LMFDB - Embedded newform 1300.2.ba.c.849.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1300,2,Mod(49,1300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1300, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("1300.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1300 = 2^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1300.ba (of order $6$, 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:	$10.3805522628$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			849.4
Root			$1.20036 + 0.747754i$ of defining polynomial
Character	$\chi$	$=$	1300.849
Dual form			1300.2.ba.c.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.44811 + 1.41342i) q^{3} +(-1.04739 - 1.81414i) q^{7} +(2.49551 + 4.32235i) q^{9} +O(q^{10})$	$q+(2.44811 + 1.41342i) q^{3} +(-1.04739 - 1.81414i) q^{7} +(2.49551 + 4.32235i) q^{9} +(1.50000 + 0.866025i) q^{11} +(-0.331331 + 3.59030i) q^{13} +(3.14218 - 1.81414i) q^{17} +(-0.926118 + 0.534695i) q^{19} -5.92163i q^{21} +(6.77046 + 3.90893i) q^{23} +5.62828i q^{27} +(-0.263457 + 0.456321i) q^{29} +5.84325i q^{31} +(2.44811 + 4.24026i) q^{33} +(-4.87423 + 8.44242i) q^{37} +(-5.88573 + 8.32114i) q^{39} +(-3.69615 - 2.13397i) q^{41} +(8.09281 - 4.67238i) q^{43} +3.46410 q^{47} +(1.30593 - 2.26194i) q^{49} +10.2566 q^{51} -12.5939i q^{53} -3.02299 q^{57} +(1.21564 - 0.701848i) q^{59} +(5.55440 + 9.62050i) q^{61} +(5.22756 - 9.05440i) q^{63} +(5.41671 - 9.38201i) q^{67} +(11.0499 + 19.1390i) q^{69} +(-12.2709 + 7.08460i) q^{71} +2.64469 q^{73} -3.62828i q^{77} -13.5729 q^{79} +(-0.468594 + 0.811629i) q^{81} -15.7925 q^{83} +(-1.28994 + 0.744750i) q^{87} +(4.78436 + 2.76225i) q^{89} +(6.86033 - 3.15937i) q^{91} +(-8.25896 + 14.3049i) q^{93} +(-7.59730 - 13.1589i) q^{97} +8.64469i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} - 6 q^{7} + 4 q^{9}+O(q^{10}) $ 8 * q + 6 * q^3 - 6 * q^7 + 4 * q^9	$ 8 q + 6 q^{3} - 6 q^{7} + 4 q^{9} + 12 q^{11} + 18 q^{17} + 6 q^{23} + 6 q^{33} - 18 q^{37} + 4 q^{39} + 12 q^{41} - 18 q^{43} + 4 q^{49} + 36 q^{57} + 24 q^{59} - 4 q^{61} + 12 q^{63} + 18 q^{67} + 24 q^{69} - 36 q^{71} - 48 q^{73} + 16 q^{79} + 8 q^{81} - 72 q^{83} - 18 q^{87} + 24 q^{89} - 48 q^{93} + 6 q^{97}+O(q^{100}) $ 8 * q + 6 * q^3 - 6 * q^7 + 4 * q^9 + 12 * q^11 + 18 * q^17 + 6 * q^23 + 6 * q^33 - 18 * q^37 + 4 * q^39 + 12 * q^41 - 18 * q^43 + 4 * q^49 + 36 * q^57 + 24 * q^59 - 4 * q^61 + 12 * q^63 + 18 * q^67 + 24 * q^69 - 36 * q^71 - 48 * q^73 + 16 * q^79 + 8 * q^81 - 72 * q^83 - 18 * q^87 + 24 * q^89 - 48 * q^93 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times$.

$n$	$301$	$651$	$677$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

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
$3$	2.44811	+	1.41342i	1.41342	+	0.816038i	0.995709	−	0.0925423i	$-0.0294993\pi$
$3$	2.44811	+	1.41342i	1.41342	+	0.816038i	0.417710	+	0.908580i	$0.362833\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.04739	−	1.81414i	−0.395878	−	0.685680i	0.597335	−	0.801992i	$-0.296226\pi$
$7$	−1.04739	−	1.81414i	−0.395878	−	0.685680i	−0.993213	+	0.116312i	$0.962893\pi$
$8$		0			0
$9$	2.49551	+	4.32235i	0.831836	+	1.44078i
$10$		0			0
$11$	1.50000	+	0.866025i	0.452267	+	0.261116i	0.708787	−	0.705422i	$-0.249243\pi$
$11$	1.50000	+	0.866025i	0.452267	+	0.261116i	−0.256520	+	0.966539i	$0.582576\pi$
$12$		0			0
$13$	−0.331331	+	3.59030i	−0.0918946	+	0.995769i
$13$	−0.331331	+	3.59030i	−0.0918946	+	0.995769i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.14218	−	1.81414i	0.762091	−	0.439993i	−0.0679550	−	0.997688i	$-0.521647\pi$
$17$	3.14218	−	1.81414i	0.762091	−	0.439993i	0.830046	+	0.557695i	$0.188314\pi$
$18$		0			0
$19$	−0.926118	+	0.534695i	−0.212466	+	0.122667i	−0.602457	−	0.798151i	$-0.705811\pi$
$19$	−0.926118	+	0.534695i	−0.212466	+	0.122667i	0.389991	+	0.920819i	$0.372478\pi$
$20$		0			0
$21$		−	5.92163i		−	1.29220i
$22$		0			0
$23$	6.77046	+	3.90893i	1.41174	+	0.815068i	0.995552	−	0.0942118i	$-0.0300331\pi$
$23$	6.77046	+	3.90893i	1.41174	+	0.815068i	0.416186	+	0.909279i	$0.363366\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			5.62828i			1.08316i
$28$		0			0
$29$	−0.263457	+	0.456321i	−0.0489227	+	0.0847366i	−0.889450	−	0.457033i	$-0.848912\pi$
$29$	−0.263457	+	0.456321i	−0.0489227	+	0.0847366i	0.840527	+	0.541770i	$0.182245\pi$
$30$		0			0
$31$			5.84325i			1.04948i	0.851263	+	0.524740i	$0.175837\pi$
$31$			5.84325i			1.04948i	−0.851263	+	0.524740i	$0.824163\pi$
$32$		0			0
$33$	2.44811	+	4.24026i	0.426162	+	0.738134i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.87423	+	8.44242i	−0.801319	+	1.38792i	0.117429	+	0.993081i	$0.462535\pi$
$37$	−4.87423	+	8.44242i	−0.801319	+	1.38792i	−0.918748	+	0.394844i	$0.870799\pi$
$38$		0			0
$39$	−5.88573	+	8.32114i	−0.942471	+	1.33245i
$40$		0			0
$41$	−3.69615	−	2.13397i	−0.577242	−	0.333271i	0.182795	−	0.983151i	$-0.441486\pi$
$41$	−3.69615	−	2.13397i	−0.577242	−	0.333271i	−0.760037	+	0.649880i	$0.774819\pi$
$42$		0			0
$43$	8.09281	−	4.67238i	1.23414	−	0.712532i	0.266251	−	0.963904i	$-0.414215\pi$
$43$	8.09281	−	4.67238i	1.23414	−	0.712532i	0.967891	+	0.251372i	$0.0808817\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.46410			0.505291			0.252646	−	0.967559i	$-0.418699\pi$
$47$	3.46410			0.505291			0.252646	+	0.967559i	$0.418699\pi$
$48$		0			0
$49$	1.30593	−	2.26194i	0.186562	−	0.323134i
$50$		0			0
$51$	10.2566			1.43621
$52$		0			0
$53$		−	12.5939i		−	1.72990i	−0.501854	−	0.864952i	$-0.667349\pi$
$53$		−	12.5939i		−	1.72990i	0.501854	−	0.864952i	$-0.332651\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−3.02299			−0.400405
$58$		0			0
$59$	1.21564	−	0.701848i	0.158262	−	0.0913729i	−0.418777	−	0.908089i	$-0.637541\pi$
$59$	1.21564	−	0.701848i	0.158262	−	0.0913729i	0.577040	+	0.816716i	$0.304208\pi$
$60$		0			0
$61$	5.55440	+	9.62050i	0.711168	+	1.23178i	0.964419	+	0.264378i	$0.0851667\pi$
$61$	5.55440	+	9.62050i	0.711168	+	1.23178i	−0.253251	+	0.967400i	$0.581500\pi$
$62$		0			0
$63$	5.22756	−	9.05440i	0.658610	−	1.14075i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	5.41671	−	9.38201i	0.661756	−	1.14620i	−0.318398	−	0.947957i	$-0.603145\pi$
$67$	5.41671	−	9.38201i	0.661756	−	1.14620i	0.980154	−	0.198238i	$-0.0635219\pi$
$68$		0			0
