LMFDB - Embedded newform 23.25.b.c.22.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [23,25,Mod(22,23)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(23, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 25, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("23.22"); S:= CuspForms(chi, 25); N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 25 $
Character orbit:	$[\chi]$	$=$	23.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [44] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$83.9424450193$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			22.14
Character	$\chi$	$=$	23.22
Dual form			23.25.b.c.22.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-4410.99 q^{2} -600091. q^{3} +2.67964e6 q^{4} +2.08680e8i q^{5} +2.64700e9 q^{6} +9.90757e8i q^{7} +6.21843e10 q^{8} +7.76795e10 q^{9} -9.20488e11i q^{10} -3.04648e12i q^{11} -1.60803e12 q^{12} -2.90487e13 q^{13} -4.37022e12i q^{14} -1.25227e14i q^{15} -3.19251e14 q^{16} +7.59542e14i q^{17} -3.42644e14 q^{18} -3.40778e15i q^{19} +5.59189e14i q^{20} -5.94544e14i q^{21} +1.34380e16i q^{22} +(-1.35383e16 + 1.72327e16i) q^{23} -3.73162e16 q^{24} +1.60571e16 q^{25} +1.28133e17 q^{26} +1.22869e17 q^{27} +2.65487e15i q^{28} -1.97404e17 q^{29} +5.52376e17i q^{30} +1.05721e18 q^{31} +3.64936e17 q^{32} +1.82817e18i q^{33} -3.35033e18i q^{34} -2.06752e17 q^{35} +2.08153e17 q^{36} +5.88277e18i q^{37} +1.50317e19i q^{38} +1.74318e19 q^{39} +1.29766e19i q^{40} +1.01351e19 q^{41} +2.62253e18i q^{42} +5.06956e19i q^{43} -8.16349e18i q^{44} +1.62102e19i q^{45} +(5.97173e19 - 7.60132e19i) q^{46} -2.15998e20 q^{47} +1.91580e20 q^{48} +1.90600e20 q^{49} -7.08279e19 q^{50} -4.55794e20i q^{51} -7.78400e19 q^{52} +6.98504e20i q^{53} -5.41973e20 q^{54} +6.35742e20 q^{55} +6.16095e19i q^{56} +2.04498e21i q^{57} +8.70748e20 q^{58} +1.97235e21 q^{59} -3.35564e20i q^{60} +2.54538e21i q^{61} -4.66336e21 q^{62} +7.69615e19i q^{63} +3.74642e21 q^{64} -6.06189e21i q^{65} -8.06403e21i q^{66} +1.45735e22i q^{67} +2.03530e21i q^{68} +(8.12421e21 - 1.03412e22i) q^{69} +9.11979e20 q^{70} -8.48225e21 q^{71} +4.83044e21 q^{72} -2.09881e22 q^{73} -2.59489e22i q^{74} -9.63574e21 q^{75} -9.13163e21i q^{76} +3.01833e21 q^{77} -7.68917e22 q^{78} -6.62640e22i q^{79} -6.66215e22i q^{80} -9.56713e22 q^{81} -4.47057e22 q^{82} -1.10895e23i q^{83} -1.59317e21i q^{84} -1.58501e23 q^{85} -2.23618e23i q^{86} +1.18460e23 q^{87} -1.89444e23i q^{88} +3.42705e23i q^{89} -7.15030e22i q^{90} -2.87802e22i q^{91} +(-3.62778e22 + 4.61774e22i) q^{92} -6.34424e23 q^{93} +9.52767e23 q^{94} +7.11137e23 q^{95} -2.18995e23 q^{96} +2.21681e23i q^{97} -8.40734e23 q^{98} -2.36649e23i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 4232 q^{2} - 434562 q^{3} + 317760360 q^{4} - 8460029520 q^{6} - 198307023760 q^{8} + 4220041988298 q^{9} - 67439597688792 q^{12} + 5771152551358 q^{13} + 18\!\cdots\!92 q^{16} + 18\!\cdots\!68 q^{18}+ \cdots - 20\!\cdots\!92 q^{98}+O(q^{100}) $ 44 * q - 4232 * q^2 - 434562 * q^3 + 317760360 * q^4 - 8460029520 * q^6 - 198307023760 * q^8 + 4220041988298 * q^9 - 67439597688792 * q^12 + 5771152551358 * q^13 + 1801550792530192 * q^16 + 1842830558165568 * q^18 - 117204213263210644 * q^23 - 186493005437450784 * q^24 - 689533084157602612 * q^25 - 548650296251047576 * q^26 + 824037505793640630 * q^27 - 1583078054945709602 * q^29 - 77249813729122274 * q^31 - 2838716832733708512 * q^32 + 3418569899175948192 * q^35 + 71181245116739335248 * q^36 + 47106572467817156310 * q^39 - 9150679195666184738 * q^41 - 153049487518536134480 * q^46 + 22735751396127769438 * q^47 - 1317482931964495330032 * q^48 - 1842110772006482246836 * q^49 + 284936617115007894520 * q^50 + 207129175371045152568 * q^52 - 381774025126375304544 * q^54 - 5430040696094013021792 * q^55 - 2168901871328366220760 * q^58 + 16048018791948427185304 * q^59 + 14054450375064171442400 * q^62 + 20310379126091866412192 * q^64 + 24476879859710435470878 * q^69 - 118028399895318845638416 * q^70 - 68204988047209908888578 * q^71 - 106777935582637627887744 * q^72 - 7319375899831086678722 * q^73 + 12913295383070041819998 * q^75 + 111116199573084838704480 * q^77 - 422583593213386075404144 * q^78 - 331350288185757013618680 * q^81 + 1000764218021118649437320 * q^82 - 113385735487939722862944 * q^85 - 248828610584854760185290 * q^87 - 4238455111972177116774696 * q^92 + 4492289396741153284965270 * q^93 - 1602622056539190351258592 * q^94 - 1668692394291208047471936 * q^95 - 12092663288748189077973504 * q^96 - 2067304853876486831513192 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$-1$

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 $

$2$	−4410.99			−1.07690			−0.538451	−	0.842657i	$-0.680990\pi$
$2$	−4410.99			−1.07690			−0.538451	+	0.842657i	$0.680990\pi$
$3$	−600091.			−1.12918			−0.564588	−	0.825373i	$-0.690965\pi$
$3$	−600091.			−1.12918			−0.564588	+	0.825373i	$0.690965\pi$
$4$	2.67964e6			0.159719
$5$			2.08680e8i			0.854755i	0.904073	+	0.427377i	$0.140562\pi$
$5$			2.08680e8i			0.854755i	−0.904073	+	0.427377i	$0.859438\pi$
$6$	2.64700e9			1.21601
$7$			9.90757e8i			0.0715798i	0.999359	+	0.0357899i	$0.0113947\pi$
$7$			9.90757e8i			0.0715798i	−0.999359	+	0.0357899i	$0.988605\pi$
$8$	6.21843e10			0.904901
$9$	7.76795e10			0.275040
$10$		−	9.20488e11i		−	0.920488i
$11$		−	3.04648e12i		−	0.970704i	−0.874319	−	0.485352i	$-0.838691\pi$
$11$		−	3.04648e12i		−	0.970704i	0.874319	−	0.485352i	$-0.161309\pi$
$12$	−1.60803e12			−0.180351
$13$	−2.90487e13			−1.24683			−0.623413	−	0.781893i	$-0.714254\pi$
$13$	−2.90487e13			−1.24683			−0.623413	+	0.781893i	$0.714254\pi$
$14$		−	4.37022e12i		−	0.0770845i
$15$		−	1.25227e14i		−	0.965169i
$16$	−3.19251e14			−1.13421
$17$			7.59542e14i			1.30366i	0.758365	+	0.651830i	$0.225999\pi$
$17$			7.59542e14i			1.30366i	−0.758365	+	0.651830i	$0.774001\pi$
$18$	−3.42644e14			−0.296191
$19$		−	3.40778e15i		−	1.53967i	−0.638241	−	0.769836i	$-0.720338\pi$
$19$		−	3.40778e15i		−	1.53967i	0.638241	−	0.769836i	$-0.279662\pi$
$20$			5.59189e14i			0.136521i
$21$		−	5.94544e14i		−	0.0808263i
$22$			1.34380e16i			1.04535i
$23$	−1.35383e16	+	1.72327e16i	−0.617775	+	0.786355i
$23$	−1.35383e16	+	1.72327e16i	−0.617775	+	0.786355i
$24$	−3.73162e16			−1.02179
$25$	1.60571e16			0.269394
$26$	1.28133e17			1.34271
$27$	1.22869e17			0.818608
$28$			2.65487e15i			0.0114327i
$29$	−1.97404e17			−0.557931			−0.278965	−	0.960301i	$-0.589991\pi$
$29$	−1.97404e17			−0.557931			−0.278965	+	0.960301i	$0.589991\pi$
$30$			5.52376e17i			1.03939i
$31$	1.05721e18			1.34221			0.671107	−	0.741360i	$-0.265819\pi$
$31$	1.05721e18			1.34221			0.671107	+	0.741360i	$0.265819\pi$
$32$	3.64936e17			0.316532
$33$			1.82817e18i			1.09610i
$34$		−	3.35033e18i		−	1.40392i
$35$	−2.06752e17			−0.0611832
$36$	2.08153e17			0.0439292
$37$			5.88277e18i			0.893638i	0.894624	+	0.446819i	$0.147443\pi$
$37$			5.88277e18i			0.893638i	−0.894624	+	0.446819i	$0.852557\pi$
$38$			1.50317e19i			1.65808i
$39$	1.74318e19			1.40789
$40$			1.29766e19i			0.773468i
$41$	1.01351e19			0.449180			0.224590	−	0.974453i	$-0.427896\pi$
$41$	1.01351e19			0.449180			0.224590	+	0.974453i	$0.427896\pi$
$42$			2.62253e18i			0.0870420i
$43$			5.06956e19i			1.26867i	0.773058	+	0.634336i	$0.218726\pi$
$43$			5.06956e19i			1.26867i	−0.773058	+	0.634336i	$0.781274\pi$
$44$		−	8.16349e18i		−	0.155040i
