LMFDB - Embedded newform 1568.2.i.p.1537.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1568,2,Mod(961,1568)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1568, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("1568.961");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1568 = 2^{5} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1568.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.5205430369$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1537.1
Root			$-1.32288 + 2.29129i$ of defining polynomial
Character	$\chi$	$=$	1568.1537
Dual form			1568.2.i.p.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32288 + 2.29129i) q^{3} +(-1.50000 - 2.59808i) q^{5} +(-2.00000 - 3.46410i) q^{9} +O(q^{10})$	\(q+(-1.32288 + 2.29129i) q^{3} +(-1.50000 - 2.59808i) q^{5} +(-2.00000 - 3.46410i) q^{9} +(-1.32288 + 2.29129i) q^{11} +4.00000 q^{13} +7.93725 q^{15} +(0.500000 - 0.866025i) q^{17} +(3.96863 + 6.87386i) q^{19} +(-1.32288 - 2.29129i) q^{23} +(-2.00000 + 3.46410i) q^{25} +2.64575 q^{27} -4.00000 q^{29} +(1.32288 - 2.29129i) q^{31} +(-3.50000 - 6.06218i) q^{33} +(2.50000 + 4.33013i) q^{37} +(-5.29150 + 9.16515i) q^{39} -8.00000 q^{41} -10.5830 q^{43} +(-6.00000 + 10.3923i) q^{45} +(-1.32288 - 2.29129i) q^{47} +(1.32288 + 2.29129i) q^{51} +(-3.50000 + 6.06218i) q^{53} +7.93725 q^{55} -21.0000 q^{57} +(-1.32288 + 2.29129i) q^{59} +(-2.50000 - 4.33013i) q^{61} +(-6.00000 - 10.3923i) q^{65} +(1.32288 - 2.29129i) q^{67} +7.00000 q^{69} +(-4.50000 + 7.79423i) q^{73} +(-5.29150 - 9.16515i) q^{75} +(-1.32288 - 2.29129i) q^{79} +(2.50000 - 4.33013i) q^{81} -10.5830 q^{83} -3.00000 q^{85} +(5.29150 - 9.16515i) q^{87} +(-4.50000 - 7.79423i) q^{89} +(3.50000 + 6.06218i) q^{93} +(11.9059 - 20.6216i) q^{95} +8.00000 q^{97} +10.5830 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{5} - 8 q^{9}+O(q^{10}) $ 4 * q - 6 * q^5 - 8 * q^9	$ 4 q - 6 q^{5} - 8 q^{9} + 16 q^{13} + 2 q^{17} - 8 q^{25} - 16 q^{29} - 14 q^{33} + 10 q^{37} - 32 q^{41} - 24 q^{45} - 14 q^{53} - 84 q^{57} - 10 q^{61} - 24 q^{65} + 28 q^{69} - 18 q^{73} + 10 q^{81} - 12 q^{85} - 18 q^{89} + 14 q^{93} + 32 q^{97}+O(q^{100}) $ 4 * q - 6 * q^5 - 8 * q^9 + 16 * q^13 + 2 * q^17 - 8 * q^25 - 16 * q^29 - 14 * q^33 + 10 * q^37 - 32 * q^41 - 24 * q^45 - 14 * q^53 - 84 * q^57 - 10 * q^61 - 24 * q^65 + 28 * q^69 - 18 * q^73 + 10 * q^81 - 12 * q^85 - 18 * q^89 + 14 * q^93 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times$.

$n$	$197$	$1471$	$1473$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.32288	+	2.29129i	−0.763763	+	1.32288i	0.177136	+	0.984186i	$0.443317\pi$
$3$	−1.32288	+	2.29129i	−0.763763	+	1.32288i	−0.940898	+	0.338689i	$0.890016\pi$
$4$		0			0
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	−0.977672	−	0.210138i	$-0.932609\pi$
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	0.306851	−	0.951757i	$-0.400725\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−2.00000	−	3.46410i	−0.666667	−	1.15470i
$10$		0			0
$11$	−1.32288	+	2.29129i	−0.398862	+	0.690849i	−0.993586	−	0.113081i	$-0.963928\pi$
$11$	−1.32288	+	2.29129i	−0.398862	+	0.690849i	0.594724	+	0.803930i	$0.297261\pi$
$12$		0			0
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$		0			0
$15$	7.93725			2.04939
$16$		0			0
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i	−0.799000	−	0.601331i	$-0.794637\pi$
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i	0.920268	+	0.391289i	$0.127971\pi$
$18$		0			0
$19$	3.96863	+	6.87386i	0.910465	+	1.57697i	0.813408	+	0.581694i	$0.197610\pi$
$19$	3.96863	+	6.87386i	0.910465	+	1.57697i	0.0970575	+	0.995279i	$0.469057\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.32288	−	2.29129i	−0.275839	−	0.477767i	0.694508	−	0.719485i	$-0.255622\pi$
$23$	−1.32288	−	2.29129i	−0.275839	−	0.477767i	−0.970346	+	0.241719i	$0.922289\pi$
$24$		0			0
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$		0			0
$27$	2.64575			0.509175
$28$		0			0
$29$	−4.00000			−0.742781			−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000			−0.742781			−0.371391	+	0.928477i	$0.621119\pi$
$30$		0			0
$31$	1.32288	−	2.29129i	0.237595	−	0.411527i	−0.722428	−	0.691446i	$-0.756974\pi$
$31$	1.32288	−	2.29129i	0.237595	−	0.411527i	0.960024	+	0.279918i	$0.0903074\pi$
$32$		0			0
$33$	−3.50000	−	6.06218i	−0.609272	−	1.05529i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.50000	+	4.33013i	0.410997	+	0.711868i	0.994999	−	0.0998840i	$-0.0318472\pi$
$37$	2.50000	+	4.33013i	0.410997	+	0.711868i	−0.584002	+	0.811752i	$0.698514\pi$
$38$		0			0
$39$	−5.29150	+	9.16515i	−0.847319	+	1.46760i
$40$		0			0
$41$	−8.00000			−1.24939			−0.624695	−	0.780869i	$-0.714777\pi$
$41$	−8.00000			−1.24939			−0.624695	+	0.780869i	$0.714777\pi$
$42$		0			0
$43$	−10.5830			−1.61389			−0.806947	−	0.590624i	$-0.798881\pi$
$43$	−10.5830			−1.61389			−0.806947	+	0.590624i	$0.798881\pi$
$44$		0			0
$45$	−6.00000	+	10.3923i	−0.894427	+	1.54919i
$46$		0			0
$47$	−1.32288	−	2.29129i	−0.192961	−	0.334219i	0.753269	−	0.657713i	$-0.228476\pi$
$47$	−1.32288	−	2.29129i	−0.192961	−	0.334219i	−0.946230	+	0.323494i	$0.895142\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	1.32288	+	2.29129i	0.185240	+	0.320844i
$52$		0			0
$53$	−3.50000	+	6.06218i	−0.480762	+	0.832704i	−0.999756	−	0.0220735i	$-0.992973\pi$
$53$	−3.50000	+	6.06218i	−0.480762	+	0.832704i	0.518994	+	0.854778i	$0.326307\pi$
$54$		0			0
$55$	7.93725			1.07026
$56$		0			0
$57$	−21.0000			−2.78152
$58$		0			0
$59$	−1.32288	+	2.29129i	−0.172224	+	0.298300i	−0.939197	−	0.343379i	$-0.888429\pi$
$59$	−1.32288	+	2.29129i	−0.172224	+	0.298300i	0.766973	+	0.641679i	$0.221762\pi$
$60$		0			0
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	0.660415	−	0.750901i	$-0.270381\pi$
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	−0.980507	+	0.196485i	$0.937047\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−6.00000	−	10.3923i	−0.744208	−	1.28901i
$66$		0			0
$67$	1.32288	−	2.29129i	0.161615	−	0.279925i	−0.773833	−	0.633390i	$-0.781663\pi$
$67$	1.32288	−	2.29129i	0.161615	−	0.279925i	0.935448	+	0.353464i	$0.114996\pi$
$68$		0			0
$69$	7.00000			0.842701
