LMFDB - Embedded newform 448.2.m.c.337.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,2,Mod(113,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("448.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.m (of order $4$, 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:	$3.57729801055$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.214798336.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 2x^{5} + 9x^{4} - 4x^{3} - 16x + 16 $ x^8 - 2x^7 - 2x^5 + 9x^4 - 4x^3 - 16*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			337.4
Root			$-0.565036 + 1.29643i$ of defining polynomial
Character	$\chi$	$=$	448.337
Dual form			448.2.m.c.113.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.96506 + 1.96506i) q^{3} +(-0.627801 + 0.627801i) q^{5} -1.00000i q^{7} +4.72294i q^{9} +(-3.72294 + 3.72294i) q^{11} +(2.22066 + 2.22066i) q^{13} -2.46733 q^{15} +3.25560 q^{17} +(1.83499 + 1.83499i) q^{19} +(1.96506 - 1.96506i) q^{21} -7.65306i q^{23} +4.21173i q^{25} +(-3.38567 + 3.38567i) q^{27} +(-1.53721 - 1.53721i) q^{29} +2.44133 q^{31} -14.6316 q^{33} +(0.627801 + 0.627801i) q^{35} +(-1.26015 + 1.26015i) q^{37} +8.72748i q^{39} -7.77589i q^{41} +(7.51575 - 7.51575i) q^{43} +(-2.96506 - 2.96506i) q^{45} -11.1158 q^{47} -1.00000 q^{49} +(6.39746 + 6.39746i) q^{51} +(2.93012 - 2.93012i) q^{53} -4.67452i q^{55} +7.21173i q^{57} +(6.83953 - 6.83953i) q^{59} +(3.37220 + 3.37220i) q^{61} +4.72294 q^{63} -2.78827 q^{65} +(-0.925579 - 0.925579i) q^{67} +(15.0387 - 15.0387i) q^{69} +12.1113i q^{71} -6.41438i q^{73} +(-8.27631 + 8.27631i) q^{75} +(3.72294 + 3.72294i) q^{77} +7.28255 q^{79} +0.862688 q^{81} +(1.96506 + 1.96506i) q^{83} +(-2.04387 + 2.04387i) q^{85} -6.04143i q^{87} +0.665433i q^{89} +(2.22066 - 2.22066i) q^{91} +(4.79736 + 4.79736i) q^{93} -2.30401 q^{95} -8.34450 q^{97} +(-17.5832 - 17.5832i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{5} + 8 q^{15} + 24 q^{17} + 12 q^{19} - 12 q^{27} - 16 q^{29} - 16 q^{31} - 24 q^{33} + 4 q^{35} + 16 q^{37} + 32 q^{43} - 8 q^{45} - 24 q^{47} - 8 q^{49} - 8 q^{51} - 8 q^{53} + 28 q^{59} + 28 q^{61}+ \cdots - 48 q^{99}+O(q^{100}) $ 8 * q - 4 * q^5 + 8 * q^15 + 24 * q^17 + 12 * q^19 - 12 * q^27 - 16 * q^29 - 16 * q^31 - 24 * q^33 + 4 * q^35 + 16 * q^37 + 32 * q^43 - 8 * q^45 - 24 * q^47 - 8 * q^49 - 8 * q^51 - 8 * q^53 + 28 * q^59 + 28 * q^61 + 8 * q^63 - 48 * q^65 + 44 * q^69 - 28 * q^75 + 24 * q^79 + 40 * q^81 - 40 * q^85 + 16 * q^93 - 16 * q^95 - 32 * q^97 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.96506	+	1.96506i	1.13453	+	1.13453i	0.989415	+	0.145114i	$0.0463549\pi$
$3$	1.96506	+	1.96506i	1.13453	+	1.13453i	0.145114	+	0.989415i	$0.453645\pi$
$4$		0			0
$5$	−0.627801	+	0.627801i	−0.280761	+	0.280761i	−0.833412	−	0.552651i	$-0.813616\pi$
$5$	−0.627801	+	0.627801i	−0.280761	+	0.280761i	0.552651	+	0.833412i	$0.313616\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		0			0
$9$			4.72294i			1.57431i
$10$		0			0
$11$	−3.72294	+	3.72294i	−1.12251	+	1.12251i	−0.131144	+	0.991363i	$0.541865\pi$
$11$	−3.72294	+	3.72294i	−1.12251	+	1.12251i	−0.991363	+	0.131144i	$0.958135\pi$
$12$		0			0
$13$	2.22066	+	2.22066i	0.615901	+	0.615901i	0.944477	−	0.328576i	$-0.106569\pi$
$13$	2.22066	+	2.22066i	0.615901	+	0.615901i	−0.328576	+	0.944477i	$0.606569\pi$
$14$		0			0
$15$	−2.46733			−0.637063
$16$		0			0
$17$	3.25560			0.789599			0.394800	−	0.918767i	$-0.370814\pi$
$17$	3.25560			0.789599			0.394800	+	0.918767i	$0.370814\pi$
$18$		0			0
$19$	1.83499	+	1.83499i	0.420975	+	0.420975i	0.885539	−	0.464564i	$-0.153789\pi$
$19$	1.83499	+	1.83499i	0.420975	+	0.420975i	−0.464564	+	0.885539i	$0.653789\pi$
$20$		0			0
$21$	1.96506	−	1.96506i	0.428812	−	0.428812i
$22$		0			0
$23$		−	7.65306i		−	1.59577i	−0.602808	−	0.797887i	$-0.705951\pi$
$23$		−	7.65306i		−	1.59577i	0.602808	−	0.797887i	$-0.294049\pi$
$24$		0			0
$25$			4.21173i			0.842347i
$26$		0			0
$27$	−3.38567	+	3.38567i	−0.651573	+	0.651573i
$28$		0			0
$29$	−1.53721	−	1.53721i	−0.285453	−	0.285453i	0.549826	−	0.835279i	$-0.314694\pi$
$29$	−1.53721	−	1.53721i	−0.285453	−	0.285453i	−0.835279	+	0.549826i	$0.814694\pi$
$30$		0			0
$31$	2.44133			0.438475			0.219238	−	0.975672i	$-0.429643\pi$
$31$	2.44133			0.438475			0.219238	+	0.975672i	$0.429643\pi$
$32$		0			0
$33$	−14.6316			−2.54703
$34$		0			0
$35$	0.627801	+	0.627801i	0.106118	+	0.106118i
$36$		0			0
$37$	−1.26015	+	1.26015i	−0.207167	+	0.207167i	−0.803062	−	0.595895i	$-0.796797\pi$
$37$	−1.26015	+	1.26015i	−0.207167	+	0.207167i	0.595895	+	0.803062i	$0.296797\pi$
$38$		0			0
$39$			8.72748i			1.39752i
$40$		0			0
$41$		−	7.77589i		−	1.21439i	−0.794553	−	0.607195i	$-0.792295\pi$
$41$		−	7.77589i		−	1.21439i	0.794553	−	0.607195i	$-0.207705\pi$
$42$		0			0
$43$	7.51575	−	7.51575i	1.14614	−	1.14614i	0.158836	−	0.987305i	$-0.449226\pi$
$43$	7.51575	−	7.51575i	1.14614	−	1.14614i	0.987305	−	0.158836i	$-0.0507740\pi$
$44$		0			0
$45$	−2.96506	−	2.96506i	−0.442005	−	0.442005i
$46$		0			0
$47$	−11.1158			−1.62141			−0.810707	−	0.585453i	$-0.800917\pi$
$47$	−11.1158			−1.62141			−0.810707	+	0.585453i	$0.800917\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	6.39746	+	6.39746i	0.895823	+	0.895823i
$52$		0			0
$53$	2.93012	−	2.93012i	0.402483	−	0.402483i	−0.476624	−	0.879107i	$-0.658140\pi$
$53$	2.93012	−	2.93012i	0.402483	−	0.402483i	0.879107	+	0.476624i	$0.158140\pi$
$54$		0			0
$55$		−	4.67452i		−	0.630312i
$56$		0			0
$57$			7.21173i			0.955217i
$58$		0			0
$59$	6.83953	−	6.83953i	0.890431	−	0.890431i	−0.104132	−	0.994563i	$-0.533206\pi$
$59$	6.83953	−	6.83953i	0.890431	−	0.890431i	0.994563	+	0.104132i	$0.0332065\pi$
$60$		0			0
$61$	3.37220	+	3.37220i	0.431766	+	0.431766i	0.889229	−	0.457463i	$-0.151242\pi$
$61$	3.37220	+	3.37220i	0.431766	+	0.431766i	−0.457463	+	0.889229i	$0.651242\pi$
$62$		0			0
$63$	4.72294			0.595034
$64$		0			0
$65$	−2.78827			−0.345842
$66$		0			0
$67$	−0.925579	−	0.925579i	−0.113077	−	0.113077i	0.648304	−	0.761382i	$-0.275479\pi$
$67$	−0.925579	−	0.925579i	−0.113077	−	0.113077i	−0.761382	+	0.648304i	$0.775479\pi$
$68$		0			0
$69$	15.0387	−	15.0387i	1.81045	−	1.81045i
$70$		0			0
$71$			12.1113i			1.43735i	0.695348	+	0.718674i	$0.255250\pi$
$71$			12.1113i			1.43735i	−0.695348	+	0.718674i	$0.744750\pi$
