LMFDB - Embedded newform 289.2.d.f.134.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,2,Mod(110,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("289.110");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	289.d (of order $8$, degree $4$, 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:	$2.30767661842$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			134.5
Character	$\chi$	$=$	289.134
Dual form			289.2.d.f.110.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32893 + 1.32893i) q^{2} +(-0.968988 - 2.33935i) q^{3} +1.53209i q^{4} +(-0.111434 + 0.0461573i) q^{5} +(1.82110 - 4.39653i) q^{6} +(1.41547 + 0.586305i) q^{7} +(0.621819 - 0.621819i) q^{8} +(-2.41228 + 2.41228i) q^{9} +O(q^{10})$	\(q+(1.32893 + 1.32893i) q^{2} +(-0.968988 - 2.33935i) q^{3} +1.53209i q^{4} +(-0.111434 + 0.0461573i) q^{5} +(1.82110 - 4.39653i) q^{6} +(1.41547 + 0.586305i) q^{7} +(0.621819 - 0.621819i) q^{8} +(-2.41228 + 2.41228i) q^{9} +(-0.209426 - 0.0867473i) q^{10} +(1.03118 - 2.48948i) q^{11} +(3.58408 - 1.48458i) q^{12} -4.57398i q^{13} +(1.10189 + 2.66021i) q^{14} +(0.215956 + 0.215956i) q^{15} +4.71688 q^{16} -6.41147 q^{18} +(1.32893 + 1.32893i) q^{19} +(-0.0707170 - 0.170726i) q^{20} -3.87939i q^{21} +(4.67869 - 1.93798i) q^{22} +(-2.83625 + 6.84731i) q^{23} +(-2.05719 - 0.852114i) q^{24} +(-3.52525 + 3.52525i) q^{25} +(6.07848 - 6.07848i) q^{26} +(0.962580 + 0.398714i) q^{27} +(-0.898271 + 2.16862i) q^{28} +(3.15179 - 1.30551i) q^{29} +0.573978i q^{30} +(1.46855 + 3.54538i) q^{31} +(5.02475 + 5.02475i) q^{32} -6.82295 q^{33} -0.184793 q^{35} +(-3.69582 - 3.69582i) q^{36} +(2.00869 + 4.84942i) q^{37} +3.53209i q^{38} +(-10.7001 + 4.43213i) q^{39} +(-0.0405900 + 0.0979930i) q^{40} +(-5.77330 - 2.39138i) q^{41} +(5.15542 - 5.15542i) q^{42} +(-3.88216 + 3.88216i) q^{43} +(3.81410 + 1.57985i) q^{44} +(0.157464 - 0.380153i) q^{45} +(-12.8687 + 5.33040i) q^{46} +7.34730i q^{47} +(-4.57060 - 11.0344i) q^{48} +(-3.28996 - 3.28996i) q^{49} -9.36959 q^{50} +7.00774 q^{52} +(-0.581912 - 0.581912i) q^{53} +(0.749337 + 1.80906i) q^{54} +0.325008i q^{55} +(1.24474 - 0.515588i) q^{56} +(1.82110 - 4.39653i) q^{57} +(5.92343 + 2.45356i) q^{58} +(-2.22237 + 2.22237i) q^{59} +(-0.330863 + 0.330863i) q^{60} +(1.13331 + 0.469431i) q^{61} +(-2.75996 + 6.66314i) q^{62} +(-4.82882 + 2.00016i) q^{63} +3.92127i q^{64} +(0.211122 + 0.509694i) q^{65} +(-9.06719 - 9.06719i) q^{66} +14.6236 q^{67} +18.7665 q^{69} +(-0.245576 - 0.245576i) q^{70} +(0.0651498 + 0.157286i) q^{71} +3.00000i q^{72} +(10.9024 - 4.51592i) q^{73} +(-3.77511 + 9.11392i) q^{74} +(11.6627 + 4.83085i) q^{75} +(-2.03603 + 2.03603i) q^{76} +(2.91919 - 2.91919i) q^{77} +(-20.1096 - 8.32968i) q^{78} +(-1.58735 + 3.83221i) q^{79} +(-0.525619 + 0.217718i) q^{80} +7.59627i q^{81} +(-4.49432 - 10.8502i) q^{82} +(-1.72093 - 1.72093i) q^{83} +5.94356 q^{84} -10.3182 q^{86} +(-6.10810 - 6.10810i) q^{87} +(-0.906801 - 2.18921i) q^{88} -15.0915i q^{89} +(0.714453 - 0.295936i) q^{90} +(2.68175 - 6.47431i) q^{91} +(-10.4907 - 4.34538i) q^{92} +(6.87087 - 6.87087i) q^{93} +(-9.76401 + 9.76401i) q^{94} +(-0.209426 - 0.0867473i) q^{95} +(6.88570 - 16.6235i) q^{96} +(10.3406 - 4.28320i) q^{97} -8.74422i q^{98} +(3.51783 + 8.49279i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 48 q^{16} - 72 q^{18} + 24 q^{35} - 168 q^{50} - 24 q^{52} + 72 q^{67} + 168 q^{69} + 24 q^{84} + 48 q^{86}+O(q^{100}) $ 24 * q + 48 * q^16 - 72 * q^18 + 24 * q^35 - 168 * q^50 - 24 * q^52 + 72 * q^67 + 168 * q^69 + 24 * q^84 + 48 * q^86

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{8}\right)$

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 $

$2$	1.32893	+	1.32893i	0.939693	+	0.939693i	0.998282	−	0.0585895i	$-0.0186603\pi$
$2$	1.32893	+	1.32893i	0.939693	+	0.939693i	−0.0585895	+	0.998282i	$0.518660\pi$
$3$	−0.968988	−	2.33935i	−0.559446	−	1.35062i	−0.910206	−	0.414156i	$-0.864077\pi$
$3$	−0.968988	−	2.33935i	−0.559446	−	1.35062i	0.350760	−	0.936465i	$-0.385923\pi$
$4$			1.53209i			0.766044i
$5$	−0.111434	+	0.0461573i	−0.0498346	+	0.0206422i	−0.407462	−	0.913222i	$-0.633586\pi$
$5$	−0.111434	+	0.0461573i	−0.0498346	+	0.0206422i	0.357627	+	0.933865i	$0.383586\pi$
$6$	1.82110	−	4.39653i	0.743462	−	1.79488i
$7$	1.41547	+	0.586305i	0.534996	+	0.221602i	0.633790	−	0.773505i	$-0.281498\pi$
$7$	1.41547	+	0.586305i	0.534996	+	0.221602i	−0.0987940	+	0.995108i	$0.531498\pi$
$8$	0.621819	−	0.621819i	0.219846	−	0.219846i
$9$	−2.41228	+	2.41228i	−0.804092	+	0.804092i
$10$	−0.209426	−	0.0867473i	−0.0662265	−	0.0274319i
$11$	1.03118	−	2.48948i	0.310911	−	0.750606i	−0.688761	−	0.724989i	$-0.741845\pi$
$11$	1.03118	−	2.48948i	0.310911	−	0.750606i	0.999672	−	0.0256173i	$-0.00815513\pi$
$12$	3.58408	−	1.48458i	1.03464	−	0.428560i
$13$		−	4.57398i		−	1.26859i	−0.773090	−	0.634297i	$-0.781290\pi$
$13$		−	4.57398i		−	1.26859i	0.773090	−	0.634297i	$-0.218710\pi$
$14$	1.10189	+	2.66021i	0.294493	+	0.710970i
$15$	0.215956	+	0.215956i	0.0557595	+	0.0557595i
$16$	4.71688			1.17922
$17$		0			0
$17$		0			0
$18$	−6.41147			−1.51120
$19$	1.32893	+	1.32893i	0.304877	+	0.304877i	0.842918	−	0.538042i	$-0.180836\pi$
$19$	1.32893	+	1.32893i	0.304877	+	0.304877i	−0.538042	+	0.842918i	$0.680836\pi$
$20$	−0.0707170	−	0.170726i	−0.0158128	−	0.0381755i
$21$		−	3.87939i		−	0.846551i
$22$	4.67869	−	1.93798i	0.997500	−	0.413178i
$23$	−2.83625	+	6.84731i	−0.591399	+	1.42776i	0.290753	+	0.956798i	$0.406094\pi$
$23$	−2.83625	+	6.84731i	−0.591399	+	1.42776i	−0.882152	+	0.470965i	$0.843906\pi$
$24$	−2.05719	−	0.852114i	−0.419921	−	0.173937i
$25$	−3.52525	+	3.52525i	−0.705049	+	0.705049i
$26$	6.07848	−	6.07848i	1.19209	−	1.19209i
$27$	0.962580	+	0.398714i	0.185249	+	0.0767325i
$28$	−0.898271	+	2.16862i	−0.169757	+	0.409830i
$29$	3.15179	−	1.30551i	0.585273	−	0.242428i	−0.0703426	−	0.997523i	$-0.522409\pi$
$29$	3.15179	−	1.30551i	0.585273	−	0.242428i	0.655615	+	0.755095i	$0.272409\pi$
$30$			0.573978i			0.104794i
$31$	1.46855	+	3.54538i	0.263759	+	0.636770i	0.999165	−	0.0408566i	$-0.0130087\pi$
$31$	1.46855	+	3.54538i	0.263759	+	0.636770i	−0.735406	+	0.677626i	$0.763009\pi$
$32$	5.02475	+	5.02475i	0.888258	+	0.888258i
$33$	−6.82295			−1.18772
$34$		0			0
$35$	−0.184793			−0.0312356
$36$	−3.69582	−	3.69582i	−0.615970	−	0.615970i
$37$	2.00869	+	4.84942i	0.330227	+	0.797239i	0.998574	+	0.0533891i	$0.0170023\pi$
$37$	2.00869	+	4.84942i	0.330227	+	0.797239i	−0.668347	+	0.743850i	$0.732998\pi$
$38$			3.53209i			0.572980i
$39$	−10.7001	+	4.43213i	−1.71339	+	0.709709i
$40$	−0.0405900	+	0.0979930i	−0.00641785	+	0.0154941i
$41$	−5.77330	−	2.39138i	−0.901637	−	0.373470i	−0.116788	−	0.993157i	$-0.537260\pi$
$41$	−5.77330	−	2.39138i	−0.901637	−	0.373470i	−0.784849	+	0.619686i	$0.787260\pi$
$42$	5.15542	−	5.15542i	0.795498	−	0.795498i
$43$	−3.88216	+	3.88216i	−0.592023	+	0.592023i	−0.938178	−	0.346154i	$-0.887487\pi$
$43$	−3.88216	+	3.88216i	−0.592023	+	0.592023i	0.346154	+	0.938178i	$0.387487\pi$
$44$	3.81410	+	1.57985i	0.574998	+	0.238172i
$45$	0.157464	−	0.380153i	0.0234734	−	0.0566698i
$46$	−12.8687	+	5.33040i	−1.89739	+	0.785925i
$47$			7.34730i			1.07171i	0.844309	+	0.535857i	$0.180011\pi$
$47$			7.34730i			1.07171i	−0.844309	+	0.535857i	$0.819989\pi$
$48$	−4.57060	−	11.0344i	−0.659710	−	1.59268i
$49$	−3.28996	−	3.28996i	−0.469994	−	0.469994i
$50$	−9.36959			−1.32506
$51$		0			0
$52$	7.00774			0.971799
$53$	−0.581912	−	0.581912i	−0.0799318	−	0.0799318i	0.666011	−	0.745942i	$-0.268001\pi$
$53$	−0.581912	−	0.581912i	−0.0799318	−	0.0799318i	−0.745942	+	0.666011i	$0.768001\pi$
$54$	0.749337	+	1.80906i	0.101972	+	0.246182i
$55$			0.325008i			0.0438240i
$56$	1.24474	−	0.515588i	0.166335	−	0.0688983i
$57$	1.82110	−	4.39653i	0.241211	−	0.582335i
$58$	5.92343	+	2.45356i	0.777784	+	0.322169i
$59$	−2.22237	+	2.22237i	−0.289328	+	0.289328i	−0.836814	−	0.547487i	$-0.815585\pi$
$59$	−2.22237	+	2.22237i	−0.289328	+	0.289328i	0.547487	+	0.836814i	$0.315585\pi$
$60$	−0.330863	+	0.330863i	−0.0427142	+	0.0427142i
$61$	1.13331	+	0.469431i	0.145105	+	0.0601044i	0.454054	−	0.890974i	$-0.349977\pi$
$61$	1.13331	+	0.469431i	0.145105	+	0.0601044i	−0.308949	+	0.951079i	$0.599977\pi$
$62$	−2.75996	+	6.66314i	−0.350516	+	0.846220i
$63$	−4.82882	+	2.00016i	−0.608375	+	0.251997i
$64$			3.92127i			0.490159i
$65$	0.211122	+	0.509694i	0.0261865	+	0.0632198i
$66$	−9.06719	−	9.06719i	−1.11609	−	1.11609i
$67$	14.6236			1.78656			0.893279	−	0.449503i	$-0.148399\pi$
$67$	14.6236			1.78656			0.893279	+	0.449503i	$0.148399\pi$
$68$		0			0
$69$	18.7665			2.25922
$70$	−0.245576	−	0.245576i	−0.0293519	−	0.0293519i
$71$	0.0651498	+	0.157286i	0.00773186	+	0.0186664i	0.927698	−	0.373331i	$-0.121784\pi$
