LMFDB - Embedded newform 351.2.r.b.316.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [351,2,Mod(10,351)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(351, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("351.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			316.9
Character	$\chi$	$=$	351.316
Dual form			351.2.r.b.10.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.21740 - 0.702869i) q^{2} +(-0.0119503 + 0.0206986i) q^{4} +(-2.61504 + 1.50979i) q^{5} +3.19463i q^{7} +2.84507i q^{8} +O(q^{10})$	\(q+(1.21740 - 0.702869i) q^{2} +(-0.0119503 + 0.0206986i) q^{4} +(-2.61504 + 1.50979i) q^{5} +3.19463i q^{7} +2.84507i q^{8} +(-2.12237 + 3.67605i) q^{10} +(0.687300 - 0.396813i) q^{11} +(-3.60510 - 0.0569665i) q^{13} +(2.24541 + 3.88916i) q^{14} +(1.97581 + 3.42221i) q^{16} +(0.0957495 + 0.165843i) q^{17} +(6.28411 - 3.62813i) q^{19} -0.0721699i q^{20} +(0.557815 - 0.966164i) q^{22} -2.54500 q^{23} +(2.05894 - 3.56619i) q^{25} +(-4.42891 + 2.46456i) q^{26} +(-0.0661242 - 0.0381768i) q^{28} +(4.22442 + 7.31690i) q^{29} +(6.22662 - 3.59494i) q^{31} +(-0.117082 - 0.0675976i) q^{32} +(0.233132 + 0.134599i) q^{34} +(-4.82322 - 8.35407i) q^{35} +(2.25703 + 1.30310i) q^{37} +(5.10020 - 8.83381i) q^{38} +(-4.29547 - 7.43997i) q^{40} +0.905916i q^{41} -3.97309 q^{43} +0.0189682i q^{44} +(-3.09830 + 1.78880i) q^{46} +(-6.60765 - 3.81493i) q^{47} -3.20565 q^{49} -5.78866i q^{50} +(0.0442612 - 0.0739396i) q^{52} -0.0692625 q^{53} +(-1.19821 + 2.07536i) q^{55} -9.08895 q^{56} +(10.2856 + 5.93842i) q^{58} +(11.7491 + 6.78334i) q^{59} +0.178857 q^{61} +(5.05354 - 8.75299i) q^{62} -8.09330 q^{64} +(9.51347 - 5.29398i) q^{65} +10.5897i q^{67} -0.00457694 q^{68} +(-11.7436 - 6.78019i) q^{70} +(-0.271545 + 0.156777i) q^{71} -6.55741i q^{73} +3.66363 q^{74} +0.173429i q^{76} +(1.26767 + 2.19567i) q^{77} +(-2.13465 + 3.69732i) q^{79} +(-10.3336 - 5.96613i) q^{80} +(0.636740 + 1.10287i) q^{82} +(7.01438 + 4.04975i) q^{83} +(-0.500776 - 0.289123i) q^{85} +(-4.83686 + 2.79256i) q^{86} +(1.12896 + 1.95542i) q^{88} +(4.56933 + 2.63810i) q^{89} +(0.181987 - 11.5170i) q^{91} +(0.0304136 - 0.0526779i) q^{92} -10.7256 q^{94} +(-10.9554 + 18.9754i) q^{95} -17.5710i q^{97} +(-3.90257 + 2.25315i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 10 q^{4} - 3 q^{5}+O(q^{10}) $ 22 * q + 10 * q^4 - 3 * q^5	$ 22 q + 10 q^{4} - 3 q^{5} - 7 q^{10} - 3 q^{11} + 3 q^{13} + 9 q^{14} - 12 q^{16} - 9 q^{17} - 6 q^{19} - 13 q^{22} + 12 q^{23} + 4 q^{25} + 12 q^{26} + 3 q^{28} + 24 q^{29} + 27 q^{31} - 15 q^{34} + 27 q^{35} + 6 q^{37} - 21 q^{38} + 13 q^{40} + 8 q^{43} - 15 q^{46} - 6 q^{47} - 14 q^{49} - 7 q^{52} + 24 q^{53} - 13 q^{55} - 18 q^{56} + 15 q^{58} + 33 q^{59} - 6 q^{61} - 24 q^{64} - 3 q^{65} - 138 q^{68} + 24 q^{70} - 9 q^{71} - 12 q^{74} - 42 q^{77} - 6 q^{79} - 105 q^{80} - 16 q^{82} + 42 q^{83} - 51 q^{85} + 45 q^{86} - 11 q^{88} + 30 q^{89} + 15 q^{91} + 3 q^{92} - 88 q^{94} + 3 q^{95} - 117 q^{98}+O(q^{100}) $ 22 * q + 10 * q^4 - 3 * q^5 - 7 * q^10 - 3 * q^11 + 3 * q^13 + 9 * q^14 - 12 * q^16 - 9 * q^17 - 6 * q^19 - 13 * q^22 + 12 * q^23 + 4 * q^25 + 12 * q^26 + 3 * q^28 + 24 * q^29 + 27 * q^31 - 15 * q^34 + 27 * q^35 + 6 * q^37 - 21 * q^38 + 13 * q^40 + 8 * q^43 - 15 * q^46 - 6 * q^47 - 14 * q^49 - 7 * q^52 + 24 * q^53 - 13 * q^55 - 18 * q^56 + 15 * q^58 + 33 * q^59 - 6 * q^61 - 24 * q^64 - 3 * q^65 - 138 * q^68 + 24 * q^70 - 9 * q^71 - 12 * q^74 - 42 * q^77 - 6 * q^79 - 105 * q^80 - 16 * q^82 + 42 * q^83 - 51 * q^85 + 45 * q^86 - 11 * q^88 + 30 * q^89 + 15 * q^91 + 3 * q^92 - 88 * q^94 + 3 * q^95 - 117 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.21740	−	0.702869i	0.860835	−	0.497003i	−0.00345668	−	0.999994i	$-0.501100\pi$
$2$	1.21740	−	0.702869i	0.860835	−	0.497003i	0.864292	+	0.502991i	$0.167767\pi$
$3$		0			0
$3$		0			0
$4$	−0.0119503	+	0.0206986i	−0.00597516	+	0.0103493i
$5$	−2.61504	+	1.50979i	−1.16948	+	0.675199i	−0.953557	−	0.301211i	$-0.902609\pi$
$5$	−2.61504	+	1.50979i	−1.16948	+	0.675199i	−0.215922	+	0.976411i	$0.569276\pi$
$6$		0			0
$7$			3.19463i			1.20746i	0.797190	+	0.603728i	$0.206319\pi$
$7$			3.19463i			1.20746i	−0.797190	+	0.603728i	$0.793681\pi$
$8$			2.84507i			1.00589i
$9$		0			0
$10$	−2.12237	+	3.67605i	−0.671153	+	1.16247i
$11$	0.687300	−	0.396813i	0.207229	−	0.119644i	−0.392794	−	0.919626i	$-0.628491\pi$
$11$	0.687300	−	0.396813i	0.207229	−	0.119644i	0.600023	+	0.799983i	$0.295158\pi$
$12$		0			0
$13$	−3.60510	−	0.0569665i	−0.999875	−	0.0157997i
$13$	−3.60510	−	0.0569665i	−0.999875	−	0.0157997i
$14$	2.24541	+	3.88916i	0.600110	+	1.03942i
$15$		0			0
$16$	1.97581	+	3.42221i	0.493953	+	0.855552i
$17$	0.0957495	+	0.165843i	0.0232227	+	0.0402228i	0.877403	−	0.479754i	$-0.159274\pi$
$17$	0.0957495	+	0.165843i	0.0232227	+	0.0402228i	−0.854181	+	0.519977i	$0.825941\pi$
$18$		0			0
$19$	6.28411	−	3.62813i	1.44167	−	0.832350i	0.443711	−	0.896170i	$-0.353662\pi$
$19$	6.28411	−	3.62813i	1.44167	−	0.832350i	0.997961	+	0.0638195i	$0.0203282\pi$
$20$		−	0.0721699i		−	0.0161377i
$21$		0			0
$22$	0.557815	−	0.966164i	0.118927	−	0.205987i
$23$	−2.54500			−0.530670			−0.265335	−	0.964156i	$-0.585483\pi$
$23$	−2.54500			−0.530670			−0.265335	+	0.964156i	$0.585483\pi$
$24$		0			0
$25$	2.05894	−	3.56619i	0.411788	−	0.713238i
$26$	−4.42891	+	2.46456i	−0.868580	+	0.483340i
$27$		0			0
$28$	−0.0661242	−	0.0381768i	−0.0124963	−	0.00721474i
$29$	4.22442	+	7.31690i	0.784454	+	1.35871i	0.929325	+	0.369264i	$0.120390\pi$
$29$	4.22442	+	7.31690i	0.784454	+	1.35871i	−0.144870	+	0.989451i	$0.546277\pi$
$30$		0			0
$31$	6.22662	−	3.59494i	1.11833	−	0.645670i	0.177358	−	0.984146i	$-0.443245\pi$
$31$	6.22662	−	3.59494i	1.11833	−	0.645670i	0.940975	+	0.338476i	$0.109911\pi$
$32$	−0.117082	−	0.0675976i	−0.0206974	−	0.0119497i
$33$		0			0
$34$	0.233132	+	0.134599i	0.0399818	+	0.0230835i
$35$	−4.82322	−	8.35407i	−0.815273	−	1.41209i
$36$		0			0
$37$	2.25703	+	1.30310i	0.371054	+	0.214228i	0.673919	−	0.738806i	$-0.264610\pi$
$37$	2.25703	+	1.30310i	0.371054	+	0.214228i	−0.302865	+	0.953033i	$0.597943\pi$
$38$	5.10020	−	8.83381i	0.827362	−	1.43303i
$39$		0			0
$40$	−4.29547	−	7.43997i	−0.679173	−	1.17636i
$41$			0.905916i			0.141480i	0.997495	+	0.0707402i	$0.0225361\pi$
$41$			0.905916i			0.141480i	−0.997495	+	0.0707402i	$0.977464\pi$
$42$		0			0
$43$	−3.97309			−0.605890			−0.302945	−	0.953008i	$-0.597970\pi$
$43$	−3.97309			−0.605890			−0.302945	+	0.953008i	$0.597970\pi$
$44$			0.0189682i			0.00285956i
$45$		0			0
$46$	−3.09830	+	1.78880i	−0.456820	+	0.263745i
$47$	−6.60765	−	3.81493i	−0.963825	−	0.556465i	−0.0664769	−	0.997788i	$-0.521176\pi$
$47$	−6.60765	−	3.81493i	−0.963825	−	0.556465i	−0.897348	+	0.441323i	$0.854509\pi$
$48$		0			0
$49$	−3.20565			−0.457950
$50$		−	5.78866i		−	0.818640i
$51$		0			0
$52$	0.0442612	−	0.0739396i	0.00613793	−	0.0102536i
$53$	−0.0692625			−0.00951393			−0.00475697	−	0.999989i	$-0.501514\pi$
$53$	−0.0692625			−0.00951393			−0.00475697	+	0.999989i	$0.501514\pi$
$54$		0			0
$55$	−1.19821	+	2.07536i	−0.161567	+	0.279841i
$56$	−9.08895			−1.21456
$57$		0			0
$58$	10.2856	+	5.93842i	1.35057	+	0.779753i
$59$	11.7491	+	6.78334i	1.52960	+	0.883116i	0.999378	+	0.0352582i	$0.0112254\pi$
$59$	11.7491	+	6.78334i	1.52960	+	0.883116i	0.530224	+	0.847858i	$0.322108\pi$
$60$		0			0
$61$	0.178857			0.0229003			0.0114501	−	0.999934i	$-0.496355\pi$
$61$	0.178857			0.0229003			0.0114501	+	0.999934i	$0.496355\pi$