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−4.50000	+	7.79423i	−0.526685	+	0.912245i	0.472831	+	0.881153i	$0.343232\pi$
$73$	−4.50000	+	7.79423i	−0.526685	+	0.912245i	−0.999517	+	0.0310925i	$0.990101\pi$
$74$		0			0
$75$	−5.29150	−	9.16515i	−0.611010	−	1.05830i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−1.32288	−	2.29129i	−0.148835	−	0.257790i	0.781962	−	0.623326i	$-0.214219\pi$
$79$	−1.32288	−	2.29129i	−0.148835	−	0.257790i	−0.930797	+	0.365536i	$0.880886\pi$
$80$		0			0
$81$	2.50000	−	4.33013i	0.277778	−	0.481125i
$82$		0			0
$83$	−10.5830			−1.16164			−0.580818	−	0.814034i	$-0.697267\pi$
$83$	−10.5830			−1.16164			−0.580818	+	0.814034i	$0.697267\pi$
$84$		0			0
$85$	−3.00000			−0.325396
$86$		0			0
$87$	5.29150	−	9.16515i	0.567309	−	0.982607i
$88$		0			0
$89$	−4.50000	−	7.79423i	−0.476999	−	0.826187i	0.522654	−	0.852545i	$-0.324942\pi$
$89$	−4.50000	−	7.79423i	−0.476999	−	0.826187i	−0.999653	+	0.0263586i	$0.991609\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	3.50000	+	6.06218i	0.362933	+	0.628619i
$94$		0			0
$95$	11.9059	−	20.6216i	1.22152	−	2.11573i
$96$		0			0
$97$	8.00000			0.812277			0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000			0.812277			0.406138	+	0.913812i	$0.366875\pi$
$98$		0			0
$99$	10.5830			1.06363
$100$		0			0
$101$	−7.50000	+	12.9904i	−0.746278	+	1.29259i	0.203317	+	0.979113i	$0.434828\pi$
$101$	−7.50000	+	12.9904i	−0.746278	+	1.29259i	−0.949595	+	0.313478i	$0.898506\pi$
$102$		0			0
$103$	1.32288	+	2.29129i	0.130347	+	0.225767i	0.923810	−	0.382851i	$-0.125058\pi$
$103$	1.32288	+	2.29129i	0.130347	+	0.225767i	−0.793463	+	0.608618i	$0.791724\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.61438	+	11.4564i	0.639436	+	1.10754i	0.985557	+	0.169346i	$0.0541655\pi$
$107$	6.61438	+	11.4564i	0.639436	+	1.10754i	−0.346121	+	0.938190i	$0.612501\pi$
$108$		0			0
$109$	−0.500000	+	0.866025i	−0.0478913	+	0.0829502i	−0.888977	−	0.457951i	$-0.848583\pi$
$109$	−0.500000	+	0.866025i	−0.0478913	+	0.0829502i	0.841086	+	0.540901i	$0.181917\pi$
$110$		0			0
$111$	−13.2288			−1.25562
$112$		0			0
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$	−3.96863	+	6.87386i	−0.370076	+	0.640991i
$116$		0			0
$117$	−8.00000	−	13.8564i	−0.739600	−	1.28103i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	2.00000	+	3.46410i	0.181818	+	0.314918i
$122$		0			0
$123$	10.5830	−	18.3303i	0.954237	−	1.65279i
$124$		0			0
$125$	−3.00000			−0.268328
$126$		0			0
$127$	−21.1660			−1.87818			−0.939090	−	0.343672i	$-0.888329\pi$
$127$	−21.1660			−1.87818			−0.939090	+	0.343672i	$0.888329\pi$
$128$		0			0
$129$	14.0000	−	24.2487i	1.23263	−	2.13498i
$130$		0			0
$131$	−3.96863	−	6.87386i	−0.346741	−	0.600572i	0.638928	−	0.769267i	$-0.279378\pi$
$131$	−3.96863	−	6.87386i	−0.346741	−	0.600572i	−0.985668	+	0.168694i	$0.946045\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−3.96863	−	6.87386i	−0.341565	−	0.591608i
$136$		0			0
$137$	−0.500000	+	0.866025i	−0.0427179	+	0.0739895i	−0.886594	−	0.462549i	$-0.846935\pi$
$137$	−0.500000	+	0.866025i	−0.0427179	+	0.0739895i	0.843876	+	0.536538i	$0.180268\pi$
$138$		0			0
$139$	−10.5830			−0.897639			−0.448819	−	0.893622i	$-0.648155\pi$
$139$	−10.5830			−0.897639			−0.448819	+	0.893622i	$0.648155\pi$
$140$		0			0
$141$	7.00000			0.589506
$142$		0			0
$143$	−5.29150	+	9.16515i	−0.442498	+	0.766428i
$144$		0			0
$145$	6.00000	+	10.3923i	0.498273	+	0.863034i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−10.5000	−	18.1865i	−0.860194	−	1.48990i	−0.871742	−	0.489966i	$-0.837009\pi$
$149$	−10.5000	−	18.1865i	−0.860194	−	1.48990i	0.0115483	−	0.999933i	$-0.496324\pi$
$150$		0			0
$151$	−1.32288	+	2.29129i	−0.107654	+	0.186462i	−0.914819	−	0.403863i	$-0.867667\pi$
$151$	−1.32288	+	2.29129i	−0.107654	+	0.186462i	0.807165	+	0.590325i	$0.201001\pi$
$152$		0			0
$153$	−4.00000			−0.323381
$154$		0			0
$155$	−7.93725			−0.637536
$156$		0			0
$157$	−4.50000	+	7.79423i	−0.359139	+	0.622047i	−0.987817	−	0.155618i	$-0.950263\pi$
$157$	−4.50000	+	7.79423i	−0.359139	+	0.622047i	0.628678	+	0.777666i	$0.283596\pi$
$158$		0			0
$159$	−9.26013	−	16.0390i	−0.734376	−	1.27198i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−6.61438	−	11.4564i	−0.518078	−	0.897338i	−0.999779	−	0.0210021i	$-0.993314\pi$
$163$	−6.61438	−	11.4564i	−0.518078	−	0.897338i	0.481701	−	0.876335i	$-0.340019\pi$
$164$		0			0
$165$	−10.5000	+	18.1865i	−0.817424	+	1.41582i
$166$		0			0
$167$	5.29150			0.409469			0.204734	−	0.978818i	$-0.434367\pi$
$167$	5.29150			0.409469			0.204734	+	0.978818i	$0.434367\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$		0			0
$171$	15.8745	−	27.4955i	1.21395	−	2.10263i
$172$		0			0
$173$	1.50000	+	2.59808i	0.114043	+	0.197528i	0.917397	−	0.397974i	$-0.130287\pi$
$173$	1.50000	+	2.59808i	0.114043	+	0.197528i	−0.803354	+	0.595502i	$0.796953\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.50000	−	6.06218i	−0.263076	−	0.455661i
$178$		0			0
$179$	−11.9059	+	20.6216i	−0.889887	+	1.54133i	−0.0498798	+	0.998755i	$0.515884\pi$
$179$	−11.9059	+	20.6216i	−0.889887	+	1.54133i	−0.840007	+	0.542575i	$0.817449\pi$
$180$		0			0
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$		0			0
$183$	13.2288			0.977898
$184$		0			0
$185$	7.50000	−	12.9904i	0.551411	−	0.955072i
$186$		0			0
$187$	1.32288	+	2.29129i	0.0967382	+	0.167556i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	11.9059	+	20.6216i	0.861479	+	1.49213i	0.870501	+	0.492167i	$0.163795\pi$
$191$	11.9059	+	20.6216i	0.861479	+	1.49213i	−0.00902170	+	0.999959i	$0.502872\pi$
$192$		0			0
$193$	3.50000	−	6.06218i	0.251936	−	0.436365i	−0.712123	−	0.702055i	$-0.752266\pi$
$193$	3.50000	−	6.06218i	0.251936	−	0.436365i	0.964059	+	0.265689i	$0.0855996\pi$
$194$		0			0
$195$	31.7490			2.27359
$196$		0			0
$197$	12.0000			0.854965			0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000			0.854965			0.427482	+	0.904024i	$0.359401\pi$
$198$		0			0
$199$	−9.26013	+	16.0390i	−0.656433	+	1.13698i	0.325099	+	0.945680i	$0.394602\pi$
$199$	−9.26013	+	16.0390i	−0.656433	+	1.13698i	−0.981532	+	0.191296i	$0.938731\pi$
$200$		0			0
$201$	3.50000	+	6.06218i	0.246871	+	0.427593i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	12.0000	+	20.7846i	0.838116	+	1.45166i
