LMFDB - Embedded newform 25.34.b.b.24.3

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} + 2 x^{8} + 325405868686 x^{7} + \cdots + 34\!\cdots\!68 $ x^10 - 2x^9 + 2x^8 + 325405868686x^7 + 327807761582101561x^6 + 230788916575056333044x^5 + 52482256238971860814088x^4 - 28868477926481009935781561728x^3 + 5099072964771111558047480848223296x^2 - 596428985476749456366946929757065984*x + 34881588984360865981321269538813997568
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{48}\cdot 3^{10}\cdot 5^{24}\cdot 11^{2} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.3
Root			$-8230.22 - 8230.22i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.34.b.b.24.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-71937.8i q^{2} +1.37573e8i q^{3} +3.41489e9 q^{4} +9.89671e12 q^{6} +1.07684e14i q^{7} -8.63600e14i q^{8} -1.33673e16 q^{9} +O(q^{10})$	\(q-71937.8i q^{2} +1.37573e8i q^{3} +3.41489e9 q^{4} +9.89671e12 q^{6} +1.07684e14i q^{7} -8.63600e14i q^{8} -1.33673e16 q^{9} -2.33530e17 q^{11} +4.69797e17i q^{12} -2.28395e18i q^{13} +7.74658e18 q^{14} -3.27918e19 q^{16} +2.09885e20i q^{17} +9.61615e20i q^{18} -6.01644e20 q^{19} -1.48145e22 q^{21} +1.67997e22i q^{22} +4.84991e22i q^{23} +1.18808e23 q^{24} -1.64302e23 q^{26} -1.07421e24i q^{27} +3.67730e23i q^{28} +8.15476e22 q^{29} -1.49925e24 q^{31} -5.05930e24i q^{32} -3.21275e25i q^{33} +1.50986e25 q^{34} -4.56479e25 q^{36} -1.78708e25i q^{37} +4.32809e25i q^{38} +3.14210e26 q^{39} -1.94621e26 q^{41} +1.06572e27i q^{42} -9.48110e26i q^{43} -7.97481e26 q^{44} +3.48891e27 q^{46} +6.29157e26i q^{47} -4.51128e27i q^{48} -3.86494e27 q^{49} -2.88745e28 q^{51} -7.79943e27i q^{52} -8.56042e27i q^{53} -7.72760e28 q^{54} +9.29963e28 q^{56} -8.27701e28i q^{57} -5.86635e27i q^{58} -5.43089e27 q^{59} +1.79220e29 q^{61} +1.07853e29i q^{62} -1.43945e30i q^{63} -6.45635e29 q^{64} -2.31118e30 q^{66} +3.33703e29i q^{67} +7.16732e29i q^{68} -6.67217e30 q^{69} -3.44997e30 q^{71} +1.15440e31i q^{72} -7.11823e30i q^{73} -1.28559e30 q^{74} -2.05455e30 q^{76} -2.51476e31i q^{77} -2.26036e31i q^{78} +1.57830e31 q^{79} +7.34723e31 q^{81} +1.40006e31i q^{82} +3.45599e31i q^{83} -5.05898e31 q^{84} -6.82049e31 q^{86} +1.12188e31i q^{87} +2.01677e32i q^{88} +2.35733e32 q^{89} +2.45946e32 q^{91} +1.65619e32i q^{92} -2.06256e32i q^{93} +4.52602e31 q^{94} +6.96024e32 q^{96} +3.55763e32i q^{97} +2.78035e32i q^{98} +3.12168e33 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2282622720 q^{4} + 25850126231520 q^{6} - 29\!\cdots\!30 q^{9}+O(q^{10}) $ 10 * q - 2282622720 * q^4 + 25850126231520 * q^6 - 29082501980817930 * q^9	$ 10 q - 2282622720 q^{4} + 25850126231520 q^{6} - 29\!\cdots\!30 q^{9}+ \cdots + 35\!\cdots\!40 q^{99}+O(q^{100}) $ 10 * q - 2282622720 * q^4 + 25850126231520 * q^6 - 29082501980817930 * q^9 - 575603603755953280 * q^11 - 23352899832544964640 * q^14 - 178360179086491914240 * q^16 - 1836729424390307895000 * q^19 - 21070231543425610826280 * q^21 + 143906401505515790361600 * q^24 - 849804721525442929523680 * q^26 + 1853754449987178542332100 * q^29 - 2672092958823642744403880 * q^31 + 137261316985027076739134560 * q^34 - 360748400001957176977117440 * q^36 + 1571583303018981507764931240 * q^39 - 2651240061509051866658512580 * q^41 + 3711878773305232716307804160 * q^44 - 5749299441668848515671371680 * q^46 - 8286468607000063583445894370 * q^49 + 14693438437830537506177750520 * q^51 - 128269435172297554561502376000 * q^54 + 289761018489691889589260313600 * q^56 - 514352424980859556364217812600 * q^59 + 1485779386335344406993238892820 * q^61 + 2078735103694502811148443975680 * q^64 - 6655035034062564292395293122560 * q^66 + 5534834351560350274144858514040 * q^69 - 11004170679364663489635588709880 * q^71 + 7277243818356708673732037512160 * q^74 + 14372679965174635117412392371200 * q^76 + 20516394009185475518243852596400 * q^79 + 157167609672604082013165294629010 * q^81 - 348890661199919432748081747133440 * q^84 + 130972229415655948195807080929120 * q^86 + 121707000777727369262632666890300 * q^89 - 537874169607477694864406415470680 * q^91 + 726874111076263788097451816894560 * q^94 - 689037206345673291941779788103680 * q^96 + 3581331178646963842559626355879040 * 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 $

$2$	− 71937.8i	− 0.776180i	−0.921622	−	0.388090i	$-0.873135\pi$
$2$	− 71937.8i	− 0.776180i	0.921622	−	0.388090i	$-0.126865\pi$
$3$	1.37573e8i	1.84516i	0.385811	+	0.922578i	$0.373922\pi$
$3$	1.37573e8i	1.84516i	−0.385811	+	0.922578i	$0.626078\pi$
$4$	3.41489e9	0.397545
$5$	0	0
$5$	0	0
$6$	9.89671e12	1.43217
$7$	1.07684e14i	1.22472i	0.790581	+	0.612358i	$0.209779\pi$
$7$	1.07684e14i	1.22472i	−0.790581	+	0.612358i	$0.790221\pi$
$8$	− 8.63600e14i	− 1.08475i
$9$	−1.33673e16	−2.40460
$10$	0	0
$11$	−2.33530e17	−1.53237	−0.766186	−	0.642619i	$-0.777848\pi$
$11$	−2.33530e17	−1.53237	−0.766186	+	0.642619i	$0.777848\pi$
$12$	4.69797e17i	0.733533i
$13$	− 2.28395e18i	− 0.951965i	−0.879455	−	0.475983i	$-0.842092\pi$
$13$	− 2.28395e18i	− 0.951965i	0.879455	−	0.475983i	$-0.157908\pi$
$14$	7.74658e18	0.950599
$15$	0	0
$16$	−3.27918e19	−0.444412
$17$	2.09885e20i	1.04610i	0.852302	+	0.523050i	$0.175206\pi$
$17$	2.09885e20i	1.04610i	−0.852302	+	0.523050i	$0.824794\pi$
$18$	9.61615e20i	1.86640i
$19$	−6.01644e20	−0.478526	−0.239263	−	0.970955i	$-0.576906\pi$
$19$	−6.01644e20	−0.478526	−0.239263	+	0.970955i	$0.576906\pi$
$20$	0	0
$21$	−1.48145e22	−2.25979
$22$	1.67997e22i	1.18940i
$23$	4.84991e22i	1.64901i	0.565853	+	0.824506i	$0.308547\pi$
$23$	4.84991e22i	1.64901i	−0.565853	+	0.824506i	$0.691453\pi$
$24$	1.18808e23	2.00153
$25$	0	0
$26$	−1.64302e23	−0.738896
$27$	− 1.07421e24i	− 2.59171i
$28$	3.67730e23i	0.486880i
$29$	8.15476e22	0.0605124	0.0302562	−	0.999542i	$-0.490368\pi$
$29$	8.15476e22	0.0605124	0.0302562	+	0.999542i	$0.490368\pi$
$30$	0	0
$31$	−1.49925e24	−0.370174	−0.185087	−	0.982722i	$-0.559257\pi$
$31$	−1.49925e24	−0.370174	−0.185087	+	0.982722i	$0.559257\pi$
$32$	− 5.05930e24i	− 0.739802i
$33$	− 3.21275e25i	− 2.82747i
$34$	1.50986e25	0.811961
$35$	0	0
$36$	−4.56479e25	−0.955938
$37$	− 1.78708e25i	− 0.238131i	−0.992886	−	0.119066i	$-0.962010\pi$
$37$	− 1.78708e25i	− 0.238131i	0.992886	−	0.119066i	$-0.0379899\pi$
$38$	4.32809e25i	0.371422i