$72$		0			0
$73$		−	6.41438i		−	0.750746i	−0.926874	−	0.375373i	$-0.877515\pi$
$73$		−	6.41438i		−	0.750746i	0.926874	−	0.375373i	$-0.122485\pi$
$74$		0			0
$75$	−8.27631	+	8.27631i	−0.955667	+	0.955667i
$76$		0			0
$77$	3.72294	+	3.72294i	0.424268	+	0.424268i
$78$		0			0
$79$	7.28255			0.819351			0.409675	−	0.912231i	$-0.365642\pi$
$79$	7.28255			0.819351			0.409675	+	0.912231i	$0.365642\pi$
$80$		0			0
$81$	0.862688			0.0958543
$82$		0			0
$83$	1.96506	+	1.96506i	0.215694	+	0.215694i	0.806681	−	0.590987i	$-0.201262\pi$
$83$	1.96506	+	1.96506i	0.215694	+	0.215694i	−0.590987	+	0.806681i	$0.701262\pi$
$84$		0			0
$85$	−2.04387	+	2.04387i	−0.221689	+	0.221689i
$86$		0			0
$87$		−	6.04143i		−	0.647709i
$88$		0			0
$89$			0.665433i			0.0705358i	0.999378	+	0.0352679i	$0.0112284\pi$
$89$			0.665433i			0.0705358i	−0.999378	+	0.0352679i	$0.988772\pi$
$90$		0			0
$91$	2.22066	−	2.22066i	0.232789	−	0.232789i
$92$		0			0
$93$	4.79736	+	4.79736i	0.497463	+	0.497463i
$94$		0			0
$95$	−2.30401			−0.236387
$96$		0			0
$97$	−8.34450			−0.847256			−0.423628	−	0.905836i	$-0.639244\pi$
$97$	−8.34450			−0.847256			−0.423628	+	0.905836i	$0.639244\pi$
$98$		0			0
$99$	−17.5832	−	17.5832i	−1.76718	−	1.76718i
$100$		0			0
$101$	−3.37944	+	3.37944i	−0.336267	+	0.336267i	−0.854960	−	0.518694i	$-0.826419\pi$
$101$	−3.37944	+	3.37944i	−0.336267	+	0.336267i	0.518694	+	0.854960i	$0.326419\pi$
$102$		0			0
$103$		−	19.2218i		−	1.89398i	−0.321268	−	0.946988i	$-0.604109\pi$
$103$		−	19.2218i		−	1.89398i	0.321268	−	0.946988i	$-0.395891\pi$
$104$		0			0
$105$			2.46733i			0.240787i
$106$		0			0
$107$	−2.46733	+	2.46733i	−0.238526	+	0.238526i	−0.816240	−	0.577713i	$-0.803945\pi$
$107$	−2.46733	+	2.46733i	−0.238526	+	0.238526i	0.577713	+	0.816240i	$0.303945\pi$
$108$		0			0
$109$	2.44587	+	2.44587i	0.234272	+	0.234272i	0.814473	−	0.580201i	$-0.197026\pi$
$109$	2.44587	+	2.44587i	0.234272	+	0.234272i	−0.580201	+	0.814473i	$0.697026\pi$
$110$		0			0
$111$	−4.95253			−0.470073
$112$		0			0
$113$	3.35149			0.315281			0.157641	−	0.987497i	$-0.449611\pi$
$113$	3.35149			0.315281			0.157641	+	0.987497i	$0.449611\pi$
$114$		0			0
$115$	4.80460	+	4.80460i	0.448031	+	0.448031i
$116$		0			0
$117$	−10.4880	+	10.4880i	−0.969620	+	0.969620i
$118$		0			0
$119$		−	3.25560i		−	0.298440i
$120$		0			0
$121$		−	16.7205i		−	1.52004i
$122$		0			0
$123$	15.2801	−	15.2801i	1.37776	−	1.37776i
$124$		0			0
$125$	−5.78313	−	5.78313i	−0.517259	−	0.517259i
$126$		0			0
$127$	5.55623			0.493036			0.246518	−	0.969138i	$-0.420714\pi$
$127$	5.55623			0.493036			0.246518	+	0.969138i	$0.420714\pi$
$128$		0			0
$129$	29.5378			2.60066
$130$		0			0
$131$	−9.67108	−	9.67108i	−0.844966	−	0.844966i	0.144534	−	0.989500i	$-0.453832\pi$
$131$	−9.67108	−	9.67108i	−0.844966	−	0.844966i	−0.989500	+	0.144534i	$0.953832\pi$
$132$		0			0
$133$	1.83499	−	1.83499i	0.159114	−	0.159114i
$134$		0			0
$135$		−	4.25106i		−	0.365873i
$136$		0			0
$137$		−	4.92558i		−	0.420821i	−0.977613	−	0.210410i	$-0.932520\pi$
$137$		−	4.92558i		−	0.420821i	0.977613	−	0.210410i	$-0.0674800\pi$
$138$		0			0
$139$	−7.58393	+	7.58393i	−0.643261	+	0.643261i	−0.951356	−	0.308095i	$-0.900309\pi$
$139$	−7.58393	+	7.58393i	−0.643261	+	0.643261i	0.308095	+	0.951356i	$0.400309\pi$
$140$		0			0
$141$	−21.8433	−	21.8433i	−1.83954	−	1.83954i
$142$		0			0
$143$	−16.5348			−1.38271
$144$		0			0
$145$	1.93012			0.160288
$146$		0			0
$147$	−1.96506	−	1.96506i	−0.162076	−	0.162076i
$148$		0			0
$149$	−2.69599	+	2.69599i	−0.220864	+	0.220864i	−0.808862	−	0.587998i	$-0.799916\pi$
$149$	−2.69599	+	2.69599i	−0.220864	+	0.220864i	0.587998	+	0.808862i	$0.299916\pi$
$150$		0			0
$151$			2.16426i			0.176125i	0.996115	+	0.0880625i	$0.0280675\pi$
$151$			2.16426i			0.176125i	−0.996115	+	0.0880625i	$0.971932\pi$
$152$		0			0
$153$			15.3760i			1.24308i
$154$		0			0
$155$	−1.53267	+	1.53267i	−0.123107	+	0.123107i
$156$		0			0
$157$	3.94266	+	3.94266i	0.314658	+	0.314658i	0.846711	−	0.532053i	$-0.178579\pi$
$157$	3.94266	+	3.94266i	0.314658	+	0.314658i	−0.532053	+	0.846711i	$0.678579\pi$
$158$		0			0
$159$	11.5157			0.913258
$160$		0			0
$161$	−7.65306			−0.603146
$162$		0			0
$163$	8.23414	+	8.23414i	0.644947	+	0.644947i	0.951768	−	0.306820i	$-0.0992650\pi$
$163$	8.23414	+	8.23414i	0.644947	+	0.644947i	−0.306820	+	0.951768i	$0.599265\pi$
$164$		0			0
$165$	9.18572	−	9.18572i	0.715108	−	0.715108i
$166$		0			0
$167$			12.4649i			0.964562i	0.876016	+	0.482281i	$0.160192\pi$
$167$			12.4649i			0.964562i	−0.876016	+	0.482281i	$0.839808\pi$
$168$		0			0
$169$		−	3.13731i		−	0.241332i
$170$		0			0
$171$	−8.66653	+	8.66653i	−0.662746	+	0.662746i
$172$		0			0
$173$	−13.9267	−	13.9267i	−1.05883	−	1.05883i	−0.998158	−	0.0606678i	$-0.980677\pi$
$173$	−13.9267	−	13.9267i	−1.05883	−	1.05883i	−0.0606678	−	0.998158i	$-0.519323\pi$
$174$		0			0
$175$	4.21173			0.318377
$176$		0			0
$177$	26.8802			2.02044
$178$		0			0
$179$	−0.977595	−	0.977595i	−0.0730689	−	0.0730689i	0.669628	−	0.742697i	$-0.266454\pi$
$179$	−0.977595	−	0.977595i	−0.0730689	−	0.0730689i	−0.742697	+	0.669628i	$0.766454\pi$
$180$		0			0
$181$	−16.0038	+	16.0038i	−1.18955	+	1.18955i	−0.212362	+	0.977191i	$0.568115\pi$
$181$	−16.0038	+	16.0038i	−1.18955	+	1.18955i	−0.977191	+	0.212362i	$0.931885\pi$
$182$		0			0
$183$			13.2532i			0.979702i
$184$		0			0
$185$		−	1.58224i		−	0.116329i
$186$		0			0
$187$	−12.1204	+	12.1204i	−0.886331	+	0.886331i
$188$		0			0
$189$	3.38567	+	3.38567i	0.246272	+	0.246272i
$190$		0			0
$191$	−2.51120			−0.181704			−0.0908521	−	0.995864i	$-0.528959\pi$
$191$	−2.51120			−0.181704			−0.0908521	+	0.995864i	$0.528959\pi$
$192$		0			0
$193$	10.0944			0.726610			0.363305	−	0.931670i	$-0.381648\pi$
$193$	10.0944			0.726610			0.363305	+	0.931670i	$0.381648\pi$
$194$		0			0
$195$	−5.47912	−	5.47912i	−0.392368	−	0.392368i
$196$		0			0
$197$	−13.5617	+	13.5617i	−0.966232	+	0.966232i	−0.999448	−	0.0332158i	$-0.989425\pi$
$197$	−13.5617	+	13.5617i	−0.966232	+	0.966232i	0.0332158	+	0.999448i	$0.489425\pi$
$198$		0			0
$199$			5.61257i			0.397865i	0.980013	+	0.198932i	$0.0637474\pi$
$199$			5.61257i			0.397865i	−0.980013	+	0.198932i	$0.936253\pi$
$200$		0			0
$201$		−	3.63764i		−	0.256579i
$202$		0			0
$203$	−1.53721	+	1.53721i	−0.107891	+	0.107891i