$45$			1.62102e19i			0.235092i
$46$	5.97173e19	−	7.60132e19i	0.665283	−	0.846828i
$47$	−2.15998e20			−1.85899			−0.929493	−	0.368841i	$-0.879755\pi$
$47$	−2.15998e20			−1.85899			−0.929493	+	0.368841i	$0.879755\pi$
$48$	1.91580e20			1.28072
$49$	1.90600e20			0.994876
$50$	−7.08279e19			−0.290111
$51$		−	4.55794e20i		−	1.47206i
$52$	−7.78400e19			−0.199142
$53$			6.98504e20i			1.42186i	0.703260	+	0.710932i	$0.251727\pi$
$53$			6.98504e20i			1.42186i	−0.703260	+	0.710932i	$0.748273\pi$
$54$	−5.41973e20			−0.881561
$55$	6.35742e20			0.829714
$56$			6.16095e19i			0.0647726i
$57$			2.04498e21i			1.73856i
$58$	8.70748e20			0.600837
$59$	1.97235e21			1.10856			0.554280	−	0.832330i	$-0.312994\pi$
$59$	1.97235e21			1.10856			0.554280	+	0.832330i	$0.312994\pi$
$60$		−	3.35564e20i		−	0.154156i
$61$			2.54538e21i			0.958948i	0.877556	+	0.479474i	$0.159173\pi$
$61$			2.54538e21i			0.958948i	−0.877556	+	0.479474i	$0.840827\pi$
$62$	−4.66336e21			−1.44543
$63$			7.69615e19i			0.0196873i
$64$	3.74642e21			0.793335
$65$		−	6.06189e21i		−	1.06573i
$66$		−	8.06403e21i		−	1.18039i
$67$			1.45735e22i			1.78101i	0.454974	+	0.890505i	$0.349649\pi$
$67$			1.45735e22i			1.78101i	−0.454974	+	0.890505i	$0.650351\pi$
$68$			2.03530e21i			0.208220i
$69$	8.12421e21	−	1.03412e22i	0.697577	−	0.887934i
$70$	9.11979e20			0.0658883
$71$	−8.48225e21			−0.516905			−0.258453	−	0.966024i	$-0.583213\pi$
$71$	−8.48225e21			−0.516905			−0.258453	+	0.966024i	$0.583213\pi$
$72$	4.83044e21			0.248884
$73$	−2.09881e22			−0.916430			−0.458215	−	0.888841i	$-0.651511\pi$
$73$	−2.09881e22			−0.916430			−0.458215	+	0.888841i	$0.651511\pi$
$74$		−	2.59489e22i		−	0.962361i
$75$	−9.63574e21			−0.304194
$76$		−	9.13163e21i		−	0.245915i
$77$	3.01833e21			0.0694828
$78$	−7.68917e22			−1.51616
$79$		−	6.62640e22i		−	1.12138i	−0.828026	−	0.560690i	$-0.810536\pi$
$79$		−	6.62640e22i		−	1.12138i	0.828026	−	0.560690i	$-0.189464\pi$
$80$		−	6.66215e22i		−	0.969471i
$81$	−9.56713e22			−1.19939
$82$	−4.47057e22			−0.483723
$83$		−	1.10895e23i		−	1.03747i	−0.854936	−	0.518734i	$-0.826404\pi$
$83$		−	1.10895e23i		−	1.03747i	0.854936	−	0.518734i	$-0.173596\pi$
$84$		−	1.59317e21i		−	0.0129095i
$85$	−1.58501e23			−1.11431
$86$		−	2.23618e23i		−	1.36624i
$87$	1.18460e23			0.630002
$88$		−	1.89444e23i		−	0.878391i
$89$			3.42705e23i			1.38752i	0.720205	+	0.693761i	$0.244048\pi$
$89$			3.42705e23i			1.38752i	−0.720205	+	0.693761i	$0.755952\pi$
$90$		−	7.15030e22i		−	0.253171i
$91$		−	2.87802e22i		−	0.0892476i
$92$	−3.62778e22	+	4.61774e22i	−0.0986704	+	0.125596i
$93$	−6.34424e23			−1.51560
$94$	9.52767e23			2.00195
$95$	7.11137e23			1.31604
$96$	−2.18995e23			−0.357420
$97$			2.21681e23i			0.319498i	0.987158	+	0.159749i	$0.0510684\pi$
$97$			2.21681e23i			0.319498i	−0.987158	+	0.159749i	$0.948932\pi$
$98$	−8.40734e23			−1.07138
$99$		−	2.36649e23i		−	0.266983i
$100$	4.30274e22			0.0430274
$101$	−4.32059e23			−0.383431			−0.191715	−	0.981451i	$-0.561405\pi$
$101$	−4.32059e23			−0.383431			−0.191715	+	0.981451i	$0.561405\pi$
$102$			2.01050e24i			1.58527i
$103$		−	1.05273e24i		−	0.738366i	−0.929357	−	0.369183i	$-0.879638\pi$
$103$		−	1.05273e24i		−	0.738366i	0.929357	−	0.369183i	$-0.120362\pi$
$104$	−1.80637e24			−1.12825
$105$	1.24070e23			0.0690866
$106$		−	3.08109e24i		−	1.53121i
$107$		−	3.32639e24i		−	1.47696i	−0.674276	−	0.738479i	$-0.735544\pi$
$107$		−	3.32639e24i		−	1.47696i	0.674276	−	0.738479i	$-0.264456\pi$
$108$	3.29244e23			0.130747
$109$			2.97757e24i			1.05863i	0.848426	+	0.529314i	$0.177551\pi$
$109$			2.97757e24i			1.05863i	−0.848426	+	0.529314i	$0.822449\pi$
$110$	−2.80425e24			−0.893521
$111$		−	3.53020e24i		−	1.00907i
$112$		−	3.16301e23i		−	0.0811865i
$113$			1.17831e23i			0.0271843i	0.999908	+	0.0135922i	$0.00432665\pi$
$113$			1.17831e23i			0.0271843i	−0.999908	+	0.0135922i	$0.995673\pi$
$114$		−	9.02038e24i		−	1.87226i
$115$	−3.59612e24	−	2.82518e24i	−0.672141	−	0.528046i
$116$	−5.28972e23			−0.0891122
$117$	−2.25648e24			−0.342927
$118$	−8.70001e24			−1.19381
$119$	−7.52521e23			−0.0933158
$120$		−	7.78716e24i		−	0.873382i
$121$	5.68665e23			0.0577341
$122$		−	1.12277e25i		−	1.03269i
$123$	−6.08196e24			−0.507204
$124$	2.83295e24			0.214377
$125$			1.57891e25i			1.08502i
$126$		−	3.39476e23i		−	0.0212013i
$127$	3.93983e24			0.223786			0.111893	−	0.993720i	$-0.464309\pi$
$127$	3.93983e24			0.223786			0.111893	+	0.993720i	$0.464309\pi$
$128$	−2.26480e25			−1.17088
$129$		−	3.04220e25i		−	1.43255i
$130$			2.67389e25i			1.14769i
$131$	1.53631e25			0.601482			0.300741	−	0.953706i	$-0.402766\pi$
$131$	1.53631e25			0.601482			0.300741	+	0.953706i	$0.402766\pi$
$132$			4.89883e24i			0.175067i
$133$	3.37628e24			0.110209
$134$		−	6.42836e25i		−	1.91797i
$135$			2.56403e25i			0.699709i
$136$			4.72316e25i			1.17968i
$137$			4.62219e25i			1.05731i	0.848838	+	0.528653i	$0.177303\pi$
$137$			4.62219e25i			1.05731i	−0.848838	+	0.528653i	$0.822697\pi$
$138$	−3.58358e25	+	4.56148e25i	−0.751222	+	0.956219i
$139$	9.74177e25			1.87267			0.936333	−	0.351114i	$-0.114197\pi$
$139$	9.74177e25			1.87267			0.936333	+	0.351114i	$0.114197\pi$
$140$	−5.54020e23			−0.00977212
$141$	1.29619e26			2.09912
$142$	3.74152e25			0.556657
$143$			8.84963e25i			1.21030i
$144$	−2.47993e25			−0.311953
$145$		−	4.11944e25i		−	0.476894i
$146$	9.25785e25			0.986906
$147$	−1.14377e26			−1.12339
$148$			1.57637e25i			0.142731i
$149$			1.58346e26i			1.32243i	0.750199	+	0.661213i	$0.229958\pi$
$149$			1.58346e26i			1.32243i	−0.750199	+	0.661213i	$0.770042\pi$
$150$	4.25032e25			0.327587
$151$	−1.00820e26			−0.717505			−0.358753	−	0.933433i	$-0.616798\pi$
$151$	−1.00820e26			−0.717505			−0.358753	+	0.933433i	$0.616798\pi$
$152$		−	2.11910e26i		−	1.39325i
$153$			5.90008e25i			0.358559i
$154$	−1.33138e25			−0.0748262
$155$			2.20620e26i			1.14726i
$156$	4.67111e25			0.224866
$157$			1.31913e26i			0.588156i	0.955781	+	0.294078i	$0.0950125\pi$
$157$			1.31913e26i			0.588156i	−0.955781	+	0.294078i	$0.904987\pi$
$158$			2.92290e26i			1.20762i
$159$		−	4.19166e26i		−	1.60554i
$160$			7.61551e25i			0.270557i
$161$	−1.70734e25	−	1.34132e25i	−0.0562872	−	0.0442202i
$162$	4.22006e26			1.29163
$163$	1.63351e26			0.464378			0.232189	−	0.972671i	$-0.425411\pi$
$163$	1.63351e26			0.464378			0.232189	+	0.972671i	$0.425411\pi$
$164$	2.71584e25			0.0717426
$165$	−3.81503e26			−0.936894
$166$			4.89157e26i			1.11725i
$167$	4.71219e26			1.00144			0.500720	−	0.865609i	$-0.333069\pi$
$167$	4.71219e26			1.00144			0.500720	+	0.865609i	$0.333069\pi$
$168$		−	3.69713e25i		−	0.0731397i
$169$	3.01024e26			0.554575
$170$	6.99149e26			1.20000
$171$		−	2.64715e26i		−	0.423472i
$172$			1.35846e26i			0.202631i
$173$	−6.15036e26			−0.855750			−0.427875	−	0.903838i	$-0.640738\pi$
$173$	−6.15036e26			−0.855750			−0.427875	+	0.903838i	$0.640738\pi$
$174$	−5.22528e26			−0.678451
$175$			1.59087e25i			0.0192832i
$176$			9.72595e26i			1.10098i
$177$	−1.18359e27			−1.25176
$178$		−	1.51167e27i		−	1.49423i
$179$	−1.12860e27			−1.04304			−0.521521	−	0.853238i	$-0.674635\pi$
$179$	−1.12860e27			−1.04304			−0.521521	+	0.853238i	$0.674635\pi$
$180$			4.34375e25i			0.0375487i
$181$		−	2.44687e27i		−	1.97910i	−0.144178	−	0.989552i	$-0.546054\pi$
$181$		−	2.44687e27i		−	1.97910i	0.144178	−	0.989552i	$-0.453946\pi$
$182$			1.26949e26i			0.0961110i
