LMFDB - Embedded newform 25.34.b.d.24.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("25.24");

S:= CuspForms(chi, 34);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			24.1
Character	$\chi$	$=$	25.24
Dual form			25.34.b.d.24.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-177167. i q^{2} -1.20911e8i q^{3} -2.27982e10 q^{4} -2.14214e13 q^{6} -1.11259e14i q^{7} +2.51723e15i q^{8} -9.06036e15 q^{9} +O(q^{10})$	\(q-177167. i q^{2} -1.20911e8i q^{3} -2.27982e10 q^{4} -2.14214e13 q^{6} -1.11259e14i q^{7} +2.51723e15i q^{8} -9.06036e15 q^{9} -1.24906e17 q^{11} +2.75655e18i q^{12} -2.26681e18i q^{13} -1.97114e19 q^{14} +2.50136e20 q^{16} +3.98383e20i q^{17} +1.60520e21i q^{18} -3.39897e20 q^{19} -1.34524e22 q^{21} +2.21292e22i q^{22} -1.96795e22i q^{23} +3.04361e23 q^{24} -4.01605e23 q^{26} +4.23345e23i q^{27} +2.53650e24i q^{28} +1.40974e23 q^{29} +3.85660e24 q^{31} -2.26929e25i q^{32} +1.51025e25i q^{33} +7.05803e25 q^{34} +2.06560e26 q^{36} -5.90970e24i q^{37} +6.02185e25i q^{38} -2.74082e26 q^{39} -8.25921e24 q^{41} +2.38332e27i q^{42} +6.30947e26i q^{43} +2.84763e27 q^{44} -3.48656e27 q^{46} +3.36586e27i q^{47} -3.02441e28i q^{48} -4.64754e27 q^{49} +4.81688e28 q^{51} +5.16793e28i q^{52} +5.10657e27i q^{53} +7.50028e28 q^{54} +2.80065e29 q^{56} +4.10972e28i q^{57} -2.49760e28i q^{58} +2.91603e29 q^{59} -3.91923e29 q^{61} -6.83262e29i q^{62} +1.00805e30i q^{63} -1.87178e30 q^{64} +2.67566e30 q^{66} -1.32177e30i q^{67} -9.08241e30i q^{68} -2.37946e30 q^{69} -4.98102e30 q^{71} -2.28071e31i q^{72} -3.33107e30i q^{73} -1.04700e30 q^{74} +7.74904e30 q^{76} +1.38969e31i q^{77} +4.85583e31i q^{78} -1.93342e31 q^{79} +8.19892e29 q^{81} +1.46326e30i q^{82} -6.11641e31i q^{83} +3.06690e32 q^{84} +1.11783e32 q^{86} -1.70453e31i q^{87} -3.14418e32i q^{88} +7.66849e31 q^{89} -2.52203e32 q^{91} +4.48657e32i q^{92} -4.66305e32i q^{93} +5.96319e32 q^{94} -2.74382e33 q^{96} +2.66508e32i q^{97} +8.23390e32i q^{98} +1.13169e33 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 98676413354 q^{4} - 35567955353446 q^{6} - 48\!\cdots\!16 q^{9}+O(q^{10}) $ 22 * q - 98676413354 * q^4 - 35567955353446 * q^6 - 48599275949251316 * q^9	$ 22 q - 98676413354 q^{4} - 35567955353446 q^{6} - 48\!\cdots\!16 q^{9}+ \cdots - 26\!\cdots\!12 q^{99}+O(q^{100}) $ 22 * q - 98676413354 * q^4 - 35567955353446 * q^6 - 48599275949251316 * q^9 - 388975069134227046 * q^11 - 19390008595334902068 * q^14 + 575591759119330759202 * q^16 + 4608842794243084808630 * q^19 + 7903359076848510896124 * q^21 + 404192556148581428871090 * q^24 + 464682665356996878920184 * q^26 - 3351264573191459117593680 * q^29 - 3759368993361156279858876 * q^31 + 89746721762579763434900102 * q^34 + 387355373506331566119004012 * q^36 + 718345493252093200854565688 * q^39 + 1099039609507795057059146334 * q^41 + 5953087248173453754548821422 * q^44 + 3376724462669734942026715164 * q^46 + 5003317848948805057160966146 * q^49 + 132635930632492996145333201114 * q^51 + 426786304479392249563776060130 * q^54 + 679074245273936256251630129820 * q^56 + 135413981096960311593168243840 * q^59 - 689538516943594572498942901796 * q^61 - 2840052535921821128029255801474 * q^64 - 320033315173213395102299074022 * q^66 - 14437009323987384127917423522852 * q^69 - 11051811216899923387221184379736 * q^71 - 16966204054892971302102433594308 * q^74 - 7588775596602318790343300932510 * q^76 - 56833627147150708379517479188380 * q^79 - 9022895406968638344517956762058 * q^81 + 599893154314490734522302146543532 * q^84 + 911820864247632195182318378176824 * q^86 + 48061740522903759998741201101110 * q^89 - 693375717774307216790074646600496 * q^91 - 465076424153121919006535311120888 * q^94 - 3684220565182840604743827051904706 * q^96 - 2601899095573470033938075107273612 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	− 177167.i	− 1.91156i	−0.294084	−	0.955780i	$-0.595014\pi$
$2$	− 177167.i	− 1.91156i	0.294084	−	0.955780i	$-0.404986\pi$
$3$	− 1.20911e8i	− 1.62168i	−0.585270	−	0.810839i	$-0.699011\pi$
$3$	− 1.20911e8i	− 1.62168i	0.585270	−	0.810839i	$-0.300989\pi$
$4$	−2.27982e10	−2.65406
$5$	0	0
$5$	0	0
$6$	−2.14214e13	−3.09993
$7$	− 1.11259e14i	− 1.26537i	−0.774410	−	0.632684i	$-0.781953\pi$
$7$	− 1.11259e14i	− 1.26537i	0.774410	−	0.632684i	$-0.218047\pi$
$8$	2.51723e15i	3.16183i
$9$	−9.06036e15	−1.62984
$10$	0	0
$11$	−1.24906e17	−0.819604	−0.409802	−	0.912174i	$-0.634402\pi$
$11$	−1.24906e17	−0.819604	−0.409802	+	0.912174i	$0.634402\pi$
$12$	2.75655e18i	4.30403i
$13$	− 2.26681e18i	− 0.944823i	−0.881378	−	0.472412i	$-0.843384\pi$
$13$	− 2.26681e18i	− 0.944823i	0.881378	−	0.472412i	$-0.156616\pi$
$14$	−1.97114e19	−2.41883
$15$	0	0
$16$	2.50136e20	3.38997
$17$	3.98383e20i	1.98561i	0.119754	+	0.992804i	$0.461789\pi$
$17$	3.98383e20i	1.98561i	−0.119754	+	0.992804i	$0.538211\pi$
$18$	1.60520e21i	3.11553i
$19$	−3.39897e20	−0.270342	−0.135171	−	0.990822i	$-0.543158\pi$
$19$	−3.39897e20	−0.270342	−0.135171	+	0.990822i	$0.543158\pi$
$20$	0	0
$21$	−1.34524e22	−2.05202
$22$	2.21292e22i	1.56672i
$23$	− 1.96795e22i	− 0.669121i	−0.942374	−	0.334561i	$-0.891412\pi$
$23$	− 1.96795e22i	− 0.669121i	0.942374	−	0.334561i	$-0.108588\pi$
$24$	3.04361e23	5.12747
$25$	0	0
$26$	−4.01605e23	−1.80609
$27$	4.23345e23i	1.02139i
$28$	2.53650e24i	3.35836i
$29$	1.40974e23	0.104610	0.0523050	−	0.998631i	$-0.483343\pi$
$29$	1.40974e23	0.104610	0.0523050	+	0.998631i	$0.483343\pi$
$30$	0	0
$31$	3.85660e24	0.952219	0.476109	−	0.879386i	$-0.342047\pi$
$31$	3.85660e24	0.952219	0.476109	+	0.879386i	$0.342047\pi$
$32$	− 2.26929e25i	− 3.31830i
$33$	1.51025e25i	1.32913i
$34$	7.05803e25	3.79561
$35$	0	0
$36$	2.06560e26	4.32568
$37$	− 5.90970e24i	− 0.0787475i	−0.999225	−	0.0393738i	$-0.987464\pi$
$37$	− 5.90970e24i	− 0.0787475i	0.999225	−	0.0393738i	$-0.0125363\pi$
$38$	6.02185e25i	0.516774i
$39$	−2.74082e26	−1.53220
$40$	0	0
$41$	−8.25921e24	−0.0202304	−0.0101152	−	0.999949i	$-0.503220\pi$
$41$	−8.25921e24	−0.0202304	−0.0101152	+	0.999949i	$0.503220\pi$
$42$	2.38332e27i	3.92256i
$43$	6.30947e26i	0.704309i	0.935942	+	0.352154i	$0.114551\pi$
$43$	6.30947e26i	0.704309i	−0.935942	+	0.352154i	$0.885449\pi$