$204$		0			0
$205$	4.88171	+	4.88171i	0.340953	+	0.340953i
$206$		0			0
$207$	36.1449			2.51224
$208$		0			0
$209$	−13.6631			−0.945096
$210$		0			0
$211$	−3.86025	−	3.86025i	−0.265750	−	0.265750i	0.561635	−	0.827385i	$-0.310173\pi$
$211$	−3.86025	−	3.86025i	−0.265750	−	0.265750i	−0.827385	+	0.561635i	$0.810173\pi$
$212$		0			0
$213$	−23.7995	+	23.7995i	−1.63071	+	1.63071i
$214$		0			0
$215$			9.43678i			0.643583i
$216$		0			0
$217$		−	2.44133i		−	0.165728i
$218$		0			0
$219$	12.6046	−	12.6046i	0.851743	−	0.851743i
$220$		0			0
$221$	7.22959	+	7.22959i	0.486315	+	0.486315i
$222$		0			0
$223$	12.5348			0.839390			0.419695	−	0.907665i	$-0.362137\pi$
$223$	12.5348			0.839390			0.419695	+	0.907665i	$0.362137\pi$
$224$		0			0
$225$	−19.8917			−1.32612
$226$		0			0
$227$	15.7043	+	15.7043i	1.04233	+	1.04233i	0.999063	+	0.0432692i	$0.0137773\pi$
$227$	15.7043	+	15.7043i	1.04233	+	1.04233i	0.0432692	+	0.999063i	$0.486223\pi$
$228$		0			0
$229$	7.29508	−	7.29508i	0.482073	−	0.482073i	−0.423720	−	0.905793i	$-0.639276\pi$
$229$	7.29508	−	7.29508i	0.482073	−	0.482073i	0.905793	+	0.423720i	$0.139276\pi$
$230$		0			0
$231$			14.6316i			0.962688i
$232$		0			0
$233$		−	0.182680i		−	0.0119678i	−0.999982	−	0.00598388i	$-0.998095\pi$
$233$		−	0.182680i		−	0.0119678i	0.999982	−	0.00598388i	$-0.00190474\pi$
$234$		0			0
$235$	6.97854	−	6.97854i	0.455230	−	0.455230i
$236$		0			0
$237$	14.3107	+	14.3107i	0.929577	+	0.929577i
$238$		0			0
$239$	−0.261087			−0.0168883			−0.00844417	−	0.999964i	$-0.502688\pi$
$239$	−0.261087			−0.0168883			−0.00844417	+	0.999964i	$0.502688\pi$
$240$		0			0
$241$	7.53022			0.485064			0.242532	−	0.970143i	$-0.422022\pi$
$241$	7.53022			0.485064			0.242532	+	0.970143i	$0.422022\pi$
$242$		0			0
$243$	11.8523	+	11.8523i	0.760323	+	0.760323i
$244$		0			0
$245$	0.627801	−	0.627801i	0.0401087	−	0.0401087i
$246$		0			0
$247$			8.14978i			0.518558i
$248$		0			0
$249$			7.72294i			0.489421i
$250$		0			0
$251$	2.22521	−	2.22521i	0.140454	−	0.140454i	−0.633384	−	0.773838i	$-0.718335\pi$
$251$	2.22521	−	2.22521i	0.140454	−	0.140454i	0.773838	+	0.633384i	$0.218335\pi$
$252$		0			0
$253$	28.4918	+	28.4918i	1.79127	+	1.79127i
$254$		0			0
$255$	−8.03266			−0.503024
$256$		0			0
$257$	−2.81428			−0.175550			−0.0877748	−	0.996140i	$-0.527976\pi$
$257$	−2.81428			−0.175550			−0.0877748	+	0.996140i	$0.527976\pi$
$258$		0			0
$259$	1.26015	+	1.26015i	0.0783016	+	0.0783016i
$260$		0			0
$261$	7.26015	−	7.26015i	0.449392	−	0.449392i
$262$		0			0
$263$			8.52568i			0.525716i	0.964835	+	0.262858i	$0.0846651\pi$
$263$			8.52568i			0.525716i	−0.964835	+	0.262858i	$0.915335\pi$
$264$		0			0
$265$			3.67907i			0.226003i
$266$		0			0
$267$	−1.30762	+	1.30762i	−0.0800249	+	0.0800249i
$268$		0			0
$269$	−11.5177	−	11.5177i	−0.702246	−	0.702246i	0.262646	−	0.964892i	$-0.415405\pi$
$269$	−11.5177	−	11.5177i	−0.702246	−	0.702246i	−0.964892	+	0.262646i	$0.915405\pi$
$270$		0			0
$271$	−26.7375			−1.62419			−0.812094	−	0.583527i	$-0.801672\pi$
$271$	−26.7375			−1.62419			−0.812094	+	0.583527i	$0.801672\pi$
$272$		0			0
$273$	8.72748			0.528211
$274$		0			0
$275$	−15.6800	−	15.6800i	−0.945540	−	0.945540i
$276$		0			0
$277$	9.06744	−	9.06744i	0.544809	−	0.544809i	−0.380126	−	0.924935i	$-0.624119\pi$
$277$	9.06744	−	9.06744i	0.544809	−	0.544809i	0.924935	+	0.380126i	$0.124119\pi$
$278$		0			0
$279$			11.5302i			0.690296i
$280$		0			0
$281$			28.4095i			1.69477i	0.530980	+	0.847384i	$0.321824\pi$
$281$			28.4095i			1.69477i	−0.530980	+	0.847384i	$0.678176\pi$
$282$		0			0
$283$	−5.34106	+	5.34106i	−0.317493	+	0.317493i	−0.847803	−	0.530311i	$-0.822075\pi$
$283$	−5.34106	+	5.34106i	−0.317493	+	0.317493i	0.530311	+	0.847803i	$0.322075\pi$
$284$		0			0
$285$	−4.52753	−	4.52753i	−0.268188	−	0.268188i
$286$		0			0
$287$	−7.77589			−0.458996
$288$		0			0
$289$	−6.40106			−0.376533
$290$		0			0
$291$	−16.3975	−	16.3975i	−0.961236	−	0.961236i
$292$		0			0
$293$	−8.64751	+	8.64751i	−0.505193	+	0.505193i	−0.913047	−	0.407854i	$-0.866277\pi$
$293$	−8.64751	+	8.64751i	−0.505193	+	0.505193i	0.407854	+	0.913047i	$0.366277\pi$
$294$		0			0
$295$			8.58773i			0.499997i
$296$		0			0
$297$		−	25.2093i		−	1.46279i
$298$		0			0
$299$	16.9949	−	16.9949i	0.982838	−	0.982838i
$300$		0			0
$301$	−7.51575	−	7.51575i	−0.433200	−	0.433200i
$302$		0			0
$303$	−13.2816			−0.763009
$304$		0			0
$305$	−4.23414			−0.242446
$306$		0			0
$307$	−22.9681	−	22.9681i	−1.31086	−	1.31086i	−0.920782	−	0.390077i	$-0.872448\pi$
$307$	−22.9681	−	22.9681i	−1.31086	−	1.31086i	−0.390077	−	0.920782i	$-0.627552\pi$
$308$		0			0
$309$	37.7720	−	37.7720i	2.14877	−	2.14877i
$310$		0			0
$311$		−	26.5457i		−	1.50527i	−0.658437	−	0.752635i	$-0.728782\pi$
$311$		−	26.5457i		−	1.50527i	0.658437	−	0.752635i	$-0.271218\pi$
$312$		0			0
$313$		−	20.1854i		−	1.14095i	−0.821317	−	0.570473i	$-0.806760\pi$
$313$		−	20.1854i		−	1.14095i	0.821317	−	0.570473i	$-0.193240\pi$
$314$		0			0
$315$	−2.96506	+	2.96506i	−0.167062	+	0.167062i
$316$		0			0
$317$	−0.930123	−	0.930123i	−0.0522409	−	0.0522409i	0.680504	−	0.732745i	$-0.261761\pi$
$317$	−0.930123	−	0.930123i	−0.0522409	−	0.0522409i	−0.732745	+	0.680504i	$0.761761\pi$
$318$		0			0
$319$	11.4459			0.640846
$320$		0			0
$321$	−9.69693			−0.541230
$322$		0			0
$323$	5.97399	+	5.97399i	0.332402	+	0.332402i
$324$		0			0
$325$	−9.35284	+	9.35284i	−0.518802	+	0.518802i
$326$		0			0
$327$			9.61257i			0.531577i
$328$		0			0
$329$			11.1158i			0.612837i
$330$		0			0
$331$	−10.4413	+	10.4413i	−0.573907	+	0.573907i	−0.933218	−	0.359311i	$-0.883012\pi$
$331$	−10.4413	+	10.4413i	−0.573907	+	0.573907i	0.359311	+	0.933218i	$0.383012\pi$
$332$		0			0
$333$	−5.95159	−	5.95159i	−0.326145	−	0.326145i
$334$		0			0
$335$	1.16216			0.0634955
$336$		0			0
$337$	−27.6212			−1.50462			−0.752312	−	0.658807i	$-0.771061\pi$
$337$	−27.6212			−1.50462			−0.752312	+	0.658807i	$0.771061\pi$
$338$		0			0
$339$	6.58588	+	6.58588i	0.357696	+	0.357696i
$340$		0			0
$341$	−9.08890	+	9.08890i	−0.492191	+	0.492191i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$			18.8827i			1.01661i
$346$		0			0
$347$	−8.35359	+	8.35359i	−0.448444	+	0.448444i	−0.894837	−	0.446393i	$-0.852708\pi$
$347$	−8.35359	+	8.35359i	−0.448444	+	0.448444i	0.446393	+	0.894837i	$0.352708\pi$
