LMFDB - Embedded newform 25.34.b.d.24.4

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			24.4
Character	$\chi$	$=$	25.24
Dual form			25.34.b.d.24.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-140551. i q^{2} -1.29136e8i q^{3} -1.11647e10 q^{4} -1.81502e13 q^{6} +4.00085e13i q^{7} +3.61884e14i q^{8} -1.11170e16 q^{9} +O(q^{10})$	\(q-140551. i q^{2} -1.29136e8i q^{3} -1.11647e10 q^{4} -1.81502e13 q^{6} +4.00085e13i q^{7} +3.61884e14i q^{8} -1.11170e16 q^{9} +2.48192e17 q^{11} +1.44176e18i q^{12} +3.61009e18i q^{13} +5.62325e18 q^{14} -4.50407e19 q^{16} +5.03453e19i q^{17} +1.56251e21i q^{18} +1.19790e21 q^{19} +5.16654e21 q^{21} -3.48837e22i q^{22} -2.35311e22i q^{23} +4.67322e22 q^{24} +5.07403e23 q^{26} +7.17728e23i q^{27} -4.46683e23i q^{28} +2.45131e24 q^{29} -2.88511e24 q^{31} +9.43908e24i q^{32} -3.20505e25i q^{33} +7.07609e24 q^{34} +1.24118e26 q^{36} -3.58819e25i q^{37} -1.68366e26i q^{38} +4.66192e26 q^{39} +6.61568e25 q^{41} -7.26162e26i q^{42} +1.70988e27i q^{43} -2.77099e27 q^{44} -3.30733e27 q^{46} -4.53211e27i q^{47} +5.81637e27i q^{48} +6.13031e27 q^{49} +6.50138e27 q^{51} -4.03056e28i q^{52} +1.11477e28i q^{53} +1.00877e29 q^{54} -1.44784e28 q^{56} -1.54691e29i q^{57} -3.44534e29i q^{58} -1.06018e29 q^{59} +9.42654e28 q^{61} +4.05506e29i q^{62} -4.44775e29i q^{63} +9.39777e29 q^{64} -4.50473e30 q^{66} -2.59250e30i q^{67} -5.62090e29i q^{68} -3.03871e30 q^{69} -4.27372e30 q^{71} -4.02306e30i q^{72} +2.23754e30i q^{73} -5.04324e30 q^{74} -1.33741e31 q^{76} +9.92980e30i q^{77} -6.55239e31i q^{78} +2.21899e31 q^{79} +3.08843e31 q^{81} -9.29841e30i q^{82} +2.60461e31i q^{83} -5.76827e31 q^{84} +2.40325e32 q^{86} -3.16552e32i q^{87} +8.98167e31i q^{88} -1.65644e32 q^{89} -1.44435e32 q^{91} +2.62718e32i q^{92} +3.72571e32i q^{93} -6.36993e32 q^{94} +1.21892e33 q^{96} +1.37226e32i q^{97} -8.61622e32i q^{98} -2.75915e33 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	− 140551.i	− 1.51649i	−0.651970	−	0.758245i	$-0.726057\pi$
$2$	− 140551.i	− 1.51649i	0.651970	−	0.758245i	$-0.273943\pi$
$3$	− 1.29136e8i	− 1.73199i	−0.500051	−	0.865996i	$-0.666685\pi$
$3$	− 1.29136e8i	− 1.73199i	0.500051	−	0.865996i	$-0.333315\pi$
$4$	−1.11647e10	−1.29974
$5$	0	0
$5$	0	0
$6$	−1.81502e13	−2.62655
$7$	4.00085e13i	0.455025i	0.973775	+	0.227512i	$0.0730592\pi$
$7$	4.00085e13i	0.455025i	−0.973775	+	0.227512i	$0.926941\pi$
$8$	3.61884e14i	0.454553i
$9$	−1.11170e16	−1.99980
$10$	0	0
$11$	2.48192e17	1.62858	0.814289	−	0.580460i	$-0.197127\pi$
$11$	2.48192e17	1.62858	0.814289	+	0.580460i	$0.197127\pi$
$12$	1.44176e18i	2.25114i
$13$	3.61009e18i	1.50471i	0.658757	+	0.752356i	$0.271083\pi$
$13$	3.61009e18i	1.50471i	−0.658757	+	0.752356i	$0.728917\pi$
$14$	5.62325e18	0.690040
$15$	0	0
$16$	−4.50407e19	−0.610416
$17$	5.03453e19i	0.250930i	0.992098	+	0.125465i	$0.0400422\pi$
$17$	5.03453e19i	0.250930i	−0.992098	+	0.125465i	$0.959958\pi$
$18$	1.56251e21i	3.03267i
$19$	1.19790e21	0.952764	0.476382	−	0.879238i	$-0.341948\pi$
$19$	1.19790e21	0.952764	0.476382	+	0.879238i	$0.341948\pi$
$20$	0	0
$21$	5.16654e21	0.788099
$22$	− 3.48837e22i	− 2.46972i
$23$	− 2.35311e22i	− 0.800081i	−0.916498	−	0.400040i	$-0.868996\pi$
$23$	− 2.35311e22i	− 0.800081i	0.916498	−	0.400040i	$-0.131004\pi$
$24$	4.67322e22	0.787282
$25$	0	0
$26$	5.07403e23	2.28188
$27$	7.17728e23i	1.73164i
$28$	− 4.46683e23i	− 0.591414i
$29$	2.45131e24	1.81899	0.909497	−	0.415711i	$-0.136467\pi$
$29$	2.45131e24	1.81899	0.909497	+	0.415711i	$0.136467\pi$
$30$	0	0
$31$	−2.88511e24	−0.712352	−0.356176	−	0.934419i	$-0.615920\pi$
$31$	−2.88511e24	−0.712352	−0.356176	+	0.934419i	$0.615920\pi$
$32$	9.43908e24i	1.38024i
$33$	− 3.20505e25i	− 2.82068i
$34$	7.07609e24	0.380532
$35$	0	0
$36$	1.24118e26	2.59922
$37$	− 3.58819e25i	− 0.478131i	−0.971003	−	0.239066i	$-0.923159\pi$
$37$	− 3.58819e25i	− 0.478131i	0.971003	−	0.239066i	$-0.0768411\pi$
$38$	− 1.68366e26i	− 1.44486i
$39$	4.66192e26	2.60615
$40$	0	0
$41$	6.61568e25	0.162047	0.0810234	−	0.996712i	$-0.474181\pi$
$41$	6.61568e25	0.162047	0.0810234	+	0.996712i	$0.474181\pi$
$42$	− 7.26162e26i	− 1.19514i
$43$	1.70988e27i	1.90869i	0.298702	+	0.954346i	$0.403446\pi$
$43$	1.70988e27i	1.90869i	−0.298702	+	0.954346i	$0.596554\pi$
$44$	−2.77099e27	−2.11673
$45$	0	0
$46$	−3.30733e27	−1.21331
$47$	− 4.53211e27i	− 1.16597i	−0.812485	−	0.582983i	$-0.801886\pi$
$47$	− 4.53211e27i	− 1.16597i	0.812485	−	0.582983i	$-0.198114\pi$
$48$	5.81637e27i	1.05724i
$49$	6.13031e27	0.792952
$50$	0	0
$51$	6.50138e27	0.434608
$52$	− 4.03056e28i	− 1.95573i
$53$	1.11477e28i	0.395031i	0.980300	+	0.197516i	$0.0632873\pi$
$53$	1.11477e28i	0.395031i	−0.980300	+	0.197516i	$0.936713\pi$
$54$	1.00877e29	2.62601
$55$	0	0
$56$	−1.44784e28	−0.206833
$57$	− 1.54691e29i	− 1.65018i
$58$	− 3.44534e29i	− 2.75848i
$59$	−1.06018e29	−0.640210	−0.320105	−	0.947382i	$-0.603718\pi$
$59$	−1.06018e29	−0.640210	−0.320105	+	0.947382i	$0.603718\pi$
$60$	0	0
$61$	9.42654e28	0.328405	0.164203	−	0.986427i	$-0.447495\pi$
$61$	9.42654e28	0.328405	0.164203	+	0.986427i	$0.447495\pi$
$62$	4.05506e29i	1.08027i
$63$	− 4.44775e29i	− 0.909957i
$64$	9.39777e29	1.48271
$65$	0	0
$66$	−4.50473e30	−4.27754
$67$	− 2.59250e30i	− 1.92081i	−0.278607	−	0.960405i	$-0.589873\pi$
$67$	− 2.59250e30i	− 1.92081i	0.278607	−	0.960405i	$-0.410127\pi$
$68$	− 5.62090e29i	− 0.326143i
$69$	−3.03871e30	−1.38573
$70$	0	0
$71$	−4.27372e30	−1.21631	−0.608153	−	0.793820i	$-0.708089\pi$
$71$	−4.27372e30	−1.21631	−0.608153	+	0.793820i	$0.708089\pi$
$72$	− 4.02306e30i	− 0.909013i
$73$	2.23754e30i	0.402664i	0.979523	+	0.201332i	$0.0645271\pi$
$73$	2.23754e30i	0.402664i	−0.979523	+	0.201332i	$0.935473\pi$
$74$	−5.04324e30	−0.725081
$75$	0	0
$76$	−1.33741e31	−1.23835
