LMFDB - Embedded newform 464.2.u.c.401.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [464,2,Mod(49,464)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(464, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("464.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 464 = 2^{4} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	464.u (of order $7$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.70505865379$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 116)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			401.1
Root			$0.222521 - 0.974928i$ of defining polynomial
Character	$\chi$	$=$	464.401
Dual form			464.2.u.c.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.346011 + 1.51597i) q^{3} +(-2.02446 - 2.53859i) q^{5} +(0.0108851 + 0.0476909i) q^{7} +(0.524459 - 0.252566i) q^{9} +O(q^{10})$	\(q+(0.346011 + 1.51597i) q^{3} +(-2.02446 - 2.53859i) q^{5} +(0.0108851 + 0.0476909i) q^{7} +(0.524459 - 0.252566i) q^{9} +(1.98039 + 0.953703i) q^{11} +(4.22737 + 2.03579i) q^{13} +(3.14795 - 3.94740i) q^{15} +4.71379 q^{17} +(-0.257865 + 1.12978i) q^{19} +(-0.0685317 + 0.0330031i) q^{21} +(3.27144 - 4.10225i) q^{23} +(-1.23341 + 5.40391i) q^{25} +(3.47285 + 4.35482i) q^{27} +(5.09783 - 1.73553i) q^{29} +(-5.51842 - 6.91988i) q^{31} +(-0.760553 + 3.33220i) q^{33} +(0.0990311 - 0.124181i) q^{35} +(-9.91939 + 4.77692i) q^{37} +(-1.62349 + 7.11297i) q^{39} +1.10992 q^{41} +(-3.40850 + 4.27413i) q^{43} +(-1.70291 - 0.820077i) q^{45} +(7.83124 + 3.77133i) q^{47} +(6.30463 - 3.03615i) q^{49} +(1.63102 + 7.14598i) q^{51} +(-2.27144 - 2.84829i) q^{53} +(-1.58815 - 6.95812i) q^{55} -1.80194 q^{57} -12.8116 q^{59} +(-0.592990 - 2.59806i) q^{61} +(0.0177539 + 0.0222627i) q^{63} +(-3.39008 - 14.8529i) q^{65} +(-0.0196143 + 0.00944576i) q^{67} +(7.35086 + 3.53999i) q^{69} +(3.31551 + 1.59667i) q^{71} +(-1.64042 + 2.05702i) q^{73} -8.61894 q^{75} +(-0.0239262 + 0.104828i) q^{77} +(6.38620 - 3.07543i) q^{79} +(-4.31133 + 5.40624i) q^{81} +(3.65399 - 16.0092i) q^{83} +(-9.54288 - 11.9664i) q^{85} +(4.39493 + 7.12766i) q^{87} +(-2.05161 - 2.57263i) q^{89} +(-0.0510733 + 0.223767i) q^{91} +(8.58091 - 10.7601i) q^{93} +(3.39008 - 1.63258i) q^{95} +(-1.90097 + 8.32869i) q^{97} +1.27950 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} - 3 q^{5} - 3 q^{7} - 6 q^{9}+O(q^{10}) $ 6 * q - 3 * q^3 - 3 * q^5 - 3 * q^7 - 6 * q^9	$ 6 q - 3 q^{3} - 3 q^{5} - 3 q^{7} - 6 q^{9} - q^{11} + 3 q^{13} + 5 q^{15} + 12 q^{17} + 11 q^{19} + 5 q^{21} + q^{23} - 4 q^{25} + 33 q^{27} - 6 q^{29} - 5 q^{31} + 11 q^{33} + 5 q^{35} - 27 q^{37} - 5 q^{39} + 8 q^{41} + 9 q^{43} + 3 q^{45} + 7 q^{47} + 26 q^{49} - 20 q^{51} + 5 q^{53} - 17 q^{55} - 2 q^{57} - 24 q^{59} + 11 q^{61} - 53 q^{63} - 19 q^{65} - 13 q^{67} + 17 q^{69} + 5 q^{71} - 21 q^{73} + 16 q^{75} + 25 q^{77} - q^{79} - 58 q^{81} + 27 q^{83} - 20 q^{85} + 3 q^{87} + 9 q^{89} + 37 q^{91} - q^{93} + 19 q^{95} - 7 q^{97} - 20 q^{99}+O(q^{100}) $ 6 * q - 3 * q^3 - 3 * q^5 - 3 * q^7 - 6 * q^9 - q^11 + 3 * q^13 + 5 * q^15 + 12 * q^17 + 11 * q^19 + 5 * q^21 + q^23 - 4 * q^25 + 33 * q^27 - 6 * q^29 - 5 * q^31 + 11 * q^33 + 5 * q^35 - 27 * q^37 - 5 * q^39 + 8 * q^41 + 9 * q^43 + 3 * q^45 + 7 * q^47 + 26 * q^49 - 20 * q^51 + 5 * q^53 - 17 * q^55 - 2 * q^57 - 24 * q^59 + 11 * q^61 - 53 * q^63 - 19 * q^65 - 13 * q^67 + 17 * q^69 + 5 * q^71 - 21 * q^73 + 16 * q^75 + 25 * q^77 - q^79 - 58 * q^81 + 27 * q^83 - 20 * q^85 + 3 * q^87 + 9 * q^89 + 37 * q^91 - q^93 + 19 * q^95 - 7 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/464\mathbb{Z}\right)^\times$.

$n$	$117$	$175$	$321$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{7}\right)$

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
$3$	0.346011	+	1.51597i	0.199769	+	0.875247i	0.971074	+	0.238780i	$0.0767476\pi$
$3$	0.346011	+	1.51597i	0.199769	+	0.875247i	−0.771304	+	0.636467i	$0.780395\pi$
$4$		0			0
$5$	−2.02446	−	2.53859i	−0.905365	−	1.13529i	−0.990306	−	0.138906i	$-0.955641\pi$
$5$	−2.02446	−	2.53859i	−0.905365	−	1.13529i	0.0849401	−	0.996386i	$-0.472930\pi$
$6$		0			0
$7$	0.0108851	+	0.0476909i	0.00411419	+	0.0180255i	0.976943	−	0.213499i	$-0.0684859\pi$
$7$	0.0108851	+	0.0476909i	0.00411419	+	0.0180255i	−0.972829	+	0.231524i	$0.925629\pi$
$8$		0			0
$9$	0.524459	−	0.252566i	0.174820	−	0.0841887i
$10$		0			0
$11$	1.98039	+	0.953703i	0.597109	+	0.287552i	0.707924	−	0.706289i	$-0.249632\pi$
$11$	1.98039	+	0.953703i	0.597109	+	0.287552i	−0.110815	+	0.993841i	$0.535346\pi$
$12$		0			0
$13$	4.22737	+	2.03579i	1.17246	+	0.564627i	0.915706	−	0.401850i	$-0.131633\pi$
$13$	4.22737	+	2.03579i	1.17246	+	0.564627i	0.256754	+	0.966477i	$0.417347\pi$
$14$		0			0
$15$	3.14795	−	3.94740i	0.812797	−	1.01921i
$16$		0			0
$17$	4.71379			1.14326			0.571631	−	0.820511i	$-0.306311\pi$
$17$	4.71379			1.14326			0.571631	+	0.820511i	$0.306311\pi$
$18$		0			0
$19$	−0.257865	+	1.12978i	−0.0591582	+	0.259189i	−0.995855	−	0.0909517i	$-0.971009\pi$
$19$	−0.257865	+	1.12978i	−0.0591582	+	0.259189i	0.936697	+	0.350141i	$0.113866\pi$
$20$		0			0
$21$	−0.0685317	+	0.0330031i	−0.0149548	+	0.00720187i
$22$		0			0
$23$	3.27144	−	4.10225i	0.682142	−	0.855379i	−0.313408	−	0.949619i	$-0.601471\pi$
$23$	3.27144	−	4.10225i	0.682142	−	0.855379i	0.995550	+	0.0942397i	$0.0300420\pi$
$24$		0			0
$25$	−1.23341	+	5.40391i	−0.246681	+	1.08078i
$26$		0			0
$27$	3.47285	+	4.35482i	0.668351	+	0.838085i
$28$		0			0
$29$	5.09783	−	1.73553i	0.946644	−	0.322281i
$29$	5.09783	−	1.73553i	0.946644	−	0.322281i
$30$		0			0
$31$	−5.51842	−	6.91988i	−0.991137	−	1.24285i	−0.970009	−	0.243070i	$-0.921846\pi$
$31$	−5.51842	−	6.91988i	−0.991137	−	1.24285i	−0.0211283	−	0.999777i	$-0.506726\pi$
$32$		0			0
$33$	−0.760553	+	3.33220i	−0.132395	+	0.580062i
$34$		0			0
$35$	0.0990311	−	0.124181i	0.0167393	−	0.0209904i
$36$		0			0
$37$	−9.91939	+	4.77692i	−1.63074	+	0.785322i	−0.630781	+	0.775961i	$0.717265\pi$
$37$	−9.91939	+	4.77692i	−1.63074	+	0.785322i	−0.999956	+	0.00936066i	$0.997020\pi$
$38$		0			0
$39$	−1.62349	+	7.11297i	−0.259966	+	1.13899i
$40$		0			0
$41$	1.10992			0.173340			0.0866699	−	0.996237i	$-0.472377\pi$
$41$	1.10992			0.173340			0.0866699	+	0.996237i	$0.472377\pi$
$42$		0			0
$43$	−3.40850	+	4.27413i	−0.519792	+	0.651798i	−0.970565	−	0.240840i	$-0.922577\pi$
$43$	−3.40850	+	4.27413i	−0.519792	+	0.651798i	0.450773	+	0.892639i	$0.351148\pi$
$44$		0			0
$45$	−1.70291	−	0.820077i	−0.253854	−	0.122250i
$46$		0			0
$47$	7.83124	+	3.77133i	1.14230	+	0.550105i	0.906713	−	0.421748i	$-0.138583\pi$
$47$	7.83124	+	3.77133i	1.14230	+	0.550105i	0.235591	+	0.971852i	$0.424298\pi$
$48$		0			0
$49$	6.30463	−	3.03615i	0.900661	−	0.433735i
$50$		0			0
$51$	1.63102	+	7.14598i	0.228389	+	1.00064i
$52$		0			0
$53$	−2.27144	−	2.84829i	−0.312006	−	0.391243i	0.600960	−	0.799279i	$-0.294785\pi$
$53$	−2.27144	−	2.84829i	−0.312006	−	0.391243i	−0.912966	+	0.408036i	$0.866214\pi$
$54$		0			0
$55$	−1.58815	−	6.95812i	−0.214146	−	0.938233i
$56$		0			0
$57$	−1.80194			−0.238672
$58$		0			0
$59$	−12.8116			−1.66793			−0.833966	−	0.551816i	$-0.813935\pi$
