LMFDB - Embedded newform 25.28.b.a.24.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,28,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, 28, names="a")

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

chi := DirichletCharacter("25.24");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 28 $
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:	$115.463893710$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{18209})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9105x^{2} + 20720704 $ x^4 + 9105*x^2 + 20720704
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{6}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 1)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.4
Root			$-66.9704i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.28.b.a.24.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+18713.6i q^{2} -3.44127e6i q^{3} -2.15981e8 q^{4} +6.43986e10 q^{6} +1.96873e11i q^{7} -1.53009e12i q^{8} -4.21675e12 q^{9} +O(q^{10})$	\(q+18713.6i q^{2} -3.44127e6i q^{3} -2.15981e8 q^{4} +6.43986e10 q^{6} +1.96873e11i q^{7} -1.53009e12i q^{8} -4.21675e12 q^{9} +2.06714e14 q^{11} +7.43249e14i q^{12} -1.66656e14i q^{13} -3.68421e15 q^{14} -3.55072e14 q^{16} +5.47219e15i q^{17} -7.89105e16i q^{18} -1.61471e17 q^{19} +6.77495e17 q^{21} +3.86837e18i q^{22} +2.80341e18i q^{23} -5.26544e18 q^{24} +3.11874e18 q^{26} -1.17308e19i q^{27} -4.25209e19i q^{28} +2.99842e18 q^{29} +9.09190e19 q^{31} -2.12009e20i q^{32} -7.11360e20i q^{33} -1.02404e20 q^{34} +9.10738e20 q^{36} -1.50001e21i q^{37} -3.02171e21i q^{38} -5.73510e20 q^{39} +5.47146e21 q^{41} +1.26784e22i q^{42} -6.81035e21i q^{43} -4.46463e22 q^{44} -5.24619e22 q^{46} +9.41657e21i q^{47} +1.22190e21i q^{48} +2.69532e22 q^{49} +1.88313e22 q^{51} +3.59946e22i q^{52} -5.35936e22i q^{53} +2.19525e23 q^{54} +3.01233e23 q^{56} +5.55667e23i q^{57} +5.61113e22i q^{58} -9.16258e23 q^{59} +1.47362e24 q^{61} +1.70142e24i q^{62} -8.30166e23i q^{63} +3.91980e24 q^{64} +1.33121e25 q^{66} +3.21915e24i q^{67} -1.18189e24i q^{68} +9.64729e24 q^{69} +3.38255e24 q^{71} +6.45199e24i q^{72} +1.32172e25i q^{73} +2.80705e25 q^{74} +3.48748e25 q^{76} +4.06965e25i q^{77} -1.07324e25i q^{78} -4.66230e25 q^{79} -7.25240e25 q^{81} +1.02391e26i q^{82} +7.14690e25i q^{83} -1.46326e26 q^{84} +1.27446e26 q^{86} -1.03184e25i q^{87} -3.16290e26i q^{88} +1.40708e26 q^{89} +3.28102e25 q^{91} -6.05484e26i q^{92} -3.12877e26i q^{93} -1.76218e26 q^{94} -7.29582e26 q^{96} -3.77568e26i q^{97} +5.04391e26i q^{98} -8.71662e26 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 381246592 q^{4} + 173765746368 q^{6} - 2470273108308 q^{9}+O(q^{10}) $ 4 * q - 381246592 * q^4 + 173765746368 * q^6 - 2470273108308 * q^9	$ 4 q - 381246592 q^{4} + 173765746368 q^{6} - 2470273108308 q^{9} + 276334675383888 q^{11} - 78\!\cdots\!24 q^{14}+ \cdots - 21\!\cdots\!76 q^{99}+O(q^{100}) $ 4 * q - 381246592 * q^4 + 173765746368 * q^6 - 2470273108308 * q^9 + 276334675383888 * q^11 - 7816680105623424 * q^14 - 28645991570333696 * q^16 - 809131620745369520 * q^19 + 1447574627166369408 * q^21 - 3354991067585064960 * q^24 - 6006918508293280032 * q^26 + 31093359990897116520 * q^29 + 57089109188934770048 * q^31 + 301876670371869719136 * q^34 + 1972689241976748422784 * q^36 + 1381980443602051054944 * q^39 + 18162687396093024509928 * q^41 - 92769082075148610599424 * q^44 - 102301447140627940559232 * q^46 + 184408226435681815380828 * q^49 - 66989949409454428929312 * q^51 + 916041559571236054270080 * q^54 + 530935521929718521978880 * q^56 - 4019241955248052977263760 * q^59 + 295714853384897880740888 * q^61 + 2468115607876274891522048 * q^64 + 23541736306288536506877696 * q^66 + 18752960979411737057391744 * q^69 - 26350397640738677196572832 * q^71 + 48468290290897051075575456 * q^74 + 57420865435885573745231360 * q^76 - 125628702071441439836358080 * q^79 - 198094311653195416476206556 * q^81 - 290304367266846887179997184 * q^84 + 504379767802394865424431168 * q^86 + 626946877522211079526988760 * q^89 + 40410730250081757073388608 * q^91 - 524930869501440083787158784 * q^94 - 1124149802196805832769011712 * q^96 - 2152083558561684671220959376 * 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 $

$2$	18713.6i	1.61530i	0.589664	+	0.807648i	$0.299260\pi$
$2$	18713.6i	1.61530i	−0.589664	+	0.807648i	$0.700740\pi$
$3$	− 3.44127e6i	− 1.24618i	−0.782149	−	0.623092i	$-0.785876\pi$
$3$	− 3.44127e6i	− 1.24618i	0.782149	−	0.623092i	$-0.214124\pi$
$4$	−2.15981e8	−1.60918
$5$	0	0
$5$	0	0
$6$	6.43986e10	2.01296
$7$	1.96873e11i	0.768004i	0.923332	+	0.384002i	$0.125454\pi$
$7$	1.96873e11i	0.768004i	−0.923332	+	0.384002i	$0.874546\pi$
$8$	− 1.53009e12i	− 0.984013i
$9$	−4.21675e12	−0.552973
$10$	0	0
$11$	2.06714e14	1.80538	0.902691	−	0.430290i	$-0.141589\pi$
$11$	2.06714e14	1.80538	0.902691	+	0.430290i	$0.141589\pi$
$12$	7.43249e14i	2.00534i
$13$	− 1.66656e14i	− 0.152611i	−0.997084	−	0.0763057i	$-0.975688\pi$
$13$	− 1.66656e14i	− 0.152611i	0.997084	−	0.0763057i	$-0.0243125\pi$
$14$	−3.68421e15	−1.24055
$15$	0	0
$16$	−3.55072e14	−0.0197105
$17$	5.47219e15i	0.133999i	0.997753	+	0.0669994i	$0.0213425\pi$
$17$	5.47219e15i	0.133999i	−0.997753	+	0.0669994i	$0.978657\pi$
$18$	− 7.89105e16i	− 0.893215i
$19$	−1.61471e17	−0.880891	−0.440445	−	0.897779i	$-0.645179\pi$
$19$	−1.61471e17	−0.880891	−0.440445	+	0.897779i	$0.645179\pi$
$20$	0	0
$21$	6.77495e17	0.957074
$22$	3.86837e18i	2.91623i
$23$	2.80341e18i	1.15974i	0.814709	+	0.579870i	$0.196897\pi$
$23$	2.80341e18i	1.15974i	−0.814709	+	0.579870i	$0.803103\pi$
$24$	−5.26544e18	−1.22626
$25$	0	0
$26$	3.11874e18	0.246513
$27$	− 1.17308e19i	− 0.557078i
$28$	− 4.25209e19i	− 1.23586i
$29$	2.99842e18	0.0542650	0.0271325	−	0.999632i	$-0.491362\pi$
$29$	2.99842e18	0.0542650	0.0271325	+	0.999632i	$0.491362\pi$
$30$	0	0
$31$	9.09190e19	0.668763	0.334381	−	0.942438i	$-0.391473\pi$
$31$	9.09190e19	0.668763	0.334381	+	0.942438i	$0.391473\pi$
$32$	− 2.12009e20i	− 1.01585i
$33$	− 7.11360e20i	− 2.24984i
$34$	−1.02404e20	−0.216448
$35$	0	0
$36$	9.10738e20	0.889835
$37$	− 1.50001e21i	− 1.01244i	−0.862404	−	0.506220i	$-0.831042\pi$
$37$	− 1.50001e21i	− 1.01244i	0.862404	−	0.506220i	$-0.168958\pi$
$38$	− 3.02171e21i	− 1.42290i
