LMFDB - Embedded newform 2184.2.bj.h.841.1

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:	8.0.8548296849.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 9x^{6} + 8x^{5} + 25x^{4} + 3x^{3} + 11x^{2} + 2x + 4 $ x^8 - 2x^7 + 9x^6 + 8x^5 + 25x^4 + 3x^3 + 11x^2 + 2*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			841.1
Root			$0.336767 - 0.583297i$ of defining polynomial
Character	$\chi$	$=$	2184.841
Dual form			2184.2.bj.h.1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} -2.89342 q^{5} +(0.500000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} -2.89342 q^{5} +(0.500000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(0.0379976 - 0.0658138i) q^{11} +(3.60495 + 0.0658138i) q^{13} +(1.44671 - 2.50577i) q^{15} +(-0.0276976 - 0.0479736i) q^{17} +(0.0975381 + 0.168941i) q^{19} -1.00000 q^{21} +(1.97441 - 3.41977i) q^{23} +3.37188 q^{25} +1.00000 q^{27} +(0.716524 - 1.24106i) q^{29} +5.66776 q^{31} +(0.0379976 + 0.0658138i) q^{33} +(-1.44671 - 2.50577i) q^{35} +(-4.34013 + 7.51732i) q^{37} +(-1.85947 + 3.08907i) q^{39} +(0.213636 - 0.370028i) q^{41} +(1.05040 + 1.81935i) q^{43} +(1.44671 + 2.50577i) q^{45} -0.156200 q^{47} +(-0.500000 + 0.866025i) q^{49} +0.0553951 q^{51} -8.24470 q^{53} +(-0.109943 + 0.190427i) q^{55} -0.195076 q^{57} +(1.45286 + 2.51644i) q^{59} +(3.81648 + 6.61034i) q^{61} +(0.500000 - 0.866025i) q^{63} +(-10.4306 - 0.190427i) q^{65} +(-4.82358 + 8.35468i) q^{67} +(1.97441 + 3.41977i) q^{69} +(0.392162 + 0.679244i) q^{71} +14.0090 q^{73} +(-1.68594 + 2.92013i) q^{75} +0.0759953 q^{77} -11.2405 q^{79} +(-0.500000 + 0.866025i) q^{81} +3.54635 q^{83} +(0.0801406 + 0.138808i) q^{85} +(0.716524 + 1.24106i) q^{87} +(-7.68930 + 13.3183i) q^{89} +(1.74548 + 3.15489i) q^{91} +(-2.83388 + 4.90842i) q^{93} +(-0.282219 - 0.488817i) q^{95} +(6.02896 + 10.4425i) q^{97} -0.0759953 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 + 4 * q^5 + 4 * q^7 - 4 * q^9	$ 8 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9} + q^{11} + q^{13} - 2 q^{15} - 3 q^{17} - 2 q^{19} - 8 q^{21} + 5 q^{23} + 4 q^{25} + 8 q^{27} + 20 q^{29} - 2 q^{31} + q^{33} + 2 q^{35} + 6 q^{37} - 2 q^{39} - 7 q^{41} - q^{43} - 2 q^{45} + 12 q^{47} - 4 q^{49} + 6 q^{51} - 20 q^{53} + 12 q^{55} + 4 q^{57} + 5 q^{59} + 2 q^{61} + 4 q^{63} - 26 q^{65} - 17 q^{67} + 5 q^{69} + 8 q^{71} + 16 q^{73} - 2 q^{75} + 2 q^{77} - 60 q^{79} - 4 q^{81} + 4 q^{83} - 7 q^{85} + 20 q^{87} - 10 q^{89} - q^{91} + q^{93} - 20 q^{95} + 19 q^{97} - 2 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 + 4 * q^5 + 4 * q^7 - 4 * q^9 + q^11 + q^13 - 2 * q^15 - 3 * q^17 - 2 * q^19 - 8 * q^21 + 5 * q^23 + 4 * q^25 + 8 * q^27 + 20 * q^29 - 2 * q^31 + q^33 + 2 * q^35 + 6 * q^37 - 2 * q^39 - 7 * q^41 - q^43 - 2 * q^45 + 12 * q^47 - 4 * q^49 + 6 * q^51 - 20 * q^53 + 12 * q^55 + 4 * q^57 + 5 * q^59 + 2 * q^61 + 4 * q^63 - 26 * q^65 - 17 * q^67 + 5 * q^69 + 8 * q^71 + 16 * q^73 - 2 * q^75 + 2 * q^77 - 60 * q^79 - 4 * q^81 + 4 * q^83 - 7 * q^85 + 20 * q^87 - 10 * q^89 - q^91 + q^93 - 20 * q^95 + 19 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$1093$	$1249$	$1457$	$1639$	$2017$
$\chi(n)$	$1$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	−2.89342			−1.29398			−0.646988	−	0.762500i	$-0.723972\pi$
$5$	−2.89342			−1.29398			−0.646988	+	0.762500i	$0.723972\pi$
$6$		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
$11$	0.0379976	−	0.0658138i	0.0114567	−	0.0198436i	−0.860240	−	0.509889i	$-0.829686\pi$
$11$	0.0379976	−	0.0658138i	0.0114567	−	0.0198436i	0.871697	+	0.490045i	$0.163020\pi$
$12$		0			0
$13$	3.60495	+	0.0658138i	0.999833	+	0.0182535i
$13$	3.60495	+	0.0658138i	0.999833	+	0.0182535i
$14$		0			0
$15$	1.44671	−	2.50577i	0.373539	−	0.646988i
$16$		0			0
$17$	−0.0276976	−	0.0479736i	−0.00671764	−	0.0116353i	0.862647	−	0.505806i	$-0.168805\pi$
$17$	−0.0276976	−	0.0479736i	−0.00671764	−	0.0116353i	−0.869365	+	0.494171i	$0.835472\pi$
$18$		0			0
$19$	0.0975381	+	0.168941i	0.0223768	+	0.0387577i	0.876997	−	0.480496i	$-0.159543\pi$
$19$	0.0975381	+	0.168941i	0.0223768	+	0.0387577i	−0.854620	+	0.519254i	$0.826210\pi$
$20$		0			0
$21$	−1.00000			−0.218218
$22$		0			0
$23$	1.97441	−	3.41977i	0.411692	−	0.713072i	−0.583383	−	0.812198i	$-0.698271\pi$
$23$	1.97441	−	3.41977i	0.411692	−	0.713072i	0.995075	+	0.0991254i	$0.0316045\pi$
$24$		0			0
$25$	3.37188			0.674375
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	0.716524	−	1.24106i	0.133055	−	0.230458i	−0.791798	−	0.610783i	$-0.790855\pi$
$29$	0.716524	−	1.24106i	0.133055	−	0.230458i	0.924853	+	0.380325i	$0.124188\pi$
$30$		0			0
$31$	5.66776			1.01796			0.508980	−	0.860779i	$-0.330023\pi$
$31$	5.66776			1.01796			0.508980	+	0.860779i	$0.330023\pi$
$32$		0			0
$33$	0.0379976	+	0.0658138i	0.00661454	+	0.0114567i
$34$		0			0
$35$	−1.44671	−	2.50577i	−0.244539	−	0.423553i
$36$		0			0
$37$	−4.34013	+	7.51732i	−0.713513	+	1.23584i	0.250017	+	0.968241i	$0.419564\pi$
$37$	−4.34013	+	7.51732i	−0.713513	+	1.23584i	−0.963530	+	0.267599i	$0.913770\pi$
$38$		0			0
$39$	−1.85947	+	3.08907i	−0.297754	+	0.494647i
$40$		0			0
$41$	0.213636	−	0.370028i	0.0333643	−	0.0577887i	−0.848861	−	0.528616i	$-0.822711\pi$
$41$	0.213636	−	0.370028i	0.0333643	−	0.0577887i	0.882225	+	0.470827i	$0.156045\pi$
$42$		0			0
$43$	1.05040	+	1.81935i	0.160185	+	0.277448i	0.934935	−	0.354819i	$-0.115458\pi$
$43$	1.05040	+	1.81935i	0.160185	+	0.277448i	−0.774750	+	0.632268i	$0.782124\pi$
$44$		0			0
$45$	1.44671	+	2.50577i	0.215663	+	0.373539i
$46$		0			0
$47$	−0.156200			−0.0227842			−0.0113921	−	0.999935i	$-0.503626\pi$
$47$	−0.156200			−0.0227842			−0.0113921	+	0.999935i	$0.503626\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$	0.0553951			0.00775687
$52$		0			0
$53$	−8.24470			−1.13250			−0.566248	−	0.824235i	$-0.691606\pi$
$53$	−8.24470			−1.13250			−0.566248	+	0.824235i	$0.691606\pi$
$54$		0			0
$55$	−0.109943	+	0.190427i	−0.0148247	+	0.0256772i
$56$		0			0
$57$	−0.195076			−0.0258385
$58$		0			0
$59$	1.45286	+	2.51644i	0.189147	+	0.327612i	0.944966	−	0.327168i	$-0.106094\pi$
$59$	1.45286	+	2.51644i	0.189147	+	0.327612i	−0.755819	+	0.654780i	$0.772761\pi$
$60$		0			0
$61$	3.81648	+	6.61034i	0.488650	+	0.846367i	0.999915	−	0.0130562i	$-0.00415603\pi$
$61$	3.81648	+	6.61034i	0.488650	+	0.846367i	−0.511264	+	0.859423i	$0.670823\pi$
$62$		0			0
$63$	0.500000	−	0.866025i	0.0629941	−	0.109109i
$64$		0			0
$65$	−10.4306	−	0.190427i	−1.29376	−	0.0236196i
$66$		0			0
$67$	−4.82358	+	8.35468i	−0.589294	+	1.02069i	0.405031	+	0.914303i	$0.367261\pi$
