LMFDB - Embedded newform 1960.2.q.p.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1960,2,Mod(361,1960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1960, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("1960.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1960 = 2^{3} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1960.q (of order $3$, 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:	$15.6506787962$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1960.361
Dual form			1960.2.q.p.961.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.207107 - 0.358719i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.41421 + 2.44949i) q^{9} +O(q^{10})$	\(q+(0.207107 - 0.358719i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.41421 + 2.44949i) q^{9} +(0.500000 - 0.866025i) q^{11} +2.41421 q^{13} +0.414214 q^{15} +(0.207107 - 0.358719i) q^{17} +(-1.00000 - 1.73205i) q^{19} +(1.12132 + 1.94218i) q^{23} +(-0.500000 + 0.866025i) q^{25} +2.41421 q^{27} +1.00000 q^{29} +(-0.878680 + 1.52192i) q^{31} +(-0.207107 - 0.358719i) q^{33} +(3.94975 + 6.84116i) q^{37} +(0.500000 - 0.866025i) q^{39} +7.41421 q^{41} -0.343146 q^{43} +(-1.41421 + 2.44949i) q^{45} +(-5.20711 - 9.01897i) q^{47} +(-0.0857864 - 0.148586i) q^{51} +(-4.70711 + 8.15295i) q^{53} +1.00000 q^{55} -0.828427 q^{57} +(-5.12132 + 8.87039i) q^{59} +(0.585786 + 1.01461i) q^{61} +(1.20711 + 2.09077i) q^{65} +(-0.707107 + 1.22474i) q^{67} +0.928932 q^{69} +14.4853 q^{71} +(2.58579 - 4.47871i) q^{73} +(0.207107 + 0.358719i) q^{75} +(7.32843 + 12.6932i) q^{79} +(-3.74264 + 6.48244i) q^{81} +11.3137 q^{83} +0.414214 q^{85} +(0.207107 - 0.358719i) q^{87} +(0.828427 + 1.43488i) q^{89} +(0.363961 + 0.630399i) q^{93} +(1.00000 - 1.73205i) q^{95} -0.0710678 q^{97} +2.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{5}+O(q^{10}) $ 4 * q - 2 * q^3 + 2 * q^5	$ 4 q - 2 q^{3} + 2 q^{5} + 2 q^{11} + 4 q^{13} - 4 q^{15} - 2 q^{17} - 4 q^{19} - 4 q^{23} - 2 q^{25} + 4 q^{27} + 4 q^{29} - 12 q^{31} + 2 q^{33} - 4 q^{37} + 2 q^{39} + 24 q^{41} - 24 q^{43} - 18 q^{47} - 6 q^{51} - 16 q^{53} + 4 q^{55} + 8 q^{57} - 12 q^{59} + 8 q^{61} + 2 q^{65} + 32 q^{69} + 24 q^{71} + 16 q^{73} - 2 q^{75} + 18 q^{79} + 2 q^{81} - 4 q^{85} - 2 q^{87} - 8 q^{89} - 24 q^{93} + 4 q^{95} + 28 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^5 + 2 * q^11 + 4 * q^13 - 4 * q^15 - 2 * q^17 - 4 * q^19 - 4 * q^23 - 2 * q^25 + 4 * q^27 + 4 * q^29 - 12 * q^31 + 2 * q^33 - 4 * q^37 + 2 * q^39 + 24 * q^41 - 24 * q^43 - 18 * q^47 - 6 * q^51 - 16 * q^53 + 4 * q^55 + 8 * q^57 - 12 * q^59 + 8 * q^61 + 2 * q^65 + 32 * q^69 + 24 * q^71 + 16 * q^73 - 2 * q^75 + 18 * q^79 + 2 * q^81 - 4 * q^85 - 2 * q^87 - 8 * q^89 - 24 * q^93 + 4 * q^95 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times$.

$n$	$981$	$1081$	$1177$	$1471$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	0.207107	−	0.358719i	0.119573	−	0.207107i	−0.800025	−	0.599966i	$-0.795181\pi$
$3$	0.207107	−	0.358719i	0.119573	−	0.207107i	0.919599	+	0.392859i	$0.128514\pi$
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.41421	+	2.44949i	0.471405	+	0.816497i
$10$		0			0
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i	−0.780750	−	0.624844i	$-0.785163\pi$
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i	0.931505	+	0.363727i	$0.118496\pi$
$12$		0			0
$13$	2.41421			0.669582			0.334791	−	0.942292i	$-0.391334\pi$
$13$	2.41421			0.669582			0.334791	+	0.942292i	$0.391334\pi$
$14$		0			0
$15$	0.414214			0.106949
$16$		0			0
$17$	0.207107	−	0.358719i	0.0502308	−	0.0870023i	−0.839817	−	0.542870i	$-0.817338\pi$
$17$	0.207107	−	0.358719i	0.0502308	−	0.0870023i	0.890048	+	0.455868i	$0.150671\pi$
$18$		0			0
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	0.728219	−	0.685344i	$-0.240348\pi$
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	−0.957635	+	0.287984i	$0.907015\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.12132	+	1.94218i	0.233811	+	0.404973i	0.958927	−	0.283654i	$-0.0915468\pi$
$23$	1.12132	+	1.94218i	0.233811	+	0.404973i	−0.725115	+	0.688628i	$0.758213\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	2.41421			0.464616
$28$		0			0
$29$	1.00000			0.185695			0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000			0.185695			0.0928477	+	0.995680i	$0.470403\pi$
$30$		0			0
$31$	−0.878680	+	1.52192i	−0.157816	+	0.273345i	−0.934081	−	0.357062i	$-0.883778\pi$
$31$	−0.878680	+	1.52192i	−0.157816	+	0.273345i	0.776265	+	0.630407i	$0.217112\pi$
$32$		0			0
$33$	−0.207107	−	0.358719i	−0.0360527	−	0.0624450i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.94975	+	6.84116i	0.649334	+	1.12468i	0.983282	+	0.182089i	$0.0582858\pi$
$37$	3.94975	+	6.84116i	0.649334	+	1.12468i	−0.333948	+	0.942592i	$0.608381\pi$
$38$		0			0
$39$	0.500000	−	0.866025i	0.0800641	−	0.138675i
$40$		0			0
$41$	7.41421			1.15791			0.578953	−	0.815361i	$-0.303462\pi$
$41$	7.41421			1.15791			0.578953	+	0.815361i	$0.303462\pi$
$42$		0			0
$43$	−0.343146			−0.0523292			−0.0261646	−	0.999658i	$-0.508329\pi$
$43$	−0.343146			−0.0523292			−0.0261646	+	0.999658i	$0.508329\pi$
$44$		0			0
$45$	−1.41421	+	2.44949i	−0.210819	+	0.365148i
$46$		0			0
$47$	−5.20711	−	9.01897i	−0.759535	−	1.31555i	−0.943088	−	0.332543i	$-0.892093\pi$
$47$	−5.20711	−	9.01897i	−0.759535	−	1.31555i	0.183554	−	0.983010i	$-0.441240\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−0.0857864	−	0.148586i	−0.0120125	−	0.0208063i
$52$		0			0
$53$	−4.70711	+	8.15295i	−0.646571	+	1.11989i	0.337365	+	0.941374i	$0.390464\pi$
$53$	−4.70711	+	8.15295i	−0.646571	+	1.11989i	−0.983936	+	0.178520i	$0.942869\pi$
$54$		0			0
$55$	1.00000			0.134840
$56$		0			0
$57$	−0.828427			−0.109728
$58$		0			0
$59$	−5.12132	+	8.87039i	−0.666739	+	1.15483i	0.312072	+	0.950059i	$0.398977\pi$
$59$	−5.12132	+	8.87039i	−0.666739	+	1.15483i	−0.978811	+	0.204767i	$0.934356\pi$
$60$		0			0
$61$	0.585786	+	1.01461i	0.0750023	+	0.129908i	0.901087	−	0.433638i	$-0.142770\pi$
$61$	0.585786	+	1.01461i	0.0750023	+	0.129908i	−0.826085	+	0.563546i	$0.809437\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.20711	+	2.09077i	0.149723	+	0.259328i
$66$		0			0
$67$	−0.707107	+	1.22474i	−0.0863868	+	0.149626i	−0.905981	−	0.423318i	$-0.860865\pi$
