LMFDB - Embedded newform 25.9.c.c.7.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,9,Mod(7,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("25.7");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	25.c (of order $4$, degree $2$, 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:	$10.1844652515$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
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} - 4 x^{11} + 8 x^{10} + 124 x^{9} + 1665 x^{8} - 2456 x^{7} + 4192 x^{6} + 50576 x^{5} + \cdots + 1000000 $ x^12 - 4x^11 + 8x^10 + 124x^9 + 1665x^8 - 2456x^7 + 4192x^6 + 50576x^5 + 221184x^4 + 133760x^3 + 3200x^2 - 80000*x + 1000000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{6}\cdot 5^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.3
Root			$-1.51110 - 1.51110i$ of defining polynomial
Character	$\chi$	$=$	25.7
Dual form			25.9.c.c.18.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0371264 - 0.0371264i) q^{2} +(-36.2471 + 36.2471i) q^{3} -255.997i q^{4} +2.69145 q^{6} +(1325.17 + 1325.17i) q^{7} +(-19.0086 + 19.0086i) q^{8} +3933.30i q^{9} +O(q^{10})$	\(q+(-0.0371264 - 0.0371264i) q^{2} +(-36.2471 + 36.2471i) q^{3} -255.997i q^{4} +2.69145 q^{6} +(1325.17 + 1325.17i) q^{7} +(-19.0086 + 19.0086i) q^{8} +3933.30i q^{9} -18438.9 q^{11} +(9279.16 + 9279.16i) q^{12} +(-25997.0 + 25997.0i) q^{13} -98.3973i q^{14} -65533.9 q^{16} +(111044. + 111044. i) q^{17} +(146.029 - 146.029i) q^{18} +43496.4i q^{19} -96066.9 q^{21} +(684.569 + 684.569i) q^{22} +(-154135. + 154135. i) q^{23} -1378.01i q^{24} +1930.35 q^{26} +(-380388. - 380388. i) q^{27} +(339239. - 339239. i) q^{28} -154042. i q^{29} +1.29801e6 q^{31} +(7299.24 + 7299.24i) q^{32} +(668356. - 668356. i) q^{33} -8245.30i q^{34} +1.00691e6 q^{36} +(-1.57267e6 - 1.57267e6i) q^{37} +(1614.86 - 1614.86i) q^{38} -1.88463e6i q^{39} -1.66047e6 q^{41} +(3566.62 + 3566.62i) q^{42} +(-1.65197e6 + 1.65197e6i) q^{43} +4.72030e6i q^{44} +11445.0 q^{46} +(3.28188e6 + 3.28188e6i) q^{47} +(2.37541e6 - 2.37541e6i) q^{48} -2.25267e6i q^{49} -8.05002e6 q^{51} +(6.65516e6 + 6.65516e6i) q^{52} +(-6.85792e6 + 6.85792e6i) q^{53} +28244.9i q^{54} -50379.2 q^{56} +(-1.57662e6 - 1.57662e6i) q^{57} +(-5719.02 + 5719.02i) q^{58} -4.67754e6i q^{59} -2.80570e6 q^{61} +(-48190.4 - 48190.4i) q^{62} +(-5.21227e6 + 5.21227e6i) q^{63} +1.67761e7i q^{64} -49627.3 q^{66} +(-1.35403e7 - 1.35403e7i) q^{67} +(2.84269e7 - 2.84269e7i) q^{68} -1.11739e7i q^{69} +3.78193e7 q^{71} +(-74766.5 - 74766.5i) q^{72} +(-1.08424e7 + 1.08424e7i) q^{73} +116775. i q^{74} +1.11350e7 q^{76} +(-2.44346e7 - 2.44346e7i) q^{77} +(-69969.6 + 69969.6i) q^{78} -5.10715e7i q^{79} +1.76954e6 q^{81} +(61647.4 + 61647.4i) q^{82} +(1.65526e7 - 1.65526e7i) q^{83} +2.45929e7i q^{84} +122663. q^{86} +(5.58357e6 + 5.58357e6i) q^{87} +(350497. - 350497. i) q^{88} +7.86587e7i q^{89} -6.89007e7 q^{91} +(3.94581e7 + 3.94581e7i) q^{92} +(-4.70491e7 + 4.70491e7i) q^{93} -243689. i q^{94} -529153. q^{96} +(3.88232e7 + 3.88232e7i) q^{97} +(-83633.5 + 83633.5i) q^{98} -7.25256e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6396 q^{6}+O(q^{10}) $ 12 * q - 6396 * q^6	$ 12 q - 6396 q^{6} - 118116 q^{11} - 1204068 q^{16} - 1365456 q^{21} + 5376024 q^{26} + 3223704 q^{31} + 14477592 q^{36} + 10940364 q^{41} - 51272856 q^{46} - 47621676 q^{51} - 64717200 q^{56} - 23597616 q^{61} + 264735828 q^{66} - 47870856 q^{71} + 432845700 q^{76} + 3008052 q^{81} - 105341616 q^{86} - 64237536 q^{91} - 1580181156 q^{96}+O(q^{100}) $ 12 * q - 6396 * q^6 - 118116 * q^11 - 1204068 * q^16 - 1365456 * q^21 + 5376024 * q^26 + 3223704 * q^31 + 14477592 * q^36 + 10940364 * q^41 - 51272856 * q^46 - 47621676 * q^51 - 64717200 * q^56 - 23597616 * q^61 + 264735828 * q^66 - 47870856 * q^71 + 432845700 * q^76 + 3008052 * q^81 - 105341616 * q^86 - 64237536 * q^91 - 1580181156 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.0371264	−	0.0371264i	−0.00232040	−	0.00232040i	0.705946	−	0.708266i	$-0.250522\pi$
$2$	−0.0371264	−	0.0371264i	−0.00232040	−	0.00232040i	−0.708266	+	0.705946i	$0.750522\pi$
$3$	−36.2471	+	36.2471i	−0.447495	+	0.447495i	−0.894521	−	0.447026i	$-0.852483\pi$
$3$	−36.2471	+	36.2471i	−0.447495	+	0.447495i	0.447026	+	0.894521i	$0.352483\pi$
$4$		−	255.997i		−	0.999989i
$5$		0			0
$5$		0			0
$6$	2.69145			0.00207673
$7$	1325.17	+	1325.17i	0.551923	+	0.551923i	0.926995	−	0.375073i	$-0.122382\pi$
$7$	1325.17	+	1325.17i	0.551923	+	0.551923i	−0.375073	+	0.926995i	$0.622382\pi$
$8$	−19.0086	+	19.0086i	−0.00464077	+	0.00464077i
$9$			3933.30i			0.599496i
$10$		0			0
$11$	−18438.9			−1.25940			−0.629700	−	0.776838i	$-0.716822\pi$
$11$	−18438.9			−1.25940			−0.629700	+	0.776838i	$0.716822\pi$
$12$	9279.16	+	9279.16i	0.447490	+	0.447490i
$13$	−25997.0	+	25997.0i	−0.910228	+	0.910228i	−0.996290	−	0.0860622i	$-0.972572\pi$
$13$	−25997.0	+	25997.0i	−0.910228	+	0.910228i	0.0860622	+	0.996290i	$0.472572\pi$
$14$		−	98.3973i		−	0.00256136i
$15$		0			0
$16$	−65533.9			−0.999968
$17$	111044.	+	111044.i	1.32953	+	1.32953i	0.905779	+	0.423751i	$0.139287\pi$
$17$	111044.	+	111044.i	1.32953	+	1.32953i	0.423751	+	0.905779i	$0.360713\pi$
$18$	146.029	−	146.029i	0.00139107	−	0.00139107i
$19$			43496.4i			0.333763i	0.985977	+	0.166882i	$0.0533698\pi$
$19$			43496.4i			0.333763i	−0.985977	+	0.166882i	$0.946630\pi$
$20$		0			0
$21$	−96066.9			−0.493965
$22$	684.569	+	684.569i	0.00292231	+	0.00292231i
$23$	−154135.	+	154135.i	−0.550795	+	0.550795i	−0.926670	−	0.375875i	$-0.877342\pi$
$23$	−154135.	+	154135.i	−0.550795	+	0.550795i	0.375875	+	0.926670i	$0.377342\pi$
$24$		−	1378.01i		−	0.00415345i
$25$		0			0
$26$	1930.35			0.00422418
$27$	−380388.	−	380388.i	−0.715767	−	0.715767i
$28$	339239.	−	339239.i	0.551917	−	0.551917i
$29$		−	154042.i		−	0.217795i	−0.994053	−	0.108897i	$-0.965268\pi$
$29$		−	154042.i		−	0.217795i	0.994053	−	0.108897i	$-0.0347320\pi$
$30$		0			0
$31$	1.29801e6			1.40550			0.702750	−	0.711437i	$-0.251955\pi$
$31$	1.29801e6			1.40550			0.702750	+	0.711437i	$0.251955\pi$
$32$	7299.24	+	7299.24i	0.00696110	+	0.00696110i
$33$	668356.	−	668356.i	0.563575	−	0.563575i
$34$		−	8245.30i		−	0.00617008i
$35$		0			0
$36$	1.00691e6			0.599490
$37$	−1.57267e6	−	1.57267e6i	−0.839131	−	0.839131i	0.149613	−	0.988745i	$-0.452197\pi$
$37$	−1.57267e6	−	1.57267e6i	−0.839131	−	0.839131i	−0.988745	+	0.149613i	$0.952197\pi$
$38$	1614.86	−	1614.86i	0.000774465	−	0.000774465i
$39$		−	1.88463e6i		−	0.814645i
$40$		0			0
$41$	−1.66047e6			−0.587620			−0.293810	−	0.955864i	$-0.594923\pi$
$41$	−1.66047e6			−0.587620			−0.293810	+	0.955864i	$0.594923\pi$
$42$	3566.62	+	3566.62i	0.00114620	+	0.00114620i
$43$	−1.65197e6	+	1.65197e6i	−0.483200	+	0.483200i	−0.906152	−	0.422952i	$-0.860994\pi$
$43$	−1.65197e6	+	1.65197e6i	−0.483200	+	0.483200i	0.422952	+	0.906152i	$0.360994\pi$
$44$			4.72030e6i			1.25939i
$45$		0			0
$46$	11445.0			0.00255613
$47$	3.28188e6	+	3.28188e6i	0.672560	+	0.672560i	0.958306	−	0.285745i	$-0.0922411\pi$
$47$	3.28188e6	+	3.28188e6i	0.672560	+	0.672560i	−0.285745	+	0.958306i	$0.592241\pi$
$48$	2.37541e6	−	2.37541e6i	0.447481	−	0.447481i
$49$		−	2.25267e6i		−	0.390763i
$50$		0			0
$51$	−8.05002e6			−1.18992
$52$	6.65516e6	+	6.65516e6i	0.910218	+	0.910218i
$53$	−6.85792e6	+	6.85792e6i	−0.869138	+	0.869138i	−0.992377	−	0.123239i	$-0.960672\pi$
$53$	−6.85792e6	+	6.85792e6i	−0.869138	+	0.869138i	0.123239	+	0.992377i	$0.460672\pi$
$54$			28244.9i			0.00332173i
$55$		0			0
$56$	−50379.2			−0.00512270
$57$	−1.57662e6	−	1.57662e6i	−0.149357	−	0.149357i
$58$	−5719.02	+	5719.02i	−0.000505371	+	0.000505371i
$59$		−	4.67754e6i		−	0.386019i	−0.981197	−	0.193010i	$-0.938175\pi$
$59$		−	4.67754e6i		−	0.386019i	0.981197	−	0.193010i	$-0.0618249\pi$
$60$		0			0
$61$	−2.80570e6			−0.202639			−0.101319	−	0.994854i	$-0.532306\pi$
$61$	−2.80570e6			−0.202639			−0.101319	+	0.994854i	$0.532306\pi$
