LMFDB - Embedded newform 225.2.h.e.46.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(46,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("225.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.h (of order $5$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	16.0.1130304400000000000000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5x^{14} + 5x^{12} - 10x^{10} + 205x^{8} - 700x^{6} + 1250x^{4} - 1250x^{2} + 625 $ x^16 - 5x^14 + 5x^12 - 10x^10 + 205x^8 - 700x^6 + 1250x^4 - 1250*x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			46.3
Root			$0.733267 + 1.75509i$ of defining polynomial
Character	$\chi$	$=$	225.46
Dual form			225.2.h.e.181.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.167451 - 0.515362i) q^{2} +(1.38048 + 1.00297i) q^{4} +(-1.16252 + 1.91012i) q^{5} +1.08833 q^{7} +(1.62484 - 1.18052i) q^{8} +O(q^{10})$	\(q+(0.167451 - 0.515362i) q^{2} +(1.38048 + 1.00297i) q^{4} +(-1.16252 + 1.91012i) q^{5} +1.08833 q^{7} +(1.62484 - 1.18052i) q^{8} +(0.789737 + 0.918969i) q^{10} +(-0.900718 + 2.77212i) q^{11} +(0.298591 + 0.918969i) q^{13} +(0.182242 - 0.560883i) q^{14} +(0.718278 + 2.21063i) q^{16} +(2.15194 - 1.56347i) q^{17} +(1.59074 - 1.15574i) q^{19} +(-3.52063 + 1.47090i) q^{20} +(1.27782 + 0.928391i) q^{22} +(2.11191 - 6.49978i) q^{23} +(-2.29710 - 4.44110i) q^{25} +0.523601 q^{26} +(1.50241 + 1.09157i) q^{28} +(-5.51425 - 4.00634i) q^{29} +(-2.01297 + 1.46251i) q^{31} +5.27639 q^{32} +(-0.445410 - 1.37083i) q^{34} +(-1.26520 + 2.07884i) q^{35} +(-2.54267 - 7.82555i) q^{37} +(-0.329253 - 1.01334i) q^{38} +(0.366018 + 4.47602i) q^{40} +(3.26498 + 10.0486i) q^{41} -7.72721 q^{43} +(-4.02379 + 2.92345i) q^{44} +(-2.99610 - 2.17679i) q^{46} +(7.29741 + 5.30188i) q^{47} -5.81554 q^{49} +(-2.67342 + 0.440172i) q^{50} +(-0.509505 + 1.56809i) q^{52} +(-4.47697 - 3.25271i) q^{53} +(-4.24798 - 4.94312i) q^{55} +(1.76836 - 1.28479i) q^{56} +(-2.98808 + 2.17097i) q^{58} +(-4.08725 - 12.5793i) q^{59} +(1.12754 - 3.47021i) q^{61} +(0.416646 + 1.28231i) q^{62} +(-0.553018 + 1.70202i) q^{64} +(-2.10246 - 0.497974i) q^{65} +(-7.15830 + 5.20081i) q^{67} +4.53882 q^{68} +(0.859493 + 1.00014i) q^{70} +(6.31844 + 4.59061i) q^{71} +(4.82987 - 14.8648i) q^{73} -4.45876 q^{74} +3.35515 q^{76} +(-0.980277 + 3.01698i) q^{77} +(5.34368 + 3.88241i) q^{79} +(-5.05758 - 1.19791i) q^{80} +5.72537 q^{82} +(1.53614 - 1.11607i) q^{83} +(0.484752 + 5.92802i) q^{85} +(-1.29393 + 3.98231i) q^{86} +(1.80902 + 5.56758i) q^{88} +(-0.353992 + 1.08948i) q^{89} +(0.324965 + 1.00014i) q^{91} +(9.43455 - 6.85460i) q^{92} +(3.95435 - 2.87300i) q^{94} +(0.358335 + 4.38207i) q^{95} +(5.01135 + 3.64096i) q^{97} +(-0.973820 + 2.99711i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{4}+O(q^{10}) $ 16 * q - 2 * q^4	$ 16 q - 2 q^{4} + 14 q^{16} + 14 q^{19} - 30 q^{22} + 10 q^{25} + 30 q^{28} + 18 q^{31} - 20 q^{34} + 10 q^{37} - 10 q^{40} - 80 q^{43} - 32 q^{49} - 40 q^{52} - 70 q^{55} - 10 q^{58} + 32 q^{61} - 8 q^{64} - 40 q^{67} + 50 q^{70} + 60 q^{73} - 88 q^{76} + 36 q^{79} + 120 q^{82} + 20 q^{88} + 30 q^{91} + 30 q^{94} + 40 q^{97}+O(q^{100}) $ 16 * q - 2 * q^4 + 14 * q^16 + 14 * q^19 - 30 * q^22 + 10 * q^25 + 30 * q^28 + 18 * q^31 - 20 * q^34 + 10 * q^37 - 10 * q^40 - 80 * q^43 - 32 * q^49 - 40 * q^52 - 70 * q^55 - 10 * q^58 + 32 * q^61 - 8 * q^64 - 40 * q^67 + 50 * q^70 + 60 * q^73 - 88 * q^76 + 36 * q^79 + 120 * q^82 + 20 * q^88 + 30 * q^91 + 30 * q^94 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	0.167451	−	0.515362i	0.118406	−	0.364416i	−0.874236	−	0.485501i	$-0.838637\pi$
$2$	0.167451	−	0.515362i	0.118406	−	0.364416i	0.992642	+	0.121085i	$0.0386373\pi$
$3$		0			0
$3$		0			0
$4$	1.38048	+	1.00297i	0.690238	+	0.501487i
$5$	−1.16252	+	1.91012i	−0.519894	+	0.854231i
$5$	−1.16252	+	1.91012i	−0.519894	+	0.854231i
$6$		0			0
$7$	1.08833			0.411349			0.205675	−	0.978620i	$-0.434061\pi$
$7$	1.08833			0.411349			0.205675	+	0.978620i	$0.434061\pi$
$8$	1.62484	−	1.18052i	0.574469	−	0.417376i
$9$		0			0
$10$	0.789737	+	0.918969i	0.249737	+	0.290604i
$11$	−0.900718	+	2.77212i	−0.271577	+	0.835827i	0.718528	+	0.695498i	$0.244816\pi$
$11$	−0.900718	+	2.77212i	−0.271577	+	0.835827i	−0.990105	+	0.140329i	$0.955184\pi$
$12$		0			0
$13$	0.298591	+	0.918969i	0.0828143	+	0.254876i	0.983887	−	0.178792i	$-0.0572189\pi$
$13$	0.298591	+	0.918969i	0.0828143	+	0.254876i	−0.901073	+	0.433668i	$0.857219\pi$
$14$	0.182242	−	0.560883i	0.0487062	−	0.149902i
$15$		0			0
$16$	0.718278	+	2.21063i	0.179569	+	0.552658i
$17$	2.15194	−	1.56347i	0.521921	−	0.379198i	−0.295406	−	0.955372i	$-0.595455\pi$
$17$	2.15194	−	1.56347i	0.521921	−	0.379198i	0.817327	+	0.576174i	$0.195455\pi$
$18$		0			0
$19$	1.59074	−	1.15574i	0.364941	−	0.265145i	−0.390169	−	0.920743i	$-0.627584\pi$
$19$	1.59074	−	1.15574i	0.364941	−	0.265145i	0.755110	+	0.655598i	$0.227584\pi$
$20$	−3.52063	+	1.47090i	−0.787236	+	0.328902i
$21$		0			0
$22$	1.27782	+	0.928391i	0.272432	+	0.197934i
$23$	2.11191	−	6.49978i	0.440363	−	1.35530i	−0.447127	−	0.894471i	$-0.647553\pi$
$23$	2.11191	−	6.49978i	0.440363	−	1.35530i	0.887490	−	0.460828i	$-0.152447\pi$
$24$		0			0
$25$	−2.29710	−	4.44110i	−0.459420	−	0.888219i
$26$	0.523601			0.102687
$27$		0			0
$28$	1.50241	+	1.09157i	0.283929	+	0.206286i
$29$	−5.51425	−	4.00634i	−1.02397	−	0.743959i	−0.0568782	−	0.998381i	$-0.518115\pi$
$29$	−5.51425	−	4.00634i	−1.02397	−	0.743959i	−0.967093	+	0.254422i	$0.918115\pi$
$30$		0			0
$31$	−2.01297	+	1.46251i	−0.361540	+	0.262674i	−0.753694	−	0.657225i	$-0.771730\pi$
$31$	−2.01297	+	1.46251i	−0.361540	+	0.262674i	0.392154	+	0.919899i	$0.371730\pi$
$32$	5.27639			0.932742
$33$		0			0
$34$	−0.445410	−	1.37083i	−0.0763872	−	0.235096i
$35$	−1.26520	+	2.07884i	−0.213858	+	0.351387i
$36$		0			0
$37$	−2.54267	−	7.82555i	−0.418013	−	1.28651i	−0.909528	−	0.415643i	$-0.863557\pi$
$37$	−2.54267	−	7.82555i	−0.418013	−	1.28651i	0.491515	−	0.870869i	$-0.336443\pi$
$38$	−0.329253	−	1.01334i	−0.0534119	−	0.164385i
$39$		0			0
$40$	0.366018	+	4.47602i	0.0578725	+	0.707720i
$41$	3.26498	+	10.0486i	0.509904	+	1.56932i	0.792367	+	0.610044i	$0.208848\pi$
$41$	3.26498	+	10.0486i	0.509904	+	1.56932i	−0.282464	+	0.959278i	$0.591152\pi$
$42$		0			0
$43$	−7.72721			−1.17839			−0.589195	−	0.807991i	$-0.700555\pi$
$43$	−7.72721			−1.17839			−0.589195	+	0.807991i	$0.700555\pi$
$44$	−4.02379	+	2.92345i	−0.606609	+	0.440727i
$45$		0			0
$46$	−2.99610	−	2.17679i	−0.441751	−	0.320951i
$47$	7.29741	+	5.30188i	1.06444	+	0.773358i	0.974904	−	0.222626i	$-0.0714627\pi$
$47$	7.29741	+	5.30188i	1.06444	+	0.773358i	0.0895324	+	0.995984i	$0.471463\pi$
$48$		0			0
$49$	−5.81554			−0.830792
$50$	−2.67342	+	0.440172i	−0.378079	+	0.0622497i
$51$		0			0
$52$	−0.509505	+	1.56809i	−0.0706556	+	0.217456i
$53$	−4.47697	−	3.25271i	−0.614960	−	0.446794i	0.236198	−	0.971705i	$-0.424099\pi$
$53$	−4.47697	−	3.25271i	−0.614960	−	0.446794i	−0.851157	+	0.524911i	$0.824099\pi$
$54$		0			0
$55$	−4.24798	−	4.94312i	−0.572798	−	0.666531i
$56$	1.76836	−	1.28479i	0.236307	−	0.171687i
$57$		0			0
$58$	−2.98808	+	2.17097i	−0.392355	+	0.285062i
$59$	−4.08725	−	12.5793i	−0.532115	−	1.63768i	−0.749802	−	0.661662i	$-0.769851\pi$
$59$	−4.08725	−	12.5793i	−0.532115	−	1.63768i	0.217687	−	0.976019i	$-0.430149\pi$
$60$		0			0
$61$	1.12754	−	3.47021i	0.144367	−	0.444315i	−0.852562	−	0.522625i	$-0.824953\pi$
$61$	1.12754	−	3.47021i	0.144367	−	0.444315i	0.996929	+	0.0783108i	$0.0249527\pi$
$62$	0.416646	+	1.28231i	0.0529141	+	0.162853i
$63$		0			0
$64$	−0.553018	+	1.70202i	−0.0691273	+	0.212752i
