LMFDB - Embedded newform 5.24.b.a.4.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,24,Mod(4,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 24, names="a")

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

chi := DirichletCharacter("5.4");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 24 $
Character orbit:	$[\chi]$	$=$	5.b (of order $2$, degree $1$, 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:	$16.7602018673$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 15644845 x^{8} + 79349217360160 x^{6} + \cdots + 34\!\cdots\!24 $ x^10 + 15644845x^8 + 79349217360160x^6 + 150324497245503837440x^4 + 76751558562242644579450880x^2 + 3490504262440921471663078375424
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{12}\cdot 5^{22} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			4.5
Root			$-224.285i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.24.b.a.4.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-448.570i q^{2} -302181. i q^{3} +8.18739e6 q^{4} +(1.05706e8 + 2.73336e7i) q^{5} -1.35549e8 q^{6} +8.28173e9i q^{7} -7.43550e9i q^{8} +2.83002e9 q^{9} +O(q^{10})$	\(q-448.570i q^{2} -302181. i q^{3} +8.18739e6 q^{4} +(1.05706e8 + 2.73336e7i) q^{5} -1.35549e8 q^{6} +8.28173e9i q^{7} -7.43550e9i q^{8} +2.83002e9 q^{9} +(1.22610e10 - 4.74167e10i) q^{10} +1.31538e11 q^{11} -2.47407e12i q^{12} +1.05183e13i q^{13} +3.71494e12 q^{14} +(8.25967e12 - 3.19424e13i) q^{15} +6.53455e13 q^{16} -6.97399e13i q^{17} -1.26946e12i q^{18} +3.53693e14 q^{19} +(8.65458e14 + 2.23791e14i) q^{20} +2.50258e15 q^{21} -5.90041e13i q^{22} -5.24907e15i q^{23} -2.24686e15 q^{24} +(1.04267e16 + 5.77865e15i) q^{25} +4.71818e15 q^{26} -2.93034e16i q^{27} +6.78058e16i q^{28} -1.00934e17 q^{29} +(-1.43284e16 - 3.70504e15i) q^{30} -1.02500e17 q^{31} -9.16855e16i q^{32} -3.97483e16i q^{33} -3.12833e16 q^{34} +(-2.26369e17 + 8.75430e17i) q^{35} +2.31705e16 q^{36} -1.24538e18i q^{37} -1.58656e17i q^{38} +3.17842e18 q^{39} +(2.03239e17 - 7.85979e17i) q^{40} +1.51172e18 q^{41} -1.12258e18i q^{42} +3.61711e18i q^{43} +1.07695e18 q^{44} +(2.99151e17 + 7.73546e16i) q^{45} -2.35458e18 q^{46} +7.84743e18i q^{47} -1.97461e19i q^{48} -4.12183e19 q^{49} +(2.59213e18 - 4.67710e18i) q^{50} -2.10741e19 q^{51} +8.61172e19i q^{52} -2.82290e19i q^{53} -1.31446e19 q^{54} +(1.39044e19 + 3.59540e18i) q^{55} +6.15788e19 q^{56} -1.06879e20i q^{57} +4.52762e19i q^{58} +2.58305e20 q^{59} +(6.76252e19 - 2.61525e20i) q^{60} -7.40067e19 q^{61} +4.59782e19i q^{62} +2.34375e19i q^{63} +5.07030e20 q^{64} +(-2.87502e20 + 1.11185e21i) q^{65} -1.78299e19 q^{66} -9.06429e20i q^{67} -5.70988e20i q^{68} -1.58617e21 q^{69} +(3.92692e20 + 1.01542e20i) q^{70} -2.88130e21 q^{71} -2.10426e19i q^{72} +3.52488e21i q^{73} -5.58641e20 q^{74} +(1.74620e21 - 3.15074e21i) q^{75} +2.89582e21 q^{76} +1.08936e21i q^{77} -1.42574e21i q^{78} +1.32853e21 q^{79} +(6.90742e21 + 1.78612e21i) q^{80} -8.58850e21 q^{81} -6.78114e20i q^{82} -1.00287e22i q^{83} +2.04896e22 q^{84} +(1.90624e21 - 7.37194e21i) q^{85} +1.62253e21 q^{86} +3.05004e22i q^{87} -9.78051e20i q^{88} -1.08101e21 q^{89} +(3.46990e19 - 1.34190e20i) q^{90} -8.71095e22 q^{91} -4.29762e22i q^{92} +3.09734e22i q^{93} +3.52012e21 q^{94} +(3.73875e22 + 9.66768e21i) q^{95} -2.77056e22 q^{96} -1.74541e22i q^{97} +1.84893e22i q^{98} +3.72256e20 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 41272680 q^{4} + 124761750 q^{5} - 2262077880 q^{6} - 189250631370 q^{9}+O(q^{10}) $ 10 * q - 41272680 * q^4 + 124761750 * q^5 - 2262077880 * q^6 - 189250631370 * q^9	$ 10 q - 41272680 q^{4} + 124761750 q^{5} - 2262077880 q^{6} - 189250631370 q^{9} - 992748199000 q^{10} - 1448637536280 q^{11} + 20750531044440 q^{14} - 14566613457000 q^{15} + 307971806876960 q^{16} + 887626815301400 q^{19} - 23\!\cdots\!00 q^{20}+ \cdots + 41\!\cdots\!60 q^{99}+O(q^{100}) $ 10 * q - 41272680 * q^4 + 124761750 * q^5 - 2262077880 * q^6 - 189250631370 * q^9 - 992748199000 * q^10 - 1448637536280 * q^11 + 20750531044440 * q^14 - 14566613457000 * q^15 + 307971806876960 * q^16 + 887626815301400 * q^19 - 2363707755099000 * q^20 - 781158183715080 * q^21 + 58473619965621600 * q^24 - 15436708968968750 * q^25 - 49259739315596880 * q^26 + 68538893585329500 * q^29 - 283259561673249000 * q^30 - 303703652281842880 * q^31 - 288299835336191360 * q^34 + 568057466315481000 * q^35 + 3242003939215214760 * q^36 - 8628905972055907440 * q^39 + 9426000384456940000 * q^40 - 6658832954283527580 * q^41 + 14990828914855427040 * q^44 - 8490880963475889750 * q^45 + 16736621075351903320 * q^46 + 51294362631233173870 * q^49 - 96456356624588250000 * q^50 - 117334349391643270080 * q^51 + 6367892697021344400 * q^54 + 8046234911696751000 * q^55 - 93285217288146540000 * q^56 + 461218638014732785800 * q^59 + 1248088814097510276000 * q^60 + 202894074812420701820 * q^61 - 2597882075263561124480 * q^64 + 404224351485216078000 * q^65 - 2067527591150630859360 * q^66 + 1761142984477245282360 * q^69 + 2651929720118465517000 * q^70 - 6362428274364321596880 * q^71 + 21369976437605310645840 * q^74 - 1268180400269994750000 * q^75 - 28533821601830896716000 * q^76 + 8008906997916696975200 * q^79 + 50390556129429851388000 * q^80 - 63620987817532049079390 * q^81 + 26983560053969205971040 * q^84 + 58719411820058643416000 * q^85 - 73642932902287825779480 * q^86 + 17045340818835962686500 * q^89 + 218378490181286718303000 * q^90 - 261754857315780277067280 * q^91 + 163995755653951693894840 * q^94 + 287254967024630517105000 * q^95 - 1029134712278532215134080 * q^96 + 411070875879864759534360 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

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

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 $

$2$		−	448.570i		−	0.154876i	−0.996997	−	0.0774382i	$-0.975326\pi$
$2$		−	448.570i		−	0.154876i	0.996997	−	0.0774382i	$-0.0246741\pi$
$3$		−	302181.i		−	0.984855i	−0.870353	−	0.492427i	$-0.836110\pi$
$3$		−	302181.i		−	0.984855i	0.870353	−	0.492427i	$-0.163890\pi$
$4$	8.18739e6			0.976013
$5$	1.05706e8	+	2.73336e7i	0.968156	+	0.250346i
$5$	1.05706e8	+	2.73336e7i	0.968156	+	0.250346i
$6$	−1.35549e8			−0.152531
$7$			8.28173e9i			1.58305i	0.611139	+	0.791523i	$0.290712\pi$
$7$			8.28173e9i			1.58305i	−0.611139	+	0.791523i	$0.709288\pi$
$8$		−	7.43550e9i		−	0.306038i
$9$	2.83002e9			0.0300609
$10$	1.22610e10	−	4.74167e10i	0.0387727	−	0.149945i
$11$	1.31538e11			0.139007			0.0695033	−	0.997582i	$-0.477859\pi$
$11$	1.31538e11			0.139007			0.0695033	+	0.997582i	$0.477859\pi$
$12$		−	2.47407e12i		−	0.961231i
$13$			1.05183e13i			1.62778i	0.581019	+	0.813890i	$0.302654\pi$
$13$			1.05183e13i			1.62778i	−0.581019	+	0.813890i	$0.697346\pi$
$14$	3.71494e12			0.245177
$15$	8.25967e12	−	3.19424e13i	0.246555	−	0.953494i
$16$	6.53455e13			0.928615
$17$		−	6.97399e13i		−	0.493536i	−0.969075	−	0.246768i	$-0.920631\pi$
$17$		−	6.97399e13i		−	0.493536i	0.969075	−	0.246768i	$-0.0793686\pi$
$18$		−	1.26946e12i		−	0.00465572i
$19$	3.53693e14			0.696562			0.348281	−	0.937390i	$-0.386766\pi$
$19$	3.53693e14			0.696562			0.348281	+	0.937390i	$0.386766\pi$
$20$	8.65458e14	+	2.23791e14i	0.944933	+	0.244341i
$21$	2.50258e15			1.55907
$22$		−	5.90041e13i		−	0.0215289i
$23$		−	5.24907e15i		−	1.14871i	−0.818605	−	0.574357i	$-0.805252\pi$
$23$		−	5.24907e15i		−	1.14871i	0.818605	−	0.574357i	$-0.194748\pi$
$24$	−2.24686e15			−0.301403
$25$	1.04267e16	+	5.77865e15i	0.874654	+	0.484749i
$26$	4.71818e15			0.252105
$27$		−	2.93034e16i		−	1.01446i
$28$			6.78058e16i			1.54507i
$29$	−1.00934e17			−1.53625			−0.768126	−	0.640299i	$-0.778810\pi$
$29$	−1.00934e17			−1.53625			−0.768126	+	0.640299i	$0.778810\pi$
$30$	−1.43284e16	−	3.70504e15i	−0.147674	−	0.0381855i
$31$	−1.02500e17			−0.724540			−0.362270	−	0.932073i	$-0.617998\pi$
$31$	−1.02500e17			−0.724540			−0.362270	+	0.932073i	$0.617998\pi$
$32$		−	9.16855e16i		−	0.449859i
$33$		−	3.97483e16i		−	0.136901i
$34$	−3.12833e16			−0.0764371
$35$	−2.26369e17	+	8.75430e17i	−0.396310	+	1.53264i
$36$	2.31705e16			0.0293398
