LMFDB - Embedded newform 5.26.b.a.4.10

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			4.10
Root			$3156.95i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.26.b.a.4.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+6313.90i q^{2} +71116.0i q^{3} -6.31093e6 q^{4} +(3.25528e8 + 4.38241e8i) q^{5} -4.49019e8 q^{6} -3.34630e10i q^{7} +1.72013e11i q^{8} +8.42231e11 q^{9} +O(q^{10})$	\(q+6313.90i q^{2} +71116.0i q^{3} -6.31093e6 q^{4} +(3.25528e8 + 4.38241e8i) q^{5} -4.49019e8 q^{6} -3.34630e10i q^{7} +1.72013e11i q^{8} +8.42231e11 q^{9} +(-2.76701e12 + 2.05535e12i) q^{10} +1.82144e13 q^{11} -4.48808e11i q^{12} +9.99300e13i q^{13} +2.11282e14 q^{14} +(-3.11659e13 + 2.31502e13i) q^{15} -1.29783e15 q^{16} -2.20067e15i q^{17} +5.31776e15i q^{18} -1.27990e16 q^{19} +(-2.05438e15 - 2.76570e15i) q^{20} +2.37975e15 q^{21} +1.15004e17i q^{22} +7.08167e16i q^{23} -1.22329e16 q^{24} +(-8.60865e16 + 2.85319e17i) q^{25} -6.30948e17 q^{26} +1.20152e17i q^{27} +2.11182e17i q^{28} -2.12993e18 q^{29} +(-1.46168e17 - 1.96779e17i) q^{30} +4.58579e18 q^{31} -2.42259e18i q^{32} +1.29534e18i q^{33} +1.38948e19 q^{34} +(1.46648e19 - 1.08931e19i) q^{35} -5.31526e18 q^{36} -1.67895e19i q^{37} -8.08114e19i q^{38} -7.10662e18 q^{39} +(-7.53830e19 + 5.59950e19i) q^{40} +4.79379e19 q^{41} +1.50255e19i q^{42} +1.55532e20i q^{43} -1.14950e20 q^{44} +(2.74170e20 + 3.69100e20i) q^{45} -4.47129e20 q^{46} +8.97966e20i q^{47} -9.22966e19i q^{48} +2.21299e20 q^{49} +(-1.80148e21 - 5.43542e20i) q^{50} +1.56503e20 q^{51} -6.30651e20i q^{52} -6.78665e21i q^{53} -7.58627e20 q^{54} +(5.92929e21 + 7.98229e21i) q^{55} +5.75606e21 q^{56} -9.10211e20i q^{57} -1.34482e22i q^{58} +8.34744e21 q^{59} +(1.96686e20 - 1.46099e20i) q^{60} -8.24148e21 q^{61} +2.89542e22i q^{62} -2.81835e22i q^{63} -2.82520e22 q^{64} +(-4.37934e22 + 3.25300e22i) q^{65} -8.17862e21 q^{66} +8.00779e21i q^{67} +1.38883e22i q^{68} -5.03620e21 q^{69} +(6.87781e22 + 9.25923e22i) q^{70} +8.71591e21 q^{71} +1.44875e23i q^{72} -1.89109e23i q^{73} +1.06007e23 q^{74} +(-2.02907e22 - 6.12213e21i) q^{75} +8.07733e22 q^{76} -6.09508e23i q^{77} -4.48705e22i q^{78} -1.13990e23 q^{79} +(-4.22480e23 - 5.68763e23i) q^{80} +7.05068e23 q^{81} +3.02675e23i q^{82} +9.87203e23i q^{83} -1.50184e22 q^{84} +(9.64422e23 - 7.16379e23i) q^{85} -9.82012e23 q^{86} -1.51472e23i q^{87} +3.13311e24i q^{88} -9.13656e23 q^{89} +(-2.33046e24 + 1.73108e24i) q^{90} +3.34395e24 q^{91} -4.46919e23i q^{92} +3.26123e23i q^{93} -5.66967e24 q^{94} +(-4.16642e24 - 5.60903e24i) q^{95} +1.72285e23 q^{96} -1.03288e24i q^{97} +1.39726e24i q^{98} +1.53407e25 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 166691544 q^{4} + 549543060 q^{5} + 10591544184 q^{6} - 3948466041036 q^{9}+O(q^{10}) $ 12 * q - 166691544 * q^4 + 549543060 * q^5 + 10591544184 * q^6 - 3948466041036 * q^9	$ 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

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			6313.90i			1.08999i	0.838439	+	0.544995i	$0.183469\pi$
$2$			6313.90i			1.08999i	−0.838439	+	0.544995i	$0.816531\pi$
$3$			71116.0i			0.0772595i	0.999254	+	0.0386297i	$0.0122993\pi$
$3$			71116.0i			0.0772595i	−0.999254	+	0.0386297i	$0.987701\pi$
$4$	−6.31093e6			−0.188080
$5$	3.25528e8	+	4.38241e8i	0.596298	+	0.802763i
$5$	3.25528e8	+	4.38241e8i	0.596298	+	0.802763i
$6$	−4.49019e8			−0.0842121
$7$		−	3.34630e10i		−	0.913774i	−0.889525	−	0.456887i	$-0.848964\pi$
$7$		−	3.34630e10i		−	0.913774i	0.889525	−	0.456887i	$-0.151036\pi$
$8$			1.72013e11i			0.884985i
$9$	8.42231e11			0.994031
$10$	−2.76701e12	+	2.05535e12i	−0.875005	+	0.649959i
$11$	1.82144e13			1.74987			0.874936	−	0.484239i	$-0.160903\pi$
$11$	1.82144e13			1.74987			0.874936	+	0.484239i	$0.160903\pi$
$12$		−	4.48808e11i		−	0.0145310i
$13$			9.99300e13i			1.18961i	0.803871	+	0.594804i	$0.202770\pi$
$13$			9.99300e13i			1.18961i	−0.803871	+	0.594804i	$0.797230\pi$
$14$	2.11282e14			0.996005
$15$	−3.11659e13	+	2.31502e13i	−0.0620211	+	0.0460696i
$16$	−1.29783e15			−1.15271
$17$		−	2.20067e15i		−	0.916100i	−0.888926	−	0.458050i	$-0.848548\pi$
$17$		−	2.20067e15i		−	0.916100i	0.888926	−	0.458050i	$-0.151452\pi$
$18$			5.31776e15i			1.08348i
$19$	−1.27990e16			−1.32665			−0.663323	−	0.748333i	$-0.730854\pi$
$19$	−1.27990e16			−1.32665			−0.663323	+	0.748333i	$0.730854\pi$
$20$	−2.05438e15	−	2.76570e15i	−0.112152	−	0.150984i
$21$	2.37975e15			0.0705977
$22$			1.15004e17i			1.90734i
$23$			7.08167e16i			0.673810i	0.941539	+	0.336905i	$0.109380\pi$
$23$			7.08167e16i			0.673810i	−0.941539	+	0.336905i	$0.890620\pi$
$24$	−1.22329e16			−0.0683735
$25$	−8.60865e16	+	2.85319e17i	−0.288858	+	0.957372i
$26$	−6.30948e17			−1.29666
$27$			1.20152e17i			0.154058i
$28$			2.11182e17i			0.171863i
$29$	−2.12993e18			−1.11787			−0.558935	−	0.829212i	$-0.688790\pi$
$29$	−2.12993e18			−1.11787			−0.558935	+	0.829212i	$0.688790\pi$
$30$	−1.46168e17	−	1.96779e17i	−0.0502155	−	0.0676024i
$31$	4.58579e18			1.04567			0.522833	−	0.852435i	$-0.324875\pi$
$31$	4.58579e18			1.04567			0.522833	+	0.852435i	$0.324875\pi$
$32$		−	2.42259e18i		−	0.371454i
$33$			1.29534e18i			0.135194i
$34$	1.38948e19			0.998541
$35$	1.46648e19	−	1.08931e19i	0.733544	−	0.544881i
$36$	−5.31526e18			−0.186958
$37$		−	1.67895e19i		−	0.419292i	−0.977777	−	0.209646i	$-0.932769\pi$
$37$		−	1.67895e19i		−	0.419292i	0.977777	−	0.209646i	$-0.0672311\pi$
$38$		−	8.08114e19i		−	1.44603i
$39$	−7.10662e18			−0.0919085
$40$	−7.53830e19	+	5.59950e19i	−0.710434	+	0.527715i
$41$	4.79379e19			0.331804			0.165902	−	0.986142i	$-0.446947\pi$
$41$	4.79379e19			0.331804			0.165902	+	0.986142i	$0.446947\pi$
$42$			1.50255e19i			0.0769508i
$43$			1.55532e20i			0.593558i	0.954946	+	0.296779i	$0.0959125\pi$
$43$			1.55532e20i			0.593558i	−0.954946	+	0.296779i	$0.904087\pi$
$44$	−1.14950e20			−0.329116
$45$	2.74170e20	+	3.69100e20i	0.592738	+	0.797972i
$46$	−4.47129e20			−0.734447
$47$			8.97966e20i			1.12729i	0.826016	+	0.563646i	$0.190602\pi$
$47$			8.97966e20i			1.12729i	−0.826016	+	0.563646i	$0.809398\pi$
$48$		−	9.22966e19i		−	0.0890574i
$49$	2.21299e20			0.165017
$50$	−1.80148e21	−	5.43542e20i	−1.04353	−	0.314853i
$51$	1.56503e20			0.0707774
$52$		−	6.30651e20i		−	0.223742i
$53$		−	6.78665e21i		−	1.89761i	−0.315863	−	0.948805i	$-0.602294\pi$
$53$		−	6.78665e21i		−	1.89761i	0.315863	−	0.948805i	$-0.397706\pi$
$54$	−7.58627e20			−0.167922
$55$	5.92929e21	+	7.98229e21i	1.04344	+	1.40473i
$56$	5.75606e21			0.808677
$57$		−	9.10211e20i		−	0.102496i
$58$		−	1.34482e22i		−	1.21847i
$59$	8.34744e21			0.610806			0.305403	−	0.952223i	$-0.401209\pi$
$59$	8.34744e21			0.610806			0.305403	+	0.952223i	$0.401209\pi$
$60$	1.96686e20	−	1.46099e20i	0.0116649	−	0.00866479i
$61$	−8.24148e21			−0.397541			−0.198771	−	0.980046i	$-0.563695\pi$
$61$	−8.24148e21			−0.397541			−0.198771	+	0.980046i	$0.563695\pi$
$62$			2.89542e22i			1.13977i
$63$		−	2.81835e22i		−	0.908320i
$64$	−2.82520e22			−0.747825
$65$	−4.37934e22	+	3.25300e22i	−0.954974	+	0.709361i
$66$	−8.17862e21			−0.147360
$67$			8.00779e21i			0.119558i	0.998212	+	0.0597789i	$0.0190396\pi$
$67$			8.00779e21i			0.119558i	−0.998212	+	0.0597789i	$0.980960\pi$
$68$			1.38883e22i			0.172300i
$69$	−5.03620e21			−0.0520582
$70$	6.87781e22	+	9.25923e22i	0.593916	+	0.799557i
$71$	8.71591e21			0.0630352			0.0315176	−	0.999503i	$-0.489966\pi$
$71$	8.71591e21			0.0630352			0.0315176	+	0.999503i	$0.489966\pi$
$72$			1.44875e23i			0.879703i
$73$		−	1.89109e23i		−	0.966444i	−0.875498	−	0.483222i	$-0.839466\pi$
