LMFDB - Embedded newform 605.2.j.k.9.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(9,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 6]))

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

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

chi := DirichletCharacter("605.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.j (of order $10$, 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			9.8
Character	$\chi$	$=$	605.9
Dual form			605.2.j.k.269.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.312280 + 0.101466i) q^{2} +(0.565450 + 0.778275i) q^{3} +(-1.53081 - 1.11220i) q^{4} +(1.86827 - 1.22865i) q^{5} +(0.0976102 + 0.300413i) q^{6} +(-1.92358 + 2.64758i) q^{7} +(-0.751190 - 1.03393i) q^{8} +(0.641073 - 1.97302i) q^{9} +O(q^{10})$	\(q+(0.312280 + 0.101466i) q^{2} +(0.565450 + 0.778275i) q^{3} +(-1.53081 - 1.11220i) q^{4} +(1.86827 - 1.22865i) q^{5} +(0.0976102 + 0.300413i) q^{6} +(-1.92358 + 2.64758i) q^{7} +(-0.751190 - 1.03393i) q^{8} +(0.641073 - 1.97302i) q^{9} +(0.708089 - 0.194116i) q^{10} -1.82028i q^{12} +(4.95243 + 1.60914i) q^{13} +(-0.869334 + 0.631608i) q^{14} +(2.01264 + 0.759289i) q^{15} +(1.03976 + 3.20006i) q^{16} +(3.42469 - 1.11275i) q^{17} +(0.400388 - 0.551087i) q^{18} +(4.05270 - 2.94446i) q^{19} +(-4.22646 - 0.197063i) q^{20} -3.14823 q^{21} -5.84372i q^{23} +(0.379917 - 1.16926i) q^{24} +(1.98086 - 4.59088i) q^{25} +(1.38327 + 1.00500i) q^{26} +(4.64280 - 1.50854i) q^{27} +(5.88927 - 1.91354i) q^{28} +(-1.65681 - 1.20374i) q^{29} +(0.551464 + 0.441325i) q^{30} +(-1.00645 + 3.09752i) q^{31} +3.66082i q^{32} +1.18237 q^{34} +(-0.340825 + 7.30978i) q^{35} +(-3.17575 + 2.30732i) q^{36} +(3.66602 - 5.04584i) q^{37} +(1.56434 - 0.508285i) q^{38} +(1.54799 + 4.76423i) q^{39} +(-2.67375 - 1.00870i) q^{40} +(-8.25648 + 5.99868i) q^{41} +(-0.983129 - 0.319438i) q^{42} +0.596820i q^{43} +(-1.22645 - 4.47378i) q^{45} +(0.592939 - 1.82488i) q^{46} +(0.565450 + 0.778275i) q^{47} +(-1.90259 + 2.61869i) q^{48} +(-1.14640 - 3.52824i) q^{49} +(1.08440 - 1.23265i) q^{50} +(2.80252 + 2.03615i) q^{51} +(-5.79154 - 7.97137i) q^{52} +(-0.374032 - 0.121530i) q^{53} +1.60292 q^{54} +4.18237 q^{56} +(4.58320 + 1.48917i) q^{57} +(-0.395249 - 0.544013i) q^{58} +(-0.426713 - 0.310025i) q^{59} +(-2.23648 - 3.40078i) q^{60} +(-1.64560 - 5.06465i) q^{61} +(-0.628585 + 0.865174i) q^{62} +(3.99057 + 5.49255i) q^{63} +(1.70807 - 5.25691i) q^{64} +(11.2295 - 3.07847i) q^{65} +8.45057i q^{67} +(-6.48016 - 2.10553i) q^{68} +(4.54802 - 3.30433i) q^{69} +(-0.848127 + 2.24812i) q^{70} +(3.87119 + 11.9143i) q^{71} +(-2.52152 + 0.819292i) q^{72} +(-5.00515 + 6.88900i) q^{73} +(1.65681 - 1.20374i) q^{74} +(4.69304 - 1.05426i) q^{75} -9.47874 q^{76} +1.64484i q^{78} +(-0.875246 + 2.69373i) q^{79} +(5.87429 + 4.70107i) q^{80} +(-1.23573 - 0.897811i) q^{81} +(-3.18699 + 1.03552i) q^{82} +(-11.5465 + 3.75168i) q^{83} +(4.81934 + 3.50146i) q^{84} +(5.03107 - 6.28665i) q^{85} +(-0.0605569 + 0.186375i) q^{86} -1.97010i q^{87} -9.00000 q^{89} +(0.0709421 - 1.52152i) q^{90} +(-13.7867 + 10.0166i) q^{91} +(-6.49938 + 8.94563i) q^{92} +(-2.97981 + 0.968201i) q^{93} +(0.0976102 + 0.300413i) q^{94} +(3.95384 - 10.4804i) q^{95} +(-2.84912 + 2.07001i) q^{96} +(10.7414 + 3.49009i) q^{97} -1.21812i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 20 q^{4} + 6 q^{5} + 20 q^{9}+O(q^{10}) $ 48 * q + 20 * q^4 + 6 * q^5 + 20 * q^9	$ 48 q + 20 q^{4} + 6 q^{5} + 20 q^{9} + 32 q^{14} - 20 q^{15} - 36 q^{16} - 26 q^{20} + 10 q^{25} - 20 q^{26} - 8 q^{31} + 48 q^{34} - 92 q^{36} - 72 q^{45} + 4 q^{49} + 192 q^{56} + 32 q^{59} + 92 q^{60} - 28 q^{64} + 16 q^{69} + 12 q^{70} - 112 q^{71} - 36 q^{75} + 106 q^{80} + 20 q^{81} + 56 q^{86} - 432 q^{89} - 72 q^{91}+O(q^{100}) $ 48 * q + 20 * q^4 + 6 * q^5 + 20 * q^9 + 32 * q^14 - 20 * q^15 - 36 * q^16 - 26 * q^20 + 10 * q^25 - 20 * q^26 - 8 * q^31 + 48 * q^34 - 92 * q^36 - 72 * q^45 + 4 * q^49 + 192 * q^56 + 32 * q^59 + 92 * q^60 - 28 * q^64 + 16 * q^69 + 12 * q^70 - 112 * q^71 - 36 * q^75 + 106 * q^80 + 20 * q^81 + 56 * q^86 - 432 * q^89 - 72 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.312280	+	0.101466i	0.220815	+	0.0717472i	0.417335	−	0.908753i	$-0.362964\pi$
$2$	0.312280	+	0.101466i	0.220815	+	0.0717472i	−0.196520	+	0.980500i	$0.562964\pi$
$3$	0.565450	+	0.778275i	0.326462	+	0.449337i	0.940427	−	0.339997i	$-0.110426\pi$
$3$	0.565450	+	0.778275i	0.326462	+	0.449337i	−0.613964	+	0.789334i	$0.710426\pi$
$4$	−1.53081	−	1.11220i	−0.765405	−	0.556099i
$5$	1.86827	−	1.22865i	0.835515	−	0.549467i
$5$	1.86827	−	1.22865i	0.835515	−	0.549467i
$6$	0.0976102	+	0.300413i	0.0398492	+	0.122643i
$7$	−1.92358	+	2.64758i	−0.727044	+	1.00069i	0.272216	+	0.962236i	$0.412243\pi$
$7$	−1.92358	+	2.64758i	−0.727044	+	1.00069i	−0.999260	+	0.0384541i	$0.987757\pi$
$8$	−0.751190	−	1.03393i	−0.265586	−	0.365548i
$9$	0.641073	−	1.97302i	0.213691	−	0.657673i
$10$	0.708089	−	0.194116i	0.223917	−	0.0613848i
$11$		0			0
$11$		0			0
$12$		−	1.82028i		−	0.525471i
$13$	4.95243	+	1.60914i	1.37356	+	0.446295i	0.900546	−	0.434762i	$-0.143167\pi$
$13$	4.95243	+	1.60914i	1.37356	+	0.446295i	0.473010	+	0.881057i	$0.343167\pi$
$14$	−0.869334	+	0.631608i	−0.232339	+	0.168804i
$15$	2.01264	+	0.759289i	0.519660	+	0.196048i
$16$	1.03976	+	3.20006i	0.259940	+	0.800014i
$17$	3.42469	−	1.11275i	0.830610	−	0.269882i	0.137308	−	0.990528i	$-0.456155\pi$
$17$	3.42469	−	1.11275i	0.830610	−	0.269882i	0.693302	+	0.720647i	$0.256155\pi$
$18$	0.400388	−	0.551087i	0.0943725	−	0.129893i
$19$	4.05270	−	2.94446i	0.929753	−	0.675505i	−0.0161792	−	0.999869i	$-0.505150\pi$
$19$	4.05270	−	2.94446i	0.929753	−	0.675505i	0.945932	+	0.324364i	$0.105150\pi$
$20$	−4.22646	−	0.197063i	−0.945066	−	0.0440646i
$21$	−3.14823			−0.687000
$22$		0			0
$23$		−	5.84372i		−	1.21850i	−0.792978	−	0.609250i	$-0.791470\pi$
$23$		−	5.84372i		−	1.21850i	0.792978	−	0.609250i	$-0.208530\pi$
$24$	0.379917	−	1.16926i	0.0775503	−	0.238675i
$25$	1.98086	−	4.59088i	0.396172	−	0.918176i
$26$	1.38327	+	1.00500i	0.271282	+	0.197098i
$27$	4.64280	−	1.50854i	0.893506	−	0.290318i
$28$	5.88927	−	1.91354i	1.11297	−	0.361625i
$29$	−1.65681	−	1.20374i	−0.307661	−	0.223529i	0.423231	−	0.906022i	$-0.360896\pi$
$29$	−1.65681	−	1.20374i	−0.307661	−	0.223529i	−0.730892	+	0.682493i	$0.760896\pi$
$30$	0.551464	+	0.441325i	0.100683	+	0.0805745i
$31$	−1.00645	+	3.09752i	−0.180763	+	0.556331i	−0.999850	−	0.0173387i	$-0.994481\pi$
$31$	−1.00645	+	3.09752i	−0.180763	+	0.556331i	0.819087	+	0.573670i	$0.194481\pi$
$32$			3.66082i			0.647147i
$33$		0			0
$34$	1.18237			0.202775
$35$	−0.340825	+	7.30978i	−0.0576100	+	1.23558i
$36$	−3.17575	+	2.30732i	−0.529292	+	0.384553i
$37$	3.66602	−	5.04584i	0.602690	−	0.829531i	−0.393261	−	0.919427i	$-0.628653\pi$
$37$	3.66602	−	5.04584i	0.602690	−	0.829531i	0.995951	+	0.0898953i	$0.0286532\pi$
$38$	1.56434	−	0.508285i	0.253769	−	0.0824547i
$39$	1.54799	+	4.76423i	0.247877	+	0.762888i
$40$	−2.67375	−	1.00870i	−0.422758	−	0.159490i
$41$	−8.25648	+	5.99868i	−1.28944	+	0.936837i	−0.999794	−	0.0202958i	$-0.993539\pi$
$41$	−8.25648	+	5.99868i	−1.28944	+	0.936837i	−0.289651	+	0.957132i	$0.593539\pi$
$42$	−0.983129	−	0.319438i	−0.151700	−	0.0492903i
$43$			0.596820i			0.0910142i	0.998964	+	0.0455071i	$0.0144904\pi$
$43$			0.596820i			0.0910142i	−0.998964	+	0.0455071i	$0.985510\pi$
$44$		0			0
$45$	−1.22645	−	4.47378i	−0.182828	−	0.666912i
$46$	0.592939	−	1.82488i	0.0874241	−	0.269064i
$47$	0.565450	+	0.778275i	0.0824793	+	0.113523i	0.848263	−	0.529575i	$-0.177649\pi$
$47$	0.565450	+	0.778275i	0.0824793	+	0.113523i	−0.765784	+	0.643098i	$0.777649\pi$
$48$	−1.90259	+	2.61869i	−0.274615	+	0.377975i
$49$	−1.14640	−	3.52824i	−0.163771	−	0.504035i
$50$	1.08440	−	1.23265i	0.153357	−	0.174323i
$51$	2.80252	+	2.03615i	0.392431	+	0.285118i
$52$	−5.79154	−	7.97137i	−0.803142	−	1.10543i
$53$	−0.374032	−	0.121530i	−0.0513772	−	0.0166935i	0.283216	−	0.959056i	$-0.408599\pi$
$53$	−0.374032	−	0.121530i	−0.0513772	−	0.0166935i	−0.334593	+	0.942363i	$0.608599\pi$
$54$	1.60292			0.218129
$55$		0			0
$56$	4.18237			0.558893
$57$	4.58320	+	1.48917i	0.607059	+	0.197245i
$58$	−0.395249	−	0.544013i	−0.0518987	−	0.0714324i
$59$	−0.426713	−	0.310025i	−0.0555533	−	0.0403619i	0.559662	−	0.828721i	$-0.310931\pi$
$59$	−0.426713	−	0.310025i	−0.0555533	−	0.0403619i	−0.615215	+	0.788359i	$0.710931\pi$
$60$	−2.23648	−	3.40078i	−0.288729	−	0.439039i
$61$	−1.64560	−	5.06465i	−0.210698	−	0.648462i	−0.999431	−	0.0337260i	$-0.989263\pi$
$61$	−1.64560	−	5.06465i	−0.210698	−	0.648462i	0.788733	−	0.614736i	$-0.210737\pi$
$62$	−0.628585	+	0.865174i	−0.0798304	+	0.109877i
$63$	3.99057	+	5.49255i	0.502764	+	0.691996i
$64$	1.70807	−	5.25691i	0.213509	−	0.657114i
$65$	11.2295	−	3.07847i	1.39285	−	0.381837i
$66$		0			0
$67$			8.45057i			1.03240i	0.856468	+	0.516201i	$0.172654\pi$
$67$			8.45057i			1.03240i	−0.856468	+	0.516201i	$0.827346\pi$
