LMFDB - Embedded newform 25.34.b.d.24.8

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			24.8
Character	$\chi$	$=$	25.24
Dual form			25.34.b.d.24.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-61242.8i q^{2} -1.16397e8i q^{3} +4.83925e9 q^{4} -7.12847e12 q^{6} +1.52684e14i q^{7} -8.22441e14i q^{8} -7.98915e15 q^{9} +O(q^{10})$	\(q-61242.8i q^{2} -1.16397e8i q^{3} +4.83925e9 q^{4} -7.12847e12 q^{6} +1.52684e14i q^{7} -8.22441e14i q^{8} -7.98915e15 q^{9} -2.70714e17 q^{11} -5.63273e17i q^{12} +3.01712e18i q^{13} +9.35077e18 q^{14} -8.79981e18 q^{16} -5.13465e19i q^{17} +4.89278e20i q^{18} +2.04320e21 q^{19} +1.77719e22 q^{21} +1.65793e22i q^{22} -2.04394e22i q^{23} -9.57295e22 q^{24} +1.84777e23 q^{26} +2.82855e23i q^{27} +7.38874e23i q^{28} -1.42015e24 q^{29} +5.31617e24 q^{31} -6.52579e24i q^{32} +3.15102e25i q^{33} -3.14460e24 q^{34} -3.86615e25 q^{36} +5.96668e25i q^{37} -1.25131e26i q^{38} +3.51183e26 q^{39} +2.10328e26 q^{41} -1.08840e27i q^{42} -3.53517e26i q^{43} -1.31005e27 q^{44} -1.25177e27 q^{46} -1.08480e27i q^{47} +1.02427e27i q^{48} -1.55813e28 q^{49} -5.97656e27 q^{51} +1.46006e28i q^{52} -1.51399e28i q^{53} +1.73228e28 q^{54} +1.25573e29 q^{56} -2.37822e29i q^{57} +8.69743e28i q^{58} +3.91155e28 q^{59} +1.55030e29 q^{61} -3.25577e29i q^{62} -1.21981e30i q^{63} -4.75248e29 q^{64} +1.92977e30 q^{66} -5.34638e29i q^{67} -2.48478e29i q^{68} -2.37908e30 q^{69} +4.86501e30 q^{71} +6.57061e30i q^{72} -5.33567e30i q^{73} +3.65416e30 q^{74} +9.88755e30 q^{76} -4.13335e31i q^{77} -2.15074e31i q^{78} -2.81314e30 q^{79} -1.14888e31 q^{81} -1.28811e31i q^{82} +2.25113e31i q^{83} +8.60025e31 q^{84} -2.16504e31 q^{86} +1.65301e32i q^{87} +2.22646e32i q^{88} -5.60122e31 q^{89} -4.60664e32 q^{91} -9.89113e31i q^{92} -6.18785e32i q^{93} -6.64360e31 q^{94} -7.59581e32 q^{96} -2.05217e32i q^{97} +9.54241e32i q^{98} +2.16277e33 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	− 61242.8i	− 0.660785i	−0.943844	−	0.330393i	$-0.892819\pi$
$2$	− 61242.8i	− 0.660785i	0.943844	−	0.330393i	$-0.107181\pi$
$3$	− 1.16397e8i	− 1.56113i	−0.625072	−	0.780567i	$-0.714930\pi$
$3$	− 1.16397e8i	− 1.56113i	0.625072	−	0.780567i	$-0.285070\pi$
$4$	4.83925e9	0.563363
$5$	0	0
$5$	0	0
$6$	−7.12847e12	−1.03157
$7$	1.52684e14i	1.73650i	0.496128	+	0.868249i	$0.334755\pi$
$7$	1.52684e14i	1.73650i	−0.496128	+	0.868249i	$0.665245\pi$
$8$	− 8.22441e14i	− 1.03305i
$9$	−7.98915e15	−1.43714
$10$	0	0
$11$	−2.70714e17	−1.77636	−0.888180	−	0.459497i	$-0.848030\pi$
$11$	−2.70714e17	−1.77636	−0.888180	+	0.459497i	$0.848030\pi$
$12$	− 5.63273e17i	− 0.879485i
$13$	3.01712e18i	1.25755i	0.777586	+	0.628777i	$0.216444\pi$
$13$	3.01712e18i	1.25755i	−0.777586	+	0.628777i	$0.783556\pi$
$14$	9.35077e18	1.14745
$15$	0	0
$16$	−8.79981e18	−0.119260
$17$	− 5.13465e19i	− 0.255920i	−0.991779	−	0.127960i	$-0.959157\pi$
$17$	− 5.13465e19i	− 0.255920i	0.991779	−	0.127960i	$-0.0408428\pi$
$18$	4.89278e20i	0.949641i
$19$	2.04320e21	1.62509	0.812543	−	0.582901i	$-0.198082\pi$
$19$	2.04320e21	1.62509	0.812543	+	0.582901i	$0.198082\pi$
$20$	0	0
$21$	1.77719e22	2.71091
$22$	1.65793e22i	1.17379i
$23$	− 2.04394e22i	− 0.694958i	−0.937688	−	0.347479i	$-0.887038\pi$
$23$	− 2.04394e22i	− 0.694958i	0.937688	−	0.347479i	$-0.112962\pi$
$24$	−9.57295e22	−1.61273
$25$	0	0
$26$	1.84777e23	0.830973
$27$	2.82855e23i	0.682435i
$28$	7.38874e23i	0.978279i
$29$	−1.42015e24	−1.05383	−0.526913	−	0.849919i	$-0.676651\pi$
$29$	−1.42015e24	−1.05383	−0.526913	+	0.849919i	$0.676651\pi$
$30$	0	0
$31$	5.31617e24	1.31260	0.656298	−	0.754502i	$-0.272122\pi$
$31$	5.31617e24	1.31260	0.656298	+	0.754502i	$0.272122\pi$
$32$	− 6.52579e24i	− 0.954242i
$33$	3.15102e25i	2.77314i
$34$	−3.14460e24	−0.169108
$35$	0	0
$36$	−3.86615e25	−0.809631
$37$	5.96668e25i	0.795068i	0.917587	+	0.397534i	$0.130134\pi$
$37$	5.96668e25i	0.795068i	−0.917587	+	0.397534i	$0.869866\pi$
$38$	− 1.25131e26i	− 1.07383i
$39$	3.51183e26	1.96321
$40$	0	0
$41$	2.10328e26	0.515186	0.257593	−	0.966253i	$-0.417071\pi$
$41$	2.10328e26	0.515186	0.257593	+	0.966253i	$0.417071\pi$
$42$	− 1.08840e27i	− 1.79133i
$43$	− 3.53517e26i	− 0.394621i	−0.980341	−	0.197311i	$-0.936779\pi$
$43$	− 3.53517e26i	− 0.394621i	0.980341	−	0.197311i	$-0.0632208\pi$
$44$	−1.31005e27	−1.00073
$45$	0	0
$46$	−1.25177e27	−0.459218
$47$	− 1.08480e27i	− 0.279083i	−0.990216	−	0.139541i	$-0.955437\pi$
$47$	− 1.08480e27i	− 0.279083i	0.990216	−	0.139541i	$-0.0445629\pi$
$48$	1.02427e27i	0.186180i
$49$	−1.55813e28	−2.01543
$50$	0	0
$51$	−5.97656e27	−0.399525
$52$	1.46006e28i	0.708459i
$53$	− 1.51399e28i	− 0.536502i	−0.963349	−	0.268251i	$-0.913554\pi$
$53$	− 1.51399e28i	− 0.536502i	0.963349	−	0.268251i	$-0.0864456\pi$
$54$	1.73228e28	0.450943
$55$	0	0
$56$	1.25573e29	1.79389
$57$	− 2.37822e29i	− 2.53698i
$58$	8.69743e28i	0.696352i
$59$	3.91155e28	0.236206	0.118103	−	0.993001i	$-0.462319\pi$
$59$	3.91155e28	0.236206	0.118103	+	0.993001i	$0.462319\pi$
$60$	0	0
$61$	1.55030e29	0.540097	0.270049	−	0.962847i	$-0.412960\pi$
$61$	1.55030e29	0.540097	0.270049	+	0.962847i	$0.412960\pi$
$62$	− 3.25577e29i	− 0.867344i
$63$	− 1.21981e30i	− 2.49559i
$64$	−4.75248e29	−0.749809
$65$	0	0
$66$	1.92977e30	1.83245
$67$	− 5.34638e29i	− 0.396119i	−0.980190	−	0.198060i	$-0.936536\pi$
$67$	− 5.34638e29i	− 0.396119i	0.980190	−	0.198060i	$-0.0634640\pi$
$68$	− 2.48478e29i	− 0.144176i
$69$	−2.37908e30	−1.08492
$70$	0	0
$71$	4.86501e30	1.38459	0.692295	−	0.721615i	$-0.256600\pi$
$71$	4.86501e30	1.38459	0.692295	+	0.721615i	$0.256600\pi$
$72$	6.57061e30i	1.48463i
$73$	− 5.33567e30i	− 0.960200i	−0.877214	−	0.480100i	$-0.840600\pi$
$73$	− 5.33567e30i	− 0.960200i	0.877214	−	0.480100i	$-0.159400\pi$
$74$	3.65416e30	0.525369
$75$	0	0
$76$	9.88755e30	0.915513
$77$	− 4.13335e31i	− 3.08465i