$206$		0			0
$207$	−5.29150	+	9.16515i	−0.367785	+	0.637022i
$208$		0			0
$209$	−21.0000			−1.45260
$210$		0			0
$211$	10.5830			0.728564			0.364282	−	0.931289i	$-0.381314\pi$
$211$	10.5830			0.728564			0.364282	+	0.931289i	$0.381314\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	15.8745	+	27.4955i	1.08263	+	1.87517i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−11.9059	−	20.6216i	−0.804525	−	1.39348i
$220$		0			0
$221$	2.00000	−	3.46410i	0.134535	−	0.233021i
$222$		0			0
$223$		0			0			−	1.00000i	$-0.5\pi$
$223$		0			0				1.00000i	$0.5\pi$
$224$		0			0
$225$	16.0000			1.06667
$226$		0			0
$227$	1.32288	−	2.29129i	0.0878023	−	0.152078i	−0.818780	−	0.574108i	$-0.805349\pi$
$227$	1.32288	−	2.29129i	0.0878023	−	0.152078i	0.906582	+	0.422030i	$0.138682\pi$
$228$		0			0
$229$	−5.50000	−	9.52628i	−0.363450	−	0.629514i	0.625076	−	0.780564i	$-0.285068\pi$
$229$	−5.50000	−	9.52628i	−0.363450	−	0.629514i	−0.988526	+	0.151050i	$0.951735\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−4.50000	−	7.79423i	−0.294805	−	0.510617i	0.680135	−	0.733087i	$-0.261921\pi$
$233$	−4.50000	−	7.79423i	−0.294805	−	0.510617i	−0.974939	+	0.222470i	$0.928588\pi$
$234$		0			0
$235$	−3.96863	+	6.87386i	−0.258885	+	0.448401i
$236$		0			0
$237$	7.00000			0.454699
$238$		0			0
$239$	−15.8745			−1.02684			−0.513418	−	0.858138i	$-0.671621\pi$
$239$	−15.8745			−1.02684			−0.513418	+	0.858138i	$0.671621\pi$
$240$		0			0
$241$	−0.500000	+	0.866025i	−0.0322078	+	0.0557856i	−0.881680	−	0.471848i	$-0.843587\pi$
$241$	−0.500000	+	0.866025i	−0.0322078	+	0.0557856i	0.849472	+	0.527633i	$0.176921\pi$
$242$		0			0
$243$	10.5830	+	18.3303i	0.678900	+	1.17589i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	15.8745	+	27.4955i	1.01007	+	1.74949i
$248$		0			0
$249$	14.0000	−	24.2487i	0.887214	−	1.53670i
$250$		0			0
$251$	5.29150			0.333997			0.166998	−	0.985957i	$-0.446593\pi$
$251$	5.29150			0.333997			0.166998	+	0.985957i	$0.446593\pi$
$252$		0			0
$253$	7.00000			0.440086
$254$		0			0
$255$	3.96863	−	6.87386i	0.248525	−	0.430458i
$256$		0			0
$257$	8.50000	+	14.7224i	0.530215	+	0.918360i	0.999379	+	0.0352486i	$0.0112223\pi$
$257$	8.50000	+	14.7224i	0.530215	+	0.918360i	−0.469163	+	0.883112i	$0.655444\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	8.00000	+	13.8564i	0.495188	+	0.857690i
$262$		0			0
$263$	−9.26013	+	16.0390i	−0.571004	+	0.989008i	0.425459	+	0.904978i	$0.360113\pi$
$263$	−9.26013	+	16.0390i	−0.571004	+	0.989008i	−0.996463	+	0.0840304i	$0.973221\pi$
$264$		0			0
$265$	21.0000			1.29002
$266$		0			0
$267$	23.8118			1.45726
$268$		0			0
$269$	7.50000	−	12.9904i	0.457283	−	0.792038i	−0.541533	−	0.840679i	$-0.682156\pi$
$269$	7.50000	−	12.9904i	0.457283	−	0.792038i	0.998816	+	0.0486418i	$0.0154893\pi$
$270$		0			0
$271$	1.32288	+	2.29129i	0.0803590	+	0.139186i	0.903404	−	0.428790i	$-0.141060\pi$
$271$	1.32288	+	2.29129i	0.0803590	+	0.139186i	−0.823045	+	0.567976i	$0.807727\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−5.29150	−	9.16515i	−0.319090	−	0.552679i
$276$		0			0
$277$	12.5000	−	21.6506i	0.751052	−	1.30086i	−0.196261	−	0.980552i	$-0.562880\pi$
$277$	12.5000	−	21.6506i	0.751052	−	1.30086i	0.947313	−	0.320309i	$-0.103787\pi$
$278$		0			0
$279$	−10.5830			−0.633588
$280$		0			0
$281$	−24.0000			−1.43172			−0.715860	−	0.698244i	$-0.753965\pi$
$281$	−24.0000			−1.43172			−0.715860	+	0.698244i	$0.753965\pi$
$282$		0			0
$283$	−9.26013	+	16.0390i	−0.550458	+	0.953420i	0.447784	+	0.894142i	$0.352213\pi$
$283$	−9.26013	+	16.0390i	−0.550458	+	0.953420i	−0.998241	+	0.0592787i	$0.981120\pi$
$284$		0			0
$285$	31.5000	+	54.5596i	1.86590	+	3.23183i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	8.00000	+	13.8564i	0.470588	+	0.815083i
$290$		0			0
$291$	−10.5830	+	18.3303i	−0.620387	+	1.07454i
$292$		0			0
$293$	10.0000			0.584206			0.292103	−	0.956387i	$-0.405645\pi$
$293$	10.0000			0.584206			0.292103	+	0.956387i	$0.405645\pi$
$294$		0			0
$295$	7.93725			0.462125
$296$		0			0
$297$	−3.50000	+	6.06218i	−0.203091	+	0.351763i
$298$		0			0
$299$	−5.29150	−	9.16515i	−0.306015	−	0.530034i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−19.8431	−	34.3693i	−1.13996	−	1.97447i
$304$		0			0
$305$	−7.50000	+	12.9904i	−0.429449	+	0.743827i
$306$		0			0
$307$	10.5830			0.604004			0.302002	−	0.953307i	$-0.402345\pi$
$307$	10.5830			0.604004			0.302002	+	0.953307i	$0.402345\pi$
$308$		0			0
$309$	−7.00000			−0.398216
$310$		0			0
$311$	−11.9059	+	20.6216i	−0.675121	+	1.16934i	0.301313	+	0.953525i	$0.402575\pi$
$311$	−11.9059	+	20.6216i	−0.675121	+	1.16934i	−0.976434	+	0.215818i	$0.930758\pi$
$312$		0			0
$313$	−8.50000	−	14.7224i	−0.480448	−	0.832161i	0.519300	−	0.854592i	$-0.326193\pi$
$313$	−8.50000	−	14.7224i	−0.480448	−	0.832161i	−0.999748	+	0.0224310i	$0.992859\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.50000	+	11.2583i	0.365076	+	0.632331i	0.988788	−	0.149323i	$-0.0477095\pi$
$317$	6.50000	+	11.2583i	0.365076	+	0.632331i	−0.623712	+	0.781654i	$0.714376\pi$
$318$		0			0
$319$	5.29150	−	9.16515i	0.296267	−	0.513150i
$320$		0			0
$321$	−35.0000			−1.95351
$322$		0			0
$323$	7.93725			0.441641
$324$		0			0
$325$	−8.00000	+	13.8564i	−0.443760	+	0.768615i
$326$		0			0
$327$	−1.32288	−	2.29129i	−0.0731552	−	0.126709i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	3.96863	+	6.87386i	0.218135	+	0.377822i	0.954238	−	0.299048i	$-0.0966692\pi$
$331$	3.96863	+	6.87386i	0.218135	+	0.377822i	−0.736102	+	0.676870i	$0.763336\pi$
$332$		0			0
$333$	10.0000	−	17.3205i	0.547997	−	0.949158i
$334$		0			0
$335$	−7.93725			−0.433659
$336$		0			0
$337$	24.0000			1.30736			0.653682	−	0.756770i	$-0.273224\pi$
$337$	24.0000			1.30736			0.653682	+	0.756770i	$0.273224\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	3.50000	+	6.06218i	0.189536	+	0.328285i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−10.5000	−	18.1865i	−0.565301	−	0.979130i
$346$		0			0
$347$	11.9059	−	20.6216i	0.639141	−	1.10702i	−0.346480	−	0.938057i	$-0.612623\pi$
$347$	11.9059	−	20.6216i	0.639141	−	1.10702i	0.985622	−	0.168968i	$-0.0540434\pi$
$348$		0			0
$349$	−20.0000			−1.07058			−0.535288	−	0.844670i	$-0.679797\pi$
