LMFDB - Embedded newform 665.2.i.d.106.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [665,2,Mod(106,665)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(665, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("665.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 665 = 5 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	665.i (of order $3$, degree $2$, 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:	$5.31005173442$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			106.1
Root			$0.403374 + 1.68443i$ of defining polynomial
Character	$\chi$	$=$	665.106
Dual form			665.2.i.d.596.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.66044 + 2.87597i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{7} +(-4.01414 - 6.95269i) q^{9} +O(q^{10})$	\(q+(-1.66044 + 2.87597i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{7} +(-4.01414 - 6.95269i) q^{9} -4.02827 q^{11} -6.64177 q^{12} +(-1.00000 - 1.73205i) q^{13} +(1.66044 + 2.87597i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(-2.32088 + 4.01989i) q^{17} +(-3.67458 + 2.34467i) q^{19} +2.00000 q^{20} +(-1.66044 + 2.87597i) q^{21} +(-0.853695 - 1.47864i) q^{23} +(-0.500000 - 0.866025i) q^{25} +16.6983 q^{27} +(1.00000 + 1.73205i) q^{28} +(-3.82088 - 6.61797i) q^{29} -7.34916 q^{31} +(6.68872 - 11.5852i) q^{33} +(0.500000 - 0.866025i) q^{35} +(8.02827 - 13.9054i) q^{36} +8.34916 q^{37} +6.64177 q^{39} +(0.514137 - 0.890511i) q^{41} +(-4.00000 + 6.92820i) q^{43} +(-4.02827 - 6.97717i) q^{44} -8.02827 q^{45} +(6.68872 + 11.5852i) q^{47} +(-6.64177 - 11.5039i) q^{48} +1.00000 q^{49} +(-7.70739 - 13.3496i) q^{51} +(2.00000 - 3.46410i) q^{52} +(-3.17458 - 5.49853i) q^{53} +(-2.01414 + 3.48859i) q^{55} +(-0.641769 - 14.4612i) q^{57} +(-1.83956 + 3.18621i) q^{59} +(-3.32088 + 5.75194i) q^{60} +(5.48133 + 9.49394i) q^{61} +(-4.01414 - 6.95269i) q^{63} -8.00000 q^{64} -2.00000 q^{65} +(5.34916 + 9.26501i) q^{67} -9.28354 q^{68} +5.67004 q^{69} +(5.01414 - 8.68474i) q^{71} +(-2.36783 + 4.10120i) q^{73} +3.32088 q^{75} +(-7.73566 - 4.01989i) q^{76} -4.02827 q^{77} +(-0.693252 + 1.20075i) q^{79} +(2.00000 + 3.46410i) q^{80} +(-15.6842 + 27.1658i) q^{81} -6.64177 q^{84} +(2.32088 + 4.01989i) q^{85} +25.3774 q^{87} +(0.646305 + 1.11943i) q^{89} +(-1.00000 - 1.73205i) q^{91} +(1.70739 - 2.95729i) q^{92} +(12.2029 - 21.1360i) q^{93} +(0.193252 + 4.35461i) q^{95} +(-0.386505 + 0.669446i) q^{97} +(16.1700 + 28.0073i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{7} - 11 q^{9}+O(q^{10}) $ 6 * q - 2 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^7 - 11 * q^9	$ 6 q - 2 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{7} - 11 q^{9} + 2 q^{11} - 8 q^{12} - 6 q^{13} + 2 q^{15} - 12 q^{16} + 2 q^{17} - q^{19} + 12 q^{20} - 2 q^{21} - 3 q^{25} + 16 q^{27} + 6 q^{28} - 7 q^{29} - 2 q^{31} + 6 q^{33} + 3 q^{35} + 22 q^{36} + 8 q^{37} + 8 q^{39} - 10 q^{41} - 24 q^{43} + 2 q^{44} - 22 q^{45} + 6 q^{47} - 8 q^{48} + 6 q^{49} - 36 q^{51} + 12 q^{52} + 2 q^{53} + q^{55} + 28 q^{57} - 19 q^{59} - 4 q^{60} + 9 q^{61} - 11 q^{63} - 48 q^{64} - 12 q^{65} - 10 q^{67} + 8 q^{68} - 24 q^{69} + 17 q^{71} + 4 q^{73} + 4 q^{75} - 10 q^{76} + 2 q^{77} - 7 q^{79} + 12 q^{80} - 23 q^{81} - 8 q^{84} - 2 q^{85} + 84 q^{87} + 9 q^{89} - 6 q^{91} + 26 q^{93} + 4 q^{95} - 8 q^{97} + 39 q^{99}+O(q^{100}) $ 6 * q - 2 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^7 - 11 * q^9 + 2 * q^11 - 8 * q^12 - 6 * q^13 + 2 * q^15 - 12 * q^16 + 2 * q^17 - q^19 + 12 * q^20 - 2 * q^21 - 3 * q^25 + 16 * q^27 + 6 * q^28 - 7 * q^29 - 2 * q^31 + 6 * q^33 + 3 * q^35 + 22 * q^36 + 8 * q^37 + 8 * q^39 - 10 * q^41 - 24 * q^43 + 2 * q^44 - 22 * q^45 + 6 * q^47 - 8 * q^48 + 6 * q^49 - 36 * q^51 + 12 * q^52 + 2 * q^53 + q^55 + 28 * q^57 - 19 * q^59 - 4 * q^60 + 9 * q^61 - 11 * q^63 - 48 * q^64 - 12 * q^65 - 10 * q^67 + 8 * q^68 - 24 * q^69 + 17 * q^71 + 4 * q^73 + 4 * q^75 - 10 * q^76 + 2 * q^77 - 7 * q^79 + 12 * q^80 - 23 * q^81 - 8 * q^84 - 2 * q^85 + 84 * q^87 + 9 * q^89 - 6 * q^91 + 26 * q^93 + 4 * q^95 - 8 * q^97 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/665\mathbb{Z}\right)^\times$.

$n$	$211$	$267$	$381$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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		−0.866025	−	0.500000i	$-0.833333\pi$
$2$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$3$	−1.66044	+	2.87597i	−0.958657	+	1.66044i	−0.232888	+	0.972504i	$0.574818\pi$
$3$	−1.66044	+	2.87597i	−0.958657	+	1.66044i	−0.725769	+	0.687939i	$0.758516\pi$
$4$	1.00000	+	1.73205i	0.500000	+	0.866025i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$		0			0
$9$	−4.01414	−	6.95269i	−1.33805	−	2.31756i
$10$		0			0
$11$	−4.02827			−1.21457			−0.607285	−	0.794484i	$-0.707741\pi$
$11$	−4.02827			−1.21457			−0.607285	+	0.794484i	$0.707741\pi$
$12$	−6.64177			−1.91731
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$		0			0
$15$	1.66044	+	2.87597i	0.428724	+	0.742572i
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	−2.32088	+	4.01989i	−0.562897	+	0.974967i	0.434345	+	0.900747i	$0.356980\pi$
$17$	−2.32088	+	4.01989i	−0.562897	+	0.974967i	−0.997242	+	0.0742198i	$0.976353\pi$
$18$		0			0
$19$	−3.67458	+	2.34467i	−0.843006	+	0.537904i
$19$	−3.67458	+	2.34467i	−0.843006	+	0.537904i
$20$	2.00000			0.447214
$21$	−1.66044	+	2.87597i	−0.362338	+	0.627588i
$22$		0			0
$23$	−0.853695	−	1.47864i	−0.178008	−	0.308318i	0.763190	−	0.646174i	$-0.223632\pi$
$23$	−0.853695	−	1.47864i	−0.178008	−	0.308318i	−0.941198	+	0.337855i	$0.890299\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	16.6983			3.21359
$28$	1.00000	+	1.73205i	0.188982	+	0.327327i
$29$	−3.82088	−	6.61797i	−0.709520	−	1.22893i	−0.965035	−	0.262120i	$-0.915578\pi$
$29$	−3.82088	−	6.61797i	−0.709520	−	1.22893i	0.255515	−	0.966805i	$-0.417755\pi$
$30$		0			0
$31$	−7.34916			−1.31995			−0.659974	−	0.751289i	$-0.729433\pi$
$31$	−7.34916			−1.31995			−0.659974	+	0.751289i	$0.729433\pi$
$32$		0			0
$33$	6.68872	−	11.5852i	1.16436	−	2.01672i
$34$		0			0
$35$	0.500000	−	0.866025i	0.0845154	−	0.146385i
$36$	8.02827	−	13.9054i	1.33805	−	2.31756i
$37$	8.34916			1.37259			0.686297	−	0.727322i	$-0.259235\pi$
$37$	8.34916			1.37259			0.686297	+	0.727322i	$0.259235\pi$
$38$		0			0
$39$	6.64177			1.06353
$40$		0			0
$41$	0.514137	−	0.890511i	0.0802947	−	0.139074i	−0.823082	−	0.567923i	$-0.807747\pi$
$41$	0.514137	−	0.890511i	0.0802947	−	0.139074i	0.903377	+	0.428848i	$0.141081\pi$
$42$		0			0
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	0.381246	+	0.924473i	$0.375495\pi$
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	−0.991241	+	0.132068i	$0.957838\pi$
$44$	−4.02827	−	6.97717i	−0.607285	−	1.05185i
$45$	−8.02827			−1.19678
$46$		0			0
$47$	6.68872	+	11.5852i	0.975650	+	1.68987i	0.677775	+	0.735270i	$0.262944\pi$
$47$	6.68872	+	11.5852i	0.975650	+	1.68987i	0.297875	+	0.954605i	$0.403722\pi$
$48$	−6.64177	−	11.5039i	−0.958657	−	1.66044i
$49$	1.00000			0.142857
$50$		0			0
$51$	−7.70739	−	13.3496i	−1.07925	−	1.86932i
$52$	2.00000	−	3.46410i	0.277350	−	0.480384i
$53$	−3.17458	−	5.49853i	−0.436062	−	0.755282i	0.561320	−	0.827599i	$-0.310294\pi$
$53$	−3.17458	−	5.49853i	−0.436062	−	0.755282i	−0.997382	+	0.0723176i	$0.976960\pi$
