LMFDB - Embedded newform 475.2.p.e.407.1

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			407.1
Root			$-3.08380 + 0.826301i$ of defining polynomial
Character	$\chi$	$=$	475.407
Dual form			475.2.p.e.468.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-2.11787 + 0.567482i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.09629 + 1.89883i) q^{6} +(1.22474 + 1.22474i) q^{7} +(-2.12132 - 2.12132i) q^{8} +(1.56527 - 0.903709i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-2.11787 + 0.567482i) 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} +(0.308663 - 1.15195i) q^{13} +(0.866025 - 1.50000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.66826 - 0.982908i) q^{17} +(-1.27804 - 1.27804i) q^{18} +(4.33013 - 0.500000i) q^{19} +(-3.28887 - 1.89883i) q^{21} +(-0.308663 - 1.15195i) q^{22} +(-1.67303 - 0.448288i) q^{23} +(5.69650 + 3.28887i) q^{24} -1.19258 q^{26} +(1.84897 - 1.84897i) q^{27} +(1.67303 + 0.448288i) q^{28} +(-1.89883 - 3.28887i) q^{29} -7.26177i q^{31} +(-4.82963 - 1.29410i) q^{32} +(-2.52574 + 0.676769i) q^{33} +(-1.89883 - 3.28887i) q^{34} +(0.903709 - 1.56527i) q^{36} +(5.92921 - 5.92921i) q^{37} +(-1.60368 - 4.05317i) q^{38} +2.61484i q^{39} +(-4.78887 - 2.76486i) q^{41} +(-0.982908 + 3.66826i) q^{42} +(2.32777 + 8.68736i) q^{43} +(1.03281 - 0.596291i) q^{44} +1.73205i q^{46} +(2.41410 - 9.00956i) q^{47} +(0.567482 - 2.11787i) q^{48} -4.00000i q^{49} +(-7.21113 + 4.16335i) q^{51} +(-0.308663 - 1.15195i) q^{52} +(1.81173 - 6.76148i) q^{53} +(-2.26451 - 1.30742i) q^{54} -5.19615i q^{56} +(-8.88691 + 3.51621i) q^{57} +(-2.68535 + 2.68535i) q^{58} +(-4.66369 + 8.07775i) q^{59} +(1.78887 + 3.09842i) q^{61} +(-7.01433 + 1.87948i) q^{62} +(3.02387 + 0.810243i) q^{63} +7.00000i q^{64} +(1.30742 + 2.26451i) q^{66} +(10.4033 + 2.78757i) q^{67} +(2.68535 - 2.68535i) q^{68} +3.79766 q^{69} +(14.0777 + 8.12779i) q^{71} +(-5.23749 - 1.40338i) q^{72} +(0.810243 + 3.02387i) q^{73} +(-7.26177 - 4.19258i) q^{74} +(3.50000 - 2.59808i) q^{76} +(1.46061 + 1.46061i) q^{77} +(2.52574 - 0.676769i) q^{78} +(-8.29457 + 14.3666i) q^{79} +(-5.57775 + 9.66094i) q^{81} +(-1.43120 + 5.34129i) 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} +(-1.67303 + 0.448288i) q^{92} +(4.12092 + 15.3795i) q^{93} -9.32738 q^{94} +10.9629 q^{96} +(-0.467794 - 1.74583i) q^{97} +(-3.86370 + 1.03528i) 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 $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i	−0.995047	−	0.0994033i	$-0.968307\pi$
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i	0.812035	−	0.583609i	$-0.198360\pi$
$3$	−2.11787	+	0.567482i	−1.22275	+	0.327636i	−0.811754	−	0.583999i	$-0.801487\pi$
$3$	−2.11787	+	0.567482i	−1.22275	+	0.327636i	−0.411000	+	0.911635i	$0.634820\pi$
$4$	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	0.899608	−	0.436698i	$-0.143852\pi$
$7$	1.22474	+	1.22474i	0.462910	+	0.462910i	−0.436698	+	0.899608i	$0.643852\pi$
$8$	−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
$13$	0.308663	−	1.15195i	0.0856077	−	0.319492i	−0.909821	−	0.415001i	$-0.863781\pi$
$13$	0.308663	−	1.15195i	0.0856077	−	0.319492i	0.995429	+	0.0955088i	$0.0304478\pi$
$14$	0.866025	−	1.50000i	0.231455	−	0.400892i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.66826	−	0.982908i	0.889684	−	0.238390i	0.215103	−	0.976591i	$-0.430991\pi$
$17$	3.66826	−	0.982908i	0.889684	−	0.238390i	0.674581	+	0.738201i	$0.264324\pi$
$18$	−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
$22$	−0.308663	−	1.15195i	−0.0658072	−	0.245596i
$23$	−1.67303	−	0.448288i	−0.348851	−	0.0934745i	0.0801385	−	0.996784i	$-0.474464\pi$
$23$	−1.67303	−	0.448288i	−0.348851	−	0.0934745i	−0.428990	+	0.903309i	$0.641130\pi$
$24$	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
$28$	1.67303	+	0.448288i	0.316173	+	0.0847184i
$29$	−1.89883	−	3.28887i	−0.352604	−	0.610728i	0.634101	−	0.773251i	$-0.281370\pi$
$29$	−1.89883	−	3.28887i	−0.352604	−	0.610728i	−0.986705	+	0.162522i	$0.948037\pi$
$30$		0			0
$31$		−	7.26177i		−	1.30425i	−0.758111	−	0.652126i	$-0.773877\pi$
$31$		−	7.26177i		−	1.30425i	0.758111	−	0.652126i	$-0.226123\pi$
$32$	−4.82963	−	1.29410i	−0.853766	−	0.228766i
$33$	−2.52574	+	0.676769i	−0.439674	+	0.117810i
$34$	−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	$-0.507937\pi$
$37$	5.92921	−	5.92921i	0.974756	−	0.974756i	0.999689	+	0.0249335i	$0.00793740\pi$
$38$	−1.60368	−	4.05317i	−0.260152	−	0.657511i
$39$			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	$0.808787\pi$
$42$	−0.982908	+	3.66826i	−0.151666	+	0.566025i
$43$	2.32777	+	8.68736i	0.354982	+	1.32481i	0.880507	+	0.474032i	$0.157202\pi$
$43$	2.32777	+	8.68736i	0.354982	+	1.32481i	−0.525526	+	0.850778i	$0.676131\pi$
$44$	1.03281	−	0.596291i	0.155701	−	0.0898943i
$45$		0			0
$46$			1.73205i			0.255377i
$47$	2.41410	−	9.00956i	0.352133	−	1.31418i	−0.531921	−	0.846794i	$-0.678530\pi$
$47$	2.41410	−	9.00956i	0.352133	−	1.31418i	0.884054	−	0.467385i	$-0.154804\pi$
$48$	0.567482	−	2.11787i	0.0819090	−	0.305688i
$49$		−	4.00000i		−	0.571429i
$50$		0			0
$51$	−7.21113	+	4.16335i	−1.00976	+	0.582985i
$52$	−0.308663	−	1.15195i	−0.0428039	−	0.159746i
$53$	1.81173	−	6.76148i	0.248861	−	0.928761i	−0.722543	−	0.691326i	$-0.757027\pi$
$53$	1.81173	−	6.76148i	0.248861	−	0.928761i	0.971404	−	0.237435i	$-0.0763066\pi$
$54$	−2.26451	−	1.30742i	−0.308161	−	0.177917i
$55$		0			0
$56$		−	5.19615i		−	0.694365i
$57$	−8.88691	+	3.51621i	−1.17710	+	0.465733i
$58$	−2.68535	+	2.68535i	−0.352604	+	0.352604i
$59$	−4.66369	+	8.07775i	−0.607161	+	1.05163i	0.384545	+	0.923106i	$0.374358\pi$
$59$	−4.66369	+	8.07775i	−0.607161	+	1.05163i	−0.991706	+	0.128527i	$0.958975\pi$
$60$		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	$0.759774\pi$
$62$	−7.01433	+	1.87948i	−0.890820	+	0.238695i
$63$	3.02387	+	0.810243i	0.380972	+	0.102081i
$64$			7.00000i			0.875000i
$65$		0			0
$66$	1.30742	+	2.26451i	0.160932	+	0.278742i
