LMFDB - Embedded newform 260.2.bf.c.93.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(37,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 7]))

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

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

chi := DirichletCharacter("260.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.bf (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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + \cdots + 9 $ x^20 + 30x^18 + 371x^16 + 2460x^14 + 9517x^12 + 21870x^10 + 29001x^8 + 20400x^6 + 6399x^4 + 666*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			93.1
Root			$0.402430i$ of defining polynomial
Character	$\chi$	$=$	260.93
Dual form			260.2.bf.c.137.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.668040 + 2.49316i) q^{3} +(-2.20341 + 0.380790i) q^{5} +(-0.432607 + 0.749297i) q^{7} +(-3.17149 - 1.83106i) q^{9} +O(q^{10})$	\(q+(-0.668040 + 2.49316i) q^{3} +(-2.20341 + 0.380790i) q^{5} +(-0.432607 + 0.749297i) q^{7} +(-3.17149 - 1.83106i) q^{9} +(0.417628 - 1.55861i) q^{11} +(-3.35321 + 1.32514i) q^{13} +(0.522592 - 5.74783i) q^{15} +(-4.99621 + 1.33873i) q^{17} +(1.16619 - 0.312480i) q^{19} +(-1.57912 - 1.57912i) q^{21} +(2.62850 + 0.704305i) q^{23} +(4.71000 - 1.67807i) q^{25} +(1.20845 - 1.20845i) q^{27} +(-5.94138 + 3.43026i) q^{29} +(0.191663 - 0.191663i) q^{31} +(3.60687 + 2.08243i) q^{33} +(0.667884 - 1.81574i) q^{35} +(4.74722 + 8.22242i) q^{37} +(-1.06370 - 9.24533i) q^{39} +(0.417297 + 0.111814i) q^{41} +(3.09480 + 11.5499i) q^{43} +(7.68533 + 2.82690i) q^{45} +1.52128 q^{47} +(3.12570 + 5.41387i) q^{49} -13.3507i q^{51} +(-4.88398 - 4.88398i) q^{53} +(-0.326700 + 3.59327i) q^{55} +3.11625i q^{57} +(3.05172 + 11.3892i) q^{59} +(-2.94152 + 5.09486i) q^{61} +(2.74402 - 1.58426i) q^{63} +(6.88388 - 4.19668i) q^{65} +(11.7116 - 6.76168i) q^{67} +(-3.51189 + 6.08277i) q^{69} +(-3.85102 - 14.3722i) q^{71} -10.9921i q^{73} +(1.03723 + 12.8638i) q^{75} +(0.987192 + 0.987192i) q^{77} -3.98168i q^{79} +(-3.28761 - 5.69431i) q^{81} -6.25583 q^{83} +(10.4989 - 4.85228i) q^{85} +(-4.58310 - 17.1044i) q^{87} +(9.80805 + 2.62806i) q^{89} +(0.457701 - 3.08581i) q^{91} +(0.349808 + 0.605885i) q^{93} +(-2.45060 + 1.13259i) q^{95} +(1.26196 + 0.728593i) q^{97} +(-4.17841 + 4.17841i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} - 6 q^{5} - 6 q^{7} + 12 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 - 6 * q^5 - 6 * q^7 + 12 * q^9	$ 20 q - 2 q^{3} - 6 q^{5} - 6 q^{7} + 12 q^{9} - 6 q^{13} + 20 q^{15} + 6 q^{17} - 20 q^{19} - 12 q^{21} + 30 q^{23} - 2 q^{25} - 20 q^{27} - 24 q^{29} + 8 q^{31} - 30 q^{33} + 30 q^{37} - 4 q^{39} + 6 q^{41} + 22 q^{43} + 36 q^{45} - 14 q^{49} + 30 q^{53} - 34 q^{55} + 24 q^{59} - 32 q^{61} - 84 q^{63} - 60 q^{65} - 54 q^{67} + 16 q^{69} + 26 q^{75} + 12 q^{77} + 2 q^{81} - 48 q^{83} + 74 q^{85} + 38 q^{87} + 30 q^{89} - 72 q^{91} - 16 q^{93} - 6 q^{95} - 6 q^{97} - 20 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 - 6 * q^5 - 6 * q^7 + 12 * q^9 - 6 * q^13 + 20 * q^15 + 6 * q^17 - 20 * q^19 - 12 * q^21 + 30 * q^23 - 2 * q^25 - 20 * q^27 - 24 * q^29 + 8 * q^31 - 30 * q^33 + 30 * q^37 - 4 * q^39 + 6 * q^41 + 22 * q^43 + 36 * q^45 - 14 * q^49 + 30 * q^53 - 34 * q^55 + 24 * q^59 - 32 * q^61 - 84 * q^63 - 60 * q^65 - 54 * q^67 + 16 * q^69 + 26 * q^75 + 12 * q^77 + 2 * q^81 - 48 * q^83 + 74 * q^85 + 38 * q^87 + 30 * q^89 - 72 * q^91 - 16 * q^93 - 6 * q^95 - 6 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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			0
$2$		0			0
$3$	−0.668040	+	2.49316i	−0.385693	+	1.43943i	0.451378	+	0.892333i	$0.350933\pi$
$3$	−0.668040	+	2.49316i	−0.385693	+	1.43943i	−0.837071	+	0.547094i	$0.815734\pi$
$4$		0			0
$5$	−2.20341	+	0.380790i	−0.985393	+	0.170295i
$5$	−2.20341	+	0.380790i	−0.985393	+	0.170295i
$6$		0			0
$7$	−0.432607	+	0.749297i	−0.163510	+	0.283208i	−0.936125	−	0.351667i	$-0.885615\pi$
$7$	−0.432607	+	0.749297i	−0.163510	+	0.283208i	0.772615	+	0.634875i	$0.218948\pi$
$8$		0			0
$9$	−3.17149	−	1.83106i	−1.05716	−	0.610354i
$10$		0			0
$11$	0.417628	−	1.55861i	0.125920	−	0.469938i	−0.873951	−	0.486014i	$-0.838451\pi$
$11$	0.417628	−	1.55861i	0.125920	−	0.469938i	0.999871	+	0.0160756i	$0.00511723\pi$
$12$		0			0
$13$	−3.35321	+	1.32514i	−0.930013	+	0.367527i
$13$	−3.35321	+	1.32514i	−0.930013	+	0.367527i
$14$		0			0
$15$	0.522592	−	5.74783i	0.134933	−	1.48408i
$16$		0			0
$17$	−4.99621	+	1.33873i	−1.21176	+	0.324690i	−0.807452	−	0.589933i	$-0.799154\pi$
$17$	−4.99621	+	1.33873i	−1.21176	+	0.324690i	−0.404308	+	0.914623i	$0.632487\pi$
$18$		0			0
$19$	1.16619	−	0.312480i	0.267543	−	0.0716878i	−0.122554	−	0.992462i	$-0.539108\pi$
$19$	1.16619	−	0.312480i	0.267543	−	0.0716878i	0.390096	+	0.920774i	$0.372442\pi$
$20$		0			0
$21$	−1.57912	−	1.57912i	−0.344592	−	0.344592i
$22$		0			0
$23$	2.62850	+	0.704305i	0.548080	+	0.146858i	0.522225	−	0.852808i	$-0.325102\pi$
$23$	2.62850	+	0.704305i	0.548080	+	0.146858i	0.0258557	+	0.999666i	$0.491769\pi$
$24$		0			0
$25$	4.71000	−	1.67807i	0.941999	−	0.335614i
$26$		0			0
$27$	1.20845	−	1.20845i	0.232567	−	0.232567i
$28$		0			0
$29$	−5.94138	+	3.43026i	−1.10329	+	0.636983i	−0.937082	−	0.349109i	$-0.886484\pi$
$29$	−5.94138	+	3.43026i	−1.10329	+	0.636983i	−0.166204	+	0.986091i	$0.553151\pi$
$30$		0			0
$31$	0.191663	−	0.191663i	0.0344237	−	0.0344237i	−0.689685	−	0.724109i	$-0.742251\pi$
$31$	0.191663	−	0.191663i	0.0344237	−	0.0344237i	0.724109	+	0.689685i	$0.242251\pi$
$32$		0			0
$33$	3.60687	+	2.08243i	0.627875	+	0.362504i
$34$		0			0
$35$	0.667884	−	1.81574i	0.112893	−	0.306916i
$36$		0			0
$37$	4.74722	+	8.22242i	0.780438	+	1.35176i	0.931687	+	0.363262i	$0.118337\pi$
$37$	4.74722	+	8.22242i	0.780438	+	1.35176i	−0.151249	+	0.988496i	$0.548330\pi$
$38$		0			0
$39$	−1.06370	−	9.24533i	−0.170328	−	1.48044i
$40$		0			0
$41$	0.417297	+	0.111814i	0.0651709	+	0.0174625i	0.291257	−	0.956645i	$-0.405926\pi$
$41$	0.417297	+	0.111814i	0.0651709	+	0.0174625i	−0.226086	+	0.974107i	$0.572593\pi$
$42$		0			0
$43$	3.09480	+	11.5499i	0.471952	+	1.76135i	0.632743	+	0.774362i	$0.281929\pi$
$43$	3.09480	+	11.5499i	0.471952	+	1.76135i	−0.160791	+	0.986989i	$0.551404\pi$
$44$		0			0
$45$	7.68533	+	2.82690i	1.14566	+	0.421409i
$46$		0			0
$47$	1.52128			0.221902			0.110951	−	0.993826i	$-0.464610\pi$
$47$	1.52128			0.221902			0.110951	+	0.993826i	$0.464610\pi$
$48$		0			0
$49$	3.12570	+	5.41387i	0.446529	+	0.773411i
$50$		0			0
$51$		−	13.3507i		−	1.86947i
$52$		0			0
$53$	−4.88398	−	4.88398i	−0.670867	−	0.670867i	0.287049	−	0.957916i	$-0.407326\pi$
$53$	−4.88398	−	4.88398i	−0.670867	−	0.670867i	−0.957916	+	0.287049i	$0.907326\pi$
$54$		0			0
$55$	−0.326700	+	3.59327i	−0.0440523	+	0.484517i
$56$		0			0
$57$			3.11625i			0.412757i
$58$		0			0
$59$	3.05172	+	11.3892i	0.397300	+	1.48274i	0.817828	+	0.575463i	$0.195178\pi$
$59$	3.05172	+	11.3892i	0.397300	+	1.48274i	−0.420528	+	0.907279i	$0.638155\pi$
