LMFDB - Embedded newform 441.2.h.b.373.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(214,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("441.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.h (of order $3$, degree $2$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.3
Root			$0.500000 + 0.224437i$ of defining polynomial
Character	$\chi$	$=$	441.373
Dual form			441.2.h.b.214.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.69963 q^{2} +(-1.29418 + 1.15113i) q^{3} +0.888736 q^{4} +(-1.79418 - 3.10761i) q^{5} +(-2.19963 + 1.95649i) q^{6} -1.88874 q^{8} +(0.349814 - 2.97954i) q^{9} +O(q^{10})$	\(q+1.69963 q^{2} +(-1.29418 + 1.15113i) q^{3} +0.888736 q^{4} +(-1.79418 - 3.10761i) q^{5} +(-2.19963 + 1.95649i) q^{6} -1.88874 q^{8} +(0.349814 - 2.97954i) q^{9} +(-3.04944 - 5.28179i) q^{10} +(1.40545 - 2.43430i) q^{11} +(-1.15019 + 1.02305i) q^{12} +(0.500000 - 0.866025i) q^{13} +(5.89926 + 1.95649i) q^{15} -4.98762 q^{16} +(-2.05563 - 3.56046i) q^{17} +(0.594554 - 5.06410i) q^{18} +(-0.444368 + 0.769668i) q^{19} +(-1.59455 - 2.76185i) q^{20} +(2.38874 - 4.13741i) q^{22} +(-2.93818 - 5.08907i) q^{23} +(2.44437 - 2.17417i) q^{24} +(-3.93818 + 6.82112i) q^{25} +(0.849814 - 1.47192i) q^{26} +(2.97710 + 4.25874i) q^{27} +(0.849814 + 1.47192i) q^{29} +(10.0265 + 3.32530i) q^{30} +6.98762 q^{31} -4.69963 q^{32} +(0.983290 + 4.76828i) q^{33} +(-3.49381 - 6.05146i) q^{34} +(0.310892 - 2.64802i) q^{36} +(-2.38255 + 4.12669i) q^{37} +(-0.755260 + 1.30815i) q^{38} +(0.349814 + 1.69636i) q^{39} +(3.38874 + 5.86946i) q^{40} +(-2.70582 + 4.68661i) q^{41} +(-2.60507 - 4.51212i) q^{43} +(1.24907 - 2.16345i) q^{44} +(-9.88688 + 4.25874i) q^{45} +(-4.99381 - 8.64953i) q^{46} +2.66621 q^{47} +(6.45489 - 5.74138i) q^{48} +(-6.69344 + 11.5934i) q^{50} +(6.75890 + 2.24159i) q^{51} +(0.444368 - 0.769668i) q^{52} +(0.0618219 + 0.107079i) q^{53} +(5.05996 + 7.23828i) q^{54} -10.0865 q^{55} +(-0.310892 - 1.50761i) q^{57} +(1.44437 + 2.50172i) q^{58} +8.87636 q^{59} +(5.24288 + 1.73880i) q^{60} -3.87636 q^{61} +11.8764 q^{62} +1.98762 q^{64} -3.58836 q^{65} +(1.67123 + 8.10430i) q^{66} +12.3090 q^{67} +(-1.82691 - 3.16431i) q^{68} +(9.66071 + 3.20397i) q^{69} -2.87636 q^{71} +(-0.660706 + 5.62755i) q^{72} +(-5.32072 - 9.21576i) q^{73} +(-4.04944 + 7.01384i) q^{74} +(-2.75526 - 13.3611i) q^{75} +(-0.394926 + 0.684031i) q^{76} +(0.594554 + 2.88318i) q^{78} -7.08650 q^{79} +(8.94870 + 15.4996i) q^{80} +(-8.75526 - 2.08457i) q^{81} +(-4.59888 + 7.96550i) q^{82} +(-2.05563 - 3.56046i) q^{83} +(-7.37636 + 12.7762i) q^{85} +(-4.42766 - 7.66893i) q^{86} +(-2.79418 - 0.926690i) q^{87} +(-2.65452 + 4.59776i) q^{88} +(4.80470 - 8.32199i) q^{89} +(-16.8040 + 7.23828i) q^{90} +(-2.61126 - 4.52284i) q^{92} +(-9.04325 + 8.04364i) q^{93} +4.53156 q^{94} +3.18911 q^{95} +(6.08217 - 5.40987i) q^{96} +(3.66071 + 6.34053i) q^{97} +(-6.76145 - 5.03913i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 2 q^{3} + 6 q^{4} - 5 q^{5} - q^{6} - 12 q^{8} - 4 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 - 2 * q^3 + 6 * q^4 - 5 * q^5 - q^6 - 12 * q^8 - 4 * q^9	$ 6 q - 2 q^{2} - 2 q^{3} + 6 q^{4} - 5 q^{5} - q^{6} - 12 q^{8} - 4 q^{9} + 2 q^{11} - 13 q^{12} + 3 q^{13} + 11 q^{15} + 6 q^{16} - 12 q^{17} + 10 q^{18} - 3 q^{19} - 16 q^{20} + 15 q^{22} + 15 q^{24} - 6 q^{25} - q^{26} + 7 q^{27} - q^{29} + 31 q^{30} + 6 q^{31} - 16 q^{32} + 13 q^{33} - 3 q^{34} - 11 q^{36} + 3 q^{37} + 8 q^{38} - 4 q^{39} + 21 q^{40} - 22 q^{41} + 3 q^{43} - 23 q^{44} + q^{45} - 12 q^{46} + 18 q^{47} + 14 q^{48} - 10 q^{50} - 12 q^{51} + 3 q^{52} + 18 q^{53} - 13 q^{54} + 12 q^{55} + 11 q^{57} + 9 q^{58} + 18 q^{59} - 17 q^{60} + 12 q^{61} + 36 q^{62} - 24 q^{64} - 10 q^{65} - 34 q^{66} + 6 q^{68} + 39 q^{69} + 18 q^{71} + 15 q^{72} + 3 q^{73} - 6 q^{74} - 4 q^{75} - 21 q^{76} + 10 q^{78} + 30 q^{79} + 11 q^{80} - 40 q^{81} + 9 q^{82} - 12 q^{83} - 9 q^{85} - 34 q^{86} - 11 q^{87} + 21 q^{88} - 2 q^{89} - 73 q^{90} - 15 q^{92} - 18 q^{93} - 48 q^{94} + 32 q^{95} + 7 q^{96} + 3 q^{97} - 46 q^{99}+O(q^{100}) $ 6 * q - 2 * q^2 - 2 * q^3 + 6 * q^4 - 5 * q^5 - q^6 - 12 * q^8 - 4 * q^9 + 2 * q^11 - 13 * q^12 + 3 * q^13 + 11 * q^15 + 6 * q^16 - 12 * q^17 + 10 * q^18 - 3 * q^19 - 16 * q^20 + 15 * q^22 + 15 * q^24 - 6 * q^25 - q^26 + 7 * q^27 - q^29 + 31 * q^30 + 6 * q^31 - 16 * q^32 + 13 * q^33 - 3 * q^34 - 11 * q^36 + 3 * q^37 + 8 * q^38 - 4 * q^39 + 21 * q^40 - 22 * q^41 + 3 * q^43 - 23 * q^44 + q^45 - 12 * q^46 + 18 * q^47 + 14 * q^48 - 10 * q^50 - 12 * q^51 + 3 * q^52 + 18 * q^53 - 13 * q^54 + 12 * q^55 + 11 * q^57 + 9 * q^58 + 18 * q^59 - 17 * q^60 + 12 * q^61 + 36 * q^62 - 24 * q^64 - 10 * q^65 - 34 * q^66 + 6 * q^68 + 39 * q^69 + 18 * q^71 + 15 * q^72 + 3 * q^73 - 6 * q^74 - 4 * q^75 - 21 * q^76 + 10 * q^78 + 30 * q^79 + 11 * q^80 - 40 * q^81 + 9 * q^82 - 12 * q^83 - 9 * q^85 - 34 * q^86 - 11 * q^87 + 21 * q^88 - 2 * q^89 - 73 * q^90 - 15 * q^92 - 18 * q^93 - 48 * q^94 + 32 * q^95 + 7 * q^96 + 3 * q^97 - 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.69963			1.20182			0.600909	−	0.799317i	$-0.294805\pi$
$2$	1.69963			1.20182			0.600909	+	0.799317i	$0.294805\pi$
$3$	−1.29418	+	1.15113i	−0.747196	+	0.664603i
$3$	−1.29418	+	1.15113i	−0.747196	+	0.664603i
$4$	0.888736			0.444368
$5$	−1.79418	−	3.10761i	−0.802383	−	1.38977i	−0.918044	−	0.396479i	$-0.870232\pi$
$5$	−1.79418	−	3.10761i	−0.802383	−	1.38977i	0.115661	−	0.993289i	$-0.463101\pi$
$6$	−2.19963	+	1.95649i	−0.897994	+	0.798733i
$7$		0			0
$7$		0			0
$8$	−1.88874			−0.667769
$9$	0.349814	−	2.97954i	0.116605	−	0.993178i
$10$	−3.04944	−	5.28179i	−0.964318	−	1.67025i
$11$	1.40545	−	2.43430i	0.423758	−	0.733970i	−0.572546	−	0.819873i	$-0.694044\pi$
$11$	1.40545	−	2.43430i	0.423758	−	0.733970i	0.996304	+	0.0859026i	$0.0273774\pi$
$12$	−1.15019	+	1.02305i	−0.332030	+	0.295328i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	−0.788320	−	0.615265i	$-0.789049\pi$
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	0.926995	+	0.375073i	$0.122382\pi$
$14$		0			0
$15$	5.89926	+	1.95649i	1.52318	+	0.505163i
$16$	−4.98762			−1.24691
$17$	−2.05563	−	3.56046i	−0.498564	−	0.863538i	0.501435	−	0.865196i	$-0.332806\pi$
$17$	−2.05563	−	3.56046i	−0.498564	−	0.863538i	−0.999999	+	0.00165734i	$0.999472\pi$
$18$	0.594554	−	5.06410i	0.140138	−	1.19362i
$19$	−0.444368	+	0.769668i	−0.101945	+	0.176574i	−0.912486	−	0.409108i	$-0.865840\pi$
$19$	−0.444368	+	0.769668i	−0.101945	+	0.176574i	0.810541	+	0.585682i	$0.199173\pi$
$20$	−1.59455	−	2.76185i	−0.356553	−	0.617568i
$21$		0			0
$22$	2.38874	−	4.13741i	0.509280	−	0.882099i
$23$	−2.93818	−	5.08907i	−0.612652	−	1.06115i	−0.990792	−	0.135396i	$-0.956769\pi$
$23$	−2.93818	−	5.08907i	−0.612652	−	1.06115i	0.378139	−	0.925749i	$-0.376564\pi$
$24$	2.44437	−	2.17417i	0.498955	−	0.443802i
$25$	−3.93818	+	6.82112i	−0.787636	+	1.36422i
$26$	0.849814	−	1.47192i	0.166662	−	0.288667i
$27$	2.97710	+	4.25874i	0.572943	+	0.819595i
$28$		0			0
$29$	0.849814	+	1.47192i	0.157807	+	0.273329i	0.934077	−	0.357071i	$-0.116224\pi$
$29$	0.849814	+	1.47192i	0.157807	+	0.273329i	−0.776271	+	0.630399i	$0.782891\pi$
$30$	10.0265	+	3.32530i	1.83059	+	0.607114i
$31$	6.98762			1.25501			0.627507	−	0.778611i	$-0.284075\pi$
$31$	6.98762			1.25501			0.627507	+	0.778611i	$0.284075\pi$
$32$	−4.69963			−0.830785
$33$	0.983290	+	4.76828i	0.171169	+	0.830051i
$34$	−3.49381	−	6.05146i	−0.599183	−	1.03782i
$35$		0			0
$36$	0.310892	−	2.64802i	0.0518154	−	0.441337i
$37$	−2.38255	+	4.12669i	−0.391688	+	0.678424i	−0.992672	−	0.120837i	$-0.961442\pi$
$37$	−2.38255	+	4.12669i	−0.391688	+	0.678424i	0.600984	+	0.799261i	$0.294775\pi$
$38$	−0.755260	+	1.30815i	−0.122519	+	0.212210i
$39$	0.349814	+	1.69636i	0.0560151	+	0.271635i
$40$	3.38874	+	5.86946i	0.535806	+	0.928044i
$41$	−2.70582	+	4.68661i	−0.422578	+	0.731926i	−0.996191	−	0.0872002i	$-0.972208\pi$
$41$	−2.70582	+	4.68661i	−0.422578	+	0.731926i	0.573613	+	0.819126i	$0.305541\pi$
$42$		0			0
$43$	−2.60507	−	4.51212i	−0.397270	−	0.688092i	0.596118	−	0.802897i	$-0.296709\pi$
$43$	−2.60507	−	4.51212i	−0.397270	−	0.688092i	−0.993388	+	0.114805i	$0.963376\pi$
$44$	1.24907	−	2.16345i	0.188304	−	0.326153i
$45$	−9.88688	+	4.25874i	−1.47385	+	0.634856i
$46$	−4.99381	−	8.64953i	−0.736297	−	1.27530i
$47$	2.66621			0.388906			0.194453	−	0.980912i	$-0.437707\pi$
$47$	2.66621			0.388906			0.194453	+	0.980912i	$0.437707\pi$
$48$	6.45489	−	5.74138i	0.931683	−	0.828697i
$49$		0			0
$50$	−6.69344	+	11.5934i	−0.946595	+	1.63955i
$51$	6.75890	+	2.24159i	0.946436	+	0.313885i
$52$	0.444368	−	0.769668i	0.0616227	−	0.106734i
$53$	0.0618219	+	0.107079i	0.00849190	+	0.0147084i	0.870240	−	0.492628i	$-0.163964\pi$
