LMFDB - Embedded newform 260.2.bf.c.93.2

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			93.2
Root			$0.676406i$ of defining polynomial
Character	$\chi$	$=$	260.93
Dual form			260.2.bf.c.137.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.223531 + 0.834228i) q^{3} +(-0.382788 - 2.20306i) q^{5} +(1.19682 - 2.07295i) q^{7} +(1.95211 + 1.12705i) q^{9} +O(q^{10})$	\(q+(-0.223531 + 0.834228i) q^{3} +(-0.382788 - 2.20306i) q^{5} +(1.19682 - 2.07295i) q^{7} +(1.95211 + 1.12705i) q^{9} +(0.0379829 - 0.141754i) q^{11} +(0.344781 - 3.58903i) q^{13} +(1.92342 + 0.173119i) q^{15} +(4.96543 - 1.33048i) q^{17} +(-4.18726 + 1.12197i) q^{19} +(1.46179 + 1.46179i) q^{21} +(8.53261 + 2.28631i) q^{23} +(-4.70695 + 1.68661i) q^{25} +(-3.20866 + 3.20866i) q^{27} +(5.00061 - 2.88710i) q^{29} +(-4.94351 + 4.94351i) q^{31} +(0.109765 + 0.0633728i) q^{33} +(-5.02496 - 1.84316i) q^{35} +(-2.17085 - 3.76003i) q^{37} +(2.91700 + 1.08988i) q^{39} +(-11.6356 - 3.11775i) q^{41} +(0.172107 + 0.642311i) q^{43} +(1.73571 - 4.73203i) q^{45} -3.88786 q^{47} +(0.635248 + 1.10028i) q^{49} +4.43971i q^{51} +(-2.38836 - 2.38836i) q^{53} +(-0.326832 - 0.0294169i) q^{55} -3.74392i q^{57} +(1.94788 + 7.26959i) q^{59} +(-5.54868 + 9.61059i) q^{61} +(4.67263 - 2.69775i) q^{63} +(-8.03882 + 0.614264i) q^{65} +(-3.33873 + 1.92761i) q^{67} +(-3.81460 + 6.60708i) q^{69} +(1.66605 + 6.21778i) q^{71} +0.839574i q^{73} +(-0.354869 - 4.30368i) q^{75} +(-0.248391 - 0.248391i) q^{77} -3.64275i q^{79} +(1.42162 + 2.46232i) q^{81} +10.3431 q^{83} +(-4.83184 - 10.4298i) q^{85} +(1.29071 + 4.81701i) q^{87} +(11.7600 + 3.15109i) q^{89} +(-7.02724 - 5.01013i) q^{91} +(-3.01899 - 5.22904i) q^{93} +(4.07460 + 8.79530i) q^{95} +(0.440943 + 0.254578i) q^{97} +(0.233910 - 0.233910i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.223531	+	0.834228i	−0.129056	+	0.481642i	−0.999952	−	0.00982510i	$-0.996873\pi$
$3$	−0.223531	+	0.834228i	−0.129056	+	0.481642i	0.870896	+	0.491467i	$0.163539\pi$
$4$		0			0
$5$	−0.382788	−	2.20306i	−0.171188	−	0.985238i
$5$	−0.382788	−	2.20306i	−0.171188	−	0.985238i
$6$		0			0
$7$	1.19682	−	2.07295i	0.452355	−	0.783502i	−0.546177	−	0.837670i	$-0.683917\pi$
$7$	1.19682	−	2.07295i	0.452355	−	0.783502i	0.998532	+	0.0541680i	$0.0172506\pi$
$8$		0			0
$9$	1.95211	+	1.12705i	0.650702	+	0.375683i
$10$		0			0
$11$	0.0379829	−	0.141754i	0.0114523	−	0.0427405i	−0.959963	−	0.280126i	$-0.909624\pi$
$11$	0.0379829	−	0.141754i	0.0114523	−	0.0427405i	0.971416	+	0.237385i	$0.0762904\pi$
$12$		0			0
$13$	0.344781	−	3.58903i	0.0956249	−	0.995417i
$13$	0.344781	−	3.58903i	0.0956249	−	0.995417i
$14$		0			0
$15$	1.92342	+	0.173119i	0.496625	+	0.0446993i
$16$		0			0
$17$	4.96543	−	1.33048i	1.20429	−	0.322689i	0.399773	−	0.916614i	$-0.369089\pi$
$17$	4.96543	−	1.33048i	1.20429	−	0.322689i	0.804521	+	0.593925i	$0.202422\pi$
$18$		0			0
$19$	−4.18726	+	1.12197i	−0.960623	+	0.257398i	−0.704864	−	0.709343i	$-0.748992\pi$
$19$	−4.18726	+	1.12197i	−0.960623	+	0.257398i	−0.255759	+	0.966741i	$0.582325\pi$
$20$		0			0
$21$	1.46179	+	1.46179i	0.318989	+	0.318989i
$22$		0			0
$23$	8.53261	+	2.28631i	1.77917	+	0.476728i	0.990432	−	0.138000i	$-0.0440674\pi$
$23$	8.53261	+	2.28631i	1.77917	+	0.476728i	0.788739	+	0.614728i	$0.210734\pi$
$24$		0			0
$25$	−4.70695	+	1.68661i	−0.941389	+	0.337322i
$26$		0			0
$27$	−3.20866	+	3.20866i	−0.617508	+	0.617508i
$28$		0			0
$29$	5.00061	−	2.88710i	0.928590	−	0.536121i	0.0422244	−	0.999108i	$-0.486556\pi$
$29$	5.00061	−	2.88710i	0.928590	−	0.536121i	0.886365	+	0.462987i	$0.153222\pi$
$30$		0			0
$31$	−4.94351	+	4.94351i	−0.887880	+	0.887880i	−0.994319	−	0.106439i	$-0.966055\pi$
$31$	−4.94351	+	4.94351i	−0.887880	+	0.887880i	0.106439	+	0.994319i	$0.466055\pi$
$32$		0			0
$33$	0.109765	+	0.0633728i	0.0191076	+	0.0110318i
$34$		0			0
$35$	−5.02496	−	1.84316i	−0.849374	−	0.311552i
$36$		0			0
$37$	−2.17085	−	3.76003i	−0.356886	−	0.618144i	0.630553	−	0.776146i	$-0.282828\pi$
$37$	−2.17085	−	3.76003i	−0.356886	−	0.618144i	−0.987439	+	0.158002i	$0.949495\pi$
$38$		0			0
$39$	2.91700	+	1.08988i	0.467094	+	0.174521i
$40$		0			0
$41$	−11.6356	−	3.11775i	−1.81718	−	0.486911i	−0.820744	−	0.571297i	$-0.806441\pi$
$41$	−11.6356	−	3.11775i	−1.81718	−	0.486911i	−0.996433	+	0.0843856i	$0.973107\pi$
$42$		0			0
$43$	0.172107	+	0.642311i	0.0262460	+	0.0979516i	0.977806	−	0.209510i	$-0.0671870\pi$
$43$	0.172107	+	0.642311i	0.0262460	+	0.0979516i	−0.951560	+	0.307462i	$0.900520\pi$
$44$		0			0
$45$	1.73571	−	4.73203i	0.258745	−	0.705409i
$46$		0			0
$47$	−3.88786			−0.567103			−0.283552	−	0.958957i	$-0.591513\pi$
$47$	−3.88786			−0.567103			−0.283552	+	0.958957i	$0.591513\pi$
$48$		0			0
$49$	0.635248	+	1.10028i	0.0907497	+	0.157183i
$50$		0			0
$51$			4.43971i			0.621683i
$52$		0			0
$53$	−2.38836	−	2.38836i	−0.328067	−	0.328067i	0.523784	−	0.851851i	$-0.324520\pi$
$53$	−2.38836	−	2.38836i	−0.328067	−	0.328067i	−0.851851	+	0.523784i	$0.824520\pi$
$54$		0			0
$55$	−0.326832	−	0.0294169i	−0.0440700	−	0.00396657i
$56$		0			0
$57$		−	3.74392i		−	0.495895i
$58$		0			0
$59$	1.94788	+	7.26959i	0.253592	+	0.946420i	0.968868	+	0.247577i	$0.0796344\pi$
$59$	1.94788	+	7.26959i	0.253592	+	0.946420i	−0.715276	+	0.698842i	$0.753699\pi$
$60$		0			0
$61$	−5.54868	+	9.61059i	−0.710435	+	1.23051i	0.254259	+	0.967136i	$0.418168\pi$
$61$	−5.54868	+	9.61059i	−0.710435	+	1.23051i	−0.964694	+	0.263373i	$0.915165\pi$
$62$		0			0
$63$	4.67263	−	2.69775i	0.588697	−	0.339884i
$64$		0			0
$65$	−8.03882	+	0.614264i	−0.997093	+	0.0761900i
$66$		0			0
$67$	−3.33873	+	1.92761i	−0.407890	+	0.235496i	−0.689883	−	0.723921i	$-0.742338\pi$
$67$	−3.33873	+	1.92761i	−0.407890	+	0.235496i	0.281993	+	0.959417i	$0.409005\pi$
$68$		0			0
$69$	−3.81460	+	6.60708i	−0.459224	+	0.795399i
$70$		0			0
$71$	1.66605	+	6.21778i	0.197724	+	0.737914i	0.991545	+	0.129763i	$0.0414218\pi$
$71$	1.66605	+	6.21778i	0.197724	+	0.737914i	−0.793821	+	0.608151i	$0.791912\pi$
$72$		0			0
$73$			0.839574i			0.0982647i	0.998792	+	0.0491323i	$0.0156456\pi$
$73$			0.839574i			0.0982647i	−0.998792	+	0.0491323i	$0.984354\pi$
$74$		0			0
$75$	−0.354869	−	4.30368i	−0.0409767	−	0.496946i
$76$		0			0
$77$	−0.248391	−	0.248391i	−0.0283067	−	0.0283067i
$78$		0			0
$79$		−	3.64275i		−	0.409841i	−0.978779	−	0.204921i	$-0.934306\pi$
$79$		−	3.64275i		−	0.409841i	0.978779	−	0.204921i	$-0.0656936\pi$
$80$		0			0
$81$	1.42162	+	2.46232i	0.157958	+	0.273591i
$82$		0			0
$83$	10.3431			1.13530			0.567651	−	0.823270i	$-0.307852\pi$
$83$	10.3431			1.13530			0.567651	+	0.823270i	$0.307852\pi$
$84$		0			0
$85$	−4.83184	−	10.4298i	−0.524087	−	1.13128i
$86$		0			0