$59$	−12.8116			−1.66793			−0.833966	+	0.551816i	$0.813935\pi$
$60$		0			0
$61$	−0.592990	−	2.59806i	−0.0759246	−	0.332648i	0.922673	−	0.385583i	$-0.126000\pi$
$61$	−0.592990	−	2.59806i	−0.0759246	−	0.332648i	−0.998598	+	0.0529350i	$0.983142\pi$
$62$		0			0
$63$	0.0177539	+	0.0222627i	0.00223678	+	0.00280483i
$64$		0			0
$65$	−3.39008	−	14.8529i	−0.420488	−	1.84228i
$66$		0			0
$67$	−0.0196143	+	0.00944576i	−0.00239627	+	0.00115398i	−0.435081	−	0.900391i	$-0.643280\pi$
$67$	−0.0196143	+	0.00944576i	−0.00239627	+	0.00115398i	0.432685	+	0.901545i	$0.357566\pi$
$68$		0			0
$69$	7.35086	+	3.53999i	0.884939	+	0.426164i
$70$		0			0
$71$	3.31551	+	1.59667i	0.393479	+	0.189489i	0.620152	−	0.784481i	$-0.287071\pi$
$71$	3.31551	+	1.59667i	0.393479	+	0.189489i	−0.226674	+	0.973971i	$0.572785\pi$
$72$		0			0
$73$	−1.64042	+	2.05702i	−0.191996	+	0.240756i	−0.868507	−	0.495677i	$-0.834920\pi$
$73$	−1.64042	+	2.05702i	−0.191996	+	0.240756i	0.676511	+	0.736433i	$0.263491\pi$
$74$		0			0
$75$	−8.61894			−0.995230
$76$		0			0
$77$	−0.0239262	+	0.104828i	−0.00272664	+	0.0119462i
$78$		0			0
$79$	6.38620	−	3.07543i	0.718504	−	0.346013i	−0.0386475	−	0.999253i	$-0.512305\pi$
$79$	6.38620	−	3.07543i	0.718504	−	0.346013i	0.757151	+	0.653240i	$0.226591\pi$
$80$		0			0
$81$	−4.31133	+	5.40624i	−0.479037	+	0.600693i
$82$		0			0
$83$	3.65399	−	16.0092i	0.401077	−	1.75724i	−0.221972	−	0.975053i	$-0.571250\pi$
$83$	3.65399	−	16.0092i	0.401077	−	1.75724i	0.623050	−	0.782182i	$-0.285893\pi$
$84$		0			0
$85$	−9.54288	−	11.9664i	−1.03507	−	1.29794i
$86$		0			0
$87$	4.39493	+	7.12766i	0.471186	+	0.764166i
$88$		0			0
$89$	−2.05161	−	2.57263i	−0.217470	−	0.272698i	0.661115	−	0.750284i	$-0.270083\pi$
$89$	−2.05161	−	2.57263i	−0.217470	−	0.272698i	−0.878585	+	0.477586i	$0.841512\pi$
$90$		0			0
$91$	−0.0510733	+	0.223767i	−0.00535393	+	0.0234571i
$92$		0			0
$93$	8.58091	−	10.7601i	0.889799	−	1.11577i
$94$		0			0
$95$	3.39008	−	1.63258i	0.347815	−	0.167499i
$96$		0			0
$97$	−1.90097	+	8.32869i	−0.193014	+	0.845650i	0.781959	+	0.623329i	$0.214220\pi$
$97$	−1.90097	+	8.32869i	−0.193014	+	0.845650i	−0.974974	+	0.222321i	$0.928637\pi$
$98$		0			0
$99$	1.27950			0.128595
$100$		0			0
$101$	−6.57942	+	8.25033i	−0.654676	+	0.820938i	−0.992752	−	0.120181i	$-0.961653\pi$
$101$	−6.57942	+	8.25033i	−0.654676	+	0.820938i	0.338076	+	0.941119i	$0.390224\pi$
$102$		0			0
$103$	−16.4623	−	7.92781i	−1.62208	−	0.781150i	−0.622077	−	0.782956i	$-0.713711\pi$
$103$	−16.4623	−	7.92781i	−1.62208	−	0.781150i	−0.999998	+	0.00180621i	$0.999425\pi$
$104$		0			0
$105$	0.222521	+	0.107160i	0.0217158	+	0.0104578i
$106$		0			0
$107$	6.11745	−	2.94601i	0.591396	−	0.284801i	−0.114152	−	0.993463i	$-0.536415\pi$
$107$	6.11745	−	2.94601i	0.591396	−	0.284801i	0.705548	+	0.708662i	$0.250701\pi$
$108$		0			0
$109$	4.16972	+	18.2687i	0.399387	+	1.74983i	0.629822	+	0.776739i	$0.283128\pi$
$109$	4.16972	+	18.2687i	0.399387	+	1.74983i	−0.230435	+	0.973088i	$0.574015\pi$
$110$		0			0
$111$	−10.6739	−	13.3846i	−1.01312	−	1.27041i
$112$		0			0
$113$	0.605072	+	2.65099i	0.0569204	+	0.249384i	0.995381	−	0.0960012i	$-0.0306053\pi$
$113$	0.605072	+	2.65099i	0.0569204	+	0.249384i	−0.938461	+	0.345386i	$0.887748\pi$
$114$		0			0
$115$	−17.0368			−1.58869
$116$		0			0
$117$	2.73125			0.252504
$118$		0			0
$119$	0.0513102	+	0.224805i	0.00470360	+	0.0206078i
$120$		0			0
$121$	−3.84601	−	4.82274i	−0.349637	−	0.438431i
$122$		0			0
$123$	0.384043	+	1.68260i	0.0346280	+	0.151715i
$124$		0			0
$125$	1.58815	−	0.764811i	0.142048	−	0.0684068i
$126$		0			0
$127$	8.07822	+	3.89027i	0.716826	+	0.345205i	0.756488	−	0.654008i	$-0.226914\pi$
$127$	8.07822	+	3.89027i	0.716826	+	0.345205i	−0.0396616	+	0.999213i	$0.512628\pi$
$128$		0			0
$129$	−7.65883	−	3.68830i	−0.674323	−	0.324737i
$130$		0			0
$131$	−8.93631	+	11.2058i	−0.780769	+	0.979054i	0.219225	+	0.975674i	$0.429647\pi$
$131$	−8.93631	+	11.2058i	−0.780769	+	0.979054i	−0.999994	+	0.00337936i	$0.998924\pi$
$132$		0			0
$133$	−0.0566871			−0.00491539
$134$		0			0
$135$	4.02446	−	17.6323i	0.346370	−	1.51755i
$136$		0			0
$137$	−8.23705	+	3.96676i	−0.703739	+	0.338903i	−0.751296	−	0.659966i	$-0.770571\pi$
$137$	−8.23705	+	3.96676i	−0.703739	+	0.338903i	0.0475567	+	0.998869i	$0.484857\pi$
$138$		0			0
$139$	−4.82640	+	6.05211i	−0.409370	+	0.513333i	−0.943185	−	0.332268i	$-0.892186\pi$
$139$	−4.82640	+	6.05211i	−0.409370	+	0.513333i	0.533816	+	0.845601i	$0.320758\pi$
$140$		0			0
$141$	−3.00753	+	13.1769i	−0.253280	+	1.10969i
$142$		0			0
$143$	6.43027	+	8.06331i	0.537726	+	0.674288i
$144$		0			0
$145$	−14.7262	−	9.42780i	−1.22294	−	0.782936i
$146$		0			0
$147$	6.78418	+	8.50710i	0.559550	+	0.701654i
$148$		0			0
$149$	−1.74214	+	7.63279i	−0.142721	+	0.625303i	0.852075	+	0.523420i	$0.175344\pi$
$149$	−1.74214	+	7.63279i	−0.142721	+	0.625303i	−0.994796	+	0.101883i	$0.967513\pi$
$150$		0			0
$151$	−10.7992	+	13.5418i	−0.878830	+	1.10202i	0.115246	+	0.993337i	$0.463234\pi$
$151$	−10.7992	+	13.5418i	−0.878830	+	1.10202i	−0.994077	+	0.108682i	$0.965337\pi$
$152$		0			0
$153$	2.47219	−	1.19054i	0.199865	−	0.0962497i
$154$		0			0
$155$	−6.39493	+	28.0180i	−0.513653	+	2.25046i
$156$		0			0
$157$	−7.82371			−0.624400			−0.312200	−	0.950016i	$-0.601066\pi$
$157$	−7.82371			−0.624400			−0.312200	+	0.950016i	$0.601066\pi$
$158$		0			0
$159$	3.53199	−	4.42898i	0.280105	−	0.351241i
$160$		0			0
$161$	0.231250	+	0.111364i	0.0182251	+	0.00877673i
$162$		0			0
$163$	12.2371	+	5.89305i	0.958480	+	0.461580i	0.846651	−	0.532148i	$-0.178615\pi$
$163$	12.2371	+	5.89305i	0.958480	+	0.461580i	0.111829	+	0.993728i	$0.464329\pi$
$164$		0			0
$165$	9.99880	−	4.81517i	0.778406	−	0.374860i
$166$		0			0
$167$	−3.48307	−	15.2603i	−0.269528	−	1.18088i	−0.910563	−	0.413369i	$-0.864352\pi$
$167$	−3.48307	−	15.2603i	−0.269528	−	1.18088i	0.641035	−	0.767512i	$-0.278505\pi$
$168$		0			0
$169$	5.62080	+	7.04826i	0.432369	+	0.542174i
$170$		0			0
$171$	0.150104	+	0.657650i	0.0114788	+	0.0502918i
$172$		0			0
$173$	9.82371			0.746883			0.373441	−	0.927654i	$-0.378178\pi$
$173$	9.82371			0.746883			0.373441	+	0.927654i	$0.378178\pi$
$174$		0			0
$175$	−0.271143			−0.0204965
$176$		0			0
$177$	−4.43296	−	19.4221i	−0.333202	−	1.45985i
$178$		0			0
$179$	−10.8415	−	13.5948i	−0.810329	−	1.01612i	−0.999416	−	0.0341601i	$-0.989124\pi$
$179$	−10.8415	−	13.5948i	−0.810329	−	1.01612i	0.189087	−	0.981960i	$-0.439447\pi$
$180$		0			0
$181$	−5.08157	−	22.2638i	−0.377710	−	1.65486i	−0.704458	−	0.709746i	$-0.748810\pi$
$181$	−5.08157	−	22.2638i	−0.377710	−	1.65486i	0.326748	−	0.945112i	$-0.394047\pi$
$182$		0			0
$183$	3.73341	−	1.79791i	0.275981	−	0.132906i
$184$		0			0
$185$	32.2080	+	15.5106i	2.36798	+	1.14036i
$186$		0			0
$187$	9.33513	+	4.49556i	0.682652	+	0.328748i
$188$		0			0
$189$	−0.169883	+	0.213026i	−0.0123571	+	0.0154954i
$190$		0			0
$191$	−4.21983			−0.305336			−0.152668	−	0.988278i	$-0.548787\pi$
$191$	−4.21983			−0.305336			−0.152668	+	0.988278i	$0.548787\pi$
$192$		0			0