$44$	2.84763e27	2.17528
$45$	0	0
$46$	−3.48656e27	−1.27906
$47$	3.36586e27i	0.865927i	0.901411	+	0.432964i	$0.142532\pi$
$47$	3.36586e27i	0.865927i	−0.901411	+	0.432964i	$0.857468\pi$
$48$	− 3.02441e28i	− 5.49744i
$49$	−4.64754e27	−0.601157
$50$	0	0
$51$	4.81688e28	3.22001
$52$	5.16793e28i	2.50762i
$53$	5.10657e27i	0.180958i	0.995898	+	0.0904790i	$0.0288398\pi$
$53$	5.10657e27i	0.180958i	−0.995898	+	0.0904790i	$0.971160\pi$
$54$	7.50028e28	1.95245
$55$	0	0
$56$	2.80065e29	4.00088
$57$	4.10972e28i	0.438407i
$58$	− 2.49760e28i	− 0.199968i
$59$	2.91603e29	1.76089	0.880447	−	0.474144i	$-0.157243\pi$
$59$	2.91603e29	1.76089	0.880447	+	0.474144i	$0.157243\pi$
$60$	0	0
$61$	−3.91923e29	−1.36540	−0.682699	−	0.730700i	$-0.739194\pi$
$61$	−3.91923e29	−1.36540	−0.682699	+	0.730700i	$0.739194\pi$
$62$	− 6.83262e29i	− 1.82022i
$63$	1.00805e30i	2.06234i
$64$	−1.87178e30	−2.95315
$65$	0	0
$66$	2.67566e30	2.54072
$67$	− 1.32177e30i	− 0.979313i	−0.871915	−	0.489657i	$-0.837122\pi$
$67$	− 1.32177e30i	− 0.979313i	0.871915	−	0.489657i	$-0.162878\pi$
$68$	− 9.08241e30i	− 5.26992i
$69$	−2.37946e30	−1.08510
$70$	0	0
$71$	−4.98102e30	−1.41761	−0.708803	−	0.705407i	$-0.750764\pi$
$71$	−4.98102e30	−1.41761	−0.708803	+	0.705407i	$0.750764\pi$
$72$	− 2.28071e31i	− 5.15327i
$73$	− 3.33107e30i	− 0.599454i	−0.954025	−	0.299727i	$-0.903104\pi$
$73$	− 3.33107e30i	− 0.599454i	0.954025	−	0.299727i	$-0.0968956\pi$
$74$	−1.04700e30	−0.150531
$75$	0	0
$76$	7.74904e30	0.717503
$77$	1.38969e31i	1.03710i
$78$	4.85583e31i	2.92889i
$79$	−1.93342e31	−0.945103	−0.472552	−	0.881303i	$-0.656667\pi$
$79$	−1.93342e31	−0.945103	−0.472552	+	0.881303i	$0.656667\pi$
$80$	0	0
$81$	8.19892e29	0.0265310
$82$	1.46326e30i	0.0386716i
$83$	− 6.11641e31i	− 1.32345i	−0.749746	−	0.661726i	$-0.769824\pi$
$83$	− 6.11641e31i	− 1.32345i	0.749746	−	0.661726i	$-0.230176\pi$
$84$	3.06690e32	5.44618
$85$	0	0
$86$	1.11783e32	1.34633
$87$	− 1.70453e31i	− 0.169644i
$88$	− 3.14418e32i	− 2.59145i
$89$	7.66849e31	0.524535	0.262268	−	0.964995i	$-0.415530\pi$
$89$	7.66849e31	0.524535	0.262268	+	0.964995i	$0.415530\pi$
$90$	0	0
$91$	−2.52203e32	−1.19555
$92$	4.48657e32i	1.77589i
$93$	− 4.66305e32i	− 1.54419i
$94$	5.96319e32	1.65527
$95$	0	0
$96$	−2.74382e33	−5.38121
$97$	2.66508e32i	0.440530i	0.975440	+	0.220265i	$0.0706923\pi$
$97$	2.66508e32i	0.440530i	−0.975440	+	0.220265i	$0.929308\pi$
$98$	8.23390e32i	1.14915i
$99$	1.13169e33	1.33582
$100$	0	0
$101$	4.53257e32	0.384629	0.192314	−	0.981333i	$-0.438401\pi$
$101$	4.53257e32	0.384629	0.192314	+	0.981333i	$0.438401\pi$
$102$	− 8.53392e33i	− 6.15525i
$103$	1.94880e33i	1.19661i	0.801269	+	0.598304i	$0.204159\pi$
$103$	1.94880e33i	1.19661i	−0.801269	+	0.598304i	$0.795841\pi$
$104$	5.70610e33	2.98737
$105$	0	0
$106$	9.04716e32	0.345912
$107$	4.03797e33i	1.32230i	0.750253	+	0.661150i	$0.229931\pi$
$107$	4.03797e33i	1.32230i	−0.750253	+	0.661150i	$0.770069\pi$
$108$	− 9.65150e33i	− 2.71083i
$109$	−3.32000e33	−0.800941	−0.400471	−	0.916310i	$-0.631153\pi$
$109$	−3.32000e33	−0.800941	−0.400471	+	0.916310i	$0.631153\pi$
$110$	0	0
$111$	−7.14546e32	−0.127703
$112$	− 2.78298e34i	− 4.28956i
$113$	− 5.18771e33i	− 0.690528i	−0.938506	−	0.345264i	$-0.887789\pi$
$113$	− 5.18771e33i	− 0.690528i	0.938506	−	0.345264i	$-0.112211\pi$
$114$	7.28107e33	0.838041
$115$	0	0
$116$	−3.21396e33	−0.277641
$117$	2.05382e34i	1.53991i
$118$	− 5.16624e34i	− 3.36605i
$119$	4.43236e34	2.51252
$120$	0	0
$121$	−7.62363e33	−0.328249
$122$	6.94359e34i	2.61004i
$123$	9.98627e32i	0.0328072i
$124$	−8.79235e34	−2.52725
$125$	0	0
$126$	1.78592e35	3.94229
$127$	4.26706e34i	0.826738i	0.910564	+	0.413369i	$0.135648\pi$
$127$	4.26706e34i	0.826738i	−0.910564	+	0.413369i	$0.864352\pi$
$128$	1.36688e35i	2.32683i
$129$	7.62883e34	1.14216
$130$	0	0
$131$	9.51459e34	1.10513	0.552566	−	0.833469i	$-0.313649\pi$
$131$	9.51459e34	1.10513	0.552566	+	0.833469i	$0.313649\pi$
$132$	− 3.44310e35i	− 3.52760i
$133$	3.78166e34i	0.342082i
$134$	−2.34174e35	−1.87202
$135$	0	0
$136$	−1.00282e36	−6.27816
$137$	3.09831e35i	1.71884i	0.511270	+	0.859420i	$0.329175\pi$
$137$	3.09831e35i	1.71884i	−0.511270	+	0.859420i	$0.670825\pi$
$138$	4.21562e35i	2.07423i
$139$	3.67774e34	0.160634	0.0803169	−	0.996769i	$-0.474407\pi$
$139$	3.67774e34	0.160634	0.0803169	+	0.996769i	$0.474407\pi$
$140$	0	0
$141$	4.06969e35	1.40425
$142$	8.82472e35i	2.70984i
$143$	2.83139e35i	0.774381i
$144$	−2.26632e36	−5.52510
$145$	0	0
$146$	−5.90155e35	−1.14589
$147$	5.61938e35i	0.974882i
$148$	1.34730e35i	0.209001i
$149$	1.01479e35	0.140865	0.0704326	−	0.997517i	$-0.477562\pi$
$149$	1.01479e35	0.140865	0.0704326	+	0.997517i	$0.477562\pi$
$150$	0	0
$151$	1.09661e36	1.22161	0.610803	−	0.791782i	$-0.290847\pi$
$151$	1.09661e36	1.22161	0.610803	+	0.791782i	$0.290847\pi$
$152$	− 8.55601e35i	− 0.854775i
$153$	− 3.60949e36i	− 3.23622i
$154$	2.46207e36	1.98248
$155$	0	0
$156$	6.24858e36	4.06655
$157$	1.18915e36i	0.696453i	0.937410	+	0.348227i	$0.113216\pi$
$157$	1.18915e36i	0.696453i	−0.937410	+	0.348227i	$0.886784\pi$
$158$	3.42538e36i	1.80662i
$159$	6.17440e35	0.293455
$160$	0	0
$161$	−2.18952e36	−0.846685
$162$	− 1.45258e35i	− 0.0507156i
$163$	3.11032e36i	0.981093i	0.871415	+	0.490547i	$0.163203\pi$
$163$	3.11032e36i	0.981093i	−0.871415	+	0.490547i	$0.836797\pi$
$164$	1.88295e35	0.0536927
$165$	0	0
$166$	−1.08363e37	−2.52986
$167$	1.39555e36i	0.295069i	0.989057	+	0.147535i	$0.0471338\pi$
$167$	1.39555e36i	0.295069i	−0.989057	+	0.147535i	$0.952866\pi$
$168$	− 3.38628e37i	− 6.48814i
$169$	6.17684e35	0.107309
$170$	0	0
$171$	3.07959e36	0.440613
$172$	− 1.43844e37i	− 1.86928i
$173$	1.01617e36i	0.120007i	0.998198	+	0.0600034i	$0.0191111\pi$
$173$	1.01617e36i	0.120007i	−0.998198	+	0.0600034i	$0.980889\pi$
$174$	−3.01987e36	−0.324284
$175$	0	0
$176$	−3.12435e37	−2.77843
$177$	− 3.52579e37i	− 2.85560i
$178$	− 1.35860e37i	− 1.00268i
$179$	−2.10377e37	−1.41555	−0.707773	−	0.706440i	$-0.750300\pi$
$179$	−2.10377e37	−1.41555	−0.707773	+	0.706440i	$0.750300\pi$
$180$	0	0
$181$	−7.67214e36	−0.429754	−0.214877	−	0.976641i	$-0.568935\pi$
$181$	−7.67214e36	−0.429754	−0.214877	+	0.976641i	$0.568935\pi$
$182$	4.46821e37i	2.28536i
