LMFDB - Embedded newform 960.2.w.g.127.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(127,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 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("960.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.w (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:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.426337261060096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 $ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.4
Root			$1.41127 + 0.0912546i$ of defining polynomial
Character	$\chi$	$=$	960.127
Dual form			960.2.w.g.703.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{3} +(-1.32001 + 1.80487i) q^{5} +(1.86678 - 1.86678i) q^{7} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{3} +(-1.32001 + 1.80487i) q^{5} +(1.86678 - 1.86678i) q^{7} +1.00000i q^{9} -0.728515i q^{11} +(3.12489 - 3.12489i) q^{13} +(-2.20963 + 0.342849i) q^{15} +(1.12489 + 1.12489i) q^{17} +3.73356 q^{19} +2.64002 q^{21} +(5.83347 + 5.83347i) q^{23} +(-1.51514 - 4.76491i) q^{25} +(-0.707107 + 0.707107i) q^{27} +2.64002i q^{29} +6.01008i q^{31} +(0.515138 - 0.515138i) q^{33} +(0.905130 + 5.83347i) q^{35} +(-3.12489 - 3.12489i) q^{37} +4.41926 q^{39} -4.24977 q^{41} +(5.10495 + 5.10495i) q^{43} +(-1.80487 - 1.32001i) q^{45} +(-2.09991 + 2.09991i) q^{47} +0.0302761i q^{49} +1.59083i q^{51} +(-0.484862 + 0.484862i) q^{53} +(1.31488 + 0.961649i) q^{55} +(2.64002 + 2.64002i) q^{57} +4.92834 q^{59} -2.31032 q^{61} +(1.86678 + 1.86678i) q^{63} +(1.51514 + 9.76491i) q^{65} +(-5.10495 + 5.10495i) q^{67} +8.24977i q^{69} -13.1240i q^{71} +(3.96972 - 3.96972i) q^{73} +(2.29793 - 4.44066i) q^{75} +(-1.35998 - 1.35998i) q^{77} +7.11388 q^{79} -1.00000 q^{81} +(3.55694 + 3.55694i) q^{83} +(-3.51514 + 0.545414i) q^{85} +(-1.86678 + 1.86678i) q^{87} -1.03028i q^{89} -11.6669i q^{91} +(-4.24977 + 4.24977i) q^{93} +(-4.92834 + 6.73860i) q^{95} +(-12.5298 - 12.5298i) q^{97} +0.728515 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q+O(q^{10}) $ 12 * q	$ 12 q + 4 q^{13} - 20 q^{17} - 20 q^{25} + 8 q^{33} - 4 q^{37} + 16 q^{41} - 4 q^{45} - 4 q^{53} + 32 q^{61} + 20 q^{65} + 44 q^{73} - 48 q^{77} - 12 q^{81} - 44 q^{85} + 16 q^{93} - 20 q^{97}+O(q^{100}) $ 12 * q + 4 * q^13 - 20 * q^17 - 20 * q^25 + 8 * q^33 - 4 * q^37 + 16 * q^41 - 4 * q^45 - 4 * q^53 + 32 * q^61 + 20 * q^65 + 44 * q^73 - 48 * q^77 - 12 * q^81 - 44 * q^85 + 16 * q^93 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		0			0
$5$	−1.32001	+	1.80487i	−0.590327	+	0.807164i
$5$	−1.32001	+	1.80487i	−0.590327	+	0.807164i
$6$		0			0
$7$	1.86678	−	1.86678i	0.705576	−	0.705576i	−0.260026	−	0.965602i	$-0.583731\pi$
$7$	1.86678	−	1.86678i	0.705576	−	0.705576i	0.965602	+	0.260026i	$0.0837311\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$		−	0.728515i		−	0.219656i	−0.993951	−	0.109828i	$-0.964970\pi$
$11$		−	0.728515i		−	0.219656i	0.993951	−	0.109828i	$-0.0350299\pi$
$12$		0			0
$13$	3.12489	−	3.12489i	0.866687	−	0.866687i	−0.125417	−	0.992104i	$-0.540027\pi$
$13$	3.12489	−	3.12489i	0.866687	−	0.866687i	0.992104	+	0.125417i	$0.0400268\pi$
$14$		0			0
$15$	−2.20963	+	0.342849i	−0.570523	+	0.0885233i
$16$		0			0
$17$	1.12489	+	1.12489i	0.272825	+	0.272825i	0.830236	−	0.557412i	$-0.188205\pi$
$17$	1.12489	+	1.12489i	0.272825	+	0.272825i	−0.557412	+	0.830236i	$0.688205\pi$
$18$		0			0
$19$	3.73356			0.856537			0.428268	−	0.903652i	$-0.359124\pi$
$19$	3.73356			0.856537			0.428268	+	0.903652i	$0.359124\pi$
$20$		0			0
$21$	2.64002			0.576100
$22$		0			0
$23$	5.83347	+	5.83347i	1.21636	+	1.21636i	0.968897	+	0.247466i	$0.0795978\pi$
$23$	5.83347	+	5.83347i	1.21636	+	1.21636i	0.247466	+	0.968897i	$0.420402\pi$
$24$		0			0
$25$	−1.51514	−	4.76491i	−0.303028	−	0.952982i
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$			2.64002i			0.490240i	0.969493	+	0.245120i	$0.0788274\pi$
$29$			2.64002i			0.490240i	−0.969493	+	0.245120i	$0.921173\pi$
$30$		0			0
$31$			6.01008i			1.07944i	0.841844	+	0.539721i	$0.181470\pi$
$31$			6.01008i			1.07944i	−0.841844	+	0.539721i	$0.818530\pi$
$32$		0			0
$33$	0.515138	−	0.515138i	0.0896740	−	0.0896740i
$34$		0			0
$35$	0.905130	+	5.83347i	0.152995	+	0.986036i
$36$		0			0
$37$	−3.12489	−	3.12489i	−0.513728	−	0.513728i	0.401939	−	0.915667i	$-0.368337\pi$
$37$	−3.12489	−	3.12489i	−0.513728	−	0.513728i	−0.915667	+	0.401939i	$0.868337\pi$
$38$		0			0
$39$	4.41926			0.707647
$40$		0			0
$41$	−4.24977			−0.663703			−0.331851	−	0.943332i	$-0.607673\pi$
$41$	−4.24977			−0.663703			−0.331851	+	0.943332i	$0.607673\pi$
$42$		0			0
$43$	5.10495	+	5.10495i	0.778498	+	0.778498i	0.979575	−	0.201077i	$-0.0644442\pi$
$43$	5.10495	+	5.10495i	0.778498	+	0.778498i	−0.201077	+	0.979575i	$0.564444\pi$
$44$		0			0
$45$	−1.80487	−	1.32001i	−0.269055	−	0.196776i
$46$		0			0
$47$	−2.09991	+	2.09991i	−0.306304	+	0.306304i	−0.843474	−	0.537170i	$-0.819493\pi$
$47$	−2.09991	+	2.09991i	−0.306304	+	0.306304i	0.537170	+	0.843474i	$0.319493\pi$
$48$		0			0
$49$			0.0302761i			0.00432516i
$50$		0			0
$51$			1.59083i			0.222761i
$52$		0			0
$53$	−0.484862	+	0.484862i	−0.0666009	+	0.0666009i	−0.739623	−	0.673022i	$-0.764996\pi$
$53$	−0.484862	+	0.484862i	−0.0666009	+	0.0666009i	0.673022	+	0.739623i	$0.264996\pi$
$54$		0			0
$55$	1.31488	+	0.961649i	0.177298	+	0.129669i
$56$		0			0
$57$	2.64002	+	2.64002i	0.349680	+	0.349680i
$58$		0			0
$59$	4.92834			0.641615			0.320808	−	0.947144i	$-0.396046\pi$
$59$	4.92834			0.641615			0.320808	+	0.947144i	$0.396046\pi$
$60$		0			0
$61$	−2.31032			−0.295807			−0.147903	−	0.989002i	$-0.547252\pi$
$61$	−2.31032			−0.295807			−0.147903	+	0.989002i	$0.547252\pi$
$62$		0			0
$63$	1.86678	+	1.86678i	0.235192	+	0.235192i
$64$		0			0
$65$	1.51514	+	9.76491i	0.187930	+	1.21119i
$66$		0			0
$67$	−5.10495	+	5.10495i	−0.623669	+	0.623669i	−0.946468	−	0.322798i	$-0.895376\pi$
$67$	−5.10495	+	5.10495i	−0.623669	+	0.623669i	0.322798	+	0.946468i	$0.395376\pi$
$68$		0			0
$69$			8.24977i			0.993156i
$70$		0			0
$71$		−	13.1240i		−	1.55753i	−0.627317	−	0.778764i	$-0.715847\pi$
$71$		−	13.1240i		−	1.55753i	0.627317	−	0.778764i	$-0.284153\pi$
$72$		0			0
$73$	3.96972	−	3.96972i	0.464621	−	0.464621i	−0.435546	−	0.900167i	$-0.643445\pi$
$73$	3.96972	−	3.96972i	0.464621	−	0.464621i	0.900167	+	0.435546i	$0.143445\pi$
$74$		0			0
$75$	2.29793	−	4.44066i	0.265343	−	0.512764i
