LMFDB - Embedded newform 25.34.b.d.24.2

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			24.2
Character	$\chi$	$=$	25.24
Dual form			25.34.b.d.24.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-171393. i q^{2} +3.66048e7i q^{3} -2.07856e10 q^{4} +6.27381e12 q^{6} -4.77732e13i q^{7} +2.09024e15i q^{8} +4.21915e15 q^{9} +O(q^{10})$	\(q-171393. i q^{2} +3.66048e7i q^{3} -2.07856e10 q^{4} +6.27381e12 q^{6} -4.77732e13i q^{7} +2.09024e15i q^{8} +4.21915e15 q^{9} -1.37621e17 q^{11} -7.60852e17i q^{12} +3.30270e18i q^{13} -8.18799e18 q^{14} +1.79706e20 q^{16} +1.37326e20i q^{17} -7.23131e20i q^{18} -8.26685e20 q^{19} +1.74873e21 q^{21} +2.35873e22i q^{22} +4.90370e22i q^{23} -7.65130e22 q^{24} +5.66060e23 q^{26} +3.57930e23i q^{27} +9.92994e23i q^{28} -2.29875e24 q^{29} -1.68439e24 q^{31} -1.28452e25i q^{32} -5.03760e24i q^{33} +2.35367e25 q^{34} -8.76973e25 q^{36} -6.34376e25i q^{37} +1.41688e26i q^{38} -1.20895e26 q^{39} +6.03512e26 q^{41} -2.99720e26i q^{42} +2.71742e26i q^{43} +2.86053e27 q^{44} +8.40459e27 q^{46} -6.74390e27i q^{47} +6.57811e27i q^{48} +5.44871e27 q^{49} -5.02679e27 q^{51} -6.86485e28i q^{52} -3.22589e28i q^{53} +6.13466e28 q^{54} +9.98577e28 q^{56} -3.02607e28i q^{57} +3.93989e29i q^{58} -4.27415e28 q^{59} +4.00547e29 q^{61} +2.88691e29i q^{62} -2.01562e29i q^{63} -6.57922e29 q^{64} -8.63409e29 q^{66} +1.15008e30i q^{67} -2.85440e30i q^{68} -1.79499e30 q^{69} -4.55510e30 q^{71} +8.81904e30i q^{72} -5.29485e30i q^{73} -1.08727e31 q^{74} +1.71831e31 q^{76} +6.57461e30i q^{77} +2.07205e31i q^{78} -1.47913e31 q^{79} +1.03525e31 q^{81} -1.03438e32i q^{82} +7.50132e30i q^{83} -3.63484e31 q^{84} +4.65745e31 q^{86} -8.41454e31i q^{87} -2.87662e32i q^{88} +1.55730e32 q^{89} +1.57781e32 q^{91} -1.01926e33i q^{92} -6.16567e31i q^{93} -1.15586e33 q^{94} +4.70198e32 q^{96} +7.66696e32i q^{97} -9.33870e32i q^{98} -5.80644e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	− 171393.i	− 1.84926i	−0.380868	−	0.924629i	$-0.624375\pi$
$2$	− 171393.i	− 1.84926i	0.380868	−	0.924629i	$-0.375625\pi$
$3$	3.66048e7i	0.490951i	0.969403	+	0.245475i	$0.0789440\pi$
$3$	3.66048e7i	0.490951i	−0.969403	+	0.245475i	$0.921056\pi$
$4$	−2.07856e10	−2.41976
$5$	0	0
$5$	0	0
$6$	6.27381e12	0.907895
$7$	− 4.77732e13i	− 0.543334i	−0.962391	−	0.271667i	$-0.912425\pi$
$7$	− 4.77732e13i	− 0.543334i	0.962391	−	0.271667i	$-0.0875750\pi$
$8$	2.09024e15i	2.62550i
$9$	4.21915e15	0.758967
$10$	0	0
$11$	−1.37621e17	−0.903038	−0.451519	−	0.892261i	$-0.649118\pi$
$11$	−1.37621e17	−0.903038	−0.451519	+	0.892261i	$0.649118\pi$
$12$	− 7.60852e17i	− 1.18798i
$13$	3.30270e18i	1.37659i	0.725431	+	0.688294i	$0.241640\pi$
$13$	3.30270e18i	1.37659i	−0.725431	+	0.688294i	$0.758360\pi$
$14$	−8.18799e18	−1.00477
$15$	0	0
$16$	1.79706e20	2.43547
$17$	1.37326e20i	0.684455i	0.939617	+	0.342228i	$0.111181\pi$
$17$	1.37326e20i	0.684455i	−0.939617	+	0.342228i	$0.888819\pi$
$18$	− 7.23131e20i	− 1.40353i
$19$	−8.26685e20	−0.657515	−0.328758	−	0.944414i	$-0.606630\pi$
$19$	−8.26685e20	−0.657515	−0.328758	+	0.944414i	$0.606630\pi$
$20$	0	0
$21$	1.74873e21	0.266750
$22$	2.35873e22i	1.66995i
$23$	4.90370e22i	1.66730i	0.552291	+	0.833651i	$0.313754\pi$
$23$	4.90370e22i	1.66730i	−0.552291	+	0.833651i	$0.686246\pi$
$24$	−7.65130e22	−1.28899
$25$	0	0
$26$	5.66060e23	2.54567
$27$	3.57930e23i	0.863566i
$28$	9.92994e23i	1.31474i
$29$	−2.29875e24	−1.70579	−0.852894	−	0.522085i	$-0.825154\pi$
$29$	−2.29875e24	−1.70579	−0.852894	+	0.522085i	$0.825154\pi$
$30$	0	0
$31$	−1.68439e24	−0.415885	−0.207943	−	0.978141i	$-0.566677\pi$
$31$	−1.68439e24	−0.415885	−0.207943	+	0.978141i	$0.566677\pi$
$32$	− 1.28452e25i	− 1.87831i
$33$	− 5.03760e24i	− 0.443347i
$34$	2.35367e25	1.26574
$35$	0	0
$36$	−8.76973e25	−1.83652
$37$	− 6.34376e25i	− 0.845314i	−0.906290	−	0.422657i	$-0.861097\pi$
$37$	− 6.34376e25i	− 0.845314i	0.906290	−	0.422657i	$-0.138903\pi$
$38$	1.41688e26i	1.21592i
$39$	−1.20895e26	−0.675837
$40$	0	0
$41$	6.03512e26	1.47827	0.739133	−	0.673560i	$-0.235236\pi$
$41$	6.03512e26	1.47827	0.739133	+	0.673560i	$0.235236\pi$
$42$	− 2.99720e26i	− 0.493290i
$43$	2.71742e26i	0.303338i	0.988431	+	0.151669i	$0.0484647\pi$
$43$	2.71742e26i	0.303338i	−0.988431	+	0.151669i	$0.951535\pi$
$44$	2.86053e27	2.18513
$45$	0	0
$46$	8.40459e27	3.08327
$47$	− 6.74390e27i	− 1.73499i	−0.497447	−	0.867494i	$-0.665729\pi$
$47$	− 6.74390e27i	− 1.73499i	0.497447	−	0.867494i	$-0.334271\pi$
$48$	6.57811e27i	1.19570i
$49$	5.44871e27	0.704788
$50$	0	0
$51$	−5.02679e27	−0.336034
$52$	− 6.86485e28i	− 3.33101i
$53$	− 3.22589e28i	− 1.14314i	−0.820554	−	0.571568i	$-0.806335\pi$
$53$	− 3.22589e28i	− 1.14314i	0.820554	−	0.571568i	$-0.193665\pi$
$54$	6.13466e28	1.59696
$55$	0	0
$56$	9.98577e28	1.42652
$57$	− 3.02607e28i	− 0.322807i
$58$	3.93989e29i	3.15444i
$59$	−4.27415e28	−0.258102	−0.129051	−	0.991638i	$-0.541193\pi$
$59$	−4.27415e28	−0.258102	−0.129051	+	0.991638i	$0.541193\pi$
$60$	0	0
$61$	4.00547e29	1.39544	0.697720	−	0.716371i	$-0.254198\pi$
$61$	4.00547e29	1.39544	0.697720	+	0.716371i	$0.254198\pi$
$62$	2.88691e29i	0.769079i
$63$	− 2.01562e29i	− 0.412373i
$64$	−6.57922e29	−1.03802
$65$	0	0
$66$	−8.63409e29	−0.819864
$67$	1.15008e30i	0.852105i	0.904699	+	0.426052i	$0.140096\pi$
$67$	1.15008e30i	0.852105i	−0.904699	+	0.426052i	$0.859904\pi$
$68$	− 2.85440e30i	− 1.65622i
$69$	−1.79499e30	−0.818563
$70$	0	0
$71$	−4.55510e30	−1.29639	−0.648194	−	0.761475i	$-0.724475\pi$
$71$	−4.55510e30	−1.29639	−0.648194	+	0.761475i	$0.724475\pi$
$72$	8.81904e30i	1.99267i
$73$	− 5.29485e30i	− 0.952854i	−0.879214	−	0.476427i	$-0.841932\pi$
$73$	− 5.29485e30i	− 0.952854i	0.879214	−	0.476427i	$-0.158068\pi$
$74$	−1.08727e31	−1.56320
$75$	0	0
$76$	1.71831e31	1.59103
$77$	6.57461e30i	0.490652i