$39$	−5.73510e20	−0.190182
$40$	0	0
$41$	5.47146e21	0.923679	0.461840	−	0.886963i	$-0.347190\pi$
$41$	5.47146e21	0.923679	0.461840	+	0.886963i	$0.347190\pi$
$42$	1.26784e22i	1.54596i
$43$	− 6.81035e21i	− 0.604429i	−0.953240	−	0.302215i	$-0.902274\pi$
$43$	− 6.81035e21i	− 0.604429i	0.953240	−	0.302215i	$-0.0977259\pi$
$44$	−4.46463e22	−2.90519
$45$	0	0
$46$	−5.24619e22	−1.87333
$47$	9.41657e21i	0.251520i	0.992061	+	0.125760i	$0.0401369\pi$
$47$	9.41657e21i	0.251520i	−0.992061	+	0.125760i	$0.959863\pi$
$48$	1.22190e21i	0.0245628i
$49$	2.69532e22	0.410169
$50$	0	0
$51$	1.88313e22	0.166987
$52$	3.59946e22i	0.245580i
$53$	− 5.35936e22i	− 0.282741i	−0.989957	−	0.141370i	$-0.954849\pi$
$53$	− 5.35936e22i	− 0.282741i	0.989957	−	0.141370i	$-0.0451509\pi$
$54$	2.19525e23	0.899846
$55$	0	0
$56$	3.01233e23	0.755726
$57$	5.55667e23i	1.09775i
$58$	5.61113e22i	0.0876541i
$59$	−9.16258e23	−1.13636	−0.568180	−	0.822904i	$-0.692352\pi$
$59$	−9.16258e23	−1.13636	−0.568180	+	0.822904i	$0.692352\pi$
$60$	0	0
$61$	1.47362e24	1.16529	0.582643	−	0.812728i	$-0.302019\pi$
$61$	1.47362e24	1.16529	0.582643	+	0.812728i	$0.302019\pi$
$62$	1.70142e24i	1.08025i
$63$	− 8.30166e23i	− 0.424685i
$64$	3.91980e24	1.62119
$65$	0	0
$66$	1.33121e25	3.63415
$67$	3.21915e24i	0.717349i	0.933463	+	0.358675i	$0.116771\pi$
$67$	3.21915e24i	0.717349i	−0.933463	+	0.358675i	$0.883229\pi$
$68$	− 1.18189e24i	− 0.215629i
$69$	9.64729e24	1.44525
$70$	0	0
$71$	3.38255e24	0.344554	0.172277	−	0.985049i	$-0.444888\pi$
$71$	3.38255e24	0.344554	0.172277	+	0.985049i	$0.444888\pi$
$72$	6.45199e24i	0.544133i
$73$	1.32172e25i	0.925295i	0.886542	+	0.462648i	$0.153100\pi$
$73$	1.32172e25i	0.925295i	−0.886542	+	0.462648i	$0.846900\pi$
$74$	2.80705e25	1.63539
$75$	0	0
$76$	3.48748e25	1.41752
$77$	4.06965e25i	1.38654i
$78$	− 1.07324e25i	− 0.307200i
$79$	−4.66230e25	−1.12366	−0.561830	−	0.827253i	$-0.689902\pi$
$79$	−4.66230e25	−1.12366	−0.561830	+	0.827253i	$0.689902\pi$
$80$	0	0
$81$	−7.25240e25	−1.24719
$82$	1.02391e26i	1.49202i
$83$	7.14690e25i	0.884226i	0.896959	+	0.442113i	$0.145771\pi$
$83$	7.14690e25i	0.884226i	−0.896959	+	0.442113i	$0.854229\pi$
$84$	−1.46326e26	−1.54011
$85$	0	0
$86$	1.27446e26	0.976332
$87$	− 1.03184e25i	− 0.0676242i
$88$	− 3.16290e26i	− 1.77652i
$89$	1.40708e26	0.678504	0.339252	−	0.940696i	$-0.389826\pi$
$89$	1.40708e26	0.678504	0.339252	+	0.940696i	$0.389826\pi$
$90$	0	0
$91$	3.28102e25	0.117206
$92$	− 6.05484e26i	− 1.86624i
$93$	− 3.12877e26i	− 0.833401i
$94$	−1.76218e26	−0.406279
$95$	0	0
$96$	−7.29582e26	−1.26594
$97$	− 3.77568e26i	− 0.569609i	−0.958586	−	0.284805i	$-0.908071\pi$
$97$	− 3.77568e26i	− 0.569609i	0.958586	−	0.284805i	$-0.0919287\pi$
$98$	5.04391e26i	0.662545i
$99$	−8.71662e26	−0.998327
$100$	0	0
$101$	−1.82546e27	−1.59600	−0.798002	−	0.602654i	$-0.794110\pi$
$101$	−1.82546e27	−1.59600	−0.798002	+	0.602654i	$0.794110\pi$
$102$	3.52401e26i	0.269734i
$103$	2.87048e27i	1.92598i	0.269534	+	0.962991i	$0.413130\pi$
$103$	2.87048e27i	1.92598i	−0.269534	+	0.962991i	$0.586870\pi$
$104$	−2.54999e26	−0.150172
$105$	0	0
$106$	1.00293e27	0.456710
$107$	1.31331e27i	0.526849i	0.964680	+	0.263425i	$0.0848520\pi$
$107$	1.31331e27i	0.526849i	−0.964680	+	0.263425i	$0.915148\pi$
$108$	2.53362e27i	0.896441i
$109$	3.16013e27	0.987296	0.493648	−	0.869662i	$-0.335663\pi$
$109$	3.16013e27	0.987296	0.493648	+	0.869662i	$0.335663\pi$
$110$	0	0
$111$	−5.16192e27	−1.26169
$112$	− 6.99043e25i	− 0.0151377i
$113$	3.68033e27i	0.706851i	0.935463	+	0.353425i	$0.114983\pi$
$113$	3.68033e27i	0.706851i	−0.935463	+	0.353425i	$0.885017\pi$
$114$	−1.03985e28	−1.77319
$115$	0	0
$116$	−6.47603e26	−0.0873224
$117$	7.02748e26i	0.0843899i
$118$	− 1.71465e28i	− 1.83556i
$119$	−1.07733e27	−0.102912
$120$	0	0
$121$	2.96208e28	2.25940
$122$	2.75767e28i	1.88228i
$123$	− 1.88288e28i	− 1.15107i
$124$	−1.96368e28	−1.07616
$125$	0	0
$126$	1.55354e28	0.685993
$127$	2.69227e28i	1.06849i	0.845331	+	0.534243i	$0.179403\pi$
$127$	2.69227e28i	1.06849i	−0.845331	+	0.534243i	$0.820597\pi$
$128$	4.48982e28i	1.60285i
$129$	−2.34363e28	−0.753229
$130$	0	0
$131$	3.17810e28	0.829860	0.414930	−	0.909853i	$-0.363806\pi$
$131$	3.17810e28	0.829860	0.414930	+	0.909853i	$0.363806\pi$
$132$	1.53640e29i	3.62040i
$133$	− 3.17894e28i	− 0.676528i
$134$	−6.02418e28	−1.15873
$135$	0	0
$136$	8.37292e27	0.131857
$137$	− 2.13194e28i	− 0.304122i	−0.988371	−	0.152061i	$-0.951409\pi$
$137$	− 2.13194e28i	− 0.304122i	0.988371	−	0.152061i	$-0.0485910\pi$
$138$	1.80536e29i	2.33451i
$139$	1.15969e29	1.36032	0.680161	−	0.733062i	$-0.261910\pi$
$139$	1.15969e29	1.36032	0.680161	+	0.733062i	$0.261910\pi$
$140$	0	0
$141$	3.24050e28	0.313439
$142$	6.32998e28i	0.556557i
$143$	− 3.44502e28i	− 0.275522i
$144$	1.49725e27	0.0108993
$145$	0	0
$146$	−2.47341e29	−1.49463
$147$	− 9.27533e28i	− 0.511146i
$148$	3.23973e29i	1.62920i
$149$	−2.70481e29	−1.24200	−0.621000	−	0.783810i	$-0.713273\pi$
$149$	−2.70481e29	−1.24200	−0.621000	+	0.783810i	$0.713273\pi$
$150$	0	0
$151$	6.43669e28	0.246873	0.123437	−	0.992352i	$-0.460608\pi$
$151$	6.43669e28	0.246873	0.123437	+	0.992352i	$0.460608\pi$
$152$	2.47065e29i	0.866808i
$153$	− 2.30748e28i	− 0.0740977i
$154$	−7.61579e29	−2.23968
$155$	0	0
$156$	1.23867e29	0.306037
$157$	7.36476e29i	1.66922i	0.550842	+	0.834609i	$0.314307\pi$
$157$	7.36476e29i	1.66922i	−0.550842	+	0.834609i	$0.685693\pi$
$158$	− 8.72484e29i	− 1.81504i
$159$	−1.84430e29	−0.352347
$160$	0	0
$161$	−5.51917e29	−0.890686
$162$	− 1.35718e30i	− 2.01459i
$163$	4.91659e29i	0.671632i	0.941928	+	0.335816i	$0.109012\pi$
$163$	4.91659e29i	0.671632i	−0.941928	+	0.335816i	$0.890988\pi$
$164$	−1.18173e30	−1.48637
$165$	0	0
$166$	−1.33744e30	−1.42829
$167$	− 6.37427e29i	− 0.627709i	−0.949471	−	0.313854i	$-0.898380\pi$
$167$	− 6.37427e29i	− 0.627709i	0.949471	−	0.313854i	$-0.101620\pi$
$168$	− 1.03663e30i	− 0.941774i
$169$	1.16476e30	0.976710
$170$	0	0
$171$	6.80884e29	0.487109
$172$	1.47091e30i	0.972638i
$173$	2.71145e30i	1.65798i	0.559265	+	0.828989i	$0.311083\pi$
$173$	2.71145e30i	1.65798i	−0.559265	+	0.828989i	$0.688917\pi$
$174$	1.93094e29	0.109233
$175$	0	0
$176$	−7.33984e28	−0.0355849
$177$	3.15309e30i	1.41611i
$178$	2.63315e30i	1.09599i
$179$	1.65055e30	0.636961	0.318481	−	0.947929i	$-0.396827\pi$