$76$		0			0
$77$	−1.35998	−	1.35998i	−0.154984	−	0.154984i
$78$		0			0
$79$	7.11388			0.800375			0.400187	−	0.916433i	$-0.368945\pi$
$79$	7.11388			0.800375			0.400187	+	0.916433i	$0.368945\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	3.55694	+	3.55694i	0.390425	+	0.390425i	0.874839	−	0.484414i	$-0.160967\pi$
$83$	3.55694	+	3.55694i	0.390425	+	0.390425i	−0.484414	+	0.874839i	$0.660967\pi$
$84$		0			0
$85$	−3.51514	+	0.545414i	−0.381270	+	0.0591585i
$86$		0			0
$87$	−1.86678	+	1.86678i	−0.200140	+	0.200140i
$88$		0			0
$89$		−	1.03028i		−	0.109209i	−0.998508	−	0.0546045i	$-0.982610\pi$
$89$		−	1.03028i		−	0.109209i	0.998508	−	0.0546045i	$-0.0173898\pi$
$90$		0			0
$91$		−	11.6669i		−	1.22303i
$92$		0			0
$93$	−4.24977	+	4.24977i	−0.440681	+	0.440681i
$94$		0			0
$95$	−4.92834	+	6.73860i	−0.505637	+	0.691366i
$96$		0			0
$97$	−12.5298	−	12.5298i	−1.27221	−	1.27221i	−0.944926	−	0.327284i	$-0.893867\pi$
$97$	−12.5298	−	12.5298i	−1.27221	−	1.27221i	−0.327284	−	0.944926i	$-0.606133\pi$
$98$		0			0
$99$	0.728515			0.0732185
$100$		0			0
$101$	5.67030			0.564216			0.282108	−	0.959383i	$-0.408966\pi$
$101$	5.67030			0.564216			0.282108	+	0.959383i	$0.408966\pi$
$102$		0			0
$103$	0.0565188	+	0.0565188i	0.00556896	+	0.00556896i	0.709886	−	0.704317i	$-0.248747\pi$
$103$	0.0565188	+	0.0565188i	0.00556896	+	0.00556896i	−0.704317	+	0.709886i	$0.748747\pi$
$104$		0			0
$105$	−3.48486	+	4.76491i	−0.340088	+	0.465007i
$106$		0			0
$107$	3.91017	−	3.91017i	0.378011	−	0.378011i	−0.492373	−	0.870384i	$-0.663871\pi$
$107$	3.91017	−	3.91017i	0.378011	−	0.378011i	0.870384	+	0.492373i	$0.163871\pi$
$108$		0			0
$109$		−	15.7796i		−	1.51141i	−0.654912	−	0.755705i	$-0.727294\pi$
$109$		−	15.7796i		−	1.51141i	0.654912	−	0.755705i	$-0.272706\pi$
$110$		0			0
$111$		−	4.41926i		−	0.419457i
$112$		0			0
$113$	−1.84484	+	1.84484i	−0.173548	+	0.173548i	−0.788536	−	0.614988i	$-0.789161\pi$
$113$	−1.84484	+	1.84484i	−0.173548	+	0.173548i	0.614988	+	0.788536i	$0.289161\pi$
$114$		0			0
$115$	−18.2289	+	2.82843i	−1.69986	+	0.263752i
$116$		0			0
$117$	3.12489	+	3.12489i	0.288896	+	0.288896i
$118$		0			0
$119$	4.19982			0.384997
$120$		0			0
$121$	10.4693			0.951751
$122$		0			0
$123$	−3.00504	−	3.00504i	−0.270955	−	0.270955i
$124$		0			0
$125$	10.6001	+	3.55510i	0.948098	+	0.317978i
$126$		0			0
$127$	−11.2572	+	11.2572i	−0.998914	+	0.998914i	−0.999999	−	0.00108535i	$-0.999655\pi$
$127$	−11.2572	+	11.2572i	−0.998914	+	0.998914i	0.00108535	+	0.999999i	$0.499655\pi$
$128$		0			0
$129$			7.21949i			0.635641i
$130$		0			0
$131$		−	4.57511i		−	0.399729i	−0.979824	−	0.199865i	$-0.935950\pi$
$131$		−	4.57511i		−	0.399729i	0.979824	−	0.199865i	$-0.0640502\pi$
$132$		0			0
$133$	6.96972	−	6.96972i	0.604352	−	0.604352i
$134$		0			0
$135$	−0.342849	−	2.20963i	−0.0295078	−	0.190174i
$136$		0			0
$137$	−4.09461	−	4.09461i	−0.349826	−	0.349826i	0.510219	−	0.860045i	$-0.329564\pi$
$137$	−4.09461	−	4.09461i	−0.349826	−	0.349826i	−0.860045	+	0.510219i	$0.829564\pi$
$138$		0			0
$139$	13.5902			1.15271			0.576354	−	0.817200i	$-0.304475\pi$
$139$	13.5902			1.15271			0.576354	+	0.817200i	$0.304475\pi$
$140$		0			0
$141$	−2.96972			−0.250096
$142$		0			0
$143$	−2.27653	−	2.27653i	−0.190373	−	0.190373i
$144$		0			0
$145$	−4.76491	−	3.48486i	−0.395704	−	0.289402i
$146$		0			0
$147$	−0.0214084	+	0.0214084i	−0.00176574	+	0.00176574i
$148$		0			0
$149$		−	5.67030i		−	0.464529i	−0.972653	−	0.232265i	$-0.925386\pi$
$149$		−	5.67030i		−	0.464529i	0.972653	−	0.232265i	$-0.0746135\pi$
$150$		0			0
$151$		−	19.2471i		−	1.56631i	−0.621829	−	0.783153i	$-0.713610\pi$
$151$		−	19.2471i		−	1.56631i	0.621829	−	0.783153i	$-0.286390\pi$
$152$		0			0
$153$	−1.12489	+	1.12489i	−0.0909416	+	0.0909416i
$154$		0			0
$155$	−10.8474	−	7.93338i	−0.871287	−	0.637224i
$156$		0			0
$157$	2.09461	+	2.09461i	0.167168	+	0.167168i	0.785733	−	0.618565i	$-0.212286\pi$
$157$	2.09461	+	2.09461i	0.167168	+	0.167168i	−0.618565	+	0.785733i	$0.712286\pi$
$158$		0			0
$159$	−0.685698			−0.0543794
$160$		0			0
$161$	21.7796			1.71647
$162$		0			0
$163$	4.28546	+	4.28546i	0.335663	+	0.335663i	0.854732	−	0.519069i	$-0.173721\pi$
$163$	4.28546	+	4.28546i	0.335663	+	0.335663i	−0.519069	+	0.854732i	$0.673721\pi$
$164$		0			0
$165$	0.249771	+	1.60975i	0.0194446	+	0.125319i
$166$		0			0
$167$	4.37644	−	4.37644i	0.338659	−	0.338659i	−0.517203	−	0.855862i	$-0.673027\pi$
$167$	4.37644	−	4.37644i	0.338659	−	0.338659i	0.855862	+	0.517203i	$0.173027\pi$
$168$		0			0
$169$		−	6.52982i		−	0.502294i
$170$		0			0
$171$			3.73356i			0.285512i
$172$		0			0
$173$	−16.4049	+	16.4049i	−1.24724	+	1.24724i	−0.290312	+	0.956932i	$0.593759\pi$
$173$	−16.4049	+	16.4049i	−1.24724	+	1.24724i	−0.956932	+	0.290312i	$0.906241\pi$
$174$		0			0
$175$	−11.7235	−	6.06660i	−0.886210	−	0.458592i
$176$		0			0
$177$	3.48486	+	3.48486i	0.261938	+	0.261938i
$178$		0			0
$179$	−24.4156			−1.82491			−0.912455	−	0.409178i	$-0.865815\pi$
$179$	−24.4156			−1.82491			−0.912455	+	0.409178i	$0.865815\pi$
$180$		0			0
$181$	−11.2800			−0.838439			−0.419220	−	0.907885i	$-0.637696\pi$
$181$	−11.2800			−0.838439			−0.419220	+	0.907885i	$0.637696\pi$
$182$		0			0
$183$	−1.63365	−	1.63365i	−0.120763	−	0.120763i
$184$		0			0
$185$	9.76491	−	1.51514i	0.717930	−	0.111395i
$186$		0			0
$187$	0.819496	−	0.819496i	0.0599275	−	0.0599275i
$188$		0			0
$189$			2.64002i			0.192033i
$190$		0			0
$191$			3.26729i			0.236413i	0.992989	+	0.118206i	$0.0377144\pi$
$191$			3.26729i			0.236413i	−0.992989	+	0.118206i	$0.962286\pi$
$192$		0			0
$193$	0.939448	−	0.939448i	0.0676229	−	0.0676229i	−0.672486	−	0.740109i	$-0.734774\pi$
$193$	0.939448	−	0.939448i	0.0676229	−	0.0676229i	0.740109	+	0.672486i	$0.234774\pi$
$194$		0			0
$195$	−5.83347	+	7.97620i	−0.417743	+	0.571187i
$196$		0			0
$197$	1.45459	+	1.45459i	0.103635	+	0.103635i	0.757023	−	0.653388i	$-0.226653\pi$
$197$	1.45459	+	1.45459i	0.103635	+	0.103635i	−0.653388	+	0.757023i	$0.726653\pi$
$198$		0			0
$199$	−5.19059			−0.367951			−0.183975	−	0.982931i	$-0.558897\pi$
$199$	−5.19059			−0.367951			−0.183975	+	0.982931i	$0.558897\pi$
$200$		0			0
$201$	−7.21949			−0.509224
$202$		0			0
$203$	4.92834	+	4.92834i	0.345902	+	0.345902i
$204$		0			0
$205$	5.60975	−	7.67030i	0.391802	−	0.535717i
$206$		0			0
$207$	−5.83347	+	5.83347i	−0.405454	+	0.405454i
$208$		0			0
