LMFDB - Embedded newform 2184.2.bj.k.1849.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2184,2,Mod(841,2184)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2184, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("2184.841");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2184 = 2^{3} \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2184.bj (of order $3$, degree $2$, 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:	$17.4393278014$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.8248090761.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 7x^{6} - 2x^{5} + 41x^{4} - 7x^{3} + 57x^{2} + 8x + 64 $ x^8 + 7x^6 - 2x^5 + 41x^4 - 7x^3 + 57x^2 + 8x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1849.1
Root			$-1.23409 - 2.13751i$ of defining polynomial
Character	$\chi$	$=$	2184.1849
Dual form			2184.2.bj.k.841.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} -2.46819 q^{5} +(-0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{3} -2.46819 q^{5} +(-0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(0.0102890 + 0.0178211i) q^{11} +(-0.0102890 - 3.60554i) q^{13} +(-1.23409 - 2.13751i) q^{15} +(-0.198409 + 0.343655i) q^{17} +(2.96819 - 5.14105i) q^{19} -1.00000 q^{21} +(1.93250 + 3.34719i) q^{23} +1.09195 q^{25} -1.00000 q^{27} +(3.01416 + 5.22068i) q^{29} -4.22694 q^{31} +(-0.0102890 + 0.0178211i) q^{33} +(1.23409 - 2.13751i) q^{35} +(-5.32604 - 9.22497i) q^{37} +(3.11734 - 1.81168i) q^{39} +(-2.62062 - 4.53905i) q^{41} +(1.15944 - 2.00822i) q^{43} +(1.23409 - 2.13751i) q^{45} +10.1060 q^{47} +(-0.500000 - 0.866025i) q^{49} -0.396818 q^{51} +13.0566 q^{53} +(-0.0253952 - 0.0439858i) q^{55} +5.93637 q^{57} +(6.71958 - 11.6386i) q^{59} +(-6.06013 + 10.4965i) q^{61} +(-0.500000 - 0.866025i) q^{63} +(0.0253952 + 8.89914i) q^{65} +(4.79036 + 8.29714i) q^{67} +(-1.93250 + 3.34719i) q^{69} +(1.79130 - 3.10263i) q^{71} +14.7029 q^{73} +(0.545973 + 0.945653i) q^{75} -0.0205780 q^{77} +3.50934 q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0835 q^{83} +(0.489711 - 0.848204i) q^{85} +(-3.01416 + 5.22068i) q^{87} +(5.81889 + 10.0786i) q^{89} +(3.12763 + 1.79386i) q^{91} +(-2.11347 - 3.66064i) q^{93} +(-7.32604 + 12.6891i) q^{95} +(5.27679 - 9.13966i) q^{97} -0.0205780 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 - 4 * q^7 - 4 * q^9	$ 8 q + 4 q^{3} - 4 q^{7} - 4 q^{9} - 3 q^{11} + 3 q^{13} + q^{17} + 4 q^{19} - 8 q^{21} + 3 q^{23} - 12 q^{25} - 8 q^{27} - 6 q^{29} - 38 q^{31} + 3 q^{33} - 12 q^{37} - 9 q^{41} + q^{43} + 28 q^{47} - 4 q^{49} + 2 q^{51} - 16 q^{53} + 4 q^{55} + 8 q^{57} + 5 q^{59} - 8 q^{61} - 4 q^{63} - 4 q^{65} + 15 q^{67} - 3 q^{69} + 20 q^{71} + 48 q^{73} - 6 q^{75} + 6 q^{77} - 4 q^{79} - 4 q^{81} - 8 q^{83} + 7 q^{85} + 6 q^{87} + 30 q^{89} - 3 q^{91} - 19 q^{93} - 28 q^{95} + 9 q^{97} + 6 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 - 4 * q^7 - 4 * q^9 - 3 * q^11 + 3 * q^13 + q^17 + 4 * q^19 - 8 * q^21 + 3 * q^23 - 12 * q^25 - 8 * q^27 - 6 * q^29 - 38 * q^31 + 3 * q^33 - 12 * q^37 - 9 * q^41 + q^43 + 28 * q^47 - 4 * q^49 + 2 * q^51 - 16 * q^53 + 4 * q^55 + 8 * q^57 + 5 * q^59 - 8 * q^61 - 4 * q^63 - 4 * q^65 + 15 * q^67 - 3 * q^69 + 20 * q^71 + 48 * q^73 - 6 * q^75 + 6 * q^77 - 4 * q^79 - 4 * q^81 - 8 * q^83 + 7 * q^85 + 6 * q^87 + 30 * q^89 - 3 * q^91 - 19 * q^93 - 28 * q^95 + 9 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2184\mathbb{Z}\right)^\times$.

$n$	$1093$	$1249$	$1457$	$1639$	$2017$
$\chi(n)$	$1$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	−2.46819			−1.10381			−0.551903	−	0.833908i	$-0.686098\pi$
$5$	−2.46819			−1.10381			−0.551903	+	0.833908i	$0.686098\pi$
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	0.0102890	+	0.0178211i	0.00310226	+	0.00537327i	0.867572	−	0.497311i	$-0.165679\pi$
$11$	0.0102890	+	0.0178211i	0.00310226	+	0.00537327i	−0.864470	+	0.502684i	$0.832346\pi$
$12$		0			0
$13$	−0.0102890	−	3.60554i	−0.00285366	−	0.999996i
$13$	−0.0102890	−	3.60554i	−0.00285366	−	0.999996i
$14$		0			0
$15$	−1.23409	−	2.13751i	−0.318642	−	0.551903i
$16$		0			0
$17$	−0.198409	+	0.343655i	−0.0481213	+	0.0833485i	−0.889083	−	0.457746i	$-0.848657\pi$
$17$	−0.198409	+	0.343655i	−0.0481213	+	0.0833485i	0.840961	+	0.541095i	$0.181990\pi$
$18$		0			0
$19$	2.96819	−	5.14105i	0.680949	−	1.17944i	−0.293743	−	0.955884i	$-0.594901\pi$
$19$	2.96819	−	5.14105i	0.680949	−	1.17944i	0.974692	−	0.223553i	$-0.0717657\pi$
$20$		0			0
$21$	−1.00000			−0.218218
$22$		0			0
$23$	1.93250	+	3.34719i	0.402955	+	0.697938i	0.994081	−	0.108641i	$-0.0346499\pi$
$23$	1.93250	+	3.34719i	0.402955	+	0.697938i	−0.591126	+	0.806579i	$0.701317\pi$
$24$		0			0
$25$	1.09195			0.218389
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	3.01416	+	5.22068i	0.559715	+	0.969456i	0.997520	+	0.0703854i	$0.0224229\pi$
$29$	3.01416	+	5.22068i	0.559715	+	0.969456i	−0.437804	+	0.899070i	$0.644244\pi$
$30$		0			0
$31$	−4.22694			−0.759181			−0.379591	−	0.925155i	$-0.623935\pi$
$31$	−4.22694			−0.759181			−0.379591	+	0.925155i	$0.623935\pi$
$32$		0			0
$33$	−0.0102890	+	0.0178211i	−0.00179109	+	0.00310226i
$34$		0			0
$35$	1.23409	−	2.13751i	0.208600	−	0.361306i
$36$		0			0
$37$	−5.32604	−	9.22497i	−0.875596	−	1.51658i	−0.856127	−	0.516766i	$-0.827136\pi$
$37$	−5.32604	−	9.22497i	−0.875596	−	1.51658i	−0.0194686	−	0.999810i	$-0.506197\pi$
$38$		0			0
$39$	3.11734	−	1.81168i	0.499174	−	0.290101i
$40$		0			0
$41$	−2.62062	−	4.53905i	−0.409273	−	0.708881i	0.585536	−	0.810646i	$-0.300884\pi$
$41$	−2.62062	−	4.53905i	−0.409273	−	0.708881i	−0.994808	+	0.101766i	$0.967551\pi$
$42$		0			0
$43$	1.15944	−	2.00822i	0.176814	−	0.306250i	−0.763974	−	0.645247i	$-0.776754\pi$
$43$	1.15944	−	2.00822i	0.176814	−	0.306250i	0.940787	+	0.338997i	$0.110088\pi$
$44$		0			0
$45$	1.23409	−	2.13751i	0.183968	−	0.318642i
$46$		0			0
$47$	10.1060			1.47411			0.737053	−	0.675835i	$-0.236217\pi$
$47$	10.1060			1.47411			0.737053	+	0.675835i	$0.236217\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$	−0.396818			−0.0555657
$52$		0			0
$53$	13.0566			1.79347			0.896734	−	0.442570i	$-0.145933\pi$
$53$	13.0566			1.79347			0.896734	+	0.442570i	$0.145933\pi$
$54$		0			0
$55$	−0.0253952	−	0.0439858i	−0.00342429	−	0.00593105i
$56$		0			0
$57$	5.93637			0.786292
$58$		0			0
$59$	6.71958	−	11.6386i	0.874814	−	1.51522i	0.0178542	−	0.999841i	$-0.494317\pi$
$59$	6.71958	−	11.6386i	0.874814	−	1.51522i	0.856960	−	0.515382i	$-0.172350\pi$
$60$		0			0
$61$	−6.06013	+	10.4965i	−0.775921	+	1.34393i	0.158355	+	0.987382i	$0.449381\pi$