$65$	−2.10246	−	0.497974i	−0.260778	−	0.0617661i
$66$		0			0
$67$	−7.15830	+	5.20081i	−0.874525	+	0.635380i	−0.931797	−	0.362979i	$-0.881760\pi$
$67$	−7.15830	+	5.20081i	−0.874525	+	0.635380i	0.0572722	+	0.998359i	$0.481760\pi$
$68$	4.53882			0.550413
$69$		0			0
$70$	0.859493	+	1.00014i	0.102729	+	0.119540i
$71$	6.31844	+	4.59061i	0.749861	+	0.544806i	0.895784	−	0.444490i	$-0.146615\pi$
$71$	6.31844	+	4.59061i	0.749861	+	0.544806i	−0.145923	+	0.989296i	$0.546615\pi$
$72$		0			0
$73$	4.82987	−	14.8648i	0.565293	−	1.73979i	−0.101785	−	0.994806i	$-0.532455\pi$
$73$	4.82987	−	14.8648i	0.565293	−	1.73979i	0.667078	−	0.744988i	$-0.267545\pi$
$74$	−4.45876			−0.518321
$75$		0			0
$76$	3.35515			0.384863
$77$	−0.980277	+	3.01698i	−0.111713	+	0.343817i
$78$		0			0
$79$	5.34368	+	3.88241i	0.601211	+	0.436805i	0.846308	−	0.532693i	$-0.178820\pi$
$79$	5.34368	+	3.88241i	0.601211	+	0.436805i	−0.245098	+	0.969498i	$0.578820\pi$
$80$	−5.05758	−	1.19791i	−0.565455	−	0.133930i
$81$		0			0
$82$	5.72537			0.632262
$83$	1.53614	−	1.11607i	0.168614	−	0.122505i	−0.500278	−	0.865865i	$-0.666769\pi$
$83$	1.53614	−	1.11607i	0.168614	−	0.122505i	0.668892	+	0.743360i	$0.266769\pi$
$84$		0			0
$85$	0.484752	+	5.92802i	0.0525788	+	0.642984i
$86$	−1.29393	+	3.98231i	−0.139528	+	0.429424i
$87$		0			0
$88$	1.80902	+	5.56758i	0.192842	+	0.593506i
$89$	−0.353992	+	1.08948i	−0.0375231	+	0.115484i	−0.968064	−	0.250705i	$-0.919338\pi$
$89$	−0.353992	+	1.08948i	−0.0375231	+	0.115484i	0.930540	+	0.366189i	$0.119338\pi$
$90$		0			0
$91$	0.324965	+	1.00014i	0.0340656	+	0.104843i
$92$	9.43455	−	6.85460i	0.983620	−	0.714642i
$93$		0			0
$94$	3.95435	−	2.87300i	0.407860	−	0.296327i
$95$	0.358335	+	4.38207i	0.0367644	+	0.449591i
$96$		0			0
$97$	5.01135	+	3.64096i	0.508825	+	0.369683i	0.812378	−	0.583132i	$-0.198173\pi$
$97$	5.01135	+	3.64096i	0.508825	+	0.369683i	−0.303553	+	0.952815i	$0.598173\pi$
$98$	−0.973820	+	2.99711i	−0.0983706	+	0.302754i
$99$		0			0
$100$	1.28321	−	8.43476i	0.128321	−	0.843476i
$101$	3.88891			0.386961			0.193481	−	0.981104i	$-0.438022\pi$
$101$	3.88891			0.386961			0.193481	+	0.981104i	$0.438022\pi$
$102$		0			0
$103$	14.3890	+	10.4542i	1.41779	+	1.03008i	0.992132	+	0.125198i	$0.0399566\pi$
$103$	14.3890	+	10.4542i	1.41779	+	1.03008i	0.425656	+	0.904885i	$0.360043\pi$
$104$	1.57002	+	1.14069i	0.153954	+	0.111854i
$105$		0			0
$106$	−2.42600	+	1.76259i	−0.235634	+	0.171198i
$107$	−7.02996			−0.679612			−0.339806	−	0.940496i	$-0.610361\pi$
$107$	−7.02996			−0.679612			−0.339806	+	0.940496i	$0.610361\pi$
$108$		0			0
$109$	−2.78917	−	8.58418i	−0.267154	−	0.822215i	−0.991189	−	0.132452i	$-0.957715\pi$
$109$	−2.78917	−	8.58418i	−0.267154	−	0.822215i	0.724036	−	0.689763i	$-0.242285\pi$
$110$	−3.25883	+	1.36152i	−0.310717	+	0.129816i
$111$		0			0
$112$	0.781722	+	2.40589i	0.0738658	+	0.227336i
$113$	−4.01303	−	12.3508i	−0.377514	−	1.16187i	−0.941767	−	0.336267i	$-0.890835\pi$
$113$	−4.01303	−	12.3508i	−0.377514	−	1.16187i	0.564252	−	0.825603i	$-0.309165\pi$
$114$		0			0
$115$	9.96022	+	11.5901i	0.928795	+	1.08078i
$116$	−3.59404	−	11.0613i	−0.333698	−	1.02702i
$117$		0			0
$118$	−7.16729			−0.659803
$119$	2.34201	−	1.70157i	0.214692	−	0.155983i
$120$		0			0
$121$	2.02580	+	1.47183i	0.184164	+	0.133803i
$122$	−1.59961	−	1.16218i	−0.144821	−	0.105219i
$123$		0			0
$124$	−4.24571			−0.381276
$125$	11.1534	+	0.775121i	0.997594	+	0.0693289i
$126$		0			0
$127$	−0.524803	+	1.61518i	−0.0465687	+	0.143324i	−0.971637	−	0.236477i	$-0.924007\pi$
$127$	−0.524803	+	1.61518i	−0.0465687	+	0.143324i	0.925068	+	0.379800i	$0.124007\pi$
$128$	9.32192	+	6.77277i	0.823949	+	0.598634i
$129$		0			0
$130$	−0.608696	+	1.00014i	−0.0533862	+	0.0877181i
$131$	−10.8568	+	7.88790i	−0.948559	+	0.689169i	−0.950466	−	0.310829i	$-0.899393\pi$
$131$	−10.8568	+	7.88790i	−0.948559	+	0.689169i	0.00190626	+	0.999998i	$0.499393\pi$
$132$		0			0
$133$	1.73125	−	1.25782i	0.150118	−	0.109067i
$134$	1.48163	+	4.56000i	0.127994	+	0.393924i
$135$		0			0
$136$	1.65085	−	5.08080i	0.141559	−	0.435675i
$137$	−1.76221	−	5.42354i	−0.150556	−	0.463364i	0.847127	−	0.531390i	$-0.178330\pi$
$137$	−1.76221	−	5.42354i	−0.150556	−	0.463364i	−0.997684	+	0.0680257i	$0.978330\pi$
$138$		0			0
$139$	−5.96328	+	18.3531i	−0.505799	+	1.55669i	0.293624	+	0.955921i	$0.405139\pi$
$139$	−5.96328	+	18.3531i	−0.505799	+	1.55669i	−0.799423	+	0.600768i	$0.794861\pi$
$140$	−3.83160	+	1.60082i	−0.323829	+	0.135294i
$141$		0			0
$142$	3.42386	−	2.48758i	0.287324	−	0.208753i
$143$	−2.81644			−0.235523
$144$		0			0
$145$	14.0630	−	5.87543i	1.16787	−	0.487928i
$146$	−6.85199	−	4.97826i	−0.567075	−	0.412004i
$147$		0			0
$148$	4.33872	−	13.3532i	0.356641	−	1.09763i
$149$	17.0295			1.39511			0.697555	−	0.716531i	$-0.254271\pi$
$149$	17.0295			1.39511			0.697555	+	0.716531i	$0.254271\pi$
$150$		0			0
$151$	−0.691471			−0.0562711			−0.0281355	−	0.999604i	$-0.508957\pi$
$151$	−0.691471			−0.0562711			−0.0281355	+	0.999604i	$0.508957\pi$
$152$	1.22033	−	3.75579i	0.0989819	−	0.304635i
$153$		0			0
$154$	1.39069	+	1.01039i	0.112065	+	0.0814199i
$155$	−0.453448	−	5.54520i	−0.0364218	−	0.445401i
$156$		0			0
$157$	−0.448304			−0.0357786			−0.0178893	−	0.999840i	$-0.505695\pi$
$157$	−0.448304			−0.0357786			−0.0178893	+	0.999840i	$0.505695\pi$
$158$	2.89565	−	2.10381i	0.230366	−	0.167370i
$159$		0			0
$160$	−6.13390	+	10.0785i	−0.484927	+	0.796777i
$161$	2.29845	−	7.07390i	0.181143	−	0.557501i
$162$		0			0
$163$	3.06353	+	9.42856i	0.239954	+	0.738502i	0.996426	+	0.0844756i	$0.0269215\pi$
$163$	3.06353	+	9.42856i	0.239954	+	0.738502i	−0.756472	+	0.654026i	$0.773079\pi$
$164$	−5.57123	+	17.1465i	−0.435040	+	1.33892i
$165$		0			0
$166$	−0.317953	−	0.978558i	−0.0246779	−	0.0759508i
$167$	−15.3063	+	11.1207i	−1.18444	+	0.860546i	−0.992666	−	0.120893i	$-0.961424\pi$
$167$	−15.3063	+	11.1207i	−1.18444	+	0.860546i	−0.191774	+	0.981439i	$0.561424\pi$
$168$		0			0
$169$	9.76187	−	7.09242i	0.750913	−	0.545570i
$170$	3.13625	+	0.742831i	0.240539	+	0.0569725i
$171$		0			0
$172$	−10.6672	−	7.75020i	−0.813369	−	0.590947i
$173$	−3.70902	+	11.4152i	−0.281991	+	0.867881i	0.705293	+	0.708916i	$0.250816\pi$
$173$	−3.70902	+	11.4152i	−0.281991	+	0.867881i	−0.987284	+	0.158964i	$0.949184\pi$
$174$		0			0
$175$	−2.50000	−	4.83337i	−0.188982	−	0.365368i
$176$	−6.77511			−0.510693
$177$		0			0
$178$	0.502198	+	0.364868i	0.0376413	+	0.0273480i
$179$	7.36920	+	5.35404i	0.550800	+	0.400180i	0.828080	−	0.560609i	$-0.189433\pi$
$179$	7.36920	+	5.35404i	0.550800	+	0.400180i	−0.277280	+	0.960789i	$0.589433\pi$
$180$		0			0
$181$	4.92946	−	3.58146i	0.366404	−	0.266208i	−0.389314	−	0.921105i	$-0.627288\pi$
$181$	4.92946	−	3.58146i	0.366404	−	0.266208i	0.755718	+	0.654897i	$0.227288\pi$
$182$	0.569850			0.0422401
$183$		0			0
$184$	−4.24159	−	13.0543i	−0.312694	−	0.962374i
$185$	17.9036	+	4.24054i	1.31630	+	0.311770i
$186$		0			0
$187$	2.39586	+	7.37368i	0.175202	+	0.539217i
$188$	4.75625	+	14.6382i	0.346885	+	1.06760i
$189$		0			0
$190$	2.31835	+	0.549110i	0.168191	+	0.0398367i
$191$	−2.85913	−	8.79950i	−0.206879	−	0.636709i	−0.999631	−	0.0271644i	$-0.991352\pi$
$191$	−2.85913	−	8.79950i	−0.206879	−	0.636709i	0.792752	−	0.609545i	$-0.208648\pi$
$192$		0			0
$193$	−24.2638			−1.74655			−0.873275	−	0.487228i	$-0.838008\pi$
$193$	−24.2638			−1.74655			−0.873275	+	0.487228i	$0.838008\pi$
$194$	2.71557	−	1.97297i	0.194966	−	0.141651i
$195$		0			0
$196$	−8.02822	−	5.83284i	−0.573444	−	0.416631i
$197$	−10.2445	−	7.44303i	−0.729887	−	0.530294i	0.159640	−	0.987175i	$-0.448967\pi$
