LMFDB - Embedded newform 5.26.b.a.4.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,26,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, 26, names="a")

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

chi := DirichletCharacter("5.4");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 26 $
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:	$19.7998389976$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 71168091 x^{10} + \cdots + 10\!\cdots\!36 $ x^12 + 71168091x^10 + 1813581965257740x^8 + 20299276558981985144320x^6 + 100647952747482434827869143040x^4 + 189155799423092547840968636818784256*x^2 + 108016131559589051821063489995287755227136
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{44}\cdot 3^{20}\cdot 5^{29} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			4.11
Root			$4680.77i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.26.b.a.4.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+9361.55i q^{2} +531494. i q^{3} -5.40841e7 q^{4} +(-5.44720e8 - 3.61012e7i) q^{5} -4.97561e9 q^{6} -1.37587e10i q^{7} -1.92189e11i q^{8} +5.64803e11 q^{9} +(3.37963e11 - 5.09942e12i) q^{10} -9.26999e12 q^{11} -2.87454e13i q^{12} -1.02027e14i q^{13} +1.28802e14 q^{14} +(1.91876e13 - 2.89515e14i) q^{15} -1.55712e13 q^{16} +3.06292e15i q^{17} +5.28743e15i q^{18} +5.00581e15 q^{19} +(2.94607e16 + 1.95250e15i) q^{20} +7.31265e15 q^{21} -8.67815e16i q^{22} -9.11014e16i q^{23} +1.02148e17 q^{24} +(2.95417e17 + 3.93301e16i) q^{25} +9.55130e17 q^{26} +7.50518e17i q^{27} +7.44125e17i q^{28} -3.16262e18 q^{29} +(2.71031e18 + 1.79626e17i) q^{30} +3.22878e18 q^{31} -6.59458e18i q^{32} -4.92695e18i q^{33} -2.86736e19 q^{34} +(-4.96704e17 + 7.49462e18i) q^{35} -3.05468e19 q^{36} -1.59124e19i q^{37} +4.68621e19i q^{38} +5.42268e19 q^{39} +(-6.93828e18 + 1.04689e20i) q^{40} -8.10389e19 q^{41} +6.84577e19i q^{42} -3.97592e20i q^{43} +5.01359e20 q^{44} +(-3.07659e20 - 2.03901e19i) q^{45} +8.52850e20 q^{46} -9.69576e20i q^{47} -8.27600e18i q^{48} +1.15177e21 q^{49} +(-3.68191e20 + 2.76556e21i) q^{50} -1.62792e21 q^{51} +5.51804e21i q^{52} -5.88324e21i q^{53} -7.02601e21 q^{54} +(5.04955e21 + 3.34658e20i) q^{55} -2.64427e21 q^{56} +2.66056e21i q^{57} -2.96070e22i q^{58} -2.11464e22 q^{59} +(-1.03774e21 + 1.56582e22i) q^{60} +7.65113e21 q^{61} +3.02264e22i q^{62} -7.77093e21i q^{63} +6.12130e22 q^{64} +(-3.68330e21 + 5.55762e22i) q^{65} +4.61238e22 q^{66} +3.72268e22i q^{67} -1.65655e23i q^{68} +4.84199e22 q^{69} +(-7.01612e22 - 4.64992e21i) q^{70} -3.96178e22 q^{71} -1.08549e23i q^{72} -4.27194e22i q^{73} +1.48965e23 q^{74} +(-2.09037e22 + 1.57012e23i) q^{75} -2.70734e23 q^{76} +1.27543e23i q^{77} +5.07646e23i q^{78} -9.25017e23 q^{79} +(8.48194e21 + 5.62139e20i) q^{80} +7.96549e22 q^{81} -7.58649e23i q^{82} +9.81159e23i q^{83} -3.95498e23 q^{84} +(1.10575e23 - 1.66843e24i) q^{85} +3.72207e24 q^{86} -1.68091e24i q^{87} +1.78160e24i q^{88} -1.32371e24 q^{89} +(1.90883e23 - 2.88017e24i) q^{90} -1.40375e24 q^{91} +4.92714e24i q^{92} +1.71608e24i q^{93} +9.07673e24 q^{94} +(-2.72676e24 - 1.80716e23i) q^{95} +3.50498e24 q^{96} -3.52916e24i q^{97} +1.07823e25i q^{98} -5.23572e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 166691544 q^{4} + 549543060 q^{5} + 10591544184 q^{6} - 3948466041036 q^{9} + 4435846671960 q^{10} - 1090673824176 q^{11} - 890646861445848 q^{14} + 443085522435120 q^{15} + 22\!\cdots\!32 q^{16}+ \cdots - 10\!\cdots\!72 q^{99}+O(q^{100}) $ 12 * q - 166691544 * q^4 + 549543060 * q^5 + 10591544184 * q^6 - 3948466041036 * q^9 + 4435846671960 * q^10 - 1090673824176 * q^11 - 890646861445848 * q^14 + 443085522435120 * q^15 + 2206145875609632 * q^16 + 6329834351210160 * q^19 - 45407795215923720 * q^20 + 13538972741781744 * q^21 - 1238774108159908320 * q^24 + 883359578467451100 * q^25 + 487725686068642704 * q^26 - 5990455853511966360 * q^29 + 8784171220269562920 * q^30 - 35669623242168576 * q^31 - 45224081273675172288 * q^34 + 37959801679716705360 * q^35 + 95509342682184062232 * q^36 + 59576177650244745888 * q^39 - 135247056564421048800 * q^40 - 149504768291960577576 * q^41 + 1795327120321140441312 * q^44 - 1757089887558453396180 * q^45 - 2632260904857596314776 * q^46 - 1924948130789206201884 * q^49 + 4613478251192179347600 * q^50 + 6601362996360626974464 * q^51 - 4543556632841187026640 * q^54 - 4976317493836251356880 * q^55 + 6789286242764162655840 * q^56 - 31976684482970870043120 * q^59 + 38198563842186313414560 * q^60 + 33892026990475241838024 * q^61 - 45154694563657190239104 * q^64 - 23988754129834728629280 * q^65 - 84625057142490628840032 * q^66 + 454638912158488569862128 * q^69 - 514001938945682971911240 * q^70 - 118991523615678935618976 * q^71 - 276076790459758393833168 * q^74 - 256450000750992984232800 * q^75 + 1770023872374606472757280 * q^76 - 741918285485353377639360 * q^79 + 504838130357233934552160 * q^80 + 2020576746978155938317372 * q^81 - 6598941205046486172215328 * q^84 - 1447445120396229235779840 * q^85 + 6309456694176729359288664 * q^86 + 576066549612764658926520 * q^89 - 14281964558091964746137880 * q^90 + 12216814388553519240480864 * q^91 - 11673168428062976516959608 * q^94 - 23618191778193292124785200 * q^95 + 57292208364908004705120384 * q^96 - 10068680551503914801051472 * q^99

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 $

$2$			9361.55i			1.61612i	0.589103	+	0.808058i	$0.299481\pi$
$2$			9361.55i			1.61612i	−0.589103	+	0.808058i	$0.700519\pi$
$3$			531494.i			0.577408i	0.957418	+	0.288704i	$0.0932243\pi$
$3$			531494.i			0.577408i	−0.957418	+	0.288704i	$0.906776\pi$
$4$	−5.40841e7			−1.61183
$5$	−5.44720e8	−	3.61012e7i	−0.997811	−	0.0661298i
$5$	−5.44720e8	−	3.61012e7i	−0.997811	−	0.0661298i
$6$	−4.97561e9			−0.933158
$7$		−	1.37587e10i		−	0.375708i	−0.982197	−	0.187854i	$-0.939847\pi$
$7$		−	1.37587e10i		−	0.375708i	0.982197	−	0.187854i	$-0.0601532\pi$
$8$		−	1.92189e11i		−	0.988791i
$9$	5.64803e11			0.666600
$10$	3.37963e11	−	5.09942e12i	0.106873	−	1.61258i
$11$	−9.26999e12			−0.890576			−0.445288	−	0.895387i	$-0.646899\pi$
$11$	−9.26999e12			−0.890576			−0.445288	+	0.895387i	$0.646899\pi$
$12$		−	2.87454e13i		−	0.930685i
$13$		−	1.02027e14i		−	1.21457i	−0.794483	−	0.607286i	$-0.792258\pi$
$13$		−	1.02027e14i		−	1.21457i	0.794483	−	0.607286i	$-0.207742\pi$
$14$	1.28802e14			0.607188
$15$	1.91876e13	−	2.89515e14i	0.0381839	−	0.576144i
$16$	−1.55712e13			−0.0138300
$17$			3.06292e15i			1.27504i	0.770434	+	0.637520i	$0.220040\pi$
$17$			3.06292e15i			1.27504i	−0.770434	+	0.637520i	$0.779960\pi$
$18$			5.28743e15i			1.07730i
$19$	5.00581e15			0.518864			0.259432	−	0.965761i	$-0.416465\pi$
$19$	5.00581e15			0.518864			0.259432	+	0.965761i	$0.416465\pi$
$20$	2.94607e16	+	1.95250e15i	1.60830	+	0.106590i
$21$	7.31265e15			0.216937
$22$		−	8.67815e16i		−	1.43927i
$23$		−	9.11014e16i		−	0.866817i	−0.901198	−	0.433408i	$-0.857311\pi$
$23$		−	9.11014e16i		−	0.866817i	0.901198	−	0.433408i	$-0.142689\pi$
$24$	1.02148e17			0.570936
$25$	2.95417e17	+	3.93301e16i	0.991254	+	0.131970i
$26$	9.55130e17			1.96289
$27$			7.50518e17i			0.962308i
$28$			7.44125e17i			0.605578i
$29$	−3.16262e18			−1.65986			−0.829930	−	0.557867i	$-0.811620\pi$
$29$	−3.16262e18			−1.65986			−0.829930	+	0.557867i	$0.811620\pi$
$30$	2.71031e18	+	1.79626e17i	0.931116	+	0.0617095i
$31$	3.22878e18			0.736237			0.368119	−	0.929779i	$-0.380002\pi$
$31$	3.22878e18			0.736237			0.368119	+	0.929779i	$0.380002\pi$
$32$		−	6.59458e18i		−	1.01114i
$33$		−	4.92695e18i		−	0.514226i
$34$	−2.86736e19			−2.06061
$35$	−4.96704e17	+	7.49462e18i	−0.0248455	+	0.374886i
$36$	−3.05468e19			−1.07445
$37$		−	1.59124e19i		−	0.397388i	−0.980062	−	0.198694i	$-0.936330\pi$
$37$		−	1.59124e19i		−	0.397388i	0.980062	−	0.198694i	$-0.0636699\pi$
$38$			4.68621e19i			0.838545i
$39$	5.42268e19			0.701303
$40$	−6.93828e18	+	1.04689e20i	−0.0653885	+	0.986627i
$41$	−8.10389e19			−0.560913			−0.280456	−	0.959867i	$-0.590486\pi$
