LMFDB - Embedded newform 784.3.s.h.705.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [784,3,Mod(129,784)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("784.129"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(784, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	784.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0,0,0,0,4,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$21.3624527258$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.339738624.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 $ x^8 - 4x^6 + 14x^4 - 8*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 7^{2} $
Twist minimal:	no (minimal twist has level 49)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			705.1
Root			$-0.662827 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	784.705
Dual form			784.3.s.h.129.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.92586 + 1.68925i) q^{3} +(-4.13779 - 2.38896i) q^{5} +(1.20711 - 2.09077i) q^{9} +(4.53553 + 7.85578i) q^{11} +7.57675i q^{13} +16.1421 q^{15} +(-19.4770 + 11.2451i) q^{17} +(2.21593 + 1.27937i) q^{19} +(-8.65685 + 14.9941i) q^{23} +(-1.08579 - 1.88064i) q^{25} -22.2500i q^{27} +35.7990 q^{29} +(-36.5302 + 21.0907i) q^{31} +(-26.5407 - 15.3233i) q^{33} +(1.65685 - 2.86976i) q^{37} +(-12.7990 - 22.1685i) q^{39} -67.8100i q^{41} +27.6985 q^{43} +(-9.98951 + 5.76745i) q^{45} +(-34.1063 - 19.6913i) q^{47} +(37.9914 - 65.8030i) q^{51} +(-25.1838 - 43.6196i) q^{53} -43.3407i q^{55} -8.64466 q^{57} +(40.7541 - 23.5294i) q^{59} +(68.5067 + 39.5524i) q^{61} +(18.1005 - 31.3510i) q^{65} +(-27.2132 - 47.1347i) q^{67} -58.4942i q^{69} +0.402020 q^{71} +(1.80006 - 1.03926i) q^{73} +(6.35372 + 3.66832i) q^{75} +(30.4437 - 52.7299i) q^{79} +(48.4497 + 83.9174i) q^{81} -82.9634i q^{83} +107.456 q^{85} +(-104.743 + 60.4733i) q^{87} +(-6.05966 - 3.49854i) q^{89} +(71.2548 - 123.417i) q^{93} +(-6.11270 - 10.5875i) q^{95} -90.5402i q^{97} +21.8995 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{9} + 8 q^{11} + 16 q^{15} - 24 q^{23} - 20 q^{25} + 128 q^{29} - 32 q^{37} + 56 q^{39} - 16 q^{43} + 72 q^{51} + 104 q^{53} - 352 q^{57} + 224 q^{65} - 48 q^{67} + 320 q^{71} + 368 q^{79} + 348 q^{81}+ \cdots + 96 q^{99}+O(q^{100}) $ 8 * q + 4 * q^9 + 8 * q^11 + 16 * q^15 - 24 * q^23 - 20 * q^25 + 128 * q^29 - 32 * q^37 + 56 * q^39 - 16 * q^43 + 72 * q^51 + 104 * q^53 - 352 * q^57 + 224 * q^65 - 48 * q^67 + 320 * q^71 + 368 * q^79 + 348 * q^81 + 656 * q^85 + 208 * q^93 + 200 * q^95 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−2.92586	+	1.68925i	−0.975287	+	0.563082i	−0.900844	−	0.434143i	$-0.857051\pi$
$3$	−2.92586	+	1.68925i	−0.975287	+	0.563082i	−0.0744430	+	0.997225i	$0.523718\pi$
$4$		0			0
$5$	−4.13779	−	2.38896i	−0.827558	−	0.477791i	0.0254576	−	0.999676i	$-0.491896\pi$
$5$	−4.13779	−	2.38896i	−0.827558	−	0.477791i	−0.853016	+	0.521885i	$0.825229\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.20711	−	2.09077i	0.134123	−	0.232308i
$10$		0			0
$11$	4.53553	+	7.85578i	0.412321	+	0.714161i	0.995143	−	0.0984386i	$-0.0313848\pi$
$11$	4.53553	+	7.85578i	0.412321	+	0.714161i	−0.582822	+	0.812600i	$0.698051\pi$
$12$		0			0
$13$			7.57675i			0.582827i	0.956597	+	0.291413i	$0.0941255\pi$
$13$			7.57675i			0.582827i	−0.956597	+	0.291413i	$0.905875\pi$
$14$		0			0
$15$	16.1421			1.07614
$16$		0			0
$17$	−19.4770	+	11.2451i	−1.14571	+	0.661475i	−0.947838	−	0.318754i	$-0.896736\pi$
$17$	−19.4770	+	11.2451i	−1.14571	+	0.661475i	−0.197870	+	0.980228i	$0.563402\pi$
$18$		0			0
$19$	2.21593	+	1.27937i	0.116628	+	0.0673351i	0.557179	−	0.830392i	$-0.311884\pi$
$19$	2.21593	+	1.27937i	0.116628	+	0.0673351i	−0.440551	+	0.897727i	$0.645217\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−8.65685	+	14.9941i	−0.376385	+	0.651918i	−0.990533	−	0.137273i	$-0.956166\pi$
$23$	−8.65685	+	14.9941i	−0.376385	+	0.651918i	0.614148	+	0.789191i	$0.289500\pi$
$24$		0			0
$25$	−1.08579	−	1.88064i	−0.0434315	−	0.0752255i
$26$		0			0
$27$		−	22.2500i		−	0.824075i
$28$		0			0
$29$	35.7990			1.23445			0.617224	−	0.786788i	$-0.288257\pi$
$29$	35.7990			1.23445			0.617224	+	0.786788i	$0.288257\pi$
$30$		0			0
$31$	−36.5302	+	21.0907i	−1.17839	+	0.680346i	−0.955642	−	0.294530i	$-0.904837\pi$
$31$	−36.5302	+	21.0907i	−1.17839	+	0.680346i	−0.222751	+	0.974875i	$0.571504\pi$
$32$		0			0
$33$	−26.5407	−	15.3233i	−0.804263	−	0.464341i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.65685	−	2.86976i	0.0447798	−	0.0775610i	−0.842767	−	0.538279i	$-0.819075\pi$
$37$	1.65685	−	2.86976i	0.0447798	−	0.0775610i	0.887547	+	0.460718i	$0.152408\pi$
$38$		0			0
$39$	−12.7990	−	22.1685i	−0.328179	−	0.568423i
$40$		0			0
$41$		−	67.8100i		−	1.65390i	−0.562274	−	0.826951i	$-0.690074\pi$
$41$		−	67.8100i		−	1.65390i	0.562274	−	0.826951i	$-0.309926\pi$
$42$		0			0
$43$	27.6985			0.644151			0.322075	−	0.946714i	$-0.395620\pi$
$43$	27.6985			0.644151			0.322075	+	0.946714i	$0.395620\pi$
$44$		0			0
$45$	−9.98951	+	5.76745i	−0.221989	+	0.128166i
$46$		0			0
$47$	−34.1063	−	19.6913i	−0.725667	−	0.418964i	0.0911682	−	0.995836i	$-0.470940\pi$
$47$	−34.1063	−	19.6913i	−0.725667	−	0.418964i	−0.816835	+	0.576872i	$0.804273\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	37.9914	−	65.8030i	0.744929	−	1.29025i
$52$		0			0
$53$	−25.1838	−	43.6196i	−0.475165	−	0.823011i	0.524430	−	0.851454i	$-0.324278\pi$
$53$	−25.1838	−	43.6196i	−0.475165	−	0.823011i	−0.999595	+	0.0284429i	$0.990945\pi$
$54$		0			0
$55$		−	43.3407i		−	0.788014i
$56$		0			0
$57$	−8.64466			−0.151661
$58$		0			0
$59$	40.7541	−	23.5294i	0.690748	−	0.398803i	−0.113144	−	0.993579i	$-0.536092\pi$
$59$	40.7541	−	23.5294i	0.690748	−	0.398803i	0.803892	+	0.594775i	$0.202759\pi$
$60$		0			0
$61$	68.5067	+	39.5524i	1.12306	+	0.648400i	0.942181	−	0.335105i	$-0.108772\pi$
$61$	68.5067	+	39.5524i	1.12306	+	0.648400i	0.180880	+	0.983505i	$0.442105\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	18.1005	−	31.3510i	0.278469	−	0.482323i
$66$		0			0
$67$	−27.2132	−	47.1347i	−0.406167	−	0.703502i	0.588289	−	0.808651i	$-0.299802\pi$
$67$	−27.2132	−	47.1347i	−0.406167	−	0.703502i	−0.994457	+	0.105148i	$0.966468\pi$
$68$		0			0
$69$		−	58.4942i		−	0.847743i
$70$		0			0
$71$	0.402020			0.00566226			0.00283113	−	0.999996i	$-0.499099\pi$