$197$	−10.2445	−	7.44303i	−0.729887	−	0.530294i	−0.889528	+	0.456881i	$0.848967\pi$
$198$		0			0
$199$	−13.8284			−0.980271			−0.490136	−	0.871646i	$-0.663053\pi$
$199$	−13.8284			−0.980271			−0.490136	+	0.871646i	$0.663053\pi$
$200$	−8.97522	−	4.50432i	−0.634644	−	0.318503i
$201$		0			0
$202$	0.651203	−	2.00420i	0.0458185	−	0.141015i
$203$	−6.00132	−	4.36021i	−0.421210	−	0.306027i
$204$		0			0
$205$	−22.9895	−	5.44515i	−1.60566	−	0.380306i
$206$	7.79715	−	5.66496i	0.543253	−	0.394696i
$207$		0			0
$208$	−1.81703	+	1.32015i	−0.125988	+	0.0915360i
$209$	1.77105	+	5.45072i	0.122506	+	0.377034i
$210$		0			0
$211$	−4.36155	+	13.4235i	−0.300261	+	0.924109i	0.681142	+	0.732151i	$0.261484\pi$
$211$	−4.36155	+	13.4235i	−0.300261	+	0.924109i	−0.981403	+	0.191958i	$0.938516\pi$
$212$	−2.91797	−	8.98058i	−0.200407	−	0.616789i
$213$		0			0
$214$	−1.17718	+	3.62297i	−0.0804700	+	0.247661i
$215$	8.98303	−	14.7599i	0.612638	−	1.00662i
$216$		0			0
$217$	−2.19077	+	1.59169i	−0.148719	+	0.108051i
$218$	−4.89101			−0.331261
$219$		0			0
$220$	−0.906412	−	11.0845i	−0.0611103	−	0.747316i
$221$	2.07933	+	1.51072i	0.139871	+	0.101622i
$222$		0			0
$223$	5.74690	−	17.6871i	0.384841	−	1.18442i	−0.551755	−	0.834006i	$-0.686042\pi$
$223$	5.74690	−	17.6871i	0.384841	−	1.18442i	0.936596	−	0.350412i	$-0.113958\pi$
$224$	5.74244			0.383683
$225$		0			0
$226$	−7.03714			−0.468104
$227$	−4.78448	+	14.7251i	−0.317557	+	0.977340i	0.657132	+	0.753776i	$0.271769\pi$
$227$	−4.78448	+	14.7251i	−0.317557	+	0.977340i	−0.974689	+	0.223565i	$0.928231\pi$
$228$		0			0
$229$	12.6240	+	9.17187i	0.834217	+	0.606094i	0.920749	−	0.390155i	$-0.127579\pi$
$229$	12.6240	+	9.17187i	0.834217	+	0.606094i	−0.0865324	+	0.996249i	$0.527579\pi$
$230$	7.64095	−	3.19234i	0.503830	−	0.210497i
$231$		0			0
$232$	−13.6894			−0.898750
$233$	−17.4961	+	12.7117i	−1.14621	+	0.832769i	−0.987972	−	0.154632i	$-0.950581\pi$
$233$	−17.4961	+	12.7117i	−1.14621	+	0.832769i	−0.158237	+	0.987401i	$0.550581\pi$
$234$		0			0
$235$	−18.6106	+	7.77538i	−1.21402	+	0.507210i
$236$	6.97433	−	21.4648i	0.453990	−	1.39724i
$237$		0			0
$238$	−0.484752	−	1.49191i	−0.0314218	−	0.0967065i
$239$	4.82997	−	14.8651i	0.312425	−	0.961544i	−0.664377	−	0.747398i	$-0.731303\pi$
$239$	4.82997	−	14.8651i	0.312425	−	0.961544i	0.976802	−	0.214146i	$-0.0686970\pi$
$240$		0			0
$241$	−3.22911	−	9.93817i	−0.208005	−	0.640174i	−0.999577	−	0.0290971i	$-0.990737\pi$
$241$	−3.22911	−	9.93817i	−0.208005	−	0.640174i	0.791572	−	0.611076i	$-0.209263\pi$
$242$	1.09775	−	0.797562i	0.0705661	−	0.0512693i
$243$		0			0
$244$	5.03707	−	3.65965i	0.322465	−	0.234285i
$245$	6.76068	−	11.1084i	0.431924	−	0.709688i
$246$		0			0
$247$	1.53707	+	1.11675i	0.0978014	+	0.0710569i
$248$	−1.54424	+	4.75269i	−0.0980595	+	0.301796i
$249$		0			0
$250$	2.26713	−	5.61826i	0.143386	−	0.355330i
$251$	−4.30657			−0.271829			−0.135914	−	0.990721i	$-0.543397\pi$
$251$	−4.30657			−0.271829			−0.135914	+	0.990721i	$0.543397\pi$
$252$		0			0
$253$	16.1160	+	11.7089i	1.01320	+	0.736135i
$254$	0.744522	+	0.540927i	0.0467154	+	0.0339408i
$255$		0			0
$256$	2.15575	−	1.56625i	0.134735	−	0.0978905i
$257$	−28.0650			−1.75065			−0.875323	−	0.483539i	$-0.839351\pi$
$257$	−28.0650			−1.75065			−0.875323	+	0.483539i	$0.839351\pi$
$258$		0			0
$259$	−2.76726	−	8.51676i	−0.171949	−	0.529206i
$260$	−2.40294	−	2.79615i	−0.149024	−	0.173410i
$261$		0			0
$262$	2.24714	+	6.91600i	0.138829	+	0.427272i
$263$	7.73879	+	23.8176i	0.477194	+	1.46865i	0.842975	+	0.537953i	$0.180802\pi$
$263$	7.73879	+	23.8176i	0.477194	+	1.46865i	−0.365781	+	0.930701i	$0.619198\pi$
$264$		0			0
$265$	11.4176	−	4.77021i	0.701379	−	0.293032i
$266$	−0.358335	−	1.10284i	−0.0219709	−	0.0676196i
$267$		0			0
$268$	−15.0981			−0.922265
$269$	−3.50453	+	2.54619i	−0.213675	+	0.155244i	−0.689475	−	0.724310i	$-0.742159\pi$
$269$	−3.50453	+	2.54619i	−0.213675	+	0.155244i	0.475800	+	0.879554i	$0.342159\pi$
$270$		0			0
$271$	19.0441	+	13.8363i	1.15685	+	0.840497i	0.989376	−	0.145380i	$-0.0464404\pi$
$271$	19.0441	+	13.8363i	1.15685	+	0.840497i	0.167469	+	0.985877i	$0.446440\pi$
$272$	5.00195	+	3.63413i	0.303288	+	0.220352i
$273$		0			0
$274$	−3.09017			−0.186684
$275$	14.3803	−	2.36768i	0.867165	−	0.142776i
$276$		0			0
$277$	4.93385	−	15.1848i	0.296446	−	0.912367i	−0.686286	−	0.727332i	$-0.740760\pi$
$277$	4.93385	−	15.1848i	0.296446	−	0.912367i	0.982732	−	0.185035i	$-0.0592399\pi$
$278$	8.45993	+	6.14650i	0.507393	+	0.368642i
$279$		0			0
$280$	0.398347	+	4.87137i	0.0238058	+	0.291120i
$281$	13.1988	−	9.58947i	0.787373	−	0.572060i	−0.119810	−	0.992797i	$-0.538229\pi$
$281$	13.1988	−	9.58947i	0.787373	−	0.572060i	0.907183	+	0.420737i	$0.138229\pi$
$282$		0			0
$283$	−13.9733	+	10.1522i	−0.830625	+	0.603484i	−0.919736	−	0.392538i	$-0.871597\pi$
$283$	−13.9733	+	10.1522i	−0.830625	+	0.603484i	0.0891113	+	0.996022i	$0.471597\pi$
$284$	4.11818	+	12.6745i	0.244369	+	0.752091i
$285$		0			0
$286$	−0.471617	+	1.45149i	−0.0278873	+	0.0858283i
$287$	3.55337	+	10.9361i	0.209749	+	0.645540i
$288$		0			0
$289$	−3.06691	+	9.43897i	−0.180406	+	0.555234i
$290$	−0.673106	−	8.23139i	−0.0395261	−	0.483364i
$291$		0			0
$292$	21.5765	−	15.6763i	1.26267	−	0.917385i
$293$	−20.4862			−1.19681			−0.598407	−	0.801192i	$-0.704199\pi$
$293$	−20.4862			−1.19681			−0.598407	+	0.801192i	$0.704199\pi$
$294$		0			0
$295$	28.7794	+	6.81650i	1.67560	+	0.396872i
$296$	−13.3696	−	9.71361i	−0.777095	−	0.564592i
$297$		0			0
$298$	2.85161	−	8.77635i	0.165189	−	0.508400i
$299$	6.60370			0.381902
$300$		0			0
$301$	−8.40974			−0.484730
$302$	−0.115788	+	0.356358i	−0.00666283	+	0.0205061i
$303$		0			0
$304$	3.69751	+	2.68640i	0.212067	+	0.154075i
$305$	5.31772	+	6.18791i	0.304492	+	0.354319i
$306$		0			0
$307$	1.57747			0.0900309			0.0450155	−	0.998986i	$-0.485666\pi$
$307$	1.57747			0.0900309			0.0450155	+	0.998986i	$0.485666\pi$
$308$	−4.37920	+	3.18168i	−0.249528	+	0.181293i
$309$		0			0
$310$	−2.93371	−	0.694860i	−0.166624	−	0.0394654i
$311$	−4.07115	+	12.5297i	−0.230854	+	0.710495i	0.766790	+	0.641898i	$0.221853\pi$
$311$	−4.07115	+	12.5297i	−0.230854	+	0.710495i	−0.997644	+	0.0685979i	$0.978147\pi$
$312$		0			0
$313$	5.69800	+	17.5366i	0.322070	+	0.991229i	0.972746	+	0.231873i	$0.0744855\pi$
$313$	5.69800	+	17.5366i	0.322070	+	0.991229i	−0.650676	+	0.759355i	$0.725514\pi$
$314$	−0.0750691	+	0.231039i	−0.00423640	+	0.0130383i
$315$		0			0
$316$	3.48286	+	10.7191i	0.195926	+	0.602999i
$317$	−0.572771	+	0.416143i	−0.0321700	+	0.0233729i	−0.603754	−	0.797171i	$-0.706329\pi$
$317$	−0.572771	+	0.416143i	−0.0321700	+	0.0233729i	0.571584	+	0.820544i	$0.306329\pi$
$318$		0			0
$319$	16.0729	−	11.6776i	0.899908	−	0.653821i
$320$	−2.60816	−	3.03496i	−0.145800	−	0.169659i
$321$		0			0
$322$	−3.26074	−	2.36907i	−0.181714	−	0.132023i
$323$	1.61620	−	4.97416i	0.0899278	−	0.276769i
$324$		0			0
$325$	3.39534	−	3.43704i	0.188339	−	0.190653i
$326$	5.37211			0.297534
$327$		0			0
$328$	17.1676	+	12.4730i	0.947921	+	0.688705i
$329$	7.94198	+	5.77018i	0.437855	+	0.318120i
$330$		0			0
$331$	6.67460	−	4.84938i	0.366869	−	0.266546i	−0.389042	−	0.921220i	$-0.627194\pi$
$331$	6.67460	−	4.84938i	0.366869	−	0.266546i	0.755911	+	0.654674i	$0.227194\pi$
$332$	3.24000			0.177818
$333$		0			0
$334$	3.16812	+	9.75048i	0.173352	+	0.533522i
$335$	−1.61250	−	19.7192i	−0.0881004	−	1.07738i
$336$		0			0
$337$	−0.799462	−	2.46049i	−0.0435495	−	0.134031i	0.926918	−	0.375265i	$-0.122448\pi$
$337$	−0.799462	−	2.46049i	−0.0435495	−	0.134031i	−0.970467	+	0.241233i	$0.922448\pi$
$338$	−2.02052	−	6.21853i	−0.109902	−	0.338244i