$37$		−	1.24538e18i		−	1.15075i	−0.817888	−	0.575377i	$-0.804855\pi$
$37$		−	1.24538e18i		−	1.15075i	0.817888	−	0.575377i	$-0.195145\pi$
$38$		−	1.58656e17i		−	0.107881i
$39$	3.17842e18			1.60313
$40$	2.03239e17	−	7.85979e17i	0.0766155	−	0.296293i
$41$	1.51172e18			0.429001			0.214500	−	0.976724i	$-0.431188\pi$
$41$	1.51172e18			0.429001			0.214500	+	0.976724i	$0.431188\pi$
$42$		−	1.12258e18i		−	0.241463i
$43$			3.61711e18i			0.593573i	0.954944	+	0.296787i	$0.0959150\pi$
$43$			3.61711e18i			0.593573i	−0.954944	+	0.296787i	$0.904085\pi$
$44$	1.07695e18			0.135672
$45$	2.99151e17	+	7.73546e16i	0.0291036	+	0.00752562i
$46$	−2.35458e18			−0.177909
$47$			7.84743e18i			0.463022i	0.972832	+	0.231511i	$0.0743670\pi$
$47$			7.84743e18i			0.463022i	−0.972832	+	0.231511i	$0.925633\pi$
$48$		−	1.97461e19i		−	0.914551i
$49$	−4.12183e19			−1.50604
$50$	2.59213e18	−	4.67710e18i	0.0750762	−	0.135463i
$51$	−2.10741e19			−0.486061
$52$			8.61172e19i			1.58873i
$53$		−	2.82290e19i		−	0.418334i	−0.977880	−	0.209167i	$-0.932925\pi$
$53$		−	2.82290e19i		−	0.418334i	0.977880	−	0.209167i	$-0.0670753\pi$
$54$	−1.31446e19			−0.157116
$55$	1.39044e19	+	3.59540e18i	0.134580	+	0.0347998i
$56$	6.15788e19			0.484472
$57$		−	1.06879e20i		−	0.686012i
$58$			4.52762e19i			0.237929i
$59$	2.58305e20			1.11516			0.557578	−	0.830125i	$-0.311731\pi$
$59$	2.58305e20			1.11516			0.557578	+	0.830125i	$0.311731\pi$
$60$	6.76252e19	−	2.61525e20i	0.240641	−	0.930622i
$61$	−7.40067e19			−0.217760			−0.108880	−	0.994055i	$-0.534726\pi$
$61$	−7.40067e19			−0.217760			−0.108880	+	0.994055i	$0.534726\pi$
$62$			4.59782e19i			0.112214i
$63$			2.34375e19i			0.0475877i
$64$	5.07030e20			0.858943
$65$	−2.87502e20	+	1.11185e21i	−0.407509	+	1.57595i
$66$	−1.78299e19			−0.0212028
$67$		−	9.06429e20i		−	0.906721i	−0.891327	−	0.453361i	$-0.850225\pi$
$67$		−	9.06429e20i		−	0.906721i	0.891327	−	0.453361i	$-0.149775\pi$
$68$		−	5.70988e20i		−	0.481698i
$69$	−1.58617e21			−1.13132
$70$	3.92692e20	+	1.01542e20i	0.237369	+	0.0613790i
$71$	−2.88130e21			−1.47951			−0.739754	−	0.672878i	$-0.765058\pi$
$71$	−2.88130e21			−1.47951			−0.739754	+	0.672878i	$0.765058\pi$
$72$		−	2.10426e19i		−	0.00919976i
$73$			3.52488e21i			1.31502i	0.753447	+	0.657508i	$0.228390\pi$
$73$			3.52488e21i			1.31502i	−0.753447	+	0.657508i	$0.771610\pi$
$74$	−5.58641e20			−0.178225
$75$	1.74620e21	−	3.15074e21i	0.477407	−	0.861407i
$76$	2.89582e21			0.679853
$77$			1.08936e21i			0.220054i
$78$		−	1.42574e21i		−	0.248287i
$79$	1.32853e21			0.199829			0.0999145	−	0.994996i	$-0.468143\pi$
$79$	1.32853e21			0.199829			0.0999145	+	0.994996i	$0.468143\pi$
$80$	6.90742e21	+	1.78612e21i	0.899045	+	0.232475i
$81$	−8.58850e21			−0.969035
$82$		−	6.78114e20i		−	0.0664421i
$83$		−	1.00287e22i		−	0.854767i	−0.904070	−	0.427383i	$-0.859435\pi$
$83$		−	1.00287e22i		−	0.854767i	0.904070	−	0.427383i	$-0.140565\pi$
$84$	2.04896e22			1.52167
$85$	1.90624e21	−	7.37194e21i	0.123555	−	0.477820i
$86$	1.62253e21			0.0919306
$87$			3.05004e22i			1.51298i
$88$		−	9.78051e20i		−	0.0425413i
$89$	−1.08101e21			−0.0412899			−0.0206449	−	0.999787i	$-0.506572\pi$
$89$	−1.08101e21			−0.0412899			−0.0206449	+	0.999787i	$0.506572\pi$
$90$	3.46990e19	−	1.34190e20i	0.00116554	−	0.00450746i
$91$	−8.71095e22			−2.57685
$92$		−	4.29762e22i		−	1.12116i
$93$			3.09734e22i			0.713567i
$94$	3.52012e21			0.0717113
$95$	3.73875e22	+	9.66768e21i	0.674381	+	0.174382i
$96$	−2.77056e22			−0.443045
$97$		−	1.74541e22i		−	0.247755i	−0.992298	−	0.123877i	$-0.960467\pi$
$97$		−	1.74541e22i		−	0.247755i	0.992298	−	0.123877i	$-0.0395329\pi$
$98$			1.84893e22i			0.233249i
$99$	3.72256e20			0.00417866
$100$	8.53673e22	+	4.73121e22i	0.853673	+	0.473121i
$101$	−1.22364e23			−1.09134			−0.545668	−	0.838001i	$-0.683724\pi$
$101$	−1.22364e23			−1.09134			−0.545668	+	0.838001i	$0.683724\pi$
$102$			9.45320e21i			0.0752795i
$103$		−	6.36214e22i		−	0.452872i	−0.974026	−	0.226436i	$-0.927293\pi$
$103$		−	6.36214e22i		−	0.452872i	0.974026	−	0.226436i	$-0.0727074\pi$
$104$	7.82086e22			0.498162
$105$	2.64538e23	+	6.84044e22i	1.50942	+	0.390308i
$106$	−1.26627e22			−0.0647902
$107$		−	2.34788e23i		−	1.07836i	−0.842191	−	0.539179i	$-0.818734\pi$
$107$		−	2.34788e23i		−	1.07836i	0.842191	−	0.539179i	$-0.181266\pi$
$108$		−	2.39919e23i		−	0.990127i
$109$	2.62018e23			0.972583			0.486291	−	0.873797i	$-0.338349\pi$
$109$	2.62018e23			0.972583			0.486291	+	0.873797i	$0.338349\pi$
$110$	1.61279e21	−	6.23710e21i	0.00538967	−	0.0208433i
$111$	−3.76330e23			−1.13333
$112$			5.41174e23i			1.47004i
$113$			5.52325e23i			1.35454i	0.735733	+	0.677271i	$0.236838\pi$
$113$			5.52325e23i			1.35454i	−0.735733	+	0.677271i	$0.763162\pi$
$114$	−4.79428e22			−0.106247
$115$	1.43476e23	−	5.54859e23i	0.287576	−	1.11214i
$116$	−8.26390e23			−1.49940
$117$			2.97670e22i			0.0489324i
$118$		−	1.15868e23i		−	0.172711i
$119$	5.77567e23			0.781290
$120$	−2.37508e23	−	6.14148e22i	−0.291805	−	0.0754551i
$121$	−8.78128e23			−0.980677
$122$			3.31972e22i			0.0337259i
$123$		−	4.56813e23i		−	0.422503i
$124$	−8.39204e23			−0.707161
$125$	9.44214e23	+	8.95838e23i	0.725446	+	0.688279i
$126$	1.05134e22			0.00737022
$127$			3.54067e23i			0.226643i	0.993558	+	0.113322i	$0.0361490\pi$
$127$			3.54067e23i			0.226643i	−0.993558	+	0.113322i	$0.963851\pi$
$128$		−	9.96553e23i		−	0.582889i
$129$	1.09302e24			0.584584
$130$	4.98741e23	+	1.28965e23i	0.244077	+	0.0631135i
$131$	3.21116e24			1.43894			0.719469	−	0.694525i	$-0.244385\pi$
$131$	3.21116e24			1.43894			0.719469	+	0.694525i	$0.244385\pi$
$132$		−	3.25435e23i		−	0.133618i
$133$			2.92919e24i			1.10269i
$134$	−4.06597e23			−0.140430
$135$	8.00967e23	−	3.09755e24i	0.253966	−	0.982156i
$136$	−5.18551e23			−0.151041
$137$		−	6.64427e24i		−	1.77894i	−0.456995	−	0.889469i	$-0.651074\pi$
$137$		−	6.64427e24i		−	1.77894i	0.456995	−	0.889469i	$-0.348926\pi$
$138$			7.11507e23i			0.175214i
$139$	−2.85476e24			−0.646993			−0.323497	−	0.946229i	$-0.604858\pi$
$139$	−2.85476e24			−0.646993			−0.323497	+	0.946229i	$0.604858\pi$
$140$	−1.85337e24	+	7.16749e24i	−0.386804	+	1.49587i
$141$	2.37134e24			0.456010
$142$			1.29246e24i			0.229141i
$143$			1.38355e24i			0.226272i
$144$	1.84929e23			0.0279150
$145$	−1.06694e25	−	2.75890e24i	−1.48733	−	0.384595i
$146$	1.58116e24			0.203665
$147$			1.24554e25i			1.48323i
$148$		−	1.01964e25i		−	1.12315i
$149$	−3.06282e24			−0.312234			−0.156117	−	0.987739i	$-0.549898\pi$
$149$	−3.06282e24			−0.312234			−0.156117	+	0.987739i	$0.549898\pi$
$150$	−1.41333e24	−	7.83292e23i	−0.133412	−	0.0739391i
$151$	9.29799e22			0.00813119			0.00406560	−	0.999992i	$-0.498706\pi$
$151$	9.29799e22			0.00813119			0.00406560	+	0.999992i	$0.498706\pi$
$152$		−	2.62988e24i		−	0.213174i
$153$		−	1.97366e23i		−	0.0148361i
$154$	4.88656e23			0.0340812
$155$	−1.08348e25	−	2.80168e24i	−0.701468	−	0.181386i
$156$	2.60229e25			1.56467
$157$			5.33483e24i			0.298040i	0.988834	+	0.149020i	$0.0476119\pi$
$157$			5.33483e24i			0.298040i	−0.988834	+	0.149020i	$0.952388\pi$
$158$		−	5.95937e23i		−	0.0309488i
$159$	−8.53027e24			−0.411999
$160$	2.50609e24	−	9.69173e24i	0.112620	−	0.435534i
$161$	4.34714e25			1.81847
$162$			3.85255e24i			0.150081i
$163$			1.58636e25i			0.575765i	0.957666	+	0.287882i	$0.0929513\pi$
$163$			1.58636e25i			0.575765i	−0.957666	+	0.287882i	$0.907049\pi$
$164$	1.23771e25			0.418710
$165$	1.08646e24	−	4.20164e24i	0.0342728	−	0.132542i
$166$	−4.49859e24			−0.132383
$167$		−	2.92212e25i		−	0.802525i	−0.915963	−	0.401263i	$-0.868571\pi$
$167$		−	2.92212e25i		−	0.802525i	0.915963	−	0.401263i	$-0.131429\pi$
$168$		−	1.86079e25i		−	0.477135i
$169$	−6.88801e25			−1.64967
$170$	−3.30683e24	−	8.55083e23i	−0.0740031	−	0.0191358i
$171$	1.00096e24			0.0209392
$172$			2.96147e25i			0.579335i
$173$			1.96813e25i			0.360183i	0.983650	+	0.180092i	$0.0576394\pi$
$173$			1.96813e25i			0.360183i	−0.983650	+	0.180092i	$0.942361\pi$
$174$	1.36816e25			0.234326
$175$	−4.78572e25	+	8.63510e25i	−0.767379	+	1.38462i
$176$	8.59542e24			0.129084
$177$		−	7.80549e25i		−	1.09827i
$178$			4.84908e23i			0.00639483i
