LMFDB - Embedded newform 5.26.b.a.4.7

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			4.7
Root			$1011.64i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.26.b.a.4.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2023.27i q^{2} -529751. i q^{3} +2.94608e7 q^{4} +(8.23814e7 - 5.39663e8i) q^{5} +1.07183e9 q^{6} -2.78390e10i q^{7} +1.27497e11i q^{8} +5.66653e11 q^{9} +(1.09188e12 + 1.66680e11i) q^{10} -1.72111e13 q^{11} -1.56069e13i q^{12} +4.19700e13i q^{13} +5.63258e13 q^{14} +(-2.85887e14 - 4.36416e13i) q^{15} +7.30580e14 q^{16} -2.71981e15i q^{17} +1.14649e15i q^{18} -2.11681e15 q^{19} +(2.42702e15 - 1.58989e16i) q^{20} -1.47477e16 q^{21} -3.48226e16i q^{22} -1.88198e17i q^{23} +6.75416e16 q^{24} +(-2.84450e17 - 8.89165e16i) q^{25} -8.49167e16 q^{26} -7.49036e17i q^{27} -8.20159e17i q^{28} +1.94107e18 q^{29} +(8.82988e16 - 5.78427e17i) q^{30} -3.33805e18 q^{31} +5.75625e18i q^{32} +9.11757e18i q^{33} +5.50290e18 q^{34} +(-1.50237e19 - 2.29341e18i) q^{35} +1.66940e19 q^{36} +6.23367e19i q^{37} -4.28289e18i q^{38} +2.22337e19 q^{39} +(6.88054e19 + 1.05034e19i) q^{40} -5.06141e19 q^{41} -2.98386e19i q^{42} -2.68901e20i q^{43} -5.07052e20 q^{44} +(4.66817e19 - 3.05802e20i) q^{45} +3.80776e20 q^{46} -1.57876e20i q^{47} -3.87025e20i q^{48} +5.66060e20 q^{49} +(1.79902e20 - 5.75519e20i) q^{50} -1.44082e21 q^{51} +1.23647e21i q^{52} +1.18565e19i q^{53} +1.51550e21 q^{54} +(-1.41787e21 + 9.28818e21i) q^{55} +3.54938e21 q^{56} +1.12138e21i q^{57} +3.92731e21i q^{58} +2.75209e21 q^{59} +(-8.42246e21 - 1.28572e21i) q^{60} -4.94352e21 q^{61} -6.75379e21i q^{62} -1.57750e22i q^{63} +1.28678e22 q^{64} +(2.26497e22 + 3.45755e21i) q^{65} -1.84473e22 q^{66} -4.65921e22i q^{67} -8.01277e22i q^{68} -9.96982e22 q^{69} +(4.64020e21 - 3.03970e22i) q^{70} +1.36659e23 q^{71} +7.22465e22i q^{72} +4.38570e22i q^{73} -1.26124e23 q^{74} +(-4.71036e22 + 1.50688e23i) q^{75} -6.23630e22 q^{76} +4.79138e23i q^{77} +4.49847e22i q^{78} +6.86566e23 q^{79} +(6.01862e22 - 3.94267e23i) q^{80} +8.33158e22 q^{81} -1.02406e23i q^{82} +1.11044e24i q^{83} -4.34480e23 q^{84} +(-1.46778e24 - 2.24062e23i) q^{85} +5.44059e23 q^{86} -1.02828e24i q^{87} -2.19436e24i q^{88} -8.75176e23 q^{89} +(6.18720e23 + 9.44496e22i) q^{90} +1.16840e24 q^{91} -5.54448e24i q^{92} +1.76834e24i q^{93} +3.19426e23 q^{94} +(-1.74386e23 + 1.14237e24i) q^{95} +3.04938e24 q^{96} +8.28877e24i q^{97} +1.14529e24i q^{98} -9.75269e24 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 $

$2$			2023.27i			0.349284i	0.984632	+	0.174642i	$0.0558768\pi$
$2$			2023.27i			0.349284i	−0.984632	+	0.174642i	$0.944123\pi$
$3$		−	529751.i		−	0.575514i	−0.957703	−	0.287757i	$-0.907090\pi$
$3$		−	529751.i		−	0.575514i	0.957703	−	0.287757i	$-0.0929095\pi$
$4$	2.94608e7			0.878001
$5$	8.23814e7	−	5.39663e8i	0.150905	−	0.988548i
$5$	8.23814e7	−	5.39663e8i	0.150905	−	0.988548i
$6$	1.07183e9			0.201018
$7$		−	2.78390e10i		−	0.760200i	−0.924945	−	0.380100i	$-0.875890\pi$
$7$		−	2.78390e10i		−	0.760200i	0.924945	−	0.380100i	$-0.124110\pi$
$8$			1.27497e11i			0.655956i
$9$	5.66653e11			0.668784
$10$	1.09188e12	+	1.66680e11i	0.345284	+	0.0527088i
$11$	−1.72111e13			−1.65348			−0.826740	−	0.562584i	$-0.809807\pi$
$11$	−1.72111e13			−1.65348			−0.826740	+	0.562584i	$0.809807\pi$
$12$		−	1.56069e13i		−	0.505302i
$13$			4.19700e13i			0.499629i	0.968294	+	0.249814i	$0.0803696\pi$
$13$			4.19700e13i			0.499629i	−0.968294	+	0.249814i	$0.919630\pi$
$14$	5.63258e13			0.265526
$15$	−2.85887e14	−	4.36416e13i	−0.568923	−	0.0868481i
$16$	7.30580e14			0.648885
$17$		−	2.71981e15i		−	1.13221i	−0.824333	−	0.566104i	$-0.808450\pi$
$17$		−	2.71981e15i		−	1.13221i	0.824333	−	0.566104i	$-0.191550\pi$
$18$			1.14649e15i			0.233596i
$19$	−2.11681e15			−0.219413			−0.109707	−	0.993964i	$-0.534991\pi$
$19$	−2.11681e15			−0.219413			−0.109707	+	0.993964i	$0.534991\pi$
$20$	2.42702e15	−	1.58989e16i	0.132495	−	0.867946i
$21$	−1.47477e16			−0.437506
$22$		−	3.48226e16i		−	0.577534i
$23$		−	1.88198e17i		−	1.79068i	−0.445383	−	0.895340i	$-0.646933\pi$
$23$		−	1.88198e17i		−	1.79068i	0.445383	−	0.895340i	$-0.353067\pi$
$24$	6.75416e16			0.377512
$25$	−2.84450e17	−	8.89165e16i	−0.954455	−	0.298354i
$26$	−8.49167e16			−0.174512
$27$		−	7.49036e17i		−	0.960408i
$28$		−	8.20159e17i		−	0.667456i
$29$	1.94107e18			1.01875			0.509374	−	0.860545i	$-0.329877\pi$
$29$	1.94107e18			1.01875			0.509374	+	0.860545i	$0.329877\pi$
$30$	8.82988e16	−	5.78427e17i	0.0303347	−	0.198716i
$31$	−3.33805e18			−0.761154			−0.380577	−	0.924749i	$-0.624275\pi$
$31$	−3.33805e18			−0.761154			−0.380577	+	0.924749i	$0.624275\pi$
$32$			5.75625e18i			0.882601i
$33$			9.11757e18i			0.951601i
$34$	5.50290e18			0.395463
$35$	−1.50237e19	−	2.29341e18i	−0.751494	−	0.114718i
$36$	1.66940e19			0.587192
$37$			6.23367e19i			1.55676i	0.627791	+	0.778382i	$0.283959\pi$
$37$			6.23367e19i			1.55676i	−0.627791	+	0.778382i	$0.716041\pi$
$38$		−	4.28289e18i		−	0.0766375i
$39$	2.22337e19			0.287543
$40$	6.88054e19	+	1.05034e19i	0.648444	+	0.0989872i
$41$	−5.06141e19			−0.350327			−0.175163	−	0.984539i	$-0.556045\pi$
$41$	−5.06141e19			−0.350327			−0.175163	+	0.984539i	$0.556045\pi$
$42$		−	2.98386e19i		−	0.152814i
$43$		−	2.68901e20i		−	1.02621i	−0.858326	−	0.513105i	$-0.828495\pi$
$43$		−	2.68901e20i		−	1.02621i	0.858326	−	0.513105i	$-0.171505\pi$
$44$	−5.07052e20			−1.45176
$45$	4.66817e19	−	3.05802e20i	0.100923	−	0.661125i
$46$	3.80776e20			0.625456
$47$		−	1.57876e20i		−	0.198195i	−0.995078	−	0.0990975i	$-0.968404\pi$
$47$		−	1.57876e20i		−	0.198195i	0.995078	−	0.0990975i	$-0.0315956\pi$
$48$		−	3.87025e20i		−	0.373443i
$49$	5.66060e20			0.422096
$50$	1.79902e20	−	5.75519e20i	0.104210	−	0.333376i
$51$	−1.44082e21			−0.651602
$52$			1.23647e21i			0.438674i
$53$			1.18565e19i			0.00331519i	0.999999	+	0.00165759i	$0.000527628\pi$
$53$			1.18565e19i			0.00331519i	−0.999999	+	0.00165759i	$0.999472\pi$
$54$	1.51550e21			0.335455
$55$	−1.41787e21	+	9.28818e21i	−0.249519	+	1.63454i
$56$	3.54938e21			0.498658
$57$			1.12138e21i			0.126275i
$58$			3.92731e21i			0.355833i
$59$	2.75209e21			0.201378			0.100689	−	0.994918i	$-0.467895\pi$
$59$	2.75209e21			0.201378			0.100689	+	0.994918i	$0.467895\pi$
$60$	−8.42246e21	−	1.28572e21i	−0.499515	−	0.0762527i
$61$	−4.94352e21			−0.238459			−0.119229	−	0.992867i	$-0.538042\pi$
$61$	−4.94352e21			−0.238459			−0.119229	+	0.992867i	$0.538042\pi$
$62$		−	6.75379e21i		−	0.265859i
$63$		−	1.57750e22i		−	0.508409i
$64$	1.28678e22			0.340607
$65$	2.26497e22	+	3.45755e21i	0.493907	+	0.0753966i
$66$	−1.84473e22			−0.332379
$67$		−	4.65921e22i		−	0.695629i	−0.937563	−	0.347814i	$-0.886924\pi$
$67$		−	4.65921e22i		−	0.695629i	0.937563	−	0.347814i	$-0.113076\pi$
$68$		−	8.01277e22i		−	0.994080i
$69$	−9.96982e22			−1.03056
$70$	4.64020e21	−	3.03970e22i	0.0400692	−	0.262485i
$71$	1.36659e23			0.988344			0.494172	−	0.869364i	$-0.335471\pi$
$71$	1.36659e23			0.988344			0.494172	+	0.869364i	$0.335471\pi$
$72$			7.22465e22i			0.438693i
$73$			4.38570e22i			0.224132i	0.993701	+	0.112066i	$0.0357468\pi$
$73$			4.38570e22i			0.224132i	−0.993701	+	0.112066i	$0.964253\pi$
$74$	−1.26124e23			−0.543753
$75$	−4.71036e22	+	1.50688e23i	−0.171707	+	0.549302i
$76$	−6.23630e22			−0.192645
$77$			4.79138e23i			1.25698i
$78$			4.49847e22i			0.100434i
$79$	6.86566e23			1.30721			0.653603	−	0.756838i	$-0.273257\pi$