$67$	−4.82358	+	8.35468i	−0.589294	+	1.02069i	−0.994325	+	0.106384i	$0.966073\pi$
$68$		0			0
$69$	1.97441	+	3.41977i	0.237691	+	0.411692i
$70$		0			0
$71$	0.392162	+	0.679244i	0.0465410	+	0.0806115i	0.888357	−	0.459152i	$-0.151847\pi$
$71$	0.392162	+	0.679244i	0.0465410	+	0.0806115i	−0.841816	+	0.539764i	$0.818514\pi$
$72$		0			0
$73$	14.0090			1.63964			0.819818	−	0.572625i	$-0.194075\pi$
$73$	14.0090			1.63964			0.819818	+	0.572625i	$0.194075\pi$
$74$		0			0
$75$	−1.68594	+	2.92013i	−0.194675	+	0.337188i
$76$		0			0
$77$	0.0759953			0.00866046
$78$		0			0
$79$	−11.2405			−1.26465			−0.632327	−	0.774702i	$-0.717900\pi$
$79$	−11.2405			−1.26465			−0.632327	+	0.774702i	$0.717900\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	3.54635			0.389263			0.194631	−	0.980876i	$-0.437649\pi$
$83$	3.54635			0.389263			0.194631	+	0.980876i	$0.437649\pi$
$84$		0			0
$85$	0.0801406	+	0.138808i	0.00869247	+	0.0150558i
$86$		0			0
$87$	0.716524	+	1.24106i	0.0768194	+	0.133055i
$88$		0			0
$89$	−7.68930	+	13.3183i	−0.815064	+	1.41173i	0.0942175	+	0.995552i	$0.469965\pi$
$89$	−7.68930	+	13.3183i	−0.815064	+	1.41173i	−0.909282	+	0.416181i	$0.863368\pi$
$90$		0			0
$91$	1.74548	+	3.15489i	0.182976	+	0.330722i
$92$		0			0
$93$	−2.83388	+	4.90842i	−0.293860	+	0.508980i
$94$		0			0
$95$	−0.282219	−	0.488817i	−0.0289550	−	0.0501516i
$96$		0			0
$97$	6.02896	+	10.4425i	0.612148	+	1.06027i	0.990878	+	0.134764i	$0.0430275\pi$
$97$	6.02896	+	10.4425i	0.612148	+	1.06027i	−0.378730	+	0.925507i	$0.623639\pi$
$98$		0			0
$99$	−0.0759953			−0.00763781
$100$		0			0
$101$	−4.88843	+	8.46700i	−0.486417	+	0.842498i	−0.999878	−	0.0156143i	$-0.995030\pi$
$101$	−4.88843	+	8.46700i	−0.486417	+	0.842498i	0.513461	+	0.858113i	$0.328363\pi$
$102$		0			0
$103$	−6.56118			−0.646492			−0.323246	−	0.946315i	$-0.604774\pi$
$103$	−6.56118			−0.646492			−0.323246	+	0.946315i	$0.604774\pi$
$104$		0			0
$105$	2.89342			0.282369
$106$		0			0
$107$	−1.49501	+	2.58943i	−0.144528	+	0.250330i	−0.929197	−	0.369586i	$-0.879500\pi$
$107$	−1.49501	+	2.58943i	−0.144528	+	0.250330i	0.784669	+	0.619915i	$0.212833\pi$
$108$		0			0
$109$	−0.250471			−0.0239908			−0.0119954	−	0.999928i	$-0.503818\pi$
$109$	−0.250471			−0.0239908			−0.0119954	+	0.999928i	$0.503818\pi$
$110$		0			0
$111$	−4.34013	−	7.51732i	−0.411947	−	0.713513i
$112$		0			0
$113$	1.01645	+	1.76055i	0.0956200	+	0.165619i	0.909867	−	0.414900i	$-0.136183\pi$
$113$	1.01645	+	1.76055i	0.0956200	+	0.165619i	−0.814247	+	0.580518i	$0.802850\pi$
$114$		0			0
$115$	−5.71279	+	9.89484i	−0.532720	+	0.922699i
$116$		0			0
$117$	−1.74548	−	3.15489i	−0.161370	−	0.291669i
$118$		0			0
$119$	0.0276976	−	0.0479736i	0.00253903	−	0.00439773i
$120$		0			0
$121$	5.49711	+	9.52128i	0.499737	+	0.865571i
$122$		0			0
$123$	0.213636	+	0.370028i	0.0192629	+	0.0333643i
$124$		0			0
$125$	4.71084			0.421351
$126$		0			0
$127$	−4.41612	+	7.64895i	−0.391868	+	0.678735i	−0.992696	−	0.120643i	$-0.961504\pi$
$127$	−4.41612	+	7.64895i	−0.391868	+	0.678735i	0.600828	+	0.799378i	$0.294838\pi$
$128$		0			0
$129$	−2.10081			−0.184966
$130$		0			0
$131$	−16.6306			−1.45303			−0.726513	−	0.687153i	$-0.758860\pi$
$131$	−16.6306			−1.45303			−0.726513	+	0.687153i	$0.758860\pi$
$132$		0			0
$133$	−0.0975381	+	0.168941i	−0.00845763	+	0.0146490i
$134$		0			0
$135$	−2.89342			−0.249026
$136$		0			0
$137$	0.475665	+	0.823876i	0.0406388	+	0.0703885i	0.885629	−	0.464393i	$-0.153727\pi$
$137$	0.475665	+	0.823876i	0.0406388	+	0.0703885i	−0.844991	+	0.534781i	$0.820394\pi$
$138$		0			0
$139$	0.390057	+	0.675598i	0.0330842	+	0.0573035i	0.882093	−	0.471075i	$-0.156134\pi$
$139$	0.390057	+	0.675598i	0.0330842	+	0.0573035i	−0.849009	+	0.528378i	$0.822800\pi$
$140$		0			0
$141$	0.0781001	−	0.135273i	0.00657722	−	0.0113921i
$142$		0			0
$143$	0.141311	−	0.234755i	0.0118170	−	0.0196312i
$144$		0			0
$145$	−2.07320	+	3.59089i	−0.172170	+	0.298207i
$146$		0			0
$147$	−0.500000	−	0.866025i	−0.0412393	−	0.0714286i
$148$		0			0
$149$	1.05656	+	1.83001i	0.0865565	+	0.149920i	0.906053	−	0.423163i	$-0.139080\pi$
$149$	1.05656	+	1.83001i	0.0865565	+	0.149920i	−0.819497	+	0.573084i	$0.805747\pi$
$150$		0			0
$151$	6.10332			0.496681			0.248341	−	0.968673i	$-0.420115\pi$
$151$	6.10332			0.496681			0.248341	+	0.968673i	$0.420115\pi$
$152$		0			0
$153$	−0.0276976	+	0.0479736i	−0.00223921	+	0.00387843i
$154$		0			0
$155$	−16.3992			−1.31722
$156$		0			0
$157$	11.7586			0.938437			0.469218	−	0.883082i	$-0.344536\pi$
$157$	11.7586			0.938437			0.469218	+	0.883082i	$0.344536\pi$
$158$		0			0
$159$	4.12235	−	7.14012i	0.326923	−	0.566248i
$160$		0			0
$161$	3.94881			0.311210
$162$		0			0
$163$	−7.80213	−	13.5137i	−0.611110	−	1.05847i	−0.991054	−	0.133464i	$-0.957390\pi$
$163$	−7.80213	−	13.5137i	−0.611110	−	1.05847i	0.379944	−	0.925010i	$-0.375943\pi$
$164$		0			0
$165$	−0.109943	−	0.190427i	−0.00855906	−	0.0148247i
$166$		0			0
$167$	9.17401	−	15.8898i	0.709906	−	1.22959i	−0.254985	−	0.966945i	$-0.582071\pi$
$167$	9.17401	−	15.8898i	0.709906	−	1.22959i	0.964892	−	0.262649i	$-0.0845960\pi$
$168$		0			0
$169$	12.9913	+	0.474511i	0.999334	+	0.0365009i
$170$		0			0
$171$	0.0975381	−	0.168941i	0.00745893	−	0.0129192i
$172$		0			0
$173$	13.0140	+	22.5410i	0.989439	+	1.71376i	0.620248	+	0.784406i	$0.287032\pi$
$173$	13.0140	+	22.5410i	0.989439	+	1.71376i	0.369191	+	0.929353i	$0.379635\pi$
$174$		0			0
$175$	1.68594	+	2.92013i	0.127445	+	0.220741i
$176$		0			0
$177$	−2.90573			−0.218408
$178$		0			0
$179$	−3.39053	+	5.87257i	−0.253420	+	0.438937i	−0.964465	−	0.264210i	$-0.914889\pi$
$179$	−3.39053	+	5.87257i	−0.253420	+	0.438937i	0.711045	+	0.703147i	$0.248222\pi$
$180$		0			0
$181$	1.97751			0.146987			0.0734937	−	0.997296i	$-0.476585\pi$
$181$	1.97751			0.146987			0.0734937	+	0.997296i	$0.476585\pi$
$182$		0			0
$183$	−7.63296			−0.564245
$184$		0			0
$185$	12.5578	−	21.7508i	0.923269	−	1.59915i
$186$		0			0
$187$	−0.00420977			−0.000307849
$188$		0			0
$189$	0.500000	+	0.866025i	0.0363696	+	0.0629941i
$190$		0			0
$191$	−9.77607	−	16.9327i	−0.707372	−	1.22520i	−0.965829	−	0.259181i	$-0.916547\pi$
$191$	−9.77607	−	16.9327i	−0.707372	−	1.22520i	0.258457	−	0.966023i	$-0.416786\pi$
$192$		0			0
$193$	−9.30135	+	16.1104i	−0.669526	+	1.15965i	0.308511	+	0.951221i	$0.400169\pi$
$193$	−9.30135	+	16.1104i	−0.669526	+	1.15965i	−0.978037	+	0.208432i	$0.933164\pi$
$194$		0			0
$195$	5.38023	−	8.93798i	0.385286	−	0.640062i
$196$		0			0
$197$	−2.29993	+	3.98360i	−0.163863	+	0.283820i	−0.936251	−	0.351332i	$-0.885729\pi$
