LMFDB - Embedded newform 475.2.p.e.293.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(107,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("475.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.p (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.14096583954457373039394816.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 127x^{12} + 13728x^{8} - 304927x^{4} + 5764801 $ x^16 - 127x^12 + 13728x^8 - 304927*x^4 + 5764801
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			293.1
Root			$-0.826301 - 3.08380i$ of defining polynomial
Character	$\chi$	$=$	475.293
Dual form			475.2.p.e.107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(-0.567482 - 2.11787i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.09629 + 1.89883i) q^{6} +(1.22474 - 1.22474i) q^{7} +(2.12132 - 2.12132i) q^{8} +(-1.56527 + 0.903709i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.567482 - 2.11787i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.09629 + 1.89883i) q^{6} +(1.22474 - 1.22474i) q^{7} +(2.12132 - 2.12132i) q^{8} +(-1.56527 + 0.903709i) q^{9} +1.19258 q^{11} +(1.55039 + 1.55039i) q^{12} +(1.15195 + 0.308663i) q^{13} +(-0.866025 + 1.50000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.982908 - 3.66826i) q^{17} +(1.27804 - 1.27804i) q^{18} +(-4.33013 + 0.500000i) q^{19} +(-3.28887 - 1.89883i) q^{21} +(-1.15195 + 0.308663i) q^{22} +(0.448288 - 1.67303i) q^{23} +(-5.69650 - 3.28887i) q^{24} -1.19258 q^{26} +(-1.84897 - 1.84897i) q^{27} +(-0.448288 + 1.67303i) q^{28} +(1.89883 + 3.28887i) q^{29} -7.26177i q^{31} +(-1.29410 + 4.82963i) q^{32} +(-0.676769 - 2.52574i) q^{33} +(1.89883 + 3.28887i) q^{34} +(0.903709 - 1.56527i) q^{36} +(-5.92921 - 5.92921i) q^{37} +(4.05317 - 1.60368i) q^{38} -2.61484i q^{39} +(-4.78887 - 2.76486i) q^{41} +(3.66826 + 0.982908i) q^{42} +(-8.68736 + 2.32777i) q^{43} +(-1.03281 + 0.596291i) q^{44} +1.73205i q^{46} +(-9.00956 - 2.41410i) q^{47} +(2.11787 + 0.567482i) q^{48} +4.00000i q^{49} +(-7.21113 + 4.16335i) q^{51} +(-1.15195 + 0.308663i) q^{52} +(6.76148 + 1.81173i) q^{53} +(2.26451 + 1.30742i) q^{54} -5.19615i q^{56} +(3.51621 + 8.88691i) q^{57} +(-2.68535 - 2.68535i) q^{58} +(4.66369 - 8.07775i) q^{59} +(1.78887 + 3.09842i) q^{61} +(1.87948 + 7.01433i) q^{62} +(-0.810243 + 3.02387i) q^{63} -7.00000i q^{64} +(1.30742 + 2.26451i) q^{66} +(2.78757 - 10.4033i) q^{67} +(2.68535 + 2.68535i) q^{68} -3.79766 q^{69} +(14.0777 + 8.12779i) q^{71} +(-1.40338 + 5.23749i) q^{72} +(-3.02387 + 0.810243i) q^{73} +(7.26177 + 4.19258i) q^{74} +(3.50000 - 2.59808i) q^{76} +(1.46061 - 1.46061i) q^{77} +(0.676769 + 2.52574i) q^{78} +(8.29457 - 14.3666i) q^{79} +(-5.57775 + 9.66094i) q^{81} +(5.34129 + 1.43120i) q^{82} +(-1.46061 - 1.46061i) q^{83} +3.79766 q^{84} +(7.78887 - 4.49691i) q^{86} +(5.88786 - 5.88786i) q^{87} +(2.52985 - 2.52985i) q^{88} +(2.59808 + 4.50000i) q^{89} +(1.78887 - 1.03281i) q^{91} +(0.448288 + 1.67303i) q^{92} +(-15.3795 + 4.12092i) q^{93} +9.32738 q^{94} +10.9629 q^{96} +(-1.74583 + 0.467794i) q^{97} +(-1.03528 - 3.86370i) q^{98} +(-1.86671 + 1.07775i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{6}+O(q^{10}) $ 16 * q - 4 * q^6	$ 16 q - 4 q^{6} - 24 q^{11} - 8 q^{16} + 12 q^{21} + 24 q^{26} + 36 q^{36} - 12 q^{41} - 180 q^{51} - 36 q^{61} + 64 q^{66} + 96 q^{71} + 56 q^{76} + 40 q^{81} + 60 q^{86} - 36 q^{91} - 40 q^{96}+O(q^{100}) $ 16 * q - 4 * q^6 - 24 * q^11 - 8 * q^16 + 12 * q^21 + 24 * q^26 + 36 * q^36 - 12 * q^41 - 180 * q^51 - 36 * q^61 + 64 * q^66 + 96 * q^71 + 56 * q^76 + 40 * q^81 + 60 * q^86 - 36 * q^91 - 40 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i	−0.583609	−	0.812035i	$-0.698360\pi$
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i	−0.0994033	+	0.995047i	$0.531693\pi$
$3$	−0.567482	−	2.11787i	−0.327636	−	1.22275i	−0.911635	−	0.411000i	$-0.865180\pi$
$3$	−0.567482	−	2.11787i	−0.327636	−	1.22275i	0.583999	−	0.811754i	$-0.301487\pi$
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	1.09629	+	1.89883i	0.447559	+	0.775195i
$7$	1.22474	−	1.22474i	0.462910	−	0.462910i	−0.436698	−	0.899608i	$-0.643852\pi$
$7$	1.22474	−	1.22474i	0.462910	−	0.462910i	0.899608	+	0.436698i	$0.143852\pi$
$8$	2.12132	−	2.12132i	0.750000	−	0.750000i
$9$	−1.56527	+	0.903709i	−0.521757	+	0.301236i
$10$		0			0
$11$	1.19258			0.359577			0.179789	−	0.983705i	$-0.442459\pi$
$11$	1.19258			0.359577			0.179789	+	0.983705i	$0.442459\pi$
$12$	1.55039	+	1.55039i	0.447559	+	0.447559i
$13$	1.15195	+	0.308663i	0.319492	+	0.0856077i	0.415001	−	0.909821i	$-0.363781\pi$
$13$	1.15195	+	0.308663i	0.319492	+	0.0856077i	−0.0955088	+	0.995429i	$0.530448\pi$
$14$	−0.866025	+	1.50000i	−0.231455	+	0.400892i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.982908	−	3.66826i	−0.238390	−	0.889684i	−0.976591	−	0.215103i	$-0.930991\pi$
$17$	−0.982908	−	3.66826i	−0.238390	−	0.889684i	0.738201	−	0.674581i	$-0.235676\pi$
$18$	1.27804	−	1.27804i	0.301236	−	0.301236i
$19$	−4.33013	+	0.500000i	−0.993399	+	0.114708i
$19$	−4.33013	+	0.500000i	−0.993399	+	0.114708i
$20$		0			0
$21$	−3.28887	−	1.89883i	−0.717691	−	0.414359i
$22$	−1.15195	+	0.308663i	−0.245596	+	0.0658072i
$23$	0.448288	−	1.67303i	0.0934745	−	0.348851i	−0.903309	−	0.428990i	$-0.858870\pi$
$23$	0.448288	−	1.67303i	0.0934745	−	0.348851i	0.996784	+	0.0801385i	$0.0255363\pi$
$24$	−5.69650	−	3.28887i	−1.16279	−	0.671339i
$25$		0			0
$26$	−1.19258			−0.233885
$27$	−1.84897	−	1.84897i	−0.355834	−	0.355834i
$28$	−0.448288	+	1.67303i	−0.0847184	+	0.316173i
$29$	1.89883	+	3.28887i	0.352604	+	0.610728i	0.986705	−	0.162522i	$-0.0519629\pi$
$29$	1.89883	+	3.28887i	0.352604	+	0.610728i	−0.634101	+	0.773251i	$0.718630\pi$
$30$		0			0
$31$		−	7.26177i		−	1.30425i	−0.758111	−	0.652126i	$-0.773877\pi$
$31$		−	7.26177i		−	1.30425i	0.758111	−	0.652126i	$-0.226123\pi$
$32$	−1.29410	+	4.82963i	−0.228766	+	0.853766i
$33$	−0.676769	−	2.52574i	−0.117810	−	0.439674i
$34$	1.89883	+	3.28887i	0.325647	+	0.564037i
$35$		0			0
$36$	0.903709	−	1.56527i	0.150618	−	0.260878i
$37$	−5.92921	−	5.92921i	−0.974756	−	0.974756i	0.0249335	−	0.999689i	$-0.492063\pi$
$37$	−5.92921	−	5.92921i	−0.974756	−	0.974756i	−0.999689	+	0.0249335i	$0.992063\pi$
$38$	4.05317	−	1.60368i	0.657511	−	0.260152i
$39$		−	2.61484i		−	0.418709i
$40$		0			0
$41$	−4.78887	−	2.76486i	−0.747896	−	0.431798i	0.0770369	−	0.997028i	$-0.475454\pi$
$41$	−4.78887	−	2.76486i	−0.747896	−	0.431798i	−0.824933	+	0.565230i	$0.808787\pi$
$42$	3.66826	+	0.982908i	0.566025	+	0.151666i
$43$	−8.68736	+	2.32777i	−1.32481	+	0.354982i	−0.850778	−	0.525526i	$-0.823869\pi$
$43$	−8.68736	+	2.32777i	−1.32481	+	0.354982i	−0.474032	+	0.880507i	$0.657202\pi$
$44$	−1.03281	+	0.596291i	−0.155701	+	0.0898943i
$45$		0			0
$46$			1.73205i			0.255377i
$47$	−9.00956	−	2.41410i	−1.31418	−	0.352133i	−0.467385	−	0.884054i	$-0.654804\pi$
$47$	−9.00956	−	2.41410i	−1.31418	−	0.352133i	−0.846794	+	0.531921i	$0.821470\pi$
$48$	2.11787	+	0.567482i	0.305688	+	0.0819090i
$49$			4.00000i			0.571429i
$50$		0			0
$51$	−7.21113	+	4.16335i	−1.00976	+	0.582985i
$52$	−1.15195	+	0.308663i	−0.159746	+	0.0428039i
$53$	6.76148	+	1.81173i	0.928761	+	0.248861i	0.691326	−	0.722543i	$-0.257027\pi$
$53$	6.76148	+	1.81173i	0.928761	+	0.248861i	0.237435	+	0.971404i	$0.423693\pi$
$54$	2.26451	+	1.30742i	0.308161	+	0.177917i
$55$		0			0
$56$		−	5.19615i		−	0.694365i
$57$	3.51621	+	8.88691i	0.465733	+	1.17710i
$58$	−2.68535	−	2.68535i	−0.352604	−	0.352604i
$59$	4.66369	−	8.07775i	0.607161	−	1.05163i	−0.384545	−	0.923106i	$-0.625642\pi$
$59$	4.66369	−	8.07775i	0.607161	−	1.05163i	0.991706	−	0.128527i	$-0.0410249\pi$
$60$		0			0
$61$	1.78887	+	3.09842i	0.229042	+	0.396712i	0.957524	−	0.288352i	$-0.0931074\pi$
$61$	1.78887	+	3.09842i	0.229042	+	0.396712i	−0.728483	+	0.685064i	$0.759774\pi$
$62$	1.87948	+	7.01433i	0.238695	+	0.890820i
$63$	−0.810243	+	3.02387i	−0.102081	+	0.380972i
$64$		−	7.00000i		−	0.875000i
$65$		0			0
$66$	1.30742	+	2.26451i	0.160932	+	0.278742i
$67$	2.78757	−	10.4033i	0.340555	−	1.27097i	−0.557164	−	0.830403i	$-0.688111\pi$
$67$	2.78757	−	10.4033i	0.340555	−	1.27097i	0.897719	−	0.440568i	$-0.145223\pi$