$39$	3.14210e26	1.75652
$40$	0	0
$41$	−1.94621e26	−0.476712	−0.238356	−	0.971178i	$-0.576608\pi$
$41$	−1.94621e26	−0.476712	−0.238356	+	0.971178i	$0.576608\pi$
$42$	1.06572e27i	1.75400i
$43$	− 9.48110e26i	− 1.05835i	−0.848513	−	0.529175i	$-0.822502\pi$
$43$	− 9.48110e26i	− 1.05835i	0.848513	−	0.529175i	$-0.177498\pi$
$44$	−7.97481e26	−0.609187
$45$	0	0
$46$	3.48891e27	1.27993
$47$	6.29157e26i	0.161862i	0.996720	+	0.0809309i	$0.0257893\pi$
$47$	6.29157e26i	0.161862i	−0.996720	+	0.0809309i	$0.974211\pi$
$48$	− 4.51128e27i	− 0.820010i
$49$	−3.86494e27	−0.499927
$50$	0	0
$51$	−2.88745e28	−1.93022
$52$	− 7.79943e27i	− 0.378449i
$53$	− 8.56042e27i	− 0.303350i	−0.988430	−	0.151675i	$-0.951533\pi$
$53$	− 8.56042e27i	− 0.303350i	0.988430	−	0.151675i	$-0.0484666\pi$
$54$	−7.72760e28	−2.01163
$55$	0	0
$56$	9.29963e28	1.32851
$57$	− 8.27701e28i	− 0.882954i
$58$	− 5.86635e27i	− 0.0469685i
$59$	−5.43089e27	−0.0327954	−0.0163977	−	0.999866i	$-0.505220\pi$
$59$	−5.43089e27	−0.0327954	−0.0163977	+	0.999866i	$0.505220\pi$
$60$	0	0
$61$	1.79220e29	0.624373	0.312186	−	0.950021i	$-0.398939\pi$
$61$	1.79220e29	0.624373	0.312186	+	0.950021i	$0.398939\pi$
$62$	1.07853e29i	0.287321i
$63$	− 1.43945e30i	− 2.94495i
$64$	−6.45635e29	−1.01863
$65$	0	0
$66$	−2.31118e30	−2.19462
$67$	3.33703e29i	0.247244i	0.992329	+	0.123622i	$0.0394510\pi$
$67$	3.33703e29i	0.247244i	−0.992329	+	0.123622i	$0.960549\pi$
$68$	7.16732e29i	0.415872i
$69$	−6.67217e30	−3.04269
$70$	0	0
$71$	−3.44997e30	−0.981866	−0.490933	−	0.871197i	$-0.663344\pi$
$71$	−3.44997e30	−0.981866	−0.490933	+	0.871197i	$0.663344\pi$
$72$	1.15440e31i	2.60838i
$73$	− 7.11823e30i	− 1.28099i	−0.767963	−	0.640494i	$-0.778730\pi$
$73$	− 7.11823e30i	− 1.28099i	0.767963	−	0.640494i	$-0.221270\pi$
$74$	−1.28559e30	−0.184833
$75$	0	0
$76$	−2.05455e30	−0.190236
$77$	− 2.51476e31i	− 1.87672i
$78$	− 2.26036e31i	− 1.36338i
$79$	1.57830e31	0.771510	0.385755	−	0.922601i	$-0.373941\pi$
$79$	1.57830e31	0.771510	0.385755	+	0.922601i	$0.373941\pi$
$80$	0	0
$81$	7.34723e31	2.37750
$82$	1.40006e31i	0.370014i
$83$	3.45599e31i	0.747798i	0.927470	+	0.373899i	$0.121979\pi$
$83$	3.45599e31i	0.747798i	−0.927470	+	0.373899i	$0.878021\pi$
$84$	−5.05898e31	−0.898369
$85$	0	0
$86$	−6.82049e31	−0.821469
$87$	1.12188e31i	0.111655i
$88$	2.01677e32i	1.66223i
$89$	2.35733e32	1.61244	0.806222	−	0.591613i	$-0.201509\pi$
$89$	2.35733e32	1.61244	0.806222	+	0.591613i	$0.201509\pi$
$90$	0	0
$91$	2.45946e32	1.16589
$92$	1.65619e32i	0.655557i
$93$	− 2.06256e32i	− 0.683029i
$94$	4.52602e31	0.125634
$95$	0	0
$96$	6.96024e32	1.36505
$97$	3.55763e32i	0.588067i	0.955795	+	0.294033i	$0.0949977\pi$
$97$	3.55763e32i	0.588067i	−0.955795	+	0.294033i	$0.905002\pi$
$98$	2.78035e32i	0.388033i
$99$	3.12168e33	3.68474
$100$	0	0
$101$	9.03859e32	0.767004	0.383502	−	0.923540i	$-0.374718\pi$
$101$	9.03859e32	0.767004	0.383502	+	0.923540i	$0.374718\pi$
$102$	2.07717e33i	1.49820i
$103$	2.36642e33i	1.45304i	0.687146	+	0.726519i	$0.258863\pi$
$103$	2.36642e33i	1.45304i	−0.687146	+	0.726519i	$0.741137\pi$
$104$	−1.97242e33	−1.03264
$105$	0	0
$106$	−6.15818e32	−0.235454
$107$	− 2.84756e33i	− 0.932482i	−0.884658	−	0.466241i	$-0.845608\pi$
$107$	− 2.84756e33i	− 0.932482i	0.884658	−	0.466241i	$-0.154392\pi$
$108$	− 3.66830e33i	− 1.03032i
$109$	−3.46217e33	−0.835241	−0.417620	−	0.908622i	$-0.637136\pi$
$109$	−3.46217e33	−0.835241	−0.417620	+	0.908622i	$0.637136\pi$
$110$	0	0
$111$	2.45855e33	0.439389
$112$	− 3.53117e33i	− 0.544279i
$113$	− 9.04247e33i	− 1.20363i	−0.798636	−	0.601815i	$-0.794444\pi$
$113$	− 9.04247e33i	− 1.20363i	0.798636	−	0.601815i	$-0.205556\pi$
$114$	−5.95430e33	−0.685331
$115$	0	0
$116$	2.78476e32	0.0240564
$117$	3.05303e34i	2.28910i
$118$	3.90687e32i	0.0254551i
$119$	−2.26013e34	−1.28117
$120$	0	0
$121$	3.13113e34	1.34816
$122$	− 1.28927e34i	− 0.484626i
$123$	− 2.67746e34i	− 0.879608i
$124$	−5.11977e33	−0.147161
$125$	0	0
$126$	−1.03551e35	−2.28581
$127$	4.59458e33i	0.0890194i	0.999009	+	0.0445097i	$0.0141726\pi$
$127$	4.59458e33i	0.0890194i	−0.999009	+	0.0445097i	$0.985827\pi$
$128$	2.98648e33i	0.0508388i
$129$	1.30434e35	1.95282
$130$	0	0
$131$	−2.50614e34	−0.291091	−0.145545	−	0.989352i	$-0.546494\pi$
$131$	−2.50614e34	−0.291091	−0.145545	+	0.989352i	$0.546494\pi$
$132$	− 1.09712e35i	− 1.12405i
$133$	− 6.47877e34i	− 0.586058i
$134$	2.40059e34	0.191906
$135$	0	0
$136$	1.81256e35	1.13475
$137$	− 2.78859e35i	− 1.54702i	−0.633784	−	0.773510i	$-0.718499\pi$
$137$	− 2.78859e35i	− 1.54702i	0.633784	−	0.773510i	$-0.281501\pi$
$138$	4.79981e35i	2.36167i
$139$	−1.40995e35	−0.615827	−0.307914	−	0.951414i	$-0.599631\pi$
$139$	−1.40995e35	−0.615827	−0.307914	+	0.951414i	$0.599631\pi$
$140$	0	0
$141$	−8.65551e34	−0.298660
$142$	2.48183e35i	0.762104i
$143$	5.33372e35i	1.45877i
$144$	4.38339e35	1.06863
$145$	0	0
$146$	−5.12070e35	−0.994277
$147$	− 5.31711e35i	− 0.922444i
$148$	− 6.10269e34i	− 0.0946680i
$149$	4.84716e35	0.672844	0.336422	−	0.941711i	$-0.390783\pi$
$149$	4.84716e35	0.672844	0.336422	+	0.941711i	$0.390783\pi$
$150$	0	0
$151$	−1.29129e35	−0.143848	−0.0719238	−	0.997410i	$-0.522914\pi$
$151$	−1.29129e35	−0.143848	−0.0719238	+	0.997410i	$0.522914\pi$
$152$	5.19580e35i	0.519079i
$153$	− 2.80559e36i	− 2.51545i
$154$	−1.80906e36	−1.45667
$155$	0	0
$156$	1.07299e36	0.698298
$157$	− 1.48727e36i	− 0.871052i	−0.900176	−	0.435526i	$-0.856562\pi$
$157$	− 1.48727e36i	− 0.871052i	0.900176	−	0.435526i	$-0.143438\pi$
$158$	− 1.13539e36i	− 0.598830i
$159$	1.17768e36	0.559727
$160$	0	0
$161$	−5.22259e36	−2.01957
$162$	− 5.28543e36i	− 1.84537i
$163$	− 5.65066e36i	− 1.78240i	−0.453615	−	0.891198i	$-0.649866\pi$
$163$	− 5.65066e36i	− 1.78240i	0.453615	−	0.891198i	$-0.350134\pi$
$164$	−6.64609e35	−0.189515
$165$	0	0
$166$	2.48616e36	0.580425
$167$	8.79383e36i	1.85933i	0.368407	+	0.929665i	$0.379903\pi$
$167$	8.79383e36i	1.85933i	−0.368407	+	0.929665i	$0.620097\pi$
$168$	1.27938e37i	2.45130i
$169$	5.39705e35	0.0937617
$170$	0	0
$171$	8.04237e36	1.15066
$172$	− 3.23769e36i	− 0.420742i
$173$	− 5.34130e36i	− 0.630792i	−0.948960	−	0.315396i	$-0.897863\pi$
$173$	− 5.34130e36i	− 0.630792i	0.948960	−	0.315396i	$-0.102137\pi$
$174$	8.07053e35	0.0866641
$175$	0	0
$176$	7.65790e36	0.681005
$177$	− 7.47145e35i	− 0.0605127i