$209$		−	2.71995i		−	0.188143i
$210$		0			0
$211$		−	11.7800i		−	0.810967i	−0.914102	−	0.405483i	$-0.867103\pi$
$211$		−	11.7800i		−	0.810967i	0.914102	−	0.405483i	$-0.132897\pi$
$212$		0			0
$213$	9.28005	−	9.28005i	0.635858	−	0.635858i
$214$		0			0
$215$	−15.9524	+	2.47520i	−1.08794	+	0.168807i
$216$		0			0
$217$	11.2195	+	11.2195i	0.761629	+	0.761629i
$218$		0			0
$219$	5.61404			0.379361
$220$		0			0
$221$	7.03028			0.472908
$222$		0			0
$223$	3.32381	+	3.32381i	0.222579	+	0.222579i	0.809583	−	0.587005i	$-0.199693\pi$
$223$	3.32381	+	3.32381i	0.222579	+	0.222579i	−0.587005	+	0.809583i	$0.699693\pi$
$224$		0			0
$225$	4.76491	−	1.51514i	0.317661	−	0.101009i
$226$		0			0
$227$	−8.83851	+	8.83851i	−0.586633	+	0.586633i	−0.936718	−	0.350085i	$-0.886153\pi$
$227$	−8.83851	+	8.83851i	−0.586633	+	0.586633i	0.350085	+	0.936718i	$0.386153\pi$
$228$		0			0
$229$			7.09083i			0.468575i	0.972167	+	0.234288i	$0.0752757\pi$
$229$			7.09083i			0.468575i	−0.972167	+	0.234288i	$0.924724\pi$
$230$		0			0
$231$		−	1.92330i		−	0.126544i
$232$		0			0
$233$	−15.3747	+	15.3747i	−1.00723	+	1.00723i	−0.00725353	+	0.999974i	$0.502309\pi$
$233$	−15.3747	+	15.3747i	−1.00723	+	1.00723i	−0.999974	+	0.00725353i	$0.997691\pi$
$234$		0			0
$235$	−1.01817	−	6.56198i	−0.0664179	−	0.428057i
$236$		0			0
$237$	5.03028	+	5.03028i	0.326752	+	0.326752i
$238$		0			0
$239$	−0.706459			−0.0456970			−0.0228485	−	0.999739i	$-0.507274\pi$
$239$	−0.706459			−0.0456970			−0.0228485	+	0.999739i	$0.507274\pi$
$240$		0			0
$241$	−24.9991			−1.61033			−0.805166	−	0.593049i	$-0.797924\pi$
$241$	−24.9991			−1.61033			−0.805166	+	0.593049i	$0.797924\pi$
$242$		0			0
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	−0.0546445	−	0.0399648i	−0.00349111	−	0.00255326i
$246$		0			0
$247$	11.6669	−	11.6669i	0.742349	−	0.742349i
$248$		0			0
$249$			5.03028i			0.318781i
$250$		0			0
$251$		−	28.6154i		−	1.80619i	−0.429440	−	0.903095i	$-0.641289\pi$
$251$		−	28.6154i		−	1.80619i	0.429440	−	0.903095i	$-0.358711\pi$
$252$		0			0
$253$	4.24977	−	4.24977i	0.267181	−	0.267181i
$254$		0			0
$255$	−2.87124	−	2.09991i	−0.179804	−	0.131502i
$256$		0			0
$257$	−3.90539	−	3.90539i	−0.243612	−	0.243612i	0.574731	−	0.818342i	$-0.305107\pi$
$257$	−3.90539	−	3.90539i	−0.243612	−	0.243612i	−0.818342	+	0.574731i	$0.805107\pi$
$258$		0			0
$259$	−11.6669			−0.724948
$260$		0			0
$261$	−2.64002			−0.163413
$262$		0			0
$263$	−0.176615	−	0.176615i	−0.0108905	−	0.0108905i	0.701641	−	0.712531i	$-0.252451\pi$
$263$	−0.176615	−	0.176615i	−0.0108905	−	0.0108905i	−0.712531	+	0.701641i	$0.752451\pi$
$264$		0			0
$265$	−0.235091	−	1.51514i	−0.0144415	−	0.0930742i
$266$		0			0
$267$	0.728515	−	0.728515i	0.0445844	−	0.0445844i
$268$		0			0
$269$			5.38934i			0.328594i	0.986411	+	0.164297i	$0.0525355\pi$
$269$			5.38934i			0.328594i	−0.986411	+	0.164297i	$0.947465\pi$
$270$		0			0
$271$		−	15.4005i		−	0.935513i	−0.883857	−	0.467757i	$-0.845062\pi$
$271$		−	15.4005i		−	0.935513i	0.883857	−	0.467757i	$-0.154938\pi$
$272$		0			0
$273$	8.24977	−	8.24977i	0.499299	−	0.499299i
$274$		0			0
$275$	−3.47131	+	1.10380i	−0.209328	+	0.0665617i
$276$		0			0
$277$	−8.59415	−	8.59415i	−0.516372	−	0.516372i	0.400099	−	0.916472i	$-0.368976\pi$
$277$	−8.59415	−	8.59415i	−0.516372	−	0.516372i	−0.916472	+	0.400099i	$0.868976\pi$
$278$		0			0
$279$	−6.01008			−0.359814
$280$		0			0
$281$	−20.7493			−1.23780			−0.618900	−	0.785470i	$-0.712421\pi$
$281$	−20.7493			−1.23780			−0.618900	+	0.785470i	$0.712421\pi$
$282$		0			0
$283$	−18.5822	−	18.5822i	−1.10459	−	1.10459i	−0.993849	−	0.110745i	$-0.964676\pi$
$283$	−18.5822	−	18.5822i	−1.10459	−	1.10459i	−0.110745	−	0.993849i	$-0.535324\pi$
$284$		0			0
$285$	−8.24977	+	1.28005i	−0.488674	+	0.0758234i
$286$		0			0
$287$	−7.93338	+	7.93338i	−0.468293	+	0.468293i
$288$		0			0
$289$		−	14.4693i		−	0.851133i
$290$		0			0
$291$		−	17.7198i		−	1.03876i
$292$		0			0
$293$	−6.23509	+	6.23509i	−0.364258	+	0.364258i	−0.865378	−	0.501120i	$-0.832922\pi$
$293$	−6.23509	+	6.23509i	−0.364258	+	0.364258i	0.501120	+	0.865378i	$0.332922\pi$
$294$		0			0
$295$	−6.50547	+	8.89503i	−0.378763	+	0.517889i
$296$		0			0
$297$	0.515138	+	0.515138i	0.0298913	+	0.0298913i
$298$		0			0
$299$	36.4578			2.10841
$300$		0			0
$301$	19.0596			1.09858
$302$		0			0
$303$	4.00951	+	4.00951i	0.230340	+	0.230340i
$304$		0			0
$305$	3.04965	−	4.16984i	0.174623	−	0.238764i
$306$		0			0
$307$	−0.905130	+	0.905130i	−0.0516585	+	0.0516585i	−0.732464	−	0.680806i	$-0.761630\pi$
$307$	−0.905130	+	0.905130i	−0.0516585	+	0.0516585i	0.680806	+	0.732464i	$0.261630\pi$
$308$		0			0
$309$			0.0799296i			0.00454704i
$310$		0			0
$311$		−	24.4377i		−	1.38573i	−0.721066	−	0.692867i	$-0.756347\pi$
$311$		−	24.4377i		−	1.38573i	0.721066	−	0.692867i	$-0.243653\pi$
$312$		0			0
$313$	18.5904	−	18.5904i	1.05079	−	1.05079i	0.0521506	−	0.998639i	$-0.483392\pi$
$313$	18.5904	−	18.5904i	1.05079	−	1.05079i	0.998639	−	0.0521506i	$-0.0166076\pi$
$314$		0			0
$315$	−5.83347	+	0.905130i	−0.328679	+	0.0509983i
$316$		0			0
$317$	−19.3141	−	19.3141i	−1.08479	−	1.08479i	−0.996055	−	0.0887327i	$-0.971718\pi$
$317$	−19.3141	−	19.3141i	−1.08479	−	1.08479i	−0.0887327	−	0.996055i	$-0.528282\pi$
$318$		0			0
$319$	1.92330			0.107684
$320$		0			0
$321$	5.52982			0.308644
$322$		0			0
$323$	4.19982	+	4.19982i	0.233684	+	0.233684i
$324$		0			0
$325$	−19.6244	−	10.1552i	−1.08857	−	0.563307i
$326$		0			0
$327$	11.1579	−	11.1579i	0.617031	−	0.617031i
$328$		0			0
$329$			7.84014i			0.432241i
$330$		0			0
$331$			11.0294i			0.606231i	0.952954	+	0.303115i	$0.0980268\pi$
$331$			11.0294i			0.606231i	−0.952954	+	0.303115i	$0.901973\pi$
$332$		0			0
$333$	3.12489	−	3.12489i	0.171243	−	0.171243i
$334$		0			0
$335$	−2.47520	−	15.9524i	−0.135235	−	0.871572i
$336$		0			0
$337$	13.6206	+	13.6206i	0.741964	+	0.741964i	0.972956	−	0.230992i	$-0.0741971\pi$
$337$	13.6206	+	13.6206i	0.741964	+	0.741964i	−0.230992	+	0.972956i	$0.574197\pi$
$338$		0			0
$339$	−2.60900			−0.141701
$340$		0			0
$341$	4.37844			0.237106
$342$		0			0
$343$	13.1240	+	13.1240i	0.708628	+	0.708628i
$344$		0			0
$345$	−14.8898	−	10.8898i	−0.801640	−	0.586287i
$346$		0			0
$347$	−17.7627	+	17.7627i	−0.953549	+	0.953549i	−0.998968	−	0.0454187i	$-0.985538\pi$
$347$	−17.7627	+	17.7627i	−0.953549	+	0.953549i	0.0454187	+	0.998968i	$0.485538\pi$
$348$		0			0