$68$	2.68535	+	2.68535i	0.325647	+	0.325647i
$69$	−3.79766			−0.457185
$70$		0			0
$71$	14.0777	+	8.12779i	1.67072	+	0.964591i	0.967235	+	0.253882i	$0.0817076\pi$
$71$	14.0777	+	8.12779i	1.67072	+	0.964591i	0.703486	+	0.710709i	$0.251626\pi$
$72$	−1.40338	+	5.23749i	−0.165390	+	0.617245i
$73$	−3.02387	+	0.810243i	−0.353917	+	0.0948318i	−0.431397	−	0.902162i	$-0.641979\pi$
$73$	−3.02387	+	0.810243i	−0.353917	+	0.0948318i	0.0774801	+	0.996994i	$0.475313\pi$
$74$	7.26177	+	4.19258i	0.844163	+	0.487378i
$75$		0			0
$76$	3.50000	−	2.59808i	0.401478	−	0.298020i
$77$	1.46061	−	1.46061i	0.166452	−	0.166452i
$78$	0.676769	+	2.52574i	0.0766290	+	0.285983i
$79$	8.29457	−	14.3666i	0.933212	−	1.61637i	0.155421	−	0.987848i	$-0.450327\pi$
$79$	8.29457	−	14.3666i	0.933212	−	1.61637i	0.777791	−	0.628523i	$-0.216340\pi$
$80$		0			0
$81$	−5.57775	+	9.66094i	−0.619750	+	1.07344i
$82$	5.34129	+	1.43120i	0.589847	+	0.158049i
$83$	−1.46061	−	1.46061i	−0.160323	−	0.160323i	0.622387	−	0.782710i	$-0.286163\pi$
$83$	−1.46061	−	1.46061i	−0.160323	−	0.160323i	−0.782710	+	0.622387i	$0.786163\pi$
$84$	3.79766			0.414359
$85$		0			0
$86$	7.78887	−	4.49691i	0.839896	−	0.484914i
$87$	5.88786	−	5.88786i	0.631245	−	0.631245i
$88$	2.52985	−	2.52985i	0.269683	−	0.269683i
$89$	2.59808	+	4.50000i	0.275396	+	0.476999i	0.970235	−	0.242166i	$-0.0778579\pi$
$89$	2.59808	+	4.50000i	0.275396	+	0.476999i	−0.694839	+	0.719165i	$0.744525\pi$
$90$		0			0
$91$	1.78887	−	1.03281i	0.187525	−	0.108268i
$92$	0.448288	+	1.67303i	0.0467372	+	0.174426i
$93$	−15.3795	+	4.12092i	−1.59478	+	0.427320i
$94$	9.32738			0.962046
$95$		0			0
$96$	10.9629			1.11890
$97$	−1.74583	+	0.467794i	−0.177262	+	0.0474973i	−0.346358	−	0.938102i	$-0.612582\pi$
$97$	−1.74583	+	0.467794i	−0.177262	+	0.0474973i	0.169096	+	0.985600i	$0.445915\pi$
$98$	−1.03528	−	3.86370i	−0.104579	−	0.390293i
$99$	−1.86671	+	1.07775i	−0.187612	+	0.108318i
$100$		0			0
$101$	−1.19258	−	2.06561i	−0.118666	−	0.205536i	0.800573	−	0.599235i	$-0.204529\pi$
$101$	−1.19258	−	2.06561i	−0.118666	−	0.205536i	−0.919239	+	0.393699i	$0.871195\pi$
$102$	5.88786	−	5.88786i	0.582985	−	0.582985i
$103$	−5.92921	+	5.92921i	−0.584222	+	0.584222i	−0.936061	−	0.351839i	$-0.885557\pi$
$103$	−5.92921	+	5.92921i	−0.584222	+	0.584222i	0.351839	+	0.936061i	$0.385557\pi$
$104$	3.09842	−	1.78887i	0.303825	−	0.175413i
$105$		0			0
$106$	−7.00000			−0.679900
$107$	12.4293	+	12.4293i	1.20159	+	1.20159i	0.973683	+	0.227907i	$0.0731883\pi$
$107$	12.4293	+	12.4293i	1.20159	+	1.20159i	0.227907	+	0.973683i	$0.426812\pi$
$108$	2.52574	+	0.676769i	0.243039	+	0.0651221i
$109$	−1.19959	+	2.07775i	−0.114900	+	0.199012i	−0.917740	−	0.397183i	$-0.869988\pi$
$109$	−1.19959	+	2.07775i	−0.114900	+	0.199012i	0.802840	+	0.596195i	$0.203321\pi$
$110$		0			0
$111$	−9.19258	+	15.9220i	−0.872521	+	1.51125i
$112$	0.448288	+	1.67303i	0.0423592	+	0.158087i
$113$	5.35828	−	5.35828i	0.504064	−	0.504064i	−0.408634	−	0.912698i	$-0.633995\pi$
$113$	5.35828	−	5.35828i	0.504064	−	0.504064i	0.912698	+	0.408634i	$0.133995\pi$
$114$	−5.69650	−	7.67404i	−0.533526	−	0.718740i
$115$		0			0
$116$	−3.28887	−	1.89883i	−0.305364	−	0.176302i
$117$	−2.08205	+	0.557883i	−0.192485	+	0.0515763i
$118$	−2.41410	+	9.00956i	−0.222236	+	0.829397i
$119$	−5.69650	−	3.28887i	−0.522197	−	0.301491i
$120$		0			0
$121$	−9.57775			−0.870704
$122$	−2.52985	−	2.52985i	−0.229042	−	0.229042i
$123$	−3.13801	+	11.7112i	−0.282945	+	1.05597i
$124$	3.63088	+	6.28887i	0.326063	+	0.564758i
$125$		0			0
$126$		−	3.13054i		−	0.278891i
$127$	1.24425	−	4.64361i	0.110409	−	0.412054i	−0.888493	−	0.458890i	$-0.848247\pi$
$127$	1.24425	−	4.64361i	0.110409	−	0.412054i	0.998903	+	0.0468363i	$0.0149139\pi$
$128$	−0.776457	−	2.89778i	−0.0686298	−	0.256130i
$129$	9.85984	+	17.0777i	0.868111	+	1.50361i
$130$		0			0
$131$	9.28887	−	16.0888i	0.811573	−	1.40569i	−0.100190	−	0.994968i	$-0.531945\pi$
$131$	9.28887	−	16.0888i	0.811573	−	1.40569i	0.911763	−	0.410717i	$-0.134721\pi$
$132$	1.84897	+	1.84897i	0.160932	+	0.160932i
$133$	−4.69093	+	5.91567i	−0.406755	+	0.512954i
$134$			10.7703i			0.930415i
$135$		0			0
$136$	−9.86662	−	5.69650i	−0.846056	−	0.488471i
$137$	19.0478	+	5.10383i	1.62736	+	0.436050i	0.953152	−	0.302492i	$-0.0978187\pi$
$137$	19.0478	+	5.10383i	1.62736	+	0.436050i	0.674207	+	0.738542i	$0.264485\pi$
$138$	3.66826	−	0.982908i	0.312263	−	0.0836707i
$139$	−13.4907	+	7.78887i	−1.14427	+	0.660644i	−0.947484	−	0.319803i	$-0.896383\pi$
$139$	−13.4907	+	7.78887i	−1.14427	+	0.660644i	−0.196784	+	0.980447i	$0.563050\pi$
$140$		0			0
$141$			20.4510i			1.72229i
$142$	−15.7017	−	4.20725i	−1.31766	−	0.353065i
$143$	1.37379	+	0.368106i	0.114882	+	0.0307826i
$144$		−	1.80742i		−	0.150618i
$145$		0			0
$146$	2.71113	−	1.56527i	0.224374	−	0.129543i
$147$	8.47149	−	2.26993i	0.698717	−	0.187221i
$148$	8.09945	+	2.17024i	0.665770	+	0.178393i
$149$	−3.13054	−	1.80742i	−0.256464	−	0.148069i	0.366257	−	0.930514i	$-0.380639\pi$
$149$	−3.13054	−	1.80742i	−0.256464	−	0.148069i	−0.622720	+	0.782444i	$0.713973\pi$
$150$		0			0
$151$		−	5.86328i		−	0.477147i	−0.971124	−	0.238573i	$-0.923320\pi$
$151$		−	5.86328i		−	0.477147i	0.971124	−	0.238573i	$-0.0766798\pi$
$152$	−8.12493	+	10.2462i	−0.659019	+	0.831080i
$153$	4.85356	+	4.85356i	0.392387	+	0.392387i
$154$	−1.03281	+	1.78887i	−0.0832259	+	0.144152i
$155$		0			0
$156$	1.30742	+	2.26451i	0.104677	+	0.181306i
$157$	2.05215	+	7.65872i	0.163779	+	0.611232i	0.998193	+	0.0600935i	$0.0191399\pi$
$157$	2.05215	+	7.65872i	0.163779	+	0.611232i	−0.834414	+	0.551139i	$0.814193\pi$
$158$	−4.29359	+	16.0239i	−0.341579	+	1.27479i
$159$		−	15.3481i		−	1.21718i
$160$		0			0
$161$	−1.50000	−	2.59808i	−0.118217	−	0.204757i
$162$	2.88725	−	10.7754i	0.226844	−	0.846594i
$163$	3.67423	+	3.67423i	0.287788	+	0.287788i	0.836205	−	0.548417i	$-0.184769\pi$
$163$	3.67423	+	3.67423i	0.287788	+	0.287788i	−0.548417	+	0.836205i	$0.684769\pi$
$164$	5.52971			0.431798
$165$		0			0
$166$	1.78887	+	1.03281i	0.138844	+	0.0801613i
$167$	−0.885744	+	3.30564i	−0.0685409	+	0.255798i	−0.991691	−	0.128641i	$-0.958939\pi$
$167$	−0.885744	+	3.30564i	−0.0685409	+	0.255798i	0.923150	+	0.384439i	$0.125605\pi$
$168$	−11.0048	+	2.94872i	−0.849038	+	0.227499i
$169$	−10.0266	−	5.78887i	−0.771279	−	0.445298i
$170$		0			0
$171$	6.32596	−	4.69581i	0.483758	−	0.359097i
$172$	6.35959	−	6.35959i	0.484914	−	0.484914i
$173$	1.81173	+	6.76148i	0.137744	+	0.514066i	0.999972	+	0.00754550i	$0.00240183\pi$
$173$	1.81173	+	6.76148i	0.137744	+	0.514066i	−0.862228	+	0.506520i	$0.830932\pi$
$174$	−4.16335	+	7.21113i	−0.315622	+	0.546674i
$175$		0			0
$176$	−0.596291	+	1.03281i	−0.0449471	+	0.0778507i
$177$	−19.7542	−	5.29312i	−1.48482	−	0.397855i
$178$	−3.67423	−	3.67423i	−0.275396	−	0.275396i
$179$	2.79698			0.209056			0.104528	−	0.994522i	$-0.466667\pi$
$179$	2.79698			0.209056			0.104528	+	0.994522i	$0.466667\pi$
$180$		0			0
$181$	0.288874	−	0.166781i	0.0214718	−	0.0123968i	−0.489226	−	0.872157i	$-0.662721\pi$
$181$	0.288874	−	0.166781i	0.0214718	−	0.0123968i	0.510697	+	0.859760i	$0.329387\pi$
$182$	−1.46061	+	1.46061i	−0.108268	+	0.108268i
$183$	5.54690	−	5.54690i	0.410039	−	0.410039i
$184$	−2.59808	−	4.50000i	−0.191533	−	0.331744i
$185$		0			0
$186$	13.7889	−	7.96101i	1.01105	−	0.583730i
$187$	−1.17220	−	4.37470i	−0.0857196	−	0.319910i
$188$	9.00956	−	2.41410i	0.657089	−	0.176067i
$189$	−4.52903			−0.329438
$190$		0			0
$191$	−0.577747			−0.0418043			−0.0209022	−	0.999782i	$-0.506654\pi$
$191$	−0.577747			−0.0418043			−0.0209022	+	0.999782i	$0.506654\pi$
$192$	−14.8251	+	3.97237i	−1.06991	+	0.286681i
$193$	−6.82898	−	25.4861i	−0.491561	−	1.83453i	−0.548497	−	0.836153i	$-0.684800\pi$
$193$	−6.82898	−	25.4861i	−0.491561	−	1.83453i	0.0569358	−	0.998378i	$-0.481867\pi$
$194$	1.56527	−	0.903709i	0.112380	−	0.0648825i
$195$		0			0
$196$	−2.00000	−	3.46410i	−0.142857	−	0.247436i
$197$	−3.91010	+	3.91010i	−0.278583	+	0.278583i	−0.832543	−	0.553960i	$-0.813116\pi$
$197$	−3.91010	+	3.91010i	−0.278583	+	0.278583i	0.553960	+	0.832543i	$0.313116\pi$
$198$	1.52416	−	1.52416i	0.108318	−	0.108318i
$199$	14.8571	−	8.57775i	1.05319	−	0.608060i	0.129650	−	0.991560i	$-0.458615\pi$