$62$	−48190.4	−	48190.4i	−0.00326132	−	0.00326132i
$63$	−5.21227e6	+	5.21227e6i	−0.330876	+	0.330876i
$64$			1.67761e7i			0.999935i
$65$		0			0
$66$	−49627.3			−0.00261544
$67$	−1.35403e7	−	1.35403e7i	−0.671937	−	0.671937i	0.286226	−	0.958162i	$-0.407599\pi$
$67$	−1.35403e7	−	1.35403e7i	−0.671937	−	0.671937i	−0.958162	+	0.286226i	$0.907599\pi$
$68$	2.84269e7	−	2.84269e7i	1.32952	−	1.32952i
$69$		−	1.11739e7i		−	0.492956i
$70$		0			0
$71$	3.78193e7			1.48826			0.744132	−	0.668033i	$-0.232863\pi$
$71$	3.78193e7			1.48826			0.744132	+	0.668033i	$0.232863\pi$
$72$	−74766.5	−	74766.5i	−0.00278213	−	0.00278213i
$73$	−1.08424e7	+	1.08424e7i	−0.381799	+	0.381799i	−0.871750	−	0.489951i	$-0.837015\pi$
$73$	−1.08424e7	+	1.08424e7i	−0.381799	+	0.381799i	0.489951	+	0.871750i	$0.337015\pi$
$74$			116775.i			0.00389424i
$75$		0			0
$76$	1.11350e7			0.333760
$77$	−2.44346e7	−	2.44346e7i	−0.695091	−	0.695091i
$78$	−69969.6	+	69969.6i	−0.00189030	+	0.00189030i
$79$		−	5.10715e7i		−	1.31120i	−0.755107	−	0.655602i	$-0.772415\pi$
$79$		−	5.10715e7i		−	1.31120i	0.755107	−	0.655602i	$-0.227585\pi$
$80$		0			0
$81$	1.76954e6			0.0411075
$82$	61647.4	+	61647.4i	0.00136351	+	0.00136351i
$83$	1.65526e7	−	1.65526e7i	0.348782	−	0.348782i	−0.510874	−	0.859656i	$-0.670678\pi$
$83$	1.65526e7	−	1.65526e7i	0.348782	−	0.348782i	0.859656	+	0.510874i	$0.170678\pi$
$84$			2.45929e7i			0.493960i
$85$		0			0
$86$	122663.			0.00224244
$87$	5.58357e6	+	5.58357e6i	0.0974620	+	0.0974620i
$88$	350497.	−	350497.i	0.00584459	−	0.00584459i
$89$			7.86587e7i			1.25368i	0.779148	+	0.626840i	$0.215652\pi$
$89$			7.86587e7i			1.25368i	−0.779148	+	0.626840i	$0.784348\pi$
$90$		0			0
$91$	−6.89007e7			−1.00475
$92$	3.94581e7	+	3.94581e7i	0.550789	+	0.550789i
$93$	−4.70491e7	+	4.70491e7i	−0.628955	+	0.628955i
$94$		−	243689.i		−	0.00312122i
$95$		0			0
$96$	−529153.			−0.00623011
$97$	3.88232e7	+	3.88232e7i	0.438535	+	0.438535i	0.891519	−	0.452984i	$-0.149640\pi$
$97$	3.88232e7	+	3.88232e7i	0.438535	+	0.438535i	−0.452984	+	0.891519i	$0.649640\pi$
$98$	−83633.5	+	83633.5i	−0.000906726	+	0.000906726i
$99$		−	7.25256e7i		−	0.755006i
$100$		0			0
$101$	−1.17157e8			−1.12586			−0.562929	−	0.826505i	$-0.690326\pi$
$101$	−1.17157e8			−1.12586			−0.562929	+	0.826505i	$0.690326\pi$
$102$	298868.	+	298868.i	0.00276108	+	0.00276108i
$103$	−3.20910e7	+	3.20910e7i	−0.285124	+	0.285124i	−0.835149	−	0.550024i	$-0.814618\pi$
$103$	−3.20910e7	+	3.20910e7i	−0.285124	+	0.285124i	0.550024	+	0.835149i	$0.314618\pi$
$104$		−	988334.i		−	0.00844832i
$105$		0			0
$106$	509219.			0.00403349
$107$	1.19508e8	+	1.19508e8i	0.911722	+	0.911722i	0.996408	−	0.0846858i	$-0.0269886\pi$
$107$	1.19508e8	+	1.19508e8i	0.911722	+	0.911722i	−0.0846858	+	0.996408i	$0.526989\pi$
$108$	−9.73782e7	+	9.73782e7i	−0.715759	+	0.715759i
$109$		−	790709.i		−	0.00560158i	−0.999996	−	0.00280079i	$-0.999108\pi$
$109$		−	790709.i		−	0.00560158i	0.999996	−	0.00280079i	$-0.000891521\pi$
$110$		0			0
$111$	1.14009e8			0.751014
$112$	−8.68433e7	−	8.68433e7i	−0.551905	−	0.551905i
$113$	1.84087e8	−	1.84087e8i	1.12904	−	1.12904i	0.138705	−	0.990334i	$-0.455706\pi$
$113$	1.84087e8	−	1.84087e8i	1.12904	−	1.12904i	0.990334	−	0.138705i	$-0.0442938\pi$
$114$			117068.i			0.000693138i
$115$		0			0
$116$	−3.94343e7			−0.217792
$117$	−1.02254e8	−	1.02254e8i	−0.545678	−	0.545678i
$118$	−173660.	+	173660.i	−0.000895720	+	0.000895720i
$119$			2.94303e8i			1.46760i
$120$		0			0
$121$	1.25633e8			0.586088
$122$	104166.	+	104166.i	0.000470203	+	0.000470203i
$123$	6.01874e7	−	6.01874e7i	0.262957	−	0.262957i
$124$		−	3.32287e8i		−	1.40549i
$125$		0			0
$126$	387026.			0.00153553
$127$	−2.54930e8	−	2.54930e8i	−0.979955	−	0.979955i	0.0198481	−	0.999803i	$-0.493682\pi$
$127$	−2.54930e8	−	2.54930e8i	−0.979955	−	0.979955i	−0.999803	+	0.0198481i	$0.993682\pi$
$128$	2.49144e6	−	2.49144e6i	0.00928135	−	0.00928135i
$129$		−	1.19758e8i		−	0.432460i
$130$		0			0
$131$	4.20292e8			1.42714			0.713569	−	0.700584i	$-0.247077\pi$
$131$	4.20292e8			1.42714			0.713569	+	0.700584i	$0.247077\pi$
$132$	−1.71097e8	−	1.71097e8i	−0.563569	−	0.563569i
$133$	−5.76400e7	+	5.76400e7i	−0.184212	+	0.184212i
$134$			1.00540e6i			0.00311832i
$135$		0			0
$136$	−4.22157e6			−0.0123401
$137$	3.53619e8	+	3.53619e8i	1.00381	+	1.00381i	0.999993	+	0.00382151i	$0.00121643\pi$
$137$	3.53619e8	+	3.53619e8i	1.00381	+	1.00381i	0.00382151	+	0.999993i	$0.498784\pi$
$138$	−414847.	+	414847.i	−0.00114386	+	0.00114386i
$139$			8.68615e7i			0.232685i	0.993209	+	0.116342i	$0.0371170\pi$
$139$			8.68615e7i			0.232685i	−0.993209	+	0.116342i	$0.962883\pi$
$140$		0			0
$141$	−2.37917e8			−0.601935
$142$	−1.40409e6	−	1.40409e6i	−0.00345337	−	0.00345337i
$143$	4.79356e8	−	4.79356e8i	1.14634	−	1.14634i
$144$		−	2.57764e8i		−	0.599477i
$145$		0			0
$146$	805079.			0.00177185
$147$	8.16527e7	+	8.16527e7i	0.174864	+	0.174864i
$148$	−4.02599e8	+	4.02599e8i	−0.839122	+	0.839122i
$149$			7.52588e8i			1.52690i	0.645864	+	0.763452i	$0.276497\pi$
$149$			7.52588e8i			1.52690i	−0.645864	+	0.763452i	$0.723503\pi$
$150$		0			0
$151$	−3.16577e8			−0.608936			−0.304468	−	0.952523i	$-0.598479\pi$
$151$	−3.16577e8			−0.608936			−0.304468	+	0.952523i	$0.598479\pi$
$152$	−826806.	−	826806.i	−0.00154892	−	0.00154892i
$153$	−4.36768e8	+	4.36768e8i	−0.797048	+	0.797048i
$154$			1.81434e6i			0.00322578i
$155$		0			0
$156$	−4.82461e8			−0.814636
$157$	4.46031e8	+	4.46031e8i	0.734119	+	0.734119i	0.971433	−	0.237314i	$-0.0762669\pi$
$157$	4.46031e8	+	4.46031e8i	0.734119	+	0.734119i	−0.237314	+	0.971433i	$0.576267\pi$
$158$	−1.89610e6	+	1.89610e6i	−0.00304252	+	0.00304252i
$159$		−	4.97159e8i		−	0.777870i
$160$		0			0
$161$	−4.08509e8			−0.607993
$162$	−65696.8	−	65696.8i	−9.53859e−5	−	9.53859e-5i
$163$	−2.63584e8	+	2.63584e8i	−0.373395	+	0.373395i	−0.868712	−	0.495318i	$-0.835052\pi$
$163$	−2.63584e8	+	2.63584e8i	−0.373395	+	0.373395i	0.495318	+	0.868712i	$0.335052\pi$
$164$			4.25077e8i			0.587614i
$165$		0			0
$166$	−1.22908e6			−0.00161863
$167$	−8.72381e7	−	8.72381e7i	−0.112161	−	0.112161i	0.648799	−	0.760960i	$-0.275272\pi$
$167$	−8.72381e7	−	8.72381e7i	−0.112161	−	0.112161i	−0.760960	+	0.648799i	$0.775272\pi$
$168$	1.82610e6	−	1.82610e6i	0.00229238	−	0.00229238i
$169$		−	5.35958e8i		−	0.657028i
$170$		0			0
$171$	−1.71084e8			−0.200090
$172$	4.22899e8	+	4.22899e8i	0.483195	+	0.483195i
$173$	5.38851e8	−	5.38851e8i	0.601567	−	0.601567i	−0.339161	−	0.940728i	$-0.610143\pi$
$173$	5.38851e8	−	5.38851e8i	0.601567	−	0.601567i	0.940728	+	0.339161i	$0.110143\pi$
$174$		−	414596.i		−	0.000452302i
$175$		0			0
$176$	1.20837e9			1.25936
$177$	1.69547e8	+	1.69547e8i	0.172742	+	0.172742i
$178$	2.92031e6	−	2.92031e6i	0.00290904	−	0.00290904i
$179$			7.15210e8i			0.696661i	0.937372	+	0.348331i	$0.113251\pi$
$179$			7.15210e8i			0.696661i	−0.937372	+	0.348331i	$0.886749\pi$
$180$		0			0
$181$	1.93495e8			0.180283			0.0901417	−	0.995929i	$-0.471268\pi$
$181$	1.93495e8			0.180283			0.0901417	+	0.995929i	$0.471268\pi$
$182$	2.55804e6	+	2.55804e6i	0.00233142	+	0.00233142i
$183$	1.01699e8	−	1.01699e8i	0.0906798	−	0.0906798i
$184$		−	5.85979e6i		−	0.00511223i
$185$		0			0
$186$	3.49353e6			0.00291885
$187$	−2.04752e9	−	2.04752e9i	−1.67441	−	1.67441i
$188$	8.40152e8	−	8.40152e8i	0.672553	−	0.672553i
$189$		−	1.00815e9i		−	0.790096i
$190$		0			0
$191$	1.01296e9			0.761127			0.380563	−	0.924755i	$-0.375730\pi$
$191$	1.01296e9			0.761127			0.380563	+	0.924755i	$0.375730\pi$
$192$	−6.08086e8	−	6.08086e8i	−0.447466	−	0.447466i
$193$	−7.64304e8	+	7.64304e8i	−0.550855	+	0.550855i	−0.926688	−	0.375833i	$-0.877357\pi$
$193$	−7.64304e8	+	7.64304e8i	−0.550855	+	0.550855i	0.375833	+	0.926688i	$0.377357\pi$
$194$		−	2.88273e6i		−	0.00203515i
$195$		0			0
$196$	−5.76677e8			−0.390759
$197$	1.36187e8	+	1.36187e8i	0.0904212	+	0.0904212i	0.750871	−	0.660449i	$-0.229634\pi$
$197$	1.36187e8	+	1.36187e8i	0.0904212	+	0.0904212i	−0.660449	+	0.750871i	$0.729634\pi$