$69$	11.0499	+	19.1390i	1.33025	+	2.30406i
$70$		0			0
$71$	−12.2709	+	7.08460i	−1.45629	+	0.840787i	−0.998826	−	0.0484428i	$-0.984574\pi$
$71$	−12.2709	+	7.08460i	−1.45629	+	0.840787i	−0.457460	+	0.889230i	$0.651241\pi$
$72$		0			0
$73$	2.64469			0.309538			0.154769	−	0.987951i	$-0.450537\pi$
$73$	2.64469			0.309538			0.154769	+	0.987951i	$0.450537\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	3.62828i		−	0.413481i
$78$		0			0
$79$	−13.5729			−1.52707			−0.763535	−	0.645766i	$-0.776538\pi$
$79$	−13.5729			−1.52707			−0.763535	+	0.645766i	$0.776538\pi$
$80$		0			0
$81$	−0.468594	+	0.811629i	−0.0520660	+	0.0901809i
$82$		0			0
$83$	−15.7925			−1.73345			−0.866724	−	0.498789i	$-0.833778\pi$
$83$	−15.7925			−1.73345			−0.866724	+	0.498789i	$0.833778\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−1.28994	+	0.744750i	−0.138297	+	0.0798456i
$88$		0			0
$89$	4.78436	+	2.76225i	0.507141	+	0.292798i	0.731658	−	0.681672i	$-0.238747\pi$
$89$	4.78436	+	2.76225i	0.507141	+	0.292798i	−0.224516	+	0.974470i	$0.572080\pi$
$90$		0			0
$91$	6.86033	−	3.15937i	0.719158	−	0.331192i
$92$		0			0
$93$	−8.25896	+	14.3049i	−0.856415	+	1.48335i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−7.59730	−	13.1589i	−0.771389	−	1.33608i	−0.936802	−	0.349860i	$-0.886229\pi$
$97$	−7.59730	−	13.1589i	−0.771389	−	1.33608i	0.165413	−	0.986224i	$-0.447104\pi$
$98$		0			0
$99$			8.64469i			0.868824i
$100$		0			0
$101$	−1.83133	+	3.17196i	−0.182224	+	0.315622i	−0.942638	−	0.333818i	$-0.891663\pi$
$101$	−1.83133	+	3.17196i	−0.182224	+	0.315622i	0.760413	+	0.649439i	$0.224996\pi$
$102$		0			0
$103$		−	13.7804i		−	1.35783i	−0.734218	−	0.678914i	$-0.762451\pi$
$103$		−	13.7804i		−	1.35783i	0.734218	−	0.678914i	$-0.237549\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.80342	−	1.61856i	−0.271017	−	0.156472i	0.358333	−	0.933594i	$-0.383345\pi$
$107$	−2.80342	−	1.61856i	−0.271017	−	0.156472i	−0.629350	+	0.777122i	$0.716679\pi$
$108$		0			0
$109$		−	9.12979i		−	0.874476i	−0.899346	−	0.437238i	$-0.855957\pi$
$109$		−	9.12979i		−	0.874476i	0.899346	−	0.437238i	$-0.144043\pi$
$110$		0			0
$111$	−23.8654	+	13.7787i	−2.26520	+	1.30781i
$112$		0			0
$113$	9.48610	−	5.47680i	0.892377	−	0.515214i	0.0176577	−	0.999844i	$-0.494379\pi$
$113$	9.48610	−	5.47680i	0.892377	−	0.515214i	0.874719	+	0.484630i	$0.161046\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−16.3453	+	7.52748i	−1.51113	+	0.695916i
$118$		0			0
$119$	−6.58220	−	3.80024i	−0.603390	−	0.348367i
$120$		0			0
$121$	−4.00000	−	6.92820i	−0.363636	−	0.629837i
$122$		0			0
$123$	−6.03240	−	10.4484i	−0.543923	−	0.942103i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	0.786022	+	0.453810i	0.0697482	+	0.0402691i	0.534469	−	0.845188i	$-0.320512\pi$
$127$	0.786022	+	0.453810i	0.0697482	+	0.0402691i	−0.464720	+	0.885458i	$0.653845\pi$
$128$		0			0
$129$	26.4161			2.32581
$130$		0			0
$131$	−13.1626			−1.15002			−0.575012	−	0.818145i	$-0.695003\pi$
$131$	−13.1626			−1.15002			−0.575012	+	0.818145i	$0.695003\pi$
$132$		0			0
$133$	1.94002	+	1.12007i	0.168221	+	0.0971225i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.03240	+	10.4484i	0.515383	+	0.892669i	0.999841	+	0.0178546i	$0.00568359\pi$
$137$	6.03240	+	10.4484i	0.515383	+	0.892669i	−0.484458	+	0.874815i	$0.660983\pi$
$138$		0			0
$139$	−2.80593	−	4.86002i	−0.237996	−	0.412221i	0.722143	−	0.691744i	$-0.243157\pi$
$139$	−2.80593	−	4.86002i	−0.237996	−	0.412221i	−0.960139	+	0.279522i	$0.909824\pi$
$140$		0			0
$141$	8.48052	+	4.89623i	0.714188	+	0.412337i
$142$		0			0
$143$	−3.60628	+	5.09850i	−0.301573	+	0.426358i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	6.39414	−	3.69166i	0.527380	−	0.304483i
$148$		0			0
$149$	−18.1767	+	10.4943i	−1.48909	+	0.859727i	−0.999922	−	0.0124625i	$-0.996033\pi$
$149$	−18.1767	+	10.4943i	−1.48909	+	0.859727i	−0.489168	+	0.872189i	$0.662700\pi$
$150$		0			0
$151$		−	6.99102i		−	0.568921i	−0.958688	−	0.284460i	$-0.908186\pi$
$151$		−	6.99102i		−	0.568921i	0.958688	−	0.284460i	$-0.0918144\pi$
$152$		0			0
$153$	15.6827	+	9.05440i	1.26787	+	0.732005i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			3.74761i			0.299092i	0.988755	+	0.149546i	$0.0477812\pi$
$157$			3.74761i			0.299092i	−0.988755	+	0.149546i	$0.952219\pi$
$158$		0			0
$159$	17.8005	−	30.8313i	1.41167	−	2.44508i
$160$		0			0
$161$		−	16.3767i		−	1.29067i
$162$		0			0
$163$	3.18915	+	5.52377i	0.249793	+	0.432655i	0.963468	−	0.267822i	$-0.0863039\pi$
$163$	3.18915	+	5.52377i	0.249793	+	0.432655i	−0.713675	+	0.700477i	$0.752971\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.76445	−	13.4484i	0.600831	−	1.04067i	−0.391864	−	0.920023i	$-0.628170\pi$
$167$	7.76445	−	13.4484i	0.600831	−	1.04067i	0.992695	−	0.120647i	$-0.0384970\pi$
$168$		0			0
$169$	−12.7804	−	2.37915i	−0.983111	−	0.183012i
$170$		0			0
$171$	−4.62227	−	2.66867i	−0.353474	−	0.204078i
$172$		0			0
$173$	−4.13617	+	2.38802i	−0.314467	+	0.181558i	−0.648924	−	0.760853i	$-0.724781\pi$
$173$	−4.13617	+	2.38802i	−0.314467	+	0.181558i	0.334456	+	0.942411i	$0.391447\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	3.96802			0.298255
$178$		0			0
$179$	−7.85134	+	13.5989i	−0.586837	+	1.01643i	0.407807	+	0.913068i	$0.366294\pi$
$179$	−7.85134	+	13.5989i	−0.586837	+	1.01643i	−0.994644	+	0.103363i	$0.967040\pi$
$180$		0			0
$181$	10.8851			0.809080			0.404540	−	0.914520i	$-0.367432\pi$
$181$	10.8851			0.809080			0.404540	+	0.914520i	$0.367432\pi$
$182$		0			0
$183$			31.4028i			2.32136i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	6.28436			0.459558
$188$		0			0
$189$	10.2105	−	5.89502i	0.742703	−	0.428800i
$190$		0			0
$191$	2.97909	+	5.15994i	0.215560	+	0.373360i	0.953446	−	0.301565i	$-0.0975091\pi$
$191$	2.97909	+	5.15994i	0.215560	+	0.373360i	−0.737886	+	0.674925i	$0.764176\pi$
$192$		0			0
$193$	6.38473	−	11.0587i	0.459583	−	0.796021i	−0.539356	−	0.842078i	$-0.681332\pi$
$193$	6.38473	−	11.0587i	0.459583	−	0.796021i	0.998939	+	0.0460568i	$0.0146655\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	8.05397	−	13.9499i	0.573822	−	0.993888i	−0.422347	−	0.906434i	$-0.638794\pi$
$197$	8.05397	−	13.9499i	0.573822	−	0.993888i	0.996169	−	0.0874540i	$-0.0278731\pi$
$198$		0			0