$62$	5.05354	−	8.75299i	0.641800	−	1.11163i
$63$		0			0
$64$	−8.09330			−1.01166
$65$	9.51347	−	5.29398i	1.18000	−	0.656638i
$66$		0			0
$67$			10.5897i			1.29374i	0.762602	+	0.646868i	$0.223922\pi$
$67$			10.5897i			1.29374i	−0.762602	+	0.646868i	$0.776078\pi$
$68$	−0.00457694			−0.000555036
$69$		0			0
$70$	−11.7436	−	6.78019i	−1.40363	−	0.810387i
$71$	−0.271545	+	0.156777i	−0.0322265	+	0.0186060i	−0.516027	−	0.856572i	$-0.672589\pi$
$71$	−0.271545	+	0.156777i	−0.0322265	+	0.0186060i	0.483800	+	0.875178i	$0.339256\pi$
$72$		0			0
$73$		−	6.55741i		−	0.767487i	−0.923440	−	0.383743i	$-0.874635\pi$
$73$		−	6.55741i		−	0.767487i	0.923440	−	0.383743i	$-0.125365\pi$
$74$	3.66363			0.425888
$75$		0			0
$76$			0.173429i			0.0198937i
$77$	1.26767	+	2.19567i	0.144464	+	0.250220i
$78$		0			0
$79$	−2.13465	+	3.69732i	−0.240167	+	0.415981i	−0.960762	−	0.277376i	$-0.910535\pi$
$79$	−2.13465	+	3.69732i	−0.240167	+	0.415981i	0.720595	+	0.693356i	$0.243869\pi$
$80$	−10.3336	−	5.96613i	−1.15534	−	0.667034i
$81$		0			0
$82$	0.636740	+	1.10287i	0.0703162	+	0.121791i
$83$	7.01438	+	4.04975i	0.769928	+	0.444518i	0.832849	−	0.553500i	$-0.186708\pi$
$83$	7.01438	+	4.04975i	0.769928	+	0.444518i	−0.0629208	+	0.998019i	$0.520042\pi$
$84$		0			0
$85$	−0.500776	−	0.289123i	−0.0543168	−	0.0313598i
$86$	−4.83686	+	2.79256i	−0.521572	+	0.301130i
$87$		0			0
$88$	1.12896	+	1.95542i	0.120348	+	0.208448i
$89$	4.56933	+	2.63810i	0.484348	+	0.279638i	0.722226	−	0.691657i	$-0.243119\pi$
$89$	4.56933	+	2.63810i	0.484348	+	0.279638i	−0.237879	+	0.971295i	$0.576452\pi$
$90$		0			0
$91$	0.181987	−	11.5170i	0.0190774	−	1.20731i
$92$	0.0304136	−	0.0526779i	0.00317084	−	0.00549205i
$93$		0			0
$94$	−10.7256			−1.10626
$95$	−10.9554	+	18.9754i	−1.12400	+	1.94683i
$96$		0			0
$97$		−	17.5710i		−	1.78406i	−0.451975	−	0.892030i	$-0.649281\pi$
$97$		−	17.5710i		−	1.78406i	0.451975	−	0.892030i	$-0.350719\pi$
$98$	−3.90257	+	2.25315i	−0.394219	+	0.227603i
$99$		0			0
$100$	0.0492100	+	0.0852342i	0.00492100	+	0.00852342i
$101$	0.748943	+	1.29721i	0.0745227	+	0.129077i	0.900879	−	0.434071i	$-0.142923\pi$
$101$	0.748943	+	1.29721i	0.0745227	+	0.129077i	−0.826356	+	0.563148i	$0.809590\pi$
$102$		0			0
$103$	1.62024	+	2.80634i	0.159647	+	0.276517i	0.934741	−	0.355329i	$-0.115631\pi$
$103$	1.62024	+	2.80634i	0.159647	+	0.276517i	−0.775094	+	0.631846i	$0.782298\pi$
$104$	0.162074	−	10.2568i	0.0158927	−	1.00576i
$105$		0			0
$106$	−0.0843205	+	0.0486825i	−0.00818993	+	0.00472846i
$107$	2.74177	−	4.74888i	0.265057	−	0.459091i	−0.702522	−	0.711662i	$-0.747943\pi$
$107$	2.74177	−	4.74888i	0.265057	−	0.459091i	0.967578	+	0.252571i	$0.0812760\pi$
$108$		0			0
$109$		−	2.75058i		−	0.263458i	−0.991286	−	0.131729i	$-0.957947\pi$
$109$		−	2.75058i		−	0.263458i	0.991286	−	0.131729i	$-0.0420529\pi$
$110$			3.36874i			0.321197i
$111$		0			0
$112$	−10.9327	+	6.31199i	−1.03304	+	0.596427i
$113$	8.25023	−	14.2898i	0.776117	−	1.34427i	−0.158048	−	0.987431i	$-0.550520\pi$
$113$	8.25023	−	14.2898i	0.776117	−	1.34427i	0.934165	−	0.356842i	$-0.116147\pi$
$114$		0			0
$115$	6.65528	−	3.84243i	0.620608	−	0.358308i
$116$	−0.201932			−0.0187490
$117$		0			0
$118$	19.0712			1.75565
$119$	−0.529806	+	0.305884i	−0.0485673	+	0.0280403i
$120$		0			0
$121$	−5.18508	+	8.98082i	−0.471371	+	0.816438i
$122$	0.217741	−	0.125713i	0.0197134	−	0.0113815i
$123$		0			0
$124$			0.171843i			0.0154319i
$125$		−	2.66363i		−	0.238243i
$126$		0			0
$127$	−7.71406	+	13.3611i	−0.684512	+	1.18561i	0.289078	+	0.957305i	$0.406651\pi$
$127$	−7.71406	+	13.3611i	−0.684512	+	1.18561i	−0.973590	+	0.228304i	$0.926682\pi$
$128$	−9.61866	+	5.55334i	−0.850178	+	0.490850i
$129$		0			0
$130$	7.86077	−	13.1316i	0.689436	−	1.15172i
$131$	−3.53140	−	6.11657i	−0.308540	−	0.534407i	0.669503	−	0.742809i	$-0.266507\pi$
$131$	−3.53140	−	6.11657i	−0.308540	−	0.534407i	−0.978043	+	0.208402i	$0.933174\pi$
$132$		0			0
$133$	11.5905	+	20.0754i	1.00503	+	1.74076i
$134$	7.44316	+	12.8919i	0.642992	+	1.11369i
$135$		0			0
$136$	−0.471835	+	0.272414i	−0.0404596	+	0.0233593i
$137$		−	6.97198i		−	0.595657i	−0.954619	−	0.297828i	$-0.903738\pi$
$137$		−	6.97198i		−	0.595657i	0.954619	−	0.297828i	$-0.0962623\pi$
$138$		0			0
$139$	5.45262	−	9.44421i	0.462485	−	0.801048i	−0.536599	−	0.843837i	$-0.680291\pi$
$139$	5.45262	−	9.44421i	0.462485	−	0.801048i	0.999084	+	0.0427897i	$0.0136245\pi$
$140$	0.230556			0.0194855
$141$		0			0
$142$	−0.220387	+	0.381722i	−0.0184945	+	0.0320334i
$143$	−2.50039	+	1.39140i	−0.209093	+	0.116355i
$144$		0			0
$145$	−22.0940	−	12.7560i	−1.83481	−	1.05933i
$146$	−4.60900	−	7.98302i	−0.381444	−	0.660680i
$147$		0			0
$148$	−0.0539445	+	0.0311448i	−0.00443421	+	0.00256009i
$149$	12.6627	+	7.31084i	1.03737	+	0.598927i	0.919088	−	0.394053i	$-0.128927\pi$
$149$	12.6627	+	7.31084i	1.03737	+	0.598927i	0.118284	+	0.992980i	$0.462261\pi$
$150$		0			0
$151$	−0.912654	−	0.526921i	−0.0742707	−	0.0428802i	0.462405	−	0.886669i	$-0.346987\pi$
$151$	−0.912654	−	0.526921i	−0.0742707	−	0.0428802i	−0.536675	+	0.843789i	$0.680320\pi$
$152$	10.3223	+	17.8787i	0.837249	+	1.45016i
$153$		0			0
$154$	3.08653	+	1.78201i	0.248720	+	0.143599i
$155$	−10.8552	+	18.8018i	−0.871912	+	1.51020i
$156$		0			0
$157$	5.59684	+	9.69401i	0.446677	+	0.773667i	0.998167	−	0.0605145i	$-0.0192741\pi$
$157$	5.59684	+	9.69401i	0.446677	+	0.773667i	−0.551491	+	0.834181i	$0.685941\pi$
$158$			6.00151i			0.477454i
$159$		0			0
$160$	0.408233			0.0322736
$161$		−	8.13034i		−	0.640761i
$162$		0			0
$163$	−1.69044	+	0.975977i	−0.132406	+	0.0764444i	−0.564740	−	0.825269i	$-0.691023\pi$
$163$	−1.69044	+	0.975977i	−0.132406	+	0.0764444i	0.432334	+	0.901713i	$0.357690\pi$
$164$	−0.0187512	−	0.0108260i	−0.00146422	−	0.000845367i
$165$		0			0
$166$	11.3858			0.883708
$167$		−	19.8679i		−	1.53742i	−0.639595	−	0.768712i	$-0.720898\pi$
$167$		−	19.8679i		−	1.53742i	0.639595	−	0.768712i	$-0.279102\pi$
$168$		0			0
$169$	12.9935	+	0.410740i	0.999501	+	0.0315954i
$170$	−0.812864			−0.0623438
$171$		0			0
$172$	0.0474797	−	0.0822372i	0.00362029	−	0.00627053i
$173$	3.37210			0.256376			0.128188	−	0.991750i	$-0.459084\pi$
$173$	3.37210			0.256376			0.128188	+	0.991750i	$0.459084\pi$
$174$		0			0
$175$	11.3926	+	6.57755i	0.861203	+	0.497216i
$176$	2.71595	+	1.56806i	0.204723	+	0.118197i
$177$		0			0
$178$	7.41696			0.555925
$179$	−6.46527	+	11.1982i	−0.483237	+	0.836990i	−0.999815	−	0.0192497i	$-0.993872\pi$
$179$	−6.46527	+	11.1982i	−0.483237	+	0.836990i	0.516578	+	0.856240i	$0.327206\pi$
$180$		0			0
$181$	−11.3925			−0.846798			−0.423399	−	0.905943i	$-0.639163\pi$
$181$	−11.3925			−0.846798			−0.423399	+	0.905943i	$0.639163\pi$
$182$	−7.87336	−	14.1487i	−0.583612	−	1.04877i
$183$		0			0
$184$		−	7.24073i		−	0.533793i
$185$	−7.86962			−0.578586
$186$		0			0
$187$	0.131617	+	0.0759893i	0.00962481	+	0.00555688i
$188$	0.157927	−	0.0911792i	0.0115180	−	0.00664993i
$189$		0			0
$190$			30.8010i			2.23454i
$191$	−3.26866			−0.236512			−0.118256	−	0.992983i	$-0.537730\pi$
$191$	−3.26866			−0.236512			−0.118256	+	0.992983i	$0.537730\pi$
$192$		0			0
$193$		−	19.0634i		−	1.37221i	−0.727501	−	0.686107i	$-0.759318\pi$
$193$		−	19.0634i		−	1.37221i	0.727501	−	0.686107i	$-0.240682\pi$
$194$	−12.3501	−	21.3910i	−0.886684	−	1.53578i
$195$		0			0
$196$	0.0383085	−	0.0663523i	0.00273632	−	0.00473945i
$197$	2.13371	+	1.23190i	0.152020	+	0.0877690i	0.574081	−	0.818799i	$-0.305360\pi$