$73$		−	1.89109e23i		−	0.966444i	0.875498	−	0.483222i	$-0.160534\pi$
$74$	1.06007e23			0.457024
$75$	−2.02907e22	−	6.12213e21i	−0.0739660	−	0.0223170i
$76$	8.07733e22			0.249516
$77$		−	6.09508e23i		−	1.59899i
$78$		−	4.48705e22i		−	0.100179i
$79$	−1.13990e23			−0.217034			−0.108517	−	0.994095i	$-0.534610\pi$
$79$	−1.13990e23			−0.217034			−0.108517	+	0.994095i	$0.534610\pi$
$80$	−4.22480e23	−	5.68763e23i	−0.687356	−	0.925350i
$81$	7.05068e23			0.982129
$82$			3.02675e23i			0.361663i
$83$			9.87203e23i			1.01375i	0.862020	+	0.506874i	$0.169199\pi$
$83$			9.87203e23i			1.01375i	−0.862020	+	0.506874i	$0.830801\pi$
$84$	−1.50184e22			−0.0132780
$85$	9.64422e23	−	7.16379e23i	0.735412	−	0.546268i
$86$	−9.82012e23			−0.646973
$87$		−	1.51472e23i		−	0.0863660i
$88$			3.13311e24i			1.54861i
$89$	−9.13656e23			−0.392110			−0.196055	−	0.980593i	$-0.562813\pi$
$89$	−9.13656e23			−0.392110			−0.196055	+	0.980593i	$0.562813\pi$
$90$	−2.33046e24	+	1.73108e24i	−0.869782	+	0.646079i
$91$	3.34395e24			1.08703
$92$		−	4.46919e23i		−	0.126730i
$93$			3.26123e23i			0.0807876i
$94$	−5.66967e24			−1.22874
$95$	−4.16642e24	−	5.60903e24i	−0.791075	−	1.06498i
$96$	1.72285e23			0.0286983
$97$		−	1.03288e24i		−	0.151149i	−0.997140	−	0.0755745i	$-0.975921\pi$
$97$		−	1.03288e24i		−	0.151149i	0.997140	−	0.0755745i	$-0.0240791\pi$
$98$			1.39726e24i			0.179867i
$99$	1.53407e25			1.73943
$100$	5.43286e23	−	1.80063e24i	0.0543286	−	0.180063i
$101$	9.50077e24			0.838960			0.419480	−	0.907765i	$-0.362212\pi$
$101$	9.50077e24			0.838960			0.419480	+	0.907765i	$0.362212\pi$
$102$			9.88143e23i			0.0771467i
$103$		−	7.31026e24i		−	0.505205i	−0.967570	−	0.252602i	$-0.918714\pi$
$103$		−	7.31026e24i		−	0.505205i	0.967570	−	0.252602i	$-0.0812864\pi$
$104$	−1.71892e25			−1.05279
$105$	7.74675e23	+	1.04290e24i	0.0420972	+	0.0566732i
$106$	4.28502e25			2.06838
$107$		−	1.98063e25i		−	0.850171i	−0.905153	−	0.425085i	$-0.860244\pi$
$107$		−	1.98063e25i		−	0.850171i	0.905153	−	0.425085i	$-0.139756\pi$
$108$		−	7.58270e23i		−	0.0289752i
$109$	−2.78064e25			−0.946922			−0.473461	−	0.880815i	$-0.656996\pi$
$109$	−2.78064e25			−0.946922			−0.473461	+	0.880815i	$0.656996\pi$
$110$	−5.03994e25	+	3.74370e25i	−1.53115	+	1.13734i
$111$	1.19400e24			0.0323943
$112$			4.34293e25i			1.05331i
$113$		−	8.19644e25i		−	1.77887i	−0.457059	−	0.889436i	$-0.651097\pi$
$113$		−	8.19644e25i		−	1.77887i	0.457059	−	0.889436i	$-0.348903\pi$
$114$	5.74698e24			0.111720
$115$	−3.10347e25	+	2.30528e25i	−0.540910	+	0.401791i
$116$	1.34419e25			0.210249
$117$			8.41642e25i			1.18251i
$118$			5.27049e25i			0.665773i
$119$	−7.36409e25			−0.837109
$120$	−3.98214e24	−	5.36094e24i	−0.0407709	−	0.0548877i
$121$	2.23417e26			2.06205
$122$		−	5.20359e25i		−	0.433316i
$123$			3.40915e24i			0.0256350i
$124$	−2.89406e25			−0.196669
$125$	−1.53062e26	+	5.51527e25i	−0.940789	+	0.338994i
$126$	1.77948e26			0.990060
$127$		−	2.00659e26i		−	1.01137i	−0.862717	−	0.505686i	$-0.831239\pi$
$127$		−	2.00659e26i		−	1.01137i	0.862717	−	0.505686i	$-0.168761\pi$
$128$		−	2.59669e26i		−	1.18658i
$129$	−1.10608e25			−0.0458580
$130$	−2.05391e26	−	2.76507e26i	−0.773197	−	1.04091i
$131$	1.88307e26			0.644133			0.322066	−	0.946717i	$-0.395623\pi$
$131$	1.88307e26			0.644133			0.322066	+	0.946717i	$0.395623\pi$
$132$		−	8.17476e24i		−	0.0254273i
$133$			4.28291e26i			1.21225i
$134$	−5.05604e25			−0.130317
$135$	−5.26554e25	+	3.91128e25i	−0.123672	+	0.0918643i
$136$	3.78543e26			0.810735
$137$			1.93039e26i			0.377257i	0.982048	+	0.188629i	$0.0604042\pi$
$137$			1.93039e26i			0.377257i	−0.982048	+	0.188629i	$0.939596\pi$
$138$		−	3.17981e25i		−	0.0567430i
$139$	−2.35098e25			−0.0383321			−0.0191661	−	0.999816i	$-0.506101\pi$
$139$	−2.35098e25			−0.0383321			−0.0191661	+	0.999816i	$0.506101\pi$
$140$	−9.25487e25	+	6.87457e25i	−0.137965	+	0.102481i
$141$	−6.38598e25			−0.0870940
$142$			5.50314e25i			0.0687078i
$143$			1.82017e27i			2.08166i
$144$	−1.09307e27			−1.14583
$145$	−6.93353e26	−	9.33424e26i	−0.666583	−	0.897385i
$146$	1.19402e27			1.05342
$147$			1.57379e25i			0.0127491i
$148$			1.05957e26i			0.0788605i
$149$	−8.08718e26			−0.553310			−0.276655	−	0.960969i	$-0.589226\pi$
$149$	−8.08718e26			−0.553310			−0.276655	+	0.960969i	$0.589226\pi$
$150$	3.86545e25	−	1.28114e26i	0.0243254	−	0.0806223i
$151$	−1.94023e27			−1.12368			−0.561838	−	0.827247i	$-0.689906\pi$
$151$	−1.94023e27			−1.12368			−0.561838	+	0.827247i	$0.689906\pi$
$152$		−	2.20159e27i		−	1.17406i
$153$		−	1.85347e27i		−	0.910632i
$154$	3.84837e27			1.74288
$155$	1.49280e27	+	2.00968e27i	0.623528	+	0.839423i
$156$	4.48494e25			0.0172862
$157$			7.20403e26i			0.256348i	0.991752	+	0.128174i	$0.0409116\pi$
$157$			7.20403e26i			0.256348i	−0.991752	+	0.128174i	$0.959088\pi$
$158$		−	7.19721e26i		−	0.236565i
$159$	4.82639e26			0.146608
$160$	1.06168e27	−	7.88620e26i	0.298190	−	0.221497i
$161$	2.36973e27			0.615710
$162$			4.45173e27i			1.07051i
$163$		−	7.26372e27i		−	1.61739i	−0.588229	−	0.808694i	$-0.700175\pi$
$163$		−	7.26372e27i		−	1.61739i	0.588229	−	0.808694i	$-0.299825\pi$
$164$	−3.02533e26			−0.0624057
$165$	−5.67668e26	+	4.21668e26i	−0.108529	+	0.0806159i
$166$	−6.23310e27			−1.10498
$167$		−	8.01662e25i		−	0.0131836i	−0.999978	−	0.00659182i	$-0.997902\pi$
$167$		−	8.01662e25i		−	0.0131836i	0.999978	−	0.00659182i	$-0.00209826\pi$
$168$			4.09348e26i			0.0624779i
$169$	−2.92960e27			−0.415168
$170$	4.52314e27	+	6.08927e27i	0.595428	+	0.801592i
$171$	−1.07797e28			−1.31873
$172$		−	9.81549e26i		−	0.111637i
$173$			7.99251e27i			0.845486i	0.906249	+	0.422743i	$0.138933\pi$
$173$			7.99251e27i			0.845486i	−0.906249	+	0.422743i	$0.861067\pi$
$174$	9.56382e26			0.0941382
$175$	9.54762e27	+	2.88071e27i	0.874822	+	0.263951i
$176$	−2.36392e28			−2.01709
$177$			5.93636e26i			0.0471905i
$178$		−	5.76873e27i		−	0.427396i
$179$	2.21151e28			1.52766			0.763829	−	0.645419i	$-0.223317\pi$
$179$	2.21151e28			1.52766			0.763829	+	0.645419i	$0.223317\pi$
$180$	−1.73026e27	−	2.32936e27i	−0.111482	−	0.150083i
$181$	1.90946e28			1.14796			0.573982	−	0.818868i	$-0.305398\pi$
$181$	1.90946e28			1.14796			0.573982	+	0.818868i	$0.305398\pi$
$182$			2.11134e28i			1.18486i
$183$		−	5.86101e26i		−	0.0307138i
$184$	−1.21814e28			−0.596312
$185$	7.35784e27	−	5.46545e27i	0.336592	−	0.250023i
$186$	−2.05911e27			−0.0880578
$187$		−	4.00838e28i		−	1.60306i
$188$		−	5.66700e27i		−	0.212021i
$189$	4.02064e27			0.140774
$190$	3.54148e28	−	2.63064e28i	1.16082	−	0.862265i
$191$	−5.19174e28			−1.59366			−0.796830	−	0.604204i	$-0.793491\pi$
$191$	−5.19174e28			−1.59366			−0.796830	+	0.604204i	$0.793491\pi$
$192$		−	2.00917e27i		−	0.0577765i
$193$			4.44868e27i			0.119885i	0.998202	+	0.0599425i	$0.0190917\pi$
$193$			4.44868e27i			0.119885i	−0.998202	+	0.0599425i	$0.980908\pi$
$194$	6.52153e27			0.164751
$195$	−2.31340e27	−	3.11441e27i	−0.0548048	−	0.0737808i
$196$	−1.39660e27			−0.0310364
$197$		−	5.37613e28i		−	1.12109i	−0.828122	−	0.560547i	$-0.810591\pi$
$197$		−	5.37613e28i		−	1.12109i	0.828122	−	0.560547i	$-0.189409\pi$
$198$			9.68599e28i			1.89596i
$199$	5.29552e28			0.973297			0.486649	−	0.873598i	$-0.338219\pi$
$199$	5.29552e28			0.973297			0.486649	+	0.873598i	$0.338219\pi$
$200$	−4.90785e28	−	1.48080e28i	−0.847260	−	0.255635i
$201$	−5.69482e26			−0.00923697
$202$			5.99869e28i			0.914459i
$203$			7.12739e28i			1.02148i
$204$	−9.87677e26			−0.0133118
$205$	1.56051e28	+	2.10084e28i	0.197854	+	0.266360i