$71$	0.402020			0.00566226			0.00283113	+	0.999996i	$0.499099\pi$
$72$		0			0
$73$	1.80006	−	1.03926i	0.0246583	−	0.0142365i	−0.487620	−	0.873056i	$-0.662135\pi$
$73$	1.80006	−	1.03926i	0.0246583	−	0.0142365i	0.512278	+	0.858819i	$0.328802\pi$
$74$		0			0
$75$	6.35372	+	3.66832i	0.0847163	+	0.0489110i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	30.4437	−	52.7299i	0.385363	−	0.667468i	−0.606457	−	0.795116i	$-0.707410\pi$
$79$	30.4437	−	52.7299i	0.385363	−	0.667468i	0.991819	+	0.127649i	$0.0407430\pi$
$80$		0			0
$81$	48.4497	+	83.9174i	0.598145	+	1.03602i
$82$		0			0
$83$		−	82.9634i		−	0.999560i	−0.866152	−	0.499780i	$-0.833414\pi$
$83$		−	82.9634i		−	0.999560i	0.866152	−	0.499780i	$-0.166586\pi$
$84$		0			0
$85$	107.456			1.26419
$86$		0			0
$87$	−104.743	+	60.4733i	−1.20394	+	0.695096i
$88$		0			0
$89$	−6.05966	−	3.49854i	−0.0680860	−	0.0393095i	0.465571	−	0.885011i	$-0.345849\pi$
$89$	−6.05966	−	3.49854i	−0.0680860	−	0.0393095i	−0.533657	+	0.845701i	$0.679182\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	71.2548	−	123.417i	0.766181	−	1.32706i
$94$		0			0
$95$	−6.11270	−	10.5875i	−0.0643442	−	0.111447i
$96$		0			0
$97$		−	90.5402i		−	0.933404i	−0.884415	−	0.466702i	$-0.845442\pi$
$97$		−	90.5402i		−	0.933404i	0.884415	−	0.466702i	$-0.154558\pi$
$98$		0			0
$99$	21.8995			0.221207
$100$		0			0
$101$	−29.5527	+	17.0622i	−0.292601	+	0.168933i	−0.639114	−	0.769112i	$-0.720699\pi$
$101$	−29.5527	+	17.0622i	−0.292601	+	0.168933i	0.346513	+	0.938045i	$0.387366\pi$
$102$		0			0
$103$	115.026	+	66.4105i	1.11676	+	0.644763i	0.940572	−	0.339594i	$-0.110290\pi$
$103$	115.026	+	66.4105i	1.11676	+	0.644763i	0.176189	+	0.984356i	$0.443623\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	64.7401	−	112.133i	0.605048	−	1.04797i	−0.386996	−	0.922081i	$-0.626487\pi$
$107$	64.7401	−	112.133i	0.605048	−	1.04797i	0.992044	−	0.125892i	$-0.0401793\pi$
$108$		0			0
$109$	−50.2843	−	87.0949i	−0.461324	−	0.799036i	0.537704	−	0.843134i	$-0.319292\pi$
$109$	−50.2843	−	87.0949i	−0.461324	−	0.799036i	−0.999027	+	0.0440980i	$0.985959\pi$
$110$		0			0
$111$			11.1953i			0.100859i
$112$		0			0
$113$	−168.693			−1.49286			−0.746431	−	0.665463i	$-0.768234\pi$
$113$	−168.693			−1.49286			−0.746431	+	0.665463i	$0.768234\pi$
$114$		0			0
$115$	71.6405	−	41.3617i	0.622961	−	0.359667i
$116$		0			0
$117$	15.8412	+	9.14594i	0.135395	+	0.0781704i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	19.3579	−	33.5288i	0.159982	−	0.277098i
$122$		0			0
$123$	114.548	+	198.402i	0.931282	+	1.61303i
$124$		0			0
$125$			129.823i			1.03859i
$126$		0			0
$127$	−26.6030			−0.209473			−0.104736	−	0.994500i	$-0.533400\pi$
$127$	−26.6030			−0.209473			−0.104736	+	0.994500i	$0.533400\pi$
$128$		0			0
$129$	−81.0419	+	46.7896i	−0.628232	+	0.362710i
$130$		0			0
$131$	−124.048	−	71.6189i	−0.946928	−	0.546709i	−0.0548030	−	0.998497i	$-0.517453\pi$
$131$	−124.048	−	71.6189i	−0.946928	−	0.546709i	−0.892125	+	0.451788i	$0.850786\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−53.1543	+	92.0660i	−0.393736	+	0.681970i
$136$		0			0
$137$	−33.7365	−	58.4334i	−0.246252	−	0.426521i	0.716231	−	0.697864i	$-0.245866\pi$
$137$	−33.7365	−	58.4334i	−0.246252	−	0.426521i	−0.962483	+	0.271342i	$0.912532\pi$
$138$		0			0
$139$			14.7727i			0.106279i	0.998587	+	0.0531394i	$0.0169228\pi$
$139$			14.7727i			0.106279i	−0.998587	+	0.0531394i	$0.983077\pi$
$140$		0			0
$141$	133.054			0.943644
$142$		0			0
$143$	−59.5212	+	34.3646i	−0.416232	+	0.240312i
$144$		0			0
$145$	−148.129	−	85.5222i	−1.02158	−	0.589808i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−43.2426	+	74.8985i	−0.290219	+	0.502674i	−0.973861	−	0.227143i	$-0.927062\pi$
$149$	−43.2426	+	74.8985i	−0.290219	+	0.502674i	0.683642	+	0.729817i	$0.260395\pi$
$150$		0			0
$151$	−104.213	−	180.503i	−0.690154	−	1.19538i	−0.971787	−	0.235859i	$-0.924210\pi$
$151$	−104.213	−	180.503i	−0.690154	−	1.19538i	0.281634	−	0.959522i	$-0.409124\pi$
$152$		0			0
$153$			54.2960i			0.354876i
$154$		0			0
$155$	201.539			1.30025
$156$		0			0
$157$	102.613	−	59.2437i	0.653586	−	0.377348i	−0.136243	−	0.990676i	$-0.543503\pi$
$157$	102.613	−	59.2437i	0.653586	−	0.377348i	0.789829	+	0.613327i	$0.210169\pi$
$158$		0			0
$159$	147.368	+	85.0832i	0.926845	+	0.535114i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−147.104	+	254.792i	−0.902479	+	1.56314i	−0.0782130	+	0.996937i	$0.524921\pi$
$163$	−147.104	+	254.792i	−0.902479	+	1.56314i	−0.824266	+	0.566203i	$0.808412\pi$
$164$		0			0
$165$	73.2132	+	126.809i	0.443716	+	0.768539i
$166$		0			0
$167$		−	59.8525i		−	0.358398i	−0.983813	−	0.179199i	$-0.942649\pi$
$167$		−	59.8525i		−	0.358398i	0.983813	−	0.179199i	$-0.0573506\pi$
$168$		0			0
$169$	111.593			0.660313
$170$		0			0
$171$	5.34972	−	3.08866i	0.0312849	−	0.0180624i
$172$		0			0
$173$	−72.9386	−	42.1111i	−0.421610	−	0.243417i	0.274156	−	0.961685i	$-0.411602\pi$
$173$	−72.9386	−	42.1111i	−0.421610	−	0.243417i	−0.695766	+	0.718268i	$0.744935\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−79.4939	+	137.687i	−0.449118	+	0.777895i
$178$		0			0
$179$	−1.11775	−	1.93600i	−0.00624441	−	0.0108156i	0.862886	−	0.505398i	$-0.168654\pi$
$179$	−1.11775	−	1.93600i	−0.00624441	−	0.0108156i	−0.869131	+	0.494582i	$0.835321\pi$
$180$		0			0
$181$		−	7.57675i		−	0.0418605i	−0.999781	−	0.0209302i	$-0.993337\pi$
$181$		−	7.57675i		−	0.0418605i	0.999781	−	0.0209302i	$-0.00666279\pi$
$182$		0			0
$183$	−267.255			−1.46041
$184$		0			0
$185$	−13.7114	+	7.91630i	−0.0741159	+	0.0427908i
$186$		0			0
$187$	−176.677	−	102.005i	−0.944799	−	0.545480i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−18.0589	+	31.2789i	−0.0945491	+	0.163764i	−0.909420	−	0.415878i	$-0.863474\pi$
$191$	−18.0589	+	31.2789i	−0.0945491	+	0.163764i	0.814871	+	0.579642i	$0.196808\pi$
$192$		0			0
$193$	−9.83705	−	17.0383i	−0.0509692	−	0.0882812i	0.839415	−	0.543491i	$-0.182898\pi$
$193$	−9.83705	−	17.0383i	−0.0509692	−	0.0882812i	−0.890384	+	0.455210i	$0.849564\pi$
$194$		0			0
$195$			122.305i			0.627204i
$196$		0			0
$197$	−256.794			−1.30352			−0.651761	−	0.758424i	$-0.725970\pi$
$197$	−256.794			−1.30352			−0.651761	+	0.758424i	$0.725970\pi$
$198$		0			0
$199$	10.5272	−	6.07787i	0.0529004	−	0.0305421i	−0.473317	−	0.880892i	$-0.656943\pi$