$178$	− 1.69581e37i	− 1.25155i
$179$	1.75097e37	1.17816	0.589080	−	0.808075i	$-0.299490\pi$
$179$	1.75097e37	1.17816	0.589080	+	0.808075i	$0.299490\pi$
$180$	0	0
$181$	1.00404e37	0.562411	0.281205	−	0.959648i	$-0.409266\pi$
$181$	1.00404e37	0.562411	0.281205	+	0.959648i	$0.409266\pi$
$182$	− 1.76928e37i	− 0.904937i
$183$	2.46559e37i	1.15207i
$184$	4.18838e37	1.78876
$185$	0	0
$186$	−1.48376e37	−0.530153
$187$	− 4.90144e37i	− 1.60301i
$188$	2.14850e36i	0.0643474i
$189$	1.15675e38	3.17410
$190$	0	0
$191$	−1.96610e37	−0.453477	−0.226739	−	0.973956i	$-0.572806\pi$
$191$	−1.96610e37	−0.453477	−0.226739	+	0.973956i	$0.572806\pi$
$192$	− 8.88220e37i	− 1.87953i
$193$	3.92456e37i	0.762246i	0.924524	+	0.381123i	$0.124463\pi$
$193$	3.92456e37i	0.762246i	−0.924524	+	0.381123i	$0.875537\pi$
$194$	2.55928e37	0.456446
$195$	0	0
$196$	−1.31983e37	−0.198744
$197$	1.18069e38i	1.63471i	0.576131	+	0.817357i	$0.304562\pi$
$197$	1.18069e38i	1.63471i	−0.576131	+	0.817357i	$0.695438\pi$
$198$	− 2.24566e38i	− 2.86002i
$199$	−1.43693e38	−1.68407	−0.842035	−	0.539423i	$-0.818642\pi$
$199$	−1.43693e38	−1.68407	−0.842035	+	0.539423i	$0.818642\pi$
$200$	0	0
$201$	−4.59086e37	−0.456204
$202$	− 6.50216e37i	− 0.595333i
$203$	8.78140e36i	0.0741104i
$204$	−9.86031e37	−0.767349
$205$	0	0
$206$	1.70235e38	1.12782
$207$	− 6.48302e38i	− 3.96522i
$208$	7.48949e37i	0.423065i
$209$	1.40502e38	0.733279
$210$	0	0
$211$	−2.97825e38	−1.32831	−0.664157	−	0.747593i	$-0.731210\pi$
$211$	−2.97825e38	−1.32831	−0.664157	+	0.747593i	$0.731210\pi$
$212$	− 2.92329e37i	− 0.120595i
$213$	− 4.74623e38i	− 1.81170i
$214$	−2.04847e38	−0.723773
$215$	0	0
$216$	−9.27685e38	−2.81134
$217$	− 1.61446e38i	− 0.453358i
$218$	2.49061e38i	0.648297i
$219$	9.79278e38	2.36362
$220$	0	0
$221$	4.79366e38	0.995851
$222$	− 1.76863e38i	− 0.341045i
$223$	− 1.05983e38i	− 0.189761i	−0.995489	−	0.0948804i	$-0.969753\pi$
$223$	− 1.05983e38i	− 0.189761i	0.995489	−	0.0948804i	$-0.0302469\pi$
$224$	5.44808e38	0.906047
$225$	0	0
$226$	−6.50496e38	−0.934233
$227$	− 7.63192e38i	− 1.01908i	−0.860448	−	0.509538i	$-0.829816\pi$
$227$	− 7.63192e38i	− 1.01908i	0.860448	−	0.509538i	$-0.170184\pi$
$228$	− 2.82651e38i	− 0.351014i
$229$	−2.74424e38	−0.317057	−0.158528	−	0.987354i	$-0.550675\pi$
$229$	−2.74424e38	−0.317057	−0.158528	+	0.987354i	$0.550675\pi$
$230$	0	0
$231$	3.45963e39	3.46284
$232$	− 7.04245e37i	− 0.0656406i
$233$	− 7.50623e38i	− 0.651702i	−0.945421	−	0.325851i	$-0.894349\pi$
$233$	− 7.50623e38i	− 0.651702i	0.945421	−	0.325851i	$-0.105651\pi$
$234$	2.19628e39	1.77675
$235$	0	0
$236$	−1.85459e37	−0.0130377
$237$	2.17131e39i	1.42356i
$238$	1.62589e39i	0.994422i
$239$	9.41651e38	0.537434	0.268717	−	0.963219i	$-0.413400\pi$
$239$	9.41651e38	0.537434	0.268717	+	0.963219i	$0.413400\pi$
$240$	0	0
$241$	−4.90507e38	−0.243985	−0.121993	−	0.992531i	$-0.538928\pi$
$241$	−4.90507e38	−0.243985	−0.121993	+	0.992531i	$0.538928\pi$
$242$	− 2.25247e39i	− 1.04642i
$243$	4.13623e39i	1.79515i
$244$	6.12016e38	0.248217
$245$	0	0
$246$	−1.92611e39	−0.682734
$247$	1.37412e39i	0.455540i
$248$	1.29475e39i	0.401545i
$249$	−4.75452e39	−1.37980
$250$	0	0
$251$	5.96650e39	1.51741	0.758705	−	0.651434i	$-0.225832\pi$
$251$	5.96650e39	1.51741	0.758705	+	0.651434i	$0.225832\pi$
$252$	− 4.91557e39i	− 1.17075i
$253$	− 1.13260e40i	− 2.52690i
$254$	3.30524e38	0.0690950
$255$	0	0
$256$	−5.33112e39	−0.979172
$257$	8.25525e39i	1.42178i	0.703301	+	0.710892i	$0.251709\pi$
$257$	8.25525e39i	1.42178i	−0.703301	+	0.710892i	$0.748291\pi$
$258$	− 9.38317e39i	− 1.51574i
$259$	1.92441e39	0.291643
$260$	0	0
$261$	−1.09007e39	−0.145508
$262$	1.80286e39i	0.225939i
$263$	6.74712e39i	0.794051i	0.917808	+	0.397026i	$0.129958\pi$
$263$	6.74712e39i	0.794051i	−0.917808	+	0.397026i	$0.870042\pi$
$264$	−2.77454e40	−3.06708
$265$	0	0
$266$	−4.66068e39	−0.454886
$267$	3.24305e40i	2.97521i
$268$	1.13956e39i	0.0982907i
$269$	2.97390e39	0.241220	0.120610	−	0.992700i	$-0.461515\pi$
$269$	2.97390e39	0.241220	0.120610	+	0.992700i	$0.461515\pi$
$270$	0	0
$271$	−7.89524e39	−0.566725	−0.283362	−	0.959013i	$-0.591450\pi$
$271$	−7.89524e39	−0.566725	−0.283362	+	0.959013i	$0.591450\pi$
$272$	− 6.88250e39i	− 0.464900i
$273$	3.38355e40i	2.15124i
$274$	−2.00605e40	−1.20076
$275$	0	0
$276$	−2.27847e40	−1.20961
$277$	− 2.12171e40i	− 1.06113i	−0.847644	−	0.530566i	$-0.821980\pi$
$277$	− 2.12171e40i	− 1.06113i	0.847644	−	0.530566i	$-0.178020\pi$
$278$	1.01429e40i	0.477993i
$279$	2.00409e40	0.890120
$280$	0	0
$281$	4.91397e40	1.93989	0.969947	−	0.243317i	$-0.0782355\pi$
$281$	4.91397e40	1.93989	0.969947	+	0.243317i	$0.0782355\pi$
$282$	6.22658e39i	0.231814i
$283$	− 4.22019e40i	− 1.48203i	−0.671491	−	0.741013i	$-0.734346\pi$
$283$	− 4.22019e40i	− 1.48203i	0.671491	−	0.741013i	$-0.265654\pi$
$284$	−1.17813e40	−0.390336
$285$	0	0
$286$	3.83696e40	1.13226
$287$	− 2.09576e40i	− 0.583836i
$288$	6.76292e40i	1.77893i
$289$	−3.79702e39	−0.0943253
$290$	0	0
$291$	−4.89434e40	−1.08508
$292$	− 2.43080e40i	− 0.509251i
$293$	2.96004e40i	0.586115i	0.956095	+	0.293057i	$0.0946727\pi$
$293$	2.96004e40i	0.586115i	−0.956095	+	0.293057i	$0.905327\pi$
$294$	−3.82502e40	−0.715982
$295$	0	0
$296$	−1.54333e40	−0.258312
$297$	2.50860e41i	3.97146i
$298$	− 3.48694e40i	− 0.522248i
$299$	1.10769e41	1.56980
$300$	0	0
$301$	1.02097e41	1.29618
$302$	9.28922e39i	0.111652i
$303$	1.24347e41i	1.41524i
$304$	1.97290e40	0.212663
$305$	0	0
$306$	−2.01828e41	−1.95244
$307$	1.70501e41i	1.56295i	0.623938	+	0.781474i	$0.285532\pi$
$307$	1.70501e41i	1.56295i	−0.623938	+	0.781474i	$0.714468\pi$
$308$	− 8.58762e40i	− 0.746081i
$309$	−3.25556e41	−2.68108
$310$	0	0
$311$	1.09238e41	0.808774	0.404387	−	0.914588i	$-0.367485\pi$
$311$	1.09238e41	0.808774	0.404387	+	0.914588i	$0.367485\pi$
$312$	− 2.71352e41i	− 1.90538i
$313$	− 2.55151e41i	− 1.69948i	−0.527205	−	0.849738i	$-0.676760\pi$
$313$	− 2.55151e41i	− 1.69948i	0.527205	−	0.849738i	$-0.323240\pi$
$314$	−1.06991e41	−0.676093
$315$	0	0
$316$	5.38971e40	0.306710
$317$	− 1.40033e41i	− 0.756400i	−0.925724	−	0.378200i	$-0.876543\pi$
$317$	− 1.40033e41i	− 0.756400i	0.925724	−	0.378200i	$-0.123457\pi$
$318$	− 8.47200e40i	− 0.434449i
$319$	−1.90438e40	−0.0927275
$320$	0	0
$321$	3.91748e41	1.72057