$348$		0			0
$349$	−7.97685	−	7.97685i	−0.426991	−	0.426991i	0.460611	−	0.887602i	$-0.347630\pi$
$349$	−7.97685	−	7.97685i	−0.426991	−	0.426991i	−0.887602	+	0.460611i	$0.847630\pi$
$350$		0			0
$351$	−15.0369			−0.802609
$352$		0			0
$353$	−10.7623			−0.572817			−0.286409	−	0.958108i	$-0.592461\pi$
$353$	−10.7623			−0.572817			−0.286409	+	0.958108i	$0.592461\pi$
$354$		0			0
$355$	−7.60348	−	7.60348i	−0.403551	−	0.403551i
$356$		0			0
$357$	6.39746	−	6.39746i	0.338589	−	0.338589i
$358$		0			0
$359$		−	17.9725i		−	0.948552i	−0.880376	−	0.474276i	$-0.842710\pi$
$359$		−	17.9725i		−	0.948552i	0.880376	−	0.474276i	$-0.157290\pi$
$360$		0			0
$361$		−	12.2656i		−	0.645560i
$362$		0			0
$363$	32.8568	−	32.8568i	1.72453	−	1.72453i
$364$		0			0
$365$	4.02695	+	4.02695i	0.210780	+	0.210780i
$366$		0			0
$367$	16.7091			0.872206			0.436103	−	0.899897i	$-0.356358\pi$
$367$	16.7091			0.872206			0.436103	+	0.899897i	$0.356358\pi$
$368$		0			0
$369$	36.7250			1.91183
$370$		0			0
$371$	−2.93012	−	2.93012i	−0.152124	−	0.152124i
$372$		0			0
$373$	−15.5786	+	15.5786i	−0.806631	+	0.806631i	−0.984122	−	0.177491i	$-0.943202\pi$
$373$	−15.5786	+	15.5786i	−0.806631	+	0.806631i	0.177491	+	0.984122i	$0.443202\pi$
$374$		0			0
$375$		−	22.7284i		−	1.17369i
$376$		0			0
$377$		−	6.82725i		−	0.351621i
$378$		0			0
$379$	−23.6361	+	23.6361i	−1.21411	+	1.21411i	−0.244443	+	0.969664i	$0.578605\pi$
$379$	−23.6361	+	23.6361i	−1.21411	+	1.21411i	−0.969664	+	0.244443i	$0.921395\pi$
$380$		0			0
$381$	10.9183	+	10.9183i	0.559364	+	0.559364i
$382$		0			0
$383$	−9.83330			−0.502458			−0.251229	−	0.967928i	$-0.580835\pi$
$383$	−9.83330			−0.502458			−0.251229	+	0.967928i	$0.580835\pi$
$384$		0			0
$385$	−4.67452			−0.238236
$386$		0			0
$387$	35.4964	+	35.4964i	1.80438	+	1.80438i
$388$		0			0
$389$	10.3490	−	10.3490i	0.524717	−	0.524717i	−0.394275	−	0.918992i	$-0.629004\pi$
$389$	10.3490	−	10.3490i	0.524717	−	0.524717i	0.918992	+	0.394275i	$0.129004\pi$
$390$		0			0
$391$		−	24.9153i		−	1.26002i
$392$		0			0
$393$		−	38.0085i		−	1.91728i
$394$		0			0
$395$	−4.57199	+	4.57199i	−0.230042	+	0.230042i
$396$		0			0
$397$	18.0543	+	18.0543i	0.906120	+	0.906120i	0.995957	−	0.0898366i	$-0.0286345\pi$
$397$	18.0543	+	18.0543i	0.906120	+	0.906120i	−0.0898366	+	0.995957i	$0.528634\pi$
$398$		0			0
$399$	7.21173			0.361038
$400$		0			0
$401$	18.8064			0.939149			0.469575	−	0.882893i	$-0.344407\pi$
$401$	18.8064			0.939149			0.469575	+	0.882893i	$0.344407\pi$
$402$		0			0
$403$	5.42136	+	5.42136i	0.270057	+	0.270057i
$404$		0			0
$405$	−0.541596	+	0.541596i	−0.0269121	+	0.0269121i
$406$		0			0
$407$		−	9.38288i		−	0.465092i
$408$		0			0
$409$			29.6077i			1.46401i	0.681301	+	0.732003i	$0.261414\pi$
$409$			29.6077i			1.46401i	−0.681301	+	0.732003i	$0.738586\pi$
$410$		0			0
$411$	9.67907	−	9.67907i	0.477433	−	0.477433i
$412$		0			0
$413$	−6.83953	−	6.83953i	−0.336551	−	0.336551i
$414$		0			0
$415$	−2.46733			−0.121117
$416$		0			0
$417$	−29.8058			−1.45960
$418$		0			0
$419$	−1.15229	−	1.15229i	−0.0562929	−	0.0562929i	0.678400	−	0.734693i	$-0.262674\pi$
$419$	−1.15229	−	1.15229i	−0.0562929	−	0.0562929i	−0.734693	+	0.678400i	$0.762674\pi$
$420$		0			0
$421$	19.7275	−	19.7275i	0.961459	−	0.961459i	−0.0378258	−	0.999284i	$-0.512043\pi$
$421$	19.7275	−	19.7275i	0.961459	−	0.961459i	0.999284	+	0.0378258i	$0.0120432\pi$
$422$		0			0
$423$		−	52.4994i		−	2.55261i
$424$		0			0
$425$			13.7117i			0.665116i
$426$		0			0
$427$	3.37220	−	3.37220i	0.163192	−	0.163192i
$428$		0			0
$429$	−32.4918	−	32.4918i	−1.56872	−	1.56872i
$430$		0			0
$431$	−20.3960			−0.982439			−0.491219	−	0.871036i	$-0.663449\pi$
$431$	−20.3960			−0.982439			−0.491219	+	0.871036i	$0.663449\pi$
$432$		0			0
$433$	28.3107			1.36052			0.680262	−	0.732969i	$-0.261866\pi$
$433$	28.3107			1.36052			0.680262	+	0.732969i	$0.261866\pi$
$434$		0			0
$435$	3.79281	+	3.79281i	0.181851	+	0.181851i
$436$		0			0
$437$	14.0433	−	14.0433i	0.671781	−	0.671781i
$438$		0			0
$439$			4.57231i			0.218224i	0.994029	+	0.109112i	$0.0348008\pi$
$439$			4.57231i			0.218224i	−0.994029	+	0.109112i	$0.965199\pi$
$440$		0			0
$441$		−	4.72294i		−	0.224902i
$442$		0			0
$443$	−7.13371	+	7.13371i	−0.338933	+	0.338933i	−0.855966	−	0.517033i	$-0.827037\pi$
$443$	−7.13371	+	7.13371i	−0.338933	+	0.338933i	0.517033	+	0.855966i	$0.327037\pi$
$444$		0			0
$445$	−0.417759	−	0.417759i	−0.0198037	−	0.0198037i
$446$		0			0
$447$	−10.5956			−0.501153
$448$		0			0
$449$	13.0695			0.616790			0.308395	−	0.951258i	$-0.400208\pi$
$449$	13.0695			0.616790			0.308395	+	0.951258i	$0.400208\pi$
$450$		0			0
$451$	28.9491	+	28.9491i	1.36316	+	1.36316i
$452$		0			0
$453$	−4.25291	+	4.25291i	−0.199819	+	0.199819i
$454$		0			0
$455$			2.78827i			0.130716i
$456$		0			0
$457$		−	31.9117i		−	1.49277i	−0.665516	−	0.746383i	$-0.731789\pi$
$457$		−	31.9117i		−	1.49277i	0.665516	−	0.746383i	$-0.268211\pi$
$458$		0			0
$459$	−11.0224	+	11.0224i	−0.514482	+	0.514482i
$460$		0			0
$461$	−11.2878	−	11.2878i	−0.525727	−	0.525727i	0.393568	−	0.919295i	$-0.371241\pi$
$461$	−11.2878	−	11.2878i	−0.525727	−	0.525727i	−0.919295	+	0.393568i	$0.871241\pi$
$462$		0			0
$463$	21.0406			0.977839			0.488919	−	0.872329i	$-0.337391\pi$
$463$	21.0406			0.977839			0.488919	+	0.872329i	$0.337391\pi$
$464$		0			0
$465$	−6.02357			−0.279336
$466$		0			0
$467$	6.75518	+	6.75518i	0.312592	+	0.312592i	0.845913	−	0.533321i	$-0.179056\pi$
$467$	6.75518	+	6.75518i	0.312592	+	0.312592i	−0.533321	+	0.845913i	$0.679056\pi$
$468$		0			0
$469$	−0.925579	+	0.925579i	−0.0427393	+	0.0427393i
$470$		0			0
$471$			15.4951i			0.713978i
$472$		0			0
$473$			55.9613i			2.57310i
$474$		0			0
$475$	−7.72848	+	7.72848i	−0.354607	+	0.354607i
$476$		0			0
$477$	13.8388	+	13.8388i	0.633634	+	0.633634i
$478$		0			0
$479$	10.5328			0.481254			0.240627	−	0.970618i	$-0.422647\pi$
$479$	10.5328			0.481254			0.240627	+	0.970618i	$0.422647\pi$
$480$		0			0
$481$	−5.59672			−0.255188
$482$		0			0
$483$	−15.0387	−	15.0387i	−0.684286	−	0.684286i
$484$		0			0
$485$	5.23868	−	5.23868i	0.237876	−	0.237876i
$486$		0			0
$487$		−	3.45941i		−	0.156761i	−0.996924	−	0.0783803i	$-0.975025\pi$
$487$		−	3.45941i		−	0.156761i	0.996924	−	0.0783803i	$-0.0249749\pi$
$488$		0			0