$41$	−8.10389e19			−0.560913			−0.280456	+	0.959867i	$0.590486\pi$
$42$			6.84577e19i			0.350595i
$43$		−	3.97592e20i		−	1.51734i	−0.651478	−	0.758668i	$-0.725851\pi$
$43$		−	3.97592e20i		−	1.51734i	0.651478	−	0.758668i	$-0.274149\pi$
$44$	5.01359e20			1.43546
$45$	−3.07659e20	−	2.03901e19i	−0.665141	−	0.0440821i
$46$	8.52850e20			1.40088
$47$		−	9.69576e20i		−	1.21719i	−0.793481	−	0.608595i	$-0.791733\pi$
$47$		−	9.69576e20i		−	1.21719i	0.793481	−	0.608595i	$-0.208267\pi$
$48$		−	8.27600e18i		−	0.00798555i
$49$	1.15177e21			0.858843
$50$	−3.68191e20	+	2.76556e21i	−0.213279	+	1.60198i
$51$	−1.62792e21			−0.736218
$52$			5.51804e21i			1.95769i
$53$		−	5.88324e21i		−	1.64501i	−0.568759	−	0.822504i	$-0.692576\pi$
$53$		−	5.88324e21i		−	1.64501i	0.568759	−	0.822504i	$-0.307424\pi$
$54$	−7.02601e21			−1.55520
$55$	5.04955e21	+	3.34658e20i	0.888626	+	0.0588936i
$56$	−2.64427e21			−0.371497
$57$			2.66056e21i			0.299596i
$58$		−	2.96070e22i		−	2.68253i
$59$	−2.11464e22			−1.54734			−0.773671	−	0.633588i	$-0.781582\pi$
$59$	−2.11464e22			−1.54734			−0.773671	+	0.633588i	$0.781582\pi$
$60$	−1.03774e21	+	1.56582e22i	−0.0615459	+	0.928647i
$61$	7.65113e21			0.369065			0.184532	−	0.982826i	$-0.440923\pi$
$61$	7.65113e21			0.369065			0.184532	+	0.982826i	$0.440923\pi$
$62$			3.02264e22i			1.18985i
$63$		−	7.77093e21i		−	0.250447i
$64$	6.12130e22			1.62029
$65$	−3.68330e21	+	5.55762e22i	−0.0803194	+	1.21191i
$66$	4.61238e22			0.831048
$67$			3.72268e22i			0.555802i	0.960610	+	0.277901i	$0.0896387\pi$
$67$			3.72268e22i			0.555802i	−0.960610	+	0.277901i	$0.910361\pi$
$68$		−	1.65655e23i		−	2.05515i
$69$	4.84199e22			0.500507
$70$	−7.01612e22	−	4.64992e21i	−0.605859	−	0.0401532i
$71$	−3.96178e22			−0.286524			−0.143262	−	0.989685i	$-0.545759\pi$
$71$	−3.96178e22			−0.286524			−0.143262	+	0.989685i	$0.545759\pi$
$72$		−	1.08549e23i		−	0.659128i
$73$		−	4.27194e22i		−	0.218318i	−0.994024	−	0.109159i	$-0.965184\pi$
$73$		−	4.27194e22i		−	0.218318i	0.994024	−	0.109159i	$-0.0348157\pi$
$74$	1.48965e23			0.642225
$75$	−2.09037e22	+	1.57012e23i	−0.0762005	+	0.572358i
$76$	−2.70734e23			−0.836322
$77$			1.27543e23i			0.334597i
$78$			5.07646e23i			1.13339i
$79$	−9.25017e23			−1.76121			−0.880605	−	0.473851i	$-0.842863\pi$
$79$	−9.25017e23			−1.76121			−0.880605	+	0.473851i	$0.842863\pi$
$80$	8.48194e21	+	5.62139e20i	0.0137997	+	0.000914575i
$81$	7.96549e22			0.110956
$82$		−	7.58649e23i		−	0.906500i
$83$			9.81159e23i			1.00754i	0.863837	+	0.503771i	$0.168054\pi$
$83$			9.81159e23i			1.00754i	−0.863837	+	0.503771i	$0.831946\pi$
$84$	−3.95498e23			−0.349666
$85$	1.10575e23	−	1.66843e24i	0.0843181	−	1.27225i
$86$	3.72207e24			2.45219
$87$		−	1.68091e24i		−	0.958416i
$88$			1.78160e24i			0.880594i
$89$	−1.32371e24			−0.568091			−0.284046	−	0.958811i	$-0.591677\pi$
$89$	−1.32371e24			−0.568091			−0.284046	+	0.958811i	$0.591677\pi$
$90$	1.90883e23	−	2.88017e24i	0.0712418	−	1.07495i
$91$	−1.40375e24			−0.456324
$92$			4.92714e24i			1.39716i
$93$			1.71608e24i			0.425109i
$94$	9.07673e24			1.96712
$95$	−2.72676e24	−	1.80716e23i	−0.517729	−	0.0343124i
$96$	3.50498e24			0.583842
$97$		−	3.52916e24i		−	0.516445i	−0.966085	−	0.258223i	$-0.916863\pi$
$97$		−	3.52916e24i		−	0.516445i	0.966085	−	0.258223i	$-0.0831368\pi$
$98$			1.07823e25i			1.38799i
$99$	−5.23572e24			−0.593658
$100$	−1.59773e25	−	2.12713e24i	−1.59773	−	0.212713i
$101$	−1.04249e25			−0.920570			−0.460285	−	0.887771i	$-0.652253\pi$
$101$	−1.04249e25			−0.920570			−0.460285	+	0.887771i	$0.652253\pi$
$102$		−	1.52399e25i		−	1.18981i
$103$		−	1.55473e25i		−	1.07446i	−0.843436	−	0.537230i	$-0.819471\pi$
$103$		−	1.55473e25i		−	1.07446i	0.843436	−	0.537230i	$-0.180529\pi$
$104$	−1.96085e25			−1.20096
$105$	−3.98334e24	−	2.63996e23i	−0.216462	−	0.0143460i
$106$	5.50762e25			2.65852
$107$			3.91524e25i			1.68059i	0.542131	+	0.840294i	$0.317618\pi$
$107$			3.91524e25i			1.68059i	−0.542131	+	0.840294i	$0.682382\pi$
$108$		−	4.05911e25i		−	1.55108i
$109$	−1.97006e25			−0.670886			−0.335443	−	0.942060i	$-0.608886\pi$
$109$	−1.97006e25			−0.670886			−0.335443	+	0.942060i	$0.608886\pi$
$110$	−3.13292e24	+	4.72716e25i	−0.0951789	+	1.43612i
$111$	8.45735e24			0.229455
$112$			2.14239e23i			0.00519604i
$113$			4.21994e25i			0.915853i	0.888990	+	0.457926i	$0.151408\pi$
$113$			4.21994e25i			0.915853i	−0.888990	+	0.457926i	$0.848592\pi$
$114$	−2.49069e25			−0.484183
$115$	−3.28887e24	+	4.96248e25i	−0.0573224	+	0.864919i
$116$	1.71047e26			2.67542
$117$		−	5.76251e25i		−	0.809634i
$118$		−	1.97963e26i		−	2.50068i
$119$	4.21416e25			0.479043
$120$	−5.56418e25	−	3.68765e24i	−0.569686	−	0.0377559i
$121$	−2.24143e25			−0.206875
$122$			7.16264e25i			0.596452i
$123$		−	4.30717e25i		−	0.323875i
$124$	−1.74626e26			−1.18669
$125$	−1.59499e26	−	3.20888e25i	−0.980357	−	0.197233i
$126$	7.27479e25			0.404752
$127$			1.11228e26i			0.560619i	0.959910	+	0.280310i	$0.0904372\pi$
$127$			1.11228e26i			0.560619i	−0.959910	+	0.280310i	$0.909563\pi$
$128$			3.51771e26i			1.60744i
$129$	2.11318e26			0.876122
$130$	−5.20279e26	−	3.44814e25i	−1.95859	−	0.129805i
$131$	2.15522e26			0.737227			0.368613	−	0.929583i	$-0.379833\pi$
$131$	2.15522e26			0.737227			0.368613	+	0.929583i	$0.379833\pi$
$132$			2.66470e26i			0.828845i
$133$		−	6.88732e25i		−	0.194942i
$134$	−3.48500e26			−0.898241
$135$	2.70946e25	−	4.08822e26i	0.0636372	−	0.960202i
$136$	5.88660e26			1.26075
$137$		−	9.54103e26i		−	1.86461i	−0.361672	−	0.932305i	$-0.617794\pi$
$137$		−	9.54103e26i		−	1.86461i	0.361672	−	0.932305i	$-0.382206\pi$
$138$			4.53285e26i			0.808877i
$139$	−2.71293e26			−0.442337			−0.221169	−	0.975236i	$-0.570987\pi$
$139$	−2.71293e26			−0.442337			−0.221169	+	0.975236i	$0.570987\pi$
$140$	2.68638e25	−	4.05340e26i	0.0400467	−	0.604253i
$141$	5.15324e26			0.702816
$142$		−	3.70884e26i		−	0.463056i
$143$			9.45790e26i			1.08167i
$144$	−8.79465e24			−0.00921908
$145$	1.72274e27	+	1.14174e26i	1.65623	+	0.109766i
$146$	3.99919e26			0.352827
$147$			6.12158e26i			0.495903i
$148$			8.60608e26i			0.640522i
$149$	−2.96654e26			−0.202966			−0.101483	−	0.994837i	$-0.532359\pi$
$149$	−2.96654e26			−0.202966			−0.101483	+	0.994837i	$0.532359\pi$
$150$	−1.46988e27	−	1.95691e26i	−0.924997	−	0.123149i
$151$	2.46628e26			0.142834			0.0714169	−	0.997447i	$-0.477248\pi$
$151$	2.46628e26			0.142834			0.0714169	+	0.997447i	$0.477248\pi$
$152$		−	9.62063e26i		−	0.513049i
$153$			1.72994e27i			0.849942i
$154$	−1.19400e27			−0.540747
$155$	−1.75878e27	−	1.16563e26i	−0.734626	−	0.0486872i
$156$	−2.93281e27			−1.13038
$157$			6.49248e26i			0.231028i	0.993306	+	0.115514i	$0.0368516\pi$
$157$			6.49248e26i			0.231028i	−0.993306	+	0.115514i	$0.963148\pi$
$158$		−	8.65959e27i		−	2.84632i
$159$	3.12691e27			0.949841
$160$	−2.38072e26	+	3.59220e27i	−0.0668666	+	1.00893i
$161$	−1.25343e27			−0.325670
$162$			7.45693e26i			0.179317i
$163$		−	4.33189e26i		−	0.0964567i	−0.998836	−	0.0482283i	$-0.984642\pi$
$163$		−	4.33189e26i		−	0.0964567i	0.998836	−	0.0482283i	$-0.0153575\pi$
$164$	4.38291e27			0.904097
$165$	−1.77869e26	+	2.68381e27i	−0.0340056	+	0.513100i
$166$	−9.18516e27			−1.62830
$167$		−	1.30454e26i		−	0.0214536i	−0.999942	−	0.0107268i	$-0.996585\pi$
$167$		−	1.30454e26i		−	0.0214536i	0.999942	−	0.0107268i	$-0.00341451\pi$
$168$		−	1.40541e27i		−	0.214505i
$169$	−3.35310e27			−0.475185
$170$	1.56191e28	+	1.03515e27i	2.05610	+	0.136268i
$171$	2.82729e27			0.345875
$172$			2.15034e28i			2.44569i
$173$		−	6.64872e27i		−	0.703335i	−0.936125	−	0.351667i	$-0.885615\pi$
$173$		−	6.64872e27i		−	0.703335i	0.936125	−	0.351667i	$-0.114385\pi$
$174$	1.57359e28			1.54891
$175$	5.41130e26	−	4.06454e27i	0.0495822	−	0.372422i
$176$	1.44345e26			0.0123167
$177$		−	1.12392e28i		−	0.893447i
$178$		−	1.23920e28i		−	0.918102i
$179$	−1.37345e28			−0.948749			−0.474375	−	0.880323i	$-0.657326\pi$
$179$	−1.37345e28			−0.948749			−0.474375	+	0.880323i	$0.657326\pi$
$180$	1.66395e28	+	1.10278e27i	1.07210	+	0.0710529i