$199$	14.8571	−	8.57775i	1.05319	−	0.608060i	0.923541	+	0.383499i	$0.125281\pi$
$200$		0			0
$201$	−23.6148			−1.66566
$202$	1.68657	+	1.68657i	0.118666	+	0.118666i
$203$	6.35362	+	1.70245i	0.445936	+	0.119488i
$204$	4.16335	−	7.21113i	0.291493	−	0.504880i
$205$		0			0
$206$	4.19258	−	7.26177i	0.292111	−	0.505951i
$207$	0.810243	+	3.02387i	0.0563158	+	0.210173i
$208$	−0.843283	+	0.843283i	−0.0584712	+	0.0584712i
$209$	−5.16403	+	0.596291i	−0.357204	+	0.0412463i
$210$		0			0
$211$	12.8666	+	7.42855i	0.885775	+	0.511402i	0.872558	−	0.488510i	$-0.162460\pi$
$211$	12.8666	+	7.42855i	0.885775	+	0.511402i	0.0132166	+	0.999913i	$0.495793\pi$
$212$	−6.76148	+	1.81173i	−0.464380	+	0.124430i
$213$	9.22475	−	34.4272i	0.632070	−	2.35892i
$214$	−15.2228	−	8.78887i	−1.04061	−	0.600795i
$215$		0			0
$216$	−7.84451			−0.533751
$217$	−8.89381	−	8.89381i	−0.603751	−	0.603751i
$218$	0.620952	−	2.31743i	0.0420562	−	0.156956i
$219$	3.43198	+	5.94437i	0.231912	+	0.401683i
$220$		0			0
$221$		−	4.52903i		−	0.304655i
$222$	4.75843	−	17.7587i	0.319365	−	1.19189i
$223$	−4.49001	−	16.7570i	−0.300673	−	1.12213i	−0.936606	−	0.350384i	$-0.886051\pi$
$223$	−4.49001	−	16.7570i	−0.300673	−	1.12213i	0.635933	−	0.771745i	$-0.280616\pi$
$224$	4.33013	+	7.50000i	0.289319	+	0.501115i
$225$		0			0
$226$	−3.78887	+	6.56252i	−0.252032	+	0.436532i
$227$	3.53553	+	3.53553i	0.234662	+	0.234662i	0.814635	−	0.579974i	$-0.196937\pi$
$227$	3.53553	+	3.53553i	0.234662	+	0.234662i	−0.579974	+	0.814635i	$0.696937\pi$
$228$	−7.48858	−	5.93819i	−0.495943	−	0.393266i
$229$			21.0000i			1.38772i	0.720110	+	0.693860i	$0.244091\pi$
$229$			21.0000i			1.38772i	−0.720110	+	0.693860i	$0.755909\pi$
$230$		0			0
$231$	−3.92225	−	2.26451i	−0.258065	−	0.148994i
$232$	11.0048	+	2.94872i	0.722500	+	0.193593i
$233$	9.39380	−	2.51706i	0.615408	−	0.164898i	0.0623689	−	0.998053i	$-0.480134\pi$
$233$	9.39380	−	2.51706i	0.615408	−	0.164898i	0.553040	+	0.833155i	$0.313468\pi$
$234$	1.86671	−	1.07775i	0.122031	−	0.0704545i
$235$		0			0
$236$			9.32738i			0.607161i
$237$	−35.1337	−	9.41404i	−2.28218	−	0.611508i
$238$	6.35362	+	1.70245i	0.411844	+	0.110353i
$239$		−	9.00000i		−	0.582162i	−0.956698	−	0.291081i	$-0.905985\pi$
$239$		−	9.00000i		−	0.582162i	0.956698	−	0.291081i	$-0.0940149\pi$
$240$		0			0
$241$	−12.2889	+	7.09498i	−0.791596	+	0.457028i	−0.840524	−	0.541774i	$-0.817753\pi$
$241$	−12.2889	+	7.09498i	−0.791596	+	0.457028i	0.0489282	+	0.998802i	$0.484419\pi$
$242$	9.25139	−	2.47890i	0.594702	−	0.159350i
$243$	16.0487	+	4.30024i	1.02952	+	0.275860i
$244$	−3.09842	−	1.78887i	−0.198356	−	0.114521i
$245$		0			0
$246$		−	12.1244i		−	0.773021i
$247$	−5.14240	−	0.760577i	−0.327203	−	0.0483944i
$248$	−15.4045	−	15.4045i	−0.978189	−	0.978189i
$249$	−2.26451	+	3.92225i	−0.143508	+	0.248563i
$250$		0			0
$251$	9.28887	+	16.0888i	0.586309	+	1.01552i	0.994711	+	0.102714i	$0.0327527\pi$
$251$	9.28887	+	16.0888i	0.586309	+	1.01552i	−0.408402	+	0.912802i	$0.633914\pi$
$252$	−0.810243	−	3.02387i	−0.0510405	−	0.190486i
$253$	0.534620	−	1.99523i	0.0336113	−	0.125439i
$254$			4.80742i			0.301644i
$255$		0			0
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	−7.39647	+	27.6040i	−0.461379	+	1.72189i	0.207246	+	0.978289i	$0.433550\pi$
$257$	−7.39647	+	27.6040i	−0.461379	+	1.72189i	−0.668624	+	0.743600i	$0.733117\pi$
$258$	−13.9439	−	13.9439i	−0.868111	−	0.868111i
$259$	−14.5235			−0.902448
$260$		0			0
$261$	−5.94437	−	3.43198i	−0.367947	−	0.212434i
$262$	−4.80827	+	17.9447i	−0.297056	+	1.10863i
$263$	15.0573	−	4.03459i	0.928472	−	0.248783i	0.237269	−	0.971444i	$-0.423748\pi$
$263$	15.0573	−	4.03459i	0.928472	−	0.248783i	0.691203	+	0.722660i	$0.257081\pi$
$264$	−6.79354	−	3.92225i	−0.418114	−	0.241398i
$265$		0			0
$266$	3.00000	−	6.92820i	0.183942	−	0.424795i
$267$	8.05606	−	8.05606i	0.493023	−	0.493023i
$268$	2.78757	+	10.4033i	0.170278	+	0.635485i
$269$	12.6247	−	21.8666i	0.769742	−	1.33323i	−0.167962	−	0.985794i	$-0.553718\pi$
$269$	12.6247	−	21.8666i	0.769742	−	1.33323i	0.937703	−	0.347438i	$-0.112948\pi$
$270$		0			0
$271$	9.28887	−	16.0888i	0.564259	−	0.977325i	−0.432859	−	0.901461i	$-0.642495\pi$
$271$	9.28887	−	16.0888i	0.564259	−	0.977325i	0.997118	−	0.0758636i	$-0.0241713\pi$
$272$	3.66826	+	0.982908i	0.222421	+	0.0595975i
$273$	−3.20251	−	3.20251i	−0.193824	−	0.193824i
$274$	−19.7197			−1.19131
$275$		0			0
$276$	3.28887	−	1.89883i	0.197967	−	0.114296i
$277$	15.6404	−	15.6404i	0.939740	−	0.939740i	−0.0585445	−	0.998285i	$-0.518646\pi$
$277$	15.6404	−	15.6404i	0.939740	−	0.939740i	0.998285	+	0.0585445i	$0.0186460\pi$
$278$	11.0151	−	11.0151i	0.660644	−	0.660644i
$279$	6.56252	+	11.3666i	0.392888	+	0.680502i
$280$		0			0
$281$	26.6555	−	15.3896i	1.59013	−	0.918064i	0.596851	−	0.802352i	$-0.296418\pi$
$281$	26.6555	−	15.3896i	1.59013	−	0.918064i	0.993283	−	0.115712i	$-0.0369148\pi$
$282$	−5.29312	−	19.7542i	−0.315201	−	1.17635i
$283$	−3.02387	+	0.810243i	−0.179750	+	0.0481640i	−0.347571	−	0.937654i	$-0.612994\pi$
$283$	−3.02387	+	0.810243i	−0.179750	+	0.0481640i	0.167821	+	0.985817i	$0.446327\pi$
$284$	−16.2556			−0.964591
$285$		0			0
$286$	−1.42225			−0.0840996
$287$	−9.25139	+	2.47890i	−0.546092	+	0.146325i
$288$	−2.33897	−	8.72916i	−0.137825	−	0.514370i
$289$	2.23239	−	1.28887i	0.131317	−	0.0758161i
$290$		0			0
$291$	1.98146	+	3.43198i	0.116155	+	0.201186i
$292$	2.21363	−	2.21363i	0.129543	−	0.129543i
$293$	−12.4293	+	12.4293i	−0.726130	+	0.726130i	−0.969847	−	0.243716i	$-0.921633\pi$
$293$	−12.4293	+	12.4293i	−0.726130	+	0.726130i	0.243716	+	0.969847i	$0.421633\pi$
$294$	−7.59533	+	4.38516i	−0.442969	+	0.255748i
$295$		0			0
$296$	−25.1555			−1.46213
$297$	−2.20505	−	2.20505i	−0.127950	−	0.127950i
$298$	3.49166	+	0.935588i	0.202267	+	0.0541972i
$299$	1.03281	−	1.78887i	0.0597288	−	0.103453i
$300$		0			0
$301$	−7.78887	+	13.4907i	−0.448943	+	0.777592i
$302$	1.51753	+	5.66349i	0.0873239	+	0.325897i
$303$	−3.69794	+	3.69794i	−0.212441	+	0.212441i
$304$	1.73205	−	4.00000i	0.0993399	−	0.229416i
$305$		0			0
$306$	−5.94437	−	3.43198i	−0.339817	−	0.196193i
$307$	16.7928	−	4.49961i	0.958415	−	0.256806i	0.254485	−	0.967077i	$-0.418094\pi$
$307$	16.7928	−	4.49961i	0.958415	−	0.256806i	0.703929	+	0.710270i	$0.251427\pi$
$308$	−0.534620	+	1.99523i	−0.0304628	+	0.113689i
$309$	15.9220	+	9.19258i	0.905772	+	0.522948i
$310$		0			0
$311$	−19.7703			−1.12107			−0.560536	−	0.828130i	$-0.689405\pi$
$311$	−19.7703			−1.12107			−0.560536	+	0.828130i	$0.689405\pi$
$312$	−5.54690	−	5.54690i	−0.314032	−	0.314032i
$313$	1.17220	−	4.37470i	0.0662566	−	0.247273i	−0.924852	−	0.380327i	$-0.875812\pi$
$313$	1.17220	−	4.37470i	0.0662566	−	0.247273i	0.991109	+	0.133054i	$0.0424783\pi$
$314$	−3.96445	−	6.86662i	−0.223727	−	0.387506i
$315$		0			0
$316$			16.5891i			0.933212i
$317$	1.03528	−	3.86370i	0.0581469	−	0.217007i	−0.930739	−	0.365685i	$-0.880835\pi$
$317$	1.03528	−	3.86370i	0.0581469	−	0.217007i	0.988886	+	0.148677i	$0.0475016\pi$
$318$	3.97237	+	14.8251i	0.222760	+	0.831351i
$319$	2.26451	+	3.92225i	0.126788	+	0.219604i
$320$		0			0
$321$	19.2703	−	33.3772i	1.07556	−	1.86293i
$322$	2.12132	+	2.12132i	0.118217	+	0.118217i
$323$	6.09025	+	15.3926i	0.338870	+	0.856466i
$324$		−	11.1555i		−	0.619750i
$325$		0			0
$326$	−4.50000	−	2.59808i	−0.249232	−	0.143894i
$327$	5.08115	+	1.36149i	0.280988	+	0.0752905i
$328$	−16.0239	+	4.29359i	−0.884771	+	0.237074i
$329$	−13.9911	+	8.07775i	−0.771353	+	0.445341i
$330$		0			0
$331$			17.3205i			0.952021i	0.879440	+	0.476011i	$0.157918\pi$
$331$			17.3205i			0.952021i	−0.879440	+	0.476011i	$0.842082\pi$
$332$	1.99523	+	0.534620i	0.109502	+	0.0293411i
$333$	14.6391	+	3.92253i	0.802217	+	0.214953i
$334$		−	3.42225i		−	0.187257i
$335$		0			0
$336$	3.28887	−	1.89883i	0.179423	−	0.103590i
$337$	0.593885	−	0.159131i	0.0323510	−	0.00866842i	−0.242607	−	0.970125i	$-0.578003\pi$
$337$	0.593885	−	0.159131i	0.0323510	−	0.00866842i	0.274958	+	0.961456i	$0.411336\pi$
$338$	11.1832	+	2.99654i	0.608288	+	0.162990i
$339$	−14.3889	−	8.30742i	−0.781496	−	0.451197i
$340$		0			0
$341$		−	8.66025i		−	0.468979i
$342$	−4.89504	+	6.17308i	−0.264694	+	0.333802i
$343$	13.4722	+	13.4722i	0.727430	+	0.727430i