$489$			32.3612i			1.46342i
$490$		0			0
$491$	−0.356972	+	0.356972i	−0.0161099	+	0.0161099i	−0.715116	−	0.699006i	$-0.753626\pi$
$491$	−0.356972	+	0.356972i	−0.0161099	+	0.0161099i	0.699006	+	0.715116i	$0.253626\pi$
$492$		0			0
$493$	−5.00454	−	5.00454i	−0.225393	−	0.225393i
$494$		0			0
$495$	22.0775			0.992308
$496$		0			0
$497$	12.1113			0.543266
$498$		0			0
$499$	−16.3040	−	16.3040i	−0.729868	−	0.729868i	0.240725	−	0.970593i	$-0.422615\pi$
$499$	−16.3040	−	16.3040i	−0.729868	−	0.729868i	−0.970593	+	0.240725i	$0.922615\pi$
$500$		0			0
$501$	−24.4943	+	24.4943i	−1.09432	+	1.09432i
$502$		0			0
$503$			27.6867i			1.23449i	0.786772	+	0.617243i	$0.211751\pi$
$503$			27.6867i			1.23449i	−0.786772	+	0.617243i	$0.788249\pi$
$504$		0			0
$505$		−	4.24323i		−	0.188821i
$506$		0			0
$507$	6.16501	−	6.16501i	0.273798	−	0.273798i
$508$		0			0
$509$	−24.0183	−	24.0183i	−1.06459	−	1.06459i	−0.997765	−	0.0668266i	$-0.978713\pi$
$509$	−24.0183	−	24.0183i	−1.06459	−	1.06459i	−0.0668266	−	0.997765i	$-0.521287\pi$
$510$		0			0
$511$	−6.41438			−0.283755
$512$		0			0
$513$	−12.4253			−0.548593
$514$		0			0
$515$	12.0674	+	12.0674i	0.531755	+	0.531755i
$516$		0			0
$517$	41.3836	−	41.3836i	1.82005	−	1.82005i
$518$		0			0
$519$		−	54.7336i		−	2.40254i
$520$		0			0
$521$		−	19.5484i		−	0.856431i	−0.903677	−	0.428216i	$-0.859142\pi$
$521$		−	19.5484i		−	0.856431i	0.903677	−	0.428216i	$-0.140858\pi$
$522$		0			0
$523$	7.20189	−	7.20189i	0.314917	−	0.314917i	−0.531894	−	0.846811i	$-0.678520\pi$
$523$	7.20189	−	7.20189i	0.314917	−	0.314917i	0.846811	+	0.531894i	$0.178520\pi$
$524$		0			0
$525$	8.27631	+	8.27631i	0.361208	+	0.361208i
$526$		0			0
$527$	7.94798			0.346220
$528$		0			0
$529$	−35.5693			−1.54649
$530$		0			0
$531$	32.3027	+	32.3027i	1.40182	+	1.40182i
$532$		0			0
$533$	17.2676	−	17.2676i	0.747944	−	0.747944i
$534$		0			0
$535$		−	3.09799i		−	0.133938i
$536$		0			0
$537$		−	3.84207i		−	0.165798i
$538$		0			0
$539$	3.72294	−	3.72294i	0.160358	−	0.160358i
$540$		0			0
$541$	−1.57325	−	1.57325i	−0.0676393	−	0.0676393i	0.672478	−	0.740117i	$-0.265230\pi$
$541$	−1.57325	−	1.57325i	−0.0676393	−	0.0676393i	−0.740117	+	0.672478i	$0.765230\pi$
$542$		0			0
$543$	−62.8969			−2.69916
$544$		0			0
$545$	−3.07104			−0.131549
$546$		0			0
$547$	6.76891	+	6.76891i	0.289418	+	0.289418i	0.836850	−	0.547432i	$-0.184395\pi$
$547$	6.76891	+	6.76891i	0.289418	+	0.289418i	−0.547432	+	0.836850i	$0.684395\pi$
$548$		0			0
$549$	−15.9267	+	15.9267i	−0.679734	+	0.679734i
$550$		0			0
$551$		−	5.64153i		−	0.240337i
$552$		0			0
$553$		−	7.28255i		−	0.309686i
$554$		0			0
$555$	3.10920	−	3.10920i	0.131978	−	0.131978i
$556$		0			0
$557$	3.32093	+	3.32093i	0.140712	+	0.140712i	0.773954	−	0.633242i	$-0.218276\pi$
$557$	3.32093	+	3.32093i	0.140712	+	0.140712i	−0.633242	+	0.773954i	$0.718276\pi$
$558$		0			0
$559$	33.3799			1.41182
$560$		0			0
$561$	−47.6346			−2.01114
$562$		0			0
$563$	−18.7697	−	18.7697i	−0.791047	−	0.791047i	0.190618	−	0.981664i	$-0.438951\pi$
$563$	−18.7697	−	18.7697i	−0.791047	−	0.791047i	−0.981664	+	0.190618i	$0.938951\pi$
$564$		0			0
$565$	−2.10406	+	2.10406i	−0.0885187	+	0.0885187i
$566$		0			0
$567$		−	0.862688i		−	0.0362295i
$568$		0			0
$569$		−	23.4973i		−	0.985059i	−0.870296	−	0.492530i	$-0.836072\pi$
$569$		−	23.4973i		−	0.985059i	0.870296	−	0.492530i	$-0.163928\pi$
$570$		0			0
$571$	−24.9670	+	24.9670i	−1.04484	+	1.04484i	−0.0458902	+	0.998946i	$0.514612\pi$
$571$	−24.9670	+	24.9670i	−1.04484	+	1.04484i	−0.998946	+	0.0458902i	$0.985388\pi$
$572$		0			0
$573$	−4.93467	−	4.93467i	−0.206149	−	0.206149i
$574$		0			0
$575$	32.2326			1.34419
$576$		0			0
$577$	−14.4181			−0.600232			−0.300116	−	0.953903i	$-0.597025\pi$
$577$	−14.4181			−0.600232			−0.300116	+	0.953903i	$0.597025\pi$
$578$		0			0
$579$	19.8361	+	19.8361i	0.824360	+	0.824360i
$580$		0			0
$581$	1.96506	−	1.96506i	0.0815245	−	0.0815245i
$582$		0			0
$583$			21.8173i			0.903581i
$584$		0			0
$585$		−	13.1688i		−	0.544463i
$586$		0			0
$587$	13.2110	−	13.2110i	0.545276	−	0.545276i	−0.379795	−	0.925071i	$-0.624005\pi$
$587$	13.2110	−	13.2110i	0.545276	−	0.545276i	0.925071	+	0.379795i	$0.124005\pi$
$588$		0			0
$589$	4.47981	+	4.47981i	0.184587	+	0.184587i
$590$		0			0
$591$	−53.2992			−2.19244
$592$		0			0
$593$	16.3859			0.672889			0.336445	−	0.941703i	$-0.390775\pi$
$593$	16.3859			0.672889			0.336445	+	0.941703i	$0.390775\pi$
$594$		0			0
$595$	2.04387	+	2.04387i	0.0837904	+	0.0837904i
$596$		0			0
$597$	−11.0291	+	11.0291i	−0.451389	+	0.451389i
$598$		0			0
$599$			34.0042i			1.38937i	0.719312	+	0.694687i	$0.244457\pi$
$599$			34.0042i			1.38937i	−0.719312	+	0.694687i	$0.755543\pi$
$600$		0			0
$601$		−	3.33457i		−	0.136020i	−0.997685	−	0.0680099i	$-0.978335\pi$
$601$		−	3.33457i		−	0.136020i	0.997685	−	0.0680099i	$-0.0216649\pi$
$602$		0			0
$603$	4.37145	−	4.37145i	0.178019	−	0.178019i
$604$		0			0
$605$	10.4971	+	10.4971i	0.426769	+	0.426769i
$606$		0			0
$607$	10.4737			0.425113			0.212556	−	0.977149i	$-0.431821\pi$
$607$	10.4737			0.425113			0.212556	+	0.977149i	$0.431821\pi$
$608$		0			0
$609$	−6.04143			−0.244811
$610$		0			0
$611$	−24.6846	−	24.6846i	−0.998630	−	0.998630i
$612$		0			0
$613$	−8.99756	+	8.99756i	−0.363408	+	0.363408i	−0.865066	−	0.501658i	$-0.832724\pi$
$613$	−8.99756	+	8.99756i	−0.363408	+	0.363408i	0.501658	+	0.865066i	$0.332724\pi$
$614$		0			0
$615$			19.1857i			0.773643i
$616$		0			0
$617$			2.93899i			0.118319i	0.998249	+	0.0591597i	$0.0188421\pi$
$617$			2.93899i			0.118319i	−0.998249	+	0.0591597i	$0.981158\pi$
$618$		0			0
$619$	−7.24761	+	7.24761i	−0.291306	+	0.291306i	−0.837596	−	0.546290i	$-0.816040\pi$
$619$	−7.24761	+	7.24761i	−0.291306	+	0.291306i	0.546290	+	0.837596i	$0.316040\pi$
$620$		0			0
$621$	25.9108	+	25.9108i	1.03976	+	1.03976i
$622$		0			0
$623$	0.665433			0.0266600
$624$		0			0
$625$	−13.7974			−0.551894
$626$		0			0
$627$	−26.8488	−	26.8488i	−1.07224	−	1.07224i
$628$		0			0
$629$	−4.10253	+	4.10253i	−0.163579	+	0.163579i
$630$		0			0
$631$		−	9.59471i		−	0.381959i	−0.981594	−	0.190980i	$-0.938834\pi$
$631$		−	9.59471i		−	0.381959i	0.981594	−	0.190980i	$-0.0611665\pi$
$632$		0			0
$633$		−	15.1712i		−	0.603003i
$634$		0			0
$635$	−3.48821	+	3.48821i	−0.138425	+	0.138425i
$636$		0			0
