LMFDB - Embedded newform 1148.2.n.e.953.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(57,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("1148.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.n (of order $5$, degree $4$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			953.2
Character	$\chi$	$=$	1148.953
Dual form			1148.2.n.e.365.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.660580 q^{3} +(0.860652 + 2.64881i) q^{5} +(0.809017 - 0.587785i) q^{7} -2.56363 q^{9} +O(q^{10})$	\(q-0.660580 q^{3} +(0.860652 + 2.64881i) q^{5} +(0.809017 - 0.587785i) q^{7} -2.56363 q^{9} +(-1.31434 + 4.04513i) q^{11} +(-2.12587 - 1.54453i) q^{13} +(-0.568529 - 1.74975i) q^{15} +(0.363137 - 1.11762i) q^{17} +(-3.50486 + 2.54643i) q^{19} +(-0.534420 + 0.388279i) q^{21} +(-6.79186 - 4.93457i) q^{23} +(-2.23041 + 1.62048i) q^{25} +3.67523 q^{27} +(1.24066 + 3.81836i) q^{29} +(1.90141 - 5.85195i) q^{31} +(0.868229 - 2.67214i) q^{33} +(2.25322 + 1.63706i) q^{35} +(-1.16042 - 3.57141i) q^{37} +(1.40431 + 1.02029i) q^{39} +(-1.69701 + 6.17415i) q^{41} +(-0.641872 - 0.466348i) q^{43} +(-2.20640 - 6.79059i) q^{45} +(-10.4153 - 7.56713i) q^{47} +(0.309017 - 0.951057i) q^{49} +(-0.239881 + 0.738277i) q^{51} +(2.26939 + 6.98447i) q^{53} -11.8460 q^{55} +(2.31524 - 1.68212i) q^{57} +(5.15250 + 3.74351i) q^{59} +(-2.46506 + 1.79097i) q^{61} +(-2.07402 + 1.50687i) q^{63} +(2.26155 - 6.96033i) q^{65} +(-2.37463 - 7.30837i) q^{67} +(4.48657 + 3.25968i) q^{69} +(-0.999222 + 3.07529i) q^{71} -4.45989 q^{73} +(1.47336 - 1.07046i) q^{75} +(1.31434 + 4.04513i) q^{77} +2.23436 q^{79} +5.26312 q^{81} -12.3979 q^{83} +3.27290 q^{85} +(-0.819556 - 2.52233i) q^{87} +(-2.23269 + 1.62214i) q^{89} -2.62772 q^{91} +(-1.25604 + 3.86568i) q^{93} +(-9.76149 - 7.09214i) q^{95} +(-0.383518 - 1.18035i) q^{97} +(3.36950 - 10.3702i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9}+O(q^{10}) $ 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9	$ 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9} - 8 q^{11} + 10 q^{15} + 8 q^{17} - 28 q^{19} + 3 q^{21} - 23 q^{23} + 17 q^{25} + 12 q^{27} - 31 q^{29} + 2 q^{31} + 12 q^{33} + 13 q^{35} + 7 q^{37} - 16 q^{39} - q^{41} - 2 q^{43} + 71 q^{45} + 15 q^{47} - 6 q^{49} + 2 q^{51} + 28 q^{53} - 16 q^{55} - 15 q^{57} + 17 q^{59} + 35 q^{61} - q^{63} + 62 q^{65} - 10 q^{67} - 9 q^{69} - 25 q^{71} - 74 q^{73} + 17 q^{75} + 8 q^{77} + 64 q^{81} + 96 q^{83} - 94 q^{85} - q^{87} - 33 q^{89} - 15 q^{93} - 29 q^{95} - 34 q^{97} - 3 q^{99}+O(q^{100}) $ 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9 - 8 * q^11 + 10 * q^15 + 8 * q^17 - 28 * q^19 + 3 * q^21 - 23 * q^23 + 17 * q^25 + 12 * q^27 - 31 * q^29 + 2 * q^31 + 12 * q^33 + 13 * q^35 + 7 * q^37 - 16 * q^39 - q^41 - 2 * q^43 + 71 * q^45 + 15 * q^47 - 6 * q^49 + 2 * q^51 + 28 * q^53 - 16 * q^55 - 15 * q^57 + 17 * q^59 + 35 * q^61 - q^63 + 62 * q^65 - 10 * q^67 - 9 * q^69 - 25 * q^71 - 74 * q^73 + 17 * q^75 + 8 * q^77 + 64 * q^81 + 96 * q^83 - 94 * q^85 - q^87 - 33 * q^89 - 15 * q^93 - 29 * q^95 - 34 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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
$3$	−0.660580			−0.381386			−0.190693	−	0.981650i	$-0.561074\pi$
$3$	−0.660580			−0.381386			−0.190693	+	0.981650i	$0.561074\pi$
$4$		0			0
$5$	0.860652	+	2.64881i	0.384895	+	1.18459i	0.936556	+	0.350517i	$0.113994\pi$
$5$	0.860652	+	2.64881i	0.384895	+	1.18459i	−0.551661	+	0.834068i	$0.686006\pi$
$6$		0			0
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$8$		0			0
$9$	−2.56363			−0.854545
$10$		0			0
$11$	−1.31434	+	4.04513i	−0.396290	+	1.21965i	0.531663	+	0.846956i	$0.321567\pi$
$11$	−1.31434	+	4.04513i	−0.396290	+	1.21965i	−0.927953	+	0.372698i	$0.878433\pi$
$12$		0			0
$13$	−2.12587	−	1.54453i	−0.589609	−	0.428376i	0.252566	−	0.967580i	$-0.418725\pi$
$13$	−2.12587	−	1.54453i	−0.589609	−	0.428376i	−0.842176	+	0.539203i	$0.818725\pi$
$14$		0			0
$15$	−0.568529	−	1.74975i	−0.146794	−	0.451784i
$16$		0			0
$17$	0.363137	−	1.11762i	0.0880736	−	0.271063i	−0.897313	−	0.441394i	$-0.854484\pi$
$17$	0.363137	−	1.11762i	0.0880736	−	0.271063i	0.985387	+	0.170332i	$0.0544840\pi$
$18$		0			0
$19$	−3.50486	+	2.54643i	−0.804071	+	0.584192i	−0.912106	−	0.409955i	$-0.865544\pi$
$19$	−3.50486	+	2.54643i	−0.804071	+	0.584192i	0.108035	+	0.994147i	$0.465544\pi$
$20$		0			0
$21$	−0.534420	+	0.388279i	−0.116620	+	0.0847295i
$22$		0			0
$23$	−6.79186	−	4.93457i	−1.41620	−	1.02893i	−0.992384	−	0.123182i	$-0.960690\pi$
$23$	−6.79186	−	4.93457i	−1.41620	−	1.02893i	−0.423816	−	0.905748i	$-0.639310\pi$
$24$		0			0
$25$	−2.23041	+	1.62048i	−0.446081	+	0.324097i
$26$		0			0
$27$	3.67523			0.707297
$28$		0			0
$29$	1.24066	+	3.81836i	0.230385	+	0.709052i	0.997700	+	0.0677821i	$0.0215923\pi$
$29$	1.24066	+	3.81836i	0.230385	+	0.709052i	−0.767315	+	0.641270i	$0.778408\pi$
$30$		0			0
$31$	1.90141	−	5.85195i	0.341504	−	1.05104i	−0.621925	−	0.783077i	$-0.713649\pi$
$31$	1.90141	−	5.85195i	0.341504	−	1.05104i	0.963429	−	0.267964i	$-0.0863509\pi$
$32$		0			0
$33$	0.868229	−	2.67214i	0.151139	−	0.465159i
$34$		0			0
$35$	2.25322	+	1.63706i	0.380863	+	0.276713i
$36$		0			0
$37$	−1.16042	−	3.57141i	−0.190772	−	0.587136i	0.809228	−	0.587495i	$-0.199886\pi$
$37$	−1.16042	−	3.57141i	−0.190772	−	0.587136i	−1.00000		0.000358916i	$0.999886\pi$
$38$		0			0
$39$	1.40431	+	1.02029i	0.224869	+	0.163377i
$40$		0			0
$41$	−1.69701	+	6.17415i	−0.265028	+	0.964241i
$41$	−1.69701	+	6.17415i	−0.265028	+	0.964241i
$42$		0			0
$43$	−0.641872	−	0.466348i	−0.0978846	−	0.0711173i	0.537766	−	0.843094i	$-0.319268\pi$
$43$	−0.641872	−	0.466348i	−0.0978846	−	0.0711173i	−0.635651	+	0.771977i	$0.719268\pi$
$44$		0			0
$45$	−2.20640	−	6.79059i	−0.328910	−	1.01228i
$46$		0			0
$47$	−10.4153	−	7.56713i	−1.51922	−	1.10378i	−0.961872	−	0.273500i	$-0.911819\pi$
$47$	−10.4153	−	7.56713i	−1.51922	−	1.10378i	−0.557349	−	0.830278i	$-0.688181\pi$
$48$		0			0
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$		0			0
$51$	−0.239881	+	0.738277i	−0.0335900	+	0.103379i
$52$		0			0
$53$	2.26939	+	6.98447i	0.311725	+	0.959390i	0.977082	+	0.212865i	$0.0682794\pi$
$53$	2.26939	+	6.98447i	0.311725	+	0.959390i	−0.665357	+	0.746525i	$0.731721\pi$
$54$		0			0
$55$	−11.8460			−1.59731
$56$		0			0
$57$	2.31524	−	1.68212i	0.306661	−	0.222803i
$58$		0			0
$59$	5.15250	+	3.74351i	0.670799	+	0.487364i	0.870293	−	0.492535i	$-0.163930\pi$
$59$	5.15250	+	3.74351i	0.670799	+	0.487364i	−0.199494	+	0.979899i	$0.563930\pi$
$60$		0			0
$61$	−2.46506	+	1.79097i	−0.315619	+	0.229311i	−0.734304	−	0.678821i	$-0.762491\pi$
$61$	−2.46506	+	1.79097i	−0.315619	+	0.229311i	0.418685	+	0.908132i	$0.362491\pi$
$62$		0			0
$63$	−2.07402	+	1.50687i	−0.261302	+	0.189847i