$183$	4.73878e37i	2.21423i
$184$	4.95379e37	2.11565
$185$	0	0
$186$	−8.26138e37	−2.95181
$187$	− 4.97604e37i	− 1.62741i
$188$	− 7.67355e37i	− 2.29822i
$189$	4.71009e37	1.29244
$190$	0	0
$191$	2.89689e37	0.668162	0.334081	−	0.942544i	$-0.391574\pi$
$191$	2.89689e37	0.668162	0.334081	+	0.942544i	$0.391574\pi$
$192$	2.26319e38i	4.78906i
$193$	1.08652e37i	0.211030i	0.994418	+	0.105515i	$0.0336490\pi$
$193$	1.08652e37i	0.211030i	−0.994418	+	0.105515i	$0.966351\pi$
$194$	4.72163e37	0.842100
$195$	0	0
$196$	1.05956e38	1.59551
$197$	8.66891e37i	1.20025i	0.799906	+	0.600125i	$0.204883\pi$
$197$	8.66891e37i	1.20025i	−0.799906	+	0.600125i	$0.795117\pi$
$198$	− 2.00499e38i	− 2.55350i
$199$	−1.33609e38	−1.56588	−0.782941	−	0.622096i	$-0.786281\pi$
$199$	−1.33609e38	−1.56588	−0.782941	+	0.622096i	$0.786281\pi$
$200$	0	0
$201$	−1.59816e38	−1.58813
$202$	− 8.03022e37i	− 0.735241i
$203$	− 1.56846e37i	− 0.132370i
$204$	−1.09816e39	−8.54611
$205$	0	0
$206$	3.45262e38	2.28739
$207$	1.78303e38i	1.09056i
$208$	− 5.67011e38i	− 3.20292i
$209$	4.24552e37	0.221573
$210$	0	0
$211$	−1.06827e38	−0.476454	−0.238227	−	0.971210i	$-0.576566\pi$
$211$	−1.06827e38	−0.476454	−0.238227	+	0.971210i	$0.576566\pi$
$212$	− 1.16421e38i	− 0.480273i
$213$	6.02259e38i	2.29890i
$214$	7.15394e38	2.52766
$215$	0	0
$216$	−1.06566e39	−3.22947
$217$	− 4.29081e38i	− 1.20491i
$218$	5.88194e38i	1.53105i
$219$	−4.02762e38	−0.972121
$220$	0	0
$221$	9.03060e38	1.87605
$222$	1.26594e38i	0.244112i
$223$	− 8.53641e38i	− 1.52843i	−0.644962	−	0.764214i	$-0.723127\pi$
$223$	− 8.53641e38i	− 1.52843i	0.644962	−	0.764214i	$-0.276873\pi$
$224$	−2.52479e39	−4.19887
$225$	0	0
$226$	−9.19091e38	−1.31999
$227$	9.76166e38i	1.30346i	0.758452	+	0.651729i	$0.225956\pi$
$227$	9.76166e38i	1.30346i	−0.758452	+	0.651729i	$0.774044\pi$
$228$	− 9.36943e38i	− 1.16356i
$229$	1.17399e39	1.35638	0.678188	−	0.734888i	$-0.262765\pi$
$229$	1.17399e39	1.35638	0.678188	+	0.734888i	$0.262765\pi$
$230$	0	0
$231$	1.68029e39	1.68184
$232$	3.54865e38i	0.330759i
$233$	− 3.61332e38i	− 0.313714i	−0.987621	−	0.156857i	$-0.949864\pi$
$233$	− 3.61332e38i	− 0.313714i	0.987621	−	0.156857i	$-0.0501362\pi$
$234$	3.63868e39	2.94363
$235$	0	0
$236$	−6.64801e39	−4.67352
$237$	2.33771e39i	1.53265i
$238$	− 7.85268e39i	− 4.80284i
$239$	2.97191e38	0.169617	0.0848087	−	0.996397i	$-0.472972\pi$
$239$	2.97191e38	0.169617	0.0848087	+	0.996397i	$0.472972\pi$
$240$	0	0
$241$	8.15459e37	0.0405621	0.0202811	−	0.999794i	$-0.493544\pi$
$241$	8.15459e37	0.0405621	0.0202811	+	0.999794i	$0.493544\pi$
$242$	1.35066e39i	0.627467i
$243$	2.25427e39i	0.978367i
$244$	8.93515e39	3.62384
$245$	0	0
$246$	1.76924e38	0.0627129
$247$	7.70484e38i	0.255425i
$248$	9.70797e39i	3.01076i
$249$	−7.39540e39	−2.14621
$250$	0	0
$251$	3.98247e39	1.01283	0.506414	−	0.862290i	$-0.330971\pi$
$251$	3.98247e39	1.01283	0.506414	+	0.862290i	$0.330971\pi$
$252$	− 2.29816e40i	− 5.47358i
$253$	2.45809e39i	0.548415i
$254$	7.55983e39	1.58036
$255$	0	0
$256$	8.13803e39	1.49472
$257$	1.37695e39i	0.237149i	0.992945	+	0.118574i	$0.0378324\pi$
$257$	1.37695e39i	0.237149i	−0.992945	+	0.118574i	$0.962168\pi$
$258$	− 1.35158e40i	− 2.18331i
$259$	−6.57506e38	−0.0996446
$260$	0	0
$261$	−1.27728e39	−0.170497
$262$	− 1.68567e40i	− 2.11252i
$263$	− 4.06217e39i	− 0.478066i	−0.971011	−	0.239033i	$-0.923170\pi$
$263$	− 4.06217e39i	− 0.478066i	0.971011	−	0.239033i	$-0.0768304\pi$
$264$	−3.80165e40	−4.20250
$265$	0	0
$266$	6.69985e39	0.653910
$267$	− 9.27203e39i	− 0.850627i
$268$	3.01340e40i	2.59916i
$269$	−9.40208e39	−0.762625	−0.381313	−	0.924446i	$-0.624528\pi$
$269$	−9.40208e39	−0.762625	−0.381313	+	0.924446i	$0.624528\pi$
$270$	0	0
$271$	−8.74843e39	−0.627967	−0.313984	−	0.949428i	$-0.601664\pi$
$271$	−8.74843e39	−0.627967	−0.313984	+	0.949428i	$0.601664\pi$
$272$	9.96498e40i	6.73115i
$273$	3.04941e40i	1.93880i
$274$	5.48918e40	3.28567
$275$	0	0
$276$	5.42475e40	2.87992
$277$	1.79091e40i	0.895691i	0.894111	+	0.447845i	$0.147808\pi$
$277$	1.79091e40i	0.895691i	−0.894111	+	0.447845i	$0.852192\pi$
$278$	− 6.51574e39i	− 0.307061i
$279$	−3.49422e40	−1.55196
$280$	0	0
$281$	−3.07657e40	−1.21454	−0.607271	−	0.794495i	$-0.707736\pi$
$281$	−3.07657e40	−1.21454	−0.607271	+	0.794495i	$0.707736\pi$
$282$	− 7.21014e40i	− 2.68432i
$283$	− 1.98938e40i	− 0.698622i	−0.937007	−	0.349311i	$-0.886416\pi$
$283$	− 1.98938e40i	− 0.698622i	0.937007	−	0.349311i	$-0.113584\pi$
$284$	1.13558e41	3.76241
$285$	0	0
$286$	5.01628e40	1.48028
$287$	9.18910e38i	0.0255989i
$288$	2.05606e41i	5.40829i
$289$	−1.18454e41	−2.94264
$290$	0	0
$291$	3.22236e40	0.714398
$292$	7.59423e40i	1.59099i
$293$	3.51689e40i	0.696375i	0.937425	+	0.348187i	$0.113203\pi$
$293$	3.51689e40i	0.696375i	−0.937425	+	0.348187i	$0.886797\pi$
$294$	9.95568e40	1.86355
$295$	0	0
$296$	1.48761e40	0.248986
$297$	− 5.28784e40i	− 0.837137i
$298$	− 1.79788e40i	− 0.269272i
$299$	−4.46098e40	−0.632201
$300$	0	0
$301$	7.01984e40	0.891210
$302$	− 1.94283e41i	− 2.33517i
$303$	− 5.48037e40i	− 0.623744i
$304$	−8.50204e40	−0.916451
$305$	0	0
$306$	−6.39483e41	−6.18622
$307$	2.17720e41i	1.99579i	0.0648506	+	0.997895i	$0.479343\pi$
$307$	2.17720e41i	1.99579i	−0.0648506	+	0.997895i	$0.520657\pi$
$308$	− 3.16824e41i	− 2.75253i
$309$	2.35630e41	1.94051
$310$	0	0
$311$	7.47866e40	0.553703	0.276852	−	0.960913i	$-0.410709\pi$
$311$	7.47866e40	0.553703	0.276852	+	0.960913i	$0.410709\pi$
$312$	− 6.89929e41i	− 4.84455i
$313$	− 1.94316e40i	− 0.129428i	−0.997904	−	0.0647139i	$-0.979387\pi$
$313$	− 1.94316e40i	− 0.129428i	0.997904	−	0.0647139i	$-0.0206135\pi$
$314$	2.10678e41	1.33131
$315$	0	0
$316$	4.40785e41	2.50836
$317$	− 2.89155e41i	− 1.56190i	−0.624595	−	0.780949i	$-0.714736\pi$
$317$	− 2.89155e41i	− 1.56190i	0.624595	−	0.780949i	$-0.285264\pi$
$318$	− 1.09390e41i	− 0.560957i
$319$	−1.76085e40	−0.0857388
$320$	0	0
$321$	4.88234e41	2.14434
$322$	3.87910e41i	1.61849i
$323$	− 1.35409e41i	− 0.536793i
$324$	−1.86920e40	−0.0704148
$325$	0	0
$326$	5.51047e41	1.87542
$327$	4.01424e41i	1.29887i
$328$	− 2.07904e40i	− 0.0639652i
$329$	3.74482e41	1.09572
$330$	0	0
$331$	4.23132e41	1.12025	0.560124	−	0.828409i	$-0.310753\pi$
