LMFDB - Embedded newform 128.2.g.b.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,2,Mod(17,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("128.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	128.g (of order $8$, degree $4$, 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:	$1.02208514587$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			81.1
Root			$0.500000 - 0.0297061i$ of defining polynomial
Character	$\chi$	$=$	128.81
Dual form			128.2.g.b.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.27882 - 0.529706i) q^{3} +(-0.707107 - 1.70711i) q^{5} +(2.74912 - 2.74912i) q^{7} +(-0.766519 - 0.766519i) q^{9} +(-0.135390 + 0.0560803i) q^{11} +(1.18073 - 2.85054i) q^{13} +2.55765i q^{15} +6.44549i q^{17} +(-0.805198 + 1.94392i) q^{19} +(-4.97186 + 2.05941i) q^{21} +(-0.749118 - 0.749118i) q^{23} +(1.12132 - 1.12132i) q^{25} +(2.16333 + 5.22274i) q^{27} +(4.32417 + 1.79113i) q^{29} -1.17157 q^{31} +0.202846 q^{33} +(-6.63696 - 2.74912i) q^{35} +(1.73172 + 4.18073i) q^{37} +(-3.01990 + 3.01990i) q^{39} +(-2.49824 - 2.49824i) q^{41} +(6.10725 - 2.52971i) q^{43} +(-0.766519 + 1.85054i) q^{45} +2.66981i q^{47} -8.11529i q^{49} +(3.41421 - 8.24264i) q^{51} +(1.64769 - 0.682497i) q^{53} +(0.191470 + 0.191470i) q^{55} +(2.05941 - 2.05941i) q^{57} +(-1.43744 - 3.47029i) q^{59} +(-3.46760 - 1.43633i) q^{61} -4.21450 q^{63} -5.70108 q^{65} +(14.0791 + 5.83176i) q^{67} +(0.561177 + 1.35480i) q^{69} +(3.40950 - 3.40950i) q^{71} +(-0.442353 - 0.442353i) q^{73} +(-2.02794 + 0.840001i) q^{75} +(-0.218031 + 0.526374i) q^{77} -7.07550i q^{79} -4.57283i q^{81} +(-2.99862 + 7.23931i) q^{83} +(11.0031 - 4.55765i) q^{85} +(-4.58107 - 4.58107i) q^{87} +(-4.21803 + 4.21803i) q^{89} +(-4.59050 - 11.0824i) q^{91} +(1.49824 + 0.620589i) q^{93} +3.88784 q^{95} +10.3267 q^{97} +(0.146766 + 0.0607923i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 8 q^{7} - 4 q^{11} - 8 q^{13} - 4 q^{19} + 8 q^{23} - 8 q^{25} - 8 q^{27} - 32 q^{31} - 16 q^{33} - 16 q^{35} - 8 q^{37} - 16 q^{39} + 8 q^{41} + 12 q^{43} + 16 q^{51} + 8 q^{53} + 16 q^{55}+ \cdots - 28 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 + 8 * q^7 - 4 * q^11 - 8 * q^13 - 4 * q^19 + 8 * q^23 - 8 * q^25 - 8 * q^27 - 32 * q^31 - 16 * q^33 - 16 * q^35 - 8 * q^37 - 16 * q^39 + 8 * q^41 + 12 * q^43 + 16 * q^51 + 8 * q^53 + 16 * q^55 + 16 * q^57 + 20 * q^59 + 24 * q^61 + 40 * q^63 + 36 * q^67 + 32 * q^69 + 24 * q^71 - 32 * q^73 + 12 * q^75 + 16 * q^77 - 20 * q^83 + 8 * q^85 - 56 * q^87 - 16 * q^89 - 40 * q^91 - 16 * q^93 + 8 * q^95 + 32 * q^97 - 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$

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
$3$	−1.27882	−	0.529706i	−0.738329	−	0.305826i	−0.0183595	−	0.999831i	$-0.505844\pi$
$3$	−1.27882	−	0.529706i	−0.738329	−	0.305826i	−0.719970	+	0.694005i	$0.755844\pi$
$4$		0			0
$5$	−0.707107	−	1.70711i	−0.316228	−	0.763441i	−0.999448	−	0.0332288i	$-0.989421\pi$
$5$	−0.707107	−	1.70711i	−0.316228	−	0.763441i	0.683220	−	0.730213i	$-0.260579\pi$
$6$		0			0
$7$	2.74912	−	2.74912i	1.03907	−	1.03907i	0.0398636	−	0.999205i	$-0.487308\pi$
$7$	2.74912	−	2.74912i	1.03907	−	1.03907i	0.999205	−	0.0398636i	$-0.0126924\pi$
$8$		0			0
$9$	−0.766519	−	0.766519i	−0.255506	−	0.255506i
$10$		0			0
$11$	−0.135390	+	0.0560803i	−0.0408216	+	0.0169089i	−0.403001	−	0.915200i	$-0.632033\pi$
$11$	−0.135390	+	0.0560803i	−0.0408216	+	0.0169089i	0.362179	+	0.932108i	$0.382033\pi$
$12$		0			0
$13$	1.18073	−	2.85054i	0.327476	−	0.790598i	−0.671302	−	0.741184i	$-0.734265\pi$
$13$	1.18073	−	2.85054i	0.327476	−	0.790598i	0.998778	−	0.0494138i	$-0.0157353\pi$
$14$		0			0
$15$			2.55765i			0.660382i
$16$		0			0
$17$			6.44549i			1.56326i	0.623742	+	0.781630i	$0.285611\pi$
$17$			6.44549i			1.56326i	−0.623742	+	0.781630i	$0.714389\pi$
$18$		0			0
$19$	−0.805198	+	1.94392i	−0.184725	+	0.445966i	−0.988929	−	0.148387i	$-0.952592\pi$
$19$	−0.805198	+	1.94392i	−0.184725	+	0.445966i	0.804204	+	0.594353i	$0.202592\pi$
$20$		0			0
$21$	−4.97186	+	2.05941i	−1.08495	+	0.449401i
$22$		0			0
$23$	−0.749118	−	0.749118i	−0.156202	−	0.156202i	0.624679	−	0.780881i	$-0.285230\pi$
$23$	−0.749118	−	0.749118i	−0.156202	−	0.156202i	−0.780881	+	0.624679i	$0.785230\pi$
$24$		0			0
$25$	1.12132	−	1.12132i	0.224264	−	0.224264i
$26$		0			0
$27$	2.16333	+	5.22274i	0.416333	+	1.00512i
$28$		0			0
$29$	4.32417	+	1.79113i	0.802978	+	0.332604i	0.746148	−	0.665780i	$-0.231901\pi$
$29$	4.32417	+	1.79113i	0.802978	+	0.332604i	0.0568292	+	0.998384i	$0.481901\pi$
$30$		0			0
$31$	−1.17157			−0.210421			−0.105210	−	0.994450i	$-0.533552\pi$
$31$	−1.17157			−0.210421			−0.105210	+	0.994450i	$0.533552\pi$
$32$		0			0
$33$	0.202846			0.0353109
$34$		0			0
$35$	−6.63696	−	2.74912i	−1.12185	−	0.464686i
$36$		0			0
$37$	1.73172	+	4.18073i	0.284692	+	0.687308i	0.999933	−	0.0115700i	$-0.00368293\pi$
$37$	1.73172	+	4.18073i	0.284692	+	0.687308i	−0.715241	+	0.698878i	$0.753683\pi$
$38$		0			0
$39$	−3.01990	+	3.01990i	−0.483571	+	0.483571i
$40$		0			0
$41$	−2.49824	−	2.49824i	−0.390159	−	0.390159i	0.484585	−	0.874744i	$-0.338971\pi$
$41$	−2.49824	−	2.49824i	−0.390159	−	0.390159i	−0.874744	+	0.484585i	$0.838971\pi$
$42$		0			0
$43$	6.10725	−	2.52971i	0.931347	−	0.385777i	0.135158	−	0.990824i	$-0.456846\pi$
$43$	6.10725	−	2.52971i	0.931347	−	0.385777i	0.796189	+	0.605048i	$0.206846\pi$
$44$		0			0
$45$	−0.766519	+	1.85054i	−0.114266	+	0.275862i
$46$		0			0
$47$			2.66981i			0.389432i	0.980860	+	0.194716i	$0.0623784\pi$
$47$			2.66981i			0.389432i	−0.980860	+	0.194716i	$0.937622\pi$
$48$		0			0
$49$		−	8.11529i		−	1.15933i
$50$		0			0
$51$	3.41421	−	8.24264i	0.478086	−	1.15420i
$52$		0			0
$53$	1.64769	−	0.682497i	0.226328	−	0.0937482i	−0.266638	−	0.963797i	$-0.585913\pi$
$53$	1.64769	−	0.682497i	0.226328	−	0.0937482i	0.492966	+	0.870049i	$0.335913\pi$
$54$		0			0
$55$	0.191470	+	0.191470i	0.0258178	+	0.0258178i
$56$		0			0
$57$	2.05941	−	2.05941i	0.272776	−	0.272776i
$58$		0			0
$59$	−1.43744	−	3.47029i	−0.187139	−	0.451794i	0.802267	−	0.596965i	$-0.203627\pi$
$59$	−1.43744	−	3.47029i	−0.187139	−	0.451794i	−0.989407	+	0.145171i	$0.953627\pi$
$60$		0			0
$61$	−3.46760	−	1.43633i	−0.443981	−	0.183903i	0.149482	−	0.988764i	$-0.452239\pi$
$61$	−3.46760	−	1.43633i	−0.443981	−	0.183903i	−0.593462	+	0.804862i	$0.702239\pi$
$62$		0			0
$63$	−4.21450			−0.530977
$64$		0			0
$65$	−5.70108			−0.707132
$66$		0			0
$67$	14.0791	+	5.83176i	1.72004	+	0.712463i	0.999825	+	0.0187090i	$0.00595560\pi$
$67$	14.0791	+	5.83176i	1.72004	+	0.712463i	0.720212	+	0.693754i	$0.244044\pi$
$68$		0			0
$69$	0.561177	+	1.35480i	0.0675578	+	0.163099i
$70$		0			0
$71$	3.40950	−	3.40950i	0.404633	−	0.404633i	−0.475229	−	0.879862i	$-0.657635\pi$
$71$	3.40950	−	3.40950i	0.404633	−	0.404633i	0.879862	+	0.475229i	$0.157635\pi$