$87$	1.29071	+	4.81701i	0.138379	+	0.516437i
$88$		0			0
$89$	11.7600	+	3.15109i	1.24656	+	0.334015i	0.821007	−	0.570918i	$-0.193412\pi$
$89$	11.7600	+	3.15109i	1.24656	+	0.334015i	0.425554	+	0.904933i	$0.360079\pi$
$90$		0			0
$91$	−7.02724	−	5.01013i	−0.736655	−	0.525204i
$92$		0			0
$93$	−3.01899	−	5.22904i	−0.313054	−	0.542226i
$94$		0			0
$95$	4.07460	+	8.79530i	0.418045	+	0.902379i
$96$		0			0
$97$	0.440943	+	0.254578i	0.0447709	+	0.0258485i	0.522218	−	0.852812i	$-0.325105\pi$
$97$	0.440943	+	0.254578i	0.0447709	+	0.0258485i	−0.477447	+	0.878660i	$0.658438\pi$
$98$		0			0
$99$	0.233910	−	0.233910i	0.0235089	−	0.0235089i
$100$		0			0
$101$	8.19497	−	4.73137i	0.815430	−	0.470789i	−0.0334079	−	0.999442i	$-0.510636\pi$
$101$	8.19497	−	4.73137i	0.815430	−	0.470789i	0.848838	+	0.528653i	$0.177303\pi$
$102$		0			0
$103$	−12.8189	+	12.8189i	−1.26308	+	1.26308i	−0.313494	+	0.949590i	$0.601500\pi$
$103$	−12.8189	+	12.8189i	−1.26308	+	1.26308i	−0.949590	+	0.313494i	$0.898500\pi$
$104$		0			0
$105$	2.66085	−	3.77996i	0.259673	−	0.368887i
$106$		0			0
$107$	−4.25910	−	1.14122i	−0.411743	−	0.110326i	0.0470007	−	0.998895i	$-0.485034\pi$
$107$	−4.25910	−	1.14122i	−0.411743	−	0.110326i	−0.458744	+	0.888569i	$0.651700\pi$
$108$		0			0
$109$	4.91337	+	4.91337i	0.470615	+	0.470615i	0.902114	−	0.431498i	$-0.142015\pi$
$109$	4.91337	+	4.91337i	0.470615	+	0.470615i	−0.431498	+	0.902114i	$0.642015\pi$
$110$		0			0
$111$	3.62197	−	0.970505i	0.343782	−	0.0921162i
$112$		0			0
$113$	1.09955	−	0.294624i	0.103437	−	0.0277159i	−0.206729	−	0.978398i	$-0.566282\pi$
$113$	1.09955	−	0.294624i	0.103437	−	0.0277159i	0.310166	+	0.950682i	$0.399615\pi$
$114$		0			0
$115$	1.77069	−	19.6730i	0.165118	−	1.83452i
$116$		0			0
$117$	4.71806	−	6.61758i	0.436185	−	0.611795i
$118$		0			0
$119$	3.18469	−	11.8854i	0.291940	−	1.08954i
$120$		0			0
$121$	9.50763	+	5.48923i	0.864330	+	0.499021i
$122$		0			0
$123$	5.20183	−	9.00984i	0.469034	−	0.812390i
$124$		0			0
$125$	5.51746	+	9.72407i	0.493497	+	0.869748i
$126$		0			0
$127$	4.19958	−	15.6730i	0.372653	−	1.39076i	−0.484092	−	0.875017i	$-0.660850\pi$
$127$	4.19958	−	15.6730i	0.372653	−	1.39076i	0.856744	−	0.515741i	$-0.172483\pi$
$128$		0			0
$129$	−0.574306			−0.0505648
$130$		0			0
$131$	−12.0412			−1.05204			−0.526022	−	0.850471i	$-0.676317\pi$
$131$	−12.0412			−1.05204			−0.526022	+	0.850471i	$0.676317\pi$
$132$		0			0
$133$	−2.68560	+	10.0228i	−0.232871	+	0.869085i
$134$		0			0
$135$	8.29712	+	5.84064i	0.714102	+	0.502682i
$136$		0			0
$137$	−0.626533	+	1.08519i	−0.0535284	+	0.0927138i	−0.891548	−	0.452926i	$-0.850380\pi$
$137$	−0.626533	+	1.08519i	−0.0535284	+	0.0927138i	0.838020	+	0.545640i	$0.183713\pi$
$138$		0			0
$139$	−17.2116	−	9.93710i	−1.45987	−	0.842854i	−0.460862	−	0.887472i	$-0.652460\pi$
$139$	−17.2116	−	9.93710i	−1.45987	−	0.842854i	−0.999004	+	0.0446175i	$0.985793\pi$
$140$		0			0
$141$	0.869057	−	3.24337i	0.0731878	−	0.273141i
$142$		0			0
$143$	−0.495664	−	0.185196i	−0.0414495	−	0.0154868i
$144$		0			0
$145$	−8.27463	−	9.91149i	−0.687171	−	0.823105i
$146$		0			0
$147$	−1.05988	+	0.283995i	−0.0874178	+	0.0234235i
$148$		0			0
$149$	0.709453	−	0.190097i	0.0581207	−	0.0155734i	−0.229642	−	0.973275i	$-0.573755\pi$
$149$	0.709453	−	0.190097i	0.0581207	−	0.0155734i	0.287762	+	0.957702i	$0.407089\pi$
$150$		0			0
$151$	13.9096	+	13.9096i	1.13195	+	1.13195i	0.989853	+	0.142093i	$0.0453834\pi$
$151$	13.9096	+	13.9096i	1.13195	+	1.13195i	0.142093	+	0.989853i	$0.454617\pi$
$152$		0			0
$153$	11.1926	+	2.99904i	0.904865	+	0.242458i
$154$		0			0
$155$	12.7832	+	8.99853i	1.02677	+	0.722779i
$156$		0			0
$157$	2.54080	−	2.54080i	0.202778	−	0.202778i	−0.598411	−	0.801189i	$-0.704201\pi$
$157$	2.54080	−	2.54080i	0.202778	−	0.202778i	0.801189	+	0.598411i	$0.204201\pi$
$158$		0			0
$159$	2.52631	−	1.45857i	0.200350	−	0.115672i
$160$		0			0
$161$	14.9514	−	14.9514i	1.17833	−	1.17833i
$162$		0			0
$163$	7.57741	+	4.37482i	0.593509	+	0.342662i	0.766484	−	0.642264i	$-0.222005\pi$
$163$	7.57741	+	4.37482i	0.593509	+	0.342662i	−0.172975	+	0.984926i	$0.555338\pi$
$164$		0			0
$165$	0.0975974	−	0.266077i	0.00759795	−	0.0207141i
$166$		0			0
$167$	3.48292	+	6.03260i	0.269517	+	0.466816i	0.968737	−	0.248090i	$-0.0798028\pi$
$167$	3.48292	+	6.03260i	0.269517	+	0.466816i	−0.699220	+	0.714906i	$0.746469\pi$
$168$		0			0
$169$	−12.7623	−	2.47485i	−0.981712	−	0.190373i
$170$		0			0
$171$	−9.43848	−	2.52903i	−0.721779	−	0.193400i
$172$		0			0
$173$	0.832640	+	3.10746i	0.0633045	+	0.236256i	0.990328	−	0.138749i	$-0.0443080\pi$
$173$	0.832640	+	3.10746i	0.0633045	+	0.236256i	−0.927023	+	0.375004i	$0.877641\pi$
$174$		0			0
$175$	−2.13711	+	11.7758i	−0.161550	+	0.890170i
$176$		0			0
$177$	−6.49991			−0.488563
$178$		0			0
$179$	1.04481	+	1.80967i	0.0780930	+	0.135261i	0.902427	−	0.430843i	$-0.141784\pi$
$179$	1.04481	+	1.80967i	0.0780930	+	0.135261i	−0.824334	+	0.566104i	$0.808450\pi$
$180$		0			0
$181$			1.36226i			0.101256i	0.998718	+	0.0506281i	$0.0161223\pi$
$181$			1.36226i			0.101256i	−0.998718	+	0.0506281i	$0.983878\pi$
$182$		0			0
$183$	−6.77713	−	6.77713i	−0.500979	−	0.500979i
$184$		0			0
$185$	−7.45259	+	6.22181i	−0.547925	+	0.457436i
$186$		0			0
$187$		−	0.754405i		−	0.0551676i
$188$		0			0
$189$	2.81121	+	10.4916i	0.204486	+	0.763151i
$190$		0			0
$191$	−1.42257	+	2.46396i	−0.102933	+	0.178286i	−0.912892	−	0.408201i	$-0.866156\pi$
$191$	−1.42257	+	2.46396i	−0.102933	+	0.178286i	0.809959	+	0.586487i	$0.199489\pi$
$192$		0			0
$193$	−0.502326	+	0.290018i	−0.0361582	+	0.0208760i	−0.517970	−	0.855399i	$-0.673312\pi$
$193$	−0.502326	+	0.290018i	−0.0361582	+	0.0208760i	0.481812	+	0.876275i	$0.339979\pi$
$194$		0			0
$195$	1.28449	−	6.84352i	0.0919841	−	0.490075i
$196$		0			0
$197$	−1.10274	+	0.636666i	−0.0785668	+	0.0453606i	−0.538769	−	0.842454i	$-0.681110\pi$
$197$	−1.10274	+	0.636666i	−0.0785668	+	0.0453606i	0.460202	+	0.887814i	$0.347777\pi$
$198$		0			0
$199$	9.35079	−	16.1960i	0.662860	−	1.14811i	−0.317001	−	0.948425i	$-0.602676\pi$
$199$	9.35079	−	16.1960i	0.662860	−	1.14811i	0.979861	−	0.199682i	$-0.0639908\pi$
$200$		0			0
$201$	−0.861762	−	3.21614i	−0.0607840	−	0.226849i
$202$		0			0
$203$		−	13.8214i		−	0.970069i
$204$		0			0
$205$	−2.41463	+	26.8274i	−0.168645	+	1.87371i
$206$		0			0
$207$	14.0798	+	14.0798i	0.978612	+	0.978612i
$208$		0			0
$209$			0.636176i			0.0440052i
$210$		0			0
$211$	−9.74267	−	16.8748i	−0.670713	−	1.16171i	−0.977702	−	0.209996i	$-0.932655\pi$
$211$	−9.74267	−	16.8748i	−0.670713	−	1.16171i	0.306989	−	0.951713i	$-0.400679\pi$
$212$		0			0
$213$	−5.55946			−0.380928
$214$		0			0
$215$	1.34917	−	0.625031i	0.0920126	−	0.0426267i