$54$		0			0
$55$	−2.01414	+	3.48859i	−0.271586	+	0.470401i
$56$		0			0
$57$	−0.641769	−	14.4612i	−0.0850044	−	1.91543i
$58$		0			0
$59$	−1.83956	+	3.18621i	−0.239490	+	0.414809i	−0.960568	−	0.278045i	$-0.910314\pi$
$59$	−1.83956	+	3.18621i	−0.239490	+	0.414809i	0.721078	+	0.692854i	$0.243647\pi$
$60$	−3.32088	+	5.75194i	−0.428724	+	0.742572i
$61$	5.48133	+	9.49394i	0.701812	+	1.21557i	0.967830	+	0.251606i	$0.0809587\pi$
$61$	5.48133	+	9.49394i	0.701812	+	1.21557i	−0.266018	+	0.963968i	$0.585708\pi$
$62$		0			0
$63$	−4.01414	−	6.95269i	−0.505734	−	0.875956i
$64$	−8.00000			−1.00000
$65$	−2.00000			−0.248069
$66$		0			0
$67$	5.34916	+	9.26501i	0.653504	+	1.13190i	0.982267	+	0.187489i	$0.0600349\pi$
$67$	5.34916	+	9.26501i	0.653504	+	1.13190i	−0.328763	+	0.944412i	$0.606632\pi$
$68$	−9.28354			−1.12579
$69$	5.67004			0.682593
$70$		0			0
$71$	5.01414	−	8.68474i	0.595069	−	1.03069i	−0.398469	−	0.917182i	$-0.630458\pi$
$71$	5.01414	−	8.68474i	0.595069	−	1.03069i	0.993537	−	0.113507i	$-0.0362084\pi$
$72$		0			0
$73$	−2.36783	+	4.10120i	−0.277134	+	0.480010i	−0.970671	−	0.240411i	$-0.922718\pi$
$73$	−2.36783	+	4.10120i	−0.277134	+	0.480010i	0.693538	+	0.720421i	$0.256051\pi$
$74$		0			0
$75$	3.32088			0.383463
$76$	−7.73566	−	4.01989i	−0.887341	−	0.461113i
$77$	−4.02827			−0.459064
$78$		0			0
$79$	−0.693252	+	1.20075i	−0.0779970	+	0.135095i	−0.902386	−	0.430929i	$-0.858186\pi$
$79$	−0.693252	+	1.20075i	−0.0779970	+	0.135095i	0.824389	+	0.566024i	$0.191519\pi$
$80$	2.00000	+	3.46410i	0.223607	+	0.387298i
$81$	−15.6842	+	27.1658i	−1.74269	+	3.01842i
$82$		0			0
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$	−6.64177			−0.724676
$85$	2.32088	+	4.01989i	0.251735	+	0.436018i
$86$		0			0
$87$	25.3774			2.72075
$88$		0			0
$89$	0.646305	+	1.11943i	0.0685082	+	0.118660i	0.898245	−	0.439495i	$-0.144843\pi$
$89$	0.646305	+	1.11943i	0.0685082	+	0.118660i	−0.829737	+	0.558155i	$0.811509\pi$
$90$		0			0
$91$	−1.00000	−	1.73205i	−0.104828	−	0.181568i
$92$	1.70739	−	2.95729i	0.178008	−	0.308318i
$93$	12.2029	−	21.1360i	1.26538	−	2.19170i
$94$		0			0
$95$	0.193252	+	4.35461i	0.0198273	+	0.446774i
$96$		0			0
$97$	−0.386505	+	0.669446i	−0.0392436	+	0.0679719i	−0.884980	−	0.465629i	$-0.845828\pi$
$97$	−0.386505	+	0.669446i	−0.0392436	+	0.0679719i	0.845736	+	0.533601i	$0.179162\pi$
$98$		0			0
$99$	16.1700	+	28.0073i	1.62515	+	2.81484i
$100$	1.00000	−	1.73205i	0.100000	−	0.173205i
$101$	−3.48133	−	6.02983i	−0.346405	−	0.599991i	0.639203	−	0.769038i	$-0.279264\pi$
$101$	−3.48133	−	6.02983i	−0.346405	−	0.599991i	−0.985608	+	0.169047i	$0.945931\pi$
$102$		0			0
$103$	16.7357			1.64901			0.824507	−	0.565852i	$-0.191453\pi$
$103$	16.7357			1.64901			0.824507	+	0.565852i	$0.191453\pi$
$104$		0			0
$105$	1.66044	+	2.87597i	0.162043	+	0.280666i
$106$		0			0
$107$	−8.93438			−0.863719			−0.431860	−	0.901941i	$-0.642142\pi$
$107$	−8.93438			−0.863719			−0.431860	+	0.901941i	$0.642142\pi$
$108$	16.6983	+	28.9223i	1.60680	+	2.78305i
$109$	−4.04241	+	7.00166i	−0.387193	+	0.670637i	−0.992071	−	0.125681i	$-0.959889\pi$
$109$	−4.04241	+	7.00166i	−0.387193	+	0.670637i	0.604878	+	0.796318i	$0.293222\pi$
$110$		0			0
$111$	−13.8633	+	24.0119i	−1.31585	+	2.27911i
$112$	−2.00000	+	3.46410i	−0.188982	+	0.327327i
$113$	−11.1222			−1.04629			−0.523143	−	0.852245i	$-0.675241\pi$
$113$	−11.1222			−1.04629			−0.523143	+	0.852245i	$0.675241\pi$
$114$		0			0
$115$	−1.70739			−0.159215
$116$	7.64177	−	13.2359i	0.709520	−	1.22893i
$117$	−8.02827	+	13.9054i	−0.742214	+	1.28555i
$118$		0			0
$119$	−2.32088	+	4.01989i	−0.212755	+	0.368503i
$120$		0			0
$121$	5.22699			0.475181
$122$		0			0
$123$	1.70739	+	2.95729i	0.153950	+	0.266649i
$124$	−7.34916	−	12.7291i	−0.659974	−	1.14311i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−4.78807	−	8.29319i	−0.424873	−	0.735901i	0.571536	−	0.820577i	$-0.306348\pi$
$127$	−4.78807	−	8.29319i	−0.424873	−	0.735901i	−0.996409	+	0.0846758i	$0.973015\pi$
$128$		0			0
$129$	−13.2835	−	23.0078i	−1.16955	−	2.02572i
$130$		0			0
$131$	−6.34916	+	10.9971i	−0.554729	+	0.960818i	0.443196	+	0.896425i	$0.353845\pi$
$131$	−6.34916	+	10.9971i	−0.554729	+	0.960818i	−0.997925	+	0.0643933i	$0.979489\pi$
$132$	26.7549			2.32871
$133$	−3.67458	+	2.34467i	−0.318626	+	0.203308i
$134$		0			0
$135$	8.34916	−	14.4612i	0.718581	−	1.24462i
$136$		0			0
$137$	−3.78807	−	6.56114i	−0.323637	−	0.560556i	0.657599	−	0.753369i	$-0.271572\pi$
$137$	−3.78807	−	6.56114i	−0.323637	−	0.560556i	−0.981236	+	0.192813i	$0.938239\pi$
$138$		0			0
$139$	4.73566	+	8.20241i	0.401674	+	0.695719i	0.993928	−	0.110032i	$-0.0350953\pi$
$139$	4.73566	+	8.20241i	0.401674	+	0.695719i	−0.592254	+	0.805751i	$0.701762\pi$
$140$	2.00000			0.169031
$141$	−44.4249			−3.74125
$142$		0			0
$143$	4.02827	+	6.97717i	0.336861	+	0.583461i
$144$	32.1131			2.67609
$145$	−7.64177			−0.634614
$146$		0			0
$147$	−1.66044	+	2.87597i	−0.136951	+	0.237206i
$148$	8.34916	+	14.4612i	0.686297	+	1.18870i
$149$	−3.30675	+	5.72745i	−0.270899	+	0.469211i	−0.969092	−	0.246698i	$-0.920654\pi$
$149$	−3.30675	+	5.72745i	−0.270899	+	0.469211i	0.698193	+	0.715910i	$0.253988\pi$
$150$		0			0
$151$	3.84049			0.312534			0.156267	−	0.987715i	$-0.450054\pi$
$151$	3.84049			0.312534			0.156267	+	0.987715i	$0.450054\pi$
$152$		0			0
$153$	37.2654			3.01273
$154$		0			0
$155$	−3.67458	+	6.36456i	−0.295149	+	0.511214i
$156$	6.64177	+	11.5039i	0.531767	+	0.921048i
$157$	−8.98133	+	15.5561i	−0.716788	+	1.24151i	0.245478	+	0.969402i	$0.421055\pi$
$157$	−8.98133	+	15.5561i	−0.716788	+	1.24151i	−0.962266	+	0.272111i	$0.912278\pi$
$158$		0			0
$159$	21.0848			1.67214
$160$		0			0
$161$	−0.853695	−	1.47864i	−0.0672806	−	0.116533i
$162$		0			0
$163$	−10.3492			−0.810609			−0.405304	−	0.914182i	$-0.632834\pi$
$163$	−10.3492			−0.810609			−0.405304	+	0.914182i	$0.632834\pi$
$164$	2.05655			0.160589
$165$	−6.68872	−	11.5852i	−0.520716	−	0.901906i
$166$		0			0
$167$	1.02827	+	1.78102i	0.0795702	+	0.137820i	0.903065	−	0.429505i	$-0.141312\pi$
$167$	1.02827	+	1.78102i	0.0795702	+	0.137820i	−0.823494	+	0.567324i	$0.807979\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$	31.0520	+	16.1364i	2.37461	+	1.23398i
$172$	−16.0000			−1.21999
$173$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$173$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$174$		0			0
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$	8.05655	−	13.9543i	0.607285	−	1.05185i
$177$	−6.10896	−	10.5810i	−0.459177	−	0.795319i
$178$		0			0
$179$	1.44305			0.107859			0.0539294	−	0.998545i	$-0.482825\pi$
$179$	1.44305			0.107859			0.0539294	+	0.998545i	$0.482825\pi$
$180$	−8.02827	−	13.9054i	−0.598392	−	1.03645i
$181$	11.3492	+	19.6573i	0.843576	+	1.46112i	0.886852	+	0.462054i	$0.152887\pi$
$181$	11.3492	+	19.6573i	0.843576	+	1.46112i	−0.0432756	+	0.999063i	$0.513779\pi$
$182$		0			0
$183$	−36.4057			−2.69119
$184$		0			0
$185$	4.17458	−	7.23058i	0.306921	−	0.531603i
$186$		0			0
$187$	9.34916	−	16.1932i	0.683678	−	1.18417i
$188$	−13.3774	+	23.1704i	−0.975650	+	1.68987i
$189$	16.6983			1.21462
$190$		0			0
$191$	12.4148			0.898302			0.449151	−	0.893456i	$-0.351727\pi$
$191$	12.4148			0.898302			0.449151	+	0.893456i	$0.351727\pi$