$197$	−2.29993	+	3.98360i	−0.163863	+	0.283820i	0.772388	+	0.635151i	$0.219062\pi$
$198$		0			0
$199$	−6.90793	−	11.9649i	−0.489690	−	0.848168i	0.510239	−	0.860032i	$-0.329557\pi$
$199$	−6.90793	−	11.9649i	−0.489690	−	0.848168i	−0.999930	+	0.0118642i	$0.996223\pi$
$200$		0			0
$201$	−4.82358	−	8.35468i	−0.340229	−	0.589294i
$202$		0			0
$203$	1.43305			0.100580
$204$		0			0
$205$	−0.618138	+	1.07065i	−0.0431726	+	0.0747772i
$206$		0			0
$207$	−3.94881			−0.274462
$208$		0			0
$209$	0.0148249			0.00102546
$210$		0			0
$211$	−9.26030	+	16.0393i	−0.637506	+	1.10419i	0.348473	+	0.937319i	$0.386700\pi$
$211$	−9.26030	+	16.0393i	−0.637506	+	1.10419i	−0.985978	+	0.166873i	$0.946633\pi$
$212$		0			0
$213$	−0.784324			−0.0537410
$214$		0			0
$215$	−3.03926	−	5.26414i	−0.207275	−	0.359012i
$216$		0			0
$217$	2.83388	+	4.90842i	0.192376	+	0.333205i
$218$		0			0
$219$	−7.00452	+	12.1322i	−0.473322	+	0.819818i
$220$		0			0
$221$	−0.0966910	−	0.174765i	−0.00650414	−	0.0117560i
$222$		0			0
$223$	3.78963	−	6.56383i	0.253772	−	0.439547i	−0.710789	−	0.703405i	$-0.751662\pi$
$223$	3.78963	−	6.56383i	0.253772	−	0.439547i	0.964561	+	0.263859i	$0.0849952\pi$
$224$		0			0
$225$	−1.68594	−	2.92013i	−0.112396	−	0.194675i
$226$		0			0
$227$	6.82157	+	11.8153i	0.452763	+	0.784209i	0.998557	−	0.0537107i	$-0.0171049\pi$
$227$	6.82157	+	11.8153i	0.452763	+	0.784209i	−0.545793	+	0.837920i	$0.683772\pi$
$228$		0			0
$229$	4.20413			0.277816			0.138908	−	0.990305i	$-0.455641\pi$
$229$	4.20413			0.277816			0.138908	+	0.990305i	$0.455641\pi$
$230$		0			0
$231$	−0.0379976	+	0.0658138i	−0.00250006	+	0.00433023i
$232$		0			0
$233$	−4.71317			−0.308770			−0.154385	−	0.988011i	$-0.549340\pi$
$233$	−4.71317			−0.308770			−0.154385	+	0.988011i	$0.549340\pi$
$234$		0			0
$235$	0.451953			0.0294822
$236$		0			0
$237$	5.62024	−	9.73455i	0.365074	−	0.632327i
$238$		0			0
$239$	2.82992			0.183053			0.0915263	−	0.995803i	$-0.470825\pi$
$239$	2.82992			0.183053			0.0915263	+	0.995803i	$0.470825\pi$
$240$		0			0
$241$	−0.568583	−	0.984814i	−0.0366256	−	0.0634375i	0.847132	−	0.531383i	$-0.178328\pi$
$241$	−0.568583	−	0.984814i	−0.0366256	−	0.0634375i	−0.883757	+	0.467946i	$0.844994\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	1.44671	−	2.50577i	0.0924269	−	0.160088i
$246$		0			0
$247$	0.340501	+	0.615443i	0.0216656	+	0.0391597i
$248$		0			0
$249$	−1.77318	+	3.07123i	−0.112370	+	0.194631i
$250$		0			0
$251$	5.95296	+	10.3108i	0.375748	+	0.650814i	0.990439	−	0.137954i	$-0.0440527\pi$
$251$	5.95296	+	10.3108i	0.375748	+	0.650814i	−0.614691	+	0.788768i	$0.710719\pi$
$252$		0			0
$253$	−0.150046	−	0.259887i	−0.00943329	−	0.0163389i
$254$		0			0
$255$	−0.160281			−0.0100372
$256$		0			0
$257$	−14.0108	+	24.2674i	−0.873968	+	1.51376i	−0.0161102	+	0.999870i	$0.505128\pi$
$257$	−14.0108	+	24.2674i	−0.873968	+	1.51376i	−0.857858	+	0.513887i	$0.828205\pi$
$258$		0			0
$259$	−8.68026			−0.539365
$260$		0			0
$261$	−1.43305			−0.0887034
$262$		0			0
$263$	12.5715	−	21.7744i	0.775191	−	1.34267i	−0.159497	−	0.987198i	$-0.550987\pi$
$263$	12.5715	−	21.7744i	0.775191	−	1.34267i	0.934687	−	0.355471i	$-0.115679\pi$
$264$		0			0
$265$	23.8554			1.46542
$266$		0			0
$267$	−7.68930	−	13.3183i	−0.470578	−	0.815064i
$268$		0			0
$269$	−4.29425	−	7.43786i	−0.261825	−	0.453494i	0.704902	−	0.709305i	$-0.250991\pi$
$269$	−4.29425	−	7.43786i	−0.261825	−	0.453494i	−0.966727	+	0.255810i	$0.917658\pi$
$270$		0			0
$271$	13.1348	−	22.7501i	0.797879	−	1.38197i	−0.123115	−	0.992392i	$-0.539288\pi$
$271$	13.1348	−	22.7501i	0.797879	−	1.38197i	0.920995	−	0.389575i	$-0.127378\pi$
$272$		0			0
$273$	−3.60495	−	0.0658138i	−0.218182	−	0.00398323i
$274$		0			0
$275$	0.128123	−	0.221916i	0.00772613	−	0.0133820i
$276$		0			0
$277$	2.53404	+	4.38909i	0.152256	+	0.263715i	0.932056	−	0.362313i	$-0.118013\pi$
$277$	2.53404	+	4.38909i	0.152256	+	0.263715i	−0.779801	+	0.626028i	$0.784680\pi$
$278$		0			0
$279$	−2.83388	−	4.90842i	−0.169660	−	0.293860i
$280$		0			0
$281$	10.8216			0.645565			0.322782	−	0.946473i	$-0.395382\pi$
$281$	10.8216			0.645565			0.322782	+	0.946473i	$0.395382\pi$
$282$		0			0
$283$	−9.32704	+	16.1549i	−0.554435	+	0.960309i	0.443512	+	0.896268i	$0.353732\pi$
$283$	−9.32704	+	16.1549i	−0.554435	+	0.960309i	−0.997947	+	0.0640411i	$0.979601\pi$
$284$		0			0
$285$	0.564437			0.0334344
$286$		0			0
$287$	0.427272			0.0252211
$288$		0			0
$289$	8.49847	−	14.7198i	0.499910	−	0.865869i
$290$		0			0
$291$	−12.0579			−0.706847
$292$		0			0
$293$	−0.259733	−	0.449871i	−0.0151738	−	0.0262817i	0.858339	−	0.513083i	$-0.171497\pi$
$293$	−0.259733	−	0.449871i	−0.0151738	−	0.0262817i	−0.873513	+	0.486802i	$0.838163\pi$
$294$		0			0
$295$	−4.20375	−	7.28110i	−0.244752	−	0.423922i
$296$		0			0
$297$	0.0379976	−	0.0658138i	0.00220485	−	0.00381891i
$298$		0			0
$299$	7.34271	−	12.1982i	0.424640	−	0.705439i
$300$		0			0
$301$	−1.05040	+	1.81935i	−0.0605442	+	0.104866i
$302$		0			0
$303$	−4.88843	−	8.46700i	−0.280833	−	0.486417i
$304$		0			0
$305$	−11.0427	−	19.1265i	−0.632302	−	1.09518i
$306$		0			0
$307$	20.7074			1.18183			0.590917	−	0.806733i	$-0.298766\pi$
$307$	20.7074			1.18183			0.590917	+	0.806733i	$0.298766\pi$
$308$		0			0
$309$	3.28059	−	5.68215i	0.186626	−	0.323246i
$310$		0			0
$311$	−2.87187			−0.162849			−0.0814244	−	0.996680i	$-0.525947\pi$
$311$	−2.87187			−0.162849			−0.0814244	+	0.996680i	$0.525947\pi$
$312$		0			0
$313$	1.27202			0.0718989			0.0359495	−	0.999354i	$-0.488554\pi$
$313$	1.27202			0.0718989			0.0359495	+	0.999354i	$0.488554\pi$
$314$		0			0
$315$	−1.44671	+	2.50577i	−0.0815129	+	0.141184i
$316$		0			0
$317$	−6.69244			−0.375885			−0.187942	−	0.982180i	$-0.560182\pi$
$317$	−6.69244			−0.375885			−0.187942	+	0.982180i	$0.560182\pi$
$318$		0			0
$319$	−0.0544524	−	0.0943143i	−0.00304875	−	0.00528059i
$320$		0			0
$321$	−1.49501	−	2.58943i	−0.0834432	−	0.144528i
$322$		0			0
$323$	0.00540314	−	0.00935850i	0.000300638	−	0.000520721i
$324$		0			0
$325$	12.1554	+	0.221916i	0.674263	+	0.0123097i
$326$		0			0
$327$	0.125236	−	0.216915i	0.00692555	−	0.0119954i
$328$		0			0
$329$	−0.0781001	−	0.135273i	−0.00430580	−	0.00745786i
$330$		0			0
$331$	11.5756	+	20.0496i	0.636254	+	1.10202i	0.986248	+	0.165272i	$0.0528502\pi$
$331$	11.5756	+	20.0496i	0.636254	+	1.10202i	−0.349994	+	0.936752i	$0.613816\pi$
$332$		0			0
$333$	8.68026			0.475675
$334$		0			0
$335$	13.9566	−	24.1736i	0.762533	−	1.32075i
$336$		0			0
$337$	0.501382			0.0273120			0.0136560	−	0.999907i	$-0.495653\pi$
$337$	0.501382			0.0273120			0.0136560	+	0.999907i	$0.495653\pi$