$183$		−	1.52746e27i		−	1.08282i
$184$	−8.41869e26	+	1.07160e27i	−0.559025	+	0.711573i
$185$	−1.22762e27			−0.763841
$186$	2.79844e27			1.63215
$187$	2.31393e27			1.26547
$188$	−5.78798e26			−0.296915
$189$			1.21733e26i			0.0585958i
$190$	−3.13682e27			−1.41725
$191$			1.33797e27i			0.567606i	0.958883	+	0.283803i	$0.0915962\pi$
$191$			1.33797e27i			0.567606i	−0.958883	+	0.283803i	$0.908404\pi$
$192$	−2.24819e27			−0.895815
$193$	1.16340e27			0.435553			0.217776	−	0.975999i	$-0.430120\pi$
$193$	1.16340e27			0.435553			0.217776	+	0.975999i	$0.430120\pi$
$194$		−	9.77834e26i		−	0.344068i
$195$			3.63768e27i			1.20340i
$196$	5.10739e26			0.158901
$197$	−7.49565e26			−0.219389			−0.109694	−	0.993965i	$-0.534987\pi$
$197$	−7.49565e26			−0.219389			−0.109694	+	0.993965i	$0.534987\pi$
$198$			1.04386e27i			0.287514i
$199$		−	7.27664e27i		−	1.88666i	−0.331855	−	0.943330i	$-0.607675\pi$
$199$		−	7.27664e27i		−	1.88666i	0.331855	−	0.943330i	$-0.392325\pi$
$200$	9.98502e26			0.243775
$201$		−	8.74542e27i		−	2.01107i
$202$	1.90581e27			0.412917
$203$		−	1.95579e26i		−	0.0399366i
$204$		−	1.22136e27i		−	0.235117i
$205$			2.11499e27i			0.383939i
$206$			4.64360e27i			0.795148i
$207$	−1.05165e27	+	1.33863e27i	−0.169913	+	0.216279i
$208$	9.27383e27			1.41416
$209$	−1.03818e28			−1.49457
$210$	−5.47270e26			−0.0743996
$211$	−9.47507e27			−1.21673			−0.608363	−	0.793659i	$-0.708174\pi$
$211$	−9.47507e27			−1.21673			−0.608363	+	0.793659i	$0.708174\pi$
$212$			1.87174e27i			0.227099i
$213$	5.09012e27			0.583678
$214$			1.46727e28i			1.59054i
$215$	−1.05792e28			−1.08440
$216$	7.64050e27			0.740759
$217$			1.04744e27i			0.0960755i
$218$		−	1.31340e28i		−	1.14004i
$219$	1.25948e28			1.03481
$220$	1.70356e27			0.132521
$221$		−	2.20637e28i		−	1.62544i
$222$			1.55717e28i			1.08668i
$223$	−2.45451e28			−1.62295			−0.811477	−	0.584384i	$-0.801336\pi$
$223$	−2.45451e28			−1.62295			−0.811477	+	0.584384i	$0.801336\pi$
$224$			3.61563e26i			0.0226573i
$225$	1.24731e27			0.0740942
$226$		−	5.19752e26i		−	0.0292748i
$227$		−	1.85135e28i		−	0.988961i	−0.869189	−	0.494481i	$-0.835358\pi$
$227$		−	1.85135e28i		−	0.988961i	0.869189	−	0.494481i	$-0.164642\pi$
$228$			5.47981e27i			0.277682i
$229$		−	2.51005e28i		−	1.20686i	−0.797416	−	0.603430i	$-0.793800\pi$
$229$		−	2.51005e28i		−	1.20686i	0.797416	−	0.603430i	$-0.206200\pi$
$230$	1.58625e28	+	1.24618e28i	0.723830	+	0.568654i
$231$	−1.81127e27			−0.0784584
$232$	−1.22754e28			−0.504872
$233$	−7.79932e27			−0.304639			−0.152320	−	0.988331i	$-0.548674\pi$
$233$	−7.79932e27			−0.304639			−0.152320	+	0.988331i	$0.548674\pi$
$234$	9.95334e27			0.369299
$235$		−	4.50746e28i		−	1.58898i
$236$	5.28519e27			0.177058
$237$			3.97644e28i			1.26624i
$238$	3.31937e27			0.100492
$239$	−1.12722e28			−0.324514			−0.162257	−	0.986749i	$-0.551877\pi$
$239$	−1.12722e28			−0.324514			−0.162257	+	0.986749i	$0.551877\pi$
$240$			3.99790e28i			1.09470i
$241$		−	3.25888e27i		−	0.0848915i	−0.999099	−	0.0424457i	$-0.986485\pi$
$241$		−	3.25888e27i		−	0.0848915i	0.999099	−	0.0424457i	$-0.0135150\pi$
$242$	−2.50838e27			−0.0621739
$243$	2.27097e28			0.535719
$244$			6.82071e27i			0.153162i
$245$			3.97744e28i			0.850375i
$246$	2.68275e28			0.546209
$247$			9.89915e28i			1.91970i
$248$	6.57420e28			1.21457
$249$			6.65470e28i			1.17148i
$250$		−	6.96457e28i		−	1.16846i
$251$			4.57088e28i			0.730996i	0.930812	+	0.365498i	$0.119101\pi$
$251$			4.57088e28i			0.730996i	−0.930812	+	0.365498i	$0.880899\pi$
$252$			2.06229e26i			0.00314444i
$253$	5.24991e28	+	4.12442e28i	0.763318	+	0.599676i
$254$	−1.73786e28			−0.240996
$255$	9.51153e28			1.25825
$256$	3.70459e28			0.467585
$257$	8.03698e28			0.968044			0.484022	−	0.875056i	$-0.339175\pi$
$257$	8.03698e28			0.968044			0.484022	+	0.875056i	$0.339175\pi$
$258$			1.34191e29i			1.54272i
$259$	−5.82840e27			−0.0639664
$260$		−	1.62437e28i		−	0.170218i
$261$	−1.53342e28			−0.153453
$262$	−6.77664e28			−0.647738
$263$			3.39866e28i			0.310341i	0.987888	+	0.155170i	$0.0495927\pi$
$263$			3.39866e28i			0.310341i	−0.987888	+	0.155170i	$0.950407\pi$
$264$			1.13683e29i			0.991858i
$265$	−1.45764e29			−1.21535
$266$	−1.48928e28			−0.118685
$267$		−	2.05654e29i		−	1.56676i
$268$			3.90518e28i			0.284461i
$269$	1.00748e29			0.701791			0.350895	−	0.936415i	$-0.385877\pi$
$269$	1.00748e29			0.701791			0.350895	+	0.936415i	$0.385877\pi$
$270$		−	1.13099e29i		−	0.753518i
$271$	9.43583e27			0.0601379			0.0300690	−	0.999548i	$-0.490427\pi$
$271$	9.43583e27			0.0601379			0.0300690	+	0.999548i	$0.490427\pi$
$272$		−	2.42485e29i		−	1.47862i
$273$			1.72707e28i			0.100776i
$274$		−	2.03884e29i		−	1.13862i
$275$		−	4.89178e28i		−	0.261502i
$276$	2.17700e28	−	2.77106e28i	0.111416	−	0.141820i
$277$	1.29492e29			0.634581			0.317291	−	0.948328i	$-0.397227\pi$
$277$	1.29492e29			0.634581			0.317291	+	0.948328i	$0.397227\pi$
$278$	−4.29709e29			−2.01668
$279$	8.21237e28			0.369163
$280$	−1.28567e28			−0.0553647
$281$		−	1.11509e29i		−	0.460079i	−0.973181	−	0.230039i	$-0.926115\pi$
$281$		−	1.11509e29i		−	0.460079i	0.973181	−	0.230039i	$-0.0738855\pi$
$282$	−5.71747e29			−2.26055
$283$		−	7.49221e28i		−	0.283905i	−0.989873	−	0.141952i	$-0.954662\pi$
$283$		−	7.49221e28i		−	0.283905i	0.989873	−	0.141952i	$-0.0453380\pi$
$284$	−2.27294e28			−0.0825597
$285$	−4.26747e29			−1.48604
$286$		−	3.90357e29i		−	1.30337i
$287$			1.00414e28i			0.0321522i
$288$	2.83481e28			0.0870590
$289$	−2.37455e29			−0.699532
$290$			1.81708e29i			0.513568i
$291$		−	1.33029e29i		−	0.360769i
$292$	−5.62406e28			−0.146371
$293$		−	1.67819e29i		−	0.419208i	−0.977786	−	0.209604i	$-0.932782\pi$
$293$		−	1.67819e29i		−	0.419208i	0.977786	−	0.209604i	$-0.0672176\pi$
$294$	5.04517e29			1.20978
$295$			4.11590e29i			0.947547i
$296$			3.65816e29i			0.808653i
$297$		−	3.74317e29i		−	0.794626i
$298$		−	6.98462e29i		−	1.42412i
$299$	3.93269e29	−	5.00586e29i	0.770257	−	0.980448i
$300$	−2.58203e28			−0.0485855
$301$	−5.02270e28			−0.0908112
$302$	4.44718e29			0.772683
$303$	2.59275e29			0.432961
$304$			1.08794e30i			1.74631i
$305$	−5.31171e29			−0.819665
$306$		−	2.60252e29i		−	0.386133i
$307$	−1.15119e30			−1.64243			−0.821216	−	0.570617i	$-0.806704\pi$
$307$	−1.15119e30			−1.64243			−0.821216	+	0.570617i	$0.806704\pi$
$308$	8.08803e27			0.0110977
$309$			6.31735e29i			0.833745i
$310$		−	9.73151e29i		−	1.23549i
$311$	5.86583e29			0.716482			0.358241	−	0.933629i	$-0.383377\pi$
$311$	5.86583e29			0.716482			0.358241	+	0.933629i	$0.383377\pi$
$312$	1.08399e30			1.27400
$313$			3.50404e29i			0.396311i	0.980171	+	0.198156i	$0.0634952\pi$
$313$			3.50404e29i			0.396311i	−0.980171	+	0.198156i	$0.936505\pi$
$314$		−	5.81868e29i		−	0.633386i
$315$	−1.60603e28			−0.0168278
$316$		−	1.77564e29i		−	0.179106i
$317$	−6.73771e29			−0.654336			−0.327168	−	0.944966i	$-0.606094\pi$
$317$	−6.73771e29			−0.654336			−0.327168	+	0.944966i	$0.606094\pi$
$318$			1.84894e30i			1.72901i
$319$			6.01388e29i			0.541585i
$320$			7.81804e29i			0.678107i
$321$			1.99614e30i			1.66775i
$322$	7.53106e28	+	5.91654e28i	0.0606158	+	0.0476208i
$323$	2.58835e30			2.00721
$324$	−2.56365e29			−0.191566
$325$	−4.66439e29			−0.335888
$326$	−7.20542e29			−0.500090
$327$		−	1.78681e30i		−	1.19538i
$328$	6.30242e29			0.406463
$329$		−	2.14002e29i		−	0.133066i
$330$	1.68281e30			1.00894