$192$	13.2835	−	23.0078i	0.958657	−	1.66044i
$193$	−3.82542	+	6.62582i	−0.275360	+	0.476937i	−0.970226	−	0.242202i	$-0.922130\pi$
$193$	−3.82542	+	6.62582i	−0.275360	+	0.476937i	0.694866	+	0.719139i	$0.255464\pi$
$194$		0			0
$195$	3.32088	−	5.75194i	0.237813	−	0.411905i
$196$	1.00000	+	1.73205i	0.0714286	+	0.123718i
$197$	13.5761			0.967261			0.483630	−	0.875272i	$-0.339318\pi$
$197$	13.5761			0.967261			0.483630	+	0.875272i	$0.339318\pi$
$198$		0			0
$199$	−10.8305	−	18.7590i	−0.767753	−	1.32979i	−0.938779	−	0.344520i	$-0.888042\pi$
$199$	−10.8305	−	18.7590i	−0.767753	−	1.32979i	0.171026	−	0.985266i	$-0.445292\pi$
$200$		0			0
$201$	−35.5279			−2.50594
$202$		0			0
$203$	−3.82088	−	6.61797i	−0.268174	−	0.464490i
$204$	15.4148	−	26.6992i	1.07925	−	1.86932i
$205$	−0.514137	−	0.890511i	−0.0359089	−	0.0621960i
$206$		0			0
$207$	−6.85369	+	11.8709i	−0.476365	+	0.825088i
$208$	8.00000			0.554700
$209$	14.8022	−	9.44496i	1.02389	−	0.653322i
$210$		0			0
$211$	3.50000	−	6.06218i	0.240950	−	0.417338i	−0.720035	−	0.693938i	$-0.755874\pi$
$211$	3.50000	−	6.06218i	0.240950	−	0.417338i	0.960985	+	0.276600i	$0.0892077\pi$
$212$	6.34916	−	10.9971i	0.436062	−	0.755282i
$213$	16.6514	+	28.8410i	1.14093	+	1.97615i
$214$		0			0
$215$	4.00000	+	6.92820i	0.272798	+	0.472500i
$216$		0			0
$217$	−7.34916			−0.498893
$218$		0			0
$219$	−7.86330	−	13.6196i	−0.531352	−	0.920329i
$220$	−8.05655			−0.543172
$221$	9.28354			0.624478
$222$		0			0
$223$	−4.75434	+	8.23475i	−0.318374	+	0.551440i	−0.980149	−	0.198263i	$-0.936470\pi$
$223$	−4.75434	+	8.23475i	−0.318374	+	0.551440i	0.661775	+	0.749703i	$0.269803\pi$
$224$		0			0
$225$	−4.01414	+	6.95269i	−0.267609	+	0.463513i
$226$		0			0
$227$	0.547875			0.0363637			0.0181819	−	0.999835i	$-0.494212\pi$
$227$	0.547875			0.0363637			0.0181819	+	0.999835i	$0.494212\pi$
$228$	24.4057	−	15.5727i	1.61631	−	1.03133i
$229$	−6.65084			−0.439500			−0.219750	−	0.975556i	$-0.570524\pi$
$229$	−6.65084			−0.439500			−0.219750	+	0.975556i	$0.570524\pi$
$230$		0			0
$231$	6.68872	−	11.5852i	0.440085	−	0.762250i
$232$		0			0
$233$	−6.96265	+	12.0597i	−0.456139	+	0.790055i	−0.998753	−	0.0499268i	$-0.984101\pi$
$233$	−6.96265	+	12.0597i	−0.456139	+	0.790055i	0.542614	+	0.839982i	$0.317435\pi$
$234$		0			0
$235$	13.3774			0.872647
$236$	−7.35823			−0.478980
$237$	−2.30221	−	3.98755i	−0.149545	−	0.259019i
$238$		0			0
$239$	17.3865			1.12464			0.562320	−	0.826920i	$-0.309909\pi$
$239$	17.3865			1.12464			0.562320	+	0.826920i	$0.309909\pi$
$240$	−13.2835			−0.857449
$241$	−11.0611	−	19.1584i	−0.712507	−	1.23410i	−0.963913	−	0.266217i	$-0.914226\pi$
$241$	−11.0611	−	19.1584i	−0.712507	−	1.23410i	0.251406	−	0.967882i	$-0.419107\pi$
$242$		0			0
$243$	−27.0379	−	46.8310i	−1.73448	−	3.00421i
$244$	−10.9627	+	18.9879i	−0.701812	+	1.21557i
$245$	0.500000	−	0.866025i	0.0319438	−	0.0553283i
$246$		0			0
$247$	7.73566	+	4.01989i	0.492208	+	0.255779i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−13.6090	−	23.5714i	−0.858990	−	1.48781i	−0.872894	−	0.487911i	$-0.837759\pi$
$251$	−13.6090	−	23.5714i	−0.858990	−	1.48781i	0.0139037	−	0.999903i	$-0.495574\pi$
$252$	8.02827	−	13.9054i	0.505734	−	0.875956i
$253$	3.43892	+	5.95638i	0.216203	+	0.374474i
$254$		0			0
$255$	−15.4148			−0.965311
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−10.7826	−	18.6760i	−0.672601	−	1.16498i	−0.977164	−	0.212487i	$-0.931844\pi$
$257$	−10.7826	−	18.6760i	−0.672601	−	1.16498i	0.304563	−	0.952492i	$-0.401490\pi$
$258$		0			0
$259$	8.34916			0.518791
$260$	−2.00000	−	3.46410i	−0.124035	−	0.214834i
$261$	−30.6751	+	53.1308i	−1.89874	+	3.28872i
$262$		0			0
$263$	6.41478	−	11.1107i	0.395552	−	0.685117i	−0.597619	−	0.801780i	$-0.703887\pi$
$263$	6.41478	−	11.1107i	0.395552	−	0.685117i	0.993172	+	0.116663i	$0.0372199\pi$
$264$		0			0
$265$	−6.34916			−0.390026
$266$		0			0
$267$	−4.29261			−0.262704
$268$	−10.6983	+	18.5300i	−0.653504	+	1.13190i
$269$	−3.03281	+	5.25298i	−0.184914	+	0.320280i	−0.943547	−	0.331237i	$-0.892534\pi$
$269$	−3.03281	+	5.25298i	−0.184914	+	0.320280i	0.758634	+	0.651517i	$0.225867\pi$
$270$		0			0
$271$	−5.09482	+	8.82449i	−0.309488	+	0.536050i	−0.978251	−	0.207427i	$-0.933491\pi$
$271$	−5.09482	+	8.82449i	−0.309488	+	0.536050i	0.668762	+	0.743476i	$0.266824\pi$
$272$	−9.28354	−	16.0796i	−0.562897	−	0.974967i
$273$	6.64177			0.401978
$274$		0			0
$275$	2.01414	+	3.48859i	0.121457	+	0.210370i
$276$	5.67004	+	9.82080i	0.341296	+	0.591143i
$277$	27.5761			1.65689			0.828445	−	0.560070i	$-0.189226\pi$
$277$	27.5761			1.65689			0.828445	+	0.560070i	$0.189226\pi$
$278$		0			0
$279$	29.5005	+	51.0964i	1.76615	+	3.05906i
$280$		0			0
$281$	5.48586	+	9.50179i	0.327259	+	0.566829i	0.981967	−	0.189053i	$-0.0605417\pi$
$281$	5.48586	+	9.50179i	0.327259	+	0.566829i	−0.654708	+	0.755882i	$0.727208\pi$
$282$		0			0
$283$	−9.33049	+	16.1609i	−0.554640	+	0.960664i	0.443292	+	0.896377i	$0.353811\pi$
$283$	−9.33049	+	16.1609i	−0.554640	+	0.960664i	−0.997931	+	0.0642868i	$0.979523\pi$
$284$	20.0565			1.19014
$285$	−12.8446	−	6.67479i	−0.760850	−	0.395381i
$286$		0			0
$287$	0.514137	−	0.890511i	0.0303485	−	0.0525652i
$288$		0			0
$289$	−2.27301	−	3.93697i	−0.133706	−	0.231586i
$290$		0			0
$291$	−1.28354	−	2.22315i	−0.0752423	−	0.130324i
$292$	−9.47133			−0.554267
$293$	−9.43398			−0.551139			−0.275569	−	0.961281i	$-0.588866\pi$
$293$	−9.43398			−0.551139			−0.275569	+	0.961281i	$0.588866\pi$
$294$		0			0
$295$	1.83956	+	3.18621i	0.107103	+	0.185508i
$296$		0			0
$297$	−67.2654			−3.90313
$298$		0			0
$299$	−1.70739	+	2.95729i	−0.0987409	+	0.171024i
$300$	3.32088	+	5.75194i	0.191731	+	0.332088i
$301$	−4.00000	+	6.92820i	−0.230556	+	0.399335i
$302$		0			0
$303$	23.1222			1.32833
$304$	−0.773010	−	17.4185i	−0.0443351	−	0.999017i
$305$	10.9627			0.627720
$306$		0			0
$307$	−10.9627	+	18.9879i	−0.625672	+	1.08370i	0.362739	+	0.931891i	$0.381842\pi$
$307$	−10.9627	+	18.9879i	−0.625672	+	1.08370i	−0.988411	+	0.151804i	$0.951492\pi$
$308$	−4.02827	−	6.97717i	−0.229532	−	0.397561i
$309$	−27.7886	+	48.1313i	−1.58084	+	2.73809i
$310$		0			0
$311$	6.82956			0.387269			0.193634	−	0.981074i	$-0.437972\pi$
$311$	6.82956			0.387269			0.193634	+	0.981074i	$0.437972\pi$
$312$		0			0
$313$	7.33049	+	12.6968i	0.414344	+	0.717664i	0.995359	−	0.0962283i	$-0.0306779\pi$
$313$	7.33049	+	12.6968i	0.414344	+	0.717664i	−0.581016	+	0.813892i	$0.697345\pi$
$314$		0			0
$315$	−8.02827			−0.452342
$316$	−2.77301			−0.155994
$317$	7.70739	+	13.3496i	0.432890	+	0.749788i	0.997121	−	0.0758295i	$-0.0241605\pi$
$317$	7.70739	+	13.3496i	0.432890	+	0.749788i	−0.564231	+	0.825617i	$0.690827\pi$
$318$		0			0
$319$	15.3916	+	26.6590i	0.861762	+	1.49262i
$320$	−4.00000	+	6.92820i	−0.223607	+	0.387298i
$321$	14.8350	−	25.6950i	0.828010	−	1.43416i
$322$		0			0
$323$	−0.897033	−	20.2131i	−0.0499123	−	1.12469i
$324$	−62.7367			−3.48537
$325$	−1.00000	+	1.73205i	−0.0554700	+	0.0960769i
$326$		0			0
$327$	−13.4244	−	23.2517i	−0.742370	−	1.28582i
$328$		0			0
$329$	6.68872	+	11.5852i	0.368761	+	0.638713i
$330$		0			0
$331$	−8.31181			−0.456858			−0.228429	−	0.973561i	$-0.573359\pi$
$331$	−8.31181			−0.456858			−0.228429	+	0.973561i	$0.573359\pi$
$332$		0			0
$333$	−33.5147	−	58.0491i	−1.83659	−	3.18107i