$64$		0			0
$65$	2.26155	−	6.96033i	0.280511	−	0.863323i
$66$		0			0
$67$	−2.37463	−	7.30837i	−0.290108	−	0.892860i	−0.984821	−	0.173573i	$-0.944469\pi$
$67$	−2.37463	−	7.30837i	−0.290108	−	0.892860i	0.694713	−	0.719287i	$-0.255531\pi$
$68$		0			0
$69$	4.48657	+	3.25968i	0.540119	+	0.392420i
$70$		0			0
$71$	−0.999222	+	3.07529i	−0.118586	+	0.364970i	−0.992678	−	0.120790i	$-0.961457\pi$
$71$	−0.999222	+	3.07529i	−0.118586	+	0.364970i	0.874092	+	0.485760i	$0.161457\pi$
$72$		0			0
$73$	−4.45989			−0.521991			−0.260995	−	0.965340i	$-0.584051\pi$
$73$	−4.45989			−0.521991			−0.260995	+	0.965340i	$0.584051\pi$
$74$		0			0
$75$	1.47336	−	1.07046i	0.170129	−	0.123606i
$76$		0			0
$77$	1.31434	+	4.04513i	0.149783	+	0.460986i
$78$		0			0
$79$	2.23436			0.251385			0.125693	−	0.992069i	$-0.459885\pi$
$79$	2.23436			0.251385			0.125693	+	0.992069i	$0.459885\pi$
$80$		0			0
$81$	5.26312			0.584791
$82$		0			0
$83$	−12.3979			−1.36085			−0.680423	−	0.732820i	$-0.738204\pi$
$83$	−12.3979			−1.36085			−0.680423	+	0.732820i	$0.738204\pi$
$84$		0			0
$85$	3.27290			0.354996
$86$		0			0
$87$	−0.819556	−	2.52233i	−0.0878657	−	0.270423i
$88$		0			0
$89$	−2.23269	+	1.62214i	−0.236664	+	0.171947i	−0.699796	−	0.714343i	$-0.746726\pi$
$89$	−2.23269	+	1.62214i	−0.236664	+	0.171947i	0.463132	+	0.886290i	$0.346726\pi$
$90$		0			0
$91$	−2.62772			−0.275459
$92$		0			0
$93$	−1.25604	+	3.86568i	−0.130245	+	0.400852i
$94$		0			0
$95$	−9.76149	−	7.09214i	−1.00151	−	0.727638i
$96$		0			0
$97$	−0.383518	−	1.18035i	−0.0389403	−	0.119846i	0.929697	−	0.368326i	$-0.120069\pi$
$97$	−0.383518	−	1.18035i	−0.0389403	−	0.119846i	−0.968637	+	0.248480i	$0.920069\pi$
$98$		0			0
$99$	3.36950	−	10.3702i	0.338647	−	1.04225i
$100$		0			0
$101$	−6.55569	+	4.76299i	−0.652316	+	0.473935i	−0.864059	−	0.503390i	$-0.832086\pi$
$101$	−6.55569	+	4.76299i	−0.652316	+	0.473935i	0.211743	+	0.977325i	$0.432086\pi$
$102$		0			0
$103$	−14.5968	+	10.6052i	−1.43827	+	1.04496i	−0.449868	+	0.893095i	$0.648529\pi$
$103$	−14.5968	+	10.6052i	−1.43827	+	1.04496i	−0.988401	+	0.151868i	$0.951471\pi$
$104$		0			0
$105$	−1.48843	−	1.08141i	−0.145256	−	0.105535i
$106$		0			0
$107$	−3.18659	+	2.31519i	−0.308059	+	0.223818i	−0.731063	−	0.682310i	$-0.760976\pi$
$107$	−3.18659	+	2.31519i	−0.308059	+	0.223818i	0.423004	+	0.906128i	$0.360976\pi$
$108$		0			0
$109$	−2.50586			−0.240018			−0.120009	−	0.992773i	$-0.538292\pi$
$109$	−2.50586			−0.240018			−0.120009	+	0.992773i	$0.538292\pi$
$110$		0			0
$111$	0.766551	+	2.35920i	0.0727578	+	0.223925i
$112$		0			0
$113$	−6.08326	+	18.7223i	−0.572265	+	1.76125i	0.0730454	+	0.997329i	$0.476728\pi$
$113$	−6.08326	+	18.7223i	−0.572265	+	1.76125i	−0.645310	+	0.763921i	$0.723272\pi$
$114$		0			0
$115$	7.22534	−	22.2373i	0.673767	−	2.07364i
$116$		0			0
$117$	5.44994	+	3.95962i	0.503848	+	0.366067i
$118$		0			0
$119$	−0.363137	−	1.11762i	−0.0332887	−	0.102452i
$120$		0			0
$121$	−5.73643	−	4.16776i	−0.521493	−	0.378887i
$122$		0			0
$123$	1.12101	−	4.07852i	0.101078	−	0.367748i
$124$		0			0
$125$	5.05411	+	3.67203i	0.452054	+	0.328436i
$126$		0			0
$127$	−3.71971	−	11.4481i	−0.330071	−	1.01585i	−0.969099	−	0.246671i	$-0.920663\pi$
$127$	−3.71971	−	11.4481i	−0.330071	−	1.01585i	0.639029	−	0.769183i	$-0.279337\pi$
$128$		0			0
$129$	0.424008	+	0.308060i	0.0373318	+	0.0271232i
$130$		0			0
$131$	−0.917345	+	2.82330i	−0.0801488	+	0.246673i	−0.983100	−	0.183071i	$-0.941396\pi$
$131$	−0.917345	+	2.82330i	−0.0801488	+	0.246673i	0.902951	+	0.429744i	$0.141396\pi$
$132$		0			0
$133$	−1.33874	+	4.12021i	−0.116083	+	0.357268i
$134$		0			0
$135$	3.16309	+	9.73499i	0.272235	+	0.837854i
$136$		0			0
$137$	11.3089			0.966186			0.483093	−	0.875569i	$-0.339513\pi$
$137$	11.3089			0.966186			0.483093	+	0.875569i	$0.339513\pi$
$138$		0			0
$139$	−6.17717	+	4.48798i	−0.523941	+	0.380665i	−0.818086	−	0.575095i	$-0.804965\pi$
$139$	−6.17717	+	4.48798i	−0.523941	+	0.380665i	0.294146	+	0.955761i	$0.404965\pi$
$140$		0			0
$141$	6.88011	+	4.99869i	0.579410	+	0.420966i
$142$		0			0
$143$	9.04196	−	6.56937i	0.756127	−	0.549358i
$144$		0			0
$145$	−9.04636	+	6.57256i	−0.751259	+	0.545822i
$146$		0			0
$147$	−0.204130	+	0.628249i	−0.0168364	+	0.0518171i
$148$		0			0
$149$	6.83270	+	21.0289i	0.559757	+	1.72275i	0.683038	+	0.730383i	$0.260658\pi$
$149$	6.83270	+	21.0289i	0.559757	+	1.72275i	−0.123281	+	0.992372i	$0.539342\pi$
$150$		0			0
$151$	7.27106	+	5.28273i	0.591710	+	0.429903i	0.842927	−	0.538028i	$-0.180831\pi$
$151$	7.27106	+	5.28273i	0.591710	+	0.429903i	−0.251217	+	0.967931i	$0.580831\pi$
$152$		0			0
$153$	−0.930949	+	2.86517i	−0.0752628	+	0.231635i
$154$		0			0
$155$	17.1372			1.37649
$156$		0			0
$157$	−4.09331	+	2.97396i	−0.326682	+	0.237348i	−0.739021	−	0.673682i	$-0.764712\pi$
$157$	−4.09331	+	2.97396i	−0.326682	+	0.237348i	0.412340	+	0.911030i	$0.364712\pi$
$158$		0			0
$159$	−1.49911	−	4.61380i	−0.118887	−	0.365898i
$160$		0			0
$161$	−8.39520			−0.661634
$162$		0			0
$163$	10.7170			0.839417			0.419709	−	0.907659i	$-0.362132\pi$
$163$	10.7170			0.839417			0.419709	+	0.907659i	$0.362132\pi$
$164$		0			0
$165$	7.82523			0.609193
$166$		0			0
$167$	19.1405			1.48113			0.740566	−	0.671983i	$-0.234557\pi$
$167$	19.1405			1.48113			0.740566	+	0.671983i	$0.234557\pi$
$168$		0			0
$169$	−1.88349	−	5.79679i	−0.144884	−	0.445907i
$170$		0			0
$171$	8.98519	−	6.52812i	0.687115	−	0.499218i
$172$		0			0
$173$	−1.80401			−0.137156			−0.0685781	−	0.997646i	$-0.521846\pi$
$173$	−1.80401			−0.137156			−0.0685781	+	0.997646i	$0.521846\pi$
$174$		0			0
$175$	−0.851939	+	2.62200i	−0.0644006	+	0.198205i
$176$		0			0
$177$	−3.40364	−	2.47289i	−0.255833	−	0.185874i
$178$		0			0
$179$	−3.19241	−	9.82522i	−0.238612	−	0.734371i	−0.996622	−	0.0821283i	$-0.973828\pi$
$179$	−3.19241	−	9.82522i	−0.238612	−	0.734371i	0.758010	−	0.652243i	$-0.226172\pi$
$180$		0			0
$181$	−1.51210	+	4.65377i	−0.112394	+	0.345912i	−0.991395	−	0.130908i	$-0.958211\pi$
$181$	−1.51210	+	4.65377i	−0.112394	+	0.345912i	0.879001	+	0.476820i	$0.158211\pi$
$182$		0			0
$183$	1.62837	−	1.18308i	0.120373	−	0.0874559i
$184$		0			0
$185$	8.46128	−	6.14748i	0.622085	−	0.451971i
$186$		0			0
$187$	4.04364	+	2.93787i	0.295700	+	0.214839i
$188$		0			0
$189$	2.97332	−	2.16024i	0.216277	−	0.157135i
$190$		0			0
$191$	9.35777			0.677105			0.338552	−	0.940948i	$-0.390063\pi$
$191$	9.35777			0.677105			0.338552	+	0.940948i	$0.390063\pi$
$192$		0			0
$193$	2.67725	+	8.23972i	0.192713	+	0.593108i	0.999996	+	0.00294386i	$0.000937061\pi$
$193$	2.67725	+	8.23972i	0.192713	+	0.593108i	−0.807283	+	0.590164i	$0.799063\pi$
$194$		0			0
$195$	−1.49393	+	4.59785i	−0.106983	+	0.329259i
$196$		0			0
$197$	5.81523	−	17.8975i	0.414318	−	1.27514i	−0.498541	−	0.866866i	$-0.666131\pi$