$60$		0			0
$61$	−2.94152	+	5.09486i	−0.376623	+	0.652330i	−0.990569	−	0.137018i	$-0.956248\pi$
$61$	−2.94152	+	5.09486i	−0.376623	+	0.652330i	0.613946	+	0.789348i	$0.289581\pi$
$62$		0			0
$63$	2.74402	−	1.58426i	0.345714	−	0.199598i
$64$		0			0
$65$	6.88388	−	4.19668i	0.853841	−	0.520535i
$66$		0			0
$67$	11.7116	−	6.76168i	1.43080	−	0.826070i	0.433614	−	0.901099i	$-0.357238\pi$
$67$	11.7116	−	6.76168i	1.43080	−	0.826070i	0.997181	+	0.0750284i	$0.0239047\pi$
$68$		0			0
$69$	−3.51189	+	6.08277i	−0.422782	+	0.732279i
$70$		0			0
$71$	−3.85102	−	14.3722i	−0.457031	−	1.70566i	−0.682046	−	0.731309i	$-0.738910\pi$
$71$	−3.85102	−	14.3722i	−0.457031	−	1.70566i	0.225015	−	0.974355i	$-0.427757\pi$
$72$		0			0
$73$		−	10.9921i		−	1.28653i	−0.765643	−	0.643266i	$-0.777579\pi$
$73$		−	10.9921i		−	1.28653i	0.765643	−	0.643266i	$-0.222421\pi$
$74$		0			0
$75$	1.03723	+	12.8638i	0.119770	+	1.48538i
$76$		0			0
$77$	0.987192	+	0.987192i	0.112501	+	0.112501i
$78$		0			0
$79$		−	3.98168i		−	0.447974i	−0.974592	−	0.223987i	$-0.928093\pi$
$79$		−	3.98168i		−	0.447974i	0.974592	−	0.223987i	$-0.0719074\pi$
$80$		0			0
$81$	−3.28761	−	5.69431i	−0.365290	−	0.632701i
$82$		0			0
$83$	−6.25583			−0.686667			−0.343333	−	0.939214i	$-0.611556\pi$
$83$	−6.25583			−0.686667			−0.343333	+	0.939214i	$0.611556\pi$
$84$		0			0
$85$	10.4989	−	4.85228i	1.13877	−	0.526304i
$86$		0			0
$87$	−4.58310	−	17.1044i	−0.491360	−	1.83378i
$88$		0			0
$89$	9.80805	+	2.62806i	1.03965	+	0.278574i	0.737969	−	0.674835i	$-0.235785\pi$
$89$	9.80805	+	2.62806i	1.03965	+	0.278574i	0.301683	+	0.953408i	$0.402452\pi$
$90$		0			0
$91$	0.457701	−	3.08581i	0.0479801	−	0.323481i
$92$		0			0
$93$	0.349808	+	0.605885i	0.0362734	+	0.0628274i
$94$		0			0
$95$	−2.45060	+	1.13259i	−0.251427	+	0.116202i
$96$		0			0
$97$	1.26196	+	0.728593i	0.128133	+	0.0739774i	0.562696	−	0.826664i	$-0.309764\pi$
$97$	1.26196	+	0.728593i	0.128133	+	0.0739774i	−0.434564	+	0.900641i	$0.643097\pi$
$98$		0			0
$99$	−4.17841	+	4.17841i	−0.419946	+	0.419946i
$100$		0			0
$101$	−10.0529	+	5.80403i	−1.00030	+	0.577523i	−0.908337	−	0.418240i	$-0.862647\pi$
$101$	−10.0529	+	5.80403i	−1.00030	+	0.577523i	−0.0919621	+	0.995763i	$0.529314\pi$
$102$		0			0
$103$	−10.8660	+	10.8660i	−1.07066	+	1.07066i	−0.0733504	+	0.997306i	$0.523369\pi$
$103$	−10.8660	+	10.8660i	−1.07066	+	1.07066i	−0.997306	+	0.0733504i	$0.976631\pi$
$104$		0			0
$105$	4.08076	+	2.87813i	0.398241	+	0.280877i
$106$		0			0
$107$	6.88942	+	1.84601i	0.666025	+	0.178461i	0.575964	−	0.817475i	$-0.304627\pi$
$107$	6.88942	+	1.84601i	0.666025	+	0.178461i	0.0900615	+	0.995936i	$0.471294\pi$
$108$		0			0
$109$	−4.56805	−	4.56805i	−0.437540	−	0.437540i	0.453643	−	0.891183i	$-0.350124\pi$
$109$	−4.56805	−	4.56805i	−0.437540	−	0.437540i	−0.891183	+	0.453643i	$0.850124\pi$
$110$		0			0
$111$	−23.6711	+	6.34266i	−2.24677	+	0.602019i
$112$		0			0
$113$	−8.34679	+	2.23652i	−0.785200	+	0.210394i	−0.629076	−	0.777344i	$-0.716567\pi$
$113$	−8.34679	+	2.23652i	−0.785200	+	0.210394i	−0.156124	+	0.987737i	$0.549900\pi$
$114$		0			0
$115$	−6.05985	−	0.550961i	−0.565084	−	0.0513774i
$116$		0			0
$117$	13.0611	+	1.93727i	1.20750	+	0.179101i
$118$		0			0
$119$	1.15829	−	4.32280i	0.106180	−	0.396270i
$120$		0			0
$121$	7.27143	+	4.19816i	0.661039	+	0.381651i
$122$		0			0
$123$	−0.557543	+	0.965692i	−0.0502719	+	0.0870735i
$124$		0			0
$125$	−9.73904	+	5.49100i	−0.871086	+	0.491130i
$126$		0			0
$127$	−1.21781	+	4.54494i	−0.108064	+	0.403299i	−0.998675	−	0.0514670i	$-0.983610\pi$
$127$	−1.21781	+	4.54494i	−0.108064	+	0.403299i	0.890611	+	0.454766i	$0.150277\pi$
$128$		0			0
$129$	−30.8633			−2.71736
$130$		0			0
$131$	15.3255			1.33900			0.669498	−	0.742814i	$-0.266509\pi$
$131$	15.3255			1.33900			0.669498	+	0.742814i	$0.266509\pi$
$132$		0			0
$133$	−0.270362	+	1.00900i	−0.0234434	+	0.0874918i
$134$		0			0
$135$	−2.20255	+	3.12288i	−0.189565	+	0.268775i
$136$		0			0
$137$	8.47191	−	14.6738i	0.723804	−	1.25367i	−0.235661	−	0.971835i	$-0.575725\pi$
$137$	8.47191	−	14.6738i	0.723804	−	1.25367i	0.959464	−	0.281830i	$-0.0909413\pi$
$138$		0			0
$139$	2.69425	+	1.55553i	0.228524	+	0.131938i	0.609891	−	0.792485i	$-0.291213\pi$
$139$	2.69425	+	1.55553i	0.228524	+	0.131938i	−0.381367	+	0.924424i	$0.624547\pi$
$140$		0			0
$141$	−1.01628	+	3.79280i	−0.0855861	+	0.319412i
$142$		0			0
$143$	0.664975	+	5.77975i	0.0556080	+	0.483327i
$144$		0			0
$145$	11.7851	−	9.82067i	0.978696	−	0.815562i
$146$		0			0
$147$	−15.5857	+	4.17619i	−1.28549	+	0.344446i
$148$		0			0
$149$	−15.9563	+	4.27549i	−1.30719	+	0.350262i	−0.844166	−	0.536082i	$-0.819904\pi$
$149$	−15.9563	+	4.27549i	−1.30719	+	0.350262i	−0.463029	+	0.886343i	$0.653237\pi$
$150$		0			0
$151$	12.3067	+	12.3067i	1.00151	+	1.00151i	0.999999	+	0.00150662i	$0.000479574\pi$
$151$	12.3067	+	12.3067i	1.00151	+	1.00151i	0.00150662	+	0.999999i	$0.499520\pi$
$152$		0			0
$153$	18.2968	+	4.90260i	1.47920	+	0.396352i
$154$		0			0
$155$	−0.349328	+	0.495295i	−0.0280587	+	0.0397830i
$156$		0			0
$157$	−5.83463	+	5.83463i	−0.465654	+	0.465654i	−0.900503	−	0.434849i	$-0.856802\pi$
$157$	−5.83463	+	5.83463i	−0.465654	+	0.465654i	0.434849	+	0.900503i	$0.356802\pi$
$158$		0			0
$159$	15.4392	−	8.91385i	1.22441	−	0.706914i
$160$		0			0
$161$	−1.66484	+	1.66484i	−0.131208	+	0.131208i
$162$		0			0
$163$	−4.57504	−	2.64140i	−0.358344	−	0.206890i	0.310010	−	0.950733i	$-0.399668\pi$
$163$	−4.57504	−	2.64140i	−0.358344	−	0.206890i	−0.668354	+	0.743843i	$0.733001\pi$
$164$		0			0
$165$	−8.74036	−	3.21497i	−0.680436	−	0.250285i
$166$		0			0
$167$	3.93382	+	6.81358i	0.304408	+	0.527251i	0.977129	−	0.212645i	$-0.0682079\pi$
$167$	3.93382	+	6.81358i	0.304408	+	0.527251i	−0.672721	+	0.739896i	$0.734875\pi$
$168$		0			0
$169$	9.48803	−	8.88692i	0.729848	−	0.683609i
$170$		0			0
$171$	−4.27073	−	1.14434i	−0.326591	−	0.0875098i
$172$		0			0
$173$	−5.16129	−	19.2622i	−0.392406	−	1.46448i	−0.826154	−	0.563444i	$-0.809476\pi$
$173$	−5.16129	−	19.2622i	−0.392406	−	1.46448i	0.433749	−	0.901034i	$-0.357191\pi$
$174$		0			0
$175$	−0.780203	+	4.25514i	−0.0589778	+	0.321658i
$176$		0			0
$177$	−30.4337			−2.28753
$178$		0			0
$179$	1.53139	+	2.65244i	0.114461	+	0.198253i	0.917564	−	0.397588i	$-0.130153\pi$
$179$	1.53139	+	2.65244i	0.114461	+	0.198253i	−0.803103	+	0.595840i	$0.796819\pi$
$180$		0			0
$181$		−	23.3657i		−	1.73676i	−0.495901	−	0.868379i	$-0.665162\pi$
$181$		−	23.3657i		−	1.73676i	0.495901	−	0.868379i	$-0.334838\pi$
$182$		0			0
$183$	−10.7372	−	10.7372i	−0.793720	−	0.793720i
$184$		0			0
$185$	−13.5911	−	16.3096i	−0.999235	−	1.19911i
$186$		0			0
$187$			8.34623i			0.610337i
$188$		0			0
$189$	0.382706	+	1.42828i	0.0278377	+	0.103892i
$190$		0			0
$191$	3.73743	−	6.47341i	0.270431	−	0.468400i	−0.698541	−	0.715570i	$-0.746167\pi$
$191$	3.73743	−	6.47341i	0.270431	−	0.468400i	0.968972	+	0.247170i	$0.0795006\pi$
$192$		0			0
$193$	1.73378	−	1.00100i	0.124800	−	0.0720536i	−0.436300	−	0.899801i	$-0.643711\pi$