$78$	− 2.15074e31i	− 1.29726i
$79$	−2.81314e30	−0.137513	−0.0687566	−	0.997633i	$-0.521903\pi$
$79$	−2.81314e30	−0.137513	−0.0687566	+	0.997633i	$0.521903\pi$
$80$	0	0
$81$	−1.14888e31	−0.371768
$82$	− 1.28811e31i	− 0.340428i
$83$	2.25113e31i	0.487092i	0.969889	+	0.243546i	$0.0783107\pi$
$83$	2.25113e31i	0.487092i	−0.969889	+	0.243546i	$0.921689\pi$
$84$	8.60025e31	1.52722
$85$	0	0
$86$	−2.16504e31	−0.260760
$87$	1.65301e32i	1.64516i
$88$	2.22646e32i	1.83506i
$89$	−5.60122e31	−0.383131	−0.191566	−	0.981480i	$-0.561356\pi$
$89$	−5.60122e31	−0.383131	−0.191566	+	0.981480i	$0.561356\pi$
$90$	0	0
$91$	−4.60664e32	−2.18374
$92$	− 9.89113e31i	− 0.391513i
$93$	− 6.18785e32i	− 2.04914i
$94$	−6.64360e31	−0.184414
$95$	0	0
$96$	−7.59581e32	−1.48970
$97$	− 2.05217e32i	− 0.339218i	−0.985511	−	0.169609i	$-0.945749\pi$
$97$	− 2.05217e32i	− 0.339218i	0.985511	−	0.169609i	$-0.0542505\pi$
$98$	9.54241e32i	1.33177i
$99$	2.16277e33	2.55288
$100$	0	0
$101$	5.72611e32	0.485911	0.242956	−	0.970037i	$-0.421883\pi$
$101$	5.72611e32	0.485911	0.242956	+	0.970037i	$0.421883\pi$
$102$	3.66022e32i	0.264000i
$103$	− 1.61083e33i	− 0.989087i	−0.869153	−	0.494544i	$-0.835335\pi$
$103$	− 1.61083e33i	− 0.989087i	0.869153	−	0.494544i	$-0.164665\pi$
$104$	2.48140e33	1.29911
$105$	0	0
$106$	−9.27210e32	−0.354512
$107$	− 7.00011e32i	− 0.229231i	−0.993410	−	0.114615i	$-0.963436\pi$
$107$	− 7.00011e32i	− 0.229231i	0.993410	−	0.114615i	$-0.0365635\pi$
$108$	1.36880e33i	0.384458i
$109$	−3.40209e32	−0.0820745	−0.0410372	−	0.999158i	$-0.513066\pi$
$109$	−3.40209e32	−0.0820745	−0.0410372	+	0.999158i	$0.513066\pi$
$110$	0	0
$111$	6.94502e33	1.24121
$112$	− 1.34359e33i	− 0.207094i
$113$	− 1.31038e34i	− 1.74423i	−0.489302	−	0.872115i	$-0.662748\pi$
$113$	− 1.31038e34i	− 1.74423i	0.489302	−	0.872115i	$-0.337252\pi$
$114$	−1.45649e34	−1.67640
$115$	0	0
$116$	−6.87248e33	−0.593686
$117$	− 2.41042e34i	− 1.80728i
$118$	− 2.39554e33i	− 0.156081i
$119$	7.83976e33	0.444404
$120$	0	0
$121$	5.00607e34	2.15545
$122$	− 9.49445e33i	− 0.356888i
$123$	− 2.44816e34i	− 0.804275i
$124$	2.57263e34	0.739467
$125$	0	0
$126$	−7.47047e34	−1.64905
$127$	− 4.66720e33i	− 0.0904264i	−0.998977	−	0.0452132i	$-0.985603\pi$
$127$	− 4.66720e33i	− 0.0904264i	0.998977	−	0.0452132i	$-0.0143967\pi$
$128$	− 2.69506e34i	− 0.458779i
$129$	−4.11482e34	−0.616057
$130$	0	0
$131$	1.00302e34	0.116502	0.0582512	−	0.998302i	$-0.481448\pi$
$131$	1.00302e34	0.116502	0.0582512	+	0.998302i	$0.481448\pi$
$132$	1.52486e35i	1.56228i
$133$	3.11963e35i	2.82196i
$134$	−3.27428e34	−0.261750
$135$	0	0
$136$	−4.22295e34	−0.264377
$137$	2.30007e35i	1.27600i	0.770036	+	0.638001i	$0.220238\pi$
$137$	2.30007e35i	1.27600i	−0.770036	+	0.638001i	$0.779762\pi$
$138$	1.45702e35i	0.716901i
$139$	−2.21338e35	−0.966745	−0.483372	−	0.875415i	$-0.660588\pi$
$139$	−2.21338e35	−0.966745	−0.483372	+	0.875415i	$0.660588\pi$
$140$	0	0
$141$	−1.26267e35	−0.435686
$142$	− 2.97947e35i	− 0.914917i
$143$	− 8.16774e35i	− 2.23387i
$144$	7.03030e34	0.171393
$145$	0	0
$146$	−3.26772e35	−0.634486
$147$	1.81361e36i	3.14635i
$148$	2.88742e35i	0.447912i
$149$	6.94142e35	0.963551	0.481776	−	0.876295i	$-0.339992\pi$
$149$	6.94142e35	0.963551	0.481776	+	0.876295i	$0.339992\pi$
$150$	0	0
$151$	−6.93068e35	−0.772070	−0.386035	−	0.922484i	$-0.626156\pi$
$151$	−6.93068e35	−0.772070	−0.386035	+	0.922484i	$0.626156\pi$
$152$	− 1.68041e36i	− 1.67879i
$153$	4.10215e35i	0.367792i
$154$	−2.53138e36	−2.03829
$155$	0	0
$156$	1.69946e36	1.10600
$157$	− 2.71872e36i	− 1.59229i	−0.605109	−	0.796143i	$-0.706870\pi$
$157$	− 2.71872e36i	− 1.59229i	0.605109	−	0.796143i	$-0.293130\pi$
$158$	1.72285e35i	0.0908667i
$159$	−1.76224e36	−0.837551
$160$	0	0
$161$	3.12076e36	1.20679
$162$	7.03607e35i	0.245659i
$163$	− 3.97714e36i	− 1.25451i	−0.778812	−	0.627257i	$-0.784178\pi$
$163$	− 3.97714e36i	− 1.25451i	0.778812	−	0.627257i	$-0.215822\pi$
$164$	1.01783e36	0.290237
$165$	0	0
$166$	1.37865e36	0.321863
$167$	3.59469e36i	0.760046i	0.924977	+	0.380023i	$0.124084\pi$
$167$	3.59469e36i	0.760046i	−0.924977	+	0.380023i	$0.875916\pi$
$168$	− 1.46163e37i	− 2.80050i
$169$	−3.34686e36	−0.581443
$170$	0	0
$171$	−1.63234e37	−2.33548
$172$	− 1.71076e36i	− 0.222315i
$173$	− 4.00036e36i	− 0.472431i	−0.971701	−	0.236216i	$-0.924093\pi$
$173$	− 4.00036e36i	− 0.472431i	0.971701	−	0.236216i	$-0.0759072\pi$
$174$	1.01235e37	1.08710
$175$	0	0
$176$	2.38223e36	0.211848
$177$	− 4.55292e36i	− 0.368749i
$178$	3.43035e36i	0.253168i
$179$	8.79988e36	0.592109	0.296055	−	0.955171i	$-0.404329\pi$
$179$	8.79988e36	0.592109	0.296055	+	0.955171i	$0.404329\pi$
$180$	0	0
$181$	−3.29934e37	−1.84812	−0.924061	−	0.382246i	$-0.875151\pi$
$181$	−3.29934e37	−1.84812	−0.924061	+	0.382246i	$0.875151\pi$
$182$	2.82124e37i	1.44298i
$183$	− 1.80449e37i	− 0.843165i
$184$	−1.68102e37	−0.717924
$185$	0	0
$186$	−3.78961e37	−1.35404
$187$	1.39002e37i	0.454605i
$188$	− 5.24960e36i	− 0.157225i
$189$	−4.31872e37	−1.18505
$190$	0	0
$191$	2.42443e37	0.559189	0.279595	−	0.960118i	$-0.409800\pi$
$191$	2.42443e37	0.559189	0.279595	+	0.960118i	$0.409800\pi$
$192$	5.53173e37i	1.17055i
$193$	− 5.35430e36i	− 0.103994i	−0.998647	−	0.0519969i	$-0.983441\pi$
$193$	− 5.35430e36i	− 0.103994i	0.998647	−	0.0519969i	$-0.0165586\pi$
$194$	−1.25681e37	−0.224151
$195$	0	0
$196$	−7.54016e37	−1.13542
$197$	− 5.10097e37i	− 0.706252i	−0.935576	−	0.353126i	$-0.885119\pi$
$197$	− 5.10097e37i	− 0.706252i	0.935576	−	0.353126i	$-0.114881\pi$
$198$	− 1.32454e38i	− 1.68690i
$199$	−8.02061e37	−0.940008	−0.470004	−	0.882664i	$-0.655747\pi$
$199$	−8.02061e37	−0.940008	−0.470004	+	0.882664i	$0.655747\pi$
$200$	0	0
$201$	−6.22302e37	−0.618395
$202$	− 3.50683e37i	− 0.321083i
$203$	− 2.16834e38i	− 1.82997i
$204$	−2.89221e37	−0.225077