$197$	5.81523	−	17.8975i	0.414318	−	1.27514i	0.912859	−	0.408274i	$-0.133869\pi$
$198$		0			0
$199$	−7.75316	−	5.63300i	−0.549607	−	0.399313i	0.278033	−	0.960571i	$-0.410317\pi$
$199$	−7.75316	−	5.63300i	−0.549607	−	0.399313i	−0.827641	+	0.561258i	$0.810317\pi$
$200$		0			0
$201$	1.56864	+	4.82777i	0.110643	+	0.340524i
$202$		0			0
$203$	3.24809	+	2.35988i	0.227972	+	0.165631i
$204$		0			0
$205$	−17.8147	+	0.818738i	−1.24423	+	0.0571832i
$206$		0			0
$207$	17.4118	+	12.6504i	1.21021	+	0.879267i
$208$		0			0
$209$	−5.69407	−	17.5245i	−0.393867	−	1.21220i
$210$		0			0
$211$	14.1667	+	10.2927i	0.975278	+	0.708581i	0.956648	−	0.291246i	$-0.0940697\pi$
$211$	14.1667	+	10.2927i	0.975278	+	0.708581i	0.0186296	+	0.999826i	$0.494070\pi$
$212$		0			0
$213$	0.660066	−	2.03147i	0.0452270	−	0.139194i
$214$		0			0
$215$	0.682839	−	2.10156i	0.0465692	−	0.143325i
$216$		0			0
$217$	−1.90141	−	5.85195i	−0.129076	−	0.397256i
$218$		0			0
$219$	2.94611			0.199080
$220$		0			0
$221$	−2.49818	+	1.81503i	−0.168046	+	0.122092i
$222$		0			0
$223$	5.19097	+	3.77146i	0.347613	+	0.252556i	0.747867	−	0.663848i	$-0.231078\pi$
$223$	5.19097	+	3.77146i	0.347613	+	0.252556i	−0.400254	+	0.916404i	$0.631078\pi$
$224$		0			0
$225$	5.71794	−	4.15433i	0.381196	−	0.276955i
$226$		0			0
$227$	−4.58368	+	3.33024i	−0.304229	+	0.221036i	−0.729416	−	0.684070i	$-0.760208\pi$
$227$	−4.58368	+	3.33024i	−0.304229	+	0.221036i	0.425187	+	0.905105i	$0.360208\pi$
$228$		0			0
$229$	4.79574	−	14.7598i	0.316912	−	0.975354i	−0.658049	−	0.752975i	$-0.728618\pi$
$229$	4.79574	−	14.7598i	0.316912	−	0.975354i	0.974960	−	0.222379i	$-0.0713821\pi$
$230$		0			0
$231$	−0.868229	−	2.67214i	−0.0571253	−	0.175814i
$232$		0			0
$233$	−2.26574	−	1.64616i	−0.148434	−	0.107843i	0.511090	−	0.859527i	$-0.329242\pi$
$233$	−2.26574	−	1.64616i	−0.148434	−	0.107843i	−0.659524	+	0.751684i	$0.729242\pi$
$234$		0			0
$235$	11.0800	−	34.1007i	0.722779	−	2.22449i
$236$		0			0
$237$	−1.47597			−0.0958748
$238$		0			0
$239$	15.7061	−	11.4111i	1.01594	−	0.738125i	0.0504954	−	0.998724i	$-0.483920\pi$
$239$	15.7061	−	11.4111i	1.01594	−	0.738125i	0.965447	+	0.260599i	$0.0839200\pi$
$240$		0			0
$241$	7.49040	+	23.0531i	0.482499	+	1.48498i	0.835571	+	0.549383i	$0.185137\pi$
$241$	7.49040	+	23.0531i	0.482499	+	1.48498i	−0.353072	+	0.935596i	$0.614863\pi$
$242$		0			0
$243$	−14.5024			−0.930329
$244$		0			0
$245$	2.78513			0.177935
$246$		0			0
$247$	11.3839			0.724342
$248$		0			0
$249$	8.18980			0.519008
$250$		0			0
$251$	−3.13619	−	9.65220i	−0.197955	−	0.609241i	−0.999929	−	0.0118836i	$-0.996217\pi$
$251$	−3.13619	−	9.65220i	−0.197955	−	0.609241i	0.801975	−	0.597358i	$-0.203783\pi$
$252$		0			0
$253$	28.8879	−	20.9883i	1.81616	−	1.31952i
$254$		0			0
$255$	−2.16201			−0.135390
$256$		0			0
$257$	3.71537	−	11.4347i	0.231758	−	0.713279i	−0.765777	−	0.643107i	$-0.777645\pi$
$257$	3.71537	−	11.4347i	0.231758	−	0.713279i	0.997535	−	0.0701721i	$-0.0223548\pi$
$258$		0			0
$259$	−3.03802	−	2.20725i	−0.188773	−	0.137152i
$260$		0			0
$261$	−3.18060	−	9.78889i	−0.196874	−	0.605917i
$262$		0			0
$263$	9.34517	−	28.7615i	0.576248	−	1.77351i	−0.0556434	−	0.998451i	$-0.517721\pi$
$263$	9.34517	−	28.7615i	0.576248	−	1.77351i	0.631891	−	0.775057i	$-0.282279\pi$
$264$		0			0
$265$	−16.5474	+	12.0224i	−1.01650	+	0.738529i
$266$		0			0
$267$	1.47487	−	1.07155i	0.0902605	−	0.0655781i
$268$		0			0
$269$	16.4112	+	11.9234i	1.00061	+	0.726984i	0.962218	−	0.272279i	$-0.0877773\pi$
$269$	16.4112	+	11.9234i	1.00061	+	0.726984i	0.0383892	+	0.999263i	$0.487777\pi$
$270$		0			0
$271$	−19.7796	+	14.3707i	−1.20152	+	0.872957i	−0.994434	−	0.105365i	$-0.966399\pi$
$271$	−19.7796	+	14.3707i	−1.20152	+	0.872957i	−0.207089	+	0.978322i	$0.566399\pi$
$272$		0			0
$273$	1.73582			0.105056
$274$		0			0
$275$	−3.62356	−	11.1522i	−0.218509	−	0.672501i
$276$		0			0
$277$	−7.02910	+	21.6333i	−0.422338	+	1.29982i	0.483183	+	0.875519i	$0.339481\pi$
$277$	−7.02910	+	21.6333i	−0.422338	+	1.29982i	−0.905521	+	0.424302i	$0.860519\pi$
$278$		0			0
$279$	−4.87453	+	15.0023i	−0.291830	+	0.898162i
$280$		0			0
$281$	1.30938	+	0.951323i	0.0781113	+	0.0567512i	0.626156	−	0.779698i	$-0.284627\pi$
$281$	1.30938	+	0.951323i	0.0781113	+	0.0567512i	−0.548044	+	0.836449i	$0.684627\pi$
$282$		0			0
$283$	5.12498	+	15.7731i	0.304649	+	0.937612i	0.979808	+	0.199940i	$0.0640748\pi$
$283$	5.12498	+	15.7731i	0.304649	+	0.937612i	−0.675159	+	0.737672i	$0.735925\pi$
$284$		0			0
$285$	6.44825	+	4.68493i	0.381961	+	0.277511i
$286$		0			0
$287$	2.25617	+	5.99247i	0.133177	+	0.353724i
$288$		0			0
$289$	12.6361	+	9.18065i	0.743299	+	0.540038i
$290$		0			0
$291$	0.253344	+	0.779713i	0.0148513	+	0.0457076i
$292$		0			0
$293$	−9.13257	−	6.63520i	−0.533530	−	0.387632i	0.288146	−	0.957586i	$-0.406961\pi$
$293$	−9.13257	−	6.63520i	−0.533530	−	0.387632i	−0.821677	+	0.569954i	$0.806961\pi$
$294$		0			0
$295$	−5.48136	+	16.8699i	−0.319137	+	0.982202i
$296$		0			0
$297$	−4.83051	+	14.8668i	−0.280295	+	0.862658i
$298$		0			0
$299$	6.81698	+	20.9805i	0.394236	+	1.21333i
$300$		0			0
$301$	−0.793398			−0.0457307
$302$		0			0
$303$	4.33056	−	3.14634i	0.248784	−	0.180752i
$304$		0			0
$305$	−6.86551	−	4.98809i	−0.393118	−	0.285617i
$306$		0			0
$307$	−16.1972	+	11.7679i	−0.924423	+	0.671632i	−0.944621	−	0.328164i	$-0.893570\pi$
$307$	−16.1972	+	11.7679i	−0.924423	+	0.671632i	0.0201983	+	0.999796i	$0.493570\pi$
$308$		0			0
$309$	9.64238	−	7.00560i	0.548536	−	0.398535i
$310$		0			0
$311$	−4.06550	+	12.5123i	−0.230533	+	0.709508i	0.767149	+	0.641468i	$0.221674\pi$
$311$	−4.06550	+	12.5123i	−0.230533	+	0.709508i	−0.997683	+	0.0680397i	$0.978326\pi$
$312$		0			0
$313$	1.98338	+	6.10423i	0.112108	+	0.345031i	0.991333	−	0.131375i	$-0.0419391\pi$
$313$	1.98338	+	6.10423i	0.112108	+	0.345031i	−0.879225	+	0.476406i	$0.841939\pi$
$314$		0			0
$315$	−5.77642	−	4.19681i	−0.325464	−	0.236464i
$316$		0			0
$317$	−4.52911	+	13.9392i	−0.254380	+	0.782902i	0.739571	+	0.673079i	$0.235029\pi$
$317$	−4.52911	+	13.9392i	−0.254380	+	0.782902i	−0.993951	+	0.109823i	$0.964971\pi$
$318$		0			0
$319$	−17.0765			−0.956098
$320$		0			0
$321$	2.10500	−	1.52937i	0.117490	−	0.0853612i
$322$		0			0
$323$	1.57320	+	4.84181i	0.0875351	+	0.269405i
$324$		0			0
$325$	7.24444			0.401849
$326$		0			0
$327$	1.65532			0.0915396
$328$		0			0
$329$	−12.8740			−0.709765
$330$		0			0
$331$	−2.84097			−0.156154			−0.0780769	−	0.996947i	$-0.524878\pi$
$331$	−2.84097			−0.156154			−0.0780769	+	0.996947i	$0.524878\pi$
$332$		0			0
$333$	2.97489	+	9.15578i	0.163023	+	0.501734i
$334$		0			0
$335$	17.3148	−	12.5799i	0.946008	−	0.687315i
$336$		0			0
$337$	−13.4878			−0.734728			−0.367364	−	0.930077i	$-0.619740\pi$
