LMFDB - Embedded newform 354.2.c.b.353.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(353,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("354.353");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.c (of order $2$, degree $1$, 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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.41542366334681088.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - x^{8} - 2x^{7} + 2x^{6} + 14x^{5} + 6x^{4} - 18x^{3} - 27x^{2} - 81x + 243 $ x^10 - x^9 - x^8 - 2x^7 + 2x^6 + 14x^5 + 6x^4 - 18x^3 - 27x^2 - 81*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			353.4
Root			$1.43134 + 0.975334i$ of defining polynomial
Character	$\chi$	$=$	354.353
Dual form			354.2.c.b.353.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.43134 + 0.975334i) q^{3} +1.00000 q^{4} -0.0999120i q^{5} +(-1.43134 + 0.975334i) q^{6} +2.48626 q^{7} +1.00000 q^{8} +(1.09745 - 2.79206i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.43134 + 0.975334i) q^{3} +1.00000 q^{4} -0.0999120i q^{5} +(-1.43134 + 0.975334i) q^{6} +2.48626 q^{7} +1.00000 q^{8} +(1.09745 - 2.79206i) q^{9} -0.0999120i q^{10} +1.50375 q^{11} +(-1.43134 + 0.975334i) q^{12} +3.74859i q^{13} +2.48626 q^{14} +(0.0974475 + 0.143008i) q^{15} +1.00000 q^{16} +6.68366i q^{17} +(1.09745 - 2.79206i) q^{18} +3.99002 q^{19} -0.0999120i q^{20} +(-3.55868 + 2.42494i) q^{21} +1.50375 q^{22} -7.31226 q^{23} +(-1.43134 + 0.975334i) q^{24} +4.99002 q^{25} +3.74859i q^{26} +(1.15238 + 5.06676i) q^{27} +2.48626 q^{28} -3.18348i q^{29} +(0.0974475 + 0.143008i) q^{30} -9.23530i q^{31} +1.00000 q^{32} +(-2.15238 + 1.46666i) q^{33} +6.68366i q^{34} -0.248408i q^{35} +(1.09745 - 2.79206i) q^{36} +0.665027i q^{37} +3.99002 q^{38} +(-3.65613 - 5.36550i) q^{39} -0.0999120i q^{40} -3.99875i q^{41} +(-3.55868 + 2.42494i) q^{42} -10.0506i q^{43} +1.50375 q^{44} +(-0.278960 - 0.109648i) q^{45} -7.31226 q^{46} -4.30475 q^{47} +(-1.43134 + 0.975334i) q^{48} -0.818487 q^{49} +4.99002 q^{50} +(-6.51880 - 9.56657i) q^{51} +3.74859i q^{52} -0.250155i q^{53} +(1.15238 + 5.06676i) q^{54} -0.150243i q^{55} +2.48626 q^{56} +(-5.71106 + 3.89160i) q^{57} -3.18348i q^{58} +(-7.65780 + 0.598474i) q^{59} +(0.0974475 + 0.143008i) q^{60} +13.2188i q^{61} -9.23530i q^{62} +(2.72855 - 6.94181i) q^{63} +1.00000 q^{64} +0.374529 q^{65} +(-2.15238 + 1.46666i) q^{66} +7.06709i q^{67} +6.68366i q^{68} +(10.4663 - 7.13189i) q^{69} -0.248408i q^{70} -10.1991i q^{71} +(1.09745 - 2.79206i) q^{72} -11.3305i q^{73} +0.665027i q^{74} +(-7.14239 + 4.86693i) q^{75} +3.99002 q^{76} +3.73873 q^{77} +(-3.65613 - 5.36550i) q^{78} -9.13074 q^{79} -0.0999120i q^{80} +(-6.59122 - 6.12828i) q^{81} -3.99875i q^{82} -5.43398 q^{83} +(-3.55868 + 2.42494i) q^{84} +0.667778 q^{85} -10.0506i q^{86} +(3.10495 + 4.55663i) q^{87} +1.50375 q^{88} +8.23497 q^{89} +(-0.278960 - 0.109648i) q^{90} +9.31999i q^{91} -7.31226 q^{92} +(9.00751 + 13.2188i) q^{93} -4.30475 q^{94} -0.398650i q^{95} +(-1.43134 + 0.975334i) q^{96} -3.83328i q^{97} -0.818487 q^{98} +(1.65029 - 4.19857i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} - q^{3} + 10 q^{4} - q^{6} - 2 q^{7} + 10 q^{8} + 3 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 - q^3 + 10 * q^4 - q^6 - 2 * q^7 + 10 * q^8 + 3 * q^9	$ 10 q + 10 q^{2} - q^{3} + 10 q^{4} - q^{6} - 2 q^{7} + 10 q^{8} + 3 q^{9} - 4 q^{11} - q^{12} - 2 q^{14} - 7 q^{15} + 10 q^{16} + 3 q^{18} - 6 q^{19} - 3 q^{21} - 4 q^{22} + 8 q^{23} - q^{24} + 4 q^{25} - 10 q^{27} - 2 q^{28} - 7 q^{30} + 10 q^{32} + 3 q^{36} - 6 q^{38} + 4 q^{39} - 3 q^{42} - 4 q^{44} - 11 q^{45} + 8 q^{46} - q^{48} + 8 q^{49} + 4 q^{50} + 2 q^{51} - 10 q^{54} - 2 q^{56} - 3 q^{57} - 20 q^{59} - 7 q^{60} - 19 q^{63} + 10 q^{64} - 16 q^{65} - 14 q^{69} + 3 q^{72} - 4 q^{75} - 6 q^{76} - 48 q^{77} + 4 q^{78} + 6 q^{79} + 7 q^{81} - 12 q^{83} - 3 q^{84} - 4 q^{85} - 15 q^{87} - 4 q^{88} + 16 q^{89} - 11 q^{90} + 8 q^{92} + 52 q^{93} - q^{96} + 8 q^{98} - 2 q^{99}+O(q^{100}) $ 10 * q + 10 * q^2 - q^3 + 10 * q^4 - q^6 - 2 * q^7 + 10 * q^8 + 3 * q^9 - 4 * q^11 - q^12 - 2 * q^14 - 7 * q^15 + 10 * q^16 + 3 * q^18 - 6 * q^19 - 3 * q^21 - 4 * q^22 + 8 * q^23 - q^24 + 4 * q^25 - 10 * q^27 - 2 * q^28 - 7 * q^30 + 10 * q^32 + 3 * q^36 - 6 * q^38 + 4 * q^39 - 3 * q^42 - 4 * q^44 - 11 * q^45 + 8 * q^46 - q^48 + 8 * q^49 + 4 * q^50 + 2 * q^51 - 10 * q^54 - 2 * q^56 - 3 * q^57 - 20 * q^59 - 7 * q^60 - 19 * q^63 + 10 * q^64 - 16 * q^65 - 14 * q^69 + 3 * q^72 - 4 * q^75 - 6 * q^76 - 48 * q^77 + 4 * q^78 + 6 * q^79 + 7 * q^81 - 12 * q^83 - 3 * q^84 - 4 * q^85 - 15 * q^87 - 4 * q^88 + 16 * q^89 - 11 * q^90 + 8 * q^92 + 52 * q^93 - q^96 + 8 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.43134	+	0.975334i	−0.826382	+	0.563109i
$3$	−1.43134	+	0.975334i	−0.826382	+	0.563109i
$4$	1.00000			0.500000
$5$		−	0.0999120i		−	0.0446820i	−0.999750	−	0.0223410i	$-0.992888\pi$
$5$		−	0.0999120i		−	0.0446820i	0.999750	−	0.0223410i	$-0.00711195\pi$
$6$	−1.43134	+	0.975334i	−0.584341	+	0.398178i
$7$	2.48626			0.939720			0.469860	−	0.882741i	$-0.344304\pi$
$7$	2.48626			0.939720			0.469860	+	0.882741i	$0.344304\pi$
$8$	1.00000			0.353553
$9$	1.09745	−	2.79206i	0.365816	−	0.930687i
$10$		−	0.0999120i		−	0.0315949i
$11$	1.50375			0.453399			0.226699	−	0.973965i	$-0.427207\pi$
$11$	1.50375			0.453399			0.226699	+	0.973965i	$0.427207\pi$
$12$	−1.43134	+	0.975334i	−0.413191	+	0.281555i
$13$			3.74859i			1.03967i	0.854266	+	0.519836i	$0.174007\pi$
$13$			3.74859i			1.03967i	−0.854266	+	0.519836i	$0.825993\pi$
$14$	2.48626			0.664482
$15$	0.0974475	+	0.143008i	0.0251608	+	0.0369244i
$16$	1.00000			0.250000
$17$			6.68366i			1.62103i	0.585721	+	0.810513i	$0.300812\pi$
$17$			6.68366i			1.62103i	−0.585721	+	0.810513i	$0.699188\pi$
$18$	1.09745	−	2.79206i	0.258671	−	0.658095i
$19$	3.99002			0.915373			0.457686	−	0.889114i	$-0.348678\pi$
$19$	3.99002			0.915373			0.457686	+	0.889114i	$0.348678\pi$
$20$		−	0.0999120i		−	0.0223410i
$21$	−3.55868	+	2.42494i	−0.776568	+	0.529165i
$22$	1.50375			0.320601
$23$	−7.31226			−1.52471			−0.762356	−	0.647158i	$-0.775957\pi$
$23$	−7.31226			−1.52471			−0.762356	+	0.647158i	$0.775957\pi$
$24$	−1.43134	+	0.975334i	−0.292170	+	0.199089i
$25$	4.99002			0.998004
$26$			3.74859i			0.735159i
$27$	1.15238	+	5.06676i	0.221775	+	0.975098i
$28$	2.48626			0.469860
$29$		−	3.18348i		−	0.591157i	−0.955318	−	0.295578i	$-0.904488\pi$
$29$		−	3.18348i		−	0.591157i	0.955318	−	0.295578i	$-0.0955124\pi$
$30$	0.0974475	+	0.143008i	0.0177914	+	0.0261095i
$31$		−	9.23530i		−	1.65871i	−0.558722	−	0.829355i	$-0.688708\pi$
$31$		−	9.23530i		−	1.65871i	0.558722	−	0.829355i	$-0.311292\pi$
$32$	1.00000			0.176777
$33$	−2.15238	+	1.46666i	−0.374681	+	0.255313i
$34$			6.68366i			1.14624i
$35$		−	0.248408i		−	0.0419885i
$36$	1.09745	−	2.79206i	0.182908	−	0.465344i
$37$			0.665027i			0.109330i	0.998505	+	0.0546649i	$0.0174090\pi$
$37$			0.665027i			0.109330i	−0.998505	+	0.0546649i	$0.982591\pi$
$38$	3.99002			0.647266
$39$	−3.65613	−	5.36550i	−0.585449	−	0.859167i
$40$		−	0.0999120i		−	0.0157975i
$41$		−	3.99875i		−	0.624499i	−0.950000	−	0.312250i	$-0.898917\pi$
$41$		−	3.99875i		−	0.624499i	0.950000	−	0.312250i	$-0.101083\pi$
$42$	−3.55868	+	2.42494i	−0.549116	+	0.374176i
$43$		−	10.0506i		−	1.53270i	−0.642424	−	0.766349i	$-0.722071\pi$
$43$		−	10.0506i		−	1.53270i	0.642424	−	0.766349i	$-0.277929\pi$
$44$	1.50375			0.226699
$45$	−0.278960	−	0.109648i	−0.0415850	−	0.0163454i
$46$	−7.31226			−1.07813
$47$	−4.30475			−0.627913			−0.313956	−	0.949437i	$-0.601655\pi$
$47$	−4.30475			−0.627913			−0.313956	+	0.949437i	$0.601655\pi$
$48$	−1.43134	+	0.975334i	−0.206596	+	0.140777i