$331$	4.23132e41	1.12025	0.560124	+	0.828409i	$0.310753\pi$
$332$	1.39443e42i	3.51252i
$333$	5.35440e40i	0.128346i
$334$	2.47246e41	0.564043
$335$	0	0
$336$	−3.36493e42	−6.95628
$337$	− 1.90258e41i	− 0.374498i	−0.982312	−	0.187249i	$-0.940043\pi$
$337$	− 1.90258e41i	− 0.374498i	0.982312	−	0.187249i	$-0.0599571\pi$
$338$	− 1.09433e41i	− 0.205127i
$339$	−6.27250e41	−1.11981
$340$	0	0
$341$	−4.81713e41	−0.780443
$342$	− 5.45602e41i	− 0.842258i
$343$	− 3.43062e41i	− 0.504684i
$344$	−1.58824e42	−2.22691
$345$	0	0
$346$	1.80032e41	0.229400
$347$	7.85300e41i	0.954112i	0.878873	+	0.477056i	$0.158296\pi$
$347$	7.85300e41i	0.954112i	−0.878873	+	0.477056i	$0.841704\pi$
$348$	3.88602e41i	0.450244i
$349$	−1.51475e42	−1.67387	−0.836937	−	0.547300i	$-0.815656\pi$
$349$	−1.51475e42	−1.67387	−0.836937	+	0.547300i	$0.815656\pi$
$350$	0	0
$351$	9.59645e41	0.965035
$352$	2.83448e42i	2.71969i
$353$	− 2.12379e42i	− 1.94459i	−0.233751	−	0.972297i	$-0.575100\pi$
$353$	− 2.12379e42i	− 1.94459i	0.233751	−	0.972297i	$-0.424900\pi$
$354$	−6.24654e42	−5.45865
$355$	0	0
$356$	−1.74828e42	−1.39215
$357$	− 5.35920e42i	− 4.07450i
$358$	3.72719e42i	2.70590i
$359$	2.70737e42	1.87711	0.938553	−	0.345135i	$-0.112167\pi$
$359$	2.70737e42	1.87711	0.938553	+	0.345135i	$0.112167\pi$
$360$	0	0
$361$	−1.46524e42	−0.926915
$362$	1.35925e42i	0.821500i
$363$	9.21779e41i	0.532314i
$364$	5.74978e42	3.17306
$365$	0	0
$366$	8.39555e42	4.23264
$367$	− 1.95306e42i	− 0.941295i	−0.882321	−	0.470648i	$-0.844020\pi$
$367$	− 1.95306e42i	− 0.941295i	0.882321	−	0.470648i	$-0.155980\pi$
$368$	− 4.92255e42i	− 2.26830i
$369$	7.48314e40	0.0329723
$370$	0	0
$371$	5.68151e41	0.228978
$372$	1.06309e43i	4.09838i
$373$	3.00107e42i	1.10683i	0.832907	+	0.553413i	$0.186675\pi$
$373$	3.00107e42i	1.10683i	−0.832907	+	0.553413i	$0.813325\pi$
$374$	−8.81590e42	−3.11089
$375$	0	0
$376$	−8.47266e42	−2.73792
$377$	− 3.19563e41i	− 0.0988379i
$378$	− 8.34472e42i	− 2.47057i
$379$	2.42202e42	0.686485	0.343242	−	0.939247i	$-0.388475\pi$
$379$	2.42202e42	0.686485	0.343242	+	0.939247i	$0.388475\pi$
$380$	0	0
$381$	5.15934e42	1.34070
$382$	− 5.13234e42i	− 1.27723i
$383$	− 5.11408e42i	− 1.21895i	−0.792804	−	0.609477i	$-0.791379\pi$
$383$	− 5.11408e42i	− 1.21895i	0.792804	−	0.609477i	$-0.208621\pi$
$384$	1.65270e43	3.77337
$385$	0	0
$386$	1.92496e42	0.403395
$387$	− 5.71660e42i	− 1.14791i
$388$	− 6.07589e42i	− 1.16919i
$389$	−4.84726e42	−0.893980	−0.446990	−	0.894539i	$-0.647504\pi$
$389$	−4.84726e42	−0.893980	−0.446990	+	0.894539i	$0.647504\pi$
$390$	0	0
$391$	7.83997e42	1.32861
$392$	− 1.16989e43i	− 1.90076i
$393$	− 1.15042e43i	− 1.79217i
$394$	1.53584e43	2.29435
$395$	0	0
$396$	−2.58006e43	−3.54535
$397$	− 1.26339e43i	− 1.66531i	−0.553791	−	0.832656i	$-0.686819\pi$
$397$	− 1.26339e43i	− 1.66531i	0.553791	−	0.832656i	$-0.313181\pi$
$398$	2.36711e43i	2.99328i
$399$	4.57243e42	0.554746
$400$	0	0
$401$	−4.14706e42	−0.463296	−0.231648	−	0.972800i	$-0.574412\pi$
$401$	−4.14706e42	−0.463296	−0.231648	+	0.972800i	$0.574412\pi$
$402$	2.83142e43i	3.03580i
$403$	− 8.74220e42i	− 0.899679i
$404$	−1.03334e43	−1.02083
$405$	0	0
$406$	−2.77880e42	−0.253033
$407$	7.38157e41i	0.0645418i
$408$	1.21252e44i	10.1811i
$409$	−2.91139e42	−0.234782	−0.117391	−	0.993086i	$-0.537453\pi$
$409$	−2.91139e42	−0.234782	−0.117391	+	0.993086i	$0.537453\pi$
$410$	0	0
$411$	3.74619e43	2.78740
$412$	− 4.44290e43i	− 3.17587i
$413$	− 3.24434e43i	− 2.22818i
$414$	3.15895e43	2.08467
$415$	0	0
$416$	−5.14406e43	−3.13521
$417$	− 4.44679e42i	− 0.260496i
$418$	− 7.52166e42i	− 0.423550i
$419$	−2.78455e43	−1.50738	−0.753691	−	0.657229i	$-0.771729\pi$
$419$	−2.78455e43	−1.50738	−0.753691	+	0.657229i	$0.771729\pi$
$420$	0	0
$421$	6.27307e42	0.313925	0.156962	−	0.987605i	$-0.449830\pi$
$421$	6.27307e42	0.313925	0.156962	+	0.987605i	$0.449830\pi$
$422$	1.89262e43i	0.910769i
$423$	− 3.04959e43i	− 1.41132i
$424$	−1.28544e43	−0.572159
$425$	0	0
$426$	1.06700e44	4.39448
$427$	4.36050e43i	1.72773i
$428$	− 9.20583e43i	− 3.50946i
$429$	3.42345e43	1.25580
$430$	0	0
$431$	2.59418e43	0.881302	0.440651	−	0.897678i	$-0.354748\pi$
$431$	2.59418e43	0.881302	0.440651	+	0.897678i	$0.354748\pi$
$432$	1.05894e44i	3.46249i
$433$	5.37170e43i	1.69068i	0.534227	+	0.845341i	$0.320603\pi$
$433$	5.37170e43i	1.69068i	−0.534227	+	0.845341i	$0.679397\pi$
$434$	−7.60190e43	−2.30325
$435$	0	0
$436$	7.56900e43	2.12575
$437$	6.68901e42i	0.180891i
$438$	7.13561e43i	1.85827i
$439$	−5.32504e43	−1.33554	−0.667772	−	0.744365i	$-0.732752\pi$
$439$	−5.32504e43	−1.33554	−0.667772	+	0.744365i	$0.732752\pi$
$440$	0	0
$441$	4.21084e43	0.979787
$442$	− 1.59992e44i	− 3.58618i
$443$	3.70109e43i	0.799224i	0.916684	+	0.399612i	$0.130855\pi$
$443$	3.70109e43i	0.799224i	−0.916684	+	0.399612i	$0.869145\pi$
$444$	1.62904e43	0.338931
$445$	0	0
$446$	−1.51237e44	−2.92168
$447$	− 1.22699e43i	− 0.228438i
$448$	2.08253e44i	3.73683i
$449$	3.12899e43	0.541178	0.270589	−	0.962695i	$-0.412782\pi$
$449$	3.12899e43	0.541178	0.270589	+	0.962695i	$0.412782\pi$
$450$	0	0
$451$	1.03162e42	0.0165809
$452$	1.18270e44i	1.83270i
$453$	− 1.32592e44i	− 1.98105i
$454$	1.72944e44	2.49164
$455$	0	0
$456$	−1.03451e44	−1.38617
$457$	− 1.28166e44i	− 1.65636i	−0.560463	−	0.828179i	$-0.689377\pi$
$457$	− 1.28166e44i	− 1.65636i	0.560463	−	0.828179i	$-0.310623\pi$
$458$	− 2.07993e44i	− 2.59279i
$459$	−1.68653e44	−2.02808
$460$	0	0
$461$	−7.43569e42	−0.0832254	−0.0416127	−	0.999134i	$-0.513250\pi$
$461$	−7.43569e42	−0.0832254	−0.0416127	+	0.999134i	$0.513250\pi$
$462$	− 2.97691e44i	− 3.21494i
$463$	1.76967e44i	1.84419i	0.386966	+	0.922094i	$0.373523\pi$
$463$	1.76967e44i	1.84419i	−0.386966	+	0.922094i	$0.626477\pi$
$464$	3.52627e43	0.354625
$465$	0	0
$466$	−6.40161e43	−0.599683
$467$	− 1.54998e44i	− 1.40152i	−0.713398	−	0.700759i	$-0.752845\pi$
$467$	− 1.54998e44i	− 1.40152i	0.713398	−	0.700759i	$-0.247155\pi$
$468$	− 4.68233e44i	− 4.08701i
$469$	−1.47059e44	−1.23919
$470$	0	0
$471$	1.43781e44	1.12942
$472$	7.34032e44i	5.56765i
$473$	− 7.88091e43i	− 0.577255i
$474$	4.14166e44	2.92976
$475$	0	0
$476$	−1.01050e45	−6.66839
$477$	− 4.62674e43i	− 0.294932i
$478$	− 5.26525e43i	− 0.324234i
