LMFDB - Embedded newform 1680.2.bg.v.1201.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1680,2,Mod(961,1680)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1680, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1680.961");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.bg (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:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.29428272.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 6x^{4} - 4x^{3} - 42x^{2} + 343 $ x^6 - 6x^4 - 4x^3 - 42*x^2 + 343
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 840)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1201.3
Root			$-2.56022 - 0.667305i$ of defining polynomial
Character	$\chi$	$=$	1680.1201
Dual form			1680.2.bg.v.961.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.56022 - 0.667305i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.56022 - 0.667305i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-2.65581 + 4.59999i) q^{11} -5.71602 q^{13} +1.00000 q^{15} +(-3.76242 + 6.51670i) q^{17} +(0.500000 + 0.866025i) q^{19} +(0.702205 - 2.55086i) q^{21} +(2.06022 + 3.56840i) q^{23} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{27} -2.71602 q^{29} +(-2.91823 + 5.05452i) q^{31} +(2.65581 + 4.59999i) q^{33} +(1.85801 + 1.88356i) q^{35} +(-2.45360 - 4.24976i) q^{37} +(-2.85801 + 4.95022i) q^{39} -8.12043 q^{41} -4.31161 q^{43} +(0.500000 - 0.866025i) q^{45} +(5.41823 + 9.38464i) q^{47} +(6.10941 - 3.41689i) q^{49} +(3.76242 + 6.51670i) q^{51} +(2.29780 - 3.97990i) q^{53} -5.31161 q^{55} +1.00000 q^{57} +(7.35801 - 12.7444i) q^{59} +(-1.85801 - 1.88356i) q^{63} +(-2.85801 - 4.95022i) q^{65} +(2.15581 - 3.73397i) q^{67} +4.12043 q^{69} +10.3337 q^{71} +(-0.439784 + 0.761729i) q^{73} +(0.500000 + 0.866025i) q^{75} +(-3.72984 + 13.5492i) q^{77} +(-3.51382 - 6.08611i) q^{79} +(-0.500000 + 0.866025i) q^{81} +2.71602 q^{83} -7.52484 q^{85} +(-1.35801 + 2.35214i) q^{87} +(-1.95360 - 3.38374i) q^{89} +(-14.6342 + 3.81433i) q^{91} +(2.91823 + 5.05452i) q^{93} +(-0.500000 + 0.866025i) q^{95} +8.00000 q^{97} +5.31161 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} + 3 q^{5} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 + 3 * q^5 - 3 * q^9	$ 6 q + 3 q^{3} + 3 q^{5} - 3 q^{9} - 3 q^{11} - 6 q^{13} + 6 q^{15} - 6 q^{17} + 3 q^{19} + 3 q^{21} - 3 q^{23} - 3 q^{25} - 6 q^{27} + 12 q^{29} + 12 q^{31} + 3 q^{33} - 3 q^{35} - 3 q^{37} - 3 q^{39} - 18 q^{41} + 3 q^{45} + 3 q^{47} + 12 q^{49} + 6 q^{51} + 15 q^{53} - 6 q^{55} + 6 q^{57} + 30 q^{59} + 3 q^{63} - 3 q^{65} - 6 q^{69} + 24 q^{71} - 18 q^{73} + 3 q^{75} + 33 q^{77} + 6 q^{79} - 3 q^{81} - 12 q^{83} - 12 q^{85} + 6 q^{87} - 30 q^{91} - 12 q^{93} - 3 q^{95} + 48 q^{97} + 6 q^{99}+O(q^{100}) $ 6 * q + 3 * q^3 + 3 * q^5 - 3 * q^9 - 3 * q^11 - 6 * q^13 + 6 * q^15 - 6 * q^17 + 3 * q^19 + 3 * q^21 - 3 * q^23 - 3 * q^25 - 6 * q^27 + 12 * q^29 + 12 * q^31 + 3 * q^33 - 3 * q^35 - 3 * q^37 - 3 * q^39 - 18 * q^41 + 3 * q^45 + 3 * q^47 + 12 * q^49 + 6 * q^51 + 15 * q^53 - 6 * q^55 + 6 * q^57 + 30 * q^59 + 3 * q^63 - 3 * q^65 - 6 * q^69 + 24 * q^71 - 18 * q^73 + 3 * q^75 + 33 * q^77 + 6 * q^79 - 3 * q^81 - 12 * q^83 - 12 * q^85 + 6 * q^87 - 30 * q^91 - 12 * q^93 - 3 * q^95 + 48 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$	$1$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	2.56022	−	0.667305i	0.967671	−	0.252218i
$7$	2.56022	−	0.667305i	0.967671	−	0.252218i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−2.65581	+	4.59999i	−0.800756	+	1.38695i	0.118364	+	0.992970i	$0.462235\pi$
$11$	−2.65581	+	4.59999i	−0.800756	+	1.38695i	−0.919119	+	0.393979i	$0.871098\pi$
$12$		0			0
$13$	−5.71602			−1.58534			−0.792670	−	0.609651i	$-0.791309\pi$
$13$	−5.71602			−1.58534			−0.792670	+	0.609651i	$0.791309\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	−3.76242	+	6.51670i	−0.912521	+	1.58053i	−0.102030	+	0.994781i	$0.532534\pi$
$17$	−3.76242	+	6.51670i	−0.912521	+	1.58053i	−0.810491	+	0.585751i	$0.800800\pi$
$18$		0			0
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	−0.802955	+	0.596040i	$0.796740\pi$
$20$		0			0
$21$	0.702205	−	2.55086i	0.153234	−	0.556644i
$22$		0			0
$23$	2.06022	+	3.56840i	0.429585	+	0.744062i	0.996836	−	0.0794821i	$-0.0253266\pi$
$23$	2.06022	+	3.56840i	0.429585	+	0.744062i	−0.567252	+	0.823545i	$0.691993\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−2.71602			−0.504353			−0.252176	−	0.967681i	$-0.581146\pi$
$29$	−2.71602			−0.504353			−0.252176	+	0.967681i	$0.581146\pi$
$30$		0			0
$31$	−2.91823	+	5.05452i	−0.524129	+	0.907818i	0.475476	+	0.879728i	$0.342276\pi$
$31$	−2.91823	+	5.05452i	−0.524129	+	0.907818i	−0.999605	+	0.0280895i	$0.991058\pi$
$32$		0			0
$33$	2.65581	+	4.59999i	0.462317	+	0.800756i
$34$		0			0
$35$	1.85801	+	1.88356i	0.314061	+	0.318380i
$36$		0			0
$37$	−2.45360	−	4.24976i	−0.403370	−	0.698657i	0.590761	−	0.806847i	$-0.298828\pi$
$37$	−2.45360	−	4.24976i	−0.403370	−	0.698657i	−0.994130	+	0.108190i	$0.965494\pi$
$38$		0			0
$39$	−2.85801	+	4.95022i	−0.457648	+	0.792670i
$40$		0			0
$41$	−8.12043			−1.26820			−0.634099	−	0.773252i	$-0.718629\pi$
$41$	−8.12043			−1.26820			−0.634099	+	0.773252i	$0.718629\pi$
$42$		0			0
$43$	−4.31161			−0.657515			−0.328757	−	0.944414i	$-0.606630\pi$
$43$	−4.31161			−0.657515			−0.328757	+	0.944414i	$0.606630\pi$
$44$		0			0
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$		0			0
$47$	5.41823	+	9.38464i	0.790330	+	1.36889i	0.925763	+	0.378105i	$0.123424\pi$
$47$	5.41823	+	9.38464i	0.790330	+	1.36889i	−0.135433	+	0.990786i	$0.543243\pi$
$48$		0			0
$49$	6.10941	−	3.41689i	0.872773	−	0.488127i
$50$		0			0
$51$	3.76242	+	6.51670i	0.526844	+	0.912521i
$52$		0			0
$53$	2.29780	−	3.97990i	0.315626	−	0.546681i	−0.663944	−	0.747782i	$-0.731119\pi$
$53$	2.29780	−	3.97990i	0.315626	−	0.546681i	0.979570	+	0.201101i	$0.0644520\pi$
$54$		0			0
$55$	−5.31161			−0.716218
$56$		0			0
$57$	1.00000			0.132453
$58$		0			0
$59$	7.35801	−	12.7444i	0.957931	−	1.65919i	0.230419	−	0.973092i	$-0.425990\pi$
$59$	7.35801	−	12.7444i	0.957931	−	1.65919i	0.727513	−	0.686094i	$-0.240676\pi$
$60$		0			0
$61$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$61$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$62$		0			0
$63$	−1.85801	−	1.88356i	−0.234087	−	0.237306i
$64$		0			0
$65$	−2.85801	−	4.95022i	−0.354493	−	0.613999i
$66$		0			0
$67$	2.15581	−	3.73397i	0.263374	−	0.456177i	−0.703763	−	0.710435i	$-0.748498\pi$
$67$	2.15581	−	3.73397i	0.263374	−	0.456177i	0.967136	+	0.254259i	$0.0818315\pi$