$205$	0	0
$206$	−9.86516e37	−0.653574
$207$	1.63293e38i	0.998752i
$208$	− 2.65501e37i	− 0.149976i
$209$	−5.53122e38	−2.88674
$210$	0	0
$211$	3.04681e38	1.35889	0.679445	−	0.733726i	$-0.262220\pi$
$211$	3.04681e38	1.35889	0.679445	+	0.733726i	$0.262220\pi$
$212$	− 7.32657e37i	− 0.302245i
$213$	− 5.66272e38i	− 2.16153i
$214$	−4.28707e37	−0.151472
$215$	0	0
$216$	2.32631e38	0.704987
$217$	8.11691e38i	2.27932i
$218$	2.08353e37i	0.0542336i
$219$	−6.21055e38	−1.49900
$220$	0	0
$221$	1.54918e38	0.321833
$222$	− 4.25333e38i	− 0.820172i
$223$	4.72155e38i	0.845385i	0.906273	+	0.422692i	$0.138915\pi$
$223$	4.72155e38i	0.845385i	−0.906273	+	0.422692i	$0.861085\pi$
$224$	9.96381e38	1.65704
$225$	0	0
$226$	−8.02515e38	−1.15256
$227$	− 2.32476e38i	− 0.310421i	−0.987881	−	0.155211i	$-0.950394\pi$
$227$	− 2.32476e38i	− 0.310421i	0.987881	−	0.155211i	$-0.0496056\pi$
$228$	− 1.15088e39i	− 1.42924i
$229$	1.88914e38	0.218262	0.109131	−	0.994027i	$-0.465193\pi$
$229$	1.88914e38	0.218262	0.109131	+	0.994027i	$0.465193\pi$
$230$	0	0
$231$	−4.81109e39	−4.81555
$232$	1.16799e39i	1.08865i
$233$	− 1.00706e39i	− 0.874345i	−0.899378	−	0.437172i	$-0.855980\pi$
$233$	− 1.00706e39i	− 0.874345i	0.899378	−	0.437172i	$-0.144020\pi$
$234$	−1.47621e39	−1.19423
$235$	0	0
$236$	1.89290e38	0.133070
$237$	3.27441e38i	0.214677i
$238$	− 4.80129e38i	− 0.293656i
$239$	1.09777e39	0.626534	0.313267	−	0.949665i	$-0.398577\pi$
$239$	1.09777e39	0.626534	0.313267	+	0.949665i	$0.398577\pi$
$240$	0	0
$241$	3.35837e39	1.67050	0.835251	−	0.549869i	$-0.185322\pi$
$241$	3.35837e39	1.67050	0.835251	+	0.549869i	$0.185322\pi$
$242$	− 3.06586e39i	− 1.42429i
$243$	2.90967e39i	1.26281i
$244$	7.50226e38	0.304271
$245$	0	0
$246$	−1.49932e39	−0.531453
$247$	6.16457e39i	2.04363i
$248$	− 4.37224e39i	− 1.35597i
$249$	2.62024e39	0.760416
$250$	0	0
$251$	5.63657e39	1.43350	0.716751	−	0.697329i	$-0.245628\pi$
$251$	5.63657e39	1.43350	0.716751	+	0.697329i	$0.245628\pi$
$252$	− 5.90297e39i	− 1.40592i
$253$	5.53322e39i	1.23449i
$254$	−2.85833e38	−0.0597524
$255$	0	0
$256$	−5.73288e39	−1.05296
$257$	− 8.42092e39i	− 1.45032i	−0.688582	−	0.725159i	$-0.741766\pi$
$257$	− 8.42092e39i	− 1.45032i	0.688582	−	0.725159i	$-0.258234\pi$
$258$	2.52003e39i	0.407081i
$259$	−9.11013e39	−1.38063
$260$	0	0
$261$	1.13458e40	1.51450
$262$	− 6.14281e38i	− 0.0769831i
$263$	− 1.45121e40i	− 1.70789i	−0.520366	−	0.853943i	$-0.674205\pi$
$263$	− 1.45121e40i	− 1.70789i	0.520366	−	0.853943i	$-0.325795\pi$
$264$	2.59153e40	2.86478
$265$	0	0
$266$	1.91055e40	1.86471
$267$	6.51964e39i	0.598119i
$268$	− 2.58725e39i	− 0.223159i
$269$	−1.80369e40	−1.46302	−0.731508	−	0.681832i	$-0.761183\pi$
$269$	−1.80369e40	−1.46302	−0.731508	+	0.681832i	$0.761183\pi$
$270$	0	0
$271$	8.00345e37	0.00574492	0.00287246	−	0.999996i	$-0.499086\pi$
$271$	8.00345e37	0.00574492	0.00287246	+	0.999996i	$0.499086\pi$
$272$	4.51840e38i	0.0305209i
$273$	5.36198e40i	3.40911i
$274$	1.40863e40	0.843163
$275$	0	0
$276$	−1.15130e40	−0.611205
$277$	− 1.33035e40i	− 0.665348i	−0.943042	−	0.332674i	$-0.892049\pi$
$277$	− 1.33035e40i	− 0.665348i	0.943042	−	0.332674i	$-0.107951\pi$
$278$	1.35554e40i	0.638811i
$279$	−4.24717e40	−1.88638
$280$	0	0
$281$	3.66368e40	1.44631	0.723157	−	0.690684i	$-0.242690\pi$
$281$	3.66368e40	1.44631	0.723157	+	0.690684i	$0.242690\pi$
$282$	7.73293e39i	0.287895i
$283$	3.20197e40i	1.12445i	0.826983	+	0.562226i	$0.190055\pi$
$283$	3.20197e40i	1.12445i	−0.826983	+	0.562226i	$0.809945\pi$
$284$	2.35430e40	0.780026
$285$	0	0
$286$	−5.00216e40	−1.47611
$287$	3.21137e40i	0.894620i
$288$	5.21355e40i	1.37138i
$289$	3.76180e40	0.934505
$290$	0	0
$291$	−2.38866e40	−0.529565
$292$	− 2.58206e40i	− 0.540941i
$293$	8.52126e40i	1.68728i	0.536907	+	0.843641i	$0.319593\pi$
$293$	8.52126e40i	1.68728i	−0.536907	+	0.843641i	$0.680407\pi$
$294$	1.11071e41	2.07906
$295$	0	0
$296$	4.90724e40	0.821343
$297$	− 7.65726e40i	− 1.21225i
$298$	− 4.25112e40i	− 0.636701i
$299$	6.16680e40	0.873947
$300$	0	0
$301$	5.39762e40	0.685260
$302$	4.24455e40i	0.510172i
$303$	− 6.66500e40i	− 0.758572i
$304$	−1.79798e40	−0.193807
$305$	0	0
$306$	2.51227e40	0.243032
$307$	1.30196e41i	1.19348i	0.802434	+	0.596740i	$0.203538\pi$
$307$	1.30196e41i	1.19348i	−0.802434	+	0.596740i	$0.796462\pi$
$308$	− 2.00023e41i	− 1.73777i
$309$	−1.87495e41	−1.54410
$310$	0	0
$311$	1.69188e41	1.25263	0.626314	−	0.779571i	$-0.284563\pi$
$311$	1.69188e41	1.25263	0.626314	+	0.779571i	$0.284563\pi$
$312$	− 2.88827e41i	− 2.02809i
$313$	8.13687e40i	0.541971i	0.962583	+	0.270985i	$0.0873495\pi$
$313$	8.13687e40i	0.541971i	−0.962583	+	0.270985i	$0.912650\pi$
$314$	−1.66502e41	−1.05216
$315$	0	0
$316$	−1.36135e40	−0.0774698
$317$	− 3.44270e40i	− 0.185961i	−0.995668	−	0.0929805i	$-0.970361\pi$
$317$	− 3.44270e40i	− 0.185961i	0.995668	−	0.0929805i	$-0.0296394\pi$
$318$	1.07924e41i	0.553442i
$319$	3.84455e41	1.87197
$320$	0	0
$321$	−8.14790e40	−0.357860
$322$	− 1.91124e41i	− 0.797431i
$323$	− 1.04911e41i	− 0.415891i
$324$	−5.55972e40	−0.209440
$325$	0	0
$326$	−2.43571e41	−0.828965
$327$	3.95992e40i	0.128129i
$328$	− 1.72983e41i	− 0.532212i
$329$	1.65630e41	0.484627
$330$	0	0
$331$	1.77844e41	0.470845	0.235422	−	0.971893i	$-0.424353\pi$
$331$	1.77844e41	0.470845	0.235422	+	0.971893i	$0.424353\pi$
$332$	1.08938e41i	0.274410i
$333$	− 4.76687e41i	− 1.14262i
$334$	2.20149e41	0.502228
$335$	0	0
$336$	−1.56389e41	−0.323302
$337$	3.38563e41i	0.666417i	0.942853	+	0.333208i	$0.108131\pi$
$337$	3.38563e41i	0.666417i	−0.942853	+	0.333208i	$0.891869\pi$
$338$	2.04971e41i	0.384209i
$339$	−1.52524e42	−2.72298
$340$	0	0
$341$	−1.43916e42	−2.33164
$342$	9.99693e41i	1.54325i
$343$	− 1.19861e42i	− 1.76329i
$344$	−2.90747e41	−0.407662
$345$	0	0
$346$	−2.44994e41	−0.312176