$53$	0.0618219	+	0.107079i	0.00849190	+	0.0147084i	−0.861748	+	0.507336i	$0.830630\pi$
$54$	5.05996	+	7.23828i	0.688574	+	0.985005i
$55$	−10.0865			−1.36006
$56$		0			0
$57$	−0.310892	−	1.50761i	−0.0411787	−	0.199688i
$58$	1.44437	+	2.50172i	0.189655	+	0.328492i
$59$	8.87636			1.15560			0.577802	−	0.816177i	$-0.303911\pi$
$59$	8.87636			1.15560			0.577802	+	0.816177i	$0.303911\pi$
$60$	5.24288	+	1.73880i	0.676853	+	0.224478i
$61$	−3.87636			−0.496317			−0.248158	−	0.968720i	$-0.579825\pi$
$61$	−3.87636			−0.496317			−0.248158	+	0.968720i	$0.579825\pi$
$62$	11.8764			1.50830
$63$		0			0
$64$	1.98762			0.248453
$65$	−3.58836			−0.445082
$66$	1.67123	+	8.10430i	0.205714	+	0.997571i
$67$	12.3090			1.50379			0.751894	−	0.659284i	$-0.229141\pi$
$67$	12.3090			1.50379			0.751894	+	0.659284i	$0.229141\pi$
$68$	−1.82691	−	3.16431i	−0.221546	−	0.383729i
$69$	9.66071	+	3.20397i	1.16301	+	0.385713i
$70$		0			0
$71$	−2.87636			−0.341361			−0.170680	−	0.985326i	$-0.554597\pi$
$71$	−2.87636			−0.341361			−0.170680	+	0.985326i	$0.554597\pi$
$72$	−0.660706	+	5.62755i	−0.0778650	+	0.663214i
$73$	−5.32072	−	9.21576i	−0.622744	−	1.07862i	−0.988973	−	0.148099i	$-0.952685\pi$
$73$	−5.32072	−	9.21576i	−0.622744	−	1.07862i	0.366229	−	0.930525i	$-0.380649\pi$
$74$	−4.04944	+	7.01384i	−0.470738	+	0.815342i
$75$	−2.75526	−	13.3611i	−0.318150	−	1.54281i
$76$	−0.394926	+	0.684031i	−0.0453011	+	0.0784638i
$77$		0			0
$78$	0.594554	+	2.88318i	0.0673200	+	0.326456i
$79$	−7.08650			−0.797294			−0.398647	−	0.917104i	$-0.630520\pi$
$79$	−7.08650			−0.797294			−0.398647	+	0.917104i	$0.630520\pi$
$80$	8.94870	+	15.4996i	1.00049	+	1.73291i
$81$	−8.75526	−	2.08457i	−0.972807	−	0.231619i
$82$	−4.59888	+	7.96550i	−0.507862	+	0.879642i
$83$	−2.05563	−	3.56046i	−0.225635	−	0.390811i	0.730875	−	0.682512i	$-0.239112\pi$
$83$	−2.05563	−	3.56046i	−0.225635	−	0.390811i	−0.956510	+	0.291700i	$0.905779\pi$
$84$		0			0
$85$	−7.37636	+	12.7762i	−0.800078	+	1.38578i
$86$	−4.42766	−	7.66893i	−0.477447	−	0.826962i
$87$	−2.79418	−	0.926690i	−0.299568	−	0.0993516i
$88$	−2.65452	+	4.59776i	−0.282972	+	0.490123i
$89$	4.80470	−	8.32199i	0.509297	−	0.882129i	−0.490645	−	0.871360i	$-0.663239\pi$
$89$	4.80470	−	8.32199i	0.509297	−	0.882129i	0.999942	−	0.0107692i	$-0.00342802\pi$
$90$	−16.8040	+	7.23828i	−1.77130	+	0.762981i
$91$		0			0
$92$	−2.61126	−	4.52284i	−0.272243	−	0.471539i
$93$	−9.04325	+	8.04364i	−0.937742	+	0.834086i
$94$	4.53156			0.467395
$95$	3.18911			0.327196
$96$	6.08217	−	5.40987i	0.620759	−	0.552142i
$97$	3.66071	+	6.34053i	0.371688	+	0.643783i	0.989825	−	0.142287i	$-0.0454456\pi$
$97$	3.66071	+	6.34053i	0.371688	+	0.643783i	−0.618137	+	0.786070i	$0.712112\pi$
$98$		0			0
$99$	−6.76145	−	5.03913i	−0.679551	−	0.506452i
$100$	−3.50000	+	6.06218i	−0.350000	+	0.606218i
$101$	1.73236	−	3.00054i	0.172376	−	0.298564i	−0.766874	−	0.641798i	$-0.778189\pi$
$101$	1.73236	−	3.00054i	0.172376	−	0.298564i	0.939250	+	0.343233i	$0.111522\pi$
$102$	11.4876	+	3.80987i	1.13744	+	0.377233i
$103$	−7.93818	−	13.7493i	−0.782172	−	1.35476i	−0.930674	−	0.365849i	$-0.880779\pi$
$103$	−7.93818	−	13.7493i	−0.782172	−	1.35476i	0.148502	−	0.988912i	$-0.452555\pi$
$104$	−0.944368	+	1.63569i	−0.0926029	+	0.160393i
$105$		0			0
$106$	0.105074	+	0.181994i	0.0102057	+	0.0176768i
$107$	2.67673	−	4.63623i	0.258769	−	0.448201i	−0.707143	−	0.707070i	$-0.750016\pi$
$107$	2.67673	−	4.63623i	0.258769	−	0.448201i	0.965912	+	0.258869i	$0.0833498\pi$
$108$	2.64586	+	3.78490i	0.254598	+	0.364202i
$109$	9.43199	+	16.3367i	0.903421	+	1.56477i	0.823023	+	0.568008i	$0.192286\pi$
$109$	9.43199	+	16.3367i	0.903421	+	1.56477i	0.0803973	+	0.996763i	$0.474381\pi$
$110$	−17.1433			−1.63455
$111$	−1.66690	−	8.08330i	−0.158215	−	0.767233i
$112$		0			0
$113$	9.27561	−	16.0658i	0.872576	−	1.51135i	0.0132538	−	0.999912i	$-0.495781\pi$
$113$	9.27561	−	16.0658i	0.872576	−	1.51135i	0.859322	−	0.511434i	$-0.170886\pi$
$114$	−0.528401	−	2.56238i	−0.0494893	−	0.239989i
$115$	−10.5433	+	18.2614i	−0.983163	+	1.70289i
$116$	0.755260	+	1.30815i	0.0701242	+	0.121459i
$117$	−2.40545	−	1.79272i	−0.222384	−	0.165737i
$118$	15.0865			1.38883
$119$		0			0
$120$	−11.1421	−	3.69529i	−1.01713	−	0.337332i
$121$	1.54944	+	2.68371i	0.140858	+	0.243974i
$122$	−6.58836			−0.596482
$123$	−1.89307	−	9.18007i	−0.170692	−	0.827739i
$124$	6.21015			0.557688
$125$	10.3214			0.923175
$126$		0			0
$127$	9.98762			0.886258			0.443129	−	0.896458i	$-0.353868\pi$
$127$	9.98762			0.886258			0.443129	+	0.896458i	$0.353868\pi$
$128$	12.7775			1.12938
$129$	8.56546	+	2.84073i	0.754147	+	0.250113i
$130$	−6.09888			−0.534908
$131$	8.02654	+	13.9024i	0.701282	+	1.21466i	0.968017	+	0.250886i	$0.0807220\pi$
$131$	8.02654	+	13.9024i	0.701282	+	1.21466i	−0.266734	+	0.963770i	$0.585945\pi$
$132$	0.873885	+	4.23774i	0.0760619	+	0.368848i
$133$		0			0
$134$	20.9208			1.80728
$135$	7.89307	−	16.8926i	0.679327	−	1.45389i
$136$	3.88255	+	6.72477i	0.332926	+	0.576644i
$137$	6.49381	−	11.2476i	0.554804	−	0.960948i	−0.443115	−	0.896465i	$-0.646127\pi$
$137$	6.49381	−	11.2476i	0.554804	−	0.960948i	0.997919	−	0.0644834i	$-0.0205400\pi$
$138$	16.4196	+	5.44556i	1.39773	+	0.463557i
$139$	0.555632	−	0.962383i	0.0471281	−	0.0816283i	−0.841499	−	0.540259i	$-0.818326\pi$
$139$	0.555632	−	0.962383i	0.0471281	−	0.0816283i	0.888627	+	0.458630i	$0.151660\pi$
$140$		0			0
$141$	−3.45056	+	3.06914i	−0.290589	+	0.258468i
$142$	−4.88874			−0.410254
$143$	−1.40545	−	2.43430i	−0.117529	−	0.203567i
$144$	−1.74474	+	14.8608i	−0.145395	+	1.23840i
$145$	3.04944	−	5.28179i	0.253242	−	0.438629i
$146$	−9.04325	−	15.6634i	−0.748425	−	1.29631i
$147$		0			0
$148$	−2.11745	+	3.66754i	−0.174054	+	0.301470i
$149$	−4.21634	−	7.30291i	−0.345416	−	0.598278i	0.640013	−	0.768364i	$-0.278929\pi$
$149$	−4.21634	−	7.30291i	−0.345416	−	0.598278i	−0.985429	+	0.170086i	$0.945595\pi$
$150$	−4.68292	−	22.7089i	−0.382359	−	1.85418i
$151$	7.42580	−	12.8619i	0.604303	−	1.04668i	−0.387858	−	0.921719i	$-0.626785\pi$
$151$	7.42580	−	12.8619i	0.604303	−	1.04668i	0.992161	−	0.124964i	$-0.0398816\pi$
$152$	0.839294	−	1.45370i	0.0680757	−	0.117911i
$153$	−11.3276	+	4.87933i	−0.915782	+	0.394470i
$154$		0			0
$155$	−12.5371	−	21.7148i	−1.00700	−	1.74418i
$156$	0.310892	+	1.50761i	0.0248913	+	0.120706i
$157$	−2.88874			−0.230546			−0.115273	−	0.993334i	$-0.536774\pi$
$157$	−2.88874			−0.230546			−0.115273	+	0.993334i	$0.536774\pi$
$158$	−12.0444			−0.958203
$159$	−0.203270	−	0.0674145i	−0.0161204	−	0.00534632i
$160$	8.43199	+	14.6046i	0.666607	+	1.15460i
$161$		0			0
$162$	−14.8807	−	3.54299i	−1.16914	−	0.278363i
$163$	5.15452	−	8.92788i	0.403733	−	0.699286i	−0.590440	−	0.807081i	$-0.701046\pi$
$163$	5.15452	−	8.92788i	0.403733	−	0.699286i	0.994173	+	0.107796i	$0.0343792\pi$
$164$	−2.40476	+	4.16516i	−0.187780	+	0.325245i
$165$	13.0538	−	11.6108i	1.01623	−	0.903903i
$166$	−3.49381	−	6.05146i	−0.271172	−	0.469684i
$167$	6.07598	−	10.5239i	0.470174	−	0.814365i	−0.529244	−	0.848469i	$-0.677525\pi$
$167$	6.07598	−	10.5239i	0.470174	−	0.814365i	0.999418	+	0.0341045i	$0.0108579\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$	−12.5371	+	21.7148i	−0.961549	+	1.66545i
$171$	2.13781	+	1.59325i	0.163482	+	0.121839i
$172$	−2.31522	−	4.01008i	−0.176534	−	0.305766i
$173$	6.60940			0.502504			0.251252	−	0.967922i	$-0.419158\pi$
$173$	6.60940			0.502504			0.251252	+	0.967922i	$0.419158\pi$
$174$	−4.74907	−	1.57503i	−0.360026	−	0.119403i
$175$		0			0
$176$	−7.00983	+	12.1414i	−0.528386	+	0.915191i
$177$	−11.4876	+	10.2178i	−0.863462	+	0.768018i
$178$	8.16621	−	14.1443i	0.612083	−	1.06016i
$179$	1.92147	+	3.32808i	0.143617	+	0.248752i	0.928856	−	0.370440i	$-0.120793\pi$
$179$	1.92147	+	3.32808i	0.143617	+	0.248752i	−0.785239	+	0.619193i	$0.787460\pi$
$180$	−8.78682	+	3.78490i	−0.654931	+	0.282109i
$181$	−18.5426			−1.37826			−0.689129	−	0.724639i	$-0.742007\pi$
$181$	−18.5426			−1.37826			−0.689129	+	0.724639i	$0.742007\pi$
$182$		0			0
$183$	5.01671	−	4.46218i	0.370846	−	0.329854i
$184$	5.54944	+	9.61192i	0.409110	+	0.708600i
$185$	17.0989			1.25713
$186$	−15.3702	+	13.6712i	−1.12700	+	1.00242i
$187$	−11.5563			−0.845082
$188$	2.36955			0.172818
$189$		0			0
$190$	5.42030			0.393230
$191$	4.63416			0.335316			0.167658	−	0.985845i	$-0.446380\pi$
$191$	4.63416			0.335316			0.167658	+	0.985845i	$0.446380\pi$
$192$	−2.57234	+	2.28800i	−0.185643	+	0.165122i
$193$	−25.2967			−1.82089			−0.910446	−	0.413627i	$-0.864262\pi$
$193$	−25.2967			−1.82089			−0.910446	+	0.413627i	$0.864262\pi$
$194$	6.22184	+	10.7765i	0.446702	+	0.773711i
$195$	4.64400	−	4.13066i	0.332563	−	0.295803i
$196$		0			0
$197$	10.7207			0.763816			0.381908	−	0.924200i	$-0.375267\pi$
$197$	10.7207			0.763816			0.381908	+	0.924200i	$0.375267\pi$
