	0	0
$786$	2.70354e47	0.454423
$787$	− 6.26036e47i	− 1.03043i	−0.857062	−	0.515213i	$-0.827713\pi$
$787$	− 6.26036e47i	− 1.03043i	0.857062	−	0.515213i	$-0.172287\pi$
$788$	1.84799e48i	2.97863i
$789$	3.00829e47	0.474842
$790$	0	0
$791$	7.50935e47	1.13682
$792$	− 4.62156e47i	− 0.685208i
$793$	− 1.89053e46i	− 0.0274521i
$794$	1.46471e48	2.08312
$795$	0	0
$796$	2.18348e48	2.97910
$797$	1.56391e47i	0.209002i	0.994525	+	0.104501i	$0.0333246\pi$
$797$	1.56391e47i	0.209002i	−0.994525	+	0.104501i	$0.966675\pi$
$798$	− 7.07833e46i	− 0.0926580i
$799$	1.08734e48	1.39425
$800$	0	0
$801$	−1.68012e47	−0.206730
$802$	− 7.96201e47i	− 0.959722i
$803$	− 4.96943e47i	− 0.586813i
$804$	−1.23559e48	−1.42938
$805$	0	0
$806$	1.69255e47	0.187937
$807$	− 5.22171e47i	− 0.568067i
$808$	− 2.51747e48i	− 2.68335i
$809$	−4.01144e47	−0.418938	−0.209469	−	0.977815i	$-0.567174\pi$
$809$	−4.01144e47	−0.418938	−0.209469	+	0.977815i	$0.567174\pi$
$810$	0	0
$811$	2.34209e47	0.234833	0.117417	−	0.993083i	$-0.462539\pi$
$811$	2.34209e47	0.234833	0.117417	+	0.993083i	$0.462539\pi$
$812$	− 1.72553e48i	− 1.69530i
$813$	− 1.27608e48i	− 1.22853i
$814$	4.23098e47	0.399152
$815$	0	0
$816$	−3.19993e48	−2.89903
$817$	− 2.48253e47i	− 0.220410i
$818$	2.97269e48i	2.58655i
$819$	−2.83137e47	−0.241442
$820$	0	0
$821$	4.03504e47	0.330510	0.165255	−	0.986251i	$-0.447155\pi$
$821$	4.03504e47	0.330510	0.165255	+	0.986251i	$0.447155\pi$
$822$	− 8.15807e47i	− 0.654942i
$823$	− 1.82505e48i	− 1.43608i	−0.696002	−	0.718039i	$-0.745040\pi$
$823$	− 1.82505e48i	− 1.43608i	0.696002	−	0.718039i	$-0.254960\pi$
$824$	−3.53640e48	−2.72749
$825$	0	0
$826$	1.11494e48	0.826195
$827$	7.52706e47i	0.546744i	0.961908	+	0.273372i	$0.0881390\pi$
$827$	7.52706e47i	0.546744i	−0.961908	+	0.273372i	$0.911861\pi$
$828$	1.75627e48i	1.25052i
$829$	2.19354e48	1.53107	0.765537	−	0.643392i	$-0.222474\pi$
$829$	2.19354e48	1.53107	0.765537	+	0.643392i	$0.222474\pi$
$830$	0	0
$831$	−7.47306e47	−0.501281
$832$	− 1.24162e48i	− 0.816499i
$833$	− 1.57074e48i	− 1.01265i
$834$	−3.31244e48	−2.09367
$835$	0	0
$836$	2.39009e47	0.145215
$837$	− 2.29055e47i	− 0.136449i
$838$	2.73408e48i	1.59693i
$839$	2.86394e48	1.64018	0.820091	−	0.572233i	$-0.193923\pi$
$839$	2.86394e48	1.64018	0.820091	+	0.572233i	$0.193923\pi$
$840$	0	0
$841$	4.63381e47	0.255155
$842$	3.54978e48i	1.91669i
$843$	1.54943e48i	0.820382i
$844$	1.16308e48	0.603892
$845$	0	0
$846$	1.50839e48	0.753185
$847$	− 9.08800e47i	− 0.445033i
$848$	− 1.64561e48i	− 0.790308i
$849$	8.06680e47	0.379948
