LMFDB - Embedded newform 1680.2.bg.u.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1680.961");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.bg (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.38363328.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 3x^{4} - 2x^{3} - 21x^{2} - 49x + 343 $ x^6 - x^5 - 3x^4 - 2x^3 - 21x^2 - 49x + 343
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 840)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$-2.33916 - 1.23625i$ of defining polynomial
Character	$\chi$	$=$	1680.961
Dual form			1680.2.bg.u.1201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-2.24021 + 1.40765i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-2.24021 + 1.40765i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-2.74021 - 4.74618i) q^{11} +0.197906 q^{13} -1.00000 q^{15} +(-1.40105 - 2.42668i) q^{17} +(-0.302094 + 0.523243i) q^{19} +(-2.33916 - 1.23625i) q^{21} +(3.93811 - 6.82101i) q^{23} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{27} +10.1587 q^{29} +(-1.83916 - 3.18552i) q^{31} +(2.74021 - 4.74618i) q^{33} +(-0.0989528 - 2.64390i) q^{35} +(2.57937 - 4.46760i) q^{37} +(0.0989528 + 0.171391i) q^{39} +7.08461 q^{41} -4.48042 q^{43} +(-0.500000 - 0.866025i) q^{45} +(-4.33916 + 7.51565i) q^{47} +(3.03707 - 6.30684i) q^{49} +(1.40105 - 2.42668i) q^{51} +(2.53707 + 4.39433i) q^{53} +5.48042 q^{55} -0.604189 q^{57} +(-3.07937 - 5.33362i) q^{59} +(-0.802094 + 1.38927i) q^{61} +(-0.0989528 - 2.64390i) q^{63} +(-0.0989528 + 0.171391i) q^{65} +(1.04230 + 1.80532i) q^{67} +7.87623 q^{69} +10.5546 q^{71} +(-2.43811 - 4.22294i) q^{73} +(0.500000 - 0.866025i) q^{75} +(12.8196 + 6.77519i) q^{77} +(5.64126 - 9.77094i) q^{79} +(-0.500000 - 0.866025i) q^{81} -11.7629 q^{83} +2.80209 q^{85} +(5.07937 + 8.79773i) q^{87} +(-3.59895 + 6.23357i) q^{89} +(-0.443350 + 0.278581i) q^{91} +(1.83916 - 3.18552i) q^{93} +(-0.302094 - 0.523243i) q^{95} +2.39581 q^{97} +5.48042 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 3 q^{5} + 2 q^{7} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 - 3 * q^5 + 2 * q^7 - 3 * q^9	$ 6 q + 3 q^{3} - 3 q^{5} + 2 q^{7} - 3 q^{9} - q^{11} + 2 q^{13} - 6 q^{15} - 8 q^{17} - q^{19} + q^{21} + 9 q^{23} - 3 q^{25} - 6 q^{27} + 4 q^{31} + q^{33} - q^{35} - 15 q^{37} + q^{39} + 10 q^{41} + 4 q^{43} - 3 q^{45} - 11 q^{47} + 4 q^{49} + 8 q^{51} + q^{53} + 2 q^{55} - 2 q^{57} + 12 q^{59} - 4 q^{61} - q^{63} - q^{65} - 10 q^{67} + 18 q^{69} + 4 q^{71} + 3 q^{75} + 31 q^{77} + 18 q^{79} - 3 q^{81} - 8 q^{83} + 16 q^{85} - 22 q^{89} + 14 q^{91} - 4 q^{93} - q^{95} + 16 q^{97} + 2 q^{99}+O(q^{100}) $ 6 * q + 3 * q^3 - 3 * q^5 + 2 * q^7 - 3 * q^9 - q^11 + 2 * q^13 - 6 * q^15 - 8 * q^17 - q^19 + q^21 + 9 * q^23 - 3 * q^25 - 6 * q^27 + 4 * q^31 + q^33 - q^35 - 15 * q^37 + q^39 + 10 * q^41 + 4 * q^43 - 3 * q^45 - 11 * q^47 + 4 * q^49 + 8 * q^51 + q^53 + 2 * q^55 - 2 * q^57 + 12 * q^59 - 4 * q^61 - q^63 - q^65 - 10 * q^67 + 18 * q^69 + 4 * q^71 + 3 * q^75 + 31 * q^77 + 18 * q^79 - 3 * q^81 - 8 * q^83 + 16 * q^85 - 22 * q^89 + 14 * q^91 - 4 * q^93 - q^95 + 16 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	−2.24021	+	1.40765i	−0.846719	+	0.532040i
$7$	−2.24021	+	1.40765i	−0.846719	+	0.532040i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−2.74021	−	4.74618i	−0.826204	−	1.43103i	−0.900996	−	0.433828i	$-0.857163\pi$
$11$	−2.74021	−	4.74618i	−0.826204	−	1.43103i	0.0747918	−	0.997199i	$-0.476171\pi$
$12$		0			0
$13$	0.197906			0.0548891			0.0274446	−	0.999623i	$-0.491263\pi$
$13$	0.197906			0.0548891			0.0274446	+	0.999623i	$0.491263\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	−1.40105	−	2.42668i	−0.339804	−	0.588558i	0.644592	−	0.764527i	$-0.277027\pi$
$17$	−1.40105	−	2.42668i	−0.339804	−	0.588558i	−0.984396	+	0.175969i	$0.943694\pi$
$18$		0			0
$19$	−0.302094	+	0.523243i	−0.0693052	+	0.120040i	−0.898596	−	0.438778i	$-0.855412\pi$
$19$	−0.302094	+	0.523243i	−0.0693052	+	0.120040i	0.829290	+	0.558818i	$0.188745\pi$
$20$		0			0
$21$	−2.33916	−	1.23625i	−0.510447	−	0.269773i
$22$		0			0
$23$	3.93811	−	6.82101i	0.821154	−	1.42228i	−0.0836703	−	0.996493i	$-0.526664\pi$
$23$	3.93811	−	6.82101i	0.821154	−	1.42228i	0.904824	−	0.425786i	$-0.140002\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	10.1587			1.88643			0.943215	−	0.332182i	$-0.107785\pi$
$29$	10.1587			1.88643			0.943215	+	0.332182i	$0.107785\pi$
$30$		0			0
$31$	−1.83916	−	3.18552i	−0.330323	−	0.572136i	0.652252	−	0.758002i	$-0.273824\pi$
$31$	−1.83916	−	3.18552i	−0.330323	−	0.572136i	−0.982575	+	0.185866i	$0.940491\pi$
$32$		0			0
$33$	2.74021	−	4.74618i	0.477009	−	0.826204i
$34$		0			0
$35$	−0.0989528	−	2.64390i	−0.0167261	−	0.446901i
$36$		0			0
$37$	2.57937	−	4.46760i	0.424046	−	0.734469i	−0.572285	−	0.820055i	$-0.693943\pi$
$37$	2.57937	−	4.46760i	0.424046	−	0.734469i	0.996331	+	0.0855860i	$0.0272762\pi$
$38$		0			0
$39$	0.0989528	+	0.171391i	0.0158451	+	0.0274446i
$40$		0			0
$41$	7.08461			1.10643			0.553215	−	0.833039i	$-0.313401\pi$
$41$	7.08461			1.10643			0.553215	+	0.833039i	$0.313401\pi$
$42$		0			0
$43$	−4.48042			−0.683257			−0.341629	−	0.939835i	$-0.610978\pi$
$43$	−4.48042			−0.683257			−0.341629	+	0.939835i	$0.610978\pi$
$44$		0			0
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$		0			0
$47$	−4.33916	+	7.51565i	−0.632932	+	1.09627i	0.354018	+	0.935239i	$0.384815\pi$
$47$	−4.33916	+	7.51565i	−0.632932	+	1.09627i	−0.986949	+	0.161031i	$0.948518\pi$
$48$		0			0
$49$	3.03707	−	6.30684i	0.433867	−	0.900977i
$50$		0			0
$51$	1.40105	−	2.42668i	0.196186	−	0.339804i
$52$		0			0
$53$	2.53707	+	4.39433i	0.348493	+	0.603607i	0.985982	−	0.166852i	$-0.0533602\pi$
$53$	2.53707	+	4.39433i	0.348493	+	0.603607i	−0.637489	+	0.770459i	$0.720027\pi$
$54$		0			0
$55$	5.48042			0.738979
$56$		0			0
$57$	−0.604189			−0.0800267
$58$		0			0
$59$	−3.07937	−	5.33362i	−0.400900	−	0.694379i	0.592935	−	0.805250i	$-0.297969\pi$
$59$	−3.07937	−	5.33362i	−0.400900	−	0.694379i	−0.993835	+	0.110872i	$0.964636\pi$
$60$		0			0
$61$	−0.802094	+	1.38927i	−0.102698	+	0.177878i	−0.912795	−	0.408418i	$-0.866081\pi$
$61$	−0.802094	+	1.38927i	−0.102698	+	0.177878i	0.810098	+	0.586295i	$0.199414\pi$
$62$		0			0
$63$	−0.0989528	−	2.64390i	−0.0124669	−	0.333100i
$64$		0			0
$65$	−0.0989528	+	0.171391i	−0.0122736	+	0.0212585i
$66$		0			0
$67$	1.04230	+	1.80532i	0.127338	+	0.220555i	0.922644	−	0.385652i	$-0.126024\pi$
$67$	1.04230	+	1.80532i	0.127338	+	0.220555i	−0.795307	+	0.606207i	$0.792690\pi$
$68$		0			0
$69$	7.87623			0.948186
