LMFDB - Embedded newform 1568.2.t.h.753.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1568,2,Mod(177,1568)]

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, 3, 2]))

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

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

chi := DirichletCharacter("1568.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1568 = 2^{5} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1568.t (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:	$12.5205430369$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 392)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			753.1
Character	$\chi$	$=$	1568.753
Dual form			1568.2.t.h.177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.48442 - 1.43438i) q^{3} +(-2.76990 + 1.59920i) q^{5} +(2.61491 + 4.52915i) q^{9} +O(q^{10})$	\(q+(-2.48442 - 1.43438i) q^{3} +(-2.76990 + 1.59920i) q^{5} +(2.61491 + 4.52915i) q^{9} +(-1.25758 - 0.726062i) q^{11} +1.14479i q^{13} +9.17548 q^{15} +(-2.79001 + 4.83244i) q^{17} +(1.27690 - 0.737219i) q^{19} +(1.64207 + 2.84415i) q^{23} +(2.61491 - 4.52915i) q^{25} -6.39682i q^{27} +3.59086i q^{29} +(-0.506184 + 0.876737i) q^{31} +(2.08290 + 3.60769i) q^{33} +(5.62493 - 3.24755i) q^{37} +(1.64207 - 2.84415i) q^{39} +7.39608 q^{41} +7.59434i q^{43} +(-14.4861 - 8.36354i) q^{45} +(-5.98186 - 10.3609i) q^{47} +(13.8631 - 8.00388i) q^{51} +(-9.54216 - 5.50917i) q^{53} +4.64449 q^{55} -4.22982 q^{57} +(-5.47043 - 3.15835i) q^{59} +(-2.76990 + 1.59920i) q^{61} +(-1.83076 - 3.17097i) q^{65} +(-2.25593 - 1.30246i) q^{67} -9.42145i q^{69} -12.4596 q^{71} +(4.60607 - 7.97794i) q^{73} +(-12.9931 + 7.50156i) q^{75} +(-6.94567 - 12.0302i) q^{79} +(-1.33076 + 2.30494i) q^{81} +7.87125i q^{83} -17.8472i q^{85} +(5.15067 - 8.92122i) q^{87} +(-1.61514 - 2.79750i) q^{89} +(2.51515 - 1.45212i) q^{93} +(-2.35793 + 4.08405i) q^{95} +0.401845 q^{97} -7.59434i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{9}+O(q^{10}) $ 24 * q + 12 * q^9	$ 24 q + 12 q^{9} + 32 q^{15} + 32 q^{23} + 12 q^{25} + 32 q^{39} - 8 q^{65} - 96 q^{71} - 80 q^{79} + 4 q^{81} - 64 q^{95}+O(q^{100}) $ 24 * q + 12 * q^9 + 32 * q^15 + 32 * q^23 + 12 * q^25 + 32 * q^39 - 8 * q^65 - 96 * q^71 - 80 * q^79 + 4 * q^81 - 64 * q^95

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
$3$	−2.48442	−	1.43438i	−1.43438	−	0.828141i	−0.436932	−	0.899495i	$-0.643935\pi$
$3$	−2.48442	−	1.43438i	−1.43438	−	0.828141i	−0.997451	+	0.0713535i	$0.977268\pi$
$4$		0			0
$5$	−2.76990	+	1.59920i	−1.23874	+	0.715186i	−0.968836	−	0.247702i	$-0.920325\pi$
$5$	−2.76990	+	1.59920i	−1.23874	+	0.715186i	−0.269902	+	0.962888i	$0.586991\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	2.61491	+	4.52915i	0.871636	+	1.50972i
$10$		0			0
$11$	−1.25758	−	0.726062i	−0.379174	−	0.218916i	0.298285	−	0.954477i	$-0.403585\pi$
$11$	−1.25758	−	0.726062i	−0.379174	−	0.218916i	−0.677459	+	0.735561i	$0.736919\pi$
$12$		0			0
$13$			1.14479i			0.317509i	0.987318	+	0.158754i	$0.0507478\pi$
$13$			1.14479i			0.317509i	−0.987318	+	0.158754i	$0.949252\pi$
$14$		0			0
$15$	9.17548			2.36910
$16$		0			0
$17$	−2.79001	+	4.83244i	−0.676676	+	1.17204i	0.299299	+	0.954159i	$0.403247\pi$
$17$	−2.79001	+	4.83244i	−0.676676	+	1.17204i	−0.975976	+	0.217879i	$0.930086\pi$
$18$		0			0
$19$	1.27690	−	0.737219i	0.292941	−	0.169130i	−0.346326	−	0.938114i	$-0.612571\pi$
$19$	1.27690	−	0.737219i	0.292941	−	0.169130i	0.639267	+	0.768985i	$0.279238\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.64207	+	2.84415i	0.342396	+	0.593047i	0.984877	−	0.173254i	$-0.0554282\pi$
$23$	1.64207	+	2.84415i	0.342396	+	0.593047i	−0.642481	+	0.766302i	$0.722095\pi$
$24$		0			0
$25$	2.61491	−	4.52915i	0.522982	−	0.905831i
$26$		0			0
$27$		−	6.39682i		−	1.23107i
$28$		0			0
$29$			3.59086i			0.666806i	0.942784	+	0.333403i	$0.108197\pi$
$29$			3.59086i			0.666806i	−0.942784	+	0.333403i	$0.891803\pi$
$30$		0			0
$31$	−0.506184	+	0.876737i	−0.0909134	+	0.157467i	−0.907896	−	0.419196i	$-0.862312\pi$
$31$	−0.506184	+	0.876737i	−0.0909134	+	0.157467i	0.816982	+	0.576663i	$0.195645\pi$
$32$		0			0
$33$	2.08290	+	3.60769i	0.362587	+	0.628018i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	5.62493	−	3.24755i	0.924733	−	0.533895i	0.0395909	−	0.999216i	$-0.487395\pi$
$37$	5.62493	−	3.24755i	0.924733	−	0.533895i	0.885142	+	0.465321i	$0.154061\pi$
$38$		0			0
$39$	1.64207	−	2.84415i	0.262942	−	0.455429i
$40$		0			0
$41$	7.39608			1.15507			0.577536	−	0.816365i	$-0.304014\pi$
$41$	7.39608			1.15507			0.577536	+	0.816365i	$0.304014\pi$
$42$		0			0
$43$			7.59434i			1.15813i	0.815283	+	0.579063i	$0.196581\pi$
$43$			7.59434i			1.15813i	−0.815283	+	0.579063i	$0.803419\pi$
$44$		0			0
$45$	−14.4861	−	8.36354i	−2.15946	−	1.24676i
$46$		0			0
$47$	−5.98186	−	10.3609i	−0.872544	−	1.51129i	−0.859356	−	0.511378i	$-0.829135\pi$
$47$	−5.98186	−	10.3609i	−0.872544	−	1.51129i	−0.0131883	−	0.999913i	$-0.504198\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	13.8631	−	8.00388i	1.94123	−	1.12077i
$52$		0			0
$53$	−9.54216	−	5.50917i	−1.31072	−	0.756743i	−0.328502	−	0.944503i	$-0.606544\pi$
$53$	−9.54216	−	5.50917i	−1.31072	−	0.756743i	−0.982215	+	0.187760i	$0.939877\pi$
$54$		0			0
$55$	4.64449			0.626262
$56$		0			0
$57$	−4.22982			−0.560253
$58$		0			0
$59$	−5.47043	−	3.15835i	−0.712189	−	0.411183i	0.0996819	−	0.995019i	$-0.468217\pi$
$59$	−5.47043	−	3.15835i	−0.712189	−	0.411183i	−0.811871	+	0.583837i	$0.801551\pi$
$60$		0			0
$61$	−2.76990	+	1.59920i	−0.354650	+	0.204757i	−0.666731	−	0.745298i	$-0.732307\pi$
$61$	−2.76990	+	1.59920i	−0.354650	+	0.204757i	0.312082	+	0.950055i	$0.398974\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.83076	−	3.17097i	−0.227078	−	0.393310i
$66$		0			0
$67$	−2.25593	−	1.30246i	−0.275606	−	0.159121i	0.355827	−	0.934552i	$-0.384199\pi$
$67$	−2.25593	−	1.30246i	−0.275606	−	0.159121i	−0.631432	+	0.775431i	$0.717533\pi$
$68$		0			0
$69$		−	9.42145i		−	1.13421i
$70$		0			0
$71$	−12.4596			−1.47869			−0.739343	−	0.673329i	$-0.764864\pi$
$71$	−12.4596			−1.47869			−0.739343	+	0.673329i	$0.764864\pi$
$72$		0			0
$73$	4.60607	−	7.97794i	0.539099	−	0.933747i	−0.459853	−	0.887995i	$-0.652098\pi$
$73$	4.60607	−	7.97794i	0.539099	−	0.933747i	0.998953	−	0.0457527i	$-0.0145686\pi$
