LMFDB - Embedded newform 5.26.b.a.4.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5,26,Mod(4,5)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	5.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			4.1
Root			$-5297.67i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.26.b.a.4.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-10595.3i q^{2} +1.42235e6i q^{3} -7.87068e7 q^{4} +(5.09516e8 + 1.96001e8i) q^{5} +1.50702e10 q^{6} -3.45094e10i q^{7} +4.78405e11i q^{8} -1.17578e12 q^{9} +(2.07670e12 - 5.39850e12i) q^{10} -7.99859e12 q^{11} -1.11948e14i q^{12} -2.45373e13i q^{13} -3.65639e14 q^{14} +(-2.78781e14 + 7.24708e14i) q^{15} +2.42790e15 q^{16} -1.75638e15i q^{17} +1.24578e16i q^{18} -1.10855e16 q^{19} +(-4.01024e16 - 1.54266e16i) q^{20} +4.90843e16 q^{21} +8.47478e16i q^{22} -1.79803e17i q^{23} -6.80457e17 q^{24} +(2.21190e17 + 1.99731e17i) q^{25} -2.59981e17 q^{26} -4.67227e17i q^{27} +2.71613e18i q^{28} -2.26075e18 q^{29} +(7.67853e18 + 2.95378e18i) q^{30} -4.56664e18 q^{31} -9.67184e18i q^{32} -1.13768e19i q^{33} -1.86094e19 q^{34} +(6.76388e18 - 1.75831e19i) q^{35} +9.25418e19 q^{36} -3.51306e19i q^{37} +1.17455e20i q^{38} +3.49005e19 q^{39} +(-9.37679e19 + 2.43755e20i) q^{40} -8.43478e19 q^{41} -5.20065e20i q^{42} -5.67281e19i q^{43} +6.29543e20 q^{44} +(-5.99078e20 - 2.30454e20i) q^{45} -1.90507e21 q^{46} -3.57511e20i q^{47} +3.45332e21i q^{48} +1.50169e20 q^{49} +(2.11622e21 - 2.34359e21i) q^{50} +2.49818e21 q^{51} +1.93125e21i q^{52} -1.71740e21i q^{53} -4.95043e21 q^{54} +(-4.07541e21 - 1.56773e21i) q^{55} +1.65095e22 q^{56} -1.57674e22i q^{57} +2.39534e22i q^{58} -9.09918e21 q^{59} +(2.19420e22 - 5.70395e22i) q^{60} -7.31924e21 q^{61} +4.83851e22i q^{62} +4.05755e22i q^{63} -2.10096e22 q^{64} +(4.80933e21 - 1.25021e22i) q^{65} -1.20541e23 q^{66} +4.11318e21i q^{67} +1.38239e23i q^{68} +2.55741e23 q^{69} +(-1.86299e23 - 7.16657e22i) q^{70} -5.06493e21 q^{71} -5.62499e23i q^{72} +1.13977e23i q^{73} -3.72221e23 q^{74} +(-2.84087e23 + 3.14609e23i) q^{75} +8.72504e23 q^{76} +2.76027e23i q^{77} -3.69782e23i q^{78} +8.56496e23 q^{79} +(1.23706e24 + 4.75871e23i) q^{80} -3.31666e23 q^{81} +8.93694e23i q^{82} -3.95018e23i q^{83} -3.86327e24 q^{84} +(3.44252e23 - 8.94903e23i) q^{85} -6.01054e23 q^{86} -3.21557e24i q^{87} -3.82656e24i q^{88} +3.25979e24 q^{89} +(-2.44174e24 + 6.34744e24i) q^{90} -8.46766e23 q^{91} +1.41517e25i q^{92} -6.49533e24i q^{93} -3.78795e24 q^{94} +(-5.64824e24 - 2.17277e24i) q^{95} +1.37567e25 q^{96} +5.43843e24i q^{97} -1.59109e24i q^{98} +9.40457e24 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 $

$2$		−	10595.3i		−	1.82911i	−0.404461	−	0.914555i	$-0.632541\pi$
$2$		−	10595.3i		−	1.82911i	0.404461	−	0.914555i	$-0.367459\pi$
$3$			1.42235e6i			1.54522i	0.634883	+	0.772609i	$0.281048\pi$
$3$			1.42235e6i			1.54522i	−0.634883	+	0.772609i	$0.718952\pi$
$4$	−7.87068e7			−2.34565
$5$	5.09516e8	+	1.96001e8i	0.933325	+	0.359032i
$5$	5.09516e8	+	1.96001e8i	0.933325	+	0.359032i
$6$	1.50702e10			2.82637
$7$		−	3.45094e10i		−	0.942350i	−0.882040	−	0.471175i	$-0.843830\pi$
$7$		−	3.45094e10i		−	0.942350i	0.882040	−	0.471175i	$-0.156170\pi$
$8$			4.78405e11i			2.46134i
$9$	−1.17578e12			−1.38770
$10$	2.07670e12	−	5.39850e12i	0.656710	−	1.70716i
$11$	−7.99859e12			−0.768431			−0.384215	−	0.923243i	$-0.625528\pi$
$11$	−7.99859e12			−0.768431			−0.384215	+	0.923243i	$0.625528\pi$
$12$		−	1.11948e14i		−	3.62453i
$13$		−	2.45373e13i		−	0.292102i	−0.989277	−	0.146051i	$-0.953344\pi$
$13$		−	2.45373e13i		−	0.292102i	0.989277	−	0.146051i	$-0.0466563\pi$
$14$	−3.65639e14			−1.72366
$15$	−2.78781e14	+	7.24708e14i	−0.554783	+	1.44219i
$16$	2.42790e15			2.15641
$17$		−	1.75638e15i		−	0.731150i	−0.930782	−	0.365575i	$-0.880872\pi$
$17$		−	1.75638e15i		−	0.731150i	0.930782	−	0.365575i	$-0.119128\pi$
$18$			1.24578e16i			2.53825i
$19$	−1.10855e16			−1.14904			−0.574520	−	0.818491i	$-0.694811\pi$
$19$	−1.10855e16			−1.14904			−0.574520	+	0.818491i	$0.694811\pi$
$20$	−4.01024e16	−	1.54266e16i	−2.18925	−	0.842163i
$21$	4.90843e16			1.45614
$22$			8.47478e16i			1.40555i
$23$		−	1.79803e17i		−	1.71079i	−0.517973	−	0.855397i	$-0.673313\pi$
$23$		−	1.79803e17i		−	1.71079i	0.517973	−	0.855397i	$-0.326687\pi$
$24$	−6.80457e17			−3.80330
$25$	2.21190e17	+	1.99731e17i	0.742192	+	0.670188i
$26$	−2.59981e17			−0.534286
$27$		−	4.67227e17i		−	0.599074i
$28$			2.71613e18i			2.21042i
$29$	−2.26075e18			−1.18653			−0.593264	−	0.805008i	$-0.702161\pi$
$29$	−2.26075e18			−1.18653			−0.593264	+	0.805008i	$0.702161\pi$
$30$	7.67853e18	+	2.95378e18i	2.63793	+	1.01476i
$31$	−4.56664e18			−1.04130			−0.520649	−	0.853771i	$-0.674310\pi$
$31$	−4.56664e18			−1.04130			−0.520649	+	0.853771i	$0.674310\pi$
$32$		−	9.67184e18i		−	1.48298i
$33$		−	1.13768e19i		−	1.18739i
$34$	−1.86094e19			−1.33735
$35$	6.76388e18	−	1.75831e19i	0.338334	−	0.879519i
$36$	9.25418e19			3.25504
$37$		−	3.51306e19i		−	0.877332i	−0.898650	−	0.438666i	$-0.855451\pi$
$37$		−	3.51306e19i		−	0.877332i	0.898650	−	0.438666i	$-0.144549\pi$
$38$			1.17455e20i			2.10172i
$39$	3.49005e19			0.451360
$40$	−9.37679e19	+	2.43755e20i	−0.883699	+	2.29723i
$41$	−8.43478e19			−0.583816			−0.291908	−	0.956446i	$-0.594290\pi$
$41$	−8.43478e19			−0.583816			−0.291908	+	0.956446i	$0.594290\pi$
$42$		−	5.20065e20i		−	2.66343i
$43$		−	5.67281e19i		−	0.216492i	−0.994124	−	0.108246i	$-0.965477\pi$
$43$		−	5.67281e19i		−	0.216492i	0.994124	−	0.108246i	$-0.0345235\pi$
$44$	6.29543e20			1.80247
$45$	−5.99078e20	−	2.30454e20i	−1.29517	−	0.498228i
$46$	−1.90507e21			−3.12923
$47$		−	3.57511e20i		−	0.448814i	−0.974495	−	0.224407i	$-0.927955\pi$
$47$		−	3.57511e20i		−	0.448814i	0.974495	−	0.224407i	$-0.0720445\pi$
$48$			3.45332e21i			3.33212i
$49$	1.50169e20			0.111977
$50$	2.11622e21	−	2.34359e21i	1.22585	−	1.35755i
$51$	2.49818e21			1.12979
$52$			1.93125e21i			0.685167i
$53$		−	1.71740e21i		−	0.480202i	−0.970748	−	0.240101i	$-0.922819\pi$
$53$		−	1.71740e21i		−	0.480202i	0.970748	−	0.240101i	$-0.0771805\pi$
$54$	−4.95043e21			−1.09577
$55$	−4.07541e21	−	1.56773e21i	−0.717196	−	0.275891i
$56$	1.65095e22			2.31944
$57$		−	1.57674e22i		−	1.77552i
$58$			2.39534e22i			2.17029i
$59$	−9.09918e21			−0.665813			−0.332906	−	0.942960i	$-0.608029\pi$
$59$	−9.09918e21			−0.665813			−0.332906	+	0.942960i	$0.608029\pi$
$60$	2.19420e22	−	5.70395e22i	1.30132	−	3.38287i
$61$	−7.31924e21			−0.353056			−0.176528	−	0.984296i	$-0.556487\pi$
$61$	−7.31924e21			−0.353056			−0.176528	+	0.984296i	$0.556487\pi$
$62$			4.83851e22i			1.90465i
$63$			4.05755e22i			1.30770i
$64$	−2.10096e22			−0.556119
$65$	4.80933e21	−	1.25021e22i	0.104874	−	0.272626i
$66$	−1.20541e23			−2.17187
$67$			4.11318e21i			0.0614105i	0.999528	+	0.0307053i	$0.00977532\pi$
$67$			4.11318e21i			0.0614105i	−0.999528	+	0.0307053i	$0.990225\pi$
$68$			1.38239e23i			1.71502i
$69$	2.55741e23			2.64355
$70$	−1.86299e23	−	7.16657e22i	−1.60874	−	0.618850i
$71$	−5.06493e21			−0.0366306			−0.0183153	−	0.999832i	$-0.505830\pi$
$71$	−5.06493e21			−0.0366306			−0.0183153	+	0.999832i	$0.505830\pi$
$72$		−	5.62499e23i		−	3.41559i
$73$			1.13977e23i			0.582478i	0.956650	+	0.291239i	$0.0940676\pi$
$73$			1.13977e23i			0.582478i	−0.956650	+	0.291239i	$0.905932\pi$
$74$	−3.72221e23			−1.60474