$70$		0			0
$71$	10.5546			1.25259			0.626297	−	0.779584i	$-0.284570\pi$
$71$	10.5546			1.25259			0.626297	+	0.779584i	$0.284570\pi$
$72$		0			0
$73$	−2.43811	−	4.22294i	−0.285360	−	0.494257i	0.687337	−	0.726339i	$-0.258780\pi$
$73$	−2.43811	−	4.22294i	−0.285360	−	0.494257i	−0.972696	+	0.232082i	$0.925446\pi$
$74$		0			0
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$		0			0
$77$	12.8196	+	6.77519i	1.46093	+	0.772105i
$78$		0			0
$79$	5.64126	−	9.77094i	0.634691	−	1.09932i	−0.351890	−	0.936041i	$-0.614461\pi$
$79$	5.64126	−	9.77094i	0.634691	−	1.09932i	0.986581	−	0.163275i	$-0.0522059\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−11.7629			−1.29115			−0.645575	−	0.763697i	$-0.723382\pi$
$83$	−11.7629			−1.29115			−0.645575	+	0.763697i	$0.723382\pi$
$84$		0			0
$85$	2.80209			0.303930
$86$		0			0
$87$	5.07937	+	8.79773i	0.544566	+	0.943215i
$88$		0			0
$89$	−3.59895	+	6.23357i	−0.381488	+	0.660757i	−0.991275	−	0.131808i	$-0.957922\pi$
$89$	−3.59895	+	6.23357i	−0.381488	+	0.660757i	0.609787	+	0.792565i	$0.291255\pi$
$90$		0			0
$91$	−0.443350	+	0.278581i	−0.0464757	+	0.0292032i
$92$		0			0
$93$	1.83916	−	3.18552i	0.190712	−	0.330323i
$94$		0			0
$95$	−0.302094	−	0.523243i	−0.0309942	−	0.0536836i
$96$		0			0
$97$	2.39581			0.243258			0.121629	−	0.992576i	$-0.461188\pi$
$97$	2.39581			0.243258			0.121629	+	0.992576i	$0.461188\pi$
$98$		0			0
$99$	5.48042			0.550803
$100$		0			0
$101$	−7.40105	−	12.8190i	−0.736432	−	1.27554i	−0.954092	−	0.299513i	$-0.903176\pi$
$101$	−7.40105	−	12.8190i	−0.736432	−	1.27554i	0.217661	−	0.976025i	$-0.430157\pi$
$102$		0			0
$103$	−0.957697	+	1.65878i	−0.0943647	+	0.163444i	−0.909343	−	0.416047i	$-0.863415\pi$
$103$	−0.957697	+	1.65878i	−0.0943647	+	0.163444i	0.814979	+	0.579491i	$0.196749\pi$
$104$		0			0
$105$	2.24021	−	1.40765i	0.218622	−	0.137372i
$106$		0			0
$107$	−2.07937	+	3.60157i	−0.201020	+	0.348177i	−0.948857	−	0.315705i	$-0.897759\pi$
$107$	−2.07937	+	3.60157i	−0.201020	+	0.348177i	0.747837	+	0.663882i	$0.231092\pi$
$108$		0			0
$109$	−8.31958	−	14.4099i	−0.796871	−	1.38022i	−0.921644	−	0.388036i	$-0.873154\pi$
$109$	−8.31958	−	14.4099i	−0.796871	−	1.38022i	0.124773	−	0.992185i	$-0.460180\pi$
$110$		0			0
$111$	5.15874			0.489646
$112$		0			0
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		0			0
$115$	3.93811	+	6.82101i	0.367231	+	0.636063i
$116$		0			0
$117$	−0.0989528	+	0.171391i	−0.00914819	+	0.0158451i
$118$		0			0
$119$	6.55455	+	3.46410i	0.600855	+	0.317554i
$120$		0			0
$121$	−9.51748	+	16.4848i	−0.865226	+	1.49861i
$122$		0			0
$123$	3.54230	+	6.13545i	0.319399	+	0.553215i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−4.59372			−0.407626			−0.203813	−	0.979010i	$-0.565334\pi$
$127$	−4.59372			−0.407626			−0.203813	+	0.979010i	$0.565334\pi$
$128$		0			0
$129$	−2.24021	−	3.88015i	−0.197239	−	0.341629i
$130$		0			0
$131$	10.4979	−	18.1829i	0.917206	−	1.58865i	0.113566	−	0.993530i	$-0.463773\pi$
$131$	10.4979	−	18.1829i	0.917206	−	1.58865i	0.803639	−	0.595117i	$-0.202894\pi$
$132$		0			0
$133$	−0.0597862	−	1.59741i	−0.00518412	−	0.138513i
$134$		0			0
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$		0			0
$137$	4.88146	+	8.45494i	0.417052	+	0.722355i	0.995641	−	0.0932641i	$-0.0297301\pi$
$137$	4.88146	+	8.45494i	0.417052	+	0.722355i	−0.578590	+	0.815619i	$0.696397\pi$
$138$		0			0
$139$	−20.2433			−1.71702			−0.858509	−	0.512798i	$-0.828609\pi$
$139$	−20.2433			−1.71702			−0.858509	+	0.512798i	$0.828609\pi$
$140$		0			0
$141$	−8.67832			−0.730847
$142$		0			0
$143$	−0.542303	−	0.939296i	−0.0453496	−	0.0785479i
$144$		0			0
$145$	−5.07937	+	8.79773i	−0.421819	+	0.730611i
$146$		0			0
$147$	6.98042	−	0.523243i	0.575735	−	0.0431563i
$148$		0			0
$149$	2.00000	−	3.46410i	0.163846	−	0.283790i	−0.772399	−	0.635138i	$-0.780943\pi$
$149$	2.00000	−	3.46410i	0.163846	−	0.283790i	0.936245	+	0.351348i	$0.114277\pi$
$150$		0			0
$151$	−3.80209	−	6.58542i	−0.309410	−	0.535914i	0.668823	−	0.743421i	$-0.266798\pi$
$151$	−3.80209	−	6.58542i	−0.309410	−	0.535914i	−0.978233	+	0.207507i	$0.933465\pi$
$152$		0			0
$153$	2.80209			0.226536
$154$		0			0
$155$	3.67832			0.295450
$156$		0			0
$157$	−11.1413	−	19.2972i	−0.889169	−	1.54009i	−0.840860	−	0.541253i	$-0.817950\pi$
$157$	−11.1413	−	19.2972i	−0.889169	−	1.54009i	−0.0483095	−	0.998832i	$-0.515383\pi$
$158$		0			0
$159$	−2.53707	+	4.39433i	−0.201202	+	0.348493i
$160$		0			0
$161$	0.779375	+	20.8240i	0.0614234	+	1.64116i
$162$		0			0
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	−0.361619	−	0.932326i	$-0.617776\pi$
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	0.988227	−	0.152992i	$-0.0488907\pi$
$164$		0			0
$165$	2.74021	+	4.74618i	0.213325	+	0.369490i
$166$		0			0
$167$	24.0454			1.86069			0.930346	−	0.366683i	$-0.119507\pi$
$167$	24.0454			1.86069			0.930346	+	0.366683i	$0.119507\pi$
$168$		0			0
$169$	−12.9608			−0.996987
$170$		0			0
$171$	−0.302094	−	0.523243i	−0.0231017	−	0.0400134i
$172$		0			0
$173$	−1.85874	+	3.21944i	−0.141318	+	0.244769i	−0.927993	−	0.372597i	$-0.878467\pi$
$173$	−1.85874	+	3.21944i	−0.141318	+	0.244769i	0.786675	+	0.617367i	$0.211801\pi$
$174$		0			0
$175$	2.33916	+	1.23625i	0.176824	+	0.0934521i
$176$		0			0
$177$	3.07937	−	5.33362i	0.231460	−	0.400900i
$178$		0			0
$179$	−8.33916	−	14.4439i	−0.623298	−	1.07958i	−0.988867	−	0.148800i	$-0.952459\pi$
$179$	−8.33916	−	14.4439i	−0.623298	−	1.07958i	0.365569	−	0.930784i	$-0.380874\pi$
$180$		0			0
$181$	−9.03497			−0.671564			−0.335782	−	0.941940i	$-0.609001\pi$
$181$	−9.03497			−0.671564			−0.335782	+	0.941940i	$0.609001\pi$
$182$		0			0
$183$	−1.60419			−0.118585
$184$		0			0
$185$	2.57937	+	4.46760i	0.189639	+	0.328464i
$186$		0			0
$187$	−7.67832	+	13.2992i	−0.561495	+	0.972537i
$188$		0			0
$189$	2.24021	−	1.40765i	0.162951	−	0.102391i
$190$		0			0
$191$	11.9608	−	20.7168i	0.865456	−	1.49901i	−0.00113863	−	0.999999i	$-0.500362\pi$
$191$	11.9608	−	20.7168i	0.865456	−	1.49901i	0.866594	−	0.499014i	$-0.166304\pi$
$192$		0			0
$193$	−9.31434	−	16.1329i	−0.670461	−	1.16127i	−0.977774	−	0.209664i	$-0.932763\pi$
$193$	−9.31434	−	16.1329i	−0.670461	−	1.16127i	0.307313	−	0.951609i	$-0.400570\pi$
$194$		0			0
$195$	−0.197906			−0.0141723
$196$		0			0
$197$	3.08461			0.219769			0.109885	−	0.993944i	$-0.464952\pi$
$197$	3.08461			0.219769			0.109885	+	0.993944i	$0.464952\pi$
$198$		0			0
$199$	10.4804	+	18.1526i	0.742937	+	1.28680i	0.951152	+	0.308722i	$0.0999012\pi$
$199$	10.4804	+	18.1526i	0.742937	+	1.28680i	−0.208215	+	0.978083i	$0.566765\pi$