$197$	2.13371	+	1.23190i	0.152020	+	0.0877690i	−0.422060	+	0.906568i	$0.638693\pi$
$198$		0			0
$199$	11.7617	+	20.3718i	0.833764	+	1.44412i	0.895033	+	0.446000i	$0.147152\pi$
$199$	11.7617	+	20.3718i	0.833764	+	1.44412i	−0.0612690	+	0.998121i	$0.519515\pi$
$200$	10.1461	+	5.85784i	0.717436	+	0.414212i
$201$		0			0
$202$	1.82353	+	1.05282i	0.128303	+	0.0740760i
$203$	−23.3748	+	13.4954i	−1.64059	+	0.947194i
$204$		0			0
$205$	−1.36774	−	2.36900i	−0.0955274	−	0.165458i
$206$	3.94498	+	2.27763i	0.274860	+	0.158690i
$207$		0			0
$208$	−6.92806	−	12.4500i	−0.480374	−	0.863250i
$209$	2.87938	−	4.98723i	0.199171	−	0.344974i
$210$		0			0
$211$	−1.44535			−0.0995020			−0.0497510	−	0.998762i	$-0.515843\pi$
$211$	−1.44535			−0.0995020			−0.0497510	+	0.998762i	$0.515843\pi$
$212$	0.000827709	−	0.00143363i	5.68473e−5	−	9.84623e-5i
$213$		0			0
$214$		−	7.70841i		−	0.526936i
$215$	10.3898	−	5.99854i	0.708576	−	0.409097i
$216$		0			0
$217$	11.4845	+	19.8917i	0.779618	+	1.35034i
$218$	−1.93330	−	3.34857i	−0.130940	−	0.226794i
$219$		0			0
$220$	−0.0286380	−	0.0496024i	−0.00193077	−	0.00334419i
$221$	−0.335739	−	0.603335i	−0.0225842	−	0.0405847i
$222$		0			0
$223$	−0.525138	+	0.303188i	−0.0351658	+	0.0203030i	−0.517480	−	0.855695i	$-0.673130\pi$
$223$	−0.525138	+	0.303188i	−0.0351658	+	0.0203030i	0.482314	+	0.875998i	$0.339796\pi$
$224$	0.215949	−	0.374035i	0.0144287	−	0.0249912i
$225$		0			0
$226$		−	23.1953i		−	1.54293i
$227$			23.0561i			1.53029i	0.643861	+	0.765143i	$0.277332\pi$
$227$			23.0561i			1.53029i	−0.643861	+	0.765143i	$0.722668\pi$
$228$		0			0
$229$	3.97688	−	2.29605i	0.262799	−	0.151727i	−0.362812	−	0.931863i	$-0.618183\pi$
$229$	3.97688	−	2.29605i	0.262799	−	0.151727i	0.625611	+	0.780135i	$0.284850\pi$
$230$	5.40144	−	9.35558i	0.356161	−	0.616888i
$231$		0			0
$232$	−20.8171	+	12.0188i	−1.36671	+	0.789071i
$233$	7.84289			0.513804			0.256902	−	0.966437i	$-0.417298\pi$
$233$	7.84289			0.513804			0.256902	+	0.966437i	$0.417298\pi$
$234$		0			0
$235$	23.0390			1.50290
$236$	−0.280811	+	0.162126i	−0.0182792	+	0.0105535i
$237$		0			0
$238$	−0.429993	+	0.744769i	−0.0278723	+	0.0482762i
$239$	1.19864	−	0.692034i	0.0775334	−	0.0447639i	−0.460732	−	0.887539i	$-0.652413\pi$
$239$	1.19864	−	0.692034i	0.0775334	−	0.0447639i	0.538266	+	0.842775i	$0.319080\pi$
$240$		0			0
$241$		−	4.04654i		−	0.260661i	−0.991471	−	0.130330i	$-0.958396\pi$
$241$		−	4.04654i		−	0.260661i	0.991471	−	0.130330i	$-0.0416038\pi$
$242$			14.5777i			0.937092i
$243$		0			0
$244$	−0.00213739	+	0.00370208i	−0.000136833	+	0.000237001i
$245$	8.38288	−	4.83986i	0.535563	−	0.309207i
$246$		0			0
$247$	−22.8615	+	12.7218i	−1.45464	+	0.809468i
$248$	10.2279	+	17.7152i	0.649470	+	1.12492i
$249$		0			0
$250$	−1.87219	−	3.24272i	−0.118407	−	0.205088i
$251$	−3.43920	−	5.95686i	−0.217080	−	0.375994i	0.736834	−	0.676074i	$-0.236320\pi$
$251$	−3.43920	−	5.95686i	−0.217080	−	0.375994i	−0.953914	+	0.300080i	$0.902987\pi$
$252$		0			0
$253$	−1.74918	+	1.00989i	−0.109970	+	0.0634913i
$254$			21.6879i			1.36082i
$255$		0			0
$256$	0.286766	−	0.496694i	0.0179229	−	0.0310434i
$257$	−7.53544			−0.470048			−0.235024	−	0.971990i	$-0.575517\pi$
$257$	−7.53544			−0.470048			−0.235024	+	0.971990i	$0.575517\pi$
$258$		0			0
$259$	−4.16291	+	7.21037i	−0.258671	+	0.448031i
$260$	−0.00411127	+	0.260180i	−0.000254970	+	0.0161357i
$261$		0			0
$262$	−8.59829	−	4.96422i	−0.531204	−	0.306691i
$263$	2.25667	+	3.90867i	0.139152	+	0.241019i	0.927176	−	0.374626i	$-0.122229\pi$
$263$	2.25667	+	3.90867i	0.139152	+	0.241019i	−0.788024	+	0.615645i	$0.788896\pi$
$264$		0			0
$265$	0.181124	−	0.104572i	0.0111263	−	0.00642380i
$266$	28.2207	+	16.2932i	1.73032	+	0.999003i
$267$		0			0
$268$	−0.219191	−	0.126550i	−0.0133892	−	0.00773028i
$269$	7.59726	+	13.1588i	0.463213	+	0.802309i	0.999119	−	0.0419692i	$-0.0133631\pi$
$269$	7.59726	+	13.1588i	0.463213	+	0.802309i	−0.535906	+	0.844278i	$0.680030\pi$
$270$		0			0
$271$	−19.0083	−	10.9744i	−1.15467	−	0.666650i	−0.204650	−	0.978835i	$-0.565606\pi$
$271$	−19.0083	−	10.9744i	−1.15467	−	0.666650i	−0.950021	+	0.312185i	$0.898939\pi$
$272$	−0.378366	+	0.655349i	−0.0229418	+	0.0397364i
$273$		0			0
$274$	−4.90039	−	8.48773i	−0.296043	−	0.512762i
$275$		−	3.26806i		−	0.197071i
$276$		0			0
$277$	6.04087			0.362961			0.181480	−	0.983395i	$-0.441911\pi$
$277$	6.04087			0.362961			0.181480	+	0.983395i	$0.441911\pi$
$278$		−	15.3299i		−	0.919427i
$279$		0			0
$280$	23.7679	−	13.7224i	1.42041	−	0.820072i
$281$	−6.56065	−	3.78780i	−0.391376	−	0.225961i	0.291380	−	0.956607i	$-0.405886\pi$
$281$	−6.56065	−	3.78780i	−0.391376	−	0.225961i	−0.682756	+	0.730646i	$0.739219\pi$
$282$		0			0
$283$	−28.0741			−1.66883			−0.834416	−	0.551135i	$-0.814195\pi$
$283$	−28.0741			−1.66883			−0.834416	+	0.551135i	$0.814195\pi$
$284$		−	0.00749413i		−	0.000444695i
$285$		0			0
$286$	−2.06602	+	3.45134i	−0.122166	+	0.204082i
$287$	−2.89406			−0.170831
$288$		0			0
$289$	8.48166	−	14.6907i	0.498921	−	0.864157i
$290$	−35.8631			−2.10595
$291$		0			0
$292$	0.135729	+	0.0783631i	0.00794293	+	0.00458586i
$293$	−19.8636	−	11.4682i	−1.16044	−	0.669982i	−0.209033	−	0.977909i	$-0.567032\pi$
$293$	−19.8636	−	11.4682i	−1.16044	−	0.669982i	−0.951410	+	0.307926i	$0.900365\pi$
$294$		0			0
$295$	−40.9657			−2.38512
$296$	−3.70741	+	6.42142i	−0.215489	+	0.373237i
$297$		0			0
$298$	20.5542			1.19068
$299$	9.17500	+	0.144980i	0.530604	+	0.00838441i
$300$		0			0
$301$		−	12.6925i		−	0.731586i
$302$	−1.48143			−0.0852465
$303$		0			0
$304$	24.8324	+	14.3370i	1.42424	+	0.822285i
$305$	−0.467717	+	0.270036i	−0.0267814	+	0.0154622i
$306$		0			0
$307$			3.31351i			0.189112i	0.995520	+	0.0945560i	$0.0301431\pi$
$307$			3.31351i			0.189112i	−0.995520	+	0.0945560i	$0.969857\pi$
$308$	−0.0605962			−0.00345279
$309$		0			0
$310$			30.5192i			1.73337i
$311$	−12.6695	−	21.9442i	−0.718421	−	1.24434i	−0.961625	−	0.274367i	$-0.911532\pi$
$311$	−12.6695	−	21.9442i	−0.718421	−	1.24434i	0.243204	−	0.969975i	$-0.421802\pi$
$312$		0			0
$313$	−8.71624	+	15.0970i	−0.492671	+	0.853331i	−0.999964	−	0.00844245i	$-0.997313\pi$
$313$	−8.71624	+	15.0970i	−0.492671	+	0.853331i	0.507294	+	0.861773i	$0.330646\pi$
$314$	13.6272	+	7.86769i	0.769030	+	0.444000i
$315$		0			0
$316$	−0.0510194	−	0.0883682i	−0.00287007	−	0.00497110i
$317$	−11.2999	−	6.52400i	−0.634666	−	0.366425i	0.147891	−	0.989004i	$-0.452752\pi$
$317$	−11.2999	−	6.52400i	−0.634666	−	0.366425i	−0.782557	+	0.622579i	$0.786085\pi$
$318$		0			0
$319$	5.80688	+	3.35261i	0.325123	+	0.187710i
$320$	21.1643	−	12.2192i	1.18312	−	0.683074i
$321$		0			0
$322$	−5.71457	−	9.89792i	−0.318460	−	0.551589i
$323$	1.20340	+	0.694783i	0.0669589	+	0.0386588i
$324$		0			0
$325$	−7.62584	+	12.7392i	−0.423006	+	0.706643i
$326$	−1.37197	+	2.37632i	−0.0759862	+	0.131612i
$327$		0			0
$328$	−2.57740			−0.142313
$329$	12.1873	−	21.1090i	0.671907	−	1.16378i
$330$		0			0
$331$			4.75617i			0.261423i	0.991420	+	0.130711i	$0.0417261\pi$
$331$			4.75617i			0.261423i	−0.991420	+	0.130711i	$0.958274\pi$
$332$	−0.167648	+	0.0967917i	−0.00920088	+	0.00531213i
$333$		0			0
$334$	−13.9645	−	24.1873i	−0.764105	−	1.32347i
$335$	−15.9882	−	27.6924i	−0.873530	−	1.51300i
$336$		0			0
$337$	−12.7677	−	22.1143i	−0.695500	−	1.20464i	−0.970012	−	0.243057i	$-0.921850\pi$
$337$	−12.7677	−	22.1143i	−0.695500	−	1.20464i	0.274512	−	0.961584i	$-0.411484\pi$
$338$	16.1071	−	8.63270i	0.876108	−	0.469557i
$339$		0			0