$181$	−2.24199e28			−1.34788			−0.673941	−	0.738786i	$-0.735400\pi$
$181$	−2.24199e28			−1.34788			−0.673941	+	0.738786i	$0.735400\pi$
$182$		−	1.31413e28i		−	0.737473i
$183$			4.06653e27i			0.213101i
$184$	−1.75087e28			−0.857101
$185$	−5.74457e26	+	8.66781e27i	−0.0262791	+	0.396518i
$186$	−1.60652e28			−0.687026
$187$		−	2.83932e28i		−	1.13552i
$188$			5.24386e28i			1.96191i
$189$	1.03261e28			0.361547
$190$	1.69178e27	−	2.55267e28i	0.0554528	−	0.836710i
$191$	−6.91841e26			−0.0212368			−0.0106184	−	0.999944i	$-0.503380\pi$
$191$	−6.91841e26			−0.0212368			−0.0106184	+	0.999944i	$0.503380\pi$
$192$			3.25343e28i			0.935570i
$193$			6.51372e28i			1.75535i	0.479259	+	0.877673i	$0.340905\pi$
$193$			6.51372e28i			1.75535i	−0.479259	+	0.877673i	$0.659095\pi$
$194$	3.30384e28			0.834636
$195$	−2.95384e28	−	1.95765e27i	−0.699768	−	0.0463770i
$196$	−6.22923e28			−1.38431
$197$		−	4.73638e27i		−	0.0987686i	−0.998780	−	0.0493843i	$-0.984274\pi$
$197$		−	4.73638e27i		−	0.0987686i	0.998780	−	0.0493843i	$-0.0157259\pi$
$198$		−	4.90144e28i		−	0.959420i
$199$	3.76031e28			0.691131			0.345565	−	0.938395i	$-0.387687\pi$
$199$	3.76031e28			0.691131			0.345565	+	0.938395i	$0.387687\pi$
$200$	7.55884e27	−	5.67760e28i	0.130491	−	0.980143i
$201$	−1.97858e28			−0.320925
$202$		−	9.75936e28i		−	1.48775i
$203$			4.35134e28i			0.623623i
$204$	8.80447e28			1.18666
$205$	4.41435e28	+	2.92560e27i	0.559685	+	0.0370930i
$206$	1.45547e29			1.73645
$207$		−	5.14543e28i		−	0.577820i
$208$			1.58868e27i			0.0167975i
$209$	−4.64038e28			−0.462088
$210$	2.47141e27	−	3.72903e28i	0.0231848	−	0.349828i
$211$	2.10105e28			0.185740			0.0928700	−	0.995678i	$-0.470396\pi$
$211$	2.10105e28			0.185740			0.0928700	+	0.995678i	$0.470396\pi$
$212$			3.18190e29i			2.65148i
$213$		−	2.10566e28i		−	0.165441i
$214$	−3.66527e29			−2.71603
$215$	−1.43536e28	+	2.16576e29i	−0.100341	+	1.51401i
$216$	1.44242e29			0.951522
$217$		−	4.44237e28i		−	0.276610i
$218$		−	1.84428e29i		−	1.08423i
$219$	2.27051e28			0.126058
$220$	−2.73100e29	−	1.80997e28i	−1.43232	−	0.0949265i
$221$	3.12500e29			1.54863
$222$			7.91739e28i			0.370826i
$223$		−	2.96364e29i		−	1.31224i	−0.754655	−	0.656122i	$-0.772196\pi$
$223$		−	2.96364e29i		−	1.31224i	0.754655	−	0.656122i	$-0.227804\pi$
$224$	−9.07325e28			−0.379894
$225$	1.66852e29	+	2.22138e28i	0.660770	+	0.0879712i
$226$	−3.95051e29			−1.48012
$227$		−	2.89017e29i		−	1.02471i	−0.858775	−	0.512354i	$-0.828774\pi$
$227$		−	2.89017e29i		−	1.02471i	0.858775	−	0.512354i	$-0.171226\pi$
$228$		−	1.43894e29i		−	0.482899i
$229$	−1.38694e29			−0.440670			−0.220335	−	0.975424i	$-0.570715\pi$
$229$	−1.38694e29			−0.440670			−0.220335	+	0.975424i	$0.570715\pi$
$230$	−4.64565e29	−	3.07889e28i	−1.39781	−	0.0926397i
$231$	−6.77882e28			−0.193199
$232$			6.07821e29i			1.64126i
$233$		−	1.00825e29i		−	0.258000i	−0.991645	−	0.129000i	$-0.958823\pi$
$233$		−	1.00825e29i		−	0.258000i	0.991645	−	0.129000i	$-0.0411768\pi$
$234$	5.39460e29			1.30846
$235$	−3.50029e28	+	5.28147e29i	−0.0804925	+	1.21453i
$236$	1.14368e30			2.49405
$237$		−	4.91641e29i		−	1.01694i
$238$			3.94511e29i			0.774189i
$239$	5.29180e29			0.985438			0.492719	−	0.870188i	$-0.336003\pi$
$239$	5.29180e29			0.985438			0.492719	+	0.870188i	$0.336003\pi$
$240$	−2.98774e26	+	4.50810e27i	−0.000528083	+	0.00796807i
$241$	−4.04250e28			−0.0678324			−0.0339162	−	0.999425i	$-0.510798\pi$
$241$	−4.04250e28			−0.0678324			−0.0339162	+	0.999425i	$0.510798\pi$
$242$		−	2.09832e29i		−	0.334333i
$243$			6.78242e29i			1.02637i
$244$	−4.13804e29			−0.594870
$245$	−6.27391e29	−	4.15802e28i	−0.856963	−	0.0567951i
$246$	4.03217e29			0.523420
$247$		−	5.10727e29i		−	0.630198i
$248$		−	6.20538e29i		−	0.727985i
$249$	−5.21480e29			−0.581763
$250$	3.00401e29	−	1.49316e30i	0.318751	−	1.58437i
$251$	4.46094e29			0.450303			0.225151	−	0.974324i	$-0.427712\pi$
$251$	4.46094e29			0.450303			0.225151	+	0.974324i	$0.427712\pi$
$252$			4.20284e29i			0.403678i
$253$			8.44510e29i			0.771966i
$254$	−1.04127e30			−0.906026
$255$	8.86762e29	+	5.87700e28i	0.734607	+	0.0486859i
$256$	−1.23915e30			−0.977517
$257$		−	9.74169e29i		−	0.731931i	−0.930628	−	0.365965i	$-0.880739\pi$
$257$		−	9.74169e29i		−	0.731931i	0.930628	−	0.365965i	$-0.119261\pi$
$258$			1.97826e30i			1.41591i
$259$	−2.18933e29			−0.149302
$260$	1.99208e29	−	3.00579e30i	0.129461	−	1.95340i
$261$	−1.78625e30			−1.10646
$262$			2.01762e30i			1.19144i
$263$			1.52948e30i			0.861188i	0.902546	+	0.430594i	$0.141696\pi$
$263$			1.52948e30i			0.861188i	−0.902546	+	0.430594i	$0.858304\pi$
$264$	−9.46907e29			−0.508462
$265$	−2.12392e29	+	3.20472e30i	−0.108784	+	1.64141i
$266$	6.44759e29			0.315048
$267$		−	7.03545e29i		−	0.328020i
$268$		−	2.01338e30i		−	0.895860i
$269$	−2.62915e29			−0.111663			−0.0558317	−	0.998440i	$-0.517781\pi$
$269$	−2.62915e29			−0.111663			−0.0558317	+	0.998440i	$0.517781\pi$
$270$	3.82721e30	+	2.53648e29i	1.55180	+	0.102845i
$271$	−2.83737e30			−1.09850			−0.549249	−	0.835658i	$-0.685086\pi$
$271$	−2.83737e30			−1.09850			−0.549249	+	0.835658i	$0.685086\pi$
$272$		−	4.76933e28i		−	0.0176338i
$273$		−	7.46087e29i		−	0.263485i
$274$	8.93188e30			3.01343
$275$	−2.73851e30	−	3.64590e29i	−0.882787	−	0.117529i
$276$	−2.61875e30			−0.806733
$277$		−	2.96419e30i		−	0.872788i	−0.899756	−	0.436394i	$-0.856255\pi$
$277$		−	2.96419e30i		−	0.872788i	0.899756	−	0.436394i	$-0.143745\pi$
$278$		−	2.53972e30i		−	0.714868i
$279$	1.82363e30			0.490776
$280$	1.44039e30	+	9.54614e28i	0.370684	+	0.0245670i
$281$	3.78581e30			0.931816			0.465908	−	0.884833i	$-0.345728\pi$
$281$	3.78581e30			0.931816			0.465908	+	0.884833i	$0.345728\pi$
$282$			4.82423e30i			1.13583i
$283$		−	5.09128e30i		−	1.14682i	−0.819267	−	0.573412i	$-0.805619\pi$
$283$		−	5.09128e30i		−	1.14682i	0.819267	−	0.573412i	$-0.194381\pi$
$284$	2.14269e30			0.461829
$285$	9.60493e28	−	1.44926e30i	0.0198122	−	0.298941i
$286$	−8.85405e30			−1.74810
$287$			1.11499e30i			0.210739i
$288$		−	3.72463e30i		−	0.674027i
$289$	−3.61083e30			−0.625727
$290$	−1.06885e30	+	1.61275e31i	−0.177395	+	2.67666i
$291$	1.87573e30			0.298200
$292$			2.31044e30i			0.351891i
$293$			6.28617e30i			0.917362i	0.888601	+	0.458681i	$0.151678\pi$
$293$			6.28617e30i			0.917362i	−0.888601	+	0.458681i	$0.848322\pi$
$294$	−5.73074e30			−0.801437
$295$	1.15189e31	+	7.63411e29i	1.54395	+	0.102325i
$296$	−3.05820e30			−0.392933
$297$		−	6.95730e30i		−	0.857008i
$298$		−	2.77714e30i		−	0.328016i
$299$	−9.29481e30			−1.05281
$300$	1.13056e30	−	8.49186e30i	0.122822	−	0.922544i
$301$	−5.47033e30			−0.570075
$302$			2.30882e30i			0.230836i
$303$		−	5.54080e30i		−	0.531544i
$304$	−7.79464e28			−0.00717590
$305$	−4.16772e30	−	2.76215e29i	−0.368257	−	0.0244062i
$306$	−1.61949e31			−1.37360
$307$			1.10314e30i			0.0898261i	0.998991	+	0.0449130i	$0.0143011\pi$
$307$			1.10314e30i			0.0898261i	−0.998991	+	0.0449130i	$0.985699\pi$
$308$		−	6.89803e30i		−	0.539313i
$309$	8.26332e30			0.620402
$310$	1.09121e30	−	1.64649e31i	0.0786842	−	1.18724i
$311$	2.41872e31			1.67525			0.837627	−	0.546242i	$-0.183942\pi$
$311$	2.41872e31			1.67525			0.837627	+	0.546242i	$0.183942\pi$
$312$		−	1.04218e31i		−	0.693443i
$313$			1.66307e31i			1.06318i	0.847002	+	0.531589i	$0.178405\pi$
$313$			1.66307e31i			1.06318i	−0.847002	+	0.531589i	$0.821595\pi$
$314$	−6.07797e30			−0.373369
$315$	−2.80540e29	+	4.23298e30i	−0.0165620	+	0.249899i
$316$	5.00287e31			2.83877
$317$			2.91127e31i			1.58797i	0.607939	+	0.793984i	$0.291997\pi$
$317$			2.91127e31i			1.58797i	−0.607939	+	0.793984i	$0.708003\pi$
$318$			2.92727e31i			1.53505i
$319$	2.93174e31			1.47823
$320$	−3.33439e31	−	2.20986e30i	−1.61675	−	0.107150i
$321$	−2.08093e31			−0.970385
$322$		−	1.17341e31i		−	0.526321i
$323$			1.53324e31i			0.661573i
$324$	−4.30806e30			−0.178842
$325$	4.01274e30	−	3.01405e31i	0.160287	−	1.20395i
$326$	4.05532e30			0.155885
$327$		−	1.04708e31i		−	0.387375i
$328$			1.55748e31i			0.554625i
$329$	−1.33401e31			−0.457308