$72$		0			0
$73$	−0.442353	−	0.442353i	−0.0517735	−	0.0517735i	0.680746	−	0.732520i	$-0.261656\pi$
$73$	−0.442353	−	0.442353i	−0.0517735	−	0.0517735i	−0.732520	+	0.680746i	$0.761656\pi$
$74$		0			0
$75$	−2.02794	+	0.840001i	−0.234166	+	0.0969949i
$76$		0			0
$77$	−0.218031	+	0.526374i	−0.0248470	+	0.0599859i
$78$		0			0
$79$		−	7.07550i		−	0.796056i	−0.917373	−	0.398028i	$-0.869695\pi$
$79$		−	7.07550i		−	0.796056i	0.917373	−	0.398028i	$-0.130305\pi$
$80$		0			0
$81$		−	4.57283i		−	0.508093i
$82$		0			0
$83$	−2.99862	+	7.23931i	−0.329141	+	0.794617i	0.669515	+	0.742798i	$0.266502\pi$
$83$	−2.99862	+	7.23931i	−0.329141	+	0.794617i	−0.998656	+	0.0518190i	$0.983498\pi$
$84$		0			0
$85$	11.0031	−	4.55765i	1.19346	−	0.494346i
$86$		0			0
$87$	−4.58107	−	4.58107i	−0.491143	−	0.491143i
$88$		0			0
$89$	−4.21803	+	4.21803i	−0.447110	+	0.447110i	−0.894393	−	0.447282i	$-0.852392\pi$
$89$	−4.21803	+	4.21803i	−0.447110	+	0.447110i	0.447282	+	0.894393i	$0.352392\pi$
$90$		0			0
$91$	−4.59050	−	11.0824i	−0.481215	−	1.16176i
$92$		0			0
$93$	1.49824	+	0.620589i	0.155360	+	0.0643521i
$94$		0			0
$95$	3.88784			0.398884
$96$		0			0
$97$	10.3267			1.04851			0.524257	−	0.851560i	$-0.324343\pi$
$97$	10.3267			1.04851			0.524257	+	0.851560i	$0.324343\pi$
$98$		0			0
$99$	0.146766	+	0.0607923i	0.0147505	+	0.00610986i
$100$		0			0
$101$	−4.31750	−	10.4234i	−0.429608	−	1.03716i	−0.979412	−	0.201871i	$-0.935298\pi$
$101$	−4.31750	−	10.4234i	−0.429608	−	1.03716i	0.549805	−	0.835293i	$-0.314702\pi$
$102$		0			0
$103$	−13.3134	+	13.3134i	−1.31181	+	1.31181i	−0.391732	+	0.920080i	$0.628124\pi$
$103$	−13.3134	+	13.3134i	−1.31181	+	1.31181i	−0.920080	+	0.391732i	$0.871876\pi$
$104$		0			0
$105$	7.03127	+	7.03127i	0.686182	+	0.686182i
$106$		0			0
$107$	−13.2507	+	5.48861i	−1.28099	+	0.530604i	−0.916288	−	0.400519i	$-0.868830\pi$
$107$	−13.2507	+	5.48861i	−1.28099	+	0.530604i	−0.364704	+	0.931124i	$0.618830\pi$
$108$		0			0
$109$	−4.87515	+	11.7697i	−0.466955	+	1.12733i	0.498531	+	0.866872i	$0.333873\pi$
$109$	−4.87515	+	11.7697i	−0.466955	+	1.12733i	−0.965486	+	0.260456i	$0.916127\pi$
$110$		0			0
$111$		−	6.26372i		−	0.594526i
$112$		0			0
$113$			5.88118i			0.553254i	0.960977	+	0.276627i	$0.0892167\pi$
$113$			5.88118i			0.553254i	−0.960977	+	0.276627i	$0.910783\pi$
$114$		0			0
$115$	−0.749118	+	1.80853i	−0.0698556	+	0.168646i
$116$		0			0
$117$	−3.09005	+	1.27994i	−0.285675	+	0.118330i
$118$		0			0
$119$	17.7194	+	17.7194i	1.62433	+	1.62433i
$120$		0			0
$121$	−7.76299	+	7.76299i	−0.705726	+	0.705726i
$122$		0			0
$123$	1.87147	+	4.51813i	0.168745	+	0.407386i
$124$		0			0
$125$	−11.2426	−	4.65685i	−1.00557	−	0.416522i
$126$		0			0
$127$	15.4022			1.36672			0.683360	−	0.730081i	$-0.260518\pi$
$127$	15.4022			1.36672			0.683360	+	0.730081i	$0.260518\pi$
$128$		0			0
$129$	−9.15010			−0.805621
$130$		0			0
$131$	2.96382	+	1.22765i	0.258950	+	0.107261i	0.508382	−	0.861132i	$-0.330244\pi$
$131$	2.96382	+	1.22765i	0.258950	+	0.107261i	−0.249432	+	0.968392i	$0.580244\pi$
$132$		0			0
$133$	3.13048	+	7.55765i	0.271447	+	0.655331i
$134$		0			0
$135$	7.38607	−	7.38607i	0.635692	−	0.635692i
$136$		0			0
$137$	10.7757	+	10.7757i	0.920628	+	0.920628i	0.997074	−	0.0764454i	$-0.0243571\pi$
$137$	10.7757	+	10.7757i	0.920628	+	0.920628i	−0.0764454	+	0.997074i	$0.524357\pi$
$138$		0			0
$139$	−4.78372	+	1.98148i	−0.405750	+	0.168067i	−0.576218	−	0.817296i	$-0.695472\pi$
$139$	−4.78372	+	1.98148i	−0.405750	+	0.168067i	0.170468	+	0.985363i	$0.445472\pi$
$140$		0			0
$141$	1.41421	−	3.41421i	0.119098	−	0.287529i
$142$		0			0
$143$			0.452150i			0.0378107i
$144$		0			0
$145$		−	8.64833i		−	0.718205i
$146$		0			0
$147$	−4.29872	+	10.3780i	−0.354553	+	0.855966i
$148$		0			0
$149$	4.32417	−	1.79113i	0.354250	−	0.146735i	−0.198460	−	0.980109i	$-0.563594\pi$
$149$	4.32417	−	1.79113i	0.354250	−	0.146735i	0.552709	+	0.833374i	$0.313594\pi$
$150$		0			0
$151$	−13.2344	−	13.2344i	−1.07700	−	1.07700i	−0.996777	−	0.0802232i	$-0.974437\pi$
$151$	−13.2344	−	13.2344i	−1.07700	−	1.07700i	−0.0802232	−	0.996777i	$-0.525563\pi$
$152$		0			0
$153$	4.94059	−	4.94059i	0.399423	−	0.399423i
$154$		0			0
$155$	0.828427	+	2.00000i	0.0665409	+	0.160644i
$156$		0			0
$157$	−15.9529	−	6.60790i	−1.27318	−	0.527368i	−0.359249	−	0.933242i	$-0.616967\pi$
$157$	−15.9529	−	6.60790i	−1.27318	−	0.527368i	−0.913929	+	0.405874i	$0.866967\pi$
$158$		0			0
$159$	−2.46863			−0.195775
$160$		0			0
$161$	−4.11882			−0.324609
$162$		0			0
$163$	−10.6488	−	4.41088i	−0.834079	−	0.345487i	−0.0755629	−	0.997141i	$-0.524075\pi$
$163$	−10.6488	−	4.41088i	−0.834079	−	0.345487i	−0.758516	+	0.651654i	$0.774075\pi$
$164$		0			0
$165$	−0.143434	−	0.346280i	−0.0111663	−	0.0269578i
$166$		0			0
$167$	2.98677	−	2.98677i	0.231123	−	0.231123i	−0.582038	−	0.813161i	$-0.697745\pi$
$167$	2.98677	−	2.98677i	0.231123	−	0.231123i	0.813161	+	0.582038i	$0.197745\pi$
$168$		0			0
$169$	2.46094	+	2.46094i	0.189303	+	0.189303i
$170$		0			0
$171$	2.10725	−	0.872852i	0.161145	−	0.0667486i
$172$		0			0
$173$	7.85054	−	18.9529i	0.596866	−	1.44096i	−0.279894	−	0.960031i	$-0.590299\pi$
$173$	7.85054	−	18.9529i	0.596866	−	1.44096i	0.876759	−	0.480930i	$-0.159701\pi$
$174$		0			0
$175$		−	6.16528i		−	0.466052i
$176$		0			0
$177$			5.19932i			0.390805i
$178$		0			0
$179$	9.60549	−	23.1897i	0.717948	−	1.73328i	0.0388344	−	0.999246i	$-0.487636\pi$
$179$	9.60549	−	23.1897i	0.717948	−	1.73328i	0.679113	−	0.734033i	$-0.262364\pi$
$180$		0			0
$181$	1.87868	−	0.778175i	0.139641	−	0.0578413i	−0.311768	−	0.950158i	$-0.600921\pi$
$181$	1.87868	−	0.778175i	0.139641	−	0.0578413i	0.451410	+	0.892317i	$0.350921\pi$
$182$		0			0
$183$	3.67362	+	3.67362i	0.271562	+	0.271562i
$184$		0			0
$185$	5.91245	−	5.91245i	0.434692	−	0.434692i
$186$		0			0
$187$	−0.361465	−	0.872654i	−0.0264329	−	0.0638148i
$188$		0			0
$189$	20.3052	+	8.41068i	1.47699	+	0.611787i
$190$		0			0
$191$	−9.05902			−0.655487			−0.327744	−	0.944767i	$-0.606288\pi$
$191$	−9.05902			−0.655487			−0.327744	+	0.944767i	$0.606288\pi$
$192$		0			0
$193$	6.24707			0.449674			0.224837	−	0.974396i	$-0.427815\pi$
$193$	6.24707			0.449674			0.224837	+	0.974396i	$0.427815\pi$
$194$		0			0
$195$	7.29068	+	3.01990i	0.522096	+	0.216259i
$196$		0			0
$197$	−1.81298	−	4.37691i	−0.129169	−	0.311842i	0.846043	−	0.533115i	$-0.178979\pi$
$197$	−1.81298	−	4.37691i	−0.129169	−	0.311842i	−0.975212	+	0.221273i	$0.928979\pi$
$198$		0			0
$199$	−6.14186	+	6.14186i	−0.435385	+	0.435385i	−0.890455	−	0.455071i	$-0.849614\pi$
$199$	−6.14186	+	6.14186i	−0.435385	+	0.435385i	0.455071	+	0.890455i	$0.349614\pi$
$200$		0			0
$201$	−14.9156	−	14.9156i	−1.05206	−	1.05206i
$202$		0			0
$203$	16.8117	−	6.96362i	1.17995	−	0.488750i
$204$		0			0
$205$	−2.49824	+	6.03127i	−0.174484	+	0.421242i
$206$		0			0
$207$			1.14843i			0.0798211i