$67$	10.4033	+	2.78757i	1.27097	+	0.340555i	0.830403	−	0.557164i	$-0.188111\pi$
$67$	10.4033	+	2.78757i	1.27097	+	0.340555i	0.440568	+	0.897719i	$0.354777\pi$
$68$	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	$0.251626\pi$
$72$	−5.23749	−	1.40338i	−0.617245	−	0.165390i
$73$	0.810243	+	3.02387i	0.0948318	+	0.353917i	0.996994	−	0.0774801i	$-0.0246874\pi$
$73$	0.810243	+	3.02387i	0.0948318	+	0.353917i	−0.902162	+	0.431397i	$0.858021\pi$
$74$	−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
$78$	2.52574	−	0.676769i	0.285983	−	0.0766290i
$79$	−8.29457	+	14.3666i	−0.933212	+	1.61637i	−0.155421	+	0.987848i	$0.549673\pi$
$79$	−8.29457	+	14.3666i	−0.933212	+	1.61637i	−0.777791	+	0.628523i	$0.783660\pi$
$80$		0			0
$81$	−5.57775	+	9.66094i	−0.619750	+	1.07344i
$82$	−1.43120	+	5.34129i	−0.158049	+	0.589847i
$83$	−1.46061	+	1.46061i	−0.160323	+	0.160323i	−0.782710	−	0.622387i	$-0.786163\pi$
$83$	−1.46061	+	1.46061i	−0.160323	+	0.160323i	0.622387	+	0.782710i	$0.286163\pi$
$84$	−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	0.694839	−	0.719165i	$-0.255475\pi$
$89$	−2.59808	−	4.50000i	−0.275396	−	0.476999i	−0.970235	+	0.242166i	$0.922142\pi$
$90$		0			0
$91$	1.78887	−	1.03281i	0.187525	−	0.108268i
$92$	−1.67303	+	0.448288i	−0.174426	+	0.0467372i
$93$	4.12092	+	15.3795i	0.427320	+	1.59478i
$94$	−9.32738			−0.962046
$95$		0			0
$96$	10.9629			1.11890
$97$	−0.467794	−	1.74583i	−0.0474973	−	0.177262i	0.938102	−	0.346358i	$-0.112582\pi$
$97$	−0.467794	−	1.74583i	−0.0474973	−	0.177262i	−0.985600	+	0.169096i	$0.945915\pi$
$98$	−3.86370	+	1.03528i	−0.390293	+	0.104579i
$99$	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	$-0.114443\pi$
$103$	5.92921	+	5.92921i	0.584222	+	0.584222i	−0.351839	+	0.936061i	$0.614443\pi$
$104$	−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	−0.227907	+	0.973683i	$0.573188\pi$
$107$	−12.4293	+	12.4293i	−1.20159	+	1.20159i	−0.973683	+	0.227907i	$0.926812\pi$
$108$	0.676769	−	2.52574i	0.0651221	−	0.243039i
$109$	1.19959	−	2.07775i	0.114900	−	0.199012i	−0.802840	−	0.596195i	$-0.796679\pi$
$109$	1.19959	−	2.07775i	0.114900	−	0.199012i	0.917740	+	0.397183i	$0.130012\pi$
$110$		0			0
$111$	−9.19258	+	15.9220i	−0.872521	+	1.51125i
$112$	−1.67303	+	0.448288i	−0.158087	+	0.0423592i
$113$	−5.35828	−	5.35828i	−0.504064	−	0.504064i	0.408634	−	0.912698i	$-0.366005\pi$
$113$	−5.35828	−	5.35828i	−0.504064	−	0.504064i	−0.912698	+	0.408634i	$0.866005\pi$
$114$	5.69650	+	7.67404i	0.533526	+	0.718740i
$115$		0			0
$116$	−3.28887	−	1.89883i	−0.305364	−	0.176302i
$117$	−0.557883	−	2.08205i	−0.0515763	−	0.192485i
$118$	9.00956	+	2.41410i	0.829397	+	0.222236i
$119$	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
$123$	11.7112	+	3.13801i	1.05597	+	0.282945i
$124$	−3.63088	−	6.28887i	−0.326063	−	0.564758i
$125$		0			0
$126$		−	3.13054i		−	0.278891i
$127$	4.64361	+	1.24425i	0.412054	+	0.110409i	0.458890	−	0.888493i	$-0.348247\pi$
$127$	4.64361	+	1.24425i	0.412054	+	0.110409i	−0.0468363	+	0.998903i	$0.514914\pi$
$128$	−2.89778	+	0.776457i	−0.256130	+	0.0686298i
$129$	−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
$133$	5.91567	+	4.69093i	0.512954	+	0.406755i
$134$		−	10.7703i		−	0.930415i
$135$		0			0
$136$	−9.86662	−	5.69650i	−0.846056	−	0.488471i
$137$	−5.10383	+	19.0478i	−0.436050	+	1.62736i	0.302492	+	0.953152i	$0.402181\pi$
$137$	−5.10383	+	19.0478i	−0.436050	+	1.62736i	−0.738542	+	0.674207i	$0.764485\pi$
$138$	−0.982908	−	3.66826i	−0.0836707	−	0.312263i
$139$	13.4907	−	7.78887i	1.14427	−	0.660644i	0.196784	−	0.980447i	$-0.436950\pi$
$139$	13.4907	−	7.78887i	1.14427	−	0.660644i	0.947484	+	0.319803i	$0.103617\pi$
$140$		0			0
$141$			20.4510i			1.72229i
$142$	4.20725	−	15.7017i	0.353065	−	1.31766i
$143$	0.368106	−	1.37379i	0.0307826	−	0.114882i
$144$			1.80742i			0.150618i
$145$		0			0
$146$	2.71113	−	1.56527i	0.224374	−	0.129543i
$147$	2.26993	+	8.47149i	0.187221	+	0.698717i
$148$	2.17024	−	8.09945i	0.178393	−	0.665770i
$149$	3.13054	+	1.80742i	0.256464	+	0.148069i	0.622720	−	0.782444i	$-0.286027\pi$
$149$	3.13054	+	1.80742i	0.256464	+	0.148069i	−0.366257	+	0.930514i	$0.619361\pi$
$150$		0			0
$151$		−	5.86328i		−	0.477147i	−0.971124	−	0.238573i	$-0.923320\pi$
$151$		−	5.86328i		−	0.477147i	0.971124	−	0.238573i	$-0.0766798\pi$
$152$	−10.2462	−	8.12493i	−0.831080	−	0.659019i
$153$	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
$157$	−7.65872	+	2.05215i	−0.611232	+	0.163779i	−0.551139	−	0.834414i	$-0.685807\pi$
$157$	−7.65872	+	2.05215i	−0.611232	+	0.163779i	−0.0600935	+	0.998193i	$0.519140\pi$
$158$	16.0239	+	4.29359i	1.27479	+	0.341579i
$159$			15.3481i			1.21718i
$160$		0			0
$161$	−1.50000	−	2.59808i	−0.118217	−	0.204757i
$162$	10.7754	+	2.88725i	0.846594	+	0.226844i
$163$	3.67423	−	3.67423i	0.287788	−	0.287788i	−0.548417	−	0.836205i	$-0.684769\pi$
$163$	3.67423	−	3.67423i	0.287788	−	0.287788i	0.836205	+	0.548417i	$0.184769\pi$
$164$	−5.52971			−0.431798
$165$		0			0
$166$	1.78887	+	1.03281i	0.138844	+	0.0801613i
$167$	−3.30564	−	0.885744i	−0.255798	−	0.0685409i	0.128641	−	0.991691i	$-0.458939\pi$
$167$	−3.30564	−	0.885744i	−0.255798	−	0.0685409i	−0.384439	+	0.923150i	$0.625605\pi$
$168$	2.94872	+	11.0048i	0.227499	+	0.849038i
$169$	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
$173$	6.76148	−	1.81173i	0.514066	−	0.137744i	0.00754550	−	0.999972i	$-0.497598\pi$
$173$	6.76148	−	1.81173i	0.514066	−	0.137744i	0.506520	+	0.862228i	$0.330932\pi$
$174$	4.16335	−	7.21113i	0.315622	−	0.546674i
$175$		0			0
$176$	−0.596291	+	1.03281i	−0.0449471	+	0.0778507i
$177$	5.29312	−	19.7542i	0.397855	−	1.48482i
$178$	−3.67423	+	3.67423i	−0.275396	+	0.275396i
$179$	−2.79698			−0.209056			−0.104528	−	0.994522i	$-0.533333\pi$
$179$	−2.79698			−0.209056			−0.104528	+	0.994522i	$0.533333\pi$
$180$		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
$187$	4.37470	−	1.17220i	0.319910	−	0.0857196i