$347$	2.23211e41i	0.271193i	0.990764	+	0.135596i	$0.0432951\pi$
$347$	2.23211e41i	0.271193i	−0.990764	+	0.135596i	$0.956705\pi$
$348$	7.99935e41i	0.926824i
$349$	−7.47321e41	−0.825824	−0.412912	−	0.910771i	$-0.635488\pi$
$349$	−7.47321e41	−0.825824	−0.412912	+	0.910771i	$0.635488\pi$
$350$	0	0
$351$	−8.53405e41	−0.858199
$352$	1.76662e42i	1.69508i
$353$	1.59110e42i	1.45685i	0.685124	+	0.728426i	$0.259748\pi$
$353$	1.59110e42i	1.45685i	−0.685124	+	0.728426i	$0.740252\pi$
$354$	−2.78834e41	−0.243664
$355$	0	0
$356$	−2.71057e41	−0.215842
$357$	− 9.12523e41i	− 0.693774i
$358$	− 5.38930e41i	− 0.391257i
$359$	1.91809e42	1.32988	0.664938	−	0.746899i	$-0.268458\pi$
$359$	1.91809e42	1.32988	0.664938	+	0.746899i	$0.268458\pi$
$360$	0	0
$361$	2.59390e42	1.64091
$362$	2.02061e42i	1.22121i
$363$	− 5.82690e42i	− 3.36495i
$364$	−2.22927e42	−1.23024
$365$	0	0
$366$	−1.10512e42	−0.557151
$367$	− 2.05163e42i	− 0.988800i	−0.869235	−	0.494400i	$-0.835388\pi$
$367$	− 2.05163e42i	− 0.988800i	0.869235	−	0.494400i	$-0.164612\pi$
$368$	1.79863e41i	0.0828805i
$369$	−1.68035e42	−0.740395
$370$	0	0
$371$	2.31161e42	0.931635
$372$	− 2.99445e42i	− 1.15441i
$373$	− 1.79481e42i	− 0.661945i	−0.943640	−	0.330972i	$-0.892623\pi$
$373$	− 1.79481e42i	− 0.661945i	0.943640	−	0.330972i	$-0.107377\pi$
$374$	8.51287e41	0.300396
$375$	0	0
$376$	−8.92181e41	−0.288306
$377$	− 4.28477e42i	− 1.32524i
$378$	2.64491e42i	0.783062i
$379$	7.45789e41	0.211382	0.105691	−	0.994399i	$-0.466294\pi$
$379$	7.45789e41	0.211382	0.105691	+	0.994399i	$0.466294\pi$
$380$	0	0
$381$	−5.43247e41	−0.141168
$382$	− 1.48479e42i	− 0.369504i
$383$	7.50246e39i	0.00178823i	1.00000		0.000894117i	$0.000284606\pi$
$383$	7.50246e39i	0.00178823i	−1.00000		0.000894117i	$0.999715\pi$
$384$	−3.13696e42	−0.716216
$385$	0	0
$386$	−3.27913e41	−0.0687176
$387$	2.82430e42i	0.567126i
$388$	− 9.93095e41i	− 0.191103i
$389$	−1.60222e41	−0.0295498	−0.0147749	−	0.999891i	$-0.504703\pi$
$389$	−1.60222e41	−0.0295498	−0.0147749	+	0.999891i	$0.504703\pi$
$390$	0	0
$391$	−1.04949e42	−0.177853
$392$	1.28147e43i	2.08203i
$393$	− 1.16749e42i	− 0.181876i
$394$	−3.12398e42	−0.466681
$395$	0	0
$396$	1.04662e43	1.43820
$397$	− 8.68103e42i	− 1.14427i	−0.820160	−	0.572134i	$-0.806116\pi$
$397$	− 8.68103e42i	− 1.14427i	0.820160	−	0.572134i	$-0.193884\pi$
$398$	4.91205e42i	0.621143i
$399$	3.63115e43	4.40546
$400$	0	0
$401$	−1.74844e43	−1.95330	−0.976650	−	0.214835i	$-0.931079\pi$
$401$	−1.74844e43	−1.95330	−0.976650	+	0.214835i	$0.931079\pi$
$402$	3.81115e42i	0.408627i
$403$	1.60395e43i	1.65066i
$404$	2.77101e42	0.273744
$405$	0	0
$406$	−1.32795e43	−1.20922
$407$	− 1.61526e43i	− 1.41233i
$408$	4.91537e42i	0.412728i
$409$	−4.63147e42	−0.373495	−0.186747	−	0.982408i	$-0.559795\pi$
$409$	−4.63147e42	−0.373495	−0.186747	+	0.982408i	$0.559795\pi$
$410$	0	0
$411$	2.67720e43	1.99201
$412$	− 7.79519e42i	− 0.557215i
$413$	5.97229e42i	0.410171i
$414$	1.00005e43	0.659961
$415$	0	0
$416$	1.96891e43	1.20001
$417$	2.57630e43i	1.50922i
$418$	3.38748e43i	1.90751i
$419$	1.92258e42	0.104077	0.0520383	−	0.998645i	$-0.483428\pi$
$419$	1.92258e42	0.104077	0.0520383	+	0.998645i	$0.483428\pi$
$420$	0	0
$421$	1.19695e43	0.598994	0.299497	−	0.954097i	$-0.403181\pi$
$421$	1.19695e43	0.598994	0.299497	+	0.954097i	$0.403181\pi$
$422$	− 1.86595e43i	− 0.897935i
$423$	8.66660e42i	0.401081i
$424$	−1.24517e43	−0.554232
$425$	0	0
$426$	−3.46801e43	−1.42831
$427$	2.36705e43i	0.937879i
$428$	− 3.38753e42i	− 0.129140i
$429$	−9.50699e43	−3.48737
$430$	0	0
$431$	3.20269e43	1.08803	0.544013	−	0.839076i	$-0.316904\pi$
$431$	3.20269e43	1.08803	0.544013	+	0.839076i	$0.316904\pi$
$432$	− 2.48907e42i	− 0.0813870i
$433$	− 3.85334e43i	− 1.21279i	−0.795162	−	0.606397i	$-0.792614\pi$
$433$	− 3.85334e43i	− 1.21279i	0.795162	−	0.606397i	$-0.207386\pi$
$434$	4.97103e43	1.50614
$435$	0	0
$436$	−1.64635e42	−0.0462377
$437$	− 4.17617e43i	− 1.12937i
$438$	3.80352e43i	0.990518i
$439$	4.54949e43	1.14103	0.570516	−	0.821287i	$-0.306743\pi$
$439$	4.54949e43	1.14103	0.570516	+	0.821287i	$0.306743\pi$
$440$	0	0
$441$	1.24481e44	2.89645
$442$	− 9.48764e42i	− 0.212662i
$443$	1.02820e43i	0.222033i	0.993819	+	0.111017i	$0.0354107\pi$
$443$	1.02820e43i	0.222033i	−0.993819	+	0.111017i	$0.964589\pi$
$444$	3.36087e43	0.699250
$445$	0	0
$446$	2.89161e43	0.558618
$447$	− 8.07959e43i	− 1.50423i
$448$	− 7.25625e43i	− 1.30204i
$449$	−5.57673e43	−0.964529	−0.482264	−	0.876026i	$-0.660186\pi$
$449$	−5.57673e43	−0.964529	−0.482264	+	0.876026i	$0.660186\pi$
$450$	0	0
$451$	−5.69388e43	−0.915156
$452$	− 6.34126e43i	− 0.982634i
$453$	8.06709e43i	1.20530i
$454$	−1.42375e43	−0.205122
$455$	0	0
$456$	−1.95595e44	−2.62082
$457$	1.36752e44i	1.76733i	0.468123	+	0.883663i	$0.344930\pi$
$457$	1.36752e44i	1.76733i	−0.468123	+	0.883663i	$0.655070\pi$
$458$	− 1.15696e43i	− 0.144224i
$459$	1.45236e43	0.174648
$460$	0	0
$461$	9.55770e43	1.06976	0.534882	−	0.844927i	$-0.320356\pi$
$461$	9.55770e43	1.06976	0.534882	+	0.844927i	$0.320356\pi$
$462$	2.94645e44i	3.18204i
$463$	− 8.83617e43i	− 0.920826i	−0.887705	−	0.460413i	$-0.847701\pi$
$463$	− 8.83617e43i	− 0.920826i	0.887705	−	0.460413i	$-0.152299\pi$
$464$	1.24971e43	0.125679
$465$	0	0
$466$	−6.16752e43	−0.577754
$467$	− 3.90426e43i	− 0.353029i	−0.984298	−	0.176514i	$-0.943518\pi$
$467$	− 3.90426e43i	− 0.353029i	0.984298	−	0.176514i	$-0.0564822\pi$
$468$	− 1.16646e44i	− 1.01816i
$469$	8.16305e43	0.687861
$470$	0	0
$471$	−3.16451e44	−2.48577
$472$	− 3.21702e43i	− 0.244012i
$473$	9.57018e43i	0.700989i
$474$	2.00534e43	0.141855
$475$	0	0
$476$	3.79386e43	0.250361
$477$	1.20955e44i	0.771028i
$478$	− 6.72303e43i	− 0.414005i
$479$	−2.78662e44	−1.65784	−0.828918	−	0.559370i	$-0.811043\pi$
$479$	−2.78662e44	−1.65784	−0.828918	+	0.559370i	$0.811043\pi$
$480$	0	0