$193$	3.88351	−	17.0148i	0.279541	−	1.22475i	−0.618834	−	0.785522i	$-0.712395\pi$
$193$	3.88351	−	17.0148i	0.279541	−	1.22475i	0.898375	−	0.439228i	$-0.144748\pi$
$194$		0			0
$195$	21.3436	−	10.2785i	1.52845	−	0.736062i
$196$		0			0
$197$	3.12767	−	3.92197i	0.222837	−	0.279429i	−0.657828	−	0.753168i	$-0.728525\pi$
$197$	3.12767	−	3.92197i	0.222837	−	0.279429i	0.880665	+	0.473739i	$0.157096\pi$
$198$		0			0
$199$	−3.80313	+	16.6626i	−0.269597	+	1.18118i	0.640886	+	0.767636i	$0.278567\pi$
$199$	−3.80313	+	16.6626i	−0.269597	+	1.18118i	−0.910483	+	0.413546i	$0.864290\pi$
$200$		0			0
$201$	−0.0211063	−	0.0264664i	−0.00148872	−	0.00186680i
$202$		0			0
$203$	0.138260	+	0.224229i	0.00970394	+	0.0157378i
$204$		0			0
$205$	−2.24698	−	2.81762i	−0.156936	−	0.196791i
$206$		0			0
$207$	0.679644	−	2.97772i	0.0472386	−	0.206966i
$208$		0			0
$209$	−1.58815	+	1.99147i	−0.109854	+	0.137753i
$210$		0			0
$211$	18.9073	−	9.10528i	1.30163	−	0.626833i	0.350774	−	0.936460i	$-0.385918\pi$
$211$	18.9073	−	9.10528i	1.30163	−	0.626833i	0.950858	+	0.309627i	$0.100204\pi$
$212$		0			0
$213$	−1.27330	+	5.57869i	−0.0872450	+	0.382245i
$214$		0			0
$215$	17.7506			1.21058
$216$		0			0
$217$	0.269946	−	0.338502i	0.0183252	−	0.0229790i
$218$		0			0
$219$	−3.68598	−	1.77507i	−0.249075	−	0.119948i
$220$		0			0
$221$	19.9269	+	9.59630i	1.34043	+	0.645517i
$222$		0			0
$223$	−5.26659	+	2.53626i	−0.352677	+	0.169840i	−0.601831	−	0.798624i	$-0.705562\pi$
$223$	−5.26659	+	2.53626i	−0.352677	+	0.169840i	0.249154	+	0.968464i	$0.419848\pi$
$224$		0			0
$225$	0.717972	+	3.14564i	0.0478648	+	0.209709i
$226$		0			0
$227$	8.70440	+	10.9150i	0.577731	+	0.724452i	0.981724	−	0.190310i	$-0.0609494\pi$
$227$	8.70440	+	10.9150i	0.577731	+	0.724452i	−0.403993	+	0.914762i	$0.632378\pi$
$228$		0			0
$229$	0.900969	+	3.94740i	0.0595377	+	0.260852i	0.995933	−	0.0900949i	$-0.0287170\pi$
$229$	0.900969	+	3.94740i	0.0595377	+	0.260852i	−0.936395	+	0.350947i	$0.885860\pi$
$230$		0			0
$231$	−0.167194			−0.0110006
$232$		0			0
$233$	8.63533			0.565720			0.282860	−	0.959161i	$-0.408717\pi$
$233$	8.63533			0.565720			0.282860	+	0.959161i	$0.408717\pi$
$234$		0			0
$235$	−6.28017	−	27.5152i	−0.409673	−	1.79489i
$236$		0			0
$237$	6.87196	+	8.61717i	0.446382	+	0.559745i
$238$		0			0
$239$	−2.74214	−	12.0141i	−0.177374	−	0.777126i	−0.982836	−	0.184479i	$-0.940940\pi$
$239$	−2.74214	−	12.0141i	−0.177374	−	0.777126i	0.805462	−	0.592647i	$-0.201917\pi$
$240$		0			0
$241$	−19.5015	+	9.39142i	−1.25620	+	0.604955i	−0.939168	−	0.343459i	$-0.888401\pi$
$241$	−19.5015	+	9.39142i	−1.25620	+	0.604955i	−0.317034	+	0.948414i	$0.602687\pi$
$242$		0			0
$243$	5.36778	+	2.58499i	0.344343	+	0.165827i
$244$		0			0
$245$	−20.4710	−	9.85831i	−1.30784	−	0.629824i
$246$		0			0
$247$	−3.39008	+	4.25103i	−0.215706	+	0.270487i
$248$		0			0
$249$	25.5338			1.61814
$250$		0			0
$251$	1.78568	−	7.82356i	0.112711	−	0.493819i	−0.886788	−	0.462176i	$-0.847069\pi$
$251$	1.78568	−	7.82356i	0.112711	−	0.493819i	0.999499	−	0.0316428i	$-0.0100739\pi$
$252$		0			0
$253$	10.3910	−	5.00406i	0.653279	−	0.314603i
$254$		0			0
$255$	14.8388	−	18.6072i	0.929240	−	1.16523i
$256$		0			0
$257$	−3.04043	+	13.3210i	−0.189657	+	0.830939i	0.787141	+	0.616773i	$0.211561\pi$
$257$	−3.04043	+	13.3210i	−0.189657	+	0.830939i	−0.976797	+	0.214166i	$0.931297\pi$
$258$		0			0
$259$	−0.335790	−	0.421067i	−0.0208649	−	0.0261638i
$260$		0			0
$261$	2.23527	−	2.19776i	0.138360	−	0.136038i
$262$		0			0
$263$	−1.91454	−	2.40076i	−0.118056	−	0.148037i	0.719292	−	0.694708i	$-0.244466\pi$
$263$	−1.91454	−	2.40076i	−0.118056	−	0.148037i	−0.837348	+	0.546671i	$0.815895\pi$
$264$		0			0
$265$	−2.63222	+	11.5325i	−0.161696	+	0.708436i
$266$		0			0
$267$	3.19016	−	4.00034i	0.195235	−	0.244817i
$268$		0			0
$269$	−7.29374	+	3.51248i	−0.444707	+	0.214160i	−0.642816	−	0.766020i	$-0.722234\pi$
$269$	−7.29374	+	3.51248i	−0.444707	+	0.214160i	0.198109	+	0.980180i	$0.436520\pi$
$270$		0			0
$271$	−6.16733	+	27.0208i	−0.374638	+	1.64140i	0.338929	+	0.940812i	$0.389935\pi$
$271$	−6.16733	+	27.0208i	−0.374638	+	1.64140i	−0.713568	+	0.700586i	$0.752922\pi$
$272$		0			0
$273$	−0.356896			−0.0216003
$274$		0			0
$275$	−7.59634	+	9.52551i	−0.458077	+	0.574410i
$276$		0			0
$277$	−0.178448	−	0.0859360i	−0.0107219	−	0.00516339i	0.428515	−	0.903535i	$-0.359037\pi$
$277$	−0.178448	−	0.0859360i	−0.0107219	−	0.00516339i	−0.439237	+	0.898371i	$0.644751\pi$
$278$		0			0
$279$	−4.64191	−	2.23542i	−0.277904	−	0.133831i
$280$		0			0
$281$	−0.743095	+	0.357856i	−0.0443293	+	0.0213479i	−0.455917	−	0.890022i	$-0.650689\pi$
$281$	−0.743095	+	0.357856i	−0.0443293	+	0.0213479i	0.411588	+	0.911370i	$0.364974\pi$
$282$		0			0
$283$	−0.940198	−	4.11927i	−0.0558889	−	0.244865i	0.939265	−	0.343192i	$-0.111508\pi$
$283$	−0.940198	−	4.11927i	−0.0558889	−	0.244865i	−0.995154	+	0.0983266i	$0.968651\pi$
$284$		0			0
$285$	3.64795	+	4.57438i	0.216086	+	0.270963i
$286$		0			0
$287$	0.0120816	+	0.0529329i	0.000713153	+	0.00312453i
$288$		0			0
$289$	5.21983			0.307049
$290$		0			0
$291$	−13.2838			−0.778711
$292$		0			0
$293$	1.10441	+	4.83873i	0.0645202	+	0.282681i	0.996888	−	0.0788293i	$-0.0251182\pi$
$293$	1.10441	+	4.83873i	0.0645202	+	0.282681i	−0.932368	+	0.361511i	$0.882261\pi$
$294$		0			0
$295$	25.9366	+	32.5235i	1.51009	+	1.89359i
$296$		0			0
$297$	2.72438	+	11.9363i	0.158085	+	0.692614i
$298$		0			0
$299$	22.1809	−	10.6818i	1.28275	−	0.617742i
$300$		0			0
$301$	−0.240939	−	0.116030i	−0.0138875	−	0.00668786i
$302$		0			0
$303$	−14.7838	−	7.11951i	−0.849308	−	0.409005i
$304$		0			0
$305$	−5.39493	+	6.76503i	−0.308913	+	0.387364i
$306$		0			0
$307$	−16.2500			−0.927434			−0.463717	−	0.885983i	$-0.653485\pi$
$307$	−16.2500			−0.927434			−0.463717	+	0.885983i	$0.653485\pi$
$308$		0			0
$309$	6.32222	−	27.6994i	0.359658	−	1.57577i
$310$		0			0
$311$	−7.41335	+	3.57008i	−0.420372	+	0.202441i	−0.632098	−	0.774889i	$-0.717806\pi$
$311$	−7.41335	+	3.57008i	−0.420372	+	0.202441i	0.211726	+	0.977329i	$0.432092\pi$
$312$		0			0
$313$	8.88740	−	11.1444i	0.502345	−	0.629921i	−0.464411	−	0.885620i	$-0.653734\pi$
$313$	8.88740	−	11.1444i	0.502345	−	0.629921i	0.966757	+	0.255699i	$0.0823055\pi$
$314$		0			0
$315$	0.0205738	−	0.0901398i	0.00115920	−	0.00507880i
$316$		0			0
$317$	−5.99731	−	7.52039i	−0.336843	−	0.422387i	0.584345	−	0.811505i	$-0.301351\pi$
$317$	−5.99731	−	7.52039i	−0.336843	−	0.422387i	−0.921188	+	0.389118i	$0.872780\pi$
$318$		0			0
$319$	11.7509	+	1.42479i	0.657922	+	0.0797732i
$320$		0			0
$321$	6.58277	+	8.25453i	0.367414	+	0.460723i
$322$		0			0
$323$	−1.21552	+	5.32554i	−0.0676334	+	0.296321i
$324$		0			0
$325$	−16.2153	+	20.3333i	−0.899462	+	1.12789i
$326$		0			0
$327$	−26.2521	+	12.6424i	−1.45175	+	0.699124i
$328$		0			0
$329$	−0.0946138	+	0.414530i	−0.00521623	+	0.0228538i
$330$		0			0
$331$	−6.31767			−0.347250			−0.173625	−	0.984812i	$-0.555548\pi$
$331$	−6.31767			−0.347250			−0.173625	+	0.984812i	$0.555548\pi$
$332$		0			0
$333$	−3.99582	+	5.01060i	−0.218970	+	0.274579i
$334$		0			0
$335$	0.0636873	+	0.0306702i	0.00347961	+	0.00167569i