$206$	4.61562e28			0.550668
$207$			5.96440e28i			0.669788i
$208$		−	1.29692e29i		−	1.37127i
$209$	−2.33125e29			−2.32146
$210$	−6.58479e27	+	4.89122e27i	−0.0617733	+	0.0458856i
$211$	3.70619e28			0.327640			0.163820	−	0.986490i	$-0.447618\pi$
$211$	3.70619e28			0.327640			0.163820	+	0.986490i	$0.447618\pi$
$212$			4.28300e28i			0.356903i
$213$			6.19840e26i			0.00487007i
$214$	1.25055e29			0.926678
$215$	−6.81603e28	+	5.06299e28i	−0.476487	+	0.353937i
$216$	−2.06677e28			−0.136339
$217$		−	1.53454e29i		−	0.955503i
$218$		−	1.75567e29i		−	1.03214i
$219$	1.34487e28			0.0746670
$220$	−3.74193e28	−	5.03756e28i	−0.196251	−	0.264203i
$221$	2.19913e29			1.08980
$222$			7.53882e27i			0.0353094i
$223$		−	2.00308e29i		−	0.886926i	−0.896293	−	0.443463i	$-0.853750\pi$
$223$		−	2.00308e29i		−	0.886926i	0.896293	−	0.443463i	$-0.146250\pi$
$224$	−8.10670e28			−0.339425
$225$	−7.25047e28	+	2.40305e29i	−0.287134	+	0.951657i
$226$	5.17515e29			1.93895
$227$			2.72579e29i			0.966427i	0.875503	+	0.483214i	$0.160531\pi$
$227$			2.72579e29i			0.966427i	−0.875503	+	0.483214i	$0.839469\pi$
$228$			5.74428e27i			0.0192775i
$229$	2.35864e29			0.749408			0.374704	−	0.927145i	$-0.377744\pi$
$229$	2.35864e29			0.749408			0.374704	+	0.927145i	$0.377744\pi$
$230$	−1.45553e29	−	1.95950e29i	−0.437949	−	0.589587i
$231$	4.33457e28			0.123537
$232$		−	3.66376e29i		−	0.989298i
$233$			2.85511e29i			0.730591i	0.930892	+	0.365295i	$0.119032\pi$
$233$			2.85511e29i			0.730591i	−0.930892	+	0.365295i	$0.880968\pi$
$234$	−5.31404e29			−1.28892
$235$	−3.93525e29	+	2.92313e29i	−0.904949	+	0.672202i
$236$	−5.26801e28			−0.114880
$237$		−	8.10650e27i		−	0.0167679i
$238$		−	4.64961e29i		−	0.912441i
$239$	−3.11095e29			−0.579321			−0.289660	−	0.957130i	$-0.593542\pi$
$239$	−3.11095e29			−0.579321			−0.289660	+	0.957130i	$0.593542\pi$
$240$	4.04481e28	−	3.00451e28i	0.0714921	−	0.0531047i
$241$	−1.05064e29			−0.176295			−0.0881475	−	0.996107i	$-0.528095\pi$
$241$	−1.05064e29			−0.176295			−0.0881475	+	0.996107i	$0.528095\pi$
$242$			1.41063e30i			2.24762i
$243$			1.51945e29i			0.229936i
$244$	5.20114e28			0.0747697
$245$	7.20390e28	+	9.69822e28i	0.0983992	+	0.132470i
$246$	−2.15251e28			−0.0279419
$247$		−	1.27900e30i		−	1.57819i
$248$			7.88815e29i			0.925399i
$249$	−7.02059e28			−0.0783217
$250$	−3.48229e29	−	9.66418e29i	−0.369500	−	1.02545i
$251$	1.05031e30			1.06022			0.530111	−	0.847928i	$-0.322150\pi$
$251$	1.05031e30			1.06022			0.530111	+	0.847928i	$0.322150\pi$
$252$			1.77864e29i			0.170837i
$253$			1.28988e30i			1.17908i
$254$	1.26694e30			1.10239
$255$	5.09460e28	+	6.85859e28i	0.0422044	+	0.0568175i
$256$	6.91545e29			0.545533
$257$		−	2.63115e30i		−	1.97688i	−0.151599	−	0.988442i	$-0.548442\pi$
$257$		−	2.63115e30i		−	1.97688i	0.151599	−	0.988442i	$-0.451558\pi$
$258$		−	6.98368e28i		−	0.0499848i
$259$	−5.61827e29			−0.383138
$260$	2.76377e29	−	2.05294e29i	0.179612	−	0.133417i
$261$	−1.79390e30			−1.11120
$262$			1.18895e30i			0.702099i
$263$		−	9.52475e29i		−	0.536298i	−0.963377	−	0.268149i	$-0.913588\pi$
$263$		−	9.52475e29i		−	0.536298i	0.963377	−	0.268149i	$-0.0864120\pi$
$264$	−2.22814e29			−0.119645
$265$	2.97418e30	−	2.20924e30i	1.52333	−	1.13154i
$266$	−2.70419e30			−1.32135
$267$		−	6.49755e28i		−	0.0302942i
$268$		−	5.05366e28i		−	0.0224865i
$269$	1.14301e30			0.485452			0.242726	−	0.970095i	$-0.421958\pi$
$269$	1.14301e30			0.485452			0.242726	+	0.970095i	$0.421958\pi$
$270$	−2.46954e29	−	3.32461e29i	−0.100131	−	0.134801i
$271$	−9.46451e29			−0.366422			−0.183211	−	0.983074i	$-0.558649\pi$
$271$	−9.46451e29			−0.366422			−0.183211	+	0.983074i	$0.558649\pi$
$272$			2.85610e30i			1.05599i
$273$			2.37809e29i			0.0839836i
$274$	−1.21883e30			−0.411207
$275$	−1.56801e30	+	5.19691e30i	−0.505465	+	1.67528i
$276$	3.17831e28			0.00979112
$277$			7.31941e29i			0.215516i	0.994177	+	0.107758i	$0.0343671\pi$
$277$			7.31941e29i			0.215516i	−0.994177	+	0.107758i	$0.965633\pi$
$278$		−	1.48438e29i		−	0.0417817i
$279$	3.86230e30			1.03943
$280$	1.87376e30	+	2.52254e30i	0.482212	+	0.649176i
$281$	−7.88433e29			−0.194060			−0.0970299	−	0.995281i	$-0.530934\pi$
$281$	−7.88433e29			−0.194060			−0.0970299	+	0.995281i	$0.530934\pi$
$282$		−	4.03204e29i		−	0.0949317i
$283$		−	6.09023e29i		−	0.137184i	−0.997645	−	0.0685920i	$-0.978149\pi$
$283$		−	6.09023e29i		−	0.137184i	0.997645	−	0.0685920i	$-0.0218507\pi$
$284$	−5.50054e28			−0.0118557
$285$	3.98892e29	−	2.96299e29i	0.0822800	−	0.0611181i
$286$	−1.14923e31			−2.26899
$287$		−	1.60415e30i		−	0.303194i
$288$		−	2.04038e30i		−	0.369237i
$289$	9.27687e29			0.160760
$290$	5.89355e30	−	4.37776e30i	0.978142	−	0.726570i
$291$	7.34546e28			0.0116777
$292$			1.19345e30i			0.181769i
$293$		−	6.89904e30i		−	1.00680i	−0.864053	−	0.503400i	$-0.832082\pi$
$293$		−	6.89904e30i		−	1.00680i	0.864053	−	0.503400i	$-0.167918\pi$
$294$	−9.93675e28			−0.0138964
$295$	2.71732e30	+	3.65819e30i	0.364222	+	0.490332i
$296$	2.88801e30			0.371067
$297$			2.18849e30i			0.269581i
$298$		−	5.10617e30i		−	0.603103i
$299$	−7.07671e30			−0.801570
$300$	1.28053e29	+	3.86363e28i	0.0139115	+	0.00419740i
$301$	5.20455e30			0.542378
$302$		−	1.22504e31i		−	1.22480i
$303$			6.75656e29i			0.0648176i
$304$	1.66109e31			1.52923
$305$	−2.68283e30	−	3.61175e30i	−0.237053	−	0.319132i
$306$	1.17026e31			0.992581
$307$			1.77035e31i			1.44155i	0.693171	+	0.720773i	$0.256213\pi$
$307$			1.77035e31i			1.44155i	−0.693171	+	0.720773i	$0.743787\pi$
$308$			3.84656e30i			0.300738i
$309$	5.19876e29			0.0390318
$310$	−1.26889e31	+	9.42541e30i	−0.914963	+	0.679640i
$311$	−1.86741e31			−1.29340			−0.646701	−	0.762743i	$-0.723852\pi$
$311$	−1.86741e31			−1.29340			−0.646701	+	0.762743i	$0.723852\pi$
$312$		−	1.22243e30i		−	0.0813377i
$313$			1.97244e31i			1.26096i	0.776207	+	0.630479i	$0.217141\pi$
$313$			1.97244e31i			1.26096i	−0.776207	+	0.630479i	$0.782859\pi$
$314$	−4.54855e30			−0.279417
$315$	1.23512e31	−	9.17453e30i	0.729166	−	0.541629i
$316$	7.19381e29			0.0408198
$317$		−	2.26583e31i		−	1.23591i	−0.786214	−	0.617954i	$-0.787962\pi$
$317$		−	2.26583e31i		−	1.23591i	0.786214	−	0.617954i	$-0.212038\pi$
$318$			3.04734e30i			0.159802i
$319$	−3.87955e31			−1.95613
$320$	−9.19682e30	−	1.23812e31i	−0.445926	−	0.600326i
$321$	1.40854e30			0.0656837
$322$			1.49623e31i			0.671118i
$323$			2.81663e31i			1.21534i
$324$	−4.44963e30			−0.184719
$325$	−2.85119e31	−	8.60263e30i	−1.13890	−	0.343628i
$326$	4.58624e31			1.76294
$327$		−	1.97748e30i		−	0.0731587i
$328$			8.24594e30i			0.293641i
$329$	3.00486e31			1.03009
$330$	−2.66237e30	−	3.58420e30i	−0.0878706	−	0.118296i
$331$	2.49464e31			0.792789			0.396394	−	0.918080i	$-0.370261\pi$
$331$	2.49464e31			0.792789			0.396394	+	0.918080i	$0.370261\pi$
$332$		−	6.23017e30i		−	0.190666i
$333$		−	1.41406e31i		−	0.416789i
$334$	5.06162e29			0.0143701
$335$	−3.50934e30	+	2.60676e30i	−0.0959766	+	0.0712920i
$336$	−3.08852e30			−0.0813784
$337$			1.07256e31i			0.272300i	0.990688	+	0.136150i	$0.0434730\pi$
$337$			1.07256e31i			0.272300i	−0.990688	+	0.136150i	$0.956527\pi$
$338$		−	1.84972e31i		−	0.452530i
$339$	5.82898e30			0.137435
$340$	−6.08640e30	+	4.52101e30i	−0.138316	+	0.102742i
$341$	8.35275e31			1.82978
$342$		−	6.80619e31i		−	1.43740i
$343$		−	5.22814e31i		−	1.06456i
$344$	−2.67535e31			−0.525290
$345$	−1.63942e30	−	2.20707e30i	−0.0310422	−	0.0417904i
$346$	−5.04639e31			−0.921573
$347$			8.48517e31i			1.49466i	0.664453	+	0.747330i	$0.268664\pi$
$347$			8.48517e31i			1.49466i	−0.664453	+	0.747330i	$0.731336\pi$