$71$	0.0651498	+	0.157286i	0.00773186	+	0.0186664i	−0.919966	+	0.391997i	$0.871784\pi$
$72$			3.00000i			0.353553i
$73$	10.9024	−	4.51592i	1.27603	−	0.528548i	0.361236	−	0.932474i	$-0.382355\pi$
$73$	10.9024	−	4.51592i	1.27603	−	0.528548i	0.914792	+	0.403926i	$0.132355\pi$
$74$	−3.77511	+	9.11392i	−0.438848	+	1.05947i
$75$	11.6627	+	4.83085i	1.34669	+	0.557818i
$76$	−2.03603	+	2.03603i	−0.233549	+	0.233549i
$77$	2.91919	−	2.91919i	0.332672	−	0.332672i
$78$	−20.1096	−	8.32968i	−2.27697	−	0.943151i
$79$	−1.58735	+	3.83221i	−0.178591	+	0.431157i	−0.987672	−	0.156541i	$-0.949966\pi$
$79$	−1.58735	+	3.83221i	−0.178591	+	0.431157i	0.809080	+	0.587698i	$0.199966\pi$
$80$	−0.525619	+	0.217718i	−0.0587660	+	0.0243417i
$81$			7.59627i			0.844030i
$82$	−4.49432	−	10.8502i	−0.496315	−	1.19821i
$83$	−1.72093	−	1.72093i	−0.188897	−	0.188897i	0.606322	−	0.795219i	$-0.292644\pi$
$83$	−1.72093	−	1.72093i	−0.188897	−	0.188897i	−0.795219	+	0.606322i	$0.792644\pi$
$84$	5.94356			0.648496
$85$		0			0
$86$	−10.3182			−1.11264
$87$	−6.10810	−	6.10810i	−0.654857	−	0.654857i
$88$	−0.906801	−	2.18921i	−0.0966653	−	0.233371i
$89$		−	15.0915i		−	1.59970i	−0.600201	−	0.799849i	$-0.704913\pi$
$89$		−	15.0915i		−	1.59970i	0.600201	−	0.799849i	$-0.295087\pi$
$90$	0.714453	−	0.295936i	0.0753100	−	0.0311944i
$91$	2.68175	−	6.47431i	0.281123	−	0.678692i
$92$	−10.4907	−	4.34538i	−1.09373	−	0.453038i
$93$	6.87087	−	6.87087i	0.712476	−	0.712476i
$94$	−9.76401	+	9.76401i	−1.00708	+	1.00708i
$95$	−0.209426	−	0.0867473i	−0.0214867	−	0.00890008i
$96$	6.88570	−	16.6235i	0.702768	−	1.69663i
$97$	10.3406	−	4.28320i	1.04992	−	0.434893i	0.210059	−	0.977689i	$-0.432634\pi$
$97$	10.3406	−	4.28320i	1.04992	−	0.434893i	0.839865	+	0.542796i	$0.182634\pi$
$98$		−	8.74422i		−	0.883300i
$99$	3.51783	+	8.49279i	0.353555	+	0.853558i
$100$	−5.40099	−	5.40099i	−0.540099	−	0.540099i
$101$	−7.78106			−0.774244			−0.387122	−	0.922028i	$-0.626531\pi$
$101$	−7.78106			−0.774244			−0.387122	+	0.922028i	$0.626531\pi$
$102$		0			0
$103$	−10.8598			−1.07005			−0.535023	−	0.844837i	$-0.679697\pi$
$103$	−10.8598			−1.07005			−0.535023	+	0.844837i	$0.679697\pi$
$104$	−2.84419	−	2.84419i	−0.278896	−	0.278896i
$105$	0.179062	+	0.432294i	0.0174746	+	0.0421875i
$106$		−	1.54664i		−	0.150223i
$107$	−11.1253	+	4.60823i	−1.07552	+	0.445495i	−0.848935	−	0.528497i	$-0.822756\pi$
$107$	−11.1253	+	4.60823i	−1.07552	+	0.445495i	−0.226584	+	0.973992i	$0.572756\pi$
$108$	−0.610865	+	1.47476i	−0.0587805	+	0.141909i
$109$	6.10760	+	2.52985i	0.585002	+	0.242316i	0.655499	−	0.755196i	$-0.272459\pi$
$109$	6.10760	+	2.52985i	0.585002	+	0.242316i	−0.0704970	+	0.997512i	$0.522459\pi$
$110$	−0.431911	+	0.431911i	−0.0411811	+	0.0411811i
$111$	9.39806	−	9.39806i	0.892024	−	0.892024i
$112$	6.67658	+	2.76553i	0.630878	+	0.261318i
$113$	−1.94651	+	4.69928i	−0.183112	+	0.442071i	−0.988605	−	0.150534i	$-0.951901\pi$
$113$	−1.94651	+	4.69928i	−0.183112	+	0.442071i	0.805493	+	0.592605i	$0.201901\pi$
$114$	8.26277	−	3.42255i	0.773880	−	0.320551i
$115$		−	0.893933i		−	0.0833597i
$116$	2.00016	+	4.82882i	0.185711	+	0.448345i
$117$	11.0337	+	11.0337i	1.02007	+	1.02007i
$118$	−5.90673			−0.543758
$119$		0			0
$120$	0.268571			0.0245170
$121$	2.64399	+	2.64399i	0.240363	+	0.240363i
$122$	0.882241	+	2.12992i	0.0798744	+	0.192834i
$123$			15.8229i			1.42671i
$124$	−5.43184	+	2.24994i	−0.487794	+	0.202051i
$125$	0.460901	−	1.11271i	0.0412243	−	0.0995242i
$126$	−9.07522	−	3.75908i	−0.808485	−	0.334885i
$127$	−1.55874	+	1.55874i	−0.138316	+	0.138316i	−0.772875	−	0.634559i	$-0.781182\pi$
$127$	−1.55874	+	1.55874i	−0.138316	+	0.138316i	0.634559	+	0.772875i	$0.281182\pi$
$128$	4.83841	−	4.83841i	0.427659	−	0.427659i
$129$	12.8435	+	5.31994i	1.13080	+	0.468395i
$130$	−0.396780	+	0.957912i	−0.0347999	+	0.0840145i
$131$	−1.84147	+	0.762762i	−0.160890	+	0.0666428i	−0.461675	−	0.887049i	$-0.652751\pi$
$131$	−1.84147	+	0.762762i	−0.160890	+	0.0666428i	0.300785	+	0.953692i	$0.402751\pi$
$132$		−	10.4534i		−	0.909848i
$133$	1.10189	+	2.66021i	0.0955462	+	0.230669i
$134$	19.4337	+	19.4337i	1.67882	+	1.67882i
$135$	−0.125667			−0.0108157
$136$		0			0
$137$	−12.6236			−1.07851			−0.539254	−	0.842143i	$-0.681294\pi$
$137$	−12.6236			−1.07851			−0.539254	+	0.842143i	$0.681294\pi$
$138$	24.9393	+	24.9393i	2.12297	+	2.12297i
$139$	−2.00313	−	4.83598i	−0.169903	−	0.410182i	0.815876	−	0.578226i	$-0.196255\pi$
$139$	−2.00313	−	4.83598i	−0.169903	−	0.410182i	−0.985779	+	0.168044i	$0.946255\pi$
$140$		−	0.283119i		−	0.0239279i
$141$	17.1879	−	7.11945i	1.44748	−	0.599565i
$142$	−0.122442	+	0.295600i	−0.0102751	+	0.0248062i
$143$	−11.3868	−	4.71658i	−0.952214	−	0.394420i
$144$	−11.3784	+	11.3784i	−0.948202	+	0.948202i
$145$	−0.290956	+	0.290956i	−0.0241626	+	0.0241626i
$146$	20.4898	+	8.48715i	1.69575	+	0.702401i
$147$	−4.50842	+	10.8843i	−0.371848	+	0.897720i
$148$	−7.42974	+	3.07750i	−0.610721	+	0.252969i
$149$		−	9.65270i		−	0.790780i	−0.918513	−	0.395390i	$-0.870609\pi$
$149$		−	9.65270i		−	0.790780i	0.918513	−	0.395390i	$-0.129391\pi$
$150$	9.07902	+	21.9187i	0.741299	+	1.78965i
$151$	0.853535	+	0.853535i	0.0694597	+	0.0694597i	0.740983	−	0.671524i	$-0.234360\pi$
$151$	0.853535	+	0.853535i	0.0694597	+	0.0694597i	−0.671524	+	0.740983i	$0.734360\pi$
$152$	1.65270			0.134052
$153$		0			0
$154$	7.75877			0.625220
$155$	−0.327291	−	0.327291i	−0.0262886	−	0.0262886i
$156$	−6.79042	−	16.3935i	−0.543669	−	1.31253i
$157$			15.0942i			1.20465i	0.798251	+	0.602324i	$0.205759\pi$
$157$			15.0942i			1.20465i	−0.798251	+	0.602324i	$0.794241\pi$
$158$	−7.20220	+	2.98325i	−0.572976	+	0.237335i
$159$	−0.797427	+	1.92516i	−0.0632401	+	0.152675i
$160$	−0.791854	−	0.327997i	−0.0626016	−	0.0259304i
$161$	−8.02922	+	8.02922i	−0.632791	+	0.632791i
$162$	−10.0949	+	10.0949i	−0.793128	+	0.793128i
$163$	−6.05546	−	2.50825i	−0.474300	−	0.196461i	0.132711	−	0.991155i	$-0.457632\pi$
$163$	−6.05546	−	2.50825i	−0.474300	−	0.196461i	−0.607011	+	0.794693i	$0.707632\pi$
$164$	3.66380	−	8.84520i	0.286095	−	0.690694i
$165$	0.760305	−	0.314929i	0.0591897	−	0.0245172i
$166$		−	4.57398i		−	0.355010i
$167$	−1.50914	−	3.64338i	−0.116780	−	0.281933i	0.854672	−	0.519169i	$-0.173759\pi$
$167$	−1.50914	−	3.64338i	−0.116780	−	0.281933i	−0.971452	+	0.237236i	$0.923759\pi$
$168$	−2.41228	−	2.41228i	−0.186111	−	0.186111i
$169$	−7.92127			−0.609329
$170$		0			0
$171$	−6.41147			−0.490298
$172$	−5.94781	−	5.94781i	−0.453516	−	0.453516i
$173$	7.24575	+	17.4928i	0.550884	+	1.32995i	0.916816	+	0.399311i	$0.130751\pi$
$173$	7.24575	+	17.4928i	0.550884	+	1.32995i	−0.365931	+	0.930642i	$0.619249\pi$
$174$		−	16.2344i		−	1.23073i
$175$	−7.05674	+	2.92300i	−0.533439	+	0.220958i
$176$	4.86393	−	11.7426i	0.366633	−	0.885130i
$177$	7.35234	+	3.04544i	0.552635	+	0.228909i
$178$	20.0555	−	20.0555i	1.50322	−	1.50322i
$179$	−5.12937	+	5.12937i	−0.383387	+	0.383387i	−0.872321	−	0.488934i	$-0.837386\pi$
$179$	−5.12937	+	5.12937i	−0.383387	+	0.383387i	0.488934	+	0.872321i	$0.337386\pi$
$180$	0.582427	+	0.241249i	0.0434116	+	0.0179817i
$181$	9.60507	−	23.1887i	0.713939	−	1.72360i	0.0240245	−	0.999711i	$-0.492352\pi$
$181$	9.60507	−	23.1887i	0.713939	−	1.72360i	0.689915	−	0.723891i	$-0.257648\pi$
$182$	12.1677	−	5.04003i	0.901931	−	0.373592i
$183$		−	3.10607i		−	0.229607i
$184$	2.49415	+	6.02142i	0.183872	+	0.443905i
$185$	−0.447672	−	0.447672i	−0.0329135	−	0.0329135i
$186$	18.2618			1.33902
$187$		0			0
$188$	−11.2567			−0.820980
$189$	1.12873	+	1.12873i	0.0821031	+	0.0821031i
$190$	−0.163032	−	0.393593i	−0.0118276	−	0.0285542i
$191$			14.1557i			1.02427i	0.858905	+	0.512135i	$0.171145\pi$
$191$			14.1557i			1.02427i	−0.858905	+	0.512135i	$0.828855\pi$
$192$	9.17321	−	3.79967i	0.662020	−	0.274218i
$193$	6.28790	−	15.1803i	0.452613	−	1.09270i	−0.518712	−	0.854949i	$-0.673588\pi$
$193$	6.28790	−	15.1803i	0.452613	−	1.09270i	0.971325	−	0.237755i	$-0.0764116\pi$
$194$	19.4339	+	8.04978i	1.39527	+	0.577940i
$195$	0.987776	−	0.987776i	0.0707361	−	0.0707361i
$196$	5.04051	−	5.04051i	0.360036	−	0.360036i
$197$	−18.6988	−	7.74531i	−1.33224	−	0.551831i	−0.400944	−	0.916102i	$-0.631318\pi$
$197$	−18.6988	−	7.74531i	−1.33224	−	0.551831i	−0.931293	+	0.364272i	$0.881318\pi$
$198$	−6.61136	+	15.9612i	−0.469849	+	1.13432i
$199$	20.4873	−	8.48612i	1.45231	−	0.601565i	0.489560	−	0.871970i	$-0.337158\pi$
$199$	20.4873	−	8.48612i	1.45231	−	0.601565i	0.962747	+	0.270405i	$0.0871575\pi$
$200$			4.38413i			0.310005i
$201$	−14.1701	−	34.2097i	−0.999482	−	2.41296i
$202$	−10.3405	−	10.3405i	−0.727552	−	0.727552i
$203$	5.22668			0.366841
$204$		0			0
$205$	0.753718			0.0526420
$206$	−14.4319	−	14.4319i	−1.00551	−	1.00551i