$349$	−20.0000			−1.07058			−0.535288	+	0.844670i	$0.679797\pi$
$350$		0			0
$351$	10.5830			0.564879
$352$		0			0
$353$	4.50000	−	7.79423i	0.239511	−	0.414845i	−0.721063	−	0.692869i	$-0.756346\pi$
$353$	4.50000	−	7.79423i	0.239511	−	0.414845i	0.960574	+	0.278024i	$0.0896796\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−9.26013	−	16.0390i	−0.488731	−	0.846507i	0.511185	−	0.859471i	$-0.329207\pi$
$359$	−9.26013	−	16.0390i	−0.488731	−	0.846507i	−0.999916	+	0.0129639i	$0.995873\pi$
$360$		0			0
$361$	−22.0000	+	38.1051i	−1.15789	+	2.00553i
$362$		0			0
$363$	−10.5830			−0.555464
$364$		0			0
$365$	27.0000			1.41324
$366$		0			0
$367$	9.26013	−	16.0390i	0.483375	−	0.837230i	−0.516443	−	0.856322i	$-0.672744\pi$
$367$	9.26013	−	16.0390i	0.483375	−	0.837230i	0.999818	+	0.0190919i	$0.00607750\pi$
$368$		0			0
$369$	16.0000	+	27.7128i	0.832927	+	1.44267i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	10.5000	+	18.1865i	0.543669	+	0.941663i	0.998689	+	0.0511818i	$0.0162988\pi$
$373$	10.5000	+	18.1865i	0.543669	+	0.941663i	−0.455020	+	0.890481i	$0.650368\pi$
$374$		0			0
$375$	3.96863	−	6.87386i	0.204939	−	0.354965i
$376$		0			0
$377$	−16.0000			−0.824042
$378$		0			0
$379$	5.29150			0.271806			0.135903	−	0.990722i	$-0.456606\pi$
$379$	5.29150			0.271806			0.135903	+	0.990722i	$0.456606\pi$
$380$		0			0
$381$	28.0000	−	48.4974i	1.43448	−	2.48460i
$382$		0			0
$383$	9.26013	+	16.0390i	0.473171	+	0.819555i	0.999528	−	0.0307077i	$-0.00977611\pi$
$383$	9.26013	+	16.0390i	0.473171	+	0.819555i	−0.526358	+	0.850263i	$0.676443\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	21.1660	+	36.6606i	1.07593	+	1.86356i
$388$		0			0
$389$	7.50000	−	12.9904i	0.380265	−	0.658638i	−0.610835	−	0.791758i	$-0.709166\pi$
$389$	7.50000	−	12.9904i	0.380265	−	0.658638i	0.991100	+	0.133120i	$0.0424994\pi$
$390$		0			0
$391$	−2.64575			−0.133801
$392$		0			0
$393$	21.0000			1.05931
$394$		0			0
$395$	−3.96863	+	6.87386i	−0.199683	+	0.345862i
$396$		0			0
$397$	2.50000	+	4.33013i	0.125471	+	0.217323i	0.921917	−	0.387387i	$-0.126622\pi$
$397$	2.50000	+	4.33013i	0.125471	+	0.217323i	−0.796446	+	0.604710i	$0.793289\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	11.5000	+	19.9186i	0.574283	+	0.994687i	0.996119	+	0.0880147i	$0.0280523\pi$
$401$	11.5000	+	19.9186i	0.574283	+	0.994687i	−0.421837	+	0.906672i	$0.638614\pi$
$402$		0			0
$403$	5.29150	−	9.16515i	0.263589	−	0.456549i
$404$		0			0
$405$	−15.0000			−0.745356
$406$		0			0
$407$	−13.2288			−0.655725
$408$		0			0
$409$	−11.5000	+	19.9186i	−0.568638	+	0.984911i	0.428063	+	0.903749i	$0.359196\pi$
$409$	−11.5000	+	19.9186i	−0.568638	+	0.984911i	−0.996701	+	0.0811615i	$0.974137\pi$
$410$		0			0
$411$	−1.32288	−	2.29129i	−0.0652526	−	0.113021i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	15.8745	+	27.4955i	0.779249	+	1.34970i
$416$		0			0
$417$	14.0000	−	24.2487i	0.685583	−	1.18746i
$418$		0			0
$419$	−31.7490			−1.55104			−0.775520	−	0.631322i	$-0.782512\pi$
$419$	−31.7490			−1.55104			−0.775520	+	0.631322i	$0.782512\pi$
$420$		0			0
$421$	−12.0000			−0.584844			−0.292422	−	0.956289i	$-0.594461\pi$
$421$	−12.0000			−0.584844			−0.292422	+	0.956289i	$0.594461\pi$
$422$		0			0
$423$	−5.29150	+	9.16515i	−0.257282	+	0.445625i
$424$		0			0
$425$	2.00000	+	3.46410i	0.0970143	+	0.168034i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−14.0000	−	24.2487i	−0.675926	−	1.17074i
$430$		0			0
$431$	−1.32288	+	2.29129i	−0.0637207	+	0.110367i	−0.896126	−	0.443800i	$-0.853630\pi$
$431$	−1.32288	+	2.29129i	−0.0637207	+	0.110367i	0.832405	+	0.554168i	$0.186963\pi$
$432$		0			0
$433$	32.0000			1.53782			0.768911	−	0.639356i	$-0.220799\pi$
$433$	32.0000			1.53782			0.768911	+	0.639356i	$0.220799\pi$
$434$		0			0
$435$	−31.7490			−1.52225
$436$		0			0
$437$	10.5000	−	18.1865i	0.502283	−	0.869980i
$438$		0			0
$439$	−11.9059	−	20.6216i	−0.568237	−	0.984215i	−0.996740	−	0.0806748i	$-0.974292\pi$
$439$	−11.9059	−	20.6216i	−0.568237	−	0.984215i	0.428504	−	0.903540i	$-0.359041\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3.96863	−	6.87386i	−0.188555	−	0.326587i	0.756214	−	0.654325i	$-0.227047\pi$
$443$	−3.96863	−	6.87386i	−0.188555	−	0.326587i	−0.944769	+	0.327738i	$0.893714\pi$
$444$		0			0
$445$	−13.5000	+	23.3827i	−0.639961	+	1.10845i
$446$		0			0
$447$	55.5608			2.62793
$448$		0			0
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$		0			0
$451$	10.5830	−	18.3303i	0.498334	−	0.863140i
$452$		0			0
$453$	−3.50000	−	6.06218i	−0.164444	−	0.284826i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−3.50000	−	6.06218i	−0.163723	−	0.283577i	0.772478	−	0.635042i	$-0.219017\pi$
$457$	−3.50000	−	6.06218i	−0.163723	−	0.283577i	−0.936201	+	0.351465i	$0.885684\pi$
$458$		0			0
$459$	1.32288	−	2.29129i	0.0617465	−	0.106948i
$460$		0			0
$461$	20.0000			0.931493			0.465746	−	0.884918i	$-0.345786\pi$
$461$	20.0000			0.931493			0.465746	+	0.884918i	$0.345786\pi$
$462$		0			0
$463$		0			0			−	1.00000i	$-0.5\pi$
$463$		0			0				1.00000i	$0.5\pi$
$464$		0			0
$465$	10.5000	−	18.1865i	0.486926	−	0.843380i
$466$		0			0
$467$	−3.96863	−	6.87386i	−0.183646	−	0.318084i	0.759473	−	0.650538i	$-0.225457\pi$
$467$	−3.96863	−	6.87386i	−0.183646	−	0.318084i	−0.943119	+	0.332454i	$0.892123\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−11.9059	−	20.6216i	−0.548594	−	0.950193i
$472$		0			0
$473$	14.0000	−	24.2487i	0.643721	−	1.11496i
$474$		0			0
$475$	−31.7490			−1.45674
$476$		0			0
$477$	28.0000			1.28203
$478$		0			0
$479$	19.8431	−	34.3693i	0.906656	−	1.57037i	0.0879772	−	0.996122i	$-0.471960\pi$
$479$	19.8431	−	34.3693i	0.906656	−	1.57037i	0.818679	−	0.574252i	$-0.194707\pi$
$480$		0			0
$481$	10.0000	+	17.3205i	0.455961	+	0.789747i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−12.0000	−	20.7846i	−0.544892	−	0.943781i
$486$		0			0
$487$	11.9059	−	20.6216i	0.539507	−	0.934453i	−0.459424	−	0.888217i	$-0.651944\pi$
$487$	11.9059	−	20.6216i	0.539507	−	0.934453i	0.998931	−	0.0462362i	$-0.0147227\pi$
$488$		0			0
$489$	35.0000			1.58275
$490$		0			0
$491$	−37.0405			−1.67162			−0.835808	−	0.549022i	$-0.815000\pi$
$491$	−37.0405			−1.67162			−0.835808	+	0.549022i	$0.815000\pi$