$74$		0			0
$75$	−12.9931	+	7.50156i	−1.50031	+	0.866205i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−6.94567	−	12.0302i	−0.781449	−	1.35351i	−0.931098	−	0.364770i	$-0.881148\pi$
$79$	−6.94567	−	12.0302i	−0.781449	−	1.35351i	0.149649	−	0.988739i	$-0.452186\pi$
$80$		0			0
$81$	−1.33076	+	2.30494i	−0.147862	+	0.256105i
$82$		0			0
$83$			7.87125i			0.863982i	0.901878	+	0.431991i	$0.142189\pi$
$83$			7.87125i			0.863982i	−0.901878	+	0.431991i	$0.857811\pi$
$84$		0			0
$85$		−	17.8472i		−	1.93580i
$86$		0			0
$87$	5.15067	−	8.92122i	0.552210	−	0.956455i
$88$		0			0
$89$	−1.61514	−	2.79750i	−0.171204	−	0.296534i	0.767637	−	0.640885i	$-0.221432\pi$
$89$	−1.61514	−	2.79750i	−0.171204	−	0.296534i	−0.938841	+	0.344351i	$0.888099\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	2.51515	−	1.45212i	0.260809	−	0.150578i
$94$		0			0
$95$	−2.35793	+	4.08405i	−0.241918	+	0.419015i
$96$		0			0
$97$	0.401845			0.0408012			0.0204006	−	0.999792i	$-0.493506\pi$
$97$	0.401845			0.0408012			0.0204006	+	0.999792i	$0.493506\pi$
$98$		0			0
$99$		−	7.59434i		−	0.763260i
$100$		0			0
$101$	5.38931	+	3.11152i	0.536256	+	0.309608i	0.743560	−	0.668669i	$-0.233136\pi$
$101$	5.38931	+	3.11152i	0.536256	+	0.309608i	−0.207304	+	0.978277i	$0.566469\pi$
$102$		0			0
$103$	3.65962	+	6.33865i	0.360593	+	0.624565i	0.988059	−	0.154079i	$-0.0492410\pi$
$103$	3.65962	+	6.33865i	0.360593	+	0.624565i	−0.627466	+	0.778644i	$0.715908\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.87084	+	2.23483i	−0.374208	+	0.216049i	−0.675295	−	0.737547i	$-0.735984\pi$
$107$	−3.87084	+	2.23483i	−0.374208	+	0.216049i	0.301087	+	0.953597i	$0.402651\pi$
$108$		0			0
$109$	10.9442	+	6.31866i	1.04827	+	0.605218i	0.922164	−	0.386799i	$-0.126419\pi$
$109$	10.9442	+	6.31866i	1.04827	+	0.605218i	0.126104	+	0.992017i	$0.459753\pi$
$110$		0			0
$111$	−18.6329			−1.76856
$112$		0			0
$113$	−10.2298			−0.962340			−0.481170	−	0.876627i	$-0.659788\pi$
$113$	−10.2298			−0.962340			−0.481170	+	0.876627i	$0.659788\pi$
$114$		0			0
$115$	−9.09677	−	5.25202i	−0.848278	−	0.489754i
$116$		0			0
$117$	−5.18495	+	2.99353i	−0.479349	+	0.276752i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−4.44567	−	7.70012i	−0.404152	−	0.700011i
$122$		0			0
$123$	−18.3750	−	10.6088i	−1.65682	−	0.956564i
$124$		0			0
$125$			0.735042i			0.0657442i
$126$		0			0
$127$	−15.0668			−1.33696			−0.668482	−	0.743728i	$-0.733056\pi$
$127$	−15.0668			−1.33696			−0.668482	+	0.743728i	$0.733056\pi$
$128$		0			0
$129$	10.8932	−	18.8676i	0.959092	−	1.66120i
$130$		0			0
$131$	4.26291	−	2.46119i	0.372452	−	0.215035i	−0.302077	−	0.953283i	$-0.597680\pi$
$131$	4.26291	−	2.46119i	0.372452	−	0.215035i	0.674529	+	0.738248i	$0.264347\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	10.2298	+	17.7186i	0.880442	+	1.52497i
$136$		0			0
$137$	−9.17548	+	15.8924i	−0.783914	+	1.35778i	0.145731	+	0.989324i	$0.453447\pi$
$137$	−9.17548	+	15.8924i	−0.783914	+	1.35778i	−0.929645	+	0.368455i	$0.879887\pi$
$138$		0			0
$139$		−	17.0567i		−	1.44673i	−0.690464	−	0.723366i	$-0.742594\pi$
$139$		−	17.0567i		−	1.44673i	0.690464	−	0.723366i	$-0.257406\pi$
$140$		0			0
$141$			34.3211i			2.89036i
$142$		0			0
$143$	0.831192	−	1.43967i	0.0695078	−	0.120391i
$144$		0			0
$145$	−5.74252	−	9.94634i	−0.476890	−	0.825998i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	17.6656	−	10.1993i	1.44723	−	0.835556i	0.448910	−	0.893577i	$-0.351812\pi$
$149$	17.6656	−	10.1993i	1.44723	−	0.835556i	0.998315	+	0.0580206i	$0.0184789\pi$
$150$		0			0
$151$	2.35793	−	4.08405i	0.191885	−	0.332355i	−0.753990	−	0.656886i	$-0.771873\pi$
$151$	2.35793	−	4.08405i	0.191885	−	0.332355i	0.945875	+	0.324531i	$0.105206\pi$
$152$		0			0
$153$	−29.1825			−2.35926
$154$		0			0
$155$		−	3.23797i		−	0.260080i
$156$		0			0
$157$	−7.80436	−	4.50585i	−0.622856	−	0.359606i	0.155124	−	0.987895i	$-0.450422\pi$
$157$	−7.80436	−	4.50585i	−0.622856	−	0.359606i	−0.777980	+	0.628289i	$0.783755\pi$
$158$		0			0
$159$	15.8045	+	27.3742i	1.25338	+	2.17092i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	4.06174	−	2.34505i	0.318140	−	0.183678i	−0.332423	−	0.943130i	$-0.607866\pi$
$163$	4.06174	−	2.34505i	0.318140	−	0.183678i	0.650563	+	0.759452i	$0.274533\pi$
$164$		0			0
$165$	−11.5389	−	6.66197i	−0.898300	−	0.518634i
$166$		0			0
$167$	13.9885			1.08246			0.541230	−	0.840875i	$-0.317959\pi$
$167$	13.9885			1.08246			0.541230	+	0.840875i	$0.317959\pi$
$168$		0			0
$169$	11.6894			0.899188
$170$		0			0
$171$	6.67795	+	3.85552i	0.510676	+	0.294839i
$172$		0			0
$173$	6.53123	−	3.77081i	0.496560	−	0.286689i	−0.230732	−	0.973017i	$-0.574112\pi$
$173$	6.53123	−	3.77081i	0.496560	−	0.286689i	0.727292	+	0.686328i	$0.240779\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	9.06058	+	15.6934i	0.681035	+	1.17959i
$178$		0			0
$179$	12.8946	+	7.44468i	0.963785	+	0.556441i	0.897336	−	0.441348i	$-0.145500\pi$
$179$	12.8946	+	7.44468i	0.963785	+	0.556441i	0.0664489	+	0.997790i	$0.478833\pi$
$180$		0			0
$181$		−	16.4911i		−	1.22577i	−0.790170	−	0.612887i	$-0.790008\pi$
$181$		−	16.4911i		−	1.22577i	0.790170	−	0.612887i	$-0.209992\pi$
$182$		0			0
$183$	9.17548			0.678271
$184$		0			0
$185$	−10.3870	+	17.9908i	−0.763668	+	1.32271i
$186$		0			0
$187$	7.01730	−	4.05144i	0.513156	−	0.296271i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.17548	+	2.03600i	0.0850550	+	0.147320i	0.905415	−	0.424528i	$-0.139560\pi$
$191$	1.17548	+	2.03600i	0.0850550	+	0.147320i	−0.820360	+	0.571848i	$0.806227\pi$
$192$		0			0
$193$	4.77643	−	8.27302i	0.343815	−	0.595505i	−0.641323	−	0.767271i	$-0.721614\pi$
$193$	4.77643	−	8.27302i	0.343815	−	0.595505i	0.985138	+	0.171766i	$0.0549474\pi$
$194$		0			0
$195$			10.5040i			0.752210i
$196$		0			0
$197$		−	12.0578i		−	0.859086i	−0.903046	−	0.429543i	$-0.858675\pi$
$197$		−	12.0578i		−	0.859086i	0.903046	−	0.429543i	$-0.141325\pi$
$198$		0			0
$199$	1.99724	−	3.45931i	0.141580	−	0.245224i	−0.786512	−	0.617575i	$-0.788115\pi$
$199$	1.99724	−	3.45931i	0.141580	−	0.245224i	0.928092	+	0.372351i	$0.121448\pi$
$200$		0			0
$201$	3.73646	+	6.47173i	0.263549	+	0.456481i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−20.4864	+	11.8278i	−1.43083	+	0.826092i
$206$		0			0
$207$	−8.58774	+	14.8744i	−0.596889	+	1.03384i