$68$		0			0
$69$	4.12043			0.496042
$70$		0			0
$71$	10.3337			1.22638			0.613190	−	0.789936i	$-0.289886\pi$
$71$	10.3337			1.22638			0.613190	+	0.789936i	$0.289886\pi$
$72$		0			0
$73$	−0.439784	+	0.761729i	−0.0514729	+	0.0891536i	−0.890614	−	0.454760i	$-0.849725\pi$
$73$	−0.439784	+	0.761729i	−0.0514729	+	0.0891536i	0.839141	+	0.543914i	$0.183058\pi$
$74$		0			0
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$		0			0
$77$	−3.72984	+	13.5492i	−0.425055	+	1.54407i
$78$		0			0
$79$	−3.51382	−	6.08611i	−0.395335	−	0.684741i	0.597809	−	0.801639i	$-0.296038\pi$
$79$	−3.51382	−	6.08611i	−0.395335	−	0.684741i	−0.993144	+	0.116898i	$0.962705\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	2.71602			0.298122			0.149061	−	0.988828i	$-0.452375\pi$
$83$	2.71602			0.298122			0.149061	+	0.988828i	$0.452375\pi$
$84$		0			0
$85$	−7.52484			−0.816184
$86$		0			0
$87$	−1.35801	+	2.35214i	−0.145594	+	0.252176i
$88$		0			0
$89$	−1.95360	−	3.38374i	−0.207081	−	0.358675i	0.743713	−	0.668500i	$-0.233063\pi$
$89$	−1.95360	−	3.38374i	−0.207081	−	0.358675i	−0.950794	+	0.309824i	$0.899730\pi$
$90$		0			0
$91$	−14.6342	+	3.81433i	−1.53409	+	0.399850i
$92$		0			0
$93$	2.91823	+	5.05452i	0.302606	+	0.524129i
$94$		0			0
$95$	−0.500000	+	0.866025i	−0.0512989	+	0.0888523i
$96$		0			0
$97$	8.00000			0.812277			0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000			0.812277			0.406138	+	0.913812i	$0.366875\pi$
$98$		0			0
$99$	5.31161			0.533837
$100$		0			0
$101$	−0.237580	+	0.411500i	−0.0236401	+	0.0409458i	−0.877603	−	0.479387i	$-0.840859\pi$
$101$	−0.237580	+	0.411500i	−0.0236401	+	0.0409458i	0.853963	+	0.520333i	$0.174192\pi$
$102$		0			0
$103$	8.87183	+	15.3665i	0.874167	+	1.51410i	0.857647	+	0.514238i	$0.171925\pi$
$103$	8.87183	+	15.3665i	0.874167	+	1.51410i	0.0165200	+	0.999864i	$0.494741\pi$
$104$		0			0
$105$	2.56022	−	0.667305i	0.249851	−	0.0651223i
$106$		0			0
$107$	−3.16683	−	5.48511i	−0.306149	−	0.530266i	0.671368	−	0.741125i	$-0.265707\pi$
$107$	−3.16683	−	5.48511i	−0.306149	−	0.530266i	−0.977516	+	0.210859i	$0.932374\pi$
$108$		0			0
$109$	−6.51382	+	11.2823i	−0.623911	+	1.08064i	0.364840	+	0.931070i	$0.381124\pi$
$109$	−6.51382	+	11.2823i	−0.623911	+	1.08064i	−0.988750	+	0.149574i	$0.952210\pi$
$110$		0			0
$111$	−4.90720			−0.465771
$112$		0			0
$113$	7.61764			0.716607			0.358304	−	0.933605i	$-0.383355\pi$
$113$	7.61764			0.716607			0.358304	+	0.933605i	$0.383355\pi$
$114$		0			0
$115$	−2.06022	+	3.56840i	−0.192116	+	0.332755i
$116$		0			0
$117$	2.85801	+	4.95022i	0.264223	+	0.457648i
$118$		0			0
$119$	−5.28398	+	19.1948i	−0.484381	+	1.75959i
$120$		0			0
$121$	−8.60661	−	14.9071i	−0.782419	−	1.35519i
$122$		0			0
$123$	−4.06022	+	7.03250i	−0.366097	+	0.634099i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−3.33366			−0.295814			−0.147907	−	0.989001i	$-0.547254\pi$
$127$	−3.33366			−0.295814			−0.147907	+	0.989001i	$0.547254\pi$
$128$		0			0
$129$	−2.15581	+	3.73397i	−0.189808	+	0.328757i
$130$		0			0
$131$	0.702205	+	1.21625i	0.0613519	+	0.106265i	0.895070	−	0.445926i	$-0.147125\pi$
$131$	0.702205	+	1.21625i	0.0613519	+	0.106265i	−0.833718	+	0.552190i	$0.813792\pi$
$132$		0			0
$133$	1.85801	+	1.88356i	0.161110	+	0.163325i
$134$		0			0
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$		0			0
$137$	−9.79005	+	16.9569i	−0.836421	+	1.44872i	0.0564475	+	0.998406i	$0.482023\pi$
$137$	−9.79005	+	16.9569i	−0.836421	+	1.44872i	−0.892868	+	0.450318i	$0.851311\pi$
$138$		0			0
$139$	−7.21323			−0.611818			−0.305909	−	0.952061i	$-0.598960\pi$
$139$	−7.21323			−0.611818			−0.305909	+	0.952061i	$0.598960\pi$
$140$		0			0
$141$	10.8365			0.912594
$142$		0			0
$143$	15.1806	−	26.2937i	1.26947	−	2.19879i
$144$		0			0
$145$	−1.35801	−	2.35214i	−0.112777	−	0.195335i
$146$		0			0
$147$	0.0955907	−	6.99935i	0.00788419	−	0.577296i
$148$		0			0
$149$	5.43204	+	9.40858i	0.445010	+	0.770781i	0.998053	−	0.0623724i	$-0.0198667\pi$
$149$	5.43204	+	9.40858i	0.445010	+	0.770781i	−0.553043	+	0.833153i	$0.686533\pi$
$150$		0			0
$151$	2.19118	−	3.79524i	0.178316	−	0.308852i	−0.762988	−	0.646413i	$-0.776268\pi$
$151$	2.19118	−	3.79524i	0.178316	−	0.308852i	0.941304	+	0.337561i	$0.109602\pi$
$152$		0			0
$153$	7.52484			0.608347
$154$		0			0
$155$	−5.83645			−0.468795
$156$		0			0
$157$	−9.53866	+	16.5214i	−0.761268	+	1.31855i	0.180930	+	0.983496i	$0.442089\pi$
$157$	−9.53866	+	16.5214i	−0.761268	+	1.31855i	−0.942197	+	0.335058i	$0.891244\pi$
$158$		0			0
$159$	−2.29780	−	3.97990i	−0.182227	−	0.315626i
$160$		0			0
$161$	7.65581	+	7.76108i	0.603362	+	0.611658i
$162$		0			0
$163$	4.00000	+	6.92820i	0.313304	+	0.542659i	0.979076	−	0.203497i	$-0.0652307\pi$
$163$	4.00000	+	6.92820i	0.313304	+	0.542659i	−0.665771	+	0.746156i	$0.731897\pi$
$164$		0			0
$165$	−2.65581	+	4.59999i	−0.206754	+	0.358109i
$166$		0			0
$167$	−8.50279			−0.657966			−0.328983	−	0.944336i	$-0.606706\pi$
$167$	−8.50279			−0.657966			−0.328983	+	0.944336i	$0.606706\pi$
$168$		0			0
$169$	19.6729			1.51330
$170$		0			0
$171$	0.500000	−	0.866025i	0.0382360	−	0.0662266i
$172$		0			0
$173$	10.5387	+	18.2535i	0.801239	+	1.38779i	0.918801	+	0.394722i	$0.129159\pi$
$173$	10.5387	+	18.2535i	0.801239	+	1.38779i	−0.117561	+	0.993066i	$0.537508\pi$
$174$		0			0
$175$	−0.702205	+	2.55086i	−0.0530817	+	0.192827i
$176$		0			0
$177$	−7.35801	−	12.7444i	−0.553062	−	0.957931i
$178$		0			0
$179$	2.82264	−	4.88895i	0.210974	−	0.365417i	−0.741046	−	0.671454i	$-0.765670\pi$
$179$	2.82264	−	4.88895i	0.210974	−	0.365417i	0.952020	+	0.306037i	$0.0990032\pi$
$180$		0			0
$181$	25.2685			1.87819			0.939096	−	0.343654i	$-0.111665\pi$
$181$	25.2685			1.87819			0.939096	+	0.343654i	$0.111665\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.45360	−	4.24976i	0.180392	−	0.312449i
$186$		0			0
$187$	−19.9845	−	34.6142i	−1.46141	−	2.53124i
$188$		0			0
$189$	−2.56022	+	0.667305i	−0.186228	+	0.0485393i
$190$		0			0
$191$	6.43204	+	11.1406i	0.465406	+	0.806107i	0.999220	−	0.0394948i	$-0.0125749\pi$
$191$	6.43204	+	11.1406i	0.465406	+	0.806107i	−0.533813	+	0.845602i	$0.679242\pi$
$192$		0			0
$193$	9.87183	−	17.0985i	0.710590	−	1.23078i	−0.254046	−	0.967192i	$-0.581762\pi$
$193$	9.87183	−	17.0985i	0.710590	−	1.23078i	0.964636	−	0.263585i	$-0.0849051\pi$
$194$		0			0
$195$	−5.71602			−0.409333
$196$		0			0
$197$	−18.7437			−1.33543			−0.667715	−	0.744417i	$-0.732728\pi$
$197$	−18.7437			−1.33543			−0.667715	+	0.744417i	$0.732728\pi$
$198$		0			0
