LMFDB - Embedded newform 25.20.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,20,Mod(1,25)]

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([0]))

N = Newforms(chi, 20, names="a")

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	25.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$57.2041741391$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-456.000 q^{2} -50652.0 q^{3} -316352. q^{4} +2.30973e7 q^{6} +1.69175e7 q^{7} +3.83332e8 q^{8} +1.40336e9 q^{9} +O(q^{10})$

\(q-456.000 q^{2} -50652.0 q^{3} -316352. q^{4} +2.30973e7 q^{6} +1.69175e7 q^{7} +3.83332e8 q^{8} +1.40336e9 q^{9} -1.62121e7 q^{11} +1.60239e10 q^{12} -5.04216e10 q^{13} -7.71440e9 q^{14} -8.93976e9 q^{16} -2.25070e11 q^{17} -6.39934e11 q^{18} -1.71028e12 q^{19} -8.56907e11 q^{21} +7.39272e9 q^{22} -1.40365e13 q^{23} -1.94165e13 q^{24} +2.29923e13 q^{26} -1.22123e13 q^{27} -5.35190e12 q^{28} +1.13784e12 q^{29} -1.04627e14 q^{31} -1.96900e14 q^{32} +8.21176e11 q^{33} +1.02632e14 q^{34} -4.43957e14 q^{36} +1.69392e14 q^{37} +7.79887e14 q^{38} +2.55396e15 q^{39} -3.30998e15 q^{41} +3.90750e14 q^{42} -1.12791e15 q^{43} +5.12873e12 q^{44} +6.40066e15 q^{46} -3.49869e15 q^{47} +4.52817e14 q^{48} -1.11127e16 q^{49} +1.14003e16 q^{51} +1.59510e16 q^{52} -2.99563e16 q^{53} +5.56881e15 q^{54} +6.48503e15 q^{56} +8.66290e16 q^{57} -5.18853e14 q^{58} +5.83914e16 q^{59} +2.33737e16 q^{61} +4.77099e16 q^{62} +2.37415e16 q^{63} +9.44733e16 q^{64} -3.74456e14 q^{66} +2.05103e17 q^{67} +7.12014e16 q^{68} +7.10979e17 q^{69} -1.77902e17 q^{71} +5.37954e17 q^{72} -2.99854e17 q^{73} -7.72429e16 q^{74} +5.41050e17 q^{76} -2.74269e14 q^{77} -1.16460e18 q^{78} -9.22271e16 q^{79} -1.01250e18 q^{81} +1.50935e18 q^{82} -1.20854e18 q^{83} +2.71084e17 q^{84} +5.14329e17 q^{86} -5.76336e16 q^{87} -6.21462e15 q^{88} +4.37120e18 q^{89} -8.53010e17 q^{91} +4.44049e18 q^{92} +5.29956e18 q^{93} +1.59540e18 q^{94} +9.97337e18 q^{96} +6.35013e17 q^{97} +5.06739e18 q^{98} -2.27515e16 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−456.000	−0.629767	−0.314883	−	0.949130i	$-0.601965\pi$
$2$	−456.000	−0.629767	−0.314883	+	0.949130i	$0.601965\pi$
$3$	−50652.0	−1.48575	−0.742873	−	0.669432i	$-0.766537\pi$
$3$	−50652.0	−1.48575	−0.742873	+	0.669432i	$0.766537\pi$
$4$	−316352.	−0.603394
$5$	0	0
$5$	0	0
$6$	2.30973e7	0.935674
$7$	1.69175e7	0.158455	0.0792275	−	0.996857i	$-0.474755\pi$
$7$	1.69175e7	0.158455	0.0792275	+	0.996857i	$0.474755\pi$
$8$	3.83332e8	1.00976
$9$	1.40336e9	1.20744
$10$	0	0
$11$	−1.62121e7	−0.00207305	−0.00103652	−	0.999999i	$-0.500330\pi$
$11$	−1.62121e7	−0.00207305	−0.00103652	+	0.999999i	$0.500330\pi$
$12$	1.60239e10	0.896490
$13$	−5.04216e10	−1.31873	−0.659364	−	0.751824i	$-0.729174\pi$
$13$	−5.04216e10	−1.31873	−0.659364	+	0.751824i	$0.729174\pi$
$14$	−7.71440e9	−0.0997897
$15$	0	0
$16$	−8.93976e9	−0.0325227
$17$	−2.25070e11	−0.460313	−0.230156	−	0.973154i	$-0.573924\pi$
$17$	−2.25070e11	−0.460313	−0.230156	+	0.973154i	$0.573924\pi$
$18$	−6.39934e11	−0.760407
$19$	−1.71028e12	−1.21593	−0.607964	−	0.793965i	$-0.708013\pi$
$19$	−1.71028e12	−1.21593	−0.607964	+	0.793965i	$0.708013\pi$
$20$	0	0
$21$	−8.56907e11	−0.235424
$22$	7.39272e9	0.00130554
$23$	−1.40365e13	−1.62497	−0.812485	−	0.582982i	$-0.801886\pi$
$23$	−1.40365e13	−1.62497	−0.812485	+	0.582982i	$0.801886\pi$
$24$	−1.94165e13	−1.50025
$25$	0	0
$26$	2.29923e13	0.830491
$27$	−1.22123e13	−0.308207
$28$	−5.35190e12	−0.0956107
$29$	1.13784e12	0.0145646	0.00728230	−	0.999973i	$-0.497682\pi$
$29$	1.13784e12	0.0145646	0.00728230	+	0.999973i	$0.497682\pi$
$30$	0	0
$31$	−1.04627e14	−0.710734	−0.355367	−	0.934727i	$-0.615644\pi$
$31$	−1.04627e14	−0.710734	−0.355367	+	0.934727i	$0.615644\pi$
$32$	−1.96900e14	−0.989283
$33$	8.21176e11	0.00308002
$34$	1.02632e14	0.289890
$35$	0	0
$36$	−4.43957e14	−0.728563
$37$	1.69392e14	0.214278	0.107139	−	0.994244i	$-0.465831\pi$
$37$	1.69392e14	0.214278	0.107139	+	0.994244i	$0.465831\pi$
$38$	7.79887e14	0.765751
$39$	2.55396e15	1.95929
$40$	0	0
$41$	−3.30998e15	−1.57899	−0.789495	−	0.613757i	$-0.789657\pi$
$41$	−3.30998e15	−1.57899	−0.789495	+	0.613757i	$0.789657\pi$
$42$	3.90750e14	0.148262
$43$	−1.12791e15	−0.342236	−0.171118	−	0.985251i	$-0.554738\pi$
$43$	−1.12791e15	−0.342236	−0.171118	+	0.985251i	$0.554738\pi$
$44$	5.12873e12	0.00125086
$45$	0	0
$46$	6.40066e15	1.02335
$47$	−3.49869e15	−0.456012	−0.228006	−	0.973660i	$-0.573221\pi$
$47$	−3.49869e15	−0.456012	−0.228006	+	0.973660i	$0.573221\pi$
$48$	4.52817e14	0.0483204
$49$	−1.11127e16	−0.974892
$50$	0	0
$51$	1.14003e16	0.683908
$52$	1.59510e16	0.795711
$53$	−2.99563e16	−1.24700	−0.623501	−	0.781822i	$-0.714290\pi$
$53$	−2.99563e16	−1.24700	−0.623501	+	0.781822i	$0.714290\pi$
$54$	5.56881e15	0.194098
$55$	0	0
$56$	6.48503e15	0.160002
$57$	8.66290e16	1.80656
$58$	−5.18853e14	−0.00917230
$59$	5.83914e16	0.877515	0.438758	−	0.898605i	$-0.355419\pi$
$59$	5.83914e16	0.877515	0.438758	+	0.898605i	$0.355419\pi$
$60$	0	0
$61$	2.33737e16	0.255914	0.127957	−	0.991780i	$-0.459158\pi$
$61$	2.33737e16	0.255914	0.127957	+	0.991780i	$0.459158\pi$
$62$	4.77099e16	0.447597
$63$	2.37415e16	0.191325
$64$	9.44733e16	0.655540
$65$	0	0
$66$	−3.74456e14	−0.00193970
$67$	2.05103e17	0.921002	0.460501	−	0.887659i	$-0.347670\pi$
$67$	2.05103e17	0.921002	0.460501	+	0.887659i	$0.347670\pi$
$68$	7.12014e16	0.277750
$69$	7.10979e17	2.41429
$70$	0	0
$71$	−1.77902e17	−0.460498	−0.230249	−	0.973132i	$-0.573954\pi$