$322$	3.75702e41i	1.56755i
$323$	− 1.26276e41i	− 0.500586i
$324$	2.50900e41	0.945164
$325$	0	0
$326$	−4.06496e41	−1.38346
$327$	− 4.76302e41i	− 1.54115i
$328$	1.68075e41i	0.517111i
$329$	−6.77504e40	−0.198235
$330$	0	0
$331$	−2.36103e41	−0.625086	−0.312543	−	0.949904i	$-0.601181\pi$
$331$	−2.36103e41	−0.625086	−0.312543	+	0.949904i	$0.601181\pi$
$332$	1.18018e41i	0.297283i
$333$	2.38885e41i	0.572611i
$334$	6.32609e41	1.44317
$335$	0	0
$336$	4.85794e41	1.00428
$337$	− 5.72695e41i	− 1.12728i	−0.826022	−	0.563638i	$-0.809401\pi$
$337$	− 5.72695e41i	− 1.12728i	0.826022	−	0.563638i	$-0.190599\pi$
$338$	− 3.88252e40i	− 0.0727759i
$339$	1.24400e42	2.22088
$340$	0	0
$341$	3.50120e41	0.567244
$342$	− 5.78550e41i	− 0.893121i
$343$	4.16314e41i	0.612446i
$344$	−8.18788e41	−1.14804
$345$	0	0
$346$	−3.84241e41	−0.489608
$347$	− 7.23409e41i	− 0.878917i	−0.898263	−	0.439458i	$-0.855170\pi$
$347$	− 7.23409e41i	− 0.878917i	0.898263	−	0.439458i	$-0.144830\pi$
$348$	3.83108e40i	0.0443878i
$349$	1.72145e42	1.90228	0.951140	−	0.308761i	$-0.0999145\pi$
$349$	1.72145e42	1.90228	0.951140	+	0.308761i	$0.0999145\pi$
$350$	0	0
$351$	−2.45343e42	−2.46721
$352$	1.18150e42i	1.13365i
$353$	− 1.10466e42i	− 1.01145i	−0.862695	−	0.505725i	$-0.831225\pi$
$353$	− 1.10466e42i	− 1.01145i	0.862695	−	0.505725i	$-0.168775\pi$
$354$	−5.37480e40	−0.0469687
$355$	0	0
$356$	8.05001e41	0.641020
$357$	− 3.10933e42i	− 2.36397i
$358$	− 1.25961e42i	− 0.914464i
$359$	−1.24115e42	−0.860528	−0.430264	−	0.902703i	$-0.641580\pi$
$359$	−1.24115e42	−0.860528	−0.430264	+	0.902703i	$0.641580\pi$
$360$	0	0
$361$	−1.21880e42	−0.771013
$362$	− 7.22283e41i	− 0.436532i
$363$	4.30760e42i	2.48757i
$364$	8.39877e41	0.463493
$365$	0	0
$366$	1.77369e42	0.894210
$367$	− 7.83869e41i	− 0.377792i	−0.981997	−	0.188896i	$-0.939509\pi$
$367$	− 7.83869e41i	− 0.377792i	0.981997	−	0.188896i	$-0.0604910\pi$
$368$	− 1.59037e42i	− 0.732842i
$369$	2.60156e42	1.14630
$370$	0	0
$371$	9.21824e41	0.371517
$372$	− 7.04343e41i	− 0.271535i
$373$	− 4.48131e42i	− 1.65276i	−0.563116	−	0.826378i	$-0.690397\pi$
$373$	− 4.48131e42i	− 1.65276i	0.563116	−	0.826378i	$-0.309603\pi$
$374$	−3.52599e42	−1.24423
$375$	0	0
$376$	5.43340e41	0.175579
$377$	− 1.86251e41i	− 0.0576057i
$378$	− 8.32142e42i	− 2.46367i
$379$	−5.32753e42	−1.51001	−0.755003	−	0.655721i	$-0.772365\pi$
$379$	−5.32753e42	−1.51001	−0.755003	+	0.655721i	$0.772365\pi$
$380$	0	0
$381$	−6.32091e41	−0.164255
$382$	1.41437e42i	0.351980i
$383$	7.66000e42i	1.82578i	0.408203	+	0.912891i	$0.366156\pi$
$383$	7.66000e42i	1.82578i	−0.408203	+	0.912891i	$0.633844\pi$
$384$	−4.10860e41	−0.0938055
$385$	0	0
$386$	2.82324e42	0.591640
$387$	1.26737e43i	2.54491i
$388$	1.21489e42i	0.233783i
$389$	−2.42415e42	−0.447085	−0.223543	−	0.974694i	$-0.571762\pi$
$389$	−2.42415e42	−0.447085	−0.223543	+	0.974694i	$0.571762\pi$
$390$	0	0
$391$	−1.01792e43	−1.72503
$392$	3.33776e42i	0.542294i
$393$	− 3.44777e42i	− 0.537108i
$394$	8.49360e42	1.26883
$395$	0	0
$396$	1.06602e43	1.46485
$397$	− 4.43937e42i	− 0.585164i	−0.956240	−	0.292582i	$-0.905486\pi$
$397$	− 4.43937e42i	− 0.585164i	0.956240	−	0.292582i	$-0.0945145\pi$
$398$	1.03370e43i	1.30714i
$399$	8.91304e42	1.08137
$400$	0	0
$401$	6.39786e41	0.0714747	0.0357374	−	0.999361i	$-0.488622\pi$
$401$	6.39786e41	0.0714747	0.0357374	+	0.999361i	$0.488622\pi$
$402$	3.30256e42i	0.354096i
$403$	3.42421e42i	0.352393i
$404$	3.08658e42	0.304919
$405$	0	0
$406$	6.31715e41	0.0575230
$407$	4.17339e42i	0.364906i
$408$	2.49360e43i	2.09380i
$409$	1.16096e43	0.936227	0.468114	−	0.883668i	$-0.344934\pi$
$409$	1.16096e43	0.936227	0.468114	+	0.883668i	$0.344934\pi$
$410$	0	0
$411$	3.83636e43	2.85449
$412$	8.08105e42i	0.577649i
$413$	− 5.84823e41i	− 0.0401650i
$414$	−4.66374e43	−3.07772
$415$	0	0
$416$	−1.15552e43	−0.704266
$417$	− 1.93971e43i	− 1.13630i
$418$	− 1.01074e43i	− 0.569156i
$419$	7.07188e42	0.382828	0.191414	−	0.981509i	$-0.438693\pi$
$419$	7.07188e42	0.382828	0.191414	+	0.981509i	$0.438693\pi$
$420$	0	0
$421$	−2.32219e43	−1.16210	−0.581050	−	0.813868i	$-0.697358\pi$
$421$	−2.32219e43	−1.16210	−0.581050	+	0.813868i	$0.697358\pi$
$422$	2.14249e43i	1.03101i
$423$	− 8.41014e42i	− 0.389213i
$424$	−7.39279e42	−0.329057
$425$	0	0
$426$	−3.41433e43	−1.40620
$427$	1.92992e43i	0.764679i
$428$	− 9.72410e42i	− 0.370704i
$429$	−7.33777e43	−2.69165
$430$	0	0
$431$	−3.01488e43	−1.02422	−0.512112	−	0.858919i	$-0.671137\pi$
$431$	−3.01488e43	−1.02422	−0.512112	+	0.858919i	$0.671137\pi$
$432$	3.52252e43i	1.15179i
$433$	3.63888e43i	1.14530i	0.819802	+	0.572648i	$0.194084\pi$
$433$	3.63888e43i	1.14530i	−0.819802	+	0.572648i	$0.805916\pi$
$434$	−1.16141e43	−0.351887
$435$	0	0
$436$	−1.18229e43	−0.332046
$437$	− 2.91792e43i	− 0.789095i
$438$	− 7.04471e43i	− 1.83460i
$439$	3.62391e42	0.0908893	0.0454446	−	0.998967i	$-0.485530\pi$
$439$	3.62391e42	0.0908893	0.0454446	+	0.998967i	$0.485530\pi$
$440$	0	0
$441$	5.16638e43	1.20213
$442$	− 3.44845e43i	− 0.772959i
$443$	2.84653e43i	0.614686i	0.951599	+	0.307343i	$0.0994400\pi$
$443$	2.84653e43i	0.614686i	−0.951599	+	0.307343i	$0.900560\pi$
$444$	8.39567e42	0.174677
$445$	0	0
$446$	−7.62419e42	−0.147288
$447$	6.66840e43i	1.24150i
$448$	− 6.95248e43i	− 1.24753i
$449$	3.05597e43	0.528548	0.264274	−	0.964448i	$-0.414868\pi$
$449$	3.05597e43	0.528548	0.264274	+	0.964448i	$0.414868\pi$
$450$	0	0
$451$	4.54499e43	0.730500
$452$	− 3.08790e43i	− 0.478497i
$453$	− 1.77646e43i	− 0.265421i
$454$	−5.49023e43	−0.790987
$455$	0	0
$456$	−7.14803e43	−0.957781
$457$	8.70256e42i	0.112468i	0.998418	+	0.0562341i	$0.0179093\pi$
$457$	8.70256e42i	0.112468i	−0.998418	+	0.0562341i	$0.982091\pi$
$458$	1.97415e43i	0.246093i
$459$	2.25459e44	2.71118
$460$	0	0
$461$	7.28964e43	0.815907	0.407954	−	0.913003i	$-0.366243\pi$
$461$	7.28964e43	0.815907	0.407954	+	0.913003i	$0.366243\pi$
$462$	− 2.48878e44i	− 2.68779i
$463$	1.54940e44i	1.61465i	0.590108	+	0.807324i	$0.299085\pi$
$463$	1.54940e44i	1.61465i	−0.590108	+	0.807324i	$0.700915\pi$
$464$	−2.67410e42	−0.0268924
$465$	0	0
$466$	−5.39982e43	−0.505838
$467$	9.15725e43i	0.828011i	0.910274	+	0.414006i	$0.135871\pi$
$467$	9.15725e43i	0.828011i	−0.910274	+	0.414006i	$0.864129\pi$
$468$	1.04257e44i	0.910020i
$469$	−3.59346e43	−0.302804
$470$	0	0
$471$	2.04608e44	1.60723