$193$	1.73378	−	1.00100i	0.124800	−	0.0720536i	0.561101	+	0.827748i	$0.310378\pi$
$194$		0			0
$195$	5.86429	+	19.9662i	0.419951	+	1.42981i
$196$		0			0
$197$	2.75469	−	1.59042i	0.196264	−	0.113313i	−0.398648	−	0.917104i	$-0.630520\pi$
$197$	2.75469	−	1.59042i	0.196264	−	0.113313i	0.594912	+	0.803791i	$0.297187\pi$
$198$		0			0
$199$	8.20225	−	14.2067i	0.581442	−	1.00709i	−0.413867	−	0.910337i	$-0.635822\pi$
$199$	8.20225	−	14.2067i	0.581442	−	1.00709i	0.995309	−	0.0967496i	$-0.0308446\pi$
$200$		0			0
$201$	9.03414	+	33.7159i	0.637219	+	2.37813i
$202$		0			0
$203$		−	5.93581i		−	0.416612i
$204$		0			0
$205$	−0.962053	−	0.0874698i	−0.0671927	−	0.00610916i
$206$		0			0
$207$	−7.04664	−	7.04664i	−0.489775	−	0.489775i
$208$		0			0
$209$		−	1.94813i		−	0.134755i
$210$		0			0
$211$	5.66213	+	9.80710i	0.389797	+	0.675149i	0.992422	−	0.122876i	$-0.0392117\pi$
$211$	5.66213	+	9.80710i	0.389797	+	0.675149i	−0.602625	+	0.798025i	$0.705878\pi$
$212$		0			0
$213$	38.4048			2.63145
$214$		0			0
$215$	−11.2172	−	24.2708i	−0.765007	−	1.65525i
$216$		0			0
$217$	0.0606978	+	0.226527i	0.00412044	+	0.0153777i
$218$		0			0
$219$	27.4051	+	7.34318i	1.85187	+	0.496206i
$220$		0			0
$221$	14.9794	−	11.1097i	1.00762	−	0.747320i
$222$		0			0
$223$	5.04810	+	8.74357i	0.338046	+	0.585513i	0.984065	−	0.177808i	$-0.0569007\pi$
$223$	5.04810	+	8.74357i	0.338046	+	0.585513i	−0.646019	+	0.763321i	$0.723567\pi$
$224$		0			0
$225$	−18.0104	−	3.30230i	−1.20069	−	0.220154i
$226$		0			0
$227$	−11.8985	−	6.86958i	−0.789728	−	0.455950i	0.0501387	−	0.998742i	$-0.484034\pi$
$227$	−11.8985	−	6.86958i	−0.789728	−	0.455950i	−0.839867	+	0.542792i	$0.817367\pi$
$228$		0			0
$229$	3.36743	−	3.36743i	0.222526	−	0.222526i	−0.587035	−	0.809561i	$-0.699705\pi$
$229$	3.36743	−	3.36743i	0.222526	−	0.222526i	0.809561	+	0.587035i	$0.199705\pi$
$230$		0			0
$231$	−3.12071	+	1.80174i	−0.205328	+	0.118546i
$232$		0			0
$233$	−19.1541	+	19.1541i	−1.25482	+	1.25482i	−0.301293	+	0.953532i	$0.597418\pi$
$233$	−19.1541	+	19.1541i	−1.25482	+	1.25482i	−0.953532	+	0.301293i	$0.902582\pi$
$234$		0			0
$235$	−3.35201	+	0.579291i	−0.218661	+	0.0377888i
$236$		0			0
$237$	9.92697	+	2.65992i	0.644826	+	0.172781i
$238$		0			0
$239$	18.4667	+	18.4667i	1.19451	+	1.19451i	0.975786	+	0.218727i	$0.0701904\pi$
$239$	18.4667	+	18.4667i	1.19451	+	1.19451i	0.218727	+	0.975786i	$0.429810\pi$
$240$		0			0
$241$	0.850786	−	0.227967i	0.0548040	−	0.0146847i	−0.231313	−	0.972879i	$-0.574302\pi$
$241$	0.850786	−	0.227967i	0.0548040	−	0.0146847i	0.286117	+	0.958195i	$0.407635\pi$
$242$		0			0
$243$	21.3454	−	5.71949i	1.36931	−	0.366905i
$244$		0			0
$245$	−8.94874	−	10.7387i	−0.571714	−	0.686072i
$246$		0			0
$247$	−3.49640	+	2.59317i	−0.222471	+	0.165000i
$248$		0			0
$249$	4.17915	−	15.5968i	0.264843	−	0.988406i
$250$		0			0
$251$	5.62276	+	3.24630i	0.354905	+	0.204905i	0.666844	−	0.745198i	$-0.267645\pi$
$251$	5.62276	+	3.24630i	0.354905	+	0.204905i	−0.311938	+	0.950102i	$0.600978\pi$
$252$		0			0
$253$	2.19547	−	3.80266i	0.138028	−	0.239071i
$254$		0			0
$255$	5.08381	+	29.4170i	0.318361	+	1.84216i
$256$		0			0
$257$	−2.77298	+	10.3489i	−0.172974	+	0.645547i	0.823914	+	0.566715i	$0.191786\pi$
$257$	−2.77298	+	10.3489i	−0.172974	+	0.645547i	−0.996888	+	0.0788324i	$0.974881\pi$
$258$		0			0
$259$	−8.21472			−0.510438
$260$		0			0
$261$	25.1240			1.55514
$262$		0			0
$263$	2.62824	−	9.80873i	0.162064	−	0.604832i	−0.836332	−	0.548223i	$-0.815304\pi$
$263$	2.62824	−	9.80873i	0.162064	−	0.604832i	0.998396	−	0.0566092i	$-0.0180289\pi$
$264$		0			0
$265$	12.6212	+	8.90162i	0.775312	+	0.546822i
$266$		0			0
$267$	−13.1043	+	22.6974i	−0.801973	+	1.38906i
$268$		0			0
$269$	16.1943	+	9.34977i	0.987383	+	0.570066i	0.904491	−	0.426493i	$-0.140251\pi$
$269$	16.1943	+	9.34977i	0.987383	+	0.570066i	0.0828917	+	0.996559i	$0.473584\pi$
$270$		0			0
$271$	−4.74484	+	17.7080i	−0.288228	+	1.07568i	0.658220	+	0.752826i	$0.271310\pi$
$271$	−4.74484	+	17.7080i	−0.288228	+	1.07568i	−0.946448	+	0.322856i	$0.895357\pi$
$272$		0			0
$273$	7.38767	+	3.20257i	0.447122	+	0.193828i
$274$		0			0
$275$	−0.648431	−	8.04185i	−0.0391019	−	0.484942i
$276$		0			0
$277$	13.0979	−	3.50958i	0.786979	−	0.210870i	0.157120	−	0.987580i	$-0.449779\pi$
$277$	13.0979	−	3.50958i	0.786979	−	0.210870i	0.629859	+	0.776709i	$0.283113\pi$
$278$		0			0
$279$	−0.958804	+	0.256911i	−0.0574021	+	0.0153809i
$280$		0			0
$281$	17.1478	+	17.1478i	1.02295	+	1.02295i	0.999730	+	0.0232200i	$0.00739181\pi$
$281$	17.1478	+	17.1478i	1.02295	+	1.02295i	0.0232200	+	0.999730i	$0.492608\pi$
$282$		0			0
$283$	8.84554	+	2.37015i	0.525813	+	0.140891i	0.511954	−	0.859013i	$-0.328922\pi$
$283$	8.84554	+	2.37015i	0.525813	+	0.140891i	0.0138586	+	0.999904i	$0.495589\pi$
$284$		0			0
$285$	−1.18664	−	6.86636i	−0.0702904	−	0.406728i
$286$		0			0
$287$	−0.264308	+	0.264308i	−0.0156016	+	0.0156016i
$288$		0			0
$289$	8.44752	−	4.87718i	0.496913	−	0.286893i
$290$		0			0
$291$	−2.65954	+	2.65954i	−0.155905	+	0.155905i
$292$		0			0
$293$	15.7458	+	9.09083i	0.919878	+	0.531092i	0.883596	−	0.468250i	$-0.155115\pi$
$293$	15.7458	+	9.09083i	0.919878	+	0.531092i	0.0362820	+	0.999342i	$0.488449\pi$
$294$		0			0
$295$	−11.0611	−	23.9329i	−0.643999	−	1.39343i
$296$		0			0
$297$	−1.37882	−	2.38819i	−0.0800073	−	0.138577i
$298$		0			0
$299$	−9.74721	+	1.12144i	−0.563696	+	0.0648546i
$300$		0			0
$301$	−9.99318	−	2.67766i	−0.575997	−	0.154338i
$302$		0			0
$303$	−7.75465	−	28.9408i	−0.445493	−	1.66260i
$304$		0			0
$305$	4.54129	−	12.3461i	0.260033	−	0.706938i
$306$		0			0
$307$	−28.0356			−1.60008			−0.800039	−	0.599948i	$-0.795188\pi$
$307$	−28.0356			−1.60008			−0.800039	+	0.599948i	$0.795188\pi$
$308$		0			0
$309$	−19.8317	−	34.3495i	−1.12819	−	1.95408i
$310$		0			0
$311$			11.5168i			0.653060i	0.945187	+	0.326530i	$0.105879\pi$
$311$			11.5168i			0.653060i	−0.945187	+	0.326530i	$0.894121\pi$
$312$		0			0
$313$	−10.3376	−	10.3376i	−0.584316	−	0.584316i	0.351771	−	0.936086i	$-0.385580\pi$
$313$	−10.3376	−	10.3376i	−0.584316	−	0.584316i	−0.936086	+	0.351771i	$0.885580\pi$
$314$		0			0
$315$	−5.44292	+	4.53567i	−0.306674	+	0.255556i
$316$		0			0
$317$		−	2.31106i		−	0.129802i	−0.997892	−	0.0649010i	$-0.979327\pi$
$317$		−	2.31106i		−	0.129802i	0.997892	−	0.0649010i	$-0.0206731\pi$
$318$		0			0
$319$	2.86514	+	10.6928i	0.160417	+	0.598685i
$320$		0			0
$321$	−9.20481	+	15.9432i	−0.513763	+	0.889863i
$322$		0			0
$323$	−5.40821	+	3.12243i	−0.300921	+	0.173737i
$324$		0			0
$325$	−13.5699	+	11.8683i	−0.752724	+	0.658336i
$326$		0			0
$327$	14.4405	−	8.33724i	0.798563	−	0.461050i
$328$		0			0
$329$	−0.658118	+	1.13989i	−0.0362832	+	0.0628444i
$330$		0			0
$331$	−9.10127	−	33.9664i	−0.500251	−	1.86696i	−0.498370	−	0.866965i	$-0.666068\pi$
$331$	−9.10127	−	33.9664i	−0.500251	−	1.86696i	−0.00188163	−	0.999998i	$-0.500599\pi$
$332$		0			0
$333$		−	34.7698i		−	1.90537i
$334$		0			0
$335$	−23.2306	+	19.3584i	−1.26922	+	1.05766i
$336$		0			0