$188$	−2.41410	−	9.00956i	−0.176067	−	0.657089i
$189$	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	$0.506654\pi$
$192$	−3.97237	−	14.8251i	−0.286681	−	1.06991i
$193$	−25.4861	+	6.82898i	−1.83453	+	0.491561i	−0.998378	−	0.0569358i	$-0.981867\pi$
$193$	−25.4861	+	6.82898i	−1.83453	+	0.491561i	−0.836153	+	0.548497i	$0.815200\pi$
$194$	−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	0.553960	−	0.832543i	$-0.313116\pi$
$197$	−3.91010	−	3.91010i	−0.278583	−	0.278583i	−0.832543	+	0.553960i	$0.813116\pi$
$198$	−1.52416	−	1.52416i	−0.108318	−	0.108318i
$199$	−14.8571	+	8.57775i	−1.05319	+	0.608060i	−0.923541	−	0.383499i	$-0.874719\pi$
$199$	−14.8571	+	8.57775i	−1.05319	+	0.608060i	−0.129650	+	0.991560i	$0.541385\pi$
$200$		0			0
$201$	−23.6148			−1.66566
$202$	−1.68657	+	1.68657i	−0.118666	+	0.118666i
$203$	1.70245	−	6.35362i	0.119488	−	0.445936i
$204$	−4.16335	+	7.21113i	−0.291493	+	0.504880i
$205$		0			0
$206$	4.19258	−	7.26177i	0.292111	−	0.505951i
$207$	−3.02387	+	0.810243i	−0.210173	+	0.0563158i
$208$	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	$0.495793\pi$
$212$	−1.81173	−	6.76148i	−0.124430	−	0.464380i
$213$	−34.4272	−	9.22475i	−2.35892	−	0.632070i
$214$	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
$218$	−2.31743	−	0.620952i	−0.156956	−	0.0420562i
$219$	−3.43198	−	5.94437i	−0.231912	−	0.401683i
$220$		0			0
$221$		−	4.52903i		−	0.304655i
$222$	17.7587	+	4.75843i	1.19189	+	0.319365i
$223$	−16.7570	+	4.49001i	−1.12213	+	0.300673i	−0.771745	−	0.635933i	$-0.780616\pi$
$223$	−16.7570	+	4.49001i	−1.12213	+	0.300673i	−0.350384	+	0.936606i	$0.613949\pi$
$224$	−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	$-0.803063\pi$
$227$	−3.53553	+	3.53553i	−0.234662	+	0.234662i	0.579974	+	0.814635i	$0.303063\pi$
$228$	−5.93819	+	7.48858i	−0.393266	+	0.495943i
$229$		−	21.0000i		−	1.38772i	−0.720110	−	0.693860i	$-0.755909\pi$
$229$		−	21.0000i		−	1.38772i	0.720110	−	0.693860i	$-0.244091\pi$
$230$		0			0
$231$	−3.92225	−	2.26451i	−0.258065	−	0.148994i
$232$	−2.94872	+	11.0048i	−0.193593	+	0.722500i
$233$	−2.51706	−	9.39380i	−0.164898	−	0.615408i	−0.998053	−	0.0623689i	$-0.980134\pi$
$233$	−2.51706	−	9.39380i	−0.164898	−	0.615408i	0.833155	−	0.553040i	$-0.186532\pi$
$234$	−1.86671	+	1.07775i	−0.122031	+	0.0704545i
$235$		0			0
$236$			9.32738i			0.607161i
$237$	9.41404	−	35.1337i	0.611508	−	2.28218i
$238$	1.70245	−	6.35362i	0.110353	−	0.411844i
$239$			9.00000i			0.582162i	0.956698	+	0.291081i	$0.0940149\pi$
$239$			9.00000i			0.582162i	−0.956698	+	0.291081i	$0.905985\pi$
$240$		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	$0.484419\pi$
$242$	2.47890	+	9.25139i	0.159350	+	0.594702i
$243$	4.30024	−	16.0487i	0.275860	−	1.02952i
$244$	3.09842	+	1.78887i	0.198356	+	0.114521i
$245$		0			0
$246$		−	12.1244i		−	0.773021i
$247$	0.760577	−	5.14240i	0.0483944	−	0.327203i
$248$	−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	$0.633914\pi$
$252$	3.02387	−	0.810243i	0.190486	−	0.0510405i
$253$	−1.99523	−	0.534620i	−0.125439	−	0.0336113i
$254$		−	4.80742i		−	0.301644i
$255$		0			0
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	−27.6040	−	7.39647i	−1.72189	−	0.461379i	−0.743600	−	0.668624i	$-0.766883\pi$
$257$	−27.6040	−	7.39647i	−1.72189	−	0.461379i	−0.978289	+	0.207246i	$0.933550\pi$
$258$	−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
$262$	−17.9447	−	4.80827i	−1.10863	−	0.297056i
$263$	−4.03459	−	15.0573i	−0.248783	−	0.928472i	−0.971444	−	0.237269i	$-0.923748\pi$
$263$	−4.03459	−	15.0573i	−0.248783	−	0.928472i	0.722660	−	0.691203i	$-0.242919\pi$
$264$	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
$268$	10.4033	−	2.78757i	0.635485	−	0.170278i
$269$	−12.6247	+	21.8666i	−0.769742	+	1.33323i	0.167962	+	0.985794i	$0.446282\pi$
$269$	−12.6247	+	21.8666i	−0.769742	+	1.33323i	−0.937703	+	0.347438i	$0.887052\pi$
$270$		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	$-0.0241713\pi$
$272$	−0.982908	+	3.66826i	−0.0595975	+	0.222421i
$273$	−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	0.998285	−	0.0585445i	$-0.0186460\pi$
$277$	15.6404	+	15.6404i	0.939740	+	0.939740i	−0.0585445	+	0.998285i	$0.518646\pi$
$278$	−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	$-0.0369148\pi$
$282$	19.7542	−	5.29312i	1.17635	−	0.315201i
$283$	0.810243	+	3.02387i	0.0481640	+	0.179750i	0.985817	−	0.167821i	$-0.0536731\pi$
$283$	0.810243	+	3.02387i	0.0481640	+	0.179750i	−0.937654	+	0.347571i	$0.887006\pi$
$284$	16.2556			0.964591
$285$		0			0
$286$	−1.42225			−0.0840996
$287$	−2.47890	−	9.25139i	−0.146325	−	0.546092i
$288$	−8.72916	+	2.33897i	−0.514370	+	0.137825i
$289$	−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	$-0.0783666\pi$
$293$	12.4293	+	12.4293i	0.726130	+	0.726130i	−0.243716	+	0.969847i	$0.578367\pi$
$294$	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
$298$	0.935588	−	3.49166i	0.0541972	−	0.202267i
$299$	−1.03281	+	1.78887i	−0.0597288	+	0.103453i
$300$		0			0
$301$	−7.78887	+	13.4907i	−0.448943	+	0.777592i
$302$	−5.66349	+	1.51753i	−0.325897	+	0.0873239i
$303$	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
$307$	4.49961	+	16.7928i	0.256806	+	0.958415i	0.967077	+	0.254485i	$0.0819061\pi$
$307$	4.49961	+	16.7928i	0.256806	+	0.958415i	−0.710270	+	0.703929i	$0.751427\pi$
$308$	1.99523	+	0.534620i	0.113689	+	0.0304628i
$309$	−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
$313$	−4.37470	−	1.17220i	−0.247273	−	0.0662566i	0.133054	−	0.991109i	$-0.457522\pi$
$313$	−4.37470	−	1.17220i	−0.247273	−	0.0662566i	−0.380327	+	0.924852i	$0.624188\pi$
$314$	3.96445	+	6.86662i	0.223727	+	0.387506i
$315$		0			0
$316$			16.5891i			0.933212i
$317$	3.86370	+	1.03528i	0.217007	+	0.0581469i	0.365685	−	0.930739i	$-0.380835\pi$
$317$	3.86370	+	1.03528i	0.217007	+	0.0581469i	−0.148677	+	0.988886i	$0.547502\pi$
$318$	14.8251	−	3.97237i	0.831351	−	0.222760i
$319$	−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