$208$		0			0
$209$		−	0.308343i		−	0.0213285i
$210$		0			0
$211$	−5.21588	+	12.5923i	−0.359076	+	0.866886i	0.636354	+	0.771397i	$0.280442\pi$
$211$	−5.21588	+	12.5923i	−0.359076	+	0.866886i	−0.995430	+	0.0954895i	$0.969558\pi$
$212$		0			0
$213$	−6.16619	+	2.55412i	−0.422500	+	0.175005i
$214$		0			0
$215$	−8.63696	−	8.63696i	−0.589036	−	0.589036i
$216$		0			0
$217$	−3.22079	+	3.22079i	−0.218642	+	0.218642i
$218$		0			0
$219$	0.331374	+	0.800008i	0.0223922	+	0.0540595i
$220$		0			0
$221$	18.3731	+	7.61040i	1.23591	+	0.511931i
$222$		0			0
$223$	0.960579			0.0643251			0.0321626	−	0.999483i	$-0.489761\pi$
$223$	0.960579			0.0643251			0.0321626	+	0.999483i	$0.489761\pi$
$224$		0			0
$225$	−1.71903			−0.114602
$226$		0			0
$227$	−14.1698	−	5.86932i	−0.940482	−	0.389561i	−0.140837	−	0.990033i	$-0.544979\pi$
$227$	−14.1698	−	5.86932i	−0.940482	−	0.389561i	−0.799646	+	0.600472i	$0.794979\pi$
$228$		0			0
$229$	1.80408	+	4.35544i	0.119217	+	0.287816i	0.972211	−	0.234105i	$-0.0752159\pi$
$229$	1.80408	+	4.35544i	0.119217	+	0.287816i	−0.852994	+	0.521920i	$0.825216\pi$
$230$		0			0
$231$	0.557647	−	0.557647i	0.0366905	−	0.0366905i
$232$		0			0
$233$	−16.7918	−	16.7918i	−1.10007	−	1.10007i	−0.994402	−	0.105663i	$-0.966303\pi$
$233$	−16.7918	−	16.7918i	−1.10007	−	1.10007i	−0.105663	−	0.994402i	$-0.533697\pi$
$234$		0			0
$235$	4.55765	−	1.88784i	0.297308	−	0.123149i
$236$		0			0
$237$	−3.74794	+	9.04832i	−0.243455	+	0.587751i
$238$		0			0
$239$			15.8414i			1.02469i	0.858779	+	0.512347i	$0.171224\pi$
$239$			15.8414i			1.02469i	−0.858779	+	0.512347i	$0.828776\pi$
$240$		0			0
$241$		−	0.313335i		−	0.0201837i	−0.999949	−	0.0100918i	$-0.996788\pi$
$241$		−	0.313335i		−	0.0201837i	0.999949	−	0.0100918i	$-0.00321239\pi$
$242$		0			0
$243$	4.06774	−	9.82038i	0.260945	−	0.629978i
$244$		0			0
$245$	−13.8537	+	5.73838i	−0.885079	+	0.366612i
$246$		0			0
$247$	4.59050	+	4.59050i	0.292086	+	0.292086i
$248$		0			0
$249$	7.66941	−	7.66941i	0.486029	−	0.486029i
$250$		0			0
$251$	3.55903	+	8.59225i	0.224644	+	0.542338i	0.995510	−	0.0946593i	$-0.0301762\pi$
$251$	3.55903	+	8.59225i	0.224644	+	0.542338i	−0.770866	+	0.636997i	$0.780176\pi$
$252$		0			0
$253$	0.143434	+	0.0594122i	0.00901760	+	0.00373521i
$254$		0			0
$255$	−16.4853			−1.03235
$256$		0			0
$257$	18.9043			1.17922			0.589609	−	0.807689i	$-0.299282\pi$
$257$	18.9043			1.17922			0.589609	+	0.807689i	$0.299282\pi$
$258$		0			0
$259$	16.2540	+	6.73263i	1.00998	+	0.418346i
$260$		0			0
$261$	−1.94162	−	4.68749i	−0.120183	−	0.290148i
$262$		0			0
$263$	16.6366	−	16.6366i	1.02585	−	1.02585i	0.0261975	−	0.999657i	$-0.491660\pi$
$263$	16.6366	−	16.6366i	1.02585	−	1.02585i	0.999657	−	0.0261975i	$-0.00833988\pi$
$264$		0			0
$265$	−2.33019	−	2.33019i	−0.143143	−	0.143143i
$266$		0			0
$267$	7.62844	−	3.15980i	0.466853	−	0.193377i
$268$		0			0
$269$	−5.01046	+	12.0963i	−0.305493	+	0.737525i	0.694347	+	0.719640i	$0.255693\pi$
$269$	−5.01046	+	12.0963i	−0.305493	+	0.737525i	−0.999840	+	0.0178850i	$0.994307\pi$
$270$		0			0
$271$			28.2141i			1.71388i	0.515412	+	0.856942i	$0.327639\pi$
$271$			28.2141i			1.71388i	−0.515412	+	0.856942i	$0.672361\pi$
$272$		0			0
$273$			16.6041i			1.00493i
$274$		0			0
$275$	−0.0889314	+	0.214699i	−0.00536277	+	0.0129469i
$276$		0			0
$277$	−21.8246	+	9.04006i	−1.31132	+	0.543165i	−0.925268	−	0.379314i	$-0.876160\pi$
$277$	−21.8246	+	9.04006i	−1.31132	+	0.543165i	−0.386047	+	0.922479i	$0.626160\pi$
$278$		0			0
$279$	0.898033	+	0.898033i	0.0537638	+	0.0537638i
$280$		0			0
$281$	3.00666	−	3.00666i	0.179363	−	0.179363i	−0.611715	−	0.791078i	$-0.709520\pi$
$281$	3.00666	−	3.00666i	0.179363	−	0.179363i	0.791078	+	0.611715i	$0.209520\pi$
$282$		0			0
$283$	−0.709521	−	1.71293i	−0.0421766	−	0.101823i	0.901387	−	0.433014i	$-0.142550\pi$
$283$	−0.709521	−	1.71293i	−0.0421766	−	0.101823i	−0.943564	+	0.331190i	$0.892550\pi$
$284$		0			0
$285$	−4.97186	−	2.05941i	−0.294508	−	0.121989i
$286$		0			0
$287$	−13.7359			−0.810804
$288$		0			0
$289$	−24.5443			−1.44378
$290$		0			0
$291$	−13.2060	−	5.47010i	−0.774148	−	0.320663i
$292$		0			0
$293$	10.5176	+	25.3917i	0.614444	+	1.48340i	0.858071	+	0.513530i	$0.171663\pi$
$293$	10.5176	+	25.3917i	0.614444	+	1.48340i	−0.243627	+	0.969869i	$0.578337\pi$
$294$		0			0
$295$	−4.90774	+	4.90774i	−0.285739	+	0.285739i
$296$		0			0
$297$	−0.585786	−	0.585786i	−0.0339908	−	0.0339908i
$298$		0			0
$299$	−3.01990	+	1.25088i	−0.174645	+	0.0723404i
$300$		0			0
$301$	9.83509	−	23.7440i	0.566885	−	1.36858i
$302$		0			0
$303$			15.6167i			0.897154i
$304$		0			0
$305$			6.93520i			0.397108i
$306$		0			0
$307$	−5.80167	+	14.0065i	−0.331119	+	0.799391i	0.667385	+	0.744713i	$0.267413\pi$
$307$	−5.80167	+	14.0065i	−0.331119	+	0.799391i	−0.998504	+	0.0546786i	$0.982587\pi$
$308$		0			0
$309$	24.0777	−	9.97332i	1.36973	−	0.567363i
$310$		0			0
$311$	−7.15481	−	7.15481i	−0.405712	−	0.405712i	0.474528	−	0.880240i	$-0.342619\pi$
$311$	−7.15481	−	7.15481i	−0.405712	−	0.405712i	−0.880240	+	0.474528i	$0.842619\pi$
$312$		0			0
$313$	−11.8512	+	11.8512i	−0.669868	+	0.669868i	−0.957685	−	0.287817i	$-0.907070\pi$
$313$	−11.8512	+	11.8512i	−0.669868	+	0.669868i	0.287817	+	0.957685i	$0.407070\pi$
$314$		0			0
$315$	2.98010	+	7.19460i	0.167910	+	0.405370i
$316$		0			0
$317$	18.9377	+	7.84425i	1.06365	+	0.440577i	0.844745	−	0.535170i	$-0.179752\pi$
$317$	18.9377	+	7.84425i	1.06365	+	0.440577i	0.218902	+	0.975747i	$0.429752\pi$
$318$		0			0
$319$	−0.685896			−0.0384028
$320$		0			0
$321$	19.8526			1.10807
$322$		0			0
$323$	−12.5295	−	5.18989i	−0.697160	−	0.288773i
$324$		0			0
$325$	−1.87239	−	4.52035i	−0.103861	−	0.250744i
$326$		0			0
$327$	12.4689	−	12.4689i	0.689533	−	0.689533i
$328$		0			0
$329$	7.33962	+	7.33962i	0.404646	+	0.404646i
$330$		0			0
$331$	−9.91107	+	4.10530i	−0.544762	+	0.225648i	−0.638055	−	0.769991i	$-0.720261\pi$
$331$	−9.91107	+	4.10530i	−0.544762	+	0.225648i	0.0932931	+	0.995639i	$0.470261\pi$
$332$		0			0
$333$	1.87722	−	4.53200i	0.102871	−	0.248352i
$334$		0			0
$335$		−	28.1582i		−	1.53845i
$336$		0			0
$337$		−	3.23412i		−	0.176174i	−0.996113	−	0.0880868i	$-0.971925\pi$
$337$		−	3.23412i		−	0.176174i	0.996113	−	0.0880868i	$-0.0280753\pi$
$338$		0			0
$339$	3.11529	−	7.52099i	0.169200	−	0.408484i
$340$		0			0
$341$	0.158619	−	0.0657022i	0.00858971	−	0.00355797i
$342$		0			0
$343$	−3.06608	−	3.06608i	−0.165553	−	0.165553i
$344$		0			0
$345$	1.91598	−	1.91598i	0.103153	−	0.103153i
$346$		0			0
$347$	9.82705	+	23.7246i	0.527544	+	1.27360i	0.933128	+	0.359545i	$0.117068\pi$
$347$	9.82705	+	23.7246i	0.527544	+	1.27360i	−0.405584	+	0.914058i	$0.632932\pi$
$348$		0			0
$349$	−12.5762	−	5.20925i	−0.673190	−	0.278845i	0.0197868	−	0.999804i	$-0.493701\pi$
$349$	−12.5762	−	5.20925i	−0.673190	−	0.278845i	−0.692977	+	0.720960i	$0.743701\pi$