$199$	10.5272	−	6.07787i	0.0529004	−	0.0305421i	0.526217	+	0.850350i	$0.323610\pi$
$200$		0			0
$201$	159.244	+	91.9396i	0.792259	+	0.457411i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−161.995	+	280.583i	−0.790219	+	1.36870i
$206$		0			0
$207$	20.8995	+	36.1990i	0.100964	+	0.174874i
$208$		0			0
$209$			23.2104i			0.111055i
$210$		0			0
$211$	188.201			0.891948			0.445974	−	0.895046i	$-0.352857\pi$
$211$	188.201			0.891948			0.445974	+	0.895046i	$0.352857\pi$
$212$		0			0
$213$	−1.17626	+	0.679111i	−0.00552232	+	0.00318832i
$214$		0			0
$215$	−114.611	−	66.1704i	−0.533072	−	0.307769i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−3.51115	+	6.08149i	−0.0160326	+	0.0277693i
$220$		0			0
$221$	−85.2010	−	147.572i	−0.385525	−	0.667749i
$222$		0			0
$223$			272.001i			1.21974i	0.792503	+	0.609868i	$0.208778\pi$
$223$			272.001i			1.21974i	−0.792503	+	0.609868i	$0.791222\pi$
$224$		0			0
$225$	−5.24264			−0.0233006
$226$		0			0
$227$	328.614	−	189.726i	1.44764	−	0.835795i	0.449299	−	0.893381i	$-0.351674\pi$
$227$	328.614	−	189.726i	1.44764	−	0.835795i	0.998341	+	0.0575860i	$0.0183403\pi$
$228$		0			0
$229$	64.6630	+	37.3332i	0.282371	+	0.163027i	0.634496	−	0.772926i	$-0.281208\pi$
$229$	64.6630	+	37.3332i	0.282371	+	0.163027i	−0.352125	+	0.935953i	$0.614541\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−48.6899	+	84.3333i	−0.208969	+	0.361946i	−0.951390	−	0.307988i	$-0.900344\pi$
$233$	−48.6899	+	84.3333i	−0.208969	+	0.361946i	0.742421	+	0.669934i	$0.233678\pi$
$234$		0			0
$235$	94.0833	+	162.957i	0.400354	+	0.693434i
$236$		0			0
$237$			205.707i			0.867963i
$238$		0			0
$239$	−438.985			−1.83676			−0.918378	−	0.395703i	$-0.870501\pi$
$239$	−438.985			−1.83676			−0.918378	+	0.395703i	$0.870501\pi$
$240$		0			0
$241$	230.332	−	132.982i	0.955735	−	0.551794i	0.0608773	−	0.998145i	$-0.480610\pi$
$241$	230.332	−	132.982i	0.955735	−	0.551794i	0.894858	+	0.446351i	$0.147277\pi$
$242$		0			0
$243$	−110.093	−	63.5620i	−0.453056	−	0.261572i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−9.69343	+	16.7895i	−0.0392447	+	0.0679738i
$248$		0			0
$249$	140.146	+	242.739i	0.562834	+	0.974857i
$250$		0			0
$251$			391.326i			1.55907i	0.626361	+	0.779533i	$0.284543\pi$
$251$			391.326i			1.55907i	−0.626361	+	0.779533i	$0.715457\pi$
$252$		0			0
$253$	−157.054			−0.620766
$254$		0			0
$255$	−314.401	+	181.519i	−1.23294	+	0.711841i
$256$		0			0
$257$	−28.9289	−	16.7021i	−0.112564	−	0.0649887i	0.442661	−	0.896689i	$-0.354034\pi$
$257$	−28.9289	−	16.7021i	−0.112564	−	0.0649887i	−0.555225	+	0.831700i	$0.687368\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	43.2132	−	74.8475i	0.165568	−	0.286772i
$262$		0			0
$263$	−201.012	−	348.163i	−0.764305	−	1.32381i	−0.940613	−	0.339480i	$-0.889749\pi$
$263$	−201.012	−	348.163i	−0.764305	−	1.32381i	0.176308	−	0.984335i	$-0.443584\pi$
$264$		0			0
$265$			240.652i			0.908119i
$266$		0			0
$267$	23.6396			0.0885379
$268$		0			0
$269$	−11.6530	+	6.72786i	−0.0433197	+	0.0250106i	−0.521503	−	0.853249i	$-0.674629\pi$
$269$	−11.6530	+	6.72786i	−0.0433197	+	0.0250106i	0.478184	+	0.878260i	$0.341295\pi$
$270$		0			0
$271$	432.511	+	249.710i	1.59598	+	0.921440i	0.992251	+	0.124250i	$0.0396525\pi$
$271$	432.511	+	249.710i	1.59598	+	0.921440i	0.603729	+	0.797190i	$0.293681\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	9.84924	−	17.0594i	0.0358154	−	0.0620341i
$276$		0			0
$277$	240.404	+	416.392i	0.867885	+	1.50322i	0.864154	+	0.503228i	$0.167854\pi$
$277$	240.404	+	416.392i	0.867885	+	1.50322i	0.00373101	+	0.999993i	$0.498812\pi$
$278$		0			0
$279$			101.835i			0.365000i
$280$		0			0
$281$	167.307			0.595397			0.297699	−	0.954660i	$-0.403781\pi$
$281$	167.307			0.595397			0.297699	+	0.954660i	$0.403781\pi$
$282$		0			0
$283$	242.380	−	139.938i	0.856467	−	0.494481i	−0.00636072	−	0.999980i	$-0.502025\pi$
$283$	242.380	−	139.938i	0.856467	−	0.494481i	0.862828	+	0.505498i	$0.168691\pi$
$284$		0			0
$285$	35.7698	+	20.6517i	0.125508	+	0.0724621i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	108.403	−	187.760i	0.375097	−	0.649687i
$290$		0			0
$291$	152.945	+	264.908i	0.525583	+	0.910337i
$292$		0			0
$293$		−	128.043i		−	0.437007i	−0.975836	−	0.218504i	$-0.929882\pi$
$293$		−	128.043i		−	0.437007i	0.975836	−	0.218504i	$-0.0701176\pi$
$294$		0			0
$295$	−224.843			−0.762179
$296$		0			0
$297$	174.791	−	100.916i	0.588523	−	0.339784i
$298$		0			0
$299$	−113.607	−	65.5908i	−0.379955	−	0.219367i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	57.6447	−	99.8435i	0.190246	−	0.329516i
$304$		0			0
$305$	−188.978	−	327.319i	−0.619599	−	1.07318i
$306$		0			0
$307$		−	513.315i		−	1.67204i	−0.548702	−	0.836018i	$-0.684878\pi$
$307$		−	513.315i		−	1.67204i	0.548702	−	0.836018i	$-0.315122\pi$
$308$		0			0
$309$	−448.735			−1.45222
$310$		0			0
$311$	189.750	−	109.552i	0.610130	−	0.352258i	−0.162887	−	0.986645i	$-0.552080\pi$
$311$	189.750	−	109.552i	0.610130	−	0.352258i	0.773016	+	0.634386i	$0.218747\pi$
$312$		0			0
$313$	441.339	+	254.807i	1.41003	+	0.814080i	0.995390	−	0.0959070i	$-0.0305751\pi$
$313$	441.339	+	254.807i	1.41003	+	0.814080i	0.414637	+	0.909987i	$0.363908\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	144.556	−	250.379i	0.456014	−	0.789839i	−0.542732	−	0.839906i	$-0.682610\pi$
$317$	144.556	−	250.379i	0.456014	−	0.789839i	0.998746	+	0.0500669i	$0.0159435\pi$
$318$		0			0
$319$	162.368	+	281.229i	0.508989	+	0.881595i
$320$		0			0
$321$			437.448i			1.36277i
$322$		0			0
$323$	−57.5462			−0.178162
$324$		0			0
$325$	14.2491	−	8.22673i	0.0438434	−	0.0253130i
$326$		0			0
$327$	294.250	+	169.885i	0.899846	+	0.519526i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	62.4838	−	108.225i	0.188773	−	0.326964i	−0.756069	−	0.654492i	$-0.772882\pi$
$331$	62.4838	−	108.225i	0.188773	−	0.326964i	0.944841	+	0.327528i	$0.106216\pi$
$332$		0			0
$333$	−4.00000	−	6.92820i	−0.0120120	−	0.0208054i
$334$		0			0
$335$			260.044i			0.776252i
$336$		0			0
$337$	−320.583			−0.951284			−0.475642	−	0.879639i	$-0.657784\pi$
$337$	−320.583			−0.951284			−0.475642	+	0.879639i	$0.657784\pi$
$338$		0			0
$339$	493.573	−	284.965i	1.45597	−	0.840604i
$340$		0			0
$341$	−331.368	−	191.315i	−0.971753	−	0.561042i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−139.740	+	242.037i	−0.405044	+	0.701556i
