LMFDB - Embedded newform 441.2.g.d.67.3

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			67.3
Root			$0.500000 + 2.05195i$ of defining polynomial
Character	$\chi$	$=$	441.67
Dual form			441.2.g.d.79.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23025 - 2.13086i) q^{2} +(-0.933463 + 1.45899i) q^{3} +(-2.02704 - 3.51094i) q^{4} +2.59358 q^{5} +(1.96050 + 3.78400i) q^{6} -5.05408 q^{8} +(-1.25729 - 2.72382i) q^{9} +O(q^{10})$	\(q+(1.23025 - 2.13086i) q^{2} +(-0.933463 + 1.45899i) q^{3} +(-2.02704 - 3.51094i) q^{4} +2.59358 q^{5} +(1.96050 + 3.78400i) q^{6} -5.05408 q^{8} +(-1.25729 - 2.72382i) q^{9} +(3.19076 - 5.52655i) q^{10} +4.51459 q^{11} +(7.01459 + 0.319901i) q^{12} +(0.500000 - 0.866025i) q^{13} +(-2.42101 + 3.78400i) q^{15} +(-2.16372 + 3.74766i) q^{16} +(-0.472958 + 0.819187i) q^{17} +(-7.35087 - 0.671871i) q^{18} +(-2.02704 - 3.51094i) q^{19} +(-5.25729 - 9.10590i) q^{20} +(5.55408 - 9.61996i) q^{22} -0.273346 q^{23} +(4.71780 - 7.37385i) q^{24} +1.72665 q^{25} +(-1.23025 - 2.13086i) q^{26} +(5.14766 + 0.708209i) q^{27} +(-1.23025 - 2.13086i) q^{29} +(5.08472 + 9.81411i) q^{30} +(1.16372 + 2.01561i) q^{31} +(0.269748 + 0.467216i) q^{32} +(-4.21420 + 6.58673i) q^{33} +(1.16372 + 2.01561i) q^{34} +(-7.01459 + 9.93559i) q^{36} +(-0.890369 - 1.54216i) q^{37} -9.97509 q^{38} +(0.796790 + 1.53790i) q^{39} -13.1082 q^{40} +(-3.20321 + 5.54812i) q^{41} +(5.21780 + 9.03749i) q^{43} +(-9.15126 - 15.8505i) q^{44} +(-3.26089 - 7.06445i) q^{45} +(-0.336285 + 0.582462i) q^{46} +(-6.08113 + 10.5328i) q^{47} +(-3.44805 - 6.65514i) q^{48} +(2.12422 - 3.67926i) q^{50} +(-0.753696 - 1.45472i) q^{51} -4.05408 q^{52} +(3.13667 - 5.43288i) q^{53} +(7.84202 - 10.0977i) q^{54} +11.7089 q^{55} +(7.01459 + 0.319901i) q^{57} -6.05408 q^{58} +(-1.36333 - 2.36135i) q^{59} +(18.1929 + 0.829688i) q^{60} +(-1.13667 + 1.96878i) q^{61} +5.72665 q^{62} -7.32743 q^{64} +(1.29679 - 2.24611i) q^{65} +(8.85087 + 17.0832i) q^{66} +(7.90856 + 13.6980i) q^{67} +3.83482 q^{68} +(0.255158 - 0.398809i) q^{69} +3.27335 q^{71} +(6.35447 + 13.7664i) q^{72} +(-0.753696 + 1.30544i) q^{73} -4.38151 q^{74} +(-1.61177 + 2.51917i) q^{75} +(-8.21780 + 14.2336i) q^{76} +(4.25729 + 0.194154i) q^{78} +(-7.35447 + 12.7383i) q^{79} +(-5.61177 + 9.71987i) q^{80} +(-5.83842 + 6.84929i) q^{81} +(7.88151 + 13.6512i) q^{82} +(-0.472958 - 0.819187i) q^{83} +(-1.22665 + 2.12463i) q^{85} +25.6768 q^{86} +(4.25729 + 0.194154i) q^{87} -22.8171 q^{88} +(-7.17830 - 12.4332i) q^{89} +(-19.0651 - 1.74255i) q^{90} +(0.554084 + 0.959702i) q^{92} +(-4.02704 - 0.183653i) q^{93} +(14.9626 + 25.9161i) q^{94} +(-5.25729 - 9.10590i) q^{95} +(-0.933463 - 0.0425706i) q^{96} +(-5.74484 - 9.95036i) q^{97} +(-5.67617 - 12.2969i) 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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.23025	−	2.13086i	0.869920	−	1.50675i	0.00784213	−	0.999969i	$-0.497504\pi$
$2$	1.23025	−	2.13086i	0.869920	−	1.50675i	0.862078	−	0.506776i	$-0.169163\pi$
$3$	−0.933463	+	1.45899i	−0.538935	+	0.842347i
$3$	−0.933463	+	1.45899i	−0.538935	+	0.842347i
$4$	−2.02704	−	3.51094i	−1.01352	−	1.75547i
$5$	2.59358			1.15988			0.579942	−	0.814658i	$-0.303075\pi$
$5$	2.59358			1.15988			0.579942	+	0.814658i	$0.303075\pi$
$6$	1.96050	+	3.78400i	0.800373	+	1.54481i
$7$		0			0
$7$		0			0
$8$	−5.05408			−1.78689
$9$	−1.25729	−	2.72382i	−0.419098	−	0.907941i
$10$	3.19076	−	5.52655i	1.00901	−	1.74765i
$11$	4.51459			1.36120			0.680600	−	0.732655i	$-0.261719\pi$
$11$	4.51459			1.36120			0.680600	+	0.732655i	$0.261719\pi$
$12$	7.01459	+	0.319901i	2.02494	+	0.0923474i
$13$	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
$15$	−2.42101	+	3.78400i	−0.625102	+	0.977025i
$16$	−2.16372	+	3.74766i	−0.540929	+	0.936916i
$17$	−0.472958	+	0.819187i	−0.114709	+	0.198682i	−0.917663	−	0.397359i	$-0.869927\pi$
$17$	−0.472958	+	0.819187i	−0.114709	+	0.198682i	0.802954	+	0.596041i	$0.203260\pi$
$18$	−7.35087	−	0.671871i	−1.73262	−	0.158362i
$19$	−2.02704	−	3.51094i	−0.465035	−	0.805465i	0.534168	−	0.845378i	$-0.320625\pi$
$19$	−2.02704	−	3.51094i	−0.465035	−	0.805465i	−0.999203	+	0.0399136i	$0.987292\pi$
$20$	−5.25729	−	9.10590i	−1.17557	−	2.03614i
$21$		0			0
$22$	5.55408	−	9.61996i	1.18413	−	2.05098i
$23$	−0.273346			−0.0569966			−0.0284983	−	0.999594i	$-0.509073\pi$
$23$	−0.273346			−0.0569966			−0.0284983	+	0.999594i	$0.509073\pi$
$24$	4.71780	−	7.37385i	0.963017	−	1.50518i