$337$	−13.4878			−0.734728			−0.367364	+	0.930077i	$0.619740\pi$
$338$		0			0
$339$	4.01848	−	12.3676i	0.218254	−	0.671716i
$340$		0			0
$341$	21.1728	+	15.3829i	1.14657	+	0.833033i
$342$		0			0
$343$	−0.309017	−	0.951057i	−0.0166853	−	0.0513522i
$344$		0			0
$345$	−4.77292	+	14.6895i	−0.256965	+	0.790858i
$346$		0			0
$347$	16.7075	−	12.1387i	0.896906	−	0.651640i	−0.0407636	−	0.999169i	$-0.512979\pi$
$347$	16.7075	−	12.1387i	0.896906	−	0.651640i	0.937669	+	0.347529i	$0.112979\pi$
$348$		0			0
$349$	−16.0772	+	11.6807i	−0.860591	+	0.625256i	−0.928046	−	0.372466i	$-0.878512\pi$
$349$	−16.0772	+	11.6807i	−0.860591	+	0.625256i	0.0674548	+	0.997722i	$0.478512\pi$
$350$		0			0
$351$	−7.81304	−	5.67651i	−0.417029	−	0.302989i
$352$		0			0
$353$	24.5980	−	17.8715i	1.30922	−	0.951203i	0.309219	−	0.950991i	$-0.399932\pi$
$353$	24.5980	−	17.8715i	1.30922	−	0.951203i	1.00000		0.000212707i	$-6.77069e-5\pi$
$354$		0			0
$355$	−9.00585			−0.477981
$356$		0			0
$357$	0.239881	+	0.738277i	0.0126958	+	0.0390738i
$358$		0			0
$359$	−4.78981	+	14.7415i	−0.252796	+	0.778027i	0.741459	+	0.670998i	$0.234134\pi$
$359$	−4.78981	+	14.7415i	−0.252796	+	0.778027i	−0.994256	+	0.107030i	$0.965866\pi$
$360$		0			0
$361$	−0.0715713	+	0.220274i	−0.00376691	+	0.0115934i
$362$		0			0
$363$	3.78937	+	2.75314i	0.198890	+	0.144502i
$364$		0			0
$365$	−3.83841	−	11.8134i	−0.200912	−	0.618342i
$366$		0			0
$367$	13.9526	+	10.1372i	0.728321	+	0.529156i	0.889032	−	0.457846i	$-0.151379\pi$
$367$	13.9526	+	10.1372i	0.728321	+	0.529156i	−0.160711	+	0.987001i	$0.551379\pi$
$368$		0			0
$369$	4.35051	−	15.8283i	0.226478	−	0.823987i
$370$		0			0
$371$	5.94134	+	4.31664i	0.308459	+	0.224109i
$372$		0			0
$373$	−2.38643	−	7.34469i	−0.123565	−	0.380294i	0.870072	−	0.492925i	$-0.164072\pi$
$373$	−2.38643	−	7.34469i	−0.123565	−	0.380294i	−0.993637	+	0.112631i	$0.964072\pi$
$374$		0			0
$375$	−3.33865	−	2.42567i	−0.172407	−	0.125261i
$376$		0			0
$377$	3.26011	−	10.0336i	0.167904	−	0.516755i
$378$		0			0
$379$	10.5989	−	32.6200i	0.544428	−	1.67558i	−0.177919	−	0.984045i	$-0.556936\pi$
$379$	10.5989	−	32.6200i	0.544428	−	1.67558i	0.722346	−	0.691531i	$-0.243064\pi$
$380$		0			0
$381$	2.45717	+	7.56238i	0.125884	+	0.387432i
$382$		0			0
$383$	−24.2389			−1.23855			−0.619275	−	0.785174i	$-0.712573\pi$
$383$	−24.2389			−1.23855			−0.619275	+	0.785174i	$0.712573\pi$
$384$		0			0
$385$	−9.58361	+	6.96290i	−0.488426	+	0.354862i
$386$		0			0
$387$	1.64553	+	1.19554i	0.0836468	+	0.0607729i
$388$		0			0
$389$	10.4570	−	7.59745i	0.530191	−	0.385206i	−0.290238	−	0.956954i	$-0.593735\pi$
$389$	10.4570	−	7.59745i	0.530191	−	0.385206i	0.820429	+	0.571748i	$0.193735\pi$
$390$		0			0
$391$	−7.98135	+	5.79879i	−0.403634	+	0.293257i
$392$		0			0
$393$	0.605980	−	1.86501i	0.0305677	−	0.0940776i
$394$		0			0
$395$	1.92301	+	5.91841i	0.0967570	+	0.297787i
$396$		0			0
$397$	18.4060	+	13.3728i	0.923773	+	0.671160i	0.944460	−	0.328626i	$-0.106585\pi$
$397$	18.4060	+	13.3728i	0.923773	+	0.671160i	−0.0206872	+	0.999786i	$0.506585\pi$
$398$		0			0
$399$	0.884344	−	2.72173i	0.0442726	−	0.136257i
$400$		0			0
$401$	−33.1881			−1.65734			−0.828669	−	0.559740i	$-0.810901\pi$
$401$	−33.1881			−1.65734			−0.828669	+	0.559740i	$0.810901\pi$
$402$		0			0
$403$	−13.0807	+	9.50367i	−0.651595	+	0.473412i
$404$		0			0
$405$	4.52971	+	13.9410i	0.225083	+	0.692735i
$406$		0			0
$407$	15.9720			0.791704
$408$		0			0
$409$	−14.4102			−0.712540			−0.356270	−	0.934383i	$-0.615952\pi$
$409$	−14.4102			−0.712540			−0.356270	+	0.934383i	$0.615952\pi$
$410$		0			0
$411$	−7.47045			−0.368490
$412$		0			0
$413$	6.36884			0.313390
$414$		0			0
$415$	−10.6703	−	32.8397i	−0.523783	−	1.61204i
$416$		0			0
$417$	4.08052	−	2.96467i	0.199824	−	0.145180i
$418$		0			0
$419$	−25.5369			−1.24756			−0.623780	−	0.781600i	$-0.714404\pi$
$419$	−25.5369			−1.24756			−0.623780	+	0.781600i	$0.714404\pi$
$420$		0			0
$421$	10.6382	−	32.7411i	0.518475	−	1.59570i	−0.258394	−	0.966040i	$-0.583193\pi$
$421$	10.6382	−	32.7411i	0.518475	−	1.59570i	0.776869	−	0.629662i	$-0.216807\pi$
$422$		0			0
$423$	26.7009	+	19.3993i	1.29824	+	0.943228i
$424$		0			0
$425$	1.00114	+	3.08120i	0.0485626	+	0.149460i
$426$		0			0
$427$	−0.941570	+	2.89785i	−0.0455658	+	0.140237i
$428$		0			0
$429$	−5.97294	+	4.33960i	−0.288376	+	0.209518i
$430$		0			0
$431$	−28.3482	+	20.5962i	−1.36549	+	0.992083i	−0.367411	+	0.930059i	$0.619756\pi$
$431$	−28.3482	+	20.5962i	−1.36549	+	0.992083i	−0.998075	+	0.0620246i	$0.980244\pi$
$432$		0			0
$433$	−2.99826	−	2.17836i	−0.144087	−	0.104685i	0.513407	−	0.858146i	$-0.328383\pi$
$433$	−2.99826	−	2.17836i	−0.144087	−	0.104685i	−0.657494	+	0.753460i	$0.728383\pi$
$434$		0			0
$435$	5.97584	−	4.34170i	0.286520	−	0.208169i
$436$		0			0
$437$	36.3701			1.73982
$438$		0			0
$439$	−6.48593	−	19.9616i	−0.309556	−	0.952717i	−0.977938	−	0.208898i	$-0.933012\pi$
$439$	−6.48593	−	19.9616i	−0.309556	−	0.952717i	0.668381	−	0.743819i	$-0.266988\pi$
$440$		0			0
$441$	−0.792206	+	2.43816i	−0.0377241	+	0.116103i
$442$		0			0
$443$	−5.76868	+	17.7542i	−0.274078	+	0.843527i	0.715383	+	0.698732i	$0.246252\pi$
$443$	−5.76868	+	17.7542i	−0.274078	+	0.843527i	−0.989462	+	0.144794i	$0.953748\pi$
$444$		0			0
$445$	−6.21831	−	4.51787i	−0.294776	−	0.214168i
$446$		0			0
$447$	−4.51355	−	13.8913i	−0.213483	−	0.657035i
$448$		0			0
$449$	19.9388	+	14.4864i	0.940970	+	0.683654i	0.948654	−	0.316316i	$-0.102446\pi$
$449$	19.9388	+	14.4864i	0.940970	+	0.683654i	−0.00768421	+	0.999970i	$0.502446\pi$
$450$		0			0
$451$	−22.7448	−	14.9796i	−1.07101	−	0.705361i
$452$		0			0
$453$	−4.80312	−	3.48967i	−0.225670	−	0.163959i
$454$		0			0
$455$	−2.26155	−	6.96033i	−0.106023	−	0.326305i
$456$		0			0
$457$	−0.343361	−	0.249466i	−0.0160617	−	0.0116695i	0.579725	−	0.814812i	$-0.303160\pi$
$457$	−0.343361	−	0.249466i	−0.0160617	−	0.0116695i	−0.595787	+	0.803142i	$0.703160\pi$
$458$		0			0
$459$	1.33461	−	4.10750i	0.0622942	−	0.191722i
$460$		0			0
$461$	−0.199643	+	0.614439i	−0.00929832	+	0.0286173i	−0.955598	−	0.294673i	$-0.904789\pi$
$461$	−0.199643	+	0.614439i	−0.00929832	+	0.0286173i	0.946300	+	0.323291i	$0.104789\pi$
$462$		0			0
$463$	−5.58609	−	17.1922i	−0.259608	−	0.798991i	−0.992887	−	0.119063i	$-0.962011\pi$
$463$	−5.58609	−	17.1922i	−0.259608	−	0.798991i	0.733279	−	0.679928i	$-0.237989\pi$
$464$		0			0
$465$	−11.3205			−0.524975
$466$		0			0
$467$	−21.5860	+	15.6832i	−0.998882	+	0.725730i	−0.961848	−	0.273584i	$-0.911791\pi$
$467$	−21.5860	+	15.6832i	−0.998882	+	0.725730i	−0.0370339	+	0.999314i	$0.511791\pi$
$468$		0			0
$469$	−6.21687	−	4.51682i	−0.287069	−	0.208568i
$470$		0			0
$471$	2.70396	−	1.96454i	0.124592	−	0.0905213i
$472$		0			0