$61$	−6.06013	+	10.4965i	−0.775921	+	1.34393i	−0.934276	+	0.356552i	$0.883952\pi$
$62$		0			0
$63$	−0.500000	−	0.866025i	−0.0629941	−	0.109109i
$64$		0			0
$65$	0.0253952	+	8.89914i	0.00314989	+	1.10380i
$66$		0			0
$67$	4.79036	+	8.29714i	0.585235	+	1.01366i	0.994846	+	0.101397i	$0.0323311\pi$
$67$	4.79036	+	8.29714i	0.585235	+	1.01366i	−0.409611	+	0.912260i	$0.634336\pi$
$68$		0			0
$69$	−1.93250	+	3.34719i	−0.232646	+	0.402955i
$70$		0			0
$71$	1.79130	−	3.10263i	0.212588	−	0.368214i	−0.739935	−	0.672678i	$-0.765144\pi$
$71$	1.79130	−	3.10263i	0.212588	−	0.368214i	0.952524	+	0.304464i	$0.0984773\pi$
$72$		0			0
$73$	14.7029			1.72084			0.860420	−	0.509585i	$-0.170201\pi$
$73$	14.7029			1.72084			0.860420	+	0.509585i	$0.170201\pi$
$74$		0			0
$75$	0.545973	+	0.945653i	0.0630436	+	0.109195i
$76$		0			0
$77$	−0.0205780			−0.00234509
$78$		0			0
$79$	3.50934			0.394832			0.197416	−	0.980320i	$-0.436745\pi$
$79$	3.50934			0.394832			0.197416	+	0.980320i	$0.436745\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	12.0835			1.32634			0.663168	−	0.748471i	$-0.269212\pi$
$83$	12.0835			1.32634			0.663168	+	0.748471i	$0.269212\pi$
$84$		0			0
$85$	0.489711	−	0.848204i	0.0531166	−	0.0920007i
$86$		0			0
$87$	−3.01416	+	5.22068i	−0.323152	+	0.559715i
$88$		0			0
$89$	5.81889	+	10.0786i	0.616801	+	1.06833i	0.990066	+	0.140606i	$0.0449050\pi$
$89$	5.81889	+	10.0786i	0.616801	+	1.06833i	−0.373265	+	0.927725i	$0.621762\pi$
$90$		0			0
$91$	3.12763	+	1.79386i	0.327865	+	0.188047i
$92$		0			0
$93$	−2.11347	−	3.66064i	−0.219157	−	0.379591i
$94$		0			0
$95$	−7.32604	+	12.6891i	−0.751636	+	1.30187i
$96$		0			0
$97$	5.27679	−	9.13966i	0.535776	−	0.927992i	−0.463349	−	0.886176i	$-0.653352\pi$
$97$	5.27679	−	9.13966i	0.535776	−	0.927992i	0.999125	−	0.0418160i	$-0.0133143\pi$
$98$		0			0
$99$	−0.0205780			−0.00206817
$100$		0			0
$101$	1.13887	+	1.97257i	0.113321	+	0.196278i	0.917107	−	0.398640i	$-0.130518\pi$
$101$	1.13887	+	1.97257i	0.113321	+	0.196278i	−0.803786	+	0.594918i	$0.797184\pi$
$102$		0			0
$103$	−19.5454			−1.92587			−0.962933	−	0.269741i	$-0.913062\pi$
$103$	−19.5454			−1.92587			−0.962933	+	0.269741i	$0.913062\pi$
$104$		0			0
$105$	2.46819			0.240870
$106$		0			0
$107$	−5.59582	−	9.69224i	−0.540968	−	0.936984i	−0.998849	−	0.0479706i	$-0.984725\pi$
$107$	−5.59582	−	9.69224i	−0.540968	−	0.936984i	0.457881	−	0.889014i	$-0.348609\pi$
$108$		0			0
$109$	6.03459			0.578009			0.289005	−	0.957328i	$-0.406676\pi$
$109$	6.03459			0.578009			0.289005	+	0.957328i	$0.406676\pi$
$110$		0			0
$111$	5.32604	−	9.22497i	0.505525	−	0.875596i
$112$		0			0
$113$	5.22600	−	9.05169i	0.491620	−	0.851511i	−0.508333	−	0.861160i	$-0.669738\pi$
$113$	5.22600	−	9.05169i	0.491620	−	0.851511i	0.999953	+	0.00964919i	$0.00307148\pi$
$114$		0			0
$115$	−4.76978	−	8.26150i	−0.444784	−	0.770389i
$116$		0			0
$117$	3.12763	+	1.79386i	0.289150	+	0.165842i
$118$		0			0
$119$	−0.198409	−	0.343655i	−0.0181881	−	0.0315028i
$120$		0			0
$121$	5.49979	−	9.52591i	0.499981	−	0.865992i
$122$		0			0
$123$	2.62062	−	4.53905i	0.236294	−	0.409273i
$124$		0			0
$125$	9.64581			0.862747
$126$		0			0
$127$	−1.79423	−	3.10769i	−0.159212	−	0.275763i	0.775373	−	0.631504i	$-0.217562\pi$
$127$	−1.79423	−	3.10769i	−0.159212	−	0.275763i	−0.934585	+	0.355741i	$0.884229\pi$
$128$		0			0
$129$	2.31889			0.204167
$130$		0			0
$131$	13.5473			1.18363			0.591816	−	0.806073i	$-0.298411\pi$
$131$	13.5473			1.18363			0.591816	+	0.806073i	$0.298411\pi$
$132$		0			0
$133$	2.96819	+	5.14105i	0.257374	+	0.445786i
$134$		0			0
$135$	2.46819			0.212428
$136$		0			0
$137$	−6.85691	+	11.8765i	−0.585825	+	1.01468i	0.408947	+	0.912558i	$0.365896\pi$
$137$	−6.85691	+	11.8765i	−0.585825	+	1.01468i	−0.994772	+	0.102121i	$0.967437\pi$
$138$		0			0
$139$	9.42499	−	16.3246i	0.799418	−	1.38463i	−0.120578	−	0.992704i	$-0.538475\pi$
$139$	9.42499	−	16.3246i	0.799418	−	1.38463i	0.919996	−	0.391928i	$-0.128192\pi$
$140$		0			0
$141$	5.05298	+	8.75202i	0.425538	+	0.737053i
$142$		0			0
$143$	0.0641488	−	0.0372808i	0.00536439	−	0.00311758i
$144$		0			0
$145$	−7.43951	−	12.8856i	−0.617818	−	1.07009i
$146$		0			0
$147$	0.500000	−	0.866025i	0.0412393	−	0.0714286i
$148$		0			0
$149$	−4.04175	+	7.00051i	−0.331113	+	0.573504i	−0.982730	−	0.185044i	$-0.940757\pi$
$149$	−4.04175	+	7.00051i	−0.331113	+	0.573504i	0.651618	+	0.758548i	$0.274091\pi$
$150$		0			0
$151$	−7.26928			−0.591565			−0.295783	−	0.955255i	$-0.595580\pi$
$151$	−7.26928			−0.591565			−0.295783	+	0.955255i	$0.595580\pi$
$152$		0			0
$153$	−0.198409	−	0.343655i	−0.0160404	−	0.0277828i
$154$		0			0
$155$	10.4329			0.837989
$156$		0			0
$157$	−3.27802			−0.261614			−0.130807	−	0.991408i	$-0.541757\pi$
$157$	−3.27802			−0.261614			−0.130807	+	0.991408i	$0.541757\pi$
$158$		0			0
$159$	6.52832	+	11.3074i	0.517729	+	0.896734i
$160$		0			0
$161$	−3.86501			−0.304605
$162$		0			0
$163$	−11.2203	+	19.4341i	−0.878843	+	1.52220i	−0.0262304	+	0.999656i	$0.508350\pi$
$163$	−11.2203	+	19.4341i	−0.878843	+	1.52220i	−0.852612	+	0.522544i	$0.824983\pi$
$164$		0			0
$165$	0.0253952	−	0.0439858i	0.00197702	−	0.00342429i
$166$		0			0
$167$	−9.53920	−	16.5224i	−0.738165	−	1.27854i	−0.953321	−	0.301960i	$-0.902359\pi$
$167$	−9.53920	−	16.5224i	−0.738165	−	1.27854i	0.215155	−	0.976580i	$-0.430974\pi$
$168$		0			0
$169$	−12.9998	+	0.0741949i	−0.999984	+	0.00570730i
$170$		0			0
$171$	2.96819	+	5.14105i	0.226983	+	0.393146i
$172$		0			0
$173$	−1.64821	+	2.85478i	−0.125311	+	0.217045i	−0.921854	−	0.387536i	$-0.873326\pi$
$173$	−1.64821	+	2.85478i	−0.125311	+	0.217045i	0.796543	+	0.604581i	$0.206660\pi$
$174$		0			0
$175$	−0.545973	+	0.945653i	−0.0412717	+	0.0714847i
$176$		0			0
$177$	13.4392			1.01015
$178$		0			0
$179$	−9.70615	−	16.8115i	−0.725472	−	1.25655i	−0.958780	−	0.284151i	$-0.908288\pi$
$179$	−9.70615	−	16.8115i	−0.725472	−	1.25655i	0.233308	−	0.972403i	$-0.425045\pi$
$180$		0			0
$181$	5.60129			0.416341			0.208170	−	0.978093i	$-0.433249\pi$
$181$	5.60129			0.416341			0.208170	+	0.978093i	$0.433249\pi$
$182$		0			0
$183$	−12.1203			−0.895956
$184$		0			0
$185$	13.1457	+	22.7690i	0.966488	+	1.67401i
$186$		0			0
$187$	−0.00816575			−0.000597139
$188$		0			0
$189$	0.500000	−	0.866025i	0.0363696	−	0.0629941i
$190$		0			0
$191$	−3.60705	+	6.24760i	−0.260997	+	0.452060i	−0.966507	−	0.256640i	$-0.917385\pi$
$191$	−3.60705	+	6.24760i	−0.260997	+	0.452060i	0.705510	+	0.708700i	$0.250718\pi$
$192$		0			0
$193$	2.10552	+	3.64686i	0.151558	+	0.262507i	0.931801	−	0.362971i	$-0.118238\pi$
$193$	2.10552	+	3.64686i	0.151558	+	0.262507i	−0.780242	+	0.625478i	$0.784904\pi$