$216$		0			0
$217$	4.33117	+	16.1641i	0.294019	+	1.09729i
$218$		0			0
$219$	−0.700396	−	0.187671i	−0.0473284	−	0.0126816i
$220$		0			0
$221$	−3.06316	−	18.2798i	−0.206050	−	1.22963i
$222$		0			0
$223$	−13.4835	−	23.3541i	−0.902922	−	1.56391i	−0.823683	−	0.567050i	$-0.808084\pi$
$223$	−13.4835	−	23.3541i	−0.902922	−	1.56391i	−0.0792386	−	0.996856i	$-0.525249\pi$
$224$		0			0
$225$	−11.0893	−	2.01252i	−0.739290	−	0.134168i
$226$		0			0
$227$	−4.11233	−	2.37425i	−0.272945	−	0.157585i	0.357280	−	0.933997i	$-0.383704\pi$
$227$	−4.11233	−	2.37425i	−0.272945	−	0.157585i	−0.630225	+	0.776412i	$0.717037\pi$
$228$		0			0
$229$	−18.5531	+	18.5531i	−1.22603	+	1.22603i	−0.260571	+	0.965455i	$0.583911\pi$
$229$	−18.5531	+	18.5531i	−1.22603	+	1.22603i	−0.965455	+	0.260571i	$0.916089\pi$
$230$		0			0
$231$	0.262737	−	0.151692i	0.0172869	−	0.00998057i
$232$		0			0
$233$	−17.8687	+	17.8687i	−1.17062	+	1.17062i	−0.188558	+	0.982062i	$0.560381\pi$
$233$	−17.8687	+	17.8687i	−1.17062	+	1.17062i	−0.982062	+	0.188558i	$0.939619\pi$
$234$		0			0
$235$	1.48823	+	8.56520i	0.0970812	+	0.558732i
$236$		0			0
$237$	3.03888	+	0.814267i	0.197397	+	0.0528923i
$238$		0			0
$239$	−8.92835	−	8.92835i	−0.577527	−	0.577527i	0.356694	−	0.934221i	$-0.383904\pi$
$239$	−8.92835	−	8.92835i	−0.577527	−	0.577527i	−0.934221	+	0.356694i	$0.883904\pi$
$240$		0			0
$241$	0.894443	−	0.239665i	0.0576162	−	0.0154382i	−0.229896	−	0.973215i	$-0.573839\pi$
$241$	0.894443	−	0.239665i	0.0576162	−	0.0154382i	0.287512	+	0.957777i	$0.407172\pi$
$242$		0			0
$243$	−15.5213	+	4.15891i	−0.995690	+	0.266794i
$244$		0			0
$245$	2.18082	−	1.82066i	0.139328	−	0.116318i
$246$		0			0
$247$	2.58311	+	15.4150i	0.164359	+	0.980834i
$248$		0			0
$249$	−2.31200	+	8.62850i	−0.146517	+	0.546809i
$250$		0			0
$251$	−5.87395	−	3.39133i	−0.370760	−	0.214059i	0.303030	−	0.952981i	$-0.402002\pi$
$251$	−5.87395	−	3.39133i	−0.370760	−	0.214059i	−0.673791	+	0.738922i	$0.735335\pi$
$252$		0			0
$253$	0.648186	−	1.12269i	0.0407511	−	0.0705830i
$254$		0			0
$255$	9.78094	−	1.69946i	0.612506	−	0.106425i
$256$		0			0
$257$	1.71988	−	6.41868i	0.107283	−	0.400386i	−0.891311	−	0.453392i	$-0.850214\pi$
$257$	1.71988	−	6.41868i	0.107283	−	0.400386i	0.998594	+	0.0530063i	$0.0168803\pi$
$258$		0			0
$259$	−10.3925			−0.645756
$260$		0			0
$261$	13.0156			0.805647
$262$		0			0
$263$	−3.05461	+	11.4000i	−0.188355	+	0.702952i	0.805532	+	0.592552i	$0.201880\pi$
$263$	−3.05461	+	11.4000i	−0.188355	+	0.702952i	−0.993887	+	0.110400i	$0.964787\pi$
$264$		0			0
$265$	−4.34747	+	6.17594i	−0.267063	+	0.379385i
$266$		0			0
$267$	−5.25746	+	9.10619i	−0.321752	+	0.557290i
$268$		0			0
$269$	14.5787	+	8.41701i	0.888878	+	0.513194i	0.873575	−	0.486689i	$-0.161796\pi$
$269$	14.5787	+	8.41701i	0.888878	+	0.513194i	0.0153026	+	0.999883i	$0.495129\pi$
$270$		0			0
$271$	3.25919	−	12.1634i	0.197981	−	0.738877i	−0.793493	−	0.608579i	$-0.791740\pi$
$271$	3.25919	−	12.1634i	0.197981	−	0.738877i	0.991475	−	0.130298i	$-0.0415934\pi$
$272$		0			0
$273$	5.75040	−	4.74241i	0.348030	−	0.287023i
$274$		0			0
$275$	0.0603002	+	0.731291i	0.00363624	+	0.0440985i
$276$		0			0
$277$	−13.8609	+	3.71401i	−0.832818	+	0.223153i	−0.649943	−	0.759983i	$-0.725207\pi$
$277$	−13.8609	+	3.71401i	−0.832818	+	0.223153i	−0.182876	+	0.983136i	$0.558541\pi$
$278$		0			0
$279$	−15.2218	+	4.07867i	−0.911307	+	0.244184i
$280$		0			0
$281$	11.1184	+	11.1184i	0.663267	+	0.663267i	0.956149	−	0.292882i	$-0.0946142\pi$
$281$	11.1184	+	11.1184i	0.663267	+	0.663267i	−0.292882	+	0.956149i	$0.594614\pi$
$282$		0			0
$283$	16.5884	+	4.44486i	0.986081	+	0.264220i	0.715603	−	0.698507i	$-0.246152\pi$
$283$	16.5884	+	4.44486i	0.986081	+	0.264220i	0.270477	+	0.962726i	$0.412819\pi$
$284$		0			0
$285$	−8.24809	+	1.43313i	−0.488575	+	0.0848912i
$286$		0			0
$287$	−20.3887	+	20.3887i	−1.20350	+	1.20350i
$288$		0			0
$289$	8.16288	−	4.71284i	0.480169	−	0.277226i
$290$		0			0
$291$	−0.310941	+	0.310941i	−0.0182277	+	0.0182277i
$292$		0			0
$293$	−21.5898	−	12.4649i	−1.26129	−	0.728205i	−0.287964	−	0.957641i	$-0.592979\pi$
$293$	−21.5898	−	12.4649i	−1.26129	−	0.728205i	−0.973324	+	0.229436i	$0.926312\pi$
$294$		0			0
$295$	15.2697	−	7.07401i	0.889037	−	0.411865i
$296$		0			0
$297$	0.332967	+	0.576716i	0.0193207	+	0.0334644i
$298$		0			0
$299$	11.1475	−	29.8355i	0.644676	−	1.72543i
$300$		0			0
$301$	1.53746	+	0.411961i	0.0886178	+	0.0237451i
$302$		0			0
$303$	2.11521	+	7.89409i	0.121516	+	0.453503i
$304$		0			0
$305$	23.2967	+	8.54525i	1.33396	+	0.489300i
$306$		0			0
$307$	10.3236			0.589199			0.294599	−	0.955621i	$-0.404814\pi$
$307$	10.3236			0.589199			0.294599	+	0.955621i	$0.404814\pi$
$308$		0			0
$309$	−7.82847	−	13.5593i	−0.445346	−	0.771362i
$310$		0			0
$311$		−	15.7703i		−	0.894254i	−0.894471	−	0.447127i	$-0.852447\pi$
$311$		−	15.7703i		−	0.894254i	0.894471	−	0.447127i	$-0.147553\pi$
$312$		0			0
$313$	−17.7618	−	17.7618i	−1.00395	−	1.00395i	−0.999992	−	0.00396212i	$-0.998739\pi$
$313$	−17.7618	−	17.7618i	−1.00395	−	1.00395i	−0.00396212	−	0.999992i	$-0.501261\pi$
$314$		0			0
$315$	−7.73192	−	9.26143i	−0.435645	−	0.521822i
$316$		0			0
$317$		−	13.4146i		−	0.753441i	−0.926327	−	0.376721i	$-0.877052\pi$
$317$		−	13.4146i		−	0.753441i	0.926327	−	0.376721i	$-0.122948\pi$
$318$		0			0
$319$	−0.219321	−	0.818517i	−0.0122796	−	0.0458282i
$320$		0			0
$321$	1.90408	−	3.29797i	0.106275	−	0.184074i
$322$		0			0
$323$	−19.2988	+	11.1421i	−1.07381	+	0.619966i
$324$		0			0
$325$	4.43042	+	17.4749i	0.245756	+	0.969332i
$326$		0			0
$327$	−5.19716	+	3.00058i	−0.287404	+	0.165933i
$328$		0			0
$329$	−4.65307	+	8.05935i	−0.256532	+	0.444326i
$330$		0			0
$331$	−3.79152	−	14.1502i	−0.208401	−	0.777763i	−0.988386	−	0.151965i	$-0.951440\pi$
$331$	−3.79152	−	14.1502i	−0.208401	−	0.777763i	0.779985	−	0.625798i	$-0.215227\pi$
$332$		0			0
$333$		−	9.78662i		−	0.536303i
$334$		0			0
$335$	5.52467	+	6.61755i	0.301845	+	0.361555i
$336$		0			0
$337$	7.93205	+	7.93205i	0.432086	+	0.432086i	0.889338	−	0.457251i	$-0.151166\pi$
$337$	7.93205	+	7.93205i	0.432086	+	0.432086i	−0.457251	+	0.889338i	$0.651166\pi$
$338$		0			0
$339$			0.983136i			0.0533966i
$340$		0			0
$341$	0.512994	+	0.888531i	0.0277802	+	0.0481166i
$342$		0			0
$343$	19.7966			1.06891
$344$		0			0
$345$	16.0160	+	5.87469i	0.862272	+	0.316282i
$346$		0			0
$347$	−7.00902	−	26.1580i	−0.376264	−	1.40424i	−0.851490	−	0.524371i	$-0.824300\pi$
$347$	−7.00902	−	26.1580i	−0.376264	−	1.40424i	0.475226	−	0.879864i	$-0.342366\pi$
$348$		0			0
$349$	7.60394	+	2.03747i	0.407030	+	0.109063i	0.456524	−	0.889711i	$-0.349094\pi$
$349$	7.60394	+	2.03747i	0.407030	+	0.109063i	−0.0494943	+	0.998774i	$0.515761\pi$