$207$	−9.67579	−	23.3594i	−0.672514	−	1.62359i
$208$		−	21.5749i		−	1.49595i
$209$	4.67869	−	1.93798i	0.323632	−	0.134053i
$210$	−0.336526	+	0.812446i	−0.0232225	+	0.0560641i
$211$	−6.64037	−	2.75053i	−0.457142	−	0.189354i	0.142216	−	0.989836i	$-0.454577\pi$
$211$	−6.64037	−	2.75053i	−0.457142	−	0.189354i	−0.599358	+	0.800481i	$0.704577\pi$
$212$	0.891541	−	0.891541i	0.0612313	−	0.0612313i
$213$	0.304816	−	0.304816i	0.0208856	−	0.0208856i
$214$	−20.9086	−	8.66064i	−1.42929	−	0.592029i
$215$	0.253413	−	0.611792i	0.0172826	−	0.0417239i
$216$	0.846479	−	0.350623i	0.0575956	−	0.0238569i
$217$			5.87939i			0.399119i
$218$	4.75456	+	11.4785i	0.322020	+	0.777424i
$219$	−21.1286	−	21.1286i	−1.42774	−	1.42774i
$220$	−0.497941			−0.0335711
$221$		0			0
$222$	24.9786			1.67646
$223$	4.25650	+	4.25650i	0.285036	+	0.285036i	0.835114	−	0.550077i	$-0.185402\pi$
$223$	4.25650	+	4.25650i	0.285036	+	0.285036i	−0.550077	+	0.835114i	$0.685402\pi$
$224$	4.16632	+	10.0584i	0.278374	+	0.672055i
$225$		−	17.0077i		−	1.13385i
$226$	−8.83176	+	3.65824i	−0.587480	+	0.243342i
$227$	−8.43246	+	20.3578i	−0.559682	+	1.35119i	0.350336	+	0.936624i	$0.386067\pi$
$227$	−8.43246	+	20.3578i	−0.559682	+	1.35119i	−0.910018	+	0.414568i	$0.863933\pi$
$228$	6.73588	+	2.79009i	0.446094	+	0.184778i
$229$	2.61604	−	2.61604i	0.172873	−	0.172873i	−0.615367	−	0.788240i	$-0.710992\pi$
$229$	2.61604	−	2.61604i	0.172873	−	0.172873i	0.788240	+	0.615367i	$0.210992\pi$
$230$	1.18797	−	1.18797i	0.0783325	−	0.0783325i
$231$	−9.65765	−	4.00033i	−0.635427	−	0.263202i
$232$	1.14805	−	2.77164i	0.0753732	−	0.181967i
$233$	−26.9317	+	11.1555i	−1.76435	+	0.730819i	−0.768499	+	0.639850i	$0.778996\pi$
$233$	−26.9317	+	11.1555i	−1.76435	+	0.730819i	−0.995854	+	0.0909687i	$0.971004\pi$
$234$			29.3259i			1.91710i
$235$	−0.339131	−	0.818735i	−0.0221225	−	0.0534084i
$236$	−3.40487	−	3.40487i	−0.221638	−	0.221638i
$237$	10.5030			0.682243
$238$		0			0
$239$	12.4834			0.807484			0.403742	−	0.914873i	$-0.367709\pi$
$239$	12.4834			0.807484			0.403742	+	0.914873i	$0.367709\pi$
$240$	1.01864	+	1.01864i	0.0657527	+	0.0657527i
$241$	−6.20605	−	14.9827i	−0.399767	−	0.965122i	−0.987721	−	0.156228i	$-0.950067\pi$
$241$	−6.20605	−	14.9827i	−0.399767	−	0.965122i	0.587954	−	0.808894i	$-0.299933\pi$
$242$			7.02734i			0.451735i
$243$	20.6580	−	8.55684i	1.32521	−	0.548921i
$244$	−0.719210	+	1.73633i	−0.0460427	+	0.111157i
$245$	0.518467	+	0.214756i	0.0331236	+	0.0137203i
$246$	−21.0275	+	21.0275i	−1.34067	+	1.34067i
$247$	6.07848	−	6.07848i	0.386764	−	0.386764i
$248$	3.11776	+	1.29142i	0.197978	+	0.0820051i
$249$	−2.35829	+	5.69341i	−0.149450	+	0.360805i
$250$	2.09122	−	0.866211i	0.132260	−	0.0547840i
$251$		−	15.9959i		−	1.00965i	−0.863221	−	0.504826i	$-0.831557\pi$
$251$		−	15.9959i		−	1.00965i	0.863221	−	0.504826i	$-0.168443\pi$
$252$	−3.06443	−	7.39819i	−0.193041	−	0.466042i
$253$	14.1216	+	14.1216i	0.887815	+	0.887815i
$254$	−4.14290			−0.259949
$255$		0			0
$256$	20.7023			1.29390
$257$	6.83097	+	6.83097i	0.426104	+	0.426104i	0.887299	−	0.461195i	$-0.152579\pi$
$257$	6.83097	+	6.83097i	0.426104	+	0.426104i	−0.461195	+	0.887299i	$0.652579\pi$
$258$	9.99822	+	24.1378i	0.622462	+	1.50276i
$259$			8.04189i			0.499699i
$260$	−0.780897	+	0.323458i	−0.0484292	+	0.0200600i
$261$	−4.45373	+	10.7523i	−0.275679	+	0.665548i
$262$	−3.46083	−	1.43352i	−0.213811	−	0.0885634i
$263$	19.7858	−	19.7858i	1.22004	−	1.22004i	0.252429	−	0.967616i	$-0.418771\pi$
$263$	19.7858	−	19.7858i	1.22004	−	1.22004i	0.967616	−	0.252429i	$-0.0812293\pi$
$264$	−4.24264	+	4.24264i	−0.261116	+	0.261116i
$265$	0.0917040	+	0.0379850i	0.00563333	+	0.00233340i
$266$	−2.07088	+	4.99955i	−0.126974	+	0.306542i
$267$	−35.3043	+	14.6235i	−2.16059	+	0.894944i
$268$			22.4047i			1.36858i
$269$	−2.54327	−	6.14001i	−0.155066	−	0.374363i	0.827186	−	0.561928i	$-0.189940\pi$
$269$	−2.54327	−	6.14001i	−0.155066	−	0.374363i	−0.982252	+	0.187565i	$0.939940\pi$
$270$	−0.167002	−	0.167002i	−0.0101634	−	0.0101634i
$271$	−17.0000			−1.03268			−0.516338	−	0.856385i	$-0.672705\pi$
$271$	−17.0000			−1.03268			−0.516338	+	0.856385i	$0.672705\pi$
$272$		0			0
$273$	−17.7442			−1.07393
$274$	−16.7758	−	16.7758i	−1.01347	−	1.01347i
$275$	5.14088	+	12.4112i	0.310007	+	0.748422i
$276$			28.7520i			1.73066i
$277$	−18.6151	+	7.71065i	−1.11848	+	0.463288i	−0.863849	−	0.503751i	$-0.831953\pi$
$277$	−18.6151	+	7.71065i	−1.11848	+	0.463288i	−0.254627	+	0.967039i	$0.581953\pi$
$278$	3.76465	−	9.08866i	0.225789	−	0.545102i
$279$	−12.0950	−	5.00991i	−0.724108	−	0.299935i
$280$	−0.114908	+	0.114908i	−0.00686704	+	0.00686704i
$281$	−11.6481	+	11.6481i	−0.694870	+	0.694870i	−0.963299	−	0.268429i	$-0.913495\pi$
$281$	−11.6481	+	11.6481i	−0.694870	+	0.694870i	0.268429	+	0.963299i	$0.413495\pi$
$282$	32.3026	+	13.3802i	1.92359	+	0.796778i
$283$	−7.05883	+	17.0415i	−0.419604	+	1.01301i	0.562858	+	0.826553i	$0.309702\pi$
$283$	−7.05883	+	17.0415i	−0.419604	+	1.01301i	−0.982462	+	0.186461i	$0.940298\pi$
$284$	−0.240975	+	0.0998153i	−0.0142993	+	0.00592295i
$285$			0.573978i			0.0339995i
$286$	−8.86426	−	21.4002i	−0.524155	−	1.26542i
$287$	−6.76982	−	6.76982i	−0.399610	−	0.399610i
$288$	−24.2422			−1.42848
$289$		0			0
$290$	−0.773318			−0.0454108
$291$	−20.0398	−	20.0398i	−1.17475	−	1.17475i
$292$	6.91879	+	16.7034i	0.404891	+	0.977494i
$293$		−	10.9513i		−	0.639782i	−0.947454	−	0.319891i	$-0.896354\pi$
$293$		−	10.9513i		−	0.639782i	0.947454	−	0.319891i	$-0.103646\pi$
$294$	−20.4558	+	8.47305i	−1.19300	+	0.494158i
$295$	0.145068	−	0.350225i	0.00844618	−	0.0203909i
$296$	4.26451	+	1.76642i	0.247869	+	0.102671i
$297$	1.98518	−	1.98518i	0.115192	−	0.115192i
$298$	12.8277	−	12.8277i	0.743090	−	0.743090i
$299$	31.3194	+	12.9729i	1.81125	+	0.750244i
$300$	−7.40128	+	17.8683i	−0.427313	+	1.03163i
$301$	−7.77119	+	3.21893i	−0.447924	+	0.185536i
$302$			2.26857i			0.130542i
$303$	7.53976	+	18.2026i	0.433148	+	1.04571i
$304$	6.26839	+	6.26839i	0.359517	+	0.359517i
$305$	−0.147956			−0.00847193
$306$		0			0
$307$	−5.78106			−0.329942			−0.164971	−	0.986298i	$-0.552753\pi$
$307$	−5.78106			−0.329942			−0.164971	+	0.986298i	$0.552753\pi$
$308$	4.47246	+	4.47246i	0.254842	+	0.254842i
$309$	10.5230	+	25.4048i	0.598633	+	1.44523i
$310$		−	0.869890i		−	0.0494064i
$311$	−0.111434	+	0.0461573i	−0.00631881	+	0.00261734i	−0.385841	−	0.922565i	$-0.626089\pi$
$311$	−0.111434	+	0.0461573i	−0.00631881	+	0.00261734i	0.379522	+	0.925183i	$0.376089\pi$
$312$	−3.89755	+	9.40952i	−0.220655	+	0.532709i
$313$	−9.59836	−	3.97577i	−0.542531	−	0.224724i	0.0945505	−	0.995520i	$-0.469859\pi$
$313$	−9.59836	−	3.97577i	−0.542531	−	0.224724i	−0.637082	+	0.770796i	$0.719859\pi$
$314$	−20.0591	+	20.0591i	−1.13200	+	1.13200i
$315$	0.445771	−	0.445771i	0.0251163	−	0.0251163i
$316$	−5.87129	−	2.43197i	−0.330286	−	0.136809i
$317$	10.6392	−	25.6853i	0.597558	−	1.44263i	−0.278505	−	0.960435i	$-0.589839\pi$
$317$	10.6392	−	25.6853i	0.597558	−	1.44263i	0.876063	−	0.482197i	$-0.160161\pi$
$318$	−3.61812	+	1.49867i	−0.202894	+	0.0840414i
$319$		−	9.19253i		−	0.514683i
$320$	−0.180995	−	0.436961i	−0.0101179	−	0.0244269i
$321$	21.5605	+	21.5605i	1.20339	+	1.20339i
$322$	−21.3405			−1.18926
$323$		0			0
$324$	−11.6382			−0.646564
$325$	16.1244	+	16.1244i	0.894421	+	0.894421i
$326$	−4.71397	−	11.3805i	−0.261083	−	0.630309i
$327$		−	16.7392i		−	0.925678i
$328$	−5.07695	+	2.10294i	−0.280328	+	0.116116i
$329$	−4.30776	+	10.3998i	−0.237494	+	0.573362i
$330$	1.42891	+	0.591872i	0.0786587	+	0.0325815i
$331$	6.20725	−	6.20725i	0.341181	−	0.341181i	−0.515630	−	0.856811i	$-0.672442\pi$
$331$	6.20725	−	6.20725i	0.341181	−	0.341181i	0.856811	+	0.515630i	$0.172442\pi$
$332$	2.63662	−	2.63662i	0.144703	−	0.144703i
$333$	−16.5437	−	6.85261i	−0.906587	−	0.375521i
$334$	2.83625	−	6.84731i	0.155193	−	0.374668i
$335$	−1.62956	+	0.674986i	−0.0890324	+	0.0368784i
$336$		−	18.2986i		−	0.998270i
$337$	0.559140	+	1.34988i	0.0304583	+	0.0735329i	0.938377	−	0.345614i	$-0.112329\pi$
$337$	0.559140	+	1.34988i	0.0304583	+	0.0735329i	−0.907919	+	0.419147i	$0.862329\pi$
$338$	−10.5268	−	10.5268i	−0.572582	−	0.572582i
$339$	12.8794			0.699512
$340$		0			0
$341$	10.3405			0.559969
$342$	−8.52037	−	8.52037i	−0.460729	−	0.460729i
$343$	−6.83204	−	16.4940i	−0.368895	−	0.890592i
$344$			4.82800i			0.260308i
$345$	−2.09122	+	0.866211i	−0.112587	+	0.0466352i
$346$	−13.6176	+	32.8757i	−0.732085	+	1.76741i
$347$	−28.9691	−	11.9994i	−1.55514	−	0.644162i	−0.570907	−	0.821014i	$-0.693409\pi$
$347$	−28.9691	−	11.9994i	−1.55514	−	0.644162i	−0.984237	+	0.176852i	$0.943409\pi$
$348$	9.35815	−	9.35815i	0.501649	−	0.501649i
$349$	21.0536	−	21.0536i	1.12697	−	1.12697i	0.136305	−	0.990667i	$-0.456477\pi$