$330$	−2.51246e31	−	1.66513e30i	−0.829229	−	0.0549570i
$331$	1.93746e31			0.615719			0.307860	−	0.951432i	$-0.400387\pi$
$331$	1.93746e31			0.615719			0.307860	+	0.951432i	$0.400387\pi$
$332$		−	5.30651e31i		−	1.62399i
$333$		−	8.98737e30i		−	0.264899i
$334$	1.22125e30			0.0346715
$335$	1.34393e30	−	2.02782e31i	0.0367551	−	0.554586i
$336$	−1.13867e29			−0.00300024
$337$			2.56947e30i			0.0652335i	0.999468	+	0.0326167i	$0.0103841\pi$
$337$			2.56947e30i			0.0652335i	−0.999468	+	0.0326167i	$0.989616\pi$
$338$		−	3.13902e31i		−	0.767954i
$339$	−2.24287e31			−0.528821
$340$	−5.98035e30	+	9.02357e31i	−0.135907	+	2.05065i
$341$	−2.99308e31			−0.655675
$342$			2.64678e31i			0.558974i
$343$		−	3.42981e31i		−	0.698383i
$344$	−7.64129e31			−1.50033
$345$	−2.63753e31	−	1.74802e30i	−0.499411	−	0.0330984i
$346$	6.22423e31			1.13667
$347$			3.68925e31i			0.649860i	0.945738	+	0.324930i	$0.105341\pi$
$347$			3.68925e31i			0.649860i	−0.945738	+	0.324930i	$0.894659\pi$
$348$			9.09106e31i			1.54481i
$349$	−8.90327e31			−1.45959			−0.729796	−	0.683665i	$-0.760385\pi$
$349$	−8.90327e31			−1.45959			−0.729796	+	0.683665i	$0.760385\pi$
$350$	3.80503e31	+	5.06581e30i	0.601877	+	0.0801306i
$351$	7.65731e31			1.16879
$352$			6.11317e31i			0.900499i
$353$		−	1.18792e32i		−	1.68890i	−0.535638	−	0.844448i	$-0.679929\pi$
$353$		−	1.18792e32i		−	1.68890i	0.535638	−	0.844448i	$-0.320071\pi$
$354$	1.05216e32			1.44391
$355$	2.15806e31	+	1.43025e30i	0.285897	+	0.0189478i
$356$	7.15917e31			0.915668
$357$			2.23980e31i			0.276603i
$358$		−	1.28577e32i		−	1.53329i
$359$	3.43106e31			0.395137			0.197569	−	0.980289i	$-0.436695\pi$
$359$	3.43106e31			0.395137			0.197569	+	0.980289i	$0.436695\pi$
$360$	−3.91876e30	+	5.91289e31i	−0.0435880	+	0.657686i
$361$	−6.80184e31			−0.730780
$362$		−	2.09885e32i		−	2.17833i
$363$		−	1.19130e31i		−	0.119451i
$364$	7.59208e31			0.735518
$365$	−1.54222e30	+	2.32701e31i	−0.0144373	+	0.217840i
$366$	−3.80690e31			−0.344396
$367$			1.81832e32i			1.58981i	0.606735	+	0.794904i	$0.292479\pi$
$367$			1.81832e32i			1.58981i	−0.606735	+	0.794904i	$0.707521\pi$
$368$			1.41856e30i			0.0119881i
$369$	−4.57710e31			−0.373904
$370$	−8.11441e31	−	5.37781e30i	−0.640819	−	0.0424702i
$371$	−8.09454e31			−0.618043
$372$		−	9.28126e31i		−	0.685205i
$373$		−	4.57515e31i		−	0.326621i	−0.986575	−	0.163311i	$-0.947783\pi$
$373$		−	4.57515e31i		−	0.326621i	0.986575	−	0.163311i	$-0.0522173\pi$
$374$	2.65804e32			1.83513
$375$	1.70550e31	−	8.47730e31i	0.113884	−	0.566066i
$376$	−1.86342e32			−1.20355
$377$			3.22672e32i			2.01602i
$378$			9.66685e31i			0.584302i
$379$	5.21676e31			0.305078			0.152539	−	0.988297i	$-0.451255\pi$
$379$	5.21676e31			0.305078			0.152539	+	0.988297i	$0.451255\pi$
$380$	1.47474e32	+	9.77385e30i	0.834492	+	0.0553058i
$381$	−5.91171e31			−0.323706
$382$		−	6.47670e30i		−	0.0343212i
$383$			1.65045e32i			0.846481i	0.906017	+	0.423240i	$0.139107\pi$
$383$			1.65045e32i			0.846481i	−0.906017	+	0.423240i	$0.860893\pi$
$384$	−1.86964e32			−0.928149
$385$	4.60445e30	−	6.94751e31i	0.0221268	−	0.333864i
$386$	−6.09785e32			−2.83684
$387$		−	2.24561e32i		−	1.01146i
$388$			1.90871e32i			0.832423i
$389$	−2.98846e32			−1.26205			−0.631025	−	0.775762i	$-0.717366\pi$
$389$	−2.98846e32			−1.26205			−0.631025	+	0.775762i	$0.717366\pi$
$390$	1.83267e31	−	2.76525e32i	0.0749507	−	1.13091i
$391$	2.79036e32			1.10523
$392$		−	2.21358e32i		−	0.849217i
$393$			1.14549e32i			0.425681i
$394$	4.43399e31			0.159622
$395$	5.03875e32	+	3.33943e31i	1.75735	+	0.116468i
$396$	2.83169e32			0.956877
$397$		−	3.98902e32i		−	1.30612i	−0.757304	−	0.653062i	$-0.773484\pi$
$397$		−	3.98902e32i		−	1.30612i	0.757304	−	0.653062i	$-0.226516\pi$
$398$			3.52023e32i			1.11695i
$399$	3.66057e31			0.112561
$400$	−4.59999e30	−	6.12417e29i	−0.0137090	−	0.00182515i
$401$	1.04555e32			0.302024			0.151012	−	0.988532i	$-0.451747\pi$
$401$	1.04555e32			0.302024			0.151012	+	0.988532i	$0.451747\pi$
$402$		−	1.85226e32i		−	0.518651i
$403$		−	3.29423e32i		−	0.894213i
$404$	5.63824e32			1.48380
$405$	−4.33896e31	−	2.87564e30i	−0.110713	−	0.00733747i
$406$	−4.07352e32			−1.00785
$407$			1.47508e32i			0.353904i
$408$			3.12869e32i			0.727966i
$409$	−5.94901e32			−1.34247			−0.671234	−	0.741246i	$-0.734235\pi$
$409$	−5.94901e32			−1.34247			−0.671234	+	0.741246i	$0.734235\pi$
$410$	−2.73882e31	+	4.13251e32i	−0.0599466	+	0.904516i
$411$	5.07100e32			1.07664
$412$			8.40864e32i			1.73185i
$413$			2.90946e32i			0.581349i
$414$	4.81692e32			0.933825
$415$	3.54210e31	−	5.34457e32i	0.0666285	−	1.00534i
$416$	−6.72825e32			−1.22810
$417$		−	1.44191e32i		−	0.255409i
$418$		−	4.34411e32i		−	0.746788i
$419$	1.11614e33			1.86227			0.931136	−	0.364671i	$-0.118819\pi$
$419$	1.11614e33			1.86227			0.931136	+	0.364671i	$0.118819\pi$
$420$	2.15436e32	+	1.42780e31i	0.348900	+	0.0231233i
$421$	−4.92553e32			−0.774331			−0.387166	−	0.922010i	$-0.626546\pi$
$421$	−4.92553e32			−0.774331			−0.387166	+	0.922010i	$0.626546\pi$
$422$			1.96691e32i			0.300177i
$423$		−	5.47619e32i		−	0.811379i
$424$	−1.13070e33			−1.62657
$425$	−1.20465e32	+	9.04837e32i	−0.168267	+	1.26389i
$426$	1.97123e32			0.267372
$427$		−	1.05269e32i		−	0.138661i
$428$		−	2.11752e33i		−	2.70883i
$429$	−5.02682e32			−0.624564
$430$	−2.02749e33	−	1.34371e32i	−2.44682	−	0.162163i
$431$	−4.71497e31			−0.0552730			−0.0276365	−	0.999618i	$-0.508798\pi$
$431$	−4.71497e31			−0.0552730			−0.0276365	+	0.999618i	$0.508798\pi$
$432$		−	1.16865e31i		−	0.0133087i
$433$			3.61224e30i			0.00399648i	0.999998	+	0.00199824i	$0.000636061\pi$
$433$			3.61224e30i			0.00399648i	−0.999998	+	0.00199824i	$0.999364\pi$
$434$	4.15875e32			0.447034
$435$	−6.06830e31	+	9.15626e32i	−0.0633799	+	0.956319i
$436$	1.06549e33			1.08136
$437$		−	4.56036e32i		−	0.449760i
$438$			2.12555e32i			0.203725i
$439$	−3.57029e32			−0.332580			−0.166290	−	0.986077i	$-0.553179\pi$
$439$	−3.57029e32			−0.332580			−0.166290	+	0.986077i	$0.553179\pi$
$440$	6.43178e31	−	9.70471e32i	0.0582335	−	0.878666i
$441$	6.50522e32			0.572505
$442$			2.92549e33i			2.50276i
$443$			1.54821e33i			1.28761i	0.765190	+	0.643805i	$0.222645\pi$
$443$			1.54821e33i			1.28761i	−0.765190	+	0.643805i	$0.777355\pi$
$444$	−4.57408e32			−0.369842
$445$	7.21052e32	+	4.77876e31i	0.566848	+	0.0375678i
$446$	2.77442e33			2.12074
$447$		−	1.57670e32i		−	0.117194i
$448$		−	8.42208e32i		−	0.608757i
$449$	−2.49721e33			−1.75540			−0.877701	−	0.479209i	$-0.840924\pi$
$449$	−2.49721e33			−1.75540			−0.877701	+	0.479209i	$0.840924\pi$
$450$	−2.07955e32	+	1.56199e33i	−0.142172	+	1.06788i
$451$	7.51230e32			0.499535
$452$		−	2.28232e33i		−	1.47620i
$453$			1.31082e32i			0.0824734i
$454$	2.70564e33			1.65605
$455$	7.64653e32	+	5.06773e31i	0.455326	+	0.0301766i
$456$	5.11331e32			0.296238
$457$		−	3.97112e32i		−	0.223851i	−0.993717	−	0.111926i	$-0.964298\pi$
$457$		−	3.97112e32i		−	0.223851i	0.993717	−	0.111926i	$-0.0357019\pi$
$458$		−	1.29839e33i		−	0.712174i
$459$	−2.29878e33			−1.22698
$460$	1.77876e32	−	2.68391e33i	0.0923941	−	1.39410i
$461$	−8.07920e32			−0.408420			−0.204210	−	0.978927i	$-0.565463\pi$
$461$	−8.07920e32			−0.408420			−0.204210	+	0.978927i	$0.565463\pi$
$462$		−	6.34602e32i		−	0.312232i
$463$			9.97158e32i			0.477531i	0.971077	+	0.238766i	$0.0767427\pi$
$463$			9.97158e32i			0.477531i	−0.971077	+	0.238766i	$0.923257\pi$
$464$	4.92457e31			0.0229559
$465$	6.19526e31	−	9.34783e32i	0.0281124	−	0.424179i
$466$	9.43880e32			0.416959
$467$		−	3.43650e33i		−	1.47793i	−0.673742	−	0.738967i	$-0.735314\pi$
$467$		−	3.43650e33i		−	1.47793i	0.673742	−	0.738967i	$-0.264686\pi$
$468$			3.11660e33i			1.30499i
$469$	5.12190e32			0.208819
$470$	−4.94428e33	−	3.27681e32i	−1.96282	−	0.130085i
$471$	−3.45072e32			−0.133398
$472$			4.06411e33i			1.53000i
$473$			3.68567e33i			1.35130i
$474$	4.60252e33			1.64349
$475$	1.47880e33	+	1.96879e32i	0.514326	+	0.0684746i
$476$	−2.27919e33			−0.772136
$477$		−	3.32287e33i		−	1.09656i