$179$	1.65055e30	0.636961	0.318481	+	0.947929i	$0.396827\pi$
$180$	0	0
$181$	4.30260e30	1.42913	0.714563	−	0.699571i	$-0.246626\pi$
$181$	4.30260e30	1.42913	0.714563	+	0.699571i	$0.246626\pi$
$182$	6.13997e29i	0.189323i
$183$	− 5.07112e30i	− 1.45216i
$184$	4.28946e30	1.14120
$185$	0	0
$186$	5.85506e30	1.34619
$187$	1.13118e30i	0.241919i
$188$	− 2.03380e30i	− 0.404741i
$189$	2.30948e30	0.427838
$190$	0	0
$191$	5.35850e30	0.861177	0.430589	−	0.902548i	$-0.358306\pi$
$191$	5.35850e30	0.861177	0.430589	+	0.902548i	$0.358306\pi$
$192$	− 1.34891e31i	− 2.02030i
$193$	2.47114e30i	0.345044i	0.985006	+	0.172522i	$0.0551915\pi$
$193$	2.47114e30i	0.345044i	−0.985006	+	0.172522i	$0.944808\pi$
$194$	7.06566e30	0.920088
$195$	0	0
$196$	−5.82138e30	−0.660038
$197$	4.41349e30i	0.467185i	0.972335	+	0.233592i	$0.0750481\pi$
$197$	4.41349e30i	0.467185i	−0.972335	+	0.233592i	$0.924952\pi$
$198$	− 1.63119e31i	− 1.61259i
$199$	1.58034e31	1.45960	0.729802	−	0.683658i	$-0.239612\pi$
$199$	1.58034e31	1.45960	0.729802	+	0.683658i	$0.239612\pi$
$200$	0	0
$201$	1.10780e31	0.893949
$202$	− 3.41610e31i	− 2.57802i
$203$	5.90310e29i	0.0416758i
$204$	−4.06720e30	−0.268713
$205$	0	0
$206$	−5.37170e31	−3.11103
$207$	− 1.18213e31i	− 0.641305i
$208$	5.91750e28i	0.00300804i
$209$	−3.33784e31	−1.59034
$210$	0	0
$211$	−1.50086e31	−0.628820	−0.314410	−	0.949287i	$-0.601807\pi$
$211$	−1.50086e31	−0.628820	−0.314410	+	0.949287i	$0.601807\pi$
$212$	1.15752e31i	0.454982i
$213$	− 1.16403e31i	− 0.429377i
$214$	−2.45768e31	−0.851018
$215$	0	0
$216$	−1.79491e31	−0.548172
$217$	1.78995e31i	0.513613i
$218$	5.91374e31i	1.59478i
$219$	4.54839e31	1.15309
$220$	0	0
$221$	9.11975e29	0.0204497
$222$	− 9.65982e31i	− 2.03800i
$223$	− 1.04534e31i	− 0.207559i	−0.994600	−	0.103779i	$-0.966906\pi$
$223$	− 1.04534e31i	− 0.207559i	0.994600	−	0.103779i	$-0.0330936\pi$
$224$	4.17390e31	0.780178
$225$	0	0
$226$	−6.88722e31	−1.14177
$227$	− 9.45028e31i	− 1.47603i	−0.674783	−	0.738016i	$-0.735763\pi$
$227$	− 9.45028e31i	− 1.47603i	0.674783	−	0.738016i	$-0.264237\pi$
$228$	− 1.20013e32i	− 1.76648i
$229$	6.26689e31	0.869508	0.434754	−	0.900549i	$-0.356835\pi$
$229$	6.26689e31	0.869508	0.434754	+	0.900549i	$0.356835\pi$
$230$	0	0
$231$	1.40048e32	1.72788
$232$	− 4.58785e30i	− 0.0533975i
$233$	7.87335e31i	0.864678i	0.901711	+	0.432339i	$0.142312\pi$
$233$	7.87335e31i	0.864678i	−0.901711	+	0.432339i	$0.857688\pi$
$234$	−1.31509e31	−0.136315
$235$	0	0
$236$	1.97894e32	1.82861
$237$	1.60442e32i	1.40029i
$238$	− 2.01607e31i	− 0.166233i
$239$	5.65108e30	0.0440311	0.0220156	−	0.999758i	$-0.492992\pi$
$239$	5.65108e30	0.0440311	0.0220156	+	0.999758i	$0.492992\pi$
$240$	0	0
$241$	−4.42939e31	−0.308400	−0.154200	−	0.988040i	$-0.549280\pi$
$241$	−4.42939e31	−0.308400	−0.154200	+	0.988040i	$0.549280\pi$
$242$	5.54311e32i	3.64961i
$243$	1.60121e32i	0.997154i
$244$	−3.18274e32	−1.87516
$245$	0	0
$246$	3.52354e32	1.85933
$247$	2.69102e31i	0.134434i
$248$	− 1.39114e32i	− 0.658071i
$249$	2.45944e32	1.10191
$250$	0	0
$251$	−3.28116e32	−1.31957	−0.659785	−	0.751454i	$-0.729353\pi$
$251$	−3.28116e32	−1.31957	−0.659785	+	0.751454i	$0.729353\pi$
$252$	1.79300e32i	0.683397i
$253$	5.79505e32i	2.09377i
$254$	−5.03822e32	−1.72592
$255$	0	0
$256$	−3.14099e32	−0.967894
$257$	− 3.48288e31i	− 0.101822i	−0.998703	−	0.0509109i	$-0.983788\pi$
$257$	− 3.48288e31i	− 0.101822i	0.998703	−	0.0509109i	$-0.0162125\pi$
$258$	− 4.38577e32i	− 1.21669i
$259$	2.95311e32	0.777559
$260$	0	0
$261$	−1.26436e31	−0.0300071
$262$	5.94736e32i	1.34047i
$263$	3.82694e31i	0.0819311i	0.999161	+	0.0409656i	$0.0130434\pi$
$263$	3.82694e31i	0.0819311i	−0.999161	+	0.0409656i	$0.986957\pi$
$264$	−1.08844e33	−2.21387
$265$	0	0
$266$	5.94895e32	1.09279
$267$	− 4.84213e32i	− 0.845541i
$268$	− 6.95274e32i	− 1.15435i
$269$	4.44965e31	0.0702539	0.0351269	−	0.999383i	$-0.488816\pi$
$269$	4.44965e31	0.0702539	0.0351269	+	0.999383i	$0.488816\pi$
$270$	0	0
$271$	3.62870e32	0.518401	0.259200	−	0.965824i	$-0.416541\pi$
$271$	3.62870e32	0.518401	0.259200	+	0.965824i	$0.416541\pi$
$272$	− 1.94302e30i	− 0.00264118i
$273$	− 1.12909e32i	− 0.146060i
$274$	3.98963e32	0.491247
$275$	0	0
$276$	−2.08363e33	−2.32567
$277$	− 1.40758e33i	− 1.49622i	−0.663574	−	0.748111i	$-0.730961\pi$
$277$	− 1.40758e33i	− 1.49622i	0.663574	−	0.748111i	$-0.269039\pi$
$278$	2.17020e33i	2.19733i
$279$	−3.83383e32	−0.369808
$280$	0	0
$281$	3.59534e32	0.314924	0.157462	−	0.987525i	$-0.449669\pi$
$281$	3.59534e32	0.314924	0.157462	+	0.987525i	$0.449669\pi$
$282$	6.06414e32i	0.506298i
$283$	− 3.59177e32i	− 0.285885i	−0.989731	−	0.142943i	$-0.954344\pi$
$283$	− 3.59177e32i	− 0.285885i	0.989731	−	0.142943i	$-0.0456565\pi$
$284$	−7.30568e32	−0.554451
$285$	0	0
$286$	6.44688e32	0.445049
$287$	1.07719e33i	0.709390i
$288$	8.93990e32i	0.561738i
$289$	1.63777e33	0.982044
$290$	0	0
$291$	−1.29931e33	−0.709838
$292$	− 2.85466e33i	− 1.48897i
$293$	3.51312e32i	0.174976i	0.996166	+	0.0874882i	$0.0278840\pi$
$293$	3.51312e32i	0.174976i	−0.996166	+	0.0874882i	$0.972116\pi$
$294$	1.73575e33	0.825653
$295$	0	0
$296$	−2.29514e33	−0.996255
$297$	− 2.42492e33i	− 1.00574i
$298$	− 5.06167e33i	− 2.00620i
$299$	4.67206e32	0.176990
$300$	0	0
$301$	1.34078e33	0.464204
$302$	1.20454e33i	0.398773i
$303$	6.28191e33i	1.98891i
$304$	5.73340e31	0.0173628
$305$	0	0
$306$	4.31813e32	0.119690
$307$	6.75654e32i	0.179208i	0.995977	+	0.0896038i	$0.0285601\pi$
$307$	6.75654e32i	0.179208i	−0.995977	+	0.0896038i	$0.971440\pi$
$308$	− 8.78968e33i	− 2.23120i
$309$	9.87810e33	2.40013
$310$	0	0
$311$	5.16690e33	1.15071	0.575354	−	0.817905i	$-0.304864\pi$
$311$	5.16690e33	1.15071	0.575354	+	0.817905i	$0.304864\pi$
$312$	8.77519e32i	0.187141i
$313$	− 1.10679e33i	− 0.226056i	−0.993592	−	0.113028i	$-0.963945\pi$
$313$	− 1.10679e33i	− 0.226056i	0.993592	−	0.113028i	$-0.0360551\pi$
$314$	−1.37821e34	−2.69628
$315$	0	0
$316$	1.00697e34	1.80817
$317$	9.49991e33i	1.63463i	0.576191	+	0.817315i	$0.304539\pi$
$317$	9.49991e33i	1.63463i	−0.576191	+	0.817315i	$0.695461\pi$
$318$	− 3.45135e33i	− 0.569145i
$319$	6.19817e32	0.0979691
$320$	0	0
$321$	4.51946e33	0.656551
$322$	− 1.03284e34i	− 1.43872i
$323$	− 8.83602e32i	− 0.118038i
$324$	1.56638e34	2.00696
$325$	0	0
$326$	−9.20072e33	−1.08489