$68$	−6.48016	−	2.10553i	−0.785834	−	0.255333i
$69$	4.54802	−	3.30433i	0.547517	−	0.397795i
$70$	−0.848127	+	2.24812i	−0.101371	+	0.268701i
$71$	3.87119	+	11.9143i	0.459426	+	1.41397i	0.865859	+	0.500288i	$0.166772\pi$
$71$	3.87119	+	11.9143i	0.459426	+	1.41397i	−0.406433	+	0.913681i	$0.633228\pi$
$72$	−2.52152	+	0.819292i	−0.297164	+	0.0965545i
$73$	−5.00515	+	6.88900i	−0.585809	+	0.806297i	−0.994317	−	0.106458i	$-0.966049\pi$
$73$	−5.00515	+	6.88900i	−0.585809	+	0.806297i	0.408508	+	0.912755i	$0.366049\pi$
$74$	1.65681	−	1.20374i	0.192600	−	0.139932i
$75$	4.69304	−	1.05426i	0.541906	−	0.121736i
$76$	−9.47874			−1.08729
$77$		0			0
$78$			1.64484i			0.186242i
$79$	−0.875246	+	2.69373i	−0.0984728	+	0.303068i	−0.988143	−	0.153535i	$-0.950934\pi$
$79$	−0.875246	+	2.69373i	−0.0984728	+	0.303068i	0.889670	+	0.456603i	$0.150934\pi$
$80$	5.87429	+	4.70107i	0.656766	+	0.525595i
$81$	−1.23573	−	0.897811i	−0.137303	−	0.0997567i
$82$	−3.18699	+	1.03552i	−0.351945	+	0.114354i
$83$	−11.5465	+	3.75168i	−1.26739	+	0.411800i	−0.864123	−	0.503281i	$-0.832126\pi$
$83$	−11.5465	+	3.75168i	−1.26739	+	0.411800i	−0.403269	+	0.915082i	$0.632126\pi$
$84$	4.81934	+	3.50146i	0.525833	+	0.382040i
$85$	5.03107	−	6.28665i	0.545697	−	0.681883i
$86$	−0.0605569	+	0.186375i	−0.00653002	+	0.0200973i
$87$		−	1.97010i		−	0.211217i
$88$		0			0
$89$	−9.00000			−0.953998			−0.476999	−	0.878904i	$-0.658275\pi$
$89$	−9.00000			−0.953998			−0.476999	+	0.878904i	$0.658275\pi$
$90$	0.0709421	−	1.52152i	0.00747795	−	0.160382i
$91$	−13.7867	+	10.0166i	−1.44524	+	1.05003i
$92$	−6.49938	+	8.94563i	−0.677608	+	0.932647i
$93$	−2.97981	+	0.968201i	−0.308992	+	0.100398i
$94$	0.0976102	+	0.300413i	0.0100677	+	0.0309853i
$95$	3.95384	−	10.4804i	0.405655	−	1.07526i
$96$	−2.84912	+	2.07001i	−0.290787	+	0.211269i
$97$	10.7414	+	3.49009i	1.09062	+	0.354365i	0.798487	−	0.602012i	$-0.205634\pi$
$97$	10.7414	+	3.49009i	1.09062	+	0.354365i	0.292136	+	0.956377i	$0.405634\pi$
$98$		−	1.21812i		−	0.123049i
$99$		0			0
$100$	−8.13829	+	4.82466i	−0.813829	+	0.482466i
$101$	4.06884	−	12.5226i	0.404865	−	1.24605i	−0.516143	−	0.856503i	$-0.672633\pi$
$101$	4.06884	−	12.5226i	0.404865	−	1.24605i	0.921008	−	0.389544i	$-0.127367\pi$
$102$	0.668570	+	0.920208i	0.0661983	+	0.0911142i
$103$	1.63539	−	2.25091i	0.161139	−	0.221789i	−0.720811	−	0.693132i	$-0.756230\pi$
$103$	1.63539	−	2.25091i	0.161139	−	0.221789i	0.881950	+	0.471342i	$0.156230\pi$
$104$	−2.05648	−	6.32921i	−0.201655	−	0.620630i
$105$	−5.88174	+	3.86806i	−0.573999	+	0.377484i
$106$	−0.104471	−	0.0759030i	−0.0101472	−	0.00737235i
$107$	9.37530	+	12.9040i	0.906345	+	1.24748i	0.968400	+	0.249404i	$0.0802346\pi$
$107$	9.37530	+	12.9040i	0.906345	+	1.24748i	−0.0620550	+	0.998073i	$0.519765\pi$
$108$	−8.78503	−	2.85443i	−0.845340	−	0.274668i
$109$	3.90911			0.374425			0.187212	−	0.982319i	$-0.440055\pi$
$109$	3.90911			0.374425			0.187212	+	0.982319i	$0.440055\pi$
$110$		0			0
$111$	6.00000			0.569495
$112$	−10.4725	−	3.40271i	−0.989555	−	0.321526i
$113$	−5.80589	−	7.99112i	−0.546172	−	0.751742i	0.443314	−	0.896366i	$-0.353803\pi$
$113$	−5.80589	−	7.99112i	−0.546172	−	0.751742i	−0.989487	+	0.144625i	$0.953803\pi$
$114$	1.28014	+	0.930076i	0.119896	+	0.0871096i
$115$	−7.17987	−	10.9176i	−0.669526	−	1.01808i
$116$	1.19746	+	3.68539i	0.111181	+	0.342180i
$117$	6.34973	−	8.73966i	0.587033	−	0.807981i
$118$	−0.101797	−	0.140112i	−0.00937118	−	0.0128983i
$119$	−3.64157	+	11.2076i	−0.333822	+	1.02740i
$120$	−0.726825	−	2.65129i	−0.0663497	−	0.242028i
$121$		0			0
$122$		−	1.74856i		−	0.158307i
$123$	−9.33724	−	3.03385i	−0.841911	−	0.273553i
$124$	4.98574	−	3.62235i	0.447732	−	0.325297i
$125$	−1.93979	−	11.0108i	−0.173500	−	0.984834i
$126$	0.688868	+	2.12012i	0.0613693	+	0.188875i
$127$	−5.15080	+	1.67360i	−0.457060	+	0.148508i	−0.528493	−	0.848938i	$-0.677243\pi$
$127$	−5.15080	+	1.67360i	−0.457060	+	0.148508i	0.0714331	+	0.997445i	$0.477243\pi$
$128$	5.37034	−	7.39164i	0.474676	−	0.653335i
$129$	−0.464490	+	0.337472i	−0.0408961	+	0.0297127i
$130$	3.81912	+	0.178070i	0.334959	+	0.0156178i
$131$	−19.1241			−1.67088			−0.835440	−	0.549582i	$-0.814787\pi$
$131$	−19.1241			−1.67088			−0.835440	+	0.549582i	$0.814787\pi$
$132$		0			0
$133$			16.3937i			1.42152i
$134$	−0.857445	+	2.63894i	−0.0740719	+	0.227970i
$135$	6.82053	−	8.52270i	0.587018	−	0.733517i
$136$	−3.72310	−	2.70499i	−0.319253	−	0.231951i
$137$	−15.2577	+	4.95751i	−1.30355	+	0.423549i	−0.876815	−	0.480828i	$-0.840336\pi$
$137$	−15.2577	+	4.95751i	−1.30355	+	0.423549i	−0.426735	+	0.904377i	$0.640336\pi$
$138$	1.75553	−	0.570407i	0.149441	−	0.0485563i
$139$	−10.1688	−	7.38809i	−0.862509	−	0.626649i	0.0660576	−	0.997816i	$-0.478958\pi$
$139$	−10.1688	−	7.38809i	−0.862509	−	0.626649i	−0.928566	+	0.371167i	$0.878958\pi$
$140$	8.65167	−	10.8108i	0.731200	−	0.913682i
$141$	−0.285978	+	0.880150i	−0.0240837	+	0.0741220i
$142$			4.11339i			0.345188i
$143$		0			0
$144$	6.98034			0.581695
$145$	−4.57433	−	0.213282i	−0.379877	−	0.0177121i
$146$	−2.26201	+	1.64345i	−0.187205	+	0.136012i
$147$	2.09771	−	2.88726i	0.173017	−	0.238137i
$148$	−11.2240	+	3.64689i	−0.922604	+	0.299772i
$149$	−4.30397	−	13.2463i	−0.352595	−	1.08518i	−0.957391	−	0.288795i	$-0.906745\pi$
$149$	−4.30397	−	13.2463i	−0.352595	−	1.08518i	0.604796	−	0.796380i	$-0.293255\pi$
$150$	1.57251	+	0.146959i	0.128395	+	0.0119992i
$151$	−12.9713	+	9.42423i	−1.05559	+	0.766933i	−0.973268	−	0.229672i	$-0.926235\pi$
$151$	−12.9713	+	9.42423i	−1.05559	+	0.766933i	−0.0823251	+	0.996606i	$0.526235\pi$
$152$	−6.08870	−	1.97834i	−0.493859	−	0.160464i
$153$		−	7.47034i		−	0.603941i
$154$		0			0
$155$	1.92544	+	7.02357i	0.154655	+	0.564146i
$156$	2.92909	−	9.01482i	0.234515	−	0.721763i
$157$	−1.33714	−	1.84042i	−0.106715	−	0.146881i	0.752319	−	0.658799i	$-0.228935\pi$
$157$	−1.33714	−	1.84042i	−0.106715	−	0.146881i	−0.859034	+	0.511918i	$0.828935\pi$
$158$	−0.546643	+	0.752390i	−0.0434886	+	0.0598570i
$159$	−0.116912	−	0.359819i	−0.00927174	−	0.0285355i
$160$	4.49785	+	6.83939i	0.355586	+	0.540701i
$161$	15.4717	+	11.2409i	1.21934	+	0.885904i
$162$	−0.294797	−	0.405753i	−0.0231614	−	0.0318790i
$163$	21.4648	+	6.97433i	1.68125	+	0.546272i	0.985154	−	0.171674i	$-0.0549176\pi$
$163$	21.4648	+	6.97433i	1.68125	+	0.546272i	0.696099	+	0.717946i	$0.254918\pi$
$164$	19.3108			1.50792
$165$		0			0
$166$	−3.98640			−0.309405
$167$	−3.62307	−	1.17721i	−0.280362	−	0.0910951i	0.165461	−	0.986216i	$-0.447089\pi$
$167$	−3.62307	−	1.17721i	−0.280362	−	0.0910951i	−0.445823	+	0.895121i	$0.647089\pi$
$168$	2.36492	+	3.25503i	0.182457	+	0.251131i
$169$	11.4200	+	8.29709i	0.878459	+	0.638238i
$170$	2.20898	−	1.45271i	0.169421	−	0.111418i
$171$	−3.21140	−	9.88367i	−0.245582	−	0.755823i
$172$	0.663783	−	0.913618i	0.0506130	−	0.0696628i
$173$	0.558191	+	0.768284i	0.0424385	+	0.0584115i	0.829709	−	0.558196i	$-0.188506\pi$
$173$	0.558191	+	0.768284i	0.0424385	+	0.0584115i	−0.787270	+	0.616608i	$0.788506\pi$
$174$	0.199898	−	0.615224i	0.0151543	−	0.0466400i
$175$	8.34438	+	14.0754i	0.630776	+	1.06400i
$176$		0			0
$177$		−	0.507404i		−	0.0381388i
$178$	−2.81052	−	0.913193i	−0.210657	−	0.0684467i
$179$	2.94099	−	2.13675i	0.219820	−	0.159708i	−0.472426	−	0.881370i	$-0.656622\pi$
$179$	2.94099	−	2.13675i	0.219820	−	0.159708i	0.692246	+	0.721662i	$0.256622\pi$
$180$	−3.09828	+	8.21257i	−0.230932	+	0.612128i
$181$	3.88396	+	11.9536i	0.288692	+	0.888503i	0.985268	+	0.171020i	$0.0547061\pi$
$181$	3.88396	+	11.9536i	0.288692	+	0.888503i	−0.696576	+	0.717483i	$0.745294\pi$
$182$	−5.32166	+	1.72911i	−0.394467	+	0.128170i
$183$	3.01118	−	4.14453i	0.222593	−	0.306373i
$184$	−6.04197	+	4.38975i	−0.445420	+	0.323617i
$185$	0.649557	−	13.9312i	0.0477563	−	1.02424i
$186$	−1.02878			−0.0754335
$187$		0			0
$188$		−	1.82028i		−	0.132758i
$189$	−4.93681	+	15.1939i	−0.359100	+	1.10520i
$190$	2.29810	−	2.87163i	0.166722	−	0.208330i
$191$	2.16538	+	1.57324i	0.156681	+	0.113836i	0.663364	−	0.748297i	$-0.269128\pi$
$191$	2.16538	+	1.57324i	0.156681	+	0.113836i	−0.506682	+	0.862133i	$0.669128\pi$
$192$	5.05715	−	1.64317i	0.364969	−	0.118585i
$193$	−0.369230	+	0.119970i	−0.0265778	+	0.00863564i	−0.322276	−	0.946646i	$-0.604448\pi$
$193$	−0.369230	+	0.119970i	−0.0265778	+	0.00863564i	0.295698	+	0.955281i	$0.404448\pi$
$194$	3.00020	+	2.17977i	0.215402	+	0.156498i
$195$	8.74563	+	6.99894i	0.626287	+	0.501204i
$196$	−2.16919	+	6.67610i	−0.154942	+	0.476864i
$197$		−	18.5416i		−	1.32104i	−0.750810	−	0.660518i	$-0.770337\pi$
$197$		−	18.5416i		−	1.32104i	0.750810	−	0.660518i	$-0.229663\pi$
$198$		0			0
$199$	−10.1491			−0.719451			−0.359726	−	0.933058i	$-0.617130\pi$
$199$	−10.1491			−0.719451			−0.359726	+	0.933058i	$0.617130\pi$
$200$	−6.23463	+	1.40057i	−0.440855	+	0.0990351i
$201$	−6.57686	+	4.77837i	−0.463896	+	0.337040i
$202$	2.54124	−	3.49771i	0.178801	−	0.246098i
$203$	6.37399	−	2.07103i	0.447366	−	0.145358i