$49$	−0.818487			−0.116927
$50$	4.99002			0.705695
$51$	−6.51880	−	9.56657i	−0.912815	−	1.33959i
$52$			3.74859i			0.519836i
$53$		−	0.250155i		−	0.0343614i	−0.999852	−	0.0171807i	$-0.994531\pi$
$53$		−	0.250155i		−	0.0343614i	0.999852	−	0.0171807i	$-0.00546906\pi$
$54$	1.15238	+	5.06676i	0.156819	+	0.689498i
$55$		−	0.150243i		−	0.0202587i
$56$	2.48626			0.332241
$57$	−5.71106	+	3.89160i	−0.756448	+	0.515455i
$58$		−	3.18348i		−	0.418011i
$59$	−7.65780	+	0.598474i	−0.996960	+	0.0779147i
$59$	−7.65780	+	0.598474i	−0.996960	+	0.0779147i
$60$	0.0974475	+	0.143008i	0.0125804	+	0.0184622i
$61$			13.2188i			1.69250i	0.532788	+	0.846249i	$0.321144\pi$
$61$			13.2188i			1.69250i	−0.532788	+	0.846249i	$0.678856\pi$
$62$		−	9.23530i		−	1.17288i
$63$	2.72855	−	6.94181i	0.343764	−	0.874585i
$64$	1.00000			0.125000
$65$	0.374529			0.0464546
$66$	−2.15238	+	1.46666i	−0.264939	+	0.180533i
$67$			7.06709i			0.863382i	0.902022	+	0.431691i	$0.142083\pi$
$67$			7.06709i			0.863382i	−0.902022	+	0.431691i	$0.857917\pi$
$68$			6.68366i			0.810513i
$69$	10.4663	−	7.13189i	1.25999	−	0.858579i
$70$		−	0.248408i		−	0.0296904i
$71$		−	10.1991i		−	1.21041i	−0.796071	−	0.605203i	$-0.793092\pi$
$71$		−	10.1991i		−	1.21041i	0.796071	−	0.605203i	$-0.206908\pi$
$72$	1.09745	−	2.79206i	0.129335	−	0.329048i
$73$		−	11.3305i		−	1.32613i	−0.748562	−	0.663065i	$-0.769255\pi$
$73$		−	11.3305i		−	1.32613i	0.748562	−	0.663065i	$-0.230745\pi$
$74$			0.665027i			0.0773078i
$75$	−7.14239	+	4.86693i	−0.824733	+	0.561985i
$76$	3.99002			0.457686
$77$	3.73873			0.426068
$78$	−3.65613	−	5.36550i	−0.413975	−	0.607523i
$79$	−9.13074			−1.02729			−0.513645	−	0.858003i	$-0.671705\pi$
$79$	−9.13074			−1.02729			−0.513645	+	0.858003i	$0.671705\pi$
$80$		−	0.0999120i		−	0.0111705i
$81$	−6.59122	−	6.12828i	−0.732358	−	0.680920i
$82$		−	3.99875i		−	0.441588i
$83$	−5.43398			−0.596456			−0.298228	−	0.954495i	$-0.596396\pi$
$83$	−5.43398			−0.596456			−0.298228	+	0.954495i	$0.596396\pi$
$84$	−3.55868	+	2.42494i	−0.388284	+	0.264582i
$85$	0.667778			0.0724307
$86$		−	10.0506i		−	1.08378i
$87$	3.10495	+	4.55663i	0.332886	+	0.488522i
$88$	1.50375			0.160301
$89$	8.23497			0.872906			0.436453	−	0.899727i	$-0.356235\pi$
$89$	8.23497			0.872906			0.436453	+	0.899727i	$0.356235\pi$
$90$	−0.278960	−	0.109648i	−0.0294050	−	0.0115579i
$91$			9.31999i			0.977001i
$92$	−7.31226			−0.762356
$93$	9.00751	+	13.2188i	0.934035	+	1.37073i
$94$	−4.30475			−0.444001
$95$		−	0.398650i		−	0.0409007i
$96$	−1.43134	+	0.975334i	−0.146085	+	0.0995446i
$97$		−	3.83328i		−	0.389211i	−0.980882	−	0.194605i	$-0.937657\pi$
$97$		−	3.83328i		−	0.389211i	0.980882	−	0.194605i	$-0.0623426\pi$
$98$	−0.818487			−0.0826797
$99$	1.65029	−	4.19857i	0.165860	−	0.421972i
$100$	4.99002			0.499002
$101$	9.73873			0.969040			0.484520	−	0.874780i	$-0.338994\pi$
$101$	9.73873			0.969040			0.484520	+	0.874780i	$0.338994\pi$
$102$	−6.51880	−	9.56657i	−0.645458	−	0.947231i
$103$		−	1.88836i		−	0.186066i	−0.995663	−	0.0930330i	$-0.970344\pi$
$103$		−	1.88836i		−	0.186066i	0.995663	−	0.0930330i	$-0.0296562\pi$
$104$			3.74859i			0.367580i
$105$	0.242280	+	0.355555i	0.0236441	+	0.0346986i
$106$		−	0.250155i		−	0.0242972i
$107$		−	1.98828i		−	0.192214i	−0.995371	−	0.0961069i	$-0.969361\pi$
$107$		−	1.98828i		−	0.192214i	0.995371	−	0.0961069i	$-0.0306391\pi$
$108$	1.15238	+	5.06676i	0.110887	+	0.487549i
$109$			9.53579i			0.913363i	0.889630	+	0.456682i	$0.150962\pi$
$109$			9.53579i			0.913363i	−0.889630	+	0.456682i	$0.849038\pi$
$110$		−	0.150243i		−	0.0143251i
$111$	−0.648623	−	0.951877i	−0.0615646	−	0.0903482i
$112$	2.48626			0.234930
$113$	−13.6203			−1.28129			−0.640647	−	0.767836i	$-0.721334\pi$
$113$	−13.6203			−1.28129			−0.640647	+	0.767836i	$0.721334\pi$
$114$	−5.71106	+	3.89160i	−0.534890	+	0.364482i
$115$			0.730582i			0.0681271i
$116$		−	3.18348i		−	0.295578i
$117$	10.4663	+	4.11388i	0.967610	+	0.380329i
$118$	−7.65780	+	0.598474i	−0.704957	+	0.0550940i
$119$			16.6174i			1.52331i
$120$	0.0974475	+	0.143008i	0.00889570	+	0.0130547i
$121$	−8.73873			−0.794430
$122$			13.2188i			1.19678i
$123$	3.90011	+	5.72355i	0.351661	+	0.516075i
$124$		−	9.23530i		−	0.829355i
$125$		−	0.998122i		−	0.0892748i
$126$	2.72855	−	6.94181i	0.243078	−	0.618425i
$127$	−1.08727			−0.0964792			−0.0482396	−	0.998836i	$-0.515361\pi$
$127$	−1.08727			−0.0964792			−0.0482396	+	0.998836i	$0.515361\pi$
$128$	1.00000			0.0883883
$129$	9.80267	+	14.3858i	0.863077	+	1.26659i
$130$	0.374529			0.0328484
$131$	−2.06978			−0.180837			−0.0904186	−	0.995904i	$-0.528821\pi$
$131$	−2.06978			−0.180837			−0.0904186	+	0.995904i	$0.528821\pi$
$132$	−2.15238	+	1.46666i	−0.187340	+	0.127656i
$133$	9.92024			0.860194
$134$			7.06709i			0.610503i
$135$	0.506230	−	0.115136i	0.0435693	−	0.00990934i
$136$			6.68366i			0.573119i
$137$		−	3.26816i		−	0.279218i	−0.990207	−	0.139609i	$-0.955415\pi$
$137$		−	3.26816i		−	0.279218i	0.990207	−	0.139609i	$-0.0445846\pi$
$138$	10.4663	−	7.13189i	0.890951	−	0.607107i
$139$	16.2500			1.37831			0.689153	−	0.724616i	$-0.257983\pi$
$139$	16.2500			1.37831			0.689153	+	0.724616i	$0.257983\pi$
$140$		−	0.248408i		−	0.0209943i
$141$	6.16155	−	4.19857i	0.518896	−	0.353583i
$142$		−	10.1991i		−	0.855887i
$143$			5.63696i			0.471386i
$144$	1.09745	−	2.79206i	0.0914540	−	0.232672i
$145$	−0.318067			−0.0264141
$146$		−	11.3305i		−	0.937716i
$147$	1.17153	−	0.798298i	0.0966262	−	0.0658425i
$148$			0.665027i			0.0546649i
$149$	−4.42980			−0.362904			−0.181452	−	0.983400i	$-0.558080\pi$
$149$	−4.42980			−0.362904			−0.181452	+	0.983400i	$0.558080\pi$
$150$	−7.14239	+	4.86693i	−0.583174	+	0.397383i
$151$		−	12.6194i		−	1.02695i	−0.858105	−	0.513474i	$-0.828358\pi$
$151$		−	12.6194i		−	1.02695i	0.858105	−	0.513474i	$-0.171642\pi$
$152$	3.99002			0.323633
$153$	18.6612	+	7.33497i	1.50867	+	0.592997i
$154$	3.73873			0.301275
$155$	−0.922717			−0.0741144
$156$	−3.65613	−	5.36550i	−0.292725	−	0.429583i
$157$			15.4024i			1.22925i	0.788820	+	0.614624i	$0.210692\pi$
$157$			15.4024i			1.22925i	−0.788820	+	0.614624i	$0.789308\pi$
$158$	−9.13074			−0.726403
$159$	0.243984	+	0.358056i	0.0193492	+	0.0283957i
$160$		−	0.0999120i		−	0.00789873i
$161$	−18.1802			−1.43280
$162$	−6.59122	−	6.12828i	−0.517855	−	0.481483i
$163$	−11.2458			−0.880840			−0.440420	−	0.897792i	$-0.645170\pi$
$163$	−11.2458			−0.880840			−0.440420	+	0.897792i	$0.645170\pi$
$164$		−	3.99875i		−	0.312250i
$165$	0.146537	+	0.215048i	0.0114079	+	0.0167415i
$166$	−5.43398			−0.421758
$167$		−	7.44685i		−	0.576255i	−0.957592	−	0.288127i	$-0.906967\pi$
$167$		−	7.44685i		−	0.576255i	0.957592	−	0.288127i	$-0.0930327\pi$
$168$	−3.55868	+	2.42494i	−0.274558	+	0.187088i
$169$	−1.05194			−0.0809185
$170$	0.667778			0.0512162
$171$	4.37883	−	11.1404i	0.334858	−	0.851926i
$172$		−	10.0506i		−	0.766349i
$173$	−1.87828			−0.142803			−0.0714016	−	0.997448i	$-0.522747\pi$
$173$	−1.87828			−0.142803			−0.0714016	+	0.997448i	$0.522747\pi$
$174$	3.10495	+	4.55663i	0.235386	+	0.345437i
$175$	12.4065			0.937844
$176$	1.50375			0.113350
$177$	10.3772	−	8.32553i	0.779996	−	0.625785i
$178$	8.23497			0.617237
$179$	14.4415			1.07941			0.539703	−	0.841855i	$-0.318536\pi$
$179$	14.4415			1.07941			0.539703	+	0.841855i	$0.318536\pi$
$180$	−0.278960	−	0.109648i	−0.0207925	−	0.00817269i
$181$	−19.5756			−1.45504			−0.727520	−	0.686087i	$-0.759327\pi$
$181$	−19.5756			−1.45504			−0.727520	+	0.686087i	$0.759327\pi$
$182$			9.31999i			0.690844i
$183$	−12.8928	−	18.9206i	−0.953061	−	1.39865i
$184$	−7.31226			−0.539067
$185$	0.0664441			0.00488507
$186$	9.00751	+	13.2188i	0.660462	+	0.969251i
$187$			10.0506i			0.734971i
$188$	−4.30475			−0.313956