$349$			14.6888i			0.786271i	0.919480	+	0.393136i	$0.128610\pi$
$349$			14.6888i			0.786271i	−0.919480	+	0.393136i	$0.871390\pi$
$350$		0			0
$351$			4.41926i			0.235882i
$352$		0			0
$353$	−18.4049	+	18.4049i	−0.979596	+	0.979596i	−0.999796	−	0.0202002i	$-0.993570\pi$
$353$	−18.4049	+	18.4049i	−0.979596	+	0.979596i	0.0202002	+	0.999796i	$0.493570\pi$
$354$		0			0
$355$	23.6871	+	17.3238i	1.25718	+	0.919451i
$356$		0			0
$357$	2.96972	+	2.96972i	0.157174	+	0.157174i
$358$		0			0
$359$	9.63060			0.508284			0.254142	−	0.967167i	$-0.418207\pi$
$359$	9.63060			0.508284			0.254142	+	0.967167i	$0.418207\pi$
$360$		0			0
$361$	−5.06055			−0.266345
$362$		0			0
$363$	7.40289	+	7.40289i	0.388551	+	0.388551i
$364$		0			0
$365$	1.92477	+	12.4049i	0.100747	+	0.649304i
$366$		0			0
$367$	−15.4570	+	15.4570i	−0.806850	+	0.806850i	−0.984156	−	0.177306i	$-0.943262\pi$
$367$	−15.4570	+	15.4570i	−0.806850	+	0.806850i	0.177306	+	0.984156i	$0.443262\pi$
$368$		0			0
$369$		−	4.24977i		−	0.221234i
$370$		0			0
$371$			1.81026i			0.0939840i
$372$		0			0
$373$	−3.37466	+	3.37466i	−0.174733	+	0.174733i	−0.789055	−	0.614322i	$-0.789430\pi$
$373$	−3.37466	+	3.37466i	−0.174733	+	0.174733i	0.614322	+	0.789055i	$0.289430\pi$
$374$		0			0
$375$	4.98154	+	10.0092i	0.257245	+	0.516873i
$376$		0			0
$377$	8.24977	+	8.24977i	0.424885	+	0.424885i
$378$		0			0
$379$	−5.89705			−0.302911			−0.151455	−	0.988464i	$-0.548396\pi$
$379$	−5.89705			−0.302911			−0.151455	+	0.988464i	$0.548396\pi$
$380$		0			0
$381$	−15.9201			−0.815610
$382$		0			0
$383$	0.642881	+	0.642881i	0.0328497	+	0.0328497i	0.723341	−	0.690491i	$-0.242606\pi$
$383$	0.642881	+	0.642881i	0.0328497	+	0.0328497i	−0.690491	+	0.723341i	$0.742606\pi$
$384$		0			0
$385$	4.24977	−	0.659401i	0.216588	−	0.0336062i
$386$		0			0
$387$	−5.10495	+	5.10495i	−0.259499	+	0.259499i
$388$		0			0
$389$		−	18.8292i		−	0.954680i	−0.878719	−	0.477340i	$-0.841601\pi$
$389$		−	18.8292i		−	0.954680i	0.878719	−	0.477340i	$-0.158399\pi$
$390$		0			0
$391$			13.1240i			0.663708i
$392$		0			0
$393$	3.23509	−	3.23509i	0.163189	−	0.163189i
$394$		0			0
$395$	−9.39041	+	12.8397i	−0.472483	+	0.646034i
$396$		0			0
$397$	24.3444	+	24.3444i	1.22181	+	1.22181i	0.966988	+	0.254821i	$0.0820166\pi$
$397$	24.3444	+	24.3444i	1.22181	+	1.22181i	0.254821	+	0.966988i	$0.417983\pi$
$398$		0			0
$399$	9.85668			0.493451
$400$		0			0
$401$	15.9394			0.795978			0.397989	−	0.917390i	$-0.369708\pi$
$401$	15.9394			0.795978			0.397989	+	0.917390i	$0.369708\pi$
$402$		0			0
$403$	18.7808	+	18.7808i	0.935539	+	0.935539i
$404$		0			0
$405$	1.32001	−	1.80487i	0.0655919	−	0.0896849i
$406$		0			0
$407$	−2.27653	+	2.27653i	−0.112843	+	0.112843i
$408$		0			0
$409$			23.4087i			1.15749i	0.815510	+	0.578743i	$0.196457\pi$
$409$			23.4087i			1.15749i	−0.815510	+	0.578743i	$0.803543\pi$
$410$		0			0
$411$		−	5.79065i		−	0.285632i
$412$		0			0
$413$	9.20012	−	9.20012i	0.452708	−	0.452708i
$414$		0			0
$415$	−11.1150	+	1.72463i	−0.545616	+	0.0846586i
$416$		0			0
$417$	9.60975	+	9.60975i	0.470591	+	0.470591i
$418$		0			0
$419$	28.0361			1.36966			0.684828	−	0.728705i	$-0.259878\pi$
$419$	28.0361			1.36966			0.684828	+	0.728705i	$0.259878\pi$
$420$		0			0
$421$	−17.4087			−0.848449			−0.424224	−	0.905557i	$-0.639453\pi$
$421$	−17.4087			−0.848449			−0.424224	+	0.905557i	$0.639453\pi$
$422$		0			0
$423$	−2.09991	−	2.09991i	−0.102101	−	0.102101i
$424$		0			0
$425$	3.65562	−	7.06433i	0.177324	−	0.342670i
$426$		0			0
$427$	−4.31286	+	4.31286i	−0.208714	+	0.208714i
$428$		0			0
$429$		−	3.21949i		−	0.155439i
$430$		0			0
$431$			31.1542i			1.50065i	0.661071	+	0.750323i	$0.270102\pi$
$431$			31.1542i			1.50065i	−0.661071	+	0.750323i	$0.729898\pi$
$432$		0			0
$433$	−12.1589	+	12.1589i	−0.584321	+	0.584321i	−0.936088	−	0.351766i	$-0.885581\pi$
$433$	−12.1589	+	12.1589i	−0.584321	+	0.584321i	0.351766	+	0.936088i	$0.385581\pi$
$434$		0			0
$435$	−0.905130	−	5.83347i	−0.0433977	−	0.279693i
$436$		0			0
$437$	21.7796	+	21.7796i	1.04186	+	1.04186i
$438$		0			0
$439$	14.2967			0.682344			0.341172	−	0.940001i	$-0.389176\pi$
$439$	14.2967			0.682344			0.341172	+	0.940001i	$0.389176\pi$
$440$		0			0
$441$	−0.0302761			−0.00144172
$442$		0			0
$443$	−7.02825	−	7.02825i	−0.333922	−	0.333922i	0.520152	−	0.854074i	$-0.325875\pi$
$443$	−7.02825	−	7.02825i	−0.333922	−	0.333922i	−0.854074	+	0.520152i	$0.825875\pi$
$444$		0			0
$445$	1.85952	+	1.35998i	0.0881496	+	0.0644691i
$446$		0			0
$447$	4.00951	−	4.00951i	0.189643	−	0.189643i
$448$		0			0
$449$		−	38.4608i		−	1.81508i	−0.419969	−	0.907538i	$-0.637959\pi$
$449$		−	38.4608i		−	1.81508i	0.419969	−	0.907538i	$-0.362041\pi$
$450$		0			0
$451$			3.09602i			0.145786i
$452$		0			0
$453$	13.6097	−	13.6097i	0.639442	−	0.639442i
$454$		0			0
$455$	21.0573	+	15.4005i	0.987184	+	0.721986i
$456$		0			0
$457$	4.93945	+	4.93945i	0.231058	+	0.231058i	0.813134	−	0.582076i	$-0.197760\pi$
$457$	4.93945	+	4.93945i	0.231058	+	0.231058i	−0.582076	+	0.813134i	$0.697760\pi$
$458$		0			0
$459$	−1.59083			−0.0742535
$460$		0			0
$461$	−27.1689			−1.26538			−0.632691	−	0.774404i	$-0.718050\pi$
$461$	−27.1689			−1.26538			−0.632691	+	0.774404i	$0.718050\pi$
$462$		0			0
$463$	4.96280	+	4.96280i	0.230641	+	0.230641i	0.812960	−	0.582319i	$-0.197855\pi$
$463$	4.96280	+	4.96280i	0.230641	+	0.230641i	−0.582319	+	0.812960i	$0.697855\pi$
$464$		0			0
$465$	−2.06055	−	13.2800i	−0.0955558	−	0.615847i
$466$		0			0
$467$	21.2340	−	21.2340i	0.982591	−	0.982591i	−0.0172604	−	0.999851i	$-0.505494\pi$
$467$	21.2340	−	21.2340i	0.982591	−	0.982591i	0.999851	+	0.0172604i	$0.00549442\pi$
$468$		0			0
$469$			19.0596i			0.880092i
$470$		0			0
$471$			2.96222i			0.136492i
$472$		0			0
$473$	3.71904	−	3.71904i	0.171001	−	0.171001i
$474$		0			0
$475$	−5.65685	−	17.7901i	−0.259554	−	0.816264i
$476$		0			0
$477$	−0.484862	−	0.484862i	−0.0222003	−	0.0222003i
$478$		0			0
$479$	18.7808			0.858118			0.429059	−	0.903277i	$-0.358845\pi$
$479$	18.7808			0.858118			0.429059	+	0.903277i	$0.358845\pi$
$480$		0			0
$481$	−19.5298			−0.890483
$482$		0			0
$483$	15.4005	+	15.4005i	0.700747	+	0.700747i
$484$		0			0
$485$	39.1542	−	6.07523i	1.77790	−	0.275862i
$486$		0			0
$487$	2.97058	−	2.97058i	0.134610	−	0.134610i	−0.636591	−	0.771201i	$-0.719656\pi$
$487$	2.97058	−	2.97058i	0.134610	−	0.134610i	0.771201	+	0.636591i	$0.219656\pi$
$488$		0			0
$489$			6.06055i			0.274068i
