LMFDB - Embedded newform 26.2.b.a.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [26,2,Mod(25,26)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(26, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("26.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	26.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:	$0.207611045255$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			25.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	26.25
Dual form			26.2.b.a.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -3.00000i q^{5} -1.00000i q^{6} +3.00000i q^{7} -1.00000i q^{8} -2.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -3.00000i q^{5} -1.00000i q^{6} +3.00000i q^{7} -1.00000i q^{8} -2.00000 q^{9} +3.00000 q^{10} +1.00000 q^{12} +(2.00000 + 3.00000i) q^{13} -3.00000 q^{14} +3.00000i q^{15} +1.00000 q^{16} +3.00000 q^{17} -2.00000i q^{18} -6.00000i q^{19} +3.00000i q^{20} -3.00000i q^{21} -6.00000 q^{23} +1.00000i q^{24} -4.00000 q^{25} +(-3.00000 + 2.00000i) q^{26} +5.00000 q^{27} -3.00000i q^{28} -3.00000 q^{30} +1.00000i q^{32} +3.00000i q^{34} +9.00000 q^{35} +2.00000 q^{36} +3.00000i q^{37} +6.00000 q^{38} +(-2.00000 - 3.00000i) q^{39} -3.00000 q^{40} +3.00000 q^{42} -1.00000 q^{43} +6.00000i q^{45} -6.00000i q^{46} +3.00000i q^{47} -1.00000 q^{48} -2.00000 q^{49} -4.00000i q^{50} -3.00000 q^{51} +(-2.00000 - 3.00000i) q^{52} -6.00000 q^{53} +5.00000i q^{54} +3.00000 q^{56} +6.00000i q^{57} -6.00000i q^{59} -3.00000i q^{60} -8.00000 q^{61} -6.00000i q^{63} -1.00000 q^{64} +(9.00000 - 6.00000i) q^{65} -12.0000i q^{67} -3.00000 q^{68} +6.00000 q^{69} +9.00000i q^{70} +15.0000i q^{71} +2.00000i q^{72} +6.00000i q^{73} -3.00000 q^{74} +4.00000 q^{75} +6.00000i q^{76} +(3.00000 - 2.00000i) q^{78} +10.0000 q^{79} -3.00000i q^{80} +1.00000 q^{81} +6.00000i q^{83} +3.00000i q^{84} -9.00000i q^{85} -1.00000i q^{86} -6.00000i q^{89} -6.00000 q^{90} +(-9.00000 + 6.00000i) q^{91} +6.00000 q^{92} -3.00000 q^{94} -18.0000 q^{95} -1.00000i q^{96} -12.0000i q^{97} -2.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - 2 q^{4} - 4 q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 - 2 * q^4 - 4 * q^9	$ 2 q - 2 q^{3} - 2 q^{4} - 4 q^{9} + 6 q^{10} + 2 q^{12} + 4 q^{13} - 6 q^{14} + 2 q^{16} + 6 q^{17} - 12 q^{23} - 8 q^{25} - 6 q^{26} + 10 q^{27} - 6 q^{30} + 18 q^{35} + 4 q^{36} + 12 q^{38} - 4 q^{39} - 6 q^{40} + 6 q^{42} - 2 q^{43} - 2 q^{48} - 4 q^{49} - 6 q^{51} - 4 q^{52} - 12 q^{53} + 6 q^{56} - 16 q^{61} - 2 q^{64} + 18 q^{65} - 6 q^{68} + 12 q^{69} - 6 q^{74} + 8 q^{75} + 6 q^{78} + 20 q^{79} + 2 q^{81} - 12 q^{90} - 18 q^{91} + 12 q^{92} - 6 q^{94} - 36 q^{95}+O(q^{100}) $ 2 * q - 2 * q^3 - 2 * q^4 - 4 * q^9 + 6 * q^10 + 2 * q^12 + 4 * q^13 - 6 * q^14 + 2 * q^16 + 6 * q^17 - 12 * q^23 - 8 * q^25 - 6 * q^26 + 10 * q^27 - 6 * q^30 + 18 * q^35 + 4 * q^36 + 12 * q^38 - 4 * q^39 - 6 * q^40 + 6 * q^42 - 2 * q^43 - 2 * q^48 - 4 * q^49 - 6 * q^51 - 4 * q^52 - 12 * q^53 + 6 * q^56 - 16 * q^61 - 2 * q^64 + 18 * q^65 - 6 * q^68 + 12 * q^69 - 6 * q^74 + 8 * q^75 + 6 * q^78 + 20 * q^79 + 2 * q^81 - 12 * q^90 - 18 * q^91 + 12 * q^92 - 6 * q^94 - 36 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.00000			−0.577350			−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000			−0.577350			−0.288675	+	0.957427i	$0.593215\pi$
$4$	−1.00000			−0.500000
$5$		−	3.00000i		−	1.34164i	−0.741620	−	0.670820i	$-0.765942\pi$
$5$		−	3.00000i		−	1.34164i	0.741620	−	0.670820i	$-0.234058\pi$
$6$		−	1.00000i		−	0.408248i
$7$			3.00000i			1.13389i	0.823754	+	0.566947i	$0.191875\pi$
$7$			3.00000i			1.13389i	−0.823754	+	0.566947i	$0.808125\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−2.00000			−0.666667
$10$	3.00000			0.948683
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$	1.00000			0.288675
$13$	2.00000	+	3.00000i	0.554700	+	0.832050i
$13$	2.00000	+	3.00000i	0.554700	+	0.832050i
$14$	−3.00000			−0.801784
$15$			3.00000i			0.774597i
$16$	1.00000			0.250000
$17$	3.00000			0.727607			0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000			0.727607			0.363803	+	0.931476i	$0.381478\pi$
$18$		−	2.00000i		−	0.471405i
$19$		−	6.00000i		−	1.37649i	−0.725476	−	0.688247i	$-0.758380\pi$
$19$		−	6.00000i		−	1.37649i	0.725476	−	0.688247i	$-0.241620\pi$
$20$			3.00000i			0.670820i
$21$		−	3.00000i		−	0.654654i
$22$		0			0
$23$	−6.00000			−1.25109			−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000			−1.25109			−0.625543	+	0.780189i	$0.715123\pi$
$24$			1.00000i			0.204124i
$25$	−4.00000			−0.800000
$26$	−3.00000	+	2.00000i	−0.588348	+	0.392232i
$27$	5.00000			0.962250
$28$		−	3.00000i		−	0.566947i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$	−3.00000			−0.547723
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$			3.00000i			0.514496i
$35$	9.00000			1.52128
$36$	2.00000			0.333333
$37$			3.00000i			0.493197i	0.969118	+	0.246598i	$0.0793129\pi$
$37$			3.00000i			0.493197i	−0.969118	+	0.246598i	$0.920687\pi$
$38$	6.00000			0.973329
$39$	−2.00000	−	3.00000i	−0.320256	−	0.480384i
$40$	−3.00000			−0.474342
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$	3.00000			0.462910
$43$	−1.00000			−0.152499			−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000			−0.152499			−0.0762493	+	0.997089i	$0.524294\pi$
$44$		0			0
$45$			6.00000i			0.894427i
$46$		−	6.00000i		−	0.884652i
$47$			3.00000i			0.437595i	0.975770	+	0.218797i	$0.0702134\pi$
$47$			3.00000i			0.437595i	−0.975770	+	0.218797i	$0.929787\pi$
$48$	−1.00000			−0.144338
$49$	−2.00000			−0.285714
$50$		−	4.00000i		−	0.565685i
$51$	−3.00000			−0.420084
$52$	−2.00000	−	3.00000i	−0.277350	−	0.416025i
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$			5.00000i			0.680414i
$55$		0			0
$56$	3.00000			0.400892
$57$			6.00000i			0.794719i
$58$		0			0
$59$		−	6.00000i		−	0.781133i	−0.920575	−	0.390567i	$-0.872279\pi$
$59$		−	6.00000i		−	0.781133i	0.920575	−	0.390567i	$-0.127721\pi$
$60$		−	3.00000i		−	0.387298i
$61$	−8.00000			−1.02430			−0.512148	−	0.858898i	$-0.671150\pi$
$61$	−8.00000			−1.02430			−0.512148	+	0.858898i	$0.671150\pi$
$62$		0			0
$63$		−	6.00000i		−	0.755929i
$64$	−1.00000			−0.125000
$65$	9.00000	−	6.00000i	1.11631	−	0.744208i
$66$		0			0
$67$		−	12.0000i		−	1.46603i	−0.680211	−	0.733017i	$-0.738112\pi$
$67$		−	12.0000i		−	1.46603i	0.680211	−	0.733017i	$-0.261888\pi$
$68$	−3.00000			−0.363803
$69$	6.00000			0.722315
$70$			9.00000i			1.07571i
$71$			15.0000i			1.78017i	0.455792	+	0.890086i	$0.349356\pi$
