LMFDB - Embedded newform 1248.2.bb.f.655.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1248,2,Mod(463,1248)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1248, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 0, 1]))

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

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

chi := DirichletCharacter("1248.463");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1248 = 2^{5} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1248.bb (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:	$9.96533017226$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			655.3
Character	$\chi$	$=$	1248.655
Dual form			1248.2.bb.f.463.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} +(-1.67211 - 1.67211i) q^{5} +(1.16012 - 1.16012i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} +(-1.67211 - 1.67211i) q^{5} +(1.16012 - 1.16012i) q^{7} +1.00000 q^{9} +(0.391951 + 0.391951i) q^{11} +(-3.59209 - 0.311317i) q^{13} +(-1.67211 - 1.67211i) q^{15} -2.95889i q^{17} +(0.785637 - 0.785637i) q^{19} +(1.16012 - 1.16012i) q^{21} -2.14814 q^{23} +0.591934i q^{25} +1.00000 q^{27} -9.69684i q^{29} +(-1.16012 - 1.16012i) q^{31} +(0.391951 + 0.391951i) q^{33} -3.87971 q^{35} +(1.87575 - 1.87575i) q^{37} +(-3.59209 - 0.311317i) q^{39} +(-1.21870 + 1.21870i) q^{41} +6.64295i q^{43} +(-1.67211 - 1.67211i) q^{45} +(-5.19778 + 5.19778i) q^{47} +4.30823i q^{49} -2.95889i q^{51} -13.9505i q^{53} -1.31077i q^{55} +(0.785637 - 0.785637i) q^{57} +(-8.86339 - 8.86339i) q^{59} +5.77916i q^{61} +(1.16012 - 1.16012i) q^{63} +(5.48582 + 6.52694i) q^{65} +(5.85732 - 5.85732i) q^{67} -2.14814 q^{69} +(-5.33062 - 5.33062i) q^{71} +(-5.90017 - 5.90017i) q^{73} +0.591934i q^{75} +0.909421 q^{77} +1.82465i q^{79} +1.00000 q^{81} +(-3.29212 + 3.29212i) q^{83} +(-4.94759 + 4.94759i) q^{85} -9.69684i q^{87} +(-7.48582 - 7.48582i) q^{89} +(-4.52842 + 3.80609i) q^{91} +(-1.16012 - 1.16012i) q^{93} -2.62735 q^{95} +(4.94128 - 4.94128i) q^{97} +(0.391951 + 0.391951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{3} + 24 q^{9}+O(q^{10}) $ 24 * q + 24 * q^3 + 24 * q^9	$ 24 q + 24 q^{3} + 24 q^{9} - 8 q^{11} - 20 q^{19} + 24 q^{27} - 8 q^{33} - 16 q^{35} - 12 q^{41} - 20 q^{57} + 16 q^{59} - 76 q^{65} - 28 q^{67} - 8 q^{73} + 24 q^{81} + 72 q^{83} + 28 q^{89} + 4 q^{91} + 24 q^{97} - 8 q^{99}+O(q^{100}) $ 24 * q + 24 * q^3 + 24 * q^9 - 8 * q^11 - 20 * q^19 + 24 * q^27 - 8 * q^33 - 16 * q^35 - 12 * q^41 - 20 * q^57 + 16 * q^59 - 76 * q^65 - 28 * q^67 - 8 * q^73 + 24 * q^81 + 72 * q^83 + 28 * q^89 + 4 * q^91 + 24 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1248\mathbb{Z}\right)^\times$.

$n$	$703$	$769$	$833$	$1093$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$		0			0
$5$	−1.67211	−	1.67211i	−0.747792	−	0.747792i	0.226272	−	0.974064i	$-0.427346\pi$
$5$	−1.67211	−	1.67211i	−0.747792	−	0.747792i	−0.974064	+	0.226272i	$0.927346\pi$
$6$		0			0
$7$	1.16012	−	1.16012i	0.438485	−	0.438485i	−0.453017	−	0.891502i	$-0.649652\pi$
$7$	1.16012	−	1.16012i	0.438485	−	0.438485i	0.891502	+	0.453017i	$0.149652\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	0.391951	+	0.391951i	0.118178	+	0.118178i	0.763722	−	0.645545i	$-0.223370\pi$
$11$	0.391951	+	0.391951i	0.118178	+	0.118178i	−0.645545	+	0.763722i	$0.723370\pi$
$12$		0			0
$13$	−3.59209	−	0.311317i	−0.996265	−	0.0863438i
$13$	−3.59209	−	0.311317i	−0.996265	−	0.0863438i
$14$		0			0
$15$	−1.67211	−	1.67211i	−0.431738	−	0.431738i
$16$		0			0
$17$		−	2.95889i		−	0.717635i	−0.933408	−	0.358818i	$-0.883180\pi$
$17$		−	2.95889i		−	0.717635i	0.933408	−	0.358818i	$-0.116820\pi$
$18$		0			0
$19$	0.785637	−	0.785637i	0.180238	−	0.180238i	−0.611222	−	0.791459i	$-0.709322\pi$
$19$	0.785637	−	0.785637i	0.180238	−	0.180238i	0.791459	+	0.611222i	$0.209322\pi$
$20$		0			0
$21$	1.16012	−	1.16012i	0.253159	−	0.253159i
$22$		0			0
$23$	−2.14814			−0.447918			−0.223959	−	0.974599i	$-0.571898\pi$
$23$	−2.14814			−0.447918			−0.223959	+	0.974599i	$0.571898\pi$
$24$		0			0
$25$			0.591934i			0.118387i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$		−	9.69684i		−	1.80066i	−0.435210	−	0.900329i	$-0.643326\pi$
$29$		−	9.69684i		−	1.80066i	0.435210	−	0.900329i	$-0.356674\pi$
$30$		0			0
$31$	−1.16012	−	1.16012i	−0.208364	−	0.208364i	0.595208	−	0.803572i	$-0.297070\pi$
$31$	−1.16012	−	1.16012i	−0.208364	−	0.208364i	−0.803572	+	0.595208i	$0.797070\pi$
$32$		0			0
$33$	0.391951	+	0.391951i	0.0682298	+	0.0682298i
$34$		0			0
$35$	−3.87971			−0.655791
$36$		0			0
$37$	1.87575	−	1.87575i	0.308372	−	0.308372i	−0.535906	−	0.844278i	$-0.680030\pi$
$37$	1.87575	−	1.87575i	0.308372	−	0.308372i	0.844278	+	0.535906i	$0.180030\pi$
$38$		0			0
$39$	−3.59209	−	0.311317i	−0.575194	−	0.0498506i
$40$		0			0
$41$	−1.21870	+	1.21870i	−0.190329	+	0.190329i	−0.795838	−	0.605509i	$-0.792970\pi$
$41$	−1.21870	+	1.21870i	−0.190329	+	0.190329i	0.605509	+	0.795838i	$0.292970\pi$
$42$		0			0
$43$			6.64295i			1.01304i	0.862228	+	0.506521i	$0.169069\pi$
$43$			6.64295i			1.01304i	−0.862228	+	0.506521i	$0.830931\pi$
$44$		0			0
$45$	−1.67211	−	1.67211i	−0.249264	−	0.249264i
$46$		0			0
$47$	−5.19778	+	5.19778i	−0.758174	+	0.758174i	−0.975990	−	0.217816i	$-0.930107\pi$
$47$	−5.19778	+	5.19778i	−0.758174	+	0.758174i	0.217816	+	0.975990i	$0.430107\pi$
$48$		0			0
$49$			4.30823i			0.615462i
$50$		0			0
$51$		−	2.95889i		−	0.414327i
$52$		0			0
$53$		−	13.9505i		−	1.91625i	−0.286355	−	0.958124i	$-0.592444\pi$
$53$		−	13.9505i		−	1.91625i	0.286355	−	0.958124i	$-0.407556\pi$
$54$		0			0
$55$		−	1.31077i		−	0.176745i
$56$		0			0
$57$	0.785637	−	0.785637i	0.104060	−	0.104060i
$58$		0			0
$59$	−8.86339	−	8.86339i	−1.15392	−	1.15392i	−0.985761	−	0.168155i	$-0.946219\pi$
$59$	−8.86339	−	8.86339i	−1.15392	−	1.15392i	−0.168155	−	0.985761i	$-0.553781\pi$
$60$		0			0
$61$			5.77916i			0.739945i	0.929043	+	0.369972i	$0.120633\pi$
$61$			5.77916i			0.739945i	−0.929043	+	0.369972i	$0.879367\pi$
$62$		0			0
$63$	1.16012	−	1.16012i	0.146162	−	0.146162i
$64$		0			0
$65$	5.48582	+	6.52694i	0.680432	+	0.809567i
$66$		0			0
$67$	5.85732	−	5.85732i	0.715585	−	0.715585i	−0.252113	−	0.967698i	$-0.581125\pi$
$67$	5.85732	−	5.85732i	0.715585	−	0.715585i	0.967698	+	0.252113i	$0.0811254\pi$