$340$	0.0119689	−	0.00691023i	0.000649103	−	0.000374760i
$341$	2.85304	−	4.94160i	0.154501	−	0.267603i
$342$		0			0
$343$			12.1215i			0.654502i
$344$		−	11.3037i		−	0.609456i
$345$		0			0
$346$	4.10521	−	2.37014i	0.220697	−	0.127420i
$347$	2.71373	−	4.70031i	0.145680	−	0.252326i	−0.783946	−	0.620829i	$-0.786796\pi$
$347$	2.71373	−	4.70031i	0.145680	−	0.252326i	0.929627	+	0.368503i	$0.120130\pi$
$348$		0			0
$349$	22.8603	−	13.1984i	1.22368	−	0.706493i	0.257981	−	0.966150i	$-0.416943\pi$
$349$	22.8603	−	13.1984i	1.22368	−	0.706493i	0.965701	+	0.259657i	$0.0836096\pi$
$350$	18.4926			0.988472
$351$		0			0
$352$	−0.107294			−0.00571881
$353$	25.8786	−	14.9410i	1.37738	−	0.795230i	0.385535	−	0.922693i	$-0.374017\pi$
$353$	25.8786	−	14.9410i	1.37738	−	0.795230i	0.991843	+	0.127463i	$0.0406836\pi$
$354$		0			0
$355$	0.473401	−	0.819954i	0.0251255	−	0.0435186i
$356$	−0.109210	+	0.0630523i	−0.00578811	+	0.00334176i
$357$		0			0
$358$			18.1769i			0.960681i
$359$		−	27.5815i		−	1.45570i	−0.685738	−	0.727849i	$-0.740520\pi$
$359$		−	27.5815i		−	1.45570i	0.685738	−	0.727849i	$-0.259480\pi$
$360$		0			0
$361$	16.8267	−	29.1446i	0.885614	−	1.53393i
$362$	−13.8693	+	8.00743i	−0.728953	+	0.420861i
$363$		0			0
$364$	0.236210	+	0.141398i	0.0123807	+	0.00741128i
$365$	9.90032	+	17.1479i	0.518207	+	0.897560i
$366$		0			0
$367$	−10.7197	−	18.5671i	−0.559565	−	0.969196i	−0.997533	−	0.0702047i	$-0.977635\pi$
$367$	−10.7197	−	18.5671i	−0.559565	−	0.969196i	0.437967	−	0.898991i	$-0.355699\pi$
$368$	−5.02845	−	8.70954i	−0.262126	−	0.454016i
$369$		0			0
$370$	−9.58051	+	5.53131i	−0.498067	+	0.287559i
$371$		−	0.221268i		−	0.0114877i
$372$		0			0
$373$	12.4225	−	21.5164i	0.643211	−	1.11407i	−0.341500	−	0.939882i	$-0.610935\pi$
$373$	12.4225	−	21.5164i	0.643211	−	1.11407i	0.984712	−	0.174193i	$-0.0557317\pi$
$374$	0.213642			0.0110472
$375$		0			0
$376$	10.8538	−	18.7993i	0.559740	−	0.969498i
$377$	−14.8126	−	26.6188i	−0.762889	−	1.37094i
$378$		0			0
$379$	−0.763882	−	0.441027i	−0.0392380	−	0.0226540i	0.480253	−	0.877130i	$-0.340545\pi$
$379$	−0.763882	−	0.441027i	−0.0392380	−	0.0226540i	−0.519491	+	0.854476i	$0.673878\pi$
$380$	−0.261842	−	0.453524i	−0.0134322	−	0.0232653i
$381$		0			0
$382$	−3.97928	+	2.29744i	−0.203598	+	0.117547i
$383$	−2.48536	−	1.43492i	−0.126996	−	0.0733210i	0.435156	−	0.900355i	$-0.356693\pi$
$383$	−2.48536	−	1.43492i	−0.126996	−	0.0733210i	−0.562152	+	0.827034i	$0.690026\pi$
$384$		0			0
$385$	−6.63000	−	3.82783i	−0.337896	−	0.195084i
$386$	−13.3991	−	23.2079i	−0.681995	−	1.18125i
$387$		0			0
$388$	0.363693	+	0.209979i	0.0184637	+	0.0106600i
$389$	−6.00741	+	10.4051i	−0.304588	+	0.527561i	−0.977169	−	0.212462i	$-0.931852\pi$
$389$	−6.00741	+	10.4051i	−0.304588	+	0.527561i	0.672582	+	0.740023i	$0.265185\pi$
$390$		0			0
$391$	−0.243683	−	0.422071i	−0.0123236	−	0.0213450i
$392$		−	9.12031i		−	0.460645i
$393$		0			0
$394$	3.46345			0.174486
$395$		−	12.8915i		−	0.648641i
$396$		0			0
$397$	7.80521	−	4.50634i	0.391732	−	0.226167i	−0.291178	−	0.956669i	$-0.594047\pi$
$397$	7.80521	−	4.50634i	0.391732	−	0.226167i	0.682910	+	0.730502i	$0.260714\pi$
$398$	28.6375	+	16.5339i	1.43547	+	0.828767i
$399$		0			0
$400$	16.2723			0.813616
$401$			33.2406i			1.65996i	0.557795	+	0.829979i	$0.311647\pi$
$401$			33.2406i			1.65996i	−0.557795	+	0.829979i	$0.688353\pi$
$402$		0			0
$403$	−22.6524	+	12.6054i	−1.12840	+	0.627920i
$404$	−0.0358004			−0.00178114
$405$		0			0
$406$	−18.9710	+	32.8588i	−0.941517	+	1.63076i
$407$	2.06834			0.102524
$408$		0			0
$409$	29.3655	+	16.9542i	1.45203	+	0.838332i	0.998597	−	0.0529572i	$-0.0168647\pi$
$409$	29.3655	+	16.9542i	1.45203	+	0.838332i	0.453436	+	0.891289i	$0.350198\pi$
$410$	−3.33020	−	1.92269i	−0.164467	−	0.0949549i
$411$		0			0
$412$	−0.0774496			−0.00381567
$413$	−21.6703	+	37.5340i	−1.06632	+	1.84693i
$414$		0			0
$415$	−24.4571			−1.20055
$416$	0.418243	+	0.250366i	0.0205061	+	0.0122752i
$417$		0			0
$418$		−	8.09530i		−	0.395954i
$419$	−25.3790			−1.23984			−0.619921	−	0.784664i	$-0.712836\pi$
$419$	−25.3790			−1.23984			−0.619921	+	0.784664i	$0.712836\pi$
$420$		0			0
$421$	−10.2213	−	5.90124i	−0.498153	−	0.287609i	0.229797	−	0.973239i	$-0.426194\pi$
$421$	−10.2213	−	5.90124i	−0.498153	−	0.287609i	−0.727951	+	0.685630i	$0.759527\pi$
$422$	−1.75958	+	1.01589i	−0.0856549	+	0.0494529i
$423$		0			0
$424$		−	0.197057i		−	0.00956993i
$425$	0.788570			0.0382512
$426$		0			0
$427$			0.571381i			0.0276511i
$428$	0.0655299	+	0.113501i	0.00316751	+	0.00548629i
$429$		0			0
$430$	8.43237	−	14.6053i	0.406645	−	0.704330i
$431$	−9.96641	−	5.75411i	−0.480065	−	0.277166i	0.240379	−	0.970679i	$-0.422728\pi$
$431$	−9.96641	−	5.75411i	−0.480065	−	0.277166i	−0.720444	+	0.693514i	$0.756062\pi$
$432$		0			0
$433$	7.00567	+	12.1342i	0.336671	+	0.583131i	0.983804	−	0.179246i	$-0.0573657\pi$
$433$	7.00567	+	12.1342i	0.336671	+	0.583131i	−0.647133	+	0.762377i	$0.724032\pi$
$434$	27.9626	+	16.1442i	1.34225	+	0.774946i
$435$		0			0
$436$	0.0569331	+	0.0328703i	0.00272660	+	0.00157420i
$437$	−15.9931	+	9.23361i	−0.765053	+	0.441703i
$438$		0			0
$439$	17.0399	+	29.5140i	0.813271	+	1.40863i	0.910563	+	0.413371i	$0.135649\pi$
$439$	17.0399	+	29.5140i	0.813271	+	1.40863i	−0.0972920	+	0.995256i	$0.531018\pi$
$440$	−5.90455	−	3.40900i	−0.281489	−	0.162517i
$441$		0			0
$442$	−0.832796	−	0.498522i	−0.0396121	−	0.0237123i
$443$	−16.3341	+	28.2916i	−0.776058	+	1.34417i	0.158139	+	0.987417i	$0.449451\pi$
$443$	−16.3341	+	28.2916i	−0.776058	+	1.34417i	−0.934198	+	0.356756i	$0.883883\pi$
$444$		0			0
$445$	−15.9319			−0.755246
$446$	−0.426204	+	0.738206i	−0.0201813	+	0.0349551i
$447$		0			0
$448$		−	25.8551i		−	1.22154i
$449$	−7.66848	+	4.42740i	−0.361898	+	0.208942i	−0.669913	−	0.742440i	$-0.733669\pi$
$449$	−7.66848	+	4.42740i	−0.361898	+	0.208942i	0.308015	+	0.951381i	$0.400335\pi$
$450$		0			0
$451$	0.359479	+	0.622636i	0.0169272	+	0.0293188i
$452$	0.197186	+	0.341536i	0.00927484	+	0.0160645i
$453$		0			0
$454$	16.2054	+	28.0686i	0.760557	+	1.31732i
$455$	16.9123	+	30.3920i	0.792861	+	1.42480i
$456$		0			0
$457$	13.1806	−	7.60982i	0.616563	−	0.355973i	−0.158967	−	0.987284i	$-0.550816\pi$
$457$	13.1806	−	7.60982i	0.616563	−	0.355973i	0.775530	+	0.631311i	$0.217483\pi$
$458$	3.22764	−	5.59044i	0.150818	−	0.261224i
$459$		0			0
$460$			0.183673i			0.00856379i
$461$		−	34.8112i		−	1.62132i	−0.585519	−	0.810658i	$-0.699109\pi$
$461$		−	34.8112i		−	1.62132i	0.585519	−	0.810658i	$-0.300891\pi$
$462$		0			0
$463$	23.7329	−	13.7022i	1.10296	−	0.636795i	0.165963	−	0.986132i	$-0.446927\pi$
$463$	23.7329	−	13.7022i	1.10296	−	0.636795i	0.936997	+	0.349337i	$0.113593\pi$
$464$	−16.6933	+	28.9137i	−0.774968	+	1.34228i
$465$		0			0
$466$	9.54797	−	5.51252i	0.442301	−	0.255363i
$467$	9.34092			0.432246			0.216123	−	0.976366i	$-0.430659\pi$
$467$	9.34092			0.432246			0.216123	+	0.976366i	$0.430659\pi$
$468$		0			0
$469$	−33.8301			−1.56213
$470$	28.0478	−	16.1934i	1.29375	−	0.746946i
$471$		0			0
$472$	−19.2991	+	33.4270i	−0.888314	+	1.53860i
$473$	−2.73070	+	1.57657i	−0.125558	+	0.0724909i
$474$		0			0
$475$		−	29.8804i		−	1.37101i
$476$		−	0.0146216i		−	0.000670182i
$477$		0			0
$478$	0.972818	−	1.68497i	0.0444957	−	0.0770687i
$479$	9.55816	−	5.51841i	0.436723	−	0.252142i	−0.265483	−	0.964115i	$-0.585532\pi$
$479$	9.55816	−	5.51841i	0.436723	−	0.252142i	0.702207	+	0.711973i	$0.252198\pi$
$480$		0			0
$481$	−8.06259	−	4.82637i	−0.367622	−	0.220064i