$490$		0			0
$491$			29.5480i			1.33348i	0.745290	+	0.666741i	$0.232311\pi$
$491$			29.5480i			1.33348i	−0.745290	+	0.666741i	$0.767689\pi$
$492$		0			0
$493$	−2.96972	+	2.96972i	−0.133750	+	0.133750i
$494$		0			0
$495$	−0.961649	+	1.31488i	−0.0432229	+	0.0590994i
$496$		0			0
$497$	−24.4995	−	24.4995i	−1.09895	−	1.09895i
$498$		0			0
$499$	−15.0473			−0.673608			−0.336804	−	0.941575i	$-0.609346\pi$
$499$	−15.0473			−0.673608			−0.336804	+	0.941575i	$0.609346\pi$
$500$		0			0
$501$	6.18922			0.276514
$502$		0			0
$503$	13.4136	+	13.4136i	0.598084	+	0.598084i	0.939802	−	0.341719i	$-0.111009\pi$
$503$	13.4136	+	13.4136i	0.598084	+	0.598084i	−0.341719	+	0.939802i	$0.611009\pi$
$504$		0			0
$505$	−7.48486	+	10.2342i	−0.333072	+	0.455415i
$506$		0			0
$507$	4.61728	−	4.61728i	0.205061	−	0.205061i
$508$		0			0
$509$		−	41.4187i		−	1.83585i	−0.396752	−	0.917926i	$-0.629863\pi$
$509$		−	41.4187i		−	1.83585i	0.396752	−	0.917926i	$-0.370137\pi$
$510$		0			0
$511$		−	14.8212i		−	0.655651i
$512$		0			0
$513$	−2.64002	+	2.64002i	−0.116560	+	0.116560i
$514$		0			0
$515$	−0.176615	+	0.0274038i	−0.00778257	+	0.00120756i
$516$		0			0
$517$	1.52982	+	1.52982i	0.0672813	+	0.0672813i
$518$		0			0
$519$	−23.2001			−1.01837
$520$		0			0
$521$	30.8392			1.35109			0.675545	−	0.737318i	$-0.263908\pi$
$521$	30.8392			1.35109			0.675545	+	0.737318i	$0.263908\pi$
$522$		0			0
$523$	17.1251	+	17.1251i	0.748829	+	0.748829i	0.974259	−	0.225430i	$-0.0723787\pi$
$523$	17.1251	+	17.1251i	0.748829	+	0.748829i	−0.225430	+	0.974259i	$0.572379\pi$
$524$		0			0
$525$	−4.00000	−	12.5795i	−0.174574	−	0.549013i
$526$		0			0
$527$	−6.76066	+	6.76066i	−0.294499	+	0.294499i
$528$		0			0
$529$			45.0587i			1.95907i
$530$		0			0
$531$			4.92834i			0.213872i
$532$		0			0
$533$	−13.2800	+	13.2800i	−0.575223	+	0.575223i
$534$		0			0
$535$	1.89589	+	12.2188i	0.0819666	+	0.528266i
$536$		0			0
$537$	−17.2645	−	17.2645i	−0.745016	−	0.745016i
$538$		0			0
$539$	0.0220566			0.000950045
$540$		0			0
$541$	22.3397			0.960458			0.480229	−	0.877143i	$-0.340554\pi$
$541$	22.3397			0.960458			0.480229	+	0.877143i	$0.340554\pi$
$542$		0			0
$543$	−7.97620	−	7.97620i	−0.342291	−	0.342291i
$544$		0			0
$545$	28.4802	+	20.8292i	1.21996	+	0.892227i
$546$		0			0
$547$	25.3428	−	25.3428i	1.08358	−	1.08358i	0.0874075	−	0.996173i	$-0.472142\pi$
$547$	25.3428	−	25.3428i	1.08358	−	1.08358i	0.996173	−	0.0874075i	$-0.0278582\pi$
$548$		0			0
$549$		−	2.31032i		−	0.0986022i
$550$		0			0
$551$			9.85668i			0.419909i
$552$		0			0
$553$	13.2800	−	13.2800i	0.564725	−	0.564725i
$554$		0			0
$555$	7.97620	+	5.83347i	0.338571	+	0.247617i
$556$		0			0
$557$	−21.1055	−	21.1055i	−0.894269	−	0.894269i	0.100653	−	0.994922i	$-0.467907\pi$
$557$	−21.1055	−	21.1055i	−0.894269	−	0.894269i	−0.994922	+	0.100653i	$0.967907\pi$
$558$		0			0
$559$	31.9048			1.34943
$560$		0			0
$561$	1.15894			0.0489306
$562$		0			0
$563$	−10.2955	−	10.2955i	−0.433905	−	0.433905i	0.456049	−	0.889955i	$-0.349264\pi$
$563$	−10.2955	−	10.2955i	−0.433905	−	0.433905i	−0.889955	+	0.456049i	$0.849264\pi$
$564$		0			0
$565$	−0.894492	−	5.76491i	−0.0376316	−	0.242532i
$566$		0			0
$567$	−1.86678	+	1.86678i	−0.0783973	+	0.0783973i
$568$		0			0
$569$		−	28.3179i		−	1.18715i	−0.804780	−	0.593574i	$-0.797717\pi$
$569$		−	28.3179i		−	1.18715i	0.804780	−	0.593574i	$-0.202283\pi$
$570$		0			0
$571$			27.2387i			1.13990i	0.821678	+	0.569952i	$0.193038\pi$
$571$			27.2387i			1.13990i	−0.821678	+	0.569952i	$0.806962\pi$
$572$		0			0
$573$	−2.31032	+	2.31032i	−0.0965151	+	0.0965151i
$574$		0			0
$575$	18.9574	−	36.6345i	0.790580	−	1.52776i
$576$		0			0
$577$	4.81078	+	4.81078i	0.200275	+	0.200275i	0.800118	−	0.599843i	$-0.204770\pi$
$577$	4.81078	+	4.81078i	0.200275	+	0.200275i	−0.599843	+	0.800118i	$0.704770\pi$
$578$		0			0
$579$	1.32858			0.0552139
$580$		0			0
$581$	13.2800			0.550949
$582$		0			0
$583$	0.353229	+	0.353229i	0.0146293	+	0.0146293i
$584$		0			0
$585$	−9.76491	+	1.51514i	−0.403729	+	0.0626432i
$586$		0			0
$587$	−4.84271	+	4.84271i	−0.199880	+	0.199880i	−0.799948	−	0.600069i	$-0.795140\pi$
$587$	−4.84271	+	4.84271i	−0.199880	+	0.199880i	0.600069	+	0.799948i	$0.295140\pi$
$588$		0			0
$589$			22.4390i			0.924582i
$590$		0			0
$591$			2.05710i			0.0846176i
$592$		0			0
$593$	18.8439	−	18.8439i	0.773827	−	0.773827i	−0.204946	−	0.978773i	$-0.565702\pi$
$593$	18.8439	−	18.8439i	0.773827	−	0.773827i	0.978773	+	0.204946i	$0.0657019\pi$
$594$		0			0
$595$	−5.54382	+	7.58015i	−0.227274	+	0.310756i
$596$		0			0
$597$	−3.67030	−	3.67030i	−0.150215	−	0.150215i
$598$		0			0
$599$	−30.2765			−1.23706			−0.618532	−	0.785760i	$-0.712272\pi$
$599$	−30.2765			−1.23706			−0.618532	+	0.785760i	$0.712272\pi$
$600$		0			0
$601$	30.1505			1.22986			0.614932	−	0.788581i	$-0.289184\pi$
$601$	30.1505			1.22986			0.614932	+	0.788581i	$0.289184\pi$
$602$		0			0
$603$	−5.10495	−	5.10495i	−0.207890	−	0.207890i
$604$		0			0
$605$	−13.8196	+	18.8957i	−0.561845	+	0.768220i
$606$		0			0
$607$	19.5438	−	19.5438i	0.793258	−	0.793258i	−0.188764	−	0.982022i	$-0.560448\pi$
$607$	19.5438	−	19.5438i	0.793258	−	0.793258i	0.982022	+	0.188764i	$0.0604482\pi$
$608$		0			0
$609$			6.96972i			0.282427i
$610$		0			0
$611$			13.1240i			0.530939i
$612$		0			0
$613$	−23.4040	+	23.4040i	−0.945279	+	0.945279i	−0.998579	−	0.0532993i	$-0.983026\pi$
$613$	−23.4040	+	23.4040i	−0.945279	+	0.945279i	0.0532993	+	0.998579i	$0.483026\pi$
$614$		0			0
$615$	9.39041	−	1.45703i	0.378658	−	0.0587531i
$616$		0			0
$617$	−17.9348	−	17.9348i	−0.722026	−	0.722026i	0.246992	−	0.969018i	$-0.420558\pi$
$617$	−17.9348	−	17.9348i	−0.722026	−	0.722026i	−0.969018	+	0.246992i	$0.920558\pi$
$618$		0			0
$619$	38.9056			1.56375			0.781875	−	0.623435i	$-0.214264\pi$
$619$	38.9056			1.56375			0.781875	+	0.623435i	$0.214264\pi$
$620$		0			0
$621$	−8.24977			−0.331052
$622$		0			0
$623$	−1.92330	−	1.92330i	−0.0770553	−	0.0770553i
$624$		0			0
$625$	−20.4087	+	14.4390i	−0.816349	+	0.577560i
$626$		0			0
$627$	1.92330	−	1.92330i	0.0768091	−	0.0768091i
$628$		0			0
$629$		−	7.03028i		−	0.280315i
$630$		0			0
$631$		−	12.7707i		−	0.508395i	−0.967152	−	0.254198i	$-0.918189\pi$
$631$		−	12.7707i		−	0.508395i	0.967152	−	0.254198i	$-0.0818113\pi$
$632$		0			0
$633$	8.32970	−	8.32970i	0.331076	−	0.331076i
$634$		0			0
$635$	−5.45818	−	35.1774i	−0.216601	−	1.39597i