$336$		0			0
$337$	−5.26659	−	2.53626i	−0.286890	−	0.138159i	0.284904	−	0.958556i	$-0.408038\pi$
$337$	−5.26659	−	2.53626i	−0.286890	−	0.138159i	−0.571794	+	0.820397i	$0.693752\pi$
$338$		0			0
$339$	−3.80947	+	1.83454i	−0.206902	+	0.0996388i
$340$		0			0
$341$	−4.32908	−	18.9670i	−0.234433	−	1.02712i
$342$		0			0
$343$	0.426919	+	0.535340i	0.0230515	+	0.0289056i
$344$		0			0
$345$	−5.89493	−	25.8274i	−0.317372	−	1.39050i
$346$		0			0
$347$	25.8732			1.38895			0.694474	−	0.719518i	$-0.255637\pi$
$347$	25.8732			1.38895			0.694474	+	0.719518i	$0.255637\pi$
$348$		0			0
$349$	−19.9651			−1.06871			−0.534353	−	0.845261i	$-0.679445\pi$
$349$	−19.9651			−1.06871			−0.534353	+	0.845261i	$0.679445\pi$
$350$		0			0
$351$	5.81551	+	25.4794i	0.310409	+	1.35999i
$352$		0			0
$353$	−10.4574	−	13.1132i	−0.556592	−	0.697945i	0.421331	−	0.906907i	$-0.361563\pi$
$353$	−10.4574	−	13.1132i	−0.556592	−	0.697945i	−0.977924	+	0.208962i	$0.932991\pi$
$354$		0			0
$355$	−2.65883	−	11.6491i	−0.141116	−	0.618271i
$356$		0			0
$357$	−0.323044	+	0.155570i	−0.0170973	+	0.00823363i
$358$		0			0
$359$	16.3034	+	7.85132i	0.860462	+	0.414377i	0.811450	−	0.584421i	$-0.198679\pi$
$359$	16.3034	+	7.85132i	0.860462	+	0.414377i	0.0490118	+	0.998798i	$0.484393\pi$
$360$		0			0
$361$	15.9085	+	7.66113i	0.837290	+	0.403217i
$362$		0			0
$363$	5.98039	−	7.49917i	0.313889	−	0.393604i
$364$		0			0
$365$	8.54288			0.447155
$366$		0			0
$367$	−4.20224	+	18.4112i	−0.219355	+	0.961058i	0.738601	+	0.674143i	$0.235487\pi$
$367$	−4.20224	+	18.4112i	−0.219355	+	0.961058i	−0.957956	+	0.286915i	$0.907370\pi$
$368$		0			0
$369$	0.582105	−	0.280327i	0.0303032	−	0.0145932i
$370$		0			0
$371$	0.111113	−	0.139331i	0.00576868	−	0.00723370i
$372$		0			0
$373$	5.32424	−	23.3270i	0.275679	−	1.20783i	−0.627519	−	0.778602i	$-0.715929\pi$
$373$	5.32424	−	23.3270i	0.275679	−	1.20783i	0.903197	−	0.429226i	$-0.141214\pi$
$374$		0			0
$375$	1.70895	+	2.14295i	0.0882497	+	0.110662i
$376$		0			0
$377$	25.0836	+	3.04139i	1.29187	+	0.156640i
$378$		0			0
$379$	−3.56734	−	4.47330i	−0.183242	−	0.229778i	0.681723	−	0.731610i	$-0.261231\pi$
$379$	−3.56734	−	4.47330i	−0.183242	−	0.229778i	−0.864965	+	0.501832i	$0.832659\pi$
$380$		0			0
$381$	−3.10238	+	13.5924i	−0.158940	+	0.696361i
$382$		0			0
$383$	−1.48158	+	1.85785i	−0.0757053	+	0.0949315i	−0.818242	−	0.574874i	$-0.805051\pi$
$383$	−1.48158	+	1.85785i	−0.0757053	+	0.0949315i	0.742537	+	0.669805i	$0.233622\pi$
$384$		0			0
$385$	0.314552	−	0.151480i	0.0160310	−	0.00772014i
$386$		0			0
$387$	−0.708119	+	3.10247i	−0.0359957	+	0.157708i
$388$		0			0
$389$	−13.7560			−0.697457			−0.348729	−	0.937224i	$-0.613386\pi$
$389$	−13.7560			−0.697457			−0.348729	+	0.937224i	$0.613386\pi$
$390$		0			0
$391$	15.4209	−	19.3372i	0.779867	−	0.977923i
$392$		0			0
$393$	−20.0797	−	9.66988i	−1.01289	−	0.487781i
$394$		0			0
$395$	−20.7359	−	9.98586i	−1.04333	−	0.502443i
$396$		0			0
$397$	−0.354740	+	0.170834i	−0.0178039	+	0.00857390i	−0.442765	−	0.896638i	$-0.646002\pi$
$397$	−0.354740	+	0.170834i	−0.0178039	+	0.00857390i	0.424961	+	0.905212i	$0.360288\pi$
$398$		0			0
$399$	−0.0196143	−	0.0859360i	−0.000981945	−	0.00430218i
$400$		0			0
$401$	−0.496648	−	0.622776i	−0.0248014	−	0.0311000i	0.769276	−	0.638916i	$-0.220617\pi$
$401$	−0.496648	−	0.622776i	−0.0248014	−	0.0311000i	−0.794078	+	0.607816i	$0.792046\pi$
$402$		0			0
$403$	−9.24094	−	40.4872i	−0.460324	−	2.01681i
$404$		0			0
$405$	22.4523			1.11567
$406$		0			0
$407$	−24.2000			−1.19955
$408$		0			0
$409$	−2.22641	−	9.75452i	−0.110089	−	0.482330i	−0.999673	−	0.0255596i	$-0.991863\pi$
$409$	−2.22641	−	9.75452i	−0.110089	−	0.482330i	0.889585	−	0.456770i	$-0.150994\pi$
$410$		0			0
$411$	−8.86360	−	11.1146i	−0.437209	−	0.548243i
$412$		0			0
$413$	−0.139456	−	0.610998i	−0.00686219	−	0.0300652i
$414$		0			0
$415$	−48.0381	+	23.1339i	−2.35810	+	1.13560i
$416$		0			0
$417$	−10.8448	−	5.22259i	−0.531073	−	0.255751i
$418$		0			0
$419$	−12.4037	−	5.97329i	−0.605958	−	0.291814i	0.105636	−	0.994405i	$-0.466312\pi$
$419$	−12.4037	−	5.97329i	−0.605958	−	0.291814i	−0.711594	+	0.702591i	$0.752026\pi$
$420$		0			0
$421$	−23.9581	+	30.0425i	−1.16765	+	1.46418i	−0.309407	+	0.950930i	$0.600131\pi$
$421$	−23.9581	+	30.0425i	−1.16765	+	1.46418i	−0.858238	+	0.513252i	$0.828441\pi$
$422$		0			0
$423$	5.05967			0.246010
$424$		0			0
$425$	−5.81402	+	25.4729i	−0.282021	+	1.23562i
$426$		0			0
$427$	0.117449	−	0.0565605i	0.00568376	−	0.00273715i
$428$		0			0
$429$	−9.99880	+	12.5381i	−0.482747	+	0.605345i
$430$		0			0
$431$	−4.13049	+	18.0969i	−0.198959	+	0.871695i	0.772599	+	0.634894i	$0.218956\pi$
$431$	−4.13049	+	18.0969i	−0.198959	+	0.871695i	−0.971558	+	0.236801i	$0.923901\pi$
$432$		0			0
$433$	9.57942	+	12.0122i	0.460357	+	0.577270i	0.956781	−	0.290811i	$-0.0939250\pi$
$433$	9.57942	+	12.0122i	0.460357	+	0.577270i	−0.496423	+	0.868081i	$0.665354\pi$
$434$		0			0
$435$	9.19687	−	25.5866i	0.440956	−	1.22678i
$436$		0			0
$437$	3.79105	+	4.75383i	0.181351	+	0.227407i
$438$		0			0
$439$	−0.820593	+	3.59525i	−0.0391647	+	0.171592i	−0.990728	−	0.135862i	$-0.956620\pi$
$439$	−0.820593	+	3.59525i	−0.0391647	+	0.171592i	0.951563	+	0.307454i	$0.0994769\pi$
$440$		0			0
$441$	2.53969	−	3.18467i	0.120938	−	0.151651i
$442$		0			0
$443$	33.0323	−	15.9075i	1.56941	−	0.755789i	0.571513	−	0.820593i	$-0.306357\pi$
$443$	33.0323	−	15.9075i	1.56941	−	0.755789i	0.997898	+	0.0648041i	$0.0206423\pi$
$444$		0			0
$445$	−2.37747	+	10.4164i	−0.112703	+	0.493784i
$446$		0			0
$447$	−12.1739			−0.575806
$448$		0			0
$449$	19.2623	−	24.1542i	0.909046	−	1.13991i	−0.0806527	−	0.996742i	$-0.525700\pi$
$449$	19.2623	−	24.1542i	0.909046	−	1.13991i	0.989699	−	0.143165i	$-0.0457281\pi$
$450$		0			0
$451$	2.19806	+	1.05853i	0.103503	+	0.0498443i
$452$		0			0
$453$	−24.2657	−	11.6857i	−1.14010	−	0.549044i
$454$		0			0
$455$	0.671448	−	0.323352i	0.0314780	−	0.0151590i
$456$		0			0
$457$	5.77359	+	25.2958i	0.270077	+	1.18329i	0.909921	+	0.414781i	$0.136142\pi$
$457$	5.77359	+	25.2958i	0.270077	+	1.18329i	−0.639844	+	0.768505i	$0.721001\pi$
$458$		0			0
$459$	16.3703	+	20.5277i	0.764100	+	0.958152i
$460$		0			0
$461$	−6.03803	−	26.4543i	−0.281219	−	1.23210i	−0.896232	−	0.443585i	$-0.853706\pi$
$461$	−6.03803	−	26.4543i	−0.281219	−	1.23210i	0.615013	−	0.788517i	$-0.289151\pi$
$462$		0			0
$463$	9.32975			0.433590			0.216795	−	0.976217i	$-0.430440\pi$
$463$	9.32975			0.433590			0.216795	+	0.976217i	$0.430440\pi$
$464$		0			0
$465$	−44.6872			−2.07232
$466$		0			0
$467$	−5.92035	−	25.9387i	−0.273961	−	1.20030i	−0.905293	−	0.424788i	$-0.860348\pi$
$467$	−5.92035	−	25.9387i	−0.273961	−	1.20030i	0.631332	−	0.775513i	$-0.282509\pi$
$468$		0			0
$469$	−0.000663981	0	0.000832606i	−3.06598e−5	0	3.84462e-5i
$470$		0			0
$471$	−2.70709	−	11.8605i	−0.124736	−	0.546504i
$472$		0			0
$473$	−10.8264	+	5.21372i	−0.497798	+	0.239727i
$474$		0			0
$475$	−5.78717	−	2.78695i	−0.265533	−	0.127874i
$476$		0			0
$477$	−1.91066	−	0.920124i	−0.0874830	−	0.0421296i
$478$		0			0