$77$	9.92980e30i	0.741043i
$78$	− 6.55239e31i	− 3.95220i
$79$	2.21899e31	1.08470	0.542349	−	0.840153i	$-0.317535\pi$
$79$	2.21899e31	1.08470	0.542349	+	0.840153i	$0.317535\pi$
$80$	0	0
$81$	3.08843e31	0.999390
$82$	− 9.29841e30i	− 0.245742i
$83$	2.60461e31i	0.563579i	0.959476	+	0.281790i	$0.0909280\pi$
$83$	2.60461e31i	0.563579i	−0.959476	+	0.281790i	$0.909072\pi$
$84$	−5.76827e31	−1.02432
$85$	0	0
$86$	2.40325e32	2.89451
$87$	− 3.16552e32i	− 3.15048i
$88$	8.98167e31i	0.740275i
$89$	−1.65644e32	−1.13302	−0.566512	−	0.824053i	$-0.691708\pi$
$89$	−1.65644e32	−1.13302	−0.566512	+	0.824053i	$0.691708\pi$
$90$	0	0
$91$	−1.44435e32	−0.684681
$92$	2.62718e32i	1.03990i
$93$	3.72571e32i	1.23379i
$94$	−6.36993e32	−1.76817
$95$	0	0
$96$	1.21892e33	2.39057
$97$	1.37226e32i	0.226831i	0.993548	+	0.113416i	$0.0361792\pi$
$97$	1.37226e32i	0.226831i	−0.993548	+	0.113416i	$0.963821\pi$
$98$	− 8.61622e32i	− 1.20250i
$99$	−2.75915e33	−3.25682
$100$	0	0
$101$	1.03548e33	0.878698	0.439349	−	0.898317i	$-0.355209\pi$
$101$	1.03548e33	0.878698	0.439349	+	0.898317i	$0.355209\pi$
$102$	− 9.13777e32i	− 0.659079i
$103$	− 2.45463e33i	− 1.50720i	−0.657333	−	0.753600i	$-0.728316\pi$
$103$	− 2.45463e33i	− 1.50720i	0.657333	−	0.753600i	$-0.271684\pi$
$104$	−1.30643e33	−0.683971
$105$	0	0
$106$	1.56681e33	0.599061
$107$	− 1.11407e33i	− 0.364822i	−0.983222	−	0.182411i	$-0.941610\pi$
$107$	− 1.11407e33i	− 0.364822i	0.983222	−	0.182411i	$-0.0583901\pi$
$108$	− 8.01320e33i	− 2.25068i
$109$	2.70218e33	0.651894	0.325947	−	0.945388i	$-0.394317\pi$
$109$	2.70218e33	0.651894	0.325947	+	0.945388i	$0.394317\pi$
$110$	0	0
$111$	−4.63364e33	−0.828120
$112$	− 1.80201e33i	− 0.277754i
$113$	− 2.20215e33i	− 0.293124i	−0.989201	−	0.146562i	$-0.953179\pi$
$113$	− 2.20215e33i	− 0.293124i	0.989201	−	0.146562i	$-0.0468209\pi$
$114$	−2.17421e34	−2.50248
$115$	0	0
$116$	−2.73681e34	−2.36422
$117$	− 4.01334e34i	− 3.00912i
$118$	1.49010e34i	0.970872i
$119$	−2.01424e33	−0.114179
$120$	0	0
$121$	3.83741e34	1.65227
$122$	− 1.32491e34i	− 0.498023i
$123$	− 8.54321e33i	− 0.280664i
$124$	3.22114e34	0.925872
$125$	0	0
$126$	−6.25136e34	−1.37994
$127$	− 4.18545e34i	− 0.810925i	−0.914112	−	0.405463i	$-0.867110\pi$
$127$	− 4.18545e34i	− 0.810925i	0.914112	−	0.405463i	$-0.132890\pi$
$128$	− 5.10056e34i	− 0.868267i
$129$	2.20807e35	3.30584
$130$	0	0
$131$	1.65700e35	1.92463	0.962314	−	0.271941i	$-0.0876655\pi$
$131$	1.65700e35	1.92463	0.962314	+	0.271941i	$0.0876655\pi$
$132$	3.57833e35i	3.66616i
$133$	4.79261e34i	0.433531i
$134$	−3.64379e35	−2.91289
$135$	0	0
$136$	−1.82192e34	−0.114061
$137$	1.27396e35i	0.706751i	0.935482	+	0.353375i	$0.114966\pi$
$137$	1.27396e35i	0.706751i	−0.935482	+	0.353375i	$0.885034\pi$
$138$	4.27094e35i	2.10145i
$139$	2.10212e35	0.918148	0.459074	−	0.888398i	$-0.348181\pi$
$139$	2.10212e35	0.918148	0.459074	+	0.888398i	$0.348181\pi$
$140$	0	0
$141$	−5.85257e35	−2.01944
$142$	6.00676e35i	1.84452i
$143$	8.95997e35i	2.45054i
$144$	5.00717e35	1.22071
$145$	0	0
$146$	3.14488e35	0.610636
$147$	− 7.91642e35i	− 1.37339i
$148$	4.00610e35i	0.621446i
$149$	−3.92609e35	−0.544987	−0.272494	−	0.962158i	$-0.587848\pi$
$149$	−3.92609e35	−0.544987	−0.272494	+	0.962158i	$0.587848\pi$
$150$	0	0
$151$	1.34206e36	1.49504	0.747521	−	0.664239i	$-0.231244\pi$
$151$	1.34206e36	1.49504	0.747521	+	0.664239i	$0.231244\pi$
$152$	4.33500e35i	0.433082i
$153$	− 5.59689e35i	− 0.501808i
$154$	1.39564e36	1.12378
$155$	0	0
$156$	−5.20489e36	−3.38732
$157$	− 1.18714e36i	− 0.695279i	−0.937628	−	0.347640i	$-0.886983\pi$
$157$	− 1.18714e36i	− 0.695279i	0.937628	−	0.347640i	$-0.113017\pi$
$158$	− 3.11882e36i	− 1.64493i
$159$	1.43956e36	0.684191
$160$	0	0
$161$	9.41447e35	0.364057
$162$	− 4.34082e36i	− 1.51556i
$163$	2.79919e36i	0.882950i	0.897273	+	0.441475i	$0.145545\pi$
$163$	2.79919e36i	0.882950i	−0.897273	+	0.441475i	$0.854455\pi$
$164$	−7.38619e35	−0.210619
$165$	0	0
$166$	3.66082e36	0.854662
$167$	− 1.00045e36i	− 0.211531i	−0.994391	−	0.105766i	$-0.966271\pi$
$167$	− 1.00045e36i	− 0.211531i	0.994391	−	0.105766i	$-0.0337294\pi$
$168$	1.86969e36i	0.358233i
$169$	−7.27665e36	−1.26416
$170$	0	0
$171$	−1.33170e37	−1.90533
$172$	− 1.90903e37i	− 2.48080i
$173$	− 3.30706e36i	− 0.390554i	−0.980748	−	0.195277i	$-0.937439\pi$
$173$	− 3.30706e36i	− 0.390554i	0.980748	−	0.195277i	$-0.0625606\pi$
$174$	−4.44917e37	−4.77767
$175$	0	0
$176$	−1.11787e37	−0.994109
$177$	1.36908e37i	1.10884i
$178$	2.32814e37i	1.71822i
$179$	−7.68220e36	−0.516905	−0.258452	−	0.966024i	$-0.583213\pi$
$179$	−7.68220e36	−0.516905	−0.258452	+	0.966024i	$0.583213\pi$
$180$	0	0
$181$	1.70691e37	0.956123	0.478062	−	0.878326i	$-0.341340\pi$
$181$	1.70691e37	0.956123	0.478062	+	0.878326i	$0.341340\pi$
$182$	2.03005e37i	1.03831i
$183$	− 1.21730e37i	− 0.568795i
$184$	8.51554e36	0.363679
$185$	0	0
$186$	5.23653e37	1.87103
$187$	1.24953e37i	0.408658i
$188$	5.05995e37i	1.51545i
$189$	−2.87152e37	−0.787939
$190$	0	0
$191$	3.12199e37	0.720080	0.360040	−	0.932937i	$-0.382763\pi$
$191$	3.12199e37	0.720080	0.360040	+	0.932937i	$0.382763\pi$
$192$	− 1.21359e38i	− 2.56804i
$193$	− 3.37722e37i	− 0.655940i	−0.944688	−	0.327970i	$-0.893635\pi$
$193$	− 3.37722e37i	− 0.655940i	0.944688	−	0.327970i	$-0.106365\pi$
$194$	1.92873e37	0.343987
$195$	0	0
$196$	−6.84430e37	−1.03063
$197$	1.81875e37i	0.251814i	0.992042	+	0.125907i	$0.0401840\pi$
$197$	1.81875e37i	0.251814i	−0.992042	+	0.125907i	$0.959816\pi$
$198$	3.87801e38i	4.93894i
$199$	−1.94624e37	−0.228098	−0.114049	−	0.993475i	$-0.536382\pi$
$199$	−1.94624e37	−0.228098	−0.114049	+	0.993475i	$0.536382\pi$
$200$	0	0
$201$	−3.34785e38	−3.32683
$202$	− 1.45538e38i	− 1.33254i
$203$	9.80733e37i	0.827687i
$204$	−7.25859e37	−0.564878
$205$	0	0
$206$	−3.45000e38	−2.28565