$636$		0			0
$637$	0.0946093	+	0.0946093i	0.00374856	+	0.00374856i
$638$		0			0
$639$	13.1240			0.519176
$640$		0			0
$641$	−16.4683			−0.650461			−0.325230	−	0.945635i	$-0.605442\pi$
$641$	−16.4683			−0.650461			−0.325230	+	0.945635i	$0.605442\pi$
$642$		0			0
$643$	−5.74249	−	5.74249i	−0.226462	−	0.226462i	0.584751	−	0.811213i	$-0.301192\pi$
$643$	−5.74249	−	5.74249i	−0.226462	−	0.226462i	−0.811213	+	0.584751i	$0.801192\pi$
$644$		0			0
$645$	−13.0303	−	9.52982i	−0.513067	−	0.375236i
$646$		0			0
$647$	−4.61663	+	4.61663i	−0.181498	+	0.181498i	−0.792009	−	0.610510i	$-0.790964\pi$
$647$	−4.61663	+	4.61663i	−0.181498	+	0.181498i	0.610510	+	0.792009i	$0.290964\pi$
$648$		0			0
$649$		−	3.59037i		−	0.140934i
$650$		0			0
$651$			15.8668i			0.621867i
$652$		0			0
$653$	−14.4655	+	14.4655i	−0.566078	+	0.566078i	−0.931027	−	0.364949i	$-0.881086\pi$
$653$	−14.4655	+	14.4655i	−0.566078	+	0.566078i	0.364949	+	0.931027i	$0.381086\pi$
$654$		0			0
$655$	8.25750	+	6.03920i	0.322647	+	0.235971i
$656$		0			0
$657$	3.96972	+	3.96972i	0.154874	+	0.154874i
$658$		0			0
$659$	−35.5474			−1.38473			−0.692364	−	0.721548i	$-0.743431\pi$
$659$	−35.5474			−1.38473			−0.692364	+	0.721548i	$0.743431\pi$
$660$		0			0
$661$	−15.1883			−0.590756			−0.295378	−	0.955380i	$-0.595446\pi$
$661$	−15.1883			−0.590756			−0.295378	+	0.955380i	$0.595446\pi$
$662$		0			0
$663$	4.97116	+	4.97116i	0.193064	+	0.193064i
$664$		0			0
$665$	3.37935	+	21.7796i	0.131046	+	0.844576i
$666$		0			0
$667$	−15.4005	+	15.4005i	−0.596310	+	0.596310i
$668$		0			0
$669$			4.70058i			0.181735i
$670$		0			0
$671$			1.68311i			0.0649756i
$672$		0			0
$673$	−20.3700	+	20.3700i	−0.785204	+	0.785204i	−0.980704	−	0.195500i	$-0.937367\pi$
$673$	−20.3700	+	20.3700i	−0.785204	+	0.785204i	0.195500	+	0.980704i	$0.437367\pi$
$674$		0			0
$675$	4.44066	+	2.29793i	0.170921	+	0.0884476i
$676$		0			0
$677$	−9.06433	−	9.06433i	−0.348371	−	0.348371i	0.511132	−	0.859502i	$-0.329226\pi$
$677$	−9.06433	−	9.06433i	−0.348371	−	0.348371i	−0.859502	+	0.511132i	$0.829226\pi$
$678$		0			0
$679$	−46.7808			−1.79528
$680$		0			0
$681$	−12.4995			−0.478983
$682$		0			0
$683$	24.8545	+	24.8545i	0.951030	+	0.951030i	0.998856	−	0.0478253i	$-0.0152291\pi$
$683$	24.8545	+	24.8545i	0.951030	+	0.951030i	−0.0478253	+	0.998856i	$0.515229\pi$
$684$		0			0
$685$	12.7952	−	1.98532i	0.488879	−	0.0758552i
$686$		0			0
$687$	−5.01397	+	5.01397i	−0.191295	+	0.191295i
$688$		0			0
$689$			3.03028i			0.115444i
$690$		0			0
$691$		−	40.8979i		−	1.55583i	−0.628371	−	0.777914i	$-0.716278\pi$
$691$		−	40.8979i		−	1.55583i	0.628371	−	0.777914i	$-0.283722\pi$
$692$		0			0
$693$	1.35998	−	1.35998i	0.0516612	−	0.0516612i
$694$		0			0
$695$	−17.9393	+	24.5287i	−0.680475	+	0.930425i
$696$		0			0
$697$	−4.78051	−	4.78051i	−0.181075	−	0.181075i
$698$		0			0
$699$	−21.7430			−0.822398
$700$		0			0
$701$	43.1396			1.62936			0.814679	−	0.579912i	$-0.196913\pi$
$701$	43.1396			1.62936			0.814679	+	0.579912i	$0.196913\pi$
$702$		0			0
$703$	−11.6669	−	11.6669i	−0.440027	−	0.440027i
$704$		0			0
$705$	3.92007	−	5.35998i	0.147638	−	0.201868i
$706$		0			0
$707$	10.5852	−	10.5852i	0.398097	−	0.398097i
$708$		0			0
$709$			18.4702i			0.693662i	0.937928	+	0.346831i	$0.112742\pi$
$709$			18.4702i			0.693662i	−0.937928	+	0.346831i	$0.887258\pi$
$710$		0			0
$711$			7.11388i			0.266792i
$712$		0			0
$713$	−35.0596	+	35.0596i	−1.31299	+	1.31299i
$714$		0			0
$715$	7.11388	−	1.10380i	0.266044	−	0.0412798i
$716$		0			0
$717$	−0.499542	−	0.499542i	−0.0186557	−	0.0186557i
$718$		0			0
$719$	33.3725			1.24458			0.622292	−	0.782785i	$-0.286201\pi$
$719$	33.3725			1.24458			0.622292	+	0.782785i	$0.286201\pi$
$720$		0			0
$721$	0.211016			0.00785865
$722$		0			0
$723$	−17.6770	−	17.6770i	−0.657415	−	0.657415i
$724$		0			0
$725$	12.5795	−	4.00000i	0.467190	−	0.148556i
$726$		0			0
$727$	−23.2774	+	23.2774i	−0.863309	+	0.863309i	−0.991721	−	0.128412i	$-0.959012\pi$
$727$	−23.2774	+	23.2774i	−0.863309	+	0.863309i	0.128412	+	0.991721i	$0.459012\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$			11.4850i			0.424787i
$732$		0			0
$733$	16.2157	−	16.2157i	0.598941	−	0.598941i	−0.341090	−	0.940031i	$-0.610796\pi$
$733$	16.2157	−	16.2157i	0.598941	−	0.598941i	0.940031	+	0.341090i	$0.110796\pi$
$734$		0			0
$735$	−0.0103801	−	0.0668989i	−0.000382877	−	0.00246760i
$736$		0			0
$737$	3.71904	+	3.71904i	0.136992	+	0.136992i
$738$		0			0
$739$	−14.3408			−0.527535			−0.263768	−	0.964586i	$-0.584965\pi$
$739$	−14.3408			−0.527535			−0.263768	+	0.964586i	$0.584965\pi$
$740$		0			0
$741$	16.4995			0.606126
$742$		0			0
$743$	−11.6034	−	11.6034i	−0.425686	−	0.425686i	0.461470	−	0.887156i	$-0.347322\pi$
$743$	−11.6034	−	11.6034i	−0.425686	−	0.425686i	−0.887156	+	0.461470i	$0.847322\pi$
$744$		0			0
$745$	10.2342	+	7.48486i	0.374951	+	0.274224i
$746$		0			0
$747$	−3.55694	+	3.55694i	−0.130142	+	0.130142i
$748$		0			0
$749$		−	14.5988i		−	0.533430i
$750$		0			0
$751$			35.1721i			1.28345i	0.766936	+	0.641724i	$0.221780\pi$
$751$			35.1721i			1.28345i	−0.766936	+	0.641724i	$0.778220\pi$
$752$		0			0
$753$	20.2342	−	20.2342i	0.737374	−	0.737374i
$754$		0			0
$755$	34.7386	+	25.4064i	1.26427	+	0.924633i
$756$		0			0
$757$	15.7455	+	15.7455i	0.572281	+	0.572281i	0.932765	−	0.360484i	$-0.117389\pi$
$757$	15.7455	+	15.7455i	0.572281	+	0.572281i	−0.360484	+	0.932765i	$0.617389\pi$
$758$		0			0
$759$	6.01008			0.218152
$760$		0			0
$761$	−24.4002			−0.884508			−0.442254	−	0.896890i	$-0.645821\pi$
$761$	−24.4002			−0.884508			−0.442254	+	0.896890i	$0.645821\pi$
$762$		0			0
$763$	−29.4570	−	29.4570i	−1.06641	−	1.06641i
$764$		0			0
$765$	−0.545414	−	3.51514i	−0.0197195	−	0.127090i
$766$		0			0
$767$	15.4005	−	15.4005i	0.556080	−	0.556080i
$768$		0			0
$769$		−	15.9688i		−	0.575850i	−0.957653	−	0.287925i	$-0.907035\pi$
$769$		−	15.9688i		−	0.575850i	0.957653	−	0.287925i	$-0.0929654\pi$
$770$		0			0
$771$		−	5.52306i		−	0.198908i
$772$		0			0
$773$	2.84392	−	2.84392i	0.102289	−	0.102289i	−0.654110	−	0.756399i	$-0.726957\pi$
$773$	2.84392	−	2.84392i	0.102289	−	0.102289i	0.756399	+	0.654110i	$0.226957\pi$
$774$		0			0
$775$	28.6375	−	9.10611i	1.02869	−	0.327101i
$776$		0			0
$777$	−8.24977	−	8.24977i	−0.295959	−	0.295959i
$778$		0			0
$779$	−15.8668			−0.568486
$780$		0			0
$781$	−9.56101			−0.342120
$782$		0			0
$783$	−1.86678	−	1.86678i	−0.0667132	−	0.0667132i