$473$	2.73008	−	1.98352i	0.125529	−	0.0912023i
$474$		0			0
$475$	3.69081	−	11.3592i	0.169346	−	0.521194i
$476$		0			0
$477$	−5.81789	−	17.9056i	−0.266383	−	0.819842i
$478$		0			0
$479$	18.3854	+	13.3577i	0.840048	+	0.610331i	0.922384	−	0.386274i	$-0.126238\pi$
$479$	18.3854	+	13.3577i	0.840048	+	0.610331i	−0.0823360	+	0.996605i	$0.526238\pi$
$480$		0			0
$481$	−3.04926	+	9.38465i	−0.139034	+	0.427903i
$482$		0			0
$483$	5.54570			0.252338
$484$		0			0
$485$	2.79644	−	2.03173i	0.126980	−	0.0922562i
$486$		0			0
$487$	0.611173	+	1.88100i	0.0276949	+	0.0852362i	0.963949	−	0.266088i	$-0.0857313\pi$
$487$	0.611173	+	1.88100i	0.0276949	+	0.0852362i	−0.936254	+	0.351325i	$0.885731\pi$
$488$		0			0
$489$	−7.07941			−0.320142
$490$		0			0
$491$	−7.53842			−0.340204			−0.170102	−	0.985426i	$-0.554410\pi$
$491$	−7.53842			−0.340204			−0.170102	+	0.985426i	$0.554410\pi$
$492$		0			0
$493$	4.71801			0.212488
$494$		0			0
$495$	30.3688			1.36498
$496$		0			0
$497$	0.999222	+	3.07529i	0.0448212	+	0.137946i
$498$		0			0
$499$	−18.0927	+	13.1451i	−0.809940	+	0.588456i	−0.913813	−	0.406134i	$-0.866876\pi$
$499$	−18.0927	+	13.1451i	−0.809940	+	0.588456i	0.103873	+	0.994591i	$0.466876\pi$
$500$		0			0
$501$	−12.6438			−0.564883
$502$		0			0
$503$	−2.96962	+	9.13956i	−0.132409	+	0.407513i	−0.995178	−	0.0980854i	$-0.968728\pi$
$503$	−2.96962	+	9.13956i	−0.132409	+	0.407513i	0.862769	+	0.505598i	$0.168728\pi$
$504$		0			0
$505$	−18.2584	−	13.2655i	−0.812490	−	0.590308i
$506$		0			0
$507$	1.24420	+	3.82925i	0.0552567	+	0.170063i
$508$		0			0
$509$	−5.54112	+	17.0538i	−0.245606	+	0.755897i	0.749930	+	0.661517i	$0.230087\pi$
$509$	−5.54112	+	17.0538i	−0.245606	+	0.755897i	−0.995536	+	0.0943804i	$0.969913\pi$
$510$		0			0
$511$	−3.60813	+	2.62146i	−0.159614	+	0.115966i
$512$		0			0
$513$	−12.8812	+	9.35871i	−0.568717	+	0.413197i
$514$		0			0
$515$	−40.6540	−	29.5369i	−1.79143	−	1.30155i
$516$		0			0
$517$	44.2993	−	32.1853i	1.94828	−	1.41551i
$518$		0			0
$519$	1.19169			0.0523095
$520$		0			0
$521$	−12.5708	−	38.6889i	−0.550736	−	1.69499i	−0.706947	−	0.707266i	$-0.749928\pi$
$521$	−12.5708	−	38.6889i	−0.550736	−	1.69499i	0.156212	−	0.987724i	$-0.450072\pi$
$522$		0			0
$523$	−11.1383	+	34.2802i	−0.487044	+	1.49897i	0.341955	+	0.939716i	$0.388911\pi$
$523$	−11.1383	+	34.2802i	−0.487044	+	1.49897i	−0.828999	+	0.559251i	$0.811089\pi$
$524$		0			0
$525$	0.562774	−	1.73204i	0.0245615	−	0.0755924i
$526$		0			0
$527$	−5.84978	−	4.25011i	−0.254820	−	0.185138i
$528$		0			0
$529$	14.6719	+	45.1556i	0.637910	+	1.96329i
$530$		0			0
$531$	−13.2091	−	9.59700i	−0.573228	−	0.416474i
$532$		0			0
$533$	13.1438	−	10.5043i	0.569321	−	0.454994i
$534$		0			0
$535$	−8.87506	−	6.44811i	−0.383702	−	0.278776i
$536$		0			0
$537$	2.10884	+	6.49034i	0.0910031	+	0.280079i
$538$		0			0
$539$	3.44100	+	2.50003i	0.148214	+	0.107684i
$540$		0			0
$541$	6.99007	−	21.5132i	0.300527	−	0.924926i	−0.680782	−	0.732486i	$-0.738360\pi$
$541$	6.99007	−	21.5132i	0.300527	−	0.924926i	0.981309	−	0.192440i	$-0.0616400\pi$
$542$		0			0
$543$	0.998865	−	3.07419i	0.0428654	−	0.131926i
$544$		0			0
$545$	−2.15668	−	6.63757i	−0.0923819	−	0.284322i
$546$		0			0
$547$	4.39316			0.187838			0.0939189	−	0.995580i	$-0.470061\pi$
$547$	4.39316			0.187838			0.0939189	+	0.995580i	$0.470061\pi$
$548$		0			0
$549$	6.31952	−	4.59140i	0.269710	−	0.195956i
$550$		0			0
$551$	−14.0716	−	10.2236i	−0.599468	−	0.435539i
$552$		0			0
$553$	1.80764	−	1.31332i	0.0768685	−	0.0558482i
$554$		0			0
$555$	−5.58935	+	4.06090i	−0.237255	+	0.172376i
$556$		0			0
$557$	11.7778	−	36.2485i	0.499043	−	1.53590i	−0.311517	−	0.950241i	$-0.600837\pi$
$557$	11.7778	−	36.2485i	0.499043	−	1.53590i	0.810560	−	0.585656i	$-0.199163\pi$
$558$		0			0
$559$	0.644246	+	1.98279i	0.0272487	+	0.0838629i
$560$		0			0
$561$	−2.67114	−	1.94070i	−0.112776	−	0.0819364i
$562$		0			0
$563$	4.39644	−	13.5308i	0.185288	−	0.570257i	−0.814666	−	0.579931i	$-0.803079\pi$
$563$	4.39644	−	13.5308i	0.185288	−	0.570257i	0.999953	+	0.00967428i	$0.00307947\pi$
$564$		0			0
$565$	−54.8275			−2.30661
$566$		0			0
$567$	4.25795	−	3.09359i	0.178817	−	0.129918i
$568$		0			0
$569$	13.9111	+	42.8140i	0.583184	+	1.79486i	0.606443	+	0.795127i	$0.292596\pi$
$569$	13.9111	+	42.8140i	0.583184	+	1.79486i	−0.0232591	+	0.999729i	$0.507404\pi$
$570$		0			0
$571$	24.3157			1.01758			0.508790	−	0.860891i	$-0.330093\pi$
$571$	24.3157			1.01758			0.508790	+	0.860891i	$0.330093\pi$
$572$		0			0
$573$	−6.18156			−0.258238
$574$		0			0
$575$	23.1450			0.965213
$576$		0			0
$577$	−44.2583			−1.84250			−0.921249	−	0.388973i	$-0.872830\pi$
$577$	−44.2583			−1.84250			−0.921249	+	0.388973i	$0.872830\pi$
$578$		0			0
$579$	−1.76854	−	5.44300i	−0.0734979	−	0.226203i
$580$		0			0
$581$	−10.0301	+	7.28730i	−0.416119	+	0.302328i
$582$		0			0
$583$	−31.2359			−1.29366
$584$		0			0
$585$	−5.79778	+	17.8437i	−0.239709	+	0.737748i
$586$		0			0
$587$	12.5201	+	9.09639i	0.516760	+	0.375448i	0.815382	−	0.578923i	$-0.196527\pi$
$587$	12.5201	+	9.09639i	0.516760	+	0.375448i	−0.298622	+	0.954372i	$0.596527\pi$
$588$		0			0
$589$	8.23740	+	25.3521i	0.339416	+	1.04462i
$590$		0			0
$591$	−3.84143	+	11.8227i	−0.158015	+	0.486321i
$592$		0			0
$593$	3.18853	−	2.31661i	0.130937	−	0.0951316i	−0.520389	−	0.853929i	$-0.674213\pi$
$593$	3.18853	−	2.31661i	0.130937	−	0.0951316i	0.651326	+	0.758798i	$0.274213\pi$
$594$		0			0
$595$	2.64783	−	1.92376i	0.108551	−	0.0788666i
$596$		0			0
$597$	5.12158	+	3.72105i	0.209612	+	0.152292i
$598$		0			0
$599$	−8.33494	+	6.05569i	−0.340556	+	0.247429i	−0.744897	−	0.667180i	$-0.767501\pi$
$599$	−8.33494	+	6.05569i	−0.340556	+	0.247429i	0.404340	+	0.914609i	$0.367501\pi$
$600$		0			0
$601$	−23.5385			−0.960154			−0.480077	−	0.877226i	$-0.659391\pi$
$601$	−23.5385			−0.960154			−0.480077	+	0.877226i	$0.659391\pi$
$602$		0			0
$603$	6.08769	+	18.7360i	0.247910	+	0.762989i
$604$		0			0
$605$	6.10255	−	18.7817i	0.248104	−	0.763585i
$606$		0			0
$607$	10.3029	−	31.7089i	0.418180	−	1.28703i	−0.491196	−	0.871049i	$-0.663440\pi$
$607$	10.3029	−	31.7089i	0.418180	−	1.28703i	0.909375	−	0.415976i	$-0.136560\pi$
$608$		0			0
$609$	−2.14563	−	1.55889i	−0.0869452	−	0.0631694i
$610$		0			0
$611$	10.4538	+	32.1734i	0.422914	+	1.30160i
$612$		0			0
$613$	−3.17767	−	2.30871i	−0.128345	−	0.0932479i	0.521761	−	0.853092i	$-0.325275\pi$
$613$	−3.17767	−	2.30871i	−0.128345	−	0.0932479i	−0.650106	+	0.759844i	$0.725275\pi$
$614$		0			0
$615$	11.7680	−	0.540842i	0.474533	−	0.0218089i
$616$		0			0
$617$	11.9094	+	8.65269i	0.479454	+	0.348344i	0.801114	−	0.598511i	$-0.204241\pi$
$617$	11.9094	+	8.65269i	0.479454	+	0.348344i	−0.321660	+	0.946855i	$0.604241\pi$
$618$		0			0
$619$	−5.19031	−	15.9741i	−0.208616	−	0.642055i	−0.999545	−	0.0301471i	$-0.990402\pi$