$199$	11.8365	−	20.5013i	0.839064	−	1.45330i	−0.0516143	−	0.998667i	$-0.516437\pi$
$199$	11.8365	−	20.5013i	0.839064	−	1.45330i	0.890678	−	0.454634i	$-0.150230\pi$
$200$		0			0
$201$	−2.15581	−	3.73397i	−0.152059	−	0.263374i
$202$		0			0
$203$	−6.95360	+	1.81242i	−0.488047	+	0.127207i
$204$		0			0
$205$	−4.06022	−	7.03250i	−0.283578	−	0.491171i
$206$		0			0
$207$	2.06022	−	3.56840i	0.143195	−	0.248021i
$208$		0			0
$209$	−5.31161			−0.367412
$210$		0			0
$211$	−9.64527			−0.664008			−0.332004	−	0.943278i	$-0.607725\pi$
$211$	−9.64527			−0.664008			−0.332004	+	0.943278i	$0.607725\pi$
$212$		0			0
$213$	5.16683	−	8.94921i	0.354025	−	0.613190i
$214$		0			0
$215$	−2.15581	−	3.73397i	−0.147025	−	0.254654i
$216$		0			0
$217$	−4.09838	+	14.8880i	−0.278216	+	1.01066i
$218$		0			0
$219$	0.439784	+	0.761729i	0.0297179	+	0.0514729i
$220$		0			0
$221$	21.5061	−	37.2496i	1.44666	−	2.50568i
$222$		0			0
$223$	−6.56796			−0.439823			−0.219911	−	0.975520i	$-0.570577\pi$
$223$	−6.56796			−0.439823			−0.219911	+	0.975520i	$0.570577\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−2.16683	+	3.75306i	−0.143818	+	0.249099i	−0.928931	−	0.370252i	$-0.879271\pi$
$227$	−2.16683	+	3.75306i	−0.143818	+	0.249099i	0.785114	+	0.619352i	$0.212605\pi$
$228$		0			0
$229$	3.08177	+	5.33779i	0.203649	+	0.352731i	0.949702	−	0.313156i	$-0.101386\pi$
$229$	3.08177	+	5.33779i	0.203649	+	0.352731i	−0.746052	+	0.665887i	$0.768053\pi$
$230$		0			0
$231$	9.86903	+	10.0047i	0.649335	+	0.658263i
$232$		0			0
$233$	1.71602	+	2.97224i	0.112420	+	0.194718i	0.916746	−	0.399472i	$-0.130806\pi$
$233$	1.71602	+	2.97224i	0.112420	+	0.194718i	−0.804325	+	0.594189i	$0.797473\pi$
$234$		0			0
$235$	−5.41823	+	9.38464i	−0.353446	+	0.612187i
$236$		0			0
$237$	−7.02763			−0.456494
$238$		0			0
$239$	28.8641			1.86706			0.933531	−	0.358496i	$-0.116710\pi$
$239$	28.8641			1.86706			0.933531	+	0.358496i	$0.116710\pi$
$240$		0			0
$241$	−8.29780	+	14.3722i	−0.534508	+	0.925795i	0.464679	+	0.885479i	$0.346170\pi$
$241$	−8.29780	+	14.3722i	−0.534508	+	0.925795i	−0.999187	+	0.0403158i	$0.987164\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	6.01382	+	3.58246i	0.384209	+	0.228875i
$246$		0			0
$247$	−2.85801	−	4.95022i	−0.181851	−	0.314975i
$248$		0			0
$249$	1.35801	−	2.35214i	0.0860604	−	0.149061i
$250$		0			0
$251$	11.1260			0.702268			0.351134	−	0.936325i	$-0.385796\pi$
$251$	11.1260			0.702268			0.351134	+	0.936325i	$0.385796\pi$
$252$		0			0
$253$	−21.8861			−1.37597
$254$		0			0
$255$	−3.76242	+	6.51670i	−0.235612	+	0.408092i
$256$		0			0
$257$	−6.54919	−	11.3435i	−0.408527	−	0.707590i	0.586198	−	0.810168i	$-0.300624\pi$
$257$	−6.54919	−	11.3435i	−0.408527	−	0.707590i	−0.994725	+	0.102578i	$0.967291\pi$
$258$		0			0
$259$	−9.11764	−	9.24301i	−0.566542	−	0.574333i
$260$		0			0
$261$	1.35801	+	2.35214i	0.0840588	+	0.145594i
$262$		0			0
$263$	2.71602	−	4.70429i	0.167477	−	0.290079i	−0.770055	−	0.637977i	$-0.779771\pi$
$263$	2.71602	−	4.70429i	0.167477	−	0.290079i	0.937532	+	0.347899i	$0.113105\pi$
$264$		0			0
$265$	4.59559			0.282305
$266$		0			0
$267$	−3.90720			−0.239117
$268$		0			0
$269$	3.12043	−	5.40475i	0.190256	−	0.329533i	−0.755079	−	0.655634i	$-0.772402\pi$
$269$	3.12043	−	5.40475i	0.190256	−	0.329533i	0.945335	+	0.326101i	$0.105735\pi$
$270$		0			0
$271$	10.4044	+	18.0210i	0.632023	+	1.09470i	0.987138	+	0.159873i	$0.0511085\pi$
$271$	10.4044	+	18.0210i	0.632023	+	1.09470i	−0.355115	+	0.934823i	$0.615558\pi$
$272$		0			0
$273$	−4.01382	+	14.5808i	−0.242927	+	0.882470i
$274$		0			0
$275$	−2.65581	−	4.59999i	−0.160151	−	0.277390i
$276$		0			0
$277$	13.4674	−	23.3263i	0.809179	−	1.40154i	−0.104255	−	0.994551i	$-0.533246\pi$
$277$	13.4674	−	23.3263i	0.809179	−	1.40154i	0.913433	−	0.406988i	$-0.133421\pi$
$278$		0			0
$279$	5.83645			0.349419
$280$		0			0
$281$	8.41000			0.501698			0.250849	−	0.968026i	$-0.419290\pi$
$281$	8.41000			0.501698			0.250849	+	0.968026i	$0.419290\pi$
$282$		0			0
$283$	6.84419	−	11.8545i	0.406845	−	0.704676i	−0.587689	−	0.809087i	$-0.699962\pi$
$283$	6.84419	−	11.8545i	0.406845	−	0.704676i	0.994534	+	0.104410i	$0.0332955\pi$
$284$		0			0
$285$	0.500000	+	0.866025i	0.0296174	+	0.0512989i
$286$		0			0
$287$	−20.7901	+	5.41880i	−1.22720	+	0.319862i
$288$		0			0
$289$	−19.8116	−	34.3147i	−1.16539	−	2.01851i
$290$		0			0
$291$	4.00000	−	6.92820i	0.234484	−	0.406138i
$292$		0			0
$293$	−5.97237			−0.348909			−0.174455	−	0.984665i	$-0.555816\pi$
$293$	−5.97237			−0.348909			−0.174455	+	0.984665i	$0.555816\pi$
$294$		0			0
$295$	14.7160			0.856800
$296$		0			0
$297$	2.65581	−	4.59999i	0.154106	−	0.266919i
$298$		0			0
$299$	−11.7762	−	20.3970i	−0.681037	−	1.17959i
$300$		0			0
$301$	−11.0387	+	2.87716i	−0.636258	+	0.165837i
$302$		0			0
$303$	0.237580	+	0.411500i	0.0136486	+	0.0236401i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−32.9789			−1.88221			−0.941104	−	0.338119i	$-0.890209\pi$
$307$	−32.9789			−1.88221			−0.941104	+	0.338119i	$0.890209\pi$
$308$		0			0
$309$	17.7437			1.00940
$310$		0			0
$311$	−10.3856	+	17.9885i	−0.588916	+	1.02003i	0.405459	+	0.914113i	$0.367112\pi$
$311$	−10.3856	+	17.9885i	−0.588916	+	1.02003i	−0.994375	+	0.105919i	$0.966222\pi$
$312$		0			0
$313$	−1.77344	−	3.07169i	−0.100241	−	0.173622i	0.811543	−	0.584293i	$-0.198628\pi$
$313$	−1.77344	−	3.07169i	−0.100241	−	0.173622i	−0.911784	+	0.410670i	$0.865295\pi$
$314$		0			0
$315$	0.702205	−	2.55086i	0.0395648	−	0.143725i
$316$		0			0
$317$	3.64199	+	6.30811i	0.204554	+	0.354299i	0.949991	−	0.312278i	$-0.101092\pi$
$317$	3.64199	+	6.30811i	0.204554	+	0.354299i	−0.745436	+	0.666577i	$0.767759\pi$
$318$		0			0
$319$	7.21323	−	12.4937i	0.403863	−	0.699512i
$320$		0			0
$321$	−6.33366			−0.353510
$322$		0			0
$323$	−7.52484			−0.418693
$324$		0			0
$325$	2.85801	−	4.95022i	0.158534	−	0.274589i
$326$		0			0
$327$	6.51382	+	11.2823i	0.360215	+	0.623911i
$328$		0			0
$329$	20.1342	+	20.4111i	1.11004	+	1.12530i
$330$		0			0
$331$	−11.0525	−	19.1434i	−0.607499	−	1.05222i	−0.991651	−	0.128949i	$-0.958840\pi$
$331$	−11.0525	−	19.1434i	−0.607499	−	1.05222i	0.384152	−	0.923270i	$-0.374494\pi$
$332$		0			0
$333$	−2.45360	+	4.24976i	−0.134457	+	0.232886i
$334$		0			0
$335$	4.31161			0.235569
$336$		0			0
$337$	−36.1701			−1.97031			−0.985156	−	0.171663i	$-0.945086\pi$
$337$	−36.1701			−1.97031			−0.985156	+	0.171663i	$0.945086\pi$
$338$		0			0
$339$	3.80882	−	6.59707i	0.206867	−	0.358304i
$340$		0			0
$341$	−15.5005	−	26.8476i	−0.839399	−	1.45388i
$342$		0			0
$343$	13.3613	−	12.8248i	0.721442	−	0.692475i