$75$	−2.84087e23	+	3.14609e23i	−1.03559	+	1.14685i
$76$	8.72504e23			2.69524
$77$			2.76027e23i			0.724131i
$78$		−	3.69782e23i		−	0.825588i
$79$	8.56496e23			1.63075			0.815373	−	0.578935i	$-0.196532\pi$
$79$	8.56496e23			1.63075			0.815373	+	0.578935i	$0.196532\pi$
$80$	1.23706e24	+	4.75871e23i	2.01263	+	0.774221i
$81$	−3.31666e23			−0.461996
$82$			8.93694e23i			1.06786i
$83$		−	3.95018e23i		−	0.405640i	−0.979216	−	0.202820i	$-0.934989\pi$
$83$		−	3.95018e23i		−	0.405640i	0.979216	−	0.202820i	$-0.0650106\pi$
$84$	−3.86327e24			−3.41558
$85$	3.44252e23	−	8.94903e23i	0.262506	−	0.682401i
$86$	−6.01054e23			−0.395989
$87$		−	3.21557e24i		−	1.83344i
$88$		−	3.82656e24i		−	1.89137i
$89$	3.25979e24			1.39899			0.699496	−	0.714637i	$-0.253408\pi$
$89$	3.25979e24			1.39899			0.699496	+	0.714637i	$0.253408\pi$
$90$	−2.44174e24	+	6.34744e24i	−0.911313	+	2.36901i
$91$	−8.46766e23			−0.275262
$92$			1.41517e25i			4.01292i
$93$		−	6.49533e24i		−	1.60903i
$94$	−3.78795e24			−0.820931
$95$	−5.64824e24	−	2.17277e24i	−1.07243	−	0.412542i
$96$	1.37567e25			2.29152
$97$			5.43843e24i			0.795842i	0.917420	+	0.397921i	$0.130268\pi$
$97$			5.43843e24i			0.795842i	−0.917420	+	0.397921i	$0.869732\pi$
$98$		−	1.59109e24i		−	0.204818i
$99$	9.40457e24			1.06635
$100$	−1.74092e25	−	1.57202e25i	−1.74092	−	1.57202i
$101$	9.23453e24			0.815450			0.407725	−	0.913105i	$-0.366322\pi$
$101$	9.23453e24			0.815450			0.407725	+	0.913105i	$0.366322\pi$
$102$		−	2.64690e25i		−	2.06650i
$103$			3.18418e24i			0.220055i	0.993929	+	0.110028i	$0.0350939\pi$
$103$			3.18418e24i			0.220055i	−0.993929	+	0.110028i	$0.964906\pi$
$104$	1.17387e25			0.718960
$105$	2.50093e25	+	9.62058e24i	1.35905	+	0.522799i
$106$	−1.81965e25			−0.878342
$107$		−	1.08629e24i		−	0.0466284i	−0.999728	−	0.0233142i	$-0.992578\pi$
$107$		−	1.08629e24i		−	0.0466284i	0.999728	−	0.0233142i	$-0.00742181\pi$
$108$			3.67740e25i			1.40522i
$109$	−2.83630e25			−0.965877			−0.482938	−	0.875654i	$-0.660430\pi$
$109$	−2.83630e25			−0.965877			−0.482938	+	0.875654i	$0.660430\pi$
$110$	−1.66107e25	+	4.31804e25i	−0.504636	+	1.31183i
$111$	4.99678e25			1.35567
$112$		−	8.37855e25i		−	2.03209i
$113$			8.67305e25i			1.88231i	0.337974	+	0.941156i	$0.390258\pi$
$113$			8.67305e25i			1.88231i	−0.337974	+	0.941156i	$0.609742\pi$
$114$	−1.67061e26			−3.24761
$115$	3.52415e25	−	9.16123e25i	0.614230	−	1.59673i
$116$	1.77937e26			2.78318
$117$			2.88504e25i			0.405348i
$118$			9.64089e25i			1.21784i
$119$	−6.06116e25			−0.688999
$120$	−3.46704e26	−	1.33370e26i	−3.54971	−	1.36551i
$121$	−4.43697e25			−0.409514
$122$			7.75499e25i			0.645778i
$123$		−	1.19972e26i		−	0.902122i
$124$	3.59425e26			2.44252
$125$	7.35525e25	+	1.45120e26i	0.452087	+	0.891974i
$126$	4.29911e26			2.39192
$127$		−	2.83457e26i		−	1.42870i	−0.699789	−	0.714349i	$-0.746723\pi$
$127$		−	2.83457e26i		−	1.42870i	0.699789	−	0.714349i	$-0.253277\pi$
$128$		−	1.01929e26i		−	0.465773i
$129$	8.06870e25			0.334528
$130$	−1.32464e26	−	5.09565e25i	−0.498663	−	0.191826i
$131$	−5.09764e26			−1.74373			−0.871863	−	0.489750i	$-0.837088\pi$
$131$	−5.09764e26			−1.74373			−0.871863	+	0.489750i	$0.837088\pi$
$132$			8.95429e26i			2.78520i
$133$			3.82554e26i			1.08280i
$134$	4.35806e25			0.112327
$135$	9.15770e25	−	2.38060e26i	0.215087	−	0.559131i
$136$	8.40260e26			1.79961
$137$			9.32766e25i			0.182291i	0.995838	+	0.0911456i	$0.0290529\pi$
$137$			9.32766e25i			0.182291i	−0.995838	+	0.0911456i	$0.970947\pi$
$138$		−	2.70967e27i		−	4.83534i
$139$	−8.82441e26			−1.43880			−0.719400	−	0.694596i	$-0.755583\pi$
$139$	−8.82441e26			−1.43880			−0.719400	+	0.694596i	$0.755583\pi$
$140$	−5.32364e26	+	1.38391e27i	−0.793612	+	2.06304i
$141$	5.08505e26			0.693515
$142$			5.36647e25i			0.0670015i
$143$			1.96263e26i			0.224460i
$144$	−2.85468e27			−2.99244
$145$	−1.15189e27	−	4.43110e26i	−1.10742	−	0.426002i
$146$	1.20762e27			1.06542
$147$			2.13592e26i			0.173029i
$148$			2.76502e27i			2.05791i
$149$	1.54631e27			1.05796			0.528979	−	0.848635i	$-0.322575\pi$
$149$	1.54631e27			1.05796			0.528979	+	0.848635i	$0.322575\pi$
$150$	3.33339e27	+	3.01000e27i	2.09771	+	1.89420i
$151$	−3.84188e25			−0.0222501			−0.0111251	−	0.999938i	$-0.503541\pi$
$151$	−3.84188e25			−0.0222501			−0.0111251	+	0.999938i	$0.503541\pi$
$152$		−	5.30335e27i		−	2.82817i
$153$			2.06511e27i			1.01461i
$154$	2.92460e27			1.32452
$155$	−2.32677e27	−	8.95065e26i	−0.971870	−	0.373860i
$156$	−2.74690e27			−1.05873
$157$			1.81649e27i			0.646381i	0.946334	+	0.323190i	$0.104755\pi$
$157$			1.81649e27i			0.646381i	−0.946334	+	0.323190i	$0.895245\pi$
$158$		−	9.07486e27i		−	2.98282i
$159$	2.44274e27			0.742016
$160$	1.89569e27	−	4.92796e27i	0.532437	−	1.38410i
$161$	−6.20488e27			−1.61217
$162$			3.51411e27i			0.845042i
$163$			4.94120e27i			1.10024i	0.835086	+	0.550120i	$0.185418\pi$
$163$			4.94120e27i			1.10024i	−0.835086	+	0.550120i	$0.814582\pi$
$164$	6.63875e27			1.36942
$165$	2.22986e27	−	5.79664e27i	0.426312	−	1.10822i
$166$	−4.18535e27			−0.741961
$167$			1.18612e25i			0.00195062i	1.00000		0.000975312i	$0.000310451\pi$
$167$			1.18612e25i			0.00195062i	−1.00000		0.000975312i	$0.999690\pi$
$168$			2.34822e28i			3.58404i
$169$	6.45433e27			0.914677
$170$	−9.48180e27	−	3.64747e27i	−1.24819	−	0.480153i
$171$	1.30341e28			1.59452
$172$			4.46489e27i			0.507815i
$173$			7.57007e27i			0.800800i	0.916341	+	0.400400i	$0.131129\pi$
$173$			7.57007e27i			0.800800i	−0.916341	+	0.400400i	$0.868871\pi$
$174$	−3.40701e28			−3.35357
$175$	6.89262e27	−	7.63315e27i	0.631551	−	0.699404i
$176$	−1.94198e28			−1.65705
$177$		−	1.29422e28i		−	1.02882i
$178$		−	3.45386e28i		−	2.55891i
$179$	−2.53660e28			−1.75222			−0.876112	−	0.482108i	$-0.839871\pi$
$179$	−2.53660e28			−1.75222			−0.876112	+	0.482108i	$0.839871\pi$
$180$	4.71516e28	+	1.81383e28i	3.03801	+	1.16867i
$181$	−4.15985e27			−0.250090			−0.125045	−	0.992151i	$-0.539907\pi$
$181$	−4.15985e27			−0.250090			−0.125045	+	0.992151i	$0.539907\pi$
$182$			8.97178e27i			0.503485i
$183$		−	1.04105e28i		−	0.545548i
$184$	8.60184e28			4.21084
$185$	6.88563e27	−	1.78996e28i	0.314990	−	0.818836i
$186$	−6.88203e28			−2.94310
$187$			1.40485e28i			0.561838i
$188$			2.81386e28i			1.05276i
$189$	−1.61237e28			−0.564538
$190$	−2.30212e28	+	5.98450e28i	−0.754585	+	1.96159i
$191$	5.07164e28			1.55680			0.778398	−	0.627771i	$-0.216033\pi$
$191$	5.07164e28			1.55680			0.778398	+	0.627771i	$0.216033\pi$
$192$		−	2.98829e28i		−	0.859325i
$193$		−	3.94350e28i		−	1.06271i	−0.847148	−	0.531357i	$-0.821682\pi$
$193$		−	3.94350e28i		−	1.06271i	0.847148	−	0.531357i	$-0.178318\pi$
$194$	5.76221e28			1.45568
$195$	1.77824e28	+	6.84053e27i	0.421266	+	0.162053i
$196$	−1.18193e28			−0.262658
$197$		−	4.28378e27i		−	0.0893303i	−0.999002	−	0.0446652i	$-0.985778\pi$
$197$		−	4.28378e27i		−	0.0893303i	0.999002	−	0.0446652i	$-0.0142221\pi$
$198$		−	9.96446e28i		−	1.95047i
$199$	2.53583e28			0.466077			0.233038	−	0.972468i	$-0.425133\pi$
$199$	2.53583e28			0.466077			0.233038	+	0.972468i	$0.425133\pi$
$200$	−9.55525e28	+	1.05819e29i	−1.64956	+	1.82678i
$201$	−5.85037e27			−0.0948926
$202$		−	9.78430e28i		−	1.49155i
$203$			7.80173e28i			1.11812i
$204$	−1.96624e29			−2.65008
$205$	−4.29766e28	−	1.65323e28i	−0.544890	−	0.209609i
$206$	3.37374e28			0.402505
$207$			2.11408e29i			2.37406i