$68$		0			0
$69$	−2.14814			−0.258606
$70$		0			0
$71$	−5.33062	−	5.33062i	−0.632629	−	0.632629i	0.316098	−	0.948727i	$-0.397627\pi$
$71$	−5.33062	−	5.33062i	−0.632629	−	0.632629i	−0.948727	+	0.316098i	$0.897627\pi$
$72$		0			0
$73$	−5.90017	−	5.90017i	−0.690563	−	0.690563i	0.271793	−	0.962356i	$-0.412383\pi$
$73$	−5.90017	−	5.90017i	−0.690563	−	0.690563i	−0.962356	+	0.271793i	$0.912383\pi$
$74$		0			0
$75$			0.591934i			0.0683507i
$76$		0			0
$77$	0.909421			0.103638
$78$		0			0
$79$			1.82465i			0.205289i	0.994718	+	0.102644i	$0.0327304\pi$
$79$			1.82465i			0.205289i	−0.994718	+	0.102644i	$0.967270\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−3.29212	+	3.29212i	−0.361357	+	0.361357i	−0.864312	−	0.502955i	$-0.832246\pi$
$83$	−3.29212	+	3.29212i	−0.361357	+	0.361357i	0.502955	+	0.864312i	$0.332246\pi$
$84$		0			0
$85$	−4.94759	+	4.94759i	−0.536642	+	0.536642i
$86$		0			0
$87$		−	9.69684i		−	1.03961i
$88$		0			0
$89$	−7.48582	−	7.48582i	−0.793496	−	0.793496i	0.188565	−	0.982061i	$-0.439616\pi$
$89$	−7.48582	−	7.48582i	−0.793496	−	0.793496i	−0.982061	+	0.188565i	$0.939616\pi$
$90$		0			0
$91$	−4.52842	+	3.80609i	−0.474708	+	0.398987i
$92$		0			0
$93$	−1.16012	−	1.16012i	−0.120299	−	0.120299i
$94$		0			0
$95$	−2.62735			−0.269561
$96$		0			0
$97$	4.94128	−	4.94128i	0.501711	−	0.501711i	−0.410258	−	0.911969i	$-0.634561\pi$
$97$	4.94128	−	4.94128i	0.501711	−	0.501711i	0.911969	+	0.410258i	$0.134561\pi$
$98$		0			0
$99$	0.391951	+	0.391951i	0.0393925	+	0.0393925i
$100$		0			0
$101$	2.09896			0.208854			0.104427	−	0.994533i	$-0.466699\pi$
$101$	2.09896			0.208854			0.104427	+	0.994533i	$0.466699\pi$
$102$		0			0
$103$	15.6849			1.54548			0.772741	−	0.634722i	$-0.218885\pi$
$103$	15.6849			1.54548			0.772741	+	0.634722i	$0.218885\pi$
$104$		0			0
$105$	−3.87971			−0.378621
$106$		0			0
$107$	11.8062			1.14134			0.570672	−	0.821178i	$-0.306683\pi$
$107$	11.8062			1.14134			0.570672	+	0.821178i	$0.306683\pi$
$108$		0			0
$109$	9.84874	+	9.84874i	0.943338	+	0.943338i	0.998479	−	0.0551405i	$-0.0175607\pi$
$109$	9.84874	+	9.84874i	0.943338	+	0.943338i	−0.0551405	+	0.998479i	$0.517561\pi$
$110$		0			0
$111$	1.87575	−	1.87575i	0.178039	−	0.178039i
$112$		0			0
$113$	9.39629			0.883929			0.441964	−	0.897033i	$-0.354282\pi$
$113$	9.39629			0.883929			0.441964	+	0.897033i	$0.354282\pi$
$114$		0			0
$115$	3.59193	+	3.59193i	0.334950	+	0.334950i
$116$		0			0
$117$	−3.59209	−	0.311317i	−0.332088	−	0.0287813i
$118$		0			0
$119$	−3.43267	−	3.43267i	−0.314672	−	0.314672i
$120$		0			0
$121$		−	10.6927i		−	0.972068i
$122$		0			0
$123$	−1.21870	+	1.21870i	−0.109887	+	0.109887i
$124$		0			0
$125$	−7.37079	+	7.37079i	−0.659264	+	0.659264i
$126$		0			0
$127$	4.36241			0.387101			0.193551	−	0.981090i	$-0.438000\pi$
$127$	4.36241			0.387101			0.193551	+	0.981090i	$0.438000\pi$
$128$		0			0
$129$			6.64295i			0.584880i
$130$		0			0
$131$	20.5049			1.79152			0.895759	−	0.444540i	$-0.146633\pi$
$131$	20.5049			1.79152			0.895759	+	0.444540i	$0.146633\pi$
$132$		0			0
$133$		−	1.82287i		−	0.158063i
$134$		0			0
$135$	−1.67211	−	1.67211i	−0.143913	−	0.143913i
$136$		0			0
$137$	9.80009	+	9.80009i	0.837278	+	0.837278i	0.988500	−	0.151222i	$-0.0483208\pi$
$137$	9.80009	+	9.80009i	0.837278	+	0.837278i	−0.151222	+	0.988500i	$0.548321\pi$
$138$		0			0
$139$	3.50388			0.297195			0.148598	−	0.988898i	$-0.452524\pi$
$139$	3.50388			0.297195			0.148598	+	0.988898i	$0.452524\pi$
$140$		0			0
$141$	−5.19778	+	5.19778i	−0.437732	+	0.437732i
$142$		0			0
$143$	−1.28590	−	1.52994i	−0.107532	−	0.127940i
$144$		0			0
$145$	−16.2142	+	16.2142i	−1.34652	+	1.34652i
$146$		0			0
$147$			4.30823i			0.355337i
$148$		0			0
$149$	3.27548	+	3.27548i	0.268338	+	0.268338i	0.828430	−	0.560092i	$-0.189234\pi$
$149$	3.27548	+	3.27548i	0.268338	+	0.268338i	−0.560092	+	0.828430i	$0.689234\pi$
$150$		0			0
$151$	−7.01121	+	7.01121i	−0.570564	+	0.570564i	−0.932286	−	0.361722i	$-0.882189\pi$
$151$	−7.01121	+	7.01121i	−0.570564	+	0.570564i	0.361722	+	0.932286i	$0.382189\pi$
$152$		0			0
$153$		−	2.95889i		−	0.239212i
$154$		0			0
$155$			3.87971i			0.311626i
$156$		0			0
$157$			23.5918i			1.88283i	0.337252	+	0.941414i	$0.390503\pi$
$157$			23.5918i			1.88283i	−0.337252	+	0.941414i	$0.609497\pi$
$158$		0			0
$159$		−	13.9505i		−	1.10635i
$160$		0			0
$161$	−2.49210	+	2.49210i	−0.196405	+	0.196405i
$162$		0			0
$163$	−14.2947	−	14.2947i	−1.11965	−	1.11965i	−0.991793	−	0.127856i	$-0.959190\pi$
$163$	−14.2947	−	14.2947i	−1.11965	−	1.11965i	−0.127856	−	0.991793i	$-0.540810\pi$
$164$		0			0
$165$		−	1.31077i		−	0.102043i
$166$		0			0
$167$	9.66616	−	9.66616i	0.747990	−	0.747990i	−0.226111	−	0.974101i	$-0.572601\pi$
$167$	9.66616	−	9.66616i	0.747990	−	0.747990i	0.974101	+	0.226111i	$0.0726013\pi$
$168$		0			0
$169$	12.8062	+	2.23655i	0.985090	+	0.172043i
$170$		0			0
$171$	0.785637	−	0.785637i	0.0600792	−	0.0600792i
$172$		0			0
$173$	−4.90900			−0.373224			−0.186612	−	0.982434i	$-0.559751\pi$
$173$	−4.90900			−0.373224			−0.186612	+	0.982434i	$0.559751\pi$
$174$		0			0
$175$	0.686716	+	0.686716i	0.0519109	+	0.0519109i
$176$		0			0
$177$	−8.86339	−	8.86339i	−0.666213	−	0.666213i
$178$		0			0
$179$			15.4884i			1.15766i	0.815448	+	0.578830i	$0.196490\pi$
$179$			15.4884i			1.15766i	−0.815448	+	0.578830i	$0.803510\pi$
$180$		0			0
$181$	13.7660			1.02322			0.511610	−	0.859217i	$-0.329049\pi$
$181$	13.7660			1.02322			0.511610	+	0.859217i	$0.329049\pi$
$182$		0			0
$183$			5.77916i			0.427207i
$184$		0			0
$185$	−6.27295			−0.461196
$186$		0			0
$187$	1.15974	−	1.15974i	0.0848083	−	0.0848083i
$188$		0			0
$189$	1.16012	−	1.16012i	0.0843865	−	0.0843865i
$190$		0			0
$191$			9.49269i			0.686867i	0.939177	+	0.343433i	$0.111590\pi$
$191$			9.49269i			0.686867i	−0.939177	+	0.343433i	$0.888410\pi$
$192$		0			0
$193$	−4.70473	−	4.70473i	−0.338654	−	0.338654i	0.517207	−	0.855861i	$-0.326972\pi$
$193$	−4.70473	−	4.70473i	−0.338654	−	0.338654i	−0.855861	+	0.517207i	$0.826972\pi$
$194$		0			0
$195$	5.48582	+	6.52694i	0.392848	+	0.467404i
$196$		0			0
$197$	−13.2304	−	13.2304i	−0.942629	−	0.942629i	0.0558125	−	0.998441i	$-0.482225\pi$
$197$	−13.2304	−	13.2304i	−0.942629	−	0.942629i	−0.998441	+	0.0558125i	$0.982225\pi$
$198$		0			0
