LMFDB - Embedded newform 1600.2.l.f.1201.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(401,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("1600.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.l (of order $4$, degree $2$, not 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:	$12.7760643234$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.4767670494822400.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 $ x^12 - 4x^11 + 7x^10 - 4x^9 - 8x^8 + 24x^7 - 38x^6 + 48x^5 - 32x^4 - 32x^3 + 112x^2 - 128*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 400)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1201.3
Root			$-1.41313 - 0.0554252i$ of defining polynomial
Character	$\chi$	$=$	1600.1201
Dual form			1600.2.l.f.401.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.488516 + 0.488516i) q^{3} +4.71540i q^{7} +2.52270i q^{9} +O(q^{10})$	$q+(-0.488516 + 0.488516i) q^{3} +4.71540i q^{7} +2.52270i q^{9} +(3.91360 + 3.91360i) q^{11} +(0.0878822 - 0.0878822i) q^{13} -4.67442 q^{17} +(-1.81249 + 1.81249i) q^{19} +(-2.30355 - 2.30355i) q^{21} -1.63007i q^{23} +(-2.69793 - 2.69793i) q^{27} +(3.26362 - 3.26362i) q^{29} +2.12875 q^{31} -3.82371 q^{33} +(-3.97797 - 3.97797i) q^{37} +0.0858637i q^{39} -8.25504i q^{41} +(2.27336 + 2.27336i) q^{43} -4.06129 q^{47} -15.2350 q^{49} +(2.28353 - 2.28353i) q^{51} +(5.03938 + 5.03938i) q^{53} -1.77086i q^{57} +(5.16453 + 5.16453i) q^{59} +(7.12726 - 7.12726i) q^{61} -11.8956 q^{63} +(-7.49920 + 7.49920i) q^{67} +(0.796314 + 0.796314i) q^{69} -4.54072i q^{71} +8.30557i q^{73} +(-18.4542 + 18.4542i) q^{77} -11.5317 q^{79} -4.93215 q^{81} +(-1.16919 + 1.16919i) q^{83} +3.18866i q^{87} +3.24572i q^{89} +(0.414400 + 0.414400i) q^{91} +(-1.03993 + 1.03993i) q^{93} +13.9581 q^{97} +(-9.87285 + 9.87285i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3}+O(q^{10}) $ 12 * q - 2 * q^3	$ 12 q - 2 q^{3} + 2 q^{11} - 4 q^{13} - 8 q^{17} + 14 q^{19} - 20 q^{21} + 10 q^{27} + 4 q^{31} + 28 q^{33} + 8 q^{37} - 8 q^{47} + 4 q^{49} - 10 q^{51} - 16 q^{53} - 20 q^{59} + 4 q^{61} + 8 q^{63} - 50 q^{67} - 8 q^{77} - 12 q^{79} - 8 q^{81} + 2 q^{83} - 44 q^{93} - 12 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 + 2 * q^11 - 4 * q^13 - 8 * q^17 + 14 * q^19 - 20 * q^21 + 10 * q^27 + 4 * q^31 + 28 * q^33 + 8 * q^37 - 8 * q^47 + 4 * q^49 - 10 * q^51 - 16 * q^53 - 20 * q^59 + 4 * q^61 + 8 * q^63 - 50 * q^67 - 8 * q^77 - 12 * q^79 - 8 * q^81 + 2 * q^83 - 44 * q^93 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.488516	+	0.488516i	−0.282045	+	0.282045i	−0.833924	−	0.551879i	$-0.813911\pi$
$3$	−0.488516	+	0.488516i	−0.282045	+	0.282045i	0.551879	+	0.833924i	$0.313911\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			4.71540i			1.78226i	0.453753	+	0.891128i	$0.350085\pi$
$7$			4.71540i			1.78226i	−0.453753	+	0.891128i	$0.649915\pi$
$8$		0			0
$9$			2.52270i			0.840901i
$10$		0			0
$11$	3.91360	+	3.91360i	1.17999	+	1.17999i	0.979745	+	0.200249i	$0.0641750\pi$
$11$	3.91360	+	3.91360i	1.17999	+	1.17999i	0.200249	+	0.979745i	$0.435825\pi$
$12$		0			0
$13$	0.0878822	−	0.0878822i	0.0243741	−	0.0243741i	−0.694815	−	0.719189i	$-0.744514\pi$
$13$	0.0878822	−	0.0878822i	0.0243741	−	0.0243741i	0.719189	+	0.694815i	$0.244514\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.67442			−1.13371			−0.566857	−	0.823816i	$-0.691841\pi$
$17$	−4.67442			−1.13371			−0.566857	+	0.823816i	$0.691841\pi$
$18$		0			0
$19$	−1.81249	+	1.81249i	−0.415813	+	0.415813i	−0.883758	−	0.467945i	$-0.844995\pi$
$19$	−1.81249	+	1.81249i	−0.415813	+	0.415813i	0.467945	+	0.883758i	$0.344995\pi$
$20$		0			0
$21$	−2.30355	−	2.30355i	−0.502676	−	0.502676i
$22$		0			0
$23$		−	1.63007i		−	0.339893i	−0.985453	−	0.169946i	$-0.945641\pi$
$23$		−	1.63007i		−	0.339893i	0.985453	−	0.169946i	$-0.0543594\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−2.69793	−	2.69793i	−0.519217	−	0.519217i
$28$		0			0
$29$	3.26362	−	3.26362i	0.606039	−	0.606039i	−0.335869	−	0.941909i	$-0.609030\pi$
$29$	3.26362	−	3.26362i	0.606039	−	0.606039i	0.941909	+	0.335869i	$0.109030\pi$
$30$		0			0
$31$	2.12875			0.382334			0.191167	−	0.981557i	$-0.438773\pi$
$31$	2.12875			0.382334			0.191167	+	0.981557i	$0.438773\pi$
$32$		0			0
$33$	−3.82371			−0.665622
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.97797	−	3.97797i	−0.653974	−	0.653974i	0.299973	−	0.953948i	$-0.403022\pi$
$37$	−3.97797	−	3.97797i	−0.653974	−	0.653974i	−0.953948	+	0.299973i	$0.903022\pi$
$38$		0			0
$39$			0.0858637i			0.0137492i
$40$		0			0
$41$		−	8.25504i		−	1.28922i	−0.764511	−	0.644611i	$-0.777020\pi$
$41$		−	8.25504i		−	1.28922i	0.764511	−	0.644611i	$-0.222980\pi$
$42$		0			0
$43$	2.27336	+	2.27336i	0.346685	+	0.346685i	0.858873	−	0.512188i	$-0.171165\pi$
$43$	2.27336	+	2.27336i	0.346685	+	0.346685i	−0.512188	+	0.858873i	$0.671165\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.06129			−0.592400			−0.296200	−	0.955126i	$-0.595719\pi$
$47$	−4.06129			−0.592400			−0.296200	+	0.955126i	$0.595719\pi$
$48$		0			0
$49$	−15.2350			−2.17643
$50$		0			0
$51$	2.28353	−	2.28353i	0.319758	−	0.319758i
$52$		0			0
$53$	5.03938	+	5.03938i	0.692211	+	0.692211i	0.962718	−	0.270507i	$-0.0871912\pi$
$53$	5.03938	+	5.03938i	0.692211	+	0.692211i	−0.270507	+	0.962718i	$0.587191\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	1.77086i		−	0.234556i
$58$		0			0
$59$	5.16453	+	5.16453i	0.672365	+	0.672365i	0.958261	−	0.285896i	$-0.0922911\pi$
$59$	5.16453	+	5.16453i	0.672365	+	0.672365i	−0.285896	+	0.958261i	$0.592291\pi$
$60$		0			0
$61$	7.12726	−	7.12726i	0.912552	−	0.912552i	−0.0839206	−	0.996472i	$-0.526744\pi$
$61$	7.12726	−	7.12726i	0.912552	−	0.912552i	0.996472	+	0.0839206i	$0.0267442\pi$
$62$		0			0
$63$	−11.8956			−1.49870
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−7.49920	+	7.49920i	−0.916173	+	0.916173i	−0.996748	−	0.0805758i	$-0.974324\pi$
$67$	−7.49920	+	7.49920i	−0.916173	+	0.916173i	0.0805758	+	0.996748i	$0.474324\pi$