$208$		−	5.95740e28i		−	0.629891i
$209$	8.86683e28			0.882957
$210$	1.01933e29	−	2.64982e29i	0.956258	−	2.48585i
$211$	−9.77644e28			−0.864271			−0.432136	−	0.901809i	$-0.642240\pi$
$211$	−9.77644e28			−0.864271			−0.432136	+	0.901809i	$0.642240\pi$
$212$			1.35171e29i			1.12638i
$213$		−	7.20409e27i		−	0.0566023i
$214$	−1.15097e28			−0.0852884
$215$	1.11188e28	−	2.89039e28i	0.0777278	−	0.202058i
$216$	2.23524e29			1.47452
$217$			1.57592e29i			0.981267i
$218$			3.00516e29i			1.76670i
$219$	−1.62114e29			−0.900056
$220$	3.20763e29	+	1.23391e29i	1.68229	+	0.647144i
$221$	−4.30967e28			−0.213570
$222$		−	5.29426e29i		−	2.47967i
$223$		−	4.09784e29i		−	1.81445i	−0.420650	−	0.907223i	$-0.638198\pi$
$223$		−	4.09784e29i		−	1.81445i	0.420650	−	0.907223i	$-0.361802\pi$
$224$	−3.33770e29			−1.39748
$225$	−2.60071e29	−	2.34840e29i	−1.02994	−	0.930017i
$226$	9.18939e29			3.44296
$227$		−	5.57436e28i		−	0.197639i	−0.995105	−	0.0988193i	$-0.968493\pi$
$227$		−	5.57436e28i		−	0.197639i	0.995105	−	0.0988193i	$-0.0315066\pi$
$228$			1.24100e30i			4.16473i
$229$	4.45181e29			1.41447			0.707234	−	0.706980i	$-0.249943\pi$
$229$	4.45181e29			1.41447			0.707234	+	0.706980i	$0.249943\pi$
$230$	−9.70664e29	−	3.73396e29i	−2.92059	−	1.12350i
$231$	−3.92605e29			−1.11894
$232$		−	1.08156e30i		−	2.92044i
$233$		−	4.02754e29i		−	1.03060i	−0.857009	−	0.515301i	$-0.827680\pi$
$233$		−	4.02754e29i		−	1.03060i	0.857009	−	0.515301i	$-0.172320\pi$
$234$	3.05680e29			0.741427
$235$	7.00726e28	−	1.82158e29i	0.161139	−	0.418890i
$236$	7.16167e29			1.56176
$237$			1.21823e30i			2.51986i
$238$			6.42200e29i			1.26026i
$239$	−6.36932e29			−1.18610			−0.593048	−	0.805167i	$-0.702075\pi$
$239$	−6.36932e29			−1.18610			−0.593048	+	0.805167i	$0.702075\pi$
$240$	−6.76854e29	+	1.75952e30i	−1.19634	+	3.10995i
$241$	−5.68201e29			−0.953430			−0.476715	−	0.879058i	$-0.658173\pi$
$241$	−5.68201e29			−0.953430			−0.476715	+	0.879058i	$0.658173\pi$
$242$			4.70112e29i			0.749047i
$243$		−	8.67620e29i		−	1.31296i
$244$	5.76074e29			0.828144
$245$	7.65134e28	+	2.94332e28i	0.104511	+	0.0402033i
$246$	−1.27114e30			−1.65008
$247$			2.72007e29i			0.335636i
$248$		−	2.18470e30i		−	2.56299i
$249$	5.61852e29			0.626802
$250$	1.53760e30	−	7.79314e29i	1.63152	−	0.826918i
$251$	1.77131e30			1.78802			0.894012	−	0.448044i	$-0.147879\pi$
$251$	1.77131e30			1.78802			0.894012	+	0.448044i	$0.147879\pi$
$252$		−	3.19357e30i		−	3.06739i
$253$			1.43817e30i			1.31463i
$254$	−3.00332e30			−2.61325
$255$	1.27286e30	+	4.89645e29i	1.05446	+	0.405629i
$256$	−1.78494e30			−1.40807
$257$			1.14766e30i			0.862285i	0.902284	+	0.431143i	$0.141889\pi$
$257$			1.14766e30i			0.862285i	−0.902284	+	0.431143i	$0.858111\pi$
$258$		−	8.54907e29i		−	0.611889i
$259$	−1.21234e30			−0.826753
$260$	−3.78527e29	+	9.84003e29i	−0.245997	+	0.639484i
$261$	2.65815e30			1.64654
$262$			5.40113e30i			3.18947i
$263$		−	3.50470e30i		−	1.97335i	−0.162698	−	0.986676i	$-0.552020\pi$
$263$		−	3.50470e30i		−	1.97335i	0.162698	−	0.986676i	$-0.447980\pi$
$264$	5.44270e30			2.92257
$265$	3.36613e29	−	8.75045e29i	0.172408	−	0.448184i
$266$	4.05329e30			1.98056
$267$			4.63655e30i			2.16175i
$268$		−	3.23735e29i		−	0.144047i
$269$	−2.50073e30			−1.06210			−0.531048	−	0.847342i	$-0.678202\pi$
$269$	−2.50073e30			−1.06210			−0.531048	+	0.847342i	$0.678202\pi$
$270$	−2.52232e30	−	9.70289e29i	−1.02271	−	0.393418i
$271$	−2.61531e30			−1.01253			−0.506264	−	0.862379i	$-0.668974\pi$
$271$	−2.61531e30			−1.01253			−0.506264	+	0.862379i	$0.668974\pi$
$272$		−	4.26431e30i		−	1.57666i
$273$		−	1.20439e30i		−	0.425339i
$274$	9.88298e29			0.333431
$275$	−1.76921e30	−	1.59757e30i	−0.570323	−	0.514993i
$276$	−2.01286e31			−6.20083
$277$		−	6.52093e30i		−	1.92005i	−0.279916	−	0.960024i	$-0.590307\pi$
$277$		−	6.52093e30i		−	1.92005i	0.279916	−	0.960024i	$-0.409693\pi$
$278$			9.34976e30i			2.63173i
$279$	5.36935e30			1.44501
$280$	8.41185e30	+	3.23588e30i	2.16479	+	0.832754i
$281$	2.68754e30			0.661493			0.330747	−	0.943720i	$-0.392699\pi$
$281$	2.68754e30			0.661493			0.330747	+	0.943720i	$0.392699\pi$
$282$		−	5.38778e30i		−	1.26852i
$283$			1.77405e30i			0.399608i	0.979836	+	0.199804i	$0.0640306\pi$
$283$			1.77405e30i			0.399608i	−0.979836	+	0.199804i	$0.935969\pi$
$284$	3.98645e29			0.0859225
$285$	3.09043e30	−	8.03375e30i	0.637467	−	1.65713i
$286$	2.07948e30			0.410562
$287$			2.91079e30i			0.550158i
$288$			1.13719e31i			2.05792i
$289$	2.68576e30			0.465420
$290$	−4.69490e30	+	1.22047e31i	−0.779205	+	2.02559i
$291$	−7.73533e30			−1.22975
$292$		−	8.97073e30i		−	1.36629i
$293$			5.33007e30i			0.777835i	0.921273	+	0.388917i	$0.127151\pi$
$293$			5.33007e30i			0.777835i	−0.921273	+	0.388917i	$0.872849\pi$
$294$	2.26308e30			0.316488
$295$	−4.63618e30	−	1.78345e30i	−0.621420	−	0.239048i
$296$	1.68066e31			2.15941
$297$			3.73716e30i			0.460347i
$298$		−	1.63837e31i		−	1.93512i
$299$	−4.41186e30			−0.499726
$300$	2.23596e31	−	2.47619e31i	2.42912	−	2.69010i
$301$	−1.95766e30			−0.204012
$302$			4.07061e29i			0.0406979i
$303$			1.31347e31i			1.26005i
$304$	−2.69145e31			−2.47780
$305$	−3.72927e30	−	1.43458e30i	−0.329516	−	0.126758i
$306$	2.18806e31			1.85584
$307$			6.07610e30i			0.494761i	0.968918	+	0.247381i	$0.0795698\pi$
$307$			6.07610e30i			0.494761i	−0.968918	+	0.247381i	$0.920430\pi$
$308$		−	2.17252e31i		−	1.69855i
$309$	−4.52900e30			−0.340033
$310$	−9.48352e30	+	2.46530e31i	−0.683831	+	1.77766i
$311$	5.39356e30			0.373569			0.186784	−	0.982401i	$-0.440193\pi$
$311$	5.39356e30			0.373569			0.186784	+	0.982401i	$0.440193\pi$
$312$			1.66966e31i			1.11095i
$313$		−	9.42715e30i		−	0.602665i	−0.953519	−	0.301333i	$-0.902569\pi$
$313$		−	9.42715e30i		−	0.602665i	0.953519	−	0.301333i	$-0.0974315\pi$
$314$	1.92464e31			1.18230
$315$	−7.95283e30	+	2.06739e31i	−0.469505	+	1.22050i
$316$	−6.74121e31			−3.82516
$317$		−	9.40226e30i		−	0.512851i	−0.966564	−	0.256426i	$-0.917455\pi$
$317$		−	9.40226e30i		−	0.512851i	0.966564	−	0.256426i	$-0.0825449\pi$
$318$		−	2.58817e31i		−	1.35723i
$319$	1.80828e31			0.911765
$320$	−1.07047e31	−	4.11790e30i	−0.519040	−	0.199665i
$321$	1.54509e30			0.0720509
$322$			6.57428e31i			2.94883i
$323$			1.94703e31i			0.840120i
$324$	2.61044e31			1.08368
$325$	4.90086e30	−	5.42740e30i	0.195763	−	0.216795i
$326$	5.23537e31			2.01246
$327$		−	4.03421e31i		−	1.49249i
$328$		−	4.03524e31i		−	1.43697i
$329$	−1.23375e31			−0.422940
$330$	−6.14174e31	−	2.36261e31i	−2.02706	−	0.779772i
$331$	−1.45278e31			−0.461691			−0.230845	−	0.972990i	$-0.574149\pi$
$331$	−1.45278e31			−0.461691			−0.230845	+	0.972990i	$0.574149\pi$
$332$			3.10906e31i			0.951488i
$333$			4.13058e31i			1.21747i
$334$	1.25674e29			0.00356791
$335$	−8.06188e29	+	2.09573e30i	−0.0220484	+	0.0573160i
$336$	1.19172e32			3.14002
$337$		−	3.76453e31i		−	0.955734i	−0.878432	−	0.477867i	$-0.841410\pi$
$337$		−	3.76453e31i		−	0.955734i	0.878432	−	0.477867i	$-0.158590\pi$
$338$		−	6.83859e31i		−	1.67304i
$339$	−1.23361e32			−2.90858
$340$	−2.70950e31	+	7.04350e31i	−0.615747	+	1.60067i
$341$	3.65266e31			0.800166
$342$		−	1.38101e32i		−	2.91655i
$343$		−	5.14617e31i		−	1.04787i
$344$	2.71390e31			0.532861
$345$	1.30304e32	+	5.01256e31i	2.46729	+	0.949119i
$346$	8.02075e31			1.46475
$347$			1.22537e31i			0.215849i	0.994159	+	0.107924i	$0.0344204\pi$