$619$	−5.19031	−	15.9741i	−0.208616	−	0.642055i	0.790929	−	0.611908i	$-0.209598\pi$
$620$		0			0
$621$	−24.9616	−	18.1357i	−1.00168	−	0.727760i
$622$		0			0
$623$	−0.852810	+	2.62468i	−0.0341671	+	0.105156i
$624$		0			0
$625$	−9.63638	+	29.6577i	−0.385455	+	1.18631i
$626$		0			0
$627$	3.76139	+	11.5764i	0.150215	+	0.462315i
$628$		0			0
$629$	−4.41287			−0.175953
$630$		0			0
$631$	−30.9180	+	22.4633i	−1.23083	+	0.894249i	−0.996952	−	0.0780179i	$-0.975141\pi$
$631$	−30.9180	+	22.4633i	−1.23083	+	0.894249i	−0.233876	+	0.972267i	$0.575141\pi$
$632$		0			0
$633$	−9.35826	−	6.79917i	−0.371957	−	0.270243i
$634$		0			0
$635$	27.1225	−	19.7056i	1.07632	−	0.781994i
$636$		0			0
$637$	−2.12587	+	1.54453i	−0.0842299	+	0.0611966i
$638$		0			0
$639$	2.56164	−	7.88391i	0.101337	−	0.311883i
$640$		0			0
$641$	9.19389	+	28.2959i	0.363137	+	1.11762i	0.951139	+	0.308762i	$0.0999145\pi$
$641$	9.19389	+	28.2959i	0.363137	+	1.11762i	−0.588002	+	0.808859i	$0.700085\pi$
$642$		0			0
$643$	−6.48194	−	4.70941i	−0.255623	−	0.185721i	0.452592	−	0.891718i	$-0.350499\pi$
$643$	−6.48194	−	4.70941i	−0.255623	−	0.185721i	−0.708215	+	0.705997i	$0.750499\pi$
$644$		0			0
$645$	−0.451070	+	1.38825i	−0.0177609	+	0.0546623i
$646$		0			0
$647$	−10.7034			−0.420795			−0.210398	−	0.977616i	$-0.567476\pi$
$647$	−10.7034			−0.420795			−0.210398	+	0.977616i	$0.567476\pi$
$648$		0			0
$649$	−21.9152	+	15.9223i	−0.860246	+	0.625005i
$650$		0			0
$651$	1.25604	+	3.86568i	0.0492279	+	0.151508i
$652$		0			0
$653$	23.3092			0.912159			0.456079	−	0.889939i	$-0.349253\pi$
$653$	23.3092			0.912159			0.456079	+	0.889939i	$0.349253\pi$
$654$		0			0
$655$	−8.26791			−0.323054
$656$		0			0
$657$	11.4335			0.446064
$658$		0			0
$659$	42.2917			1.64745			0.823726	−	0.566988i	$-0.191891\pi$
$659$	42.2917			1.64745			0.823726	+	0.566988i	$0.191891\pi$
$660$		0			0
$661$	−7.85189	−	24.1656i	−0.305403	−	0.939934i	−0.979526	−	0.201315i	$-0.935478\pi$
$661$	−7.85189	−	24.1656i	−0.305403	−	0.939934i	0.674123	−	0.738619i	$-0.264522\pi$
$662$		0			0
$663$	1.65025	−	1.19898i	0.0640903	−	0.0465643i
$664$		0			0
$665$	−12.0659			−0.467894
$666$		0			0
$667$	10.4156	−	32.0559i	0.403294	−	1.24121i
$668$		0			0
$669$	−3.42905	−	2.49135i	−0.132575	−	0.0963213i
$670$		0			0
$671$	−4.00479	−	12.3255i	−0.154603	−	0.475819i
$672$		0			0
$673$	2.79177	−	8.59218i	0.107615	−	0.331204i	−0.882720	−	0.469898i	$-0.844291\pi$
$673$	2.79177	−	8.59218i	0.107615	−	0.331204i	0.990335	+	0.138694i	$0.0442905\pi$
$674$		0			0
$675$	−8.19724	+	5.95565i	−0.315512	+	0.229233i
$676$		0			0
$677$	34.8330	−	25.3077i	1.33874	−	0.972652i	0.339252	−	0.940696i	$-0.389826\pi$
$677$	34.8330	−	25.3077i	1.33874	−	0.972652i	0.999489	−	0.0319568i	$-0.0101739\pi$
$678$		0			0
$679$	−1.00406	−	0.729494i	−0.0385324	−	0.0279954i
$680$		0			0
$681$	3.02789	−	2.19989i	0.116029	−	0.0842999i
$682$		0			0
$683$	−1.09807			−0.0420163			−0.0210082	−	0.999779i	$-0.506688\pi$
$683$	−1.09807			−0.0420163			−0.0210082	+	0.999779i	$0.506688\pi$
$684$		0			0
$685$	9.73304	+	29.9552i	0.371880	+	1.14453i
$686$		0			0
$687$	−3.16797	+	9.75002i	−0.120866	+	0.371986i
$688$		0			0
$689$	5.96331	−	18.3532i	0.227184	−	0.699201i
$690$		0			0
$691$	−7.75351	−	5.63325i	−0.294957	−	0.214299i	0.430458	−	0.902611i	$-0.358352\pi$
$691$	−7.75351	−	5.63325i	−0.294957	−	0.214299i	−0.725415	+	0.688312i	$0.758352\pi$
$692$		0			0
$693$	−3.36950	−	10.3702i	−0.127997	−	0.393933i
$694$		0			0
$695$	−17.2042	−	12.4996i	−0.652593	−	0.474136i
$696$		0			0
$697$	6.28411	+	4.13867i	0.238028	+	0.156763i
$698$		0			0
$699$	1.49671	+	1.08742i	0.0566106	+	0.0411300i
$700$		0			0
$701$	−8.81022	−	27.1151i	−0.332757	−	1.02412i	−0.967816	−	0.251658i	$-0.919024\pi$
$701$	−8.81022	−	27.1151i	−0.332757	−	1.02412i	0.635059	−	0.772464i	$-0.280976\pi$
$702$		0			0
$703$	13.1615	+	9.56237i	0.496394	+	0.360651i
$704$		0			0
$705$	−7.31922	+	22.5263i	−0.275658	+	0.848388i
$706$		0			0
$707$	−2.50405	+	7.70668i	−0.0941746	+	0.289840i
$708$		0			0
$709$	−4.35984	−	13.4182i	−0.163737	−	0.503932i	0.835204	−	0.549941i	$-0.185350\pi$
$709$	−4.35984	−	13.4182i	−0.163737	−	0.503932i	−0.998941	+	0.0460090i	$0.985350\pi$
$710$		0			0
$711$	−5.72808			−0.214820
$712$		0			0
$713$	−41.7910	+	30.3630i	−1.56509	+	1.13710i
$714$		0			0
$715$	25.1830	+	18.2965i	0.941791	+	0.684252i
$716$		0			0
$717$	−10.3751	+	7.53797i	−0.387466	+	0.281511i
$718$		0			0
$719$	−6.78742	+	4.93135i	−0.253128	+	0.183908i	−0.707112	−	0.707102i	$-0.750002\pi$
$719$	−6.78742	+	4.93135i	−0.253128	+	0.183908i	0.453984	+	0.891010i	$0.350002\pi$
$720$		0			0
$721$	−5.57549	+	17.1596i	−0.207642	+	0.639057i
$722$		0			0
$723$	−4.94801	−	15.2284i	−0.184018	−	0.566350i
$724$		0			0
$725$	−8.95478	−	6.50603i	−0.332572	−	0.241628i
$726$		0			0
$727$	−15.7364	+	48.4317i	−0.583631	+	1.79623i	0.0210681	+	0.999778i	$0.493293\pi$
$727$	−15.7364	+	48.4317i	−0.583631	+	1.79623i	−0.604699	+	0.796454i	$0.706707\pi$
$728$		0			0
$729$	−6.20937			−0.229977
$730$		0			0
$731$	−0.754287	+	0.548021i	−0.0278983	+	0.0202693i
$732$		0			0
$733$	−5.54421	−	17.0633i	−0.204780	−	0.630248i	−0.999722	−	0.0235631i	$-0.992499\pi$
$733$	−5.54421	−	17.0633i	−0.204780	−	0.630248i	0.794942	−	0.606685i	$-0.207501\pi$
$734$		0			0
$735$	−1.83980			−0.0678620
$736$		0			0
$737$	32.6844			1.20395
$738$		0			0
$739$	−36.5321			−1.34386			−0.671928	−	0.740617i	$-0.734533\pi$
$739$	−36.5321			−1.34386			−0.671928	+	0.740617i	$0.734533\pi$
$740$		0			0
$741$	−7.51999			−0.276254
$742$		0			0
$743$	2.64444	+	8.13875i	0.0970151	+	0.298582i	0.987774	−	0.155895i	$-0.0498262\pi$
$743$	2.64444	+	8.13875i	0.0970151	+	0.298582i	−0.890759	+	0.454477i	$0.849826\pi$
$744$		0			0
$745$	−49.8210	+	36.1971i	−1.82530	+	1.32616i
$746$		0			0
$747$	31.7837			1.16290
$748$		0			0
$749$	−1.21717	+	3.74606i	−0.0444744	+	0.136878i
$750$		0			0
$751$	−3.78998	−	2.75358i	−0.138298	−	0.100480i	0.516485	−	0.856296i	$-0.327240\pi$
$751$	−3.78998	−	2.75358i	−0.138298	−	0.100480i	−0.654783	+	0.755817i	$0.727240\pi$
$752$		0			0
$753$	2.07170	+	6.37605i	0.0754971	+	0.232356i
$754$		0			0
$755$	−7.73513	+	23.8063i	−0.281510	+	0.866399i
$756$		0			0
$757$	−19.4584	+	14.1374i	−0.707229	+	0.513832i	−0.882278	−	0.470728i	$-0.843991\pi$
$757$	−19.4584	+	14.1374i	−0.707229	+	0.513832i	0.175050	+	0.984560i	$0.443991\pi$
$758$		0			0
$759$	−19.0827	+	13.8644i	−0.692660	+	0.503247i
$760$		0			0
$761$	−9.76788	−	7.09678i	−0.354085	−	0.257258i	0.396496	−	0.918037i	$-0.370226\pi$
$761$	−9.76788	−	7.09678i	−0.354085	−	0.257258i	−0.750581	+	0.660779i	$0.770226\pi$
$762$		0			0
$763$	−2.02729	+	1.47291i	−0.0733927	+	0.0533229i
$764$		0			0
$765$	−8.39052			−0.303360
$766$		0			0
