LMFDB - Embedded newform 260.2.r.b.213.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(177,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("260.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.r (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			213.1
Root			$-0.618034i$ of defining polynomial
Character	$\chi$	$=$	260.213
Dual form			260.2.r.b.177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.618034 - 0.618034i) q^{3} -2.23607 q^{5} -2.23607i q^{9} +O(q^{10})$	$q+(-0.618034 - 0.618034i) q^{3} -2.23607 q^{5} -2.23607i q^{9} +(-2.61803 - 2.61803i) q^{11} +(-3.00000 - 2.00000i) q^{13} +(1.38197 + 1.38197i) q^{15} +(2.23607 + 2.23607i) q^{17} +(-5.85410 - 5.85410i) q^{19} +(-3.38197 + 3.38197i) q^{23} +5.00000 q^{25} +(-3.23607 + 3.23607i) q^{27} +5.23607i q^{29} +(5.85410 - 5.85410i) q^{31} +3.23607i q^{33} +9.70820 q^{37} +(0.618034 + 3.09017i) q^{39} +(3.76393 - 3.76393i) q^{41} +(3.85410 - 3.85410i) q^{43} +5.00000i q^{45} -8.94427 q^{47} -7.00000 q^{49} -2.76393i q^{51} +(1.47214 + 1.47214i) q^{53} +(5.85410 + 5.85410i) q^{55} +7.23607i q^{57} +(3.38197 - 3.38197i) q^{59} +5.70820 q^{61} +(6.70820 + 4.47214i) q^{65} +0.291796i q^{67} +4.18034 q^{69} +(2.61803 - 2.61803i) q^{71} +11.7082i q^{73} +(-3.09017 - 3.09017i) q^{75} +3.70820i q^{79} -2.70820 q^{81} -10.4721 q^{83} +(-5.00000 - 5.00000i) q^{85} +(3.23607 - 3.23607i) q^{87} +(2.23607 - 2.23607i) q^{89} -7.23607 q^{93} +(13.0902 + 13.0902i) q^{95} -15.4164i q^{97} +(-5.85410 + 5.85410i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3}+O(q^{10}) $ 4 * q + 2 * q^3	$ 4 q + 2 q^{3} - 6 q^{11} - 12 q^{13} + 10 q^{15} - 10 q^{19} - 18 q^{23} + 20 q^{25} - 4 q^{27} + 10 q^{31} + 12 q^{37} - 2 q^{39} + 24 q^{41} + 2 q^{43} - 28 q^{49} - 12 q^{53} + 10 q^{55} + 18 q^{59} - 4 q^{61} - 28 q^{69} + 6 q^{71} + 10 q^{75} + 16 q^{81} - 24 q^{83} - 20 q^{85} + 4 q^{87} - 20 q^{93} + 30 q^{95} - 10 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 6 * q^11 - 12 * q^13 + 10 * q^15 - 10 * q^19 - 18 * q^23 + 20 * q^25 - 4 * q^27 + 10 * q^31 + 12 * q^37 - 2 * q^39 + 24 * q^41 + 2 * q^43 - 28 * q^49 - 12 * q^53 + 10 * q^55 + 18 * q^59 - 4 * q^61 - 28 * q^69 + 6 * q^71 + 10 * q^75 + 16 * q^81 - 24 * q^83 - 20 * q^85 + 4 * q^87 - 20 * q^93 + 30 * q^95 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.618034	−	0.618034i	−0.356822	−	0.356822i	0.505818	−	0.862640i	$-0.331191\pi$
$3$	−0.618034	−	0.618034i	−0.356822	−	0.356822i	−0.862640	+	0.505818i	$0.831191\pi$
$4$		0			0
$5$	−2.23607			−1.00000
$5$	−2.23607			−1.00000
$6$		0			0
$7$		0			0			−	1.00000i	$-0.5\pi$
$7$		0			0				1.00000i	$0.5\pi$
$8$		0			0
$9$		−	2.23607i		−	0.745356i
$10$		0			0
$11$	−2.61803	−	2.61803i	−0.789367	−	0.789367i	0.192023	−	0.981390i	$-0.438495\pi$
$11$	−2.61803	−	2.61803i	−0.789367	−	0.789367i	−0.981390	+	0.192023i	$0.938495\pi$
$12$		0			0
$13$	−3.00000	−	2.00000i	−0.832050	−	0.554700i
$13$	−3.00000	−	2.00000i	−0.832050	−	0.554700i
$14$		0			0
$15$	1.38197	+	1.38197i	0.356822	+	0.356822i
$16$		0			0
$17$	2.23607	+	2.23607i	0.542326	+	0.542326i	0.924210	−	0.381884i	$-0.124725\pi$
$17$	2.23607	+	2.23607i	0.542326	+	0.542326i	−0.381884	+	0.924210i	$0.624725\pi$
$18$		0			0
$19$	−5.85410	−	5.85410i	−1.34302	−	1.34302i	−0.893034	−	0.449989i	$-0.851428\pi$
$19$	−5.85410	−	5.85410i	−1.34302	−	1.34302i	−0.449989	−	0.893034i	$-0.648572\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.38197	+	3.38197i	−0.705189	+	0.705189i	−0.965519	−	0.260331i	$-0.916168\pi$
$23$	−3.38197	+	3.38197i	−0.705189	+	0.705189i	0.260331	+	0.965519i	$0.416168\pi$
$24$		0			0
$25$	5.00000			1.00000
$26$		0			0
$27$	−3.23607	+	3.23607i	−0.622782	+	0.622782i
$28$		0			0
$29$			5.23607i			0.972313i	0.873872	+	0.486157i	$0.161602\pi$
$29$			5.23607i			0.972313i	−0.873872	+	0.486157i	$0.838398\pi$
$30$		0			0
$31$	5.85410	−	5.85410i	1.05143	−	1.05143i	0.0528239	−	0.998604i	$-0.483178\pi$
$31$	5.85410	−	5.85410i	1.05143	−	1.05143i	0.998604	−	0.0528239i	$-0.0168222\pi$
$32$		0			0
$33$			3.23607i			0.563327i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	9.70820			1.59602			0.798009	−	0.602645i	$-0.205886\pi$
$37$	9.70820			1.59602			0.798009	+	0.602645i	$0.205886\pi$
$38$		0			0
$39$	0.618034	+	3.09017i	0.0989646	+	0.494823i
$40$		0			0
$41$	3.76393	−	3.76393i	0.587827	−	0.587827i	−0.349215	−	0.937043i	$-0.613552\pi$
$41$	3.76393	−	3.76393i	0.587827	−	0.587827i	0.937043	+	0.349215i	$0.113552\pi$
$42$		0			0
$43$	3.85410	−	3.85410i	0.587745	−	0.587745i	−0.349275	−	0.937020i	$-0.613572\pi$
$43$	3.85410	−	3.85410i	0.587745	−	0.587745i	0.937020	+	0.349275i	$0.113572\pi$
$44$		0			0
$45$			5.00000i			0.745356i
$46$		0			0
$47$	−8.94427			−1.30466			−0.652328	−	0.757937i	$-0.726208\pi$
$47$	−8.94427			−1.30466			−0.652328	+	0.757937i	$0.726208\pi$
$48$		0			0
$49$	−7.00000			−1.00000
$50$		0			0
$51$		−	2.76393i		−	0.387028i
$52$		0			0
$53$	1.47214	+	1.47214i	0.202213	+	0.202213i	0.800948	−	0.598734i	$-0.204329\pi$
$53$	1.47214	+	1.47214i	0.202213	+	0.202213i	−0.598734	+	0.800948i	$0.704329\pi$
$54$		0			0
$55$	5.85410	+	5.85410i	0.789367	+	0.789367i
$56$		0			0
$57$			7.23607i			0.958441i
$58$		0			0
$59$	3.38197	−	3.38197i	0.440294	−	0.440294i	−0.451816	−	0.892111i	$-0.649224\pi$
$59$	3.38197	−	3.38197i	0.440294	−	0.440294i	0.892111	+	0.451816i	$0.149224\pi$
$60$		0			0
$61$	5.70820			0.730861			0.365430	−	0.930839i	$-0.380922\pi$
$61$	5.70820			0.730861			0.365430	+	0.930839i	$0.380922\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	6.70820	+	4.47214i	0.832050	+	0.554700i
$66$		0			0
$67$			0.291796i			0.0356486i	0.999841	+	0.0178243i	$0.00567395\pi$
$67$			0.291796i			0.0356486i	−0.999841	+	0.0178243i	$0.994326\pi$
$68$		0			0
$69$	4.18034			0.503254
$70$		0			0
$71$	2.61803	−	2.61803i	0.310703	−	0.310703i	−0.534479	−	0.845182i	$-0.679492\pi$
$71$	2.61803	−	2.61803i	0.310703	−	0.310703i	0.845182	+	0.534479i	$0.179492\pi$
$72$		0			0
$73$			11.7082i			1.37034i	0.728382	+	0.685171i	$0.240272\pi$