$198$	−2.69261e6	+	2.69261e6i	−0.00175192	+	0.00175192i
$199$		−	8.19357e8i		−	0.522469i	−0.965275	−	0.261235i	$-0.915870\pi$
$199$		−	8.19357e8i		−	0.522469i	0.965275	−	0.261235i	$-0.0841296\pi$
$200$		0			0
$201$	9.81591e8			0.601377
$202$	4.34963e6	+	4.34963e6i	0.00261244	+	0.00261244i
$203$	2.04131e8	−	2.04131e8i	0.120206	−	0.120206i
$204$			2.06078e9i			1.18990i
$205$		0			0
$206$	2.38284e6			0.00132320
$207$	−6.06259e8	−	6.06259e8i	−0.330200	−	0.330200i
$208$	1.70368e9	−	1.70368e9i	0.910198	−	0.910198i
$209$		−	8.02024e8i		−	0.420342i
$210$		0			0
$211$	1.19972e9			0.605269			0.302634	−	0.953107i	$-0.402134\pi$
$211$	1.19972e9			0.605269			0.302634	+	0.953107i	$0.402134\pi$
$212$	1.75561e9	+	1.75561e9i	0.869128	+	0.869128i
$213$	−1.37084e9	+	1.37084e9i	−0.665990	+	0.665990i
$214$		−	8.87381e6i		−	0.00423112i
$215$		0			0
$216$	1.44613e7			0.00664342
$217$	1.72008e9	+	1.72008e9i	0.775728	+	0.775728i
$218$	−29356.2	+	29356.2i	−1.29979e−5	+	1.29979e-5i
$219$		−	7.86012e8i		−	0.341706i
$220$		0			0
$221$	−5.77361e9			−2.42035
$222$	−4.23275e6	−	4.23275e6i	−0.00174265	−	0.00174265i
$223$	−6.38952e8	+	6.38952e8i	−0.258374	+	0.258374i	−0.824393	−	0.566018i	$-0.808483\pi$
$223$	−6.38952e8	+	6.38952e8i	−0.258374	+	0.258374i	0.566018	+	0.824393i	$0.308483\pi$
$224$			1.93454e7i			0.00768398i
$225$		0			0
$226$	−1.36690e7			−0.00523964
$227$	−3.56390e8	−	3.56390e8i	−0.134222	−	0.134222i	0.636804	−	0.771026i	$-0.280256\pi$
$227$	−3.56390e8	−	3.56390e8i	−0.134222	−	0.134222i	−0.771026	+	0.636804i	$0.780256\pi$
$228$	−4.03610e8	+	4.03610e8i	−0.149356	+	0.149356i
$229$			1.79306e9i			0.652008i	0.945368	+	0.326004i	$0.105702\pi$
$229$			1.79306e9i			0.652008i	−0.945368	+	0.326004i	$0.894298\pi$
$230$		0			0
$231$	1.77136e9			0.622100
$232$	2.92812e6	+	2.92812e6i	0.00101074	+	0.00101074i
$233$	−3.47531e9	+	3.47531e9i	−1.17915	+	1.17915i	−0.199192	+	0.979960i	$0.563832\pi$
$233$	−3.47531e9	+	3.47531e9i	−1.17915	+	1.17915i	−0.979960	+	0.199192i	$0.936168\pi$
$234$			7.59264e6i			0.00253238i
$235$		0			0
$236$	−1.19744e9			−0.386015
$237$	1.85119e9	+	1.85119e9i	0.586757	+	0.586757i
$238$	1.09264e7	−	1.09264e7i	0.00340541	−	0.00340541i
$239$		−	2.07630e8i		−	0.0636353i	−0.999494	−	0.0318177i	$-0.989870\pi$
$239$		−	2.07630e8i		−	0.0636353i	0.999494	−	0.0318177i	$-0.0101296\pi$
$240$		0			0
$241$	−4.79222e9			−1.42059			−0.710294	−	0.703905i	$-0.751438\pi$
$241$	−4.79222e9			−1.42059			−0.710294	+	0.703905i	$0.751438\pi$
$242$	−4.66431e6	−	4.66431e6i	−0.00135996	−	0.00135996i
$243$	2.43158e9	−	2.43158e9i	0.697371	−	0.697371i
$244$			7.18252e8i			0.202637i
$245$		0			0
$246$	−4.46908e6			−0.00122033
$247$	−1.13078e9	−	1.13078e9i	−0.303801	−	0.303801i
$248$	−2.46734e7	+	2.46734e7i	−0.00652261	+	0.00652261i
$249$			1.19997e9i			0.312157i
$250$		0			0
$251$	4.92208e9			1.24009			0.620046	−	0.784566i	$-0.287114\pi$
$251$	4.92208e9			1.24009			0.620046	+	0.784566i	$0.287114\pi$
$252$	1.33433e9	+	1.33433e9i	0.330872	+	0.330872i
$253$	2.84208e9	−	2.84208e9i	0.693671	−	0.693671i
$254$			1.89293e7i			0.00454777i
$255$		0			0
$256$	4.29450e9			0.999892
$257$	−1.28291e9	−	1.28291e9i	−0.294078	−	0.294078i	0.544611	−	0.838689i	$-0.316677\pi$
$257$	−1.28291e9	−	1.28291e9i	−0.294078	−	0.294078i	−0.838689	+	0.544611i	$0.816677\pi$
$258$	−4.44618e6	+	4.44618e6i	−0.00100348	+	0.00100348i
$259$		−	4.16809e9i		−	0.926271i
$260$		0			0
$261$	6.05893e8			0.130567
$262$	−1.56039e7	−	1.56039e7i	−0.00331153	−	0.00331153i
$263$	6.13430e8	−	6.13430e8i	0.128216	−	0.128216i	−0.640087	−	0.768303i	$-0.721102\pi$
$263$	6.13430e8	−	6.13430e8i	0.128216	−	0.128216i	0.768303	+	0.640087i	$0.221102\pi$
$264$			2.54090e7i			0.00523085i
$265$		0			0
$266$	4.27993e6			0.000854889
$267$	−2.85115e9	−	2.85115e9i	−0.561015	−	0.561015i
$268$	−3.46627e9	+	3.46627e9i	−0.671929	+	0.671929i
$269$		−	3.11121e9i		−	0.594184i	−0.954849	−	0.297092i	$-0.903983\pi$
$269$		−	3.11121e9i		−	0.594184i	0.954849	−	0.297092i	$-0.0960168\pi$
$270$		0			0
$271$	4.62618e9			0.857719			0.428860	−	0.903371i	$-0.358915\pi$
$271$	4.62618e9			0.857719			0.428860	+	0.903371i	$0.358915\pi$
$272$	−7.27712e9	−	7.27712e9i	−1.32949	−	1.32949i
$273$	2.49745e9	−	2.49745e9i	0.449621	−	0.449621i
$274$		−	2.62572e7i		−	0.00465850i
$275$		0			0
$276$	−2.86049e9			−0.492951
$277$	1.93042e9	+	1.93042e9i	0.327893	+	0.327893i	0.851785	−	0.523892i	$-0.175520\pi$
$277$	1.93042e9	+	1.93042e9i	0.327893	+	0.327893i	−0.523892	+	0.851785i	$0.675520\pi$
$278$	3.22485e6	−	3.22485e6i	0.000539922	−	0.000539922i
$279$			5.10546e9i			0.842593i
$280$		0			0
$281$	3.04932e9			0.489078			0.244539	−	0.969640i	$-0.421363\pi$
$281$	3.04932e9			0.489078			0.244539	+	0.969640i	$0.421363\pi$
$282$	8.83301e6	+	8.83301e6i	0.00139673	+	0.00139673i
$283$	6.02007e9	−	6.02007e9i	0.938547	−	0.938547i	−0.0596715	−	0.998218i	$-0.519005\pi$
$283$	6.02007e9	−	6.02007e9i	0.938547	−	0.938547i	0.998218	+	0.0596715i	$0.0190053\pi$
$284$		−	9.68163e9i		−	1.48825i
$285$		0			0
$286$	−3.55935e7			−0.00531994
$287$	−2.20040e9	−	2.20040e9i	−0.324321	−	0.324321i
$288$	−2.87101e7	+	2.87101e7i	−0.00417315	+	0.00417315i
$289$			1.76856e10i			2.53530i
$290$		0			0
$291$	−2.81446e9			−0.392485
$292$	2.77563e9	+	2.77563e9i	0.381795	+	0.381795i
$293$	−6.98416e9	+	6.98416e9i	−0.947640	+	0.947640i	−0.998696	−	0.0510555i	$-0.983741\pi$
$293$	−6.98416e9	+	6.98416e9i	−0.947640	+	0.947640i	0.0510555	+	0.998696i	$0.483741\pi$
$294$		−	6.06294e6i		−	0.000811511i
$295$		0			0
$296$	5.97885e7			0.00778844
$297$	7.01392e9	+	7.01392e9i	0.901436	+	0.901436i
$298$	2.79409e7	−	2.79409e7i	0.00354303	−	0.00354303i
$299$		−	8.01410e9i		−	1.00270i
$300$		0			0
$301$	−4.37826e9			−0.533379
$302$	1.17534e7	+	1.17534e7i	0.00141298	+	0.00141298i
$303$	4.24661e9	−	4.24661e9i	0.503816	−	0.503816i
$304$		−	2.85049e9i		−	0.333753i
$305$		0			0
$306$	3.24312e7			0.00369894
$307$	3.47041e9	+	3.47041e9i	0.390685	+	0.390685i	0.874932	−	0.484247i	$-0.160906\pi$
$307$	3.47041e9	+	3.47041e9i	0.390685	+	0.390685i	−0.484247	+	0.874932i	$0.660906\pi$
$308$	−6.25518e9	+	6.25518e9i	−0.695084	+	0.695084i
$309$		−	2.32641e9i		−	0.255183i
$310$		0			0
$311$	−1.16644e9			−0.124687			−0.0623435	−	0.998055i	$-0.519857\pi$
$311$	−1.16644e9			−0.124687			−0.0623435	+	0.998055i	$0.519857\pi$
$312$	3.58242e7	+	3.58242e7i	0.00378058	+	0.00378058i
$313$	−4.28427e9	+	4.28427e9i	−0.446375	+	0.446375i	−0.894147	−	0.447773i	$-0.852217\pi$
$313$	−4.28427e9	+	4.28427e9i	−0.446375	+	0.446375i	0.447773	+	0.894147i	$0.352217\pi$
$314$		−	3.31191e7i		−	0.00340690i
$315$		0			0
$316$	−1.30742e10			−1.31119
$317$	6.76878e9	+	6.76878e9i	0.670307	+	0.670307i	0.957787	−	0.287480i	$-0.0928175\pi$
$317$	6.76878e9	+	6.76878e9i	0.670307	+	0.670307i	−0.287480	+	0.957787i	$0.592818\pi$
$318$	−1.84577e7	+	1.84577e7i	−0.00180497	+	0.00180497i
$319$			2.84036e9i			0.274290i
$320$		0			0
$321$	−8.66365e9			−0.815982
$322$	1.51665e7	+	1.51665e7i	0.00141079	+	0.00141079i
$323$	−4.83000e9	+	4.83000e9i	−0.443748	+	0.443748i
$324$		−	4.52998e8i		−	0.0411071i
$325$		0			0
$326$	1.95718e7			0.00173285
$327$	2.86609e7	+	2.86609e7i	0.00250668	+	0.00250668i
$328$	3.15633e7	−	3.15633e7i	0.00272701	−	0.00272701i
$329$			8.69807e9i			0.742403i
$330$		0			0
$331$	1.93877e10			1.61515			0.807577	−	0.589762i	$-0.200778\pi$
$331$	1.93877e10			1.61515			0.807577	+	0.589762i	$0.200778\pi$
$332$	−4.23742e9	−	4.23742e9i	−0.348778	−	0.348778i
$333$	6.18577e9	−	6.18577e9i	0.503056	−	0.503056i
$334$			6.47767e6i			0.000520515i
$335$		0			0
$336$	6.29563e9			0.493949
$337$	2.59603e8	+	2.59603e8i	0.0201275	+	0.0201275i	0.717099	−	0.696971i	$-0.245470\pi$
$337$	2.59603e8	+	2.59603e8i	0.0201275	+	0.0201275i	−0.696971	+	0.717099i	$0.745470\pi$
$338$	−1.98982e7	+	1.98982e7i	−0.00152457	+	0.00152457i
$339$			1.33452e10i			1.01048i
$340$		0			0
$341$	−2.39338e10			−1.77009