$208$		0			0
$209$	−2.14107			−0.148101
$210$		0			0
$211$		−	6.44154i		−	0.443454i	−0.975109	−	0.221727i	$-0.928831\pi$
$211$		−	6.44154i		−	0.443454i	0.975109	−	0.221727i	$-0.0711694\pi$
$212$		0			0
$213$	30.9550	+	17.8719i	2.12100	+	1.22456i
$214$		0			0
$215$	−12.1449	−	21.0356i	−0.828275	−	1.43461i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−22.8868	+	13.2137i	−1.54655	+	0.892901i
$220$		0			0
$221$	−5.53215	−	3.19399i	−0.372132	−	0.214851i
$222$		0			0
$223$	19.2830			1.29128			0.645641	−	0.763641i	$-0.276590\pi$
$223$	19.2830			1.29128			0.645641	+	0.763641i	$0.276590\pi$
$224$		0			0
$225$	27.3510			1.82340
$226$		0			0
$227$	8.39083	+	4.84445i	0.556919	+	0.321537i	0.751908	−	0.659268i	$-0.229134\pi$
$227$	8.39083	+	4.84445i	0.556919	+	0.321537i	−0.194989	+	0.980805i	$0.562467\pi$
$228$		0			0
$229$	8.10535	−	4.67962i	0.535616	−	0.309238i	−0.207684	−	0.978196i	$-0.566593\pi$
$229$	8.10535	−	4.67962i	0.535616	−	0.309238i	0.743301	+	0.668958i	$0.233259\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−8.45963	−	14.6525i	−0.554209	−	0.959918i	−0.997965	−	0.0637701i	$-0.979688\pi$
$233$	−8.45963	−	14.6525i	−0.554209	−	0.959918i	0.443756	−	0.896148i	$-0.353646\pi$
$234$		0			0
$235$	33.1384	+	19.1324i	2.16171	+	1.24806i
$236$		0			0
$237$			39.8510i			2.58860i
$238$		0			0
$239$	4.71585			0.305043			0.152522	−	0.988300i	$-0.451261\pi$
$239$	4.71585			0.305043			0.152522	+	0.988300i	$0.451261\pi$
$240$		0			0
$241$	−4.44356	+	7.69648i	−0.286235	+	0.495774i	−0.972908	−	0.231193i	$-0.925737\pi$
$241$	−4.44356	+	7.69648i	−0.286235	+	0.495774i	0.686673	+	0.726967i	$0.259070\pi$
$242$		0			0
$243$	−10.0071	+	5.77759i	−0.641954	+	0.370632i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.843964	+	1.46179i	0.0537001	+	0.0930114i
$248$		0			0
$249$	11.2904	−	19.5555i	0.715499	−	1.23928i
$250$		0			0
$251$			16.3974i			1.03500i	0.855684	+	0.517499i	$0.173137\pi$
$251$			16.3974i			1.03500i	−0.855684	+	0.517499i	$0.826863\pi$
$252$		0			0
$253$		−	4.76899i		−	0.299824i
$254$		0			0
$255$	−25.5997	+	44.3399i	−1.60311	+	2.77667i
$256$		0			0
$257$	−6.36396	−	11.0227i	−0.396973	−	0.687577i	0.596378	−	0.802704i	$-0.296606\pi$
$257$	−6.36396	−	11.0227i	−0.396973	−	0.687577i	−0.993351	+	0.115126i	$0.963273\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−16.2636	+	9.38977i	−1.00669	+	0.581212i
$262$		0			0
$263$	10.9457	−	18.9585i	0.674939	−	1.16903i	−0.301548	−	0.953451i	$-0.597503\pi$
$263$	10.9457	−	18.9585i	0.674939	−	1.16903i	0.976487	−	0.215577i	$-0.0691633\pi$
$264$		0			0
$265$	35.2412			2.16485
$266$		0			0
$267$			9.26689i			0.567125i
$268$		0			0
$269$	−16.0367	−	9.25880i	−0.977776	−	0.564519i	−0.0761780	−	0.997094i	$-0.524272\pi$
$269$	−16.0367	−	9.25880i	−0.977776	−	0.564519i	−0.901598	+	0.432575i	$0.857605\pi$
$270$		0			0
$271$	6.96673	+	12.0667i	0.423199	+	0.733001i	0.996250	−	0.0865177i	$-0.0275739\pi$
$271$	6.96673	+	12.0667i	0.423199	+	0.733001i	−0.573052	+	0.819519i	$0.694241\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−6.57689	+	3.79717i	−0.396601	+	0.228978i
$276$		0			0
$277$	12.0573	+	6.96130i	0.724454	+	0.418264i	0.816390	−	0.577501i	$-0.195972\pi$
$277$	12.0573	+	6.96130i	0.724454	+	0.418264i	−0.0919358	+	0.995765i	$0.529305\pi$
$278$		0			0
$279$	−5.29450			−0.316973
$280$		0			0
$281$	1.43171			0.0854084			0.0427042	−	0.999088i	$-0.486403\pi$
$281$	1.43171			0.0854084			0.0427042	+	0.999088i	$0.486403\pi$
$282$		0			0
$283$	−3.89631	−	2.24953i	−0.231611	−	0.133721i	0.379704	−	0.925108i	$-0.376026\pi$
$283$	−3.89631	−	2.24953i	−0.231611	−	0.133721i	−0.611315	+	0.791387i	$0.709359\pi$
$284$		0			0
$285$	11.7162	−	6.76434i	0.694006	−	0.400685i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−7.06829	−	12.2426i	−0.415782	−	0.720156i
$290$		0			0
$291$	−0.998353	−	0.576399i	−0.0585245	−	0.0337891i
$292$		0			0
$293$			8.04068i			0.469741i	0.972027	+	0.234871i	$0.0754667\pi$
$293$			8.04068i			0.469741i	−0.972027	+	0.234871i	$0.924533\pi$
$294$		0			0
$295$	20.2034			1.17629
$296$		0			0
$297$	−4.64449	+	8.04449i	−0.269500	+	0.466788i
$298$		0			0
$299$	−3.25597	+	1.87984i	−0.188298	+	0.108714i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−8.92622	−	15.4607i	−0.512798	−	0.888192i
$304$		0			0
$305$	5.11491	−	8.85928i	0.292879	−	0.507281i
$306$		0			0
$307$		−	11.9785i		−	0.683648i	−0.939764	−	0.341824i	$-0.888955\pi$
$307$		−	11.9785i		−	0.683648i	0.939764	−	0.341824i	$-0.111045\pi$
$308$		0			0
$309$		−	20.9972i		−	1.19449i
$310$		0			0
$311$	10.8350	−	18.7668i	0.614398	−	1.06417i	−0.376092	−	0.926582i	$-0.622732\pi$
$311$	10.8350	−	18.7668i	0.614398	−	1.06417i	0.990490	−	0.137586i	$-0.0439344\pi$
$312$		0			0
$313$	−4.71041	−	8.15866i	−0.266248	−	0.461155i	0.701642	−	0.712530i	$-0.252451\pi$
$313$	−4.71041	−	8.15866i	−0.266248	−	0.461155i	−0.967890	+	0.251375i	$0.919117\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.92725	+	4.57680i	−0.445239	+	0.257059i	−0.705817	−	0.708394i	$-0.749420\pi$
$317$	−7.92725	+	4.57680i	−0.445239	+	0.257059i	0.260579	+	0.965453i	$0.416087\pi$
$318$		0			0
$319$	2.60719	−	4.51578i	0.145975	−	0.252835i
$320$		0			0
$321$	12.8224			0.715678
$322$		0			0
$323$			8.22739i			0.457784i
$324$		0			0
$325$	5.18495	+	2.99353i	0.287609	+	0.166051i
$326$		0			0
$327$	−18.1268	−	31.3965i	−1.00241	−	1.73623i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	17.2155	−	9.93939i	0.946251	−	0.546318i	0.0543365	−	0.998523i	$-0.482696\pi$
$331$	17.2155	−	9.93939i	0.946251	−	0.546318i	0.891914	+	0.452205i	$0.149362\pi$
$332$		0			0
$333$	29.4173	+	16.9841i	1.61206	+	0.930724i
$334$		0			0
$335$	8.33161			0.455204
$336$		0			0
$337$	−19.5529			−1.06511			−0.532556	−	0.846395i	$-0.678768\pi$
$337$	−19.5529			−1.06511			−0.532556	+	0.846395i	$0.678768\pi$
$338$		0			0
$339$	25.4152	+	14.6735i	1.38036	+	0.796953i
$340$		0			0
$341$	1.27313	−	0.735042i	0.0689439	−	0.0398048i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	15.0668	+	26.0965i	0.811170	+	1.40499i
$346$		0			0
$347$	−26.8505	−	15.5021i	−1.44141	−	0.832198i	−0.443465	−	0.896292i	$-0.646251\pi$
$347$	−26.8505	−	15.5021i	−1.44141	−	0.832198i	−0.997944	+	0.0640940i	$0.979584\pi$
$348$		0			0
$349$		−	14.6735i		−	0.785453i	−0.919655	−	0.392726i	$-0.871532\pi$
