LMFDB - Embedded newform 1300.2.ba.c.49.4

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			49.4
Root			$1.20036 - 0.747754i$ of defining polynomial
Character	$\chi$	$=$	1300.49
Dual form			1300.2.ba.c.849.4

$q$-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 $\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times$.

$n$	$301$	$651$	$677$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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	0.417710	−	0.908580i	$-0.362833\pi$
$3$	2.44811	−	1.41342i	1.41342	−	0.816038i	0.995709	+	0.0925423i	$0.0294993\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.04739	+	1.81414i	−0.395878	+	0.685680i	−0.993213	−	0.116312i	$-0.962893\pi$
$7$	−1.04739	+	1.81414i	−0.395878	+	0.685680i	0.597335	+	0.801992i	$0.296226\pi$
$8$		0			0
$9$	2.49551	−	4.32235i	0.831836	−	1.44078i
$10$		0			0
$11$	1.50000	−	0.866025i	0.452267	−	0.261116i	−0.256520	−	0.966539i	$-0.582576\pi$
$11$	1.50000	−	0.866025i	0.452267	−	0.261116i	0.708787	+	0.705422i	$0.249243\pi$
$12$		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	0.830046	−	0.557695i	$-0.188314\pi$
$17$	3.14218	+	1.81414i	0.762091	+	0.439993i	−0.0679550	+	0.997688i	$0.521647\pi$
$18$		0			0
$19$	−0.926118	−	0.534695i	−0.212466	−	0.122667i	0.389991	−	0.920819i	$-0.372478\pi$
$19$	−0.926118	−	0.534695i	−0.212466	−	0.122667i	−0.602457	+	0.798151i	$0.705811\pi$
$20$		0			0
$21$			5.92163i			1.29220i
$22$		0			0
$23$	6.77046	−	3.90893i	1.41174	−	0.815068i	0.416186	−	0.909279i	$-0.363366\pi$
$23$	6.77046	−	3.90893i	1.41174	−	0.815068i	0.995552	+	0.0942118i	$0.0300331\pi$
$24$		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	0.840527	−	0.541770i	$-0.182245\pi$
$29$	−0.263457	−	0.456321i	−0.0489227	−	0.0847366i	−0.889450	+	0.457033i	$0.848912\pi$
$30$		0			0
$31$		−	5.84325i		−	1.04948i	−0.851263	−	0.524740i	$-0.824163\pi$
$31$		−	5.84325i		−	1.04948i	0.851263	−	0.524740i	$-0.175837\pi$
$32$		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	−0.918748	−	0.394844i	$-0.870799\pi$
$37$	−4.87423	−	8.44242i	−0.801319	−	1.38792i	0.117429	−	0.993081i	$-0.462535\pi$
$38$		0			0
$39$	−5.88573	−	8.32114i	−0.942471	−	1.33245i
$40$		0			0
$41$	−3.69615	+	2.13397i	−0.577242	+	0.333271i	−0.760037	−	0.649880i	$-0.774819\pi$
$41$	−3.69615	+	2.13397i	−0.577242	+	0.333271i	0.182795	+	0.983151i	$0.441486\pi$
$42$		0			0
$43$	8.09281	+	4.67238i	1.23414	+	0.712532i	0.967891	−	0.251372i	$-0.0808817\pi$
$43$	8.09281	+	4.67238i	1.23414	+	0.712532i	0.266251	+	0.963904i	$0.414215\pi$
$44$		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	$0.332651\pi$
$53$			12.5939i			1.72990i	−0.501854	+	0.864952i	$0.667349\pi$
$54$		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	0.577040	−	0.816716i	$-0.304208\pi$
$59$	1.21564	+	0.701848i	0.158262	+	0.0913729i	−0.418777	+	0.908089i	$0.637541\pi$
$60$		0			0
$61$	5.55440	−	9.62050i	0.711168	−	1.23178i	−0.253251	−	0.967400i	$-0.581500\pi$
$61$	5.55440	−	9.62050i	0.711168	−	1.23178i	0.964419	−	0.264378i	$-0.0851667\pi$
$62$		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	0.980154	+	0.198238i	$0.0635219\pi$
$67$	5.41671	+	9.38201i	0.661756	+	1.14620i	−0.318398	+	0.947957i	$0.603145\pi$
$68$		0			0
$69$	11.0499	−	19.1390i	1.33025	−	2.30406i
$70$		0			0
$71$	−12.2709	−	7.08460i	−1.45629	−	0.840787i	−0.457460	−	0.889230i	$-0.651241\pi$
$71$	−12.2709	−	7.08460i	−1.45629	−	0.840787i	−0.998826	+	0.0484428i	$0.984574\pi$