$79$	6.86566e23			1.30721			0.653603	+	0.756838i	$0.273257\pi$
$80$	6.01862e22	−	3.94267e23i	0.0979202	−	0.641455i
$81$	8.33158e22			0.116055
$82$		−	1.02406e23i		−	0.122364i
$83$			1.11044e24i			1.14030i	0.821539	+	0.570152i	$0.193116\pi$
$83$			1.11044e24i			1.14030i	−0.821539	+	0.570152i	$0.806884\pi$
$84$	−4.34480e23			−0.384130
$85$	−1.46778e24	−	2.24062e23i	−1.11924	−	0.170856i
$86$	5.44059e23			0.358439
$87$		−	1.02828e24i		−	0.586304i
$88$		−	2.19436e24i		−	1.08461i
$89$	−8.75176e23			−0.375596			−0.187798	−	0.982208i	$-0.560135\pi$
$89$	−8.75176e23			−0.375596			−0.187798	+	0.982208i	$0.560135\pi$
$90$	6.18720e23	+	9.44496e22i	0.230920	+	0.0352508i
$91$	1.16840e24			0.379818
$92$		−	5.54448e24i		−	1.57222i
$93$			1.76834e24i			0.438055i
$94$	3.19426e23			0.0692264
$95$	−1.74386e23	+	1.14237e24i	−0.0331106	+	0.216900i
$96$	3.04938e24			0.507949
$97$			8.28877e24i			1.21295i	0.795102	+	0.606475i	$0.207417\pi$
$97$			8.28877e24i			1.21295i	−0.795102	+	0.606475i	$0.792583\pi$
$98$			1.14529e24i			0.147432i
$99$	−9.75269e24			−1.10582
$100$	−8.38012e24	−	2.61955e24i	−0.838012	−	0.261955i
$101$	2.00440e25			1.76998			0.884989	−	0.465612i	$-0.154166\pi$
$101$	2.00440e25			1.76998			0.884989	+	0.465612i	$0.154166\pi$
$102$		−	2.91517e24i		−	0.227594i
$103$			1.74513e25i			1.20604i	0.797726	+	0.603020i	$0.206036\pi$
$103$			1.74513e25i			1.20604i	−0.797726	+	0.603020i	$0.793964\pi$
$104$	−5.35105e24			−0.327734
$105$	−1.21494e24	+	7.95880e24i	−0.0660219	+	0.432495i
$106$	−2.39889e22			−0.00115794
$107$			1.85608e25i			0.796711i	0.917231	+	0.398355i	$0.130419\pi$
$107$			1.85608e25i			0.796711i	−0.917231	+	0.398355i	$0.869581\pi$
$108$		−	2.20672e25i		−	0.843239i
$109$	1.23903e25			0.421940			0.210970	−	0.977493i	$-0.432338\pi$
$109$	1.23903e25			0.421940			0.210970	+	0.977493i	$0.432338\pi$
$110$	−1.87925e25	−	2.86874e24i	−0.570921	−	0.0871530i
$111$	3.30229e25			0.895939
$112$		−	2.03386e25i		−	0.493283i
$113$		−	6.56029e25i		−	1.42378i	−0.702291	−	0.711890i	$-0.747840\pi$
$113$		−	6.56029e25i		−	1.42378i	0.702291	−	0.711890i	$-0.252160\pi$
$114$	−2.26886e24			−0.0441060
$115$	−1.01564e26	−	1.55041e25i	−1.77017	−	0.270223i
$116$	5.71856e25			0.894461
$117$			2.37824e25i			0.334143i
$118$			5.56822e24i			0.0703383i
$119$	−7.57166e25			−0.860705
$120$	5.56417e24	−	3.64497e25i	0.0569685	−	0.373189i
$121$	1.87873e26			1.73400
$122$		−	1.00021e25i		−	0.0832899i
$123$			2.68129e25i			0.201618i
$124$	−9.83418e25			−0.668293
$125$	−7.14183e25	+	1.46182e26i	−0.438970	+	0.898502i
$126$	3.19172e25			0.177579
$127$		−	8.15832e25i		−	0.411201i	−0.978636	−	0.205600i	$-0.934085\pi$
$127$		−	8.15832e25i		−	0.411201i	0.978636	−	0.205600i	$-0.0659147\pi$
$128$			2.19183e26i			1.00157i
$129$	−1.42450e26			−0.590598
$130$	−6.99556e24	+	4.58264e25i	−0.0263348	+	0.172514i
$131$	4.56659e26			1.56207			0.781036	−	0.624486i	$-0.214692\pi$
$131$	4.56659e26			1.56207			0.781036	+	0.624486i	$0.214692\pi$
$132$			2.68611e26i			0.835506i
$133$			5.89299e25i			0.166798i
$134$	9.42685e25			0.242972
$135$	−4.04228e26	−	6.17067e25i	−0.949410	−	0.144931i
$136$	3.46767e26			0.742679
$137$		−	6.16258e26i		−	1.20436i	−0.798361	−	0.602179i	$-0.794299\pi$
$137$		−	6.16258e26i		−	1.20436i	0.798361	−	0.602179i	$-0.205701\pi$
$138$		−	2.01716e26i		−	0.359959i
$139$	−4.40596e26			−0.718382			−0.359191	−	0.933264i	$-0.616947\pi$
$139$	−4.40596e26			−0.718382			−0.359191	+	0.933264i	$0.616947\pi$
$140$	−4.42610e26	−	6.75659e25i	−0.659812	−	0.100723i
$141$	−8.36349e25			−0.114064
$142$			2.76498e26i			0.345213i
$143$		−	7.22348e26i		−	0.826126i
$144$	4.13985e26			0.433964
$145$	1.59908e26	−	1.04753e27i	0.153734	−	1.00708i
$146$	−8.87346e25			−0.0782857
$147$		−	2.99871e26i		−	0.242922i
$148$			1.83649e27i			1.36684i
$149$	6.48784e26			0.443887			0.221943	−	0.975060i	$-0.428760\pi$
$149$	6.48784e26			0.443887			0.221943	+	0.975060i	$0.428760\pi$
$150$	−3.04882e26	−	9.53033e25i	−0.191863	−	0.0599745i
$151$	6.60374e26			0.382453			0.191227	−	0.981546i	$-0.438753\pi$
$151$	6.60374e26			0.382453			0.191227	+	0.981546i	$0.438753\pi$
$152$		−	2.69887e26i		−	0.143925i
$153$		−	1.54119e27i		−	0.757203i
$154$	−9.69426e26			−0.439042
$155$	−2.74994e26	+	1.80143e27i	−0.114862	+	0.752437i
$156$	6.55021e26			0.252463
$157$			4.50634e27i			1.60354i	0.597636	+	0.801768i	$0.296107\pi$
$157$			4.50634e27i			1.60354i	−0.597636	+	0.801768i	$0.703893\pi$
$158$			1.38911e27i			0.456586i
$159$	6.28098e24			0.00190794
$160$	3.10643e27	+	4.74208e26i	0.872494	+	0.133189i
$161$	−5.23925e27			−1.36127
$162$			1.68570e26i			0.0405363i
$163$		−	1.31731e27i		−	0.293321i	−0.989187	−	0.146661i	$-0.953147\pi$
$163$		−	1.31731e27i		−	0.293321i	0.989187	−	0.146661i	$-0.0468525\pi$
$164$	−1.49113e27			−0.307587
$165$	4.92042e27	+	7.51118e26i	0.940703	+	0.143602i
$166$	−2.24673e27			−0.398290
$167$		−	5.52465e27i		−	0.908550i	−0.890861	−	0.454275i	$-0.849898\pi$
$167$		−	5.52465e27i		−	0.908550i	0.890861	−	0.454275i	$-0.150102\pi$
$168$		−	1.88029e27i		−	0.286984i
$169$	5.29493e27			0.750371
$170$	4.53337e26	−	2.96972e27i	0.0596774	−	0.390934i
$171$	−1.19950e27			−0.146740
$172$		−	7.92203e27i		−	0.901012i
$173$		−	1.57879e27i		−	0.167012i	−0.996507	−	0.0835058i	$-0.973388\pi$
$173$		−	1.57879e27i		−	0.167012i	0.996507	−	0.0835058i	$-0.0266117\pi$
$174$	2.08050e27			0.204787
$175$	−2.47534e27	+	7.91879e27i	−0.226809	+	0.725577i
$176$	−1.25741e28			−1.07292
$177$		−	1.45792e27i		−	0.115896i
$178$		−	1.77072e27i		−	0.131190i
$179$	8.29286e27			0.572850			0.286425	−	0.958103i	$-0.407533\pi$
$179$	8.29286e27			0.572850			0.286425	+	0.958103i	$0.407533\pi$
$180$	1.37528e27	−	9.00917e27i	0.0886104	−	0.580468i
$181$	−2.78734e28			−1.67574			−0.837872	−	0.545867i	$-0.816200\pi$
$181$	−2.78734e28			−1.67574			−0.837872	+	0.545867i	$0.816200\pi$
$182$			2.36399e27i			0.132664i
$183$			2.61883e27i			0.137236i
$184$	2.39947e28			1.17461
$185$	3.36409e28	+	5.13539e27i	1.53894	+	0.234924i
$186$	−3.57782e27			−0.153006
$187$			4.68107e28i			1.87208i
$188$		−	4.65115e27i		−	0.174015i
$189$	−2.08524e28			−0.730102
$190$	−2.31132e27	−	3.52830e26i	−0.0757599	−	0.0115650i
$191$	−9.53907e26			−0.0292812			−0.0146406	−	0.999893i	$-0.504660\pi$
$191$	−9.53907e26			−0.0292812			−0.0146406	+	0.999893i	$0.504660\pi$
$192$		−	6.81670e27i		−	0.196024i
$193$			5.56387e28i			1.49938i	0.661791	+	0.749688i	$0.269797\pi$
$193$			5.56387e28i			1.49938i	−0.661791	+	0.749688i	$0.730203\pi$
$194$	−1.67704e28			−0.423665
$195$	1.83164e27	−	1.19987e28i	0.0433918	−	0.284250i
$196$	1.66766e28			0.370601
$197$		−	5.10086e28i		−	1.06369i	−0.846841	−	0.531846i	$-0.821498\pi$
$197$		−	5.10086e28i		−	1.06369i	0.846841	−	0.531846i	$-0.178502\pi$
$198$		−	1.97323e28i		−	0.386246i
$199$	2.20419e28			0.405122			0.202561	−	0.979270i	$-0.435074\pi$
$199$	2.20419e28			0.405122			0.202561	+	0.979270i	$0.435074\pi$
$200$	1.13366e28	−	3.62665e28i	0.195707	−	0.626081i
$201$	−2.46822e28			−0.400344
$202$			4.05545e28i			0.618225i
$203$		−	5.40375e28i		−	0.774452i
$204$	−4.24477e28			−0.572107
$205$	−4.16966e27	+	2.73146e28i	−0.0528662	+	0.346315i
$206$	−3.53086e28			−0.421251
$207$		−	1.06643e29i		−	1.19758i
$208$			3.06625e28i			0.324202i
$209$	3.64326e28			0.362795
$210$	−1.61028e28	−	2.45815e27i	−0.151064	−	0.0230604i