$344$	−13.4907	+	23.3666i	−0.727371	+	1.25984i
$345$		0			0
$346$	−3.50000	−	6.06218i	−0.188161	−	0.325905i
$347$	2.05215	+	7.65872i	0.110165	+	0.411142i	0.998880	−	0.0473189i	$-0.0150677\pi$
$347$	2.05215	+	7.65872i	0.110165	+	0.411142i	−0.888715	+	0.458461i	$0.848401\pi$
$348$	−2.15511	+	8.04297i	−0.115526	+	0.431148i
$349$			31.3110i			1.67604i	0.545640	+	0.838019i	$0.316286\pi$
$349$			31.3110i			1.67604i	−0.545640	+	0.838019i	$0.683714\pi$
$350$		0			0
$351$	−1.55920	−	2.70062i	−0.0832241	−	0.144148i
$352$	−1.54332	+	5.75973i	−0.0822590	+	0.306995i
$353$	−6.59545	−	6.59545i	−0.351041	−	0.351041i	0.509456	−	0.860497i	$-0.329847\pi$
$353$	−6.59545	−	6.59545i	−0.351041	−	0.351041i	−0.860497	+	0.509456i	$0.829847\pi$
$354$	20.4510			1.08696
$355$		0			0
$356$	−4.50000	−	2.59808i	−0.238500	−	0.137698i
$357$	−3.73275	+	13.9308i	−0.197558	+	0.737298i
$358$	−2.70167	+	0.723911i	−0.142788	+	0.0382599i
$359$	6.22896	+	3.59629i	0.328752	+	0.189805i	0.655287	−	0.755380i	$-0.272548\pi$
$359$	6.22896	+	3.59629i	0.328752	+	0.189805i	−0.326535	+	0.945185i	$0.605881\pi$
$360$		0			0
$361$	18.5000	−	4.33013i	0.973684	−	0.227901i
$362$	−0.235864	+	0.235864i	−0.0123968	+	0.0123968i
$363$	5.43520	+	20.2844i	0.285274	+	1.06466i
$364$	−1.03281	+	1.78887i	−0.0541338	+	0.0937625i
$365$		0			0
$366$	−3.92225	+	6.79354i	−0.205019	+	0.355104i
$367$	−24.3890	−	6.53503i	−1.27310	−	0.341126i	−0.441881	−	0.897074i	$-0.645689\pi$
$367$	−24.3890	−	6.53503i	−1.27310	−	0.341126i	−0.831217	+	0.555948i	$0.812355\pi$
$368$	1.22474	+	1.22474i	0.0638442	+	0.0638442i
$369$	9.99450			0.520293
$370$		0			0
$371$	10.5000	−	6.06218i	0.545133	−	0.314733i
$372$	11.2586	−	11.2586i	0.583730	−	0.583730i
$373$	−10.1456	+	10.1456i	−0.525320	+	0.525320i	−0.919173	−	0.393853i	$-0.871142\pi$
$373$	−10.1456	+	10.1456i	−0.525320	+	0.525320i	0.393853	+	0.919173i	$0.371142\pi$
$374$	2.26451	+	3.92225i	0.117095	+	0.202815i
$375$		0			0
$376$	−24.2332	+	13.9911i	−1.24973	+	0.721534i
$377$	1.17220	+	4.37470i	0.0603713	+	0.225309i
$378$	4.37470	−	1.17220i	0.225011	−	0.0602914i
$379$	2.79698			0.143671			0.0718355	−	0.997416i	$-0.477114\pi$
$379$	2.79698			0.143671			0.0718355	+	0.997416i	$0.477114\pi$
$380$		0			0
$381$	−10.5407			−0.540014
$382$	0.558061	−	0.149532i	0.0285529	−	0.00765072i
$383$	4.39992	+	16.4207i	0.224826	+	0.839061i	0.982474	+	0.186398i	$0.0596814\pi$
$383$	4.39992	+	16.4207i	0.224826	+	0.839061i	−0.757649	+	0.652663i	$0.773652\pi$
$384$	−5.69650	+	3.28887i	−0.290698	+	0.167835i
$385$		0			0
$386$	13.1926	+	22.8502i	0.671485	+	1.16305i
$387$	11.4944	−	11.4944i	0.584295	−	0.584295i
$388$	1.27804	−	1.27804i	0.0648825	−	0.0648825i
$389$	−13.4907	+	7.78887i	−0.684007	+	0.394912i	−0.801363	−	0.598178i	$-0.795891\pi$
$389$	−13.4907	+	7.78887i	−0.684007	+	0.394912i	0.117356	+	0.993090i	$0.462558\pi$
$390$		0			0
$391$	−6.57775			−0.332651
$392$	8.48528	+	8.48528i	0.428571	+	0.428571i
$393$	−39.3453	−	10.5425i	−1.98471	−	0.531801i
$394$	2.76486	−	4.78887i	0.139292	−	0.241260i
$395$		0			0
$396$	1.07775	−	1.86671i	0.0541588	−	0.0938059i
$397$	6.89698	+	25.7399i	0.346150	+	1.29185i	0.891264	+	0.453486i	$0.149820\pi$
$397$	6.89698	+	25.7399i	0.346150	+	1.29185i	−0.545114	+	0.838362i	$0.683514\pi$
$398$	−12.1308	+	12.1308i	−0.608060	+	0.608060i
$399$	15.1907	+	6.57775i	0.760484	+	0.329299i
$400$		0			0
$401$	16.7332	+	9.66094i	0.835618	+	0.482444i	0.855772	−	0.517352i	$-0.173082\pi$
$401$	16.7332	+	9.66094i	0.835618	+	0.482444i	−0.0201542	+	0.999797i	$0.506416\pi$
$402$	22.8102	−	6.11197i	1.13767	−	0.304837i
$403$	2.24144	−	8.36516i	0.111654	−	0.416698i
$404$	2.06561	+	1.19258i	0.102768	+	0.0593332i
$405$		0			0
$406$	−6.57775			−0.326448
$407$	−7.07107	−	7.07107i	−0.350500	−	0.350500i
$408$	−6.46532	+	24.1289i	−0.320081	+	1.19456i
$409$	1.06493	+	1.84451i	0.0526572	+	0.0912049i	0.891153	−	0.453704i	$-0.149898\pi$
$409$	1.06493	+	1.84451i	0.0526572	+	0.0912049i	−0.838495	+	0.544909i	$0.816564\pi$
$410$		0			0
$411$		−	43.2370i		−	2.13273i
$412$	2.17024	−	8.09945i	0.106920	−	0.399031i
$413$	−4.18135	−	15.6050i	−0.205751	−	0.767872i
$414$	−1.56527	−	2.71113i	−0.0769288	−	0.133245i
$415$		0			0
$416$	−2.98146	+	5.16403i	−0.146178	+	0.253188i
$417$	24.1516	+	24.1516i	1.18271	+	1.18271i
$418$	4.83374	−	1.91252i	0.236426	−	0.0935446i
$419$		−	24.0000i		−	1.17248i	−0.810139	−	0.586238i	$-0.800608\pi$
$419$		−	24.0000i		−	1.17248i	0.810139	−	0.586238i	$-0.199392\pi$
$420$		0			0
$421$	19.1555	+	11.0594i	0.933582	+	0.539004i	0.887943	−	0.459954i	$-0.152134\pi$
$421$	19.1555	+	11.0594i	0.933582	+	0.539004i	0.0456391	+	0.998958i	$0.485468\pi$
$422$	−14.3509	−	3.84530i	−0.698588	−	0.187186i
$423$	16.2840	−	4.36329i	0.791757	−	0.212151i
$424$	18.1865	−	10.5000i	0.883216	−	0.509925i
$425$		0			0
$426$			35.6417i			1.72685i
$427$	5.98569	+	1.60386i	0.289668	+	0.0776162i
$428$	−16.9788	−	4.54946i	−0.820701	−	0.219906i
$429$		−	3.11841i		−	0.150558i
$430$		0			0
$431$	−4.78887	+	2.76486i	−0.230672	+	0.133178i	−0.610882	−	0.791722i	$-0.709185\pi$
$431$	−4.78887	+	2.76486i	−0.230672	+	0.133178i	0.380210	+	0.924900i	$0.375852\pi$
$432$	2.52574	−	0.676769i	0.121520	−	0.0325611i
$433$	17.9806	+	4.81787i	0.864090	+	0.231532i	0.663530	−	0.748149i	$-0.269057\pi$
$433$	17.9806	+	4.81787i	0.864090	+	0.231532i	0.200560	+	0.979681i	$0.435724\pi$
$434$	10.8926	+	6.28887i	0.522864	+	0.301876i
$435$		0			0
$436$		−	2.39918i		−	0.114900i
$437$	−1.10463	+	7.46859i	−0.0528415	+	0.357271i
$438$	−4.85356	−	4.85356i	−0.231912	−	0.231912i
$439$	13.3239	−	23.0777i	0.635917	−	1.10144i	−0.350403	−	0.936599i	$-0.613955\pi$
$439$	13.3239	−	23.0777i	0.635917	−	1.10144i	0.986320	−	0.164842i	$-0.0527113\pi$
$440$		0			0
$441$	−3.61484	−	6.26108i	−0.172135	−	0.298147i
$442$	1.17220	+	4.37470i	0.0557558	+	0.208083i
$443$	−2.51706	+	9.39380i	−0.119589	+	0.446313i	−0.999589	−	0.0286607i	$-0.990876\pi$
$443$	−2.51706	+	9.39380i	−0.119589	+	0.446313i	0.880000	+	0.474974i	$0.157542\pi$
$444$		−	18.3852i		−	0.872521i
$445$		0			0
$446$	8.67404	+	15.0239i	0.410728	+	0.711401i
$447$	−2.05135	+	7.65576i	−0.0970257	+	0.362105i
$448$	−8.57321	−	8.57321i	−0.405046	−	0.405046i
$449$	5.86328			0.276705			0.138353	−	0.990383i	$-0.455819\pi$
$449$	5.86328			0.276705			0.138353	+	0.990383i	$0.455819\pi$
$450$		0			0
$451$	−5.71113	−	3.29732i	−0.268926	−	0.155265i
$452$	−1.96127	+	7.31954i	−0.0922502	+	0.344282i
$453$	−12.4177	+	3.32730i	−0.583433	+	0.156330i
$454$	−4.33013	−	2.50000i	−0.203223	−	0.117331i
$455$		0			0
$456$	26.3110	+	11.3930i	1.23212	+	0.533526i
$457$	−2.92122	+	2.92122i	−0.136649	+	0.136649i	−0.772123	−	0.635474i	$-0.780805\pi$
$457$	−2.92122	+	2.92122i	−0.136649	+	0.136649i	0.635474	+	0.772123i	$0.280805\pi$
$458$	−5.43520	−	20.2844i	−0.253970	−	0.947830i
$459$	−4.96513	+	8.59986i	−0.231753	+	0.401407i
$460$		0			0
$461$	9.28887	−	16.0888i	0.432626	−	0.749330i	−0.564473	−	0.825452i	$-0.690920\pi$
$461$	9.28887	−	16.0888i	0.432626	−	0.749330i	0.997099	+	0.0761217i	$0.0242537\pi$
$462$	4.37470	+	1.17220i	0.203530	+	0.0545356i
$463$	−9.56209	−	9.56209i	−0.444388	−	0.444388i	0.449096	−	0.893484i	$-0.351746\pi$
$463$	−9.56209	−	9.56209i	−0.444388	−	0.444388i	−0.893484	+	0.449096i	$0.851746\pi$
$464$	−3.79766			−0.176302
$465$		0			0
$466$	−8.42225	+	4.86259i	−0.390153	+	0.225255i
$467$	27.8878	−	27.8878i	1.29050	−	1.29050i	0.356015	−	0.934480i	$-0.384135\pi$
$467$	27.8878	−	27.8878i	1.29050	−	1.29050i	0.934480	−	0.356015i	$-0.115865\pi$
$468$	1.52416	−	1.52416i	0.0704545	−	0.0704545i
$469$	−9.32738	−	16.1555i	−0.430698	−	0.745991i
$470$		0			0
$471$	15.0556	−	8.69237i	0.693727	−	0.400523i
$472$	−7.24231	−	27.0287i	−0.333354	−	1.24410i
$473$	−10.3604	+	2.77606i	−0.476371	+	0.127643i
$474$	36.3731			1.67067
$475$		0			0
$476$	6.57775			0.301491
$477$	−12.2208	+	3.27456i	−0.559553	+	0.149932i
$478$	2.32937	+	8.69333i	0.106543	+	0.397624i
$479$	33.7108	−	19.4629i	1.54028	−	0.889283i	0.541463	−	0.840724i	$-0.317871\pi$
$479$	33.7108	−	19.4629i	1.54028	−	0.889283i	0.998820	−	0.0485587i	$-0.0154628\pi$
$480$		0			0
$481$	−5.00000	−	8.66025i	−0.227980	−	0.394874i
$482$	10.0338	−	10.0338i	0.457028	−	0.457028i