$850$	0	0
$851$	−9.43013e47	−0.427248
$852$	8.42012e47i	0.374166i
$853$	− 4.28657e48i	− 1.86832i	−0.356859	−	0.934158i	$-0.616152\pi$
$853$	− 4.28657e48i	− 1.86832i	0.356859	−	0.934158i	$-0.383848\pi$
$854$	−9.36073e46	−0.0400180
$855$	0	0
$856$	−1.47638e48	−0.607270
$857$	− 8.64522e47i	− 0.348813i	−0.984674	−	0.174406i	$-0.944199\pi$
$857$	− 8.64522e47i	− 0.348813i	0.984674	−	0.174406i	$-0.0558007\pi$
$858$	1.42788e48i	0.565134i
$859$	−2.35883e48	−0.915817	−0.457909	−	0.888999i	$-0.651401\pi$
$859$	−2.35883e48	−0.915817	−0.457909	+	0.888999i	$0.651401\pi$
$860$	0	0
$861$	−6.43555e47	−0.240455
$862$	3.68860e48i	1.35205i
$863$	6.27316e46i	0.0225584i	0.999936	+	0.0112792i	$0.00359036\pi$
$863$	6.27316e46i	0.0225584i	−0.999936	+	0.0112792i	$0.996410\pi$
$864$	−5.64951e48	−1.99312
$865$	0	0
$866$	4.49666e48	1.52702
$867$	3.80669e48i	1.26833i
$868$	− 5.92890e47i	− 0.193820i
$869$	−4.56861e47	−0.146541
$870$	0	0
$871$	−2.11901e48	−0.654386
$872$	− 9.24541e48i	− 2.80159i
$873$	1.09203e48i	0.324712i
$874$	−7.52982e47	−0.219708
$875$	0	0
$876$	−6.73715e48	−1.89303
$877$	− 2.00783e48i	− 0.553647i	−0.960921	−	0.276823i	$-0.910718\pi$
$877$	− 2.00783e48i	− 0.553647i	0.960921	−	0.276823i	$-0.0892817\pi$
$878$	2.57194e48i	0.695988i
$879$	7.49818e47	0.199131
$880$	0	0
$881$	−4.20296e48	−1.07511	−0.537555	−	0.843229i	$-0.680652\pi$
$881$	−4.20296e48	−1.07511	−0.537555	+	0.843229i	$0.680652\pi$
$882$	− 2.17898e48i	− 0.547042i
$883$	− 7.94997e48i	− 1.95891i	−0.201672	−	0.979453i	$-0.564638\pi$
$883$	− 7.94997e48i	− 1.95891i	0.201672	−	0.979453i	$-0.435362\pi$
$884$	−1.32067e49	−3.19399
$885$	0	0
$886$	−1.77675e48	−0.413971
$887$	− 7.43922e48i	− 1.70133i	−0.525710	−	0.850664i	$-0.676200\pi$
$887$	− 7.43922e48i	− 1.70133i	0.525710	−	0.850664i	$-0.323800\pi$
$888$	− 3.36422e48i	− 0.755216i
$889$	3.91811e48	0.863371
$890$	0	0
$891$	7.01859e47	0.149028
$892$	9.67400e48i	2.01644i
$893$	4.57523e47i	0.0936189i
$894$	1.58888e48	0.319170
$895$	0	0
$896$	−1.01136e47	−0.0195804
$897$	− 3.18250e48i	− 0.604913i
$898$	− 5.22659e47i	− 0.0975345i
$899$	7.83220e47	0.143499
$900$	0	0
$901$	−3.06398e48	−0.541161
$902$	− 3.07159e48i	− 0.532666i
$903$	− 5.19523e48i	− 0.884620i
$904$	2.84986e49	4.76480
$905$	0	0
$906$	1.24311e49	2.00399
$907$	8.96944e48i	1.41986i	0.704273	+	0.709929i	$0.251273\pi$
$907$	8.96944e48i	1.41986i	−0.704273	+	0.709929i	$0.748727\pi$
$908$	5.43871e48i	0.845433i
$909$	−3.25918e48	−0.497513
$910$	0	0
$911$	2.25421e48	0.331850	0.165925	−	0.986138i	$-0.446939\pi$