$198$	−11.4920	−	8.56465i	−0.816697	−	0.608663i
$199$	−4.38323	−	7.59199i	−0.310719	−	0.538182i	0.667799	−	0.744342i	$-0.267237\pi$
$199$	−4.38323	−	7.59199i	−0.310719	−	0.538182i	−0.978518	+	0.206160i	$0.933903\pi$
$200$	7.43818	−	12.8833i	0.525959	−	0.910987i
$201$	−15.9301	+	14.1693i	−1.12362	+	0.999422i
$202$	2.94437	−	5.09979i	0.207165	−	0.358820i
$203$		0			0
$204$	6.00688	+	1.99218i	0.420566	+	0.139481i
$205$	19.4189			1.35628
$206$	−13.4920	−	23.3687i	−0.940029	−	1.62818i
$207$	−16.1909	+	6.97418i	−1.12534	+	0.484739i
$208$	−2.49381	+	4.31941i	−0.172915	+	0.299497i
$209$	1.24907	+	2.16345i	0.0864000	+	0.149649i
$210$		0			0
$211$	−5.26509	+	9.11941i	−0.362464	+	0.627806i	−0.988366	−	0.152096i	$-0.951398\pi$
$211$	−5.26509	+	9.11941i	−0.362464	+	0.627806i	0.625902	+	0.779902i	$0.284731\pi$
$212$	0.0549434	+	0.0951647i	0.00377353	+	0.00653594i
$213$	3.72253	−	3.31105i	0.255063	−	0.226869i
$214$	4.54944	−	7.87987i	0.310993	−	0.538656i
$215$	−9.34795	+	16.1911i	−0.637525	+	1.10423i
$216$	−5.62296	−	8.04364i	−0.382594	−	0.547300i
$217$		0			0
$218$	16.0309	+	27.7663i	1.08575	+	1.88057i
$219$	17.4945	+	5.80205i	1.18217	+	0.392066i
$220$	−8.96424			−0.604369
$221$	−4.11126			−0.276554
$222$	−2.83310	−	13.7386i	−0.190145	−	0.922075i
$223$	−2.83379	−	4.90827i	−0.189765	−	0.328682i	0.755407	−	0.655256i	$-0.227439\pi$
$223$	−2.83379	−	4.90827i	−0.189765	−	0.328682i	−0.945172	+	0.326574i	$0.894106\pi$
$224$		0			0
$225$	18.9462	+	14.1201i	1.26308	+	0.941338i
$226$	15.7651	−	27.3059i	1.04868	−	1.81636i
$227$	−5.54944	+	9.61192i	−0.368329	+	0.637965i	−0.989304	−	0.145865i	$-0.953403\pi$
$227$	−5.54944	+	9.61192i	−0.368329	+	0.637965i	0.620975	+	0.783830i	$0.286737\pi$
$228$	−0.276301	−	1.33987i	−0.0182985	−	0.0887351i
$229$	9.82141	+	17.0112i	0.649017	+	1.12413i	0.983358	+	0.181679i	$0.0581530\pi$
$229$	9.82141	+	17.0112i	0.649017	+	1.12413i	−0.334341	+	0.942452i	$0.608514\pi$
$230$	−17.9196	+	31.0377i	−1.18158	+	2.04656i
$231$		0			0
$232$	−1.60507	−	2.78007i	−0.105378	−	0.182521i
$233$	−4.48143	+	7.76207i	−0.293588	+	0.508510i	−0.974656	−	0.223711i	$-0.928183\pi$
$233$	−4.48143	+	7.76207i	−0.293588	+	0.508510i	0.681067	+	0.732221i	$0.261516\pi$
$234$	−4.08836	−	3.04695i	−0.267265	−	0.199185i
$235$	−4.78366	−	8.28554i	−0.312052	−	0.540489i
$236$	7.88874			0.513513
$237$	9.17123	−	8.15747i	0.595735	−	0.529884i
$238$		0			0
$239$	−5.61126	+	9.71899i	−0.362963	+	0.628670i	−0.988447	−	0.151567i	$-0.951568\pi$
$239$	−5.61126	+	9.71899i	−0.362963	+	0.628670i	0.625484	+	0.780237i	$0.284901\pi$
$240$	−29.4233	−	9.75822i	−1.89926	−	0.629890i
$241$	−3.49312	+	6.05026i	−0.225012	+	0.389732i	−0.956323	−	0.292312i	$-0.905575\pi$
$241$	−3.49312	+	6.05026i	−0.225012	+	0.389732i	0.731311	+	0.682044i	$0.238909\pi$
$242$	2.63348	+	4.56131i	0.169286	+	0.293212i
$243$	13.7305	−	7.38061i	0.880812	−	0.473466i
$244$	−3.44506			−0.220547
$245$		0			0
$246$	−3.21751	−	15.6027i	−0.205141	−	0.994792i
$247$	0.444368	+	0.769668i	0.0282745	+	0.0489728i
$248$	−13.1978			−0.838059
$249$	6.75890	+	2.24159i	0.428328	+	0.142055i
$250$	17.5426			1.10949
$251$	−4.62041			−0.291638			−0.145819	−	0.989311i	$-0.546582\pi$
$251$	−4.62041			−0.291638			−0.145819	+	0.989311i	$0.546582\pi$
$252$		0			0
$253$	−16.5178			−1.03847
$254$	16.9752			1.06512
$255$	−5.16071	−	25.0259i	−0.323176	−	1.56718i
$256$	17.7417			1.10886
$257$	−0.712008	−	1.23323i	−0.0444138	−	0.0769270i	0.842964	−	0.537970i	$-0.180809\pi$
$257$	−0.712008	−	1.23323i	−0.0444138	−	0.0769270i	−0.887378	+	0.461043i	$0.847475\pi$
$258$	14.5581	+	4.82819i	0.906348	+	0.300590i
$259$		0			0
$260$	−3.18911			−0.197780
$261$	4.68292	−	2.01715i	0.289865	−	0.124859i
$262$	13.6421	+	23.6289i	0.842814	+	1.45980i
$263$	−8.13162	+	14.0844i	−0.501417	+	0.868480i	0.498582	+	0.866843i	$0.333854\pi$
$263$	−8.13162	+	14.0844i	−0.501417	+	0.868480i	−0.999999	+	0.00163692i	$0.999479\pi$
$264$	−1.85717	−	9.00602i	−0.114301	−	0.554282i
$265$	0.221840	−	0.384237i	0.0136275	−	0.0236035i
$266$		0			0
$267$	3.36151	+	16.3010i	0.205721	+	0.997604i
$268$	10.9395			0.668235
$269$	−9.32691	−	16.1547i	−0.568672	−	0.984969i	−0.996698	−	0.0812022i	$-0.974124\pi$
$269$	−9.32691	−	16.1547i	−0.568672	−	0.984969i	0.428026	−	0.903767i	$-0.359209\pi$
$270$	13.4153	−	28.7112i	0.816428	−	1.74731i
$271$	1.98143	−	3.43194i	0.120363	−	0.208475i	−0.799548	−	0.600603i	$-0.794927\pi$
$271$	1.98143	−	3.43194i	0.120363	−	0.208475i	0.919911	+	0.392127i	$0.128261\pi$
$272$	10.2527	+	17.7582i	0.621662	+	1.07675i
$273$		0			0
$274$	11.0371	−	19.1168i	0.666773	−	1.15489i
$275$	11.0698	+	19.1734i	0.667534	+	1.15620i
$276$	8.58582	+	2.84748i	0.516805	+	0.171398i
$277$	1.16690	−	2.02112i	0.0701120	−	0.121438i	−0.828838	−	0.559488i	$-0.810998\pi$
$277$	1.16690	−	2.02112i	0.0701120	−	0.121438i	0.898950	+	0.438051i	$0.144331\pi$
$278$	0.944368	−	1.63569i	0.0566394	−	0.0981024i
$279$	2.44437	−	20.8199i	0.146340	−	1.24645i
$280$		0			0
$281$	−13.9975	−	24.2443i	−0.835018	−	1.44629i	−0.894016	−	0.448035i	$-0.852124\pi$
$281$	−13.9975	−	24.2443i	−0.835018	−	1.44629i	0.0589978	−	0.998258i	$-0.481210\pi$
$282$	−5.86467	+	5.21640i	−0.349236	+	0.310632i
$283$	−10.3200			−0.613462			−0.306731	−	0.951796i	$-0.599235\pi$
$283$	−10.3200			−0.613462			−0.306731	+	0.951796i	$0.599235\pi$
$284$	−2.55632			−0.151690
$285$	−4.12729	+	3.67107i	−0.244479	+	0.217455i
$286$	−2.38874	−	4.13741i	−0.141249	−	0.244650i
$287$		0			0
$288$	−1.64400	+	14.0027i	−0.0968734	+	0.825117i
$289$	0.0487535	−	0.0844436i	0.00286785	−	0.00496727i
$290$	5.18292	−	8.97708i	0.304351	−	0.527152i
$291$	−12.0364	−	3.99186i	−0.705585	−	0.234007i
$292$	−4.72872	−	8.19038i	−0.276727	−	0.479306i
$293$	−15.3480	+	26.5834i	−0.896637	+	1.55302i	−0.0648718	+	0.997894i	$0.520664\pi$
$293$	−15.3480	+	26.5834i	−0.896637	+	1.55302i	−0.831765	+	0.555127i	$0.812670\pi$
$294$		0			0
$295$	−15.9258	−	27.5843i	−0.927236	−	1.60602i
$296$	4.50000	−	7.79423i	0.261557	−	0.453030i
$297$	14.5512	−	1.26174i	0.844348	−	0.0732133i
$298$	−7.16621	−	12.4122i	−0.415127	−	0.719021i
$299$	−5.87636			−0.339838
$300$	−2.44870	−	11.8745i	−0.141376	−	0.685575i
$301$		0			0
$302$	12.6211	−	21.8604i	0.726262	−	1.25792i
$303$	1.21201	+	5.87741i	0.0696280	+	0.337648i
$304$	2.21634	−	3.83881i	0.127116	−	0.220171i
$305$	6.95489	+	12.0462i	0.398236	+	0.689765i
$306$	−19.2527	+	8.29305i	−1.10060	+	0.474082i
$307$	11.4437			0.653125			0.326563	−	0.945176i	$-0.394110\pi$
$307$	11.4437			0.653125			0.326563	+	0.945176i	$0.394110\pi$
$308$		0			0
$309$	26.1007	+	8.65628i	1.48482	+	0.492439i
$310$	−21.3083	−	36.9071i	−1.21023	−	2.09618i
$311$	−11.9629			−0.678352			−0.339176	−	0.940723i	$-0.610148\pi$
$311$	−11.9629			−0.678352			−0.339176	+	0.940723i	$0.610148\pi$
$312$	−0.660706	−	3.20397i	−0.0374051	−	0.181389i
$313$	13.5439			0.765549			0.382774	−	0.923842i	$-0.374969\pi$
$313$	13.5439			0.765549			0.382774	+	0.923842i	$0.374969\pi$
$314$	−4.90978			−0.277075
$315$		0			0
$316$	−6.29803			−0.354292
$317$	−29.9629			−1.68288			−0.841441	−	0.540349i	$-0.818292\pi$
$317$	−29.9629			−1.68288			−0.841441	+	0.540349i	$0.818292\pi$
$318$	−0.345483	−	0.114580i	−0.0193738	−	0.00642530i
$319$	4.77747			0.267487
$320$	−3.56615	−	6.17676i	−0.199354	−	0.345291i
$321$	1.87271	+	9.08138i	0.104525	+	0.506873i
$322$		0			0
$323$	3.65383			0.203304
$324$	−7.78111	−	1.85263i	−0.432284	−	0.102924i
$325$	3.93818	+	6.82112i	0.218451	+	0.378368i
$326$	8.76076	−	15.1741i	0.485214	−	0.840415i
$327$	−31.0123	−	10.2852i	−1.71498	−	0.568774i
$328$	5.11058	−	8.85178i	0.282184	−	0.488758i
$329$		0			0
$330$	22.1866	−	19.7341i	1.22133	−	1.08633i
$331$	2.08650			0.114685			0.0573423	−	0.998355i	$-0.481737\pi$
$331$	2.08650			0.114685			0.0573423	+	0.998355i	$0.481737\pi$
$332$	−1.82691	−	3.16431i	−0.100265	−	0.173664i
$333$	11.4622	+	8.54245i	0.628123	+	0.468124i
$334$	10.3269	−	17.8867i	0.565064	−	0.978719i
$335$	−22.0846	−	38.2517i	−1.20661	−	2.08992i
$336$		0			0
$337$	8.10439	−	14.0372i	0.441474	−	0.764655i	−0.556325	−	0.830965i	$-0.687789\pi$
$337$	8.10439	−	14.0372i	0.441474	−	0.764655i	0.997799	+	0.0663093i	$0.0211224\pi$
$338$	10.1978	+	17.6631i	0.554686	+	0.960743i
$339$	6.48948	+	31.4695i	0.352460	+	1.70919i
$340$	−6.55563	+	11.3547i	−0.355529	+	0.615794i
$341$	9.82072	−	17.0100i	0.531822	−	0.921143i
$342$	3.63348	+	2.70793i	0.196476	+	0.146428i
$343$		0			0
$344$	4.92030	+	8.52220i	0.265285	+	0.459486i
$345$	−7.37636	−	35.7703i	−0.397130	−	1.92581i
$346$	11.2335			0.603918
$347$	11.2670			0.604842			0.302421	−	0.953175i	$-0.402205\pi$
$347$	11.2670			0.604842			0.302421	+	0.953175i	$0.402205\pi$
$348$	−2.48329	−	0.823583i	−0.133118	−	0.0441487i