$339$		0			0
$340$	−5.27646	+	8.66968i	−0.286156	+	0.470180i
$341$	−2.24114	−	6.89751i	−0.121364	−	0.373521i
$342$		0			0
$343$	−13.9475			−0.753095
$344$	−12.5555	+	9.12211i	−0.676948	+	0.491831i
$345$		0			0
$346$	5.26187	+	3.82297i	0.282880	+	0.205524i
$347$	−12.4477	−	9.04380i	−0.668229	−	0.485497i	0.201203	−	0.979550i	$-0.435515\pi$
$347$	−12.4477	−	9.04380i	−0.668229	−	0.485497i	−0.869432	+	0.494053i	$0.835515\pi$
$348$		0			0
$349$	1.86531			0.0998477			0.0499239	−	0.998753i	$-0.484102\pi$
$349$	1.86531			0.0998477			0.0499239	+	0.998753i	$0.484102\pi$
$350$	−2.90956	+	0.479051i	−0.155523	+	0.0256064i
$351$		0			0
$352$	−4.75254	+	14.6268i	−0.253311	+	0.779611i
$353$	−2.64868	−	1.92438i	−0.140975	−	0.102425i	0.515062	−	0.857153i	$-0.327769\pi$
$353$	−2.64868	−	1.92438i	−0.140975	−	0.102425i	−0.656038	+	0.754728i	$0.727769\pi$
$354$		0			0
$355$	−16.1139	+	6.73229i	−0.855238	+	0.357313i
$356$	−1.58139	+	1.14895i	−0.0838137	+	0.0608942i
$357$		0			0
$358$	3.99325	−	2.90127i	0.211050	−	0.153337i
$359$	−2.30894	−	7.10619i	−0.121861	−	0.375050i	0.871455	−	0.490476i	$-0.163177\pi$
$359$	−2.30894	−	7.10619i	−0.121861	−	0.375050i	−0.993316	+	0.115425i	$0.963177\pi$
$360$		0			0
$361$	−4.67661	+	14.3931i	−0.246137	+	0.757532i
$362$	−1.02031	−	3.14018i	−0.0536261	−	0.165044i
$363$		0			0
$364$	−0.554508	+	1.70660i	−0.0290641	+	0.0894502i
$365$	22.7787	+	26.5062i	1.19229	+	1.38740i
$366$		0			0
$367$	3.85822	−	2.80316i	0.201397	−	0.146324i	−0.482516	−	0.875887i	$-0.660277\pi$
$367$	3.85822	−	2.80316i	0.201397	−	0.146324i	0.683913	+	0.729564i	$0.260277\pi$
$368$	15.8856			0.828092
$369$		0			0
$370$	5.18339	−	8.51676i	0.269472	−	0.442765i
$371$	−4.87242	−	3.54002i	−0.252963	−	0.183789i
$372$		0			0
$373$	8.56051	−	26.3466i	0.443247	−	1.36417i	−0.441149	−	0.897434i	$-0.645429\pi$
$373$	8.56051	−	26.3466i	0.443247	−	1.36417i	0.884395	−	0.466739i	$-0.154571\pi$
$374$	4.20130			0.217244
$375$		0			0
$376$	18.1161			0.934267
$377$	2.03520	−	6.26369i	0.104818	−	0.322596i
$378$		0			0
$379$	13.6265	+	9.90026i	0.699948	+	0.508542i	0.879915	−	0.475131i	$-0.157599\pi$
$379$	13.6265	+	9.90026i	0.699948	+	0.508542i	−0.179967	+	0.983673i	$0.557599\pi$
$380$	−3.90043	+	6.40874i	−0.200088	+	0.328761i
$381$		0			0
$382$	−5.01369			−0.256523
$383$	10.6767	−	7.75708i	0.545554	−	0.396368i	−0.280590	−	0.959828i	$-0.590530\pi$
$383$	10.6767	−	7.75708i	0.545554	−	0.396368i	0.826144	+	0.563460i	$0.190530\pi$
$384$		0			0
$385$	−4.62320	−	5.37974i	−0.235620	−	0.274177i
$386$	−4.06301	+	12.5047i	−0.206802	+	0.636471i
$387$		0			0
$388$	3.26626	+	10.0525i	0.165819	+	0.510339i
$389$	−4.59578	+	14.1444i	−0.233015	+	0.717147i	0.764363	+	0.644786i	$0.223054\pi$
$389$	−4.59578	+	14.1444i	−0.233015	+	0.717147i	−0.997378	+	0.0723615i	$0.976946\pi$
$390$		0			0
$391$	−5.61755	−	17.2890i	−0.284092	−	0.874344i
$392$	−9.44934	+	6.86535i	−0.477264	+	0.346753i
$393$		0			0
$394$	−5.55130	+	4.03326i	−0.279671	+	0.203193i
$395$	−13.6280	+	5.69368i	−0.685698	+	0.286480i
$396$		0			0
$397$	7.96973	+	5.79034i	0.399989	+	0.290609i	0.769537	−	0.638603i	$-0.220487\pi$
$397$	7.96973	+	5.79034i	0.399989	+	0.290609i	−0.369547	+	0.929212i	$0.620487\pi$
$398$	−2.31559	+	7.12665i	−0.116070	+	0.357226i
$399$		0			0
$400$	8.16767	−	8.26799i	0.408384	−	0.413399i
$401$	−1.90738			−0.0952498			−0.0476249	−	0.998865i	$-0.515165\pi$
$401$	−1.90738			−0.0952498			−0.0476249	+	0.998865i	$0.515165\pi$
$402$		0			0
$403$	−1.94505	−	1.41316i	−0.0968900	−	0.0703947i
$404$	5.36855	+	3.90048i	0.267095	+	0.194056i
$405$		0			0
$406$	−3.25202	+	2.36273i	−0.161395	+	0.117260i
$407$	23.9836			1.18882
$408$		0			0
$409$	−6.26989	−	19.2967i	−0.310026	−	0.954162i	−0.977754	−	0.209756i	$-0.932733\pi$
$409$	−6.26989	−	19.2967i	−0.310026	−	0.954162i	0.667728	−	0.744406i	$-0.267267\pi$
$410$	−6.65585	+	10.9361i	−0.328709	+	0.540097i
$411$		0			0
$412$	9.37834	+	28.8635i	0.462037	+	1.42200i
$413$	−4.44827	−	13.6904i	−0.218885	−	0.673659i
$414$		0			0
$415$	0.346037	+	4.23167i	0.0169863	+	0.207725i
$416$	1.57548	+	4.84884i	0.0772444	+	0.237734i
$417$		0			0
$418$	3.10566			0.151903
$419$	28.7486	−	20.8871i	1.40446	−	1.02040i	0.410364	−	0.911922i	$-0.365402\pi$
$419$	28.7486	−	20.8871i	1.40446	−	1.02040i	0.994099	−	0.108480i	$-0.0345982\pi$
$420$		0			0
$421$	−6.31397	−	4.58737i	−0.307724	−	0.223575i	0.423195	−	0.906039i	$-0.360908\pi$
$421$	−6.31397	−	4.58737i	−0.307724	−	0.223575i	−0.730919	+	0.682464i	$0.760908\pi$
$422$	6.18760	+	4.49555i	0.301207	+	0.218840i
$423$		0			0
$424$	−11.1143			−0.539756
$425$	−11.8867	−	5.96550i	−0.576592	−	0.289369i
$426$		0			0
$427$	1.22713	−	3.77672i	0.0593851	−	0.182769i
$428$	−9.70469	−	7.05087i	−0.469094	−	0.340817i
$429$		0			0
$430$	−6.10247	−	7.10107i	−0.294287	−	0.342444i
$431$	−13.4653	+	9.78311i	−0.648601	+	0.471236i	−0.862794	−	0.505555i	$-0.831288\pi$
$431$	−13.4653	+	9.78311i	−0.648601	+	0.471236i	0.214194	+	0.976791i	$0.431288\pi$
$432$		0			0
$433$	0.0247524	−	0.0179837i	0.00118952	−	0.000864240i	−0.587190	−	0.809449i	$-0.699766\pi$
$433$	0.0247524	−	0.0179837i	0.00118952	−	0.000864240i	0.588380	+	0.808585i	$0.299766\pi$
$434$	0.453448	+	1.39557i	0.0217662	+	0.0669895i
$435$		0			0
$436$	4.75933	−	14.6477i	0.227931	−	0.701498i
$437$	−4.15256	−	12.7803i	−0.198644	−	0.611363i
$438$		0			0
$439$	3.81957	−	11.7554i	0.182298	−	0.561057i	−0.817593	−	0.575797i	$-0.804692\pi$
$439$	3.81957	−	11.7554i	0.182298	−	0.561057i	0.999891	+	0.0147399i	$0.00469204\pi$
$440$	−12.7378	−	3.01698i	−0.607249	−	0.143829i
$441$		0			0
$442$	1.12676	−	0.818637i	0.0535944	−	0.0389386i
$443$	29.8515			1.41829			0.709143	−	0.705065i	$-0.249082\pi$
$443$	29.8515			1.41829			0.709143	+	0.705065i	$0.249082\pi$
$444$		0			0
$445$	−1.66950	−	1.94270i	−0.0791421	−	0.0920929i
$446$	−8.15295	−	5.92346i	−0.386053	−	0.280484i
$447$		0			0
$448$	−0.601866	+	1.85235i	−0.0284355	+	0.0875154i
$449$	−31.5217			−1.48760			−0.743799	−	0.668403i	$-0.766978\pi$
$449$	−31.5217			−1.48760			−0.743799	+	0.668403i	$0.766978\pi$
$450$		0			0
$451$	−30.7967			−1.45016
$452$	6.84769	−	21.0750i	0.322088	−	0.991286i
$453$		0			0
$454$	6.78760	+	4.93148i	0.318558	+	0.231446i
$455$	−2.28816	−	0.541960i	−0.107271	−	0.0254075i
$456$		0			0
$457$	−14.8832			−0.696206			−0.348103	−	0.937456i	$-0.613174\pi$
$457$	−14.8832			−0.696206			−0.348103	+	0.937456i	$0.613174\pi$
$458$	6.84073	−	4.97008i	0.319646	−	0.232237i
$459$		0			0
$460$	2.12526	+	25.9897i	0.0990907	+	1.21178i
$461$	3.24185	−	9.97739i	0.150988	−	0.464694i	−0.846744	−	0.532000i	$-0.821441\pi$
$461$	3.24185	−	9.97739i	0.150988	−	0.464694i	0.997732	+	0.0673066i	$0.0214406\pi$
$462$		0			0
$463$	−5.84565	−	17.9911i	−0.271670	−	0.836115i	−0.990081	−	0.140496i	$-0.955130\pi$
$463$	−5.84565	−	17.9911i	−0.271670	−	0.836115i	0.718411	−	0.695619i	$-0.244870\pi$
$464$	4.89578	−	15.0677i	0.227281	−	0.699498i
$465$		0			0
$466$	3.62137	+	11.1454i	0.167757	+	0.516302i
$467$	10.1969	−	7.40848i	0.471856	−	0.342824i	−0.326308	−	0.945264i	$-0.605805\pi$
$467$	10.1969	−	7.40848i	0.471856	−	0.342824i	0.798164	+	0.602440i	$0.205805\pi$
$468$		0			0
$469$	−7.79058	+	5.66019i	−0.359735	+	0.261363i
$470$	0.890769	+	10.8932i	0.0410881	+	0.502465i
$471$		0			0
$472$	−21.4912	−	15.6143i	−0.989212	−	0.718705i
$473$	6.96004	−	21.4208i	0.320023	−	0.984929i
$474$		0			0
$475$	−8.78684	−	4.40977i	−0.403168	−	0.202334i
$476$	4.93973			0.226412
$477$		0			0
$478$	−6.85213	−	4.97836i	−0.313409	−	0.227705i
$479$	−18.6364	−	13.5401i	−0.851518	−	0.618664i	0.0740459	−	0.997255i	$-0.476409\pi$