$478$			4.95394e33i			1.59258i
$479$	−4.30103e33			−1.34704			−0.673518	−	0.739171i	$-0.735218\pi$
$479$	−4.30103e33			−1.34704			−0.673518	+	0.739171i	$0.735218\pi$
$480$	−1.90923e33	−	1.26534e32i	−0.582564	−	0.0386093i
$481$	−1.62350e33			−0.482656
$482$		−	3.78440e32i		−	0.109625i
$483$		−	6.66193e32i		−	0.188045i
$484$	1.21225e33			0.333447
$485$	−1.27407e32	+	1.92240e33i	−0.0341524	+	0.515315i
$486$	−6.34939e33			−1.65874
$487$			1.77385e33i			0.451654i	0.974167	+	0.225827i	$0.0725083\pi$
$487$			1.77385e33i			0.451654i	−0.974167	+	0.225827i	$0.927492\pi$
$488$		−	1.47047e33i		−	0.364928i
$489$	2.30237e32			0.0556948
$490$	3.89255e32	−	5.87335e33i	0.0917875	−	1.38495i
$491$	7.59245e33			1.74527			0.872637	−	0.488370i	$-0.162408\pi$
$491$	7.59245e33			1.74527			0.872637	+	0.488370i	$0.162408\pi$
$492$			2.32949e33i			0.522033i
$493$		−	9.68683e33i		−	2.11639i
$494$	4.78120e33			1.01847
$495$	2.85200e33	+	1.89016e32i	0.592358	+	0.0392585i
$496$	−5.02760e31			−0.0101822
$497$			5.45088e32i			0.107649i
$498$		−	4.88186e33i		−	0.940196i
$499$	−2.93681e33			−0.551593			−0.275797	−	0.961216i	$-0.588942\pi$
$499$	−2.93681e33			−0.551593			−0.275797	+	0.961216i	$0.588942\pi$
$500$	8.62639e33	+	1.73549e33i	1.58017	+	0.317906i
$501$	6.93353e31			0.0123875
$502$			4.17613e33i			0.727742i
$503$			4.24338e33i			0.721294i	0.932702	+	0.360647i	$0.117444\pi$
$503$			4.24338e33i			0.721294i	−0.932702	+	0.360647i	$0.882556\pi$
$504$	−1.49349e33			−0.247640
$505$	5.67868e33	+	3.76354e32i	0.918555	+	0.0608771i
$506$	−7.90592e33			−1.24759
$507$		−	1.78215e33i		−	0.274376i
$508$		−	6.01567e33i		−	0.903624i
$509$	−2.39447e33			−0.350943			−0.175472	−	0.984484i	$-0.556145\pi$
$509$	−2.39447e33			−0.350943			−0.175472	+	0.984484i	$0.556145\pi$
$510$	−5.50178e32	+	8.30146e33i	−0.0786821	+	1.18721i
$511$	−5.87761e32			−0.0820237
$512$			2.03101e32i			0.0276591i
$513$			3.75695e33i			0.499307i
$514$	9.11972e33			1.18289
$515$	−5.61278e32	+	8.46894e33i	−0.0710538	+	1.07211i
$516$	−1.14289e34			−1.41216
$517$			8.98796e33i			1.08400i
$518$		−	2.04955e33i		−	0.241289i
$519$	3.53376e33			0.406111
$520$	1.06811e34	+	7.07891e32i	1.19833	+	0.0794191i
$521$	8.32276e33			0.911582			0.455791	−	0.890087i	$-0.349356\pi$
$521$	8.32276e33			0.911582			0.455791	+	0.890087i	$0.349356\pi$
$522$		−	1.67221e34i		−	1.78817i
$523$		−	1.32749e34i		−	1.38599i	−0.720944	−	0.692993i	$-0.756292\pi$
$523$		−	1.32749e34i		−	1.38599i	0.720944	−	0.692993i	$-0.243708\pi$
$524$	−1.16563e34			−1.18829
$525$	2.16028e33	+	2.87607e32i	0.215039	+	0.0286292i
$526$	−1.43183e34			−1.39178
$527$			9.88950e33i			0.938732i
$528$			7.67185e31i			0.00711174i
$529$	2.74629e33			0.248629
$530$	−3.00011e34	−	1.98832e33i	−2.65270	−	0.175808i
$531$	−1.19435e34			−1.03146
$532$			3.72494e33i			0.314213i
$533$			8.26815e33i			0.681269i
$534$	6.58627e33			0.530119
$535$	1.41345e33	−	2.13271e34i	0.111137	−	1.67691i
$536$	7.15459e33			0.549572
$537$		−	7.29983e33i		−	0.547815i
$538$		−	2.46129e33i		−	0.180461i
$539$	−1.06769e34			−0.764865
$540$	−1.46539e33	+	2.21108e34i	−0.102572	+	1.54768i
$541$	1.45952e34			0.998260			0.499130	−	0.866527i	$-0.333653\pi$
$541$	1.45952e34			0.998260			0.499130	+	0.866527i	$0.333653\pi$
$542$		−	2.65622e34i		−	1.77530i
$543$		−	1.19160e34i		−	0.778277i
$544$	2.01986e34			1.28925
$545$	1.07313e34	+	7.11217e32i	0.669418	+	0.0443655i
$546$	6.98453e33			0.425823
$547$			3.28646e34i			1.95834i	0.203054	+	0.979168i	$0.434913\pi$
$547$			3.28646e34i			1.95834i	−0.203054	+	0.979168i	$0.565087\pi$
$548$			5.16018e34i			3.00544i
$549$	4.32138e33			0.246019
$550$	3.41313e33	−	2.56367e34i	0.189941	−	1.42669i
$551$	−1.58314e34			−0.861242
$552$		−	9.30579e33i		−	0.494897i
$553$			1.27270e34i			0.661701i
$554$	2.77494e34			1.41053
$555$	−4.60689e33	−	3.05321e32i	−0.228952	−	0.0151738i
$556$	1.46726e34			0.712973
$557$		−	2.79942e34i		−	1.33008i	−0.746806	−	0.665042i	$-0.768414\pi$
$557$		−	2.79942e34i		−	1.33008i	0.746806	−	0.665042i	$-0.231586\pi$
$558$			1.70720e34i			0.793151i
$559$	−4.05651e34			−1.84291
$560$	7.73428e30	−	1.16700e32i	0.000343613	−	0.00518467i
$561$	1.50908e34			0.655658
$562$			3.54410e34i			1.50592i
$563$		−	2.94294e34i		−	1.22300i	−0.791244	−	0.611500i	$-0.790566\pi$
$563$		−	2.94294e34i		−	1.22300i	0.791244	−	0.611500i	$-0.209434\pi$
$564$	−2.78708e34			−1.13282
$565$	1.52345e33	−	2.29869e34i	0.0605651	−	0.913848i
$566$	4.76623e34			1.85340
$567$		−	1.09594e33i		−	0.0416869i
$568$			7.61413e33i			0.283313i
$569$	−1.44033e34			−0.524275			−0.262137	−	0.965031i	$-0.584427\pi$
$569$	−1.44033e34			−0.524275			−0.262137	+	0.965031i	$0.584427\pi$
$570$	1.35673e34	+	8.99170e32i	0.483123	+	0.0320189i
$571$	−6.02200e33			−0.209792			−0.104896	−	0.994483i	$-0.533451\pi$
$571$	−6.02200e33			−0.209792			−0.104896	+	0.994483i	$0.533451\pi$
$572$		−	5.11522e34i		−	1.74347i
$573$		−	3.67710e32i		−	0.0122623i
$574$	−1.04380e34			−0.340579
$575$	3.58303e33	−	2.69129e34i	0.114394	−	0.859235i
$576$	3.45732e34			1.08009
$577$			3.36622e34i			1.02907i	0.857470	+	0.514534i	$0.172035\pi$
$577$			3.36622e34i			1.02907i	−0.857470	+	0.514534i	$0.827965\pi$
$578$		−	3.38030e34i		−	1.01125i
$579$	−3.46201e34			−1.01355
$580$	−9.31729e34	−	6.17502e33i	−2.66956	−	0.176925i
$581$	1.34994e34			0.378542
$582$			1.75597e34i			0.481925i
$583$			5.45376e34i			1.46500i
$584$	−8.21021e33			−0.215871
$585$	−2.08034e33	+	3.13896e34i	−0.0535409	+	0.807861i
$586$	−5.88482e34			−1.48256
$587$			2.29972e34i			0.567152i	0.958950	+	0.283576i	$0.0915208\pi$
$587$			2.29972e34i			0.567152i	−0.958950	+	0.283576i	$0.908479\pi$
$588$		−	3.31080e34i		−	0.799312i
$589$	1.61627e34			0.382007
$590$	−7.14671e33	+	1.07834e35i	−0.165370	+	2.49521i
$591$	2.51736e33			0.0570298
$592$			2.47775e32i			0.00549587i
$593$		−	2.56446e34i		−	0.556945i	−0.960444	−	0.278472i	$-0.910172\pi$
$593$		−	2.56446e34i		−	0.556945i	0.960444	−	0.278472i	$-0.0898280\pi$
$594$	6.51311e34			1.38503
$595$	−2.29554e34	−	1.52136e33i	−0.477994	−	0.0316790i
$596$	1.60443e34			0.327146
$597$			1.99858e34i			0.399064i
$598$		−	8.70138e34i		−	1.70147i
$599$	6.53223e34			1.25091			0.625455	−	0.780260i	$-0.284913\pi$
$599$	6.53223e34			1.25091			0.625455	+	0.780260i	$0.284913\pi$
$600$	3.01761e34	+	4.01748e33i	0.565942	+	0.0753464i
$601$	1.46105e34			0.268370			0.134185	−	0.990956i	$-0.457158\pi$
$601$	1.46105e34			0.268370			0.134185	+	0.990956i	$0.457158\pi$
$602$		−	5.12107e34i		−	0.921308i
$603$			2.10258e34i			0.370498i
$604$	−1.33387e34			−0.230224
$605$	1.22095e34	+	8.09182e32i	0.206422	+	0.0136806i
$606$	5.18704e34			0.859038
$607$			1.63446e34i			0.265165i	0.991172	+	0.132582i	$0.0423269\pi$
$607$			1.63446e34i			0.265165i	−0.991172	+	0.132582i	$0.957673\pi$
$608$		−	3.30112e34i		−	0.524646i
$609$	−2.31271e34			−0.360085
$610$	2.58580e33	−	3.90163e34i	0.0394432	−	0.595146i
$611$	−9.89229e34			−1.47837
$612$		−	9.35625e34i		−	1.36996i
$613$		−	6.22253e34i		−	0.892712i	−0.894855	−	0.446356i	$-0.852722\pi$
$613$		−	6.22253e34i		−	0.892712i	0.894855	−	0.446356i	$-0.147278\pi$
$614$	−1.03271e34			−0.145169
$615$	−1.55494e33	+	2.34620e34i	−0.0214178	+	0.323166i
$616$	2.45124e34			0.330846
$617$		−	4.34980e34i		−	0.575314i	−0.957733	−	0.287657i	$-0.907124\pi$
$617$		−	4.34980e34i		−	0.575314i	0.957733	−	0.287657i	$-0.0928763\pi$
$618$			7.73574e34i			1.00264i
$619$	1.76940e34			0.224747			0.112373	−	0.993666i	$-0.464155\pi$
$619$	1.76940e34			0.224747			0.112373	+	0.993666i	$0.464155\pi$
$620$	9.51222e34	+	6.30421e33i	1.18409	+	0.0784756i
$621$	6.83733e34			0.834145
$622$			2.26430e35i			2.70741i
$623$			1.82125e34i			0.213437i
$624$	−8.44376e32			−0.00969903
$625$	8.57241e34	+	2.32375e34i	0.965168	+	0.261632i
$626$	−1.55689e35			−1.71822
$627$		−	2.46633e34i		−	0.266813i
$628$		−	3.51140e34i		−	0.372379i
$629$	4.87384e34			0.506685
$630$	−3.96272e34	−	2.62629e33i	−0.403866	−	0.0267661i
$631$	1.04208e35			1.04120			0.520601	−	0.853800i	$-0.325708\pi$