$483$	−4.65117	+	4.65117i	−0.211636	+	0.211636i
$484$	8.29457	−	4.78887i	0.377026	−	0.217676i
$485$		0			0
$486$	−16.6148			−0.753664
$487$	16.5358	+	16.5358i	0.749309	+	0.749309i	0.974349	−	0.225040i	$-0.0722514\pi$
$487$	16.5358	+	16.5358i	0.749309	+	0.749309i	−0.225040	+	0.974349i	$0.572251\pi$
$488$	10.3675	+	2.77797i	0.469315	+	0.125753i
$489$	5.69650	−	9.86662i	0.257604	−	0.446184i
$490$		0			0
$491$	−17.0777	+	29.5795i	−0.770708	+	1.33491i	0.166468	+	0.986047i	$0.446764\pi$
$491$	−17.0777	+	29.5795i	−0.770708	+	1.33491i	−0.937175	+	0.348858i	$0.886569\pi$
$492$	−3.13801	−	11.7112i	−0.141473	−	0.527983i
$493$	10.1981	−	10.1981i	0.459298	−	0.459298i
$494$	5.16403	−	0.596291i	0.232341	−	0.0268284i
$495$		0			0
$496$	6.28887	+	3.63088i	0.282379	+	0.163031i
$497$	27.1961	−	7.28718i	1.21991	−	0.326875i
$498$	1.17220	−	4.37470i	0.0525275	−	0.196035i
$499$	24.3834	+	14.0777i	1.09155	+	0.630207i	0.933989	−	0.357303i	$-0.116304\pi$
$499$	24.3834	+	14.0777i	1.09155	+	0.630207i	0.157561	+	0.987509i	$0.449637\pi$
$500$		0			0
$501$	7.50357			0.335235
$502$	−13.1365	−	13.1365i	−0.586309	−	0.586309i
$503$	−7.79356	+	29.0859i	−0.347497	+	1.29688i	0.542170	+	0.840269i	$0.317603\pi$
$503$	−7.79356	+	29.0859i	−0.347497	+	1.29688i	−0.889667	+	0.456609i	$0.849064\pi$
$504$	4.69581	+	8.13338i	0.209168	+	0.362290i
$505$		0			0
$506$			2.06561i			0.0918277i
$507$	−6.57016	+	24.5202i	−0.291791	+	1.08898i
$508$	1.24425	+	4.64361i	0.0552047	+	0.206027i
$509$	−17.6541	−	30.5777i	−0.782503	−	1.35533i	−0.930480	−	0.366344i	$-0.880609\pi$
$509$	−17.6541	−	30.5777i	−0.782503	−	1.35533i	0.147977	−	0.988991i	$-0.452724\pi$
$510$		0			0
$511$	−2.71113	+	4.69581i	−0.119933	+	0.207730i
$512$	−7.77817	−	7.77817i	−0.343750	−	0.343750i
$513$	8.93075	+	7.08178i	0.394302	+	0.312668i
$514$		−	28.5777i		−	1.26051i
$515$		0			0
$516$	−17.0777	−	9.85984i	−0.751806	−	0.434055i
$517$	−10.7446	−	2.87902i	−0.472549	−	0.126619i
$518$	14.0287	−	3.75897i	0.616384	−	0.165160i
$519$	13.2918	−	7.67404i	0.583446	−	0.336853i
$520$		0			0
$521$		−	40.7736i		−	1.78632i	−0.449734	−	0.893162i	$-0.648481\pi$
$521$		−	40.7736i		−	1.78632i	0.449734	−	0.893162i	$-0.351519\pi$
$522$	6.63008	+	1.77652i	0.290191	+	0.0777564i
$523$	9.88110	+	2.64763i	0.432070	+	0.115773i	0.468298	−	0.883571i	$-0.344867\pi$
$523$	9.88110	+	2.64763i	0.432070	+	0.115773i	−0.0362274	+	0.999344i	$0.511534\pi$
$524$			18.5777i			0.811573i
$525$		0			0
$526$	−13.5000	+	7.79423i	−0.588628	+	0.339845i
$527$	−26.6381	+	7.13765i	−1.16037	+	0.310921i
$528$	2.52574	+	0.676769i	0.109919	+	0.0294526i
$529$	17.3205	+	10.0000i	0.753066	+	0.434783i
$530$		0			0
$531$			16.8585i			0.731595i
$532$	1.10463	−	7.46859i	0.0478916	−	0.323804i
$533$	−4.66312	−	4.66312i	−0.201982	−	0.201982i
$534$	−5.69650	+	9.86662i	−0.246511	+	0.426970i
$535$		0			0
$536$	−16.1555	−	27.9821i	−0.697811	−	1.20864i
$537$	−1.58723	−	5.92364i	−0.0684942	−	0.255624i
$538$	−6.53503	+	24.3890i	−0.281745	+	1.05149i
$539$			4.77033i			0.205473i
$540$		0			0
$541$	21.8666	+	37.8741i	0.940119	+	1.62833i	0.765240	+	0.643745i	$0.222620\pi$
$541$	21.8666	+	37.8741i	0.940119	+	1.62833i	0.174879	+	0.984590i	$0.444047\pi$
$542$	−4.80827	+	17.9447i	−0.206533	+	0.770792i
$543$	−0.517152	−	0.517152i	−0.0221931	−	0.0221931i
$544$	18.9883			0.814118
$545$		0			0
$546$	3.92225	+	2.26451i	0.167857	+	0.0969122i
$547$	−10.2339	+	38.1933i	−0.437569	+	1.63303i	0.297274	+	0.954792i	$0.403923\pi$
$547$	−10.2339	+	38.1933i	−0.437569	+	1.63303i	−0.734843	+	0.678237i	$0.762744\pi$
$548$	−19.0478	+	5.10383i	−0.813680	+	0.218025i
$549$	−5.60014	−	3.23324i	−0.239008	−	0.137991i
$550$		0			0
$551$	−9.86662	−	13.2918i	−0.420332	−	0.566251i
$552$	−8.05606	+	8.05606i	−0.342889	+	0.342889i
$553$	−7.43671	−	27.7542i	−0.316241	−	1.18023i
$554$	−11.0594	+	19.1555i	−0.469870	+	0.813839i
$555$		0			0
$556$	7.78887	−	13.4907i	0.330322	−	0.572134i
$557$	−7.65872	−	2.05215i	−0.324510	−	0.0869523i	0.0928862	−	0.995677i	$-0.470391\pi$
$557$	−7.65872	−	2.05215i	−0.324510	−	0.0869523i	−0.417397	+	0.908724i	$0.637057\pi$
$558$	−9.28081	−	9.28081i	−0.392888	−	0.392888i
$559$	−10.7259			−0.453656
$560$		0			0
$561$	−8.59986	+	4.96513i	−0.363086	+	0.209628i
$562$	−21.7641	+	21.7641i	−0.918064	+	0.918064i
$563$	−1.82274	+	1.82274i	−0.0768194	+	0.0768194i	−0.744473	−	0.667653i	$-0.767299\pi$
$563$	−1.82274	+	1.82274i	−0.0768194	+	0.0768194i	0.667653	+	0.744473i	$0.267299\pi$
$564$	−10.2255	−	17.7111i	−0.430572	−	0.745773i
$565$		0			0
$566$	2.71113	−	1.56527i	0.113957	−	0.0657932i
$567$	5.00087	+	18.6635i	0.210017	+	0.783794i
$568$	47.1051	−	12.6218i	1.97648	−	0.529597i
$569$	−14.5235			−0.608858			−0.304429	−	0.952535i	$-0.598466\pi$
$569$	−14.5235			−0.608858			−0.304429	+	0.952535i	$0.598466\pi$
$570$		0			0
$571$	−13.1555			−0.550540			−0.275270	−	0.961367i	$-0.588767\pi$
$571$	−13.1555			−0.550540			−0.275270	+	0.961367i	$0.588767\pi$
$572$	−1.37379	+	0.368106i	−0.0574411	+	0.0153913i
$573$	0.327861	+	1.22359i	0.0136966	+	0.0511164i
$574$	8.29457	−	4.78887i	0.346209	−	0.199884i
$575$		0			0
$576$	6.32596	+	10.9569i	0.263582	+	0.456537i
$577$	7.34847	−	7.34847i	0.305921	−	0.305921i	−0.537404	−	0.843325i	$-0.680595\pi$
$577$	7.34847	−	7.34847i	0.305921	−	0.305921i	0.843325	+	0.537404i	$0.180595\pi$
$578$	−1.82274	+	1.82274i	−0.0758161	+	0.0758161i
$579$	−50.1010	+	28.9258i	−2.08213	+	1.20212i
$580$		0			0
$581$	−3.57775			−0.148430
$582$	−2.80220	−	2.80220i	−0.116155	−	0.116155i
$583$	8.06362	+	2.16064i	0.333961	+	0.0894846i
$584$	−4.69581	+	8.13338i	−0.194314	+	0.336562i
$585$		0			0
$586$	8.78887	−	15.2228i	0.363065	−	0.628847i
$587$	−7.34527	−	27.4129i	−0.303172	−	1.13145i	−0.934508	−	0.355943i	$-0.884160\pi$
$587$	−7.34527	−	27.4129i	−0.303172	−	1.13145i	0.631336	−	0.775509i	$-0.282507\pi$
$588$	−6.20156	+	6.20156i	−0.255748	+	0.255748i
$589$	3.63088	+	31.4444i	0.149608	+	1.29564i
$590$		0			0
$591$	10.5000	+	6.06218i	0.431912	+	0.249365i
$592$	8.09945	−	2.17024i	0.332885	−	0.0891963i
$593$	−4.03459	+	15.0573i	−0.165681	+	0.618329i	0.832272	+	0.554368i	$0.187040\pi$
$593$	−4.03459	+	15.0573i	−0.165681	+	0.618329i	−0.997952	+	0.0639609i	$0.979627\pi$
$594$	2.70062	+	1.55920i	0.110808	+	0.0639749i
$595$		0			0
$596$	3.61484			0.148069
$597$	−26.5977	−	26.5977i	−1.08857	−	1.08857i
$598$	−0.534620	+	1.99523i	−0.0218622	+	0.0815910i
$599$	−15.4217	−	26.7111i	−0.630113	−	1.09139i	−0.987528	−	0.157442i	$-0.949675\pi$
$599$	−15.4217	−	26.7111i	−0.630113	−	1.09139i	0.357416	−	0.933945i	$-0.383658\pi$
$600$		0			0
$601$		−	11.7266i		−	0.478336i	−0.970978	−	0.239168i	$-0.923125\pi$
$601$		−	11.7266i		−	0.478336i	0.970978	−	0.239168i	$-0.0768747\pi$
$602$	4.03182	−	15.0469i	0.164325	−	0.613268i
$603$	5.03830	+	18.8032i	0.205175	+	0.765725i
$604$	2.93164	+	5.07775i	0.119287	+	0.206611i
$605$		0			0
$606$	2.61484	−	4.52903i	0.106220	−	0.183979i
$607$	7.64200	+	7.64200i	0.310179	+	0.310179i	0.844979	−	0.534800i	$-0.179613\pi$
$607$	7.64200	+	7.64200i	0.310179	+	0.310179i	−0.534800	+	0.844979i	$0.679613\pi$
$608$	3.18878	−	21.5600i	0.129322	−	0.874372i
$609$		−	14.4223i		−	0.584419i
$610$		0			0
$611$	−9.63338	−	5.56183i	−0.389725	−	0.225008i
$612$	−6.63008	−	1.77652i	−0.268005	−	0.0718118i
$613$	−32.4320	+	8.69013i	−1.30992	+	0.350991i	−0.845191	−	0.534464i	$-0.820514\pi$
$613$	−32.4320	+	8.69013i	−1.30992	+	0.350991i	−0.464725	+	0.885455i	$0.653847\pi$
$614$	−15.0560	+	8.69258i	−0.607610	+	0.350804i
$615$		0			0
$616$		−	6.19684i		−	0.249678i
$617$	16.3461	+	4.37992i	0.658068	+	0.176329i	0.572374	−	0.819993i	$-0.306023\pi$
$617$	16.3461	+	4.37992i	0.658068	+	0.176329i	0.0856943	+	0.996321i	$0.472689\pi$
$618$	−17.7587	−	4.75843i	−0.714360	−	0.191412i
$619$			18.5777i			0.746703i	0.927690	+	0.373351i	$0.121791\pi$
$619$			18.5777i			0.746703i	−0.927690	+	0.373351i	$0.878209\pi$
$620$		0			0
$621$	−3.92225	+	2.26451i	−0.157395	+	0.0908718i
$622$	19.0967	−	5.11694i	0.765707	−	0.205171i
$623$	8.69333	+	2.32937i	0.348291	+	0.0933243i
$624$	2.26451	+	1.30742i	0.0906531	+	0.0523386i
$625$		0			0
$626$			4.52903i			0.181016i
$627$	4.19336	+	10.5984i	0.167467	+	0.423258i
$628$	−5.60657	−	5.60657i	−0.223727	−	0.223727i