$342$	6.35174e6	+	6.35174e6i	0.000464289	+	0.000464289i
$343$	1.06245e10	−	1.06245e10i	0.767593	−	0.767593i
$344$		−	6.28032e7i		−	0.00448485i
$345$		0			0
$346$	−4.00112e7			−0.00279175
$347$	−8.23958e9	−	8.23958e9i	−0.568312	−	0.568312i	0.363343	−	0.931655i	$-0.381635\pi$
$347$	−8.23958e9	−	8.23958e9i	−0.568312	−	0.568312i	−0.931655	+	0.363343i	$0.881635\pi$
$348$	1.42938e9	−	1.42938e9i	0.0974609	−	0.0974609i
$349$		−	2.38809e10i		−	1.60971i	−0.593470	−	0.804856i	$-0.702243\pi$
$349$		−	2.38809e10i		−	1.60971i	0.593470	−	0.804856i	$-0.297757\pi$
$350$		0			0
$351$	1.97779e10			1.30302
$352$	−1.34590e8	−	1.34590e8i	−0.00876681	−	0.00876681i
$353$	−5.64415e9	+	5.64415e9i	−0.363496	+	0.363496i	−0.865098	−	0.501602i	$-0.832744\pi$
$353$	−5.64415e9	+	5.64415e9i	−0.363496	+	0.363496i	0.501602	+	0.865098i	$0.332744\pi$
$354$		−	1.25893e7i		−	0.000801660i
$355$		0			0
$356$	2.01364e10			1.25367
$357$	−1.06676e10	−	1.06676e10i	−0.656741	−	0.656741i
$358$	2.65532e7	−	2.65532e7i	0.00161653	−	0.00161653i
$359$		−	2.31997e10i		−	1.39671i	−0.715753	−	0.698353i	$-0.753916\pi$
$359$		−	2.31997e10i		−	1.39671i	0.715753	−	0.698353i	$-0.246084\pi$
$360$		0			0
$361$	1.50916e10			0.888602
$362$	−7.18378e6	−	7.18378e6i	−0.000418329	−	0.000418329i
$363$	−4.55384e9	+	4.55384e9i	−0.262271	+	0.262271i
$364$			1.76384e10i			1.00474i
$365$		0			0
$366$	−7.55141e6			−0.000420827
$367$	−1.57789e10	−	1.57789e10i	−0.869787	−	0.869787i	0.122662	−	0.992449i	$-0.460857\pi$
$367$	−1.57789e10	−	1.57789e10i	−0.869787	−	0.869787i	−0.992449	+	0.122662i	$0.960857\pi$
$368$	1.01011e10	−	1.01011e10i	0.550777	−	0.550777i
$369$		−	6.53114e9i		−	0.352276i
$370$		0			0
$371$	−1.81758e10			−0.959394
$372$	1.20444e10	+	1.20444e10i	0.628948	+	0.628948i
$373$	8.47950e9	−	8.47950e9i	0.438062	−	0.438062i	−0.453298	−	0.891359i	$-0.649753\pi$
$373$	8.47950e9	−	8.47950e9i	0.438062	−	0.438062i	0.891359	+	0.453298i	$0.149753\pi$
$374$			1.52034e8i			0.00777060i
$375$		0			0
$376$	−1.24768e8			−0.00624240
$377$	4.00463e9	+	4.00463e9i	0.198243	+	0.198243i
$378$	−3.74291e7	+	3.74291e7i	−0.00183334	+	0.00183334i
$379$			1.84736e10i			0.895356i	0.894195	+	0.447678i	$0.147749\pi$
$379$			1.84736e10i			0.895356i	−0.894195	+	0.447678i	$0.852251\pi$
$380$		0			0
$381$	1.84809e10			0.877050
$382$	−3.76074e7	−	3.76074e7i	−0.00176612	−	0.00176612i
$383$	−2.19194e9	+	2.19194e9i	−0.101867	+	0.101867i	−0.756204	−	0.654336i	$-0.772948\pi$
$383$	−2.19194e9	+	2.19194e9i	−0.101867	+	0.101867i	0.654336	+	0.756204i	$0.272948\pi$
$384$			1.80615e8i			0.00830672i
$385$		0			0
$386$	5.67517e7			0.00255641
$387$	−6.49767e9	−	6.49767e9i	−0.289677	−	0.289677i
$388$	9.93864e9	−	9.93864e9i	0.438531	−	0.438531i
$389$			8.45767e9i			0.369362i	0.982799	+	0.184681i	$0.0591252\pi$
$389$			8.45767e9i			0.369362i	−0.982799	+	0.184681i	$0.940875\pi$
$390$		0			0
$391$	−3.42314e10			−1.46460
$392$	4.28201e7	+	4.28201e7i	0.00181344	+	0.00181344i
$393$	−1.52344e10	+	1.52344e10i	−0.638638	+	0.638638i
$394$		−	1.01123e7i		−	0.000419627i
$395$		0			0
$396$	−1.85663e10			−0.754998
$397$	1.31777e10	+	1.31777e10i	0.530491	+	0.530491i	0.920718	−	0.390228i	$-0.127604\pi$
$397$	1.31777e10	+	1.31777e10i	0.530491	+	0.530491i	−0.390228	+	0.920718i	$0.627604\pi$
$398$	−3.04198e7	+	3.04198e7i	−0.00121234	+	0.00121234i
$399$		−	4.17856e9i		−	0.164868i
$400$		0			0
$401$	1.07626e10			0.416235			0.208118	−	0.978104i	$-0.433266\pi$
$401$	1.07626e10			0.416235			0.208118	+	0.978104i	$0.433266\pi$
$402$	−3.64430e7	−	3.64430e7i	−0.00139543	−	0.00139543i
$403$	−3.37444e10	+	3.37444e10i	−1.27933	+	1.27933i
$404$			2.99919e10i			1.12585i
$405$		0			0
$406$	−1.51573e7			−0.000557851
$407$	2.89982e10	+	2.89982e10i	1.05680	+	1.05680i
$408$	1.53020e8	−	1.53020e8i	0.00552213	−	0.00552213i
$409$		−	5.07853e10i		−	1.81487i	−0.420194	−	0.907434i	$-0.638038\pi$
$409$		−	5.07853e10i		−	1.81487i	0.420194	−	0.907434i	$-0.361962\pi$
$410$		0			0
$411$	−2.56353e10			−0.898404
$412$	8.21520e9	+	8.21520e9i	0.285121	+	0.285121i
$413$	6.19851e9	−	6.19851e9i	0.213053	−	0.213053i
$414$			4.50164e7i			0.00153239i
$415$		0			0
$416$	−3.79517e8			−0.0126724
$417$	−3.14848e9	−	3.14848e9i	−0.104125	−	0.104125i
$418$	−2.97763e7	+	2.97763e7i	−0.000975361	+	0.000975361i
$419$		−	6.71861e9i		−	0.217983i	−0.994043	−	0.108992i	$-0.965238\pi$
$419$		−	6.71861e9i		−	0.217983i	0.994043	−	0.108992i	$-0.0347622\pi$
$420$		0			0
$421$	−1.93070e10			−0.614590			−0.307295	−	0.951614i	$-0.599424\pi$
$421$	−1.93070e10			−0.614590			−0.307295	+	0.951614i	$0.599424\pi$
$422$	−4.45411e7	−	4.45411e7i	−0.00140447	−	0.00140447i
$423$	−1.29086e10	+	1.29086e10i	−0.403198	+	0.403198i
$424$		−	2.60719e8i		−	0.00806695i
$425$		0			0
$426$	1.01789e8			0.00309073
$427$	−3.71802e9	−	3.71802e9i	−0.111841	−	0.111841i
$428$	3.05938e10	−	3.05938e10i	0.911712	−	0.911712i
$429$			3.47505e10i			1.02596i
$430$		0			0
$431$	2.49648e10			0.723467			0.361733	−	0.932282i	$-0.382185\pi$
$431$	2.49648e10			0.723467			0.361733	+	0.932282i	$0.382185\pi$
$432$	2.49283e10	+	2.49283e10i	0.715744	+	0.715744i
$433$	−1.35555e10	+	1.35555e10i	−0.385624	+	0.385624i	−0.873123	−	0.487499i	$-0.837909\pi$
$433$	−1.35555e10	+	1.35555e10i	−0.385624	+	0.385624i	0.487499	+	0.873123i	$0.337909\pi$
$434$		−	1.27721e8i		−	0.00360000i
$435$		0			0
$436$	−2.02419e8			−0.00560152
$437$	−6.70432e9	−	6.70432e9i	−0.183835	−	0.183835i
$438$	−2.91818e7	+	2.91818e7i	−0.000792895	+	0.000792895i
$439$			2.64207e10i			0.711354i	0.934609	+	0.355677i	$0.115750\pi$
$439$			2.64207e10i			0.711354i	−0.934609	+	0.355677i	$0.884250\pi$
$440$		0			0
$441$	8.86042e9			0.234261
$442$	2.14353e8	+	2.14353e8i	0.00561618	+	0.00561618i
$443$	2.91624e10	−	2.91624e10i	0.757196	−	0.757196i	−0.218616	−	0.975811i	$-0.570154\pi$
$443$	2.91624e10	−	2.91624e10i	0.757196	−	0.757196i	0.975811	+	0.218616i	$0.0701540\pi$
$444$		−	2.91861e10i		−	0.751006i
$445$		0			0
$446$	4.74440e7			0.00119906
$447$	−2.72791e10	−	2.72791e10i	−0.683282	−	0.683282i
$448$	−2.22312e10	+	2.22312e10i	−0.551887	+	0.551887i
$449$			3.26728e10i			0.803899i	0.915662	+	0.401950i	$0.131667\pi$
$449$			3.26728e10i			0.803899i	−0.915662	+	0.401950i	$0.868333\pi$
$450$		0			0
$451$	3.06173e10			0.740049
$452$	−4.71257e10	−	4.71257e10i	−1.12903	−	1.12903i
$453$	1.14750e10	−	1.14750e10i	0.272496	−	0.272496i
$454$			2.64630e7i			0.000622895i
$455$		0			0
$456$	5.99386e7			0.00138627
$457$	−4.03333e10	−	4.03333e10i	−0.924695	−	0.924695i	0.0726618	−	0.997357i	$-0.476851\pi$
$457$	−4.03333e10	−	4.03333e10i	−0.924695	−	0.924695i	−0.997357	+	0.0726618i	$0.976851\pi$
$458$	6.65699e7	−	6.65699e7i	0.00151292	−	0.00151292i
$459$		−	8.44793e10i		−	1.90327i
$460$		0			0
$461$	2.16556e10			0.479475			0.239738	−	0.970838i	$-0.422939\pi$
$461$	2.16556e10			0.479475			0.239738	+	0.970838i	$0.422939\pi$
$462$	−6.57644e7	−	6.57644e7i	−0.00144352	−	0.00144352i
$463$	2.04303e10	−	2.04303e10i	0.444581	−	0.444581i	−0.448967	−	0.893548i	$-0.648208\pi$
$463$	2.04303e10	−	2.04303e10i	0.444581	−	0.444581i	0.893548	+	0.448967i	$0.148208\pi$
$464$			1.00950e10i			0.217788i
$465$		0			0
$466$	2.58052e8			0.00547221
$467$	4.03881e10	+	4.03881e10i	0.849152	+	0.849152i	0.990027	−	0.140875i	$-0.0449916\pi$
$467$	4.03881e10	+	4.03881e10i	0.849152	+	0.849152i	−0.140875	+	0.990027i	$0.544992\pi$
$468$	−2.61767e10	+	2.61767e10i	−0.545672	+	0.545672i
$469$		−	3.58862e10i		−	0.741714i
$470$		0			0
$471$	−3.23347e10			−0.657030
$472$	8.89135e7	+	8.89135e7i	0.00179143	+	0.00179143i
$473$	3.04604e10	−	3.04604e10i	0.608543	−	0.608543i
$474$		−	1.37456e8i		−	0.00272302i
$475$		0			0
$476$	7.53407e10			1.46758
$477$	−2.69742e10	−	2.69742e10i	−0.521045	−	0.521045i
$478$	−7.70855e6	+	7.70855e6i	−0.000147659	+	0.000147659i
$479$			9.78748e10i			1.85921i	0.368555	+	0.929606i	$0.379853\pi$
$479$			9.78748e10i			1.85921i	−0.368555	+	0.929606i	$0.620147\pi$
$480$		0			0
$481$	8.17693e10			1.52760