$68$		0			0
$69$	0.796314	+	0.796314i	0.0958649	+	0.0958649i
$70$		0			0
$71$		−	4.54072i		−	0.538884i	−0.963017	−	0.269442i	$-0.913161\pi$
$71$		−	4.54072i		−	0.538884i	0.963017	−	0.269442i	$-0.0868393\pi$
$72$		0			0
$73$			8.30557i			0.972093i	0.873933	+	0.486047i	$0.161561\pi$
$73$			8.30557i			0.972093i	−0.873933	+	0.486047i	$0.838439\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−18.4542	+	18.4542i	−2.10305	+	2.10305i
$78$		0			0
$79$	−11.5317			−1.29742			−0.648709	−	0.761037i	$-0.724691\pi$
$79$	−11.5317			−1.29742			−0.648709	+	0.761037i	$0.724691\pi$
$80$		0			0
$81$	−4.93215			−0.548017
$82$		0			0
$83$	−1.16919	+	1.16919i	−0.128335	+	0.128335i	−0.768357	−	0.640022i	$-0.778925\pi$
$83$	−1.16919	+	1.16919i	−0.128335	+	0.128335i	0.640022	+	0.768357i	$0.278925\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$			3.18866i			0.341861i
$88$		0			0
$89$			3.24572i			0.344046i	0.985093	+	0.172023i	$0.0550304\pi$
$89$			3.24572i			0.344046i	−0.985093	+	0.172023i	$0.944970\pi$
$90$		0			0
$91$	0.414400	+	0.414400i	0.0434409	+	0.0434409i
$92$		0			0
$93$	−1.03993	+	1.03993i	−0.107835	+	0.107835i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	13.9581			1.41723			0.708613	−	0.705598i	$-0.249321\pi$
$97$	13.9581			1.41723			0.708613	+	0.705598i	$0.249321\pi$
$98$		0			0
$99$	−9.87285	+	9.87285i	−0.992258	+	0.992258i
$100$		0			0
$101$	13.4088	+	13.4088i	1.33422	+	1.33422i	0.901552	+	0.432672i	$0.142429\pi$
$101$	13.4088	+	13.4088i	1.33422	+	1.33422i	0.432672	+	0.901552i	$0.357571\pi$
$102$		0			0
$103$		−	13.7638i		−	1.35618i	−0.734977	−	0.678092i	$-0.762807\pi$
$103$		−	13.7638i		−	1.35618i	0.734977	−	0.678092i	$-0.237193\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.327996	−	0.327996i	−0.0317086	−	0.0317086i	0.691075	−	0.722783i	$-0.257138\pi$
$107$	−0.327996	−	0.327996i	−0.0317086	−	0.0317086i	−0.722783	+	0.691075i	$0.757138\pi$
$108$		0			0
$109$	−0.149698	+	0.149698i	−0.0143385	+	0.0143385i	−0.714240	−	0.699901i	$-0.753227\pi$
$109$	−0.149698	+	0.149698i	−0.0143385	+	0.0143385i	0.699901	+	0.714240i	$0.253227\pi$
$110$		0			0
$111$	3.88660			0.368900
$112$		0			0
$113$	−5.97999			−0.562550			−0.281275	−	0.959627i	$-0.590757\pi$
$113$	−5.97999			−0.562550			−0.281275	+	0.959627i	$0.590757\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.221701	+	0.221701i	0.0204962	+	0.0204962i
$118$		0			0
$119$		−	22.0418i		−	2.02057i
$120$		0			0
$121$			19.6325i			1.78477i
$122$		0			0
$123$	4.03272	+	4.03272i	0.363618	+	0.363618i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−2.73076			−0.242315			−0.121158	−	0.992633i	$-0.538661\pi$
$127$	−2.73076			−0.242315			−0.121158	+	0.992633i	$0.538661\pi$
$128$		0			0
$129$	−2.22115			−0.195561
$130$		0			0
$131$	0.813555	−	0.813555i	0.0710806	−	0.0710806i	−0.670673	−	0.741753i	$-0.733994\pi$
$131$	0.813555	−	0.813555i	0.0710806	−	0.0710806i	0.741753	+	0.670673i	$0.233994\pi$
$132$		0			0
$133$	−8.54661	−	8.54661i	−0.741085	−	0.741085i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	0.199812i		−	0.0170711i	−0.999964	−	0.00853557i	$-0.997283\pi$
$137$		−	0.199812i		−	0.0170711i	0.999964	−	0.00853557i	$-0.00271699\pi$
$138$		0			0
$139$	11.6301	+	11.6301i	0.986448	+	0.986448i	0.999909	−	0.0134610i	$-0.00428488\pi$
$139$	11.6301	+	11.6301i	0.986448	+	0.986448i	−0.0134610	+	0.999909i	$0.504285\pi$
$140$		0			0
$141$	1.98400	−	1.98400i	0.167083	−	0.167083i
$142$		0			0
$143$	0.687871			0.0575227
$144$		0			0
$145$		0			0
$146$		0			0
$147$	7.44256	−	7.44256i	0.613852	−	0.613852i
$148$		0			0
$149$	−1.13384	−	1.13384i	−0.0928880	−	0.0928880i	0.659136	−	0.752024i	$-0.270922\pi$
$149$	−1.13384	−	1.13384i	−0.0928880	−	0.0928880i	−0.752024	+	0.659136i	$0.770922\pi$
$150$		0			0
$151$		−	7.12216i		−	0.579593i	−0.957088	−	0.289797i	$-0.906412\pi$
$151$		−	7.12216i		−	0.579593i	0.957088	−	0.289797i	$-0.0935877\pi$
$152$		0			0
$153$		−	11.7922i		−	0.953341i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	5.32145	−	5.32145i	0.424698	−	0.424698i	−0.462120	−	0.886818i	$-0.652911\pi$
$157$	5.32145	−	5.32145i	0.424698	−	0.424698i	0.886818	+	0.462120i	$0.152911\pi$
$158$		0			0
$159$	−4.92363			−0.390469
$160$		0			0
$161$	7.68643			0.605775
$162$		0			0
$163$	−12.3010	+	12.3010i	−0.963488	+	0.963488i	−0.999357	−	0.0358685i	$-0.988580\pi$
$163$	−12.3010	+	12.3010i	−0.963488	+	0.963488i	0.0358685	+	0.999357i	$0.488580\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			9.86820i			0.763624i	0.924240	+	0.381812i	$0.124700\pi$
$167$			9.86820i			0.763624i	−0.924240	+	0.381812i	$0.875300\pi$
$168$		0			0
$169$			12.9846i			0.998812i
$170$		0			0
$171$	−4.57237	−	4.57237i	−0.349658	−	0.349658i
$172$		0			0
$173$	13.4089	−	13.4089i	1.01946	−	1.01946i	0.0196525	−	0.999807i	$-0.493744\pi$
$173$	13.4089	−	13.4089i	1.01946	−	1.01946i	0.999807	−	0.0196525i	$-0.00625599\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−5.04591			−0.379274
$178$		0			0
$179$	−0.419587	+	0.419587i	−0.0313614	+	0.0313614i	−0.722614	−	0.691252i	$-0.757059\pi$
$179$	−0.419587	+	0.419587i	−0.0313614	+	0.0313614i	0.691252	+	0.722614i	$0.257059\pi$
$180$		0			0
$181$	−14.2605	−	14.2605i	−1.05998	−	1.05998i	−0.998083	−	0.0618956i	$-0.980285\pi$
$181$	−14.2605	−	14.2605i	−1.05998	−	1.05998i	−0.0618956	−	0.998083i	$-0.519715\pi$
$182$		0			0
$183$			6.96356i			0.514761i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−18.2938	−	18.2938i	−1.33777	−	1.33777i
$188$		0			0
$189$	12.7218	−	12.7218i	0.925377	−	0.925377i
$190$		0			0
$191$	−17.3304			−1.25399			−0.626993	−	0.779025i	$-0.715715\pi$
$191$	−17.3304			−1.25399			−0.626993	+	0.779025i	$0.715715\pi$
$192$		0			0
$193$	−16.8667			−1.21409			−0.607045	−	0.794667i	$-0.707645\pi$
$193$	−16.8667			−1.21409			−0.607045	+	0.794667i	$0.707645\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	3.58908	+	3.58908i	0.255712	+	0.255712i	0.823307	−	0.567596i	$-0.192126\pi$