$350$		0			0
$351$	10.4097	+	12.6223i	0.555629	+	0.673727i
$352$		0			0
$353$	14.2741	+	24.7235i	0.759734	+	1.31590i	0.942986	+	0.332831i	$0.108004\pi$
$353$	14.2741	+	24.7235i	0.759734	+	1.31590i	−0.183253	+	0.983066i	$0.558663\pi$
$354$		0			0
$355$	13.0604	−	6.05049i	0.693174	−	0.321127i
$356$		0			0
$357$	9.20330	+	5.31353i	0.487090	+	0.281222i
$358$		0			0
$359$	9.94522	−	9.94522i	0.524889	−	0.524889i	−0.394155	−	0.919044i	$-0.628963\pi$
$359$	9.94522	−	9.94522i	0.524889	−	0.524889i	0.919044	+	0.394155i	$0.128963\pi$
$360$		0			0
$361$	−0.180183	+	0.104029i	−0.00948333	+	0.00547520i
$362$		0			0
$363$	−6.70452	+	6.70452i	−0.351896	+	0.351896i
$364$		0			0
$365$	1.84963	−	0.321379i	0.0968141	−	0.0168217i
$366$		0			0
$367$	25.4933	+	6.83092i	1.33074	+	0.356571i	0.852992	−	0.521925i	$-0.174786\pi$
$367$	25.4933	+	6.83092i	1.33074	+	0.356571i	0.477750	+	0.878496i	$0.341452\pi$
$368$		0			0
$369$	−19.2001	−	19.2001i	−0.999516	−	0.999516i
$370$		0			0
$371$	−7.80940	+	2.09252i	−0.405444	+	0.108638i
$372$		0			0
$373$	0.823363	−	0.220619i	0.0426321	−	0.0114232i	−0.237440	−	0.971402i	$-0.576308\pi$
$373$	0.823363	−	0.220619i	0.0426321	−	0.0114232i	0.280072	+	0.959979i	$0.409642\pi$
$374$		0			0
$375$	−9.34542	+	2.42919i	−0.482595	+	0.125443i
$376$		0			0
$377$	−8.63778	−	18.9427i	−0.444868	−	0.975601i
$378$		0			0
$379$	−5.74031	+	21.4231i	−0.294860	+	1.10043i	0.646469	+	0.762940i	$0.276245\pi$
$379$	−5.74031	+	21.4231i	−0.294860	+	1.10043i	−0.941329	+	0.337491i	$0.890422\pi$
$380$		0			0
$381$	12.1362	+	7.00682i	0.621755	+	0.358970i
$382$		0			0
$383$	−6.72928	+	11.6555i	−0.343850	+	0.595566i	−0.985144	−	0.171729i	$-0.945065\pi$
$383$	−6.72928	+	11.6555i	−0.343850	+	0.595566i	0.641294	+	0.767295i	$0.278398\pi$
$384$		0			0
$385$	−0.452139	+	0.642300i	−0.0230431	+	0.0327347i
$386$		0			0
$387$	−0.387945	+	1.44783i	−0.0197204	+	0.0735974i
$388$		0			0
$389$	10.4988			0.532310			0.266155	−	0.963930i	$-0.414247\pi$
$389$	10.4988			0.532310			0.266155	+	0.963930i	$0.414247\pi$
$390$		0			0
$391$	45.4100			2.29648
$392$		0			0
$393$	2.69158	−	10.0451i	0.135772	−	0.506708i
$394$		0			0
$395$	−8.02519	+	1.39440i	−0.403791	+	0.0701599i
$396$		0			0
$397$	11.6920	−	20.2512i	0.586805	−	1.01638i	−0.407843	−	0.913052i	$-0.633719\pi$
$397$	11.6920	−	20.2512i	0.586805	−	1.01638i	0.994648	−	0.103324i	$-0.0329479\pi$
$398$		0			0
$399$	−7.76097	−	4.48080i	−0.388535	−	0.224321i
$400$		0			0
$401$	8.35969	−	31.1988i	0.417463	−	1.55799i	−0.362388	−	0.932027i	$-0.618038\pi$
$401$	8.35969	−	31.1988i	0.417463	−	1.55799i	0.779851	−	0.625966i	$-0.215295\pi$
$402$		0			0
$403$	16.0380	+	19.4468i	0.798908	+	0.968715i
$404$		0			0
$405$	4.88046	−	4.07447i	0.242512	−	0.202462i
$406$		0			0
$407$	−0.615454	+	0.164910i	−0.0305069	+	0.00817431i
$408$		0			0
$409$	−9.26291	+	2.48199i	−0.458022	+	0.122726i	−0.480450	−	0.877022i	$-0.659527\pi$
$409$	−9.26291	+	2.48199i	−0.458022	+	0.122726i	0.0224288	+	0.999748i	$0.492860\pi$
$410$		0			0
$411$	−0.765245	−	0.765245i	−0.0377467	−	0.0377467i
$412$		0			0
$413$	17.4008	+	4.66252i	0.856236	+	0.229428i
$414$		0			0
$415$	−3.95921	−	22.7864i	−0.194350	−	1.11854i
$416$		0			0
$417$	12.1371	−	12.1371i	0.594358	−	0.594358i
$418$		0			0
$419$	10.4021	−	6.00568i	0.508178	−	0.293397i	−0.223906	−	0.974611i	$-0.571881\pi$
$419$	10.4021	−	6.00568i	0.508178	−	0.293397i	0.732084	+	0.681214i	$0.238548\pi$
$420$		0			0
$421$	−9.06775	+	9.06775i	−0.441935	+	0.441935i	−0.892662	−	0.450727i	$-0.851165\pi$
$421$	−9.06775	+	9.06775i	−0.441935	+	0.441935i	0.450727	+	0.892662i	$0.351165\pi$
$422$		0			0
$423$	−7.58952	−	4.38181i	−0.369015	−	0.213051i
$424$		0			0
$425$	−21.1280	+	14.6372i	−1.02486	+	0.710011i
$426$		0			0
$427$	13.2815	+	23.0043i	0.642738	+	1.11325i
$428$		0			0
$429$	0.265292	−	0.372100i	0.0128084	−	0.0179651i
$430$		0			0
$431$	6.85071	+	1.83564i	0.329987	+	0.0884197i	0.420009	−	0.907520i	$-0.362027\pi$
$431$	6.85071	+	1.83564i	0.329987	+	0.0884197i	−0.0900218	+	0.995940i	$0.528694\pi$
$432$		0			0
$433$	−3.73685	−	13.9461i	−0.179582	−	0.670208i	−0.995726	−	0.0923594i	$-0.970559\pi$
$433$	−3.73685	−	13.9461i	−0.179582	−	0.670208i	0.816144	−	0.577848i	$-0.196108\pi$
$434$		0			0
$435$	10.1181	−	4.68741i	0.485125	−	0.224744i
$436$		0			0
$437$	−38.2934			−1.83182
$438$		0			0
$439$	−15.9695	−	27.6599i	−0.762181	−	1.32014i	−0.941724	−	0.336386i	$-0.890795\pi$
$439$	−15.9695	−	27.6599i	−0.762181	−	1.32014i	0.179543	−	0.983750i	$-0.442538\pi$
$440$		0			0
$441$			2.86382i			0.136372i
$442$		0			0
$443$	−1.63712	−	1.63712i	−0.0777820	−	0.0777820i	0.667145	−	0.744927i	$-0.267516\pi$
$443$	−1.63712	−	1.63712i	−0.0777820	−	0.0777820i	−0.744927	+	0.667145i	$0.767516\pi$
$444$		0			0
$445$	2.44045	−	27.1143i	0.115688	−	1.28534i
$446$		0			0
$447$			0.634339i			0.0300032i
$448$		0			0
$449$	−1.13708	−	4.24365i	−0.0536622	−	0.200270i	0.933890	−	0.357560i	$-0.116391\pi$
$449$	−1.13708	−	4.24365i	−0.0536622	−	0.200270i	−0.987553	+	0.157289i	$0.949724\pi$
$450$		0			0
$451$	−0.883908	+	1.53097i	−0.0416216	+	0.0720907i
$452$		0			0
$453$	−14.7130	+	8.49456i	−0.691277	+	0.399109i
$454$		0			0
$455$	−8.34768	+	17.3993i	−0.391345	+	0.815690i
$456$		0			0
$457$	12.4765	−	7.20333i	0.583627	−	0.336957i	−0.178946	−	0.983859i	$-0.557269\pi$
$457$	12.4765	−	7.20333i	0.583627	−	0.336957i	0.762574	+	0.646901i	$0.223935\pi$
$458$		0			0
$459$	−11.6633	+	20.2015i	−0.544397	+	0.942924i
$460$		0			0
$461$	4.86355	+	18.1510i	0.226518	+	0.845377i	0.981791	+	0.189966i	$0.0608379\pi$
$461$	4.86355	+	18.1510i	0.226518	+	0.845377i	−0.755272	+	0.655411i	$0.772495\pi$
$462$		0			0
$463$		−	32.2068i		−	1.49678i	−0.663260	−	0.748389i	$-0.730828\pi$
$463$		−	32.2068i		−	1.49678i	0.663260	−	0.748389i	$-0.269172\pi$
$464$		0			0
$465$	−10.3643	+	8.65262i	−0.480631	+	0.401256i
$466$		0			0
$467$	−12.3536	−	12.3536i	−0.571656	−	0.571656i	0.360935	−	0.932591i	$-0.382458\pi$
$467$	−12.3536	−	12.3536i	−0.571656	−	0.571656i	−0.932591	+	0.360935i	$0.882458\pi$
$468$		0			0
$469$			9.22802i			0.426111i
$470$		0			0
$471$	1.55166	+	2.68756i	0.0714968	+	0.123836i
$472$		0			0
$473$	0.0975874			0.00448707
$474$		0			0
$475$	17.8169	−	12.3433i	0.817494	−	0.566351i
$476$		0			0
$477$	−1.97053	−	7.35413i	−0.0902246	−	0.336723i
$478$		0			0
$479$	17.8406	+	4.78038i	0.815158	+	0.218421i	0.642228	−	0.766513i	$-0.278010\pi$
$479$	17.8406	+	4.78038i	0.815158	+	0.218421i	0.172930	+	0.984934i	$0.444677\pi$
$480$		0			0
$481$	−14.2433	+	6.49487i	−0.649439	+	0.296140i
$482$		0			0
$483$	9.13078	+	15.8150i	0.415465	+	0.719606i
$484$		0			0
$485$	0.392064	−	1.06887i	0.0178027	−	0.0485350i