$479$	−1.90950e44	−1.13602	−0.568008	−	0.823023i	$-0.692286\pi$
$479$	−1.90950e44	−1.13602	−0.568008	+	0.823023i	$0.692286\pi$
$480$	0	0
$481$	−1.33962e43	−0.0744025
$482$	− 1.44472e43i	− 0.0775369i
$483$	2.64736e44i	1.37305i
$484$	1.73805e44	0.871192
$485$	0	0
$486$	3.99382e44	1.87021
$487$	9.86519e43i	0.446558i	0.974755	+	0.223279i	$0.0716760\pi$
$487$	9.86519e43i	0.446558i	−0.974755	+	0.223279i	$0.928324\pi$
$488$	− 9.86563e44i	− 4.31716i
$489$	3.76072e44	1.59102
$490$	0	0
$491$	9.91478e43	0.392138	0.196069	−	0.980590i	$-0.437182\pi$
$491$	9.91478e43	0.392138	0.196069	+	0.980590i	$0.437182\pi$
$492$	− 2.27669e43i	− 0.0870722i
$493$	5.61617e43i	0.207714i
$494$	1.36504e44	0.488260
$495$	0	0
$496$	9.64674e44	3.22799
$497$	5.54182e44i	1.79379i
$498$	1.31022e45i	4.10261i
$499$	−2.18397e44	−0.661588	−0.330794	−	0.943703i	$-0.607316\pi$
$499$	−2.18397e44	−0.661588	−0.330794	+	0.943703i	$0.607316\pi$
$500$	0	0
$501$	1.68737e44	0.478507
$502$	− 7.05561e44i	− 1.93608i
$503$	− 4.26115e44i	− 1.13150i	−0.824577	−	0.565750i	$-0.808587\pi$
$503$	− 4.26115e44i	− 1.13150i	0.824577	−	0.565750i	$-0.191413\pi$
$504$	−2.53749e45	−6.52079
$505$	0	0
$506$	4.35492e44	1.04833
$507$	− 7.46846e43i	− 0.174020i
$508$	− 9.72814e44i	− 2.19421i
$509$	4.45432e44	0.972607	0.486304	−	0.873790i	$-0.338345\pi$
$509$	4.45432e44	0.972607	0.486304	+	0.873790i	$0.338345\pi$
$510$	0	0
$511$	−3.70611e44	−0.758530
$512$	− 2.67653e44i	− 0.530417i
$513$	− 1.43894e44i	− 0.276125i
$514$	2.43950e44	0.453324
$515$	0	0
$516$	−1.73923e45	−3.03136
$517$	− 4.20416e44i	− 0.709718i
$518$	1.16488e44i	0.190477i
$519$	1.22866e44	0.194612
$520$	0	0
$521$	7.95638e44	1.18275	0.591375	−	0.806397i	$-0.298585\pi$
$521$	7.95638e44	1.18275	0.591375	+	0.806397i	$0.298585\pi$
$522$	2.26292e44i	0.325915i
$523$	5.07858e43i	0.0708703i	0.999372	+	0.0354352i	$0.0112817\pi$
$523$	5.07858e43i	0.0708703i	−0.999372	+	0.0354352i	$0.988718\pi$
$524$	−2.16916e45	−2.93308
$525$	0	0
$526$	−7.19682e44	−0.913852
$527$	1.53640e45i	1.89073i
$528$	3.77767e45i	4.50572i
$529$	4.77722e44	0.552277
$530$	0	0
$531$	−2.64203e45	−2.86997
$532$	− 8.62150e44i	− 0.907906i
$533$	1.87221e43i	0.0191142i
$534$	−1.64270e45	−1.62602
$535$	0	0
$536$	3.32720e45	3.09642
$537$	2.54369e45i	2.29556i
$538$	1.66574e45i	1.45780i
$539$	5.80506e44	0.492711
$540$	0	0
$541$	5.77848e44	0.461380	0.230690	−	0.973027i	$-0.425902\pi$
$541$	5.77848e44	0.461380	0.230690	+	0.973027i	$0.425902\pi$
$542$	1.54993e45i	1.20040i
$543$	9.27644e44i	0.696922i
$544$	9.04046e45	6.58884
$545$	0	0
$546$	5.40254e45	3.70612
$547$	− 1.52755e45i	− 1.01673i	−0.861143	−	0.508363i	$-0.830251\pi$
$547$	− 1.52755e45i	− 1.01673i	0.861143	−	0.508363i	$-0.169749\pi$
$548$	− 7.06359e45i	− 4.56190i
$549$	3.55097e45	2.22537
$550$	0	0
$551$	−4.79168e43	−0.0282804
$552$	− 5.98967e45i	− 3.43090i
$553$	2.15110e45i	1.19590i
$554$	3.17290e45	1.71217
$555$	0	0
$556$	−8.38459e44	−0.426332
$557$	− 2.40408e45i	− 1.18669i	−0.804948	−	0.593345i	$-0.797807\pi$
$557$	− 2.40408e45i	− 1.18669i	0.804948	−	0.593345i	$-0.202193\pi$
$558$	6.19060e45i	2.96667i
$559$	1.43024e45	0.665447
$560$	0	0
$561$	−6.01657e45	−2.63914
$562$	5.45066e45i	2.32167i
$563$	− 6.97447e44i	− 0.288485i	−0.989542	−	0.144242i	$-0.953926\pi$
$563$	− 6.97447e44i	− 0.288485i	0.989542	−	0.144242i	$-0.0460745\pi$
$564$	−9.27816e45	−3.72697
$565$	0	0
$566$	−3.52453e45	−1.33546
$567$	− 9.12202e43i	− 0.0335715i
$568$	− 1.25384e46i	− 4.48223i
$569$	−3.28369e45	−1.14028	−0.570138	−	0.821549i	$-0.693110\pi$
$569$	−3.28369e45	−1.14028	−0.570138	+	0.821549i	$0.693110\pi$
$570$	0	0
$571$	−4.65773e45	−1.52644	−0.763218	−	0.646141i	$-0.776382\pi$
$571$	−4.65773e45	−1.52644	−0.763218	+	0.646141i	$0.776382\pi$
$572$	− 6.45505e45i	− 2.05525i
$573$	− 3.50266e45i	− 1.08354i
$574$	1.62800e44	0.0489338
$575$	0	0
$576$	1.69590e46	4.81316
$577$	− 5.19987e45i	− 1.43414i	−0.697001	−	0.717070i	$-0.745483\pi$
$577$	− 5.19987e45i	− 1.43414i	0.697001	−	0.717070i	$-0.254517\pi$
$578$	2.09862e46i	5.62502i
$579$	1.31372e45	0.342222
$580$	0	0
$581$	−6.80505e45	−1.67465
$582$	− 5.70896e45i	− 1.36561i
$583$	− 6.37842e44i	− 0.148314i
$584$	8.38507e45	1.89537
$585$	0	0
$586$	6.23077e45	1.33116
$587$	1.42187e45i	0.295346i	0.989036	+	0.147673i	$0.0471783\pi$
$587$	1.42187e45i	0.295346i	−0.989036	+	0.147673i	$0.952822\pi$
$588$	− 1.28112e46i	− 2.58740i
$589$	−1.31085e45	−0.257424
$590$	0	0
$591$	1.04817e46	1.94642
$592$	− 1.47823e45i	− 0.266952i
$593$	1.86285e44i	0.0327171i	0.999866	+	0.0163586i	$0.00520732\pi$
$593$	1.86285e44i	0.0327171i	−0.999866	+	0.0163586i	$0.994793\pi$
$594$	−9.36830e45	−1.60024
$595$	0	0
$596$	−2.31354e45	−0.373864
$597$	1.61547e46i	2.53936i
$598$	7.90338e45i	1.20849i
$599$	1.86132e45	0.276871	0.138436	−	0.990371i	$-0.455793\pi$
$599$	1.86132e45	0.276871	0.138436	+	0.990371i	$0.455793\pi$
$600$	0	0
$601$	−7.31474e45	−1.02984	−0.514921	−	0.857238i	$-0.672179\pi$
$601$	−7.31474e45	−1.02984	−0.514921	+	0.857238i	$0.672179\pi$
$602$	− 1.24368e46i	− 1.70360i
$603$	1.19757e46i	1.59612i
$604$	−2.50007e46	−3.24222
$605$	0	0
$606$	−9.70940e45	−1.19232
$607$	1.20958e46i	1.44551i	0.691104	+	0.722755i	$0.257125\pi$
$607$	1.20958e46i	1.44551i	−0.691104	+	0.722755i	$0.742875\pi$
$608$	7.71326e45i	0.897075i
$609$	−1.89644e45	−0.214662
$610$	0	0
$611$	7.62978e45	0.818148
$612$	8.22899e46i	8.58911i
$613$	4.67729e45i	0.475222i	0.971360	+	0.237611i	$0.0763643\pi$
$613$	4.67729e45i	0.475222i	−0.971360	+	0.237611i	$0.923636\pi$
$614$	3.85728e46	3.81507
$615$	0	0
$616$	−3.49818e46	−3.27914
$617$	− 7.40374e45i	− 0.675687i	−0.941202	−	0.337844i	$-0.890303\pi$
$617$	− 7.40374e45i	− 0.675687i	0.941202	−	0.337844i	$-0.109697\pi$
$618$	− 4.17459e46i	− 3.70940i
$619$	5.69692e45	0.492884	0.246442	−	0.969158i	$-0.420739\pi$
$619$	5.69692e45	0.492884	0.246442	+	0.969158i	$0.420739\pi$
$620$	0	0
$621$	8.33122e45	0.683435
$622$	− 1.32497e46i	− 1.05844i
$623$	− 8.53187e45i	− 0.663730i
$624$	−6.85578e46	−5.19411
$625$	0	0
$626$	−3.44264e45	−0.247409
$627$	− 5.13329e45i	− 0.359320i
$628$	− 2.71105e46i	− 1.84843i
$629$	2.35432e45	0.156362
$630$	0	0
$631$	1.42939e46	0.900877	0.450439	−	0.892807i	$-0.351268\pi$
$631$	1.42939e46	0.900877	0.450439	+	0.892807i	$0.351268\pi$