$334$		0			0
$335$	10.6983			0.584511
$336$	−6.64177	−	11.5039i	−0.362338	−	0.627588i
$337$	2.17458	−	3.76648i	0.118457	−	0.205173i	−0.800699	−	0.599066i	$-0.795539\pi$
$337$	2.17458	−	3.76648i	0.118457	−	0.205173i	0.919156	+	0.393893i	$0.128872\pi$
$338$		0			0
$339$	18.4677	−	31.9870i	1.00303	−	1.73730i
$340$	−4.64177	+	8.03978i	−0.251735	+	0.436018i
$341$	29.6044			1.60317
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	2.83502	−	4.91040i	0.152632	−	0.264367i
$346$		0			0
$347$	4.29261	−	7.43502i	0.230439	−	0.399133i	−0.727498	−	0.686110i	$-0.759317\pi$
$347$	4.29261	−	7.43502i	0.230439	−	0.399133i	0.957937	+	0.286977i	$0.0926503\pi$
$348$	25.3774	+	43.9550i	1.36037	+	2.35624i
$349$	−2.31181			−0.123748			−0.0618742	−	0.998084i	$-0.519708\pi$
$349$	−2.31181			−0.123748			−0.0618742	+	0.998084i	$0.519708\pi$
$350$		0			0
$351$	−16.6983	−	28.9223i	−0.891290	−	1.54376i
$352$		0			0
$353$	15.5652			0.828453			0.414227	−	0.910174i	$-0.364052\pi$
$353$	15.5652			0.828453			0.414227	+	0.910174i	$0.364052\pi$
$354$		0			0
$355$	−5.01414	−	8.68474i	−0.266123	−	0.460938i
$356$	−1.29261	+	2.23887i	−0.0685082	+	0.118660i
$357$	−7.70739	−	13.3496i	−0.407918	−	0.706535i
$358$		0			0
$359$	−10.8916	+	18.8648i	−0.574835	+	0.995643i	0.421225	+	0.906956i	$0.361600\pi$
$359$	−10.8916	+	18.8648i	−0.574835	+	0.995643i	−0.996060	+	0.0886871i	$0.971733\pi$
$360$		0			0
$361$	8.00506	−	17.2313i	0.421319	−	0.906912i
$362$		0			0
$363$	−8.67912	+	15.0327i	−0.455535	+	0.789011i
$364$	2.00000	−	3.46410i	0.104828	−	0.181568i
$365$	2.36783	+	4.10120i	0.123938	+	0.214667i
$366$		0			0
$367$	−10.3492	−	17.9253i	−0.540222	−	0.935691i	−0.998891	−	0.0470843i	$-0.985007\pi$
$367$	−10.3492	−	17.9253i	−0.540222	−	0.935691i	0.458669	−	0.888607i	$-0.348326\pi$
$368$	6.82956			0.356015
$369$	−8.25526			−0.429752
$370$		0			0
$371$	−3.17458	−	5.49853i	−0.164816	−	0.285470i
$372$	48.8114			2.53075
$373$	0.773010			0.0400249			0.0200125	−	0.999800i	$-0.493629\pi$
$373$	0.773010			0.0400249			0.0200125	+	0.999800i	$0.493629\pi$
$374$		0			0
$375$	1.66044	−	2.87597i	0.0857449	−	0.148514i
$376$		0			0
$377$	−7.64177	+	13.2359i	−0.393571	+	0.681685i
$378$		0			0
$379$	−9.38650			−0.482152			−0.241076	−	0.970506i	$-0.577500\pi$
$379$	−9.38650			−0.482152			−0.241076	+	0.970506i	$0.577500\pi$
$380$	−7.34916	+	4.68934i	−0.377004	+	0.240558i
$381$	31.8013			1.62923
$382$		0			0
$383$	8.12217	−	14.0680i	0.415023	−	0.718842i	−0.580408	−	0.814326i	$-0.697107\pi$
$383$	8.12217	−	14.0680i	0.415023	−	0.718842i	0.995431	+	0.0954846i	$0.0304401\pi$
$384$		0			0
$385$	−2.01414	+	3.48859i	−0.102650	+	0.177795i
$386$		0			0
$387$	64.2262			3.26480
$388$	−1.54602			−0.0784872
$389$	7.00506	+	12.1331i	0.355171	+	0.615174i	0.987147	−	0.159814i	$-0.0510894\pi$
$389$	7.00506	+	12.1331i	0.355171	+	0.615174i	−0.631976	+	0.774988i	$0.717756\pi$
$390$		0			0
$391$	7.92531			0.400800
$392$		0			0
$393$	−21.0848	−	36.5200i	−1.06359	−	1.84219i
$394$		0			0
$395$	0.693252	+	1.20075i	0.0348813	+	0.0604162i
$396$	−32.3401	+	56.0147i	−1.62515	+	2.81484i
$397$	10.7357	−	18.5947i	0.538807	−	0.933242i	−0.460161	−	0.887835i	$-0.652208\pi$
$397$	10.7357	−	18.5947i	0.538807	−	0.933242i	0.998969	−	0.0454065i	$-0.0144583\pi$
$398$		0			0
$399$	−0.641769	−	14.4612i	−0.0321286	−	0.723964i
$400$	4.00000			0.200000
$401$	13.5848	−	23.5296i	0.678394	−	1.17501i	−0.297071	−	0.954855i	$-0.596010\pi$
$401$	13.5848	−	23.5296i	0.678394	−	1.17501i	0.975465	−	0.220157i	$-0.0706569\pi$
$402$		0			0
$403$	7.34916	+	12.7291i	0.366088	+	0.634082i
$404$	6.96265	−	12.0597i	0.346405	−	0.599991i
$405$	15.6842	+	27.1658i	0.779353	+	1.34988i
$406$		0			0
$407$	−33.6327			−1.66711
$408$		0			0
$409$	8.48133	+	14.6901i	0.419375	+	0.726378i	0.995877	−	0.0907176i	$-0.0289161\pi$
$409$	8.48133	+	14.6901i	0.419375	+	0.726378i	−0.576502	+	0.817096i	$0.695583\pi$
$410$		0			0
$411$	25.1595			1.24103
$412$	16.7357	+	28.9870i	0.824507	+	1.42809i
$413$	−1.83956	+	3.18621i	−0.0905187	+	0.156783i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−31.4532			−1.54027
$418$		0			0
$419$	−29.2070			−1.42685			−0.713427	−	0.700729i	$-0.752858\pi$
$419$	−29.2070			−1.42685			−0.713427	+	0.700729i	$0.752858\pi$
$420$	−3.32088	+	5.75194i	−0.162043	+	0.280666i
$421$	−13.0424	+	22.5901i	−0.635648	+	1.10097i	0.350729	+	0.936477i	$0.385934\pi$
$421$	−13.0424	+	22.5901i	−0.635648	+	1.10097i	−0.986377	+	0.164498i	$0.947400\pi$
$422$		0			0
$423$	53.6988	−	93.0091i	2.61093	−	4.52226i
$424$		0			0
$425$	4.64177			0.225159
$426$		0			0
$427$	5.48133	+	9.49394i	0.265260	+	0.459444i
$428$	−8.93438	−	15.4748i	−0.431860	−	0.748003i
$429$	−26.7549			−1.29174
$430$		0			0
$431$	−2.34409	−	4.06009i	−0.112911	−	0.195568i	0.804032	−	0.594586i	$-0.202684\pi$
$431$	−2.34409	−	4.06009i	−0.112911	−	0.195568i	−0.916943	+	0.399019i	$0.869351\pi$
$432$	−33.3966	+	57.8447i	−1.60680	+	2.78305i
$433$	−17.9813	−	31.1446i	−0.864127	−	1.49671i	−0.867911	−	0.496720i	$-0.834538\pi$
$433$	−17.9813	−	31.1446i	−0.864127	−	1.49671i	0.00378358	−	0.999993i	$-0.498796\pi$
$434$		0			0
$435$	12.6887	−	21.9775i	0.608377	−	1.05374i
$436$	−16.1696			−0.774385
$437$	6.60389	+	3.43176i	0.315907	+	0.164163i
$438$		0			0
$439$	15.7594	−	27.2961i	0.752155	−	1.30277i	−0.194621	−	0.980879i	$-0.562348\pi$
$439$	15.7594	−	27.2961i	0.752155	−	1.30277i	0.946776	−	0.321892i	$-0.104319\pi$
$440$		0			0
$441$	−4.01414	−	6.95269i	−0.191149	−	0.331080i
$442$		0			0
$443$	12.8970	+	22.3383i	0.612757	+	1.06133i	0.990774	+	0.135527i	$0.0432727\pi$
$443$	12.8970	+	22.3383i	0.612757	+	1.06133i	−0.378017	+	0.925799i	$0.623394\pi$
$444$	−55.4532			−2.63169
$445$	1.29261			0.0612756
$446$		0			0
$447$	−10.9813	−	19.0202i	−0.519399	−	0.899625i
$448$	−8.00000			−0.377964
$449$	−1.07469			−0.0507179			−0.0253589	−	0.999678i	$-0.508073\pi$
$449$	−1.07469			−0.0507179			−0.0253589	+	0.999678i	$0.508073\pi$
$450$		0			0
$451$	−2.07108	+	3.58722i	−0.0975236	+	0.168916i
$452$	−11.1222	−	19.2642i	−0.523143	−	0.906110i
$453$	−6.37690	+	11.0451i	−0.299613	+	0.518945i
$454$		0			0
$455$	−2.00000			−0.0937614
$456$		0			0
$457$	−9.30168			−0.435114			−0.217557	−	0.976048i	$-0.569809\pi$
$457$	−9.30168			−0.435114			−0.217557	+	0.976048i	$0.569809\pi$
$458$		0			0
$459$	−38.7549	+	67.1254i	−1.80892	+	3.13315i
$460$	−1.70739	−	2.95729i	−0.0796074	−	0.137884i
$461$	10.5752	−	18.3168i	0.492537	−	0.853099i	−0.507426	−	0.861695i	$-0.669403\pi$
$461$	10.5752	−	18.3168i	0.492537	−	0.853099i	0.999963	+	0.00859603i	$0.00273624\pi$
$462$		0			0
$463$	2.52867			0.117517			0.0587587	−	0.998272i	$-0.481286\pi$
$463$	2.52867			0.117517			0.0587587	+	0.998272i	$0.481286\pi$
$464$	30.5671			1.41904
$465$	−12.2029	−	21.1360i	−0.565894	−	0.980157i
$466$		0			0
$467$	−0.659914			−0.0305372			−0.0152686	−	0.999883i	$-0.504860\pi$
$467$	−0.659914			−0.0305372			−0.0152686	+	0.999883i	$0.504860\pi$
$468$	−32.1131			−1.48443
$469$	5.34916	+	9.26501i	0.247001	+	0.427819i
$470$		0			0
$471$	−29.8259	−	51.6601i	−1.37431	−	2.38037i
$472$		0			0
$473$	16.1131	−	27.9087i	0.740881	−	1.28324i
$474$		0			0
$475$	3.86783	+	2.00994i	0.177468	+	0.0922226i
$476$	−9.28354			−0.425510
$477$	−25.4864	+	44.1437i	−1.16694	+	2.02120i
$478$		0			0