$211$	1.08789e29			0.961731			0.480865	−	0.876794i	$-0.340323\pi$
$211$	1.08789e29			0.961731			0.480865	+	0.876794i	$0.340323\pi$
$212$			3.49302e26i			0.00291073i
$213$		−	7.23951e28i		−	0.568806i
$214$	−3.75536e28			−0.278278
$215$	−1.45116e29	−	2.21524e28i	−1.01446	−	0.154860i
$216$	9.54998e28			0.629986
$217$			9.29280e28i			0.578629i
$218$			2.50689e28i			0.147377i
$219$	2.32333e28			0.128991
$220$	−4.17716e28	+	2.73637e29i	−0.219078	+	1.43513i
$221$	1.14150e29			0.565684
$222$			6.68143e28i			0.312937i
$223$			1.88668e29i			0.835388i	0.908588	+	0.417694i	$0.137162\pi$
$223$			1.88668e29i			0.835388i	−0.908588	+	0.417694i	$0.862838\pi$
$224$	1.60248e29			0.670953
$225$	−1.61184e29	−	5.03848e28i	−0.638324	−	0.199534i
$226$	1.32732e29			0.497304
$227$		−	7.62292e28i		−	0.270270i	−0.990827	−	0.135135i	$-0.956853\pi$
$227$		−	7.62292e28i		−	0.270270i	0.990827	−	0.135135i	$-0.0431469\pi$
$228$			3.30369e28i			0.110870i
$229$	−4.98149e29			−1.58276			−0.791382	−	0.611322i	$-0.790638\pi$
$229$	−4.98149e29			−1.58276			−0.791382	+	0.611322i	$0.790638\pi$
$230$	3.13689e28	−	2.05491e29i	0.0943846	−	0.618294i
$231$	2.53824e29			0.723407
$232$			2.47481e29i			0.668254i
$233$		−	2.73818e29i		−	0.700669i	−0.936625	−	0.350334i	$-0.886068\pi$
$233$		−	2.73818e29i		−	0.700669i	0.936625	−	0.350334i	$-0.113932\pi$
$234$	−4.81183e28			−0.116711
$235$	−8.51998e28	−	1.30060e28i	−0.195925	−	0.0299087i
$236$	8.10788e28			0.176810
$237$		−	3.63709e29i		−	0.752315i
$238$		−	1.53195e29i		−	0.300631i
$239$	−3.89671e29			−0.725645			−0.362822	−	0.931858i	$-0.618187\pi$
$239$	−3.89671e29			−0.725645			−0.362822	+	0.931858i	$0.618187\pi$
$240$	−2.08863e29	−	3.18837e28i	−0.369166	−	0.0563545i
$241$	1.08446e30			1.81971			0.909854	−	0.414928i	$-0.136193\pi$
$241$	1.08446e30			1.81971			0.909854	+	0.414928i	$0.136193\pi$
$242$			3.80119e29i			0.605657i
$243$		−	6.78787e29i		−	1.02720i
$244$	−1.45640e29			−0.209367
$245$	4.66328e28	−	3.05482e29i	0.0636965	−	0.417263i
$246$	−5.42497e28			−0.0704220
$247$		−	8.88427e28i		−	0.109625i
$248$		−	4.25592e29i		−	0.499283i
$249$	5.88259e29			0.656261
$250$	−2.95766e29	−	1.44499e29i	−0.313832	−	0.153325i
$251$	−1.81453e30			−1.83165			−0.915826	−	0.401576i	$-0.868462\pi$
$251$	−1.81453e30			−1.83165			−0.915826	+	0.401576i	$0.868462\pi$
$252$		−	4.64745e29i		−	0.446384i
$253$			3.23909e30i			2.96085i
$254$	1.65065e29			0.143626
$255$	−1.18697e29	+	7.77558e29i	−0.0983302	+	0.644140i
$256$	−1.16951e28			−0.00922581
$257$		−	3.71565e29i		−	0.279171i	−0.990210	−	0.139585i	$-0.955423\pi$
$257$		−	3.71565e29i		−	0.279171i	0.990210	−	0.139585i	$-0.0445770\pi$
$258$		−	2.88215e29i		−	0.206287i
$259$	1.73539e30			1.18345
$260$	6.67278e29	+	1.01862e29i	0.433651	+	0.0661982i
$261$	1.09991e30			0.681322
$262$			9.23945e29i			0.545607i
$263$			3.58787e29i			0.202018i	0.994886	+	0.101009i	$0.0322071\pi$
$263$			3.58787e29i			0.202018i	−0.994886	+	0.101009i	$0.967793\pi$
$264$	−1.16246e30			−0.624208
$265$	6.39851e27	+	9.76755e26i	0.00327722	+	0.000500279i
$266$	−1.19231e29			−0.0582598
$267$			4.63625e29i			0.216160i
$268$		−	1.37264e30i		−	0.610763i
$269$	−3.68420e29			−0.156473			−0.0782366	−	0.996935i	$-0.524929\pi$
$269$	−3.68420e29			−0.156473			−0.0782366	+	0.996935i	$0.524929\pi$
$270$	1.24849e29	−	8.17862e29i	0.0506220	−	0.331614i
$271$	−3.05825e30			−1.18401			−0.592007	−	0.805933i	$-0.701664\pi$
$271$	−3.05825e30			−1.18401			−0.592007	+	0.805933i	$0.701664\pi$
$272$		−	1.98704e30i		−	0.734674i
$273$		−	6.18962e29i		−	0.218590i
$274$	1.24686e30			0.420663
$275$	4.89568e30	+	1.53035e30i	1.57817	+	0.493323i
$276$	−2.93719e30			−0.904833
$277$		−	5.78873e29i		−	0.170446i	−0.996362	−	0.0852229i	$-0.972840\pi$
$277$		−	5.78873e29i		−	0.170446i	0.996362	−	0.0852229i	$-0.0271602\pi$
$278$		−	8.91445e29i		−	0.250920i
$279$	−1.89152e30			−0.509047
$280$	2.92403e29	−	1.91547e30i	0.0752500	−	0.492947i
$281$	−5.20581e30			−1.28132			−0.640662	−	0.767823i	$-0.721340\pi$
$281$	−5.20581e30			−1.28132			−0.640662	+	0.767823i	$0.721340\pi$
$282$		−	1.69216e29i		−	0.0398407i
$283$		−	5.35308e30i		−	1.20580i	−0.797819	−	0.602898i	$-0.794013\pi$
$283$		−	5.35308e30i		−	1.20580i	0.797819	−	0.602898i	$-0.205987\pi$
$284$	4.02608e30			0.867767
$285$	6.05170e29	+	9.23812e28i	0.124829	+	0.0190556i
$286$	1.46151e30			0.288553
$287$			1.40905e30i			0.266318i
$288$			3.26179e30i			0.590269i
$289$	−1.62672e30			−0.281897
$290$	2.11943e30	+	3.23538e29i	0.351758	+	0.0536970i
$291$	4.39098e30			0.698070
$292$			1.29206e30i			0.196788i
$293$			5.03168e30i			0.734290i	0.930164	+	0.367145i	$0.119665\pi$
$293$			5.03168e30i			0.734290i	−0.930164	+	0.367145i	$0.880335\pi$
$294$	6.06720e29			0.0848489
$295$	2.26721e29	−	1.48520e30i	0.0303890	−	0.199072i
$296$	−7.94774e30			−1.02117
$297$			1.28917e31i			1.58802i
$298$			1.31267e30i			0.155043i
$299$	7.89869e30			0.894675
$300$	−1.38771e30	+	4.43938e30i	−0.150759	+	0.482288i
$301$	−7.48592e30			−0.780124
$302$			1.33612e30i			0.133585i
$303$		−	1.06183e31i		−	1.01865i
$304$	−1.54650e30			−0.142374
$305$	−4.07254e29	+	2.66784e30i	−0.0359847	+	0.235728i
$306$	3.11824e30			0.264479
$307$		−	1.98181e31i		−	1.61374i	−0.590730	−	0.806870i	$-0.701160\pi$
$307$		−	1.98181e31i		−	1.61374i	0.590730	−	0.806870i	$-0.298840\pi$
$308$			1.41158e31i			1.10362i
$309$	9.24482e30			0.694093
$310$	−3.64477e30	−	5.56387e29i	−0.262814	−	0.0401195i
$311$	4.40038e30			0.304779			0.152390	−	0.988321i	$-0.451303\pi$
$311$	4.40038e30			0.304779			0.152390	+	0.988321i	$0.451303\pi$
$312$			2.83472e30i			0.188616i
$313$		−	9.30499e30i		−	0.594855i	−0.954744	−	0.297428i	$-0.903871\pi$
$313$		−	9.30499e30i		−	0.594855i	0.954744	−	0.297428i	$-0.0961287\pi$
$314$	−9.11755e30			−0.560090
$315$	−8.51321e30	−	1.29957e30i	−0.502587	−	0.0767216i
$316$	2.02268e31			1.14773
$317$		−	1.57166e31i		−	0.857268i	−0.903478	−	0.428634i	$-0.858995\pi$
$317$		−	1.57166e31i		−	0.857268i	0.903478	−	0.428634i	$-0.141005\pi$
$318$			1.27081e28i			0.000666412i
$319$	−3.34079e31			−1.68448
$320$	1.06006e30	−	6.94426e30i	0.0513993	−	0.336706i
$321$	9.83262e30			0.458518
$322$		−	1.06004e31i		−	0.475472i
$323$			5.75732e30i			0.248421i
$324$	2.45455e30			0.101897
$325$	3.73183e30	−	1.19384e31i	0.149066	−	0.476873i
$326$	2.66528e30			0.102452
$327$		−	6.56377e30i		−	0.242832i
$328$		−	6.45314e30i		−	0.229799i
$329$	−4.39510e30			−0.150668
$330$	−1.51972e30	+	9.95533e30i	−0.0501577	+	0.328573i
$331$	3.48836e31			1.10859			0.554295	−	0.832320i	$-0.312988\pi$
$331$	3.48836e31			1.10859			0.554295	+	0.832320i	$0.312988\pi$
$332$			3.27146e31i			1.00119i
$333$			3.53233e31i			1.04114i
$334$	1.11779e31			0.317342
$335$	−2.51441e31	−	3.83833e30i	−0.687663	−	0.104974i
$336$	−1.07744e31			−0.283891
$337$			4.49684e31i			1.14165i	0.821071	+	0.570826i	$0.193377\pi$
$337$			4.49684e31i			1.14165i	−0.821071	+	0.570826i	$0.806623\pi$
$338$			1.07131e31i			0.262093i
$339$	−3.47532e31			−0.819405
$340$	−4.32420e31	−	6.60104e30i	−0.982696	−	0.150012i
$341$	5.74514e31			1.25855
$342$		−	2.42691e30i		−	0.0512539i
$343$		−	5.30925e31i		−	1.08108i
$344$	3.42840e31			0.673148
$345$	−8.21328e30	+	5.38035e31i	−0.155517	+	1.01876i
$346$	3.19431e30			0.0583345
$347$			3.65658e31i			0.644106i	0.946722	+	0.322053i	$0.104373\pi$
$347$			3.65658e31i			0.644106i	−0.946722	+	0.322053i	$0.895627\pi$
$348$		−	3.02941e31i		−	0.514775i