$631$	1.04208e35			1.04120			0.520601	+	0.853800i	$0.325708\pi$
$632$			1.77778e35i			1.74147i
$633$			1.11669e34i			0.107248i
$634$	−2.72540e35			−2.56634
$635$	4.01547e33	−	6.05882e34i	0.0370736	−	0.559392i
$636$	−1.69116e35			−1.53098
$637$		−	1.17511e35i		−	1.04313i
$638$			2.74457e35i			2.38899i
$639$	−2.23762e34			−0.190997
$640$	1.26994e34	−	1.91616e35i	0.106300	−	1.60392i
$641$	−8.19994e34			−0.673109			−0.336555	−	0.941664i	$-0.609262\pi$
$641$	−8.19994e34			−0.673109			−0.336555	+	0.941664i	$0.609262\pi$
$642$		−	1.94807e35i		−	1.56825i
$643$		−	5.73324e34i		−	0.452650i	−0.974052	−	0.226325i	$-0.927329\pi$
$643$		−	5.73324e34i		−	0.452650i	0.974052	−	0.226325i	$-0.0726712\pi$
$644$	6.77908e34			0.524925
$645$	−1.15109e35	−	7.62883e33i	−0.874204	−	0.0579377i
$646$	−1.43535e35			−1.06918
$647$		−	1.81756e35i		−	1.32796i	−0.747751	−	0.663979i	$-0.768866\pi$
$647$		−	1.81756e35i		−	1.32796i	0.747751	−	0.663979i	$-0.231134\pi$
$648$		−	1.53088e34i		−	0.109712i
$649$	1.96027e35			1.37803
$650$	2.82161e35	+	3.75654e34i	1.94572	+	0.259043i
$651$	2.36110e34			0.159717
$652$			2.34286e34i			0.155472i
$653$			1.90602e35i			1.24083i	0.784274	+	0.620415i	$0.213036\pi$
$653$			1.90602e35i			1.24083i	−0.784274	+	0.620415i	$0.786964\pi$
$654$	9.80226e34			0.626043
$655$	−1.17399e35	−	7.78062e33i	−0.735613	−	0.0487526i
$656$	1.26187e33			0.00775742
$657$		−	2.41280e34i		−	0.145531i
$658$		−	1.24884e35i		−	0.739064i
$659$	6.08809e34			0.353520			0.176760	−	0.984254i	$-0.443438\pi$
$659$	6.08809e34			0.353520			0.176760	+	0.984254i	$0.443438\pi$
$660$	9.61988e33	−	1.45151e35i	0.0548113	−	0.827031i
$661$	−2.17257e35			−1.21466			−0.607332	−	0.794448i	$-0.707760\pi$
$661$	−2.17257e35			−1.21466			−0.607332	+	0.794448i	$0.707760\pi$
$662$			1.81376e35i			0.995074i
$663$			1.66092e35i			0.894190i
$664$	1.88568e35			0.996249
$665$	−2.48641e33	+	3.75166e34i	−0.0128914	+	0.194515i
$666$	8.41357e34			0.428107
$667$			2.88119e35i			1.43879i
$668$			7.05547e33i			0.0345796i
$669$	1.57516e35			0.757700
$670$	1.89835e35	+	1.25813e34i	0.896275	+	0.0594005i
$671$	−7.09259e34			−0.328680
$672$		−	4.82238e34i		−	0.219354i
$673$			7.80776e34i			0.348609i	0.984692	+	0.174304i	$0.0557676\pi$
$673$			7.80776e34i			0.348609i	−0.984692	+	0.174304i	$0.944232\pi$
$674$	−2.40542e34			−0.105425
$675$	−2.95180e34	+	2.21716e35i	−0.126996	+	0.953892i
$676$	1.81349e35			0.765918
$677$		−	2.43537e35i		−	1.00973i	−0.863198	−	0.504866i	$-0.831542\pi$
$677$		−	2.43537e35i		−	1.00973i	0.863198	−	0.504866i	$-0.168458\pi$
$678$		−	2.09968e35i		−	0.854636i
$679$	−4.85565e34			−0.194033
$680$	−3.20655e35	−	2.12514e34i	−1.25799	−	0.0833730i
$681$	1.53611e35			0.591674
$682$		−	2.80199e35i		−	1.05965i
$683$		−	4.30905e35i		−	1.60001i	−0.599994	−	0.800004i	$-0.704830\pi$
$683$		−	4.30905e35i		−	1.60001i	0.599994	−	0.800004i	$-0.295170\pi$
$684$	−1.52912e35			−0.557492
$685$	−3.44443e34	+	5.19719e35i	−0.123306	+	1.86053i
$686$	3.21083e35			1.12867
$687$		−	7.37149e34i		−	0.254446i
$688$			6.19098e33i			0.0209848i
$689$	−6.00249e35			−1.99798
$690$	1.63641e34	−	2.46913e35i	0.0534909	−	0.807107i
$691$	2.98951e35			0.959675			0.479838	−	0.877357i	$-0.340696\pi$
$691$	2.98951e35			0.959675			0.479838	+	0.877357i	$0.340696\pi$
$692$			3.59590e35i			1.13366i
$693$			7.20364e34i			0.223042i
$694$	−3.45371e35			−1.05025
$695$	1.47779e35	+	9.79401e33i	0.441369	+	0.0292517i
$696$	−3.23053e35			−0.947674
$697$		−	2.48215e35i		−	0.715186i
$698$		−	8.33483e35i		−	2.35887i
$699$	5.35880e34			0.148971
$700$	−2.92665e34	+	2.19827e35i	−0.0799182	+	0.600282i
$701$	−5.64961e35			−1.51546			−0.757728	−	0.652570i	$-0.773691\pi$
$701$	−5.64961e35			−1.51546			−0.757728	+	0.652570i	$0.773691\pi$
$702$			7.16843e35i			1.88890i
$703$		−	7.96544e34i		−	0.206190i
$704$	−5.67444e35			−1.44299
$705$	−2.80707e35	−	1.86038e34i	−0.701277	−	0.0464770i
$706$	1.11208e36			2.72945
$707$			1.43433e35i			0.345866i
$708$			6.07861e35i			1.44009i
$709$	3.85512e35			0.897345			0.448672	−	0.893696i	$-0.351897\pi$
$709$	3.85512e35			0.897345			0.448672	+	0.893696i	$0.351897\pi$
$710$	−1.33894e34	+	2.02028e35i	−0.0306218	+	0.462043i
$711$	−5.22452e35			−1.17402
$712$			2.54403e35i			0.561724i
$713$		−	2.94147e35i		−	0.638183i
$714$	−2.09680e35			−0.447023
$715$	3.41442e34	−	5.15191e35i	0.0715305	−	1.07930i
$716$	7.42821e35			1.52922
$717$			2.81256e35i			0.569000i
$718$			3.21200e35i			0.638588i
$719$	9.36871e35			1.83050			0.915248	−	0.402892i	$-0.131995\pi$
$719$	9.36871e35			1.83050			0.915248	+	0.402892i	$0.131995\pi$
$720$	4.79062e33	+	3.17498e32i	0.00919890	+	0.000609656i
$721$	−2.13910e35			−0.403684
$722$		−	6.36757e35i		−	1.18102i
$723$		−	2.14856e34i		−	0.0391669i
$724$	1.21256e36			2.17256
$725$	−9.34289e35	−	1.24386e35i	−1.64534	−	0.219052i
$726$	1.11525e35			0.193047
$727$		−	3.25564e35i		−	0.553931i	−0.960880	−	0.276966i	$-0.910671\pi$
$727$		−	3.25564e35i		−	0.553931i	0.960880	−	0.276966i	$-0.0893288\pi$
$728$			2.69787e35i			0.451210i
$729$	−2.92991e35			−0.481681
$730$	−2.17844e35	−	1.44376e34i	−0.352055	−	0.0233324i
$731$	1.21779e36			1.93466
$732$		−	2.19935e35i		−	0.343483i
$733$			2.07689e35i			0.318870i	0.987208	+	0.159435i	$0.0509673\pi$
$733$			2.07689e35i			0.318870i	−0.987208	+	0.159435i	$0.949033\pi$
$734$	−1.70223e36			−2.56931
$735$	2.20997e34	−	3.33455e35i	0.0327940	−	0.494818i
$736$	−6.00776e35			−0.876475
$737$		−	3.45092e35i		−	0.494984i
$738$		−	4.28487e35i		−	0.604273i
$739$	1.12620e36			1.56156			0.780781	−	0.624805i	$-0.214821\pi$
$739$	1.12620e36			1.56156			0.780781	+	0.624805i	$0.214821\pi$
$740$	3.10690e34	−	4.68790e35i	0.0423576	−	0.639120i
$741$	2.71449e35			0.363881
$742$		−	7.57774e35i		−	0.998829i
$743$			7.41657e35i			0.961264i	0.876922	+	0.480632i	$0.159593\pi$
$743$			7.41657e35i			0.961264i	−0.876922	+	0.480632i	$0.840407\pi$
$744$	3.29812e35			0.420344
$745$	1.61594e35	+	1.07096e34i	0.202521	+	0.0134221i
$746$	4.28304e35			0.527858
$747$			5.54161e35i			0.671628i
$748$			1.53562e36i			1.83027i
$749$	5.38685e35			0.631411
$750$	7.93607e35	+	1.59661e35i	0.914828	+	0.184049i
$751$	−9.24971e35			−1.04865			−0.524323	−	0.851520i	$-0.675681\pi$
$751$	−9.24971e35			−1.04865			−0.524323	+	0.851520i	$0.675681\pi$
$752$			1.50975e34i			0.0168338i
$753$			2.37096e35i			0.260008i
$754$	−3.02071e36			−3.25812
$755$	−1.34343e35	−	8.90359e33i	−0.142521	−	0.00944557i
$756$	−5.58479e35			−0.582753
$757$			2.20319e35i			0.226127i	0.993588	+	0.113064i	$0.0360664\pi$
$757$			2.20319e35i			0.226127i	−0.993588	+	0.113064i	$0.963934\pi$
$758$			4.88369e35i			0.493041i
$759$	−4.48852e35			−0.445739
$760$	−3.47317e34	+	5.24055e35i	−0.0339278	+	0.511926i
$761$	−3.87186e35			−0.372059			−0.186029	−	0.982544i	$-0.559562\pi$
$761$	−3.87186e35			−0.372059			−0.186029	+	0.982544i	$0.559562\pi$
$762$		−	5.53427e35i		−	0.523147i
$763$			2.71054e35i			0.252057i
$764$	3.74176e34			0.0342302
$765$	6.24531e34	−	9.42335e35i	0.0562064	−	0.848081i
$766$	−1.54507e36			−1.36801
$767$			2.15750e36i			1.87936i
$768$		−	6.58601e35i		−	0.564426i
$769$	5.73844e35			0.483854			0.241927	−	0.970294i	$-0.422221\pi$
$769$	5.73844e35			0.483854			0.241927	+	0.970294i	$0.422221\pi$
$770$	6.50394e35	+	4.31047e34i	0.539563	+	0.0357595i
$771$	5.17765e35			0.422623
$772$		−	3.52289e36i		−	2.82932i
$773$			1.94109e35i			0.153392i	0.997055	+	0.0766959i	$0.0244371\pi$
$773$			1.94109e35i			0.153392i	−0.997055	+	0.0766959i	$0.975563\pi$
$774$	2.10224e36			1.63463
$775$	9.53836e35	+	1.26988e35i	0.729798	+	0.0971613i
$776$	−6.78267e35			−0.510657
$777$		−	1.16362e35i		−	0.0862080i
$778$		−	2.79766e36i		−	2.03962i
$779$	−4.05665e35			−0.291038
$780$	1.59756e36	+	1.05878e35i	1.12791	+	0.0747520i
$781$	3.67257e35			0.255171
$782$			2.61221e36i			1.78617i
$783$		−	2.37360e36i		−	1.59730i
$784$	−1.79344e34			−0.0118778
$785$	2.34387e34	−	3.53658e35i	0.0152778	−	0.230523i
$786$	−1.07235e36			−0.687949