$479$	0.711926	+	1.23309i	0.0325287	+	0.0563414i	0.881831	−	0.471565i	$-0.156311\pi$
$479$	0.711926	+	1.23309i	0.0325287	+	0.0563414i	−0.849303	+	0.527906i	$0.822977\pi$
$480$		0			0
$481$	−8.34916	−	14.4612i	−0.380689	−	0.659372i
$482$		0			0
$483$	5.67004			0.257996
$484$	5.22699	+	9.05341i	0.237590	+	0.411519i
$485$	0.386505	+	0.669446i	0.0175503	+	0.0303980i
$486$		0			0
$487$	29.5015			1.33684			0.668419	−	0.743785i	$-0.266971\pi$
$487$	29.5015			1.33684			0.668419	+	0.743785i	$0.266971\pi$
$488$		0			0
$489$	17.1842	−	29.7639i	0.777095	−	1.34597i
$490$		0			0
$491$	−15.1418	+	26.2263i	−0.683338	+	1.18358i	0.290617	+	0.956839i	$0.406139\pi$
$491$	−15.1418	+	26.2263i	−0.683338	+	1.18358i	−0.973956	+	0.226738i	$0.927194\pi$
$492$	−3.41478	+	5.91457i	−0.153950	+	0.266649i
$493$	35.4713			1.59755
$494$		0			0
$495$	32.3401			1.45358
$496$	14.6983	−	25.4582i	0.659974	−	1.14311i
$497$	5.01414	−	8.68474i	0.224915	−	0.389564i
$498$		0			0
$499$	7.76940	−	13.4570i	0.347806	−	0.602418i	−0.638053	−	0.769992i	$-0.720260\pi$
$499$	7.76940	−	13.4570i	0.347806	−	0.602418i	0.985859	+	0.167574i	$0.0535934\pi$
$500$	−1.00000	−	1.73205i	−0.0447214	−	0.0774597i
$501$	−6.82956			−0.305122
$502$		0			0
$503$	21.6231	+	37.4523i	0.964126	+	1.66992i	0.711945	+	0.702236i	$0.247815\pi$
$503$	21.6231	+	37.4523i	0.964126	+	1.66992i	0.252182	+	0.967680i	$0.418852\pi$
$504$		0			0
$505$	−6.96265			−0.309834
$506$		0			0
$507$	14.9440	+	25.8837i	0.663685	+	1.14954i
$508$	9.57615	−	16.5864i	0.424873	−	0.735901i
$509$	−13.6418	−	23.6282i	−0.604661	−	1.04730i	−0.992105	−	0.125410i	$-0.959975\pi$
$509$	−13.6418	−	23.6282i	−0.604661	−	1.04730i	0.387444	−	0.921893i	$-0.373358\pi$
$510$		0			0
$511$	−2.36783	+	4.10120i	−0.104747	+	0.181427i
$512$		0			0
$513$	−61.3593	+	39.1520i	−2.70908	+	1.72860i
$514$		0			0
$515$	8.36783	−	14.4935i	0.368731	−	0.638660i
$516$	26.5671	−	46.0155i	1.16955	−	2.02572i
$517$	−26.9440	−	46.6683i	−1.18499	−	2.05247i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	25.3310			1.10977			0.554886	−	0.831926i	$-0.312762\pi$
$521$	25.3310			1.10977			0.554886	+	0.831926i	$0.312762\pi$
$522$		0			0
$523$	6.10349	+	10.5716i	0.266887	+	0.462262i	0.968056	−	0.250733i	$-0.0806716\pi$
$523$	6.10349	+	10.5716i	0.266887	+	0.462262i	−0.701169	+	0.712995i	$0.747338\pi$
$524$	−25.3966			−1.10946
$525$	3.32088			0.144935
$526$		0			0
$527$	17.0565	−	29.5428i	0.742995	−	1.28690i
$528$	26.7549	+	46.3408i	1.16436	+	2.01672i
$529$	10.0424	−	17.3940i	0.436627	−	0.756259i
$530$		0			0
$531$	29.5369			1.28179
$532$	−7.73566	−	4.01989i	−0.335384	−	0.174284i
$533$	−2.05655			−0.0890790
$534$		0			0
$535$	−4.46719	+	7.73740i	−0.193133	+	0.334517i
$536$		0			0
$537$	−2.39611	+	4.15018i	−0.103400	+	0.179093i
$538$		0			0
$539$	−4.02827			−0.173510
$540$	33.3966			1.43716
$541$	1.42892	+	2.47495i	0.0614339	+	0.106407i	0.895107	−	0.445852i	$-0.147099\pi$
$541$	1.42892	+	2.47495i	0.0614339	+	0.106407i	−0.833673	+	0.552259i	$0.813766\pi$
$542$		0			0
$543$	−75.3785			−3.23480
$544$		0			0
$545$	4.04241	+	7.00166i	0.173158	+	0.299918i
$546$		0			0
$547$	11.2594	+	19.5019i	0.481417	+	0.833839i	0.999773	−	0.0213262i	$-0.00678887\pi$
$547$	11.2594	+	19.5019i	0.481417	+	0.833839i	−0.518355	+	0.855165i	$0.673456\pi$
$548$	7.57615	−	13.1223i	0.323637	−	0.560556i
$549$	44.0056	−	76.2199i	1.87811	−	3.25299i
$550$		0			0
$551$	29.5571	+	15.3595i	1.25917	+	0.654338i
$552$		0			0
$553$	−0.693252	+	1.20075i	−0.0294801	+	0.0510610i
$554$		0			0
$555$	13.8633	+	24.0119i	0.588464	+	1.01925i
$556$	−9.47133	+	16.4048i	−0.401674	+	0.695719i
$557$	13.4016	+	23.2122i	0.567843	+	0.983532i	0.996779	+	0.0801977i	$0.0255552\pi$
$557$	13.4016	+	23.2122i	0.567843	+	0.983532i	−0.428936	+	0.903335i	$0.641112\pi$
$558$		0			0
$559$	16.0000			0.676728
$560$	2.00000	+	3.46410i	0.0845154	+	0.146385i
$561$	31.0475	+	53.7758i	1.31083	+	2.27042i
$562$		0			0
$563$	−41.2280			−1.73755			−0.868777	−	0.495203i	$-0.835094\pi$
$563$	−41.2280			−1.73755			−0.868777	+	0.495203i	$0.835094\pi$
$564$	−44.4249	−	76.9462i	−1.87063	−	3.24002i
$565$	−5.56108	+	9.63208i	−0.233957	+	0.405225i
$566$		0			0
$567$	−15.6842	+	27.1658i	−0.658674	+	1.14086i
$568$		0			0
$569$	5.25526			0.220312			0.110156	−	0.993914i	$-0.464865\pi$
$569$	5.25526			0.220312			0.110156	+	0.993914i	$0.464865\pi$
$570$		0			0
$571$	18.3966			0.769875			0.384938	−	0.922943i	$-0.374223\pi$
$571$	18.3966			0.769875			0.384938	+	0.922943i	$0.374223\pi$
$572$	−8.05655	+	13.9543i	−0.336861	+	0.583461i
$573$	−20.6140	+	35.7045i	−0.861163	+	1.49158i
$574$		0			0
$575$	−0.853695	+	1.47864i	−0.0356015	+	0.0616637i
$576$	32.1131	+	55.6215i	1.33805	+	2.31756i
$577$	−4.69832			−0.195593			−0.0977967	−	0.995206i	$-0.531180\pi$
$577$	−4.69832			−0.195593			−0.0977967	+	0.995206i	$0.531180\pi$
$578$		0			0
$579$	−12.7038	−	22.0036i	−0.527951	−	0.914438i
$580$	−7.64177	−	13.2359i	−0.317307	−	0.549592i
$581$		0			0
$582$		0			0
$583$	12.7881	+	22.1496i	0.529628	+	0.917342i
$584$		0			0
$585$	8.02827	+	13.9054i	0.331928	+	0.574917i
$586$		0			0
$587$	−4.29261	+	7.43502i	−0.177175	+	0.306876i	−0.940912	−	0.338652i	$-0.890029\pi$
$587$	−4.29261	+	7.43502i	−0.177175	+	0.306876i	0.763737	+	0.645528i	$0.223363\pi$
$588$	−6.64177			−0.273902
$589$	27.0051	−	17.2313i	1.11272	−	0.710005i
$590$		0			0
$591$	−22.5424	+	39.0446i	−0.927271	+	1.60608i
$592$	−16.6983	+	28.9223i	−0.686297	+	1.18870i
$593$	13.6514	+	23.6449i	0.560595	+	0.970978i	0.997445	+	0.0714439i	$0.0227607\pi$
$593$	13.6514	+	23.6449i	0.560595	+	0.970978i	−0.436850	+	0.899534i	$0.643906\pi$
$594$		0			0
$595$	2.32088	+	4.01989i	0.0951470	+	0.164799i
$596$	−13.2270			−0.541799
$597$	71.9336			2.94405
$598$		0			0
$599$	10.8916	+	18.8648i	0.445017	+	0.770793i	0.998053	−	0.0623645i	$-0.0198641\pi$
$599$	10.8916	+	18.8648i	0.445017	+	0.770793i	−0.553036	+	0.833157i	$0.686531\pi$
$600$		0			0
$601$	34.3593			1.40154			0.700772	−	0.713385i	$-0.252839\pi$
$601$	34.3593			1.40154			0.700772	+	0.713385i	$0.252839\pi$
$602$		0			0
$603$	42.9445	−	74.3821i	1.74884	−	3.02907i
$604$	3.84049	+	6.65192i	0.156267	+	0.270663i
$605$	2.61350	−	4.52671i	0.106254	−	0.184037i
$606$		0			0
$607$	31.4713			1.27738			0.638691	−	0.769463i	$-0.279476\pi$
$607$	31.4713			1.27738			0.638691	+	0.769463i	$0.279476\pi$
$608$		0			0
$609$	25.3774			1.02835
$610$		0			0
$611$	13.3774	−	23.1704i	0.541193	−	0.937374i
$612$	37.2654	+	64.5456i	1.50636	+	2.60910i
$613$	−12.2967	+	21.2986i	−0.496661	+	0.860242i	−0.999993	−	0.00385133i	$-0.998774\pi$
$613$	−12.2967	+	21.2986i	−0.496661	+	0.860242i	0.503332	+	0.864093i	$0.332107\pi$
$614$		0			0
$615$	3.41478			0.137697
$616$		0			0
$617$	−4.09389	−	7.09083i	−0.164814	−	0.285466i	0.771775	−	0.635895i	$-0.219369\pi$
$617$	−4.09389	−	7.09083i	−0.164814	−	0.285466i	−0.936589	+	0.350429i	$0.886036\pi$
$618$		0			0
$619$	−11.9253			−0.479319			−0.239659	−	0.970857i	$-0.577036\pi$
$619$	−11.9253			−0.479319			−0.239659	+	0.970857i	$0.577036\pi$
$620$	−14.6983			−0.590299
$621$	−14.2553	−	24.6908i	−0.572044	−	0.990809i
$622$		0			0
$623$	0.646305	+	1.11943i	0.0258937	+	0.0448492i
$624$	−13.2835	+	23.0078i	−0.531767	+	0.921048i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	2.58522	+	58.2535i	0.103244	+	2.32642i