$767$	−5.17156	−	15.9164i	−0.186734	−	0.574709i
$768$		0			0
$769$	1.55946	−	4.79954i	0.0562357	−	0.173076i	−0.918993	−	0.394273i	$-0.870996\pi$
$769$	1.55946	−	4.79954i	0.0562357	−	0.173076i	0.975229	+	0.221197i	$0.0709964\pi$
$770$		0			0
$771$	−2.45430	+	7.55355i	−0.0883894	+	0.272035i
$772$		0			0
$773$	−33.1362	−	24.0748i	−1.19183	−	0.865912i	−0.198370	−	0.980127i	$-0.563565\pi$
$773$	−33.1362	−	24.0748i	−1.19183	−	0.865912i	−0.993456	+	0.114215i	$0.963565\pi$
$774$		0			0
$775$	5.24207	+	16.1334i	0.188301	+	0.579530i
$776$		0			0
$777$	2.00686	+	1.45807i	0.0719956	+	0.0523078i
$778$		0			0
$779$	−9.77428	−	25.9609i	−0.350200	−	0.930145i
$780$		0			0
$781$	−11.1266	−	8.08397i	−0.398142	−	0.289267i
$782$		0			0
$783$	4.55971	+	14.0333i	0.162951	+	0.501511i
$784$		0			0
$785$	−11.4004	−	8.28287i	−0.406897	−	0.295628i
$786$		0			0
$787$	9.67450	−	29.7750i	0.344859	−	1.06137i	−0.616801	−	0.787119i	$-0.711572\pi$
$787$	9.67450	−	29.7750i	0.344859	−	1.06137i	0.961659	−	0.274246i	$-0.0884284\pi$
$788$		0			0
$789$	−6.17323	+	18.9993i	−0.219773	+	0.676391i
$790$		0			0
$791$	6.08326	+	18.7223i	0.216296	+	0.665690i
$792$		0			0
$793$	8.00661			0.284323
$794$		0			0
$795$	10.9309	−	7.94175i	0.387678	−	0.281665i
$796$		0			0
$797$	5.15538	+	3.74560i	0.182613	+	0.132676i	0.675336	−	0.737510i	$-0.263999\pi$
$797$	5.15538	+	3.74560i	0.182613	+	0.132676i	−0.492723	+	0.870186i	$0.663999\pi$
$798$		0			0
$799$	−12.2393	+	8.89239i	−0.432996	+	0.314590i
$800$		0			0
$801$	5.72379	−	4.15858i	0.202240	−	0.146936i
$802$		0			0
$803$	5.86183	−	18.0409i	0.206859	−	0.636648i
$804$		0			0
$805$	−7.22534	−	22.2373i	−0.254660	−	0.783762i
$806$		0			0
$807$	−10.8409	−	7.87638i	−0.381618	−	0.277262i
$808$		0			0
$809$	14.3192	−	44.0700i	0.503437	−	1.54942i	−0.299947	−	0.953956i	$-0.596969\pi$
$809$	14.3192	−	44.0700i	0.503437	−	1.54942i	0.803383	−	0.595462i	$-0.203031\pi$
$810$		0			0
$811$	25.7425			0.903942			0.451971	−	0.892033i	$-0.350721\pi$
$811$	25.7425			0.903942			0.451971	+	0.892033i	$0.350721\pi$
$812$		0			0
$813$	13.0660	−	9.49299i	0.458244	−	0.332934i
$814$		0			0
$815$	9.22357	+	28.3872i	0.323088	+	0.994361i
$816$		0			0
$817$	3.43720			0.120252
$818$		0			0
$819$	6.73650			0.235392
$820$		0			0
$821$	−17.1090			−0.597107			−0.298554	−	0.954393i	$-0.596504\pi$
$821$	−17.1090			−0.597107			−0.298554	+	0.954393i	$0.596504\pi$
$822$		0			0
$823$	50.8710			1.77325			0.886626	−	0.462487i	$-0.153043\pi$
$823$	50.8710			1.77325			0.886626	+	0.462487i	$0.153043\pi$
$824$		0			0
$825$	2.39365	+	7.36690i	0.0833362	+	0.256482i
$826$		0			0
$827$	−24.9860	+	18.1534i	−0.868848	+	0.631255i	−0.930277	−	0.366857i	$-0.880434\pi$
$827$	−24.9860	+	18.1534i	−0.868848	+	0.631255i	0.0614299	+	0.998111i	$0.480434\pi$
$828$		0			0
$829$	28.7745			0.999381			0.499690	−	0.866204i	$-0.333447\pi$
$829$	28.7745			0.999381			0.499690	+	0.866204i	$0.333447\pi$
$830$		0			0
$831$	4.64328	−	14.2906i	0.161074	−	0.495734i
$832$		0			0
$833$	−0.950704	−	0.690727i	−0.0329399	−	0.0239323i
$834$		0			0
$835$	16.4733	+	50.6995i	0.570081	+	1.75453i
$836$		0			0
$837$	6.98812	−	21.5072i	0.241545	−	0.743399i
$838$		0			0
$839$	16.8423	−	12.2367i	0.581462	−	0.422457i	−0.257789	−	0.966201i	$-0.582994\pi$
$839$	16.8423	−	12.2367i	0.581462	−	0.422457i	0.839251	+	0.543744i	$0.182994\pi$
$840$		0			0
$841$	10.4208	−	7.57118i	0.359339	−	0.261075i
$842$		0			0
$843$	−0.864953	−	0.628425i	−0.0297906	−	0.0216441i
$844$		0			0
$845$	13.7336	−	9.97804i	0.472450	−	0.343255i
$846$		0			0
$847$	−7.09061			−0.243636
$848$		0			0
$849$	−3.38546	−	10.4194i	−0.116189	−	0.357592i
$850$		0			0
$851$	−9.74197	+	29.9827i	−0.333950	+	1.02779i
$852$		0			0
$853$	7.01337	−	21.5849i	0.240133	−	0.739054i	−0.756266	−	0.654264i	$-0.772978\pi$
$853$	7.01337	−	21.5849i	0.240133	−	0.739054i	0.996399	−	0.0847891i	$-0.0270217\pi$
$854$		0			0
$855$	25.0249	+	18.1816i	0.855833	+	0.621799i
$856$		0			0
$857$	−8.11365	−	24.9712i	−0.277157	−	0.853002i	−0.988641	−	0.150299i	$-0.951976\pi$
$857$	−8.11365	−	24.9712i	−0.277157	−	0.853002i	0.711484	−	0.702703i	$-0.248024\pi$
$858$		0			0
$859$	−43.2439	−	31.4185i	−1.47546	−	1.07199i	−0.978984	−	0.203936i	$-0.934627\pi$
$859$	−43.2439	−	31.4185i	−1.47546	−	1.07199i	−0.496477	−	0.868050i	$-0.665373\pi$
$860$		0			0
$861$	−1.49038	−	3.95851i	−0.0507920	−	0.134906i
$862$		0			0
$863$	−19.3401	−	14.0514i	−0.658345	−	0.478316i	0.207759	−	0.978180i	$-0.433383\pi$
$863$	−19.3401	−	14.0514i	−0.658345	−	0.478316i	−0.866104	+	0.499864i	$0.833383\pi$
$864$		0			0
$865$	−1.55262	−	4.77848i	−0.0527908	−	0.162473i
$866$		0			0
$867$	−8.34714	−	6.06456i	−0.283484	−	0.205963i
$868$		0			0
$869$	−2.93672	+	9.03829i	−0.0996214	+	0.306603i
$870$		0			0
$871$	−6.23987	+	19.2043i	−0.211430	+	0.650714i
$872$		0			0
$873$	0.983199	+	3.02597i	0.0332762	+	0.102414i
$874$		0			0
$875$	6.24723			0.211195
$876$		0			0
$877$	37.4177	−	27.1856i	1.26351	−	0.917991i	0.264582	−	0.964363i	$-0.414766\pi$
$877$	37.4177	−	27.1856i	1.26351	−	0.917991i	0.998924	+	0.0463724i	$0.0147661\pi$
$878$		0			0
$879$	6.03279	+	4.38308i	0.203481	+	0.147838i
$880$		0			0
$881$	−24.5635	+	17.8464i	−0.827564	+	0.601261i	−0.918869	−	0.394562i	$-0.870896\pi$
$881$	−24.5635	+	17.8464i	−0.827564	+	0.601261i	0.0913050	+	0.995823i	$0.470896\pi$
$882$		0			0
$883$	−35.4858	+	25.7819i	−1.19419	+	0.867631i	−0.993701	−	0.112065i	$-0.964254\pi$
$883$	−35.4858	+	25.7819i	−1.19419	+	0.867631i	−0.200490	+	0.979696i	$0.564254\pi$
$884$		0			0
$885$	3.62087	−	11.1439i	0.121714	−	0.374598i
$886$		0			0
$887$	4.99047	+	15.3591i	0.167564	+	0.515708i	0.999216	−	0.0395887i	$-0.0126048\pi$
$887$	4.99047	+	15.3591i	0.167564	+	0.515708i	−0.831652	+	0.555297i	$0.812605\pi$
$888$		0			0
$889$	−9.73833	−	7.07531i	−0.326613	−	0.237298i
$890$		0			0
$891$	−6.91755	+	21.2900i	−0.231747	+	0.713243i
$892$		0			0
$893$	55.7732			1.86638
$894$		0			0
$895$	23.2776	−	16.9122i	0.778085	−	0.565312i
$896$		0			0
$897$	−4.50316	−	13.8593i	−0.150356	−	0.462748i
$898$		0			0
$899$	24.7039			0.823921
$900$		0			0
$901$	8.63008			0.287510
$902$		0			0
$903$	0.524103			0.0174410
$904$		0			0
$905$	−13.6284			−0.453022
$906$		0			0
$907$	−5.82801	−	17.9368i	−0.193516	−	0.595580i	−0.999991	−	0.00431196i	$-0.998627\pi$
$907$	−5.82801	−	17.9368i	−0.193516	−	0.595580i	0.806475	−	0.591268i	$-0.201373\pi$
$908$		0			0
$909$	16.8064	−	12.2106i	0.557433	−	0.404999i
$910$		0			0
$911$	−8.37060			−0.277330			−0.138665	−	0.990339i	$-0.544281\pi$
$911$	−8.37060			−0.277330			−0.138665	+	0.990339i	$0.544281\pi$
$912$		0			0
$913$	16.2951	−	50.1511i	0.539289	−	1.65976i
$914$		0			0
$915$	4.53522	+	3.29503i	0.149930	+	0.108930i
$916$		0			0
$917$	0.917345	+	2.82330i	0.0302934	+	0.0932335i