$784$		0			0
$785$	−6.54541	+	1.01560i	−0.233616	+	0.0362482i
$786$		0			0
$787$	7.49452	−	7.49452i	0.267151	−	0.267151i	−0.560800	−	0.827951i	$-0.689506\pi$
$787$	7.49452	−	7.49452i	0.267151	−	0.267151i	0.827951	+	0.560800i	$0.189506\pi$
$788$		0			0
$789$		−	0.249771i		−	0.00889208i
$790$		0			0
$791$			6.88781i			0.244902i
$792$		0			0
$793$	−7.21949	+	7.21949i	−0.256372	+	0.256372i
$794$		0			0
$795$	0.905130	−	1.23760i	0.0321016	−	0.0438931i
$796$		0			0
$797$	−26.1552	−	26.1552i	−0.926463	−	0.926463i	0.0710121	−	0.997475i	$-0.477377\pi$
$797$	−26.1552	−	26.1552i	−0.926463	−	0.926463i	−0.997475	+	0.0710121i	$0.977377\pi$
$798$		0			0
$799$	−4.72432			−0.167134
$800$		0			0
$801$	1.03028			0.0364030
$802$		0			0
$803$	−2.89200	−	2.89200i	−0.102057	−	0.102057i
$804$		0			0
$805$	−28.7493	+	39.3094i	−1.01328	+	1.38547i
$806$		0			0
$807$	−3.81084	+	3.81084i	−0.134148	+	0.134148i
$808$		0			0
$809$		−	23.7115i		−	0.833651i	−0.908987	−	0.416826i	$-0.863143\pi$
$809$		−	23.7115i		−	0.833651i	0.908987	−	0.416826i	$-0.136857\pi$
$810$		0			0
$811$			26.0077i			0.913255i	0.889658	+	0.456628i	$0.150943\pi$
$811$			26.0077i			0.913255i	−0.889658	+	0.456628i	$0.849057\pi$
$812$		0			0
$813$	10.8898	−	10.8898i	0.381922	−	0.381922i
$814$		0			0
$815$	−13.3916	+	2.07786i	−0.469086	+	0.0727841i
$816$		0			0
$817$	19.0596	+	19.0596i	0.666812	+	0.666812i
$818$		0			0
$819$	11.6669			0.407676
$820$		0			0
$821$	−33.0790			−1.15447			−0.577233	−	0.816580i	$-0.695867\pi$
$821$	−33.0790			−1.15447			−0.577233	+	0.816580i	$0.695867\pi$
$822$		0			0
$823$	−17.9737	−	17.9737i	−0.626525	−	0.626525i	0.320667	−	0.947192i	$-0.396093\pi$
$823$	−17.9737	−	17.9737i	−0.626525	−	0.626525i	−0.947192	+	0.320667i	$0.896093\pi$
$824$		0			0
$825$	−3.23509	−	1.67408i	−0.112631	−	0.0582840i
$826$		0			0
$827$	−18.8665	+	18.8665i	−0.656051	+	0.656051i	−0.954443	−	0.298392i	$-0.903550\pi$
$827$	−18.8665	+	18.8665i	−0.656051	+	0.656051i	0.298392	+	0.954443i	$0.403550\pi$
$828$		0			0
$829$		−	3.28005i		−	0.113921i	−0.998376	−	0.0569604i	$-0.981859\pi$
$829$		−	3.28005i		−	0.113921i	0.998376	−	0.0569604i	$-0.0181409\pi$
$830$		0			0
$831$		−	12.1540i		−	0.421616i
$832$		0			0
$833$	−0.0340571	+	0.0340571i	−0.00118001	+	0.00118001i
$834$		0			0
$835$	2.12197	+	13.6759i	0.0734337	+	0.473273i
$836$		0			0
$837$	−4.24977	−	4.24977i	−0.146894	−	0.146894i
$838$		0			0
$839$	−54.8854			−1.89486			−0.947428	−	0.319969i	$-0.896327\pi$
$839$	−54.8854			−1.89486			−0.947428	+	0.319969i	$0.896327\pi$
$840$		0			0
$841$	22.0303			0.759665
$842$		0			0
$843$	−14.6720	−	14.6720i	−0.505330	−	0.505330i
$844$		0			0
$845$	11.7855	+	8.61944i	0.405433	+	0.296518i
$846$		0			0
$847$	19.5438	−	19.5438i	0.671533	−	0.671533i
$848$		0			0
$849$		−	26.2791i		−	0.901897i
$850$		0			0
$851$		−	36.4578i		−	1.24976i
$852$		0			0
$853$	17.9348	−	17.9348i	0.614074	−	0.614074i	−0.329931	−	0.944005i	$-0.607025\pi$
$853$	17.9348	−	17.9348i	0.614074	−	0.614074i	0.944005	+	0.329931i	$0.107025\pi$
$854$		0			0
$855$	−6.73860	−	4.92834i	−0.230455	−	0.168546i
$856$		0			0
$857$	−9.00378	−	9.00378i	−0.307563	−	0.307563i	0.536400	−	0.843964i	$-0.319784\pi$
$857$	−9.00378	−	9.00378i	−0.307563	−	0.307563i	−0.843964	+	0.536400i	$0.819784\pi$
$858$		0			0
$859$	−24.6779			−0.841998			−0.420999	−	0.907061i	$-0.638320\pi$
$859$	−24.6779			−0.841998			−0.420999	+	0.907061i	$0.638320\pi$
$860$		0			0
$861$	−11.2195			−0.382359
$862$		0			0
$863$	−40.4811	−	40.4811i	−1.37799	−	1.37799i	−0.848009	−	0.529982i	$-0.822198\pi$
$863$	−40.4811	−	40.4811i	−1.37799	−	1.37799i	−0.529982	−	0.848009i	$-0.677802\pi$
$864$		0			0
$865$	−7.95413	−	51.2635i	−0.270448	−	1.74301i
$866$		0			0
$867$	10.2313	−	10.2313i	0.347474	−	0.347474i
$868$		0			0
$869$		−	5.18257i		−	0.175807i
$870$		0			0
$871$			31.9048i			1.08105i
$872$		0			0
$873$	12.5298	−	12.5298i	0.424070	−	0.424070i
$874$		0			0
$875$	26.4246	−	13.1514i	0.893313	−	0.444598i
$876$		0			0
$877$	1.59507	+	1.59507i	0.0538616	+	0.0538616i	0.733525	−	0.679663i	$-0.237874\pi$
$877$	1.59507	+	1.59507i	0.0538616	+	0.0538616i	−0.679663	+	0.733525i	$0.737874\pi$
$878$		0			0
$879$	−8.81775			−0.297415
$880$		0			0
$881$	33.2876			1.12149			0.560744	−	0.827989i	$-0.310515\pi$
$881$	33.2876			1.12149			0.560744	+	0.827989i	$0.310515\pi$
$882$		0			0
$883$	−29.4296	−	29.4296i	−0.990385	−	0.990385i	0.00956956	−	0.999954i	$-0.496954\pi$
$883$	−29.4296	−	29.4296i	−0.990385	−	0.990385i	−0.999954	+	0.00956956i	$0.996954\pi$
$884$		0			0
$885$	−10.8898	+	1.68968i	−0.366056	+	0.0567979i
$886$		0			0
$887$	30.9776	−	30.9776i	1.04013	−	1.04013i	0.0409656	−	0.999161i	$-0.486957\pi$
$887$	30.9776	−	30.9776i	1.04013	−	1.04013i	0.999161	−	0.0409656i	$-0.0130434\pi$
$888$		0			0
$889$			42.0294i			1.40962i
$890$		0			0
$891$			0.728515i			0.0244062i
$892$		0			0
$893$	−7.84014	+	7.84014i	−0.262360	+	0.262360i
$894$		0			0
$895$	32.2289	−	44.0671i	1.07729	−	1.47300i
$896$		0			0
$897$	25.7796	+	25.7796i	0.860755	+	0.860755i
$898$		0			0
$899$	−15.8668			−0.529186
$900$		0			0
$901$	−1.09083			−0.0363408
$902$		0			0
$903$	13.4772	+	13.4772i	0.448493	+	0.448493i
$904$		0			0
$905$	14.8898	−	20.3591i	0.494954	−	0.676758i
$906$		0			0
$907$	−28.6790	+	28.6790i	−0.952271	+	0.952271i	−0.998912	−	0.0466405i	$-0.985148\pi$
$907$	−28.6790	+	28.6790i	−0.952271	+	0.952271i	0.0466405	+	0.998912i	$0.485148\pi$
$908$		0			0
$909$			5.67030i			0.188072i
$910$		0			0
$911$		−	31.8607i		−	1.05559i	−0.849371	−	0.527796i	$-0.823019\pi$
$911$		−	31.8607i		−	1.05559i	0.849371	−	0.527796i	$-0.176981\pi$
$912$		0			0
$913$	2.59129	−	2.59129i	0.0857591	−	0.0857591i
$914$		0			0
$915$	5.10495	−	0.792092i	0.168765	−	0.0261858i
$916$		0			0
$917$	−8.54072	−	8.54072i	−0.282039	−	0.282039i
$918$		0			0
$919$	−55.4206			−1.82816			−0.914079	−	0.405536i	$-0.867085\pi$
$919$	−55.4206			−1.82816			−0.914079	+	0.405536i	$0.867085\pi$
$920$		0			0
$921$	−1.28005			−0.0421790
$922$		0			0
$923$	−41.0109	−	41.0109i	−1.34989	−	1.34989i
$924$		0			0
$925$	−10.1552	+	19.6244i	−0.333900	+	0.645247i
$926$		0			0
$927$	−0.0565188	+	0.0565188i	−0.00185632	+	0.00185632i
$928$		0			0
$929$			46.9603i			1.54072i	0.637610	+	0.770359i	$0.279923\pi$
$929$			46.9603i			1.54072i	−0.637610	+	0.770359i	$0.720077\pi$
$930$		0			0
$931$			0.113038i			0.00370466i
$932$		0			0