$482$	−2.84419	−	4.92628i	−0.129549	−	0.224386i
$483$		0			0
$484$	−0.123927	−	0.214647i	−0.00563303	−	0.00975669i
$485$	26.5285	+	45.9487i	1.20460	+	2.08642i
$486$		0			0
$487$	9.99524	−	5.77075i	0.452928	−	0.261498i	−0.256138	−	0.966640i	$-0.582450\pi$
$487$	9.99524	−	5.77075i	0.452928	−	0.261498i	0.709066	+	0.705142i	$0.249117\pi$
$488$			0.508861i			0.0230350i
$489$		0			0
$490$	6.80357	−	11.7841i	0.307354	−	0.532353i
$491$	21.2444			0.958747			0.479373	−	0.877611i	$-0.340864\pi$
$491$	21.2444			0.958747			0.479373	+	0.877611i	$0.340864\pi$
$492$		0			0
$493$	−0.808971	+	1.40118i	−0.0364342	+	0.0631059i
$494$	−18.8900	+	31.5562i	−0.849900	+	1.41978i
$495$		0			0
$496$	24.6053	+	14.2059i	1.10481	+	0.637862i
$497$	−0.500844	−	0.867487i	−0.0224659	−	0.0389121i
$498$		0			0
$499$	−11.3888	+	6.57531i	−0.509832	+	0.294351i	−0.732764	−	0.680482i	$-0.761770\pi$
$499$	−11.3888	+	6.57531i	−0.509832	+	0.294351i	0.222933	+	0.974834i	$0.428437\pi$
$500$	0.0551334	+	0.0318313i	0.00246564	+	0.00142354i
$501$		0			0
$502$	−8.37379	−	4.83461i	−0.373740	−	0.215779i
$503$	3.54282	+	6.13635i	0.157967	+	0.273606i	0.934135	−	0.356919i	$-0.116173\pi$
$503$	3.54282	+	6.13635i	0.157967	+	0.273606i	−0.776169	+	0.630525i	$0.782839\pi$
$504$		0			0
$505$	−3.91703	−	2.26150i	−0.174305	−	0.100635i
$506$	−1.41964	+	2.45889i	−0.0631108	+	0.109311i
$507$		0			0
$508$	−0.184371	−	0.319340i	−0.00818013	−	0.0141684i
$509$		−	8.66992i		−	0.384288i	−0.981367	−	0.192144i	$-0.938456\pi$
$509$		−	8.66992i		−	0.384288i	0.981367	−	0.192144i	$-0.0615440\pi$
$510$		0			0
$511$	20.9485			0.926707
$512$		−	23.0196i		−	1.01733i
$513$		0			0
$514$	−9.17368	+	5.29643i	−0.404634	+	0.233615i
$515$	−8.47398	−	4.89245i	−0.373408	−	0.215587i
$516$		0			0
$517$	−6.05525			−0.266310
$518$			11.7039i			0.514241i
$519$		0			0
$520$	15.0618	+	27.0665i	0.660502	+	1.18695i
$521$	−27.2897			−1.19558			−0.597792	−	0.801651i	$-0.703955\pi$
$521$	−27.2897			−1.19558			−0.597792	+	0.801651i	$0.703955\pi$
$522$		0			0
$523$	2.33445	−	4.04338i	0.102078	−	0.176805i	−0.810463	−	0.585790i	$-0.800784\pi$
$523$	2.33445	−	4.04338i	0.102078	−	0.176805i	0.912541	+	0.408986i	$0.134117\pi$
$524$	0.168805			0.00737430
$525$		0			0
$526$	5.49456	+	3.17229i	0.239574	+	0.138318i
$527$	1.19239	+	0.688427i	0.0519413	+	0.0299883i
$528$		0			0
$529$	−16.5230			−0.718389
$530$	0.147001	−	0.254613i	0.00638530	−	0.0110597i
$531$		0			0
$532$	−0.554042			−0.0240208
$533$	0.0516069	−	3.26592i	0.00223534	−	0.141463i
$534$		0			0
$535$			16.5580i			0.715864i
$536$	−30.1285			−1.30135
$537$		0			0
$538$	18.4979	+	10.6798i	0.797500	+	0.460437i
$539$	−2.20324	+	1.27204i	−0.0949004	+	0.0547908i
$540$		0			0
$541$			39.9796i			1.71886i	0.511255	+	0.859429i	$0.329181\pi$
$541$			39.9796i			1.71886i	−0.511255	+	0.859429i	$0.670819\pi$
$542$	−30.8544			−1.32531
$543$		0			0
$544$		−	0.0258897i		−	0.00111001i
$545$	4.15281	+	7.19287i	0.177887	+	0.308109i
$546$		0			0
$547$	5.31092	−	9.19878i	0.227078	−	0.393311i	−0.729863	−	0.683594i	$-0.760416\pi$
$547$	5.31092	−	9.19878i	0.227078	−	0.393311i	0.956941	+	0.290283i	$0.0937493\pi$
$548$	0.144310	+	0.0833174i	0.00616462	+	0.00355914i
$549$		0			0
$550$	−2.29702	−	3.97855i	−0.0979451	−	0.169646i
$551$	53.0934	+	30.6535i	2.26185	+	1.30588i
$552$		0			0
$553$	−11.8116	−	6.81940i	−0.502278	−	0.289990i
$554$	7.35418	−	4.24594i	0.312449	−	0.180393i
$555$		0			0
$556$	0.130321	+	0.225723i	0.00552684	+	0.00957277i
$557$	27.4337	+	15.8389i	1.16240	+	0.671114i	0.951879	−	0.306474i	$-0.0991493\pi$
$557$	27.4337	+	15.8389i	1.16240	+	0.671114i	0.210525	+	0.977588i	$0.432483\pi$
$558$		0			0
$559$	14.3234	+	0.226333i	0.605815	+	0.00957287i
$560$	19.0596	−	33.0122i	0.805414	−	1.39502i
$561$		0			0
$562$	−10.6493			−0.449213
$563$	10.6403	−	18.4295i	0.448435	−	0.776713i	−0.549849	−	0.835264i	$-0.685315\pi$
$563$	10.6403	−	18.4295i	0.448435	−	0.776713i	0.998284	+	0.0585513i	$0.0186481\pi$
$564$		0			0
$565$			49.8245i			2.09613i
$566$	−34.1776	+	19.7324i	−1.43659	+	0.829415i
$567$		0			0
$568$	−0.446042	−	0.772567i	−0.0187155	−	0.0324162i
$569$	−1.90257	−	3.29536i	−0.0797601	−	0.138148i	0.823386	−	0.567481i	$-0.192082\pi$
$569$	−1.90257	−	3.29536i	−0.0797601	−	0.138148i	−0.903146	+	0.429333i	$0.858749\pi$
$570$		0			0
$571$	16.1472	+	27.9678i	0.675740	+	1.17042i	0.976252	+	0.216638i	$0.0695092\pi$
$571$	16.1472	+	27.9678i	0.675740	+	1.17042i	−0.300512	+	0.953778i	$0.597157\pi$
$572$	0.00108055	−	0.0683821i	4.51801e−5	−	0.00285920i
$573$		0			0
$574$	−3.52325	+	2.03415i	−0.147058	+	0.0849037i
$575$	−5.24001	+	9.07597i	−0.218524	+	0.378494i
$576$		0			0
$577$			5.48831i			0.228481i	0.993453	+	0.114241i	$0.0364435\pi$
$577$			5.48831i			0.228481i	−0.993453	+	0.114241i	$0.963557\pi$
$578$		−	23.8460i		−	0.991863i
$579$		0			0
$580$	0.528060	−	0.304876i	0.0219265	−	0.0126593i
$581$	−12.9375	+	22.4083i	−0.536736	+	0.929654i
$582$		0			0
$583$	−0.0476041	+	0.0274843i	−0.00197156	+	0.00113828i
$584$	18.6563			0.772004
$585$		0			0
$586$	−32.2427			−1.33193
$587$	−16.6886	+	9.63518i	−0.688813	+	0.397687i	−0.803167	−	0.595753i	$-0.796854\pi$
$587$	−16.6886	+	9.63518i	−0.688813	+	0.397687i	0.114354	+	0.993440i	$0.463520\pi$
$588$		0			0
$589$	26.0858	−	45.1820i	1.07485	−	1.86169i
$590$	−49.8719	+	28.7935i	−2.05319	+	1.18541i
$591$		0			0
$592$			10.2987i			0.423274i
$593$		−	17.9934i		−	0.738902i	−0.929250	−	0.369451i	$-0.879546\pi$
$593$		−	17.9934i		−	0.738902i	0.929250	−	0.369451i	$-0.120454\pi$
$594$		0			0
$595$	0.923642	−	1.59979i	0.0378656	−	0.0655852i
$596$	−0.302647	+	0.174734i	−0.0123969	+	0.00715737i
$597$		0			0
$598$	11.2716	−	6.27232i	0.460930	−	0.256494i
$599$	1.96620	+	3.40556i	0.0803367	+	0.139147i	0.903395	−	0.428810i	$-0.141067\pi$
$599$	1.96620	+	3.40556i	0.0803367	+	0.139147i	−0.823058	+	0.567958i	$0.807734\pi$
$600$		0			0
$601$	−12.2462	−	21.2110i	−0.499533	−	0.865216i	0.500467	−	0.865756i	$-0.333162\pi$
$601$	−12.2462	−	21.2110i	−0.499533	−	0.865216i	−1.00000		0.000539252i	$0.999828\pi$
$602$	−8.92119	−	15.4520i	−0.363601	−	0.629775i
$603$		0			0
$604$	0.0218130	−	0.0125937i	0.000887559	−	0.000512432i
$605$		−	31.3135i		−	1.27308i
$606$		0			0
$607$	−6.72493	+	11.6479i	−0.272956	+	0.472774i	−0.969617	−	0.244626i	$-0.921335\pi$
$607$	−6.72493	+	11.6479i	−0.272956	+	0.472774i	0.696661	+	0.717400i	$0.254668\pi$
$608$	−0.981011			−0.0397853
$609$		0			0
$610$	−0.379600	+	0.657487i	−0.0153696	+	0.0266209i
$611$	23.6039	+	14.1296i	0.954913	+	0.571623i
$612$		0			0
$613$	20.2969	+	11.7184i	0.819784	+	0.473303i	0.850342	−	0.526230i	$-0.176395\pi$
$613$	20.2969	+	11.7184i	0.819784	+	0.473303i	−0.0305579	+	0.999533i	$0.509728\pi$
$614$	2.32896	+	4.03388i	0.0939893	+	0.162794i
$615$		0			0
$616$	−6.24684	+	3.60661i	−0.251692	+	0.145315i
$617$	20.1193	+	11.6159i	0.809974	+	0.467639i	0.846947	−	0.531677i	$-0.178438\pi$
$617$	20.1193	+	11.6159i	0.809974	+	0.467639i	−0.0369726	+	0.999316i	$0.511771\pi$
$618$		0			0
$619$	1.01355	+	0.585173i	0.0407380	+	0.0235201i	0.520231	−	0.854026i	$-0.325846\pi$
$619$	1.01355	+	0.585173i	0.0407380	+	0.0235201i	−0.479493	+	0.877546i	$0.659179\pi$
$620$	−0.259446	−	0.449374i	−0.0104196	−	0.0180473i
$621$		0			0
$622$	−30.8478	−	17.8100i	−1.23688	−	0.714116i
$623$	−8.42775	+	14.5973i	−0.337651	+	0.584828i
$624$		0			0
$625$	14.3162	+	24.7964i	0.572649	+	0.991858i
$626$			24.5055i			0.979436i
$627$		0			0
$628$	−0.267536			−0.0106759