$637$	−2.22066	−	2.22066i	−0.0879859	−	0.0879859i
$638$		0			0
$639$	−57.2009			−2.26283
$640$		0			0
$641$	−15.8289			−0.625202			−0.312601	−	0.949885i	$-0.601200\pi$
$641$	−15.8289			−0.625202			−0.312601	+	0.949885i	$0.601200\pi$
$642$		0			0
$643$	−10.3033	−	10.3033i	−0.406321	−	0.406321i	0.474132	−	0.880454i	$-0.342762\pi$
$643$	−10.3033	−	10.3033i	−0.406321	−	0.406321i	−0.880454	+	0.474132i	$0.842762\pi$
$644$		0			0
$645$	−18.5439	+	18.5439i	−0.730164	+	0.730164i
$646$		0			0
$647$		−	10.5272i		−	0.413866i	−0.978355	−	0.206933i	$-0.933652\pi$
$647$		−	10.5272i		−	0.413866i	0.978355	−	0.206933i	$-0.0663482\pi$
$648$		0			0
$649$			50.9263i			1.99903i
$650$		0			0
$651$	4.79736	−	4.79736i	0.188023	−	0.188023i
$652$		0			0
$653$	23.6147	+	23.6147i	0.924114	+	0.924114i	0.997317	−	0.0732033i	$-0.0233222\pi$
$653$	23.6147	+	23.6147i	0.924114	+	0.924114i	−0.0732033	+	0.997317i	$0.523322\pi$
$654$		0			0
$655$	12.1430			0.474467
$656$		0			0
$657$	30.2947			1.18191
$658$		0			0
$659$	14.9087	+	14.9087i	0.580759	+	0.580759i	0.935112	−	0.354353i	$-0.115299\pi$
$659$	14.9087	+	14.9087i	0.580759	+	0.580759i	−0.354353	+	0.935112i	$0.615299\pi$
$660$		0			0
$661$	22.2104	−	22.2104i	0.863884	−	0.863884i	−0.127903	−	0.991787i	$-0.540824\pi$
$661$	22.2104	−	22.2104i	0.863884	−	0.863884i	0.991787	+	0.127903i	$0.0408245\pi$
$662$		0			0
$663$			28.4132i			1.10348i
$664$		0			0
$665$			2.30401i			0.0893458i
$666$		0			0
$667$	−11.7644	+	11.7644i	−0.455518	+	0.455518i
$668$		0			0
$669$	24.6316	+	24.6316i	0.952312	+	0.952312i
$670$		0			0
$671$	−25.1090			−0.969321
$672$		0			0
$673$	45.9274			1.77037			0.885186	−	0.465237i	$-0.154031\pi$
$673$	45.9274			1.77037			0.885186	+	0.465237i	$0.154031\pi$
$674$		0			0
$675$	−14.2596	−	14.2596i	−0.548851	−	0.548851i
$676$		0			0
$677$	30.9708	−	30.9708i	1.19030	−	1.19030i	0.213323	−	0.976982i	$-0.431571\pi$
$677$	30.9708	−	30.9708i	1.19030	−	1.19030i	0.976982	−	0.213323i	$-0.0684286\pi$
$678$		0			0
$679$			8.34450i			0.320233i
$680$		0			0
$681$			61.7199i			2.36511i
$682$		0			0
$683$	12.6125	−	12.6125i	0.482603	−	0.482603i	−0.423359	−	0.905962i	$-0.639149\pi$
$683$	12.6125	−	12.6125i	0.482603	−	0.482603i	0.905962	+	0.423359i	$0.139149\pi$
$684$		0			0
$685$	3.09228	+	3.09228i	0.118150	+	0.118150i
$686$		0			0
$687$	28.6706			1.09385
$688$		0			0
$689$	13.0136			0.495780
$690$		0			0
$691$	−23.0900	−	23.0900i	−0.878385	−	0.878385i	0.114983	−	0.993368i	$-0.463319\pi$
$691$	−23.0900	−	23.0900i	−0.878385	−	0.878385i	−0.993368	+	0.114983i	$0.963319\pi$
$692$		0			0
$693$	−17.5832	+	17.5832i	−0.667930	+	0.667930i
$694$		0			0
$695$		−	9.52239i		−	0.361205i
$696$		0			0
$697$		−	25.3152i		−	0.958882i
$698$		0			0
$699$	0.358977	−	0.358977i	0.0135778	−	0.0135778i
$700$		0			0
$701$	23.1180	+	23.1180i	0.873153	+	0.873153i	0.992815	−	0.119662i	$-0.0381810\pi$
$701$	23.1180	+	23.1180i	0.873153	+	0.873153i	−0.119662	+	0.992815i	$0.538181\pi$
$702$		0			0
$703$	−4.62471			−0.174424
$704$		0			0
$705$	27.4265			1.03294
$706$		0			0
$707$	3.37944	+	3.37944i	0.127097	+	0.127097i
$708$		0			0
$709$	−29.5978	+	29.5978i	−1.11157	+	1.11157i	−0.118628	+	0.992939i	$0.537850\pi$
$709$	−29.5978	+	29.5978i	−1.11157	+	1.11157i	−0.992939	+	0.118628i	$0.962150\pi$
$710$		0			0
$711$			34.3950i			1.28991i
$712$		0			0
$713$		−	18.6836i		−	0.699707i
$714$		0			0
$715$	10.3805	−	10.3805i	0.388210	−	0.388210i
$716$		0			0
$717$	−0.513053	−	0.513053i	−0.0191603	−	0.0191603i
$718$		0			0
$719$	47.9973			1.79000			0.894999	−	0.446068i	$-0.147176\pi$
$719$	47.9973			1.79000			0.894999	+	0.446068i	$0.147176\pi$
$720$		0			0
$721$	−19.2218			−0.715856
$722$		0			0
$723$	14.7974	+	14.7974i	0.550320	+	0.550320i
$724$		0			0
$725$	6.47432	−	6.47432i	0.240450	−	0.240450i
$726$		0			0
$727$		−	35.3027i		−	1.30931i	−0.755930	−	0.654653i	$-0.772815\pi$
$727$		−	35.3027i		−	1.30931i	0.755930	−	0.654653i	$-0.227185\pi$
$728$		0			0
$729$			43.9928i			1.62936i
$730$		0			0
$731$	24.4683	−	24.4683i	0.904992	−	0.904992i
$732$		0			0
$733$	−6.33921	−	6.33921i	−0.234144	−	0.234144i	0.580276	−	0.814420i	$-0.302945\pi$
$733$	−6.33921	−	6.33921i	−0.234144	−	0.234144i	−0.814420	+	0.580276i	$0.802945\pi$
$734$		0			0
$735$	2.46733			0.0910090
$736$		0			0
$737$	6.89174			0.253861
$738$		0			0
$739$	−0.840283	−	0.840283i	−0.0309103	−	0.0309103i	0.691483	−	0.722393i	$-0.256958\pi$
$739$	−0.840283	−	0.840283i	−0.0309103	−	0.0309103i	−0.722393	+	0.691483i	$0.756958\pi$
$740$		0			0
$741$	−16.0148	+	16.0148i	−0.588319	+	0.588319i
$742$		0			0
$743$			46.9253i			1.72152i	0.509008	+	0.860762i	$0.330012\pi$
$743$			46.9253i			1.72152i	−0.509008	+	0.860762i	$0.669988\pi$
$744$		0			0
$745$		−	3.38508i		−	0.124020i
$746$		0			0
$747$	−9.28086	+	9.28086i	−0.339569	+	0.339569i
$748$		0			0
$749$	2.46733	+	2.46733i	0.0901544	+	0.0901544i
$750$		0			0
$751$	11.5182			0.420305			0.210152	−	0.977669i	$-0.432604\pi$
$751$	11.5182			0.420305			0.210152	+	0.977669i	$0.432604\pi$
$752$		0			0
$753$	8.74534			0.318698
$754$		0			0
$755$	−1.35872	−	1.35872i	−0.0494491	−	0.0494491i
$756$		0			0
$757$	−14.6371	+	14.6371i	−0.531994	+	0.531994i	−0.921165	−	0.389172i	$-0.872761\pi$
$757$	−14.6371	+	14.6371i	−0.531994	+	0.531994i	0.389172	+	0.921165i	$0.372761\pi$
$758$		0			0
$759$			111.976i			4.06449i
$760$		0			0
$761$		−	6.74979i		−	0.244680i	−0.992488	−	0.122340i	$-0.960960\pi$
$761$		−	6.74979i		−	0.244680i	0.992488	−	0.122340i	$-0.0390398\pi$
$762$		0			0
$763$	2.44587	−	2.44587i	0.0885465	−	0.0885465i
$764$		0			0
$765$	−9.65306	−	9.65306i	−0.349007	−	0.349007i
$766$		0			0
$767$	30.3766			1.09684
$768$		0			0
$769$	−2.23508			−0.0805990			−0.0402995	−	0.999188i	$-0.512831\pi$
$769$	−2.23508			−0.0805990			−0.0402995	+	0.999188i	$0.512831\pi$
$770$		0			0
$771$	−5.53022	−	5.53022i	−0.199166	−	0.199166i
$772$		0			0
$773$	16.6209	−	16.6209i	0.597813	−	0.597813i	−0.341917	−	0.939730i	$-0.611076\pi$
$773$	16.6209	−	16.6209i	0.597813	−	0.597813i	0.939730	+	0.341917i	$0.111076\pi$
$774$		0			0
$775$			10.2822i			0.369348i
$776$		0			0
$777$			4.95253i			0.177671i
$778$		0			0
$779$	14.2687	−	14.2687i	0.511228	−	0.511228i
$780$		0			0
$781$	−45.0896	−	45.0896i	−1.61343	−	1.61343i
$782$		0			0
$783$	10.4090			0.371987