$479$	−18.6364	−	13.5401i	−0.851518	−	0.618664i	−0.925564	+	0.378591i	$0.876409\pi$
$480$		0			0
$481$	6.43222	−	4.67328i	0.293284	−	0.213083i
$482$	−5.66247			−0.257918
$483$		0			0
$484$	1.32036	+	4.06366i	0.0600165	+	0.184712i
$485$	−12.7804	+	5.33958i	−0.580330	+	0.242458i
$486$		0			0
$487$	−9.02735	−	27.7833i	−0.409068	−	1.25898i	−0.917450	−	0.397850i	$-0.869756\pi$
$487$	−9.02735	−	27.7833i	−0.409068	−	1.25898i	0.508382	−	0.861132i	$-0.330244\pi$
$488$	−2.26457	−	6.96962i	−0.102512	−	0.315500i
$489$		0			0
$490$	−4.59275	−	5.34431i	−0.207479	−	0.241431i
$491$	11.6621	+	35.8921i	0.526301	+	1.61979i	0.761728	+	0.647897i	$0.224351\pi$
$491$	11.6621	+	35.8921i	0.526301	+	1.61979i	−0.235427	+	0.971892i	$0.575649\pi$
$492$		0			0
$493$	−18.1301			−0.816540
$494$	0.832913	−	0.605147i	0.0374745	−	0.0272268i
$495$		0			0
$496$	−4.67894	−	3.39945i	−0.210090	−	0.152640i
$497$	6.87653	+	4.99609i	0.308455	+	0.224105i
$498$		0			0
$499$	−34.5121			−1.54497			−0.772487	−	0.635031i	$-0.780987\pi$
$499$	−34.5121			−1.54497			−0.772487	+	0.635031i	$0.780987\pi$
$500$	14.6196	+	12.2567i	0.653810	+	0.548134i
$501$		0			0
$502$	−0.721141	+	2.21944i	−0.0321861	+	0.0990586i
$503$	−1.35651	−	0.985565i	−0.0604840	−	0.0439442i	0.557132	−	0.830424i	$-0.311902\pi$
$503$	−1.35651	−	0.985565i	−0.0604840	−	0.0439442i	−0.617616	+	0.786479i	$0.711902\pi$
$504$		0			0
$505$	−4.52093	+	7.42828i	−0.201179	+	0.330554i
$506$	8.73298	−	6.34488i	0.388228	−	0.282064i
$507$		0			0
$508$	−2.34446	+	1.70335i	−0.104019	+	0.0755739i
$509$	2.83938	+	8.73871i	0.125853	+	0.387337i	0.994056	−	0.108874i	$-0.0347245\pi$
$509$	2.83938	+	8.73871i	0.125853	+	0.387337i	−0.868202	+	0.496210i	$0.834724\pi$
$510$		0			0
$511$	5.25648	−	16.1778i	0.232533	−	0.715663i
$512$	6.67511	+	20.5439i	0.295001	+	0.907920i
$513$		0			0
$514$	−4.69952	+	14.4636i	−0.207287	+	0.637963i
$515$	−36.6962	+	15.3314i	−1.61703	+	0.675584i
$516$		0			0
$517$	−21.2704	+	15.4538i	−0.935470	+	0.679659i
$518$	−4.85260			−0.213211
$519$		0			0
$520$	−4.00403	+	1.67286i	−0.175588	+	0.0733597i
$521$	31.5663	+	22.9343i	1.38295	+	1.00477i	0.996598	+	0.0824162i	$0.0262637\pi$
$521$	31.5663	+	22.9343i	1.38295	+	1.00477i	0.386348	+	0.922353i	$0.373736\pi$
$522$		0			0
$523$	−1.71010	+	5.26313i	−0.0747773	+	0.230141i	−0.981458	−	0.191676i	$-0.938608\pi$
$523$	−1.71010	+	5.26313i	−0.0747773	+	0.230141i	0.906681	+	0.421817i	$0.138608\pi$
$524$	−22.8989			−1.00034
$525$		0			0
$526$	13.5705			0.591703
$527$	−2.04519	+	6.29444i	−0.0890898	+	0.274190i
$528$		0			0
$529$	−19.1796	−	13.9348i	−0.833897	−	0.605862i
$530$	−0.546489	−	6.68299i	−0.0237379	−	0.290290i
$531$		0			0
$532$	3.65151			0.158313
$533$	−8.25943	+	6.00083i	−0.357756	+	0.259925i
$534$		0			0
$535$	8.17246	−	13.4280i	0.353326	−	0.580545i
$536$	−5.49147	+	16.9010i	−0.237195	+	0.730012i
$537$		0			0
$538$	0.725372	+	2.23246i	0.0312730	+	0.0962484i
$539$	5.23816	−	16.1214i	0.225624	−	0.694398i
$540$		0			0
$541$	−4.05717	−	12.4867i	−0.174431	−	0.536844i	0.825176	−	0.564876i	$-0.191076\pi$
$541$	−4.05717	−	12.4867i	−0.174431	−	0.536844i	−0.999607	+	0.0280318i	$0.991076\pi$
$542$	10.3197	−	7.49768i	0.443268	−	0.322053i
$543$		0			0
$544$	11.3544	−	8.24949i	0.486818	−	0.353694i
$545$	19.6392	+	4.65162i	0.841253	+	0.199254i
$546$		0			0
$547$	20.7349	+	15.0648i	0.886562	+	0.644125i	0.934979	−	0.354702i	$-0.115418\pi$
$547$	20.7349	+	15.0648i	0.886562	+	0.644125i	−0.0484176	+	0.998827i	$0.515418\pi$
$548$	3.00698	−	9.25452i	0.128452	−	0.395333i
$549$		0			0
$550$	1.18779	−	7.80753i	0.0506475	−	0.332914i
$551$	−13.4020			−0.570946
$552$		0			0
$553$	5.81567	+	4.22533i	0.247308	+	0.179679i
$554$	−6.99950	−	5.08543i	−0.297380	−	0.216059i
$555$		0			0
$556$	−26.6399	+	19.3550i	−1.12978	+	0.820834i
$557$	38.4002			1.62707			0.813534	−	0.581517i	$-0.197541\pi$
$557$	38.4002			1.62707			0.813534	+	0.581517i	$0.197541\pi$
$558$		0			0
$559$	−2.30728	−	7.10107i	−0.0975875	−	0.300343i
$560$	−5.50431	−	1.30371i	−0.232599	−	0.0550920i
$561$		0			0
$562$	−2.73190	−	8.40791i	−0.115238	−	0.354666i
$563$	−6.95797	−	21.4144i	−0.293244	−	0.902511i	−0.983806	−	0.179238i	$-0.942637\pi$
$563$	−6.95797	−	21.4144i	−0.293244	−	0.902511i	0.690562	−	0.723273i	$-0.257363\pi$
$564$		0			0
$565$	28.2568	+	6.69272i	1.18877	+	0.281565i
$566$	2.89220	+	8.90129i	0.121568	+	0.374149i
$567$		0			0
$568$	15.6858			0.658160
$569$	−19.6403	+	14.2695i	−0.823366	+	0.598210i	−0.917675	−	0.397333i	$-0.869936\pi$
$569$	−19.6403	+	14.2695i	−0.823366	+	0.598210i	0.0943089	+	0.995543i	$0.469936\pi$
$570$		0			0
$571$	−12.4149	−	9.01996i	−0.519548	−	0.377474i	0.296886	−	0.954913i	$-0.404052\pi$
$571$	−12.4149	−	9.01996i	−0.519548	−	0.377474i	−0.816434	+	0.577439i	$0.804052\pi$
$572$	−3.88803	−	2.82482i	−0.162567	−	0.118112i
$573$		0			0
$574$	6.23108			0.260080
$575$	−33.7174	+	5.55148i	−1.40611	+	0.231513i
$576$		0			0
$577$	−3.16623	+	9.74466i	−0.131812	+	0.405675i	−0.995081	−	0.0990695i	$-0.968413\pi$
$577$	−3.16623	+	9.74466i	−0.131812	+	0.405675i	0.863269	+	0.504745i	$0.168413\pi$
$578$	4.35093	+	3.16113i	0.180975	+	0.131486i
$579$		0			0
$580$	25.3066	+	5.99394i	1.05080	+	0.248885i
$581$	1.67183	−	1.21465i	0.0693591	−	0.0503924i
$582$		0			0
$583$	13.0494	−	9.48095i	0.540451	−	0.392661i
$584$	−9.70039	−	29.8547i	−0.401405	−	1.23540i
$585$		0			0
$586$	−3.43043	+	10.5578i	−0.141710	+	0.436138i
$587$	11.1976	+	34.4627i	0.462175	+	1.42243i	0.862501	+	0.506055i	$0.168897\pi$
$587$	11.1976	+	34.4627i	0.462175	+	1.42243i	−0.400327	+	0.916372i	$0.631103\pi$
$588$		0			0
$589$	−1.51183	+	4.65293i	−0.0622939	+	0.191721i
$590$	8.33211	−	13.6904i	0.343027	−	0.563624i
$591$		0			0
$592$	15.4731	−	11.2418i	0.635939	−	0.462037i
$593$	5.53608			0.227339			0.113670	−	0.993519i	$-0.463739\pi$
$593$	5.53608			0.227339			0.113670	+	0.993519i	$0.463739\pi$
$594$		0			0
$595$	0.527570	+	6.45163i	0.0216283	+	0.264491i
$596$	23.5088	+	17.0801i	0.962958	+	0.699630i
$597$		0			0
$598$	1.10580	−	3.40329i	0.0452194	−	0.139171i
$599$	−22.4935			−0.919059			−0.459530	−	0.888162i	$-0.651982\pi$
$599$	−22.4935			−0.919059			−0.459530	+	0.888162i	$0.651982\pi$
$600$		0			0
$601$	8.51096			0.347169			0.173585	−	0.984819i	$-0.444465\pi$
$601$	8.51096			0.347169			0.173585	+	0.984819i	$0.444465\pi$
$602$	−1.40822	+	4.33406i	−0.0573948	+	0.176643i
$603$		0			0
$604$	−0.954559	−	0.693528i	−0.0388404	−	0.0282192i
$605$	−5.16641	+	2.15849i	−0.210044	+	0.0877552i
$606$		0			0
$607$	28.6926			1.16460			0.582298	−	0.812975i	$-0.302154\pi$
$607$	28.6926			1.16460			0.582298	+	0.812975i	$0.302154\pi$
$608$	8.39335	−	6.09813i	0.340395	−	0.247312i
$609$		0			0
$610$	4.07947	−	1.70438i	0.165173	−	0.0690082i
$611$	−2.69332	+	8.28919i	−0.108960	+	0.335345i
$612$		0			0
$613$	5.09174	+	15.6708i	0.205653	+	0.632936i	0.999686	+	0.0250610i	$0.00797799\pi$
$613$	5.09174	+	15.6708i	0.205653	+	0.632936i	−0.794032	+	0.607875i	$0.792022\pi$
$614$	0.264149	−	0.812968i	0.0106602	−	0.0328087i
$615$		0			0
$616$	1.96880	+	6.05936i	0.0793254	+	0.244138i
$617$	8.08557	−	5.87451i	0.325513	−	0.236499i	−0.413012	−	0.910726i	$-0.635523\pi$
$617$	8.08557	−	5.87451i	0.325513	−	0.236499i	0.738524	+	0.674227i	$0.235523\pi$
$618$		0			0
$619$	0.0893807	−	0.0649389i	0.00359251	−	0.00261011i	−0.585988	−	0.810320i	$-0.699293\pi$
$619$	0.0893807	−	0.0649389i	0.00359251	−	0.00261011i	0.589580	+	0.807710i	$0.299293\pi$
$620$	4.93572	−	8.10981i	0.198223	−	0.325698i
$621$		0			0
$622$	5.77562	+	4.19624i	0.231581	+	0.168254i
$623$	−0.385260	+	1.18571i	−0.0154351	+	0.0475044i
$624$		0			0