$629$			0.499083i			0.0198998i
$630$		0			0
$631$	−4.36496	+	2.52011i	−0.173766	+	0.100324i	−0.584361	−	0.811494i	$-0.698655\pi$
$631$	−4.36496	+	2.52011i	−0.173766	+	0.100324i	0.410594	+	0.911818i	$0.365321\pi$
$632$	−10.5191	−	6.07323i	−0.418429	−	0.241580i
$633$		0			0
$634$	−18.3421			−0.728457
$635$		−	46.5865i		−	1.84873i
$636$		0			0
$637$	11.5567	+	0.182615i	0.457893	+	0.00723546i
$638$	9.42577			0.373170
$639$		0			0
$640$	16.7688	−	29.0443i	0.662844	−	1.14808i
$641$	34.6823			1.36987			0.684934	−	0.728605i	$-0.259831\pi$
$641$	34.6823			1.36987			0.684934	+	0.728605i	$0.259831\pi$
$642$		0			0
$643$	−33.4281	−	19.2997i	−1.31827	−	0.761106i	−0.334824	−	0.942281i	$-0.608677\pi$
$643$	−33.4281	−	19.2997i	−1.31827	−	0.761106i	−0.983451	+	0.181174i	$0.942010\pi$
$644$	0.168286	+	0.0971602i	0.00663141	+	0.00382865i
$645$		0			0
$646$	1.95337			0.0768542
$647$	18.4314	−	31.9241i	0.724612	−	1.25507i	−0.234521	−	0.972111i	$-0.575352\pi$
$647$	18.4314	−	31.9241i	0.724612	−	1.25507i	0.959133	−	0.282954i	$-0.0913145\pi$
$648$		0			0
$649$	10.7669			0.422637
$650$	−0.329760	+	20.8687i	−0.0129342	+	0.818538i
$651$		0			0
$652$		−	0.0466529i		−	0.00182707i
$653$	32.6420			1.27738			0.638690	−	0.769464i	$-0.279477\pi$
$653$	32.6420			1.27738			0.638690	+	0.769464i	$0.279477\pi$
$654$		0			0
$655$	18.4695	+	10.6634i	0.721662	+	0.416652i
$656$	−3.10024	+	1.78992i	−0.121044	+	0.0698847i
$657$		0			0
$658$		−	34.2642i		−	1.33576i
$659$	−8.86611			−0.345375			−0.172687	−	0.984977i	$-0.555245\pi$
$659$	−8.86611			−0.345375			−0.172687	+	0.984977i	$0.555245\pi$
$660$		0			0
$661$			19.1922i			0.746491i	0.927733	+	0.373245i	$0.121755\pi$
$661$			19.1922i			0.746491i	−0.927733	+	0.373245i	$0.878245\pi$
$662$	3.34296	+	5.79018i	0.129928	+	0.225042i
$663$		0			0
$664$	−11.5219	+	19.9564i	−0.447135	+	0.774460i
$665$	−60.6193	−	34.9986i	−2.35071	−	1.35719i
$666$		0			0
$667$	−10.7512	−	18.6215i	−0.416286	−	0.721029i
$668$	0.411237	+	0.237428i	0.0159112	+	0.00918635i
$669$		0			0
$670$	−38.9283	−	22.4753i	−1.50393	−	0.868295i
$671$	0.122928	−	0.0709727i	0.00474559	−	0.00273987i
$672$		0			0
$673$	−2.67791	−	4.63828i	−0.103226	−	0.178792i	0.809786	−	0.586725i	$-0.199583\pi$
$673$	−2.67791	−	4.63828i	−0.103226	−	0.178792i	−0.913012	+	0.407933i	$0.866250\pi$
$674$	−31.0869	−	17.9480i	−1.19742	−	0.691331i
$675$		0			0
$676$	−0.163778	+	0.264038i	−0.00629916	+	0.0101553i
$677$	−1.63177	+	2.82630i	−0.0627139	+	0.108624i	−0.895678	−	0.444704i	$-0.853309\pi$
$677$	−1.63177	+	2.82630i	−0.0627139	+	0.108624i	0.832964	+	0.553328i	$0.186642\pi$
$678$		0			0
$679$	56.1327			2.15417
$680$	0.822578	−	1.42475i	0.0315444	−	0.0546365i
$681$		0			0
$682$		−	8.02124i		−	0.307149i
$683$	22.0781	−	12.7468i	0.844794	−	0.487742i	−0.0140968	−	0.999901i	$-0.504487\pi$
$683$	22.0781	−	12.7468i	0.844794	−	0.487742i	0.858891	+	0.512159i	$0.171154\pi$
$684$		0			0
$685$	10.5262	+	18.2320i	0.402187	+	0.696608i
$686$	8.51986	+	14.7568i	0.325290	+	0.563418i
$687$		0			0
$688$	−7.85008	−	13.5967i	−0.299282	−	0.518371i
$689$	0.249698	+	0.00394564i	0.00951275	+	0.000150317i
$690$		0			0
$691$	19.2220	−	11.0978i	0.731240	−	0.422182i	−0.0876354	−	0.996153i	$-0.527931\pi$
$691$	19.2220	−	11.0978i	0.731240	−	0.422182i	0.818876	+	0.573971i	$0.194598\pi$
$692$	−0.0402976	+	0.0697975i	−0.00153189	+	0.00265330i
$693$		0			0
$694$		−	7.62958i		−	0.289615i
$695$			32.9293i			1.24908i
$696$		0			0
$697$	−0.150240	+	0.0867410i	−0.00569074	+	0.00328555i
$698$	18.5535	−	32.1355i	0.702259	−	1.21635i
$699$		0			0
$700$	−0.272291	+	0.157208i	−0.0102916	+	0.00594189i
$701$	−35.2587			−1.33170			−0.665851	−	0.746085i	$-0.731931\pi$
$701$	−35.2587			−1.33170			−0.665851	+	0.746085i	$0.731931\pi$
$702$		0			0
$703$	18.9112			0.713250
$704$	−5.56253	+	3.21153i	−0.209646	+	0.121039i
$705$		0			0
$706$	21.0031	−	36.3785i	0.790464	−	1.36912i
$707$	−4.14410	+	2.39260i	−0.155855	+	0.0899828i
$708$		0			0
$709$		−	19.8184i		−	0.744297i	−0.928173	−	0.372149i	$-0.878621\pi$
$709$		−	19.8184i		−	0.744297i	0.928173	−	0.372149i	$-0.121379\pi$
$710$		−	1.33095i		−	0.0499498i
$711$		0			0
$712$	−7.50559	+	13.0001i	−0.281284	+	0.487198i
$713$	−15.8468	+	9.14913i	−0.593466	+	0.342638i
$714$		0			0
$715$	4.43789	−	7.41363i	0.165968	−	0.277254i
$716$	−0.154524	−	0.267643i	−0.00577483	−	0.0100023i
$717$		0			0
$718$	−19.3862	−	33.5779i	−0.723487	−	1.25312i
$719$	−12.5408	−	21.7214i	−0.467695	−	0.810071i	0.531624	−	0.846981i	$-0.321582\pi$
$719$	−12.5408	−	21.7214i	−0.467695	−	0.810071i	−0.999319	+	0.0369095i	$0.988249\pi$
$720$		0			0
$721$	−8.96521	+	5.17607i	−0.333882	+	0.192767i
$722$		−	47.3078i		−	1.76061i
$723$		0			0
$724$	0.136144	−	0.235808i	0.00505975	−	0.00876374i
$725$	34.7913			1.29212
$726$		0			0
$727$	−5.05060	+	8.74790i	−0.187317	+	0.324442i	−0.944355	−	0.328929i	$-0.893312\pi$
$727$	−5.05060	+	8.74790i	−0.187317	+	0.324442i	0.757038	+	0.653371i	$0.226646\pi$
$728$	32.7666	+	0.517766i	1.21441	+	0.0191897i
$729$		0			0
$730$	24.1054	+	13.9173i	0.892181	+	0.515101i
$731$	−0.380421	−	0.658909i	−0.0140704	−	0.0243706i
$732$		0			0
$733$	−10.3089	+	5.95182i	−0.380766	+	0.219836i	−0.678152	−	0.734922i	$-0.737219\pi$
$733$	−10.3089	+	5.95182i	−0.380766	+	0.219836i	0.297385	+	0.954758i	$0.403885\pi$
$734$	−26.1005	−	15.0691i	−0.963387	−	0.556212i
$735$		0			0
$736$	0.297975	+	0.172036i	0.0109835	+	0.00634133i
$737$	4.20213	+	7.27830i	0.154787	+	0.268100i
$738$		0			0
$739$	22.7597	+	13.1403i	0.837231	+	0.483375i	0.856322	−	0.516442i	$-0.172744\pi$
$739$	22.7597	+	13.1403i	0.837231	+	0.483375i	−0.0190912	+	0.999818i	$0.506077\pi$
$740$	0.0940444	−	0.162890i	0.00345714	−	0.00598795i
$741$		0			0
$742$	−0.155522	−	0.269373i	−0.00570940	−	0.00988898i
$743$			7.21139i			0.264560i	0.991212	+	0.132280i	$0.0422299\pi$
$743$			7.21139i			0.264560i	−0.991212	+	0.132280i	$0.957770\pi$
$744$		0			0
$745$	−44.1513			−1.61758
$746$		−	34.9255i		−	1.27871i
$747$		0			0
$748$	−0.00314574	+	0.00181619i	−0.000115019	+	6.64065e-5i
$749$	15.1709	+	8.75892i	0.554333	+	0.320044i
$750$		0			0
$751$	−0.499000			−0.0182088			−0.00910439	−	0.999959i	$-0.502898\pi$
$751$	−0.499000			−0.0182088			−0.00910439	+	0.999959i	$0.502898\pi$
$752$		−	30.1504i		−	1.09947i
$753$		0			0
$754$	−36.7425	−	21.9945i	−1.33808	−	0.800994i
$755$	3.18216			0.115811
$756$		0			0
$757$	24.1489	−	41.8272i	0.877708	−	1.52024i	0.0238592	−	0.999715i	$-0.492405\pi$
$757$	24.1489	−	41.8272i	0.877708	−	1.52024i	0.853849	−	0.520520i	$-0.174262\pi$
$758$	−1.23994			−0.0450366
$759$		0			0
$760$	−53.9864	−	31.1690i	−1.95829	−	1.13062i
$761$	27.4526	+	15.8498i	0.995157	+	0.574554i	0.906812	−	0.421536i	$-0.138509\pi$
$761$	27.4526	+	15.8498i	0.995157	+	0.574554i	0.0883449	+	0.996090i	$0.471842\pi$
$762$		0			0
$763$	8.78709			0.318114
$764$	0.0390615	−	0.0676565i	0.00141320	−	0.00244773i
$765$		0			0
$766$	−4.03424			−0.145763
$767$	−41.9703	−	25.1239i	−1.51546	−	0.907173i
$768$		0			0
$769$		−	8.88528i		−	0.320411i	−0.987084	−	0.160206i	$-0.948784\pi$
$769$		−	8.88528i		−	0.320411i	0.987084	−	0.160206i	$-0.0512158\pi$
$770$	−10.7619			−0.387831
$771$		0			0
$772$	0.394585	+	0.227814i	0.0142014	+	0.00819919i
$773$	−39.3502	+	22.7188i	−1.41533	+	0.817140i	−0.995884	−	0.0906413i	$-0.971108\pi$
$773$	−39.3502	+	22.7188i	−1.41533	+	0.817140i	−0.419444	+	0.907781i	$0.637775\pi$
$774$		0			0
$775$		−	29.6071i		−	1.06352i
$776$	49.9907			1.79456
$777$		0			0