$197$	3.58908	+	3.58908i	0.255712	+	0.255712i	−0.567596	+	0.823307i	$0.692126\pi$
$198$		0			0
$199$		−	6.64501i		−	0.471052i	−0.971868	−	0.235526i	$-0.924319\pi$
$199$		−	6.64501i		−	0.471052i	0.971868	−	0.235526i	$-0.0756813\pi$
$200$		0			0
$201$		−	7.32695i		−	0.516803i
$202$		0			0
$203$	15.3893	+	15.3893i	1.08012	+	1.08012i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	4.11218			0.285816
$208$		0			0
$209$	−14.1867			−0.981314
$210$		0			0
$211$	−1.90906	+	1.90906i	−0.131425	+	0.131425i	−0.769759	−	0.638334i	$-0.779624\pi$
$211$	−1.90906	+	1.90906i	−0.131425	+	0.131425i	0.638334	+	0.769759i	$0.279624\pi$
$212$		0			0
$213$	2.21821	+	2.21821i	0.151989	+	0.151989i
$214$		0			0
$215$		0			0
$216$		0			0
$217$			10.0379i			0.681418i
$218$		0			0
$219$	−4.05740	−	4.05740i	−0.274174	−	0.274174i
$220$		0			0
$221$	−0.410798	+	0.410798i	−0.0276333	+	0.0276333i
$222$		0			0
$223$	24.1071			1.61433			0.807165	−	0.590326i	$-0.201001\pi$
$223$	24.1071			1.61433			0.807165	+	0.590326i	$0.201001\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.67411	−	6.67411i	0.442977	−	0.442977i	−0.450035	−	0.893011i	$-0.648588\pi$
$227$	6.67411	−	6.67411i	0.442977	−	0.442977i	0.893011	+	0.450035i	$0.148588\pi$
$228$		0			0
$229$	16.0807	+	16.0807i	1.06264	+	1.06264i	0.997902	+	0.0647388i	$0.0206214\pi$
$229$	16.0807	+	16.0807i	1.06264	+	1.06264i	0.0647388	+	0.997902i	$0.479379\pi$
$230$		0			0
$231$		−	18.0303i		−	1.18631i
$232$		0			0
$233$			16.4976i			1.08079i	0.841411	+	0.540396i	$0.181726\pi$
$233$			16.4976i			1.08079i	−0.841411	+	0.540396i	$0.818274\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	5.63342	−	5.63342i	0.365930	−	0.365930i
$238$		0			0
$239$	−5.25917			−0.340188			−0.170094	−	0.985428i	$-0.554407\pi$
$239$	−5.25917			−0.340188			−0.170094	+	0.985428i	$0.554407\pi$
$240$		0			0
$241$	−14.1126			−0.909075			−0.454538	−	0.890728i	$-0.650196\pi$
$241$	−14.1126			−0.909075			−0.454538	+	0.890728i	$0.650196\pi$
$242$		0			0
$243$	10.5032	−	10.5032i	0.673782	−	0.673782i
$244$		0			0
$245$		0			0
$246$		0			0
$247$			0.318571i			0.0202702i
$248$		0			0
$249$		−	1.14234i		−	0.0723927i
$250$		0			0
$251$	9.98825	+	9.98825i	0.630453	+	0.630453i	0.948182	−	0.317729i	$-0.102920\pi$
$251$	9.98825	+	9.98825i	0.630453	+	0.630453i	−0.317729	+	0.948182i	$0.602920\pi$
$252$		0			0
$253$	6.37943	−	6.37943i	0.401071	−	0.401071i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	8.44760			0.526947			0.263474	−	0.964667i	$-0.415132\pi$
$257$	8.44760			0.526947			0.263474	+	0.964667i	$0.415132\pi$
$258$		0			0
$259$	18.7577	−	18.7577i	1.16555	−	1.16555i
$260$		0			0
$261$	8.23315	+	8.23315i	0.509619	+	0.509619i
$262$		0			0
$263$			18.3064i			1.12882i	0.825494	+	0.564410i	$0.190896\pi$
$263$			18.3064i			1.12882i	−0.825494	+	0.564410i	$0.809104\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.58559	−	1.58559i	−0.0970364	−	0.0970364i
$268$		0			0
$269$	13.5631	−	13.5631i	0.826955	−	0.826955i	−0.160140	−	0.987094i	$-0.551194\pi$
$269$	13.5631	−	13.5631i	0.826955	−	0.826955i	0.987094	+	0.160140i	$0.0511945\pi$
$270$		0			0
$271$	2.24520			0.136386			0.0681930	−	0.997672i	$-0.478277\pi$
$271$	2.24520			0.136386			0.0681930	+	0.997672i	$0.478277\pi$
$272$		0			0
$273$	−0.404882			−0.0245046
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−7.28255	−	7.28255i	−0.437566	−	0.437566i	0.453626	−	0.891192i	$-0.350130\pi$
$277$	−7.28255	−	7.28255i	−0.437566	−	0.437566i	−0.891192	+	0.453626i	$0.850130\pi$
$278$		0			0
$279$			5.37020i			0.321506i
$280$		0			0
$281$			6.04084i			0.360367i	0.983633	+	0.180183i	$0.0576691\pi$
$281$			6.04084i			0.360367i	−0.983633	+	0.180183i	$0.942331\pi$
$282$		0			0
$283$	−15.1350	−	15.1350i	−0.899682	−	0.899682i	0.0957259	−	0.995408i	$-0.469483\pi$
$283$	−15.1350	−	15.1350i	−0.899682	−	0.899682i	−0.995408	+	0.0957259i	$0.969483\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	38.9259			2.29772
$288$		0			0
$289$	4.85021			0.285306
$290$		0			0
$291$	−6.81873	+	6.81873i	−0.399721	+	0.399721i
$292$		0			0
$293$	10.7777	+	10.7777i	0.629637	+	0.629637i	0.947977	−	0.318339i	$-0.103125\pi$
$293$	10.7777	+	10.7777i	0.629637	+	0.629637i	−0.318339	+	0.947977i	$0.603125\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		−	21.1172i		−	1.22534i
$298$		0			0
$299$	−0.143254	−	0.143254i	−0.00828459	−	0.00828459i
$300$		0			0
$301$	−10.7198	+	10.7198i	−0.617881	+	0.617881i
$302$		0			0
$303$	−13.1008			−0.752621
$304$		0			0
$305$		0			0
$306$		0			0
$307$	7.94378	−	7.94378i	0.453376	−	0.453376i	−0.443098	−	0.896473i	$-0.646120\pi$
$307$	7.94378	−	7.94378i	0.453376	−	0.453376i	0.896473	+	0.443098i	$0.146120\pi$
$308$		0			0
$309$	6.72382	+	6.72382i	0.382505	+	0.382505i
$310$		0			0
$311$			31.1649i			1.76720i	0.468244	+	0.883599i	$0.344887\pi$
$311$			31.1649i			1.76720i	−0.468244	+	0.883599i	$0.655113\pi$
$312$		0			0
$313$		−	5.35842i		−	0.302876i	−0.988467	−	0.151438i	$-0.951610\pi$
$313$		−	5.35842i		−	0.302876i	0.988467	−	0.151438i	$-0.0483903\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	8.88165	−	8.88165i	0.498843	−	0.498843i	−0.412235	−	0.911078i	$-0.635252\pi$
$317$	8.88165	−	8.88165i	0.498843	−	0.498843i	0.911078	+	0.412235i	$0.135252\pi$
$318$		0			0
$319$	25.5450			1.43025
$320$		0			0
$321$	0.320463			0.0178865
$322$		0			0
$323$	8.47233	−	8.47233i	0.471413	−	0.471413i
$324$		0			0
$325$		0			0
$326$		0			0
$327$		−	0.146260i		−	0.00808817i
$328$		0			0
$329$		−	19.1506i		−	1.05581i
$330$		0			0
$331$	−6.07281	−	6.07281i	−0.333792	−	0.333792i	0.520233	−	0.854025i	$-0.325845\pi$
$331$	−6.07281	−	6.07281i	−0.333792	−	0.333792i	−0.854025	+	0.520233i	$0.825845\pi$
$332$		0			0
$333$	10.0352	−	10.0352i	0.549928	−	0.549928i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	22.0227			1.19965			0.599827	−	0.800130i	$-0.295236\pi$
$337$	22.0227			1.19965			0.599827	+	0.800130i	$0.295236\pi$
$338$		0			0
$339$	2.92132	−	2.92132i	0.158664	−	0.158664i
$340$		0			0