$348$			9.55931e29i			0.0162437i
$349$	−2.89637e31			−0.474829			−0.237414	−	0.971408i	$-0.576300\pi$
$349$	−2.89637e31			−0.474829			−0.237414	+	0.971408i	$0.576300\pi$
$350$	−1.81885e31	+	6.02827e31i	−0.287705	+	0.953548i
$351$	−1.20068e31			−0.183268
$352$		−	4.41260e31i		−	0.649997i
$353$		−	8.84461e31i		−	1.25746i	−0.777623	−	0.628731i	$-0.783575\pi$
$353$		−	8.84461e31i		−	1.25746i	0.777623	−	0.628731i	$-0.216425\pi$
$354$	−3.74816e30			−0.0514372
$355$	2.83727e30	+	3.81966e30i	0.0375877	+	0.0506024i
$356$	5.76601e30			0.0737481
$357$		−	5.23704e30i		−	0.0646746i
$358$			1.39633e32i			1.66513i
$359$	−2.72715e31			−0.314072			−0.157036	−	0.987593i	$-0.550194\pi$
$359$	−2.72715e31			−0.314072			−0.157036	+	0.987593i	$0.550194\pi$
$360$	−6.34899e31	+	4.71607e31i	−0.706193	+	0.524565i
$361$	7.07370e31			0.759988
$362$			1.20561e32i			1.25127i
$363$			1.58885e31i			0.159313i
$364$	−2.11034e31			−0.204450
$365$	8.28753e31	−	6.15603e31i	0.775826	−	0.576288i
$366$	3.70059e30			0.0334778
$367$			1.20849e32i			1.05661i	0.849054	+	0.528306i	$0.177173\pi$
$367$			1.20849e32i			1.05661i	−0.849054	+	0.528306i	$0.822827\pi$
$368$		−	9.19081e31i		−	0.776705i
$369$	4.03748e31			0.329823
$370$	3.45083e31	+	4.64567e31i	0.272522	+	0.366882i
$371$	−2.27101e32			−1.73399
$372$		−	2.05814e30i		−	0.0151946i
$373$		−	1.72298e32i		−	1.23004i	−0.788512	−	0.615020i	$-0.789148\pi$
$373$		−	1.72298e32i		−	1.23004i	0.788512	−	0.615020i	$-0.210852\pi$
$374$	2.53085e32			1.74732
$375$	−3.92224e30	−	1.08852e31i	−0.0261905	−	0.0726848i
$376$	−1.54462e32			−0.997637
$377$		−	2.12844e32i		−	1.32983i
$378$			2.53859e31i			0.153442i
$379$	−7.65880e31			−0.447889			−0.223945	−	0.974602i	$-0.571893\pi$
$379$	−7.65880e31			−0.447889			−0.223945	+	0.974602i	$0.571893\pi$
$380$	2.62940e31	+	3.53982e31i	0.148786	+	0.200302i
$381$	1.42700e31			0.0781381
$382$		−	3.27801e32i		−	1.73707i
$383$			2.34216e32i			1.20125i	0.799532	+	0.600623i	$0.205081\pi$
$383$			2.34216e32i			1.20125i	−0.799532	+	0.600623i	$0.794919\pi$
$384$	1.84666e31			0.0916742
$385$	2.67111e32	−	1.98412e32i	1.28361	−	0.953472i
$386$	−2.80885e31			−0.130674
$387$			1.30994e32i			0.590015i
$388$			6.51846e30i			0.0284281i
$389$	−1.78957e32			−0.755752			−0.377876	−	0.925856i	$-0.623345\pi$
$389$	−1.78957e32			−0.755752			−0.377876	+	0.925856i	$0.623345\pi$
$390$	1.96641e31	−	1.46066e31i	0.0804204	−	0.0597368i
$391$	1.55844e32			0.617278
$392$			3.80663e31i			0.146037i
$393$			1.33916e31i			0.0497653i
$394$	3.39444e32			1.22198
$395$	−3.71069e31	−	4.99550e31i	−0.129417	−	0.174227i
$396$	−9.68142e31			−0.327152
$397$			2.80991e32i			0.920048i	0.887906	+	0.460024i	$0.152159\pi$
$397$			2.80991e32i			0.920048i	−0.887906	+	0.460024i	$0.847841\pi$
$398$			3.34354e32i			1.06089i
$399$	−3.04584e31			−0.0936581
$400$	1.11726e32	−	3.70296e32i	0.332969	−	1.10357i
$401$	−6.22371e32			−1.79781			−0.898907	−	0.438140i	$-0.855637\pi$
$401$	−6.22371e32			−1.79781			−0.898907	+	0.438140i	$0.855637\pi$
$402$		−	3.59565e30i		−	0.0100682i
$403$			4.58258e32i			1.24393i
$404$	−5.99586e31			−0.157792
$405$	2.29519e32	+	3.08990e32i	0.585641	+	0.788417i
$406$	−4.50016e32			−1.11340
$407$		−	3.05811e32i		−	0.733707i
$408$			2.69205e31i			0.0626370i
$409$	2.80739e32			0.633521			0.316760	−	0.948506i	$-0.397405\pi$
$409$	2.80739e32			0.633521			0.316760	+	0.948506i	$0.397405\pi$
$410$	−1.32645e32	+	9.85293e31i	−0.290330	+	0.215659i
$411$	−1.37281e31			−0.0291467
$412$			4.61345e31i			0.0950190i
$413$		−	2.79330e32i		−	0.558138i
$414$	−3.76586e32			−0.730063
$415$	−4.32633e32	+	3.21362e32i	−0.813801	+	0.604496i
$416$	2.42089e32			0.441885
$417$		−	1.67192e30i		−	0.00296152i
$418$		−	1.47193e33i		−	2.53037i
$419$	−8.22274e32			−1.37196			−0.685980	−	0.727620i	$-0.740626\pi$
$419$	−8.22274e32			−1.37196			−0.685980	+	0.727620i	$0.740626\pi$
$420$	−4.88892e30	−	6.58169e30i	−0.00791766	−	0.0106591i
$421$	1.22311e33			1.92282			0.961410	−	0.275121i	$-0.0887180\pi$
$421$	1.22311e33			1.92282			0.961410	+	0.275121i	$0.0887180\pi$
$422$			2.34005e32i			0.357125i
$423$			7.56295e32i			1.12056i
$424$	1.16739e33			1.67936
$425$	6.27893e32	+	1.89448e32i	0.877049	+	0.264623i
$426$	−3.91361e30			−0.00530833
$427$			2.75784e32i			0.363263i
$428$			1.24996e32i			0.159900i
$429$	−1.29443e32			−0.160828
$430$	−3.19672e32	−	4.30358e32i	−0.385789	−	0.519366i
$431$	3.42455e30			0.00401456			0.00200728	−	0.999998i	$-0.499361\pi$
$431$	3.42455e30			0.00401456			0.00200728	+	0.999998i	$0.499361\pi$
$432$		−	1.55937e32i		−	0.177583i
$433$		−	1.57159e33i		−	1.73876i	−0.494141	−	0.869382i	$-0.664517\pi$
$433$		−	1.57159e33i		−	1.73876i	0.494141	−	0.869382i	$-0.335483\pi$
$434$	9.68895e32			1.04149
$435$	6.63814e31	−	4.93085e31i	0.0693315	−	0.0514998i
$436$	1.75484e32			0.178097
$437$		−	9.06380e32i		−	0.893907i
$438$			8.49137e31i			0.0813863i
$439$	−1.28443e33			−1.19648			−0.598240	−	0.801317i	$-0.704133\pi$
$439$	−1.28443e33			−1.19648			−0.598240	+	0.801317i	$0.704133\pi$
$440$	−1.37306e33	+	1.01991e33i	−1.24317	+	0.923433i
$441$	1.86385e32			0.164032
$442$			1.38851e33i			1.18787i
$443$		−	2.78771e32i		−	0.231847i	−0.993258	−	0.115923i	$-0.963017\pi$
$443$		−	2.78771e32i		−	0.231847i	0.993258	−	0.115923i	$-0.0369827\pi$
$444$	−7.53526e30			−0.00609272
$445$	−2.97420e32	−	4.00401e32i	−0.233814	−	0.314771i
$446$	1.26472e33			0.966741
$447$		−	5.75128e31i		−	0.0427484i
$448$			9.45396e32i			0.683343i
$449$	−1.77478e33			−1.24757			−0.623785	−	0.781596i	$-0.714406\pi$
$449$	−1.77478e33			−1.24757			−0.623785	+	0.781596i	$0.714406\pi$
$450$	−1.51726e33	−	4.57788e32i	−1.03730	−	0.312974i
$451$	8.73161e32			0.580614
$452$			5.17271e32i			0.334571i
$453$		−	1.37981e32i		−	0.0868147i
$454$	−1.72104e33			−1.05340
$455$	1.08855e33	+	1.46546e33i	0.648195	+	0.872631i
$456$	1.56568e32			0.0907073
$457$		−	5.67070e32i		−	0.319657i	−0.987145	−	0.159829i	$-0.948906\pi$
$457$		−	5.67070e32i		−	0.319657i	0.987145	−	0.159829i	$-0.0510942\pi$
$458$			1.48922e33i			0.816848i
$459$	2.64414e32			0.141132
$460$	1.95858e32	−	1.45484e32i	0.101735	−	0.0755690i
$461$	2.05579e33			1.03924			0.519622	−	0.854397i	$-0.326073\pi$
$461$	2.05579e33			1.03924			0.519622	+	0.854397i	$0.326073\pi$
$462$			2.73681e32i			0.134654i
$463$			1.15042e33i			0.550929i	0.961311	+	0.275465i	$0.0888317\pi$
$463$			1.15042e33i			0.550929i	−0.961311	+	0.275465i	$0.911168\pi$
$464$	2.76430e33			1.28858
$465$	−1.42920e32	+	1.06162e32i	−0.0648534	+	0.0481735i
$466$	−1.80269e33			−0.796337
$467$		−	1.30592e33i		−	0.561639i	−0.959761	−	0.280819i	$-0.909394\pi$
$467$		−	1.30592e33i		−	0.561639i	0.959761	−	0.280819i	$-0.0906061\pi$
$468$		−	5.31154e32i		−	0.222406i
$469$	2.67964e32			0.109249
$470$	−1.84564e33	−	2.48468e33i	−0.732694	−	0.986387i
$471$	−5.12322e31			−0.0198053
$472$			1.43587e33i			0.540554i
$473$			2.83292e33i			1.03865i
$474$	5.11837e31			0.0182769
$475$	1.10182e33	−	3.65179e33i	0.383213	−	1.27009i
$476$	4.64742e32			0.157444
$477$		−	5.71593e33i		−	1.88628i
$478$		−	1.96422e33i		−	0.631454i
$479$	−4.71822e32			−0.147769			−0.0738847	−	0.997267i	$-0.523540\pi$
$479$	−4.71822e32			−0.147769			−0.0738847	+	0.997267i	$0.523540\pi$
$480$	5.60835e31	+	7.55022e31i	0.0171127	+	0.0230380i
$481$	1.67778e33			0.498793
$482$		−	6.63362e32i		−	0.192160i
$483$			1.68526e32i			0.0475694i
$484$	−1.40997e33			−0.387831
$485$	4.52652e32	−	3.36233e32i	0.121337	−	0.0901297i
$486$	−9.59365e32			−0.250629