$778$			16.8897i			0.605524i
$779$	3.28678	+	5.69287i	0.117761	+	0.203968i
$780$		0			0
$781$	−0.124422	+	0.215506i	−0.00445218	+	0.00771139i
$782$	−0.593321	−	0.342554i	−0.0212171	−	0.0122497i
$783$		0			0
$784$	−6.33376	−	10.9704i	−0.226206	−	0.391800i
$785$	−29.2719	−	16.9001i	−1.04476	−	0.603191i
$786$		0			0
$787$	−4.22481	−	2.43919i	−0.150598	−	0.0869478i	0.422807	−	0.906220i	$-0.361045\pi$
$787$	−4.22481	−	2.43919i	−0.150598	−	0.0869478i	−0.573405	+	0.819272i	$0.694378\pi$
$788$	−0.0509969	+	0.0294431i	−0.00181669	+	0.00104887i
$789$		0			0
$790$	−9.06102	−	15.6942i	−0.322377	−	0.558373i
$791$	45.6507	+	26.3564i	1.62315	+	0.937127i
$792$		0			0
$793$	−0.644797	−	0.0101889i	−0.0228974	−	0.000361817i
$794$	6.33473	−	10.9721i	0.224811	−	0.389385i
$795$		0			0
$796$	−0.562223			−0.0199275
$797$	17.9543	−	31.0978i	0.635974	−	1.10154i	−0.350333	−	0.936625i	$-0.613932\pi$
$797$	17.9543	−	31.0978i	0.635974	−	1.10154i	0.986308	−	0.164915i	$-0.0527350\pi$
$798$		0			0
$799$		−	1.46111i		−	0.0516903i
$800$	−0.482131	+	0.278359i	−0.0170459	+	0.00984146i
$801$		0			0
$802$	23.3638	+	40.4673i	0.825004	+	1.42895i
$803$	−2.60207	−	4.50691i	−0.0918249	−	0.159045i
$804$		0			0
$805$	12.2751	+	21.2611i	0.432641	+	0.749356i
$806$	−18.7172	+	31.2675i	−0.659284	+	1.10135i
$807$		0			0
$808$	−3.69065	+	2.13080i	−0.129837	+	0.0749613i
$809$	12.1005	−	20.9587i	0.425430	−	0.736867i	−0.571030	−	0.820929i	$-0.693456\pi$
$809$	12.1005	−	20.9587i	0.425430	−	0.736867i	0.996461	+	0.0840620i	$0.0267894\pi$
$810$		0			0
$811$		−	14.3469i		−	0.503789i	−0.967755	−	0.251894i	$-0.918946\pi$
$811$		−	14.3469i		−	0.503789i	0.967755	−	0.251894i	$-0.0810536\pi$
$812$		−	0.645099i		−	0.0226385i
$813$		0			0
$814$	2.51801	−	1.45377i	0.0882563	−	0.0509548i
$815$	2.94704	−	5.10443i	0.103230	−	0.178800i
$816$		0			0
$817$	−24.9673	+	14.4149i	−0.873496	+	0.504313i
$818$	47.6663			1.66661
$819$		0			0
$820$	0.0653799			0.00228317
$821$	4.33057	−	2.50026i	0.151138	−	0.0872596i	−0.422524	−	0.906352i	$-0.638856\pi$
$821$	4.33057	−	2.50026i	0.151138	−	0.0872596i	0.573662	+	0.819092i	$0.305522\pi$
$822$		0			0
$823$	−2.26172	+	3.91741i	−0.0788385	+	0.136552i	−0.902749	−	0.430168i	$-0.858454\pi$
$823$	−2.26172	+	3.91741i	−0.0788385	+	0.136552i	0.823911	+	0.566720i	$0.191788\pi$
$824$	−7.98425	+	4.60971i	−0.278144	+	0.160587i
$825$		0			0
$826$			60.9254i			2.11987i
$827$			7.63184i			0.265385i	0.991157	+	0.132693i	$0.0423623\pi$
$827$			7.63184i			0.265385i	−0.991157	+	0.132693i	$0.957638\pi$
$828$		0			0
$829$	8.47700	−	14.6826i	0.294418	−	0.509948i	−0.680431	−	0.732812i	$-0.738207\pi$
$829$	8.47700	−	14.6826i	0.294418	−	0.509948i	0.974849	+	0.222864i	$0.0715407\pi$
$830$	−29.7742	+	17.1902i	−1.03348	+	0.596679i
$831$		0			0
$832$	29.1772	+	0.461047i	1.01154	+	0.0159839i
$833$	−0.306939	−	0.531634i	−0.0106348	−	0.0184200i
$834$		0			0
$835$	29.9964	+	51.9553i	1.03807	+	1.79799i
$836$	0.0688190	+	0.119198i	0.00238015	+	0.00412255i
$837$		0			0
$838$	−30.8965	+	17.8381i	−1.06730	+	0.616206i
$839$			22.9697i			0.793003i	0.918034	+	0.396501i	$0.129776\pi$
$839$			22.9697i			0.793003i	−0.918034	+	0.396501i	$0.870224\pi$
$840$		0			0
$841$	−21.1914	+	36.7045i	−0.730737	+	1.26567i
$842$	−16.5912			−0.571771
$843$		0			0
$844$	0.0172724	−	0.0299167i	0.000594540	−	0.00102977i
$845$	−34.5986	+	18.5434i	−1.19023	+	0.637912i
$846$		0			0
$847$	−28.6904	−	16.5644i	−0.985813	−	0.569159i
$848$	−0.136850	−	0.237031i	−0.00469944	−	0.00813967i
$849$		0			0
$850$	0.960008	−	0.554261i	0.0329280	−	0.0190110i
$851$	−5.74415	−	3.31639i	−0.196907	−	0.113684i
$852$		0			0
$853$	−16.0483	−	9.26548i	−0.549483	−	0.317244i	0.199430	−	0.979912i	$-0.436091\pi$
$853$	−16.0483	−	9.26548i	−0.549483	−	0.317244i	−0.748913	+	0.662668i	$0.769424\pi$
$854$	0.401606	+	0.695602i	0.0137427	+	0.0238030i
$855$		0			0
$856$	13.5109	+	7.80053i	0.461793	+	0.266617i
$857$	−20.7985	+	36.0241i	−0.710464	+	1.23056i	0.254219	+	0.967147i	$0.418181\pi$
$857$	−20.7985	+	36.0241i	−0.710464	+	1.23056i	−0.964683	+	0.263413i	$0.915152\pi$
$858$		0			0
$859$	−7.48523	−	12.9648i	−0.255393	−	0.442353i	0.709609	−	0.704595i	$-0.248871\pi$
$859$	−7.48523	−	12.9648i	−0.255393	−	0.442353i	−0.965002	+	0.262242i	$0.915538\pi$
$860$			0.286738i			0.00977767i
$861$		0			0
$862$	−16.1775			−0.551009
$863$			30.1011i			1.02465i	0.858791	+	0.512327i	$0.171216\pi$
$863$			30.1011i			1.02465i	−0.858791	+	0.512327i	$0.828784\pi$
$864$		0			0
$865$	−8.81815	+	5.09116i	−0.299826	+	0.173105i
$866$	17.0575	+	9.84813i	0.579636	+	0.334653i
$867$		0			0
$868$	−0.548973			−0.0186334
$869$			3.38822i			0.114938i
$870$		0			0
$871$	0.603258	−	38.1769i	0.0204406	−	1.29358i
$872$	7.82562			0.265009
$873$		0			0
$874$	−12.9800	+	22.4821i	−0.439056	+	0.760468i
$875$	8.50932			0.287667
$876$		0			0
$877$	3.98782	+	2.30237i	0.134659	+	0.0777454i	0.565816	−	0.824531i	$-0.308561\pi$
$877$	3.98782	+	2.30237i	0.134659	+	0.0777454i	−0.431157	+	0.902277i	$0.641895\pi$
$878$	41.4890	+	23.9537i	1.40018	+	0.808397i
$879$		0			0
$880$	−9.46976			−0.319225
$881$	23.1838	−	40.1555i	0.781082	−	1.35287i	−0.150229	−	0.988651i	$-0.548001\pi$
$881$	23.1838	−	40.1555i	0.781082	−	1.35287i	0.931312	−	0.364223i	$-0.118666\pi$
$882$		0			0
$883$	−20.7632			−0.698737			−0.349368	−	0.936985i	$-0.613604\pi$
$883$	−20.7632			−0.698737			−0.349368	+	0.936985i	$0.613604\pi$
$884$	0.0165003		0.000260733i	0.000554967		8.76939e-6i
$885$		0			0
$886$			45.9230i			1.54281i
$887$	−38.6528			−1.29783			−0.648916	−	0.760860i	$-0.724778\pi$
$887$	−38.6528			−1.29783			−0.648916	+	0.760860i	$0.724778\pi$
$888$		0			0
$889$	−42.6839	−	24.6435i	−1.43157	−	0.826518i
$890$	−19.3956	+	11.1981i	−0.650142	+	0.375360i
$891$		0			0
$892$		−	0.0144928i		−	0.000485255i
$893$	−55.3643			−1.85269
$894$		0			0
$895$		−	39.0448i		−	1.30512i
$896$	−17.7408	−	30.7280i	−0.592680	−	1.02655i
$897$		0			0
$898$	−6.22376	+	10.7799i	−0.207690	+	0.359729i
$899$	52.6076	+	30.3730i	1.75456	+	1.01300i
$900$		0			0
$901$	−0.00663185	−	0.0114867i	−0.000220939	−	0.000382677i
$902$	0.875264	+	0.505334i	0.0291431	+	0.0168258i
$903$		0			0
$904$	40.6556	+	23.4725i	1.35219	+	0.780685i
$905$	29.7918	−	17.2003i	0.990312	−	0.571757i
$906$		0			0
$907$	11.6137	+	20.1154i	0.385625	+	0.667922i	0.991856	−	0.127367i	$-0.0406524\pi$
$907$	11.6137	+	20.1154i	0.385625	+	0.667922i	−0.606230	+	0.795289i	$0.707319\pi$
$908$	−0.477227	−	0.275527i	−0.0158373	−	0.00914370i
$909$		0			0
$910$	41.9507	+	25.1123i	1.39065	+	0.832463i
$911$	28.3835	−	49.1616i	0.940386	−	1.62880i	0.175649	−	0.984453i	$-0.443798\pi$
$911$	28.3835	−	49.1616i	0.940386	−	1.62880i	0.764737	−	0.644343i	$-0.222869\pi$
$912$		0			0
$913$	6.42798			0.212735
$914$	10.6974	−	18.5285i	0.353839	−	0.612867i
$915$		0			0
$916$			0.109754i			0.00362638i
$917$	19.5401	−	11.2815i	0.645273	−	0.372548i
$918$		0			0
$919$	10.2662	+	17.7815i	0.338649	+	0.586557i	0.984179	−	0.177178i	$-0.0566967\pi$
$919$	10.2662	+	17.7815i	0.338649	+	0.586557i	−0.645530	+	0.763735i	$0.723363\pi$
$920$	10.9320	+	18.9348i	0.360417	+	0.624260i
$921$		0			0
$922$	−24.4677	−	42.3793i	−0.805800	−	1.39569i
$923$	0.987880	−	0.549727i	0.0325165	−	0.0180945i
$924$		0			0
$925$	9.29418	−	5.36600i	0.305591	−	0.176433i
$926$	19.2617	−	33.3622i	0.632978	−	1.09635i
$927$		0			0
$928$		−	1.14224i		−	0.0374959i
$929$		−	43.6220i		−	1.43119i	−0.698515	−	0.715595i	$-0.746155\pi$
$929$		−	43.6220i		−	1.43119i	0.698515	−	0.715595i	$-0.253845\pi$