$346$		0			0
$347$	119.933	+	207.729i	0.345627	+	0.598643i	0.985467	−	0.169864i	$-0.0543330\pi$
$347$	119.933	+	207.729i	0.345627	+	0.598643i	−0.639841	+	0.768508i	$0.721000\pi$
$348$		0			0
$349$		−	278.817i		−	0.798901i	−0.916755	−	0.399451i	$-0.869201\pi$
$349$		−	278.817i		−	0.798901i	0.916755	−	0.399451i	$-0.130799\pi$
$350$		0			0
$351$	168.583			0.480293
$352$		0			0
$353$	89.1600	−	51.4766i	0.252578	−	0.145826i	−0.368366	−	0.929681i	$-0.620083\pi$
$353$	89.1600	−	51.4766i	0.252578	−	0.145826i	0.620944	+	0.783855i	$0.286749\pi$
$354$		0			0
$355$	−1.66348	−	0.960408i	−0.00468585	−	0.00270538i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−206.647	+	357.923i	−0.575618	+	0.996999i	0.420357	+	0.907359i	$0.361905\pi$
$359$	−206.647	+	357.923i	−0.575618	+	0.996999i	−0.995974	+	0.0896401i	$0.971428\pi$
$360$		0			0
$361$	−177.226	−	306.965i	−0.490932	−	0.850319i
$362$		0			0
$363$			130.801i			0.360333i
$364$		0			0
$365$	−9.93102			−0.0272083
$366$		0			0
$367$	−504.739	+	291.411i	−1.37531	+	0.794036i	−0.991591	−	0.129413i	$-0.958691\pi$
$367$	−504.739	+	291.411i	−1.37531	+	0.794036i	−0.383720	+	0.923449i	$0.625357\pi$
$368$		0			0
$369$	−141.775	−	81.8539i	−0.384214	−	0.221826i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−142.238	+	246.363i	−0.381334	+	0.660490i	−0.991253	−	0.131974i	$-0.957869\pi$
$373$	−142.238	+	246.363i	−0.381334	+	0.660490i	0.609919	+	0.792464i	$0.291202\pi$
$374$		0			0
$375$	−219.304	−	379.845i	−0.584810	−	1.01292i
$376$		0			0
$377$			271.240i			0.719469i
$378$		0			0
$379$	−158.111			−0.417178			−0.208589	−	0.978003i	$-0.566887\pi$
$379$	−158.111			−0.417178			−0.208589	+	0.978003i	$0.566887\pi$
$380$		0			0
$381$	77.8368	−	44.9391i	0.204296	−	0.117950i
$382$		0			0
$383$	−64.4698	−	37.2217i	−0.168329	−	0.0971845i	0.413469	−	0.910518i	$-0.364317\pi$
$383$	−64.4698	−	37.2217i	−0.168329	−	0.0971845i	−0.581797	+	0.813334i	$0.697650\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	33.4350	−	57.9112i	0.0863954	−	0.149641i
$388$		0			0
$389$	−28.7868	−	49.8602i	−0.0740020	−	0.128175i	0.826650	−	0.562717i	$-0.190244\pi$
$389$	−28.7868	−	49.8602i	−0.0740020	−	0.128175i	−0.900652	+	0.434541i	$0.856910\pi$
$390$		0			0
$391$		−	389.388i		−	0.995876i
$392$		0			0
$393$	483.928			1.23137
$394$		0			0
$395$	−251.939	+	145.457i	−0.637820	+	0.368246i
$396$		0			0
$397$	−447.692	−	258.475i	−1.12769	−	0.651071i	−0.184336	−	0.982863i	$-0.559013\pi$
$397$	−447.692	−	258.475i	−1.12769	−	0.651071i	−0.943353	+	0.331792i	$0.892347\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	205.943	−	356.704i	0.513574	−	0.889536i	−0.486302	−	0.873791i	$-0.661654\pi$
$401$	205.943	−	356.704i	0.513574	−	0.889536i	0.999876	−	0.0157456i	$-0.00501219\pi$
$402$		0			0
$403$	−159.799	−	276.780i	−0.396524	−	0.686799i
$404$		0			0
$405$		−	462.977i		−	1.14315i
$406$		0			0
$407$	30.0589			0.0738547
$408$		0			0
$409$	−149.391	+	86.2510i	−0.365260	+	0.210883i	−0.671385	−	0.741108i	$-0.734300\pi$
$409$	−149.391	+	86.2510i	−0.365260	+	0.210883i	0.306126	+	0.951991i	$0.400967\pi$
$410$		0			0
$411$	197.417	+	113.979i	0.480333	+	0.277320i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−198.196	+	343.285i	−0.477581	+	0.827194i
$416$		0			0
$417$	−24.9548	−	43.2230i	−0.0598436	−	0.103652i
$418$		0			0
$419$		−	96.5939i		−	0.230534i	−0.993335	−	0.115267i	$-0.963228\pi$
$419$		−	96.5939i		−	0.230534i	0.993335	−	0.115267i	$-0.0367724\pi$
$420$		0			0
$421$	233.377			0.554339			0.277170	−	0.960821i	$-0.410604\pi$
$421$	233.377			0.554339			0.277170	+	0.960821i	$0.410604\pi$
$422$		0			0
$423$	−82.3400	+	47.5390i	−0.194657	+	0.112385i
$424$		0			0
$425$	42.2958	+	24.4195i	0.0995195	+	0.0574576i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	116.101	−	201.092i	0.270631	−	0.468746i
$430$		0			0
$431$	−204.203	−	353.690i	−0.473789	−	0.820627i	0.525761	−	0.850633i	$-0.323781\pi$
$431$	−204.203	−	353.690i	−0.473789	−	0.820627i	−0.999550	+	0.0300058i	$0.990447\pi$
$432$		0			0
$433$		−	345.865i		−	0.798765i	−0.916784	−	0.399382i	$-0.869225\pi$
$433$		−	345.865i		−	0.798765i	0.916784	−	0.399382i	$-0.130775\pi$
$434$		0			0
$435$	577.872			1.32844
$436$		0			0
$437$	−38.3659	+	22.1506i	−0.0877939	+	0.0506878i
$438$		0			0
$439$	−439.610	−	253.809i	−1.00139	−	0.578152i	−0.0927303	−	0.995691i	$-0.529559\pi$
$439$	−439.610	−	253.809i	−1.00139	−	0.578152i	−0.908659	+	0.417539i	$0.862893\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	360.233	−	623.941i	0.813166	−	1.40844i	−0.0974713	−	0.995238i	$-0.531075\pi$
$443$	360.233	−	623.941i	0.813166	−	1.40844i	0.910637	−	0.413207i	$-0.135591\pi$
$444$		0			0
$445$	16.7157	+	28.9525i	0.0375634	+	0.0650618i
$446$		0			0
$447$		−	292.190i		−	0.653669i
$448$		0			0
$449$	363.598			0.809795			0.404898	−	0.914362i	$-0.367307\pi$
$449$	363.598			0.809795			0.404898	+	0.914362i	$0.367307\pi$
$450$		0			0
$451$	532.700	−	307.554i	1.18115	−	0.681939i
$452$		0			0
$453$	609.827	+	352.084i	1.34620	+	0.777226i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−229.986	+	398.348i	−0.503252	+	0.871659i	0.496741	+	0.867899i	$0.334530\pi$
$457$	−229.986	+	398.348i	−0.503252	+	0.871659i	−0.999993	+	0.00375958i	$0.998803\pi$
$458$		0			0
$459$	250.203	+	433.364i	0.545105	+	0.944149i
$460$		0			0
$461$			506.119i			1.09787i	0.835864	+	0.548936i	$0.184967\pi$
$461$			506.119i			1.09787i	−0.835864	+	0.548936i	$0.815033\pi$
$462$		0			0
$463$	−12.6030			−0.0272204			−0.0136102	−	0.999907i	$-0.504332\pi$
$463$	−12.6030			−0.0272204			−0.0136102	+	0.999907i	$0.504332\pi$
$464$		0			0
$465$	−589.675	+	340.449i	−1.26812	+	0.732149i
$466$		0			0
$467$	−567.795	−	327.817i	−1.21584	−	0.701963i	−0.251811	−	0.967776i	$-0.581026\pi$
$467$	−567.795	−	327.817i	−1.21584	−	0.701963i	−0.964025	+	0.265813i	$0.914360\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−200.154	+	346.677i	−0.424956	+	0.736046i
$472$		0			0
$473$	125.627	+	217.593i	0.265597	+	0.460028i
$474$		0			0
$475$		−	5.55648i		−	0.0116978i
$476$		0			0
$477$	−121.598			−0.254922
$478$		0			0
$479$	−666.063	+	384.551i	−1.39053	+	0.802821i	−0.993374	−	0.114931i	$-0.963335\pi$
$479$	−666.063	+	384.551i	−1.39053	+	0.802821i	−0.397154	+	0.917752i	$0.630002\pi$