$207$	2.61595e38i	1.60000i
$208$	− 1.62601e38i	− 0.918499i
$209$	2.97309e38	1.55165
$210$	0	0
$211$	−4.61601e37	−0.205876	−0.102938	−	0.994688i	$-0.532824\pi$
$211$	−4.61601e37	−0.205876	−0.102938	+	0.994688i	$0.532824\pi$
$212$	− 1.24460e38i	− 0.513438i
$213$	5.51890e38i	2.10663i
$214$	−1.56584e38	−0.553249
$215$	0	0
$216$	−2.59734e38	−0.787122
$217$	− 1.15429e38i	− 0.324138i
$218$	− 3.79795e38i	− 0.988591i
$219$	2.88946e38	0.697411
$220$	0	0
$221$	−1.81751e38	−0.377577
$222$	6.51263e38i	1.25583i
$223$	3.65945e38i	0.655218i	0.944813	+	0.327609i	$0.106243\pi$
$223$	3.65945e38i	0.655218i	−0.944813	+	0.327609i	$0.893757\pi$
$224$	−3.77644e38	−0.628044
$225$	0	0
$226$	−3.09514e38	−0.444520
$227$	− 8.68482e38i	− 1.15967i	−0.814734	−	0.579834i	$-0.803117\pi$
$227$	− 8.68482e38i	− 1.15967i	0.814734	−	0.579834i	$-0.196883\pi$
$228$	1.72708e39i	2.14481i
$229$	−3.80140e38	−0.439195	−0.219598	−	0.975591i	$-0.570474\pi$
$229$	−3.80140e38	−0.439195	−0.219598	+	0.975591i	$0.570474\pi$
$230$	0	0
$231$	1.28229e39	1.28348
$232$	8.87089e38i	0.826829i
$233$	7.33719e38i	0.637026i	0.947918	+	0.318513i	$0.103183\pi$
$233$	7.33719e38i	0.637026i	−0.947918	+	0.318513i	$0.896817\pi$
$234$	−5.64079e39	−4.56329
$235$	0	0
$236$	1.18366e39	0.832107
$237$	− 2.86551e39i	− 1.87869i
$238$	2.83104e38i	0.173152i
$239$	2.06579e39	1.17902	0.589509	−	0.807762i	$-0.299321\pi$
$239$	2.06579e39	1.17902	0.589509	+	0.807762i	$0.299321\pi$
$240$	0	0
$241$	1.68438e39	0.837833	0.418917	−	0.908025i	$-0.362410\pi$
$241$	1.68438e39	0.837833	0.418917	+	0.908025i	$0.362410\pi$
$242$	− 5.39353e39i	− 2.50564i
$243$	1.62204e36i	0 0.000703975i
$244$	−1.05244e39	−0.426842
$245$	0	0
$246$	−1.20076e39	−0.425624
$247$	4.32452e39i	1.43364i
$248$	− 1.04408e39i	− 0.323802i
$249$	3.36349e39	0.976115
$250$	0	0
$251$	3.13801e39	0.798065	0.399032	−	0.916937i	$-0.369346\pi$
$251$	3.13801e39	0.798065	0.399032	+	0.916937i	$0.369346\pi$
$252$	4.96577e39i	1.18271i
$253$	− 5.84024e39i	− 1.30299i
$254$	−5.88270e39	−1.22976
$255$	0	0
$256$	9.03730e38	0.165989
$257$	6.46986e39i	1.11429i	0.830415	+	0.557145i	$0.188103\pi$
$257$	6.46986e39i	1.11429i	−0.830415	+	0.557145i	$0.811897\pi$
$258$	− 3.10346e40i	− 5.01327i
$259$	1.43558e39	0.217562
$260$	0	0
$261$	−2.72512e40	−3.63762
$262$	− 2.32894e40i	− 2.91868i
$263$	9.40764e39i	1.10716i	0.832796	+	0.553581i	$0.186739\pi$
$263$	9.40764e39i	1.10716i	−0.832796	+	0.553581i	$0.813261\pi$
$264$	1.15985e40	1.28215
$265$	0	0
$266$	6.73607e39	0.657446
$267$	2.13905e40i	1.96239i
$268$	2.89444e40i	2.49655i
$269$	1.06054e40	0.860229	0.430115	−	0.902774i	$-0.358473\pi$
$269$	1.06054e40	0.860229	0.430115	+	0.902774i	$0.358473\pi$
$270$	0	0
$271$	5.90847e39	0.424113	0.212057	−	0.977257i	$-0.431984\pi$
$271$	5.90847e39	0.424113	0.212057	+	0.977257i	$0.431984\pi$
$272$	− 2.26759e39i	− 0.153171i
$273$	1.86517e40i	1.18586i
$274$	1.79056e40	1.07178
$275$	0	0
$276$	3.39263e40	1.80109
$277$	− 4.69522e39i	− 0.234822i	−0.993083	−	0.117411i	$-0.962540\pi$
$277$	− 4.69522e39i	− 0.234822i	0.993083	−	0.117411i	$-0.0374596\pi$
$278$	− 2.95455e40i	− 1.39236i
$279$	3.20738e40	1.42456
$280$	0	0
$281$	−2.77236e40	−1.09445	−0.547225	−	0.836986i	$-0.684316\pi$
$281$	−2.77236e40	−1.09445	−0.547225	+	0.836986i	$0.684316\pi$
$282$	8.22586e40i	3.06246i
$283$	− 1.78562e40i	− 0.627064i	−0.949578	−	0.313532i	$-0.898488\pi$
$283$	− 1.78562e40i	− 0.627064i	0.949578	−	0.313532i	$-0.101512\pi$
$284$	4.77147e40	1.58088
$285$	0	0
$286$	1.25933e41	3.71622
$287$	2.64684e39i	0.0737353i
$288$	− 1.04934e41i	− 2.76020i
$289$	3.77198e40	0.937034
$290$	0	0
$291$	1.77208e40	0.392870
$292$	− 2.49814e40i	− 0.523359i
$293$	7.90450e40i	1.56516i	0.622551	+	0.782580i	$0.286096\pi$
$293$	7.90450e40i	1.56516i	−0.622551	+	0.782580i	$0.713904\pi$
$294$	−1.11266e41	−2.08273
$295$	0	0
$296$	1.29851e40	0.217336
$297$	1.78134e41i	2.82011i
$298$	5.51816e40i	0.826468i
$299$	8.49496e40	1.20389
$300$	0	0
$301$	−6.84098e40	−0.868503
$302$	− 1.88628e41i	− 2.26721i
$303$	− 1.33718e41i	− 1.52190i
$304$	−5.39542e40	−0.581582
$305$	0	0
$306$	−7.86649e40	−0.760987
$307$	− 1.77046e41i	− 1.62294i	−0.584393	−	0.811471i	$-0.698667\pi$
$307$	− 1.77046e41i	− 1.62294i	0.584393	−	0.811471i	$-0.301333\pi$
$308$	− 1.10863e41i	− 0.963164i
$309$	−3.16980e41	−2.61046
$310$	0	0
$311$	6.58911e40	0.487843	0.243922	−	0.969795i	$-0.421566\pi$
$311$	6.58911e40	0.487843	0.243922	+	0.969795i	$0.421566\pi$
$312$	1.68707e41i	1.18463i
$313$	− 1.43570e41i	− 0.956276i	−0.878285	−	0.478138i	$-0.841312\pi$
$313$	− 1.43570e41i	− 0.956276i	0.878285	−	0.478138i	$-0.158688\pi$
$314$	−1.66854e41	−1.05438
$315$	0	0
$316$	−2.47744e41	−1.40983
$317$	− 1.92102e41i	− 1.03766i	−0.854877	−	0.518830i	$-0.826368\pi$
$317$	− 1.92102e41i	− 1.03766i	0.854877	−	0.518830i	$-0.173632\pi$
$318$	− 2.02332e41i	− 1.03757i
$319$	6.08395e41	2.96237
$320$	0	0
$321$	−1.43867e41	−0.631869
$322$	− 1.32321e41i	− 0.552088i
$323$	6.03086e40i	0.239077i
$324$	−3.44814e41	−1.29895
$325$	0	0
$326$	3.93429e41	1.33898
$327$	− 3.48948e41i	− 1.12908i
$328$	2.39411e40i	0.0736589i
$329$	1.81323e41	0.530543
$330$	0	0
$331$	6.51390e41	1.72456	0.862282	−	0.506429i	$-0.169035\pi$
$331$	6.51390e41	1.72456	0.862282	+	0.506429i	$0.169035\pi$
$332$	− 2.90797e41i	− 0.732507i
$333$	3.98899e41i	0.956165i
$334$	−1.40615e41	−0.320785
$335$	0	0
$336$	−2.32704e41	−0.481068
$337$	− 1.11640e41i	− 0.219749i	−0.993945	−	0.109874i	$-0.964955\pi$
$337$	− 1.11640e41i	− 0.219749i	0.993945	−	0.109874i	$-0.0350448\pi$
$338$	1.02274e42i	1.91708i
$339$	−2.84376e41	−0.507689
$340$	0	0
$341$	−7.16062e41	−1.16012
$342$	1.87172e42i	2.88942i
$343$	5.54571e41i	0.815838i
$344$	−6.18778e41	−0.867602
$345$	0	0
$346$	−4.64810e41	−0.592271
$347$	− 4.51461e41i	− 0.548509i	−0.961657	−	0.274255i	$-0.911569\pi$