$347$			1.22537e31i			0.215849i	−0.994159	+	0.107924i	$0.965580\pi$
$348$			2.53087e32i			4.30061i
$349$	4.18405e31			0.685928			0.342964	−	0.939349i	$-0.388569\pi$
$349$	4.18405e31			0.685928			0.342964	+	0.939349i	$0.388569\pi$
$350$	−8.08758e31	−	7.30296e31i	−1.27929	−	1.15518i
$351$	−1.14645e31			−0.174991
$352$			7.73611e31i			1.13957i
$353$		−	1.27324e31i		−	0.181020i	−0.995896	−	0.0905098i	$-0.971150\pi$
$353$		−	1.27324e31i		−	0.181020i	0.995896	−	0.0905098i	$-0.0288496\pi$
$354$	−1.37127e32			−1.88183
$355$	−2.58067e30	−	9.92732e29i	−0.0341883	−	0.0131516i
$356$	−2.56568e32			−3.28154
$357$		−	8.62106e31i		−	1.06465i
$358$			2.68762e32i			3.20501i
$359$	4.96532e31			0.571830			0.285915	−	0.958255i	$-0.407703\pi$
$359$	4.96532e31			0.571830			0.285915	+	0.958255i	$0.407703\pi$
$360$	1.10250e32	−	2.86602e32i	1.22631	−	3.18785i
$361$	2.98116e31			0.320291
$362$			4.40751e31i			0.457442i
$363$		−	6.31090e31i		−	0.632788i
$364$	6.66463e31			0.645667
$365$	−2.23395e31	+	5.80729e31i	−0.209129	+	0.543642i
$366$	−1.10303e32			−0.997867
$367$		−	1.01189e32i		−	0.884727i	−0.896836	−	0.442364i	$-0.854140\pi$
$367$		−	1.01189e32i		−	0.884727i	0.896836	−	0.442364i	$-0.145860\pi$
$368$		−	4.36543e32i		−	3.68917i
$369$	9.91744e31			0.810158
$370$	−1.89652e32	−	7.29556e31i	−1.49774	−	0.576152i
$371$	−5.92666e31			−0.452518
$372$			5.11227e32i			3.77422i
$373$			3.75463e31i			0.268044i	0.990978	+	0.134022i	$0.0427894\pi$
$373$			3.75463e31i			0.268044i	−0.990978	+	0.134022i	$0.957211\pi$
$374$	1.48849e32			1.02766
$375$	−2.06411e32	+	1.04617e32i	−1.37829	+	0.698573i
$376$	1.71035e32			1.10468
$377$			5.54727e31i			0.346587i
$378$			1.70836e32i			1.03260i
$379$	−1.09299e32			−0.639186			−0.319593	−	0.947555i	$-0.603546\pi$
$379$	−1.09299e32			−0.639186			−0.319593	+	0.947555i	$0.603546\pi$
$380$	4.44555e32	+	1.71012e32i	2.51554	+	0.967678i
$381$	4.03174e32			2.20765
$382$		−	5.37358e32i		−	2.84755i
$383$			3.01872e32i			1.54824i	0.633039	+	0.774120i	$0.281807\pi$
$383$			3.01872e32i			1.54824i	−0.633039	+	0.774120i	$0.718193\pi$
$384$	1.44979e32			0.719721
$385$	−5.41015e31	+	1.40640e32i	−0.259986	+	0.675849i
$386$	−4.17828e32			−1.94382
$387$			6.66998e31i			0.300426i
$388$		−	4.28042e32i		−	1.86676i
$389$	2.39462e32			1.01127			0.505635	−	0.862748i	$-0.331258\pi$
$389$	2.39462e32			1.01127			0.505635	+	0.862748i	$0.331258\pi$
$390$	7.24777e31	−	1.88410e32i	0.296413	−	0.770542i
$391$	−3.15801e32			−1.25085
$392$			7.18414e31i			0.275613i
$393$		−	7.25061e32i		−	2.69443i
$394$	−4.53881e31			−0.163395
$395$	4.36398e32	+	1.67874e32i	1.52202	+	0.585491i
$396$	−7.40204e32			−2.50128
$397$			2.94125e31i			0.0963053i	0.998840	+	0.0481526i	$0.0153334\pi$
$397$			2.94125e31i			0.0963053i	−0.998840	+	0.0481526i	$0.984667\pi$
$398$		−	2.68680e32i		−	0.852506i
$399$	−5.44124e32			−1.67316
$400$	5.37029e32	+	4.84928e32i	1.60047	+	1.44520i
$401$	−1.75755e32			−0.507696			−0.253848	−	0.967244i	$-0.581696\pi$
$401$	−1.75755e32			−0.507696			−0.253848	+	0.967244i	$0.581696\pi$
$402$			6.19866e31i			0.173569i
$403$			1.12053e32i			0.304165i
$404$	−7.26820e32			−1.91276
$405$	−1.68989e32	−	6.50069e31i	−0.431192	−	0.165871i
$406$	8.26619e32			2.04517
$407$			2.80995e32i			0.674169i
$408$			1.19514e33i			2.78078i
$409$	−2.79549e32			−0.630837			−0.315418	−	0.948953i	$-0.602145\pi$
$409$	−2.79549e32			−0.630837			−0.315418	+	0.948953i	$0.602145\pi$
$410$	−1.75165e32	+	4.55352e32i	−0.383397	+	0.996664i
$411$	−1.32672e32			−0.281680
$412$		−	2.50616e32i		−	0.516172i
$413$			3.14007e32i			0.627428i
$414$	2.23994e33			4.34242
$415$	7.74240e31	−	2.01268e32i	0.145638	−	0.378594i
$416$	−2.37320e32			−0.433180
$417$		−	1.25514e33i		−	2.22326i
$418$		−	9.39470e32i		−	1.61503i
$419$	−8.65982e32			−1.44489			−0.722443	−	0.691431i	$-0.756981\pi$
$419$	−8.65982e32			−1.44489			−0.722443	+	0.691431i	$0.756981\pi$
$420$	−1.96840e33	−	7.57205e32i	−3.18784	−	1.22630i
$421$	3.83750e32			0.603284			0.301642	−	0.953421i	$-0.402465\pi$
$421$	3.83750e32			0.603284			0.301642	+	0.953421i	$0.402465\pi$
$422$			1.03585e33i			1.58085i
$423$			4.20354e32i			0.622818i
$424$	8.21614e32			1.18194
$425$	3.50804e32	−	3.88494e32i	0.490008	−	0.542653i
$426$	−7.63298e31			−0.103532
$427$			2.52583e32i			0.332702i
$428$			8.54988e31i			0.109374i
$429$	−2.79154e32			−0.346839
$430$	−3.06247e32	−	1.17807e32i	−0.369586	−	0.142173i
$431$	4.84509e32			0.567983			0.283992	−	0.958827i	$-0.408341\pi$
$431$	4.84509e32			0.567983			0.283992	+	0.958827i	$0.408341\pi$
$432$		−	1.13438e33i		−	1.29185i
$433$		−	4.17279e32i		−	0.461666i	−0.972993	−	0.230833i	$-0.925855\pi$
$433$		−	4.17279e32i		−	0.461666i	0.972993	−	0.230833i	$-0.0741450\pi$
$434$	1.66974e33			1.79485
$435$	6.30256e32	−	1.63839e33i	0.658265	−	1.71120i
$436$	2.23237e33			2.26561
$437$			1.99320e33i			1.96577i
$438$			1.71765e33i			1.64630i
$439$	−1.42703e33			−1.32931			−0.664653	−	0.747152i	$-0.731421\pi$
$439$	−1.42703e33			−1.32931			−0.664653	+	0.747152i	$0.731421\pi$
$440$	7.50011e32	−	1.94970e33i	0.679061	−	1.76526i
$441$	−1.76565e32			−0.155390
$442$			4.56624e32i			0.390643i
$443$			1.52145e33i			1.26536i	0.774415	+	0.632678i	$0.218044\pi$
$443$			1.52145e33i			1.26536i	−0.774415	+	0.632678i	$0.781956\pi$
$444$	−3.93281e33			−3.17992
$445$	1.66092e33	+	6.38923e32i	1.30571	+	0.502283i
$446$	−4.34180e33			−3.31882
$447$			2.19939e33i			1.63477i
$448$			7.25029e32i			0.524059i
$449$	1.36887e33			0.962242			0.481121	−	0.876654i	$-0.340230\pi$
$449$	1.36887e33			0.962242			0.481121	+	0.876654i	$0.340230\pi$
$450$	−2.48821e33	+	2.75554e33i	−1.70110	+	1.88387i
$451$	6.74663e32			0.448622
$452$		−	6.82628e33i		−	4.41524i
$453$		−	5.46449e31i		−	0.0343813i
$454$	−5.90622e32			−0.361503
$455$	−4.31441e32	−	1.65967e32i	−0.256909	−	0.0988279i
$456$	7.54320e33			4.37014
$457$		−	1.70778e33i		−	0.962672i	−0.876536	−	0.481336i	$-0.840152\pi$
$457$		−	1.70778e33i		−	0.962672i	0.876536	−	0.481336i	$-0.159848\pi$
$458$		−	4.71684e33i		−	2.58722i
$459$	−8.20627e32			−0.438013
$460$	−2.77375e33	+	7.21051e33i	−1.44077	+	3.74536i
$461$	3.32758e33			1.68216			0.841080	−	0.540910i	$-0.181920\pi$
$461$	3.32758e33			1.68216			0.841080	+	0.540910i	$0.181920\pi$
$462$			4.15979e33i			2.04666i
$463$		−	1.16782e33i		−	0.559258i	−0.960108	−	0.279629i	$-0.909788\pi$
$463$		−	1.16782e33i		−	0.559258i	0.960108	−	0.279629i	$-0.0902115\pi$
$464$	−5.48889e33			−2.55864
$465$	1.27309e33	−	3.30948e33i	0.577694	−	1.50175i
$466$	−4.26732e33			−1.88509
$467$			2.01085e33i			0.864806i	0.901680	+	0.432403i	$0.142334\pi$
$467$			2.01085e33i			0.864806i	−0.901680	+	0.432403i	$0.857666\pi$
$468$		−	2.27072e33i		−	0.950804i
$469$	1.41943e32			0.0578702
$470$	−1.93002e33	−	7.42443e32i	−0.766195	−	0.294741i
$471$	−2.58368e33			−0.998799
$472$		−	4.35309e33i		−	1.63879i
$473$			4.53745e32i			0.166359i
$474$	1.29076e34			4.60910
$475$	−2.45200e33	−	2.21412e33i	−0.852807	−	0.770072i
$476$	4.77055e33			1.61615
$477$			2.01929e33i			0.666374i
$478$			6.74851e33i			2.16950i
$479$	1.79260e33			0.561422			0.280711	−	0.959792i	$-0.409430\pi$
$479$	1.79260e33			0.561422			0.280711	+	0.959792i	$0.409430\pi$
$480$	7.00926e33	+	2.69633e33i	2.13873	+	0.822730i
$481$	−8.62008e32			−0.256270
$482$			6.02028e33i			1.74393i
$483$		−	8.82549e33i		−	2.49115i