$200$		0			0
$201$	−1.04230	+	1.80532i	−0.0735184	+	0.127338i
$202$		0			0
$203$	−22.7577	+	14.2999i	−1.59728	+	1.00366i
$204$		0			0
$205$	−3.54230	+	6.13545i	−0.247405	+	0.428518i
$206$		0			0
$207$	3.93811	+	6.82101i	0.273718	+	0.474093i
$208$		0			0
$209$	3.31121			0.229041
$210$		0			0
$211$	−7.63916			−0.525901			−0.262951	−	0.964809i	$-0.584696\pi$
$211$	−7.63916			−0.525901			−0.262951	+	0.964809i	$0.584696\pi$
$212$		0			0
$213$	5.27728	+	9.14051i	0.361593	+	0.626297i
$214$		0			0
$215$	2.24021	−	3.88015i	0.152781	−	0.264624i
$216$		0			0
$217$	8.60419	+	4.54734i	0.584090	+	0.308694i
$218$		0			0
$219$	2.43811	−	4.22294i	0.164752	−	0.285360i
$220$		0			0
$221$	−0.277275	−	0.480255i	−0.0186515	−	0.0323054i
$222$		0			0
$223$	16.3175			1.09270			0.546350	−	0.837557i	$-0.316017\pi$
$223$	16.3175			1.09270			0.546350	+	0.837557i	$0.316017\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	9.88146	+	17.1152i	0.655856	+	1.13598i	0.981679	+	0.190545i	$0.0610254\pi$
$227$	9.88146	+	17.1152i	0.655856	+	1.13598i	−0.325823	+	0.945431i	$0.605641\pi$
$228$		0			0
$229$	1.51748	−	2.62836i	0.100278	−	0.173687i	−0.811521	−	0.584323i	$-0.801360\pi$
$229$	1.51748	−	2.62836i	0.100278	−	0.173687i	0.911799	+	0.410636i	$0.134693\pi$
$230$		0			0
$231$	0.542303	+	14.4897i	0.0356809	+	0.953351i
$232$		0			0
$233$	8.19791	−	14.1992i	0.537063	−	0.930220i	−0.461998	−	0.886881i	$-0.652867\pi$
$233$	8.19791	−	14.1992i	0.537063	−	0.930220i	0.999060	−	0.0433387i	$-0.0137995\pi$
$234$		0			0
$235$	−4.33916	−	7.51565i	−0.283056	−	0.490267i
$236$		0			0
$237$	11.2825			0.732878
$238$		0			0
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$		0			0
$241$	2.94335	+	5.09803i	0.189598	+	0.328393i	0.945116	−	0.326734i	$-0.105948\pi$
$241$	2.94335	+	5.09803i	0.189598	+	0.328393i	−0.755518	+	0.655127i	$0.772615\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	3.94335	+	5.78360i	0.251931	+	0.369500i
$246$		0			0
$247$	−0.0597862	+	0.103553i	−0.00380410	+	0.00658890i
$248$		0			0
$249$	−5.88146	−	10.1870i	−0.372723	−	0.645575i
$250$		0			0
$251$	9.87623			0.623382			0.311691	−	0.950184i	$-0.399105\pi$
$251$	9.87623			0.623382			0.311691	+	0.950184i	$0.399105\pi$
$252$		0			0
$253$	−43.1650			−2.71376
$254$		0			0
$255$	1.40105	+	2.42668i	0.0877370	+	0.151965i
$256$		0			0
$257$	3.88146	−	6.72289i	0.242119	−	0.419363i	−0.719199	−	0.694805i	$-0.755491\pi$
$257$	3.88146	−	6.72289i	0.242119	−	0.419363i	0.961318	+	0.275442i	$0.0888242\pi$
$258$		0			0
$259$	0.510472	+	13.6392i	0.0317192	+	0.847498i
$260$		0			0
$261$	−5.07937	+	8.79773i	−0.314405	+	0.544566i
$262$		0			0
$263$	−2.80209	−	4.85337i	−0.172785	−	0.299272i	0.766608	−	0.642116i	$-0.221943\pi$
$263$	−2.80209	−	4.85337i	−0.172785	−	0.299272i	−0.939392	+	0.342844i	$0.888610\pi$
$264$		0			0
$265$	−5.07413			−0.311702
$266$		0			0
$267$	−7.19791			−0.440505
$268$		0			0
$269$	−10.8762	−	18.8382i	−0.663135	−	1.14858i	−0.979787	−	0.200042i	$-0.935892\pi$
$269$	−10.8762	−	18.8382i	−0.663135	−	1.14858i	0.316652	−	0.948542i	$-0.397441\pi$
$270$		0			0
$271$	−10.0846	+	17.4670i	−0.612596	+	1.06105i	0.378205	+	0.925722i	$0.376541\pi$
$271$	−10.0846	+	17.4670i	−0.612596	+	1.06105i	−0.990801	+	0.135326i	$0.956792\pi$
$272$		0			0
$273$	−0.462933	−	0.244662i	−0.0280180	−	0.0148076i
$274$		0			0
$275$	−2.74021	+	4.74618i	−0.165241	+	0.286205i
$276$		0			0
$277$	8.11644	+	14.0581i	0.487669	+	0.844668i	0.999899	−	0.0141801i	$-0.00451382\pi$
$277$	8.11644	+	14.0581i	0.487669	+	0.844668i	−0.512230	+	0.858848i	$0.671180\pi$
$278$		0			0
$279$	3.67832			0.220215
$280$		0			0
$281$	−14.6783			−0.875635			−0.437818	−	0.899064i	$-0.644248\pi$
$281$	−14.6783			−0.875635			−0.437818	+	0.899064i	$0.644248\pi$
$282$		0			0
$283$	−2.03183	−	3.51923i	−0.120780	−	0.209197i	0.799296	−	0.600938i	$-0.205206\pi$
$283$	−2.03183	−	3.51923i	−0.120780	−	0.209197i	−0.920075	+	0.391741i	$0.871873\pi$
$284$		0			0
$285$	0.302094	−	0.523243i	0.0178945	−	0.0309942i
$286$		0			0
$287$	−15.8710	+	9.97261i	−0.936835	+	0.588665i
$288$		0			0
$289$	4.57413	−	7.92263i	0.269067	−	0.466037i
$290$		0			0
$291$	1.19791	+	2.07483i	0.0702225	+	0.121629i
$292$		0			0
$293$	2.67832			0.156469			0.0782346	−	0.996935i	$-0.475072\pi$
$293$	2.67832			0.156469			0.0782346	+	0.996935i	$0.475072\pi$
$294$		0			0
$295$	6.15874			0.358576
$296$		0			0
$297$	2.74021	+	4.74618i	0.159003	+	0.275401i
$298$		0			0
$299$	0.779375	−	1.34992i	0.0450724	−	0.0780677i
$300$		0			0
$301$	10.0371	−	6.30684i	0.578527	−	0.363520i
$302$		0			0
$303$	7.40105	−	12.8190i	0.425179	−	0.736432i
$304$		0			0
$305$	−0.802094	−	1.38927i	−0.0459278	−	0.0795493i
$306$		0			0
$307$	−31.1937			−1.78032			−0.890159	−	0.455649i	$-0.849407\pi$
$307$	−31.1937			−1.78032			−0.890159	+	0.455649i	$0.849407\pi$
$308$		0			0
$309$	−1.91539			−0.108963
$310$		0			0
$311$	0.192670	+	0.333714i	0.0109253	+	0.0189232i	0.871436	−	0.490509i	$-0.163189\pi$
$311$	0.192670	+	0.333714i	0.0109253	+	0.0189232i	−0.860511	+	0.509432i	$0.829856\pi$
$312$		0			0
$313$	−4.24021	+	7.34426i	−0.239671	+	0.415122i	−0.960620	−	0.277866i	$-0.910373\pi$
$313$	−4.24021	+	7.34426i	−0.239671	+	0.415122i	0.720949	+	0.692988i	$0.243706\pi$
$314$		0			0
$315$	2.33916	+	1.23625i	0.131797	+	0.0696550i
$316$		0			0
$317$	−13.4360	+	23.2719i	−0.754642	+	1.30708i	0.190910	+	0.981607i	$0.438856\pi$
$317$	−13.4360	+	23.2719i	−0.754642	+	1.30708i	−0.945552	+	0.325470i	$0.894477\pi$
$318$		0			0
$319$	−27.8371	−	48.2152i	−1.55858	−	2.69953i
$320$		0			0
$321$	−4.15874			−0.232118
$322$		0			0
$323$	1.69299			0.0942007
$324$		0			0
$325$	−0.0989528	−	0.171391i	−0.00548891	−	0.00950708i
$326$		0			0
$327$	8.31958	−	14.4099i	0.460074	−	0.796871i
$328$		0			0
$329$	−0.858744	−	22.9446i	−0.0473441	−	1.26498i
$330$		0			0
$331$	−4.58461	+	7.94077i	−0.251993	+	0.436464i	−0.964074	−	0.265632i	$-0.914419\pi$
$331$	−4.58461	+	7.94077i	−0.251993	+	0.436464i	0.712082	+	0.702097i	$0.247753\pi$
$332$		0			0
$333$	2.57937	+	4.46760i	0.141349	+	0.244823i
$334$		0			0
$335$	−2.08461			−0.113894
$336$		0			0
$337$	24.0063			1.30770			0.653852	−	0.756622i	$-0.273152\pi$
$337$	24.0063			1.30770			0.653852	+	0.756622i	$0.273152\pi$
$338$		0			0
$339$	−3.00000	−	5.19615i	−0.162938	−	0.282216i
$340$		0			0
$341$	−10.0794	+	17.4580i	−0.545828	+	0.945403i
$342$		0			0
$343$	2.07413	+	18.4037i	0.111993	+	0.993709i
$344$		0			0
$345$	−3.93811	+	6.82101i	−0.212021	+	0.367231i
$346$		0			0
$347$	−1.71749	−	2.97478i	−0.0921996	−	0.159694i	0.816237	−	0.577718i	$-0.196056\pi$