$341$	8.33106	+	8.33106i	0.451152	+	0.451152i
$342$		0			0
$343$		−	38.8315i		−	2.09670i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	11.8920	+	11.8920i	0.638395	+	0.638395i	0.950159	−	0.311765i	$-0.100920\pi$
$347$	11.8920	+	11.8920i	0.638395	+	0.638395i	−0.311765	+	0.950159i	$0.600920\pi$
$348$		0			0
$349$	−8.65696	+	8.65696i	−0.463396	+	0.463396i	−0.899767	−	0.436371i	$-0.856264\pi$
$349$	−8.65696	+	8.65696i	−0.463396	+	0.463396i	0.436371	+	0.899767i	$0.356264\pi$
$350$		0			0
$351$	−0.474200			−0.0253109
$352$		0			0
$353$	26.6153			1.41659			0.708296	−	0.705916i	$-0.249464\pi$
$353$	26.6153			1.41659			0.708296	+	0.705916i	$0.249464\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	10.7678	+	10.7678i	0.569890	+	0.569890i
$358$		0			0
$359$			4.85032i			0.255990i	0.991775	+	0.127995i	$0.0408542\pi$
$359$			4.85032i			0.255990i	−0.991775	+	0.127995i	$0.959146\pi$
$360$		0			0
$361$			12.4298i			0.654199i
$362$		0			0
$363$	−9.59078	−	9.59078i	−0.503385	−	0.503385i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−15.6741			−0.818182			−0.409091	−	0.912494i	$-0.634154\pi$
$367$	−15.6741			−0.818182			−0.409091	+	0.912494i	$0.634154\pi$
$368$		0			0
$369$	20.8250			1.08411
$370$		0			0
$371$	−23.7627	+	23.7627i	−1.23370	+	1.23370i
$372$		0			0
$373$	−5.44481	−	5.44481i	−0.281922	−	0.281922i	0.551953	−	0.833875i	$-0.313883\pi$
$373$	−5.44481	−	5.44481i	−0.281922	−	0.281922i	−0.833875	+	0.551953i	$0.813883\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	0.573629i		−	0.0295434i
$378$		0			0
$379$	17.4103	+	17.4103i	0.894309	+	0.894309i	0.994925	−	0.100616i	$-0.0320814\pi$
$379$	17.4103	+	17.4103i	0.894309	+	0.894309i	−0.100616	+	0.994925i	$0.532081\pi$
$380$		0			0
$381$	1.33402	−	1.33402i	0.0683438	−	0.0683438i
$382$		0			0
$383$	−9.04928			−0.462396			−0.231198	−	0.972907i	$-0.574265\pi$
$383$	−9.04928			−0.462396			−0.231198	+	0.972907i	$0.574265\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−5.73503	+	5.73503i	−0.291528	+	0.291528i
$388$		0			0
$389$	−15.3617	−	15.3617i	−0.778871	−	0.778871i	0.200768	−	0.979639i	$-0.435656\pi$
$389$	−15.3617	−	15.3617i	−0.778871	−	0.778871i	−0.979639	+	0.200768i	$0.935656\pi$
$390$		0			0
$391$			7.61962i			0.385341i
$392$		0			0
$393$			0.794869i			0.0400959i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	9.44519	−	9.44519i	0.474041	−	0.474041i	−0.429179	−	0.903220i	$-0.641197\pi$
$397$	9.44519	−	9.44519i	0.474041	−	0.474041i	0.903220	+	0.429179i	$0.141197\pi$
$398$		0			0
$399$	8.35031			0.418038
$400$		0			0
$401$	−21.5765			−1.07748			−0.538739	−	0.842473i	$-0.681099\pi$
$401$	−21.5765			−1.07748			−0.538739	+	0.842473i	$0.681099\pi$
$402$		0			0
$403$	0.187079	−	0.187079i	0.00931907	−	0.00931907i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	31.1363i		−	1.54337i
$408$		0			0
$409$		−	4.17336i		−	0.206359i	−0.994663	−	0.103180i	$-0.967098\pi$
$409$		−	4.17336i		−	0.206359i	0.994663	−	0.103180i	$-0.0329017\pi$
$410$		0			0
$411$	0.0976116	+	0.0976116i	0.00481482	+	0.00481482i
$412$		0			0
$413$	−24.3529	+	24.3529i	−1.19833	+	1.19833i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−11.3629			−0.556445
$418$		0			0
$419$	−27.1191	+	27.1191i	−1.32485	+	1.32485i	−0.415060	+	0.909794i	$0.636239\pi$
$419$	−27.1191	+	27.1191i	−1.32485	+	1.32485i	−0.909794	+	0.415060i	$0.863761\pi$
$420$		0			0
$421$	−26.9594	−	26.9594i	−1.31392	−	1.31392i	−0.918500	−	0.395421i	$-0.870599\pi$
$421$	−26.9594	−	26.9594i	−1.31392	−	1.31392i	−0.395421	−	0.918500i	$-0.629401\pi$
$422$		0			0
$423$		−	10.2454i		−	0.498150i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	33.6079	+	33.6079i	1.62640	+	1.62640i
$428$		0			0
$429$	−0.336036	+	0.336036i	−0.0162240	+	0.0162240i
$430$		0			0
$431$	22.4059			1.07925			0.539626	−	0.841905i	$-0.318566\pi$
$431$	22.4059			1.07925			0.539626	+	0.841905i	$0.318566\pi$
$432$		0			0
$433$	16.8061			0.807649			0.403824	−	0.914837i	$-0.367681\pi$
$433$	16.8061			0.807649			0.403824	+	0.914837i	$0.367681\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.95448	+	2.95448i	0.141332	+	0.141332i
$438$		0			0
$439$		−	9.08322i		−	0.433519i	−0.976225	−	0.216759i	$-0.930451\pi$
$439$		−	9.08322i		−	0.433519i	0.976225	−	0.216759i	$-0.0695487\pi$
$440$		0			0
$441$		−	38.4335i		−	1.83017i
$442$		0			0
$443$	12.5397	+	12.5397i	0.595781	+	0.595781i	0.939187	−	0.343406i	$-0.111581\pi$
$443$	12.5397	+	12.5397i	0.595781	+	0.595781i	−0.343406	+	0.939187i	$0.611581\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	1.10780			0.0523972
$448$		0			0
$449$	18.0707			0.852811			0.426406	−	0.904532i	$-0.359780\pi$
$449$	18.0707			0.852811			0.426406	+	0.904532i	$0.359780\pi$
$450$		0			0
$451$	32.3069	−	32.3069i	1.52127	−	1.52127i
$452$		0			0
$453$	3.47929	+	3.47929i	0.163471	+	0.163471i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	18.6637i		−	0.873052i	−0.899692	−	0.436526i	$-0.856209\pi$
$457$		−	18.6637i		−	0.873052i	0.899692	−	0.436526i	$-0.143791\pi$
$458$		0			0
$459$	12.6113	+	12.6113i	0.588643	+	0.588643i
$460$		0			0
$461$	−0.831229	+	0.831229i	−0.0387142	+	0.0387142i	−0.726199	−	0.687485i	$-0.758715\pi$
$461$	−0.831229	+	0.831229i	−0.0387142	+	0.0387142i	0.687485	+	0.726199i	$0.258715\pi$
$462$		0			0
$463$	7.82533			0.363674			0.181837	−	0.983329i	$-0.441796\pi$
$463$	7.82533			0.363674			0.181837	+	0.983329i	$0.441796\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	8.75068	−	8.75068i	0.404933	−	0.404933i	−0.475034	−	0.879967i	$-0.657564\pi$
$467$	8.75068	−	8.75068i	0.404933	−	0.404933i	0.879967	+	0.475034i	$0.157564\pi$
$468$		0			0
$469$	−35.3617	−	35.3617i	−1.63285	−	1.63285i
$470$		0			0
$471$			5.19922i			0.239568i
$472$		0			0
$473$			17.7941i			0.818172i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−12.7129	+	12.7129i	−0.582082	+	0.582082i
$478$		0			0
$479$	−2.10417			−0.0961421			−0.0480710	−	0.998844i	$-0.515307\pi$
$479$	−2.10417			−0.0961421			−0.0480710	+	0.998844i	$0.515307\pi$
$480$		0			0