$487$			3.91800e33i			0.997591i	0.866720	+	0.498796i	$0.166224\pi$
$487$			3.91800e33i			0.997591i	−0.866720	+	0.498796i	$0.833776\pi$
$488$		−	1.41764e33i		−	0.351818i
$489$	5.16567e32			0.124959
$490$	−6.12336e32	+	4.54847e32i	−0.144391	+	0.107254i
$491$	−1.49234e33			−0.343043			−0.171521	−	0.985180i	$-0.554868\pi$
$491$	−1.49234e33			−0.343043			−0.171521	+	0.985180i	$0.554868\pi$
$492$		−	2.15149e31i		−	0.00482143i
$493$			4.68728e33i			1.02408i
$494$	8.07549e33			1.72021
$495$	4.99383e33	+	6.72293e33i	1.03722	+	1.39635i
$496$	−5.95159e33			−1.20535
$497$		−	2.91660e32i		−	0.0575999i
$498$		−	4.43273e32i		−	0.0853699i
$499$	−7.73935e33			−1.45361			−0.726805	−	0.686844i	$-0.758996\pi$
$499$	−7.73935e33			−1.45361			−0.726805	+	0.686844i	$0.758996\pi$
$500$	9.65963e32	−	3.48064e32i	0.176944	−	0.0637580i
$501$	5.70110e30			0.00101856
$502$			6.63157e33i			1.15563i
$503$		−	8.35964e33i		−	1.42098i	−0.703708	−	0.710489i	$-0.748474\pi$
$503$		−	8.35964e33i		−	1.42098i	0.703708	−	0.710489i	$-0.251526\pi$
$504$	4.84793e33			0.803850
$505$	3.09276e33	+	4.16362e33i	0.500270	+	0.673487i
$506$	−8.14419e33			−1.28519
$507$		−	2.08341e32i		−	0.0320757i
$508$			1.26634e33i			0.190219i
$509$	−1.26637e34			−1.85605			−0.928023	−	0.372522i	$-0.878493\pi$
$509$	−1.26637e34			−1.85605			−0.928023	+	0.372522i	$0.878493\pi$
$510$	−4.33044e32	+	3.21668e32i	−0.0619306	+	0.0460024i
$511$	−6.32815e33			−0.883112
$512$		−	4.34670e33i		−	0.591950i
$513$		−	1.53782e33i		−	0.204380i
$514$	1.66128e34			2.15479
$515$	3.20365e33	−	2.37969e33i	0.405560	−	0.301252i
$516$	6.98039e31			0.00862498
$517$			1.63559e34i			1.97262i
$518$		−	3.54732e33i		−	0.417617i
$519$	−5.68395e32			−0.0653218
$520$	−5.59558e33	−	7.53303e33i	−0.627774	−	0.845138i
$521$	−2.92449e33			−0.320316			−0.160158	−	0.987091i	$-0.551200\pi$
$521$	−2.92449e33			−0.320316			−0.160158	+	0.987091i	$0.551200\pi$
$522$		−	1.13265e34i		−	1.21119i
$523$		−	7.60851e33i		−	0.794380i	−0.917736	−	0.397190i	$-0.869985\pi$
$523$		−	7.60851e33i		−	0.794380i	0.917736	−	0.397190i	$-0.130015\pi$
$524$	−1.18839e33			−0.121149
$525$	−2.04865e32	+	6.78988e32i	−0.0203927	+	0.0675882i
$526$	6.01383e33			0.584560
$527$		−	1.00918e34i		−	0.957936i
$528$		−	1.68113e33i		−	0.155839i
$529$	6.03077e33			0.545980
$530$	1.39489e34	+	1.87787e34i	1.23337	+	1.66042i
$531$	7.03047e33			0.607160
$532$		−	2.70291e33i		−	0.228001i
$533$			4.79044e33i			0.394716i
$534$	4.10249e32			0.0330204
$535$	8.67992e33	−	6.44750e33i	0.682486	−	0.506955i
$536$	−1.37744e33			−0.105807
$537$			1.57274e33i			0.118026i
$538$			7.21685e33i			0.529138i
$539$	4.03083e33			0.288758
$540$	3.32305e32	−	2.46838e32i	0.0232602	−	0.0172779i
$541$	−1.94229e34			−1.32846			−0.664230	−	0.747528i	$-0.731241\pi$
$541$	−1.94229e34			−1.32846			−0.664230	+	0.747528i	$0.731241\pi$
$542$		−	5.97580e33i		−	0.399397i
$543$			1.35793e33i			0.0886910i
$544$	−5.33132e33			−0.340289
$545$	−9.05177e33	−	1.21859e34i	−0.564647	−	0.760154i
$546$	−1.50150e33			−0.0915414
$547$			1.91244e34i			1.13958i	0.821790	+	0.569791i	$0.192976\pi$
$547$			1.91244e34i			1.13958i	−0.821790	+	0.569791i	$0.807024\pi$
$548$		−	1.21825e33i		−	0.0709546i
$549$	−6.94123e33			−0.395168
$550$	−3.28128e34	−	9.90029e33i	−1.82604	−	0.550952i
$551$	2.72610e34			1.48302
$552$		−	8.66290e32i		−	0.0460707i
$553$			3.81444e33i			0.198320i
$554$	−4.62140e33			−0.234910
$555$	3.88681e32	+	5.23260e32i	0.0193166	+	0.0260049i
$556$	1.48368e32			0.00720952
$557$			4.52903e33i			0.215187i	0.994195	+	0.107593i	$0.0343144\pi$
$557$			4.52903e33i			0.215187i	−0.994195	+	0.107593i	$0.965686\pi$
$558$			2.43862e34i			1.13296i
$559$	−1.55423e34			−0.706102
$560$	−1.90325e34	+	1.41374e34i	−0.845561	+	0.628088i
$561$	2.85060e33			0.123851
$562$		−	4.97809e33i		−	0.211523i
$563$			3.42883e34i			1.42492i	0.701712	+	0.712461i	$0.252419\pi$
$563$			3.42883e34i			1.42492i	−0.701712	+	0.712461i	$0.747581\pi$
$564$	4.03014e32			0.0163807
$565$	3.59201e34	−	2.66817e34i	1.42801	−	1.06074i
$566$	3.84531e33			0.149529
$567$		−	2.35937e34i		−	0.897444i
$568$			1.49925e33i			0.0557852i
$569$	−1.19665e34			−0.435577			−0.217788	−	0.975996i	$-0.569884\pi$
$569$	−1.19665e34			−0.435577			−0.217788	+	0.975996i	$0.569884\pi$
$570$	1.87080e33	+	2.51856e33i	0.0666181	+	0.0896844i
$571$	5.39502e34			1.87950			0.939749	−	0.341864i	$-0.111058\pi$
$571$	5.39502e34			1.87950			0.939749	+	0.341864i	$0.111058\pi$
$572$		−	1.14869e34i		−	0.391520i
$573$		−	3.69216e33i		−	0.123125i
$574$	1.01284e34			0.330478
$575$	−2.02053e34	−	6.09636e33i	−0.645087	−	0.194636i
$576$	−2.37947e34			−0.743361
$577$			3.46528e34i			1.05935i	0.848200	+	0.529677i	$0.177687\pi$
$577$			3.46528e34i			1.05935i	−0.848200	+	0.529677i	$0.822313\pi$
$578$			5.85732e33i			0.175227i
$579$	−3.16372e32			−0.00926225
$580$	4.37570e33	+	5.89077e33i	0.125371	+	0.168780i
$581$	3.30347e34			0.926338
$582$			4.63785e32i			0.0127286i
$583$		−	1.23615e35i		−	3.32057i
$584$	3.25292e34			0.855289
$585$	−3.68842e34	+	2.73978e34i	−0.949274	+	0.705126i
$586$	4.35599e34			1.09740
$587$		−	5.34642e34i		−	1.31852i	−0.751915	−	0.659260i	$-0.770870\pi$
$587$		−	5.34642e34i		−	1.31852i	0.751915	−	0.659260i	$-0.229130\pi$
$588$		−	9.93207e31i		−	0.00239786i
$589$	−5.86934e34			−1.38723
$590$	−2.30974e34	+	1.71569e34i	−0.534458	+	0.396999i
$591$	3.82329e33			0.0866151
$592$			2.17900e34i			0.483320i
$593$			3.72971e34i			0.810012i	0.914314	+	0.405006i	$0.132731\pi$
$593$			3.72971e34i			0.810012i	−0.914314	+	0.405006i	$0.867269\pi$
$594$	−1.38179e34			−0.293841
$595$	−2.39722e34	−	3.22724e34i	−0.499166	−	0.672000i
$596$	5.10376e33			0.104067
$597$			3.76596e33i			0.0751964i
$598$		−	4.46816e34i		−	0.873704i
$599$	5.17432e34			0.990874			0.495437	−	0.868644i	$-0.335008\pi$
$599$	5.17432e34			0.990874			0.495437	+	0.868644i	$0.335008\pi$
$600$	1.05308e33	−	3.49027e33i	0.0197503	−	0.0654588i
$601$	−5.13702e34			−0.943584			−0.471792	−	0.881710i	$-0.656393\pi$
$601$	−5.13702e34			−0.943584			−0.471792	+	0.881710i	$0.656393\pi$
$602$			3.28610e34i			0.591187i
$603$			6.74441e33i			0.118844i
$604$	1.22447e34			0.211341
$605$	7.27285e34	+	9.79105e34i	1.22960	+	1.65534i
$606$	−4.26603e33			−0.0706506
$607$			8.79446e34i			1.42676i	0.700778	+	0.713379i	$0.252836\pi$
$607$			8.79446e34i			1.42676i	−0.700778	+	0.713379i	$0.747164\pi$
$608$			3.10066e34i			0.492788i
$609$	−5.06871e33			−0.0789190
$610$	2.28042e34	−	1.69391e34i	0.347851	−	0.258386i
$611$	−8.97338e34			−1.34104
$612$			1.16971e34i			0.171272i
$613$			1.70622e33i			0.0244782i	0.999925	+	0.0122391i	$0.00389593\pi$
$613$			1.70622e33i			0.0244782i	−0.999925	+	0.0122391i	$0.996104\pi$
$614$	−1.11778e35			−1.57127
$615$	−1.49403e33	+	1.10977e33i	−0.0205788	+	0.0152861i
$616$	1.04843e35			1.41508
$617$		−	1.12122e34i		−	0.148295i	−0.997247	−	0.0741475i	$-0.976376\pi$
$617$		−	1.12122e34i		−	0.148295i	0.997247	−	0.0741475i	$-0.0236236\pi$
$618$			3.28245e33i			0.0425443i
$619$	7.85440e34			0.997654			0.498827	−	0.866701i	$-0.333764\pi$
$619$	7.85440e34			0.997654			0.498827	+	0.866701i	$0.333764\pi$
$620$	−9.42097e33	−	1.26829e34i	−0.117273	−	0.157879i
$621$	−8.50875e33			−0.103806
$622$		−	1.17906e35i		−	1.40980i
$623$			3.05736e34i			0.358300i
$624$	9.22320e33			0.105943
$625$	−7.39961e34	−	4.91242e34i	−0.833122	−	0.553090i
$626$	−1.24538e35			−1.37443
$627$		−	1.65789e34i		−	0.179355i
$628$		−	4.54641e33i		−	0.0482140i
$629$	−3.69481e34			−0.384113
$630$	5.79271e34	+	7.79841e34i	0.590371	+	0.794784i