$204$	−2.02552	−	6.23391i	−0.141815	−	0.436461i
$205$	−8.05506	+	21.3514i	−0.562590	+	1.49125i
$206$	0.739089	−	0.536980i	0.0514948	−	0.0374132i
$207$	−11.5298	−	3.74625i	−0.801375	−	0.260383i
$208$			17.5212i			1.21487i
$209$		0			0
$210$	−2.22922	+	0.611121i	−0.153831	+	0.0421714i
$211$	2.61846	−	8.05879i	0.180262	−	0.554790i	−0.819572	−	0.572976i	$-0.805789\pi$
$211$	2.61846	−	8.05879i	0.180262	−	0.554790i	0.999835	+	0.0181856i	$0.00578896\pi$
$212$	0.437406	+	0.602038i	0.0300412	+	0.0413481i
$213$	−7.08364	+	9.74979i	−0.485363	+	0.668045i
$214$	1.61840	+	4.98093i	0.110632	+	0.340490i
$215$	0.733281	+	1.11502i	0.0500093	+	0.0760438i
$216$	−5.04734	−	3.66710i	−0.343428	−	0.249515i
$217$	−6.26495	−	8.62296i	−0.425292	−	0.585365i
$218$	1.22074	+	0.396641i	0.0826787	+	0.0268639i
$219$	−8.19170			−0.553544
$220$		0			0
$221$	18.7511			1.26134
$222$	1.87368	+	0.608796i	0.125753	+	0.0408597i
$223$	13.9345	+	19.1793i	0.933126	+	1.28434i	0.958628	+	0.284663i	$0.0918817\pi$
$223$	13.9345	+	19.1793i	0.933126	+	1.28434i	−0.0255016	+	0.999675i	$0.508118\pi$
$224$	−9.69230	−	7.04187i	−0.647594	−	0.470504i
$225$	−7.78803	−	6.85136i	−0.519202	−	0.456758i
$226$	−1.00224	−	3.08457i	−0.0666678	−	0.205182i
$227$	0.421197	−	0.579727i	0.0279558	−	0.0384779i	−0.794810	−	0.606858i	$-0.792430\pi$
$227$	0.421197	−	0.579727i	0.0279558	−	0.0384779i	0.822766	+	0.568380i	$0.192430\pi$
$228$	−5.35975	−	7.37706i	−0.354958	−	0.488558i
$229$	−4.06330	+	12.5055i	−0.268510	+	0.826390i	0.722354	+	0.691524i	$0.243060\pi$
$229$	−4.06330	+	12.5055i	−0.268510	+	0.826390i	−0.990864	+	0.134866i	$0.956940\pi$
$230$	−1.13436	−	4.13788i	−0.0747975	−	0.272843i
$231$		0			0
$232$			2.61725i			0.171831i
$233$	25.6145	+	8.32265i	1.67806	+	0.545235i	0.984534	−	0.175195i	$-0.0560557\pi$
$233$	25.6145	+	8.32265i	1.67806	+	0.545235i	0.693527	+	0.720430i	$0.256056\pi$
$234$	2.86967	−	2.08494i	0.187596	−	0.136297i
$235$	2.01264	+	0.759289i	0.131290	+	0.0495306i
$236$	0.308407	+	0.949180i	0.0200756	+	0.0617864i
$237$	−2.59137	+	0.841987i	−0.168327	+	0.0546929i
$238$	−2.27438	+	3.13041i	−0.147426	+	0.202915i
$239$	4.05270	−	2.94446i	0.262147	−	0.190461i	−0.448946	−	0.893559i	$-0.648200\pi$
$239$	4.05270	−	2.94446i	0.262147	−	0.190461i	0.711093	+	0.703098i	$0.248200\pi$
$240$	−0.337107	+	7.23003i	−0.0217602	+	0.466696i
$241$	−4.69354			−0.302337			−0.151169	−	0.988508i	$-0.548304\pi$
$241$	−4.69354			−0.302337			−0.151169	+	0.988508i	$0.548304\pi$
$242$		0			0
$243$		−	16.1146i		−	1.03375i
$244$	−3.11379	+	9.58326i	−0.199340	+	0.613505i
$245$	−6.47674	−	5.18320i	−0.413784	−	0.331142i
$246$	−2.60800	−	1.89482i	−0.166280	−	0.120810i
$247$	24.8087	−	8.06085i	1.57854	−	0.512900i
$248$	3.95864	−	1.28624i	0.251374	−	0.0816762i
$249$	−9.44879	−	6.86495i	−0.598793	−	0.435048i
$250$	0.511460	−	3.63527i	0.0323476	−	0.229915i
$251$	1.35298	−	4.16404i	0.0853994	−	0.262832i	−0.899234	−	0.437469i	$-0.855875\pi$
$251$	1.35298	−	4.16404i	0.0853994	−	0.262832i	0.984633	+	0.174637i	$0.0558751\pi$
$252$		−	12.8464i		−	0.809244i
$253$		0			0
$254$	−1.77831			−0.111581
$255$	7.73756	+	0.360771i	0.484545	+	0.0225924i
$256$	−6.51655	+	4.73455i	−0.407284	+	0.295909i
$257$	−3.83010	+	5.27169i	−0.238915	+	0.328839i	−0.911591	−	0.411099i	$-0.865145\pi$
$257$	−3.83010	+	5.27169i	−0.238915	+	0.328839i	0.672675	+	0.739938i	$0.265145\pi$
$258$	−0.179293	+	0.0582557i	−0.0111623	+	0.00362684i
$259$	6.30739	+	19.4121i	0.391922	+	1.20621i
$260$	−20.6141	−	7.77691i	−1.27844	−	0.482304i
$261$	−3.43713	+	2.49722i	−0.212753	+	0.154574i
$262$	−5.97207	−	1.94044i	−0.368956	−	0.119881i
$263$		−	4.28212i		−	0.264047i	−0.991247	−	0.132023i	$-0.957853\pi$
$263$		−	4.28212i		−	0.264047i	0.991247	−	0.132023i	$-0.0421474\pi$
$264$		0			0
$265$	−0.848110	+	0.232501i	−0.0520990	+	0.0142824i
$266$	−1.66341	+	5.11943i	−0.101990	+	0.313893i
$267$	−5.08905	−	7.00447i	−0.311445	−	0.428667i
$268$	9.39871	−	12.9362i	0.574118	−	0.790205i
$269$	−3.28227	−	10.1018i	−0.200124	−	0.615918i	−0.999878	−	0.0155908i	$-0.995037\pi$
$269$	−3.28227	−	10.1018i	−0.200124	−	0.615918i	0.799755	−	0.600327i	$-0.204963\pi$
$270$	2.99468	−	1.96942i	0.182250	−	0.119855i
$271$	−8.61649	−	6.26025i	−0.523415	−	0.380283i	0.294474	−	0.955659i	$-0.404856\pi$
$271$	−8.61649	−	6.26025i	−0.523415	−	0.380283i	−0.817889	+	0.575376i	$0.804856\pi$
$272$	7.12173	+	9.80222i	0.431818	+	0.594347i
$273$	−15.5914	−	5.06594i	−0.943632	−	0.306605i
$274$	−5.26768			−0.318232
$275$		0			0
$276$	−10.6372			−0.640286
$277$	6.99082	+	2.27145i	0.420037	+	0.136478i	0.511407	−	0.859339i	$-0.329124\pi$
$277$	6.99082	+	2.27145i	0.420037	+	0.136478i	−0.0913696	+	0.995817i	$0.529124\pi$
$278$	−2.42588	−	3.33894i	−0.145495	−	0.200256i
$279$	5.46626	+	3.97147i	0.327257	+	0.237766i
$280$	7.81379	−	5.13865i	0.466963	−	0.307093i
$281$	8.72335	+	26.8477i	0.520391	+	1.60160i	0.773253	+	0.634097i	$0.218628\pi$
$281$	8.72335	+	26.8477i	0.520391	+	1.60160i	−0.252862	+	0.967502i	$0.581372\pi$
$282$	−0.178610	+	0.245836i	−0.0106361	+	0.0146393i
$283$	−5.91415	−	8.14012i	−0.351559	−	0.483880i	0.596213	−	0.802826i	$-0.296671\pi$
$283$	−5.91415	−	8.14012i	−0.351559	−	0.483880i	−0.947773	+	0.318946i	$0.896671\pi$
$284$	7.32502	−	22.5441i	0.434660	−	1.33775i
$285$	10.3923	−	2.84895i	0.615587	−	0.168757i
$286$		0			0
$287$		−	33.3986i		−	1.97146i
$288$	7.22286	+	2.34685i	0.425611	+	0.138290i
$289$	−3.26297	+	2.37069i	−0.191940	+	0.139452i
$290$	−1.40683	−	0.530742i	−0.0826119	−	0.0311663i
$291$	3.35747	+	10.3332i	0.196818	+	0.605744i
$292$	15.3239	−	4.97903i	0.896762	−	0.291376i
$293$	−0.0143892	+	0.0198050i	−0.000840625	+	0.00115702i	−0.809437	−	0.587207i	$-0.800228\pi$
$293$	−0.0143892	+	0.0198050i	−0.000840625	+	0.00115702i	0.808596	+	0.588364i	$0.200228\pi$
$294$	0.948032	−	0.688786i	0.0552904	−	0.0401708i
$295$	−1.17813	−	0.0549313i	−0.0685932	−	0.00319822i
$296$	−7.97090			−0.463299
$297$		0			0
$298$		−	4.57325i		−	0.264921i
$299$	9.40337	−	28.9406i	0.543811	−	1.67368i
$300$	−8.35671	−	3.60572i	−0.482475	−	0.208177i
$301$	−1.58013	−	1.14803i	−0.0910770	−	0.0661713i
$302$	−5.00693	+	1.62685i	−0.288116	+	0.0936147i
$303$	12.0468	−	3.91423i	0.692068	−	0.224867i
$304$	13.6363	+	9.90734i	0.782094	+	0.568225i
$305$	−9.29709	−	7.44026i	−0.532350	−	0.426028i
$306$	0.757985	−	2.33284i	0.0433311	−	0.133359i
$307$			32.9698i			1.88169i	0.338839	+	0.940844i	$0.389966\pi$
$307$			32.9698i			1.88169i	−0.338839	+	0.940844i	$0.610034\pi$
$308$		0			0
$309$	2.67656			0.152264
$310$	−0.111375	+	2.38869i	−0.00632566	+	0.135668i
$311$	3.90405	−	2.83646i	0.221378	−	0.160841i	−0.471569	−	0.881829i	$-0.656312\pi$
$311$	3.90405	−	2.83646i	0.221378	−	0.160841i	0.692947	+	0.720989i	$0.256312\pi$
$312$	3.76302	−	5.17936i	0.213039	−	0.293223i
$313$	16.2309	−	5.27374i	0.917424	−	0.298089i	0.188014	−	0.982166i	$-0.439795\pi$
$313$	16.2309	−	5.27374i	0.917424	−	0.298089i	0.729410	+	0.684077i	$0.239795\pi$
$314$	−0.230823	−	0.710399i	−0.0130261	−	0.0400902i
$315$	14.2038	+	5.35856i	0.800296	+	0.301921i
$316$	4.33580	−	3.15014i	0.243908	−	0.177209i
$317$	−1.63255	−	0.530448i	−0.0916932	−	0.0297929i	0.262811	−	0.964847i	$-0.415350\pi$
$317$	−1.63255	−	0.530448i	−0.0916932	−	0.0297929i	−0.354504	+	0.935054i	$0.615350\pi$
$318$		−	0.124227i		−	0.00696629i
$319$		0			0
$320$	−3.26774	−	11.9199i	−0.182672	−	0.666345i
$321$	−4.74159	+	14.5931i	−0.264650	+	0.814508i
$322$	3.69094	+	5.08015i	0.205688	+	0.283105i
$323$	10.6028	−	14.5935i	0.589956	−	0.812005i
$324$	0.893125	+	2.74876i	0.0496181	+	0.152709i
$325$	17.1974	−	19.5485i	0.953942	−	1.08436i
$326$	5.99537	+	4.35589i	0.332053	+	0.241250i
$327$	2.21040	+	3.04236i	0.122236	+	0.168243i
$328$	12.4044	+	4.03042i	0.684917	+	0.222543i
$329$	−3.14823			−0.173567
$330$		0			0
$331$	0.892186			0.0490390			0.0245195	−	0.999699i	$-0.492194\pi$
$331$	0.892186			0.0490390			0.0245195	+	0.999699i	$0.492194\pi$
$332$	21.8481	+	7.09888i	1.19907	+	0.389601i
$333$	−7.60536	−	10.4679i	−0.416771	−	0.573636i
$334$	−1.01197	−	0.735237i	−0.0553724	−	0.0402304i
$335$	10.3828	+	15.7879i	0.567271	+	0.862587i
$336$	−3.27341	−	10.0745i	−0.178579	−	0.549610i
$337$	−11.0419	+	15.1979i	−0.601491	+	0.827881i	−0.995844	−	0.0910780i	$-0.970969\pi$
$337$	−11.0419	+	15.1979i	−0.601491	+	0.827881i	0.394353	+	0.918959i	$0.370969\pi$
$338$	2.72435	+	3.74975i	0.148185	+	0.203960i
$339$	2.93635	−	9.03715i	0.159481	−	0.490831i
$340$	−14.6936	+	4.02812i	−0.796874	+	0.218456i
$341$		0			0
$342$		−	3.41232i		−	0.184517i
$343$	−10.2404	−	3.32731i	−0.552930	−	0.179658i
$344$	0.617067	−	0.448326i	0.0332700	−	0.0241721i
$345$	4.43708	−	11.7613i	0.238884	−	0.633206i
$346$	0.0963572	+	0.296557i	0.00518020	+	0.0159430i
$347$	19.9340	−	6.47695i	1.07011	−	0.347701i	0.279581	−	0.960122i	$-0.409804\pi$
$347$	19.9340	−	6.47695i	1.07011	−	0.347701i	0.790531	+	0.612421i	$0.209804\pi$
$348$	−2.19115	+	3.01586i	−0.117458	+	0.161667i
$349$	21.9945	−	15.9799i	1.17734	−	0.855385i	0.185468	−	0.982650i	$-0.440620\pi$