$189$	2.86511	+	12.5973i	0.208406	+	0.916319i
$190$		−	0.398650i		−	0.0289211i
$191$	2.00333			0.144956			0.0724780	−	0.997370i	$-0.476909\pi$
$191$	2.00333			0.144956			0.0724780	+	0.997370i	$0.476909\pi$
$192$	−1.43134	+	0.975334i	−0.103298	+	0.0703887i
$193$	6.79102			0.488828			0.244414	−	0.969671i	$-0.421404\pi$
$193$	6.79102			0.488828			0.244414	+	0.969671i	$0.421404\pi$
$194$		−	3.83328i		−	0.275213i
$195$	−0.536077	+	0.365291i	−0.0383893	+	0.0261590i
$196$	−0.818487			−0.0584634
$197$			3.36517i			0.239758i	0.992789	+	0.119879i	$0.0382507\pi$
$197$			3.36517i			0.239758i	−0.992789	+	0.119879i	$0.961749\pi$
$198$	1.65029	−	4.19857i	0.117281	−	0.298379i
$199$	−12.2483			−0.868258			−0.434129	−	0.900851i	$-0.642944\pi$
$199$	−12.2483			−0.868258			−0.434129	+	0.900851i	$0.642944\pi$
$200$	4.99002			0.352848
$201$	−6.89277	−	10.1154i	−0.486179	−	0.713484i
$202$	9.73873			0.685214
$203$		−	7.91497i		−	0.555522i
$204$	−6.51880	−	9.56657i	−0.456407	−	0.669794i
$205$	−0.399523			−0.0279039
$206$		−	1.88836i		−	0.131569i
$207$	−8.02482	+	20.4163i	−0.557763	+	1.41903i
$208$			3.74859i			0.259918i
$209$	6.00000			0.415029
$210$	0.242280	+	0.355555i	0.0167189	+	0.0245356i
$211$			2.12329i			0.146174i	0.997326	+	0.0730868i	$0.0232850\pi$
$211$			2.12329i			0.146174i	−0.997326	+	0.0730868i	$0.976715\pi$
$212$		−	0.250155i		−	0.0171807i
$213$	9.94750	+	14.5983i	0.681591	+	1.00026i
$214$		−	1.98828i		−	0.135916i
$215$	−1.00417			−0.0684840
$216$	1.15238	+	5.06676i	0.0784093	+	0.344749i
$217$		−	22.9614i		−	1.55872i
$218$			9.53579i			0.645845i
$219$	11.0510	+	16.2177i	0.746756	+	1.09589i
$220$		−	0.150243i		−	0.0101294i
$221$	−25.0543			−1.68534
$222$	−0.648623	−	0.951877i	−0.0435327	−	0.0638858i
$223$	5.17553			0.346579			0.173290	−	0.984871i	$-0.444560\pi$
$223$	5.17553			0.346579			0.173290	+	0.984871i	$0.444560\pi$
$224$	2.48626			0.166121
$225$	5.47628	−	13.9324i	0.365085	−	0.928829i
$226$	−13.6203			−0.906012
$227$	29.3591			1.94863			0.974315	−	0.225190i	$-0.0723001\pi$
$227$	29.3591			1.94863			0.974315	+	0.225190i	$0.0723001\pi$
$228$	−5.71106	+	3.89160i	−0.378224	+	0.257727i
$229$		−	7.00153i		−	0.462674i	−0.972874	−	0.231337i	$-0.925690\pi$
$229$		−	7.00153i		−	0.462674i	0.972874	−	0.231337i	$-0.0743100\pi$
$230$			0.730582i			0.0481731i
$231$	−5.35138	+	3.64651i	−0.352095	+	0.239923i
$232$		−	3.18348i		−	0.209006i
$233$	24.8628			1.62882			0.814409	−	0.580292i	$-0.197061\pi$
$233$	24.8628			1.62882			0.814409	+	0.580292i	$0.197061\pi$
$234$	10.4663	+	4.11388i	0.684203	+	0.268933i
$235$			0.430096i			0.0280564i
$236$	−7.65780	+	0.598474i	−0.498480	+	0.0389574i
$237$	13.0692	−	8.90552i	0.848934	−	0.578476i
$238$			16.6174i			1.07714i
$239$			3.43288i			0.222055i	0.993817	+	0.111027i	$0.0354141\pi$
$239$			3.43288i			0.222055i	−0.993817	+	0.111027i	$0.964586\pi$
$240$	0.0974475	+	0.143008i	0.00629021	+	0.00923110i
$241$	8.12675			0.523490			0.261745	−	0.965137i	$-0.415702\pi$
$241$	8.12675			0.523490			0.261745	+	0.965137i	$0.415702\pi$
$242$	−8.73873			−0.561747
$243$	15.4114	+	2.34300i	0.988640	+	0.150303i
$244$			13.2188i			0.846249i
$245$			0.0817767i			0.00522452i
$246$	3.90011	+	5.72355i	0.248662	+	0.364920i
$247$			14.9569i			0.951688i
$248$		−	9.23530i		−	0.586442i
$249$	7.77785	−	5.29994i	0.492901	−	0.335870i
$250$		−	0.998122i		−	0.0631268i
$251$			19.2860i			1.21732i	0.793429	+	0.608662i	$0.208294\pi$
$251$			19.2860i			1.21732i	−0.793429	+	0.608662i	$0.791706\pi$
$252$	2.72855	−	6.94181i	0.171882	−	0.437293i
$253$	−10.9958			−0.691302
$254$	−1.08727			−0.0682211
$255$	−0.955814	+	0.651306i	−0.0598554	+	0.0407864i
$256$	1.00000			0.0625000
$257$			31.2661i			1.95033i	0.221483	+	0.975164i	$0.428910\pi$
$257$			31.2661i			1.95033i	−0.221483	+	0.975164i	$0.571090\pi$
$258$	9.80267	+	14.3858i	0.610287	+	0.895618i
$259$			1.65343i			0.102739i
$260$	0.374529			0.0232273
$261$	−8.88846	−	3.49370i	−0.550182	−	0.216255i
$262$	−2.06978			−0.127871
$263$			21.5816i			1.33078i	0.746496	+	0.665390i	$0.231735\pi$
$263$			21.5816i			1.33078i	−0.746496	+	0.665390i	$0.768265\pi$
$264$	−2.15238	+	1.46666i	−0.132470	+	0.0902667i
$265$	−0.0249935			−0.00153534
$266$	9.92024			0.608249
$267$	−11.7870	+	8.03185i	−0.721354	+	0.491541i
$268$			7.06709i			0.431691i
$269$	−1.12922			−0.0688500			−0.0344250	−	0.999407i	$-0.510960\pi$
$269$	−1.12922			−0.0688500			−0.0344250	+	0.999407i	$0.510960\pi$
$270$	0.506230	−	0.115136i	0.0308082	−	0.00700696i
$271$	−1.65329			−0.100430			−0.0502151	−	0.998738i	$-0.515991\pi$
$271$	−1.65329			−0.100430			−0.0502151	+	0.998738i	$0.515991\pi$
$272$			6.68366i			0.405256i
$273$	−9.09010	−	13.3400i	−0.550158	−	0.807376i
$274$		−	3.26816i		−	0.197437i
$275$	7.50375			0.452493
$276$	10.4663	−	7.13189i	0.629997	−	0.429289i
$277$	2.31824			0.139290			0.0696448	−	0.997572i	$-0.477813\pi$
$277$	2.31824			0.139290			0.0696448	+	0.997572i	$0.477813\pi$
$278$	16.2500			0.974609
$279$	−25.7855	−	10.1353i	−1.54374	−	0.606782i
$280$		−	0.248408i		−	0.0148452i
$281$		−	23.6300i		−	1.40965i	−0.709381	−	0.704825i	$-0.751026\pi$
$281$		−	23.6300i		−	1.40965i	0.709381	−	0.704825i	$-0.248974\pi$
$282$	6.16155	−	4.19857i	0.366915	−	0.250021i
$283$		−	23.8843i		−	1.41977i	−0.704317	−	0.709886i	$-0.748746\pi$
$283$		−	23.8843i		−	1.41977i	0.704317	−	0.709886i	$-0.251254\pi$
$284$		−	10.1991i		−	0.605203i
$285$	0.388817	+	0.570603i	0.0230316	+	0.0337996i
$286$			5.63696i			0.333320i
$287$		−	9.94194i		−	0.586854i
$288$	1.09745	−	2.79206i	0.0646677	−	0.164524i
$289$	−27.6713			−1.62773
$290$	−0.318067			−0.0186776
$291$	3.73873	+	5.48671i	0.219168	+	0.321637i
$292$		−	11.3305i		−	0.663065i
$293$			6.61014i			0.386168i	0.981182	+	0.193084i	$0.0618490\pi$
$293$			6.61014i			0.386168i	−0.981182	+	0.193084i	$0.938151\pi$
$294$	1.17153	−	0.798298i	0.0683250	−	0.0465577i
$295$	0.0597947	+	0.765105i	0.00348138	+	0.0445462i
$296$			0.665027i			0.0386539i
$297$	1.73289	+	7.61915i	0.100552	+	0.442108i
$298$	−4.42980			−0.256612
$299$		−	27.4107i		−	1.58520i
$300$	−7.14239	+	4.86693i	−0.412366	+	0.280993i
$301$		−	24.9884i		−	1.44031i
$302$		−	12.6194i		−	0.726162i
$303$	−13.9394	+	9.49851i	−0.800797	+	0.545675i
$304$	3.99002			0.228843
$305$	1.32072			0.0756241
$306$	18.6612	+	7.33497i	1.06679	+	0.419312i
$307$	−27.6453			−1.57780			−0.788901	−	0.614520i	$-0.789350\pi$
$307$	−27.6453			−1.57780			−0.788901	+	0.614520i	$0.789350\pi$
$308$	3.73873			0.213034
$309$	1.84178	+	2.70288i	0.104775	+	0.153762i
$310$	−0.922717			−0.0524068
$311$		−	23.5349i		−	1.33454i	−0.744814	−	0.667272i	$-0.767462\pi$
$311$		−	23.5349i		−	1.33454i	0.744814	−	0.667272i	$-0.232538\pi$
$312$	−3.65613	−	5.36550i	−0.206988	−	0.303761i
$313$			26.8677i			1.51866i	0.650709	+	0.759328i	$0.274472\pi$
$313$			26.8677i			1.51866i	−0.650709	+	0.759328i	$0.725528\pi$
$314$			15.4024i			0.869210i
$315$	−0.693569	−	0.272614i	−0.0390782	−	0.0153601i
$316$	−9.13074			−0.513645
$317$		−	32.1230i		−	1.80421i	−0.431518	−	0.902104i	$-0.642022\pi$
$317$		−	32.1230i		−	1.80421i	0.431518	−	0.902104i	$-0.357978\pi$
$318$	0.243984	+	0.358056i	0.0136820	+	0.0200788i
$319$		−	4.78716i		−	0.268030i
$320$		−	0.0999120i		−	0.00558525i
$321$	1.93923	+	2.84589i	0.108237	+	0.158842i
$322$	−18.1802			−1.01314
$323$			26.6679i			1.48384i
$324$	−6.59122	−	6.12828i	−0.366179	−	0.340460i
$325$			18.7055i			1.03760i
$326$	−11.2458			−0.622848
$327$	−9.30058	−	13.6489i	−0.514323	−	0.754787i
$328$		−	3.99875i		−	0.220794i
$329$	−10.7028			−0.590062
$330$	0.146537	+	0.215048i	0.00806660	+	0.0118380i
$331$	−19.7922			−1.08788			−0.543939	−	0.839125i	$-0.683068\pi$
$331$	−19.7922			−1.08788			−0.543939	+	0.839125i	$0.683068\pi$