$179$	4.88685e25			0.604253			0.302127	−	0.953268i	$-0.402303\pi$
$179$	4.88685e25			0.604253			0.302127	+	0.953268i	$0.402303\pi$
$180$	2.44927e24	+	6.33333e23i	0.0284055	+	0.00734511i
$181$	−1.48889e26			−1.62016			−0.810082	−	0.586316i	$-0.800578\pi$
$181$	−1.48889e26			−1.62016			−0.810082	+	0.586316i	$0.800578\pi$
$182$			3.90747e25i			0.399094i
$183$			2.23634e25i			0.214462i
$184$	−3.90295e25			−0.351550
$185$	3.40407e25	−	1.31645e26i	0.288087	−	1.11411i
$186$	1.38937e25			0.110515
$187$		−	9.17346e24i		−	0.0686048i
$188$			6.42500e25i			0.451916i
$189$	2.42683e26			1.60594
$190$	4.33663e24	−	1.67709e25i	0.0270076	−	0.104446i
$191$	1.61479e26			0.946742			0.473371	−	0.880863i	$-0.343037\pi$
$191$	1.61479e26			0.946742			0.473371	+	0.880863i	$0.343037\pi$
$192$		−	1.53215e26i		−	0.845934i
$193$		−	6.35702e25i		−	0.330632i	−0.986241	−	0.165316i	$-0.947136\pi$
$193$		−	6.35702e25i		−	0.330632i	0.986241	−	0.165316i	$-0.0528644\pi$
$194$	−7.82937e24			−0.0383713
$195$	3.35978e26	+	8.68774e25i	1.55208	+	0.401337i
$196$	−3.37470e26			−1.46991
$197$			4.67741e26i			1.92152i	0.277386	+	0.960758i	$0.410532\pi$
$197$			4.67741e26i			1.92152i	−0.277386	+	0.960758i	$0.589468\pi$
$198$		−	1.66983e23i		−	0.000647176i
$199$	−5.85962e25			−0.214318			−0.107159	−	0.994242i	$-0.534175\pi$
$199$	−5.85962e25			−0.214318			−0.107159	+	0.994242i	$0.534175\pi$
$200$	4.29672e25	−	7.75276e25i	0.148351	−	0.267677i
$201$	−2.73905e26			−0.892989
$202$			5.48890e25i			0.169022i
$203$		−	8.35912e26i		−	2.43196i
$204$	−1.72542e26			−0.474402
$205$	1.59799e26	+	4.13208e25i	0.415340	+	0.107399i
$206$	−2.85387e25			−0.0701392
$207$		−	1.48550e25i		−	0.0345313i
$208$			6.87321e26i			1.51158i
$209$	4.65241e25			0.0968267
$210$	3.06842e25	−	1.18664e26i	0.0604495	−	0.233774i
$211$	−8.76218e26			−1.63442			−0.817210	−	0.576340i	$-0.804480\pi$
$211$	−8.76218e26			−1.63442			−0.817210	+	0.576340i	$0.804480\pi$
$212$		−	2.31122e26i		−	0.408300i
$213$			8.70672e26i			1.45710i
$214$	−1.05319e26			−0.167012
$215$	−9.88685e25	+	3.82351e26i	−0.148599	+	0.574672i
$216$	−2.17886e26			−0.310463
$217$		−	8.48874e26i		−	1.14698i
$218$		−	1.17534e26i		−	0.150630i
$219$	1.06515e27			1.29510
$220$	1.13841e26	+	2.94370e25i	0.131352	+	0.0339651i
$221$	7.33543e26			0.803368
$222$			1.68811e26i			0.175526i
$223$		−	8.85073e26i		−	0.873923i	−0.899480	−	0.436961i	$-0.856055\pi$
$223$		−	8.85073e26i		−	0.873923i	0.899480	−	0.436961i	$-0.143945\pi$
$224$	7.59315e26			0.712147
$225$	2.95078e25	+	1.63537e25i	0.0262928	+	0.0145720i
$226$	2.47757e26			0.209787
$227$		−	1.25273e26i		−	0.100823i	−0.998729	−	0.0504117i	$-0.983947\pi$
$227$		−	1.25273e26i		−	0.100823i	0.998729	−	0.0504117i	$-0.0160534\pi$
$228$		−	8.75061e26i		−	0.669557i
$229$	−7.49748e26			−0.545515			−0.272758	−	0.962083i	$-0.587936\pi$
$229$	−7.49748e26			−0.545515			−0.272758	+	0.962083i	$0.587936\pi$
$230$	−2.48893e26	−	6.43589e25i	−0.172244	−	0.0445388i
$231$	3.29184e26			0.216721
$232$			7.50498e26i			0.470151i
$233$			1.77705e27i			1.05951i	0.848150	+	0.529757i	$0.177717\pi$
$233$			1.77705e27i			1.05951i	−0.848150	+	0.529757i	$0.822283\pi$
$234$	1.33526e25			0.00757849
$235$	−2.14498e26	+	8.29522e26i	−0.115916	+	0.448278i
$236$	2.11485e27			1.08841
$237$		−	4.01455e26i		−	0.196803i
$238$		−	2.59079e26i		−	0.121004i
$239$	−3.55752e27			−1.58333			−0.791666	−	0.610954i	$-0.790786\pi$
$239$	−3.55752e27			−1.58333			−0.791666	+	0.610954i	$0.790786\pi$
$240$	5.39732e26	−	2.08729e27i	0.228954	−	0.885429i
$241$	−4.31970e26			−0.174686			−0.0873429	−	0.996178i	$-0.527838\pi$
$241$	−4.31970e26			−0.174686			−0.0873429	+	0.996178i	$0.527838\pi$
$242$			3.93902e26i			0.151884i
$243$		−	1.63439e26i		−	0.0601011i
$244$	−6.05922e26			−0.212537
$245$	−4.35703e27	−	1.12664e27i	−1.45808	−	0.377030i
$246$	−2.04913e26			−0.0654358
$247$			3.72023e27i			1.13385i
$248$			7.62135e26i			0.221737i
$249$	−3.03049e27			−0.841821
$250$	4.01846e26	−	4.23546e26i	0.106598	−	0.112355i
$251$	5.77138e27			1.46229			0.731143	−	0.682224i	$-0.238987\pi$
$251$	5.77138e27			1.46229			0.731143	+	0.682224i	$0.238987\pi$
$252$			1.91892e26i			0.0464462i
$253$		−	6.90452e26i		−	0.159679i
$254$	1.58824e26			0.0351017
$255$	−2.22766e27	−	5.76029e26i	−0.470583	−	0.121684i
$256$	3.80625e27			0.768667
$257$		−	4.52366e27i		−	0.873492i	−0.899585	−	0.436746i	$-0.856131\pi$
$257$		−	4.52366e27i		−	0.873492i	0.899585	−	0.436746i	$-0.143869\pi$
$258$		−	4.90296e26i		−	0.0905383i
$259$	1.03139e28			1.82170
$260$	−2.35389e27	+	9.10312e27i	−0.397734	+	1.53814i
$261$	−2.85647e26			−0.0461810
$262$		−	1.44043e27i		−	0.222858i
$263$		−	4.90619e27i		−	0.726530i	−0.931686	−	0.363265i	$-0.881662\pi$
$263$		−	4.90619e27i		−	0.726530i	0.931686	−	0.363265i	$-0.118338\pi$
$264$	−2.95548e26			−0.0418970
$265$	7.71600e26	−	2.98399e27i	0.104728	−	0.405013i
$266$	1.31395e27			0.170781
$267$			3.26660e26i			0.0406645i
$268$		−	7.42129e27i		−	0.884972i
$269$	−4.42638e27			−0.505705			−0.252853	−	0.967505i	$-0.581369\pi$
$269$	−4.42638e27			−0.505705			−0.252853	+	0.967505i	$0.581369\pi$
$270$	−1.38947e27	−	3.59290e26i	−0.152113	−	0.0393334i
$271$	9.10090e27			0.954855			0.477427	−	0.878671i	$-0.341569\pi$
$271$	9.10090e27			0.954855			0.477427	+	0.878671i	$0.341569\pi$
$272$		−	4.55719e27i		−	0.458305i
$273$			2.63228e28i			2.53782i
$274$	−2.98042e27			−0.275516
$275$	1.37151e27	+	7.60113e26i	0.121583	+	0.0673833i
$276$	−1.29866e28			−1.10418
$277$		−	3.21248e27i		−	0.262013i	−0.991381	−	0.131007i	$-0.958179\pi$
$277$		−	3.21248e27i		−	0.262013i	0.991381	−	0.131007i	$-0.0418209\pi$
$278$			1.28056e27i			0.100204i
$279$	−2.90076e26			−0.0217803
$280$	6.50926e27	+	1.68317e27i	0.469045	+	0.121286i
$281$	−1.62849e28			−1.12632			−0.563162	−	0.826347i	$-0.690415\pi$
$281$	−1.62849e28			−1.12632			−0.563162	+	0.826347i	$0.690415\pi$
$282$		−	1.06371e27i		−	0.0706252i
$283$		−	1.42599e28i		−	0.909015i	−0.890743	−	0.454507i	$-0.849815\pi$
$283$		−	1.42599e28i		−	0.909015i	0.890743	−	0.454507i	$-0.150185\pi$
$284$	−2.35903e28			−1.44402
$285$	2.92139e27	−	1.12978e28i	0.171741	−	0.664167i
$286$	6.20621e26			0.0350443
$287$			1.25197e28i			0.679128i
$288$		−	2.59472e26i		−	0.0135231i
$289$	1.51039e28			0.756422
$290$	−1.23756e27	+	4.78597e27i	−0.0595647	+	0.230353i
$291$	−5.27428e27			−0.244002
$292$			2.88596e28i			1.28347i
$293$		−	2.58150e28i		−	1.10381i	−0.833906	−	0.551906i	$-0.813901\pi$
$293$		−	2.58150e28i		−	1.10381i	0.833906	−	0.551906i	$-0.186099\pi$
$294$	5.58711e27			0.229717
$295$	2.73045e28	+	7.06041e27i	1.07964	+	0.279175i
$296$	−9.26004e27			−0.352175
$297$		−	3.85452e27i		−	0.141017i
$298$			1.37389e27i			0.0483577i
$299$	5.52111e28			1.86985
$300$	1.42968e28	−	2.57964e28i	0.465956	−	0.840744i
$301$	−2.99559e28			−0.939654
$302$		−	4.17080e25i		−	0.00125933i
$303$			3.69761e28i			1.07481i
$304$	2.31122e28			0.646838
$305$	−7.82297e27	−	2.02287e27i	−0.210826	−	0.0545154i
$306$	−8.85324e25			−0.00229777
$307$		−	6.24975e28i		−	1.56233i	−0.624327	−	0.781163i	$-0.714627\pi$
$307$		−	6.24975e28i		−	1.56233i	0.624327	−	0.781163i	$-0.285373\pi$
$308$			8.91904e27i			0.214776i
$309$	−1.92252e28			−0.446013
$310$	−1.25675e27	+	4.86019e27i	−0.0280924	+	0.108641i
$311$	−3.68771e28			−0.794350			−0.397175	−	0.917743i	$-0.630009\pi$
$311$	−3.68771e28			−0.794350			−0.397175	+	0.917743i	$0.630009\pi$
$312$		−	2.36331e28i		−	0.490618i
$313$		−	3.94526e27i		−	0.0789434i	−0.999221	−	0.0394717i	$-0.987432\pi$
$313$		−	3.94526e27i		−	0.0789434i	0.999221	−	0.0394717i	$-0.0125675\pi$
$314$	2.39305e27			0.0461594
$315$	−6.40630e26	+	2.47749e27i	−0.0119134	+	0.0460724i
$316$	1.08772e28			0.195036
$317$			1.02232e29i			1.76768i	0.467789	+	0.883840i	$0.345051\pi$
$317$			1.02232e29i			1.76768i	−0.467789	+	0.883840i	$0.654949\pi$
$318$			3.82642e27i			0.0638089i
$319$	−1.32767e28			−0.213549
$320$	5.35963e28	+	1.38589e28i	0.831591	+	0.215033i
$321$	−7.09485e28			−1.06203
$322$		−	1.95000e28i		−	0.281638i
$323$		−	2.46665e28i		−	0.343778i
$324$	−7.03174e28			−0.945792
$325$	−6.07814e28	+	1.09671e29i	−0.789064	+	1.42374i