$25$	1.72665			0.345331
$26$	−1.23025	−	2.13086i	−0.241272	−	0.417896i
$27$	5.14766	+	0.708209i	0.990668	+	0.136295i
$28$		0			0
$29$	−1.23025	−	2.13086i	−0.228452	−	0.395691i	0.728897	−	0.684623i	$-0.240033\pi$
$29$	−1.23025	−	2.13086i	−0.228452	−	0.395691i	−0.957350	+	0.288932i	$0.906700\pi$
$30$	5.08472	+	9.81411i	0.928340	+	1.79180i
$31$	1.16372	+	2.01561i	0.209009	+	0.362015i	0.951403	−	0.307949i	$-0.0996427\pi$
$31$	1.16372	+	2.01561i	0.209009	+	0.362015i	−0.742393	+	0.669964i	$0.766309\pi$
$32$	0.269748	+	0.467216i	0.0476851	+	0.0825930i
$33$	−4.21420	+	6.58673i	−0.733598	+	1.14660i
$34$	1.16372	+	2.01561i	0.199576	+	0.345675i
$35$		0			0
$36$	−7.01459	+	9.93559i	−1.16910	+	1.65593i
$37$	−0.890369	−	1.54216i	−0.146376	−	0.253530i	0.783510	−	0.621380i	$-0.213428\pi$
$37$	−0.890369	−	1.54216i	−0.146376	−	0.253530i	−0.929885	+	0.367849i	$0.880094\pi$
$38$	−9.97509			−1.61817
$39$	0.796790	+	1.53790i	0.127588	+	0.246261i
$40$	−13.1082			−2.07258
$41$	−3.20321	+	5.54812i	−0.500257	+	0.866471i	0.499743	+	0.866174i	$0.333428\pi$
$41$	−3.20321	+	5.54812i	−0.500257	+	0.866471i	−1.00000		0.000297253i	$0.999905\pi$
$42$		0			0
$43$	5.21780	+	9.03749i	0.795707	+	1.37820i	0.922389	+	0.386262i	$0.126234\pi$
$43$	5.21780	+	9.03749i	0.795707	+	1.37820i	−0.126682	+	0.991943i	$0.540433\pi$
$44$	−9.15126	−	15.8505i	−1.37960	−	2.38955i
$45$	−3.26089	−	7.06445i	−0.486105	−	1.05311i
$46$	−0.336285	+	0.582462i	−0.0495825	+	0.0858794i
$47$	−6.08113	+	10.5328i	−0.887023	+	1.53637i	−0.0436467	+	0.999047i	$0.513898\pi$
$47$	−6.08113	+	10.5328i	−0.887023	+	1.53637i	−0.843377	+	0.537323i	$0.819436\pi$
$48$	−3.44805	−	6.65514i	−0.497683	−	0.960587i
$49$		0			0
$50$	2.12422	−	3.67926i	0.300410	−	0.520326i
$51$	−0.753696	−	1.45472i	−0.105539	−	0.203702i
$52$	−4.05408			−0.562200
$53$	3.13667	−	5.43288i	0.430855	−	0.746263i	−0.566092	−	0.824342i	$-0.691545\pi$
$53$	3.13667	−	5.43288i	0.430855	−	0.746263i	0.996947	+	0.0780790i	$0.0248786\pi$
$54$	7.84202	−	10.0977i	1.06716	−	1.37412i
$55$	11.7089			1.57883
$56$		0			0
$57$	7.01459	+	0.319901i	0.929105	+	0.0423719i
$58$	−6.05408			−0.794940
$59$	−1.36333	−	2.36135i	−0.177490	−	0.307422i	0.763530	−	0.645772i	$-0.223464\pi$
$59$	−1.36333	−	2.36135i	−0.177490	−	0.307422i	−0.941020	+	0.338350i	$0.890131\pi$
$60$	18.1929	+	0.829688i	2.34869	+	0.107112i
$61$	−1.13667	+	1.96878i	−0.145536	+	0.252076i	−0.929573	−	0.368639i	$-0.879824\pi$
$61$	−1.13667	+	1.96878i	−0.145536	+	0.252076i	0.784037	+	0.620714i	$0.213157\pi$
$62$	5.72665			0.727286
$63$		0			0
$64$	−7.32743			−0.915929
$65$	1.29679	−	2.24611i	0.160847	−	0.278595i
$66$	8.85087	+	17.0832i	1.08947	+	2.10280i
$67$	7.90856	+	13.6980i	0.966184	+	1.67348i	0.706400	+	0.707813i	$0.250318\pi$
$67$	7.90856	+	13.6980i	0.966184	+	1.67348i	0.259784	+	0.965667i	$0.416349\pi$
$68$	3.83482			0.465041
$69$	0.255158	−	0.398809i	0.0307175	−	0.0480110i
$70$		0			0
$71$	3.27335			0.388475			0.194237	−	0.980955i	$-0.437777\pi$
$71$	3.27335			0.388475			0.194237	+	0.980955i	$0.437777\pi$
$72$	6.35447	+	13.7664i	0.748882	+	1.62239i
$73$	−0.753696	+	1.30544i	−0.0882134	+	0.152790i	−0.906756	−	0.421656i	$-0.861449\pi$
$73$	−0.753696	+	1.30544i	−0.0882134	+	0.152790i	0.818543	+	0.574446i	$0.194782\pi$
$74$	−4.38151			−0.509341
$75$	−1.61177	+	2.51917i	−0.186111	+	0.290888i
$76$	−8.21780	+	14.2336i	−0.942646	+	1.63271i
$77$		0			0
$78$	4.25729	+	0.194154i	0.482044	+	0.0219836i
$79$	−7.35447	+	12.7383i	−0.827443	+	1.43317i	0.0725952	+	0.997361i	$0.476872\pi$
$79$	−7.35447	+	12.7383i	−0.827443	+	1.43317i	−0.900038	+	0.435811i	$0.856461\pi$
$80$	−5.61177	+	9.71987i	−0.627415	+	1.08671i
$81$	−5.83842	+	6.84929i	−0.648713	+	0.761033i
$82$	7.88151	+	13.6512i	0.870368	+	1.50752i
$83$	−0.472958	−	0.819187i	−0.0519139	−	0.0899175i	0.838901	−	0.544285i	$-0.183199\pi$
$83$	−0.472958	−	0.819187i	−0.0519139	−	0.0899175i	−0.890815	+	0.454367i	$0.849865\pi$
$84$		0			0
$85$	−1.22665	+	2.12463i	−0.133049	+	0.230448i
$86$	25.6768			2.76881
$87$	4.25729	+	0.194154i	0.456430	+	0.0208155i
$88$	−22.8171			−2.43231
$89$	−7.17830	−	12.4332i	−0.760899	−	1.31792i	−0.942388	−	0.334522i	$-0.891425\pi$
$89$	−7.17830	−	12.4332i	−0.760899	−	1.31792i	0.181489	−	0.983393i	$-0.441908\pi$
$90$	−19.0651	−	1.74255i	−2.00964	−	0.183681i
$91$		0			0
$92$	0.554084	+	0.959702i	0.0577673	+	0.100056i
$93$	−4.02704	−	0.183653i	−0.417585	−	0.0190440i
$94$	14.9626	+	25.9161i	1.54328	+	2.67304i