$78$	2.07205e31i	1.24980i
$79$	−1.47913e31	−0.723036	−0.361518	−	0.932365i	$-0.617741\pi$
$79$	−1.47913e31	−0.723036	−0.361518	+	0.932365i	$0.617741\pi$
$80$	0	0
$81$	1.03525e31	0.334999
$82$	− 1.03438e32i	− 2.73369i
$83$	7.50132e30i	0.162311i	0.996701	+	0.0811557i	$0.0258611\pi$
$83$	7.50132e30i	0.162311i	−0.996701	+	0.0811557i	$0.974139\pi$
$84$	−3.63484e31	−0.645471
$85$	0	0
$86$	4.65745e31	0.560950
$87$	− 8.41454e31i	− 0.837457i
$88$	− 2.87662e32i	− 2.37093i
$89$	1.55730e32	1.06521	0.532606	−	0.846363i	$-0.321213\pi$
$89$	1.55730e32	1.06521	0.532606	+	0.846363i	$0.321213\pi$
$90$	0	0
$91$	1.57781e32	0.747948
$92$	− 1.01926e33i	− 4.03447i
$93$	− 6.16567e31i	− 0.204179i
$94$	−1.15586e33	−3.20844
$95$	0	0
$96$	4.70198e32	0.922159
$97$	7.66696e32i	1.26733i	0.773607	+	0.633665i	$0.218450\pi$
$97$	7.66696e32i	1.26733i	−0.773607	+	0.633665i	$0.781550\pi$
$98$	− 9.33870e32i	− 1.30334i
$99$	−5.80644e32	−0.685377
$100$	0	0
$101$	4.91257e32	0.416875	0.208438	−	0.978036i	$-0.433162\pi$
$101$	4.91257e32	0.416875	0.208438	+	0.978036i	$0.433162\pi$
$102$	8.61556e32i	0.621414i
$103$	− 1.79651e33i	− 1.10310i	−0.834141	−	0.551551i	$-0.814036\pi$
$103$	− 1.79651e33i	− 1.10310i	0.834141	−	0.551551i	$-0.185964\pi$
$104$	−6.90345e33	−3.61423
$105$	0	0
$106$	−5.52895e33	−2.11396
$107$	− 4.34220e33i	− 1.42193i	−0.703228	−	0.710965i	$-0.748259\pi$
$107$	− 4.34220e33i	− 1.42193i	0.703228	−	0.710965i	$-0.251741\pi$
$108$	− 7.43977e33i	− 2.08962i
$109$	−6.72572e33	−1.62256	−0.811282	−	0.584655i	$-0.801230\pi$
$109$	−6.72572e33	−1.62256	−0.811282	+	0.584655i	$0.801230\pi$
$110$	0	0
$111$	2.32212e33	0.415008
$112$	− 8.58513e33i	− 1.32327i
$113$	3.23457e32i	0.0430548i	0.999768	+	0.0215274i	$0.00685292\pi$
$113$	3.23457e32i	0.0430548i	−0.999768	+	0.0215274i	$0.993147\pi$
$114$	−5.18646e33	−0.596954
$115$	0	0
$116$	4.77808e34	4.12759
$117$	1.39346e34i	1.04479i
$118$	7.32558e33i	0.477297i
$119$	6.56050e33	0.371888
$120$	0	0
$121$	−4.28554e33	−0.184522
$122$	− 6.86508e34i	− 2.58053i
$123$	2.20915e34i	0.725755i
$124$	3.50109e34	1.00634
$125$	0	0
$126$	−3.45463e34	−0.762584
$127$	8.16772e33i	0.158248i	0.996865	+	0.0791242i	$0.0252124\pi$
$127$	8.16772e33i	0.158248i	−0.996865	+	0.0791242i	$0.974788\pi$
$128$	2.42318e33i	0.0412497i
$129$	−9.94706e33	−0.148924
$130$	0	0
$131$	−9.77336e34	−1.13519	−0.567594	−	0.823309i	$-0.692126\pi$
$131$	−9.77336e34	−1.13519	−0.567594	+	0.823309i	$0.692126\pi$
$132$	1.04709e35i	1.07279i
$133$	3.94934e34i	0.357250i
$134$	1.97115e35	1.57576
$135$	0	0
$136$	−2.87044e35	−1.79704
$137$	2.75196e35i	1.52670i	0.645988	+	0.763348i	$0.276446\pi$
$137$	2.75196e35i	1.52670i	−0.645988	+	0.763348i	$0.723554\pi$
$138$	3.07649e35i	1.51374i
$139$	−1.50687e35	−0.658160	−0.329080	−	0.944302i	$-0.606739\pi$
$139$	−1.50687e35	−0.658160	−0.329080	+	0.944302i	$0.606739\pi$
$140$	0	0
$141$	2.46860e35	0.851794
$142$	7.80711e35i	2.39736i
$143$	− 4.54522e35i	− 1.24311i
$144$	7.58205e35	1.84844
$145$	0	0
$146$	−9.07499e35	−1.76207
$147$	1.99449e35i	0.346016i
$148$	1.31859e36i	2.04546i
$149$	4.93298e35	0.684757	0.342378	−	0.939562i	$-0.388768\pi$
$149$	4.93298e35	0.684757	0.342378	+	0.939562i	$0.388768\pi$
$150$	0	0
$151$	−1.03123e36	−1.14878	−0.574390	−	0.818582i	$-0.694761\pi$
$151$	−1.03123e36	−1.14878	−0.574390	+	0.818582i	$0.694761\pi$
$152$	− 1.72797e36i	− 1.72630i
$153$	5.79398e35i	0.519479i
$154$	1.12684e36	0.907342
$155$	0	0
$156$	2.51287e36	1.63536
$157$	− 2.53133e36i	− 1.48253i	−0.671211	−	0.741267i	$-0.734225\pi$
$157$	− 2.53133e36i	− 1.48253i	0.671211	−	0.741267i	$-0.265775\pi$
$158$	2.53512e36i	1.33708i
$159$	1.18083e36	0.561224
$160$	0	0
$161$	2.34266e36	0.905903
$162$	− 1.77435e36i	− 0.619500i
$163$	− 5.19792e35i	− 0.163958i	−0.996634	−	0.0819792i	$-0.973876\pi$
$163$	− 5.19792e35i	− 0.163958i	0.996634	−	0.0819792i	$-0.0261241\pi$
$164$	−1.25443e37	−3.57704
$165$	0	0
$166$	1.28567e36	0.300156
$167$	5.08052e36i	1.07420i	0.843518	+	0.537101i	$0.180481\pi$
$167$	5.08052e36i	1.07420i	−0.843518	+	0.537101i	$0.819519\pi$
$168$	3.65527e36i	0.700353i
$169$	−5.15172e36	−0.894997
$170$	0	0
$171$	−3.48791e36	−0.499032
$172$	− 5.64830e36i	− 0.734004i
$173$	− 9.63409e36i	− 1.13776i	−0.822421	−	0.568879i	$-0.807377\pi$
$173$	− 9.63409e36i	− 1.13776i	0.822421	−	0.568879i	$-0.192623\pi$
$174$	−1.44219e37	−1.54868
$175$	0	0
$176$	−2.47313e37	−2.19932
$177$	− 1.56454e36i	− 0.126715i
$178$	− 2.66909e37i	− 1.96985i
$179$	1.49381e36	0.100512	0.0502562	−	0.998736i	$-0.483996\pi$
$179$	1.49381e36	0.100512	0.0502562	+	0.998736i	$0.483996\pi$
$180$	0	0
$181$	−7.35855e35	−0.0412188	−0.0206094	−	0.999788i	$-0.506561\pi$
$181$	−7.35855e35	−0.0412188	−0.0206094	+	0.999788i	$0.506561\pi$
$182$	− 2.70425e37i	− 1.38315i
$183$	1.46620e37i	0.685092i
$184$	−1.02499e38	−4.37750
$185$	0	0
$186$	−1.05675e37	−0.377580
$187$	− 1.88990e37i	− 0.618090i
$188$	1.40176e38i	4.19825i
$189$	1.70995e37	0.469205
$190$	0	0
$191$	5.91065e37	1.36328	0.681639	−	0.731689i	$-0.261268\pi$
$191$	5.91065e37	1.36328	0.681639	+	0.731689i	$0.261268\pi$
$192$	− 2.40831e37i	− 0.509615i
$193$	− 2.53053e37i	− 0.491491i	−0.969334	−	0.245745i	$-0.920967\pi$
$193$	− 2.53053e37i	− 0.491491i	0.969334	−	0.245745i	$-0.0790327\pi$
$194$	1.31406e38	2.34362
$195$	0	0
$196$	−1.13254e38	−1.70542
$197$	− 7.69807e37i	− 1.06583i	−0.846168	−	0.532916i	$-0.821096\pi$
$197$	− 7.69807e37i	− 1.06583i	0.846168	−	0.532916i	$-0.178904\pi$
$198$	9.95182e37i	1.26744i
$199$	−1.90947e37	−0.223788	−0.111894	−	0.993720i	$-0.535692\pi$
$199$	−1.90947e37	−0.223788	−0.111894	+	0.993720i	$0.535692\pi$
$200$	0	0
$201$	−4.20984e37	−0.418341
$202$	− 8.41979e37i	− 0.770910i
$203$	1.09819e38i	0.926813i
$204$	1.04485e38	0.813121
$205$	0	0
$206$	−3.07909e38	−2.03992
$207$	2.06894e38i	1.26543i