$631$	−6.73578e34			−0.673009			−0.336504	−	0.941682i	$-0.609245\pi$
$631$	−6.73578e34			−0.673009			−0.336504	+	0.941682i	$0.609245\pi$
$632$		−	1.96077e34i		−	0.192072i
$633$			2.63569e33i			0.0253133i
$634$	1.43062e35			1.34713
$635$	8.79367e34	−	6.53199e34i	0.811893	−	0.603079i
$636$	−3.04590e33			−0.0275741
$637$			2.21144e34i			0.196305i
$638$		−	2.44951e35i		−	2.13216i
$639$	7.34081e33			0.0626590
$640$	1.13798e35	−	8.45295e34i	0.952540	−	0.707552i
$641$	7.31472e34			0.600444			0.300222	−	0.953869i	$-0.402939\pi$
$641$	7.31472e34			0.600444			0.300222	+	0.953869i	$0.402939\pi$
$642$			8.89341e33i			0.0715946i
$643$			2.10086e35i			1.65867i	0.558749	+	0.829337i	$0.311281\pi$
$643$			2.10086e35i			1.65867i	−0.558749	+	0.829337i	$0.688719\pi$
$644$	−1.49552e34			−0.115803
$645$	−3.60060e33	−	4.84729e33i	−0.0273450	−	0.0368131i
$646$	−1.77839e35			−1.32471
$647$		−	1.38944e34i		−	0.101516i	−0.998711	−	0.0507582i	$-0.983836\pi$
$647$		−	1.38944e34i		−	0.101516i	0.998711	−	0.0507582i	$-0.0161638\pi$
$648$			1.21281e35i			0.869169i
$649$	1.52044e35			1.06883
$650$	5.43161e34	−	1.80022e35i	0.374552	−	1.24139i
$651$	1.09130e34			0.0738216
$652$			4.58408e34i			0.304199i
$653$			6.94252e34i			0.451962i	0.974132	+	0.225981i	$0.0725588\pi$
$653$			6.94252e34i			0.451962i	−0.974132	+	0.225981i	$0.927441\pi$
$654$	1.24856e34			0.0797423
$655$	6.12992e34	+	8.25238e34i	0.384095	+	0.517086i
$656$	−6.22154e34			−0.382472
$657$		−	1.59274e35i		−	0.960676i
$658$			1.89724e35i			1.12279i
$659$	−5.89779e34			−0.342469			−0.171235	−	0.985230i	$-0.554776\pi$
$659$	−5.89779e34			−0.342469			−0.171235	+	0.985230i	$0.554776\pi$
$660$	3.58251e33	−	2.66111e33i	0.0204121	−	0.0151623i
$661$	−1.44684e35			−0.808913			−0.404457	−	0.914557i	$-0.632539\pi$
$661$	−1.44684e35			−0.808913			−0.404457	+	0.914557i	$0.632539\pi$
$662$			1.57509e35i			0.864132i
$663$			1.56393e34i			0.0841974i
$664$	−1.69812e35			−0.897153
$665$	−1.87695e35	+	1.39421e35i	−0.973153	+	0.722864i
$666$	8.92826e34			0.454296
$667$		−	1.50835e35i		−	0.753232i
$668$			5.05923e32i			0.00247958i
$669$	1.42451e34			0.0685234
$670$	−1.64588e34	−	2.21576e34i	−0.0777076	−	0.104614i
$671$	−1.50114e35			−0.695646
$672$		−	5.76516e33i		−	0.0262238i
$673$		−	2.30536e35i		−	1.02932i	−0.857394	−	0.514661i	$-0.827918\pi$
$673$		−	2.30536e35i		−	1.02932i	0.857394	−	0.514661i	$-0.172082\pi$
$674$	−6.77204e34			−0.296805
$675$	−3.42816e34	−	1.03435e34i	−0.147491	−	0.0445009i
$676$	1.84885e34			0.0780850
$677$		−	7.48456e34i		−	0.310319i	−0.987889	−	0.155159i	$-0.950411\pi$
$677$		−	7.48456e34i		−	0.310319i	0.987889	−	0.155159i	$-0.0495891\pi$
$678$			3.68036e34i			0.149803i
$679$	−3.45634e34			−0.138116
$680$	1.23226e35	+	1.65893e35i	0.483439	+	0.650829i
$681$	−1.93847e34			−0.0746656
$682$			5.27384e35i			1.99445i
$683$		−	7.67141e34i		−	0.284850i	−0.989806	−	0.142425i	$-0.954510\pi$
$683$		−	7.67141e34i		−	0.284850i	0.989806	−	0.142425i	$-0.0454900\pi$
$684$	6.80298e34			0.248026
$685$	−8.45975e34	+	6.28395e34i	−0.302848	+	0.224958i
$686$	3.30100e35			1.16036
$687$			1.67737e34i			0.0578988i
$688$		−	2.01854e35i		−	0.684198i
$689$	6.78190e35			2.25741
$690$	1.39352e34	−	1.03512e34i	0.0455512	−	0.0338357i
$691$	1.00480e35			0.322555			0.161278	−	0.986909i	$-0.448439\pi$
$691$	1.00480e35			0.322555			0.161278	+	0.986909i	$0.448439\pi$
$692$		−	5.04401e34i		−	0.159019i
$693$		−	5.13346e35i		−	1.58944i
$694$	−5.35746e35			−1.62917
$695$	−7.65308e33	−	1.03029e34i	−0.0228574	−	0.0307716i
$696$	2.60552e34			0.0764326
$697$		−	1.05495e35i		−	0.303965i
$698$		−	1.82874e35i		−	0.517559i
$699$	−2.03044e34			−0.0564450
$700$	−6.02543e34	−	1.81799e34i	−0.164537	−	0.0496440i
$701$	5.43593e35			1.45814			0.729070	−	0.684440i	$-0.239953\pi$
$701$	5.43593e35			1.45814			0.729070	+	0.684440i	$0.239953\pi$
$702$		−	7.58096e34i		−	0.199761i
$703$			2.14888e35i			0.556252i
$704$	−5.14593e35			−1.30860
$705$	−2.07881e34	−	2.79859e34i	−0.0519339	−	0.0699159i
$706$	5.58440e35			1.37062
$707$		−	3.17924e35i		−	0.766620i
$708$		−	3.74639e33i		−	0.00887560i
$709$	−2.08778e35			−0.485967			−0.242984	−	0.970030i	$-0.578126\pi$
$709$	−2.08778e35			−0.485967			−0.242984	+	0.970030i	$0.578126\pi$
$710$	−2.41170e34	+	1.79142e34i	−0.0551561	+	0.0409703i
$711$	−9.60058e34			−0.215738
$712$		−	1.57160e35i		−	0.347011i
$713$			3.24750e35i			0.704581i
$714$	3.30662e34			0.0704947
$715$	−7.97670e35	+	5.92514e35i	−1.67108	+	1.24129i
$716$	−1.39567e35			−0.287322
$717$		−	2.21238e34i		−	0.0447580i
$718$		−	1.72190e35i		−	0.342335i
$719$	4.27958e35			0.836162			0.418081	−	0.908410i	$-0.362703\pi$
$719$	4.27958e35			0.836162			0.418081	+	0.908410i	$0.362703\pi$
$720$	−3.55826e35	−	4.79030e35i	−0.683253	−	0.919827i
$721$	−2.44623e35			−0.461643
$722$			4.46627e35i			0.828380i
$723$		−	7.47171e33i		−	0.0136204i
$724$	−1.20505e35			−0.215909
$725$	1.83359e35	−	6.07711e35i	0.322906	−	1.07022i
$726$	−1.00319e35			−0.173650
$727$			8.01009e35i			1.36288i	0.731875	+	0.681439i	$0.238646\pi$
$727$			8.01009e35i			1.36288i	−0.731875	+	0.681439i	$0.761354\pi$
$728$			5.75203e35i			0.962008i
$729$	5.86590e35			0.964364
$730$	3.88686e35	+	5.23267e35i	0.628149	+	0.845644i
$731$	3.42274e35			0.543759
$732$			3.69884e33i			0.00577666i
$733$			4.73921e35i			0.727622i	0.931473	+	0.363811i	$0.118525\pi$
$733$			4.73921e35i			0.727622i	−0.931473	+	0.363811i	$0.881475\pi$
$734$	−7.63026e35			−1.15170
$735$	−6.89699e33	+	5.12312e33i	−0.0102345	+	0.00760227i
$736$	1.71560e35			0.250289
$737$			1.45857e35i			0.209211i
$738$			2.54923e35i			0.359504i
$739$	−4.23795e35			−0.587626			−0.293813	−	0.955863i	$-0.594924\pi$
$739$	−4.23795e35			−0.587626			−0.293813	+	0.955863i	$0.594924\pi$
$740$	−4.64348e34	+	3.44921e34i	−0.0633063	+	0.0470243i
$741$	9.09574e34			0.121930
$742$		−	1.43390e36i		−	1.89003i
$743$		−	2.79773e35i		−	0.362614i	−0.983427	−	0.181307i	$-0.941967\pi$
$743$		−	2.79773e35i		−	0.362614i	0.983427	−	0.181307i	$-0.0580328\pi$
$744$	−5.60974e34			−0.0714959
$745$	−2.63260e35	−	3.54413e35i	−0.329938	−	0.444177i
$746$	1.08787e36			1.34073
$747$			8.31453e35i			1.00770i
$748$			2.52966e35i			0.301504i
$749$	−6.62777e35			−0.776864
$750$	6.87278e34	−	2.47646e34i	0.0792258	−	0.0285474i
$751$	−4.10259e35			−0.465114			−0.232557	−	0.972583i	$-0.574709\pi$
$751$	−4.10259e35			−0.465114			−0.232557	+	0.972583i	$0.574709\pi$
$752$		−	1.16541e36i		−	1.29944i
$753$			7.46940e34i			0.0819122i
$754$	1.34388e36			1.44950
$755$	−6.31599e35	−	8.50288e35i	−0.670046	−	0.902047i
$756$	−2.53739e34			−0.0264768
$757$		−	1.01875e36i		−	1.04561i	−0.852451	−	0.522807i	$-0.824885\pi$
$757$		−	1.01875e36i		−	1.04561i	0.852451	−	0.522807i	$-0.175115\pi$
$758$		−	4.83569e35i		−	0.488195i
$759$	−9.17313e34			−0.0910952
$760$	9.64825e35	−	7.16678e35i	0.942494	−	0.700090i
$761$	−1.41828e36			−1.36287			−0.681434	−	0.731879i	$-0.738644\pi$
$761$	−1.41828e36			−1.36287			−0.681434	+	0.731879i	$0.738644\pi$
$762$			9.00996e34i			0.0851698i
$763$			9.30486e35i			0.865273i
$764$	3.27647e35			0.299736
$765$	8.12266e35	−	6.03356e35i	0.731022	−	0.543008i
$766$	−1.47882e36			−1.30935
$767$			8.34159e35i			0.726619i
$768$			4.91799e34i			0.0421475i
$769$	2.13487e36			1.80008			0.900040	−	0.435808i	$-0.143537\pi$
$769$	2.13487e36			1.80008			0.900040	+	0.435808i	$0.143537\pi$
$770$	1.25275e36	+	1.68651e36i	1.03928	+	1.39912i
$771$	1.87117e35			0.152733
$772$		−	2.80753e34i		−	0.0225480i
$773$		−	5.07472e35i		−	0.401022i	−0.979691	−	0.200511i	$-0.935740\pi$