$95$	−5.25729	−	9.10590i	−0.539387	−	0.934246i
$96$	−0.933463	−	0.0425706i	−0.0952711	−	0.00434485i
$97$	−5.74484	−	9.95036i	−0.583300	−	1.01031i	−0.995085	−	0.0990246i	$-0.968428\pi$
$97$	−5.74484	−	9.95036i	−0.583300	−	1.01031i	0.411785	−	0.911281i	$-0.364906\pi$
$98$		0			0
$99$	−5.67617	−	12.2969i	−0.570476	−	1.23589i
$100$	−3.50000	−	6.06218i	−0.350000	−	0.606218i
$101$	3.67977			0.366150			0.183075	−	0.983099i	$-0.441395\pi$
$101$	3.67977			0.366150			0.183075	+	0.983099i	$0.441395\pi$
$102$	−4.02704	−	0.183653i	−0.398737	−	0.0181844i
$103$	9.72665			0.958396			0.479198	−	0.877707i	$-0.340928\pi$
$103$	9.72665			0.958396			0.479198	+	0.877707i	$0.340928\pi$
$104$	−2.52704	+	4.37697i	−0.247797	+	0.429197i
$105$		0			0
$106$	−7.71780	−	13.3676i	−0.749619	−	1.29838i
$107$	0.687159	+	1.19019i	0.0664301	+	0.115060i	0.897327	−	0.441365i	$-0.145506\pi$
$107$	0.687159	+	1.19019i	0.0664301	+	0.115060i	−0.830897	+	0.556426i	$0.812172\pi$
$108$	−7.94805	−	19.5087i	−0.764802	−	1.87723i
$109$	1.69961	−	2.94381i	0.162793	−	0.281966i	−0.773076	−	0.634313i	$-0.781283\pi$
$109$	1.69961	−	2.94381i	0.162793	−	0.281966i	0.935869	+	0.352347i	$0.114616\pi$
$110$	14.4050	−	24.9501i	1.37346	−	2.37890i
$111$	3.08113	+	0.140515i	0.292448	+	0.0133371i
$112$		0			0
$113$	−5.19436	+	8.99689i	−0.488644	+	0.846356i	−0.999915	−	0.0130636i	$-0.995842\pi$
$113$	−5.19436	+	8.99689i	−0.488644	+	0.846356i	0.511271	+	0.859420i	$0.329175\pi$
$114$	9.31138	−	14.5535i	0.872091	−	1.36306i
$115$	−0.708945			−0.0661095
$116$	−4.98755	+	8.63868i	−0.463082	+	0.802082i
$117$	−2.98755	−	0.273062i	−0.276199	−	0.0252446i
$118$	−6.70895			−0.617608
$119$		0			0
$120$	12.2360	−	19.1247i	1.11699	−	1.74584i
$121$	9.38151			0.852865
$122$	2.79679	+	4.84418i	0.253209	+	0.438572i
$123$	−5.10457	−	9.85241i	−0.460264	−	0.888362i
$124$	4.71780	−	8.17147i	0.423671	−	0.733820i
$125$	−8.48968			−0.759340
$126$		0			0
$127$	0.672570			0.0596809			0.0298405	−	0.999555i	$-0.490500\pi$
$127$	0.672570			0.0596809			0.0298405	+	0.999555i	$0.490500\pi$
$128$	−9.55408	+	16.5482i	−0.844470	+	1.46266i
$129$	−18.0562	−	0.823455i	−1.58976	−	0.0725012i
$130$	−3.19076	−	5.52655i	−0.279848	−	0.484711i
$131$	−7.91381			−0.691433			−0.345717	−	0.938339i	$-0.612364\pi$
$131$	−7.91381			−0.691433			−0.345717	+	0.938339i	$0.612364\pi$
$132$	31.6680	+	1.44422i	2.75634	+	0.125703i
$133$		0			0
$134$	38.9181			3.36201
$135$	13.3509	+	1.83680i	1.14906	+	0.158086i
$136$	2.39037	−	4.14024i	0.204972	−	0.355023i
$137$	−3.67257			−0.313769			−0.156884	−	0.987617i	$-0.550145\pi$
$137$	−3.67257			−0.313769			−0.156884	+	0.987617i	$0.550145\pi$
$138$	−0.535897	−	1.03434i	−0.0456185	−	0.0880491i
$139$	−1.02704	+	1.77889i	−0.0871126	+	0.150883i	−0.906289	−	0.422658i	$-0.861097\pi$
$139$	−1.02704	+	1.77889i	−0.0871126	+	0.150883i	0.819177	+	0.573541i	$0.194431\pi$
$140$		0			0
$141$	−9.69076	−	18.7043i	−0.816109	−	1.57519i
$142$	4.02704	−	6.97504i	0.337942	−	0.585332i
$143$	2.25729	−	3.90975i	0.188764	−	0.326950i
$144$	12.9284	+	1.18166i	1.07737	+	0.0984715i
$145$	−3.19076	−	5.52655i	−0.264978	−	0.458955i
$146$	1.85447	+	3.21204i	0.153477	+	0.265830i
$147$		0			0
$148$	−3.60963	+	6.25206i	−0.296710	+	0.513917i
$149$	−13.5438			−1.10955			−0.554774	−	0.832001i	$-0.687195\pi$
$149$	−13.5438			−1.10955			−0.554774	+	0.832001i	$0.687195\pi$
$150$	3.38511	+	6.53366i	0.276393	+	0.533471i
$151$	9.92821			0.807946			0.403973	−	0.914771i	$-0.367629\pi$
$151$	9.92821			0.807946			0.403973	+	0.914771i	$0.367629\pi$
$152$	10.2448	+	17.7446i	0.830966	+	1.43928i
$153$	2.82597	+	0.258294i	0.228466	+	0.0208818i
$154$		0			0
$155$	3.01819	+	5.22765i	0.242427	+	0.419895i
$156$	3.78434	−	5.91486i	0.302989	−	0.473568i
$157$	3.02704	+	5.24299i	0.241584	+	0.418436i	0.961166	−	0.275972i	$-0.0889996\pi$
$157$	3.02704	+	5.24299i	0.241584	+	0.418436i	−0.719581	+	0.694408i	$0.755666\pi$
$158$	18.0957	+	31.3427i	1.43962	+	2.49349i
$159$	4.99854	+	9.64776i	0.396410	+	0.765117i
$160$	0.699612	+	1.21176i	0.0553092	+	0.0957983i
$161$		0			0
$162$	7.41216	+	20.8672i	0.582354	+	1.63948i
$163$	−8.90856	−	15.4301i	−0.697772	−	1.20858i	−0.969237	−	0.246128i	$-0.920842\pi$
$163$	−8.90856	−	15.4301i	−0.697772	−	1.20858i	0.271465	−	0.962448i	$-0.412492\pi$
$164$	25.9722			2.02809
$165$	−10.9299	+	17.0832i	−0.850889	+	1.32993i
$166$	−2.32743			−0.180644
$167$	−4.23385	+	7.33325i	−0.327625	+	0.567464i	−0.982040	−	0.188672i	$-0.939582\pi$