$481$	−1.80022e44	−0.999841
$482$	− 2.05676e44i	− 1.10384i
$483$	− 3.63246e44i	− 1.88397i
$484$	2.42256e44	1.21430
$485$	0	0
$486$	1.78196e44	0.834449
$487$	− 3.84992e44i	− 1.74271i	−0.490656	−	0.871353i	$-0.663243\pi$
$487$	− 3.84992e44i	− 1.74271i	0.490656	−	0.871353i	$-0.336757\pi$
$488$	− 1.27503e44i	− 0.557946i
$489$	−4.62926e44	−1.95847
$490$	0	0
$491$	−2.78220e44	−1.10038	−0.550191	−	0.835039i	$-0.685445\pi$
$491$	−2.78220e44	−1.10038	−0.550191	+	0.835039i	$0.685445\pi$
$492$	− 1.18472e44i	− 0.453099i
$493$	7.29199e43i	0.269695i
$494$	3.77536e44	1.35040
$495$	0	0
$496$	−4.67813e43	−0.156540
$497$	7.42807e44i	2.40434i
$498$	− 1.60471e44i	− 0.502472i
$499$	−5.63211e43	−0.170613	−0.0853065	−	0.996355i	$-0.527187\pi$
$499$	−5.63211e43	−0.170613	−0.0853065	+	0.996355i	$0.527187\pi$
$500$	0	0
$501$	4.18411e44	1.18653
$502$	− 3.45199e44i	− 0.947237i
$503$	− 3.86793e44i	− 1.02709i	−0.858064	−	0.513543i	$-0.828333\pi$
$503$	− 3.86793e44i	− 1.02709i	0.858064	−	0.513543i	$-0.171667\pi$
$504$	−1.00322e45	−2.57806
$505$	0	0
$506$	3.38870e44	0.815736
$507$	3.89564e44i	0.907710i
$508$	− 2.25858e43i	− 0.0509429i
$509$	4.99727e44	1.09116	0.545582	−	0.838058i	$-0.316309\pi$
$509$	4.99727e44	1.09116	0.545582	+	0.838058i	$0.316309\pi$
$510$	0	0
$511$	8.14669e44	1.66739
$512$	1.19594e44i	0.237004i
$513$	5.77929e44i	1.10902i
$514$	−5.15721e44	−0.958349
$515$	0	0
$516$	−1.99126e44	−0.347064
$517$	2.93669e44i	0.495752i
$518$	5.57930e44i	0.912303i
$519$	−4.65629e44	−0.737529
$520$	0	0
$521$	−3.45348e44	−0.513374	−0.256687	−	0.966495i	$-0.582631\pi$
$521$	−3.45348e44	−0.513374	−0.256687	+	0.966495i	$0.582631\pi$
$522$	− 6.94851e44i	− 1.00076i
$523$	− 9.61952e44i	− 1.34238i	−0.741285	−	0.671190i	$-0.765783\pi$
$523$	− 9.61952e44i	− 1.34238i	0.741285	−	0.671190i	$-0.234217\pi$
$524$	4.85388e43	0.0656331
$525$	0	0
$526$	−8.88759e44	−1.12855
$527$	− 2.72967e44i	− 0.335919i
$528$	− 2.77284e44i	− 0.330723i
$529$	4.47237e44	0.517034
$530$	0	0
$531$	−3.12500e44	−0.339461
$532$	1.50967e45i	1.58979i
$533$	6.34585e44i	0.647875i
$534$	3.99281e44	0.395228
$535$	0	0
$536$	−4.39709e44	−0.409210
$537$	− 1.02428e45i	− 0.924362i
$538$	1.10463e45i	0.966740i
$539$	4.21806e45	3.58012
$540$	0	0
$541$	4.75196e44	0.379418	0.189709	−	0.981840i	$-0.439245\pi$
$541$	4.75196e44	0.379418	0.189709	+	0.981840i	$0.439245\pi$
$542$	− 4.90154e42i	− 0.00379616i
$543$	3.84032e45i	2.88517i
$544$	−3.35076e44	−0.244209
$545$	0	0
$546$	3.28383e45	2.25269
$547$	− 1.24806e45i	− 0.830699i	−0.909662	−	0.415350i	$-0.863659\pi$
$547$	− 1.24806e45i	− 0.830699i	0.909662	−	0.415350i	$-0.136341\pi$
$548$	1.11306e45i	0.718852i
$549$	−1.23855e45	−0.776196
$550$	0	0
$551$	−2.90166e45	−1.71256
$552$	1.95665e45i	1.12078i
$553$	− 4.29520e44i	− 0.238792i
$554$	−8.14743e44	−0.439653
$555$	0	0
$556$	−1.07111e45	−0.544628
$557$	− 1.39942e45i	− 0.690777i	−0.938460	−	0.345389i	$-0.887747\pi$
$557$	− 1.39942e45i	− 0.690777i	0.938460	−	0.345389i	$-0.112253\pi$
$558$	2.60109e45i	1.24649i
$559$	1.06660e45	0.496258
$560$	0	0
$561$	1.61794e45	0.709700
$562$	− 2.24374e45i	− 0.955703i
$563$	− 2.98083e45i	− 1.23296i	−0.787371	−	0.616479i	$-0.788559\pi$
$563$	− 2.98083e45i	− 1.23296i	0.787371	−	0.616479i	$-0.211441\pi$
$564$	−6.11036e44	−0.245449
$565$	0	0
$566$	1.96098e45	0.743022
$567$	− 1.75415e45i	− 0.645575i
$568$	− 4.00119e45i	− 1.43035i
$569$	3.72006e45	1.29181	0.645904	−	0.763419i	$-0.276481\pi$
$569$	3.72006e45	1.29181	0.645904	+	0.763419i	$0.276481\pi$
$570$	0	0
$571$	4.39952e45	1.44181	0.720907	−	0.693032i	$-0.243725\pi$
$571$	4.39952e45	1.44181	0.720907	+	0.693032i	$0.243725\pi$
$572$	− 3.95257e45i	− 1.25848i
$573$	− 2.82196e45i	− 0.872970i
$574$	1.96673e45	0.591152
$575$	0	0
$576$	3.79683e45	1.07758
$577$	3.96283e44i	0.109296i	0.998506	+	0.0546480i	$0.0174037\pi$
$577$	3.96283e44i	0.109296i	−0.998506	+	0.0546480i	$0.982596\pi$
$578$	− 2.30384e45i	− 0.617507i
$579$	−6.23224e44	−0.162348
$580$	0	0
$581$	−3.43710e45	−0.845835
$582$	1.46288e45i	0.349929i
$583$	4.09858e45i	0.953020i
$584$	−4.38828e45	−0.991932
$585$	0	0
$586$	5.21866e45	1.11493
$587$	3.03944e45i	0.631343i	0.948868	+	0.315672i	$0.102230\pi$
$587$	3.03944e45i	0.631343i	−0.948868	+	0.315672i	$0.897770\pi$
$588$	8.77651e45i	1.77254i
$589$	1.08620e46	2.13308
$590$	0	0
$591$	−5.93736e45	−1.10255
$592$	− 5.25057e44i	− 0.0948196i
$593$	1.87676e45i	0.329614i	0.986326	+	0.164807i	$0.0527001\pi$
$593$	1.87676e45i	0.329614i	−0.986326	+	0.164807i	$0.947300\pi$
$594$	−4.68952e45	−0.801037
$595$	0	0
$596$	3.35913e45	0.542829
$597$	9.33573e45i	1.46748i
$598$	− 3.77672e45i	− 0.577491i
$599$	−1.10721e46	−1.64698	−0.823490	−	0.567330i	$-0.807976\pi$
$599$	−1.10721e46	−1.64698	−0.823490	+	0.567330i	$0.807976\pi$
$600$	0	0
$601$	−9.12305e45	−1.28443	−0.642216	−	0.766524i	$-0.721985\pi$
$601$	−9.12305e45	−1.28443	−0.642216	+	0.766524i	$0.721985\pi$
$602$	− 3.30566e45i	− 0.452809i
$603$	4.27131e45i	0.569279i
$604$	−3.35393e45	−0.434955
$605$	0	0
$606$	−4.08184e45	−0.501254
$607$	5.35422e45i	0.639857i	0.947442	+	0.319928i	$0.103659\pi$
$607$	5.35422e45i	0.639857i	−0.947442	+	0.319928i	$0.896341\pi$
$608$	− 1.33335e46i	− 1.55073i
$609$	−2.52388e46	−2.85682
$610$	0	0
$611$	3.27296e45	0.350962
$612$	1.98513e45i	0.207200i
$613$	− 1.25482e44i	− 0.0127492i	−0.999980	−	0.00637459i	$-0.997971\pi$
$613$	− 1.25482e44i	− 0.0127492i	0.999980	−	0.00637459i	$-0.00202911\pi$
$614$	7.97359e45	0.788635
$615$	0	0
$616$	−3.39944e46	−3.18658
$617$	− 8.06814e45i	− 0.736323i	−0.929762	−	0.368162i	$-0.879987\pi$
$617$	− 8.06814e45i	− 0.736323i	0.929762	−	0.368162i	$-0.120013\pi$
$618$	1.14827e46i	1.02032i
$619$	2.05474e46	1.77771	0.888856	−	0.458186i	$-0.151501\pi$
$619$	2.05474e46	1.77771	0.888856	+	0.458186i	$0.151501\pi$
$620$	0	0
$621$	5.78137e45	0.474263