$208$	5.93515e38i	3.35264i
$209$	1.13769e38	0.593761
$210$	0	0
$211$	2.10132e38	0.937200	0.468600	−	0.883410i	$-0.344759\pi$
$211$	2.10132e38	0.937200	0.468600	+	0.883410i	$0.344759\pi$
$212$	6.70520e38i	2.76611i
$213$	− 1.66739e38i	− 0.636462i
$214$	−7.44223e38	−2.62951
$215$	0	0
$216$	−7.48160e38	−2.26729
$217$	8.04685e37i	0.225965i
$218$	1.15274e39i	3.00054i
$219$	1.93817e38	0.467804
$220$	0	0
$221$	−4.53547e38	−0.942214
$222$	− 3.97995e38i	− 0.767456i
$223$	− 6.11348e38i	− 1.09461i	−0.836934	−	0.547304i	$-0.815654\pi$
$223$	− 6.11348e38i	− 1.09461i	0.836934	−	0.547304i	$-0.184346\pi$
$224$	−6.13659e38	−1.02055
$225$	0	0
$226$	5.54381e37	0.0796195
$227$	2.63987e38i	0.352498i	0.984346	+	0.176249i	$0.0563964\pi$
$227$	2.63987e38i	0.352498i	−0.984346	+	0.176249i	$0.943604\pi$
$228$	6.28985e38i	0.781116i
$229$	−4.19874e38	−0.485102	−0.242551	−	0.970139i	$-0.577984\pi$
$229$	−4.19874e38	−0.485102	−0.242551	+	0.970139i	$0.577984\pi$
$230$	0	0
$231$	−2.40663e38	−0.240886
$232$	− 4.80495e39i	− 4.47854i
$233$	− 4.94181e38i	− 0.429055i	−0.976718	−	0.214528i	$-0.931179\pi$
$233$	− 4.94181e38i	− 0.429055i	0.976718	−	0.214528i	$-0.0688212\pi$
$234$	2.38829e39	1.93208
$235$	0	0
$236$	8.88405e38	0.624544
$237$	− 5.41434e38i	− 0.354975i
$238$	− 1.12442e39i	− 0.687717i
$239$	−2.17853e39	−1.24336	−0.621681	−	0.783270i	$-0.713550\pi$
$239$	−2.17853e39	−1.24336	−0.621681	+	0.783270i	$0.713550\pi$
$240$	0	0
$241$	1.88932e39	0.939776	0.469888	−	0.882726i	$-0.344294\pi$
$241$	1.88932e39	0.939776	0.469888	+	0.882726i	$0.344294\pi$
$242$	7.34511e38i	0.341228i
$243$	2.36871e39i	1.02803i
$244$	−8.32559e39	−3.37662
$245$	0	0
$246$	3.78632e39	1.34211
$247$	− 2.73030e39i	− 0.905128i
$248$	− 3.52077e39i	− 1.09191i
$249$	−2.74585e38	−0.0796869
$250$	0	0
$251$	−1.73726e39	−0.441823	−0.220911	−	0.975294i	$-0.570903\pi$
$251$	−1.73726e39	−0.441823	−0.220911	+	0.975294i	$0.570903\pi$
$252$	4.18958e39i	0.997843i
$253$	− 6.74853e39i	− 1.50564i
$254$	1.39989e39	0.292642
$255$	0	0
$256$	−5.23619e39	−0.961736
$257$	− 1.02874e39i	− 0.177177i	−0.996068	−	0.0885885i	$-0.971764\pi$
$257$	− 1.02874e39i	− 0.177177i	0.996068	−	0.0885885i	$-0.0282356\pi$
$258$	1.70485e39i	0.275399i
$259$	−3.03062e39	−0.459288
$260$	0	0
$261$	−9.69876e39	−1.29464
$262$	1.67508e40i	2.09926i
$263$	4.10260e39i	0.482824i	0.970423	+	0.241412i	$0.0776106\pi$
$263$	4.10260e39i	0.482824i	−0.970423	+	0.241412i	$0.922389\pi$
$264$	1.05298e40	1.16401
$265$	0	0
$266$	6.76889e39	0.660648
$267$	5.70046e39i	0.522967i
$268$	− 2.39050e40i	− 2.06189i
$269$	1.25402e40	1.01717	0.508584	−	0.861012i	$-0.330169\pi$
$269$	1.25402e40	1.01717	0.508584	+	0.861012i	$0.330169\pi$
$270$	0	0
$271$	2.45955e40	1.76548	0.882738	−	0.469865i	$-0.155697\pi$
$271$	2.45955e40	1.76548	0.882738	+	0.469865i	$0.155697\pi$
$272$	2.46783e40i	1.66697i
$273$	5.77554e39i	0.367206i
$274$	4.71666e40	2.82325
$275$	0	0
$276$	3.73099e40	1.98072
$277$	− 8.59097e39i	− 0.429661i	−0.976651	−	0.214831i	$-0.931080\pi$
$277$	− 8.59097e39i	− 0.429661i	0.976651	−	0.214831i	$-0.0689199\pi$
$278$	2.58267e40i	1.21711i
$279$	−7.10667e39	−0.315643
$280$	0	0
$281$	−4.59581e39	−0.181430	−0.0907148	−	0.995877i	$-0.528915\pi$
$281$	−4.59581e39	−0.181430	−0.0907148	+	0.995877i	$0.528915\pi$
$282$	− 4.23099e40i	− 1.57519i
$283$	1.32266e40i	0.464485i	0.972658	+	0.232243i	$0.0746063\pi$
$283$	1.32266e40i	0.464485i	−0.972658	+	0.232243i	$0.925394\pi$
$284$	9.46802e40	3.13694
$285$	0	0
$286$	−7.79018e40	−2.29884
$287$	− 2.88317e40i	− 0.803192i
$288$	− 5.41960e40i	− 1.42558i
$289$	2.13961e40	0.531521
$290$	0	0
$291$	−2.80648e40	−0.622197
$292$	1.10056e41i	2.30568i
$293$	− 6.49706e40i	− 1.28647i	−0.765667	−	0.643237i	$-0.777591\pi$
$293$	− 6.49706e40i	− 1.28647i	0.765667	−	0.643237i	$-0.222409\pi$
$294$	3.41842e40	0.639873
$295$	0	0
$296$	1.32600e41	2.21937
$297$	− 4.92587e40i	− 0.779834i
$298$	− 8.45478e40i	− 1.26629i
$299$	−1.61955e41	−2.29519
$300$	0	0
$301$	1.29820e40	0.164814
$302$	1.76746e41i	2.12439i
$303$	1.79824e40i	0.204665i
$304$	−1.48560e41	−1.60136
$305$	0	0
$306$	9.93046e40	0.960652
$307$	1.37051e41i	1.25632i	0.778086	+	0.628158i	$0.216191\pi$
$307$	1.37051e41i	1.25632i	−0.778086	+	0.628158i	$0.783809\pi$
$308$	− 1.36657e41i	− 1.18726i
$309$	6.57610e40	0.541568
$310$	0	0
$311$	−2.13529e41	−1.58092	−0.790462	−	0.612511i	$-0.790159\pi$
$311$	−2.13529e41	−1.58092	−0.790462	+	0.612511i	$0.790159\pi$
$312$	− 2.52700e41i	− 1.77441i
$313$	− 1.66200e40i	− 0.110700i	−0.998467	−	0.0553502i	$-0.982372\pi$
$313$	− 1.66200e40i	− 0.110700i	0.998467	−	0.0553502i	$-0.0176275\pi$
$314$	−4.33852e41	−2.74159
$315$	0	0
$316$	3.07446e41	1.74957
$317$	− 2.50993e41i	− 1.35576i	−0.735172	−	0.677881i	$-0.762899\pi$
$317$	− 2.50993e41i	− 1.35576i	0.735172	−	0.677881i	$-0.237101\pi$
$318$	− 2.02386e41i	− 1.03785i
$319$	3.16357e41	1.54039
$320$	0	0
$321$	1.58946e41	0.698097
$322$	− 4.01514e41i	− 1.67525i
$323$	− 1.13525e41i	− 0.450040i
$324$	−2.15183e41	−0.810616
$325$	0	0
$326$	−8.90886e40	−0.303202
$327$	− 2.46194e41i	− 0.796599i
$328$	1.26149e42i	3.88118i
$329$	−3.22178e41	−0.942679
$330$	0	0
$331$	−5.26370e41	−1.39357	−0.696786	−	0.717279i	$-0.745387\pi$
$331$	−5.26370e41	−1.39357	−0.696786	+	0.717279i	$0.745387\pi$
$332$	− 1.55919e41i	− 0.392754i
$333$	− 2.67652e41i	− 0.641566i
$334$	8.70764e41	1.98648
$335$	0	0
$336$	3.14257e41	0.649662
$337$	6.13456e41i	1.20751i	0.797171	+	0.603754i	$0.206329\pi$
$337$	6.13456e41i	1.20751i	−0.797171	+	0.603754i	$0.793671\pi$
$338$	8.82968e41i	1.65508i
$339$	−1.18401e40	−0.0211378
$340$	0	0
$341$	2.31807e41	0.375560
$342$	5.97802e41i	0.922840i
$343$	− 6.29637e41i	− 0.926270i
$344$	−5.68006e41	−0.796413
$345$	0	0
$346$	−1.65121e42	−2.10401
$347$	− 5.31978e41i	− 0.646334i	−0.946342	−	0.323167i	$-0.895252\pi$