$332$	−5.43398			−0.298228
$333$	1.85680	+	0.729832i	0.101752	+	0.0399946i
$334$		−	7.44685i		−	0.407474i
$335$	0.706087			0.0385776
$336$	−3.55868	+	2.42494i	−0.194142	+	0.132291i
$337$			13.2034i			0.719237i	0.933099	+	0.359618i	$0.117093\pi$
$337$			13.2034i			0.719237i	−0.933099	+	0.359618i	$0.882907\pi$
$338$	−1.05194			−0.0572180
$339$	19.4953	−	13.2844i	1.05884	−	0.721509i
$340$	0.667778			0.0362153
$341$		−	13.8876i		−	0.752056i
$342$	4.37883	−	11.1404i	0.236780	−	0.602403i
$343$	−19.4388			−1.04960
$344$		−	10.0506i		−	0.541891i
$345$	−0.712561	−	1.04571i	−0.0383630	−	0.0562991i
$346$	−1.87828			−0.100977
$347$	22.1634			1.18979			0.594897	−	0.803802i	$-0.297193\pi$
$347$	22.1634			1.18979			0.594897	+	0.803802i	$0.297193\pi$
$348$	3.10495	+	4.55663i	0.166443	+	0.244261i
$349$		−	4.57136i		−	0.244700i	−0.992487	−	0.122350i	$-0.960957\pi$
$349$		−	4.57136i		−	0.244700i	0.992487	−	0.122350i	$-0.0390430\pi$
$350$	12.4065			0.663156
$351$	−18.9932	+	4.31979i	−1.01378	+	0.230573i
$352$	1.50375			0.0801503
$353$	−15.9218			−0.847430			−0.423715	−	0.905796i	$-0.639274\pi$
$353$	−15.9218			−0.847430			−0.423715	+	0.905796i	$0.639274\pi$
$354$	10.3772	−	8.32553i	0.551540	−	0.442497i
$355$	−1.01901			−0.0540834
$356$	8.23497			0.436453
$357$	−16.2075	−	23.7850i	−0.857790	−	1.25884i
$358$	14.4415			0.763256
$359$		−	37.7987i		−	1.99494i	−0.0710832	−	0.997470i	$-0.522646\pi$
$359$		−	37.7987i		−	1.99494i	0.0710832	−	0.997470i	$-0.477354\pi$
$360$	−0.278960	−	0.109648i	−0.0147025	−	0.00577896i
$361$	−3.07976			−0.162093
$362$	−19.5756			−1.02887
$363$	12.5081	−	8.52318i	0.656503	−	0.447351i
$364$			9.31999i			0.488500i
$365$	−1.13205			−0.0592541
$366$	−12.8928	−	18.9206i	−0.673916	−	0.988995i
$367$			14.5489i			0.759445i	0.925100	+	0.379723i	$0.123981\pi$
$367$			14.5489i			0.759445i	−0.925100	+	0.379723i	$0.876019\pi$
$368$	−7.31226			−0.381178
$369$	−11.1647	−	4.38841i	−0.581214	−	0.228452i
$370$	0.0664441			0.00345427
$371$		−	0.621951i		−	0.0322901i
$372$	9.00751	+	13.2188i	0.467017	+	0.685364i
$373$	20.4733			1.06007			0.530033	−	0.847977i	$-0.322179\pi$
$373$	20.4733			1.06007			0.530033	+	0.847977i	$0.322179\pi$
$374$			10.0506i			0.519703i
$375$	0.973502	+	1.42865i	0.0502714	+	0.0737751i
$376$	−4.30475			−0.222001
$377$	11.9336			0.614609
$378$	2.86511	+	12.5973i	0.147365	+	0.647935i
$379$	−11.5722			−0.594425			−0.297213	−	0.954811i	$-0.596057\pi$
$379$	−11.5722			−0.594425			−0.297213	+	0.954811i	$0.596057\pi$
$380$		−	0.398650i		−	0.0204503i
$381$	1.55624	−	1.06045i	0.0797287	−	0.0543283i
$382$	2.00333			0.102499
$383$			10.0251i			0.512256i	0.966643	+	0.256128i	$0.0824469\pi$
$383$			10.0251i			0.512256i	−0.966643	+	0.256128i	$0.917553\pi$
$384$	−1.43134	+	0.975334i	−0.0730426	+	0.0497723i
$385$		−	0.373544i		−	0.0190375i
$386$	6.79102			0.345654
$387$	−28.0618	−	11.0300i	−1.42646	−	0.560685i
$388$		−	3.83328i		−	0.194605i
$389$			29.0531i			1.47305i	0.676410	+	0.736525i	$0.263535\pi$
$389$			29.0531i			1.47305i	−0.676410	+	0.736525i	$0.736465\pi$
$390$	−0.536077	+	0.365291i	−0.0271453	+	0.0184972i
$391$		−	48.8727i		−	2.47160i
$392$	−0.818487			−0.0413398
$393$	2.96255	−	2.01872i	0.149441	−	0.101831i
$394$			3.36517i			0.169535i
$395$			0.912271i			0.0459013i
$396$	1.65029	−	4.19857i	0.0829302	−	0.210986i
$397$		−	37.9877i		−	1.90655i	−0.302109	−	0.953273i	$-0.597691\pi$
$397$		−	37.9877i		−	1.90655i	0.302109	−	0.953273i	$-0.402309\pi$
$398$	−12.2483			−0.613951
$399$	−14.1992	+	9.67555i	−0.710849	+	0.484383i
$400$	4.99002			0.249501
$401$	−5.22747			−0.261047			−0.130524	−	0.991445i	$-0.541666\pi$
$401$	−5.22747			−0.261047			−0.130524	+	0.991445i	$0.541666\pi$
$402$	−6.89277	−	10.1154i	−0.343780	−	0.504509i
$403$	34.6194			1.72451
$404$	9.73873			0.484520
$405$	−0.612289	+	0.658541i	−0.0304249	+	0.0327232i
$406$		−	7.91497i		−	0.392813i
$407$			1.00004i			0.0495699i
$408$	−6.51880	−	9.56657i	−0.322729	−	0.473616i
$409$			19.5017i			0.964296i	0.876090	+	0.482148i	$0.160143\pi$
$409$			19.5017i			0.964296i	−0.876090	+	0.482148i	$0.839857\pi$
$410$	−0.399523			−0.0197310
$411$	3.18755	+	4.67784i	0.157230	+	0.230741i
$412$		−	1.88836i		−	0.0930330i
$413$	−19.0393	+	1.48797i	−0.936863	+	0.0732180i
$414$	−8.02482	+	20.4163i	−0.394398	+	1.00341i
$415$			0.542919i			0.0266509i
$416$			3.74859i			0.183790i
$417$	−23.2592	+	15.8492i	−1.13901	+	0.776137i
$418$	6.00000			0.293470
$419$	−28.2270			−1.37898			−0.689490	−	0.724295i	$-0.742165\pi$
$419$	−28.2270			−1.37898			−0.689490	+	0.724295i	$0.742165\pi$
$420$	0.242280	+	0.355555i	0.0118221	+	0.0173493i
$421$		−	12.3690i		−	0.602830i	−0.953493	−	0.301415i	$-0.902541\pi$
$421$		−	12.3690i		−	0.602830i	0.953493	−	0.301415i	$-0.0974589\pi$
$422$			2.12329i			0.103360i
$423$	−4.72424	+	12.0191i	−0.229700	+	0.584390i
$424$		−	0.250155i		−	0.0121486i
$425$			33.3516i			1.61779i
$426$	9.94750	+	14.5983i	0.481958	+	0.707290i
$427$			32.8655i			1.59047i
$428$		−	1.98828i		−	0.0961069i
$429$	−5.49791	−	8.06838i	−0.265442	−	0.389545i
$430$	−1.00417			−0.0484255
$431$	15.4958			0.746406			0.373203	−	0.927750i	$-0.378259\pi$
$431$	15.4958			0.746406			0.373203	+	0.927750i	$0.378259\pi$
$432$	1.15238	+	5.06676i	0.0554437	+	0.243774i
$433$	24.9628			1.19963			0.599817	−	0.800137i	$-0.295240\pi$
$433$	24.9628			1.19963			0.599817	+	0.800137i	$0.295240\pi$
$434$		−	22.9614i		−	1.10218i
$435$	0.455261	−	0.310222i	0.0218281	−	0.0148740i
$436$			9.53579i			0.456682i
$437$	−29.1760			−1.39568
$438$	11.0510	+	16.2177i	0.528036	+	0.774912i
$439$	40.6897			1.94201			0.971006	−	0.239055i	$-0.0768376\pi$
$439$	40.6897			1.94201			0.971006	+	0.239055i	$0.0768376\pi$
$440$		−	0.150243i		−	0.00716255i
$441$	−0.898247	+	2.28527i	−0.0427737	+	0.108822i
$442$	−25.0543			−1.19171
$443$	32.3516			1.53707			0.768535	−	0.639808i	$-0.220986\pi$
$443$	32.3516			1.53707			0.768535	+	0.639808i	$0.220986\pi$
$444$	−0.648623	−	0.951877i	−0.0307823	−	0.0451741i
$445$		−	0.822772i		−	0.0390032i
$446$	5.17553			0.245068
$447$	6.34054	−	4.32054i	0.299897	−	0.204354i
$448$	2.48626			0.117465
$449$		−	29.6661i		−	1.40003i	−0.714129	−	0.700014i	$-0.753177\pi$
$449$		−	29.6661i		−	1.40003i	0.714129	−	0.700014i	$-0.246823\pi$
$450$	5.47628	−	13.9324i	0.258154	−	0.656781i
$451$		−	6.01313i		−	0.283147i
$452$	−13.6203			−0.640647
$453$	12.3081	+	18.0625i	0.578284	+	0.848652i
$454$	29.3591			1.37789
$455$	0.931179			0.0436543
$456$	−5.71106	+	3.89160i	−0.267445	+	0.182241i
$457$		−	15.2368i		−	0.712747i	−0.934343	−	0.356374i	$-0.884013\pi$
$457$		−	15.2368i		−	0.712747i	0.934343	−	0.356374i	$-0.115987\pi$
$458$		−	7.00153i		−	0.327160i
$459$	−33.8645	+	7.70209i	−1.58066	+	0.359503i
$460$			0.730582i			0.0340636i
$461$			19.8024i			0.922290i	0.887325	+	0.461145i	$0.152561\pi$
$461$			19.8024i			0.922290i	−0.887325	+	0.461145i	$0.847439\pi$
$462$	−5.35138	+	3.64651i	−0.248969	+	0.169651i
$463$			22.7494i			1.05725i	0.848854	+	0.528627i	$0.177293\pi$
$463$			22.7494i			1.05725i	−0.848854	+	0.528627i	$0.822707\pi$
$464$		−	3.18348i		−	0.147789i
$465$	1.32072	−	0.899957i	0.0612469	−	0.0417345i
$466$	24.8628			1.15175
$467$	10.9522			0.506809			0.253404	−	0.967360i	$-0.418450\pi$
$467$	10.9522			0.506809			0.253404	+	0.967360i	$0.418450\pi$
$468$	10.4663	+	4.11388i	0.483805	+	0.190164i
$469$			17.5707i			0.811337i
$470$			0.430096i			0.0198389i
$471$	−15.0225	−	22.0461i	−0.692201	−	1.01583i
$472$	−7.65780	+	0.598474i	−0.352479	+	0.0275470i
$473$		−	15.1136i		−	0.694923i
$474$	13.0692	−	8.90552i	0.600287	−	0.409044i
$475$	19.9103			0.913545
$476$			16.6174i			0.761655i
$477$	−0.698448	−	0.274532i	−0.0319797	−	0.0125699i
$478$			3.43288i			0.157016i
