LMFDB - Embedded newform 441.2.g.e.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(67,441)]

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([2, 4]))

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

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

chi := DirichletCharacter("441.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.g (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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	441.79
Dual form			441.2.g.e.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.849814 - 1.47192i) q^{2} +(-1.64400 + 0.545231i) q^{3} +(-0.444368 + 0.769668i) q^{4} -3.58836 q^{5} +(2.19963 + 1.95649i) q^{6} -1.88874 q^{8} +(2.40545 - 1.79272i) q^{9} +O(q^{10})$	\(q+(-0.849814 - 1.47192i) q^{2} +(-1.64400 + 0.545231i) q^{3} +(-0.444368 + 0.769668i) q^{4} -3.58836 q^{5} +(2.19963 + 1.95649i) q^{6} -1.88874 q^{8} +(2.40545 - 1.79272i) q^{9} +(3.04944 + 5.28179i) q^{10} -2.81089 q^{11} +(0.310892 - 1.50761i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(5.89926 - 1.95649i) q^{15} +(2.49381 + 4.31941i) q^{16} +(2.05563 + 3.56046i) q^{17} +(-4.68292 - 2.01715i) q^{18} +(0.444368 - 0.769668i) q^{19} +(1.59455 - 2.76185i) q^{20} +(2.38874 + 4.13741i) q^{22} +5.87636 q^{23} +(3.10507 - 1.02980i) q^{24} +7.87636 q^{25} +(-0.849814 + 1.47192i) q^{26} +(-2.97710 + 4.25874i) q^{27} +(0.849814 - 1.47192i) q^{29} +(-7.89307 - 7.02059i) q^{30} +(3.49381 - 6.05146i) q^{31} +(2.34981 - 4.07000i) q^{32} +(4.62110 - 1.53259i) q^{33} +(3.49381 - 6.05146i) q^{34} +(0.310892 + 2.64802i) q^{36} +(-2.38255 + 4.12669i) q^{37} -1.51052 q^{38} +(1.29418 + 1.15113i) q^{39} +6.77747 q^{40} +(2.70582 + 4.68661i) q^{41} +(-2.60507 + 4.51212i) q^{43} +(1.24907 - 2.16345i) q^{44} +(-8.63162 + 6.43292i) q^{45} +(-4.99381 - 8.64953i) q^{46} +(1.33310 + 2.30900i) q^{47} +(-6.45489 - 5.74138i) q^{48} +(-6.69344 - 11.5934i) q^{50} +(-5.32072 - 4.73259i) q^{51} +0.888736 q^{52} +(0.0618219 + 0.107079i) q^{53} +(8.79851 + 0.762918i) q^{54} +10.0865 q^{55} +(-0.310892 + 1.50761i) q^{57} -2.88874 q^{58} +(4.43818 - 7.68715i) q^{59} +(-1.11559 + 5.40987i) q^{60} +(-1.93818 - 3.35702i) q^{61} -11.8764 q^{62} +1.98762 q^{64} +(1.79418 + 3.10761i) q^{65} +(-6.18292 - 5.49948i) q^{66} +(-6.15452 + 10.6599i) q^{67} -3.65383 q^{68} +(-9.66071 + 3.20397i) q^{69} -2.87636 q^{71} +(-4.54325 + 3.38597i) q^{72} +(5.32072 + 9.21576i) q^{73} +8.09888 q^{74} +(-12.9487 + 4.29443i) q^{75} +(0.394926 + 0.684031i) q^{76} +(0.594554 - 2.88318i) q^{78} +(3.54325 + 6.13709i) q^{79} +(-8.94870 - 15.4996i) q^{80} +(2.57234 - 8.62456i) q^{81} +(4.59888 - 7.96550i) q^{82} +(2.05563 - 3.56046i) q^{83} +(-7.37636 - 12.7762i) q^{85} +8.85532 q^{86} +(-0.594554 + 2.88318i) q^{87} +5.30903 q^{88} +(-4.80470 + 8.32199i) q^{89} +(16.8040 + 7.23828i) q^{90} +(-2.61126 + 4.52284i) q^{92} +(-2.44437 + 11.8535i) q^{93} +(2.26578 - 3.92445i) q^{94} +(-1.59455 + 2.76185i) q^{95} +(-1.64400 + 7.97225i) q^{96} +(-3.66071 + 6.34053i) q^{97} +(-6.76145 + 5.03913i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} + 2 q^{3} - 3 q^{4} - 10 q^{5} + q^{6} - 12 q^{8} + 8 q^{9}+O(q^{10}) $ 6 * q + q^2 + 2 * q^3 - 3 * q^4 - 10 * q^5 + q^6 - 12 * q^8 + 8 * q^9	$ 6 q + q^{2} + 2 q^{3} - 3 q^{4} - 10 q^{5} + q^{6} - 12 q^{8} + 8 q^{9} - 4 q^{11} - 11 q^{12} - 3 q^{13} + 11 q^{15} - 3 q^{16} + 12 q^{17} - 23 q^{18} + 3 q^{19} + 16 q^{20} + 15 q^{22} + 12 q^{25} + q^{26} - 7 q^{27} - q^{29} - 5 q^{30} + 3 q^{31} + 8 q^{32} + 5 q^{33} + 3 q^{34} - 11 q^{36} + 3 q^{37} + 16 q^{38} + 2 q^{39} + 42 q^{40} + 22 q^{41} + 3 q^{43} - 23 q^{44} - 4 q^{45} - 12 q^{46} + 9 q^{47} - 14 q^{48} - 10 q^{50} + 3 q^{51} + 6 q^{52} + 18 q^{53} + 4 q^{54} - 12 q^{55} + 11 q^{57} - 18 q^{58} + 9 q^{59} + 37 q^{60} + 6 q^{61} - 36 q^{62} - 24 q^{64} + 5 q^{65} - 32 q^{66} + 12 q^{68} - 39 q^{69} + 18 q^{71} + 9 q^{72} - 3 q^{73} + 12 q^{74} - 35 q^{75} + 21 q^{76} + 10 q^{78} - 15 q^{79} - 11 q^{80} + 8 q^{81} - 9 q^{82} + 12 q^{83} - 9 q^{85} + 68 q^{86} - 10 q^{87} - 42 q^{88} + 2 q^{89} + 73 q^{90} - 15 q^{92} - 15 q^{93} - 24 q^{94} - 16 q^{95} + 2 q^{96} - 3 q^{97} - 46 q^{99}+O(q^{100}) $ 6 * q + q^2 + 2 * q^3 - 3 * q^4 - 10 * q^5 + q^6 - 12 * q^8 + 8 * q^9 - 4 * q^11 - 11 * q^12 - 3 * q^13 + 11 * q^15 - 3 * q^16 + 12 * q^17 - 23 * q^18 + 3 * q^19 + 16 * q^20 + 15 * q^22 + 12 * q^25 + q^26 - 7 * q^27 - q^29 - 5 * q^30 + 3 * q^31 + 8 * q^32 + 5 * q^33 + 3 * q^34 - 11 * q^36 + 3 * q^37 + 16 * q^38 + 2 * q^39 + 42 * q^40 + 22 * q^41 + 3 * q^43 - 23 * q^44 - 4 * q^45 - 12 * q^46 + 9 * q^47 - 14 * q^48 - 10 * q^50 + 3 * q^51 + 6 * q^52 + 18 * q^53 + 4 * q^54 - 12 * q^55 + 11 * q^57 - 18 * q^58 + 9 * q^59 + 37 * q^60 + 6 * q^61 - 36 * q^62 - 24 * q^64 + 5 * q^65 - 32 * q^66 + 12 * q^68 - 39 * q^69 + 18 * q^71 + 9 * q^72 - 3 * q^73 + 12 * q^74 - 35 * q^75 + 21 * q^76 + 10 * q^78 - 15 * q^79 - 11 * q^80 + 8 * q^81 - 9 * q^82 + 12 * q^83 - 9 * q^85 + 68 * q^86 - 10 * q^87 - 42 * q^88 + 2 * q^89 + 73 * q^90 - 15 * q^92 - 15 * q^93 - 24 * q^94 - 16 * q^95 + 2 * q^96 - 3 * q^97 - 46 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.849814	−	1.47192i	−0.600909	−	1.04081i	−0.992684	−	0.120744i	$-0.961472\pi$
$2$	−0.849814	−	1.47192i	−0.600909	−	1.04081i	0.391774	−	0.920061i	$-0.371861\pi$
$3$	−1.64400	+	0.545231i	−0.949162	+	0.314789i
$3$	−1.64400	+	0.545231i	−0.949162	+	0.314789i
$4$	−0.444368	+	0.769668i	−0.222184	+	0.384834i
$5$	−3.58836			−1.60477			−0.802383	−	0.596810i	$-0.796435\pi$
$5$	−3.58836			−1.60477			−0.802383	+	0.596810i	$0.796435\pi$
$6$	2.19963	+	1.95649i	0.897994	+	0.798733i
$7$		0			0
$7$		0			0
$8$	−1.88874			−0.667769
$9$	2.40545	−	1.79272i	0.801815	−	0.597572i
$10$	3.04944	+	5.28179i	0.964318	+	1.67025i
$11$	−2.81089			−0.847516			−0.423758	−	0.905775i	$-0.639289\pi$
$11$	−2.81089			−0.847516			−0.423758	+	0.905775i	$0.639289\pi$
$12$	0.310892	−	1.50761i	0.0897469	−	0.435211i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	0.788320	−	0.615265i	$-0.210951\pi$
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	−0.926995	+	0.375073i	$0.877618\pi$
$14$		0			0
$15$	5.89926	−	1.95649i	1.52318	−	0.505163i
$16$	2.49381	+	4.31941i	0.623453	+	1.07985i
$17$	2.05563	+	3.56046i	0.498564	+	0.863538i	0.999999	−	0.00165734i	$-0.000527549\pi$
$17$	2.05563	+	3.56046i	0.498564	+	0.863538i	−0.501435	+	0.865196i	$0.667194\pi$
$18$	−4.68292	−	2.01715i	−1.10377	−	0.475447i
$19$	0.444368	−	0.769668i	0.101945	−	0.176574i	−0.810541	−	0.585682i	$-0.800827\pi$
$19$	0.444368	−	0.769668i	0.101945	−	0.176574i	0.912486	+	0.409108i	$0.134160\pi$
$20$	1.59455	−	2.76185i	0.356553	−	0.617568i
$21$		0			0
$22$	2.38874	+	4.13741i	0.509280	+	0.882099i
$23$	5.87636			1.22530			0.612652	−	0.790352i	$-0.290103\pi$
$23$	5.87636			1.22530			0.612652	+	0.790352i	$0.290103\pi$
$24$	3.10507	−	1.02980i	0.633821	−	0.210207i
$25$	7.87636			1.57527
$26$	−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	−0.776271	−	0.630399i	$-0.782891\pi$
$29$	0.849814	−	1.47192i	0.157807	−	0.273329i	0.934077	+	0.357071i	$0.116224\pi$
$30$	−7.89307	−	7.02059i	−1.44107	−	1.28178i
$31$	3.49381	−	6.05146i	0.627507	−	1.08687i	−0.360544	−	0.932742i	$-0.617409\pi$
$31$	3.49381	−	6.05146i	0.627507	−	1.08687i	0.988050	−	0.154131i	$-0.0492579\pi$
$32$	2.34981	−	4.07000i	0.415392	−	0.719481i
$33$	4.62110	−	1.53259i	0.804430	−	0.266789i
$34$	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	$0.294775\pi$
$38$	−1.51052			−0.245039
$39$	1.29418	+	1.15113i	0.207235	+	0.184328i
$40$	6.77747			1.07161
$41$	2.70582	+	4.68661i	0.422578	+	0.731926i	0.996191	−	0.0872002i	$-0.0277920\pi$
$41$	2.70582	+	4.68661i	0.422578	+	0.731926i	−0.573613	+	0.819126i	$0.694459\pi$
$42$		0			0
$43$	−2.60507	+	4.51212i	−0.397270	+	0.688092i	−0.993388	−	0.114805i	$-0.963376\pi$
$43$	−2.60507	+	4.51212i	−0.397270	+	0.688092i	0.596118	+	0.802897i	$0.296709\pi$