$199$	4.26403	+	7.38551i	0.302269	+	0.523545i	0.976650	−	0.214839i	$-0.0689226\pi$
$199$	4.26403	+	7.38551i	0.302269	+	0.523545i	−0.674381	+	0.738384i	$0.735589\pi$
$200$		0			0
$201$	26.5214	−	15.3122i	1.87068	−	1.08004i
$202$		0			0
$203$	1.10377			0.0774696
$204$		0			0
$205$		0			0
$206$		0			0
$207$			39.0190i			2.71201i
$208$		0			0
$209$	−1.85224			−0.128122
$210$		0			0
$211$	2.09030	−	3.62050i	0.143902	−	0.249245i	−0.785061	−	0.619419i	$-0.787368\pi$
$211$	2.09030	−	3.62050i	0.143902	−	0.249245i	0.928963	+	0.370173i	$0.120702\pi$
$212$		0			0
$213$	−40.0540			−2.74446
$214$		0			0
$215$		0			0
$216$		0			0
$217$	10.6005	−	6.12019i	0.719607	−	0.415465i
$218$		0			0
$219$	6.47451	+	3.73806i	0.437507	+	0.252595i
$220$		0			0
$221$	5.47219	+	11.8824i	0.368100	+	0.799299i
$222$		0			0
$223$	−5.24955	+	9.09249i	−0.351536	+	0.608878i	−0.986519	−	0.163648i	$-0.947674\pi$
$223$	−5.24955	+	9.09249i	−0.351536	+	0.608878i	0.634983	+	0.772526i	$0.281007\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.79288	+	13.4977i	0.517232	+	0.895872i	0.999800	+	0.0200131i	$0.00637079\pi$
$227$	7.79288	+	13.4977i	0.517232	+	0.895872i	−0.482568	+	0.875858i	$0.660296\pi$
$228$		0			0
$229$		−	19.2714i		−	1.27349i	−0.771074	−	0.636745i	$-0.780280\pi$
$229$		−	19.2714i		−	1.27349i	0.771074	−	0.636745i	$-0.219720\pi$
$230$		0			0
$231$	5.12828	−	8.88244i	0.337416	−	0.584422i
$232$		0			0
$233$		−	2.48794i		−	0.162991i	−0.996674	−	0.0814953i	$-0.974030\pi$
$233$		−	2.48794i		−	0.162991i	0.996674	−	0.0814953i	$-0.0259696\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−33.2280	−	19.1842i	−2.15839	−	1.24615i
$238$		0			0
$239$		−	16.7775i		−	1.08525i	−0.839976	−	0.542624i	$-0.817431\pi$
$239$		−	16.7775i		−	1.08525i	0.839976	−	0.542624i	$-0.182569\pi$
$240$		0			0
$241$	25.1835	−	14.5397i	1.62221	−	0.936585i	0.635887	−	0.771782i	$-0.280634\pi$
$241$	25.1835	−	14.5397i	1.62221	−	0.936585i	0.986326	−	0.164803i	$-0.0526990\pi$
$242$		0			0
$243$	12.3284	−	7.11778i	0.790864	−	0.456606i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1.61286	−	3.50220i	−0.102624	−	0.222840i
$248$		0			0
$249$	−38.6617	−	22.3214i	−2.45009	−	1.41456i
$250$		0			0
$251$	9.56040	+	16.5591i	0.603447	+	1.04520i	0.992295	+	0.123899i	$0.0395400\pi$
$251$	9.56040	+	16.5591i	0.603447	+	1.04520i	−0.388847	+	0.921302i	$0.627127\pi$
$252$		0			0
$253$	6.77046	+	11.7268i	0.425655	+	0.737256i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	11.8724	+	6.85453i	0.740580	+	0.427574i	0.822280	−	0.569083i	$-0.192702\pi$
$257$	11.8724	+	6.85453i	0.740580	+	0.427574i	−0.0817004	+	0.996657i	$0.526035\pi$
$258$		0			0
$259$	20.4210			1.26890
$260$		0			0
$261$	−2.62983			−0.162783
$262$		0			0
$263$	−10.3174	−	5.95675i	−0.636197	−	0.367309i	0.146951	−	0.989144i	$-0.453054\pi$
$263$	−10.3174	−	5.95675i	−0.636197	−	0.367309i	−0.783148	+	0.621835i	$0.786387\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	7.80844	+	13.5246i	0.477869	+	0.827693i
$268$		0			0
$269$	−10.4656	−	18.1270i	−0.638100	−	1.10522i	−0.985849	−	0.167634i	$-0.946387\pi$
$269$	−10.4656	−	18.1270i	−0.638100	−	1.10522i	0.347749	−	0.937588i	$-0.386946\pi$
$270$		0			0
$271$	1.69014	+	0.975805i	0.102669	+	0.0592760i	0.550455	−	0.834865i	$-0.314454\pi$
$271$	1.69014	+	0.975805i	0.102669	+	0.0592760i	−0.447786	+	0.894141i	$0.647787\pi$
$272$		0			0
$273$	21.2604	+	1.96202i	1.28674	+	0.118747i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−10.8084	+	6.24026i	−0.649416	+	0.374941i	−0.788233	−	0.615377i	$-0.789004\pi$
$277$	−10.8084	+	6.24026i	−0.649416	+	0.374941i	0.138816	+	0.990318i	$0.455670\pi$
$278$		0			0
$279$	−25.2566	+	14.5819i	−1.51207	+	0.872994i
$280$		0			0
$281$		−	2.29553i		−	0.136940i	−0.997653	−	0.0684698i	$-0.978188\pi$
$281$		−	2.29553i		−	0.136940i	0.997653	−	0.0684698i	$-0.0218117\pi$
$282$		0			0
$283$	−12.9295	−	7.46484i	−0.768578	−	0.443739i	0.0637892	−	0.997963i	$-0.479681\pi$
$283$	−12.9295	−	7.46484i	−0.768578	−	0.443739i	−0.832367	+	0.554225i	$0.813015\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			8.94045i			0.527738i
$288$		0			0
$289$	−1.91780	+	3.32172i	−0.112812	+	0.195395i
$290$		0			0
$291$		−	42.9527i		−	2.51793i
$292$		0			0
$293$	−0.716063	−	1.24026i	−0.0418329	−	0.0724566i	0.844351	−	0.535791i	$-0.179986\pi$
$293$	−0.716063	−	1.24026i	−0.0418329	−	0.0724566i	−0.886184	+	0.463334i	$0.846653\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−4.87423	+	8.44242i	−0.282832	+	0.489879i
$298$		0			0
$299$	−16.2775	+	23.0128i	−0.941350	+	1.33086i
$300$		0			0
$301$	−16.9527	−	9.78765i	−0.977138	−	0.564151i
$302$		0			0
$303$	−8.96661	+	5.17688i	−0.515118	+	0.297404i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−17.3833			−0.992118			−0.496059	−	0.868289i	$-0.665220\pi$
$307$	−17.3833			−0.992118			−0.496059	+	0.868289i	$0.665220\pi$
$308$		0			0
$309$	19.4775	−	33.7361i	1.10804	−	1.91918i
$310$		0			0
$311$	−20.2164			−1.14637			−0.573185	−	0.819426i	$-0.694292\pi$
$311$	−20.2164			−1.14637			−0.573185	+	0.819426i	$0.694292\pi$
$312$		0			0
$313$			4.86425i			0.274944i	0.990506	+	0.137472i	$0.0438977\pi$
$313$			4.86425i			0.274944i	−0.990506	+	0.137472i	$0.956102\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	23.6177			1.32650			0.663252	−	0.748396i	$-0.269176\pi$
$317$	23.6177			1.32650			0.663252	+	0.748396i	$0.269176\pi$
$318$		0			0
$319$	−0.790371	+	0.456321i	−0.0442523	+	0.0255491i
$320$		0			0
$321$	−4.57540	−	7.92482i	−0.255374	−	0.442320i
$322$		0			0
$323$	−1.94002	+	3.36022i	−0.107946	+	0.186967i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	12.9042	−	22.3508i	0.713605	−	1.23600i
$328$		0			0
$329$	−3.62828	−	6.28436i	−0.200033	−	0.346468i
$330$		0			0
$331$	−12.8863	+	7.43991i	−0.708295	+	0.408934i	−0.810429	−	0.585836i	$-0.800766\pi$
$331$	−12.8863	+	7.43991i	−0.708295	+	0.408934i	0.102134	+	0.994771i	$0.467433\pi$
$332$		0			0
$333$	−48.6547			−2.66626
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	29.1906i		−	1.59012i	−0.606534	−	0.795058i	$-0.707441\pi$
$337$		−	29.1906i		−	1.59012i	0.606534	−	0.795058i	$-0.292559\pi$
$338$		0			0
$339$	30.9641			1.68174
$340$		0			0
$341$	−5.06040	+	8.76488i	−0.274036	+	0.474645i
$342$		0			0
$343$	−20.1348			−1.08718