$622$	− 1.03615e46i	− 0.827718i
$623$	− 8.55214e45i	− 0.665307i
$624$	−3.09034e45	−0.234132
$625$	0	0
$626$	4.98325e45	0.358126
$627$	6.43816e46i	4.50658i
$628$	− 1.31566e46i	− 0.897034i
$629$	3.06368e45	0.203473
$630$	0	0
$631$	1.16488e45	0.0734170	0.0367085	−	0.999326i	$-0.488313\pi$
$631$	1.16488e45	0.0734170	0.0367085	+	0.999326i	$0.488313\pi$
$632$	2.31364e45i	0.142058i
$633$	− 3.54639e46i	− 2.12141i
$634$	−2.10841e45	−0.122880
$635$	0	0
$636$	−8.52790e45	−0.471845
$637$	− 4.70105e46i	− 2.53451i
$638$	− 2.35451e46i	− 1.23697i
$639$	−3.88673e46	−1.98985
$640$	0	0
$641$	−9.00359e45	−0.437783	−0.218891	−	0.975749i	$-0.570244\pi$
$641$	−9.00359e45	−0.437783	−0.218891	+	0.975749i	$0.570244\pi$
$642$	4.99001e45i	0.236468i
$643$	3.03445e46i	1.40152i	0.713398	+	0.700759i	$0.247155\pi$
$643$	3.03445e46i	1.40152i	−0.713398	+	0.700759i	$0.752845\pi$
$644$	1.51021e46	0.679862
$645$	0	0
$646$	−6.42506e45	−0.274815
$647$	− 3.19654e46i	− 1.33278i	−0.745602	−	0.666392i	$-0.767838\pi$
$647$	− 3.19654e46i	− 1.33278i	0.745602	−	0.666392i	$-0.232162\pi$
$648$	9.44887e45i	0.384054i
$649$	−1.05891e46	−0.419587
$650$	0	0
$651$	9.44783e46	3.55832
$652$	− 1.92464e46i	− 0.706747i
$653$	− 2.96852e46i	− 1.06285i	−0.847105	−	0.531426i	$-0.821656\pi$
$653$	− 2.96852e46i	− 1.06285i	0.847105	−	0.531426i	$-0.178344\pi$
$654$	2.42517e45	0.0846659
$655$	0	0
$656$	−1.85085e45	−0.0614410
$657$	4.26275e46i	1.37994i
$658$	− 1.01437e46i	− 0.320235i
$659$	−7.90933e45	−0.243518	−0.121759	−	0.992560i	$-0.538853\pi$
$659$	−7.90933e45	−0.243518	−0.121759	+	0.992560i	$0.538853\pi$
$660$	0	0
$661$	−5.80040e45	−0.169877	−0.0849384	−	0.996386i	$-0.527069\pi$
$661$	−5.80040e45	−0.169877	−0.0849384	+	0.996386i	$0.527069\pi$
$662$	− 1.08917e46i	− 0.311127i
$663$	− 1.80320e46i	− 0.502424i
$664$	1.85142e46	0.503189
$665$	0	0
$666$	−2.91937e46	−0.755029
$667$	2.90271e46i	0.732364i
$668$	1.73956e46i	0.428182i
$669$	5.49573e46	1.31976
$670$	0	0
$671$	−4.19686e46	−0.959407
$672$	− 1.15976e47i	− 2.58686i
$673$	− 4.73930e46i	− 1.03149i	−0.856742	−	0.515745i	$-0.827515\pi$
$673$	− 4.73930e46i	− 1.03149i	0.856742	−	0.515745i	$-0.172485\pi$
$674$	2.07346e46	0.440359
$675$	0	0
$676$	−1.61963e46	−0.327563
$677$	3.10009e46i	0.611874i	0.952052	+	0.305937i	$0.0989697\pi$
$677$	3.10009e46i	0.611874i	−0.952052	+	0.305937i	$0.901030\pi$
$678$	9.34102e46i	1.79930i
$679$	3.13332e46	0.589052
$680$	0	0
$681$	−2.70594e46	−0.484609
$682$	8.81382e46i	1.54071i
$683$	− 1.45608e46i	− 0.248453i	−0.992254	−	0.124227i	$-0.960355\pi$
$683$	− 1.45608e46i	− 0.248453i	0.992254	−	0.124227i	$-0.0396450\pi$
$684$	−7.89931e46	−1.31572
$685$	0	0
$686$	−7.34061e46	−1.16516
$687$	− 2.19889e46i	− 0.340736i
$688$	3.11088e45i	0.0470624i
$689$	4.56788e46	0.674680
$690$	0	0
$691$	2.89366e46	0.407436	0.203718	−	0.979030i	$-0.434697\pi$
$691$	2.89366e46	0.407436	0.203718	+	0.979030i	$0.434697\pi$
$692$	− 1.93588e46i	− 0.266150i
$693$	3.30220e47i	4.43307i
$694$	1.36700e46	0.179200
$695$	0	0
$696$	1.35951e47	1.69953
$697$	− 1.07996e46i	− 0.131846i
$698$	4.57681e46i	0.545693i
$699$	−1.17219e47	−1.36497
$700$	0	0
$701$	7.65232e46	0.850052	0.425026	−	0.905181i	$-0.360265\pi$
$701$	7.65232e46	0.850052	0.425026	+	0.905181i	$0.360265\pi$
$702$	5.22650e46i	0.567085i
$703$	1.21911e47i	1.29205i
$704$	1.28656e47	1.33193
$705$	0	0
$706$	9.74437e46	0.962667
$707$	8.74282e46i	0.843784i
$708$	− 2.20327e46i	− 0.207740i
$709$	1.52586e47	1.40557	0.702784	−	0.711403i	$-0.251940\pi$
$709$	1.52586e47	1.40557	0.702784	+	0.711403i	$0.251940\pi$
$710$	0	0
$711$	2.24746e46	0.197626
$712$	4.60668e46i	0.395793i
$713$	− 1.08659e47i	− 0.912198i
$714$	−5.58855e46	−0.458436
$715$	0	0
$716$	4.25848e46	0.333572
$717$	− 1.27777e47i	− 0.978104i
$718$	− 1.17469e47i	− 0.878762i
$719$	−6.69791e46	−0.489680	−0.244840	−	0.969563i	$-0.578735\pi$
$719$	−6.69791e46	−0.489680	−0.244840	+	0.969563i	$0.578735\pi$
$720$	0	0
$721$	2.45947e47	1.71755
$722$	− 1.58858e47i	− 1.08429i
$723$	− 3.90903e47i	− 2.60788i
$724$	−1.59663e47	−1.04116
$725$	0	0
$726$	−3.56856e47	−2.22351
$727$	− 9.79650e46i	− 0.596696i	−0.954457	−	0.298348i	$-0.903564\pi$
$727$	− 9.79650e46i	− 0.596696i	0.954457	−	0.298348i	$-0.0964356\pi$
$728$	3.78869e47i	2.25591i
$729$	2.74809e47	1.59966
$730$	0	0
$731$	−1.81518e46	−0.100991
$732$	− 8.73239e46i	− 0.475008i
$733$	− 6.92215e45i	− 0.0368150i	−0.999831	−	0.0184075i	$-0.994140\pi$
$733$	− 6.92215e45i	− 0.0368150i	0.999831	−	0.0184075i	$-0.00585962\pi$
$734$	−1.25647e47	−0.653384
$735$	0	0
$736$	−1.33383e47	−0.663158
$737$	1.44734e47i	0.703650i
$738$	1.02909e47i	0.489242i
$739$	1.98349e47	0.922140	0.461070	−	0.887364i	$-0.347466\pi$
$739$	1.98349e47	0.922140	0.461070	+	0.887364i	$0.347466\pi$
$740$	0	0
$741$	7.17536e47	3.19039
$742$	− 1.41570e47i	− 0.615611i
$743$	− 8.20980e45i	− 0.0349154i	−0.999848	−	0.0174577i	$-0.994443\pi$
$743$	− 8.20980e45i	− 0.0349154i	0.999848	−	0.0174577i	$-0.00555724\pi$
$744$	−5.08914e47	−2.11686
$745$	0	0
$746$	−1.09919e47	−0.437403
$747$	− 1.79846e47i	− 0.700020i
$748$	6.72665e46i	0.256108i
$749$	1.06880e47	0.398059
$750$	0	0
$751$	−3.70104e47	−1.31906	−0.659531	−	0.751677i	$-0.729245\pi$
$751$	−3.70104e47	−1.31906	−0.659531	+	0.751677i	$0.729245\pi$
$752$	9.54600e45i	0.0332834i
$753$	− 6.56078e47i	− 2.23789i
$754$	−2.62412e47	−0.875701
$755$	0	0
$756$	−2.08994e47	−0.667611
$757$	4.25190e47i	1.32893i	0.747321	+	0.664463i	$0.231340\pi$
$757$	4.25190e47i	1.32893i	−0.747321	+	0.664463i	$0.768660\pi$
$758$	− 4.56742e46i	− 0.139678i
$759$	6.44049e47	1.92721
$760$	0	0
$761$	−8.75693e46	−0.250903	−0.125451	−	0.992100i	$-0.540038\pi$
$761$	−8.75693e46	−0.250903	−0.125451	+	0.992100i	$0.540038\pi$
$762$	3.32700e46i	0.0932816i
$763$	− 5.19443e46i	− 0.142522i
$764$	1.17324e47	0.315027