$625$	−14.4467	+	20.4033i	−0.577866	+	0.816132i
$626$	9.99185			0.399355
$627$		0			0
$628$	−0.618874	−	0.449638i	−0.0246957	−	0.0179425i
$629$	−17.7067	−	12.8647i	−0.706013	−	0.512948i
$630$		0			0
$631$	22.4429	−	16.3057i	0.893438	−	0.649121i	−0.0433339	−	0.999061i	$-0.513798\pi$
$631$	22.4429	−	16.3057i	0.893438	−	0.649121i	0.936772	+	0.349940i	$0.113798\pi$
$632$	13.2659			0.527689
$633$		0			0
$634$	0.118553	+	0.364868i	0.00470834	+	0.0144908i
$635$	−2.47508	−	2.88011i	−0.0982207	−	0.114294i
$636$		0			0
$637$	−1.73647	−	5.34431i	−0.0688014	−	0.211749i
$638$	−3.32678	−	10.2388i	−0.131708	−	0.405357i
$639$		0			0
$640$	−23.7737	+	9.93250i	−0.939738	+	0.392616i
$641$	−8.19865	−	25.2329i	−0.323827	−	0.996638i	−0.971967	−	0.235117i	$-0.924453\pi$
$641$	−8.19865	−	25.2329i	−0.323827	−	0.996638i	0.648140	−	0.761521i	$-0.275547\pi$
$642$		0			0
$643$	26.7379			1.05444			0.527220	−	0.849729i	$-0.323234\pi$
$643$	26.7379			1.05444			0.527220	+	0.849729i	$0.323234\pi$
$644$	10.2679	−	7.46006i	0.404612	−	0.293968i
$645$		0			0
$646$	−2.29286	−	1.66586i	−0.0902112	−	0.0655423i
$647$	23.9789	+	17.4217i	0.942708	+	0.684917i	0.949071	−	0.315063i	$-0.102026\pi$
$647$	23.9789	+	17.4217i	0.942708	+	0.684917i	−0.00636329	+	0.999980i	$0.502026\pi$
$648$		0			0
$649$	38.5528			1.51333
$650$	−1.20277	−	2.32536i	−0.0471763	−	0.0912083i
$651$		0			0
$652$	−5.22748	+	16.0885i	−0.204724	+	0.630076i
$653$	−10.9720	−	7.97163i	−0.429368	−	0.311954i	0.352028	−	0.935989i	$-0.385492\pi$
$653$	−10.9720	−	7.97163i	−0.429368	−	0.311954i	−0.781396	+	0.624035i	$0.785492\pi$
$654$		0			0
$655$	−2.44563	−	29.9075i	−0.0955587	−	1.16858i
$656$	−19.8685	+	14.4353i	−0.775735	+	0.563605i
$657$		0			0
$658$	4.30363	−	3.12677i	0.167773	−	0.121894i
$659$	−0.196198	−	0.603835i	−0.00764279	−	0.0235221i	0.947162	−	0.320754i	$-0.103936\pi$
$659$	−0.196198	−	0.603835i	−0.00764279	−	0.0235221i	−0.954805	+	0.297232i	$0.903936\pi$
$660$		0			0
$661$	−3.39475	+	10.4480i	−0.132041	+	0.406379i	−0.995118	−	0.0986926i	$-0.968534\pi$
$661$	−3.39475	+	10.4480i	−0.132041	+	0.406379i	0.863077	+	0.505072i	$0.168534\pi$
$662$	−1.38152	−	4.25187i	−0.0536941	−	0.165254i
$663$		0			0
$664$	1.17845	−	3.62689i	0.0457326	−	0.140751i
$665$	0.389986	+	4.76913i	0.0151230	+	0.184939i
$666$		0			0
$667$	−37.6859	+	27.3804i	−1.45921	+	1.06017i
$668$	−32.2838			−1.24910
$669$		0			0
$670$	−10.4326	−	2.47099i	−0.403045	−	0.0954625i
$671$	8.60425	+	6.25136i	0.332164	+	0.241331i
$672$		0			0
$673$	−4.49212	+	13.8253i	−0.173158	+	0.532927i	−0.999545	−	0.0301771i	$-0.990393\pi$
$673$	−4.49212	+	13.8253i	−0.173158	+	0.532927i	0.826386	+	0.563104i	$0.190393\pi$
$674$	−1.40191			−0.0539997
$675$		0			0
$676$	20.5895			0.791906
$677$	8.10777	−	24.9531i	0.311607	−	0.959027i	−0.665522	−	0.746378i	$-0.731791\pi$
$677$	8.10777	−	24.9531i	0.311607	−	0.959027i	0.977129	−	0.212649i	$-0.0682090\pi$
$678$		0			0
$679$	5.45399	+	3.96256i	0.209305	+	0.152069i
$680$	7.78578	+	9.05984i	0.298571	+	0.347429i
$681$		0			0
$682$	−3.92999			−0.150487
$683$	32.3719	−	23.5196i	1.23868	−	0.899951i	0.241167	−	0.970484i	$-0.422470\pi$
$683$	32.3719	−	23.5196i	1.23868	−	0.899951i	0.997509	+	0.0705328i	$0.0224700\pi$
$684$		0			0
$685$	12.4082	+	2.93893i	0.474093	+	0.112291i
$686$	−2.33553	+	7.18802i	−0.0891709	+	0.274440i
$687$		0			0
$688$	−5.55029	−	17.0820i	−0.211603	−	0.651246i
$689$	1.65236	−	5.08543i	0.0629498	−	0.193740i
$690$		0			0
$691$	8.36431	+	25.7427i	0.318193	+	0.979298i	0.974420	+	0.224734i	$0.0721515\pi$
$691$	8.36431	+	25.7427i	0.318193	+	0.979298i	−0.656227	+	0.754564i	$0.727849\pi$
$692$	−16.5694	+	12.0383i	−0.629872	+	0.457629i
$693$		0			0
$694$	−6.74522	+	4.90069i	−0.256045	+	0.186028i
$695$	−28.1241	−	32.7264i	−1.06681	−	1.24138i
$696$		0			0
$697$	22.7367	+	16.5192i	0.861213	+	0.625708i
$698$	0.312348	−	0.961310i	0.0118226	−	0.0363861i
$699$		0			0
$700$	1.39656	−	9.17979i	0.0527849	−	0.346963i
$701$	34.7236			1.31149			0.655745	−	0.754982i	$-0.272354\pi$
$701$	34.7236			1.31149			0.655745	+	0.754982i	$0.272354\pi$
$702$		0			0
$703$	−13.0890	−	9.50973i	−0.493662	−	0.358666i
$704$	−4.22009	−	3.06607i	−0.159050	−	0.115557i
$705$		0			0
$706$	−1.43528	+	1.04279i	−0.0540174	+	0.0392460i
$707$	4.23241			0.159176
$708$		0			0
$709$	11.7018	+	36.0146i	0.439472	+	1.35256i	0.888434	+	0.459005i	$0.151794\pi$
$709$	11.7018	+	36.0146i	0.439472	+	1.35256i	−0.448962	+	0.893551i	$0.648206\pi$
$710$	0.771270	+	9.43183i	0.0289452	+	0.353970i
$711$		0			0
$712$	0.710964	+	2.18812i	0.0266445	+	0.0820033i
$713$	5.25478	+	16.1725i	0.196793	+	0.605666i
$714$		0			0
$715$	3.27417	−	5.37974i	0.122447	−	0.201191i
$716$	4.80304	+	14.7822i	0.179498	+	0.552439i
$717$		0			0
$718$	−4.04889			−0.151103
$719$	−10.4762	+	7.61139i	−0.390696	+	0.283857i	−0.765740	−	0.643150i	$-0.777627\pi$
$719$	−10.4762	+	7.61139i	−0.390696	+	0.283857i	0.375045	+	0.927007i	$0.377627\pi$
$720$		0			0
$721$	15.6599	+	11.3776i	0.583206	+	0.423724i
$722$	6.63456	+	4.82029i	0.246913	+	0.179393i
$723$		0			0
$724$	10.3971			0.386406
$725$	−5.12574	+	33.6923i	−0.190365	+	1.25130i
$726$		0			0
$727$	12.3895	−	38.1308i	0.459500	−	1.41419i	−0.406270	−	0.913753i	$-0.633171\pi$
$727$	12.3895	−	38.1308i	0.459500	−	1.41419i	0.865770	−	0.500442i	$-0.166829\pi$
$728$	1.70870	+	1.24144i	0.0633287	+	0.0460110i
$729$		0			0
$730$	17.4746	−	7.30078i	0.646765	−	0.270214i
$731$	−16.6285	+	12.0813i	−0.615026	+	0.446843i
$732$		0			0
$733$	−12.3797	+	8.99437i	−0.457254	+	0.332214i	−0.792453	−	0.609933i	$-0.791196\pi$
$733$	−12.3797	+	8.99437i	−0.457254	+	0.332214i	0.335199	+	0.942147i	$0.391196\pi$
$734$	−0.798578	−	2.45777i	−0.0294760	−	0.0907179i
$735$		0			0
$736$	11.1432	−	34.2954i	0.410745	−	1.26414i
$737$	−7.96968	−	24.5282i	−0.293567	−	0.903506i
$738$		0			0
$739$	4.77650	−	14.7006i	0.175706	−	0.540768i	−0.823959	−	0.566650i	$-0.808239\pi$
$739$	4.77650	−	14.7006i	0.175706	−	0.540768i	0.999665	+	0.0258814i	$0.00823922\pi$
$740$	20.4624	+	23.8108i	0.752212	+	0.875304i
$741$		0			0
$742$	−2.64028	+	1.91828i	−0.0969278	+	0.0704222i
$743$	−2.02309			−0.0742199			−0.0371100	−	0.999311i	$-0.511815\pi$
$743$	−2.02309			−0.0742199			−0.0371100	+	0.999311i	$0.511815\pi$
$744$		0			0
$745$	−19.7971	+	32.5283i	−0.725310	+	1.19175i
$746$	−12.1445	−	8.82353i	−0.444643	−	0.323052i
$747$		0			0
$748$	−4.08820	+	12.5822i	−0.149479	+	0.460050i
$749$	−7.65090			−0.279558
$750$		0			0
$751$	5.78809			0.211210			0.105605	−	0.994408i	$-0.466322\pi$
$751$	5.78809			0.211210			0.105605	+	0.994408i	$0.466322\pi$
$752$	−6.47893	+	19.9401i	−0.236262	+	0.727141i
$753$		0			0
$754$	−2.88727	−	2.09773i	−0.105148	−	0.0763946i
$755$	0.803848	−	1.32079i	0.0292550	−	0.0480685i
$756$		0			0
$757$	44.7826			1.62765			0.813826	−	0.581109i	$-0.197381\pi$
$757$	44.7826			1.62765			0.813826	+	0.581109i	$0.197381\pi$
$758$	7.38399	−	5.36479i	0.268199	−	0.194858i
$759$		0			0
$760$	5.75535	+	6.69715i	0.208768	+	0.242931i
$761$	4.23262	−	13.0267i	0.153432	−	0.472216i	−0.844566	−	0.535451i	$-0.820142\pi$
$761$	4.23262	−	13.0267i	0.153432	−	0.472216i	0.997999	+	0.0632347i	$0.0201417\pi$
$762$		0			0
$763$	−3.03553	−	9.34240i	−0.109894	−	0.338218i
$764$	4.87871	−	15.0151i	0.176506	−	0.543228i
$765$		0			0
$766$	−2.20988	−	6.80130i	−0.0798461	−	0.245741i
$767$	10.3395	−	7.51212i	0.373339	−	0.271247i
$768$		0			0
$769$	−16.5102	+	11.9954i	−0.595373	+	0.432564i	−0.844234	−	0.535975i	$-0.819944\pi$
$769$	−16.5102	+	11.9954i	−0.595373	+	0.432564i	0.248860	+	0.968539i	$0.419944\pi$
$770$	−3.54667	+	1.48178i	−0.127813	+	0.0533995i