$72$		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	−0.224516	−	0.974470i	$-0.572080\pi$
$89$	4.78436	−	2.76225i	0.507141	−	0.292798i	0.731658	+	0.681672i	$0.238747\pi$
$90$		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	0.165413	+	0.986224i	$0.447104\pi$
$97$	−7.59730	+	13.1589i	−0.771389	+	1.33608i	−0.936802	+	0.349860i	$0.886229\pi$
$98$		0			0
$99$		−	8.64469i		−	0.868824i
$100$		0			0
$101$	−1.83133	−	3.17196i	−0.182224	−	0.315622i	0.760413	−	0.649439i	$-0.224996\pi$
$101$	−1.83133	−	3.17196i	−0.182224	−	0.315622i	−0.942638	+	0.333818i	$0.891663\pi$
$102$		0			0
$103$			13.7804i			1.35783i	0.734218	+	0.678914i	$0.237549\pi$
$103$			13.7804i			1.35783i	−0.734218	+	0.678914i	$0.762451\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.80342	+	1.61856i	−0.271017	+	0.156472i	−0.629350	−	0.777122i	$-0.716679\pi$
$107$	−2.80342	+	1.61856i	−0.271017	+	0.156472i	0.358333	+	0.933594i	$0.383345\pi$
$108$		0			0
$109$			9.12979i			0.874476i	0.899346	+	0.437238i	$0.144043\pi$
$109$			9.12979i			0.874476i	−0.899346	+	0.437238i	$0.855957\pi$
$110$		0			0
$111$	−23.8654	−	13.7787i	−2.26520	−	1.30781i
$112$		0			0
$113$	9.48610	+	5.47680i	0.892377	+	0.515214i	0.874719	−	0.484630i	$-0.161046\pi$
$113$	9.48610	+	5.47680i	0.892377	+	0.515214i	0.0176577	+	0.999844i	$0.494379\pi$
$114$		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	−0.464720	−	0.885458i	$-0.653845\pi$
$127$	0.786022	−	0.453810i	0.0697482	−	0.0402691i	0.534469	+	0.845188i	$0.320512\pi$
$128$		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	−0.484458	−	0.874815i	$-0.660983\pi$
$137$	6.03240	−	10.4484i	0.515383	−	0.892669i	0.999841	−	0.0178546i	$-0.00568359\pi$
$138$		0			0
$139$	−2.80593	+	4.86002i	−0.237996	+	0.412221i	−0.960139	−	0.279522i	$-0.909824\pi$
$139$	−2.80593	+	4.86002i	−0.237996	+	0.412221i	0.722143	+	0.691744i	$0.243157\pi$
$140$		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	−0.489168	−	0.872189i	$-0.662700\pi$
$149$	−18.1767	−	10.4943i	−1.48909	−	0.859727i	−0.999922	+	0.0124625i	$0.996033\pi$
$150$		0			0
$151$			6.99102i			0.568921i	0.958688	+	0.284460i	$0.0918144\pi$
$151$			6.99102i			0.568921i	−0.958688	+	0.284460i	$0.908186\pi$
$152$		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	$-0.952219\pi$
$157$		−	3.74761i		−	0.299092i	0.988755	−	0.149546i	$-0.0477812\pi$
$158$		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	−0.713675	−	0.700477i	$-0.752971\pi$
$163$	3.18915	−	5.52377i	0.249793	−	0.432655i	0.963468	+	0.267822i	$0.0863039\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.76445	+	13.4484i	0.600831	+	1.04067i	0.992695	+	0.120647i	$0.0384970\pi$
$167$	7.76445	+	13.4484i	0.600831	+	1.04067i	−0.391864	+	0.920023i	$0.628170\pi$
$168$		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	0.334456	−	0.942411i	$-0.391447\pi$
$173$	−4.13617	−	2.38802i	−0.314467	−	0.181558i	−0.648924	+	0.760853i	$0.724781\pi$
$174$		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	−0.994644	−	0.103363i	$-0.967040\pi$
$179$	−7.85134	−	13.5989i	−0.586837	−	1.01643i	0.407807	−	0.913068i	$-0.366294\pi$
$180$		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	−0.737886	−	0.674925i	$-0.764176\pi$
$191$	2.97909	−	5.15994i	0.215560	−	0.373360i	0.953446	+	0.301565i	$0.0975091\pi$
$192$		0			0
$193$	6.38473	+	11.0587i	0.459583	+	0.796021i	0.998939	−	0.0460568i	$-0.0146655\pi$