$632$	− 4.86687e46i	− 2.98826i
$633$	1.29165e46i	0.772654i
$634$	−5.12287e46	−2.98566
$635$	0	0
$636$	−1.40765e46	−0.778848
$637$	1.05351e46i	0.567987i
$638$	3.11965e45i	0.163895i
$639$	4.51298e46	2.31047
$640$	0	0
$641$	3.81314e46	1.85407	0.927034	−	0.374978i	$-0.122350\pi$
$641$	3.81314e46	1.85407	0.927034	+	0.374978i	$0.122350\pi$
$642$	− 8.64989e46i	− 4.09904i
$643$	8.01593e44i	0.0370231i	0.999829	+	0.0185116i	$0.00589275\pi$
$643$	8.01593e44i	0.0370231i	−0.999829	+	0.0185116i	$0.994107\pi$
$644$	4.99171e46	2.24715
$645$	0	0
$646$	−2.39900e46	−1.02611
$647$	4.41584e46i	1.84116i	0.390548	+	0.920582i	$0.372285\pi$
$647$	4.41584e46i	1.84116i	−0.390548	+	0.920582i	$0.627715\pi$
$648$	2.06386e45i	0.0838866i
$649$	−3.64229e46	−1.44324
$650$	0	0
$651$	−5.18805e46	−1.95397
$652$	− 7.09098e46i	− 2.60388i
$653$	4.02818e46i	1.44225i	0.692803	+	0.721127i	$0.256375\pi$
$653$	4.02818e46i	1.44225i	−0.692803	+	0.721127i	$0.743625\pi$
$654$	7.11190e46	2.48286
$655$	0	0
$656$	−2.06592e45	−0.0685805
$657$	3.01807e46i	0.977012i
$658$	− 6.63458e46i	− 2.09453i
$659$	−2.34159e46	−0.720942	−0.360471	−	0.932770i	$-0.617384\pi$
$659$	−2.34159e46	−0.720942	−0.360471	+	0.932770i	$0.617384\pi$
$660$	0	0
$661$	5.49451e45	0.160918	0.0804591	−	0.996758i	$-0.474361\pi$
$661$	5.49451e45	0.160918	0.0804591	+	0.996758i	$0.474361\pi$
$662$	− 7.49651e46i	− 2.14142i
$663$	− 1.09190e47i	− 3.04234i
$664$	1.53964e47	4.18453
$665$	0	0
$666$	9.48623e45	0.245340
$667$	− 2.77430e45i	− 0.0699967i
$668$	− 3.18161e46i	− 0.783132i
$669$	−1.03214e47	−2.47862
$670$	0	0
$671$	4.89536e46	1.11909
$672$	3.05274e47i	6.80921i
$673$	− 6.08553e45i	− 0.132449i	−0.997805	−	0.0662247i	$-0.978905\pi$
$673$	− 6.08553e45i	− 0.132449i	0.997805	−	0.0662247i	$-0.0210954\pi$
$674$	−3.37074e46	−0.715875
$675$	0	0
$676$	−1.40821e46	−0.284804
$677$	− 4.63043e46i	− 0.913920i	−0.889487	−	0.456960i	$-0.848938\pi$
$677$	− 4.63043e46i	− 0.913920i	0.889487	−	0.456960i	$-0.151062\pi$
$678$	1.11128e47i	2.14059i
$679$	2.96513e46	0.557433
$680$	0	0
$681$	1.18029e47	2.11379
$682$	8.53436e46i	1.49186i
$683$	3.95290e46i	0.674488i	0.941417	+	0.337244i	$0.109495\pi$
$683$	3.95290e46i	0.674488i	−0.941417	+	0.337244i	$0.890505\pi$
$684$	−7.02091e46	−1.16941
$685$	0	0
$686$	−6.07792e46	−0.964732
$687$	− 1.41948e47i	− 2.19960i
$688$	1.57822e47i	2.38759i
$689$	1.15756e46	0.170973
$690$	0	0
$691$	−1.31488e46	−0.185139	−0.0925694	−	0.995706i	$-0.529508\pi$
$691$	−1.31488e46	−0.185139	−0.0925694	+	0.995706i	$0.529508\pi$
$692$	− 2.31668e46i	− 0.318505i
$693$	− 1.25911e47i	− 1.69031i
$694$	1.39129e47	1.82384
$695$	0	0
$696$	4.29071e46	0.536385
$697$	− 3.29033e45i	− 0.0401696i
$698$	2.68364e47i	3.19971i
$699$	−4.36889e46	−0.508743
$700$	0	0
$701$	−1.78515e46	−0.198303	−0.0991513	−	0.995072i	$-0.531613\pi$
$701$	−1.78515e46	−0.198303	−0.0991513	+	0.995072i	$0.531613\pi$
$702$	− 1.70017e47i	− 1.84472i
$703$	2.00869e45i	0.0212887i
$704$	2.33797e47	2.42042
$705$	0	0
$706$	−3.76265e47	−3.71721
$707$	− 5.04289e46i	− 0.486697i
$708$	8.03817e47i	7.57894i
$709$	1.04358e47	0.961309	0.480655	−	0.876910i	$-0.340399\pi$
$709$	1.04358e47	0.961309	0.480655	+	0.876910i	$0.340399\pi$
$710$	0	0
$711$	1.75175e47	1.54036
$712$	1.93034e47i	1.65849i
$713$	− 7.58960e46i	− 0.637150i
$714$	−9.49474e47	−7.78865
$715$	0	0
$716$	4.79623e47	3.75694
$717$	− 3.59336e46i	− 0.275065i
$718$	− 4.79656e47i	− 3.58820i
$719$	−1.34958e47	−0.986667	−0.493334	−	0.869840i	$-0.664222\pi$
$719$	−1.34958e47	−0.986667	−0.493334	+	0.869840i	$0.664222\pi$
$720$	0	0
$721$	2.16821e47	1.51415
$722$	2.59592e47i	1.77185i
$723$	− 9.85978e45i	− 0.0657787i
$724$	1.74911e47	1.14059
$725$	0	0
$726$	1.63309e47	1.01755
$727$	1.33195e47i	0.811279i	0.914033	+	0.405639i	$0.132951\pi$
$727$	1.33195e47i	0.811279i	−0.914033	+	0.405639i	$0.867049\pi$
$728$	− 6.34854e47i	− 3.78013i
$729$	2.77123e47	1.61313
$730$	0	0
$731$	−2.51358e47	−1.39848
$732$	− 1.08036e48i	− 5.87671i
$733$	− 1.24873e47i	− 0.664131i	−0.943256	−	0.332065i	$-0.892255\pi$
$733$	− 1.24873e47i	− 0.664131i	0.943256	−	0.332065i	$-0.107745\pi$
$734$	−3.46018e47	−1.79934
$735$	0	0
$736$	−4.46585e47	−2.22034
$737$	1.65097e47i	0.802649i
$738$	− 1.32576e46i	− 0.0630284i
$739$	1.60801e47	0.747578	0.373789	−	0.927514i	$-0.378058\pi$
$739$	1.60801e47	0.747578	0.373789	+	0.927514i	$0.378058\pi$
$740$	0	0
$741$	9.31598e46	0.414217
$742$	− 1.00658e47i	− 0.437706i
$743$	− 2.88596e47i	− 1.22737i	−0.789552	−	0.613683i	$-0.789687\pi$
$743$	− 2.88596e47i	− 1.22737i	0.789552	−	0.613683i	$-0.210313\pi$
$744$	1.17380e48	4.88247
$745$	0	0
$746$	5.31690e47	2.11577
$747$	5.54169e47i	2.15701i
$748$	1.13445e48i	4.31925i
$749$	4.49259e47	1.67320
$750$	0	0
$751$	4.31988e47	1.53962	0.769809	−	0.638274i	$-0.220351\pi$
$751$	4.31988e47	1.53962	0.769809	+	0.638274i	$0.220351\pi$
$752$	8.41922e47i	2.93547i
$753$	− 4.81523e47i	− 1.64248i
$754$	−5.66159e46	−0.188935
$755$	0	0
$756$	−1.07382e48	−3.43020
$757$	3.86378e47i	1.20762i	0.797128	+	0.603810i	$0.206351\pi$
$757$	3.86378e47i	1.20762i	−0.797128	+	0.603810i	$0.793649\pi$
$758$	− 4.29102e47i	− 1.31226i
$759$	2.97210e47	0.889351
$760$	0	0
$761$	−1.73723e47	−0.497750	−0.248875	−	0.968536i	$-0.580061\pi$
$761$	−1.73723e47	−0.497750	−0.248875	+	0.968536i	$0.580061\pi$
$762$	− 9.14065e47i	− 2.56283i
$763$	3.69379e47i	1.01349i
$764$	−6.60440e47	−1.77334
$765$	0	0
$766$	−9.06045e47	−2.33010
$767$	− 6.61009e47i	− 1.66373i
$768$	− 9.83976e47i	− 2.42395i
$769$	5.01555e47	1.20930	0.604649	−	0.796492i	$-0.293313\pi$
$769$	5.01555e47	1.20930	0.604649	+	0.796492i	$0.293313\pi$
$770$	0	0
$771$	1.66488e47	0.384579
$772$	− 2.47708e47i	− 0.560085i
$773$	− 2.46977e47i	− 0.546633i	−0.961924	−	0.273316i	$-0.911879\pi$
$773$	− 2.46977e47i	− 0.546633i	0.961924	−	0.273316i	$-0.0881206\pi$
$774$	−1.01279e48	−2.19430
$775$	0	0
$776$	−6.70862e47	−1.39288
$777$	7.94996e46i	0.161591i
$778$	8.58774e47i	1.70890i
$779$	2.80728e45	0.00546912
$780$	0	0
$781$	6.22159e47	1.16188
$782$	− 1.38898e48i	− 2.53972i
$783$	5.96808e46i	0.106848i
$784$	−1.16252e48	−2.03790
$785$	0	0
$786$	−2.03816e48	−3.42583
$787$	3.46347e47i	0.570069i	0.958517	+	0.285035i	$0.0920051\pi$