$323$	15.3926	−	6.09025i	0.856466	−	0.338870i
$324$			11.1555i			0.619750i
$325$		0			0
$326$	−4.50000	−	2.59808i	−0.249232	−	0.143894i
$327$	−1.36149	+	5.08115i	−0.0752905	+	0.280988i
$328$	4.29359	+	16.0239i	0.237074	+	0.884771i
$329$	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	$0.842082\pi$
$332$	−0.534620	+	1.99523i	−0.0293411	+	0.109502i
$333$	3.92253	−	14.6391i	0.214953	−	0.802217i
$334$			3.42225i			0.187257i
$335$		0			0
$336$	3.28887	−	1.89883i	0.179423	−	0.103590i
$337$	0.159131	+	0.593885i	0.00866842	+	0.0323510i	0.970125	−	0.242607i	$-0.0780026\pi$
$337$	0.159131	+	0.593885i	0.00866842	+	0.0323510i	−0.961456	+	0.274958i	$0.911336\pi$
$338$	2.99654	−	11.1832i	0.162990	−	0.608288i
$339$	14.3889	+	8.30742i	0.781496	+	0.451197i
$340$		0			0
$341$		−	8.66025i		−	0.468979i
$342$	−6.17308	−	4.89504i	−0.333802	−	0.264694i
$343$	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
$347$	−7.65872	+	2.05215i	−0.411142	+	0.110165i	−0.458461	−	0.888715i	$-0.651599\pi$
$347$	−7.65872	+	2.05215i	−0.411142	+	0.110165i	0.0473189	+	0.998880i	$0.484932\pi$
$348$	8.04297	+	2.15511i	0.431148	+	0.115526i
$349$		−	31.3110i		−	1.67604i	−0.545640	−	0.838019i	$-0.683714\pi$
$349$		−	31.3110i		−	1.67604i	0.545640	−	0.838019i	$-0.316286\pi$
$350$		0			0
$351$	−1.55920	−	2.70062i	−0.0832241	−	0.144148i
$352$	−5.75973	−	1.54332i	−0.306995	−	0.0822590i
$353$	−6.59545	+	6.59545i	−0.351041	+	0.351041i	−0.860497	−	0.509456i	$-0.829847\pi$
$353$	−6.59545	+	6.59545i	−0.351041	+	0.351041i	0.509456	+	0.860497i	$0.329847\pi$
$354$	−20.4510			−1.08696
$355$		0			0
$356$	−4.50000	−	2.59808i	−0.238500	−	0.137698i
$357$	−13.9308	−	3.73275i	−0.737298	−	0.197558i
$358$	0.723911	+	2.70167i	0.0382599	+	0.142788i
$359$	−6.22896	−	3.59629i	−0.328752	−	0.189805i	0.326535	−	0.945185i	$-0.394119\pi$
$359$	−6.22896	−	3.59629i	−0.328752	−	0.189805i	−0.655287	+	0.755380i	$0.727452\pi$
$360$		0			0
$361$	18.5000	−	4.33013i	0.973684	−	0.227901i
$362$	−0.235864	−	0.235864i	−0.0123968	−	0.0123968i
$363$	20.2844	−	5.43520i	1.06466	−	0.285274i
$364$	1.03281	−	1.78887i	0.0541338	−	0.0937625i
$365$		0			0
$366$	−3.92225	+	6.79354i	−0.205019	+	0.355104i
$367$	6.53503	−	24.3890i	0.341126	−	1.27310i	−0.555948	−	0.831217i	$-0.687645\pi$
$367$	6.53503	−	24.3890i	0.341126	−	1.27310i	0.897074	−	0.441881i	$-0.145689\pi$
$368$	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	$-0.128858\pi$
$373$	10.1456	+	10.1456i	0.525320	+	0.525320i	−0.393853	+	0.919173i	$0.628858\pi$
$374$	−2.26451	−	3.92225i	−0.117095	−	0.202815i
$375$		0			0
$376$	−24.2332	+	13.9911i	−1.24973	+	0.721534i
$377$	−4.37470	+	1.17220i	−0.225309	+	0.0603713i
$378$	−1.17220	−	4.37470i	−0.0602914	−	0.225011i
$379$	−2.79698			−0.143671			−0.0718355	−	0.997416i	$-0.522886\pi$
$379$	−2.79698			−0.143671			−0.0718355	+	0.997416i	$0.522886\pi$
$380$		0			0
$381$	−10.5407			−0.540014
$382$	0.149532	+	0.558061i	0.00765072	+	0.0285529i
$383$	16.4207	−	4.39992i	0.839061	−	0.224826i	0.186398	−	0.982474i	$-0.440319\pi$
$383$	16.4207	−	4.39992i	0.839061	−	0.224826i	0.652663	+	0.757649i	$0.273652\pi$
$384$	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	−0.117356	−	0.993090i	$-0.537442\pi$
$389$	13.4907	−	7.78887i	0.684007	−	0.394912i	0.801363	+	0.598178i	$0.204109\pi$
$390$		0			0
$391$	−6.57775			−0.332651
$392$	−8.48528	+	8.48528i	−0.428571	+	0.428571i
$393$	−10.5425	+	39.3453i	−0.531801	+	1.98471i
$394$	−2.76486	+	4.78887i	−0.139292	+	0.241260i
$395$		0			0
$396$	1.07775	−	1.86671i	0.0541588	−	0.0938059i
$397$	−25.7399	+	6.89698i	−1.29185	+	0.346150i	−0.838362	−	0.545114i	$-0.816486\pi$
$397$	−25.7399	+	6.89698i	−1.29185	+	0.346150i	−0.453486	+	0.891264i	$0.649820\pi$
$398$	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	$0.506416\pi$
$402$	6.11197	+	22.8102i	0.304837	+	1.13767i
$403$	−8.36516	−	2.24144i	−0.416698	−	0.111654i
$404$	−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
$408$	24.1289	+	6.46532i	1.19456	+	0.320081i
$409$	−1.06493	−	1.84451i	−0.0526572	−	0.0912049i	0.838495	−	0.544909i	$-0.183436\pi$
$409$	−1.06493	−	1.84451i	−0.0526572	−	0.0912049i	−0.891153	+	0.453704i	$0.850102\pi$
$410$		0			0
$411$		−	43.2370i		−	2.13273i
$412$	8.09945	+	2.17024i	0.399031	+	0.106920i
$413$	−15.6050	+	4.18135i	−0.767872	+	0.205751i
$414$	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
$418$	−1.91252	−	4.83374i	−0.0935446	−	0.236426i
$419$			24.0000i			1.17248i	0.810139	+	0.586238i	$0.199392\pi$
$419$			24.0000i			1.17248i	−0.810139	+	0.586238i	$0.800608\pi$
$420$		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	$0.485468\pi$
$422$	3.84530	−	14.3509i	0.187186	−	0.698588i
$423$	−4.36329	−	16.2840i	−0.212151	−	0.791757i
$424$	−18.1865	+	10.5000i	−0.883216	+	0.509925i
$425$		0			0
$426$			35.6417i			1.72685i
$427$	−1.60386	+	5.98569i	−0.0776162	+	0.289668i
$428$	−4.54946	+	16.9788i	−0.219906	+	0.820701i
$429$			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	$0.375852\pi$
$432$	0.676769	+	2.52574i	0.0325611	+	0.121520i
$433$	4.81787	−	17.9806i	0.231532	−	0.864090i	−0.748149	−	0.663530i	$-0.769057\pi$
$433$	4.81787	−	17.9806i	0.231532	−	0.864090i	0.979681	−	0.200560i	$-0.0642760\pi$
$434$	−10.8926	−	6.28887i	−0.522864	−	0.301876i
$435$		0			0
$436$		−	2.39918i		−	0.114900i
$437$	−7.46859	−	1.10463i	−0.357271	−	0.0528415i
$438$	−4.85356	+	4.85356i	−0.231912	+	0.231912i
$439$	−13.3239	+	23.0777i	−0.635917	+	1.10144i	0.350403	+	0.936599i	$0.386045\pi$
$439$	−13.3239	+	23.0777i	−0.635917	+	1.10144i	−0.986320	+	0.164842i	$0.947289\pi$
$440$		0			0
$441$	−3.61484	−	6.26108i	−0.172135	−	0.298147i
$442$	−4.37470	+	1.17220i	−0.208083	+	0.0557558i
$443$	9.39380	+	2.51706i	0.446313	+	0.119589i	0.474974	−	0.880000i	$-0.342458\pi$
$443$	9.39380	+	2.51706i	0.446313	+	0.119589i	−0.0286607	+	0.999589i	$0.509124\pi$
$444$			18.3852i			0.872521i
$445$		0			0
$446$	8.67404	+	15.0239i	0.410728	+	0.711401i
$447$	−7.65576	−	2.05135i	−0.362105	−	0.0970257i