$193$	6.38473	+	11.0587i	0.459583	+	0.796021i	−0.539356	+	0.842078i	$0.681332\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	8.05397	+	13.9499i	0.573822	+	0.993888i	0.996169	+	0.0874540i	$0.0278731\pi$
$197$	8.05397	+	13.9499i	0.573822	+	0.993888i	−0.422347	+	0.906434i	$0.638794\pi$
$198$		0			0
$199$	4.26403	−	7.38551i	0.302269	−	0.523545i	−0.674381	−	0.738384i	$-0.735589\pi$
$199$	4.26403	−	7.38551i	0.302269	−	0.523545i	0.976650	+	0.214839i	$0.0689226\pi$
$200$		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	0.928963	−	0.370173i	$-0.120702\pi$
$211$	2.09030	+	3.62050i	0.143902	+	0.249245i	−0.785061	+	0.619419i	$0.787368\pi$
$212$		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	0.634983	−	0.772526i	$-0.281007\pi$
$223$	−5.24955	−	9.09249i	−0.351536	−	0.608878i	−0.986519	+	0.163648i	$0.947674\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.79288	−	13.4977i	0.517232	−	0.895872i	−0.482568	−	0.875858i	$-0.660296\pi$
$227$	7.79288	−	13.4977i	0.517232	−	0.895872i	0.999800	−	0.0200131i	$-0.00637079\pi$
$228$		0			0
$229$			19.2714i			1.27349i	0.771074	+	0.636745i	$0.219720\pi$
$229$			19.2714i			1.27349i	−0.771074	+	0.636745i	$0.780280\pi$
$230$		0			0
$231$	5.12828	+	8.88244i	0.337416	+	0.584422i
$232$		0			0
$233$			2.48794i			0.162991i	0.996674	+	0.0814953i	$0.0259696\pi$
$233$			2.48794i			0.162991i	−0.996674	+	0.0814953i	$0.974030\pi$
$234$		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	$0.182569\pi$
$239$			16.7775i			1.08525i	−0.839976	+	0.542624i	$0.817431\pi$
$240$		0			0
$241$	25.1835	+	14.5397i	1.62221	+	0.936585i	0.986326	+	0.164803i	$0.0526990\pi$
$241$	25.1835	+	14.5397i	1.62221	+	0.936585i	0.635887	+	0.771782i	$0.280634\pi$
$242$		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	−0.388847	−	0.921302i	$-0.627127\pi$
$251$	9.56040	−	16.5591i	0.603447	−	1.04520i	0.992295	−	0.123899i	$-0.0395400\pi$
$252$		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	−0.0817004	−	0.996657i	$-0.526035\pi$
$257$	11.8724	−	6.85453i	0.740580	−	0.427574i	0.822280	+	0.569083i	$0.192702\pi$
$258$		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	−0.783148	−	0.621835i	$-0.786387\pi$
$263$	−10.3174	+	5.95675i	−0.636197	+	0.367309i	0.146951	+	0.989144i	$0.453054\pi$
$264$		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	0.347749	+	0.937588i	$0.386946\pi$
$269$	−10.4656	+	18.1270i	−0.638100	+	1.10522i	−0.985849	+	0.167634i	$0.946387\pi$
$270$		0			0
$271$	1.69014	−	0.975805i	0.102669	−	0.0592760i	−0.447786	−	0.894141i	$-0.647787\pi$
$271$	1.69014	−	0.975805i	0.102669	−	0.0592760i	0.550455	+	0.834865i	$0.314454\pi$
$272$		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	0.138816	−	0.990318i	$-0.455670\pi$
$277$	−10.8084	−	6.24026i	−0.649416	−	0.374941i	−0.788233	+	0.615377i	$0.789004\pi$
$278$		0			0
$279$	−25.2566	−	14.5819i	−1.51207	−	0.872994i
$280$		0			0
$281$			2.29553i			0.136940i	0.997653	+	0.0684698i	$0.0218117\pi$
$281$			2.29553i			0.136940i	−0.997653	+	0.0684698i	$0.978188\pi$
$282$		0			0
$283$	−12.9295	+	7.46484i	−0.768578	+	0.443739i	−0.832367	−	0.554225i	$-0.813015\pi$
$283$	−12.9295	+	7.46484i	−0.768578	+	0.443739i	0.0637892	+	0.997963i	$0.479681\pi$
$284$		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	−0.886184	−	0.463334i	$-0.846653\pi$
$293$	−0.716063	+	1.24026i	−0.0418329	+	0.0724566i	0.844351	+	0.535791i	$0.179986\pi$
$294$		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	$-0.956102\pi$