$327$	− 1.08749e34i	− 1.23035i
$328$	− 8.37180e33i	− 0.908913i
$329$	−1.85387e33	−0.193168
$330$	0	0
$331$	−1.25351e34	−1.20351	−0.601757	−	0.798679i	$-0.705533\pi$
$331$	−1.25351e34	−1.20351	−0.601757	+	0.798679i	$0.705533\pi$
$332$	− 1.54359e34i	− 1.42288i
$333$	6.32514e33i	0.559852i
$334$	1.19286e34	1.01394
$335$	0	0
$336$	−2.40560e32	−0.0188644
$337$	3.36740e33i	0.253683i	0.991923	+	0.126842i	$0.0404840\pi$
$337$	3.36740e33i	0.253683i	−0.991923	+	0.126842i	$0.959516\pi$
$338$	2.17968e34i	1.57768i
$339$	1.26650e34	0.880865
$340$	0	0
$341$	1.87943e34	1.20737
$342$	1.27418e34i	0.786825i
$343$	1.82434e34i	1.08302i
$344$	−1.04204e34	−0.594766
$345$	0	0
$346$	−5.07409e34	−2.67813
$347$	1.91545e34i	0.972353i	0.873861	+	0.486177i	$0.161609\pi$
$347$	1.91545e34i	0.972353i	−0.873861	+	0.486177i	$0.838391\pi$
$348$	2.22858e33i	0.108820i
$349$	−1.45433e34	−0.683158	−0.341579	−	0.939853i	$-0.610962\pi$
$349$	−1.45433e34	−0.683158	−0.341579	+	0.939853i	$0.610962\pi$
$350$	0	0
$351$	−1.95501e33	−0.0850164
$352$	− 4.38253e34i	− 1.83400i
$353$	− 4.39359e33i	− 0.176954i	−0.996078	−	0.0884772i	$-0.971800\pi$
$353$	− 4.39359e33i	− 0.176954i	0.996078	−	0.0884772i	$-0.0282000\pi$
$354$	−5.90057e34	−2.28744
$355$	0	0
$356$	−3.03902e34	−1.09184
$357$	3.70738e33i	0.128247i
$358$	3.08877e34i	1.02888i
$359$	−2.60550e34	−0.835828	−0.417914	−	0.908487i	$-0.637239\pi$
$359$	−2.60550e34	−0.835828	−0.417914	+	0.908487i	$0.637239\pi$
$360$	0	0
$361$	−7.52760e33	−0.224032
$362$	8.05172e34i	2.30846i
$363$	− 1.01933e35i	− 2.81563i
$364$	−7.08639e33	−0.188606
$365$	0	0
$366$	9.48990e34	2.34567
$367$	− 3.50053e34i	− 0.833953i	−0.908917	−	0.416977i	$-0.863090\pi$
$367$	− 3.50053e34i	− 0.833953i	0.908917	−	0.416977i	$-0.136910\pi$
$368$	− 9.95413e32i	− 0.0228590i
$369$	−2.30718e34	−0.510770
$370$	0	0
$371$	1.05512e34	0.217146
$372$	6.75755e34i	1.34110i
$373$	− 2.06100e34i	− 0.394464i	−0.980357	−	0.197232i	$-0.936805\pi$
$373$	− 2.06100e34i	− 0.394464i	0.980357	−	0.197232i	$-0.0631953\pi$
$374$	−2.11684e34	−0.390771
$375$	0	0
$376$	1.44082e34	0.247499
$377$	− 4.99707e32i	− 0.00828146i
$378$	4.32186e34i	0.691086i
$379$	3.69120e34	0.569559	0.284779	−	0.958593i	$-0.408080\pi$
$379$	3.69120e34	0.569559	0.284779	+	0.958593i	$0.408080\pi$
$380$	0	0
$381$	9.26485e34	1.33153
$382$	1.00277e35i	1.39106i
$383$	6.12833e34i	0.820652i	0.911939	+	0.410326i	$0.134585\pi$
$383$	6.12833e34i	0.820652i	−0.911939	+	0.410326i	$0.865415\pi$
$384$	1.54507e35	1.99745
$385$	0	0
$386$	−4.62439e34	−0.557348
$387$	2.87175e34i	0.334233i
$388$	8.15476e34i	0.916606i
$389$	−5.65060e34	−0.613444	−0.306722	−	0.951799i	$-0.599232\pi$
$389$	−5.65060e34	−0.613444	−0.306722	+	0.951799i	$0.599232\pi$
$390$	0	0
$391$	−1.53408e34	−0.155404
$392$	− 4.12407e34i	− 0.403612i
$393$	− 1.09367e35i	− 1.03416i
$394$	−8.25924e34	−0.754642
$395$	0	0
$396$	1.88262e35	1.60649
$397$	2.20649e35i	1.81983i	0.414794	+	0.909915i	$0.363854\pi$
$397$	2.20649e35i	1.81983i	−0.414794	+	0.909915i	$0.636146\pi$
$398$	2.95739e35i	2.35769i
$399$	−1.09396e35	−0.843078
$400$	0	0
$401$	−1.87612e35	−1.35148	−0.675741	−	0.737139i	$-0.736176\pi$
$401$	−1.87612e35	−1.35148	−0.675741	+	0.737139i	$0.736176\pi$
$402$	2.07308e35i	1.44399i
$403$	− 1.51522e34i	− 0.102061i
$404$	3.94265e35	2.56827
$405$	0	0
$406$	−1.10468e34	−0.0673188
$407$	− 3.10072e35i	− 1.82784i
$408$	− 2.88135e34i	− 0.164317i
$409$	−2.22853e35	−1.22957	−0.614786	−	0.788694i	$-0.710758\pi$
$409$	−2.22853e35	−1.22957	−0.614786	+	0.788694i	$0.710758\pi$
$410$	0	0
$411$	−7.33658e34	−0.378991
$412$	− 6.19970e35i	− 3.09926i
$413$	− 1.80387e35i	− 0.872729i
$414$	2.21219e35	1.03590
$415$	0	0
$416$	−3.53327e34	−0.155030
$417$	− 3.99081e35i	− 1.69521i
$418$	− 6.24631e35i	− 2.56888i
$419$	5.47879e34	0.218170	0.109085	−	0.994032i	$-0.465208\pi$
$419$	5.47879e34	0.218170	0.109085	+	0.994032i	$0.465208\pi$
$420$	0	0
$421$	−1.97758e35	−0.738458	−0.369229	−	0.929338i	$-0.620378\pi$
$421$	−1.97758e35	−0.738458	−0.369229	+	0.929338i	$0.620378\pi$
$422$	− 2.80864e35i	− 1.01573i
$423$	− 3.97073e34i	− 0.139083i
$424$	−8.20028e34	−0.278221
$425$	0	0
$426$	2.17832e35	0.693572
$427$	2.90116e35i	0.894945i
$428$	− 2.83650e35i	− 0.847798i
$429$	−1.18553e35	−0.343350
$430$	0	0
$431$	−4.94928e35	−1.34617	−0.673083	−	0.739567i	$-0.735030\pi$
$431$	−4.94928e35	−1.34617	−0.673083	+	0.739567i	$0.735030\pi$
$432$	4.16527e33i	0.0109803i
$433$	3.12882e35i	0.799454i	0.916634	+	0.399727i	$0.130895\pi$
$433$	3.12882e35i	0.799454i	−0.916634	+	0.399727i	$0.869105\pi$
$434$	−3.34965e35	−0.829637
$435$	0	0
$436$	−6.82528e35	−1.58874
$437$	− 4.52671e35i	− 1.02160i
$438$	8.51168e35i	1.86258i
$439$	−7.22790e35	−1.53370	−0.766852	−	0.641824i	$-0.778178\pi$
$439$	−7.22790e35	−1.53370	−0.766852	+	0.641824i	$0.778178\pi$
$440$	0	0
$441$	−1.13655e35	−0.226813
$442$	1.70663e34i	0.0330324i
$443$	− 7.68142e35i	− 1.44209i	−0.692891	−	0.721043i	$-0.743663\pi$
$443$	− 7.68142e35i	− 1.44209i	0.692891	−	0.721043i	$-0.256337\pi$
$444$	1.11488e36	2.03029
$445$	0	0
$446$	1.95620e35	0.335269
$447$	9.30798e35i	1.54776i
$448$	7.71705e35i	1.24508i
$449$	6.52536e35	1.02160	0.510798	−	0.859701i	$-0.329350\pi$
$449$	6.52536e35	1.02160	0.510798	+	0.859701i	$0.329350\pi$
$450$	0	0
$451$	1.13103e36	1.66759
$452$	− 7.94881e35i	− 1.13745i
$453$	− 2.21504e35i	− 0.307649i
$454$	1.76849e36	2.38423
$455$	0	0
$456$	8.50218e35	1.08020
$457$	− 6.21081e35i	− 0.766090i	−0.923730	−	0.383045i	$-0.874875\pi$
$457$	− 6.21081e35i	− 0.766090i	0.923730	−	0.383045i	$-0.125125\pi$
$458$	1.17276e36i	1.40451i
$459$	6.41930e34	0.0746477
$460$	0	0
$461$	1.02161e36	1.12027	0.560133	−	0.828402i	$-0.310750\pi$
$461$	1.02161e36	1.12027	0.560133	+	0.828402i	$0.310750\pi$
$462$	2.62080e36i	2.79105i
$463$	− 1.10341e36i	− 1.14129i	−0.821199	−	0.570643i	$-0.806694\pi$
$463$	− 1.10341e36i	− 1.14129i	0.821199	−	0.570643i	$-0.193306\pi$
$464$	−1.06466e33	−0.00106959
$465$	0	0
$466$	−1.47339e36	−1.39671
$467$	− 8.66440e35i	− 0.797922i	−0.916968	−	0.398961i	$-0.869371\pi$
$467$	− 8.66440e35i	− 0.797922i	0.916968	−	0.398961i	$-0.130629\pi$
$468$	− 1.51780e35i	− 0.135799i
$469$	−6.33764e35	−0.550927
$470$	0	0
$471$	2.53441e36	2.08015
$472$	1.40195e36i	1.11819i
$473$	− 1.40780e36i	− 1.09123i