$337$	4.04414	+	4.04414i	0.220298	+	0.220298i	0.808624	−	0.588326i	$-0.200213\pi$
$337$	4.04414	+	4.04414i	0.220298	+	0.220298i	−0.588326	+	0.808624i	$0.700213\pi$
$338$		0			0
$339$		−	22.3040i		−	1.21139i
$340$		0			0
$341$	−0.218684	−	0.378771i	−0.0118424	−	0.0205116i
$342$		0			0
$343$	−11.4653			−0.619068
$344$		0			0
$345$	5.42185	−	14.7401i	0.291903	−	0.793580i
$346$		0			0
$347$	0.0579124	+	0.216132i	0.00310890	+	0.0116026i	0.967463	−	0.253013i	$-0.0814216\pi$
$347$	0.0579124	+	0.216132i	0.00310890	+	0.0116026i	−0.964354	+	0.264616i	$0.914755\pi$
$348$		0			0
$349$	11.9175	+	3.19329i	0.637930	+	0.170933i	0.563266	−	0.826276i	$-0.309545\pi$
$349$	11.9175	+	3.19329i	0.637930	+	0.170933i	0.0746643	+	0.997209i	$0.476211\pi$
$350$		0			0
$351$	−2.45083	+	5.65356i	−0.130816	+	0.301765i
$352$		0			0
$353$	−6.36920	−	11.0318i	−0.338998	−	0.587162i	0.645246	−	0.763975i	$-0.276755\pi$
$353$	−6.36920	−	11.0318i	−0.338998	−	0.587162i	−0.984245	+	0.176812i	$0.943421\pi$
$354$		0			0
$355$	13.9581	+	30.2013i	0.740821	+	1.60292i
$356$		0			0
$357$	10.0036	+	5.77560i	0.529449	+	0.305677i
$358$		0			0
$359$	−18.8285	+	18.8285i	−0.993730	+	0.993730i	−0.999980	−	0.00625094i	$-0.998010\pi$
$359$	−18.8285	+	18.8285i	−0.993730	+	0.993730i	0.00625094	+	0.999980i	$0.498010\pi$
$360$		0			0
$361$	−15.1921	+	8.77118i	−0.799586	+	0.461641i
$362$		0			0
$363$	−15.3243	+	15.3243i	−0.804317	+	0.804317i
$364$		0			0
$365$	4.18570	+	24.2201i	0.219089	+	1.26774i
$366$		0			0
$367$	−20.0032	−	5.35985i	−1.04416	−	0.279782i	−0.304324	−	0.952569i	$-0.598431\pi$
$367$	−20.0032	−	5.35985i	−1.04416	−	0.279782i	−0.739837	+	0.672787i	$0.765097\pi$
$368$		0			0
$369$	−1.11872	−	1.11872i	−0.0582380	−	0.0582380i
$370$		0			0
$371$	5.77240	−	1.54671i	0.299688	−	0.0803012i
$372$		0			0
$373$	−4.11130	+	1.10162i	−0.212875	+	0.0570397i	−0.363680	−	0.931524i	$-0.618480\pi$
$373$	−4.11130	+	1.10162i	−0.212875	+	0.0570397i	0.150805	+	0.988563i	$0.451813\pi$
$374$		0			0
$375$	−7.18386	−	27.9492i	−0.370973	−	1.44329i
$376$		0			0
$377$	15.3771	−	19.3755i	0.791962	−	0.997889i
$378$		0			0
$379$	−2.81310	+	10.4986i	−0.144499	+	0.539278i	0.855278	+	0.518169i	$0.173386\pi$
$379$	−2.81310	+	10.4986i	−0.144499	+	0.539278i	−0.999777	+	0.0211086i	$0.993280\pi$
$380$		0			0
$381$	−10.5177	−	6.07241i	−0.538839	−	0.311099i
$382$		0			0
$383$	6.75134	−	11.6937i	0.344977	−	0.597518i	−0.640372	−	0.768065i	$-0.721220\pi$
$383$	6.75134	−	11.6937i	0.344977	−	0.597518i	0.985350	+	0.170546i	$0.0545533\pi$
$384$		0			0
$385$	−2.55110	−	1.79927i	−0.130016	−	0.0916994i
$386$		0			0
$387$	11.3335	−	42.2973i	0.576116	−	2.15009i
$388$		0			0
$389$	7.82344			0.396664			0.198332	−	0.980135i	$-0.436448\pi$
$389$	7.82344			0.396664			0.198332	+	0.980135i	$0.436448\pi$
$390$		0			0
$391$	−14.0754			−0.711825
$392$		0			0
$393$	−10.2381	+	38.2090i	−0.516442	+	1.92739i
$394$		0			0
$395$	1.51619	+	8.77327i	0.0762877	+	0.441431i
$396$		0			0
$397$	6.04313	−	10.4670i	0.303296	−	0.525324i	−0.673584	−	0.739110i	$-0.735246\pi$
$397$	6.04313	−	10.4670i	0.303296	−	0.525324i	0.976881	+	0.213786i	$0.0685795\pi$
$398$		0			0
$399$	−2.33500	−	1.34811i	−0.116896	−	0.0674900i
$400$		0			0
$401$	−3.23948	+	12.0899i	−0.161772	+	0.603740i	0.836658	+	0.547725i	$0.184506\pi$
$401$	−3.23948	+	12.0899i	−0.161772	+	0.603740i	−0.998430	+	0.0560149i	$0.982161\pi$
$402$		0			0
$403$	−0.388707	+	0.896666i	−0.0193629	+	0.0446661i
$404$		0			0
$405$	9.41228	+	11.2950i	0.467700	+	0.561253i
$406$		0			0
$407$	14.7981	−	3.96514i	0.733515	−	0.196545i
$408$		0			0
$409$	−12.0227	+	3.22147i	−0.594484	+	0.159292i	−0.543502	−	0.839408i	$-0.682902\pi$
$409$	−12.0227	+	3.22147i	−0.594484	+	0.159292i	−0.0509825	+	0.998700i	$0.516235\pi$
$410$		0			0
$411$	30.9245	+	30.9245i	1.52539	+	1.52539i
$412$		0			0
$413$	−9.85406	−	2.64039i	−0.484887	−	0.129925i
$414$		0			0
$415$	13.7841	−	2.38216i	0.676637	−	0.116936i
$416$		0			0
$417$	−5.67805	+	5.67805i	−0.278055	+	0.278055i
$418$		0			0
$419$	6.12710	−	3.53748i	0.299328	−	0.172817i	−0.342813	−	0.939404i	$-0.611380\pi$
$419$	6.12710	−	3.53748i	0.299328	−	0.172817i	0.642141	+	0.766586i	$0.278046\pi$
$420$		0			0
$421$	−12.6378	+	12.6378i	−0.615930	+	0.615930i	−0.944485	−	0.328555i	$-0.893438\pi$
$421$	−12.6378	+	12.6378i	−0.615930	+	0.615930i	0.328555	+	0.944485i	$0.393438\pi$
$422$		0			0
$423$	−4.82474	−	2.78557i	−0.234587	−	0.135439i
$424$		0			0
$425$	−21.2857	+	14.6894i	−1.03251	+	0.712542i
$426$		0			0
$427$	−2.54504	−	4.40815i	−0.123163	−	0.213325i
$428$		0			0
$429$	−14.8541	−	2.20322i	−0.717162	−	0.106372i
$430$		0			0
$431$	1.66350	+	0.445735i	0.0801282	+	0.0214703i	0.298660	−	0.954359i	$-0.403460\pi$
$431$	1.66350	+	0.445735i	0.0801282	+	0.0214703i	−0.218532	+	0.975830i	$0.570127\pi$
$432$		0			0
$433$	4.16531	+	15.5451i	0.200172	+	0.747052i	0.990867	+	0.134842i	$0.0430527\pi$
$433$	4.16531	+	15.5451i	0.200172	+	0.747052i	−0.790695	+	0.612210i	$0.790281\pi$
$434$		0			0
$435$	16.6116	+	35.9426i	0.796465	+	1.72332i
$436$		0			0
$437$	3.28541			0.157163
$438$		0			0
$439$	7.54892	+	13.0751i	0.360290	+	0.624041i	0.988008	−	0.154400i	$-0.0493443\pi$
$439$	7.54892	+	13.0751i	0.360290	+	0.624041i	−0.627718	+	0.778441i	$0.716011\pi$
$440$		0			0
$441$		−	22.8934i		−	1.09016i
$442$		0			0
$443$	−13.3798	−	13.3798i	−0.635694	−	0.635694i	0.313797	−	0.949490i	$-0.398399\pi$
$443$	−13.3798	−	13.3798i	−0.635694	−	0.635694i	−0.949490	+	0.313797i	$0.898399\pi$
$444$		0			0
$445$	−22.6119	−	2.05587i	−1.07191	−	0.0974576i
$446$		0			0
$447$		−	42.6379i		−	2.01670i
$448$		0			0
$449$	4.77864	+	17.8341i	0.225518	+	0.841645i	0.982196	+	0.187858i	$0.0601544\pi$
$449$	4.77864	+	17.8341i	0.225518	+	0.841645i	−0.756678	+	0.653788i	$0.773179\pi$
$450$		0			0
$451$	0.348550	−	0.603706i	0.0164126	−	0.0284274i
$452$		0			0
$453$	−38.9040	+	22.4612i	−1.82787	+	1.05532i
$454$		0			0
$455$	0.166548	+	6.97359i	0.00780788	+	0.326927i
$456$		0			0
$457$	−13.0318	+	7.52390i	−0.609601	+	0.351953i	−0.772809	−	0.634638i	$-0.781149\pi$
$457$	−13.0318	+	7.52390i	−0.609601	+	0.351953i	0.163208	+	0.986592i	$0.447816\pi$
$458$		0			0
$459$	−4.41990	+	7.65549i	−0.206303	+	0.357328i
$460$		0			0
$461$	3.12241	+	11.6530i	0.145425	+	0.542734i	0.999736	+	0.0229718i	$0.00731278\pi$
$461$	3.12241	+	11.6530i	0.145425	+	0.542734i	−0.854311	+	0.519762i	$0.826021\pi$
$462$		0			0
$463$		−	32.5516i		−	1.51280i	−0.654109	−	0.756400i	$-0.726956\pi$
$463$		−	32.5516i		−	1.51280i	0.654109	−	0.756400i	$-0.273044\pi$
$464$		0			0
$465$	−1.00148	−	1.20181i	−0.0464427	−	0.0557325i
$466$		0			0
$467$	19.4091	+	19.4091i	0.898145	+	0.898145i	0.995272	−	0.0971268i	$-0.0309652\pi$
$467$	19.4091	+	19.4091i	0.898145	+	0.898145i	−0.0971268	+	0.995272i	$0.530965\pi$
$468$		0			0
$469$			11.7006i			0.540283i
$470$		0			0
$471$	−10.6489	−	18.4444i	−0.490675	−	0.849874i
$472$		0			0
$473$	19.2943			0.887153
$474$		0			0
$475$	4.96839	−	3.42873i	0.227965	−	0.157321i
$476$		0			0