$486$		0			0
$487$	−30.5221	−	17.6219i	−1.38309	−	0.798526i	−0.390563	−	0.920576i	$-0.627720\pi$
$487$	−30.5221	−	17.6219i	−1.38309	−	0.798526i	−0.992524	+	0.122051i	$0.961053\pi$
$488$		0			0
$489$	−5.34338	+	5.34338i	−0.241636	+	0.241636i
$490$		0			0
$491$	−31.7390	+	18.3245i	−1.43236	+	0.826975i	−0.997301	−	0.0734250i	$-0.976607\pi$
$491$	−31.7390	+	18.3245i	−1.43236	+	0.826975i	−0.435062	+	0.900400i	$0.643274\pi$
$492$		0			0
$493$	20.9889	−	20.9889i	0.945294	−	0.945294i
$494$		0			0
$495$	−0.604856	−	0.425780i	−0.0271863	−	0.0191374i
$496$		0			0
$497$	14.8831	+	3.98792i	0.667599	+	0.178883i
$498$		0			0
$499$	26.6823	+	26.6823i	1.19447	+	1.19447i	0.975800	+	0.218666i	$0.0701706\pi$
$499$	26.6823	+	26.6823i	1.19447	+	1.19447i	0.218666	+	0.975800i	$0.429829\pi$
$500$		0			0
$501$	−5.81111	+	1.55708i	−0.259621	+	0.0695652i
$502$		0			0
$503$	−3.45317	+	0.925275i	−0.153969	+	0.0412560i	−0.334980	−	0.942225i	$-0.608730\pi$
$503$	−3.45317	+	0.925275i	−0.153969	+	0.0412560i	0.181011	+	0.983481i	$0.442063\pi$
$504$		0			0
$505$	−13.5604	−	16.2429i	−0.603431	−	0.722800i
$506$		0			0
$507$	4.91735	−	10.0934i	0.218387	−	0.448265i
$508$		0			0
$509$	7.47999	−	27.9157i	0.331545	−	1.23734i	−0.576022	−	0.817434i	$-0.695396\pi$
$509$	7.47999	−	27.9157i	0.331545	−	1.23734i	0.907567	−	0.419908i	$-0.137938\pi$
$510$		0			0
$511$	1.74040	+	1.00482i	0.0769906	+	0.0444505i
$512$		0			0
$513$	9.83547	−	17.0355i	0.434247	−	0.752137i
$514$		0			0
$515$	33.1477	+	23.3339i	1.46066	+	1.02821i
$516$		0			0
$517$	−0.147672	+	0.551120i	−0.00649462	+	0.0242382i
$518$		0			0
$519$	−2.77845			−0.121960
$520$		0			0
$521$	−20.7651			−0.909737			−0.454869	−	0.890559i	$-0.650314\pi$
$521$	−20.7651			−0.909737			−0.454869	+	0.890559i	$0.650314\pi$
$522$		0			0
$523$	−7.27456	+	27.1490i	−0.318094	+	1.18714i	0.602980	+	0.797756i	$0.293980\pi$
$523$	−7.27456	+	27.1490i	−0.318094	+	1.18714i	−0.921074	+	0.389387i	$0.872687\pi$
$524$		0			0
$525$	−9.34603	−	4.41510i	−0.407894	−	0.192691i
$526$		0			0
$527$	−17.9694	+	31.1239i	−0.782759	+	1.35578i
$528$		0			0
$529$	47.6596	+	27.5163i	2.07216	+	1.19636i
$530$		0			0
$531$	−4.39071	+	16.3864i	−0.190541	+	0.711107i
$532$		0			0
$533$	−15.2014	+	40.6856i	−0.658447	+	1.76229i
$534$		0			0
$535$	−0.883851	+	9.81990i	−0.0382122	+	0.424551i
$536$		0			0
$537$	−1.74323	+	0.467096i	−0.0752257	+	0.0201567i
$538$		0			0
$539$	0.180098	−	0.0482571i	0.00775737	−	0.00207858i
$540$		0			0
$541$	−17.0864	−	17.0864i	−0.734604	−	0.734604i	0.236924	−	0.971528i	$-0.423861\pi$
$541$	−17.0864	−	17.0864i	−0.734604	−	0.734604i	−0.971528	+	0.236924i	$0.923861\pi$
$542$		0			0
$543$	−1.13644	−	0.304508i	−0.0487692	−	0.0130677i
$544$		0			0
$545$	8.94367	−	12.7052i	0.383105	−	0.544232i
$546$		0			0
$547$	−18.9349	+	18.9349i	−0.809597	+	0.809597i	−0.984573	−	0.174976i	$-0.944015\pi$
$547$	−18.9349	+	18.9349i	−0.809597	+	0.809597i	0.174976	+	0.984573i	$0.444015\pi$
$548$		0			0
$549$	−21.6632	+	12.5073i	−0.924563	+	0.533797i
$550$		0			0
$551$	−17.6996	+	17.6996i	−0.754028	+	0.754028i
$552$		0			0
$553$	−7.55124	−	4.35971i	−0.321111	−	0.185394i
$554$		0			0
$555$	−3.52453	−	7.60792i	−0.149608	−	0.322938i
$556$		0			0
$557$	13.2845	+	23.0094i	0.562882	+	0.974940i	0.997243	+	0.0742015i	$0.0236408\pi$
$557$	13.2845	+	23.0094i	0.562882	+	0.974940i	−0.434361	+	0.900739i	$0.643026\pi$
$558$		0			0
$559$	2.36461	−	0.396240i	0.100012	−	0.0167592i
$560$		0			0
$561$	0.629346	+	0.168633i	0.0265710	+	0.00711968i
$562$		0			0
$563$	−1.53630	−	5.73354i	−0.0647472	−	0.241640i	0.925966	−	0.377606i	$-0.123253\pi$
$563$	−1.53630	−	5.73354i	−0.0647472	−	0.241640i	−0.990713	+	0.135967i	$0.956586\pi$
$564$		0			0
$565$	−1.06997	−	2.30960i	−0.0450140	−	0.0971657i
$566$		0			0
$567$	6.80570			0.285812
$568$		0			0
$569$	−3.07382	−	5.32402i	−0.128861	−	0.223195i	0.794374	−	0.607429i	$-0.207799\pi$
$569$	−3.07382	−	5.32402i	−0.128861	−	0.223195i	−0.923236	+	0.384234i	$0.874466\pi$
$570$		0			0
$571$		−	17.9884i		−	0.752792i	−0.926459	−	0.376396i	$-0.877163\pi$
$571$		−	17.9884i		−	0.752792i	0.926459	−	0.376396i	$-0.122837\pi$
$572$		0			0
$573$	−1.73751	−	1.73751i	−0.0725857	−	0.0725857i
$574$		0			0
$575$	−44.0186	+	3.62965i	−1.83570	+	0.151367i
$576$		0			0
$577$			38.3328i			1.59582i	0.602780	+	0.797908i	$0.294060\pi$
$577$			38.3328i			1.59582i	−0.602780	+	0.797908i	$0.705940\pi$
$578$		0			0
$579$	−0.129656	−	0.483883i	−0.00538832	−	0.0201095i
$580$		0			0
$581$	12.3788	−	21.4407i	0.513559	−	0.889511i
$582$		0			0
$583$	−0.429277	+	0.247843i	−0.0177788	+	0.0102646i
$584$		0			0
$585$	−16.3849	−	7.86104i	−0.677434	−	0.325014i
$586$		0			0
$587$	1.58584	−	0.915584i	0.0654545	−	0.0377902i	−0.466916	−	0.884302i	$-0.654635\pi$
$587$	1.58584	−	0.915584i	0.0654545	−	0.0377902i	0.532370	+	0.846512i	$0.321301\pi$
$588$		0			0
$589$	15.1533	−	26.2462i	0.624379	−	1.08146i
$590$		0			0
$591$	−0.284629	−	1.06225i	−0.0117081	−	0.0436951i
$592$		0			0
$593$		−	47.6121i		−	1.95519i	−0.210488	−	0.977596i	$-0.567505\pi$
$593$		−	47.6121i		−	1.95519i	0.210488	−	0.977596i	$-0.432495\pi$
$594$		0			0
$595$	−27.4034	−	2.46647i	−1.12343	−	0.101116i
$596$		0			0
$597$	11.4210	+	11.4210i	0.467431	+	0.467431i
$598$		0			0
$599$			35.0349i			1.43149i	0.698364	+	0.715743i	$0.253912\pi$
$599$			35.0349i			1.43149i	−0.698364	+	0.715743i	$0.746088\pi$
$600$		0			0
$601$	5.18695	+	8.98405i	0.211580	+	0.366467i	0.952209	−	0.305447i	$-0.0988058\pi$
$601$	5.18695	+	8.98405i	0.211580	+	0.366467i	−0.740629	+	0.671914i	$0.765472\pi$
$602$		0			0
$603$	−8.69006			−0.353887
$604$		0			0
$605$	8.45370	−	23.0471i	0.343692	−	0.936997i
$606$		0			0
$607$	−2.29676	−	8.57162i	−0.0932226	−	0.347911i	0.903521	−	0.428543i	$-0.140973\pi$
$607$	−2.29676	−	8.57162i	−0.0932226	−	0.347911i	−0.996744	+	0.0806315i	$0.974306\pi$
$608$		0			0
$609$	11.5302	+	3.08950i	0.467226	+	0.125193i
$610$		0			0
$611$	−1.34046	+	13.9537i	−0.0542292	+	0.564504i
$612$		0			0
$613$	7.97961	+	13.8211i	0.322293	+	0.558229i	0.980961	−	0.194206i	$-0.0622129\pi$
$613$	7.97961	+	13.8211i	0.322293	+	0.558229i	−0.658667	+	0.752434i	$0.728880\pi$
$614$		0			0
$615$	−21.8404	−	8.01110i	−0.880691	−	0.323039i
$616$		0			0
$617$	−23.4123	−	13.5171i	−0.942543	−	0.544178i	−0.0517867	−	0.998658i	$-0.516492\pi$
$617$	−23.4123	−	13.5171i	−0.942543	−	0.544178i	−0.890757	+	0.454481i	$0.849825\pi$
$618$		0			0
$619$	−23.9718	+	23.9718i	−0.963509	+	0.963509i	−0.999357	−	0.0358482i	$-0.988587\pi$
$619$	−23.9718	+	23.9718i	−0.963509	+	0.963509i	0.0358482	+	0.999357i	$0.488587\pi$
$620$		0			0
$621$	−34.7143	+	20.0423i	−1.39304	+	0.804269i
$622$		0			0
$623$	20.6067	−	20.6067i	0.825590	−	0.825590i