$482$	1.77918e8	+	1.77918e8i	0.00329633	+	0.00329633i
$483$	1.48073e10	−	1.48073e10i	0.272074	−	0.272074i
$484$		−	3.21617e10i		−	0.586082i
$485$		0			0
$486$	−1.80552e8			−0.00323636
$487$	2.88570e10	+	2.88570e10i	0.513022	+	0.513022i	0.915451	−	0.402429i	$-0.131834\pi$
$487$	2.88570e10	+	2.88570e10i	0.513022	+	0.513022i	−0.402429	+	0.915451i	$0.631834\pi$
$488$	5.33325e7	−	5.33325e7i	0.000940401	−	0.000940401i
$489$		−	1.91083e10i		−	0.334184i
$490$		0			0
$491$	−8.30227e10			−1.42847			−0.714235	−	0.699906i	$-0.753225\pi$
$491$	−8.30227e10			−1.42847			−0.714235	+	0.699906i	$0.753225\pi$
$492$	−1.54078e10	−	1.54078e10i	−0.262954	−	0.262954i
$493$	1.71054e10	−	1.71054e10i	0.289564	−	0.289564i
$494$			8.39633e7i			0.00140988i
$495$		0			0
$496$	−8.50636e10			−1.40546
$497$	5.01168e10	+	5.01168e10i	0.821406	+	0.821406i
$498$	4.45505e7	−	4.45505e7i	0.000724328	−	0.000724328i
$499$			3.98464e9i			0.0642669i	0.999484	+	0.0321334i	$0.0102302\pi$
$499$			3.98464e9i			0.0642669i	−0.999484	+	0.0321334i	$0.989770\pi$
$500$		0			0
$501$	6.32426e9			0.100383
$502$	−1.82739e8	−	1.82739e8i	−0.00287751	−	0.00287751i
$503$	−4.18276e10	+	4.18276e10i	−0.653418	+	0.653418i	−0.953815	−	0.300396i	$-0.902881\pi$
$503$	−4.18276e10	+	4.18276e10i	−0.653418	+	0.653418i	0.300396	+	0.953815i	$0.402881\pi$
$504$		−	1.98156e8i		−	0.00307104i
$505$		0			0
$506$	−2.11032e8			−0.00321919
$507$	1.94269e10	+	1.94269e10i	0.294017	+	0.294017i
$508$	−6.52614e10	+	6.52614e10i	−0.979944	+	0.979944i
$509$			5.50776e10i			0.820549i	0.911962	+	0.410274i	$0.134567\pi$
$509$			5.50776e10i			0.820549i	−0.911962	+	0.410274i	$0.865433\pi$
$510$		0			0
$511$	−2.87360e10			−0.421447
$512$	−7.97249e8	−	7.97249e8i	−0.0116015	−	0.0116015i
$513$	1.65455e10	−	1.65455e10i	0.238897	−	0.238897i
$514$			9.52594e7i			0.00136476i
$515$		0			0
$516$	−3.06577e10			−0.432455
$517$	−6.05142e10	−	6.05142e10i	−0.847022	−	0.847022i
$518$	−1.54746e8	+	1.54746e8i	−0.00214932	+	0.00214932i
$519$			3.90636e10i			0.538397i
$520$		0			0
$521$	−6.60269e10			−0.896128			−0.448064	−	0.894002i	$-0.647886\pi$
$521$	−6.60269e10			−0.896128			−0.448064	+	0.894002i	$0.647886\pi$
$522$	−2.24946e7	−	2.24946e7i	−0.000302968	−	0.000302968i
$523$	−3.80766e10	+	3.80766e10i	−0.508922	+	0.508922i	−0.914196	−	0.405273i	$-0.867176\pi$
$523$	−3.80766e10	+	3.80766e10i	−0.508922	+	0.508922i	0.405273	+	0.914196i	$0.367176\pi$
$524$		−	1.07594e11i		−	1.42712i
$525$		0			0
$526$	−4.55489e7			−0.000595025
$527$	1.44136e11	+	1.44136e11i	1.86865	+	1.86865i
$528$	−4.37999e10	+	4.37999e10i	−0.563557	+	0.563557i
$529$			3.07958e10i			0.393250i
$530$		0			0
$531$	1.83981e10			0.231417
$532$	1.47557e10	+	1.47557e10i	0.184210	+	0.184210i
$533$	4.31674e10	−	4.31674e10i	0.534868	−	0.534868i
$534$			2.11706e8i			0.00260356i
$535$		0			0
$536$	5.14764e8			0.00623661
$537$	−2.59243e10	−	2.59243e10i	−0.311752	−	0.311752i
$538$	−1.15508e8	+	1.15508e8i	−0.00137874	+	0.00137874i
$539$			4.15367e10i			0.492127i
$540$		0			0
$541$	6.43974e9			0.0751760			0.0375880	−	0.999293i	$-0.488033\pi$
$541$	6.43974e9			0.0751760			0.0375880	+	0.999293i	$0.488033\pi$
$542$	−1.71753e8	−	1.71753e8i	−0.00199025	−	0.00199025i
$543$	−7.01363e9	+	7.01363e9i	−0.0806759	+	0.0806759i
$544$			1.62107e9i			0.0185100i
$545$		0			0
$546$	−1.85443e8			−0.00208660
$547$	1.79659e10	+	1.79659e10i	0.200677	+	0.200677i	0.800290	−	0.599613i	$-0.204679\pi$
$547$	1.79659e10	+	1.79659e10i	0.200677	+	0.200677i	−0.599613	+	0.800290i	$0.704679\pi$
$548$	9.05255e10	−	9.05255e10i	1.00380	−	1.00380i
$549$		−	1.10357e10i		−	0.121481i
$550$		0			0
$551$	6.70027e9			0.0726919
$552$	2.12400e8	+	2.12400e8i	0.00228770	+	0.00228770i
$553$	6.76782e10	−	6.76782e10i	0.723683	−	0.723683i
$554$		−	1.43339e8i		−	0.00152169i
$555$		0			0
$556$	2.22363e10			0.232682
$557$	−7.06042e10	−	7.06042e10i	−0.733516	−	0.733516i	0.237798	−	0.971315i	$-0.423574\pi$
$557$	−7.06042e10	−	7.06042e10i	−0.733516	−	0.733516i	−0.971315	+	0.237798i	$0.923574\pi$
$558$	1.89547e8	−	1.89547e8i	0.00195515	−	0.00195515i
$559$		−	8.58924e10i		−	0.879645i
$560$		0			0
$561$	1.48433e11			1.49858
$562$	−1.13210e8	−	1.13210e8i	−0.00113486	−	0.00113486i
$563$	−1.05238e11	+	1.05238e11i	−1.04746	+	1.04746i	−0.0486443	+	0.998816i	$0.515490\pi$
$563$	−1.05238e11	+	1.05238e11i	−1.04746	+	1.04746i	−0.998816	+	0.0486443i	$0.984510\pi$
$564$			6.09062e10i			0.601928i
$565$		0			0
$566$	−4.47007e8			−0.00435561
$567$	2.34494e9	+	2.34494e9i	0.0226882	+	0.0226882i
$568$	−7.18892e8	+	7.18892e8i	−0.00690670	+	0.00690670i
$569$		−	1.74081e10i		−	0.166074i	−0.996546	−	0.0830372i	$-0.973538\pi$
$569$		−	1.74081e10i		−	0.166074i	0.996546	−	0.0830372i	$-0.0264620\pi$
$570$		0			0
$571$	2.99831e10			0.282054			0.141027	−	0.990006i	$-0.454960\pi$
$571$	2.99831e10			0.282054			0.141027	+	0.990006i	$0.454960\pi$
$572$	−1.22714e11	−	1.22714e11i	−1.14633	−	1.14633i
$573$	−3.67167e10	+	3.67167e10i	−0.340600	+	0.340600i
$574$			1.63386e8i			0.00150511i
$575$		0			0
$576$	−6.59855e10			−0.599458
$577$	−7.88313e10	−	7.88313e10i	−0.711206	−	0.711206i	0.255581	−	0.966788i	$-0.417733\pi$
$577$	−7.88313e10	−	7.88313e10i	−0.711206	−	0.711206i	−0.966788	+	0.255581i	$0.917733\pi$
$578$	6.56604e8	−	6.56604e8i	0.00588291	−	0.00588291i
$579$		−	5.54076e10i		−	0.493010i
$580$		0			0
$581$	4.38699e10			0.385002
$582$	1.04491e8	+	1.04491e8i	0.000910722	+	0.000910722i
$583$	1.26452e11	−	1.26452e11i	1.09459	−	1.09459i
$584$		−	4.12198e8i		−	0.00354368i
$585$		0			0
$586$	5.18593e8			0.00439781
$587$	−1.16013e11	−	1.16013e11i	−0.977136	−	0.977136i	0.0226089	−	0.999744i	$-0.492803\pi$
$587$	−1.16013e11	−	1.16013e11i	−0.977136	−	0.977136i	−0.999744	+	0.0226089i	$0.992803\pi$
$588$	2.09029e10	−	2.09029e10i	0.174862	−	0.174862i
$589$			5.64587e10i			0.469105i
$590$		0			0
$591$	−9.87275e9			−0.0809260
$592$	1.03063e11	+	1.03063e11i	0.839104	+	0.839104i
$593$	1.57104e10	−	1.57104e10i	0.127048	−	0.127048i	−0.640724	−	0.767772i	$-0.721366\pi$
$593$	1.57104e10	−	1.57104e10i	0.127048	−	0.127048i	0.767772	+	0.640724i	$0.221366\pi$
$594$		−	5.20803e8i		−	0.00418339i
$595$		0			0
$596$	1.92660e11			1.52689
$597$	2.96993e10	+	2.96993e10i	0.233802	+	0.233802i
$598$	−2.97535e8	+	2.97535e8i	−0.00232666	+	0.00232666i
$599$		−	6.59679e10i		−	0.512419i	−0.966621	−	0.256209i	$-0.917526\pi$
$599$		−	6.59679e10i		−	0.512419i	0.966621	−	0.256209i	$-0.0824737\pi$
$600$		0			0
$601$	−2.95727e10			−0.226670			−0.113335	−	0.993557i	$-0.536153\pi$
$601$	−2.95727e10			−0.226670			−0.113335	+	0.993557i	$0.536153\pi$
$602$	1.62549e8	+	1.62549e8i	0.00123765	+	0.00123765i
$603$	5.32579e10	−	5.32579e10i	0.402824	−	0.402824i
$604$			8.10429e10i			0.608930i
$605$		0			0
$606$	−3.15323e8			−0.00233811
$607$	2.68867e10	+	2.68867e10i	0.198054	+	0.198054i	0.799165	−	0.601111i	$-0.205275\pi$
$607$	2.68867e10	+	2.68867e10i	0.198054	+	0.198054i	−0.601111	+	0.799165i	$0.705275\pi$
$608$	−3.17491e8	+	3.17491e8i	−0.00232336	+	0.00232336i
$609$			1.47983e10i			0.107583i
$610$		0			0
$611$	−1.70638e11			−1.22437
$612$	1.11811e11	+	1.11811e11i	0.797040	+	0.797040i
$613$	−1.13107e11	+	1.13107e11i	−0.801027	+	0.801027i	−0.983256	−	0.182229i	$-0.941669\pi$
$613$	−1.13107e11	+	1.13107e11i	−0.801027	+	0.801027i	0.182229	+	0.983256i	$0.441669\pi$
$614$		−	2.57687e8i		−	0.00181309i
$615$		0			0
$616$	9.28935e8			0.00645152
$617$	1.39434e10	+	1.39434e10i	0.0962115	+	0.0962115i	0.753574	−	0.657363i	$-0.228328\pi$
$617$	1.39434e10	+	1.39434e10i	0.0962115	+	0.0962115i	−0.657363	+	0.753574i	$0.728328\pi$
$618$	−8.63712e7	+	8.63712e7i	−0.000592127	+	0.000592127i
$619$		−	1.14721e10i		−	0.0781410i	−0.999236	−	0.0390705i	$-0.987560\pi$
$619$		−	1.14721e10i		−	0.0781410i	0.999236	−	0.0390705i	$-0.0124397\pi$
$620$		0			0
$621$	1.17262e11			0.788482
$622$	4.33057e7	+	4.33057e7i	0.000289324	+	0.000289324i
$623$	−1.04236e11	+	1.04236e11i	−0.691934	+	0.691934i
$624$			1.23507e11i			0.814618i