$344$		0			0
$345$	2.06022	+	3.56840i	0.110918	+	0.192116i
$346$		0			0
$347$	−4.21323	+	7.29752i	−0.226178	+	0.391752i	−0.956672	−	0.291167i	$-0.905956\pi$
$347$	−4.21323	+	7.29752i	−0.226178	+	0.391752i	0.730494	+	0.682919i	$0.239290\pi$
$348$		0			0
$349$	−19.6729			−1.05307			−0.526533	−	0.850155i	$-0.676508\pi$
$349$	−19.6729			−1.05307			−0.526533	+	0.850155i	$0.676508\pi$
$350$		0			0
$351$	5.71602			0.305099
$352$		0			0
$353$	−16.0740	+	27.8410i	−0.855534	+	1.48183i	0.0206139	+	0.999788i	$0.493438\pi$
$353$	−16.0740	+	27.8410i	−0.855534	+	1.48183i	−0.876148	+	0.482042i	$0.839895\pi$
$354$		0			0
$355$	5.16683	+	8.94921i	0.274227	+	0.474975i
$356$		0			0
$357$	13.9812	+	14.1735i	0.739965	+	0.750140i
$358$		0			0
$359$	4.79005	+	8.29662i	0.252809	+	0.437879i	0.964298	−	0.264819i	$-0.0853121\pi$
$359$	4.79005	+	8.29662i	0.252809	+	0.437879i	−0.711489	+	0.702697i	$0.751979\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$		0			0
$363$	−17.2132			−0.903460
$364$		0			0
$365$	−0.879569			−0.0460387
$366$		0			0
$367$	−13.6668	+	23.6716i	−0.713403	+	1.23565i	0.250170	+	0.968202i	$0.419514\pi$
$367$	−13.6668	+	23.6716i	−0.713403	+	1.23565i	−0.963572	+	0.267448i	$0.913820\pi$
$368$		0			0
$369$	4.06022	+	7.03250i	0.211366	+	0.366097i
$370$		0			0
$371$	3.22705	−	11.7227i	0.167540	−	0.608614i
$372$		0			0
$373$	−14.1127	−	24.4439i	−0.730727	−	1.26566i	−0.956573	−	0.291494i	$-0.905848\pi$
$373$	−14.1127	−	24.4439i	−0.730727	−	1.26566i	0.225845	−	0.974163i	$-0.427486\pi$
$374$		0			0
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$		0			0
$377$	15.5248			0.799570
$378$		0			0
$379$	9.86409			0.506684			0.253342	−	0.967377i	$-0.418470\pi$
$379$	9.86409			0.506684			0.253342	+	0.967377i	$0.418470\pi$
$380$		0			0
$381$	−1.66683	+	2.88703i	−0.0853943	+	0.147907i
$382$		0			0
$383$	7.48898	+	12.9713i	0.382669	+	0.662802i	0.991443	−	0.130542i	$-0.0416717\pi$
$383$	7.48898	+	12.9713i	0.382669	+	0.662802i	−0.608774	+	0.793344i	$0.708338\pi$
$384$		0			0
$385$	−13.5989	+	3.54447i	−0.693063	+	0.180643i
$386$		0			0
$387$	2.15581	+	3.73397i	0.109586	+	0.189808i
$388$		0			0
$389$	2.45081	−	4.24492i	0.124261	−	0.215226i	−0.797183	−	0.603738i	$-0.793677\pi$
$389$	2.45081	−	4.24492i	0.124261	−	0.215226i	0.921444	+	0.388512i	$0.127011\pi$
$390$		0			0
$391$	−31.0056			−1.56802
$392$		0			0
$393$	1.40441			0.0708431
$394$		0			0
$395$	3.51382	−	6.08611i	0.176799	−	0.306225i
$396$		0			0
$397$	−1.46742	−	2.54164i	−0.0736476	−	0.127561i	0.826850	−	0.562423i	$-0.190131\pi$
$397$	−1.46742	−	2.54164i	−0.0736476	−	0.127561i	−0.900497	+	0.434861i	$0.856797\pi$
$398$		0			0
$399$	2.56022	−	0.667305i	0.128171	−	0.0334070i
$400$		0			0
$401$	−9.72984	−	16.8526i	−0.485885	−	0.841577i	0.513983	−	0.857800i	$-0.328169\pi$
$401$	−9.72984	−	16.8526i	−0.485885	−	0.841577i	−0.999868	+	0.0162226i	$0.994836\pi$
$402$		0			0
$403$	16.6806	−	28.8917i	0.830922	−	1.43920i
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	26.0652			1.29200
$408$		0			0
$409$	12.7547	−	22.0918i	0.630678	−	1.09237i	−0.356735	−	0.934206i	$-0.616110\pi$
$409$	12.7547	−	22.0918i	0.630678	−	1.09237i	0.987413	−	0.158161i	$-0.0505566\pi$
$410$		0			0
$411$	9.79005	+	16.9569i	0.482908	+	0.836421i
$412$		0			0
$413$	10.3337	−	37.5386i	0.508486	−	1.84715i
$414$		0			0
$415$	1.35801	+	2.35214i	0.0666621	+	0.115462i
$416$		0			0
$417$	−3.60661	+	6.24684i	−0.176617	+	0.305909i
$418$		0			0
$419$	9.83087			0.480269			0.240135	−	0.970740i	$-0.422808\pi$
$419$	9.83087			0.480269			0.240135	+	0.970740i	$0.422808\pi$
$420$		0			0
$421$	8.26291			0.402710			0.201355	−	0.979518i	$-0.435466\pi$
$421$	8.26291			0.402710			0.201355	+	0.979518i	$0.435466\pi$
$422$		0			0
$423$	5.41823	−	9.38464i	0.263443	−	0.456297i
$424$		0			0
$425$	−3.76242	−	6.51670i	−0.182504	−	0.316107i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−15.1806	−	26.2937i	−0.732929	−	1.26947i
$430$		0			0
$431$	5.12043	−	8.86885i	0.246642	−	0.427197i	−0.715950	−	0.698152i	$-0.754006\pi$
$431$	5.12043	−	8.86885i	0.246642	−	0.427197i	0.962592	+	0.270955i	$0.0873393\pi$
$432$		0			0
$433$	−2.11484			−0.101633			−0.0508164	−	0.998708i	$-0.516182\pi$
$433$	−2.11484			−0.101633			−0.0508164	+	0.998708i	$0.516182\pi$
$434$		0			0
$435$	−2.71602			−0.130223
$436$		0			0
$437$	−2.06022	+	3.56840i	−0.0985535	+	0.170700i
$438$		0			0
$439$	3.50279	+	6.06702i	0.167179	+	0.289563i	0.937427	−	0.348182i	$-0.113201\pi$
$439$	3.50279	+	6.06702i	0.167179	+	0.289563i	−0.770248	+	0.637745i	$0.779867\pi$
$440$		0			0
$441$	−6.01382	−	3.58246i	−0.286372	−	0.170593i
$442$		0			0
$443$	−2.71602	−	4.70429i	−0.129042	−	0.223507i	0.794264	−	0.607573i	$-0.207857\pi$
$443$	−2.71602	−	4.70429i	−0.129042	−	0.223507i	−0.923306	+	0.384066i	$0.874524\pi$
$444$		0			0
$445$	1.95360	−	3.38374i	0.0926096	−	0.160405i
$446$		0			0
$447$	10.8641			0.513854
$448$		0			0
$449$	9.21882			0.435063			0.217531	−	0.976053i	$-0.430200\pi$
$449$	9.21882			0.435063			0.217531	+	0.976053i	$0.430200\pi$
$450$		0			0
$451$	21.5663	−	37.3539i	1.01552	−	1.75893i
$452$		0			0
$453$	−2.19118	−	3.79524i	−0.102951	−	0.178316i
$454$		0			0
$455$	−10.6204	−	10.7665i	−0.497893	−	0.504740i
$456$		0			0
$457$	19.3039	+	33.4353i	0.902997	+	1.56404i	0.823584	+	0.567195i	$0.191971\pi$
$457$	19.3039	+	33.4353i	0.902997	+	1.56404i	0.0794135	+	0.996842i	$0.474695\pi$
$458$		0			0
$459$	3.76242	−	6.51670i	0.175615	−	0.304174i
$460$		0			0
$461$	−25.2840			−1.17759			−0.588796	−	0.808282i	$-0.700398\pi$
$461$	−25.2840			−1.17759			−0.588796	+	0.808282i	$0.700398\pi$
$462$		0			0
$463$	3.57452			0.166122			0.0830611	−	0.996544i	$-0.473530\pi$
$463$	3.57452			0.166122			0.0830611	+	0.996544i	$0.473530\pi$
$464$		0			0
$465$	−2.91823	+	5.05452i	−0.135330	+	0.234398i
$466$		0			0
$467$	19.0276	+	32.9568i	0.880494	+	1.52506i	0.850793	+	0.525501i	$0.176122\pi$
$467$	19.0276	+	32.9568i	0.880494	+	1.52506i	0.0297012	+	0.999559i	$0.490544\pi$
$468$		0			0
$469$	3.02763	−	10.9983i	0.139803	−	0.507856i
$470$		0			0
$471$	9.53866	+	16.5214i	0.439518	+	0.761268i
$472$		0			0
$473$	11.4508	−	19.8334i	0.526509	−	0.911940i
$474$		0			0
$475$	−1.00000			−0.0458831
$476$		0			0
$477$	−4.59559			−0.210418
$478$		0			0
$479$	9.40441	−	16.2889i	0.429698	−	0.744260i	−0.567148	−	0.823616i	$-0.691953\pi$
$479$	9.40441	−	16.2889i	0.429698	−	0.744260i	0.996846	+	0.0793565i	$0.0252865\pi$
$480$		0			0
$481$	14.0248	+	24.2917i	0.639478	+	1.10761i
$482$		0			0
$483$	10.5492	−	2.74958i	0.480005	−	0.125110i