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−20.9795	+	12.1125i	−1.12624	+	0.650234i	−0.942986	−	0.332833i	$-0.891996\pi$
$347$	−20.9795	+	12.1125i	−1.12624	+	0.650234i	−0.183252	+	0.983066i	$0.558662\pi$
$348$		0			0
$349$	11.1557	+	6.44076i	0.597152	+	0.344766i	0.767920	−	0.640545i	$-0.221292\pi$
$349$	11.1557	+	6.44076i	0.597152	+	0.344766i	−0.170768	+	0.985311i	$0.554625\pi$
$350$		0			0
$351$	−20.2072	−	1.86482i	−1.07858	−	0.0995368i
$352$		0			0
$353$	8.10837	−	14.0441i	0.431565	−	0.747492i	−0.565443	−	0.824787i	$-0.691295\pi$
$353$	8.10837	−	14.0441i	0.431565	−	0.747492i	0.997008	+	0.0772948i	$0.0246283\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−10.7427	−	18.6068i	−0.568562	−	0.984777i
$358$		0			0
$359$		−	9.19261i		−	0.485167i	−0.970131	−	0.242584i	$-0.922005\pi$
$359$		−	9.19261i		−	0.485167i	0.970131	−	0.242584i	$-0.0779949\pi$
$360$		0			0
$361$	−8.92820	+	15.4641i	−0.469905	+	0.813900i
$362$		0			0
$363$		−	22.6147i		−	1.18696i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	3.98486	+	2.30066i	0.208008	+	0.120094i	0.600385	−	0.799711i	$-0.295014\pi$
$367$	3.98486	+	2.30066i	0.208008	+	0.120094i	−0.392377	+	0.919804i	$0.628347\pi$
$368$		0			0
$369$		−	21.3014i		−	1.10891i
$370$		0			0
$371$	−22.8471	+	13.1908i	−1.18616	+	0.684831i
$372$		0			0
$373$	17.7471	−	10.2463i	0.918908	−	0.530532i	0.0356212	−	0.999365i	$-0.488659\pi$
$373$	17.7471	−	10.2463i	0.918908	−	0.530532i	0.883286	+	0.468834i	$0.155326\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.55103	−	1.09708i	−0.0798823	−	0.0565025i
$378$		0			0
$379$	−6.95307	−	4.01436i	−0.357155	−	0.206204i	0.310677	−	0.950516i	$-0.399444\pi$
$379$	−6.95307	−	4.01436i	−0.357155	−	0.206204i	−0.667832	+	0.744312i	$0.732778\pi$
$380$		0			0
$381$	1.28285	+	2.22196i	0.0657223	+	0.113834i
$382$		0			0
$383$	15.0712	+	26.1041i	0.770104	+	1.33386i	0.937505	+	0.347971i	$0.113129\pi$
$383$	15.0712	+	26.1041i	0.770104	+	1.33386i	−0.167401	+	0.985889i	$0.553538\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	40.3913	+	23.3199i	2.05321	+	1.18542i
$388$		0			0
$389$	35.8264			1.81647			0.908236	−	0.418459i	$-0.137430\pi$
$389$	35.8264			1.81647			0.908236	+	0.418459i	$0.137430\pi$
$390$		0			0
$391$	28.3654			1.43450
$392$		0			0
$393$	−32.2236	−	18.6043i	−1.62547	−	0.938463i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−7.69152	−	13.3221i	−0.386026	−	0.668617i	0.605885	−	0.795552i	$-0.292819\pi$
$397$	−7.69152	−	13.3221i	−0.386026	−	0.668617i	−0.991911	+	0.126935i	$0.959486\pi$
$398$		0			0
$399$	3.16626	+	5.48413i	0.158511	+	0.274550i
$400$		0			0
$401$	−8.46704	−	4.88845i	−0.422824	−	0.244117i	0.273461	−	0.961883i	$-0.411832\pi$
$401$	−8.46704	−	4.88845i	−0.422824	−	0.244117i	−0.696285	+	0.717766i	$0.745165\pi$
$402$		0			0
$403$	−20.9790	−	1.93605i	−1.04504	−	0.0964415i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−14.6227	+	8.44242i	−0.724820	+	0.418475i
$408$		0			0
$409$	−0.871721	+	0.503289i	−0.0431039	+	0.0248860i	−0.521397	−	0.853314i	$-0.674589\pi$
$409$	−0.871721	+	0.503289i	−0.0431039	+	0.0248860i	0.478293	+	0.878200i	$0.341256\pi$
$410$		0			0
$411$			34.1052i			1.68229i
$412$		0			0
$413$	−2.54650	−	1.47022i	−0.125305	−	0.0723450i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	15.8638i		−	0.776855i
$418$		0			0
$419$	4.85134	−	8.40278i	0.237004	−	0.410502i	−0.722849	−	0.691006i	$-0.757168\pi$
$419$	4.85134	−	8.40278i	0.237004	−	0.410502i	0.959853	+	0.280503i	$0.0905013\pi$
$420$		0			0
$421$			14.2955i			0.696721i	0.937361	+	0.348361i	$0.113262\pi$
$421$			14.2955i			0.696721i	−0.937361	+	0.348361i	$0.886738\pi$
$422$		0			0
$423$	8.64469	+	14.9730i	0.420319	+	0.728014i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	11.6353	−	20.1529i	0.563071	−	0.975267i
$428$		0			0
$429$	−16.0349	+	7.38452i	−0.774173	+	0.356528i
$430$		0			0
$431$	10.5197	+	6.07357i	0.506718	+	0.292554i	0.731483	−	0.681859i	$-0.238828\pi$
$431$	10.5197	+	6.07357i	0.506718	+	0.292554i	−0.224766	+	0.974413i	$0.572162\pi$
$432$		0			0
$433$	−0.181016	+	0.104510i	−0.00869909	+	0.00502242i	−0.504343	−	0.863503i	$-0.668265\pi$
$433$	−0.181016	+	0.104510i	−0.00869909	+	0.00502242i	0.495644	+	0.868526i	$0.334932\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−8.36033			−0.399929
$438$		0			0
$439$	13.8603	−	24.0068i	0.661517	−	1.14578i	−0.318700	−	0.947856i	$-0.603246\pi$
$439$	13.8603	−	24.0068i	0.661517	−	1.14578i	0.980217	−	0.197926i	$-0.0634206\pi$
$440$		0			0
$441$	13.0359			0.620755
$442$		0			0
$443$			7.98798i			0.379521i	0.981830	+	0.189760i	$0.0607711\pi$
$443$			7.98798i			0.379521i	−0.981830	+	0.189760i	$0.939229\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−59.3314			−2.80628
$448$		0			0
$449$	−6.17667	+	3.56610i	−0.291495	+	0.168295i	−0.638616	−	0.769526i	$-0.720493\pi$
$449$	−6.17667	+	3.56610i	−0.291495	+	0.168295i	0.347121	+	0.937820i	$0.387159\pi$
$450$		0			0
$451$	−3.69615	−	6.40192i	−0.174045	−	0.301455i
$452$		0			0
$453$	9.88124	−	17.1148i	0.464261	−	0.804124i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	15.8404	−	27.4364i	0.740984	−	1.28342i	−0.211064	−	0.977472i	$-0.567693\pi$
$457$	15.8404	−	27.4364i	0.740984	−	1.28342i	0.952048	−	0.305949i	$-0.0989737\pi$
$458$		0			0
$459$	10.2105	+	17.6851i	0.476584	+	0.825468i
$460$		0			0
$461$	−10.2649	+	5.92643i	−0.478083	+	0.276021i	−0.719617	−	0.694371i	$-0.755683\pi$
$461$	−10.2649	+	5.92643i	−0.478083	+	0.276021i	0.241534	+	0.970392i	$0.422349\pi$
$462$		0			0
$463$	−12.7655			−0.593263			−0.296632	−	0.954992i	$-0.595863\pi$
$463$	−12.7655			−0.593263			−0.296632	+	0.954992i	$0.595863\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			31.3402i			1.45025i	0.688617	+	0.725125i	$0.258218\pi$
$467$			31.3402i			1.45025i	−0.688617	+	0.725125i	$0.741782\pi$
$468$		0			0
$469$	−22.6937			−1.04790
$470$		0			0
$471$	−5.29695	+	9.17458i	−0.244070	+	0.422742i
$472$		0			0
$473$	16.1856			0.744215
$474$		0			0
$475$		0			0
$476$		0			0
$477$	54.4352	−	31.4282i	2.49242	−	1.43900i
$478$		0			0
$479$	−13.9656	−	8.06303i	−0.638103	−	0.368409i	0.145780	−	0.989317i	$-0.453431\pi$
$479$	−13.9656	−	8.06303i	−0.638103	−	0.368409i	−0.783884	+	0.620908i	$0.786764\pi$
$480$		0			0
$481$	−28.6958	−	20.2972i	−1.30842	−	0.925471i
$482$		0			0