$326$	7.11595e27			0.0891725
$327$		−	7.91768e28i		−	0.957853i
$328$		−	1.12404e28i		−	0.131290i
$329$	−6.49903e28			−0.732986
$330$	−1.88473e27	−	4.87354e26i	−0.0205276	−	0.00530804i
$331$	9.05001e28			0.951978			0.475989	−	0.879451i	$-0.342090\pi$
$331$	9.05001e28			0.951978			0.475989	+	0.879451i	$0.342090\pi$
$332$		−	8.21091e28i		−	0.834264i
$333$		−	3.52446e27i		−	0.0345927i
$334$	−1.31078e28			−0.124292
$335$	2.47759e28	−	9.58152e28i	0.226994	−	0.877848i
$336$	1.63532e29			1.44778
$337$			1.45621e29i			1.24589i	0.782267	+	0.622944i	$0.214063\pi$
$337$			1.45621e29i			1.24589i	−0.782267	+	0.622944i	$0.785937\pi$
$338$			3.08975e28i			0.255495i
$339$	1.66902e29			1.33403
$340$	1.56071e28	−	6.03570e28i	0.120591	−	0.466359i
$341$	−1.34826e28			−0.100716
$342$		−	4.49000e26i		−	0.00324300i
$343$		−	1.14698e29i		−	0.801077i
$344$	2.68950e28			0.181656
$345$	−1.67668e29	−	4.33556e28i	−1.09529	−	0.283221i
$346$	8.82844e27			0.0557839
$347$			1.64255e29i			1.00399i	0.864871	+	0.501994i	$0.167400\pi$
$347$			1.64255e29i			1.00399i	−0.864871	+	0.501994i	$0.832600\pi$
$348$			2.49719e29i			1.47669i
$349$	−9.00037e28			−0.514953			−0.257477	−	0.966285i	$-0.582891\pi$
$349$	−9.00037e28			−0.514953			−0.257477	+	0.966285i	$0.582891\pi$
$350$	3.87345e28	+	2.14673e28i	0.214445	+	0.118849i
$351$	3.08221e29			1.65132
$352$		−	1.20601e28i		−	0.0625334i
$353$		−	2.76696e29i		−	1.38865i	−0.719660	−	0.694327i	$-0.755702\pi$
$353$		−	2.76696e29i		−	1.38865i	0.719660	−	0.694327i	$-0.244298\pi$
$354$	−3.50131e28			−0.170096
$355$	−3.04571e29	−	7.87561e28i	−1.43239	−	0.370389i
$356$	−8.85063e27			−0.0402995
$357$		−	1.74530e29i		−	0.769458i
$358$		−	2.19209e28i		−	0.0935846i
$359$	2.41821e29			0.999789			0.499895	−	0.866086i	$-0.333372\pi$
$359$	2.41821e29			0.999789			0.499895	+	0.866086i	$0.333372\pi$
$360$	5.75170e26	−	2.22434e27i	0.00230313	−	0.00890681i
$361$	−1.32731e29			−0.514802
$362$			6.67872e28i			0.250925i
$363$			2.65353e29i			0.965825i
$364$	−7.13199e29			−2.51504
$365$	−9.63475e28	+	3.72602e29i	−0.329209	+	1.27314i
$366$	1.00316e28			0.0332151
$367$			1.07500e29i			0.344945i	0.985014	+	0.172472i	$0.0551755\pi$
$367$			1.07500e29i			0.344945i	−0.985014	+	0.172472i	$0.944824\pi$
$368$		−	3.43003e29i		−	1.06671i
$369$	4.27821e27			0.0128961
$370$	−5.90519e28	−	1.52697e28i	−0.172549	−	0.0446179i
$371$	2.33785e29			0.662243
$372$			2.53591e29i			0.696451i
$373$			3.98056e29i			1.05997i	0.848008	+	0.529984i	$0.177802\pi$
$373$			3.98056e29i			1.05997i	−0.848008	+	0.529984i	$0.822198\pi$
$374$	−4.11494e27			−0.0106253
$375$	2.70705e29	−	2.85323e29i	0.677855	−	0.714459i
$376$	5.83495e28			0.141702
$377$		−	1.06166e30i		−	2.50068i
$378$		−	1.08860e29i		−	0.248722i
$379$	3.47509e29			0.770220			0.385110	−	0.922871i	$-0.374163\pi$
$379$	3.47509e29			0.770220			0.385110	+	0.922871i	$0.374163\pi$
$380$	3.06106e29	+	7.91531e28i	0.658204	+	0.170199i
$381$	1.06992e29			0.223211
$382$		−	7.24345e28i		−	0.146628i
$383$			7.01936e29i			1.37883i	0.724365	+	0.689417i	$0.242133\pi$
$383$			7.01936e29i			1.37883i	−0.724365	+	0.689417i	$0.757867\pi$
$384$	−3.01139e29			−0.574061
$385$	−2.97762e28	+	1.15152e29i	−0.0550897	+	0.213047i
$386$	−2.85157e28			−0.0512071
$387$			1.02365e28i			0.0178433i
$388$		−	1.42903e29i		−	0.241812i
$389$	6.11916e29			1.00524			0.502622	−	0.864506i	$-0.332369\pi$
$389$	6.11916e29			1.00524			0.502622	+	0.864506i	$0.332369\pi$
$390$	3.89706e28	−	1.50710e29i	0.0621576	−	0.240380i
$391$	−3.66070e29			−0.566932
$392$			3.06479e29i			0.460904i
$393$		−	9.70350e29i		−	1.41714i
$394$	2.09815e29			0.297598
$395$	1.40433e29	+	3.63133e28i	0.193466	+	0.0500264i
$396$	3.04781e27			0.00407843
$397$			1.10711e30i			1.43913i	0.694426	+	0.719564i	$0.255658\pi$
$397$			1.10711e30i			1.43913i	−0.694426	+	0.719564i	$0.744342\pi$
$398$			2.62845e28i			0.0331929i
$399$	8.85144e29			1.08599
$400$	6.81337e29	+	3.77609e29i	0.812217	+	0.450145i
$401$	−1.50507e30			−1.74340			−0.871700	−	0.490039i	$-0.836982\pi$
$401$	−1.50507e30			−1.74340			−0.871700	+	0.490039i	$0.836982\pi$
$402$			1.22866e29i			0.138303i
$403$		−	1.07812e30i		−	1.17939i
$404$	−1.00184e30			−1.06516
$405$	−9.07858e29	−	2.34754e29i	−0.938178	−	0.242594i
$406$	−3.74965e29			−0.376653
$407$		−	1.63815e29i		−	0.159963i
$408$			1.56696e29i			0.148753i
$409$	3.99507e29			0.368729			0.184364	−	0.982858i	$-0.440977\pi$
$409$	3.99507e29			0.368729			0.184364	+	0.982858i	$0.440977\pi$
$410$	1.85353e28	−	7.16809e28i	0.0166335	−	0.0643263i
$411$	−2.00777e30			−1.75200
$412$		−	5.20893e29i		−	0.442009i
$413$			2.13922e30i			1.76534i
$414$	−6.66351e27			−0.00534809
$415$	2.74121e29	−	1.06010e30i	0.213988	−	0.827548i
$416$	9.64373e29			0.732271
$417$			8.62654e29i			0.637194i
$418$		−	2.08693e28i		−	0.0149962i
$419$	3.22107e28			0.0225185			0.0112592	−	0.999937i	$-0.496416\pi$
$419$	3.22107e28			0.0225185			0.0112592	+	0.999937i	$0.496416\pi$
$420$	2.16588e30	+	5.60053e29i	1.47322	+	0.380945i
$421$	−5.89545e29			−0.390187			−0.195093	−	0.980785i	$-0.562501\pi$
$421$	−5.89545e29			−0.390187			−0.195093	+	0.980785i	$0.562501\pi$
$422$			3.93045e29i			0.253133i
$423$			2.22084e28i			0.0139188i
$424$	−2.09897e29			−0.128026
$425$	4.03003e29	−	7.27156e29i	0.239241	−	0.431673i
$426$	3.90558e29			0.225671
$427$		−	6.12903e29i		−	0.344724i
$428$		−	1.92231e30i		−	1.05249i
$429$	4.18083e29			0.222845
$430$	1.71511e29	+	4.43494e28i	0.0890032	+	0.0230145i
$431$	5.69231e29			0.287607			0.143804	−	0.989606i	$-0.454067\pi$
$431$	5.69231e29			0.287607			0.143804	+	0.989606i	$0.454067\pi$
$432$		−	1.91485e30i		−	0.942043i
$433$			8.60930e29i			0.412437i	0.978506	+	0.206218i	$0.0661157\pi$
$433$			8.60930e29i			0.412437i	−0.978506	+	0.206218i	$0.933884\pi$
$434$	−3.80779e29			−0.177640
$435$	−8.33685e29	+	3.22409e30i	−0.378770	+	1.46481i
$436$	2.14524e30			0.949254
$437$		−	1.85656e30i		−	0.800151i
$438$		−	4.77795e29i		−	0.200581i
$439$	2.12796e30			0.870207			0.435103	−	0.900381i	$-0.356712\pi$
$439$	2.12796e30			0.870207			0.435103	+	0.900381i	$0.356712\pi$
$440$	2.67336e28	−	1.03386e29i	0.0106501	−	0.0411867i
$441$	−1.16649e29			−0.0452727
$442$		−	3.29046e29i		−	0.124423i
$443$		−	8.39480e29i		−	0.309291i	−0.987970	−	0.154646i	$-0.950576\pi$
$443$		−	8.39480e29i		−	0.309291i	0.987970	−	0.154646i	$-0.0494236\pi$
$444$	−3.08116e30			−1.10614
$445$	−1.14269e29	−	2.95478e28i	−0.0399751	−	0.0103368i
$446$	−3.97017e29			−0.135350
$447$			9.25526e29i			0.307505i
$448$			4.19909e30i			1.35975i
$449$	1.44706e30			0.456724			0.228362	−	0.973576i	$-0.426663\pi$
$449$	1.44706e30			0.456724			0.228362	+	0.973576i	$0.426663\pi$
$450$	7.33580e27	−	1.32363e28i	0.00225685	−	0.00407214i
$451$	1.98849e29			0.0596339
$452$			4.52210e30i			1.32205i
$453$		−	2.80967e28i		−	0.00800804i
$454$	−5.61939e28			−0.0156152
$455$	−9.20801e30	−	2.38101e30i	−2.49479	−	0.645105i
$456$	−7.94699e29			−0.209946
$457$		−	3.32229e30i		−	0.855857i	−0.903813	−	0.427928i	$-0.859244\pi$
$457$		−	3.32229e30i		−	0.855857i	0.903813	−	0.427928i	$-0.140756\pi$
$458$			3.36314e29i			0.0844875i
$459$	−2.04362e30			−0.500673
$460$	1.17469e30	−	4.54285e30i	0.280678	−	1.08546i
$461$	4.28913e30			0.999559			0.499780	−	0.866153i	$-0.333414\pi$
$461$	4.28913e30			0.999559			0.499780	+	0.866153i	$0.333414\pi$
$462$		−	1.47662e29i		−	0.0335650i
$463$		−	3.74937e30i		−	0.831337i	−0.909516	−	0.415668i	$-0.863548\pi$
$463$		−	3.74937e30i		−	0.831337i	0.909516	−	0.415668i	$-0.136452\pi$
$464$	−6.59561e30			−1.42659
$465$	−8.46613e29	+	3.27408e30i	−0.178639	+	0.690844i
$466$	7.97131e29			0.164094
$467$			6.06791e30i			1.21870i	0.792903	+	0.609348i	$0.208569\pi$
$467$			6.06791e30i			1.21870i	−0.792903	+	0.609348i	$0.791431\pi$
$468$			2.43714e29i			0.0477587i
$469$	7.50680e30			1.43538
$470$	3.72099e29	+	9.62174e28i	0.0694277	+	0.0179526i
$471$	1.61208e30			0.293526
$472$		−	1.92063e30i		−	0.341280i
$473$			4.75788e29i			0.0825107i
$474$	−1.80081e29			−0.0304801
$475$	3.68784e30	+	2.04387e30i	0.609250	+	0.337657i
$476$	4.72877e30			0.762550
$477$		−	7.98889e28i		−	0.0125755i