$479$			29.5038i			1.34806i	0.738702	+	0.674032i	$0.235439\pi$
$479$			29.5038i			1.34806i	−0.738702	+	0.674032i	$0.764561\pi$
$480$	0.0974475	+	0.143008i	0.00444785	+	0.00652737i
$481$	−2.49291			−0.113667
$482$	8.12675			0.370163
$483$	26.0220	−	17.7318i	1.18404	−	0.806824i
$484$	−8.73873			−0.397215
$485$	−0.382990			−0.0173907
$486$	15.4114	+	2.34300i	0.699074	+	0.106280i
$487$	14.4863			0.656435			0.328218	−	0.944602i	$-0.393552\pi$
$487$	14.4863			0.656435			0.328218	+	0.944602i	$0.393552\pi$
$488$			13.2188i			0.598388i
$489$	16.0965	−	10.9684i	0.727911	−	0.496009i
$490$			0.0817767i			0.00369429i
$491$			18.1129i			0.817423i	0.912664	+	0.408711i	$0.134022\pi$
$491$			18.1129i			0.817423i	−0.912664	+	0.408711i	$0.865978\pi$
$492$	3.90011	+	5.72355i	0.175831	+	0.258038i
$493$	21.2773			0.958281
$494$			14.9569i			0.672945i
$495$	−0.419487	−	0.164884i	−0.0188546	−	0.00741097i
$496$		−	9.23530i		−	0.414677i
$497$		−	25.3576i		−	1.13744i
$498$	7.77785	−	5.29994i	0.348534	−	0.237496i
$499$	21.6305			0.968314			0.484157	−	0.874981i	$-0.339126\pi$
$499$	21.6305			0.968314			0.484157	+	0.874981i	$0.339126\pi$
$500$		−	0.998122i		−	0.0446374i
$501$	7.26317	+	10.6590i	0.324494	+	0.476207i
$502$			19.2860i			0.860778i
$503$	−34.7181			−1.54801			−0.774003	−	0.633182i	$-0.781748\pi$
$503$	−34.7181			−1.54801			−0.774003	+	0.633182i	$0.781748\pi$
$504$	2.72855	−	6.94181i	0.121539	−	0.309213i
$505$		−	0.973015i		−	0.0432986i
$506$	−10.9958			−0.488824
$507$	1.50568	−	1.02599i	0.0668697	−	0.0455660i
$508$	−1.08727			−0.0482396
$509$	−40.8081			−1.80879			−0.904393	−	0.426701i	$-0.859676\pi$
$509$	−40.8081			−1.80879			−0.904393	+	0.426701i	$0.859676\pi$
$510$	−0.955814	+	0.651306i	−0.0423242	+	0.0288403i
$511$		−	28.1705i		−	1.24619i
$512$	1.00000			0.0441942
$513$	4.59800	+	20.2165i	0.203007	+	0.892578i
$514$			31.2661i			1.37909i
$515$	−0.188670			−0.00831380
$516$	9.80267	+	14.3858i	0.431538	+	0.633297i
$517$	−6.47328			−0.284695
$518$			1.65343i			0.0726477i
$519$	2.68845	−	1.83195i	0.118010	−	0.0804138i
$520$	0.374529			0.0164242
$521$			19.7972i			0.867330i	0.901074	+	0.433665i	$0.142780\pi$
$521$			19.7972i			0.867330i	−0.901074	+	0.433665i	$0.857220\pi$
$522$	−8.88846	−	3.49370i	−0.389038	−	0.152915i
$523$	−28.8761			−1.26267			−0.631333	−	0.775512i	$-0.717492\pi$
$523$	−28.8761			−1.26267			−0.631333	+	0.775512i	$0.717492\pi$
$524$	−2.06978			−0.0904186
$525$	−17.7579	+	12.1005i	−0.775018	+	0.528108i
$526$			21.5816i			0.941003i
$527$	61.7256			2.68881
$528$	−2.15238	+	1.46666i	−0.0936701	+	0.0638282i
$529$	30.4691			1.32474
$530$	−0.0249935			−0.00108565
$531$	−6.73305	+	22.0378i	−0.292190	+	0.956360i
$532$	9.92024			0.430097
$533$	14.9897			0.649275
$534$	−11.7870	+	8.03185i	−0.510074	+	0.347572i
$535$	−0.198652			−0.00858850
$536$			7.06709i			0.305252i
$537$	−20.6706	+	14.0853i	−0.892003	+	0.607824i
$538$	−1.12922			−0.0486843
$539$	−1.23080			−0.0530144
$540$	0.506230	−	0.115136i	0.0217847	−	0.00495467i
$541$			8.25440i			0.354884i	0.984131	+	0.177442i	$0.0567823\pi$
$541$			8.25440i			0.354884i	−0.984131	+	0.177442i	$0.943218\pi$
$542$	−1.65329			−0.0710149
$543$	28.0192	−	19.0927i	1.20242	−	0.819346i
$544$			6.68366i			0.286560i
$545$	0.952739			0.0408109
$546$	−9.09010	−	13.3400i	−0.389021	−	0.570901i
$547$	−11.9184			−0.509595			−0.254798	−	0.966994i	$-0.582009\pi$
$547$	−11.9184			−0.509595			−0.254798	+	0.966994i	$0.582009\pi$
$548$		−	3.26816i		−	0.139609i
$549$	36.9078	+	14.5070i	1.57519	+	0.619142i
$550$	7.50375			0.319961
$551$		−	12.7021i		−	0.541129i
$552$	10.4663	−	7.13189i	0.445475	−	0.303554i
$553$	−22.7014			−0.965364
$554$	2.31824			0.0984927
$555$	−0.0951039	+	0.0648052i	−0.00403694	+	0.00275083i
$556$	16.2500			0.689153
$557$			39.6450i			1.67981i	0.542731	+	0.839907i	$0.317390\pi$
$557$			39.6450i			1.67981i	−0.542731	+	0.839907i	$0.682610\pi$
$558$	−25.7855	−	10.1353i	−1.09159	−	0.429060i
$559$	37.6755			1.59350
$560$		−	0.248408i		−	0.0104971i
$561$	−9.80267	−	14.3858i	−0.413869	−	0.607367i
$562$		−	23.6300i		−	0.996773i
$563$	13.2738			0.559423			0.279711	−	0.960084i	$-0.409761\pi$
$563$	13.2738			0.559423			0.279711	+	0.960084i	$0.409761\pi$
$564$	6.16155	−	4.19857i	0.259448	−	0.176792i
$565$			1.36084i			0.0572508i
$566$		−	23.8843i		−	1.00393i
$567$	−16.3875	−	15.2365i	−0.688211	−	0.639874i
$568$		−	10.1991i		−	0.427943i
$569$	36.7964			1.54258			0.771292	−	0.636481i	$-0.219611\pi$
$569$	36.7964			1.54258			0.771292	+	0.636481i	$0.219611\pi$
$570$	0.388817	+	0.570603i	0.0162858	+	0.0238999i
$571$			35.3960i			1.48128i	0.671904	+	0.740638i	$0.265477\pi$
$571$			35.3960i			1.48128i	−0.671904	+	0.740638i	$0.734523\pi$
$572$			5.63696i			0.235693i
$573$	−2.86744	+	1.95392i	−0.119789	+	0.0816261i
$574$		−	9.94194i		−	0.414969i
$575$	−36.4883			−1.52167
$576$	1.09745	−	2.79206i	0.0457270	−	0.116336i
$577$	−6.36488			−0.264973			−0.132487	−	0.991185i	$-0.542296\pi$
$577$	−6.36488			−0.264973			−0.132487	+	0.991185i	$0.542296\pi$
$578$	−27.6713			−1.15098
$579$	−9.72023	+	6.62351i	−0.403959	+	0.275264i
$580$	−0.318067			−0.0132070
$581$	−13.5103			−0.560502
$582$	3.73873	+	5.48671i	0.154975	+	0.227432i
$583$		−	0.376171i		−	0.0155794i
$584$		−	11.3305i		−	0.468858i
$585$	0.411026	−	1.04571i	0.0169938	−	0.0432347i
$586$			6.61014i			0.273062i
$587$	33.9804			1.40252			0.701260	−	0.712906i	$-0.252621\pi$
$587$	33.9804			1.40252			0.701260	+	0.712906i	$0.252621\pi$
$588$	1.17153	−	0.798298i	0.0483131	−	0.0329213i
$589$		−	36.8490i		−	1.51834i
$590$	0.0597947	+	0.765105i	0.00246171	+	0.0314989i
$591$	−3.28216	−	4.81668i	−0.135010	−	0.198132i
$592$			0.665027i			0.0273324i
$593$		−	18.0122i		−	0.739673i	−0.929097	−	0.369836i	$-0.879414\pi$
$593$		−	18.0122i		−	0.739673i	0.929097	−	0.369836i	$-0.120586\pi$
$594$	1.73289	+	7.61915i	0.0711013	+	0.312618i
$595$	1.66027			0.0680645
$596$	−4.42980			−0.181452
$597$	17.5314	−	11.9462i	0.717513	−	0.488924i
$598$		−	27.4107i		−	1.12091i
$599$			8.90046i			0.363663i	0.983330	+	0.181832i	$0.0582025\pi$
$599$			8.90046i			0.363663i	−0.983330	+	0.181832i	$0.941797\pi$
$600$	−7.14239	+	4.86693i	−0.291587	+	0.198692i
$601$			23.4646i			0.957140i	0.878050	+	0.478570i	$0.158845\pi$
$601$			23.4646i			0.957140i	−0.878050	+	0.478570i	$0.841155\pi$
$602$		−	24.9884i		−	1.01845i
$603$	19.7317	+	7.75576i	0.803539	+	0.315839i
$604$		−	12.6194i		−	0.513474i
$605$			0.873103i			0.0354967i
$606$	−13.9394	+	9.49851i	−0.566249	+	0.385851i
$607$	−32.2918			−1.31068			−0.655341	−	0.755333i	$-0.727475\pi$
$607$	−32.2918			−1.31068			−0.655341	+	0.755333i	$0.727475\pi$
$608$	3.99002			0.161817
$609$	7.71974	+	11.3290i	0.312819	+	0.459073i
$610$	1.32072			0.0534743
$611$		−	16.1368i		−	0.652823i
$612$	18.6612	+	7.33497i	0.754334	+	0.296498i
$613$			13.0996i			0.529088i	0.964374	+	0.264544i	$0.0852215\pi$
$613$			13.0996i			0.529088i	−0.964374	+	0.264544i	$0.914778\pi$
$614$	−27.6453			−1.11567
$615$	0.571851	−	0.389668i	0.0230593	−	0.0157129i
$616$	3.73873			0.150638
$617$		−	24.6994i		−	0.994359i	−0.867648	−	0.497180i	$-0.834369\pi$
$617$		−	24.6994i		−	0.994359i	0.867648	−	0.497180i	$-0.165631\pi$
$618$	1.84178	+	2.70288i	0.0740875	+	0.108726i
$619$	14.6113			0.587278			0.293639	−	0.955916i	$-0.405134\pi$
$619$	14.6113			0.587278			0.293639	+	0.955916i	$0.405134\pi$
$620$	−0.922717			−0.0370572
$621$	−8.42647	−	37.0494i	−0.338143	−	1.48674i
$622$		−	23.5349i		−	0.943665i
$623$	20.4743			0.820287
$624$	−3.65613	−	5.36550i	−0.146362	−	0.214792i
$625$	24.8504			0.994015
$626$			26.8677i			1.07385i
$627$	−8.58802	+	5.85200i	−0.342972	+	0.233707i
$628$			15.4024i			0.614624i
$629$	−4.44481			−0.177226
$630$	−0.693569	−	0.272614i	−0.0276325	−	0.0108612i