$194$		0			0
$195$	−7.69418	+	4.47156i	−0.550992	+	0.320215i
$196$		0			0
$197$	4.87355	+	8.44124i	0.347226	+	0.601413i	0.985756	−	0.168184i	$-0.0537903\pi$
$197$	4.87355	+	8.44124i	0.347226	+	0.601413i	−0.638530	+	0.769597i	$0.720457\pi$
$198$		0			0
$199$	6.61326	−	11.4545i	0.468801	−	0.811988i	−0.530563	−	0.847646i	$-0.678019\pi$
$199$	6.61326	−	11.4545i	0.468801	−	0.811988i	0.999364	+	0.0356578i	$0.0113526\pi$
$200$		0			0
$201$	−4.79036	+	8.29714i	−0.337886	+	0.585235i
$202$		0			0
$203$	−6.02832			−0.423105
$204$		0			0
$205$	6.46819	+	11.2032i	0.451758	+	0.782467i
$206$		0			0
$207$	−3.86501			−0.268636
$208$		0			0
$209$	0.122159			0.00844991
$210$		0			0
$211$	−3.38011	−	5.85452i	−0.232696	−	0.403042i	0.725904	−	0.687796i	$-0.241422\pi$
$211$	−3.38011	−	5.85452i	−0.232696	−	0.403042i	−0.958601	+	0.284754i	$0.908088\pi$
$212$		0			0
$213$	3.58260			0.245476
$214$		0			0
$215$	−2.86172	+	4.95665i	−0.195168	+	0.338041i
$216$		0			0
$217$	2.11347	−	3.66064i	0.143472	−	0.248500i
$218$		0			0
$219$	7.35144	+	12.7331i	0.496764	+	0.860420i
$220$		0			0
$221$	1.24110	+	0.711836i	0.0834855	+	0.0478833i
$222$		0			0
$223$	−11.2980	−	19.5686i	−0.756567	−	1.31041i	−0.944592	−	0.328248i	$-0.893542\pi$
$223$	−11.2980	−	19.5686i	−0.756567	−	1.31041i	0.188025	−	0.982164i	$-0.439792\pi$
$224$		0			0
$225$	−0.545973	+	0.945653i	−0.0363982	+	0.0630436i
$226$		0			0
$227$	0.319834	−	0.553968i	0.0212281	−	0.0367682i	−0.855216	−	0.518271i	$-0.826576\pi$
$227$	0.319834	−	0.553968i	0.0212281	−	0.0367682i	0.876444	+	0.481503i	$0.159909\pi$
$228$		0			0
$229$	15.8587			1.04797			0.523987	−	0.851726i	$-0.324444\pi$
$229$	15.8587			1.04797			0.523987	+	0.851726i	$0.324444\pi$
$230$		0			0
$231$	−0.0102890	−	0.0178211i	−0.000676968	−	0.00117254i
$232$		0			0
$233$	−21.0504			−1.37906			−0.689528	−	0.724259i	$-0.742182\pi$
$233$	−21.0504			−1.37906			−0.689528	+	0.724259i	$0.742182\pi$
$234$		0			0
$235$	−24.9434			−1.62713
$236$		0			0
$237$	1.75467	+	3.03918i	0.113978	+	0.197416i
$238$		0			0
$239$	−19.5741			−1.26615			−0.633073	−	0.774092i	$-0.718207\pi$
$239$	−19.5741			−1.26615			−0.633073	+	0.774092i	$0.718207\pi$
$240$		0			0
$241$	15.0576	−	26.0805i	0.969944	−	1.67999i	0.274245	−	0.961660i	$-0.411572\pi$
$241$	15.0576	−	26.0805i	0.969944	−	1.67999i	0.695699	−	0.718333i	$-0.255095\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	1.23409	+	2.13751i	0.0788433	+	0.136561i
$246$		0			0
$247$	−18.5668	−	10.6490i	−1.18138	−	0.677580i
$248$		0			0
$249$	6.04175	+	10.4646i	0.382880	+	0.663168i
$250$		0			0
$251$	9.30511	−	16.1169i	0.587333	−	1.01729i	−0.407247	−	0.913318i	$-0.633511\pi$
$251$	9.30511	−	16.1169i	0.587333	−	1.01729i	0.994580	−	0.103973i	$-0.0331555\pi$
$252$		0			0
$253$	−0.0397671	+	0.0688787i	−0.00250014	+	0.00433037i
$254$		0			0
$255$	0.979422			0.0613338
$256$		0			0
$257$	12.5322	+	21.7064i	0.781737	+	1.35401i	0.930929	+	0.365199i	$0.118999\pi$
$257$	12.5322	+	21.7064i	0.781737	+	1.35401i	−0.149193	+	0.988808i	$0.547667\pi$
$258$		0			0
$259$	10.6521			0.661888
$260$		0			0
$261$	−6.02832			−0.373144
$262$		0			0
$263$	−2.67689	−	4.63650i	−0.165064	−	0.285899i	0.771614	−	0.636091i	$-0.219450\pi$
$263$	−2.67689	−	4.63650i	−0.165064	−	0.285899i	−0.936678	+	0.350192i	$0.886116\pi$
$264$		0			0
$265$	−32.2262			−1.97964
$266$		0			0
$267$	−5.81889	+	10.0786i	−0.356110	+	0.616801i
$268$		0			0
$269$	−7.31794	+	12.6750i	−0.446183	+	0.772811i	−0.998134	−	0.0610653i	$-0.980550\pi$
$269$	−7.31794	+	12.6750i	−0.446183	+	0.772811i	0.551951	+	0.833877i	$0.313884\pi$
$270$		0			0
$271$	10.1173	+	17.5237i	0.614585	+	1.06449i	0.990457	+	0.137821i	$0.0440097\pi$
$271$	10.1173	+	17.5237i	0.614585	+	1.06449i	−0.375872	+	0.926671i	$0.622657\pi$
$272$		0			0
$273$	0.0102890	+	3.60554i	0.000622720	+	0.218217i
$274$		0			0
$275$	0.0112351	+	0.0194597i	0.000677500	+	0.00117346i
$276$		0			0
$277$	1.31889	−	2.28438i	0.0792443	−	0.137255i	−0.823680	−	0.567055i	$-0.808083\pi$
$277$	1.31889	−	2.28438i	0.0792443	−	0.137255i	0.902924	+	0.429800i	$0.141416\pi$
$278$		0			0
$279$	2.11347	−	3.66064i	0.126530	−	0.219157i
$280$		0			0
$281$	18.8933			1.12708			0.563541	−	0.826088i	$-0.309439\pi$
$281$	18.8933			1.12708			0.563541	+	0.826088i	$0.309439\pi$
$282$		0			0
$283$	−3.32991	−	5.76758i	−0.197943	−	0.342847i	0.749919	−	0.661530i	$-0.230093\pi$
$283$	−3.32991	−	5.76758i	−0.197943	−	0.342847i	−0.947861	+	0.318683i	$0.896759\pi$
$284$		0			0
$285$	−14.6521			−0.867914
$286$		0			0
$287$	5.24125			0.309381
$288$		0			0
$289$	8.42127	+	14.5861i	0.495369	+	0.858004i
$290$		0			0
$291$	10.5536			0.618661
$292$		0			0
$293$	−2.54671	+	4.41103i	−0.148780	+	0.257695i	−0.930777	−	0.365588i	$-0.880868\pi$
$293$	−2.54671	+	4.41103i	−0.148780	+	0.257695i	0.781997	+	0.623283i	$0.214201\pi$
$294$		0			0
$295$	−16.5852	+	28.7264i	−0.965626	+	1.67251i
$296$		0			0
$297$	−0.0102890	−	0.0178211i	−0.000597030	−	0.00103409i
$298$		0			0
$299$	12.0485	−	7.00215i	0.696785	−	0.404945i
$300$		0			0
$301$	1.15944	+	2.00822i	0.0668292	+	0.115752i
$302$		0			0
$303$	−1.13887	+	1.97257i	−0.0654261	+	0.113321i
$304$		0			0
$305$	14.9575	−	25.9072i	0.856466	−	1.48344i
$306$		0			0
$307$	20.7484			1.18417			0.592087	−	0.805874i	$-0.298304\pi$
$307$	20.7484			1.18417			0.592087	+	0.805874i	$0.298304\pi$
$308$		0			0
$309$	−9.77270	−	16.9268i	−0.555950	−	0.962933i
$310$		0			0
$311$	−30.0151			−1.70200			−0.850999	−	0.525167i	$-0.824003\pi$
$311$	−30.0151			−1.70200			−0.850999	+	0.525167i	$0.824003\pi$
$312$		0			0
$313$	−28.9376			−1.63565			−0.817824	−	0.575469i	$-0.804820\pi$
$313$	−28.9376			−1.63565			−0.817824	+	0.575469i	$0.804820\pi$
$314$		0			0
$315$	1.23409	+	2.13751i	0.0695333	+	0.120435i
$316$		0			0
$317$	9.39989			0.527950			0.263975	−	0.964529i	$-0.414966\pi$
$317$	9.39989			0.527950			0.263975	+	0.964529i	$0.414966\pi$
$318$		0			0
$319$	−0.0620255	+	0.107431i	−0.00347276	+	0.00601500i
$320$		0			0
$321$	5.59582	−	9.69224i	0.312328	−	0.540968i
$322$		0			0
$323$	1.17783	+	2.04006i	0.0655363	+	0.113512i
$324$		0			0
$325$	−0.0112351	−	3.93705i	−0.000623209	−	0.218388i
$326$		0			0
$327$	3.01730	+	5.22611i	0.166857	+	0.289005i
$328$		0			0
$329$	−5.05298	+	8.75202i	−0.278580	+	0.482514i
$330$		0			0
$331$	10.2302	−	17.7193i	0.562304	−	0.973939i	−0.434991	−	0.900435i	$-0.643248\pi$
$331$	10.2302	−	17.7193i	0.562304	−	0.973939i	0.997295	−	0.0735041i	$-0.0234182\pi$
$332$		0			0
$333$	10.6521			0.583730
$334$		0			0
$335$	−11.8235	−	20.4789i	−0.645986	−	1.11888i