$347$	−1.71749	−	2.97478i	−0.0921996	−	0.159694i	−0.908436	+	0.418023i	$0.862723\pi$
$348$		0			0
$349$	16.6434			0.890898			0.445449	−	0.895307i	$-0.353044\pi$
$349$	16.6434			0.890898			0.445449	+	0.895307i	$0.353044\pi$
$350$		0			0
$351$	−0.197906			−0.0105634
$352$		0			0
$353$	−3.88146	−	6.72289i	−0.206589	−	0.357823i	0.744049	−	0.668126i	$-0.232903\pi$
$353$	−3.88146	−	6.72289i	−0.206589	−	0.357823i	−0.950638	+	0.310302i	$0.899570\pi$
$354$		0			0
$355$	−5.27728	+	9.14051i	−0.280089	+	0.485128i
$356$		0			0
$357$	0.277275	+	7.40846i	0.0146750	+	0.392097i
$358$		0			0
$359$	−15.0794	+	26.1182i	−0.795859	+	1.37847i	0.126434	+	0.991975i	$0.459647\pi$
$359$	−15.0794	+	26.1182i	−0.795859	+	1.37847i	−0.922292	+	0.386493i	$0.873686\pi$
$360$		0			0
$361$	9.31748	+	16.1383i	0.490394	+	0.849387i
$362$		0			0
$363$	−19.0350			−0.999077
$364$		0			0
$365$	4.87623			0.255233
$366$		0			0
$367$	8.09895	+	14.0278i	0.422762	+	0.732245i	0.996208	−	0.0869979i	$-0.0277273\pi$
$367$	8.09895	+	14.0278i	0.422762	+	0.732245i	−0.573447	+	0.819243i	$0.694394\pi$
$368$		0			0
$369$	−3.54230	+	6.13545i	−0.184405	+	0.319399i
$370$		0			0
$371$	−11.8692	−	6.27292i	−0.616219	−	0.325674i
$372$		0			0
$373$	−1.24021	+	2.14810i	−0.0642156	+	0.111225i	−0.896346	−	0.443356i	$-0.853788\pi$
$373$	−1.24021	+	2.14810i	−0.0642156	+	0.111225i	0.832130	+	0.554580i	$0.187121\pi$
$374$		0			0
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$		0			0
$377$	2.01047			0.103545
$378$		0			0
$379$	−6.92167			−0.355542			−0.177771	−	0.984072i	$-0.556889\pi$
$379$	−6.92167			−0.355542			−0.177771	+	0.984072i	$0.556889\pi$
$380$		0			0
$381$	−2.29686	−	3.97828i	−0.117672	−	0.203813i
$382$		0			0
$383$	2.53707	−	4.39433i	0.129638	−	0.224540i	−0.793898	−	0.608051i	$-0.791952\pi$
$383$	2.53707	−	4.39433i	0.129638	−	0.224540i	0.923536	+	0.383511i	$0.125285\pi$
$384$		0			0
$385$	−12.2773	+	7.71449i	−0.625708	+	0.393167i
$386$		0			0
$387$	2.24021	−	3.88015i	0.113876	−	0.197239i
$388$		0			0
$389$	3.11854	+	5.40146i	0.158116	+	0.273865i	0.934189	−	0.356778i	$-0.116125\pi$
$389$	3.11854	+	5.40146i	0.158116	+	0.273865i	−0.776073	+	0.630643i	$0.782791\pi$
$390$		0			0
$391$	−22.0699			−1.11612
$392$		0			0
$393$	20.9958			1.05910
$394$		0			0
$395$	5.64126	+	9.77094i	0.283842	+	0.491629i
$396$		0			0
$397$	−13.7206	+	23.7648i	−0.688618	+	1.19272i	0.283666	+	0.958923i	$0.408449\pi$
$397$	−13.7206	+	23.7648i	−0.688618	+	1.19272i	−0.972285	+	0.233799i	$0.924884\pi$
$398$		0			0
$399$	1.35351	−	0.850484i	0.0677602	−	0.0425774i
$400$		0			0
$401$	15.4979	−	26.8432i	0.773928	−	1.34048i	−0.161467	−	0.986878i	$-0.551622\pi$
$401$	15.4979	−	26.8432i	0.773928	−	1.34048i	0.935395	−	0.353605i	$-0.115044\pi$
$402$		0			0
$403$	−0.363980	−	0.630432i	−0.0181312	−	0.0314041i
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	−28.2720			−1.40139
$408$		0			0
$409$	13.5175	+	23.4130i	0.668397	+	1.15770i	0.978352	+	0.206946i	$0.0663524\pi$
$409$	13.5175	+	23.4130i	0.668397	+	1.15770i	−0.309956	+	0.950751i	$0.600314\pi$
$410$		0			0
$411$	−4.88146	+	8.45494i	−0.240785	+	0.417052i
$412$		0			0
$413$	14.4063	+	7.61377i	0.708887	+	0.374649i
$414$		0			0
$415$	5.88146	−	10.1870i	0.288710	−	0.500060i
$416$		0			0
$417$	−10.1217	−	17.5313i	−0.495660	−	0.858509i
$418$		0			0
$419$	12.9259			0.631470			0.315735	−	0.948847i	$-0.397749\pi$
$419$	12.9259			0.631470			0.315735	+	0.948847i	$0.397749\pi$
$420$		0			0
$421$	−18.0741			−0.880879			−0.440440	−	0.897782i	$-0.645177\pi$
$421$	−18.0741			−0.880879			−0.440440	+	0.897782i	$0.645177\pi$
$422$		0			0
$423$	−4.33916	−	7.51565i	−0.210977	−	0.365423i
$424$		0			0
$425$	−1.40105	+	2.42668i	−0.0679608	+	0.117712i
$426$		0			0
$427$	−0.158739	−	4.24131i	−0.00768192	−	0.205252i
$428$		0			0
$429$	0.542303	−	0.939296i	0.0261826	−	0.0453496i
$430$		0			0
$431$	17.0454	+	29.5236i	0.821050	+	1.42210i	0.904901	+	0.425622i	$0.139945\pi$
$431$	17.0454	+	29.5236i	0.821050	+	1.42210i	−0.0838512	+	0.996478i	$0.526722\pi$
$432$		0			0
$433$	7.51958			0.361368			0.180684	−	0.983541i	$-0.442169\pi$
$433$	7.51958			0.361368			0.180684	+	0.983541i	$0.442169\pi$
$434$		0			0
$435$	−10.1587			−0.487074
$436$		0			0
$437$	2.37936	+	4.12118i	0.113820	+	0.197143i
$438$		0			0
$439$	9.67832	−	16.7633i	0.461921	−	0.800071i	−0.537136	−	0.843496i	$-0.680494\pi$
$439$	9.67832	−	16.7633i	0.461921	−	0.800071i	0.999057	+	0.0434251i	$0.0138270\pi$
$440$		0			0
$441$	3.94335	+	5.78360i	0.187779	+	0.275409i
$442$		0			0
$443$	−8.15874	+	14.1314i	−0.387633	+	0.671401i	−0.992131	−	0.125206i	$-0.960041\pi$
$443$	−8.15874	+	14.1314i	−0.387633	+	0.671401i	0.604497	+	0.796607i	$0.293374\pi$
$444$		0			0
$445$	−3.59895	−	6.23357i	−0.170607	−	0.295500i
$446$		0			0
$447$	4.00000			0.189194
$448$		0			0
$449$	−25.2433			−1.19131			−0.595654	−	0.803241i	$-0.703107\pi$
$449$	−25.2433			−1.19131			−0.595654	+	0.803241i	$0.703107\pi$
$450$		0			0
$451$	−19.4133	−	33.6248i	−0.914136	−	1.58333i
$452$		0			0
$453$	3.80209	−	6.58542i	0.178638	−	0.309410i
$454$		0			0
$455$	−0.0195833	−	0.523243i	−0.000918080	−	0.0245300i
$456$		0			0
$457$	−14.5122	+	25.1360i	−0.678854	+	1.17581i	0.296472	+	0.955042i	$0.404190\pi$
$457$	−14.5122	+	25.1360i	−0.678854	+	1.17581i	−0.975326	+	0.220769i	$0.929143\pi$
$458$		0			0
$459$	1.40105	+	2.42668i	0.0653953	+	0.113268i
$460$		0			0
$461$	21.3462			0.994190			0.497095	−	0.867696i	$-0.334400\pi$
$461$	21.3462			0.994190			0.497095	+	0.867696i	$0.334400\pi$
$462$		0			0
$463$	20.3462			0.945567			0.472783	−	0.881179i	$-0.343249\pi$
$463$	20.3462			0.945567			0.472783	+	0.881179i	$0.343249\pi$
$464$		0			0
$465$	1.83916	+	3.18552i	0.0852891	+	0.147725i
$466$		0			0
$467$	−19.0350	+	32.9695i	−0.880833	+	1.52565i	−0.0304171	+	0.999537i	$0.509684\pi$
$467$	−19.0350	+	32.9695i	−0.880833	+	1.52565i	−0.850416	+	0.526111i	$0.823650\pi$
$468$		0			0
$469$	−4.87623	−	2.57710i	−0.225163	−	0.119000i
$470$		0			0
$471$	11.1413	−	19.2972i	0.513362	−	0.889169i
$472$		0			0
$473$	12.2773	+	21.2649i	0.564510	+	0.977760i
$474$		0			0
$475$	0.604189			0.0277221
$476$		0			0
$477$	−5.07413			−0.232329
$478$		0			0
$479$	5.88670	+	10.1961i	0.268970	+	0.465870i	0.968596	−	0.248639i	$-0.0799834\pi$
$479$	5.88670	+	10.1961i	0.268970	+	0.465870i	−0.699626	+	0.714509i	$0.746650\pi$
$480$		0			0
$481$	0.510472	−	0.884163i	0.0232755	−	0.0403144i
$482$		0			0
$483$	−17.6444	+	11.0869i	−0.802848	+	0.504473i
$484$		0			0
$485$	−1.19791	+	2.07483i	−0.0543941	+	0.0942133i
$486$		0			0