$199$	−2.89962			−0.205549			−0.102774	−	0.994705i	$-0.532772\pi$
$199$	−2.89962			−0.205549			−0.102774	+	0.994705i	$0.532772\pi$
$200$		0			0
$201$	5.85732	−	5.85732i	0.413143	−	0.413143i
$202$		0			0
$203$	−11.2495	−	11.2495i	−0.789561	−	0.789561i
$204$		0			0
$205$	4.07562			0.284654
$206$		0			0
$207$	−2.14814			−0.149306
$208$		0			0
$209$	0.615862			0.0426001
$210$		0			0
$211$	−23.3268			−1.60588			−0.802942	−	0.596057i	$-0.796733\pi$
$211$	−23.3268			−1.60588			−0.802942	+	0.596057i	$0.796733\pi$
$212$		0			0
$213$	−5.33062	−	5.33062i	−0.365248	−	0.365248i
$214$		0			0
$215$	11.1078	−	11.1078i	0.757544	−	0.757544i
$216$		0			0
$217$	−2.69177			−0.182729
$218$		0			0
$219$	−5.90017	−	5.90017i	−0.398696	−	0.398696i
$220$		0			0
$221$	−0.921151	+	10.6286i	−0.0619633	+	0.714955i
$222$		0			0
$223$	18.2336	+	18.2336i	1.22101	+	1.22101i	0.967274	+	0.253736i	$0.0816594\pi$
$223$	18.2336	+	18.2336i	1.22101	+	1.22101i	0.253736	+	0.967274i	$0.418341\pi$
$224$		0			0
$225$			0.591934i			0.0394623i
$226$		0			0
$227$	−2.94277	+	2.94277i	−0.195319	+	0.195319i	−0.797990	−	0.602671i	$-0.794103\pi$
$227$	−2.94277	+	2.94277i	−0.195319	+	0.195319i	0.602671	+	0.797990i	$0.294103\pi$
$228$		0			0
$229$	2.08468	−	2.08468i	0.137759	−	0.137759i	−0.634864	−	0.772624i	$-0.718944\pi$
$229$	2.08468	−	2.08468i	0.137759	−	0.137759i	0.772624	+	0.634864i	$0.218944\pi$
$230$		0			0
$231$	0.909421			0.0598355
$232$		0			0
$233$		−	16.1555i		−	1.05838i	−0.848502	−	0.529191i	$-0.822495\pi$
$233$		−	16.1555i		−	1.05838i	0.848502	−	0.529191i	$-0.177505\pi$
$234$		0			0
$235$	17.3826			1.13391
$236$		0			0
$237$			1.82465i			0.118524i
$238$		0			0
$239$	11.3906	+	11.3906i	0.736799	+	0.736799i	0.971957	−	0.235158i	$-0.0755607\pi$
$239$	11.3906	+	11.3906i	0.736799	+	0.736799i	−0.235158	+	0.971957i	$0.575561\pi$
$240$		0			0
$241$	8.56378	+	8.56378i	0.551642	+	0.551642i	0.926914	−	0.375273i	$-0.122451\pi$
$241$	8.56378	+	8.56378i	0.551642	+	0.551642i	−0.375273	+	0.926914i	$0.622451\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	7.20386	−	7.20386i	0.460238	−	0.460238i
$246$		0			0
$247$	−3.06666	+	2.57749i	−0.195127	+	0.164002i
$248$		0			0
$249$	−3.29212	+	3.29212i	−0.208630	+	0.208630i
$250$		0			0
$251$		−	1.13387i		−	0.0715692i	−0.999360	−	0.0357846i	$-0.988607\pi$
$251$		−	1.13387i		−	0.0715692i	0.999360	−	0.0357846i	$-0.0113930\pi$
$252$		0			0
$253$	−0.841964	−	0.841964i	−0.0529338	−	0.0529338i
$254$		0			0
$255$	−4.94759	+	4.94759i	−0.309830	+	0.309830i
$256$		0			0
$257$		−	11.6824i		−	0.728728i	−0.931257	−	0.364364i	$-0.881286\pi$
$257$		−	11.6824i		−	0.728728i	0.931257	−	0.364364i	$-0.118714\pi$
$258$		0			0
$259$		−	4.35220i		−	0.270433i
$260$		0			0
$261$		−	9.69684i		−	0.600219i
$262$		0			0
$263$			2.49816i			0.154043i	0.997029	+	0.0770214i	$0.0245410\pi$
$263$			2.49816i			0.154043i	−0.997029	+	0.0770214i	$0.975459\pi$
$264$		0			0
$265$	−23.3268	+	23.3268i	−1.43296	+	1.43296i
$266$		0			0
$267$	−7.48582	−	7.48582i	−0.458125	−	0.458125i
$268$		0			0
$269$			17.3767i			1.05948i	0.848161	+	0.529739i	$0.177710\pi$
$269$			17.3767i			1.05948i	−0.848161	+	0.529739i	$0.822290\pi$
$270$		0			0
$271$	−19.5790	+	19.5790i	−1.18934	+	1.18934i	−0.212089	+	0.977250i	$0.568027\pi$
$271$	−19.5790	+	19.5790i	−1.18934	+	1.18934i	−0.977250	+	0.212089i	$0.931973\pi$
$272$		0			0
$273$	−4.52842	+	3.80609i	−0.274073	+	0.230355i
$274$		0			0
$275$	−0.232009	+	0.232009i	−0.0139907	+	0.0139907i
$276$		0			0
$277$	28.2035			1.69459			0.847293	−	0.531126i	$-0.178231\pi$
$277$	28.2035			1.69459			0.847293	+	0.531126i	$0.178231\pi$
$278$		0			0
$279$	−1.16012	−	1.16012i	−0.0694547	−	0.0694547i
$280$		0			0
$281$	−6.00608	−	6.00608i	−0.358292	−	0.358292i	0.504891	−	0.863183i	$-0.331533\pi$
$281$	−6.00608	−	6.00608i	−0.358292	−	0.358292i	−0.863183	+	0.504891i	$0.831533\pi$
$282$		0			0
$283$			29.1306i			1.73164i	0.500359	+	0.865818i	$0.333201\pi$
$283$			29.1306i			1.73164i	−0.500359	+	0.865818i	$0.666799\pi$
$284$		0			0
$285$	−2.62735			−0.155631
$286$		0			0
$287$			2.82769i			0.166913i
$288$		0			0
$289$	8.24500			0.485000
$290$		0			0
$291$	4.94128	−	4.94128i	0.289663	−	0.289663i
$292$		0			0
$293$	5.43420	−	5.43420i	0.317469	−	0.317469i	−0.530325	−	0.847794i	$-0.677930\pi$
$293$	5.43420	−	5.43420i	0.317469	−	0.317469i	0.847794	+	0.530325i	$0.177930\pi$
$294$		0			0
$295$			29.6412i			1.72578i
$296$		0			0
$297$	0.391951	+	0.391951i	0.0227433	+	0.0227433i
$298$		0			0
$299$	7.71630	+	0.668752i	0.446245	+	0.0386749i
$300$		0			0
$301$	7.70664	+	7.70664i	0.444203	+	0.444203i
$302$		0			0
$303$	2.09896			0.120582
$304$		0			0
$305$	9.66341	−	9.66341i	0.553325	−	0.553325i
$306$		0			0
$307$	−11.4314	−	11.4314i	−0.652427	−	0.652427i	0.301150	−	0.953577i	$-0.402630\pi$
$307$	−11.4314	−	11.4314i	−0.652427	−	0.652427i	−0.953577	+	0.301150i	$0.902630\pi$
$308$		0			0
$309$	15.6849			0.892284
$310$		0			0
$311$	−16.2544			−0.921700			−0.460850	−	0.887478i	$-0.652455\pi$
$311$	−16.2544			−0.921700			−0.460850	+	0.887478i	$0.652455\pi$
$312$		0			0
$313$	19.1736			1.08376			0.541878	−	0.840457i	$-0.317713\pi$
$313$	19.1736			1.08376			0.541878	+	0.840457i	$0.317713\pi$
$314$		0			0
$315$	−3.87971			−0.218597
$316$		0			0
$317$	6.77764	+	6.77764i	0.380670	+	0.380670i	0.871344	−	0.490673i	$-0.163249\pi$
$317$	6.77764	+	6.77764i	0.380670	+	0.380670i	−0.490673	+	0.871344i	$0.663249\pi$
$318$		0			0
$319$	3.80068	−	3.80068i	0.212797	−	0.212797i
$320$		0			0
$321$	11.8062			0.658956
$322$		0			0
$323$	−2.32461	−	2.32461i	−0.129345	−	0.129345i
$324$		0			0
$325$	0.184279	−	2.12628i	0.0102220	−	0.117945i
$326$		0			0
$327$	9.84874	+	9.84874i	0.544637	+	0.544637i
$328$		0			0
$329$			12.0601i			0.664896i
$330$		0			0
$331$	13.9517	−	13.9517i	0.766855	−	0.766855i	−0.210697	−	0.977551i	$-0.567573\pi$
$331$	13.9517	−	13.9517i	0.766855	−	0.766855i	0.977551	+	0.210697i	$0.0675732\pi$
$332$		0			0
$333$	1.87575	−	1.87575i	0.102791	−	0.102791i
$334$		0			0
$335$	−19.5882			−1.07022
$336$		0			0
$337$		−	20.3092i		−	1.10631i	−0.833077	−	0.553157i	$-0.813423\pi$
$337$		−	20.3092i		−	1.10631i	0.833077	−	0.553157i	$-0.186577\pi$
$338$		0			0
$339$	9.39629			0.510336
$340$		0			0
$341$		−	0.909421i		−	0.0492479i
$342$		0			0
$343$	13.1189	+	13.1189i	0.708356	+	0.708356i