$349$	21.0536	−	21.0536i	1.12697	−	1.12697i	0.990667	−	0.136305i	$-0.0435228\pi$
$350$	−13.2623	−	5.49343i	−0.708901	−	0.293636i
$351$	1.82371	−	4.40282i	0.0973423	−	0.235005i
$352$	17.6904	−	7.32761i	0.942902	−	0.390563i
$353$			28.3141i			1.50701i	0.657444	+	0.753503i	$0.271638\pi$
$353$			28.3141i			1.50701i	−0.657444	+	0.753503i	$0.728362\pi$
$354$	5.72355	+	13.8179i	0.304203	+	0.734412i
$355$	−0.0145197	−	0.0145197i	−0.000770628	−	0.000770628i
$356$	23.1215			1.22544
$357$		0			0
$358$	−13.6331			−0.720532
$359$	1.99255	+	1.99255i	0.105163	+	0.105163i	0.757731	−	0.652568i	$-0.226308\pi$
$359$	1.99255	+	1.99255i	0.105163	+	0.105163i	−0.652568	+	0.757731i	$0.726308\pi$
$360$	−0.138472	−	0.334301i	−0.00729811	−	0.0176192i
$361$		−	15.4679i		−	0.814101i
$362$	43.5805	−	18.0516i	2.29054	−	0.948773i
$363$	3.62321	−	8.74721i	0.190169	−	0.459109i
$364$	9.91922	+	4.10867i	0.519908	+	0.215353i
$365$	−1.00645	+	1.00645i	−0.0526799	+	0.0526799i
$366$	4.12773	−	4.12773i	0.215760	−	0.215760i
$367$	−7.68502	−	3.18324i	−0.401155	−	0.166164i	0.172979	−	0.984926i	$-0.444661\pi$
$367$	−7.68502	−	3.18324i	−0.401155	−	0.166164i	−0.574133	+	0.818762i	$0.694661\pi$
$368$	−13.3782	+	32.2979i	−0.697389	+	1.68365i
$369$	19.6954	−	8.15812i	1.02530	−	0.424695i
$370$		−	1.18984i		−	0.0618571i
$371$	−0.482499	−	1.16485i	−0.0250501	−	0.0604763i
$372$	10.5268	+	10.5268i	0.545789	+	0.545789i
$373$	9.21894			0.477339			0.238669	−	0.971101i	$-0.423289\pi$
$373$	9.21894			0.477339			0.238669	+	0.971101i	$0.423289\pi$
$374$		0			0
$375$	−3.04963			−0.157482
$376$	4.56869	+	4.56869i	0.235612	+	0.235612i
$377$	−5.97140	−	14.4162i	−0.307542	−	0.742473i
$378$			3.00000i			0.154303i
$379$	9.57396	−	3.96566i	0.491781	−	0.203702i	−0.122990	−	0.992408i	$-0.539248\pi$
$379$	9.57396	−	3.96566i	0.491781	−	0.203702i	0.614771	+	0.788705i	$0.289248\pi$
$380$	0.132905	−	0.320860i	0.00681786	−	0.0164598i
$381$	5.15684	+	2.13603i	0.264193	+	0.109432i
$382$	−18.8119	+	18.8119i	−0.962499	+	0.962499i
$383$	−9.38420	+	9.38420i	−0.479510	+	0.479510i	−0.904975	−	0.425465i	$-0.860111\pi$
$383$	−9.38420	+	9.38420i	−0.479510	+	0.479510i	0.425465	+	0.904975i	$0.360111\pi$
$384$	−16.0071	−	6.63035i	−0.816858	−	0.338354i
$385$	−0.190554	+	0.460037i	−0.00971151	+	0.0234457i
$386$	28.5297	−	11.8174i	1.45212	−	0.601489i
$387$		−	18.7297i		−	0.952083i
$388$	6.56224	+	15.8426i	0.333147	+	0.804288i
$389$	−18.5802	−	18.5802i	−0.942051	−	0.942051i	0.0563592	−	0.998411i	$-0.482051\pi$
$389$	−18.5802	−	18.5802i	−0.942051	−	0.942051i	−0.998411	+	0.0563592i	$0.982051\pi$
$390$	2.62536			0.132940
$391$		0			0
$392$	−4.09152			−0.206653
$393$	3.56873	+	3.56873i	0.180018	+	0.180018i
$394$	−14.5564	−	35.1423i	−0.733342	−	1.77044i
$395$		−	0.500305i		−	0.0251731i
$396$	−13.0117	+	5.38963i	−0.653863	+	0.270839i
$397$	9.74947	−	23.5373i	0.489312	−	1.18130i	−0.465755	−	0.884913i	$-0.654217\pi$
$397$	9.74947	−	23.5373i	0.489312	−	1.18130i	0.955067	−	0.296390i	$-0.0957827\pi$
$398$	38.5035	+	15.9487i	1.93001	+	0.799435i
$399$	5.15542	−	5.15542i	0.258094	−	0.258094i
$400$	−16.6282	+	16.6282i	−0.831409	+	0.831409i
$401$	0.832176	+	0.344698i	0.0415569	+	0.0172134i	0.403365	−	0.915039i	$-0.367840\pi$
$401$	0.832176	+	0.344698i	0.0415569	+	0.0172134i	−0.361808	+	0.932253i	$0.617840\pi$
$402$	26.6311	−	64.2931i	1.32824	−	3.20665i
$403$	16.2165	−	6.71710i	0.807802	−	0.334602i
$404$		−	11.9213i		−	0.593106i
$405$	−0.350623	−	0.846479i	−0.0174226	−	0.0420619i
$406$	6.94587	+	6.94587i	0.344718	+	0.344718i
$407$	14.1438			0.701084
$408$		0			0
$409$	−15.3259			−0.757819			−0.378910	−	0.925434i	$-0.623701\pi$
$409$	−15.3259			−0.757819			−0.378910	+	0.925434i	$0.623701\pi$
$410$	1.00164	+	1.00164i	0.0494673	+	0.0494673i
$411$	12.2321	+	29.5310i	0.603366	+	1.45666i
$412$		−	16.6382i		−	0.819703i
$413$	−4.44867	+	1.84270i	−0.218905	+	0.0906733i
$414$	18.1845	−	43.9013i	0.893721	−	2.15763i
$415$	0.271203	+	0.112336i	0.0133128	+	0.00551435i
$416$	22.9831	−	22.9831i	1.12684	−	1.12684i
$417$	−9.37201	+	9.37201i	−0.458949	+	0.458949i
$418$	8.79306	+	3.64221i	0.430083	+	0.178146i
$419$	−0.912368	+	2.20265i	−0.0445721	+	0.107607i	−0.944598	−	0.328231i	$-0.893548\pi$
$419$	−0.912368	+	2.20265i	−0.0445721	+	0.107607i	0.900025	+	0.435837i	$0.143548\pi$
$420$	−0.662312	+	0.274339i	−0.0323175	+	0.0133864i
$421$			8.28581i			0.403826i	0.979404	+	0.201913i	$0.0647157\pi$
$421$			8.28581i			0.403826i	−0.979404	+	0.201913i	$0.935284\pi$
$422$	−5.16931	−	12.4798i	−0.251638	−	0.607507i
$423$	−17.7237	−	17.7237i	−0.861756	−	0.861756i
$424$	−0.723689			−0.0351454
$425$		0			0
$426$	0.810155			0.0392521
$427$	1.32893	+	1.32893i	0.0643112	+	0.0643112i
$428$	−7.06022	−	17.0449i	−0.341269	−	0.823895i
$429$			31.2080i			1.50674i
$430$	1.14979	−	0.476260i	0.0554480	−	0.0229673i
$431$	12.3680	−	29.8590i	0.595745	−	1.43826i	−0.282134	−	0.959375i	$-0.591042\pi$
$431$	12.3680	−	29.8590i	0.595745	−	1.43826i	0.877879	−	0.478882i	$-0.158958\pi$
$432$	4.54038	+	1.88069i	0.218449	+	0.0904845i
$433$	−10.6520	+	10.6520i	−0.511902	+	0.511902i	−0.915109	−	0.403207i	$-0.867895\pi$
$433$	−10.6520	+	10.6520i	−0.511902	+	0.511902i	0.403207	+	0.915109i	$0.367895\pi$
$434$	−7.81327	+	7.81327i	−0.375049	+	0.375049i
$435$	0.962580	+	0.398714i	0.0461522	+	0.0191169i
$436$	−3.87595	+	9.35738i	−0.185625	+	0.448137i
$437$	−12.8687	+	5.33040i	−0.615595	+	0.254988i
$438$		−	56.1566i		−	2.68327i
$439$	0.984661	+	2.37718i	0.0469953	+	0.113457i	0.945634	−	0.325233i	$-0.105443\pi$
$439$	0.984661	+	2.37718i	0.0469953	+	0.113457i	−0.898639	+	0.438690i	$0.855443\pi$
$440$	0.202096	+	0.202096i	0.00963455	+	0.00963455i
$441$	15.8726			0.755837
$442$		0			0
$443$	23.4662			1.11491			0.557455	−	0.830207i	$-0.311778\pi$
$443$	23.4662			1.11491			0.557455	+	0.830207i	$0.311778\pi$
$444$	14.3987	+	14.3987i	0.683330	+	0.683330i
$445$	0.696583	+	1.68170i	0.0330212	+	0.0797203i
$446$			11.3131i			0.535693i
$447$	−22.5810	+	9.35336i	−1.06804	+	0.442399i
$448$	−2.29906	+	5.55043i	−0.108621	+	0.262233i
$449$	17.4225	+	7.21666i	0.822221	+	0.340575i	0.753818	−	0.657083i	$-0.228210\pi$
$449$	17.4225	+	7.21666i	0.822221	+	0.340575i	0.0684024	+	0.997658i	$0.478210\pi$
$450$	22.6020	−	22.6020i	1.06547	−	1.06547i
$451$	−11.9066	+	11.9066i	−0.560658	+	0.560658i
$452$	−7.19972	−	2.98222i	−0.338646	−	0.140272i
$453$	1.16965	−	2.82378i	0.0549548	−	0.132673i
$454$	−38.2601	+	15.8478i	−1.79563	+	0.743776i
$455$			0.845237i			0.0396253i
$456$	−1.60145	−	3.86624i	−0.0749948	−	0.181053i
$457$	−1.49045	−	1.49045i	−0.0697205	−	0.0697205i	0.671387	−	0.741107i	$-0.265699\pi$
$457$	−1.49045	−	1.49045i	−0.0697205	−	0.0697205i	−0.741107	+	0.671387i	$0.765699\pi$
$458$	6.95306			0.324895
$459$		0			0
$460$	1.36959			0.0638572
$461$	15.4911	+	15.4911i	0.721490	+	0.721490i	0.968909	−	0.247418i	$-0.0795822\pi$
$461$	15.4911	+	15.4911i	0.721490	+	0.721490i	−0.247418	+	0.968909i	$0.579582\pi$
$462$	−7.51816	−	18.1504i	−0.349776	−	0.844435i
$463$			14.1557i			0.657871i	0.944352	+	0.328936i	$0.106690\pi$
$463$			14.1557i			0.657871i	−0.944352	+	0.328936i	$0.893310\pi$
$464$	14.8666	−	6.15796i	0.690166	−	0.285876i
$465$	−0.448505	+	1.08279i	−0.0207989	+	0.0502130i
$466$	−50.6150	−	20.9654i	−2.34469	−	0.971204i
$467$	−20.9924	+	20.9924i	−0.971414	+	0.971414i	−0.999603	−	0.0281886i	$-0.991026\pi$
$467$	−20.9924	+	20.9924i	−0.971414	+	0.971414i	0.0281886	+	0.999603i	$0.491026\pi$
$468$	−16.9046	+	16.9046i	−0.781416	+	0.781416i
$469$	20.6992	+	8.57389i	0.955801	+	0.395906i
$470$	0.637358	−	1.53872i	0.0293991	−	0.0709758i
$471$	35.3106	−	14.6261i	1.62702	−	0.673936i
$472$			2.76382i			0.127215i
$473$	5.66136	+	13.6677i	0.260310	+	0.628443i
$474$	13.9577	+	13.9577i	0.641098	+	0.641098i
$475$	−9.36959			−0.429906
$476$		0			0
$477$	2.80747			0.128545
$478$	16.5895	+	16.5895i	0.758786	+	0.758786i
$479$	−14.6552	−	35.3808i	−0.669614	−	1.61659i	−0.782258	−	0.622955i	$-0.785932\pi$
$479$	−14.6552	−	35.3808i	−0.669614	−	1.61659i	0.112644	−	0.993635i	$-0.464068\pi$
$480$			2.17024i			0.0990577i
$481$	22.1811	−	9.18772i	1.01137	−	0.418924i
$482$	11.6636	−	28.1583i	0.531260	−	1.28258i
$483$	26.5634	+	11.0029i	1.20867	+	0.500649i
$484$	−4.05083	+	4.05083i	−0.184129	+	0.184129i
$485$	−0.954583	+	0.954583i	−0.0433454	+	0.0433454i
$486$	38.8244	+	16.0816i	1.76111	+	0.729476i
$487$	−8.93601	+	21.5734i	−0.404929	+	0.977586i	0.581522	+	0.813531i	$0.302457\pi$
$487$	−8.93601	+	21.5734i	−0.404929	+	0.977586i	−0.986451	+	0.164055i	$0.947543\pi$
$488$	0.996613	−	0.412810i	0.0451145	−	0.0186871i
$489$			16.5963i			0.750509i
$490$	0.403609	+	0.974399i	0.0182332	+	0.0440189i
$491$	22.1981	+	22.1981i	1.00178	+	1.00178i	0.999998	+	0.00178634i	$0.000568609\pi$