$481$	−0.699186			−0.0318801
$482$		0			0
$483$	−3.75494	+	3.75494i	−0.170856	+	0.170856i
$484$		0			0
$485$		0			0
$486$		0			0
$487$			4.87183i			0.220764i	0.993889	+	0.110382i	$0.0352074\pi$
$487$			4.87183i			0.220764i	−0.993889	+	0.110382i	$0.964793\pi$
$488$		0			0
$489$		−	12.0185i		−	0.543494i
$490$		0			0
$491$	−14.3582	−	14.3582i	−0.647975	−	0.647975i	0.304528	−	0.952503i	$-0.401501\pi$
$491$	−14.3582	−	14.3582i	−0.647975	−	0.647975i	−0.952503	+	0.304528i	$0.901501\pi$
$492$		0			0
$493$	−15.2555	+	15.2555i	−0.687075	+	0.687075i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	21.4113			0.960429
$498$		0			0
$499$	25.1060	−	25.1060i	1.12390	−	1.12390i	0.132748	−	0.991150i	$-0.457620\pi$
$499$	25.1060	−	25.1060i	1.12390	−	1.12390i	0.991150	−	0.132748i	$-0.0423801\pi$
$500$		0			0
$501$	−4.82077	−	4.82077i	−0.215376	−	0.215376i
$502$		0			0
$503$			18.8868i			0.842120i	0.907033	+	0.421060i	$0.138342\pi$
$503$			18.8868i			0.842120i	−0.907033	+	0.421060i	$0.861658\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−6.34316	−	6.34316i	−0.281710	−	0.281710i
$508$		0			0
$509$	−22.9756	+	22.9756i	−1.01837	+	1.01837i	−0.0185459	+	0.999828i	$0.505904\pi$
$509$	−22.9756	+	22.9756i	−1.01837	+	1.01837i	−0.999828	+	0.0185459i	$0.994096\pi$
$510$		0			0
$511$	−39.1641			−1.73252
$512$		0			0
$513$	9.77993			0.431794
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−15.8942	−	15.8942i	−0.699028	−	0.699028i
$518$		0			0
$519$			13.1009i			0.575066i
$520$		0			0
$521$			20.2089i			0.885367i	0.896678	+	0.442683i	$0.145973\pi$
$521$			20.2089i			0.885367i	−0.896678	+	0.442683i	$0.854027\pi$
$522$		0			0
$523$	−3.93445	−	3.93445i	−0.172042	−	0.172042i	0.615834	−	0.787876i	$-0.288819\pi$
$523$	−3.93445	−	3.93445i	−0.172042	−	0.172042i	−0.787876	+	0.615834i	$0.788819\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−9.95066			−0.433458
$528$		0			0
$529$	20.3429			0.884473
$530$		0			0
$531$	−13.0286	+	13.0286i	−0.565393	+	0.565393i
$532$		0			0
$533$	−0.725471	−	0.725471i	−0.0314237	−	0.0314237i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		−	0.409950i		−	0.0176906i
$538$		0			0
$539$	−59.6238	−	59.6238i	−2.56818	−	2.56818i
$540$		0			0
$541$	−3.17895	+	3.17895i	−0.136674	+	0.136674i	−0.772134	−	0.635460i	$-0.780811\pi$
$541$	−3.17895	+	3.17895i	−0.136674	+	0.136674i	0.635460	+	0.772134i	$0.280811\pi$
$542$		0			0
$543$	13.9330			0.597923
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.32918	+	1.32918i	−0.0568317	+	0.0568317i	−0.734951	−	0.678120i	$-0.762795\pi$
$547$	−1.32918	+	1.32918i	−0.0568317	+	0.0568317i	0.678120	+	0.734951i	$0.262795\pi$
$548$		0			0
$549$	17.9800	+	17.9800i	0.767366	+	0.767366i
$550$		0			0
$551$			11.8306i			0.503998i
$552$		0			0
$553$		−	54.3766i		−	2.31233i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	24.9082	−	24.9082i	1.05539	−	1.05539i	0.0570196	−	0.998373i	$-0.481840\pi$
$557$	24.9082	−	24.9082i	1.05539	−	1.05539i	0.998373	−	0.0570196i	$-0.0181598\pi$
$558$		0			0
$559$	0.399576			0.0169003
$560$		0			0
$561$	17.8736			0.754625
$562$		0			0
$563$	−3.80804	+	3.80804i	−0.160490	+	0.160490i	−0.782784	−	0.622294i	$-0.786201\pi$
$563$	−3.80804	+	3.80804i	−0.160490	+	0.160490i	0.622294	+	0.782784i	$0.286201\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		−	23.2571i		−	0.976706i
$568$		0			0
$569$		−	8.43971i		−	0.353811i	−0.984228	−	0.176905i	$-0.943391\pi$
$569$		−	8.43971i		−	0.353811i	0.984228	−	0.176905i	$-0.0566087\pi$
$570$		0			0
$571$	21.2821	+	21.2821i	0.890629	+	0.890629i	0.994582	−	0.103953i	$-0.0331491\pi$
$571$	21.2821	+	21.2821i	0.890629	+	0.890629i	−0.103953	+	0.994582i	$0.533149\pi$
$572$		0			0
$573$	8.46619	−	8.46619i	0.353680	−	0.353680i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−36.3491			−1.51323			−0.756615	−	0.653860i	$-0.773148\pi$
$577$	−36.3491			−1.51323			−0.756615	+	0.653860i	$0.773148\pi$
$578$		0			0
$579$	8.23964	−	8.23964i	0.342428	−	0.342428i
$580$		0			0
$581$	−5.51321	−	5.51321i	−0.228726	−	0.228726i
$582$		0			0
$583$			39.4442i			1.63361i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	6.55994	+	6.55994i	0.270758	+	0.270758i	0.829405	−	0.558647i	$-0.188679\pi$
$587$	6.55994	+	6.55994i	0.270758	+	0.270758i	−0.558647	+	0.829405i	$0.688679\pi$
$588$		0			0
$589$	−3.85833	+	3.85833i	−0.158980	+	0.158980i
$590$		0			0
$591$	−3.50665			−0.144244
$592$		0			0
$593$	−1.40974			−0.0578911			−0.0289455	−	0.999581i	$-0.509215\pi$
$593$	−1.40974			−0.0578911			−0.0289455	+	0.999581i	$0.509215\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	3.24619	+	3.24619i	0.132858	+	0.132858i
$598$		0			0
$599$			23.3593i			0.954435i	0.878785	+	0.477218i	$0.158355\pi$
$599$			23.3593i			0.954435i	−0.878785	+	0.477218i	$0.841645\pi$
$600$		0			0
$601$		−	20.4138i		−	0.832695i	−0.909206	−	0.416347i	$-0.863310\pi$
$601$		−	20.4138i		−	0.832695i	0.909206	−	0.416347i	$-0.136690\pi$
$602$		0			0
$603$	−18.9183	−	18.9183i	−0.770411	−	0.770411i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−0.758240			−0.0307760			−0.0153880	−	0.999882i	$-0.504898\pi$
$607$	−0.758240			−0.0307760			−0.0153880	+	0.999882i	$0.504898\pi$
$608$		0			0
$609$	−15.0358			−0.609283
$610$		0			0
$611$	−0.356915	+	0.356915i	−0.0144392	+	0.0144392i
$612$		0			0
$613$	12.0341	+	12.0341i	0.486052	+	0.486052i	0.907058	−	0.421006i	$-0.138323\pi$
$613$	12.0341	+	12.0341i	0.486052	+	0.486052i	−0.421006	+	0.907058i	$0.638323\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			32.6899i			1.31605i	0.752998	+	0.658023i	$0.228607\pi$
$617$			32.6899i			1.31605i	−0.752998	+	0.658023i	$0.771393\pi$
$618$		0			0
$619$	−26.3836	−	26.3836i	−1.06045	−	1.06045i	−0.998052	−	0.0623934i	$-0.980127\pi$
$619$	−26.3836	−	26.3836i	−1.06045	−	1.06045i	−0.0623934	−	0.998052i	$-0.519873\pi$
$620$		0			0
$621$	−4.39781	+	4.39781i	−0.176478	+	0.176478i
$622$		0			0
$623$	−15.3049			−0.613178
$624$		0			0
$625$		0			0
$626$		0			0