$347$	− 4.51461e41i	− 0.548509i	0.961657	−	0.274255i	$-0.0884311\pi$
$348$	3.53420e42i	4.09481i
$349$	−1.08192e42	−1.19557	−0.597783	−	0.801658i	$-0.703952\pi$
$349$	−1.08192e42	−1.19557	−0.597783	+	0.801658i	$0.703952\pi$
$350$	0	0
$351$	−2.59107e42	−2.60562
$352$	2.34271e42i	2.24783i
$353$	− 1.02423e41i	− 0.0937809i	−0.998900	−	0.0468904i	$-0.985069\pi$
$353$	− 1.02423e41i	− 0.0937809i	0.998900	−	0.0468904i	$-0.0149312\pi$
$354$	1.92425e42	1.68154
$355$	0	0
$356$	1.84936e42	1.47264
$357$	2.60111e41i	0.197758i
$358$	1.07974e42i	0.783881i
$359$	6.14289e40	0.0425907	0.0212953	−	0.999773i	$-0.493221\pi$
$359$	6.14289e40	0.0425907	0.0212953	+	0.999773i	$0.493221\pi$
$360$	0	0
$361$	−1.45811e41	−0.0922407
$362$	− 2.39908e42i	− 1.44995i
$363$	− 4.95547e42i	− 2.86171i
$364$	1.61257e42	0.889908
$365$	0	0
$366$	−1.71093e42	−0.862572
$367$	− 2.92870e42i	− 1.41151i	−0.708454	−	0.705757i	$-0.750607\pi$
$367$	− 2.92870e42i	− 1.41151i	0.708454	−	0.705757i	$-0.249393\pi$
$368$	1.05986e42i	0.488382i
$369$	−7.35464e41	−0.324061
$370$	0	0
$371$	−4.46001e41	−0.179749
$372$	− 4.15964e42i	− 1.60360i
$373$	− 2.72869e42i	− 1.00637i	−0.864178	−	0.503186i	$-0.832161\pi$
$373$	− 2.72869e42i	− 1.00637i	0.864178	−	0.503186i	$-0.167839\pi$
$374$	1.75623e42	0.619726
$375$	0	0
$376$	1.64010e42	0.529993
$377$	8.84946e42i	2.73706i
$378$	4.03596e42i	1.19490i
$379$	−2.51319e42	−0.712327	−0.356163	−	0.934424i	$-0.615915\pi$
$379$	−2.51319e42	−0.712327	−0.356163	+	0.934424i	$0.615915\pi$
$380$	0	0
$381$	−5.40492e42	−1.40452
$382$	− 4.38799e42i	− 1.09199i
$383$	5.53799e42i	1.31999i	0.751268	+	0.659997i	$0.229443\pi$
$383$	5.53799e42i	1.31999i	−0.751268	+	0.659997i	$0.770557\pi$
$384$	−6.58665e42	−1.50383
$385$	0	0
$386$	−4.74672e42	−0.994726
$387$	− 1.90087e43i	− 3.81700i
$388$	− 1.53209e42i	− 0.294822i
$389$	−6.43527e42	−1.18686	−0.593428	−	0.804887i	$-0.702226\pi$
$389$	−6.43527e42	−1.18686	−0.593428	+	0.804887i	$0.702226\pi$
$390$	0	0
$391$	1.18468e42	0.200764
$392$	2.21846e42i	0.360439i
$393$	− 2.13978e43i	− 3.33344i
$394$	2.55627e42	0.381873
$395$	0	0
$396$	3.08050e43	4.23303
$397$	− 2.59182e41i	− 0.0341634i	−0.999854	−	0.0170817i	$-0.994562\pi$
$397$	− 2.59182e41i	− 0.0341634i	0.999854	−	0.0170817i	$-0.00543753\pi$
$398$	2.73547e42i	0.345908i
$399$	6.18898e42	0.750873
$400$	0	0
$401$	−2.15733e41	−0.0241010	−0.0120505	−	0.999927i	$-0.503836\pi$
$401$	−2.15733e41	−0.0241010	−0.0120505	+	0.999927i	$0.503836\pi$
$402$	4.70543e43i	5.04510i
$403$	− 1.04155e43i	− 1.07188i
$404$	−1.15608e43	−1.14208
$405$	0	0
$406$	1.37843e43	1.25518
$407$	− 8.90561e42i	− 0.778674i
$408$	2.35275e42i	0.197552i
$409$	−3.07671e42	−0.248114	−0.124057	−	0.992275i	$-0.539591\pi$
$409$	−3.07671e42	−0.248114	−0.124057	+	0.992275i	$0.539591\pi$
$410$	0	0
$411$	1.64514e43	1.22409
$412$	2.74051e43i	1.95897i
$413$	− 4.24164e42i	− 0.291312i
$414$	3.67675e43	2.42638
$415$	0	0
$416$	−3.40760e43	−2.07687
$417$	− 2.71458e43i	− 1.59022i
$418$	− 4.17871e43i	− 2.35306i
$419$	−8.31146e42	−0.449931	−0.224966	−	0.974367i	$-0.572227\pi$
$419$	−8.31146e42	−0.449931	−0.224966	+	0.974367i	$0.572227\pi$
$420$	0	0
$421$	−2.48499e43	−1.24357	−0.621786	−	0.783187i	$-0.713593\pi$
$421$	−2.48499e43	−1.24357	−0.621786	+	0.783187i	$0.713593\pi$
$422$	6.48786e42i	0.312209i
$423$	5.03834e43i	2.33169i
$424$	−4.03415e42	−0.179563
$425$	0	0
$426$	7.75687e43	3.19469
$427$	3.77142e42i	0.149433i
$428$	1.24383e43i	0.474174i
$429$	1.15705e44	4.24432
$430$	0	0
$431$	−5.49619e43	−1.86718	−0.933591	−	0.358340i	$-0.883343\pi$
$431$	−5.49619e43	−1.86718	−0.933591	+	0.358340i	$0.883343\pi$
$432$	− 3.23270e43i	− 1.05702i
$433$	1.92976e43i	0.607369i	0.952773	+	0.303685i	$0.0982169\pi$
$433$	1.92976e43i	0.607369i	−0.952773	+	0.303685i	$0.901783\pi$
$434$	−1.62237e43	−0.491552
$435$	0	0
$436$	−3.01690e43	−0.847293
$437$	− 2.81879e43i	− 0.762288i
$438$	− 4.06117e43i	− 1.05762i
$439$	4.45489e43	1.11731	0.558653	−	0.829401i	$-0.311318\pi$
$439$	4.45489e43	1.11731	0.558653	+	0.829401i	$0.311318\pi$
$440$	0	0
$441$	−6.81506e43	−1.58574
$442$	2.55454e43i	0.572591i
$443$	− 4.76827e43i	− 1.02967i	−0.857288	−	0.514837i	$-0.827853\pi$
$443$	− 4.76827e43i	− 1.02967i	0.857288	−	0.514837i	$-0.172147\pi$
$444$	5.17331e43	1.07634
$445$	0	0
$446$	5.14340e43	0.993631
$447$	5.06998e43i	0.943914i
$448$	3.75991e43i	0.674668i
$449$	−7.03065e43	−1.21599	−0.607996	−	0.793940i	$-0.708026\pi$
$449$	−7.03065e43	−1.21599	−0.607996	+	0.793940i	$0.708026\pi$
$450$	0	0
$451$	1.64196e43	0.263906
$452$	2.45863e43i	0.380986i
$453$	− 1.73308e44i	− 2.58940i
$454$	−1.22066e44	−1.75863
$455$	0	0
$456$	5.59803e43	0.750094
$457$	1.29751e44i	1.67685i	0.545018	+	0.838424i	$0.316523\pi$
$457$	1.29751e44i	1.67685i	−0.545018	+	0.838424i	$0.683477\pi$
$458$	5.34291e43i	0.666035i
$459$	−3.61342e43	−0.434520
$460$	0	0
$461$	−1.60383e43	−0.179512	−0.0897561	−	0.995964i	$-0.528609\pi$
$461$	−1.60383e43	−0.179512	−0.0897561	+	0.995964i	$0.528609\pi$
$462$	− 1.80228e44i	− 1.94639i
$463$	− 8.21430e43i	− 0.856020i	−0.903774	−	0.428010i	$-0.859215\pi$
$463$	− 8.21430e43i	− 0.856020i	0.903774	−	0.428010i	$-0.140785\pi$
$464$	−1.10409e44	−1.11034
$465$	0	0
$466$	1.03125e44	0.966044
$467$	− 2.45616e43i	− 0.222089i	−0.993815	−	0.111045i	$-0.964580\pi$
$467$	− 2.45616e43i	− 0.222089i	0.993815	−	0.111045i	$-0.0354196\pi$
$468$	4.48077e44i	3.91107i
$469$	1.03722e44	0.874016
$470$	0	0
$471$	−1.53303e44	−1.20422
$472$	− 3.83663e43i	− 0.291010i
$473$	4.24378e44i	3.10845i
$474$	−4.02751e44	−2.84901
$475$	0	0
$476$	2.24884e43	0.148403
$477$	− 1.23928e44i	− 0.789982i
$478$	− 2.90349e44i	− 1.78797i
$479$	−2.62104e44	−1.55933	−0.779664	−	0.626199i	$-0.784610\pi$
$479$	−2.62104e44	−1.55933	−0.779664	+	0.626199i	$0.784610\pi$