$338$		0			0
$339$	−2.03291			−0.110412
$340$		0			0
$341$	0.215361	−	0.373017i	0.0116625	−	0.0202000i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$	−5.71279	−	9.89484i	−0.307566	−	0.532720i
$346$		0			0
$347$	10.4049	+	18.0218i	0.558563	+	0.967460i	0.997617	+	0.0689991i	$0.0219806\pi$
$347$	10.4049	+	18.0218i	0.558563	+	0.967460i	−0.439053	+	0.898461i	$0.644686\pi$
$348$		0			0
$349$	1.97136	−	3.41450i	0.105524	−	0.182774i	−0.808428	−	0.588595i	$-0.799681\pi$
$349$	1.97136	−	3.41450i	0.105524	−	0.182774i	0.913952	+	0.405821i	$0.133015\pi$
$350$		0			0
$351$	3.60495	+	0.0658138i	0.192418	+	0.00351288i
$352$		0			0
$353$	10.6107	−	18.3783i	0.564752	−	0.978180i	−0.432320	−	0.901720i	$-0.642305\pi$
$353$	10.6107	−	18.3783i	0.564752	−	0.978180i	0.997073	−	0.0764597i	$-0.0243616\pi$
$354$		0			0
$355$	−1.13469	−	1.96534i	−0.0602230	−	0.104309i
$356$		0			0
$357$	0.0276976	+	0.0479736i	0.00146591	+	0.00253903i
$358$		0			0
$359$	−2.08240			−0.109905			−0.0549524	−	0.998489i	$-0.517501\pi$
$359$	−2.08240			−0.109905			−0.0549524	+	0.998489i	$0.517501\pi$
$360$		0			0
$361$	9.48097	−	16.4215i	0.498999	−	0.864291i
$362$		0			0
$363$	−10.9942			−0.577047
$364$		0			0
$365$	−40.5341			−2.12165
$366$		0			0
$367$	−4.05461	+	7.02279i	−0.211649	+	0.366587i	−0.952231	−	0.305379i	$-0.901217\pi$
$367$	−4.05461	+	7.02279i	−0.211649	+	0.366587i	0.740582	+	0.671966i	$0.234550\pi$
$368$		0			0
$369$	−0.427272			−0.0222429
$370$		0			0
$371$	−4.12235	−	7.14012i	−0.214022	−	0.370696i
$372$		0			0
$373$	−1.98251	−	3.43380i	−0.102650	−	0.177796i	0.810125	−	0.586257i	$-0.199399\pi$
$373$	−1.98251	−	3.43380i	−0.102650	−	0.177796i	−0.912776	+	0.408461i	$0.866066\pi$
$374$		0			0
$375$	−2.35542	+	4.07971i	−0.121633	+	0.210675i
$376$		0			0
$377$	2.66471	−	4.42679i	0.137240	−	0.227991i
$378$		0			0
$379$	−6.88343	+	11.9225i	−0.353578	+	0.612416i	−0.986874	−	0.161495i	$-0.948369\pi$
$379$	−6.88343	+	11.9225i	−0.353578	+	0.612416i	0.633295	+	0.773910i	$0.281702\pi$
$380$		0			0
$381$	−4.41612	−	7.64895i	−0.226245	−	0.391868i
$382$		0			0
$383$	10.5320	+	18.2420i	0.538160	+	0.932121i	0.999003	+	0.0446391i	$0.0142138\pi$
$383$	10.5320	+	18.2420i	0.538160	+	0.932121i	−0.460843	+	0.887482i	$0.652453\pi$
$384$		0			0
$385$	−0.219886			−0.0112064
$386$		0			0
$387$	1.05040	−	1.81935i	0.0533950	−	0.0924828i
$388$		0			0
$389$	13.3555			0.677150			0.338575	−	0.940939i	$-0.390055\pi$
$389$	13.3555			0.677150			0.338575	+	0.940939i	$0.390055\pi$
$390$		0			0
$391$	−0.218745			−0.0110624
$392$		0			0
$393$	8.31532	−	14.4026i	0.419452	−	0.726513i
$394$		0			0
$395$	32.5234			1.63643
$396$		0			0
$397$	−2.61494	−	4.52920i	−0.131240	−	0.227314i	0.792915	−	0.609332i	$-0.208562\pi$
$397$	−2.61494	−	4.52920i	−0.131240	−	0.227314i	−0.924155	+	0.382018i	$0.875229\pi$
$398$		0			0
$399$	−0.0975381	−	0.168941i	−0.00488301	−	0.00845763i
$400$		0			0
$401$	−4.00867	+	6.94322i	−0.200183	+	0.346728i	−0.948587	−	0.316515i	$-0.897487\pi$
$401$	−4.00867	+	6.94322i	−0.200183	+	0.346728i	0.748404	+	0.663243i	$0.230820\pi$
$402$		0			0
$403$	20.4320	+	0.373017i	1.01779	+	0.0185813i
$404$		0			0
$405$	1.44671	−	2.50577i	0.0718876	−	0.124513i
$406$		0			0
$407$	0.329829	+	0.571281i	0.0163490	+	0.0283173i
$408$		0			0
$409$	16.7543	+	29.0193i	0.828447	+	1.43491i	0.899256	+	0.437423i	$0.144109\pi$
$409$	16.7543	+	29.0193i	0.828447	+	1.43491i	−0.0708087	+	0.997490i	$0.522558\pi$
$410$		0			0
$411$	−0.951330			−0.0469257
$412$		0			0
$413$	−1.45286	+	2.51644i	−0.0714908	+	0.123826i
$414$		0			0
$415$	−10.2611			−0.503697
$416$		0			0
$417$	−0.780114			−0.0382023
$418$		0			0
$419$	−1.48150	+	2.56604i	−0.0723762	+	0.125359i	−0.899942	−	0.436009i	$-0.856392\pi$
$419$	−1.48150	+	2.56604i	−0.0723762	+	0.125359i	0.827566	+	0.561368i	$0.189725\pi$
$420$		0			0
$421$	−39.3657			−1.91857			−0.959283	−	0.282447i	$-0.908854\pi$
$421$	−39.3657			−1.91857			−0.959283	+	0.282447i	$0.908854\pi$
$422$		0			0
$423$	0.0781001	+	0.135273i	0.00379736	+	0.00657722i
$424$		0			0
$425$	−0.0933927	−	0.161761i	−0.00453021	−	0.00784656i
$426$		0			0
$427$	−3.81648	+	6.61034i	−0.184692	+	0.319897i
$428$		0			0
$429$	0.132648	+	0.239756i	0.00640431	+	0.0115755i
$430$		0			0
$431$	4.27754	−	7.40892i	0.206042	−	0.356875i	−0.744422	−	0.667709i	$-0.767275\pi$
$431$	4.27754	−	7.40892i	0.206042	−	0.356875i	0.950464	+	0.310834i	$0.100608\pi$
$432$		0			0
$433$	3.26828	+	5.66083i	0.157063	+	0.272042i	0.933808	−	0.357773i	$-0.116464\pi$
$433$	3.26828	+	5.66083i	0.157063	+	0.272042i	−0.776745	+	0.629815i	$0.783131\pi$
$434$		0			0
$435$	−2.07320	−	3.59089i	−0.0994025	−	0.172170i
$436$		0			0
$437$	0.770320			0.0368494
$438$		0			0
$439$	16.6458	−	28.8314i	0.794463	−	1.37605i	−0.128717	−	0.991681i	$-0.541086\pi$
$439$	16.6458	−	28.8314i	0.794463	−	1.37605i	0.923180	−	0.384368i	$-0.125581\pi$
$440$		0			0
$441$	1.00000			0.0476190
$442$		0			0
$443$	−23.2762			−1.10589			−0.552944	−	0.833219i	$-0.686495\pi$
$443$	−23.2762			−1.10589			−0.552944	+	0.833219i	$0.686495\pi$
$444$		0			0
$445$	22.2484	−	38.5353i	1.05467	−	1.82675i
$446$		0			0
$447$	−2.11311			−0.0999469
$448$		0			0
$449$	3.58483	+	6.20910i	0.169178	+	0.293026i	0.938131	−	0.346280i	$-0.112555\pi$
$449$	3.58483	+	6.20910i	0.169178	+	0.293026i	−0.768953	+	0.639305i	$0.779222\pi$
$450$		0			0
$451$	−0.0162353	−	0.0281204i	−0.000764491	−	0.00132414i
$452$		0			0
$453$	−3.05166	+	5.28563i	−0.143380	+	0.248341i
$454$		0			0
$455$	−5.05040	−	9.12841i	−0.236767	−	0.427946i
$456$		0			0
$457$	6.30571	−	10.9218i	0.294969	−	0.510901i	−0.680009	−	0.733204i	$-0.738024\pi$
$457$	6.30571	−	10.9218i	0.294969	−	0.510901i	0.974978	+	0.222303i	$0.0713574\pi$
$458$		0			0
$459$	−0.0276976	−	0.0479736i	−0.00129281	−	0.00223921i
$460$		0			0
$461$	6.16456	+	10.6773i	0.287112	+	0.497293i	0.973119	−	0.230302i	$-0.0739715\pi$
$461$	6.16456	+	10.6773i	0.287112	+	0.497293i	−0.686007	+	0.727595i	$0.740638\pi$
$462$		0			0
$463$	7.48537			0.347875			0.173937	−	0.984757i	$-0.444351\pi$
$463$	7.48537			0.347875			0.173937	+	0.984757i	$0.444351\pi$
$464$		0			0
$465$	8.19960	−	14.2021i	0.380247	−	0.658608i
$466$		0			0
$467$	4.42746			0.204879			0.102439	−	0.994739i	$-0.467335\pi$
$467$	4.42746			0.204879			0.102439	+	0.994739i	$0.467335\pi$
$468$		0			0
$469$	−9.64716			−0.445464
$470$		0			0
$471$	−5.87929	+	10.1832i	−0.270903	+	0.469218i
$472$		0			0
$473$	0.159651			0.00734077
$474$		0			0
$475$	0.328887	+	0.569648i	0.0150903	+	0.0261373i
$476$		0			0
$477$	4.12235	+	7.14012i	0.188749	+	0.326923i
$478$		0			0