$491$	22.1981	+	22.1981i	1.00178	+	1.00178i	0.00178634	+	0.999998i	$0.499431\pi$
$492$	−24.2422			−1.09292
$493$		0			0
$494$	16.1557			0.726879
$495$	−0.784008	−	0.784008i	−0.0352386	−	0.0352386i
$496$	6.92696	+	16.7232i	0.311030	+	0.750892i
$497$			0.260830i			0.0116998i
$498$	−10.7001	+	4.43213i	−0.479484	+	0.198609i
$499$	−6.17308	+	14.9031i	−0.276345	+	0.667156i	−0.999729	−	0.0232901i	$-0.992586\pi$
$499$	−6.17308	+	14.9031i	−0.276345	+	0.667156i	0.723384	+	0.690446i	$0.242586\pi$
$500$	1.70478	+	0.706142i	0.0762399	+	0.0315796i
$501$	−7.06078	+	7.06078i	−0.315452	+	0.315452i
$502$	21.2573	−	21.2573i	0.948762	−	0.948762i
$503$	−31.7479	−	13.1504i	−1.41557	−	0.586348i	−0.461827	−	0.886970i	$-0.652806\pi$
$503$	−31.7479	−	13.1504i	−1.41557	−	0.586348i	−0.953743	+	0.300622i	$0.902806\pi$
$504$	−1.75892	+	4.24640i	−0.0783483	+	0.189150i
$505$	0.867071	−	0.359152i	0.0385841	−	0.0159821i
$506$			37.5330i			1.66855i
$507$	7.67562	+	18.5306i	0.340886	+	0.822973i
$508$	−2.38813	−	2.38813i	−0.105956	−	0.105956i
$509$	−20.0283			−0.887738			−0.443869	−	0.896092i	$-0.646394\pi$
$509$	−20.0283			−0.887738			−0.443869	+	0.896092i	$0.646394\pi$
$510$		0			0
$511$	18.0797			0.799797
$512$	17.8350	+	17.8350i	0.788205	+	0.788205i
$513$	0.749337	+	1.80906i	0.0330840	+	0.0798719i
$514$			18.1557i			0.800813i
$515$	1.21014	−	0.501258i	0.0533253	−	0.0220881i
$516$	−8.15062	+	19.6773i	−0.358811	+	0.866247i
$517$	18.2909	+	7.57636i	0.804435	+	0.333208i
$518$	−10.6871	+	10.6871i	−0.469563	+	0.469563i
$519$	33.9006	−	33.9006i	1.48807	−	1.48807i
$520$	0.448218	+	0.185658i	0.0196556	+	0.00814164i
$521$	−2.13761	+	5.16064i	−0.0936503	+	0.226092i	−0.963762	−	0.266762i	$-0.914046\pi$
$521$	−2.13761	+	5.16064i	−0.0936503	+	0.226092i	0.870112	+	0.492854i	$0.164046\pi$
$522$	−20.2076	+	8.37027i	−0.884464	+	0.366357i
$523$		−	5.51249i		−	0.241044i	−0.992711	−	0.120522i	$-0.961543\pi$
$523$		−	5.51249i		−	0.241044i	0.992711	−	0.120522i	$-0.0384569\pi$
$524$	−1.16862	−	2.82130i	−0.0510514	−	0.123249i
$525$	13.6758	+	13.6758i	0.596860	+	0.596860i
$526$	52.5877			2.29293
$527$		0			0
$528$	−32.1830			−1.40059
$529$	−22.5779	−	22.5779i	−0.981647	−	0.981647i
$530$	0.0713885	+	0.172347i	0.00310092	+	0.00748628i
$531$		−	10.7219i		−	0.465292i
$532$	−4.07567	+	1.68820i	−0.176703	+	0.0731927i
$533$	−10.9381	+	26.4069i	−0.473782	+	1.14381i
$534$	−66.3503	−	27.4832i	−2.87126	−	1.18931i
$535$	1.02702	−	1.02702i	0.0444021	−	0.0444021i
$536$	9.09324	−	9.09324i	0.392768	−	0.392768i
$537$	16.9697	+	7.02906i	0.732295	+	0.303327i
$538$	4.77979	−	11.5394i	0.206071	−	0.497501i
$539$	−11.5828	+	4.79776i	−0.498907	+	0.206654i
$540$		−	0.192533i		−	0.00828531i
$541$	5.35563	+	12.9296i	0.230257	+	0.555889i	0.996207	−	0.0870104i	$-0.0277314\pi$
$541$	5.35563	+	12.9296i	0.230257	+	0.555889i	−0.765951	+	0.642899i	$0.777731\pi$
$542$	−22.5917	−	22.5917i	−0.970398	−	0.970398i
$543$	−63.5536			−2.72734
$544$		0			0
$545$	−0.797362			−0.0341552
$546$	−23.5808	−	23.5808i	−1.00916	−	1.00916i
$547$	11.2576	+	27.1782i	0.481339	+	1.16206i	0.958973	+	0.283497i	$0.0914945\pi$
$547$	11.2576	+	27.1782i	0.481339	+	1.16206i	−0.477634	+	0.878559i	$0.658506\pi$
$548$		−	19.3405i		−	0.826185i
$549$	−3.86624	+	1.60145i	−0.165007	+	0.0683483i
$550$	−9.66169	+	23.3254i	−0.411976	+	0.994598i
$551$	5.92343	+	2.45356i	0.252347	+	0.104525i
$552$	11.6694	−	11.6694i	0.496682	−	0.496682i
$553$	−4.49369	+	4.49369i	−0.191091	+	0.191091i
$554$	−34.9850	−	14.4913i	−1.48637	−	0.615675i
$555$	−0.613470	+	1.48105i	−0.0260403	+	0.0628669i
$556$	7.40914	−	3.06897i	0.314218	−	0.130153i
$557$		−	32.0574i		−	1.35831i	−0.733993	−	0.679157i	$-0.762345\pi$
$557$		−	32.0574i		−	1.35831i	0.733993	−	0.679157i	$-0.237655\pi$
$558$	−9.41555	−	22.7311i	−0.398592	−	0.962286i
$559$	17.7569	+	17.7569i	0.751037	+	0.751037i
$560$	−0.871644			−0.0368337
$561$		0			0
$562$	−30.9590			−1.30593
$563$	−13.1863	−	13.1863i	−0.555737	−	0.555737i	0.372354	−	0.928091i	$-0.378551\pi$
$563$	−13.1863	−	13.1863i	−0.555737	−	0.555737i	−0.928091	+	0.372354i	$0.878551\pi$
$564$	10.9076	+	26.3333i	0.459294	+	1.10883i
$565$		−	0.613503i		−	0.0258103i
$566$	−32.0276	+	13.2663i	−1.34622	+	0.557623i
$567$	−4.45373	+	10.7523i	−0.187039	+	0.451552i
$568$	0.138315	+	0.0572918i	0.00580355	+	0.00240391i
$569$	19.5553	−	19.5553i	0.819801	−	0.819801i	−0.166278	−	0.986079i	$-0.553175\pi$
$569$	19.5553	−	19.5553i	0.819801	−	0.819801i	0.986079	+	0.166278i	$0.0531748\pi$
$570$	−0.762774	+	0.762774i	−0.0319491	+	0.0319491i
$571$	30.6508	+	12.6960i	1.28270	+	0.531311i	0.916801	−	0.399345i	$-0.130762\pi$
$571$	30.6508	+	12.6960i	1.28270	+	0.531311i	0.365897	+	0.930655i	$0.380762\pi$
$572$	7.22621	−	17.4456i	0.302143	−	0.729438i
$573$	33.1151	−	13.7167i	1.38340	−	0.573024i
$574$		−	17.9932i		−	0.751021i
$575$	−14.1400	−	34.1369i	−0.589678	−	1.42361i
$576$	−9.45920	−	9.45920i	−0.394133	−	0.394133i
$577$	−2.70233			−0.112500			−0.0562498	−	0.998417i	$-0.517914\pi$
$577$	−2.70233			−0.112500			−0.0562498	+	0.998417i	$0.517914\pi$
$578$		0			0
$579$	−41.6049			−1.72904
$580$	−0.445771	−	0.445771i	−0.0185096	−	0.0185096i
$581$	−1.42693	−	3.44491i	−0.0591989	−	0.142919i
$582$		−	53.2627i		−	2.20781i
$583$	−2.04871	+	0.848604i	−0.0848490	+	0.0351456i
$584$	3.97123	−	9.58740i	0.164331	−	0.396729i
$585$	−1.73881	−	0.720238i	−0.0718909	−	0.0297782i
$586$	14.5535	−	14.5535i	0.601198	−	0.601198i
$587$	−4.46574	+	4.46574i	−0.184321	+	0.184321i	−0.793236	−	0.608915i	$-0.791605\pi$
$587$	−4.46574	+	4.46574i	−0.184321	+	0.184321i	0.608915	+	0.793236i	$0.291605\pi$
$588$	−16.6757	−	6.90729i	−0.687694	−	0.284852i
$589$	−2.75996	+	6.66314i	−0.113722	+	0.274550i
$590$	0.658207	−	0.272638i	0.0270980	−	0.0112243i
$591$			51.2481i			2.10807i
$592$	9.47477	+	22.8741i	0.389411	+	0.940121i
$593$	−7.22297	−	7.22297i	−0.296612	−	0.296612i	0.543073	−	0.839685i	$-0.317261\pi$
$593$	−7.22297	−	7.22297i	−0.296612	−	0.296612i	−0.839685	+	0.543073i	$0.817261\pi$
$594$	5.27631			0.216490
$595$		0			0
$596$	14.7888			0.605773
$597$	−39.7039	−	39.7039i	−1.62497	−	1.62497i
$598$	24.3811	+	58.8613i	0.997019	+	2.40702i
$599$		−	21.4347i		−	0.875798i	−0.899024	−	0.437899i	$-0.855723\pi$
$599$		−	21.4347i		−	0.875798i	0.899024	−	0.437899i	$-0.144277\pi$
$600$	10.2560	−	4.24817i	0.418699	−	0.173431i
$601$	−6.68002	+	16.1270i	−0.272484	+	0.657834i	−0.999588	−	0.0286930i	$-0.990865\pi$
$601$	−6.68002	+	16.1270i	−0.272484	+	0.657834i	0.727105	+	0.686527i	$0.240865\pi$
$602$	−14.6051	−	6.04961i	−0.595258	−	0.246564i
$603$	−35.2762	+	35.2762i	−1.43656	+	1.43656i
$604$	−1.30769	+	1.30769i	−0.0532092	+	0.0532092i
$605$	−0.416669	−	0.172590i	−0.0169400	−	0.00701678i
$606$	−14.1701	+	34.2097i	−0.575621	+	1.38967i
$607$	−7.86203	+	3.25656i	−0.319110	+	0.132180i	−0.536488	−	0.843908i	$-0.680249\pi$
$607$	−7.86203	+	3.25656i	−0.319110	+	0.132180i	0.217378	+	0.976087i	$0.430249\pi$
$608$			13.3550i			0.541618i
$609$	−5.06459	−	12.2270i	−0.205228	−	0.495464i
$610$	−0.196622	−	0.196622i	−0.00796101	−	0.00796101i
$611$	33.6064			1.35957
$612$		0			0
$613$	9.78106			0.395053			0.197527	−	0.980298i	$-0.436709\pi$
$613$	9.78106			0.395053			0.197527	+	0.980298i	$0.436709\pi$
$614$	−7.68260	−	7.68260i	−0.310045	−	0.310045i
$615$	−0.730344	−	1.76321i	−0.0294503	−	0.0710994i
$616$		−	3.63041i		−	0.146274i
$617$	−21.1118	+	8.74478i	−0.849928	+	0.352052i	−0.764760	−	0.644315i	$-0.777143\pi$
$617$	−21.1118	+	8.74478i	−0.849928	+	0.352052i	−0.0851678	+	0.996367i	$0.527143\pi$
$618$	−19.7768	+	47.7454i	−0.795539	+	1.92060i
$619$	38.1218	+	15.7906i	1.53224	+	0.634676i	0.979998	−	0.199006i	$-0.0637714\pi$
$619$	38.1218	+	15.7906i	1.53224	+	0.634676i	0.552245	+	0.833682i	$0.313771\pi$
$620$	0.501438	−	0.501438i	0.0201382	−	0.0201382i
$621$	−5.46023	+	5.46023i	−0.219112	+	0.219112i
$622$	−0.209426	−	0.0867473i	−0.00839724	−	0.00347825i
$623$	8.84823	−	21.3615i	0.354497	−	0.855831i
$624$	−50.4712	+	20.9058i	−2.02046	+	0.836903i
$625$		−	24.7820i		−	0.991280i
$626$	−7.47200	−	18.0390i	−0.298641	−	0.720984i
$627$	−9.06719	−	9.06719i	−0.362109	−	0.362109i
$628$	−23.1257			−0.922815
$629$		0			0
$630$	1.18479			0.0472033
$631$	−6.74758	−	6.74758i	−0.268617	−	0.268617i	0.559926	−	0.828543i	$-0.310830\pi$
$631$	−6.74758	−	6.74758i	−0.268617	−	0.268617i	−0.828543	+	0.559926i	$0.810830\pi$
$632$	1.39590	+	3.36999i	0.0555257	+	0.134051i
$633$			18.1993i			0.723359i
$634$	48.2726	−	19.9952i	1.91715	−	0.794110i
$635$	0.101749	−	0.245643i	0.00403778	−	0.00974805i
$636$	−2.94952	−	1.22173i	−0.116956	−	0.0484447i
$637$	−15.0482	+	15.0482i	−0.596231	+	0.596231i
$638$	12.2162	−	12.2162i	0.483644	−	0.483644i