$773$		−	5.07472e35i		−	0.401022i	0.979691	−	0.200511i	$-0.0642603\pi$
$774$	−8.27081e35			−0.643111
$775$	−3.94775e35	+	1.30841e36i	−0.302050	+	1.00109i
$776$	1.77669e35			0.133765
$777$		−	3.99549e34i		−	0.0296010i
$778$		−	1.12992e36i		−	0.823763i
$779$	−6.13556e35			−0.440186
$780$	1.45997e34	+	1.96548e34i	0.0103077	+	0.0138767i
$781$	1.58755e35			0.110304
$782$			9.83983e35i			0.672827i
$783$		−	2.55916e35i		−	0.172217i
$784$	−2.87209e35			−0.190216
$785$	−3.15710e35	+	2.34511e35i	−0.205787	+	0.152860i
$786$	−8.45535e34			−0.0542438
$787$			4.72481e35i			0.298332i	0.988812	+	0.149166i	$0.0476589\pi$
$787$			4.72481e35i			0.298332i	−0.988812	+	0.149166i	$0.952341\pi$
$788$			3.39284e35i			0.210856i
$789$	6.77362e34			0.0414341
$790$	3.15411e35	−	2.34289e35i	0.189906	−	0.141063i
$791$	−2.74277e36			−1.62549
$792$			2.63880e36i			1.53937i
$793$		−	8.23571e35i		−	0.472919i
$794$	−1.77415e36			−1.00284
$795$	1.57112e35	+	2.11512e35i	0.0874222	+	0.117692i
$796$	−3.34197e35			−0.183058
$797$			1.69149e36i			0.912096i	0.889955	+	0.456048i	$0.150735\pi$
$797$			1.69149e36i			0.912096i	−0.889955	+	0.456048i	$0.849265\pi$
$798$		−	1.92311e35i		−	0.102086i
$799$	1.97613e36			1.03271
$800$	6.91211e35	+	2.08552e35i	0.355620	+	0.107298i
$801$	−7.69509e35			−0.389769
$802$		−	3.92959e36i		−	1.95960i
$803$		−	3.44451e36i		−	1.69115i
$804$	3.59396e33			0.00173729
$805$	7.71415e35	+	1.03851e36i	0.367146	+	0.494270i
$806$	−2.89340e36			−1.35588
$807$			8.12863e34i			0.0375058i
$808$			1.63425e36i			0.742467i
$809$	1.61569e34			0.00722771			0.00361386	−	0.999993i	$-0.498850\pi$
$809$	1.61569e34			0.00722771			0.00361386	+	0.999993i	$0.498850\pi$
$810$	−1.95093e36	+	1.44916e36i	−0.859367	+	0.638343i
$811$	8.38978e35			0.363907			0.181953	−	0.983307i	$-0.441758\pi$
$811$	8.38978e35			0.363907			0.181953	+	0.983307i	$0.441758\pi$
$812$		−	4.49804e35i		−	0.192120i
$813$		−	6.73078e34i		−	0.0283096i
$814$	1.93086e36			0.799734
$815$	3.18326e36	−	2.36454e36i	1.29838	−	0.964445i
$816$	−2.03114e35			−0.0815856
$817$		−	1.99065e36i		−	0.787441i
$818$			1.77256e36i			0.690532i
$819$	2.81638e36			1.08054
$820$	−9.84828e34	−	1.32582e35i	−0.0372124	−	0.0500970i
$821$	4.82346e36			1.79502			0.897510	−	0.440993i	$-0.145374\pi$
$821$	4.82346e36			1.79502			0.897510	+	0.440993i	$0.145374\pi$
$822$		−	8.66782e34i		−	0.0317696i
$823$			2.05555e36i			0.742046i	0.928624	+	0.371023i	$0.120993\pi$
$823$			2.05555e36i			0.742046i	−0.928624	+	0.371023i	$0.879007\pi$
$824$	1.25746e36			0.447099
$825$	−3.69584e35	−	1.11511e35i	−0.129431	−	0.0390520i
$826$	1.76366e36			0.608366
$827$			1.61138e36i			0.547494i	0.961802	+	0.273747i	$0.0882631\pi$
$827$			1.61138e36i			0.547494i	−0.961802	+	0.273747i	$0.911737\pi$
$828$		−	3.76409e35i		−	0.125974i
$829$	−5.88426e36			−1.93982			−0.969908	−	0.243472i	$-0.921714\pi$
$829$	−5.88426e36			−1.93982			−0.969908	+	0.243472i	$0.921714\pi$
$830$	−2.02905e36	−	2.73160e36i	−0.658895	−	0.887035i
$831$	−5.20527e34			−0.0166506
$832$		−	2.82322e36i		−	0.889618i
$833$		−	4.87006e35i		−	0.151172i
$834$	1.05563e34			0.00322803
$835$	3.51321e34	−	2.60963e34i	0.0105833	−	0.00786137i
$836$	1.47124e36			0.436621
$837$			5.50992e35i			0.161093i
$838$		−	5.19176e36i		−	1.49542i
$839$	−2.56435e36			−0.727702			−0.363851	−	0.931457i	$-0.618538\pi$
$839$	−2.56435e36			−0.727702			−0.363851	+	0.931457i	$0.618538\pi$
$840$	−1.79393e35	+	1.33254e35i	−0.0501550	+	0.0372554i
$841$	9.06258e35			0.249633
$842$			7.72258e36i			2.09586i
$843$		−	5.60702e34i		−	0.0149930i
$844$	−2.33895e35			−0.0616226
$845$	−9.53666e35	−	1.28387e36i	−0.247564	−	0.333282i
$846$	−4.77517e36			−1.22140
$847$		−	7.47620e36i		−	1.88425i
$848$			8.80792e36i			2.18739i
$849$	4.33113e34			0.0105988
$850$	−1.19616e36	+	3.96445e36i	−0.288437	+	0.955975i
$851$	1.18898e36			0.282523
$852$		−	3.91177e33i		−	0.000915963i
$853$			5.96355e36i			1.37607i	0.725675	+	0.688037i	$0.241528\pi$
$853$			5.96355e36i			1.37607i	−0.725675	+	0.688037i	$0.758472\pi$
$854$	−1.74128e36			−0.395953
$855$	−3.50909e36	−	4.72410e36i	−0.786353	−	1.05863i
$856$	3.40694e36			0.752388
$857$			4.07011e35i			0.0885820i	0.999019	+	0.0442910i	$0.0141029\pi$
$857$			4.07011e35i			0.0885820i	−0.999019	+	0.0442910i	$0.985897\pi$
$858$		−	8.17289e35i		−	0.175301i
$859$	−4.17556e35			−0.0882673			−0.0441336	−	0.999026i	$-0.514053\pi$
$859$	−4.17556e35			−0.0882673			−0.0441336	+	0.999026i	$0.514053\pi$
$860$	4.30155e35	−	3.19522e35i	0.0896178	−	0.0665686i
$861$	1.14080e35			0.0234246
$862$			2.16223e34i			0.00437583i
$863$			2.97664e36i			0.593734i	0.954919	+	0.296867i	$0.0959418\pi$
$863$			2.97664e36i			0.593734i	−0.954919	+	0.296867i	$0.904058\pi$
$864$	2.91079e35			0.0572254
$865$	−3.50264e36	+	2.60178e36i	−0.678726	+	0.504162i
$866$	9.92286e36			1.89524
$867$			6.59734e34i			0.0124202i
$868$			9.68438e35i			0.179711i
$869$	−2.07626e36			−0.379781
$870$	3.11329e35	+	4.19125e35i	0.0561344	+	0.0755707i
$871$	−8.00219e35			−0.142227
$872$		−	4.78306e36i		−	0.838012i
$873$		−	8.69927e35i		−	0.150247i
$874$	5.72279e36			0.974350
$875$	1.84557e36	+	5.12191e36i	0.309763	+	0.859668i
$876$	−8.48737e34			−0.0140434
$877$			1.00528e37i			1.63980i	0.572508	+	0.819899i	$0.305970\pi$
$877$			1.00528e37i			1.63980i	−0.572508	+	0.819899i	$0.694030\pi$
$878$		−	8.10980e36i		−	1.30415i
$879$	4.90632e35			0.0777849
$880$	−7.69522e36	−	1.03597e37i	−1.20278	−	1.61924i
$881$	2.24336e36			0.345700			0.172850	−	0.984948i	$-0.444702\pi$
$881$	2.24336e36			0.345700			0.172850	+	0.984948i	$0.444702\pi$
$882$			1.17682e36i			0.178793i
$883$		−	3.14992e36i		−	0.471835i	−0.971773	−	0.235918i	$-0.924190\pi$
$883$		−	3.14992e36i		−	0.471835i	0.971773	−	0.235918i	$-0.0758095\pi$
$884$	−1.38785e36			−0.204970
$885$	−2.60156e35	+	1.93245e35i	−0.0378828	+	0.0281396i
$886$	1.76013e36			0.252711
$887$		−	9.57382e36i		−	1.35531i	−0.735378	−	0.677657i	$-0.762996\pi$
$887$		−	9.57382e36i		−	1.35531i	0.735378	−	0.677657i	$-0.237004\pi$
$888$			2.05384e35i			0.0286684i
$889$	−6.71463e36			−0.924166
$890$	2.52809e36	−	1.87788e36i	0.343098	−	0.254855i
$891$	1.28424e37			1.71860
$892$			1.26413e36i			0.166813i
$893$		−	1.14930e37i		−	1.49552i
$894$	3.63130e35			0.0465954
$895$	7.19908e36	+	9.69174e36i	0.910939	+	1.22635i
$896$	−8.68929e36			−1.08426
$897$		−	5.03267e35i		−	0.0619289i
$898$		−	1.12058e37i		−	1.35984i
$899$	−9.76744e36			−1.16892
$900$	4.57572e35	−	1.51654e36i	0.0540043	−	0.178988i
$901$	−1.49352e37			−1.73840
$902$			5.51305e36i			0.632864i
$903$			3.70127e35i			0.0419038i
$904$	1.40989e37			1.57428
$905$	6.21582e36	+	8.36803e36i	0.684528	+	0.921543i
$906$	8.71201e35			0.0946272
$907$			3.90194e36i			0.418013i	0.977914	+	0.209007i	$0.0670230\pi$
$907$			3.90194e36i			0.418013i	−0.977914	+	0.209007i	$0.932977\pi$
$908$		−	1.72023e36i		−	0.181766i
$909$	8.00184e36			0.833953
$910$	−9.25275e36	+	6.87300e36i	−0.951160	+	0.706527i
$911$	3.83962e36			0.389322			0.194661	−	0.980871i	$-0.437639\pi$
$911$	3.83962e36			0.389322			0.194661	+	0.980871i	$0.437639\pi$
$912$			1.18130e36i			0.118148i
$913$			1.79813e37i			1.77393i
$914$	3.58043e36			0.348423
$915$	2.56853e35	−	1.90792e35i	0.0246559	−	0.0183146i
$916$	−1.48852e36			−0.140949
$917$		−	6.30131e36i		−	0.588592i
$918$			1.66949e36i			0.153833i
$919$	−5.06195e36			−0.460123			−0.230062	−	0.973176i	$-0.573893\pi$
$919$	−5.06195e36			−0.460123			−0.230062	+	0.973176i	$0.573893\pi$
$920$	−3.96538e36	−	5.33837e36i	−0.355579	−	0.478697i