$479$	7.50330	−	12.9961i	0.342834	−	0.593807i	−0.642123	−	0.766601i	$-0.721946\pi$
$479$	7.50330	−	12.9961i	0.342834	−	0.593807i	0.984958	+	0.172795i	$0.0552797\pi$
$480$		0			0
$481$	−16.1407	+	26.8139i	−0.735952	+	1.22261i
$482$		0			0
$483$	−1.97441	+	3.41977i	−0.0898386	+	0.155605i
$484$		0			0
$485$	−17.4443	−	30.2144i	−0.792105	−	1.37197i
$486$		0			0
$487$	6.07358	+	10.5197i	0.275220	+	0.476695i	0.970191	−	0.242343i	$-0.0779160\pi$
$487$	6.07358	+	10.5197i	0.275220	+	0.476695i	−0.694971	+	0.719038i	$0.744583\pi$
$488$		0			0
$489$	15.6043			0.705649
$490$		0			0
$491$	−13.9394	+	24.1437i	−0.629076	+	1.08959i	0.358661	+	0.933468i	$0.383233\pi$
$491$	−13.9394	+	24.1437i	−0.629076	+	1.08959i	−0.987737	+	0.156124i	$0.950100\pi$
$492$		0			0
$493$	−0.0793838			−0.00357527
$494$		0			0
$495$	0.219886			0.00988315
$496$		0			0
$497$	−0.392162	+	0.679244i	−0.0175909	+	0.0304683i
$498$		0			0
$499$	−2.00673			−0.0898334			−0.0449167	−	0.998991i	$-0.514302\pi$
$499$	−2.00673			−0.0898334			−0.0449167	+	0.998991i	$0.514302\pi$
$500$		0			0
$501$	9.17401	+	15.8898i	0.409864	+	0.709906i
$502$		0			0
$503$	−2.20271	−	3.81520i	−0.0982139	−	0.170111i	0.812732	−	0.582638i	$-0.197980\pi$
$503$	−2.20271	−	3.81520i	−0.0982139	−	0.170111i	−0.910945	+	0.412527i	$0.864646\pi$
$504$		0			0
$505$	14.1443	−	24.4986i	0.629412	−	1.09017i
$506$		0			0
$507$	−6.90661	+	11.0136i	−0.306733	+	0.489130i
$508$		0			0
$509$	−13.4958	+	23.3754i	−0.598191	+	1.03610i	0.394897	+	0.918725i	$0.370780\pi$
$509$	−13.4958	+	23.3754i	−0.598191	+	1.03610i	−0.993088	+	0.117371i	$0.962553\pi$
$510$		0			0
$511$	7.00452	+	12.1322i	0.309862	+	0.536697i
$512$		0			0
$513$	0.0975381	+	0.168941i	0.00430641	+	0.00745893i
$514$		0			0
$515$	18.9842			0.836546
$516$		0			0
$517$	−0.00593524	+	0.0102801i	−0.000261032	+	0.000452120i
$518$		0			0
$519$	−26.0281			−1.14251
$520$		0			0
$521$	−12.0048			−0.525942			−0.262971	−	0.964804i	$-0.584702\pi$
$521$	−12.0048			−0.525942			−0.262971	+	0.964804i	$0.584702\pi$
$522$		0			0
$523$	11.4690	−	19.8649i	0.501505	−	0.868632i	−0.498494	−	0.866893i	$-0.666113\pi$
$523$	11.4690	−	19.8649i	0.501505	−	0.868632i	0.999998	−	0.00173853i	$-0.000553392\pi$
$524$		0			0
$525$	−3.37188			−0.147161
$526$		0			0
$527$	−0.156983	−	0.271903i	−0.00683829	−	0.0118443i
$528$		0			0
$529$	3.70343	+	6.41453i	0.161019	+	0.278893i
$530$		0			0
$531$	1.45286	−	2.51644i	0.0630489	−	0.109204i
$532$		0			0
$533$	0.794500	−	1.31987i	0.0344136	−	0.0571701i
$534$		0			0
$535$	4.32568	−	7.49230i	0.187016	−	0.323921i
$536$		0			0
$537$	−3.39053	−	5.87257i	−0.146312	−	0.253420i
$538$		0			0
$539$	0.0379976	+	0.0658138i	0.00163667	+	0.00283480i
$540$		0			0
$541$	−15.6818			−0.674215			−0.337107	−	0.941466i	$-0.609449\pi$
$541$	−15.6818			−0.674215			−0.337107	+	0.941466i	$0.609449\pi$
$542$		0			0
$543$	−0.988757	+	1.71258i	−0.0424316	+	0.0734937i
$544$		0			0
$545$	0.724719			0.0310435
$546$		0			0
$547$	15.0217			0.642281			0.321140	−	0.947032i	$-0.395934\pi$
$547$	15.0217			0.642281			0.321140	+	0.947032i	$0.395934\pi$
$548$		0			0
$549$	3.81648	−	6.61034i	0.162883	−	0.282122i
$550$		0			0
$551$	0.279553			0.0119094
$552$		0			0
$553$	−5.62024	−	9.73455i	−0.238997	−	0.413955i
$554$		0			0
$555$	12.5578	+	21.7508i	0.533050	+	0.923269i
$556$		0			0
$557$	19.1019	−	33.0854i	0.809371	−	1.40187i	−0.103929	−	0.994585i	$-0.533141\pi$
$557$	19.1019	−	33.0854i	0.809371	−	1.40187i	0.913300	−	0.407288i	$-0.133525\pi$
$558$		0			0
$559$	3.66691	+	6.62780i	0.155094	+	0.280326i
$560$		0			0
$561$	0.00210488	−	0.00364576i	8.88682e−5	−	0.000153924i
$562$		0			0
$563$	−17.3117	−	29.9848i	−0.729603	−	1.26371i	−0.957051	−	0.289919i	$-0.906372\pi$
$563$	−17.3117	−	29.9848i	−0.729603	−	1.26371i	0.227448	−	0.973790i	$-0.426962\pi$
$564$		0			0
$565$	−2.94103	−	5.09401i	−0.123730	−	0.214307i
$566$		0			0
$567$	−1.00000			−0.0419961
$568$		0			0
$569$	1.39747	−	2.42049i	0.0585850	−	0.101472i	−0.835245	−	0.549877i	$-0.814674\pi$
$569$	1.39747	−	2.42049i	0.0585850	−	0.101472i	0.893830	+	0.448405i	$0.148008\pi$
$570$		0			0
$571$	3.32566			0.139175			0.0695873	−	0.997576i	$-0.477832\pi$
$571$	3.32566			0.139175			0.0695873	+	0.997576i	$0.477832\pi$
$572$		0			0
$573$	19.5521			0.816802
$574$		0			0
$575$	6.65746	−	11.5311i	0.277635	−	0.480878i
$576$		0			0
$577$	29.1820			1.21486			0.607430	−	0.794373i	$-0.292200\pi$
$577$	29.1820			1.21486			0.607430	+	0.794373i	$0.292200\pi$
$578$		0			0
$579$	−9.30135	−	16.1104i	−0.386551	−	0.669526i
$580$		0			0
$581$	1.77318	+	3.07123i	0.0735638	+	0.127416i
$582$		0			0
$583$	−0.313279	+	0.542615i	−0.0129747	+	0.0224728i
$584$		0			0
$585$	5.05040	+	9.12841i	0.208808	+	0.377413i
$586$		0			0
$587$	14.7933	−	25.6228i	0.610585	−	1.05756i	−0.380557	−	0.924758i	$-0.624268\pi$
$587$	14.7933	−	25.6228i	0.610585	−	1.05756i	0.991142	−	0.132807i	$-0.0423990\pi$
$588$		0			0
$589$	0.552822	+	0.957517i	0.0227787	+	0.0394538i
$590$		0			0
$591$	−2.29993	−	3.98360i	−0.0946065	−	0.163863i
$592$		0			0
$593$	−22.3788			−0.918987			−0.459493	−	0.888181i	$-0.651969\pi$
$593$	−22.3788			−0.918987			−0.459493	+	0.888181i	$0.651969\pi$
$594$		0			0
$595$	−0.0801406	+	0.138808i	−0.00328545	+	0.00569056i
$596$		0			0
$597$	13.8159			0.565445
$598$		0			0
$599$	11.5677			0.472644			0.236322	−	0.971675i	$-0.424058\pi$
$599$	11.5677			0.472644			0.236322	+	0.971675i	$0.424058\pi$
$600$		0			0
$601$	7.98729	−	13.8344i	0.325808	−	0.564316i	−0.655867	−	0.754876i	$-0.727697\pi$
$601$	7.98729	−	13.8344i	0.325808	−	0.564316i	0.981676	+	0.190560i	$0.0610303\pi$
$602$		0			0
$603$	9.64716			0.392863
$604$		0			0
$605$	−15.9055	−	27.5491i	−0.646649	−	1.12003i
$606$		0			0
$607$	−14.5465	−	25.1952i	−0.590422	−	1.02264i	−0.994175	−	0.107774i	$-0.965628\pi$
$607$	−14.5465	−	25.1952i	−0.590422	−	1.02264i	0.403753	−	0.914868i	$-0.367706\pi$
$608$		0			0
$609$	−0.716524	+	1.24106i	−0.0290350	+	0.0502901i
$610$		0			0
$611$	−0.563094	−	0.0102801i	−0.0227804	−	0.000415890i
$612$		0			0
$613$	19.5774	−	33.9090i	0.790722	−	1.36957i	−0.134799	−	0.990873i	$-0.543039\pi$
$613$	19.5774	−	33.9090i	0.790722	−	1.36957i	0.925520	−	0.378698i	$-0.123628\pi$
$614$		0			0
$615$	−0.618138	−	1.07065i	−0.0249257	−	0.0431726i
$616$		0			0
$617$	−1.70968	−	2.96126i	−0.0688292	−	0.119216i	0.829557	−	0.558422i	$-0.188593\pi$
$617$	−1.70968	−	2.96126i	−0.0688292	−	0.119216i	−0.898386	+	0.439206i	$0.855260\pi$
$618$		0			0
$619$	−21.8671			−0.878911			−0.439456	−	0.898264i	$-0.644829\pi$
$619$	−21.8671			−0.878911			−0.439456	+	0.898264i	$0.644829\pi$