$349$	1.78800e31			0.293122			0.146561	−	0.989202i	$-0.453180\pi$
$349$	1.78800e31			0.293122			0.146561	+	0.989202i	$0.453180\pi$
$350$	−1.60219e31	−	5.00829e30i	−0.253432	−	0.0792207i
$351$	3.14371e31			0.479848
$352$		−	9.90711e31i		−	1.45936i
$353$			4.44335e31i			0.631723i	0.948805	+	0.315862i	$0.102294\pi$
$353$			4.44335e31i			0.631723i	−0.948805	+	0.315862i	$0.897706\pi$
$354$	2.94977e30			0.0404806
$355$	1.12581e31	−	7.37497e31i	0.149146	−	0.977026i
$356$	−2.57834e31			−0.329773
$357$			4.01109e31i			0.495348i
$358$			1.67787e31i			0.200088i
$359$	−5.83509e31			−0.671996			−0.335998	−	0.941863i	$-0.609074\pi$
$359$	−5.83509e31			−0.671996			−0.335998	+	0.941863i	$0.609074\pi$
$360$	3.89888e31	+	5.95177e30i	0.433669	+	0.0662010i
$361$	−8.85956e31			−0.951858
$362$		−	5.63954e31i		−	0.585311i
$363$		−	9.95260e31i		−	0.997939i
$364$	3.44221e31			0.333480
$365$	2.36680e31	+	3.61301e30i	0.221565	+	0.0338227i
$366$	−5.29861e30			−0.0479345
$367$		−	5.85632e31i		−	0.512035i	−0.966672	−	0.256017i	$-0.917590\pi$
$367$		−	5.85632e31i		−	0.512035i	0.966672	−	0.256017i	$-0.0824104\pi$
$368$		−	1.37494e32i		−	1.16195i
$369$	−2.86806e31			−0.234293
$370$	−1.03903e31	+	6.80645e31i	−0.0820551	+	0.537526i
$371$	3.30073e29			0.00252020
$372$			5.20966e31i			0.384612i
$373$			2.48400e32i			1.77333i	0.462409	+	0.886667i	$0.346985\pi$
$373$			2.48400e32i			1.77333i	−0.462409	+	0.886667i	$0.653015\pi$
$374$	−9.47108e31			−0.653890
$375$	7.74401e31	+	3.78339e31i	0.517100	+	0.252633i
$376$	2.01287e31			0.130007
$377$			8.14669e31i			0.508996i
$378$		−	4.21901e31i		−	0.255013i
$379$	1.58347e32			0.926020			0.463010	−	0.886353i	$-0.346769\pi$
$379$	1.58347e32			0.926020			0.463010	+	0.886353i	$0.346769\pi$
$380$	−5.13756e30	+	3.36550e31i	−0.0290711	+	0.190439i
$381$	−4.32187e31			−0.236652
$382$		−	1.93001e30i		−	0.0102275i
$383$			9.64738e31i			0.494794i	0.968914	+	0.247397i	$0.0795752\pi$
$383$			9.64738e31i			0.494794i	−0.968914	+	0.247397i	$0.920425\pi$
$384$	1.16112e32			0.576418
$385$	2.58573e32	+	3.94721e31i	1.24258	+	0.189684i
$386$	−1.12572e32			−0.523709
$387$		−	1.52373e32i		−	0.686312i
$388$			2.44194e32i			1.06497i
$389$	−3.69637e31			−0.156101			−0.0780504	−	0.996949i	$-0.524870\pi$
$389$	−3.69637e31			−0.156101			−0.0780504	+	0.996949i	$0.524870\pi$
$390$	2.42766e31	+	3.70590e30i	0.0992842	+	0.0151561i
$391$	−5.11863e32			−2.02742
$392$			7.21709e31i			0.276877i
$393$		−	2.41915e32i		−	0.898994i
$394$	1.03204e32			0.371531
$395$	5.65603e31	−	3.70515e32i	0.197264	−	1.29224i
$396$	−2.87322e32			−0.970911
$397$			4.44703e32i			1.45609i	0.685528	+	0.728046i	$0.259571\pi$
$397$			4.44703e32i			1.45609i	−0.685528	+	0.728046i	$0.740429\pi$
$398$			4.45968e31i			0.141503i
$399$	3.12182e31			0.0959945
$400$	−2.07813e32	−	6.49606e31i	−0.619332	−	0.193598i
$401$	3.32269e32			0.959809			0.479904	−	0.877321i	$-0.340671\pi$
$401$	3.32269e32			0.959809			0.479904	+	0.877321i	$0.340671\pi$
$402$		−	4.99388e31i		−	0.139834i
$403$		−	1.40098e32i		−	0.380294i
$404$	5.90513e32			1.55404
$405$	6.86368e30	−	4.49625e31i	0.0175133	−	0.114726i
$406$	1.09332e32			0.270504
$407$		−	1.07288e33i		−	2.57408i
$408$		−	1.83700e32i		−	0.427422i
$409$	−5.29054e32			−1.19388			−0.596938	−	0.802288i	$-0.703616\pi$
$409$	−5.29054e32			−1.19388			−0.596938	+	0.802288i	$0.703616\pi$
$410$	−5.52648e31	−	8.43636e30i	−0.120962	−	0.0184653i
$411$	−3.26463e32			−0.693125
$412$			5.14128e32i			1.05890i
$413$		−	7.66154e31i		−	0.153088i
$414$	2.15768e32			0.418295
$415$	5.99266e32	+	9.14800e31i	1.12725	+	0.172078i
$416$	−2.41590e32			−0.440973
$417$			2.33406e32i			0.413439i
$418$			7.37130e31i			0.126719i
$419$	−6.29624e32			−1.05052			−0.525262	−	0.850941i	$-0.676033\pi$
$419$	−6.29624e32			−1.05052			−0.525262	+	0.850941i	$0.676033\pi$
$420$	−3.57931e31	+	2.34473e32i	−0.0579672	+	0.379731i
$421$	4.32266e32			0.679555			0.339778	−	0.940506i	$-0.389648\pi$
$421$	4.32266e32			0.679555			0.339778	+	0.940506i	$0.389648\pi$
$422$			2.20109e32i			0.335917i
$423$		−	8.94608e31i		−	0.132550i
$424$	−1.51167e30			−0.00217462
$425$	−2.41836e32	+	7.73649e32i	−0.337799	+	1.08064i
$426$	1.46475e32			0.198675
$427$			1.37622e32i			0.181276i
$428$			5.46818e32i			0.699512i
$429$	−3.82665e32			−0.475447
$430$	4.48203e31	−	2.93608e32i	0.0540903	−	0.354334i
$431$	1.21421e33			1.42341			0.711704	−	0.702480i	$-0.247924\pi$
$431$	1.21421e33			1.42341			0.711704	+	0.702480i	$0.247924\pi$
$432$		−	5.47231e32i		−	0.623195i
$433$			4.46703e32i			0.494220i	0.968987	+	0.247110i	$0.0794809\pi$
$433$			4.46703e32i			0.494220i	−0.968987	+	0.247110i	$0.920519\pi$
$434$	−1.88019e32			−0.202106
$435$	−5.54927e32	−	8.47116e31i	−0.579590	−	0.0884763i
$436$	3.65028e32			0.370463
$437$			3.98381e32i			0.392899i
$438$			4.70072e31i			0.0450545i
$439$	1.89182e32			0.176227			0.0881135	−	0.996110i	$-0.471916\pi$
$439$	1.89182e32			0.176227			0.0881135	+	0.996110i	$0.471916\pi$
$440$	−1.18421e33	−	1.80774e32i	−1.07219	−	0.163673i
$441$	3.20760e32			0.282291
$442$			2.30957e32i			0.197585i
$443$		−	9.50307e32i		−	0.790346i	−0.918607	−	0.395173i	$-0.870685\pi$
$443$		−	9.50307e32i		−	0.790346i	0.918607	−	0.395173i	$-0.129315\pi$
$444$	9.72882e32			0.786635
$445$	−7.20983e31	+	4.72301e32i	−0.0566793	+	0.371294i
$446$	−3.81727e32			−0.291788
$447$		−	3.43694e32i		−	0.255463i
$448$		−	3.58225e32i		−	0.258929i
$449$	−6.79168e32			−0.477417			−0.238709	−	0.971091i	$-0.576724\pi$
$449$	−6.79168e32			−0.477417			−0.238709	+	0.971091i	$0.576724\pi$
$450$	1.01942e32	−	3.26119e32i	0.0696942	−	0.222957i
$451$	8.71123e32			0.579259
$452$		−	1.93272e33i		−	1.25008i
$453$		−	3.49834e32i		−	0.220107i
$454$	1.54232e32			0.0944011
$455$	9.62547e31	−	6.30544e32i	0.0573165	−	0.375468i
$456$	−1.42973e32			−0.0828310
$457$			7.89422e32i			0.444996i	0.974933	+	0.222498i	$0.0714212\pi$
$457$			7.89422e32i			0.444996i	−0.974933	+	0.222498i	$0.928579\pi$
$458$		−	1.00789e33i		−	0.552834i
$459$	−2.03723e33			−1.08738
$460$	−2.99215e33	−	4.56762e32i	−1.55421	−	0.237256i
$461$	2.02758e33			1.02498			0.512492	−	0.858692i	$-0.328722\pi$
$461$	2.02758e33			1.02498			0.512492	+	0.858692i	$0.328722\pi$
$462$			5.13554e32i			0.252675i
$463$		−	1.88726e32i		−	0.0903794i	−0.998978	−	0.0451897i	$-0.985611\pi$
$463$		−	1.88726e32i		−	0.0903794i	0.998978	−	0.0451897i	$-0.0143892\pi$
$464$	1.41811e33			0.661051
$465$	9.54307e32	+	1.45678e32i	0.433038	+	0.0661047i
$466$	5.54007e32			0.244733
$467$			1.70273e33i			0.732291i	0.930558	+	0.366145i	$0.119323\pi$
$467$			1.70273e33i			0.732291i	−0.930558	+	0.366145i	$0.880677\pi$
$468$			7.00650e32i			0.293378i
$469$	−1.29708e33			−0.528817
$470$	2.63147e31	−	1.72382e32i	0.0104466	−	0.0684336i
$471$	2.38724e33			0.922857
$472$			3.50883e32i			0.132095i
$473$			4.62806e33i			1.69682i
$474$	7.35881e32			0.262772
$475$	6.02127e32	+	1.88220e32i	0.209420	+	0.0654628i
$476$	−2.23067e33			−0.755699
$477$			6.71851e30i			0.00221714i
$478$		−	7.88409e32i		−	0.253456i
$479$	−3.94704e33			−1.23617			−0.618084	−	0.786112i	$-0.712091\pi$
$479$	−3.94704e33			−1.23617			−0.618084	+	0.786112i	$0.712091\pi$
$480$	2.51212e32	−	1.64564e33i	0.0766522	−	0.502133i
$481$	−2.61627e33			−0.777803
$482$			2.19416e33i			0.635596i
$483$			2.77550e33i			0.783433i
$484$	5.53490e33			1.52245
$485$	4.47314e33	+	6.82840e32i	1.19906	+	0.183041i