$472$	4.69012e42i	0.0355747i
$473$	2.21413e44i	1.62179i
$474$	1.56199e44	1.10494
$475$	0	0
$476$	−7.71809e43	−0.509325
$477$	1.14430e44i	0.729434i
$478$	− 6.77403e43i	− 0.417145i
$479$	−3.67745e43	−0.218782	−0.109391	−	0.993999i	$-0.534890\pi$
$479$	−3.67745e43	−0.218782	−0.109391	+	0.993999i	$0.534890\pi$
$480$	0	0
$481$	−4.08161e43	−0.226693
$482$	3.52860e43i	0.189376i
$483$	− 7.18488e44i	− 3.72642i
$484$	1.06925e44	0.535957
$485$	0	0
$486$	2.97552e44	1.39336
$487$	− 2.46290e44i	− 1.11485i	−0.830226	−	0.557427i	$-0.811789\pi$
$487$	− 2.46290e44i	− 1.11485i	0.830226	−	0.557427i	$-0.188211\pi$
$488$	− 1.54774e44i	− 0.677286i
$489$	7.77380e44	3.28880
$490$	0	0
$491$	1.21128e44	0.479071	0.239535	−	0.970888i	$-0.423005\pi$
$491$	1.21128e44	0.479071	0.239535	+	0.970888i	$0.423005\pi$
$492$	− 9.14324e43i	− 0.349684i
$493$	1.71156e43i	0.0633020i
$494$	9.88515e43	0.353581
$495$	0	0
$496$	4.91632e43	0.164510
$497$	− 3.71508e44i	− 1.20251i
$498$	3.42029e44i	1.07097i
$499$	−4.07835e44	−1.23545	−0.617726	−	0.786393i	$-0.711946\pi$
$499$	−4.07835e44	−1.23545	−0.617726	+	0.786393i	$0.711946\pi$
$500$	0	0
$501$	−1.20980e45	−3.43075
$502$	− 4.29217e44i	− 1.17778i
$503$	− 5.88791e44i	− 1.56347i	−0.623612	−	0.781734i	$-0.714335\pi$
$503$	− 5.88791e44i	− 1.56347i	0.623612	−	0.781734i	$-0.285665\pi$
$504$	−1.24311e45	−3.19452
$505$	0	0
$506$	−8.14768e44	−1.96133
$507$	7.42489e43i	0.173005i
$508$	1.56900e43i	0.0353892i
$509$	−7.13633e44	−1.55823	−0.779115	−	0.626881i	$-0.784331\pi$
$509$	−7.13633e44	−1.55823	−0.779115	+	0.626881i	$0.784331\pi$
$510$	0	0
$511$	7.66523e44	1.56885
$512$	4.09163e44i	0.810852i
$513$	6.46290e44i	1.24020i
$514$	5.93864e44	1.10356
$515$	0	0
$516$	4.45419e44	0.776335
$517$	− 1.46927e44i	− 0.248033i
$518$	− 1.38438e44i	− 0.226367i
$519$	7.34820e44	1.16391
$520$	0	0
$521$	−1.39893e44	−0.207957	−0.103978	−	0.994580i	$-0.533157\pi$
$521$	−1.39893e44	−0.207957	−0.103978	+	0.994580i	$0.533157\pi$
$522$	7.84174e43i	0.112940i
$523$	− 4.12677e44i	− 0.575880i	−0.957648	−	0.287940i	$-0.907030\pi$
$523$	− 4.12677e44i	− 0.575880i	0.957648	−	0.287940i	$-0.0929704\pi$
$524$	−8.55818e43	−0.115722
$525$	0	0
$526$	4.85373e44	0.616326
$527$	− 3.14669e44i	− 0.387239i
$528$	1.05352e45i	1.25656i
$529$	−1.48715e45	−1.71924
$530$	0	0
$531$	7.25965e43	0.0788599
$532$	− 2.21243e44i	− 0.232984i
$533$	4.44504e44i	0.453813i
$534$	2.33298e45	2.30930
$535$	0	0
$536$	2.88186e44	0.268197
$537$	2.40887e45i	2.17389i
$538$	− 2.13936e44i	− 0.187230i
$539$	9.02580e44	0.766075
$540$	0	0
$541$	−2.35683e45	−1.88180	−0.940899	−	0.338687i	$-0.890017\pi$
$541$	−2.35683e45	−1.88180	−0.940899	+	0.338687i	$0.890017\pi$
$542$	5.67966e44i	0.439880i
$543$	1.38129e45i	1.03774i
$544$	1.06187e45	0.773907
$545$	0	0
$546$	2.43405e45	1.66975
$547$	− 2.11321e45i	− 1.40654i	−0.710923	−	0.703270i	$-0.751723\pi$
$547$	− 2.11321e45i	− 1.40654i	0.710923	−	0.703270i	$-0.248277\pi$
$548$	− 9.52274e44i	− 0.615010i
$549$	−2.39569e45	−1.50137
$550$	0	0
$551$	−4.90626e43	−0.0289567
$552$	5.76209e45i	3.30054i
$553$	1.69958e45i	0.944880i
$554$	−1.52631e45	−0.823628
$555$	0	0
$556$	−4.81482e44	−0.244819
$557$	− 2.27438e45i	− 1.12267i	−0.827589	−	0.561335i	$-0.810288\pi$
$557$	− 2.27438e45i	− 1.12267i	0.827589	−	0.561335i	$-0.189712\pi$
$558$	− 1.44170e45i	− 0.690893i
$559$	−2.16544e45	−1.00751
$560$	0	0
$561$	6.74307e45	2.95781
$562$	− 3.53500e45i	− 1.50571i
$563$	− 1.75752e45i	− 0.726962i	−0.931602	−	0.363481i	$-0.881588\pi$
$563$	− 1.75752e45i	− 0.726962i	0.931602	−	0.363481i	$-0.118412\pi$
$564$	−2.95576e44	−0.118731
$565$	0	0
$566$	−3.03591e45	−1.15032
$567$	7.91182e45i	2.91176i
$568$	2.97939e45i	1.06508i
$569$	−9.61177e44	−0.333773	−0.166886	−	0.985976i	$-0.553371\pi$
$569$	−9.61177e44	−0.333773	−0.166886	+	0.985976i	$0.553371\pi$
$570$	0	0
$571$	−5.28842e45	−1.73313	−0.866563	−	0.499067i	$-0.833676\pi$
$571$	−5.28842e45	−1.73313	−0.866563	+	0.499067i	$0.833676\pi$
$572$	1.82141e45i	0.579925i
$573$	− 2.70483e45i	− 0.836737i
$574$	−1.50765e45	−0.453162
$575$	0	0
$576$	8.63040e45	2.44940
$577$	1.11538e45i	0.307626i	0.988100	+	0.153813i	$0.0491554\pi$
$577$	1.11538e45i	0.307626i	−0.988100	+	0.153813i	$0.950845\pi$
$578$	2.73149e44i	0.0732134i
$579$	−5.39914e45	−1.40646
$580$	0	0
$581$	−3.72156e45	−0.915839
$582$	3.52088e45i	0.842213i
$583$	1.99912e45i	0.464845i
$584$	−6.14731e45	−1.38955
$585$	0	0
$586$	2.12939e45	0.454930
$587$	− 3.02679e45i	− 0.628714i	−0.949305	−	0.314357i	$-0.898211\pi$
$587$	− 3.02679e45i	− 0.628714i	0.949305	−	0.314357i	$-0.101789\pi$
$588$	− 1.81574e45i	− 0.366713i
$589$	9.02014e44	0.177138
$590$	0	0
$591$	−1.62431e46	−3.01630
$592$	5.86018e44i	0.105829i
$593$	2.02049e45i	0.354857i	0.984134	+	0.177428i	$0.0567778\pi$
$593$	2.02049e45i	0.354857i	−0.984134	+	0.177428i	$0.943222\pi$
$594$	1.80463e46	3.08256
$595$	0	0
$596$	1.65525e45	0.267486
$597$	− 1.97683e46i	− 3.10737i
$598$	− 7.96851e45i	− 1.21845i
$599$	7.17593e45	1.06742	0.533710	−	0.845667i	$-0.320797\pi$
$599$	7.17593e45	1.06742	0.533710	+	0.845667i	$0.320797\pi$
$600$	0	0
$601$	−8.79572e44	−0.123835	−0.0619174	−	0.998081i	$-0.519722\pi$
$601$	−8.79572e44	−0.123835	−0.0619174	+	0.998081i	$0.519722\pi$
$602$	− 7.34461e45i	− 1.00607i
$603$	− 4.46071e45i	− 0.594523i
$604$	−4.40960e44	−0.0571859
$605$	0	0
$606$	8.94523e45	1.09848
$607$	1.35040e46i	1.61380i	0.590686	+	0.806902i	$0.298857\pi$
$607$	1.35040e46i	1.61380i	−0.590686	+	0.806902i	$0.701143\pi$
$608$	3.04390e45i	0.354014i
$609$	−1.20809e45	−0.136745
$610$	0	0
$611$	1.43696e45	0.154087
$612$	− 9.58079e45i	− 1.00001i
$613$	− 1.09063e45i	− 0.110810i	−0.998464	−	0.0554052i	$-0.982355\pi$
$613$	− 1.09063e45i	− 0.110810i	0.998464	−	0.0554052i	$-0.0176450\pi$
$614$	1.22655e46	1.21313
$615$	0	0
$616$	−2.17175e46	−2.03576
$617$	− 1.20780e46i	− 1.10227i	−0.834415	−	0.551137i	$-0.814194\pi$
$617$	− 1.20780e46i	− 1.10227i	0.834415	−	0.551137i	$-0.185806\pi$
$618$	2.34197e46i	2.08100i
$619$	3.00533e45	0.260014	0.130007	−	0.991513i	$-0.458500\pi$
$619$	3.00533e45	0.260014	0.130007	+	0.991513i	$0.458500\pi$
$620$	0	0
$621$	5.20980e46	4.27376
$622$	− 7.85834e45i	− 0.627754i
$623$	2.53847e46i	1.97478i
$624$	−1.03035e46	−0.780621
$625$	0	0
$626$	−1.83550e46	−1.31910
$627$	1.93293e46i	1.35301i