$44$	1.24907	−	2.16345i	0.188304	−	0.326153i
$45$	−8.63162	+	6.43292i	−1.28673	+	0.958962i
$46$	−4.99381	−	8.64953i	−0.736297	−	1.27530i
$47$	1.33310	+	2.30900i	0.194453	+	0.336803i	0.946721	−	0.322055i	$-0.104373\pi$
$47$	1.33310	+	2.30900i	0.194453	+	0.336803i	−0.752268	+	0.658857i	$0.771040\pi$
$48$	−6.45489	−	5.74138i	−0.931683	−	0.828697i
$49$		0			0
$50$	−6.69344	−	11.5934i	−0.946595	−	1.63955i
$51$	−5.32072	−	4.73259i	−0.745050	−	0.662695i
$52$	0.888736			0.123245
$53$	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	$0.830630\pi$
$54$	8.79851	+	0.762918i	1.19733	+	0.103820i
$55$	10.0865			1.36006
$56$		0			0
$57$	−0.310892	+	1.50761i	−0.0411787	+	0.199688i
$58$	−2.88874			−0.379310
$59$	4.43818	−	7.68715i	0.577802	−	1.00078i	−0.417929	−	0.908479i	$-0.637244\pi$
$59$	4.43818	−	7.68715i	0.577802	−	1.00078i	0.995731	−	0.0923022i	$-0.0294226\pi$
$60$	−1.11559	+	5.40987i	−0.144023	+	0.698411i
$61$	−1.93818	−	3.35702i	−0.248158	−	0.429823i	0.714857	−	0.699271i	$-0.246492\pi$
$61$	−1.93818	−	3.35702i	−0.248158	−	0.429823i	−0.963015	+	0.269448i	$0.913159\pi$
$62$	−11.8764			−1.50830
$63$		0			0
$64$	1.98762			0.248453
$65$	1.79418	+	3.10761i	0.222541	+	0.385452i
$66$	−6.18292	−	5.49948i	−0.761065	−	0.676939i
$67$	−6.15452	+	10.6599i	−0.751894	+	1.30232i	0.195010	+	0.980801i	$0.437526\pi$
$67$	−6.15452	+	10.6599i	−0.751894	+	1.30232i	−0.946904	+	0.321517i	$0.895807\pi$
$68$	−3.65383			−0.443092
$69$	−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	$0.554597\pi$
$72$	−4.54325	+	3.38597i	−0.535427	+	0.399040i
$73$	5.32072	+	9.21576i	0.622744	+	1.07862i	0.988973	+	0.148099i	$0.0473154\pi$
$73$	5.32072	+	9.21576i	0.622744	+	1.07862i	−0.366229	+	0.930525i	$0.619351\pi$
$74$	8.09888			0.941476
$75$	−12.9487	+	4.29443i	−1.49519	+	0.495879i
$76$	0.394926	+	0.684031i	0.0453011	+	0.0784638i
$77$		0			0
$78$	0.594554	−	2.88318i	0.0673200	−	0.326456i
$79$	3.54325	+	6.13709i	0.398647	+	0.690477i	0.993559	−	0.113314i	$-0.0361465\pi$
$79$	3.54325	+	6.13709i	0.398647	+	0.690477i	−0.594912	+	0.803791i	$0.702813\pi$
$80$	−8.94870	−	15.4996i	−1.00049	−	1.73291i
$81$	2.57234	−	8.62456i	0.285816	−	0.958285i
$82$	4.59888	−	7.96550i	0.507862	−	0.879642i
$83$	2.05563	−	3.56046i	0.225635	−	0.390811i	−0.730875	−	0.682512i	$-0.760888\pi$
$83$	2.05563	−	3.56046i	0.225635	−	0.390811i	0.956510	+	0.291700i	$0.0942210\pi$
$84$		0			0
$85$	−7.37636	−	12.7762i	−0.800078	−	1.38578i
$86$	8.85532			0.954893
$87$	−0.594554	+	2.88318i	−0.0637429	+	0.309109i
$88$	5.30903			0.565945
$89$	−4.80470	+	8.32199i	−0.509297	+	0.882129i	0.490645	+	0.871360i	$0.336761\pi$
$89$	−4.80470	+	8.32199i	−0.509297	+	0.882129i	−0.999942	+	0.0107692i	$0.996572\pi$
$90$	16.8040	+	7.23828i	1.77130	+	0.762981i
$91$		0			0
$92$	−2.61126	+	4.52284i	−0.272243	+	0.471539i
$93$	−2.44437	+	11.8535i	−0.253469	+	1.22915i
$94$	2.26578	−	3.92445i	0.233697	−	0.404776i
$95$	−1.59455	+	2.76185i	−0.163598	+	0.283360i
$96$	−1.64400	+	7.97225i	−0.167790	+	0.813664i
$97$	−3.66071	+	6.34053i	−0.371688	+	0.643783i	−0.989825	−	0.142287i	$-0.954554\pi$
$97$	−3.66071	+	6.34053i	−0.371688	+	0.643783i	0.618137	+	0.786070i	$0.287888\pi$
$98$		0			0
$99$	−6.76145	+	5.03913i	−0.679551	+	0.506452i
$100$	−3.50000	+	6.06218i	−0.350000	+	0.606218i
$101$	3.46472			0.344753			0.172376	−	0.985031i	$-0.444856\pi$
$101$	3.46472			0.344753			0.172376	+	0.985031i	$0.444856\pi$
$102$	−2.44437	+	11.8535i	−0.242028	+	1.17367i
$103$	−15.8764			−1.56434			−0.782172	−	0.623063i	$-0.785888\pi$
$103$	−15.8764			−1.56434			−0.782172	+	0.623063i	$0.785888\pi$
$104$	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	$0.0833498\pi$
$108$	−1.95489	−	4.18383i	−0.188109	−	0.402589i
$109$	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	$0.474381\pi$
$110$	−8.57165	−	14.8465i	−0.817275	−	1.41556i
$111$	1.66690	−	8.08330i	0.158215	−	0.767233i
$112$		0			0
$113$	9.27561	+	16.0658i	0.872576	+	1.51135i	0.859322	+	0.511434i	$0.170886\pi$
$113$	9.27561	+	16.0658i	0.872576	+	1.51135i	0.0132538	+	0.999912i	$0.495781\pi$
$114$	2.48329	−	0.823583i	0.232581	−	0.0771356i
$115$	−21.0865			−1.96633
$116$	0.755260	+	1.30815i	0.0701242	+	0.121459i
$117$	−2.75526	−	1.18682i	−0.254724	−	0.109722i
$118$	−15.0865			−1.38883
$119$		0			0
$120$	−11.1421	+	3.69529i	−1.01713	+	0.337332i
$121$	−3.09888			−0.281717
$122$	−3.29418	+	5.70569i	−0.298241	+	0.516569i
$123$	−7.00364	−	6.22948i	−0.631497	−	0.561693i
$124$	3.10507	+	5.37815i	0.278844	+	0.482972i
$125$	−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	$0.353868\pi$
$128$	−6.38874	−	11.0656i	−0.564690	−	0.978071i
$129$	1.82258	−	8.83828i	0.160470	−	0.778167i
$130$	3.04944	−	5.28179i	0.267454	−	0.463244i
$131$	16.0531			1.40256			0.701282	−	0.712884i	$-0.252611\pi$
$131$	16.0531			1.40256			0.701282	+	0.712884i	$0.252611\pi$
$132$	−0.873885	+	4.23774i	−0.0760619	+	0.368848i
$133$		0			0
$134$	20.9208			1.80728
$135$	10.6829	−	15.2819i	0.919439	−	1.31526i
$136$	−3.88255	−	6.72477i	−0.332926	−	0.576644i
$137$	−12.9876			−1.10961			−0.554804	−	0.831981i	$-0.687207\pi$
$137$	−12.9876			−1.10961			−0.554804	+	0.831981i	$0.687207\pi$
$138$	12.9258	+	11.4970i	1.10032	+	0.978691i
$139$	−0.555632	−	0.962383i	−0.0471281	−	0.0816283i	0.841499	−	0.540259i	$-0.181674\pi$
$139$	−0.555632	−	0.962383i	−0.0471281	−	0.0816283i	−0.888627	+	0.458630i	$0.848340\pi$
$140$		0			0
$141$	−3.45056	−	3.06914i	−0.290589	−	0.258468i
$142$	2.44437	+	4.23377i	0.205127	+	0.355290i
$143$	1.40545	+	2.43430i	0.117529	+	0.203567i
$144$	13.7422	+	5.91941i	1.14518	+	0.493284i
$145$	−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
$149$	8.43268			0.690832			0.345416	−	0.938450i	$-0.387738\pi$
$149$	8.43268			0.690832			0.345416	+	0.938450i	$0.387738\pi$
$150$	17.3251	+	15.4100i	1.41458	+	1.25822i
$151$	−14.8516			−1.20861			−0.604303	−	0.796755i	$-0.706548\pi$
$151$	−14.8516			−1.20861			−0.604303	+	0.796755i	$0.706548\pi$
$152$	−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
$156$	−1.46108	+	0.484566i	−0.116980	+	0.0387964i
$157$	−1.44437	+	2.50172i	−0.115273	+	0.199659i	−0.917889	−	0.396837i	$-0.870108\pi$
$157$	−1.44437	+	2.50172i	−0.115273	+	0.199659i	0.802616	+	0.596496i	$0.203441\pi$
$158$	6.02221	−	10.4308i	0.479101	−	0.829828i
$159$	−0.160018	−	0.142330i	−0.0126902	−	0.0112875i
$160$	−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	$0.0343792\pi$
$164$	−4.80951			−0.375560
$165$	−16.5822	+	5.49948i	−1.29092	+	0.428134i
$166$	−6.98762			−0.542345
$167$	−6.07598	−	10.5239i	−0.470174	−	0.814365i	0.529244	−	0.848469i	$-0.322475\pi$
$167$	−6.07598	−	10.5239i	−0.470174	−	0.814365i	−0.999418	+	0.0341045i	$0.989142\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$	−12.5371	+	21.7148i	−0.961549	+	1.66545i
$171$	−0.310892	−	2.64802i	−0.0237745	−	0.202499i
$172$	−2.31522	−	4.01008i	−0.176534	−	0.305766i
$173$	3.30470	+	5.72391i	0.251252	+	0.435181i	0.963871	−	0.266370i	$-0.0858244\pi$
$173$	3.30470	+	5.72391i	0.251252	+	0.435181i	−0.712619	+	0.701551i	$0.752491\pi$
$174$	4.74907	−	1.57503i	0.360026	−	0.119403i
$175$		0			0
$176$	−7.00983	−	12.1414i	−0.528386	−	0.915191i
$177$	−3.10507	+	15.0575i	−0.233392	+	1.13179i
$178$	16.3324			1.22417
$179$	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	$0.787460\pi$
$180$	−1.11559	−	9.50206i	−0.0831515	−	0.708242i
$181$	18.5426			1.37826			0.689129	−	0.724639i	$-0.257993\pi$
$181$	18.5426			1.37826			0.689129	+	0.724639i	$0.257993\pi$
$182$		0			0
$183$	5.01671	+	4.46218i	0.370846	+	0.329854i
$184$	−11.0989			−0.818221
$185$	8.54944	−	14.8081i	0.628567	−	1.08871i
$186$	19.5247	−	6.47536i	1.43162	−	0.474796i
$187$	−5.77816	−	10.0081i	−0.422541	−	0.731862i
$188$	−2.36955			−0.172818
$189$		0			0
$190$	5.42030			0.393230
$191$	−2.31708	−	4.01330i	−0.167658	−	0.290392i	0.769938	−	0.638119i	$-0.220287\pi$
$191$	−2.31708	−	4.01330i	−0.167658	−	0.290392i	−0.937596	+	0.347726i	$0.886954\pi$