$787$		−	7.50226e35i		−	0.473705i	−0.971546	−	0.236852i	$-0.923884\pi$
$787$		−	7.50226e35i		−	0.473705i	0.971546	−	0.236852i	$-0.0761158\pi$
$788$			2.56163e35i			0.159198i
$789$	−8.12912e35			−0.497257
$790$	−3.12622e35	+	4.71705e36i	−0.188226	+	2.84009i
$791$	5.80607e35			0.344093
$792$			1.00625e36i			0.587004i
$793$		−	7.80622e35i		−	0.448256i
$794$	3.73434e36			2.11085
$795$	−1.70329e36	−	1.12885e35i	−0.947761	−	0.0628127i
$796$	−2.03373e36			−1.11399
$797$			2.78320e36i			1.50077i	0.660998	+	0.750387i	$0.270133\pi$
$797$			2.78320e36i			1.50077i	−0.660998	+	0.750387i	$0.729867\pi$
$798$			3.42686e35i			0.181911i
$799$	2.96973e36			1.55197
$800$	2.59366e35	−	1.94815e36i	0.133440	−	1.00230i
$801$	−7.47636e35			−0.378690
$802$			9.78801e35i			0.488107i
$803$			3.96008e35i			0.194429i
$804$	1.07010e36			0.517276
$805$	6.82770e35	+	4.52505e34i	0.324957	+	0.0215365i
$806$	3.08391e36			1.44515
$807$		−	1.39738e35i		−	0.0644754i
$808$			2.00357e36i			0.910252i
$809$	−2.84960e36			−1.27476			−0.637379	−	0.770550i	$-0.719982\pi$
$809$	−2.84960e36			−1.27476			−0.637379	+	0.770550i	$0.719982\pi$
$810$	2.69204e34	−	4.06194e35i	0.0118582	−	0.178925i
$811$	−2.18452e36			−0.947535			−0.473767	−	0.880650i	$-0.657106\pi$
$811$	−2.18452e36			−0.947535			−0.473767	+	0.880650i	$0.657106\pi$
$812$		−	2.35338e36i		−	1.00518i
$813$		−	1.50804e36i		−	0.634282i
$814$	−1.38090e36			−0.571950
$815$	−1.56387e34	+	2.35967e35i	−0.00637866	+	0.0962455i
$816$	2.53487e34			0.0101819
$817$		−	1.99027e36i		−	0.787291i
$818$		−	5.56920e36i		−	2.16958i
$819$	−7.92844e35			−0.304186
$820$	−2.38746e36	−	1.58229e35i	−0.902118	−	0.0597877i
$821$	−3.44892e36			−1.28349			−0.641746	−	0.766917i	$-0.721790\pi$
$821$	−3.44892e36			−1.28349			−0.641746	+	0.766917i	$0.721790\pi$
$822$			4.74724e36i			1.73998i
$823$		−	6.75510e35i		−	0.243856i	−0.992539	−	0.121928i	$-0.961092\pi$
$823$		−	6.75510e35i		−	0.243856i	0.992539	−	0.121928i	$-0.0389078\pi$
$824$	−2.98803e36			−1.06242
$825$	1.93777e35	−	1.45550e36i	0.0678624	−	0.509728i
$826$	−2.72370e36			−0.939527
$827$		−	1.98402e36i		−	0.674105i	−0.941486	−	0.337053i	$-0.890570\pi$
$827$		−	1.98402e36i		−	0.674105i	0.941486	−	0.337053i	$-0.109430\pi$
$828$			2.78286e36i			0.931349i
$829$	−1.25430e36			−0.413496			−0.206748	−	0.978394i	$-0.566288\pi$
$829$	−1.25430e36			−0.413496			−0.206748	+	0.978394i	$0.566288\pi$
$830$	5.00334e36	+	3.31596e35i	1.62474	+	0.107679i
$831$	1.57545e36			0.503955
$832$		−	6.24537e36i		−	1.96796i
$833$			3.52777e36i			1.09506i
$834$	1.34985e36			0.412771
$835$	−4.70954e33	+	7.10607e34i	−0.00141872	+	0.0214066i
$836$	2.50971e36			0.744808
$837$			2.42326e36i			0.708487i
$838$			1.04488e37i			3.00965i
$839$	−3.59072e36			−1.01896			−0.509480	−	0.860483i	$-0.670162\pi$
$839$	−3.59072e36			−1.01896			−0.509480	+	0.860483i	$0.670162\pi$
$840$	−5.07371e34	+	7.65557e35i	−0.0141852	+	0.214036i
$841$	6.37178e36			1.75514
$842$		−	4.61106e36i		−	1.25141i
$843$			2.01214e36i			0.538038i
$844$	−1.13633e36			−0.299381
$845$	1.82650e36	+	1.21051e35i	0.474145	+	0.0314239i
$846$	5.12656e36			1.31128
$847$			3.08390e35i			0.0777245i
$848$			9.16091e34i			0.0227505i
$849$	2.70599e36			0.662185
$850$	−8.47067e36	−	1.12774e36i	−2.04259	−	0.271939i
$851$	−1.44964e36			−0.344462
$852$			1.13883e36i			0.266664i
$853$			4.77260e35i			0.110127i	0.998483	+	0.0550633i	$0.0175361\pi$
$853$			4.77260e35i			0.110127i	−0.998483	+	0.0550633i	$0.982464\pi$
$854$	9.85483e35			0.224092
$855$	−1.54008e36	−	1.02069e35i	−0.345118	−	0.0228726i
$856$	7.52468e36			1.66175
$857$			3.37504e36i			0.734545i	0.930113	+	0.367272i	$0.119708\pi$
$857$			3.37504e36i			0.734545i	−0.930113	+	0.367272i	$0.880292\pi$
$858$		−	4.70588e36i		−	1.00937i
$859$	−4.53153e36			−0.957923			−0.478961	−	0.877836i	$-0.658987\pi$
$859$	−4.53153e36			−0.957923			−0.478961	+	0.877836i	$0.658987\pi$
$860$	7.76299e35	−	1.17133e37i	0.161733	−	2.44034i
$861$	−5.92608e35			−0.121683
$862$		−	4.41394e35i		−	0.0893276i
$863$		−	2.57027e36i		−	0.512677i	−0.966587	−	0.256338i	$-0.917484\pi$
$863$		−	2.57027e36i		−	0.512677i	0.966587	−	0.256338i	$-0.0825161\pi$
$864$	4.94935e36			0.973030
$865$	−2.40027e35	+	3.62169e36i	−0.0465114	+	0.701795i
$866$	−3.38162e34			−0.00645878
$867$		−	1.91914e36i		−	0.361299i
$868$			2.40262e36i			0.445849i
$869$	8.57490e36			1.56849
$870$	−8.57168e36	−	5.68087e35i	−1.54552	−	0.102429i
$871$	3.79814e36			0.675062
$872$			3.78625e36i			0.663366i
$873$		−	1.99328e36i		−	0.344262i
$874$	4.26920e36			0.726865
$875$	−4.41499e35	+	2.19450e36i	−0.0741019	+	0.368328i
$876$	−1.22798e36			−0.203185
$877$		−	1.02943e37i		−	1.67919i	−0.543213	−	0.839595i	$-0.682792\pi$
$877$		−	1.02943e37i		−	1.67919i	0.543213	−	0.839595i	$-0.317208\pi$
$878$		−	3.34234e36i		−	0.537488i
$879$	−3.34106e36			−0.529692
$880$	−7.86276e34	−	5.21103e33i	−0.0122897	−	0.000814498i
$881$	−1.32860e36			−0.204737			−0.102369	−	0.994747i	$-0.532642\pi$
$881$	−1.32860e36			−0.204737			−0.102369	+	0.994747i	$0.532642\pi$
$882$			6.08989e36i			0.925235i
$883$			8.24109e36i			1.23446i	0.786784	+	0.617228i	$0.211745\pi$
$883$			8.24109e36i			1.23446i	−0.786784	+	0.617228i	$0.788255\pi$
$884$	−1.69013e37			−2.49613
$885$	−4.05748e35	+	6.12221e36i	−0.0590835	+	0.891492i
$886$	−1.44937e37			−2.08093
$887$			2.45432e36i			0.347445i	0.984795	+	0.173722i	$0.0555795\pi$
$887$			2.45432e36i			0.347445i	−0.984795	+	0.173722i	$0.944421\pi$
$888$		−	1.62541e36i		−	0.226883i
$889$	1.53035e36			0.210629
$890$	−4.47366e35	+	6.75016e36i	−0.0607139	+	0.916092i
$891$	−7.38400e35			−0.0988144
$892$			1.60286e37i			2.11512i
$893$		−	4.85351e36i		−	0.631557i
$894$	1.47604e36			0.189399
$895$	7.48148e36	+	4.95834e35i	0.946673	+	0.0627406i
$896$	4.83989e36			0.603928
$897$		−	4.94014e36i		−	0.607902i
$898$		−	2.33778e37i		−	2.83693i
$899$	−1.02114e37			−1.22205
$900$	−9.02405e36	−	1.20141e36i	−1.06505	−	0.141795i
$901$	1.80199e37			2.09745
$902$			7.03267e36i			0.807307i
$903$		−	2.90745e36i		−	0.329166i
$904$	8.11028e36			0.905587
$905$	1.22126e37	+	8.09386e35i	1.34493	+	0.0891351i
$906$	−1.22713e36			−0.133287
$907$		−	7.87438e36i		−	0.843578i	−0.906694	−	0.421789i	$-0.861402\pi$
$907$		−	7.87438e36i		−	0.843578i	0.906694	−	0.421789i	$-0.138598\pi$
$908$			1.56312e37i			1.65166i
$909$	−5.88804e36			−0.613652
$910$	−4.74418e35	+	7.15834e36i	−0.0487689	+	0.735859i
$911$	−1.36078e37			−1.37978			−0.689889	−	0.723915i	$-0.742341\pi$
$911$	−1.36078e37			−1.37978			−0.689889	+	0.723915i	$0.742341\pi$
$912$		−	4.14280e34i		−	0.00414342i
$913$		−	9.09534e36i		−	0.897293i
$914$	3.71758e36			0.361770
$915$	1.46807e35	−	2.21512e36i	0.0140923	−	0.212634i
$916$	7.50112e36			0.710286
$917$		−	2.96530e36i		−	0.276982i
$918$		−	2.15201e37i		−	1.98294i
$919$	9.86137e35			0.0896382			0.0448191	−	0.998995i	$-0.485729\pi$
$919$	9.86137e35			0.0896382			0.0448191	+	0.998995i	$0.485729\pi$
$920$	9.53736e36	+	6.32087e35i	0.855225	+	0.0566799i
$921$	−5.86315e35			−0.0518663
$922$		−	7.56338e36i		−	0.660054i
$923$			4.04209e36i			0.348004i
$924$	3.66626e36			0.311404
$925$	6.25837e35	−	4.70079e36i	0.0524432	−	0.393912i
$926$	−9.33494e36			−0.771746
$927$		−	8.78117e36i		−	0.716236i
$928$			2.08561e37i			1.67835i
$929$	−3.38052e36			−0.268403			−0.134202	−	0.990954i	$-0.542847\pi$
$929$	−3.38052e36			−0.268403			−0.134202	+	0.990954i	$0.542847\pi$
$930$	8.75101e36	+	5.79972e35i	0.685522	+	0.0454329i
$931$	5.76553e36			0.445623
$932$			5.45304e36i			0.415853i
$933$			1.28554e37i			0.967305i
$934$	3.21709e37			2.38851
$935$	−1.02503e36	+	1.54664e37i	−0.0750917	+	1.13303i
$936$	−1.10749e37			−0.800559
$937$			1.23256e37i			0.879151i	0.898206	+	0.439576i	$0.144871\pi$
$937$			1.23256e37i			0.879151i	−0.898206	+	0.439576i	$0.855129\pi$
$938$			4.79489e36i			0.337476i
$939$	−8.83912e36			−0.613888
$940$	1.89310e36	−	2.85644e37i	0.129740	−	1.95761i
$941$	6.55312e36			0.443178			0.221589	−	0.975140i	$-0.428876\pi$
$941$	6.55312e36			0.443178			0.221589	+	0.975140i	$0.428876\pi$