$484$	3.49219e33			0.960575
$485$	−1.06594e33	+	2.77097e33i	−0.285733	+	0.742780i
$486$	−9.19273e33			−2.40155
$487$		−	5.66689e33i		−	1.44289i	−0.692473	−	0.721444i	$-0.743479\pi$
$487$		−	5.66689e33i		−	1.44289i	0.692473	−	0.721444i	$-0.256521\pi$
$488$		−	3.50156e33i		−	0.868989i
$489$	−7.02809e33			−1.70011
$490$	3.11855e32	−	8.10685e32i	0.0735363	−	0.191162i
$491$	1.64815e32			0.0378859			0.0189429	−	0.999821i	$-0.493970\pi$
$491$	1.64815e32			0.0378859			0.0189429	+	0.999821i	$0.493970\pi$
$492$			9.44260e33i			2.11606i
$493$			3.97074e33i			0.867530i
$494$	2.88201e33			0.613916
$495$	4.79178e33	+	1.84331e33i	0.995250	+	0.382853i
$496$	−1.10873e34			−2.24547
$497$			1.74788e32i			0.0345189i
$498$		−	5.95302e33i		−	1.14649i
$499$	2.46424e33			0.462834			0.231417	−	0.972855i	$-0.425664\pi$
$499$	2.46424e33			0.462834			0.231417	+	0.972855i	$0.425664\pi$
$500$	−5.78908e33	−	1.14219e34i	−1.06044	−	2.09225i
$501$	−1.68708e31			−0.00301414
$502$		−	1.87676e34i		−	3.27049i
$503$			1.37835e33i			0.234293i	0.993115	+	0.117146i	$0.0373747\pi$
$503$			1.37835e33i			0.234293i	−0.993115	+	0.117146i	$0.962625\pi$
$504$	−1.94115e34			−3.21868
$505$	4.70514e33	+	1.80998e33i	0.761080	+	0.292773i
$506$	1.52379e34			2.40460
$507$			9.18029e33i			1.41337i
$508$			2.23100e34i			3.35122i
$509$	−8.86612e33			−1.29946			−0.649728	−	0.760167i	$-0.725117\pi$
$509$	−8.86612e33			−1.29946			−0.649728	+	0.760167i	$0.725117\pi$
$510$	5.18796e33	−	1.34864e34i	0.741941	−	1.92872i
$511$	3.93327e33			0.548898
$512$			1.54919e34i			2.10974i
$513$			5.17944e33i			0.688360i
$514$	1.21599e34			1.57722
$515$	−6.24102e32	+	1.62239e33i	−0.0790069	+	0.205383i
$516$	−6.35062e33			−0.784684
$517$			2.85959e33i			0.344883i
$518$			1.28451e34i			1.51222i
$519$	−1.07673e34			−1.23741
$520$	5.98108e33	+	2.30081e33i	0.671024	+	0.258130i
$521$	−2.37193e32			−0.0259795			−0.0129898	−	0.999916i	$-0.504135\pi$
$521$	−2.37193e32			−0.0259795			−0.0129898	+	0.999916i	$0.504135\pi$
$522$		−	2.81640e34i		−	3.01170i
$523$		−	3.41717e33i		−	0.356775i	−0.983960	−	0.178388i	$-0.942912\pi$
$523$		−	3.41717e33i		−	0.356775i	0.983960	−	0.178388i	$-0.0570881\pi$
$524$	4.01219e34			4.09016
$525$	1.08570e34	+	9.80368e33i	1.08073	+	0.975884i
$526$	−3.71335e34			−3.60948
$527$			8.02074e33i			0.761345i
$528$		−	2.76217e34i		−	2.56051i
$529$	−2.12832e34			−1.92682
$530$	−9.27140e33	−	3.56653e33i	−0.819779	−	0.315353i
$531$	1.06986e34			0.923945
$532$		−	3.01096e34i		−	2.53986i
$533$			2.06966e33i			0.170533i
$534$	4.91259e34			3.95407
$535$	2.12915e32	−	5.53484e32i	0.0167411	−	0.0435194i
$536$	−1.96777e33			−0.151152
$537$		−	3.60793e34i		−	2.70757i
$538$			2.64961e34i			1.94269i
$539$	−1.20114e33			−0.0860464
$540$	−7.20773e33	+	1.87369e34i	−0.504518	+	1.31152i
$541$	−4.03613e33			−0.276057			−0.138029	−	0.990428i	$-0.544077\pi$
$541$	−4.03613e33			−0.276057			−0.138029	+	0.990428i	$0.544077\pi$
$542$			2.77101e34i			1.85203i
$543$		−	5.91675e33i		−	0.386443i
$544$	−1.69874e34			−1.08428
$545$	−1.44514e34	−	5.55919e33i	−0.901477	−	0.346781i
$546$	−1.27610e34			−0.777993
$547$			9.55148e33i			0.569153i	0.958653	+	0.284577i	$0.0918530\pi$
$547$			9.55148e33i			0.569153i	−0.958653	+	0.284577i	$0.908147\pi$
$548$		−	7.34151e33i		−	0.427591i
$549$	8.60581e33			0.489934
$550$	−1.69268e34	+	1.87454e34i	−0.941979	+	1.04318i
$551$	2.50615e34			1.36337
$552$			1.22348e35i			6.50666i
$553$		−	2.95572e34i		−	1.53673i
$554$	−6.90915e34			−3.51198
$555$	2.54594e34	+	9.79375e33i	1.26528	+	0.486728i
$556$	6.94541e34			3.37492
$557$		−	2.92625e34i		−	1.39034i	−0.718845	−	0.695170i	$-0.755329\pi$
$557$		−	2.92625e34i		−	1.39034i	0.718845	−	0.695170i	$-0.244671\pi$
$558$		−	5.68901e34i		−	2.64308i
$559$	−1.39195e33			−0.0632378
$560$	1.64220e34	−	4.26901e34i	0.729587	−	1.89660i
$561$	−1.99819e34			−0.868162
$562$		−	2.84754e34i		−	1.20994i
$563$		−	7.52283e33i		−	0.312627i	−0.987708	−	0.156313i	$-0.950039\pi$
$563$		−	7.52283e33i		−	0.312627i	0.987708	−	0.156313i	$-0.0499610\pi$
$564$	−4.00228e34			−1.62674
$565$	−1.69993e34	+	4.41906e34i	−0.675810	+	1.75681i
$566$	1.87966e34			0.730928
$567$			1.14456e34i			0.435362i
$568$		−	2.42309e33i		−	0.0901603i
$569$	−6.20348e33			−0.225804			−0.112902	−	0.993606i	$-0.536015\pi$
$569$	−6.20348e33			−0.225804			−0.112902	+	0.993606i	$0.536015\pi$
$570$	−8.51203e34	−	3.27441e34i	−3.03108	−	1.16600i
$571$	−1.53335e34			−0.534184			−0.267092	−	0.963671i	$-0.586063\pi$
$571$	−1.53335e34			−0.534184			−0.267092	+	0.963671i	$0.586063\pi$
$572$		−	1.54473e34i		−	0.526504i
$573$			7.21363e34i			2.40559i
$574$	3.08409e34			1.00630
$575$	3.59122e34	−	3.97706e34i	1.14655	−	1.26974i
$576$	2.47026e34			0.771724
$577$		−	4.85990e34i		−	1.48569i	−0.669461	−	0.742847i	$-0.733475\pi$
$577$		−	4.85990e34i		−	1.48569i	0.669461	−	0.742847i	$-0.266525\pi$
$578$		−	2.84566e34i		−	0.851304i
$579$	5.60903e34			1.64212
$580$	9.06616e34	+	3.48758e34i	2.59761	+	0.999250i
$581$	−1.36318e34			−0.382255
$582$			8.19585e34i			2.24935i
$583$			1.37368e34i			0.369002i
$584$	−5.45270e34			−1.43368
$585$	−5.65471e33	+	1.46997e34i	−0.145533	+	0.378322i
$586$	5.64739e34			1.42275
$587$		−	3.71292e34i		−	0.915671i	−0.889037	−	0.457836i	$-0.848625\pi$
$587$		−	3.71292e34i		−	0.915671i	0.889037	−	0.457836i	$-0.151375\pi$
$588$		−	1.68111e34i		−	0.405864i
$589$	5.06234e34			1.19649
$590$	−1.88962e34	+	4.91219e34i	−0.437246	+	1.13665i
$591$	6.09301e33			0.138035
$592$		−	8.52936e34i		−	1.89189i
$593$			5.21268e34i			1.13208i	0.824378	+	0.566040i	$0.191525\pi$
$593$			5.21268e34i			1.13208i	−0.824378	+	0.566040i	$0.808475\pi$
$594$	3.95964e34			0.842026
$595$	−3.08826e34	−	1.18799e34i	−0.643060	−	0.247373i
$596$	−1.21705e35			−2.48160
$597$			3.60683e34i			0.720190i
$598$			4.67452e34i			0.914054i
$599$	9.33366e32			0.0178738			0.00893690	−	0.999960i	$-0.497155\pi$
$599$	9.33366e32			0.0178738			0.00893690	+	0.999960i	$0.497155\pi$
$600$	−1.50511e35	−	1.35909e35i	−2.82278	−	2.54892i
$601$	5.57712e34			1.02442			0.512211	−	0.858860i	$-0.328827\pi$
$601$	5.57712e34			1.02442			0.512211	+	0.858860i	$0.328827\pi$
$602$			2.07420e34i			0.373160i
$603$		−	4.83619e33i		−	0.0852191i
$604$	3.02383e33			0.0521909
$605$	−2.26071e34	−	8.69650e33i	−0.382210	−	0.147029i
$606$	1.39167e35			2.30477
$607$		−	2.75826e34i		−	0.447483i	−0.974649	−	0.223741i	$-0.928173\pi$
$607$		−	2.75826e34i		−	0.447483i	0.974649	−	0.223741i	$-0.0718271\pi$
$608$			1.07217e35i			1.70400i
$609$	−1.10968e35			−1.72775
$610$	−1.51999e34	+	3.95129e34i	−0.231855	+	0.602721i
$611$	−8.77235e33			−0.131099
$612$		−	1.62538e35i		−	2.37993i
$613$			1.02854e35i			1.47559i	0.675022	+	0.737797i	$0.264134\pi$
$613$			1.02854e35i			1.47559i	−0.675022	+	0.737797i	$0.735866\pi$
$614$	6.43784e34			0.904973
$615$	2.35146e34	−	6.11276e34i	0.323891	−	0.841973i
$616$	−1.32053e35			−1.78233
$617$		−	1.88558e34i		−	0.249391i	−0.992195	−	0.124695i	$-0.960205\pi$
$617$		−	1.88558e34i		−	0.249391i	0.992195	−	0.124695i	$-0.0397954\pi$
$618$			4.79863e34i			0.621958i
$619$	−1.03460e35			−1.31413			−0.657066	−	0.753833i	$-0.728203\pi$
$619$	−1.03460e35			−1.31413			−0.657066	+	0.753833i	$0.728203\pi$
$620$	1.83133e35	+	7.04478e34i	2.27966	+	0.876942i
$621$	−8.40086e34			−1.02489
$622$		−	5.71466e34i		−	0.683299i
$623$		−	1.12494e35i		−	1.31834i