$73$			11.7082i			1.37034i	−0.728382	+	0.685171i	$0.759728\pi$
$74$		0			0
$75$	−3.09017	−	3.09017i	−0.356822	−	0.356822i
$76$		0			0
$77$		0			0
$78$		0			0
$79$			3.70820i			0.417206i	0.978000	+	0.208603i	$0.0668916\pi$
$79$			3.70820i			0.417206i	−0.978000	+	0.208603i	$0.933108\pi$
$80$		0			0
$81$	−2.70820			−0.300912
$82$		0			0
$83$	−10.4721			−1.14947			−0.574733	−	0.818341i	$-0.694894\pi$
$83$	−10.4721			−1.14947			−0.574733	+	0.818341i	$0.694894\pi$
$84$		0			0
$85$	−5.00000	−	5.00000i	−0.542326	−	0.542326i
$86$		0			0
$87$	3.23607	−	3.23607i	0.346943	−	0.346943i
$88$		0			0
$89$	2.23607	−	2.23607i	0.237023	−	0.237023i	−0.578593	−	0.815616i	$-0.696398\pi$
$89$	2.23607	−	2.23607i	0.237023	−	0.237023i	0.815616	+	0.578593i	$0.196398\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−7.23607			−0.750345
$94$		0			0
$95$	13.0902	+	13.0902i	1.34302	+	1.34302i
$96$		0			0
$97$		−	15.4164i		−	1.56530i	−0.622463	−	0.782650i	$-0.713868\pi$
$97$		−	15.4164i		−	1.56530i	0.622463	−	0.782650i	$-0.286132\pi$
$98$		0			0
$99$	−5.85410	+	5.85410i	−0.588359	+	0.588359i
$100$		0			0
$101$		−	1.52786i		−	0.152028i	−0.997107	−	0.0760141i	$-0.975781\pi$
$101$		−	1.52786i		−	0.152028i	0.997107	−	0.0760141i	$-0.0242194\pi$
$102$		0			0
$103$	3.85410	−	3.85410i	0.379756	−	0.379756i	−0.491258	−	0.871014i	$-0.663463\pi$
$103$	3.85410	−	3.85410i	0.379756	−	0.379756i	0.871014	+	0.491258i	$0.163463\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.61803	+	2.61803i	−0.253095	+	0.253095i	−0.822238	−	0.569143i	$-0.807275\pi$
$107$	−2.61803	+	2.61803i	−0.253095	+	0.253095i	0.569143	+	0.822238i	$0.307275\pi$
$108$		0			0
$109$	−4.70820	−	4.70820i	−0.450964	−	0.450964i	0.444710	−	0.895674i	$-0.353307\pi$
$109$	−4.70820	−	4.70820i	−0.450964	−	0.450964i	−0.895674	+	0.444710i	$0.853307\pi$
$110$		0			0
$111$	−6.00000	−	6.00000i	−0.569495	−	0.569495i
$112$		0			0
$113$	−11.9443	−	11.9443i	−1.12362	−	1.12362i	−0.991192	−	0.132430i	$-0.957722\pi$
$113$	−11.9443	−	11.9443i	−1.12362	−	1.12362i	−0.132430	−	0.991192i	$-0.542278\pi$
$114$		0			0
$115$	7.56231	−	7.56231i	0.705189	−	0.705189i
$116$		0			0
$117$	−4.47214	+	6.70820i	−0.413449	+	0.620174i
$118$		0			0
$119$		0			0
$120$		0			0
$121$			2.70820i			0.246200i
$122$		0			0
$123$	−4.65248			−0.419500
$124$		0			0
$125$	−11.1803			−1.00000
$126$		0			0
$127$	0.145898	+	0.145898i	0.0129464	+	0.0129464i	0.713550	−	0.700604i	$-0.247086\pi$
$127$	0.145898	+	0.145898i	0.0129464	+	0.0129464i	−0.700604	+	0.713550i	$0.747086\pi$
$128$		0			0
$129$	−4.76393			−0.419441
$130$		0			0
$131$	−7.41641			−0.647975			−0.323987	−	0.946061i	$-0.605024\pi$
$131$	−7.41641			−0.647975			−0.323987	+	0.946061i	$0.605024\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	7.23607	−	7.23607i	0.622782	−	0.622782i
$136$		0			0
$137$	16.4721			1.40731			0.703655	−	0.710542i	$-0.251550\pi$
$137$	16.4721			1.40731			0.703655	+	0.710542i	$0.251550\pi$
$138$		0			0
$139$		−	23.1246i		−	1.96140i	−0.195509	−	0.980702i	$-0.562636\pi$
$139$		−	23.1246i		−	1.96140i	0.195509	−	0.980702i	$-0.437364\pi$
$140$		0			0
$141$	5.52786	+	5.52786i	0.465530	+	0.465530i
$142$		0			0
$143$	2.61803	+	13.0902i	0.218931	+	1.09466i
$144$		0			0
$145$		−	11.7082i		−	0.972313i
$146$		0			0
$147$	4.32624	+	4.32624i	0.356822	+	0.356822i
$148$		0			0
$149$	−5.94427	−	5.94427i	−0.486974	−	0.486974i	0.420376	−	0.907350i	$-0.361898\pi$
$149$	−5.94427	−	5.94427i	−0.486974	−	0.486974i	−0.907350	+	0.420376i	$0.861898\pi$
$150$		0			0
$151$	−0.145898	−	0.145898i	−0.0118730	−	0.0118730i	0.701145	−	0.713018i	$-0.252672\pi$
$151$	−0.145898	−	0.145898i	−0.0118730	−	0.0118730i	−0.713018	+	0.701145i	$0.752672\pi$
$152$		0			0
$153$	5.00000	−	5.00000i	0.404226	−	0.404226i
$154$		0			0
$155$	−13.0902	+	13.0902i	−1.05143	+	1.05143i
$156$		0			0
$157$	−5.00000	+	5.00000i	−0.399043	+	0.399043i	−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−5.00000	+	5.00000i	−0.399043	+	0.399043i	0.478852	+	0.877896i	$0.341053\pi$
$158$		0			0
$159$		−	1.81966i		−	0.144308i
$160$		0			0
$161$		0			0
$162$		0			0
$163$			4.29180i			0.336159i	0.985773	+	0.168080i	$0.0537566\pi$
$163$			4.29180i			0.336159i	−0.985773	+	0.168080i	$0.946243\pi$
$164$		0			0
$165$		−	7.23607i		−	0.563327i
$166$		0			0
$167$	−13.5279			−1.04682			−0.523409	−	0.852082i	$-0.675340\pi$
$167$	−13.5279			−1.04682			−0.523409	+	0.852082i	$0.675340\pi$
$168$		0			0
$169$	5.00000	+	12.0000i	0.384615	+	0.923077i
$170$		0			0
$171$	−13.0902	+	13.0902i	−1.00103	+	1.00103i
$172$		0			0
$173$	17.1803	−	17.1803i	1.30620	−	1.30620i	0.382059	−	0.924138i	$-0.375215\pi$
$173$	17.1803	−	17.1803i	1.30620	−	1.30620i	0.924138	−	0.382059i	$-0.124785\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−4.18034			−0.314214
$178$		0			0
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$			8.29180i			0.616324i	0.951334	+	0.308162i	$0.0997139\pi$
$181$			8.29180i			0.616324i	−0.951334	+	0.308162i	$0.900286\pi$
$182$		0			0
$183$	−3.52786	−	3.52786i	−0.260787	−	0.260787i
$184$		0			0
$185$	−21.7082			−1.59602
$186$		0			0
$187$		−	11.7082i		−	0.856189i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	7.41641			0.536632			0.268316	−	0.963331i	$-0.413533\pi$
$191$	7.41641			0.536632			0.268316	+	0.963331i	$0.413533\pi$
$192$		0			0
$193$			3.41641i			0.245918i	0.992412	+	0.122959i	$0.0392384\pi$
$193$			3.41641i			0.245918i	−0.992412	+	0.122959i	$0.960762\pi$
$194$		0			0
$195$	−1.38197	−	6.90983i	−0.0989646	−	0.494823i
$196$		0			0
$197$		−	12.0000i		−	0.854965i	−0.904024	−	0.427482i	$-0.859401\pi$
$197$		−	12.0000i		−	0.854965i	0.904024	−	0.427482i	$-0.140599\pi$
$198$		0			0
$199$	11.4164			0.809288			0.404644	−	0.914474i	$-0.367395\pi$
$199$	11.4164			0.809288			0.404644	+	0.914474i	$0.367395\pi$
$200$		0			0
$201$	0.180340	−	0.180340i	0.0127202	−	0.0127202i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−8.41641	+	8.41641i	−0.587827	+	0.587827i
$206$		0			0
$207$	7.56231	+	7.56231i	0.525617	+	0.525617i
$208$		0			0
$209$			30.6525i			2.12028i
$210$		0			0