$625$		0			0
$626$	3.18119e8			0.00207154
$627$	2.90711e10	+	2.90711e10i	0.188101	+	0.188101i
$628$	1.14183e11	−	1.14183e11i	0.734112	−	0.734112i
$629$		−	3.49269e11i		−	2.23130i
$630$		0			0
$631$	−1.75295e11			−1.10574			−0.552868	−	0.833269i	$-0.686467\pi$
$631$	−1.75295e11			−1.10574			−0.552868	+	0.833269i	$0.686467\pi$
$632$	9.70798e8	+	9.70798e8i	0.00608500	+	0.00608500i
$633$	−4.34862e10	+	4.34862e10i	−0.270855	+	0.270855i
$634$		−	5.02601e8i		−	0.00311076i
$635$		0			0
$636$	−1.27271e11			−0.777861
$637$	5.85627e10	+	5.85627e10i	0.355683	+	0.355683i
$638$	1.05452e8	−	1.05452e8i	0.000636464	−	0.000636464i
$639$			1.48754e11i			0.892209i
$640$		0			0
$641$	−2.29834e11			−1.36139			−0.680695	−	0.732567i	$-0.738322\pi$
$641$	−2.29834e11			−1.36139			−0.680695	+	0.732567i	$0.738322\pi$
$642$	3.21650e8	+	3.21650e8i	0.00189340	+	0.00189340i
$643$	−1.98174e11	+	1.98174e11i	−1.15932	+	1.15932i	−0.174694	+	0.984623i	$0.555893\pi$
$643$	−1.98174e11	+	1.98174e11i	−1.15932	+	1.15932i	−0.984623	+	0.174694i	$0.944107\pi$
$644$			1.04577e11i			0.607986i
$645$		0			0
$646$	3.58641e8			0.00205935
$647$	1.74867e10	+	1.74867e10i	0.0997906	+	0.0997906i	0.755240	−	0.655449i	$-0.227521\pi$
$647$	1.74867e10	+	1.74867e10i	0.0997906	+	0.0997906i	−0.655449	+	0.755240i	$0.727521\pi$
$648$	−3.36366e7	+	3.36366e7i	−0.000190771	+	0.000190771i
$649$			8.62485e10i			0.486153i
$650$		0			0
$651$	−1.24696e11			−0.694269
$652$	6.74767e10	+	6.74767e10i	0.373390	+	0.373390i
$653$	−1.02593e11	+	1.02593e11i	−0.564241	+	0.564241i	−0.930509	−	0.366268i	$-0.880635\pi$
$653$	−1.02593e11	+	1.02593e11i	−0.564241	+	0.564241i	0.366268	+	0.930509i	$0.380635\pi$
$654$		−	2.12815e6i		−	1.16330e-5i
$655$		0			0
$656$	1.08817e11			0.587601
$657$	−4.26464e10	−	4.26464e10i	−0.228887	−	0.228887i
$658$	3.22928e8	−	3.22928e8i	0.00172267	−	0.00172267i
$659$			4.63683e10i			0.245855i	0.992416	+	0.122928i	$0.0392283\pi$
$659$			4.63683e10i			0.245855i	−0.992416	+	0.122928i	$0.960772\pi$
$660$		0			0
$661$	1.89326e11			0.991756			0.495878	−	0.868392i	$-0.334846\pi$
$661$	1.89326e11			0.991756			0.495878	+	0.868392i	$0.334846\pi$
$662$	−7.19795e8	−	7.19795e8i	−0.00374781	−	0.00374781i
$663$	2.09276e11	−	2.09276e11i	1.08309	−	1.08309i
$664$			6.29285e8i			0.00323724i
$665$		0			0
$666$	−4.59311e8			−0.00233458
$667$	2.37433e10	+	2.37433e10i	0.119960	+	0.119960i
$668$	−2.23327e10	+	2.23327e10i	−0.112159	+	0.112159i
$669$		−	4.63203e10i		−	0.231242i
$670$		0			0
$671$	5.17340e10			0.255203
$672$	−7.01215e8	−	7.01215e8i	−0.00343854	−	0.00343854i
$673$	2.24267e11	−	2.24267e11i	1.09321	−	1.09321i	0.0980297	−	0.995183i	$-0.468746\pi$
$673$	2.24267e11	−	2.24267e11i	1.09321	−	1.09321i	0.995183	−	0.0980297i	$-0.0312540\pi$
$674$		−	1.92762e7i		−	9.34076e-5i
$675$		0			0
$676$	−1.37204e11			−0.657021
$677$	7.12288e10	+	7.12288e10i	0.339079	+	0.339079i	0.856021	−	0.516942i	$-0.172930\pi$
$677$	7.12288e10	+	7.12288e10i	0.339079	+	0.339079i	−0.516942	+	0.856021i	$0.672930\pi$
$678$	4.95460e8	−	4.95460e8i	0.00234471	−	0.00234471i
$679$			1.02894e11i			0.484075i
$680$		0			0
$681$	2.58362e10			0.120127
$682$	8.88577e8	+	8.88577e8i	0.00410731	+	0.00410731i
$683$	−2.71176e11	+	2.71176e11i	−1.24614	+	1.24614i	−0.288735	+	0.957409i	$0.593235\pi$
$683$	−2.71176e11	+	2.71176e11i	−1.24614	+	1.24614i	−0.957409	+	0.288735i	$0.906765\pi$
$684$			4.37971e10i			0.200088i
$685$		0			0
$686$	−7.88898e8			−0.00356225
$687$	−6.49932e10	−	6.49932e10i	−0.291770	−	0.291770i
$688$	1.08260e11	−	1.08260e11i	0.483185	−	0.483185i
$689$		−	3.56571e11i		−	1.58223i
$690$		0			0
$691$	4.28187e11			1.87811			0.939055	−	0.343767i	$-0.111703\pi$
$691$	4.28187e11			1.87811			0.939055	+	0.343767i	$0.111703\pi$
$692$	−1.37944e11	−	1.37944e11i	−0.601561	−	0.601561i
$693$	9.61084e10	−	9.61084e10i	0.416705	−	0.416705i
$694$			6.11812e8i			0.00263742i
$695$		0			0
$696$	−2.12272e8			−0.000904598
$697$	−1.84385e11	−	1.84385e11i	−0.781258	−	0.781258i
$698$	−8.86610e8	+	8.86610e8i	−0.00373517	+	0.00373517i
$699$		−	2.51940e11i		−	1.05533i
$700$		0			0
$701$	1.13474e10			0.0469921			0.0234960	−	0.999724i	$-0.492520\pi$
$701$	1.13474e10			0.0469921			0.0234960	+	0.999724i	$0.492520\pi$
$702$	−7.34282e8	−	7.34282e8i	−0.00302353	−	0.00302353i
$703$	6.84054e10	−	6.84054e10i	0.280071	−	0.280071i
$704$		−	3.09333e11i		−	1.25932i
$705$		0			0
$706$	4.19094e8			0.00168691
$707$	−1.55253e11	−	1.55253e11i	−0.621387	−	0.621387i
$708$	4.34036e10	−	4.34036e10i	0.172740	−	0.172740i
$709$			4.05605e11i			1.60516i	0.596543	+	0.802581i	$0.296540\pi$
$709$			4.05605e11i			1.60516i	−0.596543	+	0.802581i	$0.703460\pi$
$710$		0			0
$711$	2.00879e11			0.786062
$712$	−1.49519e9	−	1.49519e9i	−0.00581805	−	0.00581805i
$713$	−2.00069e11	+	2.00069e11i	−0.774143	+	0.774143i
$714$			7.92100e8i			0.00304781i
$715$		0			0
$716$	1.83092e11			0.696654
$717$	7.52598e9	+	7.52598e9i	0.0284765	+	0.0284765i
$718$	−8.61322e8	+	8.61322e8i	−0.00324092	+	0.00324092i
$719$			3.63833e11i			1.36140i	0.732561	+	0.680701i	$0.238325\pi$
$719$			3.63833e11i			1.36140i	−0.732561	+	0.680701i	$0.761675\pi$
$720$		0			0
$721$	−8.50517e10			−0.314733
$722$	−5.60298e8	−	5.60298e8i	−0.00206191	−	0.00206191i
$723$	1.73704e11	−	1.73704e11i	0.635706	−	0.635706i
$724$		−	4.95342e10i		−	0.180281i
$725$		0			0
$726$	3.38135e8			0.00121715
$727$	−1.46957e11	−	1.46957e11i	−0.526082	−	0.526082i	0.393320	−	0.919402i	$-0.371327\pi$
$727$	−1.46957e11	−	1.46957e11i	−0.526082	−	0.526082i	−0.919402	+	0.393320i	$0.871327\pi$
$728$	1.30971e9	−	1.30971e9i	0.00466282	−	0.00466282i
$729$			1.87886e11i			0.665248i
$730$		0			0
$731$	−3.66881e11			−1.28486
$732$	−2.60346e10	−	2.60346e10i	−0.0906788	−	0.0906788i
$733$	2.24637e11	−	2.24637e11i	0.778155	−	0.778155i	−0.201362	−	0.979517i	$-0.564537\pi$
$733$	2.24637e11	−	2.24637e11i	0.778155	−	0.778155i	0.979517	+	0.201362i	$0.0645368\pi$
$734$			1.17163e9i			0.00403651i
$735$		0			0
$736$	−2.25014e9			−0.00766828
$737$	2.49667e11	+	2.49667e11i	0.846237	+	0.846237i
$738$	−2.42478e8	+	2.42478e8i	−0.000817422	+	0.000817422i
$739$		−	4.45714e11i		−	1.49444i	−0.664576	−	0.747220i	$-0.731388\pi$
$739$		−	4.45714e11i		−	1.49444i	0.664576	−	0.747220i	$-0.268612\pi$
$740$		0			0
$741$	8.19747e10			0.271899
$742$	6.74800e8	+	6.74800e8i	0.00222618	+	0.00222618i
$743$	2.67262e11	−	2.67262e11i	0.876965	−	0.876965i	−0.116255	−	0.993219i	$-0.537089\pi$
$743$	2.67262e11	−	2.67262e11i	0.876965	−	0.876965i	0.993219	+	0.116255i	$0.0370889\pi$
$744$		−	1.78868e9i		−	0.00583767i
$745$		0			0
$746$	−6.29627e8			−0.00203296
$747$	6.51063e10	+	6.51063e10i	0.209094	+	0.209094i
$748$	−5.24159e11	+	5.24159e11i	−1.67439	+	1.67439i
$749$			3.16736e11i			1.00640i
$750$		0			0
$751$	2.41249e11			0.758413			0.379206	−	0.925312i	$-0.376197\pi$
$751$	2.41249e11			0.758413			0.379206	+	0.925312i	$0.376197\pi$
$752$	−2.15074e11	−	2.15074e11i	−0.672539	−	0.672539i
$753$	−1.78411e11	+	1.78411e11i	−0.554935	+	0.554935i
$754$		−	2.97355e8i		−	0.000920004i
$755$		0			0
$756$	−2.58085e11			−0.790087
$757$	4.55253e11	+	4.55253e11i	1.38634	+	1.38634i	0.832869	+	0.553470i	$0.186697\pi$
$757$	4.55253e11	+	4.55253e11i	1.38634	+	1.38634i	0.553470	+	0.832869i	$0.313303\pi$
$758$	6.85860e8	−	6.85860e8i	0.00207758	−	0.00207758i
$759$			2.06034e11i			0.620829i
$760$		0			0
$761$	−3.96496e11			−1.18222			−0.591112	−	0.806590i	$-0.701311\pi$
$761$	−3.96496e11			−1.18222			−0.591112	+	0.806590i	$0.701311\pi$
$762$	−6.86131e8	−	6.86131e8i	−0.00203511	−	0.00203511i
$763$	1.04782e9	−	1.04782e9i	0.00309164	−	0.00309164i
$764$		−	2.59314e11i		−	0.761119i
$765$		0			0
$766$	1.62758e8			0.000472745
$767$	1.21602e11	+	1.21602e11i	0.351366	+	0.351366i
$768$	−1.55663e11	+	1.55663e11i	−0.447447	+	0.447447i
$769$		−	3.69440e11i		−	1.05642i	−0.849113	−	0.528212i	$-0.822863\pi$
$769$		−	3.69440e11i		−	1.05642i	0.849113	−	0.528212i	$-0.177137\pi$
$770$		0			0
$771$	9.30033e10			0.263197