$639$	−0.536575	−	0.222257i	−0.0212266	−	0.00879234i
$640$	−0.315833	+	0.762489i	−0.0124844	+	0.0301400i
$641$	8.71099	−	3.60821i	0.344064	−	0.142516i	−0.203959	−	0.978979i	$-0.565381\pi$
$641$	8.71099	−	3.60821i	0.344064	−	0.142516i	0.548022	+	0.836464i	$0.315381\pi$
$642$			57.3046i			2.26163i
$643$	4.21181	+	10.1682i	0.166098	+	0.400995i	0.984910	−	0.173066i	$-0.0553673\pi$
$643$	4.21181	+	10.1682i	0.166098	+	0.400995i	−0.818813	+	0.574061i	$0.805367\pi$
$644$	−12.3015	−	12.3015i	−0.484746	−	0.484746i
$645$	−1.67675			−0.0660219
$646$		0			0
$647$	28.9840			1.13948			0.569740	−	0.821825i	$-0.307044\pi$
$647$	28.9840			1.13948			0.569740	+	0.821825i	$0.307044\pi$
$648$	4.72350	+	4.72350i	0.185557	+	0.185557i
$649$	3.24089	+	7.82419i	0.127216	+	0.307126i
$650$			42.8563i			1.68096i
$651$	13.7539	−	5.69706i	0.539058	−	0.223285i
$652$	3.84286	−	9.27750i	0.150498	−	0.363335i
$653$	13.5975	+	5.63226i	0.532111	+	0.220408i	0.632527	−	0.774538i	$-0.282018\pi$
$653$	13.5975	+	5.63226i	0.532111	+	0.220408i	−0.100417	+	0.994945i	$0.532018\pi$
$654$	22.2451	−	22.2451i	0.869853	−	0.869853i
$655$	0.169994	−	0.169994i	0.00664223	−	0.00664223i
$656$	−27.2320	−	11.2798i	−1.06323	−	0.440404i
$657$	−15.4059	+	37.1932i	−0.601043	+	1.45105i
$658$	−19.5453	+	8.09593i	−0.761956	+	0.315612i
$659$		−	2.19759i		−	0.0856058i	−0.999084	−	0.0428029i	$-0.986371\pi$
$659$		−	2.19759i		−	0.0856058i	0.999084	−	0.0428029i	$-0.0136287\pi$
$660$	0.482499	+	1.16485i	0.0187812	+	0.0453419i
$661$	−18.8106	−	18.8106i	−0.731649	−	0.731649i	0.239297	−	0.970946i	$-0.423083\pi$
$661$	−18.8106	−	18.8106i	−0.731649	−	0.731649i	−0.970946	+	0.239297i	$0.923083\pi$
$662$	16.4979			0.641211
$663$		0			0
$664$	−2.14022			−0.0830565
$665$	−0.245576	−	0.245576i	−0.00952301	−	0.00952301i
$666$	−12.8787	−	31.0919i	−0.499039	−	1.20479i
$667$			25.2841i			0.979002i
$668$	5.58198	−	2.31213i	0.215973	−	0.0894590i
$669$	5.83292	−	14.0819i	0.225514	−	0.544439i
$670$	−3.06257	−	1.26856i	−0.118317	−	0.0490087i
$671$	2.33728	−	2.33728i	0.0902295	−	0.0902295i
$672$	19.4929	−	19.4929i	0.751956	−	0.751956i
$673$	6.69251	+	2.77213i	0.257977	+	0.106858i	0.507924	−	0.861402i	$-0.330413\pi$
$673$	6.69251	+	2.77213i	0.257977	+	0.106858i	−0.249947	+	0.968260i	$0.580413\pi$
$674$	−1.05084	+	2.53695i	−0.0404768	+	0.0977197i
$675$	−4.79890	+	1.98777i	−0.184710	+	0.0765092i
$676$		−	12.1361i		−	0.466773i
$677$	8.77388	+	21.1820i	0.337208	+	0.814091i	0.997981	+	0.0635063i	$0.0202283\pi$
$677$	8.77388	+	21.1820i	0.337208	+	0.814091i	−0.660774	+	0.750585i	$0.729772\pi$
$678$	17.1158	+	17.1158i	0.657326	+	0.657326i
$679$	17.1480			0.658078
$680$		0			0
$681$	55.7948			2.13806
$682$	13.7417	+	13.7417i	0.526199	+	0.526199i
$683$	−1.64397	−	3.96890i	−0.0629049	−	0.151866i	0.889301	−	0.457322i	$-0.151191\pi$
$683$	−1.64397	−	3.96890i	−0.0629049	−	0.151866i	−0.952206	+	0.305456i	$0.901191\pi$
$684$		−	9.82295i		−	0.375590i
$685$	1.40669	−	0.582671i	0.0537470	−	0.0222627i
$686$	12.8400	−	30.9986i	0.490235	−	1.18353i
$687$	−8.65475	−	3.58491i	−0.330199	−	0.136773i
$688$	−18.3117	+	18.3117i	−0.698126	+	0.698126i
$689$	−2.66165	+	2.66165i	−0.101401	+	0.101401i
$690$	−3.93020	−	1.62794i	−0.149620	−	0.0619748i
$691$	7.89595	−	19.0625i	0.300376	−	0.725172i	−0.699568	−	0.714566i	$-0.746624\pi$
$691$	7.89595	−	19.0625i	0.300376	−	0.725172i	0.999944	−	0.0106055i	$-0.00337590\pi$
$692$	−26.8005	+	11.1011i	−1.01880	+	0.422002i
$693$			14.0838i			0.534998i
$694$	−22.5515	−	54.4442i	−0.856044	−	2.06667i
$695$	0.446431	+	0.446431i	0.0169341	+	0.0169341i
$696$	−7.59627			−0.287936
$697$		0			0
$698$	55.9573			2.11801
$699$	52.1930	+	52.1930i	1.97412	+	1.97412i
$700$	−4.47829	−	10.8115i	−0.169263	−	0.408638i
$701$		−	28.2772i		−	1.06802i	−0.845479	−	0.534008i	$-0.820685\pi$
$701$		−	28.2772i		−	1.06802i	0.845479	−	0.534008i	$-0.179315\pi$
$702$	8.27459	−	3.42745i	0.312304	−	0.129361i
$703$	−3.77511	+	9.11392i	−0.142381	+	0.343738i
$704$	9.76193	+	4.04352i	0.367917	+	0.152396i
$705$	−1.58669	+	1.58669i	−0.0597582	+	0.0597582i
$706$	−37.6273	+	37.6273i	−1.41612	+	1.41612i
$707$	−11.0138	−	4.56207i	−0.414217	−	0.171574i
$708$	−4.66588	+	11.2644i	−0.175355	+	0.423343i
$709$	−25.0373	+	10.3708i	−0.940296	+	0.389483i	−0.799575	−	0.600566i	$-0.794942\pi$
$709$	−25.0373	+	10.3708i	−0.940296	+	0.389483i	−0.140721	+	0.990049i	$0.544942\pi$
$710$		−	0.0385913i		−	0.00144831i
$711$	−5.41522	−	13.0735i	−0.203087	−	0.490294i
$712$	−9.38420	−	9.38420i	−0.351688	−	0.351688i
$713$	−28.4415			−1.06514
$714$		0			0
$715$	1.48658			0.0555949
$716$	−7.85865	−	7.85865i	−0.293691	−	0.293691i
$717$	−12.0963	−	29.2030i	−0.451743	−	1.09060i
$718$			5.29591i			0.197642i
$719$	−23.8732	+	9.88861i	−0.890321	+	0.368783i	−0.780491	−	0.625167i	$-0.785031\pi$
$719$	−23.8732	+	9.88861i	−0.890321	+	0.368783i	−0.109830	+	0.993950i	$0.535031\pi$
$720$	0.742741	−	1.79313i	0.0276803	−	0.0668262i
$721$	−15.3717	−	6.36715i	−0.572470	−	0.237125i
$722$	20.5557	−	20.5557i	0.765004	−	0.765004i
$723$	−29.0362	+	29.0362i	−1.07987	+	1.07987i
$724$	35.5271	+	14.7158i	1.32036	+	0.546909i
$725$	−6.50858	+	15.7131i	−0.241723	+	0.583570i
$726$	16.4394	−	6.80941i	0.610122	−	0.252721i
$727$			31.6290i			1.17305i	0.809930	+	0.586527i	$0.199505\pi$
$727$			31.6290i			1.17305i	−0.809930	+	0.586527i	$0.800495\pi$
$728$	−2.35829	−	5.69341i	−0.0874040	−	0.211012i
$729$	−23.9207	−	23.9207i	−0.885951	−	0.885951i
$730$	−2.67499			−0.0990059
$731$		0			0
$732$	4.75877			0.175889
$733$	−18.1048	−	18.1048i	−0.668715	−	0.668715i	0.288704	−	0.957419i	$-0.406776\pi$
$733$	−18.1048	−	18.1048i	−0.668715	−	0.668715i	−0.957419	+	0.288704i	$0.906776\pi$
$734$	−5.98253	−	14.4431i	−0.220819	−	0.533105i
$735$		−	1.42097i		−	0.0524133i
$736$	−48.6574	+	20.1546i	−1.79354	+	0.742907i
$737$	15.0795	−	36.4052i	0.555461	−	1.34100i
$738$	37.0153	+	15.3323i	1.36255	+	0.564388i
$739$	15.3005	−	15.3005i	0.562837	−	0.562837i	−0.367275	−	0.930112i	$-0.619709\pi$
$739$	15.3005	−	15.3005i	0.562837	−	0.562837i	0.930112	+	0.367275i	$0.119709\pi$
$740$	0.685873	−	0.685873i	0.0252132	−	0.0252132i
$741$	−20.1096	−	8.32968i	−0.738746	−	0.305999i
$742$	0.906801	−	2.18921i	0.0332897	−	0.0803685i
$743$	24.7181	−	10.2386i	0.906818	−	0.375616i	0.119980	−	0.992776i	$-0.461717\pi$
$743$	24.7181	−	10.2386i	0.906818	−	0.375616i	0.786838	+	0.617160i	$0.211717\pi$
$744$		−	8.54488i		−	0.313271i
$745$	0.445542	+	1.07563i	0.0163234	+	0.0394082i
$746$	12.2513	+	12.2513i	0.448552	+	0.448552i
$747$	8.30272			0.303781
$748$		0			0
$749$	−18.4492			−0.674121
$750$	−4.05273	−	4.05273i	−0.147985	−	0.147985i
$751$	16.0541	+	38.7580i	0.585821	+	1.41430i	0.887464	+	0.460877i	$0.152465\pi$
$751$	16.0541	+	38.7580i	0.585821	+	1.41430i	−0.301643	+	0.953421i	$0.597535\pi$
$752$			34.6563i			1.26379i
$753$	−37.4199	+	15.4998i	−1.36366	+	0.564845i
$754$	11.2226	−	27.0936i	0.408701	−	0.986692i
$755$	−0.134509	−	0.0557156i	−0.00489529	−	0.00202770i
$756$	−1.72932	+	1.72932i	−0.0628946	+	0.0628946i
$757$	3.53072	−	3.53072i	0.128326	−	0.128326i	−0.640027	−	0.768353i	$-0.721077\pi$
$757$	3.53072	−	3.53072i	0.128326	−	0.128326i	0.768353	+	0.640027i	$0.221077\pi$
$758$	17.9932	+	7.45301i	0.653541	+	0.270705i
$759$	19.3516	−	46.7188i	0.702418	−	1.69579i
$760$	−0.184167	+	0.0762843i	−0.00668042	+	0.00276712i
$761$		−	13.2935i		−	0.481891i	−0.970539	−	0.240945i	$-0.922543\pi$
$761$		−	13.2935i		−	0.481891i	0.970539	−	0.240945i	$-0.0774575\pi$
$762$	4.01443	+	9.69168i	0.145427	+	0.351093i
$763$	7.16183	+	7.16183i	0.259276	+	0.259276i
$764$	−21.6878			−0.784637
$765$		0			0
$766$	−24.9418			−0.901184
$767$	10.1651	+	10.1651i	0.367039	+	0.367039i
$768$	−20.0603	−	48.4299i	−0.723865	−	1.74756i
$769$			8.25166i			0.297562i	0.988870	+	0.148781i	$0.0475350\pi$
$769$			8.25166i			0.297562i	−0.988870	+	0.148781i	$0.952465\pi$
$770$	−0.864587	+	0.358124i	−0.0311576	+	0.0129059i
$771$	9.36086	−	22.5991i	0.337123	−	0.813887i
$772$	23.2576	+	9.63362i	0.837060	+	0.346722i
$773$	18.4585	−	18.4585i	0.663907	−	0.663907i	−0.292391	−	0.956299i	$-0.594451\pi$
$773$	18.4585	−	18.4585i	0.663907	−	0.663907i	0.956299	+	0.292391i	$0.0944510\pi$
$774$	24.8904	−	24.8904i	0.894665	−	0.894665i
$775$	−17.6753	−	7.32137i	−0.634917	−	0.262991i
$776$	3.76658	−	9.09333i	0.135212	−	0.326431i
$777$	18.8128	−	7.79250i	0.674904	−	0.279554i
$778$		−	49.3833i		−	1.77048i
$779$	−4.49432	−	10.8502i	−0.161026	−	0.388750i
$780$	1.51336	+	1.51336i	0.0541870	+	0.0541870i
$781$	0.458740			0.0164150
$782$		0			0
$783$	3.55438			0.127023
$784$	−15.5183	−	15.5183i	−0.554227	−	0.554227i
$785$	−0.696707	−	1.68200i	−0.0248666	−	0.0600332i
$786$			9.48515i			0.338324i