$349$	21.9945	−	15.9799i	1.17734	−	0.855385i	0.991869	+	0.127265i	$0.0406199\pi$
$350$	1.17761	+	5.24213i	0.0629459	+	0.280204i
$351$	25.4205			1.35685
$352$		0			0
$353$			8.66841i			0.461373i	0.973028	+	0.230686i	$0.0740972\pi$
$353$			8.66841i			0.461373i	−0.973028	+	0.230686i	$0.925903\pi$
$354$	0.0514842	−	0.158452i	0.00273635	−	0.00842163i
$355$	21.8709	+	17.5028i	1.16079	+	0.928953i
$356$	13.7773	+	10.0098i	0.730195	+	0.530518i
$357$	−10.7817	+	3.50319i	−0.570629	+	0.185409i
$358$	1.13522	−	0.368855i	0.0599982	−	0.0194946i
$359$	5.58598	+	4.05845i	0.294817	+	0.214197i	0.725354	−	0.688376i	$-0.241676\pi$
$359$	5.58598	+	4.05845i	0.294817	+	0.214197i	−0.430537	+	0.902573i	$0.641676\pi$
$360$	−3.70426	+	4.62872i	−0.195232	+	0.243955i
$361$	1.88322	−	5.79595i	0.0991167	−	0.305050i
$362$			4.12695i			0.216908i
$363$		0			0
$364$	32.2453			1.69011
$365$	−0.886828	+	19.0201i	−0.0464187	+	0.995556i
$366$	1.36086	−	0.988723i	0.0711333	−	0.0516814i
$367$	−9.57503	+	13.1789i	−0.499813	+	0.687933i	−0.982160	−	0.188047i	$-0.939784\pi$
$367$	−9.57503	+	13.1789i	−0.499813	+	0.687933i	0.482347	+	0.875980i	$0.339784\pi$
$368$	18.7003	−	6.07608i	0.974818	−	0.316738i
$369$	6.54251	+	20.1358i	0.340590	+	1.04823i
$370$	1.61639	−	4.28454i	0.0840320	−	0.222742i
$371$	1.04124	−	0.756505i	0.0540585	−	0.0392758i
$372$	5.63836	+	1.83202i	0.292336	+	0.0949856i
$373$			3.69622i			0.191383i	0.995411	+	0.0956915i	$0.0305062\pi$
$373$			3.69622i			0.191383i	−0.995411	+	0.0956915i	$0.969494\pi$
$374$		0			0
$375$	7.47255	−	7.73573i	0.385881	−	0.399471i
$376$	0.379917	−	1.16926i	0.0195927	−	0.0603002i
$377$	−6.26822	−	8.62746i	−0.322830	−	0.444337i
$378$	−3.08334	+	4.24385i	−0.158590	+	0.218280i
$379$	1.14391	+	3.52060i	0.0587588	+	0.180841i	0.976128	−	0.217197i	$-0.0696913\pi$
$379$	1.14391	+	3.52060i	0.0587588	+	0.180841i	−0.917369	+	0.398038i	$0.869691\pi$
$380$	−17.7088	+	11.6460i	−0.908444	+	0.597428i
$381$	−4.21504	−	3.06241i	−0.215943	−	0.156892i
$382$	0.516575	+	0.711004i	0.0264303	+	0.0363781i
$383$	−29.8355	−	9.69413i	−1.52452	−	0.495347i	−0.577465	−	0.816415i	$-0.695958\pi$
$383$	−29.8355	−	9.69413i	−1.52452	−	0.495347i	−0.947056	+	0.321068i	$0.895958\pi$
$384$	8.78939			0.448532
$385$		0			0
$386$	−0.127476			−0.00648836
$387$	1.17754	+	0.382605i	0.0598576	+	0.0194489i
$388$	−12.5614	−	17.2892i	−0.637707	−	0.877728i
$389$	−11.1852	−	8.12652i	−0.567112	−	0.412031i	0.266943	−	0.963712i	$-0.413987\pi$
$389$	−11.1852	−	8.12652i	−0.567112	−	0.412031i	−0.834055	+	0.551681i	$0.813987\pi$
$390$	2.02093	+	3.07301i	0.102334	+	0.155608i
$391$	−6.50261	−	20.0130i	−0.328851	−	1.01210i
$392$	−2.78678	+	3.83567i	−0.140754	+	0.193731i
$393$	−10.8137	−	14.8838i	−0.545479	−	0.750788i
$394$	1.88134	−	5.79018i	0.0947807	−	0.291705i
$395$	1.67445	+	6.10798i	0.0842505	+	0.307326i
$396$		0			0
$397$			9.73413i			0.488542i	0.969707	+	0.244271i	$0.0785486\pi$
$397$			9.73413i			0.488542i	−0.969707	+	0.244271i	$0.921451\pi$
$398$	−3.16936	−	1.02979i	−0.158866	−	0.0516187i
$399$	−12.7588	+	9.26983i	−0.638740	+	0.464072i
$400$	16.7507	+	1.56544i	0.837535	+	0.0782719i
$401$	−8.08908	−	24.8956i	−0.403949	−	1.24323i	−0.921769	−	0.387739i	$-0.873256\pi$
$401$	−8.08908	−	24.8956i	−0.403949	−	1.24323i	0.517820	−	0.855490i	$-0.326744\pi$
$402$	−2.53866	+	0.824862i	−0.126617	+	0.0411404i
$403$	−9.96869	+	13.7207i	−0.496576	+	0.683478i
$404$	−20.1563	+	14.6444i	−1.00281	+	0.728585i
$405$	−3.41177	−	0.159077i	−0.169532	−	0.00790459i
$406$	2.20061			0.109214
$407$		0			0
$408$		−	4.42713i		−	0.219175i
$409$	0.817540	−	2.51613i	0.0404248	−	0.124415i	−0.928808	−	0.370563i	$-0.879165\pi$
$409$	0.817540	−	2.51613i	0.0404248	−	0.124415i	0.969232	+	0.246148i	$0.0791649\pi$
$410$	−4.68188	+	5.85031i	−0.231221	+	0.288926i
$411$	−12.4857	−	9.07142i	−0.615876	−	0.447460i
$412$	−5.00693	+	1.62685i	−0.246674	+	0.0801492i
$413$	1.64163	−	0.533399i	0.0807795	−	0.0262468i
$414$	−3.22040	−	2.33976i	−0.158274	−	0.114993i
$415$	−16.9625	+	21.1957i	−0.832654	+	1.04046i
$416$	−5.89077	+	18.1299i	−0.288819	+	0.888893i
$417$		−	12.0917i		−	0.592135i
$418$		0			0
$419$	−24.3118			−1.18771			−0.593855	−	0.804572i	$-0.702395\pi$
$419$	−24.3118			−1.18771			−0.593855	+	0.804572i	$0.702395\pi$
$420$	13.3059	+	0.620399i	0.649260	+	0.0302724i
$421$	22.5653	−	16.3946i	1.09976	−	0.799025i	0.118742	−	0.992925i	$-0.462114\pi$
$421$	22.5653	−	16.3946i	1.09976	−	0.799025i	0.981021	+	0.193900i	$0.0621139\pi$
$422$	1.63539	−	2.25091i	0.0796093	−	0.109573i
$423$	1.89805	−	0.616712i	0.0922861	−	0.0299856i
$424$	0.155316	+	0.478013i	0.00754281	+	0.0232144i
$425$	1.67533	−	17.9266i	0.0812653	−	0.869566i
$426$	−3.20135	+	2.32592i	−0.155106	+	0.112691i
$427$	16.5745	+	5.38538i	0.802096	+	0.260617i
$428$		−	30.1808i		−	1.45884i
$429$		0			0
$430$	0.115852	+	0.422602i	0.00558689	+	0.0203797i
$431$	−6.19197	+	19.0569i	−0.298257	+	0.917940i	0.683851	+	0.729622i	$0.260304\pi$
$431$	−6.19197	+	19.0569i	−0.298257	+	0.917940i	−0.982108	+	0.188319i	$0.939696\pi$
$432$	9.65480	+	13.2887i	0.464517	+	0.639353i
$433$	−2.57728	+	3.54732i	−0.123856	+	0.170473i	−0.866442	−	0.499277i	$-0.833599\pi$
$433$	−2.57728	+	3.54732i	−0.123856	+	0.170473i	0.742586	+	0.669750i	$0.233599\pi$
$434$	−1.08148	−	3.32846i	−0.0519128	−	0.159771i
$435$	−2.42056	−	3.68068i	−0.116057	−	0.176475i
$436$	−5.98410	−	4.34771i	−0.286587	−	0.208217i
$437$	−17.2066	−	23.6829i	−0.823104	−	1.13290i
$438$	−2.55810	−	0.831178i	−0.122231	−	0.0397152i
$439$	−34.2675			−1.63550			−0.817750	−	0.575573i	$-0.804779\pi$
$439$	−34.2675			−1.63550			−0.817750	+	0.575573i	$0.804779\pi$
$440$		0			0
$441$	−7.69622			−0.366487
$442$	5.85560	+	1.90260i	0.278522	+	0.0904974i
$443$	10.8700	+	14.9613i	0.516450	+	0.710832i	0.984990	−	0.172610i	$-0.0552199\pi$
$443$	10.8700	+	14.9613i	0.516450	+	0.710832i	−0.468540	+	0.883442i	$0.655220\pi$
$444$	−9.18486	−	6.67319i	−0.435894	−	0.316696i
$445$	−16.8144	+	11.0578i	−0.797080	+	0.524191i
$446$	2.40544	+	7.40318i	0.113901	+	0.350551i
$447$	7.87554	−	10.8398i	0.372500	−	0.512703i
$448$	10.6325	+	14.6343i	0.502337	+	0.691408i
$449$	−5.80049	+	17.8521i	−0.273742	+	0.842491i	0.715808	+	0.698298i	$0.246059\pi$
$449$	−5.80049	+	17.8521i	−0.273742	+	0.842491i	−0.989550	+	0.144194i	$0.953941\pi$
$450$	−1.73686	−	2.92976i	−0.0818766	−	0.138110i
$451$		0			0
$452$			18.6902i			0.879113i
$453$	−14.6693	−	4.76634i	−0.689223	−	0.223942i
$454$	0.190354	−	0.138300i	0.00893375	−	0.00649075i
$455$	−13.4504	+	35.6527i	−0.630564	+	1.67143i
$456$	−1.90316	−	5.85733i	−0.0891237	−	0.274295i
$457$	−13.7894	+	4.48045i	−0.645041	+	0.209586i	−0.613226	−	0.789907i	$-0.710129\pi$
$457$	−13.7894	+	4.48045i	−0.645041	+	0.209586i	−0.0318145	+	0.999494i	$0.510129\pi$
$458$	−2.53777	+	3.49295i	−0.118582	+	0.163215i
$459$	14.2215	−	10.3325i	0.663804	−	0.482282i
$460$	−1.15158	+	24.6983i	−0.0536927	+	1.15156i
$461$	15.2150			0.708632			0.354316	−	0.935126i	$-0.384714\pi$
$461$	15.2150			0.708632			0.354316	+	0.935126i	$0.384714\pi$
$462$		0			0
$463$			9.08060i			0.422011i	0.977485	+	0.211006i	$0.0676739\pi$
$463$			9.08060i			0.422011i	−0.977485	+	0.211006i	$0.932326\pi$
$464$	2.12935	−	6.55347i	0.0988527	−	0.304237i
$465$	−4.37752	+	5.47000i	−0.203003	+	0.253665i
$466$	7.15443	+	5.19800i	0.331422	+	0.240792i
$467$	16.4381	−	5.34105i	0.760663	−	0.247154i	0.0970999	−	0.995275i	$-0.469043\pi$
$467$	16.4381	−	5.34105i	0.760663	−	0.247154i	0.663563	+	0.748120i	$0.269043\pi$
$468$	−19.4405	+	6.31659i	−0.898636	+	0.291985i
$469$	−22.3735	−	16.2553i	−1.03311	−	0.750601i
$470$	0.551464	+	0.441325i	0.0254371	+	0.0203568i
$471$	0.676264	−	2.08133i	0.0311606	−	0.0959024i
$472$			0.674078i			0.0310269i
$473$		0			0
$474$	−0.894665			−0.0410933
$475$	−5.48984	−	24.4380i	−0.251891	−	1.12129i
$476$	18.0396	−	13.1066i	0.826846	−	0.600738i
$477$	−0.479563	+	0.660062i	−0.0219577	+	0.0302222i
$478$	1.56434	−	0.508285i	0.0715512	−	0.0232484i
$479$	−10.0834	−	31.0335i	−0.460722	−	1.41796i	−0.864284	−	0.503005i	$-0.832228\pi$
$479$	−10.0834	−	31.0335i	−0.460722	−	1.41796i	0.403561	−	0.914953i	$-0.367772\pi$
$480$	−2.77962	+	7.36789i	−0.126872	+	0.336297i
$481$	26.2752	−	19.0900i	1.19804	−	0.870430i
$482$	−1.46570	−	0.476234i	−0.0667607	−	0.0216919i
$483$			18.3974i			0.837110i
$484$		0			0
$485$	24.3559	−	6.67694i	1.10594	−	0.303184i
$486$	1.63508	−	5.03226i	0.0741687	−	0.228268i
$487$	8.96742	+	12.3426i	0.406353	+	0.559297i	0.962324	−	0.271905i	$-0.0876536\pi$
$487$	8.96742	+	12.3426i	0.406353	+	0.559297i	−0.555971	+	0.831201i	$0.687654\pi$
$488$	−4.00030	+	5.50595i	−0.181085	+	0.249242i
$489$	6.70931	+	20.6491i	0.303406	+	0.933786i
$490$	−1.49664	−	2.27578i	−0.0676112	−	0.102809i
$491$	−5.39609	−	3.92049i	−0.243522	−	0.176929i	0.459329	−	0.888266i	$-0.348090\pi$
$491$	−5.39609	−	3.92049i	−0.243522	−	0.176929i	−0.702851	+	0.711337i	$0.748090\pi$
$492$	10.9193	+	15.0291i	0.492280	+	0.677565i