$67$	−0.707107	+	1.22474i	−0.0863868	+	0.149626i	0.819594	+	0.572944i	$0.194199\pi$
$68$		0			0
$69$	0.928932			0.111830
$70$		0			0
$71$	14.4853			1.71909			0.859543	−	0.511063i	$-0.170748\pi$
$71$	14.4853			1.71909			0.859543	+	0.511063i	$0.170748\pi$
$72$		0			0
$73$	2.58579	−	4.47871i	0.302643	−	0.524194i	−0.674090	−	0.738649i	$-0.735464\pi$
$73$	2.58579	−	4.47871i	0.302643	−	0.524194i	0.976734	+	0.214455i	$0.0687975\pi$
$74$		0			0
$75$	0.207107	+	0.358719i	0.0239146	+	0.0414214i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	7.32843	+	12.6932i	0.824512	+	1.42810i	0.902291	+	0.431127i	$0.141884\pi$
$79$	7.32843	+	12.6932i	0.824512	+	1.42810i	−0.0777789	+	0.996971i	$0.524783\pi$
$80$		0			0
$81$	−3.74264	+	6.48244i	−0.415849	+	0.720272i
$82$		0			0
$83$	11.3137			1.24184			0.620920	−	0.783874i	$-0.286759\pi$
$83$	11.3137			1.24184			0.620920	+	0.783874i	$0.286759\pi$
$84$		0			0
$85$	0.414214			0.0449278
$86$		0			0
$87$	0.207107	−	0.358719i	0.0222042	−	0.0384588i
$88$		0			0
$89$	0.828427	+	1.43488i	0.0878131	+	0.152097i	0.906586	−	0.422020i	$-0.138679\pi$
$89$	0.828427	+	1.43488i	0.0878131	+	0.152097i	−0.818773	+	0.574117i	$0.805346\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	0.363961	+	0.630399i	0.0377410	+	0.0653693i
$94$		0			0
$95$	1.00000	−	1.73205i	0.102598	−	0.177705i
$96$		0			0
$97$	−0.0710678			−0.00721584			−0.00360792	−	0.999993i	$-0.501148\pi$
$97$	−0.0710678			−0.00721584			−0.00360792	+	0.999993i	$0.501148\pi$
$98$		0			0
$99$	2.82843			0.284268
$100$		0			0
$101$	3.24264	−	5.61642i	0.322655	−	0.558855i	−0.658380	−	0.752686i	$-0.728758\pi$
$101$	3.24264	−	5.61642i	0.322655	−	0.558855i	0.981035	+	0.193831i	$0.0620914\pi$
$102$		0			0
$103$	−7.62132	−	13.2005i	−0.750951	−	1.30069i	−0.947362	−	0.320164i	$-0.896262\pi$
$103$	−7.62132	−	13.2005i	−0.750951	−	1.30069i	0.196411	−	0.980522i	$-0.437071\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.24264	−	2.15232i	−0.120131	−	0.208072i	0.799688	−	0.600415i	$-0.204998\pi$
$107$	−1.24264	−	2.15232i	−0.120131	−	0.208072i	−0.919819	+	0.392343i	$0.871665\pi$
$108$		0			0
$109$	−2.15685	+	3.73578i	−0.206589	+	0.357823i	−0.950638	−	0.310302i	$-0.899570\pi$
$109$	−2.15685	+	3.73578i	−0.206589	+	0.357823i	0.744049	+	0.668125i	$0.232903\pi$
$110$		0			0
$111$	3.27208			0.310572
$112$		0			0
$113$	5.07107			0.477046			0.238523	−	0.971137i	$-0.423337\pi$
$113$	5.07107			0.477046			0.238523	+	0.971137i	$0.423337\pi$
$114$		0			0
$115$	−1.12132	+	1.94218i	−0.104564	+	0.181110i
$116$		0			0
$117$	3.41421	+	5.91359i	0.315644	+	0.546712i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$		0			0
$123$	1.53553	−	2.65962i	0.138454	−	0.239810i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	12.2426			1.08636			0.543179	−	0.839617i	$-0.317220\pi$
$127$	12.2426			1.08636			0.543179	+	0.839617i	$0.317220\pi$
$128$		0			0
$129$	−0.0710678	+	0.123093i	−0.00625717	+	0.0108377i
$130$		0			0
$131$	−5.87868	−	10.1822i	−0.513623	−	0.889620i	−0.999875	−	0.0158021i	$-0.994970\pi$
$131$	−5.87868	−	10.1822i	−0.513623	−	0.889620i	0.486253	−	0.873818i	$-0.338364\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	1.20711	+	2.09077i	0.103891	+	0.179945i
$136$		0			0
$137$	−1.65685	+	2.86976i	−0.141555	+	0.245180i	−0.928082	−	0.372375i	$-0.878543\pi$
$137$	−1.65685	+	2.86976i	−0.141555	+	0.245180i	0.786528	+	0.617555i	$0.211877\pi$
$138$		0			0
$139$	−1.41421			−0.119952			−0.0599760	−	0.998200i	$-0.519102\pi$
$139$	−1.41421			−0.119952			−0.0599760	+	0.998200i	$0.519102\pi$
$140$		0			0
$141$	−4.31371			−0.363280
$142$		0			0
$143$	1.20711	−	2.09077i	0.100943	−	0.174839i
$144$		0			0
$145$	0.500000	+	0.866025i	0.0415227	+	0.0719195i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	7.41421	+	12.8418i	0.607396	+	1.05204i	0.991668	+	0.128821i	$0.0411192\pi$
$149$	7.41421	+	12.8418i	0.607396	+	1.05204i	−0.384272	+	0.923220i	$0.625547\pi$
$150$		0			0
$151$	−2.32843	+	4.03295i	−0.189485	+	0.328197i	−0.945079	−	0.326843i	$-0.894015\pi$
$151$	−2.32843	+	4.03295i	−0.189485	+	0.328197i	0.755594	+	0.655040i	$0.227348\pi$
$152$		0			0
$153$	1.17157			0.0947161
$154$		0			0
$155$	−1.75736			−0.141154
$156$		0			0
$157$	3.24264	−	5.61642i	0.258791	−	0.448239i	−0.707127	−	0.707086i	$-0.750009\pi$
$157$	3.24264	−	5.61642i	0.258791	−	0.448239i	0.965918	+	0.258847i	$0.0833426\pi$
$158$		0			0
$159$	1.94975	+	3.37706i	0.154625	+	0.267818i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−8.53553	−	14.7840i	−0.668555	−	1.15797i	−0.978308	−	0.207154i	$-0.933580\pi$
$163$	−8.53553	−	14.7840i	−0.668555	−	1.15797i	0.309754	−	0.950817i	$-0.399753\pi$
$164$		0			0
$165$	0.207107	−	0.358719i	0.0161232	−	0.0279263i
$166$		0			0
$167$	10.4142			0.805876			0.402938	−	0.915227i	$-0.367989\pi$
$167$	10.4142			0.805876			0.402938	+	0.915227i	$0.367989\pi$
$168$		0			0
$169$	−7.17157			−0.551659
$170$		0			0
$171$	2.82843	−	4.89898i	0.216295	−	0.374634i
$172$		0			0
$173$	−5.86396	−	10.1567i	−0.445829	−	0.772198i	0.552281	−	0.833658i	$-0.313758\pi$
$173$	−5.86396	−	10.1567i	−0.445829	−	0.772198i	−0.998110	+	0.0614602i	$0.980424\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	2.12132	+	3.67423i	0.159448	+	0.276172i
$178$		0			0
$179$	12.0711	−	20.9077i	0.902234	−	1.56272i	0.0776462	−	0.996981i	$-0.475260\pi$
$179$	12.0711	−	20.9077i	0.902234	−	1.56272i	0.824588	−	0.565734i	$-0.191407\pi$
$180$		0			0
$181$	5.55635			0.413000			0.206500	−	0.978447i	$-0.433793\pi$
$181$	5.55635			0.413000			0.206500	+	0.978447i	$0.433793\pi$
$182$		0			0
$183$	0.485281			0.0358730
$184$		0			0
$185$	−3.94975	+	6.84116i	−0.290391	+	0.502972i
$186$		0			0
$187$	−0.207107	−	0.358719i	−0.0151451	−	0.0262322i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.08579	−	7.07679i	−0.295637	−	0.512059i	0.679496	−	0.733679i	$-0.262199\pi$
$191$	−4.08579	−	7.07679i	−0.295637	−	0.512059i	−0.975133	+	0.221621i	$0.928865\pi$
$192$		0			0
$193$	−11.6569	+	20.1903i	−0.839079	+	1.45333i	0.0515871	+	0.998668i	$0.483572\pi$
$193$	−11.6569	+	20.1903i	−0.839079	+	1.45333i	−0.890666	+	0.454658i	$0.849761\pi$
$194$		0			0
$195$	1.00000			0.0716115
$196$		0			0
$197$	−3.75736			−0.267701			−0.133850	−	0.991002i	$-0.542734\pi$
$197$	−3.75736			−0.267701			−0.133850	+	0.991002i	$0.542734\pi$
$198$		0			0