$487$	13.2010	+	22.8649i	0.598196	+	1.03611i	0.993087	+	0.117378i	$0.0374490\pi$
$487$	13.2010	+	22.8649i	0.598196	+	1.03611i	−0.394891	+	0.918728i	$0.629218\pi$
$488$		0			0
$489$	16.0000			0.723545
$490$		0			0
$491$	24.3175			1.09743			0.548716	−	0.836009i	$-0.315117\pi$
$491$	24.3175			1.09743			0.548716	+	0.836009i	$0.315117\pi$
$492$		0			0
$493$	−14.2329	−	24.6521i	−0.641016	−	1.11027i
$494$		0			0
$495$	−2.74021	+	4.74618i	−0.123163	+	0.213325i
$496$		0			0
$497$	−23.6444	+	14.8571i	−1.06060	+	0.666431i
$498$		0			0
$499$	−11.3300	+	19.6242i	−0.507203	+	0.878501i	0.492763	+	0.870164i	$0.335987\pi$
$499$	−11.3300	+	19.6242i	−0.507203	+	0.878501i	−0.999965	+	0.00833700i	$0.997346\pi$
$500$		0			0
$501$	12.0227	+	20.8240i	0.537135	+	0.930346i
$502$		0			0
$503$	12.9608			0.577895			0.288947	−	0.957345i	$-0.406695\pi$
$503$	12.9608			0.577895			0.288947	+	0.957345i	$0.406695\pi$
$504$		0			0
$505$	14.8021			0.658685
$506$		0			0
$507$	−6.48042	−	11.2244i	−0.287805	−	0.498494i
$508$		0			0
$509$	−16.3671	+	28.3487i	−0.725460	+	1.25653i	0.233325	+	0.972399i	$0.425039\pi$
$509$	−16.3671	+	28.3487i	−0.725460	+	1.25653i	−0.958785	+	0.284134i	$0.908294\pi$
$510$		0			0
$511$	11.4063	+	6.02826i	0.504584	+	0.266674i
$512$		0			0
$513$	0.302094	−	0.523243i	0.0133378	−	0.0231017i
$514$		0			0
$515$	−0.957697	−	1.65878i	−0.0422012	−	0.0730946i
$516$		0			0
$517$	47.5608			2.09172
$518$		0			0
$519$	−3.71749			−0.163180
$520$		0			0
$521$	−12.4238	−	21.5186i	−0.544295	−	0.942747i	−0.998651	−	0.0519265i	$-0.983464\pi$
$521$	−12.4238	−	21.5186i	−0.544295	−	0.942747i	0.454356	−	0.890820i	$-0.349869\pi$
$522$		0			0
$523$	−7.24021	+	12.5404i	−0.316592	+	0.548354i	−0.979775	−	0.200104i	$-0.935872\pi$
$523$	−7.24021	+	12.5404i	−0.316592	+	0.548354i	0.663182	+	0.748458i	$0.269205\pi$
$524$		0			0
$525$	0.0989528	+	2.64390i	0.00431866	+	0.115389i
$526$		0			0
$527$	−5.15350	+	8.92613i	−0.224490	+	0.388828i
$528$		0			0
$529$	−19.5175	−	33.8053i	−0.848586	−	1.46979i
$530$		0			0
$531$	6.15874			0.267267
$532$		0			0
$533$	1.40208			0.0607310
$534$		0			0
$535$	−2.07937	−	3.60157i	−0.0898990	−	0.155710i
$536$		0			0
$537$	8.33916	−	14.4439i	0.359861	−	0.623298i
$538$		0			0
$539$	−38.2556	+	2.86759i	−1.64778	+	0.123516i
$540$		0			0
$541$	5.51748	−	9.55656i	0.237215	−	0.410869i	−0.722699	−	0.691163i	$-0.757099\pi$
$541$	5.51748	−	9.55656i	0.237215	−	0.410869i	0.959914	+	0.280294i	$0.0904320\pi$
$542$		0			0
$543$	−4.51748	−	7.82451i	−0.193864	−	0.335782i
$544$		0			0
$545$	16.6392			0.712743
$546$		0			0
$547$	13.1091			0.560505			0.280252	−	0.959926i	$-0.409582\pi$
$547$	13.1091			0.560505			0.280252	+	0.959926i	$0.409582\pi$
$548$		0			0
$549$	−0.802094	−	1.38927i	−0.0342326	−	0.0592925i
$550$		0			0
$551$	−3.06890	+	5.31549i	−0.130739	+	0.226447i
$552$		0			0
$553$	1.11644	+	29.8298i	0.0474757	+	1.26849i
$554$		0			0
$555$	−2.57937	+	4.46760i	−0.109488	+	0.189639i
$556$		0			0
$557$	1.54754	+	2.68042i	0.0655713	+	0.113573i	0.896947	−	0.442138i	$-0.145780\pi$
$557$	1.54754	+	2.68042i	0.0655713	+	0.113573i	−0.831376	+	0.555710i	$0.812446\pi$
$558$		0			0
$559$	−0.886700			−0.0375034
$560$		0			0
$561$	−15.3566			−0.648358
$562$		0			0
$563$	−7.39581	−	12.8099i	−0.311696	−	0.539874i	0.667033	−	0.745028i	$-0.267564\pi$
$563$	−7.39581	−	12.8099i	−0.311696	−	0.539874i	−0.978730	+	0.205154i	$0.934230\pi$
$564$		0			0
$565$	3.00000	−	5.19615i	0.126211	−	0.218604i
$566$		0			0
$567$	2.33916	+	1.23625i	0.0982355	+	0.0519178i
$568$		0			0
$569$	9.54230	−	16.5278i	0.400034	−	0.692879i	−0.593695	−	0.804690i	$-0.702332\pi$
$569$	9.54230	−	16.5278i	0.400034	−	0.692879i	0.993730	+	0.111810i	$0.0356649\pi$
$570$		0			0
$571$	−13.3937	−	23.1986i	−0.560509	−	0.970831i	−0.997452	−	0.0713413i	$-0.977272\pi$
$571$	−13.3937	−	23.1986i	−0.560509	−	0.970831i	0.436943	−	0.899489i	$-0.356061\pi$
$572$		0			0
$573$	23.9217			0.999342
$574$		0			0
$575$	−7.87623			−0.328461
$576$		0			0
$577$	6.11644	+	10.5940i	0.254631	+	0.441033i	0.964795	−	0.263003i	$-0.0847128\pi$
$577$	6.11644	+	10.5940i	0.254631	+	0.441033i	−0.710165	+	0.704036i	$0.751379\pi$
$578$		0			0
$579$	9.31434	−	16.1329i	0.387091	−	0.670461i
$580$		0			0
$581$	26.3514	−	16.5580i	1.09324	−	0.686943i
$582$		0			0
$583$	13.9042	−	24.0828i	0.575852	−	0.997406i
$584$		0			0
$585$	−0.0989528	−	0.171391i	−0.00409120	−	0.00708616i
$586$		0			0
$587$	45.7629			1.88884			0.944419	−	0.328744i	$-0.106625\pi$
$587$	45.7629			1.88884			0.944419	+	0.328744i	$0.106625\pi$
$588$		0			0
$589$	2.22240			0.0915724
$590$		0			0
$591$	1.54230	+	2.67135i	0.0634419	+	0.109885i
$592$		0			0
$593$	6.67309	−	11.5581i	0.274031	−	0.474635i	−0.695859	−	0.718178i	$-0.744976\pi$
$593$	6.67309	−	11.5581i	0.274031	−	0.474635i	0.969890	+	0.243543i	$0.0783096\pi$
$594$		0			0
$595$	−6.27728	+	3.94436i	−0.257343	+	0.161703i
$596$		0			0
$597$	−10.4804	+	18.1526i	−0.428935	+	0.742937i
$598$		0			0
$599$	−9.48042	−	16.4206i	−0.387359	−	0.670926i	0.604734	−	0.796427i	$-0.293279\pi$
$599$	−9.48042	−	16.4206i	−0.387359	−	0.670926i	−0.992093	+	0.125501i	$0.959946\pi$
$600$		0			0
$601$	27.9958			1.14197			0.570986	−	0.820960i	$-0.306561\pi$
$601$	27.9958			1.14197			0.570986	+	0.820960i	$0.306561\pi$
$602$		0			0
$603$	−2.08461			−0.0848917
$604$		0			0
$605$	−9.51748	−	16.4848i	−0.386941	−	0.670201i
$606$		0			0
$607$	−20.1836	+	34.9589i	−0.819225	+	1.41894i	0.0870284	+	0.996206i	$0.472263\pi$
$607$	−20.1836	+	34.9589i	−0.819225	+	1.41894i	−0.906254	+	0.422734i	$0.861070\pi$
$608$		0			0
$609$	−23.7629	−	12.5588i	−0.962922	−	0.508908i
$610$		0			0
$611$	−0.858744	+	1.48739i	−0.0347411	+	0.0601733i
$612$		0			0
$613$	−10.5371	−	18.2507i	−0.425588	−	0.737140i	0.570887	−	0.821029i	$-0.306599\pi$
$613$	−10.5371	−	18.2507i	−0.425588	−	0.737140i	−0.996475	+	0.0838884i	$0.973266\pi$
$614$		0			0
$615$	−7.08461			−0.285679
$616$		0			0
$617$	−18.8825			−0.760181			−0.380090	−	0.924949i	$-0.624107\pi$
$617$	−18.8825			−0.760181			−0.380090	+	0.924949i	$0.624107\pi$
$618$		0			0
$619$	−14.8671	−	25.7506i	−0.597560	−	1.03500i	−0.993180	−	0.116590i	$-0.962804\pi$
$619$	−14.8671	−	25.7506i	−0.597560	−	1.03500i	0.395620	−	0.918414i	$-0.370530\pi$
$620$		0			0
$621$	−3.93811	+	6.82101i	−0.158031	+	0.273718i
$622$		0			0
$623$	−0.712253	−	19.0305i	−0.0285358	−	0.762443i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	1.65560	+	2.86759i	0.0661184	+	0.114520i
$628$		0			0
$629$	−14.4553			−0.576369
$630$		0			0
$631$	−36.8616			−1.46744			−0.733718	−	0.679454i	$-0.762217\pi$