$347$	− 5.31978e41i	− 0.646334i	0.946342	−	0.323167i	$-0.104748\pi$
$348$	1.74901e42i	2.02644i
$349$	4.87219e41	0.538399	0.269200	−	0.963084i	$-0.413241\pi$
$349$	4.87219e41	0.538399	0.269200	+	0.963084i	$0.413241\pi$
$350$	0	0
$351$	−1.18214e42	−1.18878
$352$	1.76778e42i	1.69619i
$353$	1.44982e41i	0.132749i	0.997795	+	0.0663747i	$0.0211433\pi$
$353$	1.44982e41i	0.132749i	−0.997795	+	0.0663747i	$0.978857\pi$
$354$	−2.68152e41	−0.234329
$355$	0	0
$356$	−3.23693e42	−2.57756
$357$	2.40146e41i	0.182579i
$358$	− 2.56028e41i	− 0.185873i
$359$	1.84745e42	1.28090	0.640450	−	0.768000i	$-0.278748\pi$
$359$	1.84745e42	1.28090	0.640450	+	0.768000i	$0.278748\pi$
$360$	0	0
$361$	−8.97362e41	−0.567674
$362$	1.26120e41i	0.0762243i
$363$	− 1.56872e41i	− 0.0905910i
$364$	−3.27956e42	−1.80985
$365$	0	0
$366$	2.51295e42	1.26691
$367$	− 2.26409e41i	− 0.109120i	−0.998510	−	0.0545600i	$-0.982624\pi$
$367$	− 2.26409e41i	− 0.109120i	0.998510	−	0.0545600i	$-0.0173756\pi$
$368$	8.81223e42i	4.06066i
$369$	2.54631e42	1.12196
$370$	0	0
$371$	−1.54111e42	−0.621105
$372$	1.28157e42i	0.494064i
$373$	1.81120e41i	0.0667993i	0.999442	+	0.0333996i	$0.0106334\pi$
$373$	1.81120e41i	0.0667993i	−0.999442	+	0.0333996i	$0.989367\pi$
$374$	−3.23915e42	−1.14301
$375$	0	0
$376$	1.40964e43	4.55521
$377$	− 7.59209e42i	− 2.34817i
$378$	− 2.93073e42i	− 0.867682i
$379$	−7.20050e41	−0.204087	−0.102044	−	0.994780i	$-0.532538\pi$
$379$	−7.20050e41	−0.204087	−0.102044	+	0.994780i	$0.532538\pi$
$380$	0	0
$381$	−2.98978e41	−0.0776922
$382$	− 1.01304e43i	− 2.52105i
$383$	− 3.83359e42i	− 0.913747i	−0.889532	−	0.456873i	$-0.848969\pi$
$383$	− 3.83359e42i	− 0.913747i	0.889532	−	0.456873i	$-0.151031\pi$
$384$	−8.87001e40	−0.0202516
$385$	0	0
$386$	−4.33714e42	−0.908894
$387$	1.14652e42i	0.230223i
$388$	− 1.59362e43i	− 3.06663i
$389$	2.90997e42	0.536685	0.268343	−	0.963324i	$-0.413524\pi$
$389$	2.90997e42	0.536685	0.268343	+	0.963324i	$0.413524\pi$
$390$	0	0
$391$	−6.73405e42	−1.14119
$392$	1.13891e43i	1.85042i
$393$	− 3.57753e42i	− 0.557321i
$394$	−1.31939e43	−1.97100
$395$	0	0
$396$	1.20690e43	1.65845
$397$	− 8.66553e42i	− 1.14223i	−0.820872	−	0.571113i	$-0.806512\pi$
$397$	− 8.66553e42i	− 1.14223i	0.820872	−	0.571113i	$-0.193488\pi$
$398$	3.27269e42i	0.413842i
$399$	−1.44565e42	−0.175392
$400$	0	0
$401$	−1.77117e43	−1.97869	−0.989347	−	0.145575i	$-0.953497\pi$
$401$	−1.77117e43	−1.97869	−0.989347	+	0.145575i	$0.953497\pi$
$402$	7.21537e42i	0.773621i
$403$	− 5.56302e42i	− 0.572503i
$404$	−1.02110e43	−1.00874
$405$	0	0
$406$	1.88221e43	1.71392
$407$	8.73036e42i	0.763351i
$408$	− 1.05072e43i	− 0.882257i
$409$	−3.25831e42	−0.262759	−0.131379	−	0.991332i	$-0.541941\pi$
$409$	−3.25831e42	−0.262759	−0.131379	+	0.991332i	$0.541941\pi$
$410$	0	0
$411$	−1.00735e43	−0.749532
$412$	3.73415e43i	2.66924i
$413$	2.04190e42i	0.140236i
$414$	3.54602e43	2.34010
$415$	0	0
$416$	4.24240e43	2.58566
$417$	− 5.51587e42i	− 0.323124i
$418$	− 1.94993e43i	− 1.09802i
$419$	9.33890e42	0.505550	0.252775	−	0.967525i	$-0.418657\pi$
$419$	9.33890e42	0.505550	0.252775	+	0.967525i	$0.418657\pi$
$420$	0	0
$421$	−3.27277e43	−1.63780	−0.818900	−	0.573936i	$-0.805416\pi$
$421$	−3.27277e43	−1.63780	−0.818900	+	0.573936i	$0.805416\pi$
$422$	− 3.60152e43i	− 1.73313i
$423$	− 2.84535e43i	− 1.31680i
$424$	6.74290e43	3.00130
$425$	0	0
$426$	−2.85778e43	−1.17698
$427$	− 1.91354e43i	− 0.758190i
$428$	9.02551e43i	3.44072i
$429$	1.66377e43	0.610307
$430$	0	0
$431$	6.45303e41	0.0219224	0.0109612	−	0.999940i	$-0.496511\pi$
$431$	6.45303e41	0.0219224	0.0109612	+	0.999940i	$0.496511\pi$
$432$	6.43221e43i	2.10319i
$433$	− 3.48487e43i	− 1.09682i	−0.836209	−	0.548411i	$-0.815233\pi$
$433$	− 3.48487e43i	− 1.09682i	0.836209	−	0.548411i	$-0.184767\pi$
$434$	1.37917e43	0.417867
$435$	0	0
$436$	1.39798e44	3.92621
$437$	− 4.05381e43i	− 1.09628i
$438$	− 3.32189e43i	− 0.865091i
$439$	7.82812e43	1.96333	0.981664	−	0.190617i	$-0.0610490\pi$
$439$	7.82812e43	1.96333	0.981664	+	0.190617i	$0.0610490\pi$
$440$	0	0
$441$	2.29889e43	0.534911
$442$	7.77346e43i	1.74240i
$443$	7.93586e43i	1.71369i	0.515573	+	0.856845i	$0.327579\pi$
$443$	7.93586e43i	1.71369i	−0.515573	+	0.856845i	$0.672421\pi$
$444$	−4.82666e43	−1.00422
$445$	0	0
$446$	−1.04781e44	−2.02421
$447$	1.80571e43i	0.336182i
$448$	3.14311e43i	0.563990i
$449$	−9.44847e43	−1.63417	−0.817084	−	0.576519i	$-0.804411\pi$
$449$	−9.44847e43	−1.63417	−0.817084	+	0.576519i	$0.804411\pi$
$450$	0	0
$451$	−8.30561e43	−1.33493
$452$	− 6.72323e42i	− 0.104182i
$453$	− 3.77481e43i	− 0.563994i
$454$	4.52455e43	0.651860
$455$	0	0
$456$	6.32521e43	0.847531
$457$	− 1.52574e43i	− 0.197181i	−0.995128	−	0.0985903i	$-0.968567\pi$
$457$	− 1.52574e43i	− 0.197181i	0.995128	−	0.0985903i	$-0.0314333\pi$
$458$	7.19634e43i	0.897080i
$459$	−4.91530e43	−0.591073
$460$	0	0
$461$	−1.34257e44	−1.50269	−0.751347	−	0.659907i	$-0.770596\pi$
$461$	−1.34257e44	−1.50269	−0.751347	+	0.659907i	$0.770596\pi$
$462$	4.12479e43i	0.445460i
$463$	− 1.48404e44i	− 1.54654i	−0.634079	−	0.773268i	$-0.718621\pi$
$463$	− 1.48404e44i	− 1.54654i	0.634079	−	0.773268i	$-0.281379\pi$
$464$	−4.13099e44	−4.15439
$465$	0	0
$466$	−8.46990e43	−0.793434
$467$	− 1.50337e44i	− 1.35937i	−0.733503	−	0.679687i	$-0.762116\pi$
$467$	− 1.50337e44i	− 1.35937i	0.733503	−	0.679687i	$-0.237884\pi$
$468$	− 2.89638e44i	− 2.52813i
$469$	5.49429e43	0.462978
$470$	0	0
$471$	9.26589e43	0.727851
$472$	− 8.93400e43i	− 0.677646i
$473$	− 3.73974e43i	− 0.273926i
$474$	−9.27978e43	−0.656440
$475$	0	0
$476$	−1.36364e44	−0.899879
$477$	− 1.36105e44i	− 0.867604i
$478$	3.73384e44i	2.29930i
$479$	−1.66652e43	−0.0991459	−0.0495730	−	0.998771i	$-0.515786\pi$
$479$	−1.66652e43	−0.0991459	−0.0495730	+	0.998771i	$0.515786\pi$