$336$		0			0
$337$	14.7032			0.800932			0.400466	−	0.916312i	$-0.368848\pi$
$337$	14.7032			0.800932			0.400466	+	0.916312i	$0.368848\pi$
$338$		0			0
$339$	10.4520			0.567674
$340$		0			0
$341$	−0.0434911	−	0.0753288i	−0.00235517	−	0.00407928i
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	4.76978	−	8.26150i	0.256796	−	0.444784i
$346$		0			0
$347$	−11.5029	+	19.9237i	−0.617509	+	1.06956i	0.372429	+	0.928061i	$0.378525\pi$
$347$	−11.5029	+	19.9237i	−0.617509	+	1.06956i	−0.989939	+	0.141497i	$0.954808\pi$
$348$		0			0
$349$	−3.77752	−	6.54286i	−0.202206	−	0.350231i	0.747033	−	0.664787i	$-0.231478\pi$
$349$	−3.77752	−	6.54286i	−0.202206	−	0.350231i	−0.949239	+	0.314556i	$0.898144\pi$
$350$		0			0
$351$	0.0102890	+	3.60554i	0.000549187	+	0.192449i
$352$		0			0
$353$	−16.7450	−	29.0031i	−0.891245	−	1.54368i	−0.838384	−	0.545080i	$-0.816499\pi$
$353$	−16.7450	−	29.0031i	−0.891245	−	1.54368i	−0.0528607	−	0.998602i	$-0.516834\pi$
$354$		0			0
$355$	−4.42127	+	7.65786i	−0.234657	+	0.406437i
$356$		0			0
$357$	0.198409	−	0.343655i	0.0105009	−	0.0181881i
$358$		0			0
$359$	−12.1708			−0.642349			−0.321174	−	0.947020i	$-0.604078\pi$
$359$	−12.1708			−0.642349			−0.321174	+	0.947020i	$0.604078\pi$
$360$		0			0
$361$	−8.12027	−	14.0647i	−0.427382	−	0.740248i
$362$		0			0
$363$	10.9996			0.577328
$364$		0			0
$365$	−36.2894			−1.89948
$366$		0			0
$367$	−10.5272	−	18.2337i	−0.549517	−	0.951791i	−0.998308	−	0.0581543i	$-0.981478\pi$
$367$	−10.5272	−	18.2337i	−0.549517	−	0.951791i	0.448791	−	0.893637i	$-0.351855\pi$
$368$		0			0
$369$	5.24125			0.272848
$370$		0			0
$371$	−6.52832	+	11.3074i	−0.338934	+	0.587050i
$372$		0			0
$373$	−4.96272	+	8.59567i	−0.256960	+	0.445067i	−0.965426	−	0.260677i	$-0.916054\pi$
$373$	−4.96272	+	8.59567i	−0.256960	+	0.445067i	0.708466	+	0.705745i	$0.249387\pi$
$374$		0			0
$375$	4.82290	+	8.35351i	0.249054	+	0.431374i
$376$		0			0
$377$	18.7923	−	10.9214i	0.967854	−	0.562480i
$378$		0			0
$379$	1.09195	+	1.89131i	0.0560895	+	0.0971499i	0.892707	−	0.450638i	$-0.148803\pi$
$379$	1.09195	+	1.89131i	0.0560895	+	0.0971499i	−0.836617	+	0.547788i	$0.815470\pi$
$380$		0			0
$381$	1.79423	−	3.10769i	0.0919210	−	0.159212i
$382$		0			0
$383$	14.5982	−	25.2847i	0.745931	−	1.29199i	−0.203828	−	0.979007i	$-0.565338\pi$
$383$	14.5982	−	25.2847i	0.745931	−	1.29199i	0.949759	−	0.312983i	$-0.101328\pi$
$384$		0			0
$385$	0.0507905			0.00258852
$386$		0			0
$387$	1.15944	+	2.00822i	0.0589378	+	0.102083i
$388$		0			0
$389$	10.4694			0.530818			0.265409	−	0.964136i	$-0.414493\pi$
$389$	10.4694			0.530818			0.265409	+	0.964136i	$0.414493\pi$
$390$		0			0
$391$	−1.53371			−0.0775628
$392$		0			0
$393$	6.77365	+	11.7323i	0.341685	+	0.591816i
$394$		0			0
$395$	−8.66171			−0.435818
$396$		0			0
$397$	6.87529	−	11.9084i	0.345061	−	0.597663i	−0.640304	−	0.768122i	$-0.721192\pi$
$397$	6.87529	−	11.9084i	0.345061	−	0.597663i	0.985365	+	0.170458i	$0.0545248\pi$
$398$		0			0
$399$	−2.96819	+	5.14105i	−0.148595	+	0.257374i
$400$		0			0
$401$	4.14602	+	7.18111i	0.207042	+	0.358608i	0.950781	−	0.309862i	$-0.100283\pi$
$401$	4.14602	+	7.18111i	0.207042	+	0.358608i	−0.743739	+	0.668470i	$0.766950\pi$
$402$		0			0
$403$	0.0434911	+	15.2404i	0.00216645	+	0.759178i
$404$		0			0
$405$	1.23409	+	2.13751i	0.0613226	+	0.106214i
$406$		0			0
$407$	0.109599	−	0.189832i	0.00543264	−	0.00940962i
$408$		0			0
$409$	−13.4156	+	23.2365i	−0.663358	+	1.14897i	0.316370	+	0.948636i	$0.397536\pi$
$409$	−13.4156	+	23.2365i	−0.663358	+	1.14897i	−0.979728	+	0.200334i	$0.935797\pi$
$410$		0			0
$411$	−13.7138			−0.676453
$412$		0			0
$413$	6.71958	+	11.6386i	0.330649	+	0.572700i
$414$		0			0
$415$	−29.8243			−1.46402
$416$		0			0
$417$	18.8500			0.923088
$418$		0			0
$419$	−0.603772	−	1.04576i	−0.0294962	−	0.0510889i	0.850901	−	0.525327i	$-0.176057\pi$
$419$	−0.603772	−	1.04576i	−0.0294962	−	0.0510889i	−0.880397	+	0.474238i	$0.842724\pi$
$420$		0			0
$421$	−1.20447			−0.0587023			−0.0293512	−	0.999569i	$-0.509344\pi$
$421$	−1.20447			−0.0587023			−0.0293512	+	0.999569i	$0.509344\pi$
$422$		0			0
$423$	−5.05298	+	8.75202i	−0.245684	+	0.425538i
$424$		0			0
$425$	−0.216652	+	0.375253i	−0.0105092	+	0.0182024i
$426$		0			0
$427$	−6.06013	−	10.4965i	−0.293270	−	0.507959i
$428$		0			0
$429$	0.0643605	+	0.0369141i	0.00310736	+	0.00178223i
$430$		0			0
$431$	−8.50373	−	14.7289i	−0.409610	−	0.709466i	0.585236	−	0.810863i	$-0.301002\pi$
$431$	−8.50373	−	14.7289i	−0.409610	−	0.709466i	−0.994846	+	0.101398i	$0.967669\pi$
$432$		0			0
$433$	3.92828	−	6.80397i	0.188781	−	0.326978i	−0.756063	−	0.654499i	$-0.772880\pi$
$433$	3.92828	−	6.80397i	0.188781	−	0.326978i	0.944844	+	0.327521i	$0.106213\pi$
$434$		0			0
$435$	7.43951	−	12.8856i	0.356697	−	0.617818i
$436$		0			0
$437$	22.9441			1.09757
$438$		0			0
$439$	−0.627041	−	1.08607i	−0.0299270	−	0.0518351i	0.850674	−	0.525694i	$-0.176194\pi$
$439$	−0.627041	−	1.08607i	−0.0299270	−	0.0518351i	−0.880601	+	0.473858i	$0.842861\pi$
$440$		0			0
$441$	1.00000			0.0476190
$442$		0			0
$443$	19.0155			0.903453			0.451726	−	0.892156i	$-0.350808\pi$
$443$	19.0155			0.903453			0.451726	+	0.892156i	$0.350808\pi$
$444$		0			0
$445$	−14.3621	−	24.8759i	−0.680829	−	1.17923i
$446$		0			0
$447$	−8.08349			−0.382336
$448$		0			0
$449$	−10.7325	+	18.5892i	−0.506498	+	0.877280i	0.493474	+	0.869761i	$0.335727\pi$
$449$	−10.7325	+	18.5892i	−0.506498	+	0.877280i	−0.999972	+	0.00751916i	$0.997607\pi$
$450$		0			0
$451$	0.0539273	−	0.0934048i	0.00253934	−	0.00439826i
$452$		0			0
$453$	−3.63464	−	6.29538i	−0.170770	−	0.295783i
$454$		0			0
$455$	−7.71958	−	4.42758i	−0.361899	−	0.207568i
$456$		0			0
$457$	−9.98329	−	17.2916i	−0.466999	−	0.808866i	0.532290	−	0.846562i	$-0.321331\pi$
$457$	−9.98329	−	17.2916i	−0.466999	−	0.808866i	−0.999289	+	0.0376962i	$0.987998\pi$
$458$		0			0
$459$	0.198409	−	0.343655i	0.00926095	−	0.0160404i
$460$		0			0
$461$	0.354716	−	0.614387i	0.0165208	−	0.0286148i	−0.857647	−	0.514239i	$-0.828074\pi$
$461$	0.354716	−	0.614387i	0.0165208	−	0.0286148i	0.874168	+	0.485624i	$0.161408\pi$
$462$		0			0
$463$	2.94803			0.137007			0.0685033	−	0.997651i	$-0.478178\pi$
$463$	2.94803			0.137007			0.0685033	+	0.997651i	$0.478178\pi$
$464$		0			0
$465$	5.21644	+	9.03514i	0.241907	+	0.418995i
$466$		0			0
$467$	−7.02903			−0.325265			−0.162632	−	0.986687i	$-0.551998\pi$
$467$	−7.02903			−0.325265			−0.162632	+	0.986687i	$0.551998\pi$
$468$		0			0
$469$	−9.58071			−0.442396
$470$		0			0
$471$	−1.63901	−	2.83885i	−0.0755216	−	0.130807i
$472$		0			0
$473$	0.0477182			0.00219408
$474$		0			0