$480$	0	0
$481$	1.29537e44	0.719450
$482$	− 2.36741e44i	− 1.27057i
$483$	− 1.21574e44i	− 0.630543i
$484$	−4.28435e44	−2.14752
$485$	0	0
$486$	2.27979e41	0.00106757
$487$	1.10024e43i	0.0498037i	0.999690	+	0.0249018i	$0.00792732\pi$
$487$	1.10024e43i	0.0498037i	−0.999690	+	0.0249018i	$0.992073\pi$
$488$	3.41131e43i	0.149278i
$489$	3.61475e44	1.52926
$490$	0	0
$491$	−2.25640e44	−0.892426	−0.446213	−	0.894927i	$-0.647228\pi$
$491$	−2.25640e44	−0.892426	−0.446213	+	0.894927i	$0.647228\pi$
$492$	9.53822e43i	0.364790i
$493$	1.23412e44i	0.456439i
$494$	6.07817e44	2.17409
$495$	0	0
$496$	1.29947e44	0.434831
$497$	− 1.70985e44i	− 0.553450i
$498$	− 4.72742e44i	− 1.48027i
$499$	4.29566e44	1.30128	0.650641	−	0.759386i	$-0.274500\pi$
$499$	4.29566e44	1.30128	0.650641	+	0.759386i	$0.274500\pi$
$500$	0	0
$501$	−1.29194e44	−0.366371
$502$	− 4.41051e44i	− 1.21026i
$503$	2.02877e44i	0.538717i	0.963040	+	0.269359i	$0.0868117\pi$
$503$	2.02877e44i	0.538717i	−0.963040	+	0.269359i	$0.913188\pi$
$504$	1.60957e44	0.413624
$505$	0	0
$506$	−8.20853e44	−1.97598
$507$	9.39676e44i	2.18951i
$508$	4.67292e44i	1.05399i
$509$	−4.74147e44	−1.03531	−0.517654	−	0.855590i	$-0.673194\pi$
$509$	−4.74147e44	−1.03531	−0.517654	+	0.855590i	$0.673194\pi$
$510$	0	0
$511$	−8.95206e43	−0.183222
$512$	− 5.65155e44i	− 1.11999i
$513$	8.59764e44i	1.64984i
$514$	9.09346e44	1.68981
$515$	0	0
$516$	−2.46524e45	−4.29673
$517$	− 1.12483e45i	− 1.89886i
$518$	− 2.01773e44i	− 0.329930i
$519$	−4.27059e44	−0.676436
$520$	0	0
$521$	1.04032e45	1.54648	0.773240	−	0.634113i	$-0.218635\pi$
$521$	1.04032e45	1.54648	0.773240	+	0.634113i	$0.218635\pi$
$522$	3.83018e45i	5.51641i
$523$	− 7.60705e44i	− 1.06154i	−0.847514	−	0.530772i	$-0.821902\pi$
$523$	− 7.60705e44i	− 1.06154i	0.847514	−	0.530772i	$-0.178098\pi$
$524$	−1.84999e45	−2.50152
$525$	0	0
$526$	1.32225e45	1.67900
$527$	− 1.45252e44i	− 0.178750i
$528$	1.44358e45i	1.72179i
$529$	3.11290e44	0.359871
$530$	0	0
$531$	1.17860e45	1.28029
$532$	− 5.35080e44i	− 0.563478i
$533$	2.38832e44i	0.243834i
$534$	3.00646e45	2.97594
$535$	0	0
$536$	9.38184e44	0.873110
$537$	9.92047e44i	0.895275i
$538$	− 1.49060e45i	− 1.30453i
$539$	1.52149e45	1.29138
$540$	0	0
$541$	9.20989e44	0.735359	0.367680	−	0.929953i	$-0.380152\pi$
$541$	9.20989e44	0.735359	0.367680	+	0.929953i	$0.380152\pi$
$542$	− 8.30442e44i	− 0.643163i
$543$	− 2.20423e45i	− 1.65600i
$544$	−4.75214e44	−0.346344
$545$	0	0
$546$	2.62151e45	1.79835
$547$	− 2.34454e45i	− 1.56051i	−0.625463	−	0.780254i	$-0.715090\pi$
$547$	− 2.34454e45i	− 1.56051i	0.625463	−	0.780254i	$-0.284910\pi$
$548$	− 1.42234e45i	− 0.918593i
$549$	−1.04795e45	−0.656744
$550$	0	0
$551$	2.93642e45	1.73307
$552$	− 1.09966e45i	− 0.629889i
$553$	8.87787e44i	0.493565i
$554$	−6.59918e44	−0.356106
$555$	0	0
$556$	−2.34695e45	−1.19335
$557$	9.31697e44i	0.459900i	0.973202	+	0.229950i	$0.0738563\pi$
$557$	9.31697e44i	0.459900i	−0.973202	+	0.229950i	$0.926144\pi$
$558$	− 4.50800e45i	− 2.16033i
$559$	−6.17283e45	−2.87203
$560$	0	0
$561$	1.61359e45	0.707793
$562$	3.89659e45i	1.65972i
$563$	1.76320e45i	0.729312i	0.931142	+	0.364656i	$0.118813\pi$
$563$	1.76320e45i	0.729312i	−0.931142	+	0.364656i	$0.881187\pi$
$564$	6.53421e45	2.62475
$565$	0	0
$566$	−2.50970e45	−0.950936
$567$	1.23564e45i	0.454747i
$568$	− 1.54659e45i	− 0.552875i
$569$	−1.99581e45	−0.693054	−0.346527	−	0.938040i	$-0.612639\pi$
$569$	−1.99581e45	−0.693054	−0.346527	+	0.938040i	$0.612639\pi$
$570$	0	0
$571$	−1.67320e45	−0.548342	−0.274171	−	0.961681i	$-0.588404\pi$
$571$	−1.67320e45	−0.548342	−0.274171	+	0.961681i	$0.588404\pi$
$572$	− 1.00035e46i	− 3.18507i
$573$	− 4.03161e45i	− 1.24717i
$574$	3.72016e44	0.111819
$575$	0	0
$576$	−1.04475e46	−2.96511
$577$	6.81345e44i	0.187917i	0.995576	+	0.0939586i	$0.0299521\pi$
$577$	6.81345e44i	0.187917i	−0.995576	+	0.0939586i	$0.970048\pi$
$578$	− 5.30157e45i	− 1.42100i
$579$	−4.36120e45	−1.13608
$580$	0	0
$581$	−1.04207e45	−0.256443
$582$	− 2.49068e45i	− 0.595783i
$583$	2.76676e45i	0.643339i
$584$	−8.09729e44	−0.183032
$585$	0	0
$586$	1.11099e46	2.37355
$587$	7.97410e45i	1.65635i	0.560467	+	0.828176i	$0.310622\pi$
$587$	7.97410e45i	1.65635i	−0.560467	+	0.828176i	$0.689378\pi$
$588$	8.83844e45i	1.78505i
$589$	−3.45607e45	−0.678703
$590$	0	0
$591$	2.34865e45	0.436139
$592$	1.61615e45i	0.291859i
$593$	− 9.65663e45i	− 1.69599i	−0.530005	−	0.847994i	$-0.677810\pi$
$593$	− 9.65663e45i	− 1.69599i	0.530005	−	0.847994i	$-0.322190\pi$
$594$	2.50370e46	4.27667
$595$	0	0
$596$	4.38335e45	0.708342
$597$	2.51330e45i	0.395064i
$598$	− 1.19398e46i	− 1.82569i
$599$	8.55789e45	1.27299	0.636494	−	0.771282i	$-0.280384\pi$
$599$	8.55789e45	1.27299	0.636494	+	0.771282i	$0.280384\pi$
$600$	0	0
$601$	−3.47394e45	−0.489095	−0.244548	−	0.969637i	$-0.578639\pi$
$601$	−3.47394e45	−0.489095	−0.244548	+	0.969637i	$0.578639\pi$
$602$	9.61507e45i	1.31707i
$603$	2.88208e46i	3.84123i
$604$	−1.49837e46	−1.94317
$605$	0	0
$606$	−1.87942e46	−2.30794
$607$	− 3.78540e45i	− 0.452375i	−0.974084	−	0.226188i	$-0.927374\pi$
$607$	− 3.78540e45i	− 0.452375i	0.974084	−	0.226188i	$-0.0726262\pi$
$608$	1.13071e46i	1.31504i
$609$	1.26648e46	1.43355
$610$	0	0
$611$	1.63613e46	1.75444
$612$	6.24875e45i	0.652220i
$613$	9.19782e45i	0.934517i	0.884121	+	0.467258i	$0.154758\pi$
$613$	9.19782e45i	0.934517i	−0.884121	+	0.467258i	$0.845242\pi$
$614$	−2.48840e46	−2.46117
$615$	0	0
$616$	−3.59344e45	−0.336843
$617$	− 3.00505e45i	− 0.274250i	−0.990554	−	0.137125i	$-0.956214\pi$
$617$	− 3.00505e45i	− 0.274250i	0.990554	−	0.137125i	$-0.0437862\pi$
$618$	4.45519e46i	3.95873i
$619$	8.07148e45	0.698325	0.349162	−	0.937062i	$-0.386466\pi$
$619$	8.07148e45	0.698325	0.349162	+	0.937062i	$0.386466\pi$
$620$	0	0
$621$	1.68890e46	1.38545