$331$	1.22926e30			0.710734			0.355367	−	0.934727i	$-0.384356\pi$
$331$	1.22926e30			0.710734			0.355367	+	0.934727i	$0.384356\pi$
$332$		−	2.97159e29i		−	0.165703i
$333$			4.56971e29i			0.245786i
$334$	−2.07854e30			−1.07845
$335$	−3.04120e30			−1.52233
$336$			1.89809e29i			0.0916739i
$337$		−	2.09567e30i		−	0.976704i	−0.872647	−	0.488352i	$-0.837598\pi$
$337$		−	2.09567e30i		−	0.976704i	0.872647	−	0.488352i	$-0.162402\pi$
$338$	−1.32781e30			−0.597224
$339$		−	7.07093e28i		−	0.0306959i
$340$	−4.24727e29			−0.177977
$341$		−	3.22078e30i		−	1.30289i
$342$			1.16765e30i			0.456038i
$343$			3.78648e29i			0.142793i
$344$			3.15247e30i			1.14802i
$345$	2.15800e30	+	1.69536e30i	0.758966	+	0.596257i
$346$	2.71292e30			0.921560
$347$	2.58156e30			0.847086			0.423543	−	0.905876i	$-0.360786\pi$
$347$	2.58156e30			0.847086			0.423543	+	0.905876i	$0.360786\pi$
$348$	3.17431e29			0.100623
$349$	3.64197e30			1.11540			0.557702	−	0.830042i	$-0.311683\pi$
$349$	3.64197e30			1.11540			0.557702	+	0.830042i	$0.311683\pi$
$350$		−	7.01733e28i		−	0.0207661i
$351$	−3.56917e30			−1.02066
$352$		−	1.11177e30i		−	0.307259i
$353$	−6.16437e30			−1.64662			−0.823308	−	0.567594i	$-0.807874\pi$
$353$	−6.16437e30			−1.64662			−0.823308	+	0.567594i	$0.807874\pi$
$354$	5.22080e30			1.34802
$355$		−	1.77008e30i		−	0.441827i
$356$			9.18325e29i			0.221614i
$357$	4.51581e29			0.105370
$358$	4.97822e30			1.12325
$359$			2.59830e30i			0.566964i	0.958978	+	0.283482i	$0.0914896\pi$
$359$			2.59830e30i			0.566964i	−0.958978	+	0.283482i	$0.908510\pi$
$360$			1.00802e30i			0.212735i
$361$	−6.71421e30			−1.37059
$362$			1.07931e31i			2.13130i
$363$	−3.41251e29			−0.0651919
$364$		−	7.71205e28i		−	0.0142545i
$365$		−	4.37981e30i		−	0.783323i
$366$			6.73762e30i			1.16609i
$367$			2.11320e30i			0.353955i	0.984215	+	0.176977i	$0.0566319\pi$
$367$			2.11320e30i			0.353955i	−0.984215	+	0.176977i	$0.943368\pi$
$368$	4.32212e30	−	5.50156e30i	0.700685	−	0.891891i
$369$	7.87287e29			0.123543
$370$	5.41502e30			0.822582
$371$	−6.92047e29			−0.101777
$372$	−1.70003e30			−0.242070
$373$		−	8.27959e29i		−	0.114157i	−0.998370	−	0.0570785i	$-0.981821\pi$
$373$		−	8.27959e29i		−	0.114157i	0.998370	−	0.0570785i	$-0.0181785\pi$
$374$	−1.02067e31			−1.36279
$375$		−	9.47491e30i		−	1.22518i
$376$	−1.34317e31			−1.68220
$377$	5.73432e30			0.695642
$378$		−	5.36963e29i		−	0.0631020i
$379$		−	1.30508e31i		−	1.48582i	−0.669393	−	0.742909i	$-0.733446\pi$
$379$		−	1.30508e31i		−	1.48582i	0.669393	−	0.742909i	$-0.266554\pi$
$380$	1.90559e30			0.210197
$381$	−2.36426e30			−0.252694
$382$		−	5.90179e30i		−	0.611256i
$383$			3.64171e30i			0.365527i	0.983157	+	0.182764i	$0.0585043\pi$
$383$			3.64171e30i			0.365527i	−0.983157	+	0.182764i	$0.941496\pi$
$384$	1.35909e31			1.32213
$385$			6.29865e29i			0.0593908i
$386$	−5.13174e30			−0.469048
$387$			3.93801e30i			0.348935i
$388$			5.94026e29i			0.0510299i
$389$			6.66496e30i			0.555140i	0.960705	+	0.277570i	$0.0895291\pi$
$389$			6.66496e30i			0.555140i	−0.960705	+	0.277570i	$0.910471\pi$
$390$		−	1.60458e31i		−	1.29594i
$391$	−1.30889e31	−	1.02829e31i	−1.02514	−	0.805368i
$392$	1.18523e31			0.900264
$393$	−9.21924e30			−0.679180
$394$	3.30633e30			0.236261
$395$	1.38280e31			0.958504
$396$		−	6.34135e29i		−	0.0426422i
$397$	−5.59012e30			−0.364699			−0.182350	−	0.983234i	$-0.558370\pi$
$397$	−5.59012e30			−0.364699			−0.182350	+	0.983234i	$0.558370\pi$
$398$			3.20972e31i			2.03175i
$399$	−2.02608e30			−0.124446
$400$	−5.12627e30			−0.305549
$401$		−	2.62935e31i		−	1.52095i	−0.649365	−	0.760477i	$-0.724965\pi$
$401$		−	2.62935e31i		−	1.52095i	0.649365	−	0.760477i	$-0.275035\pi$
$402$			3.85760e31i			2.16573i
$403$	−3.07106e31			−1.67351
$404$	−1.15776e30			−0.0612412
$405$		−	1.99647e31i		−	1.02519i
$406$			8.62699e29i			0.0430078i
$407$	1.79218e31			0.867457
$408$		−	2.83432e31i		−	1.33207i
$409$	−3.22952e31			−1.47387			−0.736934	−	0.675965i	$-0.763727\pi$
$409$	−3.22952e31			−1.47387			−0.736934	+	0.675965i	$0.763727\pi$
$410$		−	9.32921e30i		−	0.413465i
$411$		−	2.77373e31i		−	1.19389i
$412$		−	2.82095e30i		−	0.117931i
$413$			1.95412e30i			0.0793505i
$414$	4.63881e30	−	5.90467e30i	0.182980	−	0.232912i
$415$	2.31416e31			0.886780
$416$	−1.06009e31			−0.394660
$417$	−5.84595e31			−2.11457
$418$	4.57938e31			1.60950
$419$			4.07204e31i			1.39073i	0.718655	+	0.695367i	$0.244758\pi$
$419$			4.07204e31i			1.39073i	−0.718655	+	0.695367i	$0.755242\pi$
$420$	3.32462e29			0.0110345
$421$		−	2.74059e31i		−	0.884014i	−0.897012	−	0.442007i	$-0.854267\pi$
$421$		−	2.74059e31i		−	0.884014i	0.897012	−	0.442007i	$-0.145733\pi$
$422$	4.17945e31			1.31030
$423$	−1.67786e31			−0.511296
$424$			4.34360e31i			1.28665i
$425$			1.21961e31i			0.351199i
$426$	−2.24525e31			−0.628564
$427$	−2.52185e30			−0.0686413
$428$		−	8.91354e30i		−	0.235898i
$429$		−	5.31058e31i		−	1.36664i
$430$	4.66647e31			1.16780
$431$		−	1.39542e31i		−	0.339608i	−0.985478	−	0.169804i	$-0.945687\pi$
$431$		−	1.39542e31i		−	0.339608i	0.985478	−	0.169804i	$-0.0543135\pi$
$432$	−3.92260e31			−0.928472
$433$			3.93119e30i			0.0905042i	0.998976	+	0.0452521i	$0.0144091\pi$
$433$			3.93119e30i			0.0905042i	−0.998976	+	0.0452521i	$0.985591\pi$
$434$		−	4.62025e30i		−	0.103464i
$435$			2.47204e31i			0.538497i
$436$			7.97881e30i			0.169083i
$437$	5.87252e31	+	4.61355e31i	1.21073	+	0.951171i
$438$	−5.55555e31			−1.11439
$439$	5.82675e31			1.13724			0.568620	−	0.822600i	$-0.307477\pi$
$439$	5.82675e31			1.13724			0.568620	+	0.822600i	$0.307477\pi$
$440$	3.95331e31			0.750809
$441$	1.48057e31			0.273631
$442$			9.73227e31i			1.75044i
$443$	−2.10094e31			−0.367763			−0.183881	−	0.982948i	$-0.558866\pi$
$443$	−2.10094e31			−0.367763			−0.183881	+	0.982948i	$0.558866\pi$
$444$		−	9.45967e30i		−	0.161169i
$445$	−7.15157e31			−1.18599
$446$	1.08268e32			1.74776
$447$		−	9.50218e31i		−	1.49325i
$448$			3.71179e30i			0.0567868i
$449$	−9.13734e31			−1.36102			−0.680509	−	0.732740i	$-0.738241\pi$
$449$	−9.13734e31			−1.36102			−0.680509	+	0.732740i	$0.738241\pi$
$450$	−5.50188e30			−0.0797922
$451$		−	3.08763e31i		−	0.436021i
$452$			3.15745e29i			0.00434185i
$453$	6.05014e31			0.810190
$454$			8.16631e31i			1.06501i
$455$	6.00585e30			0.0762848
$456$			1.27166e32i			1.57323i
$457$		−	4.64917e31i		−	0.560248i	−0.959964	−	0.280124i	$-0.909624\pi$
$457$		−	4.64917e31i		−	0.560248i	0.959964	−	0.280124i	$-0.0903756\pi$
$458$			1.10718e32i			1.29967i
$459$			9.33239e31i			1.06719i
$460$	−9.63632e30	−	7.57046e30i	−0.107354	−	0.0843390i
$461$	9.65031e31			1.04744			0.523721	−	0.851890i	$-0.324543\pi$
$461$	9.65031e31			1.04744			0.523721	+	0.851890i	$0.324543\pi$
$462$	7.98950e30			0.0844920
$463$	−7.76934e31			−0.800594			−0.400297	−	0.916386i	$-0.631093\pi$
$463$	−7.76934e31			−0.800594			−0.400297	+	0.916386i	$0.631093\pi$
$464$	6.30215e31			0.632810
$465$		−	1.32392e32i		−	1.29546i
$466$	3.44027e31			0.328067
$467$			1.29167e32i			1.20046i	0.799826	+	0.600231i	$0.204925\pi$
$467$			1.29167e32i			1.20046i	−0.799826	+	0.600231i	$0.795075\pi$
$468$	−6.04657e30			−0.0547720
$469$	−1.44388e31			−0.127484
$470$			1.98824e32i			1.71117i
$471$		−	7.91599e31i		−	0.664132i
$472$	1.22649e32			1.00314
$473$	1.54443e32			1.23150
$474$		−	1.75401e32i		−	1.36361i
$475$		−	5.47192e31i		−	0.414779i
$476$	−2.01649e30			−0.0149043
$477$			5.42594e31i			0.391070i