$199$	−12.1924	+	21.1178i	−0.864295	+	1.49700i	0.00344954	+	0.999994i	$0.498902\pi$
$199$	−12.1924	+	21.1178i	−0.864295	+	1.49700i	−0.867745	+	0.497010i	$0.834431\pi$
$200$		0			0
$201$	0.292893	+	0.507306i	0.0206591	+	0.0357826i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	3.70711	+	6.42090i	0.258916	+	0.448455i
$206$		0			0
$207$	−3.17157	+	5.49333i	−0.220440	+	0.381813i
$208$		0			0
$209$	−2.00000			−0.138343
$210$		0			0
$211$	−11.1421			−0.767056			−0.383528	−	0.923529i	$-0.625291\pi$
$211$	−11.1421			−0.767056			−0.383528	+	0.923529i	$0.625291\pi$
$212$		0			0
$213$	3.00000	−	5.19615i	0.205557	−	0.356034i
$214$		0			0
$215$	−0.171573	−	0.297173i	−0.0117012	−	0.0202670i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−1.07107	−	1.85514i	−0.0723761	−	0.125359i
$220$		0			0
$221$	0.500000	−	0.866025i	0.0336336	−	0.0582552i
$222$		0			0
$223$	19.3848			1.29810			0.649050	−	0.760745i	$-0.275166\pi$
$223$	19.3848			1.29810			0.649050	+	0.760745i	$0.275166\pi$
$224$		0			0
$225$	−2.82843			−0.188562
$226$		0			0
$227$	−2.20711	+	3.82282i	−0.146491	+	0.253730i	−0.929928	−	0.367741i	$-0.880131\pi$
$227$	−2.20711	+	3.82282i	−0.146491	+	0.253730i	0.783437	+	0.621471i	$0.213465\pi$
$228$		0			0
$229$	11.9497	+	20.6976i	0.789662	+	1.36773i	0.926174	+	0.377096i	$0.123077\pi$
$229$	11.9497	+	20.6976i	0.789662	+	1.36773i	−0.136513	+	0.990638i	$0.543589\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−10.2426	−	17.7408i	−0.671018	−	1.16224i	−0.977616	−	0.210398i	$-0.932524\pi$
$233$	−10.2426	−	17.7408i	−0.671018	−	1.16224i	0.306598	−	0.951839i	$-0.400809\pi$
$234$		0			0
$235$	5.20711	−	9.01897i	0.339674	−	0.588333i
$236$		0			0
$237$	6.07107			0.394358
$238$		0			0
$239$	6.65685			0.430596			0.215298	−	0.976548i	$-0.430928\pi$
$239$	6.65685			0.430596			0.215298	+	0.976548i	$0.430928\pi$
$240$		0			0
$241$	13.1924	−	22.8499i	0.849796	−	1.47189i	−0.0315933	−	0.999501i	$-0.510058\pi$
$241$	13.1924	−	22.8499i	0.849796	−	1.47189i	0.881390	−	0.472390i	$-0.156609\pi$
$242$		0			0
$243$	5.17157	+	8.95743i	0.331757	+	0.574619i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−2.41421	−	4.18154i	−0.153613	−	0.266065i
$248$		0			0
$249$	2.34315	−	4.05845i	0.148491	−	0.257194i
$250$		0			0
$251$	−23.5563			−1.48686			−0.743432	−	0.668812i	$-0.766803\pi$
$251$	−23.5563			−1.48686			−0.743432	+	0.668812i	$0.766803\pi$
$252$		0			0
$253$	2.24264			0.140994
$254$		0			0
$255$	0.0857864	−	0.148586i	0.00537216	−	0.00930485i
$256$		0			0
$257$	3.24264	+	5.61642i	0.202270	+	0.350343i	0.949260	−	0.314494i	$-0.101835\pi$
$257$	3.24264	+	5.61642i	0.202270	+	0.350343i	−0.746989	+	0.664836i	$0.768501\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	1.41421	+	2.44949i	0.0875376	+	0.151620i
$262$		0			0
$263$	7.48528	−	12.9649i	0.461562	−	0.799449i	−0.537477	−	0.843279i	$-0.680622\pi$
$263$	7.48528	−	12.9649i	0.461562	−	0.799449i	0.999039	+	0.0438293i	$0.0139558\pi$
$264$		0			0
$265$	−9.41421			−0.578311
$266$		0			0
$267$	0.686292			0.0420004
$268$		0			0
$269$	−10.7071	+	18.5453i	−0.652824	+	1.13072i	0.329611	+	0.944117i	$0.393082\pi$
$269$	−10.7071	+	18.5453i	−0.652824	+	1.13072i	−0.982435	+	0.186607i	$0.940251\pi$
$270$		0			0
$271$	−6.82843	−	11.8272i	−0.414797	−	0.718450i	0.580610	−	0.814182i	$-0.302814\pi$
$271$	−6.82843	−	11.8272i	−0.414797	−	0.718450i	−0.995407	+	0.0957318i	$0.969481\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$		0			0
$277$	−0.535534	+	0.927572i	−0.0321771	+	0.0557324i	−0.881666	−	0.471875i	$-0.843577\pi$
$277$	−0.535534	+	0.927572i	−0.0321771	+	0.0557324i	0.849488	+	0.527607i	$0.176911\pi$
$278$		0			0
$279$	−4.97056			−0.297580
$280$		0			0
$281$	−4.31371			−0.257334			−0.128667	−	0.991688i	$-0.541070\pi$
$281$	−4.31371			−0.257334			−0.128667	+	0.991688i	$0.541070\pi$
$282$		0			0
$283$	11.5208	−	19.9546i	0.684841	−	1.18618i	−0.288645	−	0.957436i	$-0.593205\pi$
$283$	11.5208	−	19.9546i	0.684841	−	1.18618i	0.973487	−	0.228744i	$-0.0734619\pi$
$284$		0			0
$285$	−0.414214	−	0.717439i	−0.0245359	−	0.0424974i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	8.41421	+	14.5738i	0.494954	+	0.857285i
$290$		0			0
$291$	−0.0147186	+	0.0254934i	−0.000862821	+	0.00149445i
$292$		0			0
$293$	−15.5858			−0.910531			−0.455266	−	0.890356i	$-0.650456\pi$
$293$	−15.5858			−0.910531			−0.455266	+	0.890356i	$0.650456\pi$
$294$		0			0
$295$	−10.2426			−0.596350
$296$		0			0
$297$	1.20711	−	2.09077i	0.0700434	−	0.121319i
$298$		0			0
$299$	2.70711	+	4.68885i	0.156556	+	0.271163i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−1.34315	−	2.32640i	−0.0771617	−	0.133648i
$304$		0			0
$305$	−0.585786	+	1.01461i	−0.0335420	+	0.0580965i
$306$		0			0
$307$	−26.0711			−1.48795			−0.743977	−	0.668205i	$-0.767063\pi$
$307$	−26.0711			−1.48795			−0.743977	+	0.668205i	$0.767063\pi$
$308$		0			0
$309$	−6.31371			−0.359174
$310$		0			0
$311$	−5.00000	+	8.66025i	−0.283524	+	0.491078i	−0.972250	−	0.233944i	$-0.924837\pi$
$311$	−5.00000	+	8.66025i	−0.283524	+	0.491078i	0.688726	+	0.725022i	$0.258170\pi$
$312$		0			0
$313$	−0.863961	−	1.49642i	−0.0488340	−	0.0845829i	0.840575	−	0.541695i	$-0.182217\pi$
$313$	−0.863961	−	1.49642i	−0.0488340	−	0.0845829i	−0.889409	+	0.457112i	$0.848884\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−11.8284	−	20.4874i	−0.664351	−	1.15069i	−0.979461	−	0.201634i	$-0.935375\pi$
$317$	−11.8284	−	20.4874i	−0.664351	−	1.15069i	0.315110	−	0.949055i	$-0.397958\pi$
$318$		0			0
$319$	0.500000	−	0.866025i	0.0279946	−	0.0484881i
$320$		0			0
$321$	−1.02944			−0.0574576
$322$		0			0
$323$	−0.828427			−0.0460949
$324$		0			0
$325$	−1.20711	+	2.09077i	−0.0669582	+	0.115975i
$326$		0			0
$327$	0.893398	+	1.54741i	0.0494050	+	0.0855720i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−13.2426	−	22.9369i	−0.727881	−	1.26073i	−0.957777	−	0.287512i	$-0.907172\pi$
$331$	−13.2426	−	22.9369i	−0.727881	−	1.26073i	0.229896	−	0.973215i	$-0.426162\pi$
$332$		0			0
$333$	−11.1716	+	19.3497i	−0.612198	+	1.06036i
$334$		0			0
$335$	−1.41421			−0.0772667
$336$		0			0
$337$	1.07107			0.0583448			0.0291724	−	0.999574i	$-0.490713\pi$
$337$	1.07107			0.0583448			0.0291724	+	0.999574i	$0.490713\pi$
$338$		0			0
$339$	1.05025	−	1.81909i	0.0570419	−	0.0987994i
$340$		0			0