$484$		0			0
$485$	4.00000	+	6.92820i	0.181631	+	0.314594i
$486$		0			0
$487$	8.24860	−	14.2870i	0.373780	−	0.647406i	−0.616364	−	0.787462i	$-0.711395\pi$
$487$	8.24860	−	14.2870i	0.373780	−	0.647406i	0.990144	+	0.140056i	$0.0447282\pi$
$488$		0			0
$489$	8.00000			0.361773
$490$		0			0
$491$	7.81441			0.352659			0.176330	−	0.984331i	$-0.443578\pi$
$491$	7.81441			0.352659			0.176330	+	0.984331i	$0.443578\pi$
$492$		0			0
$493$	10.2188	−	17.6995i	0.460232	−	0.797146i
$494$		0			0
$495$	2.65581	+	4.59999i	0.119370	+	0.206754i
$496$		0			0
$497$	26.4564	−	6.89570i	1.18673	−	0.309315i
$498$		0			0
$499$	14.5415	+	25.1865i	0.650965	+	1.12750i	0.982889	+	0.184198i	$0.0589688\pi$
$499$	14.5415	+	25.1865i	0.650965	+	1.12750i	−0.331924	+	0.943306i	$0.607698\pi$
$500$		0			0
$501$	−4.25140	+	7.36364i	−0.189938	+	0.328983i
$502$		0			0
$503$	−30.2409			−1.34837			−0.674187	−	0.738561i	$-0.735506\pi$
$503$	−30.2409			−1.34837			−0.674187	+	0.738561i	$0.735506\pi$
$504$		0			0
$505$	−0.475159			−0.0211443
$506$		0			0
$507$	9.83645	−	17.0372i	0.436852	−	0.756650i
$508$		0			0
$509$	11.7160	+	20.2927i	0.519304	+	0.899460i	0.999748	+	0.0224351i	$0.00714192\pi$
$509$	11.7160	+	20.2927i	0.519304	+	0.899460i	−0.480445	+	0.877025i	$0.659525\pi$
$510$		0			0
$511$	−0.617637	+	2.24366i	−0.0273227	+	0.0992537i
$512$		0			0
$513$	−0.500000	−	0.866025i	−0.0220755	−	0.0382360i
$514$		0			0
$515$	−8.87183	+	15.3665i	−0.390939	+	0.677127i
$516$		0			0
$517$	−57.5590			−2.53144
$518$		0			0
$519$	21.0773			0.925191
$520$		0			0
$521$	−0.865752	+	1.49953i	−0.0379293	+	0.0656954i	−0.884367	−	0.466793i	$-0.845409\pi$
$521$	−0.865752	+	1.49953i	−0.0379293	+	0.0656954i	0.846438	+	0.532488i	$0.178743\pi$
$522$		0			0
$523$	18.9923	+	32.8956i	0.830474	+	1.43842i	0.897663	+	0.440682i	$0.145263\pi$
$523$	18.9923	+	32.8956i	0.830474	+	1.43842i	−0.0671897	+	0.997740i	$0.521403\pi$
$524$		0			0
$525$	1.85801	+	1.88356i	0.0810902	+	0.0822053i
$526$		0			0
$527$	−21.9592	−	38.0344i	−0.956557	−	1.65681i
$528$		0			0
$529$	3.01102	−	5.21525i	0.130914	−	0.226750i
$530$		0			0
$531$	−14.7160			−0.638621
$532$		0			0
$533$	46.4166			2.01052
$534$		0			0
$535$	3.16683	−	5.48511i	0.136914	−	0.237142i
$536$		0			0
$537$	−2.82264	−	4.88895i	−0.121806	−	0.210974i
$538$		0			0
$539$	−0.507741	+	37.1778i	−0.0218699	+	1.60136i
$540$		0			0
$541$	4.51382	+	7.81816i	0.194064	+	0.336129i	0.946593	−	0.322430i	$-0.104500\pi$
$541$	4.51382	+	7.81816i	0.194064	+	0.336129i	−0.752529	+	0.658559i	$0.771166\pi$
$542$		0			0
$543$	12.6342	−	21.8832i	0.542187	−	0.939096i
$544$		0			0
$545$	−13.0276			−0.558043
$546$		0			0
$547$	11.8144			0.505148			0.252574	−	0.967578i	$-0.418723\pi$
$547$	11.8144			0.505148			0.252574	+	0.967578i	$0.418723\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.35801	−	2.35214i	−0.0578532	−	0.100205i
$552$		0			0
$553$	−13.0574	−	13.2370i	−0.555258	−	0.562893i
$554$		0			0
$555$	−2.45360	−	4.24976i	−0.104150	−	0.180392i
$556$		0			0
$557$	1.77295	−	3.07085i	0.0751225	−	0.130116i	−0.826017	−	0.563645i	$-0.809399\pi$
$557$	1.77295	−	3.07085i	0.0751225	−	0.130116i	0.901140	+	0.433529i	$0.142732\pi$
$558$		0			0
$559$	24.6453			1.04238
$560$		0			0
$561$	−39.9690			−1.68749
$562$		0			0
$563$	−14.6729	+	25.4142i	−0.618389	+	1.07108i	0.371390	+	0.928477i	$0.378881\pi$
$563$	−14.6729	+	25.4142i	−0.618389	+	1.07108i	−0.989780	+	0.142605i	$0.954452\pi$
$564$		0			0
$565$	3.80882	+	6.59707i	0.160238	+	0.277541i
$566$		0			0
$567$	−0.702205	+	2.55086i	−0.0294898	+	0.107126i
$568$		0			0
$569$	−14.0602	−	24.3530i	−0.589435	−	1.02093i	−0.994307	−	0.106558i	$-0.966017\pi$
$569$	−14.0602	−	24.3530i	−0.589435	−	1.02093i	0.404872	−	0.914374i	$-0.367316\pi$
$570$		0			0
$571$	7.51382	−	13.0143i	0.314443	−	0.544632i	−0.664876	−	0.746954i	$-0.731515\pi$
$571$	7.51382	−	13.0143i	0.314443	−	0.544632i	0.979319	+	0.202322i	$0.0648488\pi$
$572$		0			0
$573$	12.8641			0.537405
$574$		0			0
$575$	−4.12043			−0.171834
$576$		0			0
$577$	12.3690	−	21.4238i	0.514930	−	0.891884i	−0.484920	−	0.874558i	$-0.661151\pi$
$577$	12.3690	−	21.4238i	0.514930	−	0.891884i	0.999850	−	0.0173259i	$-0.00551529\pi$
$578$		0			0
$579$	−9.87183	−	17.0985i	−0.410259	−	0.710590i
$580$		0			0
$581$	6.95360	−	1.81242i	0.288484	−	0.0751917i
$582$		0			0
$583$	12.2050	+	21.1397i	0.505479	+	0.875516i
$584$		0			0
$585$	−2.85801	+	4.95022i	−0.118164	+	0.204666i
$586$		0			0
$587$	−17.9625			−0.741391			−0.370695	−	0.928755i	$-0.620881\pi$
$587$	−17.9625			−0.741391			−0.370695	+	0.928755i	$0.620881\pi$
$588$		0			0
$589$	−5.83645			−0.240487
$590$		0			0
$591$	−9.37183	+	16.2325i	−0.385505	+	0.667715i
$592$		0			0
$593$	−10.1668	−	17.6095i	−0.417502	−	0.723134i	0.578186	−	0.815905i	$-0.303761\pi$
$593$	−10.1668	−	17.6095i	−0.417502	−	0.723134i	−0.995687	+	0.0927710i	$0.970428\pi$
$594$		0			0
$595$	−19.2652	+	5.02136i	−0.789797	+	0.205856i
$596$		0			0
$597$	−11.8365	−	20.5013i	−0.484434	−	0.839064i
$598$		0			0
$599$	−14.3613	+	24.8745i	−0.586787	+	1.01634i	0.407864	+	0.913043i	$0.366274\pi$
$599$	−14.3613	+	24.8745i	−0.586787	+	1.01634i	−0.994650	+	0.103301i	$0.967059\pi$
$600$		0			0
$601$	29.0717			1.18586			0.592930	−	0.805254i	$-0.297971\pi$
$601$	29.0717			1.18586			0.592930	+	0.805254i	$0.297971\pi$
$602$		0			0
$603$	−4.31161			−0.175582
$604$		0			0
$605$	8.60661	−	14.9071i	0.349909	−	0.606060i
$606$		0			0
$607$	12.7873	+	22.1482i	0.519019	+	0.898967i	0.999756	+	0.0221022i	$0.00703591\pi$
$607$	12.7873	+	22.1482i	0.519019	+	0.898967i	−0.480737	+	0.876865i	$0.659631\pi$
$608$		0			0
$609$	−1.90720	+	6.92820i	−0.0772838	+	0.280745i
$610$		0			0
$611$	−30.9707	−	53.6428i	−1.25294	−	2.17016i
$612$		0			0
$613$	−5.82264	+	10.0851i	−0.235174	+	0.407333i	−0.959323	−	0.282310i	$-0.908899\pi$
$613$	−5.82264	+	10.0851i	−0.235174	+	0.407333i	0.724149	+	0.689643i	$0.242233\pi$
$614$		0			0
$615$	−8.12043			−0.327447
$616$		0			0
$617$	−36.6232			−1.47440			−0.737198	−	0.675677i	$-0.763851\pi$
$617$	−36.6232			−1.47440			−0.737198	+	0.675677i	$0.763851\pi$
$618$		0			0
$619$	−7.02484	+	12.1674i	−0.282352	+	0.489048i	−0.971964	−	0.235131i	$-0.924448\pi$
$619$	−7.02484	+	12.1674i	−0.282352	+	0.489048i	0.689611	+	0.724180i	$0.257781\pi$
$620$		0			0
$621$	−2.06022	−	3.56840i	−0.0826736	−	0.143195i
$622$		0			0
$623$	−7.25963	−	7.35945i	−0.290851	−	0.294850i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−2.65581	+	4.59999i	−0.106063	+	0.183706i
$628$		0			0
$629$	36.9259			1.47233
$630$		0			0