$350$		0			0
$351$	17.4420			0.930983
$352$		0			0
$353$	−8.67371			−0.461655			−0.230828	−	0.972995i	$-0.574143\pi$
$353$	−8.67371			−0.461655			−0.230828	+	0.972995i	$0.574143\pi$
$354$		0			0
$355$	−8.23127	−	3.40950i	−0.436870	−	0.180958i
$356$		0			0
$357$	−13.2739	−	32.0461i	−0.702530	−	1.69606i
$358$		0			0
$359$	−13.6307	+	13.6307i	−0.719399	+	0.719399i	−0.968482	−	0.249083i	$-0.919871\pi$
$359$	−13.6307	+	13.6307i	−0.719399	+	0.719399i	0.249083	+	0.968482i	$0.419871\pi$
$360$		0			0
$361$	10.3045	+	10.3045i	0.542345	+	0.542345i
$362$		0			0
$363$	14.0396	−	5.81539i	0.736888	−	0.305229i
$364$		0			0
$365$	−0.442353	+	1.06793i	−0.0231538	+	0.0558982i
$366$		0			0
$367$		−	28.9800i		−	1.51274i	−0.654142	−	0.756371i	$-0.726970\pi$
$367$		−	28.9800i		−	1.51274i	0.654142	−	0.756371i	$-0.273030\pi$
$368$		0			0
$369$			3.82989i			0.199376i
$370$		0			0
$371$	2.65344	−	6.40597i	0.137760	−	0.332581i
$372$		0			0
$373$	−5.56367	+	2.30455i	−0.288076	+	0.119325i	−0.522042	−	0.852920i	$-0.674830\pi$
$373$	−5.56367	+	2.30455i	−0.288076	+	0.119325i	0.233966	+	0.972245i	$0.424830\pi$
$374$		0			0
$375$	11.9106	+	11.9106i	0.615060	+	0.615060i
$376$		0			0
$377$	10.2114	−	10.2114i	0.525912	−	0.525912i
$378$		0			0
$379$	−8.55274	−	20.6481i	−0.439325	−	1.06062i	−0.976183	−	0.216951i	$-0.930389\pi$
$379$	−8.55274	−	20.6481i	−0.439325	−	1.06062i	0.536858	−	0.843673i	$-0.319611\pi$
$380$		0			0
$381$	−19.6966	−	8.15862i	−1.00909	−	0.417979i
$382$		0			0
$383$	30.5667			1.56188			0.780942	−	0.624603i	$-0.214739\pi$
$383$	30.5667			1.56188			0.780942	+	0.624603i	$0.214739\pi$
$384$		0			0
$385$	1.05275			0.0536530
$386$		0			0
$387$	−6.62039	−	2.74226i	−0.336533	−	0.139397i
$388$		0			0
$389$	−7.06634	−	17.0597i	−0.358278	−	0.864959i	−0.995543	−	0.0943139i	$-0.969934\pi$
$389$	−7.06634	−	17.0597i	−0.358278	−	0.864959i	0.637265	−	0.770645i	$-0.280066\pi$
$390$		0			0
$391$	4.82843	−	4.82843i	0.244184	−	0.244184i
$392$		0			0
$393$	−3.13990	−	3.13990i	−0.158387	−	0.158387i
$394$		0			0
$395$	−12.0786	+	5.00313i	−0.607742	+	0.251735i
$396$		0			0
$397$	7.15759	−	17.2799i	0.359229	−	0.867255i	−0.636180	−	0.771541i	$-0.719486\pi$
$397$	7.15759	−	17.2799i	0.359229	−	0.867255i	0.995409	−	0.0957146i	$-0.0305136\pi$
$398$		0			0
$399$		−	11.3231i		−	0.566866i
$400$		0			0
$401$		−	11.0004i		−	0.549332i	−0.961540	−	0.274666i	$-0.911433\pi$
$401$		−	11.0004i		−	0.549332i	0.961540	−	0.274666i	$-0.0885674\pi$
$402$		0			0
$403$	−1.38331	+	3.33962i	−0.0689078	+	0.166358i
$404$		0			0
$405$	−7.80631	+	3.23348i	−0.387899	+	0.160673i
$406$		0			0
$407$	−0.468914	−	0.468914i	−0.0232432	−	0.0232432i
$408$		0			0
$409$	−1.15862	+	1.15862i	−0.0572900	+	0.0572900i	−0.735171	−	0.677881i	$-0.762898\pi$
$409$	−1.15862	+	1.15862i	−0.0572900	+	0.0572900i	0.677881	+	0.735171i	$0.262898\pi$
$410$		0			0
$411$	−8.07225	−	19.4881i	−0.398175	−	0.961279i
$412$		0			0
$413$	−13.4919	−	5.58855i	−0.663895	−	0.274994i
$414$		0			0
$415$	14.4786			0.710727
$416$		0			0
$417$	7.16714			0.350976
$418$		0			0
$419$	32.0362	+	13.2698i	1.56507	+	0.648273i	0.985961	−	0.166978i	$-0.0534009\pi$
$419$	32.0362	+	13.2698i	1.56507	+	0.648273i	0.579108	+	0.815251i	$0.303401\pi$
$420$		0			0
$421$	9.34602	+	22.5633i	0.455497	+	1.09967i	0.970202	+	0.242299i	$0.0779016\pi$
$421$	9.34602	+	22.5633i	0.455497	+	1.09967i	−0.514705	+	0.857368i	$0.672098\pi$
$422$		0			0
$423$	2.04646	−	2.04646i	0.0995022	−	0.0995022i
$424$		0			0
$425$	7.22746	+	7.22746i	0.350583	+	0.350583i
$426$		0			0
$427$	−13.4815	+	5.58421i	−0.652414	+	0.270239i
$428$		0			0
$429$	0.239507	−	0.578221i	0.0115635	−	0.0279168i
$430$		0			0
$431$			4.47586i			0.215594i	0.994173	+	0.107797i	$0.0343797\pi$
$431$			4.47586i			0.215594i	−0.994173	+	0.107797i	$0.965620\pi$
$432$		0			0
$433$		−	1.44196i		−	0.0692960i	−0.999400	−	0.0346480i	$-0.988969\pi$
$433$		−	1.44196i		−	0.0692960i	0.999400	−	0.0346480i	$-0.0110310\pi$
$434$		0			0
$435$	−4.58107	+	11.0597i	−0.219646	+	0.530272i
$436$		0			0
$437$	2.05941	−	0.853036i	0.0985150	−	0.0408063i
$438$		0			0
$439$	−0.854615	−	0.854615i	−0.0407885	−	0.0407885i	0.686418	−	0.727207i	$-0.259182\pi$
$439$	−0.854615	−	0.854615i	−0.0407885	−	0.0407885i	−0.727207	+	0.686418i	$0.759182\pi$
$440$		0			0
$441$	−6.22053	+	6.22053i	−0.296216	+	0.296216i
$442$		0			0
$443$	−4.68913	−	11.3206i	−0.222787	−	0.537857i	0.772479	−	0.635040i	$-0.219017\pi$
$443$	−4.68913	−	11.3206i	−0.222787	−	0.537857i	−0.995266	+	0.0971838i	$0.969017\pi$
$444$		0			0
$445$	10.1832	+	4.21803i	0.482731	+	0.199954i
$446$		0			0
$447$	−6.47862			−0.306428
$448$		0			0
$449$	−24.5573			−1.15893			−0.579464	−	0.814998i	$-0.696738\pi$
$449$	−24.5573			−1.15893			−0.579464	+	0.814998i	$0.696738\pi$
$450$		0			0
$451$	0.478338	+	0.198134i	0.0225240	+	0.00932976i
$452$		0			0
$453$	9.91412	+	23.9348i	0.465806	+	1.12456i
$454$		0			0
$455$	−15.6729	+	15.6729i	−0.734759	+	0.734759i
$456$		0			0
$457$	14.1684	+	14.1684i	0.662771	+	0.662771i	0.956032	−	0.293262i	$-0.0947407\pi$
$457$	14.1684	+	14.1684i	0.662771	+	0.662771i	−0.293262	+	0.956032i	$0.594741\pi$
$458$		0			0
$459$	−33.6631	+	13.9437i	−1.57126	+	0.650837i
$460$		0			0
$461$	−11.7965	+	28.4793i	−0.549417	+	1.32641i	0.368496	+	0.929630i	$0.379873\pi$
$461$	−11.7965	+	28.4793i	−0.549417	+	1.32641i	−0.917913	+	0.396782i	$0.870127\pi$
$462$		0			0
$463$			14.8190i			0.688697i	0.938842	+	0.344349i	$0.111900\pi$
$463$			14.8190i			0.688697i	−0.938842	+	0.344349i	$0.888100\pi$
$464$		0			0
$465$		−	2.99647i		−	0.138958i
$466$		0			0
$467$	−5.43521	+	13.1218i	−0.251512	+	0.607203i	−0.998326	−	0.0578293i	$-0.981582\pi$
$467$	−5.43521	+	13.1218i	−0.251512	+	0.607203i	0.746815	+	0.665032i	$0.231582\pi$
$468$		0			0
$469$	54.7373	−	22.6729i	2.52753	−	1.04694i
$470$		0			0
$471$	16.9007	+	16.9007i	0.778742	+	0.778742i
$472$		0			0
$473$	−0.684993	+	0.684993i	−0.0314960	+	0.0314960i
$474$		0			0
$475$	1.27687	+	3.08264i	0.0585869	+	0.141441i
$476$		0			0
$477$	−1.78614	−	0.739842i	−0.0817816	−	0.0338750i
$478$		0			0
$479$	−32.3727			−1.47915			−0.739574	−	0.673076i	$-0.764973\pi$
$479$	−32.3727			−1.47915			−0.739574	+	0.673076i	$0.764973\pi$
$480$		0			0
$481$	13.9620			0.636614
$482$		0			0
$483$	5.26725	+	2.18177i	0.239668	+	0.0992738i
$484$		0			0
$485$	−7.30205	−	17.6287i	−0.331569	−	0.800479i
$486$		0			0
$487$	1.89478	−	1.89478i	0.0858608	−	0.0858608i	−0.662872	−	0.748733i	$-0.730663\pi$
$487$	1.89478	−	1.89478i	0.0858608	−	0.0858608i	0.748733	+	0.662872i	$0.230663\pi$
$488$		0			0
$489$	11.2815	+	11.2815i	0.510166	+	0.510166i
$490$		0			0
$491$	18.2886	−	7.57539i	0.825354	−	0.341873i	0.0702922	−	0.997526i	$-0.477607\pi$
$491$	18.2886	−	7.57539i	0.825354	−	0.341873i	0.755062	+	0.655654i	$0.227607\pi$
$492$		0			0
$493$	−11.5447	+	27.8714i	−0.519947	+	1.25526i