$349$	−0.0988844	−	0.171273i	−0.00529316	−	0.00916803i	0.863367	−	0.504577i	$-0.168352\pi$
$349$	−0.0988844	−	0.171273i	−0.00529316	−	0.00916803i	−0.868660	+	0.495409i	$0.835018\pi$
$350$		0			0
$351$	5.17673	−	0.448873i	0.276313	−	0.0239591i
$352$	−6.60507	+	11.4403i	−0.352052	+	0.609771i
$353$	−6.25093	+	10.8269i	−0.332703	+	0.576259i	−0.983041	−	0.183386i	$-0.941294\pi$
$353$	−6.25093	+	10.8269i	−0.332703	+	0.576259i	0.650338	+	0.759645i	$0.274627\pi$
$354$	−19.5247	+	17.3665i	−1.03773	+	0.923018i
$355$	5.16071	+	8.93861i	0.273902	+	0.474412i
$356$	4.27011	−	7.39605i	0.226315	−	0.391990i
$357$		0			0
$358$	3.26578	+	5.65650i	0.172602	+	0.298955i
$359$	−10.0098	+	17.3375i	−0.528299	+	0.915040i	0.471157	+	0.882049i	$0.343837\pi$
$359$	−10.0098	+	17.3375i	−0.528299	+	0.915040i	−0.999456	+	0.0329908i	$0.989497\pi$
$360$	18.6737	−	8.04364i	0.984190	−	0.423937i
$361$	9.10507	+	15.7705i	0.479214	+	0.830024i
$362$	−31.5155			−1.65642
$363$	−5.09455	−	1.68961i	−0.267395	−	0.0886814i
$364$		0			0
$365$	−19.0927	+	33.0695i	−0.999357	+	1.73094i
$366$	8.52654	−	7.58404i	0.445689	−	0.396424i
$367$	15.0364	−	26.0438i	0.784892	−	1.35947i	−0.144171	−	0.989553i	$-0.546052\pi$
$367$	15.0364	−	26.0438i	0.784892	−	1.35947i	0.929063	−	0.369921i	$-0.120615\pi$
$368$	14.6545	+	25.3824i	0.763919	+	1.32315i
$369$	13.0174	+	9.70152i	0.677659	+	0.505041i
$370$	29.0617			1.51085
$371$		0			0
$372$	−8.03706	+	7.14867i	−0.416702	+	0.370641i
$373$	−3.50619	−	6.07290i	−0.181544	−	0.314443i	0.760863	−	0.648913i	$-0.224776\pi$
$373$	−3.50619	−	6.07290i	−0.181544	−	0.314443i	−0.942406	+	0.334470i	$0.891443\pi$
$374$	−19.6414			−1.01564
$375$	−13.3578	+	11.8813i	−0.689793	+	0.613545i
$376$	−5.03576			−0.259700
$377$	1.69963			0.0875353
$378$		0			0
$379$	−19.0741			−0.979772			−0.489886	−	0.871787i	$-0.662962\pi$
$379$	−19.0741			−0.979772			−0.489886	+	0.871787i	$0.662962\pi$
$380$	2.83427			0.145395
$381$	−12.9258	+	11.4970i	−0.662209	+	0.589010i
$382$	7.87636			0.402989
$383$	1.60507	+	2.78007i	0.0820155	+	0.142055i	0.904116	−	0.427288i	$-0.140531\pi$
$383$	1.60507	+	2.78007i	0.0820155	+	0.142055i	−0.822100	+	0.569343i	$0.807198\pi$
$384$	−16.5364	+	14.7085i	−0.843868	+	0.750590i
$385$		0			0
$386$	−42.9949			−2.18838
$387$	−14.3553	+	6.18351i	−0.729722	+	0.314325i
$388$	3.25340	+	5.63506i	0.165166	+	0.286077i
$389$	−2.56801	+	4.44793i	−0.130203	+	0.225519i	−0.923755	−	0.382984i	$-0.874896\pi$
$389$	−2.56801	+	4.44793i	−0.130203	+	0.225519i	0.793552	+	0.608503i	$0.208230\pi$
$390$	7.89307	−	7.02059i	0.399681	−	0.355501i
$391$	−12.0796	+	20.9225i	−0.610893	+	1.05810i
$392$		0			0
$393$	−26.3912	−	8.75264i	−1.33126	−	0.441512i
$394$	18.2212			0.917968
$395$	12.7145	+	22.0221i	0.639735	+	1.10805i
$396$	−6.00914	−	4.47846i	−0.301971	−	0.225051i
$397$	11.4691	−	19.8650i	0.575615	−	0.996995i	−0.420359	−	0.907358i	$-0.638096\pi$
$397$	11.4691	−	19.8650i	0.575615	−	0.996995i	0.995975	−	0.0896370i	$-0.0285707\pi$
$398$	−7.44987	−	12.9036i	−0.373428	−	0.646797i
$399$		0			0
$400$	19.6421	−	34.0212i	0.982107	−	1.70106i
$401$	9.10507	+	15.7705i	0.454686	+	0.787539i	0.998670	−	0.0515566i	$-0.0164183\pi$
$401$	9.10507	+	15.7705i	0.454686	+	0.787539i	−0.543984	+	0.839095i	$0.683085\pi$
$402$	−27.0753	+	24.0825i	−1.35039	+	1.20112i
$403$	3.49381	−	6.05146i	0.174039	−	0.301445i
$404$	1.53961	−	2.66668i	0.0765985	−	0.132672i
$405$	9.23050	+	30.9481i	0.458667	+	1.53782i
$406$		0			0
$407$	6.69708	+	11.5997i	0.331962	+	0.574975i
$408$	−12.7658	−	4.23377i	−0.632000	−	0.209603i
$409$	15.3324			0.758139			0.379070	−	0.925368i	$-0.376244\pi$
$409$	15.3324			0.758139			0.379070	+	0.925368i	$0.376244\pi$
$410$	33.0049			1.63000
$411$	4.54325	+	22.0317i	0.224102	+	1.08674i
$412$	−7.05494	−	12.2195i	−0.347572	−	0.602013i
$413$		0			0
$414$	−27.5185	+	11.8535i	−1.35246	+	0.582568i
$415$	−7.37636	+	12.7762i	−0.362091	+	0.627160i
$416$	−2.34981	+	4.07000i	−0.115209	+	0.199548i
$417$	0.388736	+	1.88510i	0.0190365	+	0.0923138i
$418$	2.12296	+	3.67707i	0.103837	+	0.179851i
$419$	5.28435	−	9.15276i	0.258157	−	0.447142i	−0.707591	−	0.706622i	$-0.750218\pi$
$419$	5.28435	−	9.15276i	0.258157	−	0.447142i	0.965748	+	0.259481i	$0.0835513\pi$
$420$		0			0
$421$	18.0858	+	31.3256i	0.881449	+	1.52671i	0.849731	+	0.527217i	$0.176765\pi$
$421$	18.0858	+	31.3256i	0.881449	+	1.52671i	0.0317181	+	0.999497i	$0.489902\pi$
$422$	−8.94870	+	15.4996i	−0.435616	+	0.754509i
$423$	0.932677	−	7.94406i	0.0453483	−	0.386253i
$424$	−0.116765	−	0.202243i	−0.00567062	−	0.00982181i
$425$	32.3818			1.57075
$426$	6.32691	−	5.62755i	0.306540	−	0.272656i
$427$		0			0
$428$	2.37890	−	4.12038i	0.114989	−	0.199166i
$429$	4.62110	+	1.53259i	0.223109	+	0.0739939i
$430$	−15.8880	+	27.5189i	−0.766190	+	1.32708i
$431$	−17.5494	−	30.3965i	−0.845327	−	1.46415i	−0.885337	−	0.464950i	$-0.846072\pi$
$431$	−17.5494	−	30.3965i	−0.845327	−	1.46415i	0.0400101	−	0.999199i	$-0.487261\pi$
$432$	−14.8486	−	21.2410i	−0.714406	−	1.02196i
$433$	41.1730			1.97865			0.989324	−	0.145731i	$-0.0465533\pi$
$433$	41.1730			1.97865			0.989324	+	0.145731i	$0.0465533\pi$
$434$		0			0
$435$	2.13348	+	10.3459i	0.102292	+	0.496047i
$436$	8.38255	+	14.5190i	0.401451	+	0.695334i
$437$	5.22253			0.249827
$438$	29.7341	+	9.86132i	1.42075	+	0.471192i
$439$	4.67859			0.223297			0.111648	−	0.993748i	$-0.464387\pi$
$439$	4.67859			0.223297			0.111648	+	0.993748i	$0.464387\pi$
$440$	19.0507			0.908209
$441$		0			0
$442$	−6.98762			−0.332367
$443$	30.1730			1.43356			0.716781	−	0.697298i	$-0.245615\pi$
$443$	30.1730			1.43356			0.716781	+	0.697298i	$0.245615\pi$
$444$	−1.48143	−	7.18392i	−0.0703056	−	0.340934i
$445$	−34.4820			−1.63461
$446$	−4.81639	−	8.34224i	−0.228063	−	0.395016i
$447$	13.8633	+	4.59776i	0.655711	+	0.217466i
$448$		0			0
$449$	0.333792			0.0157526			0.00787632	−	0.999969i	$-0.497493\pi$
$449$	0.333792			0.0157526			0.00787632	+	0.999969i	$0.497493\pi$
$450$	32.2014	+	23.9989i	1.51799	+	1.13132i
$451$	7.60576	+	13.1736i	0.358141	+	0.620319i
$452$	8.24357	−	14.2783i	0.387745	−	0.671594i
$453$	5.19530	+	25.1936i	0.244096	+	1.18370i
$454$	−9.43199	+	16.3367i	−0.442665	+	0.766719i
$455$		0			0
$456$	0.587193	+	2.84748i	0.0274979	+	0.133346i
$457$	−19.3090			−0.903238			−0.451619	−	0.892211i	$-0.649153\pi$
$457$	−19.3090			−0.903238			−0.451619	+	0.892211i	$0.649153\pi$
$458$	16.6927	+	28.9127i	0.780001	+	1.35100i
$459$	9.04325	−	19.3542i	0.422103	−	0.903379i
$460$	−9.37017	+	16.2296i	−0.436886	+	0.756709i
$461$	19.5538	+	33.8681i	0.910710	+	1.57740i	0.813064	+	0.582175i	$0.197798\pi$
$461$	19.5538	+	33.8681i	0.910710	+	1.57740i	0.0976463	+	0.995221i	$0.468869\pi$
$462$		0			0
$463$	−10.9382	+	18.9455i	−0.508340	+	0.880471i	0.491613	+	0.870814i	$0.336407\pi$
$463$	−10.9382	+	18.9455i	−0.508340	+	0.880471i	−0.999953	+	0.00965741i	$0.996926\pi$
$464$	−4.23855	−	7.34138i	−0.196770	−	0.340815i
$465$	41.2218	+	13.6712i	1.91161	+	0.633986i
$466$	−7.61677	+	13.1926i	−0.352840	+	0.611137i
$467$	−6.16002	+	10.6695i	−0.285052	+	0.493724i	−0.972622	−	0.232394i	$-0.925344\pi$
$467$	−6.16002	+	10.6695i	−0.285052	+	0.493724i	0.687570	+	0.726118i	$0.258677\pi$
$468$	−2.13781	−	1.59325i	−0.0988201	−	0.0736480i
$469$		0			0
$470$	−8.13045	−	14.0823i	−0.375029	−	0.649570i
$471$	3.73855	−	3.32530i	0.172263	−	0.153222i
$472$	−16.7651			−0.771676
$473$	−14.6452			−0.673385
$474$	15.5877	−	13.8647i	0.715966	−	0.636825i
$475$	−3.50000	−	6.06218i	−0.160591	−	0.278152i
$476$		0			0
$477$	0.340671	−	0.146743i	0.0155983	−	0.00671890i
$478$	−9.53706	+	16.5187i	−0.436215	+	0.755547i
$479$	6.74474	−	11.6822i	0.308175	−	0.533775i	−0.669788	−	0.742552i	$-0.733615\pi$
$479$	6.74474	−	11.6822i	0.308175	−	0.533775i	0.977963	+	0.208777i	$0.0669484\pi$
$480$	−27.7243	−	9.19476i	−1.26544	−	0.419682i
$481$	2.38255	+	4.12669i	0.108635	+	0.188161i
$482$	−5.93701	+	10.2832i	−0.270423	+	0.468387i
$483$		0			0
$484$	1.37704	+	2.38511i	0.0625929	+	0.108414i
$485$	13.1359	−	22.7521i	0.596473	−	1.03312i
$486$	23.3367	−	12.5443i	1.05858	−	0.569020i
$487$	−3.77197	−	6.53324i	−0.170924	−	0.296050i	0.767819	−	0.640667i	$-0.221342\pi$
$487$	−3.77197	−	6.53324i	−0.170924	−	0.296050i	−0.938743	+	0.344617i	$0.888009\pi$
$488$	7.32141			0.331425
$489$	3.60624	+	17.4878i	0.163080	+	0.790826i
$490$		0			0
$491$	8.06979	−	13.9773i	0.364185	−	0.630786i	−0.624460	−	0.781057i	$-0.714681\pi$
$491$	8.06979	−	13.9773i	0.364185	−	0.630786i	0.988645	+	0.150270i	$0.0480143\pi$
$492$	−1.68244	−	8.15866i	−0.0758501	−	0.367821i
$493$	3.49381	−	6.05146i	0.157353	−	0.272544i
$494$	0.755260	+	1.30815i	0.0339808	+	0.0588564i
$495$	−3.52840	+	30.0531i	−0.158590	+	1.35079i
$496$	−34.8516			−1.56488
$497$		0			0
$498$	11.4876	+	3.80987i	0.514773	+	0.170724i