$627$	6.93042	−	6.93042i	0.276774	−	0.276774i
$628$		0			0
$629$	18.5947	+	18.5947i	0.741420	+	0.741420i
$630$		0			0
$631$			6.08765i			0.242345i	0.992631	+	0.121173i	$0.0386655\pi$
$631$			6.08765i			0.242345i	−0.992631	+	0.121173i	$0.961335\pi$
$632$		0			0
$633$		−	1.86521i		−	0.0741354i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−1.33889	+	1.33889i	−0.0530487	+	0.0530487i
$638$		0			0
$639$	11.4549			0.453149
$640$		0			0
$641$	11.1680			0.441111			0.220555	−	0.975374i	$-0.429213\pi$
$641$	11.1680			0.441111			0.220555	+	0.975374i	$0.429213\pi$
$642$		0			0
$643$	21.9585	−	21.9585i	0.865957	−	0.865957i	−0.126065	−	0.992022i	$-0.540235\pi$
$643$	21.9585	−	21.9585i	0.865957	−	0.865957i	0.992022	+	0.126065i	$0.0402348\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			36.9848i			1.45402i	0.686625	+	0.727011i	$0.259091\pi$
$647$			36.9848i			1.45402i	−0.686625	+	0.727011i	$0.740909\pi$
$648$		0			0
$649$			40.4238i			1.58677i
$650$		0			0
$651$	−4.90368	−	4.90368i	−0.192190	−	0.192190i
$652$		0			0
$653$	−18.4157	+	18.4157i	−0.720663	+	0.720663i	−0.968740	−	0.248077i	$-0.920201\pi$
$653$	−18.4157	+	18.4157i	−0.720663	+	0.720663i	0.248077	+	0.968740i	$0.420201\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−20.9525			−0.817435
$658$		0			0
$659$	15.5421	−	15.5421i	0.605434	−	0.605434i	−0.336316	−	0.941749i	$-0.609181\pi$
$659$	15.5421	−	15.5421i	0.605434	−	0.605434i	0.941749	+	0.336316i	$0.109181\pi$
$660$		0			0
$661$	29.6677	+	29.6677i	1.15394	+	1.15394i	0.985755	+	0.168185i	$0.0537906\pi$
$661$	29.6677	+	29.6677i	1.15394	+	1.15394i	0.168185	+	0.985755i	$0.446209\pi$
$662$		0			0
$663$		−	0.401363i		−	0.0155877i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−5.31992	−	5.31992i	−0.205988	−	0.205988i
$668$		0			0
$669$	−11.7767	+	11.7767i	−0.455313	+	0.455313i
$670$		0			0
$671$	55.7864			2.15361
$672$		0			0
$673$	−29.2198			−1.12634			−0.563171	−	0.826340i	$-0.690419\pi$
$673$	−29.2198			−1.12634			−0.563171	+	0.826340i	$0.690419\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	17.2591	+	17.2591i	0.663320	+	0.663320i	0.956161	−	0.292841i	$-0.0946006\pi$
$677$	17.2591	+	17.2591i	0.663320	+	0.663320i	−0.292841	+	0.956161i	$0.594601\pi$
$678$		0			0
$679$			65.8179i			2.52586i
$680$		0			0
$681$			6.52082i			0.249878i
$682$		0			0
$683$	−1.10407	−	1.10407i	−0.0422459	−	0.0422459i	0.685668	−	0.727914i	$-0.259510\pi$
$683$	−1.10407	−	1.10407i	−0.0422459	−	0.0422459i	−0.727914	+	0.685668i	$0.759510\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−15.7113			−0.599425
$688$		0			0
$689$	0.885743			0.0337441
$690$		0			0
$691$	28.4233	−	28.4233i	1.08127	−	1.08127i	0.0848830	−	0.996391i	$-0.472948\pi$
$691$	28.4233	−	28.4233i	1.08127	−	1.08127i	0.996391	−	0.0848830i	$-0.0270517\pi$
$692$		0			0
$693$	−46.5545	−	46.5545i	−1.76846	−	1.76846i
$694$		0			0
$695$		0			0
$696$		0			0
$697$			38.5875i			1.46161i
$698$		0			0
$699$	−8.05933	−	8.05933i	−0.304832	−	0.304832i
$700$		0			0
$701$	−23.7991	+	23.7991i	−0.898880	+	0.898880i	−0.995337	−	0.0964573i	$-0.969249\pi$
$701$	−23.7991	+	23.7991i	−0.898880	+	0.898880i	0.0964573	+	0.995337i	$0.469249\pi$
$702$		0			0
$703$	14.4200			0.543862
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−63.2278	+	63.2278i	−2.37793	+	2.37793i
$708$		0			0
$709$	1.49921	+	1.49921i	0.0563039	+	0.0563039i	0.734698	−	0.678394i	$-0.237324\pi$
$709$	1.49921	+	1.49921i	0.0563039	+	0.0563039i	−0.678394	+	0.734698i	$0.737324\pi$
$710$		0			0
$711$		−	29.0911i		−	1.09100i
$712$		0			0
$713$		−	3.47000i		−	0.129953i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	2.56919	−	2.56919i	0.0959482	−	0.0959482i
$718$		0			0
$719$	−7.37612			−0.275083			−0.137541	−	0.990496i	$-0.543920\pi$
$719$	−7.37612			−0.275083			−0.137541	+	0.990496i	$0.543920\pi$
$720$		0			0
$721$	64.9017			2.41707
$722$		0			0
$723$	6.89425	−	6.89425i	0.256400	−	0.256400i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	30.1470i		−	1.11809i	−0.829137	−	0.559045i	$-0.811168\pi$
$727$		−	30.1470i		−	1.11809i	0.829137	−	0.559045i	$-0.188832\pi$
$728$		0			0
$729$		−	4.53447i		−	0.167943i
$730$		0			0
$731$	−10.6267	−	10.6267i	−0.393041	−	0.393041i
$732$		0			0
$733$	−1.43297	+	1.43297i	−0.0529279	+	0.0529279i	−0.733075	−	0.680147i	$-0.761916\pi$
$733$	−1.43297	+	1.43297i	−0.0529279	+	0.0529279i	0.680147	+	0.733075i	$0.261916\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−58.6977			−2.16216
$738$		0			0
$739$	−31.0001	+	31.0001i	−1.14036	+	1.14036i	−0.151973	+	0.988385i	$0.548563\pi$
$739$	−31.0001	+	31.0001i	−1.14036	+	1.14036i	−0.988385	+	0.151973i	$0.951437\pi$
$740$		0			0
$741$	−0.155627	−	0.155627i	−0.00571710	−	0.00571710i
$742$		0			0
$743$			38.5395i			1.41388i	0.707276	+	0.706938i	$0.249924\pi$
$743$			38.5395i			1.41388i	−0.707276	+	0.706938i	$0.750076\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−2.94952	−	2.94952i	−0.107917	−	0.107917i
$748$		0			0
$749$	1.54664	−	1.54664i	0.0565128	−	0.0565128i
$750$		0			0
$751$	−26.9523			−0.983503			−0.491751	−	0.870736i	$-0.663643\pi$
$751$	−26.9523			−0.983503			−0.491751	+	0.870736i	$0.663643\pi$
$752$		0			0
$753$	−9.75884			−0.355632
$754$		0			0
$755$		0			0
$756$		0			0
$757$	17.0688	+	17.0688i	0.620377	+	0.620377i	0.945628	−	0.325251i	$-0.105449\pi$
$757$	17.0688	+	17.0688i	0.620377	+	0.620377i	−0.325251	+	0.945628i	$0.605449\pi$
$758$		0			0
$759$			6.23290i			0.226240i
$760$		0			0
$761$		−	6.89608i		−	0.249983i	−0.992158	−	0.124991i	$-0.960110\pi$
$761$		−	6.89608i		−	0.249983i	0.992158	−	0.124991i	$-0.0398903\pi$
$762$		0			0
$763$	−0.705886	−	0.705886i	−0.0255548	−	0.0255548i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.907741			0.0327766
$768$		0			0
$769$	11.8443			0.427117			0.213558	−	0.976930i	$-0.431495\pi$
$769$	11.8443			0.427117			0.213558	+	0.976930i	$0.431495\pi$
$770$		0			0
$771$	−4.12679	+	4.12679i	−0.148623	+	0.148623i
$772$		0			0
$773$	−3.58865	−	3.58865i	−0.129075	−	0.129075i	0.639618	−	0.768693i	$-0.279093\pi$