$344$		0			0
$345$	3.59193	+	3.59193i	0.193383	+	0.193383i
$346$		0			0
$347$	−18.8537			−1.01212			−0.506060	−	0.862498i	$-0.668899\pi$
$347$	−18.8537			−1.01212			−0.506060	+	0.862498i	$0.668899\pi$
$348$		0			0
$349$	4.93319	−	4.93319i	0.264068	−	0.264068i	−0.562637	−	0.826704i	$-0.690213\pi$
$349$	4.93319	−	4.93319i	0.264068	−	0.264068i	0.826704	+	0.562637i	$0.190213\pi$
$350$		0			0
$351$	−3.59209	−	0.311317i	−0.191731	−	0.0166169i
$352$		0			0
$353$	−15.4858	+	15.4858i	−0.824227	+	0.824227i	−0.986711	−	0.162484i	$-0.948049\pi$
$353$	−15.4858	+	15.4858i	−0.824227	+	0.824227i	0.162484	+	0.986711i	$0.448049\pi$
$354$		0			0
$355$			17.8268i			0.946150i
$356$		0			0
$357$	−3.43267	−	3.43267i	−0.181676	−	0.181676i
$358$		0			0
$359$	12.6928	−	12.6928i	0.669902	−	0.669902i	−0.287791	−	0.957693i	$-0.592921\pi$
$359$	12.6928	−	12.6928i	0.669902	−	0.669902i	0.957693	+	0.287791i	$0.0929210\pi$
$360$		0			0
$361$			17.7655i			0.935029i
$362$		0			0
$363$		−	10.6927i		−	0.561224i
$364$		0			0
$365$			19.7315i			1.03279i
$366$		0			0
$367$			1.60603i			0.0838342i	0.999121	+	0.0419171i	$0.0133465\pi$
$367$			1.60603i			0.0838342i	−0.999121	+	0.0419171i	$0.986653\pi$
$368$		0			0
$369$	−1.21870	+	1.21870i	−0.0634431	+	0.0634431i
$370$		0			0
$371$	−16.1843	−	16.1843i	−0.840245	−	0.840245i
$372$		0			0
$373$		−	12.5988i		−	0.652341i	−0.945311	−	0.326170i	$-0.894242\pi$
$373$		−	12.5988i		−	0.652341i	0.945311	−	0.326170i	$-0.105758\pi$
$374$		0			0
$375$	−7.37079	+	7.37079i	−0.380626	+	0.380626i
$376$		0			0
$377$	−3.01879	+	34.8319i	−0.155476	+	1.79393i
$378$		0			0
$379$	−3.97178	+	3.97178i	−0.204017	+	0.204017i	−0.801718	−	0.597702i	$-0.796081\pi$
$379$	−3.97178	+	3.97178i	−0.204017	+	0.204017i	0.597702	+	0.801718i	$0.296081\pi$
$380$		0			0
$381$	4.36241			0.223493
$382$		0			0
$383$	24.1673	+	24.1673i	1.23489	+	1.23489i	0.962062	+	0.272832i	$0.0879604\pi$
$383$	24.1673	+	24.1673i	1.23489	+	1.23489i	0.272832	+	0.962062i	$0.412040\pi$
$384$		0			0
$385$	−1.52066	−	1.52066i	−0.0774998	−	0.0774998i
$386$		0			0
$387$			6.64295i			0.337680i
$388$		0			0
$389$	19.5120			0.989298			0.494649	−	0.869093i	$-0.335297\pi$
$389$	19.5120			0.989298			0.494649	+	0.869093i	$0.335297\pi$
$390$		0			0
$391$			6.35610i			0.321442i
$392$		0			0
$393$	20.5049			1.03433
$394$		0			0
$395$	3.05102	−	3.05102i	0.153513	−	0.153513i
$396$		0			0
$397$	−12.4820	+	12.4820i	−0.626454	+	0.626454i	−0.947174	−	0.320720i	$-0.896075\pi$
$397$	−12.4820	+	12.4820i	−0.626454	+	0.626454i	0.320720	+	0.947174i	$0.396075\pi$
$398$		0			0
$399$		−	1.82287i		−	0.0912576i
$400$		0			0
$401$	−5.08810	−	5.08810i	−0.254088	−	0.254088i	0.568557	−	0.822644i	$-0.307502\pi$
$401$	−5.08810	−	5.08810i	−0.254088	−	0.254088i	−0.822644	+	0.568557i	$0.807502\pi$
$402$		0			0
$403$	3.80609	+	4.52842i	0.189595	+	0.225577i
$404$		0			0
$405$	−1.67211	−	1.67211i	−0.0830880	−	0.0830880i
$406$		0			0
$407$	1.47040			0.0728852
$408$		0			0
$409$	18.2904	−	18.2904i	0.904403	−	0.904403i	−0.0914099	−	0.995813i	$-0.529137\pi$
$409$	18.2904	−	18.2904i	0.904403	−	0.904403i	0.995813	+	0.0914099i	$0.0291373\pi$
$410$		0			0
$411$	9.80009	+	9.80009i	0.483403	+	0.483403i
$412$		0			0
$413$	−20.5652			−1.01195
$414$		0			0
$415$	11.0096			0.540440
$416$		0			0
$417$	3.50388			0.171586
$418$		0			0
$419$	19.2388			0.939875			0.469938	−	0.882700i	$-0.344276\pi$
$419$	19.2388			0.939875			0.469938	+	0.882700i	$0.344276\pi$
$420$		0			0
$421$	−22.4944	−	22.4944i	−1.09631	−	1.09631i	−0.994839	−	0.101471i	$-0.967645\pi$
$421$	−22.4944	−	22.4944i	−1.09631	−	1.09631i	−0.101471	−	0.994839i	$-0.532355\pi$
$422$		0			0
$423$	−5.19778	+	5.19778i	−0.252725	+	0.252725i
$424$		0			0
$425$	1.75147			0.0849586
$426$		0			0
$427$	6.70452	+	6.70452i	0.324455	+	0.324455i
$428$		0			0
$429$	−1.28590	−	1.52994i	−0.0620838	−	0.0738662i
$430$		0			0
$431$	−23.8969	−	23.8969i	−1.15107	−	1.15107i	−0.986338	−	0.164735i	$-0.947323\pi$
$431$	−23.8969	−	23.8969i	−1.15107	−	1.15107i	−0.164735	−	0.986338i	$-0.552677\pi$
$432$		0			0
$433$		−	33.4534i		−	1.60767i	−0.594854	−	0.803834i	$-0.702790\pi$
$433$		−	33.4534i		−	1.60767i	0.594854	−	0.803834i	$-0.297210\pi$
$434$		0			0
$435$	−16.2142	+	16.2142i	−0.777413	+	0.777413i
$436$		0			0
$437$	−1.68766	+	1.68766i	−0.0807316	+	0.0807316i
$438$		0			0
$439$	2.89421			0.138133			0.0690665	−	0.997612i	$-0.477998\pi$
$439$	2.89421			0.138133			0.0690665	+	0.997612i	$0.477998\pi$
$440$		0			0
$441$			4.30823i			0.205154i
$442$		0			0
$443$	19.6887			0.935440			0.467720	−	0.883877i	$-0.345076\pi$
$443$	19.6887			0.935440			0.467720	+	0.883877i	$0.345076\pi$
$444$		0			0
$445$			25.0343i			1.18674i
$446$		0			0
$447$	3.27548	+	3.27548i	0.154925	+	0.154925i
$448$		0			0
$449$	−13.5405	−	13.5405i	−0.639017	−	0.639017i	0.311296	−	0.950313i	$-0.399237\pi$
$449$	−13.5405	−	13.5405i	−0.639017	−	0.639017i	−0.950313	+	0.311296i	$0.899237\pi$
$450$		0			0
$451$	−0.955342			−0.0449853
$452$		0			0
$453$	−7.01121	+	7.01121i	−0.329416	+	0.329416i
$454$		0			0
$455$	13.9363	+	1.20782i	0.653342	+	0.0566235i
$456$		0			0
$457$	−3.88236	+	3.88236i	−0.181609	+	0.181609i	−0.792057	−	0.610447i	$-0.790990\pi$
$457$	−3.88236	+	3.88236i	−0.181609	+	0.181609i	0.610447	+	0.792057i	$0.290990\pi$
$458$		0			0
$459$		−	2.95889i		−	0.138109i
$460$		0			0
$461$	17.4455	+	17.4455i	0.812517	+	0.812517i	0.985011	−	0.172494i	$-0.0551825\pi$
$461$	17.4455	+	17.4455i	0.812517	+	0.812517i	−0.172494	+	0.985011i	$0.555182\pi$
$462$		0			0
$463$	30.0459	−	30.0459i	1.39635	−	1.39635i	0.586140	−	0.810210i	$-0.300647\pi$
$463$	30.0459	−	30.0459i	1.39635	−	1.39635i	0.810210	−	0.586140i	$-0.199353\pi$
$464$		0			0
$465$			3.87971i			0.179917i
$466$		0			0
$467$			8.61820i			0.398803i	0.979918	+	0.199401i	$0.0638998\pi$
$467$			8.61820i			0.398803i	−0.979918	+	0.199401i	$0.936100\pi$
$468$		0			0
$469$		−	13.5904i		−	0.627547i
$470$		0			0
$471$			23.5918i			1.08705i
$472$		0			0
$473$	−2.60371	+	2.60371i	−0.119719	+	0.119719i
$474$		0			0
$475$	0.465046	+	0.465046i	0.0213378	+	0.0213378i
$476$		0			0
$477$		−	13.9505i		−	0.638749i
$478$		0			0
$479$	4.53008	−	4.53008i	0.206985	−	0.206985i	−0.596000	−	0.802984i	$-0.703244\pi$
$479$	4.53008	−	4.53008i	0.206985	−	0.206985i	0.802984	+	0.596000i	$0.203244\pi$