$492$		0			0
$493$	−2.00000	+	3.46410i	−0.0900755	+	0.156015i
$494$		0			0
$495$	−15.8745	−	27.4955i	−0.713506	−	1.23583i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−6.61438	−	11.4564i	−0.296100	−	0.512861i	0.679140	−	0.734009i	$-0.262353\pi$
$499$	−6.61438	−	11.4564i	−0.296100	−	0.512861i	−0.975240	+	0.221148i	$0.929020\pi$
$500$		0			0
$501$	−7.00000	+	12.1244i	−0.312737	+	0.541676i
$502$		0			0
$503$	21.1660			0.943746			0.471873	−	0.881667i	$-0.343578\pi$
$503$	21.1660			0.943746			0.471873	+	0.881667i	$0.343578\pi$
$504$		0			0
$505$	45.0000			2.00247
$506$		0			0
$507$	−3.96863	+	6.87386i	−0.176253	+	0.305279i
$508$		0			0
$509$	−9.50000	−	16.4545i	−0.421080	−	0.729332i	0.574965	−	0.818178i	$-0.305016\pi$
$509$	−9.50000	−	16.4545i	−0.421080	−	0.729332i	−0.996045	+	0.0888457i	$0.971682\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	10.5000	+	18.1865i	0.463586	+	0.802955i
$514$		0			0
$515$	3.96863	−	6.87386i	0.174879	−	0.302899i
$516$		0			0
$517$	7.00000			0.307860
$518$		0			0
$519$	−7.93725			−0.348407
$520$		0			0
$521$	11.5000	−	19.9186i	0.503824	−	0.872649i	−0.496166	−	0.868228i	$-0.665259\pi$
$521$	11.5000	−	19.9186i	0.503824	−	0.872649i	0.999990	−	0.00442139i	$-0.00140738\pi$
$522$		0			0
$523$	−17.1974	−	29.7867i	−0.751989	−	1.30248i	−0.946857	−	0.321654i	$-0.895761\pi$
$523$	−17.1974	−	29.7867i	−0.751989	−	1.30248i	0.194868	−	0.980829i	$-0.437572\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.32288	−	2.29129i	−0.0576254	−	0.0998101i
$528$		0			0
$529$	8.00000	−	13.8564i	0.347826	−	0.602452i
$530$		0			0
$531$	10.5830			0.459263
$532$		0			0
$533$	−32.0000			−1.38607
$534$		0			0
$535$	19.8431	−	34.3693i	0.857894	−	1.48592i
$536$		0			0
$537$	−31.5000	−	54.5596i	−1.35933	−	2.35442i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−10.5000	−	18.1865i	−0.451430	−	0.781900i	0.547045	−	0.837103i	$-0.315753\pi$
$541$	−10.5000	−	18.1865i	−0.451430	−	0.781900i	−0.998475	+	0.0552031i	$0.982419\pi$
$542$		0			0
$543$	−7.93725	+	13.7477i	−0.340620	+	0.589971i
$544$		0			0
$545$	3.00000			0.128506
$546$		0			0
$547$	−26.4575			−1.13124			−0.565621	−	0.824665i	$-0.691363\pi$
$547$	−26.4575			−1.13124			−0.565621	+	0.824665i	$0.691363\pi$
$548$		0			0
$549$	−10.0000	+	17.3205i	−0.426790	+	0.739221i
$550$		0			0
$551$	−15.8745	−	27.4955i	−0.676277	−	1.17135i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	19.8431	+	34.3693i	0.842294	+	1.45890i
$556$		0			0
$557$	19.5000	−	33.7750i	0.826242	−	1.43109i	−0.0747252	−	0.997204i	$-0.523808\pi$
$557$	19.5000	−	33.7750i	0.826242	−	1.43109i	0.900967	−	0.433888i	$-0.142859\pi$
$558$		0			0
$559$	−42.3320			−1.79045
$560$		0			0
$561$	−7.00000			−0.295540
$562$		0			0
$563$	−1.32288	+	2.29129i	−0.0557526	+	0.0965663i	−0.892555	−	0.450939i	$-0.851089\pi$
$563$	−1.32288	+	2.29129i	−0.0557526	+	0.0965663i	0.836802	+	0.547505i	$0.184422\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$	16.5000	+	28.5788i	0.691716	+	1.19809i	0.971275	+	0.237959i	$0.0764783\pi$
$569$	16.5000	+	28.5788i	0.691716	+	1.19809i	−0.279559	+	0.960128i	$0.590188\pi$
$570$		0			0
$571$	−1.32288	+	2.29129i	−0.0553606	+	0.0958874i	−0.892378	−	0.451290i	$-0.850964\pi$
$571$	−1.32288	+	2.29129i	−0.0553606	+	0.0958874i	0.837017	+	0.547177i	$0.184298\pi$
$572$		0			0
$573$	−63.0000			−2.63186
$574$		0			0
$575$	10.5830			0.441342
$576$		0			0
$577$	−20.5000	+	35.5070i	−0.853426	+	1.47818i	0.0246713	+	0.999696i	$0.492146\pi$
$577$	−20.5000	+	35.5070i	−0.853426	+	1.47818i	−0.878097	+	0.478482i	$0.841187\pi$
$578$		0			0
$579$	9.26013	+	16.0390i	0.384838	+	0.666559i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−9.26013	−	16.0390i	−0.383515	−	0.664268i
$584$		0			0
$585$	−24.0000	+	41.5692i	−0.992278	+	1.71868i
$586$		0			0
$587$	31.7490			1.31042			0.655211	−	0.755446i	$-0.272580\pi$
$587$	31.7490			1.31042			0.655211	+	0.755446i	$0.272580\pi$
$588$		0			0
$589$	21.0000			0.865290
$590$		0			0
$591$	−15.8745	+	27.4955i	−0.652990	+	1.13101i
$592$		0			0
$593$	16.5000	+	28.5788i	0.677574	+	1.17359i	0.975709	+	0.219069i	$0.0703019\pi$
$593$	16.5000	+	28.5788i	0.677574	+	1.17359i	−0.298136	+	0.954524i	$0.596365\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−24.5000	−	42.4352i	−1.00272	−	1.73676i
$598$		0			0
$599$	11.9059	−	20.6216i	0.486461	−	0.842575i	−0.513418	−	0.858139i	$-0.671621\pi$
$599$	11.9059	−	20.6216i	0.486461	−	0.842575i	0.999879	+	0.0155634i	$0.00495420\pi$
$600$		0			0
$601$	−8.00000			−0.326327			−0.163163	−	0.986599i	$-0.552170\pi$
$601$	−8.00000			−0.326327			−0.163163	+	0.986599i	$0.552170\pi$
$602$		0			0
$603$	−10.5830			−0.430973
$604$		0			0
$605$	6.00000	−	10.3923i	0.243935	−	0.422507i
$606$		0			0
$607$	19.8431	+	34.3693i	0.805408	+	1.39501i	0.916015	+	0.401143i	$0.131387\pi$
$607$	19.8431	+	34.3693i	0.805408	+	1.39501i	−0.110607	+	0.993864i	$0.535280\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−5.29150	−	9.16515i	−0.214071	−	0.370782i
$612$		0			0
$613$	−20.5000	+	35.5070i	−0.827987	+	1.43412i	0.0716275	+	0.997431i	$0.477181\pi$
$613$	−20.5000	+	35.5070i	−0.827987	+	1.43412i	−0.899615	+	0.436684i	$0.856153\pi$
$614$		0			0
$615$	−63.4980			−2.56049
$616$		0			0
$617$	−32.0000			−1.28827			−0.644136	−	0.764911i	$-0.722783\pi$
$617$	−32.0000			−1.28827			−0.644136	+	0.764911i	$0.722783\pi$
$618$		0			0
$619$	−22.4889	+	38.9519i	−0.903905	+	1.56561i	−0.0815238	+	0.996671i	$0.525979\pi$
$619$	−22.4889	+	38.9519i	−0.903905	+	1.56561i	−0.822381	+	0.568937i	$0.807355\pi$
$620$		0			0
$621$	−3.50000	−	6.06218i	−0.140450	−	0.243267i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$		0			0
$627$	27.7804	−	48.1170i	1.10944	−	1.92161i
$628$		0			0
$629$	5.00000			0.199363
$630$		0			0
$631$	42.3320			1.68521			0.842606	−	0.538531i	$-0.181021\pi$
$631$	42.3320			1.68521			0.842606	+	0.538531i	$0.181021\pi$
$632$		0			0
$633$	−14.0000	+	24.2487i	−0.556450	+	0.963800i
$634$		0			0
$635$	31.7490	+	54.9909i	1.25992	+	2.18225i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.500000	−	0.866025i	0.0197488	−	0.0342059i	−0.855982	−	0.517005i	$-0.827047\pi$
$641$	0.500000	−	0.866025i	0.0197488	−	0.0342059i	0.875731	+	0.482800i	$0.160380\pi$