$631$	−22.1980			−0.883690			−0.441845	−	0.897091i	$-0.645676\pi$
$631$	−22.1980			−0.883690			−0.441845	+	0.897091i	$0.645676\pi$
$632$	−9.13074			−0.363202
$633$	−2.07092	−	3.03915i	−0.0823117	−	0.120795i
$634$		−	32.1230i		−	1.27577i
$635$			0.108631i			0.00431088i
$636$	0.243984	+	0.358056i	0.00967461	+	0.0141978i
$637$		−	3.06817i		−	0.121565i
$638$		−	4.78716i		−	0.189526i
$639$	−28.4764	−	11.1929i	−1.12651	−	0.442786i
$640$		−	0.0999120i		−	0.00394937i
$641$		−	7.03082i		−	0.277701i	−0.990313	−	0.138850i	$-0.955659\pi$
$641$		−	7.03082i		−	0.277701i	0.990313	−	0.138850i	$-0.0443407\pi$
$642$	1.93923	+	2.84589i	0.0765354	+	0.112318i
$643$	16.0565			0.633205			0.316603	−	0.948558i	$-0.397458\pi$
$643$	16.0565			0.633205			0.316603	+	0.948558i	$0.397458\pi$
$644$	−18.1802			−0.716401
$645$	1.43731	−	0.979404i	0.0565940	−	0.0385640i
$646$			26.6679i			1.04924i
$647$			22.9346i			0.901651i	0.892612	+	0.450825i	$0.148870\pi$
$647$			22.9346i			0.901651i	−0.892612	+	0.450825i	$0.851130\pi$
$648$	−6.59122	−	6.12828i	−0.258927	−	0.240742i
$649$	−11.5154	+	0.899957i	−0.452020	+	0.0353264i
$650$			18.7055i			0.733692i
$651$	22.3950	+	32.8655i	0.877731	+	1.28810i
$652$	−11.2458			−0.440420
$653$		−	32.5353i		−	1.27321i	−0.771192	−	0.636603i	$-0.780339\pi$
$653$		−	32.5353i		−	1.27321i	0.771192	−	0.636603i	$-0.219661\pi$
$654$	−9.30058	−	13.6489i	−0.363681	−	0.533715i
$655$			0.206795i			0.00808017i
$656$		−	3.99875i		−	0.156125i
$657$	−31.6354	−	12.4346i	−1.23421	−	0.485120i
$658$	−10.7028			−0.417237
$659$	20.1685			0.785654			0.392827	−	0.919612i	$-0.371497\pi$
$659$	20.1685			0.785654			0.392827	+	0.919612i	$0.371497\pi$
$660$	0.146537	+	0.215048i	0.00570394	+	0.00837074i
$661$	1.93525			0.0752726			0.0376363	−	0.999292i	$-0.488017\pi$
$661$	1.93525			0.0752726			0.0376363	+	0.999292i	$0.488017\pi$
$662$	−19.7922			−0.769245
$663$	35.8612	−	24.4363i	1.39273	−	0.949028i
$664$	−5.43398			−0.210879
$665$		−	0.991151i		−	0.0384352i
$666$	1.85680	+	0.729832i	0.0719494	+	0.0282804i
$667$			23.2784i			0.901343i
$668$		−	7.44685i		−	0.288127i
$669$	−7.40792	+	5.04787i	−0.286407	+	0.195162i
$670$	0.706087			0.0272785
$671$			19.8778i			0.767376i
$672$	−3.55868	+	2.42494i	−0.137279	+	0.0935440i
$673$		−	16.8416i		−	0.649195i	−0.945852	−	0.324597i	$-0.894771\pi$
$673$		−	16.8416i		−	0.649195i	0.945852	−	0.324597i	$-0.105229\pi$
$674$			13.2034i			0.508577i
$675$	5.75038	+	25.2832i	0.221332	+	0.973151i
$676$	−1.05194			−0.0404593
$677$		−	30.0998i		−	1.15683i	−0.815743	−	0.578415i	$-0.803672\pi$
$677$		−	30.0998i		−	1.15683i	0.815743	−	0.578415i	$-0.196328\pi$
$678$	19.4953	−	13.2844i	0.748712	−	0.510184i
$679$		−	9.53055i		−	0.365749i
$680$	0.667778			0.0256081
$681$	−42.0227	+	28.6349i	−1.61031	+	1.09729i
$682$		−	13.8876i		−	0.531784i
$683$	−20.1948			−0.772734			−0.386367	−	0.922345i	$-0.626270\pi$
$683$	−20.1948			−0.772734			−0.386367	+	0.922345i	$0.626270\pi$
$684$	4.37883	−	11.1404i	0.167429	−	0.425963i
$685$	−0.326529			−0.0124760
$686$	−19.4388			−0.742178
$687$	6.82883	+	10.0215i	0.260536	+	0.382346i
$688$		−	10.0506i		−	0.383175i
$689$	0.937728			0.0357246
$690$	−0.712561	−	1.04571i	−0.0271267	−	0.0398094i
$691$			33.9577i			1.29181i	0.763417	+	0.645906i	$0.223520\pi$
$691$			33.9577i			1.29181i	−0.763417	+	0.645906i	$0.776480\pi$
$692$	−1.87828			−0.0714016
$693$	4.10306	−	10.4388i	0.155862	−	0.396536i
$694$	22.1634			0.841311
$695$		−	1.62357i		−	0.0615854i
$696$	3.10495	+	4.55663i	0.117693	+	0.172718i
$697$	26.7263			1.01233
$698$		−	4.57136i		−	0.173029i
$699$	−35.5871	+	24.2496i	−1.34603	+	0.917202i
$700$	12.4065			0.468922
$701$	3.59083			0.135624			0.0678119	−	0.997698i	$-0.478398\pi$
$701$	3.59083			0.135624			0.0678119	+	0.997698i	$0.478398\pi$
$702$	−18.9932	+	4.31979i	−0.716852	+	0.163040i
$703$			2.65347i			0.100077i
$704$	1.50375			0.0566748
$705$	−0.419487	−	0.615612i	−0.0157988	−	0.0231853i
$706$	−15.9218			−0.599223
$707$	24.2131			0.910626
$708$	10.3772	−	8.32553i	0.389998	−	0.312892i
$709$	11.3787			0.427337			0.213668	−	0.976906i	$-0.431459\pi$
$709$	11.3787			0.427337			0.213668	+	0.976906i	$0.431459\pi$
$710$	−1.01901			−0.0382427
$711$	−10.0205	+	25.4936i	−0.375799	+	0.956085i
$712$	8.23497			0.308619
$713$			67.5309i			2.52905i
$714$	−16.2075	−	23.7850i	−0.606549	−	0.890132i
$715$	0.563199			0.0210625
$716$	14.4415			0.539703
$717$	−3.34821	−	4.91361i	−0.125041	−	0.183502i
$718$		−	37.7987i		−	1.41064i
$719$	−6.27578			−0.234047			−0.117023	−	0.993129i	$-0.537335\pi$
$719$	−6.27578			−0.234047			−0.117023	+	0.993129i	$0.537335\pi$
$720$	−0.278960	−	0.109648i	−0.0103962	−	0.00408634i
$721$		−	4.69497i		−	0.174850i
$722$	−3.07976			−0.114617
$723$	−11.6321	+	7.92629i	−0.432603	+	0.294782i
$724$	−19.5756			−0.727520
$725$		−	15.8856i		−	0.589977i
$726$	12.5081	−	8.52318i	0.464218	−	0.316325i
$727$	10.8245			0.401457			0.200729	−	0.979647i	$-0.435669\pi$
$727$	10.8245			0.401457			0.200729	+	0.979647i	$0.435669\pi$
$728$			9.31999i			0.345422i
$729$	−24.3441	+	11.6776i	−0.901632	+	0.432504i
$730$	−1.13205			−0.0418990
$731$	67.1746			2.48454
$732$	−12.8928	−	18.9206i	−0.476530	−	0.699325i
$733$	−17.4775			−0.645545			−0.322772	−	0.946477i	$-0.604615\pi$
$733$	−17.4775			−0.645545			−0.322772	+	0.946477i	$0.604615\pi$
$734$			14.5489i			0.537009i
$735$	−0.0797595	−	0.117050i	−0.00294198	−	0.00431745i
$736$	−7.31226			−0.269533
$737$			10.6272i			0.391456i
$738$	−11.1647	−	4.38841i	−0.410980	−	0.161540i
$739$			16.8480i			0.619762i	0.950775	+	0.309881i	$0.100289\pi$
$739$			16.8480i			0.619762i	−0.950775	+	0.309881i	$0.899711\pi$
$740$	0.0664441			0.00244253
$741$	−14.5880	−	21.4084i	−0.535904	−	0.786458i
$742$		−	0.621951i		−	0.0228325i
$743$			19.6522i			0.720968i	0.932765	+	0.360484i	$0.117388\pi$
$743$			19.6522i			0.720968i	−0.932765	+	0.360484i	$0.882612\pi$
$744$	9.00751	+	13.2188i	0.330231	+	0.484626i
$745$			0.442590i			0.0162153i
$746$	20.4733			0.749580
$747$	−5.96350	+	15.1720i	−0.218193	+	0.555114i
$748$			10.0506i			0.367485i
$749$		−	4.94338i		−	0.180627i
$750$	0.973502	+	1.42865i	0.0355473	+	0.0521669i
$751$			24.7561i			0.903362i	0.892179	+	0.451681i	$0.149176\pi$
$751$			24.7561i			0.903362i	−0.892179	+	0.451681i	$0.850824\pi$
$752$	−4.30475			−0.156978
$753$	−18.8103	−	27.6048i	−0.685487	−	1.00598i
$754$	11.9336			0.434594
$755$	−1.26082			−0.0458861
$756$	2.86511	+	12.5973i	0.104203	+	0.458159i
$757$	−37.6335			−1.36781			−0.683907	−	0.729569i	$-0.739721\pi$
$757$	−37.6335			−1.36781			−0.683907	+	0.729569i	$0.739721\pi$
$758$	−11.5722			−0.420322
$759$	15.7387	−	10.7246i	0.571280	−	0.389278i
$760$		−	0.398650i		−	0.0144606i
$761$		−	0.789332i		−	0.0286133i	−0.999898	−	0.0143066i	$-0.995446\pi$
$761$		−	0.789332i		−	0.0286133i	0.999898	−	0.0143066i	$-0.00455410\pi$
$762$	1.55624	−	1.06045i	0.0563767	−	0.0384159i
$763$			23.7085i			0.858305i
$764$	2.00333			0.0724780
$765$	0.732851	−	1.86448i	0.0264963	−	0.0674103i
$766$			10.0251i			0.362220i
$767$	−2.24344	−	28.7059i	−0.0810058	−	1.03651i
$768$	−1.43134	+	0.975334i	−0.0516489	+	0.0351943i
$769$			16.3975i			0.591308i	0.955295	+	0.295654i	$0.0955376\pi$
$769$			16.3975i			0.591308i	−0.955295	+	0.295654i	$0.904462\pi$
$770$		−	0.373544i		−	0.0134616i
$771$	−30.4949	−	44.7524i	−1.09825	−	1.61172i
$772$	6.79102			0.244414
$773$	−23.4991			−0.845205			−0.422603	−	0.906315i	$-0.638883\pi$
$773$	−23.4991			−0.845205			−0.422603	+	0.906315i	$0.638883\pi$
$774$	−28.0618	−	11.0300i	−1.00866	−	0.396464i
$775$		−	46.0843i		−	1.65540i
$776$		−	3.83328i		−	0.137607i
$777$	−1.61265	−	2.36662i	−0.0578535	−	0.0849020i
$778$			29.0531i			1.04160i
$779$		−	15.9551i		−	0.571650i