$493$	−7.01351	−	2.27883i	−0.315873	−	0.102633i
$494$	8.56518			0.385365
$495$		0			0
$496$	−10.9587			−0.492060
$497$	−38.9906	−	12.6688i	−1.74897	−	0.568274i
$498$	−2.25411	−	3.10252i	−0.101009	−	0.139027i
$499$	−4.97474	−	3.61436i	−0.222700	−	0.161801i	0.470841	−	0.882218i	$-0.343950\pi$
$499$	−4.97474	−	3.61436i	−0.222700	−	0.161801i	−0.693541	+	0.720417i	$0.743950\pi$
$500$	−9.27672	+	19.0128i	−0.414868	+	0.850280i
$501$	−1.13247	−	3.48540i	−0.0505952	−	0.155716i
$502$	0.845017	−	1.16307i	0.0377150	−	0.0519102i
$503$	15.1108	+	20.7983i	0.673759	+	0.927350i	0.999838	−	0.0179929i	$-0.00572762\pi$
$503$	15.1108	+	20.7983i	0.673759	+	0.927350i	−0.326079	+	0.945342i	$0.605728\pi$
$504$	2.68120	−	8.25190i	0.119430	−	0.367569i
$505$	−7.78416	−	28.3948i	−0.346391	−	1.26355i
$506$		0			0
$507$			13.5795i			0.603085i
$508$	9.74628	+	3.16676i	0.432421	+	0.140502i
$509$	−13.6282	+	9.90144i	−0.604058	+	0.438873i	−0.847317	−	0.531088i	$-0.821783\pi$
$509$	−13.6282	+	9.90144i	−0.604058	+	0.438873i	0.243259	+	0.969961i	$0.421783\pi$
$510$	2.37968	+	0.897760i	0.105374	+	0.0397535i
$511$	−8.61137	−	26.5031i	−0.380944	−	1.17243i
$512$	−19.8942	+	6.46401i	−0.879207	+	0.285672i
$513$	14.3740	−	19.7842i	0.634629	−	0.873492i
$514$	−1.73096	+	1.25762i	−0.0763494	+	0.0554711i
$515$	0.289763	−	6.21462i	0.0127685	−	0.273849i
$516$	1.08638			0.0478253
$517$		0			0
$518$			6.70201i			0.294469i
$519$	−0.282307	+	0.868851i	−0.0123919	+	0.0381383i
$520$	−11.6184	−	9.29797i	−0.509501	−	0.407743i
$521$	20.3636	+	14.7950i	0.892144	+	0.648180i	0.936436	−	0.350838i	$-0.114103\pi$
$521$	20.3636	+	14.7950i	0.892144	+	0.648180i	−0.0442923	+	0.999019i	$0.514103\pi$
$522$	−1.32673	+	0.431081i	−0.0580695	+	0.0188679i
$523$	−17.0329	+	5.53431i	−0.744795	+	0.241998i	−0.656740	−	0.754117i	$-0.728065\pi$
$523$	−17.0329	+	5.53431i	−0.744795	+	0.241998i	−0.0880547	+	0.996116i	$0.528065\pi$
$524$	29.2754	+	21.2698i	1.27890	+	0.929175i
$525$	−6.23619	+	14.4531i	−0.272170	+	0.630787i
$526$	0.434489	−	1.33722i	0.0189446	−	0.0583055i
$527$			11.7280i			0.510879i
$528$		0			0
$529$	−11.1491			−0.484744
$530$	−0.288439	−	0.0134487i	−0.0125290	−	0.000584175i
$531$	−0.885241	+	0.643165i	−0.0384162	+	0.0279110i
$532$	18.2331	−	25.0957i	0.790505	−	1.08804i
$533$	−50.5423	+	16.4222i	−2.18923	+	0.711324i
$534$	−0.878492	−	2.70372i	−0.0380161	−	0.117001i
$535$	33.3700	+	12.5892i	1.44271	+	0.544279i
$536$	8.73725	−	6.34799i	0.377392	−	0.274191i
$537$	3.32596	+	1.08067i	0.143526	+	0.0466344i
$538$		−	3.48763i		−	0.150362i
$539$		0			0
$540$	−19.9199	+	5.46085i	−0.857215	+	0.234998i
$541$	−2.91857	+	8.98243i	−0.125479	+	0.386185i	−0.993988	−	0.109489i	$-0.965079\pi$
$541$	−2.91857	+	8.98243i	−0.125479	+	0.386185i	0.868509	+	0.495673i	$0.165079\pi$
$542$	−2.05556	−	2.82923i	−0.0882937	−	0.121526i
$543$	−7.10699	+	9.78193i	−0.304990	+	0.419783i
$544$	4.07358	+	12.5372i	0.174653	+	0.537527i
$545$	7.30327	−	4.80291i	0.312838	−	0.205734i
$546$	−4.35485	−	3.16398i	−0.186370	−	0.135406i
$547$	−8.99572	−	12.3815i	−0.384629	−	0.529397i	0.572174	−	0.820132i	$-0.306100\pi$
$547$	−8.99572	−	12.3815i	−0.384629	−	0.529397i	−0.956804	+	0.290735i	$0.906100\pi$
$548$	28.8703	+	9.38054i	1.23328	+	0.400717i
$549$	−11.0476			−0.471500
$550$		0			0
$551$	−10.2589			−0.437044
$552$	−6.83286	−	2.22013i	−0.290826	−	0.0944951i
$553$	−5.44825	−	7.49888i	−0.231683	−	0.318885i
$554$	1.95262	+	1.41866i	0.0829587	+	0.0602731i
$555$	11.2096	−	7.37188i	0.475822	−	0.312919i
$556$	7.34953	+	22.6195i	0.311689	+	0.959281i
$557$	5.84755	−	8.04846i	0.247768	−	0.341024i	−0.666960	−	0.745094i	$-0.732405\pi$
$557$	5.84755	−	8.04846i	0.247768	−	0.341024i	0.914728	+	0.404070i	$0.132405\pi$
$558$	1.30404	+	1.79485i	0.0552042	+	0.0759821i
$559$	−0.960367	+	2.95571i	−0.0406192	+	0.125013i
$560$	−23.7461	+	6.50977i	−1.00346	+	0.275088i
$561$		0			0
$562$			9.26912i			0.390994i
$563$	−26.6695	−	8.66544i	−1.12398	−	0.365205i	−0.312697	−	0.949853i	$-0.601233\pi$
$563$	−26.6695	−	8.66544i	−1.12398	−	0.365205i	−0.811287	+	0.584648i	$0.801233\pi$
$564$	1.41668	−	1.02928i	0.0596530	−	0.0433404i
$565$	−20.6652	−	7.79618i	−0.869393	−	0.327988i
$566$	−1.02092	−	3.14208i	−0.0429126	−	0.132072i
$567$	4.75405	−	1.54468i	0.199651	−	0.0648706i
$568$	9.41050	−	12.9524i	0.394856	−	0.543472i
$569$	−16.4854	+	11.9773i	−0.691104	+	0.502116i	−0.877023	−	0.480449i	$-0.840474\pi$
$569$	−16.4854	+	11.9773i	−0.691104	+	0.502116i	0.185919	+	0.982565i	$0.440474\pi$
$570$	3.53438	+	0.164794i	0.148039	+	0.00690245i
$571$	43.6546			1.82689			0.913444	−	0.406964i	$-0.133412\pi$
$571$	43.6546			1.82689			0.913444	+	0.406964i	$0.133412\pi$
$572$		0			0
$573$			2.57485i			0.107566i
$574$	3.38882	−	10.4297i	0.141447	−	0.435328i
$575$	−26.8278	−	11.5756i	−1.11880	−	0.482736i
$576$	−9.27699	−	6.74013i	−0.386541	−	0.280839i
$577$	−35.6308	+	11.5771i	−1.48333	+	0.481963i	−0.935106	−	0.354369i	$-0.884696\pi$
$577$	−35.6308	+	11.5771i	−1.48333	+	0.481963i	−0.548223	+	0.836332i	$0.684696\pi$
$578$	−1.25951	+	0.409238i	−0.0523885	+	0.0170221i
$579$	−0.302151	−	0.219525i	−0.0125570	−	0.00912317i
$580$	6.76522	+	5.41406i	0.280910	+	0.224807i
$581$	12.2777	−	37.7869i	0.509365	−	1.56766i
$582$			3.56753i			0.147879i
$583$		0			0
$584$	10.8825			0.450322
$585$	1.12506	−	24.1296i	0.0465157	−	0.997636i
$586$	−0.00650298	+	0.00472469i	−0.000268636	+	0.000195175i
$587$	3.53798	−	4.86961i	0.146028	−	0.200990i	−0.729737	−	0.683728i	$-0.760358\pi$
$587$	3.53798	−	4.86961i	0.146028	−	0.200990i	0.875765	+	0.482738i	$0.160358\pi$
$588$	−6.42241	+	2.08677i	−0.264856	+	0.0860568i
$589$	5.04170	+	15.5168i	0.207740	+	0.639357i
$590$	−0.362332	−	0.136694i	−0.0149170	−	0.00562759i
$591$	14.4305	−	10.4844i	0.593590	−	0.431269i
$592$	19.9588	+	6.48500i	0.820300	+	0.266532i
$593$			14.3574i			0.589589i	0.955561	+	0.294794i	$0.0952511\pi$
$593$			14.3574i			0.589589i	−0.955561	+	0.294794i	$0.904749\pi$
$594$		0			0
$595$	6.96674	+	25.4130i	0.285609	+	1.04183i
$596$	−8.14391	+	25.0644i	−0.333587	+	1.02668i
$597$	−5.73881	−	7.89880i	−0.234874	−	0.323276i
$598$	5.87297	−	8.08345i	0.240164	−	0.330557i
$599$	−8.63612	−	26.5793i	−0.352862	−	1.08600i	−0.957239	−	0.289300i	$-0.906578\pi$
$599$	−8.63612	−	26.5793i	−0.352862	−	1.08600i	0.604376	−	0.796699i	$-0.293422\pi$
$600$	−4.61540	−	4.06030i	−0.188423	−	0.165761i
$601$	16.6365	+	12.0871i	0.678616	+	0.493043i	0.872898	−	0.487902i	$-0.162238\pi$
$601$	16.6365	+	12.0871i	0.678616	+	0.493043i	−0.194282	+	0.980946i	$0.562238\pi$
$602$	−0.376956	−	0.518836i	−0.0153636	−	0.0211462i
$603$	16.6731	+	5.41743i	0.678983	+	0.220615i
$604$	30.3383			1.23445
$605$		0			0
$606$	4.15912			0.168953
$607$	−18.2354	−	5.92504i	−0.740152	−	0.240490i	−0.0854138	−	0.996346i	$-0.527221\pi$
$607$	−18.2354	−	5.92504i	−0.740152	−	0.240490i	−0.654738	+	0.755856i	$0.727221\pi$
$608$	10.7791	+	14.8362i	0.437151	+	0.601687i
$609$	5.21600	+	3.78965i	0.211363	+	0.153564i
$610$	−2.14836	−	3.26678i	−0.0869846	−	0.132268i
$611$	1.54799	+	4.76423i	0.0626251	+	0.192740i
$612$	−8.30851	+	11.4357i	−0.335851	+	0.462260i
$613$	−10.6117	−	14.6057i	−0.428601	−	0.589919i	0.539030	−	0.842286i	$-0.318791\pi$
$613$	−10.6117	−	14.6057i	−0.428601	−	0.589919i	−0.967631	+	0.252368i	$0.918791\pi$
$614$	−3.34532	+	10.2958i	−0.135006	+	0.415506i
$615$	−21.1720	+	5.80411i	−0.853738	+	0.234044i
$616$		0			0
$617$			32.0433i			1.29001i	0.764176	+	0.645007i	$0.223146\pi$
$617$			32.0433i			1.29001i	−0.764176	+	0.645007i	$0.776854\pi$
$618$	0.835835	+	0.271579i	0.0336222	+	0.0109245i
$619$	−4.29576	+	3.12105i	−0.172661	+	0.125446i	−0.670760	−	0.741675i	$-0.734032\pi$
$619$	−4.29576	+	3.12105i	−0.172661	+	0.125446i	0.498099	+	0.867120i	$0.334032\pi$
$620$	4.86411	−	12.8932i	0.195347	−	0.517804i
$621$	−8.81547	−	27.1312i	−0.353752	−	1.08874i
$622$	1.50696	−	0.489641i	0.0604236	−	0.0196328i
$623$	17.3122	−	23.8282i	0.693599	−	0.954657i
$624$	−13.6363	+	9.90734i	−0.545888	+	0.396611i
$625$	−17.1524	−	18.1878i	−0.686096	−	0.727511i
$626$	5.60369			0.223968
$627$		0			0
$628$			4.30450i			0.171768i
$629$	6.94023	−	21.3598i	0.276725	−	0.851672i
$630$	3.89187	+	3.11458i	0.155056	+	0.124088i
$631$	−31.8692	−	23.1543i	−1.26869	−	0.921758i	−0.269541	−	0.962989i	$-0.586872\pi$
$631$	−31.8692	−	23.1543i	−1.26869	−	0.921758i	−0.999150	+	0.0412309i	$0.986872\pi$
$632$	3.44259	−	1.11857i	0.136939	−	0.0444941i
$633$	7.75256	−	2.51896i	0.308137	−	0.100120i
$634$	−0.455991	−	0.331297i	−0.0181097	−	0.0131575i
$635$	−7.56683	+	9.45525i	−0.300280	+	0.375220i
$636$	−0.221220	+	0.680844i	−0.00877193	+	0.0269972i
$637$		−	19.3181i		−	0.765410i
$638$		0			0
$639$	25.9889			1.02810
$640$	0.951534	−	20.4078i	0.0376127	−	0.806690i
$641$	38.2382	−	27.7816i	1.51032	−	1.09731i	0.544280	−	0.838904i	$-0.316803\pi$
$641$	38.2382	−	27.7816i	1.51032	−	1.09731i	0.966037	−	0.258405i	$-0.0831970\pi$
$642$	−2.96141	+	4.07603i	−0.116877	+	0.160868i