$349$		−	14.6735i		−	0.785453i	0.919655	−	0.392726i	$-0.128468\pi$
$350$		0			0
$351$	7.32304			0.390875
$352$		0			0
$353$	−12.8333	+	22.2280i	−0.683049	+	1.18308i	0.290996	+	0.956724i	$0.406013\pi$
$353$	−12.8333	+	22.2280i	−0.683049	+	1.18308i	−0.974046	+	0.226352i	$0.927320\pi$
$354$		0			0
$355$	34.5120	−	19.9255i	1.83170	−	1.05754i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2.10170	−	3.64026i	−0.110924	−	0.192125i	0.805219	−	0.592977i	$-0.202048\pi$
$359$	−2.10170	−	3.64026i	−0.110924	−	0.192125i	−0.916143	+	0.400852i	$0.868714\pi$
$360$		0			0
$361$	−8.41302	+	14.5718i	−0.442790	+	0.766935i
$362$		0			0
$363$			25.5072i			1.33878i
$364$		0			0
$365$			29.4642i			1.54222i
$366$		0			0
$367$	−17.8018	+	30.8335i	−0.929244	+	1.60950i	−0.144655	+	0.989482i	$0.546207\pi$
$367$	−17.8018	+	30.8335i	−0.929244	+	1.60950i	−0.784589	+	0.620016i	$0.787126\pi$
$368$		0			0
$369$	19.3401	+	33.4980i	1.00680	+	1.74383i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−8.64192	+	4.98942i	−0.447462	+	0.258342i	−0.706758	−	0.707456i	$-0.749843\pi$
$373$	−8.64192	+	4.98942i	−0.447462	+	0.258342i	0.259296	+	0.965798i	$0.416510\pi$
$374$		0			0
$375$	1.05433	−	1.82616i	0.0544455	−	0.0943023i
$376$		0			0
$377$	−4.11080			−0.211717
$378$		0			0
$379$		−	24.5283i		−	1.25993i	−0.776622	−	0.629967i	$-0.783068\pi$
$379$		−	24.5283i		−	1.25993i	0.776622	−	0.629967i	$-0.216932\pi$
$380$		0			0
$381$	37.4324	+	21.6116i	1.91772	+	1.10719i
$382$		0			0
$383$	4.31948	+	7.48156i	0.220715	+	0.382290i	0.955025	−	0.296524i	$-0.0958276\pi$
$383$	4.31948	+	7.48156i	0.220715	+	0.382290i	−0.734310	+	0.678814i	$0.762494\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−34.3959	+	19.8585i	−1.74844	+	1.00946i
$388$		0			0
$389$	10.9442	+	6.31866i	0.554895	+	0.320369i	0.751094	−	0.660195i	$-0.229526\pi$
$389$	10.9442	+	6.31866i	0.554895	+	0.320369i	−0.196199	+	0.980564i	$0.562860\pi$
$390$		0			0
$391$	−18.3256			−0.926765
$392$		0			0
$393$	−14.1212			−0.712318
$394$		0			0
$395$	38.4776	+	22.2151i	1.93602	+	1.11776i
$396$		0			0
$397$	1.62799	−	0.939919i	0.0817063	−	0.0471732i	−0.458590	−	0.888648i	$-0.651645\pi$
$397$	1.62799	−	0.939919i	0.0817063	−	0.0471732i	0.540297	+	0.841475i	$0.318312\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−7.29039	−	12.6273i	−0.364065	−	0.630579i	0.624561	−	0.780976i	$-0.285278\pi$
$401$	−7.29039	−	12.6273i	−0.364065	−	0.630579i	−0.988626	+	0.150398i	$0.951945\pi$
$402$		0			0
$403$	−1.00368	−	0.579477i	−0.0499970	−	0.0288658i
$404$		0			0
$405$		−	8.51263i		−	0.422996i
$406$		0			0
$407$	−9.43171			−0.467512
$408$		0			0
$409$	15.0974	−	26.1495i	0.746519	−	1.29301i	−0.202963	−	0.979186i	$-0.565057\pi$
$409$	15.0974	−	26.1495i	0.746519	−	1.29301i	0.949482	−	0.313822i	$-0.101610\pi$
$410$		0			0
$411$	45.5916	−	26.3223i	2.24887	−	1.29838i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−12.5877	−	21.8026i	−0.617908	−	1.07025i
$416$		0			0
$417$	−24.4659	+	42.3761i	−1.19810	+	2.07517i
$418$		0			0
$419$			7.28773i			0.356029i	0.984028	+	0.178014i	$0.0569673\pi$
$419$			7.28773i			0.356029i	−0.984028	+	0.178014i	$0.943033\pi$
$420$		0			0
$421$		−	2.30560i		−	0.112368i	−0.998420	−	0.0561840i	$-0.982107\pi$
$421$		−	2.30560i		−	0.112368i	0.998420	−	0.0561840i	$-0.0178933\pi$
$422$		0			0
$423$	31.2840	−	54.1855i	1.52108	−	2.63459i
$424$		0			0
$425$	14.5912	+	25.2727i	0.707779	+	1.22591i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−4.13007	+	2.38449i	−0.199401	+	0.115124i
$430$		0			0
$431$	−1.18244	+	2.04805i	−0.0569563	+	0.0986512i	−0.893098	−	0.449863i	$-0.851473\pi$
$431$	−1.18244	+	2.04805i	−0.0569563	+	0.0986512i	0.836141	+	0.548514i	$0.184806\pi$
$432$		0			0
$433$	−11.0832			−0.532624			−0.266312	−	0.963887i	$-0.585805\pi$
$433$	−11.0832			−0.532624			−0.266312	+	0.963887i	$0.585805\pi$
$434$		0			0
$435$			32.9479i			1.57973i
$436$		0			0
$437$	4.19353	+	2.42113i	0.200604	+	0.115819i
$438$		0			0
$439$	−3.33461	−	5.77572i	−0.159152	−	0.275660i	0.775411	−	0.631457i	$-0.217543\pi$
$439$	−3.33461	−	5.77572i	−0.159152	−	0.275660i	−0.934563	+	0.355797i	$0.884209\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.15946	+	0.669416i	−0.0550877	+	0.0318049i	−0.527291	−	0.849685i	$-0.676792\pi$
$443$	−1.15946	+	0.669416i	−0.0550877	+	0.0318049i	0.472203	+	0.881490i	$0.343459\pi$
$444$		0			0
$445$	8.94754	+	5.16586i	0.424154	+	0.244885i
$446$		0			0
$447$	−58.5186			−2.76783
$448$		0			0
$449$	−4.35097			−0.205335			−0.102667	−	0.994716i	$-0.532738\pi$
$449$	−4.35097			−0.205335			−0.102667	+	0.994716i	$0.532738\pi$
$450$		0			0
$451$	−9.30113	−	5.37001i	−0.437973	−	0.252864i
$452$		0			0
$453$	−11.7162	+	6.76434i	−0.550474	+	0.317816i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	11.0062	+	19.0634i	0.514850	+	0.891747i	0.999851	+	0.0172334i	$0.00548584\pi$
$457$	11.0062	+	19.0634i	0.514850	+	0.891747i	−0.485001	+	0.874514i	$0.661181\pi$
$458$		0			0
$459$	30.9122	+	17.8472i	1.44286	+	0.833035i
$460$		0			0
$461$			6.80657i			0.317014i	0.987358	+	0.158507i	$0.0506680\pi$
$461$			6.80657i			0.317014i	−0.987358	+	0.158507i	$0.949332\pi$
$462$		0			0
$463$	−1.43171			−0.0665370			−0.0332685	−	0.999446i	$-0.510592\pi$
$463$	−1.43171			−0.0665370			−0.0332685	+	0.999446i	$0.510592\pi$
$464$		0			0
$465$	−4.64449	+	8.04449i	−0.215383	+	0.373054i
$466$		0			0
$467$	−29.2694	+	16.8987i	−1.35443	+	0.781978i	−0.988866	−	0.148810i	$-0.952456\pi$
$467$	−29.2694	+	16.8987i	−1.35443	+	0.781978i	−0.365560	+	0.930788i	$0.619122\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	12.9262	+	22.3889i	0.595609	+	1.03162i
$472$		0			0
$473$	5.51396	−	9.55046i	0.253532	−	0.439131i
$474$		0			0
$475$		−	7.71104i		−	0.353807i
$476$		0			0
$477$		−	57.6239i		−	2.63842i
$478$		0			0
$479$	10.9789	−	19.0159i	0.501637	−	0.868860i	−0.498361	−	0.866969i	$-0.666065\pi$
$479$	10.9789	−	19.0159i	0.501637	−	0.868860i	0.999998	−	0.00189103i	$-0.000601935\pi$
$480$		0			0
$481$	3.71778	+	6.43939i	0.169516	+	0.293611i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.11307	+	0.642632i	−0.0505420	+	0.0291804i
$486$		0			0
$487$	−18.5613	+	32.1492i	−0.841094	+	1.45682i	0.0478760	+	0.998853i	$0.484755\pi$
$487$	−18.5613	+	32.1492i	−0.841094	+	1.45682i	−0.888970	+	0.457965i	$0.848579\pi$