$71$	−1.77902e17	−0.460498	−0.230249	+	0.973132i	$0.573954\pi$
$72$	5.37954e17	1.21923
$73$	−2.99854e17	−0.596132	−0.298066	−	0.954545i	$-0.596342\pi$
$73$	−2.99854e17	−0.596132	−0.298066	+	0.954545i	$0.596342\pi$
$74$	−7.72429e16	−0.134945
$75$	0	0
$76$	5.41050e17	0.733683
$77$	−2.74269e14	−0.000328485 0
$78$	−1.16460e18	−1.23390
$79$	−9.22271e16	−0.0865767	−0.0432884	−	0.999063i	$-0.513783\pi$
$79$	−9.22271e16	−0.0865767	−0.0432884	+	0.999063i	$0.513783\pi$
$80$	0	0
$81$	−1.01250e18	−0.749525
$82$	1.50935e18	0.994396
$83$	−1.20854e18	−0.709611	−0.354805	−	0.934940i	$-0.615453\pi$
$83$	−1.20854e18	−0.709611	−0.354805	+	0.934940i	$0.615453\pi$
$84$	2.71084e17	0.142053
$85$	0	0
$86$	5.14329e17	0.215529
$87$	−5.76336e16	−0.0216393
$88$	−6.21462e15	−0.00209329
$89$	4.37120e18	1.32250	0.661250	−	0.750166i	$-0.270026\pi$
$89$	4.37120e18	1.32250	0.661250	+	0.750166i	$0.270026\pi$
$90$	0	0
$91$	−8.53010e17	−0.208959
$92$	4.44049e18	0.980497
$93$	5.29956e18	1.05597
$94$	1.59540e18	0.287181
$95$	0	0
$96$	9.97337e18	1.46982
$97$	6.35013e17	0.0848108	0.0424054	−	0.999100i	$-0.486498\pi$
$97$	6.35013e17	0.0848108	0.0424054	+	0.999100i	$0.486498\pi$
$98$	5.06739e18	0.613955
$99$	−2.27515e16	−0.00250308
$100$	0	0
$101$	−1.42252e19	−1.29421	−0.647105	−	0.762401i	$-0.724021\pi$
$101$	−1.42252e19	−1.29421	−0.647105	+	0.762401i	$0.724021\pi$
$102$	−5.19851e18	−0.430703
$103$	−4.90729e18	−0.370586	−0.185293	−	0.982683i	$-0.559323\pi$
$103$	−4.90729e18	−0.370586	−0.185293	+	0.982683i	$0.559323\pi$
$104$	−1.93282e19	−1.33160
$105$	0	0
$106$	1.36601e19	0.785321
$107$	−2.64625e19	−1.39151	−0.695753	−	0.718281i	$-0.744929\pi$
$107$	−2.64625e19	−1.39151	−0.695753	+	0.718281i	$0.744929\pi$
$108$	3.86339e18	0.185970
$109$	−1.84178e19	−0.812242	−0.406121	−	0.913819i	$-0.633119\pi$
$109$	−1.84178e19	−0.812242	−0.406121	+	0.913819i	$0.633119\pi$
$110$	0	0
$111$	−8.58006e18	−0.318363
$112$	−1.51239e17	−0.00515338
$113$	−2.57421e19	−0.806118	−0.403059	−	0.915174i	$-0.632053\pi$
$113$	−2.57421e19	−0.806118	−0.403059	+	0.915174i	$0.632053\pi$
$114$	−3.95028e19	−1.13771
$115$	0	0
$116$	−3.59956e17	−0.00878818
$117$	−7.07599e19	−1.59229
$118$	−2.66265e19	−0.552630
$119$	−3.80763e18	−0.0729389
$120$	0	0
$121$	−6.11588e19	−0.999996
$122$	−1.06584e19	−0.161166
$123$	1.67657e20	2.34598
$124$	3.30989e19	0.428852
$125$	0	0
$126$	−1.08261e19	−0.120490
$127$	−8.80720e19	−0.909290	−0.454645	−	0.890673i	$-0.650234\pi$
$127$	−8.80720e19	−0.909290	−0.454645	+	0.890673i	$0.650234\pi$
$128$	6.01524e19	0.576445
$129$	5.71311e19	0.508476
$130$	0	0
$131$	7.19289e19	0.553129	0.276564	−	0.960995i	$-0.410804\pi$
$131$	7.19289e19	0.553129	0.276564	+	0.960995i	$0.410804\pi$
$132$	−2.59781e17	−0.00185846
$133$	−2.89337e19	−0.192670
$134$	−9.35268e19	−0.580016
$135$	0	0
$136$	−8.62765e19	−0.464807
$137$	2.95426e20	1.48458	0.742290	−	0.670079i	$-0.233740\pi$
$137$	2.95426e20	1.48458	0.742290	+	0.670079i	$0.233740\pi$
$138$	−3.24206e20	−1.52044
$139$	1.38478e20	0.606375	0.303187	−	0.952931i	$-0.401949\pi$
$139$	1.38478e20	0.606375	0.303187	+	0.952931i	$0.401949\pi$
$140$	0	0
$141$	1.77216e20	0.677518
$142$	8.11235e19	0.290006
$143$	8.17441e17	0.00273378
$144$	−1.25457e19	−0.0392692
$145$	0	0
$146$	1.36733e20	0.375424
$147$	5.62880e20	1.44844
$148$	−5.35876e19	−0.129294
$149$	−2.66021e20	−0.602070	−0.301035	−	0.953613i	$-0.597332\pi$
$149$	−2.66021e20	−0.602070	−0.301035	+	0.953613i	$0.597332\pi$
$150$	0	0
$151$	5.75578e20	1.14769	0.573844	−	0.818965i	$-0.305452\pi$
$151$	5.75578e20	1.14769	0.573844	+	0.818965i	$0.305452\pi$
$152$	−6.55604e20	−1.22780
$153$	−3.15855e20	−0.555801
$154$	1.25067e17	0.000206869 0
$155$	0	0
$156$	−8.07949e20	−1.18223
$157$	1.07238e21	1.47673	0.738363	−	0.674403i	$-0.235599\pi$
$157$	1.07238e21	1.47673	0.738363	+	0.674403i	$0.235599\pi$
$158$	4.20556e19	0.0545232
$159$	1.51735e21	1.85273
$160$	0	0
$161$	−2.37464e20	−0.257485
$162$	4.61699e20	0.472026
$163$	5.80765e20	0.560039	0.280019	−	0.959994i	$-0.409659\pi$
$163$	5.80765e20	0.560039	0.280019	+	0.959994i	$0.409659\pi$
$164$	1.04712e21	0.952752
$165$	0	0
$166$	5.51096e20	0.446889
$167$	−2.43392e20	−0.186423	−0.0932117	−	0.995646i	$-0.529713\pi$
$167$	−2.43392e20	−0.186423	−0.0932117	+	0.995646i	$0.529713\pi$
$168$	−3.28480e20	−0.237723
$169$	1.08042e21	0.739041
$170$	0	0
$171$	−2.40014e21	−1.46816
$172$	3.56818e20	0.206503
$173$	1.19350e21	0.653711	0.326855	−	0.945074i	$-0.394011\pi$
$173$	1.19350e21	0.653711	0.326855	+	0.945074i	$0.394011\pi$
$174$	2.62809e19	0.0136277
$175$	0	0
$176$	1.44932e17	6.74210e−5 0
$177$	−2.95764e21	−1.30377
$178$	−1.99327e21	−0.832867
$179$	−4.14664e21	−1.64283	−0.821415	−	0.570331i	$-0.806815\pi$
$179$	−4.14664e21	−1.64283	−0.821415	+	0.570331i	$0.806815\pi$
$180$	0	0
$181$	3.32364e21	1.18486	0.592430	−	0.805622i	$-0.298169\pi$
$181$	3.32364e21	1.18486	0.592430	+	0.805622i	$0.298169\pi$
$182$	3.88973e20	0.131595
$183$	−1.18392e21	−0.380223
$184$	−5.38065e21	−1.64084
$185$	0	0
$186$	−2.41660e21	−0.665015
$187$	3.64886e18	0.000954250 0
$188$	1.10682e21	0.275155
$189$	−2.06602e20	−0.0488369
$190$	0	0
$191$	6.19380e21	1.32477	0.662384	−	0.749164i	$-0.269545\pi$
$191$	6.19380e21	1.32477	0.662384	+	0.749164i	$0.269545\pi$
$192$	−4.78526e21	−0.973966
$193$	5.20697e21	1.00877	0.504383	−	0.863480i	$-0.331720\pi$
$193$	5.20697e21	1.00877	0.504383	+	0.863480i	$0.331720\pi$
$194$	−2.89566e20	−0.0534111