$167$	−4.23385	+	7.33325i	−0.327625	+	0.567464i	0.654415	+	0.756136i	$0.272915\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$	3.01819	+	5.22765i	0.231484	+	0.400943i
$171$	−7.01459	+	9.93559i	−0.536419	+	0.759793i
$172$	21.1534	−	36.6388i	1.61293	−	2.79368i
$173$	8.67830	−	15.0313i	0.659799	−	1.14281i	−0.320868	−	0.947124i	$-0.603975\pi$
$173$	8.67830	−	15.0313i	0.659799	−	1.14281i	0.980667	−	0.195682i	$-0.0626920\pi$
$174$	5.65126	−	8.83284i	0.428421	−	0.669616i
$175$		0			0
$176$	−9.76829	+	16.9192i	−0.736312	+	1.27533i
$177$	4.71780	+	0.215155i	0.354612	+	0.0161721i
$178$	−35.3245			−2.64768
$179$	5.67471	−	9.82888i	0.424147	−	0.734645i	−0.572193	−	0.820119i	$-0.693907\pi$
$179$	5.67471	−	9.82888i	0.424147	−	0.734645i	0.996340	+	0.0854741i	$0.0272405\pi$
$180$	−18.1929	+	25.7687i	−1.35602	+	1.92069i
$181$	−21.8889			−1.62699			−0.813495	−	0.581572i	$-0.802438\pi$
$181$	−21.8889			−1.62699			−0.813495	+	0.581572i	$0.802438\pi$
$182$		0			0
$183$	−1.81138	−	3.49617i	−0.133901	−	0.258444i
$184$	1.38151			0.101847
$185$	−2.30924	−	3.99973i	−0.169779	−	0.294066i
$186$	−5.34562	+	8.35512i	−0.391960	+	0.612627i
$187$	−2.13521	+	3.69829i	−0.156142	+	0.270446i
$188$	49.3068			3.59607
$189$		0			0
$190$	−25.8712			−1.87689
$191$	0.350874	−	0.607731i	0.0253883	−	0.0439739i	−0.853052	−	0.521826i	$-0.825251\pi$
$191$	0.350874	−	0.607731i	0.0253883	−	0.0439739i	0.878440	+	0.477852i	$0.158584\pi$
$192$	6.83988	−	10.6906i	0.493626	−	0.771530i
$193$	−6.07227	−	10.5175i	−0.437092	−	0.757065i	0.560372	−	0.828241i	$-0.310658\pi$
$193$	−6.07227	−	10.5175i	−0.437092	−	0.757065i	−0.997464	+	0.0711760i	$0.977325\pi$
$194$	−28.2704			−2.02970
$195$	2.06654	+	3.98866i	0.147988	+	0.285634i
$196$		0			0
$197$	−16.4107			−1.16921			−0.584607	−	0.811317i	$-0.698751\pi$
$197$	−16.4107			−1.16921			−0.584607	+	0.811317i	$0.698751\pi$
$198$	−33.1862	−	3.03322i	−2.35844	−	0.215562i
$199$	11.3530	−	19.6640i	0.804794	−	1.39394i	−0.111637	−	0.993749i	$-0.535609\pi$
$199$	11.3530	−	19.6640i	0.804794	−	1.39394i	0.916430	−	0.400194i	$-0.131057\pi$
$200$	−8.72665			−0.617068
$201$	−27.3676	−	1.24810i	−1.93036	−	0.0880342i
$202$	4.52704	−	7.84107i	0.318522	−	0.551696i
$203$		0			0
$204$	−3.57966	+	5.59496i	−0.250627	+	0.391726i
$205$	−8.30778	+	14.3895i	−0.580241	+	1.00501i
$206$	11.9662	−	20.7261i	0.833727	−	1.44406i
$207$	0.343677	+	0.744547i	0.0238872	+	0.0517496i
$208$	2.16372	+	3.74766i	0.150027	+	0.259854i
$209$	−9.15126	−	15.8505i	−0.633006	−	1.09640i
$210$		0			0
$211$	−2.28074	+	3.95035i	−0.157012	+	0.271954i	−0.933790	−	0.357822i	$-0.883520\pi$
$211$	−2.28074	+	3.95035i	−0.157012	+	0.271954i	0.776778	+	0.629775i	$0.216853\pi$
$212$	−25.4327			−1.74672
$213$	−3.05555	+	4.77577i	−0.209363	+	0.327231i
$214$	3.38151			0.231156
$215$	13.5328	+	23.4395i	0.922928	+	1.59856i
$216$	−26.0167	−	3.57935i	−1.77021	−	0.243544i
$217$		0			0
$218$	−4.18190	−	7.24327i	−0.283234	−	0.490576i
$219$	−1.20107	−	2.31821i	−0.0811611	−	0.156650i
$220$	−23.7345	−	41.1094i	−1.60018	−	2.77160i
$221$	0.472958	+	0.819187i	0.0318146	+	0.0551045i
$222$	4.08998	−	6.39258i	0.274502	−	0.429042i
$223$	6.66225	+	11.5394i	0.446137	+	0.772733i	0.998131	−	0.0611159i	$-0.0194659\pi$
$223$	6.66225	+	11.5394i	0.446137	+	0.772733i	−0.551993	+	0.833849i	$0.686133\pi$
$224$		0			0
$225$	−2.17091	−	4.70310i	−0.144727	−	0.313540i
$226$	12.7807	+	22.1369i	0.850162	+	1.47252i
$227$	−1.38151			−0.0916943			−0.0458472	−	0.998948i	$-0.514599\pi$
$227$	−1.38151			−0.0916943			−0.0458472	+	0.998948i	$0.514599\pi$
$228$	−13.0957	−	25.2763i	−0.867285	−	1.67396i
$229$	17.9794			1.18811			0.594055	−	0.804424i	$-0.297526\pi$
$229$	17.9794			1.18811			0.594055	+	0.804424i	$0.297526\pi$
$230$	−0.872181	+	1.51066i	−0.0575099	+	0.0996101i
$231$		0			0
$232$	6.21780	+	10.7695i	0.408219	+	0.707055i
$233$	9.49115	+	16.4391i	0.621786	+	1.07696i	0.989153	+	0.146888i	$0.0469258\pi$
$233$	9.49115	+	16.4391i	0.621786	+	1.07696i	−0.367367	+	0.930076i	$0.619741\pi$
$234$	−4.25729	+	6.03011i	−0.278308	+	0.394200i
$235$	−15.7719	+	27.3177i	−1.02884	+	1.78201i
$236$	−5.52704	+	9.57312i	−0.359780	+	0.623157i
$237$	−11.7199	−	22.6208i	−0.761292	−	1.46938i
$238$		0			0
$239$	−2.44592	+	4.23645i	−0.158213	+	0.274033i	−0.934224	−	0.356686i	$-0.883907\pi$
$239$	−2.44592	+	4.23645i	−0.158213	+	0.274033i	0.776011	+	0.630719i	$0.217240\pi$
$240$	−8.94280	−	17.2606i	−0.577255	−	1.11417i
$241$	26.1593			1.68507			0.842535	−	0.538641i	$-0.181062\pi$