$478$			1.59580e30i			0.245221i
$479$	−3.01378e30			−0.452120			−0.226060	−	0.974113i	$-0.572585\pi$
$479$	−3.01378e30			−0.452120			−0.226060	+	0.974113i	$0.572585\pi$
$480$	−2.92865e30	−	7.57292e29i	−0.428937	−	0.110915i
$481$	1.30993e31			1.87318
$482$			1.93769e29i			0.0270547i
$483$		−	1.31362e31i		−	1.79093i
$484$	−7.18958e30			−0.957154
$485$	4.77082e29	−	1.84500e30i	0.0620244	−	0.239865i
$486$	−7.33137e28			−0.00930825
$487$			8.39432e30i			1.04088i	0.853897	+	0.520442i	$0.174233\pi$
$487$			8.39432e30i			1.04088i	−0.853897	+	0.520442i	$0.825767\pi$
$488$			5.50277e29i			0.0666428i
$489$	4.79368e30			0.567045
$490$	−5.05378e29	+	1.95443e30i	−0.0583931	+	0.225822i
$491$	−2.64316e30			−0.298323			−0.149161	−	0.988813i	$-0.547657\pi$
$491$	−2.64316e30			−0.298323			−0.149161	+	0.988813i	$0.547657\pi$
$492$		−	3.74011e30i		−	0.412369i
$493$			7.03916e30i			0.758196i
$494$	1.66879e30			0.175607
$495$	3.93498e28	+	1.01751e28i	0.00404560	+	0.00104611i
$496$	−6.69788e30			−0.672819
$497$		−	2.38621e31i		−	2.34213i
$498$			1.35939e30i			0.130378i
$499$	−3.04753e30			−0.285622			−0.142811	−	0.989750i	$-0.545614\pi$
$499$	−3.04753e30			−0.285622			−0.142811	+	0.989750i	$0.545614\pi$
$500$	7.73065e30	+	7.33458e30i	0.708045	+	0.671769i
$501$	−8.83008e30			−0.790371
$502$		−	2.58887e30i		−	0.226474i
$503$			2.02438e31i			1.73086i	0.501034	+	0.865428i	$0.332953\pi$
$503$			2.02438e31i			1.73086i	−0.501034	+	0.865428i	$0.667047\pi$
$504$	1.74269e29			0.0145636
$505$	−1.29347e31	−	3.34465e30i	−1.05658	−	0.273212i
$506$	−3.09716e29			−0.0247305
$507$			2.08142e31i			1.62468i
$508$			2.89889e30i			0.221207i
$509$	6.74069e30			0.502863			0.251431	−	0.967875i	$-0.419099\pi$
$509$	6.74069e30			0.502863			0.251431	+	0.967875i	$0.419099\pi$
$510$	−2.58389e29	+	9.99262e29i	−0.0188459	+	0.0728823i
$511$	−2.91921e31			−2.08173
$512$		−	1.00671e31i		−	0.701937i
$513$		−	1.03644e31i		−	0.706634i
$514$	−2.02918e30			−0.135283
$515$	1.73900e30	−	6.72518e30i	0.113375	−	0.438451i
$516$	8.94899e30			0.570561
$517$			1.03224e30i			0.0643632i
$518$		−	4.62652e30i		−	0.282138i
$519$	5.94730e30			0.354728
$520$	8.26713e30	+	2.13772e30i	0.482299	+	0.124713i
$521$	−8.68856e30			−0.495808			−0.247904	−	0.968785i	$-0.579742\pi$
$521$	−8.68856e30			−0.495808			−0.247904	+	0.968785i	$0.579742\pi$
$522$			1.28133e29i			0.00715236i
$523$		−	2.50430e31i		−	1.36747i	−0.729731	−	0.683734i	$-0.760355\pi$
$523$		−	2.50430e31i		−	1.36747i	0.729731	−	0.683734i	$-0.239645\pi$
$524$	2.62910e31			1.40442
$525$	2.60936e31	+	1.44615e31i	1.36365	+	0.755757i
$526$	−2.20077e30			−0.112522
$527$			7.14831e30i			0.357587i
$528$		−	2.59737e30i		−	0.127129i
$529$	−6.67226e30			−0.319545
$530$	−1.33853e30	−	3.46117e29i	−0.0627270	−	0.0162200i
$531$	7.31011e29			0.0335225
$532$			2.39824e31i			1.07624i
$533$			1.59007e31i			0.698319i
$534$	1.46530e29			0.00629798
$535$	6.41760e30	−	2.48186e31i	0.269963	−	1.04402i
$536$	−6.73976e30			−0.277491
$537$		−	1.47671e31i		−	0.595102i
$538$			1.98554e30i			0.0783218i
$539$	−5.42178e30			−0.209349
$540$	6.55783e30	−	2.53609e31i	0.247875	−	0.958598i
$541$	1.42855e30			0.0528598			0.0264299	−	0.999651i	$-0.491586\pi$
$541$	1.42855e30			0.0528598			0.0264299	+	0.999651i	$0.491586\pi$
$542$		−	4.08239e30i		−	0.147885i
$543$			4.49914e31i			1.59563i
$544$	−6.39414e30			−0.222021
$545$	2.76969e31	+	7.16189e30i	0.941612	+	0.243482i
$546$	1.18076e31			0.393049
$547$			1.36802e30i			0.0445902i	0.999751	+	0.0222951i	$0.00709734\pi$
$547$			1.36802e30i			0.0445902i	−0.999751	+	0.0222951i	$0.992903\pi$
$548$		−	5.43993e31i		−	1.73627i
$549$	−2.09441e29			−0.00654605
$550$	3.40964e29	−	6.15217e29i	0.0104361	−	0.0188303i
$551$	−3.56998e31			−1.07009
$552$			1.17939e31i			0.346226i
$553$			1.10025e31i			0.316338i
$554$	−1.44102e30			−0.0405797
$555$	−3.97805e31	−	1.02864e31i	−1.09724	−	0.283724i
$556$	−2.33731e31			−0.631474
$557$			3.27739e30i			0.0867348i	0.999059	+	0.0433674i	$0.0138086\pi$
$557$			3.27739e30i			0.0867348i	−0.999059	+	0.0433674i	$0.986191\pi$
$558$			1.30120e29i			0.00337326i
$559$	−3.80457e31			−0.966207
$560$	−1.47922e31	+	5.72054e31i	−0.368019	+	1.42323i
$561$	−2.77204e30			−0.0675658
$562$			7.30494e30i			0.174441i
$563$			1.96163e30i			0.0458955i	0.999737	+	0.0229478i	$0.00730514\pi$
$563$			1.96163e30i			0.0458955i	−0.999737	+	0.0229478i	$0.992695\pi$
$564$	1.94151e31			0.445072
$565$	−1.50970e31	+	5.83842e31i	−0.339105	+	1.31141i
$566$	−6.39654e30			−0.140785
$567$		−	7.11276e31i		−	1.53403i
$568$			2.14239e31i			0.452785i
$569$	3.45236e31			0.715032			0.357516	−	0.933907i	$-0.383624\pi$
$569$	3.45236e31			0.715032			0.357516	+	0.933907i	$0.383624\pi$
$570$	−5.06785e30	−	1.31045e30i	−0.102864	−	0.0265986i
$571$	6.79955e31			1.35259			0.676293	−	0.736633i	$-0.263585\pi$
$571$	6.79955e31			1.35259			0.676293	+	0.736633i	$0.263585\pi$
$572$			1.13277e31i			0.220845i
$573$		−	4.87957e31i		−	0.932403i
$574$	5.61596e30			0.105181
$575$	3.03326e31	−	5.47304e31i	0.556838	−	1.00473i
$576$	1.43491e30			0.0258205
$577$		−	1.16391e31i		−	0.205304i	−0.994717	−	0.102652i	$-0.967267\pi$
$577$		−	1.16391e31i		−	0.205304i	0.994717	−	0.102652i	$-0.0327327\pi$
$578$		−	6.77516e30i		−	0.117152i
$579$	−1.92097e31			−0.325624
$580$	−8.73546e31	−	2.25882e31i	−1.45166	−	0.375370i
$581$	8.30552e31			1.35314
$582$			2.36588e30i			0.0377902i
$583$		−	3.71319e30i		−	0.0581513i
$584$	2.62092e31			0.402445
$585$	−8.13637e29	+	3.14655e30i	−0.0122501	+	0.0473743i
$586$	−1.15799e31			−0.170955
$587$			5.91729e31i			0.856613i	0.903634	+	0.428306i	$0.140890\pi$
$587$			5.91729e31i			0.856613i	−0.903634	+	0.428306i	$0.859110\pi$
$588$			1.01977e32i			1.44765i
$589$	−3.62533e31			−0.504687
$590$	3.16709e30	−	1.22480e31i	0.0432376	−	0.167212i
$591$	1.41342e32			1.89242
$592$		−	8.13801e31i		−	1.06861i
$593$		−	1.23535e31i		−	0.159096i	−0.996831	−	0.0795482i	$-0.974652\pi$
$593$		−	1.23535e31i		−	0.159096i	0.996831	−	0.0795482i	$-0.0253478\pi$
$594$	−1.72902e30			−0.0218402
$595$	6.10525e31	+	1.57870e31i	0.756411	+	0.195593i
$596$	−2.50766e31			−0.304744
$597$			1.77066e31i			0.211072i
$598$		−	2.47661e31i		−	0.289596i
$599$	−3.67204e31			−0.421210			−0.210605	−	0.977571i	$-0.567543\pi$
$599$	−3.67204e31			−0.421210			−0.210605	+	0.977571i	$0.567543\pi$
$600$	−2.34273e31	−	1.29839e31i	−0.263623	−	0.146105i
$601$	6.53454e31			0.721371			0.360686	−	0.932687i	$-0.382543\pi$
$601$	6.53454e31			0.721371			0.360686	+	0.932687i	$0.382543\pi$
$602$			1.34373e31i			0.145530i
$603$		−	2.56522e30i		−	0.0272568i
$604$	7.61263e29			0.00793615
$605$	−9.28236e31	−	2.40024e31i	−0.949449	−	0.245509i
$606$	1.65864e31			0.166463
$607$			1.25990e32i			1.24070i	0.784326	+	0.620349i	$0.213009\pi$
$607$			1.25990e32i			1.24070i	−0.784326	+	0.620349i	$0.786991\pi$
$608$		−	3.24285e31i		−	0.313354i
$609$	−2.52596e32			−2.39513
$610$	−9.07397e29	+	3.50915e30i	−0.00844315	+	0.0326519i
$611$	−8.25413e31			−0.753698
$612$		−	1.61591e30i		−	0.0144802i
$613$		−	8.59467e31i		−	0.755847i	−0.925837	−	0.377923i	$-0.876638\pi$
$613$		−	8.59467e31i		−	0.755847i	0.925837	−	0.377923i	$-0.123362\pi$
$614$	−2.80345e31			−0.241967
$615$	1.24863e31	−	4.82880e31i	0.105772	−	0.409049i
$616$	8.09996e30			0.0673449
$617$			4.44519e31i			0.362753i	0.983414	+	0.181377i	$0.0580553\pi$
$617$			4.44519e31i			0.362753i	−0.983414	+	0.181377i	$0.941945\pi$
$618$			8.62383e30i			0.0690769i
$619$	1.46179e32			1.14933			0.574664	−	0.818389i	$-0.305133\pi$
$619$	1.46179e32			1.14933			0.574664	+	0.818389i	$0.305133\pi$
$620$	−8.87091e31	−	2.29384e31i	−0.684642	−	0.177035i
$621$	−1.53816e32			−1.16533
$622$			1.65420e31i			0.123026i
$623$		−	8.95261e30i		−	0.0653638i
$624$	2.07695e32			1.48869
$625$	7.53229e31	+	1.20504e32i	0.530038	+	0.847974i
$626$	−1.76973e30			−0.0122265
$627$		−	1.40587e31i		−	0.0953603i
$628$			4.36783e31i			0.290891i
$629$	−8.68528e31			−0.567939
$630$	1.11133e30	+	2.87368e29i	0.00713552	+	0.00184511i
$631$	2.21285e32			1.39513			0.697564	−	0.716523i	$-0.254267\pi$
$631$	2.21285e32			1.39513			0.697564	+	0.716523i	$0.254267\pi$