$480$		0			0
$481$	21.7434	+	12.5536i	0.0452046	+	0.0260989i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−216.296	+	374.636i	−0.445972	+	0.772446i
$486$		0			0
$487$	207.184	+	358.853i	0.425429	+	0.736864i	0.996460	−	0.0840639i	$-0.0267900\pi$
$487$	207.184	+	358.853i	0.425429	+	0.736864i	−0.571032	+	0.820928i	$0.693457\pi$
$488$		0			0
$489$		−	993.980i		−	2.03268i
$490$		0			0
$491$	474.995			0.967403			0.483702	−	0.875233i	$-0.339292\pi$
$491$	474.995			0.967403			0.483702	+	0.875233i	$0.339292\pi$
$492$		0			0
$493$	−697.258	+	402.562i	−1.41432	+	0.816556i
$494$		0			0
$495$	−90.6155	−	52.3169i	−0.183062	−	0.105691i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−22.1594	+	38.3812i	−0.0444076	+	0.0769162i	−0.887375	−	0.461049i	$-0.847473\pi$
$499$	−22.1594	+	38.3812i	−0.0444076	+	0.0769162i	0.842967	+	0.537965i	$0.180807\pi$
$500$		0			0
$501$	101.106	+	175.120i	0.201807	+	0.349541i
$502$		0			0
$503$			182.603i			0.363029i	0.983388	+	0.181514i	$0.0580999\pi$
$503$			182.603i			0.363029i	−0.983388	+	0.181514i	$0.941900\pi$
$504$		0			0
$505$	163.044			0.322859
$506$		0			0
$507$	−326.505	+	188.508i	−0.643995	+	0.371811i
$508$		0			0
$509$	−577.993	−	333.704i	−1.13555	−	0.655608i	−0.190222	−	0.981741i	$-0.560921\pi$
$509$	−577.993	−	333.704i	−1.13555	−	0.655608i	−0.945324	+	0.326133i	$0.894254\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	28.4659	−	49.3045i	0.0554892	−	0.0961101i
$514$		0			0
$515$	−317.304	−	549.586i	−0.616124	−	1.06716i
$516$		0			0
$517$		−	357.242i		−	0.690991i
$518$		0			0
$519$	284.544			0.548255
$520$		0			0
$521$	401.675	−	231.907i	0.770969	−	0.445119i	−0.0622514	−	0.998060i	$-0.519828\pi$
$521$	401.675	−	231.907i	0.770969	−	0.445119i	0.833220	+	0.552942i	$0.186495\pi$
$522$		0			0
$523$	216.499	+	124.996i	0.413956	+	0.238998i	0.692488	−	0.721429i	$-0.256515\pi$
$523$	216.499	+	124.996i	0.413956	+	0.238998i	−0.278532	+	0.960427i	$0.589848\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	474.333	−	821.569i	0.900063	−	1.55895i
$528$		0			0
$529$	114.618	+	198.524i	0.216669	+	0.375281i
$530$		0			0
$531$		−	113.610i		−	0.213955i
$532$		0			0
$533$	513.779			0.963938
$534$		0			0
$535$	−535.762	+	309.322i	−1.00142	+	0.578173i
$536$		0			0
$537$	6.54076	+	3.77631i	0.0121802	+	0.00703223i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	196.044	−	339.558i	0.362373	−	0.627648i	−0.625978	−	0.779841i	$-0.715300\pi$
$541$	196.044	−	339.558i	0.362373	−	0.627648i	0.988351	+	0.152192i	$0.0486334\pi$
$542$		0			0
$543$	12.7990	+	22.1685i	0.0235709	+	0.0408260i
$544$		0			0
$545$			480.507i			0.881665i
$546$		0			0
$547$	−209.307			−0.382645			−0.191322	−	0.981527i	$-0.561278\pi$
$547$	−209.307			−0.382645			−0.191322	+	0.981527i	$0.561278\pi$
$548$		0			0
$549$	165.390	−	95.4879i	0.301257	−	0.173931i
$550$		0			0
$551$	79.3280	+	45.8000i	0.143971	+	0.0831216i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	26.7452	−	46.3240i	0.0481895	−	0.0834666i
$556$		0			0
$557$	−104.088	−	180.286i	−0.186873	−	0.323674i	0.757333	−	0.653029i	$-0.226502\pi$
$557$	−104.088	−	180.286i	−0.186873	−	0.323674i	−0.944206	+	0.329355i	$0.893169\pi$
$558$		0			0
$559$			209.864i			0.375428i
$560$		0			0
$561$	689.245			1.22860
$562$		0			0
$563$	−739.970	+	427.222i	−1.31433	+	0.758831i	−0.982811	−	0.184617i	$-0.940896\pi$
$563$	−739.970	+	427.222i	−1.31433	+	0.758831i	−0.331523	+	0.943447i	$0.607562\pi$
$564$		0			0
$565$	698.018	+	403.001i	1.23543	+	0.713276i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	477.948	−	827.831i	0.839979	−	1.45489i	−0.0499316	−	0.998753i	$-0.515900\pi$
$569$	477.948	−	827.831i	0.839979	−	1.45489i	0.889911	−	0.456134i	$-0.150766\pi$
$570$		0			0
$571$	119.641	+	207.224i	0.209529	+	0.362915i	0.951566	−	0.307444i	$-0.0994736\pi$
$571$	119.641	+	207.224i	0.209529	+	0.362915i	−0.742037	+	0.670359i	$0.766140\pi$
$572$		0			0
$573$		−	122.024i		−	0.212956i
$574$		0			0
$575$	37.5980			0.0653878
$576$		0			0
$577$	−185.304	+	106.985i	−0.321150	+	0.185416i	−0.651905	−	0.758301i	$-0.726030\pi$
$577$	−185.304	+	106.985i	−0.321150	+	0.185416i	0.330755	+	0.943717i	$0.392697\pi$
$578$		0			0
$579$	57.5637	+	33.2344i	0.0994191	+	0.0573997i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	228.444	−	395.676i	0.391842	−	0.678690i
$584$		0			0
$585$	−43.6985	−	75.6880i	−0.0746983	−	0.129381i
$586$		0			0
$587$		−	496.638i		−	0.846062i	−0.906115	−	0.423031i	$-0.860966\pi$
$587$		−	496.638i		−	0.846062i	0.906115	−	0.423031i	$-0.139034\pi$
$588$		0			0
$589$	−107.931			−0.183245
$590$		0			0
$591$	751.343	−	433.788i	1.27131	−	0.733990i
$592$		0			0
$593$	−720.974	−	416.254i	−1.21581	−	0.701947i	−0.251789	−	0.967782i	$-0.581019\pi$
$593$	−720.974	−	416.254i	−1.21581	−	0.701947i	−0.964018	+	0.265836i	$0.914352\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−20.5341	+	35.5660i	−0.0343954	+	0.0595746i
$598$		0			0
$599$	−281.615	−	487.772i	−0.470142	−	0.814310i	0.529275	−	0.848450i	$-0.322464\pi$
$599$	−281.615	−	487.772i	−0.470142	−	0.814310i	−0.999417	+	0.0341402i	$0.989131\pi$
$600$		0			0
$601$		−	679.242i		−	1.13019i	−0.825027	−	0.565093i	$-0.808840\pi$
$601$		−	679.242i		−	1.13019i	0.825027	−	0.565093i	$-0.191160\pi$
$602$		0			0
$603$	−131.397			−0.217905
$604$		0			0
$605$	−160.198	+	92.4901i	−0.264789	+	0.152876i
$606$		0			0
$607$	45.8393	+	26.4653i	0.0755178	+	0.0436002i	0.537283	−	0.843402i	$-0.319451\pi$
$607$	45.8393	+	26.4653i	0.0755178	+	0.0436002i	−0.461766	+	0.887002i	$0.652784\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	149.196	−	258.415i	0.244183	−	0.422938i
$612$		0			0
$613$	−150.274	−	260.282i	−0.245145	−	0.424604i	0.717027	−	0.697045i	$-0.245502\pi$
$613$	−150.274	−	260.282i	−0.245145	−	0.424604i	−0.962173	+	0.272441i	$0.912169\pi$
$614$		0			0
$615$		−	1094.60i		−	1.77983i
$616$		0			0
$617$	−1186.18			−1.92250			−0.961249	−	0.275683i	$-0.911096\pi$
$617$	−1186.18			−1.92250			−0.961249	+	0.275683i	$0.911096\pi$
$618$		0			0
$619$	355.520	−	205.260i	0.574346	−	0.331599i	−0.184537	−	0.982826i	$-0.559079\pi$
$619$	355.520	−	205.260i	0.574346	−	0.331599i	0.758883	+	0.651227i	$0.225745\pi$
$620$		0			0
$621$	333.619	+	192.615i	0.537229	+	0.310170i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	282.997	−	490.166i	0.452796	−	0.784266i