$620$		0			0
$621$	1.97441	−	3.41977i	0.0792302	−	0.137231i
$622$		0			0
$623$	−15.3786			−0.616131
$624$		0			0
$625$	−30.4898			−1.21959
$626$		0			0
$627$	−0.00741243	+	0.0128387i	−0.000296024	+	0.000512729i
$628$		0			0
$629$	0.480844			0.0191725
$630$		0			0
$631$	0.604636	+	1.04726i	0.0240702	+	0.0416907i	0.877810	−	0.479010i	$-0.159004\pi$
$631$	0.604636	+	1.04726i	0.0240702	+	0.0416907i	−0.853739	+	0.520701i	$0.825671\pi$
$632$		0			0
$633$	−9.26030	−	16.0393i	−0.368064	−	0.637506i
$634$		0			0
$635$	12.7777	−	22.1316i	0.507068	−	0.878267i
$636$		0			0
$637$	−1.85947	+	3.08907i	−0.0736750	+	0.122393i
$638$		0			0
$639$	0.392162	−	0.679244i	0.0155137	−	0.0268705i
$640$		0			0
$641$	3.82474	+	6.62465i	0.151068	+	0.261658i	0.931620	−	0.363433i	$-0.118395\pi$
$641$	3.82474	+	6.62465i	0.151068	+	0.261658i	−0.780552	+	0.625091i	$0.785062\pi$
$642$		0			0
$643$	14.4694	+	25.0618i	0.570618	+	0.988339i	0.996503	+	0.0835619i	$0.0266296\pi$
$643$	14.4694	+	25.0618i	0.570618	+	0.988339i	−0.425885	+	0.904778i	$0.640037\pi$
$644$		0			0
$645$	6.07851			0.239341
$646$		0			0
$647$	0.0964998	−	0.167143i	0.00379380	−	0.00657105i	−0.864122	−	0.503282i	$-0.832126\pi$
$647$	0.0964998	−	0.167143i	0.00379380	−	0.00657105i	0.867916	+	0.496711i	$0.165459\pi$
$648$		0			0
$649$	0.220822			0.00866801
$650$		0			0
$651$	−5.66776			−0.222137
$652$		0			0
$653$	15.7160	−	27.2209i	0.615014	−	1.06524i	−0.375368	−	0.926876i	$-0.622483\pi$
$653$	15.7160	−	27.2209i	0.615014	−	1.06524i	0.990382	−	0.138360i	$-0.0441832\pi$
$654$		0			0
$655$	48.1194			1.88018
$656$		0			0
$657$	−7.00452	−	12.1322i	−0.273273	−	0.473322i
$658$		0			0
$659$	−6.55078	−	11.3463i	−0.255182	−	0.441989i	0.709763	−	0.704441i	$-0.248802\pi$
$659$	−6.55078	−	11.3463i	−0.255182	−	0.441989i	−0.964945	+	0.262452i	$0.915469\pi$
$660$		0			0
$661$	−23.2498	+	40.2698i	−0.904312	+	1.56631i	−0.0824741	+	0.996593i	$0.526282\pi$
$661$	−23.2498	+	40.2698i	−0.904312	+	1.56631i	−0.821838	+	0.569721i	$0.807051\pi$
$662$		0			0
$663$	0.199697	+	0.00364576i	0.00775557	+	0.000141590i
$664$		0			0
$665$	0.282219	−	0.488817i	0.0109440	−	0.0189555i
$666$		0			0
$667$	−2.82942	−	4.90070i	−0.109556	−	0.189756i
$668$		0			0
$669$	3.78963	+	6.56383i	0.146516	+	0.253772i
$670$		0			0
$671$	0.580069			0.0223933
$672$		0			0
$673$	−9.02839	+	15.6376i	−0.348019	+	0.602786i	−0.985897	−	0.167351i	$-0.946479\pi$
$673$	−9.02839	+	15.6376i	−0.348019	+	0.602786i	0.637879	+	0.770137i	$0.279812\pi$
$674$		0			0
$675$	3.37188			0.129784
$676$		0			0
$677$	−44.1828			−1.69808			−0.849041	−	0.528327i	$-0.822820\pi$
$677$	−44.1828			−1.69808			−0.849041	+	0.528327i	$0.822820\pi$
$678$		0			0
$679$	−6.02896	+	10.4425i	−0.231370	+	0.400745i
$680$		0			0
$681$	−13.6431			−0.522806
$682$		0			0
$683$	−2.02980	−	3.51572i	−0.0776682	−	0.134525i	0.824575	−	0.565752i	$-0.191414\pi$
$683$	−2.02980	−	3.51572i	−0.0776682	−	0.134525i	−0.902243	+	0.431227i	$0.858081\pi$
$684$		0			0
$685$	−1.37630	−	2.38382i	−0.0525857	−	0.0910810i
$686$		0			0
$687$	−2.10206	+	3.64088i	−0.0801987	+	0.138908i
$688$		0			0
$689$	−29.7217	−	0.542615i	−1.13231	−	0.0206720i
$690$		0			0
$691$	−9.66698	+	16.7437i	−0.367749	+	0.636960i	−0.989213	−	0.146482i	$-0.953205\pi$
$691$	−9.66698	+	16.7437i	−0.367749	+	0.636960i	0.621464	+	0.783443i	$0.286538\pi$
$692$		0			0
$693$	−0.0379976	−	0.0658138i	−0.00144341	−	0.00250006i
$694$		0			0
$695$	−1.12860	−	1.95479i	−0.0428102	−	0.0741494i
$696$		0			0
$697$	−0.0236688			−0.000896518
$698$		0			0
$699$	2.35658	−	4.08172i	0.0891342	−	0.154385i
$700$		0			0
$701$	−32.7040			−1.23521			−0.617607	−	0.786487i	$-0.711898\pi$
$701$	−32.7040			−1.23521			−0.617607	+	0.786487i	$0.711898\pi$
$702$		0			0
$703$	−1.69331			−0.0638645
$704$		0			0
$705$	−0.225976	+	0.391403i	−0.00851077	+	0.0147411i
$706$		0			0
$707$	−9.77685			−0.367696
$708$		0			0
$709$	−5.89719	−	10.2142i	−0.221473	−	0.383603i	0.733782	−	0.679385i	$-0.237753\pi$
$709$	−5.89719	−	10.2142i	−0.221473	−	0.383603i	−0.955256	+	0.295782i	$0.904420\pi$
$710$		0			0
$711$	5.62024	+	9.73455i	0.210776	+	0.365074i
$712$		0			0
$713$	11.1905	−	19.3825i	0.419086	−	0.725878i
$714$		0			0
$715$	−0.408872	+	0.679244i	−0.0152909	+	0.0254023i
$716$		0			0
$717$	−1.41496	+	2.45079i	−0.0528427	+	0.0915263i
$718$		0			0
$719$	−5.07006	−	8.78160i	−0.189081	−	0.327498i	0.755863	−	0.654730i	$-0.227218\pi$
$719$	−5.07006	−	8.78160i	−0.189081	−	0.327498i	−0.944944	+	0.327231i	$0.893884\pi$
$720$		0			0
$721$	−3.28059	−	5.68215i	−0.122176	−	0.211614i
$722$		0			0
$723$	1.13717			0.0422916
$724$		0			0
$725$	2.41603	−	4.18468i	0.0897291	−	0.155415i
$726$		0			0
$727$	−9.75795			−0.361902			−0.180951	−	0.983492i	$-0.557918\pi$
$727$	−9.75795			−0.361902			−0.180951	+	0.983492i	$0.557918\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	0.0581872	−	0.100783i	0.00215213	−	0.00372760i
$732$		0			0
$733$	15.2177			0.562078			0.281039	−	0.959696i	$-0.409321\pi$
$733$	15.2177			0.562078			0.281039	+	0.959696i	$0.409321\pi$
$734$		0			0
$735$	1.44671	+	2.50577i	0.0533627	+	0.0924269i
$736$		0			0
$737$	0.366569	+	0.634916i	0.0135027	+	0.0233874i
$738$		0			0
$739$	24.9158	−	43.1553i	0.916541	−	1.58750i	0.111911	−	0.993718i	$-0.464303\pi$
$739$	24.9158	−	43.1553i	0.916541	−	1.58750i	0.804630	−	0.593777i	$-0.202364\pi$
$740$		0			0
$741$	−0.703240	−	0.0128387i	−0.0258342	−	0.000471642i
$742$		0			0
$743$	9.15256	−	15.8527i	0.335775	−	0.581579i	−0.647858	−	0.761761i	$-0.724335\pi$
$743$	9.15256	−	15.8527i	0.335775	−	0.581579i	0.983633	+	0.180182i	$0.0576685\pi$
$744$		0			0
$745$	−3.05706	−	5.29499i	−0.112002	−	0.193993i
$746$		0			0
$747$	−1.77318	−	3.07123i	−0.0648771	−	0.112370i
$748$		0			0
$749$	−2.99001			−0.109253
$750$		0			0
$751$	−8.93296	+	15.4723i	−0.325968	+	0.564594i	−0.981708	−	0.190394i	$-0.939024\pi$
$751$	−8.93296	+	15.4723i	−0.325968	+	0.564594i	0.655740	+	0.754987i	$0.272357\pi$
$752$		0			0
$753$	−11.9059			−0.433876
$754$		0			0
$755$	−17.6595			−0.642694
$756$		0			0
$757$	−3.99596	+	6.92120i	−0.145236	+	0.251555i	−0.929461	−	0.368921i	$-0.879727\pi$
$757$	−3.99596	+	6.92120i	−0.145236	+	0.251555i	0.784225	+	0.620476i	$0.213061\pi$
$758$		0			0
$759$	0.300091			0.0108926
$760$		0			0
$761$	8.69483	+	15.0599i	0.315187	+	0.545920i	0.979477	−	0.201555i	$-0.0645993\pi$
$761$	8.69483	+	15.0599i	0.315187	+	0.545920i	−0.664290	+	0.747475i	$0.731266\pi$
$762$		0			0
$763$	−0.125236	−	0.216915i	−0.00453384	−	0.00785283i
$764$		0			0
$765$	0.0801406	−	0.138808i	0.00289749	−	0.00501860i