$499$	15.4327	+	26.7302i	0.690862	+	1.19661i	0.971556	+	0.236810i	$0.0761019\pi$
$499$	15.4327	+	26.7302i	0.690862	+	1.19661i	−0.280694	+	0.959797i	$0.590565\pi$
$500$	9.17301			0.410229
$501$	4.25093	+	20.6141i	0.189918	+	0.920970i
$502$	−7.85297			−0.350495
$503$	−24.6304			−1.09822			−0.549109	−	0.835751i	$-0.685033\pi$
$503$	−24.6304			−1.09822			−0.549109	+	0.835751i	$0.685033\pi$
$504$		0			0
$505$	−12.4327			−0.553247
$506$	−28.0741			−1.24805
$507$	−19.7280	−	6.54277i	−0.876149	−	0.290575i
$508$	8.87636			0.393825
$509$	6.79487	+	11.7691i	0.301177	+	0.521654i	0.976403	−	0.215957i	$-0.0692870\pi$
$509$	6.79487	+	11.7691i	0.301177	+	0.521654i	−0.675226	+	0.737611i	$0.735954\pi$
$510$	−8.77128	−	42.5347i	−0.388399	−	1.88347i
$511$		0			0
$512$	4.59937			0.203265
$513$	−4.60074	+	0.398930i	−0.203128	+	0.0176132i
$514$	−1.21015	−	2.09604i	−0.0533774	−	0.0924523i
$515$	−28.4851	+	49.3376i	−1.25520	+	2.17407i
$516$	7.61243	+	2.52466i	0.335119	+	0.111142i
$517$	3.74721	−	6.49036i	0.164802	−	0.285446i
$518$		0			0
$519$	−8.55377	+	7.60826i	−0.375469	+	0.333966i
$520$	6.77747			0.297212
$521$	−19.5865	−	33.9248i	−0.858100	−	1.48627i	−0.873739	−	0.486396i	$-0.838311\pi$
$521$	−19.5865	−	33.9248i	−0.858100	−	1.48627i	0.0156383	−	0.999878i	$-0.495022\pi$
$522$	7.95922	−	3.42841i	0.348366	−	0.150057i
$523$	9.56182	−	16.5616i	0.418109	−	0.724187i	−0.577640	−	0.816292i	$-0.696026\pi$
$523$	9.56182	−	16.5616i	0.418109	−	0.724187i	0.995749	+	0.0921051i	$0.0293596\pi$
$524$	7.13348	+	12.3555i	0.311627	+	0.539754i
$525$		0			0
$526$	−13.8207	+	23.9382i	−0.602612	+	1.04375i
$527$	−14.3640	−	24.8791i	−0.625705	−	1.08375i
$528$	−4.90428	−	23.7824i	−0.213431	−	1.03499i
$529$	−5.76578	+	9.98663i	−0.250686	+	0.434201i
$530$	0.377045	−	0.653061i	0.0163778	−	0.0283671i
$531$	3.10507	−	26.4474i	0.134749	−	1.14772i
$532$		0			0
$533$	2.70582	+	4.68661i	0.117202	+	0.203000i
$534$	5.71331	+	27.7056i	0.247239	+	1.19894i
$535$	−19.2101			−0.830527
$536$	−23.2485			−1.00418
$537$	−6.31777	−	2.09529i	−0.272632	−	0.0904183i
$538$	−15.8523	−	27.4570i	−0.683441	−	1.18375i
$539$		0			0
$540$	7.01485	−	15.0131i	0.301871	−	0.646061i
$541$	−1.26509	+	2.19120i	−0.0543906	+	0.0942072i	−0.891939	−	0.452156i	$-0.850655\pi$
$541$	−1.26509	+	2.19120i	−0.0543906	+	0.0942072i	0.837548	+	0.546363i	$0.183988\pi$
$542$	3.36769	−	5.83302i	0.144655	−	0.250550i
$543$	23.9975	−	21.3448i	1.02983	−	0.915995i
$544$	9.66071	+	16.7328i	0.414199	+	0.717414i
$545$	33.8454	−	58.6220i	1.44978	−	2.51109i
$546$		0			0
$547$	−8.92580	−	15.4599i	−0.381640	−	0.661019i	0.609657	−	0.792665i	$-0.291307\pi$
$547$	−8.92580	−	15.4599i	−0.381640	−	0.661019i	−0.991297	+	0.131646i	$0.957974\pi$
$548$	5.77128	−	9.99615i	0.246537	−	0.427015i
$549$	−1.35600	+	11.5497i	−0.0578728	+	0.492931i
$550$	18.8145	+	32.5877i	0.802254	+	1.38955i
$551$	−1.51052			−0.0643503
$552$	−18.2465	−	6.05146i	−0.776624	−	0.257567i
$553$		0			0
$554$	1.98329	−	3.43516i	0.0842619	−	0.145946i
$555$	−22.1291	+	19.6830i	−0.939327	+	0.835496i
$556$	0.493810	−	0.855304i	0.0209422	−	0.0362730i
$557$	−20.6804	−	35.8195i	−0.876255	−	1.51772i	−0.855419	−	0.517936i	$-0.826701\pi$
$557$	−20.6804	−	35.8195i	−0.876255	−	1.51772i	−0.0208360	−	0.999783i	$-0.506633\pi$
$558$	4.15452	−	35.3860i	0.175875	−	1.49801i
$559$	−5.21015			−0.220366
$560$		0			0
$561$	14.9560	−	13.3028i	0.631442	−	0.561644i
$562$	−23.7905	−	41.2063i	−1.00354	−	1.73818i
$563$	20.7366			0.873944			0.436972	−	0.899475i	$-0.356051\pi$
$563$	20.7366			0.873944			0.436972	+	0.899475i	$0.356051\pi$
$564$	−3.06663	+	2.72766i	−0.129129	+	0.114855i
$565$	−66.5685			−2.80056
$566$	−17.5402			−0.737271
$567$		0			0
$568$	5.43268			0.227950
$569$	−0.268329			−0.0112489			−0.00562446	−	0.999984i	$-0.501790\pi$
$569$	−0.268329			−0.0112489			−0.00562446	+	0.999984i	$0.501790\pi$
$570$	−7.01485	+	6.23945i	−0.293820	+	0.261342i
$571$	35.9367			1.50391			0.751953	−	0.659217i	$-0.229112\pi$
$571$	35.9367			1.50391			0.751953	+	0.659217i	$0.229112\pi$
$572$	−1.24907	−	2.16345i	−0.0522263	−	0.0904585i
$573$	−5.99745	+	5.33451i	−0.250547	+	0.222852i
$574$		0			0
$575$	46.2843			1.93019
$576$	0.695298	−	5.92218i	0.0289707	−	0.246758i
$577$	2.71565	+	4.70364i	0.113054	+	0.195815i	0.917000	−	0.398887i	$-0.130603\pi$
$577$	2.71565	+	4.70364i	0.113054	+	0.195815i	−0.803946	+	0.594702i	$0.797270\pi$
$578$	0.0828628	−	0.143523i	0.00344664	−	0.00596976i
$579$	32.7385	−	29.1197i	1.36056	−	1.21017i
$580$	2.71015	−	4.69412i	0.112533	−	0.194913i
$581$		0			0
$582$	−20.4574	−	6.78468i	−0.847985	−	0.281234i
$583$	0.347550			0.0143940
$584$	10.0494	+	17.4061i	0.415849	+	0.720271i
$585$	−1.25526	+	10.6917i	−0.0518986	+	0.442046i
$586$	−26.0858	+	45.1820i	−1.07760	+	1.86645i
$587$	17.5822	+	30.4532i	0.725694	+	1.25694i	0.958688	+	0.284461i	$0.0918145\pi$
$587$	17.5822	+	30.4532i	0.725694	+	1.25694i	−0.232994	+	0.972478i	$0.574852\pi$
$588$		0			0
$589$	−3.10507	+	5.37815i	−0.127942	+	0.221603i
$590$	−27.0679	−	46.8830i	−1.11437	−	1.93014i
$591$	−13.8745	+	12.3408i	−0.570721	+	0.507635i
$592$	11.8832	−	20.5824i	0.488398	−	0.845930i
$593$	−16.7534	+	29.0177i	−0.687980	+	1.19162i	0.284511	+	0.958673i	$0.408169\pi$
$593$	−16.7534	+	29.0177i	−0.687980	+	1.19162i	−0.972490	+	0.232943i	$0.925164\pi$
$594$	24.7317	−	2.14448i	1.01475	−	0.0879891i
$595$		0			0
$596$	−3.74721	−	6.49036i	−0.153492	−	0.265856i
$597$	14.4120	+	4.77975i	0.589846	+	0.195622i
$598$	−9.98762			−0.408424
$599$	6.24729			0.255257			0.127629	−	0.991822i	$-0.459263\pi$
$599$	6.24729			0.255257			0.127629	+	0.991822i	$0.459263\pi$
$600$	5.20396	+	25.2356i	0.212451	+	1.03024i
$601$	11.2040	+	19.4058i	0.457019	+	0.791580i	0.998802	−	0.0489384i	$-0.0155838\pi$
$601$	11.2040	+	19.4058i	0.457019	+	0.791580i	−0.541783	+	0.840519i	$0.682250\pi$
$602$		0			0
$603$	4.30587	−	36.6752i	0.175349	−	1.49353i
$604$	6.59957	−	11.4308i	0.268533	−	0.465112i
$605$	5.55996	−	9.63014i	0.226045	−	0.391521i
$606$	2.05996	+	9.98940i	0.0836803	+	0.405792i
$607$	7.47524	+	12.9475i	0.303411	+	0.525523i	0.976906	−	0.213669i	$-0.0685413\pi$
$607$	7.47524	+	12.9475i	0.303411	+	0.525523i	−0.673496	+	0.739191i	$0.735208\pi$
$608$	2.08836	−	3.61715i	0.0846943	−	0.146695i
$609$		0			0
$610$	11.8207	+	20.4741i	0.478607	+	0.828972i
$611$	1.33310	−	2.30900i	0.0539316	−	0.0934123i
$612$	−10.0672	+	4.33643i	−0.406944	+	0.175290i
$613$	−17.5989	−	30.4822i	−0.710812	−	1.23116i	−0.964553	−	0.263891i	$-0.914994\pi$
$613$	−17.5989	−	30.4822i	−0.710812	−	1.23116i	0.253740	−	0.967272i	$-0.418339\pi$
$614$	19.4500			0.784938
$615$	−25.1316	+	22.3536i	−1.01340	+	0.901386i
$616$		0			0
$617$	1.00619	−	1.74277i	0.0405077	−	0.0701614i	−0.845061	−	0.534670i	$-0.820436\pi$
$617$	1.00619	−	1.74277i	0.0405077	−	0.0701614i	0.885568	+	0.464509i	$0.153769\pi$
$618$	44.3614	+	14.7125i	1.78448	+	0.591822i
$619$	19.6909	−	34.1056i	0.791444	−	1.37082i	−0.133629	−	0.991031i	$-0.542663\pi$
$619$	19.6909	−	34.1056i	0.791444	−	1.37082i	0.925073	−	0.379789i	$-0.124004\pi$
$620$	−11.1421	−	19.2987i	−0.447479	−	0.775056i
$621$	12.9258	−	27.6636i	0.518694	−	1.11010i
$622$	−20.3324			−0.815256
$623$		0			0
$624$	−1.74474	−	8.46079i	−0.0698455	−	0.338703i
$625$	1.17240	+	2.03065i	0.0468959	+	0.0812261i
$626$	23.0197			0.920051
$627$	−4.10693	−	1.36206i	−0.164015	−	0.0543956i
$628$	−2.56732			−0.102447
$629$	19.5906			0.781126
$630$		0			0
$631$	44.3832			1.76687			0.883433	−	0.468558i	$-0.155226\pi$
$631$	44.3832			1.76687			0.883433	+	0.468558i	$0.155226\pi$
$632$	13.3845			0.532408
$633$	−3.68361	−	17.8630i	−0.146410	−	0.709989i
$634$	−50.9257			−2.02252
$635$	−17.9196	−	31.0377i	−0.711118	−	1.23169i
$636$	−0.180653	−	0.0599137i	−0.00716337	−	0.00237573i
$637$		0			0
$638$	8.11993			0.321471
$639$	−1.00619	+	8.57020i	−0.0398043	+	0.339032i
$640$	−22.9251	−	39.7075i	−0.906195	−	1.56957i
$641$	7.49312	−	12.9785i	0.295961	−	0.512619i	−0.679247	−	0.733909i	$-0.737694\pi$
$641$	7.49312	−	12.9785i	0.295961	−	0.512619i	0.975208	+	0.221291i	$0.0710270\pi$
$642$	3.18292	+	15.4350i	0.125620	+	0.609169i
$643$	−5.32691	+	9.22649i	−0.210073	+	0.363857i	−0.951737	−	0.306914i	$-0.900703\pi$
$643$	−5.32691	+	9.22649i	−0.210073	+	0.363857i	0.741664	+	0.670771i	$0.234037\pi$
$644$		0			0
$645$	−6.54009	−	31.7150i	−0.257516	−	1.24878i
$646$	6.21015			0.244335
$647$	1.06478	+	1.84424i	0.0418606	+	0.0725047i	0.886197	−	0.463309i	$-0.153338\pi$
$647$	1.06478	+	1.84424i	0.0418606	+	0.0725047i	−0.844336	+	0.535814i	$0.820005\pi$
$648$	16.5364	+	3.93720i	0.649610	+	0.154668i
$649$	12.4752	−	21.6078i	0.489696	−	0.848178i
$650$	6.69344	+	11.5934i	0.262538	+	0.454730i
$651$		0			0
$652$	4.58100	−	7.93453i	0.179406	−	0.310740i
$653$	−5.58582	−	9.67492i	−0.218590	−	0.378609i	0.735787	−	0.677213i	$-0.236812\pi$