$480$		0			0
$481$	−7.32182	+	6.15391i	−0.333846	+	0.280594i
$482$		0			0
$483$	−2.49210	+	2.49210i	−0.113395	+	0.113395i
$484$		0			0
$485$	−16.5248			−0.750352
$486$		0			0
$487$	−14.1789	−	14.1789i	−0.642507	−	0.642507i	0.308664	−	0.951171i	$-0.400118\pi$
$487$	−14.1789	−	14.1789i	−0.642507	−	0.642507i	−0.951171	+	0.308664i	$0.900118\pi$
$488$		0			0
$489$	−14.2947	−	14.2947i	−0.646430	−	0.646430i
$490$		0			0
$491$			19.7677i			0.892104i	0.895007	+	0.446052i	$0.147170\pi$
$491$			19.7677i			0.892104i	−0.895007	+	0.446052i	$0.852830\pi$
$492$		0			0
$493$	−28.6918			−1.29222
$494$		0			0
$495$		−	1.31077i		−	0.0589148i
$496$		0			0
$497$	−12.3683			−0.554796
$498$		0			0
$499$	14.8709	−	14.8709i	0.665713	−	0.665713i	−0.291008	−	0.956721i	$-0.593991\pi$
$499$	14.8709	−	14.8709i	0.665713	−	0.665713i	0.956721	+	0.291008i	$0.0939906\pi$
$500$		0			0
$501$	9.66616	−	9.66616i	0.431852	−	0.431852i
$502$		0			0
$503$		−	30.0549i		−	1.34008i	−0.742324	−	0.670041i	$-0.766276\pi$
$503$		−	30.0549i		−	1.34008i	0.742324	−	0.670041i	$-0.233724\pi$
$504$		0			0
$505$	−3.50970	−	3.50970i	−0.156180	−	0.156180i
$506$		0			0
$507$	12.8062	+	2.23655i	0.568742	+	0.0993288i
$508$		0			0
$509$	−0.547453	−	0.547453i	−0.0242654	−	0.0242654i	0.694870	−	0.719135i	$-0.255462\pi$
$509$	−0.547453	−	0.547453i	−0.0242654	−	0.0242654i	−0.719135	+	0.694870i	$0.755462\pi$
$510$		0			0
$511$	−13.6898			−0.605602
$512$		0			0
$513$	0.785637	−	0.785637i	0.0346867	−	0.0346867i
$514$		0			0
$515$	−26.2270	−	26.2270i	−1.15570	−	1.15570i
$516$		0			0
$517$	−4.07454			−0.179198
$518$		0			0
$519$	−4.90900			−0.215481
$520$		0			0
$521$	10.9111			0.478025			0.239012	−	0.971017i	$-0.423176\pi$
$521$	10.9111			0.478025			0.239012	+	0.971017i	$0.423176\pi$
$522$		0			0
$523$	−36.6897			−1.60433			−0.802165	−	0.597103i	$-0.796318\pi$
$523$	−36.6897			−1.60433			−0.802165	+	0.597103i	$0.796318\pi$
$524$		0			0
$525$	0.686716	+	0.686716i	0.0299707	+	0.0299707i
$526$		0			0
$527$	−3.43267	+	3.43267i	−0.149529	+	0.149529i
$528$		0			0
$529$	−18.3855			−0.799370
$530$		0			0
$531$	−8.86339	−	8.86339i	−0.384639	−	0.384639i
$532$		0			0
$533$	4.75709	−	3.99828i	0.206052	−	0.173185i
$534$		0			0
$535$	−19.7413	−	19.7413i	−0.853489	−	0.853489i
$536$		0			0
$537$			15.4884i			0.668375i
$538$		0			0
$539$	−1.68861	+	1.68861i	−0.0727338	+	0.0727338i
$540$		0			0
$541$	−2.29349	+	2.29349i	−0.0986047	+	0.0986047i	−0.754688	−	0.656084i	$-0.772212\pi$
$541$	−2.29349	+	2.29349i	−0.0986047	+	0.0986047i	0.656084	+	0.754688i	$0.272212\pi$
$542$		0			0
$543$	13.7660			0.590757
$544$		0			0
$545$		−	32.9364i		−	1.41084i
$546$		0			0
$547$	29.3860			1.25646			0.628228	−	0.778029i	$-0.283780\pi$
$547$	29.3860			1.25646			0.628228	+	0.778029i	$0.283780\pi$
$548$		0			0
$549$			5.77916i			0.246648i
$550$		0			0
$551$	−7.61820	−	7.61820i	−0.324546	−	0.324546i
$552$		0			0
$553$	2.11681	+	2.11681i	0.0900161	+	0.0900161i
$554$		0			0
$555$	−6.27295			−0.266272
$556$		0			0
$557$	15.4424	−	15.4424i	0.654316	−	0.654316i	−0.299713	−	0.954029i	$-0.596891\pi$
$557$	15.4424	−	15.4424i	0.654316	−	0.654316i	0.954029	+	0.299713i	$0.0968910\pi$
$558$		0			0
$559$	2.06806	−	23.8621i	0.0874698	−	1.00926i
$560$		0			0
$561$	1.15974	−	1.15974i	0.0489641	−	0.0489641i
$562$		0			0
$563$			28.2354i			1.18998i	0.803733	+	0.594990i	$0.202844\pi$
$563$			28.2354i			1.18998i	−0.803733	+	0.594990i	$0.797156\pi$
$564$		0			0
$565$	−15.7117	−	15.7117i	−0.660995	−	0.660995i
$566$		0			0
$567$	1.16012	−	1.16012i	0.0487205	−	0.0487205i
$568$		0			0
$569$		−	8.54680i		−	0.358301i	−0.983822	−	0.179150i	$-0.942665\pi$
$569$		−	8.54680i		−	0.358301i	0.983822	−	0.179150i	$-0.0573348\pi$
$570$		0			0
$571$		−	37.8236i		−	1.58287i	−0.611254	−	0.791435i	$-0.709335\pi$
$571$		−	37.8236i		−	1.58287i	0.611254	−	0.791435i	$-0.290665\pi$
$572$		0			0
$573$			9.49269i			0.396563i
$574$		0			0
$575$		−	1.27156i		−	0.0530276i
$576$		0			0
$577$	−14.3094	+	14.3094i	−0.595709	+	0.595709i	−0.939168	−	0.343459i	$-0.888401\pi$
$577$	−14.3094	+	14.3094i	−0.595709	+	0.595709i	0.343459	+	0.939168i	$0.388401\pi$
$578$		0			0
$579$	−4.70473	−	4.70473i	−0.195522	−	0.195522i
$580$		0			0
$581$			7.63852i			0.316899i
$582$		0			0
$583$	5.46790	−	5.46790i	0.226457	−	0.226457i
$584$		0			0
$585$	5.48582	+	6.52694i	0.226811	+	0.269856i
$586$		0			0
$587$	−5.61673	+	5.61673i	−0.231827	+	0.231827i	−0.813455	−	0.581628i	$-0.802416\pi$
$587$	−5.61673	+	5.61673i	−0.231827	+	0.231827i	0.581628	+	0.813455i	$0.302416\pi$
$588$		0			0
$589$	−1.82287			−0.0751100
$590$		0			0
$591$	−13.2304	−	13.2304i	−0.544227	−	0.544227i
$592$		0			0
$593$	9.10077	+	9.10077i	0.373724	+	0.373724i	0.868832	−	0.495108i	$-0.164871\pi$
$593$	9.10077	+	9.10077i	0.373724	+	0.373724i	−0.495108	+	0.868832i	$0.664871\pi$
$594$		0			0
$595$			11.4796i			0.470619i
$596$		0			0
$597$	−2.89962			−0.118674
$598$		0			0
$599$		−	22.5156i		−	0.919962i	−0.887929	−	0.459981i	$-0.847856\pi$
$599$		−	22.5156i		−	0.919962i	0.887929	−	0.459981i	$-0.152144\pi$
$600$		0			0
$601$	6.23544			0.254349			0.127174	−	0.991880i	$-0.459409\pi$
$601$	6.23544			0.254349			0.127174	+	0.991880i	$0.459409\pi$
$602$		0			0
$603$	5.85732	−	5.85732i	0.238528	−	0.238528i
$604$		0			0
$605$	−17.8795	+	17.8795i	−0.726905	+	0.726905i
$606$		0			0
$607$		−	46.7547i		−	1.89772i	−0.315704	−	0.948858i	$-0.602241\pi$
$607$		−	46.7547i		−	1.89772i	0.315704	−	0.948858i	$-0.397759\pi$
$608$		0			0
$609$	−11.2495	−	11.2495i	−0.455853	−	0.455853i
$610$		0			0
$611$	20.2890	−	17.0527i	0.820806	−	0.689879i
$612$		0			0
$613$	−13.4628	−	13.4628i	−0.543757	−	0.543757i	0.380871	−	0.924628i	$-0.375624\pi$
$613$	−13.4628	−	13.4628i	−0.543757	−	0.543757i	−0.924628	+	0.380871i	$0.875624\pi$
$614$		0			0
$615$	4.07562			0.164345
$616$		0			0
$617$	13.6695	−	13.6695i	0.550313	−	0.550313i	−0.376218	−	0.926531i	$-0.622776\pi$
$617$	13.6695	−	13.6695i	0.550313	−	0.550313i	0.926531	+	0.376218i	$0.122776\pi$
$618$		0			0
$619$	−11.8988	−	11.8988i	−0.478255	−	0.478255i	0.426318	−	0.904573i	$-0.359810\pi$
$619$	−11.8988	−	11.8988i	−0.478255	−	0.478255i	−0.904573	+	0.426318i	$0.859810\pi$
$620$		0			0
$621$	−2.14814			−0.0862018
$622$		0			0
$623$	−17.3689			−0.695872
$624$		0			0
$625$	27.6093			1.10437