$195$	0	0
$196$	3.51552e21	0.588244
$197$	−2.42384e21	−0.386433	−0.193216	−	0.981156i	$-0.561892\pi$
$197$	−2.42384e21	−0.386433	−0.193216	+	0.981156i	$0.561892\pi$
$198$	1.03747e19	0.00157636
$199$	−1.05907e21	−0.153399	−0.0766993	−	0.997054i	$-0.524438\pi$
$199$	−1.05907e21	−0.153399	−0.0766993	+	0.997054i	$0.524438\pi$
$200$	0	0
$201$	−1.03889e22	−1.36837
$202$	6.48668e21	0.815051
$203$	1.92494e19	0.00230783
$204$	−3.60649e21	−0.412666
$205$	0	0
$206$	2.23773e21	0.233383
$207$	−1.96984e22	−1.96206
$208$	4.50757e20	0.0428885
$209$	2.77272e19	0.00252067
$210$	0	0
$211$	−1.32424e22	−1.09972	−0.549861	−	0.835256i	$-0.685319\pi$
$211$	−1.32424e22	−1.09972	−0.549861	+	0.835256i	$0.685319\pi$
$212$	9.47673e21	0.752433
$213$	9.01111e21	0.684183
$214$	1.20669e22	0.876325
$215$	0	0
$216$	−4.68137e21	−0.311216
$217$	−1.77003e21	−0.112619
$218$	8.39851e21	0.511523
$219$	1.51882e22	0.885701
$220$	0	0
$221$	1.13484e22	0.607027
$222$	3.91251e21	0.200494
$223$	−2.00921e22	−0.986575	−0.493287	−	0.869866i	$-0.664205\pi$
$223$	−2.00921e22	−0.986575	−0.493287	+	0.869866i	$0.664205\pi$
$224$	−3.33106e21	−0.156757
$225$	0	0
$226$	1.17384e22	0.507667
$227$	2.03494e22	0.843929	0.421965	−	0.906612i	$-0.361341\pi$
$227$	2.03494e22	0.843929	0.421965	+	0.906612i	$0.361341\pi$
$228$	−2.74053e22	−1.09007
$229$	−3.99900e22	−1.52586	−0.762930	−	0.646481i	$-0.776240\pi$
$229$	−3.99900e22	−1.52586	−0.762930	+	0.646481i	$0.776240\pi$
$230$	0	0
$231$	1.38923e19	0.000488045 0
$232$	4.36168e20	0.0147068
$233$	−2.42170e22	−0.783862	−0.391931	−	0.919995i	$-0.628193\pi$
$233$	−2.42170e22	−0.783862	−0.391931	+	0.919995i	$0.628193\pi$
$234$	3.22665e22	1.00277
$235$	0	0
$236$	−1.84722e22	−0.529487
$237$	4.67149e21	0.128631
$238$	1.73628e21	0.0459345
$239$	2.62411e22	0.667116	0.333558	−	0.942730i	$-0.391751\pi$
$239$	2.62411e22	0.667116	0.333558	+	0.942730i	$0.391751\pi$
$240$	0	0
$241$	7.36445e22	1.72973	0.864865	−	0.502004i	$-0.167404\pi$
$241$	7.36445e22	1.72973	0.864865	+	0.502004i	$0.167404\pi$
$242$	2.78884e22	0.629764
$243$	6.54789e22	1.42181
$244$	−7.39431e21	−0.154417
$245$	0	0
$246$	−7.64518e22	−1.47742
$247$	8.62350e22	1.60348
$248$	−4.01068e22	−0.717674
$249$	6.12151e22	1.05430
$250$	0	0
$251$	7.29309e22	1.16416	0.582078	−	0.813133i	$-0.302240\pi$
$251$	7.29309e22	1.16416	0.582078	+	0.813133i	$0.302240\pi$
$252$	−7.51066e21	−0.115444
$253$	2.27562e20	0.00336864
$254$	4.01608e22	0.572641
$255$	0	0
$256$	−7.69607e22	−1.01857
$257$	6.38120e22	0.813838	0.406919	−	0.913464i	$-0.366603\pi$
$257$	6.38120e22	0.813838	0.406919	+	0.913464i	$0.366603\pi$
$258$	−2.60518e22	−0.320221
$259$	2.86570e21	0.0339534
$260$	0	0
$261$	1.59680e21	0.0175859
$262$	−3.27996e22	−0.348342
$263$	1.35820e23	1.39118	0.695590	−	0.718439i	$-0.255143\pi$
$263$	1.35820e23	1.39118	0.695590	+	0.718439i	$0.255143\pi$
$264$	3.14783e20	0.00311010
$265$	0	0
$266$	1.31938e22	0.121337
$267$	−2.21410e23	−1.96490
$268$	−6.48846e22	−0.555726
$269$	−1.33672e23	−1.10508	−0.552540	−	0.833486i	$-0.686341\pi$
$269$	−1.33672e23	−1.10508	−0.552540	+	0.833486i	$0.686341\pi$
$270$	0	0
$271$	2.00548e23	1.54529	0.772643	−	0.634840i	$-0.218934\pi$
$271$	2.00548e23	1.54529	0.772643	+	0.634840i	$0.218934\pi$
$272$	2.01207e21	0.0149706
$273$	4.32067e22	0.310460
$274$	−1.34714e23	−0.934939
$275$	0	0
$276$	−2.24919e23	−1.45677
$277$	−2.00223e23	−1.25301	−0.626507	−	0.779416i	$-0.715516\pi$
$277$	−2.00223e23	−1.25301	−0.626507	+	0.779416i	$0.715516\pi$
$278$	−6.31461e22	−0.381875
$279$	−1.46830e23	−0.858170
$280$	0	0
$281$	−1.19239e23	−0.651194	−0.325597	−	0.945509i	$-0.605565\pi$
$281$	−1.19239e23	−0.651194	−0.325597	+	0.945509i	$0.605565\pi$
$282$	−8.08104e22	−0.426679
$283$	3.46108e21	0.0176702	0.00883509	−	0.999961i	$-0.497188\pi$
$283$	3.46108e21	0.0176702	0.00883509	+	0.999961i	$0.497188\pi$
$284$	5.62798e22	0.277861
$285$	0	0
$286$	−3.72753e20	−0.00172165
$287$	−5.59968e22	−0.250199
$288$	−2.76322e23	−1.19450
$289$	−1.88416e23	−0.788112
$290$	0	0
$291$	−3.21647e22	−0.126007
$292$	9.48593e22	0.359702
$293$	2.13236e23	0.782739	0.391370	−	0.920234i	$-0.372001\pi$
$293$	2.13236e23	0.782739	0.391370	+	0.920234i	$0.372001\pi$
$294$	−2.56673e23	−0.912181
$295$	0	0
$296$	6.49335e22	0.216370
$297$	1.97987e20	0.000638927 0
$298$	1.21306e23	0.379164
$299$	7.07745e23	2.14289
$300$	0	0
$301$	−1.90815e22	−0.0542290
$302$	−2.62464e23	−0.722776
$303$	7.20534e23	1.92287
$304$	1.52895e22	0.0395452
$305$	0	0
$306$	1.44030e23	0.350025
$307$	−1.91887e23	−0.452097	−0.226048	−	0.974116i	$-0.572581\pi$
$307$	−1.91887e23	−0.452097	−0.226048	+	0.974116i	$0.572581\pi$
$308$	8.67656e19	0.000198205 0
$309$	2.48564e23	0.550596
$310$	0	0
$311$	−1.54522e23	−0.321933	−0.160967	−	0.986960i	$-0.551461\pi$
$311$	−1.54522e23	−0.321933	−0.160967	+	0.986960i	$0.551461\pi$
$312$	9.79013e23	1.97843
$313$	−2.87408e23	−0.563413	−0.281707	−	0.959501i	$-0.590900\pi$
$313$	−2.87408e23	−0.563413	−0.281707	+	0.959501i	$0.590900\pi$
$314$	−4.89003e23	−0.929994
$315$	0	0
$316$	2.91762e22	0.0522398
$317$	−2.63533e22	−0.0457901	−0.0228950	−	0.999738i	$-0.507288\pi$
$317$	−2.63533e22	−0.0457901	−0.0228950	+	0.999738i	$0.507288\pi$
$318$	−6.91910e23	−1.16679
$319$	−1.84467e19	−3.01931e−5 0
$320$	0	0
$321$	1.34038e24	2.06743
$322$	1.08283e23	0.162155
$323$	3.84933e23	0.559707
$324$	3.20306e23	0.452259
$325$	0	0
$326$	−2.64829e23	−0.352694
$327$	9.32897e23	1.20679
$328$	−1.26882e24	−1.59441
$329$	−5.91893e22	−0.0722574