$622$	− 9.26106e45i	− 0.739809i
$623$	− 6.62716e45i	− 0.515554i
$624$	−2.09976e46	−1.59083
$625$	0	0
$626$	−2.01790e46	−1.45018
$627$	− 3.83932e46i	− 2.68745i
$628$	1.32541e46i	0.903682i
$629$	1.80649e45	0.119977
$630$	0	0
$631$	−1.34115e46	−0.845264	−0.422632	−	0.906301i	$-0.638894\pi$
$631$	−1.34115e46	−0.845264	−0.422632	+	0.906301i	$0.638894\pi$
$632$	8.03018e45i	0.493053i
$633$	5.96092e45i	0.356576i
$634$	−2.70002e46	−1.57360
$635$	0	0
$636$	−1.60722e46	−0.889271
$637$	2.21310e46i	1.19316i
$638$	− 8.55107e46i	− 4.49241i
$639$	4.75109e46	2.43237
$640$	0	0
$641$	−1.68745e46	−0.820489	−0.410244	−	0.911976i	$-0.634557\pi$
$641$	−1.68745e46	−0.820489	−0.410244	+	0.911976i	$0.634557\pi$
$642$	2.02206e46i	0.958222i
$643$	− 3.29909e45i	− 0.152375i	−0.997094	−	0.0761874i	$-0.975725\pi$
$643$	− 3.29909e45i	− 0.152375i	0.997094	−	0.0761874i	$-0.0242747\pi$
$644$	−1.05110e46	−0.473179
$645$	0	0
$646$	8.47644e45	0.362557
$647$	1.31901e46i	0.549953i	0.961451	+	0.274977i	$0.0886701\pi$
$647$	1.31901e46i	0.549953i	−0.961451	+	0.274977i	$0.911330\pi$
$648$	1.11765e46i	0.454276i
$649$	−2.63129e46	−1.04263
$650$	0	0
$651$	−1.49060e46	−0.561404
$652$	− 3.12520e46i	− 1.14761i
$653$	− 3.26301e46i	− 1.16829i	−0.811649	−	0.584146i	$-0.801430\pi$
$653$	− 3.26301e46i	− 1.16829i	0.811649	−	0.584146i	$-0.198570\pi$
$654$	−4.90451e46	−1.71223
$655$	0	0
$656$	−2.97975e45	−0.0989159
$657$	− 2.48747e46i	− 0.805247i
$658$	− 2.54852e46i	− 0.804563i
$659$	−1.87303e46	−0.576682	−0.288341	−	0.957528i	$-0.593104\pi$
$659$	−1.87303e46	−0.576682	−0.288341	+	0.957528i	$0.593104\pi$
$660$	0	0
$661$	−1.63902e46	−0.480021	−0.240011	−	0.970770i	$-0.577151\pi$
$661$	−1.63902e46	−0.480021	−0.240011	+	0.970770i	$0.577151\pi$
$662$	− 9.15536e46i	− 2.61528i
$663$	2.34706e46i	0.653960i
$664$	−9.42568e45	−0.256177
$665$	0	0
$666$	5.60657e46	1.45001
$667$	− 5.76821e46i	− 1.45534i
$668$	1.11697e46i	0.274936i
$669$	4.72566e46	1.13483
$670$	0	0
$671$	2.33959e46	0.534834
$672$	4.87674e46i	1.08777i
$673$	8.65953e46i	1.88472i	0.334606	+	0.942358i	$0.391397\pi$
$673$	8.65953e46i	1.88472i	−0.334606	+	0.942358i	$0.608603\pi$
$674$	−1.56911e46	−0.333246
$675$	0	0
$676$	8.12415e46	1.64308
$677$	4.79310e45i	0.0946027i	0.998881	+	0.0473014i	$0.0150621\pi$
$677$	4.79310e45i	0.0946027i	−0.998881	+	0.0473014i	$0.984938\pi$
$678$	3.99694e46i	0.769905i
$679$	−5.49021e45	−0.103214
$680$	0	0
$681$	−1.12152e47	−2.00854
$682$	1.00643e47i	1.75931i
$683$	− 6.64508e46i	− 1.13386i	−0.823767	−	0.566929i	$-0.808131\pi$
$683$	− 6.64508e46i	− 1.13386i	0.823767	−	0.566929i	$-0.191869\pi$
$684$	1.48680e47	2.47644
$685$	0	0
$686$	7.79455e46	1.23721
$687$	4.90896e46i	0.760683i
$688$	− 7.70142e46i	− 1.16510i
$689$	−4.02441e46	−0.594408
$690$	0	0
$691$	4.37178e46	0.615560	0.307780	−	0.951458i	$-0.400414\pi$
$691$	4.37178e46	0.615560	0.307780	+	0.951458i	$0.400414\pi$
$692$	3.69222e46i	0.507619i
$693$	− 1.10390e47i	− 1.48194i
$694$	−6.34534e46	−0.831809
$695$	0	0
$696$	1.14555e47	1.43206
$697$	3.33068e45i	0.0406624i
$698$	1.52064e47i	1.81306i
$699$	9.47494e46	1.10332
$700$	0	0
$701$	9.99204e46	1.10996	0.554979	−	0.831864i	$-0.312726\pi$
$701$	9.99204e46	1.10996	0.554979	+	0.831864i	$0.312726\pi$
$702$	3.64177e47i	3.95139i
$703$	− 4.29829e46i	− 0.455546i
$704$	2.33245e47	2.41470
$705$	0	0
$706$	−1.43956e46	−0.142218
$707$	4.14281e46i	0.399829i
$708$	− 1.52853e47i	− 1.44120i
$709$	3.22308e46	0.296898	0.148449	−	0.988920i	$-0.452572\pi$
$709$	3.22308e46	0.296898	0.148449	+	0.988920i	$0.452572\pi$
$710$	0	0
$711$	−2.46685e47	−2.16918
$712$	− 5.99437e46i	− 0.515020i
$713$	6.78900e46i	0.569939i
$714$	3.65589e46	0.299897
$715$	0	0
$716$	8.57693e46	0.671842
$717$	− 2.66767e47i	− 2.04205i
$718$	− 8.63391e45i	− 0.0645883i
$719$	2.25121e47	1.64585	0.822923	−	0.568153i	$-0.192342\pi$
$719$	2.25121e47	1.64585	0.822923	+	0.568153i	$0.192342\pi$
$720$	0	0
$721$	9.82060e46	0.685814
$722$	2.04940e46i	0.139882i
$723$	− 2.17513e47i	− 1.45112i
$724$	−1.90571e47	−1.24271
$725$	0	0
$726$	−6.96497e47	−4.33976
$727$	1.90515e46i	0.116041i	0.998315	+	0.0580205i	$0.0184789\pi$
$727$	1.90515e46i	0.116041i	−0.998315	+	0.0580205i	$0.981521\pi$
$728$	− 5.22686e46i	− 0.311224i
$729$	1.71897e47	1.00061
$730$	0	0
$731$	−8.60844e46	−0.478948
$732$	1.35908e47i	0.739286i
$733$	2.27821e47i	1.21165i	0.795597	+	0.605826i	$0.207157\pi$
$733$	2.27821e47i	1.21165i	−0.795597	+	0.605826i	$0.792843\pi$
$734$	−4.11633e47	−2.14055
$735$	0	0
$736$	2.22112e47	1.10430
$737$	− 6.43438e47i	− 3.12819i
$738$	1.03370e47i	0.491435i
$739$	−3.27147e47	−1.52093	−0.760467	−	0.649377i	$-0.775030\pi$
$739$	−3.27147e47	−1.52093	−0.760467	+	0.649377i	$0.775030\pi$
$740$	0	0
$741$	5.58451e47	2.48304
$742$	6.26860e46i	0.272588i
$743$	− 1.23139e47i	− 0.523698i	−0.965109	−	0.261849i	$-0.915668\pi$
$743$	− 1.23139e47i	− 0.523698i	0.965109	−	0.261849i	$-0.0843322\pi$
$744$	−1.34827e47	−0.560822
$745$	0	0
$746$	−3.83520e47	−1.52615
$747$	− 2.89555e47i	− 1.12704i
$748$	− 1.39506e47i	− 0.531150i
$749$	4.45724e46	0.166003
$750$	0	0
$751$	4.24124e47	1.51159	0.755795	−	0.654808i	$-0.227251\pi$
$751$	4.24124e47	1.51159	0.755795	+	0.654808i	$0.227251\pi$
$752$	2.04129e47i	0.711723i
$753$	− 4.05230e47i	− 1.38224i
$754$	1.24380e48	4.15072
$755$	0	0
$756$	3.20597e47	1.02412
$757$	− 4.38259e47i	− 1.36977i	−0.728649	−	0.684887i	$-0.759852\pi$
$757$	− 4.38259e47i	− 1.36977i	0.728649	−	0.684887i	$-0.240148\pi$
$758$	3.53232e47i	1.08024i
$759$	−7.54184e47	−2.25677
$760$	0	0
$761$	−6.43868e47	−1.84480	−0.922401	−	0.386232i	$-0.873776\pi$
$761$	−6.43868e47	−1.84480	−0.922401	+	0.386232i	$0.873776\pi$
$762$	7.59667e47i	2.12993i
$763$	1.08110e47i	0.296628i
$764$	−3.48560e47	−0.935918
$765$	0	0
$766$	7.78370e47	2.00176
$767$	− 3.82736e47i	− 0.963332i