$71$			15.0000i			1.78017i	−0.455792	+	0.890086i	$0.650644\pi$
$72$			2.00000i			0.235702i
$73$			6.00000i			0.702247i	0.936329	+	0.351123i	$0.114200\pi$
$73$			6.00000i			0.702247i	−0.936329	+	0.351123i	$0.885800\pi$
$74$	−3.00000			−0.348743
$75$	4.00000			0.461880
$76$			6.00000i			0.688247i
$77$		0			0
$78$	3.00000	−	2.00000i	0.339683	−	0.226455i
$79$	10.0000			1.12509			0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000			1.12509			0.562544	+	0.826767i	$0.309823\pi$
$80$		−	3.00000i		−	0.335410i
$81$	1.00000			0.111111
$82$		0			0
$83$			6.00000i			0.658586i	0.944228	+	0.329293i	$0.106810\pi$
$83$			6.00000i			0.658586i	−0.944228	+	0.329293i	$0.893190\pi$
$84$			3.00000i			0.327327i
$85$		−	9.00000i		−	0.976187i
$86$		−	1.00000i		−	0.107833i
$87$		0			0
$88$		0			0
$89$		−	6.00000i		−	0.635999i	−0.948091	−	0.317999i	$-0.896989\pi$
$89$		−	6.00000i		−	0.635999i	0.948091	−	0.317999i	$-0.103011\pi$
$90$	−6.00000			−0.632456
$91$	−9.00000	+	6.00000i	−0.943456	+	0.628971i
$92$	6.00000			0.625543
$93$		0			0
$94$	−3.00000			−0.309426
$95$	−18.0000			−1.84676
$96$		−	1.00000i		−	0.102062i
$97$		−	12.0000i		−	1.21842i	−0.793011	−	0.609208i	$-0.791488\pi$
$97$		−	12.0000i		−	1.21842i	0.793011	−	0.609208i	$-0.208512\pi$
$98$		−	2.00000i		−	0.202031i
$99$		0			0
$100$	4.00000			0.400000
$101$	12.0000			1.19404			0.597022	−	0.802225i	$-0.296350\pi$
$101$	12.0000			1.19404			0.597022	+	0.802225i	$0.296350\pi$
$102$		−	3.00000i		−	0.297044i
$103$	14.0000			1.37946			0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000			1.37946			0.689730	+	0.724066i	$0.257729\pi$
$104$	3.00000	−	2.00000i	0.294174	−	0.196116i
$105$	−9.00000			−0.878310
$106$		−	6.00000i		−	0.582772i
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$	−5.00000			−0.481125
$109$			9.00000i			0.862044i	0.902342	+	0.431022i	$0.141847\pi$
$109$			9.00000i			0.862044i	−0.902342	+	0.431022i	$0.858153\pi$
$110$		0			0
$111$		−	3.00000i		−	0.284747i
$112$			3.00000i			0.283473i
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$	−6.00000			−0.561951
$115$			18.0000i			1.67851i
$116$		0			0
$117$	−4.00000	−	6.00000i	−0.369800	−	0.554700i
$118$	6.00000			0.552345
$119$			9.00000i			0.825029i
$120$	3.00000			0.273861
$121$	11.0000			1.00000
$122$		−	8.00000i		−	0.724286i
$123$		0			0
$124$		0			0
$125$		−	3.00000i		−	0.268328i
$126$	6.00000			0.534522
$127$	−2.00000			−0.177471			−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000			−0.177471			−0.0887357	+	0.996055i	$0.528283\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	1.00000			0.0880451
$130$	6.00000	+	9.00000i	0.526235	+	0.789352i
$131$	−3.00000			−0.262111			−0.131056	−	0.991375i	$-0.541837\pi$
$131$	−3.00000			−0.262111			−0.131056	+	0.991375i	$0.541837\pi$
$132$		0			0
$133$	18.0000			1.56080
$134$	12.0000			1.03664
$135$		−	15.0000i		−	1.29099i
$136$		−	3.00000i		−	0.257248i
$137$			18.0000i			1.53784i	0.639343	+	0.768922i	$0.279207\pi$
$137$			18.0000i			1.53784i	−0.639343	+	0.768922i	$0.720793\pi$
$138$			6.00000i			0.510754i
$139$	5.00000			0.424094			0.212047	−	0.977259i	$-0.431987\pi$
$139$	5.00000			0.424094			0.212047	+	0.977259i	$0.431987\pi$
$140$	−9.00000			−0.760639
$141$		−	3.00000i		−	0.252646i
$142$	−15.0000			−1.25877
$143$		0			0
$144$	−2.00000			−0.166667
$145$		0			0
$146$	−6.00000			−0.496564
$147$	2.00000			0.164957
$148$		−	3.00000i		−	0.246598i
$149$		−	6.00000i		−	0.491539i	−0.969328	−	0.245770i	$-0.920959\pi$
$149$		−	6.00000i		−	0.491539i	0.969328	−	0.245770i	$-0.0790407\pi$
$150$			4.00000i			0.326599i
$151$		−	15.0000i		−	1.22068i	−0.792139	−	0.610341i	$-0.791032\pi$
$151$		−	15.0000i		−	1.22068i	0.792139	−	0.610341i	$-0.208968\pi$
$152$	−6.00000			−0.486664
$153$	−6.00000			−0.485071
$154$		0			0
$155$		0			0
$156$	2.00000	+	3.00000i	0.160128	+	0.240192i
$157$	−22.0000			−1.75579			−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000			−1.75579			−0.877896	+	0.478852i	$0.841053\pi$
$158$			10.0000i			0.795557i
$159$	6.00000			0.475831
$160$	3.00000			0.237171
$161$		−	18.0000i		−	1.41860i
$162$			1.00000i			0.0785674i
$163$			6.00000i			0.469956i	0.972001	+	0.234978i	$0.0755019\pi$
$163$			6.00000i			0.469956i	−0.972001	+	0.234978i	$0.924498\pi$
$164$		0			0
$165$		0			0
$166$	−6.00000			−0.465690
$167$		−	12.0000i		−	0.928588i	−0.885681	−	0.464294i	$-0.846308\pi$
$167$		−	12.0000i		−	0.928588i	0.885681	−	0.464294i	$-0.153692\pi$
$168$	−3.00000			−0.231455
$169$	−5.00000	+	12.0000i	−0.384615	+	0.923077i
$170$	9.00000			0.690268
$171$			12.0000i			0.917663i
$172$	1.00000			0.0762493
$173$	−6.00000			−0.456172			−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000			−0.456172			−0.228086	+	0.973641i	$0.573247\pi$
$174$		0			0
$175$		−	12.0000i		−	0.907115i
$176$		0			0
$177$			6.00000i			0.450988i
$178$	6.00000			0.449719
$179$	15.0000			1.12115			0.560576	−	0.828103i	$-0.310580\pi$
$179$	15.0000			1.12115			0.560576	+	0.828103i	$0.310580\pi$
$180$		−	6.00000i		−	0.447214i
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	−6.00000	−	9.00000i	−0.444750	−	0.667124i
$183$	8.00000			0.591377
$184$			6.00000i			0.442326i
$185$	9.00000			0.661693
$186$		0			0
$187$		0			0
$188$		−	3.00000i		−	0.218797i
$189$			15.0000i			1.09109i
$190$		−	18.0000i		−	1.30586i
$191$	12.0000			0.868290			0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000			0.868290			0.434145	+	0.900843i	$0.357051\pi$
$192$	1.00000			0.0721688
$193$			6.00000i			0.431889i	0.976406	+	0.215945i	$0.0692831\pi$
$193$			6.00000i			0.431889i	−0.976406	+	0.215945i	$0.930717\pi$
$194$	12.0000			0.861550
$195$	−9.00000	+	6.00000i	−0.644503	+	0.429669i
$196$	2.00000			0.142857
$197$			3.00000i			0.213741i	0.994273	+	0.106871i	$0.0340831\pi$
$197$			3.00000i			0.213741i	−0.994273	+	0.106871i	$0.965917\pi$
$198$		0			0
$199$	−20.0000			−1.41776			−0.708881	−	0.705328i	$-0.750800\pi$
$199$	−20.0000			−1.41776			−0.708881	+	0.705328i	$0.750800\pi$
$200$			4.00000i			0.282843i
$201$			12.0000i			0.846415i
$202$			12.0000i			0.844317i
$203$		0			0
$204$	3.00000			0.210042
$205$		0			0
$206$			14.0000i			0.975426i
$207$	12.0000			0.834058
$208$	2.00000	+	3.00000i	0.138675	+	0.208013i
$209$		0			0
$210$		−	9.00000i		−	0.621059i
$211$	−23.0000			−1.58339			−0.791693	−	0.610920i	$-0.790800\pi$
$211$	−23.0000			−1.58339			−0.791693	+	0.610920i	$0.790800\pi$
$212$	6.00000			0.412082
$213$		−	15.0000i		−	1.02778i
$214$		−	12.0000i		−	0.820303i