$631$	−20.0553			−0.798388			−0.399194	−	0.916867i	$-0.630710\pi$
$631$	−20.0553			−0.798388			−0.399194	+	0.916867i	$0.630710\pi$
$632$		0			0
$633$	−4.82264	+	8.35305i	−0.191683	+	0.332004i
$634$		0			0
$635$	−1.66683	−	2.88703i	−0.0661461	−	0.114568i
$636$		0			0
$637$	−34.9215	+	19.5310i	−1.38364	+	0.773847i
$638$		0			0
$639$	−5.16683	−	8.94921i	−0.204397	−	0.354025i
$640$		0			0
$641$	2.93978	−	5.09186i	0.116115	−	0.201116i	−0.802110	−	0.597176i	$-0.796289\pi$
$641$	2.93978	−	5.09186i	0.116115	−	0.201116i	0.918225	+	0.396060i	$0.129623\pi$
$642$		0			0
$643$	6.35571			0.250645			0.125322	−	0.992116i	$-0.460004\pi$
$643$	6.35571			0.250645			0.125322	+	0.992116i	$0.460004\pi$
$644$		0			0
$645$	−4.31161			−0.169770
$646$		0			0
$647$	−3.06022	+	5.30045i	−0.120309	+	0.208382i	−0.919890	−	0.392177i	$-0.871722\pi$
$647$	−3.06022	+	5.30045i	−0.120309	+	0.208382i	0.799580	+	0.600559i	$0.205055\pi$
$648$		0			0
$649$	39.0829	+	67.6936i	1.53414	+	2.65721i
$650$		0			0
$651$	10.8442	+	10.9933i	0.425017	+	0.430862i
$652$		0			0
$653$	20.2514	+	35.0764i	0.792498	+	1.37265i	0.924416	+	0.381387i	$0.124553\pi$
$653$	20.2514	+	35.0764i	0.792498	+	1.37265i	−0.131917	+	0.991261i	$0.542113\pi$
$654$		0			0
$655$	−0.702205	+	1.21625i	−0.0274374	+	0.0475230i
$656$		0			0
$657$	0.879569			0.0343152
$658$		0			0
$659$	−41.7282			−1.62550			−0.812749	−	0.582613i	$-0.802030\pi$
$659$	−41.7282			−1.62550			−0.812749	+	0.582613i	$0.802030\pi$
$660$		0			0
$661$	−10.2298	+	17.7186i	−0.397895	+	0.689174i	−0.993466	−	0.114129i	$-0.963592\pi$
$661$	−10.2298	+	17.7186i	−0.397895	+	0.689174i	0.595571	+	0.803302i	$0.296926\pi$
$662$		0			0
$663$	−21.5061	−	37.2496i	−0.835227	−	1.44666i
$664$		0			0
$665$	−0.702205	+	2.55086i	−0.0272303	+	0.0989183i
$666$		0			0
$667$	−5.59559	−	9.69185i	−0.216662	−	0.375270i
$668$		0			0
$669$	−3.28398	+	5.68802i	−0.126966	+	0.219911i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.30602			0.0503436			0.0251718	−	0.999683i	$-0.491987\pi$
$673$	1.30602			0.0503436			0.0251718	+	0.999683i	$0.491987\pi$
$674$		0			0
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$		0			0
$677$	−0.628172	−	1.08803i	−0.0241426	−	0.0418162i	0.853702	−	0.520762i	$-0.174352\pi$
$677$	−0.628172	−	1.08803i	−0.0241426	−	0.0418162i	−0.877844	+	0.478946i	$0.841019\pi$
$678$		0			0
$679$	20.4817	−	5.33844i	0.786016	−	0.204871i
$680$		0			0
$681$	2.16683	+	3.75306i	0.0830331	+	0.143818i
$682$		0			0
$683$	−5.28726	+	9.15780i	−0.202311	+	0.350414i	−0.949273	−	0.314454i	$-0.898179\pi$
$683$	−5.28726	+	9.15780i	−0.202311	+	0.350414i	0.746961	+	0.664867i	$0.231512\pi$
$684$		0			0
$685$	−19.5801			−0.748118
$686$		0			0
$687$	6.16355			0.235154
$688$		0			0
$689$	−13.1342	+	22.7492i	−0.500375	+	0.866675i
$690$		0			0
$691$	−8.25189	−	14.2927i	−0.313917	−	0.543719i	0.665290	−	0.746585i	$-0.268308\pi$
$691$	−8.25189	−	14.2927i	−0.313917	−	0.543719i	−0.979207	+	0.202866i	$0.934975\pi$
$692$		0			0
$693$	13.5989	−	3.54447i	0.516578	−	0.134643i
$694$		0			0
$695$	−3.60661	−	6.24684i	−0.136807	−	0.236956i
$696$		0			0
$697$	30.5525	−	52.9184i	1.15726	−	2.00443i
$698$		0			0
$699$	3.43204			0.129812
$700$		0			0
$701$	11.9072			0.449729			0.224864	−	0.974390i	$-0.427806\pi$
$701$	11.9072			0.449729			0.224864	+	0.974390i	$0.427806\pi$
$702$		0			0
$703$	2.45360	−	4.24976i	0.0925393	−	0.160283i
$704$		0			0
$705$	5.41823	+	9.38464i	0.204062	+	0.353446i
$706$		0			0
$707$	−0.333659	+	1.21207i	−0.0125485	+	0.0455845i
$708$		0			0
$709$	4.24086	+	7.34539i	0.159269	+	0.275862i	0.934605	−	0.355687i	$-0.115753\pi$
$709$	4.24086	+	7.34539i	0.159269	+	0.275862i	−0.775336	+	0.631549i	$0.782420\pi$
$710$		0			0
$711$	−3.51382	+	6.08611i	−0.131778	+	0.228247i
$712$		0			0
$713$	−24.0487			−0.900631
$714$		0			0
$715$	30.3613			1.13545
$716$		0			0
$717$	14.4320	−	24.9970i	0.538975	−	0.933531i
$718$		0			0
$719$	13.3337	+	23.0946i	0.497262	+	0.861282i	0.999995	−	0.00315917i	$-0.00100560\pi$
$719$	13.3337	+	23.0946i	0.497262	+	0.861282i	−0.502733	+	0.864441i	$0.667672\pi$
$720$		0			0
$721$	32.9679	+	33.4212i	1.22779	+	1.24467i
$722$		0			0
$723$	8.29780	+	14.3722i	0.308598	+	0.534508i
$724$		0			0
$725$	1.35801	−	2.35214i	0.0504353	−	0.0873564i
$726$		0			0
$727$	−18.5689			−0.688684			−0.344342	−	0.938844i	$-0.611898\pi$
$727$	−18.5689			−0.688684			−0.344342	+	0.938844i	$0.611898\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	16.2221	−	28.0975i	0.599996	−	1.03922i
$732$		0			0
$733$	0.114355	+	0.198068i	0.00422378	+	0.00731581i	0.868130	−	0.496338i	$-0.165322\pi$
$733$	0.114355	+	0.198068i	0.00422378	+	0.00731581i	−0.863906	+	0.503653i	$0.831989\pi$
$734$		0			0
$735$	6.10941	−	3.41689i	0.225349	−	0.126034i
$736$		0			0
$737$	11.4508	+	19.8334i	0.421796	+	0.730572i
$738$		0			0
$739$	14.4072	−	24.9540i	0.529978	−	0.917948i	−0.469411	−	0.882980i	$-0.655534\pi$
$739$	14.4072	−	24.9540i	0.529978	−	0.917948i	0.999388	−	0.0349682i	$-0.0111330\pi$
$740$		0			0
$741$	−5.71602			−0.209983
$742$		0			0
$743$	32.5581			1.19444			0.597220	−	0.802078i	$-0.296272\pi$
$743$	32.5581			1.19444			0.597220	+	0.802078i	$0.296272\pi$
$744$		0			0
$745$	−5.43204	+	9.40858i	−0.199015	+	0.344704i
$746$		0			0
$747$	−1.35801	−	2.35214i	−0.0496870	−	0.0860604i
$748$		0			0
$749$	−11.7680	−	11.9298i	−0.429994	−	0.435906i
$750$		0			0
$751$	22.4210	+	38.8343i	0.818155	+	1.41709i	0.907040	+	0.421044i	$0.138336\pi$
$751$	22.4210	+	38.8343i	0.818155	+	1.41709i	−0.0888857	+	0.996042i	$0.528331\pi$
$752$		0			0
$753$	5.56301	−	9.63542i	0.202727	−	0.351134i
$754$		0			0
$755$	4.38236			0.159491
$756$		0			0
$757$	28.8641			1.04908			0.524542	−	0.851385i	$-0.324237\pi$
$757$	28.8641			1.04908			0.524542	+	0.851385i	$0.324237\pi$
$758$		0			0
$759$	−10.9431	+	18.9539i	−0.397208	+	0.687985i
$760$		0			0
$761$	9.39387	+	16.2707i	0.340528	+	0.589811i	0.984531	−	0.175212i	$-0.0560610\pi$
$761$	9.39387	+	16.2707i	0.340528	+	0.589811i	−0.644003	+	0.765023i	$0.722728\pi$
$762$		0			0
$763$	−9.14807	+	33.2317i	−0.331182	+	1.20307i
$764$		0			0
$765$	3.76242	+	6.51670i	0.136031	+	0.235612i
$766$		0			0
$767$	−42.0586	+	72.8475i	−1.51865	+	2.63037i
$768$		0			0
$769$	33.7226			1.21607			0.608034	−	0.793911i	$-0.291959\pi$
$769$	33.7226			1.21607			0.608034	+	0.793911i	$0.291959\pi$
$770$		0			0
$771$	−13.0984			−0.471727
$772$		0			0
$773$	−8.87462	+	15.3713i	−0.319198	+	0.552867i	−0.980321	−	0.197410i	$-0.936747\pi$
$773$	−8.87462	+	15.3713i	−0.319198	+	0.552867i	0.661123	+	0.750278i	$0.270080\pi$
$774$		0			0