$479$	−14.7412	+	18.4849i	−0.673544	+	0.844598i	−0.994742	−	0.102414i	$-0.967343\pi$
$479$	−14.7412	+	18.4849i	−0.673544	+	0.844598i	0.321198	+	0.947012i	$0.395915\pi$
$480$		0			0
$481$	−51.6577			−2.35539
$482$		0			0
$483$	−0.0888100	+	0.389102i	−0.00404099	+	0.0177048i
$484$		0			0
$485$	24.9916	−	12.0353i	1.13481	−	0.546495i
$486$		0			0
$487$	9.06667	−	11.3692i	0.410850	−	0.515190i	−0.532752	−	0.846271i	$-0.678842\pi$
$487$	9.06667	−	11.3692i	0.410850	−	0.515190i	0.943602	+	0.331082i	$0.107414\pi$
$488$		0			0
$489$	−4.69955	+	20.5901i	−0.212521	+	0.931116i
$490$		0			0
$491$	−22.2268	−	27.8716i	−1.00308	−	1.25783i	−0.966008	−	0.258514i	$-0.916767\pi$
$491$	−22.2268	−	27.8716i	−1.00308	−	1.25783i	−0.0370753	−	0.999312i	$-0.511804\pi$
$492$		0			0
$493$	24.0301	−	8.18095i	1.08226	−	0.368451i
$494$		0			0
$495$	−2.59030	−	3.24814i	−0.116425	−	0.145993i
$496$		0			0
$497$	−0.0400566	+	0.175500i	−0.00179679	+	0.00787223i
$498$		0			0
$499$	−4.59448	+	5.76130i	−0.205677	+	0.257911i	−0.873962	−	0.485995i	$-0.838457\pi$
$499$	−4.59448	+	5.76130i	−0.205677	+	0.257911i	0.668285	+	0.743906i	$0.267029\pi$
$500$		0			0
$501$	21.9291	−	10.5605i	0.979719	−	0.471808i
$502$		0			0
$503$	7.63760	−	33.4625i	0.340544	−	1.49202i	−0.457386	−	0.889268i	$-0.651214\pi$
$503$	7.63760	−	33.4625i	0.340544	−	1.49202i	0.797930	−	0.602751i	$-0.205929\pi$
$504$		0			0
$505$	34.2640			1.52473
$506$		0			0
$507$	−8.74011	+	10.9598i	−0.388162	+	0.486740i
$508$		0			0
$509$	−6.34697	−	3.05654i	−0.281325	−	0.135479i	0.287901	−	0.957660i	$-0.407043\pi$
$509$	−6.34697	−	3.05654i	−0.281325	−	0.135479i	−0.569226	+	0.822181i	$0.692757\pi$
$510$		0			0
$511$	−0.115957	−	0.0558420i	−0.00512964	−	0.00247030i
$512$		0			0
$513$	−5.81551	+	2.80060i	−0.256761	+	0.123650i
$514$		0			0
$515$	13.2017	+	57.8405i	0.581737	+	2.54876i
$516$		0			0
$517$	11.9121	+	14.9374i	0.523896	+	0.656944i
$518$		0			0
$519$	3.39911	+	14.8925i	0.149204	+	0.653707i
$520$		0			0
$521$	−27.1594			−1.18988			−0.594938	−	0.803772i	$-0.702823\pi$
$521$	−27.1594			−1.18988			−0.594938	+	0.803772i	$0.702823\pi$
$522$		0			0
$523$	3.82371			0.167199			0.0835995	−	0.996499i	$-0.473358\pi$
$523$	3.82371			0.167199			0.0835995	+	0.996499i	$0.473358\pi$
$524$		0			0
$525$	−0.0938183	−	0.411045i	−0.00409457	−	0.0179395i
$526$		0			0
$527$	−26.0127	−	32.6189i	−1.13313	−	1.42090i
$528$		0			0
$529$	−1.00820	−	4.41720i	−0.0438346	−	0.192052i
$530$		0			0
$531$	−6.71917	+	3.23578i	−0.291587	+	0.140421i
$532$		0			0
$533$	4.69202	+	2.25956i	0.203234	+	0.0978723i
$534$		0			0
$535$	−19.8632	−	9.56563i	−0.858762	−	0.413558i
$536$		0			0
$537$	16.8580	−	21.1393i	0.727477	−	0.912228i
$538$		0			0
$539$	15.3812			0.662514
$540$		0			0
$541$	−6.73437	+	29.5052i	−0.289533	+	1.26853i	0.595635	+	0.803255i	$0.296901\pi$
$541$	−6.73437	+	29.5052i	−0.289533	+	1.26853i	−0.885168	+	0.465272i	$0.845957\pi$
$542$		0			0
$543$	31.9931	−	15.4070i	1.37295	−	0.661180i
$544$		0			0
$545$	37.9354	−	47.5695i	1.62497	−	2.03765i
$546$		0			0
$547$	−0.602679	+	2.64051i	−0.0257687	+	0.112900i	−0.986177	−	0.165698i	$-0.947012\pi$
$547$	−0.602679	+	2.64051i	−0.0257687	+	0.112900i	0.960408	+	0.278598i	$0.0898696\pi$
$548$		0			0
$549$	−0.967181	−	1.21281i	−0.0412783	−	0.0517613i
$550$		0			0
$551$	0.646220	+	6.20696i	0.0275299	+	0.264425i
$552$		0			0
$553$	0.216185	+	0.271087i	0.00919311	+	0.0115278i
$554$		0			0
$555$	−12.3693	+	54.1933i	−0.525046	+	2.30038i
$556$		0			0
$557$	−3.20373	+	4.01736i	−0.135747	+	0.170221i	−0.845058	−	0.534674i	$-0.820434\pi$
$557$	−3.20373	+	4.01736i	−0.135747	+	0.170221i	0.709312	+	0.704895i	$0.249006\pi$
$558$		0			0
$559$	−23.1102	+	11.1293i	−0.977458	+	0.470719i
$560$		0			0
$561$	−3.58509	+	15.7073i	−0.151363	+	0.663163i
$562$		0			0
$563$	4.13062			0.174085			0.0870425	−	0.996205i	$-0.472258\pi$
$563$	4.13062			0.174085			0.0870425	+	0.996205i	$0.472258\pi$
$564$		0			0
$565$	5.50484	−	6.90286i	0.231591	−	0.290405i
$566$		0			0
$567$	−0.304758	−	0.146764i	−0.0127986	−	0.00616349i
$568$		0			0
$569$	−23.5722	−	11.3518i	−0.988197	−	0.475891i	−0.131280	−	0.991345i	$-0.541909\pi$
$569$	−23.5722	−	11.3518i	−0.988197	−	0.475891i	−0.856917	+	0.515455i	$0.827623\pi$
$570$		0			0
$571$	13.6899	−	6.59269i	0.572903	−	0.275896i	−0.124919	−	0.992167i	$-0.539867\pi$
$571$	13.6899	−	6.59269i	0.572903	−	0.275896i	0.697822	+	0.716271i	$0.254153\pi$
$572$		0			0
$573$	−1.46011	−	6.39715i	−0.0609969	−	0.267245i
$574$		0			0
$575$	18.1332	+	22.7383i	0.756206	+	0.948252i
$576$		0			0
$577$	0.597302	+	2.61695i	0.0248660	+	0.108945i	0.985838	−	0.167701i	$-0.0536342\pi$
$577$	0.597302	+	2.61695i	0.0248660	+	0.108945i	−0.960972	+	0.276646i	$0.910777\pi$
$578$		0			0
$579$	27.1377			1.12780
$580$		0			0
$581$	0.803266			0.0333251
$582$		0			0
$583$	−1.78190	−	7.80700i	−0.0737986	−	0.323333i
$584$		0			0
$585$	−5.52930	−	6.93353i	−0.228609	−	0.286666i
$586$		0			0
$587$	9.34840	+	40.9580i	0.385850	+	1.69052i	0.678745	+	0.734374i	$0.262524\pi$
$587$	9.34840	+	40.9580i	0.385850	+	1.69052i	−0.292895	+	0.956145i	$0.594619\pi$
$588$		0			0
$589$	9.24094	−	4.45020i	0.380766	−	0.183367i
$590$		0			0
$591$	7.02781	+	3.38442i	0.289086	+	0.139216i
$592$		0			0
$593$	−20.3034	−	9.77762i	−0.833762	−	0.401519i	−0.0322372	−	0.999480i	$-0.510263\pi$
$593$	−20.3034	−	9.77762i	−0.833762	−	0.401519i	−0.801525	+	0.597962i	$0.795977\pi$
$594$		0			0
$595$	0.466812	−	0.585364i	0.0191374	−	0.0239976i
$596$		0			0
$597$	−26.5760			−1.08768
$598$		0			0
$599$	2.11649	−	9.27295i	0.0864774	−	0.378882i	−0.913107	−	0.407721i	$-0.866324\pi$
$599$	2.11649	−	9.27295i	0.0864774	−	0.378882i	0.999584	+	0.0288384i	$0.00918083\pi$
$600$		0			0
$601$	37.5306	−	18.0738i	1.53090	−	0.737244i	0.536601	−	0.843836i	$-0.319708\pi$
$601$	37.5306	−	18.0738i	1.53090	−	0.737244i	0.994303	+	0.106592i	$0.0339939\pi$
$602$		0			0
$603$	−0.00790123	+	0.00990783i	−0.000321763	+	0.000403478i
$604$		0			0
$605$	−4.45689	+	19.5269i	−0.181198	+	0.793881i
$606$		0			0
$607$	−4.40180	−	5.51968i	−0.178663	−	0.224037i	0.684433	−	0.729075i	$-0.260050\pi$
$607$	−4.40180	−	5.51968i	−0.178663	−	0.224037i	−0.863097	+	0.505039i	$0.831478\pi$
$608$		0			0
$609$	−0.292085	+	0.287184i	−0.0118359	+	0.0116373i
$610$		0			0
$611$	25.4279	+	31.8856i	1.02870	+	1.28995i
$612$		0			0
$613$	8.28070	−	36.2801i	0.334454	−	1.46534i	−0.475952	−	0.879471i	$-0.657896\pi$
$613$	8.28070	−	36.2801i	0.334454	−	1.46534i	0.810406	−	0.585869i	$-0.199247\pi$
$614$		0			0
$615$	3.49396	−	4.38129i	0.140890	−	0.176671i
$616$		0			0
$617$	9.94653	−	4.79000i	0.400432	−	0.192838i	−0.222819	−	0.974860i	$-0.571526\pi$
$617$	9.94653	−	4.79000i	0.400432	−	0.192838i	0.623251	+	0.782022i	$0.285811\pi$
$618$		0			0
$619$	9.19149	−	40.2705i	0.369437	−	1.61861i	−0.358890	−	0.933380i	$-0.616845\pi$
$619$	9.19149	−	40.2705i	0.369437	−	1.61861i	0.728327	−	0.685230i	$-0.240298\pi$
$620$		0			0
$621$	29.2258			1.17279
$622$		0			0
$623$	0.100359	−	0.125846i	0.00402080	−	0.00504193i
$624$		0			0
$625$	19.8131	+	9.54149i	0.792525	+	0.381660i
$626$		0			0
$627$	−3.56853	−	1.71851i	−0.142513	−	0.0686308i