$241$	26.1593			1.68507			0.842535	+	0.538641i	$0.181062\pi$
$242$	11.5416	−	19.9907i	0.741924	−	1.28505i
$243$	−4.54309	−	14.9118i	−0.291440	−	0.956589i
$244$	9.21634			0.590016
$245$		0			0
$246$	−27.2740	−	1.24383i	−1.73893	−	0.0793039i
$247$	−4.05408			−0.257955
$248$	−5.88151	−	10.1871i	−0.373477	−	0.646880i
$249$	1.63667	+	0.0746406i	0.103720	+	0.00473015i
$250$	−10.4445	+	18.0903i	−0.660565	+	1.14413i
$251$	−18.4576			−1.16503			−0.582516	−	0.812819i	$-0.697932\pi$
$251$	−18.4576			−1.16503			−0.582516	+	0.812819i	$0.697932\pi$
$252$		0			0
$253$	−1.23405			−0.0775838
$254$	0.827430	−	1.43315i	0.0519176	−	0.0899239i
$255$	−1.95477	−	3.77293i	−0.122412	−	0.236270i
$256$	16.1804	+	28.0253i	1.01128	+	1.75158i
$257$	11.7339			0.731938			0.365969	−	0.930627i	$-0.380738\pi$
$257$	11.7339			0.731938			0.365969	+	0.930627i	$0.380738\pi$
$258$	−23.9684	+	37.4622i	−1.49221	+	2.33230i
$259$		0			0
$260$	−10.5146			−0.652087
$261$	−4.25729	+	6.03011i	−0.263520	+	0.373254i
$262$	−9.73599	+	16.8632i	−0.601491	+	1.04181i
$263$	−7.52179			−0.463813			−0.231907	−	0.972738i	$-0.574496\pi$
$263$	−7.52179			−0.463813			−0.231907	+	0.972738i	$0.574496\pi$
$264$	21.2989	−	33.2899i	1.31086	−	2.04885i
$265$	8.13521	−	14.0906i	0.499742	−	0.865579i
$266$		0			0
$267$	24.8406	+	1.13285i	1.52022	+	0.0693296i
$268$	32.0620	−	55.5329i	1.95850	−	3.39221i
$269$	−9.41741	+	16.3114i	−0.574190	+	0.994526i	0.421939	+	0.906624i	$0.361349\pi$
$269$	−9.41741	+	16.3114i	−0.574190	+	0.994526i	−0.996129	+	0.0879017i	$0.971984\pi$
$270$	20.3389	−	26.1891i	1.23779	−	1.59382i
$271$	−11.9911	−	20.7693i	−0.728410	−	1.26164i	−0.957555	−	0.288251i	$-0.906926\pi$
$271$	−11.9911	−	20.7693i	−0.728410	−	1.26164i	0.229145	−	0.973392i	$-0.426407\pi$
$272$	−2.04669	−	3.54498i	−0.124099	−	0.214946i
$273$		0			0
$274$	−4.51819	+	7.82573i	−0.272954	+	0.472770i
$275$	7.79513			0.470064
$276$	−1.91741	−	0.0874436i	−0.115415	−	0.00526349i
$277$	7.16225			0.430338			0.215169	−	0.976577i	$-0.430970\pi$
$277$	7.16225			0.430338			0.215169	+	0.976577i	$0.430970\pi$
$278$	2.52704	+	4.37697i	0.151562	+	0.262513i
$279$	4.02704	−	5.70397i	0.241093	−	0.341488i
$280$		0			0
$281$	−7.44085	−	12.8879i	−0.443884	−	0.768830i	0.554090	−	0.832457i	$-0.313067\pi$
$281$	−7.44085	−	12.8879i	−0.443884	−	0.768830i	−0.997974	+	0.0636271i	$0.979733\pi$
$282$	−51.7783	−	2.36135i	−3.08335	−	0.140616i
$283$	9.99854	+	17.3180i	0.594351	+	1.02945i	0.993638	+	0.112621i	$0.0359245\pi$
$283$	9.99854	+	17.3180i	0.594351	+	1.02945i	−0.399287	+	0.916826i	$0.630742\pi$
$284$	−6.63521	−	11.4925i	−0.393727	−	0.681956i
$285$	18.1929	+	0.829688i	1.07765	+	0.0491465i
$286$	−5.55408	−	9.61996i	−0.328420	−	0.568840i
$287$		0			0
$288$	0.933463	−	1.32217i	0.0550048	−	0.0779098i
$289$	8.05262	+	13.9475i	0.473684	+	0.820444i
$290$	−15.7017			−0.922038
$291$	19.8801	+	0.906631i	1.16539	+	0.0531476i
$292$	6.11109			0.357625
$293$	7.53278	−	13.0472i	0.440070	−	0.762223i	−0.557625	−	0.830093i	$-0.688287\pi$
$293$	7.53278	−	13.0472i	0.440070	−	0.762223i	0.997694	+	0.0678705i	$0.0216205\pi$
$294$		0			0
$295$	−3.53590	−	6.12435i	−0.205868	−	0.356574i
$296$	4.50000	+	7.79423i	0.261557	+	0.453030i
$297$	23.2396	+	3.19727i	1.34850	+	0.185525i
$298$	−16.6623	+	28.8599i	−0.965218	+	1.67181i
$299$	−0.136673	+	0.236725i	−0.00790401	+	0.0136901i
$300$	12.1118	+	0.552358i	0.699273	+	0.0318904i
$301$		0			0
$302$	12.2142	−	21.1556i	0.702848	−	1.21737i
$303$	−3.43493	+	5.36874i	−0.197331	+	0.308426i
$304$	17.5438			1.00620
$305$	−2.94805	+	5.10618i	−0.168805	+	0.292379i
$306$	4.02704	−	5.70397i	0.230211	−	0.326075i
$307$	27.2704			1.55641			0.778203	−	0.628013i	$-0.216132\pi$
$307$	27.2704			1.55641			0.778203	+	0.628013i	$0.216132\pi$
$308$		0			0
$309$	−9.07947	+	14.1911i	−0.516513	+	0.807302i
$310$	14.8525			0.843567
$311$	−7.99115	−	13.8411i	−0.453136	−	0.784855i	0.545443	−	0.838148i	$-0.316362\pi$
$311$	−7.99115	−	13.8411i	−0.453136	−	0.784855i	−0.998579	+	0.0532931i	$0.983028\pi$
$312$	−4.02704	−	7.77266i	−0.227986	−	0.440040i
$313$	5.79893	−	10.0440i	0.327775	−	0.567722i	−0.654295	−	0.756239i	$-0.727035\pi$
$313$	5.79893	−	10.0440i	0.327775	−	0.567722i	0.982070	+	0.188517i	$0.0603680\pi$
$314$	14.8961			0.840636
$315$		0			0
$316$	59.6313			3.35452
$317$	1.00885	−	1.74739i	0.0566629	−	0.0981430i	−0.836303	−	0.548268i	$-0.815287\pi$
$317$	1.00885	−	1.74739i	0.0566629	−	0.0981430i	0.892965	+	0.450125i	$0.148621\pi$