$211$	3.41641			0.235195			0.117598	−	0.993061i	$-0.462481\pi$
$211$	3.41641			0.235195			0.117598	+	0.993061i	$0.462481\pi$
$212$		0			0
$213$	−3.23607			−0.221732
$214$		0			0
$215$	−8.61803	+	8.61803i	−0.587745	+	0.587745i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	7.23607	−	7.23607i	0.488968	−	0.488968i
$220$		0			0
$221$	−2.23607	−	11.1803i	−0.150414	−	0.752071i
$222$		0			0
$223$	7.41641			0.496639			0.248320	−	0.968678i	$-0.420122\pi$
$223$	7.41641			0.496639			0.248320	+	0.968678i	$0.420122\pi$
$224$		0			0
$225$		−	11.1803i		−	0.745356i
$226$		0			0
$227$		−	8.29180i		−	0.550346i	−0.961395	−	0.275173i	$-0.911265\pi$
$227$		−	8.29180i		−	0.550346i	0.961395	−	0.275173i	$-0.0887351\pi$
$228$		0			0
$229$	−8.41641	+	8.41641i	−0.556172	+	0.556172i	−0.928215	−	0.372043i	$-0.878657\pi$
$229$	−8.41641	+	8.41641i	−0.556172	+	0.556172i	0.372043	+	0.928215i	$0.378657\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	7.47214	−	7.47214i	0.489516	−	0.489516i	−0.418638	−	0.908153i	$-0.637492\pi$
$233$	7.47214	−	7.47214i	0.489516	−	0.489516i	0.908153	+	0.418638i	$0.137492\pi$
$234$		0			0
$235$	20.0000			1.30466
$236$		0			0
$237$	2.29180	−	2.29180i	0.148868	−	0.148868i
$238$		0			0
$239$	8.61803	+	8.61803i	0.557454	+	0.557454i	0.928582	−	0.371128i	$-0.121029\pi$
$239$	8.61803	+	8.61803i	0.557454	+	0.557454i	−0.371128	+	0.928582i	$0.621029\pi$
$240$		0			0
$241$	−2.70820	−	2.70820i	−0.174451	−	0.174451i	0.614481	−	0.788932i	$-0.289365\pi$
$241$	−2.70820	−	2.70820i	−0.174451	−	0.174451i	−0.788932	+	0.614481i	$0.789365\pi$
$242$		0			0
$243$	11.3820	+	11.3820i	0.730153	+	0.730153i
$244$		0			0
$245$	15.6525			1.00000
$246$		0			0
$247$	5.85410	+	29.2705i	0.372488	+	1.86244i
$248$		0			0
$249$	6.47214	+	6.47214i	0.410155	+	0.410155i
$250$		0			0
$251$			26.1803i			1.65249i	0.563312	+	0.826244i	$0.309527\pi$
$251$			26.1803i			1.65249i	−0.563312	+	0.826244i	$0.690473\pi$
$252$		0			0
$253$	17.7082			1.11331
$254$		0			0
$255$			6.18034i			0.387028i
$256$		0			0
$257$	−17.1803	−	17.1803i	−1.07168	−	1.07168i	−0.997224	−	0.0744558i	$-0.976278\pi$
$257$	−17.1803	−	17.1803i	−1.07168	−	1.07168i	−0.0744558	−	0.997224i	$-0.523722\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	11.7082			0.724720
$262$		0			0
$263$	22.0344	+	22.0344i	1.35870	+	1.35870i	0.875520	+	0.483182i	$0.160519\pi$
$263$	22.0344	+	22.0344i	1.35870	+	1.35870i	0.483182	+	0.875520i	$0.339481\pi$
$264$		0			0
$265$	−3.29180	−	3.29180i	−0.202213	−	0.202213i
$266$		0			0
$267$	−2.76393			−0.169150
$268$		0			0
$269$			13.5279i			0.824808i	0.911001	+	0.412404i	$0.135311\pi$
$269$			13.5279i			0.824808i	−0.911001	+	0.412404i	$0.864689\pi$
$270$		0			0
$271$	−7.56231	−	7.56231i	−0.459377	−	0.459377i	0.439074	−	0.898451i	$-0.355307\pi$
$271$	−7.56231	−	7.56231i	−0.459377	−	0.459377i	−0.898451	+	0.439074i	$0.855307\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−13.0902	−	13.0902i	−0.789367	−	0.789367i
$276$		0			0
$277$	2.70820	+	2.70820i	0.162720	+	0.162720i	0.783771	−	0.621050i	$-0.213294\pi$
$277$	2.70820	+	2.70820i	0.162720	+	0.162720i	−0.621050	+	0.783771i	$0.713294\pi$
$278$		0			0
$279$	−13.0902	−	13.0902i	−0.783688	−	0.783688i
$280$		0			0
$281$	2.23607	+	2.23607i	0.133393	+	0.133393i	0.770651	−	0.637258i	$-0.219931\pi$
$281$	2.23607	+	2.23607i	0.133393	+	0.133393i	−0.637258	+	0.770651i	$0.719931\pi$
$282$		0			0
$283$	15.8541	−	15.8541i	0.942429	−	0.942429i	−0.0560021	−	0.998431i	$-0.517835\pi$
$283$	15.8541	−	15.8541i	0.942429	−	0.942429i	0.998431	+	0.0560021i	$0.0178354\pi$
$284$		0			0
$285$		−	16.1803i		−	0.958441i
$286$		0			0
$287$		0			0
$288$		0			0
$289$		−	7.00000i		−	0.411765i
$290$		0			0
$291$	−9.52786	+	9.52786i	−0.558533	+	0.558533i
$292$		0			0
$293$			27.7082i			1.61873i	0.587306	+	0.809365i	$0.300189\pi$
$293$			27.7082i			1.61873i	−0.587306	+	0.809365i	$0.699811\pi$
$294$		0			0
$295$	−7.56231	+	7.56231i	−0.440294	+	0.440294i
$296$		0			0
$297$	16.9443			0.983206
$298$		0			0
$299$	16.9098	−	3.38197i	0.977921	−	0.195584i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−0.944272	+	0.944272i	−0.0542470	+	0.0542470i
$304$		0			0
$305$	−12.7639			−0.730861
$306$		0			0
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$		0			0
$309$	−4.76393			−0.271011
$310$		0			0
$311$			2.18034i			0.123636i	0.998087	+	0.0618179i	$0.0196898\pi$
$311$			2.18034i			0.123636i	−0.998087	+	0.0618179i	$0.980310\pi$
$312$		0			0
$313$	−14.7082	−	14.7082i	−0.831357	−	0.831357i	0.156346	−	0.987702i	$-0.450029\pi$
$313$	−14.7082	−	14.7082i	−0.831357	−	0.831357i	−0.987702	+	0.156346i	$0.950029\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			3.70820i			0.208273i	0.994563	+	0.104137i	$0.0332080\pi$
$317$			3.70820i			0.208273i	−0.994563	+	0.104137i	$0.966792\pi$
$318$		0			0
$319$	13.7082	−	13.7082i	0.767512	−	0.767512i
$320$		0			0
$321$	3.23607			0.180620
$322$		0			0
$323$		−	26.1803i		−	1.45671i
$324$		0			0
$325$	−15.0000	−	10.0000i	−0.832050	−	0.554700i
$326$		0			0
$327$			5.81966i			0.321828i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−15.8541	+	15.8541i	−0.871420	+	0.871420i	−0.992627	−	0.121207i	$-0.961324\pi$
$331$	−15.8541	+	15.8541i	−0.871420	+	0.871420i	0.121207	+	0.992627i	$0.461324\pi$
$332$		0			0
$333$		−	21.7082i		−	1.18960i
$334$		0			0
$335$		−	0.652476i		−	0.0356486i
$336$		0			0
$337$	−14.4164	−	14.4164i	−0.785312	−	0.785312i	0.195410	−	0.980722i	$-0.437396\pi$
$337$	−14.4164	−	14.4164i	−0.785312	−	0.785312i	−0.980722	+	0.195410i	$0.937396\pi$
$338$		0			0
$339$			14.7639i			0.801867i
$340$		0			0
$341$	−30.6525			−1.65992
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−9.34752			−0.503254
$346$		0			0
$347$	7.09017	−	7.09017i	0.380620	−	0.380620i	−0.490705	−	0.871326i	$-0.663261\pi$
$347$	7.09017	−	7.09017i	0.380620	−	0.380620i	0.871326	+	0.490705i	$0.163261\pi$
$348$		0			0
$349$	−16.7082	+	16.7082i	−0.894370	+	0.894370i	−0.994931	−	0.100561i	$-0.967936\pi$
$349$	−16.7082	+	16.7082i	−0.894370	+	0.894370i	0.100561	+	0.994931i	$0.467936\pi$