$330$	0	0
$331$	−1.05338e24	−1.21400	−0.606998	−	0.794703i	$-0.707626\pi$
$331$	−1.05338e24	−1.21400	−0.606998	+	0.794703i	$0.707626\pi$
$332$	3.82325e23	0.428175
$333$	2.37719e23	0.258728
$334$	1.10987e23	0.117403
$335$	0	0
$336$	7.66055e21	0.00765661
$337$	−6.76160e23	−0.657000	−0.328500	−	0.944504i	$-0.606543\pi$
$337$	−6.76160e23	−0.657000	−0.328500	+	0.944504i	$0.606543\pi$
$338$	−4.92671e23	−0.465424
$339$	1.30389e24	1.19769
$340$	0	0
$341$	1.69622e21	0.00147338
$342$	1.09447e24	0.924600
$343$	−3.80841e23	−0.312932
$344$	−4.32365e23	−0.345578
$345$	0	0
$346$	−5.44237e23	−0.411685
$347$	−1.06325e24	−0.782535	−0.391268	−	0.920277i	$-0.627963\pi$
$347$	−1.06325e24	−0.782535	−0.391268	+	0.920277i	$0.627963\pi$
$348$	1.82325e22	0.0130570
$349$	−7.14667e23	−0.498037	−0.249019	−	0.968499i	$-0.580108\pi$
$349$	−7.14667e23	−0.498037	−0.249019	+	0.968499i	$0.580108\pi$
$350$	0	0
$351$	6.15764e23	0.406440
$352$	3.19216e21	0.00205083
$353$	5.07321e23	0.317266	0.158633	−	0.987338i	$-0.449291\pi$
$353$	5.07321e23	0.317266	0.158633	+	0.987338i	$0.449291\pi$
$354$	1.34868e24	0.821068
$355$	0	0
$356$	−1.38284e24	−0.797988
$357$	1.92864e23	0.108369
$358$	1.89087e24	1.03460
$359$	3.32006e24	1.76909	0.884544	−	0.466458i	$-0.154470\pi$
$359$	3.32006e24	1.76909	0.884544	+	0.466458i	$0.154470\pi$
$360$	0	0
$361$	9.46633e23	0.478479
$362$	−1.51558e24	−0.746186
$363$	3.09782e24	1.48574
$364$	2.69851e23	0.126084
$365$	0	0
$366$	5.39869e23	0.239452
$367$	2.24430e24	0.969958	0.484979	−	0.874526i	$-0.338827\pi$
$367$	2.24430e24	0.969958	0.484979	+	0.874526i	$0.338827\pi$
$368$	1.25483e23	0.0528484
$369$	−4.64511e24	−1.90654
$370$	0	0
$371$	−5.06787e23	−0.197594
$372$	−1.67653e24	−0.637166
$373$	−5.10606e24	−1.89170	−0.945850	−	0.324603i	$-0.894769\pi$
$373$	−5.10606e24	−1.89170	−0.945850	+	0.324603i	$0.894769\pi$
$374$	−1.66388e21	−0.000600955 0
$375$	0	0
$376$	−1.34116e24	−0.460465
$377$	−5.73715e22	−0.0192067
$378$	9.42106e22	0.0307559
$379$	−4.28975e24	−1.36571	−0.682857	−	0.730552i	$-0.739263\pi$
$379$	−4.28975e24	−1.36571	−0.682857	+	0.730552i	$0.739263\pi$
$380$	0	0
$381$	4.46102e24	1.35098
$382$	−2.82437e24	−0.834295
$383$	1.86803e24	0.538264	0.269132	−	0.963103i	$-0.413263\pi$
$383$	1.86803e24	0.538264	0.269132	+	0.963103i	$0.413263\pi$
$384$	−3.04684e24	−0.856451
$385$	0	0
$386$	−2.37438e24	−0.635288
$387$	−1.58287e24	−0.413230
$388$	−2.00888e23	−0.0511743
$389$	−6.47448e24	−1.60947	−0.804737	−	0.593632i	$-0.797694\pi$
$389$	−6.47448e24	−1.60947	−0.804737	+	0.593632i	$0.797694\pi$
$390$	0	0
$391$	3.15920e24	0.747995
$392$	−4.25985e24	−0.984411
$393$	−3.64334e24	−0.821809
$394$	1.10527e24	0.243363
$395$	0	0
$396$	7.19748e21	0.00151034
$397$	−1.22760e24	−0.251505	−0.125752	−	0.992062i	$-0.540134\pi$
$397$	−1.22760e24	−0.251505	−0.125752	+	0.992062i	$0.540134\pi$
$398$	4.82937e23	0.0966054
$399$	1.46555e24	0.286258
$400$	0	0
$401$	−5.17895e23	−0.0964651	−0.0482326	−	0.998836i	$-0.515359\pi$
$401$	−5.17895e23	−0.0964651	−0.0482326	+	0.998836i	$0.515359\pi$
$402$	4.73732e24	0.861757
$403$	5.27546e24	0.937264
$404$	4.50017e24	0.780918
$405$	0	0
$406$	−8.77772e21	−0.00145340
$407$	−2.74621e21	−0.000444208 0
$408$	4.37008e24	0.690586
$409$	2.81877e24	0.435199	0.217599	−	0.976038i	$-0.430177\pi$
$409$	2.81877e24	0.435199	0.217599	+	0.976038i	$0.430177\pi$
$410$	0	0
$411$	−1.49639e25	−2.20571
$412$	1.55243e24	0.223609
$413$	9.87839e23	0.139047
$414$	8.98245e24	1.23564
$415$	0	0
$416$	9.92800e24	1.30459
$417$	−7.01420e24	−0.900919
$418$	−1.26436e22	−0.00158744
$419$	8.65571e24	1.06235	0.531177	−	0.847261i	$-0.321750\pi$
$419$	8.65571e24	1.06235	0.531177	+	0.847261i	$0.321750\pi$
$420$	0	0
$421$	−5.21652e24	−0.611929	−0.305964	−	0.952043i	$-0.598979\pi$
$421$	−5.21652e24	−0.611929	−0.305964	+	0.952043i	$0.598979\pi$
$422$	6.03853e24	0.692569
$423$	−4.90994e24	−0.550608
$424$	−1.14832e25	−1.25918
$425$	0	0
$426$	−4.10907e24	−0.430876
$427$	3.95425e23	0.0405508
$428$	8.37147e24	0.839626
$429$	−4.14050e22	−0.00406171
$430$	0	0
$431$	1.04364e25	0.979526	0.489763	−	0.871856i	$-0.337083\pi$
$431$	1.04364e25	0.979526	0.489763	+	0.871856i	$0.337083\pi$
$432$	1.09175e23	0.0100237
$433$	−1.45110e25	−1.30335	−0.651675	−	0.758499i	$-0.725933\pi$
$433$	−1.45110e25	−1.30335	−0.651675	+	0.758499i	$0.725933\pi$
$434$	8.07134e23	0.0709240
$435$	0	0
$436$	5.82650e24	0.490102
$437$	2.40064e25	1.97585
$438$	−6.92582e24	−0.557785
$439$	1.79857e25	1.41747	0.708735	−	0.705474i	$-0.249266\pi$
$439$	1.79857e25	1.41747	0.708735	+	0.705474i	$0.249266\pi$
$440$	0	0
$441$	−1.55951e25	−1.17713
$442$	−5.17487e24	−0.382286
$443$	−8.73685e24	−0.631712	−0.315856	−	0.948807i	$-0.602292\pi$
$443$	−8.73685e24	−0.631712	−0.315856	+	0.948807i	$0.602292\pi$
$444$	2.71432e24	0.192098
$445$	0	0
$446$	9.16201e24	0.621312
$447$	1.34745e25	0.894523
$448$	1.59826e24	0.103874
$449$	−1.60576e25	−1.02174	−0.510870	−	0.859658i	$-0.670677\pi$
$449$	−1.60576e25	−1.02174	−0.510870	+	0.859658i	$0.670677\pi$
$450$	0	0
$451$	5.36618e22	0.00327332
$452$	8.14357e24	0.486407
$453$	−2.91542e25	−1.70517
$454$	−9.27933e24	−0.531479
$455$	0	0
$456$	3.32077e25	1.82420
$457$	2.67587e24	0.143966	0.0719831	−	0.997406i	$-0.477067\pi$
$457$	2.67587e24	0.143966	0.0719831	+	0.997406i	$0.477067\pi$
$458$	1.82355e25	0.960936
$459$	2.74863e24	0.141871
$460$	0	0
$461$	6.96807e24	0.345107	0.172553	−	0.985000i	$-0.444798\pi$
$461$	6.96807e24	0.345107	0.172553	+	0.985000i	$0.444798\pi$