$478$	4.97215e31			0.349470
$479$			2.47226e32i			1.69460i	0.531112	+	0.847302i	$0.321774\pi$
$479$			2.47226e32i			1.69460i	−0.531112	+	0.847302i	$0.678226\pi$
$480$		−	4.56999e31i		−	0.305507i
$481$		−	1.70887e32i		−	1.11421i
$482$			1.43749e31i			0.0914199i
$483$	1.02456e31	+	8.04911e30i	0.0635582	+	0.0499324i
$484$	1.52382e30			0.00922123
$485$	−4.62605e31			−0.273092
$486$	−1.00173e32			−0.576917
$487$	−1.08375e32			−0.608952			−0.304476	−	0.952520i	$-0.598481\pi$
$487$	−1.08375e32			−0.608952			−0.304476	+	0.952520i	$0.598481\pi$
$488$			1.58283e32i			0.867753i
$489$	−9.80256e31			−0.524365
$490$		−	1.75445e32i		−	0.915771i
$491$	−1.54420e32			−0.786548			−0.393274	−	0.919421i	$-0.628658\pi$
$491$	−1.54420e32			−0.786548			−0.393274	+	0.919421i	$0.628658\pi$
$492$	−1.62975e31			−0.0810101
$493$		−	1.49937e32i		−	0.727352i
$494$		−	4.36651e32i		−	2.06733i
$495$	4.93841e31			0.228205
$496$	−3.37517e32			−1.52235
$497$		−	8.40385e30i		−	0.0370000i
$498$		−	2.93538e32i		−	1.26157i
$499$	−9.58770e31			−0.402261			−0.201130	−	0.979564i	$-0.564461\pi$
$499$	−9.58770e31			−0.402261			−0.201130	+	0.979564i	$0.564461\pi$
$500$			4.23092e31i			0.173299i
$501$	−2.82774e32			−1.13080
$502$		−	2.01621e32i		−	0.787212i
$503$		−	2.55312e31i		−	0.0973321i	−0.998815	−	0.0486660i	$-0.984503\pi$
$503$		−	2.55312e31i		−	0.0973321i	0.998815	−	0.0486660i	$-0.0154970\pi$
$504$			4.78579e30i			0.0178151i
$505$		−	9.01623e31i		−	0.327739i
$506$	−2.31573e32	−	1.81928e32i	−0.822019	−	0.645793i
$507$	−1.80642e32			−0.626214
$508$	1.05573e31			0.0357429
$509$	2.44999e32			0.810122			0.405061	−	0.914290i	$-0.367250\pi$
$509$	2.44999e32			0.810122			0.405061	+	0.914290i	$0.367250\pi$
$510$	−4.19553e32			−1.35502
$511$		−	2.07941e31i		−	0.0655979i
$512$	2.16562e32			0.667333
$513$		−	4.18709e32i		−	1.26039i
$514$	−3.54510e32			−1.04249
$515$	2.19685e32			0.631122
$516$		−	8.15200e31i		−	0.228806i
$517$			6.58035e32i			1.80452i
$518$	2.57090e31			0.0688856
$519$	3.69077e32			0.966293
$520$		−	3.76954e32i		−	0.964380i
$521$		−	1.39895e32i		−	0.349744i	−0.984591	−	0.174872i	$-0.944049\pi$
$521$		−	1.39895e32i		−	0.349744i	0.984591	−	0.174872i	$-0.0559511\pi$
$522$	6.76392e31			0.165254
$523$			4.80620e32i			1.14758i	0.819004	+	0.573788i	$0.194527\pi$
$523$			4.80620e32i			1.14758i	−0.819004	+	0.573788i	$0.805473\pi$
$524$	4.11676e31			0.0960682
$525$		−	9.54668e30i		−	0.0217741i
$526$		−	1.49915e32i		−	0.334207i
$527$			8.02997e32i			1.74979i
$528$		−	5.83645e32i		−	1.24320i
$529$	−1.13680e32	−	4.66602e32i	−0.236709	−	0.971581i
$530$	6.42964e32			1.30881
$531$	1.53211e32			0.304899
$532$	9.04723e30			0.0176026
$533$	−2.94410e32			−0.560049
$534$			9.07138e32i			1.68725i
$535$	6.94153e32			1.26244
$536$			9.06243e32i			1.61164i
$537$	6.77260e32			1.17778
$538$	−4.44397e32			−0.755760
$539$		−	5.80659e32i		−	0.965730i
$540$			6.87067e31i			0.111757i
$541$	2.83872e32			0.451601			0.225801	−	0.974174i	$-0.427500\pi$
$541$	2.83872e32			0.451601			0.225801	+	0.974174i	$0.427500\pi$
$542$	−4.16214e31			−0.0647627
$543$			1.46835e33i			2.23476i
$544$			2.77184e32i			0.412650i
$545$	−6.21360e32			−0.904868
$546$		−	7.61810e31i		−	0.108526i
$547$	2.53339e32			0.353065			0.176533	−	0.984295i	$-0.443512\pi$
$547$	2.53339e32			0.353065			0.176533	+	0.984295i	$0.443512\pi$
$548$			1.23858e32i			0.168872i
$549$			1.97724e32i			0.263749i
$550$			2.15776e32i			0.281612i
$551$			6.72710e32i			0.859030i
$552$	5.05198e32	−	6.43059e32i	0.631238	−	0.803492i
$553$	6.56515e31			0.0802681
$554$	−5.71190e32			−0.683382
$555$	7.36683e32			0.862512
$556$	2.61044e32			0.299100
$557$		−	8.05399e32i		−	0.903127i	−0.892239	−	0.451564i	$-0.850866\pi$
$557$		−	8.05399e32i		−	0.903127i	0.892239	−	0.451564i	$-0.149134\pi$
$558$	−3.62247e32			−0.397553
$559$		−	1.47264e33i		−	1.58181i
$560$	6.60057e31			0.0693945
$561$	−1.38857e33			−1.42894
$562$			4.91863e32i			0.495460i
$563$			4.99664e31i			0.0492694i	0.999697	+	0.0246347i	$0.00784227\pi$
$563$			4.99664e31i			0.0492694i	−0.999697	+	0.0246347i	$0.992158\pi$
$564$	3.47331e32			0.335270
$565$	−2.45890e31			−0.0232359
$566$			3.30481e32i			0.305738i
$567$		−	9.47870e31i		−	0.0858523i
$568$	−5.27463e32			−0.467748
$569$			6.57173e32i			0.570601i	0.958438	+	0.285300i	$0.0920934\pi$
$569$			6.57173e32i			0.570601i	−0.958438	+	0.285300i	$0.907907\pi$
$570$	1.88238e33			1.60033
$571$			1.30947e32i			0.109009i	0.998514	+	0.0545045i	$0.0173579\pi$
$571$			1.30947e32i			0.109009i	−0.998514	+	0.0545045i	$0.982642\pi$
$572$			2.37138e32i			0.193308i
$573$		−	8.02905e32i		−	0.640927i
$574$		−	4.42925e31i		−	0.0346248i
$575$	−2.17386e32	+	2.76708e32i	−0.166425	+	0.211840i
$576$	2.91020e32			0.218199
$577$	−1.59489e33			−1.17117			−0.585586	−	0.810610i	$-0.699135\pi$
$577$	−1.59489e33			−1.17117			−0.585586	+	0.810610i	$0.699135\pi$
$578$	1.04741e33			0.753328
$579$	−6.98145e32			−0.491816
$580$		−	1.10386e32i		−	0.0761690i
$581$	1.09870e32			0.0742617
$582$			5.86789e32i			0.388513i
$583$	2.12798e33			1.38021
$584$	−1.30513e33			−0.829278
$585$		−	4.70884e32i		−	0.293119i
$586$			7.40249e32i			0.451447i
$587$	1.06280e33			0.635028			0.317514	−	0.948254i	$-0.397152\pi$
$587$	1.06280e33			0.635028			0.317514	+	0.948254i	$0.397152\pi$
$588$	−3.06490e32			−0.179427
$589$		−	3.60275e33i		−	2.06657i
$590$		−	1.81552e33i		−	1.02042i
$591$	4.49807e32			0.247729
$592$		−	1.87808e33i		−	1.01357i
$593$	−1.30642e33			−0.690919			−0.345460	−	0.938434i	$-0.612277\pi$
$593$	−1.30642e33			−0.690919			−0.345460	+	0.938434i	$0.612277\pi$
$594$			1.65111e33i			0.855734i
$595$		−	1.57036e32i		−	0.0797621i
$596$			4.24310e32i			0.211217i
$597$			4.36664e33i			2.13037i
$598$	−1.73471e33	+	2.20808e33i	−0.829492	+	1.05585i
$599$	−2.64114e33			−1.23785			−0.618927	−	0.785448i	$-0.712432\pi$
$599$	−2.64114e33			−1.23785			−0.618927	+	0.785448i	$0.712432\pi$
$600$	−5.99192e32			−0.275265
$601$	3.08301e33			1.38829			0.694146	−	0.719835i	$-0.255782\pi$
$601$	3.08301e33			1.38829			0.694146	+	0.719835i	$0.255782\pi$
$602$	2.21551e32			0.0977949
$603$			1.13206e33i			0.489849i
$604$	−2.70162e32			−0.114599
$605$			1.18669e32i			0.0493485i
$606$	−1.14366e33			−0.466257
$607$	−3.56136e33			−1.42348			−0.711741	−	0.702442i	$-0.752093\pi$
$607$	−3.56136e33			−1.42348			−0.711741	+	0.702442i	$0.752093\pi$
$608$		−	1.24362e33i		−	0.487355i
$609$			1.17365e32i			0.0450954i
$610$	2.34299e33			0.882700
$611$	6.27446e33			2.31783
$612$			1.58101e32i			0.0572687i
$613$			3.59488e33i			1.27691i	0.769661	+	0.638453i	$0.220425\pi$
$613$			3.59488e33i			1.27691i	−0.769661	+	0.638453i	$0.779575\pi$
$614$	5.07790e33			1.76874
$615$		−	1.26919e33i		−	0.433535i
$616$	1.87692e32			0.0628750
$617$		−	5.62527e33i		−	1.84808i	−0.382292	−	0.924042i	$-0.624865\pi$
$617$		−	5.62527e33i		−	1.84808i	0.382292	−	0.924042i	$-0.375135\pi$
$618$		−	2.78658e33i		−	0.897862i
$619$			5.20978e33i			1.64639i	0.567761	+	0.823193i	$0.307810\pi$
$619$			5.20978e33i			1.64639i	−0.567761	+	0.823193i	$0.692190\pi$
$620$			5.91181e32i			0.183240i
$621$	−1.66343e33	+	2.11736e33i	−0.505715	+	0.643717i
$622$	−2.58741e33			−0.771581
$623$	−3.39537e32			−0.0993186
$624$	−5.56514e33			−1.59684
$625$	−2.33780e33			−0.658033
$626$		−	1.54563e33i		−	0.426789i
$627$	6.22999e33			1.68763
$628$			3.53480e32i			0.0939397i
$629$	−4.46821e33			−1.16500