$477$	6.54664	+	24.4324i	0.299750	+	1.11868i
$478$		0			0
$479$	−5.16289	−	1.38339i	−0.235899	−	0.0632088i	0.138933	−	0.990302i	$-0.455633\pi$
$479$	−5.16289	−	1.38339i	−0.235899	−	0.0632088i	−0.374831	+	0.927093i	$0.622299\pi$
$480$		0			0
$481$	−26.8142	−	21.2808i	−1.22262	−	0.970321i
$482$		0			0
$483$	−3.03853	−	5.26290i	−0.138258	−	0.239470i
$484$		0			0
$485$	−3.05805	−	1.12484i	−0.138859	−	0.0510765i
$486$		0			0
$487$	−10.2752	−	5.93242i	−0.465616	−	0.268823i	0.248787	−	0.968558i	$-0.419968\pi$
$487$	−10.2752	−	5.93242i	−0.465616	−	0.268823i	−0.714403	+	0.699735i	$0.753301\pi$
$488$		0			0
$489$	9.64173	−	9.64173i	0.436014	−	0.436014i
$490$		0			0
$491$	16.9915	−	9.81007i	0.766817	−	0.442722i	−0.0649209	−	0.997890i	$-0.520680\pi$
$491$	16.9915	−	9.81007i	0.766817	−	0.442722i	0.831738	+	0.555168i	$0.187346\pi$
$492$		0			0
$493$	25.0922	−	25.0922i	1.13010	−	1.13010i
$494$		0			0
$495$	7.61564	−	10.7978i	0.342297	−	0.485326i
$496$		0			0
$497$	12.4350	+	3.33195i	0.557787	+	0.149459i
$498$		0			0
$499$	−25.2879	−	25.2879i	−1.13204	−	1.13204i	−0.989837	−	0.142203i	$-0.954581\pi$
$499$	−25.2879	−	25.2879i	−1.13204	−	1.13204i	−0.142203	−	0.989837i	$-0.545419\pi$
$500$		0			0
$501$	−19.6153	+	5.25591i	−0.876347	+	0.234817i
$502$		0			0
$503$	13.7984	−	3.69726i	0.615239	−	0.164853i	0.0622762	−	0.998059i	$-0.480164\pi$
$503$	13.7984	−	3.69726i	0.615239	−	0.164853i	0.552962	+	0.833206i	$0.313497\pi$
$504$		0			0
$505$	19.9405	−	16.6167i	0.887339	−	0.739433i
$506$		0			0
$507$	15.8181	+	29.5920i	0.702508	+	1.31423i
$508$		0			0
$509$	−9.01986	+	33.6626i	−0.399798	+	1.49207i	0.413653	+	0.910435i	$0.364253\pi$
$509$	−9.01986	+	33.6626i	−0.399798	+	1.49207i	−0.813451	+	0.581633i	$0.802414\pi$
$510$		0			0
$511$	8.23637	+	4.75527i	0.364356	+	0.210361i
$512$		0			0
$513$	1.03167	−	1.78690i	0.0455493	−	0.0788938i
$514$		0			0
$515$	19.8045	−	28.0798i	0.872691	−	1.23734i
$516$		0			0
$517$	0.635331	−	2.37109i	0.0279418	−	0.104280i
$518$		0			0
$519$	51.4717			2.25936
$520$		0			0
$521$	20.2982			0.889281			0.444641	−	0.895709i	$-0.353331\pi$
$521$	20.2982			0.889281			0.444641	+	0.895709i	$0.353331\pi$
$522$		0			0
$523$	−4.88891	+	18.2457i	−0.213777	+	0.797827i	0.772816	+	0.634630i	$0.218847\pi$
$523$	−4.88891	+	18.2457i	−0.213777	+	0.797827i	−0.986593	+	0.163197i	$0.947819\pi$
$524$		0			0
$525$	−10.0875	−	4.78777i	−0.440256	−	0.208955i
$526$		0			0
$527$	−0.701004	+	1.21417i	−0.0305362	+	0.0528903i
$528$		0			0
$529$	−13.5056	−	7.79747i	−0.587201	−	0.339020i
$530$		0			0
$531$	11.1758	−	41.7085i	0.484987	−	1.80999i
$532$		0			0
$533$	−1.54745	+	0.178038i	−0.0670277	+	0.00771170i
$534$		0			0
$535$	−15.8831	−	1.44409i	−0.686688	−	0.0624336i
$536$		0			0
$537$	−7.63598	+	2.04605i	−0.329517	+	0.0882938i
$538$		0			0
$539$	9.74349	−	2.61076i	0.419682	−	0.112453i
$540$		0			0
$541$	−20.5158	−	20.5158i	−0.882042	−	0.882042i	0.111700	−	0.993742i	$-0.464371\pi$
$541$	−20.5158	−	20.5158i	−0.882042	−	0.882042i	−0.993742	+	0.111700i	$0.964371\pi$
$542$		0			0
$543$	58.2544	+	15.6092i	2.49993	+	0.669856i
$544$		0			0
$545$	11.8047	+	8.32580i	0.505660	+	0.356638i
$546$		0			0
$547$	−28.8176	+	28.8176i	−1.23215	+	1.23215i	−0.269018	+	0.963135i	$0.586699\pi$
$547$	−28.8176	+	28.8176i	−1.23215	+	1.23215i	−0.963135	+	0.269018i	$0.913301\pi$
$548$		0			0
$549$	18.6580	−	10.7722i	0.796304	−	0.459747i
$550$		0			0
$551$	−5.85689	+	5.85689i	−0.249512	+	0.249512i
$552$		0			0
$553$	2.98347	+	1.72250i	0.126870	+	0.0732484i
$554$		0			0
$555$	49.7419	−	22.9892i	2.11143	−	0.975838i
$556$		0			0
$557$	−3.75786	−	6.50881i	−0.159226	−	0.275787i	0.775364	−	0.631515i	$-0.217566\pi$
$557$	−3.75786	−	6.50881i	−0.159226	−	0.275787i	−0.934590	+	0.355727i	$0.884233\pi$
$558$		0			0
$559$	−25.6828	−	34.6284i	−1.08627	−	1.46462i
$560$		0			0
$561$	−20.8085	−	5.57562i	−0.878535	−	0.235403i
$562$		0			0
$563$	6.18074	+	23.0668i	0.260487	+	0.972151i	0.964955	+	0.262415i	$0.0845190\pi$
$563$	6.18074	+	23.0668i	0.260487	+	0.972151i	−0.704468	+	0.709736i	$0.748814\pi$
$564$		0			0
$565$	17.5397	−	8.10633i	0.737902	−	0.341036i
$566$		0			0
$567$	5.68898			0.238915
$568$		0			0
$569$	−1.39258	−	2.41202i	−0.0583801	−	0.101117i	0.835358	−	0.549706i	$-0.185260\pi$
$569$	−1.39258	−	2.41202i	−0.0583801	−	0.101117i	−0.893738	+	0.448589i	$0.851927\pi$
$570$		0			0
$571$		−	28.8794i		−	1.20857i	−0.796769	−	0.604284i	$-0.793459\pi$
$571$		−	28.8794i		−	1.20857i	0.796769	−	0.604284i	$-0.206541\pi$
$572$		0			0
$573$	13.6425	+	13.6425i	0.569924	+	0.569924i
$574$		0			0
$575$	13.5621	−	1.09354i	0.565579	−	0.0456038i
$576$		0			0
$577$		−	4.20458i		−	0.175039i	−0.996163	−	0.0875196i	$-0.972106\pi$
$577$		−	4.20458i		−	0.175039i	0.996163	−	0.0875196i	$-0.0278940\pi$
$578$		0			0
$579$	1.33742	+	4.99131i	0.0555811	+	0.207432i
$580$		0			0
$581$	2.70632	−	4.68748i	0.112277	−	0.194469i
$582$		0			0
$583$	−9.65190	+	5.57253i	−0.399741	+	0.230790i
$584$		0			0
$585$	−29.5166	+	0.704933i	−1.22036	+	0.0291454i
$586$		0			0
$587$	4.69510	−	2.71072i	0.193787	−	0.111883i	−0.399967	−	0.916530i	$-0.630978\pi$
$587$	4.69510	−	2.71072i	0.193787	−	0.111883i	0.593754	+	0.804646i	$0.297645\pi$
$588$		0			0
$589$	0.163625	−	0.283406i	0.00674204	−	0.0116776i
$590$		0			0
$591$	2.12493	+	7.93036i	0.0874081	+	0.326211i
$592$		0			0
$593$		−	15.8446i		−	0.650660i	−0.945601	−	0.325330i	$-0.894525\pi$
$593$		−	15.8446i		−	0.650660i	0.945601	−	0.325330i	$-0.105475\pi$
$594$		0			0
$595$	−0.906103	+	9.96594i	−0.0371466	+	0.408564i
$596$		0			0
$597$	29.9402	+	29.9402i	1.22537	+	1.22537i
$598$		0			0
$599$			34.8884i			1.42550i	0.701418	+	0.712750i	$0.252550\pi$
$599$			34.8884i			1.42550i	−0.701418	+	0.712750i	$0.747450\pi$
$600$		0			0
$601$	11.6867	+	20.2419i	0.476710	+	0.825686i	0.999644	−	0.0266875i	$-0.00849591\pi$
$601$	11.6867	+	20.2419i	0.476710	+	0.825686i	−0.522934	+	0.852373i	$0.675163\pi$
$602$		0			0
$603$	−49.5242			−2.01678
$604$		0			0
$605$	−17.6205	−	6.48137i	−0.716377	−	0.263505i
$606$		0			0
$607$	8.38242	+	31.2836i	0.340232	+	1.26976i	0.898085	+	0.439823i	$0.144959\pi$
$607$	8.38242	+	31.2836i	0.340232	+	1.26976i	−0.557853	+	0.829940i	$0.688375\pi$
$608$		0			0
$609$	14.7989	+	3.96536i	0.599683	+	0.160685i
$610$		0			0
$611$	−5.10118	+	2.01591i	−0.206372	+	0.0815549i
$612$		0			0
$613$	19.5519	+	33.8649i	0.789695	+	1.36779i	0.926154	+	0.377146i	$0.123095\pi$
$613$	19.5519	+	33.8649i	0.789695	+	1.36779i	−0.136458	+	0.990646i	$0.543572\pi$
$614$		0			0
$615$	0.860766	−	2.34012i	0.0347094	−	0.0943627i
$616$		0			0
$617$	−12.3761	−	7.14533i	−0.498242	−	0.287660i	0.229745	−	0.973251i	$-0.426211\pi$
$617$	−12.3761	−	7.14533i	−0.498242	−	0.287660i	−0.727987	+	0.685591i	$0.759544\pi$
$618$		0			0
$619$	6.85038	−	6.85038i	0.275340	−	0.275340i	−0.555906	−	0.831245i	$-0.687628\pi$
$619$	6.85038	−	6.85038i	0.275340	−	0.275340i	0.831245	+	0.555906i	$0.187628\pi$
$620$		0			0
$621$	4.02754	−	2.32530i	0.161620	−	0.0933111i
$622$		0			0