$629$	−15.9220	+	27.5777i	−0.634853	+	1.09960i
$630$		0			0
$631$	−23.3666	−	40.4722i	−0.930210	−	1.61117i	−0.782960	−	0.622073i	$-0.786291\pi$
$631$	−23.3666	−	40.4722i	−0.930210	−	1.61117i	−0.147251	−	0.989099i	$-0.547042\pi$
$632$	−12.8808	−	48.0717i	−0.512369	−	1.91219i
$633$	8.43113	−	31.4654i	0.335108	−	1.25064i
$634$			4.00000i			0.158860i
$635$		0			0
$636$	7.67404	+	13.2918i	0.304295	+	0.527055i
$637$	−1.23465	+	4.60778i	−0.0489187	+	0.182567i
$638$	−3.20251	−	3.20251i	−0.126788	−	0.126788i
$639$	−29.3806			−1.16228
$640$		0			0
$641$	5.36662	+	3.09842i	0.211969	+	0.122380i	0.602226	−	0.798326i	$-0.294281\pi$
$641$	5.36662	+	3.09842i	0.211969	+	0.122380i	−0.390257	+	0.920706i	$0.627614\pi$
$642$	−9.97506	+	37.2274i	−0.393684	+	1.46925i
$643$	20.7208	−	5.55212i	0.817148	−	0.218954i	0.174049	−	0.984737i	$-0.444315\pi$
$643$	20.7208	−	5.55212i	0.817148	−	0.218954i	0.643099	+	0.765783i	$0.277648\pi$
$644$	2.59808	+	1.50000i	0.102379	+	0.0591083i
$645$		0			0
$646$	−9.86662	−	13.2918i	−0.388197	−	0.522960i
$647$	−16.3480	+	16.3480i	−0.642706	+	0.642706i	−0.951220	−	0.308514i	$-0.900168\pi$
$647$	−16.3480	+	16.3480i	−0.642706	+	0.642706i	0.308514	+	0.951220i	$0.400168\pi$
$648$	8.66176	+	32.3261i	0.340266	+	1.26989i
$649$	5.56183	−	9.63338i	0.218321	−	0.378143i
$650$		0			0
$651$	−13.7889	+	23.8830i	−0.540429	+	0.936050i
$652$	−5.01910	−	1.34486i	−0.196563	−	0.0526689i
$653$	1.69647	+	1.69647i	0.0663881	+	0.0663881i	0.739521	−	0.673133i	$-0.235052\pi$
$653$	1.69647	+	1.69647i	0.0663881	+	0.0663881i	−0.673133	+	0.739521i	$0.735052\pi$
$654$	−5.26039			−0.205698
$655$		0			0
$656$	4.78887	−	2.76486i	0.186974	−	0.107950i
$657$	4.00095	−	4.00095i	0.156092	−	0.156092i
$658$	11.4237	−	11.4237i	0.445341	−	0.445341i
$659$	3.99656	+	6.92225i	0.155684	+	0.269653i	0.933308	−	0.359077i	$-0.116908\pi$
$659$	3.99656	+	6.92225i	0.155684	+	0.269653i	−0.777624	+	0.628730i	$0.783575\pi$
$660$		0			0
$661$	30.5221	−	17.6220i	1.18717	−	0.685414i	0.229510	−	0.973306i	$-0.426288\pi$
$661$	30.5221	−	17.6220i	1.18717	−	0.685414i	0.957663	+	0.287892i	$0.0929544\pi$
$662$	−4.48288	−	16.7303i	−0.174232	−	0.650243i
$663$	−9.59190	+	2.57014i	−0.372519	+	0.0998160i
$664$	−6.19684			−0.240484
$665$		0			0
$666$	−15.1555			−0.587263
$667$	6.35362	−	1.70245i	0.246013	−	0.0659190i
$668$	−0.885744	−	3.30564i	−0.0342705	−	0.127899i
$669$	−32.9411	+	19.0185i	−1.27358	+	0.735299i
$670$		0			0
$671$	2.13338	+	3.69512i	0.0823582	+	0.142649i
$672$	13.4268	−	13.4268i	0.517949	−	0.517949i
$673$	−2.96460	+	2.96460i	−0.114277	+	0.114277i	−0.761933	−	0.647656i	$-0.775749\pi$
$673$	−2.96460	+	2.96460i	−0.114277	+	0.114277i	0.647656	+	0.761933i	$0.275749\pi$
$674$	−0.532463	+	0.307418i	−0.0205097	+	0.0118413i
$675$		0			0
$676$	11.5777			0.445298
$677$	−6.96112	−	6.96112i	−0.267537	−	0.267537i	0.560570	−	0.828107i	$-0.310582\pi$
$677$	−6.96112	−	6.96112i	−0.267537	−	0.267537i	−0.828107	+	0.560570i	$0.810582\pi$
$678$	16.0487	+	4.30024i	0.616347	+	0.165150i
$679$	−1.56527	+	2.71113i	−0.0600695	+	0.104043i
$680$		0			0
$681$	5.48146	−	9.49416i	0.210050	−	0.363817i
$682$	2.24144	+	8.36516i	0.0858291	+	0.320319i
$683$	17.8976	−	17.8976i	0.684832	−	0.684832i	−0.276253	−	0.961085i	$-0.589093\pi$
$683$	17.8976	−	17.8976i	0.684832	−	0.684832i	0.961085	+	0.276253i	$0.0890929\pi$
$684$	−3.13054	+	7.22967i	−0.119699	+	0.276433i
$685$		0			0
$686$	−16.5000	−	9.52628i	−0.629973	−	0.363715i
$687$	44.4753	−	11.9171i	1.69684	−	0.454667i
$688$	2.32777	−	8.68736i	0.0887454	−	0.331202i
$689$	7.22965	+	4.17404i	0.275428	+	0.159018i
$690$		0			0
$691$	−10.7332			−0.408312			−0.204156	−	0.978938i	$-0.565445\pi$
$691$	−10.7332			−0.408312			−0.204156	+	0.978938i	$0.565445\pi$
$692$	−4.94975	−	4.94975i	−0.188161	−	0.188161i
$693$	−0.966282	+	3.60621i	−0.0367060	+	0.136989i
$694$	−3.96445	−	6.86662i	−0.150488	−	0.260653i
$695$		0			0
$696$		−	24.9801i		−	0.946867i
$697$	−5.43520	+	20.2844i	−0.205873	+	0.768328i
$698$	−8.10388	−	30.2441i	−0.306736	−	1.14476i
$699$	−10.6616	−	18.4665i	−0.403260	−	0.698467i
$700$		0			0
$701$	−16.7518	+	29.0149i	−0.632706	+	1.09588i	0.354290	+	0.935136i	$0.384723\pi$
$701$	−16.7518	+	29.0149i	−0.632706	+	1.09588i	−0.986996	+	0.160744i	$0.948611\pi$
$702$	2.20505	+	2.20505i	0.0832241	+	0.0832241i
$703$	28.6388	+	22.7096i	1.08013	+	0.856509i
$704$		−	8.34808i		−	0.314630i
$705$		0			0
$706$	8.07775	+	4.66369i	0.304010	+	0.175520i
$707$	−3.99046	−	1.06924i	−0.150077	−	0.0402129i
$708$	19.7542	−	5.29312i	0.742408	−	0.198928i
$709$	−2.46341	+	1.42225i	−0.0925155	+	0.0534138i	−0.545544	−	0.838082i	$-0.683677\pi$
$709$	−2.46341	+	1.42225i	−0.0925155	+	0.0534138i	0.453029	+	0.891496i	$0.350344\pi$
$710$		0			0
$711$			29.9835i			1.12447i
$712$	15.0573	+	4.03459i	0.564296	+	0.151203i
$713$	−12.1492	−	3.25536i	−0.454990	−	0.121914i
$714$		−	14.4223i		−	0.539739i
$715$		0			0
$716$	−2.42225	+	1.39849i	−0.0905238	+	0.0522640i
$717$	−19.0608	+	5.10734i	−0.711840	+	0.190737i
$718$	−6.94750	−	1.86158i	−0.259278	−	0.0694734i
$719$	−30.6445	−	17.6926i	−1.14285	−	0.659822i	−0.195712	−	0.980661i	$-0.562702\pi$
$719$	−30.6445	−	17.6926i	−1.14285	−	0.659822i	−0.947134	+	0.320840i	$0.896035\pi$
$720$		0			0
$721$			14.5235i			0.540885i
$722$	−16.7489	+	8.97073i	−0.623330	+	0.333856i
$723$	22.0000	+	22.0000i	0.818188	+	0.818188i
$724$	−0.166781	+	0.288874i	−0.00619838	+	0.0107359i
$725$		0			0
$726$	−10.5000	−	18.1865i	−0.389692	−	0.674966i
$727$	−11.8979	−	44.4034i	−0.441267	−	1.64683i	−0.725609	−	0.688108i	$-0.758442\pi$
$727$	−11.8979	−	44.4034i	−0.441267	−	1.64683i	0.284342	−	0.958723i	$-0.408225\pi$
$728$	1.60386	−	5.98569i	0.0594430	−	0.221844i
$729$		−	2.96291i		−	0.109737i
$730$		0			0
$731$	17.0777	+	29.5795i	0.631643	+	1.09404i
$732$	−2.03031	+	7.57721i	−0.0750423	+	0.280062i
$733$	−14.6969	−	14.6969i	−0.542844	−	0.542844i	0.381518	−	0.924362i	$-0.375402\pi$
$733$	−14.6969	−	14.6969i	−0.542844	−	0.542844i	−0.924362	+	0.381518i	$0.875402\pi$
$734$	25.2494			0.931972
$735$		0			0
$736$	7.50000	+	4.33013i	0.276454	+	0.159611i
$737$	3.32440	−	12.4068i	0.122456	−	0.457012i
$738$	−9.65395	+	2.58677i	−0.355367	+	0.0952202i
$739$	11.5277	+	6.65549i	0.424052	+	0.244826i	0.696809	−	0.717256i	$-0.254602\pi$
$739$	11.5277	+	6.65549i	0.424052	+	0.244826i	−0.272758	+	0.962083i	$0.587936\pi$
$740$		0			0
$741$	1.30742	+	11.3226i	0.0480292	+	0.415945i
$742$	−8.57321	+	8.57321i	−0.314733	+	0.314733i
$743$	−11.2097	−	41.8352i	−0.411244	−	1.53478i	−0.792241	−	0.610208i	$-0.791086\pi$
$743$	−11.2097	−	41.8352i	−0.411244	−	1.53478i	0.380997	−	0.924576i	$-0.375581\pi$
$744$	−23.8830	+	41.3666i	−0.875594	+	1.51657i
$745$		0			0
$746$	7.17404	−	12.4258i	0.262660	−	0.454941i
$747$	3.60621	+	0.966282i	0.131944	+	0.0353544i
$748$	3.20251	+	3.20251i	0.117095	+	0.117095i
$749$	30.4456			1.11246
$750$		0			0
$751$	−3.57775	+	2.06561i	−0.130554	+	0.0753753i	−0.563855	−	0.825874i	$-0.690682\pi$
$751$	−3.57775	+	2.06561i	−0.130554	+	0.0753753i	0.433301	+	0.901249i	$0.357349\pi$
$752$	6.59545	−	6.59545i	0.240511	−	0.240511i
$753$	28.8028	−	28.8028i	1.04963	−	1.04963i
$754$	−2.26451	−	3.92225i	−0.0824687	−	0.142840i
$755$		0			0
$756$	3.92225	−	2.26451i	0.142651	−	0.0823596i
$757$	−11.8979	−	44.4034i	−0.432435	−	1.61387i	−0.747131	−	0.664676i	$-0.768569\pi$
$757$	−11.8979	−	44.4034i	−0.432435	−	1.61387i	0.314697	−	0.949192i	$-0.398097\pi$
$758$	−2.70167	+	0.723911i	−0.0981291	+	0.0262936i
$759$	−4.52903			−0.164393
$760$		0			0
$761$	−31.2297			−1.13207			−0.566037	−	0.824380i	$-0.691524\pi$
$761$	−31.2297			−1.13207			−0.566037	+	0.824380i	$0.691524\pi$
$762$	10.1815	−	2.72812i	0.368837	−	0.0988295i
$763$	1.07552	+	4.01390i	0.0389365	+	0.145313i
$764$	0.500344	−	0.288874i	0.0181018	−	0.0104511i
$765$		0			0
$766$	−8.50000	−	14.7224i	−0.307117	−	0.531943i
$767$	7.86562	−	7.86562i	0.284011	−	0.284011i
$768$	26.3566	−	26.3566i	0.951063	−	0.951063i
$769$	−37.3738	+	21.5777i	−1.34773	+	0.778113i	−0.987928	−	0.154914i	$-0.950490\pi$
$769$	−37.3738	+	21.5777i	−1.34773	+	0.778113i	−0.359804	+	0.933028i	$0.617156\pi$
$770$		0			0
$771$	62.6591			2.25661
$772$	18.6571	+	18.6571i	0.671485	+	0.671485i