$773$	−3.58865	−	3.58865i	−0.129075	−	0.129075i	−0.768693	+	0.639618i	$0.779093\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$			18.3269i			0.657474i
$778$		0			0
$779$	14.9622	+	14.9622i	0.536075	+	0.536075i
$780$		0			0
$781$	17.7705	−	17.7705i	0.635880	−	0.635880i
$782$		0			0
$783$	−17.6100			−0.629332
$784$		0			0
$785$		0			0
$786$		0			0
$787$	22.4800	−	22.4800i	0.801326	−	0.801326i	−0.181977	−	0.983303i	$-0.558250\pi$
$787$	22.4800	−	22.4800i	0.801326	−	0.801326i	0.983303	+	0.181977i	$0.0582497\pi$
$788$		0			0
$789$	−8.94296	−	8.94296i	−0.318378	−	0.318378i
$790$		0			0
$791$		−	28.1981i		−	1.00261i
$792$		0			0
$793$		−	1.25272i		−	0.0444853i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−8.67589	+	8.67589i	−0.307316	+	0.307316i	−0.843867	−	0.536552i	$-0.819727\pi$
$797$	−8.67589	+	8.67589i	−0.307316	+	0.307316i	0.536552	+	0.843867i	$0.319727\pi$
$798$		0			0
$799$	18.9842			0.671612
$800$		0			0
$801$	−8.18800			−0.289309
$802$		0			0
$803$	−32.5046	+	32.5046i	−1.14706	+	1.14706i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			13.2515i			0.466476i
$808$		0			0
$809$		−	27.9066i		−	0.981143i	−0.871401	−	0.490571i	$-0.836788\pi$
$809$		−	27.9066i		−	0.981143i	0.871401	−	0.490571i	$-0.163212\pi$
$810$		0			0
$811$	−15.2635	−	15.2635i	−0.535974	−	0.535974i	0.386370	−	0.922344i	$-0.373729\pi$
$811$	−15.2635	−	15.2635i	−0.535974	−	0.535974i	−0.922344	+	0.386370i	$0.873729\pi$
$812$		0			0
$813$	−1.09681	+	1.09681i	−0.0384670	+	0.0384670i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−8.24089			−0.288312
$818$		0			0
$819$	−1.04541	+	1.04541i	−0.0365295	+	0.0365295i
$820$		0			0
$821$	25.2883	+	25.2883i	0.882567	+	0.882567i	0.993795	−	0.111228i	$-0.0354782\pi$
$821$	25.2883	+	25.2883i	0.882567	+	0.882567i	−0.111228	+	0.993795i	$0.535478\pi$
$822$		0			0
$823$			7.12228i			0.248267i	0.992266	+	0.124133i	$0.0396151\pi$
$823$			7.12228i			0.248267i	−0.992266	+	0.124133i	$0.960385\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−32.1618	−	32.1618i	−1.11837	−	1.11837i	−0.991980	−	0.126394i	$-0.959660\pi$
$827$	−32.1618	−	32.1618i	−1.11837	−	1.11837i	−0.126394	−	0.991980i	$-0.540340\pi$
$828$		0			0
$829$	−34.9802	+	34.9802i	−1.21491	+	1.21491i	−0.245522	+	0.969391i	$0.578959\pi$
$829$	−34.9802	+	34.9802i	−1.21491	+	1.21491i	−0.969391	+	0.245522i	$0.921041\pi$
$830$		0			0
$831$	7.11529			0.246827
$832$		0			0
$833$	71.2149			2.46745
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−5.74321	−	5.74321i	−0.198514	−	0.198514i
$838$		0			0
$839$		−	11.1147i		−	0.383721i	−0.981422	−	0.191861i	$-0.938548\pi$
$839$		−	11.1147i		−	0.383721i	0.981422	−	0.191861i	$-0.0614521\pi$
$840$		0			0
$841$			7.69754i			0.265432i
$842$		0			0
$843$	−2.95105	−	2.95105i	−0.101640	−	0.101640i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−92.5750			−3.18092
$848$		0			0
$849$	14.7874			0.507501
$850$		0			0
$851$	−6.48436	+	6.48436i	−0.222281	+	0.222281i
$852$		0			0
$853$	28.9107	+	28.9107i	0.989884	+	0.989884i	0.999949	−	0.0100656i	$-0.00320402\pi$
$853$	28.9107	+	28.9107i	0.989884	+	0.989884i	−0.0100656	+	0.999949i	$0.503204\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	34.1485i		−	1.16649i	−0.812296	−	0.583245i	$-0.801783\pi$
$857$		−	34.1485i		−	1.16649i	0.812296	−	0.583245i	$-0.198217\pi$
$858$		0			0
$859$	−20.4589	−	20.4589i	−0.698047	−	0.698047i	0.265942	−	0.963989i	$-0.414317\pi$
$859$	−20.4589	−	20.4589i	−0.698047	−	0.698047i	−0.963989	+	0.265942i	$0.914317\pi$
$860$		0			0
$861$	−19.0159	+	19.0159i	−0.648060	+	0.648060i
$862$		0			0
$863$	35.3591			1.20364			0.601818	−	0.798633i	$-0.294443\pi$
$863$	35.3591			1.20364			0.601818	+	0.798633i	$0.294443\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−2.36940	+	2.36940i	−0.0804692	+	0.0804692i
$868$		0			0
$869$	−45.1304	−	45.1304i	−1.53094	−	1.53094i
$870$		0			0
$871$			1.31809i			0.0446618i
$872$		0			0
$873$			35.2120i			1.19175i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−3.15415	+	3.15415i	−0.106508	+	0.106508i	−0.758353	−	0.651845i	$-0.773995\pi$
$877$	−3.15415	+	3.15415i	−0.106508	+	0.106508i	0.651845	+	0.758353i	$0.273995\pi$
$878$		0			0
$879$	−10.5301			−0.355172
$880$		0			0
$881$	20.3066			0.684146			0.342073	−	0.939673i	$-0.388871\pi$
$881$	20.3066			0.684146			0.342073	+	0.939673i	$0.388871\pi$
$882$		0			0
$883$	−0.523303	+	0.523303i	−0.0176105	+	0.0176105i	−0.715857	−	0.698247i	$-0.753964\pi$
$883$	−0.523303	+	0.523303i	−0.0176105	+	0.0176105i	0.698247	+	0.715857i	$0.253964\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		−	34.8129i		−	1.16890i	−0.811429	−	0.584452i	$-0.801310\pi$
$887$		−	34.8129i		−	1.16890i	0.811429	−	0.584452i	$-0.198690\pi$
$888$		0			0
$889$		−	12.8766i		−	0.431868i
$890$		0			0
$891$	−19.3024	−	19.3024i	−0.646656	−	0.646656i
$892$		0			0
$893$	7.36103	−	7.36103i	0.246328	−	0.246328i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.139964			0.00467325
$898$		0			0
$899$	6.94743	−	6.94743i	0.231710	−	0.231710i
$900$		0			0
$901$	−23.5562	−	23.5562i	−0.784770	−	0.784770i
$902$		0			0
$903$		−	10.4736i		−	0.348540i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	13.3188	+	13.3188i	0.442244	+	0.442244i	0.892766	−	0.450521i	$-0.148762\pi$
$907$	13.3188	+	13.3188i	0.442244	+	0.442244i	−0.450521	+	0.892766i	$0.648762\pi$
$908$		0			0
$909$	−33.8264	+	33.8264i	−1.12195	+	1.12195i
$910$		0			0
$911$	47.0117			1.55757			0.778783	−	0.627294i	$-0.215837\pi$
$911$	47.0117			1.55757			0.778783	+	0.627294i	$0.215837\pi$
$912$		0			0
$913$	−9.15148			−0.302870
$914$		0			0
$915$		0			0
$916$		0			0
$917$	3.83624	+	3.83624i	0.126684	+	0.126684i
$918$		0			0
$919$		−	31.3426i		−	1.03390i	−0.856016	−	0.516949i	$-0.827068\pi$
$919$		−	31.3426i		−	1.03390i	0.856016	−	0.516949i	$-0.172932\pi$
$920$		0			0
$921$			7.76133i			0.255745i
$922$		0			0
$923$	−0.399048	−	0.399048i	−0.0131348	−	0.0131348i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	34.7219			1.14042