$628$	−35.9253			−1.43358
$629$	−19.3774	+	33.5627i	−0.772629	+	1.33823i
$630$		0			0
$631$	−15.4964	−	26.8405i	−0.616902	−	1.06850i	−0.990048	−	0.140732i	$-0.955054\pi$
$631$	−15.4964	−	26.8405i	−0.616902	−	1.06850i	0.373146	−	0.927773i	$-0.378279\pi$
$632$		0			0
$633$	11.6231	+	20.1318i	0.461977	+	0.800167i
$634$		0			0
$635$	−9.57615			−0.380018
$636$	21.0848	+	36.5200i	0.836068	+	1.44811i
$637$	−1.00000	−	1.73205i	−0.0396214	−	0.0686264i
$638$		0			0
$639$	−80.5097			−3.18492
$640$		0			0
$641$	13.4198	−	23.2438i	0.530052	−	0.918077i	−0.469333	−	0.883021i	$-0.655506\pi$
$641$	13.4198	−	23.2438i	0.530052	−	0.918077i	0.999385	−	0.0350558i	$-0.0111609\pi$
$642$		0			0
$643$	−3.03735	+	5.26084i	−0.119781	+	0.207467i	−0.919681	−	0.392667i	$-0.871553\pi$
$643$	−3.03735	+	5.26084i	−0.119781	+	0.207467i	0.799900	+	0.600134i	$0.204886\pi$
$644$	1.70739	−	2.95729i	0.0672806	−	0.116533i
$645$	−26.5671			−1.04608
$646$		0			0
$647$	−26.8861			−1.05700			−0.528501	−	0.848933i	$-0.677246\pi$
$647$	−26.8861			−1.05700			−0.528501	+	0.848933i	$0.677246\pi$
$648$		0			0
$649$	7.41024	−	12.8349i	0.290877	−	0.503815i
$650$		0			0
$651$	12.2029	−	21.1360i	0.478268	−	0.828384i
$652$	−10.3492	−	17.9253i	−0.405304	−	0.702008i
$653$	−31.8770			−1.24744			−0.623722	−	0.781646i	$-0.714380\pi$
$653$	−31.8770			−1.24744			−0.623722	+	0.781646i	$0.714380\pi$
$654$		0			0
$655$	6.34916	+	10.9971i	0.248082	+	0.429691i
$656$	2.05655	+	3.56205i	0.0802947	+	0.139074i
$657$	38.0192			1.48327
$658$		0			0
$659$	3.99454	+	6.91874i	0.155605	+	0.269516i	0.933279	−	0.359152i	$-0.116934\pi$
$659$	3.99454	+	6.91874i	0.155605	+	0.269516i	−0.777674	+	0.628668i	$0.783601\pi$
$660$	13.3774	−	23.1704i	0.520716	−	0.901906i
$661$	2.21699	+	3.83994i	0.0862309	+	0.149356i	0.905915	−	0.423459i	$-0.139184\pi$
$661$	2.21699	+	3.83994i	0.0862309	+	0.149356i	−0.819684	+	0.572816i	$0.805851\pi$
$662$		0			0
$663$	−15.4148	+	26.6992i	−0.598660	+	1.03691i
$664$		0			0
$665$	0.193252	+	4.35461i	0.00749401	+	0.168865i
$666$		0			0
$667$	−6.52374	+	11.2994i	−0.252600	+	0.437516i
$668$	−2.05655	+	3.56205i	−0.0795702	+	0.137820i
$669$	−15.7886	−	27.3467i	−0.610423	−	1.05728i
$670$		0			0
$671$	−22.0803	−	38.2442i	−0.852400	−	1.47640i
$672$		0			0
$673$	10.6682			0.411228			0.205614	−	0.978633i	$-0.434081\pi$
$673$	10.6682			0.411228			0.205614	+	0.978633i	$0.434081\pi$
$674$		0			0
$675$	−8.34916	−	14.4612i	−0.321359	−	0.556611i
$676$	18.0000			0.692308
$677$	45.8314			1.76144			0.880722	−	0.473633i	$-0.157058\pi$
$677$	45.8314			1.76144			0.880722	+	0.473633i	$0.157058\pi$
$678$		0			0
$679$	−0.386505	+	0.669446i	−0.0148327	+	0.0256910i
$680$		0			0
$681$	−0.909714	+	1.57567i	−0.0348603	+	0.0603799i
$682$		0			0
$683$	−42.7367			−1.63528			−0.817638	−	0.575733i	$-0.804717\pi$
$683$	−42.7367			−1.63528			−0.817638	+	0.575733i	$0.804717\pi$
$684$	3.10297	+	69.9200i	0.118645	+	2.67346i
$685$	−7.57615			−0.289470
$686$		0			0
$687$	11.0433	−	19.1276i	0.421330	−	0.729764i
$688$	−16.0000	−	27.7128i	−0.609994	−	1.05654i
$689$	−6.34916	+	10.9971i	−0.241884	+	0.418955i
$690$		0			0
$691$	14.3665			0.546528			0.273264	−	0.961939i	$-0.411897\pi$
$691$	14.3665			0.546528			0.273264	+	0.961939i	$0.411897\pi$
$692$		0			0
$693$	16.1700	+	28.0073i	0.614249	+	1.06391i
$694$		0			0
$695$	9.47133			0.359268
$696$		0			0
$697$	2.38650	+	4.13355i	0.0903953	+	0.156569i
$698$		0			0
$699$	−23.1222	−	40.0488i	−0.874561	−	1.51478i
$700$	1.00000	−	1.73205i	0.0377964	−	0.0654654i
$701$	−12.5333	+	21.7084i	−0.473378	+	0.819914i	−0.999536	−	0.0304727i	$-0.990299\pi$
$701$	−12.5333	+	21.7084i	−0.473378	+	0.819914i	0.526158	+	0.850387i	$0.323632\pi$
$702$		0			0
$703$	−30.6796	+	19.5760i	−1.15710	+	0.738323i
$704$	32.2262			1.21457
$705$	−22.2125	+	38.4731i	−0.836569	+	1.44898i
$706$		0			0
$707$	−3.48133	−	6.02983i	−0.130929	−	0.226775i
$708$	12.2179	−	21.1621i	0.459177	−	0.795319i
$709$	5.30675	+	9.19156i	0.199299	+	0.345196i	0.948301	−	0.317371i	$-0.102800\pi$
$709$	5.30675	+	9.19156i	0.199299	+	0.345196i	−0.749002	+	0.662567i	$0.769467\pi$
$710$		0			0
$711$	11.1312			0.417454
$712$		0			0
$713$	6.27394	+	10.8668i	0.234961	+	0.406964i
$714$		0			0
$715$	8.05655			0.301298
$716$	1.44305	+	2.49944i	0.0539294	+	0.0934085i
$717$	−28.8693	+	50.0031i	−1.07814	+	1.86740i
$718$		0			0
$719$	3.74566	−	6.48768i	0.139690	−	0.241950i	−0.787689	−	0.616072i	$-0.788723\pi$
$719$	3.74566	−	6.48768i	0.139690	−	0.241950i	0.927379	+	0.374123i	$0.122056\pi$
$720$	16.0565	−	27.8108i	0.598392	−	1.03645i
$721$	16.7357			0.623269
$722$		0			0
$723$	73.4652			2.73220
$724$	−22.6983	+	39.3146i	−0.843576	+	1.46112i
$725$	−3.82088	+	6.61797i	−0.141904	+	0.245785i
$726$		0			0
$727$	7.73566	−	13.3986i	0.286900	−	0.496925i	−0.686168	−	0.727443i	$-0.740709\pi$
$727$	7.73566	−	13.3986i	0.286900	−	0.496925i	0.973068	+	0.230518i	$0.0740420\pi$
$728$		0			0
$729$	85.4742			3.16571
$730$		0			0
$731$	−18.5671	−	32.1591i	−0.686728	−	1.18945i
$732$	−36.4057	−	63.0565i	−1.34559	−	2.33064i
$733$	−15.8880			−0.586835			−0.293418	−	0.955984i	$-0.594793\pi$
$733$	−15.8880			−0.586835			−0.293418	+	0.955984i	$0.594793\pi$
$734$		0			0
$735$	1.66044	+	2.87597i	0.0612463	+	0.106082i
$736$		0			0
$737$	−21.5479	−	37.3220i	−0.793726	−	1.37477i
$738$		0			0
$739$	−22.1610	+	38.3839i	−0.815204	+	1.41198i	0.0939765	+	0.995574i	$0.470042\pi$
$739$	−22.1610	+	38.3839i	−0.815204	+	1.41198i	−0.909181	+	0.416401i	$0.863291\pi$
$740$	16.6983			0.613842
$741$	−24.4057	+	15.5727i	−0.896566	+	0.572079i
$742$		0			0
$743$	−10.4672	+	18.1297i	−0.384004	+	0.665114i	−0.991630	−	0.129109i	$-0.958788\pi$
$743$	−10.4672	+	18.1297i	−0.384004	+	0.665114i	0.607627	+	0.794223i	$0.292122\pi$
$744$		0			0
$745$	3.30675	+	5.72745i	0.121150	+	0.209838i
$746$		0			0
$747$		0			0
$748$	37.3966			1.36736
$749$	−8.93438			−0.326455
$750$		0			0
$751$	16.4964	+	28.5726i	0.601962	+	1.04263i	0.992524	+	0.122052i	$0.0389474\pi$
$751$	16.4964	+	28.5726i	0.601962	+	1.04263i	−0.390562	+	0.920577i	$0.627719\pi$
$752$	−53.5097			−1.95130
$753$	90.3876			3.29391
$754$		0			0
$755$	1.92024	−	3.32596i	0.0698848	−	0.121044i
$756$	16.6983	+	28.9223i	0.607312	+	1.05190i
$757$	2.96265	−	5.13147i	0.107679	−	0.186506i	−0.807150	−	0.590346i	$-0.798991\pi$
$757$	2.96265	−	5.13147i	0.107679	−	0.186506i	0.914830	+	0.403840i	$0.132325\pi$
$758$		0			0
$759$	−22.8405			−0.829057
$760$		0			0
$761$	−48.6055			−1.76195			−0.880974	−	0.473165i	$-0.843111\pi$
$761$	−48.6055			−1.76195			−0.880974	+	0.473165i	$0.843111\pi$
$762$		0			0
$763$	−4.04241	+	7.00166i	−0.146345	+	0.253477i
$764$	12.4148	+	21.5030i	0.449151	+	0.777952i
$765$	18.6327	−	32.2728i	0.673667	−	1.16682i
$766$		0			0
$767$	7.35823			0.265690
$768$	53.1342			1.91731
$769$	0.938916	+	1.62625i	0.0338582	+	0.0586441i	0.882458	−	0.470391i	$-0.155887\pi$
$769$	0.938916	+	1.62625i	0.0338582	+	0.0586441i	−0.848600	+	0.529035i	$0.822554\pi$
$770$		0			0
$771$	71.6156			2.57917
$772$	−15.3017			−0.550720
$773$	−11.3305	−	19.6250i	−0.407529	−	0.705861i	0.587083	−	0.809527i	$-0.300276\pi$
$773$	−11.3305	−	19.6250i	−0.407529	−	0.705861i	−0.994612	+	0.103665i	$0.966943\pi$
$774$		0			0
$775$	3.67458	+	6.36456i	0.131995	+	0.228622i
$776$		0			0