$350$		0			0
$351$	16.1803	−	3.23607i	0.863643	−	0.172729i
$352$		0			0
$353$	−12.7639			−0.679356			−0.339678	−	0.940542i	$-0.610318\pi$
$353$	−12.7639			−0.679356			−0.339678	+	0.940542i	$0.610318\pi$
$354$		0			0
$355$	−5.85410	+	5.85410i	−0.310703	+	0.310703i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	13.0902	−	13.0902i	0.690873	−	0.690873i	−0.271551	−	0.962424i	$-0.587537\pi$
$359$	13.0902	−	13.0902i	0.690873	−	0.690873i	0.962424	+	0.271551i	$0.0875366\pi$
$360$		0			0
$361$			49.5410i			2.60742i
$362$		0			0
$363$	1.67376	−	1.67376i	0.0878497	−	0.0878497i
$364$		0			0
$365$		−	26.1803i		−	1.37034i
$366$		0			0
$367$	11.8541	−	11.8541i	0.618779	−	0.618779i	−0.326439	−	0.945218i	$-0.605849\pi$
$367$	11.8541	−	11.8541i	0.618779	−	0.618779i	0.945218	+	0.326439i	$0.105849\pi$
$368$		0			0
$369$	−8.41641	−	8.41641i	−0.438141	−	0.438141i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−0.416408	−	0.416408i	−0.0215608	−	0.0215608i	0.696244	−	0.717805i	$-0.254853\pi$
$373$	−0.416408	−	0.416408i	−0.0215608	−	0.0215608i	−0.717805	+	0.696244i	$0.754853\pi$
$374$		0			0
$375$	6.90983	+	6.90983i	0.356822	+	0.356822i
$376$		0			0
$377$	10.4721	−	15.7082i	0.539342	−	0.809014i
$378$		0			0
$379$	3.85410	+	3.85410i	0.197972	+	0.197972i	0.799130	−	0.601158i	$-0.205294\pi$
$379$	3.85410	+	3.85410i	0.197972	+	0.197972i	−0.601158	+	0.799130i	$0.705294\pi$
$380$		0			0
$381$		−	0.180340i		−	0.00923909i
$382$		0			0
$383$	−17.8885			−0.914062			−0.457031	−	0.889451i	$-0.651087\pi$
$383$	−17.8885			−0.914062			−0.457031	+	0.889451i	$0.651087\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−8.61803	−	8.61803i	−0.438079	−	0.438079i
$388$		0			0
$389$	25.4164			1.28866			0.644332	−	0.764746i	$-0.277136\pi$
$389$	25.4164			1.28866			0.644332	+	0.764746i	$0.277136\pi$
$390$		0			0
$391$	−15.1246			−0.764884
$392$		0			0
$393$	4.58359	+	4.58359i	0.231212	+	0.231212i
$394$		0			0
$395$		−	8.29180i		−	0.417206i
$396$		0			0
$397$	−5.12461			−0.257197			−0.128598	−	0.991697i	$-0.541048\pi$
$397$	−5.12461			−0.257197			−0.128598	+	0.991697i	$0.541048\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	2.23607	+	2.23607i	0.111664	+	0.111664i	0.760731	−	0.649067i	$-0.224841\pi$
$401$	2.23607	+	2.23607i	0.111664	+	0.111664i	−0.649067	+	0.760731i	$0.724841\pi$
$402$		0			0
$403$	−29.2705	+	5.85410i	−1.45807	+	0.291614i
$404$		0			0
$405$	6.05573			0.300912
$406$		0			0
$407$	−25.4164	−	25.4164i	−1.25984	−	1.25984i
$408$		0			0
$409$	−3.29180	−	3.29180i	−0.162769	−	0.162769i	0.621023	−	0.783792i	$-0.286717\pi$
$409$	−3.29180	−	3.29180i	−0.162769	−	0.162769i	−0.783792	+	0.621023i	$0.786717\pi$
$410$		0			0
$411$	−10.1803	−	10.1803i	−0.502159	−	0.502159i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	23.4164			1.14947
$416$		0			0
$417$	−14.2918	+	14.2918i	−0.699872	+	0.699872i
$418$		0			0
$419$		−	21.5967i		−	1.05507i	−0.849533	−	0.527535i	$-0.823116\pi$
$419$		−	21.5967i		−	1.05507i	0.849533	−	0.527535i	$-0.176884\pi$
$420$		0			0
$421$	3.29180	−	3.29180i	0.160432	−	0.160432i	−0.622326	−	0.782758i	$-0.713812\pi$
$421$	3.29180	−	3.29180i	0.160432	−	0.160432i	0.782758	+	0.622326i	$0.213812\pi$
$422$		0			0
$423$			20.0000i			0.972433i
$424$		0			0
$425$	11.1803	+	11.1803i	0.542326	+	0.542326i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	6.47214	−	9.70820i	0.312478	−	0.468717i
$430$		0			0
$431$	16.9098	−	16.9098i	0.814518	−	0.814518i	−0.170790	−	0.985308i	$-0.554632\pi$
$431$	16.9098	−	16.9098i	0.814518	−	0.814518i	0.985308	+	0.170790i	$0.0546319\pi$
$432$		0			0
$433$	17.0000	−	17.0000i	0.816968	−	0.816968i	−0.168700	−	0.985668i	$-0.553957\pi$
$433$	17.0000	−	17.0000i	0.816968	−	0.816968i	0.985668	+	0.168700i	$0.0539568\pi$
$434$		0			0
$435$	−7.23607	+	7.23607i	−0.346943	+	0.346943i
$436$		0			0
$437$	39.5967			1.89417
$438$		0			0
$439$	−20.0000			−0.954548			−0.477274	−	0.878755i	$-0.658375\pi$
$439$	−20.0000			−0.954548			−0.477274	+	0.878755i	$0.658375\pi$
$440$		0			0
$441$			15.6525i			0.745356i
$442$		0			0
$443$	0.326238	+	0.326238i	0.0155000	+	0.0155000i	0.714814	−	0.699314i	$-0.246511\pi$
$443$	0.326238	+	0.326238i	0.0155000	+	0.0155000i	−0.699314	+	0.714814i	$0.746511\pi$
$444$		0			0
$445$	−5.00000	+	5.00000i	−0.237023	+	0.237023i
$446$		0			0
$447$			7.34752i			0.347526i
$448$		0			0
$449$	10.5279	−	10.5279i	0.496841	−	0.496841i	−0.413612	−	0.910453i	$-0.635733\pi$
$449$	10.5279	−	10.5279i	0.496841	−	0.496841i	0.910453	+	0.413612i	$0.135733\pi$
$450$		0			0
$451$	−19.7082			−0.928023
$452$		0			0
$453$			0.180340i			0.00847311i
$454$		0			0
$455$		0			0
$456$		0			0
$457$			23.4164i			1.09537i	0.836684	+	0.547687i	$0.184491\pi$
$457$			23.4164i			1.09537i	−0.836684	+	0.547687i	$0.815509\pi$
$458$		0			0
$459$	−14.4721			−0.675501
$460$		0			0
$461$	17.1803	−	17.1803i	0.800168	−	0.800168i	−0.182953	−	0.983122i	$-0.558566\pi$
$461$	17.1803	−	17.1803i	0.800168	−	0.800168i	0.983122	+	0.182953i	$0.0585657\pi$
$462$		0			0
$463$			4.29180i			0.199457i	0.995015	+	0.0997283i	$0.0317974\pi$
$463$			4.29180i			0.199457i	−0.995015	+	0.0997283i	$0.968203\pi$
$464$		0			0
$465$	16.1803			0.750345
$466$		0			0
$467$	−16.0344	−	16.0344i	−0.741985	−	0.741985i	0.230974	−	0.972960i	$-0.425809\pi$
$467$	−16.0344	−	16.0344i	−0.741985	−	0.741985i	−0.972960	+	0.230974i	$0.925809\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	6.18034			0.284775
$472$		0			0
$473$	−20.1803			−0.927893
$474$		0			0
$475$	−29.2705	−	29.2705i	−1.34302	−	1.34302i
$476$		0			0
$477$	3.29180	−	3.29180i	0.150721	−	0.150721i
$478$		0			0
$479$	−25.7426	+	25.7426i	−1.17621	+	1.17621i	−0.195510	+	0.980702i	$0.562636\pi$
$479$	−25.7426	+	25.7426i	−1.17621	+	1.17621i	−0.980702	+	0.195510i	$0.937364\pi$
$480$		0			0
$481$	−29.1246	−	19.4164i	−1.32797	−	0.885312i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			34.4721i			1.56530i
$486$		0			0
$487$			15.1246i			0.685362i	0.939452	+	0.342681i	$0.111335\pi$
$487$			15.1246i			0.685362i	−0.939452	+	0.342681i	$0.888665\pi$