$215$			3.00000i			0.204598i
$216$		−	5.00000i		−	0.340207i
$217$		0			0
$218$	−9.00000			−0.609557
$219$		−	6.00000i		−	0.405442i
$220$		0			0
$221$	6.00000	+	9.00000i	0.403604	+	0.605406i
$222$	3.00000			0.201347
$223$		−	9.00000i		−	0.602685i	−0.953516	−	0.301342i	$-0.902565\pi$
$223$		−	9.00000i		−	0.602685i	0.953516	−	0.301342i	$-0.0974347\pi$
$224$	−3.00000			−0.200446
$225$	8.00000			0.533333
$226$		−	6.00000i		−	0.399114i
$227$		−	12.0000i		−	0.796468i	−0.917284	−	0.398234i	$-0.869623\pi$
$227$		−	12.0000i		−	0.796468i	0.917284	−	0.398234i	$-0.130377\pi$
$228$		−	6.00000i		−	0.397360i
$229$			9.00000i			0.594737i	0.954763	+	0.297368i	$0.0961089\pi$
$229$			9.00000i			0.594737i	−0.954763	+	0.297368i	$0.903891\pi$
$230$	−18.0000			−1.18688
$231$		0			0
$232$		0			0
$233$	−21.0000			−1.37576			−0.687878	−	0.725826i	$-0.741458\pi$
$233$	−21.0000			−1.37576			−0.687878	+	0.725826i	$0.741458\pi$
$234$	6.00000	−	4.00000i	0.392232	−	0.261488i
$235$	9.00000			0.587095
$236$			6.00000i			0.390567i
$237$	−10.0000			−0.649570
$238$	−9.00000			−0.583383
$239$			9.00000i			0.582162i	0.956698	+	0.291081i	$0.0940149\pi$
$239$			9.00000i			0.582162i	−0.956698	+	0.291081i	$0.905985\pi$
$240$			3.00000i			0.193649i
$241$		−	30.0000i		−	1.93247i	−0.257663	−	0.966235i	$-0.582952\pi$
$241$		−	30.0000i		−	1.93247i	0.257663	−	0.966235i	$-0.417048\pi$
$242$			11.0000i			0.707107i
$243$	−16.0000			−1.02640
$244$	8.00000			0.512148
$245$			6.00000i			0.383326i
$246$		0			0
$247$	18.0000	−	12.0000i	1.14531	−	0.763542i
$248$		0			0
$249$		−	6.00000i		−	0.380235i
$250$	3.00000			0.189737
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$			6.00000i			0.377964i
$253$		0			0
$254$		−	2.00000i		−	0.125491i
$255$			9.00000i			0.563602i
$256$	1.00000			0.0625000
$257$	3.00000			0.187135			0.0935674	−	0.995613i	$-0.470173\pi$
$257$	3.00000			0.187135			0.0935674	+	0.995613i	$0.470173\pi$
$258$			1.00000i			0.0622573i
$259$	−9.00000			−0.559233
$260$	−9.00000	+	6.00000i	−0.558156	+	0.372104i
$261$		0			0
$262$		−	3.00000i		−	0.185341i
$263$	24.0000			1.47990			0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000			1.47990			0.739952	+	0.672660i	$0.234848\pi$
$264$		0			0
$265$			18.0000i			1.10573i
$266$			18.0000i			1.10365i
$267$			6.00000i			0.367194i
$268$			12.0000i			0.733017i
$269$		0			0			−	1.00000i	$-0.5\pi$
$269$		0			0				1.00000i	$0.5\pi$
$270$	15.0000			0.912871
$271$			15.0000i			0.911185i	0.890188	+	0.455593i	$0.150573\pi$
$271$			15.0000i			0.911185i	−0.890188	+	0.455593i	$0.849427\pi$
$272$	3.00000			0.181902
$273$	9.00000	−	6.00000i	0.544705	−	0.363137i
$274$	−18.0000			−1.08742
$275$		0			0
$276$	−6.00000			−0.361158
$277$	8.00000			0.480673			0.240337	−	0.970690i	$-0.422742\pi$
$277$	8.00000			0.480673			0.240337	+	0.970690i	$0.422742\pi$
$278$			5.00000i			0.299880i
$279$		0			0
$280$		−	9.00000i		−	0.537853i
$281$		−	30.0000i		−	1.78965i	−0.446417	−	0.894825i	$-0.647300\pi$
$281$		−	30.0000i		−	1.78965i	0.446417	−	0.894825i	$-0.352700\pi$
$282$	3.00000			0.178647
$283$	4.00000			0.237775			0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000			0.237775			0.118888	+	0.992908i	$0.462067\pi$
$284$		−	15.0000i		−	0.890086i
$285$	18.0000			1.06623
$286$		0			0
$287$		0			0
$288$		−	2.00000i		−	0.117851i
$289$	−8.00000			−0.470588
$290$		0			0
$291$			12.0000i			0.703452i
$292$		−	6.00000i		−	0.351123i
$293$		−	9.00000i		−	0.525786i	−0.964825	−	0.262893i	$-0.915323\pi$
$293$		−	9.00000i		−	0.525786i	0.964825	−	0.262893i	$-0.0846766\pi$
$294$			2.00000i			0.116642i
$295$	−18.0000			−1.04800
$296$	3.00000			0.174371
$297$		0			0
$298$	6.00000			0.347571
$299$	−12.0000	−	18.0000i	−0.693978	−	1.04097i
$300$	−4.00000			−0.230940
$301$		−	3.00000i		−	0.172917i
$302$	15.0000			0.863153
$303$	−12.0000			−0.689382
$304$		−	6.00000i		−	0.344124i
$305$			24.0000i			1.37424i
$306$		−	6.00000i		−	0.342997i
$307$			18.0000i			1.02731i	0.857996	+	0.513657i	$0.171710\pi$
$307$			18.0000i			1.02731i	−0.857996	+	0.513657i	$0.828290\pi$
$308$		0			0
$309$	−14.0000			−0.796432
$310$		0			0
$311$	−18.0000			−1.02069			−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000			−1.02069			−0.510343	+	0.859971i	$0.670482\pi$
$312$	−3.00000	+	2.00000i	−0.169842	+	0.113228i
$313$	19.0000			1.07394			0.536972	−	0.843600i	$-0.319568\pi$
$313$	19.0000			1.07394			0.536972	+	0.843600i	$0.319568\pi$
$314$		−	22.0000i		−	1.24153i
$315$	−18.0000			−1.01419
$316$	−10.0000			−0.562544
$317$			18.0000i			1.01098i	0.862832	+	0.505490i	$0.168688\pi$
$317$			18.0000i			1.01098i	−0.862832	+	0.505490i	$0.831312\pi$
$318$			6.00000i			0.336463i
$319$		0			0
$320$			3.00000i			0.167705i
$321$	12.0000			0.669775
$322$	18.0000			1.00310
$323$		−	18.0000i		−	1.00155i
$324$	−1.00000			−0.0555556
$325$	−8.00000	−	12.0000i	−0.443760	−	0.665640i
$326$	−6.00000			−0.332309
$327$		−	9.00000i		−	0.497701i
$328$		0			0
$329$	−9.00000			−0.496186
$330$		0			0
$331$			30.0000i			1.64895i	0.565899	+	0.824475i	$0.308529\pi$
$331$			30.0000i			1.64895i	−0.565899	+	0.824475i	$0.691471\pi$
$332$		−	6.00000i		−	0.329293i
$333$		−	6.00000i		−	0.328798i
$334$	12.0000			0.656611
$335$	−36.0000			−1.96689
$336$		−	3.00000i		−	0.163663i
$337$	13.0000			0.708155			0.354078	−	0.935216i	$-0.384795\pi$
$337$	13.0000			0.708155			0.354078	+	0.935216i	$0.384795\pi$
$338$	−12.0000	−	5.00000i	−0.652714	−	0.271964i
$339$	6.00000			0.325875
$340$			9.00000i			0.488094i
$341$		0			0
$342$	−12.0000			−0.648886
$343$			15.0000i			0.809924i
$344$			1.00000i			0.0539164i
$345$		−	18.0000i		−	0.969087i
$346$		−	6.00000i		−	0.322562i
$347$	33.0000			1.77153			0.885766	−	0.464131i	$-0.153633\pi$
$347$	33.0000			1.77153			0.885766	+	0.464131i	$0.153633\pi$
$348$		0			0
$349$		−	21.0000i		−	1.12410i	−0.827102	−	0.562052i	$-0.810012\pi$
$349$		−	21.0000i		−	1.12410i	0.827102	−	0.562052i	$-0.189988\pi$
$350$	12.0000			0.641427
$351$	10.0000	+	15.0000i	0.533761	+	0.800641i
$352$		0			0
$353$			6.00000i			0.319348i	0.987170	+	0.159674i	$0.0510443\pi$
$353$			6.00000i			0.319348i	−0.987170	+	0.159674i	$0.948956\pi$
$354$	−6.00000			−0.318896
$355$	45.0000			2.38835
$356$			6.00000i			0.317999i
$357$		−	9.00000i		−	0.476331i
$358$			15.0000i			0.792775i
$359$			24.0000i			1.26667i	0.773877	+	0.633336i	$0.218315\pi$
$359$			24.0000i			1.26667i	−0.773877	+	0.633336i	$0.781685\pi$
$360$	6.00000			0.316228
$361$	−17.0000			−0.894737
$362$			2.00000i			0.105118i
$363$	−11.0000			−0.577350