$624$	8.47349e34			0.973318
$625$	9.03252e33	+	8.83574e34i	0.101697	+	0.994815i
$626$	−9.98839e34			−1.10234
$627$			1.26117e35i			1.36436i
$628$		−	1.42971e35i		−	1.51618i
$629$	−6.17026e34			−0.641461
$630$	2.19047e35	+	8.42630e34i	2.23244	+	0.858776i
$631$	1.73782e35			1.73635			0.868177	−	0.496255i	$-0.165292\pi$
$631$	1.73782e35			1.73635			0.868177	+	0.496255i	$0.165292\pi$
$632$			4.09752e35i			4.01382i
$633$		−	1.39055e35i		−	1.33549i
$634$	−9.96202e34			−0.938062
$635$	5.55579e34	−	1.44426e35i	0.512949	−	1.33344i
$636$	−1.92260e35			−1.74051
$637$		−	3.68473e33i		−	0.0327086i
$638$		−	1.91594e35i		−	1.66772i
$639$	5.95524e33			0.0508322
$640$	1.99783e34	−	5.19347e34i	0.167228	−	0.434718i
$641$	−3.63882e34			−0.298700			−0.149350	−	0.988784i	$-0.547718\pi$
$641$	−3.63882e34			−0.298700			−0.149350	+	0.988784i	$0.547718\pi$
$642$		−	1.63707e34i		−	0.131789i
$643$			6.70807e34i			0.529615i	0.964301	+	0.264808i	$0.0853084\pi$
$643$			6.70807e34i			0.529615i	−0.964301	+	0.264808i	$0.914692\pi$
$644$	4.88366e35			3.78157
$645$	4.11114e34	+	1.58147e34i	0.312223	+	0.120106i
$646$	2.06295e35			1.53667
$647$			2.02794e35i			1.48167i	0.671687	+	0.740835i	$0.265570\pi$
$647$			2.02794e35i			1.48167i	−0.671687	+	0.740835i	$0.734430\pi$
$648$		−	1.58671e35i		−	1.13713i
$649$	7.27806e34			0.511631
$650$	−5.75052e34	−	5.19263e34i	−0.396543	−	0.358072i
$651$	−2.24150e35			−1.51627
$652$		−	3.88906e35i		−	2.58077i
$653$		−	4.83092e34i		−	0.314496i	−0.987559	−	0.157248i	$-0.949738\pi$
$653$		−	4.83092e34i		−	0.314496i	0.987559	−	0.157248i	$-0.0502621\pi$
$654$	−4.27438e35			−2.72993
$655$	−2.59733e35	−	9.99143e34i	−1.62746	−	0.626054i
$656$	−2.04788e35			−1.25895
$657$		−	1.34011e35i		−	0.808303i
$658$			1.30720e35i			0.773604i
$659$	1.92840e34			0.111977			0.0559885	−	0.998431i	$-0.482169\pi$
$659$	1.92840e34			0.111977			0.0559885	+	0.998431i	$0.482169\pi$
$660$	−1.75505e35	+	4.56235e35i	−0.999977	+	2.59950i
$661$	−1.24428e35			−0.695666			−0.347833	−	0.937556i	$-0.613082\pi$
$661$	−1.24428e35			−0.695666			−0.347833	+	0.937556i	$0.613082\pi$
$662$			1.53927e35i			0.844484i
$663$		−	6.12984e34i		−	0.330012i
$664$	1.88979e35			0.998416
$665$	−7.49810e34	+	1.94917e35i	−0.388759	+	1.01060i
$666$	4.37649e35			2.22689
$667$			4.06489e35i			2.02991i
$668$		−	9.33559e32i		−	0.00457547i
$669$	5.82854e35			2.80371
$670$	2.22050e34	+	8.54184e33i	0.104837	+	0.0403289i
$671$	5.85436e34			0.271299
$672$		−	4.74736e35i		−	2.15942i
$673$		−	1.95858e35i		−	0.874485i	−0.899344	−	0.437242i	$-0.855955\pi$
$673$		−	1.95858e35i		−	0.874485i	0.899344	−	0.437242i	$-0.144045\pi$
$674$	−3.98865e35			−1.74814
$675$	9.33199e34	−	1.03346e35i	0.401492	−	0.444628i
$676$	−5.08000e35			−2.14551
$677$		−	2.72177e35i		−	1.12848i	−0.825611	−	0.564240i	$-0.809169\pi$
$677$		−	2.72177e35i		−	1.12848i	0.825611	−	0.564240i	$-0.190831\pi$
$678$			1.30705e36i			5.32011i
$679$	1.87677e35			0.749962
$680$	4.28126e35	+	1.64692e35i	1.67962	+	0.646116i
$681$	7.92867e34			0.305394
$682$		−	3.87012e35i		−	1.46359i
$683$		−	1.73040e35i		−	0.642523i	−0.946991	−	0.321261i	$-0.895893\pi$
$683$		−	1.73040e35i		−	0.642523i	0.946991	−	0.321261i	$-0.104107\pi$
$684$	−1.02587e36			−3.74017
$685$	−1.82823e34	+	4.75260e34i	−0.0654484	+	0.170137i
$686$	−5.45255e35			−1.91667
$687$			6.33201e35i			2.18566i
$688$		−	1.37730e35i		−	0.466847i
$689$	−4.21403e34			−0.140268
$690$	5.31098e35	−	1.38062e36i	1.73604	−	4.51295i
$691$	1.53972e35			0.494271			0.247135	−	0.968981i	$-0.420511\pi$
$691$	1.53972e35			0.494271			0.247135	+	0.968981i	$0.420511\pi$
$692$		−	5.95816e35i		−	1.87839i
$693$		−	3.24546e35i		−	1.00487i
$694$	1.29832e35			0.394811
$695$	−4.49618e35	−	1.72959e35i	−1.34287	−	0.516576i
$696$	1.53835e36			4.51272
$697$			1.48147e35i			0.426857i
$698$		−	4.43314e35i		−	1.25464i
$699$	5.72856e35			1.59250
$700$	−5.42496e35	+	6.00781e35i	−1.48140	+	1.64055i
$701$	4.71238e35			1.26405			0.632027	−	0.774947i	$-0.282223\pi$
$701$	4.71238e35			1.26405			0.632027	+	0.774947i	$0.282223\pi$
$702$			1.21470e35i			0.320077i
$703$			3.89440e35i			1.00809i
$704$	1.68047e35			0.427339
$705$	2.59091e35	+	9.96675e34i	0.647275	+	0.248994i
$706$	−1.34904e35			−0.331105
$707$		−	3.18678e35i		−	0.768439i
$708$			1.01864e36i			2.41326i
$709$	−7.10076e35			−1.65283			−0.826413	−	0.563065i	$-0.809622\pi$
$709$	−7.10076e35			−1.65283			−0.826413	+	0.563065i	$0.809622\pi$
$710$	−1.05183e34	+	2.73430e34i	−0.0240557	+	0.0625342i
$711$	−1.00705e36			−2.26298
$712$			1.55950e36i			3.44339i
$713$			8.21093e35i			1.78145i
$714$	−9.13431e35			−1.94737
$715$	−3.84678e34	+	9.99994e34i	−0.0805883	+	0.209494i
$716$	1.99648e36			4.11010
$717$		−	9.05938e35i		−	1.83277i
$718$		−	5.26093e35i		−	1.04594i
$719$	5.05048e35			0.986783			0.493391	−	0.869807i	$-0.335757\pi$
$719$	5.05048e35			0.986783			0.493391	+	0.869807i	$0.335757\pi$
$720$	−1.45450e36	−	5.59520e35i	−2.79292	−	1.07438i
$721$	1.09884e35			0.207369
$722$		−	3.15864e35i		−	0.585848i
$723$		−	8.08178e35i		−	1.47326i
$724$	3.27409e35			0.586622
$725$	−5.00057e35	−	4.51543e35i	−0.880631	−	0.795196i
$726$	−6.68661e35			−1.15744
$727$			3.77374e35i			0.642083i	0.947065	+	0.321042i	$0.104033\pi$
$727$			3.77374e35i			0.642083i	−0.947065	+	0.321042i	$0.895967\pi$
$728$		−	4.05097e35i		−	0.677512i
$729$	9.53038e35			1.56681
$730$	6.15302e35	+	2.36695e35i	0.994381	+	0.382519i
$731$	−9.96361e34			−0.158288
$732$			8.19377e35i			1.27966i
$733$		−	9.19254e35i		−	1.41135i	−0.708534	−	0.705677i	$-0.750643\pi$
$733$		−	9.19254e35i		−	1.41135i	0.708534	−	0.705677i	$-0.249357\pi$
$734$	−1.07214e36			−1.61826
$735$	−4.18642e34	+	1.08828e35i	−0.0621228	+	0.161492i
$736$	−1.73902e36			−2.53707
$737$		−	3.28996e34i		−	0.0471897i
$738$		−	1.05079e36i		−	1.48187i
$739$	−8.81803e35			−1.22269			−0.611345	−	0.791365i	$-0.709371\pi$
$739$	−8.81803e35			−1.22269			−0.611345	+	0.791365i	$0.709371\pi$
$740$	−5.41946e35	+	1.40882e36i	−0.738856	+	1.92070i
$741$	−3.86889e35			−0.518631
$742$			6.27950e35i			0.827706i
$743$		−	6.06624e35i		−	0.786248i	−0.919486	−	0.393124i	$-0.871394\pi$
$743$		−	6.06624e35i		−	0.786248i	0.919486	−	0.393124i	$-0.128606\pi$
$744$	3.10740e36			3.96037
$745$	7.87870e35	+	3.03079e35i	0.987419	+	0.379841i
$746$	3.97816e35			0.490283
$747$			4.64454e35i			0.562905i
$748$		−	1.10572e36i		−	1.31787i
$749$	−3.74874e34			−0.0439402
$750$	1.10845e36	+	2.18699e36i	1.27777	+	2.52105i
$751$	−5.99727e35			−0.679915			−0.339958	−	0.940441i	$-0.610413\pi$
$751$	−5.99727e35			−0.679915			−0.339958	+	0.940441i	$0.610413\pi$
$752$		−	8.68003e35i		−	0.967828i
$753$			2.51942e36i			2.76288i
$754$	5.87752e35			0.633946
$755$	−1.95750e34	−	7.53014e33i	−0.0207666	−	0.00798851i
$756$	1.26905e36			1.32421
$757$		−	7.10585e35i		−	0.729319i	−0.931141	−	0.364660i	$-0.881185\pi$
$757$		−	7.10585e35i		−	0.729319i	0.931141	−	0.364660i	$-0.118815\pi$
$758$			1.15806e36i			1.16914i
$759$	−2.04557e36			−2.03138
$760$	1.03946e36	−	2.70215e36i	1.01540	−	2.63960i
$761$	1.73020e36			1.66260			0.831302	−	0.555822i	$-0.187596\pi$
$761$	1.73020e36			1.66260			0.831302	+	0.555822i	$0.187596\pi$
$762$		−	4.27176e36i		−	4.03804i
$763$			9.78792e35i			0.910194i
$764$	−3.99173e36			−3.65169
$765$	−4.04764e35	+	1.05221e36i	−0.364279	+	0.946965i
$766$	3.19844e36			2.83190