$653$	−5.58582	−	9.67492i	−0.218590	−	0.378609i	−0.954377	+	0.298604i	$0.903479\pi$
$654$	−52.7094	−	17.4811i	−2.06110	−	0.683564i
$655$	28.8022	−	49.8868i	1.12539	−	1.94924i
$656$	13.4956	−	23.3751i	0.526914	−	0.912642i
$657$	−29.3200	+	12.6295i	−1.14388	+	0.492723i
$658$		0			0
$659$	5.65452	+	9.79391i	0.220269	+	0.381517i	0.954890	−	0.296961i	$-0.0959733\pi$
$659$	5.65452	+	9.79391i	0.220269	+	0.381517i	−0.734621	+	0.678478i	$0.762640\pi$
$660$	11.6014	−	10.3190i	0.451582	−	0.401666i
$661$	−32.3570			−1.25854			−0.629271	−	0.777186i	$-0.716646\pi$
$661$	−32.3570			−1.25854			−0.629271	+	0.777186i	$0.716646\pi$
$662$	3.54628			0.137830
$663$	5.32072	−	4.73259i	0.206640	−	0.183798i
$664$	3.88255	+	6.72477i	0.150672	+	0.260972i
$665$		0			0
$666$	19.4814	+	14.5190i	0.754890	+	0.562600i
$667$	4.99381	−	8.64953i	0.193361	−	0.334911i
$668$	5.39995	−	9.35298i	0.208930	−	0.361878i
$669$	9.31749	+	3.09014i	0.360235	+	0.119472i
$670$	−37.5357	−	65.0137i	−1.45013	−	2.51170i
$671$	−5.44801	+	9.43623i	−0.210318	+	0.364282i
$672$		0			0
$673$	12.0803	+	20.9237i	0.465662	+	0.806550i	0.999231	−	0.0392063i	$-0.0124830\pi$
$673$	12.0803	+	20.9237i	0.465662	+	0.806550i	−0.533569	+	0.845756i	$0.679150\pi$
$674$	13.7744	−	23.8580i	0.530572	−	0.918977i
$675$	−40.7738	+	3.53549i	−1.56938	+	0.136081i
$676$	5.33242	+	9.23601i	0.205093	+	0.355231i
$677$	−25.0741			−0.963677			−0.481838	−	0.876260i	$-0.660031\pi$
$677$	−25.0741			−0.963677			−0.481838	+	0.876260i	$0.660031\pi$
$678$	11.0297	+	53.4865i	0.423593	+	2.05414i
$679$		0			0
$680$	13.9320	−	24.1309i	0.534267	−	0.925378i
$681$	−3.88255	−	18.8277i	−0.148779	−	0.721478i
$682$	16.6916	−	28.9107i	0.639154	−	1.10705i
$683$	23.8392	+	41.2907i	0.912182	+	1.57995i	0.810975	+	0.585081i	$0.198937\pi$
$683$	23.8392	+	41.2907i	0.912182	+	1.57995i	0.101207	+	0.994865i	$0.467729\pi$
$684$	1.89995	+	1.41598i	0.0726462	+	0.0541413i
$685$	−46.6043			−1.78066
$686$		0			0
$687$	−32.2927	−	10.7099i	−1.23204	−	0.408607i
$688$	12.9931	+	22.5047i	0.495358	+	0.857985i
$689$	0.123644			0.00471046
$690$	−12.5371	−	60.7961i	−0.477278	−	2.31447i
$691$	24.6800			0.938870			0.469435	−	0.882967i	$-0.344458\pi$
$691$	24.6800			0.938870			0.469435	+	0.882967i	$0.344458\pi$
$692$	5.87402			0.223297
$693$		0			0
$694$	19.1496			0.726910
$695$	−3.98762			−0.151259
$696$	5.27747	+	1.75027i	0.200042	+	0.0663439i
$697$	22.2487			0.842728
$698$	−0.168067	−	0.291100i	−0.00636142	−	0.0110183i
$699$	−3.13533	−	15.2042i	−0.118589	−	0.575076i
$700$		0			0
$701$	−29.6784			−1.12094			−0.560469	−	0.828175i	$-0.689379\pi$
$701$	−29.6784			−1.12094			−0.560469	+	0.828175i	$0.689379\pi$
$702$	8.79851	−	0.762918i	0.332078	−	0.0287945i
$703$	−2.11745	−	3.66754i	−0.0798613	−	0.138324i
$704$	2.79349	−	4.83847i	0.105284	−	0.182357i
$705$	15.7286	+	5.21640i	0.592375	+	0.196461i
$706$	−10.6243	+	18.4018i	−0.399849	+	0.692559i
$707$		0			0
$708$	−10.2095	+	9.08094i	−0.383695	+	0.341282i
$709$	−29.2581			−1.09881			−0.549406	−	0.835555i	$-0.685146\pi$
$709$	−29.2581			−1.09881			−0.549406	+	0.835555i	$0.685146\pi$
$710$	8.77128	+	15.1923i	0.329180	+	0.570157i
$711$	−2.47896	+	21.1145i	−0.0929682	+	0.791855i
$712$	−9.07481	+	15.7180i	−0.340093	+	0.589058i
$713$	−20.5309	−	35.5605i	−0.768887	−	1.33175i
$714$		0			0
$715$	−5.04325	+	8.73517i	−0.188607	+	0.326677i
$716$	1.70768	+	2.95778i	0.0638189	+	0.110538i
$717$	−3.92580	−	19.0374i	−0.146612	−	0.710966i
$718$	−17.0130	+	29.4674i	−0.634919	+	1.09971i
$719$	0.537063	−	0.930220i	0.0200291	−	0.0346913i	−0.855837	−	0.517245i	$-0.826957\pi$
$719$	0.537063	−	0.930220i	0.0200291	−	0.0346913i	0.875866	+	0.482554i	$0.160291\pi$
$720$	49.3120	−	21.2410i	1.83775	−	0.791605i
$721$		0			0
$722$	15.4752	+	26.8039i	0.575929	+	0.997538i
$723$	−2.44389	−	11.8512i	−0.0908891	−	0.440750i
$724$	−16.4794			−0.612454
$725$	−13.3869			−0.497176
$726$	−8.65885	−	2.87171i	−0.321360	−	0.106579i
$727$	12.7163	+	22.0253i	0.471623	+	0.816875i	0.999473	−	0.0324628i	$-0.0103350\pi$
$727$	12.7163	+	22.0253i	0.471623	+	0.816875i	−0.527850	+	0.849338i	$0.677002\pi$
$728$		0			0
$729$	−9.27375	+	25.3574i	−0.343472	+	0.939163i
$730$	−32.4505	+	56.2059i	−1.20105	+	2.08027i
$731$	−10.7101	+	18.5505i	−0.396129	+	0.686116i
$732$	4.45853	−	3.96570i	0.164792	−	0.146576i
$733$	−5.69777	−	9.86883i	−0.210452	−	0.364513i	0.741404	−	0.671059i	$-0.234160\pi$
$733$	−5.69777	−	9.86883i	−0.210452	−	0.364513i	−0.951856	+	0.306545i	$0.900827\pi$
$734$	25.5562	−	44.2647i	0.943298	−	1.63384i
$735$		0			0
$736$	13.8083	+	23.9168i	0.508982	+	0.881583i
$737$	17.2997	−	29.9639i	0.637242	−	1.10374i
$738$	22.1247	+	16.4890i	0.814423	+	0.606968i
$739$	14.9697	+	25.9283i	0.550671	+	0.953790i	0.998226	+	0.0595336i	$0.0189613\pi$
$739$	14.9697	+	25.9283i	0.550671	+	0.953790i	−0.447556	+	0.894256i	$0.647705\pi$
$740$	15.1964			0.558630
$741$	−1.46108	−	0.484566i	−0.0536740	−	0.0178010i
$742$		0			0
$743$	9.50069	−	16.4557i	0.348546	−	0.603700i	−0.637445	−	0.770496i	$-0.720009\pi$
$743$	9.50069	−	16.4557i	0.348546	−	0.603700i	0.985991	+	0.166796i	$0.0533420\pi$
$744$	17.0803	−	15.1923i	0.626195	−	0.556977i
$745$	−15.1298	+	26.2055i	−0.554311	+	0.960096i
$746$	−5.95922	−	10.3217i	−0.218183	−	0.377903i
$747$	−11.3276	+	4.87933i	−0.414455	+	0.178525i
$748$	−10.2705			−0.375527
$749$		0			0
$750$	−22.7033	+	20.1937i	−0.829006	+	0.737370i
$751$	−0.0130684	−	0.0226352i	−0.000476873	−	0.000825969i	0.865787	−	0.500413i	$-0.166818\pi$
$751$	−0.0130684	−	0.0226352i	−0.000476873	−	0.000825969i	−0.866264	+	0.499587i	$0.833485\pi$
$752$	−13.2980			−0.484929
$753$	5.97965	−	5.31867i	0.217910	−	0.193823i
$754$	2.88874			0.105202
$755$	−53.2929			−1.93953
$756$		0			0
$757$	−13.6910			−0.497607			−0.248803	−	0.968554i	$-0.580037\pi$
$757$	−13.6910			−0.497607			−0.248803	+	0.968554i	$0.580037\pi$
$758$	−32.4189			−1.17751
$759$	21.3770	−	19.0141i	0.775938	−	0.690168i
$760$	−6.02338			−0.218491
$761$	−7.32141	−	12.6811i	−0.265401	−	0.459688i	0.702268	−	0.711913i	$-0.252171\pi$
$761$	−7.32141	−	12.6811i	−0.265401	−	0.459688i	−0.967669	+	0.252225i	$0.918838\pi$
$762$	−21.9691	+	19.5407i	−0.795855	+	0.707883i
$763$		0			0
$764$	4.11855			0.149004
$765$	35.4869	+	26.4474i	1.28303	+	0.956208i
$766$	2.72803	+	4.72509i	0.0985677	+	0.170724i
$767$	4.43818	−	7.68715i	0.160253	−	0.277567i
$768$	−22.9610	+	20.4230i	−0.828534	+	0.736950i
$769$	24.5672	−	42.5517i	0.885918	−	1.53445i	0.0412592	−	0.999148i	$-0.486863\pi$
$769$	24.5672	−	42.5517i	0.885918	−	1.53445i	0.844658	−	0.535306i	$-0.179804\pi$
$770$		0			0
$771$	2.34108	+	0.776418i	0.0843118	+	0.0279620i
$772$	−22.4820			−0.809146
$773$	6.22067	+	10.7745i	0.223742	+	0.387532i	0.955941	−	0.293558i	$-0.0948394\pi$
$773$	6.22067	+	10.7745i	0.223742	+	0.387532i	−0.732199	+	0.681090i	$0.761506\pi$
$774$	−24.3987	+	10.5097i	−0.876993	+	0.377762i
$775$	−27.5185	+	47.6634i	−0.988493	+	1.71212i
$776$	−6.91411	−	11.9756i	−0.248202	−	0.429898i
$777$		0			0
$778$	−4.36467	+	7.55982i	−0.156481	+	0.271033i
$779$	−2.40476	−	4.16516i	−0.0861594	−	0.149232i
$780$	4.12729	−	3.67107i	0.147781	−	0.131445i
$781$	−4.04256	+	7.00193i	−0.144654	+	0.250549i
$782$	−20.5309	+	35.5605i	−0.734183	+	1.27164i
$783$	−3.73855	+	8.00119i	−0.133605	+	0.285939i
$784$		0			0
$785$	5.18292	+	8.97708i	0.184986	+	0.320406i
$786$	−44.8552	−	14.8762i	−1.59993	−	0.530618i
$787$	32.9133			1.17323			0.586617	−	0.809865i	$-0.300459\pi$
$787$	32.9133			1.17323			0.586617	+	0.809865i	$0.300459\pi$
$788$	9.52784			0.339415
$789$	−5.68911	−	27.5883i	−0.202538	−	0.982168i
$790$	21.6099	+	37.4294i	0.768845	+	1.33168i
$791$		0			0
$792$	12.7706	+	9.51759i	0.453783	+	0.338193i
$793$	−1.93818	+	3.35702i	−0.0688267	+	0.119211i
$794$	19.4931	−	33.7631i	0.691785	−	1.19821i
$795$	0.155205	+	0.752639i	0.00550456	+	0.0266933i
$796$	−3.89554	−	6.74727i	−0.138074	−	0.239151i
$797$	13.1989	−	22.8612i	0.467530	−	0.809786i	−0.531781	−	0.846882i	$-0.678477\pi$
$797$	13.1989	−	22.8612i	0.467530	−	0.809786i	0.999312	+	0.0370953i	$0.0118105\pi$
$798$		0			0
$799$	−5.48074	−	9.49292i	−0.193895	−	0.335835i
$800$	18.5080	−	32.0567i	0.654356	−	1.13338i
$801$	−23.1149	−	17.2269i	−0.816725	−	0.608684i
$802$	15.4752	+	26.8039i	0.546450	+	0.946479i
$803$	−29.9120			−1.05557
$804$	−14.1577	+	12.5927i	−0.499303	+	0.444111i
$805$		0			0
$806$	5.93818	−	10.2852i	0.209163	−	0.362282i
$807$	30.6668	+	10.1706i	1.07952	+	0.358024i
$808$	−3.27197	+	5.66722i	−0.115108	+	0.199372i
$809$	−17.7960	−	30.8235i	−0.625673	−	1.08370i	−0.988410	−	0.151806i	$-0.951491\pi$
$809$	−17.7960	−	30.8235i	−0.625673	−	1.08370i	0.362738	−	0.931891i	$-0.381842\pi$
$810$	15.6884	+	52.6002i	0.551235	+	1.84818i
$811$	37.8268			1.32828			0.664140	−	0.747608i	$-0.268798\pi$