$488$		0			0
$489$	−13.4548			−0.608446
$490$		0			0
$491$			3.31071i			0.149410i	0.997206	+	0.0747051i	$0.0238016\pi$
$491$			3.31071i			0.149410i	−0.997206	+	0.0747051i	$0.976198\pi$
$492$		0			0
$493$	−17.3526	−	10.0185i	−0.781522	−	0.451212i
$494$		0			0
$495$	12.1449	+	21.0356i	0.545873	+	0.945479i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−21.2475	+	12.2672i	−0.951168	+	0.549157i	−0.893443	−	0.449176i	$-0.851718\pi$
$499$	−21.2475	+	12.2672i	−0.951168	+	0.549157i	−0.0577242	+	0.998333i	$0.518384\pi$
$500$		0			0
$501$	−34.7533	−	20.0648i	−1.55266	−	0.896429i
$502$		0			0
$503$	3.68712			0.164401			0.0822003	−	0.996616i	$-0.473805\pi$
$503$	3.68712			0.164401			0.0822003	+	0.996616i	$0.473805\pi$
$504$		0			0
$505$	−19.9038			−0.885708
$506$		0			0
$507$	−29.0415	−	16.7671i	−1.28978	−	0.744655i
$508$		0			0
$509$	−25.7701	+	14.8783i	−1.14224	+	0.659471i	−0.946984	−	0.321282i	$-0.895886\pi$
$509$	−25.7701	+	14.8783i	−1.14224	+	0.659471i	−0.195254	+	0.980753i	$0.562553\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−4.71585	−	8.16810i	−0.208210	−	0.360630i
$514$		0			0
$515$	−20.2736	−	11.7050i	−0.893361	−	0.515782i
$516$		0			0
$517$			17.3728i			0.764055i
$518$		0			0
$519$	−21.6351			−0.949676
$520$		0			0
$521$	15.0974	−	26.1495i	0.661430	−	1.14563i	−0.318810	−	0.947818i	$-0.603283\pi$
$521$	15.0974	−	26.1495i	0.661430	−	1.14563i	0.980240	−	0.197811i	$-0.0633833\pi$
$522$		0			0
$523$	−36.8342	+	21.2662i	−1.61064	+	0.929906i	−0.621424	+	0.783474i	$0.713446\pi$
$523$	−36.8342	+	21.2662i	−1.61064	+	0.929906i	−0.989221	+	0.146432i	$0.953221\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.82452	−	4.89221i	−0.123038	−	0.213108i
$528$		0			0
$529$	6.10719	−	10.5780i	0.265530	−	0.459911i
$530$		0			0
$531$		−	33.0352i		−	1.43361i
$532$		0			0
$533$			8.46699i			0.366746i
$534$		0			0
$535$	7.14791	−	12.3805i	0.309031	−	0.535257i
$536$		0			0
$537$	−21.3570	−	36.9915i	−0.921624	−	1.59630i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	4.51186	−	2.60492i	0.193980	−	0.111994i	−0.399864	−	0.916574i	$-0.630943\pi$
$541$	4.51186	−	2.60492i	0.193980	−	0.111994i	0.593844	+	0.804580i	$0.297609\pi$
$542$		0			0
$543$	−23.6546	+	40.9709i	−1.01511	+	1.75823i
$544$		0			0
$545$	−40.4193			−1.73137
$546$		0			0
$547$		−	37.1465i		−	1.58827i	−0.607743	−	0.794134i	$-0.707925\pi$
$547$		−	37.1465i		−	1.58827i	0.607743	−	0.794134i	$-0.292075\pi$
$548$		0			0
$549$	−14.4861	−	8.36354i	−0.618251	−	0.356947i
$550$		0			0
$551$	2.64725	+	4.58517i	0.112777	+	0.195335i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	51.6115	−	29.7979i	2.19078	−	1.26485i
$556$		0			0
$557$	−26.6894	−	15.4091i	−1.13086	−	0.652905i	−0.186712	−	0.982415i	$-0.559783\pi$
$557$	−26.6894	−	15.4091i	−1.13086	−	0.652905i	−0.944152	+	0.329510i	$0.893117\pi$
$558$		0			0
$559$	−8.69396			−0.367715
$560$		0			0
$561$	−23.2453			−0.981415
$562$		0			0
$563$	17.6920	+	10.2145i	0.745627	+	0.430488i	0.824112	−	0.566427i	$-0.191675\pi$
$563$	17.6920	+	10.2145i	0.745627	+	0.430488i	−0.0784846	+	0.996915i	$0.525008\pi$
$564$		0			0
$565$	28.3356	−	16.3596i	1.19209	−	0.688252i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−14.0062	−	24.2595i	−0.587172	−	1.01701i	−0.994601	−	0.103775i	$-0.966908\pi$
$569$	−14.0062	−	24.2595i	−0.587172	−	1.01701i	0.407429	−	0.913237i	$-0.366426\pi$
$570$		0			0
$571$	12.6109	+	7.28090i	0.527749	+	0.304696i	0.740099	−	0.672498i	$-0.234778\pi$
$571$	12.6109	+	7.28090i	0.527749	+	0.304696i	−0.212350	+	0.977194i	$0.568112\pi$
$572$		0			0
$573$		−	6.74437i		−	0.281750i
$574$		0			0
$575$	17.1755			0.716267
$576$		0			0
$577$	10.1586	−	17.5952i	0.422907	−	0.732497i	−0.573315	−	0.819335i	$-0.694343\pi$
$577$	10.1586	−	17.5952i	0.422907	−	0.732497i	0.996222	+	0.0868380i	$0.0276763\pi$
$578$		0			0
$579$	−23.7333	+	13.7025i	−0.986324	+	0.569454i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	8.00000	+	13.8564i	0.331326	+	0.573874i
$584$		0			0
$585$	9.57454	−	16.5836i	0.395858	−	0.685647i
$586$		0			0
$587$			8.05859i			0.332614i	0.986074	+	0.166307i	$0.0531842\pi$
$587$			8.05859i			0.332614i	−0.986074	+	0.166307i	$0.946816\pi$
$588$		0			0
$589$			1.49267i			0.0615046i
$590$		0			0
$591$	−17.2956	+	29.9568i	−0.711445	+	1.23226i
$592$		0			0
$593$	13.0332	+	22.5741i	0.535209	+	0.927009i	0.999153	+	0.0411444i	$0.0131004\pi$
$593$	13.0332	+	22.5741i	0.535209	+	0.927009i	−0.463944	+	0.885864i	$0.653566\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−9.92396	+	5.72960i	−0.406161	+	0.234497i
$598$		0			0
$599$	23.7438	−	41.1254i	0.970144	−	1.68034i	0.275037	−	0.961434i	$-0.411310\pi$
$599$	23.7438	−	41.1254i	0.970144	−	1.68034i	0.695107	−	0.718906i	$-0.255357\pi$
$600$		0			0
$601$	2.00922			0.0819580			0.0409790	−	0.999160i	$-0.486952\pi$
$601$	2.00922			0.0819580			0.0409790	+	0.999160i	$0.486952\pi$
$602$		0			0
$603$		−	13.6233i		−	0.554782i
$604$		0			0
$605$	24.6281	+	14.2191i	1.00128	+	0.578087i
$606$		0			0
$607$	−20.7740	−	35.9816i	−0.843191	−	1.46045i	−0.887183	−	0.461418i	$-0.847341\pi$
$607$	−20.7740	−	35.9816i	−0.843191	−	1.46045i	0.0439917	−	0.999032i	$-0.485992\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	11.8611	−	6.84800i	0.479848	−	0.277041i
$612$		0			0
$613$	30.3176	+	17.5039i	1.22452	+	0.706974i	0.965877	−	0.259000i	$-0.0833929\pi$
$613$	30.3176	+	17.5039i	1.22452	+	0.706974i	0.258638	+	0.965974i	$0.416726\pi$
$614$		0			0
$615$	67.8626			2.73648
$616$		0			0
$617$	6.58078			0.264932			0.132466	−	0.991188i	$-0.457710\pi$
$617$	6.58078			0.264932			0.132466	+	0.991188i	$0.457710\pi$
$618$		0			0
$619$	0.339345	+	0.195921i	0.0136394	+	0.00787473i	0.506804	−	0.862061i	$-0.330827\pi$
$619$	0.339345	+	0.195921i	0.0136394	+	0.00787473i	−0.493165	+	0.869936i	$0.664160\pi$
$620$		0			0
$621$	18.1935	−	10.5040i	0.730081	−	0.421513i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	11.8991	+	20.6098i	0.475962	+	0.824391i
$626$		0			0
$627$	5.31932	+	3.07111i	0.212433	+	0.122648i
$628$		0			0
$629$			36.2428i			1.44510i
$630$		0			0
$631$	−23.4876			−0.935025			−0.467512	−	0.883987i	$-0.654850\pi$
$631$	−23.4876			−0.935025			−0.467512	+	0.883987i	$0.654850\pi$
$632$		0			0
$633$	−9.23964	+	16.0035i	−0.367243	+	0.636083i
$634$		0			0