$624$		0			0
$625$	19.3107	−	15.8776i	0.772428	−	0.635102i
$626$		0			0
$627$	−0.530716	−	0.142205i	−0.0211948	−	0.00567912i
$628$		0			0
$629$	−15.7819	−	15.7819i	−0.629264	−	0.629264i
$630$		0			0
$631$	−18.6213	+	4.98955i	−0.741301	+	0.198631i	−0.609656	−	0.792666i	$-0.708692\pi$
$631$	−18.6213	+	4.98955i	−0.741301	+	0.198631i	−0.131645	+	0.991297i	$0.542026\pi$
$632$		0			0
$633$	16.2552	−	4.35558i	0.646087	−	0.173119i
$634$		0			0
$635$	−36.1362	−	3.25248i	−1.43402	−	0.129071i
$636$		0			0
$637$	4.16796	−	1.90057i	0.165141	−	0.0753032i
$638$		0			0
$639$	−3.75543	+	14.0155i	−0.148563	+	0.554443i
$640$		0			0
$641$	−18.8267	−	10.8696i	−0.743609	−	0.429323i	0.0797710	−	0.996813i	$-0.474581\pi$
$641$	−18.8267	−	10.8696i	−0.743609	−	0.429323i	−0.823380	+	0.567490i	$0.807914\pi$
$642$		0			0
$643$	20.0899	−	34.7968i	0.792270	−	1.37225i	−0.132289	−	0.991211i	$-0.542233\pi$
$643$	20.0899	−	34.7968i	0.792270	−	1.37225i	0.924558	−	0.381040i	$-0.124434\pi$
$644$		0			0
$645$	0.219837	+	1.26523i	0.00865608	+	0.0498184i
$646$		0			0
$647$	7.37512	−	27.5243i	0.289946	−	1.08209i	−0.655203	−	0.755453i	$-0.727417\pi$
$647$	7.37512	−	27.5243i	0.289946	−	1.08209i	0.945149	−	0.326640i	$-0.105916\pi$
$648$		0			0
$649$	1.10448			0.0433546
$650$		0			0
$651$	−14.4527			−0.566447
$652$		0			0
$653$	−0.828184	+	3.09082i	−0.0324093	+	0.120953i	−0.980235	−	0.197835i	$-0.936609\pi$
$653$	−0.828184	+	3.09082i	−0.0324093	+	0.120953i	0.947826	+	0.318788i	$0.103276\pi$
$654$		0			0
$655$	4.60922	+	26.5275i	0.180097	+	1.03651i
$656$		0			0
$657$	−0.946240	+	1.63894i	−0.0369164	+	0.0639410i
$658$		0			0
$659$	6.29598	+	3.63499i	0.245257	+	0.141599i	0.617590	−	0.786500i	$-0.288109\pi$
$659$	6.29598	+	3.63499i	0.245257	+	0.141599i	−0.372334	+	0.928099i	$0.621442\pi$
$660$		0			0
$661$	−10.9236	+	40.7674i	−0.424878	+	1.58567i	0.339311	+	0.940674i	$0.389806\pi$
$661$	−10.9236	+	40.7674i	−0.424878	+	1.58567i	−0.764189	+	0.644992i	$0.776861\pi$
$662$		0			0
$663$	15.9342	+	1.53072i	0.618834	+	0.0594484i
$664$		0			0
$665$	23.1088	+	2.07993i	0.896121	+	0.0806563i
$666$		0			0
$667$	49.2690	−	13.2016i	1.90770	−	0.511168i
$668$		0			0
$669$	22.4966	−	6.02795i	0.869770	−	0.233054i
$670$		0			0
$671$	1.15159	+	1.15159i	0.0444565	+	0.0444565i
$672$		0			0
$673$	17.5690	+	4.70761i	0.677236	+	0.181465i	0.581012	−	0.813895i	$-0.302657\pi$
$673$	17.5690	+	4.70761i	0.677236	+	0.181465i	0.0962240	+	0.995360i	$0.469323\pi$
$674$		0			0
$675$	9.69125	−	20.5148i	0.373016	−	0.789614i
$676$		0			0
$677$	35.6038	−	35.6038i	1.36836	−	1.36836i	0.505589	−	0.862774i	$-0.331275\pi$
$677$	35.6038	−	35.6038i	1.36836	−	1.36836i	0.862774	−	0.505589i	$-0.168725\pi$
$678$		0			0
$679$	1.05546	−	0.609368i	0.0405047	−	0.0233854i
$680$		0			0
$681$	2.89990	−	2.89990i	0.111125	−	0.111125i
$682$		0			0
$683$	32.5158	+	18.7730i	1.24418	+	0.718329i	0.969943	−	0.243332i	$-0.0782404\pi$
$683$	32.5158	+	18.7730i	1.24418	+	0.718329i	0.274240	+	0.961661i	$0.411574\pi$
$684$		0			0
$685$	2.63056	+	0.964894i	0.100509	+	0.0368667i
$686$		0			0
$687$	−11.3304	−	19.6248i	−0.432280	−	0.748731i
$688$		0			0
$689$	−9.39536	+	7.74844i	−0.357935	+	0.295192i
$690$		0			0
$691$	37.6457	+	10.0871i	1.43211	+	0.383733i	0.889764	−	0.456421i	$-0.150869\pi$
$691$	37.6457	+	10.0871i	1.43211	+	0.383733i	0.542348	+	0.840154i	$0.317536\pi$
$692$		0			0
$693$	−0.204936	−	0.764833i	−0.00778489	−	0.0290536i
$694$		0			0
$695$	−15.3037	+	41.7219i	−0.580501	+	1.58260i
$696$		0			0
$697$	−61.9239			−2.34554
$698$		0			0
$699$	−10.9124	−	18.9008i	−0.412745	−	0.714895i
$700$		0			0
$701$		−	24.5879i		−	0.928672i	−0.885659	−	0.464336i	$-0.846293\pi$
$701$		−	24.5879i		−	0.928672i	0.885659	−	0.464336i	$-0.153707\pi$
$702$		0			0
$703$	13.3086	+	13.3086i	0.501942	+	0.501942i
$704$		0			0
$705$	−7.47799	−	0.673065i	−0.281638	−	0.0253491i
$706$		0			0
$707$		−	22.6504i		−	0.851855i
$708$		0			0
$709$	4.35703	+	16.2607i	0.163632	+	0.610682i	0.998211	+	0.0597936i	$0.0190443\pi$
$709$	4.35703	+	16.2607i	0.163632	+	0.610682i	−0.834579	+	0.550888i	$0.814289\pi$
$710$		0			0
$711$	4.10555	−	7.11103i	0.153970	−	0.266684i
$712$		0			0
$713$	−53.4834	+	30.8786i	−2.00297	+	1.15641i
$714$		0			0
$715$	−0.218263	+	1.16287i	−0.00816259	+	0.0434888i
$716$		0			0
$717$	9.44404	−	5.45252i	0.352694	−	0.203628i
$718$		0			0
$719$	8.79659	−	15.2361i	0.328057	−	0.568212i	−0.654069	−	0.756435i	$-0.726939\pi$
$719$	8.79659	−	15.2361i	0.328057	−	0.568212i	0.982126	+	0.188223i	$0.0602728\pi$
$720$		0			0
$721$	11.2311	+	41.9149i	0.418266	+	1.56099i
$722$		0			0
$723$			0.799743i			0.0297427i
$724$		0			0
$725$	−18.6682	+	22.0235i	−0.693319	+	0.817933i
$726$		0			0
$727$	−18.0270	−	18.0270i	−0.668585	−	0.668585i	0.288803	−	0.957388i	$-0.406743\pi$
$727$	−18.0270	−	18.0270i	−0.668585	−	0.668585i	−0.957388	+	0.288803i	$0.906743\pi$
$728$		0			0
$729$		−	5.34819i		−	0.198081i
$730$		0			0
$731$	1.70917	+	2.96037i	0.0632159	+	0.109493i
$732$		0			0
$733$	24.4764			0.904056			0.452028	−	0.892004i	$-0.350701\pi$
$733$	24.4764			0.904056			0.452028	+	0.892004i	$0.350701\pi$
$734$		0			0
$735$	1.03137	+	2.22628i	0.0380426	+	0.0821175i
$736$		0			0
$737$	0.146433	+	0.546494i	0.00539392	+	0.0201304i
$738$		0			0
$739$	12.3388	+	3.30617i	0.453890	+	0.121619i	0.478519	−	0.878077i	$-0.341174\pi$
$739$	12.3388	+	3.30617i	0.453890	+	0.121619i	−0.0246292	+	0.999697i	$0.507840\pi$
$740$		0			0
$741$	−13.4371	−	1.29083i	−0.493622	−	0.0474199i
$742$		0			0
$743$	−7.53145	−	13.0449i	−0.276302	−	0.478569i	0.694161	−	0.719820i	$-0.255776\pi$
$743$	−7.53145	−	13.0449i	−0.276302	−	0.478569i	−0.970463	+	0.241251i	$0.922442\pi$
$744$		0			0
$745$	−0.690366	−	1.49020i	−0.0252931	−	0.0545968i
$746$		0			0
$747$	20.1908	+	11.6572i	0.738743	+	0.426513i
$748$		0			0
$749$	−7.46308	+	7.46308i	−0.272695	+	0.272695i
$750$		0			0
$751$	−0.0168245	+	0.00971361i	−0.000613933	+	0.000354455i	−0.500307	−	0.865848i	$-0.666779\pi$
$751$	−0.0168245	+	0.00971361i	−0.000613933	+	0.000354455i	0.499693	+	0.866203i	$0.333446\pi$
$752$		0			0
$753$	4.14215	−	4.14215i	0.150948	−	0.150948i
$754$		0			0
$755$	25.3192	−	35.9681i	0.921462	−	1.30901i
$756$		0			0
$757$	39.0825	+	10.4721i	1.42048	+	0.380616i	0.885653	−	0.464347i	$-0.153711\pi$
$757$	39.0825	+	10.4721i	1.42048	+	0.380616i	0.534825	+	0.844963i	$0.320378\pi$
$758$		0			0
$759$	0.791691	+	0.791691i	0.0287366	+	0.0287366i
$760$		0			0
$761$	23.2860	−	6.23947i	0.844118	−	0.226181i	0.189255	−	0.981928i	$-0.439393\pi$
$761$	23.2860	−	6.23947i	0.844118	−	0.226181i	0.654863	+	0.755747i	$0.272726\pi$
$762$		0			0
$763$	16.0656	−	4.30476i	0.581613	−	0.155843i