$632$		−	9.87825e30i		−	0.0611552i
$633$			2.64776e32i			1.60967i
$634$	4.58580e31			0.273772
$635$	−9.67791e30	+	3.74271e31i	−0.0567393	+	0.219426i
$636$	−6.98407e31			−0.402116
$637$		−	4.33545e32i		−	2.45149i
$638$			5.95554e30i			0.0330738i
$639$	−8.15414e30			−0.0444752
$640$	2.72393e31	−	1.05342e32i	0.145924	−	0.564327i
$641$	−1.47537e32			−0.776308			−0.388154	−	0.921595i	$-0.626887\pi$
$641$	−1.47537e32			−0.776308			−0.388154	+	0.921595i	$0.626887\pi$
$642$			3.18254e31i			0.164483i
$643$		−	2.39840e32i		−	1.21757i	−0.793334	−	0.608786i	$-0.791657\pi$
$643$		−	2.39840e32i		−	1.21757i	0.793334	−	0.608786i	$-0.208343\pi$
$644$	3.55917e32			1.77485
$645$	1.15539e32	+	2.98761e31i	0.565968	+	0.146348i
$646$	−1.10647e31			−0.0532432
$647$		−	6.15724e30i		−	0.0291063i	−0.999894	−	0.0145532i	$-0.995367\pi$
$647$		−	6.15724e30i		−	0.0291063i	0.999894	−	0.0145532i	$-0.00463258\pi$
$648$			6.38598e31i			0.296562i
$649$	3.39770e31			0.155014
$650$	4.91950e31	+	2.72647e31i	0.220504	+	0.122207i
$651$	−2.56513e32			−1.12961
$652$			1.29882e32i			0.561954i
$653$			1.31379e31i			0.0558500i	0.999610	+	0.0279250i	$0.00888996\pi$
$653$			1.31379e31i			0.0558500i	−0.999610	+	0.0279250i	$0.991110\pi$
$654$	−3.55164e31			−0.148349
$655$	3.39439e32	+	8.77724e31i	1.39312	+	0.360233i
$656$	9.87843e31			0.398376
$657$			9.97549e30i			0.0395305i
$658$			2.91527e31i			0.113522i
$659$	−2.54141e32			−0.972506			−0.486253	−	0.873818i	$-0.661637\pi$
$659$	−2.54141e32			−0.972506			−0.486253	+	0.873818i	$0.661637\pi$
$660$	8.89529e30	−	3.44005e31i	0.0334507	−	0.129363i
$661$	−3.16549e32			−1.16983			−0.584917	−	0.811093i	$-0.698873\pi$
$661$	−3.16549e32			−1.16983			−0.584917	+	0.811093i	$0.698873\pi$
$662$		−	4.05956e31i		−	0.147439i
$663$		−	2.21663e32i		−	0.791201i
$664$	−7.45686e31			−0.261591
$665$	−8.00651e31	+	3.09633e32i	−0.276054	+	1.06758i
$666$	−1.58097e30			−0.00535759
$667$			5.29812e32i			1.76471i
$668$		−	2.39245e32i		−	0.783275i
$669$	−2.67452e32			−0.860687
$670$	−4.29799e31	−	1.11137e31i	−0.135958	−	0.0351561i
$671$	−9.73470e30			−0.0302701
$672$		−	2.29450e32i		−	0.701361i
$673$			2.36325e32i			0.710127i	0.934842	+	0.355063i	$0.115541\pi$
$673$			2.36325e32i			0.710127i	−0.934842	+	0.355063i	$0.884459\pi$
$674$	6.53210e31			0.192959
$675$	1.69334e32	−	3.05538e32i	0.491758	−	0.887301i
$676$	−5.63948e32			−1.61010
$677$		−	1.16353e31i		−	0.0326595i	−0.999867	−	0.0163297i	$-0.994802\pi$
$677$		−	1.16353e31i		−	0.0326595i	0.999867	−	0.0163297i	$-0.00519815\pi$
$678$		−	7.48672e31i		−	0.206610i
$679$	1.44550e32			0.392207
$680$	−5.48141e31	−	1.41739e31i	−0.146231	−	0.0378125i
$681$	−3.78552e31			−0.0992965
$682$			6.04789e30i			0.0155985i
$683$			2.63629e32i			0.668582i	0.942470	+	0.334291i	$0.108497\pi$
$683$			2.63629e32i			0.668582i	−0.942470	+	0.334291i	$0.891503\pi$
$684$	8.19524e30			0.0204370
$685$	1.81612e32	−	7.02341e32i	0.445350	−	1.72229i
$686$	−5.14502e31			−0.124068
$687$			2.26559e32i			0.537253i
$688$			2.36362e32i			0.551201i
$689$	2.96921e32			0.680956
$690$	−1.94480e31	+	7.52108e31i	−0.0438643	+	0.169635i
$691$	5.50229e32			1.22052			0.610262	−	0.792200i	$-0.291064\pi$
$691$	5.50229e32			1.22052			0.610262	+	0.792200i	$0.291064\pi$
$692$			1.61138e32i			0.351543i
$693$			3.08292e30i			0.00661501i
$694$	7.36798e31			0.155494
$695$	−3.01766e32	−	7.80308e31i	−0.626391	−	0.161972i
$696$	2.26786e32			0.463031
$697$		−	1.05427e32i		−	0.211727i
$698$			4.03730e31i			0.0797541i
$699$	5.36990e32			1.04347
$700$	−3.91826e32	+	7.06989e32i	−0.748973	+	1.35140i
$701$	3.64948e32			0.686236			0.343118	−	0.939292i	$-0.388517\pi$
$701$	3.64948e32			0.686236			0.343118	+	0.939292i	$0.388517\pi$
$702$		−	1.38259e32i		−	0.255750i
$703$		−	4.40482e32i		−	0.801572i
$704$	6.66938e31			0.119399
$705$	2.50665e32	+	6.48172e31i	0.441489	+	0.114160i
$706$	−1.24118e32			−0.215070
$707$		−	1.01339e33i		−	1.72764i
$708$		−	6.39066e32i		−	1.07192i
$709$	−3.85906e32			−0.636869			−0.318434	−	0.947945i	$-0.603157\pi$
$709$	−3.85906e32			−0.636869			−0.318434	+	0.947945i	$0.603157\pi$
$710$	−3.53276e31	+	1.36622e32i	−0.0573646	+	0.221844i
$711$	3.75976e30			0.00600703
$712$			8.03783e30i			0.0126363i
$713$			5.38027e32i			0.832290i
$714$	−7.82888e31			−0.119171
$715$	−3.78174e31	+	1.46250e32i	−0.0566464	+	0.219067i
$716$	4.00105e32			0.589759
$717$			1.07501e33i			1.55935i
$718$		−	1.08474e32i		−	0.154844i
$719$	1.78348e32			0.250545			0.125273	−	0.992122i	$-0.460019\pi$
$719$	1.78348e32			0.250545			0.125273	+	0.992122i	$0.460019\pi$
$720$	1.95482e31	+	5.05478e30i	0.0270260	+	0.00698841i
$721$	5.26895e32			0.716917
$722$			5.95392e31i			0.0797307i
$723$			1.30533e32i			0.172040i
$724$	−1.21901e33			−1.58130
$725$	−1.05241e33	−	5.83265e32i	−1.34369	−	0.744696i
$726$	1.19030e32			0.149584
$727$		−	1.17673e33i		−	1.45556i	−0.685810	−	0.727781i	$-0.740552\pi$
$727$		−	1.17673e33i		−	1.45556i	0.685810	−	0.727781i	$-0.259448\pi$
$728$			6.47702e32i			0.788614i
$729$	−8.57937e32			−1.02823
$730$	1.67138e32	+	4.32186e31i	0.197180	+	0.0509868i
$731$	2.52257e32			0.292950
$732$			1.83098e32i			0.209318i
$733$			9.99183e32i			1.12447i	0.826976	+	0.562237i	$0.190059\pi$
$733$			9.99183e32i			1.12447i	−0.826976	+	0.562237i	$0.809941\pi$
$734$	4.82214e31			0.0534238
$735$	−3.40450e32	+	1.31661e33i	−0.371320	+	1.43599i
$736$	−4.81264e32			−0.516759
$737$		−	1.19230e32i		−	0.126040i
$738$		−	1.91908e30i		−	0.00199731i
$739$	−1.30194e33			−1.33408			−0.667039	−	0.745022i	$-0.732439\pi$
$739$	−1.30194e33			−1.33408			−0.667039	+	0.745022i	$0.732439\pi$
$740$	2.78705e32	−	1.07783e33i	0.281177	−	1.08739i
$741$	1.12418e33			1.11668
$742$		−	1.04869e32i		−	0.102566i
$743$		−	9.92153e32i		−	0.955449i	−0.878510	−	0.477724i	$-0.841462\pi$
$743$		−	9.92153e32i		−	0.955449i	0.878510	−	0.477724i	$-0.158538\pi$
$744$	2.30303e32			0.218379
$745$	−3.23760e32	−	8.37179e31i	−0.302291	−	0.0781666i
$746$	1.78556e32			0.164164
$747$		−	2.83815e31i		−	0.0256950i
$748$		−	7.51067e31i		−	0.0669592i
$749$	1.94445e33			1.70709
$750$	−1.27988e32	−	1.21430e32i	−0.110653	−	0.104984i
$751$	−4.69843e31			−0.0400030			−0.0200015	−	0.999800i	$-0.506367\pi$
$751$	−4.69843e31			−0.0400030			−0.0200015	+	0.999800i	$0.506367\pi$
$752$			5.12794e32i			0.429970i
$753$		−	1.74400e33i		−	1.44014i
$754$	−4.76227e32			−0.387296
$755$	9.82856e30	+	2.54147e30i	0.00787227	+	0.00203561i
$756$	1.98694e33			1.56742
$757$			1.32997e33i			1.03333i	0.856187	+	0.516666i	$0.172827\pi$
$757$			1.32997e33i			1.03333i	−0.856187	+	0.516666i	$0.827173\pi$
$758$		−	1.55882e32i		−	0.119289i
$759$	−2.08641e32			−0.157261
$760$	7.18840e31	−	2.77995e32i	0.0533674	−	0.206386i
$761$	−1.37543e33			−1.00581			−0.502903	−	0.864343i	$-0.667735\pi$
$761$	−1.37543e33			−1.00581			−0.502903	+	0.864343i	$0.667735\pi$
$762$		−	4.79935e31i		−	0.0345701i
$763$			2.16996e33i			1.53964i
$764$	1.32209e33			0.924033
$765$	5.39471e30	−	2.08628e31i	0.00371417	−	0.0143637i
$766$	3.14868e32			0.213549
$767$			2.71693e33i			1.81523i
$768$		−	1.15018e33i		−	0.757025i
$769$	1.99445e33			1.29321			0.646606	−	0.762824i	$-0.276188\pi$
$769$	1.99445e33			1.29321			0.646606	+	0.762824i	$0.276188\pi$
$770$	5.16540e31	+	1.33567e31i	0.0329959	+	0.00853210i
$771$	−1.36696e33			−0.860263
$772$		−	5.20474e32i		−	0.322701i
$773$		−	2.90186e33i		−	1.77261i	−0.463103	−	0.886305i	$-0.653264\pi$
$773$		−	2.90186e33i		−	1.77261i	0.463103	−	0.886305i	$-0.346736\pi$
$774$	4.59179e30			0.00276351
$775$	−1.06873e33	−	5.92309e32i	−0.633722	−	0.351220i
$776$	−1.29780e32			−0.0758223
$777$		−	3.11667e33i		−	1.79411i
$778$		−	2.74487e32i		−	0.155689i
$779$	5.34685e32			0.298825
$780$	2.75079e33	+	7.11300e32i	1.51485	+	0.391710i
$781$	−3.79000e32			−0.205661
$782$			1.64208e32i			0.0878045i
$783$			2.95772e33i			1.55847i
$784$	−2.69343e33			−1.39853
$785$	−1.45820e32	+	5.63925e32i	−0.0746132	+	0.288549i
$786$	−4.35270e32			−0.219482
$787$		−	2.39501e33i		−	1.19014i	−0.803674	−	0.595070i	$-0.797124\pi$
$787$		−	2.39501e33i		−	1.19014i	0.803674	−	0.595070i	$-0.202876\pi$