$767$			2.23269e35i			0.194485i
$768$		−	2.53880e36i		−	2.17577i
$769$	5.62477e35			0.474270			0.237135	−	0.971477i	$-0.423792\pi$
$769$	5.62477e35			0.474270			0.237135	+	0.971477i	$0.423792\pi$
$770$	1.49013e36	+	5.73224e35i	1.23620	+	0.475544i
$771$	−1.63238e36			−1.33242
$772$			3.10381e36i			2.49275i
$773$			1.69568e36i			1.33999i	0.742367	+	0.669993i	$0.233703\pi$
$773$			1.69568e36i			1.33999i	−0.742367	+	0.669993i	$0.766297\pi$
$774$	7.06707e35			0.549512
$775$	−1.01010e36	−	9.12101e35i	−0.772843	−	0.697865i
$776$	−2.60177e36			−1.95884
$777$		−	1.72436e36i		−	1.27751i
$778$		−	2.53718e36i		−	1.84972i
$779$	9.35037e35			0.670827
$780$	−1.39959e36	−	5.38396e35i	−0.988141	−	0.380119i
$781$	4.05123e34			0.0281481
$782$			3.34602e36i			2.28794i
$783$			1.05628e36i			0.710819i
$784$	3.64595e35			0.241468
$785$	−3.56035e35	+	9.25534e35i	−0.232072	+	0.603284i
$786$	−7.68227e36			−4.92842
$787$		−	1.06016e36i		−	0.669404i	−0.942324	−	0.334702i	$-0.891364\pi$
$787$		−	1.06016e36i		−	0.669404i	0.942324	−	0.334702i	$-0.108636\pi$
$788$			3.37162e35i			0.209537i
$789$	4.98490e36			3.04926
$790$	1.77868e36	−	4.62379e36i	1.07093	−	2.78394i
$791$	2.99302e36			1.77380
$792$			4.49919e36i			2.62464i
$793$			1.79594e35i			0.103128i
$794$	3.11635e35			0.176153
$795$	1.24462e36	+	4.78780e35i	0.692542	+	0.266408i
$796$	−1.99587e36			−1.09325
$797$		−	1.65168e36i		−	0.890630i	−0.895374	−	0.445315i	$-0.853092\pi$
$797$		−	1.65168e36i		−	0.890630i	0.895374	−	0.445315i	$-0.146908\pi$
$798$			5.76518e36i			3.06039i
$799$	−6.27925e35			−0.328151
$800$	1.93177e36	−	2.13932e36i	0.993873	−	1.10065i
$801$	−3.83280e36			−1.94137
$802$			1.86219e36i			0.928632i
$803$		−	9.11652e35i		−	0.447594i
$804$	4.60464e35			0.222584
$805$	−3.16149e36	−	1.21616e36i	−1.50468	−	0.578820i
$806$	1.18724e36			0.556351
$807$		−	3.55690e36i		−	1.64117i
$808$			4.41784e36i			2.00710i
$809$	−1.36648e36			−0.611289			−0.305645	−	0.952146i	$-0.598872\pi$
$809$	−1.36648e36			−0.611289			−0.305645	+	0.952146i	$0.598872\pi$
$810$	−6.88770e35	+	1.79050e36i	−0.303397	+	0.788699i
$811$	−1.87428e36			−0.812968			−0.406484	−	0.913658i	$-0.633245\pi$
$811$	−1.87428e36			−0.812968			−0.406484	+	0.913658i	$0.633245\pi$
$812$		−	6.14049e36i		−	2.62272i
$813$		−	3.71987e36i		−	1.56458i
$814$	2.97724e36			1.23313
$815$	−9.68480e35	+	2.51762e36i	−0.395021	+	1.02688i
$816$	6.06533e36			2.43628
$817$			6.28859e35i			0.248758i
$818$			2.96192e36i			1.15387i
$819$	9.95610e35			0.381980
$820$	3.38255e36	+	1.30120e36i	1.27812	+	0.491668i
$821$	5.70590e35			0.212341			0.106171	−	0.994348i	$-0.466141\pi$
$821$	5.70590e35			0.212341			0.106171	+	0.994348i	$0.466141\pi$
$822$			1.40570e36i			0.515223i
$823$		−	9.91550e35i		−	0.357945i	−0.983854	−	0.178973i	$-0.942723\pi$
$823$		−	9.91550e35i		−	0.357945i	0.983854	−	0.178973i	$-0.0572773\pi$
$824$	−1.52333e36			−0.541630
$825$	2.27230e36	−	2.51643e36i	0.795776	−	0.881273i
$826$	3.32701e36			1.14764
$827$			1.80765e36i			0.614178i	0.951681	+	0.307089i	$0.0993550\pi$
$827$			1.80765e36i			0.614178i	−0.951681	+	0.307089i	$0.900645\pi$
$828$		−	1.66393e37i		−	5.56871i
$829$	−2.73751e36			−0.902450			−0.451225	−	0.892410i	$-0.649013\pi$
$829$	−2.73751e36			−0.902450			−0.451225	+	0.892410i	$0.649013\pi$
$830$	−2.13250e36	−	8.20333e35i	−0.692490	−	0.266388i
$831$	9.27501e36			2.96689
$832$			5.15518e35i			0.162443i
$833$		−	2.63753e35i		−	0.0818719i
$834$	−1.32986e37			−4.06659
$835$	−2.32481e33	+	6.04348e33i	−0.000700337	+	0.00182057i
$836$	−6.97880e36			−2.07111
$837$			2.13366e36i			0.623815i
$838$			9.17537e36i			2.64286i
$839$	1.83813e36			0.521618			0.260809	−	0.965390i	$-0.416011\pi$
$839$	1.83813e36			0.521618			0.260809	+	0.965390i	$0.416011\pi$
$840$	−4.60253e36	+	1.19646e37i	−1.28679	+	3.34507i
$841$	1.48064e36			0.407849
$842$		−	4.06596e36i		−	1.10347i
$843$			3.82261e36i			1.02215i
$844$	7.69472e36			2.02727
$845$	3.28859e36	+	1.26506e36i	0.853691	+	0.328398i
$846$	4.45380e36			1.13920
$847$			1.53117e36i			0.385906i
$848$		−	4.16969e36i		−	1.03551i
$849$	−2.52331e36			−0.617482
$850$	−4.11623e36	−	3.71689e36i	−0.992573	−	0.896278i
$851$	−6.31657e36			−1.50093
$852$			5.67011e35i			0.132769i
$853$		−	3.94597e36i		−	0.910524i	−0.890358	−	0.455262i	$-0.849546\pi$
$853$		−	3.94597e36i		−	0.910524i	0.890358	−	0.455262i	$-0.150454\pi$
$854$	2.67620e36			0.608549
$855$	6.64108e36	+	2.55469e36i	1.48820	+	0.572483i
$856$	5.19689e35			0.114768
$857$			5.86390e36i			1.27622i	0.769945	+	0.638111i	$0.220284\pi$
$857$			5.86390e36i			1.27622i	−0.769945	+	0.638111i	$0.779716\pi$
$858$			2.95774e36i			0.634407i
$859$	3.10698e35			0.0656786			0.0328393	−	0.999461i	$-0.489545\pi$
$859$	3.10698e35			0.0656786			0.0328393	+	0.999461i	$0.489545\pi$
$860$	−8.75124e35	+	2.27493e36i	−0.182322	+	0.473956i
$861$	−4.14016e36			−0.850114
$862$		−	5.13353e36i		−	1.03890i
$863$		−	2.75565e36i		−	0.549654i	−0.961494	−	0.274827i	$-0.911379\pi$
$863$		−	2.75565e36i		−	0.549654i	0.961494	−	0.274827i	$-0.0886206\pi$
$864$	−4.51895e36			−0.888414
$865$	−1.48374e36	+	3.85708e36i	−0.287513	+	0.747406i
$866$	−4.42121e36			−0.844438
$867$			3.82008e36i			0.719174i
$868$		−	1.24036e37i		−	2.30171i
$869$	−6.85076e36			−1.25312
$870$	−1.73593e37	−	6.67777e36i	−3.12997	−	1.20404i
$871$	1.00926e35			0.0179381
$872$		−	1.35690e37i		−	2.37735i
$873$		−	6.39440e36i		−	1.10439i
$874$	2.11186e37			3.59561
$875$	5.00801e36	−	2.53825e36i	0.840551	−	0.426024i
$876$	1.27595e37			2.11121
$877$			1.07892e37i			1.75992i	0.475048	+	0.879960i	$0.342431\pi$
$877$			1.07892e37i			1.75992i	−0.475048	+	0.879960i	$0.657569\pi$
$878$			1.51198e37i			2.43145i
$879$	−7.58120e36			−1.20192
$880$	−9.89470e36	−	3.80630e36i	−1.54657	−	0.594935i
$881$	4.77723e36			0.736168			0.368084	−	0.929793i	$-0.380014\pi$
$881$	4.77723e36			0.736168			0.368084	+	0.929793i	$0.380014\pi$
$882$			1.87077e36i			0.284225i
$883$		−	4.17167e35i		−	0.0624886i	−0.999512	−	0.0312443i	$-0.990053\pi$
$883$		−	4.17167e35i		−	0.0624886i	0.999512	−	0.0312443i	$-0.00994700\pi$
$884$	3.39200e36			0.500960
$885$	2.53668e36	−	6.59425e36i	0.369381	−	0.960228i
$886$	1.61203e37			2.31447
$887$		−	4.66827e36i		−	0.660862i	−0.943830	−	0.330431i	$-0.892806\pi$
$887$		−	4.66827e36i		−	0.660862i	0.943830	−	0.330431i	$-0.107194\pi$
$888$			2.39049e37i			3.33675i
$889$	−9.78194e36			−1.34633
$890$	6.76961e36	−	1.75980e37i	0.918731	−	2.38830i
$891$	2.65286e36			0.355012
$892$			3.22528e37i			4.25605i
$893$			3.96319e36i			0.515705i
$894$	2.33033e37			2.99018
$895$	−1.29244e37	−	4.97177e36i	−1.63539	−	0.629105i
$896$	−3.51752e36			−0.438922
$897$		−	6.27519e36i		−	0.772185i
$898$		−	1.45037e37i		−	1.76005i
$899$	1.03240e37			1.23553
$900$	2.04694e37	+	1.84835e37i	2.41587	+	2.18149i
$901$	−3.01641e36			−0.351100
$902$		−	7.14829e36i		−	0.820579i
$903$		−	2.78446e36i		−	0.315242i
$904$	−4.14923e37			−4.63300
$905$	−2.11951e36	−	8.15336e35i	−0.233415	−	0.0897903i
$906$	−5.78981e35			−0.0628872
$907$		−	1.12014e37i		−	1.20000i	−0.799999	−	0.600002i	$-0.795167\pi$
$907$		−	1.12014e37i		−	1.20000i	0.799999	−	0.600002i	$-0.204833\pi$
$908$			4.38740e36i			0.463590i
$909$	−1.08578e37			−1.13160
$910$	−1.75848e36	+	4.57127e36i	−0.180767	+	0.469915i
$911$	7.03174e36			0.712989			0.356495	−	0.934297i	$-0.383972\pi$