$313$		−	4.86425i		−	0.274944i	0.990506	−	0.137472i	$-0.0438977\pi$
$314$		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	0.102134	−	0.994771i	$-0.467433\pi$
$331$	−12.8863	−	7.43991i	−0.708295	−	0.408934i	−0.810429	+	0.585836i	$0.800766\pi$
$332$		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	$0.292559\pi$
$337$			29.1906i			1.59012i	−0.606534	+	0.795058i	$0.707441\pi$
$338$		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	−0.183252	−	0.983066i	$-0.558662\pi$
$347$	−20.9795	−	12.1125i	−1.12624	−	0.650234i	−0.942986	+	0.332833i	$0.891996\pi$
$348$		0			0
$349$	11.1557	−	6.44076i	0.597152	−	0.344766i	−0.170768	−	0.985311i	$-0.554625\pi$
$349$	11.1557	−	6.44076i	0.597152	−	0.344766i	0.767920	+	0.640545i	$0.221292\pi$
$350$		0			0
$351$	−20.2072	+	1.86482i	−1.07858	+	0.0995368i
$352$		0			0
$353$	8.10837	+	14.0441i	0.431565	+	0.747492i	0.997008	−	0.0772948i	$-0.0246283\pi$
$353$	8.10837	+	14.0441i	0.431565	+	0.747492i	−0.565443	+	0.824787i	$0.691295\pi$
$354$		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	$0.0779949\pi$
$359$			9.19261i			0.485167i	−0.970131	+	0.242584i	$0.922005\pi$
$360$		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	−0.392377	−	0.919804i	$-0.628347\pi$
$367$	3.98486	−	2.30066i	0.208008	−	0.120094i	0.600385	+	0.799711i	$0.295014\pi$
$368$		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	0.883286	−	0.468834i	$-0.155326\pi$
$373$	17.7471	+	10.2463i	0.918908	+	0.530532i	0.0356212	+	0.999365i	$0.488659\pi$
$374$		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	−0.667832	−	0.744312i	$-0.732778\pi$
$379$	−6.95307	+	4.01436i	−0.357155	+	0.206204i	0.310677	+	0.950516i	$0.399444\pi$
$380$		0			0
$381$	1.28285	−	2.22196i	0.0657223	−	0.113834i
$382$		0			0
$383$	15.0712	−	26.1041i	0.770104	−	1.33386i	−0.167401	−	0.985889i	$-0.553538\pi$
$383$	15.0712	−	26.1041i	0.770104	−	1.33386i	0.937505	−	0.347971i	$-0.113129\pi$
$384$		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	−0.991911	−	0.126935i	$-0.959486\pi$
$397$	−7.69152	+	13.3221i	−0.386026	+	0.668617i	0.605885	+	0.795552i	$0.292819\pi$
$398$		0			0
$399$	3.16626	−	5.48413i	0.158511	−	0.274550i
$400$		0			0
$401$	−8.46704	+	4.88845i	−0.422824	+	0.244117i	−0.696285	−	0.717766i	$-0.745165\pi$
$401$	−8.46704	+	4.88845i	−0.422824	+	0.244117i	0.273461	+	0.961883i	$0.411832\pi$
$402$		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	0.478293	−	0.878200i	$-0.341256\pi$
$409$	−0.871721	−	0.503289i	−0.0431039	−	0.0248860i	−0.521397	+	0.853314i	$0.674589\pi$
$410$		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	0.959853	−	0.280503i	$-0.0905013\pi$
$419$	4.85134	+	8.40278i	0.237004	+	0.410502i	−0.722849	+	0.691006i	$0.757168\pi$
$420$		0			0
$421$		−	14.2955i		−	0.696721i	−0.937361	−	0.348361i	$-0.886738\pi$
$421$		−	14.2955i		−	0.696721i	0.937361	−	0.348361i	$-0.113262\pi$
$422$		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	−0.224766	−	0.974413i	$-0.572162\pi$
$431$	10.5197	−	6.07357i	0.506718	−	0.292554i	0.731483	+	0.681859i	$0.238828\pi$
$432$		0			0
$433$	−0.181016	−	0.104510i	−0.00869909	−	0.00502242i	0.495644	−	0.868526i	$-0.334932\pi$
$433$	−0.181016	−	0.104510i	−0.00869909	−	0.00502242i	−0.504343	+	0.863503i	$0.668265\pi$
$434$		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	0.980217	+	0.197926i	$0.0634206\pi$
$439$	13.8603	+	24.0068i	0.661517	+	1.14578i	−0.318700	+	0.947856i	$0.603246\pi$
$440$		0			0
$441$	13.0359			0.620755