$642$		0			0
$643$	−10.5830			−0.417353			−0.208676	−	0.977985i	$-0.566916\pi$
$643$	−10.5830			−0.417353			−0.208676	+	0.977985i	$0.566916\pi$
$644$		0			0
$645$	−84.0000			−3.30750
$646$		0			0
$647$	19.8431	−	34.3693i	0.780114	−	1.35120i	−0.151761	−	0.988417i	$-0.548494\pi$
$647$	19.8431	−	34.3693i	0.780114	−	1.35120i	0.931875	−	0.362780i	$-0.118172\pi$
$648$		0			0
$649$	−3.50000	−	6.06218i	−0.137387	−	0.237961i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−9.50000	−	16.4545i	−0.371764	−	0.643914i	0.618073	−	0.786121i	$-0.287914\pi$
$653$	−9.50000	−	16.4545i	−0.371764	−	0.643914i	−0.989837	+	0.142207i	$0.954580\pi$
$654$		0			0
$655$	−11.9059	+	20.6216i	−0.465201	+	0.805752i
$656$		0			0
$657$	36.0000			1.40449
$658$		0			0
$659$	31.7490			1.23677			0.618383	−	0.785877i	$-0.287788\pi$
$659$	31.7490			1.23677			0.618383	+	0.785877i	$0.287788\pi$
$660$		0			0
$661$	−16.5000	+	28.5788i	−0.641776	+	1.11159i	0.343261	+	0.939240i	$0.388469\pi$
$661$	−16.5000	+	28.5788i	−0.641776	+	1.11159i	−0.985036	+	0.172348i	$0.944865\pi$
$662$		0			0
$663$	5.29150	+	9.16515i	0.205505	+	0.355945i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	5.29150	+	9.16515i	0.204888	+	0.354876i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	13.2288			0.510690
$672$		0			0
$673$	−24.0000			−0.925132			−0.462566	−	0.886585i	$-0.653071\pi$
$673$	−24.0000			−0.925132			−0.462566	+	0.886585i	$0.653071\pi$
$674$		0			0
$675$	−5.29150	+	9.16515i	−0.203670	+	0.352767i
$676$		0			0
$677$	−1.50000	−	2.59808i	−0.0576497	−	0.0998522i	0.835760	−	0.549095i	$-0.185027\pi$
$677$	−1.50000	−	2.59808i	−0.0576497	−	0.0998522i	−0.893410	+	0.449242i	$0.851694\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	3.50000	+	6.06218i	0.134120	+	0.232303i
$682$		0			0
$683$	−11.9059	+	20.6216i	−0.455566	+	0.789063i	−0.998721	−	0.0505694i	$-0.983896\pi$
$683$	−11.9059	+	20.6216i	−0.455566	+	0.789063i	0.543155	+	0.839633i	$0.317230\pi$
$684$		0			0
$685$	3.00000			0.114624
$686$		0			0
$687$	29.1033			1.11036
$688$		0			0
$689$	−14.0000	+	24.2487i	−0.533358	+	0.923802i
$690$		0			0
$691$	−14.5516	−	25.2042i	−0.553570	−	0.958812i	−0.998013	−	0.0630046i	$-0.979932\pi$
$691$	−14.5516	−	25.2042i	−0.553570	−	0.958812i	0.444443	−	0.895807i	$-0.353402\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	15.8745	+	27.4955i	0.602154	+	1.04296i
$696$		0			0
$697$	−4.00000	+	6.92820i	−0.151511	+	0.262424i
$698$		0			0
$699$	23.8118			0.900644
$700$		0			0
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$		0			0
$703$	−19.8431	+	34.3693i	−0.748398	+	1.29626i
$704$		0			0
$705$	−10.5000	−	18.1865i	−0.395453	−	0.684944i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	18.5000	+	32.0429i	0.694782	+	1.20340i	0.970254	+	0.242089i	$0.0778325\pi$
$709$	18.5000	+	32.0429i	0.694782	+	1.20340i	−0.275472	+	0.961309i	$0.588834\pi$
$710$		0			0
$711$	−5.29150	+	9.16515i	−0.198447	+	0.343720i
$712$		0			0
$713$	−7.00000			−0.262152
$714$		0			0
$715$	31.7490			1.18735
$716$		0			0
$717$	21.0000	−	36.3731i	0.784259	−	1.35838i
$718$		0			0
$719$	−19.8431	−	34.3693i	−0.740024	−	1.28176i	−0.952484	−	0.304589i	$-0.901481\pi$
$719$	−19.8431	−	34.3693i	−0.740024	−	1.28176i	0.212460	−	0.977170i	$-0.431853\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−1.32288	−	2.29129i	−0.0491983	−	0.0852139i
$724$		0			0
$725$	8.00000	−	13.8564i	0.297113	−	0.514614i
$726$		0			0
$727$	42.3320			1.57001			0.785004	−	0.619491i	$-0.212661\pi$
$727$	42.3320			1.57001			0.785004	+	0.619491i	$0.212661\pi$
$728$		0			0
$729$	−41.0000			−1.51852
$730$		0			0
$731$	−5.29150	+	9.16515i	−0.195713	+	0.338985i
$732$		0			0
$733$	5.50000	+	9.52628i	0.203147	+	0.351861i	0.949541	−	0.313644i	$-0.101550\pi$
$733$	5.50000	+	9.52628i	0.203147	+	0.351861i	−0.746394	+	0.665505i	$0.768216\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.50000	+	6.06218i	0.128924	+	0.223303i
$738$		0			0
$739$	−22.4889	+	38.9519i	−0.827267	+	1.43287i	0.0729072	+	0.997339i	$0.476772\pi$
$739$	−22.4889	+	38.9519i	−0.827267	+	1.43287i	−0.900174	+	0.435530i	$0.856561\pi$
$740$		0			0
$741$	−84.0000			−3.08582
$742$		0			0
$743$	21.1660			0.776506			0.388253	−	0.921553i	$-0.373079\pi$
$743$	21.1660			0.776506			0.388253	+	0.921553i	$0.373079\pi$
$744$		0			0
$745$	−31.5000	+	54.5596i	−1.15407	+	1.99891i
$746$		0			0
$747$	21.1660	+	36.6606i	0.774424	+	1.34134i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−19.8431	−	34.3693i	−0.724086	−	1.25415i	−0.959349	−	0.282222i	$-0.908928\pi$
$751$	−19.8431	−	34.3693i	−0.724086	−	1.25415i	0.235263	−	0.971932i	$-0.424405\pi$
$752$		0			0
$753$	−7.00000	+	12.1244i	−0.255094	+	0.441836i
$754$		0			0
$755$	7.93725			0.288866
$756$		0			0
$757$	4.00000			0.145382			0.0726912	−	0.997354i	$-0.476841\pi$
$757$	4.00000			0.145382			0.0726912	+	0.997354i	$0.476841\pi$
$758$		0			0
$759$	−9.26013	+	16.0390i	−0.336121	+	0.582179i
$760$		0			0
$761$	4.50000	+	7.79423i	0.163125	+	0.282541i	0.935988	−	0.352032i	$-0.114509\pi$
$761$	4.50000	+	7.79423i	0.163125	+	0.282541i	−0.772863	+	0.634573i	$0.781176\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	6.00000	+	10.3923i	0.216930	+	0.375735i
$766$		0			0
$767$	−5.29150	+	9.16515i	−0.191065	+	0.330934i
$768$		0			0
$769$	24.0000			0.865462			0.432731	−	0.901523i	$-0.357550\pi$
$769$	24.0000			0.865462			0.432731	+	0.901523i	$0.357550\pi$
$770$		0			0
$771$	−44.9778			−1.61983
$772$		0			0
$773$	16.5000	−	28.5788i	0.593464	−	1.02791i	−0.400298	−	0.916385i	$-0.631093\pi$
$773$	16.5000	−	28.5788i	0.593464	−	1.02791i	0.993762	−	0.111524i	$-0.0355733\pi$
$774$		0			0
$775$	5.29150	+	9.16515i	0.190076	+	0.329222i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−31.7490	−	54.9909i	−1.13753	−	1.97025i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−10.5830			−0.378206
$784$		0			0
$785$	27.0000			0.963671
$786$		0			0
$787$	9.26013	−	16.0390i	0.330088	−	0.571729i	−0.652441	−	0.757840i	$-0.726255\pi$
$787$	9.26013	−	16.0390i	0.330088	−	0.571729i	0.982529	+	0.186111i	$0.0595882\pi$
$788$		0			0
$789$	−24.5000	−	42.4352i	−0.872223	−	1.51073i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−10.0000	−	17.3205i	−0.355110	−	0.615069i