$486$	1.37337e33			0.358785
$487$		−	3.91855e33i		−	0.997730i	−0.866680	−	0.498865i	$-0.833750\pi$
$487$		−	3.91855e33i		−	0.997730i	0.866680	−	0.498865i	$-0.166250\pi$
$488$		−	6.30283e32i		−	0.156418i
$489$	−6.97847e32			−0.168811
$490$	6.18072e32	+	9.43508e31i	0.145743	+	0.0222482i
$491$	−2.40038e33			−0.551773			−0.275887	−	0.961190i	$-0.588971\pi$
$491$	−2.40038e33			−0.551773			−0.275887	+	0.961190i	$0.588971\pi$
$492$			7.89929e32i			0.177021i
$493$		−	5.27934e33i		−	1.15344i
$494$	1.79753e32			0.0382903
$495$	−8.03441e32	+	5.26317e33i	−0.166874	+	1.09316i
$496$	−2.43872e33			−0.493901
$497$		−	3.80444e33i		−	0.751339i
$498$			1.19021e33i			0.229222i
$499$	−2.69345e33			−0.505886			−0.252943	−	0.967481i	$-0.581399\pi$
$499$	−2.69345e33			−0.505886			−0.252943	+	0.967481i	$0.581399\pi$
$500$	−2.10404e33	+	4.30664e33i	−0.385416	+	0.788885i
$501$	−2.92669e33			−0.522883
$502$		−	3.67129e33i		−	0.639767i
$503$		−	4.57498e33i		−	0.777659i	−0.921310	−	0.388829i	$-0.872880\pi$
$503$		−	4.57498e33i		−	0.777659i	0.921310	−	0.388829i	$-0.127120\pi$
$504$	2.01127e33			0.333494
$505$	1.65126e33	−	1.08170e34i	0.267099	−	1.74971i
$506$	−6.55356e33			−1.03418
$507$		−	2.80499e33i		−	0.431849i
$508$		−	2.40351e33i		−	0.361035i
$509$	1.09929e34			1.61117			0.805586	−	0.592479i	$-0.201851\pi$
$509$	1.09929e34			1.61117			0.805586	+	0.592479i	$0.201851\pi$
$510$	−1.57321e33	−	2.40156e32i	−0.224988	−	0.0343452i
$511$	1.22093e33			0.170385
$512$			7.33088e33i			0.998348i
$513$			1.58557e33i			0.210726i
$514$	7.51776e32			0.0975100
$515$	9.41781e33	+	1.43766e33i	1.19223	+	0.181998i
$516$	−4.19670e33			−0.518545
$517$			2.71721e33i			0.327711i
$518$			3.51116e33i			0.413361i
$519$	−8.36363e32			−0.0961175
$520$	−4.40827e32	+	2.88776e33i	−0.0494568	+	0.323981i
$521$	−9.13391e33			−1.00043			−0.500213	−	0.865902i	$-0.666745\pi$
$521$	−9.13391e33			−1.00043			−0.500213	+	0.865902i	$0.666745\pi$
$522$			2.22542e33i			0.237975i
$523$		−	2.09183e33i		−	0.218402i	−0.994020	−	0.109201i	$-0.965171\pi$
$523$		−	2.09183e33i		−	0.218402i	0.994020	−	0.109201i	$-0.0348292\pi$
$524$	1.34535e34			1.37150
$525$	4.19499e33	+	1.31132e33i	0.417580	+	0.130532i
$526$	−7.25923e32			−0.0705617
$527$			9.07887e33i			0.861785i
$528$			6.66111e33i			0.617480i
$529$	−2.43729e34			−2.20653
$530$	−1.97624e30	+	1.29459e31i	−0.000174739	+	0.00114468i
$531$	1.55948e33			0.134679
$532$			1.73612e33i			0.146449i
$533$		−	2.12428e33i		−	0.175033i
$534$	−9.38039e32			−0.0755014
$535$	1.00166e34	+	1.52907e33i	0.787587	+	0.120228i
$536$	5.94035e33			0.456302
$537$		−	4.39315e33i		−	0.329683i
$538$		−	7.45414e32i		−	0.0546537i
$539$	−9.74249e33			−0.697928
$540$	−1.19089e34	−	1.81793e33i	−0.833582	−	0.127249i
$541$	1.05050e34			0.718503			0.359251	−	0.933241i	$-0.383032\pi$
$541$	1.05050e34			0.718503			0.359251	+	0.933241i	$0.383032\pi$
$542$		−	6.18766e33i		−	0.413557i
$543$			1.47659e34i			0.964414i
$544$	1.56559e34			0.999289
$545$	1.02073e33	−	6.68659e33i	0.0636729	−	0.417108i
$546$	1.25233e33			0.0763502
$547$			1.22596e34i			0.730523i	0.930905	+	0.365261i	$0.119020\pi$
$547$			1.22596e34i			0.730523i	−0.930905	+	0.365261i	$0.880980\pi$
$548$		−	1.81555e34i		−	1.05743i
$549$	−2.80126e33			−0.159477
$550$	−3.09630e33	+	9.90529e33i	−0.172310	+	0.551231i
$551$	−4.10889e33			−0.223527
$552$		−	1.27112e34i		−	0.676003i
$553$		−	1.91133e34i		−	0.993737i
$554$	1.17122e33			0.0595340
$555$	2.72048e33	−	1.78213e34i	0.135202	−	0.885679i
$556$	−1.29803e34			−0.630740
$557$		−	1.79762e34i		−	0.854100i	−0.904228	−	0.427050i	$-0.859553\pi$
$557$		−	1.79762e34i		−	0.854100i	0.904228	−	0.427050i	$-0.140447\pi$
$558$		−	3.82705e33i		−	0.177802i
$559$	1.12858e34			0.512724
$560$	−1.09760e34	−	1.67552e33i	−0.487634	−	0.0744389i
$561$	2.47980e34			1.07741
$562$		−	1.05328e34i		−	0.447547i
$563$			3.62981e34i			1.50844i	0.656619	+	0.754222i	$0.271986\pi$
$563$			3.62981e34i			1.50844i	−0.656619	+	0.754222i	$0.728014\pi$
$564$	−2.46395e33			−0.100148
$565$	−3.54035e34	−	5.40446e33i	−1.40747	−	0.214856i
$566$	1.08307e34			0.421165
$567$		−	2.31943e33i		−	0.0882252i
$568$			1.74236e34i			0.648310i
$569$	−3.88784e34			−1.41516			−0.707579	−	0.706635i	$-0.750212\pi$
$569$	−3.88784e34			−1.41516			−0.707579	+	0.706635i	$0.750212\pi$
$570$	−1.86912e32	+	1.22442e33i	−0.00665582	+	0.0436009i
$571$	3.32205e34			1.15732			0.578662	−	0.815567i	$-0.303575\pi$
$571$	3.32205e34			1.15732			0.578662	+	0.815567i	$0.303575\pi$
$572$		−	2.12810e34i		−	0.725339i
$573$			5.05333e32i			0.0168517i
$574$	−2.85088e33			−0.0930208
$575$	−1.67339e34	+	5.35330e34i	−0.534257	+	1.70912i
$576$	7.29155e33			0.227792
$577$			5.11740e34i			1.56441i	0.623018	+	0.782207i	$0.285906\pi$
$577$			5.11740e34i			1.56441i	−0.623018	+	0.782207i	$0.714094\pi$
$578$		−	3.29130e33i		−	0.0984622i
$579$	2.94746e34			0.862912
$580$	4.71103e33	−	3.08610e34i	0.134979	−	0.884218i
$581$	3.09136e34			0.866859
$582$			8.88414e33i			0.243825i
$583$		−	2.04063e32i		−	0.00548159i
$584$	−5.59163e33			−0.147021
$585$	1.28345e34	+	1.95923e33i	0.330317	+	0.0504240i
$586$	−1.01805e34			−0.256476
$587$		−	5.17586e33i		−	0.127646i	−0.997961	−	0.0638228i	$-0.979671\pi$
$587$		−	5.17586e33i		−	0.127646i	0.997961	−	0.0638228i	$-0.0203293\pi$
$588$		−	8.83443e33i		−	0.213286i
$589$	7.06604e33			0.167007
$590$	3.00497e33	+	4.58718e32i	0.0695328	+	0.0106144i
$591$	−2.70219e34			−0.612170
$592$			4.55420e34i			1.01016i
$593$		−	3.22963e34i		−	0.701406i	−0.936487	−	0.350703i	$-0.885943\pi$
$593$		−	3.22963e34i		−	0.701406i	0.936487	−	0.350703i	$-0.114057\pi$
$594$	−2.60834e34			−0.554669
$595$	−6.23765e33	+	4.08615e34i	−0.129885	+	0.850848i
$596$	1.91137e34			0.389733
$597$		−	1.16767e34i		−	0.233153i
$598$			1.59812e34i			0.312496i
$599$	−5.78815e34			−1.10842			−0.554211	−	0.832376i	$-0.686980\pi$
$599$	−5.78815e34			−1.10842			−0.554211	+	0.832376i	$0.686980\pi$
$600$	−1.92122e34	−	6.00556e33i	−0.360318	−	0.112632i
$601$	4.54517e34			0.834872			0.417436	−	0.908706i	$-0.362929\pi$
$601$	4.54517e34			0.834872			0.417436	+	0.908706i	$0.362929\pi$
$602$		−	1.51460e34i		−	0.272485i
$603$		−	2.64016e34i		−	0.465225i
$604$	1.94552e34			0.335794
$605$	1.54773e34	−	1.01388e35i	0.261669	−	1.71414i
$606$	2.14838e34			0.355797
$607$			2.97089e34i			0.481979i	0.970528	+	0.240990i	$0.0774720\pi$
$607$			2.97089e34i			0.481979i	−0.970528	+	0.240990i	$0.922528\pi$
$608$		−	1.21849e34i		−	0.193654i
$609$	−2.86264e34			−0.445708
$610$	−5.39775e33	−	8.23985e32i	−0.0823361	−	0.0125689i
$611$	6.62606e33			0.0990239
$612$		−	4.54046e34i		−	0.664825i
$613$		−	6.35057e34i		−	0.911080i	−0.890215	−	0.455540i	$-0.849446\pi$
$613$		−	6.35057e34i		−	0.911080i	0.890215	−	0.455540i	$-0.150554\pi$
$614$	4.00975e34			0.563654
$615$	1.44699e34	+	2.20888e33i	0.199309	+	0.0304252i
$616$	−6.10886e34			−0.824520
$617$		−	6.33497e34i		−	0.837876i	−0.908015	−	0.418938i	$-0.862402\pi$
$617$		−	6.33497e34i		−	0.837876i	0.908015	−	0.418938i	$-0.137598\pi$
$618$			1.87048e34i			0.242436i
$619$	−5.34076e32			−0.00678375			−0.00339188	−	0.999994i	$-0.501080\pi$
$619$	−5.34076e32			−0.00678375			−0.00339188	+	0.999994i	$0.501080\pi$
$620$	−8.10154e33	+	5.30715e34i	−0.100849	+	0.660640i
$621$	−1.40967e35			−1.71978
$622$			8.90316e33i			0.106455i
$623$			2.43640e34i			0.285528i
$624$	1.62435e34			0.186583