$775$	−2.91823	−	5.05452i	−0.104826	−	0.181564i
$776$		0			0
$777$	−12.5635	+	3.27460i	−0.450713	+	0.117476i
$778$		0			0
$779$	−4.06022	−	7.03250i	−0.145472	−	0.251965i
$780$		0			0
$781$	−27.4442	+	47.5347i	−0.982031	+	1.70093i
$782$		0			0
$783$	2.71602			0.0970627
$784$		0			0
$785$	−19.0773			−0.680899
$786$		0			0
$787$	−16.5028	+	28.5837i	−0.588261	+	1.01890i	0.406199	+	0.913785i	$0.366854\pi$
$787$	−16.5028	+	28.5837i	−0.588261	+	1.01890i	−0.994460	+	0.105113i	$0.966479\pi$
$788$		0			0
$789$	−2.71602	−	4.70429i	−0.0966929	−	0.167477i
$790$		0			0
$791$	19.5028	−	5.08329i	0.693440	−	0.180741i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	2.29780	−	3.97990i	0.0814944	−	0.141152i
$796$		0			0
$797$	−45.0122			−1.59441			−0.797206	−	0.603707i	$-0.793690\pi$
$797$	−45.0122			−1.59441			−0.797206	+	0.603707i	$0.793690\pi$
$798$		0			0
$799$	−81.5426			−2.88477
$800$		0			0
$801$	−1.95360	+	3.38374i	−0.0690271	+	0.119558i
$802$		0			0
$803$	−2.33596	−	4.04601i	−0.0824344	−	0.142781i
$804$		0			0
$805$	−2.89339	+	10.5107i	−0.101978	+	0.370452i
$806$		0			0
$807$	−3.12043	−	5.40475i	−0.109844	−	0.190256i
$808$		0			0
$809$	12.8503	−	22.2573i	0.451791	−	0.782526i	−0.546706	−	0.837325i	$-0.684118\pi$
$809$	12.8503	−	22.2573i	0.451791	−	0.782526i	0.998497	+	0.0547989i	$0.0174518\pi$
$810$		0			0
$811$	17.0332			0.598117			0.299059	−	0.954235i	$-0.403327\pi$
$811$	17.0332			0.598117			0.299059	+	0.954235i	$0.403327\pi$
$812$		0			0
$813$	20.8088			0.729797
$814$		0			0
$815$	−4.00000	+	6.92820i	−0.140114	+	0.242684i
$816$		0			0
$817$	−2.15581	−	3.73397i	−0.0754221	−	0.130635i
$818$		0			0
$819$	10.6204	+	10.7665i	0.371108	+	0.376211i
$820$		0			0
$821$	9.64199	+	16.7004i	0.336508	+	0.582848i	0.983773	−	0.179416i	$-0.0574208\pi$
$821$	9.64199	+	16.7004i	0.336508	+	0.582848i	−0.647266	+	0.762265i	$0.724088\pi$
$822$		0			0
$823$	7.68839	−	13.3167i	0.268000	−	0.464190i	−0.700345	−	0.713805i	$-0.746971\pi$
$823$	7.68839	−	13.3167i	0.268000	−	0.464190i	0.968345	+	0.249614i	$0.0803038\pi$
$824$		0			0
$825$	−5.31161			−0.184927
$826$		0			0
$827$	−3.43204			−0.119344			−0.0596719	−	0.998218i	$-0.519005\pi$
$827$	−3.43204			−0.119344			−0.0596719	+	0.998218i	$0.519005\pi$
$828$		0			0
$829$	3.18016	−	5.50820i	0.110451	−	0.191308i	−0.805501	−	0.592595i	$-0.798104\pi$
$829$	3.18016	−	5.50820i	0.110451	−	0.191308i	0.915952	+	0.401287i	$0.131437\pi$
$830$		0			0
$831$	−13.4674	−	23.3263i	−0.467180	−	0.809179i
$832$		0			0
$833$	−0.719305	+	52.6690i	−0.0249224	+	1.82487i
$834$		0			0
$835$	−4.25140	−	7.36364i	−0.147126	−	0.254829i
$836$		0			0
$837$	2.91823	−	5.05452i	0.100869	−	0.174710i
$838$		0			0
$839$	22.5304			0.777837			0.388918	−	0.921272i	$-0.372849\pi$
$839$	22.5304			0.777837			0.388918	+	0.921272i	$0.372849\pi$
$840$		0			0
$841$	−21.6232			−0.745628
$842$		0			0
$843$	4.20500	−	7.28327i	0.144828	−	0.250849i
$844$		0			0
$845$	9.83645	+	17.0372i	0.338384	+	0.586099i
$846$		0			0
$847$	−31.9824	−	32.4221i	−1.09893	−	1.11404i
$848$		0			0
$849$	−6.84419	−	11.8545i	−0.234892	−	0.406845i
$850$		0			0
$851$	10.1099	−	17.5109i	0.346563	−	0.600264i
$852$		0			0
$853$	−46.7216			−1.59972			−0.799859	−	0.600188i	$-0.795092\pi$
$853$	−46.7216			−1.59972			−0.799859	+	0.600188i	$0.795092\pi$
$854$		0			0
$855$	1.00000			0.0341993
$856$		0			0
$857$	−1.54919	+	2.68328i	−0.0529194	+	0.0916591i	−0.891272	−	0.453470i	$-0.850186\pi$
$857$	−1.54919	+	2.68328i	−0.0529194	+	0.0916591i	0.838352	+	0.545129i	$0.183519\pi$
$858$		0			0
$859$	8.55247	+	14.8133i	0.291807	+	0.505424i	0.974237	−	0.225527i	$-0.0724103\pi$
$859$	8.55247	+	14.8133i	0.291807	+	0.505424i	−0.682430	+	0.730951i	$0.739077\pi$
$860$		0			0
$861$	−5.70220	+	20.7141i	−0.194331	+	0.705935i
$862$		0			0
$863$	−17.7795	−	30.7950i	−0.605222	−	1.04828i	−0.992016	−	0.126109i	$-0.959751\pi$
$863$	−17.7795	−	30.7950i	−0.605222	−	1.04828i	0.386794	−	0.922166i	$-0.373582\pi$
$864$		0			0
$865$	−10.5387	+	18.2535i	−0.358325	+	0.620637i
$866$		0			0
$867$	−39.6232			−1.34568
$868$		0			0
$869$	37.3281			1.26627
$870$		0			0
$871$	−12.3226	+	21.3434i	−0.417537	+	0.723195i
$872$		0			0
$873$	−4.00000	−	6.92820i	−0.135379	−	0.234484i
$874$		0			0
$875$	−2.56022	+	0.667305i	−0.0865511	+	0.0225590i
$876$		0			0
$877$	24.2270	+	41.9625i	0.818089	+	1.41697i	0.907088	+	0.420940i	$0.138300\pi$
$877$	24.2270	+	41.9625i	0.818089	+	1.41697i	−0.0889991	+	0.996032i	$0.528367\pi$
$878$		0			0
$879$	−2.98618	+	5.17222i	−0.100721	+	0.174455i
$880$		0			0
$881$	−49.3182			−1.66157			−0.830786	−	0.556592i	$-0.812109\pi$
$881$	−49.3182			−1.66157			−0.830786	+	0.556592i	$0.812109\pi$
$882$		0			0
$883$	−47.7437			−1.60670			−0.803351	−	0.595506i	$-0.796952\pi$
$883$	−47.7437			−1.60670			−0.803351	+	0.595506i	$0.796952\pi$
$884$		0			0
$885$	7.35801	−	12.7444i	0.247337	−	0.428400i
$886$		0			0
$887$	8.97565	+	15.5463i	0.301373	+	0.521993i	0.976447	−	0.215757i	$-0.0692218\pi$
$887$	8.97565	+	15.5463i	0.301373	+	0.521993i	−0.675074	+	0.737750i	$0.735888\pi$
$888$		0			0
$889$	−8.53489	+	2.22457i	−0.286251	+	0.0746096i
$890$		0			0
$891$	−2.65581	−	4.59999i	−0.0889729	−	0.154106i
$892$		0			0
$893$	−5.41823	+	9.38464i	−0.181314	+	0.314045i
$894$		0			0
$895$	5.64527			0.188701
$896$		0			0
$897$	−23.5525			−0.786394
$898$		0			0
$899$	7.92597	−	13.7282i	0.264346	−	0.457860i
$900$		0			0
$901$	17.2905	+	29.9481i	0.576032	+	0.997716i
$902$		0			0
$903$	−3.02763	+	10.9983i	−0.100753	+	0.366002i
$904$		0			0
$905$	12.6342	+	21.8832i	0.419977	+	0.727421i
$906$		0			0
$907$	23.0630	−	39.9463i	0.765795	−	1.32640i	−0.174031	−	0.984740i	$-0.555679\pi$
$907$	23.0630	−	39.9463i	0.765795	−	1.32640i	0.939825	−	0.341655i	$-0.110987\pi$
$908$		0			0
$909$	0.475159			0.0157600
$910$		0			0
$911$	−9.71043			−0.321721			−0.160861	−	0.986977i	$-0.551427\pi$
$911$	−9.71043			−0.321721			−0.160861	+	0.986977i	$0.551427\pi$
$912$		0			0
$913$	−7.21323	+	12.4937i	−0.238723	+	0.413480i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	2.60941	+	2.64529i	0.0861702	+	0.0873551i
$918$		0			0
$919$	−5.01661	−	8.68903i	−0.165483	−	0.286624i	0.771344	−	0.636419i	$-0.219585\pi$
$919$	−5.01661	−	8.68903i	−0.165483	−	0.286624i	−0.936827	+	0.349794i	$0.886252\pi$
$920$		0			0
$921$	−16.4895	+	28.5606i	−0.543346	+	0.941104i
$922$		0			0
$923$	−59.0674			−1.94423
$924$		0			0
$925$	4.90720			0.161348
$926$		0			0
$927$	8.87183	−	15.3665i	0.291389	−	0.504701i
$928$		0			0
$929$	−8.20828	−	14.2172i	−0.269305	−	0.466450i	0.699378	−	0.714752i	$-0.253461\pi$