$494$		0			0
$495$		−	0.293531i		−	0.0131932i
$496$		0			0
$497$		−	18.7462i		−	0.840884i
$498$		0			0
$499$	9.54921	−	23.0538i	0.427481	−	1.03203i	−0.552602	−	0.833445i	$-0.686365\pi$
$499$	9.54921	−	23.0538i	0.427481	−	1.03203i	0.980083	−	0.198586i	$-0.0636349\pi$
$500$		0			0
$501$	−5.40166	+	2.23744i	−0.241328	+	0.0999614i
$502$		0			0
$503$	−22.6436	−	22.6436i	−1.00963	−	1.00963i	−0.999953	−	0.00967595i	$-0.996920\pi$
$503$	−22.6436	−	22.6436i	−1.00963	−	1.00963i	−0.00967595	−	0.999953i	$-0.503080\pi$
$504$		0			0
$505$	−14.7409	+	14.7409i	−0.655960	+	0.655960i
$506$		0			0
$507$	−1.84353	−	4.45068i	−0.0818741	−	0.197661i
$508$		0			0
$509$	−21.3715	−	8.85238i	−0.947276	−	0.392375i	−0.145070	−	0.989421i	$-0.546341\pi$
$509$	−21.3715	−	8.85238i	−0.947276	−	0.392375i	−0.802206	+	0.597047i	$0.796341\pi$
$510$		0			0
$511$	−2.43216			−0.107592
$512$		0			0
$513$	−11.8945			−0.525155
$514$		0			0
$515$	32.1415	+	13.3134i	1.41632	+	0.586660i
$516$		0			0
$517$	−0.149724	−	0.361465i	−0.00658484	−	0.0158972i
$518$		0			0
$519$	−20.0789	+	20.0789i	−0.881366	+	0.881366i
$520$		0			0
$521$	−9.76588	−	9.76588i	−0.427851	−	0.427851i	0.460045	−	0.887896i	$-0.347833\pi$
$521$	−9.76588	−	9.76588i	−0.427851	−	0.427851i	−0.887896	+	0.460045i	$0.847833\pi$
$522$		0			0
$523$	16.9370	−	7.01552i	0.740601	−	0.306767i	0.0197010	−	0.999806i	$-0.493729\pi$
$523$	16.9370	−	7.01552i	0.740601	−	0.306767i	0.720900	+	0.693039i	$0.243729\pi$
$524$		0			0
$525$	−3.26579	+	7.88431i	−0.142531	+	0.344099i
$526$		0			0
$527$		−	7.55136i		−	0.328942i
$528$		0			0
$529$		−	21.8776i		−	0.951202i
$530$		0			0
$531$	−1.55822	+	3.76187i	−0.0676209	+	0.163251i
$532$		0			0
$533$	−10.0711	+	4.17157i	−0.436226	+	0.180691i
$534$		0			0
$535$	18.7393	+	18.7393i	0.810170	+	0.810170i
$536$		0			0
$537$	−24.5674	+	24.5674i	−1.06016	+	1.06016i
$538$		0			0
$539$	0.455108	+	1.09873i	0.0196029	+	0.0473256i
$540$		0			0
$541$	14.2214	+	5.89071i	0.611427	+	0.253261i	0.666839	−	0.745202i	$-0.267647\pi$
$541$	14.2214	+	5.89071i	0.611427	+	0.253261i	−0.0554115	+	0.998464i	$0.517647\pi$
$542$		0			0
$543$	−2.81470			−0.120791
$544$		0			0
$545$	23.5393			1.00831
$546$		0			0
$547$	9.67342	+	4.00686i	0.413606	+	0.171321i	0.579776	−	0.814776i	$-0.303140\pi$
$547$	9.67342	+	4.00686i	0.413606	+	0.171321i	−0.166170	+	0.986097i	$0.553140\pi$
$548$		0			0
$549$	1.55701	+	3.75895i	0.0664515	+	0.160428i
$550$		0			0
$551$	−6.96362	+	6.96362i	−0.296660	+	0.296660i
$552$		0			0
$553$	−19.4514	−	19.4514i	−0.827157	−	0.827157i
$554$		0			0
$555$	−10.6928	+	4.42912i	−0.453886	+	0.188006i
$556$		0			0
$557$	−3.08965	+	7.45908i	−0.130913	+	0.316051i	−0.975721	−	0.219018i	$-0.929715\pi$
$557$	−3.08965	+	7.45908i	−0.130913	+	0.316051i	0.844808	+	0.535070i	$0.179715\pi$
$558$		0			0
$559$		−	20.3959i		−	0.862653i
$560$		0			0
$561$			1.30744i			0.0552002i
$562$		0			0
$563$	−10.1815	+	24.5802i	−0.429097	+	1.03593i	0.550477	+	0.834850i	$0.314446\pi$
$563$	−10.1815	+	24.5802i	−0.429097	+	1.03593i	−0.979574	+	0.201082i	$0.935554\pi$
$564$		0			0
$565$	10.0398	−	4.15862i	0.422377	−	0.174954i
$566$		0			0
$567$	−12.5713	−	12.5713i	−0.527943	−	0.527943i
$568$		0			0
$569$	8.12862	−	8.12862i	0.340770	−	0.340770i	−0.515887	−	0.856657i	$-0.672538\pi$
$569$	8.12862	−	8.12862i	0.340770	−	0.340770i	0.856657	+	0.515887i	$0.172538\pi$
$570$		0			0
$571$	7.40930	+	17.8876i	0.310070	+	0.748574i	0.999702	+	0.0244147i	$0.00777221\pi$
$571$	7.40930	+	17.8876i	0.310070	+	0.748574i	−0.689632	+	0.724160i	$0.742228\pi$
$572$		0			0
$573$	11.5849	+	4.79862i	0.483965	+	0.200465i
$574$		0			0
$575$	−1.68000			−0.0700609
$576$		0			0
$577$	−11.9134			−0.495959			−0.247980	−	0.968765i	$-0.579767\pi$
$577$	−11.9134			−0.495959			−0.247980	+	0.968765i	$0.579767\pi$
$578$		0			0
$579$	−7.98890	−	3.30911i	−0.332008	−	0.137522i
$580$		0			0
$581$	11.6582	+	28.1453i	0.483662	+	1.16766i
$582$		0			0
$583$	−0.184807	+	0.184807i	−0.00765391	+	0.00765391i
$584$		0			0
$585$	4.36999	+	4.36999i	0.180677	+	0.180677i
$586$		0			0
$587$	23.6011	−	9.77588i	0.974120	−	0.403494i	0.161876	−	0.986811i	$-0.448246\pi$
$587$	23.6011	−	9.77588i	0.974120	−	0.403494i	0.812244	+	0.583318i	$0.198246\pi$
$588$		0			0
$589$	0.943348	−	2.27744i	0.0388700	−	0.0938404i
$590$		0			0
$591$			6.55765i			0.269746i
$592$		0			0
$593$		−	12.5549i		−	0.515567i	−0.966203	−	0.257784i	$-0.917008\pi$
$593$		−	12.5549i		−	0.515567i	0.966203	−	0.257784i	$-0.0829922\pi$
$594$		0			0
$595$	17.7194	−	42.7784i	0.726425	−	1.75374i
$596$		0			0
$597$	11.1077	−	4.60097i	0.454609	−	0.188305i
$598$		0			0
$599$	6.66010	+	6.66010i	0.272124	+	0.272124i	0.829955	−	0.557830i	$-0.188366\pi$
$599$	6.66010	+	6.66010i	0.272124	+	0.272124i	−0.557830	+	0.829955i	$0.688366\pi$
$600$		0			0
$601$	27.4318	−	27.4318i	1.11896	−	1.11896i	0.127071	−	0.991894i	$-0.459442\pi$
$601$	27.4318	−	27.4318i	1.11896	−	1.11896i	0.991894	−	0.127071i	$-0.0405577\pi$
$602$		0			0
$603$	−6.32175	−	15.2621i	−0.257442	−	0.621519i
$604$		0			0
$605$	18.7415	+	7.76299i	0.761951	+	0.315610i
$606$		0			0
$607$	20.3361			0.825416			0.412708	−	0.910863i	$-0.364583\pi$
$607$	20.3361			0.825416			0.412708	+	0.910863i	$0.364583\pi$
$608$		0			0
$609$	−25.1878			−1.02066
$610$		0			0
$611$	7.61040	+	3.15233i	0.307884	+	0.127530i
$612$		0			0
$613$	−13.3277	−	32.1759i	−0.538301	−	1.29957i	−0.925908	−	0.377748i	$-0.876699\pi$
$613$	−13.3277	−	32.1759i	−0.538301	−	1.29957i	0.387608	−	0.921824i	$-0.373301\pi$
$614$		0			0
$615$	6.38960	−	6.38960i	0.257654	−	0.257654i
$616$		0			0
$617$	−11.3168	−	11.3168i	−0.455599	−	0.455599i	0.441609	−	0.897208i	$-0.354408\pi$
$617$	−11.3168	−	11.3168i	−0.455599	−	0.455599i	−0.897208	+	0.441609i	$0.854408\pi$
$618$		0			0
$619$	0.224799	−	0.0931149i	0.00903545	−	0.00374260i	−0.378161	−	0.925740i	$-0.623443\pi$
$619$	0.224799	−	0.0931149i	0.00903545	−	0.00374260i	0.387197	+	0.921997i	$0.373443\pi$
$620$		0			0
$621$	2.29186	−	5.53304i	0.0919691	−	0.222033i
$622$		0			0
$623$			23.1917i			0.929157i
$624$		0			0
$625$			14.5563i			0.582254i
$626$		0			0
$627$	−0.163331	+	0.394316i	−0.00652282	+	0.0157475i
$628$		0			0
$629$	−26.9469	+	11.1618i	−1.07444	+	0.445048i
$630$		0			0
$631$	−1.15481	−	1.15481i	−0.0459722	−	0.0459722i	0.683747	−	0.729719i	$-0.260349\pi$
$631$	−1.15481	−	1.15481i	−0.0459722	−	0.0459722i	−0.729719	+	0.683747i	$0.760349\pi$
$632$		0			0
$633$	13.3404	−	13.3404i	0.530233	−	0.530233i
$634$		0			0
$635$	−10.8910	−	26.2931i	−0.432195	−	1.04341i
$636$		0			0
$637$	−23.1330	−	9.58199i	−0.916562	−	0.379652i
$638$		0			0
$639$	−5.22690			−0.206773
$640$		0			0
$641$	−14.1953			−0.560679			−0.280339	−	0.959901i	$-0.590447\pi$
$641$	−14.1953			−0.560679			−0.280339	+	0.959901i	$0.590447\pi$
$642$		0			0
$643$	−33.9334	−	14.0557i	−1.33820	−	0.554302i	−0.405219	−	0.914219i	$-0.632805\pi$