$192$	−3.26764	+	1.08371i	−0.235822	+	0.0782102i
$193$	12.6483	−	21.9075i	0.910446	−	1.57694i	0.0970118	−	0.995283i	$-0.469072\pi$
$193$	12.6483	−	21.9075i	0.910446	−	1.57694i	0.813435	−	0.581656i	$-0.197595\pi$
$194$	12.4437			0.893404
$195$	−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	$0.375267\pi$
$198$	13.1632	+	5.67000i	0.935466	+	0.402949i
$199$	4.38323	+	7.59199i	0.310719	+	0.538182i	0.978518	−	0.206160i	$-0.0660968\pi$
$199$	4.38323	+	7.59199i	0.310719	+	0.538182i	−0.667799	+	0.744342i	$0.732763\pi$
$200$	−14.8764			−1.05192
$201$	4.30587	−	20.8805i	0.303713	−	1.47280i
$202$	−2.94437	−	5.09979i	−0.207165	−	0.358820i
$203$		0			0
$204$	6.00688	−	1.99218i	0.420566	−	0.139481i
$205$	−9.70946	−	16.8173i	−0.678138	−	1.17457i
$206$	13.4920	+	23.3687i	0.940029	+	1.62818i
$207$	14.1353	−	10.5346i	0.982468	−	0.732208i
$208$	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	0.625902	−	0.779902i	$-0.284731\pi$
$211$	−5.26509	−	9.11941i	−0.362464	−	0.627806i	−0.988366	+	0.152096i	$0.951398\pi$
$212$	−0.109887			−0.00754705
$213$	4.72872	−	1.56828i	0.324006	−	0.107457i
$214$	−9.09888			−0.621987
$215$	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
$219$	−13.7720	−	12.2497i	−0.930624	−	0.827755i
$220$	−4.48212	+	7.76326i	−0.302184	+	0.523399i
$221$	2.05563	−	3.56046i	0.138277	−	0.239502i
$222$	−13.3145	+	4.41576i	−0.893613	+	0.296367i
$223$	2.83379	−	4.90827i	0.189765	−	0.328682i	−0.755407	−	0.655256i	$-0.772561\pi$
$223$	2.83379	−	4.90827i	0.189765	−	0.328682i	0.945172	+	0.326574i	$0.105894\pi$
$224$		0			0
$225$	18.9462	−	14.1201i	1.26308	−	0.941338i
$226$	15.7651	−	27.3059i	1.04868	−	1.81636i
$227$	−11.0989			−0.736659			−0.368329	−	0.929695i	$-0.620070\pi$
$227$	−11.0989			−0.736659			−0.368329	+	0.929695i	$0.620070\pi$
$228$	−1.02221	−	0.909219i	−0.0676976	−	0.0602145i
$229$	19.6428			1.29803			0.649017	−	0.760774i	$-0.275180\pi$
$229$	19.6428			1.29803			0.649017	+	0.760774i	$0.275180\pi$
$230$	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	$0.261516\pi$
$234$	0.594554	+	5.06410i	0.0388672	+	0.331051i
$235$	−4.78366	−	8.28554i	−0.312052	−	0.540489i
$236$	3.94437	+	6.83185i	0.256756	+	0.444715i
$237$	−9.17123	−	8.15747i	−0.595735	−	0.529884i
$238$		0			0
$239$	−5.61126	−	9.71899i	−0.362963	−	0.628670i	0.625484	−	0.780237i	$-0.284901\pi$
$239$	−5.61126	−	9.71899i	−0.362963	−	0.628670i	−0.988447	+	0.151567i	$0.951568\pi$
$240$	23.1625	+	20.6022i	1.49513	+	1.32986i
$241$	−6.98624			−0.450023			−0.225012	−	0.974356i	$-0.572242\pi$
$241$	−6.98624			−0.450023			−0.225012	+	0.974356i	$0.572242\pi$
$242$	2.63348	+	4.56131i	0.169286	+	0.293212i
$243$	0.473458	+	15.5813i	0.0303723	+	0.999539i
$244$	3.44506			0.220547
$245$		0			0
$246$	−3.21751	+	15.6027i	−0.205141	+	0.994792i
$247$	−0.888736			−0.0565489
$248$	−6.59888	+	11.4296i	−0.419030	+	0.725781i
$249$	−1.43818	+	6.97418i	−0.0911408	+	0.441970i
$250$	8.77128	+	15.1923i	0.554745	+	0.960846i
$251$	4.62041			0.291638			0.145819	−	0.989311i	$-0.453418\pi$
$251$	4.62041			0.291638			0.145819	+	0.989311i	$0.453418\pi$
$252$		0			0
$253$	−16.5178			−1.03847
$254$	−8.48762	−	14.7010i	−0.532561	−	0.922422i
$255$	19.0927	+	16.9822i	1.19563	+	1.06347i
$256$	−8.87085	+	15.3648i	−0.554428	+	0.960298i
$257$	−1.42402			−0.0888277			−0.0444138	−	0.999013i	$-0.514142\pi$
$257$	−1.42402			−0.0888277			−0.0444138	+	0.999013i	$0.514142\pi$
$258$	−14.5581	+	4.82819i	−0.906348	+	0.300590i
$259$		0			0
$260$	−3.18911			−0.197780
$261$	−0.594554	−	5.06410i	−0.0368020	−	0.313460i
$262$	−13.6421	−	23.6289i	−0.842814	−	1.45980i
$263$	16.2632			1.00283			0.501417	−	0.865206i	$-0.332812\pi$
$263$	16.2632			1.00283			0.501417	+	0.865206i	$0.332812\pi$
$264$	−8.72803	+	2.89465i	−0.537173	+	0.178153i
$265$	−0.221840	−	0.384237i	−0.0136275	−	0.0236035i
$266$		0			0
$267$	3.36151	−	16.3010i	0.205721	−	0.997604i
$268$	−5.46974	−	9.47387i	−0.334118	−	0.578709i
$269$	9.32691	+	16.1547i	0.568672	+	0.984969i	0.996698	+	0.0812022i	$0.0258759\pi$
$269$	9.32691	+	16.1547i	0.568672	+	0.984969i	−0.428026	+	0.903767i	$0.640791\pi$
$270$	−31.5723	−	2.73763i	−1.92143	−	0.166607i
$271$	−1.98143	+	3.43194i	−0.120363	+	0.208475i	−0.919911	−	0.392127i	$-0.871739\pi$
$271$	−1.98143	+	3.43194i	−0.120363	+	0.208475i	0.799548	+	0.600603i	$0.205073\pi$
$272$	−10.2527	+	17.7582i	−0.621662	+	1.07675i
$273$		0			0
$274$	11.0371	+	19.1168i	0.666773	+	1.15489i
$275$	−22.1396			−1.33507
$276$	1.82691	−	8.85928i	0.109967	−	0.533266i
$277$	−2.33379			−0.140224			−0.0701120	−	0.997539i	$-0.522336\pi$
$277$	−2.33379			−0.140224			−0.0701120	+	0.997539i	$0.522336\pi$
$278$	−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	0.0589978	+	0.998258i	$0.481210\pi$
$281$	−13.9975	+	24.2443i	−0.835018	+	1.44629i	−0.894016	+	0.448035i	$0.852124\pi$
$282$	−1.58520	+	7.68715i	−0.0943975	+	0.457763i
$283$	−5.16002	+	8.93741i	−0.306731	+	0.531274i	−0.977645	−	0.210261i	$-0.932569\pi$
$283$	−5.16002	+	8.93741i	−0.306731	+	0.531274i	0.670914	+	0.741535i	$0.265902\pi$
$284$	1.27816	−	2.21384i	0.0758449	−	0.131367i
$285$	1.11559	−	5.40987i	0.0660821	−	0.320453i
$286$	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
$290$	10.3658			0.608703
$291$	2.56113	−	12.4197i	0.150136	−	0.728058i
$292$	−9.45744			−0.553455
$293$	15.3480	+	26.5834i	0.896637	+	1.55302i	0.831765	+	0.555127i	$0.187330\pi$
$293$	15.3480	+	26.5834i	0.896637	+	1.55302i	0.0648718	+	0.997894i	$0.479336\pi$
$294$		0			0
$295$	−15.9258	+	27.5843i	−0.927236	+	1.60602i
$296$	4.50000	−	7.79423i	0.261557	−	0.453030i
$297$	8.36831	−	11.9709i	0.485578	−	0.694620i
$298$	−7.16621	−	12.4122i	−0.415127	−	0.719021i
$299$	−2.93818	−	5.08907i	−0.169919	−	0.294309i
$300$	2.44870	−	11.8745i	0.141376	−	0.685575i
$301$		0			0
$302$	12.6211	+	21.8604i	0.726262	+	1.25792i
$303$	−5.69599	+	1.88907i	−0.327226	+	0.108524i
$304$	4.43268			0.254231
$305$	6.95489	+	12.0462i	0.398236	+	0.689765i
$306$	−2.44437	−	20.8199i	−0.139735	−	1.19019i
$307$	−11.4437			−0.653125			−0.326563	−	0.945176i	$-0.605890\pi$
$307$	−11.4437			−0.653125			−0.326563	+	0.945176i	$0.605890\pi$
$308$		0			0
$309$	26.1007	−	8.65628i	1.48482	−	0.492439i
$310$	42.6167			2.42047
$311$	−5.98143	+	10.3601i	−0.339176	+	0.587470i	−0.984278	−	0.176627i	$-0.943481\pi$
$311$	−5.98143	+	10.3601i	−0.339176	+	0.587470i	0.645102	+	0.764096i	$0.276815\pi$
$312$	−2.44437	−	2.17417i	−0.138385	−	0.123088i
$313$	6.77197	+	11.7294i	0.382774	+	0.662985i	0.991458	−	0.130429i	$-0.0416353\pi$
$313$	6.77197	+	11.7294i	0.382774	+	0.662985i	−0.608683	+	0.793413i	$0.708302\pi$
$314$	4.90978			0.277075
$315$		0			0
$316$	−6.29803			−0.354292
$317$	14.9814	+	25.9486i	0.841441	+	1.45742i	0.888676	+	0.458535i	$0.151626\pi$
$317$	14.9814	+	25.9486i	0.841441	+	1.45742i	−0.0472355	+	0.998884i	$0.515041\pi$
$318$	−0.0735129	+	0.356487i	−0.00412240	+	0.0199908i
$319$	−2.38874	+	4.13741i	−0.133744	+	0.231651i
$320$	−7.13231			−0.398708
$321$	−1.87271	+	9.08138i	−0.104525	+	0.506873i
$322$		0			0
$323$	3.65383			0.203304
$324$	5.49498	+	5.81233i	0.305277	+	0.322907i
$325$	−3.93818	−	6.82112i	−0.218451	−	0.378368i
$326$	−17.5215			−0.970427
$327$	−24.4134	−	21.7148i	−1.35007	−	1.20083i
$328$	−5.11058	−	8.85178i	−0.282184	−	0.488758i
$329$		0			0
$330$	22.1866	+	19.7341i	1.22133	+	1.08633i
$331$	−1.04325	−	1.80697i	−0.0573423	−	0.0993198i	0.835929	−	0.548837i	$-0.184929\pi$
$331$	−1.04325	−	1.80697i	−0.0573423	−	0.0993198i	−0.893272	+	0.449517i	$0.851596\pi$
$332$	1.82691	+	3.16431i	0.100265	+	0.173664i
$333$	1.66690	+	14.1978i	0.0913454	+	0.778032i
$334$	−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	0.997799	−	0.0663093i	$-0.0211224\pi$
$337$	8.10439	+	14.0372i	0.441474	+	0.764655i	−0.556325	+	0.830965i	$0.687789\pi$
$338$	−20.3955			−1.10937
$339$	−24.0087	−	21.3548i	−1.30397	−	1.15983i
$340$	13.1113			0.711058
$341$	−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
$345$	34.6661	−	11.4970i	1.86636	−	0.618979i