$442$		0			0
$443$		−	7.98798i		−	0.379521i	−0.981830	−	0.189760i	$-0.939229\pi$
$443$		−	7.98798i		−	0.379521i	0.981830	−	0.189760i	$-0.0607711\pi$
$444$		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	0.347121	−	0.937820i	$-0.387159\pi$
$449$	−6.17667	−	3.56610i	−0.291495	−	0.168295i	−0.638616	+	0.769526i	$0.720493\pi$
$450$		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	0.952048	+	0.305949i	$0.0989737\pi$
$457$	15.8404	+	27.4364i	0.740984	+	1.28342i	−0.211064	+	0.977472i	$0.567693\pi$
$458$		0			0
$459$	10.2105	−	17.6851i	0.476584	−	0.825468i
$460$		0			0
$461$	−10.2649	−	5.92643i	−0.478083	−	0.276021i	0.241534	−	0.970392i	$-0.422349\pi$
$461$	−10.2649	−	5.92643i	−0.478083	−	0.276021i	−0.719617	+	0.694371i	$0.755683\pi$
$462$		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	$-0.741782\pi$
$467$		−	31.3402i		−	1.45025i	0.688617	−	0.725125i	$-0.258218\pi$
$468$		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	−0.783884	−	0.620908i	$-0.786764\pi$
$479$	−13.9656	+	8.06303i	−0.638103	+	0.368409i	0.145780	+	0.989317i	$0.453431\pi$
$480$		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	−0.922378	−	0.386288i	$-0.873757\pi$
$487$	−2.79501	+	4.84109i	−0.126654	+	0.219371i	0.795724	+	0.605659i	$0.207090\pi$
$488$		0			0
$489$		−	18.0304i		−	0.815364i
$490$		0			0
$491$	−9.14772	−	15.8443i	−0.412831	−	0.715044i	0.582367	−	0.812926i	$-0.302127\pi$
$491$	−9.14772	−	15.8443i	−0.412831	−	0.715044i	−0.995198	+	0.0978817i	$0.968793\pi$
$492$		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	$0.00394627\pi$
$499$			0.553868i			0.0247945i	−0.999923	+	0.0123973i	$0.996054\pi$
$500$		0			0
$501$	38.0165	+	21.9489i	1.69845	+	0.980602i
$502$		0			0
$503$	−12.7161	−	7.34162i	−0.566981	−	0.327347i	0.188962	−	0.981984i	$-0.439488\pi$
$503$	−12.7161	−	7.34162i	−0.566981	−	0.327347i	−0.755943	+	0.654638i	$0.772821\pi$
$504$		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	−0.626952	−	0.779058i	$-0.715698\pi$
$509$	−5.99545	+	3.46148i	−0.265744	+	0.153427i	0.361208	+	0.932485i	$0.382364\pi$
$510$		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	−0.804326	−	0.594188i	$-0.797474\pi$
$523$	−15.8234	+	9.13563i	−0.691908	+	0.399473i	0.112418	+	0.993661i	$0.464140\pi$
$524$		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	$0.240411\pi$
$541$			31.8881i			1.37098i	−0.728084	+	0.685488i	$0.759589\pi$
$542$		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	$-0.592933\pi$
$547$		−	44.7966i		−	1.91537i	0.287826	−	0.957683i	$-0.407067\pi$
$548$		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	−0.997719	−	0.0675037i	$-0.978497\pi$
$557$	−13.1532	−	22.7820i	−0.557319	−	0.965306i	0.440400	−	0.897802i	$-0.354837\pi$
$558$		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	0.390604	−	0.920559i	$-0.372266\pi$
$563$	−5.01415	−	2.89492i	−0.211321	−	0.122006i	−0.601925	+	0.798552i	$0.705599\pi$
$564$		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	0.504534	−	0.863392i	$-0.331664\pi$
$569$	−11.8184	−	20.4700i	−0.495452	−	0.858149i	−0.999986	+	0.00524320i	$0.998331\pi$
$570$		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	0.918303	−	0.395878i	$-0.129560\pi$
$587$	2.81800	+	4.88091i	0.116311	+	0.201457i	−0.801992	+	0.597335i	$0.796226\pi$
$588$		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	0.761566	+	0.648087i	$0.224431\pi$
$601$	23.0945	+	40.0008i	0.942043	+	1.63167i	0.180476	+	0.983579i	$0.442236\pi$