$771$		0			0
$772$	−33.4957	−	24.3360i	−1.20554	−	0.875873i
$773$	1.25986	−	3.87745i	0.0453140	−	0.139462i	−0.925840	−	0.377916i	$-0.876641\pi$
$773$	1.25986	−	3.87745i	0.0453140	−	0.139462i	0.971154	+	0.238454i	$0.0766407\pi$
$774$		0			0
$775$	11.1191	+	5.58026i	0.399411	+	0.200449i
$776$	12.4409			0.446601
$777$		0			0
$778$	6.51990	+	4.73698i	0.233750	+	0.169829i
$779$	16.8072	+	12.2112i	0.602182	+	0.437511i
$780$		0			0
$781$	−18.4169	+	13.3806i	−0.659008	+	0.478797i
$782$	−9.85077			−0.352263
$783$		0			0
$784$	−4.17718	−	12.8560i	−0.149185	−	0.459144i
$785$	0.521162	−	0.856314i	0.0186011	−	0.0305632i
$786$		0			0
$787$	−9.73607	−	29.9645i	−0.347053	−	1.06812i	−0.960475	−	0.278365i	$-0.910207\pi$
$787$	−9.73607	−	29.9645i	−0.347053	−	1.06812i	0.613422	−	0.789755i	$-0.289793\pi$
$788$	−6.67705	−	20.5499i	−0.237860	−	0.732058i
$789$		0			0
$790$	0.652284	+	7.97676i	0.0232072	+	0.283800i
$791$	−4.36750	−	13.4418i	−0.155290	−	0.477935i
$792$		0			0
$793$	3.52569			0.125201
$794$	4.31866	−	3.13769i	0.153264	−	0.111353i
$795$		0			0
$796$	−19.0898	−	13.8696i	−0.676621	−	0.491594i
$797$	−29.0512	−	21.1069i	−1.02905	−	0.747646i	−0.0609293	−	0.998142i	$-0.519406\pi$
$797$	−29.0512	−	21.1069i	−1.02905	−	0.747646i	−0.968118	+	0.250496i	$0.919406\pi$
$798$		0			0
$799$	23.9929			0.848808
$800$	−12.1204	−	23.4329i	−0.428521	−	0.828479i
$801$		0			0
$802$	−0.319392	+	0.982989i	−0.0112781	+	0.0347105i
$803$	36.8567	+	26.7780i	1.30065	+	0.944975i
$804$		0			0
$805$	10.8400	+	12.6138i	0.382059	+	0.444580i
$806$	−1.05399	+	0.765771i	−0.0371253	+	0.0269731i
$807$		0			0
$808$	6.31887	−	4.59093i	0.222297	−	0.161508i
$809$	16.2431	+	49.9910i	0.571076	+	1.75759i	0.649169	+	0.760644i	$0.275117\pi$
$809$	16.2431	+	49.9910i	0.571076	+	1.75759i	−0.0780930	+	0.996946i	$0.524883\pi$
$810$		0			0
$811$	−4.40971	+	13.5717i	−0.154846	+	0.476567i	−0.998145	−	0.0608773i	$-0.980610\pi$
$811$	−4.40971	+	13.5717i	−0.154846	+	0.476567i	0.843299	+	0.537444i	$0.180610\pi$
$812$	−3.91149	−	12.0383i	−0.137267	−	0.422463i
$813$		0			0
$814$	4.01609	−	12.3602i	0.140764	−	0.433226i
$815$	−21.5711	−	5.10918i	−0.755602	−	0.178967i
$816$		0			0
$817$	−12.2920	+	8.93065i	−0.430042	+	0.312444i
$818$	−10.9947			−0.384421
$819$		0			0
$820$	−26.2752	−	30.5748i	−0.917568	−	1.06772i
$821$	−18.9927	−	13.7990i	−0.662851	−	0.481589i	0.204774	−	0.978809i	$-0.434354\pi$
$821$	−18.9927	−	13.7990i	−0.662851	−	0.481589i	−0.867624	+	0.497220i	$0.834354\pi$
$822$		0			0
$823$	−11.3829	+	35.0328i	−0.396781	+	1.22117i	0.530784	+	0.847507i	$0.321898\pi$
$823$	−11.3829	+	35.0328i	−0.396781	+	1.22117i	−0.927566	+	0.373661i	$0.878102\pi$
$824$	35.7212			1.24441
$825$		0			0
$826$	−7.80036			−0.271409
$827$	4.72636	−	14.5462i	0.164352	−	0.505822i	−0.834636	−	0.550801i	$-0.814322\pi$
$827$	4.72636	−	14.5462i	0.164352	−	0.505822i	0.998988	+	0.0449792i	$0.0143222\pi$
$828$		0			0
$829$	−25.5445	−	18.5592i	−0.887198	−	0.644587i	0.0479481	−	0.998850i	$-0.484732\pi$
$829$	−25.5445	−	18.5592i	−0.887198	−	0.644587i	−0.935146	+	0.354263i	$0.884732\pi$
$830$	2.23879	+	0.530264i	0.0777094	+	0.0184057i
$831$		0			0
$832$	−1.72923			−0.0599502
$833$	−12.5147	+	9.09244i	−0.433608	+	0.315035i
$834$		0			0
$835$	−3.44796	−	42.1649i	−0.119321	−	1.45918i
$836$	−3.02205	+	9.30091i	−0.104520	+	0.321679i
$837$		0			0
$838$	−5.95042	−	18.3135i	−0.205554	−	0.632630i
$839$	3.97764	−	12.2419i	0.137323	−	0.422638i	−0.858621	−	0.512611i	$-0.828678\pi$
$839$	3.97764	−	12.2419i	0.137323	−	0.422638i	0.995944	+	0.0899734i	$0.0286782\pi$
$840$		0			0
$841$	5.39475	+	16.6033i	0.186026	+	0.572529i
$842$	−3.42144	+	2.48582i	−0.117911	+	0.0856670i
$843$		0			0
$844$	−19.4844	+	14.1562i	−0.670681	+	0.487278i
$845$	2.19899	+	26.8914i	0.0756476	+	0.925092i
$846$		0			0
$847$	2.20474	+	1.60184i	0.0757558	+	0.0550398i
$848$	3.97484	−	12.2333i	0.136496	−	0.420093i
$849$		0			0
$850$	−5.06484	+	5.12705i	−0.173723	+	0.175856i
$851$	−56.2342			−1.92768
$852$		0			0
$853$	−23.5227	−	17.0903i	−0.805403	−	0.585160i	0.107091	−	0.994249i	$-0.465846\pi$
$853$	−23.5227	−	17.0903i	−0.805403	−	0.585160i	−0.912494	+	0.409090i	$0.865846\pi$
$854$	−1.74090	−	1.26483i	−0.0595722	−	0.0432817i
$855$		0			0
$856$	−11.4226	+	8.29899i	−0.390416	+	0.283654i
$857$	−5.81897			−0.198772			−0.0993862	−	0.995049i	$-0.531688\pi$
$857$	−5.81897			−0.198772			−0.0993862	+	0.995049i	$0.531688\pi$
$858$		0			0
$859$	2.39087	+	7.35834i	0.0815755	+	0.251063i	0.983523	−	0.180782i	$-0.0578627\pi$
$859$	2.39087	+	7.35834i	0.0815755	+	0.251063i	−0.901948	+	0.431845i	$0.857863\pi$
$860$	27.2046	−	11.3659i	0.927671	−	0.387575i
$861$		0			0
$862$	2.78706	+	8.57770i	0.0949277	+	0.292158i
$863$	14.0642	+	43.2852i	0.478751	+	1.47345i	0.840831	+	0.541298i	$0.182067\pi$
$863$	14.0642	+	43.2852i	0.478751	+	1.47345i	−0.362079	+	0.932147i	$0.617933\pi$
$864$		0			0
$865$	−17.4925	−	20.3550i	−0.594765	−	0.692092i
$866$	−0.00512328	−	0.0157678i	−0.000174096	−	0.000535812i
$867$		0			0
$868$	−4.62073			−0.156838
$869$	−15.5757	+	11.3164i	−0.528368	+	0.383882i
$870$		0			0
$871$	−6.91679	−	5.02534i	−0.234366	−	0.170277i
$872$	−14.6657	−	10.6553i	−0.496644	−	0.360833i
$873$		0			0
$874$	−7.28182			−0.246311
$875$	12.1386	+	0.843586i	0.410360	+	0.0285184i
$876$		0			0
$877$	−4.58403	+	14.1082i	−0.154792	+	0.476399i	−0.998140	−	0.0609682i	$-0.980581\pi$
$877$	−4.58403	+	14.1082i	−0.154792	+	0.476399i	0.843348	+	0.537368i	$0.180581\pi$
$878$	−5.41871	−	3.93693i	−0.182873	−	0.132865i
$879$		0			0
$880$	7.87619	−	12.9413i	0.265506	−	0.436250i
$881$	14.1895	−	10.3093i	0.478058	−	0.347329i	−0.322515	−	0.946564i	$-0.604528\pi$
$881$	14.1895	−	10.3093i	0.478058	−	0.347329i	0.800573	+	0.599235i	$0.204528\pi$
$882$		0			0
$883$	−10.2678	+	7.46001i	−0.345540	+	0.251049i	−0.746996	−	0.664829i	$-0.768504\pi$
$883$	−10.2678	+	7.46001i	−0.345540	+	0.251049i	0.401456	+	0.915878i	$0.368504\pi$
$884$	1.35525	+	4.17104i	0.0455821	+	0.140287i
$885$		0			0
$886$	4.99866	−	15.3843i	0.167933	−	0.516846i
$887$	6.97166	+	21.4566i	0.234086	+	0.720441i	0.997241	+	0.0742268i	$0.0236489\pi$
$887$	6.97166	+	21.4566i	0.234086	+	0.720441i	−0.763156	+	0.646215i	$0.776351\pi$
$888$		0			0
$889$	−0.571158	+	1.75784i	−0.0191560	+	0.0589561i
$890$	−1.28076	+	0.535091i	−0.0429310	+	0.0179363i
$891$		0			0
$892$	25.6732	−	18.6527i	0.859602	−	0.624537i
$893$	17.7359			0.593508
$894$		0			0
$895$	−18.7937	+	7.85188i	−0.628204	+	0.262459i
$896$	10.1453	+	7.37100i	0.338931	+	0.246248i
$897$		0			0
$898$	−5.27834	+	16.2451i	−0.176140	+	0.542105i
$899$	16.9593			0.565625
$900$		0			0
$901$	−14.7197			−0.490384
$902$	−5.15694	+	15.8714i	−0.171707	+	0.528461i
$903$		0			0
$904$	−21.1009	−	15.3307i	−0.701807	−	0.509893i
$905$	1.11043	+	13.5794i	0.0369119	+	0.451394i
$906$		0			0
$907$	−40.3527			−1.33989			−0.669945	−	0.742411i	$-0.733682\pi$
$907$	−40.3527			−1.33989			−0.669945	+	0.742411i	$0.733682\pi$
$908$	−21.3738	+	15.5290i	−0.709314	+	0.515346i
$909$		0			0
$910$	−0.662461	+	1.08848i	−0.0219604	+	0.0360828i
$911$	9.55502	−	29.4073i	0.316572	−	0.974308i	−0.658531	−	0.752554i	$-0.728822\pi$
$911$	9.55502	−	29.4073i	0.316572	−	0.974308i	0.975103	−	0.221754i	$-0.0711783\pi$
$912$		0			0
$913$	1.71026	+	5.26365i	0.0566014	+	0.174201i
$914$	−2.49221	+	7.67022i	−0.0824349	+	0.253708i
$915$		0			0
$916$	8.22797	+	25.3231i	0.271860	+	0.836698i
$917$	−11.8157	+	8.58462i	−0.390189	+	0.283489i
$918$		0			0
$919$	19.9965	−	14.5283i	0.659625	−	0.479245i	−0.206911	−	0.978360i	$-0.566341\pi$
$919$	19.9965	−	14.5283i	0.659625	−	0.479245i	0.866536	+	0.499114i	$0.166341\pi$