$341$	0.878680	+	1.52192i	0.0475832	+	0.0824165i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	0.464466	+	0.804479i	0.0250060	+	0.0433117i
$346$		0			0
$347$	12.4350	−	21.5381i	0.667547	−	1.15623i	−0.311041	−	0.950397i	$-0.600678\pi$
$347$	12.4350	−	21.5381i	0.667547	−	1.15623i	0.978588	−	0.205829i	$-0.0659892\pi$
$348$		0			0
$349$	−29.3137			−1.56913			−0.784563	−	0.620049i	$-0.787113\pi$
$349$	−29.3137			−1.56913			−0.784563	+	0.620049i	$0.787113\pi$
$350$		0			0
$351$	5.82843			0.311098
$352$		0			0
$353$	6.10660	−	10.5769i	0.325022	−	0.562954i	−0.656495	−	0.754330i	$-0.727962\pi$
$353$	6.10660	−	10.5769i	0.325022	−	0.562954i	0.981517	+	0.191376i	$0.0612951\pi$
$354$		0			0
$355$	7.24264	+	12.5446i	0.384399	+	0.665799i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	9.17157	+	15.8856i	0.484057	+	0.838411i	0.999832	−	0.0183125i	$-0.00582936\pi$
$359$	9.17157	+	15.8856i	0.484057	+	0.838411i	−0.515775	+	0.856724i	$0.672496\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$		0			0
$363$	4.14214			0.217406
$364$		0			0
$365$	5.17157			0.270692
$366$		0			0
$367$	−1.37868	+	2.38794i	−0.0719665	+	0.124650i	−0.899763	−	0.436379i	$-0.856261\pi$
$367$	−1.37868	+	2.38794i	−0.0719665	+	0.124650i	0.827797	+	0.561028i	$0.189594\pi$
$368$		0			0
$369$	10.4853	+	18.1610i	0.545842	+	0.945426i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−8.58579	−	14.8710i	−0.444555	−	0.769992i	0.553466	−	0.832872i	$-0.313305\pi$
$373$	−8.58579	−	14.8710i	−0.444555	−	0.769992i	−0.998021	+	0.0628797i	$0.979972\pi$
$374$		0			0
$375$	−0.207107	+	0.358719i	−0.0106949	+	0.0185242i
$376$		0			0
$377$	2.41421			0.124338
$378$		0			0
$379$	−16.6274			−0.854093			−0.427047	−	0.904230i	$-0.640446\pi$
$379$	−16.6274			−0.854093			−0.427047	+	0.904230i	$0.640446\pi$
$380$		0			0
$381$	2.53553	−	4.39167i	0.129899	−	0.224992i
$382$		0			0
$383$	−8.58579	−	14.8710i	−0.438713	−	0.759874i	0.558877	−	0.829250i	$-0.311232\pi$
$383$	−8.58579	−	14.8710i	−0.438713	−	0.759874i	−0.997591	+	0.0693768i	$0.977899\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−0.485281	−	0.840532i	−0.0246682	−	0.0427266i
$388$		0			0
$389$	14.3995	−	24.9407i	0.730083	−	1.26454i	−0.226764	−	0.973950i	$-0.572815\pi$
$389$	14.3995	−	24.9407i	0.730083	−	1.26454i	0.956847	−	0.290592i	$-0.0938521\pi$
$390$		0			0
$391$	0.928932			0.0469781
$392$		0			0
$393$	−4.87006			−0.245662
$394$		0			0
$395$	−7.32843	+	12.6932i	−0.368733	+	0.638665i
$396$		0			0
$397$	4.20711	+	7.28692i	0.211149	+	0.365720i	0.952074	−	0.305867i	$-0.0989463\pi$
$397$	4.20711	+	7.28692i	0.211149	+	0.365720i	−0.740926	+	0.671587i	$0.765613\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−13.2279	−	22.9114i	−0.660571	−	1.14414i	−0.980466	−	0.196689i	$-0.936981\pi$
$401$	−13.2279	−	22.9114i	−0.660571	−	1.14414i	0.319895	−	0.947453i	$-0.396352\pi$
$402$		0			0
$403$	−2.12132	+	3.67423i	−0.105670	+	0.183027i
$404$		0			0
$405$	−7.48528			−0.371947
$406$		0			0
$407$	7.89949			0.391563
$408$		0			0
$409$	−14.5563	+	25.2123i	−0.719765	+	1.24667i	0.241328	+	0.970444i	$0.422417\pi$
$409$	−14.5563	+	25.2123i	−0.719765	+	1.24667i	−0.961093	+	0.276226i	$0.910916\pi$
$410$		0			0
$411$	0.686292	+	1.18869i	0.0338523	+	0.0586338i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	5.65685	+	9.79796i	0.277684	+	0.480963i
$416$		0			0
$417$	−0.292893	+	0.507306i	−0.0143430	+	0.0248429i
$418$		0			0
$419$	−31.4142			−1.53468			−0.767342	−	0.641238i	$-0.778421\pi$
$419$	−31.4142			−1.53468			−0.767342	+	0.641238i	$0.778421\pi$
$420$		0			0
$421$	−3.68629			−0.179659			−0.0898294	−	0.995957i	$-0.528632\pi$
$421$	−3.68629			−0.179659			−0.0898294	+	0.995957i	$0.528632\pi$
$422$		0			0
$423$	14.7279	−	25.5095i	0.716096	−	1.24031i
$424$		0			0
$425$	0.207107	+	0.358719i	0.0100462	+	0.0174005i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−0.500000	−	0.866025i	−0.0241402	−	0.0418121i
$430$		0			0
$431$	−5.67157	+	9.82345i	−0.273190	+	0.473179i	−0.969677	−	0.244391i	$-0.921412\pi$
$431$	−5.67157	+	9.82345i	−0.273190	+	0.473179i	0.696487	+	0.717570i	$0.254745\pi$
$432$		0			0
$433$	−26.9706			−1.29612			−0.648061	−	0.761588i	$-0.724420\pi$
$433$	−26.9706			−1.29612			−0.648061	+	0.761588i	$0.724420\pi$
$434$		0			0
$435$	0.414214			0.0198600
$436$		0			0
$437$	2.24264	−	3.88437i	0.107280	−	0.185815i
$438$		0			0
$439$	6.12132	+	10.6024i	0.292155	+	0.506027i	0.974319	−	0.225172i	$-0.0722945\pi$
$439$	6.12132	+	10.6024i	0.292155	+	0.506027i	−0.682164	+	0.731199i	$0.738961\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−19.3848	−	33.5754i	−0.920999	−	1.59522i	−0.797873	−	0.602825i	$-0.794042\pi$
$443$	−19.3848	−	33.5754i	−0.920999	−	1.59522i	−0.123125	−	0.992391i	$-0.539292\pi$
$444$		0			0
$445$	−0.828427	+	1.43488i	−0.0392712	+	0.0680197i
$446$		0			0
$447$	6.14214			0.290513
$448$		0			0
$449$	−10.5147			−0.496220			−0.248110	−	0.968732i	$-0.579809\pi$
$449$	−10.5147			−0.496220			−0.248110	+	0.968732i	$0.579809\pi$
$450$		0			0
$451$	3.70711	−	6.42090i	0.174561	−	0.302348i
$452$		0			0
$453$	0.964466	+	1.67050i	0.0453146	+	0.0784871i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−9.53553	−	16.5160i	−0.446053	−	0.772587i	0.552071	−	0.833797i	$-0.313838\pi$
$457$	−9.53553	−	16.5160i	−0.446053	−	0.772587i	−0.998125	+	0.0612095i	$0.980504\pi$
$458$		0			0
$459$	0.500000	−	0.866025i	0.0233380	−	0.0404226i
$460$		0			0
$461$	24.2843			1.13103			0.565516	−	0.824738i	$-0.308677\pi$
$461$	24.2843			1.13103			0.565516	+	0.824738i	$0.308677\pi$
$462$		0			0
$463$	−25.4558			−1.18303			−0.591517	−	0.806293i	$-0.701471\pi$
$463$	−25.4558			−1.18303			−0.591517	+	0.806293i	$0.701471\pi$
$464$		0			0
$465$	−0.363961	+	0.630399i	−0.0168783	+	0.0292341i
$466$		0			0
$467$	−2.79289	−	4.83743i	−0.129240	−	0.223850i	0.794143	−	0.607732i	$-0.207920\pi$
$467$	−2.79289	−	4.83743i	−0.129240	−	0.223850i	−0.923382	+	0.383882i	$0.874587\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−1.34315	−	2.32640i	−0.0618889	−	0.107195i
$472$		0			0
$473$	−0.171573	+	0.297173i	−0.00788893	+	0.0136640i
$474$		0			0
$475$	2.00000			0.0917663
$476$		0			0
$477$	−26.6274			−1.21919
$478$		0			0
$479$	−12.2635	+	21.2409i	−0.560332	+	0.970523i	0.437136	+	0.899396i	$0.355993\pi$
$479$	−12.2635	+	21.2409i	−0.560332	+	0.970523i	−0.997467	+	0.0711272i	$0.977340\pi$