$488$		0			0
$489$	2.65248	−	2.65248i	0.119949	−	0.119949i
$490$		0			0
$491$		−	24.6525i		−	1.11255i	−0.830998	−	0.556275i	$-0.812230\pi$
$491$		−	24.6525i		−	1.11255i	0.830998	−	0.556275i	$-0.187770\pi$
$492$		0			0
$493$	−11.7082	+	11.7082i	−0.527311	+	0.527311i
$494$		0			0
$495$	13.0902	−	13.0902i	0.588359	−	0.588359i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	20.9787	+	20.9787i	0.939136	+	0.939136i	0.998251	−	0.0591150i	$-0.0188279\pi$
$499$	20.9787	+	20.9787i	0.939136	+	0.939136i	−0.0591150	+	0.998251i	$0.518828\pi$
$500$		0			0
$501$	8.36068	+	8.36068i	0.373528	+	0.373528i
$502$		0			0
$503$	−11.6738	−	11.6738i	−0.520507	−	0.520507i	0.397217	−	0.917725i	$-0.369976\pi$
$503$	−11.6738	−	11.6738i	−0.520507	−	0.520507i	−0.917725	+	0.397217i	$0.869976\pi$
$504$		0			0
$505$			3.41641i			0.152028i
$506$		0			0
$507$	4.32624	−	10.5066i	0.192135	−	0.466614i
$508$		0			0
$509$	9.76393	+	9.76393i	0.432779	+	0.432779i	0.889573	−	0.456794i	$-0.151002\pi$
$509$	9.76393	+	9.76393i	0.432779	+	0.432779i	−0.456794	+	0.889573i	$0.651002\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	37.8885			1.67282
$514$		0			0
$515$	−8.61803	+	8.61803i	−0.379756	+	0.379756i
$516$		0			0
$517$	23.4164	+	23.4164i	1.02985	+	1.02985i
$518$		0			0
$519$	−21.2361			−0.932160
$520$		0			0
$521$	41.1246			1.80170			0.900851	−	0.434128i	$-0.142944\pi$
$521$	41.1246			1.80170			0.900851	+	0.434128i	$0.142944\pi$
$522$		0			0
$523$	25.2705	+	25.2705i	1.10500	+	1.10500i	0.993798	+	0.111205i	$0.0354709\pi$
$523$	25.2705	+	25.2705i	1.10500	+	1.10500i	0.111205	+	0.993798i	$0.464529\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	26.1803			1.14043
$528$		0			0
$529$			0.124612i			0.00541790i
$530$		0			0
$531$	−7.56231	−	7.56231i	−0.328176	−	0.328176i
$532$		0			0
$533$	−18.8197	+	3.76393i	−0.815170	+	0.163034i
$534$		0			0
$535$	5.85410	−	5.85410i	0.253095	−	0.253095i
$536$		0			0
$537$	−7.41641	−	7.41641i	−0.320042	−	0.320042i
$538$		0			0
$539$	18.3262	+	18.3262i	0.789367	+	0.789367i
$540$		0			0
$541$	14.4164	+	14.4164i	0.619810	+	0.619810i	0.945483	−	0.325673i	$-0.105591\pi$
$541$	14.4164	+	14.4164i	0.619810	+	0.619810i	−0.325673	+	0.945483i	$0.605591\pi$
$542$		0			0
$543$	5.12461	−	5.12461i	0.219918	−	0.219918i
$544$		0			0
$545$	10.5279	+	10.5279i	0.450964	+	0.450964i
$546$		0			0
$547$	−7.56231	+	7.56231i	−0.323341	+	0.323341i	−0.850047	−	0.526706i	$-0.823427\pi$
$547$	−7.56231	+	7.56231i	−0.323341	+	0.323341i	0.526706	+	0.850047i	$0.323427\pi$
$548$		0			0
$549$		−	12.7639i		−	0.544751i
$550$		0			0
$551$	30.6525	−	30.6525i	1.30584	−	1.30584i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	13.4164	+	13.4164i	0.569495	+	0.569495i
$556$		0			0
$557$	−35.2361			−1.49300			−0.746500	−	0.665385i	$-0.768267\pi$
$557$	−35.2361			−1.49300			−0.746500	+	0.665385i	$0.768267\pi$
$558$		0			0
$559$	−19.2705	+	3.85410i	−0.815056	+	0.163011i
$560$		0			0
$561$	−7.23607	+	7.23607i	−0.305507	+	0.305507i
$562$		0			0
$563$	−1.09017	+	1.09017i	−0.0459452	+	0.0459452i	−0.729706	−	0.683761i	$-0.760343\pi$
$563$	−1.09017	+	1.09017i	−0.0459452	+	0.0459452i	0.683761	+	0.729706i	$0.260343\pi$
$564$		0			0
$565$	26.7082	+	26.7082i	1.12362	+	1.12362i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	17.1246			0.717901			0.358951	−	0.933357i	$-0.383135\pi$
$569$	17.1246			0.717901			0.358951	+	0.933357i	$0.383135\pi$
$570$		0			0
$571$			8.29180i			0.347001i	0.984834	+	0.173500i	$0.0555078\pi$
$571$			8.29180i			0.347001i	−0.984834	+	0.173500i	$0.944492\pi$
$572$		0			0
$573$	−4.58359	−	4.58359i	−0.191482	−	0.191482i
$574$		0			0
$575$	−16.9098	+	16.9098i	−0.705189	+	0.705189i
$576$		0			0
$577$			27.1246i			1.12921i	0.825360	+	0.564606i	$0.190972\pi$
$577$			27.1246i			1.12921i	−0.825360	+	0.564606i	$0.809028\pi$
$578$		0			0
$579$	2.11146	−	2.11146i	0.0877491	−	0.0877491i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		−	7.70820i		−	0.319241i
$584$		0			0
$585$	10.0000	−	15.0000i	0.413449	−	0.620174i
$586$		0			0
$587$			23.1246i			0.954455i	0.878780	+	0.477227i	$0.158358\pi$
$587$			23.1246i			0.954455i	−0.878780	+	0.477227i	$0.841642\pi$
$588$		0			0
$589$	−68.5410			−2.82418
$590$		0			0
$591$	−7.41641	+	7.41641i	−0.305070	+	0.305070i
$592$		0			0
$593$			16.5836i			0.681007i	0.940243	+	0.340503i	$0.110597\pi$
$593$			16.5836i			0.681007i	−0.940243	+	0.340503i	$0.889403\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−7.05573	−	7.05573i	−0.288772	−	0.288772i
$598$		0			0
$599$		−	41.0132i		−	1.67575i	−0.545861	−	0.837876i	$-0.683797\pi$
$599$		−	41.0132i		−	1.67575i	0.545861	−	0.837876i	$-0.316203\pi$
$600$		0			0
$601$	14.0000			0.571072			0.285536	−	0.958368i	$-0.407828\pi$
$601$	14.0000			0.571072			0.285536	+	0.958368i	$0.407828\pi$
$602$		0			0
$603$	0.652476			0.0265709
$604$		0			0
$605$		−	6.05573i		−	0.246200i
$606$		0			0
$607$	−29.2705	+	29.2705i	−1.18805	+	1.18805i	−0.210448	+	0.977605i	$0.567492\pi$
$607$	−29.2705	+	29.2705i	−1.18805	+	1.18805i	−0.977605	+	0.210448i	$0.932508\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	26.8328	+	17.8885i	1.08554	+	0.723693i
$612$		0			0
$613$	13.4164			0.541884			0.270942	−	0.962596i	$-0.412665\pi$
$613$	13.4164			0.541884			0.270942	+	0.962596i	$0.412665\pi$
$614$		0			0
$615$	10.4033			0.419500
$616$		0			0
$617$		−	4.58359i		−	0.184528i	−0.995735	−	0.0922642i	$-0.970590\pi$
$617$		−	4.58359i		−	0.184528i	0.995735	−	0.0922642i	$-0.0294104\pi$
$618$		0			0
$619$	17.2705	−	17.2705i	0.694160	−	0.694160i	−0.268984	−	0.963145i	$-0.586688\pi$
$619$	17.2705	−	17.2705i	0.694160	−	0.694160i	0.963145	+	0.268984i	$0.0866879\pi$
$620$		0			0
$621$		−	21.8885i		−	0.878357i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	25.0000			1.00000
$626$		0			0
$627$	18.9443	−	18.9443i	0.756561	−	0.756561i
$628$		0			0
$629$	21.7082	+	21.7082i	0.865563	+	0.865563i
$630$		0			0
$631$	−29.2705	−	29.2705i	−1.16524	−	1.16524i	−0.983312	−	0.181929i	$-0.941766\pi$