$475$	3.24110	−	5.61375i	0.148712	−	0.257577i
$476$		0			0
$477$	−6.52832	+	11.3074i	−0.298911	+	0.517729i
$478$		0			0
$479$	12.5244	+	21.6930i	0.572257	+	0.991178i	0.996334	+	0.0855516i	$0.0272652\pi$
$479$	12.5244	+	21.6930i	0.572257	+	0.991178i	−0.424077	+	0.905626i	$0.639401\pi$
$480$		0			0
$481$	−33.2062	+	19.2981i	−1.51407	+	0.879920i
$482$		0			0
$483$	−1.93250	−	3.34719i	−0.0879319	−	0.152303i
$484$		0			0
$485$	−13.0241	+	22.5584i	−0.591394	+	1.02432i
$486$		0			0
$487$	14.9409	−	25.8784i	0.677037	−	1.17266i	−0.298832	−	0.954306i	$-0.596597\pi$
$487$	14.9409	−	25.8784i	0.677037	−	1.17266i	0.975869	−	0.218356i	$-0.0700695\pi$
$488$		0			0
$489$	−22.4406			−1.01480
$490$		0			0
$491$	8.44244	+	14.6227i	0.381002	+	0.659914i	0.991206	−	0.132330i	$-0.0422458\pi$
$491$	8.44244	+	14.6227i	0.381002	+	0.659914i	−0.610204	+	0.792244i	$0.708913\pi$
$492$		0			0
$493$	−2.39215			−0.107737
$494$		0			0
$495$	0.0507905			0.00228286
$496$		0			0
$497$	1.79130	+	3.10263i	0.0803509	+	0.139172i
$498$		0			0
$499$	−22.5420			−1.00912			−0.504560	−	0.863376i	$-0.668345\pi$
$499$	−22.5420			−1.00912			−0.504560	+	0.863376i	$0.668345\pi$
$500$		0			0
$501$	9.53920	−	16.5224i	0.426180	−	0.738165i
$502$		0			0
$503$	−10.8603	+	18.8105i	−0.484235	+	0.838720i	−0.999836	−	0.0181087i	$-0.994236\pi$
$503$	−10.8603	+	18.8105i	−0.484235	+	0.838720i	0.515601	+	0.856829i	$0.327569\pi$
$504$		0			0
$505$	−2.81093	−	4.86868i	−0.125085	−	0.216653i
$506$		0			0
$507$	−6.56415	−	11.2210i	−0.291524	−	0.498344i
$508$		0			0
$509$	−2.57297	−	4.45651i	−0.114045	−	0.197531i	0.803353	−	0.595504i	$-0.203047\pi$
$509$	−2.57297	−	4.45651i	−0.114045	−	0.197531i	−0.917398	+	0.397972i	$0.869714\pi$
$510$		0			0
$511$	−7.35144	+	12.7331i	−0.325208	+	0.563277i
$512$		0			0
$513$	−2.96819	+	5.14105i	−0.131049	+	0.226983i
$514$		0			0
$515$	48.2417			2.12578
$516$		0			0
$517$	0.103980	+	0.180099i	0.00457306	+	0.00792077i
$518$		0			0
$519$	−3.29642			−0.144697
$520$		0			0
$521$	−11.7709			−0.515692			−0.257846	−	0.966186i	$-0.583013\pi$
$521$	−11.7709			−0.515692			−0.257846	+	0.966186i	$0.583013\pi$
$522$		0			0
$523$	3.13280	+	5.42618i	0.136988	+	0.237270i	0.926355	−	0.376651i	$-0.122925\pi$
$523$	3.13280	+	5.42618i	0.136988	+	0.237270i	−0.789367	+	0.613921i	$0.789591\pi$
$524$		0			0
$525$	−1.09195			−0.0476565
$526$		0			0
$527$	0.838664	−	1.45261i	0.0365328	−	0.0632766i
$528$		0			0
$529$	4.03087	−	6.98167i	0.175255	−	0.303551i
$530$		0			0
$531$	6.71958	+	11.6386i	0.291605	+	0.505074i
$532$		0			0
$533$	−16.3388	+	9.49545i	−0.707710	+	0.411294i
$534$		0			0
$535$	13.8115	+	23.9223i	0.597124	+	1.03425i
$536$		0			0
$537$	9.70615	−	16.8115i	0.418851	−	0.725472i
$538$		0			0
$539$	0.0102890	−	0.0178211i	0.000443180	−	0.000767609i
$540$		0			0
$541$	5.93680			0.255243			0.127621	−	0.991823i	$-0.459266\pi$
$541$	5.93680			0.255243			0.127621	+	0.991823i	$0.459266\pi$
$542$		0			0
$543$	2.80064	+	4.85086i	0.120187	+	0.208170i
$544$		0			0
$545$	−14.8945			−0.638011
$546$		0			0
$547$	−2.11762			−0.0905428			−0.0452714	−	0.998975i	$-0.514415\pi$
$547$	−2.11762			−0.0905428			−0.0452714	+	0.998975i	$0.514415\pi$
$548$		0			0
$549$	−6.06013	−	10.4965i	−0.258640	−	0.447978i
$550$		0			0
$551$	35.7864			1.52455
$552$		0			0
$553$	−1.75467	+	3.03918i	−0.0746162	+	0.129239i
$554$		0			0
$555$	−13.1457	+	22.7690i	−0.558002	+	0.966488i
$556$		0			0
$557$	−16.6394	−	28.8203i	−0.705034	−	1.22115i	−0.966679	−	0.255990i	$-0.917599\pi$
$557$	−16.6394	−	28.8203i	−0.705034	−	1.22115i	0.261646	−	0.965164i	$-0.415735\pi$
$558$		0			0
$559$	−7.25262	−	4.15975i	−0.306753	−	0.175939i
$560$		0			0
$561$	−0.00408287	−	0.00707174i	−0.000172379	−	0.000298569i
$562$		0			0
$563$	−1.25861	+	2.17998i	−0.0530441	+	0.0918751i	−0.891328	−	0.453359i	$-0.850226\pi$
$563$	−1.25861	+	2.17998i	−0.0530441	+	0.0918751i	0.838284	+	0.545234i	$0.183559\pi$
$564$		0			0
$565$	−12.8987	+	22.3413i	−0.542654	+	0.939904i
$566$		0			0
$567$	1.00000			0.0419961
$568$		0			0
$569$	−4.57684	−	7.92732i	−0.191871	−	0.332331i	0.753999	−	0.656875i	$-0.228122\pi$
$569$	−4.57684	−	7.92732i	−0.191871	−	0.332331i	−0.945870	+	0.324545i	$0.894789\pi$
$570$		0			0
$571$	−24.6436			−1.03130			−0.515652	−	0.856798i	$-0.672450\pi$
$571$	−24.6436			−1.03130			−0.515652	+	0.856798i	$0.672450\pi$
$572$		0			0
$573$	−7.21411			−0.301374
$574$		0			0
$575$	2.11019	+	3.65496i	0.0880010	+	0.152422i
$576$		0			0
$577$	33.2384			1.38373			0.691865	−	0.722027i	$-0.256789\pi$
$577$	33.2384			1.38373			0.691865	+	0.722027i	$0.256789\pi$
$578$		0			0
$579$	−2.10552	+	3.64686i	−0.0875023	+	0.151558i
$580$		0			0
$581$	−6.04175	+	10.4646i	−0.250654	+	0.434145i
$582$		0			0
$583$	0.134340	+	0.232684i	0.00556380	+	0.00963678i
$584$		0			0
$585$	−7.71958	−	4.42758i	−0.319165	−	0.183058i
$586$		0			0
$587$	−6.45630	−	11.1826i	−0.266480	−	0.461557i	0.701470	−	0.712699i	$-0.252527\pi$
$587$	−6.45630	−	11.1826i	−0.266480	−	0.461557i	−0.967950	+	0.251142i	$0.919194\pi$
$588$		0			0
$589$	−12.5464	+	21.7309i	−0.516963	+	0.895407i
$590$		0			0
$591$	−4.87355	+	8.44124i	−0.200471	+	0.347226i
$592$		0			0
$593$	−27.6591			−1.13582			−0.567912	−	0.823089i	$-0.692249\pi$
$593$	−27.6591			−1.13582			−0.567912	+	0.823089i	$0.692249\pi$
$594$		0			0
$595$	0.489711	+	0.848204i	0.0200762	+	0.0347730i
$596$		0			0
$597$	13.2265			0.541325
$598$		0			0
$599$	18.6826			0.763350			0.381675	−	0.924297i	$-0.375347\pi$
$599$	18.6826			0.763350			0.381675	+	0.924297i	$0.375347\pi$
$600$		0			0
$601$	9.93578	+	17.2093i	0.405289	+	0.701981i	0.994355	−	0.106104i	$-0.0338375\pi$
$601$	9.93578	+	17.2093i	0.405289	+	0.701981i	−0.589066	+	0.808085i	$0.700504\pi$
$602$		0			0
$603$	−9.58071			−0.390157
$604$		0			0
$605$	−13.5745	+	23.5117i	−0.551882	+	0.955888i
$606$		0			0
$607$	−4.47739	+	7.75506i	−0.181731	+	0.314768i	−0.942470	−	0.334290i	$-0.891503\pi$
$607$	−4.47739	+	7.75506i	−0.181731	+	0.314768i	0.760739	+	0.649058i	$0.224837\pi$
$608$		0			0
$609$	−3.01416	−	5.22068i	−0.122140	−	0.211553i
$610$		0			0
$611$	−0.103980	−	36.4374i	−0.00420660	−	1.47410i
$612$		0			0
$613$	−17.6795	−	30.6218i	−0.714069	−	1.23680i	−0.963317	−	0.268364i	$-0.913517\pi$
$613$	−17.6795	−	30.6218i	−0.714069	−	1.23680i	0.249248	−	0.968440i	$-0.419816\pi$
$614$		0			0
$615$	−6.46819	+	11.2032i	−0.260822	+	0.451758i
$616$		0			0
$617$	−14.1922	+	24.5817i	−0.571357	+	0.989620i	0.425069	+	0.905161i	$0.360250\pi$
$617$	−14.1922	+	24.5817i	−0.571357	+	0.989620i	−0.996427	+	0.0844594i	$0.973084\pi$
$618$		0			0