$772$	1.95660e11	+	1.95660e11i	0.550849	+	0.550849i
$773$	−8.77771e10	+	8.77771e10i	−0.245846	+	0.245846i	−0.819263	−	0.573417i	$-0.805617\pi$
$773$	−8.77771e10	+	8.77771e10i	−0.245846	+	0.245846i	0.573417	+	0.819263i	$0.305617\pi$
$774$			4.82470e8i			0.00134433i
$775$		0			0
$776$	−1.47595e9			−0.00407029
$777$	1.51081e11	+	1.51081e11i	0.414502	+	0.414502i
$778$	3.14003e8	−	3.14003e8i	0.000857067	−	0.000857067i
$779$		−	7.22246e10i		−	0.196126i
$780$		0			0
$781$	−6.97345e11			−1.87432
$782$	1.27089e9	+	1.27089e9i	0.00339845	+	0.00339845i
$783$	−5.85957e10	+	5.85957e10i	−0.155890	+	0.155890i
$784$			1.47626e11i			0.390750i
$785$		0			0
$786$	1.13120e9			0.00296379
$787$	−2.61315e11	−	2.61315e11i	−0.681186	−	0.681186i	0.279081	−	0.960267i	$-0.409970\pi$
$787$	−2.61315e11	−	2.61315e11i	−0.681186	−	0.681186i	−0.960267	+	0.279081i	$0.909970\pi$
$788$	3.48634e10	−	3.48634e10i	0.0904202	−	0.0904202i
$789$			4.44701e10i			0.114752i
$790$		0			0
$791$	4.87891e11			1.24628
$792$	1.37861e9	+	1.37861e9i	0.00350381	+	0.00350381i
$793$	7.29399e10	−	7.29399e10i	0.184447	−	0.184447i
$794$		−	9.78482e8i		−	0.00246190i
$795$		0			0
$796$	−2.09753e11			−0.522464
$797$	1.14052e11	+	1.14052e11i	0.282662	+	0.282662i	0.834170	−	0.551508i	$-0.185947\pi$
$797$	1.14052e11	+	1.14052e11i	0.282662	+	0.282662i	−0.551508	+	0.834170i	$0.685947\pi$
$798$	−1.55135e8	+	1.55135e8i	−0.000382559	+	0.000382559i
$799$			7.28864e11i			1.78838i
$800$		0			0
$801$	−3.09388e11			−0.751577
$802$	−3.99576e8	−	3.99576e8i	−0.000965833	−	0.000965833i
$803$	1.99922e11	−	1.99922e11i	0.480837	−	0.480837i
$804$		−	2.51285e11i		−	0.601370i
$805$		0			0
$806$	2.50561e9			0.00593709
$807$	1.12772e11	+	1.12772e11i	0.265894	+	0.265894i
$808$	2.22700e9	−	2.22700e9i	0.00522486	−	0.00522486i
$809$			4.48710e11i			1.04754i	0.851859	+	0.523772i	$0.175475\pi$
$809$			4.48710e11i			1.04754i	−0.851859	+	0.523772i	$0.824525\pi$
$810$		0			0
$811$	−1.17339e11			−0.271243			−0.135621	−	0.990761i	$-0.543303\pi$
$811$	−1.17339e11			−0.271243			−0.135621	+	0.990761i	$0.543303\pi$
$812$	−5.22570e10	−	5.22570e10i	−0.120204	−	0.120204i
$813$	−1.67686e11	+	1.67686e11i	−0.383825	+	0.383825i
$814$		−	2.15320e9i		−	0.00490441i
$815$		0			0
$816$	5.27549e11			1.18988
$817$	−7.18546e10	−	7.18546e10i	−0.161275	−	0.161275i
$818$	−1.88548e9	+	1.88548e9i	−0.00421122	+	0.00421122i
$819$		−	2.71007e11i		−	0.602344i
$820$		0			0
$821$	6.09671e11			1.34191			0.670954	−	0.741499i	$-0.265885\pi$
$821$	6.09671e11			1.34191			0.670954	+	0.741499i	$0.265885\pi$
$822$	9.51747e8	+	9.51747e8i	0.00208466	+	0.00208466i
$823$	2.74061e11	−	2.74061e11i	0.597376	−	0.597376i	−0.342238	−	0.939613i	$-0.611185\pi$
$823$	2.74061e11	−	2.74061e11i	0.597376	−	0.597376i	0.939613	+	0.342238i	$0.111185\pi$
$824$		−	1.22001e9i		−	0.00264639i
$825$		0			0
$826$	−4.60257e8			−0.000988736
$827$	−2.40819e11	−	2.40819e11i	−0.514835	−	0.514835i	0.401169	−	0.916004i	$-0.368604\pi$
$827$	−2.40819e11	−	2.40819e11i	−0.514835	−	0.514835i	−0.916004	+	0.401169i	$0.868604\pi$
$828$	−1.55201e11	+	1.55201e11i	−0.330196	+	0.330196i
$829$		−	3.90117e11i		−	0.825994i	−0.910732	−	0.412997i	$-0.864482\pi$
$829$		−	3.90117e11i		−	0.825994i	0.910732	−	0.412997i	$-0.135518\pi$
$830$		0			0
$831$	−1.39944e11			−0.293461
$832$	−4.36129e11	−	4.36129e11i	−0.910169	−	0.910169i
$833$	2.50145e11	−	2.50145e11i	0.519531	−	0.519531i
$834$			2.33783e8i			0.000483225i
$835$		0			0
$836$	−2.05316e11			−0.420337
$837$	−4.93747e11	−	4.93747e11i	−1.00601	−	1.00601i
$838$	−2.49438e8	+	2.49438e8i	−0.000505808	+	0.000505808i
$839$		−	6.94091e11i		−	1.40078i	−0.713762	−	0.700388i	$-0.753010\pi$
$839$		−	6.94091e11i		−	1.40078i	0.713762	−	0.700388i	$-0.246990\pi$
$840$		0			0
$841$	4.76517e11			0.952566
$842$	7.16798e8	+	7.16798e8i	0.00142609	+	0.00142609i
$843$	−1.10529e11	+	1.10529e11i	−0.218860	+	0.218860i
$844$		−	3.07124e11i		−	0.605262i
$845$		0			0
$846$	9.58500e8			0.00187116
$847$	1.66485e11	+	1.66485e11i	0.323475	+	0.323475i
$848$	4.49426e11	−	4.49426e11i	0.869110	−	0.869110i
$849$			4.36420e11i			0.839990i
$850$		0			0
$851$	4.84806e11			0.924379
$852$	3.50931e11	+	3.50931e11i	0.665983	+	0.665983i
$853$	−6.70378e11	+	6.70378e11i	−1.26626	+	1.26626i	−0.318258	+	0.948004i	$0.603098\pi$
$853$	−6.70378e11	+	6.70378e11i	−1.26626	+	1.26626i	−0.948004	+	0.318258i	$0.896902\pi$
$854$			2.76074e8i			0.000519031i
$855$		0			0
$856$	−4.54337e9			−0.00846219
$857$	1.54804e11	+	1.54804e11i	0.286985	+	0.286985i	0.835887	−	0.548902i	$-0.184954\pi$
$857$	1.54804e11	+	1.54804e11i	0.286985	+	0.286985i	−0.548902	+	0.835887i	$0.684954\pi$
$858$	1.29016e9	−	1.29016e9i	0.00238064	−	0.00238064i
$859$		−	3.86664e11i		−	0.710168i	−0.934834	−	0.355084i	$-0.884452\pi$
$859$		−	3.86664e11i		−	0.710168i	0.934834	−	0.355084i	$-0.115548\pi$
$860$		0			0
$861$	1.59517e11			0.290264
$862$	−9.26852e8	−	9.26852e8i	−0.00167873	−	0.00167873i
$863$	7.17384e11	−	7.17384e11i	1.29333	−	1.29333i	0.360613	−	0.932716i	$-0.382568\pi$
$863$	7.17384e11	−	7.17384e11i	1.29333	−	1.29333i	0.932716	−	0.360613i	$-0.117432\pi$
$864$		−	5.55308e9i		−	0.00996505i
$865$		0			0
$866$	1.00653e9			0.00178961
$867$	−6.41053e11	−	6.41053e11i	−1.13453	−	1.13453i
$868$	4.40335e11	−	4.40335e11i	0.775719	−	0.775719i
$869$			9.41701e11i			1.65133i
$870$		0			0
$871$	7.04013e11			1.22323
$872$	1.50303e7	+	1.50303e7i	2.59957e−5	+	2.59957e-5i
$873$	−1.52703e11	+	1.52703e11i	−0.262900	+	0.262900i
$874$			4.97814e8i			0.000853143i
$875$		0			0
$876$	−2.01217e11			−0.341702
$877$	−1.61999e11	−	1.61999e11i	−0.273850	−	0.273850i	0.556798	−	0.830648i	$-0.312030\pi$
$877$	−1.61999e11	−	1.61999e11i	−0.273850	−	0.273850i	−0.830648	+	0.556798i	$0.812030\pi$
$878$	9.80904e8	−	9.80904e8i	0.00165063	−	0.00165063i
$879$		−	5.06311e11i		−	0.848129i
$880$		0			0
$881$	−7.85866e11			−1.30450			−0.652251	−	0.758003i	$-0.726175\pi$
$881$	−7.85866e11			−1.30450			−0.652251	+	0.758003i	$0.726175\pi$
$882$	−3.28955e8	−	3.28955e8i	−0.000543579	−	0.000543579i
$883$	−5.74398e11	+	5.74398e11i	−0.944865	+	0.944865i	−0.998558	−	0.0536922i	$-0.982901\pi$
$883$	−5.74398e11	+	5.74398e11i	−0.944865	+	0.944865i	0.0536922	+	0.998558i	$0.482901\pi$
$884$			1.47803e12i			2.42032i
$885$		0			0
$886$	−2.16539e9			−0.00351399
$887$	5.42004e11	+	5.42004e11i	0.875604	+	0.875604i	0.993076	−	0.117472i	$-0.0374791\pi$
$887$	5.42004e11	+	5.42004e11i	0.875604	+	0.875604i	−0.117472	+	0.993076i	$0.537479\pi$
$888$	−2.16716e9	+	2.16716e9i	−0.00348529	+	0.00348529i
$889$		−	6.75649e11i		−	1.08172i
$890$		0			0
$891$	−3.26284e10			−0.0517708
$892$	1.63570e11	+	1.63570e11i	0.258371	+	0.258371i
$893$	−1.42750e11	+	1.42750e11i	−0.224476	+	0.224476i
$894$			2.02555e9i			0.00317098i
$895$		0			0
$896$	6.60315e9			0.0102452
$897$	2.90488e11	+	2.90488e11i	0.448702	+	0.448702i
$898$	1.21303e9	−	1.21303e9i	0.00186537	−	0.00186537i
$899$		−	1.99948e11i		−	0.306110i
$900$		0			0
$901$	−1.52306e12			−2.31109
$902$	−1.13671e9	−	1.13671e9i	−0.00171721	−	0.00171721i
$903$	1.58699e11	−	1.58699e11i	0.238684	−	0.238684i
$904$			6.99847e9i			0.0104792i
$905$		0			0
$906$	−8.52051e8			−0.00126460
$907$	−4.62012e11	−	4.62012e11i	−0.682691	−	0.682691i	0.277915	−	0.960606i	$-0.410357\pi$
$907$	−4.62012e11	−	4.62012e11i	−0.682691	−	0.682691i	−0.960606	+	0.277915i	$0.910357\pi$
$908$	−9.12349e10	+	9.12349e10i	−0.134220	+	0.134220i
$909$		−	4.60814e11i		−	0.674948i
$910$		0			0
$911$	−9.07943e10			−0.131821			−0.0659105	−	0.997826i	$-0.520995\pi$
$911$	−9.07943e10			−0.131821			−0.0659105	+	0.997826i	$0.520995\pi$
$912$	1.03322e11	+	1.03322e11i	0.149353	+	0.149353i
$913$	−3.05212e11	+	3.05212e11i	−0.439256	+	0.439256i
$914$			2.99486e9i			0.00429132i
$915$		0			0
$916$	4.59019e11			0.652001
$917$	5.56957e11	+	5.56957e11i	0.787670	+	0.787670i
$918$	−3.13641e9	+	3.13641e9i	−0.00441634	+	0.00441634i
$919$			7.68364e11i			1.07722i	0.842555	+	0.538611i	$0.181051\pi$