$777$	−13.8633	+	24.0119i	−0.497343	+	0.861423i
$778$		0			0
$779$	0.198716	+	4.47773i	0.00711975	+	0.160431i
$780$	13.2835			0.475627
$781$	−20.1983	+	34.9845i	−0.722753	+	1.25184i
$782$		0			0
$783$	−63.8023	−	110.509i	−2.28011	−	3.94927i
$784$	−2.00000	+	3.46410i	−0.0714286	+	0.123718i
$785$	8.98133	+	15.5561i	0.320557	+	0.555222i
$786$		0			0
$787$	8.52867			0.304014			0.152007	−	0.988379i	$-0.451426\pi$
$787$	8.52867			0.304014			0.152007	+	0.988379i	$0.451426\pi$
$788$	13.5761	+	23.5146i	0.483630	+	0.837672i
$789$	21.3027	+	36.8974i	0.758398	+	1.31358i
$790$		0			0
$791$	−11.1222			−0.395459
$792$		0			0
$793$	10.9627	−	18.9879i	0.389295	−	0.674279i
$794$		0			0
$795$	10.5424	−	18.2600i	0.373901	−	0.647615i
$796$	21.6610	−	37.5179i	0.767753	−	1.32979i
$797$	−5.18964			−0.183827			−0.0919133	−	0.995767i	$-0.529298\pi$
$797$	−5.18964			−0.183827			−0.0919133	+	0.995767i	$0.529298\pi$
$798$		0			0
$799$	−62.0950			−2.19676
$800$		0			0
$801$	5.18872	−	8.98712i	0.183334	−	0.317544i
$802$		0			0
$803$	9.53827	−	16.5208i	0.336598	−	0.583006i
$804$	−35.5279	−	61.5361i	−1.25297	−	2.17021i
$805$	−1.70739			−0.0601776
$806$		0			0
$807$	−10.0716	−	17.4445i	−0.354538	−	0.614077i
$808$		0			0
$809$	54.5207			1.91684			0.958422	−	0.285354i	$-0.0921113\pi$
$809$	54.5207			1.91684			0.958422	+	0.285354i	$0.0921113\pi$
$810$		0			0
$811$	−23.8780	−	41.3578i	−0.838469	−	1.45227i	−0.891175	−	0.453660i	$-0.850118\pi$
$811$	−23.8780	−	41.3578i	−0.838469	−	1.45227i	0.0527062	−	0.998610i	$-0.483215\pi$
$812$	7.64177	−	13.2359i	0.268174	−	0.464490i
$813$	−16.9193	−	29.3051i	−0.593386	−	1.02778i
$814$		0			0
$815$	−5.17458	+	8.96263i	−0.181258	+	0.313947i
$816$	61.6591			2.15850
$817$	−1.54602	−	34.8369i	−0.0540884	−	1.21879i
$818$		0			0
$819$	−8.02827	+	13.9054i	−0.280531	+	0.485893i
$820$	1.02827	−	1.78102i	0.0359089	−	0.0621960i
$821$	−19.3350	−	33.4892i	−0.674797	−	1.16878i	−0.976528	−	0.215390i	$-0.930898\pi$
$821$	−19.3350	−	33.4892i	−0.674797	−	1.16878i	0.301731	−	0.953393i	$-0.402435\pi$
$822$		0			0
$823$	15.6610	+	27.1256i	0.545907	+	0.945539i	0.998549	+	0.0538466i	$0.0171482\pi$
$823$	15.6610	+	27.1256i	0.545907	+	0.945539i	−0.452642	+	0.891692i	$0.649518\pi$
$824$		0			0
$825$	−13.3774			−0.465742
$826$		0			0
$827$	23.4298	+	40.5817i	0.814735	+	1.41116i	0.909518	+	0.415665i	$0.136451\pi$
$827$	23.4298	+	40.5817i	0.814735	+	1.41116i	−0.0947822	+	0.995498i	$0.530215\pi$
$828$	−27.4148			−0.952729
$829$	−12.4540			−0.432545			−0.216272	−	0.976333i	$-0.569390\pi$
$829$	−12.4540			−0.432545			−0.216272	+	0.976333i	$0.569390\pi$
$830$		0			0
$831$	−45.7886	+	79.3082i	−1.58839	+	2.75117i
$832$	8.00000	+	13.8564i	0.277350	+	0.480384i
$833$	−2.32088	+	4.01989i	−0.0804139	+	0.139281i
$834$		0			0
$835$	2.05655			0.0711698
$836$	31.1614	+	16.1932i	1.07774	+	0.560054i
$837$	−122.719			−4.24177
$838$		0			0
$839$	14.7549	−	25.5562i	0.509394	−	0.882297i	−0.490546	−	0.871415i	$-0.663203\pi$
$839$	14.7549	−	25.5562i	0.509394	−	0.882297i	0.999941	−	0.0108820i	$-0.00346392\pi$
$840$		0			0
$841$	−14.6983	+	25.4582i	−0.506839	+	0.877870i
$842$		0			0
$843$	−36.4358			−1.25492
$844$	14.0000			0.481900
$845$	−4.50000	−	7.79423i	−0.154805	−	0.268130i
$846$		0			0
$847$	5.22699			0.179602
$848$	25.3966			0.872124
$849$	−30.9855	−	53.6684i	−1.06342	−	1.84189i
$850$		0			0
$851$	−7.12763	−	12.3454i	−0.244332	−	0.423196i
$852$	−33.3027	+	57.6820i	−1.14093	+	1.97615i
$853$	3.01867	−	5.22850i	0.103357	−	0.179020i	−0.809709	−	0.586832i	$-0.800375\pi$
$853$	3.01867	−	5.22850i	0.103357	−	0.179020i	0.913066	+	0.407812i	$0.133708\pi$
$854$		0			0
$855$	29.5005	−	18.8236i	1.00890	−	0.643755i
$856$		0			0
$857$	−6.54787	+	11.3413i	−0.223671	+	0.387410i	−0.955920	−	0.293627i	$-0.905137\pi$
$857$	−6.54787	+	11.3413i	−0.223671	+	0.387410i	0.732249	+	0.681037i	$0.238471\pi$
$858$		0			0
$859$	−4.25073	−	7.36248i	−0.145033	−	0.251204i	0.784352	−	0.620316i	$-0.212995\pi$
$859$	−4.25073	−	7.36248i	−0.145033	−	0.251204i	−0.929385	+	0.369111i	$0.879662\pi$
$860$	−8.00000	+	13.8564i	−0.272798	+	0.472500i
$861$	1.70739	+	2.95729i	0.0581877	+	0.100784i
$862$		0			0
$863$	−8.05655			−0.274248			−0.137124	−	0.990554i	$-0.543786\pi$
$863$	−8.05655			−0.274248			−0.137124	+	0.990554i	$0.543786\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	15.0968			0.512714
$868$	−7.34916	−	12.7291i	−0.249447	−	0.432054i
$869$	2.79261	−	4.83694i	0.0947328	−	0.164082i
$870$		0			0
$871$	10.6983	−	18.5300i	0.362499	−	0.627866i
$872$		0			0
$873$	6.20593			0.210039
$874$		0			0
$875$	−1.00000			−0.0338062
$876$	15.7266	−	27.2393i	0.531352	−	0.920329i
$877$	−0.0373465	+	0.0646860i	−0.00126110	+	0.00218429i	−0.866655	−	0.498907i	$-0.833735\pi$
$877$	−0.0373465	+	0.0646860i	−0.00126110	+	0.00218429i	0.865394	+	0.501092i	$0.167068\pi$
$878$		0			0
$879$	15.6646	−	27.1318i	0.528353	−	0.915134i
$880$	−8.05655	−	13.9543i	−0.271586	−	0.470401i
$881$	−18.3665			−0.618783			−0.309392	−	0.950935i	$-0.600125\pi$
$881$	−18.3665			−0.618783			−0.309392	+	0.950935i	$0.600125\pi$
$882$		0			0
$883$	17.7881	+	30.8098i	0.598616	+	1.03683i	0.993026	+	0.117899i	$0.0376159\pi$
$883$	17.7881	+	30.8098i	0.598616	+	1.03683i	−0.394409	+	0.918935i	$0.629051\pi$
$884$	9.28354	+	16.0796i	0.312239	+	0.540814i
$885$	−12.2179			−0.410701
$886$		0			0
$887$	−7.43345	−	12.8751i	−0.249591	−	0.432304i	0.713821	−	0.700328i	$-0.246963\pi$
$887$	−7.43345	−	12.8751i	−0.249591	−	0.432304i	−0.963412	+	0.268024i	$0.913629\pi$
$888$		0			0
$889$	−4.78807	−	8.29319i	−0.160587	−	0.278145i
$890$		0			0
$891$	63.1802	−	109.431i	2.11662	−	3.66609i
$892$	−19.0173			−0.636748
$893$	−51.7417	−	26.8879i	−1.73147	−	0.899769i
$894$		0			0
$895$	0.721526	−	1.24972i	0.0241180	−	0.0417735i
$896$		0			0
$897$	−5.67004	−	9.82080i	−0.189317	−	0.327907i
$898$		0			0
$899$	28.0803	+	48.6365i	0.936530	+	1.62212i
$900$	−16.0565			−0.535218
$901$	29.4713			0.981832
$902$		0			0
$903$	−13.2835	−	23.0078i	−0.442048	−	0.765650i
$904$		0			0
$905$	22.6983			0.754518
$906$		0			0
$907$	26.5237	−	45.9405i	0.880706	−	1.52543i	0.0301491	−	0.999545i	$-0.490402\pi$
$907$	26.5237	−	45.9405i	0.880706	−	1.52543i	0.850557	−	0.525883i	$-0.176265\pi$
$908$	0.547875	+	0.948947i	0.0181819	+	0.0314919i
$909$	−27.9490	+	48.4092i	−0.927011	+	1.60563i
$910$		0			0
$911$	−0.0848216			−0.00281026			−0.00140513	−	0.999999i	$-0.500447\pi$
$911$	−0.0848216			−0.00281026			−0.00140513	+	0.999999i	$0.500447\pi$
$912$	51.3785	+	26.6992i	1.70131	+	0.884098i
$913$		0			0
$914$		0			0
$915$	−18.2029	+	31.5283i	−0.601768	+	1.04229i
$916$	−6.65084	−	11.5196i	−0.219750	−	0.380618i
$917$	−6.34916	+	10.9971i	−0.209668	+	0.363155i
$918$		0			0
$919$	−52.9354			−1.74618			−0.873089	−	0.487560i	$-0.837887\pi$
$919$	−52.9354			−1.74618			−0.873089	+	0.487560i	$0.837887\pi$
$920$		0			0
$921$	−36.4057	−	63.0565i	−1.19961	−	2.07778i
$922$		0			0
$923$	−20.0565			−0.660169
$924$	26.7549			0.880170
$925$	−4.17458	−	7.23058i	−0.137259	−	0.237740i
$926$		0			0
$927$	−67.1792	−	116.358i	−2.20646	−	3.82169i
$928$		0			0
$929$	−26.6035	+	46.0786i	−0.872832	+	1.51179i	−0.0137783	+	0.999905i	$0.504386\pi$
$929$	−26.6035	+	46.0786i	−0.872832	+	1.51179i	−0.859054	+	0.511885i	$0.828947\pi$
$930$		0			0