$619$	12.9301			0.519705			0.259852	−	0.965648i	$-0.416326\pi$
$619$	12.9301			0.519705			0.259852	+	0.965648i	$0.416326\pi$
$620$		0			0
$621$	−1.93250	−	3.34719i	−0.0775487	−	0.134318i
$622$		0			0
$623$	−11.6378			−0.466258
$624$		0			0
$625$	−29.2674			−1.17070
$626$		0			0
$627$	0.0610795	+	0.105793i	0.00243928	+	0.00422496i
$628$		0			0
$629$	4.22694			0.168539
$630$		0			0
$631$	4.04911	−	7.01326i	0.161193	−	0.279194i	−0.774104	−	0.633058i	$-0.781799\pi$
$631$	4.04911	−	7.01326i	0.161193	−	0.279194i	0.935297	+	0.353865i	$0.115133\pi$
$632$		0			0
$633$	3.38011	−	5.85452i	0.134347	−	0.232696i
$634$		0			0
$635$	4.42849	+	7.67036i	0.175739	+	0.304389i
$636$		0			0
$637$	−3.11734	+	1.81168i	−0.123514	+	0.0717813i
$638$		0			0
$639$	1.79130	+	3.10263i	0.0708628	+	0.122738i
$640$		0			0
$641$	−5.14543	+	8.91214i	−0.203232	+	0.352008i	−0.949568	−	0.313561i	$-0.898478\pi$
$641$	−5.14543	+	8.91214i	−0.203232	+	0.352008i	0.746336	+	0.665570i	$0.231811\pi$
$642$		0			0
$643$	20.8506	−	36.1142i	0.822266	−	1.42421i	−0.0817247	−	0.996655i	$-0.526043\pi$
$643$	20.8506	−	36.1142i	0.822266	−	1.42421i	0.903991	−	0.427552i	$-0.140624\pi$
$644$		0			0
$645$	−5.72345			−0.225361
$646$		0			0
$647$	17.3474	+	30.0465i	0.681995	+	1.18125i	0.974371	+	0.224946i	$0.0722207\pi$
$647$	17.3474	+	30.0465i	0.681995	+	1.18125i	−0.292376	+	0.956303i	$0.594446\pi$
$648$		0			0
$649$	0.276552			0.0108556
$650$		0			0
$651$	4.22694			0.165667
$652$		0			0
$653$	13.4011	+	23.2113i	0.524424	+	0.908330i	0.999596	+	0.0284362i	$0.00905276\pi$
$653$	13.4011	+	23.2113i	0.524424	+	0.908330i	−0.475171	+	0.879893i	$0.657614\pi$
$654$		0			0
$655$	−33.4373			−1.30650
$656$		0			0
$657$	−7.35144	+	12.7331i	−0.286807	+	0.496764i
$658$		0			0
$659$	5.25307	−	9.09859i	0.204631	−	0.354431i	−0.745384	−	0.666635i	$-0.767734\pi$
$659$	5.25307	−	9.09859i	0.204631	−	0.354431i	0.950015	+	0.312204i	$0.101067\pi$
$660$		0			0
$661$	16.0557	+	27.8093i	0.624494	+	1.08166i	0.988638	+	0.150313i	$0.0480282\pi$
$661$	16.0557	+	27.8093i	0.624494	+	1.08166i	−0.364144	+	0.931343i	$0.618639\pi$
$662$		0			0
$663$	0.00408287	+	1.43074i	0.000158566	+	0.0555655i
$664$		0			0
$665$	−7.32604	−	12.6891i	−0.284092	−	0.492061i
$666$		0			0
$667$	−11.6497	+	20.1780i	−0.451080	+	0.781293i
$668$		0			0
$669$	11.2980	−	19.5686i	0.436804	−	0.756567i
$670$		0			0
$671$	−0.249411			−0.00962842
$672$		0			0
$673$	−8.27030	−	14.3246i	−0.318797	−	0.552172i	0.661441	−	0.749998i	$-0.269945\pi$
$673$	−8.27030	−	14.3246i	−0.318797	−	0.552172i	−0.980237	+	0.197826i	$0.936612\pi$
$674$		0			0
$675$	−1.09195			−0.0420290
$676$		0			0
$677$	−17.2129			−0.661546			−0.330773	−	0.943710i	$-0.607310\pi$
$677$	−17.2129			−0.661546			−0.330773	+	0.943710i	$0.607310\pi$
$678$		0			0
$679$	5.27679	+	9.13966i	0.202504	+	0.350748i
$680$		0			0
$681$	0.639668			0.0245121
$682$		0			0
$683$	−16.9957	+	29.4374i	−0.650323	+	1.12639i	0.332722	+	0.943025i	$0.392033\pi$
$683$	−16.9957	+	29.4374i	−0.650323	+	1.12639i	−0.983045	+	0.183367i	$0.941300\pi$
$684$		0			0
$685$	16.9241	−	29.3134i	0.646638	−	1.12001i
$686$		0			0
$687$	7.92937	+	13.7341i	0.302524	+	0.523987i
$688$		0			0
$689$	−0.134340	−	47.0762i	−0.00511795	−	1.79346i
$690$		0			0
$691$	3.99731	+	6.92354i	0.152065	+	0.263384i	0.931986	−	0.362493i	$-0.118074\pi$
$691$	3.99731	+	6.92354i	0.152065	+	0.263384i	−0.779922	+	0.625877i	$0.784741\pi$
$692$		0			0
$693$	0.0102890	−	0.0178211i	0.000390848	−	0.000676968i
$694$		0			0
$695$	−23.2626	+	40.2921i	−0.882403	+	1.52837i
$696$		0			0
$697$	2.07982			0.0787789
$698$		0			0
$699$	−10.5252	−	18.2302i	−0.398099	−	0.689528i
$700$		0			0
$701$	28.6792			1.08320			0.541600	−	0.840637i	$-0.317819\pi$
$701$	28.6792			1.08320			0.541600	+	0.840637i	$0.317819\pi$
$702$		0			0
$703$	−63.2347			−2.38494
$704$		0			0
$705$	−12.4717	−	21.6016i	−0.469711	−	0.813564i
$706$		0			0
$707$	−2.27773			−0.0856629
$708$		0			0
$709$	−6.47987	+	11.2235i	−0.243357	+	0.421506i	−0.961668	−	0.274216i	$-0.911582\pi$
$709$	−6.47987	+	11.2235i	−0.243357	+	0.421506i	0.718312	+	0.695721i	$0.244915\pi$
$710$		0			0
$711$	−1.75467	+	3.03918i	−0.0658053	+	0.113978i
$712$		0			0
$713$	−8.16858	−	14.1484i	−0.305916	−	0.529861i
$714$		0			0
$715$	−0.158331	+	0.0920160i	−0.00592125	+	0.00344120i
$716$		0			0
$717$	−9.78707	−	16.9517i	−0.365505	−	0.633073i
$718$		0			0
$719$	0.319690	−	0.553719i	0.0119224	−	0.0206502i	−0.860003	−	0.510290i	$-0.829538\pi$
$719$	0.319690	−	0.553719i	0.0119224	−	0.0206502i	0.871925	+	0.489639i	$0.162872\pi$
$720$		0			0
$721$	9.77270	−	16.9268i	0.363954	−	0.630388i
$722$		0			0
$723$	30.1152			1.12000
$724$		0			0
$725$	3.29130	+	5.70070i	0.122236	+	0.211719i
$726$		0			0
$727$	26.2751			0.974491			0.487245	−	0.873265i	$-0.338002\pi$
$727$	26.2751			0.974491			0.487245	+	0.873265i	$0.338002\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	0.460089	+	0.796897i	0.0170170	+	0.0294743i
$732$		0			0
$733$	−47.9027			−1.76933			−0.884664	−	0.466230i	$-0.845612\pi$
$733$	−47.9027			−1.76933			−0.884664	+	0.466230i	$0.845612\pi$
$734$		0			0
$735$	−1.23409	+	2.13751i	−0.0455202	+	0.0788433i
$736$		0			0
$737$	−0.0985762	+	0.170739i	−0.00363110	+	0.00628925i
$738$		0			0
$739$	−10.5703	−	18.3083i	−0.388834	−	0.673480i	0.603459	−	0.797394i	$-0.293789\pi$
$739$	−10.5703	−	18.3083i	−0.388834	−	0.673480i	−0.992293	+	0.123914i	$0.960455\pi$
$740$		0			0
$741$	−0.0610795	−	21.4038i	−0.00224381	−	0.786289i
$742$		0			0
$743$	9.51570	+	16.4817i	0.349097	+	0.604654i	0.986089	−	0.166216i	$-0.0531550\pi$
$743$	9.51570	+	16.4817i	0.349097	+	0.604654i	−0.636992	+	0.770870i	$0.719822\pi$
$744$		0			0
$745$	9.97578	−	17.2786i	0.365484	−	0.633038i
$746$		0			0
$747$	−6.04175	+	10.4646i	−0.221056	+	0.382880i
$748$		0			0
$749$	11.1916			0.408933
$750$		0			0
$751$	16.6902	+	28.9082i	0.609033	+	1.05488i	0.991400	+	0.130866i	$0.0417758\pi$
$751$	16.6902	+	28.9082i	0.609033	+	1.05488i	−0.382367	+	0.924011i	$0.624891\pi$
$752$		0			0
$753$	18.6102			0.678194
$754$		0			0
$755$	17.9419			0.652974
$756$		0			0
$757$	16.1319	+	27.9412i	0.586323	+	1.01554i	0.994709	+	0.102732i	$0.0327584\pi$
$757$	16.1319	+	27.9412i	0.586323	+	1.01554i	−0.408386	+	0.912809i	$0.633908\pi$
$758$		0			0
$759$	−0.0795342			−0.00288691
$760$		0			0
$761$	−13.9160	+	24.1033i	−0.504456	+	0.873743i	0.495531	+	0.868590i	$0.334973\pi$
$761$	−13.9160	+	24.1033i	−0.504456	+	0.873743i	−0.999987	+	0.00515265i	$0.998360\pi$
$762$		0			0
$763$	−3.01730	+	5.22611i	−0.109233	+	0.189198i
$764$		0			0
$765$	0.489711	+	0.848204i	0.0177055	+	0.0306669i