$623$	−6.21223	+	6.21223i	−0.248888	+	0.248888i
$624$		0			0
$625$	19.3681	−	15.8074i	0.774726	−	0.632297i
$626$		0			0
$627$	4.85701	+	1.30143i	0.193970	+	0.0519742i
$628$		0			0
$629$	−34.7257	−	34.7257i	−1.38461	−	1.38461i
$630$		0			0
$631$	37.2254	−	9.97452i	1.48192	−	0.397080i	0.574921	−	0.818209i	$-0.305033\pi$
$631$	37.2254	−	9.97452i	1.48192	−	0.397080i	0.907000	+	0.421130i	$0.138366\pi$
$632$		0			0
$633$	−28.2332	+	7.56506i	−1.12217	+	0.300684i
$634$		0			0
$635$	0.952668	−	10.4781i	0.0378055	−	0.415810i
$636$		0			0
$637$	−17.6553	−	14.0119i	−0.699527	−	0.555171i
$638$		0			0
$639$	−14.1029	+	52.6327i	−0.557902	+	2.08212i
$640$		0			0
$641$	6.48111	+	3.74187i	0.255988	+	0.147795i	0.622503	−	0.782617i	$-0.286116\pi$
$641$	6.48111	+	3.74187i	0.255988	+	0.147795i	−0.366515	+	0.930412i	$0.619449\pi$
$642$		0			0
$643$	11.9973	−	20.7800i	0.473128	−	0.819482i	−0.526399	−	0.850238i	$-0.676458\pi$
$643$	11.9973	−	20.7800i	0.473128	−	0.819482i	0.999527	+	0.0307558i	$0.00979141\pi$
$644$		0			0
$645$	68.0044	−	11.7525i	2.67767	−	0.462752i
$646$		0			0
$647$	6.03995	−	22.5414i	0.237455	−	0.886195i	−0.739572	−	0.673078i	$-0.764972\pi$
$647$	6.03995	−	22.5414i	0.237455	−	0.886195i	0.977027	−	0.213117i	$-0.0683615\pi$
$648$		0			0
$649$	19.0257			0.746825
$650$		0			0
$651$	−0.605318			−0.0237243
$652$		0			0
$653$	−5.46196	+	20.3843i	−0.213743	+	0.797700i	0.772862	+	0.634574i	$0.218824\pi$
$653$	−5.46196	+	20.3843i	−0.213743	+	0.797700i	−0.986605	+	0.163126i	$0.947842\pi$
$654$		0			0
$655$	−33.7683	+	5.83581i	−1.31944	+	0.228024i
$656$		0			0
$657$	−20.1273	+	34.8614i	−0.785239	+	1.36007i
$658$		0			0
$659$	−13.0042	−	7.50797i	−0.506571	−	0.292469i	0.224852	−	0.974393i	$-0.427810\pi$
$659$	−13.0042	−	7.50797i	−0.506571	−	0.292469i	−0.731423	+	0.681924i	$0.761144\pi$
$660$		0			0
$661$	1.43378	−	5.35096i	0.0557677	−	0.208128i	−0.932420	−	0.361377i	$-0.882307\pi$
$661$	1.43378	−	5.35096i	0.0557677	−	0.208128i	0.988188	+	0.153249i	$0.0489735\pi$
$662$		0			0
$663$	17.6915	+	44.7676i	0.687080	+	1.73863i
$664$		0			0
$665$	0.211498	−	2.32620i	0.00820154	−	0.0902061i
$666$		0			0
$667$	−18.0329	+	4.83189i	−0.698235	+	0.187092i
$668$		0			0
$669$	−25.1715	+	6.74467i	−0.973185	+	0.260764i
$670$		0			0
$671$	6.71243	+	6.71243i	0.259130	+	0.259130i
$672$		0			0
$673$	30.3890	+	8.14271i	1.17141	+	0.313878i	0.791514	−	0.611151i	$-0.209293\pi$
$673$	30.3890	+	8.14271i	1.17141	+	0.313878i	0.379896	+	0.925029i	$0.375960\pi$
$674$		0			0
$675$	3.66394	−	7.71969i	0.141025	−	0.297131i
$676$		0			0
$677$	19.4080	−	19.4080i	0.745910	−	0.745910i	−0.227798	−	0.973708i	$-0.573153\pi$
$677$	19.4080	−	19.4080i	0.745910	−	0.745910i	0.973708	+	0.227798i	$0.0731527\pi$
$678$		0			0
$679$	−1.09187	+	0.630389i	−0.0419019	+	0.0241921i
$680$		0			0
$681$	25.0756	−	25.0756i	0.960899	−	0.960899i
$682$		0			0
$683$	−21.0802	−	12.1706i	−0.806610	−	0.465697i	0.0391672	−	0.999233i	$-0.487530\pi$
$683$	−21.0802	−	12.1706i	−0.806610	−	0.465697i	−0.845777	+	0.533536i	$0.820863\pi$
$684$		0			0
$685$	−13.0794	+	35.5583i	−0.499739	+	1.35861i
$686$		0			0
$687$	6.14597	+	10.6451i	0.234483	+	0.406137i
$688$		0			0
$689$	22.8490	+	9.90507i	0.870476	+	0.377353i
$690$		0			0
$691$	−11.5308	−	3.08967i	−0.438652	−	0.117537i	0.0327325	−	0.999464i	$-0.489579\pi$
$691$	−11.5308	−	3.08967i	−0.438652	−	0.117537i	−0.471385	+	0.881928i	$0.656246\pi$
$692$		0			0
$693$	−1.32326	−	4.93848i	−0.0502666	−	0.187597i
$694$		0			0
$695$	−6.52886	−	2.40151i	−0.247654	−	0.0910946i
$696$		0			0
$697$	−2.23460			−0.0846413
$698$		0			0
$699$	−34.9585	−	60.5498i	−1.32225	−	2.29020i
$700$		0			0
$701$			21.2613i			0.803029i	0.915853	+	0.401515i	$0.131516\pi$
$701$			21.2613i			0.803029i	−0.915853	+	0.401515i	$0.868484\pi$
$702$		0			0
$703$	8.10550	+	8.10550i	0.305705	+	0.305705i
$704$		0			0
$705$	0.795011	−	8.74408i	0.0299419	−	0.329321i
$706$		0			0
$707$		−	10.0435i		−	0.377723i
$708$		0			0
$709$	5.58329	+	20.8371i	0.209685	+	0.782555i	0.987970	+	0.154644i	$0.0494231\pi$
$709$	5.58329	+	20.8371i	0.209685	+	0.782555i	−0.778285	+	0.627911i	$0.783910\pi$
$710$		0			0
$711$	−7.29071	+	12.6279i	−0.273423	+	0.473582i
$712$		0			0
$713$	0.638775	−	0.368797i	0.0239223	−	0.0138116i
$714$		0			0
$715$	−3.66608	−	12.4819i	−0.137104	−	0.466798i
$716$		0			0
$717$	−58.3770	+	33.7040i	−2.18013	+	1.25870i
$718$		0			0
$719$	4.13804	−	7.16730i	0.154323	−	0.267295i	−0.778489	−	0.627658i	$-0.784014\pi$
$719$	4.13804	−	7.16730i	0.154323	−	0.267295i	0.932812	+	0.360363i	$0.117347\pi$
$720$		0			0
$721$	−3.44115	−	12.8425i	−0.128155	−	0.478282i
$722$		0			0
$723$			2.27344i			0.0845500i
$724$		0			0
$725$	−22.2277	+	26.1266i	−0.825514	+	0.970316i
$726$		0			0
$727$	2.41639	+	2.41639i	0.0896190	+	0.0896190i	0.750495	−	0.660876i	$-0.229815\pi$
$727$	2.41639	+	2.41639i	0.0896190	+	0.0896190i	−0.660876	+	0.750495i	$0.729815\pi$
$728$		0			0
$729$			37.3127i			1.38195i
$730$		0			0
$731$	−30.9246	−	53.5629i	−1.14379	−	1.98110i
$732$		0			0
$733$	−32.4183			−1.19740			−0.598699	−	0.800974i	$-0.704315\pi$
$733$	−32.4183			−1.19740			−0.598699	+	0.800974i	$0.704315\pi$
$734$		0			0
$735$	32.7515	−	15.1367i	1.20806	−	0.558327i
$736$		0			0
$737$	−5.64773	−	21.0776i	−0.208037	−	0.776404i
$738$		0			0
$739$	−43.7773	−	11.7301i	−1.61038	−	0.431499i	−0.662221	−	0.749309i	$-0.730386\pi$
$739$	−43.7773	−	11.7301i	−1.61038	−	0.431499i	−0.948154	+	0.317810i	$0.897053\pi$
$740$		0			0
$741$	−4.12945	−	10.4494i	−0.151699	−	0.383870i
$742$		0			0
$743$	7.57500	+	13.1203i	0.277900	+	0.481336i	0.970863	−	0.239637i	$-0.0770284\pi$
$743$	7.57500	+	13.1203i	0.277900	+	0.481336i	−0.692963	+	0.720973i	$0.743695\pi$
$744$		0			0
$745$	33.5302	−	15.4967i	1.22845	−	0.567754i
$746$		0			0
$747$	19.8403	+	11.4548i	0.725919	+	0.419110i
$748$		0			0
$749$	−4.36362	+	4.36362i	−0.159443	+	0.159443i
$750$		0			0
$751$	−5.51200	+	3.18236i	−0.201136	+	0.116126i	−0.597185	−	0.802103i	$-0.703714\pi$
$751$	−5.51200	+	3.18236i	−0.201136	+	0.116126i	0.396049	+	0.918229i	$0.370381\pi$
$752$		0			0
$753$	−11.8498	+	11.8498i	−0.431830	+	0.431830i
$754$		0			0
$755$	−31.8029	−	22.4304i	−1.15743	−	0.816326i
$756$		0			0
$757$	27.3061	+	7.31666i	0.992459	+	0.265928i	0.718283	−	0.695751i	$-0.244928\pi$
$757$	27.3061	+	7.31666i	0.992459	+	0.265928i	0.274176	+	0.961680i	$0.411595\pi$
$758$		0			0
$759$	8.01399	+	8.01399i	0.290889	+	0.290889i
$760$		0			0
$761$	31.4842	−	8.43618i	1.14130	−	0.305811i	0.361828	−	0.932245i	$-0.382153\pi$
$761$	31.4842	−	8.43618i	1.14130	−	0.305811i	0.779475	+	0.626434i	$0.215486\pi$
$762$		0			0
$763$	5.39900	−	1.44666i	0.195457	−	0.0523725i
$764$		0			0
$765$	−42.1820	−	3.83519i	−1.52509	−	0.138662i
$766$		0			0
$767$	−25.3252	−	34.1463i	−0.914441	−	1.23295i
$768$		0			0
$769$	10.7440	−	40.0972i	0.387439	−	1.44594i	−0.446848	−	0.894610i	$-0.647453\pi$
$769$	10.7440	−	40.0972i	0.387439	−	1.44594i	0.834286	−	0.551331i	$-0.185880\pi$
$770$		0			0
$771$	−23.9490	−	13.8270i	−0.862503	−	0.497966i