$480$		0			0
$481$	9.53553	+	16.5160i	0.434783	+	0.753066i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.0355339	−	0.0615465i	−0.00161351	−	0.00279468i
$486$		0			0
$487$	−13.3640	+	23.1471i	−0.605579	+	1.04889i	0.386381	+	0.922339i	$0.373725\pi$
$487$	−13.3640	+	23.1471i	−0.605579	+	1.04889i	−0.991960	+	0.126554i	$0.959608\pi$
$488$		0			0
$489$	−7.07107			−0.319765
$490$		0			0
$491$	5.48528			0.247547			0.123774	−	0.992310i	$-0.460500\pi$
$491$	5.48528			0.247547			0.123774	+	0.992310i	$0.460500\pi$
$492$		0			0
$493$	0.207107	−	0.358719i	0.00932762	−	0.0161559i
$494$		0			0
$495$	1.41421	+	2.44949i	0.0635642	+	0.110096i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−6.39949	−	11.0843i	−0.286481	−	0.496199i	0.686486	−	0.727143i	$-0.259152\pi$
$499$	−6.39949	−	11.0843i	−0.286481	−	0.496199i	−0.972967	+	0.230943i	$0.925819\pi$
$500$		0			0
$501$	2.15685	−	3.73578i	0.0963611	−	0.166902i
$502$		0			0
$503$	31.0416			1.38408			0.692039	−	0.721860i	$-0.256713\pi$
$503$	31.0416			1.38408			0.692039	+	0.721860i	$0.256713\pi$
$504$		0			0
$505$	6.48528			0.288591
$506$		0			0
$507$	−1.48528	+	2.57258i	−0.0659637	+	0.114252i
$508$		0			0
$509$	−3.87868	−	6.71807i	−0.171919	−	0.297773i	0.767171	−	0.641442i	$-0.221664\pi$
$509$	−3.87868	−	6.71807i	−0.171919	−	0.297773i	−0.939091	+	0.343669i	$0.888330\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−2.41421	−	4.18154i	−0.106590	−	0.184620i
$514$		0			0
$515$	7.62132	−	13.2005i	0.335836	−	0.581684i
$516$		0			0
$517$	−10.4142			−0.458017
$518$		0			0
$519$	−4.85786			−0.213237
$520$		0			0
$521$	−3.00000	+	5.19615i	−0.131432	+	0.227648i	−0.924229	−	0.381839i	$-0.875291\pi$
$521$	−3.00000	+	5.19615i	−0.131432	+	0.227648i	0.792797	+	0.609486i	$0.208624\pi$
$522$		0			0
$523$	16.2426	+	28.1331i	0.710241	+	1.23017i	0.964767	+	0.263108i	$0.0847474\pi$
$523$	16.2426	+	28.1331i	0.710241	+	1.23017i	−0.254525	+	0.967066i	$0.581919\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.363961	+	0.630399i	0.0158544	+	0.0274606i
$528$		0			0
$529$	8.98528	−	15.5630i	0.390664	−	0.676651i
$530$		0			0
$531$	−28.9706			−1.25722
$532$		0			0
$533$	17.8995			0.775313
$534$		0			0
$535$	1.24264	−	2.15232i	0.0537240	−	0.0930528i
$536$		0			0
$537$	−5.00000	−	8.66025i	−0.215766	−	0.373718i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−5.15685	−	8.93193i	−0.221710	−	0.384014i	0.733617	−	0.679563i	$-0.237831\pi$
$541$	−5.15685	−	8.93193i	−0.221710	−	0.384014i	−0.955327	+	0.295549i	$0.904497\pi$
$542$		0			0
$543$	1.15076	−	1.99317i	0.0493837	−	0.0855351i
$544$		0			0
$545$	−4.31371			−0.184779
$546$		0			0
$547$	−27.1127			−1.15926			−0.579628	−	0.814881i	$-0.696802\pi$
$547$	−27.1127			−1.15926			−0.579628	+	0.814881i	$0.696802\pi$
$548$		0			0
$549$	−1.65685	+	2.86976i	−0.0707128	+	0.122478i
$550$		0			0
$551$	−1.00000	−	1.73205i	−0.0426014	−	0.0737878i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	1.63604	+	2.83370i	0.0694460	+	0.120284i
$556$		0			0
$557$	13.0711	−	22.6398i	0.553839	−	0.959277i	−0.444154	−	0.895950i	$-0.646496\pi$
$557$	13.0711	−	22.6398i	0.553839	−	0.959277i	0.997993	−	0.0633267i	$-0.0201710\pi$
$558$		0			0
$559$	−0.828427			−0.0350387
$560$		0			0
$561$	−0.171573			−0.00724381
$562$		0			0
$563$	19.9706	−	34.5900i	0.841659	−	1.45780i	−0.0468326	−	0.998903i	$-0.514913\pi$
$563$	19.9706	−	34.5900i	0.841659	−	1.45780i	0.888491	−	0.458893i	$-0.151754\pi$
$564$		0			0
$565$	2.53553	+	4.39167i	0.106671	+	0.184759i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	2.92893	+	5.07306i	0.122787	+	0.212674i	0.920866	−	0.389880i	$-0.127483\pi$
$569$	2.92893	+	5.07306i	0.122787	+	0.212674i	−0.798079	+	0.602553i	$0.794150\pi$
$570$		0			0
$571$	−13.7279	+	23.7775i	−0.574496	+	0.995056i	0.421601	+	0.906782i	$0.361468\pi$
$571$	−13.7279	+	23.7775i	−0.574496	+	0.995056i	−0.996096	+	0.0882740i	$0.971865\pi$
$572$		0			0
$573$	−3.38478			−0.141401
$574$		0			0
$575$	−2.24264			−0.0935246
$576$		0			0
$577$	16.7929	−	29.0861i	0.699097	−	1.21087i	−0.269683	−	0.962949i	$-0.586919\pi$
$577$	16.7929	−	29.0861i	0.699097	−	1.21087i	0.968780	−	0.247923i	$-0.0797479\pi$
$578$		0			0
$579$	4.82843	+	8.36308i	0.200663	+	0.347558i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	4.70711	+	8.15295i	0.194948	+	0.337661i
$584$		0			0
$585$	−3.41421	+	5.91359i	−0.141160	+	0.244497i
$586$		0			0
$587$	−42.1421			−1.73939			−0.869696	−	0.493588i	$-0.835685\pi$
$587$	−42.1421			−1.73939			−0.869696	+	0.493588i	$0.835685\pi$
$588$		0			0
$589$	3.51472			0.144821
$590$		0			0
$591$	−0.778175	+	1.34784i	−0.0320098	+	0.0554426i
$592$		0			0
$593$	−20.2782	−	35.1228i	−0.832725	−	1.44232i	−0.895869	−	0.444317i	$-0.853446\pi$
$593$	−20.2782	−	35.1228i	−0.832725	−	1.44232i	0.0631447	−	0.998004i	$-0.479887\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	5.05025	+	8.74729i	0.206693	+	0.358003i
$598$		0			0
$599$	6.84315	−	11.8527i	0.279603	−	0.484287i	−0.691683	−	0.722201i	$-0.743130\pi$
$599$	6.84315	−	11.8527i	0.279603	−	0.484287i	0.971286	+	0.237914i	$0.0764637\pi$
$600$		0			0
$601$	38.2843			1.56165			0.780824	−	0.624751i	$-0.214800\pi$
$601$	38.2843			1.56165			0.780824	+	0.624751i	$0.214800\pi$
$602$		0			0
$603$	−4.00000			−0.162893
$604$		0			0
$605$	−5.00000	+	8.66025i	−0.203279	+	0.352089i
$606$		0			0
$607$	−2.96447	−	5.13461i	−0.120324	−	0.208407i	0.799571	−	0.600571i	$-0.205060\pi$
$607$	−2.96447	−	5.13461i	−0.120324	−	0.208407i	−0.919895	+	0.392164i	$0.871727\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−12.5711	−	21.7737i	−0.508571	−	0.880871i
$612$		0			0
$613$	−3.34315	+	5.79050i	−0.135028	+	0.233876i	−0.925608	−	0.378483i	$-0.876446\pi$
$613$	−3.34315	+	5.79050i	−0.135028	+	0.233876i	0.790580	+	0.612359i	$0.209779\pi$
$614$		0			0
$615$	3.07107			0.123837
$616$		0			0
$617$	−8.58579			−0.345651			−0.172825	−	0.984952i	$-0.555290\pi$
$617$	−8.58579			−0.345651			−0.172825	+	0.984952i	$0.555290\pi$
$618$		0			0
$619$	0.464466	−	0.804479i	0.0186685	−	0.0323347i	−0.856540	−	0.516080i	$-0.827391\pi$
$619$	0.464466	−	0.804479i	0.0186685	−	0.0323347i	0.875209	+	0.483745i	$0.160724\pi$
$620$		0			0
$621$	2.70711	+	4.68885i	0.108632	+	0.188157i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−0.414214	+	0.717439i	−0.0165421	+	0.0286518i