$766$		0			0
$767$	−42.0327	−	24.1079i	−1.51771	−	0.870487i
$768$		0			0
$769$	−25.1346	−	43.5344i	−0.906376	−	1.56989i	−0.819060	−	0.573708i	$-0.805504\pi$
$769$	−25.1346	−	43.5344i	−0.906376	−	1.56989i	−0.0873161	−	0.996181i	$-0.527829\pi$
$770$		0			0
$771$	−12.5322	+	21.7064i	−0.451336	+	0.781737i
$772$		0			0
$773$	−2.11107	+	3.65648i	−0.0759298	+	0.131514i	−0.901490	−	0.432799i	$-0.857526\pi$
$773$	−2.11107	+	3.65648i	−0.0759298	+	0.131514i	0.825560	+	0.564314i	$0.190859\pi$
$774$		0			0
$775$	−4.61559			−0.165797
$776$		0			0
$777$	5.32604	+	9.22497i	0.191071	+	0.330944i
$778$		0			0
$779$	−31.1140			−1.11477
$780$		0			0
$781$	0.0737230			0.00263802
$782$		0			0
$783$	−3.01416	−	5.22068i	−0.107717	−	0.186572i
$784$		0			0
$785$	8.09077			0.288772
$786$		0			0
$787$	0.406309	−	0.703747i	0.0144833	−	0.0250859i	−0.858693	−	0.512490i	$-0.828723\pi$
$787$	0.406309	−	0.703747i	0.0144833	−	0.0250859i	0.873176	+	0.487405i	$0.162056\pi$
$788$		0			0
$789$	2.67689	−	4.63650i	0.0952996	−	0.165064i
$790$		0			0
$791$	5.22600	+	9.05169i	0.185815	+	0.321841i
$792$		0			0
$793$	37.9077	+	21.7420i	1.34614	+	0.772082i
$794$		0			0
$795$	−16.1131	−	27.9087i	−0.571473	−	0.989821i
$796$		0			0
$797$	−8.87697	+	15.3754i	−0.314439	+	0.544624i	−0.979318	−	0.202327i	$-0.935150\pi$
$797$	−8.87697	+	15.3754i	−0.314439	+	0.544624i	0.664879	+	0.746951i	$0.268483\pi$
$798$		0			0
$799$	−2.00512	+	3.47296i	−0.0709359	+	0.122865i
$800$		0			0
$801$	−11.6378			−0.411201
$802$		0			0
$803$	0.151278	+	0.262021i	0.00533849	+	0.00924654i
$804$		0			0
$805$	9.53956			0.336225
$806$		0			0
$807$	−14.6359			−0.515208
$808$		0			0
$809$	22.5266	+	39.0172i	0.791992	+	1.37177i	0.924732	+	0.380620i	$0.124289\pi$
$809$	22.5266	+	39.0172i	0.791992	+	1.37177i	−0.132740	+	0.991151i	$0.542377\pi$
$810$		0			0
$811$	43.6533			1.53287			0.766437	−	0.642319i	$-0.222028\pi$
$811$	43.6533			1.53287			0.766437	+	0.642319i	$0.222028\pi$
$812$		0			0
$813$	−10.1173	+	17.5237i	−0.354831	+	0.614585i
$814$		0			0
$815$	27.6938	−	47.9671i	0.970072	−	1.68021i
$816$		0			0
$817$	−6.88289	−	11.9215i	−0.240802	−	0.417081i
$818$		0			0
$819$	−3.11734	+	1.81168i	−0.108929	+	0.0633052i
$820$		0			0
$821$	16.2308	+	28.1126i	0.566460	+	0.981138i	0.996912	+	0.0785242i	$0.0250208\pi$
$821$	16.2308	+	28.1126i	0.566460	+	0.981138i	−0.430452	+	0.902613i	$0.641646\pi$
$822$		0			0
$823$	−2.78861	+	4.83002i	−0.0972049	+	0.168364i	−0.910527	−	0.413450i	$-0.864324\pi$
$823$	−2.78861	+	4.83002i	−0.0972049	+	0.168364i	0.813322	+	0.581814i	$0.197657\pi$
$824$		0			0
$825$	−0.0112351	+	0.0194597i	−0.000391155	+	0.000677500i
$826$		0			0
$827$	36.9740			1.28571			0.642857	−	0.765986i	$-0.277749\pi$
$827$	36.9740			1.28571			0.642857	+	0.765986i	$0.277749\pi$
$828$		0			0
$829$	17.2708	+	29.9139i	0.599840	+	1.03895i	0.992844	+	0.119417i	$0.0381025\pi$
$829$	17.2708	+	29.9139i	0.599840	+	1.03895i	−0.393004	+	0.919537i	$0.628564\pi$
$830$		0			0
$831$	2.63778			0.0915034
$832$		0			0
$833$	0.396818			0.0137489
$834$		0			0
$835$	23.5445	+	40.7803i	0.814792	+	1.41126i
$836$		0			0
$837$	4.22694			0.146104
$838$		0			0
$839$	13.1472	−	22.7716i	0.453892	−	0.786163i	−0.544732	−	0.838610i	$-0.683369\pi$
$839$	13.1472	−	22.7716i	0.453892	−	0.786163i	0.998624	+	0.0524467i	$0.0167020\pi$
$840$		0			0
$841$	−3.67032	+	6.35719i	−0.126563	+	0.219213i
$842$		0			0
$843$	9.44666	+	16.3621i	0.325360	+	0.563541i
$844$		0			0
$845$	32.0859	−	0.183127i	1.10379	−	0.00629976i
$846$		0			0
$847$	5.49979	+	9.52591i	0.188975	+	0.327314i
$848$		0			0
$849$	3.32991	−	5.76758i	0.114282	−	0.197943i
$850$		0			0
$851$	20.5852	−	35.6546i	0.705651	−	1.22222i
$852$		0			0
$853$	−35.1534			−1.20363			−0.601815	−	0.798636i	$-0.705556\pi$
$853$	−35.1534			−1.20363			−0.601815	+	0.798636i	$0.705556\pi$
$854$		0			0
$855$	−7.32604	−	12.6891i	−0.250545	−	0.433957i
$856$		0			0
$857$	−16.8437			−0.575370			−0.287685	−	0.957725i	$-0.592886\pi$
$857$	−16.8437			−0.575370			−0.287685	+	0.957725i	$0.592886\pi$
$858$		0			0
$859$	23.0292			0.785747			0.392873	−	0.919593i	$-0.371481\pi$
$859$	23.0292			0.785747			0.392873	+	0.919593i	$0.371481\pi$
$860$		0			0
$861$	2.62062	+	4.53905i	0.0893106	+	0.154690i
$862$		0			0
$863$	−0.585093			−0.0199168			−0.00995840	−	0.999950i	$-0.503170\pi$
$863$	−0.585093			−0.0199168			−0.00995840	+	0.999950i	$0.503170\pi$
$864$		0			0
$865$	4.06809	−	7.04613i	0.138319	−	0.239576i
$866$		0			0
$867$	−8.42127	+	14.5861i	−0.286001	+	0.495369i
$868$		0			0
$869$	0.0361077	+	0.0625404i	0.00122487	+	0.00212154i
$870$		0			0
$871$	29.8664	−	17.3572i	1.01198	−	0.588125i
$872$		0			0
$873$	5.27679	+	9.13966i	0.178592	+	0.309331i
$874$		0			0
$875$	−4.82290	+	8.35351i	−0.163044	+	0.282400i
$876$		0			0
$877$	12.6565	−	21.9218i	0.427381	−	0.740246i	−0.569258	−	0.822159i	$-0.692770\pi$
$877$	12.6565	−	21.9218i	0.427381	−	0.740246i	0.996639	+	0.0819130i	$0.0261030\pi$
$878$		0			0
$879$	−5.09342			−0.171797
$880$		0			0
$881$	20.0742	+	34.7696i	0.676318	+	1.17142i	0.976082	+	0.217403i	$0.0697587\pi$
$881$	20.0742	+	34.7696i	0.676318	+	1.17142i	−0.299764	+	0.954013i	$0.596908\pi$
$882$		0			0
$883$	25.4319			0.855851			0.427925	−	0.903814i	$-0.359245\pi$
$883$	25.4319			0.855851			0.427925	+	0.903814i	$0.359245\pi$
$884$		0			0
$885$	−33.1703			−1.11501
$886$		0			0
$887$	5.07451	+	8.78930i	0.170385	+	0.295116i	0.938555	−	0.345131i	$-0.112165\pi$
$887$	5.07451	+	8.78930i	0.170385	+	0.295116i	−0.768169	+	0.640247i	$0.778832\pi$
$888$		0			0
$889$	3.58845			0.120353
$890$		0			0
$891$	0.0102890	−	0.0178211i	0.000344695	−	0.000597030i
$892$		0			0
$893$	29.9964	−	51.9553i	1.00379	−	1.73862i
$894$		0			0
$895$	23.9566	+	41.4940i	0.800781	+	1.38699i
$896$		0			0
$897$	12.0883	+	6.93327i	0.403617	+	0.231495i
$898$		0			0
$899$	−12.7407	−	22.0675i	−0.424925	−	0.735992i
$900$		0			0
$901$	−2.59056	+	4.48698i	−0.0863040	+	0.149483i
$902$		0			0
$903$	−1.15944	+	2.00822i	−0.0385839	+	0.0668292i
$904$		0			0
$905$	−13.8250			−0.459560
$906$		0			0
$907$	−5.97185	−	10.3435i	−0.198292	−	0.343452i	0.749683	−	0.661797i	$-0.230206\pi$
$907$	−5.97185	−	10.3435i	−0.198292	−	0.343452i	−0.947975	+	0.318346i	$0.896873\pi$
$908$		0			0
$909$	−2.27773			−0.0755476
$910$		0			0
$911$	27.3764			0.907021			0.453511	−	0.891251i	$-0.350171\pi$
$911$	27.3764			0.907021			0.453511	+	0.891251i	$0.350171\pi$
$912$		0			0
$913$	0.124327	+	0.215341i	0.00411463	+	0.00712675i
$914$		0			0
$915$	29.9151			0.988962
$916$		0			0
$917$	−6.77365	+	11.7323i	−0.223686	+	0.387435i
$918$		0			0