$462$	−6.33488e21	−0.000307354 0
$463$	2.49843e25	1.18754	0.593770	−	0.804635i	$-0.297639\pi$
$463$	2.49843e25	1.18754	0.593770	+	0.804635i	$0.297639\pi$
$464$	−1.01720e22	−0.000473679 0
$465$	0	0
$466$	1.10430e25	0.493650
$467$	−1.94531e25	−0.852075	−0.426037	−	0.904706i	$-0.640091\pi$
$467$	−1.94531e25	−0.852075	−0.426037	+	0.904706i	$0.640091\pi$
$468$	2.23850e25	0.960776
$469$	3.46983e24	0.145937
$470$	0	0
$471$	−5.43180e25	−2.19404
$472$	2.23833e25	0.886084
$473$	1.82859e22	0.000709471 0
$474$	−2.13020e24	−0.0810076
$475$	0	0
$476$	1.20455e24	0.0440108
$477$	−4.20396e25	−1.50568
$478$	−1.19659e25	−0.420128
$479$	3.34153e25	1.15016	0.575080	−	0.818097i	$-0.304971\pi$
$479$	3.34153e25	1.15016	0.575080	+	0.818097i	$0.304971\pi$
$480$	0	0
$481$	−8.54103e24	−0.282574
$482$	−3.35819e25	−1.08933
$483$	1.20280e25	0.382557
$484$	1.93477e25	0.603391
$485$	0	0
$486$	−2.98584e25	−0.895410
$487$	4.86181e25	1.42979	0.714896	−	0.699231i	$-0.246474\pi$
$487$	4.86181e25	1.42979	0.714896	+	0.699231i	$0.246474\pi$
$488$	8.95988e24	0.258413
$489$	−2.94169e25	−0.832075
$490$	0	0
$491$	9.86730e24	0.268488	0.134244	−	0.990948i	$-0.457139\pi$
$491$	9.86730e24	0.268488	0.134244	+	0.990948i	$0.457139\pi$
$492$	−5.30387e25	−1.41555
$493$	−2.56093e23	−0.00670427
$494$	−3.93232e25	−1.00982
$495$	0	0
$496$	9.35339e23	0.0231150
$497$	−3.00967e24	−0.0729681
$498$	−2.79141e25	−0.663964
$499$	−3.54150e25	−0.826481	−0.413240	−	0.910622i	$-0.635603\pi$
$499$	−3.54150e25	−0.826481	−0.413240	+	0.910622i	$0.635603\pi$
$500$	0	0
$501$	1.23283e25	0.276978
$502$	−3.32565e25	−0.733147
$503$	−1.47204e25	−0.318436	−0.159218	−	0.987243i	$-0.550897\pi$
$503$	−1.47204e25	−0.318436	−0.159218	+	0.987243i	$0.550897\pi$
$504$	9.10086e24	0.193193
$505$	0	0
$506$	−1.03768e23	−0.00212146
$507$	−5.47254e25	−1.09803
$508$	2.78618e25	0.548660
$509$	−4.88290e25	−0.943754	−0.471877	−	0.881664i	$-0.656423\pi$
$509$	−4.88290e25	−0.943754	−0.471877	+	0.881664i	$0.656423\pi$
$510$	0	0
$511$	−5.07279e24	−0.0944601
$512$	3.55692e24	0.0650143
$513$	2.08864e25	0.374757
$514$	−2.90983e25	−0.512528
$515$	0	0
$516$	−1.80735e25	−0.306811
$517$	5.67212e22	0.000945334 0
$518$	−1.30676e24	−0.0213827
$519$	−6.04533e25	−0.971248
$520$	0	0
$521$	7.14445e25	1.10665	0.553325	−	0.832965i	$-0.313359\pi$
$521$	7.14445e25	1.10665	0.553325	+	0.832965i	$0.313359\pi$
$522$	−7.28139e23	−0.0110750
$523$	−8.99895e25	−1.34408	−0.672041	−	0.740514i	$-0.734582\pi$
$523$	−8.99895e25	−1.34408	−0.672041	+	0.740514i	$0.734582\pi$
$524$	−2.27548e25	−0.333754
$525$	0	0
$526$	−6.19338e25	−0.876120
$527$	2.35484e25	0.327160
$528$	−7.34111e21	−0.000100170 0
$529$	1.22409e26	1.64053
$530$	0	0
$531$	8.19444e25	1.05955
$532$	9.15324e24	0.116256
$533$	1.66895e26	2.08226
$534$	1.00963e26	1.23743
$535$	0	0
$536$	7.86223e25	0.929995
$537$	2.10036e26	2.44083
$538$	6.09544e25	0.695943
$539$	1.80160e23	0.00202100
$540$	0	0
$541$	−9.33602e25	−1.01109	−0.505543	−	0.862802i	$-0.668708\pi$
$541$	−9.33602e25	−1.01109	−0.505543	+	0.862802i	$0.668708\pi$
$542$	−9.14497e25	−0.973171
$543$	−1.68349e26	−1.76040
$544$	4.43162e25	0.455379
$545$	0	0
$546$	−1.97022e25	−0.195517
$547$	2.74670e25	0.267875	0.133938	−	0.990990i	$-0.457238\pi$
$547$	2.74670e25	0.267875	0.133938	+	0.990990i	$0.457238\pi$
$548$	−9.34587e25	−0.895786
$549$	3.28018e25	0.309001
$550$	0	0
$551$	−1.94602e24	−0.0177095
$552$	2.72541e26	2.43787
$553$	−1.56026e24	−0.0137185
$554$	9.13016e25	0.789106
$555$	0	0
$556$	−4.38079e25	−0.365882
$557$	−1.42589e26	−1.17074	−0.585370	−	0.810766i	$-0.699051\pi$
$557$	−1.42589e26	−1.17074	−0.585370	+	0.810766i	$0.699051\pi$
$558$	6.69543e25	0.540447
$559$	5.68712e25	0.451316
$560$	0	0
$561$	−1.84822e23	−0.00141777
$562$	5.43732e25	0.410100
$563$	1.72252e26	1.27742	0.638712	−	0.769446i	$-0.279467\pi$
$563$	1.72252e26	1.27742	0.638712	+	0.769446i	$0.279467\pi$
$564$	−5.60626e25	−0.408810
$565$	0	0
$566$	−1.57825e24	−0.0111281
$567$	−1.71290e25	−0.118766
$568$	−6.81956e25	−0.464994
$569$	5.24893e25	0.351969	0.175984	−	0.984393i	$-0.443689\pi$
$569$	5.24893e25	0.351969	0.175984	+	0.984393i	$0.443689\pi$
$570$	0	0
$571$	−3.21674e24	−0.0208628	−0.0104314	−	0.999946i	$-0.503320\pi$
$571$	−3.21674e24	−0.0208628	−0.0104314	+	0.999946i	$0.503320\pi$
$572$	−2.58599e23	−0.00164955
$573$	−3.13728e26	−1.96827
$574$	2.55345e25	0.157567
$575$	0	0
$576$	1.32580e26	0.791527
$577$	−1.17453e26	−0.689752	−0.344876	−	0.938648i	$-0.612079\pi$
$577$	−1.17453e26	−0.689752	−0.344876	+	0.938648i	$0.612079\pi$
$578$	8.59176e25	0.496327
$579$	−2.63744e26	−1.49877
$580$	0	0
$581$	−2.04456e25	−0.112441
$582$	1.46671e25	0.0793553
$583$	4.85655e23	0.00258509
$584$	−1.14943e26	−0.601953
$585$	0	0
$586$	−9.72354e25	−0.492943
$587$	−1.86886e24	−0.00932213	−0.00466107	−	0.999989i	$-0.501484\pi$
$587$	−1.86886e24	−0.00932213	−0.00466107	+	0.999989i	$0.501484\pi$
$588$	−1.78068e26	−0.873981
$589$	1.78941e26	0.864201
$590$	0	0
$591$	1.22772e26	0.574141
$592$	−1.51433e24	−0.00696889
$593$	1.50165e26	0.680063	0.340032	−	0.940414i	$-0.389562\pi$
$593$	1.50165e26	0.680063	0.340032	+	0.940414i	$0.389562\pi$
$594$	−9.02822e22	−0.000402375 0
$595$	0	0
$596$	8.41563e25	0.363285
$597$	5.36441e25	0.227911
$598$	−3.22732e26	−1.34952
$599$	1.65804e26	0.682403	0.341201	−	0.939990i	$-0.389166\pi$
$599$	1.65804e26	0.682403	0.341201	+	0.939990i	$0.389166\pi$
$600$	0	0
$601$	−2.54795e26	−1.01598	−0.507989	−	0.861364i	$-0.669611\pi$