$911$	7.03174e36			0.712989			0.356495	+	0.934297i	$0.383972\pi$
$912$		−	3.82817e37i		−	3.82874i
$913$			3.15959e36i			0.311706i
$914$	−1.80945e37			−1.76083
$915$	2.04047e36	−	5.30432e36i	0.195869	−	0.509173i
$916$	−3.50388e37			−3.31784
$917$			1.75917e37i			1.64320i
$918$			8.69482e36i			0.801175i
$919$	−4.20471e36			−0.382201			−0.191100	−	0.981570i	$-0.561206\pi$
$919$	−4.20471e36			−0.382201			−0.191100	+	0.981570i	$0.561206\pi$
$920$	4.38278e37	+	1.68597e37i	3.93008	+	1.51183i
$921$	−8.64232e36			−0.764513
$922$		−	3.52569e37i		−	3.07686i
$923$			1.24280e35i			0.0106999i
$924$	3.09007e37			2.62464
$925$	7.01668e36	−	7.77055e36i	0.587977	−	0.651148i
$926$	−1.23734e37			−1.02295
$927$		−	3.74389e36i		−	0.305370i
$928$			2.18656e37i			1.75959i
$929$	1.27316e37			1.01085			0.505423	−	0.862872i	$-0.331336\pi$
$929$	1.27316e37			1.01085			0.505423	+	0.862872i	$0.331336\pi$
$930$	−3.50651e37	−	1.34889e37i	−2.74687	−	1.05667i
$931$	−1.66469e36			−0.128666
$932$			3.16995e37i			2.41743i
$933$			7.67151e36i			0.577245i
$934$	2.13056e37			1.58183
$935$	−2.75353e36	+	7.15796e36i	−0.201718	+	0.524378i
$936$	−1.38022e37			−0.997698
$937$			2.49322e37i			1.77834i	0.457573	+	0.889172i	$0.348719\pi$
$937$			2.49322e37i			1.77834i	−0.457573	+	0.889172i	$0.651281\pi$
$938$		−	1.50394e36i		−	0.105851i
$939$	1.34087e37			0.931249
$940$	−5.51519e36	+	1.43371e37i	−0.377975	+	0.982567i
$941$	5.03146e36			0.340270			0.170135	−	0.985421i	$-0.445580\pi$
$941$	5.03146e36			0.340270			0.170135	+	0.985421i	$0.445580\pi$
$942$			2.73750e37i			1.82691i
$943$			1.51660e37i			0.998788i
$944$	−2.20919e37			−1.43577
$945$	−8.21530e36	−	3.16027e36i	−0.526897	−	0.202687i
$946$	4.80758e36			0.304290
$947$		−	1.59118e37i		−	0.993902i	−0.867779	−	0.496951i	$-0.834453\pi$
$947$		−	1.59118e37i		−	0.993902i	0.867779	−	0.496951i	$-0.165547\pi$
$948$		−	9.58833e37i		−	5.91070i
$949$	2.79667e36			0.170143
$950$	−2.34594e37	+	2.59798e37i	−1.40855	+	1.55988i
$951$	1.33733e37			0.792467
$952$		−	2.89969e37i		−	1.69586i
$953$		−	2.51935e37i		−	1.45421i	−0.686526	−	0.727105i	$-0.740865\pi$
$953$		−	2.51935e37i		−	1.45421i	0.686526	−	0.727105i	$-0.259135\pi$
$954$	2.13950e37			1.21887
$955$	2.58408e37	+	9.94048e36i	1.45300	+	0.558940i
$956$	5.01309e37			2.78216
$957$			2.57200e37i			1.40887i
$958$		−	1.89932e37i		−	1.02690i
$959$	3.21892e36			0.171782
$960$	5.85708e36	−	1.52258e37i	0.308525	−	0.802030i
$961$	1.62137e36			0.0843022
$962$			9.13327e36i			0.468746i
$963$			1.27724e36i			0.0647060i
$964$	4.47213e37			2.23641
$965$	7.72931e36	−	2.00928e37i	0.381548	−	0.991857i
$966$	−9.35090e37			−4.55659
$967$		−	3.28494e37i		−	1.58014i	−0.613014	−	0.790072i	$-0.710043\pi$
$967$		−	3.28494e37i		−	1.58014i	0.613014	−	0.790072i	$-0.289957\pi$
$968$		−	2.12267e37i		−	1.00795i
$969$	−2.76935e37			−1.29817
$970$	2.93594e37	+	1.12940e37i	1.35863	+	0.522637i
$971$	−1.54652e37			−0.706503			−0.353251	−	0.935528i	$-0.614924\pi$
$971$	−1.54652e37			−0.706503			−0.353251	+	0.935528i	$0.614924\pi$
$972$			6.82876e37i			3.07974i
$973$			3.04525e37i			1.35585i
$974$	−6.00426e37			−2.63920
$975$	7.71965e36	+	6.97072e36i	0.334996	+	0.302496i
$976$	−1.77704e37			−0.761333
$977$		−	3.01576e37i		−	1.27560i	−0.770202	−	0.637800i	$-0.779844\pi$
$977$		−	3.01576e37i		−	1.27560i	0.770202	−	0.637800i	$-0.220156\pi$
$978$			7.44650e37i			3.10969i
$979$	−2.60737e37			−1.07503
$980$	−6.02212e36	−	2.31659e36i	−0.245145	−	0.0943027i
$981$	3.33487e37			1.34034
$982$		−	1.74627e36i		−	0.0692975i
$983$			1.01888e37i			0.399212i	0.979876	+	0.199606i	$0.0639663\pi$
$983$			1.01888e37i			0.399212i	−0.979876	+	0.199606i	$0.936034\pi$
$984$	5.73951e37			2.22042
$985$	8.39625e35	−	2.18265e36i	0.0320725	−	0.0833743i
$986$	4.20713e37			1.58681
$987$		−	1.75482e37i		−	0.653534i
$988$		−	2.14088e37i		−	0.787284i
$989$	−1.01999e37			−0.370374
$990$	1.95305e37	−	5.07706e37i	0.700281	−	1.82042i
$991$	1.92327e36			0.0680957			0.0340479	−	0.999420i	$-0.489160\pi$
$991$	1.92327e36			0.0680957			0.0340479	+	0.999420i	$0.489160\pi$
$992$			4.41678e37i			1.54422i
$993$		−	2.06636e37i		−	0.713413i
$994$	1.85194e36			0.0631388
$995$	1.29205e37	+	4.97026e36i	0.435001	+	0.167337i
$996$	−4.42216e37			−1.47026
$997$			2.06375e37i			0.677592i	0.940860	+	0.338796i	$0.110020\pi$
$997$			2.06375e37i			0.677592i	−0.940860	+	0.338796i	$0.889980\pi$
$998$		−	2.61094e37i		−	0.846575i
$999$	−1.64140e37			−0.525587

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.26.b.a.4.1	✓	12
3.2	odd	2		45.26.b.b.19.12		12
5.2	odd	4		25.26.a.f.1.12		12
5.3	odd	4		25.26.a.f.1.1		12
5.4	even	2	inner	5.26.b.a.4.12	yes	12
15.14	odd	2		45.26.b.b.19.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.26.b.a.4.1	✓	12	1.1	even	1	trivial
5.26.b.a.4.12	yes	12	5.4	even	2	inner
25.26.a.f.1.1		12	5.3	odd	4
25.26.a.f.1.12		12	5.2	odd	4
45.26.b.b.19.1		12	15.14	odd	2
45.26.b.b.19.12		12	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	5.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-10595.3i q^{2} +1.42235e6i q^{3} -7.87068e7 q^{4} +(5.09516e8 + 1.96001e8i) q^{5} +1.50702e10 q^{6} -3.45094e10i q^{7} +4.78405e11i q^{8} -1.17578e12 q^{9} +(2.07670e12 - 5.39850e12i) q^{10} -7.99859e12 q^{11} -1.11948e14i q^{12} -2.45373e13i q^{13} -3.65639e14 q^{14} +(-2.78781e14 + 7.24708e14i) q^{15} +2.42790e15 q^{16} -1.75638e15i q^{17} +1.24578e16i q^{18} -1.10855e16 q^{19} +(-4.01024e16 - 1.54266e16i) q^{20} +4.90843e16 q^{21} +8.47478e16i q^{22} -1.79803e17i q^{23} -6.80457e17 q^{24} +(2.21190e17 + 1.99731e17i) q^{25} -2.59981e17 q^{26} -4.67227e17i q^{27} +2.71613e18i q^{28} -2.26075e18 q^{29} +(7.67853e18 + 2.95378e18i) q^{30} -4.56664e18 q^{31} -9.67184e18i q^{32} -1.13768e19i q^{33} -1.86094e19 q^{34} +(6.76388e18 - 1.75831e19i) q^{35} +9.25418e19 q^{36} -3.51306e19i q^{37} +1.17455e20i q^{38} +3.49005e19 q^{39} +(-9.37679e19 + 2.43755e20i) q^{40} -8.43478e19 q^{41} -5.20065e20i q^{42} -5.67281e19i q^{43} +6.29543e20 q^{44} +(-5.99078e20 - 2.30454e20i) q^{45} -1.90507e21 q^{46} -3.57511e20i q^{47} +3.45332e21i q^{48} +1.50169e20 q^{49} +(2.11622e21 - 2.34359e21i) q^{50} +2.49818e21 q^{51} +1.93125e21i q^{52} -1.71740e21i q^{53} -4.95043e21 q^{54} +(-4.07541e21 - 1.56773e21i) q^{55} +1.65095e22 q^{56} -1.57674e22i q^{57} +2.39534e22i q^{58} -9.09918e21 q^{59} +(2.19420e22 - 5.70395e22i) q^{60} -7.31924e21 q^{61} +4.83851e22i q^{62} +4.05755e22i q^{63} -2.10096e22 q^{64} +(4.80933e21 - 1.25021e22i) q^{65} -1.20541e23 q^{66} +4.11318e21i q^{67} +1.38239e23i q^{68} +2.55741e23 q^{69} +(-1.86299e23 - 7.16657e22i) q^{70} -5.06493e21 q^{71} -5.62499e23i q^{72} +1.13977e23i q^{73} -3.72221e23 q^{74} +(-2.84087e23 + 3.14609e23i) q^{75} +8.72504e23 q^{76} +2.76027e23i q^{77} -3.69782e23i q^{78} +8.56496e23 q^{79} +(1.23706e24 + 4.75871e23i) q^{80} -3.31666e23 q^{81} +8.93694e23i q^{82} -3.95018e23i q^{83} -3.86327e24 q^{84} +(3.44252e23 - 8.94903e23i) q^{85} -6.01054e23 q^{86} -3.21557e24i q^{87} -3.82656e24i q^{88} +3.25979e24 q^{89} +(-2.44174e24 + 6.34744e24i) q^{90} -8.46766e23 q^{91} +1.41517e25i q^{92} -6.49533e24i q^{93} -3.78795e24 q^{94} +(-5.64824e24 - 2.17277e24i) q^{95} +1.37567e25 q^{96} +5.43843e24i q^{97} -1.59109e24i q^{98} +9.40457e24 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

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