$942$		−	3.23040e36i		−	0.215586i
$943$			7.38276e36i			0.486208i
$944$	3.29275e35			0.0213997
$945$	−5.62485e36	−	3.72786e35i	−0.360756	−	0.0239090i
$946$	−3.45036e37			−2.18386
$947$		−	1.42694e37i		−	0.891316i	−0.895203	−	0.445658i	$-0.852970\pi$
$947$		−	1.42694e37i		−	0.891316i	0.895203	−	0.445658i	$-0.147030\pi$
$948$			2.65900e37i			1.63913i
$949$	−4.35853e36			−0.265163
$950$	−1.84309e36	+	1.38438e37i	−0.110663	+	0.831211i
$951$	−1.54732e37			−0.916905
$952$		−	8.09918e36i		−	0.473673i
$953$			2.38480e36i			0.137655i	0.997629	+	0.0688274i	$0.0219258\pi$
$953$			2.38480e36i			0.137655i	−0.997629	+	0.0688274i	$0.978074\pi$
$954$	3.11072e37			1.77217
$955$	3.76860e35	+	2.49763e34i	0.0211903	+	0.00140439i
$956$	−2.86202e37			−1.58836
$957$			1.55820e37i			0.853543i
$958$		−	4.02643e37i		−	2.17697i
$959$	−1.31272e37			−0.700549
$960$	1.17453e36	−	1.77221e37i	0.0618690	−	0.933522i
$961$	−8.80775e36			−0.457955
$962$		−	1.51984e37i		−	0.780028i
$963$			2.21134e37i			1.12028i
$964$	2.18635e36			0.109334
$965$	2.35153e36	−	3.54816e37i	0.116081	−	1.75150i
$966$	6.23659e36			0.303902
$967$			1.64185e37i			0.789774i	0.918730	+	0.394887i	$0.129216\pi$
$967$			1.64185e37i			0.789774i	−0.918730	+	0.394887i	$0.870784\pi$
$968$			4.30778e36i			0.204556i
$969$	−8.14906e36			−0.381997
$970$	−1.79967e37	−	1.19273e36i	−0.832809	−	0.0551943i
$971$	2.07297e37			0.947007			0.473503	−	0.880792i	$-0.342989\pi$
$971$	2.07297e37			0.947007			0.473503	+	0.880792i	$0.342989\pi$
$972$		−	3.66821e37i		−	1.65434i
$973$			3.73263e36i			0.166190i
$974$	−1.66060e37			−0.729925
$975$	1.60195e37	+	2.13275e36i	0.695170	+	0.0925510i
$976$	−1.19137e35			−0.00510417
$977$			3.93106e36i			0.166275i	0.996538	+	0.0831376i	$0.0264941\pi$
$977$			3.93106e36i			0.166275i	−0.996538	+	0.0831376i	$0.973506\pi$
$978$			2.15538e36i			0.0900093i
$979$	1.22708e37			0.505929
$980$	3.39319e37	+	2.24883e36i	1.38128	+	0.0915442i
$981$	−1.11270e37			−0.447213
$982$			7.10771e37i			2.82056i
$983$		−	9.80814e36i		−	0.384298i	−0.981366	−	0.192149i	$-0.938454\pi$
$983$		−	9.80814e36i		−	0.384298i	0.981366	−	0.192149i	$-0.0615456\pi$
$984$	−8.27792e36			−0.320245
$985$	−1.70989e35	+	2.58000e36i	−0.00653155	+	0.0985524i
$986$	9.06837e37			3.42033
$987$		−	7.09017e36i		−	0.264054i
$988$			2.76222e37i			1.01577i
$989$	−3.62212e37			−1.31525
$990$	−1.76948e36	+	2.66991e37i	−0.0634462	+	0.957320i
$991$	−9.07369e36			−0.321265			−0.160632	−	0.987014i	$-0.551353\pi$
$991$	−9.07369e36			−0.321265			−0.160632	+	0.987014i	$0.551353\pi$
$992$		−	2.12925e37i		−	0.744441i
$993$			1.02975e37i			0.355521i
$994$	−5.10287e36			−0.173974
$995$	−2.04832e37	−	1.35752e36i	−0.689618	−	0.0457043i
$996$	2.82038e37			0.937704
$997$			1.44463e37i			0.474315i	0.971471	+	0.237158i	$0.0762158\pi$
$997$			1.44463e37i			0.474315i	−0.971471	+	0.237158i	$0.923784\pi$
$998$		−	2.74931e37i		−	0.891439i
$999$	1.19425e37			0.382409

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.26.b.a.4.11	yes	12
3.2	odd	2		45.26.b.b.19.2		12
5.2	odd	4		25.26.a.f.1.2		12
5.3	odd	4		25.26.a.f.1.11		12
5.4	even	2	inner	5.26.b.a.4.2	✓	12
15.14	odd	2		45.26.b.b.19.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.26.b.a.4.2	✓	12	5.4	even	2	inner
5.26.b.a.4.11	yes	12	1.1	even	1	trivial
25.26.a.f.1.2		12	5.2	odd	4
25.26.a.f.1.11		12	5.3	odd	4
45.26.b.b.19.2		12	3.2	odd	2
45.26.b.b.19.11		12	15.14	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:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	5.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+9361.55i q^{2} +531494. i q^{3} -5.40841e7 q^{4} +(-5.44720e8 - 3.61012e7i) q^{5} -4.97561e9 q^{6} -1.37587e10i q^{7} -1.92189e11i q^{8} +5.64803e11 q^{9} +(3.37963e11 - 5.09942e12i) q^{10} -9.26999e12 q^{11} -2.87454e13i q^{12} -1.02027e14i q^{13} +1.28802e14 q^{14} +(1.91876e13 - 2.89515e14i) q^{15} -1.55712e13 q^{16} +3.06292e15i q^{17} +5.28743e15i q^{18} +5.00581e15 q^{19} +(2.94607e16 + 1.95250e15i) q^{20} +7.31265e15 q^{21} -8.67815e16i q^{22} -9.11014e16i q^{23} +1.02148e17 q^{24} +(2.95417e17 + 3.93301e16i) q^{25} +9.55130e17 q^{26} +7.50518e17i q^{27} +7.44125e17i q^{28} -3.16262e18 q^{29} +(2.71031e18 + 1.79626e17i) q^{30} +3.22878e18 q^{31} -6.59458e18i q^{32} -4.92695e18i q^{33} -2.86736e19 q^{34} +(-4.96704e17 + 7.49462e18i) q^{35} -3.05468e19 q^{36} -1.59124e19i q^{37} +4.68621e19i q^{38} +5.42268e19 q^{39} +(-6.93828e18 + 1.04689e20i) q^{40} -8.10389e19 q^{41} +6.84577e19i q^{42} -3.97592e20i q^{43} +5.01359e20 q^{44} +(-3.07659e20 - 2.03901e19i) q^{45} +8.52850e20 q^{46} -9.69576e20i q^{47} -8.27600e18i q^{48} +1.15177e21 q^{49} +(-3.68191e20 + 2.76556e21i) q^{50} -1.62792e21 q^{51} +5.51804e21i q^{52} -5.88324e21i q^{53} -7.02601e21 q^{54} +(5.04955e21 + 3.34658e20i) q^{55} -2.64427e21 q^{56} +2.66056e21i q^{57} -2.96070e22i q^{58} -2.11464e22 q^{59} +(-1.03774e21 + 1.56582e22i) q^{60} +7.65113e21 q^{61} +3.02264e22i q^{62} -7.77093e21i q^{63} +6.12130e22 q^{64} +(-3.68330e21 + 5.55762e22i) q^{65} +4.61238e22 q^{66} +3.72268e22i q^{67} -1.65655e23i q^{68} +4.84199e22 q^{69} +(-7.01612e22 - 4.64992e21i) q^{70} -3.96178e22 q^{71} -1.08549e23i q^{72} -4.27194e22i q^{73} +1.48965e23 q^{74} +(-2.09037e22 + 1.57012e23i) q^{75} -2.70734e23 q^{76} +1.27543e23i q^{77} +5.07646e23i q^{78} -9.25017e23 q^{79} +(8.48194e21 + 5.62139e20i) q^{80} +7.96549e22 q^{81} -7.58649e23i q^{82} +9.81159e23i q^{83} -3.95498e23 q^{84} +(1.10575e23 - 1.66843e24i) q^{85} +3.72207e24 q^{86} -1.68091e24i q^{87} +1.78160e24i q^{88} -1.32371e24 q^{89} +(1.90883e23 - 2.88017e24i) q^{90} -1.40375e24 q^{91} +4.92714e24i q^{92} +1.71608e24i q^{93} +9.07673e24 q^{94} +(-2.72676e24 - 1.80716e23i) q^{95} +3.50498e24 q^{96} -3.52916e24i q^{97} +1.07823e25i q^{98} -5.23572e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 166691544 q^{4} + 549543060 q^{5} + 10591544184 q^{6} - 3948466041036 q^{9} + 4435846671960 q^{10} - 1090673824176 q^{11} - 890646861445848 q^{14} + 443085522435120 q^{15} + 22\!\cdots\!32 q^{16}+ \cdots - 10\!\cdots\!72 q^{99}+O(q^{100}) \) 12 * q - 166691544 * q^4 + 549543060 * q^5 + 10591544184 * q^6 - 3948466041036 * q^9 + 4435846671960 * q^10 - 1090673824176 * q^11 - 890646861445848 * q^14 + 443085522435120 * q^15 + 2206145875609632 * q^16 + 6329834351210160 * q^19 - 45407795215923720 * q^20 + 13538972741781744 * q^21 - 1238774108159908320 * q^24 + 883359578467451100 * q^25 + 487725686068642704 * q^26 - 5990455853511966360 * q^29 + 8784171220269562920 * q^30 - 35669623242168576 * q^31 - 45224081273675172288 * q^34 + 37959801679716705360 * q^35 + 95509342682184062232 * q^36 + 59576177650244745888 * q^39 - 135247056564421048800 * q^40 - 149504768291960577576 * q^41 + 1795327120321140441312 * q^44 - 1757089887558453396180 * q^45 - 2632260904857596314776 * q^46 - 1924948130789206201884 * q^49 + 4613478251192179347600 * q^50 + 6601362996360626974464 * q^51 - 4543556632841187026640 * q^54 - 4976317493836251356880 * q^55 + 6789286242764162655840 * q^56 - 31976684482970870043120 * q^59 + 38198563842186313414560 * q^60 + 33892026990475241838024 * q^61 - 45154694563657190239104 * q^64 - 23988754129834728629280 * q^65 - 84625057142490628840032 * q^66 + 454638912158488569862128 * q^69 - 514001938945682971911240 * q^70 - 118991523615678935618976 * q^71 - 276076790459758393833168 * q^74 - 256450000750992984232800 * q^75 + 1770023872374606472757280 * q^76 - 741918285485353377639360 * q^79 + 504838130357233934552160 * q^80 + 2020576746978155938317372 * q^81 - 6598941205046486172215328 * q^84 - 1447445120396229235779840 * q^85 + 6309456694176729359288664 * q^86 + 576066549612764658926520 * q^89 - 14281964558091964746137880 * q^90 + 12216814388553519240480864 * q^91 - 11673168428062976516959608 * q^94 - 23618191778193292124785200 * q^95 + 57292208364908004705120384 * q^96 - 10068680551503914801051472 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more