$601$	−2.54795e26	−1.01598	−0.507989	+	0.861364i	$0.669611\pi$
$602$	8.70118e24	0.0341516
$603$	2.87833e26	1.11206
$604$	−1.82085e26	−0.692507
$605$	0	0
$606$	−3.28564e26	−1.21096
$607$	−3.14191e26	−1.13999	−0.569996	−	0.821648i	$-0.693055\pi$
$607$	−3.14191e26	−1.13999	−0.569996	+	0.821648i	$0.693055\pi$
$608$	3.36753e26	1.20290
$609$	−9.75020e23	−0.00342885
$610$	0	0
$611$	1.76410e26	0.601355
$612$	9.99214e25	0.335367
$613$	3.91478e26	1.29370	0.646848	−	0.762619i	$-0.276087\pi$
$613$	3.91478e26	1.29370	0.646848	+	0.762619i	$0.276087\pi$
$614$	8.75005e25	0.284715
$615$	0	0
$616$	−1.05136e23	−0.000331692 0
$617$	−4.86066e26	−1.51003	−0.755016	−	0.655706i	$-0.772371\pi$
$617$	−4.86066e26	−1.51003	−0.755016	+	0.655706i	$0.772371\pi$
$618$	−1.13345e26	−0.346747
$619$	−4.51098e26	−1.35897	−0.679485	−	0.733689i	$-0.737797\pi$
$619$	−4.51098e26	−1.35897	−0.679485	+	0.733689i	$0.737797\pi$
$620$	0	0
$621$	1.71418e26	0.500827
$622$	7.04619e25	0.202743
$623$	7.39500e25	0.209557
$624$	−2.28318e25	−0.0637215
$625$	0	0
$626$	1.31058e26	0.354819
$627$	−1.40444e24	−0.00374508
$628$	−3.39248e26	−0.891047
$629$	−3.81251e25	−0.0986349
$630$	0	0
$631$	2.03805e26	0.511607	0.255803	−	0.966729i	$-0.417660\pi$
$631$	2.03805e26	0.511607	0.255803	+	0.966729i	$0.417660\pi$
$632$	−3.53536e25	−0.0874221
$633$	6.70753e26	1.63391
$634$	1.20171e25	0.0288371
$635$	0	0
$636$	−4.80016e26	−1.11793
$637$	5.60320e26	1.28562
$638$	8.41170e21	1.90146e−5 0
$639$	−2.49662e26	−0.556024
$640$	0	0
$641$	5.77927e26	1.24946	0.624729	−	0.780842i	$-0.285209\pi$
$641$	5.77927e26	1.24946	0.624729	+	0.780842i	$0.285209\pi$
$642$	−6.11213e26	−1.30200
$643$	−7.72049e26	−1.62047	−0.810235	−	0.586106i	$-0.800660\pi$
$643$	−7.72049e26	−1.62047	−0.810235	+	0.586106i	$0.800660\pi$
$644$	7.51221e25	0.155365
$645$	0	0
$646$	−1.75529e26	−0.352485
$647$	1.39226e24	0.00275504	0.00137752	−	0.999999i	$-0.499562\pi$
$647$	1.39226e24	0.00275504	0.00137752	+	0.999999i	$0.499562\pi$
$648$	−3.88123e26	−0.756844
$649$	−9.46648e23	−0.00181913
$650$	0	0
$651$	8.96556e25	0.167324
$652$	−1.83726e26	−0.337924
$653$	6.19470e26	1.12291	0.561455	−	0.827507i	$-0.310242\pi$
$653$	6.19470e26	1.12291	0.561455	+	0.827507i	$0.310242\pi$
$654$	−4.25401e26	−0.759994
$655$	0	0
$656$	2.95905e25	0.0513530
$657$	−4.20804e26	−0.719795
$658$	2.69903e25	0.0455053
$659$	−7.96627e25	−0.132386	−0.0661932	−	0.997807i	$-0.521085\pi$
$659$	−7.96627e25	−0.132386	−0.0661932	+	0.997807i	$0.521085\pi$
$660$	0	0
$661$	−1.85436e26	−0.299420	−0.149710	−	0.988730i	$-0.547834\pi$
$661$	−1.85436e26	−0.299420	−0.149710	+	0.988730i	$0.547834\pi$
$662$	4.80339e26	0.764535
$663$	−5.74819e26	−0.901888
$664$	−4.63273e26	−0.716540
$665$	0	0
$666$	−1.08400e26	−0.162938
$667$	−1.59713e25	−0.0236670
$668$	7.69977e25	0.112487
$669$	1.01771e27	1.46580
$670$	0	0
$671$	−3.78937e23	−0.000530521 0
$672$	1.68725e26	0.232901
$673$	−5.91532e26	−0.805073	−0.402536	−	0.915404i	$-0.631871\pi$
$673$	−5.91532e26	−0.805073	−0.402536	+	0.915404i	$0.631871\pi$
$674$	3.08329e26	0.413757
$675$	0	0
$676$	−3.41793e26	−0.445933
$677$	2.97418e26	0.382626	0.191313	−	0.981529i	$-0.438725\pi$
$677$	2.97418e26	0.382626	0.191313	+	0.981529i	$0.438725\pi$
$678$	−5.94573e26	−0.754264
$679$	1.07429e25	0.0134387
$680$	0	0
$681$	−1.03074e27	−1.25387
$682$	−7.73477e23	−0.000927889 0
$683$	1.25943e27	1.48997	0.744983	−	0.667084i	$-0.232458\pi$
$683$	1.25943e27	1.48997	0.744983	+	0.667084i	$0.232458\pi$
$684$	7.59290e26	0.885880
$685$	0	0
$686$	1.73663e26	0.197074
$687$	2.02558e27	2.26704
$688$	1.00833e25	0.0111304
$689$	1.51044e27	1.64446
$690$	0	0
$691$	3.19965e25	0.0338891	0.0169446	−	0.999856i	$-0.494606\pi$
$691$	3.19965e25	0.0338891	0.0169446	+	0.999856i	$0.494606\pi$
$692$	−3.77567e26	−0.394445
$693$	−3.84899e23	−0.000396626 0
$694$	4.84840e26	0.492815
$695$	0	0
$696$	−2.20928e25	−0.0218506
$697$	7.44979e26	0.726829
$698$	3.25888e26	0.313648
$699$	1.22664e27	1.16462
$700$	0	0
$701$	2.06463e27	1.90775	0.953874	−	0.300208i	$-0.0970562\pi$
$701$	2.06463e27	1.90775	0.953874	+	0.300208i	$0.0970562\pi$
$702$	−2.80788e26	−0.255963
$703$	−2.89708e26	−0.260546
$704$	−1.53161e24	−0.00135897
$705$	0	0
$706$	−2.31338e26	−0.199803
$707$	−2.40655e26	−0.205074
$708$	9.35656e26	0.786684
$709$	−1.44096e27	−1.19539	−0.597697	−	0.801722i	$-0.703918\pi$
$709$	−1.44096e27	−1.19539	−0.597697	+	0.801722i	$0.703918\pi$
$710$	0	0
$711$	−1.29428e26	−0.104536
$712$	1.67562e27	1.33541
$713$	1.46860e27	1.15492
$714$	−8.79461e25	−0.0682470
$715$	0	0
$716$	1.31180e27	0.991273
$717$	−1.32916e27	−0.991165
$718$	−1.51395e27	−1.11411
$719$	−1.26393e27	−0.917907	−0.458953	−	0.888460i	$-0.651776\pi$
$719$	−1.26393e27	−0.917907	−0.458953	+	0.888460i	$0.651776\pi$
$720$	0	0
$721$	−8.30194e25	−0.0587211
$722$	−4.31665e26	−0.301331
$723$	−3.73024e27	−2.56994
$724$	−1.05144e27	−0.714937
$725$	0	0
$726$	−1.41260e27	−0.935670
$727$	−5.54468e26	−0.362493	−0.181246	−	0.983438i	$-0.558013\pi$
$727$	−5.54468e26	−0.362493	−0.181246	+	0.983438i	$0.558013\pi$
$728$	−3.26986e26	−0.210999
$729$	−2.13985e27	−1.36293
$730$	0	0
$731$	2.53860e26	0.157536
$732$	3.74537e26	0.229424
$733$	−8.06563e26	−0.487698	−0.243849	−	0.969813i	$-0.578410\pi$
$733$	−8.06563e26	−0.487698	−0.243849	+	0.969813i	$0.578410\pi$
$734$	−1.02340e27	−0.610848
$735$	0	0
$736$	2.76379e27	1.60755
$737$	−3.32514e24	−0.00190928
$738$	2.11817e27	1.20068