$628$		0			0
$629$	3.27208			0.130466
$630$		0			0
$631$	7.62742			0.303643			0.151821	−	0.988408i	$-0.451486\pi$
$631$	7.62742			0.303643			0.151821	+	0.988408i	$0.451486\pi$
$632$		0			0
$633$	−2.30761	+	3.99690i	−0.0917193	+	0.158863i
$634$		0			0
$635$	6.12132	+	10.6024i	0.242917	+	0.420745i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	20.4853	+	35.4815i	0.810385	+	1.40363i
$640$		0			0
$641$	12.1421	−	21.0308i	0.479586	−	0.830666i	−0.520140	−	0.854081i	$-0.674120\pi$
$641$	12.1421	−	21.0308i	0.479586	−	0.830666i	0.999726	+	0.0234143i	$0.00745369\pi$
$642$		0			0
$643$	12.2132			0.481642			0.240821	−	0.970570i	$-0.422583\pi$
$643$	12.2132			0.481642			0.240821	+	0.970570i	$0.422583\pi$
$644$		0			0
$645$	−0.142136			−0.00559658
$646$		0			0
$647$	5.07107	−	8.78335i	0.199364	−	0.345309i	−0.748958	−	0.662617i	$-0.769446\pi$
$647$	5.07107	−	8.78335i	0.199364	−	0.345309i	0.948322	+	0.317308i	$0.102779\pi$
$648$		0			0
$649$	5.12132	+	8.87039i	0.201029	+	0.348193i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−17.1421	−	29.6910i	−0.670824	−	1.16190i	−0.977671	−	0.210142i	$-0.932607\pi$
$653$	−17.1421	−	29.6910i	−0.670824	−	1.16190i	0.306847	−	0.951759i	$-0.400726\pi$
$654$		0			0
$655$	5.87868	−	10.1822i	0.229699	−	0.397850i
$656$		0			0
$657$	14.6274			0.570670
$658$		0			0
$659$	0.514719			0.0200506			0.0100253	−	0.999950i	$-0.496809\pi$
$659$	0.514719			0.0200506			0.0100253	+	0.999950i	$0.496809\pi$
$660$		0			0
$661$	12.5858	−	21.7992i	0.489530	−	0.847891i	−0.510397	−	0.859939i	$-0.670502\pi$
$661$	12.5858	−	21.7992i	0.489530	−	0.847891i	0.999927	+	0.0120474i	$0.00383490\pi$
$662$		0			0
$663$	−0.207107	−	0.358719i	−0.00804336	−	0.0139315i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	1.12132	+	1.94218i	0.0434177	+	0.0752017i
$668$		0			0
$669$	4.01472	−	6.95370i	0.155218	−	0.268845i
$670$		0			0
$671$	1.17157			0.0452281
$672$		0			0
$673$	45.1716			1.74124			0.870618	−	0.491959i	$-0.163719\pi$
$673$	45.1716			1.74124			0.870618	+	0.491959i	$0.163719\pi$
$674$		0			0
$675$	−1.20711	+	2.09077i	−0.0464616	+	0.0804738i
$676$		0			0
$677$	−10.9645	−	18.9910i	−0.421399	−	0.729884i	0.574678	−	0.818380i	$-0.305127\pi$
$677$	−10.9645	−	18.9910i	−0.421399	−	0.729884i	−0.996077	+	0.0884958i	$0.971794\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	0.914214	+	1.58346i	0.0350327	+	0.0606785i
$682$		0			0
$683$	9.41421	−	16.3059i	0.360225	−	0.623928i	−0.627773	−	0.778397i	$-0.716033\pi$
$683$	9.41421	−	16.3059i	0.360225	−	0.623928i	0.987998	+	0.154469i	$0.0493666\pi$
$684$		0			0
$685$	−3.31371			−0.126610
$686$		0			0
$687$	9.89949			0.377689
$688$		0			0
$689$	−11.3640	+	19.6830i	−0.432932	+	0.749861i
$690$		0			0
$691$	9.07107	+	15.7116i	0.345080	+	0.597696i	0.985368	−	0.170439i	$-0.0545186\pi$
$691$	9.07107	+	15.7116i	0.345080	+	0.597696i	−0.640289	+	0.768134i	$0.721185\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.707107	−	1.22474i	−0.0268221	−	0.0464572i
$696$		0			0
$697$	1.53553	−	2.65962i	0.0581625	−	0.100740i
$698$		0			0
$699$	−8.48528			−0.320943
$700$		0			0
$701$	−8.85786			−0.334557			−0.167278	−	0.985910i	$-0.553498\pi$
$701$	−8.85786			−0.334557			−0.167278	+	0.985910i	$0.553498\pi$
$702$		0			0
$703$	7.89949	−	13.6823i	0.297935	−	0.516039i
$704$		0			0
$705$	−2.15685	−	3.73578i	−0.0812318	−	0.140698i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	16.3284	+	28.2817i	0.613227	+	1.06214i	0.990693	+	0.136117i	$0.0434622\pi$
$709$	16.3284	+	28.2817i	0.613227	+	1.06214i	−0.377466	+	0.926024i	$0.623204\pi$
$710$		0			0
$711$	−20.7279	+	35.9018i	−0.777358	+	1.34642i
$712$		0			0
$713$	−3.94113			−0.147596
$714$		0			0
$715$	2.41421			0.0902865
$716$		0			0
$717$	1.37868	−	2.38794i	0.0514877	−	0.0891794i
$718$		0			0
$719$	4.84924	+	8.39913i	0.180846	+	0.313235i	0.942169	−	0.335138i	$-0.108783\pi$
$719$	4.84924	+	8.39913i	0.180846	+	0.313235i	−0.761323	+	0.648373i	$0.775450\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−5.46447	−	9.46473i	−0.203226	−	0.351997i
$724$		0			0
$725$	−0.500000	+	0.866025i	−0.0185695	+	0.0321634i
$726$		0			0
$727$	18.6863			0.693036			0.346518	−	0.938043i	$-0.387364\pi$
$727$	18.6863			0.693036			0.346518	+	0.938043i	$0.387364\pi$
$728$		0			0
$729$	−18.1716			−0.673021
$730$		0			0
$731$	−0.0710678	+	0.123093i	−0.00262854	+	0.00455276i
$732$		0			0
$733$	−16.3492	−	28.3177i	−0.603873	−	1.04594i	−0.992228	−	0.124429i	$-0.960290\pi$
$733$	−16.3492	−	28.3177i	−0.603873	−	1.04594i	0.388355	−	0.921510i	$-0.373043\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.707107	+	1.22474i	0.0260466	+	0.0451141i
$738$		0			0
$739$	−17.3995	+	30.1368i	−0.640051	+	1.10860i	0.345370	+	0.938467i	$0.387753\pi$
$739$	−17.3995	+	30.1368i	−0.640051	+	1.10860i	−0.985421	+	0.170134i	$0.945580\pi$
$740$		0			0
$741$	−2.00000			−0.0734718
$742$		0			0
$743$	13.8995			0.509923			0.254962	−	0.966951i	$-0.417937\pi$
$743$	13.8995			0.509923			0.254962	+	0.966951i	$0.417937\pi$
$744$		0			0
$745$	−7.41421	+	12.8418i	−0.271636	+	0.470487i
$746$		0			0
$747$	16.0000	+	27.7128i	0.585409	+	1.01396i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	9.81371	+	16.9978i	0.358107	+	0.620260i	0.987645	−	0.156710i	$-0.0500889\pi$
$751$	9.81371	+	16.9978i	0.358107	+	0.620260i	−0.629537	+	0.776970i	$0.716756\pi$
$752$		0			0
$753$	−4.87868	+	8.45012i	−0.177789	+	0.307940i
$754$		0			0
$755$	−4.65685			−0.169480
$756$		0			0
$757$	36.7696			1.33641			0.668206	−	0.743976i	$-0.267062\pi$
$757$	36.7696			1.33641			0.668206	+	0.743976i	$0.267062\pi$
$758$		0			0
$759$	0.464466	−	0.804479i	0.0168591	−	0.0292007i
$760$		0			0
$761$	−17.7782	−	30.7927i	−0.644458	−	1.11623i	−0.984426	−	0.175798i	$-0.943750\pi$
$761$	−17.7782	−	30.7927i	−0.644458	−	1.11623i	0.339968	−	0.940437i	$-0.389584\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.585786	+	1.01461i	0.0211792	+	0.0366834i
$766$		0			0
$767$	−12.3640	+	21.4150i	−0.446437	+	0.773251i
$768$		0			0
$769$	−1.51472			−0.0546222			−0.0273111	−	0.999627i	$-0.508694\pi$
$769$	−1.51472			−0.0546222			−0.0273111	+	0.999627i	$0.508694\pi$
$770$		0			0
$771$	2.68629			0.0967444
$772$		0			0
$773$	−7.69239	+	13.3236i	−0.276676	+	0.479217i	−0.970557	−	0.240873i	$-0.922566\pi$