$602$		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	0.866716	−	0.498801i	$-0.166226\pi$
$607$	21.3877	+	12.3482i	0.868100	+	0.501198i	0.00138384	+	0.999999i	$0.499560\pi$
$608$		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	0.647552	−	0.762021i	$-0.275793\pi$
$613$	−8.32277	−	14.4155i	−0.336154	−	0.582235i	−0.983706	+	0.179786i	$0.942459\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.807820	+	1.39918i	−0.0325216	+	0.0563291i	−0.881828	−	0.471571i	$-0.843687\pi$
$617$	−0.807820	+	1.39918i	−0.0325216	+	0.0563291i	0.849307	+	0.527900i	$0.177020\pi$
$618$		0			0
$619$		−	23.3922i		−	0.940213i	−0.882610	−	0.470106i	$-0.844216\pi$
$619$		−	23.3922i		−	0.940213i	0.882610	−	0.470106i	$-0.155784\pi$
$620$		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	0.554209	−	0.832377i	$-0.313021\pi$
$631$	2.77458	+	1.60190i	0.110454	+	0.0637708i	−0.443755	+	0.896148i	$0.646354\pi$
$632$		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	−0.993037	−	0.117801i	$-0.962416\pi$
$641$	−9.98794	+	17.2996i	−0.394500	+	0.683294i	0.598537	+	0.801095i	$0.295749\pi$
$642$		0			0
$643$	14.2684	−	24.7136i	0.562690	−	0.974607i	−0.434571	−	0.900638i	$-0.643100\pi$
$643$	14.2684	−	24.7136i	0.562690	−	0.974607i	0.997260	−	0.0739696i	$-0.0235668\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	5.27107	−	3.04325i	0.207227	−	0.119643i	−0.392795	−	0.919626i	$-0.628492\pi$
$647$	5.27107	−	3.04325i	0.207227	−	0.119643i	0.600022	+	0.799983i	$0.295158\pi$
$648$		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	−0.129016	−	0.991643i	$-0.541182\pi$
$653$	17.0001	−	9.81499i	0.665264	−	0.384090i	0.794280	+	0.607552i	$0.207848\pi$
$654$		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	−0.991299	−	0.131627i	$-0.957980\pi$
$659$	−9.79752	+	16.9698i	−0.381657	+	0.661049i	0.609642	+	0.792677i	$0.291313\pi$
$660$		0			0
$661$	30.0735	−	17.3630i	1.16972	−	0.675341i	0.216109	−	0.976369i	$-0.430663\pi$
$661$	30.0735	−	17.3630i	1.16972	−	0.675341i	0.953615	+	0.301029i	$0.0973300\pi$
$662$		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	0.190082	−	0.981768i	$-0.439125\pi$
$673$	29.4538	−	17.0051i	1.13536	−	0.655500i	0.945277	+	0.326268i	$0.105791\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	29.9209i		−	1.14995i	−0.818169	−	0.574977i	$-0.805011\pi$
$677$		−	29.9209i		−	1.14995i	0.818169	−	0.574977i	$-0.194989\pi$
$678$		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	0.466295	+	0.884629i	$0.345589\pi$
$683$	−13.9286	+	24.1251i	−0.532964	+	0.923121i	−0.999259	+	0.0384916i	$0.987745\pi$
$684$		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	0.236809	−	0.971556i	$-0.423899\pi$
$691$	31.4550	−	18.1606i	1.19661	−	0.690860i	0.959797	+	0.280696i	$0.0905652\pi$
$692$		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	0.998242	+	0.0592680i	$0.0188767\pi$
$709$	41.2371	+	23.8082i	1.54869	+	0.894137i	0.550449	+	0.834869i	$0.314457\pi$
$710$		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	−0.612417	−	0.790535i	$-0.709803\pi$
$719$	10.1469	−	17.5749i	0.378414	−	0.655433i	0.990832	+	0.135102i	$0.0431361\pi$
$720$		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	$-0.934200\pi$
$727$		−	11.0681i		−	0.410494i	0.978710	−	0.205247i	$-0.0657998\pi$
$728$		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	−0.0335372	−	0.999437i	$-0.510677\pi$
$739$	22.1617	−	12.7951i	0.815232	−	0.470675i	0.848770	+	0.528763i	$0.177344\pi$