$764$		0			0
$765$	2.32269	−	25.8059i	0.0839769	−	0.933013i
$766$		0			0
$767$	26.7623	−	4.48459i	0.966332	−	0.161929i
$768$		0			0
$769$	−2.93059	+	10.9371i	−0.105680	+	0.394402i	−0.998421	−	0.0561669i	$-0.982112\pi$
$769$	−2.93059	+	10.9371i	−0.105680	+	0.394402i	0.892742	+	0.450569i	$0.148779\pi$
$770$		0			0
$771$	4.97020	+	2.86954i	0.178997	+	0.103344i
$772$		0			0
$773$	13.2804	−	23.0024i	0.477664	−	0.827338i	−0.522008	−	0.852940i	$-0.674817\pi$
$773$	13.2804	−	23.0024i	0.477664	−	0.827338i	0.999672	+	0.0256023i	$0.00815036\pi$
$774$		0			0
$775$	14.9311	−	31.6066i	0.536340	−	1.13534i
$776$		0			0
$777$	2.32304	−	8.66969i	0.0833385	−	0.311023i
$778$		0			0
$779$	52.2193			1.87095
$780$		0			0
$781$	0.944676			0.0338032
$782$		0			0
$783$	−6.78153	+	25.3090i	−0.242352	+	0.904470i
$784$		0			0
$785$	−6.57013	−	4.62495i	−0.234498	−	0.165072i
$786$		0			0
$787$	−0.669088	+	1.15890i	−0.0238504	+	0.0413102i	−0.877704	−	0.479203i	$-0.840926\pi$
$787$	−0.669088	+	1.15890i	−0.0238504	+	0.0413102i	0.853854	+	0.520513i	$0.174259\pi$
$788$		0			0
$789$	−8.82737	−	5.09649i	−0.314263	−	0.181440i
$790$		0			0
$791$	0.705224	−	2.63193i	0.0250749	−	0.0935807i
$792$		0			0
$793$	32.5796	+	23.2279i	1.15694	+	0.824847i
$794$		0			0
$795$	−4.18035	−	5.00730i	−0.148262	−	0.177590i
$796$		0			0
$797$	−51.4349	+	13.7819i	−1.82192	+	0.488182i	−0.997023	−	0.0771042i	$-0.975433\pi$
$797$	−51.4349	+	13.7819i	−1.82192	+	0.488182i	−0.824895	+	0.565286i	$0.808766\pi$
$798$		0			0
$799$	−19.3049	+	5.17274i	−0.682959	+	0.182998i
$800$		0			0
$801$	19.4054	+	19.4054i	0.685656	+	0.685656i
$802$		0			0
$803$	0.119013	+	0.0318894i	0.00419988	+	0.00112535i
$804$		0			0
$805$	−38.6620	−	27.2156i	−1.36266	−	0.959224i
$806$		0			0
$807$	−10.2805	+	10.2805i	−0.361890	+	0.361890i
$808$		0			0
$809$	26.9017	−	15.5317i	0.945814	−	0.546066i	0.0540362	−	0.998539i	$-0.482791\pi$
$809$	26.9017	−	15.5317i	0.945814	−	0.546066i	0.891778	+	0.452473i	$0.149458\pi$
$810$		0			0
$811$	−23.2698	+	23.2698i	−0.817114	+	0.817114i	−0.985689	−	0.168574i	$-0.946084\pi$
$811$	−23.2698	+	23.2698i	−0.817114	+	0.817114i	0.168574	+	0.985689i	$0.446084\pi$
$812$		0			0
$813$	9.41857	+	5.43781i	0.330324	+	0.190712i
$814$		0			0
$815$	6.73745	−	18.3681i	0.236003	−	0.643407i
$816$		0			0
$817$	−1.44131	−	2.49642i	−0.0504251	−	0.0873388i
$818$		0			0
$819$	−8.07126	−	17.7003i	−0.282032	−	0.618500i
$820$		0			0
$821$	33.6762	+	9.02350i	1.17531	+	0.314922i	0.793063	−	0.609139i	$-0.208485\pi$
$821$	33.6762	+	9.02350i	1.17531	+	0.314922i	0.382243	+	0.924062i	$0.375152\pi$
$822$		0			0
$823$	−9.54424	−	35.6196i	−0.332691	−	1.24162i	−0.906350	−	0.422527i	$-0.861143\pi$
$823$	−9.54424	−	35.6196i	−0.332691	−	1.24162i	0.573659	−	0.819094i	$-0.305524\pi$
$824$		0			0
$825$	−0.623543	−	0.113162i	−0.0217090	−	0.00393979i
$826$		0			0
$827$	30.9231			1.07530			0.537651	−	0.843168i	$-0.319312\pi$
$827$	30.9231			1.07530			0.537651	+	0.843168i	$0.319312\pi$
$828$		0			0
$829$	−15.3995	−	26.6727i	−0.534846	−	0.926381i	−0.999171	−	0.0407156i	$-0.987036\pi$
$829$	−15.3995	−	26.6727i	−0.534846	−	0.926381i	0.464325	−	0.885665i	$-0.346297\pi$
$830$		0			0
$831$		−	12.3933i		−	0.429919i
$832$		0			0
$833$	4.61819	+	4.61819i	0.160011	+	0.160011i
$834$		0			0
$835$	11.9570	−	9.98229i	0.413788	−	0.345451i
$836$		0			0
$837$		−	31.7241i		−	1.09655i
$838$		0			0
$839$	4.42837	+	16.5269i	0.152884	+	0.570571i	0.999277	+	0.0380128i	$0.0121028\pi$
$839$	4.42837	+	16.5269i	0.152884	+	0.570571i	−0.846393	+	0.532559i	$0.821231\pi$
$840$		0			0
$841$	2.17072	−	3.75980i	0.0748525	−	0.129648i
$842$		0			0
$843$	−11.7606	+	6.78997i	−0.405055	+	0.233859i
$844$		0			0
$845$	−0.567019	+	29.0634i	−0.0195061	+	0.999810i
$846$		0			0
$847$	22.7578	−	13.1392i	0.781968	−	0.451469i
$848$		0			0
$849$	−7.41606	+	12.8450i	−0.254518	+	0.440839i
$850$		0			0
$851$	−9.92646	−	37.0461i	−0.340275	−	1.26992i
$852$		0			0
$853$		−	2.23760i		−	0.0766141i	−0.999266	−	0.0383071i	$-0.987804\pi$
$853$		−	2.23760i		−	0.0766141i	0.999266	−	0.0383071i	$-0.0121965\pi$
$854$		0			0
$855$	−1.95868	+	21.7616i	−0.0669854	+	0.744232i
$856$		0			0
$857$	13.2191	+	13.2191i	0.451556	+	0.451556i	0.895871	−	0.444315i	$-0.146553\pi$
$857$	13.2191	+	13.2191i	0.451556	+	0.451556i	−0.444315	+	0.895871i	$0.646553\pi$
$858$		0			0
$859$			26.7421i			0.912427i	0.889870	+	0.456214i	$0.150795\pi$
$859$			26.7421i			0.912427i	−0.889870	+	0.456214i	$0.849205\pi$
$860$		0			0
$861$	−12.4513	−	21.5663i	−0.424339	−	0.734978i
$862$		0			0
$863$	−21.5085			−0.732157			−0.366079	−	0.930584i	$-0.619300\pi$
$863$	−21.5085			−0.732157			−0.366079	+	0.930584i	$0.619300\pi$
$864$		0			0
$865$	6.52719	−	3.02385i	0.221931	−	0.102814i
$866$		0			0
$867$	2.10693	+	7.86317i	0.0715551	+	0.267047i
$868$		0			0
$869$	−0.516374	−	0.138362i	−0.0175168	−	0.00469361i
$870$		0			0
$871$	5.76714	+	12.6474i	0.195412	+	0.428540i
$872$		0			0
$873$	0.573844	+	0.993927i	0.0194217	+	0.0336393i
$874$		0			0
$875$	26.7609	+	0.200528i	0.904685	+	0.00677908i
$876$		0			0
$877$	−14.3382	−	8.27817i	−0.484167	−	0.279534i	0.237984	−	0.971269i	$-0.423513\pi$
$877$	−14.3382	−	8.27817i	−0.484167	−	0.279534i	−0.722151	+	0.691735i	$0.756847\pi$
$878$		0			0
$879$	15.2245	−	15.2245i	0.513510	−	0.513510i
$880$		0			0
$881$	−41.3063	+	23.8482i	−1.39165	+	0.803467i	−0.993497	−	0.113854i	$-0.963680\pi$
$881$	−41.3063	+	23.8482i	−1.39165	+	0.803467i	−0.398148	+	0.917321i	$0.630347\pi$
$882$		0			0
$883$	−23.3722	+	23.3722i	−0.786536	+	0.786536i	−0.980925	−	0.194388i	$-0.937728\pi$
$883$	−23.3722	+	23.3722i	−0.786536	+	0.786536i	0.194388	+	0.980925i	$0.437728\pi$
$884$		0			0
$885$	2.48808	+	14.3197i	0.0836361	+	0.481351i
$886$		0			0
$887$	−54.5002	−	14.6033i	−1.82994	−	0.490330i	−0.832015	−	0.554753i	$-0.812813\pi$
$887$	−54.5002	−	14.6033i	−1.82994	−	0.490330i	−0.997923	+	0.0644228i	$0.979479\pi$
$888$		0			0
$889$	−27.4633	−	27.4633i	−0.921091	−	0.921091i
$890$		0			0
$891$	0.403041	−	0.107995i	0.0135024	−	0.00361796i
$892$		0			0
$893$	16.2795	−	4.36207i	0.544772	−	0.145971i
$894$		0			0
$895$	3.58687	−	2.99451i	0.119896	−	0.100095i
$896$		0			0
$897$	22.3978	+	15.9687i	0.747841	+	0.533180i
$898$		0			0
$899$	−10.4481	+	38.9930i	−0.348465	+	1.30049i
$900$		0			0
$901$	−15.0369	−	8.68157i	−0.500952	−	0.289225i
$902$		0			0
$903$	−0.687340	+	1.19051i	−0.0228732	+	0.0396176i
$904$		0			0
$905$	3.00115	−	0.521458i	0.0997615	−	0.0173338i
$906$		0			0
$907$	9.27353	−	34.6093i	0.307923	−	1.14918i	−0.622478	−	0.782638i	$-0.713874\pi$
$907$	9.27353	−	34.6093i	0.307923	−	1.14918i	0.930400	−	0.366545i	$-0.119460\pi$
$908$		0			0
$909$	21.3299			0.707469