$483$	23.1472	−	40.0921i	1.05323	−	1.82426i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−2.79501	−	4.84109i	−0.126654	−	0.219371i	0.795724	−	0.605659i	$-0.207090\pi$
$487$	−2.79501	−	4.84109i	−0.126654	−	0.219371i	−0.922378	+	0.386288i	$0.873757\pi$
$488$		0			0
$489$			18.0304i			0.815364i
$490$		0			0
$491$	−9.14772	+	15.8443i	−0.412831	+	0.715044i	−0.995198	−	0.0978817i	$-0.968793\pi$
$491$	−9.14772	+	15.8443i	−0.412831	+	0.715044i	0.582367	+	0.812926i	$0.302127\pi$
$492$		0			0
$493$			1.91179i			0.0861027i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	25.7049	+	14.8407i	1.15302	+	0.665698i
$498$		0			0
$499$		−	0.553868i		−	0.0247945i	−0.999923	−	0.0123973i	$-0.996054\pi$
$499$		−	0.553868i		−	0.0247945i	0.999923	−	0.0123973i	$-0.00394627\pi$
$500$		0			0
$501$	38.0165	−	21.9489i	1.69845	−	0.980602i
$502$		0			0
$503$	−12.7161	+	7.34162i	−0.566981	+	0.327347i	−0.755943	−	0.654638i	$-0.772821\pi$
$503$	−12.7161	+	7.34162i	−0.566981	+	0.327347i	0.188962	+	0.981984i	$0.439488\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−27.9252	−	23.8886i	−1.24020	−	1.06093i
$508$		0			0
$509$	−5.99545	−	3.46148i	−0.265744	−	0.153427i	0.361208	−	0.932485i	$-0.382364\pi$
$509$	−5.99545	−	3.46148i	−0.265744	−	0.153427i	−0.626952	+	0.779058i	$0.715698\pi$
$510$		0			0
$511$	−2.77003	−	4.79784i	−0.122539	−	0.212244i
$512$		0			0
$513$	−3.00941	−	5.21245i	−0.132869	−	0.230135i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	5.19615	+	3.00000i	0.228527	+	0.131940i
$518$		0			0
$519$	−13.5011			−0.592632
$520$		0			0
$521$	−18.3551			−0.804152			−0.402076	−	0.915606i	$-0.631711\pi$
$521$	−18.3551			−0.804152			−0.402076	+	0.915606i	$0.631711\pi$
$522$		0			0
$523$	−15.8234	−	9.13563i	−0.691908	−	0.399473i	0.112418	−	0.993661i	$-0.464140\pi$
$523$	−15.8234	−	9.13563i	−0.691908	−	0.399473i	−0.804326	+	0.594188i	$0.797474\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	10.6005	+	18.3606i	0.461764	+	0.799798i
$528$		0			0
$529$	19.0594	+	33.0119i	0.828670	+	1.43530i
$530$		0			0
$531$	6.06726	+	3.50294i	0.263297	+	0.152014i
$532$		0			0
$533$	8.88625	−	12.5632i	0.384906	−	0.544174i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−38.4420	+	22.1945i	−1.65889	+	0.957763i
$538$		0			0
$539$	3.91780	−	2.26194i	0.168751	−	0.0974287i
$540$		0			0
$541$		−	31.8881i		−	1.37098i	−0.728084	−	0.685488i	$-0.759589\pi$
$541$		−	31.8881i		−	1.37098i	0.728084	−	0.685488i	$-0.240411\pi$
$542$		0			0
$543$	26.6479	+	15.3852i	1.14357	+	0.660240i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			44.7966i			1.91537i	0.287826	+	0.957683i	$0.407067\pi$
$547$			44.7966i			1.91537i	−0.287826	+	0.957683i	$0.592933\pi$
$548$		0			0
$549$	−27.7221	+	48.0161i	−1.18315	+	2.04928i
$550$		0			0
$551$		−	0.563476i		−	0.0240049i
$552$		0			0
$553$	14.2162	+	24.6231i	0.604533	+	1.04708i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−13.1532	+	22.7820i	−0.557319	+	0.965306i	0.440400	+	0.897802i	$0.354837\pi$
$557$	−13.1532	+	22.7820i	−0.557319	+	0.965306i	−0.997719	+	0.0675037i	$0.978497\pi$
$558$		0			0
$559$	14.0938	+	30.6037i	0.596106	+	1.29440i
$560$		0			0
$561$	15.3848	+	8.88244i	0.649548	+	0.375017i
$562$		0			0
$563$	−5.01415	+	2.89492i	−0.211321	+	0.122006i	−0.601925	−	0.798552i	$-0.705599\pi$
$563$	−5.01415	+	2.89492i	−0.211321	+	0.122006i	0.390604	+	0.920559i	$0.372266\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	1.96321			0.0824471
$568$		0			0
$569$	−11.8184	+	20.4700i	−0.495452	+	0.858149i	−0.999986	−	0.00524320i	$-0.998331\pi$
$569$	−11.8184	+	20.4700i	−0.495452	+	0.858149i	0.504534	+	0.863392i	$0.331664\pi$
$570$		0			0
$571$	−11.4641			−0.479758			−0.239879	−	0.970803i	$-0.577108\pi$
$571$	−11.4641			−0.479758			−0.239879	+	0.970803i	$0.577108\pi$
$572$		0			0
$573$			16.8428i			0.703620i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−34.2415			−1.42549			−0.712746	−	0.701422i	$-0.752549\pi$
$577$	−34.2415			−1.42549			−0.712746	+	0.701422i	$0.752549\pi$
$578$		0			0
$579$	31.2611	−	18.0486i	1.29917	−	0.750074i
$580$		0			0
$581$	16.5409	+	28.6497i	0.686233	+	1.18859i
$582$		0			0
$583$	10.9066	−	18.8908i	0.451707	−	0.782379i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	2.81800	−	4.88091i	0.116311	−	0.201457i	−0.801992	−	0.597335i	$-0.796226\pi$
$587$	2.81800	−	4.88091i	0.116311	−	0.201457i	0.918303	+	0.395878i	$0.129560\pi$
$588$		0			0
$589$	−3.12436	−	5.41154i	−0.128737	−	0.222979i
$590$		0			0
$591$	39.4341	−	22.7673i	1.62210	−	0.936521i
$592$		0			0
$593$	15.3014			0.628353			0.314177	−	0.949365i	$-0.398272\pi$
$593$	15.3014			0.628353			0.314177	+	0.949365i	$0.398272\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$			24.1074i			0.986651i
$598$		0			0
$599$	−9.82414			−0.401404			−0.200702	−	0.979652i	$-0.564322\pi$
$599$	−9.82414			−0.401404			−0.200702	+	0.979652i	$0.564322\pi$
$600$		0			0
$601$	23.0945	−	40.0008i	0.942043	−	1.63167i	0.180476	−	0.983579i	$-0.442236\pi$
$601$	23.0945	−	40.0008i	0.942043	−	1.63167i	0.761566	−	0.648087i	$-0.224431\pi$
$602$		0			0
$603$	54.0697			2.20189
$604$		0			0
$605$		0			0
$606$		0			0
$607$	21.3877	−	12.3482i	0.868100	−	0.501198i	0.00138384	−	0.999999i	$-0.499560\pi$
$607$	21.3877	−	12.3482i	0.868100	−	0.501198i	0.866716	+	0.498801i	$0.166226\pi$
$608$		0			0
$609$	2.70216	+	1.56009i	0.109497	+	0.0632182i
$610$		0			0
$611$	−1.14776	+	12.4371i	−0.0464335	+	0.503153i
$612$		0			0
$613$	−8.32277	+	14.4155i	−0.336154	+	0.582235i	−0.983706	−	0.179786i	$-0.942459\pi$
$613$	−8.32277	+	14.4155i	−0.336154	+	0.582235i	0.647552	+	0.762021i	$0.275793\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.807820	−	1.39918i	−0.0325216	−	0.0563291i	0.849307	−	0.527900i	$-0.177020\pi$
$617$	−0.807820	−	1.39918i	−0.0325216	−	0.0563291i	−0.881828	+	0.471571i	$0.843687\pi$
$618$		0			0
$619$			23.3922i			0.940213i	0.882610	+	0.470106i	$0.155784\pi$
$619$			23.3922i			0.940213i	−0.882610	+	0.470106i	$0.844216\pi$
$620$		0			0
$621$	−22.0005	+	38.1060i	−0.882851	+	1.52914i
$622$		0			0
$623$		−	11.5727i		−	0.463649i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−4.53449	−	2.61799i	−0.181090	−	0.104552i
$628$		0			0
$629$			35.3701i			1.41030i
$630$		0			0
$631$	2.77458	−	1.60190i	0.110454	−	0.0637708i	−0.443755	−	0.896148i	$-0.646354\pi$