$929$	−8.20828	−	14.2172i	−0.269305	−	0.466450i	−0.968683	+	0.248303i	$0.920127\pi$
$930$		0			0
$931$	6.01382	+	3.58246i	0.197095	+	0.117410i
$932$		0			0
$933$	10.3856	+	17.9885i	0.340011	+	0.588916i
$934$		0			0
$935$	19.9845	−	34.6142i	0.653564	−	1.13201i
$936$		0			0
$937$	45.0895			1.47301			0.736504	−	0.676433i	$-0.236475\pi$
$937$	45.0895			1.47301			0.736504	+	0.676433i	$0.236475\pi$
$938$		0			0
$939$	−3.54689			−0.115748
$940$		0			0
$941$	7.14478	−	12.3751i	0.232913	−	0.403418i	−0.725751	−	0.687958i	$-0.758508\pi$
$941$	7.14478	−	12.3751i	0.232913	−	0.403418i	0.958664	+	0.284540i	$0.0918408\pi$
$942$		0			0
$943$	−16.7298	−	28.9769i	−0.544799	−	0.943619i
$944$		0			0
$945$	−1.85801	−	1.88356i	−0.0604411	−	0.0612722i
$946$		0			0
$947$	21.1513	+	36.6352i	0.687326	+	1.19048i	0.972700	+	0.232068i	$0.0745491\pi$
$947$	21.1513	+	36.6352i	0.687326	+	1.19048i	−0.285373	+	0.958416i	$0.592118\pi$
$948$		0			0
$949$	2.51382	−	4.35406i	0.0816020	−	0.141339i
$950$		0			0
$951$	7.28398			0.236199
$952$		0			0
$953$	49.0609			1.58924			0.794619	−	0.607109i	$-0.207671\pi$
$953$	49.0609			1.58924			0.794619	+	0.607109i	$0.207671\pi$
$954$		0			0
$955$	−6.43204	+	11.1406i	−0.208136	+	0.360502i
$956$		0			0
$957$	−7.21323	−	12.4937i	−0.233171	−	0.403863i
$958$		0			0
$959$	−13.7492	+	49.9462i	−0.443986	+	1.61285i
$960$		0			0
$961$	−1.53209	−	2.65366i	−0.0494223	−	0.0856020i
$962$		0			0
$963$	−3.16683	+	5.48511i	−0.102050	+	0.176755i
$964$		0			0
$965$	19.7437			0.635571
$966$		0			0
$967$	25.9292			0.833828			0.416914	−	0.908946i	$-0.363112\pi$
$967$	25.9292			0.833828			0.416914	+	0.908946i	$0.363112\pi$
$968$		0			0
$969$	−3.76242	+	6.51670i	−0.120866	+	0.209347i
$970$		0			0
$971$	−28.2767	−	48.9767i	−0.907443	−	1.57174i	−0.817603	−	0.575782i	$-0.804698\pi$
$971$	−28.2767	−	48.9767i	−0.907443	−	1.57174i	−0.0898399	−	0.995956i	$-0.528636\pi$
$972$		0			0
$973$	−18.4674	+	4.81342i	−0.592038	+	0.154311i
$974$		0			0
$975$	−2.85801	−	4.95022i	−0.0915296	−	0.158534i
$976$		0			0
$977$	−12.1945	+	21.1214i	−0.390135	+	0.675734i	−0.992467	−	0.122512i	$-0.960905\pi$
$977$	−12.1945	+	21.1214i	−0.390135	+	0.675734i	0.602332	+	0.798246i	$0.294238\pi$
$978$		0			0
$979$	20.7535			0.663286
$980$		0			0
$981$	13.0276			0.415940
$982$		0			0
$983$	−6.06022	+	10.4966i	−0.193291	+	0.334790i	−0.946339	−	0.323176i	$-0.895249\pi$
$983$	−6.06022	+	10.4966i	−0.193291	+	0.334790i	0.753048	+	0.657966i	$0.228583\pi$
$984$		0			0
$985$	−9.37183	−	16.2325i	−0.298611	−	0.517210i
$986$		0			0
$987$	27.7437	−	7.23122i	0.883090	−	0.230172i
$988$		0			0
$989$	−8.88285	−	15.3856i	−0.282458	−	0.489232i
$990$		0			0
$991$	1.24532	−	2.15696i	0.0395589	−	0.0685180i	−0.845568	−	0.533868i	$-0.820738\pi$
$991$	1.24532	−	2.15696i	0.0395589	−	0.0685180i	0.885127	+	0.465350i	$0.154071\pi$
$992$		0			0
$993$	−22.1049			−0.701479
$994$		0			0
$995$	23.6729			0.750482
$996$		0			0
$997$	19.9646	−	34.5797i	0.632286	−	1.09515i	−0.354797	−	0.934943i	$-0.615450\pi$
$997$	19.9646	−	34.5797i	0.632286	−	1.09515i	0.987083	−	0.160208i	$-0.0512166\pi$
$998$		0			0
$999$	2.45360	+	4.24976i	0.0776285	+	0.134457i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.bg.v.1201.3		6
4.3	odd	2		840.2.bg.j.361.1	yes	6
7.2	even	3	inner	1680.2.bg.v.961.3		6
12.11	even	2		2520.2.bi.n.361.1		6
28.3	even	6		5880.2.a.bu.1.1		3
28.11	odd	6		5880.2.a.bv.1.1		3
28.23	odd	6		840.2.bg.j.121.1	✓	6
84.23	even	6		2520.2.bi.n.1801.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bg.j.121.1	✓	6	28.23	odd	6
840.2.bg.j.361.1	yes	6	4.3	odd	2
1680.2.bg.v.961.3		6	7.2	even	3	inner
1680.2.bg.v.1201.3		6	1.1	even	1	trivial
2520.2.bi.n.361.1		6	12.11	even	2
2520.2.bi.n.1801.1		6	84.23	even	6
5880.2.a.bu.1.1		3	28.3	even	6
5880.2.a.bv.1.1		3	28.11	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:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.bg (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.56022 - 0.667305i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.56022 - 0.667305i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-2.65581 + 4.59999i) q^{11} -5.71602 q^{13} +1.00000 q^{15} +(-3.76242 + 6.51670i) q^{17} +(0.500000 + 0.866025i) q^{19} +(0.702205 - 2.55086i) q^{21} +(2.06022 + 3.56840i) q^{23} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{27} -2.71602 q^{29} +(-2.91823 + 5.05452i) q^{31} +(2.65581 + 4.59999i) q^{33} +(1.85801 + 1.88356i) q^{35} +(-2.45360 - 4.24976i) q^{37} +(-2.85801 + 4.95022i) q^{39} -8.12043 q^{41} -4.31161 q^{43} +(0.500000 - 0.866025i) q^{45} +(5.41823 + 9.38464i) q^{47} +(6.10941 - 3.41689i) q^{49} +(3.76242 + 6.51670i) q^{51} +(2.29780 - 3.97990i) q^{53} -5.31161 q^{55} +1.00000 q^{57} +(7.35801 - 12.7444i) q^{59} +(-1.85801 - 1.88356i) q^{63} +(-2.85801 - 4.95022i) q^{65} +(2.15581 - 3.73397i) q^{67} +4.12043 q^{69} +10.3337 q^{71} +(-0.439784 + 0.761729i) q^{73} +(0.500000 + 0.866025i) q^{75} +(-3.72984 + 13.5492i) q^{77} +(-3.51382 - 6.08611i) q^{79} +(-0.500000 + 0.866025i) q^{81} +2.71602 q^{83} -7.52484 q^{85} +(-1.35801 + 2.35214i) q^{87} +(-1.95360 - 3.38374i) q^{89} +(-14.6342 + 3.81433i) q^{91} +(2.91823 + 5.05452i) q^{93} +(-0.500000 + 0.866025i) q^{95} +8.00000 q^{97} +5.31161 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} + 3 q^{5} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 + 3 * q^5 - 3 * q^9	\( 6 q + 3 q^{3} + 3 q^{5} - 3 q^{9} - 3 q^{11} - 6 q^{13} + 6 q^{15} - 6 q^{17} + 3 q^{19} + 3 q^{21} - 3 q^{23} - 3 q^{25} - 6 q^{27} + 12 q^{29} + 12 q^{31} + 3 q^{33} - 3 q^{35} - 3 q^{37} - 3 q^{39} - 18 q^{41} + 3 q^{45} + 3 q^{47} + 12 q^{49} + 6 q^{51} + 15 q^{53} - 6 q^{55} + 6 q^{57} + 30 q^{59} + 3 q^{63} - 3 q^{65} - 6 q^{69} + 24 q^{71} - 18 q^{73} + 3 q^{75} + 33 q^{77} + 6 q^{79} - 3 q^{81} - 12 q^{83} - 12 q^{85} + 6 q^{87} - 30 q^{91} - 12 q^{93} - 3 q^{95} + 48 q^{97} + 6 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 + 3 * q^5 - 3 * q^9 - 3 * q^11 - 6 * q^13 + 6 * q^15 - 6 * q^17 + 3 * q^19 + 3 * q^21 - 3 * q^23 - 3 * q^25 - 6 * q^27 + 12 * q^29 + 12 * q^31 + 3 * q^33 - 3 * q^35 - 3 * q^37 - 3 * q^39 - 18 * q^41 + 3 * q^45 + 3 * q^47 + 12 * q^49 + 6 * q^51 + 15 * q^53 - 6 * q^55 + 6 * q^57 + 30 * q^59 + 3 * q^63 - 3 * q^65 - 6 * q^69 + 24 * q^71 - 18 * q^73 + 3 * q^75 + 33 * q^77 + 6 * q^79 - 3 * q^81 - 12 * q^83 - 12 * q^85 + 6 * q^87 - 30 * q^91 - 12 * q^93 - 3 * q^95 + 48 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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