$787$	3.46347e47i	0.570069i	−0.958517	+	0.285035i	$0.907995\pi$
$788$	− 1.97636e48i	− 3.18554i
$789$	−4.91160e47	−0.775269
$790$	0	0
$791$	−5.77179e47	−0.873773
$792$	2.84874e48i	4.22364i
$793$	8.88418e47i	1.29006i
$794$	−2.23832e48	−3.18334
$795$	0	0
$796$	3.04604e48	4.15594
$797$	1.83743e47i	0.245555i	0.992434	+	0.122778i	$0.0391802\pi$
$797$	1.83743e47i	0.245555i	−0.992434	+	0.122778i	$0.960820\pi$
$798$	− 8.10084e47i	− 1.06043i
$799$	−1.34090e48	−1.71939
$800$	0	0
$801$	−6.94793e47	−0.854907
$802$	7.34723e47i	0.885618i
$803$	4.16070e47i	0.491315i
$804$	3.64352e48	4.21499
$805$	0	0
$806$	−1.54883e48	−1.71979
$807$	1.13681e48i	1.23673i
$808$	1.14095e48i	1.21613i
$809$	4.02171e47	0.420011	0.210005	−	0.977700i	$-0.432652\pi$
$809$	4.02171e47	0.420011	0.210005	+	0.977700i	$0.432652\pi$
$810$	0	0
$811$	−1.31777e48	−1.32128	−0.660640	−	0.750703i	$-0.729715\pi$
$811$	−1.31777e48	−1.32128	−0.660640	+	0.750703i	$0.729715\pi$
$812$	3.57582e47i	0.351318i
$813$	1.05778e48i	1.01836i
$814$	1.30777e47	0.123375
$815$	0	0
$816$	1.20487e49	10.9158
$817$	− 2.14457e47i	− 0.190404i
$818$	5.15802e47i	0.448800i
$819$	2.28505e48	1.94855
$820$	0	0
$821$	7.93981e47	0.650352	0.325176	−	0.945654i	$-0.394577\pi$
$821$	7.93981e47	0.650352	0.325176	+	0.945654i	$0.394577\pi$
$822$	− 6.63701e48i	− 5.32829i
$823$	2.50063e47i	0.196767i	0.995149	+	0.0983836i	$0.0313672\pi$
$823$	2.50063e47i	0.196767i	−0.995149	+	0.0983836i	$0.968633\pi$
$824$	−4.90557e48	−3.78348
$825$	0	0
$826$	−5.74789e48	−4.25930
$827$	2.45832e48i	1.78566i	0.450395	+	0.892829i	$0.351283\pi$
$827$	2.45832e48i	1.78566i	−0.450395	+	0.892829i	$0.648717\pi$
$828$	− 4.06500e48i	− 2.89441i
$829$	−3.63215e47	−0.253521	−0.126760	−	0.991933i	$-0.540458\pi$
$829$	−3.63215e47	−0.253521	−0.126760	+	0.991933i	$0.540458\pi$
$830$	0	0
$831$	2.16541e48	1.45252
$832$	4.24299e48i	2.79021i
$833$	− 1.85150e48i	− 1.19366i
$834$	−7.87824e47	−0.497954
$835$	0	0
$836$	−9.67902e47	−0.588069
$837$	1.63267e48i	0.972588i
$838$	4.93330e48i	2.88145i
$839$	6.95183e46	0.0398132	0.0199066	−	0.999802i	$-0.493663\pi$
$839$	6.95183e46	0.0398132	0.0199066	+	0.999802i	$0.493663\pi$
$840$	0	0
$841$	−1.79620e48	−0.989057
$842$	− 1.11138e48i	− 0.600086i
$843$	3.71990e48i	1.96959i
$844$	2.43546e48	1.26454
$845$	0	0
$846$	−5.40287e48	−2.69782
$847$	8.48196e47i	0.415356i
$848$	1.27734e48i	0.613442i
$849$	−2.40538e48	−1.13294
$850$	0	0
$851$	−1.16300e47	−0.0526916
$852$	− 1.37304e49i	− 6.10141i
$853$	− 1.76186e48i	− 0.767913i	−0.923351	−	0.383957i	$-0.874561\pi$
$853$	− 1.76186e48i	− 0.767913i	0.923351	−	0.383957i	$-0.125439\pi$
$854$	7.72536e48	3.30266
$855$	0	0
$856$	−1.01645e49	−4.18089
$857$	1.03657e48i	0.418229i	0.977891	+	0.209114i	$0.0670581\pi$
$857$	1.03657e48i	0.418229i	−0.977891	+	0.209114i	$0.932942\pi$
$858$	− 6.06523e48i	− 2.40053i
$859$	1.92702e48	0.748168	0.374084	−	0.927395i	$-0.377957\pi$
$859$	1.92702e48	0.748168	0.374084	+	0.927395i	$0.377957\pi$
$860$	0	0
$861$	1.11106e47	0.0415132
$862$	− 4.59603e48i	− 1.68466i
$863$	1.63147e48i	0.586681i	0.956008	+	0.293341i	$0.0947670\pi$
$863$	1.63147e48i	0.586681i	−0.956008	+	0.293341i	$0.905233\pi$
$864$	9.60693e48	3.38928
$865$	0	0
$866$	9.51689e48	3.23184
$867$	1.43224e49i	4.77201i
$868$	9.78227e48i	3.19790i
$869$	2.41496e48	0.774610
$870$	0	0
$871$	−2.99621e48	−0.925278
$872$	− 8.35721e48i	− 2.53244i
$873$	− 2.41465e48i	− 0.717993i
$874$	1.18507e48	0.345785
$875$	0	0
$876$	9.18224e48	2.58007
$877$	− 2.98707e48i	− 0.823668i	−0.911259	−	0.411834i	$-0.864888\pi$
$877$	− 2.98707e48i	− 0.823668i	0.911259	−	0.411834i	$-0.135112\pi$
$878$	9.43422e48i	2.55297i
$879$	4.25230e48	1.12930
$880$	0	0
$881$	3.94938e48	1.01025	0.505123	−	0.863047i	$-0.331447\pi$
$881$	3.94938e48	1.01025	0.505123	+	0.863047i	$0.331447\pi$
$882$	− 7.46021e48i	− 1.87292i
$883$	− 5.17634e48i	− 1.27547i	−0.770255	−	0.637736i	$-0.779871\pi$
$883$	− 5.17634e48i	− 1.27547i	0.770255	−	0.637736i	$-0.220129\pi$
$884$	−2.05881e49	−4.97914
$885$	0	0
$886$	6.55712e48	1.52776
$887$	− 7.45605e47i	− 0.170518i	−0.996359	−	0.0852588i	$-0.972828\pi$
$887$	− 7.45605e47i	− 0.170518i	0.996359	−	0.0852588i	$-0.0271717\pi$
$888$	− 1.79868e48i	− 0.403776i
$889$	4.74749e48	1.04613
$890$	0	0
$891$	−1.02409e47	−0.0217449
$892$	1.94615e49i	4.05654i
$893$	− 1.14405e48i	− 0.234096i
$894$	−2.17383e48	−0.436672
$895$	0	0
$896$	1.52077e49	2.94430
$897$	5.39380e48i	1.02523i
$898$	− 5.54354e48i	− 1.03449i
$899$	5.43682e47	0.0996116
$900$	0	0
$901$	−2.03437e48	−0.359311
$902$	− 1.82770e47i	− 0.0316954i
$903$	− 8.48775e48i	− 1.44525i
$904$	1.30587e49	2.18334
$905$	0	0
$906$	−2.34909e49	−3.78690
$907$	2.76026e48i	0.436948i	0.975843	+	0.218474i	$0.0701079\pi$
$907$	2.76026e48i	0.436948i	−0.975843	+	0.218474i	$0.929892\pi$
$908$	− 2.22548e49i	− 3.45946i
$909$	−4.10667e48	−0.626882
$910$	0	0
$911$	−1.69247e48	−0.249155	−0.124577	−	0.992210i	$-0.539757\pi$
$911$	−1.69247e48	−0.249155	−0.124577	+	0.992210i	$0.539757\pi$
$912$	1.02799e49i	1.48619i
$913$	7.63977e48i	1.08471i
$914$	−2.27067e49	−3.16623
$915$	0	0
$916$	−2.67649e49	−3.59990
$917$	− 1.05858e49i	− 1.39840i
$918$	2.98798e49i	3.87680i
$919$	1.77855e48	0.226652	0.113326	−	0.993558i	$-0.463850\pi$
$919$	1.77855e48	0.226652	0.113326	+	0.993558i	$0.463850\pi$
$920$	0	0
$921$	2.63247e49	3.23653
$922$	1.31736e48i	0.159090i
$923$	1.12910e49i	1.33939i
$924$	−3.83075e49	−4.46371
$925$	0	0
$926$	3.13526e49	3.52527
$927$	− 1.76568e49i	− 1.95028i
$928$	− 3.19912e48i	− 0.347127i
$929$	1.77834e48	0.189564	0.0947818	−	0.995498i	$-0.469785\pi$
$929$	1.77834e48	0.189564	0.0947818	+	0.995498i	$0.469785\pi$
$930$	0	0
$931$	1.57969e48	0.162518
$932$	8.23772e48i	0.832615i
$933$	− 9.04250e48i	− 0.897928i
$934$	−2.74606e49	−2.67909
$935$	0	0
$936$	−5.16993e49	−4.86893
$937$	− 1.51116e49i	− 1.39832i	−0.714964	−	0.699162i	$-0.753557\pi$
$937$	− 1.51116e49i	− 1.39832i	0.714964	−	0.699162i	$-0.246443\pi$
$938$	2.60539e49i	2.36879i
$939$	−2.34949e48	−0.209890
$940$	0	0
$941$	1.64231e49	1.41654	0.708268	−	0.705944i	$-0.249477\pi$
$941$	1.64231e49	1.41654	0.708268	+	0.705944i	$0.249477\pi$
$942$	− 2.54732e49i	− 2.15896i
$943$	1.62537e47i	0.0135366i