$635$	41.7336	−	24.0949i	1.65615	−	0.956178i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−32.5808	−	56.4316i	−1.28888	−	2.23240i
$640$		0			0
$641$	7.96735	−	13.7999i	0.314691	−	0.545061i	−0.664680	−	0.747128i	$-0.731432\pi$
$641$	7.96735	−	13.7999i	0.314691	−	0.545061i	0.979372	+	0.202066i	$0.0647656\pi$
$642$		0			0
$643$		−	44.8491i		−	1.76868i	−0.466847	−	0.884338i	$-0.654610\pi$
$643$		−	44.8491i		−	1.76868i	0.466847	−	0.884338i	$-0.345390\pi$
$644$		0			0
$645$			69.6817i			2.74372i
$646$		0			0
$647$	−11.9912	+	20.7694i	−0.471424	+	0.816530i	−0.999466	−	0.0326885i	$-0.989593\pi$
$647$	−11.9912	+	20.7694i	−0.471424	+	0.816530i	0.528042	+	0.849218i	$0.322926\pi$
$648$		0			0
$649$	4.58632	+	7.94374i	0.180029	+	0.311819i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	7.85107	−	4.53282i	0.307236	−	0.177383i	−0.338453	−	0.940983i	$-0.609904\pi$
$653$	7.85107	−	4.53282i	0.307236	−	0.177383i	0.645689	+	0.763600i	$0.276570\pi$
$654$		0			0
$655$	−7.87189	+	13.6345i	−0.307580	+	0.532744i
$656$		0			0
$657$	48.1778			1.87959
$658$		0			0
$659$			21.9578i			0.855354i	0.903932	+	0.427677i	$0.140668\pi$
$659$			21.9578i			0.855354i	−0.903932	+	0.427677i	$0.859332\pi$
$660$		0			0
$661$	−22.5721	−	13.0320i	−0.877955	−	0.506887i	−0.00797124	−	0.999968i	$-0.502537\pi$
$661$	−22.5721	−	13.0320i	−0.877955	−	0.506887i	−0.869984	+	0.493081i	$0.835871\pi$
$662$		0			0
$663$	9.16280	+	15.8704i	0.355854	+	0.616357i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−10.2130	+	5.89646i	−0.395448	+	0.228312i
$668$		0			0
$669$	−47.9070	−	27.6591i	−1.85219	−	1.06936i
$670$		0			0
$671$	4.64449			0.179298
$672$		0			0
$673$	30.5683			1.17832			0.589161	−	0.808016i	$-0.299459\pi$
$673$	30.5683			1.17832			0.589161	+	0.808016i	$0.299459\pi$
$674$		0			0
$675$	−28.9722	−	16.7271i	−1.11514	−	0.643826i
$676$		0			0
$677$	−10.3160	+	5.95596i	−0.396477	+	0.228906i	−0.684963	−	0.728578i	$-0.740182\pi$
$677$	−10.3160	+	5.95596i	−0.396477	+	0.228906i	0.288486	+	0.957484i	$0.406848\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−13.8976	−	24.0713i	−0.532556	−	0.922415i
$682$		0			0
$683$	16.4027	+	9.47012i	0.627633	+	0.362364i	0.779835	−	0.625985i	$-0.215303\pi$
$683$	16.4027	+	9.47012i	0.627633	+	0.362364i	−0.152202	+	0.988349i	$0.548636\pi$
$684$		0			0
$685$		−	58.6939i		−	2.24258i
$686$		0			0
$687$	−26.8495			−1.02437
$688$		0			0
$689$	6.30687	−	10.9238i	0.240273	−	0.416164i
$690$		0			0
$691$	7.41115	−	4.27883i	0.281933	−	0.162774i	−0.352365	−	0.935863i	$-0.614622\pi$
$691$	7.41115	−	4.27883i	0.281933	−	0.162774i	0.634298	+	0.773088i	$0.281289\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	27.2772	+	47.2455i	1.03468	+	1.79212i
$696$		0			0
$697$	−20.6351	+	35.7411i	−0.781611	+	1.35379i
$698$		0			0
$699$			48.5374i			1.83585i
$700$		0			0
$701$		−	3.59086i		−	0.135625i	−0.997698	−	0.0678125i	$-0.978398\pi$
$701$		−	3.59086i		−	0.135625i	0.997698	−	0.0678125i	$-0.0216020\pi$
$702$		0			0
$703$	4.78832	−	8.29361i	0.180595	−	0.312799i
$704$		0			0
$705$	−54.8865	−	95.0662i	−2.06714	−	3.58040i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	31.9325	−	18.4362i	1.19925	−	0.692387i	0.238862	−	0.971054i	$-0.423226\pi$
$709$	31.9325	−	18.4362i	1.19925	−	0.692387i	0.960388	+	0.278666i	$0.0898923\pi$
$710$		0			0
$711$	36.3246	−	62.9160i	1.36228	−	2.35953i
$712$		0			0
$713$	−3.32477			−0.124514
$714$		0			0
$715$			5.31698i			0.198844i
$716$		0			0
$717$	−11.7162	−	6.76434i	−0.437549	−	0.252619i
$718$		0			0
$719$	21.9951	+	38.0966i	0.820277	+	1.42076i	0.905476	+	0.424398i	$0.139514\pi$
$719$	21.9951	+	38.0966i	0.820277	+	1.42076i	−0.0851984	+	0.996364i	$0.527152\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	22.0794	−	12.7475i	0.821141	−	0.474086i
$724$		0			0
$725$	16.2636	+	9.38977i	0.604013	+	0.348727i
$726$		0			0
$727$	50.1870			1.86133			0.930666	−	0.365870i	$-0.119228\pi$
$727$	50.1870			1.86133			0.930666	+	0.365870i	$0.119228\pi$
$728$		0			0
$729$	41.1336			1.52347
$730$		0			0
$731$	−36.6992	−	21.1883i	−1.35737	−	0.783677i
$732$		0			0
$733$	5.46246	−	3.15375i	0.201760	−	0.116486i	−0.395716	−	0.918373i	$-0.629504\pi$
$733$	5.46246	−	3.15375i	0.201760	−	0.116486i	0.597476	+	0.801887i	$0.296170\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.89134	+	3.27589i	0.0696682	+	0.120669i
$738$		0			0
$739$	−29.7913	−	17.2000i	−1.09589	−	0.632712i	−0.160752	−	0.986995i	$-0.551392\pi$
$739$	−29.7913	−	17.2000i	−1.09589	−	0.632712i	−0.935138	+	0.354282i	$0.884725\pi$
$740$		0			0
$741$		−	4.84227i		−	0.177885i
$742$		0			0
$743$	9.93023			0.364305			0.182152	−	0.983270i	$-0.441694\pi$
$743$	9.93023			0.364305			0.182152	+	0.983270i	$0.441694\pi$
$744$		0			0
$745$	−32.6214	+	56.5019i	−1.19516	+	2.07007i
$746$		0			0
$747$	−35.6501	+	20.5826i	−1.30437	+	0.753078i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	5.38585	+	9.32857i	0.196532	+	0.340404i	0.947402	−	0.320047i	$-0.103699\pi$
$751$	5.38585	+	9.32857i	0.196532	+	0.340404i	−0.750869	+	0.660451i	$0.770365\pi$
$752$		0			0
$753$	23.5202	−	40.7382i	0.857124	−	1.48458i
$754$		0			0
$755$			15.0832i			0.548935i
$756$		0			0
$757$			16.2090i			0.589127i	0.955632	+	0.294563i	$0.0951742\pi$
$757$			16.2090i			0.589127i	−0.955632	+	0.294563i	$0.904826\pi$
$758$		0			0
$759$	−6.84056	+	11.8482i	−0.248296	+	0.430062i
$760$		0			0
$761$	2.68567	+	4.65172i	0.0973554	+	0.168625i	0.910589	−	0.413313i	$-0.135628\pi$
$761$	2.68567	+	4.65172i	0.0973554	+	0.168625i	−0.813234	+	0.581937i	$0.802295\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	80.8326	−	46.6687i	2.92251	−	1.68731i
$766$		0			0
$767$	3.61567	−	6.26252i	0.130554	−	0.226126i
$768$		0			0
$769$	10.1872			0.367358			0.183679	−	0.982986i	$-0.441199\pi$
$769$	10.1872			0.367358			0.183679	+	0.982986i	$0.441199\pi$
$770$		0			0
$771$			36.5134i			1.31500i
$772$		0			0
$773$	−44.5035	−	25.6941i	−1.60068	−	0.924153i	−0.991351	−	0.131236i	$-0.958105\pi$
$773$	−44.5035	−	25.6941i	−1.60068	−	0.924153i	−0.609329	−	0.792917i	$-0.708561\pi$
$774$		0			0
$775$	2.64725	+	4.58517i	0.0950920	+	0.164704i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	9.44405	−	5.45253i	0.338368	−	0.195357i
$780$		0			0
$781$	15.6689	+	9.04646i	0.560679	+	0.323708i
$782$		0			0
$783$	22.9701			0.820884