$784$		0			0
$785$	−4.95040			−0.176688
$786$		0			0
$787$	−4.01279	−	4.01279i	−0.143040	−	0.143040i	0.631960	−	0.775001i	$-0.282251\pi$
$787$	−4.01279	−	4.01279i	−0.143040	−	0.143040i	−0.775001	+	0.631960i	$0.782251\pi$
$788$		0			0
$789$	−16.7535	+	16.7535i	−0.596440	+	0.596440i
$790$		0			0
$791$		−	3.35149i		−	0.119165i
$792$		0			0
$793$			14.9770i			0.531850i
$794$		0			0
$795$	−7.22959	+	7.22959i	−0.256407	+	0.256407i
$796$		0			0
$797$	26.5404	+	26.5404i	0.940110	+	0.940110i	0.998305	−	0.0581955i	$-0.0185347\pi$
$797$	26.5404	+	26.5404i	0.940110	+	0.940110i	−0.0581955	+	0.998305i	$0.518535\pi$
$798$		0			0
$799$	−36.1888			−1.28027
$800$		0			0
$801$	−3.14280			−0.111045
$802$		0			0
$803$	23.8803	+	23.8803i	0.842718	+	0.842718i
$804$		0			0
$805$	4.80460	−	4.80460i	0.169340	−	0.169340i
$806$		0			0
$807$		−	45.2659i		−	1.59344i
$808$		0			0
$809$			6.28804i			0.221076i	0.993872	+	0.110538i	$0.0352573\pi$
$809$			6.28804i			0.221076i	−0.993872	+	0.110538i	$0.964743\pi$
$810$		0			0
$811$	−28.2328	+	28.2328i	−0.991388	+	0.991388i	−0.999963	−	0.00857565i	$-0.997270\pi$
$811$	−28.2328	+	28.2328i	−0.991388	+	0.991388i	0.00857565	+	0.999963i	$0.497270\pi$
$812$		0			0
$813$	−52.5409	−	52.5409i	−1.84269	−	1.84269i
$814$		0			0
$815$	−10.3388			−0.362152
$816$		0			0
$817$	27.5826			0.964994
$818$		0			0
$819$	10.4880	+	10.4880i	0.366482	+	0.366482i
$820$		0			0
$821$	−11.9785	+	11.9785i	−0.418054	+	0.418054i	−0.884532	−	0.466479i	$-0.845522\pi$
$821$	−11.9785	+	11.9785i	−0.418054	+	0.418054i	0.466479	+	0.884532i	$0.345522\pi$
$822$		0			0
$823$		−	37.3388i		−	1.30155i	−0.759272	−	0.650774i	$-0.774445\pi$
$823$		−	37.3388i		−	1.30155i	0.759272	−	0.650774i	$-0.225555\pi$
$824$		0			0
$825$		−	61.6244i		−	2.14549i
$826$		0			0
$827$	5.32642	−	5.32642i	0.185218	−	0.185218i	−0.608407	−	0.793625i	$-0.708191\pi$
$827$	5.32642	−	5.32642i	0.185218	−	0.185218i	0.793625	+	0.608407i	$0.208191\pi$
$828$		0			0
$829$	−5.78119	−	5.78119i	−0.200789	−	0.200789i	0.599549	−	0.800338i	$-0.295347\pi$
$829$	−5.78119	−	5.78119i	−0.200789	−	0.200789i	−0.800338	+	0.599549i	$0.795347\pi$
$830$		0			0
$831$	35.6361			1.23620
$832$		0			0
$833$	−3.25560			−0.112800
$834$		0			0
$835$	−7.82547	−	7.82547i	−0.270811	−	0.270811i
$836$		0			0
$837$	−8.26553	+	8.26553i	−0.285699	+	0.285699i
$838$		0			0
$839$			7.20540i			0.248758i	0.992235	+	0.124379i	$0.0396939\pi$
$839$			7.20540i			0.248758i	−0.992235	+	0.124379i	$0.960306\pi$
$840$		0			0
$841$		−	24.2740i		−	0.837033i
$842$		0			0
$843$	−55.8264	+	55.8264i	−1.92276	+	1.92276i
$844$		0			0
$845$	1.96961	+	1.96961i	0.0677565	+	0.0677565i
$846$		0			0
$847$	−16.7205			−0.574523
$848$		0			0
$849$	−20.9910			−0.720410
$850$		0			0
$851$	9.64397	+	9.64397i	0.330591	+	0.330591i
$852$		0			0
$853$	−13.0316	+	13.0316i	−0.446192	+	0.446192i	−0.894086	−	0.447894i	$-0.852174\pi$
$853$	−13.0316	+	13.0316i	−0.446192	+	0.446192i	0.447894	+	0.894086i	$0.352174\pi$
$854$		0			0
$855$		−	10.8817i		−	0.372147i
$856$		0			0
$857$		−	13.6289i		−	0.465556i	−0.972530	−	0.232778i	$-0.925219\pi$
$857$		−	13.6289i		−	0.465556i	0.972530	−	0.232778i	$-0.0747815\pi$
$858$		0			0
$859$	31.9028	−	31.9028i	1.08851	−	1.08851i	0.0928263	−	0.995682i	$-0.470410\pi$
$859$	31.9028	−	31.9028i	1.08851	−	1.08851i	0.995682	−	0.0928263i	$-0.0295901\pi$
$860$		0			0
$861$	−15.2801	−	15.2801i	−0.520745	−	0.520745i
$862$		0			0
$863$	51.1845			1.74234			0.871171	−	0.490980i	$-0.163361\pi$
$863$	51.1845			1.74234			0.871171	+	0.490980i	$0.163361\pi$
$864$		0			0
$865$	17.4864			0.594554
$866$		0			0
$867$	−12.5785	−	12.5785i	−0.427188	−	0.427188i
$868$		0			0
$869$	−27.1125	+	27.1125i	−0.919727	+	0.919727i
$870$		0			0
$871$		−	4.11080i		−	0.139289i
$872$		0			0
$873$		−	39.4105i		−	1.33384i
$874$		0			0
$875$	−5.78313	+	5.78313i	−0.195506	+	0.195506i
$876$		0			0
$877$	21.4095	+	21.4095i	0.722947	+	0.722947i	0.969204	−	0.246257i	$-0.0792008\pi$
$877$	21.4095	+	21.4095i	0.722947	+	0.722947i	−0.246257	+	0.969204i	$0.579201\pi$
$878$		0			0
$879$	−33.9858			−1.14631
$880$		0			0
$881$	29.7369			1.00186			0.500930	−	0.865488i	$-0.332991\pi$
$881$	29.7369			1.00186			0.500930	+	0.865488i	$0.332991\pi$
$882$		0			0
$883$	−14.3040	−	14.3040i	−0.481368	−	0.481368i	0.424200	−	0.905568i	$-0.360555\pi$
$883$	−14.3040	−	14.3040i	−0.481368	−	0.481368i	−0.905568	+	0.424200i	$0.860555\pi$
$884$		0			0
$885$	−16.8754	+	16.8754i	−0.567261	+	0.567261i
$886$		0			0
$887$		−	56.7057i		−	1.90399i	−0.306113	−	0.951995i	$-0.599029\pi$
$887$		−	56.7057i		−	1.90399i	0.306113	−	0.951995i	$-0.400971\pi$
$888$		0			0
$889$		−	5.55623i		−	0.186350i
$890$		0			0
$891$	−3.21173	+	3.21173i	−0.107597	+	0.107597i
$892$		0			0
$893$	−20.3975	−	20.3975i	−0.682575	−	0.682575i
$894$		0			0
$895$	1.22747			0.0410298
$896$		0			0
$897$	66.7919			2.23012
$898$		0			0
$899$	−3.75283	−	3.75283i	−0.125164	−	0.125164i
$900$		0			0
$901$	9.53931	−	9.53931i	0.317801	−	0.317801i
$902$		0			0
$903$		−	29.5378i		−	0.982957i
$904$		0			0
$905$		−	20.0944i		−	0.667960i
$906$		0			0
$907$	15.2487	−	15.2487i	0.506325	−	0.506325i	−0.407071	−	0.913396i	$-0.633450\pi$
$907$	15.2487	−	15.2487i	0.506325	−	0.506325i	0.913396	+	0.407071i	$0.133450\pi$
$908$		0			0
$909$	−15.9609	−	15.9609i	−0.529389	−	0.529389i
$910$		0			0
$911$	7.88055			0.261094			0.130547	−	0.991442i	$-0.458327\pi$
$911$	7.88055			0.261094			0.130547	+	0.991442i	$0.458327\pi$
$912$		0			0
$913$	−14.6316			−0.484235
$914$		0			0
$915$	−8.32034	−	8.32034i	−0.275062	−	0.275062i
$916$		0			0
$917$	−9.67108	+	9.67108i	−0.319367	+	0.319367i
$918$		0			0
$919$			2.11851i			0.0698832i	0.999389	+	0.0349416i	$0.0111245\pi$
$919$			2.11851i			0.0698832i	−0.999389	+	0.0349416i	$0.988875\pi$
$920$		0			0
$921$		−	90.2675i		−	2.97442i
$922$		0			0
$923$	−26.8951	+	26.8951i	−0.885264	+	0.885264i
$924$		0			0
$925$	−5.30740	−	5.30740i	−0.174506	−	0.174506i
$926$		0			0
$927$	90.7831			2.98171
$928$		0			0
$929$	−32.2066			−1.05667			−0.528333	−	0.849037i	$-0.677183\pi$
$929$	−32.2066			−1.05667			−0.528333	+	0.849037i	$0.677183\pi$
$930$		0			0
$931$	−1.83499	−	1.83499i	−0.0601393	−	0.0601393i
$932$		0			0
$933$	52.1640	−	52.1640i	1.70777	−	1.70777i
$934$		0			0
$935$		−	15.2184i		−	0.497694i
$936$		0			0