$631$	−29.2705	−	29.2705i	−1.16524	−	1.16524i	−0.181929	−	0.983312i	$-0.558234\pi$
$632$		0			0
$633$	−2.11146	−	2.11146i	−0.0839228	−	0.0839228i
$634$		0			0
$635$	−0.326238	−	0.326238i	−0.0129464	−	0.0129464i
$636$		0			0
$637$	21.0000	+	14.0000i	0.832050	+	0.554700i
$638$		0			0
$639$	−5.85410	−	5.85410i	−0.231585	−	0.231585i
$640$		0			0
$641$		−	32.9443i		−	1.30122i	−0.759412	−	0.650610i	$-0.774513\pi$
$641$		−	32.9443i		−	1.30122i	0.759412	−	0.650610i	$-0.225487\pi$
$642$		0			0
$643$	43.4164			1.71218			0.856088	−	0.516830i	$-0.172888\pi$
$643$	43.4164			1.71218			0.856088	+	0.516830i	$0.172888\pi$
$644$		0			0
$645$	10.6525			0.419441
$646$		0			0
$647$	1.09017	+	1.09017i	0.0428590	+	0.0428590i	0.728211	−	0.685352i	$-0.240352\pi$
$647$	1.09017	+	1.09017i	0.0428590	+	0.0428590i	−0.685352	+	0.728211i	$0.740352\pi$
$648$		0			0
$649$	−17.7082			−0.695108
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−29.0689	−	29.0689i	−1.13755	−	1.13755i	−0.988887	−	0.148666i	$-0.952502\pi$
$653$	−29.0689	−	29.0689i	−1.13755	−	1.13755i	−0.148666	−	0.988887i	$-0.547498\pi$
$654$		0			0
$655$	16.5836			0.647975
$656$		0			0
$657$	26.1803			1.02139
$658$		0			0
$659$			32.0689i			1.24923i	0.780934	+	0.624613i	$0.214743\pi$
$659$			32.0689i			1.24923i	−0.780934	+	0.624613i	$0.785257\pi$
$660$		0			0
$661$	10.7082	+	10.7082i	0.416501	+	0.416501i	0.883996	−	0.467495i	$-0.154843\pi$
$661$	10.7082	+	10.7082i	0.416501	+	0.416501i	−0.467495	+	0.883996i	$0.654843\pi$
$662$		0			0
$663$	−5.52786	+	8.29180i	−0.214684	+	0.322027i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−17.7082	−	17.7082i	−0.685664	−	0.685664i
$668$		0			0
$669$	−4.58359	−	4.58359i	−0.177212	−	0.177212i
$670$		0			0
$671$	−14.9443	−	14.9443i	−0.576917	−	0.576917i
$672$		0			0
$673$	−30.1246	+	30.1246i	−1.16122	+	1.16122i	−0.177009	+	0.984209i	$0.556642\pi$
$673$	−30.1246	+	30.1246i	−1.16122	+	1.16122i	−0.984209	+	0.177009i	$0.943358\pi$
$674$		0			0
$675$	−16.1803	+	16.1803i	−0.622782	+	0.622782i
$676$		0			0
$677$	−0.0557281	+	0.0557281i	−0.00214180	+	0.00214180i	−0.708177	−	0.706035i	$-0.750482\pi$
$677$	−0.0557281	+	0.0557281i	−0.00214180	+	0.00214180i	0.706035	+	0.708177i	$0.250482\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−5.12461	+	5.12461i	−0.196376	+	0.196376i
$682$		0			0
$683$			35.1246i			1.34401i	0.740548	+	0.672003i	$0.234566\pi$
$683$			35.1246i			1.34401i	−0.740548	+	0.672003i	$0.765434\pi$
$684$		0			0
$685$	−36.8328			−1.40731
$686$		0			0
$687$	10.4033			0.396909
$688$		0			0
$689$	−1.47214	−	7.36068i	−0.0560839	−	0.280420i
$690$		0			0
$691$	34.9787	−	34.9787i	1.33065	−	1.33065i	0.425867	−	0.904786i	$-0.359969\pi$
$691$	34.9787	−	34.9787i	1.33065	−	1.33065i	0.904786	−	0.425867i	$-0.140031\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			51.7082i			1.96140i
$696$		0			0
$697$	16.8328			0.637588
$698$		0			0
$699$	−9.23607			−0.349340
$700$		0			0
$701$		−	28.3607i		−	1.07117i	−0.844482	−	0.535584i	$-0.820092\pi$
$701$		−	28.3607i		−	1.07117i	0.844482	−	0.535584i	$-0.179908\pi$
$702$		0			0
$703$	−56.8328	−	56.8328i	−2.14349	−	2.14349i
$704$		0			0
$705$	−12.3607	−	12.3607i	−0.465530	−	0.465530i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	18.4164	−	18.4164i	0.691643	−	0.691643i	−0.270951	−	0.962593i	$-0.587338\pi$
$709$	18.4164	−	18.4164i	0.691643	−	0.691643i	0.962593	+	0.270951i	$0.0873380\pi$
$710$		0			0
$711$	8.29180			0.310967
$712$		0			0
$713$			39.5967i			1.48291i
$714$		0			0
$715$	−5.85410	−	29.2705i	−0.218931	−	1.09466i
$716$		0			0
$717$		−	10.6525i		−	0.397824i
$718$		0			0
$719$	−31.4164			−1.17163			−0.585817	−	0.810443i	$-0.699226\pi$
$719$	−31.4164			−1.17163			−0.585817	+	0.810443i	$0.699226\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$			3.34752i			0.124496i
$724$		0			0
$725$			26.1803i			0.972313i
$726$		0			0
$727$	21.8541	+	21.8541i	0.810524	+	0.810524i	0.984712	−	0.174189i	$-0.0557302\pi$
$727$	21.8541	+	21.8541i	0.810524	+	0.810524i	−0.174189	+	0.984712i	$0.555730\pi$
$728$		0			0
$729$		−	5.94427i		−	0.220158i
$730$		0			0
$731$	17.2361			0.637499
$732$		0			0
$733$	−30.0000			−1.10808			−0.554038	−	0.832492i	$-0.686914\pi$
$733$	−30.0000			−1.10808			−0.554038	+	0.832492i	$0.686914\pi$
$734$		0			0
$735$	−9.67376	−	9.67376i	−0.356822	−	0.356822i
$736$		0			0
$737$	0.763932	−	0.763932i	0.0281398	−	0.0281398i
$738$		0			0
$739$	7.56231	−	7.56231i	0.278184	−	0.278184i	−0.554200	−	0.832384i	$-0.686976\pi$
$739$	7.56231	−	7.56231i	0.278184	−	0.278184i	0.832384	+	0.554200i	$0.186976\pi$
$740$		0			0
$741$	14.4721	−	21.7082i	0.531647	−	0.797471i
$742$		0			0
$743$	−37.3050			−1.36859			−0.684293	−	0.729207i	$-0.739889\pi$
$743$	−37.3050			−1.36859			−0.684293	+	0.729207i	$0.739889\pi$
$744$		0			0
$745$	13.2918	+	13.2918i	0.486974	+	0.486974i
$746$		0			0
$747$			23.4164i			0.856762i
$748$		0			0
$749$		0			0
$750$		0			0
$751$			11.1246i			0.405943i	0.979185	+	0.202971i	$0.0650599\pi$
$751$			11.1246i			0.405943i	−0.979185	+	0.202971i	$0.934940\pi$
$752$		0			0
$753$	16.1803	−	16.1803i	0.589644	−	0.589644i
$754$		0			0
$755$	0.326238	+	0.326238i	0.0118730	+	0.0118730i
$756$		0			0
$757$	−13.2918	+	13.2918i	−0.483099	+	0.483099i	−0.906120	−	0.423021i	$-0.860970\pi$
$757$	−13.2918	+	13.2918i	−0.483099	+	0.483099i	0.423021	+	0.906120i	$0.360970\pi$
$758$		0			0
$759$	−10.9443	−	10.9443i	−0.397252	−	0.397252i
$760$		0			0
$761$	−25.4721	−	25.4721i	−0.923364	−	0.923364i	0.0739013	−	0.997266i	$-0.476455\pi$
$761$	−25.4721	−	25.4721i	−0.923364	−	0.923364i	−0.997266	+	0.0739013i	$0.976455\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−11.1803	+	11.1803i	−0.404226	+	0.404226i
$766$		0			0
$767$	−16.9098	+	3.38197i	−0.610579	+	0.122116i
$768$		0			0
$769$	5.00000	+	5.00000i	0.180305	+	0.180305i	0.791489	−	0.611184i	$-0.209306\pi$
$769$	5.00000	+	5.00000i	0.180305	+	0.180305i	−0.611184	+	0.791489i	$0.709306\pi$
$770$		0			0
$771$			21.2361i			0.764798i
$772$		0			0
$773$	30.6525			1.10249			0.551246	−	0.834342i	$-0.314152\pi$