$448$	−8.57321	+	8.57321i	−0.405046	+	0.405046i
$449$	−5.86328			−0.276705			−0.138353	−	0.990383i	$-0.544181\pi$
$449$	−5.86328			−0.276705			−0.138353	+	0.990383i	$0.544181\pi$
$450$		0			0
$451$	−5.71113	−	3.29732i	−0.268926	−	0.155265i
$452$	−7.31954	−	1.96127i	−0.344282	−	0.0922502i
$453$	3.32730	+	12.4177i	0.156330	+	0.583433i
$454$	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	0.635474	−	0.772123i	$-0.280805\pi$
$457$	−2.92122	−	2.92122i	−0.136649	−	0.136649i	−0.772123	+	0.635474i	$0.780805\pi$
$458$	−20.2844	+	5.43520i	−0.947830	+	0.253970i
$459$	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	$0.0242537\pi$
$462$	−1.17220	+	4.37470i	−0.0545356	+	0.203530i
$463$	−9.56209	+	9.56209i	−0.444388	+	0.444388i	−0.893484	−	0.449096i	$-0.851746\pi$
$463$	−9.56209	+	9.56209i	−0.444388	+	0.444388i	0.449096	+	0.893484i	$0.351746\pi$
$464$	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	0.934480	+	0.356015i	$0.115865\pi$
$467$	27.8878	+	27.8878i	1.29050	+	1.29050i	0.356015	+	0.934480i	$0.384135\pi$
$468$	−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
$472$	27.0287	−	7.24231i	1.24410	−	0.333354i
$473$	2.77606	+	10.3604i	0.127643	+	0.476371i
$474$	−36.3731			−1.67067
$475$		0			0
$476$	6.57775			0.301491
$477$	−3.27456	−	12.2208i	−0.149932	−	0.559553i
$478$	8.69333	−	2.32937i	0.397624	−	0.106543i
$479$	−33.7108	+	19.4629i	−1.54028	+	0.889283i	−0.541463	+	0.840724i	$0.682129\pi$
$479$	−33.7108	+	19.4629i	−1.54028	+	0.889283i	−0.998820	+	0.0485587i	$0.984537\pi$
$480$		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	$-0.927749\pi$
$487$	−16.5358	+	16.5358i	−0.749309	+	0.749309i	0.225040	+	0.974349i	$0.427749\pi$
$488$	2.77797	−	10.3675i	0.125753	−	0.469315i
$489$	−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	$0.886569\pi$
$492$	11.7112	−	3.13801i	0.527983	−	0.141473i
$493$	−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
$497$	7.28718	+	27.1961i	0.326875	+	1.21991i
$498$	−4.37470	−	1.17220i	−0.196035	−	0.0525275i
$499$	−24.3834	−	14.0777i	−1.09155	−	0.630207i	−0.157561	−	0.987509i	$-0.550363\pi$
$499$	−24.3834	−	14.0777i	−1.09155	−	0.630207i	−0.933989	+	0.357303i	$0.883696\pi$
$500$		0			0
$501$	7.50357			0.335235
$502$	13.1365	−	13.1365i	0.586309	−	0.586309i
$503$	29.0859	+	7.79356i	1.29688	+	0.347497i	0.840269	−	0.542170i	$-0.182397\pi$
$503$	29.0859	+	7.79356i	1.29688	+	0.347497i	0.456609	+	0.889667i	$0.349064\pi$
$504$	−4.69581	−	8.13338i	−0.209168	−	0.362290i
$505$		0			0
$506$			2.06561i			0.0918277i
$507$	−24.5202	−	6.57016i	−1.08898	−	0.291791i
$508$	4.64361	−	1.24425i	0.206027	−	0.0552047i
$509$	17.6541	+	30.5777i	0.782503	+	1.35533i	0.930480	+	0.366344i	$0.119391\pi$
$509$	17.6541	+	30.5777i	0.782503	+	1.35533i	−0.147977	+	0.988991i	$0.547276\pi$
$510$		0			0
$511$	−2.71113	+	4.69581i	−0.119933	+	0.207730i
$512$	7.77817	−	7.77817i	0.343750	−	0.343750i
$513$	7.08178	−	8.93075i	0.312668	−	0.394302i
$514$			28.5777i			1.26051i
$515$		0			0
$516$	−17.0777	−	9.85984i	−0.751806	−	0.434055i
$517$	2.87902	−	10.7446i	0.126619	−	0.472549i
$518$	−3.75897	−	14.0287i	−0.165160	−	0.616384i
$519$	−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	$-0.351519\pi$
$522$	−1.77652	+	6.63008i	−0.0777564	+	0.290191i
$523$	2.64763	−	9.88110i	0.115773	−	0.432070i	−0.883571	−	0.468298i	$-0.844867\pi$
$523$	2.64763	−	9.88110i	0.115773	−	0.432070i	0.999344	+	0.0362274i	$0.0115341\pi$
$524$		−	18.5777i		−	0.811573i
$525$		0			0
$526$	−13.5000	+	7.79423i	−0.588628	+	0.339845i
$527$	−7.13765	−	26.6381i	−0.310921	−	1.16037i
$528$	0.676769	−	2.52574i	0.0294526	−	0.109919i
$529$	−17.3205	−	10.0000i	−0.753066	−	0.434783i
$530$		0			0
$531$			16.8585i			0.731595i
$532$	7.46859	+	1.10463i	0.323804	+	0.0478916i
$533$	−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
$537$	5.92364	−	1.58723i	0.255624	−	0.0684942i
$538$	24.3890	+	6.53503i	1.05149	+	0.281745i
$539$		−	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	$0.444047\pi$
$542$	−17.9447	−	4.80827i	−0.770792	−	0.206533i
$543$	−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
$547$	−38.1933	−	10.2339i	−1.63303	−	0.437569i	−0.678237	−	0.734843i	$-0.737256\pi$
$547$	−38.1933	−	10.2339i	−1.63303	−	0.437569i	−0.954792	+	0.297274i	$0.903923\pi$
$548$	5.10383	+	19.0478i	0.218025	+	0.813680i
$549$	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
$553$	−27.7542	+	7.43671i	−1.18023	+	0.316241i
$554$	11.0594	−	19.1555i	0.469870	−	0.813839i
$555$		0			0
$556$	7.78887	−	13.4907i	0.330322	−	0.572134i
$557$	2.05215	−	7.65872i	0.0869523	−	0.324510i	−0.908724	−	0.417397i	$-0.862943\pi$
$557$	2.05215	−	7.65872i	0.0869523	−	0.324510i	0.995677	+	0.0928862i	$0.0296093\pi$
$558$	−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	$-0.232701\pi$
$563$	1.82274	+	1.82274i	0.0768194	+	0.0768194i	−0.667653	+	0.744473i	$0.732701\pi$
$564$	10.2255	+	17.7111i	0.430572	+	0.745773i
$565$		0			0
$566$	2.71113	−	1.56527i	0.113957	−	0.0657932i
$567$	−18.6635	+	5.00087i	−0.783794	+	0.210017i
$568$	−12.6218	−	47.1051i	−0.529597	−	1.97648i
$569$	14.5235			0.608858			0.304429	−	0.952535i	$-0.401534\pi$
$569$	14.5235			0.608858			0.304429	+	0.952535i	$0.401534\pi$
$570$		0			0
$571$	−13.1555			−0.550540			−0.275270	−	0.961367i	$-0.588767\pi$
$571$	−13.1555			−0.550540			−0.275270	+	0.961367i	$0.588767\pi$
$572$	−0.368106	−	1.37379i	−0.0153913	−	0.0574411i
$573$	1.22359	−	0.327861i	0.0511164	−	0.0136966i
$574$	−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	0.843325	−	0.537404i	$-0.180595\pi$
$577$	7.34847	+	7.34847i	0.305921	+	0.305921i	−0.537404	+	0.843325i	$0.680595\pi$
$578$	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
$583$	2.16064	−	8.06362i	0.0894846	−	0.333961i
$584$	4.69581	−	8.13338i	0.194314	−	0.336562i
$585$		0			0
$586$	8.78887	−	15.2228i	0.363065	−	0.628847i
$587$	27.4129	−	7.34527i	1.13145	−	0.303172i	0.355943	−	0.934508i	$-0.384160\pi$