$628$	− 5.07885e45i	− 0.346283i
$629$	3.75081e45	0.249109
$630$	0	0
$631$	−2.08614e46	−1.31480	−0.657400	−	0.753542i	$-0.728344\pi$
$631$	−2.08614e46	−1.31480	−0.657400	+	0.753542i	$0.728344\pi$
$632$	− 1.36302e46i	− 0.836892i
$633$	− 4.09728e46i	− 2.45095i
$634$	−1.00736e46	−0.587102
$635$	0	0
$636$	4.02166e45	0.222517
$637$	8.82732e45i	0.475914i
$638$	1.36997e45i	0.0719732i
$639$	4.61168e46	2.36099
$640$	0	0
$641$	−1.91329e46	−0.930299	−0.465149	−	0.885232i	$-0.653999\pi$
$641$	−1.91329e46	−0.930299	−0.465149	+	0.885232i	$0.653999\pi$
$642$	− 2.81815e46i	− 1.33547i
$643$	− 3.18460e46i	− 1.47087i	−0.677597	−	0.735434i	$-0.736978\pi$
$643$	− 3.18460e46i	− 1.47087i	0.677597	−	0.735434i	$-0.263022\pi$
$644$	−1.78346e46	−0.802871
$645$	0	0
$646$	−9.08400e45	−0.388544
$647$	− 3.25342e46i	− 1.35650i	−0.734831	−	0.678250i	$-0.762739\pi$
$647$	− 3.25342e46i	− 1.35650i	0.734831	−	0.678250i	$-0.237261\pi$
$648$	− 6.34507e46i	− 2.57898i
$649$	1.26828e45	0.0502548
$650$	0	0
$651$	2.22106e46	0.836516
$652$	− 1.92964e46i	− 0.708583i
$653$	1.98304e46i	0.710009i	0.934865	+	0.355005i	$0.115521\pi$
$653$	1.98304e46i	0.710009i	−0.934865	+	0.355005i	$0.884479\pi$
$654$	−3.42641e46	−1.19621
$655$	0	0
$656$	6.38198e45	0.211857
$657$	9.51517e46i	3.08026i
$658$	4.87381e45i	0.153866i
$659$	−2.96542e45	−0.0913011	−0.0456506	−	0.998957i	$-0.514536\pi$
$659$	−2.96542e45	−0.0913011	−0.0456506	+	0.998957i	$0.514536\pi$
$660$	0	0
$661$	1.20833e46	0.353886	0.176943	−	0.984221i	$-0.443379\pi$
$661$	1.20833e46	0.353886	0.176943	+	0.984221i	$0.443379\pi$
$662$	1.69847e46i	0.485179i
$663$	6.59479e46i	1.83750i
$664$	2.98460e46	0.811170
$665$	0	0
$666$	1.71849e46	0.444449
$667$	3.95498e45i	0.0997857i
$668$	3.00300e46i	0.739168i
$669$	1.45804e46	0.350138
$670$	0	0
$671$	−4.18533e46	−0.956772
$672$	7.49509e46i	1.67180i
$673$	2.52503e46i	0.549565i	0.961506	+	0.274782i	$0.0886058\pi$
$673$	2.52503e46i	0.549565i	−0.961506	+	0.274782i	$0.911394\pi$
$674$	−4.11984e46	−0.874968
$675$	0	0
$676$	1.84303e45	0.0372745
$677$	− 3.98633e46i	− 0.786793i	−0.919369	−	0.393396i	$-0.871300\pi$
$677$	− 3.98633e46i	− 0.786793i	0.919369	−	0.393396i	$-0.128700\pi$
$678$	− 8.94908e46i	− 1.72381i
$679$	−3.83101e46	−0.720215
$680$	0	0
$681$	1.04995e47	1.88036
$682$	− 2.51869e46i	− 0.440284i
$683$	− 3.89128e46i	− 0.663973i	−0.943284	−	0.331986i	$-0.892281\pi$
$683$	− 3.89128e46i	− 0.663973i	0.943284	−	0.331986i	$-0.107719\pi$
$684$	2.74638e46	0.457441
$685$	0	0
$686$	2.99487e46	0.475368
$687$	− 3.77534e46i	− 0.585019i
$688$	3.10903e46i	0.470344i
$689$	−1.95516e46	−0.288778
$690$	0	0
$691$	−3.16293e46	−0.445350	−0.222675	−	0.974893i	$-0.571479\pi$
$691$	−3.16293e46	−0.445350	−0.222675	+	0.974893i	$0.571479\pi$
$692$	− 1.82399e46i	− 0.250769i
$693$	3.36156e47i	4.51276i
$694$	−5.20405e46	−0.682197
$695$	0	0
$696$	9.68853e45	0.121117
$697$	− 4.08479e46i	− 0.498688i
$698$	− 1.23837e47i	− 1.47651i
$699$	1.03266e47	1.20249
$700$	0	0
$701$	−5.26072e46	−0.584384	−0.292192	−	0.956360i	$-0.594385\pi$
$701$	−5.26072e46	−0.584384	−0.292192	+	0.956360i	$0.594385\pi$
$702$	1.76495e47i	1.91500i
$703$	1.07519e46i	0.113952i
$704$	1.50775e47	1.56092
$705$	0	0
$706$	−7.94665e46	−0.785066
$707$	9.73315e46i	0.939362i
$708$	− 2.55142e45i	− 0.0240565i
$709$	−1.31306e47	−1.20954	−0.604771	−	0.796399i	$-0.706735\pi$
$709$	−1.31306e47	−1.20954	−0.604771	+	0.796399i	$0.706735\pi$
$710$	0	0
$711$	−2.10976e47	−1.85517
$712$	− 2.03579e47i	− 1.74909i
$713$	− 7.27122e46i	− 0.610422i
$714$	−2.23678e47	−1.83486
$715$	0	0
$716$	5.97938e46	0.468372
$717$	1.29546e47i	0.991649i
$718$	8.92855e46i	0.667925i
$719$	−1.58298e47	−1.15731	−0.578653	−	0.815574i	$-0.696421\pi$
$719$	−1.58298e47	−1.15731	−0.578653	+	0.815574i	$0.696421\pi$
$720$	0	0
$721$	−2.54826e47	−1.77956
$722$	8.76774e46i	0.598445i
$723$	− 6.74806e46i	− 0.450191i
$724$	3.42868e46	0.223584
$725$	0	0
$726$	3.09879e47	1.93080
$727$	2.56013e47i	1.55935i	0.626184	+	0.779676i	$0.284616\pi$
$727$	2.56013e47i	1.55935i	−0.626184	+	0.779676i	$0.715384\pi$
$728$	− 2.12399e47i	− 1.26469i
$729$	−1.60598e47	−0.934838
$730$	0	0
$731$	1.98994e47	1.10714
$732$	8.41970e46i	0.457998i
$733$	− 5.58232e46i	− 0.296893i	−0.988920	−	0.148446i	$-0.952573\pi$
$733$	− 5.58232e46i	− 0.296893i	0.988920	−	0.148446i	$-0.0474272\pi$
$734$	−5.63898e46	−0.293235
$735$	0	0
$736$	2.45371e47	1.21994
$737$	− 7.79298e46i	− 0.378870i
$738$	− 1.87150e47i	− 0.889736i
$739$	−1.40164e47	−0.651634	−0.325817	−	0.945433i	$-0.605639\pi$
$739$	−1.40164e47	−0.651634	−0.325817	+	0.945433i	$0.605639\pi$
$740$	0	0
$741$	−1.89043e47	−0.840542
$742$	− 6.63140e46i	− 0.288364i
$743$	3.74285e46i	0.159180i	0.996828	+	0.0795898i	$0.0253610\pi$
$743$	3.74285e46i	0.159180i	−0.996828	+	0.0795898i	$0.974639\pi$
$744$	−1.78123e47	−0.740913
$745$	0	0
$746$	−3.22375e47	−1.28284
$747$	− 4.61973e47i	− 1.79815i
$748$	− 1.67379e47i	− 0.637271i
$749$	3.06638e47	1.14202
$750$	0	0
$751$	2.45331e47	0.874365	0.437182	−	0.899373i	$-0.355976\pi$
$751$	2.45331e47	0.874365	0.437182	+	0.899373i	$0.355976\pi$
$752$	− 2.06312e46i	− 0.0719334i
$753$	8.20830e47i	2.79986i
$754$	−1.33985e46	−0.0447124
$755$	0	0
$756$	3.95018e47	1.26185
$757$	− 3.89117e47i	− 1.21618i	−0.793868	−	0.608090i	$-0.791936\pi$
$757$	− 3.89117e47i	− 1.21618i	0.793868	−	0.608090i	$-0.208064\pi$
$758$	3.83251e47i	1.17204i
$759$	1.55815e48	4.66253
$760$	0	0
$761$	−2.57108e47	−0.736662	−0.368331	−	0.929695i	$-0.620071\pi$
$761$	−2.57108e47	−0.736662	−0.368331	+	0.929695i	$0.620071\pi$
$762$	4.54712e46i	0.127491i
$763$	− 3.72822e47i	− 1.02293i
$764$	−6.71402e46	−0.180278
$765$	0	0
$766$	5.51044e47	1.41714
$767$	1.24039e46i	0.0312201i
$768$	− 7.33419e47i	− 1.80672i
$769$	−1.74753e47	−0.421348	−0.210674	−	0.977556i	$-0.567566\pi$
$769$	−1.74753e47	−0.421348	−0.210674	+	0.977556i	$0.567566\pi$
$770$	0	0
$771$	−1.13570e48	−2.62341
$772$	1.34019e47i	0.303027i
$773$	1.07838e47i	0.238676i	0.992854	+	0.119338i	$0.0380772\pi$
$773$	1.07838e47i	0.238676i	−0.992854	+	0.119338i	$0.961923\pi$
$774$	9.11717e47	1.97531
$775$	0	0
$776$	3.07237e47	0.637903
$777$	2.64747e47i	0.538127i
$778$	1.74388e47i	0.347019i
$779$	1.17093e47	0.228119
$780$	0	0
$781$	8.05672e47	1.50458
$782$	7.32269e47i	1.33893i
$783$	− 8.75990e46i	− 0.156830i