$474$	−3.00246e36	−2.26188
$475$	0	0
$476$	2.32683e35	0.165604
$477$	2.25991e35i	0.156348i
$478$	1.05752e35i	0.0711234i
$479$	2.57345e36	1.68262	0.841311	−	0.540552i	$-0.181785\pi$
$479$	2.57345e36	1.68262	0.841311	+	0.540552i	$0.181785\pi$
$480$	0	0
$481$	−2.49985e35	−0.154510
$482$	− 8.28899e35i	− 0.498157i
$483$	1.89930e36i	1.10996i
$484$	−6.39752e36	−3.63580
$485$	0	0
$486$	−2.99643e36	−1.61070
$487$	2.28927e36i	1.19690i	0.801162	+	0.598448i	$0.204216\pi$
$487$	2.28927e36i	1.19690i	−0.801162	+	0.598448i	$0.795784\pi$
$488$	− 2.25476e36i	− 1.14666i
$489$	1.69193e36	0.836977
$490$	0	0
$491$	1.74114e36	0.815142	0.407571	−	0.913174i	$-0.366376\pi$
$491$	1.74114e36	0.815142	0.407571	+	0.913174i	$0.366376\pi$
$492$	4.06666e36i	1.85229i
$493$	1.64079e34i	0.00727145i
$494$	−5.03587e35	−0.217151
$495$	0	0
$496$	−3.22828e34	−0.0131816
$497$	6.65935e35i	0.264619i
$498$	4.60250e36i	1.77991i
$499$	−2.80174e36	−1.05456	−0.527278	−	0.849693i	$-0.676787\pi$
$499$	−2.80174e36	−1.05456	−0.527278	+	0.849693i	$0.676787\pi$
$500$	0	0
$501$	−2.19356e36	−0.782240
$502$	− 6.14024e36i	− 2.13150i
$503$	3.44032e36i	1.16260i	0.813688	+	0.581301i	$0.197456\pi$
$503$	3.44032e36i	1.16260i	−0.813688	+	0.581301i	$0.802544\pi$
$504$	−1.27022e36	−0.417896
$505$	0	0
$506$	−1.08446e37	−3.38207
$507$	− 4.00825e36i	− 1.21716i
$508$	− 5.81480e36i	− 1.71939i
$509$	−1.50719e35	−0.0433989	−0.0216995	−	0.999765i	$-0.506908\pi$
$509$	−1.50719e35	−0.0433989	−0.0216995	+	0.999765i	$0.506908\pi$
$510$	0	0
$511$	−2.60211e36	−0.710631
$512$	1.48198e35i	0.0394183i
$513$	1.89418e36i	0.490725i
$514$	6.51772e35	0.164473
$515$	0	0
$516$	5.06179e36	1.21208
$517$	1.94654e36i	0.454089i
$518$	5.52634e36i	1.25599i
$519$	9.33082e36	2.06614
$520$	0	0
$521$	8.14778e36	1.71289	0.856446	−	0.516236i	$-0.172667\pi$
$521$	8.14778e36	1.71289	0.856446	+	0.516236i	$0.172667\pi$
$522$	− 2.36607e35i	− 0.0484704i
$523$	− 4.14380e36i	− 0.827229i	−0.910452	−	0.413615i	$-0.864266\pi$
$523$	− 4.14380e36i	− 0.827229i	0.910452	−	0.413615i	$-0.135734\pi$
$524$	−6.86409e36	−1.33540
$525$	0	0
$526$	−7.16158e35	−0.132343
$527$	4.97526e35i	0.0896133i
$528$	2.52584e35i	0.0443453i
$529$	−2.01590e36	−0.344999
$530$	0	0
$531$	3.86363e36	0.628376
$532$	6.86591e36i	1.08866i
$533$	− 9.11854e35i	− 0.140964i
$534$	9.06137e36	1.36580
$535$	0	0
$536$	4.92557e36	0.705881
$537$	− 5.67999e36i	− 0.793770i
$538$	8.32690e35i	0.113481i
$539$	5.57161e36	0.740512
$540$	0	0
$541$	1.06017e37	1.34033	0.670163	−	0.742214i	$-0.266224\pi$
$541$	1.06017e37	1.34033	0.670163	+	0.742214i	$0.266224\pi$
$542$	6.79060e36i	0.837371i
$543$	− 1.48064e37i	− 1.78095i
$544$	1.16016e36	0.136123
$545$	0	0
$546$	2.11293e36	0.235931
$547$	− 8.42305e36i	− 0.917573i	−0.888547	−	0.458786i	$-0.848284\pi$
$547$	− 8.42305e36i	− 0.917573i	0.888547	−	0.458786i	$-0.151716\pi$
$548$	4.60459e36i	0.489388i
$549$	−6.21388e36	−0.644371
$550$	0	0
$551$	−4.84160e35	−0.0478016
$552$	− 1.47612e37i	− 1.42214i
$553$	− 9.17883e36i	− 0.862975i
$554$	2.63409e37	2.41684
$555$	0	0
$556$	−2.50471e37	−2.18901
$557$	5.59363e36i	0.477143i	0.971125	+	0.238571i	$0.0766791\pi$
$557$	5.59363e36i	0.477143i	−0.971125	+	0.238571i	$0.923321\pi$
$558$	− 7.17447e36i	− 0.597349i
$559$	−1.13499e36	−0.0922427
$560$	0	0
$561$	3.89269e36	0.301475
$562$	6.72818e36i	0.508695i
$563$	2.06136e37i	1.52157i	0.649006	+	0.760783i	$0.275185\pi$
$563$	2.06136e37i	1.52157i	−0.649006	+	0.760783i	$0.724815\pi$
$564$	−6.99886e36	−0.504382
$565$	0	0
$566$	6.72150e36	0.461790
$567$	− 1.42780e37i	− 0.957850i
$568$	− 5.17560e36i	− 0.339046i
$569$	−4.96854e36	−0.317844	−0.158922	−	0.987291i	$-0.550802\pi$
$569$	−4.96854e36	−0.317844	−0.158922	+	0.987291i	$0.550802\pi$
$570$	0	0
$571$	1.02940e36	0.0628055	0.0314028	−	0.999507i	$-0.490003\pi$
$571$	1.02940e36	0.0628055	0.0314028	+	0.999507i	$0.490003\pi$
$572$	7.44060e36i	0.443365i
$573$	− 1.84400e37i	− 1.07318i
$574$	−2.01580e37	−1.14587
$575$	0	0
$576$	−1.65288e37	−0.896475
$577$	4.63258e36i	0.245442i	0.992441	+	0.122721i	$0.0391620\pi$
$577$	4.63258e36i	0.245442i	−0.992441	+	0.122721i	$0.960838\pi$
$578$	3.06485e37i	1.58629i
$579$	8.50387e36	0.429987
$580$	0	0
$581$	−1.40703e37	−0.679090
$582$	− 2.43149e37i	− 1.14660i
$583$	− 1.10786e37i	− 0.510455i
$584$	2.02234e37	0.910503
$585$	0	0
$586$	−6.57430e36	−0.282639
$587$	− 2.64137e36i	− 0.110972i	−0.998459	−	0.0554862i	$-0.982329\pi$
$587$	− 2.64137e36i	− 0.110972i	0.998459	−	0.0554862i	$-0.0176709\pi$
$588$	2.00330e37i	0.822529i
$589$	−1.46808e37	−0.589107
$590$	0	0
$591$	1.51880e37	0.582198
$592$	5.32610e35i	0.0199557i
$593$	− 3.52090e37i	− 1.28948i	−0.764401	−	0.644741i	$-0.776965\pi$
$593$	− 3.52090e37i	− 1.28948i	0.764401	−	0.644741i	$-0.223035\pi$
$594$	4.53789e37	1.62457
$595$	0	0
$596$	5.84187e37	1.99861
$597$	− 5.43839e37i	− 1.81893i
$598$	8.74311e36i	0.285891i
$599$	−4.76915e37	−1.52468	−0.762341	−	0.647176i	$-0.775950\pi$
$599$	−4.76915e37	−1.52468	−0.762341	+	0.647176i	$0.775950\pi$
$600$	0	0
$601$	−2.39124e37	−0.730831	−0.365416	−	0.930844i	$-0.619073\pi$
$601$	−2.39124e37	−0.730831	−0.365416	+	0.930844i	$0.619073\pi$
$602$	2.50908e37i	0.749827i
$603$	− 1.35743e37i	− 0.396675i
$604$	−1.39020e37	−0.397264
$605$	0	0
$606$	−1.17557e38	−3.21269
$607$	− 3.35424e37i	− 0.896493i	−0.893910	−	0.448246i	$-0.852049\pi$
$607$	− 3.35424e37i	− 0.896493i	0.893910	−	0.448246i	$-0.147951\pi$
$608$	3.42334e37i	0.894854i
$609$	2.03142e36	0.0519357
$610$	0	0
$611$	1.56933e36	0.0383847
$612$	4.98373e36i	0.119237i
$613$	− 6.25036e37i	− 1.46281i	−0.681942	−	0.731407i	$-0.738864\pi$
$613$	− 6.25036e37i	− 1.46281i	0.681942	−	0.731407i	$-0.261136\pi$
$614$	−1.26439e37	−0.289474
$615$	0	0
$616$	6.22692e37	1.36437
$617$	6.57455e37i	1.40934i	0.709534	+	0.704671i	$0.248906\pi$
$617$	6.57455e37i	1.40934i	−0.709534	+	0.704671i	$0.751094\pi$
$618$	1.84855e38i	3.87692i
$619$	−2.39694e37	−0.491851	−0.245926	−	0.969289i	$-0.579092\pi$
$619$	−2.39694e37	−0.491851	−0.245926	+	0.969289i	$0.579092\pi$
$620$	0	0
$621$	3.28862e37	0.646066
$622$	9.66913e37i	1.85873i
$623$	2.77016e37i	0.521094i
$624$	2.03637e35	0.00374857
$625$	0	0
$626$	2.07120e37	0.365148
$627$	1.14864e38i	1.98186i
$628$	− 1.59065e38i	− 2.68608i
$629$	8.20831e36	0.135666
$630$	0	0