$480$	0	0
$481$	2.09516e44	1.16365
$482$	− 3.23816e44i	− 1.73789i
$483$	8.57526e43i	0.444754i
$484$	8.90774e43	0.446498
$485$	0	0
$486$	4.05979e44	1.90110
$487$	9.90451e43i	0.448338i	0.974550	+	0.224169i	$0.0719667\pi$
$487$	9.90451e43i	0.448338i	−0.974550	+	0.224169i	$0.928033\pi$
$488$	8.37240e44i	3.66372i
$489$	1.90269e43	0.0804955
$490$	0	0
$491$	−1.43839e43	−0.0568894	−0.0284447	−	0.999595i	$-0.509055\pi$
$491$	−1.43839e43	−0.0568894	−0.0284447	+	0.999595i	$0.509055\pi$
$492$	− 4.59184e44i	− 1.75615i
$493$	− 3.15678e44i	− 1.16754i
$494$	−4.67953e44	−1.67382
$495$	0	0
$496$	−3.02694e44	−1.01288
$497$	2.17612e44i	0.704372i
$498$	4.70618e43i	0.147362i
$499$	2.57012e44	0.778564	0.389282	−	0.921119i	$-0.372723\pi$
$499$	2.57012e44	0.778564	0.389282	+	0.921119i	$0.372723\pi$
$500$	0	0
$501$	−1.85972e44	−0.527381
$502$	2.97754e44i	0.817044i
$503$	4.24762e44i	1.12791i	0.825806	+	0.563954i	$0.190720\pi$
$503$	4.24762e44i	1.12791i	−0.825806	+	0.563954i	$0.809280\pi$
$504$	4.21314e44	1.08268
$505$	0	0
$506$	−1.15665e45	−2.78431
$507$	− 1.88578e44i	− 0.439399i
$508$	− 1.69771e44i	− 0.382923i
$509$	−4.46104e43	−0.0974076	−0.0487038	−	0.998813i	$-0.515509\pi$
$509$	−4.46104e43	−0.0974076	−0.0487038	+	0.998813i	$0.515509\pi$
$510$	0	0
$511$	−2.52952e44	−0.517718
$512$	9.18260e44i	1.81975i
$513$	− 2.95895e44i	− 0.567808i
$514$	−1.76318e44	−0.327646
$515$	0	0
$516$	2.06755e44	0.360360
$517$	9.28104e44i	1.56676i
$518$	5.19426e44i	0.849343i
$519$	3.52654e44	0.558583
$520$	0	0
$521$	9.23592e44	1.37296	0.686480	−	0.727149i	$-0.259155\pi$
$521$	9.23592e44	1.37296	0.686480	+	0.727149i	$0.259155\pi$
$522$	1.66230e45i	2.39412i
$523$	1.77827e44i	0.248154i	0.992273	+	0.124077i	$0.0395969\pi$
$523$	1.77827e44i	0.248154i	−0.992273	+	0.124077i	$0.960403\pi$
$524$	2.03145e45	2.74688
$525$	0	0
$526$	7.03156e44	0.892867
$527$	− 2.31310e44i	− 0.284655i
$528$	− 9.05287e44i	− 1.07976i
$529$	−1.53962e45	−1.77990
$530$	0	0
$531$	−1.80332e44	−0.195891
$532$	− 8.20893e44i	− 0.864459i
$533$	1.99322e45i	2.03496i
$534$	9.77018e44	0.967101
$535$	0	0
$536$	−2.40394e45	−2.23720
$537$	5.46806e43i	0.0493466i
$538$	− 2.14931e45i	− 1.88101i
$539$	−7.49858e44	−0.636451
$540$	0	0
$541$	1.32094e45	1.05470	0.527348	−	0.849649i	$-0.323186\pi$
$541$	1.32094e45	1.05470	0.527348	+	0.849649i	$0.323186\pi$
$542$	− 4.21549e45i	− 3.26482i
$543$	− 2.69359e43i	− 0.0202364i
$544$	1.76399e45	1.28562
$545$	0	0
$546$	9.89887e44	0.679058
$547$	1.10958e45i	0.738531i	0.929324	+	0.369265i	$0.120391\pi$
$547$	1.10958e45i	0.738531i	−0.929324	+	0.369265i	$0.879609\pi$
$548$	− 5.72010e45i	− 3.69423i
$549$	1.68996e45	1.05909
$550$	0	0
$551$	1.90034e45	1.12158
$552$	− 3.75197e45i	− 2.14914i
$553$	7.06629e44i	0.392850i
$554$	−1.47243e45	−0.794554
$555$	0	0
$556$	3.13211e45	1.59259
$557$	1.45999e45i	0.720674i	0.932822	+	0.360337i	$0.117338\pi$
$557$	1.45999e45i	0.720674i	−0.932822	+	0.360337i	$0.882662\pi$
$558$	1.21803e45i	0.583706i
$559$	−8.97482e44	−0.417571
$560$	0	0
$561$	6.91794e44	0.303452
$562$	7.87689e44i	0.335510i
$563$	7.08631e44i	0.293111i	0.989202	+	0.146555i	$0.0468186\pi$
$563$	7.08631e44i	0.293111i	−0.989202	+	0.146555i	$0.953181\pi$
$564$	−5.13111e45	−2.06113
$565$	0	0
$566$	2.26694e45	0.858953
$567$	− 4.94574e44i	− 0.182016i
$568$	− 9.52125e45i	− 3.40366i
$569$	−4.72865e44	−0.164204	−0.0821022	−	0.996624i	$-0.526163\pi$
$569$	−4.72865e44	−0.164204	−0.0821022	+	0.996624i	$0.526163\pi$
$570$	0	0
$571$	2.38231e45	0.780732	0.390366	−	0.920660i	$-0.372348\pi$
$571$	2.38231e45	0.780732	0.390366	+	0.920660i	$0.372348\pi$
$572$	9.44750e45i	3.00803i
$573$	2.16358e45i	0.669302i
$574$	−4.94155e45	−1.48531
$575$	0	0
$576$	−2.77587e45	−0.787821
$577$	− 3.46702e45i	− 0.956215i	−0.878301	−	0.478108i	$-0.841323\pi$
$577$	− 3.46702e45i	− 0.956215i	0.878301	−	0.478108i	$-0.158677\pi$
$578$	− 3.66714e45i	− 0.982919i
$579$	9.26296e44	0.241298
$580$	0	0
$581$	3.58362e44	0.0881893
$582$	4.81011e45i	1.15060i
$583$	4.43952e45i	1.03230i
$584$	1.10675e46	2.50172
$585$	0	0
$586$	−1.11355e46	−2.37902
$587$	6.69381e45i	1.39042i	0.718809	+	0.695208i	$0.244688\pi$
$587$	6.69381e45i	1.39042i	−0.718809	+	0.695208i	$0.755312\pi$
$588$	− 4.14566e45i	− 0.837275i
$589$	1.39246e45	0.273451
$590$	0	0
$591$	2.81787e45	0.523271
$592$	− 1.14001e46i	− 2.05874i
$593$	− 5.07532e45i	− 0.891376i	−0.895188	−	0.445688i	$-0.852959\pi$
$593$	− 5.07532e45i	− 0.891376i	0.895188	−	0.445688i	$-0.147041\pi$
$594$	−8.44259e45	−1.44211
$595$	0	0
$596$	−1.02535e46	−1.65695
$597$	− 6.98959e44i	− 0.109869i
$598$	2.77579e46i	4.24440i
$599$	−1.79145e45	−0.266479	−0.133239	−	0.991084i	$-0.542538\pi$
$599$	−1.79145e45	−0.266479	−0.133239	+	0.991084i	$0.542538\pi$
$600$	0	0
$601$	2.80960e45	0.395563	0.197782	−	0.980246i	$-0.436626\pi$
$601$	2.80960e45	0.395563	0.197782	+	0.980246i	$0.436626\pi$
$602$	− 2.22502e45i	− 0.304783i
$603$	4.85235e45i	0.646720i
$604$	2.14347e46	2.77977
$605$	0	0
$606$	3.08205e45	0.378479
$607$	− 3.36655e44i	− 0.0402320i	−0.999798	−	0.0201160i	$-0.993596\pi$
$607$	− 3.36655e44i	− 0.0402320i	0.999798	−	0.0201160i	$-0.00640356\pi$
$608$	1.06190e46i	1.23502i
$609$	−4.01990e45	−0.455019
$610$	0	0
$611$	2.22731e46	2.38837
$612$	− 1.20431e46i	− 1.25701i
$613$	5.70670e45i	0.579812i	0.957055	+	0.289906i	$0.0936240\pi$
$613$	5.70670e45i	0.579812i	−0.957055	+	0.289906i	$0.906376\pi$
$614$	2.34895e46	2.32325
$615$	0	0
$616$	−1.37425e46	−1.28821
$617$	− 9.19098e45i	− 0.838796i	−0.907802	−	0.419398i	$-0.862241\pi$
$617$	− 9.19098e45i	− 0.838796i	0.907802	−	0.419398i	$-0.137759\pi$
$618$	− 1.12710e46i	− 1.00150i
$619$	6.17013e45	0.533825	0.266912	−	0.963721i	$-0.413997\pi$
$619$	6.17013e45	0.533825	0.266912	+	0.963721i	$0.413997\pi$
$620$	0	0
$621$	−1.75518e46	−1.43983