$794$		0			0
$795$	−27.7804	+	48.1170i	−0.985269	+	1.70654i
$796$		0			0
$797$	52.0000			1.84193			0.920967	−	0.389640i	$-0.127401\pi$
$797$	52.0000			1.84193			0.920967	+	0.389640i	$0.127401\pi$
$798$		0			0
$799$	−2.64575			−0.0936000
$800$		0			0
$801$	−18.0000	+	31.1769i	−0.635999	+	1.10158i
$802$		0			0
$803$	−11.9059	−	20.6216i	−0.420149	−	0.727720i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	19.8431	+	34.3693i	0.698511	+	1.20986i
$808$		0			0
$809$	−15.5000	+	26.8468i	−0.544951	+	0.943883i	0.453659	+	0.891175i	$0.350118\pi$
$809$	−15.5000	+	26.8468i	−0.544951	+	0.943883i	−0.998610	+	0.0527074i	$0.983215\pi$
$810$		0			0
$811$	10.5830			0.371620			0.185810	−	0.982586i	$-0.440509\pi$
$811$	10.5830			0.371620			0.185810	+	0.982586i	$0.440509\pi$
$812$		0			0
$813$	−7.00000			−0.245501
$814$		0			0
$815$	−19.8431	+	34.3693i	−0.695075	+	1.20390i
$816$		0			0
$817$	−42.0000	−	72.7461i	−1.46939	−	2.54507i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−6.50000	−	11.2583i	−0.226852	−	0.392918i	0.730022	−	0.683424i	$-0.239510\pi$
$821$	−6.50000	−	11.2583i	−0.226852	−	0.392918i	−0.956873	+	0.290505i	$0.906177\pi$
$822$		0			0
$823$	−9.26013	+	16.0390i	−0.322788	+	0.559085i	−0.981062	−	0.193693i	$-0.937953\pi$
$823$	−9.26013	+	16.0390i	−0.322788	+	0.559085i	0.658274	+	0.752778i	$0.271287\pi$
$824$		0			0
$825$	28.0000			0.974835
$826$		0			0
$827$	31.7490			1.10402			0.552011	−	0.833837i	$-0.313861\pi$
$827$	31.7490			1.10402			0.552011	+	0.833837i	$0.313861\pi$
$828$		0			0
$829$	−7.50000	+	12.9904i	−0.260486	+	0.451175i	−0.966371	−	0.257152i	$-0.917216\pi$
$829$	−7.50000	+	12.9904i	−0.260486	+	0.451175i	0.705885	+	0.708326i	$0.250549\pi$
$830$		0			0
$831$	33.0719	+	57.2822i	1.14725	+	1.98710i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−7.93725	−	13.7477i	−0.274680	−	0.475760i
$836$		0			0
$837$	3.50000	−	6.06218i	0.120978	−	0.209540i
$838$		0			0
$839$	21.1660			0.730732			0.365366	−	0.930864i	$-0.380944\pi$
$839$	21.1660			0.730732			0.365366	+	0.930864i	$0.380944\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$		0			0
$843$	31.7490	−	54.9909i	1.09349	−	1.89399i
$844$		0			0
$845$	−4.50000	−	7.79423i	−0.154805	−	0.268130i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−24.5000	−	42.4352i	−0.840838	−	1.45637i
$850$		0			0
$851$	6.61438	−	11.4564i	0.226738	−	0.392722i
$852$		0			0
$853$	36.0000			1.23262			0.616308	−	0.787505i	$-0.288628\pi$
$853$	36.0000			1.23262			0.616308	+	0.787505i	$0.288628\pi$
$854$		0			0
$855$	−95.2470			−3.25738
$856$		0			0
$857$	7.50000	−	12.9904i	0.256195	−	0.443743i	−0.709024	−	0.705184i	$-0.750864\pi$
$857$	7.50000	−	12.9904i	0.256195	−	0.443743i	0.965219	+	0.261441i	$0.0841977\pi$
$858$		0			0
$859$	14.5516	+	25.2042i	0.496495	+	0.859955i	0.999992	−	0.00404218i	$-0.00128667\pi$
$859$	14.5516	+	25.2042i	0.496495	+	0.859955i	−0.503497	+	0.863997i	$0.667953\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	19.8431	+	34.3693i	0.675468	+	1.16995i	0.976332	+	0.216278i	$0.0693918\pi$
$863$	19.8431	+	34.3693i	0.675468	+	1.16995i	−0.300864	+	0.953667i	$0.597275\pi$
$864$		0			0
$865$	4.50000	−	7.79423i	0.153005	−	0.265012i
$866$		0			0
$867$	−42.3320			−1.43767
$868$		0			0
$869$	7.00000			0.237459
$870$		0			0
$871$	5.29150	−	9.16515i	0.179296	−	0.310549i
$872$		0			0
$873$	−16.0000	−	27.7128i	−0.541518	−	0.937937i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−18.5000	−	32.0429i	−0.624701	−	1.08201i	−0.988599	−	0.150574i	$-0.951888\pi$
$877$	−18.5000	−	32.0429i	−0.624701	−	1.08201i	0.363898	−	0.931439i	$-0.381446\pi$
$878$		0			0
$879$	−13.2288	+	22.9129i	−0.446195	+	0.772832i
$880$		0			0
$881$	−46.0000			−1.54978			−0.774890	−	0.632096i	$-0.782195\pi$
$881$	−46.0000			−1.54978			−0.774890	+	0.632096i	$0.782195\pi$
$882$		0			0
$883$	10.5830			0.356146			0.178073	−	0.984017i	$-0.443014\pi$
$883$	10.5830			0.356146			0.178073	+	0.984017i	$0.443014\pi$
$884$		0			0
$885$	−10.5000	+	18.1865i	−0.352954	+	0.611334i
$886$		0			0
$887$	−1.32288	−	2.29129i	−0.0444178	−	0.0769339i	0.842962	−	0.537973i	$-0.180810\pi$
$887$	−1.32288	−	2.29129i	−0.0444178	−	0.0769339i	−0.887380	+	0.461040i	$0.847477\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	6.61438	+	11.4564i	0.221590	+	0.383805i
$892$		0			0
$893$	10.5000	−	18.1865i	0.351369	−	0.608589i
$894$		0			0
$895$	71.4353			2.38782
$896$		0			0
$897$	28.0000			0.934893
$898$		0			0
$899$	−5.29150	+	9.16515i	−0.176481	+	0.305675i
$900$		0			0
$901$	3.50000	+	6.06218i	0.116602	+	0.201960i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−9.00000	−	15.5885i	−0.299170	−	0.518178i
$906$		0			0
$907$	−9.26013	+	16.0390i	−0.307478	+	0.532567i	−0.977810	−	0.209494i	$-0.932818\pi$
$907$	−9.26013	+	16.0390i	−0.307478	+	0.532567i	0.670332	+	0.742061i	$0.266152\pi$
$908$		0			0
$909$	60.0000			1.99007
$910$		0			0
$911$	21.1660			0.701261			0.350631	−	0.936514i	$-0.385967\pi$
$911$	21.1660			0.701261			0.350631	+	0.936514i	$0.385967\pi$
$912$		0			0
$913$	14.0000	−	24.2487i	0.463332	−	0.802515i
$914$		0			0
$915$	−19.8431	−	34.3693i	−0.655994	−	1.13621i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−9.26013	−	16.0390i	−0.305463	−	0.529078i	0.671901	−	0.740641i	$-0.265478\pi$
$919$	−9.26013	−	16.0390i	−0.305463	−	0.529078i	−0.977364	+	0.211563i	$0.932145\pi$
$920$		0			0
$921$	−14.0000	+	24.2487i	−0.461316	+	0.799022i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−20.0000			−0.657596
$926$		0			0
$927$	5.29150	−	9.16515i	0.173796	−	0.301023i
$928$		0			0
$929$	−4.50000	−	7.79423i	−0.147640	−	0.255720i	0.782715	−	0.622381i	$-0.213834\pi$
$929$	−4.50000	−	7.79423i	−0.147640	−	0.255720i	−0.930355	+	0.366660i	$0.880501\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−31.5000	−	54.5596i	−1.03126	−	1.78620i
$934$		0			0
$935$	3.96863	−	6.87386i	0.129788	−	0.224799i
$936$		0			0
$937$	22.0000			0.718709			0.359354	−	0.933201i	$-0.382997\pi$
$937$	22.0000			0.718709			0.359354	+	0.933201i	$0.382997\pi$
$938$		0			0
$939$	44.9778			1.46779
$940$		0			0
$941$	−0.500000	+	0.866025i	−0.0162995	+	0.0282316i	−0.874060	−	0.485818i	$-0.838522\pi$