$739$	6.63850e26	0.371490	0.185745	−	0.982598i	$-0.440530\pi$
$739$	6.63850e26	0.371490	0.185745	+	0.982598i	$0.440530\pi$
$740$	0	0
$741$	−4.36798e27	−2.38236
$742$	2.31095e26	0.124438
$743$	3.64095e27	1.93562	0.967811	−	0.251677i	$-0.0809820\pi$
$743$	3.64095e27	1.93562	0.967811	+	0.251677i	$0.0809820\pi$
$744$	2.03149e27	1.06628
$745$	0	0
$746$	2.32837e27	1.19133
$747$	−1.69603e27	−0.856814
$748$	−1.15432e24	−0.000575788 0
$749$	−4.47681e26	−0.220491
$750$	0	0
$751$	−1.55458e27	−0.746505	−0.373253	−	0.927730i	$-0.621758\pi$
$751$	−1.55458e27	−0.746505	−0.373253	+	0.927730i	$0.621758\pi$
$752$	3.12775e25	0.0148307
$753$	−3.69410e27	−1.72964
$754$	2.61614e25	0.0120958
$755$	0	0
$756$	6.53590e25	0.0294679
$757$	−1.33406e27	−0.593970	−0.296985	−	0.954882i	$-0.595981\pi$
$757$	−1.33406e27	−0.593970	−0.296985	+	0.954882i	$0.595981\pi$
$758$	1.95613e27	0.860081
$759$	−1.15265e25	−0.00500494
$760$	0	0
$761$	−6.89829e25	−0.0292137	−0.0146069	−	0.999893i	$-0.504650\pi$
$761$	−6.89829e25	−0.0292137	−0.0146069	+	0.999893i	$0.504650\pi$
$762$	−2.03423e27	−0.850799
$763$	−3.11584e26	−0.128704
$764$	−1.95942e27	−0.799357
$765$	0	0
$766$	−8.51822e26	−0.338981
$767$	−2.94419e27	−1.15720
$768$	3.89821e27	1.51333
$769$	−8.09673e26	−0.310463	−0.155231	−	0.987878i	$-0.549612\pi$
$769$	−8.09673e26	−0.310463	−0.155231	+	0.987878i	$0.549612\pi$
$770$	0	0
$771$	−3.23221e27	−1.20916
$772$	−1.64724e27	−0.608683
$773$	−1.00924e27	−0.368374	−0.184187	−	0.982891i	$-0.558965\pi$
$773$	−1.00924e27	−0.368374	−0.184187	+	0.982891i	$0.558965\pi$
$774$	7.21790e26	0.260239
$775$	0	0
$776$	2.43421e26	0.0856389
$777$	−1.45154e26	−0.0504461
$778$	2.95236e27	1.01359
$779$	5.66100e27	1.91994
$780$	0	0
$781$	2.88417e24	0.000954633 0
$782$	−1.44060e27	−0.471062
$783$	−1.38956e25	−0.00448890
$784$	9.93448e25	0.0317061
$785$	0	0
$786$	1.66136e27	0.517548
$787$	4.88307e27	1.50291	0.751456	−	0.659784i	$-0.229352\pi$
$787$	4.88307e27	1.50291	0.751456	+	0.659784i	$0.229352\pi$
$788$	7.66785e26	0.233171
$789$	−6.87955e27	−2.06694
$790$	0	0
$791$	−4.35493e26	−0.127733
$792$	−8.72137e24	−0.00252752
$793$	−1.17854e27	−0.337480
$794$	5.59784e26	0.158389
$795$	0	0
$796$	3.35040e26	0.0925598
$797$	−1.18346e27	−0.323072	−0.161536	−	0.986867i	$-0.551645\pi$
$797$	−1.18346e27	−0.323072	−0.161536	+	0.986867i	$0.551645\pi$
$798$	−6.68291e26	−0.180276
$799$	7.87451e26	0.209908
$800$	0	0
$801$	6.13438e27	1.59684
$802$	2.36160e26	0.0607506
$803$	4.86126e24	0.00123581
$804$	3.28653e27	0.825669
$805$	0	0
$806$	−2.40561e27	−0.590258
$807$	6.77075e27	1.64187
$808$	−5.45297e27	−1.30685
$809$	−5.08495e27	−1.20441	−0.602207	−	0.798340i	$-0.705712\pi$
$809$	−5.08495e27	−1.20441	−0.602207	+	0.798340i	$0.705712\pi$
$810$	0	0
$811$	−2.72133e25	−0.00629627	−0.00314813	−	0.999995i	$-0.501002\pi$
$811$	−2.72133e25	−0.00629627	−0.00314813	+	0.999995i	$0.501002\pi$
$812$	−6.08958e24	−0.00139253
$813$	−1.01581e28	−2.29590
$814$	1.25227e24	0.000279748 0
$815$	0	0
$816$	−1.01916e26	−0.0222425
$817$	1.92905e27	0.416134
$818$	−1.28536e27	−0.274074
$819$	−1.19708e27	−0.252306
$820$	0	0
$821$	−5.16381e26	−0.106343	−0.0531716	−	0.998585i	$-0.516933\pi$
$821$	−5.16381e26	−0.106343	−0.0531716	+	0.998585i	$0.516933\pi$
$822$	6.82355e27	1.38908
$823$	1.97624e27	0.397687	0.198843	−	0.980031i	$-0.436282\pi$
$823$	1.97624e27	0.397687	0.198843	+	0.980031i	$0.436282\pi$
$824$	−1.88112e27	−0.374204
$825$	0	0
$826$	−4.50455e26	−0.0875670
$827$	1.16795e27	0.224450	0.112225	−	0.993683i	$-0.464202\pi$
$827$	1.16795e27	0.224450	0.112225	+	0.993683i	$0.464202\pi$
$828$	6.23162e27	1.18389
$829$	4.20809e27	0.790345	0.395173	−	0.918607i	$-0.370685\pi$
$829$	4.20809e27	0.790345	0.395173	+	0.918607i	$0.370685\pi$
$830$	0	0
$831$	1.01417e28	1.86166
$832$	−4.76350e27	−0.864479
$833$	2.50113e27	0.448755
$834$	3.19848e27	0.567369
$835$	0	0
$836$	−8.77156e24	−0.00152096
$837$	1.27774e27	0.219053
$838$	−3.94700e27	−0.669036
$839$	8.49254e27	1.42331	0.711654	−	0.702530i	$-0.247947\pi$
$839$	8.49254e27	1.42331	0.711654	+	0.702530i	$0.247947\pi$
$840$	0	0
$841$	−6.10197e27	−0.999788
$842$	2.37873e27	0.385372
$843$	6.03972e27	0.967508
$844$	4.18926e27	0.663565
$845$	0	0
$846$	2.23893e27	0.346755
$847$	−1.03466e27	−0.158454
$848$	2.67802e26	0.0405558
$849$	−1.75311e26	−0.0262534
$850$	0	0
$851$	−2.37768e27	−0.348195
$852$	−2.85068e27	−0.412831
$853$	9.33345e27	1.33668	0.668338	−	0.743857i	$-0.267006\pi$
$853$	9.33345e27	1.33668	0.668338	+	0.743857i	$0.267006\pi$
$854$	−1.80314e26	−0.0255376
$855$	0	0
$856$	−1.01439e28	−1.40509
$857$	1.11037e28	1.52108	0.760539	−	0.649292i	$-0.224935\pi$
$857$	1.11037e28	1.52108	0.760539	+	0.649292i	$0.224935\pi$
$858$	1.88807e25	0.00255793
$859$	1.11478e28	1.49367	0.746834	−	0.665011i	$-0.231573\pi$
$859$	1.11478e28	1.49367	0.746834	+	0.665011i	$0.231573\pi$
$860$	0	0
$861$	2.83635e27	0.371732
$862$	−4.75899e27	−0.616873
$863$	−1.15445e28	−1.48004	−0.740021	−	0.672583i	$-0.765185\pi$
$863$	−1.15445e28	−1.48004	−0.740021	+	0.672583i	$0.765185\pi$
$864$	2.40460e27	0.304903
$865$	0	0
$866$	6.61699e27	0.820806
$867$	9.54364e27	1.17093
$868$	5.59952e26	0.0679538
$869$	1.49520e24	0.000179478 0
$870$	0	0
$871$	−1.03416e28	−1.21455
$872$	−7.06012e27	−0.820173
$873$	8.91154e26	0.102404
$874$	−1.09469e28	−1.24432
$875$	0	0
$876$	−4.80482e27	−0.534426
$877$	−1.55912e28	−1.71547	−0.857734	−	0.514094i	$-0.828128\pi$
$877$	−1.55912e28	−1.71547	−0.857734	+	0.514094i	$0.828128\pi$