$628$		0			0
$629$	−46.7579	+	22.5174i	−1.86436	+	0.897829i
$630$		0			0
$631$	2.47530	+	10.8450i	0.0985403	+	0.431733i	0.999999	−	0.00113108i	$-0.000360035\pi$
$631$	2.47530	+	10.8450i	0.0985403	+	0.431733i	−0.901459	+	0.432864i	$0.857503\pi$
$632$		0			0
$633$	20.3455	+	25.5124i	0.808660	+	1.01403i
$634$		0			0
$635$	−6.47823	−	28.3830i	−0.257081	−	1.12634i
$636$		0			0
$637$	32.8329			1.30089
$638$		0			0
$639$	2.14211			0.0847406
$640$		0			0
$641$	3.01865	+	13.2256i	0.119230	+	0.522379i	0.998904	+	0.0468031i	$0.0149033\pi$
$641$	3.01865	+	13.2256i	0.119230	+	0.522379i	−0.879674	+	0.475576i	$0.842240\pi$
$642$		0			0
$643$	−7.34750	−	9.21348i	−0.289757	−	0.363344i	0.615553	−	0.788096i	$-0.288933\pi$
$643$	−7.34750	−	9.21348i	−0.289757	−	0.363344i	−0.905310	+	0.424752i	$0.860361\pi$
$644$		0			0
$645$	6.14191	+	26.9095i	0.241837	+	1.05956i
$646$		0			0
$647$	−21.4448	+	10.3273i	−0.843082	+	0.406007i	−0.805005	−	0.593268i	$-0.797838\pi$
$647$	−21.4448	+	10.3273i	−0.843082	+	0.406007i	−0.0380771	+	0.999275i	$0.512123\pi$
$648$		0			0
$649$	−25.3720	−	12.2185i	−0.995937	−	0.479618i
$650$		0			0
$651$	0.606564	+	0.292106i	0.0237731	+	0.0114485i
$652$		0			0
$653$	9.62833	−	12.0735i	0.376786	−	0.472474i	−0.556894	−	0.830584i	$-0.688007\pi$
$653$	9.62833	−	12.0735i	0.376786	−	0.472474i	0.933680	+	0.358109i	$0.116578\pi$
$654$		0			0
$655$	46.5381			1.81839
$656$		0			0
$657$	−0.340798	+	1.49313i	−0.0132958	+	0.0582527i
$658$		0			0
$659$	−29.9485	+	14.4224i	−1.16663	+	0.561818i	−0.913987	−	0.405743i	$-0.867013\pi$
$659$	−29.9485	+	14.4224i	−1.16663	+	0.561818i	−0.252639	+	0.967561i	$0.581298\pi$
$660$		0			0
$661$	−3.32036	+	4.16359i	−0.129147	+	0.161945i	−0.842201	−	0.539164i	$-0.818740\pi$
$661$	−3.32036	+	4.16359i	−0.129147	+	0.161945i	0.713054	+	0.701109i	$0.247312\pi$
$662$		0			0
$663$	−7.65279	+	33.5291i	−0.297210	+	1.30216i
$664$		0			0
$665$	0.114761	+	0.143905i	0.00445023	+	0.00558041i
$666$		0			0
$667$	9.55765	−	26.5903i	0.370074	−	1.02958i
$668$		0			0
$669$	−5.66719	−	7.10644i	−0.219106	−	0.274751i
$670$		0			0
$671$	1.30343	−	5.71070i	0.0503183	−	0.220459i
$672$		0			0
$673$	−17.6923	+	22.1855i	−0.681989	+	0.855187i	−0.995536	−	0.0943859i	$-0.969911\pi$
$673$	−17.6923	+	22.1855i	−0.681989	+	0.855187i	0.313547	+	0.949573i	$0.398483\pi$
$674$		0			0
$675$	−27.8165	+	13.3957i	−1.07066	+	0.515601i
$676$		0			0
$677$	−8.78674	+	38.4972i	−0.337702	+	1.47957i	0.466132	+	0.884715i	$0.345647\pi$
$677$	−8.78674	+	38.4972i	−0.337702	+	1.47957i	−0.803834	+	0.594854i	$0.797210\pi$
$678$		0			0
$679$	−0.417895			−0.0160373
$680$		0			0
$681$	−13.5350	+	16.9723i	−0.518661	+	0.650381i
$682$		0			0
$683$	−5.71595	−	2.75266i	−0.218715	−	0.105327i	0.321318	−	0.946971i	$-0.395874\pi$
$683$	−5.71595	−	2.75266i	−0.218715	−	0.105327i	−0.540033	+	0.841644i	$0.681588\pi$
$684$		0			0
$685$	26.7455	+	12.8800i	1.02189	+	0.492119i
$686$		0			0
$687$	−5.67241	+	2.73169i	−0.216416	+	0.104220i
$688$		0			0
$689$	−3.80367	−	16.6650i	−0.144908	−	0.634884i
$690$		0			0
$691$	13.5824	+	17.0318i	0.516699	+	0.647920i	0.969904	−	0.243486i	$-0.0782911\pi$
$691$	13.5824	+	17.0318i	0.516699	+	0.647920i	−0.453205	+	0.891406i	$0.649720\pi$
$692$		0			0
$693$	0.0139276	+	0.0610206i	0.000529064	+	0.00231798i
$694$		0			0
$695$	25.1347			0.953412
$696$		0			0
$697$	5.23191			0.198173
$698$		0			0
$699$	2.98792	+	13.0909i	0.113013	+	0.495144i
$700$		0			0
$701$	20.9393	+	26.2570i	0.790866	+	0.991715i	0.999905	+	0.0138076i	$0.00439522\pi$
$701$	20.9393	+	26.2570i	0.790866	+	0.991715i	−0.209038	+	0.977907i	$0.567033\pi$
$702$		0			0
$703$	−2.83901	−	12.4385i	−0.107075	−	0.469128i
$704$		0			0
$705$	39.5393	−	19.0411i	1.48914	−	0.717130i
$706$		0			0
$707$	−0.465083	−	0.223972i	−0.0174913	−	0.00842334i
$708$		0			0
$709$	−10.8192	−	5.21023i	−0.406322	−	0.195674i	0.219548	−	0.975602i	$-0.429542\pi$
$709$	−10.8192	−	5.21023i	−0.406322	−	0.195674i	−0.625870	+	0.779927i	$0.715256\pi$
$710$		0			0
$711$	2.57255	−	3.22587i	0.0964781	−	0.120980i
$712$		0			0
$713$	−46.4403			−1.73920
$714$		0			0
$715$	7.45162	−	32.6477i	0.278675	−	1.22095i
$716$		0			0
$717$	17.2642	−	8.31400i	0.644743	−	0.310492i
$718$		0			0
$719$	3.45071	−	4.32706i	0.128690	−	0.161372i	−0.713312	−	0.700847i	$-0.752806\pi$
$719$	3.45071	−	4.32706i	0.128690	−	0.161372i	0.842002	+	0.539475i	$0.181377\pi$
$720$		0			0
$721$	0.198890	−	0.871395i	0.00740706	−	0.0324524i
$722$		0			0
$723$	−20.9849	−	26.3142i	−0.780435	−	0.978635i
$724$		0			0
$725$	3.09097	+	29.6888i	0.114796	+	1.10262i
$726$		0			0
$727$	−4.32036	−	5.41755i	−0.160233	−	0.200926i	0.695233	−	0.718784i	$-0.255301\pi$
$727$	−4.32036	−	5.41755i	−0.160233	−	0.200926i	−0.855467	+	0.517858i	$0.826730\pi$
$728$		0			0
$729$	−6.67755	+	29.2562i	−0.247317	+	1.08356i
$730$		0			0
$731$	−16.0670	+	20.1473i	−0.594258	+	0.745176i
$732$		0			0
$733$	21.2937	−	10.2545i	0.786502	−	0.378760i	0.00287900	−	0.999996i	$-0.499084\pi$
$733$	21.2937	−	10.2545i	0.786502	−	0.378760i	0.783623	+	0.621236i	$0.213369\pi$
$734$		0			0
$735$	7.86174	−	34.4445i	0.289985	−	1.27051i
$736$		0			0
$737$	−0.0478524			−0.00176267
$738$		0			0
$739$	24.6598	−	30.9224i	0.907125	−	1.13750i	−0.0828929	−	0.996558i	$-0.526416\pi$
$739$	24.6598	−	30.9224i	0.907125	−	1.13750i	0.990018	−	0.140941i	$-0.0450126\pi$
$740$		0			0
$741$	−7.61745	−	3.66837i	−0.279834	−	0.134761i
$742$		0			0
$743$	8.94116	+	4.30583i	0.328019	+	0.157966i	0.590644	−	0.806932i	$-0.298874\pi$
$743$	8.94116	+	4.30583i	0.328019	+	0.157966i	−0.262625	+	0.964898i	$0.584588\pi$
$744$		0			0
$745$	22.9034	−	11.0297i	0.839116	−	0.404097i
$746$		0			0
$747$	−2.12701	−	9.31902i	−0.0778231	−	0.340965i
$748$		0			0
$749$	0.207087	+	0.259679i	0.00756679	+	0.00948846i
$750$		0			0
$751$	6.31754	+	27.6789i	0.230530	+	1.01002i	0.949202	+	0.314669i	$0.101893\pi$
$751$	6.31754	+	27.6789i	0.230530	+	1.01002i	−0.718671	+	0.695350i	$0.755249\pi$
$752$		0			0
$753$	12.4782			0.454729
$754$		0			0
$755$	56.2398			2.04678
$756$		0			0
$757$	−6.32855	−	27.7272i	−0.230015	−	1.00776i	−0.949626	−	0.313385i	$-0.898537\pi$
$757$	−6.32855	−	27.7272i	−0.230015	−	1.00776i	0.719611	−	0.694377i	$-0.244320\pi$
$758$		0			0
$759$	11.1814	+	14.0211i	0.405860	+	0.508933i
$760$		0			0
$761$	5.83890	+	25.5819i	0.211660	+	0.927344i	0.963439	+	0.267928i	$0.0863390\pi$
$761$	5.83890	+	25.5819i	0.211660	+	0.927344i	−0.751779	+	0.659415i	$0.770804\pi$
$762$		0			0
$763$	−0.825864	+	0.397715i	−0.0298983	+	0.0143983i
$764$		0			0
$765$	−8.02715	−	3.86567i	−0.290222	−	0.139764i
$766$		0			0
$767$	−54.1594	−	26.0818i	−1.95558	−	0.941759i
$768$		0			0
$769$	8.45071	−	10.5969i	0.304741	−	0.382133i	−0.605755	−	0.795651i	$-0.707129\pi$
$769$	8.45071	−	10.5969i	0.304741	−	0.382133i	0.910496	+	0.413519i	$0.135700\pi$
$770$		0			0
$771$	−21.2462			−0.765165
$772$		0			0
$773$	9.49037	−	41.5800i	0.341345	−	1.49553i	−0.454893	−	0.890546i	$-0.650323\pi$
$773$	9.49037	−	41.5800i	0.341345	−	1.49553i	0.796238	−	0.604984i	$-0.206820\pi$
$774$		0			0
$775$	44.2008	−	21.2860i	1.58774	−	0.764615i