$643$	−2.26218	+	0.735027i	−0.0892117	+	0.0289866i	−0.353283	−	0.935517i	$-0.614935\pi$
$643$	−2.26218	+	0.735027i	−0.0892117	+	0.0289866i	0.264071	+	0.964503i	$0.414935\pi$
$644$	−11.1822	−	34.4152i	−0.440640	−	1.35615i
$645$	−0.453159	+	1.20118i	−0.0178431	+	0.0472965i
$646$	4.79179	−	3.48144i	0.188530	−	0.136975i
$647$	0.846705	+	0.275111i	0.0332874	+	0.0108157i	0.325613	−	0.945503i	$-0.394429\pi$
$647$	0.846705	+	0.275111i	0.0332874	+	0.0108157i	−0.292326	+	0.956319i	$0.594429\pi$
$648$			1.95208i			0.0766849i
$649$		0			0
$650$	7.35392	−	4.35966i	0.288445	−	0.171000i
$651$	3.16852	−	9.75170i	0.124184	−	0.382199i
$652$	−25.1017	−	34.5495i	−0.983058	−	1.35306i
$653$	−7.67244	+	10.5602i	−0.300246	+	0.413253i	−0.932308	−	0.361665i	$-0.882209\pi$
$653$	−7.67244	+	10.5602i	−0.300246	+	0.413253i	0.632063	+	0.774917i	$0.282209\pi$
$654$	0.381569	+	1.17435i	0.0149205	+	0.0459207i
$655$	−35.7289	+	23.4967i	−1.39605	+	0.918093i
$656$	−27.7809	−	20.1840i	−1.08466	−	0.788053i
$657$	10.3835	+	14.2916i	0.405098	+	0.557569i
$658$	−0.983129	−	0.319438i	−0.0383263	−	0.0124530i
$659$	−24.8805			−0.969205			−0.484603	−	0.874734i	$-0.661036\pi$
$659$	−24.8805			−0.969205			−0.484603	+	0.874734i	$0.661036\pi$
$660$		0			0
$661$	−33.1788			−1.29051			−0.645253	−	0.763969i	$-0.723248\pi$
$661$	−33.1788			−1.29051			−0.645253	+	0.763969i	$0.723248\pi$
$662$	0.278612	+	0.0905265i	0.0108286	+	0.00351841i
$663$	10.6028	+	14.5935i	0.411779	+	0.566765i
$664$	12.5526	+	9.11997i	0.487134	+	0.353924i
$665$	20.1421	+	30.6279i	0.781077	+	1.18770i
$666$	−1.31287	−	4.04059i	−0.0508726	−	0.156570i
$667$	−7.03432	+	9.68191i	−0.272370	+	0.374885i
$668$	4.23695	+	5.83166i	0.163932	+	0.225634i
$669$	−7.04744	+	21.6898i	−0.272470	+	0.838576i
$670$	1.64039	+	5.98375i	0.0633738	+	0.231173i
$671$		0			0
$672$		−	11.5251i		−	0.444590i
$673$	22.6539	+	7.36070i	0.873243	+	0.283734i	0.711149	−	0.703041i	$-0.248175\pi$
$673$	22.6539	+	7.36070i	0.873243	+	0.283734i	0.162094	+	0.986775i	$0.448175\pi$
$674$	−4.99023	+	3.62562i	−0.192217	+	0.139654i
$675$	2.27121	−	24.3027i	0.0874190	−	0.935412i
$676$	−8.25379	−	25.4025i	−0.317453	−	0.977021i
$677$	−1.77882	+	0.577972i	−0.0683654	+	0.0222133i	−0.343000	−	0.939335i	$-0.611443\pi$
$677$	−1.77882	+	0.577972i	−0.0683654	+	0.0222133i	0.274635	+	0.961549i	$0.411443\pi$
$678$	1.83393	−	2.52418i	0.0704315	−	0.0969407i
$679$	−29.9022	+	21.7252i	−1.14754	+	0.833737i
$680$	−10.2792	−	0.479278i	−0.394190	−	0.0183795i
$681$	0.689352			0.0264160
$682$		0			0
$683$		−	9.51629i		−	0.364131i	−0.983286	−	0.182065i	$-0.941722\pi$
$683$		−	9.51629i		−	0.364131i	0.983286	−	0.182065i	$-0.0582782\pi$
$684$	−6.07656	+	18.7017i	−0.232343	+	0.715079i
$685$	−22.4144	+	28.0082i	−0.856410	+	1.07014i
$686$	−2.86027	−	2.07811i	−0.109206	−	0.0793425i
$687$	−12.0303	+	3.90889i	−0.458986	+	0.149134i
$688$	−1.90986	+	0.620551i	−0.0728127	+	0.0236583i
$689$	−1.65681	−	1.20374i	−0.0631193	−	0.0458588i
$690$	2.57898	−	3.22260i	0.0981801	−	0.122682i
$691$	−1.41121	+	4.34326i	−0.0536849	+	0.165225i	−0.974304	−	0.225236i	$-0.927685\pi$
$691$	−1.41121	+	4.34326i	−0.0536849	+	0.165225i	0.920619	+	0.390462i	$0.127685\pi$
$692$		−	1.79692i		−	0.0683085i
$693$		0			0
$694$	6.88217			0.261244
$695$	−28.0754	−	1.30904i	−1.06496	−	0.0496549i
$696$	−2.03694	+	1.47992i	−0.0772100	+	0.0560963i
$697$	−21.6009	+	29.7310i	−0.818191	+	1.12614i
$698$	8.48985	−	2.75852i	0.321345	−	0.104411i
$699$	8.00639	+	24.6411i	0.302830	+	0.932014i
$700$	2.88097	−	30.8274i	0.108891	−	1.16517i
$701$	23.2637	−	16.9021i	0.878658	−	0.638382i	−0.0542383	−	0.998528i	$-0.517273\pi$
$701$	23.2637	−	16.9021i	0.878658	−	0.638382i	0.932896	+	0.360146i	$0.117273\pi$
$702$	7.93833	+	2.57932i	0.299613	+	0.0973501i
$703$		−	31.2437i		−	1.17838i
$704$		0			0
$705$	0.547109	+	1.99572i	0.0206053	+	0.0751633i
$706$	−0.879548	+	2.70697i	−0.0331022	+	0.101878i
$707$	25.3278	+	34.8608i	0.952552	+	1.31108i
$708$	−0.564334	+	0.776739i	−0.0212090	+	0.0291916i
$709$	11.2526	+	34.6318i	0.422599	+	1.30063i	0.905275	+	0.424827i	$0.139665\pi$
$709$	11.2526	+	34.6318i	0.422599	+	1.30063i	−0.482676	+	0.875799i	$0.660335\pi$
$710$	5.05391	+	7.68493i	0.189670	+	0.288410i
$711$	4.75368	+	3.45375i	0.178277	+	0.129526i
$712$	6.76071	+	9.30533i	0.253368	+	0.348732i
$713$	18.1011	+	5.88139i	0.677890	+	0.220260i
$714$	−3.72237			−0.139306
$715$		0			0
$716$	−6.87859			−0.257065
$717$	4.58320	+	1.48917i	0.171163	+	0.0556141i
$718$	1.33260	+	1.83416i	0.0497320	+	0.0684503i
$719$	31.6519	+	22.9964i	1.18042	+	0.857623i	0.992219	−	0.124508i	$-0.0397354\pi$
$719$	31.6519	+	22.9964i	1.18042	+	0.857623i	0.188198	+	0.982131i	$0.439735\pi$
$720$	13.0411	−	8.57636i	0.486015	−	0.319622i
$721$	2.81368	+	8.65962i	0.104787	+	0.322501i
$722$	1.17618	−	1.61888i	0.0437730	−	0.0602483i
$723$	−2.65396	−	3.65286i	−0.0987018	−	0.135851i
$724$	7.34917	−	22.6184i	0.273130	−	0.840606i
$725$	−8.80812	+	5.22176i	−0.327126	+	0.193931i
$726$		0			0
$727$		−	32.8912i		−	1.21987i	−0.792453	−	0.609933i	$-0.791196\pi$
$727$		−	32.8912i		−	1.21987i	0.792453	−	0.609933i	$-0.208804\pi$
$728$	20.7129	+	6.73002i	0.767670	+	0.249431i
$729$	8.83437	−	6.41855i	0.327199	−	0.237724i
$730$	−2.20683	+	5.84960i	−0.0816784	+	0.216504i
$731$	0.664112	+	2.04393i	0.0245631	+	0.0755973i
$732$	−9.21909	+	2.99547i	−0.340748	+	0.110716i
$733$	−7.00972	+	9.64805i	−0.258910	+	0.356359i	−0.918607	−	0.395173i	$-0.870685\pi$
$733$	−7.00972	+	9.64805i	−0.258910	+	0.356359i	0.659697	+	0.751532i	$0.270685\pi$
$734$	−4.32730	+	3.14397i	−0.159724	+	0.116046i
$735$	0.371679	−	7.97152i	0.0137096	−	0.294034i
$736$	21.3928			0.788549
$737$		0			0
$738$			6.95184i			0.255901i
$739$	−11.5087	+	35.4201i	−0.423355	+	1.30295i	0.481207	+	0.876607i	$0.340199\pi$
$739$	−11.5087	+	35.4201i	−0.423355	+	1.30295i	−0.904561	+	0.426344i	$0.859801\pi$
$740$	−16.4886	+	20.6036i	−0.606135	+	0.757405i
$741$	20.3016	+	14.7500i	0.745800	+	0.541855i
$742$	0.401918	−	0.130591i	0.0147549	−	0.00479415i
$743$	12.6921	−	4.12391i	0.465628	−	0.151292i	−0.0668013	−	0.997766i	$-0.521279\pi$
$743$	12.6921	−	4.12391i	0.465628	−	0.151292i	0.532429	+	0.846475i	$0.321279\pi$
$744$	3.23946	+	2.35360i	0.118764	+	0.0862872i
$745$	−24.3159	−	19.4595i	−0.890867	−	0.712941i
$746$	−0.375040	+	1.15425i	−0.0137312	+	0.0422603i
$747$			25.1865i			0.921527i
$748$		0			0
$749$	−52.1984			−1.90729
$750$	3.11844	−	1.65750i	0.113869	−	0.0605235i
$751$	−0.643974	+	0.467874i	−0.0234989	+	0.0170730i	−0.599473	−	0.800395i	$-0.704623\pi$
$751$	−0.643974	+	0.467874i	−0.0234989	+	0.0170730i	0.575974	+	0.817468i	$0.304623\pi$
$752$	−1.90259	+	2.61869i	−0.0693803	+	0.0954938i
$753$	4.00581	−	1.30157i	0.145980	−	0.0474317i
$754$	−1.08205	−	3.33019i	−0.0394058	−	0.121279i
$755$	−12.6549	+	33.5442i	−0.460560	+	1.22080i
$756$	24.4560	−	17.7683i	0.889457	−	0.646228i
$757$	−38.6788	−	12.5675i	−1.40581	−	0.456774i	−0.494742	−	0.869040i	$-0.664737\pi$
$757$	−38.6788	−	12.5675i	−1.40581	−	0.456774i	−0.911063	+	0.412266i	$0.864737\pi$
$758$			1.21548i			0.0441483i
$759$		0			0
$760$	−13.8060	+	3.78479i	−0.500796	+	0.137289i
$761$	1.78312	−	5.48788i	0.0646380	−	0.198935i	−0.913522	−	0.406790i	$-0.866648\pi$
$761$	1.78312	−	5.48788i	0.0646380	−	0.198935i	0.978160	+	0.207855i	$0.0666481\pi$
$762$	−1.00554	−	1.38401i	−0.0364270	−	0.0501374i
$763$	−7.51947	+	10.3497i	−0.272223	+	0.374683i
$764$	−1.56503	−	4.81667i	−0.0566208	−	0.174261i
$765$	−9.17840	−	13.9566i	−0.331846	−	0.504602i
$766$	−8.33340	−	6.05457i	−0.301098	−	0.218760i
$767$	−1.61439	−	2.22202i	−0.0582923	−	0.0802325i
$768$	−7.36956	−	2.39451i	−0.265926	−	0.0864046i
$769$	−16.4209			−0.592152			−0.296076	−	0.955164i	$-0.595678\pi$
$769$	−16.4209			−0.592152			−0.296076	+	0.955164i	$0.595678\pi$
$770$		0			0
$771$	−6.26855			−0.225756
$772$	0.698652	+	0.227006i	0.0251451	+	0.00817012i
$773$	−14.4501	−	19.8889i	−0.519736	−	0.715355i	0.465787	−	0.884897i	$-0.345771\pi$
$773$	−14.4501	−	19.8889i	−0.519736	−	0.715355i	−0.985523	+	0.169542i	$0.945771\pi$
$774$	0.328900	+	0.238960i	0.0118221	+	0.00858923i
$775$	12.2267	+	10.7562i	0.439197	+	0.386375i
$776$	−4.46034	−	13.7275i	−0.160117	−	0.492789i
$777$	−11.5415	+	15.8855i	−0.414048	+	0.569888i
$778$	−2.66835	−	3.67267i	−0.0956650	−	0.131672i
$779$	−15.7982	+	48.6217i	−0.566027	+	1.74205i
$780$	−5.60369	−	20.4409i	−0.200644	−	0.731902i
$781$		0			0
$782$		−	6.90944i		−	0.247081i
$783$	−9.50809	−	3.08937i	−0.339792	−	0.110405i
$784$	10.0986	−	7.33707i	0.360665	−	0.262038i
$785$	−4.75936	−	1.79552i	−0.169869	−	0.0640849i
$786$	−1.86671	−	5.74513i	−0.0665832	−	0.204922i
$787$	1.74515	−	0.567033i	0.0622078	−	0.0202125i	−0.277748	−	0.960654i	$-0.589588\pi$
$787$	1.74515	−	0.567033i	0.0622078	−	0.0202125i	0.339956	+	0.940441i	$0.389588\pi$
$788$	−20.6220	+	28.3837i	−0.734627	+	1.01113i
$789$	3.33266	−	2.42132i	0.118646	−	0.0862013i
$790$	−0.0968560	+	2.07730i	−0.00344598	+	0.0739070i
$791$	32.3252			1.14935
$792$		0			0