$937$			17.8409i			0.582836i	0.956596	+	0.291418i	$0.0941271\pi$
$937$			17.8409i			0.582836i	−0.956596	+	0.291418i	$0.905873\pi$
$938$		0			0
$939$	39.6655	−	39.6655i	1.29444	−	1.29444i
$940$		0			0
$941$	−20.0164	−	20.0164i	−0.652517	−	0.652517i	0.301082	−	0.953598i	$-0.402652\pi$
$941$	−20.0164	−	20.0164i	−0.652517	−	0.652517i	−0.953598	+	0.301082i	$0.902652\pi$
$942$		0			0
$943$	−59.5094			−1.93789
$944$		0			0
$945$	−4.25106			−0.138287
$946$		0			0
$947$	−16.8118	−	16.8118i	−0.546311	−	0.546311i	0.379061	−	0.925372i	$-0.376247\pi$
$947$	−16.8118	−	16.8118i	−0.546311	−	0.546311i	−0.925372	+	0.379061i	$0.876247\pi$
$948$		0			0
$949$	14.2442	−	14.2442i	0.462385	−	0.462385i
$950$		0			0
$951$		−	3.65550i		−	0.118538i
$952$		0			0
$953$			30.3038i			0.981636i	0.871262	+	0.490818i	$0.163302\pi$
$953$			30.3038i			0.981636i	−0.871262	+	0.490818i	$0.836698\pi$
$954$		0			0
$955$	1.57653	−	1.57653i	0.0510155	−	0.0510155i
$956$		0			0
$957$	22.4918	+	22.4918i	0.727058	+	0.727058i
$958$		0			0
$959$	−4.92558			−0.159055
$960$		0			0
$961$	−25.0399			−0.807740
$962$		0			0
$963$	−11.6531	−	11.6531i	−0.375515	−	0.375515i
$964$		0			0
$965$	−6.33726	+	6.33726i	−0.204004	+	0.204004i
$966$		0			0
$967$			13.3675i			0.429869i	0.976629	+	0.214934i	$0.0689537\pi$
$967$			13.3675i			0.429869i	−0.976629	+	0.214934i	$0.931046\pi$
$968$		0			0
$969$			23.4785i			0.754239i
$970$		0			0
$971$	−9.35224	+	9.35224i	−0.300128	+	0.300128i	−0.841064	−	0.540936i	$-0.818070\pi$
$971$	−9.35224	+	9.35224i	−0.300128	+	0.300128i	0.540936	+	0.841064i	$0.318070\pi$
$972$		0			0
$973$	7.58393	+	7.58393i	0.243130	+	0.243130i
$974$		0			0
$975$	−36.7578			−1.17719
$976$		0			0
$977$	53.2312			1.70302			0.851509	−	0.524340i	$-0.175688\pi$
$977$	53.2312			1.70302			0.851509	+	0.524340i	$0.175688\pi$
$978$		0			0
$979$	−2.47736	−	2.47736i	−0.0791769	−	0.0791769i
$980$		0			0
$981$	−11.5517	+	11.5517i	−0.368817	+	0.368817i
$982$		0			0
$983$			0.295483i			0.00942446i	0.999989	+	0.00471223i	$0.00149995\pi$
$983$			0.295483i			0.00942446i	−0.999989	+	0.00471223i	$0.998500\pi$
$984$		0			0
$985$		−	17.0281i		−	0.542561i
$986$		0			0
$987$	−21.8433	+	21.8433i	−0.695281	+	0.695281i
$988$		0			0
$989$	−57.5185	−	57.5185i	−1.82898	−	1.82898i
$990$		0			0
$991$	42.0364			1.33533			0.667665	−	0.744461i	$-0.267294\pi$
$991$	42.0364			1.33533			0.667665	+	0.744461i	$0.267294\pi$
$992$		0			0
$993$	−41.0357			−1.30223
$994$		0			0
$995$	−3.52358	−	3.52358i	−0.111705	−	0.111705i
$996$		0			0
$997$	−32.5746	+	32.5746i	−1.03165	+	1.03165i	−0.0321655	+	0.999483i	$0.510240\pi$
$997$	−32.5746	+	32.5746i	−1.03165	+	1.03165i	−0.999483	+	0.0321655i	$0.989760\pi$
$998$		0			0
$999$		−	8.53289i		−	0.269969i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.2.m.c.337.4		8
4.3	odd	2		112.2.m.c.29.3	✓	8
8.3	odd	2		896.2.m.e.673.4		8
8.5	even	2		896.2.m.f.673.1		8
16.3	odd	4		896.2.m.e.225.4		8
16.5	even	4	inner	448.2.m.c.113.4		8
16.11	odd	4		112.2.m.c.85.3	yes	8
16.13	even	4		896.2.m.f.225.1		8
28.3	even	6		784.2.x.j.765.3		16
28.11	odd	6		784.2.x.k.765.3		16
28.19	even	6		784.2.x.j.557.1		16
28.23	odd	6		784.2.x.k.557.1		16
28.27	even	2		784.2.m.g.589.3		8
32.5	even	8		7168.2.a.bd.1.1		8
32.11	odd	8		7168.2.a.bc.1.1		8
32.21	even	8		7168.2.a.bd.1.8		8
32.27	odd	8		7168.2.a.bc.1.8		8
112.11	odd	12		784.2.x.k.373.1		16
112.27	even	4		784.2.m.g.197.3		8
112.59	even	12		784.2.x.j.373.1		16
112.75	even	12		784.2.x.j.165.3		16
112.107	odd	12		784.2.x.k.165.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.c.29.3	✓	8	4.3	odd	2
112.2.m.c.85.3	yes	8	16.11	odd	4
448.2.m.c.113.4		8	16.5	even	4	inner
448.2.m.c.337.4		8	1.1	even	1	trivial
784.2.m.g.197.3		8	112.27	even	4
784.2.m.g.589.3		8	28.27	even	2
784.2.x.j.165.3		16	112.75	even	12
784.2.x.j.373.1		16	112.59	even	12
784.2.x.j.557.1		16	28.19	even	6
784.2.x.j.765.3		16	28.3	even	6
784.2.x.k.165.3		16	112.107	odd	12
784.2.x.k.373.1		16	112.11	odd	12
784.2.x.k.557.1		16	28.23	odd	6
784.2.x.k.765.3		16	28.11	odd	6
896.2.m.e.225.4		8	16.3	odd	4
896.2.m.e.673.4		8	8.3	odd	2
896.2.m.f.225.1		8	16.13	even	4
896.2.m.f.673.1		8	8.5	even	2
7168.2.a.bc.1.1		8	32.11	odd	8
7168.2.a.bc.1.8		8	32.27	odd	8
7168.2.a.bd.1.1		8	32.5	even	8
7168.2.a.bd.1.8		8	32.21	even	8

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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.m (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.96506 + 1.96506i) q^{3} +(-0.627801 + 0.627801i) q^{5} -1.00000i q^{7} +4.72294i q^{9} +(-3.72294 + 3.72294i) q^{11} +(2.22066 + 2.22066i) q^{13} -2.46733 q^{15} +3.25560 q^{17} +(1.83499 + 1.83499i) q^{19} +(1.96506 - 1.96506i) q^{21} -7.65306i q^{23} +4.21173i q^{25} +(-3.38567 + 3.38567i) q^{27} +(-1.53721 - 1.53721i) q^{29} +2.44133 q^{31} -14.6316 q^{33} +(0.627801 + 0.627801i) q^{35} +(-1.26015 + 1.26015i) q^{37} +8.72748i q^{39} -7.77589i q^{41} +(7.51575 - 7.51575i) q^{43} +(-2.96506 - 2.96506i) q^{45} -11.1158 q^{47} -1.00000 q^{49} +(6.39746 + 6.39746i) q^{51} +(2.93012 - 2.93012i) q^{53} -4.67452i q^{55} +7.21173i q^{57} +(6.83953 - 6.83953i) q^{59} +(3.37220 + 3.37220i) q^{61} +4.72294 q^{63} -2.78827 q^{65} +(-0.925579 - 0.925579i) q^{67} +(15.0387 - 15.0387i) q^{69} +12.1113i q^{71} -6.41438i q^{73} +(-8.27631 + 8.27631i) q^{75} +(3.72294 + 3.72294i) q^{77} +7.28255 q^{79} +0.862688 q^{81} +(1.96506 + 1.96506i) q^{83} +(-2.04387 + 2.04387i) q^{85} -6.04143i q^{87} +0.665433i q^{89} +(2.22066 - 2.22066i) q^{91} +(4.79736 + 4.79736i) q^{93} -2.30401 q^{95} -8.34450 q^{97} +(-17.5832 - 17.5832i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{5} + 8 q^{15} + 24 q^{17} + 12 q^{19} - 12 q^{27} - 16 q^{29} - 16 q^{31} - 24 q^{33} + 4 q^{35} + 16 q^{37} + 32 q^{43} - 8 q^{45} - 24 q^{47} - 8 q^{49} - 8 q^{51} - 8 q^{53} + 28 q^{59} + 28 q^{61}+ \cdots - 48 q^{99}+O(q^{100}) \) 8 * q - 4 * q^5 + 8 * q^15 + 24 * q^17 + 12 * q^19 - 12 * q^27 - 16 * q^29 - 16 * q^31 - 24 * q^33 + 4 * q^35 + 16 * q^37 + 32 * q^43 - 8 * q^45 - 24 * q^47 - 8 * q^49 - 8 * q^51 - 8 * q^53 + 28 * q^59 + 28 * q^61 + 8 * q^63 - 48 * q^65 + 44 * q^69 - 28 * q^75 + 24 * q^79 + 40 * q^81 - 40 * q^85 + 16 * q^93 - 16 * q^95 - 32 * q^97 - 48 * q^99

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