$878$	−8.20147e27	−0.892676
$879$	−1.08008e28	−1.16295
$880$	0	0
$881$	3.35920e26	0.0353969	0.0176985	−	0.999843i	$-0.494366\pi$
$881$	3.35920e26	0.0353969	0.0176985	+	0.999843i	$0.494366\pi$
$882$	7.11139e27	0.741315
$883$	1.34374e26	0.0138576	0.00692882	−	0.999976i	$-0.497794\pi$
$883$	1.34374e26	0.0138576	0.00692882	+	0.999976i	$0.497794\pi$
$884$	−3.59009e27	−0.366276
$885$	0	0
$886$	3.98400e27	0.397832
$887$	−9.23887e27	−0.912735	−0.456367	−	0.889791i	$-0.650850\pi$
$887$	−9.23887e27	−0.912735	−0.456367	+	0.889791i	$0.650850\pi$
$888$	−3.28901e27	−0.321471
$889$	−1.48996e27	−0.144082
$890$	0	0
$891$	1.64147e25	0.00155380
$892$	6.35619e27	0.595293
$893$	5.98374e27	0.554478
$894$	−6.14437e27	−0.563341
$895$	0	0
$896$	1.01763e27	0.0913406
$897$	−3.58487e28	−3.18379
$898$	7.32226e27	0.643458
$899$	−1.19048e26	−0.0103516
$900$	0	0
$901$	6.74227e27	0.574011
$902$	−2.44698e25	−0.00206143
$903$	9.66517e26	0.0805705
$904$	−9.86777e27	−0.813990
$905$	0	0
$906$	1.32943e28	1.07386
$907$	1.80585e28	1.44349	0.721743	−	0.692161i	$-0.243341\pi$
$907$	1.80585e28	1.44349	0.721743	+	0.692161i	$0.243341\pi$
$908$	−6.43758e27	−0.509222
$909$	−1.99631e28	−1.56268
$910$	0	0
$911$	−1.99304e28	−1.52789	−0.763943	−	0.645283i	$-0.776739\pi$
$911$	−1.99304e28	−1.52789	−0.763943	+	0.645283i	$0.776739\pi$
$912$	−7.74443e26	−0.0587541
$913$	1.95930e25	0.00147106
$914$	−1.22020e27	−0.0906651
$915$	0	0
$916$	1.26509e28	0.920694
$917$	1.21686e27	0.0876460
$918$	−1.25337e27	−0.0893460
$919$	1.04320e28	0.735984	0.367992	−	0.929829i	$-0.380045\pi$
$919$	1.04320e28	0.735984	0.367992	+	0.929829i	$0.380045\pi$
$920$	0	0
$921$	9.71946e27	0.671701
$922$	−3.17744e27	−0.217337
$923$	8.97012e27	0.607271
$924$	−4.39485e24	−0.000294483 0
$925$	0	0
$926$	−1.13929e28	−0.747874
$927$	−6.88672e27	−0.447461
$928$	−2.24039e26	−0.0144085
$929$	−5.17736e27	−0.329578	−0.164789	−	0.986329i	$-0.552694\pi$
$929$	−5.17736e27	−0.329578	−0.164789	+	0.986329i	$0.552694\pi$
$930$	0	0
$931$	1.90058e28	1.18540
$932$	7.66111e27	0.472977
$933$	7.82683e27	0.478311
$934$	8.87060e27	0.536609
$935$	0	0
$936$	−2.71245e28	−1.60783
$937$	−9.33202e27	−0.547582	−0.273791	−	0.961789i	$-0.588278\pi$
$937$	−9.33202e27	−0.547582	−0.273791	+	0.961789i	$0.588278\pi$
$938$	−1.58224e27	−0.0919065
$939$	1.45578e28	0.837089
$940$	0	0
$941$	4.50115e27	0.253642	0.126821	−	0.991926i	$-0.459523\pi$
$941$	4.50115e27	0.253642	0.126821	+	0.991926i	$0.459523\pi$
$942$	2.47690e28	1.38173
$943$	4.64607e28	2.56581
$944$	−5.22005e26	−0.0285391
$945$	0	0
$946$	−8.33835e24	−0.000446801 0
$947$	−1.76126e28	−0.934324	−0.467162	−	0.884172i	$-0.654724\pi$
$947$	−1.76126e28	−0.934324	−0.467162	+	0.884172i	$0.654724\pi$
$948$	−1.47783e27	−0.0776151
$949$	1.51191e28	0.786135
$950$	0	0
$951$	1.33485e27	0.0680325
$952$	−1.45959e27	−0.0736511
$953$	−5.93730e27	−0.296624	−0.148312	−	0.988941i	$-0.547384\pi$
$953$	−5.93730e27	−0.296624	−0.148312	+	0.988941i	$0.547384\pi$
$954$	1.91700e28	0.948230
$955$	0	0
$956$	−8.30141e27	−0.402534
$957$	9.34363e23	4.48593e−5 0
$958$	−1.52374e28	−0.724333
$959$	4.99789e27	0.235239
$960$	0	0
$961$	−1.07239e28	−0.494857
$962$	3.89471e27	0.177956
$963$	−3.71365e28	−1.68016
$964$	−2.32976e28	−1.04371
$965$	0	0
$966$	−5.48477e27	−0.240922
$967$	2.58489e28	1.12432	0.562160	−	0.827028i	$-0.309970\pi$
$967$	2.58489e28	1.12432	0.562160	+	0.827028i	$0.309970\pi$
$968$	−2.34441e28	−1.00976
$969$	−1.94976e28	−0.831583
$970$	0	0
$971$	2.05732e28	0.860438	0.430219	−	0.902725i	$-0.358436\pi$
$971$	2.05732e28	0.860438	0.430219	+	0.902725i	$0.358436\pi$
$972$	−2.07144e28	−0.857912
$973$	2.34271e27	0.0960831
$974$	−2.21698e28	−0.900435
$975$	0	0
$976$	−2.08955e26	−0.00832300
$977$	2.34524e28	0.925099	0.462550	−	0.886593i	$-0.346935\pi$
$977$	2.34524e28	0.925099	0.462550	+	0.886593i	$0.346935\pi$
$978$	1.34141e28	0.524014
$979$	−7.08664e25	−0.00274160
$980$	0	0
$981$	−2.58468e28	−0.980736
$982$	−4.49949e27	−0.169085
$983$	−4.25526e28	−1.58368	−0.791840	−	0.610729i	$-0.790877\pi$
$983$	−4.25526e28	−1.58368	−0.791840	+	0.610729i	$0.790877\pi$
$984$	6.42684e28	2.36889
$985$	0	0
$986$	1.16778e26	0.00422213
$987$	2.99806e27	0.107356
$988$	−2.72806e28	−0.967527
$989$	1.58320e28	0.556123
$990$	0	0
$991$	5.21472e28	1.79693	0.898466	−	0.439044i	$-0.144683\pi$
$991$	5.21472e28	1.79693	0.898466	+	0.439044i	$0.144683\pi$
$992$	2.06010e28	0.703117
$993$	5.33556e28	1.80369
$994$	1.37241e27	0.0459529
$995$	0	0
$996$	−1.93655e28	−0.636159
$997$	1.61541e27	0.0525629	0.0262815	−	0.999655i	$-0.491633\pi$
$997$	1.61541e27	0.0525629	0.0262815	+	0.999655i	$0.491633\pi$
$998$	1.61493e28	0.520490
$999$	−2.06867e27	−0.0660419

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.20.a.a.1.1		1
5.2	odd	4		25.20.b.a.24.1		2
5.3	odd	4		25.20.b.a.24.2		2
5.4	even	2		1.20.a.a.1.1	✓	1
15.14	odd	2		9.20.a.a.1.1		1
20.19	odd	2		16.20.a.a.1.1		1
35.34	odd	2		49.20.a.b.1.1		1
40.19	odd	2		64.20.a.h.1.1		1
40.29	even	2		64.20.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.20.a.a.1.1	✓	1	5.4	even	2
9.20.a.a.1.1		1	15.14	odd	2
16.20.a.a.1.1		1	20.19	odd	2
25.20.a.a.1.1		1	1.1	even	1	trivial
25.20.b.a.24.1		2	5.2	odd	4
25.20.b.a.24.2		2	5.3	odd	4
49.20.a.b.1.1		1	35.34	odd	2
64.20.a.b.1.1		1	40.29	even	2
64.20.a.h.1.1		1	40.19	odd	2

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:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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