$346$	5.61677	−	9.72852i	0.301959	−	0.523009i
$347$	−5.63348	+	9.75747i	−0.302421	+	0.523808i	−0.976684	−	0.214683i	$-0.931128\pi$
$347$	−5.63348	+	9.75747i	−0.302421	+	0.523808i	0.674263	+	0.738491i	$0.264461\pi$
$348$	−1.95489	−	1.73880i	−0.104793	−	0.0932095i
$349$	0.0988844	−	0.171273i	0.00529316	−	0.00916803i	−0.863367	−	0.504577i	$-0.831648\pi$
$349$	0.0988844	−	0.171273i	0.00529316	−	0.00916803i	0.868660	+	0.495409i	$0.164982\pi$
$350$		0			0
$351$	5.17673	+	0.448873i	0.276313	+	0.0239591i
$352$	−6.60507	+	11.4403i	−0.352052	+	0.609771i
$353$	−12.5019			−0.665407			−0.332703	−	0.943032i	$-0.607961\pi$
$353$	−12.5019			−0.665407			−0.332703	+	0.943032i	$0.607961\pi$
$354$	24.8022	−	8.22563i	1.31822	−	0.437187i
$355$	10.3214			0.547804
$356$	−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	$0.989497\pi$
$360$	16.3028	−	12.1501i	0.859235	−	0.640365i
$361$	9.10507	+	15.7705i	0.479214	+	0.830024i
$362$	−15.7577	−	27.2932i	−0.828208	−	1.43450i
$363$	5.09455	−	1.68961i	0.267395	−	0.0886814i
$364$		0			0
$365$	−19.0927	−	33.0695i	−0.999357	−	1.73094i
$366$	2.30470	−	11.1762i	0.120469	−	0.584191i
$367$	30.0727			1.56978			0.784892	−	0.619632i	$-0.212718\pi$
$367$	30.0727			1.56978			0.784892	+	0.619632i	$0.212718\pi$
$368$	14.6545	+	25.3824i	0.763919	+	1.32315i
$369$	14.9105	+	6.42264i	0.776208	+	0.334349i
$370$	−29.0617			−1.51085
$371$		0			0
$372$	−8.03706	−	7.14867i	−0.416702	−	0.370641i
$373$	7.01238			0.363087			0.181544	−	0.983383i	$-0.441891\pi$
$373$	7.01238			0.363087			0.181544	+	0.983383i	$0.441891\pi$
$374$	−9.82072	+	17.0100i	−0.507818	+	0.879566i
$375$	16.9684	−	5.62755i	0.876242	−	0.290606i
$376$	−2.51788	−	4.36110i	−0.129850	−	0.224906i
$377$	−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	$0.662962\pi$
$380$	−1.41714	−	2.45455i	−0.0726976	−	0.125916i
$381$	−16.4196	+	5.44556i	−0.841202	+	0.278985i
$382$	−3.93818	+	6.82112i	−0.201495	+	0.348999i
$383$	3.21015			0.164031			0.0820155	−	0.996631i	$-0.473864\pi$
$383$	3.21015			0.164031			0.0820155	+	0.996631i	$0.473864\pi$
$384$	16.5364	+	14.7085i	0.843868	+	0.750590i
$385$		0			0
$386$	−42.9949			−2.18838
$387$	1.82258	+	15.5238i	0.0926471	+	0.789120i
$388$	−3.25340	−	5.63506i	−0.165166	−	0.286077i
$389$	5.13602			0.260407			0.130203	−	0.991487i	$-0.458437\pi$
$389$	5.13602			0.260407			0.130203	+	0.991487i	$0.458437\pi$
$390$	−2.13348	+	10.3459i	−0.108033	+	0.523885i
$391$	12.0796	+	20.9225i	0.610893	+	1.05810i
$392$		0			0
$393$	−26.3912	+	8.75264i	−1.33126	+	0.441512i
$394$	−9.11058	−	15.7800i	−0.458984	−	0.794984i
$395$	−12.7145	−	22.0221i	−0.639735	−	1.10805i
$396$	−0.873885	−	7.44330i	−0.0439144	−	0.374040i
$397$	−11.4691	+	19.8650i	−0.575615	+	0.996995i	0.420359	+	0.907358i	$0.361904\pi$
$397$	−11.4691	+	19.8650i	−0.575615	+	0.996995i	−0.995975	+	0.0896370i	$0.971429\pi$
$398$	7.44987	−	12.9036i	0.373428	−	0.646797i
$399$		0			0
$400$	19.6421	+	34.0212i	0.982107	+	1.70106i
$401$	−18.2101			−0.909371			−0.454686	−	0.890652i	$-0.650248\pi$
$401$	−18.2101			−0.909371			−0.454686	+	0.890652i	$0.650248\pi$
$402$	−34.3937	+	11.4067i	−1.71540	+	0.568912i
$403$	−6.98762			−0.348078
$404$	−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
$408$	10.0494	+	8.93861i	0.497522	+	0.442527i
$409$	7.66621	−	13.2783i	0.379070	−	0.656568i	−0.611858	−	0.790968i	$-0.709577\pi$
$409$	7.66621	−	13.2783i	0.379070	−	0.656568i	0.990927	+	0.134400i	$0.0429108\pi$
$410$	−16.5025	+	28.5831i	−0.814999	+	1.41162i
$411$	21.3516	−	7.08125i	1.05320	−	0.349293i
$412$	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
$416$	−4.69963			−0.230418
$417$	1.43818	+	1.27921i	0.0704279	+	0.0626430i
$418$	4.24591			0.207674
$419$	−5.28435	−	9.15276i	−0.258157	−	0.447142i	0.707591	−	0.706622i	$-0.249782\pi$
$419$	−5.28435	−	9.15276i	−0.258157	−	0.447142i	−0.965748	+	0.259481i	$0.916449\pi$
$420$		0			0
$421$	18.0858	−	31.3256i	0.881449	−	1.52671i	0.0317181	−	0.999497i	$-0.489902\pi$
$421$	18.0858	−	31.3256i	0.881449	−	1.52671i	0.849731	−	0.527217i	$-0.176765\pi$
$422$	−8.94870	+	15.4996i	−0.435616	+	0.754509i
$423$	7.34610	+	3.16431i	0.357179	+	0.153854i
$424$	−0.116765	−	0.202243i	−0.00567062	−	0.00982181i
$425$	16.1909	+	28.0434i	0.785374	+	1.36031i
$426$	−6.32691	−	5.62755i	−0.306540	−	0.272656i
$427$		0			0
$428$	2.37890	+	4.12038i	0.114989	+	0.199166i
$429$	−3.63781	−	3.23569i	−0.175635	−	0.156221i
$430$	−31.7761			−1.53238
$431$	−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	$-0.487261\pi$
$432$	−25.8196	−	2.23881i	−1.24224	−	0.107715i
$433$	−41.1730			−1.97865			−0.989324	−	0.145731i	$-0.953447\pi$
$433$	−41.1730			−1.97865			−0.989324	+	0.145731i	$0.953447\pi$
$434$		0			0
$435$	2.13348	−	10.3459i	0.102292	−	0.496047i
$436$	−16.7651			−0.802902
$437$	2.61126	−	4.52284i	0.124914	−	0.216357i
$438$	−6.32691	+	30.6812i	−0.302312	+	1.46600i
$439$	2.33929	+	4.05178i	0.111648	+	0.193381i	0.916435	−	0.400184i	$-0.131054\pi$
$439$	2.33929	+	4.05178i	0.111648	+	0.193381i	−0.804787	+	0.593564i	$0.797720\pi$
$440$	−19.0507			−0.908209
$441$		0			0
$442$	−6.98762			−0.332367
$443$	−15.0865	−	26.1306i	−0.716781	−	1.24150i	−0.962268	−	0.272102i	$-0.912281\pi$
$443$	−15.0865	−	26.1306i	−0.716781	−	1.24150i	0.245487	−	0.969400i	$-0.421052\pi$
$444$	5.48074	+	4.87492i	0.260104	+	0.231353i
$445$	17.2410	−	29.8623i	0.817303	−	1.41561i
$446$	−9.63279			−0.456126
$447$	−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	$0.497493\pi$
$450$	−36.8843	−	15.8878i	−1.73874	−	0.748959i
$451$	−7.60576	−	13.1736i	−0.358141	−	0.620319i
$452$	−16.4871			−0.775490
$453$	24.4160	−	8.09755i	1.14716	−	0.380456i
$454$	9.43199	+	16.3367i	0.442665	+	0.766719i
$455$		0			0
$456$	0.587193	−	2.84748i	0.0274979	−	0.133346i
$457$	9.65452	+	16.7221i	0.451619	+	0.782227i	0.998487	−	0.0549917i	$-0.0175132\pi$
$457$	9.65452	+	16.7221i	0.451619	+	0.782227i	−0.546868	+	0.837219i	$0.684180\pi$
$458$	−16.6927	−	28.9127i	−0.780001	−	1.35100i
$459$	−21.2829	−	1.84544i	−0.993401	−	0.0861376i
$460$	9.37017	−	16.2296i	0.436886	−	0.756709i
$461$	−19.5538	+	33.8681i	−0.910710	+	1.57740i	−0.0976463	+	0.995221i	$0.531131\pi$
$461$	−19.5538	+	33.8681i	−0.910710	+	1.57740i	−0.813064	+	0.582175i	$0.802202\pi$
$462$		0			0
$463$	−10.9382	−	18.9455i	−0.508340	−	0.880471i	−0.999953	−	0.00965741i	$-0.996926\pi$
$463$	−10.9382	−	18.9455i	−0.508340	−	0.880471i	0.491613	−	0.870814i	$-0.336407\pi$
$464$	8.47710			0.393539
$465$	8.77128	−	42.5347i	0.406758	−	1.97250i
$466$	15.2335			0.705680
$467$	6.16002	−	10.6695i	0.285052	−	0.493724i	−0.687570	−	0.726118i	$-0.741323\pi$
$467$	6.16002	−	10.6695i	0.285052	−	0.493724i	0.972622	+	0.232394i	$0.0746559\pi$
$468$	2.13781	−	1.59325i	0.0988201	−	0.0736480i
$469$		0			0
$470$	−8.13045	+	14.0823i	−0.375029	+	0.649570i
$471$	1.01052	−	4.90033i	0.0465623	−	0.225795i
$472$	−8.38255	+	14.5190i	−0.385838	+	0.668291i
$473$	7.32258	−	12.6831i	0.336693	−	0.583169i
$474$	−4.21331	+	20.4317i	−0.193524	+	0.938457i
$475$	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
$479$	13.4895			0.616350			0.308175	−	0.951330i	$-0.400282\pi$
$479$	13.4895			0.616350			0.308175	+	0.951330i	$0.400282\pi$
$480$	5.89926	−	28.6073i	0.269263	−	1.30574i
$481$	4.76509			0.217269
$482$	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
$486$	22.5320	−	13.9381i	1.02207	−	0.632244i
$487$	−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	$0.888009\pi$
$488$	3.66071	+	6.34053i	0.165712	+	0.287022i
$489$	−3.60624	+	17.4878i	−0.163080	+	0.790826i
$490$		0			0
$491$	8.06979	+	13.9773i	0.364185	+	0.630786i	0.988645	−	0.150270i	$-0.0480143\pi$
$491$	8.06979	+	13.9773i	0.364185	+	0.630786i	−0.624460	+	0.781057i	$0.714681\pi$
$492$	7.90682	−	2.62230i	0.356467	−	0.118222i
$493$	6.98762			0.314707
$494$	0.755260	+	1.30815i	0.0339808	+	0.0588564i
$495$	24.2625	−	18.0822i	1.09052	−	0.812736i
$496$	34.8516			1.56488
$497$		0			0