$630$	7.08421e31			0.0181219
$631$			9.76546e32i			0.245098i	0.992462	+	0.122549i	$0.0391069\pi$
$631$			9.76546e32i			0.245098i	−0.992462	+	0.122549i	$0.960893\pi$
$632$		−	4.12058e33i		−	1.01474i
$633$	5.68590e33			1.37390
$634$	2.97200e33			0.704657
$635$			8.22165e32i			0.191282i
$636$		−	1.12321e33i		−	0.256435i
$637$	−5.53666e33			−1.24044
$638$		−	2.65272e33i		−	0.583235i
$639$	−6.58897e32			−0.142170
$640$		−	4.72620e33i		−	1.00081i
$641$			4.09971e33i			0.852034i	0.904715	+	0.426017i	$0.140084\pi$
$641$			4.09971e33i			0.852034i	−0.904715	+	0.426017i	$0.859916\pi$
$642$		−	8.80495e33i		−	1.79600i
$643$		−	8.64543e33i		−	1.73083i	−0.501054	−	0.865416i	$-0.667054\pi$
$643$		−	8.64543e33i		−	1.73083i	0.501054	−	0.865416i	$-0.332946\pi$
$644$	−4.57506e31	−	3.59425e31i	−0.00899014	−	0.00706281i
$645$	6.34847e33			1.22448
$646$	−1.14172e34			−2.16157
$647$	−1.00030e34			−1.85900			−0.929500	−	0.368822i	$-0.879761\pi$
$647$	−1.00030e34			−1.85900			−0.929500	+	0.368822i	$0.879761\pi$
$648$	−5.94925e33			−1.08533
$649$		−	6.00873e33i		−	1.07608i
$650$	2.05746e33			0.361718
$651$		−	6.28560e32i		−	0.108486i
$652$	4.37723e32			0.0741700
$653$	−6.23459e32			−0.103717			−0.0518585	−	0.998654i	$-0.516514\pi$
$653$	−6.23459e32			−0.103717			−0.0518585	+	0.998654i	$0.516514\pi$
$654$			7.88161e33i			1.28731i
$655$			3.20597e33i			0.514120i
$656$	−3.23564e33			−0.509464
$657$	−1.63035e33			−0.252055
$658$			9.43960e32i			0.143299i
$659$		−	4.43499e33i		−	0.661101i	−0.943788	−	0.330550i	$-0.892766\pi$
$659$		−	4.43499e33i		−	0.661101i	0.943788	−	0.330550i	$-0.107234\pi$
$660$	−1.02229e33			−0.149640
$661$			3.31246e33i			0.476138i	0.971248	+	0.238069i	$0.0765144\pi$
$661$			3.31246e33i			0.476138i	−0.971248	+	0.238069i	$0.923486\pi$
$662$	−5.42225e33			−0.765391
$663$			1.32402e34i			1.83541i
$664$		−	6.89592e33i		−	0.938805i
$665$			7.04564e32i			0.0942021i
$666$		−	2.01569e33i		−	0.264688i
$667$	2.67251e33	−	3.40180e33i	0.344675	−	0.438732i
$668$	1.26270e33			0.159949
$669$	1.47293e34			1.83260
$670$	1.34147e34			1.63940
$671$	7.75447e33			0.930854
$672$		−	2.16971e32i		−	0.0255841i
$673$	−1.94600e32			−0.0225405			−0.0112702	−	0.999936i	$-0.503588\pi$
$673$	−1.94600e32			−0.0225405			−0.0112702	+	0.999936i	$0.503588\pi$
$674$			9.24396e33i			1.05182i
$675$	1.97292e33			0.220528
$676$	8.06636e32			0.0885763
$677$		−	2.93763e33i		−	0.316908i	−0.987366	−	0.158454i	$-0.949349\pi$
$677$		−	2.93763e33i		−	0.316908i	0.987366	−	0.158454i	$-0.0506510\pi$
$678$			3.11898e32i			0.0330565i
$679$	−2.19632e32			−0.0228696
$680$	−9.85630e33			−1.00834
$681$			1.11098e34i			1.11671i
$682$			1.42068e34i			1.40309i
$683$	8.72835e33			0.847000			0.423500	−	0.905896i	$-0.360801\pi$
$683$	8.72835e33			0.847000			0.423500	+	0.905896i	$0.360801\pi$
$684$		−	7.09340e32i		−	0.0676365i
$685$	−9.64560e33			−0.903737
$686$		−	1.67021e33i		−	0.153774i
$687$			1.50626e34i			1.36276i
$688$		−	1.61847e34i		−	1.43894i
$689$		−	2.02906e34i		−	1.77282i
$690$	−9.51892e33	−	7.47823e33i	−0.817332	−	0.642111i
$691$	1.92819e34			1.62710			0.813548	−	0.581498i	$-0.197533\pi$
$691$	1.92819e34			1.62710			0.813548	+	0.581498i	$0.197533\pi$
$692$	−1.64808e33			−0.136680
$693$	2.34462e32			0.0191106
$694$	−1.13872e34			−0.912229
$695$			2.03292e34i			1.60067i
$696$	7.36638e33			0.570089
$697$			7.69801e33i			0.585578i
$698$	−1.60647e34			−1.20118
$699$	4.68030e33			0.343991
$700$			4.26297e31i			0.00307989i
$701$			9.36458e32i			0.0665077i	0.999447	+	0.0332539i	$0.0105870\pi$
$701$			9.36458e32i			0.0665077i	−0.999447	+	0.0332539i	$0.989413\pi$
$702$	1.57436e34			1.09915
$703$	2.00472e34			1.37591
$704$		−	1.14134e34i		−	0.770093i
$705$			2.70489e34i			1.79424i
$706$	2.71910e34			1.77325
$707$		−	4.28066e32i		−	0.0274459i
$708$	−3.17159e33			−0.199930
$709$		−	1.59340e33i		−	0.0987573i	−0.998780	−	0.0493786i	$-0.984276\pi$
$709$		−	1.59340e33i		−	0.0987573i	0.998780	−	0.0493786i	$-0.0157241\pi$
$710$			7.80781e33i			0.475805i
$711$		−	5.14735e33i		−	0.308424i
$712$			2.13108e34i			1.25557i
$713$	−1.43129e34	+	1.82186e34i	−0.829186	+	1.05546i
$714$	−1.99192e33			−0.113473
$715$	−1.84674e34			−1.03451
$716$	−3.02423e33			−0.166594
$717$	6.76433e33			0.366433
$718$		−	1.14611e34i		−	0.610565i
$719$	−6.65329e33			−0.348570			−0.174285	−	0.984695i	$-0.555761\pi$
$719$	−6.65329e33			−0.348570			−0.174285	+	0.984695i	$0.555761\pi$
$720$		−	5.17512e33i		−	0.266643i
$721$	1.04300e33			0.0528521
$722$	2.96163e34			1.47599
$723$			1.95563e33i			0.0958575i
$724$		−	6.55674e33i		−	0.316101i
$725$	−3.16975e33			−0.150303
$726$	1.50525e33			0.0702054
$727$			1.97357e34i			0.905397i	0.891664	+	0.452699i	$0.149539\pi$
$727$			1.97357e34i			0.905397i	−0.891664	+	0.452699i	$0.850461\pi$
$728$		−	1.78967e33i		−	0.0807602i
$729$	1.33925e34			0.594472
$730$			1.93193e34i			0.843562i
$731$	−3.85054e34			−1.65392
$732$		−	4.09305e33i		−	0.172947i
$733$			2.89176e33i			0.120203i	0.998192	+	0.0601014i	$0.0191424\pi$
$733$			2.89176e33i			0.120203i	−0.998192	+	0.0601014i	$0.980858\pi$
$734$		−	9.32131e33i		−	0.381175i
$735$		−	2.38683e34i		−	0.960224i
$736$	−4.94062e33	+	6.28883e33i	−0.195545	+	0.248906i
$737$	4.43979e34			1.72883
$738$	−3.47272e33			−0.133043
$739$	−1.71747e34			−0.647374			−0.323687	−	0.946164i	$-0.604923\pi$
$739$	−1.71747e34			−0.647374			−0.323687	+	0.946164i	$0.604923\pi$
$740$	−3.28958e33			−0.122000
$741$		−	5.94039e34i		−	2.16769i
$742$	3.05262e33			0.109604
$743$		−	2.38671e34i		−	0.843207i	−0.906780	−	0.421604i	$-0.861467\pi$
$743$		−	2.38671e34i		−	0.843207i	0.906780	−	0.421604i	$-0.138533\pi$
$744$	−3.94512e34			−1.37147
$745$	−3.30436e34			−1.13035
$746$			3.65212e33i			0.122936i
$747$		−	8.61426e33i		−	0.285345i
$748$	6.20051e33			0.202120
$749$	3.29565e33			0.105720
$750$			4.17938e34i			1.31940i
$751$		−	4.82931e34i		−	1.50039i	−0.661214	−	0.750197i	$-0.729958\pi$
$751$		−	4.82931e34i		−	1.50039i	0.661214	−	0.750197i	$-0.270042\pi$
$752$	6.89577e34			2.10848
$753$		−	2.74294e34i		−	0.825424i
$754$	−2.52941e34			−0.749139
$755$		−	2.10392e34i		−	0.613291i
$756$			3.26201e32i			0.00935887i
$757$		−	2.20584e33i		−	0.0622908i	−0.999515	−	0.0311454i	$-0.990085\pi$
$757$		−	2.20584e33i		−	0.0622908i	0.999515	−	0.0311454i	$-0.00991549\pi$
$758$			5.75668e34i			1.60008i
$759$	−3.15042e34	−	2.47503e34i	−0.861921	−	0.677140i
$760$	4.42216e34			1.19089
$761$	−4.55885e34			−1.20848			−0.604240	−	0.796803i	$-0.706523\pi$
$761$	−4.55885e34			−1.20848			−0.604240	+	0.796803i	$0.706523\pi$
$762$	1.04287e34			0.272127
$763$	−2.95004e33			−0.0757764
$764$			3.58529e33i			0.0906575i
$765$	−1.23123e34			−0.306480
$766$		−	1.60635e34i		−	0.393637i
$767$	−5.72941e34			−1.38218
$768$	−2.22309e34			−0.527986
$769$			2.21352e34i			0.517569i	0.965935	+	0.258784i	$0.0833219\pi$
$769$			2.21352e34i			0.517569i	−0.965935	+	0.258784i	$0.916678\pi$
$770$		−	2.77833e33i		−	0.0639581i
$771$	−4.82292e34			−1.09309
$772$	3.11749e33			0.0695661
$773$		−	4.16692e34i		−	0.915507i	−0.889079	−	0.457753i	$-0.848654\pi$
$773$		−	4.16692e34i		−	0.915507i	0.889079	−	0.457753i	$-0.151346\pi$
$774$		−	1.73705e34i		−	0.375769i
$775$	1.69758e34			0.361585
$776$			1.37851e34i			0.289114i
$777$	3.49757e33			0.0722294
$778$		−	2.93991e34i		−	0.597832i
$779$		−	3.45381e34i		−	0.691590i
$780$			9.74768e33i			0.192206i