$587$	27.4129	−	7.34527i	1.13145	−	0.303172i	0.775509	+	0.631336i	$0.217493\pi$
$588$	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
$592$	2.17024	+	8.09945i	0.0891963	+	0.332885i
$593$	15.0573	+	4.03459i	0.618329	+	0.165681i	0.554368	−	0.832272i	$-0.312960\pi$
$593$	15.0573	+	4.03459i	0.618329	+	0.165681i	0.0639609	+	0.997952i	$0.479627\pi$
$594$	−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
$598$	1.99523	+	0.534620i	0.0815910	+	0.0218622i
$599$	15.4217	+	26.7111i	0.630113	+	1.09139i	0.987528	+	0.157442i	$0.0503246\pi$
$599$	15.4217	+	26.7111i	0.630113	+	1.09139i	−0.357416	+	0.933945i	$0.616342\pi$
$600$		0			0
$601$		−	11.7266i		−	0.478336i	−0.970978	−	0.239168i	$-0.923125\pi$
$601$		−	11.7266i		−	0.478336i	0.970978	−	0.239168i	$-0.0768747\pi$
$602$	15.0469	+	4.03182i	0.613268	+	0.164325i
$603$	18.8032	−	5.03830i	0.765725	−	0.205175i
$604$	−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	$-0.820387\pi$
$607$	−7.64200	+	7.64200i	−0.310179	+	0.310179i	0.534800	+	0.844979i	$0.320387\pi$
$608$	−21.5600	−	3.18878i	−0.874372	−	0.129322i
$609$			14.4223i			0.584419i
$610$		0			0
$611$	−9.63338	−	5.56183i	−0.389725	−	0.225008i
$612$	1.77652	−	6.63008i	0.0718118	−	0.268005i
$613$	8.69013	+	32.4320i	0.350991	+	1.30992i	0.885455	+	0.464725i	$0.153847\pi$
$613$	8.69013	+	32.4320i	0.350991	+	1.30992i	−0.534464	+	0.845191i	$0.679486\pi$
$614$	15.0560	−	8.69258i	0.607610	−	0.350804i
$615$		0			0
$616$		−	6.19684i		−	0.249678i
$617$	−4.37992	+	16.3461i	−0.176329	+	0.658068i	0.819993	+	0.572374i	$0.193977\pi$
$617$	−4.37992	+	16.3461i	−0.176329	+	0.658068i	−0.996321	+	0.0856943i	$0.972689\pi$
$618$	−4.75843	+	17.7587i	−0.191412	+	0.714360i
$619$		−	18.5777i		−	0.746703i	−0.927690	−	0.373351i	$-0.878209\pi$
$619$		−	18.5777i		−	0.746703i	0.927690	−	0.373351i	$-0.121791\pi$
$620$		0			0
$621$	−3.92225	+	2.26451i	−0.157395	+	0.0908718i
$622$	5.11694	+	19.0967i	0.205171	+	0.765707i
$623$	2.32937	−	8.69333i	0.0933243	−	0.348291i
$624$	−2.26451	−	1.30742i	−0.0906531	−	0.0523386i
$625$		0			0
$626$			4.52903i			0.181016i
$627$	−10.5984	+	4.19336i	−0.423258	+	0.167467i
$628$	−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	$-0.547042\pi$
$632$	48.0717	−	12.8808i	1.91219	−	0.512369i
$633$	−31.4654	−	8.43113i	−1.25064	−	0.335108i
$634$		−	4.00000i		−	0.158860i
$635$		0			0
$636$	7.67404	+	13.2918i	0.304295	+	0.527055i
$637$	−4.60778	−	1.23465i	−0.182567	−	0.0489187i
$638$	−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	$0.627614\pi$
$642$	−37.2274	−	9.97506i	−1.46925	−	0.393684i
$643$	−5.55212	−	20.7208i	−0.218954	−	0.817148i	−0.984737	−	0.174049i	$-0.944315\pi$
$643$	−5.55212	−	20.7208i	−0.218954	−	0.817148i	0.765783	−	0.643099i	$-0.222352\pi$
$644$	−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	0.308514	−	0.951220i	$-0.400168\pi$
$647$	−16.3480	−	16.3480i	−0.642706	−	0.642706i	−0.951220	+	0.308514i	$0.900168\pi$
$648$	32.3261	−	8.66176i	1.26989	−	0.340266i
$649$	−5.56183	+	9.63338i	−0.218321	+	0.378143i
$650$		0			0
$651$	−13.7889	+	23.8830i	−0.540429	+	0.936050i
$652$	1.34486	−	5.01910i	0.0526689	−	0.196563i
$653$	1.69647	−	1.69647i	0.0663881	−	0.0663881i	−0.673133	−	0.739521i	$-0.735052\pi$
$653$	1.69647	−	1.69647i	0.0663881	−	0.0663881i	0.739521	+	0.673133i	$0.235052\pi$
$654$	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	0.777624	−	0.628730i	$-0.216425\pi$
$659$	−3.99656	−	6.92225i	−0.155684	−	0.269653i	−0.933308	+	0.359077i	$0.883092\pi$
$660$		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	$0.0929544\pi$
$662$	16.7303	−	4.48288i	0.650243	−	0.174232i
$663$	2.57014	+	9.59190i	0.0998160	+	0.372519i
$664$	6.19684			0.240484
$665$		0			0
$666$	−15.1555			−0.587263
$667$	1.70245	+	6.35362i	0.0659190	+	0.246013i
$668$	−3.30564	+	0.885744i	−0.127899	+	0.0342705i
$669$	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	$-0.224251\pi$
$673$	2.96460	+	2.96460i	0.114277	+	0.114277i	−0.647656	+	0.761933i	$0.724251\pi$
$674$	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	$-0.689418\pi$
$677$	6.96112	−	6.96112i	0.267537	−	0.267537i	0.828107	+	0.560570i	$0.189418\pi$
$678$	4.30024	−	16.0487i	0.165150	−	0.616347i
$679$	1.56527	−	2.71113i	0.0600695	−	0.104043i
$680$		0			0
$681$	5.48146	−	9.49416i	0.210050	−	0.363817i
$682$	−8.36516	+	2.24144i	−0.320319	+	0.0858291i
$683$	−17.8976	−	17.8976i	−0.684832	−	0.684832i	0.276253	−	0.961085i	$-0.410907\pi$
$683$	−17.8976	−	17.8976i	−0.684832	−	0.684832i	−0.961085	+	0.276253i	$0.910907\pi$
$684$	3.13054	−	7.22967i	0.119699	−	0.276433i
$685$		0			0
$686$	−16.5000	−	9.52628i	−0.629973	−	0.363715i
$687$	11.9171	+	44.4753i	0.454667	+	1.69684i
$688$	−8.68736	−	2.32777i	−0.331202	−	0.0887454i
$689$	−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
$693$	3.60621	+	0.966282i	0.136989	+	0.0367060i
$694$	3.96445	+	6.86662i	0.150488	+	0.260653i
$695$		0			0
$696$		−	24.9801i		−	0.946867i
$697$	−20.2844	−	5.43520i	−0.768328	−	0.205873i
$698$	−30.2441	+	8.10388i	−1.14476	+	0.306736i
$699$	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
$703$	22.7096	−	28.6388i	0.856509	−	1.08013i
$704$			8.34808i			0.314630i
$705$		0			0
$706$	8.07775	+	4.66369i	0.304010	+	0.175520i
$707$	1.06924	−	3.99046i	0.0402129	−	0.150077i
$708$	−5.29312	−	19.7542i	−0.198928	−	0.742408i
$709$	2.46341	−	1.42225i	0.0925155	−	0.0534138i	−0.453029	−	0.891496i	$-0.649656\pi$
$709$	2.46341	−	1.42225i	0.0925155	−	0.0534138i	0.545544	+	0.838082i	$0.316323\pi$
$710$		0			0
$711$			29.9835i			1.12447i
$712$	−4.03459	+	15.0573i	−0.151203	+	0.564296i
$713$	−3.25536	+	12.1492i	−0.121914	+	0.454990i
$714$			14.4223i			0.539739i
$715$		0			0
$716$	−2.42225	+	1.39849i	−0.0905238	+	0.0522640i
$717$	−5.10734	−	19.0608i	−0.190737	−	0.711840i
$718$	−1.86158	+	6.94750i	−0.0694734	+	0.259278i
$719$	30.6445	+	17.6926i	1.14285	+	0.659822i	0.947134	−	0.320840i	$-0.103965\pi$
$719$	30.6445	+	17.6926i	1.14285	+	0.659822i	0.195712	+	0.980661i	$0.437298\pi$