$626$		0			0
$627$	0.615862			0.0245952
$628$		0			0
$629$	−5.55014	−	5.55014i	−0.221298	−	0.221298i
$630$		0			0
$631$	−11.8137	+	11.8137i	−0.470295	+	0.470295i	−0.902010	−	0.431715i	$-0.857909\pi$
$631$	−11.8137	+	11.8137i	−0.470295	+	0.470295i	0.431715	+	0.902010i	$0.357909\pi$
$632$		0			0
$633$	−23.3268			−0.927158
$634$		0			0
$635$	−7.29445	−	7.29445i	−0.289471	−	0.289471i
$636$		0			0
$637$	1.34123	−	15.4755i	0.0531413	−	0.613164i
$638$		0			0
$639$	−5.33062	−	5.33062i	−0.210876	−	0.210876i
$640$		0			0
$641$			12.0489i			0.475902i	0.971277	+	0.237951i	$0.0764757\pi$
$641$			12.0489i			0.475902i	−0.971277	+	0.237951i	$0.923524\pi$
$642$		0			0
$643$	28.4624	−	28.4624i	1.12245	−	1.12245i	0.131076	−	0.991372i	$-0.458157\pi$
$643$	28.4624	−	28.4624i	1.12245	−	1.12245i	0.991372	−	0.131076i	$-0.0418432\pi$
$644$		0			0
$645$	11.1078	−	11.1078i	0.437368	−	0.437368i
$646$		0			0
$647$	−9.55223			−0.375537			−0.187768	−	0.982213i	$-0.560125\pi$
$647$	−9.55223			−0.375537			−0.187768	+	0.982213i	$0.560125\pi$
$648$		0			0
$649$		−	6.94802i		−	0.272734i
$650$		0			0
$651$	−2.69177			−0.105499
$652$		0			0
$653$			21.6730i			0.848130i	0.905632	+	0.424065i	$0.139397\pi$
$653$			21.6730i			0.848130i	−0.905632	+	0.424065i	$0.860603\pi$
$654$		0			0
$655$	−34.2865	−	34.2865i	−1.33968	−	1.33968i
$656$		0			0
$657$	−5.90017	−	5.90017i	−0.230188	−	0.230188i
$658$		0			0
$659$	12.1786			0.474409			0.237205	−	0.971460i	$-0.423769\pi$
$659$	12.1786			0.474409			0.237205	+	0.971460i	$0.423769\pi$
$660$		0			0
$661$	−16.9361	+	16.9361i	−0.658738	+	0.658738i	−0.955082	−	0.296343i	$-0.904233\pi$
$661$	−16.9361	+	16.9361i	−0.658738	+	0.658738i	0.296343	+	0.955082i	$0.404233\pi$
$662$		0			0
$663$	−0.921151	+	10.6286i	−0.0357745	+	0.412779i
$664$		0			0
$665$	−3.04805	+	3.04805i	−0.118198	+	0.118198i
$666$		0			0
$667$			20.8302i			0.806547i
$668$		0			0
$669$	18.2336	+	18.2336i	0.704950	+	0.704950i
$670$		0			0
$671$	−2.26514	+	2.26514i	−0.0874449	+	0.0874449i
$672$		0			0
$673$			31.5099i			1.21462i	0.794466	+	0.607308i	$0.207751\pi$
$673$			31.5099i			1.21462i	−0.794466	+	0.607308i	$0.792249\pi$
$674$		0			0
$675$			0.591934i			0.0227836i
$676$		0			0
$677$		−	32.9475i		−	1.26627i	−0.774040	−	0.633137i	$-0.781767\pi$
$677$		−	32.9475i		−	1.26627i	0.774040	−	0.633137i	$-0.218233\pi$
$678$		0			0
$679$		−	11.4650i		−	0.439986i
$680$		0			0
$681$	−2.94277	+	2.94277i	−0.112767	+	0.112767i
$682$		0			0
$683$	12.5106	+	12.5106i	0.478704	+	0.478704i	0.904717	−	0.426013i	$-0.140082\pi$
$683$	12.5106	+	12.5106i	0.478704	+	0.478704i	−0.426013	+	0.904717i	$0.640082\pi$
$684$		0			0
$685$		−	32.7737i		−	1.25222i
$686$		0			0
$687$	2.08468	−	2.08468i	0.0795355	−	0.0795355i
$688$		0			0
$689$	−4.34302	+	50.1114i	−0.165456	+	1.90909i
$690$		0			0
$691$	−36.4803	+	36.4803i	−1.38777	+	1.38777i	−0.557797	+	0.829978i	$0.688353\pi$
$691$	−36.4803	+	36.4803i	−1.38777	+	1.38777i	−0.829978	+	0.557797i	$0.811647\pi$
$692$		0			0
$693$	0.909421			0.0345460
$694$		0			0
$695$	−5.85889	−	5.85889i	−0.222240	−	0.222240i
$696$		0			0
$697$	3.60600	+	3.60600i	0.136587	+	0.136587i
$698$		0			0
$699$		−	16.1555i		−	0.611058i
$700$		0			0
$701$	−41.5365			−1.56881			−0.784407	−	0.620247i	$-0.787033\pi$
$701$	−41.5365			−1.56881			−0.784407	+	0.620247i	$0.787033\pi$
$702$		0			0
$703$		−	2.94732i		−	0.111160i
$704$		0			0
$705$	17.3826			0.654665
$706$		0			0
$707$	2.43505	−	2.43505i	0.0915795	−	0.0915795i
$708$		0			0
$709$	26.1966	−	26.1966i	0.983834	−	0.983834i	−0.0160378	−	0.999871i	$-0.505105\pi$
$709$	26.1966	−	26.1966i	0.983834	−	0.983834i	0.999871	+	0.0160378i	$0.00510519\pi$
$710$		0			0
$711$			1.82465i			0.0684296i
$712$		0			0
$713$	2.49210	+	2.49210i	0.0933300	+	0.0933300i
$714$		0			0
$715$	−0.408066	+	4.70841i	−0.0152608	+	0.176084i
$716$		0			0
$717$	11.3906	+	11.3906i	0.425391	+	0.425391i
$718$		0			0
$719$	−1.99265			−0.0743134			−0.0371567	−	0.999309i	$-0.511830\pi$
$719$	−1.99265			−0.0743134			−0.0371567	+	0.999309i	$0.511830\pi$
$720$		0			0
$721$	18.1964	−	18.1964i	0.677670	−	0.677670i
$722$		0			0
$723$	8.56378	+	8.56378i	0.318491	+	0.318491i
$724$		0			0
$725$	5.73989			0.213174
$726$		0			0
$727$	−18.2357			−0.676325			−0.338162	−	0.941088i	$-0.609805\pi$
$727$	−18.2357			−0.676325			−0.338162	+	0.941088i	$0.609805\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	19.6557			0.726994
$732$		0			0
$733$	−18.4701	−	18.4701i	−0.682209	−	0.682209i	0.278289	−	0.960497i	$-0.410233\pi$
$733$	−18.4701	−	18.4701i	−0.682209	−	0.682209i	−0.960497	+	0.278289i	$0.910233\pi$
$734$		0			0
$735$	7.20386	−	7.20386i	0.265718	−	0.265718i
$736$		0			0
$737$	4.59156			0.169132
$738$		0			0
$739$	17.9656	+	17.9656i	0.660876	+	0.660876i	0.955587	−	0.294710i	$-0.0952232\pi$
$739$	17.9656	+	17.9656i	0.660876	+	0.660876i	−0.294710	+	0.955587i	$0.595223\pi$
$740$		0			0
$741$	−3.06666	+	2.57749i	−0.112657	+	0.0946866i
$742$		0			0
$743$	18.0076	+	18.0076i	0.660635	+	0.660635i	0.955530	−	0.294895i	$-0.0952845\pi$
$743$	18.0076	+	18.0076i	0.660635	+	0.660635i	−0.294895	+	0.955530i	$0.595285\pi$
$744$		0			0
$745$		−	10.9540i		−	0.401322i
$746$		0			0
$747$	−3.29212	+	3.29212i	−0.120452	+	0.120452i
$748$		0			0
$749$	13.6966	−	13.6966i	0.500462	−	0.500462i
$750$		0			0
$751$	−42.4965			−1.55072			−0.775359	−	0.631521i	$-0.782431\pi$
$751$	−42.4965			−1.55072			−0.775359	+	0.631521i	$0.782431\pi$
$752$		0			0
$753$		−	1.13387i		−	0.0413205i
$754$		0			0
$755$	23.4471			0.853328
$756$		0			0
$757$		−	16.7233i		−	0.607817i	−0.952701	−	0.303908i	$-0.901708\pi$
$757$		−	16.7233i		−	0.607817i	0.952701	−	0.303908i	$-0.0982917\pi$
$758$		0			0
$759$	−0.841964	−	0.841964i	−0.0305614	−	0.0305614i
$760$		0			0
$761$	−1.74539	−	1.74539i	−0.0632703	−	0.0632703i	0.674764	−	0.738034i	$-0.264246\pi$
$761$	−1.74539	−	1.74539i	−0.0632703	−	0.0632703i	−0.738034	+	0.674764i	$0.764246\pi$
$762$		0			0
$763$	22.8515			0.827279
$764$		0			0
$765$	−4.94759	+	4.94759i	−0.178881	+	0.178881i
$766$		0			0
$767$	29.0787	+	34.5974i	1.04997	+	1.24924i
$768$		0			0
$769$	−6.50326	+	6.50326i	−0.234514	+	0.234514i	−0.814574	−	0.580060i	$-0.803029\pi$
$769$	−6.50326	+	6.50326i	−0.234514	+	0.234514i	0.580060	+	0.814574i	$0.303029\pi$
$770$		0			0
$771$		−	11.6824i		−	0.420732i