$781$			2.58411e34i			0.501762i
$782$	5.77352e34	+	4.53578e34i	1.10398	+	0.867303i
$783$	−2.42548e34			−0.456726
$784$	−6.08492e34			−1.12840
$785$	−2.75277e34			−0.502729
$786$	4.06660e34			0.731410
$787$		−	2.48536e34i		−	0.440243i	−0.975472	−	0.220121i	$-0.929355\pi$
$787$		−	2.48536e34i		−	0.440243i	0.975472	−	0.220121i	$-0.0706454\pi$
$788$	−2.00857e33			−0.0350406
$789$		−	2.03951e34i		−	0.350430i
$790$	−6.09952e34			−1.03222
$791$	−1.16742e32			−0.00194585
$792$		−	1.47159e34i		−	0.241593i
$793$		−	7.39400e34i		−	1.19564i
$794$	2.46580e34			0.392746
$795$	8.74717e34			1.37234
$796$		−	1.94988e34i		−	0.301336i
$797$			4.17727e34i			0.635906i	0.948107	+	0.317953i	$0.102995\pi$
$797$			4.17727e34i			0.635906i	−0.948107	+	0.317953i	$0.897005\pi$
$798$	8.93701e33			0.134016
$799$		−	1.64060e35i		−	2.42349i
$800$	5.85984e33			0.0852718
$801$			2.66211e34i			0.381624i
$802$			1.15980e35i			1.63792i
$803$			6.39400e34i			0.889582i
$804$		−	2.34346e34i		−	0.321207i
$805$	2.79906e33	−	3.56288e33i	0.0377974	−	0.0481117i
$806$	1.35464e35			1.80221
$807$	−6.04577e34			−0.792446
$808$	−2.68673e34			−0.346967
$809$	5.65741e34			0.719839			0.359920	−	0.932983i	$-0.382804\pi$
$809$	5.65741e34			0.719839			0.359920	+	0.932983i	$0.382804\pi$
$810$			8.80643e34i			1.10403i
$811$	−1.57646e35			−1.94730			−0.973649	−	0.228053i	$-0.926764\pi$
$811$	−1.57646e35			−1.94730			−0.973649	+	0.228053i	$0.926764\pi$
$812$		−	5.24083e32i		−	0.00637863i
$813$	−5.66235e33			−0.0679064
$814$	−7.90528e34			−0.934167
$815$			3.40882e34i			0.396929i
$816$			1.45513e35i			1.66963i
$817$	1.72760e35			1.95334
$818$	1.42454e35			1.58721
$819$		−	2.23563e33i		−	0.0245467i
$820$			5.66742e33i			0.0613224i
$821$	2.63899e34			0.281397			0.140699	−	0.990052i	$-0.455065\pi$
$821$	2.63899e34			0.281397			0.140699	+	0.990052i	$0.455065\pi$
$822$			1.22349e35i			1.28570i
$823$	5.96975e34			0.618242			0.309121	−	0.951023i	$-0.399965\pi$
$823$	5.96975e34			0.618242			0.309121	+	0.951023i	$0.399965\pi$
$824$		−	6.54634e34i		−	0.668147i
$825$			2.93551e34i			0.295282i
$826$		−	8.61960e33i		−	0.0854528i
$827$		−	1.86687e34i		−	0.182410i	−0.995832	−	0.0912051i	$-0.970928\pi$
$827$		−	1.86687e34i		−	0.182410i	0.995832	−	0.0912051i	$-0.0290719\pi$
$828$	−2.81804e33	+	3.58704e33i	−0.0271383	+	0.0345439i
$829$	1.04755e35			0.994304			0.497152	−	0.867663i	$-0.334379\pi$
$829$	1.04755e35			0.994304			0.497152	+	0.867663i	$0.334379\pi$
$830$	−1.02077e35			−0.954976
$831$	−7.77072e34			−0.716554
$832$	−1.08828e35			−0.989151
$833$			1.44768e35i			1.29698i
$834$	2.57864e35			2.27719
$835$			9.83341e34i			0.855986i
$836$	−2.78194e34			−0.238711
$837$	1.29898e35			1.09875
$838$		−	1.79618e35i		−	1.49769i
$839$			1.47806e35i			1.21493i	0.794348	+	0.607463i	$0.207813\pi$
$839$			1.47806e35i			1.21493i	−0.794348	+	0.607463i	$0.792187\pi$
$840$	7.71519e33			0.0625165
$841$	−8.62165e34			−0.688714
$842$			1.20887e35i			0.951997i
$843$			6.69152e34i			0.519510i
$844$	−2.53898e34			−0.194334
$845$			6.28178e34i			0.474026i
$846$	7.40104e34			0.550615
$847$			5.63409e32i			0.00413259i
$848$		−	2.22998e35i		−	1.61269i
$849$			4.49601e34i			0.320579i
$850$		−	5.37968e34i		−	0.378207i
$851$	−1.01376e35	−	7.96427e34i	−0.702717	−	0.552067i
$852$	1.36397e34			0.0932244
$853$	−1.34913e35			−0.909212			−0.454606	−	0.890693i	$-0.650220\pi$
$853$	−1.34913e35			−0.909212			−0.454606	+	0.890693i	$0.650220\pi$
$854$	1.11239e34			0.0739200
$855$	5.52407e34			0.361965
$856$		−	2.06849e35i		−	1.33650i
$857$	−5.21216e34			−0.332084			−0.166042	−	0.986119i	$-0.553099\pi$
$857$	−5.21216e34			−0.332084			−0.166042	+	0.986119i	$0.553099\pi$
$858$			2.34249e35i			1.47174i
$859$	−1.43968e35			−0.891965			−0.445982	−	0.895042i	$-0.647146\pi$
$859$	−1.43968e35			−0.891965			−0.445982	+	0.895042i	$0.647146\pi$
$860$	−2.83484e34			−0.173200
$861$		−	6.02575e33i		−	0.0363055i
$862$			6.15519e34i			0.365725i
$863$	2.66313e35			1.56050			0.780249	−	0.625469i	$-0.215092\pi$
$863$	2.66313e35			1.56050			0.780249	+	0.625469i	$0.215092\pi$
$864$	4.48392e34			0.259115
$865$		−	1.28346e35i		−	0.731457i
$866$		−	1.73404e34i		−	0.0974642i
$867$	1.42495e35			0.789895
$868$			2.80677e33i			0.0153451i
$869$	−2.01872e35			−1.08853
$870$		−	1.09041e35i		−	0.579909i
$871$		−	4.23341e35i		−	2.22061i
$872$			1.85158e35i			0.957953i
$873$			1.72201e34i			0.0878747i
$874$	−2.59036e35	−	2.03504e35i	−1.30384	−	1.02432i
$875$	−1.56432e34			−0.0776656
$876$	3.37495e34			0.165279
$877$	1.98741e35			0.960047			0.480024	−	0.877256i	$-0.340628\pi$
$877$	1.98741e35			0.960047			0.480024	+	0.877256i	$0.340628\pi$
$878$	−2.57018e35			−1.22470
$879$			1.00707e35i			0.473360i
$880$	−2.02961e35			−0.941069
$881$		−	3.75023e35i		−	1.71533i	−0.514211	−	0.857664i	$-0.671915\pi$
$881$		−	3.75023e35i		−	1.71533i	0.514211	−	0.857664i	$-0.328085\pi$
$882$	−6.53077e34			−0.294674
$883$	−2.65749e35			−1.18289			−0.591443	−	0.806347i	$-0.701441\pi$
$883$	−2.65749e35			−1.18289			−0.591443	+	0.806347i	$0.701441\pi$
$884$		−	5.91227e34i		−	0.259614i
$885$		−	2.46992e35i		−	1.06995i
$886$	9.26721e34			0.396045
$887$	4.00688e35			1.68936			0.844681	−	0.535270i	$-0.179790\pi$
$887$	4.00688e35			1.68936			0.844681	+	0.535270i	$0.179790\pi$
$888$		−	2.19523e35i		−	0.913112i
$889$			3.90341e33i			0.0160186i
$890$	3.15455e35			1.27720
$891$			2.91461e35i			1.16426i
$892$	−6.57720e34			−0.259217
$893$			7.36075e35i			2.86223i
$894$			4.19141e35i			1.60809i
$895$		−	2.35516e35i		−	0.891545i
$896$		−	2.24387e34i		−	0.0838111i
$897$	−2.35997e35	+	3.00397e35i	−0.869757	+	1.10710i
$898$	4.03048e35			1.46568
$899$	−2.08698e35			−0.748863
$900$	3.34234e33			0.0118343
$901$	−5.30543e35			−1.85363
$902$			1.36195e35i			0.469552i
$903$	3.01408e34			0.102542
$904$			7.32724e33i			0.0245991i
$905$	5.10614e35			1.69165
$906$	−2.66871e35			−0.872496
$907$			1.71582e35i			0.553585i	0.960930	+	0.276792i	$0.0892714\pi$
$907$			1.71582e35i			0.553585i	−0.960930	+	0.276792i	$0.910729\pi$
$908$		−	4.96097e34i		−	0.157956i
$909$	−3.35621e34			−0.105459
$910$	−2.64918e34			−0.0821513
$911$			1.09030e35i			0.333675i	0.985984	+	0.166838i	$0.0533556\pi$
$911$			1.09030e35i			0.333675i	−0.985984	+	0.166838i	$0.946644\pi$
$912$		−	6.52862e35i		−	1.97189i
$913$	−3.37840e35			−1.00707
$914$			2.05074e35i			0.603333i
$915$	3.18751e35			0.925547
$916$		−	6.72604e34i		−	0.192759i
$917$			1.52211e34i			0.0430540i
$918$		−	4.11651e35i		−	1.14926i
$919$		−	2.45751e35i		−	0.677188i	−0.940933	−	0.338594i	$-0.890049\pi$
$919$		−	2.45751e35i		−	0.677188i	0.940933	−	0.338594i	$-0.109951\pi$
$920$	−2.23622e35	−	1.75682e35i	−0.608221	−	0.477829i
$921$	6.90820e35			1.85460
$922$	−4.25674e35			−1.12799
$923$	2.46398e35			0.644491
$924$	−4.85355e33			−0.0125313
$925$			9.44605e34i			0.240741i
$926$	3.42705e35			0.862161
$927$		−	8.17757e34i		−	0.203080i
$928$	−7.20399e34			−0.176603
$929$	3.00096e35			0.726227			0.363113	−	0.931745i	$-0.381714\pi$
$929$	3.00096e35			0.726227			0.363113	+	0.931745i	$0.381714\pi$
$930$			5.83979e35i			1.39509i
$931$		−	6.49522e35i		−	1.53178i
$932$	−2.08994e34			−0.0486567
$933$	−3.52003e35			−0.809034
$934$		−	5.69754e35i		−	1.29278i
$935$			4.82872e35i			1.08167i
$936$	−1.40318e35			−0.310315
$937$		−	4.35312e35i		−	0.950443i	−0.879866	−	0.475221i	$-0.842368\pi$