$787$	24.8186	−	10.2802i	0.884686	−	0.366449i	0.106374	−	0.994326i	$-0.466076\pi$
$787$	24.8186	−	10.2802i	0.884686	−	0.366449i	0.778312	+	0.627877i	$0.216076\pi$
$788$	11.8665	−	28.6483i	0.422727	−	1.02055i
$789$	−65.4580	−	27.1136i	−2.33037	−	0.965269i
$790$	0.664868	−	0.664868i	0.0236549	−	0.0236549i
$791$	−5.51043	+	5.51043i	−0.195928	+	0.195928i
$792$	7.46844	+	3.09353i	0.265379	+	0.109924i
$793$	2.14717	−	5.18372i	0.0762481	−	0.184079i
$794$	44.2356	−	18.3230i	1.56986	−	0.650259i
$795$		−	0.251334i		−	0.00891391i
$796$	13.0015	+	31.3884i	0.460826	+	1.11253i
$797$	−13.3086	−	13.3086i	−0.471415	−	0.471415i	0.430958	−	0.902372i	$-0.358176\pi$
$797$	−13.3086	−	13.3086i	−0.471415	−	0.471415i	−0.902372	+	0.430958i	$0.858176\pi$
$798$	13.7023			0.485057
$799$		0			0
$800$	−35.4270			−1.25253
$801$	36.4049	+	36.4049i	1.28630	+	1.28630i
$802$	0.647821	+	1.56398i	0.0228754	+	0.0552260i
$803$		−	31.7980i		−	1.12213i
$804$	52.4122	−	21.7099i	1.84844	−	0.765648i
$805$	0.524118	−	1.26533i	0.0184727	−	0.0445971i
$806$	30.4771	+	12.6240i	1.07351	+	0.444662i
$807$	−11.8992	+	11.8992i	−0.418871	+	0.418871i
$808$	−4.83841	+	4.83841i	−0.170215	+	0.170215i
$809$	−23.7967	−	9.85691i	−0.836647	−	0.346550i	−0.0771162	−	0.997022i	$-0.524571\pi$
$809$	−23.7967	−	9.85691i	−0.836647	−	0.346550i	−0.759530	+	0.650472i	$0.774571\pi$
$810$	0.658956	−	1.59086i	0.0231533	−	0.0558971i
$811$	−24.4351	+	10.1213i	−0.858031	+	0.355408i	−0.767937	−	0.640525i	$-0.778717\pi$
$811$	−24.4351	+	10.1213i	−0.858031	+	0.355408i	−0.0900937	+	0.995933i	$0.528717\pi$
$812$			8.00774i			0.281017i
$813$	16.4728	+	39.7689i	0.577726	+	1.39476i
$814$	18.7961	+	18.7961i	0.658803	+	0.658803i
$815$	0.790555			0.0276919
$816$		0			0
$817$	−10.3182			−0.360988
$818$	−20.3670	−	20.3670i	−0.712117	−	0.712117i
$819$	9.14871	+	22.0869i	0.319682	+	0.771780i
$820$			1.15476i			0.0403261i
$821$	29.1050	−	12.0557i	1.01577	−	0.420746i	0.188214	−	0.982128i	$-0.439730\pi$
$821$	29.1050	−	12.0557i	1.01577	−	0.420746i	0.827557	+	0.561382i	$0.189730\pi$
$822$	−22.9889	+	55.5001i	−0.801829	+	1.93579i
$823$	10.7997	+	4.47339i	0.376455	+	0.155933i	0.562884	−	0.826536i	$-0.309692\pi$
$823$	10.7997	+	4.47339i	0.376455	+	0.155933i	−0.186430	+	0.982468i	$0.559692\pi$
$824$	−6.75282	+	6.75282i	−0.235246	+	0.235246i
$825$	24.0526	−	24.0526i	0.837403	−	0.837403i
$826$	−8.36077	−	3.46314i	−0.290908	−	0.120498i
$827$	−1.27152	+	3.06972i	−0.0442151	+	0.106745i	−0.944444	−	0.328672i	$-0.893399\pi$
$827$	−1.27152	+	3.06972i	−0.0442151	+	0.106745i	0.900229	+	0.435417i	$0.143399\pi$
$828$	35.7887	−	14.8242i	1.24374	−	0.515175i
$829$		−	6.01186i		−	0.208801i	−0.994535	−	0.104400i	$-0.966708\pi$
$829$		−	6.01186i		−	0.208801i	0.994535	−	0.104400i	$-0.0332923\pi$
$830$	0.211122	+	0.509694i	0.00732816	+	0.0176918i
$831$	36.0757	+	36.0757i	1.25145	+	1.25145i
$832$	17.9358			0.621813
$833$		0			0
$834$	−24.9094			−0.862542
$835$	0.336337	+	0.336337i	0.0116394	+	0.0116394i
$836$	2.96915	+	7.16817i	0.102690	+	0.247916i
$837$			3.99825i			0.138200i
$838$	−4.13963	+	1.71469i	−0.143001	+	0.0592330i
$839$	−15.8475	+	38.2592i	−0.547116	+	1.32085i	0.372499	+	0.928033i	$0.378501\pi$
$839$	−15.8475	+	38.2592i	−0.547116	+	1.32085i	−0.919615	+	0.392822i	$0.871499\pi$
$840$	0.380153	+	0.157464i	0.0131165	+	0.00543304i
$841$	−12.2767	+	12.2767i	−0.423334	+	0.423334i
$842$	−11.0112	+	11.0112i	−0.379472	+	0.379472i
$843$	38.5359	+	15.9621i	1.32725	+	0.549764i
$844$	4.21406	−	10.1736i	0.145054	−	0.350191i
$845$	0.882695	−	0.365624i	0.0303656	−	0.0125779i
$846$		−	47.1070i		−	1.61957i
$847$	2.19229	+	5.29267i	0.0753281	+	0.181858i
$848$	−2.74481	−	2.74481i	−0.0942572	−	0.0942572i
$849$	46.7060			1.60294
$850$		0			0
$851$	−38.9026			−1.33356
$852$	0.467005	+	0.467005i	0.0159993	+	0.0159993i
$853$	−9.18373	−	22.1715i	−0.314445	−	0.759137i	−0.999529	−	0.0306737i	$-0.990235\pi$
$853$	−9.18373	−	22.1715i	−0.314445	−	0.759137i	0.685084	−	0.728464i	$-0.259765\pi$
$854$			3.53209i			0.120866i
$855$	0.714453	−	0.295936i	0.0244338	−	0.0101208i
$856$	−4.05241	+	9.78338i	−0.138509	+	0.334389i
$857$	−29.4305	−	12.1905i	−1.00533	−	0.416420i	−0.181579	−	0.983376i	$-0.558121\pi$
$857$	−29.4305	−	12.1905i	−1.00533	−	0.416420i	−0.823748	+	0.566956i	$0.808121\pi$
$858$	−41.4731	+	41.4731i	−1.41587	+	1.41587i
$859$	−17.0276	+	17.0276i	−0.580973	+	0.580973i	−0.935170	−	0.354198i	$-0.884754\pi$
$859$	−17.0276	+	17.0276i	−0.580973	+	0.580973i	0.354198	+	0.935170i	$0.384754\pi$
$860$	0.937320	+	0.388251i	0.0319623	+	0.0132392i
$861$	−9.27707	+	22.3968i	−0.316162	+	0.763282i
$862$	56.1165	−	23.2442i	1.91134	−	0.791702i
$863$			20.8590i			0.710047i	0.934857	+	0.355024i	$0.115527\pi$
$863$			20.8590i			0.710047i	−0.934857	+	0.355024i	$0.884473\pi$
$864$	2.83329	+	6.84016i	0.0963904	+	0.232707i
$865$	−1.61484	−	1.61484i	−0.0549062	−	0.0549062i
$866$	−28.3114			−0.962060
$867$		0			0
$868$	−9.00774			−0.305743
$869$	7.90337	+	7.90337i	0.268103	+	0.268103i
$870$	0.749337	+	1.80906i	0.0254049	+	0.0613328i
$871$		−	66.8881i		−	2.26642i
$872$	5.37093	−	2.22471i	0.181883	−	0.0753383i
$873$	−14.6120	+	35.2765i	−0.494542	+	1.19393i
$874$	−24.1853	−	10.0179i	−0.818080	−	0.338860i
$875$	1.30478	−	1.30478i	0.0441096	−	0.0441096i
$876$	32.3709	−	32.3709i	1.09371	−	1.09371i
$877$	20.6643	+	8.55944i	0.697784	+	0.289032i	0.703239	−	0.710953i	$-0.251736\pi$
$877$	20.6643	+	8.55944i	0.697784	+	0.289032i	−0.00545474	+	0.999985i	$0.501736\pi$
$878$	−1.85056	+	4.46764i	−0.0624533	+	0.150776i
$879$	−25.6189	+	10.6117i	−0.864103	+	0.357923i
$880$			1.53302i			0.0516782i
$881$	21.5940	+	52.1326i	0.727521	+	1.75639i	0.650686	+	0.759347i	$0.274482\pi$
$881$	21.5940	+	52.1326i	0.727521	+	1.75639i	0.0768353	+	0.997044i	$0.475518\pi$
$882$	21.0935	+	21.0935i	0.710255	+	0.710255i
$883$	45.4219			1.52857			0.764284	−	0.644879i	$-0.223092\pi$
$883$	45.4219			1.52857			0.764284	+	0.644879i	$0.223092\pi$
$884$		0			0
$885$	−0.959866			−0.0322655
$886$	31.1848	+	31.1848i	1.04767	+	1.04767i
$887$	−6.68993	−	16.1509i	−0.224626	−	0.542295i	0.770881	−	0.636979i	$-0.219816\pi$
$887$	−6.68993	−	16.1509i	−0.224626	−	0.542295i	−0.995507	+	0.0946836i	$0.969816\pi$
$888$		−	11.6878i		−	0.392216i
$889$	−3.12024	+	1.29245i	−0.104650	+	0.0433473i
$890$	−1.30915	+	3.16056i	−0.0438828	+	0.105942i
$891$	18.9107	+	7.83309i	0.633534	+	0.262418i
$892$	−6.52134	+	6.52134i	−0.218351	+	0.218351i
$893$	−9.76401	+	9.76401i	−0.326740	+	0.326740i
$894$	−42.4384	−	17.5786i	−1.41935	−	0.587915i
$895$	0.334826	−	0.808341i	0.0111920	−	0.0270199i
$896$	9.68539	−	4.01182i	0.323566	−	0.134026i
$897$		−	85.8376i		−	2.86603i
$898$	13.5629	+	32.7437i	0.452599	+	1.09267i
$899$	9.25710	+	9.25710i	0.308742	+	0.308742i
$900$	26.0574			0.868579
$901$		0			0
$902$	−31.6459			−1.05369
$903$	15.0604	+	15.0604i	0.501178	+	0.501178i
$904$	1.71173	+	4.13248i	0.0569313	+	0.137444i
$905$			3.02734i			0.100632i
$906$	5.30697	−	2.19822i	0.176312	−	0.0730309i
$907$	3.98520	−	9.62113i	0.132327	−	0.319464i	−0.843803	−	0.536653i	$-0.819689\pi$
$907$	3.98520	−	9.62113i	0.132327	−	0.319464i	0.976130	+	0.217188i	$0.0696885\pi$
$908$	−31.1899	−	12.9193i	−1.03507	−	0.428741i
$909$	18.7701	−	18.7701i	0.622564	−	0.622564i
$910$	−1.12326	+	1.12326i	−0.0372356	+	0.0372356i
$911$	40.9022	+	16.9422i	1.35515	+	0.561321i	0.937721	−	0.347389i	$-0.112932\pi$
$911$	40.9022	+	16.9422i	1.35515	+	0.561321i	0.417428	+	0.908710i	$0.362932\pi$
$912$	8.58993	−	20.7379i	0.284441	−	0.686701i
$913$	−6.05880	+	2.50964i	−0.200517	+	0.0830569i
$914$		−	3.96141i		−	0.131032i
$915$	0.143368	+	0.346120i	0.00473959	+	0.0114424i
$916$	4.00801	+	4.00801i	0.132428	+	0.132428i
$917$	−3.05375			−0.100844
$918$		0			0
$919$	−31.0615			−1.02462			−0.512312	−	0.858799i	$-0.671211\pi$
$919$	−31.0615			−1.02462			−0.512312	+	0.858799i	$0.671211\pi$
$920$	−0.555865	−	0.555865i	−0.0183263	−	0.0183263i
$921$	5.60178	+	13.5239i	0.184585	+	0.445627i
$922$			41.1729i			1.35596i
$923$	0.719420	−	0.297994i	0.0236800	−	0.00980858i
$924$	6.12886	−	14.7964i	0.201625	−	0.486765i
$925$	−24.1765	−	10.0142i	−0.794919	−	0.329266i
$926$	−18.8119	+	18.8119i	−0.618197	+	0.618197i
$927$	26.1968	−	26.1968i	0.860416	−	0.860416i
$928$	22.3968	+	9.27707i	0.735212	+	0.304535i
$929$	8.57093	−	20.6921i	0.281203	−	0.678885i	−0.718661	−	0.695361i	$-0.755245\pi$
$929$	8.57093	−	20.6921i	0.281203	−	0.678885i	0.999864	+	0.0164760i	$0.00524471\pi$
$930$	−2.03497	+	0.842913i	−0.0667294	+	0.0276402i
$931$		−	8.74422i		−	0.286580i
$932$	−17.0912	−	41.2617i	−0.559840	−	1.35157i
$933$	0.215956	+	0.215956i	0.00707007	+	0.00707007i
$934$	−55.7948			−1.82566
$935$		0			0
$936$	13.7219			0.448515
$937$	−41.1297	−	41.1297i	−1.34365	−	1.34365i	−0.892398	−	0.451250i	$-0.850978\pi$