$788$			3.82958e33i			1.87543i
$789$	−1.48256e33			−0.715526
$790$	1.62891e31	−	6.29943e31i	0.00774792	−	0.0299633i
$791$	−4.57421e33			−2.14430
$792$		−	2.76791e30i		−	0.00127883i
$793$		−	7.78422e32i		−	0.354465i
$794$	4.96616e32			0.222887
$795$	−9.01703e32	−	2.33163e32i	−0.398879	−	0.103142i
$796$	−4.79750e32			−0.209177
$797$			2.15419e33i			0.925793i	0.886412	+	0.462896i	$0.153190\pi$
$797$			2.15419e33i			0.925793i	−0.886412	+	0.462896i	$0.846810\pi$
$798$		−	3.97049e32i		−	0.168194i
$799$	5.47279e32			0.228518
$800$	5.29819e32	−	9.55976e32i	0.218068	−	0.393470i
$801$	−3.05928e30			−0.00124121
$802$			6.75131e32i			0.270012i
$803$			4.63656e32i			0.182796i
$804$	−2.24257e33			−0.871569
$805$	4.59519e33	+	1.18823e33i	1.76056	+	0.455247i
$806$	−4.83612e32			−0.182660
$807$			1.33757e33i			0.498046i
$808$			9.09840e32i			0.333991i
$809$	3.40486e33			1.23223			0.616114	−	0.787657i	$-0.288706\pi$
$809$	3.40486e33			1.23223			0.616114	+	0.787657i	$0.288706\pi$
$810$	−1.05304e32	+	4.07238e32i	−0.0375722	+	0.145302i
$811$	1.95755e33			0.688608			0.344304	−	0.938858i	$-0.388115\pi$
$811$	1.95755e33			0.688608			0.344304	+	0.938858i	$0.388115\pi$
$812$		−	6.84394e33i		−	2.37362i
$813$		−	2.75011e33i		−	0.940393i
$814$	−7.34826e31			−0.0247744
$815$	−4.33610e32	+	1.67688e33i	−0.144141	+	0.557431i
$816$	−1.37709e33			−0.451364
$817$			1.27934e33i			0.413460i
$818$		−	1.79207e32i		−	0.0571074i
$819$	−2.46522e32			−0.0774623
$820$	1.30833e33	+	3.38309e32i	0.405377	+	0.104823i
$821$	−2.75076e33			−0.840438			−0.420219	−	0.907423i	$-0.638047\pi$
$821$	−2.75076e33			−0.840438			−0.420219	+	0.907423i	$0.638047\pi$
$822$			9.00626e32i			0.271343i
$823$		−	4.11882e33i		−	1.22370i	−0.790974	−	0.611849i	$-0.790426\pi$
$823$		−	4.11882e33i		−	1.22370i	0.790974	−	0.611849i	$-0.209574\pi$
$824$	−4.73057e32			−0.138596
$825$	2.29691e32	−	4.14443e32i	0.0663628	−	0.119741i
$826$	9.59588e32			0.273410
$827$		−	1.35807e33i		−	0.381600i	−0.981629	−	0.190800i	$-0.938892\pi$
$827$		−	1.35807e33i		−	0.381600i	0.981629	−	0.190800i	$-0.0611082\pi$
$828$		−	1.21624e32i		−	0.0337030i
$829$	6.52663e33			1.78366			0.891830	−	0.452371i	$-0.149422\pi$
$829$	6.52663e33			1.78366			0.891830	+	0.452371i	$0.149422\pi$
$830$	−4.75529e32	−	1.22962e32i	−0.128168	−	0.0331417i
$831$	−9.70750e32			−0.258045
$832$			5.33308e33i			1.39817i
$833$			2.87456e33i			0.743283i
$834$	3.86961e32			0.0986864
$835$	7.98719e32	−	3.08886e33i	0.200909	−	0.776970i
$836$	3.80911e32			0.0945042
$837$			3.00359e33i			0.735017i
$838$		−	1.44488e31i		−	0.00348758i
$839$	6.44324e33			1.53406			0.767029	−	0.641612i	$-0.221734\pi$
$839$	6.44324e33			1.53406			0.767029	+	0.641612i	$0.221734\pi$
$840$	5.08621e32	−	1.96697e33i	0.119449	−	0.461941i
$841$	5.87104e33			1.36007
$842$			2.64452e32i			0.0604307i
$843$			4.92099e33i			1.10927i
$844$	−7.17394e33			−1.59522
$845$	−7.28105e33	−	1.88274e33i	−1.59714	−	0.412988i
$846$	9.96203e30			0.00215570
$847$		−	7.27242e33i		−	1.55246i
$848$		−	1.84464e33i		−	0.388472i
$849$	−4.30905e33			−0.895248
$850$	−3.26181e32	−	1.80775e32i	−0.0668560	−	0.0370528i
$851$	−6.53709e33			−1.32189
$852$			7.12854e33i			1.42215i
$853$		−	8.01201e32i		−	0.157699i	−0.996887	−	0.0788493i	$-0.974875\pi$
$853$		−	8.01201e32i		−	0.157699i	0.996887	−	0.0788493i	$-0.0251246\pi$
$854$	−2.74930e32			−0.0533896
$855$	1.05808e32	+	2.73598e31i	0.0202725	+	0.00524206i
$856$	−1.74577e33			−0.330019
$857$			1.18824e33i			0.221628i	0.993841	+	0.110814i	$0.0353457\pi$
$857$			1.18824e33i			0.221628i	−0.993841	+	0.110814i	$0.964654\pi$
$858$		−	1.87540e32i		−	0.0345135i
$859$	−4.00333e33			−0.726943			−0.363471	−	0.931605i	$-0.618409\pi$
$859$	−4.00333e33			−0.726943			−0.363471	+	0.931605i	$0.618409\pi$
$860$	−8.09475e32	+	3.13046e33i	−0.145034	+	0.560887i
$861$	3.78321e33			0.668842
$862$		−	2.55340e32i		−	0.0445436i
$863$		−	8.84592e32i		−	0.152272i	−0.997097	−	0.0761358i	$-0.975742\pi$
$863$		−	8.84592e32i		−	0.152272i	0.997097	−	0.0761358i	$-0.0242582\pi$
$864$	−2.68670e33			−0.456364
$865$	−5.37959e32	+	2.08043e33i	−0.0901705	+	0.348713i
$866$	3.86188e32			0.0638767
$867$		−	4.56411e33i		−	0.744966i
$868$		−	6.95006e33i		−	1.11947i
$869$	1.74752e32			0.0277776
$870$	1.44623e33	+	3.73966e32i	0.226864	+	0.0586626i
$871$	9.53407e33			1.47594
$872$		−	1.94824e33i		−	0.297647i
$873$		−	4.93954e31i		−	0.00744771i
$874$	−8.32796e32			−0.123925
$875$	−7.41909e33	+	7.81973e33i	−1.08958	+	1.14842i
$876$	8.72080e33			1.26404
$877$			8.56753e33i			1.22563i	0.790225	+	0.612817i	$0.209964\pi$
$877$			8.56753e33i			1.22563i	−0.790225	+	0.612817i	$0.790036\pi$
$878$		−	9.54541e32i		−	0.134775i
$879$	−7.80081e33			−1.08710
$880$	9.08589e32	+	2.34943e32i	0.124973	+	0.0323156i
$881$	4.76522e33			0.646934			0.323467	−	0.946239i	$-0.395152\pi$
$881$	4.76522e33			0.646934			0.323467	+	0.946239i	$0.395152\pi$
$882$			5.23252e31i			0.00701168i
$883$			5.97151e33i			0.789835i	0.918717	+	0.394917i	$0.129227\pi$
$883$			5.97151e33i			0.789835i	−0.918717	+	0.394917i	$0.870773\pi$
$884$	6.00581e33			0.784098
$885$	2.13352e33	−	8.25089e33i	0.274947	−	1.06329i
$886$	−3.76566e32			−0.0479019
$887$		−	7.37111e33i		−	0.925574i	−0.886470	−	0.462787i	$-0.846850\pi$
$887$		−	7.37111e33i		−	0.925574i	0.886470	−	0.462787i	$-0.153150\pi$
$888$			2.79820e33i			0.346841i
$889$	−2.93229e33			−0.358787
$890$	−1.32543e31	+	5.12578e31i	−0.00160092	+	0.00619120i
$891$	−1.12972e33			−0.134702
$892$		−	7.24644e33i		−	0.852960i
$893$			2.77558e33i			0.322524i
$894$	4.15164e32			0.0476253
$895$	5.16570e33	+	1.33575e33i	0.585011	+	0.151272i
$896$	8.25318e33			0.922740
$897$		−	1.66837e34i		−	1.84154i
$898$		−	6.49108e32i		−	0.0707358i
$899$	1.03457e34			1.11308
$900$	2.41592e32	+	1.33894e32i	0.0256622	+	0.0142224i
$901$	−1.96869e33			−0.206463
$902$		−	8.91978e31i		−	0.00923590i
$903$			9.05210e33i			0.925423i
$904$	4.10681e33			0.414541
$905$	−1.57385e34	−	4.06967e33i	−1.56857	−	0.405602i
$906$	−1.26034e31			−0.00124026
$907$			1.64019e34i			1.59372i	0.604166	+	0.796859i	$0.293507\pi$
$907$			1.64019e34i			1.59372i	−0.604166	+	0.796859i	$0.706493\pi$
$908$		−	1.02566e33i		−	0.0984051i
$909$	−3.46294e32			−0.0328065
$910$	−1.06805e33	+	4.13044e33i	−0.0999116	+	0.386385i
$911$	8.41201e33			0.777031			0.388515	−	0.921442i	$-0.372988\pi$
$911$	8.41201e33			0.777031			0.388515	+	0.921442i	$0.372988\pi$
$912$		−	6.98406e33i		−	0.637041i
$913$		−	1.31916e33i		−	0.118818i
$914$	−1.49028e33			−0.132552
$915$	−6.11271e32	+	2.36395e33i	−0.0536897	+	0.207633i
$916$	−6.13848e33			−0.532430
$917$			2.65940e34i			2.27790i
$918$			9.16707e32i			0.0775425i
$919$	−1.29076e34			−1.07824			−0.539122	−	0.842227i	$-0.681244\pi$
$919$	−1.29076e34			−1.07824			−0.539122	+	0.842227i	$0.681244\pi$
$920$	−4.12566e33	−	1.06681e33i	−0.340356	−	0.0880093i
$921$	−1.88855e34			−1.53866
$922$		−	1.92398e33i		−	0.154808i
$923$		−	3.03063e34i		−	2.40831i
$924$	2.69516e33			0.211523
$925$	7.19663e33	−	1.29852e34i	0.557827	−	1.00651i
$926$	−1.68186e33			−0.128755
$927$		−	1.80050e32i		−	0.0136137i
$928$			9.25423e33i			0.691096i
$929$	1.74424e33			0.128655			0.0643274	−	0.997929i	$-0.479510\pi$
$929$	1.74424e33			0.128655			0.0643274	+	0.997929i	$0.479510\pi$
$930$	1.46865e33	+	3.79765e32i	0.106996	+	0.0276670i
$931$	−1.45786e34			−1.04905
$932$			1.45494e34i			1.03410i
$933$			1.11435e34i			0.782319i
$934$	2.72189e33			0.188747
$935$	2.50743e32	−	9.69692e32i	0.0171750	−	0.0664202i
$936$	2.21332e32			0.0149752
$937$		−	1.34695e34i		−	0.900216i	−0.892974	−	0.450108i	$-0.851385\pi$
$937$		−	1.34695e34i		−	0.900216i	0.892974	−	0.450108i	$-0.148615\pi$
$938$		−	3.36733e33i		−	0.222307i
$939$	−1.19218e33			−0.0777478
$940$	−1.75618e33	+	6.79162e33i	−0.113135	+	0.437525i
$941$	−6.18067e33			−0.393328			−0.196664	−	0.980471i	$-0.563011\pi$
$941$	−6.18067e33			−0.393328			−0.196664	+	0.980471i	$0.563011\pi$
$942$		−	7.23132e32i		−	0.0454603i
$943$		−	7.93514e33i		−	0.492799i
$944$	1.68791e34			1.03555
$945$	2.56531e34	+	6.63339e33i	1.55480	+	0.402040i
$946$	2.13424e32			0.0127790