$364$	9.00000	−	6.00000i	0.471728	−	0.314485i
$365$	18.0000			0.942163
$366$			8.00000i			0.418167i
$367$	8.00000			0.417597			0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000			0.417597			0.208798	+	0.977959i	$0.433045\pi$
$368$	−6.00000			−0.312772
$369$		0			0
$370$			9.00000i			0.467888i
$371$		−	18.0000i		−	0.934513i
$372$		0			0
$373$	4.00000			0.207112			0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000			0.207112			0.103556	+	0.994624i	$0.466978\pi$
$374$		0			0
$375$			3.00000i			0.154919i
$376$	3.00000			0.154713
$377$		0			0
$378$	−15.0000			−0.771517
$379$		−	6.00000i		−	0.308199i	−0.988055	−	0.154100i	$-0.950752\pi$
$379$		−	6.00000i		−	0.308199i	0.988055	−	0.154100i	$-0.0492477\pi$
$380$	18.0000			0.923381
$381$	2.00000			0.102463
$382$			12.0000i			0.613973i
$383$		−	9.00000i		−	0.459879i	−0.973205	−	0.229939i	$-0.926147\pi$
$383$		−	9.00000i		−	0.459879i	0.973205	−	0.229939i	$-0.0738528\pi$
$384$			1.00000i			0.0510310i
$385$		0			0
$386$	−6.00000			−0.305392
$387$	2.00000			0.101666
$388$			12.0000i			0.609208i
$389$	−30.0000			−1.52106			−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000			−1.52106			−0.760530	+	0.649303i	$0.775061\pi$
$390$	−6.00000	−	9.00000i	−0.303822	−	0.455733i
$391$	−18.0000			−0.910299
$392$			2.00000i			0.101015i
$393$	3.00000			0.151330
$394$	−3.00000			−0.151138
$395$		−	30.0000i		−	1.50946i
$396$		0			0
$397$			18.0000i			0.903394i	0.892171	+	0.451697i	$0.149181\pi$
$397$			18.0000i			0.903394i	−0.892171	+	0.451697i	$0.850819\pi$
$398$		−	20.0000i		−	1.00251i
$399$	−18.0000			−0.901127
$400$	−4.00000			−0.200000
$401$			30.0000i			1.49813i	0.662497	+	0.749064i	$0.269497\pi$
$401$			30.0000i			1.49813i	−0.662497	+	0.749064i	$0.730503\pi$
$402$	−12.0000			−0.598506
$403$		0			0
$404$	−12.0000			−0.597022
$405$		−	3.00000i		−	0.149071i
$406$		0			0
$407$		0			0
$408$			3.00000i			0.148522i
$409$		−	6.00000i		−	0.296681i	−0.988936	−	0.148340i	$-0.952607\pi$
$409$		−	6.00000i		−	0.296681i	0.988936	−	0.148340i	$-0.0473931\pi$
$410$		0			0
$411$		−	18.0000i		−	0.887875i
$412$	−14.0000			−0.689730
$413$	18.0000			0.885722
$414$			12.0000i			0.589768i
$415$	18.0000			0.883585
$416$	−3.00000	+	2.00000i	−0.147087	+	0.0980581i
$417$	−5.00000			−0.244851
$418$		0			0
$419$	15.0000			0.732798			0.366399	−	0.930458i	$-0.380591\pi$
$419$	15.0000			0.732798			0.366399	+	0.930458i	$0.380591\pi$
$420$	9.00000			0.439155
$421$		−	15.0000i		−	0.731055i	−0.930800	−	0.365528i	$-0.880889\pi$
$421$		−	15.0000i		−	0.731055i	0.930800	−	0.365528i	$-0.119111\pi$
$422$		−	23.0000i		−	1.11962i
$423$		−	6.00000i		−	0.291730i
$424$			6.00000i			0.291386i
$425$	−12.0000			−0.582086
$426$	15.0000			0.726752
$427$		−	24.0000i		−	1.16144i
$428$	12.0000			0.580042
$429$		0			0
$430$	−3.00000			−0.144673
$431$		−	15.0000i		−	0.722525i	−0.932464	−	0.361262i	$-0.882346\pi$
$431$		−	15.0000i		−	0.722525i	0.932464	−	0.361262i	$-0.117654\pi$
$432$	5.00000			0.240563
$433$	−11.0000			−0.528626			−0.264313	−	0.964437i	$-0.585145\pi$
$433$	−11.0000			−0.528626			−0.264313	+	0.964437i	$0.585145\pi$
$434$		0			0
$435$		0			0
$436$		−	9.00000i		−	0.431022i
$437$			36.0000i			1.72211i
$438$	6.00000			0.286691
$439$	−10.0000			−0.477274			−0.238637	−	0.971109i	$-0.576701\pi$
$439$	−10.0000			−0.477274			−0.238637	+	0.971109i	$0.576701\pi$
$440$		0			0
$441$	4.00000			0.190476
$442$	−9.00000	+	6.00000i	−0.428086	+	0.285391i
$443$	−21.0000			−0.997740			−0.498870	−	0.866677i	$-0.666252\pi$
$443$	−21.0000			−0.997740			−0.498870	+	0.866677i	$0.666252\pi$
$444$			3.00000i			0.142374i
$445$	−18.0000			−0.853282
$446$	9.00000			0.426162
$447$			6.00000i			0.283790i
$448$		−	3.00000i		−	0.141737i
$449$			24.0000i			1.13263i	0.824189	+	0.566315i	$0.191631\pi$
$449$			24.0000i			1.13263i	−0.824189	+	0.566315i	$0.808369\pi$
$450$			8.00000i			0.377124i
$451$		0			0
$452$	6.00000			0.282216
$453$			15.0000i			0.704761i
$454$	12.0000			0.563188
$455$	18.0000	+	27.0000i	0.843853	+	1.26578i
$456$	6.00000			0.280976
$457$			18.0000i			0.842004i	0.907060	+	0.421002i	$0.138322\pi$
$457$			18.0000i			0.842004i	−0.907060	+	0.421002i	$0.861678\pi$
$458$	−9.00000			−0.420542
$459$	15.0000			0.700140
$460$		−	18.0000i		−	0.839254i
$461$		−	15.0000i		−	0.698620i	−0.937007	−	0.349310i	$-0.886416\pi$
$461$		−	15.0000i		−	0.698620i	0.937007	−	0.349310i	$-0.113584\pi$
$462$		0			0
$463$		−	24.0000i		−	1.11537i	−0.830051	−	0.557687i	$-0.811689\pi$
$463$		−	24.0000i		−	1.11537i	0.830051	−	0.557687i	$-0.188311\pi$
$464$		0			0
$465$		0			0
$466$		−	21.0000i		−	0.972806i
$467$	−12.0000			−0.555294			−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000			−0.555294			−0.277647	+	0.960683i	$0.589555\pi$
$468$	4.00000	+	6.00000i	0.184900	+	0.277350i
$469$	36.0000			1.66233
$470$			9.00000i			0.415139i
$471$	22.0000			1.01371
$472$	−6.00000			−0.276172
$473$		0			0
$474$		−	10.0000i		−	0.459315i
$475$			24.0000i			1.10120i
$476$		−	9.00000i		−	0.412514i
$477$	12.0000			0.549442
$478$	−9.00000			−0.411650
$479$			39.0000i			1.78196i	0.454047	+	0.890978i	$0.349980\pi$
$479$			39.0000i			1.78196i	−0.454047	+	0.890978i	$0.650020\pi$
$480$	−3.00000			−0.136931
$481$	−9.00000	+	6.00000i	−0.410365	+	0.273576i
$482$	30.0000			1.36646
$483$			18.0000i			0.819028i
$484$	−11.0000			−0.500000
$485$	−36.0000			−1.63468
$486$		−	16.0000i		−	0.725775i
$487$		−	12.0000i		−	0.543772i	−0.962329	−	0.271886i	$-0.912353\pi$
$487$		−	12.0000i		−	0.543772i	0.962329	−	0.271886i	$-0.0876473\pi$
$488$			8.00000i			0.362143i
$489$		−	6.00000i		−	0.271329i
$490$	−6.00000			−0.271052
$491$	27.0000			1.21849			0.609246	−	0.792981i	$-0.291472\pi$
$491$	27.0000			1.21849			0.609246	+	0.792981i	$0.291472\pi$
$492$		0			0
$493$		0			0
$494$	12.0000	+	18.0000i	0.539906	+	0.809858i
$495$		0			0
$496$		0			0
$497$	−45.0000			−2.01853
$498$	6.00000			0.268866
$499$		−	36.0000i		−	1.61158i	−0.592200	−	0.805791i	$-0.701741\pi$
$499$		−	36.0000i		−	1.61158i	0.592200	−	0.805791i	$-0.298259\pi$
$500$			3.00000i			0.134164i
$501$			12.0000i			0.536120i
$502$			12.0000i			0.535586i
$503$	−6.00000			−0.267527			−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000			−0.267527			−0.133763	+	0.991013i	$0.542706\pi$
$504$	−6.00000			−0.267261
$505$		−	36.0000i		−	1.60198i
$506$		0			0
$507$	5.00000	−	12.0000i	0.222058	−	0.532939i
$508$	2.00000			0.0887357
$509$		−	6.00000i		−	0.265945i	−0.991120	−	0.132973i	$-0.957548\pi$