$768$	− 1.16704e47i	− 0.287491i
$769$	−1.83655e46	−0.0442812	−0.0221406	−	0.999755i	$-0.507048\pi$
$769$	−1.83655e46	−0.0442812	−0.0221406	+	0.999755i	$0.507048\pi$
$770$	0	0
$771$	8.35491e47	1.92994
$772$	3.77056e47i	0.852552i
$773$	1.27125e47i	0.281364i	0.990055	+	0.140682i	$0.0449295\pi$
$773$	1.27125e47i	0.281364i	−0.990055	+	0.140682i	$0.955070\pi$
$774$	−2.67170e48	−5.78844
$775$	0	0
$776$	−4.96599e46	−0.103107
$777$	− 1.85385e47i	− 0.376815i
$778$	9.04484e47i	1.79986i
$779$	7.92490e46	0.154392
$780$	0	0
$781$	−1.06070e48	−1.98085
$782$	− 1.66509e47i	− 0.304456i
$783$	1.75937e48i	3.14984i
$784$	−2.76114e47	−0.484031
$785$	0	0
$786$	−3.00749e48	−5.05513
$787$	1.07309e48i	1.76626i	0.469133	+	0.883128i	$0.344567\pi$
$787$	1.07309e48i	1.76626i	−0.469133	+	0.883128i	$0.655433\pi$
$788$	− 2.03057e47i	− 0.327292i
$789$	1.21486e48	1.91759
$790$	0	0
$791$	8.81047e46	0.133379
$792$	− 9.98491e47i	− 1.48040i
$793$	3.40307e47i	0.494155i
$794$	−3.64283e46	−0.0518084
$795$	0	0
$796$	2.17292e47	0.296468
$797$	8.32944e47i	1.11315i	0.830798	+	0.556575i	$0.187885\pi$
$797$	8.32944e47i	1.11315i	−0.830798	+	0.556575i	$0.812115\pi$
$798$	− 8.69868e47i	− 1.13869i
$799$	2.28170e47	0.292575
$800$	0	0
$801$	1.84146e48	2.26582
$802$	3.03216e46i	0.0365489i
$803$	5.55339e47i	0.655770i
$804$	3.73776e48	4.32401
$805$	0	0
$806$	−1.46391e48	−1.62550
$807$	− 1.36954e48i	− 1.48991i
$808$	3.74724e47i	0.399415i
$809$	4.91569e47	0.513374	0.256687	−	0.966495i	$-0.417369\pi$
$809$	4.91569e47	0.513374	0.256687	+	0.966495i	$0.417369\pi$
$810$	0	0
$811$	1.31202e48	1.31551	0.657757	−	0.753230i	$-0.271505\pi$
$811$	1.31202e48	1.31551	0.657757	+	0.753230i	$0.271505\pi$
$812$	− 1.09496e48i	− 1.07578i
$813$	− 7.62995e47i	− 0.734560i
$814$	−1.25169e48	−1.18085
$815$	0	0
$816$	−2.92827e47	−0.265292
$817$	2.04826e48i	1.81853i
$818$	4.32435e47i	0.376262i
$819$	1.60568e48	1.36922
$820$	0	0
$821$	−1.18387e48	−0.969711	−0.484855	−	0.874594i	$-0.661128\pi$
$821$	−1.18387e48	−0.969711	−0.484855	+	0.874594i	$0.661128\pi$
$822$	− 2.31226e48i	− 1.85631i
$823$	− 1.23245e48i	− 0.969776i	−0.874576	−	0.484888i	$-0.838860\pi$
$823$	− 1.23245e48i	− 0.969776i	0.874576	−	0.484888i	$-0.161140\pi$
$824$	8.88289e47	0.685102
$825$	0	0
$826$	−5.96167e47	−0.441771
$827$	− 4.69422e45i	− 0.00340975i	−0.999999	−	0.00170487i	$-0.999457\pi$
$827$	− 4.69422e45i	− 0.00340975i	0.999999	−	0.00170487i	$-0.000542678\pi$
$828$	− 2.92063e48i	− 2.07958i
$829$	4.02684e47	0.281070	0.140535	−	0.990076i	$-0.455118\pi$
$829$	4.02684e47	0.281070	0.140535	+	0.990076i	$0.455118\pi$
$830$	0	0
$831$	−6.06321e47	−0.406711
$832$	3.39268e48i	2.23105i
$833$	3.08632e47i	0.198975i
$834$	−3.81538e48	−2.41156
$835$	0	0
$836$	−3.31936e48	−2.01674
$837$	− 2.07072e48i	− 1.23354i
$838$	1.16819e48i	0.682316i
$839$	−5.27811e46	−0.0302278	−0.0151139	−	0.999886i	$-0.504811\pi$
$839$	−5.27811e46	−0.0302278	−0.0151139	+	0.999886i	$0.504811\pi$
$840$	0	0
$841$	4.19284e48	2.30874
$842$	3.49269e48i	1.88586i
$843$	3.58011e48i	1.89558i
$844$	5.15363e47	0.267586
$845$	0	0
$846$	7.08144e48	3.53599
$847$	1.53529e48i	0.751822i
$848$	− 5.02098e47i	− 0.241133i
$849$	−2.30587e48	−1.08607
$850$	0	0
$851$	−8.44342e47	−0.382544
$852$	− 6.16167e48i	− 2.73808i
$853$	3.55498e48i	1.54945i	0.632298	+	0.774725i	$0.282112\pi$
$853$	3.55498e48i	1.54945i	−0.632298	+	0.774725i	$0.717888\pi$
$854$	5.30078e47	0.226613
$855$	0	0
$856$	4.03165e47	0.165831
$857$	1.12728e48i	0.454827i	0.973798	+	0.227414i	$0.0730269\pi$
$857$	1.12728e48i	0.454827i	−0.973798	+	0.227414i	$0.926973\pi$
$858$	− 1.62625e49i	− 6.43646i
$859$	−1.80056e48	−0.699070	−0.349535	−	0.936923i	$-0.613660\pi$
$859$	−1.80056e48	−0.699070	−0.349535	+	0.936923i	$0.613660\pi$
$860$	0	0
$861$	3.41801e47	0.127709
$862$	7.72496e48i	2.83156i
$863$	2.38697e48i	0.858359i	0.903219	+	0.429180i	$0.141197\pi$
$863$	2.38697e48i	0.858359i	−0.903219	+	0.429180i	$0.858803\pi$
$864$	−6.77469e48	−2.39008
$865$	0	0
$866$	2.71230e48	0.921069
$867$	− 4.87098e48i	− 1.62294i
$868$	1.28873e48i	0.421295i
$869$	5.50737e48	1.76652
$870$	0	0
$871$	9.35917e48	2.89027
$872$	9.77876e47i	0.296320i
$873$	− 1.52554e48i	− 0.453616i
$874$	−3.96184e48	−1.15600
$875$	0	0
$876$	−3.22599e48	−0.906454
$877$	− 1.44993e48i	− 0.399811i	−0.979815	−	0.199905i	$-0.935936\pi$
$877$	− 1.44993e48i	− 0.399811i	0.979815	−	0.199905i	$-0.0640635\pi$
$878$	− 6.26140e48i	− 1.69438i
$879$	1.02075e49	2.71084
$880$	0	0
$881$	−4.86343e48	−1.24406	−0.622029	−	0.782994i	$-0.713691\pi$
$881$	−4.86343e48	−1.24406	−0.622029	+	0.782994i	$0.713691\pi$
$882$	9.57864e48i	2.40476i
$883$	− 2.25361e48i	− 0.555299i	−0.960682	−	0.277650i	$-0.910445\pi$
$883$	− 2.25361e48i	− 0.555299i	0.960682	−	0.277650i	$-0.0895554\pi$
$884$	2.02920e48	0.490752
$885$	0	0
$886$	−6.70186e48	−1.56149
$887$	− 7.86411e48i	− 1.79850i	−0.437439	−	0.899248i	$-0.644114\pi$
$887$	− 7.86411e48i	− 1.79850i	0.437439	−	0.899248i	$-0.355886\pi$
$888$	− 1.67684e48i	− 0.376424i
$889$	1.67454e48	0.368991
$890$	0	0
$891$	7.66524e48	1.62758
$892$	− 4.08566e48i	− 0.851613i
$893$	− 5.42900e48i	− 1.11089i
$894$	7.12592e48	1.43144
$895$	0	0
$896$	2.04066e48	0.395083
$897$	− 1.09700e49i	− 2.08513i
$898$	9.88165e48i	1.84404i
$899$	−7.07230e48	−1.29576
$900$	0	0
$901$	−5.61232e47	−0.0991251
$902$	− 2.30779e48i	− 0.400211i
$903$	8.83415e48i	1.50424i
$904$	7.96922e47	0.133241
$905$	0	0
$906$	−2.43587e49	−3.92680
$907$	− 1.83168e48i	− 0.289954i	−0.989435	−	0.144977i	$-0.953689\pi$
$907$	− 1.83168e48i	− 0.289954i	0.989435	−	0.144977i	$-0.0463108\pi$
$908$	9.69632e48i	1.50727i
$909$	−1.15114e49	−1.75722
$910$	0	0
$911$	4.44938e48	0.655007	0.327504	−	0.944850i	$-0.393793\pi$
$911$	4.44938e48	0.655007	0.327504	+	0.944850i	$0.393793\pi$
$912$	6.96742e48i	1.00730i