$625$	7.30056e34	+	5.05846e34i	0.821970	+	0.569531i
$626$	1.88265e34			0.207774
$627$		−	1.93002e34i		−	0.208794i
$628$			1.32761e35i			1.40791i
$629$	1.69544e35			1.76258
$630$	2.62938e33	−	1.72245e34i	0.0267976	−	0.175546i
$631$	−9.67889e34			−0.967071			−0.483536	−	0.875325i	$-0.660648\pi$
$631$	−9.67889e34			−0.967071			−0.483536	+	0.875325i	$0.660648\pi$
$632$			8.75350e34i			0.857469i
$633$		−	5.76309e34i		−	0.553490i
$634$	3.17988e34			0.299430
$635$	−4.40274e34	−	6.72094e33i	−0.406492	−	0.0620524i
$636$	1.85043e32			0.00167517
$637$			2.37576e34i			0.210891i
$638$		−	6.75932e34i		−	0.588362i
$639$	7.74381e34			0.660989
$640$	1.18285e35	+	1.80566e34i	0.990100	+	0.151142i
$641$	−7.48249e34			−0.614216			−0.307108	−	0.951675i	$-0.599361\pi$
$641$	−7.48249e34			−0.614216			−0.307108	+	0.951675i	$0.599361\pi$
$642$			1.98941e34i			0.160153i
$643$			1.50707e35i			1.18986i	0.803777	+	0.594931i	$0.202821\pi$
$643$			1.50707e35i			1.18986i	−0.803777	+	0.594931i	$0.797179\pi$
$644$	−1.54353e35			−1.19520
$645$	−1.17353e34	+	7.68752e34i	−0.0891243	+	0.583835i
$646$	−1.16486e34			−0.0867697
$647$		−	6.07630e34i		−	0.443952i	−0.975052	−	0.221976i	$-0.928749\pi$
$647$		−	6.07630e34i		−	0.443952i	0.975052	−	0.221976i	$-0.0712507\pi$
$648$			1.06225e34i			0.0761271i
$649$	−4.73664e34			−0.332975
$650$	2.41545e34	+	7.55049e33i	0.166564	+	0.0520665i
$651$	4.92287e34			0.333009
$652$		−	3.88091e34i		−	0.257536i
$653$			9.70389e34i			0.631730i	0.948804	+	0.315865i	$0.102295\pi$
$653$			9.70389e34i			0.631730i	−0.948804	+	0.315865i	$0.897705\pi$
$654$	1.32803e34			0.0848175
$655$	3.76202e34	−	2.46442e35i	0.235725	−	1.54418i
$656$	−3.69777e34			−0.227322
$657$			2.48517e34i			0.149896i
$658$		−	8.89248e33i		−	0.0526259i
$659$	3.95203e34			0.229484			0.114742	−	0.993395i	$-0.463396\pi$
$659$	3.95203e34			0.229484			0.114742	+	0.993395i	$0.463396\pi$
$660$	1.44959e35	+	2.21286e34i	0.825938	+	0.126082i
$661$	−1.83055e35			−1.02344			−0.511720	−	0.859152i	$-0.670992\pi$
$661$	−1.83055e35			−1.02344			−0.511720	+	0.859152i	$0.670992\pi$
$662$			7.05789e34i			0.387213i
$663$		−	6.04712e34i		−	0.325559i
$664$	−1.41578e35			−0.747989
$665$	3.18023e34	+	4.85473e33i	0.164888	+	0.0251707i
$666$	−7.14686e34			−0.363653
$667$		−	3.65307e35i		−	1.82425i
$668$		−	1.62761e35i		−	0.797707i
$669$	9.99472e34			0.480778
$670$	7.76597e33	−	5.08733e34i	0.0366658	−	0.240190i
$671$	8.50832e34			0.394287
$672$		−	8.48915e34i		−	0.386143i
$673$		−	2.04061e35i		−	0.911111i	−0.890207	−	0.455556i	$-0.849441\pi$
$673$		−	2.04061e35i		−	0.911111i	0.890207	−	0.455556i	$-0.150559\pi$
$674$	−9.09832e34			−0.398761
$675$	−6.66017e34	+	2.13063e35i	−0.286542	+	0.916667i
$676$	1.55993e35			0.658826
$677$			3.54375e35i			1.46928i	0.678456	+	0.734641i	$0.262650\pi$
$677$			3.54375e35i			1.46928i	−0.678456	+	0.734641i	$0.737350\pi$
$678$		−	7.03151e34i		−	0.286205i
$679$	2.30751e35			0.922085
$680$	2.85672e34	−	1.87137e35i	0.112074	−	0.734174i
$681$	−4.03825e34			−0.155544
$682$			1.16240e35i			0.439592i
$683$			2.42881e35i			0.901852i	0.892561	+	0.450926i	$0.148906\pi$
$683$			2.42881e35i			0.901852i	−0.892561	+	0.450926i	$0.851094\pi$
$684$	−3.53382e34			−0.128838
$685$	−3.32572e35	−	5.07682e34i	−1.19057	−	0.181744i
$686$	1.07420e35			0.377603
$687$			2.63895e35i			0.910902i
$688$		−	1.96453e35i		−	0.665892i
$689$	−4.97617e32			−0.00165636
$690$	−1.08859e35	−	1.66177e34i	−0.355837	−	0.0543197i
$691$	2.57346e34			0.0826116			0.0413058	−	0.999147i	$-0.486848\pi$
$691$	2.57346e34			0.0826116			0.0413058	+	0.999147i	$0.486848\pi$
$692$		−	4.65123e34i		−	0.146636i
$693$			2.71505e35i			0.840644i
$694$	−7.39826e34			−0.224976
$695$	−3.62969e34	+	2.37774e35i	−0.108408	+	0.710156i
$696$	1.31103e35			0.384589
$697$			1.37661e35i			0.396643i
$698$			3.61760e34i			0.102383i
$699$	−1.45055e35			−0.403245
$700$	−7.29256e34	+	2.33294e35i	−0.199138	+	0.637057i
$701$	2.69685e35			0.723405			0.361702	−	0.932294i	$-0.382196\pi$
$701$	2.69685e35			0.723405			0.361702	+	0.932294i	$0.382196\pi$
$702$			6.36057e34i			0.167603i
$703$		−	1.31955e35i		−	0.341574i
$704$	−2.21468e35			−0.563186
$705$	−6.88996e33	+	4.51347e34i	−0.0172129	+	0.112758i
$706$	−8.99010e34			−0.220651
$707$		−	5.58005e35i		−	1.34554i
$708$		−	4.29516e34i		−	0.101757i
$709$	6.58497e35			1.53277			0.766383	−	0.642384i	$-0.222055\pi$
$709$	6.58497e35			1.53277			0.766383	+	0.642384i	$0.222055\pi$
$710$	1.49216e35	+	2.27783e34i	0.341260	+	0.0520945i
$711$	3.89045e35			0.874237
$712$		−	1.11582e35i		−	0.246374i
$713$			6.28217e35i			1.36298i
$714$	−8.11553e34			−0.173017
$715$	−3.89825e35	−	5.95081e34i	−0.816665	−	0.124667i
$716$	2.44314e35			0.502963
$717$			2.06428e35i			0.417619i
$718$		−	1.18060e35i		−	0.234718i
$719$	−3.88717e35			−0.759492			−0.379746	−	0.925091i	$-0.623989\pi$
$719$	−3.88717e35			−0.759492			−0.379746	+	0.925091i	$0.623989\pi$
$720$	3.41047e34	−	2.23413e35i	0.0654874	−	0.428994i
$721$	4.85825e35			0.916831
$722$		−	1.79253e35i		−	0.332469i
$723$		−	5.74495e35i		−	1.04727i
$724$	−8.21172e35			−1.47130
$725$	−5.52138e35	−	1.72593e35i	−0.972349	−	0.303948i
$726$	2.01368e35			0.348564
$727$		−	9.07249e35i		−	1.54364i	−0.635840	−	0.771821i	$-0.719346\pi$
$727$		−	9.07249e35i		−	1.54364i	0.635840	−	0.771821i	$-0.280654\pi$
$728$			1.48968e35i			0.249144i
$729$	−2.88995e35			−0.475113
$730$	−7.31009e33	+	4.78868e34i	−0.0118137	+	0.0773892i
$731$	−7.31358e35			−1.16188
$732$			7.71529e34i			0.120494i
$733$		−	5.01082e35i		−	0.769323i	−0.923058	−	0.384662i	$-0.874318\pi$
$733$		−	5.01082e35i		−	0.769323i	0.923058	−	0.384662i	$-0.125682\pi$
$734$	1.18489e35			0.178846
$735$	−1.61829e35	−	2.47038e34i	−0.240140	−	0.0366582i
$736$	1.08332e36			1.58046
$737$			8.01900e35i			1.15021i
$738$		−	5.80287e34i		−	0.0818348i
$739$	2.61583e35			0.362706			0.181353	−	0.983418i	$-0.441952\pi$
$739$	2.61583e35			0.362706			0.181353	+	0.983418i	$0.441952\pi$
$740$	9.91087e35	+	1.51293e35i	1.35119	+	0.206263i
$741$	−4.70645e34			−0.0630908
$742$			6.67826e32i			0.000880267i
$743$		−	6.51807e35i		−	0.844810i	−0.906407	−	0.422405i	$-0.861186\pi$
$743$		−	6.51807e35i		−	0.844810i	0.906407	−	0.422405i	$-0.138814\pi$
$744$	−2.25457e35			−0.287344
$745$	5.34478e34	−	3.50125e35i	0.0669848	−	0.438803i
$746$	−5.02579e35			−0.619397
$747$			6.29236e35i			0.762617i
$748$			1.37908e36i			1.64369i
$749$	5.16715e35			0.605659
$750$	−7.65482e34	+	1.56682e35i	−0.0882408	+	0.180615i
$751$	−8.22563e35			−0.932545			−0.466272	−	0.884641i	$-0.654403\pi$
$751$	−8.22563e35			−0.932545			−0.466272	+	0.884641i	$0.654403\pi$
$752$		−	1.15341e35i		−	0.128606i
$753$			9.61249e35i			1.05414i
$754$	−1.64829e35			−0.177784
$755$	5.44026e34	−	3.56380e35i	0.0577142	−	0.378073i
$756$	−6.14329e35			−0.641030
$757$		−	1.14364e34i		−	0.0117379i	−0.999983	−	0.00586895i	$-0.998132\pi$
$757$		−	1.14364e34i		−	0.0117379i	0.999983	−	0.00586895i	$-0.00186816\pi$
$758$			3.20379e35i			0.323444i
$759$	1.71591e36			1.70401
$760$	−1.45648e35	−	2.22337e34i	−0.142277	−	0.0217191i
$761$	9.84364e35			0.945905			0.472953	−	0.881088i	$-0.343188\pi$
$761$	9.84364e35			0.945905			0.472953	+	0.881088i	$0.343188\pi$
$762$		−	8.74432e34i		−	0.0826588i
$763$		−	3.44933e35i		−	0.320759i
$764$	−2.81029e34			−0.0257089
$765$	−8.31722e35	−	1.26965e35i	−0.748532	−	0.114266i
$766$	−1.95193e35			−0.172824
$767$			1.15505e35i			0.100614i