$509$		−	6.00000i		−	0.265945i	0.991120	−	0.132973i	$-0.0424523\pi$
$510$	−9.00000			−0.398527
$511$	−18.0000			−0.796273
$512$			1.00000i			0.0441942i
$513$		−	30.0000i		−	1.32453i
$514$			3.00000i			0.132324i
$515$		−	42.0000i		−	1.85074i
$516$	−1.00000			−0.0440225
$517$		0			0
$518$		−	9.00000i		−	0.395437i
$519$	6.00000			0.263371
$520$	−6.00000	−	9.00000i	−0.263117	−	0.394676i
$521$	27.0000			1.18289			0.591446	−	0.806345i	$-0.298557\pi$
$521$	27.0000			1.18289			0.591446	+	0.806345i	$0.298557\pi$
$522$		0			0
$523$	−16.0000			−0.699631			−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000			−0.699631			−0.349816	+	0.936819i	$0.613756\pi$
$524$	3.00000			0.131056
$525$			12.0000i			0.523723i
$526$			24.0000i			1.04645i
$527$		0			0
$528$		0			0
$529$	13.0000			0.565217
$530$	−18.0000			−0.781870
$531$			12.0000i			0.520756i
$532$	−18.0000			−0.780399
$533$		0			0
$534$	−6.00000			−0.259645
$535$			36.0000i			1.55642i
$536$	−12.0000			−0.518321
$537$	−15.0000			−0.647298
$538$		0			0
$539$		0			0
$540$			15.0000i			0.645497i
$541$		−	15.0000i		−	0.644900i	−0.946586	−	0.322450i	$-0.895494\pi$
$541$		−	15.0000i		−	0.644900i	0.946586	−	0.322450i	$-0.104506\pi$
$542$	−15.0000			−0.644305
$543$	−2.00000			−0.0858282
$544$			3.00000i			0.128624i
$545$	27.0000			1.15655
$546$	6.00000	+	9.00000i	0.256776	+	0.385164i
$547$	−37.0000			−1.58201			−0.791003	−	0.611812i	$-0.790441\pi$
$547$	−37.0000			−1.58201			−0.791003	+	0.611812i	$0.790441\pi$
$548$		−	18.0000i		−	0.768922i
$549$	16.0000			0.682863
$550$		0			0
$551$		0			0
$552$		−	6.00000i		−	0.255377i
$553$			30.0000i			1.27573i
$554$			8.00000i			0.339887i
$555$	−9.00000			−0.382029
$556$	−5.00000			−0.212047
$557$		−	27.0000i		−	1.14403i	−0.820244	−	0.572013i	$-0.806163\pi$
$557$		−	27.0000i		−	1.14403i	0.820244	−	0.572013i	$-0.193837\pi$
$558$		0			0
$559$	−2.00000	−	3.00000i	−0.0845910	−	0.126886i
$560$	9.00000			0.380319
$561$		0			0
$562$	30.0000			1.26547
$563$	39.0000			1.64365			0.821827	−	0.569737i	$-0.192955\pi$
$563$	39.0000			1.64365			0.821827	+	0.569737i	$0.192955\pi$
$564$			3.00000i			0.126323i
$565$			18.0000i			0.757266i
$566$			4.00000i			0.168133i
$567$			3.00000i			0.125988i
$568$	15.0000			0.629386
$569$	45.0000			1.88650			0.943249	−	0.332086i	$-0.107752\pi$
$569$	45.0000			1.88650			0.943249	+	0.332086i	$0.107752\pi$
$570$			18.0000i			0.753937i
$571$	−23.0000			−0.962520			−0.481260	−	0.876578i	$-0.659821\pi$
$571$	−23.0000			−0.962520			−0.481260	+	0.876578i	$0.659821\pi$
$572$		0			0
$573$	−12.0000			−0.501307
$574$		0			0
$575$	24.0000			1.00087
$576$	2.00000			0.0833333
$577$		−	42.0000i		−	1.74848i	−0.485491	−	0.874241i	$-0.661359\pi$
$577$		−	42.0000i		−	1.74848i	0.485491	−	0.874241i	$-0.338641\pi$
$578$		−	8.00000i		−	0.332756i
$579$		−	6.00000i		−	0.249351i
$580$		0			0
$581$	−18.0000			−0.746766
$582$	−12.0000			−0.497416
$583$		0			0
$584$	6.00000			0.248282
$585$	−18.0000	+	12.0000i	−0.744208	+	0.496139i
$586$	9.00000			0.371787
$587$			18.0000i			0.742940i	0.928445	+	0.371470i	$0.121146\pi$
$587$			18.0000i			0.742940i	−0.928445	+	0.371470i	$0.878854\pi$
$588$	−2.00000			−0.0824786
$589$		0			0
$590$		−	18.0000i		−	0.741048i
$591$		−	3.00000i		−	0.123404i
$592$			3.00000i			0.123299i
$593$			36.0000i			1.47834i	0.673517	+	0.739171i	$0.264783\pi$
$593$			36.0000i			1.47834i	−0.673517	+	0.739171i	$0.735217\pi$
$594$		0			0
$595$	27.0000			1.10689
$596$			6.00000i			0.245770i
$597$	20.0000			0.818546
$598$	18.0000	−	12.0000i	0.736075	−	0.490716i
$599$	−30.0000			−1.22577			−0.612883	−	0.790173i	$-0.709990\pi$
$599$	−30.0000			−1.22577			−0.612883	+	0.790173i	$0.709990\pi$
$600$		−	4.00000i		−	0.163299i
$601$	37.0000			1.50926			0.754631	−	0.656150i	$-0.227816\pi$
$601$	37.0000			1.50926			0.754631	+	0.656150i	$0.227816\pi$
$602$	3.00000			0.122271
$603$			24.0000i			0.977356i
$604$			15.0000i			0.610341i
$605$		−	33.0000i		−	1.34164i
$606$		−	12.0000i		−	0.487467i
$607$	−22.0000			−0.892952			−0.446476	−	0.894795i	$-0.647321\pi$
$607$	−22.0000			−0.892952			−0.446476	+	0.894795i	$0.647321\pi$
$608$	6.00000			0.243332
$609$		0			0
$610$	−24.0000			−0.971732
$611$	−9.00000	+	6.00000i	−0.364101	+	0.242734i
$612$	6.00000			0.242536
$613$			6.00000i			0.242338i	0.992632	+	0.121169i	$0.0386643\pi$
$613$			6.00000i			0.242338i	−0.992632	+	0.121169i	$0.961336\pi$
$614$	−18.0000			−0.726421
$615$		0			0
$616$		0			0
$617$		−	12.0000i		−	0.483102i	−0.970388	−	0.241551i	$-0.922344\pi$
$617$		−	12.0000i		−	0.483102i	0.970388	−	0.241551i	$-0.0776561\pi$
$618$		−	14.0000i		−	0.563163i
$619$			24.0000i			0.964641i	0.875995	+	0.482321i	$0.160206\pi$
$619$			24.0000i			0.964641i	−0.875995	+	0.482321i	$0.839794\pi$
$620$		0			0
$621$	−30.0000			−1.20386
$622$		−	18.0000i		−	0.721734i
$623$	18.0000			0.721155
$624$	−2.00000	−	3.00000i	−0.0800641	−	0.120096i
$625$	−29.0000			−1.16000
$626$			19.0000i			0.759393i
$627$		0			0
$628$	22.0000			0.877896
$629$			9.00000i			0.358854i
$630$		−	18.0000i		−	0.717137i
$631$		−	15.0000i		−	0.597141i	−0.954388	−	0.298570i	$-0.903490\pi$
$631$		−	15.0000i		−	0.597141i	0.954388	−	0.298570i	$-0.0965097\pi$
$632$		−	10.0000i		−	0.397779i
$633$	23.0000			0.914168
$634$	−18.0000			−0.714871
$635$			6.00000i			0.238103i
$636$	−6.00000			−0.237915
$637$	−4.00000	−	6.00000i	−0.158486	−	0.237729i
$638$		0			0
$639$		−	30.0000i		−	1.18678i
$640$	−3.00000			−0.118585
$641$	−18.0000			−0.710957			−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000			−0.710957			−0.355479	+	0.934684i	$0.615682\pi$
$642$			12.0000i			0.473602i
$643$			36.0000i			1.41970i	0.704352	+	0.709851i	$0.251238\pi$
$643$			36.0000i			1.41970i	−0.704352	+	0.709851i	$0.748762\pi$
$644$			18.0000i			0.709299i
$645$		−	3.00000i		−	0.118125i
$646$	18.0000			0.708201
$647$	−42.0000			−1.65119			−0.825595	−	0.564263i	$-0.809160\pi$
$647$	−42.0000			−1.65119			−0.825595	+	0.564263i	$0.809160\pi$
$648$		−	1.00000i		−	0.0392837i
$649$		0			0
$650$	12.0000	−	8.00000i	0.470679	−	0.313786i
$651$		0			0
$652$		−	6.00000i		−	0.234978i
$653$	−36.0000			−1.40879			−0.704394	−	0.709809i	$-0.748781\pi$
$653$	−36.0000			−1.40879			−0.704394	+	0.709809i	$0.748781\pi$
$654$	9.00000			0.351928
$655$			9.00000i			0.351659i
$656$		0			0
$657$		−	12.0000i		−	0.468165i
$658$		−	9.00000i		−	0.350857i
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$			30.0000i			1.16686i	0.812162	+	0.583432i	$0.198291\pi$
$661$			30.0000i			1.16686i	−0.812162	+	0.583432i	$0.801709\pi$