$740$		0			0
$741$	1.00161	+	10.8534i	0.0367951	+	0.398711i
$742$		0			0
$743$	4.20712	+	7.28694i	0.154344	+	0.267332i	0.932820	−	0.360343i	$-0.117340\pi$
$743$	4.20712	+	7.28694i	0.154344	+	0.267332i	−0.778476	+	0.627675i	$0.784007\pi$
$744$		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	0.952820	+	0.303535i	$0.0981671\pi$
$751$	20.2595	+	35.0905i	0.739279	+	1.28047i	−0.213541	+	0.976934i	$0.568500\pi$
$752$		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	−0.310588	−	0.950545i	$-0.600526\pi$
$757$	9.83100	−	5.67593i	0.357314	−	0.206295i	0.667902	+	0.744249i	$0.267193\pi$
$758$		0			0
$759$		−	38.2780i		−	1.38940i
$760$		0			0
$761$	−5.86364	−	3.38538i	−0.212557	−	0.122720i	0.389942	−	0.920839i	$-0.372495\pi$
$761$	−5.86364	−	3.38538i	−0.212557	−	0.122720i	−0.602499	+	0.798120i	$0.705828\pi$
$762$		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	−0.0926975	−	0.995694i	$-0.529549\pi$
$769$	20.0563	−	11.5795i	0.723250	−	0.417569i	0.815948	+	0.578126i	$0.196216\pi$
$770$		0			0
$771$	19.3766	−	33.5613i	0.697833	−	1.20868i
$772$		0			0
$773$	−20.9770	+	36.3333i	−0.754491	+	1.30682i	0.191136	+	0.981564i	$0.438783\pi$
$773$	−20.9770	+	36.3333i	−0.754491	+	1.30682i	−0.945627	+	0.325253i	$0.894551\pi$
$774$		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	−0.311923	−	0.950107i	$-0.600973\pi$
$787$	18.7076	−	32.4026i	0.666856	−	1.15503i	0.978779	−	0.204920i	$-0.0656936\pi$
$788$		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	−0.450712	−	0.892670i	$-0.648830\pi$
$797$	−40.9110	−	23.6200i	−1.44914	−	0.836663i	−0.998430	+	0.0560071i	$0.982163\pi$
$798$		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	−0.907903	−	0.419180i	$-0.862318\pi$
$809$	−23.2371	−	40.2478i	−0.816972	−	1.41504i	0.0909313	−	0.995857i	$-0.471016\pi$
$810$		0			0
$811$			11.4041i			0.400453i	0.979750	+	0.200227i	$0.0641678\pi$
$811$			11.4041i			0.400453i	−0.979750	+	0.200227i	$0.935832\pi$
$812$		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	−0.822926	−	0.568148i	$-0.807660\pi$
$821$	−21.2709	+	12.2808i	−0.742359	+	0.428601i	0.0805674	+	0.996749i	$0.474327\pi$
$822$		0			0
$823$	2.56731	+	1.48224i	0.0894909	+	0.0516676i	0.544078	−	0.839035i	$-0.316880\pi$
$823$	2.56731	+	1.48224i	0.0894909	+	0.0516676i	−0.454587	+	0.890702i	$0.650213\pi$
$824$		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	0.948858	−	0.315703i	$-0.102240\pi$
$829$	5.78791	+	10.0250i	0.201022	+	0.348181i	−0.747836	+	0.663884i	$0.768907\pi$
$830$		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	−0.304815	−	0.952412i	$-0.598595\pi$
$839$	−37.1348	−	21.4398i	−1.28203	−	0.740183i	−0.977220	+	0.212229i	$0.931928\pi$
$840$		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	$0.0579204\pi$
$857$			10.5950i			0.361919i	−0.983491	+	0.180960i	$0.942080\pi$
$858$		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	−0.644898	−	0.764268i	$-0.723100\pi$
$877$	10.0518	−	17.4103i	0.339427	−	0.587904i	0.984325	+	0.176364i	$0.0564336\pi$
$878$		0			0
$879$			4.04839i			0.136549i
$880$		0			0
$881$	1.56698	+	2.71409i	0.0527930	+	0.0914401i	0.891214	−	0.453583i	$-0.149854\pi$
$881$	1.56698	+	2.71409i	0.0527930	+	0.0914401i	−0.838421	+	0.545023i	$0.816521\pi$
$882$		0			0
$883$		−	34.0429i		−	1.14563i	−0.819683	−	0.572817i	$-0.805851\pi$
$883$		−	34.0429i		−	1.14563i	0.819683	−	0.572817i	$-0.194149\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−44.0001	+	25.4034i	−1.47738	+	0.852964i	−0.999673	−	0.0255565i	$-0.991864\pi$