$776$		0			0
$777$	0.522139	−	0.654741i	0.0187316	−	0.0234887i
$778$		0			0
$779$	−0.286208	+	1.25396i	−0.0102545	+	0.0449278i
$780$		0			0
$781$	5.04325	+	6.32403i	0.180461	+	0.226292i
$782$		0			0
$783$	25.2620	+	16.1729i	0.902789	+	0.577972i
$784$		0			0
$785$	15.8388	+	19.8612i	0.565310	+	0.708876i
$786$		0			0
$787$	−0.527680	+	2.31192i	−0.0188097	+	0.0824109i	−0.983462	−	0.181117i	$-0.942029\pi$
$787$	−0.527680	+	2.31192i	−0.0188097	+	0.0824109i	0.964652	+	0.263528i	$0.0848860\pi$
$788$		0			0
$789$	2.97703	−	3.73308i	0.105985	−	0.132901i
$790$		0			0
$791$	−0.119842	+	0.0577128i	−0.00426109	+	0.00205203i
$792$		0			0
$793$	2.78232	−	12.1902i	0.0988032	−	0.432885i
$794$		0			0
$795$	−18.3937			−0.652358
$796$		0			0
$797$	20.4822	−	25.6838i	0.725516	−	0.909768i	−0.273120	−	0.961980i	$-0.588056\pi$
$797$	20.4822	−	25.6838i	0.725516	−	0.909768i	0.998636	+	0.0522119i	$0.0166271\pi$
$798$		0			0
$799$	36.9148	+	17.7772i	1.30595	+	0.628914i
$800$		0			0
$801$	−1.72574	−	0.831073i	−0.0609761	−	0.0293645i
$802$		0			0
$803$	−5.21044	+	2.50922i	−0.183872	+	0.0885483i
$804$		0			0
$805$	−0.185448	−	0.812502i	−0.00653619	−	0.0286369i
$806$		0			0
$807$	−7.84854	−	9.84175i	−0.276282	−	0.346446i
$808$		0			0
$809$	2.36108	+	10.3446i	0.0830110	+	0.363695i	0.999324	−	0.0367683i	$-0.0117063\pi$
$809$	2.36108	+	10.3446i	0.0830110	+	0.363695i	−0.916313	+	0.400463i	$0.868849\pi$
$810$		0			0
$811$	47.7211			1.67571			0.837857	−	0.545890i	$-0.183808\pi$
$811$	47.7211			1.67571			0.837857	+	0.545890i	$0.183808\pi$
$812$		0			0
$813$	−43.0968			−1.51147
$814$		0			0
$815$	−9.81336	−	42.9951i	−0.343747	−	1.50605i
$816$		0			0
$817$	−3.94989	−	4.95300i	−0.138189	−	0.173284i
$818$		0			0
$819$	0.0297300	+	0.130256i	0.00103885	+	0.00455150i
$820$		0			0
$821$	−13.8705	+	6.67967i	−0.484083	+	0.233122i	−0.659975	−	0.751287i	$-0.729433\pi$
$821$	−13.8705	+	6.67967i	−0.484083	+	0.233122i	0.175892	+	0.984409i	$0.443719\pi$
$822$		0			0
$823$	25.1073	+	12.0910i	0.875185	+	0.421467i	0.816864	−	0.576831i	$-0.195711\pi$
$823$	25.1073	+	12.0910i	0.875185	+	0.421467i	0.0583215	+	0.998298i	$0.481425\pi$
$824$		0			0
$825$	−17.0688	−	8.21991i	−0.594260	−	0.286181i
$826$		0			0
$827$	−11.8699	+	14.8844i	−0.412758	+	0.517582i	−0.944138	−	0.329552i	$-0.893102\pi$
$827$	−11.8699	+	14.8844i	−0.412758	+	0.517582i	0.531379	+	0.847134i	$0.321674\pi$
$828$		0			0
$829$	−18.1280			−0.629610			−0.314805	−	0.949156i	$-0.601939\pi$
$829$	−18.1280			−0.629610			−0.314805	+	0.949156i	$0.601939\pi$
$830$		0			0
$831$	0.0685317	−	0.300257i	0.00237734	−	0.0104158i
$832$		0			0
$833$	29.7187	−	14.3118i	1.02969	−	0.495873i
$834$		0			0
$835$	−31.6884	+	39.7360i	−1.09662	+	1.37512i
$836$		0			0
$837$	10.9702	−	48.0634i	0.379184	−	1.66132i
$838$		0			0
$839$	−8.88202	−	11.1377i	−0.306641	−	0.384516i	0.604503	−	0.796603i	$-0.293372\pi$
$839$	−8.88202	−	11.1377i	−0.306641	−	0.384516i	−0.911145	+	0.412086i	$0.864800\pi$
$840$		0			0
$841$	22.9758	−	17.6949i	0.792270	−	0.610170i
$842$		0			0
$843$	−0.799618	−	1.00269i	−0.0275403	−	0.0345344i
$844$		0			0
$845$	6.51357	−	28.5378i	0.224074	−	0.981731i
$846$		0			0
$847$	0.188137	−	0.235916i	0.00646445	−	0.00810616i
$848$		0			0
$849$	5.91939	−	2.85063i	0.203153	−	0.0978332i
$850$		0			0
$851$	−12.8545	+	56.3193i	−0.440647	+	1.93060i
$852$		0			0
$853$	9.70650			0.332344			0.166172	−	0.986097i	$-0.446859\pi$
$853$	9.70650			0.332344			0.166172	+	0.986097i	$0.446859\pi$
$854$		0			0
$855$	1.36563	−	1.71244i	0.0467034	−	0.0585642i
$856$		0			0
$857$	−39.7601	−	19.1474i	−1.35818	−	0.654064i	−0.393949	−	0.919132i	$-0.628891\pi$
$857$	−39.7601	−	19.1474i	−1.35818	−	0.654064i	−0.964230	+	0.265068i	$0.914606\pi$
$858$		0			0
$859$	−7.35666	−	3.54278i	−0.251006	−	0.120878i	0.304151	−	0.952624i	$-0.401627\pi$
$859$	−7.35666	−	3.54278i	−0.251006	−	0.120878i	−0.555157	+	0.831746i	$0.687342\pi$
$860$		0			0
$861$	−0.0760644	+	0.0366307i	−0.00259227	+	0.00124837i
$862$		0			0
$863$	−3.88159	−	17.0064i	−0.132131	−	0.578903i	−0.997034	−	0.0769642i	$-0.975477\pi$
$863$	−3.88159	−	17.0064i	−0.132131	−	0.578903i	0.864903	−	0.501939i	$-0.167380\pi$
$864$		0			0
$865$	−19.8877	−	24.9384i	−0.676202	−	0.847930i
$866$		0			0
$867$	1.80612	+	7.91312i	0.0613390	+	0.268744i
$868$		0			0
$869$	15.5802			0.528522
$870$		0			0
$871$	−0.102147			−0.00346110
$872$		0			0
$873$	1.10656	+	4.84817i	0.0374515	+	0.164086i
$874$		0			0
$875$	0.0537617	+	0.0674150i	0.00181748	+	0.00227904i
$876$		0			0
$877$	7.91736	+	34.6882i	0.267350	+	1.17134i	0.913083	+	0.407774i	$0.133695\pi$
$877$	7.91736	+	34.6882i	0.267350	+	1.17134i	−0.645732	+	0.763564i	$0.723448\pi$
$878$		0			0
$879$	−6.95324	+	3.34850i	−0.234527	+	0.112942i
$880$		0			0
$881$	39.1030	+	18.8310i	1.31741	+	0.634433i	0.954728	−	0.297479i	$-0.0961460\pi$
$881$	39.1030	+	18.8310i	1.31741	+	0.634433i	0.362684	+	0.931912i	$0.381860\pi$
$882$		0			0
$883$	−12.1664	−	5.85901i	−0.409431	−	0.197171i	0.217820	−	0.975989i	$-0.430106\pi$
$883$	−12.1664	−	5.85901i	−0.409431	−	0.197171i	−0.627251	+	0.778818i	$0.715820\pi$
$884$		0			0
$885$	−40.3303	+	50.5726i	−1.35569	+	1.69998i
$886$		0			0
$887$	−11.5168			−0.386696			−0.193348	−	0.981130i	$-0.561935\pi$
$887$	−11.5168			−0.386696			−0.193348	+	0.981130i	$0.561935\pi$
$888$		0			0
$889$	−0.0975977	+	0.427603i	−0.00327332	+	0.0143414i
$890$		0			0
$891$	−13.6940	+	6.59470i	−0.458768	+	0.220931i
$892$		0			0
$893$	−6.28017	+	7.87508i	−0.210158	+	0.263530i
$894$		0			0
$895$	−12.5635	+	55.0441i	−0.419950	+	1.83992i
$896$		0			0
$897$	23.8681	+	29.9296i	0.796932	+	0.999321i
$898$		0			0
$899$	−40.1417	−	25.6990i	−1.33880	−	0.857109i
$900$		0			0
$901$	−10.7071	−	13.4263i	−0.356705	−	0.447294i
$902$		0			0
$903$	0.0925309	−	0.405404i	0.00307923	−	0.0134910i
$904$		0			0
$905$	−46.2313	+	57.9722i	−1.53678	+	1.92706i
$906$		0			0
$907$	−34.5577	+	16.6421i	−1.14747	+	0.552592i	−0.908273	−	0.418379i	$-0.862598\pi$
$907$	−34.5577	+	16.6421i	−1.14747	+	0.552592i	−0.239197	+	0.970971i	$0.576884\pi$
$908$		0			0
$909$	−1.36688	+	5.98869i	−0.0453365	+	0.198632i
$910$		0			0
$911$	23.4517			0.776991			0.388496	−	0.921451i	$-0.372995\pi$
$911$	23.4517			0.776991			0.388496	+	0.921451i	$0.372995\pi$
$912$		0			0
$913$	22.5043	−	28.2195i	0.744784	−	0.933930i
$914$		0			0
$915$	−12.1223	−	5.83779i	−0.400751	−	0.192991i
$916$		0			0
$917$	−0.631687	−	0.304204i	−0.0208601	−	0.0100457i
$918$		0			0
$919$	18.6289	−	8.97119i	0.614510	−	0.295932i	−0.100619	−	0.994925i	$-0.532082\pi$
$919$	18.6289	−	8.97119i	0.614510	−	0.295932i	0.715129	+	0.698993i	$0.246368\pi$
$920$		0			0
$921$	−5.62266	−	24.6345i	−0.185273	−	0.811734i
$922$		0			0
$923$	10.7654	+	13.4994i	0.354347	+	0.444338i
$924$		0			0
$925$	−13.5794	−	59.4953i	−0.446488	−	1.95619i
$926$		0			0
$927$	−10.6361			−0.349334
$928$		0			0
$929$	44.7138			1.46701			0.733506	−	0.679683i	$-0.237883\pi$
$929$	44.7138			1.46701			0.733506	+	0.679683i	$0.237883\pi$
$930$		0			0
$931$	1.80444	+	7.90575i	0.0591380	+	0.259101i
$932$		0			0