$662$	−30.0000			−1.16598
$663$	−6.00000	−	9.00000i	−0.233021	−	0.349531i
$664$	6.00000			0.232845
$665$		−	54.0000i		−	2.09403i
$666$	6.00000			0.232495
$667$		0			0
$668$			12.0000i			0.464294i
$669$			9.00000i			0.347960i
$670$		−	36.0000i		−	1.39080i
$671$		0			0
$672$	3.00000			0.115728
$673$	−1.00000			−0.0385472			−0.0192736	−	0.999814i	$-0.506135\pi$
$673$	−1.00000			−0.0385472			−0.0192736	+	0.999814i	$0.506135\pi$
$674$			13.0000i			0.500741i
$675$	−20.0000			−0.769800
$676$	5.00000	−	12.0000i	0.192308	−	0.461538i
$677$	18.0000			0.691796			0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000			0.691796			0.345898	+	0.938272i	$0.387574\pi$
$678$			6.00000i			0.230429i
$679$	36.0000			1.38155
$680$	−9.00000			−0.345134
$681$			12.0000i			0.459841i
$682$		0			0
$683$			6.00000i			0.229584i	0.993390	+	0.114792i	$0.0366201\pi$
$683$			6.00000i			0.229584i	−0.993390	+	0.114792i	$0.963380\pi$
$684$		−	12.0000i		−	0.458831i
$685$	54.0000			2.06323
$686$	−15.0000			−0.572703
$687$		−	9.00000i		−	0.343371i
$688$	−1.00000			−0.0381246
$689$	−12.0000	−	18.0000i	−0.457164	−	0.685745i
$690$	18.0000			0.685248
$691$		0			0		1.00000			$0$
$691$		0			0		−1.00000			$\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$			33.0000i			1.25266i
$695$		−	15.0000i		−	0.568982i
$696$		0			0
$697$		0			0
$698$	21.0000			0.794862
$699$	21.0000			0.794293
$700$			12.0000i			0.453557i
$701$	42.0000			1.58632			0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000			1.58632			0.793159	+	0.609015i	$0.208435\pi$
$702$	−15.0000	+	10.0000i	−0.566139	+	0.377426i
$703$	18.0000			0.678883
$704$		0			0
$705$	−9.00000			−0.338960
$706$	−6.00000			−0.225813
$707$			36.0000i			1.35392i
$708$		−	6.00000i		−	0.225494i
$709$		−	6.00000i		−	0.225335i	−0.993633	−	0.112667i	$-0.964061\pi$
$709$		−	6.00000i		−	0.225335i	0.993633	−	0.112667i	$-0.0359394\pi$
$710$			45.0000i			1.68882i
$711$	−20.0000			−0.750059
$712$	−6.00000			−0.224860
$713$		0			0
$714$	9.00000			0.336817
$715$		0			0
$716$	−15.0000			−0.560576
$717$		−	9.00000i		−	0.336111i
$718$	−24.0000			−0.895672
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$			6.00000i			0.223607i
$721$			42.0000i			1.56416i
$722$		−	17.0000i		−	0.632674i
$723$			30.0000i			1.11571i
$724$	−2.00000			−0.0743294
$725$		0			0
$726$		−	11.0000i		−	0.408248i
$727$	28.0000			1.03846			0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000			1.03846			0.519231	+	0.854634i	$0.326218\pi$
$728$	6.00000	+	9.00000i	0.222375	+	0.333562i
$729$	13.0000			0.481481
$730$			18.0000i			0.666210i
$731$	−3.00000			−0.110959
$732$	−8.00000			−0.295689
$733$		−	9.00000i		−	0.332423i	−0.986090	−	0.166211i	$-0.946847\pi$
$733$		−	9.00000i		−	0.332423i	0.986090	−	0.166211i	$-0.0531534\pi$
$734$			8.00000i			0.295285i
$735$		−	6.00000i		−	0.221313i
$736$		−	6.00000i		−	0.221163i
$737$		0			0
$738$		0			0
$739$		−	36.0000i		−	1.32428i	−0.749380	−	0.662141i	$-0.769648\pi$
$739$		−	36.0000i		−	1.32428i	0.749380	−	0.662141i	$-0.230352\pi$
$740$	−9.00000			−0.330847
$741$	−18.0000	+	12.0000i	−0.661247	+	0.440831i
$742$	18.0000			0.660801
$743$		−	39.0000i		−	1.43077i	−0.698730	−	0.715386i	$-0.746251\pi$
$743$		−	39.0000i		−	1.43077i	0.698730	−	0.715386i	$-0.253749\pi$
$744$		0			0
$745$	−18.0000			−0.659469
$746$			4.00000i			0.146450i
$747$		−	12.0000i		−	0.439057i
$748$		0			0
$749$		−	36.0000i		−	1.31541i
$750$	−3.00000			−0.109545
$751$	32.0000			1.16770			0.583848	−	0.811863i	$-0.301546\pi$
$751$	32.0000			1.16770			0.583848	+	0.811863i	$0.301546\pi$
$752$			3.00000i			0.109399i
$753$	−12.0000			−0.437304
$754$		0			0
$755$	−45.0000			−1.63772
$756$		−	15.0000i		−	0.545545i
$757$	−2.00000			−0.0726912			−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000			−0.0726912			−0.0363456	+	0.999339i	$0.511572\pi$
$758$	6.00000			0.217930
$759$		0			0
$760$			18.0000i			0.652929i
$761$		−	30.0000i		−	1.08750i	−0.839248	−	0.543750i	$-0.817004\pi$
$761$		−	30.0000i		−	1.08750i	0.839248	−	0.543750i	$-0.182996\pi$
$762$			2.00000i			0.0724524i
$763$	−27.0000			−0.977466
$764$	−12.0000			−0.434145
$765$			18.0000i			0.650791i
$766$	9.00000			0.325183
$767$	18.0000	−	12.0000i	0.649942	−	0.433295i
$768$	−1.00000			−0.0360844
$769$			24.0000i			0.865462i	0.901523	+	0.432731i	$0.142450\pi$
$769$			24.0000i			0.865462i	−0.901523	+	0.432731i	$0.857550\pi$
$770$		0			0
$771$	−3.00000			−0.108042
$772$		−	6.00000i		−	0.215945i
$773$			21.0000i			0.755318i	0.925945	+	0.377659i	$0.123271\pi$
$773$			21.0000i			0.755318i	−0.925945	+	0.377659i	$0.876729\pi$
$774$			2.00000i			0.0718885i
$775$		0			0
$776$	−12.0000			−0.430775
$777$	9.00000			0.322873
$778$		−	30.0000i		−	1.07555i
$779$		0			0
$780$	9.00000	−	6.00000i	0.322252	−	0.214834i
$781$		0			0
$782$		−	18.0000i		−	0.643679i
$783$		0			0
$784$	−2.00000			−0.0714286
$785$			66.0000i			2.35564i
$786$			3.00000i			0.107006i
$787$		−	12.0000i		−	0.427754i	−0.976861	−	0.213877i	$-0.931391\pi$
$787$		−	12.0000i		−	0.427754i	0.976861	−	0.213877i	$-0.0686091\pi$
$788$		−	3.00000i		−	0.106871i
$789$	−24.0000			−0.854423
$790$	30.0000			1.06735
$791$		−	18.0000i		−	0.640006i
$792$		0			0
$793$	−16.0000	−	24.0000i	−0.568177	−	0.852265i
$794$	−18.0000			−0.638796
$795$		−	18.0000i		−	0.638394i
$796$	20.0000			0.708881
$797$	18.0000			0.637593			0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000			0.637593			0.318796	+	0.947823i	$0.396721\pi$
$798$		−	18.0000i		−	0.637193i
$799$			9.00000i			0.318397i
$800$		−	4.00000i		−	0.141421i
$801$			12.0000i			0.423999i
$802$	−30.0000			−1.05934
$803$		0			0
$804$		−	12.0000i		−	0.423207i
$805$	−54.0000			−1.90325
$806$		0			0
$807$		0			0
$808$		−	12.0000i		−	0.422159i
$809$	15.0000			0.527372			0.263686	−	0.964609i	$-0.415062\pi$
$809$	15.0000			0.527372			0.263686	+	0.964609i	$0.415062\pi$
$810$	3.00000			0.105409
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$		0			0
$813$		−	15.0000i		−	0.526073i
$814$		0			0
$815$	18.0000			0.630512
$816$	−3.00000			−0.105021
$817$			6.00000i			0.209913i
$818$	6.00000			0.209785
$819$	18.0000	−	12.0000i	0.628971	−	0.419314i
$820$		0			0
$821$			45.0000i			1.57051i	0.619172	+	0.785255i	$0.287468\pi$
$821$			45.0000i			1.57051i	−0.619172	+	0.785255i	$0.712532\pi$
$822$	18.0000			0.627822
$823$	14.0000			0.488009			0.244005	−	0.969774i	$-0.421539\pi$
$823$	14.0000			0.488009			0.244005	+	0.969774i	$0.421539\pi$
$824$		−	14.0000i		−	0.487713i