$887$	−44.0001	+	25.4034i	−1.47738	+	0.852964i	−0.477704	+	0.878521i	$0.658531\pi$
$888$		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	−0.999253	−	0.0386406i	$-0.987697\pi$
$907$	−44.1331	+	25.4803i	−1.46542	+	0.846058i	−0.466163	+	0.884699i	$0.654364\pi$
$908$		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	0.271528	+	0.962431i	$0.412471\pi$
$919$	−21.1516	+	36.6356i	−0.697725	+	1.20850i	−0.969253	+	0.246065i	$0.920862\pi$
$920$		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	0.677262	−	0.735742i	$-0.263166\pi$
$929$	11.5432	+	6.66449i	0.378721	+	0.218655i	−0.298541	+	0.954397i	$0.596500\pi$
$930$		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	$-0.926106\pi$
$937$		−	14.0848i		−	0.460129i	0.973175	−	0.230065i	$-0.0738937\pi$
$938$		0			0
$939$	−6.87523	−	11.9082i	−0.224365	−	0.388611i
$940$		0			0
$941$		−	49.0399i		−	1.59866i	−0.600895	−	0.799328i	$-0.705189\pi$
$941$		−	49.0399i		−	1.59866i	0.600895	−	0.799328i	$-0.294811\pi$
$942$		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	0.974143	−	0.225933i	$-0.0725430\pi$
$947$	8.96760	+	15.5323i	0.291408	+	0.504733i	−0.682735	+	0.730666i	$0.739210\pi$
$948$		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	0.970126	−	0.242601i	$-0.0780006\pi$
$953$	38.4368	+	22.1915i	1.24509	+	0.718853i	0.274964	+	0.961454i	$0.411334\pi$
$954$		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	−0.856447	−	0.516235i	$-0.827333\pi$
$971$	0.587359	−	1.01734i	0.0188492	−	0.0326478i	0.875296	+	0.483587i	$0.160666\pi$
$972$		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	0.750610	−	0.660746i	$-0.229760\pi$
$977$	−6.15505	−	10.6609i	−0.196917	−	0.341071i	−0.947527	+	0.319675i	$0.896426\pi$
$978$		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	0.640633	−	0.767848i	$-0.278672\pi$
$991$	−10.8499	−	18.7926i	−0.344659	−	0.596967i	−0.985292	+	0.170880i	$0.945339\pi$
$992$		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	0.215260	−	0.976557i	$-0.430940\pi$
$997$	−16.5086	−	9.53125i	−0.522833	−	0.301858i	−0.738093	+	0.674699i	$0.764273\pi$
$998$		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.49.4		8
5.2	odd	4		260.2.x.a.101.1	✓	8
5.3	odd	4		1300.2.y.b.101.4		8
5.4	even	2		1300.2.ba.b.49.1		8
13.4	even	6		1300.2.ba.b.849.1		8
15.2	even	4		2340.2.dj.d.361.3		8
20.7	even	4		1040.2.da.c.881.4		8
65.2	even	12		3380.2.a.p.1.4		4
65.4	even	6	inner	1300.2.ba.c.849.4		8
65.17	odd	12		260.2.x.a.121.1	yes	8
65.37	even	12		3380.2.a.q.1.4		4
65.42	odd	12		3380.2.f.i.3041.7		8
65.43	odd	12		1300.2.y.b.901.4		8
65.62	odd	12		3380.2.f.i.3041.8		8
195.17	even	12		2340.2.dj.d.901.1		8
260.147	even	12		1040.2.da.c.641.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.x.a.101.1	✓	8	5.2	odd	4
260.2.x.a.121.1	yes	8	65.17	odd	12
1040.2.da.c.641.4		8	260.147	even	12
1040.2.da.c.881.4		8	20.7	even	4
1300.2.y.b.101.4		8	5.3	odd	4
1300.2.y.b.901.4		8	65.43	odd	12
1300.2.ba.b.49.1		8	5.4	even	2
1300.2.ba.b.849.1		8	13.4	even	6
1300.2.ba.c.49.4		8	1.1	even	1	trivial
1300.2.ba.c.849.4		8	65.4	even	6	inner
2340.2.dj.d.361.3		8	15.2	even	4
2340.2.dj.d.901.1		8	195.17	even	12
3380.2.a.p.1.4		4	65.2	even	12
3380.2.a.q.1.4		4	65.37	even	12
3380.2.f.i.3041.7		8	65.42	odd	12
3380.2.f.i.3041.8		8	65.62	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

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