$933$	−7.97724	−	10.0031i	−0.261163	−	0.327488i
$934$		0			0
$935$	−7.48619	−	32.7991i	−0.244825	−	1.07265i
$936$		0			0
$937$	−35.6676	+	17.1766i	−1.16521	+	0.561136i	−0.913569	−	0.406685i	$-0.866685\pi$
$937$	−35.6676	+	17.1766i	−1.16521	+	0.561136i	−0.251642	+	0.967820i	$0.580970\pi$
$938$		0			0
$939$	19.9698	+	9.61695i	0.651690	+	0.313837i
$940$		0			0
$941$	−51.5620	−	24.8310i	−1.68087	−	0.809466i	−0.996790	−	0.0800628i	$-0.974488\pi$
$941$	−51.5620	−	24.8310i	−1.68087	−	0.809466i	−0.684084	−	0.729403i	$-0.739798\pi$
$942$		0			0
$943$	3.63102	−	4.55316i	0.118242	−	0.148271i
$944$		0			0
$945$	0.884707			0.0287795
$946$		0			0
$947$	−4.40462	+	19.2979i	−0.143131	+	0.627097i	0.851566	+	0.524247i	$0.175653\pi$
$947$	−4.40462	+	19.2979i	−0.143131	+	0.627097i	−0.994697	+	0.102850i	$0.967204\pi$
$948$		0			0
$949$	−11.1223	+	5.35621i	−0.361045	+	0.173870i
$950$		0			0
$951$	9.32557	−	11.6939i	0.302402	−	0.379200i
$952$		0			0
$953$	6.04234	−	26.4732i	0.195731	−	0.857552i	−0.777712	−	0.628621i	$-0.783620\pi$
$953$	6.04234	−	26.4732i	0.195731	−	0.857552i	0.973443	−	0.228931i	$-0.0735231\pi$
$954$		0			0
$955$	8.54288	+	10.7124i	0.276441	+	0.346646i
$956$		0			0
$957$	1.90598	+	18.3070i	0.0616115	+	0.591781i
$958$		0			0
$959$	−0.278840	−	0.349654i	−0.00900420	−	0.0112909i
$960$		0			0
$961$	−10.5336	+	46.1508i	−0.339794	+	1.48873i
$962$		0			0
$963$	2.46429	−	3.09012i	0.0794106	−	0.0995777i
$964$		0			0
$965$	−51.0555	+	24.5871i	−1.64354	+	0.791485i
$966$		0			0
$967$	−0.458320	+	2.00803i	−0.0147386	+	0.0645739i	−0.981762	−	0.190112i	$-0.939115\pi$
$967$	−0.458320	+	2.00803i	−0.0147386	+	0.0645739i	0.967024	+	0.254686i	$0.0819721\pi$
$968$		0			0
$969$	−8.49396			−0.272865
$970$		0			0
$971$	−13.7044	+	17.1848i	−0.439795	+	0.551486i	−0.951489	−	0.307682i	$-0.900447\pi$
$971$	−13.7044	+	17.1848i	−0.439795	+	0.551486i	0.511694	+	0.859168i	$0.329018\pi$
$972$		0			0
$973$	−0.341166	−	0.164297i	−0.0109373	−	0.00526712i
$974$		0			0
$975$	−36.4354	−	17.5464i	−1.16687	−	0.561934i
$976$		0			0
$977$	−27.2303	+	13.1134i	−0.871176	+	0.419536i	−0.815394	−	0.578907i	$-0.803480\pi$
$977$	−27.2303	+	13.1134i	−0.871176	+	0.419536i	−0.0557823	+	0.998443i	$0.517765\pi$
$978$		0			0
$979$	−1.60944	−	7.05143i	−0.0514380	−	0.225365i
$980$		0			0
$981$	6.80091	+	8.52807i	0.217136	+	0.272280i
$982$		0			0
$983$	3.13719	+	13.7449i	0.100061	+	0.438396i	0.999997	+	0.00237419i	$0.000755729\pi$
$983$	3.13719	+	13.7449i	0.100061	+	0.438396i	−0.899936	+	0.436022i	$0.856387\pi$
$984$		0			0
$985$	−16.2881			−0.518983
$986$		0			0
$987$	−0.661154			−0.0210447
$988$		0			0
$989$	6.38285	+	27.9651i	0.202963	+	0.889238i
$990$		0			0
$991$	−0.613269	−	0.769015i	−0.0194811	−	0.0244286i	0.771996	−	0.635628i	$-0.219259\pi$
$991$	−0.613269	−	0.769015i	−0.0194811	−	0.0244286i	−0.791477	+	0.611199i	$0.790687\pi$
$992$		0			0
$993$	−2.18598	−	9.57741i	−0.0693700	−	0.303930i
$994$		0			0
$995$	49.9989	−	24.0782i	1.58507	−	0.763330i
$996$		0			0
$997$	−23.5015	−	11.3177i	−0.744300	−	0.358436i	0.0229907	−	0.999736i	$-0.492681\pi$
$997$	−23.5015	−	11.3177i	−0.744300	−	0.358436i	−0.767290	+	0.641300i	$0.778395\pi$
$998$		0			0
$999$	−55.2512	−	26.6076i	−1.74807	−	0.841827i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	464.2.u.c.401.1		6
4.3	odd	2		116.2.g.a.53.1	✓	6
12.11	even	2		1044.2.u.a.865.1		6
29.23	even	7	inner	464.2.u.c.81.1		6
116.23	odd	14		116.2.g.a.81.1	yes	6
116.67	odd	14		3364.2.a.i.1.2		3
116.79	even	28		3364.2.c.h.1681.2		6
116.95	even	28		3364.2.c.h.1681.5		6
116.107	odd	14		3364.2.a.j.1.2		3
348.23	even	14		1044.2.u.a.1009.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
116.2.g.a.53.1	✓	6	4.3	odd	2
116.2.g.a.81.1	yes	6	116.23	odd	14
464.2.u.c.81.1		6	29.23	even	7	inner
464.2.u.c.401.1		6	1.1	even	1	trivial
1044.2.u.a.865.1		6	12.11	even	2
1044.2.u.a.1009.1		6	348.23	even	14
3364.2.a.i.1.2		3	116.67	odd	14
3364.2.a.j.1.2		3	116.107	odd	14
3364.2.c.h.1681.2		6	116.79	even	28
3364.2.c.h.1681.5		6	116.95	even	28

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:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	464.u (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.346011 + 1.51597i) q^{3} +(-2.02446 - 2.53859i) q^{5} +(0.0108851 + 0.0476909i) q^{7} +(0.524459 - 0.252566i) q^{9} +O(q^{10})\)	\(q+(0.346011 + 1.51597i) q^{3} +(-2.02446 - 2.53859i) q^{5} +(0.0108851 + 0.0476909i) q^{7} +(0.524459 - 0.252566i) q^{9} +(1.98039 + 0.953703i) q^{11} +(4.22737 + 2.03579i) q^{13} +(3.14795 - 3.94740i) q^{15} +4.71379 q^{17} +(-0.257865 + 1.12978i) q^{19} +(-0.0685317 + 0.0330031i) q^{21} +(3.27144 - 4.10225i) q^{23} +(-1.23341 + 5.40391i) q^{25} +(3.47285 + 4.35482i) q^{27} +(5.09783 - 1.73553i) q^{29} +(-5.51842 - 6.91988i) q^{31} +(-0.760553 + 3.33220i) q^{33} +(0.0990311 - 0.124181i) q^{35} +(-9.91939 + 4.77692i) q^{37} +(-1.62349 + 7.11297i) q^{39} +1.10992 q^{41} +(-3.40850 + 4.27413i) q^{43} +(-1.70291 - 0.820077i) q^{45} +(7.83124 + 3.77133i) q^{47} +(6.30463 - 3.03615i) q^{49} +(1.63102 + 7.14598i) q^{51} +(-2.27144 - 2.84829i) q^{53} +(-1.58815 - 6.95812i) q^{55} -1.80194 q^{57} -12.8116 q^{59} +(-0.592990 - 2.59806i) q^{61} +(0.0177539 + 0.0222627i) q^{63} +(-3.39008 - 14.8529i) q^{65} +(-0.0196143 + 0.00944576i) q^{67} +(7.35086 + 3.53999i) q^{69} +(3.31551 + 1.59667i) q^{71} +(-1.64042 + 2.05702i) q^{73} -8.61894 q^{75} +(-0.0239262 + 0.104828i) q^{77} +(6.38620 - 3.07543i) q^{79} +(-4.31133 + 5.40624i) q^{81} +(3.65399 - 16.0092i) q^{83} +(-9.54288 - 11.9664i) q^{85} +(4.39493 + 7.12766i) q^{87} +(-2.05161 - 2.57263i) q^{89} +(-0.0510733 + 0.223767i) q^{91} +(8.58091 - 10.7601i) q^{93} +(3.39008 - 1.63258i) q^{95} +(-1.90097 + 8.32869i) q^{97} +1.27950 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} - 3 q^{5} - 3 q^{7} - 6 q^{9}+O(q^{10}) \) 6 * q - 3 * q^3 - 3 * q^5 - 3 * q^7 - 6 * q^9	\( 6 q - 3 q^{3} - 3 q^{5} - 3 q^{7} - 6 q^{9} - q^{11} + 3 q^{13} + 5 q^{15} + 12 q^{17} + 11 q^{19} + 5 q^{21} + q^{23} - 4 q^{25} + 33 q^{27} - 6 q^{29} - 5 q^{31} + 11 q^{33} + 5 q^{35} - 27 q^{37} - 5 q^{39} + 8 q^{41} + 9 q^{43} + 3 q^{45} + 7 q^{47} + 26 q^{49} - 20 q^{51} + 5 q^{53} - 17 q^{55} - 2 q^{57} - 24 q^{59} + 11 q^{61} - 53 q^{63} - 19 q^{65} - 13 q^{67} + 17 q^{69} + 5 q^{71} - 21 q^{73} + 16 q^{75} + 25 q^{77} - q^{79} - 58 q^{81} + 27 q^{83} - 20 q^{85} + 3 q^{87} + 9 q^{89} + 37 q^{91} - q^{93} + 19 q^{95} - 7 q^{97} - 20 q^{99}+O(q^{100}) \) 6 * q - 3 * q^3 - 3 * q^5 - 3 * q^7 - 6 * q^9 - q^11 + 3 * q^13 + 5 * q^15 + 12 * q^17 + 11 * q^19 + 5 * q^21 + q^23 - 4 * q^25 + 33 * q^27 - 6 * q^29 - 5 * q^31 + 11 * q^33 + 5 * q^35 - 27 * q^37 - 5 * q^39 + 8 * q^41 + 9 * q^43 + 3 * q^45 + 7 * q^47 + 26 * q^49 - 20 * q^51 + 5 * q^53 - 17 * q^55 - 2 * q^57 - 24 * q^59 + 11 * q^61 - 53 * q^63 - 19 * q^65 - 13 * q^67 + 17 * q^69 + 5 * q^71 - 21 * q^73 + 16 * q^75 + 25 * q^77 - q^79 - 58 * q^81 + 27 * q^83 - 20 * q^85 + 3 * q^87 + 9 * q^89 + 37 * q^91 - q^93 + 19 * q^95 - 7 * q^97 - 20 * q^99

Introduction

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