$772$		0			0
$773$	1.11886	−	1.93793i	0.0402427	−	0.0697025i	−0.845202	−	0.534446i	$-0.820520\pi$
$773$	1.11886	−	1.93793i	0.0402427	−	0.0697025i	0.885445	+	0.464744i	$0.153854\pi$
$774$		0			0
$775$	0.581108	−	1.22436i	0.0208740	−	0.0439802i
$776$		0			0
$777$	5.48776	−	20.4806i	0.196872	−	0.734738i
$778$		0			0
$779$	0.521588			0.0186878
$780$		0			0
$781$	−24.0089			−0.859106
$782$		0			0
$783$	−3.03457	+	11.3252i	−0.108447	+	0.404729i
$784$		0			0
$785$	10.6343	−	15.0778i	0.379554	−	0.538150i
$786$		0			0
$787$	21.6174	−	37.4425i	0.770577	−	1.33468i	−0.166669	−	0.986013i	$-0.553301\pi$
$787$	21.6174	−	37.4425i	0.770577	−	1.33468i	0.937247	−	0.348666i	$-0.113365\pi$
$788$		0			0
$789$	22.6990	+	13.1053i	0.808105	+	0.466559i
$790$		0			0
$791$	1.93507	−	7.22176i	0.0688030	−	0.256776i
$792$		0			0
$793$	3.11215	−	20.9820i	0.110516	−	0.745094i
$794$		0			0
$795$	−30.6246	+	25.5200i	−1.08614	+	0.905099i
$796$		0			0
$797$	21.9836	−	5.89049i	0.778699	−	0.208652i	0.152488	−	0.988305i	$-0.451271\pi$
$797$	21.9836	−	5.89049i	0.778699	−	0.208652i	0.626211	+	0.779653i	$0.284605\pi$
$798$		0			0
$799$	−7.60066	+	2.03659i	−0.268892	+	0.0720494i
$800$		0			0
$801$	−26.2940	−	26.2940i	−0.929053	−	0.929053i
$802$		0			0
$803$	−17.1324	−	4.59062i	−0.604590	−	0.161999i
$804$		0			0
$805$	3.03437	−	4.30228i	0.106947	−	0.151635i
$806$		0			0
$807$	−34.1289	+	34.1289i	−1.20139	+	1.20139i
$808$		0			0
$809$	−25.3301	+	14.6243i	−0.890558	+	0.514164i	−0.874125	−	0.485701i	$-0.838564\pi$
$809$	−25.3301	+	14.6243i	−0.890558	+	0.514164i	−0.0164333	+	0.999865i	$0.505231\pi$
$810$		0			0
$811$	−16.1564	+	16.1564i	−0.567327	+	0.567327i	−0.931379	−	0.364052i	$-0.881393\pi$
$811$	−16.1564	+	16.1564i	−0.567327	+	0.567327i	0.364052	+	0.931379i	$0.381393\pi$
$812$		0			0
$813$	−40.9790	−	23.6593i	−1.43720	−	0.829767i
$814$		0			0
$815$	11.0865	+	4.07794i	0.388342	+	0.142844i
$816$		0			0
$817$	7.21825	+	12.5024i	0.252535	+	0.437403i
$818$		0			0
$819$	−7.10191	+	8.94856i	−0.248161	+	0.312688i
$820$		0			0
$821$	25.6639	+	6.87663i	0.895677	+	0.239996i	0.677159	−	0.735837i	$-0.263211\pi$
$821$	25.6639	+	6.87663i	0.895677	+	0.239996i	0.218518	+	0.975833i	$0.429878\pi$
$822$		0			0
$823$	10.8708	+	40.5702i	0.378931	+	1.41419i	0.847516	+	0.530770i	$0.178097\pi$
$823$	10.8708	+	40.5702i	0.378931	+	1.41419i	−0.468585	+	0.883418i	$0.655236\pi$
$824$		0			0
$825$	20.4828	+	3.75564i	0.713119	+	0.130754i
$826$		0			0
$827$	48.4948			1.68633			0.843165	−	0.537655i	$-0.180690\pi$
$827$	48.4948			1.68633			0.843165	+	0.537655i	$0.180690\pi$
$828$		0			0
$829$	−20.4336	−	35.3921i	−0.709689	−	1.22922i	−0.964973	−	0.262351i	$-0.915502\pi$
$829$	−20.4336	−	35.3921i	−0.709689	−	1.22922i	0.255284	−	0.966866i	$-0.417831\pi$
$830$		0			0
$831$			34.9998i			1.21413i
$832$		0			0
$833$	−22.8644	−	22.8644i	−0.792205	−	0.792205i
$834$		0			0
$835$	−11.2624	−	13.5151i	−0.389750	−	0.467710i
$836$		0			0
$837$		−	0.463232i		−	0.0160116i
$838$		0			0
$839$	−7.70239	−	28.7457i	−0.265916	−	0.992412i	−0.961687	−	0.274149i	$-0.911604\pi$
$839$	−7.70239	−	28.7457i	−0.265916	−	0.992412i	0.695771	−	0.718263i	$-0.255063\pi$
$840$		0			0
$841$	9.03332	−	15.6462i	0.311494	−	0.539523i
$842$		0			0
$843$	−54.2075	+	31.2967i	−1.86701	+	1.07792i
$844$		0			0
$845$	−17.5219	+	23.1944i	−0.602773	+	0.797913i
$846$		0			0
$847$	−6.29135	+	3.63231i	−0.216173	+	0.124808i
$848$		0			0
$849$	−11.8183	+	20.4700i	−0.405605	+	0.702528i
$850$		0			0
$851$	6.68697	+	24.9561i	0.229227	+	0.855485i
$852$		0			0
$853$		−	8.67930i		−	0.297174i	−0.988899	−	0.148587i	$-0.952528\pi$
$853$		−	8.67930i		−	0.297174i	0.988899	−	0.148587i	$-0.0474724\pi$
$854$		0			0
$855$	9.84592	+	0.895190i	0.336723	+	0.0306149i
$856$		0			0
$857$	2.38807	+	2.38807i	0.0815751	+	0.0815751i	0.746717	−	0.665142i	$-0.231629\pi$
$857$	2.38807	+	2.38807i	0.0815751	+	0.0815751i	−0.665142	+	0.746717i	$0.731629\pi$
$858$		0			0
$859$		−	0.237935i		−	0.00811823i	−0.999992	−	0.00405912i	$-0.998708\pi$
$859$		−	0.237935i		−	0.00811823i	0.999992	−	0.00405912i	$-0.00129206\pi$
$860$		0			0
$861$	−0.482394	−	0.835530i	−0.0164399	−	0.0284748i
$862$		0			0
$863$	48.8736			1.66368			0.831839	−	0.555017i	$-0.187288\pi$
$863$	48.8736			1.66368			0.831839	+	0.555017i	$0.187288\pi$
$864$		0			0
$865$	18.7073	+	40.4771i	0.636067	+	1.37626i
$866$		0			0
$867$	6.51630	+	24.3192i	0.221305	+	0.825922i
$868$		0			0
$869$	−6.20588	−	1.66286i	−0.210520	−	0.0564087i
$870$		0			0
$871$	−30.3112	+	38.1927i	−1.02706	+	1.29411i
$872$		0			0
$873$	−2.66820	−	4.62145i	−0.0903048	−	0.156412i
$874$		0			0
$875$	0.0987891	−	9.67288i	0.00333968	−	0.327003i
$876$		0			0
$877$	−30.1953	−	17.4333i	−1.01962	−	0.588680i	−0.105629	−	0.994406i	$-0.533686\pi$
$877$	−30.1953	−	17.4333i	−1.01962	−	0.588680i	−0.913995	+	0.405725i	$0.867019\pi$
$878$		0			0
$879$	−33.1837	+	33.1837i	−1.11926	+	1.11926i
$880$		0			0
$881$	−24.6799	+	14.2489i	−0.831486	+	0.480058i	−0.854361	−	0.519680i	$-0.826051\pi$
$881$	−24.6799	+	14.2489i	−0.831486	+	0.480058i	0.0228755	+	0.999738i	$0.492718\pi$
$882$		0			0
$883$	10.7320	−	10.7320i	0.361160	−	0.361160i	−0.503080	−	0.864240i	$-0.667800\pi$
$883$	10.7320	−	10.7320i	0.361160	−	0.361160i	0.864240	+	0.503080i	$0.167800\pi$
$884$		0			0
$885$	67.0577	−	11.5888i	2.25412	−	0.389555i
$886$		0			0
$887$	12.5580	+	3.36490i	0.421655	+	0.112982i	0.463406	−	0.886146i	$-0.346627\pi$
$887$	12.5580	+	3.36490i	0.421655	+	0.112982i	−0.0417512	+	0.999128i	$0.513294\pi$
$888$		0			0
$889$	−2.87868	−	2.87868i	−0.0965478	−	0.0965478i
$890$		0			0
$891$	−10.2482	+	2.74600i	−0.343328	+	0.0919943i
$892$		0			0
$893$	1.77411	−	0.475371i	0.0593683	−	0.0159077i
$894$		0			0
$895$	−4.38429	−	5.26126i	−0.146551	−	0.175865i
$896$		0			0
$897$	3.71560	−	25.0505i	0.124060	−	0.836413i
$898$		0			0
$899$	−0.481289	+	1.79620i	−0.0160519	+	0.0599065i
$900$		0			0
$901$	30.9398	+	17.8631i	1.03075	+	0.595105i
$902$		0			0
$903$	13.3517	−	23.1258i	0.444316	−	0.769578i
$904$		0			0
$905$	8.89743	+	51.4841i	0.295761	+	1.71139i
$906$		0			0
$907$	13.2347	−	49.3926i	0.439451	−	1.64006i	−0.290732	−	0.956804i	$-0.593899\pi$
$907$	13.2347	−	49.3926i	0.439451	−	1.64006i	0.730184	−	0.683251i	$-0.239434\pi$
$908$		0			0
$909$	42.5102			1.40997
$910$		0			0
$911$	−45.3842			−1.50365			−0.751823	−	0.659365i	$-0.770825\pi$
$911$	−45.3842			−1.50365			−0.751823	+	0.659365i	$0.770825\pi$
$912$		0			0
$913$	−2.61261	+	9.75039i	−0.0864647	+	0.322691i
$914$		0			0
$915$	27.7472	+	19.5699i	0.917293	+	0.646960i
$916$		0			0
$917$	−6.62993	+	11.4834i	−0.218940	+	0.379214i
$918$		0			0
$919$	26.3431	+	15.2092i	0.868977	+	0.501704i	0.867008	−	0.498294i	$-0.166040\pi$
$919$	26.3431	+	15.2092i	0.868977	+	0.501704i	0.00196918	+	0.999998i	$0.499373\pi$
$920$		0			0
$921$	18.7289	−	69.8973i	0.617139	−	2.30319i
$922$		0			0
$923$	31.9584	+	43.0898i	1.05192	+	1.41832i
$924$		0			0
$925$	36.1572	+	30.7614i	1.18884	+	1.01143i
$926$		0			0