$626$		0			0
$627$	−39.2082	−	67.9105i	−0.0625329	−	0.108310i
$628$		0			0
$629$			74.5257i			0.118483i
$630$		0			0
$631$	743.980			1.17905			0.589524	−	0.807751i	$-0.299315\pi$
$631$	743.980			1.17905			0.589524	+	0.807751i	$0.299315\pi$
$632$		0			0
$633$	−550.650	+	317.918i	−0.869905	+	0.502240i
$634$		0			0
$635$	110.078	+	63.5534i	0.173351	+	0.100084i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	0.485281	−	0.840532i	0.000759439	−	0.00131539i
$640$		0			0
$641$	−257.179	−	445.447i	−0.401215	−	0.694924i	0.592658	−	0.805454i	$-0.298079\pi$
$641$	−257.179	−	445.447i	−0.401215	−	0.694924i	−0.993873	+	0.110530i	$0.964745\pi$
$642$		0			0
$643$		−	514.076i		−	0.799497i	−0.916625	−	0.399748i	$-0.869097\pi$
$643$		−	514.076i		−	0.799497i	0.916625	−	0.399748i	$-0.130903\pi$
$644$		0			0
$645$	447.113			0.693198
$646$		0			0
$647$	711.658	−	410.876i	1.09994	−	0.635048i	0.163732	−	0.986505i	$-0.447647\pi$
$647$	711.658	−	410.876i	1.09994	−	0.635048i	0.936204	+	0.351457i	$0.114314\pi$
$648$		0			0
$649$	369.683	+	213.437i	0.569620	+	0.328870i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	494.933	−	857.249i	0.757937	−	1.31279i	−0.185963	−	0.982557i	$-0.559541\pi$
$653$	494.933	−	857.249i	0.757937	−	1.31279i	0.943901	−	0.330229i	$-0.107126\pi$
$654$		0			0
$655$	342.189	+	592.688i	0.522426	+	0.904868i
$656$		0			0
$657$		−	5.01801i		−	0.00763777i
$658$		0			0
$659$	−564.281			−0.856269			−0.428135	−	0.903715i	$-0.640829\pi$
$659$	−564.281			−0.856269			−0.428135	+	0.903715i	$0.640829\pi$
$660$		0			0
$661$	355.800	−	205.421i	0.538275	−	0.310773i	−0.206105	−	0.978530i	$-0.566079\pi$
$661$	355.800	−	205.421i	0.538275	−	0.310773i	0.744379	+	0.667757i	$0.232745\pi$
$662$		0			0
$663$	498.573	+	287.851i	0.751995	+	0.434164i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−309.907	+	536.774i	−0.464628	+	0.804759i
$668$		0			0
$669$	−459.477	−	795.838i	−0.686812	−	1.18959i
$670$		0			0
$671$			717.565i			1.06940i
$672$		0			0
$673$	−930.663			−1.38286			−0.691429	−	0.722445i	$-0.743018\pi$
$673$	−930.663			−1.38286			−0.691429	+	0.722445i	$0.743018\pi$
$674$		0			0
$675$	−41.8442	+	24.1588i	−0.0619915	+	0.0357908i
$676$		0			0
$677$	−122.521	−	70.7374i	−0.180976	−	0.104487i	0.406775	−	0.913528i	$-0.366653\pi$
$677$	−122.521	−	70.7374i	−0.180976	−	0.104487i	−0.587751	+	0.809042i	$0.699987\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−640.986	+	1110.22i	−0.941243	+	1.63028i
$682$		0			0
$683$	−83.7960	−	145.139i	−0.122688	−	0.212502i	0.798139	−	0.602474i	$-0.205818\pi$
$683$	−83.7960	−	145.139i	−0.122688	−	0.212502i	−0.920827	+	0.389972i	$0.872485\pi$
$684$		0			0
$685$			322.380i			0.470628i
$686$		0			0
$687$	−252.260			−0.367191
$688$		0			0
$689$	330.494	−	190.811i	0.479672	−	0.276939i
$690$		0			0
$691$	377.163	+	217.755i	0.545822	+	0.315130i	0.747435	−	0.664335i	$-0.231285\pi$
$691$	377.163	+	217.755i	0.545822	+	0.315130i	−0.201613	+	0.979465i	$0.564618\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	35.2914	−	61.1265i	0.0507790	−	0.0879518i
$696$		0			0
$697$	762.528	+	1320.74i	1.09401	+	1.89489i
$698$		0			0
$699$		−	328.997i		−	0.470668i
$700$		0			0
$701$	742.010			1.05850			0.529251	−	0.848465i	$-0.322473\pi$
$701$	742.010			1.05850			0.529251	+	0.848465i	$0.322473\pi$
$702$		0			0
$703$	7.34294	−	4.23945i	0.0104451	−	0.00603051i
$704$		0			0
$705$	−550.549	−	317.860i	−0.780921	−	0.450865i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−58.7351	+	101.732i	−0.0828421	+	0.143487i	−0.904470	−	0.426538i	$-0.859733\pi$
$709$	−58.7351	+	101.732i	−0.0828421	+	0.143487i	0.821628	+	0.570025i	$0.193066\pi$
$710$		0			0
$711$	−73.4975	−	127.301i	−0.103372	−	0.179046i
$712$		0			0
$713$		−	730.317i		−	1.02429i
$714$		0			0
$715$	328.382			0.459275
$716$		0			0
$717$	1284.41	−	741.554i	1.79136	−	1.03424i
$718$		0			0
$719$	35.0808	+	20.2539i	0.0487911	+	0.0281695i	0.524197	−	0.851597i	$-0.324366\pi$
$719$	35.0808	+	20.2539i	0.0487911	+	0.0281695i	−0.475406	+	0.879766i	$0.657699\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−449.280	+	778.175i	−0.621411	+	1.07631i
$724$		0			0
$725$	−38.8701	−	67.3249i	−0.0536139	−	0.0928620i
$726$		0			0
$727$		−	362.922i		−	0.499205i	−0.968348	−	0.249603i	$-0.919700\pi$
$727$		−	362.922i		−	0.499205i	0.968348	−	0.249603i	$-0.0803000\pi$
$728$		0			0
$729$	−442.608			−0.607144
$730$		0			0
$731$	−539.484	+	311.471i	−0.738008	+	0.426089i
$732$		0			0
$733$	−493.431	−	284.882i	−0.673166	−	0.388653i	0.124109	−	0.992269i	$-0.460393\pi$
$733$	−493.431	−	284.882i	−0.673166	−	0.388653i	−0.797275	+	0.603616i	$0.793726\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	246.853	−	427.562i	0.334943	−	0.580138i
$738$		0			0
$739$	−22.4695	−	38.9183i	−0.0304053	−	0.0526635i	0.850422	−	0.526101i	$-0.176346\pi$
$739$	−22.4695	−	38.9183i	−0.0304053	−	0.0526635i	−0.880828	+	0.473437i	$0.843013\pi$
$740$		0			0
$741$		−	65.4984i		−	0.0883919i
$742$		0			0
$743$	−1256.37			−1.69094			−0.845472	−	0.534019i	$-0.820681\pi$
$743$	−1256.37			−1.69094			−0.845472	+	0.534019i	$0.820681\pi$
$744$		0			0
$745$	357.858	−	206.609i	0.480346	−	0.277328i
$746$		0			0
$747$	−173.458	−	100.146i	−0.232206	−	0.134064i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	524.217	−	907.971i	0.698026	−	1.20902i	−0.271124	−	0.962544i	$-0.587395\pi$
$751$	524.217	−	907.971i	0.698026	−	1.20902i	0.969150	−	0.246472i	$-0.0792713\pi$
$752$		0			0
$753$	−661.045	−	1144.96i	−0.877882	−	1.52054i
$754$		0			0
$755$			995.843i			1.31900i
$756$		0			0
$757$	1089.95			1.43983			0.719914	−	0.694063i	$-0.244181\pi$
$757$	1089.95			1.43983			0.719914	+	0.694063i	$0.244181\pi$
$758$		0			0
$759$	459.518	−	265.303i	0.605425	−	0.349542i
$760$		0			0
$761$	192.462	+	111.118i	0.252907	+	0.146016i	0.621095	−	0.783736i	$-0.286688\pi$
$761$	192.462	+	111.118i	0.252907	+	0.146016i	−0.368188	+	0.929751i	$0.620022\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	129.711	−	224.665i	0.169556	−	0.293680i
$766$		0			0
$767$	178.276	+	308.784i	0.232433	+	0.402586i
$768$		0			0
$769$			776.217i			1.00938i	0.863299	+	0.504692i	$0.168394\pi$
$769$			776.217i			1.00938i	−0.863299	+	0.504692i	$0.831606\pi$
$770$		0			0
$771$	112.856			0.146376
$772$		0			0