$772$		0			0
$773$	−10.4555	−	10.4555i	−0.376058	−	0.376058i	0.493620	−	0.869678i	$-0.335674\pi$
$773$	−10.4555	−	10.4555i	−0.376058	−	0.376058i	−0.869678	+	0.493620i	$0.835674\pi$
$774$		0			0
$775$	0.686716	−	0.686716i	0.0246676	−	0.0246676i
$776$		0			0
$777$		−	4.35220i		−	0.156134i
$778$		0			0
$779$			1.91492i			0.0686090i
$780$		0			0
$781$		−	4.17868i		−	0.149525i
$782$		0			0
$783$		−	9.69684i		−	0.346537i
$784$		0			0
$785$	39.4482	−	39.4482i	1.40797	−	1.40797i
$786$		0			0
$787$	−5.07056	−	5.07056i	−0.180746	−	0.180746i	0.610935	−	0.791681i	$-0.290794\pi$
$787$	−5.07056	−	5.07056i	−0.180746	−	0.180746i	−0.791681	+	0.610935i	$0.790794\pi$
$788$		0			0
$789$			2.49816i			0.0889367i
$790$		0			0
$791$	10.9008	−	10.9008i	0.387589	−	0.387589i
$792$		0			0
$793$	1.79915	−	20.7592i	0.0638896	−	0.737182i
$794$		0			0
$795$	−23.3268	+	23.3268i	−0.827317	+	0.827317i
$796$		0			0
$797$	24.5139			0.868327			0.434163	−	0.900834i	$-0.357044\pi$
$797$	24.5139			0.868327			0.434163	+	0.900834i	$0.357044\pi$
$798$		0			0
$799$	15.3796	+	15.3796i	0.544092	+	0.544092i
$800$		0			0
$801$	−7.48582	−	7.48582i	−0.264499	−	0.264499i
$802$		0			0
$803$		−	4.62515i		−	0.163218i
$804$		0			0
$805$	8.33416			0.293741
$806$		0			0
$807$			17.3767i			0.611690i
$808$		0			0
$809$	25.7049			0.903738			0.451869	−	0.892084i	$-0.350758\pi$
$809$	25.7049			0.903738			0.451869	+	0.892084i	$0.350758\pi$
$810$		0			0
$811$	−5.86079	+	5.86079i	−0.205800	+	0.205800i	−0.802480	−	0.596679i	$-0.796486\pi$
$811$	−5.86079	+	5.86079i	−0.205800	+	0.205800i	0.596679	+	0.802480i	$0.296486\pi$
$812$		0			0
$813$	−19.5790	+	19.5790i	−0.686665	+	0.686665i
$814$		0			0
$815$			47.8048i			1.67453i
$816$		0			0
$817$	5.21895	+	5.21895i	0.182588	+	0.182588i
$818$		0			0
$819$	−4.52842	+	3.80609i	−0.158236	+	0.132996i
$820$		0			0
$821$	4.28711	+	4.28711i	0.149621	+	0.149621i	0.777949	−	0.628328i	$-0.216260\pi$
$821$	4.28711	+	4.28711i	0.149621	+	0.149621i	−0.628328	+	0.777949i	$0.716260\pi$
$822$		0			0
$823$	−7.17762			−0.250196			−0.125098	−	0.992144i	$-0.539925\pi$
$823$	−7.17762			−0.250196			−0.125098	+	0.992144i	$0.539925\pi$
$824$		0			0
$825$	−0.232009	+	0.232009i	−0.00807752	+	0.00807752i
$826$		0			0
$827$	−29.8057	−	29.8057i	−1.03644	−	1.03644i	−0.999310	−	0.0371341i	$-0.988177\pi$
$827$	−29.8057	−	29.8057i	−1.03644	−	1.03644i	−0.0371341	−	0.999310i	$-0.511823\pi$
$828$		0			0
$829$	−16.9928			−0.590184			−0.295092	−	0.955469i	$-0.595350\pi$
$829$	−16.9928			−0.590184			−0.295092	+	0.955469i	$0.595350\pi$
$830$		0			0
$831$	28.2035			0.978370
$832$		0			0
$833$	12.7476			0.441677
$834$		0			0
$835$	−32.3259			−1.11868
$836$		0			0
$837$	−1.16012	−	1.16012i	−0.0400997	−	0.0400997i
$838$		0			0
$839$	7.08206	−	7.08206i	0.244500	−	0.244500i	−0.574209	−	0.818709i	$-0.694690\pi$
$839$	7.08206	−	7.08206i	0.244500	−	0.244500i	0.818709	+	0.574209i	$0.194690\pi$
$840$		0			0
$841$	−65.0287			−2.24237
$842$		0			0
$843$	−6.00608	−	6.00608i	−0.206860	−	0.206860i
$844$		0			0
$845$	−17.6736	−	25.1531i	−0.607990	−	0.865295i
$846$		0			0
$847$	−12.4049	−	12.4049i	−0.426237	−	0.426237i
$848$		0			0
$849$			29.1306i			0.999761i
$850$		0			0
$851$	−4.02938	+	4.02938i	−0.138125	+	0.138125i
$852$		0			0
$853$	27.2045	−	27.2045i	0.931464	−	0.931464i	−0.0663337	−	0.997797i	$-0.521130\pi$
$853$	27.2045	−	27.2045i	0.931464	−	0.931464i	0.997797	+	0.0663337i	$0.0211302\pi$
$854$		0			0
$855$	−2.62735			−0.0898535
$856$		0			0
$857$		−	28.0509i		−	0.958202i	−0.877760	−	0.479101i	$-0.840963\pi$
$857$		−	28.0509i		−	0.958202i	0.877760	−	0.479101i	$-0.159037\pi$
$858$		0			0
$859$	13.4573			0.459158			0.229579	−	0.973290i	$-0.426265\pi$
$859$	13.4573			0.459158			0.229579	+	0.973290i	$0.426265\pi$
$860$		0			0
$861$			2.82769i			0.0963673i
$862$		0			0
$863$	−7.81239	−	7.81239i	−0.265937	−	0.265937i	0.561524	−	0.827461i	$-0.310215\pi$
$863$	−7.81239	−	7.81239i	−0.265937	−	0.265937i	−0.827461	+	0.561524i	$0.810215\pi$
$864$		0			0
$865$	8.20840	+	8.20840i	0.279094	+	0.279094i
$866$		0			0
$867$	8.24500			0.280015
$868$		0			0
$869$	−0.715172	+	0.715172i	−0.0242605	+	0.0242605i
$870$		0			0
$871$	−22.8635	+	19.2165i	−0.774699	+	0.651126i
$872$		0			0
$873$	4.94128	−	4.94128i	0.167237	−	0.167237i
$874$		0			0
$875$			17.1020i			0.578154i
$876$		0			0
$877$	11.8817	+	11.8817i	0.401216	+	0.401216i	0.878661	−	0.477445i	$-0.158437\pi$
$877$	11.8817	+	11.8817i	0.401216	+	0.401216i	−0.477445	+	0.878661i	$0.658437\pi$
$878$		0			0
$879$	5.43420	−	5.43420i	0.183291	−	0.183291i
$880$		0			0
$881$			20.0497i			0.675493i	0.941237	+	0.337746i	$0.109665\pi$
$881$			20.0497i			0.675493i	−0.941237	+	0.337746i	$0.890335\pi$
$882$		0			0
$883$		−	32.1521i		−	1.08201i	−0.841021	−	0.541003i	$-0.818045\pi$
$883$		−	32.1521i		−	1.08201i	0.841021	−	0.541003i	$-0.181955\pi$
$884$		0			0
$885$			29.6412i			0.996379i
$886$		0			0
$887$			36.2082i			1.21575i	0.794032	+	0.607876i	$0.207978\pi$
$887$			36.2082i			1.21575i	−0.794032	+	0.607876i	$0.792022\pi$
$888$		0			0
$889$	5.06093	−	5.06093i	0.169738	−	0.169738i
$890$		0			0
$891$	0.391951	+	0.391951i	0.0131308	+	0.0131308i
$892$		0			0
$893$			8.16714i			0.273303i
$894$		0			0
$895$	25.8984	−	25.8984i	0.865689	−	0.865689i
$896$		0			0
$897$	7.71630	+	0.668752i	0.257640	+	0.0223290i
$898$		0			0
$899$	−11.2495	+	11.2495i	−0.375192	+	0.375192i
$900$		0			0
$901$	−41.2779			−1.37517
$902$		0			0
$903$	7.70664	+	7.70664i	0.256461	+	0.256461i
$904$		0			0
$905$	−23.0184	−	23.0184i	−0.765157	−	0.765157i
$906$		0			0
$907$		−	22.5108i		−	0.747460i	−0.927538	−	0.373730i	$-0.878079\pi$
$907$		−	22.5108i		−	0.747460i	0.927538	−	0.373730i	$-0.121921\pi$
$908$		0			0
$909$	2.09896			0.0696182
$910$		0			0
$911$			42.8030i			1.41813i	0.705146	+	0.709063i	$0.250882\pi$
$911$			42.8030i			1.41813i	−0.705146	+	0.709063i	$0.749118\pi$
$912$		0			0
$913$	−2.58070			−0.0854086
$914$		0			0
$915$	9.66341	−	9.66341i	0.319462	−	0.319462i
$916$		0			0
$917$	23.7881	−	23.7881i	0.785554	−	0.785554i
$918$		0			0
$919$		−	3.91723i		−	0.129218i	−0.997911	−	0.0646088i	$-0.979420\pi$
$919$		−	3.91723i		−	0.129218i	0.997911	−	0.0646088i	$-0.0205800\pi$
$920$		0			0
$921$	−11.4314	−	11.4314i	−0.376679	−	0.376679i
$922$		0			0