$911$	2.25421e48	0.331850	0.165925	+	0.986138i	$0.446939\pi$
$912$	− 1.34645e48i	− 0.194659i
$913$	3.38820e48i	0.481063i
$914$	−1.39679e49	−1.94769
$915$	0	0
$916$	1.91322e49	2.57329
$917$	− 1.62415e48i	− 0.214551i
$918$	2.52632e49i	3.27781i
$919$	7.04277e48	0.897507	0.448754	−	0.893656i	$-0.351868\pi$
$919$	7.04277e48	0.897507	0.448754	+	0.893656i	$0.351868\pi$
$920$	0	0
$921$	−1.56155e48	−0.191987
$922$	− 1.62673e49i	− 1.96452i
$923$	1.44404e48i	0.171297i
$924$	5.00178e48	0.582823
$925$	0	0
$926$	1.17335e49	1.31931
$927$	4.57831e48i	0.505696i
$928$	− 1.93177e49i	− 2.09611i
$929$	−1.56732e49	−1.67070	−0.835348	−	0.549721i	$-0.814734\pi$
$929$	−1.56732e49	−1.67070	−0.835348	+	0.549721i	$0.814734\pi$
$930$	0	0
$931$	6.60926e47	0.0679959
$932$	1.48276e48i	0.149868i
$933$	1.20205e49i	1.19365i
$934$	1.95123e49	1.90364
$935$	0	0
$936$	−1.07453e49	−1.01197
$937$	4.17295e48i	0.386136i	0.981185	+	0.193068i	$0.0618437\pi$
$937$	4.17295e48i	0.386136i	−0.981185	+	0.193068i	$0.938156\pi$
$938$	1.04920e49i	0.953922i
$939$	−6.29740e48	−0.562573
$940$	0	0
$941$	−5.21719e48	−0.449995	−0.224998	−	0.974359i	$-0.572237\pi$
$941$	−5.21719e48	−0.449995	−0.224998	+	0.974359i	$0.572237\pi$
$942$	2.54631e49i	2.15810i
$943$	6.84604e48i	0.570160i
$944$	2.12086e49	1.73570
$945$	0	0
$946$	2.47960e49	1.95965
$947$	− 1.05918e49i	− 0.822616i	−0.911496	−	0.411308i	$-0.865072\pi$
$947$	− 1.05918e49i	− 0.822616i	0.911496	−	0.411308i	$-0.134928\pi$
$948$	6.19376e48i	0.472734i
$949$	−1.15541e49	−0.866650
$950$	0	0
$951$	−4.82423e48	−0.349502
$952$	3.83527e49i	2.73078i
$953$	− 1.49599e49i	− 1.04688i	−0.852064	−	0.523438i	$-0.824649\pi$
$953$	− 1.49599e49i	− 1.04688i	0.852064	−	0.523438i	$-0.175351\pi$
$954$	−4.25044e48	−0.292338
$955$	0	0
$956$	−3.80536e49	−2.52837
$957$	6.60745e48i	0.431506i
$958$	− 4.17619e49i	− 2.68071i
$959$	−4.90095e48	−0.309224
$960$	0	0
$961$	−1.61344e49	−0.983594
$962$	− 9.83718e48i	− 0.589498i
$963$	1.91136e48i	0.112592i
$964$	6.34261e49	3.67280
$965$	0	0
$966$	−1.57578e49	−0.881803
$967$	− 2.39619e49i	− 1.31821i	−0.752050	−	0.659106i	$-0.770935\pi$
$967$	− 2.39619e49i	− 1.31821i	0.752050	−	0.659106i	$-0.229065\pi$
$968$	− 3.44897e49i	− 1.86529i
$969$	−2.50696e48	−0.133292
$970$	0	0
$971$	−1.35152e47	−0.00694552	−0.00347276	−	0.999994i	$-0.501105\pi$
$971$	−1.35152e47	−0.00694552	−0.00347276	+	0.999994i	$0.501105\pi$
$972$	4.14760e49i	2.09558i
$973$	1.98994e49i	0.988505i
$974$	−2.66999e49	−1.30403
$975$	0	0
$976$	−1.78061e48	−0.0840711