$910$		0			0
$911$	26.4864			0.877534			0.438767	−	0.898601i	$-0.355415\pi$
$911$	26.4864			0.877534			0.438767	+	0.898601i	$0.355415\pi$
$912$		0			0
$913$	0.392860	−	1.46617i	0.0130018	−	0.0485233i
$914$		0			0
$915$	−12.3362	+	17.5246i	−0.407823	+	0.579346i
$916$		0			0
$917$	−14.4111	+	24.9608i	−0.475897	+	0.824278i
$918$		0			0
$919$	−15.4599	−	8.92578i	−0.509975	−	0.294434i	0.222848	−	0.974853i	$-0.428465\pi$
$919$	−15.4599	−	8.92578i	−0.509975	−	0.294434i	−0.732823	+	0.680419i	$0.761798\pi$
$920$		0			0
$921$	−2.30764	+	8.61223i	−0.0760394	+	0.283783i
$922$		0			0
$923$	22.8902	−	3.83573i	0.753440	−	0.126254i
$924$		0			0
$925$	16.5598	+	14.0369i	0.544482	+	0.461529i
$926$		0			0
$927$	−39.4714	+	10.5763i	−1.29641	+	0.347372i
$928$		0			0
$929$	3.69827	−	0.990949i	0.121336	−	0.0325120i	−0.197640	−	0.980275i	$-0.563328\pi$
$929$	3.69827	−	0.990949i	0.121336	−	0.0325120i	0.318976	+	0.947763i	$0.396661\pi$
$930$		0			0
$931$	−3.89443	−	3.89443i	−0.127635	−	0.127635i
$932$		0			0
$933$	13.1561	+	3.52516i	0.430710	+	0.115408i
$934$		0			0
$935$	−1.66200	+	0.288777i	−0.0543532	+	0.00944402i
$936$		0			0
$937$	−19.7005	+	19.7005i	−0.643586	+	0.643586i	−0.951435	−	0.307849i	$-0.900391\pi$
$937$	−19.7005	+	19.7005i	−0.643586	+	0.643586i	0.307849	+	0.951435i	$0.400391\pi$
$938$		0			0
$939$	18.7877	−	10.8471i	0.613112	−	0.353981i
$940$		0			0
$941$	−9.21977	+	9.21977i	−0.300556	+	0.300556i	−0.841231	−	0.540675i	$-0.818169\pi$
$941$	−9.21977	+	9.21977i	−0.300556	+	0.300556i	0.540675	+	0.841231i	$0.318169\pi$
$942$		0			0
$943$	−92.1540	−	53.2051i	−3.00095	−	1.73260i
$944$		0			0
$945$	22.0375	−	10.2093i	0.716880	−	0.332109i
$946$		0			0
$947$	13.4215	+	23.2467i	0.436139	+	0.755415i	0.997388	−	0.0722321i	$-0.0230122\pi$
$947$	13.4215	+	23.2467i	0.436139	+	0.755415i	−0.561249	+	0.827647i	$0.689679\pi$
$948$		0			0
$949$	3.01325	+	0.289469i	0.0978144	+	0.00939655i
$950$		0			0
$951$	11.1909	+	2.99859i	0.362889	+	0.0972358i
$952$		0			0
$953$	9.05483	+	33.7931i	0.293315	+	1.09467i	0.942547	+	0.334075i	$0.108424\pi$
$953$	9.05483	+	33.7931i	0.293315	+	1.09467i	−0.649232	+	0.760590i	$0.724910\pi$
$954$		0			0
$955$	5.97278	+	2.19083i	0.193275	+	0.0708934i
$956$		0			0
$957$	0.731855			0.0236575
$958$		0			0
$959$	1.49969	+	2.59755i	0.0484276	+	0.0838791i
$960$		0			0
$961$		−	17.8765i		−	0.576662i
$962$		0			0
$963$	−7.02800	−	7.02800i	−0.226474	−	0.226474i
$964$		0			0
$965$	0.831212	+	0.995640i	0.0267577	+	0.0320508i
$966$		0			0
$967$		−	10.4047i		−	0.334594i	−0.985907	−	0.167297i	$-0.946496\pi$
$967$		−	10.4047i		−	0.334594i	0.985907	−	0.167297i	$-0.0535039\pi$
$968$		0			0
$969$	−4.98123	−	18.5902i	−0.160020	−	0.597203i
$970$		0			0
$971$	3.92930	−	6.80575i	0.126097	−	0.218407i	−0.796064	−	0.605212i	$-0.793088\pi$
$971$	3.92930	−	6.80575i	0.126097	−	0.218407i	0.922161	+	0.386805i	$0.126421\pi$
$972$		0			0
$973$	−41.1983	+	23.7858i	−1.32076	+	0.762539i
$974$		0			0
$975$	−15.5684	−	0.210189i	−0.498587	−	0.00673145i
$976$		0			0
$977$	−45.3725	+	26.1958i	−1.45159	+	0.838078i	−0.998572	−	0.0534218i	$-0.982987\pi$
$977$	−45.3725	+	26.1958i	−1.45159	+	0.838078i	−0.453021	+	0.891500i	$0.649654\pi$
$978$		0			0
$979$	0.893361	−	1.54735i	0.0285519	−	0.0494534i
$980$		0			0
$981$	4.05381	+	15.1290i	0.129428	+	0.483032i
$982$		0			0
$983$		−	38.1526i		−	1.21688i	−0.793600	−	0.608439i	$-0.791796\pi$
$983$		−	38.1526i		−	1.21688i	0.793600	−	0.608439i	$-0.208204\pi$
$984$		0			0
$985$	1.82473	+	2.18569i	0.0581406	+	0.0696418i
$986$		0			0
$987$	−5.68324	−	5.68324i	−0.180899	−	0.180899i
$988$		0			0
$989$			5.87408i			0.186785i
$990$		0			0
$991$	−4.01794	−	6.95928i	−0.127634	−	0.221069i	0.795125	−	0.606445i	$-0.207405\pi$
$991$	−4.01794	−	6.95928i	−0.127634	−	0.221069i	−0.922760	+	0.385376i	$0.874072\pi$
$992$		0			0
$993$	12.6520			0.401499
$994$		0			0
$995$	−39.2602	−	14.4007i	−1.24463	−	0.456533i
$996$		0			0
$997$	7.06984	+	26.3850i	0.223904	+	0.835621i	0.982841	+	0.184456i	$0.0590525\pi$
$997$	7.06984	+	26.3850i	0.223904	+	0.835621i	−0.758937	+	0.651164i	$0.774281\pi$
$998$		0			0
$999$	19.0302	+	5.09912i	0.602089	+	0.161329i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bf.c.93.2	✓	20
5.2	odd	4		260.2.bk.c.197.4	yes	20
5.3	odd	4		1300.2.bs.d.457.2		20
5.4	even	2		1300.2.bn.d.93.4		20
13.7	odd	12		260.2.bk.c.33.4	yes	20
65.7	even	12	inner	260.2.bf.c.137.2	yes	20
65.33	even	12		1300.2.bn.d.657.4		20
65.59	odd	12		1300.2.bs.d.293.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.c.93.2	✓	20	1.1	even	1	trivial
260.2.bf.c.137.2	yes	20	65.7	even	12	inner
260.2.bk.c.33.4	yes	20	13.7	odd	12
260.2.bk.c.197.4	yes	20	5.2	odd	4
1300.2.bn.d.93.4		20	5.4	even	2
1300.2.bn.d.657.4		20	65.33	even	12
1300.2.bs.d.293.2		20	65.59	odd	12
1300.2.bs.d.457.2		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)

\(f(q)\)	\(=\)	\(q+(-0.223531 + 0.834228i) q^{3} +(-0.382788 - 2.20306i) q^{5} +(1.19682 - 2.07295i) q^{7} +(1.95211 + 1.12705i) q^{9} +O(q^{10})\)	\(q+(-0.223531 + 0.834228i) q^{3} +(-0.382788 - 2.20306i) q^{5} +(1.19682 - 2.07295i) q^{7} +(1.95211 + 1.12705i) q^{9} +(0.0379829 - 0.141754i) q^{11} +(0.344781 - 3.58903i) q^{13} +(1.92342 + 0.173119i) q^{15} +(4.96543 - 1.33048i) q^{17} +(-4.18726 + 1.12197i) q^{19} +(1.46179 + 1.46179i) q^{21} +(8.53261 + 2.28631i) q^{23} +(-4.70695 + 1.68661i) q^{25} +(-3.20866 + 3.20866i) q^{27} +(5.00061 - 2.88710i) q^{29} +(-4.94351 + 4.94351i) q^{31} +(0.109765 + 0.0633728i) q^{33} +(-5.02496 - 1.84316i) q^{35} +(-2.17085 - 3.76003i) q^{37} +(2.91700 + 1.08988i) q^{39} +(-11.6356 - 3.11775i) q^{41} +(0.172107 + 0.642311i) q^{43} +(1.73571 - 4.73203i) q^{45} -3.88786 q^{47} +(0.635248 + 1.10028i) q^{49} +4.43971i q^{51} +(-2.38836 - 2.38836i) q^{53} +(-0.326832 - 0.0294169i) q^{55} -3.74392i q^{57} +(1.94788 + 7.26959i) q^{59} +(-5.54868 + 9.61059i) q^{61} +(4.67263 - 2.69775i) q^{63} +(-8.03882 + 0.614264i) q^{65} +(-3.33873 + 1.92761i) q^{67} +(-3.81460 + 6.60708i) q^{69} +(1.66605 + 6.21778i) q^{71} +0.839574i q^{73} +(-0.354869 - 4.30368i) q^{75} +(-0.248391 - 0.248391i) q^{77} -3.64275i q^{79} +(1.42162 + 2.46232i) q^{81} +10.3431 q^{83} +(-4.83184 - 10.4298i) q^{85} +(1.29071 + 4.81701i) q^{87} +(11.7600 + 3.15109i) q^{89} +(-7.02724 - 5.01013i) q^{91} +(-3.01899 - 5.22904i) q^{93} +(4.07460 + 8.79530i) q^{95} +(0.440943 + 0.254578i) q^{97} +(0.233910 - 0.233910i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} - 6 q^{5} - 6 q^{7} + 12 q^{9}+O(q^{10}) \) 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

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Database

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