$720$		0			0
$721$			14.5235i			0.540885i
$722$	−8.97073	−	16.7489i	−0.333856	−	0.623330i
$723$	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
$727$	44.4034	−	11.8979i	1.64683	−	0.441267i	0.688108	−	0.725609i	$-0.258442\pi$
$727$	44.4034	−	11.8979i	1.64683	−	0.441267i	0.958723	+	0.284342i	$0.0917751\pi$
$728$	−5.98569	−	1.60386i	−0.221844	−	0.0594430i
$729$			2.96291i			0.109737i
$730$		0			0
$731$	17.0777	+	29.5795i	0.631643	+	1.09404i
$732$	−7.57721	−	2.03031i	−0.280062	−	0.0750423i
$733$	−14.6969	+	14.6969i	−0.542844	+	0.542844i	−0.924362	−	0.381518i	$-0.875402\pi$
$733$	−14.6969	+	14.6969i	−0.542844	+	0.542844i	0.381518	+	0.924362i	$0.375402\pi$
$734$	−25.2494			−0.931972
$735$		0			0
$736$	7.50000	+	4.33013i	0.276454	+	0.159611i
$737$	12.4068	+	3.32440i	0.457012	+	0.122456i
$738$	2.58677	+	9.65395i	0.0952202	+	0.355367i
$739$	−11.5277	−	6.65549i	−0.424052	−	0.244826i	0.272758	−	0.962083i	$-0.412064\pi$
$739$	−11.5277	−	6.65549i	−0.424052	−	0.244826i	−0.696809	+	0.717256i	$0.745398\pi$
$740$		0			0
$741$	1.30742	+	11.3226i	0.0480292	+	0.415945i
$742$	−8.57321	−	8.57321i	−0.314733	−	0.314733i
$743$	−41.8352	+	11.2097i	−1.53478	+	0.411244i	−0.924576	−	0.380997i	$-0.875581\pi$
$743$	−41.8352	+	11.2097i	−1.53478	+	0.411244i	−0.610208	+	0.792241i	$0.708914\pi$
$744$	23.8830	−	41.3666i	0.875594	−	1.51657i
$745$		0			0
$746$	7.17404	−	12.4258i	0.262660	−	0.454941i
$747$	−0.966282	+	3.60621i	−0.0353544	+	0.131944i
$748$	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
$757$	44.4034	−	11.8979i	1.61387	−	0.432435i	0.664676	−	0.747131i	$-0.268569\pi$
$757$	44.4034	−	11.8979i	1.61387	−	0.432435i	0.949192	+	0.314697i	$0.101903\pi$
$758$	0.723911	+	2.70167i	0.0262936	+	0.0981291i
$759$	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	$0.691524\pi$
$762$	2.72812	+	10.1815i	0.0988295	+	0.368837i
$763$	4.01390	−	1.07552i	0.145313	−	0.0389365i
$764$	−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	0.359804	−	0.933028i	$-0.382844\pi$
$769$	37.3738	−	21.5777i	1.34773	−	0.778113i	0.987928	+	0.154914i	$0.0495102\pi$
$770$		0			0
$771$	62.6591			2.25661
$772$	−18.6571	+	18.6571i	−0.671485	+	0.671485i
$773$	−4.69899	+	17.5369i	−0.169011	+	0.630757i	0.828484	+	0.560013i	$0.189204\pi$
$773$	−4.69899	+	17.5369i	−0.169011	+	0.630757i	−0.997495	+	0.0707438i	$0.977463\pi$
$774$	8.12779	−	14.0777i	0.292147	−	0.506014i
$775$		0			0
$776$	−2.71113	+	4.69581i	−0.0973238	+	0.168570i
$777$	−30.7590	+	8.24184i	−1.10347	+	0.295675i
$778$	−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
$782$	1.70245	+	6.35362i	0.0608794	+	0.227205i
$783$	−9.59190	−	2.57014i	−0.342787	−	0.0918494i
$784$	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	$-0.886847\pi$
$787$	−16.5358	+	16.5358i	−0.589438	+	0.589438i	0.348041	+	0.937479i	$0.386847\pi$
$788$	−5.34129	−	1.43120i	−0.190276	−	0.0509842i
$789$	17.0895	+	29.5999i	0.608402	+	1.05378i
$790$		0			0
$791$		−	13.1250i		−	0.466673i
$792$	−6.24614	−	1.67365i	−0.221947	−	0.0594705i
$793$	4.12137	−	1.10432i	0.146354	−	0.0392155i
$794$	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	$-0.707151\pi$
$797$	5.35828	−	5.35828i	0.189800	−	0.189800i	0.795610	+	0.605810i	$0.207151\pi$
$798$	−2.42198	+	16.3755i	−0.0857373	+	0.579686i
$799$		−	35.4223i		−	1.25315i
$800$		0			0
$801$	−8.13338	−	4.69581i	−0.287379	−	0.165918i
$802$	5.00087	−	18.6635i	0.176587	−	0.659031i
$803$	0.966282	+	3.60621i	0.0340993	+	0.127260i
$804$	−20.4510	+	11.8074i	−0.721253	+	0.416416i
$805$		0			0
$806$			8.66025i			0.305044i
$807$	14.3286	−	53.4750i	0.504390	−	1.88241i
$808$	−1.85198	+	6.91168i	−0.0651524	+	0.243152i
$809$			26.4223i			0.928957i	0.885584	+	0.464478i	$0.153758\pi$
$809$			26.4223i			0.928957i	−0.885584	+	0.464478i	$0.846242\pi$
$810$		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	$0.300146\pi$
$812$	−1.70245	−	6.35362i	−0.0597442	−	0.222968i
$813$	−10.5425	+	39.3453i	−0.369743	+	1.37990i
$814$	−8.66025	−	5.00000i	−0.303542	−	0.175250i
$815$		0			0
$816$		−	8.32669i		−	0.291493i
$817$	14.4232	+	36.4535i	0.504605	+	1.27535i
$818$	−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	$0.650369\pi$
$822$	−41.7638	+	11.1906i	−1.45668	+	0.390316i
$823$	−43.4988	−	11.6555i	−1.51627	−	0.406285i	−0.597761	−	0.801674i	$-0.703943\pi$
$823$	−43.4988	−	11.6555i	−1.51627	−	0.406285i	−0.918513	+	0.395390i	$0.870610\pi$
$824$		−	25.1555i		−	0.876333i
$825$		0			0
$826$	8.07775	+	13.9911i	0.281061	+	0.486812i
$827$	37.9715	+	10.1744i	1.32040	+	0.353800i	0.849127	−	0.528189i	$-0.177129\pi$
$827$	37.9715	+	10.1744i	1.32040	+	0.353800i	0.471271	+	0.881988i	$0.343795\pi$
$828$	−2.21363	+	2.21363i	−0.0769288	+	0.0769288i
$829$	−1.66781			−0.0579255			−0.0289628	−	0.999580i	$-0.509220\pi$
$829$	−1.66781			−0.0579255			−0.0289628	+	0.999580i	$0.509220\pi$
$830$		0			0
$831$	−42.0000	−	24.2487i	−1.45696	−	0.841178i
$832$	8.06362	+	2.16064i	0.279556	+	0.0749068i
$833$	−3.93163	−	14.6730i	−0.136223	−	0.508391i
$834$	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
$838$	23.1822	−	6.21166i	0.800816	−	0.214578i
$839$	−3.96445	+	6.86662i	−0.136868	+	0.237062i	−0.926309	−	0.376764i	$-0.877037\pi$
$839$	−3.96445	+	6.86662i	−0.136868	+	0.237062i	0.789442	+	0.613826i	$0.210370\pi$
$840$		0			0
$841$	7.28887	−	12.6247i	0.251340	−	0.435334i
$842$	5.72478	−	21.3652i	0.197289	−	0.736293i
$843$	−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
$852$	−34.4272	+	9.22475i	−1.17946	+	0.316035i
$853$	2.32777	+	8.68736i	0.0797014	+	0.297450i	0.994258	−	0.107008i	$-0.0341270\pi$
$853$	2.32777	+	8.68736i	0.0797014	+	0.297450i	−0.914557	+	0.404457i	$0.867460\pi$
$854$	6.19684			0.212051
$855$		0			0
$856$	52.7332			1.80239
$857$	6.25190	+	23.3324i	0.213561	+	0.797020i	0.986668	+	0.162745i	$0.0520347\pi$
$857$	6.25190	+	23.3324i	0.213561	+	0.797020i	−0.773107	+	0.634275i	$0.781299\pi$
$858$	3.01215	−	0.807103i	0.102833	−	0.0275540i