$780$	−0.536077	+	0.365291i	−0.0191946	+	0.0130795i
$781$		−	15.3369i		−	0.548797i
$782$		−	48.8727i		−	1.74768i
$783$	16.1299	−	3.66856i	0.576436	−	0.131104i
$784$	−0.818487			−0.0292317
$785$	1.53889			0.0549252
$786$	2.96255	−	2.01872i	0.105671	−	0.0720055i
$787$	−24.2500			−0.864419			−0.432209	−	0.901773i	$-0.642266\pi$
$787$	−24.2500			−0.864419			−0.432209	+	0.901773i	$0.642266\pi$
$788$			3.36517i			0.119879i
$789$	−21.0493	−	30.8905i	−0.749374	−	1.09973i
$790$			0.912271i			0.0324571i
$791$	−33.8638			−1.20406
$792$	1.65029	−	4.19857i	0.0586405	−	0.149190i
$793$	−49.5520			−1.75964
$794$		−	37.9877i		−	1.34813i
$795$	0.0357740	−	0.0243770i	0.00126877	−	0.000864562i
$796$	−12.2483			−0.434129
$797$	16.8858			0.598125			0.299063	−	0.954233i	$-0.403326\pi$
$797$	16.8858			0.598125			0.299063	+	0.954233i	$0.403326\pi$
$798$	−14.1992	+	9.67555i	−0.502646	+	0.342511i
$799$		−	28.7715i		−	1.01786i
$800$	4.99002			0.176424
$801$	9.03745	−	22.9926i	0.319323	−	0.812402i
$802$	−5.22747			−0.184588
$803$		−	17.0382i		−	0.601266i
$804$	−6.89277	−	10.1154i	−0.243089	−	0.356742i
$805$			1.81642i			0.0640204i
$806$	34.6194			1.21942
$807$	1.61630	−	1.10137i	0.0568964	−	0.0387701i
$808$	9.73873			0.342607
$809$	38.5731			1.35616			0.678079	−	0.734989i	$-0.262813\pi$
$809$	38.5731			1.35616			0.678079	+	0.734989i	$0.262813\pi$
$810$	−0.612289	+	0.658541i	−0.0215136	+	0.0231388i
$811$		−	12.1112i		−	0.425282i	−0.977130	−	0.212641i	$-0.931794\pi$
$811$		−	12.1112i		−	0.425282i	0.977130	−	0.212641i	$-0.0682065\pi$
$812$		−	7.91497i		−	0.277761i
$813$	2.36641	−	1.61251i	0.0829937	−	0.0565532i
$814$			1.00004i			0.0350512i
$815$			1.12359i			0.0393577i
$816$	−6.51880	−	9.56657i	−0.228204	−	0.334897i
$817$		−	40.1020i		−	1.40299i
$818$			19.5017i			0.681860i
$819$	26.0220	+	10.2282i	0.909282	+	0.357402i
$820$	−0.399523			−0.0139519
$821$	−20.9298			−0.730454			−0.365227	−	0.930918i	$-0.619009\pi$
$821$	−20.9298			−0.730454			−0.365227	+	0.930918i	$0.619009\pi$
$822$	3.18755	+	4.67784i	0.111179	+	0.163159i
$823$			8.57928i			0.299055i	0.988758	+	0.149527i	$0.0477752\pi$
$823$			8.57928i			0.299055i	−0.988758	+	0.149527i	$0.952225\pi$
$824$		−	1.88836i		−	0.0657843i
$825$	−10.7404	+	7.31866i	−0.373933	+	0.254803i
$826$	−19.0393	+	1.48797i	−0.662462	+	0.0517730i
$827$		−	15.5408i		−	0.540406i	−0.962803	−	0.270203i	$-0.912909\pi$
$827$		−	15.5408i		−	0.540406i	0.962803	−	0.270203i	$-0.0870908\pi$
$828$	−8.02482	+	20.4163i	−0.278882	+	0.709515i
$829$	41.6019			1.44489			0.722447	−	0.691426i	$-0.243017\pi$
$829$	41.6019			1.44489			0.722447	+	0.691426i	$0.243017\pi$
$830$			0.542919i			0.0188450i
$831$	−3.31818	+	2.26106i	−0.115107	+	0.0784353i
$832$			3.74859i			0.129959i
$833$		−	5.47049i		−	0.189541i
$834$	−23.2592	+	15.8492i	−0.805400	+	0.548812i
$835$	−0.744030			−0.0257482
$836$	6.00000			0.207514
$837$	46.7930	−	10.6425i	1.61740	−	0.367860i
$838$	−28.2270			−0.975086
$839$	−28.1769			−0.972774			−0.486387	−	0.873744i	$-0.661685\pi$
$839$	−28.1769			−0.972774			−0.486387	+	0.873744i	$0.661685\pi$
$840$	0.242280	+	0.355555i	0.00835947	+	0.0122678i
$841$	18.8655			0.650534
$842$		−	12.3690i		−	0.426265i
$843$	23.0472	+	33.8225i	0.793787	+	1.16491i
$844$			2.12329i			0.0730868i
$845$			0.105101i			0.00361560i
$846$	−4.72424	+	12.0191i	−0.162423	+	0.413226i
$847$	−21.7268			−0.746541
$848$		−	0.250155i		−	0.00859035i
$849$	23.2951	+	34.1864i	0.799487	+	1.17327i
$850$			33.3516i			1.14395i
$851$		−	4.86285i		−	0.166696i
$852$	9.94750	+	14.5983i	0.340796	+	0.500129i
$853$	−20.7376			−0.710043			−0.355021	−	0.934858i	$-0.615526\pi$
$853$	−20.7376			−0.710043			−0.355021	+	0.934858i	$0.615526\pi$
$854$			32.8655i			1.12463i
$855$	−1.11306	−	0.437498i	−0.0380657	−	0.0149621i
$856$		−	1.98828i		−	0.0679579i
$857$	2.80382			0.0957768			0.0478884	−	0.998853i	$-0.484751\pi$
$857$	2.80382			0.0957768			0.0478884	+	0.998853i	$0.484751\pi$
$858$	−5.49791	−	8.06838i	−0.187696	−	0.275450i
$859$			8.56652i			0.292286i	0.989263	+	0.146143i	$0.0466859\pi$
$859$			8.56652i			0.292286i	−0.989263	+	0.146143i	$0.953314\pi$
$860$	−1.00417			−0.0342420
$861$	9.69671	+	14.2303i	0.330463	+	0.484966i
$862$	15.4958			0.527789
$863$	−18.8863			−0.642897			−0.321448	−	0.946927i	$-0.604170\pi$
$863$	−18.8863			−0.642897			−0.321448	+	0.946927i	$0.604170\pi$
$864$	1.15238	+	5.06676i	0.0392046	+	0.172375i
$865$			0.187663i			0.00638073i
$866$	24.9628			0.848269
$867$	39.6070	−	26.9888i	1.34512	−	0.916587i
$868$		−	22.9614i		−	0.779361i
$869$	−13.7304			−0.465771
$870$	0.455261	−	0.310222i	0.0154348	−	0.0105175i
$871$	−26.4916			−0.897635
$872$			9.53579i			0.322923i
$873$	−10.7028	−	4.20682i	−0.362233	−	0.142379i
$874$	−29.1760			−0.986894
$875$		−	2.48160i		−	0.0838933i
$876$	11.0510	+	16.2177i	0.373378	+	0.547945i
$877$	−43.7408			−1.47702			−0.738510	−	0.674242i	$-0.764470\pi$
$877$	−43.7408			−1.47702			−0.738510	+	0.674242i	$0.764470\pi$
$878$	40.6897			1.37321
$879$	−6.44709	−	9.46133i	−0.217455	−	0.319123i
$880$		−	0.150243i		−	0.00506469i
$881$	26.5001			0.892811			0.446405	−	0.894831i	$-0.352704\pi$
$881$	26.5001			0.892811			0.446405	+	0.894831i	$0.352704\pi$
$882$	−0.898247	+	2.28527i	−0.0302455	+	0.0769489i
$883$	0.00682396			0.000229645			0.000114822	−	1.00000i	$-0.499963\pi$
$883$	0.00682396			0.000229645			0.000114822		1.00000i	$0.499963\pi$
$884$	−25.0543			−0.842668
$885$	−0.831820	−	1.03680i	−0.0279613	−	0.0348518i
$886$	32.3516			1.08687
$887$	34.3521			1.15343			0.576715	−	0.816946i	$-0.304334\pi$
$887$	34.3521			1.15343			0.576715	+	0.816946i	$0.304334\pi$
$888$	−0.648623	−	0.951877i	−0.0217664	−	0.0319429i
$889$	−2.70323			−0.0906634
$890$		−	0.822772i		−	0.0275794i
$891$	−9.91156	−	9.21542i	−0.332050	−	0.308728i
$892$	5.17553			0.173290
$893$	−17.1760			−0.574774
$894$	6.34054	−	4.32054i	0.212059	−	0.144500i
$895$		−	1.44288i		−	0.0482300i
$896$	2.48626			0.0830603
$897$	26.7346	+	39.2339i	0.892641	+	1.30998i
$898$		−	29.6661i		−	0.989969i
$899$	−29.4004			−0.980558
$900$	5.47628	−	13.9324i	0.182543	−	0.464415i
$901$	1.67195			0.0557007
$902$		−	6.01313i		−	0.200215i
$903$	24.3720	+	35.7668i	0.811050	+	1.19024i
$904$	−13.6203			−0.453006
$905$			1.95583i			0.0650141i
$906$	12.3081	+	18.0625i	0.408909	+	0.600088i
$907$	−11.8888			−0.394760			−0.197380	−	0.980327i	$-0.563243\pi$
$907$	−11.8888			−0.394760			−0.197380	+	0.980327i	$0.563243\pi$
$908$	29.3591			0.974315
$909$	10.6877	−	27.1911i	0.354490	−	0.901873i
$910$	0.931179			0.0308683
$911$		−	37.1603i		−	1.23118i	−0.788068	−	0.615589i	$-0.788918\pi$
$911$		−	37.1603i		−	1.23118i	0.788068	−	0.615589i	$-0.211082\pi$
$912$	−5.71106	+	3.89160i	−0.189112	+	0.128864i
$913$	−8.17136			−0.270432
$914$		−	15.2368i		−	0.503989i
$915$	−1.89039	+	1.28814i	−0.0624945	+	0.0425847i
$916$		−	7.00153i		−	0.231337i
$917$	−5.14601			−0.169936
$918$	−33.8645	+	7.70209i	−1.11769	+	0.254207i
$919$		−	24.7932i		−	0.817853i	−0.912567	−	0.408926i	$-0.865903\pi$
$919$		−	24.7932i		−	0.817853i	0.912567	−	0.408926i	$-0.134097\pi$
$920$			0.730582i			0.0240866i
$921$	39.5698	−	26.9634i	1.30387	−	0.888475i
$922$			19.8024i			0.652158i
$923$	38.2321			1.25843
$924$	−5.35138	+	3.64651i	−0.176047	+	0.119961i
$925$			3.31850i			0.109111i
$926$			22.7494i			0.747591i
$927$	−5.27243	−	2.07238i	−0.173169	−	0.0680659i
$928$		−	3.18348i		−	0.104503i
$929$	−38.7083			−1.26998			−0.634988	−	0.772522i	$-0.718995\pi$
$929$	−38.7083			−1.26998			−0.634988	+	0.772522i	$0.718995\pi$
$930$	1.32072	−	0.899957i	0.0433081	−	0.0295108i
$931$	−3.26578			−0.107032
$932$	24.8628			0.814409
$933$	22.9544	+	33.6864i	0.751494	+	1.10284i
$934$	10.9522			0.358368
$935$	1.00417			0.0328400