$773$	30.6525			1.10249			0.551246	+	0.834342i	$0.314152\pi$
$774$		0			0
$775$	29.2705	−	29.2705i	1.05143	−	1.05143i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−44.0689			−1.57893
$780$		0			0
$781$	−13.7082			−0.490518
$782$		0			0
$783$	−16.9443	−	16.9443i	−0.605539	−	0.605539i
$784$		0			0
$785$	11.1803	−	11.1803i	0.399043	−	0.399043i
$786$		0			0
$787$	16.5836			0.591141			0.295571	−	0.955321i	$-0.404490\pi$
$787$	16.5836			0.591141			0.295571	+	0.955321i	$0.404490\pi$
$788$		0			0
$789$		−	27.2361i		−	0.969630i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−17.1246	−	11.4164i	−0.608113	−	0.405409i
$794$		0			0
$795$			4.06888i			0.144308i
$796$		0			0
$797$	−26.8885	−	26.8885i	−0.952441	−	0.952441i	0.0464782	−	0.998919i	$-0.485200\pi$
$797$	−26.8885	−	26.8885i	−0.952441	−	0.952441i	−0.998919	+	0.0464782i	$0.985200\pi$
$798$		0			0
$799$	−20.0000	−	20.0000i	−0.707549	−	0.707549i
$800$		0			0
$801$	−5.00000	−	5.00000i	−0.176666	−	0.176666i
$802$		0			0
$803$	30.6525	−	30.6525i	1.08170	−	1.08170i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	8.36068	−	8.36068i	0.294310	−	0.294310i
$808$		0			0
$809$		−	26.1803i		−	0.920452i	−0.887802	−	0.460226i	$-0.847768\pi$
$809$		−	26.1803i		−	0.920452i	0.887802	−	0.460226i	$-0.152232\pi$
$810$		0			0
$811$	3.56231	−	3.56231i	0.125089	−	0.125089i	−0.641791	−	0.766880i	$-0.721808\pi$
$811$	3.56231	−	3.56231i	0.125089	−	0.125089i	0.766880	+	0.641791i	$0.221808\pi$
$812$		0			0
$813$			9.34752i			0.327832i
$814$		0			0
$815$		−	9.59675i		−	0.336159i
$816$		0			0
$817$	−45.1246			−1.57871
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−37.3607	+	37.3607i	−1.30390	+	1.30390i	−0.378154	+	0.925743i	$0.623441\pi$
$821$	−37.3607	+	37.3607i	−1.30390	+	1.30390i	−0.925743	+	0.378154i	$0.876559\pi$
$822$		0			0
$823$	−22.9787	+	22.9787i	−0.800988	+	0.800988i	−0.983250	−	0.182262i	$-0.941658\pi$
$823$	−22.9787	+	22.9787i	−0.800988	+	0.800988i	0.182262	+	0.983250i	$0.441658\pi$
$824$		0			0
$825$			16.1803i			0.563327i
$826$		0			0
$827$	22.4721			0.781433			0.390716	−	0.920511i	$-0.372227\pi$
$827$	22.4721			0.781433			0.390716	+	0.920511i	$0.372227\pi$
$828$		0			0
$829$	13.7082			0.476106			0.238053	−	0.971252i	$-0.423491\pi$
$829$	13.7082			0.476106			0.238053	+	0.971252i	$0.423491\pi$
$830$		0			0
$831$		−	3.34752i		−	0.116124i
$832$		0			0
$833$	−15.6525	−	15.6525i	−0.542326	−	0.542326i
$834$		0			0
$835$	30.2492			1.04682
$836$		0			0
$837$			37.8885i			1.30962i
$838$		0			0
$839$	22.7984	−	22.7984i	0.787087	−	0.787087i	−0.193928	−	0.981016i	$-0.562123\pi$
$839$	22.7984	−	22.7984i	0.787087	−	0.787087i	0.981016	+	0.193928i	$0.0621230\pi$
$840$		0			0
$841$	1.58359			0.0546066
$842$		0			0
$843$		−	2.76393i		−	0.0951949i
$844$		0			0
$845$	−11.1803	−	26.8328i	−0.384615	−	0.923077i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−19.5967			−0.672559
$850$		0			0
$851$	−32.8328	+	32.8328i	−1.12549	+	1.12549i
$852$		0			0
$853$		−	4.87539i		−	0.166930i	−0.996511	−	0.0834651i	$-0.973401\pi$
$853$		−	4.87539i		−	0.166930i	0.996511	−	0.0834651i	$-0.0265987\pi$
$854$		0			0
$855$	29.2705	−	29.2705i	1.00103	−	1.00103i
$856$		0			0
$857$	9.65248	+	9.65248i	0.329722	+	0.329722i	0.852481	−	0.522759i	$-0.175097\pi$
$857$	9.65248	+	9.65248i	0.329722	+	0.329722i	−0.522759	+	0.852481i	$0.675097\pi$
$858$		0			0
$859$			51.7082i			1.76426i	0.471005	+	0.882131i	$0.343891\pi$
$859$			51.7082i			1.76426i	−0.471005	+	0.882131i	$0.656109\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−34.4721			−1.17345			−0.586723	−	0.809788i	$-0.699582\pi$
$863$	−34.4721			−1.17345			−0.586723	+	0.809788i	$0.699582\pi$
$864$		0			0
$865$	−38.4164	+	38.4164i	−1.30620	+	1.30620i
$866$		0			0
$867$	−4.32624	+	4.32624i	−0.146927	+	0.146927i
$868$		0			0
$869$	9.70820	−	9.70820i	0.329328	−	0.329328i
$870$		0			0
$871$	0.583592	−	0.875388i	0.0197743	−	0.0296614i
$872$		0			0
$873$	−34.4721			−1.16671
$874$		0			0
$875$		0			0
$876$		0			0
$877$		−	46.8328i		−	1.58143i	−0.612183	−	0.790716i	$-0.709709\pi$
$877$		−	46.8328i		−	1.58143i	0.612183	−	0.790716i	$-0.290291\pi$
$878$		0			0
$879$	17.1246	−	17.1246i	0.577599	−	0.577599i
$880$		0			0
$881$		−	20.0689i		−	0.676138i	−0.941121	−	0.338069i	$-0.890226\pi$
$881$		−	20.0689i		−	0.676138i	0.941121	−	0.338069i	$-0.109774\pi$
$882$		0			0
$883$	27.8541	−	27.8541i	0.937365	−	0.937365i	−0.0607857	−	0.998151i	$-0.519361\pi$
$883$	27.8541	−	27.8541i	0.937365	−	0.937365i	0.998151	+	0.0607857i	$0.0193606\pi$
$884$		0			0
$885$	9.34752			0.314214
$886$		0			0
$887$	21.3820	−	21.3820i	0.717936	−	0.717936i	−0.250246	−	0.968182i	$-0.580512\pi$
$887$	21.3820	−	21.3820i	0.717936	−	0.717936i	0.968182	+	0.250246i	$0.0805115\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	7.09017	+	7.09017i	0.237530	+	0.237530i
$892$		0			0
$893$	52.3607	+	52.3607i	1.75218	+	1.75218i
$894$		0			0
$895$	−26.8328			−0.896922
$896$		0			0
$897$	−12.5410	−	8.36068i	−0.418732	−	0.279155i
$898$		0			0
$899$	30.6525	+	30.6525i	1.02232	+	1.02232i
$900$		0			0
$901$			6.58359i			0.219331i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	18.5410i		−	0.616324i
$906$		0			0
$907$	5.27051	+	5.27051i	0.175004	+	0.175004i	0.789174	−	0.614170i	$-0.210509\pi$
$907$	5.27051	+	5.27051i	0.175004	+	0.175004i	−0.614170	+	0.789174i	$0.710509\pi$
$908$		0			0
$909$	−3.41641			−0.113315
$910$		0			0
$911$	50.8328			1.68417			0.842083	−	0.539348i	$-0.181329\pi$
$911$	50.8328			1.68417			0.842083	+	0.539348i	$0.181329\pi$
$912$		0			0
$913$	27.4164	+	27.4164i	0.907351	+	0.907351i
$914$		0			0
$915$	7.88854	+	7.88854i	0.260787	+	0.260787i
$916$		0			0
$917$		0			0
$918$		0			0
$919$			35.1246i			1.15865i	0.815095	+	0.579327i	$0.196685\pi$
$919$			35.1246i			1.15865i	−0.815095	+	0.579327i	$0.803315\pi$
$920$		0			0
$921$	7.41641	+	7.41641i	0.244379	+	0.244379i
$922$		0			0
$923$	−13.0902	+	2.61803i	−0.430868	+	0.0861736i
$924$		0			0
$925$	48.5410			1.59602
$926$		0			0
$927$	−8.61803	−	8.61803i	−0.283053	−	0.283053i
$928$		0			0