$859$	−21.5543	+	12.4444i	−0.735422	+	0.424596i	−0.820403	−	0.571786i	$-0.806251\pi$
$859$	−21.5543	+	12.4444i	−0.735422	+	0.424596i	0.0849801	+	0.996383i	$0.472917\pi$
$860$		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	0.995846	+	0.0910557i	$0.0290241\pi$
$863$	31.9298	+	31.9298i	1.08690	+	1.08690i	0.0910557	+	0.995846i	$0.470976\pi$
$864$	−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
$868$	3.25536	−	12.1492i	0.110494	−	0.412370i
$869$	−9.89196	+	17.1334i	−0.335562	+	0.581210i
$870$		0			0
$871$	6.42225	−	11.1237i	0.217610	−	0.376911i
$872$	−6.95228	+	1.86286i	−0.235434	+	0.0630843i
$873$	−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
$877$	−7.60544	−	28.3839i	−0.256817	−	0.958456i	−0.967070	−	0.254509i	$-0.918086\pi$
$877$	−7.60544	−	28.3839i	−0.256817	−	0.958456i	0.710253	−	0.703947i	$-0.248581\pi$
$878$	25.7399	+	6.89698i	0.868679	+	0.232762i
$879$	−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
$883$	−4.63485	−	1.24190i	−0.155975	−	0.0417934i	0.179986	−	0.983669i	$-0.442395\pi$
$883$	−4.63485	−	1.24190i	−0.155975	−	0.0417934i	−0.335962	+	0.941876i	$0.609061\pi$
$884$	−2.26451	−	3.92225i	−0.0761638	−	0.131920i
$885$		0			0
$886$		−	9.72518i		−	0.326724i
$887$	1.52399	+	0.408351i	0.0511705	+	0.0137111i	0.284313	−	0.958731i	$-0.408234\pi$
$887$	1.52399	+	0.408351i	0.0511705	+	0.0137111i	−0.233143	+	0.972442i	$0.574901\pi$
$888$	53.2761	−	14.2753i	1.78783	−	0.479047i
$889$	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
$893$	5.94860	−	40.2196i	0.199062	−	1.34590i
$894$			7.92582i			0.265079i
$895$		0			0
$896$	−4.50000	−	2.59808i	−0.150334	−	0.0867956i
$897$	1.17220	−	4.37470i	0.0391386	−	0.146067i
$898$	1.51753	+	5.66349i	0.0506406	+	0.188993i
$899$	−23.8830	+	13.7889i	−0.796544	+	0.459885i
$900$		0			0
$901$		−	26.5836i		−	0.885630i
$902$	−1.70682	+	6.36993i	−0.0568308	+	0.212096i
$903$	8.84009	−	32.9917i	0.294180	−	1.09789i
$904$			22.7332i			0.756096i
$905$		0			0
$906$	11.1334	−	6.42786i	0.369882	−	0.213551i
$907$	−9.14876	−	34.1436i	−0.303779	−	1.13372i	−0.933991	−	0.357297i	$-0.883698\pi$
$907$	−9.14876	−	34.1436i	−0.303779	−	1.13372i	0.630211	−	0.776424i	$-0.282968\pi$
$908$	−1.29410	+	4.82963i	−0.0429461	+	0.160277i
$909$	−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	$0.876063\pi$
$912$	1.39833	−	9.45440i	0.0463034	−	0.313066i
$913$	−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
$917$	31.0812	−	8.32818i	1.02639	−	0.275021i
$918$	−9.59190	−	2.57014i	−0.316580	−	0.0848273i
$919$			16.5777i			0.546849i	0.961893	+	0.273425i	$0.0881564\pi$
$919$			16.5777i			0.546849i	−0.961893	+	0.273425i	$0.911844\pi$
$920$		0			0
$921$	−19.0592	−	33.0115i	−0.628022	−	1.08777i
$922$	−17.9447	−	4.80827i	−0.590978	−	0.158352i
$923$	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
$927$	14.6391	+	3.92253i	0.480811	+	0.128833i
$928$	4.91454	+	18.3413i	0.161328	+	0.602083i
$929$	−52.4619	−	30.2889i	−1.72122	−	0.993746i	−0.916442	−	0.400167i	$-0.868952\pi$
$929$	−52.4619	−	30.2889i	−1.72122	−	0.993746i	−0.804776	−	0.593579i	$-0.797714\pi$
$930$		0			0
$931$	−2.00000	−	17.3205i	−0.0655474	−	0.567657i
$932$	−6.87674	−	6.87674i	−0.225255	−	0.225255i
$933$	41.8710	−	11.2193i	1.37080	−	0.367304i
$934$	19.7197	−	34.1555i	0.645248	−	1.11760i
$935$		0			0
$936$	−3.23324	+	5.60014i	−0.105682	+	0.183046i
$937$	1.25853	−	4.69690i	0.0411144	−	0.153441i	−0.942317	−	0.334722i	$-0.891358\pi$
$937$	1.25853	−	4.69690i	0.0411144	−	0.153441i	0.983431	+	0.181281i	$0.0580243\pi$
$938$	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
$947$	21.7494	−	5.82774i	0.706761	−	0.189376i	0.112504	−	0.993651i	$-0.464113\pi$
$947$	21.7494	−	5.82774i	0.706761	−	0.189376i	0.594257	+	0.804275i	$0.297446\pi$
$948$	−9.41404	−	35.1337i	−0.305754	−	1.14109i
$949$	3.73343			0.121192
$950$		0			0
$951$	−8.77033			−0.284397
$952$	−5.10734	−	19.0608i	−0.165530	−	0.617766i
$953$	28.5699	−	7.65528i	0.925470	−	0.247979i	0.235548	−	0.971863i	$-0.424311\pi$
$953$	28.5699	−	7.65528i	0.925470	−	0.247979i	0.689922	+	0.723884i	$0.257645\pi$
$954$	−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
$963$	−8.22277	+	30.6878i	−0.264975	+	0.988900i
$964$	−7.09498	+	12.2889i	−0.228514	+	0.395798i
$965$		0			0
$966$	3.28887	−	5.69650i	0.105818	−	0.183282i
$967$	−8.74941	+	2.34440i	−0.281362	+	0.0753907i	−0.396740	−	0.917931i	$-0.629859\pi$
$967$	−8.74941	+	2.34440i	−0.281362	+	0.0753907i	0.115378	+	0.993322i	$0.463192\pi$
$968$	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	$0.643514\pi$
$972$	−4.30024	−	16.0487i	−0.137930	−	0.514762i
$973$	26.0621	+	6.98331i	0.835512	+	0.223875i
$974$	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	$-0.761544\pi$
$977$	−1.60284	+	1.60284i	−0.0512794	+	0.0512794i	0.681002	+	0.732281i	$0.261544\pi$
$978$	11.0048	+	2.94872i	0.351894	+	0.0942898i
$979$	−3.09842	−	5.36662i	−0.0990259	−	0.171518i
$980$		0			0
$981$		−	4.33631i		−	0.138448i
$982$	32.9917	+	8.84009i	1.05281	+	0.282099i
$983$	26.2302	−	7.02836i	0.836613	−	0.224170i	0.185017	−	0.982735i	$-0.440766\pi$
$983$	26.2302	−	7.02836i	0.836613	−	0.224170i	0.651597	+	0.758566i	$0.274099\pi$
$984$	−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
$988$	−1.91252	−	4.83374i	−0.0608455	−	0.153782i
$989$		−	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	$0.694659\pi$
$992$	−9.39742	+	35.0716i	−0.298368	+	1.11353i
$993$	−9.82908	−	36.6826i	−0.311916	−	1.16409i
$994$	24.3834	−	14.0777i	0.773394	−	0.446519i
$995$		0			0
$996$		−	4.52903i		−	0.143508i
$997$	−3.65601	+	13.6444i	−0.115787	+	0.432123i	−0.999345	−	0.0361997i	$-0.988475\pi$
$997$	−3.65601	+	13.6444i	−0.115787	+	0.432123i	0.883558	+	0.468322i	$0.155141\pi$
$998$	−7.28718	+	27.1961i	−0.230672	+	0.860878i
$999$		−	21.9258i		−	0.693702i

Twists

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

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

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