$923$	17.4885	+	20.8076i	0.575642	+	0.684889i
$924$		0			0
$925$	1.11032	+	1.11032i	0.0365072	+	0.0365072i
$926$		0			0
$927$	15.6849			0.515160
$928$		0			0
$929$	−16.9835	+	16.9835i	−0.557212	+	0.557212i	−0.928513	−	0.371301i	$-0.878912\pi$
$929$	−16.9835	+	16.9835i	−0.557212	+	0.557212i	0.371301	+	0.928513i	$0.378912\pi$
$930$		0			0
$931$	3.38471	+	3.38471i	0.110929	+	0.110929i
$932$		0			0
$933$	−16.2544			−0.532144
$934$		0			0
$935$	−3.87842			−0.126838
$936$		0			0
$937$	16.7414			0.546919			0.273459	−	0.961884i	$-0.411832\pi$
$937$	16.7414			0.546919			0.273459	+	0.961884i	$0.411832\pi$
$938$		0			0
$939$	19.1736			0.625707
$940$		0			0
$941$	30.5678	+	30.5678i	0.996481	+	0.996481i	0.999994	−	0.00351291i	$-0.00111820\pi$
$941$	30.5678	+	30.5678i	0.996481	+	0.996481i	−0.00351291	+	0.999994i	$0.501118\pi$
$942$		0			0
$943$	2.61794	−	2.61794i	0.0852519	−	0.0852519i
$944$		0			0
$945$	−3.87971			−0.126207
$946$		0			0
$947$	−34.2563	−	34.2563i	−1.11318	−	1.11318i	−0.992718	−	0.120461i	$-0.961563\pi$
$947$	−34.2563	−	34.2563i	−1.11318	−	1.11318i	−0.120461	−	0.992718i	$-0.538437\pi$
$948$		0			0
$949$	19.3571	+	23.0307i	0.628358	+	0.747609i
$950$		0			0
$951$	6.77764	+	6.77764i	0.219780	+	0.219780i
$952$		0			0
$953$			14.8870i			0.482236i	0.970496	+	0.241118i	$0.0775141\pi$
$953$			14.8870i			0.482236i	−0.970496	+	0.241118i	$0.922486\pi$
$954$		0			0
$955$	15.8729	−	15.8729i	0.513634	−	0.513634i
$956$		0			0
$957$	3.80068	−	3.80068i	0.122859	−	0.122859i
$958$		0			0
$959$	22.7386			0.734267
$960$		0			0
$961$		−	28.3082i		−	0.913169i
$962$		0			0
$963$	11.8062			0.380448
$964$		0			0
$965$			15.7337i			0.506486i
$966$		0			0
$967$	3.08494	+	3.08494i	0.0992049	+	0.0992049i	0.754967	−	0.655762i	$-0.227653\pi$
$967$	3.08494	+	3.08494i	0.0992049	+	0.0992049i	−0.655762	+	0.754967i	$0.727653\pi$
$968$		0			0
$969$	−2.32461	−	2.32461i	−0.0746772	−	0.0746772i
$970$		0			0
$971$	−40.4168			−1.29704			−0.648519	−	0.761199i	$-0.724611\pi$
$971$	−40.4168			−1.29704			−0.648519	+	0.761199i	$0.724611\pi$
$972$		0			0
$973$	4.06493	−	4.06493i	0.130316	−	0.130316i
$974$		0			0
$975$	0.184279	−	2.12628i	0.00590166	−	0.0680954i
$976$		0			0
$977$	−40.2981	+	40.2981i	−1.28925	+	1.28925i	−0.354008	+	0.935242i	$0.615182\pi$
$977$	−40.2981	+	40.2981i	−1.28925	+	1.28925i	−0.935242	+	0.354008i	$0.884818\pi$
$978$		0			0
$979$		−	5.86814i		−	0.187547i
$980$		0			0
$981$	9.84874	+	9.84874i	0.314446	+	0.314446i
$982$		0			0
$983$	−4.02628	+	4.02628i	−0.128418	+	0.128418i	−0.768395	−	0.639976i	$-0.778944\pi$
$983$	−4.02628	+	4.02628i	−0.128418	+	0.128418i	0.639976	+	0.768395i	$0.278944\pi$
$984$		0			0
$985$			44.2456i			1.40978i
$986$		0			0
$987$			12.0601i			0.383878i
$988$		0			0
$989$		−	14.2700i		−	0.453759i
$990$		0			0
$991$		−	17.6322i		−	0.560104i	−0.959985	−	0.280052i	$-0.909648\pi$
$991$		−	17.6322i		−	0.560104i	0.959985	−	0.280052i	$-0.0903517\pi$
$992$		0			0
$993$	13.9517	−	13.9517i	0.442744	−	0.442744i
$994$		0			0
$995$	4.84850	+	4.84850i	0.153708	+	0.153708i
$996$		0			0
$997$		−	0.131010i		−	0.00414912i	−0.999998	−	0.00207456i	$-0.999340\pi$
$997$		−	0.131010i		−	0.00414912i	0.999998	−	0.00207456i	$-0.000660353\pi$
$998$		0			0
$999$	1.87575	−	1.87575i	0.0593462	−	0.0593462i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1248.2.bb.f.655.3		24
4.3	odd	2		312.2.t.e.187.9	✓	24
8.3	odd	2	inner	1248.2.bb.f.655.10		24
8.5	even	2		312.2.t.e.187.10	yes	24
12.11	even	2		936.2.w.j.811.4		24
13.8	odd	4	inner	1248.2.bb.f.463.10		24
24.5	odd	2		936.2.w.j.811.3		24
52.47	even	4		312.2.t.e.307.10	yes	24
104.21	odd	4		312.2.t.e.307.9	yes	24
104.99	even	4	inner	1248.2.bb.f.463.3		24
156.47	odd	4		936.2.w.j.307.3		24
312.125	even	4		936.2.w.j.307.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.t.e.187.9	✓	24	4.3	odd	2
312.2.t.e.187.10	yes	24	8.5	even	2
312.2.t.e.307.9	yes	24	104.21	odd	4
312.2.t.e.307.10	yes	24	52.47	even	4
936.2.w.j.307.3		24	156.47	odd	4
936.2.w.j.307.4		24	312.125	even	4
936.2.w.j.811.3		24	24.5	odd	2
936.2.w.j.811.4		24	12.11	even	2
1248.2.bb.f.463.3		24	104.99	even	4	inner
1248.2.bb.f.463.10		24	13.8	odd	4	inner
1248.2.bb.f.655.3		24	1.1	even	1	trivial
1248.2.bb.f.655.10		24	8.3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1248.bb (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +(-1.67211 - 1.67211i) q^{5} +(1.16012 - 1.16012i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} +(-1.67211 - 1.67211i) q^{5} +(1.16012 - 1.16012i) q^{7} +1.00000 q^{9} +(0.391951 + 0.391951i) q^{11} +(-3.59209 - 0.311317i) q^{13} +(-1.67211 - 1.67211i) q^{15} -2.95889i q^{17} +(0.785637 - 0.785637i) q^{19} +(1.16012 - 1.16012i) q^{21} -2.14814 q^{23} +0.591934i q^{25} +1.00000 q^{27} -9.69684i q^{29} +(-1.16012 - 1.16012i) q^{31} +(0.391951 + 0.391951i) q^{33} -3.87971 q^{35} +(1.87575 - 1.87575i) q^{37} +(-3.59209 - 0.311317i) q^{39} +(-1.21870 + 1.21870i) q^{41} +6.64295i q^{43} +(-1.67211 - 1.67211i) q^{45} +(-5.19778 + 5.19778i) q^{47} +4.30823i q^{49} -2.95889i q^{51} -13.9505i q^{53} -1.31077i q^{55} +(0.785637 - 0.785637i) q^{57} +(-8.86339 - 8.86339i) q^{59} +5.77916i q^{61} +(1.16012 - 1.16012i) q^{63} +(5.48582 + 6.52694i) q^{65} +(5.85732 - 5.85732i) q^{67} -2.14814 q^{69} +(-5.33062 - 5.33062i) q^{71} +(-5.90017 - 5.90017i) q^{73} +0.591934i q^{75} +0.909421 q^{77} +1.82465i q^{79} +1.00000 q^{81} +(-3.29212 + 3.29212i) q^{83} +(-4.94759 + 4.94759i) q^{85} -9.69684i q^{87} +(-7.48582 - 7.48582i) q^{89} +(-4.52842 + 3.80609i) q^{91} +(-1.16012 - 1.16012i) q^{93} -2.62735 q^{95} +(4.94128 - 4.94128i) q^{97} +(0.391951 + 0.391951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{3} + 24 q^{9}+O(q^{10}) \) 24 * q + 24 * q^3 + 24 * q^9	\( 24 q + 24 q^{3} + 24 q^{9} - 8 q^{11} - 20 q^{19} + 24 q^{27} - 8 q^{33} - 16 q^{35} - 12 q^{41} - 20 q^{57} + 16 q^{59} - 76 q^{65} - 28 q^{67} - 8 q^{73} + 24 q^{81} + 72 q^{83} + 28 q^{89} + 4 q^{91} + 24 q^{97} - 8 q^{99}+O(q^{100}) \) 24 * q + 24 * q^3 + 24 * q^9 - 8 * q^11 - 20 * q^19 + 24 * q^27 - 8 * q^33 - 16 * q^35 - 12 * q^41 - 20 * q^57 + 16 * q^59 - 76 * q^65 - 28 * q^67 - 8 * q^73 + 24 * q^81 + 72 * q^83 + 28 * q^89 + 4 * q^91 + 24 * q^97 - 8 * q^99

Introduction

L-functions

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