$919$	24.4068	−	42.2737i	0.805104	−	1.39448i	−0.111116	−	0.993807i	$-0.535443\pi$
$919$	24.4068	−	42.2737i	0.805104	−	1.39448i	0.916221	−	0.400674i	$-0.131224\pi$
$920$		0			0
$921$	10.3742	+	17.9686i	0.341842	+	0.592087i
$922$		0			0
$923$	−11.2051	−	6.42668i	−0.368819	−	0.211537i
$924$		0			0
$925$	−5.81575	−	10.0732i	−0.191221	−	0.331204i
$926$		0			0
$927$	9.77270	−	16.9268i	0.320978	−	0.555950i
$928$		0			0
$929$	20.5528	−	35.5984i	0.674314	−	1.16795i	−0.302354	−	0.953196i	$-0.597773\pi$
$929$	20.5528	−	35.5984i	0.674314	−	1.16795i	0.976669	−	0.214751i	$-0.0688941\pi$
$930$		0			0
$931$	−5.93637			−0.194557
$932$		0			0
$933$	−15.0075	−	25.9938i	−0.491324	−	0.850999i
$934$		0			0
$935$	0.0201546			0.000659126
$936$		0			0
$937$	26.7099			0.872574			0.436287	−	0.899807i	$-0.356293\pi$
$937$	26.7099			0.872574			0.436287	+	0.899807i	$0.356293\pi$
$938$		0			0
$939$	−14.4688	−	25.0607i	−0.472171	−	0.817824i
$940$		0			0
$941$	−59.7172			−1.94673			−0.973363	−	0.229270i	$-0.926366\pi$
$941$	−59.7172			−1.94673			−0.973363	+	0.229270i	$0.926366\pi$
$942$		0			0
$943$	10.1287	−	17.5435i	0.329837	−	0.571294i
$944$		0			0
$945$	−1.23409	+	2.13751i	−0.0401451	+	0.0695333i
$946$		0			0
$947$	12.0956	+	20.9502i	0.393054	+	0.680790i	0.992851	−	0.119363i	$-0.0380851\pi$
$947$	12.0956	+	20.9502i	0.393054	+	0.680790i	−0.599796	+	0.800153i	$0.704752\pi$
$948$		0			0
$949$	−0.151278	−	53.0117i	−0.00491070	−	1.72083i
$950$		0			0
$951$	4.69995	+	8.14054i	0.152406	+	0.263975i
$952$		0			0
$953$	−21.6992	+	37.5842i	−0.702907	+	1.21747i	0.264534	+	0.964376i	$0.414782\pi$
$953$	−21.6992	+	37.5842i	−0.702907	+	1.21747i	−0.967442	+	0.253095i	$0.918552\pi$
$954$		0			0
$955$	8.90288	−	15.4202i	0.288090	−	0.498987i
$956$		0			0
$957$	−0.124051			−0.00401000
$958$		0			0
$959$	−6.85691	−	11.8765i	−0.221421	−	0.383513i
$960$		0			0
$961$	−13.1330			−0.423644
$962$		0			0
$963$	11.1916			0.360645
$964$		0			0
$965$	−5.19681	−	9.00114i	−0.167291	−	0.289757i
$966$		0			0
$967$	19.9001			0.639943			0.319972	−	0.947427i	$-0.396327\pi$
$967$	19.9001			0.639943			0.319972	+	0.947427i	$0.396327\pi$
$968$		0			0
$969$	−1.17783	+	2.04006i	−0.0378374	+	0.0655363i
$970$		0			0
$971$	19.8960	−	34.4610i	0.638494	−	1.10590i	−0.347269	−	0.937766i	$-0.612891\pi$
$971$	19.8960	−	34.4610i	0.638494	−	1.10590i	0.985763	−	0.168139i	$-0.0537758\pi$
$972$		0			0
$973$	9.42499	+	16.3246i	0.302151	+	0.523342i
$974$		0			0
$975$	3.40397	−	1.97826i	0.109014	−	0.0633549i
$976$		0			0
$977$	−14.7152	−	25.4875i	−0.470781	−	0.815416i	0.528661	−	0.848833i	$-0.322694\pi$
$977$	−14.7152	−	25.4875i	−0.470781	−	0.815416i	−0.999441	+	0.0334170i	$0.989361\pi$
$978$		0			0
$979$	−0.119741	+	0.207398i	−0.00382695	+	0.00662847i
$980$		0			0
$981$	−3.01730	+	5.22611i	−0.0963349	+	0.166857i
$982$		0			0
$983$	−21.1327			−0.674028			−0.337014	−	0.941500i	$-0.609417\pi$
$983$	−21.1327			−0.674028			−0.337014	+	0.941500i	$0.609417\pi$
$984$		0			0
$985$	−12.0288	−	20.8345i	−0.383270	−	0.663844i
$986$		0			0
$987$	−10.1060			−0.321676
$988$		0			0
$989$	8.96251			0.284991
$990$		0			0
$991$	21.5982	+	37.4092i	0.686090	+	1.18834i	0.973093	+	0.230414i	$0.0740079\pi$
$991$	21.5982	+	37.4092i	0.686090	+	1.18834i	−0.287002	+	0.957930i	$0.592659\pi$
$992$		0			0
$993$	20.4604			0.649293
$994$		0			0
$995$	−16.3228	+	28.2718i	−0.517466	+	0.896278i
$996$		0			0
$997$	14.5439	−	25.1907i	0.460609	−	0.797798i	−0.538382	−	0.842701i	$-0.680964\pi$
$997$	14.5439	−	25.1907i	0.460609	−	0.797798i	0.998991	+	0.0449024i	$0.0142977\pi$
$998$		0			0
$999$	5.32604	+	9.22497i	0.168508	+	0.291865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2184.2.bj.k.1849.1	yes	8
13.9	even	3	inner	2184.2.bj.k.841.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2184.2.bj.k.841.1	✓	8	13.9	even	3	inner
2184.2.bj.k.1849.1	yes	8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2184 = 2^{3} \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2184.bj (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} -2.46819 q^{5} +(-0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} -2.46819 q^{5} +(-0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(0.0102890 + 0.0178211i) q^{11} +(-0.0102890 - 3.60554i) q^{13} +(-1.23409 - 2.13751i) q^{15} +(-0.198409 + 0.343655i) q^{17} +(2.96819 - 5.14105i) q^{19} -1.00000 q^{21} +(1.93250 + 3.34719i) q^{23} +1.09195 q^{25} -1.00000 q^{27} +(3.01416 + 5.22068i) q^{29} -4.22694 q^{31} +(-0.0102890 + 0.0178211i) q^{33} +(1.23409 - 2.13751i) q^{35} +(-5.32604 - 9.22497i) q^{37} +(3.11734 - 1.81168i) q^{39} +(-2.62062 - 4.53905i) q^{41} +(1.15944 - 2.00822i) q^{43} +(1.23409 - 2.13751i) q^{45} +10.1060 q^{47} +(-0.500000 - 0.866025i) q^{49} -0.396818 q^{51} +13.0566 q^{53} +(-0.0253952 - 0.0439858i) q^{55} +5.93637 q^{57} +(6.71958 - 11.6386i) q^{59} +(-6.06013 + 10.4965i) q^{61} +(-0.500000 - 0.866025i) q^{63} +(0.0253952 + 8.89914i) q^{65} +(4.79036 + 8.29714i) q^{67} +(-1.93250 + 3.34719i) q^{69} +(1.79130 - 3.10263i) q^{71} +14.7029 q^{73} +(0.545973 + 0.945653i) q^{75} -0.0205780 q^{77} +3.50934 q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0835 q^{83} +(0.489711 - 0.848204i) q^{85} +(-3.01416 + 5.22068i) q^{87} +(5.81889 + 10.0786i) q^{89} +(3.12763 + 1.79386i) q^{91} +(-2.11347 - 3.66064i) q^{93} +(-7.32604 + 12.6891i) q^{95} +(5.27679 - 9.13966i) q^{97} -0.0205780 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 - 4 * q^7 - 4 * q^9	\( 8 q + 4 q^{3} - 4 q^{7} - 4 q^{9} - 3 q^{11} + 3 q^{13} + q^{17} + 4 q^{19} - 8 q^{21} + 3 q^{23} - 12 q^{25} - 8 q^{27} - 6 q^{29} - 38 q^{31} + 3 q^{33} - 12 q^{37} - 9 q^{41} + q^{43} + 28 q^{47} - 4 q^{49} + 2 q^{51} - 16 q^{53} + 4 q^{55} + 8 q^{57} + 5 q^{59} - 8 q^{61} - 4 q^{63} - 4 q^{65} + 15 q^{67} - 3 q^{69} + 20 q^{71} + 48 q^{73} - 6 q^{75} + 6 q^{77} - 4 q^{79} - 4 q^{81} - 8 q^{83} + 7 q^{85} + 6 q^{87} + 30 q^{89} - 3 q^{91} - 19 q^{93} - 28 q^{95} + 9 q^{97} + 6 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 - 4 * q^7 - 4 * q^9 - 3 * q^11 + 3 * q^13 + q^17 + 4 * q^19 - 8 * q^21 + 3 * q^23 - 12 * q^25 - 8 * q^27 - 6 * q^29 - 38 * q^31 + 3 * q^33 - 12 * q^37 - 9 * q^41 + q^43 + 28 * q^47 - 4 * q^49 + 2 * q^51 - 16 * q^53 + 4 * q^55 + 8 * q^57 + 5 * q^59 - 8 * q^61 - 4 * q^63 - 4 * q^65 + 15 * q^67 - 3 * q^69 + 20 * q^71 + 48 * q^73 - 6 * q^75 + 6 * q^77 - 4 * q^79 - 4 * q^81 - 8 * q^83 + 7 * q^85 + 6 * q^87 + 30 * q^89 - 3 * q^91 - 19 * q^93 - 28 * q^95 + 9 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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