$937$		−	4.35312e35i		−	0.950443i	0.879866	−	0.475221i	$-0.157632\pi$
$938$	6.36894e34			0.137288
$939$		−	2.10274e35i		−	0.447506i
$940$		−	1.20784e35i		−	0.253790i
$941$			8.81005e35i			1.82769i	0.406061	+	0.913846i	$0.366902\pi$
$941$			8.81005e35i			1.82769i	−0.406061	+	0.913846i	$0.633098\pi$
$942$			3.49174e35i			0.715205i
$943$	−1.37212e35	+	1.74654e35i	−0.277492	+	0.353215i
$944$	−6.29675e35			−1.25734
$945$	−2.54033e34			−0.0500850
$946$	−6.81249e35			−1.32621
$947$	−2.35216e35			−0.452133			−0.226067	−	0.974112i	$-0.572587\pi$
$947$	−2.35216e35			−0.452133			−0.226067	+	0.974112i	$0.572587\pi$
$948$			1.06554e35i			0.202242i
$949$	6.09677e35			1.14263
$950$			2.41366e35i			0.446676i
$951$	4.04324e35			0.738862
$952$	−4.67950e34			−0.0844415
$953$		−	3.94863e35i		−	0.703609i	−0.936074	−	0.351804i	$-0.885568\pi$
$953$		−	3.94863e35i		−	0.703609i	0.936074	−	0.351804i	$-0.114432\pi$
$954$		−	2.39338e35i		−	0.421144i
$955$	−2.79209e35			−0.485164
$956$	−3.02054e34			−0.0518310
$957$		−	3.60888e35i		−	0.611546i
$958$		−	1.09051e36i		−	1.82492i
$959$	−4.57946e34			−0.0756818
$960$		−	4.69153e35i		−	0.765703i
$961$	4.97286e35			0.801541
$962$			7.53780e35i			1.19990i
$963$		−	2.58392e35i		−	0.406223i
$964$		−	8.73264e33i		−	0.0135588i
$965$			2.42778e35i			0.372291i
$966$	−4.51932e34	−	3.55046e34i	−0.0684459	−	0.0537723i
$967$	−8.15090e35			−1.21924			−0.609618	−	0.792696i	$-0.708677\pi$
$967$	−8.15090e35			−1.21924			−0.609618	+	0.792696i	$0.708677\pi$
$968$	3.53620e34			0.0522436
$969$	−1.55325e36			−2.26650
$970$	2.04055e35			0.294094
$971$			1.09725e35i			0.156198i	0.996946	+	0.0780992i	$0.0248851\pi$
$971$			1.09725e35i			0.156198i	−0.996946	+	0.0780992i	$0.975115\pi$
$972$	6.08540e34			0.0855645
$973$			9.65172e34i			0.134045i
$974$	4.78043e35			0.655782
$975$	2.79905e35			0.379277
$976$		−	8.12617e35i		−	1.08765i
$977$			4.17329e35i			0.551752i	0.961193	+	0.275876i	$0.0889679\pi$
$977$			4.17329e35i			0.551752i	−0.961193	+	0.275876i	$0.911032\pi$
$978$	4.32390e35			0.564690
$979$	1.04404e36			1.34687
$980$			1.06581e35i			0.135821i
$981$			2.31296e35i			0.291165i
$982$	6.81145e35			0.847036
$983$			6.42724e35i			0.789554i	0.918777	+	0.394777i	$0.129178\pi$
$983$			6.42724e35i			0.789554i	−0.918777	+	0.394777i	$0.870822\pi$
$984$	−3.78203e35			−0.458969
$985$		−	1.56420e35i		−	0.187524i
$986$			6.61369e35i			0.783287i
$987$			1.28420e35i			0.150255i
$988$			2.65262e35i			0.306613i
$989$	−8.73622e35	−	6.86332e35i	−0.997626	−	0.783753i
$990$	−2.17833e35			−0.245754
$991$	−6.75133e35			−0.752498			−0.376249	−	0.926519i	$-0.622786\pi$
$991$	−6.75133e35			−0.752498			−0.376249	+	0.926519i	$0.622786\pi$
$992$	3.85815e35			0.424854
$993$	−7.37666e35			−0.802544
$994$			3.70693e34i			0.0398454i
$995$	1.51849e36			1.61263
$996$			1.78322e35i			0.187108i
$997$	−2.66318e34			−0.0276095			−0.0138047	−	0.999905i	$-0.504394\pi$
$997$	−2.66318e34			−0.0276095			−0.0138047	+	0.999905i	$0.504394\pi$
$998$	4.22913e35			0.433196
$999$			7.22808e35i			0.731539i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.25.b.c.22.14	yes	44
23.22	odd	2	inner	23.25.b.c.22.13	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.25.b.c.22.13	✓	44	23.22	odd	2	inner
23.25.b.c.22.14	yes	44	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 25 \)
Character orbit:	\([\chi]\)	\(=\)	23.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4410.99 q^{2} -600091. q^{3} +2.67964e6 q^{4} +2.08680e8i q^{5} +2.64700e9 q^{6} +9.90757e8i q^{7} +6.21843e10 q^{8} +7.76795e10 q^{9} -9.20488e11i q^{10} -3.04648e12i q^{11} -1.60803e12 q^{12} -2.90487e13 q^{13} -4.37022e12i q^{14} -1.25227e14i q^{15} -3.19251e14 q^{16} +7.59542e14i q^{17} -3.42644e14 q^{18} -3.40778e15i q^{19} +5.59189e14i q^{20} -5.94544e14i q^{21} +1.34380e16i q^{22} +(-1.35383e16 + 1.72327e16i) q^{23} -3.73162e16 q^{24} +1.60571e16 q^{25} +1.28133e17 q^{26} +1.22869e17 q^{27} +2.65487e15i q^{28} -1.97404e17 q^{29} +5.52376e17i q^{30} +1.05721e18 q^{31} +3.64936e17 q^{32} +1.82817e18i q^{33} -3.35033e18i q^{34} -2.06752e17 q^{35} +2.08153e17 q^{36} +5.88277e18i q^{37} +1.50317e19i q^{38} +1.74318e19 q^{39} +1.29766e19i q^{40} +1.01351e19 q^{41} +2.62253e18i q^{42} +5.06956e19i q^{43} -8.16349e18i q^{44} +1.62102e19i q^{45} +(5.97173e19 - 7.60132e19i) q^{46} -2.15998e20 q^{47} +1.91580e20 q^{48} +1.90600e20 q^{49} -7.08279e19 q^{50} -4.55794e20i q^{51} -7.78400e19 q^{52} +6.98504e20i q^{53} -5.41973e20 q^{54} +6.35742e20 q^{55} +6.16095e19i q^{56} +2.04498e21i q^{57} +8.70748e20 q^{58} +1.97235e21 q^{59} -3.35564e20i q^{60} +2.54538e21i q^{61} -4.66336e21 q^{62} +7.69615e19i q^{63} +3.74642e21 q^{64} -6.06189e21i q^{65} -8.06403e21i q^{66} +1.45735e22i q^{67} +2.03530e21i q^{68} +(8.12421e21 - 1.03412e22i) q^{69} +9.11979e20 q^{70} -8.48225e21 q^{71} +4.83044e21 q^{72} -2.09881e22 q^{73} -2.59489e22i q^{74} -9.63574e21 q^{75} -9.13163e21i q^{76} +3.01833e21 q^{77} -7.68917e22 q^{78} -6.62640e22i q^{79} -6.66215e22i q^{80} -9.56713e22 q^{81} -4.47057e22 q^{82} -1.10895e23i q^{83} -1.59317e21i q^{84} -1.58501e23 q^{85} -2.23618e23i q^{86} +1.18460e23 q^{87} -1.89444e23i q^{88} +3.42705e23i q^{89} -7.15030e22i q^{90} -2.87802e22i q^{91} +(-3.62778e22 + 4.61774e22i) q^{92} -6.34424e23 q^{93} +9.52767e23 q^{94} +7.11137e23 q^{95} -2.18995e23 q^{96} +2.21681e23i q^{97} -8.40734e23 q^{98} -2.36649e23i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 4232 q^{2} - 434562 q^{3} + 317760360 q^{4} - 8460029520 q^{6} - 198307023760 q^{8} + 4220041988298 q^{9} - 67439597688792 q^{12} + 5771152551358 q^{13} + 18\!\cdots\!92 q^{16} + 18\!\cdots\!68 q^{18}+ \cdots - 20\!\cdots\!92 q^{98}+O(q^{100}) \) 44 * q - 4232 * q^2 - 434562 * q^3 + 317760360 * q^4 - 8460029520 * q^6 - 198307023760 * q^8 + 4220041988298 * q^9 - 67439597688792 * q^12 + 5771152551358 * q^13 + 1801550792530192 * q^16 + 1842830558165568 * q^18 - 117204213263210644 * q^23 - 186493005437450784 * q^24 - 689533084157602612 * q^25 - 548650296251047576 * q^26 + 824037505793640630 * q^27 - 1583078054945709602 * q^29 - 77249813729122274 * q^31 - 2838716832733708512 * q^32 + 3418569899175948192 * q^35 + 71181245116739335248 * q^36 + 47106572467817156310 * q^39 - 9150679195666184738 * q^41 - 153049487518536134480 * q^46 + 22735751396127769438 * q^47 - 1317482931964495330032 * q^48 - 1842110772006482246836 * q^49 + 284936617115007894520 * q^50 + 207129175371045152568 * q^52 - 381774025126375304544 * q^54 - 5430040696094013021792 * q^55 - 2168901871328366220760 * q^58 + 16048018791948427185304 * q^59 + 14054450375064171442400 * q^62 + 20310379126091866412192 * q^64 + 24476879859710435470878 * q^69 - 118028399895318845638416 * q^70 - 68204988047209908888578 * q^71 - 106777935582637627887744 * q^72 - 7319375899831086678722 * q^73 + 12913295383070041819998 * q^75 + 111116199573084838704480 * q^77 - 422583593213386075404144 * q^78 - 331350288185757013618680 * q^81 + 1000764218021118649437320 * q^82 - 113385735487939722862944 * q^85 - 248828610584854760185290 * q^87 - 4238455111972177116774696 * q^92 + 4492289396741153284965270 * q^93 - 1602622056539190351258592 * q^94 - 1668692394291208047471936 * q^95 - 12092663288748189077973504 * q^96 - 2067304853876486831513192 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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