$318$	26.7075	+	1.21800i	1.49768	+	0.0683018i
$319$	−5.55408	−	9.61996i	−0.310969	−	0.538614i
$320$	−19.0043			−1.06237
$321$	−2.37792	−	0.108445i	−0.132722	−	0.00605281i
$322$		0			0
$323$	3.83482			0.213375
$324$	35.8822	+	6.61454i	1.99345	+	0.367474i
$325$	0.863327	−	1.49533i	0.0478888	−	0.0829458i
$326$	−43.8391			−2.42802
$327$	2.70847	+	5.22765i	0.149779	+	0.289090i
$328$	16.1893	−	28.0407i	0.893904	−	1.54829i
$329$		0			0
$330$	22.9554	+	44.3067i	1.26366	+	2.43900i
$331$	9.85447	−	17.0684i	0.541651	−	0.938167i	−0.457159	−	0.889385i	$-0.651133\pi$
$331$	9.85447	−	17.0684i	0.541651	−	0.938167i	0.998809	−	0.0487815i	$-0.0155338\pi$
$332$	−1.91741	+	3.32105i	−0.105232	+	0.182266i
$333$	−3.08113	+	4.36416i	−0.168845	+	0.239155i
$334$	10.4174	+	18.0435i	0.570015	+	0.987296i
$335$	20.5115	+	35.5269i	1.12066	+	1.94104i
$336$		0			0
$337$	14.5256	−	25.1590i	0.791259	−	1.37050i	−0.133929	−	0.990991i	$-0.542759\pi$
$337$	14.5256	−	25.1590i	0.791259	−	1.37050i	0.925188	−	0.379509i	$-0.123907\pi$
$338$	29.5261			1.60601
$339$	−8.27762	−	15.9768i	−0.449579	−	0.867739i
$340$	9.94592			0.539393
$341$	5.25370	+	9.09967i	0.284504	+	0.492775i
$342$	12.5416	+	27.1704i	0.678174	+	1.46921i
$343$		0			0
$344$	−26.3712	−	45.6763i	−1.42184	−	2.46270i
$345$	0.661774	−	1.03434i	0.0356287	−	0.0556871i
$346$	−21.3530	−	36.9845i	−1.14794	−	1.98830i
$347$	−14.5416	−	25.1868i	−0.780636	−	1.35210i	−0.931572	−	0.363557i	$-0.881562\pi$
$347$	−14.5416	−	25.1868i	−0.780636	−	1.35210i	0.150936	−	0.988544i	$-0.451771\pi$
$348$	−7.94805	−	15.3407i	−0.426060	−	0.822346i
$349$	12.3815	+	21.4454i	0.662767	+	1.14795i	0.979885	+	0.199561i	$0.0639515\pi$
$349$	12.3815	+	21.4454i	0.662767	+	1.14795i	−0.317118	+	0.948386i	$0.602715\pi$
$350$		0			0
$351$	3.18716	−	4.10390i	0.170118	−	0.219050i
$352$	1.21780	+	2.10929i	0.0649089	+	0.112426i
$353$	33.3025			1.77251			0.886257	−	0.463193i	$-0.153296\pi$
$353$	33.3025			1.77251			0.886257	+	0.463193i	$0.153296\pi$
$354$	6.26255	−	9.78827i	0.332851	−	0.520241i
$355$	8.48968			0.450586
$356$	−29.1015	+	50.4052i	−1.54237	+	2.67147i
$357$		0			0
$358$	−13.9626	−	24.1840i	−0.737949	−	1.27816i
$359$	−12.7683	−	22.1153i	−0.673884	−	1.16720i	−0.976794	−	0.214182i	$-0.931291\pi$
$359$	−12.7683	−	22.1153i	−0.673884	−	1.16720i	0.302909	−	0.953019i	$-0.402042\pi$
$360$	16.4808	+	35.7043i	0.868616	+	1.88178i
$361$	1.28220	−	2.22084i	0.0674842	−	0.116886i
$362$	−26.9289	+	46.6422i	−1.41535	+	2.45146i
$363$	−8.75729	+	13.6875i	−0.459639	+	0.718409i
$364$		0			0
$365$	−1.95477	+	3.38576i	−0.102317	+	0.177219i
$366$	−9.67830	−	0.441380i	−0.505893	−	0.0230713i
$367$	−27.4504			−1.43290			−0.716449	−	0.697639i	$-0.754234\pi$
$367$	−27.4504			−1.43290			−0.716449	+	0.697639i	$0.754234\pi$
$368$	0.591443	−	1.02441i	0.0308311	−	0.0534011i
$369$	19.1395	+	1.74935i	0.996362	+	0.0910676i
$370$	−11.3638			−0.590776
$371$		0			0
$372$	7.51819	+	14.5110i	0.389800	+	0.752359i
$373$	16.3274			0.845402			0.422701	−	0.906269i	$-0.361082\pi$
$373$	16.3274			0.845402			0.422701	+	0.906269i	$0.361082\pi$
$374$	5.25370	+	9.09967i	0.271662	+	0.470533i
$375$	7.92480	−	12.3863i	0.409235	−	0.639628i
$376$	30.7345	−	53.2338i	1.58501	−	2.74532i
$377$	−2.46050			−0.126722
$378$		0			0
$379$	12.0364			0.618267			0.309134	−	0.951019i	$-0.399961\pi$
$379$	12.0364			0.618267			0.309134	+	0.951019i	$0.399961\pi$
$380$	−21.3135	+	36.9161i	−1.09336	+	1.89376i
$381$	−0.627819	+	0.981271i	−0.0321641	+	0.0502721i
$382$	−0.863327	−	1.49533i	−0.0441716	−	0.0765075i
$383$	12.4356			0.635429			0.317715	−	0.948186i	$-0.397085\pi$
$383$	12.4356			0.635429			0.317715	+	0.948186i	$0.397085\pi$
$384$	−15.2252	−	29.3864i	−0.776957	−	1.49962i
$385$		0			0
$386$	−29.8817			−1.52094
$387$	18.0562	−	25.5752i	0.917849	−	1.30006i
$388$	−23.2901	+	40.3396i	−1.18237	+	2.04793i
$389$	20.6008			1.04450			0.522250	−	0.852792i	$-0.325093\pi$
$389$	20.6008			1.04450			0.522250	+	0.852792i	$0.325093\pi$
$390$	11.0416	+	0.503554i	0.559115	+	0.0254985i
$391$	0.129281	−	0.223922i	0.00653803	−	0.0113242i
$392$		0			0
$393$	7.38725	−	11.5462i	0.372637	−	0.582427i
$394$	−20.1893	+	34.9689i	−1.01712	+	1.76171i
$395$	−19.0744	+	33.0378i	−0.959738	+	1.66231i
$396$	−31.6680	+	44.8551i	−1.59138	+	2.25405i
$397$	−11.8186	−	20.4704i	−0.593157	−	1.02738i	−0.993804	−	0.111146i	$-0.964548\pi$
$397$	−11.8186	−	20.4704i	−0.593157	−	1.02738i	0.400647	−	0.916233i	$-0.368785\pi$