$913$	6.46445e48i	0.917833i
$914$	1.82367e49	2.54292
$915$	0	0
$916$	4.24414e48	0.570840
$917$	6.62943e48i	0.875754i
$918$	5.07871e48i	0.658945i
$919$	1.19748e49	1.52603	0.763013	−	0.646383i	$-0.223719\pi$
$919$	1.19748e49	1.52603	0.763013	+	0.646383i	$0.223719\pi$
$920$	0	0
$921$	−2.28630e49	−2.81092
$922$	2.25421e48i	0.272228i
$923$	− 1.54285e49i	− 1.83019i
$924$	−1.43164e49	−1.66819
$925$	0	0
$926$	−1.15453e49	−1.29815
$927$	2.72880e49i	3.01409i
$928$	2.31381e49i	2.51065i
$929$	6.38779e48	0.680912	0.340456	−	0.940260i	$-0.389419\pi$
$929$	6.38779e48	0.680912	0.340456	+	0.940260i	$0.389419\pi$
$930$	0	0
$931$	7.34348e48	0.755496
$932$	− 8.19175e48i	− 0.827969i
$933$	− 8.50889e48i	− 0.844940i
$934$	−3.45215e48	−0.336796
$935$	0	0
$936$	1.45236e49	1.36780
$937$	2.98186e47i	0.0275921i	0.999905	+	0.0137960i	$0.00439155\pi$
$937$	2.98186e47i	0.0275921i	−0.999905	+	0.0137960i	$0.995608\pi$
$938$	− 1.45783e49i	− 1.32544i
$939$	−1.85401e49	−1.65626
$940$	0	0
$941$	6.14468e48	0.529993	0.264997	−	0.964249i	$-0.414629\pi$
$941$	6.14468e48	0.529993	0.264997	+	0.964249i	$0.414629\pi$
$942$	2.15469e49i	1.82618i
$943$	− 1.55674e48i	− 0.129651i
$944$	4.77514e48	0.390794
$945$	0	0
$946$	5.96469e49	4.71394
$947$	4.27472e46i	0.00331996i	0.999999	+	0.00165998i	$0.000528388\pi$
$947$	4.27472e46i	0.00331996i	−0.999999	+	0.00165998i	$0.999472\pi$
$948$	3.19926e49i	2.44181i
$949$	−8.07772e48	−0.605894
$950$	0	0
$951$	−2.48073e49	−1.79722
$952$	− 7.28922e47i	− 0.0519005i
$953$	− 1.36139e49i	− 0.952684i	−0.879260	−	0.476342i	$-0.841962\pi$
$953$	− 1.36139e49i	− 0.952684i	0.879260	−	0.476342i	$-0.158038\pi$
$954$	−1.74183e49	−1.19800
$955$	0	0
$956$	−2.30639e49	−1.53242
$957$	− 7.85656e49i	− 5.13081i
$958$	3.68390e49i	2.36470i
$959$	−5.09693e48	−0.321589
$960$	0	0
$961$	−8.07961e48	−0.492555
$962$	− 1.82066e49i	− 1.09104i
$963$	1.23851e49i	0.729570i
$964$	−1.88055e49	−1.08897
$965$	0	0
$966$	−1.70874e49	−0.956212
$967$	1.39797e49i	0.769060i	0.923113	+	0.384530i	$0.125636\pi$
$967$	1.39797e49i	0.769060i	−0.923113	+	0.384530i	$0.874364\pi$
$968$	1.38870e49i	0.751042i
$969$	7.78799e48	0.414079
$970$	0	0
$971$	2.21572e49	1.13867	0.569334	−	0.822107i	$-0.307201\pi$
$971$	2.21572e49	1.13867	0.569334	+	0.822107i	$0.307201\pi$
$972$	− 1.81095e46i	0 0.000914985i
$973$	8.41026e48i	0.417780i
$974$	1.54641e48	0.0755268
$975$	0	0
$976$	−4.24578e48	−0.200464
$977$	− 1.12838e49i	− 0.523835i	−0.965090	−	0.261918i	$-0.915645\pi$
$977$	− 1.12838e49i	− 0.523835i	0.965090	−	0.261918i	$-0.0843549\pi$
$978$	− 5.08057e49i	− 2.31911i
$979$	−4.11114e49	−1.84522
$980$	0	0
$981$	−3.00401e49	−1.30366
$982$	3.17140e49i	1.35335i
$983$	2.75705e49i	1.15694i	0.815703	+	0.578471i	$0.196350\pi$
$983$	2.75705e49i	1.15694i	−0.815703	+	0.578471i	$0.803650\pi$
$984$	3.09165e48	0.127577
$985$	0	0
$986$	1.73457e49	0.692185
$987$	− 2.34153e49i	− 0.918896i
$988$	− 4.82819e49i	− 1.86335i
$989$	4.02354e49	1.52711
$990$	0	0
$991$	2.93272e49	1.07660	0.538300	−	0.842753i	$-0.319067\pi$
$991$	2.93272e49	1.07660	0.538300	+	0.842753i	$0.319067\pi$
$992$	− 2.72328e49i	− 0.983218i
$993$	− 8.41178e49i	− 2.98693i
$994$	−2.40322e49	−0.839300
$995$	0	0
$996$	−3.75523e49	−1.26870
$997$	− 1.66255e49i	− 0.552464i	−0.961091	−	0.276232i	$-0.910914\pi$
$997$	− 1.66255e49i	− 0.552464i	0.961091	−	0.276232i	$-0.0890857\pi$
$998$	− 6.03760e49i	− 1.97338i
$999$	2.57534e49	0.827951

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.b.d.24.4		22
5.2	odd	4		25.34.a.e.1.10	yes	11
5.3	odd	4		25.34.a.d.1.2	✓	11
5.4	even	2	inner	25.34.b.d.24.19		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.34.a.d.1.2	✓	11	5.3	odd	4
25.34.a.e.1.10	yes	11	5.2	odd	4
25.34.b.d.24.4		22	1.1	even	1	trivial
25.34.b.d.24.19		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)

\(f(q)\)	\(=\)	\(q-140551. i q^{2} -1.29136e8i q^{3} -1.11647e10 q^{4} -1.81502e13 q^{6} +4.00085e13i q^{7} +3.61884e14i q^{8} -1.11170e16 q^{9} +O(q^{10})\)	\(q-140551. i q^{2} -1.29136e8i q^{3} -1.11647e10 q^{4} -1.81502e13 q^{6} +4.00085e13i q^{7} +3.61884e14i q^{8} -1.11170e16 q^{9} +2.48192e17 q^{11} +1.44176e18i q^{12} +3.61009e18i q^{13} +5.62325e18 q^{14} -4.50407e19 q^{16} +5.03453e19i q^{17} +1.56251e21i q^{18} +1.19790e21 q^{19} +5.16654e21 q^{21} -3.48837e22i q^{22} -2.35311e22i q^{23} +4.67322e22 q^{24} +5.07403e23 q^{26} +7.17728e23i q^{27} -4.46683e23i q^{28} +2.45131e24 q^{29} -2.88511e24 q^{31} +9.43908e24i q^{32} -3.20505e25i q^{33} +7.07609e24 q^{34} +1.24118e26 q^{36} -3.58819e25i q^{37} -1.68366e26i q^{38} +4.66192e26 q^{39} +6.61568e25 q^{41} -7.26162e26i q^{42} +1.70988e27i q^{43} -2.77099e27 q^{44} -3.30733e27 q^{46} -4.53211e27i q^{47} +5.81637e27i q^{48} +6.13031e27 q^{49} +6.50138e27 q^{51} -4.03056e28i q^{52} +1.11477e28i q^{53} +1.00877e29 q^{54} -1.44784e28 q^{56} -1.54691e29i q^{57} -3.44534e29i q^{58} -1.06018e29 q^{59} +9.42654e28 q^{61} +4.05506e29i q^{62} -4.44775e29i q^{63} +9.39777e29 q^{64} -4.50473e30 q^{66} -2.59250e30i q^{67} -5.62090e29i q^{68} -3.03871e30 q^{69} -4.27372e30 q^{71} -4.02306e30i q^{72} +2.23754e30i q^{73} -5.04324e30 q^{74} -1.33741e31 q^{76} +9.92980e30i q^{77} -6.55239e31i q^{78} +2.21899e31 q^{79} +3.08843e31 q^{81} -9.29841e30i q^{82} +2.60461e31i q^{83} -5.76827e31 q^{84} +2.40325e32 q^{86} -3.16552e32i q^{87} +8.98167e31i q^{88} -1.65644e32 q^{89} -1.44435e32 q^{91} +2.62718e32i q^{92} +3.72571e32i q^{93} -6.36993e32 q^{94} +1.21892e33 q^{96} +1.37226e32i q^{97} -8.61622e32i q^{98} -2.75915e33 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 98676413354 q^{4} - 35567955353446 q^{6} - 48\!\cdots\!16 q^{9}+O(q^{10}) \) 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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