$631$	−2.72032e37	−0.430748	−0.215374	−	0.976532i	$-0.569097\pi$
$631$	−2.72032e37	−0.430748	−0.215374	+	0.976532i	$0.569097\pi$
$632$	7.13372e37i	1.10570i
$633$	5.16486e37i	0.783625i
$634$	−1.77778e38	−2.64041
$635$	0	0
$636$	3.98334e37	0.566991
$637$	− 4.49192e36i	− 0.0625965i
$638$	1.15990e37i	0.158249i
$639$	−1.42634e37	−0.190529
$640$	0	0
$641$	6.03099e37	0.772334	0.386167	−	0.922429i	$-0.373799\pi$
$641$	6.03099e37	0.772334	0.386167	+	0.922429i	$0.373799\pi$
$642$	8.45753e37i	1.06052i
$643$	− 1.01937e38i	− 1.25165i	−0.779965	−	0.625823i	$-0.784763\pi$
$643$	− 1.01937e38i	− 1.25165i	0.779965	−	0.625823i	$-0.215237\pi$
$644$	1.19204e38	1.43328
$645$	0	0
$646$	1.65354e37	0.190667
$647$	− 1.38190e36i	− 0.0156052i	−0.999970	−	0.00780260i	$-0.997516\pi$
$647$	− 1.38190e36i	− 0.0156052i	0.999970	−	0.00780260i	$-0.00248367\pi$
$648$	1.10968e38i	1.22726i
$649$	−1.89404e38	−2.05156
$650$	0	0
$651$	6.15972e37	0.640055
$652$	− 1.06189e38i	− 1.08078i
$653$	− 1.67383e38i	− 1.66872i	−0.551224	−	0.834358i	$-0.685839\pi$
$653$	− 1.67383e38i	− 1.66872i	0.551224	−	0.834358i	$-0.314161\pi$
$654$	2.03508e38	1.98738
$655$	0	0
$656$	−1.94276e36	−0.0182061
$657$	− 5.57335e37i	− 0.511663i
$658$	− 3.46926e37i	− 0.312024i
$659$	1.83021e38	1.61268	0.806339	−	0.591454i	$-0.201446\pi$
$659$	1.83021e38	1.61268	0.806339	+	0.591454i	$0.201446\pi$
$660$	0	0
$661$	6.09366e37	0.515417	0.257708	−	0.966223i	$-0.417033\pi$
$661$	6.09366e37	0.515417	0.257708	+	0.966223i	$0.417033\pi$
$662$	− 2.34578e38i	− 1.94403i
$663$	− 3.13835e36i	− 0.0254841i
$664$	1.09354e38	0.870090
$665$	0	0
$666$	−1.18366e38	−0.904327
$667$	8.40581e36i	0.0629334i
$668$	1.37672e38i	1.01010i
$669$	−3.59729e37	−0.258656
$670$	0	0
$671$	3.04618e38	2.10379
$672$	− 1.43635e38i	− 0.972245i
$673$	− 6.36340e37i	− 0.422168i	−0.977468	−	0.211084i	$-0.932301\pi$
$673$	− 6.36340e37i	− 0.422168i	0.977468	−	0.211084i	$-0.0676994\pi$
$674$	−6.30163e37	−0.409774
$675$	0	0
$676$	−2.51566e38	−1.57171
$677$	5.37104e37i	0.328936i	0.986382	+	0.164468i	$0.0525907\pi$
$677$	5.37104e37i	0.328936i	−0.986382	+	0.164468i	$0.947409\pi$
$678$	2.37008e38i	1.42286i
$679$	7.43332e37	0.437462
$680$	0	0
$681$	−3.25210e38	−1.83941
$682$	3.51708e38i	1.95026i
$683$	1.59190e38i	0.865437i	0.901529	+	0.432718i	$0.142446\pi$
$683$	1.59190e38i	0.865437i	−0.901529	+	0.432718i	$0.857554\pi$
$684$	−1.47058e38	−0.783847
$685$	0	0
$686$	−3.41399e38	−1.74939
$687$	− 2.15661e38i	− 1.08357i
$688$	2.41817e36i	0.0119136i
$689$	−8.93171e36	−0.0431495
$690$	0	0
$691$	−1.11503e38	−0.518006	−0.259003	−	0.965877i	$-0.583394\pi$
$691$	−1.11503e38	−0.518006	−0.259003	+	0.965877i	$0.583394\pi$
$692$	− 5.85621e38i	− 2.66799i
$693$	− 1.71607e38i	− 0.766719i
$694$	−3.58451e38	−1.57064
$695$	0	0
$696$	−1.57880e37	−0.0665431
$697$	2.99409e37i	0.123772i
$698$	− 2.72158e38i	− 1.10350i
$699$	2.70943e38	1.07755
$700$	0	0
$701$	9.04824e37	0.346235	0.173117	−	0.984901i	$-0.444616\pi$
$701$	9.04824e37	0.346235	0.173117	+	0.984901i	$0.444616\pi$
$702$	− 3.65852e37i	− 0.137327i
$703$	2.42208e38i	0.891849i
$704$	8.10278e38	2.92687
$705$	0	0
$706$	8.22199e37	0.285834
$707$	− 3.59385e38i	− 1.22574i
$708$	− 6.81008e38i	− 2.27879i
$709$	−2.52263e38	−0.828190	−0.414095	−	0.910234i	$-0.635902\pi$
$709$	−2.52263e38	−0.828190	−0.414095	+	0.910234i	$0.635902\pi$
$710$	0	0
$711$	1.96598e38	0.621353
$712$	− 2.15295e38i	− 0.667657i
$713$	2.54883e38i	0.775591i
$714$	−6.93784e37	−0.207157
$715$	0	0
$716$	−3.56488e38	−1.02499
$717$	− 1.94469e37i	− 0.0548709i
$718$	− 4.87584e38i	− 1.35011i
$719$	2.15368e38	0.585249	0.292624	−	0.956227i	$-0.405471\pi$
$719$	2.15368e38	0.585249	0.292624	+	0.956227i	$0.405471\pi$
$720$	0	0
$721$	−5.65122e38	−1.47916
$722$	− 1.40869e38i	− 0.361878i
$723$	1.52427e38i	0.384323i
$724$	−9.29280e38	−2.29973
$725$	0	0
$726$	1.90753e39	4.54808
$727$	6.18554e38i	1.44765i	0.689985	+	0.723824i	$0.257617\pi$
$727$	6.18554e38i	1.44765i	−0.689985	+	0.723824i	$0.742383\pi$
$728$	− 5.02025e37i	− 0.115332i
$729$	−2.02058e36	−0.00455675
$730$	0	0
$731$	3.72675e37	0.0809927
$732$	1.09527e39i	2.33679i
$733$	− 5.13013e36i	− 0.0107455i	−0.999986	−	0.00537273i	$-0.998290\pi$
$733$	− 5.13013e36i	− 0.0107455i	0.999986	−	0.00537273i	$-0.00171020\pi$
$734$	6.55075e38	1.34708
$735$	0	0
$736$	5.94349e38	1.17812
$737$	6.65443e38i	1.29509i
$738$	− 4.31756e38i	− 0.825044i
$739$	5.22466e38	0.980298	0.490149	−	0.871639i	$-0.336942\pi$
$739$	5.22466e38	0.980298	0.490149	+	0.871639i	$0.336942\pi$
$740$	0	0
$741$	9.26054e37	0.167529
$742$	1.97450e38i	0.350756i
$743$	1.00984e39i	1.76158i	0.473509	+	0.880789i	$0.342987\pi$
$743$	1.00984e39i	1.76158i	−0.473509	+	0.880789i	$0.657013\pi$
$744$	−4.78729e38	−0.820077
$745$	0	0
$746$	3.85686e38	0.637177
$747$	− 3.01367e38i	− 0.488953i
$748$	− 2.44313e38i	− 0.389292i
$749$	−2.58556e38	−0.404622
$750$	0	0
$751$	−4.44629e38	−0.671210	−0.335605	−	0.942003i	$-0.608941\pi$
$751$	−4.44629e38	−0.671210	−0.335605	+	0.942003i	$0.608941\pi$
$752$	− 3.34356e36i	− 0.00495757i
$753$	1.12914e39i	1.64443i
$754$	9.35131e36	0.0133770
$755$	0	0
$756$	−4.98803e38	−0.688470
$757$	− 8.24934e38i	− 1.11847i	−0.829009	−	0.559235i	$-0.811095\pi$
$757$	− 8.24934e38i	− 1.11847i	0.829009	−	0.559235i	$-0.188905\pi$
$758$	6.90757e38i	0.920007i
$759$	1.99423e39	2.60923
$760$	0	0
$761$	−5.69669e38	−0.719333	−0.359666	−	0.933081i	$-0.617109\pi$
$761$	−5.69669e38	−0.719333	−0.359666	+	0.933081i	$0.617109\pi$
$762$	1.73379e39i	2.15082i
$763$	6.22146e38i	0.758248i
$764$	−1.15733e39	−1.38579
$765$	0	0
$766$	−1.14683e39	−1.32560
$767$	1.52700e38i	0.173421i
$768$	1.08090e39i	1.20617i
$769$	−1.47938e39	−1.62209	−0.811043	−	0.584986i	$-0.801100\pi$
$769$	−1.47938e39	−1.62209	−0.811043	+	0.584986i	$0.801100\pi$
$770$	0	0
$771$	−1.19855e38	−0.126889
$772$	− 5.33720e38i	− 0.555239i
$773$	− 1.83758e39i	− 1.87855i	−0.343160	−	0.939277i	$-0.611497\pi$
$773$	− 1.83758e39i	− 1.87855i	0.343160	−	0.939277i	$-0.388503\pi$
$774$	−5.37408e38	−0.539885
$775$	0	0
$776$	−5.77712e38	−0.560503
$777$	− 1.01625e39i	− 0.968981i
$778$	− 1.05743e39i	− 0.990894i
$779$	−8.83484e38	−0.813660
$780$	0	0
$781$	6.99222e38	0.622051
$782$	− 2.87081e38i	− 0.251023i
$783$	− 3.51738e37i	− 0.0302298i
$784$	−9.57033e36	−0.00808463
$785$	0	0
$786$	2.04665e39	1.67047