$931$	−3.67458	+	2.34467i	−0.120429	+	0.0768434i
$932$	−27.8506			−0.912277
$933$	−11.3401	+	19.6416i	−0.371258	+	0.643037i
$934$		0			0
$935$	−9.34916	−	16.1932i	−0.305750	−	0.529575i
$936$		0			0
$937$	18.5761	+	32.1748i	0.606856	+	1.05111i	0.991755	+	0.128147i	$0.0409030\pi$
$937$	18.5761	+	32.1748i	0.606856	+	1.05111i	−0.384899	+	0.922959i	$0.625764\pi$
$938$		0			0
$939$	−48.6874			−1.58885
$940$	13.3774	+	23.1704i	0.436324	+	0.755735i
$941$	−4.64084	−	8.03817i	−0.151287	−	0.262037i	0.780414	−	0.625263i	$-0.215008\pi$
$941$	−4.64084	−	8.03817i	−0.151287	−	0.262037i	−0.931701	+	0.363226i	$0.881675\pi$
$942$		0			0
$943$	−1.75566			−0.0571723
$944$	−7.35823	−	12.7448i	−0.239490	−	0.414809i
$945$	8.34916	−	14.4612i	0.271598	−	0.470422i
$946$		0			0
$947$	13.8355	−	23.9639i	0.449595	−	0.778721i	−0.548765	−	0.835977i	$-0.684902\pi$
$947$	13.8355	−	23.9639i	0.449595	−	0.778721i	0.998360	+	0.0572556i	$0.0182350\pi$
$948$	4.60442	−	7.97509i	0.149545	−	0.259019i
$949$	9.47133			0.307452
$950$		0			0
$951$	−51.1907			−1.65997
$952$		0			0
$953$	−13.5520	+	23.4728i	−0.438993	+	0.760358i	−0.997612	−	0.0690665i	$-0.977998\pi$
$953$	−13.5520	+	23.4728i	−0.438993	+	0.760358i	0.558619	+	0.829424i	$0.311331\pi$
$954$		0			0
$955$	6.20739	−	10.7515i	0.200866	−	0.347911i
$956$	17.3865	+	30.1143i	0.562320	+	0.973966i
$957$	−102.227			−3.30454
$958$		0			0
$959$	−3.78807	−	6.56114i	−0.122323	−	0.211870i
$960$	−13.2835	−	23.0078i	−0.428724	−	0.742572i
$961$	23.0101			0.742262
$962$		0			0
$963$	35.8638	+	62.1180i	1.15570	+	2.00172i
$964$	22.1222	−	38.3167i	0.712507	−	1.23410i
$965$	3.82542	+	6.62582i	0.123145	+	0.213293i
$966$		0			0
$967$	27.0475	−	46.8476i	0.869788	−	1.50652i	0.00757521	−	0.999971i	$-0.497589\pi$
$967$	27.0475	−	46.8476i	0.869788	−	1.50652i	0.862213	−	0.506546i	$-0.169078\pi$
$968$		0			0
$969$	59.6218	+	30.9829i	1.91533	+	0.995313i
$970$		0			0
$971$	9.96265	−	17.2558i	0.319717	−	0.553766i	−0.660712	−	0.750639i	$-0.729746\pi$
$971$	9.96265	−	17.2558i	0.319717	−	0.553766i	0.980429	+	0.196874i	$0.0630789\pi$
$972$	54.0757	−	93.6619i	1.73448	−	3.00421i
$973$	4.73566	+	8.20241i	0.151818	+	0.262957i
$974$		0			0
$975$	−3.32088	−	5.75194i	−0.106353	−	0.184210i
$976$	−43.8506			−1.40362
$977$	−42.5671			−1.36184			−0.680921	−	0.732357i	$-0.738420\pi$
$977$	−42.5671			−1.36184			−0.680921	+	0.732357i	$0.738420\pi$
$978$		0			0
$979$	−2.60349	−	4.50939i	−0.0832081	−	0.144121i
$980$	2.00000			0.0638877
$981$	64.9072			2.07233
$982$		0			0
$983$	1.43345	−	2.48281i	0.0457200	−	0.0791894i	−0.842260	−	0.539072i	$-0.818775\pi$
$983$	1.43345	−	2.48281i	0.0457200	−	0.0791894i	0.887980	+	0.459882i	$0.152108\pi$
$984$		0			0
$985$	6.78807	−	11.7573i	0.216286	−	0.374618i
$986$		0			0
$987$	−44.4249			−1.41406
$988$	0.773010	+	17.4185i	0.0245927	+	0.554155i
$989$	13.6591			0.434335
$990$		0			0
$991$	5.08482	−	8.80717i	0.161525	−	0.279769i	−0.773891	−	0.633319i	$-0.781692\pi$
$991$	5.08482	−	8.80717i	0.161525	−	0.279769i	0.935416	+	0.353550i	$0.115026\pi$
$992$		0			0
$993$	13.8013	−	23.9045i	0.437970	−	0.758587i
$994$		0			0
$995$	−21.6610			−0.686699
$996$		0			0
$997$	3.42385	+	5.93028i	0.108434	+	0.187814i	0.915136	−	0.403145i	$-0.132083\pi$
$997$	3.42385	+	5.93028i	0.108434	+	0.187814i	−0.806702	+	0.590959i	$0.798750\pi$
$998$		0			0
$999$	139.417			4.41096

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	665.2.i.d.106.1	✓	6
19.7	even	3	inner	665.2.i.d.596.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
665.2.i.d.106.1	✓	6	1.1	even	1	trivial
665.2.i.d.596.1	yes	6	19.7	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 665 = 5 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	665.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.66044 + 2.87597i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{7} +(-4.01414 - 6.95269i) q^{9} +O(q^{10})\)	\(q+(-1.66044 + 2.87597i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{7} +(-4.01414 - 6.95269i) q^{9} -4.02827 q^{11} -6.64177 q^{12} +(-1.00000 - 1.73205i) q^{13} +(1.66044 + 2.87597i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(-2.32088 + 4.01989i) q^{17} +(-3.67458 + 2.34467i) q^{19} +2.00000 q^{20} +(-1.66044 + 2.87597i) q^{21} +(-0.853695 - 1.47864i) q^{23} +(-0.500000 - 0.866025i) q^{25} +16.6983 q^{27} +(1.00000 + 1.73205i) q^{28} +(-3.82088 - 6.61797i) q^{29} -7.34916 q^{31} +(6.68872 - 11.5852i) q^{33} +(0.500000 - 0.866025i) q^{35} +(8.02827 - 13.9054i) q^{36} +8.34916 q^{37} +6.64177 q^{39} +(0.514137 - 0.890511i) q^{41} +(-4.00000 + 6.92820i) q^{43} +(-4.02827 - 6.97717i) q^{44} -8.02827 q^{45} +(6.68872 + 11.5852i) q^{47} +(-6.64177 - 11.5039i) q^{48} +1.00000 q^{49} +(-7.70739 - 13.3496i) q^{51} +(2.00000 - 3.46410i) q^{52} +(-3.17458 - 5.49853i) q^{53} +(-2.01414 + 3.48859i) q^{55} +(-0.641769 - 14.4612i) q^{57} +(-1.83956 + 3.18621i) q^{59} +(-3.32088 + 5.75194i) q^{60} +(5.48133 + 9.49394i) q^{61} +(-4.01414 - 6.95269i) q^{63} -8.00000 q^{64} -2.00000 q^{65} +(5.34916 + 9.26501i) q^{67} -9.28354 q^{68} +5.67004 q^{69} +(5.01414 - 8.68474i) q^{71} +(-2.36783 + 4.10120i) q^{73} +3.32088 q^{75} +(-7.73566 - 4.01989i) q^{76} -4.02827 q^{77} +(-0.693252 + 1.20075i) q^{79} +(2.00000 + 3.46410i) q^{80} +(-15.6842 + 27.1658i) q^{81} -6.64177 q^{84} +(2.32088 + 4.01989i) q^{85} +25.3774 q^{87} +(0.646305 + 1.11943i) q^{89} +(-1.00000 - 1.73205i) q^{91} +(1.70739 - 2.95729i) q^{92} +(12.2029 - 21.1360i) q^{93} +(0.193252 + 4.35461i) q^{95} +(-0.386505 + 0.669446i) q^{97} +(16.1700 + 28.0073i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{7} - 11 q^{9}+O(q^{10}) \) 6 * q - 2 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^7 - 11 * q^9	\( 6 q - 2 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{7} - 11 q^{9} + 2 q^{11} - 8 q^{12} - 6 q^{13} + 2 q^{15} - 12 q^{16} + 2 q^{17} - q^{19} + 12 q^{20} - 2 q^{21} - 3 q^{25} + 16 q^{27} + 6 q^{28} - 7 q^{29} - 2 q^{31} + 6 q^{33} + 3 q^{35} + 22 q^{36} + 8 q^{37} + 8 q^{39} - 10 q^{41} - 24 q^{43} + 2 q^{44} - 22 q^{45} + 6 q^{47} - 8 q^{48} + 6 q^{49} - 36 q^{51} + 12 q^{52} + 2 q^{53} + q^{55} + 28 q^{57} - 19 q^{59} - 4 q^{60} + 9 q^{61} - 11 q^{63} - 48 q^{64} - 12 q^{65} - 10 q^{67} + 8 q^{68} - 24 q^{69} + 17 q^{71} + 4 q^{73} + 4 q^{75} - 10 q^{76} + 2 q^{77} - 7 q^{79} + 12 q^{80} - 23 q^{81} - 8 q^{84} - 2 q^{85} + 84 q^{87} + 9 q^{89} - 6 q^{91} + 26 q^{93} + 4 q^{95} - 8 q^{97} + 39 q^{99}+O(q^{100}) \) 6 * q - 2 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^7 - 11 * q^9 + 2 * q^11 - 8 * q^12 - 6 * q^13 + 2 * q^15 - 12 * q^16 + 2 * q^17 - q^19 + 12 * q^20 - 2 * q^21 - 3 * q^25 + 16 * q^27 + 6 * q^28 - 7 * q^29 - 2 * q^31 + 6 * q^33 + 3 * q^35 + 22 * q^36 + 8 * q^37 + 8 * q^39 - 10 * q^41 - 24 * q^43 + 2 * q^44 - 22 * q^45 + 6 * q^47 - 8 * q^48 + 6 * q^49 - 36 * q^51 + 12 * q^52 + 2 * q^53 + q^55 + 28 * q^57 - 19 * q^59 - 4 * q^60 + 9 * q^61 - 11 * q^63 - 48 * q^64 - 12 * q^65 - 10 * q^67 + 8 * q^68 - 24 * q^69 + 17 * q^71 + 4 * q^73 + 4 * q^75 - 10 * q^76 + 2 * q^77 - 7 * q^79 + 12 * q^80 - 23 * q^81 - 8 * q^84 - 2 * q^85 + 84 * q^87 + 9 * q^89 - 6 * q^91 + 26 * q^93 + 4 * q^95 - 8 * q^97 + 39 * q^99

Introduction

L-functions

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