$768$			6.19549e33i			0.00530959i
$769$	−5.41990e35			−0.456995			−0.228498	−	0.973544i	$-0.573381\pi$
$769$	−5.41990e35			−0.456995			−0.228498	+	0.973544i	$0.573381\pi$
$770$	−7.98627e34	+	5.23164e35i	−0.0662537	+	0.434014i
$771$	−1.96837e35			−0.160667
$772$			1.63916e36i			1.31645i
$773$		−	9.78778e34i		−	0.0773465i	−0.999252	−	0.0386732i	$-0.987687\pi$
$773$		−	9.78778e34i		−	0.0773465i	0.999252	−	0.0386732i	$-0.0123131\pi$
$774$	3.08292e35			0.239718
$775$	9.49509e35	+	2.96808e35i	0.726487	+	0.227093i
$776$	−1.05679e36			−0.795642
$777$		−	9.19325e35i		−	0.681093i
$778$		−	7.47875e34i		−	0.0545236i
$779$	1.07141e35			0.0768663
$780$	5.39616e34	−	3.53491e35i	0.0380980	−	0.249572i
$781$	−2.35204e36			−1.63421
$782$		−	1.03564e36i		−	0.708147i
$783$		−	1.45393e36i		−	0.978414i
$784$	4.13552e35			0.273892
$785$	2.43191e36	+	3.71239e35i	1.58517	+	0.241982i
$786$	4.89460e35			0.314004
$787$		−	7.88622e35i		−	0.497949i	−0.968510	−	0.248975i	$-0.919906\pi$
$787$		−	7.88622e35i		−	0.497949i	0.968510	−	0.248975i	$-0.0800936\pi$
$788$		−	1.50276e36i		−	0.933922i
$789$	1.90068e35			0.116264
$790$	7.49651e35	+	1.14437e35i	0.451357	+	0.0689012i
$791$	−1.82632e36			−1.08236
$792$		−	1.24344e36i		−	0.725369i
$793$		−	2.07480e35i		−	0.119141i
$794$	−8.99755e35			−0.508590
$795$	5.17437e32	−	3.38962e33i	0.000287917	−	0.00188609i
$796$	6.49373e35			0.355697
$797$			7.07299e35i			0.381394i	0.981649	+	0.190697i	$0.0610749\pi$
$797$			7.07299e35i			0.381394i	−0.981649	+	0.190697i	$0.938925\pi$
$798$			6.31628e34i			0.0335294i
$799$	−4.29392e35			−0.224398
$800$	5.11825e35	−	1.63736e36i	0.263328	−	0.842404i
$801$	−4.95921e35			−0.251192
$802$			6.72269e35i			0.335246i
$803$		−	7.54826e35i		−	0.370597i
$804$	−7.27158e35			−0.351502
$805$	−4.31617e35	+	2.82743e36i	−0.205423	+	1.34569i
$806$	2.83457e35			0.132831
$807$			1.95171e35i			0.0900526i
$808$			2.55555e36i			1.16103i
$809$	3.00518e35			0.134435			0.0672177	−	0.997738i	$-0.478588\pi$
$809$	3.00518e35			0.134435			0.0672177	+	0.997738i	$0.478588\pi$
$810$	9.09713e34	+	1.38871e34i	0.0400721	+	0.00611713i
$811$	1.26185e36			0.547327			0.273664	−	0.961825i	$-0.411765\pi$
$811$	1.26185e36			0.547327			0.273664	+	0.961825i	$0.411765\pi$
$812$		−	1.59199e36i		−	0.679969i
$813$			1.62011e36i			0.681416i
$814$	2.17073e36			0.899084
$815$	−7.10905e35	−	1.08522e35i	−0.289962	−	0.0442637i
$816$	−1.05263e36			−0.422815
$817$			5.69212e35i			0.225164i
$818$		−	1.07042e36i		−	0.417002i
$819$	6.62079e35			0.254016
$820$	−1.22842e35	+	8.04710e35i	−0.0464165	+	0.304065i
$821$	−4.10231e35			−0.152665			−0.0763324	−	0.997082i	$-0.524321\pi$
$821$	−4.10231e35			−0.152665			−0.0763324	+	0.997082i	$0.524321\pi$
$822$		−	6.60523e35i		−	0.242097i
$823$			4.60163e36i			1.66117i	0.556893	+	0.830584i	$0.311993\pi$
$823$			4.60163e36i			1.66117i	−0.556893	+	0.830584i	$0.688007\pi$
$824$	−2.22498e36			−0.791109
$825$	8.10702e35	−	2.59349e36i	0.283914	−	0.908260i
$826$	1.55014e35			0.0534711
$827$			4.81186e36i			1.63491i	0.575991	+	0.817456i	$0.304616\pi$
$827$			4.81186e36i			1.63491i	−0.575991	+	0.817456i	$0.695384\pi$
$828$		−	3.14179e36i		−	1.05147i
$829$	3.18080e36			1.04859			0.524294	−	0.851538i	$-0.324329\pi$
$829$	3.18080e36			1.04859			0.524294	+	0.851538i	$0.324329\pi$
$830$	−1.85089e35	+	1.21248e36i	−0.0601041	+	0.393729i
$831$	−3.06659e35			−0.0980940
$832$			5.40060e35i			0.170177i
$833$		−	1.53957e36i		−	0.477901i
$834$	−4.72244e35			−0.144408
$835$	−2.98145e36	−	4.55129e35i	−0.898146	−	0.137105i
$836$	1.07333e36			0.318534
$837$			2.50032e36i			0.731018i
$838$		−	1.27390e36i		−	0.366931i
$839$	−2.92525e36			−0.830116			−0.415058	−	0.909795i	$-0.636239\pi$
$839$	−2.92525e36			−0.830116			−0.415058	+	0.909795i	$0.636239\pi$
$840$	−1.01472e36	−	1.54901e35i	−0.283698	−	0.0433074i
$841$	1.37400e35			0.0378475
$842$			8.74591e35i			0.237358i
$843$			2.75778e36i			0.737420i
$844$	3.20501e36			0.844400
$845$	4.36204e35	−	2.85748e36i	0.113235	−	0.741778i
$846$	1.81003e35			0.0462975
$847$		−	5.23020e36i		−	1.31818i
$848$			8.66212e33i			0.00215118i
$849$	−2.83580e36			−0.693952
$850$	−1.56530e36	−	4.89299e35i	−0.377451	−	0.117988i
$851$	1.17317e37			2.78766
$852$		−	2.13282e36i		−	0.499412i
$853$		−	5.67373e36i		−	1.30920i	−0.755975	−	0.654600i	$-0.772837\pi$
$853$		−	5.67373e36i		−	1.30920i	0.755975	−	0.654600i	$-0.227163\pi$
$854$	−2.78447e35			−0.0633169
$855$	−9.88164e34	+	6.47325e35i	−0.0221438	+	0.145059i
$856$	−2.36645e36			−0.522607
$857$		−	5.81493e36i		−	1.26557i	−0.774330	−	0.632783i	$-0.781913\pi$
$857$		−	5.81493e36i		−	1.26557i	0.774330	−	0.632783i	$-0.218087\pi$
$858$		−	7.74234e35i		−	0.166066i
$859$	−2.94784e36			−0.623144			−0.311572	−	0.950222i	$-0.600856\pi$
$859$	−2.94784e36			−0.623144			−0.311572	+	0.950222i	$0.600856\pi$
$860$	−4.27523e36	−	6.52628e35i	−0.890694	−	0.135967i
$861$	7.46443e35			0.153270
$862$			2.45668e36i			0.497174i
$863$			3.06311e36i			0.610981i	0.952195	+	0.305491i	$0.0988205\pi$
$863$			3.06311e36i			0.610981i	−0.952195	+	0.305491i	$0.901180\pi$
$864$	4.31164e36			0.847658
$865$	−8.52012e35	−	1.30063e35i	−0.165099	−	0.0252029i
$866$	−9.03801e35			−0.172623
$867$			8.61758e35i			0.162236i
$868$			2.73773e36i			0.508036i
$869$	−1.18165e37			−2.16144
$870$	1.71394e35	−	1.12277e36i	0.0309034	−	0.202441i
$871$	1.95547e36			0.347556
$872$			1.57972e36i			0.276774i
$873$			4.69685e36i			0.811202i
$874$	−8.06032e35			−0.137233
$875$	4.06956e36	+	1.98821e36i	0.683041	+	0.333705i
$876$	6.84472e35			0.113254
$877$		−	4.68999e36i		−	0.765027i	−0.923950	−	0.382513i	$-0.875059\pi$
$877$		−	4.68999e36i		−	0.765027i	0.923950	−	0.382513i	$-0.124941\pi$
$878$			3.82765e35i			0.0615533i
$879$	2.66554e36			0.422594
$880$	−1.03587e36	+	6.78576e36i	−0.161909	+	1.06063i
$881$	5.55944e36			0.856707			0.428354	−	0.903611i	$-0.359094\pi$
$881$	5.55944e36			0.856707			0.428354	+	0.903611i	$0.359094\pi$
$882$			6.48983e35i			0.0985998i
$883$		−	6.59997e36i		−	0.988629i	−0.869283	−	0.494315i	$-0.835419\pi$
$883$		−	6.59997e36i		−	0.988629i	0.869283	−	0.494315i	$-0.164581\pi$
$884$	3.36296e36			0.496671
$885$	−7.86787e35	−	1.20106e35i	−0.114569	−	0.0174893i
$886$	1.92273e36			0.276055
$887$			7.82318e36i			1.10749i	0.832688	+	0.553743i	$0.186801\pi$
$887$			7.82318e36i			1.10749i	−0.832688	+	0.553743i	$0.813199\pi$
$888$			4.21032e36i			0.587696i
$889$	−2.27119e36			−0.312595
$890$	−9.55592e35	−	1.45874e35i	−0.129687	−	0.0197972i
$891$	−1.43395e36			−0.191895
$892$			5.55832e36i			0.733471i
$893$			3.34194e35i			0.0434866i
$894$	6.95386e35			0.0892292
$895$	6.83177e35	−	4.47535e36i	0.0864461	−	0.566290i
$896$	6.10182e36			0.761393
$897$		−	4.18434e36i		−	0.514898i
$898$		−	1.37414e36i		−	0.166754i
$899$	−6.47941e36			−0.775424
$900$	−4.74862e36	−	1.48438e36i	−0.560449	−	0.175191i
$901$	3.22474e34			0.00375348
$902$			1.76252e36i			0.202326i
$903$			3.96567e36i			0.448972i
$904$	8.36417e36			0.933937
$905$	−2.29625e36	+	1.50422e37i	−0.252878	+	1.65655i
$906$	7.07808e35			0.0768799
$907$		−	1.93438e36i		−	0.207229i	−0.994618	−	0.103615i	$-0.966959\pi$
$907$		−	1.93438e36i		−	0.207229i	0.994618	−	0.103615i	$-0.0330408\pi$
$908$		−	2.24577e36i		−	0.237297i
$909$	1.13580e37			1.18373
$910$	1.27576e36	+	1.94749e35i	0.131145	+	0.0200197i
$911$	−1.32299e37			−1.34146			−0.670728	−	0.741704i	$-0.734018\pi$