$787$	3.93218e38i	0.315482i	0.987481	+	0.157741i	$0.0504210\pi$
$787$	3.93218e38i	0.315482i	−0.987481	+	0.157741i	$0.949579\pi$
$788$	− 9.53231e38i	− 0.751786i
$789$	1.31695e38	0.102101
$790$	0	0
$791$	−7.24559e38	−0.542864
$792$	1.33372e39i	0.982367i
$793$	− 2.45588e38i	− 0.177836i
$794$	−4.12914e39	−2.93957
$795$	0	0
$796$	−3.41324e39	−2.34877
$797$	1.32458e39i	0.896168i	0.893991	+	0.448084i	$0.147893\pi$
$797$	1.32458e39i	0.896168i	−0.893991	+	0.448084i	$0.852107\pi$
$798$	− 2.04719e39i	− 1.36182i
$799$	−5.15293e37	−0.0337033
$800$	0	0
$801$	−5.93329e38	−0.375194
$802$	− 3.51089e39i	− 2.18305i
$803$	2.73218e39i	1.67051i
$804$	−2.39263e39	−1.43853
$805$	0	0
$806$	2.83553e38	0.164858
$807$	− 1.53125e38i	− 0.0875492i
$808$	2.79311e39i	1.57049i
$809$	2.19258e39	1.21241	0.606206	−	0.795308i	$-0.292691\pi$
$809$	2.19258e39	1.21241	0.606206	+	0.795308i	$0.292691\pi$
$810$	0	0
$811$	2.76373e39	1.47813	0.739066	−	0.673633i	$-0.235267\pi$
$811$	2.76373e39	1.47813	0.739066	+	0.673633i	$0.235267\pi$
$812$	− 1.27496e38i	− 0.0670640i
$813$	− 1.24873e39i	− 0.646022i
$814$	5.80257e39	2.95251
$815$	0	0
$816$	−6.68646e36	−0.00329139
$817$	1.09968e39i	0.532436i
$818$	− 4.17038e39i	− 1.98612i
$819$	−1.38352e38	−0.0648118
$820$	0	0
$821$	−9.42212e38	−0.427087	−0.213543	−	0.976934i	$-0.568500\pi$
$821$	−9.42212e38	−0.427087	−0.213543	+	0.976934i	$0.568500\pi$
$822$	− 1.37294e39i	− 0.612183i
$823$	2.17900e39i	0.955782i	0.878419	+	0.477891i	$0.158599\pi$
$823$	2.17900e39i	0.955782i	−0.878419	+	0.477891i	$0.841401\pi$
$824$	4.39208e39	1.89519
$825$	0	0
$826$	3.37569e39	1.40972
$827$	8.15484e38i	0.335036i	0.985869	+	0.167518i	$0.0535752\pi$
$827$	8.15484e38i	0.335036i	−0.985869	+	0.167518i	$0.946425\pi$
$828$	2.55317e39i	1.03198i
$829$	−1.51577e39	−0.602763	−0.301382	−	0.953504i	$-0.597448\pi$
$829$	−1.51577e39	−0.602763	−0.301382	+	0.953504i	$0.597448\pi$
$830$	0	0
$831$	−4.84386e39	−1.86457
$832$	− 6.53260e38i	− 0.247412i
$833$	1.47493e38i	0.0549622i
$834$	7.46823e39	2.73827
$835$	0	0
$836$	7.20911e39	2.55916
$837$	− 1.06655e39i	− 0.372553i
$838$	1.02528e39i	0.352409i
$839$	−3.04177e39	−1.02882	−0.514410	−	0.857544i	$-0.671989\pi$
$839$	−3.04177e39	−1.02882	−0.514410	+	0.857544i	$0.671989\pi$
$840$	0	0
$841$	−3.04414e39	−0.997055
$842$	− 3.70077e39i	− 1.19283i
$843$	− 1.23726e39i	− 0.392453i
$844$	3.24157e39	1.01189
$845$	0	0
$846$	7.43067e38	0.224661
$847$	5.83154e39i	1.73523i
$848$	1.90296e37i	0.00557295i
$849$	−1.23603e39	−0.356266
$850$	0	0
$851$	4.20513e39	1.17417
$852$	2.51408e39i	0.690947i
$853$	− 9.78044e38i	− 0.264574i	−0.991211	−	0.132287i	$-0.957768\pi$
$853$	− 9.78044e38i	− 0.264574i	0.991211	−	0.132287i	$-0.0422320\pi$
$854$	−5.42912e39	−1.44560
$855$	0	0
$856$	2.00948e39	0.518427
$857$	6.93851e39i	1.76208i	0.473044	+	0.881039i	$0.343155\pi$
$857$	6.93851e39i	1.76208i	−0.473044	+	0.881039i	$0.656845\pi$
$858$	− 2.21855e39i	− 0.554613i
$859$	6.79141e39	1.67129	0.835646	−	0.549268i	$-0.185093\pi$
$859$	6.79141e39	1.67129	0.835646	+	0.549268i	$0.185093\pi$
$860$	0	0
$861$	3.70689e39	0.884030
$862$	− 9.26188e39i	− 2.17446i
$863$	− 5.27048e38i	− 0.121816i	−0.998143	−	0.0609080i	$-0.980600\pi$
$863$	− 5.27048e38i	− 0.121816i	0.998143	−	0.0609080i	$-0.0193996\pi$
$864$	−2.48703e39	−0.565908
$865$	0	0
$866$	−5.85514e39	−1.29136
$867$	− 5.63600e39i	− 1.22381i
$868$	− 3.86596e39i	− 0.826497i
$869$	−9.63764e39	−2.02863
$870$	0	0
$871$	5.36491e38	0.109476
$872$	− 4.83527e39i	− 0.971512i
$873$	1.59211e39i	0.314978i
$874$	8.47110e39	1.65019
$875$	0	0
$876$	−9.82366e39	−1.85553
$877$	− 3.42049e39i	− 0.636200i	−0.948057	−	0.318100i	$-0.896955\pi$
$877$	− 3.42049e39i	− 0.636200i	0.948057	−	0.318100i	$-0.103045\pi$
$878$	− 1.35260e40i	− 2.47739i
$879$	1.20896e39	0.218053
$880$	0	0
$881$	−7.31752e39	−1.27994	−0.639969	−	0.768401i	$-0.721053\pi$
$881$	−7.31752e39	−1.27994	−0.639969	+	0.768401i	$0.721053\pi$
$882$	− 2.12689e39i	− 0.366370i
$883$	− 2.06213e39i	− 0.349821i	−0.984584	−	0.174910i	$-0.944036\pi$
$883$	− 2.06213e39i	− 0.349821i	0.984584	−	0.174910i	$-0.0559636\pi$
$884$	−1.96969e38	−0.0329074
$885$	0	0
$886$	1.43747e40	2.32940
$887$	− 6.98969e39i	− 1.11555i	−0.829992	−	0.557775i	$-0.811655\pi$
$887$	− 6.98969e39i	− 1.11555i	0.829992	−	0.557775i	$-0.188345\pi$
$888$	7.89819e39i	1.24152i
$889$	−5.30037e39	−0.820602
$890$	0	0
$891$	−1.49917e40	−2.25166
$892$	2.25773e39i	0.334000i
$893$	− 1.52051e39i	− 0.221561i
$894$	−1.74186e40	−2.50009
$895$	0	0
$896$	−8.83926e39	−1.23100
$897$	− 1.60778e39i	− 0.220561i
$898$	1.22113e40i	1.65018i
$899$	2.72614e38	0.0362904
$900$	0	0
$901$	2.93274e38	0.0378869
$902$	2.11656e40i	2.69366i
$903$	− 4.61398e39i	− 0.578483i
$904$	5.63122e39	0.695550
$905$	0	0
$906$	4.14514e39	0.496945
$907$	2.28488e39i	0.269876i	0.990854	+	0.134938i	$0.0430835\pi$
$907$	2.28488e39i	0.269876i	−0.990854	+	0.134938i	$0.956916\pi$
$908$	2.04108e40i	2.37521i
$909$	7.69751e39	0.882547
$910$	0	0
$911$	7.51662e39	0.836612	0.418306	−	0.908306i	$-0.362624\pi$
$911$	7.51662e39	0.836612	0.418306	+	0.908306i	$0.362624\pi$
$912$	− 1.97302e38i	− 0.0216372i
$913$	1.47737e40i	1.59637i
$914$	1.16227e40	1.23746
$915$	0	0
$916$	−1.35353e40	−1.39920
$917$	6.25683e39i	0.637336i
$918$	1.20128e39i	0.120578i
$919$	−5.26405e39	−0.520668	−0.260334	−	0.965519i	$-0.583833\pi$
$919$	−5.26405e39	−0.520668	−0.260334	+	0.965519i	$0.583833\pi$
$920$	0	0
$921$	2.32511e39	0.223326
$922$	1.91179e40i	1.80956i
$923$	− 5.63724e38i	− 0.0525828i
$924$	−3.02477e40	−2.78048
$925$	0	0
$926$	2.06488e40	1.84351
$927$	− 1.21041e40i	− 1.06502i
$928$	− 6.35694e38i	− 0.0551252i
$929$	2.48177e39	0.212104	0.106052	−	0.994361i	$-0.466179\pi$
$929$	2.48177e39	0.212104	0.106052	+	0.994361i	$0.466179\pi$
$930$	0	0
$931$	−4.35217e39	−0.361314
$932$	− 1.70049e40i	− 1.39143i
$933$	− 1.77807e40i	− 1.43399i
$934$	1.62142e40	1.28888
$935$	0	0
$936$	1.07526e39	0.0830408
$937$	2.96211e39i	0.225485i	0.993624	+	0.112742i	$0.0359635\pi$
$937$	2.96211e39i	0.225485i	−0.993624	+	0.112742i	$0.964037\pi$
$938$	− 1.18600e40i	− 0.889911i
$939$	−3.80877e39	−0.281708
$940$	0	0
$941$	1.23582e40	0.888168	0.444084	−	0.895985i	$-0.353529\pi$
$941$	1.23582e40	0.888168	0.444084	+	0.895985i	$0.353529\pi$
$942$	4.74280e40i	3.36006i
$943$	1.53388e40i	1.07123i