$920$	29.8661	+	7.07390i	0.984657	+	0.233219i
$921$		0			0
$922$	−4.59912	−	3.34145i	−0.151464	−	0.110045i
$923$	−2.33200	+	7.17717i	−0.0767588	+	0.236239i
$924$		0			0
$925$	−28.9132	+	29.2683i	−0.950661	+	0.962337i
$926$	−10.2508			−0.336861
$927$		0			0
$928$	−29.0953	−	21.1390i	−0.955101	−	0.693922i
$929$	35.7481	+	25.9725i	1.17286	+	0.852131i	0.991348	−	0.131258i	$-0.0419016\pi$
$929$	35.7481	+	25.9725i	1.17286	+	0.852131i	0.181510	+	0.983389i	$0.441902\pi$
$930$		0			0
$931$	−9.25101	+	6.72125i	−0.303190	+	0.220280i
$932$	−36.9025			−1.20878
$933$		0			0
$934$	−2.11057	−	6.49566i	−0.0690598	−	0.212544i
$935$	−16.8698	−	3.99568i	−0.551703	−	0.130673i
$936$		0			0
$937$	−12.3012	−	37.8591i	−0.401862	−	1.23680i	−0.923488	−	0.383628i	$-0.874674\pi$
$937$	−12.3012	−	37.8591i	−0.401862	−	1.23680i	0.521626	−	0.853174i	$-0.325326\pi$
$938$	1.61250	+	4.96277i	0.0526501	+	0.162040i
$939$		0			0
$940$	−33.4900	−	7.93222i	−1.09232	−	0.258720i
$941$	−5.11938	−	15.7558i	−0.166887	−	0.513626i	0.832283	−	0.554351i	$-0.187033\pi$
$941$	−5.11938	−	15.7558i	−0.166887	−	0.513626i	−0.999170	+	0.0407249i	$0.987033\pi$
$942$		0			0
$943$	72.2088			2.35144
$944$	24.8723	−	18.0708i	0.809526	−	0.588155i
$945$		0			0
$946$	−9.87400	−	7.17388i	−0.321031	−	0.233243i
$947$	1.78180	+	1.29456i	0.0579008	+	0.0420674i	0.616359	−	0.787465i	$-0.288607\pi$
$947$	1.78180	+	1.29456i	0.0579008	+	0.0420674i	−0.558458	+	0.829533i	$0.688607\pi$
$948$		0			0
$949$	15.1025			0.490247
$950$	−3.74400	+	3.78998i	−0.121471	+	0.122963i
$951$		0			0
$952$	1.79667	−	5.52958i	0.0582303	−	0.179215i
$953$	−23.3773	−	16.9846i	−0.757267	−	0.550186i	0.140804	−	0.990037i	$-0.455031\pi$
$953$	−23.3773	−	16.9846i	−0.757267	−	0.550186i	−0.898071	+	0.439851i	$0.855031\pi$
$954$		0			0
$955$	20.1319	+	4.76830i	0.651452	+	0.154299i
$956$	21.5770	−	15.6766i	0.697849	−	0.507017i
$957$		0			0
$958$	−10.0988	+	7.33717i	−0.326276	+	0.237053i
$959$	−1.91787	−	5.90259i	−0.0619312	−	0.190605i
$960$		0			0
$961$	−7.66641	+	23.5948i	−0.247304	+	0.761122i
$962$	−1.33135	−	4.09747i	−0.0429244	−	0.132108i
$963$		0			0
$964$	5.51002	−	16.9581i	0.177466	−	0.546184i
$965$	28.2072	−	46.3468i	0.908021	−	1.49196i
$966$		0			0
$967$	−11.6208	+	8.44300i	−0.373700	+	0.271509i	−0.758743	−	0.651390i	$-0.774186\pi$
$967$	−11.6208	+	8.44300i	−0.373700	+	0.271509i	0.385044	+	0.922898i	$0.374186\pi$
$968$	5.02914			0.161643
$969$		0			0
$970$	0.611718	+	7.48067i	0.0196411	+	0.240190i
$971$	−39.5793	−	28.7561i	−1.27016	−	0.922826i	−0.270952	−	0.962593i	$-0.587339\pi$
$971$	−39.5793	−	28.7561i	−1.27016	−	0.922826i	−0.999209	+	0.0397664i	$0.987339\pi$
$972$		0			0
$973$	−6.49001	+	19.9742i	−0.208060	+	0.640343i
$974$	−15.8301			−0.507229
$975$		0			0
$976$	8.48124			0.271478
$977$	13.0168	−	40.0617i	0.416446	−	1.28169i	−0.494506	−	0.869174i	$-0.664651\pi$
$977$	13.0168	−	40.0617i	0.416446	−	1.28169i	0.910952	−	0.412513i	$-0.135349\pi$
$978$		0			0
$979$	−2.70132	−	1.96262i	−0.0863344	−	0.0627256i
$980$	20.4744	−	8.55405i	0.654030	−	0.273249i
$981$		0			0
$982$	20.4503			0.652594
$983$	−19.3125	+	14.0313i	−0.615972	+	0.447530i	−0.851512	−	0.524335i	$-0.824314\pi$
$983$	−19.3125	+	14.0313i	−0.615972	+	0.447530i	0.235540	+	0.971865i	$0.424314\pi$
$984$		0			0
$985$	26.1264	−	10.9155i	0.832458	−	0.347795i
$986$	−3.03591	+	9.34358i	−0.0966832	+	0.297560i
$987$		0			0
$988$	1.00182	+	3.08328i	0.0318721	+	0.0980923i
$989$	−16.3192	+	50.2252i	−0.518919	+	1.59707i
$990$		0			0
$991$	−18.5634	−	57.1321i	−0.589685	−	1.81486i	−0.579583	−	0.814913i	$-0.696784\pi$
$991$	−18.5634	−	57.1321i	−0.589685	−	1.81486i	−0.0101017	−	0.999949i	$-0.503216\pi$
$992$	−10.6212	+	7.71675i	−0.337223	+	0.245007i
$993$		0			0
$994$	3.72628	−	2.70730i	0.118190	−	0.0858704i
$995$	16.0758	−	26.4139i	0.509637	−	0.837378i
$996$		0			0
$997$	21.8166	+	15.8507i	0.690938	+	0.501996i	0.876968	−	0.480548i	$-0.159562\pi$
$997$	21.8166	+	15.8507i	0.690938	+	0.501996i	−0.186030	+	0.982544i	$0.559562\pi$
$998$	−5.77909	+	17.7862i	−0.182934	+	0.563013i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.h.e.46.3	yes	16
3.2	odd	2	inner	225.2.h.e.46.2	✓	16
25.6	even	5	inner	225.2.h.e.181.3	yes	16
25.9	even	10		5625.2.a.v.1.4		8
25.16	even	5		5625.2.a.w.1.5		8
75.41	odd	10		5625.2.a.w.1.4		8
75.56	odd	10	inner	225.2.h.e.181.2	yes	16
75.59	odd	10		5625.2.a.v.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.h.e.46.2	✓	16	3.2	odd	2	inner
225.2.h.e.46.3	yes	16	1.1	even	1	trivial
225.2.h.e.181.2	yes	16	75.56	odd	10	inner
225.2.h.e.181.3	yes	16	25.6	even	5	inner
5625.2.a.v.1.4		8	25.9	even	10
5625.2.a.v.1.5		8	75.59	odd	10
5625.2.a.w.1.4		8	75.41	odd	10
5625.2.a.w.1.5		8	25.16	even	5

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.167451 - 0.515362i) q^{2} +(1.38048 + 1.00297i) q^{4} +(-1.16252 + 1.91012i) q^{5} +1.08833 q^{7} +(1.62484 - 1.18052i) q^{8} +O(q^{10})\)	\(q+(0.167451 - 0.515362i) q^{2} +(1.38048 + 1.00297i) q^{4} +(-1.16252 + 1.91012i) q^{5} +1.08833 q^{7} +(1.62484 - 1.18052i) q^{8} +(0.789737 + 0.918969i) q^{10} +(-0.900718 + 2.77212i) q^{11} +(0.298591 + 0.918969i) q^{13} +(0.182242 - 0.560883i) q^{14} +(0.718278 + 2.21063i) q^{16} +(2.15194 - 1.56347i) q^{17} +(1.59074 - 1.15574i) q^{19} +(-3.52063 + 1.47090i) q^{20} +(1.27782 + 0.928391i) q^{22} +(2.11191 - 6.49978i) q^{23} +(-2.29710 - 4.44110i) q^{25} +0.523601 q^{26} +(1.50241 + 1.09157i) q^{28} +(-5.51425 - 4.00634i) q^{29} +(-2.01297 + 1.46251i) q^{31} +5.27639 q^{32} +(-0.445410 - 1.37083i) q^{34} +(-1.26520 + 2.07884i) q^{35} +(-2.54267 - 7.82555i) q^{37} +(-0.329253 - 1.01334i) q^{38} +(0.366018 + 4.47602i) q^{40} +(3.26498 + 10.0486i) q^{41} -7.72721 q^{43} +(-4.02379 + 2.92345i) q^{44} +(-2.99610 - 2.17679i) q^{46} +(7.29741 + 5.30188i) q^{47} -5.81554 q^{49} +(-2.67342 + 0.440172i) q^{50} +(-0.509505 + 1.56809i) q^{52} +(-4.47697 - 3.25271i) q^{53} +(-4.24798 - 4.94312i) q^{55} +(1.76836 - 1.28479i) q^{56} +(-2.98808 + 2.17097i) q^{58} +(-4.08725 - 12.5793i) q^{59} +(1.12754 - 3.47021i) q^{61} +(0.416646 + 1.28231i) q^{62} +(-0.553018 + 1.70202i) q^{64} +(-2.10246 - 0.497974i) q^{65} +(-7.15830 + 5.20081i) q^{67} +4.53882 q^{68} +(0.859493 + 1.00014i) q^{70} +(6.31844 + 4.59061i) q^{71} +(4.82987 - 14.8648i) q^{73} -4.45876 q^{74} +3.35515 q^{76} +(-0.980277 + 3.01698i) q^{77} +(5.34368 + 3.88241i) q^{79} +(-5.05758 - 1.19791i) q^{80} +5.72537 q^{82} +(1.53614 - 1.11607i) q^{83} +(0.484752 + 5.92802i) q^{85} +(-1.29393 + 3.98231i) q^{86} +(1.80902 + 5.56758i) q^{88} +(-0.353992 + 1.08948i) q^{89} +(0.324965 + 1.00014i) q^{91} +(9.43455 - 6.85460i) q^{92} +(3.95435 - 2.87300i) q^{94} +(0.358335 + 4.38207i) q^{95} +(5.01135 + 3.64096i) q^{97} +(-0.973820 + 2.99711i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{4}+O(q^{10}) \) 16 * q - 2 * q^4	\( 16 q - 2 q^{4} + 14 q^{16} + 14 q^{19} - 30 q^{22} + 10 q^{25} + 30 q^{28} + 18 q^{31} - 20 q^{34} + 10 q^{37} - 10 q^{40} - 80 q^{43} - 32 q^{49} - 40 q^{52} - 70 q^{55} - 10 q^{58} + 32 q^{61} - 8 q^{64} - 40 q^{67} + 50 q^{70} + 60 q^{73} - 88 q^{76} + 36 q^{79} + 120 q^{82} + 20 q^{88} + 30 q^{91} + 30 q^{94} + 40 q^{97}+O(q^{100}) \) 16 * q - 2 * q^4 + 14 * q^16 + 14 * q^19 - 30 * q^22 + 10 * q^25 + 30 * q^28 + 18 * q^31 - 20 * q^34 + 10 * q^37 - 10 * q^40 - 80 * q^43 - 32 * q^49 - 40 * q^52 - 70 * q^55 - 10 * q^58 + 32 * q^61 - 8 * q^64 - 40 * q^67 + 50 * q^70 + 60 * q^73 - 88 * q^76 + 36 * q^79 + 120 * q^82 + 20 * q^88 + 30 * q^91 + 30 * q^94 + 40 * q^97

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