$631$	−36.8616			−1.46744			−0.733718	+	0.679454i	$0.762217\pi$
$632$		0			0
$633$	−3.81958	−	6.61570i	−0.151815	−	0.262951i
$634$		0			0
$635$	2.29686	−	3.97828i	0.0911480	−	0.157873i
$636$		0			0
$637$	0.601053	−	1.24816i	0.0238146	−	0.0494539i
$638$		0			0
$639$	−5.27728	+	9.14051i	−0.208766	+	0.361593i
$640$		0			0
$641$	−11.3794	−	19.7096i	−0.449458	−	0.778484i	0.548893	−	0.835893i	$-0.315049\pi$
$641$	−11.3794	−	19.7096i	−0.449458	−	0.778484i	−0.998351	+	0.0574088i	$0.981716\pi$
$642$		0			0
$643$	−8.55875			−0.337524			−0.168762	−	0.985657i	$-0.553977\pi$
$643$	−8.55875			−0.337524			−0.168762	+	0.985657i	$0.553977\pi$
$644$		0			0
$645$	4.48042			0.176416
$646$		0			0
$647$	17.3794	+	30.1019i	0.683253	+	1.18343i	0.973982	+	0.226624i	$0.0727689\pi$
$647$	17.3794	+	30.1019i	0.683253	+	1.18343i	−0.290729	+	0.956805i	$0.593898\pi$
$648$		0			0
$649$	−16.8762	+	29.2305i	−0.662450	+	1.14740i
$650$		0			0
$651$	0.363980	+	9.72512i	0.0142655	+	0.381157i
$652$		0			0
$653$	23.8989	−	41.3942i	0.935238	−	1.61988i	0.161029	−	0.986950i	$-0.448519\pi$
$653$	23.8989	−	41.3942i	0.935238	−	1.61988i	0.774209	−	0.632930i	$-0.218148\pi$
$654$		0			0
$655$	10.4979	+	18.1829i	0.410187	+	0.710465i
$656$		0			0
$657$	4.87623			0.190240
$658$		0			0
$659$	8.79162			0.342473			0.171236	−	0.985230i	$-0.445224\pi$
$659$	8.79162			0.342473			0.171236	+	0.985230i	$0.445224\pi$
$660$		0			0
$661$	7.23497	+	12.5313i	0.281408	+	0.487413i	0.971732	−	0.236088i	$-0.0758653\pi$
$661$	7.23497	+	12.5313i	0.281408	+	0.487413i	−0.690324	+	0.723500i	$0.742532\pi$
$662$		0			0
$663$	0.277275	−	0.480255i	0.0107685	−	0.0186515i
$664$		0			0
$665$	1.41329	+	0.746931i	0.0548052	+	0.0289647i
$666$		0			0
$667$	40.0063	−	69.2929i	1.54905	−	2.68303i
$668$		0			0
$669$	8.15874	+	14.1314i	0.315435	+	0.546350i
$670$		0			0
$671$	8.79162			0.339397
$672$		0			0
$673$	−6.87623			−0.265059			−0.132530	−	0.991179i	$-0.542310\pi$
$673$	−6.87623			−0.265059			−0.132530	+	0.991179i	$0.542310\pi$
$674$		0			0
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$		0			0
$677$	−11.6906	+	20.2487i	−0.449305	+	0.778219i	−0.998341	−	0.0575796i	$-0.981662\pi$
$677$	−11.6906	+	20.2487i	−0.449305	+	0.778219i	0.549036	+	0.835799i	$0.314995\pi$
$678$		0			0
$679$	−5.36712	+	3.37245i	−0.205971	+	0.129423i
$680$		0			0
$681$	−9.88146	+	17.1152i	−0.378659	+	0.655856i
$682$		0			0
$683$	−2.59895	−	4.50152i	−0.0994462	−	0.172246i	0.812009	−	0.583644i	$-0.198374\pi$
$683$	−2.59895	−	4.50152i	−0.0994462	−	0.172246i	−0.911456	+	0.411399i	$0.865040\pi$
$684$		0			0
$685$	−9.76293			−0.373022
$686$		0			0
$687$	3.03497			0.115791
$688$		0			0
$689$	0.502100	+	0.869662i	0.0191285	+	0.0331315i
$690$		0			0
$691$	0.923767	−	1.60001i	0.0351417	−	0.0608673i	−0.847920	−	0.530125i	$-0.822145\pi$
$691$	0.923767	−	1.60001i	0.0351417	−	0.0608673i	0.883061	+	0.469258i	$0.155478\pi$
$692$		0			0
$693$	−12.2773	+	7.71449i	−0.466375	+	0.293049i
$694$		0			0
$695$	10.1217	−	17.5313i	0.383937	−	0.664998i
$696$		0			0
$697$	−9.92587	−	17.1921i	−0.375969	−	0.651197i
$698$		0			0
$699$	16.3958			0.620147
$700$		0			0
$701$	−20.0105			−0.755785			−0.377893	−	0.925849i	$-0.623351\pi$
$701$	−20.0105			−0.755785			−0.377893	+	0.925849i	$0.623351\pi$
$702$		0			0
$703$	1.55843	+	2.69927i	0.0587771	+	0.101805i
$704$		0			0
$705$	4.33916	−	7.51565i	0.163422	−	0.283056i
$706$		0			0
$707$	34.6245	+	18.2992i	1.30219	+	0.688211i
$708$		0			0
$709$	−7.19791	+	12.4671i	−0.270323	+	0.468213i	−0.968945	−	0.247278i	$-0.920464\pi$
$709$	−7.19791	+	12.4671i	−0.270323	+	0.468213i	0.698621	+	0.715491i	$0.253797\pi$
$710$		0			0
$711$	5.64126	+	9.77094i	0.211564	+	0.366439i
$712$		0			0
$713$	−28.9713			−1.08498
$714$		0			0
$715$	1.08461			0.0405619
$716$		0			0
$717$	3.00000	+	5.19615i	0.112037	+	0.194054i
$718$		0			0
$719$	6.19791	−	10.7351i	0.231143	−	0.400351i	−0.727002	−	0.686636i	$-0.759087\pi$
$719$	6.19791	−	10.7351i	0.231143	−	0.400351i	0.958145	+	0.286284i	$0.0924202\pi$
$720$		0			0
$721$	−0.189534	−	5.06411i	−0.00705860	−	0.188597i
$722$		0			0
$723$	−2.94335	+	5.09803i	−0.109464	+	0.189598i
$724$		0			0
$725$	−5.07937	−	8.79773i	−0.188643	−	0.326739i
$726$		0			0
$727$	39.2287			1.45491			0.727455	−	0.686155i	$-0.240703\pi$
$727$	39.2287			1.45491			0.727455	+	0.686155i	$0.240703\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	6.27728	+	10.8726i	0.232173	+	0.402136i
$732$		0			0
$733$	−0.222725	+	0.385771i	−0.00822653	+	0.0142488i	−0.870109	−	0.492859i	$-0.835952\pi$
$733$	−0.222725	+	0.385771i	−0.00822653	+	0.0142488i	0.861883	+	0.507107i	$0.169285\pi$
$734$		0			0
$735$	−3.03707	+	6.30684i	−0.112024	+	0.232631i
$736$		0			0
$737$	5.71225	−	9.89391i	0.210414	−	0.364447i
$738$		0			0
$739$	−3.10419	−	5.37661i	−0.114189	−	0.197782i	0.803266	−	0.595620i	$-0.203094\pi$
$739$	−3.10419	−	5.37661i	−0.114189	−	0.197782i	−0.917455	+	0.397839i	$0.869760\pi$
$740$		0			0
$741$	−0.119572			−0.00439260
$742$		0			0
$743$	33.9462			1.24536			0.622682	−	0.782475i	$-0.286043\pi$
$743$	33.9462			1.24536			0.622682	+	0.782475i	$0.286043\pi$
$744$		0			0
$745$	2.00000	+	3.46410i	0.0732743	+	0.126915i
$746$		0			0
$747$	5.88146	−	10.1870i	0.215192	−	0.372723i
$748$		0			0
$749$	−0.411519	−	10.9953i	−0.0150366	−	0.401759i
$750$		0			0
$751$	−17.6021	+	30.4877i	−0.642309	+	1.11251i	0.342607	+	0.939479i	$0.388690\pi$
$751$	−17.6021	+	30.4877i	−0.642309	+	1.11251i	−0.984916	+	0.173033i	$0.944643\pi$
$752$		0			0
$753$	4.93811	+	8.55306i	0.179955	+	0.311691i
$754$		0			0
$755$	7.60419			0.276745
$756$		0			0
$757$	52.7133			1.91590			0.957949	−	0.286940i	$-0.0926381\pi$
$757$	52.7133			1.91590			0.957949	+	0.286940i	$0.0926381\pi$
$758$		0			0
$759$	−21.5825	−	37.3820i	−0.783395	−	1.35688i
$760$		0			0
$761$	16.5773	−	28.7127i	0.600926	−	1.04083i	−0.391756	−	0.920069i	$-0.628132\pi$
$761$	16.5773	−	28.7127i	0.600926	−	1.04083i	0.992681	−	0.120764i	$-0.0385345\pi$
$762$		0			0
$763$	38.9217	+	20.5702i	1.40906	+	0.744692i
$764$		0			0
$765$	−1.40105	+	2.42668i	−0.0506550	+	0.0877370i
$766$		0			0
$767$	−0.609425	−	1.05555i	−0.0220050	−	0.0381139i
$768$		0			0
$769$	12.4350			0.448417			0.224208	−	0.974541i	$-0.428020\pi$
$769$	12.4350			0.448417			0.224208	+	0.974541i	$0.428020\pi$
$770$		0			0
$771$	7.76293			0.279575
$772$		0			0
$773$	17.3794	+	30.1019i	0.625092	+	1.08269i	0.988523	+	0.151070i	$0.0482720\pi$
$773$	17.3794	+	30.1019i	0.625092	+	1.08269i	−0.363431	+	0.931621i	$0.618395\pi$
$774$		0			0
$775$	−1.83916	+	3.18552i	−0.0660646	+	0.114427i