$765$	0	0
$766$	4.59472e44	0.00118164
$767$	1.18016e47i	0.297042i
$768$	6.67289e47i	1.64382i
$769$	−2.32456e47	−0.560475	−0.280237	−	0.959931i	$-0.590413\pi$
$769$	−2.32456e47	−0.560475	−0.280237	+	0.959931i	$0.590413\pi$
$770$	0	0
$771$	−9.80168e47	−2.26414
$772$	− 2.59108e46i	− 0.0585862i
$773$	− 8.67662e47i	− 1.92039i	−0.279333	−	0.960194i	$-0.590113\pi$
$773$	− 8.67662e47i	− 1.92039i	0.279333	−	0.960194i	$-0.409887\pi$
$774$	1.72968e47	0.374749
$775$	0	0
$776$	−1.68779e47	−0.350429
$777$	1.06039e48i	2.15536i
$778$	9.81246e45i	0.0195261i
$779$	4.29743e47	0.837222
$780$	0	0
$781$	−1.31703e48	−2.45953
$782$	6.42738e46i	0.117523i
$783$	− 4.01697e47i	− 0.719167i
$784$	1.37112e47	0.240359
$785$	0	0
$786$	−7.15003e46	−0.120181
$787$	1.53515e47i	0.252678i	0.991987	+	0.126339i	$0.0403228\pi$
$787$	1.53515e47i	0.252678i	−0.991987	+	0.126339i	$0.959677\pi$
$788$	− 2.46848e47i	− 0.397876i
$789$	−1.68916e48	−2.66624
$790$	0	0
$791$	2.00074e48	3.02885
$792$	− 1.77875e48i	− 2.63724i
$793$	4.67742e47i	0.679202i
$794$	−5.31651e47	−0.756116
$795$	0	0
$796$	−3.88137e47	−0.529565
$797$	1.58622e47i	0.211983i	0.994367	+	0.105991i	$0.0338016\pi$
$797$	1.58622e47i	0.211983i	−0.994367	+	0.105991i	$0.966198\pi$
$798$	− 2.22382e48i	− 2.91106i
$799$	−5.57004e46	−0.0714228
$800$	0	0
$801$	4.47490e47	0.550613
$802$	1.07080e48i	1.29071i
$803$	1.44444e48i	1.70566i
$804$	−3.01147e47	−0.348381
$805$	0	0
$806$	9.82304e47	1.09073
$807$	2.09944e48i	2.28397i
$808$	− 4.70939e47i	− 0.501969i
$809$	−1.81233e48	−1.89272	−0.946359	−	0.323116i	$-0.895269\pi$
$809$	−1.81233e48	−1.89272	−0.946359	+	0.323116i	$0.895269\pi$
$810$	0	0
$811$	−2.40110e47	−0.240750	−0.120375	−	0.992728i	$-0.538410\pi$
$811$	−2.40110e47	−0.240750	−0.120375	+	0.992728i	$0.538410\pi$
$812$	− 1.04931e48i	− 1.03094i
$813$	− 9.31576e45i	− 0.00896859i
$814$	−9.89232e47	−0.933244
$815$	0	0
$816$	5.25927e46	0.0476472
$817$	− 7.22306e47i	− 0.641294i
$818$	2.83645e47i	0.246800i
$819$	3.68031e48	3.13834
$820$	0	0
$821$	1.95200e48	1.59889	0.799444	−	0.600741i	$-0.205128\pi$
$821$	1.95200e48	1.59889	0.799444	+	0.600741i	$0.205128\pi$
$822$	− 1.63960e48i	− 1.31629i
$823$	1.52141e48i	1.19715i	0.801068	+	0.598574i	$0.204266\pi$
$823$	1.52141e48i	1.19715i	−0.801068	+	0.598574i	$0.795734\pi$
$824$	−1.32481e48	−1.02177
$825$	0	0
$826$	3.65760e47	0.271035
$827$	− 1.82790e48i	− 1.32774i	−0.747849	−	0.663869i	$-0.768913\pi$
$827$	− 1.82790e48i	− 1.32774i	0.747849	−	0.663869i	$-0.231087\pi$
$828$	7.90217e47i	0.562660i
$829$	7.69592e47	0.537169	0.268585	−	0.963256i	$-0.413444\pi$
$829$	7.69592e47	0.537169	0.268585	+	0.963256i	$0.413444\pi$
$830$	0	0
$831$	−1.54848e48	−1.03870
$832$	− 1.43388e48i	− 0.942925i
$833$	8.00043e47i	0.515788i
$834$	1.57780e48	0.997270
$835$	0	0
$836$	−2.67670e48	−1.62628
$837$	1.50370e48i	0.895761i
$838$	− 1.17744e47i	− 0.0687722i
$839$	−2.04370e48	−1.17043	−0.585215	−	0.810878i	$-0.698990\pi$
$839$	−2.04370e48	−1.17043	−0.585215	+	0.810878i	$0.698990\pi$
$840$	0	0
$841$	2.00764e47	0.110548
$842$	− 7.33048e47i	− 0.395806i
$843$	− 4.26440e48i	− 2.25789i
$844$	1.47443e48	0.765549
$845$	0	0
$846$	5.30767e47	0.265029
$847$	7.64344e48i	3.74294i
$848$	1.33228e47i	0.0639831i
$849$	3.72699e48	1.75542
$850$	0	0
$851$	1.21955e48	0.552539
$852$	− 2.74033e48i	− 1.21773i
$853$	2.79059e48i	1.21629i	0.793826	+	0.608145i	$0.208086\pi$
$853$	2.79059e48i	1.21629i	−0.793826	+	0.608145i	$0.791914\pi$
$854$	1.44965e48	0.619736
$855$	0	0
$856$	−5.75718e47	−0.236806
$857$	2.78683e48i	1.12441i	0.826997	+	0.562207i	$0.190048\pi$
$857$	2.78683e48i	1.12441i	−0.826997	+	0.562207i	$0.809952\pi$
$858$	5.82235e48i	2.30440i
$859$	−1.23473e48	−0.479384	−0.239692	−	0.970849i	$-0.577047\pi$
$859$	−1.23473e48	−0.479384	−0.239692	+	0.970849i	$0.577047\pi$
$860$	0	0
$861$	3.73793e48	1.39662
$862$	− 1.96142e48i	− 0.718952i
$863$	1.65114e48i	0.593755i	0.954916	+	0.296877i	$0.0959452\pi$
$863$	1.65114e48i	0.593755i	−0.954916	+	0.296877i	$0.904055\pi$
$864$	1.84585e48	0.651208
$865$	0	0
$866$	−2.35989e48	−0.801396
$867$	− 4.37862e48i	− 1.45889i
$868$	3.92798e48i	1.28408i
$869$	7.61556e47	0.244273
$870$	0	0
$871$	1.61307e48	0.498141
$872$	2.79802e47i	0.0847868i
$873$	1.63951e48i	0.487504i
$874$	−2.55761e48	−0.746269
$875$	0	0
$876$	−3.00544e48	−0.844481
$877$	− 1.37890e48i	− 0.380223i	−0.981763	−	0.190111i	$-0.939115\pi$
$877$	− 1.37890e48i	− 0.380223i	0.981763	−	0.190111i	$-0.0608849\pi$
$878$	− 2.78623e48i	− 0.753977i
$879$	9.91847e48	2.63408
$880$	0	0
$881$	−5.43818e46	−0.0139108	−0.00695538	−	0.999976i	$-0.502214\pi$
$881$	−5.43818e46	−0.0139108	−0.00695538	+	0.999976i	$0.502214\pi$
$882$	− 7.62357e48i	− 1.91393i
$883$	5.86213e47i	0.144445i	0.997389	+	0.0722227i	$0.0230092\pi$
$883$	5.86213e47i	0.144445i	−0.997389	+	0.0722227i	$0.976991\pi$
$884$	7.49688e47	0.181309
$885$	0	0
$886$	6.29701e47	0.146716
$887$	1.66488e48i	0.380753i	0.981711	+	0.190377i	$0.0609709\pi$
$887$	1.66488e48i	0.380753i	−0.981711	+	0.190377i	$0.939029\pi$
$888$	− 5.71187e48i	− 1.28223i
$889$	7.12605e47	0.157025
$890$	0	0
$891$	3.11017e48	0.660393
$892$	2.28488e48i	0.476258i
$893$	− 2.21645e48i	− 0.453534i
$894$	−4.94817e48	−0.993975
$895$	0	0
$896$	4.11491e48	0.796670
$897$	− 7.17796e48i	− 1.36435i
$898$	3.41535e48i	0.637346i
$899$	−7.54978e48	−1.38325
$900$	0	0
$901$	−7.77380e47	−0.137301
$902$	3.48709e48i	0.604722i
$903$	− 6.28266e48i	− 1.06978i
$904$	−1.07771e49	−1.80187
$905$	0	0
$906$	4.94052e48	0.796447
$907$	8.00665e48i	1.26745i	0.773559	+	0.633724i	$0.218475\pi$
$907$	8.00665e48i	1.26745i	−0.773559	+	0.633724i	$0.781525\pi$
$908$	− 1.12501e48i	− 0.174880i
$909$	−4.57467e48	−0.698322
$910$	0	0
$911$	1.44015e48	0.212009	0.106004	−	0.994366i	$-0.466194\pi$
$911$	1.44015e48	0.212009	0.106004	+	0.994366i	$0.466194\pi$