$622$	3.65974e46i	2.92354i
$623$	− 7.43971e45i	− 0.578766i
$624$	−2.17255e46	−1.64598
$625$	0	0
$626$	−2.84854e45	−0.204714
$627$	4.16451e45i	0.291508i
$628$	5.26151e46i	3.58737i
$629$	8.71162e45	0.578580
$630$	0	0
$631$	−2.22126e46	−1.39996	−0.699979	−	0.714164i	$-0.746807\pi$
$631$	−2.22126e46	−1.39996	−0.699979	+	0.714164i	$0.746807\pi$
$632$	− 3.09174e46i	− 1.89833i
$633$	7.69186e45i	0.460119i
$634$	−4.30183e46	−2.50715
$635$	0	0
$636$	−2.45443e46	−1.35803
$637$	1.79955e46i	0.970203i
$638$	− 5.42213e46i	− 2.84858i
$639$	−1.92186e46	−0.983916
$640$	0	0
$641$	1.80566e46	0.877967	0.438984	−	0.898495i	$-0.355339\pi$
$641$	1.80566e46	0.877967	0.438984	+	0.898495i	$0.355339\pi$
$642$	− 2.72422e46i	− 1.29096i
$643$	− 3.53912e46i	− 1.63461i	−0.576205	−	0.817305i	$-0.695467\pi$
$643$	− 3.53912e46i	− 1.63461i	0.576205	−	0.817305i	$-0.304533\pi$
$644$	−4.86934e46	−2.19206
$645$	0	0
$646$	−1.94574e46	−0.832240
$647$	1.83367e45i	0.0764539i	0.999269	+	0.0382269i	$0.0121710\pi$
$647$	1.83367e45i	0.0764539i	−0.999269	+	0.0382269i	$0.987829\pi$
$648$	2.16393e46i	0.879539i
$649$	5.88213e45	0.233076
$650$	0	0
$651$	−2.94554e45	−0.110938
$652$	1.08042e46i	0.396740i
$653$	3.11525e46i	1.11539i	0.830047	+	0.557693i	$0.188313\pi$
$653$	3.11525e46i	1.11539i	−0.830047	+	0.557693i	$0.811687\pi$
$654$	−4.21959e46	−1.47312
$655$	0	0
$656$	1.08455e47	3.60027
$657$	− 2.23397e46i	− 0.723185i
$658$	5.52190e46i	1.74326i
$659$	−1.47878e46	−0.455298	−0.227649	−	0.973743i	$-0.573104\pi$
$659$	−1.47878e46	−0.455298	−0.227649	+	0.973743i	$0.573104\pi$
$660$	0	0
$661$	4.35259e46	1.27475	0.637373	−	0.770556i	$-0.280021\pi$
$661$	4.35259e46	1.27475	0.637373	+	0.770556i	$0.280021\pi$
$662$	9.02160e46i	2.57707i
$663$	− 1.66020e46i	− 0.462581i
$664$	−1.56796e46	−0.426148
$665$	0	0
$666$	−4.58737e46	−1.18642
$667$	− 1.12724e47i	− 2.84406i
$668$	− 1.05601e47i	− 2.59931i
$669$	2.23783e46	0.537398
$670$	0	0
$671$	−5.51237e46	−1.26014
$672$	− 2.24629e46i	− 0.501041i
$673$	− 5.27514e46i	− 1.14812i	−0.818815	−	0.574058i	$-0.805368\pi$
$673$	− 5.27514e46i	− 1.14812i	0.818815	−	0.574058i	$-0.194632\pi$
$674$	1.05142e47	2.23299
$675$	0	0
$676$	1.07081e47	2.16568
$677$	− 8.28813e46i	− 1.63585i	−0.575325	−	0.817925i	$-0.695125\pi$
$677$	− 8.28813e46i	− 1.63585i	0.575325	−	0.817925i	$-0.304875\pi$
$678$	2.02930e45i	0.0390892i
$679$	3.66276e46	0.688584
$680$	0	0
$681$	−9.66322e45	−0.173059
$682$	− 3.97301e46i	− 0.694508i
$683$	− 6.76331e43i	− 0.00115403i	−1.00000		0.000577016i	$-0.999816\pi$
$683$	− 6.76331e43i	− 0.00115403i	1.00000		0.000577016i	$-0.000183670\pi$
$684$	7.24981e46	1.20754
$685$	0	0
$686$	−1.07915e47	−1.71291
$687$	− 1.53694e46i	− 0.238161i
$688$	4.88335e46i	0.738770i
$689$	1.06542e47	1.57363
$690$	0	0
$691$	−1.12682e46	−0.158659	−0.0793297	−	0.996848i	$-0.525278\pi$
$691$	−1.12682e46	−0.158659	−0.0793297	+	0.996848i	$0.525278\pi$
$692$	2.00250e47i	2.75310i
$693$	2.77393e46i	0.372389i
$694$	−9.11771e46	−1.19524
$695$	0	0
$696$	1.75884e47	2.19874
$697$	8.28778e46i	1.01181i
$698$	− 8.35058e46i	− 0.995639i
$699$	1.80894e46	0.210645
$700$	0	0
$701$	−1.08244e47	−1.20242	−0.601210	−	0.799091i	$-0.705315\pi$
$701$	−1.08244e47	−1.20242	−0.601210	+	0.799091i	$0.705315\pi$
$702$	2.02610e47i	2.19835i
$703$	5.24429e46i	0.555807i
$704$	9.05440e46	0.937369
$705$	0	0
$706$	2.48490e46	0.245488
$707$	− 2.34689e46i	− 0.226503i
$708$	3.25199e46i	0.306620i
$709$	−2.54935e46	−0.234837	−0.117418	−	0.993083i	$-0.537462\pi$
$709$	−2.54935e46	−0.234837	−0.117418	+	0.993083i	$0.537462\pi$
$710$	0	0
$711$	−6.24067e46	−0.548761
$712$	3.25513e47i	2.79671i
$713$	− 8.25972e46i	− 0.693407i
$714$	4.11593e46	0.337635
$715$	0	0
$716$	−3.10496e46	−0.243216
$717$	− 7.97447e46i	− 0.610430i
$718$	− 3.16640e47i	− 2.36871i
$719$	1.83170e47	1.33914	0.669572	−	0.742747i	$-0.266478\pi$
$719$	1.83170e47	1.33914	0.669572	+	0.742747i	$0.266478\pi$
$720$	0	0
$721$	−8.58251e46	−0.599353
$722$	1.53801e47i	1.04978i
$723$	6.91583e46i	0.461384i
$724$	1.52952e46	0.0997396
$725$	0	0
$726$	−2.68867e46	−0.167526
$727$	− 3.00722e47i	− 1.83167i	−0.401554	−	0.915835i	$-0.631530\pi$
$727$	− 3.00722e47i	− 1.83167i	0.401554	−	0.915835i	$-0.368470\pi$
$728$	3.29800e47i	1.96374i
$729$	−2.91558e46	−0.169715
$730$	0	0
$731$	−3.73171e46	−0.207621
$732$	− 3.04757e47i	− 1.65776i
$733$	− 6.08336e46i	− 0.323540i	−0.986829	−	0.161770i	$-0.948280\pi$
$733$	− 6.08336e46i	− 0.323540i	0.986829	−	0.161770i	$-0.0517202\pi$
$734$	−3.88050e46	−0.201791
$735$	0	0
$736$	6.29892e47	3.13172
$737$	− 1.58275e47i	− 0.769483i
$738$	− 4.36418e47i	− 2.07479i
$739$	9.38687e46	0.436403	0.218201	−	0.975904i	$-0.429981\pi$
$739$	9.38687e46	0.436403	0.218201	+	0.975904i	$0.429981\pi$
$740$	0	0
$741$	9.99421e46	0.444373
$742$	2.64136e47i	1.14858i
$743$	8.46330e46i	0.359935i	0.983673	+	0.179968i	$0.0575993\pi$
$743$	8.46330e46i	0.359935i	−0.983673	+	0.179968i	$0.942401\pi$
$744$	1.28877e47	0.536072
$745$	0	0
$746$	3.10427e46	0.123529
$747$	3.16491e46i	0.123189i
$748$	3.92825e47i	1.49563i
$749$	−2.07441e47	−0.772583
$750$	0	0
$751$	4.31778e47	1.53887	0.769433	−	0.638727i	$-0.220539\pi$
$751$	4.31778e47	1.53887	0.769433	+	0.638727i	$0.220539\pi$
$752$	− 1.21192e48i	− 4.22551i
$753$	− 6.35921e46i	− 0.216913i
$754$	−1.30123e48	−4.34237
$755$	0	0
$756$	−3.55422e47	−1.13536
$757$	4.24730e46i	0.132749i	0.997795	+	0.0663745i	$0.0211432\pi$
$757$	4.24730e46i	0.132749i	−0.997795	+	0.0663745i	$0.978857\pi$
$758$	1.23411e47i	0.377410i
$759$	2.47029e47	0.739194
$760$	0	0
$761$	−1.05002e47	−0.300850	−0.150425	−	0.988621i	$-0.548064\pi$
$761$	−1.05002e47	−0.300850	−0.150425	+	0.988621i	$0.548064\pi$
$762$	5.12427e46i	0.143673i
$763$	3.21310e47i	0.881595i
$764$	−1.22856e48	−3.29880
$765$	0	0
$766$	−6.57050e47	−1.68975