$784$		0			0
$785$	28.8231			1.02874
$786$		0			0
$787$	−39.3458	−	22.7163i	−1.40253	−	0.809749i	−0.407876	−	0.913037i	$-0.633730\pi$
$787$	−39.3458	−	22.7163i	−1.40253	−	0.809749i	−0.994651	+	0.103288i	$0.967064\pi$
$788$		0			0
$789$	−54.3874	+	31.4006i	−1.93624	+	1.11789i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−1.83076	−	3.17097i	−0.0650122	−	0.112604i
$794$		0			0
$795$	−87.5540	−	50.5493i	−3.10522	−	1.79280i
$796$		0			0
$797$		−	30.4917i		−	1.08007i	−0.841642	−	0.540036i	$-0.818410\pi$
$797$		−	30.4917i		−	1.08007i	0.841642	−	0.540036i	$-0.181590\pi$
$798$		0			0
$799$	66.7578			2.36172
$800$		0			0
$801$	8.44686	−	14.6304i	0.298455	−	0.516940i
$802$		0			0
$803$	−11.5850	+	6.68858i	−0.408824	+	0.236035i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	26.5613	+	46.0056i	0.935003	+	1.61947i
$808$		0			0
$809$	9.45339	−	16.3737i	0.332363	−	0.575670i	−0.650611	−	0.759411i	$-0.725487\pi$
$809$	9.45339	−	16.3737i	0.332363	−	0.575670i	0.982975	+	0.183741i	$0.0588206\pi$
$810$		0			0
$811$		−	34.8800i		−	1.22480i	−0.790548	−	0.612401i	$-0.790204\pi$
$811$		−	34.8800i		−	1.22480i	0.790548	−	0.612401i	$-0.209796\pi$
$812$		0			0
$813$		−	39.9718i		−	1.40187i
$814$		0			0
$815$	−7.50041	+	12.9911i	−0.262728	+	0.455058i
$816$		0			0
$817$	5.59869	+	9.69722i	0.195873	+	0.339263i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	8.96414	−	5.17545i	0.312851	−	0.180624i	−0.335351	−	0.942093i	$-0.608855\pi$
$821$	8.96414	−	5.17545i	0.312851	−	0.180624i	0.648201	+	0.761469i	$0.275521\pi$
$822$		0			0
$823$	3.66152	−	6.34194i	0.127633	−	0.221066i	−0.795126	−	0.606444i	$-0.792596\pi$
$823$	3.66152	−	6.34194i	0.127633	−	0.221066i	0.922759	+	0.385378i	$0.125929\pi$
$824$		0			0
$825$	21.7864			0.758504
$826$		0			0
$827$		−	33.6881i		−	1.17145i	−0.810510	−	0.585725i	$-0.800810\pi$
$827$		−	33.6881i		−	1.17145i	0.810510	−	0.585725i	$-0.199190\pi$
$828$		0			0
$829$	10.2926	+	5.94241i	0.357475	+	0.206388i	0.667973	−	0.744186i	$-0.267162\pi$
$829$	10.2926	+	5.94241i	0.357475	+	0.206388i	−0.310498	+	0.950574i	$0.600496\pi$
$830$		0			0
$831$	−19.9703	−	34.5896i	−0.692763	−	1.19990i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−38.7467	+	22.3704i	−1.34088	+	0.774160i
$836$		0			0
$837$	5.60833	+	3.23797i	0.193852	+	0.111921i
$838$		0			0
$839$	−53.8741			−1.85994			−0.929970	−	0.367635i	$-0.880168\pi$
$839$	−53.8741			−1.85994			−0.929970	+	0.367635i	$0.880168\pi$
$840$		0			0
$841$	16.1057			0.555369
$842$		0			0
$843$	−3.55696	−	2.05361i	−0.122508	−	0.0707302i
$844$		0			0
$845$	−32.3786	+	18.6938i	−1.11386	+	0.643087i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	6.45339	+	11.1776i	0.221480	+	0.383614i
$850$		0			0
$851$	18.4731	+	10.6654i	0.633250	+	0.365607i
$852$		0			0
$853$		−	31.6588i		−	1.08398i	−0.840386	−	0.541988i	$-0.817672\pi$
$853$		−	31.6588i		−	1.08398i	0.840386	−	0.541988i	$-0.182328\pi$
$854$		0			0
$855$	−24.6630			−0.843458
$856$		0			0
$857$	1.51080	−	2.61678i	0.0516078	−	0.0893874i	−0.839067	−	0.544027i	$-0.816899\pi$
$857$	1.51080	−	2.61678i	0.0516078	−	0.0893874i	0.890675	+	0.454640i	$0.150232\pi$
$858$		0			0
$859$	−12.9275	+	7.46368i	−0.441080	+	0.254657i	−0.704055	−	0.710145i	$-0.748629\pi$
$859$	−12.9275	+	7.46368i	−0.441080	+	0.254657i	0.262976	+	0.964802i	$0.415296\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.43171	−	2.47979i	−0.0487358	−	0.0844129i	0.840628	−	0.541612i	$-0.182186\pi$
$863$	−1.43171	−	2.47979i	−0.0487358	−	0.0844129i	−0.889364	+	0.457199i	$0.848853\pi$
$864$		0			0
$865$	−12.0606	+	20.8895i	−0.410072	+	0.710265i
$866$		0			0
$867$			40.5546i			1.37730i
$868$		0			0
$869$			20.1719i			0.684286i
$870$		0			0
$871$	1.49105	−	2.58258i	0.0505223	−	0.0875072i
$872$		0			0
$873$	1.05079	+	1.82002i	0.0355638	+	0.0615982i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−22.1941	+	12.8138i	−0.749442	+	0.432690i	−0.825492	−	0.564414i	$-0.809102\pi$
$877$	−22.1941	+	12.8138i	−0.749442	+	0.432690i	0.0760504	+	0.997104i	$0.475769\pi$
$878$		0			0
$879$	11.5334	−	19.9765i	0.389012	−	0.673789i
$880$		0			0
$881$	22.1882			0.747540			0.373770	−	0.927521i	$-0.378065\pi$
$881$	22.1882			0.747540			0.373770	+	0.927521i	$0.378065\pi$
$882$		0			0
$883$		−	26.5063i		−	0.892010i	−0.895031	−	0.446005i	$-0.852846\pi$
$883$		−	26.5063i		−	0.892010i	0.895031	−	0.446005i	$-0.147154\pi$
$884$		0			0
$885$	−50.1938	−	28.9794i	−1.68725	−	0.974133i
$886$		0			0
$887$	5.50318	+	9.53179i	0.184779	+	0.320046i	0.943502	−	0.331367i	$-0.107510\pi$
$887$	5.50318	+	9.53179i	0.184779	+	0.320046i	−0.758723	+	0.651413i	$0.774177\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	3.34707	−	1.93243i	0.112131	−	0.0647388i
$892$		0			0
$893$	−15.2765	−	8.81988i	−0.511208	−	0.295146i
$894$		0			0
$895$	−47.6222			−1.59184
$896$		0			0
$897$	10.7856			0.360121
$898$		0			0
$899$	−3.14824	−	1.81764i	−0.105000	−	0.0606216i
$900$		0			0
$901$	53.2454	−	30.7413i	1.77386	−	1.02414i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	26.3726	+	45.6788i	0.876656	+	1.51841i
$906$		0			0
$907$	49.8740	+	28.7947i	1.65604	+	0.956114i	0.974517	+	0.224316i	$0.0720147\pi$
$907$	49.8740	+	28.7947i	1.65604	+	0.956114i	0.681521	+	0.731798i	$0.261319\pi$
$908$		0			0
$909$			32.5453i			1.07946i
$910$		0			0
$911$	−2.77170			−0.0918306			−0.0459153	−	0.998945i	$-0.514620\pi$
$911$	−2.77170			−0.0918306			−0.0459153	+	0.998945i	$0.514620\pi$
$912$		0			0
$913$	5.71502	−	9.89870i	0.189140	−	0.327599i
$914$		0			0
$915$	−25.4152	+	14.6735i	−0.840200	+	0.485090i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	10.2298	+	17.7186i	0.337450	+	0.584481i	0.983952	−	0.178431i	$-0.0571021\pi$
$919$	10.2298	+	17.7186i	0.337450	+	0.584481i	−0.646502	+	0.762912i	$0.723769\pi$
$920$		0			0
$921$	−17.1817	+	29.7596i	−0.566157	+	0.980613i
$922$		0			0
$923$		−	14.2637i		−	0.469496i
$924$		0			0
$925$		−	33.9682i		−	1.11687i
$926$		0			0
$927$	−19.1391	+	33.1499i	−0.628612	+	1.08879i
$928$		0			0
$929$	−5.77211	−	9.99759i	−0.189377	−	0.328010i	0.755666	−	0.654957i	$-0.227313\pi$
$929$	−5.77211	−	9.99759i	−0.189377	−	0.328010i	−0.945043	+	0.326947i	$0.893980\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−53.8376	+	31.0831i	−1.76256	+	1.01762i
$934$		0			0
$935$	−12.9582	+	22.4442i	−0.423777	+	0.734003i