$643$	−33.9334	−	14.0557i	−1.33820	−	0.554302i	−0.932984	+	0.359917i	$0.882805\pi$
$644$		0			0
$645$	6.47010	+	15.6202i	0.254760	+	0.615045i
$646$		0			0
$647$	−8.73969	+	8.73969i	−0.343593	+	0.343593i	−0.857716	−	0.514123i	$-0.828117\pi$
$647$	−8.73969	+	8.73969i	−0.343593	+	0.343593i	0.514123	+	0.857716i	$0.328117\pi$
$648$		0			0
$649$	0.389231	+	0.389231i	0.0152786	+	0.0152786i
$650$		0			0
$651$	5.82490	−	2.41275i	0.228296	−	0.0945632i
$652$		0			0
$653$	16.1182	−	38.9127i	0.630753	−	1.52277i	−0.207926	−	0.978145i	$-0.566671\pi$
$653$	16.1182	−	38.9127i	0.630753	−	1.52277i	0.838679	−	0.544627i	$-0.183329\pi$
$654$		0			0
$655$		−	5.92763i		−	0.231612i
$656$		0			0
$657$			0.678143i			0.0264569i
$658$		0			0
$659$	8.93958	−	21.5821i	0.348237	−	0.840718i	−0.648592	−	0.761136i	$-0.724642\pi$
$659$	8.93958	−	21.5821i	0.348237	−	0.840718i	0.996828	−	0.0795812i	$-0.0253583\pi$
$660$		0			0
$661$	−22.0088	+	9.11633i	−0.856042	+	0.354584i	−0.767158	−	0.641458i	$-0.778330\pi$
$661$	−22.0088	+	9.11633i	−0.856042	+	0.354584i	−0.0888835	+	0.996042i	$0.528330\pi$
$662$		0			0
$663$	−19.4647	−	19.4647i	−0.755947	−	0.755947i
$664$		0			0
$665$	10.6881	−	10.6881i	0.414468	−	0.414468i
$666$		0			0
$667$	−1.89754	−	4.58107i	−0.0734732	−	0.177380i
$668$		0			0
$669$	−1.22841	−	0.508825i	−0.0474931	−	0.0196723i
$670$		0			0
$671$	0.550028			0.0212336
$672$		0			0
$673$	45.0980			1.73840			0.869200	−	0.494460i	$-0.164634\pi$
$673$	45.0980			1.73840			0.869200	+	0.494460i	$0.164634\pi$
$674$		0			0
$675$	8.28216	+	3.43058i	0.318780	+	0.132043i
$676$		0			0
$677$	13.6058	+	32.8474i	0.522915	+	1.26243i	0.936085	+	0.351774i	$0.114421\pi$
$677$	13.6058	+	32.8474i	0.522915	+	1.26243i	−0.413170	+	0.910654i	$0.635579\pi$
$678$		0			0
$679$	28.3892	−	28.3892i	1.08948	−	1.08948i
$680$		0			0
$681$	15.0117	+	15.0117i	0.575248	+	0.575248i
$682$		0			0
$683$	−18.8141	+	7.79305i	−0.719901	+	0.298193i	−0.712395	−	0.701779i	$-0.752389\pi$
$683$	−18.8141	+	7.79305i	−0.719901	+	0.298193i	−0.00750651	+	0.999972i	$0.502389\pi$
$684$		0			0
$685$	10.7757	−	26.0148i	0.411718	−	0.993974i
$686$		0			0
$687$		−	6.52547i		−	0.248962i
$688$		0			0
$689$		−	5.50267i		−	0.209635i
$690$		0			0
$691$	−12.6322	+	30.4967i	−0.480550	+	1.16015i	0.478798	+	0.877925i	$0.341073\pi$
$691$	−12.6322	+	30.4967i	−0.480550	+	1.16015i	−0.959348	+	0.282226i	$0.908927\pi$
$692$		0			0
$693$	0.570601	−	0.236351i	0.0216753	−	0.00897822i
$694$		0			0
$695$	6.76521	+	6.76521i	0.256619	+	0.256619i
$696$		0			0
$697$	16.1023	−	16.1023i	0.609920	−	0.609920i
$698$		0			0
$699$	12.5790	+	30.3684i	0.475782	+	1.14864i
$700$		0			0
$701$	0.915341	+	0.379146i	0.0345719	+	0.0143202i	0.399902	−	0.916558i	$-0.369044\pi$
$701$	0.915341	+	0.379146i	0.0345719	+	0.0143202i	−0.365330	+	0.930878i	$0.619044\pi$
$702$		0			0
$703$	−9.52138			−0.359106
$704$		0			0
$705$	−6.82843			−0.257173
$706$		0			0
$707$	−40.5244	−	16.7858i	−1.52408	−	0.631293i
$708$		0			0
$709$	−18.9677	−	45.7920i	−0.712346	−	1.71975i	−0.694055	−	0.719922i	$-0.744177\pi$
$709$	−18.9677	−	45.7920i	−0.712346	−	1.71975i	−0.0182911	−	0.999833i	$-0.505823\pi$
$710$		0			0
$711$	−5.42350	+	5.42350i	−0.203397	+	0.203397i
$712$		0			0
$713$	0.877646	+	0.877646i	0.0328681	+	0.0328681i
$714$		0			0
$715$	0.771869	−	0.319719i	0.0288663	−	0.0119568i
$716$		0			0
$717$	8.39128	−	20.2583i	0.313378	−	0.756561i
$718$		0			0
$719$		−	12.7931i		−	0.477102i	−0.971130	−	0.238551i	$-0.923328\pi$
$719$		−	12.7931i		−	0.477102i	0.971130	−	0.238551i	$-0.0766724\pi$
$720$		0			0
$721$			73.2004i			2.72612i
$722$		0			0
$723$	−0.165975	+	0.400700i	−0.00617269	+	0.0149022i
$724$		0			0
$725$	6.85720	−	2.84035i	0.254670	−	0.105488i
$726$		0			0
$727$	0.466154	+	0.466154i	0.0172887	+	0.0172887i	0.715698	−	0.698410i	$-0.246109\pi$
$727$	0.466154	+	0.466154i	0.0172887	+	0.0172887i	−0.698410	+	0.715698i	$0.746109\pi$
$728$		0			0
$729$	−20.1043	+	20.1043i	−0.744603	+	0.744603i
$730$		0			0
$731$	16.3052	+	39.3642i	0.603069	+	1.45594i
$732$		0			0
$733$	34.0271	+	14.0945i	1.25682	+	0.520591i	0.908932	−	0.416945i	$-0.136899\pi$
$733$	34.0271	+	14.0945i	1.25682	+	0.520591i	0.347887	+	0.937536i	$0.386899\pi$
$734$		0			0
$735$	20.7561			0.765599
$736$		0			0
$737$	−2.23322			−0.0822616
$738$		0			0
$739$	−8.25825	−	3.42068i	−0.303785	−	0.125832i	0.225584	−	0.974224i	$-0.427571\pi$
$739$	−8.25825	−	3.42068i	−0.303785	−	0.125832i	−0.529368	+	0.848392i	$0.677571\pi$
$740$		0			0
$741$	−3.43882	−	8.30205i	−0.126328	−	0.304984i
$742$		0			0
$743$	32.4060	−	32.4060i	1.18886	−	1.18886i	0.211477	−	0.977383i	$-0.432173\pi$
$743$	32.4060	−	32.4060i	1.18886	−	1.18886i	0.977383	−	0.211477i	$-0.0678273\pi$
$744$		0			0
$745$	−6.11529	−	6.11529i	−0.224047	−	0.224047i
$746$		0			0
$747$	7.84757	−	3.25057i	0.287127	−	0.118932i
$748$		0			0
$749$	−21.3388	+	51.5165i	−0.779704	+	1.88237i
$750$		0			0
$751$			21.5108i			0.784939i	0.919765	+	0.392470i	$0.128379\pi$
$751$			21.5108i			0.784939i	−0.919765	+	0.392470i	$0.871621\pi$
$752$		0			0
$753$		−	12.8732i		−	0.469126i
$754$		0			0
$755$	−13.2344	+	31.9507i	−0.481649	+	1.16280i
$756$		0			0
$757$	−17.3649	+	7.19276i	−0.631137	+	0.261425i	−0.675236	−	0.737602i	$-0.735958\pi$
$757$	−17.3649	+	7.19276i	−0.631137	+	0.261425i	0.0440993	+	0.999027i	$0.485958\pi$
$758$		0			0
$759$	−0.151955	−	0.151955i	−0.00551563	−	0.00551563i
$760$		0			0
$761$	−37.8574	+	37.8574i	−1.37233	+	1.37233i	−0.515354	+	0.856977i	$0.672340\pi$
$761$	−37.8574	+	37.8574i	−1.37233	+	1.37233i	−0.856977	+	0.515354i	$0.827660\pi$
$762$		0			0
$763$	18.9538	+	45.7585i	0.686174	+	1.65657i
$764$		0			0
$765$	−11.9276	−	4.94059i	−0.431245	−	0.178627i
$766$		0			0
$767$	−11.5894			−0.418471
$768$		0			0
$769$	3.07370			0.110840			0.0554201	−	0.998463i	$-0.482350\pi$
$769$	3.07370			0.110840			0.0554201	+	0.998463i	$0.482350\pi$
$770$		0			0
$771$	−24.1753	−	10.0137i	−0.870651	−	0.360635i
$772$		0			0
$773$	−6.55831	−	15.8332i	−0.235886	−	0.569479i	0.760964	−	0.648795i	$-0.224727\pi$
$773$	−6.55831	−	15.8332i	−0.235886	−	0.569479i	−0.996850	+	0.0793155i	$0.974727\pi$
$774$		0			0
$775$	−1.31371	+	1.31371i	−0.0471898	+	0.0471898i
$776$		0			0
$777$	−17.2197	−	17.2197i	−0.617753	−	0.617753i
$778$		0			0
$779$	6.86794	−	2.84479i	0.246070	−	0.101925i
$780$		0			0
$781$	−0.270406	+	0.652818i	−0.00967589	+	0.0233597i
$782$		0			0
$783$			26.4588i			0.945561i
$784$		0			0
$785$			31.9058i			1.13877i
$786$		0			0
$787$	6.77706	−	16.3613i	0.241576	−	0.583216i	−0.755864	−	0.654729i	$-0.772783\pi$
$787$	6.77706	−	16.3613i	0.241576	−	0.583216i	0.997440	+	0.0715129i	$0.0227827\pi$
$788$		0			0
$789$	−30.0877	+	12.4627i	−1.07115	+	0.443685i
$790$		0			0
$791$	16.1680	+	16.1680i	0.574869	+	0.574869i
$792$		0			0
$793$	−8.18862	+	8.18862i	−0.290786	+	0.290786i