$825$		0			0
$826$			18.0000i			0.626300i
$827$			18.0000i			0.625921i	0.949766	+	0.312961i	$0.101321\pi$
$827$			18.0000i			0.625921i	−0.949766	+	0.312961i	$0.898679\pi$
$828$	−12.0000			−0.417029
$829$	−20.0000			−0.694629			−0.347314	−	0.937749i	$-0.612906\pi$
$829$	−20.0000			−0.694629			−0.347314	+	0.937749i	$0.612906\pi$
$830$			18.0000i			0.624789i
$831$	−8.00000			−0.277517
$832$	−2.00000	−	3.00000i	−0.0693375	−	0.104006i
$833$	−6.00000			−0.207888
$834$		−	5.00000i		−	0.173136i
$835$	−36.0000			−1.24583
$836$		0			0
$837$		0			0
$838$			15.0000i			0.518166i
$839$			24.0000i			0.828572i	0.910147	+	0.414286i	$0.135969\pi$
$839$			24.0000i			0.828572i	−0.910147	+	0.414286i	$0.864031\pi$
$840$			9.00000i			0.310530i
$841$	−29.0000			−1.00000
$842$	15.0000			0.516934
$843$			30.0000i			1.03325i
$844$	23.0000			0.791693
$845$	36.0000	+	15.0000i	1.23844	+	0.516016i
$846$	6.00000			0.206284
$847$			33.0000i			1.13389i
$848$	−6.00000			−0.206041
$849$	−4.00000			−0.137280
$850$		−	12.0000i		−	0.411597i
$851$		−	18.0000i		−	0.617032i
$852$			15.0000i			0.513892i
$853$		−	39.0000i		−	1.33533i	−0.744460	−	0.667667i	$-0.767293\pi$
$853$		−	39.0000i		−	1.33533i	0.744460	−	0.667667i	$-0.232707\pi$
$854$	24.0000			0.821263
$855$	36.0000			1.23117
$856$			12.0000i			0.410152i
$857$	18.0000			0.614868			0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000			0.614868			0.307434	+	0.951569i	$0.400530\pi$
$858$		0			0
$859$	40.0000			1.36478			0.682391	−	0.730987i	$-0.260940\pi$
$859$	40.0000			1.36478			0.682391	+	0.730987i	$0.260940\pi$
$860$		−	3.00000i		−	0.102299i
$861$		0			0
$862$	15.0000			0.510902
$863$		−	39.0000i		−	1.32758i	−0.747921	−	0.663788i	$-0.768948\pi$
$863$		−	39.0000i		−	1.32758i	0.747921	−	0.663788i	$-0.231052\pi$
$864$			5.00000i			0.170103i
$865$			18.0000i			0.612018i
$866$		−	11.0000i		−	0.373795i
$867$	8.00000			0.271694
$868$		0			0
$869$		0			0
$870$		0			0
$871$	36.0000	−	24.0000i	1.21981	−	0.813209i
$872$	9.00000			0.304778
$873$			24.0000i			0.812277i
$874$	−36.0000			−1.21772
$875$	9.00000			0.304256
$876$			6.00000i			0.202721i
$877$			3.00000i			0.101303i	0.998716	+	0.0506514i	$0.0161297\pi$
$877$			3.00000i			0.101303i	−0.998716	+	0.0506514i	$0.983870\pi$
$878$		−	10.0000i		−	0.337484i
$879$			9.00000i			0.303562i
$880$		0			0
$881$	−33.0000			−1.11180			−0.555899	−	0.831250i	$-0.687626\pi$
$881$	−33.0000			−1.11180			−0.555899	+	0.831250i	$0.687626\pi$
$882$			4.00000i			0.134687i
$883$	−11.0000			−0.370179			−0.185090	−	0.982722i	$-0.559258\pi$
$883$	−11.0000			−0.370179			−0.185090	+	0.982722i	$0.559258\pi$
$884$	−6.00000	−	9.00000i	−0.201802	−	0.302703i
$885$	18.0000			0.605063
$886$		−	21.0000i		−	0.705509i
$887$	−12.0000			−0.402921			−0.201460	−	0.979497i	$-0.564569\pi$
$887$	−12.0000			−0.402921			−0.201460	+	0.979497i	$0.564569\pi$
$888$	−3.00000			−0.100673
$889$		−	6.00000i		−	0.201234i
$890$		−	18.0000i		−	0.603361i
$891$		0			0
$892$			9.00000i			0.301342i
$893$	18.0000			0.602347
$894$	−6.00000			−0.200670
$895$		−	45.0000i		−	1.50418i
$896$	3.00000			0.100223
$897$	12.0000	+	18.0000i	0.400668	+	0.601003i
$898$	−24.0000			−0.800890
$899$		0			0
$900$	−8.00000			−0.266667
$901$	−18.0000			−0.599667
$902$		0			0
$903$			3.00000i			0.0998337i
$904$			6.00000i			0.199557i
$905$		−	6.00000i		−	0.199447i
$906$	−15.0000			−0.498342
$907$	−17.0000			−0.564476			−0.282238	−	0.959344i	$-0.591077\pi$
$907$	−17.0000			−0.564476			−0.282238	+	0.959344i	$0.591077\pi$
$908$			12.0000i			0.398234i
$909$	−24.0000			−0.796030
$910$	−27.0000	+	18.0000i	−0.895041	+	0.596694i
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$			6.00000i			0.198680i
$913$		0			0
$914$	−18.0000			−0.595387
$915$		−	24.0000i		−	0.793416i
$916$		−	9.00000i		−	0.297368i
$917$		−	9.00000i		−	0.297206i
$918$			15.0000i			0.495074i
$919$	−20.0000			−0.659739			−0.329870	−	0.944027i	$-0.607005\pi$
$919$	−20.0000			−0.659739			−0.329870	+	0.944027i	$0.607005\pi$
$920$	18.0000			0.593442
$921$		−	18.0000i		−	0.593120i
$922$	15.0000			0.493999
$923$	−45.0000	+	30.0000i	−1.48119	+	0.987462i
$924$		0			0
$925$		−	12.0000i		−	0.394558i
$926$	24.0000			0.788689
$927$	−28.0000			−0.919641
$928$		0			0
$929$		−	36.0000i		−	1.18112i	−0.806993	−	0.590561i	$-0.798907\pi$
$929$		−	36.0000i		−	1.18112i	0.806993	−	0.590561i	$-0.201093\pi$
$930$		0			0
$931$			12.0000i			0.393284i
$932$	21.0000			0.687878
$933$	18.0000			0.589294
$934$		−	12.0000i		−	0.392652i
$935$		0			0
$936$	−6.00000	+	4.00000i	−0.196116	+	0.130744i
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$			36.0000i			1.17544i
$939$	−19.0000			−0.620042
$940$	−9.00000			−0.293548
$941$		−	45.0000i		−	1.46696i	−0.679712	−	0.733479i	$-0.737895\pi$
$941$		−	45.0000i		−	1.46696i	0.679712	−	0.733479i	$-0.262105\pi$
$942$			22.0000i			0.716799i
$943$		0			0
$944$		−	6.00000i		−	0.195283i
$945$	45.0000			1.46385
$946$		0			0
$947$			48.0000i			1.55979i	0.625910	+	0.779895i	$0.284728\pi$
$947$			48.0000i			1.55979i	−0.625910	+	0.779895i	$0.715272\pi$
$948$	10.0000			0.324785
$949$	−18.0000	+	12.0000i	−0.584305	+	0.389536i
$950$	−24.0000			−0.778663
$951$		−	18.0000i		−	0.583690i
$952$	9.00000			0.291692
$953$	9.00000			0.291539			0.145769	−	0.989319i	$-0.453434\pi$
$953$	9.00000			0.291539			0.145769	+	0.989319i	$0.453434\pi$
$954$			12.0000i			0.388514i
$955$		−	36.0000i		−	1.16493i
$956$		−	9.00000i		−	0.291081i
$957$		0			0
$958$	−39.0000			−1.26003
$959$	−54.0000			−1.74375
$960$		−	3.00000i		−	0.0968246i
$961$	31.0000			1.00000
$962$	−6.00000	−	9.00000i	−0.193448	−	0.290172i
$963$	24.0000			0.773389
$964$			30.0000i			0.966235i
$965$	18.0000			0.579441
$966$	−18.0000			−0.579141
$967$			3.00000i			0.0964735i	0.998836	+	0.0482367i	$0.0153602\pi$
$967$			3.00000i			0.0964735i	−0.998836	+	0.0482367i	$0.984640\pi$
$968$		−	11.0000i		−	0.353553i
$969$			18.0000i			0.578243i
$970$		−	36.0000i		−	1.15589i
$971$	27.0000			0.866471			0.433236	−	0.901281i	$-0.357372\pi$
$971$	27.0000			0.866471			0.433236	+	0.901281i	$0.357372\pi$
$972$	16.0000			0.513200
$973$			15.0000i			0.480878i
$974$	12.0000			0.384505
$975$	8.00000	+	12.0000i	0.256205	+	0.384308i
$976$	−8.00000			−0.256074
$977$		−	12.0000i		−	0.383914i	−0.981403	−	0.191957i	$-0.938517\pi$
$977$		−	12.0000i		−	0.383914i	0.981403	−	0.191957i	$-0.0614834\pi$
$978$	6.00000			0.191859
$979$		0			0
$980$		−	6.00000i		−	0.191663i
$981$		−	18.0000i		−	0.574696i
$982$			27.0000i			0.861605i