$498$	11.4876	−	3.80987i	0.514773	−	0.170724i
$499$	−30.8654			−1.38172			−0.690862	−	0.722987i	$-0.742769\pi$
$499$	−30.8654			−1.38172			−0.690862	+	0.722987i	$0.742769\pi$
$500$	4.58650	−	7.94406i	0.205115	−	0.355269i
$501$	15.7269	+	13.9885i	0.702624	+	0.624958i
$502$	−3.92649	−	6.80088i	−0.175248	−	0.303538i
$503$	24.6304			1.09822			0.549109	−	0.835751i	$-0.314967\pi$
$503$	24.6304			1.09822			0.549109	+	0.835751i	$0.314967\pi$
$504$		0			0
$505$	−12.4327			−0.553247
$506$	14.0371	+	24.3129i	0.624024	+	1.08084i
$507$	−4.19777	+	20.3563i	−0.186429	+	0.904055i
$508$	−4.43818	+	7.68715i	−0.196912	+	0.341062i
$509$	13.5897			0.602355			0.301177	−	0.953568i	$-0.402620\pi$
$509$	13.5897			0.602355			0.301177	+	0.953568i	$0.402620\pi$
$510$	8.77128	−	42.5347i	0.388399	−	1.88347i
$511$		0			0
$512$	4.59937			0.203265
$513$	1.95489	+	4.18383i	0.0863104	+	0.184720i
$514$	1.21015	+	2.09604i	0.0533774	+	0.0924523i
$515$	56.9701			2.51040
$516$	5.99264	+	5.33023i	0.263811	+	0.234650i
$517$	−3.74721	−	6.49036i	−0.164802	−	0.285446i
$518$		0			0
$519$	−8.55377	−	7.60826i	−0.375469	−	0.333966i
$520$	−3.38874	−	5.86946i	−0.148606	−	0.257393i
$521$	19.5865	+	33.9248i	0.858100	+	1.48627i	0.873739	+	0.486396i	$0.161689\pi$
$521$	19.5865	+	33.9248i	0.858100	+	1.48627i	−0.0156383	+	0.999878i	$0.504978\pi$
$522$	−6.94870	+	5.17868i	−0.304136	+	0.226665i
$523$	−9.56182	+	16.5616i	−0.418109	+	0.724187i	−0.995749	−	0.0921051i	$-0.970640\pi$
$523$	−9.56182	+	16.5616i	−0.418109	+	0.724187i	0.577640	+	0.816292i	$0.303974\pi$
$524$	−7.13348	+	12.3555i	−0.311627	+	0.539754i
$525$		0			0
$526$	−13.8207	−	23.9382i	−0.602612	−	1.04375i
$527$	28.7280			1.25141
$528$	18.1440	+	16.1384i	0.789616	+	0.702334i
$529$	11.5316			0.501372
$530$	−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
$534$	−26.8504	+	8.90494i	−1.16193	+	0.385354i
$535$	−9.60507	+	16.6365i	−0.415264	+	0.719258i
$536$	11.6243	−	20.1338i	0.502091	−	0.869648i
$537$	−4.97346	−	4.42371i	−0.214621	−	0.190897i
$538$	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	$0.183988\pi$
$542$	6.73539			0.289310
$543$	−30.4839	+	10.1100i	−1.30819	+	0.433861i
$544$	19.3214			0.828399
$545$	−33.8454	−	58.6220i	−1.44978	−	2.51109i
$546$		0			0
$547$	−8.92580	+	15.4599i	−0.381640	+	0.661019i	−0.991297	−	0.131646i	$-0.957974\pi$
$547$	−8.92580	+	15.4599i	−0.381640	+	0.661019i	0.609657	+	0.792665i	$0.291307\pi$
$548$	5.77128	−	9.99615i	0.246537	−	0.427015i
$549$	−10.6804	−	4.60054i	−0.455827	−	0.196346i
$550$	18.8145	+	32.5877i	0.802254	+	1.38955i
$551$	−0.755260	−	1.30815i	−0.0321752	−	0.0557290i
$552$	18.2465	−	6.05146i	0.776624	−	0.257567i
$553$		0			0
$554$	1.98329	+	3.43516i	0.0842619	+	0.145946i
$555$	−5.98143	+	29.0058i	−0.253898	+	1.23123i
$556$	0.987620			0.0418844
$557$	−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	$-0.506633\pi$
$558$	−28.5679	+	21.2909i	−1.20938	+	0.901317i
$559$	5.21015			0.220366
$560$		0			0
$561$	14.9560	+	13.3028i	0.631442	+	0.561644i
$562$	47.5809			2.00708
$563$	10.3683	−	17.9584i	0.436972	−	0.756858i	−0.560482	−	0.828166i	$-0.689384\pi$
$563$	10.3683	−	17.9584i	0.436972	−	0.756858i	0.997454	+	0.0713087i	$0.0227175\pi$
$564$	3.89554	−	1.29195i	0.164032	−	0.0544011i
$565$	−33.2843	−	57.6501i	−1.40028	−	2.42536i
$566$	17.5402			0.737271
$567$		0			0
$568$	5.43268			0.227950
$569$	0.134164	+	0.232379i	0.00562446	+	0.00974185i	0.868824	−	0.495121i	$-0.164876\pi$
$569$	0.134164	+	0.232379i	0.00562446	+	0.00974185i	−0.863199	+	0.504863i	$0.831543\pi$
$570$	−8.91095	+	2.95531i	−0.373239	+	0.123785i
$571$	−17.9684	+	31.1221i	−0.751953	+	1.30242i	0.194923	+	0.980819i	$0.437554\pi$
$571$	−17.9684	+	31.1221i	−0.751953	+	1.30242i	−0.946875	+	0.321601i	$0.895779\pi$
$572$	−2.49814			−0.104453
$573$	5.99745	+	5.33451i	0.250547	+	0.222852i
$574$		0			0
$575$	46.2843			1.93019
$576$	4.78111	−	3.56324i	0.199213	−	0.148468i
$577$	−2.71565	−	4.70364i	−0.113054	−	0.195815i	0.803946	−	0.594702i	$-0.202730\pi$
$577$	−2.71565	−	4.70364i	−0.113054	−	0.195815i	−0.917000	+	0.398887i	$0.869397\pi$
$578$	−0.165726			−0.00689328
$579$	−8.84913	+	42.9122i	−0.367757	+	1.78337i
$580$	−2.71015	−	4.69412i	−0.112533	−	0.194913i
$581$		0			0
$582$	−20.4574	+	6.78468i	−0.847985	+	0.281234i
$583$	−0.173775	−	0.300987i	−0.00719702	−	0.0124656i
$584$	−10.0494	−	17.4061i	−0.415849	−	0.720271i
$585$	9.88688	+	4.25874i	0.408772	+	0.176077i
$586$	26.0858	−	45.1820i	1.07760	−	1.86645i
$587$	−17.5822	+	30.4532i	−0.725694	+	1.25694i	0.232994	+	0.972478i	$0.425148\pi$
$587$	−17.5822	+	30.4532i	−0.725694	+	1.25694i	−0.958688	+	0.284461i	$0.908185\pi$
$588$		0			0
$589$	−3.10507	−	5.37815i	−0.127942	−	0.221603i
$590$	54.1359			2.22874
$591$	−17.6247	+	5.84524i	−0.724985	+	0.240441i
$592$	−23.7665			−0.976796
$593$	16.7534	−	29.0177i	0.687980	−	1.19162i	−0.284511	−	0.958673i	$-0.591831\pi$
$593$	16.7534	−	29.0177i	0.687980	−	1.19162i	0.972490	−	0.232943i	$-0.0748355\pi$
$594$	−24.7317	−	2.14448i	−1.01475	−	0.0879891i
$595$		0			0
$596$	−3.74721	+	6.49036i	−0.153492	+	0.265856i
$597$	−11.3454	−	10.0913i	−0.464337	−	0.413010i
$598$	−4.99381	+	8.64953i	−0.204212	+	0.353706i
$599$	−3.12364	+	5.41031i	−0.127629	+	0.221059i	−0.922757	−	0.385381i	$-0.874070\pi$
$599$	−3.12364	+	5.41031i	−0.127629	+	0.221059i	0.795129	+	0.606441i	$0.207403\pi$
$600$	24.4567	−	8.11105i	0.998439	−	0.331132i
$601$	−11.2040	+	19.4058i	−0.457019	+	0.791580i	−0.998802	−	0.0489384i	$-0.984416\pi$
$601$	−11.2040	+	19.4058i	−0.457019	+	0.791580i	0.541783	+	0.840519i	$0.317750\pi$
$602$		0			0
$603$	4.30587	+	36.6752i	0.175349	+	1.49353i
$604$	6.59957	−	11.4308i	0.268533	−	0.465112i
$605$	11.1199			0.452089
$606$	7.62110	+	6.77868i	0.309586	+	0.275365i
$607$	14.9505			0.606821			0.303411	−	0.952860i	$-0.401875\pi$
$607$	14.9505			0.606821			0.303411	+	0.952860i	$0.401875\pi$
$608$	−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
$612$	−8.78909	+	6.55027i	−0.355278	+	0.264779i
$613$	−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	$-0.418339\pi$
$614$	9.72500	+	16.8442i	0.392469	+	0.679776i
$615$	25.1316	+	22.3536i	1.01340	+	0.901386i
$616$		0			0
$617$	1.00619	+	1.74277i	0.0405077	+	0.0701614i	0.885568	−	0.464509i	$-0.153769\pi$
$617$	1.00619	+	1.74277i	0.0405077	+	0.0701614i	−0.845061	+	0.534670i	$0.820436\pi$
$618$	−34.9221	−	31.0619i	−1.40477	−	1.24949i
$619$	39.3818			1.58289			0.791444	−	0.611242i	$-0.209330\pi$
$619$	39.3818			1.58289			0.791444	+	0.611242i	$0.209330\pi$
$620$	−11.1421	−	19.2987i	−0.447479	−	0.775056i
$621$	−17.4945	+	25.0259i	−0.702030	+	1.00425i
$622$	20.3324			0.815256
$623$		0			0
$624$	−1.74474	+	8.46079i	−0.0698455	+	0.338703i
$625$	−2.34479			−0.0937918
$626$	11.5098	−	19.9356i	0.460025	−	0.796787i
$627$	0.873885	−	4.23774i	0.0348996	−	0.169239i
$628$	−1.28366	−	2.22337i	−0.0512237	−	0.0887220i
$629$	−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	$0.155226\pi$
$632$	−6.69227	−	11.5913i	−0.266204	−	0.461079i
$633$	13.6280	+	12.1216i	0.541663	+	0.481789i
$634$	25.4629	−	44.1030i	1.01126	−	1.75155i
$635$	−35.8392			−1.42224
$636$	0.180653	−	0.0599137i	0.00716337	−	0.00237573i
$637$		0			0
$638$	8.11993			0.321471
$639$	−6.91892	+	5.15649i	−0.273708	+	0.203988i
$640$	22.9251	+	39.7075i	0.906195	+	1.56957i
$641$	−14.9862			−0.591921			−0.295961	−	0.955200i	$-0.595640\pi$
$641$	−14.9862			−0.591921			−0.295961	+	0.955200i	$0.595640\pi$
$642$	14.9585	−	4.96099i	0.590366	−	0.195795i
$643$	5.32691	+	9.22649i	0.210073	+	0.363857i	0.951737	−	0.306914i	$-0.0992965\pi$
$643$	5.32691	+	9.22649i	0.210073	+	0.363857i	−0.741664	+	0.670771i	$0.765963\pi$
$644$		0			0
$645$	−6.54009	+	31.7150i	−0.257516	+	1.24878i
$646$	−3.10507	−	5.37815i	−0.122168	−	0.211600i
$647$	−1.06478	−	1.84424i	−0.0418606	−	0.0725047i	0.844336	−	0.535814i	$-0.179995\pi$
$647$	−1.06478	−	1.84424i	−0.0418606	−	0.0725047i	−0.886197	+	0.463309i	$0.846662\pi$
$648$	−4.85848	+	16.2895i	−0.190859	+	0.639913i