$767$	− 1.41162e47i	− 0.355300i
$768$	− 1.91670e47i	− 0.472165i
$769$	7.39843e47	1.78384	0.891918	−	0.452198i	$-0.149360\pi$
$769$	7.39843e47	1.78384	0.891918	+	0.452198i	$0.149360\pi$
$770$	0	0
$771$	3.76567e46	0.0869852
$772$	5.25984e47i	1.18929i
$773$	− 2.23647e47i	− 0.494996i	−0.968888	−	0.247498i	$-0.920392\pi$
$773$	− 2.23647e47i	− 0.494996i	0.968888	−	0.247498i	$-0.0796084\pi$
$774$	1.96505e47	0.425743
$775$	0	0
$776$	−1.60258e48	−3.32737
$777$	− 1.10935e47i	− 0.225488i
$778$	− 4.98748e47i	− 0.992470i
$779$	−4.98915e47	−0.971982
$780$	0	0
$781$	6.26878e47	1.17069
$782$	1.15417e48i	2.11036i
$783$	− 8.22791e47i	− 1.47306i
$784$	9.79165e47	1.71649
$785$	0	0
$786$	−6.13162e47	−1.03063
$787$	2.76167e47i	0.454557i	0.973830	+	0.227279i	$0.0729828\pi$
$787$	2.76167e47i	0.454557i	−0.973830	+	0.227279i	$0.927017\pi$
$788$	1.60009e48i	2.57906i
$789$	−1.50175e47	−0.237043
$790$	0	0
$791$	1.54526e46	0.0233932
$792$	− 1.21369e48i	− 1.79946i
$793$	1.32289e48i	1.92095i
$794$	−1.48521e48	−2.11227
$795$	0	0
$796$	3.96894e47	0.541513
$797$	− 1.10405e48i	− 1.47546i	−0.675094	−	0.737732i	$-0.735897\pi$
$797$	− 1.10405e48i	− 1.47546i	0.675094	−	0.737732i	$-0.264103\pi$
$798$	2.47774e47i	0.324346i
$799$	9.26112e47	1.18752
$800$	0	0
$801$	6.57046e47	0.808461
$802$	3.03566e48i	3.65912i
$803$	7.28684e47i	0.860464i
$804$	8.75039e47	1.01228
$805$	0	0
$806$	−9.53462e47	−1.05871
$807$	4.59033e47i	0.499380i
$808$	1.02685e48i	1.09451i
$809$	−1.07205e47	−0.111960	−0.0559801	−	0.998432i	$-0.517828\pi$
$809$	−1.07205e47	−0.111960	−0.0559801	+	0.998432i	$0.517828\pi$
$810$	0	0
$811$	1.65176e48	1.65616	0.828081	−	0.560609i	$-0.189433\pi$
$811$	1.65176e48	1.65616	0.828081	+	0.560609i	$0.189433\pi$
$812$	− 2.28264e48i	− 2.24266i
$813$	9.00314e47i	0.866762i
$814$	1.49632e48	1.41163
$815$	0	0
$816$	−9.03344e47	−0.818400
$817$	− 2.24645e47i	− 0.199449i
$818$	5.58450e47i	0.485909i
$819$	6.65700e47	0.567668
$820$	0	0
$821$	4.07665e46	0.0333919	0.0166960	−	0.999861i	$-0.494685\pi$
$821$	4.07665e46	0.0333919	0.0166960	+	0.999861i	$0.494685\pi$
$822$	1.72653e48i	1.38608i
$823$	1.04142e48i	0.819464i	0.912206	+	0.409732i	$0.134378\pi$
$823$	1.04142e48i	0.819464i	−0.912206	+	0.409732i	$0.865622\pi$
$824$	3.75514e48	2.89619
$825$	0	0
$826$	3.49967e47	0.259332
$827$	− 2.19704e48i	− 1.59587i	−0.602744	−	0.797934i	$-0.705926\pi$
$827$	− 2.19704e48i	− 1.59587i	0.602744	−	0.797934i	$-0.294074\pi$
$828$	− 4.30041e48i	− 3.06203i
$829$	−1.11304e48	−0.776893	−0.388446	−	0.921471i	$-0.626988\pi$
$829$	−1.11304e48	−0.776893	−0.388446	+	0.921471i	$0.626988\pi$
$830$	0	0
$831$	3.14471e47	0.210942
$832$	− 2.17292e48i	− 1.42892i
$833$	7.48249e47i	0.482396i
$834$	−9.45381e47	−0.597540
$835$	0	0
$836$	−2.36476e48	−1.43676
$837$	− 6.02892e47i	− 0.359144i
$838$	− 1.60062e48i	− 0.934893i
$839$	9.52969e47	0.545766	0.272883	−	0.962047i	$-0.412023\pi$
$839$	9.52969e47	0.545766	0.272883	+	0.962047i	$0.412023\pi$
$840$	0	0
$841$	3.46818e48	1.90971
$842$	5.60929e48i	3.02872i
$843$	− 1.68229e47i	− 0.0890730i
$844$	−4.36772e48	−2.26780
$845$	0	0
$846$	−4.87673e48	−2.43510
$847$	2.04734e47i	0.100257i
$848$	− 5.79712e48i	− 2.78407i
$849$	−4.84157e47	−0.228039
$850$	0	0
$851$	3.11079e48	1.40939
$852$	3.46576e48i	1.54008i
$853$	− 1.98887e48i	− 0.866858i	−0.901188	−	0.433429i	$-0.857303\pi$
$853$	− 1.98887e48i	− 0.866858i	0.901188	−	0.433429i	$-0.142697\pi$
$854$	−3.27967e48	−1.40209
$855$	0	0
$856$	9.07626e48	3.73327
$857$	1.50576e48i	0.607535i	0.952746	+	0.303768i	$0.0982447\pi$
$857$	1.50576e48i	0.607535i	−0.952746	+	0.303768i	$0.901755\pi$
$858$	− 2.85158e48i	− 1.12862i
$859$	−4.27542e48	−1.65994	−0.829968	−	0.557810i	$-0.811642\pi$
$859$	−4.27542e48	−1.65994	−0.829968	+	0.557810i	$0.811642\pi$
$860$	0	0
$861$	1.05538e48	0.394328
$862$	− 1.10600e47i	− 0.0405402i
$863$	1.32955e48i	0.478108i	0.971006	+	0.239054i	$0.0768372\pi$
$863$	1.32955e48i	0.478108i	−0.971006	+	0.239054i	$0.923163\pi$
$864$	4.59770e48	1.62205
$865$	0	0
$866$	−5.97281e48	−2.02831
$867$	7.83201e47i	0.260950i
$868$	− 1.67258e48i	− 0.546780i
$869$	2.03560e48	0.652929
$870$	0	0
$871$	−3.79837e48	−1.17300
$872$	− 1.40584e49i	− 4.26004i
$873$	3.23480e48i	0.961862i
$874$	−6.94795e48	−2.02730
$875$	0	0
$876$	−4.02860e48	−1.13197
$877$	− 8.44361e47i	− 0.232828i	−0.993201	−	0.116414i	$-0.962860\pi$
$877$	− 8.44361e47i	− 0.232828i	0.993201	−	0.116414i	$-0.0371399\pi$
$878$	− 1.34168e49i	− 3.63070i
$879$	2.37824e48	0.631595
$880$	0	0
$881$	4.97900e48	1.27362	0.636810	−	0.771021i	$-0.280254\pi$
$881$	4.97900e48	1.27362	0.636810	+	0.771021i	$0.280254\pi$
$882$	− 3.94013e48i	− 0.989189i
$883$	2.69903e47i	0.0665052i	0.999447	+	0.0332526i	$0.0105866\pi$
$883$	2.69903e47i	0.0665052i	−0.999447	+	0.0332526i	$0.989413\pi$
$884$	9.42722e48	2.27993
$885$	0	0
$886$	1.36015e49	3.16906
$887$	− 2.06378e48i	− 0.471981i	−0.971755	−	0.235990i	$-0.924167\pi$
$887$	− 2.06378e48i	− 0.471981i	0.971755	−	0.235990i	$-0.0758334\pi$
$888$	4.85380e48i	1.08960i
$889$	3.90199e47	0.0859818
$890$	0	0
$891$	−1.42473e48	−0.302517
$892$	1.27072e49i	2.64868i
$893$	5.57508e48i	1.14078i
$894$	3.09486e48	0.621687
$895$	0	0
$896$	1.15763e47	0.0224124
$897$	− 5.92832e48i	− 1.12683i
$898$	1.61940e49i	3.02200i
$899$	3.87198e48	0.709412
$900$	0	0
$901$	4.42999e48	0.782426
$902$	1.42352e49i	2.46863i
$903$	4.75203e47i	0.0809155i
$904$	−6.76103e47	−0.113040
$905$	0	0
$906$	−6.46975e48	−1.04297
$907$	− 2.89436e48i	− 0.458177i	−0.973406	−	0.229088i	$-0.926426\pi$
$907$	− 2.89436e48i	− 0.458177i	0.973406	−	0.229088i	$-0.0735745\pi$
$908$	− 5.48713e48i	− 0.852960i
$909$	2.07268e48	0.316395
$910$	0	0
$911$	−5.21685e48	−0.767989	−0.383995	−	0.923335i	$-0.625452\pi$
$911$	−5.21685e48	−0.767989	−0.383995	+	0.923335i	$0.625452\pi$
$912$	− 5.43802e48i	− 0.786187i