$776$		0			0
$777$	−11.5567	+	7.26168i	−0.414593	+	0.260511i
$778$		0			0
$779$	−2.14022	+	3.70697i	−0.0766813	+	0.132816i
$780$		0			0
$781$	−28.9217	−	50.0938i	−1.03490	−	1.79250i
$782$		0			0
$783$	−10.1587			−0.363044
$784$		0			0
$785$	22.2825			0.795297
$786$		0			0
$787$	6.91539	+	11.9778i	0.246507	+	0.426963i	0.962554	−	0.271089i	$-0.0873838\pi$
$787$	6.91539	+	11.9778i	0.246507	+	0.426963i	−0.716047	+	0.698052i	$0.754050\pi$
$788$		0			0
$789$	2.80209	−	4.85337i	0.0997572	−	0.172785i
$790$		0			0
$791$	13.4413	−	8.44587i	0.477916	−	0.300301i
$792$		0			0
$793$	−0.158739	+	0.274944i	−0.00563699	+	0.00976355i
$794$		0			0
$795$	−2.53707	−	4.39433i	−0.0899805	−	0.155851i
$796$		0			0
$797$	−31.6846			−1.12233			−0.561163	−	0.827705i	$-0.689646\pi$
$797$	−31.6846			−1.12233			−0.561163	+	0.827705i	$0.689646\pi$
$798$		0			0
$799$	24.3175			0.860291
$800$		0			0
$801$	−3.59895	−	6.23357i	−0.127163	−	0.220252i
$802$		0			0
$803$	−13.3619	+	23.1435i	−0.471531	+	0.816715i
$804$		0			0
$805$	−18.4238	−	9.73702i	−0.649352	−	0.343185i
$806$		0			0
$807$	10.8762	−	18.8382i	0.382861	−	0.663135i
$808$		0			0
$809$	10.5084	+	18.2010i	0.369455	+	0.639914i	0.989480	−	0.144667i	$-0.0462112\pi$
$809$	10.5084	+	18.2010i	0.369455	+	0.639914i	−0.620026	+	0.784582i	$0.712878\pi$
$810$		0			0
$811$	39.3916			1.38323			0.691613	−	0.722268i	$-0.256900\pi$
$811$	39.3916			1.38323			0.691613	+	0.722268i	$0.256900\pi$
$812$		0			0
$813$	−20.1692			−0.707365
$814$		0			0
$815$	8.00000	+	13.8564i	0.280228	+	0.485369i
$816$		0			0
$817$	1.35351	−	2.34435i	0.0473533	−	0.0820183i
$818$		0			0
$819$	−0.0195833	−	0.523243i	−0.000684297	−	0.0182836i
$820$		0			0
$821$	23.4360	−	40.5924i	0.817923	−	1.41668i	−0.0892877	−	0.996006i	$-0.528459\pi$
$821$	23.4360	−	40.5924i	0.817923	−	1.41668i	0.907210	−	0.420678i	$-0.138208\pi$
$822$		0			0
$823$	−13.6783	−	23.6915i	−0.476796	−	0.825835i	0.522850	−	0.852425i	$-0.324869\pi$
$823$	−13.6783	−	23.6915i	−0.476796	−	0.825835i	−0.999646	+	0.0265892i	$0.991535\pi$
$824$		0			0
$825$	−5.48042			−0.190804
$826$		0			0
$827$	−54.3175			−1.88880			−0.944402	−	0.328793i	$-0.893358\pi$
$827$	−54.3175			−1.88880			−0.944402	+	0.328793i	$0.893358\pi$
$828$		0			0
$829$	−11.0084	−	19.0671i	−0.382337	−	0.662226i	0.609059	−	0.793125i	$-0.291547\pi$
$829$	−11.0084	−	19.0671i	−0.382337	−	0.662226i	−0.991396	+	0.130898i	$0.958214\pi$
$830$		0			0
$831$	−8.11644	+	14.0581i	−0.281556	+	0.487669i
$832$		0			0
$833$	−19.5598	+	1.46618i	−0.677706	+	0.0508000i
$834$		0			0
$835$	−12.0227	+	20.8240i	−0.416063	+	0.720643i
$836$		0			0
$837$	1.83916	+	3.18552i	0.0635707	+	0.110108i
$838$		0			0
$839$	38.1587			1.31739			0.658693	−	0.752412i	$-0.271110\pi$
$839$	38.1587			1.31739			0.658693	+	0.752412i	$0.271110\pi$
$840$		0			0
$841$	74.2000			2.55862
$842$		0			0
$843$	−7.33916	−	12.7118i	−0.252774	−	0.437818i
$844$		0			0
$845$	6.48042	−	11.2244i	0.222933	−	0.386131i
$846$		0			0
$847$	−1.88356	−	50.3266i	−0.0647200	−	1.72924i
$848$		0			0
$849$	2.03183	−	3.51923i	0.0697323	−	0.120780i
$850$		0			0
$851$	−20.3157	−	35.1878i	−0.696413	−	1.20622i
$852$		0			0
$853$	−49.7937			−1.70490			−0.852452	−	0.522806i	$-0.824885\pi$
$853$	−49.7937			−1.70490			−0.852452	+	0.522806i	$0.824885\pi$
$854$		0			0
$855$	0.604189			0.0206628
$856$		0			0
$857$	−5.26680	−	9.12237i	−0.179911	−	0.311614i	0.761939	−	0.647649i	$-0.224248\pi$
$857$	−5.26680	−	9.12237i	−0.179911	−	0.311614i	−0.941850	+	0.336034i	$0.890914\pi$
$858$		0			0
$859$	21.6000	−	37.4123i	0.736982	−	1.27649i	−0.216866	−	0.976201i	$-0.569584\pi$
$859$	21.6000	−	37.4123i	0.736982	−	1.27649i	0.953848	−	0.300289i	$-0.0970832\pi$
$860$		0			0
$861$	−16.5720	−	8.75837i	−0.564773	−	0.298485i
$862$		0			0
$863$	9.00701	−	15.6006i	0.306602	−	0.531051i	−0.671015	−	0.741444i	$-0.734141\pi$
$863$	9.00701	−	15.6006i	0.306602	−	0.531051i	0.977617	+	0.210394i	$0.0674745\pi$
$864$		0			0
$865$	−1.85874	−	3.21944i	−0.0631992	−	0.109464i
$866$		0			0
$867$	9.14827			0.310691
$868$		0			0
$869$	−61.8329			−2.09754
$870$		0			0
$871$	0.206278	+	0.357283i	0.00698945	+	0.0121061i
$872$		0			0
$873$	−1.19791	+	2.07483i	−0.0405430	+	0.0702225i
$874$		0			0
$875$	−2.24021	+	1.40765i	−0.0757329	+	0.0475871i
$876$		0			0
$877$	−12.9825	+	22.4864i	−0.438388	+	0.759311i	−0.997565	−	0.0697373i	$-0.977784\pi$
$877$	−12.9825	+	22.4864i	−0.438388	+	0.759311i	0.559177	+	0.829048i	$0.311117\pi$
$878$		0			0
$879$	1.33916	+	2.31950i	0.0451688	+	0.0782346i
$880$		0			0
$881$	−25.0951			−0.845475			−0.422737	−	0.906252i	$-0.638931\pi$
$881$	−25.0951			−0.845475			−0.422737	+	0.906252i	$0.638931\pi$
$882$		0			0
$883$	50.9671			1.71518			0.857590	−	0.514334i	$-0.171961\pi$
$883$	50.9671			1.71518			0.857590	+	0.514334i	$0.171961\pi$
$884$		0			0
$885$	3.07937	+	5.33362i	0.103512	+	0.179288i
$886$		0			0
$887$	12.0402	−	20.8542i	0.404270	−	0.700217i	−0.589966	−	0.807428i	$-0.700859\pi$
$887$	12.0402	−	20.8542i	0.404270	−	0.700217i	0.994236	+	0.107211i	$0.0341921\pi$
$888$		0			0
$889$	10.2909	−	6.46633i	0.345145	−	0.216874i
$890$		0			0
$891$	−2.74021	+	4.74618i	−0.0918004	+	0.159003i
$892$		0			0
$893$	−2.62167	−	4.54087i	−0.0877309	−	0.151954i
$894$		0			0
$895$	16.6783			0.557495
$896$		0			0
$897$	1.55875			0.0520451
$898$		0			0
$899$	−18.6836	−	32.3609i	−0.623132	−	1.07930i
$900$		0			0
$901$	7.10910	−	12.3133i	0.236838	−	0.410216i
$902$		0			0
$903$	10.4804	+	5.53894i	0.348766	+	0.184324i
$904$		0			0
$905$	4.51748	−	7.82451i	0.150166	−	0.260096i
$906$		0			0
$907$	−10.1269	−	17.5403i	−0.336258	−	0.582417i	0.647467	−	0.762093i	$-0.275828\pi$
$907$	−10.1269	−	17.5403i	−0.336258	−	0.582417i	−0.983726	+	0.179676i	$0.942495\pi$
$908$		0			0
$909$	14.8021			0.490954
$910$		0			0
$911$	−38.7238			−1.28298			−0.641488	−	0.767133i	$-0.721682\pi$
$911$	−38.7238			−1.28298			−0.641488	+	0.767133i	$0.721682\pi$
$912$		0			0
$913$	32.2329	+	55.8290i	1.06675	+	1.84767i
$914$		0			0
$915$	0.802094	−	1.38927i	0.0265164	−	0.0459278i
$916$		0			0
$917$	2.07759	+	55.5108i	0.0686082	+	1.83313i
$918$		0			0
$919$	−8.68042	+	15.0349i	−0.286341	+	0.495957i	−0.972933	−	0.231086i	$-0.925772\pi$
$919$	−8.68042	+	15.0349i	−0.286341	+	0.495957i	0.686593	+	0.727042i	$0.259106\pi$
$920$		0			0
$921$	−15.5969	−	27.0145i	−0.513934	−	0.890159i
$922$		0			0
$923$	2.08881			0.0687539
$924$		0			0
$925$	−5.15874			−0.169618
$926$		0			0
$927$	−0.957697	−	1.65878i	−0.0314549	−	0.0544815i
$928$		0			0
$929$	16.0969	−	27.8806i	0.528121	−	0.914732i	−0.471342	−	0.881951i	$-0.656230\pi$