$929$	2.88854	+	2.88854i	0.0947700	+	0.0947700i	0.752902	−	0.658132i	$-0.228653\pi$
$929$	2.88854	+	2.88854i	0.0947700	+	0.0947700i	−0.658132	+	0.752902i	$0.728653\pi$
$930$		0			0
$931$	40.9787	+	40.9787i	1.34302	+	1.34302i
$932$		0			0
$933$	1.34752	−	1.34752i	0.0441160	−	0.0441160i
$934$		0			0
$935$			26.1803i			0.856189i
$936$		0			0
$937$	32.4164	−	32.4164i	1.05900	−	1.05900i	0.0608510	−	0.998147i	$-0.480619\pi$
$937$	32.4164	−	32.4164i	1.05900	−	1.05900i	0.998147	−	0.0608510i	$-0.0193815\pi$
$938$		0			0
$939$			18.1803i			0.593293i
$940$		0			0
$941$	−13.3607	+	13.3607i	−0.435546	+	0.435546i	−0.890510	−	0.454964i	$-0.849652\pi$
$941$	−13.3607	+	13.3607i	−0.435546	+	0.435546i	0.454964	+	0.890510i	$0.349652\pi$
$942$		0			0
$943$			25.4590i			0.829058i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3.05573			0.0992978			0.0496489	−	0.998767i	$-0.484190\pi$
$947$	3.05573			0.0992978			0.0496489	+	0.998767i	$0.484190\pi$
$948$		0			0
$949$	23.4164	−	35.1246i	0.760129	−	1.14019i
$950$		0			0
$951$	2.29180	−	2.29180i	0.0743166	−	0.0743166i
$952$		0			0
$953$	27.7639	−	27.7639i	0.899362	−	0.899362i	−0.0960177	−	0.995380i	$-0.530611\pi$
$953$	27.7639	−	27.7639i	0.899362	−	0.899362i	0.995380	+	0.0960177i	$0.0306105\pi$
$954$		0			0
$955$	−16.5836			−0.536632
$956$		0			0
$957$	−16.9443			−0.547731
$958$		0			0
$959$		0			0
$960$		0			0
$961$		−	37.5410i		−	1.21100i
$962$		0			0
$963$	5.85410	+	5.85410i	0.188646	+	0.188646i
$964$		0			0
$965$		−	7.63932i		−	0.245918i
$966$		0			0
$967$		−	7.12461i		−	0.229112i	−0.993417	−	0.114556i	$-0.963455\pi$
$967$		−	7.12461i		−	0.229112i	0.993417	−	0.114556i	$-0.0365445\pi$
$968$		0			0
$969$	−16.1803	+	16.1803i	−0.519787	+	0.519787i
$970$		0			0
$971$		0			0			−	1.00000i	$-0.5\pi$
$971$		0			0				1.00000i	$0.5\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	3.09017	+	15.4508i	0.0989646	+	0.494823i
$976$		0			0
$977$		−	3.70820i		−	0.118636i	−0.998239	−	0.0593180i	$-0.981107\pi$
$977$		−	3.70820i		−	0.118636i	0.998239	−	0.0593180i	$-0.0188926\pi$
$978$		0			0
$979$	−11.7082			−0.374196
$980$		0			0
$981$	−10.5279	+	10.5279i	−0.336129	+	0.336129i
$982$		0			0
$983$		−	32.2918i		−	1.02995i	−0.857206	−	0.514974i	$-0.827802\pi$
$983$		−	32.2918i		−	1.02995i	0.857206	−	0.514974i	$-0.172198\pi$
$984$		0			0
$985$			26.8328i			0.854965i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			26.0689i			0.828942i
$990$		0			0
$991$	−20.5836			−0.653859			−0.326930	−	0.945049i	$-0.606014\pi$
$991$	−20.5836			−0.653859			−0.326930	+	0.945049i	$0.606014\pi$
$992$		0			0
$993$	19.5967			0.621884
$994$		0			0
$995$	−25.5279			−0.809288
$996$		0			0
$997$	−29.0000	+	29.0000i	−0.918439	+	0.918439i	−0.996916	−	0.0784767i	$-0.974994\pi$
$997$	−29.0000	+	29.0000i	−0.918439	+	0.918439i	0.0784767	+	0.996916i	$0.474994\pi$
$998$		0			0
$999$	−31.4164	+	31.4164i	−0.993971	+	0.993971i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.r.b.213.1	yes	4
3.2	odd	2		2340.2.bp.e.1513.2		4
4.3	odd	2		1040.2.cd.j.993.2		4
5.2	odd	4		260.2.m.b.57.1	✓	4
5.3	odd	4		1300.2.m.b.57.2		4
5.4	even	2		1300.2.r.b.993.2		4
13.8	odd	4		260.2.m.b.73.1	yes	4
15.2	even	4		2340.2.u.f.577.1		4
20.7	even	4		1040.2.bg.j.577.2		4
39.8	even	4		2340.2.u.f.73.2		4
52.47	even	4		1040.2.bg.j.593.2		4
65.8	even	4		1300.2.r.b.957.2		4
65.34	odd	4		1300.2.m.b.593.2		4
65.47	even	4	inner	260.2.r.b.177.1	yes	4
195.47	odd	4		2340.2.bp.e.1477.2		4
260.47	odd	4		1040.2.cd.j.177.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.m.b.57.1	✓	4	5.2	odd	4
260.2.m.b.73.1	yes	4	13.8	odd	4
260.2.r.b.177.1	yes	4	65.47	even	4	inner
260.2.r.b.213.1	yes	4	1.1	even	1	trivial
1040.2.bg.j.577.2		4	20.7	even	4
1040.2.bg.j.593.2		4	52.47	even	4
1040.2.cd.j.177.2		4	260.47	odd	4
1040.2.cd.j.993.2		4	4.3	odd	2
1300.2.m.b.57.2		4	5.3	odd	4
1300.2.m.b.593.2		4	65.34	odd	4
1300.2.r.b.957.2		4	65.8	even	4
1300.2.r.b.993.2		4	5.4	even	2
2340.2.u.f.73.2		4	39.8	even	4
2340.2.u.f.577.1		4	15.2	even	4
2340.2.bp.e.1477.2		4	195.47	odd	4
2340.2.bp.e.1513.2		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.618034 - 0.618034i) q^{3} -2.23607 q^{5} -2.23607i q^{9} +O(q^{10})\)	\(q+(-0.618034 - 0.618034i) q^{3} -2.23607 q^{5} -2.23607i q^{9} +(-2.61803 - 2.61803i) q^{11} +(-3.00000 - 2.00000i) q^{13} +(1.38197 + 1.38197i) q^{15} +(2.23607 + 2.23607i) q^{17} +(-5.85410 - 5.85410i) q^{19} +(-3.38197 + 3.38197i) q^{23} +5.00000 q^{25} +(-3.23607 + 3.23607i) q^{27} +5.23607i q^{29} +(5.85410 - 5.85410i) q^{31} +3.23607i q^{33} +9.70820 q^{37} +(0.618034 + 3.09017i) q^{39} +(3.76393 - 3.76393i) q^{41} +(3.85410 - 3.85410i) q^{43} +5.00000i q^{45} -8.94427 q^{47} -7.00000 q^{49} -2.76393i q^{51} +(1.47214 + 1.47214i) q^{53} +(5.85410 + 5.85410i) q^{55} +7.23607i q^{57} +(3.38197 - 3.38197i) q^{59} +5.70820 q^{61} +(6.70820 + 4.47214i) q^{65} +0.291796i q^{67} +4.18034 q^{69} +(2.61803 - 2.61803i) q^{71} +11.7082i q^{73} +(-3.09017 - 3.09017i) q^{75} +3.70820i q^{79} -2.70820 q^{81} -10.4721 q^{83} +(-5.00000 - 5.00000i) q^{85} +(3.23607 - 3.23607i) q^{87} +(2.23607 - 2.23607i) q^{89} -7.23607 q^{93} +(13.0902 + 13.0902i) q^{95} -15.4164i q^{97} +(-5.85410 + 5.85410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3}+O(q^{10}) \) 4 * q + 2 * q^3	\( 4 q + 2 q^{3} - 6 q^{11} - 12 q^{13} + 10 q^{15} - 10 q^{19} - 18 q^{23} + 20 q^{25} - 4 q^{27} + 10 q^{31} + 12 q^{37} - 2 q^{39} + 24 q^{41} + 2 q^{43} - 28 q^{49} - 12 q^{53} + 10 q^{55} + 18 q^{59} - 4 q^{61} - 28 q^{69} + 6 q^{71} + 10 q^{75} + 16 q^{81} - 24 q^{83} - 20 q^{85} + 4 q^{87} - 20 q^{93} + 30 q^{95} - 10 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 6 * q^11 - 12 * q^13 + 10 * q^15 - 10 * q^19 - 18 * q^23 + 20 * q^25 - 4 * q^27 + 10 * q^31 + 12 * q^37 - 2 * q^39 + 24 * q^41 + 2 * q^43 - 28 * q^49 - 12 * q^53 + 10 * q^55 + 18 * q^59 - 4 * q^61 - 28 * q^69 + 6 * q^71 + 10 * q^75 + 16 * q^81 - 24 * q^83 - 20 * q^85 + 4 * q^87 - 20 * q^93 + 30 * q^95 - 10 * q^99

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