$944$	7.29402e49	5.96938
$945$	0	0
$946$	−1.39624e49	−1.10346
$947$	− 7.47638e48i	− 0.580653i	−0.956928	−	0.290326i	$-0.906236\pi$
$947$	− 7.47638e48i	− 0.580653i	0.956928	−	0.290326i	$-0.0937639\pi$
$948$	− 5.32956e49i	− 4.06775i
$949$	−7.55091e48	−0.566378
$950$	0	0
$951$	−3.49619e49	−2.53289
$952$	1.11573e50i	7.94418i
$953$	− 4.85671e48i	− 0.339867i	−0.985456	−	0.169934i	$-0.945645\pi$
$953$	− 4.85671e48i	− 0.339867i	0.985456	−	0.169934i	$-0.0543553\pi$
$954$	−8.19705e48	−0.563780
$955$	0	0
$956$	−6.77542e48	−0.450175
$957$	2.12906e48i	0.139041i
$958$	3.38301e49i	2.17156i
$959$	3.44714e49	2.17497
$960$	0	0
$961$	−1.53011e48	−0.0932794
$962$	2.37336e48i	0.142225i
$963$	− 3.65854e49i	− 2.15513i
$964$	−1.85910e48	−0.107654
$965$	0	0
$966$	4.69026e49	2.62467
$967$	1.05832e49i	0.582208i	0.956691	+	0.291104i	$0.0940226\pi$
$967$	1.05832e49i	0.582208i	−0.956691	+	0.291104i	$0.905977\pi$
$968$	− 1.91905e49i	− 1.03787i
$969$	−1.63724e49	−0.870504
$970$	0	0
$971$	1.10262e49	0.566644	0.283322	−	0.959025i	$-0.408564\pi$
$971$	1.10262e49	0.566644	0.283322	+	0.959025i	$0.408564\pi$
$972$	− 5.13932e49i	− 2.59664i
$973$	− 4.09181e48i	− 0.203261i
$974$	1.74778e49	0.853621
$975$	0	0
$976$	−9.80341e49	−4.62866
$977$	1.02152e49i	0.474227i	0.971482	+	0.237114i	$0.0762014\pi$
$977$	1.02152e49i	0.474227i	−0.971482	+	0.237114i	$0.923799\pi$
$978$	− 6.66275e49i	− 3.04132i
$979$	−9.57841e48	−0.429911
$980$	0	0
$981$	3.00804e49	1.30540
$982$	− 1.75657e49i	− 0.749594i
$983$	− 1.94073e49i	− 0.814388i	−0.913342	−	0.407194i	$-0.866507\pi$
$983$	− 1.94073e49i	− 0.814388i	0.913342	−	0.407194i	$-0.133493\pi$
$984$	−2.51378e48	−0.103731
$985$	0	0
$986$	9.95000e48	0.397058
$987$	− 4.52789e49i	− 1.77690i
$988$	− 1.75656e49i	− 0.677914i
$989$	1.24167e49	0.471268
$990$	0	0
$991$	9.24952e48	0.339550	0.169775	−	0.985483i	$-0.445696\pi$
$991$	9.24952e48	0.339550	0.169775	+	0.985483i	$0.445696\pi$
$992$	− 8.75175e49i	− 3.15975i
$993$	− 5.11613e49i	− 1.81668i
$994$	9.81828e49	3.42894
$995$	0	0
$996$	1.68602e50	5.69617
$997$	4.80545e49i	1.59685i	0.602095	+	0.798424i	$0.294333\pi$
$997$	4.80545e49i	1.59685i	−0.602095	+	0.798424i	$0.705667\pi$
$998$	3.86927e49i	1.26466i
$999$	2.50184e48	0.0804321

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.b.d.24.1		22
5.2	odd	4		25.34.a.d.1.11	✓	11
5.3	odd	4		25.34.a.e.1.1	yes	11
5.4	even	2	inner	25.34.b.d.24.22		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.34.a.d.1.11	✓	11	5.2	odd	4
25.34.a.e.1.1	yes	11	5.3	odd	4
25.34.b.d.24.1		22	1.1	even	1	trivial
25.34.b.d.24.22		22	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-177167. i q^{2} -1.20911e8i q^{3} -2.27982e10 q^{4} -2.14214e13 q^{6} -1.11259e14i q^{7} +2.51723e15i q^{8} -9.06036e15 q^{9} +O(q^{10})\)	\(q-177167. i q^{2} -1.20911e8i q^{3} -2.27982e10 q^{4} -2.14214e13 q^{6} -1.11259e14i q^{7} +2.51723e15i q^{8} -9.06036e15 q^{9} -1.24906e17 q^{11} +2.75655e18i q^{12} -2.26681e18i q^{13} -1.97114e19 q^{14} +2.50136e20 q^{16} +3.98383e20i q^{17} +1.60520e21i q^{18} -3.39897e20 q^{19} -1.34524e22 q^{21} +2.21292e22i q^{22} -1.96795e22i q^{23} +3.04361e23 q^{24} -4.01605e23 q^{26} +4.23345e23i q^{27} +2.53650e24i q^{28} +1.40974e23 q^{29} +3.85660e24 q^{31} -2.26929e25i q^{32} +1.51025e25i q^{33} +7.05803e25 q^{34} +2.06560e26 q^{36} -5.90970e24i q^{37} +6.02185e25i q^{38} -2.74082e26 q^{39} -8.25921e24 q^{41} +2.38332e27i q^{42} +6.30947e26i q^{43} +2.84763e27 q^{44} -3.48656e27 q^{46} +3.36586e27i q^{47} -3.02441e28i q^{48} -4.64754e27 q^{49} +4.81688e28 q^{51} +5.16793e28i q^{52} +5.10657e27i q^{53} +7.50028e28 q^{54} +2.80065e29 q^{56} +4.10972e28i q^{57} -2.49760e28i q^{58} +2.91603e29 q^{59} -3.91923e29 q^{61} -6.83262e29i q^{62} +1.00805e30i q^{63} -1.87178e30 q^{64} +2.67566e30 q^{66} -1.32177e30i q^{67} -9.08241e30i q^{68} -2.37946e30 q^{69} -4.98102e30 q^{71} -2.28071e31i q^{72} -3.33107e30i q^{73} -1.04700e30 q^{74} +7.74904e30 q^{76} +1.38969e31i q^{77} +4.85583e31i q^{78} -1.93342e31 q^{79} +8.19892e29 q^{81} +1.46326e30i q^{82} -6.11641e31i q^{83} +3.06690e32 q^{84} +1.11783e32 q^{86} -1.70453e31i q^{87} -3.14418e32i q^{88} +7.66849e31 q^{89} -2.52203e32 q^{91} +4.48657e32i q^{92} -4.66305e32i q^{93} +5.96319e32 q^{94} -2.74382e33 q^{96} +2.66508e32i q^{97} +8.23390e32i q^{98} +1.13169e33 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 98676413354 q^{4} - 35567955353446 q^{6} - 48\!\cdots\!16 q^{9}+O(q^{10}) \) 22 * q - 98676413354 * q^4 - 35567955353446 * q^6 - 48599275949251316 * q^9	\( 22 q - 98676413354 q^{4} - 35567955353446 q^{6} - 48\!\cdots\!16 q^{9}+ \cdots - 26\!\cdots\!12 q^{99}+O(q^{100}) \) 22 * q - 98676413354 * q^4 - 35567955353446 * q^6 - 48599275949251316 * q^9 - 388975069134227046 * q^11 - 19390008595334902068 * q^14 + 575591759119330759202 * q^16 + 4608842794243084808630 * q^19 + 7903359076848510896124 * q^21 + 404192556148581428871090 * q^24 + 464682665356996878920184 * q^26 - 3351264573191459117593680 * q^29 - 3759368993361156279858876 * q^31 + 89746721762579763434900102 * q^34 + 387355373506331566119004012 * q^36 + 718345493252093200854565688 * q^39 + 1099039609507795057059146334 * q^41 + 5953087248173453754548821422 * q^44 + 3376724462669734942026715164 * q^46 + 5003317848948805057160966146 * q^49 + 132635930632492996145333201114 * q^51 + 426786304479392249563776060130 * q^54 + 679074245273936256251630129820 * q^56 + 135413981096960311593168243840 * q^59 - 689538516943594572498942901796 * q^61 - 2840052535921821128029255801474 * q^64 - 320033315173213395102299074022 * q^66 - 14437009323987384127917423522852 * q^69 - 11051811216899923387221184379736 * q^71 - 16966204054892971302102433594308 * q^74 - 7588775596602318790343300932510 * q^76 - 56833627147150708379517479188380 * q^79 - 9022895406968638344517956762058 * q^81 + 599893154314490734522302146543532 * q^84 + 911820864247632195182318378176824 * q^86 + 48061740522903759998741201101110 * q^89 - 693375717774307216790074646600496 * q^91 - 465076424153121919006535311120888 * q^94 - 3684220565182840604743827051904706 * q^96 - 2601899095573470033938075107273612 * q^99

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