$398$	−27.9341	−	48.3833i	−1.40021	−	2.42524i
$399$		0			0
$400$	−3.73599	+	6.47092i	−0.186799	+	0.323546i
$401$	−2.56440			−0.128060			−0.0640300	−	0.997948i	$-0.520395\pi$
$401$	−2.56440			−0.128060			−0.0640300	+	0.997948i	$0.520395\pi$
$402$	−36.3286	+	56.7810i	−1.81191	+	2.83198i
$403$	2.32743			0.115938
$404$	−7.45904	−	12.9194i	−0.371101	−	0.642766i
$405$	−15.1424	+	17.7642i	−0.752432	+	0.882710i
$406$		0			0
$407$	−4.01965	−	6.96224i	−0.199247	−	0.345105i
$408$	3.80924	+	7.35228i	0.188586	+	0.363992i
$409$	−17.1623	−	29.7259i	−0.848619	−	1.46985i	−0.882441	−	0.470423i	$-0.844101\pi$
$409$	−17.1623	−	29.7259i	−0.848619	−	1.46985i	0.0338223	−	0.999428i	$-0.489232\pi$
$410$	20.4413	+	35.4054i	1.00953	+	1.74855i
$411$	3.42821	−	5.35824i	0.169101	−	0.264302i
$412$	−19.7163	−	34.1497i	−0.971354	−	1.68243i
$413$		0			0
$414$	2.00933	+	0.183653i	0.0987533	+	0.00902607i
$415$	−1.22665	−	2.12463i	−0.0602141	−	0.104294i
$416$	0.539495			0.0264509
$417$	−1.63667	−	3.15897i	−0.0801482	−	0.154695i
$418$	−45.0335			−2.20266
$419$	2.02850	−	3.51347i	0.0990989	−	0.171644i	−0.812213	−	0.583361i	$-0.801737\pi$
$419$	2.02850	−	3.51347i	0.0990989	−	0.171644i	0.911312	+	0.411717i	$0.135071\pi$
$420$		0			0
$421$	10.5344	+	18.2462i	0.513417	+	0.889264i	0.999879	+	0.0155624i	$0.00495387\pi$
$421$	10.5344	+	18.2462i	0.513417	+	0.889264i	−0.486462	+	0.873702i	$0.661713\pi$
$422$	5.61177	+	9.71987i	0.273177	+	0.473156i
$423$	36.3353	+	3.32105i	1.76668	+	0.161475i
$424$	−15.8530	+	27.4582i	−0.769890	+	1.33349i
$425$	−0.816635	+	1.41445i	−0.0396126	+	0.0686110i
$426$	6.41741	+	12.3863i	0.310925	+	0.600121i
$427$		0			0
$428$	2.78580	−	4.82515i	0.134657	−	0.233232i
$429$	3.59718	+	6.94297i	0.173673	+	0.335210i
$430$	66.5949			3.21149
$431$	−11.3092	+	19.5882i	−0.544747	+	0.943530i	0.453876	+	0.891065i	$0.350041\pi$
$431$	−11.3092	+	19.5882i	−0.544747	+	0.943530i	−0.998623	+	0.0524646i	$0.983292\pi$
$432$	−13.7922	+	17.7594i	−0.663578	+	0.854447i
$433$	−2.41789			−0.116196			−0.0580982	−	0.998311i	$-0.518504\pi$
$433$	−2.41789			−0.116196			−0.0580982	+	0.998311i	$0.518504\pi$
$434$		0			0
$435$	11.0416	+	0.503554i	0.529406	+	0.0241436i
$436$	−13.7807			−0.659978
$437$	0.554084	+	0.959702i	0.0265054	+	0.0459088i
$438$	−6.41741	−	0.292666i	−0.306636	−	0.0139841i
$439$	−11.7448	+	20.3427i	−0.560551	+	0.970902i	0.436898	+	0.899511i	$0.356077\pi$
$439$	−11.7448	+	20.3427i	−0.560551	+	0.970902i	−0.997448	+	0.0713911i	$0.977256\pi$
$440$	−59.1780			−2.82120
$441$		0			0
$442$	2.32743			0.110705
$443$	6.70895	−	11.6202i	0.318752	−	0.552094i	−0.661476	−	0.749966i	$-0.730070\pi$
$443$	6.70895	−	11.6202i	0.318752	−	0.552094i	0.980228	+	0.197872i	$0.0634031\pi$
$444$	−5.75223	−	11.1025i	−0.272989	−	0.526900i
$445$	−18.6175	−	32.2465i	−0.882554	−	1.52863i
$446$	32.7850			1.55242
$447$	12.6426	−	19.7602i	0.597975	−	0.934625i
$448$		0			0
$449$	−9.16225			−0.432393			−0.216197	−	0.976350i	$-0.569365\pi$
$449$	−9.16225			−0.432393			−0.216197	+	0.976350i	$0.569365\pi$
$450$	−12.6924	−	1.16009i	−0.598326	−	0.0546871i
$451$	−14.4612	+	25.0475i	−0.680950	+	1.17944i
$452$	42.1167			1.98100
$453$	−9.26761	+	14.4851i	−0.435430	+	0.680571i
$454$	−1.69961	+	2.94381i	−0.0797667	+	0.138160i
$455$		0			0
$456$	−35.4523	−	1.61680i	−1.66021	−	0.0757138i
$457$	−4.40856	+	7.63584i	−0.206224	+	0.357190i	−0.950522	−	0.310658i	$-0.899451\pi$
$457$	−4.40856	+	7.63584i	−0.206224	+	0.357190i	0.744298	+	0.667847i	$0.232784\pi$
$458$	22.1192	−	38.3115i	1.03356	−	1.79018i
$459$	−3.01478	+	3.88195i	−0.140718	+	0.181194i
$460$	1.43706	+	2.48906i	0.0670033	+	0.116053i
$461$	−2.82957	−	4.90095i	−0.131786	−	0.228260i	0.792579	−	0.609769i	$-0.208738\pi$
$461$	−2.82957	−	4.90095i	−0.131786	−	0.228260i	−0.924365	+	0.381509i	$0.875405\pi$
$462$		0			0
$463$	−7.86333	+	13.6197i	−0.365440	+	0.632960i	−0.988847	−	0.148937i	$-0.952415\pi$
$463$	−7.86333	+	13.6197i	−0.365440	+	0.632960i	0.623407	+	0.781898i	$0.285748\pi$
$464$	10.6477			0.494305
$465$	−10.4445	−	0.476320i	−0.484350	−	0.0220888i
$466$	46.7060			2.16361
$467$	−10.9985	−	19.0500i	−0.508952	−	0.881530i	−0.999946	−	0.0103675i	$-0.996700\pi$
$467$	−10.9985	−	19.0500i	−0.508952	−	0.881530i	0.490995	−	0.871163i	$-0.336633\pi$
$468$	5.09718	+	11.0426i	0.235617	+	0.510445i
$469$		0			0
$470$	38.8068	+	67.2153i	1.79002	+	3.10041i
$471$	−10.4751	−	0.477717i	−0.482667	−	0.0220120i
$472$	6.89037	+	11.9345i	0.317155	+	0.549328i