$977$	1.84460e48i	0.0856333i	0.999083	+	0.0428166i	$0.0136331\pi$
$977$	1.84460e48i	0.0856333i	−0.999083	+	0.0428166i	$0.986367\pi$
$978$	2.57683e49i	1.17624i
$979$	5.09011e48	0.228461
$980$	0	0
$981$	−1.19693e49	−0.519435
$982$	4.53233e48i	0.193411i
$983$	6.69809e48i	0.281072i	0.990076	+	0.140536i	$0.0448826\pi$
$983$	6.69809e48i	0.281072i	−0.990076	+	0.140536i	$0.955117\pi$
$984$	−2.44234e49	−1.00783
$985$	0	0
$986$	−8.63836e49	−3.44717
$987$	9.57464e48i	0.375742i
$988$	− 5.55705e48i	− 0.214464i
$989$	−5.52661e49	−2.09759
$990$	0	0
$991$	1.17168e49	0.430123	0.215062	−	0.976600i	$-0.431005\pi$
$991$	1.17168e49	0.430123	0.215062	+	0.976600i	$0.431005\pi$
$992$	− 6.63755e48i	− 0.239643i
$993$	1.55727e49i	0.552969i
$994$	7.14997e48	0.249706
$995$	0	0
$996$	4.59345e49	1.55189
$997$	2.44007e49i	0.810834i	0.914132	+	0.405417i	$0.132874\pi$
$997$	2.44007e49i	0.810834i	−0.914132	+	0.405417i	$0.867126\pi$
$998$	5.68168e49i	1.85705i
$999$	−1.33128e49	−0.427995

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.b.a.24.1		4
5.2	odd	4		25.34.a.a.1.2		2
5.3	odd	4		1.34.a.a.1.1	✓	2
5.4	even	2	inner	25.34.b.a.24.4		4
15.8	even	4		9.34.a.b.1.2		2
20.3	even	4		16.34.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.34.a.a.1.1	✓	2	5.3	odd	4
9.34.a.b.1.2		2	15.8	even	4
16.34.a.b.1.1		2	20.3	even	4
25.34.a.a.1.2		2	5.2	odd	4
25.34.b.a.24.1		4	1.1	even	1	trivial
25.34.b.a.24.4		4	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)

\(f(q)\)	\(=\)	\(q-171359. i q^{2} -5.34420e7i q^{3} -2.07741e10 q^{4} -9.15779e12 q^{6} +5.50153e13i q^{7} +2.08788e15i q^{8} +2.70301e15 q^{9} +O(q^{10})\)	\(q-171359. i q^{2} -5.34420e7i q^{3} -2.07741e10 q^{4} -9.15779e12 q^{6} +5.50153e13i q^{7} +2.08788e15i q^{8} +2.70301e15 q^{9} -8.18909e16 q^{11} +1.11021e18i q^{12} +1.90399e18i q^{13} +9.42739e18 q^{14} +1.79329e20 q^{16} -3.33893e20i q^{17} -4.63187e20i q^{18} +1.40494e20 q^{19} +2.94013e21 q^{21} +1.40328e22i q^{22} -3.12767e22i q^{23} +1.11580e23 q^{24} +3.26267e23 q^{26} -4.41542e23i q^{27} -1.14289e24i q^{28} +1.50979e24 q^{29} +5.18762e23 q^{31} -1.27950e25i q^{32} +4.37641e24i q^{33} -5.72158e25 q^{34} -5.61527e25 q^{36} -3.01507e25i q^{37} -2.40749e25i q^{38} +1.01753e26 q^{39} -2.18887e26 q^{41} -5.03818e26i q^{42} -1.76701e27i q^{43} +1.70121e27 q^{44} -5.35955e27 q^{46} +3.25654e27i q^{47} -9.58369e27i q^{48} +4.70431e27 q^{49} -1.78439e28 q^{51} -3.95538e28i q^{52} -9.17652e27i q^{53} -7.56623e28 q^{54} -1.14865e29 q^{56} -7.50826e27i q^{57} -2.58716e29i