$773$	−829.302	+	478.798i	−1.07284	+	0.619402i	−0.928955	−	0.370193i	$-0.879291\pi$
$773$	−829.302	+	478.798i	−1.07284	+	0.619402i	−0.143881	+	0.989595i	$0.545958\pi$
$774$		0			0
$775$	79.3280	+	45.8000i	0.102359	+	0.0590968i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	86.7538	−	150.262i	0.111366	−	0.192891i
$780$		0			0
$781$	1.82338	+	3.15818i	0.00233467	+	0.00404377i
$782$		0			0
$783$		−	796.529i		−	1.01728i
$784$		0			0
$785$	−566.122			−0.721174
$786$		0			0
$787$	−519.318	+	299.828i	−0.659871	+	0.380976i	−0.792228	−	0.610226i	$-0.791079\pi$
$787$	−519.318	+	299.828i	−0.659871	+	0.380976i	0.132357	+	0.991202i	$0.457745\pi$
$788$		0			0
$789$	1176.27	+	679.118i	1.49083	+	0.860733i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−299.678	+	519.058i	−0.377905	+	0.654550i
$794$		0			0
$795$	−406.520	−	704.113i	−0.511346	−	0.885677i
$796$		0			0
$797$			431.874i			0.541875i	0.962597	+	0.270938i	$0.0873337\pi$
$797$			431.874i			0.541875i	−0.962597	+	0.270938i	$0.912666\pi$
$798$		0			0
$799$	885.720			1.10854
$800$		0			0
$801$	−14.6293	+	8.44623i	−0.0182638	+	0.0105446i
$802$		0			0
$803$	16.3285	+	9.42724i	0.0203343	+	0.0117400i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	22.7300	−	39.3695i	0.0281661	−	0.0487851i
$808$		0			0
$809$	496.153	+	859.362i	0.613292	+	1.06225i	0.990682	+	0.136198i	$0.0434882\pi$
$809$	496.153	+	859.362i	0.613292	+	1.06225i	−0.377390	+	0.926054i	$0.623178\pi$
$810$		0			0
$811$			1364.92i			1.68301i	0.540252	+	0.841503i	$0.318329\pi$
$811$			1364.92i			1.68301i	−0.540252	+	0.841503i	$0.681671\pi$
$812$		0			0
$813$	−1687.29			−2.07538
$814$		0			0
$815$	1217.37	−	702.850i	1.49371	−	0.862393i
$816$		0			0
$817$	61.3778	+	35.4365i	0.0751259	+	0.0433739i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−287.745	+	498.389i	−0.350481	+	0.607051i	−0.986334	−	0.164759i	$-0.947315\pi$
$821$	−287.745	+	498.389i	−0.350481	+	0.607051i	0.635853	+	0.771811i	$0.280649\pi$
$822$		0			0
$823$	301.169	+	521.639i	0.365940	+	0.633827i	0.988927	−	0.148406i	$-0.0474142\pi$
$823$	301.169	+	521.639i	0.365940	+	0.633827i	−0.622987	+	0.782233i	$0.714081\pi$
$824$		0			0
$825$			66.5512i			0.0806681i
$826$		0			0
$827$	−52.3717			−0.0633273			−0.0316637	−	0.999499i	$-0.510081\pi$
$827$	−52.3717			−0.0633273			−0.0316637	+	0.999499i	$0.510081\pi$
$828$		0			0
$829$	−762.093	+	439.995i	−0.919292	+	0.530754i	−0.883409	−	0.468602i	$-0.844758\pi$
$829$	−762.093	+	439.995i	−0.919292	+	0.530754i	−0.0358830	+	0.999356i	$0.511424\pi$
$830$		0			0
$831$	−1406.78	−	812.204i	−1.69287	−	0.977381i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−142.985	+	247.657i	−0.171239	+	0.296595i
$836$		0			0
$837$	469.269	+	812.798i	0.560656	+	0.971085i
$838$		0			0
$839$			1400.14i			1.66882i	0.551147	+	0.834408i	$0.314190\pi$
$839$			1400.14i			1.66882i	−0.551147	+	0.834408i	$0.685810\pi$
$840$		0			0
$841$	440.568			0.523862
$842$		0			0
$843$	−489.516	+	282.622i	−0.580683	+	0.335257i
$844$		0			0
$845$	−461.748	−	266.591i	−0.546448	−	0.315492i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−472.780	+	818.879i	−0.556867	+	0.964522i
$850$		0			0
$851$	28.6863	+	49.6861i	0.0337089	+	0.0583856i
$852$		0			0
$853$			1243.31i			1.45757i	0.684741	+	0.728786i	$0.259915\pi$
$853$			1243.31i			1.45757i	−0.684741	+	0.728786i	$0.740085\pi$
$854$		0			0
$855$	−29.5147			−0.0345201
$856$		0			0
$857$	−609.720	+	352.022i	−0.711458	+	0.410761i	−0.811601	−	0.584213i	$-0.801403\pi$
$857$	−609.720	+	352.022i	−0.711458	+	0.410761i	0.100143	+	0.994973i	$0.468070\pi$
$858$		0			0
$859$	21.4346	+	12.3753i	0.0249529	+	0.0144066i	0.512425	−	0.858732i	$-0.328747\pi$
$859$	21.4346	+	12.3753i	0.0249529	+	0.0144066i	−0.487472	+	0.873139i	$0.662081\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−794.149	+	1375.51i	−0.920219	+	1.59387i	−0.121145	+	0.992635i	$0.538656\pi$
$863$	−794.149	+	1375.51i	−0.920219	+	1.59387i	−0.799075	+	0.601232i	$0.794677\pi$
$864$		0			0
$865$	201.203	+	348.494i	0.232605	+	0.402883i
$866$		0			0
$867$			732.478i			0.844842i
$868$		0			0
$869$	552.313			0.635573
$870$		0			0
$871$	357.127	−	206.188i	0.410020	−	0.236725i
$872$		0			0
$873$	−189.299	−	109.292i	−0.216837	−	0.125191i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−607.841	+	1052.81i	−0.693091	+	1.20047i	0.277729	+	0.960659i	$0.410418\pi$
$877$	−607.841	+	1052.81i	−0.693091	+	1.20047i	−0.970820	+	0.239809i	$0.922915\pi$
$878$		0			0
$879$	216.296	+	374.636i	0.246071	+	0.426208i
$880$		0			0
$881$			858.799i			0.974800i	0.873179	+	0.487400i	$0.162055\pi$
$881$			858.799i			0.974800i	−0.873179	+	0.487400i	$0.837945\pi$
$882$		0			0
$883$	−974.382			−1.10349			−0.551745	−	0.834013i	$-0.686038\pi$
$883$	−974.382			−1.10349			−0.551745	+	0.834013i	$0.686038\pi$
$884$		0			0
$885$	657.858	−	379.815i	0.743343	−	0.429169i
$886$		0			0
$887$	−1150.68	−	664.346i	−1.29727	−	0.748980i	−0.317340	−	0.948312i	$-0.602790\pi$
$887$	−1150.68	−	664.346i	−1.29727	−	0.748980i	−0.979932	+	0.199332i	$0.936123\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−439.491	+	761.221i	−0.493256	+	0.854344i
$892$		0			0
$893$	−50.3848	−	87.2690i	−0.0564219	−	0.0977256i
$894$		0			0
$895$			10.6810i			0.0119341i
$896$		0			0
$897$	443.196			0.494087
$898$		0			0
$899$	−1307.74	+	755.026i	−1.45467	+	0.839851i
$900$		0			0
$901$	981.010	+	566.386i	1.08880	+	0.628620i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−18.1005	+	31.3510i	−0.0200006	+	0.0346420i
$906$		0			0
$907$	−135.319	−	234.379i	−0.149194	−	0.258411i	0.781736	−	0.623610i	$-0.214334\pi$
$907$	−135.319	−	234.379i	−0.149194	−	0.258411i	−0.930930	+	0.365198i	$0.881001\pi$
$908$		0			0
$909$			82.3838i			0.0906312i
$910$		0			0
$911$	399.025			0.438008			0.219004	−	0.975724i	$-0.429719\pi$
$911$	399.025			0.438008			0.219004	+	0.975724i	$0.429719\pi$
$912$		0			0
$913$	651.742	−	376.284i	0.713847	−	0.412140i
$914$		0			0
$915$	1105.84	+	638.460i	1.20857	+	0.697770i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	1.03658	−	1.79541i	0.00112794	−	0.00195366i	−0.865461	−	0.500977i	$-0.832974\pi$
$919$	1.03658	−	1.79541i	0.00112794	−	0.00195366i	0.866589	+	0.499023i	$0.166308\pi$
$920$		0			0
$921$	867.115	+	1501.89i	0.941493	+	1.63071i
$922$		0			0
$923$			3.04601i			0.00330011i
$924$		0			0