$944$	3.25338e38	0.0223982
$945$	0	0
$946$	2.63449e40	1.76265
$947$	− 3.62546e39i	− 0.239132i	−0.992826	−	0.119566i	$-0.961850\pi$
$947$	− 3.62546e39i	− 0.239132i	0.992826	−	0.119566i	$-0.0381503\pi$
$948$	− 3.46525e40i	− 2.25332i
$949$	2.20273e39	0.141210
$950$	0	0
$951$	3.26918e40	2.03705
$952$	1.64841e39i	0.101266i
$953$	− 2.05559e40i	− 1.24504i	−0.782605	−	0.622519i	$-0.786109\pi$
$953$	− 2.05559e40i	− 1.24504i	0.782605	−	0.622519i	$-0.213891\pi$
$954$	−4.22910e39	−0.252548
$955$	0	0
$956$	−1.22053e39	−0.0708542
$957$	− 2.13296e39i	− 0.122087i
$958$	4.81585e40i	2.71793i
$959$	4.19722e39	0.233567
$960$	0	0
$961$	−1.02164e40	−0.552757
$962$	− 4.67813e39i	− 0.249579i
$963$	− 5.53790e39i	− 0.291333i
$964$	9.56665e39	0.496272
$965$	0	0
$966$	−3.55427e40	−1.79291
$967$	2.81961e40i	1.40259i	0.712871	+	0.701296i	$0.247395\pi$
$967$	2.81961e40i	1.40259i	−0.712871	+	0.701296i	$0.752605\pi$
$968$	− 4.53223e40i	− 2.22328i
$969$	−3.04071e39	−0.147097
$970$	0	0
$971$	−1.81766e40	−0.855170	−0.427585	−	0.903975i	$-0.640636\pi$
$971$	−1.81766e40	−0.855170	−0.427585	+	0.903975i	$0.640636\pi$
$972$	− 3.45830e40i	− 1.60461i
$973$	2.28312e40i	1.04473i
$974$	−4.28405e40	−1.93334
$975$	0	0
$976$	−5.23241e38	−0.0229683
$977$	− 2.03258e40i	− 0.879974i	−0.898004	−	0.439987i	$-0.854983\pi$
$977$	− 2.03258e40i	− 0.879974i	0.898004	−	0.439987i	$-0.145017\pi$
$978$	3.16622e40i	1.35197i
$979$	2.90863e40	1.22496
$980$	0	0
$981$	−1.33255e40	−0.545948
$982$	3.25830e40i	1.31670i
$983$	7.72807e39i	0.308034i	0.988068	+	0.154017i	$0.0492210\pi$
$983$	7.72807e39i	0.308034i	−0.988068	+	0.154017i	$0.950779\pi$
$984$	−2.88096e40	−1.13267
$985$	0	0
$986$	−3.07052e38	−0.0117455
$987$	6.37968e39i	0.240723i
$988$	− 5.81210e39i	− 0.216329i
$989$	1.90922e40	0.700981
$990$	0	0
$991$	1.25885e40	0.449758	0.224879	−	0.974387i	$-0.427801\pi$
$991$	1.25885e40	0.449758	0.224879	+	0.974387i	$0.427801\pi$
$992$	− 1.92757e40i	− 0.679364i
$993$	4.31368e40i	1.49980i
$994$	−1.24620e40	−0.427438
$995$	0	0
$996$	−5.31193e40	−1.77317
$997$	− 4.50833e40i	− 1.48467i	−0.670028	−	0.742336i	$-0.733718\pi$
$997$	− 4.50833e40i	− 1.48467i	0.670028	−	0.742336i	$-0.266282\pi$
$998$	− 5.24306e40i	− 1.70342i
$999$	−1.75962e40	−0.564008

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.28.b.a.24.4		4
5.2	odd	4		1.28.a.a.1.1	✓	2
5.3	odd	4		25.28.a.a.1.2		2
5.4	even	2	inner	25.28.b.a.24.1		4
15.2	even	4		9.28.a.d.1.2		2
20.7	even	4		16.28.a.d.1.2		2
35.27	even	4		49.28.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.28.a.a.1.1	✓	2	5.2	odd	4
9.28.a.d.1.2		2	15.2	even	4
16.28.a.d.1.2		2	20.7	even	4
25.28.a.a.1.2		2	5.3	odd	4
25.28.b.a.24.1		4	5.4	even	2	inner
25.28.b.a.24.4		4	1.1	even	1	trivial
49.28.a.b.1.1		2	35.27	even	4

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:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+18713.6i q^{2} -3.44127e6i q^{3} -2.15981e8 q^{4} +6.43986e10 q^{6} +1.96873e11i q^{7} -1.53009e12i q^{8} -4.21675e12 q^{9} +O(q^{10})\)	\(q+18713.6i q^{2} -3.44127e6i q^{3} -2.15981e8 q^{4} +6.43986e10 q^{6} +1.96873e11i q^{7} -1.53009e12i q^{8} -4.21675e12 q^{9} +2.06714e14 q^{11} +7.43249e14i q^{12} -1.66656e14i q^{13} -3.68421e15 q^{14} -3.55072e14 q^{16} +5.47219e15i q^{17} -7.89105e16i q^{18} -1.61471e17 q^{19} +6.77495e17 q^{21} +3.86837e18i q^{22} +2.80341e18i q^{23} -5.26544e18 q^{24} +3.11874e18 q^{26} -1.17308e19i q^{27} -4.25209e19i q^{28} +2.99842e18 q^{29} +9.09190e19 q^{31} -2.12009e20i q^{32} -7.11360e20i q^{33} -1.02404e20 q^{34} +9.10738e20 q^{36} -1.50001e21i q^{37} -3.02171e21i q^{38} -5.73510e20 q^{39} +5.47146e21 q^{41} +1.26784e22i q^{42} -6.81035e21i q^{43} -4.46463e22 q^{44} -5.24619e22 q^{46} +9.41657e21i q^{47} +1.22190e21i q^{48} +2.69532e22 q^{49} +1.88313e22 q^{51} +3.59946e22i q^{52} -5.35936e22i q^{53} +2.19525e23 q^{54} +3.01233e23 q^{56} +5.55667e23i q^{57} +5.61113e22i q^{58} -9.16258e23 q^{59} +1.47362e24 q^{61} +1.70142e24i q^{62} -8.30166e23i q^{63} +3.91980e24 q^{64} +1.33121e25 q^{66} +3.21915e24i q^{67} -1.18189e24i q^{68} +9.64729e24 q^{69} +3.38255e24 q^{71} +6.45199e24i q^{72} +1.32172e25i q^{73} +2.80705e25 q^{74} +3.48748e25 q^{76} +4.06965e25i q^{77} -1.07324e25i q^{78} -4.66230e25 q^{79} -7.25240e25 q^{81} +1.02391e26i q^{82} +7.14690e25i q^{83} -1.46326e26 q^{84} +1.27446e26 q^{86} -1.03184e25i q^{87} -3.16290e26i q^{88} +1.40708e26 q^{89} +3.28102e25 q^{91} -6.05484e26i q^{92} -3.12877e26i q^{93} -1.76218e26 q^{94} -7.29582e26 q^{96} -3.77568e26i q^{97} +5.04391e26i q^{98} -8.71662e26 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 381246592 q^{4} + 173765746368 q^{6} - 2470273108308 q^{9}+O(q^{10}) \) 4 * q - 381246592 * q^4 + 173765746368 * q^6 - 2470273108308 * q^9	\( 4 q - 381246592 q^{4} + 173765746368 q^{6} - 2470273108308 q^{9} + 276334675383888 q^{11} - 78\!\cdots\!24 q^{14}+ \cdots - 21\!\cdots\!76 q^{99}+O(q^{100}) \) 4 * q - 381246592 * q^4 + 173765746368 * q^6 - 2470273108308 * q^9 + 276334675383888 * q^11 - 7816680105623424 * q^14 - 28645991570333696 * q^16 - 809131620745369520 * q^19 + 1447574627166369408 * q^21 - 3354991067585064960 * q^24 - 6006918508293280032 * q^26 + 31093359990897116520 * q^29 + 57089109188934770048 * q^31 + 301876670371869719136 * q^34 + 1972689241976748422784 * q^36 + 1381980443602051054944 * q^39 + 18162687396093024509928 * q^41 - 92769082075148610599424 * q^44 - 102301447140627940559232 * q^46 + 184408226435681815380828 * q^49 - 66989949409454428929312 * q^51 + 916041559571236054270080 * q^54 + 530935521929718521978880 * q^56 - 4019241955248052977263760 * q^59 + 295714853384897880740888 * q^61 + 2468115607876274891522048 * q^64 + 23541736306288536506877696 * q^66 + 18752960979411737057391744 * q^69 - 26350397640738677196572832 * q^71 + 48468290290897051075575456 * q^74 + 57420865435885573745231360 * q^76 - 125628702071441439836358080 * q^79 - 198094311653195416476206556 * q^81 - 290304367266846887179997184 * q^84 + 504379767802394865424431168 * q^86 + 626946877522211079526988760 * q^89 + 40410730250081757073388608 * q^91 - 524930869501440083787158784 * q^94 - 1124149802196805832769011712 * q^96 - 2152083558561684671220959376 * q^99

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