$919$			7.68364e11i			1.07722i	−0.842555	+	0.538611i	$0.818949\pi$
$920$		0			0
$921$	−2.51584e11			−0.349659
$922$	−8.03994e8	−	8.03994e8i	−0.00111257	−	0.00111257i
$923$	−9.83188e11	+	9.83188e11i	−1.35466	+	1.35466i
$924$		−	4.53464e11i		−	0.622093i
$925$		0			0
$926$	−1.51701e9			−0.00206321
$927$	−1.26223e11	−	1.26223e11i	−0.170931	−	0.170931i
$928$	1.12439e9	−	1.12439e9i	0.00151609	−	0.00151609i
$929$		−	3.27428e9i		−	0.00439595i	−0.999998	−	0.00219797i	$-0.999300\pi$
$929$		−	3.27428e9i		−	0.00439595i	0.999998	−	0.00219797i	$-0.000699638\pi$
$930$		0			0
$931$	9.79830e10			0.130422
$932$	8.89670e11	+	8.89670e11i	1.17914	+	1.17914i
$933$	4.22801e10	−	4.22801e10i	0.0557968	−	0.0557968i
$934$		−	2.99893e9i		−	0.00394075i
$935$		0			0
$936$	3.88741e9			0.00506474
$937$	6.05565e11	+	6.05565e11i	0.785602	+	0.785602i	0.980770	−	0.195168i	$-0.0625252\pi$
$937$	6.05565e11	+	6.05565e11i	0.785602	+	0.785602i	−0.195168	+	0.980770i	$0.562525\pi$
$938$	−1.33233e9	+	1.33233e9i	−0.00172107	+	0.00172107i
$939$		−	3.10585e11i		−	0.399501i
$940$		0			0
$941$	−5.09340e11			−0.649604			−0.324802	−	0.945782i	$-0.605298\pi$
$941$	−5.09340e11			−0.649604			−0.324802	+	0.945782i	$0.605298\pi$
$942$	1.20047e9	+	1.20047e9i	0.00152457	+	0.00152457i
$943$	2.55937e11	−	2.55937e11i	0.323658	−	0.323658i
$944$			3.06537e11i			0.386007i
$945$		0			0
$946$	−2.26177e9			−0.00282412
$947$	−3.88892e11	−	3.88892e11i	−0.483536	−	0.483536i	0.422723	−	0.906259i	$-0.361074\pi$
$947$	−3.88892e11	−	3.88892e11i	−0.483536	−	0.483536i	−0.906259	+	0.422723i	$0.861074\pi$
$948$	4.73900e11	−	4.73900e11i	0.586751	−	0.586751i
$949$		−	5.63741e11i		−	0.695047i
$950$		0			0
$951$	−4.90697e11			−0.599918
$952$	−5.59428e9	−	5.59428e9i	−0.00681078	−	0.00681078i
$953$	7.69693e11	−	7.69693e11i	0.933138	−	0.933138i	−0.0647625	−	0.997901i	$-0.520629\pi$
$953$	7.69693e11	−	7.69693e11i	0.933138	−	0.933138i	0.997901	+	0.0647625i	$0.0206290\pi$
$954$			2.00291e9i			0.00241807i
$955$		0			0
$956$	−5.31527e10			−0.0636346
$957$	−1.02955e11	−	1.02955e11i	−0.122744	−	0.122744i
$958$	3.63374e9	−	3.63374e9i	0.00431412	−	0.00431412i
$959$			9.37208e11i			1.10806i
$960$		0			0
$961$	8.31937e11			0.975432
$962$	−3.03580e9	−	3.03580e9i	−0.00354465	−	0.00354465i
$963$	−4.70061e11	+	4.70061e11i	−0.546574	+	0.546574i
$964$			1.22679e12i			1.42057i
$965$		0			0
$966$	−1.09948e9			−0.00126264
$967$	−2.34787e11	−	2.34787e11i	−0.268514	−	0.268514i	0.559987	−	0.828501i	$-0.310806\pi$
$967$	−2.34787e11	−	2.34787e11i	−0.268514	−	0.268514i	−0.828501	+	0.559987i	$0.810806\pi$
$968$	−2.38811e9	+	2.38811e9i	−0.00271990	+	0.00271990i
$969$		−	3.50147e11i		−	0.397150i
$970$		0			0
$971$	8.22191e11			0.924903			0.462451	−	0.886645i	$-0.346970\pi$
$971$	8.22191e11			0.924903			0.462451	+	0.886645i	$0.346970\pi$
$972$	−6.22479e11	−	6.22479e11i	−0.697364	−	0.697364i
$973$	−1.15106e11	+	1.15106e11i	−0.128424	+	0.128424i
$974$		−	2.14272e9i		−	0.00238083i
$975$		0			0
$976$	1.83869e11			0.202632
$977$	−5.76953e11	−	5.76953e11i	−0.633231	−	0.633231i	0.315646	−	0.948877i	$-0.397779\pi$
$977$	−5.76953e11	−	5.76953e11i	−0.633231	−	0.633231i	−0.948877	+	0.315646i	$0.897779\pi$
$978$	−7.09422e8	+	7.09422e8i	−0.000775441	+	0.000775441i
$979$		−	1.45038e12i		−	1.57888i
$980$		0			0
$981$	3.11009e9			0.00335813
$982$	3.08234e9	+	3.08234e9i	0.00331462	+	0.00331462i
$983$	4.85960e11	−	4.85960e11i	0.520459	−	0.520459i	−0.397251	−	0.917710i	$-0.630036\pi$
$983$	4.85960e11	−	4.85960e11i	0.520459	−	0.520459i	0.917710	+	0.397251i	$0.130036\pi$
$984$			2.28816e9i			0.00244065i
$985$		0			0
$986$	−1.27012e9			−0.00134381
$987$	−3.15280e11	−	3.15280e11i	−0.332221	−	0.332221i
$988$	−2.89476e11	+	2.89476e11i	−0.303797	+	0.303797i
$989$		−	5.09252e11i		−	0.532289i
$990$		0			0
$991$	−3.32861e11			−0.345118			−0.172559	−	0.984999i	$-0.555204\pi$
$991$	−3.32861e11			−0.345118			−0.172559	+	0.984999i	$0.555204\pi$
$992$	9.47449e9	+	9.47449e9i	0.00978383	+	0.00978383i
$993$	−7.02748e11	+	7.02748e11i	−0.722774	+	0.722774i
$994$		−	3.72131e9i		−	0.00381198i
$995$		0			0
$996$	3.07189e11			0.312153
$997$	−7.44367e11	−	7.44367e11i	−0.753366	−	0.753366i	0.221740	−	0.975106i	$-0.428827\pi$
$997$	−7.44367e11	−	7.44367e11i	−0.753366	−	0.753366i	−0.975106	+	0.221740i	$0.928827\pi$
$998$	1.47935e8	−	1.47935e8i	0.000149125	−	0.000149125i
$999$			1.19645e12i			1.20124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.9.c.c.7.3	✓	12
5.2	odd	4	inner	25.9.c.c.18.4	yes	12
5.3	odd	4	inner	25.9.c.c.18.3	yes	12
5.4	even	2	inner	25.9.c.c.7.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.9.c.c.7.3	✓	12	1.1	even	1	trivial
25.9.c.c.7.4	yes	12	5.4	even	2	inner
25.9.c.c.18.3	yes	12	5.3	odd	4	inner
25.9.c.c.18.4	yes	12	5.2	odd	4	inner

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	25.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0371264 - 0.0371264i) q^{2} +(-36.2471 + 36.2471i) q^{3} -255.997i q^{4} +2.69145 q^{6} +(1325.17 + 1325.17i) q^{7} +(-19.0086 + 19.0086i) q^{8} +3933.30i q^{9} +O(q^{10})\)	\(q+(-0.0371264 - 0.0371264i) q^{2} +(-36.2471 + 36.2471i) q^{3} -255.997i q^{4} +2.69145 q^{6} +(1325.17 + 1325.17i) q^{7} +(-19.0086 + 19.0086i) q^{8} +3933.30i q^{9} -18438.9 q^{11} +(9279.16 + 9279.16i) q^{12} +(-25997.0 + 25997.0i) q^{13} -98.3973i q^{14} -65533.9 q^{16} +(111044. + 111044. i) q^{17} +(146.029 - 146.029i) q^{18} +43496.4i q^{19} -96066.9 q^{21} +(684.569 + 684.569i) q^{22} +(-154135. + 154135. i) q^{23} -1378.01i q^{24} +1930.35 q^{26} +(-380388. - 380388. i) q^{27} +(339239. - 339239. i) q^{28} -154042. i q^{29} +1.29801e6 q^{31} +(7299.24 + 7299.24i) q^{32} +(668356. - 668356. i) q^{33} -8245.30i q^{34} +1.00691e6 q^{36} +(-1.57267e6 - 1.57267e6i) q^{37} +(1614.86 - 1614.86i) q^{38} -1.88463e6i q^{39} -1.66047e6 q^{41} +(3566.62 + 3566.62i) q^{42} +(-1.65197e6 + 1.65197e6i) q^{43} +4.72030e6i q^{44} +11445.0 q^{46} +(3.28188e6 + 3.28188e6i) q^{47} +(2.37541e6 - 2.37541e6i) q^{48} -2.25267e6i q^{49} -8.05002e6 q^{51} +(6.65516e6 + 6.65516e6i) q^{52} +(-6.85792e6 + 6.85792e6i) q^{53} +28244.9i q^{54} -50379.2 q^{56} +(-1.57662e6 - 1.57662e6i) q^{57} +(-5719.02 + 5719.02i) q^{58} -4.67754e6i q^{59} -2.80570e6 q^{61} +(-48190.4 - 48190.4i) q^{62} +(-5.21227e6 + 5.21227e6i) q^{63} +1.67761e7i q^{64} -49627.3 q^{66} +(-1.35403e7 - 1.35403e7i) q^{67} +(2.84269e7 - 2.84269e7i) q^{68} -1.11739e7i q^{69} +3.78193e7 q^{71} +(-74766.5 - 74766.5i) q^{72} +(-1.08424e7 + 1.08424e7i) q^{73} +116775. i q^{74} +1.11350e7 q^{76} +(-2.44346e7 - 2.44346e7i) q^{77} +(-69969.6 + 69969.6i) q^{78} -5.10715e7i q^{79} +1.76954e6 q^{81} +(61647.4 + 61647.4i) q^{82} +(1.65526e7 - 1.65526e7i) q^{83} +2.45929e7i q^{84} +122663. q^{86} +(5.58357e6 + 5.58357e6i) q^{87} +(350497. - 350497. i) q^{88} +7.86587e7i q^{89} -6.89007e7 q^{91} +(3.94581e7 + 3.94581e7i) q^{92} +(-4.70491e7 + 4.70491e7i) q^{93} -243689. i q^{94} -529153. q^{96} +(3.88232e7 + 3.88232e7i) q^{97} +(-83633.5 + 83633.5i) q^{98} -7.25256e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6396 q^{6}+O(q^{10}) \) 12 * q - 6396 * q^6	\( 12 q - 6396 q^{6} - 118116 q^{11} - 1204068 q^{16} - 1365456 q^{21} + 5376024 q^{26} + 3223704 q^{31} + 14477592 q^{36} + 10940364 q^{41} - 51272856 q^{46} - 47621676 q^{51} - 64717200 q^{56} - 23597616 q^{61} + 264735828 q^{66} - 47870856 q^{71} + 432845700 q^{76} + 3008052 q^{81} - 105341616 q^{86} - 64237536 q^{91} - 1580181156 q^{96}+O(q^{100}) \) 12 * q - 6396 * q^6 - 118116 * q^11 - 1204068 * q^16 - 1365456 * q^21 + 5376024 * q^26 + 3223704 * q^31 + 14477592 * q^36 + 10940364 * q^41 - 51272856 * q^46 - 47621676 * q^51 - 64717200 * q^56 - 23597616 * q^61 + 264735828 * q^66 - 47870856 * q^71 + 432845700 * q^76 + 3008052 * q^81 - 105341616 * q^86 - 64237536 * q^91 - 1580181156 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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