$930$		0			0
$931$	−20.1446	+	11.6305i	−0.660214	+	0.381175i
$932$	−0.0937250	+	0.162336i	−0.00307006	+	0.00531750i
$933$		0			0
$934$	11.3717	−	6.56545i	0.372093	−	0.214828i
$935$	−0.458912			−0.0150080
$936$		0			0
$937$	−50.6045			−1.65318			−0.826588	−	0.562807i	$-0.809721\pi$
$937$	−50.6045			−1.65318			−0.826588	+	0.562807i	$0.809721\pi$
$938$	−41.1850	+	23.7781i	−1.34474	+	0.776384i
$939$		0			0
$940$	−0.275323	+	0.476874i	−0.00898005	+	0.0155539i
$941$	−6.38079	+	3.68395i	−0.208008	+	0.120093i	−0.600385	−	0.799711i	$-0.704986\pi$
$941$	−6.38079	+	3.68395i	−0.208008	+	0.120093i	0.392377	+	0.919804i	$0.371653\pi$
$942$		0			0
$943$		−	2.30556i		−	0.0750794i
$944$			53.6105i			1.74487i
$945$		0			0
$946$	−2.21625	+	3.83866i	−0.0720565	+	0.124805i
$947$	−13.4404	+	7.75979i	−0.436753	+	0.252159i	−0.702219	−	0.711961i	$-0.747807\pi$
$947$	−13.4404	+	7.75979i	−0.436753	+	0.252159i	0.265466	+	0.964120i	$0.414474\pi$
$948$		0			0
$949$	−0.373553	+	23.6401i	−0.0121260	+	0.767391i
$950$	−21.0020	−	36.3766i	−0.681395	−	1.18021i
$951$		0			0
$952$	−0.870262	−	1.50734i	−0.0282054	−	0.0488531i
$953$	11.8288	+	20.4880i	0.383171	+	0.663672i	0.991514	−	0.130003i	$-0.0414986\pi$
$953$	11.8288	+	20.4880i	0.383171	+	0.663672i	−0.608343	+	0.793675i	$0.708165\pi$
$954$		0			0
$955$	8.54766	−	4.93499i	0.276596	−	0.159693i
$956$			0.0330801i			0.00106989i
$957$		0			0
$958$	7.75743	−	13.4363i	0.250631	−	0.434106i
$959$	22.2729			0.719229
$960$		0			0
$961$	10.3472	−	17.9218i	0.333780	−	0.578123i
$962$	−13.2077	−	0.208704i	−0.425835	−	0.00672889i
$963$		0			0
$964$	0.0837575	+	0.0483574i	0.00269765	+	0.00155749i
$965$	28.7818	+	49.8515i	0.926518	+	1.60478i
$966$		0			0
$967$	12.2838	−	7.09208i	0.395022	−	0.228066i	−0.289312	−	0.957235i	$-0.593426\pi$
$967$	12.2838	−	7.09208i	0.395022	−	0.228066i	0.684334	+	0.729169i	$0.260093\pi$
$968$	−25.5511	−	14.7519i	−0.821243	−	0.474145i
$969$		0			0
$970$	64.5918	+	37.2921i	2.07392	+	1.19738i
$971$	16.0778	+	27.8476i	0.515963	+	0.893674i	0.999828	+	0.0185312i	$0.00589901\pi$
$971$	16.0778	+	27.8476i	0.515963	+	0.893674i	−0.483866	+	0.875142i	$0.660768\pi$
$972$		0			0
$973$	30.1707	+	17.4191i	0.967230	+	0.558430i
$974$	8.11217	−	14.0507i	0.259931	−	0.450213i
$975$		0			0
$976$	0.353388	+	0.612085i	0.0113117	+	0.0195924i
$977$			52.0954i			1.66668i	0.552760	+	0.833340i	$0.313575\pi$
$977$			52.0954i			1.66668i	−0.552760	+	0.833340i	$0.686425\pi$
$978$		0			0
$979$	4.18733			0.133828
$980$			0.231351i			0.00739025i
$981$		0			0
$982$	25.8630	−	14.9320i	0.825323	−	0.476500i
$983$	22.2548	+	12.8488i	0.709819	+	0.409814i	0.810994	−	0.585055i	$-0.198927\pi$
$983$	22.2548	+	12.8488i	0.709819	+	0.409814i	−0.101175	+	0.994869i	$0.532260\pi$
$984$		0			0
$985$	−7.43962			−0.237046
$986$			2.27440i			0.0724317i
$987$		0			0
$988$	0.00987966	−	0.625230i	0.000314314	−	0.0198912i
$989$	10.1115			0.321528
$990$		0			0
$991$	−6.04305	+	10.4669i	−0.191964	+	0.332491i	−0.945901	−	0.324455i	$-0.894819\pi$
$991$	−6.04305	+	10.4669i	−0.191964	+	0.332491i	0.753937	+	0.656947i	$0.228152\pi$
$992$	−0.972036			−0.0308622
$993$		0			0
$994$	−1.21946	−	0.704055i	−0.0386789	−	0.0223313i
$995$	−61.5145	−	35.5154i	−1.95014	−	1.12591i
$996$		0			0
$997$	55.5937			1.76067			0.880335	−	0.474353i	$-0.157318\pi$
$997$	55.5937			1.76067			0.880335	+	0.474353i	$0.157318\pi$
$998$	−9.24317	+	16.0096i	−0.292587	+	0.506776i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.r.b.316.9		22
3.2	odd	2		117.2.r.b.43.3	yes	22
9.4	even	3		351.2.l.b.199.9		22
9.5	odd	6		117.2.l.b.4.3	✓	22
13.10	even	6		351.2.l.b.127.3		22
39.23	odd	6		117.2.l.b.88.9	yes	22
117.23	odd	6		117.2.r.b.49.3	yes	22
117.49	even	6	inner	351.2.r.b.10.9		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.l.b.4.3	✓	22	9.5	odd	6
117.2.l.b.88.9	yes	22	39.23	odd	6
117.2.r.b.43.3	yes	22	3.2	odd	2
117.2.r.b.49.3	yes	22	117.23	odd	6
351.2.l.b.127.3		22	13.10	even	6
351.2.l.b.199.9		22	9.4	even	3
351.2.r.b.10.9		22	117.49	even	6	inner
351.2.r.b.316.9		22	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:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.21740 - 0.702869i) q^{2} +(-0.0119503 + 0.0206986i) q^{4} +(-2.61504 + 1.50979i) q^{5} +3.19463i q^{7} +2.84507i q^{8} +O(q^{10})\)	\(q+(1.21740 - 0.702869i) q^{2} +(-0.0119503 + 0.0206986i) q^{4} +(-2.61504 + 1.50979i) q^{5} +3.19463i q^{7} +2.84507i q^{8} +(-2.12237 + 3.67605i) q^{10} +(0.687300 - 0.396813i) q^{11} +(-3.60510 - 0.0569665i) q^{13} +(2.24541 + 3.88916i) q^{14} +(1.97581 + 3.42221i) q^{16} +(0.0957495 + 0.165843i) q^{17} +(6.28411 - 3.62813i) q^{19} -0.0721699i q^{20} +(0.557815 - 0.966164i) q^{22} -2.54500 q^{23} +(2.05894 - 3.56619i) q^{25} +(-4.42891 + 2.46456i) q^{26} +(-0.0661242 - 0.0381768i) q^{28} +(4.22442 + 7.31690i) q^{29} +(6.22662 - 3.59494i) q^{31} +(-0.117082 - 0.0675976i) q^{32} +(0.233132 + 0.134599i) q^{34} +(-4.82322 - 8.35407i) q^{35} +(2.25703 + 1.30310i) q^{37} +(5.10020 - 8.83381i) q^{38} +(-4.29547 - 7.43997i) q^{40} +0.905916i q^{41} -3.97309 q^{43} +0.0189682i q^{44} +(-3.09830 + 1.78880i) q^{46} +(-6.60765 - 3.81493i) q^{47} -3.20565 q^{49} -5.78866i q^{50} +(0.0442612 - 0.0739396i) q^{52} -0.0692625 q^{53} +(-1.19821 + 2.07536i) q^{55} -9.08895 q^{56} +(10.2856 + 5.93842i) q^{58} +(11.7491 + 6.78334i) q^{59} +0.178857 q^{61} +(5.05354 - 8.75299i) q^{62} -8.09330 q^{64} +(9.51347 - 5.29398i) q^{65} +10.5897i q^{67} -0.00457694 q^{68} +(-11.7436 - 6.78019i) q^{70} +(-0.271545 + 0.156777i) q^{71} -6.55741i q^{73} +3.66363 q^{74} +0.173429i q^{76} +(1.26767 + 2.19567i) q^{77} +(-2.13465 + 3.69732i) q^{79} +(-10.3336 - 5.96613i) q^{80} +(0.636740 + 1.10287i) q^{82} +(7.01438 + 4.04975i) q^{83} +(-0.500776 - 0.289123i) q^{85} +(-4.83686 + 2.79256i) q^{86} +(1.12896 + 1.95542i) q^{88} +(4.56933 + 2.63810i) q^{89} +(0.181987 - 11.5170i) q^{91} +(0.0304136 - 0.0526779i) q^{92} -10.7256 q^{94} +(-10.9554 + 18.9754i) q^{95} -17.5710i q^{97} +(-3.90257 + 2.25315i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 10 q^{4} - 3 q^{5}+O(q^{10}) \) 22 * q + 10 * q^4 - 3 * q^5	\( 22 q + 10 q^{4} - 3 q^{5} - 7 q^{10} - 3 q^{11} + 3 q^{13} + 9 q^{14} - 12 q^{16} - 9 q^{17} - 6 q^{19} - 13 q^{22} + 12 q^{23} + 4 q^{25} + 12 q^{26} + 3 q^{28} + 24 q^{29} + 27 q^{31} - 15 q^{34} + 27 q^{35} + 6 q^{37} - 21 q^{38} + 13 q^{40} + 8 q^{43} - 15 q^{46} - 6 q^{47} - 14 q^{49} - 7 q^{52} + 24 q^{53} - 13 q^{55} - 18 q^{56} + 15 q^{58} + 33 q^{59} - 6 q^{61} - 24 q^{64} - 3 q^{65} - 138 q^{68} + 24 q^{70} - 9 q^{71} - 12 q^{74} - 42 q^{77} - 6 q^{79} - 105 q^{80} - 16 q^{82} + 42 q^{83} - 51 q^{85} + 45 q^{86} - 11 q^{88} + 30 q^{89} + 15 q^{91} + 3 q^{92} - 88 q^{94} + 3 q^{95} - 117 q^{98}+O(q^{100}) \) 22 * q + 10 * q^4 - 3 * q^5 - 7 * q^10 - 3 * q^11 + 3 * q^13 + 9 * q^14 - 12 * q^16 - 9 * q^17 - 6 * q^19 - 13 * q^22 + 12 * q^23 + 4 * q^25 + 12 * q^26 + 3 * q^28 + 24 * q^29 + 27 * q^31 - 15 * q^34 + 27 * q^35 + 6 * q^37 - 21 * q^38 + 13 * q^40 + 8 * q^43 - 15 * q^46 - 6 * q^47 - 14 * q^49 - 7 * q^52 + 24 * q^53 - 13 * q^55 - 18 * q^56 + 15 * q^58 + 33 * q^59 - 6 * q^61 - 24 * q^64 - 3 * q^65 - 138 * q^68 + 24 * q^70 - 9 * q^71 - 12 * q^74 - 42 * q^77 - 6 * q^79 - 105 * q^80 - 16 * q^82 + 42 * q^83 - 51 * q^85 + 45 * q^86 - 11 * q^88 + 30 * q^89 + 15 * q^91 + 3 * q^92 - 88 * q^94 + 3 * q^95 - 117 * q^98

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