$811$	37.8268			1.32828			0.664140	+	0.747608i	$0.268798\pi$
$812$		0			0
$813$	1.38626	+	6.72243i	0.0486184	+	0.235766i
$814$	11.3825	+	19.7151i	0.398958	+	0.691016i
$815$	−36.9926			−1.29579
$816$	−33.7108	−	11.1802i	−1.18012	−	0.391385i
$817$	4.63045			0.161999
$818$	26.0594			0.911146
$819$		0			0
$820$	17.2583			0.602686
$821$	−18.3128			−0.639119			−0.319560	−	0.947566i	$-0.603535\pi$
$821$	−18.3128			−0.639119			−0.319560	+	0.947566i	$0.603535\pi$
$822$	7.72184	+	37.4456i	0.269330	+	1.30607i
$823$	−36.0000			−1.25488			−0.627441	−	0.778664i	$-0.715897\pi$
$823$	−36.0000			−1.25488			−0.627441	+	0.778664i	$0.715897\pi$
$824$	14.9931	+	25.9688i	0.522310	+	0.904668i
$825$	−36.3974	−	12.0712i	−1.26719	−	0.420265i
$826$		0			0
$827$	−28.2115			−0.981011			−0.490505	−	0.871438i	$-0.663188\pi$
$827$	−28.2115			−0.981011			−0.490505	+	0.871438i	$0.663188\pi$
$828$	−14.3894	+	6.19820i	−0.500067	+	0.215402i
$829$	−5.64214	−	9.77247i	−0.195960	−	0.339412i	0.751255	−	0.660012i	$-0.229449\pi$
$829$	−5.64214	−	9.77247i	−0.195960	−	0.339412i	−0.947215	+	0.320600i	$0.896115\pi$
$830$	−12.5371	+	21.7148i	−0.435168	+	0.753733i
$831$	0.816393	+	3.95895i	0.0283204	+	0.137334i
$832$	0.993810	−	1.72133i	0.0344542	−	0.0596764i
$833$		0			0
$834$	0.660706	+	3.20397i	0.0228784	+	0.110944i
$835$	−43.6057			−1.50904
$836$	1.11009	+	1.92274i	0.0383934	+	0.0664993i
$837$	20.8028	+	29.7585i	0.719051	+	1.02860i
$838$	8.98143	−	15.5563i	0.310258	−	0.537383i
$839$	−1.02152	−	1.76933i	−0.0352669	−	0.0610840i	0.847853	−	0.530231i	$-0.177895\pi$
$839$	−1.02152	−	1.76933i	−0.0352669	−	0.0610840i	−0.883120	+	0.469147i	$0.844561\pi$
$840$		0			0
$841$	13.0556	−	22.6130i	0.450194	−	0.779759i
$842$	30.7392	+	53.2418i	1.05934	+	1.83483i
$843$	46.0235	+	15.2637i	1.58513	+	0.525709i
$844$	−4.67928	+	8.10474i	−0.161067	+	0.278977i
$845$	21.5302	−	37.2914i	0.740661	−	1.28286i
$846$	1.58520	−	13.5019i	0.0545004	−	0.464206i
$847$		0			0
$848$	−0.308344	−	0.534068i	−0.0105886	−	0.0183400i
$849$	13.3560	−	11.8797i	0.458377	−	0.407709i
$850$	55.0370			1.88775
$851$	28.0014			0.959875
$852$	3.30834	−	2.94265i	0.113342	−	0.100814i
$853$	−24.2960	−	42.0818i	−0.831878	−	1.44085i	−0.896547	−	0.442948i	$-0.853933\pi$
$853$	−24.2960	−	42.0818i	−0.831878	−	1.44085i	0.0646692	−	0.997907i	$-0.479401\pi$
$854$		0			0
$855$	1.11559	−	9.50206i	0.0381525	−	0.324964i
$856$	−5.05563	+	8.75661i	−0.172798	+	0.299295i
$857$	−22.4487	+	38.8823i	−0.766833	+	1.32819i	0.172439	+	0.985020i	$0.444835\pi$
$857$	−22.4487	+	38.8823i	−0.766833	+	1.32819i	−0.939272	+	0.343173i	$0.888498\pi$
$858$	7.85414	+	2.60483i	0.268136	+	0.0889273i
$859$	14.9065	+	25.8189i	0.508605	+	0.880929i	0.999950	+	0.00996438i	$0.00317181\pi$
$859$	14.9065	+	25.8189i	0.508605	+	0.880929i	−0.491346	+	0.870965i	$0.663495\pi$
$860$	−8.30786	+	14.3896i	−0.283296	+	0.490683i
$861$		0			0
$862$	−29.8275	−	51.6628i	−1.01593	−	1.75964i
$863$	21.1298	−	36.5978i	0.719265	−	1.24580i	−0.242026	−	0.970270i	$-0.577812\pi$
$863$	21.1298	−	36.5978i	0.719265	−	1.24580i	0.961291	−	0.275534i	$-0.0888548\pi$
$864$	−13.9913	−	20.0145i	−0.475992	−	0.680907i
$865$	−11.8585	−	20.5395i	−0.403200	−	0.698363i
$866$	69.9788			2.37798
$867$	0.0341093	+	0.165407i	0.00115841	+	0.00561751i
$868$		0			0
$869$	−9.95970	+	17.2507i	−0.337860	+	0.585190i
$870$	3.62612	+	17.5842i	0.122937	+	0.596159i
$871$	6.15452	−	10.6599i	0.208538	−	0.361198i
$872$	−17.8145	−	30.8557i	−0.603276	−	1.04491i
$873$	20.1724	−	8.68920i	0.682732	−	0.294085i
$874$	8.87636			0.300247
$875$		0			0
$876$	15.5480	+	5.15649i	0.525318	+	0.174222i
$877$	15.2658	+	26.4411i	0.515489	+	0.892853i	0.999838	+	0.0179782i	$0.00572295\pi$
$877$	15.2658	+	26.4411i	0.515489	+	0.892853i	−0.484350	+	0.874875i	$0.660944\pi$
$878$	7.95186			0.268362
$879$	−10.7379	−	52.0712i	−0.362179	−	1.75632i
$880$	50.3077			1.69587
$881$	13.4079			0.451724			0.225862	−	0.974159i	$-0.427480\pi$
$881$	13.4079			0.451724			0.225862	+	0.974159i	$0.427480\pi$
$882$		0			0
$883$	−14.1250			−0.475345			−0.237672	−	0.971345i	$-0.576384\pi$
$883$	−14.1250			−0.475345			−0.237672	+	0.971345i	$0.576384\pi$
$884$	−3.65383			−0.122892
$885$	52.3639	+	17.3665i	1.76019	+	0.583768i
$886$	51.2829			1.72288
$887$	−19.9716	−	34.5918i	−0.670581	−	1.16148i	−0.977740	−	0.209822i	$-0.932712\pi$
$887$	−19.9716	−	34.5918i	−0.670581	−	1.16148i	0.307159	−	0.951658i	$-0.400622\pi$
$888$	3.14833	+	15.2672i	0.105651	+	0.512334i
$889$		0			0
$890$	−58.6067			−1.96450
$891$	−17.3795	+	18.3832i	−0.582236	+	0.615861i
$892$	−2.51849	−	4.36216i	−0.0843254	−	0.146056i
$893$	−1.18478	+	2.05209i	−0.0396471	+	0.0686707i
$894$	23.5624	+	7.81448i	0.788046	+	0.261355i
$895$	6.89493	−	11.9424i	0.230472	−	0.399189i
$896$		0			0
$897$	7.60507	−	6.76443i	0.253926	−	0.225858i
$898$	0.567323			0.0189318
$899$	5.93818	+	10.2852i	0.198049	+	0.343031i
$900$	16.8381	+	12.5490i	0.561271	+	0.418300i
$901$	0.254166	−	0.440229i	0.00846751	−	0.0146662i
$902$	12.9270	+	22.3902i	0.430421	+	0.745511i
$903$		0			0
$904$	−17.5192	+	30.3441i	−0.582679	+	1.00923i
$905$	33.2687	+	57.6231i	1.10589	+	1.91546i
$906$	8.83007	+	42.8198i	0.293360	+	1.42259i
$907$	−20.7101	+	35.8710i	−0.687669	+	1.19108i	0.284921	+	0.958551i	$0.408033\pi$
$907$	−20.7101	+	35.8710i	−0.687669	+	1.19108i	−0.972590	+	0.232527i	$0.925301\pi$
$908$	−4.93199	+	8.54245i	−0.163674	+	0.283491i
$909$	−8.33420	−	6.21126i	−0.276428	−	0.206014i
$910$		0			0
$911$	−0.894237	−	1.54886i	−0.0296274	−	0.0513162i	0.850832	−	0.525439i	$-0.176099\pi$
$911$	−0.894237	−	1.54886i	−0.0296274	−	0.0513162i	−0.880459	+	0.474122i	$0.842765\pi$
$912$	1.55061	+	7.51941i	0.0513459	+	0.248992i
$913$	−11.5563			−0.382458
$914$	−32.8182			−1.08553
$915$	−22.8676	−	7.58404i	−0.755980	−	0.250721i
$916$	8.72864	+	15.1185i	0.288402	+	0.499528i
$917$		0			0
$918$	15.3702	−	32.8950i	0.507291	−	1.08570i
$919$	28.7341	−	49.7690i	0.947852	−	1.64173i	0.197914	−	0.980219i	$-0.436583\pi$
$919$	28.7341	−	49.7690i	0.947852	−	1.64173i	0.749938	−	0.661508i	$-0.230083\pi$
$920$	19.9134	−	34.4911i	0.656526	−	1.13714i
$921$	−14.8102	+	13.1731i	−0.488013	+	0.434069i
$922$	33.2341	+	57.5632i	1.09451	+	1.89574i
$923$	−1.43818	+	2.49100i	−0.0473382	+	0.0819922i
$924$		0			0
$925$	−18.7658	−	32.5033i	−0.617015	−	1.06870i
$926$	−18.5908	+	32.2003i	−0.610933	+	1.05817i
$927$	−43.7435	+	18.8424i	−1.43672	+	0.618865i
$928$	−3.99381	−	6.91748i	−0.131103	−	0.227077i
$929$	−34.7352			−1.13963			−0.569813	−	0.821774i	$-0.692984\pi$
$929$	−34.7352			−1.13963			−0.569813	+	0.821774i	$0.692984\pi$
$930$	70.0617	+	23.2359i	2.29741	+	0.761937i
$931$		0			0
$932$	−3.98281	+	6.89843i	−0.130461	+	0.225965i
$933$	15.4821	−	13.7708i	0.506862	−	0.450835i
$934$	−10.4697	+	18.1341i	−0.342580	+	0.593367i
$935$	20.7341	+	35.9126i	0.678079	+	1.17447i
$936$	4.54325	+	3.38597i	0.148501	+	0.110674i
$937$	−11.6662			−0.381118			−0.190559	−	0.981676i	$-0.561030\pi$
$937$	−11.6662			−0.381118			−0.190559	+	0.981676i	$0.561030\pi$
$938$		0			0
$939$	−17.5283	+	15.5908i	−0.572015	+	0.508786i
$940$	−4.25141	−	7.36366i	−0.138666	−	0.240176i
$941$	50.3374			1.64095			0.820475	−	0.571682i	$-0.193709\pi$
$941$	50.3374			1.64095			0.820475	+	0.571682i	$0.193709\pi$
$942$	6.35414	−	5.65178i	0.207029	−	0.184145i
$943$	31.8007			1.03557
$944$	−44.2719			−1.44093
$945$		0			0
$946$	−24.8913			−0.809287
$947$	−32.3883			−1.05248			−0.526238	−	0.850337i	$-0.676398\pi$
$947$	−32.3883			−1.05248			−0.526238	+	0.850337i	$0.676398\pi$
$948$	8.15080	−	7.24983i	0.264726	−	0.235464i
$949$	−10.6414			−0.345436
$950$	−5.94870	−	10.3034i	−0.193001	−	0.334288i
$951$	38.7774	−	34.4911i	1.25744	−	1.11845i
$952$		0			0
$953$	−12.5367			−0.406102			−0.203051	−	0.979168i	$-0.565086\pi$
$953$	−12.5367			−0.406102			−0.203051	+	0.979168i	$0.565086\pi$
$954$	0.579014	−	0.249409i	0.0187463	−	0.00807490i
$955$	−8.31453	−	14.4012i	−0.269052	−	0.466012i
$956$	−4.98693	+	8.63762i	−0.161289	+	0.279361i
$957$	−6.18292	+	5.49948i	−0.199865	+	0.177773i
$958$	11.4635	−	19.8555i	0.370370	−	0.641500i
$959$		0			0
$960$	11.7255	+	3.88875i	0.378438	+	0.125509i
$961$	17.8268			0.575059
$962$	4.04944	+	7.01384i	0.130559	+	0.226135i
$963$	−12.8775	−	9.59722i	−0.414970	−	0.309266i
$964$	−3.10446	+	5.37709i	−0.0999880	+	0.173184i
$965$	45.3868	+	78.6122i	1.46105	+	2.53062i
$966$		0			0
$967$	28.9937	−	50.2186i	0.932376	−	1.61492i	0.153127	−	0.988206i	$-0.451065\pi$
$967$	28.9937	−	50.2186i	0.932376	−	1.61492i	0.779248	−	0.626715i	$-0.215601\pi$
$968$	−2.92649	−	5.06882i	−0.0940609	−	0.162918i
$969$	−4.72872	+	4.20602i	−0.151908	+	0.135117i
$970$	22.3262	−	38.6702i	0.716852	−	1.24162i
$971$	14.0185	−	24.2807i	0.449875	−	0.779206i	−0.548503	−	0.836149i	$-0.684802\pi$