$631$	2.77458	−	1.60190i	0.110454	−	0.0637708i	0.554209	+	0.832377i	$0.313021\pi$
$632$		0			0
$633$	10.2346	−	5.90893i	0.406787	−	0.234859i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	7.68834	+	5.43813i	0.304623	+	0.215467i
$638$		0			0
$639$	−61.2442	−	35.3593i	−2.42278	−	1.39879i
$640$		0			0
$641$	−9.98794	−	17.2996i	−0.394500	−	0.683294i	0.598537	−	0.801095i	$-0.295749\pi$
$641$	−9.98794	−	17.2996i	−0.394500	−	0.683294i	−0.993037	+	0.117801i	$0.962416\pi$
$642$		0			0
$643$	14.2684	+	24.7136i	0.562690	+	0.974607i	0.997260	+	0.0739696i	$0.0235668\pi$
$643$	14.2684	+	24.7136i	0.562690	+	0.974607i	−0.434571	+	0.900638i	$0.643100\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	5.27107	+	3.04325i	0.207227	+	0.119643i	0.600022	−	0.799983i	$-0.295158\pi$
$647$	5.27107	+	3.04325i	0.207227	+	0.119643i	−0.392795	+	0.919626i	$0.628492\pi$
$648$		0			0
$649$	2.43127			0.0954359
$650$		0			0
$651$	34.6016			1.35614
$652$		0			0
$653$	17.0001	+	9.81499i	0.665264	+	0.384090i	0.794280	−	0.607552i	$-0.207848\pi$
$653$	17.0001	+	9.81499i	0.665264	+	0.384090i	−0.129016	+	0.991643i	$0.541182\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	6.59985	+	11.4313i	0.257485	+	0.445976i
$658$		0			0
$659$	−9.79752	−	16.9698i	−0.381657	−	0.661049i	0.609642	−	0.792677i	$-0.291313\pi$
$659$	−9.79752	−	16.9698i	−0.381657	−	0.661049i	−0.991299	+	0.131627i	$0.957980\pi$
$660$		0			0
$661$	30.0735	+	17.3630i	1.16972	+	0.675341i	0.953615	−	0.301029i	$-0.0973300\pi$
$661$	30.0735	+	17.3630i	1.16972	+	0.675341i	0.216109	+	0.976369i	$0.430663\pi$
$662$		0			0
$663$	−3.39831	+	36.8241i	−0.131980	+	1.43013i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−3.56745	+	2.05967i	−0.138132	+	0.0797506i
$668$		0			0
$669$	−25.7030	+	14.8396i	−0.993736	+	0.573734i
$670$		0			0
$671$			19.2410i			0.742790i
$672$		0			0
$673$	29.4538	+	17.0051i	1.13536	+	0.655500i	0.945277	−	0.326268i	$-0.105791\pi$
$673$	29.4538	+	17.0051i	1.13536	+	0.655500i	0.190082	+	0.981768i	$0.439125\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			29.9209i			1.14995i	0.818169	+	0.574977i	$0.194989\pi$
$677$			29.9209i			1.14995i	−0.818169	+	0.574977i	$0.805011\pi$
$678$		0			0
$679$	−15.9147	+	27.5651i	−0.610751	+	1.05785i
$680$		0			0
$681$			44.0584i			1.68832i
$682$		0			0
$683$	−13.9286	−	24.1251i	−0.532964	−	0.923121i	−0.999259	−	0.0384916i	$-0.987745\pi$
$683$	−13.9286	−	24.1251i	−0.532964	−	0.923121i	0.466295	−	0.884629i	$-0.345589\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	27.2386	−	47.1786i	1.03922	−	1.79998i
$688$		0			0
$689$	45.2158	+	4.17274i	1.72258	+	0.158969i
$690$		0			0
$691$	31.4550	+	18.1606i	1.19661	+	0.690860i	0.959797	−	0.280696i	$-0.0905652\pi$
$691$	31.4550	+	18.1606i	1.19661	+	0.690860i	0.236809	+	0.971556i	$0.423899\pi$
$692$		0			0
$693$	15.6827	−	9.05440i	0.595736	−	0.343948i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−15.4853			−0.586548
$698$		0			0
$699$	3.51651	−	6.09077i	0.133007	−	0.230374i
$700$		0			0
$701$	2.16156			0.0816411			0.0408206	−	0.999166i	$-0.487003\pi$
$701$	2.16156			0.0816411			0.0408206	+	0.999166i	$0.487003\pi$
$702$		0			0
$703$		−	10.4249i		−	0.393183i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	7.67250			0.288554
$708$		0			0
$709$	41.2371	−	23.8082i	1.54869	−	0.894137i	0.550449	−	0.834869i	$-0.314457\pi$
$709$	41.2371	−	23.8082i	1.54869	−	0.894137i	0.998242	−	0.0592680i	$-0.0188767\pi$
$710$		0			0
$711$	−33.8713	−	58.6668i	−1.27027	−	2.20018i
$712$		0			0
$713$	−22.8408	+	39.5615i	−0.855396	+	1.48159i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	23.7137	−	41.0733i	0.885603	−	1.53391i
$718$		0			0
$719$	10.1469	+	17.5749i	0.378414	+	0.655433i	0.990832	−	0.135102i	$-0.0431361\pi$
$719$	10.1469	+	17.5749i	0.378414	+	0.655433i	−0.612417	+	0.790535i	$0.709803\pi$
$720$		0			0
$721$	−24.9996	+	14.4335i	−0.931035	+	0.537533i
$722$		0			0
$723$	82.2029			3.05716
$724$		0			0
$725$		0			0
$726$		0			0
$727$			11.0681i			0.410494i	0.978710	+	0.205247i	$0.0657998\pi$
$727$			11.0681i			0.410494i	−0.978710	+	0.205247i	$0.934200\pi$
$728$		0			0
$729$	43.0532			1.59456
$730$		0			0
$731$	16.9527	−	29.3630i	0.627019	−	1.08603i
$732$		0			0
$733$	23.4002			0.864304			0.432152	−	0.901801i	$-0.357754\pi$
$733$	23.4002			0.864304			0.432152	+	0.901801i	$0.357754\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	16.2501	−	9.38201i	0.598581	−	0.345591i
$738$		0			0
$739$	22.1617	+	12.7951i	0.815232	+	0.470675i	0.848770	−	0.528763i	$-0.177344\pi$
$739$	22.1617	+	12.7951i	0.815232	+	0.470675i	−0.0335372	+	0.999437i	$0.510677\pi$
$740$		0			0
$741$	1.00161	−	10.8534i	0.0367951	−	0.398711i
$742$		0			0
$743$	4.20712	−	7.28694i	0.154344	−	0.267332i	−0.778476	−	0.627675i	$-0.784007\pi$
$743$	4.20712	−	7.28694i	0.154344	−	0.267332i	0.932820	+	0.360343i	$0.117340\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−39.4102	−	68.2605i	−1.44194	−	2.49752i
$748$		0			0
$749$			6.78106i			0.247775i
$750$		0			0
$751$	20.2595	−	35.0905i	0.739279	−	1.28047i	−0.213541	−	0.976934i	$-0.568500\pi$
$751$	20.2595	−	35.0905i	0.739279	−	1.28047i	0.952820	−	0.303535i	$-0.0981671\pi$
$752$		0			0
$753$			54.0514i			1.96974i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	9.83100	+	5.67593i	0.357314	+	0.206295i	0.667902	−	0.744249i	$-0.267193\pi$
$757$	9.83100	+	5.67593i	0.357314	+	0.206295i	−0.310588	+	0.950545i	$0.600526\pi$
$758$		0			0
$759$			38.2780i			1.38940i
$760$		0			0
$761$	−5.86364	+	3.38538i	−0.212557	+	0.122720i	−0.602499	−	0.798120i	$-0.705828\pi$
$761$	−5.86364	+	3.38538i	−0.212557	+	0.122720i	0.389942	+	0.920839i	$0.372495\pi$
$762$		0			0
$763$	−16.5627	+	9.56249i	−0.599611	+	0.346185i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.11707	+	4.59704i	0.0764428	+	0.165990i
$768$		0			0
$769$	20.0563	+	11.5795i	0.723250	+	0.417569i	0.815948	−	0.578126i	$-0.196216\pi$
$769$	20.0563	+	11.5795i	0.723250	+	0.417569i	−0.0926975	+	0.995694i	$0.529549\pi$
$770$		0			0
$771$	19.3766	+	33.5613i	0.697833	+	1.20868i
$772$		0			0
$773$	−20.9770	−	36.3333i	−0.754491	−	1.30682i	−0.945627	−	0.325253i	$-0.894551\pi$