$773$	−17.5369	−	4.69899i	−0.630757	−	0.169011i	−0.0707438	−	0.997495i	$-0.522537\pi$
$773$	−17.5369	−	4.69899i	−0.630757	−	0.169011i	−0.560013	+	0.828484i	$0.689204\pi$
$774$	−8.12779	+	14.0777i	−0.292147	+	0.506014i
$775$		0			0
$776$	−2.71113	+	4.69581i	−0.0973238	+	0.168570i
$777$	8.24184	+	30.7590i	0.295675	+	1.10347i
$778$	11.0151	−	11.0151i	0.394912	−	0.394912i
$779$	22.1189	+	9.57775i	0.792490	+	0.343158i
$780$		0			0
$781$	16.7889	+	9.69306i	0.600753	+	0.346845i
$782$	6.35362	−	1.70245i	0.227205	−	0.0608794i
$783$	2.57014	−	9.59190i	0.0918494	−	0.342787i
$784$	−3.46410	−	2.00000i	−0.123718	−	0.0714286i
$785$		0			0
$786$	40.7332			1.45291
$787$	16.5358	+	16.5358i	0.589438	+	0.589438i	0.937479	−	0.348041i	$-0.113153\pi$
$787$	16.5358	+	16.5358i	0.589438	+	0.589438i	−0.348041	+	0.937479i	$0.613153\pi$
$788$	1.43120	−	5.34129i	0.0509842	−	0.190276i
$789$	−17.0895	−	29.5999i	−0.608402	−	1.05378i
$790$		0			0
$791$		−	13.1250i		−	0.466673i
$792$	−1.67365	+	6.24614i	−0.0594705	+	0.221947i
$793$	1.10432	+	4.12137i	0.0392155	+	0.146354i
$794$	−13.3239	−	23.0777i	−0.472849	−	0.818999i
$795$		0			0
$796$	−8.57775	+	14.8571i	−0.304030	+	0.526596i
$797$	−5.35828	−	5.35828i	−0.189800	−	0.189800i	0.605810	−	0.795610i	$-0.292849\pi$
$797$	−5.35828	−	5.35828i	−0.189800	−	0.189800i	−0.795610	+	0.605810i	$0.792849\pi$
$798$	−16.3755	−	2.42198i	−0.579686	−	0.0857373i
$799$			35.4223i			1.25315i
$800$		0			0
$801$	−8.13338	−	4.69581i	−0.287379	−	0.165918i
$802$	−18.6635	−	5.00087i	−0.659031	−	0.176587i
$803$	−3.60621	+	0.966282i	−0.127260	+	0.0340993i
$804$	20.4510	−	11.8074i	0.721253	−	0.416416i
$805$		0			0
$806$			8.66025i			0.305044i
$807$	−53.4750	−	14.3286i	−1.88241	−	0.504390i
$808$	−6.91168	−	1.85198i	−0.243152	−	0.0651524i
$809$		−	26.4223i		−	0.928957i	−0.885584	−	0.464478i	$-0.846242\pi$
$809$		−	26.4223i		−	0.928957i	0.885584	−	0.464478i	$-0.153758\pi$
$810$		0			0
$811$	5.13338	−	2.96376i	0.180257	−	0.104072i	−0.407156	−	0.913359i	$-0.633480\pi$
$811$	5.13338	−	2.96376i	0.180257	−	0.104072i	0.587414	+	0.809287i	$0.300146\pi$
$812$	−6.35362	+	1.70245i	−0.222968	+	0.0597442i
$813$	−39.3453	−	10.5425i	−1.37990	−	0.369743i
$814$	8.66025	+	5.00000i	0.303542	+	0.175250i
$815$		0			0
$816$		−	8.32669i		−	0.291493i
$817$	36.4535	−	14.4232i	1.27535	−	0.504605i
$818$	−1.50603	−	1.50603i	−0.0526572	−	0.0526572i
$819$	−1.86671	+	3.23324i	−0.0652282	+	0.112979i
$820$		0			0
$821$	15.5777	+	26.9814i	0.543667	+	0.941659i	0.998689	+	0.0511791i	$0.0162979\pi$
$821$	15.5777	+	26.9814i	0.543667	+	0.941659i	−0.455022	+	0.890480i	$0.650369\pi$
$822$	11.1906	+	41.7638i	0.390316	+	1.45668i
$823$	11.6555	−	43.4988i	0.406285	−	1.51627i	−0.395390	−	0.918513i	$-0.629390\pi$
$823$	11.6555	−	43.4988i	0.406285	−	1.51627i	0.801674	−	0.597761i	$-0.203943\pi$
$824$			25.1555i			0.876333i
$825$		0			0
$826$	8.07775	+	13.9911i	0.281061	+	0.486812i
$827$	10.1744	−	37.9715i	0.353800	−	1.32040i	−0.528189	−	0.849127i	$-0.677129\pi$
$827$	10.1744	−	37.9715i	0.353800	−	1.32040i	0.881988	−	0.471271i	$-0.156205\pi$
$828$	−2.21363	−	2.21363i	−0.0769288	−	0.0769288i
$829$	1.66781			0.0579255			0.0289628	−	0.999580i	$-0.490780\pi$
$829$	1.66781			0.0579255			0.0289628	+	0.999580i	$0.490780\pi$
$830$		0			0
$831$	−42.0000	−	24.2487i	−1.45696	−	0.841178i
$832$	2.16064	−	8.06362i	0.0749068	−	0.279556i
$833$	14.6730	−	3.93163i	0.508391	−	0.136223i
$834$	−29.5795	−	17.0777i	−1.02426	−	0.591354i
$835$		0			0
$836$	4.17404	−	3.09842i	0.144362	−	0.107161i
$837$	−13.4268	+	13.4268i	−0.464097	+	0.464097i
$838$	6.21166	+	23.1822i	0.214578	+	0.800816i
$839$	3.96445	−	6.86662i	0.136868	−	0.237062i	−0.789442	−	0.613826i	$-0.789630\pi$
$839$	3.96445	−	6.86662i	0.136868	−	0.237062i	0.926309	+	0.376764i	$0.122963\pi$
$840$		0			0
$841$	7.28887	−	12.6247i	0.251340	−	0.435334i
$842$	−21.3652	−	5.72478i	−0.736293	−	0.197289i
$843$	−47.7196	−	47.7196i	−1.64355	−	1.64355i
$844$	−14.8571			−0.511402
$845$		0			0
$846$	−14.5999	+	8.42923i	−0.501954	+	0.289803i
$847$	−11.7303	+	11.7303i	−0.403058	+	0.403058i
$848$	−4.94975	+	4.94975i	−0.169975	+	0.169975i
$849$	3.43198	+	5.94437i	0.117785	+	0.204010i
$850$		0			0
$851$	−12.5777	+	7.26177i	−0.431160	+	0.248930i
$852$	9.22475	+	34.4272i	0.316035	+	1.17946i
$853$	−8.68736	+	2.32777i	−0.297450	+	0.0797014i	−0.404457	−	0.914557i	$-0.632540\pi$
$853$	−8.68736	+	2.32777i	−0.297450	+	0.0797014i	0.107008	+	0.994258i	$0.465873\pi$
$854$	−6.19684			−0.212051
$855$		0			0
$856$	52.7332			1.80239
$857$	23.3324	−	6.25190i	0.797020	−	0.213561i	0.162745	−	0.986668i	$-0.447965\pi$
$857$	23.3324	−	6.25190i	0.797020	−	0.213561i	0.634275	+	0.773107i	$0.281299\pi$
$858$	0.807103	+	3.01215i	0.0275540	+	0.102833i
$859$	21.5543	−	12.4444i	0.735422	−	0.424596i	−0.0849801	−	0.996383i	$-0.527083\pi$
$859$	21.5543	−	12.4444i	0.735422	−	0.424596i	0.820403	+	0.571786i	$0.193749\pi$
$860$		0			0
$861$	10.5000	+	18.1865i	0.357839	+	0.619795i
$862$	3.91010	−	3.91010i	0.133178	−	0.133178i
$863$	−31.9298	+	31.9298i	−1.08690	+	1.08690i	−0.0910557	+	0.995846i	$0.529024\pi$
$863$	−31.9298	+	31.9298i	−1.08690	+	1.08690i	−0.995846	+	0.0910557i	$0.970976\pi$
$864$	11.3226	−	6.53709i	0.385202	−	0.222396i
$865$		0			0
$866$	−18.6148			−0.632558
$867$	−3.99651	−	3.99651i	−0.135729	−	0.135729i
$868$	12.1492	+	3.25536i	0.412370	+	0.110494i
$869$	9.89196	−	17.1334i	0.335562	−	0.581210i
$870$		0			0
$871$	6.42225	−	11.1237i	0.217610	−	0.376911i
$872$	1.86286	+	6.95228i	0.0630843	+	0.235434i
$873$	2.30995	−	2.30995i	0.0781799	−	0.0781799i
$874$	−0.866025	−	7.50000i	−0.0292937	−	0.253691i
$875$		0			0
$876$	−5.94437	−	3.43198i	−0.200842	−	0.115956i
$877$	−28.3839	+	7.60544i	−0.958456	+	0.256817i	−0.703947	−	0.710253i	$-0.748581\pi$
$877$	−28.3839	+	7.60544i	−0.958456	+	0.256817i	−0.254509	+	0.967070i	$0.581914\pi$
$878$	−6.89698	+	25.7399i	−0.232762	+	0.868679i
$879$	33.3772	+	19.2703i	1.12578	+	0.649972i
$880$		0			0
$881$	−38.9629			−1.31269			−0.656347	−	0.754459i	$-0.727899\pi$
$881$	−38.9629			−1.31269			−0.656347	+	0.754459i	$0.727899\pi$
$882$	5.11215	+	5.11215i	0.172135	+	0.172135i
$883$	1.24190	−	4.63485i	0.0417934	−	0.155975i	−0.941876	−	0.335962i	$-0.890939\pi$
$883$	1.24190	−	4.63485i	0.0417934	−	0.155975i	0.983669	+	0.179986i	$0.0576054\pi$
$884$	2.26451	+	3.92225i	0.0761638	+	0.131920i
$885$		0			0
$886$		−	9.72518i		−	0.326724i
$887$	0.408351	−	1.52399i	0.0137111	−	0.0511705i	−0.958731	−	0.284313i	$-0.908234\pi$
$887$	0.408351	−	1.52399i	0.0137111	−	0.0511705i	0.972442	+	0.233143i	$0.0749010\pi$
$888$	14.2753	+	53.2761i	0.479047	+	1.78783i
$889$	−4.16335	−	7.21113i	−0.139634	−	0.241853i
$890$		0			0
$891$	−6.65192	+	11.5215i	−0.222848	+	0.385984i
$892$	12.2669	+	12.2669i	0.410728	+	0.410728i
$893$	40.2196	+	5.94860i	1.34590	+	0.199062i
$894$		−	7.92582i		−	0.265079i
$895$		0			0
$896$	−4.50000	−	2.59808i	−0.150334	−	0.0867956i
$897$	−4.37470	−	1.17220i	−0.146067	−	0.0391386i
$898$	−5.66349	+	1.51753i	−0.188993	+	0.0506406i
$899$	23.8830	−	13.7889i	0.796544	−	0.459885i
$900$		0			0
$901$		−	26.5836i		−	0.885630i
$902$	6.36993	+	1.70682i	0.212096	+	0.0568308i
$903$	32.9917	+	8.84009i	1.09789	+	0.294180i
$904$		−	22.7332i		−	0.756096i
$905$		0			0
$906$	11.1334	−	6.42786i	0.369882	−	0.213551i
$907$	−34.1436	+	9.14876i	−1.13372	+	0.303779i	−0.776424	−	0.630211i	$-0.782968\pi$
$907$	−34.1436	+	9.14876i	−1.13372	+	0.303779i	−0.357297	+	0.933991i	$0.616302\pi$
$908$	−4.82963	−	1.29410i	−0.160277	−	0.0429461i
$909$	3.73343	+	2.15549i	0.123830	+	0.0714932i
$910$		0			0
$911$			22.9145i			0.759190i	0.925153	+	0.379595i	$0.123937\pi$
$911$			22.9145i			0.759190i	−0.925153	+	0.379595i	$0.876063\pi$
$912$	−9.45440	−	1.39833i	−0.313066	−	0.0463034i
$913$	−1.74190	−	1.74190i	−0.0576484	−	0.0576484i
$914$	2.06561	−	3.57775i	0.0683244	−	0.118341i
$915$		0			0
$916$	−10.5000	−	18.1865i	−0.346930	−	0.600900i
$917$	−8.32818	−	31.0812i	−0.275021	−	1.02639i
$918$	2.57014	−	9.59190i	0.0848273	−	0.316580i
$919$		−	16.5777i		−	0.546849i	−0.961893	−	0.273425i	$-0.911844\pi$
$919$		−	16.5777i		−	0.546849i	0.961893	−	0.273425i	$-0.0881564\pi$
$920$		0			0