$925$	−7.19596			−0.00777942
$926$		0			0
$927$	277.698	−	160.329i	0.299567	−	0.172955i
$928$		0			0
$929$	−942.558	−	544.186i	−1.01459	−	0.585776i	−0.102060	−	0.994778i	$-0.532544\pi$
$929$	−942.558	−	544.186i	−1.01459	−	0.585776i	−0.912533	+	0.409002i	$0.865877\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−370.122	+	641.070i	−0.396701	+	0.687106i
$934$		0			0
$935$	487.370	+	844.149i	0.521251	+	0.902833i
$936$		0			0
$937$		−	930.797i		−	0.993380i	−0.867928	−	0.496690i	$-0.834549\pi$
$937$		−	930.797i		−	0.993380i	0.867928	−	0.496690i	$-0.165451\pi$
$938$		0			0
$939$	−1721.73			−1.83358
$940$		0			0
$941$	546.168	−	315.330i	0.580412	−	0.335101i	−0.180885	−	0.983504i	$-0.557896\pi$
$941$	546.168	−	315.330i	0.580412	−	0.335101i	0.761297	+	0.648403i	$0.224563\pi$
$942$		0			0
$943$	1016.75	+	587.021i	1.07821	+	0.622504i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	199.378	−	345.333i	0.210537	−	0.364660i	−0.741346	−	0.671123i	$-0.765812\pi$
$947$	199.378	−	345.333i	0.210537	−	0.364660i	0.951883	+	0.306463i	$0.0991455\pi$
$948$		0			0
$949$	7.87424	+	13.6386i	0.00829741	+	0.0143715i
$950$		0			0
$951$			976.765i			1.02709i
$952$		0			0
$953$	−288.362			−0.302583			−0.151292	−	0.988489i	$-0.548343\pi$
$953$	−288.362			−0.302583			−0.151292	+	0.988489i	$0.548343\pi$
$954$		0			0
$955$	149.448	−	86.2837i	0.156490	−	0.0903494i
$956$		0			0
$957$	−950.130	−	548.558i	−0.992821	−	0.573205i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	409.137	−	708.645i	0.425741	−	0.737404i
$962$		0			0
$963$	−156.296	−	270.713i	−0.162302	−	0.281115i
$964$		0			0
$965$			94.0011i			0.0974104i
$966$		0			0
$967$	643.166			0.665114			0.332557	−	0.943083i	$-0.392089\pi$
$967$	643.166			0.665114			0.332557	+	0.943083i	$0.392089\pi$
$968$		0			0
$969$	168.372	−	97.2098i	0.173759	−	0.100320i
$970$		0			0
$971$	−621.221	−	358.662i	−0.639775	−	0.369374i	0.144753	−	0.989468i	$-0.453761\pi$
$971$	−621.221	−	358.662i	−0.639775	−	0.369374i	−0.784528	+	0.620094i	$0.787095\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−27.7939	+	48.1405i	−0.0285066	+	0.0493749i
$976$		0			0
$977$	−701.224	−	1214.56i	−0.717732	−	1.24315i	−0.961896	−	0.273414i	$-0.911847\pi$
$977$	−701.224	−	1214.56i	−0.717732	−	1.24315i	0.244165	−	0.969734i	$-0.421486\pi$
$978$		0			0
$979$		−	63.4711i		−	0.0648325i
$980$		0			0
$981$	−242.794			−0.247496
$982$		0			0
$983$	−81.3360	+	46.9593i	−0.0827426	+	0.0477715i	−0.540800	−	0.841151i	$-0.681879\pi$
$983$	−81.3360	+	46.9593i	−0.0827426	+	0.0477715i	0.458058	+	0.888922i	$0.348545\pi$
$984$		0			0
$985$	1062.56	+	613.469i	1.07874	+	0.622811i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−239.782	+	415.314i	−0.242449	+	0.419933i
$990$		0			0
$991$	−48.8314	−	84.5784i	−0.0492749	−	0.0853466i	0.840336	−	0.542066i	$-0.182358\pi$
$991$	−48.8314	−	84.5784i	−0.0492749	−	0.0853466i	−0.889611	+	0.456719i	$0.849024\pi$
$992$		0			0
$993$			422.202i			0.425178i
$994$		0			0
$995$	−58.0791			−0.0583709
$996$		0			0
$997$	234.779	−	135.550i	0.235485	−	0.135957i	−0.377615	−	0.925963i	$-0.623256\pi$
$997$	234.779	−	135.550i	0.235485	−	0.135957i	0.613100	+	0.790005i	$0.289922\pi$
$998$		0			0
$999$	−63.8522	−	36.8651i	−0.0639161	−	0.0369020i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.3.s.h.705.1		8
4.3	odd	2		49.3.d.b.19.4		8
7.2	even	3		784.3.c.c.97.1		4
7.3	odd	6	inner	784.3.s.h.129.1		8
7.4	even	3	inner	784.3.s.h.129.4		8
7.5	odd	6		784.3.c.c.97.4		4
7.6	odd	2	inner	784.3.s.h.705.4		8
12.11	even	2		441.3.m.l.19.2		8
28.3	even	6		49.3.d.b.31.4		8
28.11	odd	6		49.3.d.b.31.3		8
28.19	even	6		49.3.b.a.48.1	✓	4
28.23	odd	6		49.3.b.a.48.2	yes	4
28.27	even	2		49.3.d.b.19.3		8
84.11	even	6		441.3.m.l.325.1		8
84.23	even	6		441.3.d.e.244.3		4
84.47	odd	6		441.3.d.e.244.4		4
84.59	odd	6		441.3.m.l.325.2		8
84.83	odd	2		441.3.m.l.19.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.3.b.a.48.1	✓	4	28.19	even	6
49.3.b.a.48.2	yes	4	28.23	odd	6
49.3.d.b.19.3		8	28.27	even	2
49.3.d.b.19.4		8	4.3	odd	2
49.3.d.b.31.3		8	28.11	odd	6
49.3.d.b.31.4		8	28.3	even	6
441.3.d.e.244.3		4	84.23	even	6
441.3.d.e.244.4		4	84.47	odd	6
441.3.m.l.19.1		8	84.83	odd	2
441.3.m.l.19.2		8	12.11	even	2
441.3.m.l.325.1		8	84.11	even	6
441.3.m.l.325.2		8	84.59	odd	6
784.3.c.c.97.1		4	7.2	even	3
784.3.c.c.97.4		4	7.5	odd	6
784.3.s.h.129.1		8	7.3	odd	6	inner
784.3.s.h.129.4		8	7.4	even	3	inner
784.3.s.h.705.1		8	1.1	even	1	trivial
784.3.s.h.705.4		8	7.6	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	784.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.92586 + 1.68925i) q^{3} +(-4.13779 - 2.38896i) q^{5} +(1.20711 - 2.09077i) q^{9} +(4.53553 + 7.85578i) q^{11} +7.57675i q^{13} +16.1421 q^{15} +(-19.4770 + 11.2451i) q^{17} +(2.21593 + 1.27937i) q^{19} +(-8.65685 + 14.9941i) q^{23} +(-1.08579 - 1.88064i) q^{25} -22.2500i q^{27} +35.7990 q^{29} +(-36.5302 + 21.0907i) q^{31} +(-26.5407 - 15.3233i) q^{33} +(1.65685 - 2.86976i) q^{37} +(-12.7990 - 22.1685i) q^{39} -67.8100i q^{41} +27.6985 q^{43} +(-9.98951 + 5.76745i) q^{45} +(-34.1063 - 19.6913i) q^{47} +(37.9914 - 65.8030i) q^{51} +(-25.1838 - 43.6196i) q^{53} -43.3407i q^{55} -8.64466 q^{57} +(40.7541 - 23.5294i) q^{59} +(68.5067 + 39.5524i) q^{61} +(18.1005 - 31.3510i) q^{65} +(-27.2132 - 47.1347i) q^{67} -58.4942i q^{69} +0.402020 q^{71} +(1.80006 - 1.03926i) q^{73} +(6.35372 + 3.66832i) q^{75} +(30.4437 - 52.7299i) q^{79} +(48.4497 + 83.9174i) q^{81} -82.9634i q^{83} +107.456 q^{85} +(-104.743 + 60.4733i) q^{87} +(-6.05966 - 3.49854i) q^{89} +(71.2548 - 123.417i) q^{93} +(-6.11270 - 10.5875i) q^{95} -90.5402i q^{97} +21.8995 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{9} + 8 q^{11} + 16 q^{15} - 24 q^{23} - 20 q^{25} + 128 q^{29} - 32 q^{37} + 56 q^{39} - 16 q^{43} + 72 q^{51} + 104 q^{53} - 352 q^{57} + 224 q^{65} - 48 q^{67} + 320 q^{71} + 368 q^{79} + 348 q^{81}+ \cdots + 96 q^{99}+O(q^{100}) \) 8 * q + 4 * q^9 + 8 * q^11 + 16 * q^15 - 24 * q^23 - 20 * q^25 + 128 * q^29 - 32 * q^37 + 56 * q^39 - 16 * q^43 + 72 * q^51 + 104 * q^53 - 352 * q^57 + 224 * q^65 - 48 * q^67 + 320 * q^71 + 368 * q^79 + 348 * q^81 + 656 * q^85 + 208 * q^93 + 200 * q^95 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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