$793$		−	27.7303i		−	0.984732i
$794$	−0.987682	+	3.03977i	−0.0350515	+	0.107878i
$795$	−0.660513	−	0.528595i	−0.0234260	−	0.0187473i
$796$	15.5364	+	11.2878i	0.550672	+	0.400087i
$797$	39.9498	−	12.9805i	1.41509	−	0.459792i	0.501054	−	0.865416i	$-0.332946\pi$
$797$	39.9498	−	12.9805i	1.41509	−	0.459792i	0.914040	+	0.405624i	$0.132946\pi$
$798$	−4.92490	+	1.60020i	−0.174339	+	0.0566463i
$799$	2.80252	+	2.03615i	0.0991459	+	0.0720337i
$800$	16.8064	+	7.25156i	0.594195	+	0.256381i
$801$	−5.76966	+	17.7572i	−0.203861	+	0.627419i
$802$		−	8.59517i		−	0.303506i
$803$		0			0
$804$	15.3824			0.542496
$805$	42.7164	+	1.99169i	1.50555	+	0.0701978i
$806$	−4.50521	+	3.27323i	−0.158689	+	0.115294i
$807$	6.00602	−	8.26657i	0.211422	−	0.290997i
$808$	−16.0039	+	5.19999i	−0.563016	+	0.182935i
$809$	−8.36851	−	25.7556i	−0.294221	−	0.905520i	−0.983482	−	0.181006i	$-0.942065\pi$
$809$	−8.36851	−	25.7556i	−0.294221	−	0.905520i	0.689261	−	0.724513i	$-0.257935\pi$
$810$	−1.04929	−	0.395855i	−0.0368682	−	0.0139089i
$811$	0.832297	−	0.604699i	0.0292259	−	0.0212339i	−0.573076	−	0.819502i	$-0.694250\pi$
$811$	0.832297	−	0.604699i	0.0292259	−	0.0212339i	0.602302	+	0.798268i	$0.294250\pi$
$812$	−12.0608	−	3.91878i	−0.423250	−	0.137522i
$813$		−	10.2459i		−	0.359338i
$814$		0			0
$815$	48.6710	−	13.3427i	1.70487	−	0.467374i
$816$	−3.60184	+	11.0853i	−0.126090	+	0.388064i
$817$	1.75731	+	2.41873i	0.0614806	+	0.0846207i
$818$	0.510603	−	0.702784i	0.0178528	−	0.0245723i
$819$	10.9247	+	33.6228i	0.381740	+	1.17488i
$820$	36.0778	−	23.7262i	1.25989	−	0.828554i
$821$	−9.30898	−	6.76337i	−0.324886	−	0.236043i	0.413372	−	0.910562i	$-0.364351\pi$
$821$	−9.30898	−	6.76337i	−0.324886	−	0.236043i	−0.738257	+	0.674519i	$0.764351\pi$
$822$	−2.97861	−	4.09970i	−0.103891	−	0.142994i
$823$	−27.3562	−	8.88857i	−0.953578	−	0.309836i	−0.209409	−	0.977828i	$-0.567154\pi$
$823$	−27.3562	−	8.88857i	−0.953578	−	0.309836i	−0.744168	+	0.667992i	$0.767154\pi$
$824$	−3.55576			−0.123871
$825$		0			0
$826$	0.566771			0.0197205
$827$	51.4041	+	16.7022i	1.78749	+	0.580792i	0.999396	−	0.0347562i	$-0.0110655\pi$
$827$	51.4041	+	16.7022i	1.78749	+	0.580792i	0.788099	+	0.615548i	$0.211065\pi$
$828$	13.4833	+	18.5582i	0.468578	+	0.644943i
$829$	3.76100	+	2.73253i	0.130625	+	0.0949047i	0.651179	−	0.758924i	$-0.274275\pi$
$829$	3.76100	+	2.73253i	0.130625	+	0.0949047i	−0.520554	+	0.853829i	$0.674275\pi$
$830$	−7.44767	+	4.89788i	−0.258513	+	0.170008i
$831$	2.18514	+	6.72517i	0.0758016	+	0.233293i
$832$	16.9182	−	23.2859i	0.586534	−	0.807295i
$833$	−7.85211	−	10.8075i	−0.272060	−	0.374458i
$834$	1.22690	−	3.77601i	0.0424840	−	0.130752i
$835$	−8.21525	+	2.25213i	−0.284300	+	0.0779383i
$836$		0			0
$837$			15.8994i			0.549564i
$838$	−7.59209	−	2.46682i	−0.262265	−	0.0852149i
$839$	4.00068	−	2.90666i	0.138119	−	0.100349i	−0.516581	−	0.856239i	$-0.672795\pi$
$839$	4.00068	−	2.90666i	0.138119	−	0.100349i	0.654699	+	0.755890i	$0.272795\pi$
$840$	8.41759	+	3.17563i	0.290434	+	0.109570i
$841$	−7.66548	−	23.5919i	−0.264327	−	0.813514i
$842$	8.71017	−	2.83011i	0.300172	−	0.0975319i
$843$	−15.9623	+	21.9702i	−0.549770	+	0.756693i
$844$	−12.9713	+	9.42423i	−0.446492	+	0.324396i
$845$	31.5298	+	1.47010i	1.08466	+	0.0505731i
$846$	0.655297			0.0225296
$847$		0			0
$848$		−	1.32329i		−	0.0454418i
$849$	2.99110	−	9.20566i	0.102654	−	0.315937i
$850$	2.34211	−	5.42812i	0.0803336	−	0.186183i
$851$	−29.4865	−	21.4232i	−1.01078	−	0.734378i
$852$	21.6874	−	7.04667i	0.742999	−	0.241415i
$853$	27.8807	−	9.05898i	0.954616	−	0.310174i	0.210026	−	0.977696i	$-0.432645\pi$
$853$	27.8807	−	9.05898i	0.954616	−	0.310174i	0.744590	+	0.667522i	$0.232645\pi$
$854$	4.62945	+	3.36349i	0.158417	+	0.115096i
$855$	−18.1433	−	14.5197i	−0.620487	−	0.496563i
$856$	6.29913	−	19.3867i	0.215300	−	0.662624i
$857$		−	0.656701i		−	0.0224325i	−0.999937	−	0.0112162i	$-0.996430\pi$
$857$		−	0.656701i		−	0.0224325i	0.999937	−	0.0112162i	$-0.00357032\pi$
$858$		0			0
$859$	40.0569			1.36672			0.683361	−	0.730080i	$-0.260517\pi$
$859$	40.0569			1.36672			0.683361	+	0.730080i	$0.260517\pi$
$860$	0.117611	−	2.52244i	0.00401050	−	0.0860145i
$861$	25.9933	−	18.8852i	0.885848	−	0.643606i
$862$	−3.86726	+	5.32283i	−0.131719	+	0.181296i
$863$	18.9551	−	6.15889i	0.645239	−	0.209651i	0.0319255	−	0.999490i	$-0.489836\pi$
$863$	18.9551	−	6.15889i	0.645239	−	0.209651i	0.613314	+	0.789839i	$0.289836\pi$
$864$	5.52247	+	16.9964i	0.187878	+	0.578230i
$865$	1.98680	+	0.749542i	0.0675532	+	0.0254852i
$866$	−1.16476	+	0.846251i	−0.0395803	+	0.0287568i
$867$	−3.69010	−	1.19898i	−0.125322	−	0.0407197i
$868$			20.1680i			0.684546i
$869$		0			0
$870$	−0.382428	−	1.39501i	−0.0129655	−	0.0472952i
$871$	−13.5982	+	41.8508i	−0.460756	+	1.41806i
$872$	−2.93649	−	4.04173i	−0.0994419	−	0.136870i
$873$	13.7720	−	18.9556i	0.466113	−	0.641549i
$874$	−2.97028	−	9.14157i	−0.100471	−	0.309218i
$875$	32.8832	+	16.0443i	1.11166	+	0.542397i
$876$	12.5399	+	9.11080i	0.423685	+	0.307825i
$877$	2.81556	+	3.87528i	0.0950746	+	0.130859i	0.853904	−	0.520430i	$-0.174228\pi$
$877$	2.81556	+	3.87528i	0.0950746	+	0.130859i	−0.758830	+	0.651289i	$0.774228\pi$
$878$	−10.7011	−	3.47699i	−0.361143	−	0.117343i
$879$	−0.0235501			−0.000794325
$880$		0			0
$881$	33.9748			1.14464			0.572320	−	0.820031i	$-0.306044\pi$
$881$	33.9748			1.14464			0.572320	+	0.820031i	$0.306044\pi$
$882$	−2.40338	−	0.780904i	−0.0809259	−	0.0262944i
$883$	−23.0849	−	31.7736i	−0.776867	−	1.06927i	−0.995621	−	0.0934859i	$-0.970199\pi$
$883$	−23.0849	−	31.7736i	−0.776867	−	1.06927i	0.218753	−	0.975780i	$-0.429801\pi$
$884$	−28.7044	−	20.8550i	−0.965433	−	0.701428i
$885$	−0.623420	−	0.947967i	−0.0209560	−	0.0318656i
$886$	1.87643	+	5.77505i	0.0630398	+	0.194017i
$887$	19.5450	−	26.9013i	0.656256	−	0.903258i	−0.343095	−	0.939301i	$-0.611475\pi$
$887$	19.5450	−	26.9013i	0.656256	−	0.903258i	0.999350	+	0.0360425i	$0.0114752\pi$
$888$	−4.50714	−	6.20355i	−0.151250	−	0.208178i
$889$	5.47699	−	16.8564i	0.183692	−	0.565347i
$890$	−6.37280	+	1.74704i	−0.213617	+	0.0585610i
$891$		0			0
$892$		−	44.8578i		−	1.50195i
$893$	4.58320	+	1.48917i	0.153371	+	0.0498332i
$894$	3.55924	−	2.58594i	0.119039	−	0.0864868i
$895$	2.86924	−	7.60546i	0.0959083	−	0.254223i
$896$	9.23968	+	28.4368i	0.308676	+	0.950007i
$897$	27.8409	−	9.04605i	0.929580	−	0.302039i
$898$	−3.62275	+	4.98629i	−0.120893	+	0.166395i
$899$	5.39609	−	3.92049i	0.179970	−	0.130756i
$900$	4.30191	+	19.1500i	0.143397	+	0.638332i
$901$	−1.41618			−0.0471797
$902$		0			0
$903$		−	1.87893i		−	0.0625267i
$904$	−3.90089	+	12.0057i	−0.129742	+	0.399304i
$905$	21.9430	+	17.5605i	0.729410	+	0.583731i
$906$	−4.09730	−	2.97686i	−0.136124	−	0.0988997i
$907$	17.4516	−	5.67038i	0.579472	−	0.188282i	−0.00459214	−	0.999989i	$-0.501462\pi$
$907$	17.4516	−	5.67038i	0.579472	−	0.188282i	0.584064	+	0.811708i	$0.301462\pi$
$908$	−1.28954	+	0.418998i	−0.0427950	+	0.0139049i
$909$	−22.0989	−	16.0558i	−0.732975	−	0.532538i
$910$	−7.81782	+	9.76887i	−0.259158	+	0.323835i
$911$	11.9936	−	36.9125i	0.397365	−	1.22296i	−0.529739	−	0.848161i	$-0.677710\pi$
$911$	11.9936	−	36.9125i	0.397365	−	1.22296i	0.927104	−	0.374804i	$-0.122290\pi$
$912$			16.2149i			0.536928i
$913$		0			0
$914$	−4.76076			−0.157472
$915$	0.533530	−	11.4428i	0.0176380	−	0.378287i
$916$	20.1288	−	14.6244i	0.665074	−	0.483205i
$917$	36.7867	−	50.6325i	1.21480	−	1.67203i
$918$	5.48950	−	1.78365i	0.181180	−	0.0588691i
$919$	−0.303354	−	0.933629i	−0.0100067	−	0.0307976i	0.945928	−	0.324375i	$-0.105154\pi$
$919$	−0.303354	−	0.933629i	−0.0100067	−	0.0307976i	−0.955935	+	0.293578i	$0.905154\pi$
$920$	−5.89458	+	15.6247i	−0.194339	+	0.515130i
$921$	−25.6596	+	18.6428i	−0.845512	+	0.614301i
$922$	4.75133	+	1.54380i	0.156477	+	0.0508424i
$923$			65.2340i			2.14720i
$924$		0			0
$925$	−15.9030	−	26.8254i	−0.522888	−	0.882012i
$926$	−0.921372	+	2.83569i	−0.0302782	+	0.0931866i
$927$	−3.39270	−	4.66965i	−0.111431	−	0.153371i
$928$	4.40667	−	6.06526i	0.144656	−	0.199102i
$929$	−10.8187	−	33.2965i	−0.354950	−	1.09242i	−0.956039	−	0.293241i	$-0.905266\pi$
$929$	−10.8187	−	33.2965i	−0.354950	−	1.09242i	0.601089	−	0.799182i	$-0.294734\pi$
$930$	−1.92203	+	1.26400i	−0.0630259	+	0.0414482i
$931$	−15.0348	−	10.9234i	−0.492745	−	0.358000i
$932$	−29.9545	−	41.2288i	−0.981192	−	1.35049i
$933$	4.41508	+	1.43455i	0.144543	+	0.0469650i
$934$	5.67522			0.185699
$935$		0			0
$936$	−13.8060			−0.451263
$937$	29.3453	+	9.53487i	0.958670	+	0.311491i	0.746234	−	0.665684i	$-0.231860\pi$
$937$	29.3453	+	9.53487i	0.958670	+	0.311491i	0.212436	+	0.977175i	$0.431860\pi$
$938$	−5.33745	−	7.34636i	−0.174274	−	0.239867i
$939$	13.2822	+	9.65006i	0.433447	+	0.314918i
$940$	−2.23648	−	3.40078i	−0.0729461	−	0.110921i
$941$	9.29418	+	28.6046i	0.302982	+	0.932482i	0.980423	+	0.196905i	$0.0630890\pi$
$941$	9.29418	+	28.6046i	0.302982	+	0.932482i	−0.677441	+	0.735577i	$0.736911\pi$
$942$	0.422367	−	0.581339i	0.0137615	−	0.0189410i