$918$		0			0
$919$	14.1680	−	43.6047i	0.467360	−	1.43839i	−0.388630	−	0.921394i	$-0.627052\pi$
$919$	14.1680	−	43.6047i	0.467360	−	1.43839i	0.855990	−	0.516992i	$-0.172948\pi$
$920$		0			0
$921$	10.6995	−	7.77367i	0.352562	−	0.256151i
$922$		0			0
$923$	6.87410	−	4.99432i	0.226264	−	0.164390i
$924$		0			0
$925$	8.37562	+	6.08525i	0.275389	+	0.200082i
$926$		0			0
$927$	37.4209	−	27.1879i	1.22906	−	0.892968i
$928$		0			0
$929$	−8.86307			−0.290788			−0.145394	−	0.989374i	$-0.546445\pi$
$929$	−8.86307			−0.290788			−0.145394	+	0.989374i	$0.546445\pi$
$930$		0			0
$931$	1.33874	+	4.12021i	0.0438754	+	0.135035i
$932$		0			0
$933$	2.68559	−	8.26538i	0.0879221	−	0.270596i
$934$		0			0
$935$	−4.30172	+	13.2393i	−0.140681	+	0.432972i
$936$		0			0
$937$	1.92458	+	1.39829i	0.0628733	+	0.0456801i	0.618778	−	0.785566i	$-0.287628\pi$
$937$	1.92458	+	1.39829i	0.0628733	+	0.0456801i	−0.555905	+	0.831246i	$0.687628\pi$
$938$		0			0
$939$	−1.31018	−	4.03233i	−0.0427562	−	0.131590i
$940$		0			0
$941$	−20.7710	−	15.0910i	−0.677114	−	0.491952i	0.195285	−	0.980747i	$-0.437437\pi$
$941$	−20.7710	−	15.0910i	−0.677114	−	0.491952i	−0.872399	+	0.488794i	$0.837437\pi$
$942$		0			0
$943$	41.9927	−	33.5600i	1.36747	−	1.09286i
$944$		0			0
$945$	8.28107	+	6.01655i	0.269383	+	0.195718i
$946$		0			0
$947$	12.6718	+	38.9999i	0.411780	+	1.26733i	0.915100	+	0.403227i	$0.132112\pi$
$947$	12.6718	+	38.9999i	0.411780	+	1.26733i	−0.503320	+	0.864100i	$0.667888\pi$
$948$		0			0
$949$	9.48113	+	6.88845i	0.307771	+	0.223608i
$950$		0			0
$951$	2.99184	−	9.20794i	0.0970171	−	0.298588i
$952$		0			0
$953$	−3.97703	+	12.2400i	−0.128829	+	0.396493i	−0.994579	−	0.103982i	$-0.966842\pi$
$953$	−3.97703	+	12.2400i	−0.128829	+	0.396493i	0.865751	+	0.500476i	$0.166842\pi$
$954$		0			0
$955$	8.05378	+	24.7870i	0.260614	+	0.802088i
$956$		0			0
$957$	11.2804			0.364642
$958$		0			0
$959$	9.14911	−	6.64722i	0.295440	−	0.214650i
$960$		0			0
$961$	−5.55042	−	4.03261i	−0.179046	−	0.130084i
$962$		0			0
$963$	8.16925	−	5.93531i	0.263251	−	0.191263i
$964$		0			0
$965$	−19.5213	+	14.1831i	−0.628413	+	0.456569i
$966$		0			0
$967$	5.99742	−	18.4582i	0.192864	−	0.593575i	−0.807131	−	0.590373i	$-0.798981\pi$
$967$	5.99742	−	18.4582i	0.192864	−	0.593575i	0.999995	−	0.00320201i	$-0.00101923\pi$
$968$		0			0
$969$	−1.03922	−	3.19840i	−0.0333847	−	0.102747i
$970$		0			0
$971$	28.0327	+	20.3670i	0.899613	+	0.653607i	0.938367	−	0.345642i	$-0.112339\pi$
$971$	28.0327	+	20.3670i	0.899613	+	0.653607i	−0.0387535	+	0.999249i	$0.512339\pi$
$972$		0			0
$973$	−2.35947	+	7.26170i	−0.0756411	+	0.232799i
$974$		0			0
$975$	−4.78553			−0.153260
$976$		0			0
$977$	−24.8073	+	18.0235i	−0.793655	+	0.576624i	−0.909046	−	0.416696i	$-0.863188\pi$
$977$	−24.8073	+	18.0235i	−0.793655	+	0.576624i	0.115391	+	0.993320i	$0.463188\pi$
$978$		0			0
$979$	−3.62726	−	11.1636i	−0.115928	−	0.356789i
$980$		0			0
$981$	6.42412			0.205106
$982$		0			0
$983$	−12.1897			−0.388791			−0.194395	−	0.980923i	$-0.562275\pi$
$983$	−12.1897			−0.388791			−0.194395	+	0.980923i	$0.562275\pi$
$984$		0			0
$985$	52.4119			1.66998
$986$		0			0
$987$	8.50428			0.270694
$988$		0			0
$989$	2.05828	+	6.33473i	0.0654495	+	0.201433i
$990$		0			0
$991$	−47.2625	+	34.3382i	−1.50134	+	1.09079i	−0.531500	+	0.847058i	$0.678372\pi$
$991$	−47.2625	+	34.3382i	−1.50134	+	1.09079i	−0.969843	+	0.243731i	$0.921628\pi$
$992$		0			0
$993$	1.87669			0.0595549
$994$		0			0
$995$	8.24800	−	25.3847i	0.261479	−	0.804750i
$996$		0			0
$997$	−1.84567	−	1.34096i	−0.0584529	−	0.0424685i	0.558175	−	0.829723i	$-0.311502\pi$
$997$	−1.84567	−	1.34096i	−0.0584529	−	0.0424685i	−0.616628	+	0.787255i	$0.711502\pi$
$998$		0			0
$999$	−4.26481	−	13.1257i	−0.134933	−	0.415280i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.n.e.953.2	yes	24
41.37	even	5	inner	1148.2.n.e.365.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.n.e.365.2	✓	24	41.37	even	5	inner
1148.2.n.e.953.2	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-0.660580 q^{3} +(0.860652 + 2.64881i) q^{5} +(0.809017 - 0.587785i) q^{7} -2.56363 q^{9} +O(q^{10})\)	\(q-0.660580 q^{3} +(0.860652 + 2.64881i) q^{5} +(0.809017 - 0.587785i) q^{7} -2.56363 q^{9} +(-1.31434 + 4.04513i) q^{11} +(-2.12587 - 1.54453i) q^{13} +(-0.568529 - 1.74975i) q^{15} +(0.363137 - 1.11762i) q^{17} +(-3.50486 + 2.54643i) q^{19} +(-0.534420 + 0.388279i) q^{21} +(-6.79186 - 4.93457i) q^{23} +(-2.23041 + 1.62048i) q^{25} +3.67523 q^{27} +(1.24066 + 3.81836i) q^{29} +(1.90141 - 5.85195i) q^{31} +(0.868229 - 2.67214i) q^{33} +(2.25322 + 1.63706i) q^{35} +(-1.16042 - 3.57141i) q^{37} +(1.40431 + 1.02029i) q^{39} +(-1.69701 + 6.17415i) q^{41} +(-0.641872 - 0.466348i) q^{43} +(-2.20640 - 6.79059i) q^{45} +(-10.4153 - 7.56713i) q^{47} +(0.309017 - 0.951057i) q^{49} +(-0.239881 + 0.738277i) q^{51} +(2.26939 + 6.98447i) q^{53} -11.8460 q^{55} +(2.31524 - 1.68212i) q^{57} +(5.15250 + 3.74351i) q^{59} +(-2.46506 + 1.79097i) q^{61} +(-2.07402 + 1.50687i) q^{63} +(2.26155 - 6.96033i) q^{65} +(-2.37463 - 7.30837i) q^{67} +(4.48657 + 3.25968i) q^{69} +(-0.999222 + 3.07529i) q^{71} -4.45989 q^{73} +(1.47336 - 1.07046i) q^{75} +(1.31434 + 4.04513i) q^{77} +2.23436 q^{79} +5.26312 q^{81} -12.3979 q^{83} +3.27290 q^{85} +(-0.819556 - 2.52233i) q^{87} +(-2.23269 + 1.62214i) q^{89} -2.62772 q^{91} +(-1.25604 + 3.86568i) q^{93} +(-9.76149 - 7.09214i) q^{95} +(-0.383518 - 1.18035i) q^{97} +(3.36950 - 10.3702i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9}+O(q^{10}) \) 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9	\( 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9} - 8 q^{11} + 10 q^{15} + 8 q^{17} - 28 q^{19} + 3 q^{21} - 23 q^{23} + 17 q^{25} + 12 q^{27} - 31 q^{29} + 2 q^{31} + 12 q^{33} + 13 q^{35} + 7 q^{37} - 16 q^{39} - q^{41} - 2 q^{43} + 71 q^{45} + 15 q^{47} - 6 q^{49} + 2 q^{51} + 28 q^{53} - 16 q^{55} - 15 q^{57} + 17 q^{59} + 35 q^{61} - q^{63} + 62 q^{65} - 10 q^{67} - 9 q^{69} - 25 q^{71} - 74 q^{73} + 17 q^{75} + 8 q^{77} + 64 q^{81} + 96 q^{83} - 94 q^{85} - q^{87} - 33 q^{89} - 15 q^{93} - 29 q^{95} - 34 q^{97} - 3 q^{99}+O(q^{100}) \) 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9 - 8 * q^11 + 10 * q^15 + 8 * q^17 - 28 * q^19 + 3 * q^21 - 23 * q^23 + 17 * q^25 + 12 * q^27 - 31 * q^29 + 2 * q^31 + 12 * q^33 + 13 * q^35 + 7 * q^37 - 16 * q^39 - q^41 - 2 * q^43 + 71 * q^45 + 15 * q^47 - 6 * q^49 + 2 * q^51 + 28 * q^53 - 16 * q^55 - 15 * q^57 + 17 * q^59 + 35 * q^61 - q^63 + 62 * q^65 - 10 * q^67 - 9 * q^69 - 25 * q^71 - 74 * q^73 + 17 * q^75 + 8 * q^77 + 64 * q^81 + 96 * q^83 - 94 * q^85 - q^87 - 33 * q^89 - 15 * q^93 - 29 * q^95 - 34 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more