$921$	−1.25900e36			−0.111373
$922$			1.29801e37i			1.13277i
$923$			8.70981e35i			0.0749872i
$924$	−2.73552e35			−0.0232349
$925$	4.79037e36	+	1.44535e36i	0.401418	+	0.121116i
$926$	−7.26367e36			−0.600508
$927$		−	6.15693e36i		−	0.502189i
$928$			5.15996e36i			0.415237i
$929$	−1.60110e37			−1.27122			−0.635612	−	0.772008i	$-0.719252\pi$
$929$	−1.60110e37			−1.27122			−0.635612	+	0.772008i	$0.719252\pi$
$930$	−6.70298e35	−	9.02386e35i	−0.0525086	−	0.0706896i
$931$	−2.83240e36			−0.218919
$932$		−	1.80184e36i		−	0.137410i
$933$		−	1.32802e36i		−	0.0999276i
$934$	8.24548e36			0.612181
$935$	1.75664e37	−	1.30484e37i	1.28688	−	0.955900i
$936$	−1.44773e37			−1.04650
$937$			5.78467e36i			0.412604i	0.978488	+	0.206302i	$0.0661430\pi$
$937$			5.78467e36i			0.412604i	−0.978488	+	0.206302i	$0.933857\pi$
$938$			1.69190e36i			0.119080i
$939$	−1.40272e36			−0.0974209
$940$	2.48351e36	−	1.84477e36i	0.170203	−	0.126428i
$941$	−8.61297e36			−0.582483			−0.291241	−	0.956650i	$-0.594068\pi$
$941$	−8.61297e36			−0.582483			−0.291241	+	0.956650i	$0.594068\pi$
$942$		−	3.23475e35i		−	0.0215876i
$943$			3.39480e36i			0.223573i
$944$	−1.08336e37			−0.704079
$945$	1.30883e36	+	1.76201e36i	0.0839432	+	0.113008i
$946$	−1.78868e37			−1.13212
$947$		−	1.81921e37i		−	1.13634i	−0.822911	−	0.568171i	$-0.807651\pi$
$947$		−	1.81921e37i		−	1.13634i	0.822911	−	0.568171i	$-0.192349\pi$
$948$			5.11595e34i			0.00315371i
$949$	1.88977e37			1.14969
$950$	2.30570e37	+	6.95677e36i	1.38439	+	0.417698i
$951$	1.61137e36			0.0954856
$952$		−	1.26672e37i		−	0.740829i
$953$			4.55923e35i			0.0263166i	0.999913	+	0.0131583i	$0.00418854\pi$
$953$			4.55923e35i			0.0263166i	−0.999913	+	0.0131583i	$0.995811\pi$
$954$	3.60898e37			2.05603
$955$	−1.69005e37	−	2.27523e37i	−0.950296	−	1.27933i
$956$	1.96330e36			0.108959
$957$		−	2.75898e36i		−	0.151129i
$958$		−	2.97904e36i		−	0.161067i
$959$	6.45965e36			0.344728
$960$	8.80500e35	−	6.54041e35i	0.0463809	−	0.0344520i
$961$	1.79670e36			0.0934187
$962$			1.05933e37i			0.543680i
$963$		−	1.66815e37i		−	0.845096i
$964$	6.63049e35			0.0331576
$965$	−1.94959e36	+	1.44817e36i	−0.0962393	+	0.0714872i
$966$	−1.06406e36			−0.0518502
$967$			1.18549e37i			0.570251i	0.958490	+	0.285125i	$0.0920352\pi$
$967$			1.18549e37i			0.570251i	−0.958490	+	0.285125i	$0.907965\pi$
$968$			3.84306e37i			1.82488i
$969$	−2.00307e36			−0.0938965
$970$	2.12294e36	+	2.85800e36i	0.0982406	+	0.132256i
$971$	3.31536e37			1.51458			0.757288	−	0.653081i	$-0.226524\pi$
$971$	3.31536e37			1.51458			0.757288	+	0.653081i	$0.226524\pi$
$972$		−	9.58913e35i		−	0.0432465i
$973$			7.86706e35i			0.0350269i
$974$	−2.47379e37			−1.08737
$975$	6.11784e35	−	2.02765e36i	0.0265485	−	0.0879906i
$976$	1.06961e37			0.458248
$977$		−	1.59575e37i		−	0.674966i	−0.941332	−	0.337483i	$-0.890424\pi$
$977$		−	1.59575e37i		−	0.674966i	0.941332	−	0.337483i	$-0.109576\pi$
$978$			3.26155e36i			0.136204i
$979$	−1.66417e37			−0.686142
$980$	−4.54633e35	−	6.12048e35i	−0.0185069	−	0.0249149i
$981$	−2.34195e37			−0.941270
$982$		−	9.42247e36i		−	0.373913i
$983$			5.23038e36i			0.204934i	0.994736	+	0.102467i	$0.0326736\pi$
$983$			5.23038e36i			0.204934i	−0.994736	+	0.102467i	$0.967326\pi$
$984$	−5.86418e35			−0.0226866
$985$	2.35604e37	−	1.75008e37i	0.899974	−	0.668506i
$986$	−2.95950e37			−1.11624
$987$			2.13694e36i			0.0795843i
$988$			8.07168e36i			0.296826i
$989$	−1.10142e37			−0.399946
$990$	−4.24479e37	+	3.15306e37i	−1.52201	+	1.13056i
$991$	−4.04463e37			−1.43205			−0.716025	−	0.698075i	$-0.754040\pi$
$991$	−4.04463e37			−1.43205			−0.716025	+	0.698075i	$0.754040\pi$
$992$		−	1.11095e37i		−	0.388417i
$993$			1.77409e36i			0.0612504i
$994$	1.84151e36			0.0627834
$995$	1.72384e37	+	2.32071e37i	0.580375	+	0.781327i
$996$	4.43065e35			0.0147308
$997$			4.79135e37i			1.57315i	0.617498	+	0.786573i	$0.288146\pi$
$997$			4.79135e37i			1.57315i	−0.617498	+	0.786573i	$0.711854\pi$
$998$		−	4.88655e37i		−	1.58442i
$999$	2.01729e36			0.0645952

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.26.b.a.4.10	yes	12
3.2	odd	2		45.26.b.b.19.3		12
5.2	odd	4		25.26.a.f.1.3		12
5.3	odd	4		25.26.a.f.1.10		12
5.4	even	2	inner	5.26.b.a.4.3	✓	12
15.14	odd	2		45.26.b.b.19.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.26.b.a.4.3	✓	12	5.4	even	2	inner
5.26.b.a.4.10	yes	12	1.1	even	1	trivial
25.26.a.f.1.3		12	5.2	odd	4
25.26.a.f.1.10		12	5.3	odd	4
45.26.b.b.19.3		12	3.2	odd	2
45.26.b.b.19.10		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)

\(f(q)\)	\(=\)	\(q+6313.90i q^{2} +71116.0i q^{3} -6.31093e6 q^{4} +(3.25528e8 + 4.38241e8i) q^{5} -4.49019e8 q^{6} -3.34630e10i q^{7} +1.72013e11i q^{8} +8.42231e11 q^{9} +O(q^{10})\)	\(q+6313.90i q^{2} +71116.0i q^{3} -6.31093e6 q^{4} +(3.25528e8 + 4.38241e8i) q^{5} -4.49019e8 q^{6} -3.34630e10i q^{7} +1.72013e11i q^{8} +8.42231e11 q^{9} +(-2.76701e12 + 2.05535e12i) q^{10} +1.82144e13 q^{11} -4.48808e11i q^{12} +9.99300e13i q^{13} +2.11282e14 q^{14} +(-3.11659e13 + 2.31502e13i) q^{15} -1.29783e15 q^{16} -2.20067e15i q^{17} +5.31776e15i q^{18} -1.27990e16 q^{19} +(-2.05438e15 - 2.76570e15i) q^{20} +2.37975e15 q^{21} +1.15004e17i q^{22} +7.08167e16i q^{23} -1.22329e16 q^{24} +(-8.60865e16 + 2.85319e17i) q^{25} -6.30948e17 q^{26} +1.20152e17i q^{27} +2.11182e17i q^{28} -2.12993e18 q^{29} +(-1.46168e17 - 1.96779e17i) q^{30} +4.58579e18 q^{31} -2.42259e18i q^{32} +1.29534e18i q^{33} +1.38948e19 q^{34} +(1.46648e19 - 1.08931e19i) q^{35} -5.31526e18 q^{36} -1.67895e19i q^{37} -8.08114e19i q^{38} -7.10662e18 q^{39} +(-7.53830e19 + 5.59950e19i) q^{40} +4.79379e19 q^{41} +1.50255e19i q^{42} +1.55532e20i q^{43} -1.14950e20 q^{44} +(2.74170e20 + 3.69100e20i) q^{45} -4.47129e20 q^{46} +8.97966e20i q^{47} -9.22966e19i q^{48} +2.21299e20 q^{49} +(-1.80148e21 - 5.43542e20i) q^{50} +1.56503e20 q^{51} -6.30651e20i q^{52} -6.78665e21i q^{53} -7.58627e20 q^{54} +(5.92929e21 + 7.98229e21i) q^{55} +5.75606e21 q^{56} -9.10211e20i q^{57} -1.34482e22i q^{58} +8.34744e21 q^{59} +(1.96686e20 - 1.46099e20i) q^{60} -8.24148e21 q^{61} +2.89542e22i q^{62} -2.81835e22i q^{63} -2.82520e22 q^{64} +(-4.37934e22 + 3.25300e22i) q^{65} -8.17862e21 q^{66} +8.00779e21i q^{67} +1.38883e22i q^{68} -5.03620e21 q^{69} +(6.87781e22 + 9.25923e22i) q^{70} +8.71591e21 q^{71} +1.44875e23i q^{72} -1.89109e23i q^{73} +1.06007e23 q^{74} +(-2.02907e22 - 6.12213e21i) q^{75} +8.07733e22 q^{76} -6.09508e23i q^{77} -4.48705e22i q^{78} -1.13990e23 q^{79} +(-4.22480e23 - 5.68763e23i) q^{80} +7.05068e23 q^{81} +3.02675e23i q^{82} +9.87203e23i q^{83} -1.50184e22 q^{84} +(9.64422e23 - 7.16379e23i) q^{85} -9.82012e23 q^{86} -1.51472e23i q^{87} +3.13311e24i q^{88} -9.13656e23 q^{89} +(-2.33046e24 + 1.73108e24i) q^{90} +3.34395e24 q^{91} -4.46919e23i q^{92} +3.26123e23i q^{93} -5.66967e24 q^{94} +(-4.16642e24 - 5.60903e24i) q^{95} +1.72285e23 q^{96} -1.03288e24i q^{97} +1.39726e24i q^{98} +1.53407e25 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 166691544 q^{4} + 549543060 q^{5} + 10591544184 q^{6} - 3948466041036 q^{9}+O(q^{10}) \) 12 * q - 166691544 * q^4 + 549543060 * q^5 + 10591544184 * q^6 - 3948466041036 * q^9	\( 12 q - 166691544 q^{4} + 549543060 q^{5} + 10591544184 q^{6} - 3948466041036 q^{9} + 4435846671960 q^{10} - 1090673824176 q^{11} - 890646861445848 q^{14} + 443085522435120 q^{15} + 22\!\cdots\!32 q^{16}+ \cdots - 10\!\cdots\!72 q^{99}+O(q^{100}) \) 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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