$983$		−	9.00000i		−	0.287055i	−0.989646	−	0.143528i	$-0.954155\pi$
$983$		−	9.00000i		−	0.287055i	0.989646	−	0.143528i	$-0.0458446\pi$
$984$		0			0
$985$	9.00000			0.286764
$986$		0			0
$987$	9.00000			0.286473
$988$	−18.0000	+	12.0000i	−0.572656	+	0.381771i
$989$	6.00000			0.190789
$990$		0			0
$991$	2.00000			0.0635321			0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000			0.0635321			0.0317660	+	0.999495i	$0.489887\pi$
$992$		0			0
$993$		−	30.0000i		−	0.952021i
$994$		−	45.0000i		−	1.42731i
$995$			60.0000i			1.90213i
$996$			6.00000i			0.190117i
$997$	8.00000			0.253363			0.126681	−	0.991943i	$-0.459567\pi$
$997$	8.00000			0.253363			0.126681	+	0.991943i	$0.459567\pi$
$998$	36.0000			1.13956
$999$			15.0000i			0.474579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.2.b.a.25.2	yes	2
3.2	odd	2		234.2.b.b.181.1		2
4.3	odd	2		208.2.f.a.129.1		2
5.2	odd	4		650.2.c.a.649.2		2
5.3	odd	4		650.2.c.d.649.1		2
5.4	even	2		650.2.d.b.51.1		2
7.2	even	3		1274.2.n.d.753.2		4
7.3	odd	6		1274.2.n.c.961.1		4
7.4	even	3		1274.2.n.d.961.1		4
7.5	odd	6		1274.2.n.c.753.2		4
7.6	odd	2		1274.2.d.c.883.2		2
8.3	odd	2		832.2.f.b.129.2		2
8.5	even	2		832.2.f.d.129.2		2
12.11	even	2		1872.2.c.f.1585.2		2
13.2	odd	12		338.2.c.b.191.1		2
13.3	even	3		338.2.e.c.147.1		4
13.4	even	6		338.2.e.c.23.1		4
13.5	odd	4		338.2.a.d.1.1		1
13.6	odd	12		338.2.c.b.315.1		2
13.7	odd	12		338.2.c.f.315.1		2
13.8	odd	4		338.2.a.b.1.1		1
13.9	even	3		338.2.e.c.23.2		4
13.10	even	6		338.2.e.c.147.2		4
13.11	odd	12		338.2.c.f.191.1		2
13.12	even	2	inner	26.2.b.a.25.1	✓	2
39.5	even	4		3042.2.a.g.1.1		1
39.8	even	4		3042.2.a.j.1.1		1
39.38	odd	2		234.2.b.b.181.2		2
52.31	even	4		2704.2.a.j.1.1		1
52.47	even	4		2704.2.a.k.1.1		1
52.51	odd	2		208.2.f.a.129.2		2
65.12	odd	4		650.2.c.d.649.2		2
65.34	odd	4		8450.2.a.u.1.1		1
65.38	odd	4		650.2.c.a.649.1		2
65.44	odd	4		8450.2.a.h.1.1		1
65.64	even	2		650.2.d.b.51.2		2
91.12	odd	6		1274.2.n.c.753.1		4
91.25	even	6		1274.2.n.d.961.2		4
91.38	odd	6		1274.2.n.c.961.2		4
91.51	even	6		1274.2.n.d.753.1		4
91.90	odd	2		1274.2.d.c.883.1		2
104.51	odd	2		832.2.f.b.129.1		2
104.77	even	2		832.2.f.d.129.1		2
156.155	even	2		1872.2.c.f.1585.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.2.b.a.25.1	✓	2	13.12	even	2	inner
26.2.b.a.25.2	yes	2	1.1	even	1	trivial
208.2.f.a.129.1		2	4.3	odd	2
208.2.f.a.129.2		2	52.51	odd	2
234.2.b.b.181.1		2	3.2	odd	2
234.2.b.b.181.2		2	39.38	odd	2
338.2.a.b.1.1		1	13.8	odd	4
338.2.a.d.1.1		1	13.5	odd	4
338.2.c.b.191.1		2	13.2	odd	12
338.2.c.b.315.1		2	13.6	odd	12
338.2.c.f.191.1		2	13.11	odd	12
338.2.c.f.315.1		2	13.7	odd	12
338.2.e.c.23.1		4	13.4	even	6
338.2.e.c.23.2		4	13.9	even	3
338.2.e.c.147.1		4	13.3	even	3
338.2.e.c.147.2		4	13.10	even	6
650.2.c.a.649.1		2	65.38	odd	4
650.2.c.a.649.2		2	5.2	odd	4
650.2.c.d.649.1		2	5.3	odd	4
650.2.c.d.649.2		2	65.12	odd	4
650.2.d.b.51.1		2	5.4	even	2
650.2.d.b.51.2		2	65.64	even	2
832.2.f.b.129.1		2	104.51	odd	2
832.2.f.b.129.2		2	8.3	odd	2
832.2.f.d.129.1		2	104.77	even	2
832.2.f.d.129.2		2	8.5	even	2
1274.2.d.c.883.1		2	91.90	odd	2
1274.2.d.c.883.2		2	7.6	odd	2
1274.2.n.c.753.1		4	91.12	odd	6
1274.2.n.c.753.2		4	7.5	odd	6
1274.2.n.c.961.1		4	7.3	odd	6
1274.2.n.c.961.2		4	91.38	odd	6
1274.2.n.d.753.1		4	91.51	even	6
1274.2.n.d.753.2		4	7.2	even	3
1274.2.n.d.961.1		4	7.4	even	3
1274.2.n.d.961.2		4	91.25	even	6
1872.2.c.f.1585.1		2	156.155	even	2
1872.2.c.f.1585.2		2	12.11	even	2
2704.2.a.j.1.1		1	52.31	even	4
2704.2.a.k.1.1		1	52.47	even	4
3042.2.a.g.1.1		1	39.5	even	4
3042.2.a.j.1.1		1	39.8	even	4
8450.2.a.h.1.1		1	65.44	odd	4
8450.2.a.u.1.1		1	65.34	odd	4

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:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	26.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -3.00000i q^{5} -1.00000i q^{6} +3.00000i q^{7} -1.00000i q^{8} -2.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -3.00000i q^{5} -1.00000i q^{6} +3.00000i q^{7} -1.00000i q^{8} -2.00000 q^{9} +3.00000 q^{10} +1.00000 q^{12} +(2.00000 + 3.00000i) q^{13} -3.00000 q^{14} +3.00000i q^{15} +1.00000 q^{16} +3.00000 q^{17} -2.00000i q^{18} -6.00000i q^{19} +3.00000i q^{20} -3.00000i q^{21} -6.00000 q^{23} +1.00000i q^{24} -4.00000 q^{25} +(-3.00000 + 2.00000i) q^{26} +5.00000 q^{27} -3.00000i q^{28} -3.00000 q^{30} +1.00000i q^{32} +3.00000i q^{34} +9.00000 q^{35} +2.00000 q^{36} +3.00000i q^{37} +6.00000 q^{38} +(-2.00000 - 3.00000i) q^{39} -3.00000 q^{40} +3.00000 q^{42} -1.00000 q^{43} +6.00000i q^{45} -6.00000i q^{46} +3.00000i q^{47} -1.00000 q^{48} -2.00000 q^{49} -4.00000i q^{50} -3.00000 q^{51} +(-2.00000 - 3.00000i) q^{52} -6.00000 q^{53} +5.00000i q^{54} +3.00000 q^{56} +6.00000i q^{57} -6.00000i q^{59} -3.00000i q^{60} -8.00000 q^{61} -6.00000i q^{63} -1.00000 q^{64} +(9.00000 - 6.00000i) q^{65} -12.0000i q^{67} -3.00000 q^{68} +6.00000 q^{69} +9.00000i q^{70} +15.0000i q^{71} +2.00000i q^{72} +6.00000i q^{73} -3.00000 q^{74} +4.00000 q^{75} +6.00000i q^{76} +(3.00000 - 2.00000i) q^{78} +10.0000 q^{79} -3.00000i q^{80} +1.00000 q^{81} +6.00000i q^{83} +3.00000i q^{84} -9.00000i q^{85} -1.00000i q^{86} -6.00000i q^{89} -6.00000 q^{90} +(-9.00000 + 6.00000i) q^{91} +6.00000 q^{92} -3.00000 q^{94} -18.0000 q^{95} -1.00000i q^{96} -12.0000i q^{97} -2.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - 2 q^{4} - 4 q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 - 2 * q^4 - 4 * q^9	\( 2 q - 2 q^{3} - 2 q^{4} - 4 q^{9} + 6 q^{10} + 2 q^{12} + 4 q^{13} - 6 q^{14} + 2 q^{16} + 6 q^{17} - 12 q^{23} - 8 q^{25} - 6 q^{26} + 10 q^{27} - 6 q^{30} + 18 q^{35} + 4 q^{36} + 12 q^{38} - 4 q^{39} - 6 q^{40} + 6 q^{42} - 2 q^{43} - 2 q^{48} - 4 q^{49} - 6 q^{51} - 4 q^{52} - 12 q^{53} + 6 q^{56} - 16 q^{61} - 2 q^{64} + 18 q^{65} - 6 q^{68} + 12 q^{69} - 6 q^{74} + 8 q^{75} + 6 q^{78} + 20 q^{79} + 2 q^{81} - 12 q^{90} - 18 q^{91} + 12 q^{92} - 6 q^{94} - 36 q^{95}+O(q^{100}) \) 2 * q - 2 * q^3 - 2 * q^4 - 4 * q^9 + 6 * q^10 + 2 * q^12 + 4 * q^13 - 6 * q^14 + 2 * q^16 + 6 * q^17 - 12 * q^23 - 8 * q^25 - 6 * q^26 + 10 * q^27 - 6 * q^30 + 18 * q^35 + 4 * q^36 + 12 * q^38 - 4 * q^39 - 6 * q^40 + 6 * q^42 - 2 * q^43 - 2 * q^48 - 4 * q^49 - 6 * q^51 - 4 * q^52 - 12 * q^53 + 6 * q^56 - 16 * q^61 - 2 * q^64 + 18 * q^65 - 6 * q^68 + 12 * q^69 - 6 * q^74 + 8 * q^75 + 6 * q^78 + 20 * q^79 + 2 * q^81 - 12 * q^90 - 18 * q^91 + 12 * q^92 - 6 * q^94 - 36 * q^95

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