$766$		0			0
$767$	5.07189	+	9.16724i	0.183135	+	0.331010i
$768$		0			0
$769$	−9.25952	+	16.0380i	−0.333907	+	0.578344i	−0.983274	−	0.182131i	$-0.941700\pi$
$769$	−9.25952	+	16.0380i	−0.333907	+	0.578344i	0.649367	+	0.760475i	$0.275034\pi$
$770$		0			0
$771$	−14.0108	−	24.2674i	−0.504586	−	0.873968i
$772$		0			0
$773$	−6.11227	−	10.5868i	−0.219843	−	0.380779i	0.734917	−	0.678157i	$-0.237221\pi$
$773$	−6.11227	−	10.5868i	−0.219843	−	0.380779i	−0.954760	+	0.297378i	$0.903888\pi$
$774$		0			0
$775$	19.1110			0.686487
$776$		0			0
$777$	4.34013	−	7.51732i	0.155701	−	0.269683i
$778$		0			0
$779$	0.0833506			0.00298634
$780$		0			0
$781$	0.0596049			0.00213283
$782$		0			0
$783$	0.716524	−	1.24106i	0.0256065	−	0.0443517i
$784$		0			0
$785$	−34.0225			−1.21432
$786$		0			0
$787$	−13.3060	−	23.0466i	−0.474306	−	0.821523i	0.525261	−	0.850941i	$-0.323968\pi$
$787$	−13.3060	−	23.0466i	−0.474306	−	0.821523i	−0.999567	+	0.0294186i	$0.990634\pi$
$788$		0			0
$789$	12.5715	+	21.7744i	0.447556	+	0.775191i
$790$		0			0
$791$	−1.01645	+	1.76055i	−0.0361410	+	0.0625980i
$792$		0			0
$793$	13.3232	+	24.0811i	0.473120	+	0.855146i
$794$		0			0
$795$	−11.9277	+	20.6594i	−0.423031	+	0.732712i
$796$		0			0
$797$	14.5592	+	25.2172i	0.515712	+	0.893240i	0.999834	+	0.0182389i	$0.00580595\pi$
$797$	14.5592	+	25.2172i	0.515712	+	0.893240i	−0.484121	+	0.875001i	$0.660861\pi$
$798$		0			0
$799$	0.00432637	+	0.00749349i	0.000153056	+	0.000265100i
$800$		0			0
$801$	15.3786			0.543376
$802$		0			0
$803$	0.532311	−	0.921989i	0.0187848	−	0.0325363i
$804$		0			0
$805$	−11.4256			−0.402699
$806$		0			0
$807$	8.58850			0.302330
$808$		0			0
$809$	−0.777701	+	1.34702i	−0.0273425	+	0.0473586i	−0.879373	−	0.476134i	$-0.842038\pi$
$809$	−0.777701	+	1.34702i	−0.0273425	+	0.0473586i	0.852030	+	0.523492i	$0.175371\pi$
$810$		0			0
$811$	15.7871			0.554360			0.277180	−	0.960818i	$-0.410600\pi$
$811$	15.7871			0.554360			0.277180	+	0.960818i	$0.410600\pi$
$812$		0			0
$813$	13.1348	+	22.7501i	0.460656	+	0.797879i
$814$		0			0
$815$	22.5748	+	39.1008i	0.790762	+	1.36964i
$816$		0			0
$817$	−0.204909	+	0.354912i	−0.00716884	+	0.0124168i
$818$		0			0
$819$	1.85947	−	3.08907i	0.0649752	−	0.107941i
$820$		0			0
$821$	−11.2465	+	19.4796i	−0.392507	+	0.679842i	−0.992780	−	0.119953i	$-0.961726\pi$
$821$	−11.2465	+	19.4796i	−0.392507	+	0.679842i	0.600272	+	0.799796i	$0.295059\pi$
$822$		0			0
$823$	−15.3070	−	26.5124i	−0.533567	−	0.924166i	−0.999231	−	0.0392040i	$-0.987518\pi$
$823$	−15.3070	−	26.5124i	−0.533567	−	0.924166i	0.465664	−	0.884962i	$-0.345816\pi$
$824$		0			0
$825$	0.128123	+	0.221916i	0.00446068	+	0.00772613i
$826$		0			0
$827$	29.0345			1.00963			0.504814	−	0.863228i	$-0.331561\pi$
$827$	29.0345			1.00963			0.504814	+	0.863228i	$0.331561\pi$
$828$		0			0
$829$	−3.10285	+	5.37429i	−0.107766	+	0.186657i	−0.914865	−	0.403760i	$-0.867703\pi$
$829$	−3.10285	+	5.37429i	−0.107766	+	0.186657i	0.807099	+	0.590416i	$0.201036\pi$
$830$		0			0
$831$	−5.06809			−0.175810
$832$		0			0
$833$	0.0553951			0.00191933
$834$		0			0
$835$	−26.5443	+	45.9760i	−0.918602	+	1.59107i
$836$		0			0
$837$	5.66776			0.195906
$838$		0			0
$839$	5.97997	+	10.3576i	0.206452	+	0.357584i	0.950594	−	0.310436i	$-0.100475\pi$
$839$	5.97997	+	10.3576i	0.206452	+	0.357584i	−0.744143	+	0.668021i	$0.767142\pi$
$840$		0			0
$841$	13.4732	+	23.3362i	0.464593	+	0.804698i
$842$		0			0
$843$	−5.41082	+	9.37181i	−0.186358	+	0.322782i
$844$		0			0
$845$	−37.5894	−	1.37296i	−1.29311	−	0.0472313i
$846$		0			0
$847$	−5.49711	+	9.52128i	−0.188883	+	0.327155i
$848$		0			0
$849$	−9.32704	−	16.1549i	−0.320103	−	0.554435i
$850$		0			0
$851$	17.1384	+	29.6845i	0.587496	+	1.01757i
$852$		0			0
$853$	24.7369			0.846976			0.423488	−	0.905902i	$-0.360806\pi$
$853$	24.7369			0.846976			0.423488	+	0.905902i	$0.360806\pi$
$854$		0			0
$855$	−0.282219	+	0.488817i	−0.00965168	+	0.0167172i
$856$		0			0
$857$	53.5271			1.82845			0.914225	−	0.405206i	$-0.132800\pi$
$857$	53.5271			1.82845			0.914225	+	0.405206i	$0.132800\pi$
$858$		0			0
$859$	−3.25165			−0.110945			−0.0554725	−	0.998460i	$-0.517667\pi$
$859$	−3.25165			−0.110945			−0.0554725	+	0.998460i	$0.517667\pi$
$860$		0			0
$861$	−0.213636	+	0.370028i	−0.00728069	+	0.0126105i
$862$		0			0
$863$	39.2778			1.33703			0.668516	−	0.743698i	$-0.266930\pi$
$863$	39.2778			1.33703			0.668516	+	0.743698i	$0.266930\pi$
$864$		0			0
$865$	−37.6551	−	65.2205i	−1.28031	−	2.21756i
$866$		0			0
$867$	8.49847	+	14.7198i	0.288623	+	0.499910i
$868$		0			0
$869$	−0.427112	+	0.739779i	−0.0144888	+	0.0250953i
$870$		0			0
$871$	−17.9386	+	29.8008i	−0.607827	+	1.00976i
$872$		0			0
$873$	6.02896	−	10.4425i	0.204049	−	0.353424i
$874$		0			0
$875$	2.35542	+	4.07971i	0.0796278	+	0.137919i
$876$		0			0
$877$	15.2012	+	26.3293i	0.513309	+	0.889077i	0.999881	+	0.0154368i	$0.00491389\pi$
$877$	15.2012	+	26.3293i	0.513309	+	0.889077i	−0.486572	+	0.873641i	$0.661753\pi$
$878$		0			0
$879$	0.519466			0.0175212
$880$		0			0
$881$	−8.98386	+	15.5605i	−0.302674	+	0.524247i	−0.976741	−	0.214424i	$-0.931213\pi$
$881$	−8.98386	+	15.5605i	−0.302674	+	0.524247i	0.674067	+	0.738670i	$0.264546\pi$
$882$		0			0
$883$	−37.1010			−1.24855			−0.624274	−	0.781205i	$-0.714605\pi$
$883$	−37.1010			−1.24855			−0.624274	+	0.781205i	$0.714605\pi$
$884$		0			0
$885$	8.40749			0.282615
$886$		0			0
$887$	−14.1609	+	24.5274i	−0.475476	+	0.823549i	−0.999605	−	0.0280901i	$-0.991057\pi$
$887$	−14.1609	+	24.5274i	−0.475476	+	0.823549i	0.524129	+	0.851639i	$0.324391\pi$
$888$		0			0
$889$	−8.83225			−0.296224
$890$		0			0
$891$	0.0379976	+	0.0658138i	0.00127297	+	0.00220485i
$892$		0			0
$893$	−0.0152355	−	0.0263886i	−0.000509836	−	0.000883062i
$894$		0			0
$895$	9.81023	−	16.9918i	0.327920	−	0.567974i
$896$		0			0
$897$	6.89257	+	12.4581i	0.230136	+	0.415962i
$898$		0			0
$899$	4.06108	−	7.03400i	0.135445	−	0.234597i
$900$		0			0
$901$	0.228358	+	0.395528i	0.00760771	+	0.0131769i
$902$		0			0
$903$	−1.05040	−	1.81935i	−0.0349552	−	0.0605442i
$904$		0			0
$905$	−5.72178			−0.190198
$906$		0			0
$907$	13.0427	−	22.5906i	0.433075	−	0.750108i	−0.564061	−	0.825733i	$-0.690762\pi$
$907$	13.0427	−	22.5906i	0.433075	−	0.750108i	0.997136	+	0.0756248i	$0.0240951\pi$
$908$		0			0
$909$	9.77685			0.324278
$910$		0			0
$911$	−36.8574			−1.22114			−0.610570	−	0.791963i	$-0.709059\pi$
$911$	−36.8574			−1.22114			−0.610570	+	0.791963i	$0.709059\pi$
$912$		0			0
$913$	0.134753	−	0.233399i	0.00445967	−	0.00772438i
$914$		0			0
$915$	22.0854			0.730120
$916$		0			0