$773$	−20.9770	−	36.3333i	−0.754491	−	1.30682i	0.191136	−	0.981564i	$-0.438783\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	49.9928	+	28.8634i	1.79348	+	1.03547i
$778$		0			0
$779$	4.56410			0.163526
$780$		0			0
$781$	−24.5418			−0.878174
$782$		0			0
$783$	−2.56830	−	1.48281i	−0.0917835	−	0.0529913i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	18.7076	+	32.4026i	0.666856	+	1.15503i	0.978779	+	0.204920i	$0.0656936\pi$
$787$	18.7076	+	32.4026i	0.666856	+	1.15503i	−0.311923	+	0.950107i	$0.600973\pi$
$788$		0			0
$789$	−16.8388	−	29.1656i	−0.599476	−	1.03832i
$790$		0			0
$791$	−19.8714	−	11.4727i	−0.706544	−	0.407923i
$792$		0			0
$793$	−36.3808	+	16.7544i	−1.29192	+	0.594965i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−40.9110	+	23.6200i	−1.44914	+	0.836663i	−0.998430	−	0.0560071i	$-0.982163\pi$
$797$	−40.9110	+	23.6200i	−1.44914	+	0.836663i	−0.450712	+	0.892670i	$0.648830\pi$
$798$		0			0
$799$	10.8848	−	6.28436i	0.385078	−	0.222325i
$800$		0			0
$801$			27.5729i			0.974240i
$802$		0			0
$803$	3.96704	+	2.29037i	0.139994	+	0.0808254i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		−	59.1692i		−	2.08286i
$808$		0			0
$809$	−23.2371	+	40.2478i	−0.816972	+	1.41504i	0.0909313	+	0.995857i	$0.471016\pi$
$809$	−23.2371	+	40.2478i	−0.816972	+	1.41504i	−0.907903	+	0.419180i	$0.862318\pi$
$810$		0			0
$811$		−	11.4041i		−	0.400453i	−0.979750	−	0.200227i	$-0.935832\pi$
$811$		−	11.4041i		−	0.400453i	0.979750	−	0.200227i	$-0.0641678\pi$
$812$		0			0
$813$	2.75844	+	4.77777i	0.0967429	+	0.167564i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−4.99660	+	8.65436i	−0.174809	+	0.302778i
$818$		0			0
$819$	30.7759	+	21.7685i	1.07540	+	0.760652i
$820$		0			0
$821$	−21.2709	−	12.2808i	−0.742359	−	0.428601i	0.0805674	−	0.996749i	$-0.474327\pi$
$821$	−21.2709	−	12.2808i	−0.742359	−	0.428601i	−0.822926	+	0.568148i	$0.807660\pi$
$822$		0			0
$823$	2.56731	−	1.48224i	0.0894909	−	0.0516676i	−0.454587	−	0.890702i	$-0.650213\pi$
$823$	2.56731	−	1.48224i	0.0894909	−	0.0516676i	0.544078	+	0.839035i	$0.316880\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	17.7265			0.616412			0.308206	−	0.951320i	$-0.400271\pi$
$827$	17.7265			0.616412			0.308206	+	0.951320i	$0.400271\pi$
$828$		0			0
$829$	5.78791	−	10.0250i	0.201022	−	0.348181i	−0.747836	−	0.663884i	$-0.768907\pi$
$829$	5.78791	−	10.0250i	0.201022	−	0.348181i	0.948858	+	0.315703i	$0.102240\pi$
$830$		0			0
$831$	−35.2804			−1.22386
$832$		0			0
$833$		−	9.47657i		−	0.328344i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−32.8874			−1.13676
$838$		0			0
$839$	−37.1348	+	21.4398i	−1.28203	+	0.740183i	−0.977220	−	0.212229i	$-0.931928\pi$
$839$	−37.1348	+	21.4398i	−1.28203	+	0.740183i	−0.304815	+	0.952412i	$0.598595\pi$
$840$		0			0
$841$	14.3612	+	24.8743i	0.495213	+	0.857734i
$842$		0			0
$843$	3.24454	−	5.61971i	0.111748	−	0.193553i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−8.37915	+	14.5131i	−0.287911	+	0.498677i
$848$		0			0
$849$	−21.1019	−	36.5496i	−0.724215	−	1.25438i
$850$		0			0
$851$	−66.0016	+	38.1060i	−2.26251	+	1.30626i
$852$		0			0
$853$	13.4599			0.460857			0.230428	−	0.973089i	$-0.425987\pi$
$853$	13.4599			0.460857			0.230428	+	0.973089i	$0.425987\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	10.5950i		−	0.361919i	−0.983491	−	0.180960i	$-0.942080\pi$
$857$		−	10.5950i		−	0.361919i	0.983491	−	0.180960i	$-0.0579204\pi$
$858$		0			0
$859$	8.75716			0.298791			0.149395	−	0.988778i	$-0.452267\pi$
$859$	8.75716			0.298791			0.149395	+	0.988778i	$0.452267\pi$
$860$		0			0
$861$	−12.6366	+	21.8872i	−0.430654	+	0.745915i
$862$		0			0
$863$	−30.8640			−1.05062			−0.525311	−	0.850910i	$-0.676051\pi$
$863$	−30.8640			−1.05062			−0.525311	+	0.850910i	$0.676051\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−9.38997	+	5.42130i	−0.318900	+	0.184117i
$868$		0			0
$869$	−20.3593	−	11.7545i	−0.690643	−	0.398743i
$870$		0			0
$871$	31.8895	+	22.5561i	1.08053	+	0.764285i
$872$		0			0
$873$	37.9182	−	65.6763i	1.28334	−	2.22281i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	10.0518	+	17.4103i	0.339427	+	0.587904i	0.984325	−	0.176364i	$-0.0564336\pi$
$877$	10.0518	+	17.4103i	0.339427	+	0.587904i	−0.644898	+	0.764268i	$0.723100\pi$
$878$		0			0
$879$		−	4.04839i		−	0.136549i
$880$		0			0
$881$	1.56698	−	2.71409i	0.0527930	−	0.0914401i	−0.838421	−	0.545023i	$-0.816521\pi$
$881$	1.56698	−	2.71409i	0.0527930	−	0.0914401i	0.891214	+	0.453583i	$0.149854\pi$
$882$		0			0
$883$			34.0429i			1.14563i	0.819683	+	0.572817i	$0.194149\pi$
$883$			34.0429i			1.14563i	−0.819683	+	0.572817i	$0.805851\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−44.0001	−	25.4034i	−1.47738	−	0.852964i	−0.477704	−	0.878521i	$-0.658531\pi$
$887$	−44.0001	−	25.4034i	−1.47738	−	0.852964i	−0.999673	+	0.0255565i	$0.991864\pi$
$888$		0			0
$889$		−	1.90127i		−	0.0637666i
$890$		0			0
$891$	−1.40578	+	0.811629i	−0.0470955	+	0.0271906i
$892$		0			0
$893$	−3.20817	+	1.85224i	−0.107357	+	0.0619827i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−72.3758	+	33.3311i	−2.41656	+	1.11289i
$898$		0			0
$899$	−2.66640	−	1.53944i	−0.0889293	−	0.0513434i
$900$		0			0
$901$	−22.8471	−	39.5723i	−0.761147	−	1.31834i
$902$		0			0
$903$	−27.6681	−	47.9226i	−0.920737	−	1.59476i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−44.1331	−	25.4803i	−1.46542	−	0.846058i	−0.466163	−	0.884699i	$-0.654364\pi$
$907$	−44.1331	−	25.4803i	−1.46542	−	0.846058i	−0.999253	+	0.0386406i	$0.987697\pi$
$908$		0			0
$909$	−18.2804			−0.606323
$910$		0			0
$911$	−23.7176			−0.785800			−0.392900	−	0.919581i	$-0.628528\pi$
$911$	−23.7176			−0.785800			−0.392900	+	0.919581i	$0.628528\pi$
$912$		0			0
$913$	−23.6887	−	13.6767i	−0.783981	−	0.452632i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	13.7864	+	23.8788i	0.455269	+	0.788548i
$918$		0			0
$919$	−21.1516	−	36.6356i	−0.697725	−	1.20850i	−0.969253	−	0.246065i	$-0.920862\pi$
$919$	−21.1516	−	36.6356i	−0.697725	−	1.20850i	0.271528	−	0.962431i	$-0.412471\pi$
$920$		0			0
$921$	−42.5563	−	24.5699i	−1.40228	−	0.809606i
$922$		0			0
$923$	−21.3701	−	46.4034i	−0.703405	−	1.52739i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	59.5638	−	34.3892i	1.95633	−	1.12949i
$928$		0			0
$929$	11.5432	−	6.66449i	0.378721	−	0.218655i	−0.298541	−	0.954397i	$-0.596500\pi$