$794$		0			0
$795$	1.74559	+	4.21422i	0.0619096	+	0.149463i
$796$		0			0
$797$	−32.4476	−	13.4402i	−1.14935	−	0.476077i	−0.275036	−	0.961434i	$-0.588690\pi$
$797$	−32.4476	−	13.4402i	−1.14935	−	0.476077i	−0.874316	+	0.485356i	$0.838690\pi$
$798$		0			0
$799$	−17.2082			−0.608783
$800$		0			0
$801$	6.46640			0.228479
$802$		0			0
$803$	0.0846974	+	0.0350828i	0.00298891	+	0.00123805i
$804$		0			0
$805$	2.91245	+	7.03127i	0.102650	+	0.247820i
$806$		0			0
$807$	12.8150	−	12.8150i	0.451109	−	0.451109i
$808$		0			0
$809$	11.2704	+	11.2704i	0.396246	+	0.396246i	0.876907	−	0.480661i	$-0.159603\pi$
$809$	11.2704	+	11.2704i	0.396246	+	0.396246i	−0.480661	+	0.876907i	$0.659603\pi$
$810$		0			0
$811$	16.3328	−	6.76529i	0.573524	−	0.237561i	−0.0770206	−	0.997029i	$-0.524541\pi$
$811$	16.3328	−	6.76529i	0.573524	−	0.237561i	0.650545	+	0.759468i	$0.274541\pi$
$812$		0			0
$813$	14.9452	−	36.0809i	0.524150	−	1.26541i
$814$		0			0
$815$			21.2976i			0.746023i
$816$		0			0
$817$			13.9089i			0.486611i
$818$		0			0
$819$	−4.97620	+	12.0136i	−0.173882	+	0.419789i
$820$		0			0
$821$	29.5124	−	12.2244i	1.02999	−	0.426636i	0.197281	−	0.980347i	$-0.436789\pi$
$821$	29.5124	−	12.2244i	1.02999	−	0.426636i	0.832709	+	0.553711i	$0.186789\pi$
$822$		0			0
$823$	−1.00381	−	1.00381i	−0.0349906	−	0.0349906i	0.689395	−	0.724386i	$-0.257876\pi$
$823$	−1.00381	−	1.00381i	−0.0349906	−	0.0349906i	−0.724386	+	0.689395i	$0.757876\pi$
$824$		0			0
$825$	0.227455	−	0.227455i	0.00791898	−	0.00791898i
$826$		0			0
$827$	−15.7060	−	37.9176i	−0.546151	−	1.31852i	−0.920321	−	0.391165i	$-0.872072\pi$
$827$	−15.7060	−	37.9176i	−0.546151	−	1.31852i	0.374170	−	0.927360i	$-0.377928\pi$
$828$		0			0
$829$	31.9806	+	13.2468i	1.11073	+	0.460081i	0.861190	−	0.508283i	$-0.169720\pi$
$829$	31.9806	+	13.2468i	1.11073	+	0.460081i	0.249543	+	0.968364i	$0.419720\pi$
$830$		0			0
$831$	32.6984			1.13430
$832$		0			0
$833$	52.3070			1.81233
$834$		0			0
$835$	−7.21069	−	2.98677i	−0.249536	−	0.103361i
$836$		0			0
$837$	−2.53450	−	6.11882i	−0.0876051	−	0.211498i
$838$		0			0
$839$	−3.42599	+	3.42599i	−0.118278	+	0.118278i	−0.763768	−	0.645490i	$-0.776653\pi$
$839$	−3.42599	+	3.42599i	−0.118278	+	0.118278i	0.645490	+	0.763768i	$0.276653\pi$
$840$		0			0
$841$	−5.01582	−	5.01582i	−0.172959	−	0.172959i
$842$		0			0
$843$	−5.43764	+	2.25234i	−0.187282	+	0.0775749i
$844$		0			0
$845$	2.46094	−	5.94123i	0.0846588	−	0.204384i
$846$		0			0
$847$			42.6827i			1.46660i
$848$		0			0
$849$			2.56638i			0.0880779i
$850$		0			0
$851$	1.83460	−	4.42912i	0.0628893	−	0.151828i
$852$		0			0
$853$	−33.4739	+	13.8653i	−1.14612	+	0.474740i	−0.873232	−	0.487305i	$-0.837980\pi$
$853$	−33.4739	+	13.8653i	−1.14612	+	0.474740i	−0.272892	+	0.962045i	$0.587980\pi$
$854$		0			0
$855$	−2.98010	−	2.98010i	−0.101917	−	0.101917i
$856$		0			0
$857$	19.6667	−	19.6667i	0.671800	−	0.671800i	−0.286331	−	0.958131i	$-0.592436\pi$
$857$	19.6667	−	19.6667i	0.671800	−	0.671800i	0.958131	+	0.286331i	$0.0924356\pi$
$858$		0			0
$859$	−15.0121	−	36.2424i	−0.512207	−	1.23658i	−0.942597	−	0.333933i	$-0.891624\pi$
$859$	−15.0121	−	36.2424i	−0.512207	−	1.23658i	0.430390	−	0.902643i	$-0.358376\pi$
$860$		0			0
$861$	17.5658	+	7.27598i	0.598640	+	0.247965i
$862$		0			0
$863$	−28.3727			−0.965819			−0.482909	−	0.875670i	$-0.660420\pi$
$863$	−28.3727			−0.965819			−0.482909	+	0.875670i	$0.660420\pi$
$864$		0			0
$865$	−37.9058			−1.28883
$866$		0			0
$867$	31.3878	+	13.0013i	1.06599	+	0.441546i
$868$		0			0
$869$	0.396796	+	0.957951i	0.0134604	+	0.0324963i
$870$		0			0
$871$	33.2473	−	33.2473i	1.12654	−	1.12654i
$872$		0			0
$873$	−7.91558	−	7.91558i	−0.267902	−	0.267902i
$874$		0			0
$875$	−43.7096	+	18.1051i	−1.47765	+	0.612064i
$876$		0			0
$877$	−10.1396	+	24.4793i	−0.342391	+	0.826606i	0.655082	+	0.755558i	$0.272634\pi$
$877$	−10.1396	+	24.4793i	−0.342391	+	0.826606i	−0.997473	+	0.0710476i	$0.977366\pi$
$878$		0			0
$879$		−	38.0427i		−	1.28315i
$880$		0			0
$881$		−	9.35846i		−	0.315295i	−0.987495	−	0.157647i	$-0.949609\pi$
$881$		−	9.35846i		−	0.315295i	0.987495	−	0.157647i	$-0.0503909\pi$
$882$		0			0
$883$	−7.09207	+	17.1218i	−0.238667	+	0.576193i	−0.997145	−	0.0755050i	$-0.975943\pi$
$883$	−7.09207	+	17.1218i	−0.238667	+	0.576193i	0.758478	+	0.651698i	$0.225943\pi$
$884$		0			0
$885$	8.87579	−	3.67647i	0.298356	−	0.123583i
$886$		0			0
$887$	−30.8931	−	30.8931i	−1.03729	−	1.03729i	−0.999277	−	0.0380100i	$-0.987898\pi$
$887$	−30.8931	−	30.8931i	−1.03729	−	1.03729i	−0.0380100	−	0.999277i	$-0.512102\pi$
$888$		0			0
$889$	42.3424	−	42.3424i	1.42012	−	1.42012i
$890$		0			0
$891$	0.256446	+	0.619115i	0.00859126	+	0.0207411i
$892$		0			0
$893$	−5.18989	−	2.14972i	−0.173673	−	0.0719378i
$894$		0			0
$895$	−46.3794			−1.55029
$896$		0			0
$897$	4.52452			0.151069
$898$		0			0
$899$	−5.06608	−	2.09844i	−0.168963	−	0.0699868i
$900$		0			0
$901$	4.39903	+	10.6202i	0.146553	+	0.353810i
$902$		0			0
$903$	−25.1547	+	25.1547i	−0.837096	+	0.837096i
$904$		0			0
$905$	−2.65685	−	2.65685i	−0.0883168	−	0.0883168i
$906$		0			0
$907$	−12.6479	+	5.23891i	−0.419965	+	0.173955i	−0.582651	−	0.812723i	$-0.697984\pi$
$907$	−12.6479	+	5.23891i	−0.419965	+	0.173955i	0.162686	+	0.986678i	$0.447984\pi$
$908$		0			0
$909$	−4.68027	+	11.2992i	−0.155235	+	0.374770i
$910$		0			0
$911$		−	35.3498i		−	1.17119i	−0.810604	−	0.585595i	$-0.800861\pi$
$911$		−	35.3498i		−	1.17119i	0.810604	−	0.585595i	$-0.199139\pi$
$912$		0			0
$913$		−	1.14829i		−	0.0380030i
$914$		0			0
$915$	3.67362	−	8.86890i	0.121446	−	0.293197i
$916$		0			0
$917$	11.5228	−	4.77292i	0.380518	−	0.157616i
$918$		0			0
$919$	30.0652	+	30.0652i	0.991759	+	0.991759i	0.999966	−	0.00820720i	$-0.00261246\pi$
$919$	30.0652	+	30.0652i	0.991759	+	0.991759i	−0.00820720	+	0.999966i	$0.502612\pi$
$920$		0			0
$921$	14.8386	−	14.8386i	0.488949	−	0.488949i
$922$		0			0
$923$	−5.69321	−	13.7446i	−0.187394	−	0.452410i
$924$		0			0
$925$	6.62975	+	2.74613i	0.217985	+	0.0902923i
$926$		0			0
$927$	20.4100			0.670352
$928$		0			0
$929$	7.62858			0.250286			0.125143	−	0.992139i	$-0.460061\pi$
$929$	7.62858			0.250286			0.125143	+	0.992139i	$0.460061\pi$
$930$		0			0
$931$	15.7755	+	6.53442i	0.517020	+	0.214157i
$932$		0			0
$933$	5.35979	+	12.9397i	0.175472	+	0.423626i
$934$		0			0
$935$	−1.23412	+	1.23412i	−0.0403600	+	0.0403600i
$936$		0			0
$937$	−21.2074	−	21.2074i	−0.692817	−	0.692817i	0.270034	−	0.962851i	$-0.412965\pi$
$937$	−21.2074	−	21.2074i	−0.692817	−	0.692817i	−0.962851	+	0.270034i	$0.912965\pi$
$938$		0			0
$939$	21.4332	−	8.87793i	0.699446	−	0.289720i
$940$		0			0
$941$	13.0249	−	31.4448i	0.424599	−	1.02507i	−0.556375	−	0.830931i	$-0.687808\pi$
$941$	13.0249	−	31.4448i	0.424599	−	1.02507i	0.980974	−	0.194141i	$-0.0621918\pi$
$942$		0			0
$943$			3.74294i			0.121887i
$944$		0			0