$649$	−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
$653$	11.1716			0.437180			0.218590	−	0.975817i	$-0.429854\pi$
$653$	11.1716			0.437180			0.218590	+	0.975817i	$0.429854\pi$
$654$	−11.2156	+	54.3882i	−0.438567	+	2.12675i
$655$	−57.6043			−2.25079
$656$	−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	−0.734621	−	0.678478i	$-0.762640\pi$
$659$	5.65452	−	9.79391i	0.220269	−	0.381517i	0.954890	+	0.296961i	$0.0959733\pi$
$660$	3.13582	−	15.2066i	0.122062	−	0.591914i
$661$	−16.1785	+	28.0220i	−0.629271	+	1.08993i	0.358427	+	0.933558i	$0.383313\pi$
$661$	−16.1785	+	28.0220i	−0.629271	+	1.08993i	−0.987698	+	0.156372i	$0.950020\pi$
$662$	−1.77314	+	3.07117i	−0.0689151	+	0.119364i
$663$	−1.43818	+	6.97418i	−0.0558542	+	0.270855i
$664$	−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
$668$	10.7999			0.417860
$669$	−1.98260	+	9.61425i	−0.0766518	+	0.371708i
$670$	−75.0714			−2.90026
$671$	5.44801	+	9.43623i	0.210318	+	0.364282i
$672$		0			0
$673$	12.0803	−	20.9237i	0.465662	−	0.806550i	−0.533569	−	0.845756i	$-0.679150\pi$
$673$	12.0803	−	20.9237i	0.465662	−	0.806550i	0.999231	+	0.0392063i	$0.0124830\pi$
$674$	13.7744	−	23.8580i	0.530572	−	0.918977i
$675$	−23.4487	+	33.5434i	−0.902541	+	1.29108i
$676$	5.33242	+	9.23601i	0.205093	+	0.355231i
$677$	−12.5371	−	21.7148i	−0.481838	−	0.834569i	0.517944	−	0.855414i	$-0.326697\pi$
$677$	−12.5371	−	21.7148i	−0.481838	−	0.834569i	−0.999783	+	0.0208457i	$0.993364\pi$
$678$	−11.0297	+	53.4865i	−0.423593	+	2.05414i
$679$		0			0
$680$	13.9320	+	24.1309i	0.534267	+	0.925378i
$681$	18.2465	−	6.05146i	0.699208	−	0.231892i
$682$	33.3832			1.27831
$683$	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	$0.467729\pi$
$684$	2.17625	+	0.937411i	0.0832109	+	0.0358428i
$685$	46.6043			1.78066
$686$		0			0
$687$	−32.2927	+	10.7099i	−1.23204	+	0.408607i
$688$	−25.9862			−0.990716
$689$	0.0618219	−	0.107079i	0.00235523	−	0.00407937i
$690$	−46.3825	−	41.2555i	−1.76575	−	1.57057i
$691$	12.3400	+	21.3735i	0.469435	+	0.813085i	0.999389	−	0.0349408i	$-0.0111243\pi$
$691$	12.3400	+	21.3735i	0.469435	+	0.813085i	−0.529954	+	0.848026i	$0.677791\pi$
$692$	−5.87402			−0.223297
$693$		0			0
$694$	19.1496			0.726910
$695$	1.99381	+	3.45338i	0.0756295	+	0.130994i
$696$	1.12296	−	5.44556i	0.0425655	−	0.206413i
$697$	−11.1243	+	19.2679i	−0.421364	+	0.729824i
$698$	−0.336134			−0.0127228
$699$	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	$0.689379\pi$
$702$	−3.73855	−	8.00119i	−0.141102	−	0.301986i
$703$	2.11745	+	3.66754i	0.0798613	+	0.138324i
$704$	−5.58699			−0.210567
$705$	12.3819	+	11.0132i	0.466328	+	0.414781i
$706$	10.6243	+	18.4018i	0.399849	+	0.692559i
$707$		0			0
$708$	−10.2095	−	9.08094i	−0.383695	−	0.341282i
$709$	14.6291	+	25.3383i	0.549406	+	0.951599i	0.998315	+	0.0580220i	$0.0184794\pi$
$709$	14.6291	+	25.3383i	0.549406	+	0.951599i	−0.448909	+	0.893577i	$0.648187\pi$
$710$	−8.77128	−	15.1923i	−0.329180	−	0.570157i
$711$	19.5252	+	8.41040i	0.732251	+	0.315415i
$712$	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
$716$	−3.41535			−0.127638
$717$	14.5240	+	12.9186i	0.542408	+	0.482452i
$718$	34.0260			1.26984
$719$	−0.537063	+	0.930220i	−0.0200291	+	0.0346913i	−0.875866	−	0.482554i	$-0.839709\pi$
$719$	−0.537063	+	0.930220i	−0.0200291	+	0.0346913i	0.855837	+	0.517245i	$0.173043\pi$
$720$	−49.3120	−	21.2410i	−1.83775	−	0.791605i
$721$		0			0
$722$	15.4752	−	26.8039i	0.575929	−	0.997538i
$723$	11.4854	−	3.80912i	0.427145	−	0.141663i
$724$	−8.23972	+	14.2716i	−0.306227	+	0.530400i
$725$	6.69344	−	11.5934i	0.248588	−	0.430567i
$726$	−6.81639	−	6.06293i	−0.252980	−	0.225016i
$727$	−12.7163	+	22.0253i	−0.471623	+	0.816875i	−0.999473	−	0.0324628i	$-0.989665\pi$
$727$	−12.7163	+	22.0253i	−0.471623	+	0.816875i	0.527850	+	0.849338i	$0.322998\pi$
$728$		0			0
$729$	−9.27375	−	25.3574i	−0.343472	−	0.939163i
$730$	−32.4505	+	56.2059i	−1.20105	+	2.08027i
$731$	−21.4203			−0.792258
$732$	−5.66366	+	1.87835i	−0.209335	+	0.0694259i
$733$	−11.3955			−0.420904			−0.210452	−	0.977604i	$-0.567494\pi$
$733$	−11.3955			−0.420904			−0.210452	+	0.977604i	$0.567494\pi$
$734$	−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
$738$	−3.21751	−	27.4051i	−0.118438	−	1.00879i
$739$	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	$0.647705\pi$
$740$	7.59820	+	13.1605i	0.279315	+	0.483788i
$741$	1.46108	−	0.484566i	0.0536740	−	0.0178010i
$742$		0			0
$743$	9.50069	+	16.4557i	0.348546	+	0.603700i	0.985991	−	0.166796i	$-0.0533420\pi$
$743$	9.50069	+	16.4557i	0.348546	+	0.603700i	−0.637445	+	0.770496i	$0.720009\pi$
$744$	4.61677	−	22.3881i	0.169259	−	0.820789i
$745$	−30.2595			−1.10862
$746$	−5.95922	−	10.3217i	−0.218183	−	0.377903i
$747$	−1.43818	−	12.2497i	−0.0526202	−	0.448191i
$748$	10.2705			0.375527
$749$		0			0
$750$	−22.7033	−	20.1937i	−0.829006	−	0.737370i
$751$	0.0261368			0.000953747			0.000476873	−	1.00000i	$-0.499848\pi$
$751$	0.0261368			0.000953747			0.000476873		1.00000i	$0.499848\pi$
$752$	−6.64902	+	11.5164i	−0.242465	+	0.419961i
$753$	−7.59593	+	2.51919i	−0.276811	+	0.0918044i
$754$	1.44437	+	2.50172i	0.0526008	+	0.0911072i
$755$	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	$0.580037\pi$
$758$	16.2095	+	28.0756i	0.588754	+	1.01975i
$759$	27.1552	−	9.00602i	0.985672	−	0.326898i
$760$	3.01169	−	5.21640i	0.109246	−	0.189219i
$761$	−14.6428			−0.530802			−0.265401	−	0.964138i	$-0.585504\pi$
$761$	−14.6428			−0.530802			−0.265401	+	0.964138i	$0.585504\pi$
$762$	21.9691	+	19.5407i	0.795855	+	0.707883i
$763$		0			0
$764$	4.11855			0.149004
$765$	−40.6476	−	17.5088i	−1.46962	−	0.633032i
$766$	−2.72803	−	4.72509i	−0.0985677	−	0.170724i
$767$	−8.87636			−0.320507
$768$	6.20630	−	30.0963i	0.223951	−	1.08601i
$769$	−24.5672	−	42.5517i	−0.885918	−	1.53445i	−0.844658	−	0.535306i	$-0.820196\pi$
$769$	−24.5672	−	42.5517i	−0.885918	−	1.53445i	−0.0412592	−	0.999148i	$-0.513137\pi$
$770$		0			0
$771$	2.34108	−	0.776418i	0.0843118	−	0.0279620i
$772$	11.2410	+	19.4700i	0.404573	+	0.700741i
$773$	−6.22067	−	10.7745i	−0.223742	−	0.387532i	0.732199	−	0.681090i	$-0.238494\pi$
$773$	−6.22067	−	10.7745i	−0.223742	−	0.387532i	−0.955941	+	0.293558i	$0.905161\pi$
$774$	21.3010	−	15.8751i	0.765648	−	0.570617i
$775$	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
$779$	4.80951			0.172319
$780$	5.24288	−	1.73880i	0.187725	−	0.0622590i
$781$	8.08513			0.289309
$782$	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
$786$	35.3108	+	31.4077i	1.25950	+	1.12027i
$787$	16.4567	−	28.5038i	0.586617	−	1.01605i	−0.408055	−	0.912957i	$-0.633793\pi$
$787$	16.4567	−	28.5038i	0.586617	−	1.01605i	0.994672	−	0.103093i	$-0.0328739\pi$
$788$	−4.76392	+	8.25135i	−0.169708	+	0.293942i
$789$	−26.7367	+	8.86722i	−0.951851	+	0.315681i
$790$	−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
$794$	38.9862			1.38357
$795$	0.574202	+	0.510731i	0.0203648	+	0.0181138i
$796$	−7.79108			−0.276147
$797$	−13.1989	−	22.8612i	−0.467530	−	0.809786i	0.531781	−	0.846882i	$-0.321523\pi$
$797$	−13.1989	−	22.8612i	−0.467530	−	0.809786i	−0.999312	+	0.0370953i	$0.988189\pi$
$798$		0			0
$799$	−5.48074	+	9.49292i	−0.193895	+	0.335835i
$800$	18.5080	−	32.0567i	0.654356	−	1.13338i
$801$	3.36151	+	28.6316i	0.118773	+	1.01165i
$802$	15.4752	+	26.8039i	0.546450	+	0.946479i
$803$	−14.9560	−	25.9045i	−0.527785	−	0.914151i
$804$	14.1577	+	12.5927i	0.499303	+	0.444111i
$805$		0			0
$806$	5.93818	+	10.2852i	0.209163	+	0.362282i
$807$	−24.1414	−	21.4729i	−0.849819	−	0.755883i
$808$	−6.54394			−0.230215
$809$	−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	$-0.381842\pi$
$810$	53.3973	−	12.7135i	1.87619	−	0.446708i
$811$	−37.8268			−1.32828			−0.664140	−	0.747608i	$-0.731202\pi$
$811$	−37.8268			−1.32828			−0.664140	+	0.747608i	$0.731202\pi$
$812$		0			0
$813$	1.38626	−	6.72243i	0.0486184	−	0.235766i
$814$	−22.7651			−0.797916
$815$	−18.4963	+	32.0365i	−0.647896	+	1.12219i