$784$	1.26738e47	0.222174
$785$	0	0
$786$	−2.48025e47	−0.416892
$787$	2.21953e47i	0.365324i	0.983176	+	0.182662i	$0.0584714\pi$
$787$	2.21953e47i	0.365324i	−0.983176	+	0.182662i	$0.941529\pi$
$788$	4.03191e47i	0.649873i
$789$	−9.28223e47	−1.46515
$790$	0	0
$791$	9.73733e47	1.47410
$792$	− 2.69588e48i	− 3.99701i
$793$	− 4.09329e47i	− 0.594382i
$794$	−3.19358e47	−0.454192
$795$	0	0
$796$	−4.90696e47	−0.669494
$797$	− 9.77934e47i	− 1.30691i	−0.756963	−	0.653457i	$-0.773318\pi$
$797$	− 9.77934e47i	− 1.30691i	0.756963	−	0.653457i	$-0.226682\pi$
$798$	− 6.41185e47i	− 0.839335i
$799$	−1.32050e47	−0.169324
$800$	0	0
$801$	−3.15111e48	−3.87728
$802$	− 4.60248e46i	− 0.0554772i
$803$	1.66232e48i	1.96295i
$804$	−1.56773e47	−0.181362
$805$	0	0
$806$	2.46330e47	0.273520
$807$	4.09129e47i	0.445089i
$808$	− 7.80573e47i	− 0.832005i
$809$	6.43989e47	0.672555	0.336278	−	0.941763i	$-0.390832\pi$
$809$	6.43989e47	0.672555	0.336278	+	0.941763i	$0.390832\pi$
$810$	0	0
$811$	−3.92035e47	−0.393080	−0.196540	−	0.980496i	$-0.562971\pi$
$811$	−3.92035e47	−0.393080	−0.196540	+	0.980496i	$0.562971\pi$
$812$	2.99875e46i	0.0294623i
$813$	− 1.08617e48i	− 1.04570i
$814$	3.00224e47	0.283232
$815$	0	0
$816$	9.46847e47	0.857813
$817$	5.70425e47i	0.506447i
$818$	− 8.35166e47i	− 0.726680i
$819$	−3.28763e48	−2.80349
$820$	0	0
$821$	−3.66301e47	−0.300038	−0.150019	−	0.988683i	$-0.547934\pi$
$821$	−3.66301e47	−0.300038	−0.150019	+	0.988683i	$0.547934\pi$
$822$	− 2.75979e48i	− 2.21560i
$823$	6.74278e47i	0.530569i	0.964170	+	0.265284i	$0.0854658\pi$
$823$	6.74278e47i	0.530569i	−0.964170	+	0.265284i	$0.914534\pi$
$824$	2.04364e48	1.57618
$825$	0	0
$826$	−4.20708e46	−0.0311753
$827$	1.83329e48i	1.33165i	0.746106	+	0.665827i	$0.231921\pi$
$827$	1.83329e48i	1.33165i	−0.746106	+	0.665827i	$0.768079\pi$
$828$	− 2.21388e48i	− 1.57635i
$829$	−1.99989e48	−1.39591	−0.697954	−	0.716142i	$-0.745906\pi$
$829$	−1.99989e48	−1.39591	−0.697954	+	0.716142i	$0.745906\pi$
$830$	0	0
$831$	2.91890e48	1.95795
$832$	1.47460e48i	0.969702i
$833$	− 8.11190e47i	− 0.522974i
$834$	−1.39539e48	−0.881971
$835$	0	0
$836$	4.79799e47	0.291512
$837$	1.61050e48i	0.959382i
$838$	− 5.08735e47i	− 0.297143i
$839$	7.68878e47	0.440337	0.220168	−	0.975462i	$-0.429339\pi$
$839$	7.68878e47	0.440337	0.220168	+	0.975462i	$0.429339\pi$
$840$	0	0
$841$	−1.80943e48	−0.996338
$842$	1.67053e48i	0.901998i
$843$	6.76030e48i	3.57941i
$844$	−1.01704e48	−0.528065
$845$	0	0
$846$	−6.05007e47	−0.302099
$847$	3.37174e48i	1.65112i
$848$	2.80712e47i	0.134812i
$849$	5.80585e48	2.73457
$850$	0	0
$851$	8.66719e47	0.392682
$852$	− 1.62078e48i	− 0.720231i
$853$	1.63399e47i	0.0712180i	0.999366	+	0.0356090i	$0.0113371\pi$
$853$	1.63399e47i	0.0712180i	−0.999366	+	0.0356090i	$0.988663\pi$
$854$	1.38834e48	0.593528
$855$	0	0
$856$	−2.45915e48	−1.01151
$857$	5.35960e47i	0.216247i	0.994137	+	0.108123i	$0.0344841\pi$
$857$	5.35960e47i	0.216247i	−0.994137	+	0.108123i	$0.965516\pi$
$858$	5.27863e48i	2.08920i
$859$	3.45793e48	1.34255	0.671273	−	0.741210i	$-0.265748\pi$
$859$	3.45793e48	1.34255	0.671273	+	0.741210i	$0.265748\pi$
$860$	0	0
$861$	2.88321e48	1.07727
$862$	2.16884e48i	0.794982i
$863$	1.95932e48i	0.704574i	0.935892	+	0.352287i	$0.114596\pi$
$863$	1.95932e48i	0.704574i	−0.935892	+	0.352287i	$0.885404\pi$
$864$	−5.43473e48	−1.91735
$865$	0	0
$866$	2.61773e48	0.888955
$867$	− 5.22368e47i	− 0.174045i
$868$	− 5.51319e47i	− 0.180230i
$869$	−3.68580e48	−1.18224
$870$	0	0
$871$	7.62161e47	0.235368
$872$	2.98994e48i	0.906024i
$873$	− 4.75559e48i	− 1.41407i
$874$	−2.09908e48	−0.612479
$875$	0	0
$876$	3.34413e48	0.939647
$877$	− 1.31812e48i	− 0.363464i	−0.983348	−	0.181732i	$-0.941830\pi$
$877$	− 1.31812e48i	− 0.363464i	0.983348	−	0.181732i	$-0.0581703\pi$
$878$	− 2.60696e47i	− 0.0705464i
$879$	−4.07223e48	−1.08147
$880$	0	0
$881$	6.02351e48	1.54080	0.770401	−	0.637559i	$-0.220056\pi$
$881$	6.02351e48	1.54080	0.770401	+	0.637559i	$0.220056\pi$
$882$	− 3.71658e48i	− 0.933065i
$883$	− 5.51914e48i	− 1.35994i	−0.733240	−	0.679970i	$-0.761993\pi$
$883$	− 5.51914e48i	− 1.35994i	0.733240	−	0.679970i	$-0.238007\pi$
$884$	1.63698e48	0.395896
$885$	0	0
$886$	2.04773e48	0.477107
$887$	− 2.46908e48i	− 0.564672i	−0.959316	−	0.282336i	$-0.908891\pi$
$887$	− 2.46908e48i	− 0.564672i	0.959316	−	0.282336i	$-0.0911093\pi$
$888$	− 2.12320e48i	− 0.476626i
$889$	−4.94765e47	−0.109023
$890$	0	0
$891$	−1.71580e49	−3.64322
$892$	− 3.61921e47i	− 0.0754385i
$893$	− 3.78528e47i	− 0.0774550i
$894$	4.79710e48	0.963628
$895$	0	0
$896$	−3.21597e47	−0.0622631
$897$	1.52389e49i	2.89653i
$898$	− 2.19840e48i	− 0.410248i
$899$	−1.22260e47	−0.0224001
$900$	0	0
$901$	1.79670e48	0.317334
$902$	− 3.26957e48i	− 0.566999i
$903$	1.40458e49i	2.39165i
$904$	−7.80909e48	−1.30563
$905$	0	0
$906$	−1.27795e48	−0.206015
$907$	− 1.76568e48i	− 0.279507i	−0.990186	−	0.139753i	$-0.955369\pi$
$907$	− 1.76568e48i	− 0.279507i	0.990186	−	0.139753i	$-0.0446310\pi$
$908$	− 2.60621e48i	− 0.405129i
$909$	−1.20822e49	−1.84434
$910$	0	0
$911$	−4.90626e48	−0.722266	−0.361133	−	0.932514i	$-0.617610\pi$
$911$	−4.90626e48	−0.722266	−0.361133	+	0.932514i	$0.617610\pi$
$912$	2.71418e48i	0.392396i
$913$	− 8.07079e48i	− 1.14590i
$914$	6.26043e47	0.0872955
$915$	0	0
$916$	−9.37128e47	−0.126044
$917$	− 2.69872e48i	− 0.356503i
$918$	− 1.62190e49i	− 2.10437i
$919$	7.03091e48	0.895994	0.447997	−	0.894035i	$-0.352137\pi$
$919$	7.03091e48	0.895994	0.447997	+	0.894035i	$0.352137\pi$
$920$	0	0
$921$	−2.34564e49	−2.88388
$922$	− 5.24400e48i	− 0.633290i
$923$	7.87955e48i	0.934702i
$924$	1.18143e49	1.37664
$925$	0	0
$926$	1.11461e49	1.25326
$927$	− 3.16327e49i	− 3.49398i
$928$	− 4.12574e47i	− 0.0447672i
$929$	−3.42900e48	−0.365517	−0.182759	−	0.983158i	$-0.558503\pi$
$929$	−3.42900e48	−0.365517	−0.182759	+	0.983158i	$0.558503\pi$
$930$	0	0
$931$	2.32532e48	0.239228
$932$	− 2.56329e48i	− 0.259081i
$933$	1.50282e49i	1.49231i
$934$	6.58752e48	0.642686
$935$	0	0
$936$	2.63660e49	2.48309
$937$	2.88611e48i	0.267060i	0.991045	+	0.133530i	$0.0426313\pi$
$937$	2.88611e48i	0.267060i	−0.991045	+	0.133530i	$0.957369\pi$
$938$	2.58506e48i	0.235030i
$939$	3.51019e49	3.13580
$940$	0	0
$941$	−1.90690e49	−1.64475	−0.822373	−	0.568949i	$-0.807350\pi$
$941$	−1.90690e49	−1.64475	−0.822373	+	0.568949i	$0.807350\pi$