$912$	2.09279e48i	0.302559i
$913$	− 6.09410e48i	− 0.865251i
$914$	8.37509e48	1.16782
$915$	0	0
$916$	9.14200e47	0.122961
$917$	1.53145e48i	0.202306i
$918$	− 8.89466e47i	− 0.115405i
$919$	2.47134e48	0.314939	0.157469	−	0.987524i	$-0.449666\pi$
$919$	2.47134e48	0.314939	0.157469	+	0.987524i	$0.449666\pi$
$920$	0	0
$921$	1.51544e49	1.86318
$922$	− 5.85341e48i	− 0.706885i
$923$	1.46783e49i	1.74120i
$924$	−2.32820e49	−2.71290
$925$	0	0
$926$	−5.41152e48	−0.608468
$927$	1.28691e49i	1.42146i
$928$	9.26763e48i	1.00560i
$929$	9.81639e48	1.04639	0.523194	−	0.852214i	$-0.324740\pi$
$929$	9.81639e48	1.04639	0.523194	+	0.852214i	$0.324740\pi$
$930$	0	0
$931$	−3.18356e49	−3.27525
$932$	− 4.87342e48i	− 0.492573i
$933$	− 1.96929e49i	− 1.95552i
$934$	−2.39108e48	−0.233276
$935$	0	0
$936$	−1.98243e49	−1.86701
$937$	4.76155e48i	0.440601i	0.975432	+	0.220300i	$0.0707038\pi$
$937$	4.76155e48i	0.440601i	−0.975432	+	0.220300i	$0.929296\pi$
$938$	− 4.99928e48i	− 0.454528i
$939$	9.47106e48	0.846089
$940$	0	0
$941$	−7.34573e48	−0.633587	−0.316793	−	0.948495i	$-0.602606\pi$
$941$	−7.34573e48	−0.633587	−0.316793	+	0.948495i	$0.602606\pi$
$942$	1.93803e49i	1.64256i
$943$	− 4.29898e48i	− 0.358033i
$944$	−3.44209e47	−0.0281699
$945$	0	0
$946$	5.86105e48	0.463203
$947$	1.77230e49i	1.37646i	0.725493	+	0.688229i	$0.241612\pi$
$947$	1.77230e49i	1.37646i	−0.725493	+	0.688229i	$0.758388\pi$
$948$	1.58457e48i	0.120941i
$949$	1.60983e49	1.20750
$950$	0	0
$951$	−4.00720e48	−0.290310
$952$	− 6.44774e48i	− 0.459090i
$953$	− 1.70424e49i	− 1.19261i	−0.802757	−	0.596306i	$-0.796635\pi$
$953$	− 1.70424e49i	− 1.19261i	0.802757	−	0.596306i	$-0.203365\pi$
$954$	7.40762e48	0.509484
$955$	0	0
$956$	5.31237e48	0.352966
$957$	− 4.47493e49i	− 2.92240i
$958$	1.70660e49i	1.09547i
$959$	−3.51182e49	−2.21578
$960$	0	0
$961$	1.18582e49	0.722906
$962$	1.10250e49i	0.660680i
$963$	5.59249e48i	0.329436i
$964$	1.62520e49	0.941099
$965$	0	0
$966$	−2.22462e49	−1.24490
$967$	5.35097e48i	0.294371i	0.989109	+	0.147186i	$0.0470215\pi$
$967$	5.35097e48i	0.294371i	−0.989109	+	0.147186i	$0.952979\pi$
$968$	− 4.11720e49i	− 2.22668i
$969$	−1.22113e49	−0.649262
$970$	0	0
$971$	−4.10947e48	−0.211187	−0.105594	−	0.994409i	$-0.533674\pi$
$971$	−4.10947e48	−0.211187	−0.105594	+	0.994409i	$0.533674\pi$
$972$	1.40806e49i	0.711423i
$973$	− 3.37947e49i	− 1.67875i
$974$	−2.35780e49	−1.15155
$975$	0	0
$976$	−1.36423e48	−0.0644119
$977$	− 1.88993e49i	− 0.877376i	−0.898639	−	0.438688i	$-0.855443\pi$
$977$	− 1.88993e49i	− 0.877376i	0.898639	−	0.438688i	$-0.144557\pi$
$978$	2.83509e49i	1.29413i
$979$	1.51633e49	0.680579
$980$	0	0
$981$	2.71798e48	0.117953
$982$	1.70390e49i	0.727117i
$983$	− 4.64069e48i	− 0.194737i	−0.995248	−	0.0973687i	$-0.968957\pi$
$983$	− 4.64069e48i	− 0.194737i	0.995248	−	0.0973687i	$-0.0310426\pi$
$984$	−2.01346e49	−0.830854
$985$	0	0
$986$	4.46582e48	0.178210
$987$	− 1.92789e49i	− 0.756568i
$988$	2.98319e49i	1.15131i
$989$	−7.22567e48	−0.274245
$990$	0	0
$991$	−1.20728e49	−0.443193	−0.221596	−	0.975138i	$-0.571127\pi$
$991$	−1.20728e49	−0.443193	−0.221596	+	0.975138i	$0.571127\pi$
$992$	− 3.46922e49i	− 1.25253i
$993$	− 2.07005e49i	− 0.735052i
$994$	4.54916e49	1.58875
$995$	0	0
$996$	1.26800e49	0.428390
$997$	2.20246e47i	0.00731876i	0.999993	+	0.00365938i	$0.00116482\pi$
$997$	2.20246e47i	0.00731876i	−0.999993	+	0.00365938i	$0.998835\pi$
$998$	3.44926e48i	0.112739i
$999$	−1.68770e49	−0.542582

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.b.d.24.8		22
5.2	odd	4		25.34.a.d.1.8	✓	11
5.3	odd	4		25.34.a.e.1.4	yes	11
5.4	even	2	inner	25.34.b.d.24.15		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.34.a.d.1.8	✓	11	5.2	odd	4
25.34.a.e.1.4	yes	11	5.3	odd	4
25.34.b.d.24.8		22	1.1	even	1	trivial
25.34.b.d.24.15		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)

\(f(q)\)	\(=\)	\(q-61242.8i q^{2} -1.16397e8i q^{3} +4.83925e9 q^{4} -7.12847e12 q^{6} +1.52684e14i q^{7} -8.22441e14i q^{8} -7.98915e15 q^{9} +O(q^{10})\)	\(q-61242.8i q^{2} -1.16397e8i q^{3} +4.83925e9 q^{4} -7.12847e12 q^{6} +1.52684e14i q^{7} -8.22441e14i q^{8} -7.98915e15 q^{9} -2.70714e17 q^{11} -5.63273e17i q^{12} +3.01712e18i q^{13} +9.35077e18 q^{14} -8.79981e18 q^{16} -5.13465e19i q^{17} +4.89278e20i q^{18} +2.04320e21 q^{19} +1.77719e22 q^{21} +1.65793e22i q^{22} -2.04394e22i q^{23} -9.57295e22 q^{24} +1.84777e23 q^{26} +2.82855e23i q^{27} +7.38874e23i q^{28} -1.42015e24 q^{29} +5.31617e24 q^{31} -6.52579e24i q^{32} +3.15102e25i q^{33} -3.14460e24 q^{34} -3.86615e25 q^{36} +5.96668e25i q^{37} -1.25131e26i q^{38} +3.51183e26 q^{39} +2.10328e26 q^{41} -1.08840e27i q^{42} -3.53517e26i q^{43} -1.31005e27 q^{44} -1.25177e27 q^{46} -1.08480e27i q^{47} +1.02427e27i q^{48} -1.55813e28 q^{49} -5.97656e27 q^{51} +1.46006e28i q^{52} -1.51399e28i q^{53} +1.73228e28 q^{54} +1.25573e29 q^{56} -2.37822e29i q^{57} +8.69743e28i q^{58} +3.91155e28 q^{59} +1.55030e29 q^{61} -3.25577e29i q^{62} -1.21981e30i q^{63} -4.75248e29 q^{64} +1.92977e30 q^{66} -5.34638e29i q^{67} -2.48478e29i q^{68} -2.37908e30 q^{69} +4.86501e30 q^{71} +6.57061e30i q^{72} -5.33567e30i q^{73} +3.65416e30 q^{74} +9.88755e30 q^{76} -4.13335e31i q^{77} -2.15074e31i q^{78} -2.81314e30 q^{79} -1.14888e31 q^{81} -1.28811e31i q^{82} +2.25113e31i q^{83} +8.60025e31 q^{84} -2.16504e31 q^{86} +1.65301e32i q^{87} +2.22646e32i q^{88} -5.60122e31 q^{89} -4.60664e32 q^{91} -9.89113e31i q^{92} -6.18785e32i q^{93} -6.64360e31 q^{94} -7.59581e32 q^{96} -2.05217e32i q^{97} +9.54241e32i q^{98} +2.16277e33 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 98676413354 q^{4} - 35567955353446 q^{6} - 48\!\cdots\!16 q^{9}+O(q^{10}) \) 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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