$928$		0			0
$929$	30.3384			0.995369			0.497685	−	0.867358i	$-0.334184\pi$
$929$	30.3384			0.995369			0.497685	+	0.867358i	$0.334184\pi$
$930$		0			0
$931$	27.6133	−	27.6133i	0.904990	−	0.904990i
$932$		0			0
$933$	−15.2245	−	15.2245i	−0.498429	−	0.498429i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			14.5267i			0.474565i	0.971441	+	0.237283i	$0.0762567\pi$
$937$			14.5267i			0.474565i	−0.971441	+	0.237283i	$0.923743\pi$
$938$		0			0
$939$	2.61767	+	2.61767i	0.0854245	+	0.0854245i
$940$		0			0
$941$	37.2863	−	37.2863i	1.21550	−	1.21550i	0.246307	−	0.969192i	$-0.420783\pi$
$941$	37.2863	−	37.2863i	1.21550	−	1.21550i	0.969192	−	0.246307i	$-0.0792172\pi$
$942$		0			0
$943$	−13.4563			−0.438197
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−15.8961	+	15.8961i	−0.516553	+	0.516553i	−0.916527	−	0.399973i	$-0.869019\pi$
$947$	−15.8961	+	15.8961i	−0.516553	+	0.516553i	0.399973	+	0.916527i	$0.369019\pi$
$948$		0			0
$949$	0.729912	+	0.729912i	0.0236939	+	0.0236939i
$950$		0			0
$951$			8.67765i			0.281392i
$952$		0			0
$953$			33.2248i			1.07626i	0.842862	+	0.538129i	$0.180869\pi$
$953$			33.2248i			1.07626i	−0.842862	+	0.538129i	$0.819131\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−12.4791	+	12.4791i	−0.403393	+	0.403393i
$958$		0			0
$959$	0.942197			0.0304251
$960$		0			0
$961$	−26.4684			−0.853820
$962$		0			0
$963$	0.827438	−	0.827438i	0.0266638	−	0.0266638i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			1.79116i			0.0576000i	0.999585	+	0.0288000i	$0.00916859\pi$
$967$			1.79116i			0.0576000i	−0.999585	+	0.0288000i	$0.990831\pi$
$968$		0			0
$969$			8.27774i			0.265919i
$970$		0			0
$971$	−5.31278	−	5.31278i	−0.170495	−	0.170495i	0.616702	−	0.787197i	$-0.288469\pi$
$971$	−5.31278	−	5.31278i	−0.170495	−	0.170495i	−0.787197	+	0.616702i	$0.788469\pi$
$972$		0			0
$973$	−54.8404	+	54.8404i	−1.75810	+	1.75810i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	6.81676			0.218088			0.109044	−	0.994037i	$-0.465221\pi$
$977$	6.81676			0.218088			0.109044	+	0.994037i	$0.465221\pi$
$978$		0			0
$979$	−12.7025	+	12.7025i	−0.405972	+	0.405972i
$980$		0			0
$981$	−0.377643	−	0.377643i	−0.0120572	−	0.0120572i
$982$		0			0
$983$		−	5.49468i		−	0.175253i	−0.996153	−	0.0876265i	$-0.972072\pi$
$983$		−	5.49468i		−	0.175253i	0.996153	−	0.0876265i	$-0.0279282\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	9.35538	+	9.35538i	0.297785	+	0.297785i
$988$		0			0
$989$	3.70574	−	3.70574i	0.117836	−	0.117836i
$990$		0			0
$991$	−48.7524			−1.54867			−0.774335	−	0.632775i	$-0.781916\pi$
$991$	−48.7524			−1.54867			−0.774335	+	0.632775i	$0.781916\pi$
$992$		0			0
$993$	5.93333			0.188289
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−42.5246	−	42.5246i	−1.34677	−	1.34677i	−0.889149	−	0.457618i	$-0.848703\pi$
$997$	−42.5246	−	42.5246i	−1.34677	−	1.34677i	−0.457618	−	0.889149i	$-0.651297\pi$
$998$		0			0
$999$			21.4646i			0.679109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.l.f.1201.3		12
4.3	odd	2		400.2.l.g.101.1	yes	12
5.2	odd	4		1600.2.q.f.49.4		12
5.3	odd	4		1600.2.q.e.49.3		12
5.4	even	2		1600.2.l.g.1201.4		12
16.3	odd	4		400.2.l.g.301.1	yes	12
16.13	even	4	inner	1600.2.l.f.401.3		12
20.3	even	4		400.2.q.e.149.4		12
20.7	even	4		400.2.q.f.149.3		12
20.19	odd	2		400.2.l.f.101.6	✓	12
80.3	even	4		400.2.q.f.349.3		12
80.13	odd	4		1600.2.q.f.849.4		12
80.19	odd	4		400.2.l.f.301.6	yes	12
80.29	even	4		1600.2.l.g.401.4		12
80.67	even	4		400.2.q.e.349.4		12
80.77	odd	4		1600.2.q.e.849.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.l.f.101.6	✓	12	20.19	odd	2
400.2.l.f.301.6	yes	12	80.19	odd	4
400.2.l.g.101.1	yes	12	4.3	odd	2
400.2.l.g.301.1	yes	12	16.3	odd	4
400.2.q.e.149.4		12	20.3	even	4
400.2.q.e.349.4		12	80.67	even	4
400.2.q.f.149.3		12	20.7	even	4
400.2.q.f.349.3		12	80.3	even	4
1600.2.l.f.401.3		12	16.13	even	4	inner
1600.2.l.f.1201.3		12	1.1	even	1	trivial
1600.2.l.g.401.4		12	80.29	even	4
1600.2.l.g.1201.4		12	5.4	even	2
1600.2.q.e.49.3		12	5.3	odd	4
1600.2.q.e.849.3		12	80.77	odd	4
1600.2.q.f.49.4		12	5.2	odd	4
1600.2.q.f.849.4		12	80.13	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:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.488516 + 0.488516i) q^{3} +4.71540i q^{7} +2.52270i q^{9} +O(q^{10})\)	\(q+(-0.488516 + 0.488516i) q^{3} +4.71540i q^{7} +2.52270i q^{9} +(3.91360 + 3.91360i) q^{11} +(0.0878822 - 0.0878822i) q^{13} -4.67442 q^{17} +(-1.81249 + 1.81249i) q^{19} +(-2.30355 - 2.30355i) q^{21} -1.63007i q^{23} +(-2.69793 - 2.69793i) q^{27} +(3.26362 - 3.26362i) q^{29} +2.12875 q^{31} -3.82371 q^{33} +(-3.97797 - 3.97797i) q^{37} +0.0858637i q^{39} -8.25504i q^{41} +(2.27336 + 2.27336i) q^{43} -4.06129 q^{47} -15.2350 q^{49} +(2.28353 - 2.28353i) q^{51} +(5.03938 + 5.03938i) q^{53} -1.77086i q^{57} +(5.16453 + 5.16453i) q^{59} +(7.12726 - 7.12726i) q^{61} -11.8956 q^{63} +(-7.49920 + 7.49920i) q^{67} +(0.796314 + 0.796314i) q^{69} -4.54072i q^{71} +8.30557i q^{73} +(-18.4542 + 18.4542i) q^{77} -11.5317 q^{79} -4.93215 q^{81} +(-1.16919 + 1.16919i) q^{83} +3.18866i q^{87} +3.24572i q^{89} +(0.414400 + 0.414400i) q^{91} +(-1.03993 + 1.03993i) q^{93} +13.9581 q^{97} +(-9.87285 + 9.87285i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3}+O(q^{10}) \) 12 * q - 2 * q^3	\( 12 q - 2 q^{3} + 2 q^{11} - 4 q^{13} - 8 q^{17} + 14 q^{19} - 20 q^{21} + 10 q^{27} + 4 q^{31} + 28 q^{33} + 8 q^{37} - 8 q^{47} + 4 q^{49} - 10 q^{51} - 16 q^{53} - 20 q^{59} + 4 q^{61} + 8 q^{63} - 50 q^{67} - 8 q^{77} - 12 q^{79} - 8 q^{81} + 2 q^{83} - 44 q^{93} - 12 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 + 2 * q^11 - 4 * q^13 - 8 * q^17 + 14 * q^19 - 20 * q^21 + 10 * q^27 + 4 * q^31 + 28 * q^33 + 8 * q^37 - 8 * q^47 + 4 * q^49 - 10 * q^51 - 16 * q^53 - 20 * q^59 + 4 * q^61 + 8 * q^63 - 50 * q^67 - 8 * q^77 - 12 * q^79 - 8 * q^81 + 2 * q^83 - 44 * q^93 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more