$947$		−	2.85928e33i		−	0.169135i	−0.996418	−	0.0845673i	$-0.973049\pi$
$947$		−	2.85928e33i		−	0.169135i	0.996418	−	0.0845673i	$-0.0269508\pi$
$948$		−	3.28687e33i		−	0.192082i
$949$	−3.70756e34			−2.14056
$950$	9.16818e32	−	1.65426e33i	0.0522952	−	0.0943585i
$951$	3.08924e34			1.74091
$952$		−	4.29450e33i		−	0.239105i
$953$			1.98643e34i			1.09271i	0.837554	+	0.546355i	$0.183985\pi$
$953$			1.98643e34i			1.09271i	−0.837554	+	0.546355i	$0.816015\pi$
$954$	−3.58358e31			−0.00194765
$955$	1.70693e34	+	4.41379e33i	0.916594	+	0.237013i
$956$	−2.91268e34			−1.54535
$957$			4.01197e33i			0.210315i
$958$			1.35189e33i			0.0700228i
$959$	5.50261e34			2.81614
$960$	4.18790e33	−	1.61958e34i	0.211776	−	0.818996i
$961$	−9.50715e33			−0.475041
$962$		−	5.87594e33i		−	0.290111i
$963$		−	6.64457e32i		−	0.0324164i
$964$	−3.53671e33			−0.170496
$965$	1.73760e33	−	6.71977e33i	0.0827724	−	0.320103i
$966$	−5.89251e33			−0.277373
$967$			2.37516e33i			0.110481i	0.998473	+	0.0552407i	$0.0175926\pi$
$967$			2.37516e33i			0.110481i	−0.998473	+	0.0552407i	$0.982407\pi$
$968$			6.52932e33i			0.300124i
$969$	−7.45374e33			−0.338572
$970$	−8.27613e32	−	2.14005e32i	−0.0371495	−	0.00960612i
$971$	−5.00274e33			−0.221915			−0.110957	−	0.993825i	$-0.535392\pi$
$971$	−5.00274e33			−0.221915			−0.110957	+	0.993825i	$0.535392\pi$
$972$		−	1.33814e33i		−	0.0586595i
$973$		−	2.36424e34i		−	1.02422i
$974$	3.76544e33			0.161209
$975$	3.31403e34	+	1.83670e34i	1.40218	+	0.777114i
$976$	−4.83600e33			−0.202215
$977$		−	4.46851e34i		−	1.84661i	−0.384066	−	0.923306i	$-0.625476\pi$
$977$		−	4.46851e34i		−	1.84661i	0.384066	−	0.923306i	$-0.374524\pi$
$978$		−	2.15030e33i		−	0.0878219i
$979$	−1.42194e32			−0.00573957
$980$	−3.56727e34	−	9.22427e33i	−1.42310	−	0.367987i
$981$	7.41517e32			0.0292367
$982$			1.18564e33i			0.0462032i
$983$			5.04005e33i			0.194120i	0.995279	+	0.0970598i	$0.0309438\pi$
$983$			5.04005e33i			0.194120i	−0.995279	+	0.0970598i	$0.969056\pi$
$984$	−3.39664e33			−0.129302
$985$	−1.27850e34	+	4.94432e34i	−0.481045	+	1.86033i
$986$	3.15756e33			0.117427
$987$			1.96388e34i			0.721885i
$988$			3.04590e34i			1.10665i
$989$	1.89865e34			0.681846
$990$	4.56424e30	−	1.76511e31i	0.000162018	−	0.000626568i
$991$	−2.67998e34			−0.940338			−0.470169	−	0.882576i	$-0.655807\pi$
$991$	−2.67998e34			−0.940338			−0.470169	+	0.882576i	$0.655807\pi$
$992$			9.39773e33i			0.325941i
$993$		−	2.73474e34i		−	0.937560i
$994$	−1.07038e34			−0.362741
$995$	−6.19398e33	−	1.60164e33i	−0.207494	−	0.0536538i
$996$	−2.48118e34			−0.821629
$997$			2.07338e34i			0.678710i	0.940658	+	0.339355i	$0.110209\pi$
$997$			2.07338e34i			0.678710i	−0.940658	+	0.339355i	$0.889791\pi$
$998$			1.36703e33i			0.0442362i
$999$	−3.64940e34			−1.16739

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.24.b.a.4.5	✓	10
3.2	odd	2		45.24.b.b.19.6		10
5.2	odd	4		25.24.a.f.1.6		10
5.3	odd	4		25.24.a.f.1.5		10
5.4	even	2	inner	5.24.b.a.4.6	yes	10
15.14	odd	2		45.24.b.b.19.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.24.b.a.4.5	✓	10	1.1	even	1	trivial
5.24.b.a.4.6	yes	10	5.4	even	2	inner
25.24.a.f.1.5		10	5.3	odd	4
25.24.a.f.1.6		10	5.2	odd	4
45.24.b.b.19.5		10	15.14	odd	2
45.24.b.b.19.6		10	3.2	odd	2

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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	5.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-448.570i q^{2} -302181. i q^{3} +8.18739e6 q^{4} +(1.05706e8 + 2.73336e7i) q^{5} -1.35549e8 q^{6} +8.28173e9i q^{7} -7.43550e9i q^{8} +2.83002e9 q^{9} +O(q^{10})\)	\(q-448.570i q^{2} -302181. i q^{3} +8.18739e6 q^{4} +(1.05706e8 + 2.73336e7i) q^{5} -1.35549e8 q^{6} +8.28173e9i q^{7} -7.43550e9i q^{8} +2.83002e9 q^{9} +(1.22610e10 - 4.74167e10i) q^{10} +1.31538e11 q^{11} -2.47407e12i q^{12} +1.05183e13i q^{13} +3.71494e12 q^{14} +(8.25967e12 - 3.19424e13i) q^{15} +6.53455e13 q^{16} -6.97399e13i q^{17} -1.26946e12i q^{18} +3.53693e14 q^{19} +(8.65458e14 + 2.23791e14i) q^{20} +2.50258e15 q^{21} -5.90041e13i q^{22} -5.24907e15i q^{23} -2.24686e15 q^{24} +(1.04267e16 + 5.77865e15i) q^{25} +4.71818e15 q^{26} -2.93034e16i q^{27} +6.78058e16i q^{28} -1.00934e17 q^{29} +(-1.43284e16 - 3.70504e15i) q^{30} -1.02500e17 q^{31} -9.16855e16i q^{32} -3.97483e16i q^{33} -3.12833e16 q^{34} +(-2.26369e17 + 8.75430e17i) q^{35} +2.31705e16 q^{36} -1.24538e18i q^{37} -1.58656e17i q^{38} +3.17842e18 q^{39} +(2.03239e17 - 7.85979e17i) q^{40} +1.51172e18 q^{41} -1.12258e18i q^{42} +3.61711e18i q^{43} +1.07695e18 q^{44} +(2.99151e17 + 7.73546e16i) q^{45} -2.35458e18 q^{46} +7.84743e18i q^{47} -1.97461e19i q^{48} -4.12183e19 q^{49} +(2.59213e18 - 4.67710e18i) q^{50} -2.10741e19 q^{51} +8.61172e19i q^{52} -2.82290e19i q^{53} -1.31446e19 q^{54} +(1.39044e19 + 3.59540e18i) q^{55} +6.15788e19 q^{56} -1.06879e20i q^{57} +4.52762e19i q^{58} +2.58305e20 q^{59} +(6.76252e19 - 2.61525e20i) q^{60} -7.40067e19 q^{61} +4.59782e19i q^{62} +2.34375e19i q^{63} +5.07030e20 q^{64} +(-2.87502e20 + 1.11185e21i) q^{65} -1.78299e19 q^{66} -9.06429e20i q^{67} -5.70988e20i q^{68} -1.58617e21 q^{69} +(3.92692e20 + 1.01542e20i) q^{70} -2.88130e21 q^{71} -2.10426e19i q^{72} +3.52488e21i q^{73} -5.58641e20 q^{74} +(1.74620e21 - 3.15074e21i) q^{75} +2.89582e21 q^{76} +1.08936e21i q^{77} -1.42574e21i q^{78} +1.32853e21 q^{79} +(6.90742e21 + 1.78612e21i) q^{80} -8.58850e21 q^{81} -6.78114e20i q^{82} -1.00287e22i q^{83} +2.04896e22 q^{84} +(1.90624e21 - 7.37194e21i) q^{85} +1.62253e21 q^{86} +3.05004e22i q^{87} -9.78051e20i q^{88} -1.08101e21 q^{89} +(3.46990e19 - 1.34190e20i) q^{90} -8.71095e22 q^{91} -4.29762e22i q^{92} +3.09734e22i q^{93} +3.52012e21 q^{94} +(3.73875e22 + 9.66768e21i) q^{95} -2.77056e22 q^{96} -1.74541e22i q^{97} +1.84893e22i q^{98} +3.72256e20 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 41272680 q^{4} + 124761750 q^{5} - 2262077880 q^{6} - 189250631370 q^{9}+O(q^{10}) \) 10 * q - 41272680 * q^4 + 124761750 * q^5 - 2262077880 * q^6 - 189250631370 * q^9	\( 10 q - 41272680 q^{4} + 124761750 q^{5} - 2262077880 q^{6} - 189250631370 q^{9} - 992748199000 q^{10} - 1448637536280 q^{11} + 20750531044440 q^{14} - 14566613457000 q^{15} + 307971806876960 q^{16} + 887626815301400 q^{19} - 23\!\cdots\!00 q^{20}+ \cdots + 41\!\cdots\!60 q^{99}+O(q^{100}) \) 10 * q - 41272680 * q^4 + 124761750 * q^5 - 2262077880 * q^6 - 189250631370 * q^9 - 992748199000 * q^10 - 1448637536280 * q^11 + 20750531044440 * q^14 - 14566613457000 * q^15 + 307971806876960 * q^16 + 887626815301400 * q^19 - 2363707755099000 * q^20 - 781158183715080 * q^21 + 58473619965621600 * q^24 - 15436708968968750 * q^25 - 49259739315596880 * q^26 + 68538893585329500 * q^29 - 283259561673249000 * q^30 - 303703652281842880 * q^31 - 288299835336191360 * q^34 + 568057466315481000 * q^35 + 3242003939215214760 * q^36 - 8628905972055907440 * q^39 + 9426000384456940000 * q^40 - 6658832954283527580 * q^41 + 14990828914855427040 * q^44 - 8490880963475889750 * q^45 + 16736621075351903320 * q^46 + 51294362631233173870 * q^49 - 96456356624588250000 * q^50 - 117334349391643270080 * q^51 + 6367892697021344400 * q^54 + 8046234911696751000 * q^55 - 93285217288146540000 * q^56 + 461218638014732785800 * q^59 + 1248088814097510276000 * q^60 + 202894074812420701820 * q^61 - 2597882075263561124480 * q^64 + 404224351485216078000 * q^65 - 2067527591150630859360 * q^66 + 1761142984477245282360 * q^69 + 2651929720118465517000 * q^70 - 6362428274364321596880 * q^71 + 21369976437605310645840 * q^74 - 1268180400269994750000 * q^75 - 28533821601830896716000 * q^76 + 8008906997916696975200 * q^79 + 50390556129429851388000 * q^80 - 63620987817532049079390 * q^81 + 26983560053969205971040 * q^84 + 58719411820058643416000 * q^85 - 73642932902287825779480 * q^86 + 17045340818835962686500 * q^89 + 218378490181286718303000 * q^90 - 261754857315780277067280 * q^91 + 163995755653951693894840 * q^94 + 287254967024630517105000 * q^95 - 1029134712278532215134080 * q^96 + 411070875879864759534360 * q^99

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