$936$		0			0
$937$	−46.4780			−1.51837			−0.759185	−	0.650874i	$-0.774402\pi$
$937$	−46.4780			−1.51837			−0.759185	+	0.650874i	$0.774402\pi$
$938$		0			0
$939$			27.0261i			0.881964i
$940$		0			0
$941$	34.3615	+	19.8386i	1.12015	+	0.646720i	0.941440	−	0.337181i	$-0.109474\pi$
$941$	34.3615	+	19.8386i	1.12015	+	0.646720i	0.178712	+	0.983901i	$0.442807\pi$
$942$		0			0
$943$	12.1449	+	21.0356i	0.395492	+	0.685013i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	43.5231	−	25.1281i	1.41431	−	0.816552i	0.418520	−	0.908208i	$-0.362549\pi$
$947$	43.5231	−	25.1281i	1.41431	−	0.816552i	0.995791	+	0.0916553i	$0.0292158\pi$
$948$		0			0
$949$	9.13311	+	5.27300i	0.296473	+	0.171169i
$950$		0			0
$951$	26.2595			0.851524
$952$		0			0
$953$	26.4596			0.857111			0.428556	−	0.903515i	$-0.359023\pi$
$953$	26.4596			0.857111			0.428556	+	0.903515i	$0.359023\pi$
$954$		0			0
$955$	−6.51195	−	3.75967i	−0.210722	−	0.121660i
$956$		0			0
$957$	−12.9547	+	7.47941i	−0.418767	+	0.241775i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	14.9876	+	25.9592i	0.483470	+	0.837394i
$962$		0			0
$963$	−20.2438	−	11.6878i	−0.652347	−	0.376633i
$964$		0			0
$965$			30.5539i			0.983566i
$966$		0			0
$967$	6.98903			0.224752			0.112376	−	0.993666i	$-0.464154\pi$
$967$	6.98903			0.224752			0.112376	+	0.993666i	$0.464154\pi$
$968$		0			0
$969$	11.8012	−	20.4403i	0.379110	−	0.656637i
$970$		0			0
$971$	−22.7920	+	13.1590i	−0.731431	+	0.422292i	−0.818945	−	0.573872i	$-0.805441\pi$
$971$	−22.7920	+	13.1590i	−0.731431	+	0.422292i	0.0875147	+	0.996163i	$0.472108\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−8.58774	−	14.8744i	−0.275028	−	0.476362i
$976$		0			0
$977$	−16.4596	+	28.5089i	−0.526590	+	0.912081i	0.472930	+	0.881100i	$0.343196\pi$
$977$	−16.4596	+	28.5089i	−0.526590	+	0.912081i	−0.999520	+	0.0309809i	$0.990137\pi$
$978$		0			0
$979$			4.69076i			0.149917i
$980$		0			0
$981$			66.0909i			2.11012i
$982$		0			0
$983$	13.4823	−	23.3520i	0.430018	−	0.744813i	−0.566856	−	0.823817i	$-0.691841\pi$
$983$	13.4823	−	23.3520i	0.430018	−	0.744813i	0.996874	+	0.0790038i	$0.0251739\pi$
$984$		0			0
$985$	19.2830	+	33.3991i	0.614406	+	1.06418i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−21.5995	+	12.4705i	−0.686824	+	0.396538i
$990$		0			0
$991$	−6.22982	+	10.7904i	−0.197897	+	0.342767i	−0.947846	−	0.318728i	$-0.896744\pi$
$991$	−6.22982	+	10.7904i	−0.197897	+	0.342767i	0.749950	+	0.661495i	$0.230078\pi$
$992$		0			0
$993$	−57.0275			−1.80971
$994$		0			0
$995$			12.7759i			0.405025i
$996$		0			0
$997$	−38.8560	−	22.4335i	−1.23058	−	0.710477i	−0.263430	−	0.964678i	$-0.584854\pi$
$997$	−38.8560	−	22.4335i	−1.23058	−	0.710477i	−0.967151	+	0.254202i	$0.918187\pi$
$998$		0			0
$999$	−20.7740	−	35.9816i	−0.657261	−	1.13841i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1568.2.t.h.753.1		24
4.3	odd	2		392.2.p.h.165.4		24
7.2	even	3	inner	1568.2.t.h.177.12		24
7.3	odd	6		1568.2.b.g.785.2		12
7.4	even	3		1568.2.b.g.785.12		12
7.5	odd	6	inner	1568.2.t.h.177.2		24
7.6	odd	2	inner	1568.2.t.h.753.11		24
8.3	odd	2		392.2.p.h.165.11		24
8.5	even	2	inner	1568.2.t.h.753.12		24
28.3	even	6		392.2.b.g.197.6	yes	12
28.11	odd	6		392.2.b.g.197.5	✓	12
28.19	even	6		392.2.p.h.373.12		24
28.23	odd	6		392.2.p.h.373.11		24
28.27	even	2		392.2.p.h.165.3		24
56.3	even	6		392.2.b.g.197.7	yes	12
56.5	odd	6	inner	1568.2.t.h.177.11		24
56.11	odd	6		392.2.b.g.197.8	yes	12
56.13	odd	2	inner	1568.2.t.h.753.2		24
56.19	even	6		392.2.p.h.373.3		24
56.27	even	2		392.2.p.h.165.12		24
56.37	even	6	inner	1568.2.t.h.177.1		24
56.45	odd	6		1568.2.b.g.785.11		12
56.51	odd	6		392.2.p.h.373.4		24
56.53	even	6		1568.2.b.g.785.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.b.g.197.5	✓	12	28.11	odd	6
392.2.b.g.197.6	yes	12	28.3	even	6
392.2.b.g.197.7	yes	12	56.3	even	6
392.2.b.g.197.8	yes	12	56.11	odd	6
392.2.p.h.165.3		24	28.27	even	2
392.2.p.h.165.4		24	4.3	odd	2
392.2.p.h.165.11		24	8.3	odd	2
392.2.p.h.165.12		24	56.27	even	2
392.2.p.h.373.3		24	56.19	even	6
392.2.p.h.373.4		24	56.51	odd	6
392.2.p.h.373.11		24	28.23	odd	6
392.2.p.h.373.12		24	28.19	even	6
1568.2.b.g.785.1		12	56.53	even	6
1568.2.b.g.785.2		12	7.3	odd	6
1568.2.b.g.785.11		12	56.45	odd	6
1568.2.b.g.785.12		12	7.4	even	3
1568.2.t.h.177.1		24	56.37	even	6	inner
1568.2.t.h.177.2		24	7.5	odd	6	inner
1568.2.t.h.177.11		24	56.5	odd	6	inner
1568.2.t.h.177.12		24	7.2	even	3	inner
1568.2.t.h.753.1		24	1.1	even	1	trivial
1568.2.t.h.753.2		24	56.13	odd	2	inner
1568.2.t.h.753.11		24	7.6	odd	2	inner
1568.2.t.h.753.12		24	8.5	even	2	inner

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.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.48442 - 1.43438i) q^{3} +(-2.76990 + 1.59920i) q^{5} +(2.61491 + 4.52915i) q^{9} +O(q^{10})\)	\(q+(-2.48442 - 1.43438i) q^{3} +(-2.76990 + 1.59920i) q^{5} +(2.61491 + 4.52915i) q^{9} +(-1.25758 - 0.726062i) q^{11} +1.14479i q^{13} +9.17548 q^{15} +(-2.79001 + 4.83244i) q^{17} +(1.27690 - 0.737219i) q^{19} +(1.64207 + 2.84415i) q^{23} +(2.61491 - 4.52915i) q^{25} -6.39682i q^{27} +3.59086i q^{29} +(-0.506184 + 0.876737i) q^{31} +(2.08290 + 3.60769i) q^{33} +(5.62493 - 3.24755i) q^{37} +(1.64207 - 2.84415i) q^{39} +7.39608 q^{41} +7.59434i q^{43} +(-14.4861 - 8.36354i) q^{45} +(-5.98186 - 10.3609i) q^{47} +(13.8631 - 8.00388i) q^{51} +(-9.54216 - 5.50917i) q^{53} +4.64449 q^{55} -4.22982 q^{57} +(-5.47043 - 3.15835i) q^{59} +(-2.76990 + 1.59920i) q^{61} +(-1.83076 - 3.17097i) q^{65} +(-2.25593 - 1.30246i) q^{67} -9.42145i q^{69} -12.4596 q^{71} +(4.60607 - 7.97794i) q^{73} +(-12.9931 + 7.50156i) q^{75} +(-6.94567 - 12.0302i) q^{79} +(-1.33076 + 2.30494i) q^{81} +7.87125i q^{83} -17.8472i q^{85} +(5.15067 - 8.92122i) q^{87} +(-1.61514 - 2.79750i) q^{89} +(2.51515 - 1.45212i) q^{93} +(-2.35793 + 4.08405i) q^{95} +0.401845 q^{97} -7.59434i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{9}+O(q^{10}) \) 24 * q + 12 * q^9	\( 24 q + 12 q^{9} + 32 q^{15} + 32 q^{23} + 12 q^{25} + 32 q^{39} - 8 q^{65} - 96 q^{71} - 80 q^{79} + 4 q^{81} - 64 q^{95}+O(q^{100}) \) 24 * q + 12 * q^9 + 32 * q^15 + 32 * q^23 + 12 * q^25 + 32 * q^39 - 8 * q^65 - 96 * q^71 - 80 * q^79 + 4 * q^81 - 64 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more