$943$	35.0546	+	48.2486i	1.14154	+	1.57119i
$944$	0.548419	−	1.68786i	0.0178495	−	0.0549352i
$945$	9.44468	+	34.4520i	0.307236	+	1.12072i
$946$		0			0
$947$			10.1860i			0.331002i	0.986210	+	0.165501i	$0.0529241\pi$
$947$			10.1860i			0.331002i	−0.986210	+	0.165501i	$0.947076\pi$
$948$	4.90335	+	1.59320i	0.159253	+	0.0517446i
$949$	−35.8730	+	26.0633i	−1.16449	+	0.846050i
$950$	0.765260	−	8.18854i	0.0248283	−	0.265671i
$951$	−0.510291	−	1.57051i	−0.0165473	−	0.0509274i
$952$	14.3233	−	4.65393i	0.464222	−	0.150835i
$953$	−23.5980	+	32.4798i	−0.764413	+	1.05212i	0.232421	+	0.972615i	$0.425335\pi$
$953$	−23.5980	+	32.4798i	−0.764413	+	1.05212i	−0.996834	+	0.0795087i	$0.974665\pi$
$954$	−0.216732	+	0.157465i	−0.00701695	+	0.00509811i
$955$	5.97847	+	0.278752i	0.193459	+	0.00902019i
$956$	−9.47874			−0.306564
$957$		0			0
$958$		−	10.7143i		−	0.346162i
$959$	16.2239	−	49.9320i	0.523897	−	1.61239i
$960$	7.42925	−	9.28333i	0.239778	−	0.299618i
$961$	16.4978	+	11.9864i	0.532188	+	0.386657i
$962$	10.1422	−	3.29540i	0.326997	−	0.106248i
$963$	31.4701	−	10.2253i	1.01411	−	0.329504i
$964$	7.18492	+	5.22015i	0.231411	+	0.168130i
$965$	−0.542421	+	0.677790i	−0.0174611	+	0.0218188i
$966$	−1.86671	+	5.74513i	−0.0600603	+	0.184847i
$967$		−	58.0856i		−	1.86791i	−0.357395	−	0.933953i	$-0.616335\pi$
$967$		−	58.0856i		−	1.86791i	0.357395	−	0.933953i	$-0.383665\pi$
$968$		0			0
$969$	17.3531			0.557462
$970$	8.28334	+	0.386218i	0.265962	+	0.0124007i
$971$	−26.5455	+	19.2865i	−0.851886	+	0.618932i	−0.925666	−	0.378343i	$-0.876494\pi$
$971$	−26.5455	+	19.2865i	−0.851886	+	0.618932i	0.0737791	+	0.997275i	$0.476494\pi$
$972$	−17.9226	+	24.6684i	−0.574868	+	0.791238i
$973$	39.1211	−	12.7112i	1.25416	−	0.407502i
$974$	1.54799	+	4.76423i	0.0496009	+	0.152656i
$975$	24.9384	+	2.33062i	0.798668	+	0.0746395i
$976$	14.4961	−	10.5321i	0.464010	−	0.337123i
$977$	−17.0472	−	5.53896i	−0.545387	−	0.177207i	0.0233485	−	0.999727i	$-0.492567\pi$
$977$	−17.0472	−	5.53896i	−0.545387	−	0.177207i	−0.568736	+	0.822520i	$0.692567\pi$
$978$			7.12908i			0.227963i
$979$		0			0
$980$	4.14992	+	15.1379i	0.132564	+	0.483563i
$981$	2.50602	−	7.71275i	0.0800112	−	0.246249i
$982$	−1.28730	−	1.77181i	−0.0410792	−	0.0565407i
$983$	10.0374	−	13.8152i	0.320142	−	0.440638i	−0.618369	−	0.785888i	$-0.712206\pi$
$983$	10.0374	−	13.8152i	0.320142	−	0.440638i	0.938511	+	0.345251i	$0.112206\pi$
$984$	3.87727	+	11.9330i	0.123603	+	0.380410i
$985$	−22.7811	−	34.6407i	−0.725866	−	1.10375i
$986$	−1.95896	−	1.42327i	−0.0623859	−	0.0453260i
$987$	−1.78016	−	2.45019i	−0.0566633	−	0.0779903i
$988$	−46.9428	−	15.2526i	−1.49345	−	0.485251i
$989$	3.48765			0.110901
$990$		0			0
$991$	17.5551			0.557658			0.278829	−	0.960341i	$-0.410054\pi$
$991$	17.5551			0.557658			0.278829	+	0.960341i	$0.410054\pi$
$992$	−11.3395	−	3.68441i	−0.360028	−	0.116980i
$993$	0.504486	+	0.694366i	0.0160094	+	0.0220350i
$994$	−10.8905	−	7.91243i	−0.345427	−	0.250967i
$995$	−18.9613	+	12.4697i	−0.601113	+	0.395315i
$996$	6.82912	+	21.0179i	0.216389	+	0.665977i
$997$	8.93709	−	12.3009i	0.283041	−	0.389572i	−0.643697	−	0.765280i	$-0.722600\pi$
$997$	8.93709	−	12.3009i	0.283041	−	0.389572i	0.926738	+	0.375708i	$0.122600\pi$
$998$	−1.18678	−	1.63346i	−0.0375667	−	0.0517062i
$999$	9.40874	−	28.9571i	0.297679	−	0.916163i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.j.k.9.8		48
5.4	even	2	inner	605.2.j.k.9.5		48
11.2	odd	10	inner	605.2.j.k.124.8		48
11.3	even	5	inner	605.2.j.k.444.7		48
11.4	even	5		605.2.b.h.364.7	yes	12
11.5	even	5	inner	605.2.j.k.269.5		48
11.6	odd	10	inner	605.2.j.k.269.7		48
11.7	odd	10		605.2.b.h.364.5	✓	12
11.8	odd	10	inner	605.2.j.k.444.5		48
11.9	even	5	inner	605.2.j.k.124.6		48
11.10	odd	2	inner	605.2.j.k.9.6		48
55.4	even	10		605.2.b.h.364.6	yes	12
55.7	even	20		3025.2.a.bo.1.7		12
55.9	even	10	inner	605.2.j.k.124.7		48
55.14	even	10	inner	605.2.j.k.444.6		48
55.18	even	20		3025.2.a.bo.1.6		12
55.19	odd	10	inner	605.2.j.k.444.8		48
55.24	odd	10	inner	605.2.j.k.124.5		48
55.29	odd	10		605.2.b.h.364.8	yes	12
55.37	odd	20		3025.2.a.bo.1.5		12
55.39	odd	10	inner	605.2.j.k.269.6		48
55.48	odd	20		3025.2.a.bo.1.8		12
55.49	even	10	inner	605.2.j.k.269.8		48
55.54	odd	2	inner	605.2.j.k.9.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.b.h.364.5	✓	12	11.7	odd	10
605.2.b.h.364.6	yes	12	55.4	even	10
605.2.b.h.364.7	yes	12	11.4	even	5
605.2.b.h.364.8	yes	12	55.29	odd	10
605.2.j.k.9.5		48	5.4	even	2	inner
605.2.j.k.9.6		48	11.10	odd	2	inner
605.2.j.k.9.7		48	55.54	odd	2	inner
605.2.j.k.9.8		48	1.1	even	1	trivial
605.2.j.k.124.5		48	55.24	odd	10	inner
605.2.j.k.124.6		48	11.9	even	5	inner
605.2.j.k.124.7		48	55.9	even	10	inner
605.2.j.k.124.8		48	11.2	odd	10	inner
605.2.j.k.269.5		48	11.5	even	5	inner
605.2.j.k.269.6		48	55.39	odd	10	inner
605.2.j.k.269.7		48	11.6	odd	10	inner
605.2.j.k.269.8		48	55.49	even	10	inner
605.2.j.k.444.5		48	11.8	odd	10	inner
605.2.j.k.444.6		48	55.14	even	10	inner
605.2.j.k.444.7		48	11.3	even	5	inner
605.2.j.k.444.8		48	55.19	odd	10	inner
3025.2.a.bo.1.5		12	55.37	odd	20
3025.2.a.bo.1.6		12	55.18	even	20
3025.2.a.bo.1.7		12	55.7	even	20
3025.2.a.bo.1.8		12	55.48	odd	20

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.j (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.312280 + 0.101466i) q^{2} +(0.565450 + 0.778275i) q^{3} +(-1.53081 - 1.11220i) q^{4} +(1.86827 - 1.22865i) q^{5} +(0.0976102 + 0.300413i) q^{6} +(-1.92358 + 2.64758i) q^{7} +(-0.751190 - 1.03393i) q^{8} +(0.641073 - 1.97302i) q^{9} +O(q^{10})\)	\(q+(0.312280 + 0.101466i) q^{2} +(0.565450 + 0.778275i) q^{3} +(-1.53081 - 1.11220i) q^{4} +(1.86827 - 1.22865i) q^{5} +(0.0976102 + 0.300413i) q^{6} +(-1.92358 + 2.64758i) q^{7} +(-0.751190 - 1.03393i) q^{8} +(0.641073 - 1.97302i) q^{9} +(0.708089 - 0.194116i) q^{10} -1.82028i q^{12} +(4.95243 + 1.60914i) q^{13} +(-0.869334 + 0.631608i) q^{14} +(2.01264 + 0.759289i) q^{15} +(1.03976 + 3.20006i) q^{16} +(3.42469 - 1.11275i) q^{17} +(0.400388 - 0.551087i) q^{18} +(4.05270 - 2.94446i) q^{19} +(-4.22646 - 0.197063i) q^{20} -3.14823 q^{21} -5.84372i q^{23} +(0.379917 - 1.16926i) q^{24} +(1.98086 - 4.59088i) q^{25} +(1.38327 + 1.00500i) q^{26} +(4.64280 - 1.50854i) q^{27} +(5.88927 - 1.91354i) q^{28} +(-1.65681 - 1.20374i) q^{29} +(0.551464 + 0.441325i) q^{30} +(-1.00645 + 3.09752i) q^{31} +3.66082i q^{32} +1.18237 q^{34} +(-0.340825 + 7.30978i) q^{35} +(-3.17575 + 2.30732i) q^{36} +(3.66602 - 5.04584i) q^{37} +(1.56434 - 0.508285i) q^{38} +(1.54799 + 4.76423i) q^{39} +(-2.67375 - 1.00870i) q^{40} +(-8.25648 + 5.99868i) q^{41} +(-0.983129 - 0.319438i) q^{42} +0.596820i q^{43} +(-1.22645 - 4.47378i) q^{45} +(0.592939 - 1.82488i) q^{46} +(0.565450 + 0.778275i) q^{47} +(-1.90259 + 2.61869i) q^{48} +(-1.14640 - 3.52824i) q^{49} +(1.08440 - 1.23265i) q^{50} +(2.80252 + 2.03615i) q^{51} +(-5.79154 - 7.97137i) q^{52} +(-0.374032 - 0.121530i) q^{53} +1.60292 q^{54} +4.18237 q^{56} +(4.58320 + 1.48917i) q^{57} +(-0.395249 - 0.544013i) q^{58} +(-0.426713 - 0.310025i) q^{59} +(-2.23648 - 3.40078i) q^{60} +(-1.64560 - 5.06465i) q^{61} +(-0.628585 + 0.865174i) q^{62} +(3.99057 + 5.49255i) q^{63} +(1.70807 - 5.25691i) q^{64} +(11.2295 - 3.07847i) q^{65} +8.45057i q^{67} +(-6.48016 - 2.10553i) q^{68} +(4.54802 - 3.30433i) q^{69} +(-0.848127 + 2.24812i) q^{70} +(3.87119 + 11.9143i) q^{71} +(-2.52152 + 0.819292i) q^{72} +(-5.00515 + 6.88900i) q^{73} +(1.65681 - 1.20374i) q^{74} +(4.69304 - 1.05426i) q^{75} -9.47874 q^{76} +1.64484i q^{78} +(-0.875246 + 2.69373i) q^{79} +(5.87429 + 4.70107i) q^{80} +(-1.23573 - 0.897811i) q^{81} +(-3.18699 + 1.03552i) q^{82} +(-11.5465 + 3.75168i) q^{83} +(4.81934 + 3.50146i) q^{84} +(5.03107 - 6.28665i) q^{85} +(-0.0605569 + 0.186375i) q^{86} -1.97010i q^{87} -9.00000 q^{89} +(0.0709421 - 1.52152i) q^{90} +(-13.7867 + 10.0166i) q^{91} +(-6.49938 + 8.94563i) q^{92} +(-2.97981 + 0.968201i) q^{93} +(0.0976102 + 0.300413i) q^{94} +(3.95384 - 10.4804i) q^{95} +(-2.84912 + 2.07001i) q^{96} +(10.7414 + 3.49009i) q^{97} -1.21812i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 20 q^{4} + 6 q^{5} + 20 q^{9}+O(q^{10}) \) 48 * q + 20 * q^4 + 6 * q^5 + 20 * q^9	\( 48 q + 20 q^{4} + 6 q^{5} + 20 q^{9} + 32 q^{14} - 20 q^{15} - 36 q^{16} - 26 q^{20} + 10 q^{25} - 20 q^{26} - 8 q^{31} + 48 q^{34} - 92 q^{36} - 72 q^{45} + 4 q^{49} + 192 q^{56} + 32 q^{59} + 92 q^{60} - 28 q^{64} + 16 q^{69} + 12 q^{70} - 112 q^{71} - 36 q^{75} + 106 q^{80} + 20 q^{81} + 56 q^{86} - 432 q^{89} - 72 q^{91}+O(q^{100}) \) 48 * q + 20 * q^4 + 6 * q^5 + 20 * q^9 + 32 * q^14 - 20 * q^15 - 36 * q^16 - 26 * q^20 + 10 * q^25 - 20 * q^26 - 8 * q^31 + 48 * q^34 - 92 * q^36 - 72 * q^45 + 4 * q^49 + 192 * q^56 + 32 * q^59 + 92 * q^60 - 28 * q^64 + 16 * q^69 + 12 * q^70 - 112 * q^71 - 36 * q^75 + 106 * q^80 + 20 * q^81 + 56 * q^86 - 432 * q^89 - 72 * q^91

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