$936$	10.4663	+	4.11388i	0.342102	+	0.134466i
$937$			51.7494i			1.69058i	0.534308	+	0.845290i	$0.320572\pi$
$937$			51.7494i			1.69058i	−0.534308	+	0.845290i	$0.679428\pi$
$938$			17.5707i			0.573702i
$939$	−26.2050	−	38.4568i	−0.855169	−	1.25499i
$940$			0.430096i			0.0140282i
$941$	−3.35856			−0.109486			−0.0547430	−	0.998500i	$-0.517434\pi$
$941$	−3.35856			−0.109486			−0.0547430	+	0.998500i	$0.517434\pi$
$942$	−15.0225	−	22.0461i	−0.489460	−	0.718300i
$943$			29.2399i			0.952181i
$944$	−7.65780	+	0.598474i	−0.249240	+	0.0194787i
$945$	1.25862	−	0.286259i	0.0409429	−	0.00931200i
$946$		−	15.1136i		−	0.491385i
$947$			34.9802i			1.13670i	0.822785	+	0.568352i	$0.192419\pi$
$947$			34.9802i			1.13670i	−0.822785	+	0.568352i	$0.807581\pi$
$948$	13.0692	−	8.90552i	0.424467	−	0.289238i
$949$	42.4733			1.37874
$950$	19.9103			0.645974
$951$	31.3307	+	45.9789i	1.01597	+	1.49097i
$952$			16.6174i			0.538571i
$953$		−	33.7188i		−	1.09226i	−0.837701	−	0.546129i	$-0.816101\pi$
$953$		−	33.7188i		−	1.09226i	0.837701	−	0.546129i	$-0.183899\pi$
$954$	−0.698448	−	0.274532i	−0.0226131	−	0.00888830i
$955$		−	0.200157i		−	0.00647693i
$956$			3.43288i			0.111027i
$957$	4.66908	+	6.85204i	0.150930	+	0.221495i
$958$			29.5038i			0.953226i
$959$		−	8.12552i		−	0.262387i
$960$	0.0974475	+	0.143008i	0.00314511	+	0.00461555i
$961$	−54.2908			−1.75132
$962$	−2.49291			−0.0803748
$963$	−5.55139	−	2.18203i	−0.178891	−	0.0703149i
$964$	8.12675			0.261745
$965$		−	0.678504i		−	0.0218418i
$966$	26.0220	−	17.7318i	0.837244	−	0.570510i
$967$			31.3698i			1.00879i	0.863474	+	0.504393i	$0.168284\pi$
$967$			31.3698i			1.00879i	−0.863474	+	0.504393i	$0.831716\pi$
$968$	−8.73873			−0.280873
$969$	−26.0101	−	38.1708i	−0.835566	−	1.22622i
$970$	−0.382990			−0.0122971
$971$			20.6892i			0.663947i	0.943289	+	0.331973i	$0.107714\pi$
$971$			20.6892i			0.663947i	−0.943289	+	0.331973i	$0.892286\pi$
$972$	15.4114	+	2.34300i	0.494320	+	0.0751516i
$973$	40.4018			1.29522
$974$	14.4863			0.464170
$975$	−18.2441	−	26.7739i	−0.584280	−	0.857452i
$976$			13.2188i			0.423124i
$977$	−19.8156			−0.633956			−0.316978	−	0.948433i	$-0.602668\pi$
$977$	−19.8156			−0.633956			−0.316978	+	0.948433i	$0.602668\pi$
$978$	16.0965	−	10.9684i	0.514711	−	0.350731i
$979$	12.3834			0.395774
$980$			0.0817767i			0.00261226i
$981$	26.6245	+	10.4650i	0.850055	+	0.334123i
$982$			18.1129i			0.578005i
$983$	−43.7106			−1.39415			−0.697076	−	0.716997i	$-0.745516\pi$
$983$	−43.7106			−1.39415			−0.697076	+	0.716997i	$0.745516\pi$
$984$	3.90011	+	5.72355i	0.124331	+	0.182460i
$985$	0.336220			0.0107129
$986$	21.2773			0.677607
$987$	15.3192	−	10.4388i	0.487617	−	0.332269i
$988$			14.9569i			0.475844i
$989$			73.4924i			2.33692i
$990$	−0.419487	−	0.164884i	−0.0133322	−	0.00524035i
$991$			35.1492i			1.11655i	0.829656	+	0.558275i	$0.188537\pi$
$991$			35.1492i			1.11655i	−0.829656	+	0.558275i	$0.811463\pi$
$992$		−	9.23530i		−	0.293221i
$993$	28.3293	−	19.3040i	0.899003	−	0.612594i
$994$		−	25.3576i		−	0.804294i
$995$			1.22375i			0.0387955i
$996$	7.77785	−	5.29994i	0.246451	−	0.167935i
$997$	16.9857			0.537943			0.268972	−	0.963148i	$-0.413316\pi$
$997$	16.9857			0.537943			0.268972	+	0.963148i	$0.413316\pi$
$998$	21.6305			0.684701
$999$	−3.36953	+	0.766361i	−0.106607	+	0.0242466i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.c.b.353.4	yes	10
3.2	odd	2		354.2.c.a.353.3	✓	10
59.58	odd	2		354.2.c.a.353.4	yes	10
177.176	even	2	inner	354.2.c.b.353.3	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.c.a.353.3	✓	10	3.2	odd	2
354.2.c.a.353.4	yes	10	59.58	odd	2
354.2.c.b.353.3	yes	10	177.176	even	2	inner
354.2.c.b.353.4	yes	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.43134 + 0.975334i) q^{3} +1.00000 q^{4} -0.0999120i q^{5} +(-1.43134 + 0.975334i) q^{6} +2.48626 q^{7} +1.00000 q^{8} +(1.09745 - 2.79206i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.43134 + 0.975334i) q^{3} +1.00000 q^{4} -0.0999120i q^{5} +(-1.43134 + 0.975334i) q^{6} +2.48626 q^{7} +1.00000 q^{8} +(1.09745 - 2.79206i) q^{9} -0.0999120i q^{10} +1.50375 q^{11} +(-1.43134 + 0.975334i) q^{12} +3.74859i q^{13} +2.48626 q^{14} +(0.0974475 + 0.143008i) q^{15} +1.00000 q^{16} +6.68366i q^{17} +(1.09745 - 2.79206i) q^{18} +3.99002 q^{19} -0.0999120i q^{20} +(-3.55868 + 2.42494i) q^{21} +1.50375 q^{22} -7.31226 q^{23} +(-1.43134 + 0.975334i) q^{24} +4.99002 q^{25} +3.74859i q^{26} +(1.15238 + 5.06676i) q^{27} +2.48626 q^{28} -3.18348i q^{29} +(0.0974475 + 0.143008i) q^{30} -9.23530i q^{31} +1.00000 q^{32} +(-2.15238 + 1.46666i) q^{33} +6.68366i q^{34} -0.248408i q^{35} +(1.09745 - 2.79206i) q^{36} +0.665027i q^{37} +3.99002 q^{38} +(-3.65613 - 5.36550i) q^{39} -0.0999120i q^{40} -3.99875i q^{41} +(-3.55868 + 2.42494i) q^{42} -10.0506i q^{43} +1.50375 q^{44} +(-0.278960 - 0.109648i) q^{45} -7.31226 q^{46} -4.30475 q^{47} +(-1.43134 + 0.975334i) q^{48} -0.818487 q^{49} +4.99002 q^{50} +(-6.51880 - 9.56657i) q^{51} +3.74859i q^{52} -0.250155i q^{53} +(1.15238 + 5.06676i) q^{54} -0.150243i q^{55} +2.48626 q^{56} +(-5.71106 + 3.89160i) q^{57} -3.18348i q^{58} +(-7.65780 + 0.598474i) q^{59} +(0.0974475 + 0.143008i) q^{60} +13.2188i q^{61} -9.23530i q^{62} +(2.72855 - 6.94181i) q^{63} +1.00000 q^{64} +0.374529 q^{65} +(-2.15238 + 1.46666i) q^{66} +7.06709i q^{67} +6.68366i q^{68} +(10.4663 - 7.13189i) q^{69} -0.248408i q^{70} -10.1991i q^{71} +(1.09745 - 2.79206i) q^{72} -11.3305i q^{73} +0.665027i q^{74} +(-7.14239 + 4.86693i) q^{75} +3.99002 q^{76} +3.73873 q^{77} +(-3.65613 - 5.36550i) q^{78} -9.13074 q^{79} -0.0999120i q^{80} +(-6.59122 - 6.12828i) q^{81} -3.99875i q^{82} -5.43398 q^{83} +(-3.55868 + 2.42494i) q^{84} +0.667778 q^{85} -10.0506i q^{86} +(3.10495 + 4.55663i) q^{87} +1.50375 q^{88} +8.23497 q^{89} +(-0.278960 - 0.109648i) q^{90} +9.31999i q^{91} -7.31226 q^{92} +(9.00751 + 13.2188i) q^{93} -4.30475 q^{94} -0.398650i q^{95} +(-1.43134 + 0.975334i) q^{96} -3.83328i q^{97} -0.818487 q^{98} +(1.65029 - 4.19857i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} - q^{3} + 10 q^{4} - q^{6} - 2 q^{7} + 10 q^{8} + 3 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 - q^3 + 10 * q^4 - q^6 - 2 * q^7 + 10 * q^8 + 3 * q^9	\( 10 q + 10 q^{2} - q^{3} + 10 q^{4} - q^{6} - 2 q^{7} + 10 q^{8} + 3 q^{9} - 4 q^{11} - q^{12} - 2 q^{14} - 7 q^{15} + 10 q^{16} + 3 q^{18} - 6 q^{19} - 3 q^{21} - 4 q^{22} + 8 q^{23} - q^{24} + 4 q^{25} - 10 q^{27} - 2 q^{28} - 7 q^{30} + 10 q^{32} + 3 q^{36} - 6 q^{38} + 4 q^{39} - 3 q^{42} - 4 q^{44} - 11 q^{45} + 8 q^{46} - q^{48} + 8 q^{49} + 4 q^{50} + 2 q^{51} - 10 q^{54} - 2 q^{56} - 3 q^{57} - 20 q^{59} - 7 q^{60} - 19 q^{63} + 10 q^{64} - 16 q^{65} - 14 q^{69} + 3 q^{72} - 4 q^{75} - 6 q^{76} - 48 q^{77} + 4 q^{78} + 6 q^{79} + 7 q^{81} - 12 q^{83} - 3 q^{84} - 4 q^{85} - 15 q^{87} - 4 q^{88} + 16 q^{89} - 11 q^{90} + 8 q^{92} + 52 q^{93} - q^{96} + 8 q^{98} - 2 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - q^3 + 10 * q^4 - q^6 - 2 * q^7 + 10 * q^8 + 3 * q^9 - 4 * q^11 - q^12 - 2 * q^14 - 7 * q^15 + 10 * q^16 + 3 * q^18 - 6 * q^19 - 3 * q^21 - 4 * q^22 + 8 * q^23 - q^24 + 4 * q^25 - 10 * q^27 - 2 * q^28 - 7 * q^30 + 10 * q^32 + 3 * q^36 - 6 * q^38 + 4 * q^39 - 3 * q^42 - 4 * q^44 - 11 * q^45 + 8 * q^46 - q^48 + 8 * q^49 + 4 * q^50 + 2 * q^51 - 10 * q^54 - 2 * q^56 - 3 * q^57 - 20 * q^59 - 7 * q^60 - 19 * q^63 + 10 * q^64 - 16 * q^65 - 14 * q^69 + 3 * q^72 - 4 * q^75 - 6 * q^76 - 48 * q^77 + 4 * q^78 + 6 * q^79 + 7 * q^81 - 12 * q^83 - 3 * q^84 - 4 * q^85 - 15 * q^87 - 4 * q^88 + 16 * q^89 - 11 * q^90 + 8 * q^92 + 52 * q^93 - q^96 + 8 * q^98 - 2 * q^99

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