$937$	−41.1297	−	41.1297i	−1.34365	−	1.34365i	−0.451250	−	0.892398i	$-0.649022\pi$
$938$	16.1137	+	38.9018i	0.526129	+	1.27019i
$939$			26.3063i			0.858475i
$940$	1.25437	−	0.519579i	0.0409132	−	0.0169468i
$941$	−3.99512	+	9.64507i	−0.130237	+	0.314420i	−0.975524	−	0.219892i	$-0.929429\pi$
$941$	−3.99512	+	9.64507i	−0.130237	+	0.314420i	0.845287	+	0.534313i	$0.179429\pi$
$942$	66.3621	+	27.4881i	2.16220	+	0.895611i
$943$	32.7490	−	32.7490i	1.06645	−	1.06645i
$944$	−10.4826	+	10.4826i	−0.341181	+	0.341181i
$945$	−0.177878	−	0.0736793i	−0.00578636	−	0.00239679i
$946$	−10.6399	+	25.6869i	−0.345932	+	0.835155i
$947$	−3.73584	+	1.54744i	−0.121398	+	0.0502849i	−0.442556	−	0.896741i	$-0.645928\pi$
$947$	−3.73584	+	1.54744i	−0.121398	+	0.0502849i	0.321157	+	0.947026i	$0.395928\pi$
$948$			16.0915i			0.522628i
$949$	−20.6557	−	49.8673i	−0.670513	−	1.61876i
$950$	−12.4515	−	12.4515i	−0.403980	−	0.403980i
$951$	−70.3961			−2.28275
$952$		0			0
$953$	4.37639			0.141765			0.0708826	−	0.997485i	$-0.477418\pi$
$953$	4.37639			0.141765			0.0708826	+	0.997485i	$0.477418\pi$
$954$	3.73092	+	3.73092i	0.120793	+	0.120793i
$955$	−0.653388	−	1.57742i	−0.0211431	−	0.0510441i
$956$			19.1257i			0.618568i
$957$	−21.5045	+	8.90746i	−0.695142	+	0.287937i
$958$	27.5428	−	66.4942i	0.889867	−	2.14833i
$959$	−17.8683	−	7.40128i	−0.576997	−	0.239000i
$960$	−0.846821	+	0.846821i	−0.0273310	+	0.0273310i
$961$	11.5072	−	11.5072i	0.371200	−	0.371200i
$962$	41.6869	+	17.2673i	1.34404	+	0.556719i
$963$	15.7209	−	37.9535i	0.506598	−	1.22304i
$964$	22.9549	−	9.50822i	0.739327	−	0.306239i
$965$			1.98183i			0.0637974i
$966$	20.6787	+	49.9228i	0.665326	+	1.60624i
$967$	17.2796	+	17.2796i	0.555675	+	0.555675i	0.928073	−	0.372398i	$-0.121464\pi$
$967$	17.2796	+	17.2796i	0.555675	+	0.555675i	−0.372398	+	0.928073i	$0.621464\pi$
$968$	3.28817			0.105686
$969$		0			0
$970$	−2.53714			−0.0814627
$971$	−14.5136	−	14.5136i	−0.465762	−	0.465762i	0.434776	−	0.900539i	$-0.356828\pi$
$971$	−14.5136	−	14.5136i	−0.465762	−	0.465762i	−0.900539	+	0.434776i	$0.856828\pi$
$972$	13.1098	+	31.6499i	0.420498	+	1.01517i
$973$		−	8.01960i		−	0.257097i
$974$	−40.5448	+	16.7942i	−1.29914	+	0.538121i
$975$	22.0962	−	53.3449i	0.707644	−	1.70840i
$976$	5.34567	+	2.21425i	0.171111	+	0.0708764i
$977$	20.0163	−	20.0163i	0.640377	−	0.640377i	−0.310271	−	0.950648i	$-0.600420\pi$
$977$	20.0163	−	20.0163i	0.640377	−	0.640377i	0.950648	+	0.310271i	$0.100420\pi$
$978$	−22.0552	+	22.0552i	−0.705248	+	0.705248i
$979$	−37.5700	−	15.5620i	−1.20074	−	0.497364i
$980$	−0.329025	+	0.794338i	−0.0105103	+	0.0253742i
$981$	−20.8359	+	8.63052i	−0.665239	+	0.275551i
$982$			58.9992i			1.88274i
$983$	−10.2078	−	24.6437i	−0.325577	−	0.786013i	−0.998910	−	0.0466734i	$-0.985138\pi$
$983$	−10.2078	−	24.6437i	−0.325577	−	0.786013i	0.673333	−	0.739339i	$-0.264862\pi$
$984$	9.83901	+	9.83901i	0.313656	+	0.313656i
$985$	2.44118			0.0777824
$986$		0			0
$987$	28.5030			0.907260
$988$	9.31277	+	9.31277i	0.296279	+	0.296279i
$989$	−15.5716	−	37.5931i	−0.495147	−	1.19539i
$990$		−	2.08378i		−	0.0662268i
$991$	−32.2302	+	13.3502i	−1.02383	+	0.424082i	−0.830480	−	0.557048i	$-0.811934\pi$
$991$	−32.2302	+	13.3502i	−1.02383	+	0.424082i	−0.193345	+	0.981131i	$0.561934\pi$
$992$	−10.4356	+	25.1937i	−0.331330	+	0.799902i
$993$	−20.5356	−	8.50614i	−0.651679	−	0.269934i
$994$	−0.346624	+	0.346624i	−0.0109942	+	0.0109942i
$995$	−1.89128	+	1.89128i	−0.0599575	+	0.0599575i
$996$	−8.72281	−	3.61311i	−0.276393	−	0.114486i
$997$	−17.3419	+	41.8669i	−0.549222	+	1.32594i	0.368837	+	0.929494i	$0.379756\pi$
$997$	−17.3419	+	41.8669i	−0.549222	+	1.32594i	−0.918059	+	0.396445i	$0.870244\pi$
$998$	−28.0087	+	11.6016i	−0.886601	+	0.367242i
$999$			5.46884i			0.173027i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.2.d.f.134.5		24
17.2	even	8	inner	289.2.d.f.179.1		24
17.3	odd	16		289.2.b.d.288.5		6
17.4	even	4	inner	289.2.d.f.155.1		24
17.5	odd	16		289.2.a.e.1.1	yes	3
17.6	odd	16		289.2.c.d.251.5		12
17.7	odd	16		289.2.c.d.38.1		12
17.8	even	8	inner	289.2.d.f.110.5		24
17.9	even	8	inner	289.2.d.f.110.6		24
17.10	odd	16		289.2.c.d.38.2		12
17.11	odd	16		289.2.c.d.251.6		12
17.12	odd	16		289.2.a.d.1.1	✓	3
17.13	even	4	inner	289.2.d.f.155.2		24
17.14	odd	16		289.2.b.d.288.6		6
17.15	even	8	inner	289.2.d.f.179.2		24
17.16	even	2	inner	289.2.d.f.134.6		24
51.5	even	16		2601.2.a.w.1.3		3
51.29	even	16		2601.2.a.x.1.3		3
68.39	even	16		4624.2.a.bd.1.1		3
68.63	even	16		4624.2.a.bg.1.3		3
85.29	odd	16		7225.2.a.t.1.3		3
85.39	odd	16		7225.2.a.s.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.2.a.d.1.1	✓	3	17.12	odd	16
289.2.a.e.1.1	yes	3	17.5	odd	16
289.2.b.d.288.5		6	17.3	odd	16
289.2.b.d.288.6		6	17.14	odd	16
289.2.c.d.38.1		12	17.7	odd	16
289.2.c.d.38.2		12	17.10	odd	16
289.2.c.d.251.5		12	17.6	odd	16
289.2.c.d.251.6		12	17.11	odd	16
289.2.d.f.110.5		24	17.8	even	8	inner
289.2.d.f.110.6		24	17.9	even	8	inner
289.2.d.f.134.5		24	1.1	even	1	trivial
289.2.d.f.134.6		24	17.16	even	2	inner
289.2.d.f.155.1		24	17.4	even	4	inner
289.2.d.f.155.2		24	17.13	even	4	inner
289.2.d.f.179.1		24	17.2	even	8	inner
289.2.d.f.179.2		24	17.15	even	8	inner
2601.2.a.w.1.3		3	51.5	even	16
2601.2.a.x.1.3		3	51.29	even	16
4624.2.a.bd.1.1		3	68.39	even	16
4624.2.a.bg.1.3		3	68.63	even	16
7225.2.a.s.1.3		3	85.39	odd	16
7225.2.a.t.1.3		3	85.29	odd	16

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	289.d (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.32893 + 1.32893i) q^{2} +(-0.968988 - 2.33935i) q^{3} +1.53209i q^{4} +(-0.111434 + 0.0461573i) q^{5} +(1.82110 - 4.39653i) q^{6} +(1.41547 + 0.586305i) q^{7} +(0.621819 - 0.621819i) q^{8} +(-2.41228 + 2.41228i) q^{9} +O(q^{10})\)	\(q+(1.32893 + 1.32893i) q^{2} +(-0.968988 - 2.33935i) q^{3} +1.53209i q^{4} +(-0.111434 + 0.0461573i) q^{5} +(1.82110 - 4.39653i) q^{6} +(1.41547 + 0.586305i) q^{7} +(0.621819 - 0.621819i) q^{8} +(-2.41228 + 2.41228i) q^{9} +(-0.209426 - 0.0867473i) q^{10} +(1.03118 - 2.48948i) q^{11} +(3.58408 - 1.48458i) q^{12} -4.57398i q^{13} +(1.10189 + 2.66021i) q^{14} +(0.215956 + 0.215956i) q^{15} +4.71688 q^{16} -6.41147 q^{18} +(1.32893 + 1.32893i) q^{19} +(-0.0707170 - 0.170726i) q^{20} -3.87939i q^{21} +(4.67869 - 1.93798i) q^{22} +(-2.83625 + 6.84731i) q^{23} +(-2.05719 - 0.852114i) q^{24} +(-3.52525 + 3.52525i) q^{25} +(6.07848 - 6.07848i) q^{26} +(0.962580 + 0.398714i) q^{27} +(-0.898271 + 2.16862i) q^{28} +(3.15179 - 1.30551i) q^{29} +0.573978i q^{30} +(1.46855 + 3.54538i) q^{31} +(5.02475 + 5.02475i) q^{32} -6.82295 q^{33} -0.184793 q^{35} +(-3.69582 - 3.69582i) q^{36} +(2.00869 + 4.84942i) q^{37} +3.53209i q^{38} +(-10.7001 + 4.43213i) q^{39} +(-0.0405900 + 0.0979930i) q^{40} +(-5.77330 - 2.39138i) q^{41} +(5.15542 - 5.15542i) q^{42} +(-3.88216 + 3.88216i) q^{43} +(3.81410 + 1.57985i) q^{44} +(0.157464 - 0.380153i) q^{45} +(-12.8687 + 5.33040i) q^{46} +7.34730i q^{47} +(-4.57060 - 11.0344i) q^{48} +(-3.28996 - 3.28996i) q^{49} -9.36959 q^{50} +7.00774 q^{52} +(-0.581912 - 0.581912i) q^{53} +(0.749337 + 1.80906i) q^{54} +0.325008i q^{55} +(1.24474 - 0.515588i) q^{56} +(1.82110 - 4.39653i) q^{57} +(5.92343 + 2.45356i) q^{58} +(-2.22237 + 2.22237i) q^{59} +(-0.330863 + 0.330863i) q^{60} +(1.13331 + 0.469431i) q^{61} +(-2.75996 + 6.66314i) q^{62} +(-4.82882 + 2.00016i) q^{63} +3.92127i q^{64} +(0.211122 + 0.509694i) q^{65} +(-9.06719 - 9.06719i) q^{66} +14.6236 q^{67} +18.7665 q^{69} +(-0.245576 - 0.245576i) q^{70} +(0.0651498 + 0.157286i) q^{71} +3.00000i q^{72} +(10.9024 - 4.51592i) q^{73} +(-3.77511 + 9.11392i) q^{74} +(11.6627 + 4.83085i) q^{75} +(-2.03603 + 2.03603i) q^{76} +(2.91919 - 2.91919i) q^{77} +(-20.1096 - 8.32968i) q^{78} +(-1.58735 + 3.83221i) q^{79} +(-0.525619 + 0.217718i) q^{80} +7.59627i q^{81} +(-4.49432 - 10.8502i) q^{82} +(-1.72093 - 1.72093i) q^{83} +5.94356 q^{84} -10.3182 q^{86} +(-6.10810 - 6.10810i) q^{87} +(-0.906801 - 2.18921i) q^{88} -15.0915i q^{89} +(0.714453 - 0.295936i) q^{90} +(2.68175 - 6.47431i) q^{91} +(-10.4907 - 4.34538i) q^{92} +(6.87087 - 6.87087i) q^{93} +(-9.76401 + 9.76401i) q^{94} +(-0.209426 - 0.0867473i) q^{95} +(6.88570 - 16.6235i) q^{96} +(10.3406 - 4.28320i) q^{97} -8.74422i q^{98} +(3.51783 + 8.49279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 48 q^{16} - 72 q^{18} + 24 q^{35} - 168 q^{50} - 24 q^{52} + 72 q^{67} + 168 q^{69} + 24 q^{84} + 48 q^{86}+O(q^{100}) \) 24 * q + 48 * q^16 - 72 * q^18 + 24 * q^35 - 168 * q^50 - 24 * q^52 + 72 * q^67 + 168 * q^69 + 24 * q^84 + 48 * q^86

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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