$913$	− 1.03234e48i	− 0.146573i
$914$	−2.61501e48	−0.364638
$915$	0	0
$916$	8.72731e48	1.17383
$917$	4.66905e48i	0.616786i
$918$	8.42447e48i	1.09305i
$919$	1.74463e48	0.222330	0.111165	−	0.993802i	$-0.464542\pi$
$919$	1.74463e48	0.222330	0.111165	+	0.993802i	$0.464542\pi$
$920$	0	0
$921$	−5.01673e48	−0.616789
$922$	2.30106e49i	2.77887i
$923$	− 1.50441e49i	− 1.78459i
$924$	5.00231e48	0.582885
$925$	0	0
$926$	−2.54354e49	−2.85995
$927$	− 7.57974e48i	− 0.837218i
$928$	2.95280e49i	3.20400i
$929$	6.02295e48	0.642022	0.321011	−	0.947075i	$-0.395977\pi$
$929$	6.02295e48	0.642022	0.321011	+	0.947075i	$0.395977\pi$
$930$	0	0
$931$	−4.50437e48	−0.463409
$932$	1.02718e49i	1.03821i
$933$	− 7.81620e48i	− 0.776156i
$934$	−2.57668e49	−2.51383
$935$	0	0
$936$	−2.91267e49	−2.74308
$937$	− 7.30711e48i	− 0.676149i	−0.941119	−	0.338075i	$-0.890224\pi$
$937$	− 7.30711e48i	− 0.676149i	0.941119	−	0.338075i	$-0.109776\pi$
$938$	− 9.41683e48i	− 0.856165i
$939$	6.08372e47	0.0543484
$940$	0	0
$941$	−2.79803e48	−0.241337	−0.120668	−	0.992693i	$-0.538504\pi$
$941$	−2.79803e48	−0.241337	−0.120668	+	0.992693i	$0.538504\pi$
$942$	− 1.58811e49i	− 1.34598i
$943$	2.95944e49i	2.46472i
$944$	−7.68089e48	−0.628599
$945$	0	0
$946$	−6.40965e48	−0.506559
$947$	− 1.76749e49i	− 1.37272i	−0.727261	−	0.686361i	$-0.759207\pi$
$947$	− 1.76749e49i	− 1.37272i	0.727261	−	0.686361i	$-0.240793\pi$
$948$	1.12540e49i	0.858953i
$949$	1.74873e49	1.31169
$950$	0	0
$951$	9.18755e48	0.665612
$952$	1.37130e49i	0.976392i
$953$	− 7.01918e48i	− 0.491195i	−0.969372	−	0.245597i	$-0.921016\pi$
$953$	− 7.01918e48i	− 0.491195i	0.969372	−	0.245597i	$-0.0789841\pi$
$954$	−2.33274e49	−1.60442
$955$	0	0
$956$	4.52819e49	3.00864
$957$	1.15802e49i	0.756256i
$958$	2.85630e48i	0.183346i
$959$	1.31470e49	0.829506
$960$	0	0
$961$	−1.35663e49	−0.827039
$962$	− 3.59095e49i	− 2.15189i
$963$	− 1.83204e49i	− 1.07920i
$964$	−3.92706e49	−2.27403
$965$	0	0
$966$	1.46974e49	0.822464
$967$	2.67489e48i	0.147153i	0.997290	+	0.0735765i	$0.0234413\pi$
$967$	2.67489e48i	0.147153i	−0.997290	+	0.0735765i	$0.976559\pi$
$968$	− 8.95782e48i	− 0.484461i
$969$	4.15557e48	0.220947
$970$	0	0
$971$	1.24416e49	0.639380	0.319690	−	0.947522i	$-0.396421\pi$
$971$	1.24416e49	0.639380	0.319690	+	0.947522i	$0.396421\pi$
$972$	− 4.92349e49i	− 2.48759i
$973$	7.19880e48i	0.357601i
$974$	1.69756e49	0.829092
$975$	0	0
$976$	7.19806e49	3.39855
$977$	− 2.66698e49i	− 1.23811i	−0.785347	−	0.619055i	$-0.787516\pi$
$977$	− 2.66698e49i	− 1.23811i	0.785347	−	0.619055i	$-0.212484\pi$
$978$	− 3.26107e48i	− 0.148857i
$979$	−2.14317e49	−0.961927
$980$	0	0
$981$	−2.83768e49	−1.23147
$982$	2.46529e48i	0.105203i
$983$	− 3.25975e49i	− 1.36789i	−0.729534	−	0.683945i	$-0.760263\pi$
$983$	− 3.25975e49i	− 1.36789i	0.729534	−	0.683945i	$-0.239737\pi$
$984$	−4.61765e49	−1.90547
$985$	0	0
$986$	−5.41049e49	−2.15908
$987$	− 1.17933e49i	− 0.462809i
$988$	5.67507e49i	2.19019i
$989$	−1.33254e49	−0.505756
$990$	0	0
$991$	−2.53166e49	−0.929373	−0.464687	−	0.885475i	$-0.653833\pi$
$991$	−2.53166e49	−0.929373	−0.464687	+	0.885475i	$0.653833\pi$
$992$	2.16363e49i	0.781162i
$993$	− 1.92677e49i	− 0.684175i
$994$	3.72971e49	1.30257
$995$	0	0
$996$	5.70739e48	0.192823
$997$	2.00836e49i	0.667379i	0.942683	+	0.333689i	$0.108294\pi$
$997$	2.00836e49i	0.667379i	−0.942683	+	0.333689i	$0.891706\pi$
$998$	− 4.40500e49i	− 1.43977i
$999$	2.27062e49	0.729985

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.b.d.24.2		22
5.2	odd	4		25.34.a.e.1.11	yes	11
5.3	odd	4		25.34.a.d.1.1	✓	11
5.4	even	2	inner	25.34.b.d.24.21		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.34.a.d.1.1	✓	11	5.3	odd	4
25.34.a.e.1.11	yes	11	5.2	odd	4
25.34.b.d.24.2		22	1.1	even	1	trivial
25.34.b.d.24.21		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)

\(f(q)\)	\(=\)	\(q-171393. i q^{2} +3.66048e7i q^{3} -2.07856e10 q^{4} +6.27381e12 q^{6} -4.77732e13i q^{7} +2.09024e15i q^{8} +4.21915e15 q^{9} +O(q^{10})\)	\(q-171393. i q^{2} +3.66048e7i q^{3} -2.07856e10 q^{4} +6.27381e12 q^{6} -4.77732e13i q^{7} +2.09024e15i q^{8} +4.21915e15 q^{9} -1.37621e17 q^{11} -7.60852e17i q^{12} +3.30270e18i q^{13} -8.18799e18 q^{14} +1.79706e20 q^{16} +1.37326e20i q^{17} -7.23131e20i q^{18} -8.26685e20 q^{19} +1.74873e21 q^{21} +2.35873e22i q^{22} +4.90370e22i q^{23} -7.65130e22 q^{24} +5.66060e23 q^{26} +3.57930e23i q^{27} +9.92994e23i q^{28} -2.29875e24 q^{29} -1.68439e24 q^{31} -1.28452e25i q^{32} -5.03760e24i q^{33} +2.35367e25 q^{34} -8.76973e25 q^{36} -6.34376e25i q^{37} +1.41688e26i q^{38} -1.20895e26 q^{39} +6.03512e26 q^{41} -2.99720e26i q^{42} +2.71742e26i q^{43} +2.86053e27 q^{44} +8.40459e27 q^{46} -6.74390e27i q^{47} +6.57811e27i q^{48} +5.44871e27 q^{49} -5.02679e27 q^{51} -6.86485e28i q^{52} -3.22589e28i q^{53} +6.13466e28 q^{54} +9.98577e28 q^{56} -3.02607e28i q^{57} +3.93989e29i q^{58} -4.27415e28 q^{59} +4.00547e29 q^{61} +2.88691e29i q^{62} -2.01562e29i q^{63} -6.57922e29 q^{64} -8.63409e29 q^{66} +1.15008e30i q^{67} -2.85440e30i q^{68} -1.79499e30 q^{69} -4.55510e30 q^{71} +8.81904e30i q^{72} -5.29485e30i q^{73} -1.08727e31 q^{74} +1.71831e31 q^{76} +6.57461e30i q^{77} +2.07205e31i q^{78} -1.47913e31 q^{79} +1.03525e31 q^{81} -1.03438e32i q^{82} +7.50132e30i q^{83} -3.63484e31 q^{84} +4.65745e31 q^{86} -8.41454e31i q^{87} -2.87662e32i q^{88} +1.55730e32 q^{89} +1.57781e32 q^{91} -1.01926e33i q^{92} -6.16567e31i q^{93} -1.15586e33 q^{94} +4.70198e32 q^{96} +7.66696e32i q^{97} -9.33870e32i q^{98} -5.80644e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 98676413354 q^{4} - 35567955353446 q^{6} - 48\!\cdots\!16 q^{9}+O(q^{10}) \) 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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