$921$	−19.0592	−	33.0115i	−0.628022	−	1.08777i
$922$	−4.80827	+	17.9447i	−0.158352	+	0.590978i
$923$	13.7081	+	13.7081i	0.451206	+	0.451206i
$924$	4.52903			0.148994
$925$		0			0
$926$	11.7111	+	6.76142i	0.384851	+	0.222194i
$927$	3.92253	−	14.6391i	0.128833	−	0.480811i
$928$	−18.3413	+	4.91454i	−0.602083	+	0.161328i
$929$	52.4619	+	30.2889i	1.72122	+	0.993746i	0.916442	+	0.400167i	$0.131048\pi$
$929$	52.4619	+	30.2889i	1.72122	+	0.993746i	0.804776	+	0.593579i	$0.202286\pi$
$930$		0			0
$931$	−2.00000	−	17.3205i	−0.0655474	−	0.567657i
$932$	−6.87674	+	6.87674i	−0.225255	+	0.225255i
$933$	11.2193	+	41.8710i	0.367304	+	1.37080i
$934$	−19.7197	+	34.1555i	−0.645248	+	1.11760i
$935$		0			0
$936$	−3.23324	+	5.60014i	−0.105682	+	0.183046i
$937$	−4.69690	−	1.25853i	−0.153441	−	0.0411144i	0.181281	−	0.983431i	$-0.441976\pi$
$937$	−4.69690	−	1.25853i	−0.153441	−	0.0411144i	−0.334722	+	0.942317i	$0.608642\pi$
$938$	13.1909	+	13.1909i	0.430698	+	0.430698i
$939$	−9.93027			−0.324062
$940$		0			0
$941$	−28.5000	+	16.4545i	−0.929073	+	0.536401i	−0.886518	−	0.462693i	$-0.846883\pi$
$941$	−28.5000	+	16.4545i	−0.929073	+	0.536401i	−0.0425550	+	0.999094i	$0.513550\pi$
$942$	−12.2929	+	12.2929i	−0.400523	+	0.400523i
$943$	−6.77249	+	6.77249i	−0.220543	+	0.220543i
$944$	4.66369	+	8.07775i	0.151790	+	0.262908i
$945$		0			0
$946$	9.28887	−	5.36293i	0.302007	−	0.174364i
$947$	−5.82774	−	21.7494i	−0.189376	−	0.706761i	−0.993651	−	0.112504i	$-0.964113\pi$
$947$	−5.82774	−	21.7494i	−0.189376	−	0.706761i	0.804275	−	0.594257i	$-0.202554\pi$
$948$	35.1337	−	9.41404i	1.14109	−	0.305754i
$949$	−3.73343			−0.121192
$950$		0			0
$951$	−8.77033			−0.284397
$952$	−19.0608	+	5.10734i	−0.617766	+	0.165530i
$953$	7.65528	+	28.5699i	0.247979	+	0.925470i	0.971863	+	0.235548i	$0.0756885\pi$
$953$	7.65528	+	28.5699i	0.247979	+	0.925470i	−0.723884	+	0.689922i	$0.757645\pi$
$954$	10.9569	−	6.32596i	0.354742	−	0.204811i
$955$		0			0
$956$	4.50000	+	7.79423i	0.145540	+	0.252083i
$957$	7.02176	−	7.02176i	0.226981	−	0.226981i
$958$	−27.5247	+	27.5247i	−0.889283	+	0.889283i
$959$	29.5795	−	17.0777i	0.955173	−	0.551469i
$960$		0			0
$961$	−21.7332			−0.701072
$962$	7.07107	+	7.07107i	0.227980	+	0.227980i
$963$	−30.6878	−	8.22277i	−0.988900	−	0.264975i
$964$	7.09498	−	12.2889i	0.228514	−	0.395798i
$965$		0			0
$966$	3.28887	−	5.69650i	0.105818	−	0.183282i
$967$	2.34440	+	8.74941i	0.0753907	+	0.281362i	0.993322	−	0.115378i	$-0.0368080\pi$
$967$	2.34440	+	8.74941i	0.0753907	+	0.281362i	−0.917931	+	0.396740i	$0.870141\pi$
$968$	−20.3175	+	20.3175i	−0.653028	+	0.653028i
$969$	29.1434	−	21.6334i	0.936222	−	0.694964i
$970$		0			0
$971$	3.92225	+	2.26451i	0.125871	+	0.0726717i	0.561613	−	0.827400i	$-0.310181\pi$
$971$	3.92225	+	2.26451i	0.125871	+	0.0726717i	−0.435742	+	0.900071i	$0.643514\pi$
$972$	−16.0487	+	4.30024i	−0.514762	+	0.137930i
$973$	−6.98331	+	26.0621i	−0.223875	+	0.835512i
$974$	−20.2521	−	11.6926i	−0.648921	−	0.374655i
$975$		0			0
$976$	−3.57775			−0.114521
$977$	1.60284	+	1.60284i	0.0512794	+	0.0512794i	0.732281	−	0.681002i	$-0.238456\pi$
$977$	1.60284	+	1.60284i	0.0512794	+	0.0512794i	−0.681002	+	0.732281i	$0.738456\pi$
$978$	−2.94872	+	11.0048i	−0.0942898	+	0.351894i
$979$	3.09842	+	5.36662i	0.0990259	+	0.171518i
$980$		0			0
$981$		−	4.33631i		−	0.138448i
$982$	8.84009	−	32.9917i	0.282099	−	1.05281i
$983$	7.02836	+	26.2302i	0.224170	+	0.836613i	0.982735	+	0.185017i	$0.0592339\pi$
$983$	7.02836	+	26.2302i	0.224170	+	0.836613i	−0.758566	+	0.651597i	$0.774099\pi$
$984$	18.1865	+	31.5000i	0.579766	+	1.00418i
$985$		0			0
$986$	−7.21113	+	12.4900i	−0.229649	+	0.397764i
$987$	25.0473	+	25.0473i	0.797265	+	0.797265i
$988$	4.83374	−	1.91252i	0.153782	−	0.0608455i
$989$			15.5777i			0.495344i
$990$		0			0
$991$	−4.78887	−	2.76486i	−0.152124	−	0.0878286i	0.422006	−	0.906593i	$-0.361326\pi$
$991$	−4.78887	−	2.76486i	−0.152124	−	0.0878286i	−0.574130	+	0.818764i	$0.694659\pi$
$992$	35.0716	+	9.39742i	1.11353	+	0.298368i
$993$	36.6826	−	9.82908i	1.16409	−	0.311916i
$994$	−24.3834	+	14.0777i	−0.773394	+	0.446519i
$995$		0			0
$996$		−	4.52903i		−	0.143508i
$997$	13.6444	+	3.65601i	0.432123	+	0.115787i	0.468322	−	0.883558i	$-0.344859\pi$
$997$	13.6444	+	3.65601i	0.432123	+	0.115787i	−0.0361997	+	0.999345i	$0.511525\pi$
$998$	−27.1961	−	7.28718i	−0.860878	−	0.230672i
$999$			21.9258i			0.693702i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.p.e.293.1	yes	16
5.2	odd	4	inner	475.2.p.e.407.1	yes	16
5.3	odd	4	inner	475.2.p.e.407.4	yes	16
5.4	even	2	inner	475.2.p.e.293.4	yes	16
19.12	odd	6	inner	475.2.p.e.468.1	yes	16
95.12	even	12	inner	475.2.p.e.107.1	✓	16
95.69	odd	6	inner	475.2.p.e.468.4	yes	16
95.88	even	12	inner	475.2.p.e.107.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.p.e.107.1	✓	16	95.12	even	12	inner
475.2.p.e.107.4	yes	16	95.88	even	12	inner
475.2.p.e.293.1	yes	16	1.1	even	1	trivial
475.2.p.e.293.4	yes	16	5.4	even	2	inner
475.2.p.e.407.1	yes	16	5.2	odd	4	inner
475.2.p.e.407.4	yes	16	5.3	odd	4	inner
475.2.p.e.468.1	yes	16	19.12	odd	6	inner
475.2.p.e.468.4	yes	16	95.69	odd	6	inner

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.567482 - 2.11787i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.09629 + 1.89883i) q^{6} +(1.22474 - 1.22474i) q^{7} +(2.12132 - 2.12132i) q^{8} +(-1.56527 + 0.903709i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.567482 - 2.11787i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.09629 + 1.89883i) q^{6} +(1.22474 - 1.22474i) q^{7} +(2.12132 - 2.12132i) q^{8} +(-1.56527 + 0.903709i) q^{9} +1.19258 q^{11} +(1.55039 + 1.55039i) q^{12} +(1.15195 + 0.308663i) q^{13} +(-0.866025 + 1.50000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.982908 - 3.66826i) q^{17} +(1.27804 - 1.27804i) q^{18} +(-4.33013 + 0.500000i) q^{19} +(-3.28887 - 1.89883i) q^{21} +(-1.15195 + 0.308663i) q^{22} +(0.448288 - 1.67303i) q^{23} +(-5.69650 - 3.28887i) q^{24} -1.19258 q^{26} +(-1.84897 - 1.84897i) q^{27} +(-0.448288 + 1.67303i) q^{28} +(1.89883 + 3.28887i) q^{29} -7.26177i q^{31} +(-1.29410 + 4.82963i) q^{32} +(-0.676769 - 2.52574i) q^{33} +(1.89883 + 3.28887i) q^{34} +(0.903709 - 1.56527i) q^{36} +(-5.92921 - 5.92921i) q^{37} +(4.05317 - 1.60368i) q^{38} -2.61484i q^{39} +(-4.78887 - 2.76486i) q^{41} +(3.66826 + 0.982908i) q^{42} +(-8.68736 + 2.32777i) q^{43} +(-1.03281 + 0.596291i) q^{44} +1.73205i q^{46} +(-9.00956 - 2.41410i) q^{47} +(2.11787 + 0.567482i) q^{48} +4.00000i q^{49} +(-7.21113 + 4.16335i) q^{51} +(-1.15195 + 0.308663i) q^{52} +(6.76148 + 1.81173i) q^{53} +(2.26451 + 1.30742i) q^{54} -5.19615i q^{56} +(3.51621 + 8.88691i) q^{57} +(-2.68535 - 2.68535i) q^{58} +(4.66369 - 8.07775i) q^{59} +(1.78887 + 3.09842i) q^{61} +(1.87948 + 7.01433i) q^{62} +(-0.810243 + 3.02387i) q^{63} -7.00000i q^{64} +(1.30742 + 2.26451i) q^{66} +(2.78757 - 10.4033i) q^{67} +(2.68535 + 2.68535i) q^{68} -3.79766 q^{69} +(14.0777 + 8.12779i) q^{71} +(-1.40338 + 5.23749i) q^{72} +(-3.02387 + 0.810243i) q^{73} +(7.26177 + 4.19258i) q^{74} +(3.50000 - 2.59808i) q^{76} +(1.46061 - 1.46061i) q^{77} +(0.676769 + 2.52574i) q^{78} +(8.29457 - 14.3666i) q^{79} +(-5.57775 + 9.66094i) q^{81} +(5.34129 + 1.43120i) q^{82} +(-1.46061 - 1.46061i) q^{83} +3.79766 q^{84} +(7.78887 - 4.49691i) q^{86} +(5.88786 - 5.88786i) q^{87} +(2.52985 - 2.52985i) q^{88} +(2.59808 + 4.50000i) q^{89} +(1.78887 - 1.03281i) q^{91} +(0.448288 + 1.67303i) q^{92} +(-15.3795 + 4.12092i) q^{93} +9.32738 q^{94} +10.9629 q^{96} +(-1.74583 + 0.467794i) q^{97} +(-1.03528 - 3.86370i) q^{98} +(-1.86671 + 1.07775i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{6}+O(q^{10}) \) 16 * q - 4 * q^6	\( 16 q - 4 q^{6} - 24 q^{11} - 8 q^{16} + 12 q^{21} + 24 q^{26} + 36 q^{36} - 12 q^{41} - 180 q^{51} - 36 q^{61} + 64 q^{66} + 96 q^{71} + 56 q^{76} + 40 q^{81} + 60 q^{86} - 36 q^{91} - 40 q^{96}+O(q^{100}) \) 16 * q - 4 * q^6 - 24 * q^11 - 8 * q^16 + 12 * q^21 + 24 * q^26 + 36 * q^36 - 12 * q^41 - 180 * q^51 - 36 * q^61 + 64 * q^66 + 96 * q^71 + 56 * q^76 + 40 * q^81 + 60 * q^86 - 36 * q^91 - 40 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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