$942$	− 1.47190e49i	− 1.24750i
$943$	− 9.43893e48i	− 0.786104i
$944$	1.78089e47	0.0145747
$945$	0	0
$946$	1.59279e49	1.25880
$947$	− 7.16410e48i	− 0.556400i	−0.960523	−	0.278200i	$-0.910262\pi$
$947$	− 7.16410e48i	− 0.556400i	0.960523	−	0.278200i	$-0.0897378\pi$
$948$	7.41479e48i	0.565928i
$949$	−1.62577e49	−1.21946
$950$	0	0
$951$	1.92647e49	1.39568
$952$	1.95185e49i	1.38975i
$953$	3.01662e48i	0.211100i	0.994414	+	0.105550i	$0.0336603\pi$
$953$	3.01662e48i	0.211100i	−0.994414	+	0.105550i	$0.966340\pi$
$954$	8.23183e48	0.566172
$955$	0	0
$956$	3.21563e48	0.213654
$957$	− 2.61992e48i	− 0.171097i
$958$	2.64548e48i	0.169814i
$959$	3.00288e49	1.89466
$960$	0	0
$961$	−1.41557e49	−0.862971
$962$	2.93622e48i	0.175954i
$963$	3.80642e49i	2.24225i
$964$	−1.67503e48	−0.0969952
$965$	0	0
$966$	−5.16865e49	−2.89237
$967$	9.56534e48i	0.526216i	0.964766	+	0.263108i	$0.0847475\pi$
$967$	9.56534e48i	0.526216i	−0.964766	+	0.263108i	$0.915252\pi$
$968$	− 2.70405e49i	− 1.46242i
$969$	1.73722e49	0.923658
$970$	0	0
$971$	3.02376e49	1.55392	0.776961	−	0.629548i	$-0.216760\pi$
$971$	3.02376e49	1.55392	0.776961	+	0.629548i	$0.216760\pi$
$972$	1.41248e49i	0.713655i
$973$	− 1.51829e49i	− 0.754213i
$974$	−1.77175e49	−0.865327
$975$	0	0
$976$	−5.87695e48	−0.277479
$977$	− 5.10941e48i	− 0.237198i	−0.992942	−	0.118599i	$-0.962160\pi$
$977$	− 5.10941e48i	− 0.237198i	0.992942	−	0.118599i	$-0.0378403\pi$
$978$	− 5.59230e49i	− 2.55270i
$979$	−5.50508e49	−2.47086
$980$	0	0
$981$	4.62800e49	2.00842
$982$	− 8.71368e48i	− 0.371845i
$983$	− 1.15145e49i	− 0.483183i	−0.970378	−	0.241591i	$-0.922331\pi$
$983$	− 1.15145e49i	− 0.483183i	0.970378	−	0.241591i	$-0.0776694\pi$
$984$	−2.31226e49	−0.954151
$985$	0	0
$986$	1.23126e48	0.0491337
$987$	− 9.32064e48i	− 0.365774i
$988$	4.69248e48i	0.181098i
$989$	4.59824e49	1.74523
$990$	0	0
$991$	6.06784e48	0.222751	0.111375	−	0.993778i	$-0.464474\pi$
$991$	6.06784e48	0.222751	0.111375	+	0.993778i	$0.464474\pi$
$992$	7.58515e48i	0.273856i
$993$	− 3.24815e49i	− 1.15338i
$994$	−2.67254e49	−0.933361
$995$	0	0
$996$	−1.62361e49	−0.548534
$997$	− 3.14175e49i	− 1.04400i	−0.852945	−	0.522000i	$-0.825186\pi$
$997$	− 3.14175e49i	− 1.04400i	0.852945	−	0.522000i	$-0.174814\pi$
$998$	2.93388e49i	0.958932i
$999$	−1.91970e49	−0.617166

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.b.b.24.3		10
5.2	odd	4		5.34.a.a.1.4	✓	5
5.3	odd	4		25.34.a.b.1.2		5
5.4	even	2	inner	25.34.b.b.24.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.a.a.1.4	✓	5	5.2	odd	4
25.34.a.b.1.2		5	5.3	odd	4
25.34.b.b.24.3		10	1.1	even	1	trivial
25.34.b.b.24.8		10	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)

\(f(q)\)	\(=\)	\(q-71937.8i q^{2} +1.37573e8i q^{3} +3.41489e9 q^{4} +9.89671e12 q^{6} +1.07684e14i q^{7} -8.63600e14i q^{8} -1.33673e16 q^{9} +O(q^{10})\)	\(q-71937.8i q^{2} +1.37573e8i q^{3} +3.41489e9 q^{4} +9.89671e12 q^{6} +1.07684e14i q^{7} -8.63600e14i q^{8} -1.33673e16 q^{9} -2.33530e17 q^{11} +4.69797e17i q^{12} -2.28395e18i q^{13} +7.74658e18 q^{14} -3.27918e19 q^{16} +2.09885e20i q^{17} +9.61615e20i q^{18} -6.01644e20 q^{19} -1.48145e22 q^{21} +1.67997e22i q^{22} +4.84991e22i q^{23} +1.18808e23 q^{24} -1.64302e23 q^{26} -1.07421e24i q^{27} +3.67730e23i q^{28} +8.15476e22 q^{29} -1.49925e24 q^{31} -5.05930e24i q^{32} -3.21275e25i q^{33} +1.50986e25 q^{34} -4.56479e25 q^{36} -1.78708e25i q^{37} +4.32809e25i q^{38} +3.14210e26 q^{39} -1.94621e26 q^{41} +1.06572e27i q^{42} -9.48110e26i q^{43} -7.97481e26 q^{44} +3.48891e27 q^{46} +6.29157e26i q^{47} -4.51128e27i q^{48} -3.86494e27 q^{49} -2.88745e28 q^{51} -7.79943e27i q^{52} -8.56042e27i q^{53} -7.72760e28 q^{54} +9.29963e28 q^{56} -8.27701e28i q^{57} -5.86635e27i q^{58} -5.43089e27 q^{59} +1.79220e29 q^{61} +1.07853e29i q^{62} -1.43945e30i q^{63} -6.45635e29 q^{64} -2.31118e30 q^{66} +3.33703e29i q^{67} +7.16732e29i q^{68} -6.67217e30 q^{69} -3.44997e30 q^{71} +1.15440e31i q^{72} -7.11823e30i q^{73} -1.28559e30 q^{74} -2.05455e30 q^{76} -2.51476e31i q^{77} -2.26036e31i q^{78} +1.57830e31 q^{79} +7.34723e31 q^{81} +1.40006e31i q^{82} +3.45599e31i q^{83} -5.05898e31 q^{84} -6.82049e31 q^{86} +1.12188e31i q^{87} +2.01677e32i q^{88} +2.35733e32 q^{89} +2.45946e32 q^{91} +1.65619e32i q^{92} -2.06256e32i q^{93} +4.52602e31 q^{94} +6.96024e32 q^{96} +3.55763e32i q^{97} +2.78035e32i q^{98} +3.12168e33 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2282622720 q^{4} + 25850126231520 q^{6} - 29\!\cdots\!30 q^{9}+O(q^{10}) \) 10 * q - 2282622720 * q^4 + 25850126231520 * q^6 - 29082501980817930 * q^9	\( 10 q - 2282622720 q^{4} + 25850126231520 q^{6} - 29\!\cdots\!30 q^{9}+ \cdots + 35\!\cdots\!40 q^{99}+O(q^{100}) \) 10 * q - 2282622720 * q^4 + 25850126231520 * q^6 - 29082501980817930 * q^9 - 575603603755953280 * q^11 - 23352899832544964640 * q^14 - 178360179086491914240 * q^16 - 1836729424390307895000 * q^19 - 21070231543425610826280 * q^21 + 143906401505515790361600 * q^24 - 849804721525442929523680 * q^26 + 1853754449987178542332100 * q^29 - 2672092958823642744403880 * q^31 + 137261316985027076739134560 * q^34 - 360748400001957176977117440 * q^36 + 1571583303018981507764931240 * q^39 - 2651240061509051866658512580 * q^41 + 3711878773305232716307804160 * q^44 - 5749299441668848515671371680 * q^46 - 8286468607000063583445894370 * q^49 + 14693438437830537506177750520 * q^51 - 128269435172297554561502376000 * q^54 + 289761018489691889589260313600 * q^56 - 514352424980859556364217812600 * q^59 + 1485779386335344406993238892820 * q^61 + 2078735103694502811148443975680 * q^64 - 6655035034062564292395293122560 * q^66 + 5534834351560350274144858514040 * q^69 - 11004170679364663489635588709880 * q^71 + 7277243818356708673732037512160 * q^74 + 14372679965174635117412392371200 * q^76 + 20516394009185475518243852596400 * q^79 + 157167609672604082013165294629010 * q^81 - 348890661199919432748081747133440 * q^84 + 130972229415655948195807080929120 * q^86 + 121707000777727369262632666890300 * q^89 - 537874169607477694864406415470680 * q^91 + 726874111076263788097451816894560 * q^94 - 689037206345673291941779788103680 * q^96 + 3581331178646963842559626355879040 * q^99

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