$816$	7.17309	−	34.7845i	0.251108	−	1.21770i
$817$	2.31522	+	4.01008i	0.0809994	+	0.140295i
$818$	−26.0594			−0.911146
$819$		0			0
$820$	17.2583			0.602686
$821$	9.15638	+	15.8593i	0.319560	+	0.553494i	0.980396	−	0.197036i	$-0.0631317\pi$
$821$	9.15638	+	15.8593i	0.319560	+	0.553494i	−0.660836	+	0.750530i	$0.729798\pi$
$822$	−28.5679	−	25.4101i	−0.996421	−	0.886280i
$823$	18.0000	−	31.1769i	0.627441	−	1.08676i	−0.360623	−	0.932712i	$-0.617436\pi$
$823$	18.0000	−	31.1769i	0.627441	−	1.08676i	0.988063	−	0.154047i	$-0.0492308\pi$
$824$	29.9862			1.04462
$825$	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	$0.663188\pi$
$828$	1.82691	+	15.5607i	0.0634896	+	0.540772i
$829$	5.64214	+	9.77247i	0.195960	+	0.339412i	0.947215	−	0.320600i	$-0.103885\pi$
$829$	5.64214	+	9.77247i	0.195960	+	0.339412i	−0.751255	+	0.660012i	$0.770551\pi$
$830$	25.0741			0.870336
$831$	3.83675	−	1.27246i	0.133095	−	0.0441410i
$832$	−0.993810	−	1.72133i	−0.0344542	−	0.0596764i
$833$		0			0
$834$	0.660706	−	3.20397i	0.0228784	−	0.110944i
$835$	21.8028	+	37.7636i	0.754519	+	1.30686i
$836$	−1.11009	−	1.92274i	−0.0383934	−	0.0664993i
$837$	15.3702	+	32.8950i	0.531271	+	1.13702i
$838$	−8.98143	+	15.5563i	−0.310258	+	0.537383i
$839$	1.02152	−	1.76933i	0.0352669	−	0.0610840i	−0.847853	−	0.530231i	$-0.822105\pi$
$839$	1.02152	−	1.76933i	0.0352669	−	0.0610840i	0.883120	+	0.469147i	$0.155439\pi$
$840$		0			0
$841$	13.0556	+	22.6130i	0.450194	+	0.779759i
$842$	−61.4783			−2.11868
$843$	9.79301	−	47.4894i	0.337289	−	1.63562i
$844$	9.35855			0.322135
$845$	−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
$849$	3.61009	−	17.5065i	0.123898	−	0.600821i
$850$	27.5185	−	47.6634i	0.943877	−	1.63484i
$851$	−14.0007	+	24.2499i	−0.479937	+	0.831276i
$852$	−0.894237	+	4.33643i	−0.0306361	+	0.148564i
$853$	24.2960	−	42.0818i	0.831878	−	1.44085i	−0.0646692	−	0.997907i	$-0.520599\pi$
$853$	24.2960	−	42.0818i	0.831878	−	1.44085i	0.896547	−	0.442948i	$-0.146067\pi$
$854$		0			0
$855$	1.11559	+	9.50206i	0.0381525	+	0.324964i
$856$	−5.05563	+	8.75661i	−0.172798	+	0.299295i
$857$	−44.8974			−1.53367			−0.766833	−	0.641847i	$-0.778169\pi$
$857$	−44.8974			−1.53367			−0.766833	+	0.641847i	$0.778169\pi$
$858$	−1.67123	+	8.10430i	−0.0570547	+	0.276676i
$859$	29.8131			1.01721			0.508605	−	0.861000i	$-0.330162\pi$
$859$	29.8131			1.01721			0.508605	+	0.861000i	$0.330162\pi$
$860$	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	$-0.0888548\pi$
$864$	10.3374	+	22.1240i	0.351687	+	0.752675i
$865$	−11.8585	−	20.5395i	−0.403200	−	0.698363i
$866$	34.9894	+	60.6034i	1.18899	+	2.05939i
$867$	−0.0341093	+	0.165407i	−0.00115841	+	0.00561751i
$868$		0			0
$869$	−9.95970	−	17.2507i	−0.337860	−	0.585190i
$870$	−17.0414	+	5.65178i	−0.577757	+	0.191613i
$871$	12.3090			0.417076
$872$	−17.8145	−	30.8557i	−0.603276	−	1.04491i
$873$	2.56113	+	21.8144i	0.0866812	+	0.738306i
$874$	−8.87636			−0.300247
$875$		0			0
$876$	15.5480	−	5.15649i	0.525318	−	0.174222i
$877$	−30.5316			−1.03098			−0.515489	−	0.856896i	$-0.672390\pi$
$877$	−30.5316			−1.03098			−0.515489	+	0.856896i	$0.672390\pi$
$878$	3.97593	−	6.88651i	0.134181	−	0.232409i
$879$	−39.7261	−	35.3349i	−1.33993	−	1.19182i
$880$	25.1538	+	43.5677i	0.847935	+	1.46867i
$881$	−13.4079			−0.451724			−0.225862	−	0.974159i	$-0.572520\pi$
$881$	−13.4079			−0.451724			−0.225862	+	0.974159i	$0.572520\pi$
$882$		0			0
$883$	−14.1250			−0.475345			−0.237672	−	0.971345i	$-0.576384\pi$
$883$	−14.1250			−0.475345			−0.237672	+	0.971345i	$0.576384\pi$
$884$	1.82691	+	3.16431i	0.0614458	+	0.106427i
$885$	11.1421	−	54.0317i	0.374539	−	1.81626i
$886$	−25.6414	+	44.4123i	−0.861441	+	1.49206i
$887$	−39.9432			−1.34116			−0.670581	−	0.741837i	$-0.733955\pi$
$887$	−39.9432			−1.34116			−0.670581	+	0.741837i	$0.733955\pi$
$888$	−3.14833	+	15.2672i	−0.105651	+	0.512334i
$889$		0			0
$890$	−58.6067			−1.96450
$891$	−7.23058	+	24.2427i	−0.242233	+	0.812161i
$892$	2.51849	+	4.36216i	0.0843254	+	0.146056i
$893$	2.36955			0.0792941
$894$	18.5488	+	16.4984i	0.620363	+	0.551790i
$895$	−6.89493	−	11.9424i	−0.230472	−	0.399189i
$896$		0			0
$897$	7.60507	+	6.76443i	0.253926	+	0.225858i
$898$	−0.283662	−	0.491316i	−0.00946591	−	0.0163954i
$899$	−5.93818	−	10.2852i	−0.198049	−	0.343031i
$900$	2.44870	+	20.8567i	0.0816233	+	0.695225i
$901$	−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
$905$	−66.5375			−2.21178
$906$	−32.6680	−	29.0570i	−1.08532	−	0.965353i
$907$	41.4203			1.37534			0.687669	−	0.726024i	$-0.258634\pi$
$907$	41.4203			1.37534			0.687669	+	0.726024i	$0.258634\pi$
$908$	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	−0.880459	−	0.474122i	$-0.842765\pi$
$911$	−0.894237	+	1.54886i	−0.0296274	+	0.0513162i	0.850832	+	0.525439i	$0.176099\pi$
$912$	−7.28730	+	2.41683i	−0.241307	+	0.0800293i
$913$	−5.77816	+	10.0081i	−0.191229	+	0.331219i
$914$	16.4091	−	28.4214i	0.542764	−	0.940096i
$915$	−18.0018	−	16.0119i	−0.595121	−	0.529338i
$916$	−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	$-0.230083\pi$
$920$	39.8268			1.31305
$921$	18.8134	−	6.23945i	0.619921	−	0.205597i
$922$	66.4683			2.18902
$923$	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
$927$	−38.1897	+	28.4618i	−1.25431	+	0.934808i
$928$	−3.99381	−	6.91748i	−0.131103	−	0.227077i
$929$	−17.3676	−	30.0816i	−0.569813	−	0.986945i	−0.996584	−	0.0825854i	$-0.973682\pi$
$929$	−17.3676	−	30.0816i	−0.569813	−	0.986945i	0.426771	−	0.904360i	$-0.359651\pi$
$930$	−70.0617	+	23.2359i	−2.29741	+	0.761937i
$931$		0			0
$932$	−3.98281	−	6.89843i	−0.130461	−	0.225965i
$933$	4.18478	−	20.2933i	0.137003	−	0.664373i
$934$	−20.9395			−0.685161
$935$	20.7341	+	35.9126i	0.678079	+	1.17447i
$936$	5.20396	+	2.24159i	0.170097	+	0.0732686i
$937$	11.6662			0.381118			0.190559	−	0.981676i	$-0.438970\pi$
$937$	11.6662			0.381118			0.190559	+	0.981676i	$0.438970\pi$
$938$		0			0
$939$	−17.5283	−	15.5908i	−0.572015	−	0.508786i
$940$	8.50282			0.277332
$941$	25.1687	−	43.5934i	0.820475	−	1.42111i	−0.0848531	−	0.996393i	$-0.527042\pi$
$941$	25.1687	−	43.5934i	0.820475	−	1.42111i	0.905329	−	0.424712i	$-0.139625\pi$
$942$	−8.07165	+	2.67696i	−0.262989	+	0.0872202i
$943$	15.9004	+	27.5402i	0.517787	+	0.896833i
$944$	44.2719			1.44093
$945$		0			0
$946$	−24.8913			−0.809287
$947$	16.1941	+	28.0491i	0.526238	+	0.911472i	0.999533	+	0.0305673i	$0.00973139\pi$
$947$	16.1941	+	28.0491i	0.526238	+	0.911472i	−0.473294	+	0.880904i	$0.656935\pi$
$948$	10.3539	−	3.43388i	0.336280	−	0.111527i
$949$	5.32072	−	9.21576i	0.172718	−	0.299156i
$950$	−11.8974			−0.386003
$951$	−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	$0.565086\pi$
$954$	−0.0735129	−	0.626145i	−0.00238007	−	0.0202722i
$955$	8.31453	+	14.4012i	0.269052	+	0.466012i
$956$	9.97386			0.322578
$957$	1.67123	−	8.10430i	0.0540231	−	0.261975i
$958$	−11.4635	−	19.8555i	−0.370370	−	0.641500i
$959$		0			0
$960$	11.7255	−	3.88875i	0.378438	−	0.125509i
$961$	−8.91342	−	15.4385i	−0.287530	−	0.498016i
$962$	−4.04944	−	7.01384i	−0.130559	−	0.226135i
$963$	−1.87271	−	15.9508i	−0.0603474	−	0.514008i
$964$	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	0.779248	+	0.626715i	$0.215601\pi$
$967$	28.9937	+	50.2186i	0.932376	+	1.61492i	0.153127	+	0.988206i	$0.451065\pi$
$968$	5.85297			0.188122
$969$	−6.00688	+	1.99218i	−0.192969	+	0.0639981i
$970$	−44.6525			−1.43370
$971$	−14.0185	+	24.2807i	−0.449875	+	0.779206i	−0.998377	−	0.0569428i	$-0.981865\pi$
$971$	−14.0185	+	24.2807i	−0.449875	+	0.779206i	0.548503	+	0.836149i	$0.315198\pi$
$972$	−12.2028	−	6.55941i	−0.391405	−	0.210393i
$973$		0			0
$974$	−6.41095	+	11.1041i	−0.205420	+	0.355798i
$975$	10.1934	+	9.06668i	0.326451	+	0.290366i
$976$	9.66690	−	16.7436i	0.309430	−	0.535948i
$977$	−4.92030	+	8.52220i	−0.157414	+	0.272649i	−0.933935	−	0.357442i	$-0.883649\pi$
$977$	−4.92030	+	8.52220i	−0.157414	+	0.272649i	0.776521	+	0.630091i	$0.216982\pi$