$971$	14.0185	−	24.2807i	0.449875	−	0.779206i	0.998377	+	0.0569428i	$0.0181353\pi$
$972$	12.2028	−	6.55941i	0.391405	−	0.210393i
$973$		0			0
$974$	−6.41095	−	11.1041i	−0.205420	−	0.355798i
$975$	−12.9487	−	4.29443i	−0.414690	−	0.137532i
$976$	19.3338			0.618860
$977$	9.84059			0.314829			0.157414	−	0.987533i	$-0.449684\pi$
$977$	9.84059			0.314829			0.157414	+	0.987533i	$0.449684\pi$
$978$	6.12928	+	29.7228i	0.195993	+	0.950429i
$979$	−13.5055	−	23.3922i	−0.431638	−	0.747618i
$980$		0			0
$981$	51.9752	−	22.3881i	1.65944	−	0.714798i
$982$	13.7156	−	23.7562i	0.437684	−	0.758091i
$983$	−24.3447	+	42.1663i	−0.776476	+	1.34490i	0.157485	+	0.987521i	$0.449661\pi$
$983$	−24.3447	+	42.1663i	−0.776476	+	1.34490i	−0.933961	+	0.357374i	$0.883672\pi$
$984$	3.57550	+	17.3387i	0.113983	+	0.552739i
$985$	−19.2348	−	33.3157i	−0.612873	−	1.06153i
$986$	5.93818	−	10.2852i	0.189110	−	0.327548i
$987$		0			0
$988$	0.394926	+	0.684031i	0.0125643	+	0.0217619i
$989$	−15.3083	+	26.5148i	−0.486777	+	0.843123i
$990$	−5.99697	+	51.0791i	−0.190596	+	1.62340i
$991$	−1.43199	−	2.48028i	−0.0454886	−	0.0787886i	0.842385	−	0.538877i	$-0.181151\pi$
$991$	−1.43199	−	2.48028i	−0.0454886	−	0.0787886i	−0.887873	+	0.460088i	$0.847818\pi$
$992$	−32.8392			−1.04265
$993$	−2.70032	+	2.40183i	−0.0856920	+	0.0762198i
$994$		0			0
$995$	−15.7286	+	27.2428i	−0.498631	+	0.863655i
$996$	6.00688	+	1.99218i	0.190335	+	0.0631247i
$997$	−25.4203	+	44.0292i	−0.805069	+	1.39442i	0.111176	+	0.993801i	$0.464538\pi$
$997$	−25.4203	+	44.0292i	−0.805069	+	1.39442i	−0.916245	+	0.400619i	$0.868795\pi$
$998$	26.2298	+	45.4314i	0.830290	+	1.43810i
$999$	−24.6676	+	2.13892i	−0.780448	+	0.0676725i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.h.b.373.3		6
3.2	odd	2		1323.2.h.e.226.1		6
7.2	even	3		441.2.f.d.148.1		6
7.3	odd	6		441.2.g.e.67.1		6
7.4	even	3		441.2.g.d.67.1		6
7.5	odd	6		63.2.f.b.22.1	✓	6
7.6	odd	2		441.2.h.c.373.3		6
9.2	odd	6		1323.2.g.b.667.3		6
9.7	even	3		441.2.g.d.79.1		6
21.2	odd	6		1323.2.f.c.442.3		6
21.5	even	6		189.2.f.a.64.3		6
21.11	odd	6		1323.2.g.b.361.3		6
21.17	even	6		1323.2.g.c.361.3		6
21.20	even	2		1323.2.h.d.226.1		6
28.19	even	6		1008.2.r.k.337.1		6
63.2	odd	6		1323.2.f.c.883.3		6
63.5	even	6		567.2.a.g.1.1		3
63.11	odd	6		1323.2.h.e.802.1		6
63.16	even	3		441.2.f.d.295.1		6
63.20	even	6		1323.2.g.c.667.3		6
63.23	odd	6		3969.2.a.p.1.1		3
63.25	even	3	inner	441.2.h.b.214.3		6
63.34	odd	6		441.2.g.e.79.1		6
63.38	even	6		1323.2.h.d.802.1		6
63.40	odd	6		567.2.a.d.1.3		3
63.47	even	6		189.2.f.a.127.3		6
63.52	odd	6		441.2.h.c.214.3		6
63.58	even	3		3969.2.a.m.1.3		3
63.61	odd	6		63.2.f.b.43.1	yes	6
84.47	odd	6		3024.2.r.g.1009.1		6
252.47	odd	6		3024.2.r.g.2017.1		6
252.103	even	6		9072.2.a.bq.1.1		3
252.131	odd	6		9072.2.a.cd.1.3		3
252.187	even	6		1008.2.r.k.673.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.b.22.1	✓	6	7.5	odd	6
63.2.f.b.43.1	yes	6	63.61	odd	6
189.2.f.a.64.3		6	21.5	even	6
189.2.f.a.127.3		6	63.47	even	6
441.2.f.d.148.1		6	7.2	even	3
441.2.f.d.295.1		6	63.16	even	3
441.2.g.d.67.1		6	7.4	even	3
441.2.g.d.79.1		6	9.7	even	3
441.2.g.e.67.1		6	7.3	odd	6
441.2.g.e.79.1		6	63.34	odd	6
441.2.h.b.214.3		6	63.25	even	3	inner
441.2.h.b.373.3		6	1.1	even	1	trivial
441.2.h.c.214.3		6	63.52	odd	6
441.2.h.c.373.3		6	7.6	odd	2
567.2.a.d.1.3		3	63.40	odd	6
567.2.a.g.1.1		3	63.5	even	6
1008.2.r.k.337.1		6	28.19	even	6
1008.2.r.k.673.1		6	252.187	even	6
1323.2.f.c.442.3		6	21.2	odd	6
1323.2.f.c.883.3		6	63.2	odd	6
1323.2.g.b.361.3		6	21.11	odd	6
1323.2.g.b.667.3		6	9.2	odd	6
1323.2.g.c.361.3		6	21.17	even	6
1323.2.g.c.667.3		6	63.20	even	6
1323.2.h.d.226.1		6	21.20	even	2
1323.2.h.d.802.1		6	63.38	even	6
1323.2.h.e.226.1		6	3.2	odd	2
1323.2.h.e.802.1		6	63.11	odd	6
3024.2.r.g.1009.1		6	84.47	odd	6
3024.2.r.g.2017.1		6	252.47	odd	6
3969.2.a.m.1.3		3	63.58	even	3
3969.2.a.p.1.1		3	63.23	odd	6
9072.2.a.bq.1.1		3	252.103	even	6
9072.2.a.cd.1.3		3	252.131	odd	6

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.69963 q^{2} +(-1.29418 + 1.15113i) q^{3} +0.888736 q^{4} +(-1.79418 - 3.10761i) q^{5} +(-2.19963 + 1.95649i) q^{6} -1.88874 q^{8} +(0.349814 - 2.97954i) q^{9} +O(q^{10})\)	\(q+1.69963 q^{2} +(-1.29418 + 1.15113i) q^{3} +0.888736 q^{4} +(-1.79418 - 3.10761i) q^{5} +(-2.19963 + 1.95649i) q^{6} -1.88874 q^{8} +(0.349814 - 2.97954i) q^{9} +(-3.04944 - 5.28179i) q^{10} +(1.40545 - 2.43430i) q^{11} +(-1.15019 + 1.02305i) q^{12} +(0.500000 - 0.866025i) q^{13} +(5.89926 + 1.95649i) q^{15} -4.98762 q^{16} +(-2.05563 - 3.56046i) q^{17} +(0.594554 - 5.06410i) q^{18} +(-0.444368 + 0.769668i) q^{19} +(-1.59455 - 2.76185i) q^{20} +(2.38874 - 4.13741i) q^{22} +(-2.93818 - 5.08907i) q^{23} +(2.44437 - 2.17417i) q^{24} +(-3.93818 + 6.82112i) q^{25} +(0.849814 - 1.47192i) q^{26} +(2.97710 + 4.25874i) q^{27} +(0.849814 + 1.47192i) q^{29} +(10.0265 + 3.32530i) q^{30} +6.98762 q^{31} -4.69963 q^{32} +(0.983290 + 4.76828i) q^{33} +(-3.49381 - 6.05146i) q^{34} +(0.310892 - 2.64802i) q^{36} +(-2.38255 + 4.12669i) q^{37} +(-0.755260 + 1.30815i) q^{38} +(0.349814 + 1.69636i) q^{39} +(3.38874 + 5.86946i) q^{40} +(-2.70582 + 4.68661i) q^{41} +(-2.60507 - 4.51212i) q^{43} +(1.24907 - 2.16345i) q^{44} +(-9.88688 + 4.25874i) q^{45} +(-4.99381 - 8.64953i) q^{46} +2.66621 q^{47} +(6.45489 - 5.74138i) q^{48} +(-6.69344 + 11.5934i) q^{50} +(6.75890 + 2.24159i) q^{51} +(0.444368 - 0.769668i) q^{52} +(0.0618219 + 0.107079i) q^{53} +(5.05996 + 7.23828i) q^{54} -10.0865 q^{55} +(-0.310892 - 1.50761i) q^{57} +(1.44437 + 2.50172i) q^{58} +8.87636 q^{59} +(5.24288 + 1.73880i) q^{60} -3.87636 q^{61} +11.8764 q^{62} +1.98762 q^{64} -3.58836 q^{65} +(1.67123 + 8.10430i) q^{66} +12.3090 q^{67} +(-1.82691 - 3.16431i) q^{68} +(9.66071 + 3.20397i) q^{69} -2.87636 q^{71} +(-0.660706 + 5.62755i) q^{72} +(-5.32072 - 9.21576i) q^{73} +(-4.04944 + 7.01384i) q^{74} +(-2.75526 - 13.3611i) q^{75} +(-0.394926 + 0.684031i) q^{76} +(0.594554 + 2.88318i) q^{78} -7.08650 q^{79} +(8.94870 + 15.4996i) q^{80} +(-8.75526 - 2.08457i) q^{81} +(-4.59888 + 7.96550i) q^{82} +(-2.05563 - 3.56046i) q^{83} +(-7.37636 + 12.7762i) q^{85} +(-4.42766 - 7.66893i) q^{86} +(-2.79418 - 0.926690i) q^{87} +(-2.65452 + 4.59776i) q^{88} +(4.80470 - 8.32199i) q^{89} +(-16.8040 + 7.23828i) q^{90} +(-2.61126 - 4.52284i) q^{92} +(-9.04325 + 8.04364i) q^{93} +4.53156 q^{94} +3.18911 q^{95} +(6.08217 - 5.40987i) q^{96} +(3.66071 + 6.34053i) q^{97} +(-6.76145 - 5.03913i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 2 q^{3} + 6 q^{4} - 5 q^{5} - q^{6} - 12 q^{8} - 4 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 2 * q^3 + 6 * q^4 - 5 * q^5 - q^6 - 12 * q^8 - 4 * q^9	\( 6 q - 2 q^{2} - 2 q^{3} + 6 q^{4} - 5 q^{5} - q^{6} - 12 q^{8} - 4 q^{9} + 2 q^{11} - 13 q^{12} + 3 q^{13} + 11 q^{15} + 6 q^{16} - 12 q^{17} + 10 q^{18} - 3 q^{19} - 16 q^{20} + 15 q^{22} + 15 q^{24} - 6 q^{25} - q^{26} + 7 q^{27} - q^{29} + 31 q^{30} + 6 q^{31} - 16 q^{32} + 13 q^{33} - 3 q^{34} - 11 q^{36} + 3 q^{37} + 8 q^{38} - 4 q^{39} + 21 q^{40} - 22 q^{41} + 3 q^{43} - 23 q^{44} + q^{45} - 12 q^{46} + 18 q^{47} + 14 q^{48} - 10 q^{50} - 12 q^{51} + 3 q^{52} + 18 q^{53} - 13 q^{54} + 12 q^{55} + 11 q^{57} + 9 q^{58} + 18 q^{59} - 17 q^{60} + 12 q^{61} + 36 q^{62} - 24 q^{64} - 10 q^{65} - 34 q^{66} + 6 q^{68} + 39 q^{69} + 18 q^{71} + 15 q^{72} + 3 q^{73} - 6 q^{74} - 4 q^{75} - 21 q^{76} + 10 q^{78} + 30 q^{79} + 11 q^{80} - 40 q^{81} + 9 q^{82} - 12 q^{83} - 9 q^{85} - 34 q^{86} - 11 q^{87} + 21 q^{88} - 2 q^{89} - 73 q^{90} - 15 q^{92} - 18 q^{93} - 48 q^{94} + 32 q^{95} + 7 q^{96} + 3 q^{97} - 46 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 2 * q^3 + 6 * q^4 - 5 * q^5 - q^6 - 12 * q^8 - 4 * q^9 + 2 * q^11 - 13 * q^12 + 3 * q^13 + 11 * q^15 + 6 * q^16 - 12 * q^17 + 10 * q^18 - 3 * q^19 - 16 * q^20 + 15 * q^22 + 15 * q^24 - 6 * q^25 - q^26 + 7 * q^27 - q^29 + 31 * q^30 + 6 * q^31 - 16 * q^32 + 13 * q^33 - 3 * q^34 - 11 * q^36 + 3 * q^37 + 8 * q^38 - 4 * q^39 + 21 * q^40 - 22 * q^41 + 3 * q^43 - 23 * q^44 + q^45 - 12 * q^46 + 18 * q^47 + 14 * q^48 - 10 * q^50 - 12 * q^51 + 3 * q^52 + 18 * q^53 - 13 * q^54 + 12 * q^55 + 11 * q^57 + 9 * q^58 + 18 * q^59 - 17 * q^60 + 12 * q^61 + 36 * q^62 - 24 * q^64 - 10 * q^65 - 34 * q^66 + 6 * q^68 + 39 * q^69 + 18 * q^71 + 15 * q^72 + 3 * q^73 - 6 * q^74 - 4 * q^75 - 21 * q^76 + 10 * q^78 + 30 * q^79 + 11 * q^80 - 40 * q^81 + 9 * q^82 - 12 * q^83 - 9 * q^85 - 34 * q^86 - 11 * q^87 + 21 * q^88 - 2 * q^89 - 73 * q^90 - 15 * q^92 - 18 * q^93 - 48 * q^94 + 32 * q^95 + 7 * q^96 + 3 * q^97 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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