$773$	−7.69239	+	13.3236i	−0.276676	+	0.479217i	0.693881	+	0.720090i	$0.255900\pi$
$774$		0			0
$775$	−0.878680	−	1.52192i	−0.0315631	−	0.0546689i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−7.41421	−	12.8418i	−0.265642	−	0.460105i
$780$		0			0
$781$	7.24264	−	12.5446i	0.259162	−	0.448882i
$782$		0			0
$783$	2.41421			0.0862770
$784$		0			0
$785$	6.48528			0.231470
$786$		0			0
$787$	−22.4203	+	38.8331i	−0.799198	+	1.38425i	0.120941	+	0.992660i	$0.461409\pi$
$787$	−22.4203	+	38.8331i	−0.799198	+	1.38425i	−0.920139	+	0.391591i	$0.871925\pi$
$788$		0			0
$789$	−3.10051	−	5.37023i	−0.110381	−	0.191185i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	1.41421	+	2.44949i	0.0502202	+	0.0869839i
$794$		0			0
$795$	−1.94975	+	3.37706i	−0.0691504	+	0.119772i
$796$		0			0
$797$	50.0711			1.77361			0.886804	−	0.462146i	$-0.152920\pi$
$797$	50.0711			1.77361			0.886804	+	0.462146i	$0.152920\pi$
$798$		0			0
$799$	−4.31371			−0.152608
$800$		0			0
$801$	−2.34315	+	4.05845i	−0.0827910	+	0.143398i
$802$		0			0
$803$	−2.58579	−	4.47871i	−0.0912504	−	0.158050i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	4.43503	+	7.68170i	0.156120	+	0.270408i
$808$		0			0
$809$	9.47056	−	16.4035i	0.332967	−	0.576716i	−0.650125	−	0.759827i	$-0.725283\pi$
$809$	9.47056	−	16.4035i	0.332967	−	0.576716i	0.983092	+	0.183111i	$0.0586168\pi$
$810$		0			0
$811$	−8.44365			−0.296497			−0.148248	−	0.988950i	$-0.547363\pi$
$811$	−8.44365			−0.296497			−0.148248	+	0.988950i	$0.547363\pi$
$812$		0			0
$813$	−5.65685			−0.198395
$814$		0			0
$815$	8.53553	−	14.7840i	0.298987	−	0.517860i
$816$		0			0
$817$	0.343146	+	0.594346i	0.0120052	+	0.0207935i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−2.25736	−	3.90986i	−0.0787824	−	0.136455i	0.823942	−	0.566673i	$-0.191770\pi$
$821$	−2.25736	−	3.90986i	−0.0787824	−	0.136455i	−0.902725	+	0.430218i	$0.858437\pi$
$822$		0			0
$823$	−6.02082	+	10.4284i	−0.209872	+	0.363510i	−0.951674	−	0.307110i	$-0.900638\pi$
$823$	−6.02082	+	10.4284i	−0.209872	+	0.363510i	0.741802	+	0.670619i	$0.233972\pi$
$824$		0			0
$825$	0.414214			0.0144211
$826$		0			0
$827$	−5.95837			−0.207193			−0.103596	−	0.994619i	$-0.533035\pi$
$827$	−5.95837			−0.207193			−0.103596	+	0.994619i	$0.533035\pi$
$828$		0			0
$829$	−2.29289	+	3.97141i	−0.0796355	+	0.137933i	−0.903093	−	0.429446i	$-0.858709\pi$
$829$	−2.29289	+	3.97141i	−0.0796355	+	0.137933i	0.823457	+	0.567378i	$0.192042\pi$
$830$		0			0
$831$	0.221825	+	0.384213i	0.00769504	+	0.0133282i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	5.20711	+	9.01897i	0.180199	+	0.312114i
$836$		0			0
$837$	−2.12132	+	3.67423i	−0.0733236	+	0.127000i
$838$		0			0
$839$	16.2426			0.560758			0.280379	−	0.959889i	$-0.409540\pi$
$839$	16.2426			0.560758			0.280379	+	0.959889i	$0.409540\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$		0			0
$843$	−0.893398	+	1.54741i	−0.0307703	+	0.0532957i
$844$		0			0
$845$	−3.58579	−	6.21076i	−0.123355	−	0.213657i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−4.77208	−	8.26548i	−0.163777	−	0.283671i
$850$		0			0
$851$	−8.85786	+	15.3423i	−0.303644	+	0.525926i
$852$		0			0
$853$	−13.3137			−0.455853			−0.227926	−	0.973678i	$-0.573195\pi$
$853$	−13.3137			−0.455853			−0.227926	+	0.973678i	$0.573195\pi$
$854$		0			0
$855$	5.65685			0.193460
$856$		0			0
$857$	−18.7574	+	32.4887i	−0.640739	+	1.10979i	0.344529	+	0.938776i	$0.388039\pi$
$857$	−18.7574	+	32.4887i	−0.640739	+	1.10979i	−0.985268	+	0.171017i	$0.945295\pi$
$858$		0			0
$859$	1.27208	+	2.20330i	0.0434027	+	0.0751757i	0.886911	−	0.461941i	$-0.152847\pi$
$859$	1.27208	+	2.20330i	0.0434027	+	0.0751757i	−0.843508	+	0.537117i	$0.819513\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	27.0919	+	46.9245i	0.922218	+	1.59733i	0.795975	+	0.605330i	$0.206959\pi$
$863$	27.0919	+	46.9245i	0.922218	+	1.59733i	0.126244	+	0.991999i	$0.459708\pi$
$864$		0			0
$865$	5.86396	−	10.1567i	0.199381	−	0.345337i
$866$		0			0
$867$	6.97056			0.236733
$868$		0			0
$869$	14.6569			0.497200
$870$		0			0
$871$	−1.70711	+	2.95680i	−0.0578431	+	0.100187i
$872$		0			0
$873$	−0.100505	−	0.174080i	−0.00340158	−	0.00589171i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	3.48528	+	6.03668i	0.117690	+	0.203844i	0.918852	−	0.394603i	$-0.129118\pi$
$877$	3.48528	+	6.03668i	0.117690	+	0.203844i	−0.801162	+	0.598447i	$0.795785\pi$
$878$		0			0
$879$	−3.22792	+	5.59093i	−0.108875	+	0.188577i
$880$		0			0
$881$	6.34315			0.213706			0.106853	−	0.994275i	$-0.465923\pi$
$881$	6.34315			0.213706			0.106853	+	0.994275i	$0.465923\pi$
$882$		0			0
$883$	−27.1127			−0.912415			−0.456207	−	0.889873i	$-0.650793\pi$
$883$	−27.1127			−0.912415			−0.456207	+	0.889873i	$0.650793\pi$
$884$		0			0
$885$	−2.12132	+	3.67423i	−0.0713074	+	0.123508i
$886$		0			0
$887$	−19.1421	−	33.1552i	−0.642730	−	1.11324i	−0.984821	−	0.173574i	$-0.944468\pi$
$887$	−19.1421	−	33.1552i	−0.642730	−	1.11324i	0.342091	−	0.939667i	$-0.388865\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	3.74264	+	6.48244i	0.125383	+	0.217170i
$892$		0			0
$893$	−10.4142	+	18.0379i	−0.348498	+	0.603617i
$894$		0			0
$895$	24.1421			0.806983
$896$		0			0
$897$	2.24264			0.0748796
$898$		0			0
$899$	−0.878680	+	1.52192i	−0.0293056	+	0.0507588i
$900$		0			0
$901$	1.94975	+	3.37706i	0.0649555	+	0.112506i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.77817	+	4.81194i	0.0923496	+	0.159954i
$906$		0			0
$907$	−25.8492	+	44.7722i	−0.858310	+	1.48664i	0.0152299	+	0.999884i	$0.495152\pi$
$907$	−25.8492	+	44.7722i	−0.858310	+	1.48664i	−0.873540	+	0.486753i	$0.838181\pi$
$908$		0			0
$909$	18.3431			0.608404
$910$		0			0
$911$	43.3137			1.43505			0.717524	−	0.696534i	$-0.245276\pi$
$911$	43.3137			1.43505			0.717524	+	0.696534i	$0.245276\pi$
$912$		0			0
$913$	5.65685	−	9.79796i	0.187215	−	0.324265i
$914$		0			0
$915$	0.242641	+	0.420266i	0.00802145	+	0.0138936i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	25.2990	+	43.8191i	0.834537	+	1.44546i	0.894407	+	0.447254i	$0.147598\pi$
$919$	25.2990	+	43.8191i	0.834537	+	1.44546i	−0.0598704	+	0.998206i	$0.519069\pi$
$920$		0			0
$921$	−5.39949	+	9.35220i	−0.177919	+	0.308165i
$922$		0			0
$923$	34.9706			1.15107
$924$		0			0
$925$	−7.89949			−0.259734
$926$		0			0
$927$	21.5563	−	37.3367i	0.708003	−	1.22630i
$928$		0			0