$978$	28.8053	−	9.55328i	0.921092	−	0.305480i
$979$	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
$983$	−48.6894			−1.55295			−0.776476	−	0.630147i	$-0.782995\pi$
$983$	−48.6894			−1.55295			−0.776476	+	0.630147i	$0.782995\pi$
$984$	13.2280	+	11.7658i	0.421694	+	0.375081i
$985$	−38.4697			−1.22575
$986$	−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
$990$	−47.2343	−	20.3460i	−1.50120	−	0.646639i
$991$	−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	$0.847818\pi$
$992$	−16.4196	−	28.4396i	−0.521323	−	0.902958i
$993$	2.70032	+	2.40183i	0.0856920	+	0.0762198i
$994$		0			0
$995$	−15.7286	−	27.2428i	−0.498631	−	0.863655i
$996$	−4.72872	−	4.20602i	−0.149835	−	0.133273i
$997$	−50.8406			−1.61014			−0.805069	−	0.593181i	$-0.797872\pi$
$997$	−50.8406			−1.61014			−0.805069	+	0.593181i	$0.797872\pi$
$998$	26.2298	+	45.4314i	0.830290	+	1.43810i
$999$	−10.4814	−	22.4322i	−0.331618	−	0.709724i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.g.e.79.1		6
3.2	odd	2		1323.2.g.c.667.3		6
7.2	even	3		63.2.f.b.43.1	yes	6
7.3	odd	6		441.2.h.b.214.3		6
7.4	even	3		441.2.h.c.214.3		6
7.5	odd	6		441.2.f.d.295.1		6
7.6	odd	2		441.2.g.d.79.1		6
9.4	even	3		441.2.h.c.373.3		6
9.5	odd	6		1323.2.h.d.226.1		6
21.2	odd	6		189.2.f.a.127.3		6
21.5	even	6		1323.2.f.c.883.3		6
21.11	odd	6		1323.2.h.d.802.1		6
21.17	even	6		1323.2.h.e.802.1		6
21.20	even	2		1323.2.g.b.667.3		6
28.23	odd	6		1008.2.r.k.673.1		6
63.2	odd	6		567.2.a.g.1.1		3
63.4	even	3	inner	441.2.g.e.67.1		6
63.5	even	6		1323.2.f.c.442.3		6
63.13	odd	6		441.2.h.b.373.3		6
63.16	even	3		567.2.a.d.1.3		3
63.23	odd	6		189.2.f.a.64.3		6
63.31	odd	6		441.2.g.d.67.1		6
63.32	odd	6		1323.2.g.c.361.3		6
63.40	odd	6		441.2.f.d.148.1		6
63.41	even	6		1323.2.h.e.226.1		6
63.47	even	6		3969.2.a.p.1.1		3
63.58	even	3		63.2.f.b.22.1	✓	6
63.59	even	6		1323.2.g.b.361.3		6
63.61	odd	6		3969.2.a.m.1.3		3
84.23	even	6		3024.2.r.g.2017.1		6
252.23	even	6		3024.2.r.g.1009.1		6
252.79	odd	6		9072.2.a.bq.1.1		3
252.191	even	6		9072.2.a.cd.1.3		3
252.247	odd	6		1008.2.r.k.337.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.b.22.1	✓	6	63.58	even	3
63.2.f.b.43.1	yes	6	7.2	even	3
189.2.f.a.64.3		6	63.23	odd	6
189.2.f.a.127.3		6	21.2	odd	6
441.2.f.d.148.1		6	63.40	odd	6
441.2.f.d.295.1		6	7.5	odd	6
441.2.g.d.67.1		6	63.31	odd	6
441.2.g.d.79.1		6	7.6	odd	2
441.2.g.e.67.1		6	63.4	even	3	inner
441.2.g.e.79.1		6	1.1	even	1	trivial
441.2.h.b.214.3		6	7.3	odd	6
441.2.h.b.373.3		6	63.13	odd	6
441.2.h.c.214.3		6	7.4	even	3
441.2.h.c.373.3		6	9.4	even	3
567.2.a.d.1.3		3	63.16	even	3
567.2.a.g.1.1		3	63.2	odd	6
1008.2.r.k.337.1		6	252.247	odd	6
1008.2.r.k.673.1		6	28.23	odd	6
1323.2.f.c.442.3		6	63.5	even	6
1323.2.f.c.883.3		6	21.5	even	6
1323.2.g.b.361.3		6	63.59	even	6
1323.2.g.b.667.3		6	21.20	even	2
1323.2.g.c.361.3		6	63.32	odd	6
1323.2.g.c.667.3		6	3.2	odd	2
1323.2.h.d.226.1		6	9.5	odd	6
1323.2.h.d.802.1		6	21.11	odd	6
1323.2.h.e.226.1		6	63.41	even	6
1323.2.h.e.802.1		6	21.17	even	6
3024.2.r.g.1009.1		6	252.23	even	6
3024.2.r.g.2017.1		6	84.23	even	6
3969.2.a.m.1.3		3	63.61	odd	6
3969.2.a.p.1.1		3	63.47	even	6
9072.2.a.bq.1.1		3	252.79	odd	6
9072.2.a.cd.1.3		3	252.191	even	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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.849814 - 1.47192i) q^{2} +(-1.64400 + 0.545231i) q^{3} +(-0.444368 + 0.769668i) q^{4} -3.58836 q^{5} +(2.19963 + 1.95649i) q^{6} -1.88874 q^{8} +(2.40545 - 1.79272i) q^{9} +O(q^{10})\)	\(q+(-0.849814 - 1.47192i) q^{2} +(-1.64400 + 0.545231i) q^{3} +(-0.444368 + 0.769668i) q^{4} -3.58836 q^{5} +(2.19963 + 1.95649i) q^{6} -1.88874 q^{8} +(2.40545 - 1.79272i) q^{9} +(3.04944 + 5.28179i) q^{10} -2.81089 q^{11} +(0.310892 - 1.50761i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(5.89926 - 1.95649i) q^{15} +(2.49381 + 4.31941i) q^{16} +(2.05563 + 3.56046i) q^{17} +(-4.68292 - 2.01715i) q^{18} +(0.444368 - 0.769668i) q^{19} +(1.59455 - 2.76185i) q^{20} +(2.38874 + 4.13741i) q^{22} +5.87636 q^{23} +(3.10507 - 1.02980i) q^{24} +7.87636 q^{25} +(-0.849814 + 1.47192i) q^{26} +(-2.97710 + 4.25874i) q^{27} +(0.849814 - 1.47192i) q^{29} +(-7.89307 - 7.02059i) q^{30} +(3.49381 - 6.05146i) q^{31} +(2.34981 - 4.07000i) q^{32} +(4.62110 - 1.53259i) q^{33} +(3.49381 - 6.05146i) q^{34} +(0.310892 + 2.64802i) q^{36} +(-2.38255 + 4.12669i) q^{37} -1.51052 q^{38} +(1.29418 + 1.15113i) q^{39} +6.77747 q^{40} +(2.70582 + 4.68661i) q^{41} +(-2.60507 + 4.51212i) q^{43} +(1.24907 - 2.16345i) q^{44} +(-8.63162 + 6.43292i) q^{45} +(-4.99381 - 8.64953i) q^{46} +(1.33310 + 2.30900i) q^{47} +(-6.45489 - 5.74138i) q^{48} +(-6.69344 - 11.5934i) q^{50} +(-5.32072 - 4.73259i) q^{51} +0.888736 q^{52} +(0.0618219 + 0.107079i) q^{53} +(8.79851 + 0.762918i) q^{54} +10.0865 q^{55} +(-0.310892 + 1.50761i) q^{57} -2.88874 q^{58} +(4.43818 - 7.68715i) q^{59} +(-1.11559 + 5.40987i) q^{60} +(-1.93818 - 3.35702i) q^{61} -11.8764 q^{62} +1.98762 q^{64} +(1.79418 + 3.10761i) q^{65} +(-6.18292 - 5.49948i) q^{66} +(-6.15452 + 10.6599i) q^{67} -3.65383 q^{68} +(-9.66071 + 3.20397i) q^{69} -2.87636 q^{71} +(-4.54325 + 3.38597i) q^{72} +(5.32072 + 9.21576i) q^{73} +8.09888 q^{74} +(-12.9487 + 4.29443i) q^{75} +(0.394926 + 0.684031i) q^{76} +(0.594554 - 2.88318i) q^{78} +(3.54325 + 6.13709i) q^{79} +(-8.94870 - 15.4996i) q^{80} +(2.57234 - 8.62456i) q^{81} +(4.59888 - 7.96550i) q^{82} +(2.05563 - 3.56046i) q^{83} +(-7.37636 - 12.7762i) q^{85} +8.85532 q^{86} +(-0.594554 + 2.88318i) q^{87} +5.30903 q^{88} +(-4.80470 + 8.32199i) q^{89} +(16.8040 + 7.23828i) q^{90} +(-2.61126 + 4.52284i) q^{92} +(-2.44437 + 11.8535i) q^{93} +(2.26578 - 3.92445i) q^{94} +(-1.59455 + 2.76185i) q^{95} +(-1.64400 + 7.97225i) q^{96} +(-3.66071 + 6.34053i) q^{97} +(-6.76145 + 5.03913i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} + 2 q^{3} - 3 q^{4} - 10 q^{5} + q^{6} - 12 q^{8} + 8 q^{9}+O(q^{10}) \) 6 * q + q^2 + 2 * q^3 - 3 * q^4 - 10 * q^5 + q^6 - 12 * q^8 + 8 * q^9	\( 6 q + q^{2} + 2 q^{3} - 3 q^{4} - 10 q^{5} + q^{6} - 12 q^{8} + 8 q^{9} - 4 q^{11} - 11 q^{12} - 3 q^{13} + 11 q^{15} - 3 q^{16} + 12 q^{17} - 23 q^{18} + 3 q^{19} + 16 q^{20} + 15 q^{22} + 12 q^{25} + q^{26} - 7 q^{27} - q^{29} - 5 q^{30} + 3 q^{31} + 8 q^{32} + 5 q^{33} + 3 q^{34} - 11 q^{36} + 3 q^{37} + 16 q^{38} + 2 q^{39} + 42 q^{40} + 22 q^{41} + 3 q^{43} - 23 q^{44} - 4 q^{45} - 12 q^{46} + 9 q^{47} - 14 q^{48} - 10 q^{50} + 3 q^{51} + 6 q^{52} + 18 q^{53} + 4 q^{54} - 12 q^{55} + 11 q^{57} - 18 q^{58} + 9 q^{59} + 37 q^{60} + 6 q^{61} - 36 q^{62} - 24 q^{64} + 5 q^{65} - 32 q^{66} + 12 q^{68} - 39 q^{69} + 18 q^{71} + 9 q^{72} - 3 q^{73} + 12 q^{74} - 35 q^{75} + 21 q^{76} + 10 q^{78} - 15 q^{79} - 11 q^{80} + 8 q^{81} - 9 q^{82} + 12 q^{83} - 9 q^{85} + 68 q^{86} - 10 q^{87} - 42 q^{88} + 2 q^{89} + 73 q^{90} - 15 q^{92} - 15 q^{93} - 24 q^{94} - 16 q^{95} + 2 q^{96} - 3 q^{97} - 46 q^{99}+O(q^{100}) \) 6 * q + q^2 + 2 * q^3 - 3 * q^4 - 10 * q^5 + q^6 - 12 * q^8 + 8 * q^9 - 4 * q^11 - 11 * q^12 - 3 * q^13 + 11 * q^15 - 3 * q^16 + 12 * q^17 - 23 * q^18 + 3 * q^19 + 16 * q^20 + 15 * q^22 + 12 * q^25 + q^26 - 7 * q^27 - q^29 - 5 * q^30 + 3 * q^31 + 8 * q^32 + 5 * q^33 + 3 * q^34 - 11 * q^36 + 3 * q^37 + 16 * q^38 + 2 * q^39 + 42 * q^40 + 22 * q^41 + 3 * q^43 - 23 * q^44 - 4 * q^45 - 12 * q^46 + 9 * q^47 - 14 * q^48 - 10 * q^50 + 3 * q^51 + 6 * q^52 + 18 * q^53 + 4 * q^54 - 12 * q^55 + 11 * q^57 - 18 * q^58 + 9 * q^59 + 37 * q^60 + 6 * q^61 - 36 * q^62 - 24 * q^64 + 5 * q^65 - 32 * q^66 + 12 * q^68 - 39 * q^69 + 18 * q^71 + 9 * q^72 - 3 * q^73 + 12 * q^74 - 35 * q^75 + 21 * q^76 + 10 * q^78 - 15 * q^79 - 11 * q^80 + 8 * q^81 - 9 * q^82 + 12 * q^83 - 9 * q^85 + 68 * q^86 - 10 * q^87 - 42 * q^88 + 2 * q^89 + 73 * q^90 - 15 * q^92 - 15 * q^93 - 24 * q^94 - 16 * q^95 + 2 * q^96 - 3 * q^97 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more