$933$	17.2800	−	17.2800i	0.565723	−	0.565723i
$934$		0			0
$935$	0.397342	+	2.56083i	0.0129945	+	0.0837481i
$936$		0			0
$937$	10.4693	+	10.4693i	0.342016	+	0.342016i	0.857125	−	0.515109i	$-0.172248\pi$
$937$	10.4693	+	10.4693i	0.342016	+	0.342016i	−0.515109	+	0.857125i	$0.672248\pi$
$938$		0			0
$939$	26.2908			0.857966
$940$		0			0
$941$	41.1084			1.34009			0.670047	−	0.742318i	$-0.266274\pi$
$941$	41.1084			1.34009			0.670047	+	0.742318i	$0.266274\pi$
$942$		0			0
$943$	−24.7909	−	24.7909i	−0.807303	−	0.807303i
$944$		0			0
$945$	−4.76491	−	3.48486i	−0.155002	−	0.113363i
$946$		0			0
$947$	25.8091	−	25.8091i	0.838682	−	0.838682i	−0.150003	−	0.988685i	$-0.547928\pi$
$947$	25.8091	−	25.8091i	0.838682	−	0.838682i	0.988685	+	0.150003i	$0.0479284\pi$
$948$		0			0
$949$		−	24.8099i		−	0.805362i
$950$		0			0
$951$		−	27.3143i		−	0.885726i
$952$		0			0
$953$	−7.78429	+	7.78429i	−0.252158	+	0.252158i	−0.821855	−	0.569697i	$-0.807061\pi$
$953$	−7.78429	+	7.78429i	−0.252158	+	0.252158i	0.569697	+	0.821855i	$0.307061\pi$
$954$		0			0
$955$	−5.89705	−	4.31286i	−0.190824	−	0.139561i
$956$		0			0
$957$	1.35998	+	1.35998i	0.0439618	+	0.0439618i
$958$		0			0
$959$	−15.2875			−0.493658
$960$		0			0
$961$	−5.12110			−0.165197
$962$		0			0
$963$	3.91017	+	3.91017i	0.126004	+	0.126004i
$964$		0			0
$965$	0.455503	+	2.93567i	0.0146631	+	0.0945025i
$966$		0			0
$967$	11.7235	−	11.7235i	0.377001	−	0.377001i	−0.493018	−	0.870019i	$-0.664106\pi$
$967$	11.7235	−	11.7235i	0.377001	−	0.377001i	0.870019	+	0.493018i	$0.164106\pi$
$968$		0			0
$969$			5.93945i			0.190803i
$970$		0			0
$971$			12.9748i			0.416380i	0.978088	+	0.208190i	$0.0667572\pi$
$971$			12.9748i			0.416380i	−0.978088	+	0.208190i	$0.933243\pi$
$972$		0			0
$973$	25.3700	−	25.3700i	0.813324	−	0.813324i
$974$		0			0
$975$	−6.69578	−	21.0573i	−0.214437	−	0.674375i
$976$		0			0
$977$	−13.9054	−	13.9054i	−0.444873	−	0.444873i	0.448773	−	0.893646i	$-0.351861\pi$
$977$	−13.9054	−	13.9054i	−0.444873	−	0.444873i	−0.893646	+	0.448773i	$0.851861\pi$
$978$		0			0
$979$	−0.750572			−0.0239884
$980$		0			0
$981$	15.7796			0.503803
$982$		0			0
$983$	13.9381	+	13.9381i	0.444557	+	0.444557i	0.893540	−	0.448983i	$-0.148214\pi$
$983$	13.9381	+	13.9381i	0.444557	+	0.444557i	−0.448983	+	0.893540i	$0.648214\pi$
$984$		0			0
$985$	−4.54541	+	0.705273i	−0.144829	+	0.0224719i
$986$		0			0
$987$	−5.54382	+	5.54382i	−0.176462	+	0.176462i
$988$		0			0
$989$			59.5592i			1.89387i
$990$		0			0
$991$			52.9621i			1.68240i	0.540726	+	0.841199i	$0.318150\pi$
$991$			52.9621i			1.68240i	−0.540726	+	0.841199i	$0.681850\pi$
$992$		0			0
$993$	−7.79897	+	7.79897i	−0.247493	+	0.247493i
$994$		0			0
$995$	6.85164	−	9.36835i	0.217211	−	0.296997i
$996$		0			0
$997$	−1.53452	−	1.53452i	−0.0485986	−	0.0485986i	0.682390	−	0.730988i	$-0.260941\pi$
$997$	−1.53452	−	1.53452i	−0.0485986	−	0.0485986i	−0.730988	+	0.682390i	$0.760941\pi$
$998$		0			0
$999$	4.41926			0.139819

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.w.g.127.4		12
4.3	odd	2	inner	960.2.w.g.127.1		12
5.3	odd	4	inner	960.2.w.g.703.1		12
8.3	odd	2		60.2.j.a.7.3	yes	12
8.5	even	2		60.2.j.a.7.1	✓	12
20.3	even	4	inner	960.2.w.g.703.4		12
24.5	odd	2		180.2.k.e.127.6		12
24.11	even	2		180.2.k.e.127.4		12
40.3	even	4		60.2.j.a.43.1	yes	12
40.13	odd	4		60.2.j.a.43.3	yes	12
40.19	odd	2		300.2.j.d.7.4		12
40.27	even	4		300.2.j.d.43.6		12
40.29	even	2		300.2.j.d.7.6		12
40.37	odd	4		300.2.j.d.43.4		12
120.29	odd	2		900.2.k.n.307.1		12
120.53	even	4		180.2.k.e.163.4		12
120.59	even	2		900.2.k.n.307.3		12
120.77	even	4		900.2.k.n.343.3		12
120.83	odd	4		180.2.k.e.163.6		12
120.107	odd	4		900.2.k.n.343.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.j.a.7.1	✓	12	8.5	even	2
60.2.j.a.7.3	yes	12	8.3	odd	2
60.2.j.a.43.1	yes	12	40.3	even	4
60.2.j.a.43.3	yes	12	40.13	odd	4
180.2.k.e.127.4		12	24.11	even	2
180.2.k.e.127.6		12	24.5	odd	2
180.2.k.e.163.4		12	120.53	even	4
180.2.k.e.163.6		12	120.83	odd	4
300.2.j.d.7.4		12	40.19	odd	2
300.2.j.d.7.6		12	40.29	even	2
300.2.j.d.43.4		12	40.37	odd	4
300.2.j.d.43.6		12	40.27	even	4
900.2.k.n.307.1		12	120.29	odd	2
900.2.k.n.307.3		12	120.59	even	2
900.2.k.n.343.1		12	120.107	odd	4
900.2.k.n.343.3		12	120.77	even	4
960.2.w.g.127.1		12	4.3	odd	2	inner
960.2.w.g.127.4		12	1.1	even	1	trivial
960.2.w.g.703.1		12	5.3	odd	4	inner
960.2.w.g.703.4		12	20.3	even	4	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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.w (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{3} +(-1.32001 + 1.80487i) q^{5} +(1.86678 - 1.86678i) q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{3} +(-1.32001 + 1.80487i) q^{5} +(1.86678 - 1.86678i) q^{7} +1.00000i q^{9} -0.728515i q^{11} +(3.12489 - 3.12489i) q^{13} +(-2.20963 + 0.342849i) q^{15} +(1.12489 + 1.12489i) q^{17} +3.73356 q^{19} +2.64002 q^{21} +(5.83347 + 5.83347i) q^{23} +(-1.51514 - 4.76491i) q^{25} +(-0.707107 + 0.707107i) q^{27} +2.64002i q^{29} +6.01008i q^{31} +(0.515138 - 0.515138i) q^{33} +(0.905130 + 5.83347i) q^{35} +(-3.12489 - 3.12489i) q^{37} +4.41926 q^{39} -4.24977 q^{41} +(5.10495 + 5.10495i) q^{43} +(-1.80487 - 1.32001i) q^{45} +(-2.09991 + 2.09991i) q^{47} +0.0302761i q^{49} +1.59083i q^{51} +(-0.484862 + 0.484862i) q^{53} +(1.31488 + 0.961649i) q^{55} +(2.64002 + 2.64002i) q^{57} +4.92834 q^{59} -2.31032 q^{61} +(1.86678 + 1.86678i) q^{63} +(1.51514 + 9.76491i) q^{65} +(-5.10495 + 5.10495i) q^{67} +8.24977i q^{69} -13.1240i q^{71} +(3.96972 - 3.96972i) q^{73} +(2.29793 - 4.44066i) q^{75} +(-1.35998 - 1.35998i) q^{77} +7.11388 q^{79} -1.00000 q^{81} +(3.55694 + 3.55694i) q^{83} +(-3.51514 + 0.545414i) q^{85} +(-1.86678 + 1.86678i) q^{87} -1.03028i q^{89} -11.6669i q^{91} +(-4.24977 + 4.24977i) q^{93} +(-4.92834 + 6.73860i) q^{95} +(-12.5298 - 12.5298i) q^{97} +0.728515 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 12 * q	\( 12 q + 4 q^{13} - 20 q^{17} - 20 q^{25} + 8 q^{33} - 4 q^{37} + 16 q^{41} - 4 q^{45} - 4 q^{53} + 32 q^{61} + 20 q^{65} + 44 q^{73} - 48 q^{77} - 12 q^{81} - 44 q^{85} + 16 q^{93} - 20 q^{97}+O(q^{100}) \) 12 * q + 4 * q^13 - 20 * q^17 - 20 * q^25 + 8 * q^33 - 4 * q^37 + 16 * q^41 - 4 * q^45 - 4 * q^53 + 32 * q^61 + 20 * q^65 + 44 * q^73 - 48 * q^77 - 12 * q^81 - 44 * q^85 + 16 * q^93 - 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more