$927$	54.3576	−	14.5651i	1.78534	−	0.478380i
$928$		0			0
$929$	−23.9374	+	6.41401i	−0.785361	+	0.210437i	−0.629147	−	0.777286i	$-0.716596\pi$
$929$	−23.9374	+	6.41401i	−0.785361	+	0.210437i	−0.156214	+	0.987723i	$0.549929\pi$
$930$		0			0
$931$	5.33689	+	5.33689i	0.174910	+	0.174910i
$932$		0			0
$933$	−28.7133	−	7.69371i	−0.940031	−	0.251881i
$934$		0			0
$935$	−3.17817	−	18.3901i	−0.103937	−	0.601422i
$936$		0			0
$937$	25.3459	−	25.3459i	0.828014	−	0.828014i	−0.159228	−	0.987242i	$-0.550901\pi$
$937$	25.3459	−	25.3459i	0.828014	−	0.828014i	0.987242	+	0.159228i	$0.0509005\pi$
$938$		0			0
$939$	32.6792	−	18.8674i	1.06645	−	0.615713i
$940$		0			0
$941$	27.5969	−	27.5969i	0.899632	−	0.899632i	−0.0957715	−	0.995403i	$-0.530532\pi$
$941$	27.5969	−	27.5969i	0.899632	−	0.899632i	0.995403	+	0.0957715i	$0.0305318\pi$
$942$		0			0
$943$	1.01811	+	0.587809i	0.0331544	+	0.0191417i
$944$		0			0
$945$	−1.38713	−	3.00134i	−0.0451233	−	0.0976337i
$946$		0			0
$947$	26.4416	+	45.7982i	0.859237	+	1.48824i	0.872658	+	0.488332i	$0.162394\pi$
$947$	26.4416	+	45.7982i	0.859237	+	1.48824i	−0.0134210	+	0.999910i	$0.504272\pi$
$948$		0			0
$949$	14.5661	+	36.8589i	0.472835	+	1.19649i
$950$		0			0
$951$	5.76184	+	1.54388i	0.186840	+	0.0500637i
$952$		0			0
$953$	−12.2949	−	45.8852i	−0.398271	−	1.48637i	−0.816136	−	0.577860i	$-0.803888\pi$
$953$	−12.2949	−	45.8852i	−0.398271	−	1.48637i	0.417865	−	0.908509i	$-0.362779\pi$
$954$		0			0
$955$	−5.77005	+	15.6867i	−0.186715	+	0.507611i
$956$		0			0
$957$	−28.5730			−0.923634
$958$		0			0
$959$	7.33001	+	12.6960i	0.236699	+	0.409974i
$960$		0			0
$961$			30.9265i			0.997630i
$962$		0			0
$963$	−18.4696	−	18.4696i	−0.595173	−	0.595173i
$964$		0			0
$965$	−3.43906	+	2.86582i	−0.110707	+	0.0922539i
$966$		0			0
$967$			39.7754i			1.27909i	0.768753	+	0.639546i	$0.220878\pi$
$967$			39.7754i			1.27909i	−0.768753	+	0.639546i	$0.779122\pi$
$968$		0			0
$969$	−4.17182	−	15.5694i	−0.134018	−	0.500163i
$970$		0			0
$971$	−0.597739	+	1.03531i	−0.0191824	+	0.0332248i	−0.875457	−	0.483296i	$-0.839440\pi$
$971$	−0.597739	+	1.03531i	−0.0191824	+	0.0332248i	0.856275	+	0.516520i	$0.172773\pi$
$972$		0			0
$973$	−2.33111	+	1.34586i	−0.0747318	+	0.0431464i
$974$		0			0
$975$	−20.5243	−	41.7605i	−0.657305	−	1.33741i
$976$		0			0
$977$	−14.2623	+	8.23433i	−0.456291	+	0.263439i	−0.710483	−	0.703714i	$-0.751524\pi$
$977$	−14.2623	+	8.23433i	−0.456291	+	0.263439i	0.254193	+	0.967154i	$0.418190\pi$
$978$		0			0
$979$	8.19223	−	14.1894i	0.261825	−	0.453494i
$980$		0			0
$981$	6.12315	+	22.8519i	0.195497	+	0.729605i
$982$		0			0
$983$		−	1.80446i		−	0.0575534i	−0.999586	−	0.0287767i	$-0.990839\pi$
$983$		−	1.80446i		−	0.0575534i	0.999586	−	0.0287767i	$-0.00916118\pi$
$984$		0			0
$985$	−5.46409	+	4.55331i	−0.174100	+	0.145081i
$986$		0			0
$987$	−2.40229	−	2.40229i	−0.0764657	−	0.0764657i
$988$		0			0
$989$			32.5387i			1.03467i
$990$		0			0
$991$	0.661562	+	1.14586i	0.0210152	+	0.0363994i	0.876342	−	0.481690i	$-0.159977\pi$
$991$	0.661562	+	1.14586i	0.0210152	+	0.0363994i	−0.855327	+	0.518089i	$0.826643\pi$
$992$		0			0
$993$	90.7637			2.88030
$994$		0			0
$995$	−12.6631	+	34.4265i	−0.401447	+	1.09139i
$996$		0			0
$997$	−12.2028	−	45.5416i	−0.386467	−	1.44232i	−0.835841	−	0.548972i	$-0.815019\pi$
$997$	−12.2028	−	45.5416i	−0.386467	−	1.44232i	0.449373	−	0.893344i	$-0.351647\pi$
$998$		0			0
$999$	15.6732	+	4.19962i	0.495878	+	0.132870i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bf.c.93.1	✓	20
5.2	odd	4		260.2.bk.c.197.5	yes	20
5.3	odd	4		1300.2.bs.d.457.1		20
5.4	even	2		1300.2.bn.d.93.5		20
13.7	odd	12		260.2.bk.c.33.5	yes	20
65.7	even	12	inner	260.2.bf.c.137.1	yes	20
65.33	even	12		1300.2.bn.d.657.5		20
65.59	odd	12		1300.2.bs.d.293.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.c.93.1	✓	20	1.1	even	1	trivial
260.2.bf.c.137.1	yes	20	65.7	even	12	inner
260.2.bk.c.33.5	yes	20	13.7	odd	12
260.2.bk.c.197.5	yes	20	5.2	odd	4
1300.2.bn.d.93.5		20	5.4	even	2
1300.2.bn.d.657.5		20	65.33	even	12
1300.2.bs.d.293.1		20	65.59	odd	12
1300.2.bs.d.457.1		20	5.3	odd	4

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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.668040 + 2.49316i) q^{3} +(-2.20341 + 0.380790i) q^{5} +(-0.432607 + 0.749297i) q^{7} +(-3.17149 - 1.83106i) q^{9} +O(q^{10})\)	\(q+(-0.668040 + 2.49316i) q^{3} +(-2.20341 + 0.380790i) q^{5} +(-0.432607 + 0.749297i) q^{7} +(-3.17149 - 1.83106i) q^{9} +(0.417628 - 1.55861i) q^{11} +(-3.35321 + 1.32514i) q^{13} +(0.522592 - 5.74783i) q^{15} +(-4.99621 + 1.33873i) q^{17} +(1.16619 - 0.312480i) q^{19} +(-1.57912 - 1.57912i) q^{21} +(2.62850 + 0.704305i) q^{23} +(4.71000 - 1.67807i) q^{25} +(1.20845 - 1.20845i) q^{27} +(-5.94138 + 3.43026i) q^{29} +(0.191663 - 0.191663i) q^{31} +(3.60687 + 2.08243i) q^{33} +(0.667884 - 1.81574i) q^{35} +(4.74722 + 8.22242i) q^{37} +(-1.06370 - 9.24533i) q^{39} +(0.417297 + 0.111814i) q^{41} +(3.09480 + 11.5499i) q^{43} +(7.68533 + 2.82690i) q^{45} +1.52128 q^{47} +(3.12570 + 5.41387i) q^{49} -13.3507i q^{51} +(-4.88398 - 4.88398i) q^{53} +(-0.326700 + 3.59327i) q^{55} +3.11625i q^{57} +(3.05172 + 11.3892i) q^{59} +(-2.94152 + 5.09486i) q^{61} +(2.74402 - 1.58426i) q^{63} +(6.88388 - 4.19668i) q^{65} +(11.7116 - 6.76168i) q^{67} +(-3.51189 + 6.08277i) q^{69} +(-3.85102 - 14.3722i) q^{71} -10.9921i q^{73} +(1.03723 + 12.8638i) q^{75} +(0.987192 + 0.987192i) q^{77} -3.98168i q^{79} +(-3.28761 - 5.69431i) q^{81} -6.25583 q^{83} +(10.4989 - 4.85228i) q^{85} +(-4.58310 - 17.1044i) q^{87} +(9.80805 + 2.62806i) q^{89} +(0.457701 - 3.08581i) q^{91} +(0.349808 + 0.605885i) q^{93} +(-2.45060 + 1.13259i) q^{95} +(1.26196 + 0.728593i) q^{97} +(-4.17841 + 4.17841i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} - 6 q^{5} - 6 q^{7} + 12 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 - 6 * q^5 - 6 * q^7 + 12 * q^9	\( 20 q - 2 q^{3} - 6 q^{5} - 6 q^{7} + 12 q^{9} - 6 q^{13} + 20 q^{15} + 6 q^{17} - 20 q^{19} - 12 q^{21} + 30 q^{23} - 2 q^{25} - 20 q^{27} - 24 q^{29} + 8 q^{31} - 30 q^{33} + 30 q^{37} - 4 q^{39} + 6 q^{41} + 22 q^{43} + 36 q^{45} - 14 q^{49} + 30 q^{53} - 34 q^{55} + 24 q^{59} - 32 q^{61} - 84 q^{63} - 60 q^{65} - 54 q^{67} + 16 q^{69} + 26 q^{75} + 12 q^{77} + 2 q^{81} - 48 q^{83} + 74 q^{85} + 38 q^{87} + 30 q^{89} - 72 q^{91} - 16 q^{93} - 6 q^{95} - 6 q^{97} - 20 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 - 6 * q^5 - 6 * q^7 + 12 * q^9 - 6 * q^13 + 20 * q^15 + 6 * q^17 - 20 * q^19 - 12 * q^21 + 30 * q^23 - 2 * q^25 - 20 * q^27 - 24 * q^29 + 8 * q^31 - 30 * q^33 + 30 * q^37 - 4 * q^39 + 6 * q^41 + 22 * q^43 + 36 * q^45 - 14 * q^49 + 30 * q^53 - 34 * q^55 + 24 * q^59 - 32 * q^61 - 84 * q^63 - 60 * q^65 - 54 * q^67 + 16 * q^69 + 26 * q^75 + 12 * q^77 + 2 * q^81 - 48 * q^83 + 74 * q^85 + 38 * q^87 + 30 * q^89 - 72 * q^91 - 16 * q^93 - 6 * q^95 - 6 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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