$945$		−	40.6104i		−	1.32106i
$946$		0			0
$947$	18.6229	−	44.9596i	0.605162	−	1.46099i	−0.263043	−	0.964784i	$-0.584726\pi$
$947$	18.6229	−	44.9596i	0.605162	−	1.46099i	0.868205	−	0.496206i	$-0.165274\pi$
$948$		0			0
$949$	−1.78324	+	0.738644i	−0.0578866	+	0.0239774i
$950$		0			0
$951$	−20.0628	−	20.0628i	−0.650582	−	0.650582i
$952$		0			0
$953$	−33.7784	+	33.7784i	−1.09419	+	1.09419i	−0.0991142	+	0.995076i	$0.531601\pi$
$953$	−33.7784	+	33.7784i	−1.09419	+	1.09419i	−0.995076	+	0.0991142i	$0.968399\pi$
$954$		0			0
$955$	6.40569	+	15.4647i	0.207283	+	0.500426i
$956$		0			0
$957$	0.877140	+	0.363323i	0.0283539	+	0.0117446i
$958$		0			0
$959$	59.2472			1.91319
$960$		0			0
$961$	−29.6274			−0.955723
$962$		0			0
$963$	14.3640	+	5.94977i	0.462874	+	0.191729i
$964$		0			0
$965$	−4.41735	−	10.6644i	−0.142199	−	0.343300i
$966$		0			0
$967$	−19.3234	+	19.3234i	−0.621399	+	0.621399i	−0.945889	−	0.324490i	$-0.894807\pi$
$967$	−19.3234	+	19.3234i	−0.621399	+	0.621399i	0.324490	+	0.945889i	$0.394807\pi$
$968$		0			0
$969$	13.2739	+	13.2739i	0.426420	+	0.426420i
$970$		0			0
$971$	52.9160	−	21.9185i	1.69816	−	0.703399i	0.698234	−	0.715869i	$-0.253969\pi$
$971$	52.9160	−	21.9185i	1.69816	−	0.703399i	0.999922	+	0.0124699i	$0.00396940\pi$
$972$		0			0
$973$	−7.70369	+	18.5983i	−0.246969	+	0.596236i
$974$		0			0
$975$			6.77254i			0.216895i
$976$		0			0
$977$		−	12.2792i		−	0.392848i	−0.980519	−	0.196424i	$-0.937067\pi$
$977$		−	12.2792i		−	0.392848i	0.980519	−	0.196424i	$-0.0629329\pi$
$978$		0			0
$979$	0.334530	−	0.807628i	0.0106916	−	0.0258119i
$980$		0			0
$981$	12.7586	−	5.28477i	0.407349	−	0.168730i
$982$		0			0
$983$	14.1052	+	14.1052i	0.449887	+	0.449887i	0.895317	−	0.445430i	$-0.146949\pi$
$983$	14.1052	+	14.1052i	0.449887	+	0.449887i	−0.445430	+	0.895317i	$0.646949\pi$
$984$		0			0
$985$	−6.18989	+	6.18989i	−0.197226	+	0.197226i
$986$		0			0
$987$	−5.49824	−	13.2739i	−0.175011	−	0.422513i
$988$		0			0
$989$	−6.47010	−	2.68000i	−0.205737	−	0.0852191i
$990$		0			0
$991$	−39.8015			−1.26434			−0.632169	−	0.774831i	$-0.717835\pi$
$991$	−39.8015			−1.26434			−0.632169	+	0.774831i	$0.717835\pi$
$992$		0			0
$993$	14.8491			0.471222
$994$		0			0
$995$	14.8278	+	6.14186i	0.470071	+	0.194710i
$996$		0			0
$997$	2.57111	+	6.20720i	0.0814278	+	0.196584i	0.959350	−	0.282219i	$-0.0910706\pi$
$997$	2.57111	+	6.20720i	0.0814278	+	0.196584i	−0.877922	+	0.478803i	$0.841071\pi$
$998$		0			0
$999$	−18.0886	+	18.0886i	−0.572299	+	0.572299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.2.g.b.81.1		8
3.2	odd	2		1152.2.v.b.721.2		8
4.3	odd	2		32.2.g.b.29.1	yes	8
8.3	odd	2		256.2.g.d.161.1		8
8.5	even	2		256.2.g.c.161.2		8
12.11	even	2		288.2.v.b.253.2		8
16.3	odd	4		512.2.g.e.65.1		8
16.5	even	4		512.2.g.f.65.1		8
16.11	odd	4		512.2.g.h.65.2		8
16.13	even	4		512.2.g.g.65.2		8
20.3	even	4		800.2.ba.c.349.1		8
20.7	even	4		800.2.ba.d.349.2		8
20.19	odd	2		800.2.y.b.701.2		8
32.3	odd	8		512.2.g.h.449.2		8
32.5	even	8		256.2.g.c.97.2		8
32.11	odd	8		32.2.g.b.21.1	✓	8
32.13	even	8		512.2.g.g.449.2		8
32.19	odd	8		512.2.g.e.449.1		8
32.21	even	8	inner	128.2.g.b.49.1		8
32.27	odd	8		256.2.g.d.97.1		8
32.29	even	8		512.2.g.f.449.1		8
64.11	odd	16		4096.2.a.k.1.6		8
64.21	even	16		4096.2.a.q.1.6		8
64.43	odd	16		4096.2.a.k.1.3		8
64.53	even	16		4096.2.a.q.1.3		8
96.11	even	8		288.2.v.b.181.2		8
96.53	odd	8		1152.2.v.b.433.2		8
160.43	even	8		800.2.ba.d.149.2		8
160.107	even	8		800.2.ba.c.149.1		8
160.139	odd	8		800.2.y.b.501.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.b.21.1	✓	8	32.11	odd	8
32.2.g.b.29.1	yes	8	4.3	odd	2
128.2.g.b.49.1		8	32.21	even	8	inner
128.2.g.b.81.1		8	1.1	even	1	trivial
256.2.g.c.97.2		8	32.5	even	8
256.2.g.c.161.2		8	8.5	even	2
256.2.g.d.97.1		8	32.27	odd	8
256.2.g.d.161.1		8	8.3	odd	2
288.2.v.b.181.2		8	96.11	even	8
288.2.v.b.253.2		8	12.11	even	2
512.2.g.e.65.1		8	16.3	odd	4
512.2.g.e.449.1		8	32.19	odd	8
512.2.g.f.65.1		8	16.5	even	4
512.2.g.f.449.1		8	32.29	even	8
512.2.g.g.65.2		8	16.13	even	4
512.2.g.g.449.2		8	32.13	even	8
512.2.g.h.65.2		8	16.11	odd	4
512.2.g.h.449.2		8	32.3	odd	8
800.2.y.b.501.2		8	160.139	odd	8
800.2.y.b.701.2		8	20.19	odd	2
800.2.ba.c.149.1		8	160.107	even	8
800.2.ba.c.349.1		8	20.3	even	4
800.2.ba.d.149.2		8	160.43	even	8
800.2.ba.d.349.2		8	20.7	even	4
1152.2.v.b.433.2		8	96.53	odd	8
1152.2.v.b.721.2		8	3.2	odd	2
4096.2.a.k.1.3		8	64.43	odd	16
4096.2.a.k.1.6		8	64.11	odd	16
4096.2.a.q.1.3		8	64.53	even	16
4096.2.a.q.1.6		8	64.21	even	16

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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	128.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.27882 - 0.529706i) q^{3} +(-0.707107 - 1.70711i) q^{5} +(2.74912 - 2.74912i) q^{7} +(-0.766519 - 0.766519i) q^{9} +(-0.135390 + 0.0560803i) q^{11} +(1.18073 - 2.85054i) q^{13} +2.55765i q^{15} +6.44549i q^{17} +(-0.805198 + 1.94392i) q^{19} +(-4.97186 + 2.05941i) q^{21} +(-0.749118 - 0.749118i) q^{23} +(1.12132 - 1.12132i) q^{25} +(2.16333 + 5.22274i) q^{27} +(4.32417 + 1.79113i) q^{29} -1.17157 q^{31} +0.202846 q^{33} +(-6.63696 - 2.74912i) q^{35} +(1.73172 + 4.18073i) q^{37} +(-3.01990 + 3.01990i) q^{39} +(-2.49824 - 2.49824i) q^{41} +(6.10725 - 2.52971i) q^{43} +(-0.766519 + 1.85054i) q^{45} +2.66981i q^{47} -8.11529i q^{49} +(3.41421 - 8.24264i) q^{51} +(1.64769 - 0.682497i) q^{53} +(0.191470 + 0.191470i) q^{55} +(2.05941 - 2.05941i) q^{57} +(-1.43744 - 3.47029i) q^{59} +(-3.46760 - 1.43633i) q^{61} -4.21450 q^{63} -5.70108 q^{65} +(14.0791 + 5.83176i) q^{67} +(0.561177 + 1.35480i) q^{69} +(3.40950 - 3.40950i) q^{71} +(-0.442353 - 0.442353i) q^{73} +(-2.02794 + 0.840001i) q^{75} +(-0.218031 + 0.526374i) q^{77} -7.07550i q^{79} -4.57283i q^{81} +(-2.99862 + 7.23931i) q^{83} +(11.0031 - 4.55765i) q^{85} +(-4.58107 - 4.58107i) q^{87} +(-4.21803 + 4.21803i) q^{89} +(-4.59050 - 11.0824i) q^{91} +(1.49824 + 0.620589i) q^{93} +3.88784 q^{95} +10.3267 q^{97} +(0.146766 + 0.0607923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 8 q^{7} - 4 q^{11} - 8 q^{13} - 4 q^{19} + 8 q^{23} - 8 q^{25} - 8 q^{27} - 32 q^{31} - 16 q^{33} - 16 q^{35} - 8 q^{37} - 16 q^{39} + 8 q^{41} + 12 q^{43} + 16 q^{51} + 8 q^{53} + 16 q^{55}+ \cdots - 28 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 + 8 * q^7 - 4 * q^11 - 8 * q^13 - 4 * q^19 + 8 * q^23 - 8 * q^25 - 8 * q^27 - 32 * q^31 - 16 * q^33 - 16 * q^35 - 8 * q^37 - 16 * q^39 + 8 * q^41 + 12 * q^43 + 16 * q^51 + 8 * q^53 + 16 * q^55 + 16 * q^57 + 20 * q^59 + 24 * q^61 + 40 * q^63 + 36 * q^67 + 32 * q^69 + 24 * q^71 - 32 * q^73 + 12 * q^75 + 16 * q^77 - 20 * q^83 + 8 * q^85 - 56 * q^87 - 16 * q^89 - 40 * q^91 - 16 * q^93 + 8 * q^95 + 32 * q^97 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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