$929$	16.0969	−	27.8806i	0.528121	−	0.914732i	0.999463	−	0.0327812i	$-0.0104364\pi$
$930$		0			0
$931$	2.38253	+	3.49438i	0.0780842	+	0.114524i
$932$		0			0
$933$	−0.192670	+	0.333714i	−0.00630772	+	0.0109253i
$934$		0			0
$935$	−7.67832	−	13.2992i	−0.251108	−	0.434932i
$936$		0			0
$937$	−14.7070			−0.480457			−0.240229	−	0.970716i	$-0.577222\pi$
$937$	−14.7070			−0.480457			−0.240229	+	0.970716i	$0.577222\pi$
$938$		0			0
$939$	−8.48042			−0.276748
$940$		0			0
$941$	−14.9661	−	25.9220i	−0.487880	−	0.845033i	0.512023	−	0.858972i	$-0.328896\pi$
$941$	−14.9661	−	25.9220i	−0.487880	−	0.845033i	−0.999903	+	0.0139390i	$0.995563\pi$
$942$		0			0
$943$	27.9000	−	48.3242i	0.908548	−	1.57365i
$944$		0			0
$945$	0.0989528	+	2.64390i	0.00321894	+	0.0860061i
$946$		0			0
$947$	7.91643	−	13.7117i	0.257249	−	0.445569i	−0.708255	−	0.705957i	$-0.750517\pi$
$947$	7.91643	−	13.7117i	0.257249	−	0.445569i	0.965504	+	0.260388i	$0.0838505\pi$
$948$		0			0
$949$	−0.482517	−	0.835743i	−0.0156631	−	0.0271294i
$950$		0			0
$951$	−26.8720			−0.871385
$952$		0			0
$953$	−9.90072			−0.320716			−0.160358	−	0.987059i	$-0.551265\pi$
$953$	−9.90072			−0.320716			−0.160358	+	0.987059i	$0.551265\pi$
$954$		0			0
$955$	11.9608	+	20.7168i	0.387043	+	0.670379i
$956$		0			0
$957$	27.8371	−	48.2152i	0.899844	−	1.55858i
$958$		0			0
$959$	−22.8371	−	12.0695i	−0.737447	−	0.389743i
$960$		0			0
$961$	8.73497	−	15.1294i	0.281773	−	0.488046i
$962$		0			0
$963$	−2.07937	−	3.60157i	−0.0670067	−	0.116059i
$964$		0			0
$965$	18.6287			0.599679
$966$		0			0
$967$	4.48042			0.144080			0.0720402	−	0.997402i	$-0.477049\pi$
$967$	4.48042			0.144080			0.0720402	+	0.997402i	$0.477049\pi$
$968$		0			0
$969$	0.846497	+	1.46618i	0.0271934	+	0.0471003i
$970$		0			0
$971$	10.0175	−	17.3508i	0.321476	−	0.556813i	−0.659317	−	0.751865i	$-0.729154\pi$
$971$	10.0175	−	17.3508i	0.321476	−	0.556813i	0.980793	+	0.195052i	$0.0624876\pi$
$972$		0			0
$973$	45.3493	−	28.4955i	1.45383	−	0.913522i
$974$		0			0
$975$	0.0989528	−	0.171391i	0.00316903	−	0.00548891i
$976$		0			0
$977$	−5.21361	−	9.03024i	−0.166798	−	0.288903i	0.770494	−	0.637447i	$-0.220010\pi$
$977$	−5.21361	−	9.03024i	−0.166798	−	0.288903i	−0.937292	+	0.348544i	$0.886676\pi$
$978$		0			0
$979$	39.4475			1.26075
$980$		0			0
$981$	16.6392			0.531247
$982$		0			0
$983$	−3.29476	−	5.70669i	−0.105086	−	0.182015i	0.808687	−	0.588239i	$-0.200179\pi$
$983$	−3.29476	−	5.70669i	−0.105086	−	0.182015i	−0.913774	+	0.406224i	$0.866845\pi$
$984$		0			0
$985$	−1.54230	+	2.67135i	−0.0491419	+	0.0851162i
$986$		0			0
$987$	19.4413	−	12.2160i	0.618822	−	0.388840i
$988$		0			0
$989$	−17.6444	+	30.5610i	−0.561059	+	0.971783i
$990$		0			0
$991$	17.6021	+	30.4877i	0.559149	+	0.968474i	0.997568	+	0.0697034i	$0.0222053\pi$
$991$	17.6021	+	30.4877i	0.559149	+	0.968474i	−0.438419	+	0.898771i	$0.644461\pi$
$992$		0			0
$993$	−9.16921			−0.290976
$994$		0			0
$995$	−20.9608			−0.664503
$996$		0			0
$997$	−28.1164	−	48.6991i	−0.890456	−	1.54232i	−0.839329	−	0.543624i	$-0.817052\pi$
$997$	−28.1164	−	48.6991i	−0.890456	−	1.54232i	−0.0511274	−	0.998692i	$-0.516281\pi$
$998$		0			0
$999$	−2.57937	+	4.46760i	−0.0816076	+	0.141349i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.bg.u.961.1		6
4.3	odd	2		840.2.bg.i.121.3	✓	6
7.4	even	3	inner	1680.2.bg.u.1201.1		6
12.11	even	2		2520.2.bi.o.1801.3		6
28.11	odd	6		840.2.bg.i.361.3	yes	6
28.19	even	6		5880.2.a.bt.1.1		3
28.23	odd	6		5880.2.a.bw.1.1		3
84.11	even	6		2520.2.bi.o.361.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bg.i.121.3	✓	6	4.3	odd	2
840.2.bg.i.361.3	yes	6	28.11	odd	6
1680.2.bg.u.961.1		6	1.1	even	1	trivial
1680.2.bg.u.1201.1		6	7.4	even	3	inner
2520.2.bi.o.361.3		6	84.11	even	6
2520.2.bi.o.1801.3		6	12.11	even	2
5880.2.a.bt.1.1		3	28.19	even	6
5880.2.a.bw.1.1		3	28.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.bg (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-2.24021 + 1.40765i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-2.24021 + 1.40765i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-2.74021 - 4.74618i) q^{11} +0.197906 q^{13} -1.00000 q^{15} +(-1.40105 - 2.42668i) q^{17} +(-0.302094 + 0.523243i) q^{19} +(-2.33916 - 1.23625i) q^{21} +(3.93811 - 6.82101i) q^{23} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{27} +10.1587 q^{29} +(-1.83916 - 3.18552i) q^{31} +(2.74021 - 4.74618i) q^{33} +(-0.0989528 - 2.64390i) q^{35} +(2.57937 - 4.46760i) q^{37} +(0.0989528 + 0.171391i) q^{39} +7.08461 q^{41} -4.48042 q^{43} +(-0.500000 - 0.866025i) q^{45} +(-4.33916 + 7.51565i) q^{47} +(3.03707 - 6.30684i) q^{49} +(1.40105 - 2.42668i) q^{51} +(2.53707 + 4.39433i) q^{53} +5.48042 q^{55} -0.604189 q^{57} +(-3.07937 - 5.33362i) q^{59} +(-0.802094 + 1.38927i) q^{61} +(-0.0989528 - 2.64390i) q^{63} +(-0.0989528 + 0.171391i) q^{65} +(1.04230 + 1.80532i) q^{67} +7.87623 q^{69} +10.5546 q^{71} +(-2.43811 - 4.22294i) q^{73} +(0.500000 - 0.866025i) q^{75} +(12.8196 + 6.77519i) q^{77} +(5.64126 - 9.77094i) q^{79} +(-0.500000 - 0.866025i) q^{81} -11.7629 q^{83} +2.80209 q^{85} +(5.07937 + 8.79773i) q^{87} +(-3.59895 + 6.23357i) q^{89} +(-0.443350 + 0.278581i) q^{91} +(1.83916 - 3.18552i) q^{93} +(-0.302094 - 0.523243i) q^{95} +2.39581 q^{97} +5.48042 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 3 q^{5} + 2 q^{7} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 - 3 * q^5 + 2 * q^7 - 3 * q^9	\( 6 q + 3 q^{3} - 3 q^{5} + 2 q^{7} - 3 q^{9} - q^{11} + 2 q^{13} - 6 q^{15} - 8 q^{17} - q^{19} + q^{21} + 9 q^{23} - 3 q^{25} - 6 q^{27} + 4 q^{31} + q^{33} - q^{35} - 15 q^{37} + q^{39} + 10 q^{41} + 4 q^{43} - 3 q^{45} - 11 q^{47} + 4 q^{49} + 8 q^{51} + q^{53} + 2 q^{55} - 2 q^{57} + 12 q^{59} - 4 q^{61} - q^{63} - q^{65} - 10 q^{67} + 18 q^{69} + 4 q^{71} + 3 q^{75} + 31 q^{77} + 18 q^{79} - 3 q^{81} - 8 q^{83} + 16 q^{85} - 22 q^{89} + 14 q^{91} - 4 q^{93} - q^{95} + 16 q^{97} + 2 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 - 3 * q^5 + 2 * q^7 - 3 * q^9 - q^11 + 2 * q^13 - 6 * q^15 - 8 * q^17 - q^19 + q^21 + 9 * q^23 - 3 * q^25 - 6 * q^27 + 4 * q^31 + q^33 - q^35 - 15 * q^37 + q^39 + 10 * q^41 + 4 * q^43 - 3 * q^45 - 11 * q^47 + 4 * q^49 + 8 * q^51 + q^53 + 2 * q^55 - 2 * q^57 + 12 * q^59 - 4 * q^61 - q^63 - q^65 - 10 * q^67 + 18 * q^69 + 4 * q^71 + 3 * q^75 + 31 * q^77 + 18 * q^79 - 3 * q^81 - 8 * q^83 + 16 * q^85 - 22 * q^89 + 14 * q^91 - 4 * q^93 - q^95 + 16 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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