$917$	−8.31532	−	14.4026i	−0.274596	−	0.475614i
$918$		0			0
$919$	3.63833	+	6.30177i	0.120017	+	0.207876i	0.919774	−	0.392448i	$-0.128372\pi$
$919$	3.63833	+	6.30177i	0.120017	+	0.207876i	−0.799757	+	0.600324i	$0.795038\pi$
$920$		0			0
$921$	−10.3537	+	17.9331i	−0.341166	+	0.590917i
$922$		0			0
$923$	1.36902	+	2.47445i	0.0450619	+	0.0814476i
$924$		0			0
$925$	−14.6344	+	25.3475i	−0.481175	+	0.833420i
$926$		0			0
$927$	3.28059	+	5.68215i	0.107749	+	0.186626i
$928$		0			0
$929$	25.5662	+	44.2819i	0.838799	+	1.45284i	0.890899	+	0.454201i	$0.150075\pi$
$929$	25.5662	+	44.2819i	0.838799	+	1.45284i	−0.0521003	+	0.998642i	$0.516592\pi$
$930$		0			0
$931$	−0.195076			−0.00639337
$932$		0			0
$933$	1.43593	−	2.48711i	0.0470104	−	0.0814244i
$934$		0			0
$935$	0.0121806			0.000398349
$936$		0			0
$937$	−30.4036			−0.993242			−0.496621	−	0.867967i	$-0.665426\pi$
$937$	−30.4036			−0.993242			−0.496621	+	0.867967i	$0.665426\pi$
$938$		0			0
$939$	−0.636011	+	1.10160i	−0.0207554	+	0.0359495i
$940$		0			0
$941$	−51.0389			−1.66382			−0.831910	−	0.554910i	$-0.812753\pi$
$941$	−51.0389			−1.66382			−0.831910	+	0.554910i	$0.812753\pi$
$942$		0			0
$943$	−0.843609	−	1.46117i	−0.0274717	−	0.0475823i
$944$		0			0
$945$	−1.44671	−	2.50577i	−0.0470615	−	0.0815129i
$946$		0			0
$947$	−14.3146	+	24.7936i	−0.465161	+	0.805682i	−0.999209	−	0.0397719i	$-0.987337\pi$
$947$	−14.3146	+	24.7936i	−0.465161	+	0.805682i	0.534048	+	0.845454i	$0.320670\pi$
$948$		0			0
$949$	50.5019	+	0.921989i	1.63936	+	0.0299290i
$950$		0			0
$951$	3.34622	−	5.79582i	0.108509	−	0.187942i
$952$		0			0
$953$	13.4158	+	23.2369i	0.434581	+	0.752716i	0.997261	−	0.0739585i	$-0.0235632\pi$
$953$	13.4158	+	23.2369i	0.434581	+	0.752716i	−0.562681	+	0.826674i	$0.690230\pi$
$954$		0			0
$955$	28.2863	+	48.9933i	0.915322	+	1.58538i
$956$		0			0
$957$	0.108905			0.00352039
$958$		0			0
$959$	−0.475665	+	0.823876i	−0.0153600	+	0.0266043i
$960$		0			0
$961$	1.12348			0.0362414
$962$		0			0
$963$	2.99001			0.0963519
$964$		0			0
$965$	26.9127	−	46.6142i	0.866351	−	1.50056i
$966$		0			0
$967$	−6.52966			−0.209980			−0.104990	−	0.994473i	$-0.533481\pi$
$967$	−6.52966			−0.209980			−0.104990	+	0.994473i	$0.533481\pi$
$968$		0			0
$969$	0.00540314	+	0.00935850i	0.000173574	+	0.000300638i
$970$		0			0
$971$	13.8045	+	23.9100i	0.443006	+	0.767309i	0.997911	−	0.0646048i	$-0.0205787\pi$
$971$	13.8045	+	23.9100i	0.443006	+	0.767309i	−0.554905	+	0.831914i	$0.687245\pi$
$972$		0			0
$973$	−0.390057	+	0.675598i	−0.0125047	+	0.0216587i
$974$		0			0
$975$	−6.26991	+	10.4160i	−0.200798	+	0.333578i
$976$		0			0
$977$	−23.6308	+	40.9298i	−0.756016	+	1.30946i	0.188851	+	0.982006i	$0.439524\pi$
$977$	−23.6308	+	40.9298i	−0.756016	+	1.30946i	−0.944867	+	0.327453i	$0.893810\pi$
$978$		0			0
$979$	0.584350	+	1.01212i	0.0186759	+	0.0323476i
$980$		0			0
$981$	0.125236	+	0.216915i	0.00399847	+	0.00692555i
$982$		0			0
$983$	−5.84243			−0.186344			−0.0931722	−	0.995650i	$-0.529701\pi$
$983$	−5.84243			−0.186344			−0.0931722	+	0.995650i	$0.529701\pi$
$984$		0			0
$985$	6.65467	−	11.5262i	0.212035	−	0.367256i
$986$		0			0
$987$	0.156200			0.00497191
$988$		0			0
$989$	8.29569			0.263788
$990$		0			0
$991$	−23.9350	+	41.4567i	−0.760321	+	1.31692i	0.182363	+	0.983231i	$0.441625\pi$
$991$	−23.9350	+	41.4567i	−0.760321	+	1.31692i	−0.942685	+	0.333684i	$0.891708\pi$
$992$		0			0
$993$	−23.1512			−0.734683
$994$		0			0
$995$	19.9875	+	34.6194i	0.633648	+	1.09751i
$996$		0			0
$997$	6.33599	+	10.9743i	0.200663	+	0.347558i	0.948742	−	0.316051i	$-0.102357\pi$
$997$	6.33599	+	10.9743i	0.200663	+	0.347558i	−0.748079	+	0.663609i	$0.769024\pi$
$998$		0			0
$999$	−4.34013	+	7.51732i	−0.137316	+	0.237838i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2184.2.bj.h.841.1	✓	8	1.1	even	1	trivial
2184.2.bj.h.1849.1	yes	8	13.3	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} -2.89342 q^{5} +(0.500000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} -2.89342 q^{5} +(0.500000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(0.0379976 - 0.0658138i) q^{11} +(3.60495 + 0.0658138i) q^{13} +(1.44671 - 2.50577i) q^{15} +(-0.0276976 - 0.0479736i) q^{17} +(0.0975381 + 0.168941i) q^{19} -1.00000 q^{21} +(1.97441 - 3.41977i) q^{23} +3.37188 q^{25} +1.00000 q^{27} +(0.716524 - 1.24106i) q^{29} +5.66776 q^{31} +(0.0379976 + 0.0658138i) q^{33} +(-1.44671 - 2.50577i) q^{35} +(-4.34013 + 7.51732i) q^{37} +(-1.85947 + 3.08907i) q^{39} +(0.213636 - 0.370028i) q^{41} +(1.05040 + 1.81935i) q^{43} +(1.44671 + 2.50577i) q^{45} -0.156200 q^{47} +(-0.500000 + 0.866025i) q^{49} +0.0553951 q^{51} -8.24470 q^{53} +(-0.109943 + 0.190427i) q^{55} -0.195076 q^{57} +(1.45286 + 2.51644i) q^{59} +(3.81648 + 6.61034i) q^{61} +(0.500000 - 0.866025i) q^{63} +(-10.4306 - 0.190427i) q^{65} +(-4.82358 + 8.35468i) q^{67} +(1.97441 + 3.41977i) q^{69} +(0.392162 + 0.679244i) q^{71} +14.0090 q^{73} +(-1.68594 + 2.92013i) q^{75} +0.0759953 q^{77} -11.2405 q^{79} +(-0.500000 + 0.866025i) q^{81} +3.54635 q^{83} +(0.0801406 + 0.138808i) q^{85} +(0.716524 + 1.24106i) q^{87} +(-7.68930 + 13.3183i) q^{89} +(1.74548 + 3.15489i) q^{91} +(-2.83388 + 4.90842i) q^{93} +(-0.282219 - 0.488817i) q^{95} +(6.02896 + 10.4425i) q^{97} -0.0759953 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 + 4 * q^5 + 4 * q^7 - 4 * q^9	\( 8 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9} + q^{11} + q^{13} - 2 q^{15} - 3 q^{17} - 2 q^{19} - 8 q^{21} + 5 q^{23} + 4 q^{25} + 8 q^{27} + 20 q^{29} - 2 q^{31} + q^{33} + 2 q^{35} + 6 q^{37} - 2 q^{39} - 7 q^{41} - q^{43} - 2 q^{45} + 12 q^{47} - 4 q^{49} + 6 q^{51} - 20 q^{53} + 12 q^{55} + 4 q^{57} + 5 q^{59} + 2 q^{61} + 4 q^{63} - 26 q^{65} - 17 q^{67} + 5 q^{69} + 8 q^{71} + 16 q^{73} - 2 q^{75} + 2 q^{77} - 60 q^{79} - 4 q^{81} + 4 q^{83} - 7 q^{85} + 20 q^{87} - 10 q^{89} - q^{91} + q^{93} - 20 q^{95} + 19 q^{97} - 2 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 + 4 * q^5 + 4 * q^7 - 4 * q^9 + q^11 + q^13 - 2 * q^15 - 3 * q^17 - 2 * q^19 - 8 * q^21 + 5 * q^23 + 4 * q^25 + 8 * q^27 + 20 * q^29 - 2 * q^31 + q^33 + 2 * q^35 + 6 * q^37 - 2 * q^39 - 7 * q^41 - q^43 - 2 * q^45 + 12 * q^47 - 4 * q^49 + 6 * q^51 - 20 * q^53 + 12 * q^55 + 4 * q^57 + 5 * q^59 + 2 * q^61 + 4 * q^63 - 26 * q^65 - 17 * q^67 + 5 * q^69 + 8 * q^71 + 16 * q^73 - 2 * q^75 + 2 * q^77 - 60 * q^79 - 4 * q^81 + 4 * q^83 - 7 * q^85 + 20 * q^87 - 10 * q^89 - q^91 + q^93 - 20 * q^95 + 19 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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