$929$	11.5432	−	6.66449i	0.378721	−	0.218655i	0.677262	+	0.735742i	$0.263166\pi$
$930$		0			0
$931$			2.79310i			0.0915402i
$932$		0			0
$933$	−49.4922	−	28.5743i	−1.62030	−	0.935481i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			14.0848i			0.460129i	0.973175	+	0.230065i	$0.0738937\pi$
$937$			14.0848i			0.460129i	−0.973175	+	0.230065i	$0.926106\pi$
$938$		0			0
$939$	−6.87523	+	11.9082i	−0.224365	+	0.388611i
$940$		0			0
$941$			49.0399i			1.59866i	0.600895	+	0.799328i	$0.294811\pi$
$941$			49.0399i			1.59866i	−0.600895	+	0.799328i	$0.705189\pi$
$942$		0			0
$943$	−16.6831	−	28.8960i	−0.543277	−	0.940983i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	8.96760	−	15.5323i	0.291408	−	0.504733i	−0.682735	−	0.730666i	$-0.739210\pi$
$947$	8.96760	−	15.5323i	0.291408	−	0.504733i	0.974143	+	0.225933i	$0.0725430\pi$
$948$		0			0
$949$	−0.876268	+	9.49523i	−0.0284449	+	0.308228i
$950$		0			0
$951$	57.8189	+	33.3818i	1.87491	+	1.08248i
$952$		0			0
$953$	38.4368	−	22.1915i	1.24509	−	0.718853i	0.274964	−	0.961454i	$-0.411334\pi$
$953$	38.4368	−	22.1915i	1.24509	−	0.718853i	0.970126	+	0.242601i	$0.0780006\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−2.57989			−0.0833960
$958$		0			0
$959$	12.6366	−	21.8872i	0.408057	−	0.706776i
$960$		0			0
$961$	−3.14359			−0.101406
$962$		0			0
$963$		−	16.1565i		−	0.520635i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−24.3595			−0.783348			−0.391674	−	0.920104i	$-0.628104\pi$
$967$	−24.3595			−0.783348			−0.391674	+	0.920104i	$0.628104\pi$
$968$		0			0
$969$	−9.49879	+	5.48413i	−0.305145	+	0.176176i
$970$		0			0
$971$	0.587359	+	1.01734i	0.0188492	+	0.0326478i	0.875296	−	0.483587i	$-0.160666\pi$
$971$	0.587359	+	1.01734i	0.0188492	+	0.0326478i	−0.856447	+	0.516235i	$0.827333\pi$
$972$		0			0
$973$	−5.87783	+	10.1807i	−0.188435	+	0.326378i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−6.15505	+	10.6609i	−0.196917	+	0.341071i	−0.947527	−	0.319675i	$-0.896426\pi$
$977$	−6.15505	+	10.6609i	−0.196917	+	0.341071i	0.750610	+	0.660746i	$0.229760\pi$
$978$		0			0
$979$	4.78436	+	8.28676i	0.152909	+	0.264846i
$980$		0			0
$981$	39.4621	−	22.7835i	1.25993	−	0.727420i
$982$		0			0
$983$	2.29060			0.0730589			0.0365295	−	0.999333i	$-0.488370\pi$
$983$	2.29060			0.0730589			0.0365295	+	0.999333i	$0.488370\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		−	20.5131i		−	0.652940i
$988$		0			0
$989$	73.0560			2.32305
$990$		0			0
$991$	−10.8499	+	18.7926i	−0.344659	+	0.596967i	−0.985292	−	0.170880i	$-0.945339\pi$
$991$	−10.8499	+	18.7926i	−0.344659	+	0.596967i	0.640633	+	0.767848i	$0.278672\pi$
$992$		0			0
$993$	−42.0628			−1.33482
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−16.5086	+	9.53125i	−0.522833	+	0.301858i	−0.738093	−	0.674699i	$-0.764273\pi$
$997$	−16.5086	+	9.53125i	−0.522833	+	0.301858i	0.215260	+	0.976557i	$0.430940\pi$
$998$		0			0
$999$	−47.5163	−	27.4335i	−1.50335	−	0.867959i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1300.2.ba.c.849.4		8
5.2	odd	4		1300.2.y.b.901.4		8
5.3	odd	4		260.2.x.a.121.1	yes	8
5.4	even	2		1300.2.ba.b.849.1		8
13.10	even	6		1300.2.ba.b.49.1		8
15.8	even	4		2340.2.dj.d.901.1		8
20.3	even	4		1040.2.da.c.641.4		8
65.23	odd	12		260.2.x.a.101.1	✓	8
65.33	even	12		3380.2.a.p.1.4		4
65.43	odd	12		3380.2.f.i.3041.7		8
65.48	odd	12		3380.2.f.i.3041.8		8
65.49	even	6	inner	1300.2.ba.c.49.4		8
65.58	even	12		3380.2.a.q.1.4		4
65.62	odd	12		1300.2.y.b.101.4		8
195.23	even	12		2340.2.dj.d.361.3		8
260.23	even	12		1040.2.da.c.881.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.x.a.101.1	✓	8	65.23	odd	12
260.2.x.a.121.1	yes	8	5.3	odd	4
1040.2.da.c.641.4		8	20.3	even	4
1040.2.da.c.881.4		8	260.23	even	12
1300.2.y.b.101.4		8	65.62	odd	12
1300.2.y.b.901.4		8	5.2	odd	4
1300.2.ba.b.49.1		8	13.10	even	6
1300.2.ba.b.849.1		8	5.4	even	2
1300.2.ba.c.49.4		8	65.49	even	6	inner
1300.2.ba.c.849.4		8	1.1	even	1	trivial
2340.2.dj.d.361.3		8	195.23	even	12
2340.2.dj.d.901.1		8	15.8	even	4
3380.2.a.p.1.4		4	65.33	even	12
3380.2.a.q.1.4		4	65.58	even	12
3380.2.f.i.3041.7		8	65.43	odd	12
3380.2.f.i.3041.8		8	65.48	odd	12

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:	\( N \)	\(=\)	\( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1300.ba (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.44811 + 1.41342i) q^{3} +(-1.04739 - 1.81414i) q^{7} +(2.49551 + 4.32235i) q^{9} +O(q^{10})\)	\(q+(2.44811 + 1.41342i) q^{3} +(-1.04739 - 1.81414i) q^{7} +(2.49551 + 4.32235i) q^{9} +(1.50000 + 0.866025i) q^{11} +(-0.331331 + 3.59030i) q^{13} +(3.14218 - 1.81414i) q^{17} +(-0.926118 + 0.534695i) q^{19} -5.92163i q^{21} +(6.77046 + 3.90893i) q^{23} +5.62828i q^{27} +(-0.263457 + 0.456321i) q^{29} +5.84325i q^{31} +(2.44811 + 4.24026i) q^{33} +(-4.87423 + 8.44242i) q^{37} +(-5.88573 + 8.32114i) q^{39} +(-3.69615 - 2.13397i) q^{41} +(8.09281 - 4.67238i) q^{43} +3.46410 q^{47} +(1.30593 - 2.26194i) q^{49} +10.2566 q^{51} -12.5939i q^{53} -3.02299 q^{57} +(1.21564 - 0.701848i) q^{59} +(5.55440 + 9.62050i) q^{61} +(5.22756 - 9.05440i) q^{63} +(5.41671 - 9.38201i) q^{67} +(11.0499 + 19.1390i) q^{69} +(-12.2709 + 7.08460i) q^{71} +2.64469 q^{73} -3.62828i q^{77} -13.5729 q^{79} +(-0.468594 + 0.811629i) q^{81} -15.7925 q^{83} +(-1.28994 + 0.744750i) q^{87} +(4.78436 + 2.76225i) q^{89} +(6.86033 - 3.15937i) q^{91} +(-8.25896 + 14.3049i) q^{93} +(-7.59730 - 13.1589i) q^{97} +8.64469i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} - 6 q^{7} + 4 q^{9}+O(q^{10}) \) 8 * q + 6 * q^3 - 6 * q^7 + 4 * q^9	\( 8 q + 6 q^{3} - 6 q^{7} + 4 q^{9} + 12 q^{11} + 18 q^{17} + 6 q^{23} + 6 q^{33} - 18 q^{37} + 4 q^{39} + 12 q^{41} - 18 q^{43} + 4 q^{49} + 36 q^{57} + 24 q^{59} - 4 q^{61} + 12 q^{63} + 18 q^{67} + 24 q^{69} - 36 q^{71} - 48 q^{73} + 16 q^{79} + 8 q^{81} - 72 q^{83} - 18 q^{87} + 24 q^{89} - 48 q^{93} + 6 q^{97}+O(q^{100}) \) 8 * q + 6 * q^3 - 6 * q^7 + 4 * q^9 + 12 * q^11 + 18 * q^17 + 6 * q^23 + 6 * q^33 - 18 * q^37 + 4 * q^39 + 12 * q^41 - 18 * q^43 + 4 * q^49 + 36 * q^57 + 24 * q^59 - 4 * q^61 + 12 * q^63 + 18 * q^67 + 24 * q^69 - 36 * q^71 - 48 * q^73 + 16 * q^79 + 8 * q^81 - 72 * q^83 - 18 * q^87 + 24 * q^89 - 48 * q^93 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more