$911$	−1.32299e37			−1.34146			−0.670728	+	0.741704i	$0.734018\pi$
$912$			8.19260e35i			0.0819382i
$913$		−	1.91119e37i		−	1.88547i
$914$	−1.59721e36			−0.155430
$915$	1.41329e36	+	2.15743e35i	0.135665	+	0.0207097i
$916$	−1.46759e37			−1.38967
$917$		−	1.27129e37i		−	1.18749i
$918$		−	4.12188e36i		−	0.379806i
$919$	−1.20222e36			−0.109280			−0.0546401	−	0.998506i	$-0.517401\pi$
$919$	−1.20222e36			−0.109280			−0.0546401	+	0.998506i	$0.517401\pi$
$920$	1.97672e36	−	1.29491e37i	0.177254	−	1.16116i
$921$	−1.04987e37			−0.928729
$922$			4.10235e36i			0.358011i
$923$			5.73557e36i			0.493805i
$924$	7.47785e36			0.635151
$925$	5.54276e36	−	1.77317e37i	0.464467	−	1.48586i
$926$	3.81844e35			0.0315681
$927$			9.88881e36i			0.806580i
$928$			1.11733e37i			0.899148i
$929$	−1.76310e36			−0.139985			−0.0699924	−	0.997548i	$-0.522298\pi$
$929$	−1.76310e36			−0.139985			−0.0699924	+	0.997548i	$0.522298\pi$
$930$	−2.94746e35	+	1.93082e36i	−0.0230893	+	0.151253i
$931$	−1.19824e36			−0.0926135
$932$		−	8.06689e36i		−	0.615187i
$933$		−	2.33110e36i		−	0.175405i
$934$	−3.44507e36			−0.255778
$935$	2.52620e37	+	3.85634e36i	1.85065	+	0.282507i
$936$	−3.03219e36			−0.219183
$937$		−	8.36573e36i		−	0.596704i	−0.954456	−	0.298352i	$-0.903563\pi$
$937$		−	8.36573e36i		−	0.596704i	0.954456	−	0.298352i	$-0.0964370\pi$
$938$		−	2.62434e36i		−	0.184707i
$939$	−4.92932e36			−0.342348
$940$	−2.51006e36	−	3.83169e35i	−0.172023	−	0.0262598i
$941$	1.88960e37			1.27791			0.638953	−	0.769246i	$-0.279368\pi$
$941$	1.88960e37			1.27791			0.638953	+	0.769246i	$0.279368\pi$
$942$			4.83003e36i			0.322339i
$943$			9.52550e36i			0.627323i
$944$	2.01062e36			0.130671
$945$	−1.71785e36	+	1.12533e37i	−0.110176	+	0.721741i
$946$	−9.36382e36			−0.592671
$947$			2.30050e37i			1.43697i	0.695544	+	0.718484i	$0.255163\pi$
$947$			2.30050e37i			1.43697i	−0.695544	+	0.718484i	$0.744837\pi$
$948$		−	1.07152e37i		−	0.660533i
$949$	−1.84068e36			−0.111983
$950$	−3.80819e35	+	1.21827e36i	−0.0228651	+	0.0731471i
$951$	−8.32586e36			−0.493370
$952$		−	9.65363e36i		−	0.564585i
$953$			1.27736e37i			0.737312i	0.929566	+	0.368656i	$0.120182\pi$
$953$			1.27736e37i			0.737312i	−0.929566	+	0.368656i	$0.879818\pi$
$954$	−1.35934e34			−0.000774413
$955$	−7.85842e34	+	5.14789e35i	−0.00441869	+	0.0289459i
$956$	−1.14800e37			−0.637117
$957$			1.76979e37i			0.969441i
$958$		−	7.98593e36i		−	0.431774i
$959$	−1.71560e37			−0.915552
$960$	−3.67873e36	−	5.61570e35i	−0.193779	−	0.0295810i
$961$	−8.09018e36			−0.420645
$962$		−	5.29343e36i		−	0.271674i
$963$			1.05176e37i			0.532827i
$964$	3.19492e37			1.59771
$965$	3.00262e37	+	4.58360e36i	1.48221	+	0.226264i
$966$	−5.61558e36			−0.273641
$967$		−	1.55346e37i		−	0.747255i	−0.927579	−	0.373627i	$-0.878114\pi$
$967$		−	1.55346e37i		−	0.747255i	0.927579	−	0.373627i	$-0.121886\pi$
$968$			2.39533e37i			1.13742i
$969$	3.04995e36			0.142970
$970$	−1.38157e36	+	9.05038e36i	−0.0639332	+	0.418813i
$971$	−1.12959e37			−0.516039			−0.258019	−	0.966140i	$-0.583070\pi$
$971$	−1.12959e37			−0.516039			−0.258019	+	0.966140i	$0.583070\pi$
$972$		−	1.99976e37i		−	0.901882i
$973$			1.22657e37i			0.546114i
$974$	7.92828e36			0.348491
$975$	−6.32436e36	−	1.97694e36i	−0.274447	−	0.0857897i
$976$	−3.61164e36			−0.154732
$977$		−	2.48617e35i		−	0.0105160i	−0.999986	−	0.00525799i	$-0.998326\pi$
$977$		−	2.48617e35i		−	0.0105160i	0.999986	−	0.00525799i	$-0.00167368\pi$
$978$		−	1.41193e36i		−	0.0589628i
$979$	1.50627e37			0.621040
$980$	1.37384e36	−	8.99974e36i	0.0559256	−	0.366357i
$981$	7.02100e36			0.282187
$982$		−	4.85661e36i		−	0.192726i
$983$		−	3.35550e37i		−	1.31474i	−0.753569	−	0.657368i	$-0.771670\pi$
$983$		−	3.35550e37i		−	1.31474i	0.753569	−	0.657368i	$-0.228330\pi$
$984$	−3.41856e36			−0.132253
$985$	−2.75275e37	−	4.20217e36i	−1.05151	−	0.160517i
$986$	1.06815e37			0.402877
$987$			2.32831e36i			0.0867114i
$988$		−	2.61738e36i		−	0.0962509i
$989$	−5.06067e37			−1.83761
$990$	−1.06488e37	−	1.62558e36i	−0.381822	−	0.0582865i
$991$	2.43897e37			0.863547			0.431774	−	0.901982i	$-0.357888\pi$
$991$	2.43897e37			0.863547			0.431774	+	0.901982i	$0.357888\pi$
$992$		−	1.92147e37i		−	0.671795i
$993$		−	1.84796e37i		−	0.638009i
$994$	7.69741e36			0.262431
$995$	1.81584e36	−	1.18952e37i	0.0611350	−	0.400483i
$996$	1.73306e37			0.576197
$997$			1.09989e37i			0.361128i	0.983563	+	0.180564i	$0.0577923\pi$
$997$			1.09989e37i			0.361128i	−0.983563	+	0.180564i	$0.942208\pi$
$998$		−	5.44958e36i		−	0.176698i
$999$	4.66925e37			1.49513

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.26.b.a.4.7	yes	12
3.2	odd	2		45.26.b.b.19.6		12
5.2	odd	4		25.26.a.f.1.6		12
5.3	odd	4		25.26.a.f.1.7		12
5.4	even	2	inner	5.26.b.a.4.6	✓	12
15.14	odd	2		45.26.b.b.19.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.26.b.a.4.6	✓	12	5.4	even	2	inner
5.26.b.a.4.7	yes	12	1.1	even	1	trivial
25.26.a.f.1.6		12	5.2	odd	4
25.26.a.f.1.7		12	5.3	odd	4
45.26.b.b.19.6		12	3.2	odd	2
45.26.b.b.19.7		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+2023.27i q^{2} -529751. i q^{3} +2.94608e7 q^{4} +(8.23814e7 - 5.39663e8i) q^{5} +1.07183e9 q^{6} -2.78390e10i q^{7} +1.27497e11i q^{8} +5.66653e11 q^{9} +(1.09188e12 + 1.66680e11i) q^{10} -1.72111e13 q^{11} -1.56069e13i q^{12} +4.19700e13i q^{13} +5.63258e13 q^{14} +(-2.85887e14 - 4.36416e13i) q^{15} +7.30580e14 q^{16} -2.71981e15i q^{17} +1.14649e15i q^{18} -2.11681e15 q^{19} +(2.42702e15 - 1.58989e16i) q^{20} -1.47477e16 q^{21} -3.48226e16i q^{22} -1.88198e17i q^{23} +6.75416e16 q^{24} +(-2.84450e17 - 8.89165e16i) q^{25} -8.49167e16 q^{26} -7.49036e17i q^{27} -8.20159e17i q^{28} +1.94107e18 q^{29} +(8.82988e16 - 5.78427e17i) q^{30} -3.33805e18 q^{31} +5.75625e18i q^{32} +9.11757e18i q^{33} +5.50290e18 q^{34} +(-1.50237e19 - 2.29341e18i) q^{35} +1.66940e19 q^{36} +6.23367e19i q^{37} -4.28289e18i q^{38} +2.22337e19 q^{39} +(6.88054e19 + 1.05034e19i) q^{40} -5.06141e19 q^{41} -2.98386e19i q^{42} -2.68901e20i q^{43} -5.07052e20 q^{44} +(4.66817e19 - 3.05802e20i) q^{45} +3.80776e20 q^{46} -1.57876e20i q^{47} -3.87025e20i q^{48} +5.66060e20 q^{49} +(1.79902e20 - 5.75519e20i) q^{50} -1.44082e21 q^{51} +1.23647e21i q^{52} +1.18565e19i q^{53} +1.51550e21 q^{54} +(-1.41787e21 + 9.28818e21i) q^{55} +3.54938e21 q^{56} +1.12138e21i q^{57} +3.92731e21i q^{58} +2.75209e21 q^{59} +(-8.42246e21 - 1.28572e21i) q^{60} -4.94352e21 q^{61} -6.75379e21i q^{62} -1.57750e22i q^{63} +1.28678e22 q^{64} +(2.26497e22 + 3.45755e21i) q^{65} -1.84473e22 q^{66} -4.65921e22i q^{67} -8.01277e22i q^{68} -9.96982e22 q^{69} +(4.64020e21 - 3.03970e22i) q^{70} +1.36659e23 q^{71} +7.22465e22i q^{72} +4.38570e22i q^{73} -1.26124e23 q^{74} +(-4.71036e22 + 1.50688e23i) q^{75} -6.23630e22 q^{76} +4.79138e23i q^{77} +4.49847e22i q^{78} +6.86566e23 q^{79} +(6.01862e22 - 3.94267e23i) q^{80} +8.33158e22 q^{81} -1.02406e23i q^{82} +1.11044e24i q^{83} -4.34480e23 q^{84} +(-1.46778e24 - 2.24062e23i) q^{85} +5.44059e23 q^{86} -1.02828e24i q^{87} -2.19436e24i q^{88} -8.75176e23 q^{89} +(6.18720e23 + 9.44496e22i) q^{90} +1.16840e24 q^{91} -5.54448e24i q^{92} +1.76834e24i q^{93} +3.19426e23 q^{94} +(-1.74386e23 + 1.14237e24i) q^{95} +3.04938e24 q^{96} +8.28877e24i q^{97} +1.14529e24i q^{98} -9.75269e24 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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