q^{58} +1.18267e29 q^{59} -9.92930e27 q^{61} -8.88948e28i q^{62} +1.48707e29i q^{63} -6.52116e29 q^{64} +7.49940e29 q^{66} +1.11293e30i q^{67} +6.93634e30i q^{68} -1.67149e30 q^{69} +7.58425e29 q^{71} +5.64355e30i q^{72} +6.06835e30i q^{73} -5.16661e30 q^{74} -2.91863e30 q^{76} -4.50525e30i q^{77} -1.74364e31i q^{78} +5.57890e30 q^{79} -8.57067e30 q^{81} +3.75083e31i q^{82} -4.13746e31i q^{83} -6.10785e31 q^{84} -3.02793e32 q^{86} -8.06860e31i q^{87} -1.70978e32i q^{88} -6.21572e31 q^{89} -1.04749e32 q^{91} +6.49745e32i q^{92} -2.77237e31i q^{93} +5.58039e32 q^{94} -6.83789e32 q^{96} +4.04003e32i q^{97} -8.06129e32i q^{98} -2.21352e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 29304467968 q^{4} - 19857844386432 q^{6} + 16\!\cdots\!08 q^{9}+O(q^{10}) \) 4 * q - 29304467968 * q^4 - 19857844386432 * q^6 + 16042273909941708 * q^9	\( 4 q - 29304467968 q^{4} - 19857844386432 q^{6} + 16\!\cdots\!08 q^{9}+ \cdots + 18\!\cdots\!56 q^{99}+O(q^{100}) \) 4 * q - 29304467968 * q^4 - 19857844386432 * q^6 + 16042273909941708 * q^9 + 267743630883828528 * q^11 + 30993282524936680704 * q^14 + 391211958223788703744 * q^16 + 2721392886083394343600 * q^19 + 9672877686165602283648 * q^21 + 200471037176639420006400 * q^24 + 545463367269284185420608 * q^26 + 3349039943260799858219400 * q^29 - 12476602451447264674191232 * q^31 - 139721581072333832146151616 * q^34 - 47191510192394271217153536 * q^36 + 170052544876039337673566496 * q^39 + 555133226044004365464376488 * q^41 + 6044171828775532171616692224 * q^44 - 11227101269526771362941738752 * q^46 - 4979598731777777866889702628 * q^49 - 43589619182878870777337248992 * q^51 - 168100149856471058168032147200 * q^54 - 51150475590343517519644262400 * q^56 + 611572819270596866053327990800 * q^59 - 11491787966826529718134724872 * q^61 - 1728730644720761719947419189248 * q^64 + 1167116717113660076116539326976 * q^66 - 3501697060634855952551484887424 * q^69 - 5339523875912209431473620169952 * q^71 - 2915873996160038988422692385856 * q^74 + 9102629314941605097126324070400 * q^76 + 17070399945531272939460212382400 * q^79 + 36744800901410202817388860698084 * q^81 - 98939068122295455684135817199616 * q^84 - 625393771475157003834429652812672 * q^86 - 265438935311208632529877195453800 * q^89 + 53804204294904716821097774423488 * q^91 + 901012867777735797670099123060224 * q^94 - 1587582565113120422998050185674752 * q^96 + 1852201390665529560061313880141456 * q^99

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