$929$	−15.2635	−	26.4371i	−0.500778	−	0.867372i	−1.00000		0.000898297i	$-0.999714\pi$
$929$	−15.2635	−	26.4371i	−0.500778	−	0.867372i	0.499222	−	0.866474i	$-0.333619\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	2.07107	+	3.58719i	0.0678037	+	0.117439i
$934$		0			0
$935$	0.207107	−	0.358719i	0.00677312	−	0.0117314i
$936$		0			0
$937$	−28.2132			−0.921685			−0.460843	−	0.887482i	$-0.652453\pi$
$937$	−28.2132			−0.921685			−0.460843	+	0.887482i	$0.652453\pi$
$938$		0			0
$939$	−0.715729			−0.0233569
$940$		0			0
$941$	−12.0000	+	20.7846i	−0.391189	+	0.677559i	−0.992607	−	0.121376i	$-0.961269\pi$
$941$	−12.0000	+	20.7846i	−0.391189	+	0.677559i	0.601418	+	0.798935i	$0.294603\pi$
$942$		0			0
$943$	8.31371	+	14.3998i	0.270732	+	0.468921i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	4.94975	+	8.57321i	0.160845	+	0.278592i	0.935172	−	0.354194i	$-0.115245\pi$
$947$	4.94975	+	8.57321i	0.160845	+	0.278592i	−0.774327	+	0.632786i	$0.781911\pi$
$948$		0			0
$949$	6.24264	−	10.8126i	0.202645	−	0.350991i
$950$		0			0
$951$	−9.79899			−0.317754
$952$		0			0
$953$	21.6152			0.700186			0.350093	−	0.936715i	$-0.386150\pi$
$953$	21.6152			0.700186			0.350093	+	0.936715i	$0.386150\pi$
$954$		0			0
$955$	4.08579	−	7.07679i	0.132213	−	0.229000i
$956$		0			0
$957$	−0.207107	−	0.358719i	−0.00669481	−	0.0115958i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	13.9558	+	24.1722i	0.450189	+	0.779749i
$962$		0			0
$963$	3.51472	−	6.08767i	0.113260	−	0.196172i
$964$		0			0
$965$	−23.3137			−0.750495
$966$		0			0
$967$	23.1716			0.745148			0.372574	−	0.928003i	$-0.378475\pi$
$967$	23.1716			0.745148			0.372574	+	0.928003i	$0.378475\pi$
$968$		0			0
$969$	−0.171573	+	0.297173i	−0.00551171	+	0.00954657i
$970$		0			0
$971$	−24.0919	−	41.7284i	−0.773145	−	1.33913i	−0.935831	−	0.352449i	$-0.885349\pi$
$971$	−24.0919	−	41.7284i	−0.773145	−	1.33913i	0.162686	−	0.986678i	$-0.447984\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	0.500000	+	0.866025i	0.0160128	+	0.0277350i
$976$		0			0
$977$	27.0416	−	46.8375i	0.865138	−	1.49846i	−0.00177127	−	0.999998i	$-0.500564\pi$
$977$	27.0416	−	46.8375i	0.865138	−	1.49846i	0.866910	−	0.498465i	$-0.166103\pi$
$978$		0			0
$979$	1.65685			0.0529533
$980$		0			0
$981$	−12.2010			−0.389548
$982$		0			0
$983$	1.69239	−	2.93130i	0.0539788	−	0.0934940i	−0.837773	−	0.546018i	$-0.816143\pi$
$983$	1.69239	−	2.93130i	0.0539788	−	0.0934940i	0.891752	+	0.452524i	$0.149476\pi$
$984$		0			0
$985$	−1.87868	−	3.25397i	−0.0598597	−	0.103680i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.384776	−	0.666452i	−0.0122352	−	0.0211919i
$990$		0			0
$991$	−8.65685	+	14.9941i	−0.274994	+	0.476304i	−0.970134	−	0.242571i	$-0.922009\pi$
$991$	−8.65685	+	14.9941i	−0.274994	+	0.476304i	0.695140	+	0.718875i	$0.255343\pi$
$992$		0			0
$993$	−10.9706			−0.348140
$994$		0			0
$995$	−24.3848			−0.773049
$996$		0			0
$997$	−3.44975	+	5.97514i	−0.109255	+	0.189235i	−0.915469	−	0.402390i	$-0.868180\pi$
$997$	−3.44975	+	5.97514i	−0.109255	+	0.189235i	0.806214	+	0.591624i	$0.201513\pi$
$998$		0			0
$999$	9.53553	+	16.5160i	0.301691	+	0.522544i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1960.2.q.p.361.2		4
7.2	even	3	inner	1960.2.q.p.961.2		4
7.3	odd	6		1960.2.a.q.1.2	✓	2
7.4	even	3		1960.2.a.u.1.1	yes	2
7.5	odd	6		1960.2.q.v.961.1		4
7.6	odd	2		1960.2.q.v.361.1		4
28.3	even	6		3920.2.a.by.1.1		2
28.11	odd	6		3920.2.a.bn.1.2		2
35.4	even	6		9800.2.a.bs.1.2		2
35.24	odd	6		9800.2.a.ca.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1960.2.a.q.1.2	✓	2	7.3	odd	6
1960.2.a.u.1.1	yes	2	7.4	even	3
1960.2.q.p.361.2		4	1.1	even	1	trivial
1960.2.q.p.961.2		4	7.2	even	3	inner
1960.2.q.v.361.1		4	7.6	odd	2
1960.2.q.v.961.1		4	7.5	odd	6
3920.2.a.bn.1.2		2	28.11	odd	6
3920.2.a.by.1.1		2	28.3	even	6
9800.2.a.bs.1.2		2	35.4	even	6
9800.2.a.ca.1.1		2	35.24	odd	6

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:	\( N \)	\(=\)	\( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1960.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.207107 - 0.358719i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.41421 + 2.44949i) q^{9} +O(q^{10})\)	\(q+(0.207107 - 0.358719i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.41421 + 2.44949i) q^{9} +(0.500000 - 0.866025i) q^{11} +2.41421 q^{13} +0.414214 q^{15} +(0.207107 - 0.358719i) q^{17} +(-1.00000 - 1.73205i) q^{19} +(1.12132 + 1.94218i) q^{23} +(-0.500000 + 0.866025i) q^{25} +2.41421 q^{27} +1.00000 q^{29} +(-0.878680 + 1.52192i) q^{31} +(-0.207107 - 0.358719i) q^{33} +(3.94975 + 6.84116i) q^{37} +(0.500000 - 0.866025i) q^{39} +7.41421 q^{41} -0.343146 q^{43} +(-1.41421 + 2.44949i) q^{45} +(-5.20711 - 9.01897i) q^{47} +(-0.0857864 - 0.148586i) q^{51} +(-4.70711 + 8.15295i) q^{53} +1.00000 q^{55} -0.828427 q^{57} +(-5.12132 + 8.87039i) q^{59} +(0.585786 + 1.01461i) q^{61} +(1.20711 + 2.09077i) q^{65} +(-0.707107 + 1.22474i) q^{67} +0.928932 q^{69} +14.4853 q^{71} +(2.58579 - 4.47871i) q^{73} +(0.207107 + 0.358719i) q^{75} +(7.32843 + 12.6932i) q^{79} +(-3.74264 + 6.48244i) q^{81} +11.3137 q^{83} +0.414214 q^{85} +(0.207107 - 0.358719i) q^{87} +(0.828427 + 1.43488i) q^{89} +(0.363961 + 0.630399i) q^{93} +(1.00000 - 1.73205i) q^{95} -0.0710678 q^{97} +2.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{5}+O(q^{10}) \) 4 * q - 2 * q^3 + 2 * q^5	\( 4 q - 2 q^{3} + 2 q^{5} + 2 q^{11} + 4 q^{13} - 4 q^{15} - 2 q^{17} - 4 q^{19} - 4 q^{23} - 2 q^{25} + 4 q^{27} + 4 q^{29} - 12 q^{31} + 2 q^{33} - 4 q^{37} + 2 q^{39} + 24 q^{41} - 24 q^{43} - 18 q^{47} - 6 q^{51} - 16 q^{53} + 4 q^{55} + 8 q^{57} - 12 q^{59} + 8 q^{61} + 2 q^{65} + 32 q^{69} + 24 q^{71} + 16 q^{73} - 2 q^{75} + 18 q^{79} + 2 q^{81} - 4 q^{85} - 2 q^{87} - 8 q^{89} - 24 q^{93} + 4 q^{95} + 28 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^5 + 2 * q^11 + 4 * q^13 - 4 * q^15 - 2 * q^17 - 4 * q^19 - 4 * q^23 - 2 * q^25 + 4 * q^27 + 4 * q^29 - 12 * q^31 + 2 * q^33 - 4 * q^37 + 2 * q^39 + 24 * q^41 - 24 * q^43 - 18 * q^47 - 6 * q^51 - 16 * q^53 + 4 * q^55 + 8 * q^57 - 12 * q^59 + 8 * q^61 + 2 * q^65 + 32 * q^69 + 24 * q^71 + 16 * q^73 - 2 * q^75 + 18 * q^79 + 2 * q^81 - 4 * q^85 - 2 * q^87 - 8 * q^89 - 24 * q^93 + 4 * q^95 + 28 * q^97

Introduction

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