$941$	−0.500000	+	0.866025i	−0.0162995	+	0.0282316i	0.857761	+	0.514049i	$0.171855\pi$
$942$		0			0
$943$	10.5830	+	18.3303i	0.344630	+	0.596917i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	14.5516	+	25.2042i	0.472865	+	0.819025i	0.999518	−	0.0310549i	$-0.00988667\pi$
$947$	14.5516	+	25.2042i	0.472865	+	0.819025i	−0.526653	+	0.850080i	$0.676553\pi$
$948$		0			0
$949$	−18.0000	+	31.1769i	−0.584305	+	1.01205i
$950$		0			0
$951$	−34.3948			−1.11533
$952$		0			0
$953$	−16.0000			−0.518291			−0.259145	−	0.965838i	$-0.583441\pi$
$953$	−16.0000			−0.518291			−0.259145	+	0.965838i	$0.583441\pi$
$954$		0			0
$955$	35.7176	−	61.8648i	1.15580	−	2.00190i
$956$		0			0
$957$	14.0000	+	24.2487i	0.452556	+	0.783850i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	12.0000	+	20.7846i	0.387097	+	0.670471i
$962$		0			0
$963$	26.4575	−	45.8258i	0.852581	−	1.47671i
$964$		0			0
$965$	−21.0000			−0.676014
$966$		0			0
$967$	−42.3320			−1.36131			−0.680653	−	0.732606i	$-0.738304\pi$
$967$	−42.3320			−1.36131			−0.680653	+	0.732606i	$0.738304\pi$
$968$		0			0
$969$	−10.5000	+	18.1865i	−0.337309	+	0.584236i
$970$		0			0
$971$	−3.96863	−	6.87386i	−0.127359	−	0.220593i	0.795293	−	0.606225i	$-0.207317\pi$
$971$	−3.96863	−	6.87386i	−0.127359	−	0.220593i	−0.922653	+	0.385632i	$0.873983\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−21.1660	−	36.6606i	−0.677855	−	1.17408i
$976$		0			0
$977$	−20.5000	+	35.5070i	−0.655853	+	1.13597i	0.325826	+	0.945430i	$0.394358\pi$
$977$	−20.5000	+	35.5070i	−0.655853	+	1.13597i	−0.981679	+	0.190541i	$0.938976\pi$
$978$		0			0
$979$	23.8118			0.761027
$980$		0			0
$981$	4.00000			0.127710
$982$		0			0
$983$	11.9059	−	20.6216i	0.379739	−	0.657727i	−0.611285	−	0.791410i	$-0.709347\pi$
$983$	11.9059	−	20.6216i	0.379739	−	0.657727i	0.991024	+	0.133684i	$0.0426806\pi$
$984$		0			0
$985$	−18.0000	−	31.1769i	−0.573528	−	0.993379i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	14.0000	+	24.2487i	0.445174	+	0.771064i
$990$		0			0
$991$	22.4889	−	38.9519i	0.714383	−	1.23735i	−0.248814	−	0.968551i	$-0.580041\pi$
$991$	22.4889	−	38.9519i	0.714383	−	1.23735i	0.963197	−	0.268796i	$-0.0866259\pi$
$992$		0			0
$993$	−21.0000			−0.666415
$994$		0			0
$995$	55.5608			1.76140
$996$		0			0
$997$	11.5000	−	19.9186i	0.364209	−	0.630828i	−0.624440	−	0.781073i	$-0.714673\pi$
$997$	11.5000	−	19.9186i	0.364209	−	0.630828i	0.988649	+	0.150245i	$0.0480062\pi$
$998$		0			0
$999$	6.61438	+	11.4564i	0.209270	+	0.362466i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1568.2.i.p.1537.1		4
4.3	odd	2	inner	1568.2.i.p.1537.2		4
7.2	even	3	inner	1568.2.i.p.961.1		4
7.3	odd	6		1568.2.a.m.1.1		2
7.4	even	3		1568.2.a.t.1.2		2
7.5	odd	6		224.2.i.c.65.2	yes	4
7.6	odd	2		224.2.i.c.193.2	yes	4
21.5	even	6		2016.2.s.o.289.2		4
21.20	even	2		2016.2.s.o.865.2		4
28.3	even	6		1568.2.a.m.1.2		2
28.11	odd	6		1568.2.a.t.1.1		2
28.19	even	6		224.2.i.c.65.1	✓	4
28.23	odd	6	inner	1568.2.i.p.961.2		4
28.27	even	2		224.2.i.c.193.1	yes	4
56.3	even	6		3136.2.a.bv.1.1		2
56.5	odd	6		448.2.i.h.65.1		4
56.11	odd	6		3136.2.a.bg.1.2		2
56.13	odd	2		448.2.i.h.193.1		4
56.19	even	6		448.2.i.h.65.2		4
56.27	even	2		448.2.i.h.193.2		4
56.45	odd	6		3136.2.a.bv.1.2		2
56.53	even	6		3136.2.a.bg.1.1		2
84.47	odd	6		2016.2.s.o.289.1		4
84.83	odd	2		2016.2.s.o.865.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.i.c.65.1	✓	4	28.19	even	6
224.2.i.c.65.2	yes	4	7.5	odd	6
224.2.i.c.193.1	yes	4	28.27	even	2
224.2.i.c.193.2	yes	4	7.6	odd	2
448.2.i.h.65.1		4	56.5	odd	6
448.2.i.h.65.2		4	56.19	even	6
448.2.i.h.193.1		4	56.13	odd	2
448.2.i.h.193.2		4	56.27	even	2
1568.2.a.m.1.1		2	7.3	odd	6
1568.2.a.m.1.2		2	28.3	even	6
1568.2.a.t.1.1		2	28.11	odd	6
1568.2.a.t.1.2		2	7.4	even	3
1568.2.i.p.961.1		4	7.2	even	3	inner
1568.2.i.p.961.2		4	28.23	odd	6	inner
1568.2.i.p.1537.1		4	1.1	even	1	trivial
1568.2.i.p.1537.2		4	4.3	odd	2	inner
2016.2.s.o.289.1		4	84.47	odd	6
2016.2.s.o.289.2		4	21.5	even	6
2016.2.s.o.865.1		4	84.83	odd	2
2016.2.s.o.865.2		4	21.20	even	2
3136.2.a.bg.1.1		2	56.53	even	6
3136.2.a.bg.1.2		2	56.11	odd	6
3136.2.a.bv.1.1		2	56.3	even	6
3136.2.a.bv.1.2		2	56.45	odd	6

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:	\( N \)	\(=\)	\( 1568 = 2^{5} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1568.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.32288 + 2.29129i) q^{3} +(-1.50000 - 2.59808i) q^{5} +(-2.00000 - 3.46410i) q^{9} +O(q^{10})\)	\(q+(-1.32288 + 2.29129i) q^{3} +(-1.50000 - 2.59808i) q^{5} +(-2.00000 - 3.46410i) q^{9} +(-1.32288 + 2.29129i) q^{11} +4.00000 q^{13} +7.93725 q^{15} +(0.500000 - 0.866025i) q^{17} +(3.96863 + 6.87386i) q^{19} +(-1.32288 - 2.29129i) q^{23} +(-2.00000 + 3.46410i) q^{25} +2.64575 q^{27} -4.00000 q^{29} +(1.32288 - 2.29129i) q^{31} +(-3.50000 - 6.06218i) q^{33} +(2.50000 + 4.33013i) q^{37} +(-5.29150 + 9.16515i) q^{39} -8.00000 q^{41} -10.5830 q^{43} +(-6.00000 + 10.3923i) q^{45} +(-1.32288 - 2.29129i) q^{47} +(1.32288 + 2.29129i) q^{51} +(-3.50000 + 6.06218i) q^{53} +7.93725 q^{55} -21.0000 q^{57} +(-1.32288 + 2.29129i) q^{59} +(-2.50000 - 4.33013i) q^{61} +(-6.00000 - 10.3923i) q^{65} +(1.32288 - 2.29129i) q^{67} +7.00000 q^{69} +(-4.50000 + 7.79423i) q^{73} +(-5.29150 - 9.16515i) q^{75} +(-1.32288 - 2.29129i) q^{79} +(2.50000 - 4.33013i) q^{81} -10.5830 q^{83} -3.00000 q^{85} +(5.29150 - 9.16515i) q^{87} +(-4.50000 - 7.79423i) q^{89} +(3.50000 + 6.06218i) q^{93} +(11.9059 - 20.6216i) q^{95} +8.00000 q^{97} +10.5830 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{5} - 8 q^{9}+O(q^{10}) \) 4 * q - 6 * q^5 - 8 * q^9	\( 4 q - 6 q^{5} - 8 q^{9} + 16 q^{13} + 2 q^{17} - 8 q^{25} - 16 q^{29} - 14 q^{33} + 10 q^{37} - 32 q^{41} - 24 q^{45} - 14 q^{53} - 84 q^{57} - 10 q^{61} - 24 q^{65} + 28 q^{69} - 18 q^{73} + 10 q^{81} - 12 q^{85} - 18 q^{89} + 14 q^{93} + 32 q^{97}+O(q^{100}) \) 4 * q - 6 * q^5 - 8 * q^9 + 16 * q^13 + 2 * q^17 - 8 * q^25 - 16 * q^29 - 14 * q^33 + 10 * q^37 - 32 * q^41 - 24 * q^45 - 14 * q^53 - 84 * q^57 - 10 * q^61 - 24 * q^65 + 28 * q^69 - 18 * q^73 + 10 * q^81 - 12 * q^85 - 18 * q^89 + 14 * q^93 + 32 * q^97

Introduction

L-functions

Modular forms

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