$473$	23.5562	+	40.8006i	1.08312	+	1.87601i
$474$	−62.6203	−	2.85580i	−2.87625	−	0.131171i
$475$	−3.50000	−	6.06218i	−0.160591	−	0.278152i
$476$		0			0
$477$	−18.7419	−	1.71301i	−0.858133	−	0.0784336i
$478$	6.01819	+	10.4238i	0.275265	+	0.476774i
$479$	−24.9751			−1.14114			−0.570571	−	0.821249i	$-0.693278\pi$
$479$	−24.9751			−1.14114			−0.570571	+	0.821249i	$0.693278\pi$
$480$	−2.42101	−	0.110410i	−0.110503	−	0.00503952i
$481$	−1.78074			−0.0811947
$482$	32.1826	−	55.7419i	1.46588	−	2.53897i
$483$		0			0
$484$	−19.0167	−	32.9379i	−0.864397	−	1.49718i
$485$	−14.8997	−	25.8070i	−0.676561	−	1.17184i
$486$	−37.3640	−	8.66452i	−1.69487	−	0.393031i
$487$	8.79893	−	15.2402i	0.398717	−	0.690599i	−0.594851	−	0.803836i	$-0.702789\pi$
$487$	8.79893	−	15.2402i	0.398717	−	0.690599i	0.993568	+	0.113238i	$0.0361221\pi$
$488$	5.74484	−	9.95036i	0.260057	−	0.450432i
$489$	30.8281	+	1.40592i	1.39410	+	0.0635778i
$490$		0			0
$491$	−6.89757	+	11.9469i	−0.311283	+	0.539158i	−0.978640	−	0.205580i	$-0.934092\pi$
$491$	−6.89757	+	11.9469i	−0.311283	+	0.539158i	0.667358	+	0.744737i	$0.267425\pi$
$492$	−24.2441	+	37.8931i	−1.09301	+	1.70835i
$493$	2.32743			0.104822
$494$	−4.98755	+	8.63868i	−0.224400	+	0.388673i
$495$	−14.7216	−	31.8931i	−0.661686	−	1.43349i
$496$	−10.0718			−0.452237
$497$		0			0
$498$	2.17257	−	3.39569i	0.0973552	−	0.152165i
$499$	13.0875			0.585879			0.292939	−	0.956131i	$-0.405367\pi$
$499$	13.0875			0.585879			0.292939	+	0.956131i	$0.405367\pi$
$500$	17.2089	+	29.8068i	0.769607	+	1.33300i
$501$	−6.74698	−	13.0225i	−0.301433	−	0.581800i
$502$	−22.7075	+	39.3305i	−1.01348	+	1.75541i
$503$	22.3068			0.994611			0.497305	−	0.867576i	$-0.334323\pi$
$503$	22.3068			0.994611			0.497305	+	0.867576i	$0.334323\pi$
$504$		0			0
$505$	9.54377			0.424692
$506$	−1.51819	+	2.62958i	−0.0674917	+	0.116899i
$507$	−20.7630	−	0.946899i	−0.922119	−	0.0420533i
$508$	−1.36333	−	2.36135i	−0.0604879	−	0.104768i
$509$	15.8932			0.704453			0.352226	−	0.935915i	$-0.385425\pi$
$509$	15.8932			0.704453			0.352226	+	0.935915i	$0.385425\pi$
$510$	−10.4445	−	0.476320i	−0.462488	−	0.0210918i
$511$		0			0
$512$	41.4078			1.82998
$513$	−7.94805	−	19.5087i	−0.350915	−	0.861330i
$514$	14.4356	−	25.0032i	0.636727	−	1.10284i
$515$	25.2268			1.11163
$516$	33.7096	+	65.0635i	1.48398	+	2.86426i
$517$	−27.4538	+	47.5514i	−1.20742	+	2.09131i
$518$		0			0
$519$	13.8296	+	26.6927i	0.607051	+	1.17168i
$520$	−6.55408	+	11.3520i	−0.287416	+	0.497818i
$521$	2.20895	−	3.82600i	0.0967756	−	0.167620i	−0.813573	−	0.581463i	$-0.802480\pi$
$521$	2.20895	−	3.82600i	0.0967756	−	0.167620i	0.910348	+	0.413843i	$0.135814\pi$
$522$	7.61177	+	16.4903i	0.333158	+	0.721759i
$523$	12.6367	+	21.8874i	0.552563	+	0.957067i	0.998089	+	0.0617982i	$0.0196835\pi$
$523$	12.6367	+	21.8874i	0.552563	+	0.957067i	−0.445526	+	0.895269i	$0.646983\pi$
$524$	16.0416	+	27.7849i	0.700782	+	1.21379i
$525$		0			0
$526$	−9.25370	+	16.0279i	−0.403480	+	0.698848i
$527$	−2.20155			−0.0959012
$528$	−15.5665	−	30.0452i	−0.677447	−	1.30755i
$529$	−22.9253			−0.996751
$530$	−20.0167	−	34.6700i	−0.869471	−	1.50597i
$531$	−4.71780	+	6.68238i	−0.204735	+	0.289990i
$532$		0			0
$533$	3.20321	+	5.54812i	0.138746	+	0.240316i
$534$	32.9741	−	51.5380i	1.42693	−	2.23027i
$535$	1.78220	+	3.08686i	0.0770513	+	0.133457i
$536$	−39.9705	−	69.2310i	−1.72646	−	2.99032i
$537$	9.04309	+	17.4542i	0.390238	+	0.753205i
$538$	23.1716	+	40.1344i	0.998998	+	1.73032i
$539$		0			0
$540$	−20.6139	−	50.5974i	−0.887081	−	2.17736i
$541$	1.71926	+	2.97785i	0.0739168	+	0.128028i	0.900615	−	0.434618i	$-0.143117\pi$
$541$	1.71926	+	2.97785i	0.0739168	+	0.128028i	−0.826698	+	0.562646i	$0.809783\pi$
$542$	−59.0085			−2.53463
$543$	20.4325	−	31.9357i	0.876842	−	1.37049i
$544$	−0.510317			−0.0218797
$545$	4.40808	−	7.63501i	0.188821	−	0.327048i
$546$		0			0
$547$	3.46410	+	6.00000i	0.148114	+	0.256542i	0.930531	−	0.366214i	$-0.119346\pi$
$547$	3.46410	+	6.00000i	0.148114	+	0.256542i	−0.782416	+	0.622756i	$0.786013\pi$
$548$	7.44445	+	12.8942i	0.318011	+	0.550812i
$549$	6.79173	+	0.620765i	0.289864	+	0.0264936i
$550$	9.58998	−	16.6103i	0.408918	−	0.708267i
$551$	−4.98755	+	8.63868i	−0.212477	+	0.368020i
$552$	−1.28959	+	2.01561i	−0.0548887	+	0.0857902i
$553$		0			0
$554$	8.81138	−	15.2618i	0.374360	−	0.648410i
$555$	7.99115	+	0.364437i	0.339205	+	0.0154695i
$556$	8.32743			0.353162
$557$	−16.7917	+	29.0841i	−0.711488	+	1.23233i	0.252810	+	0.967516i	$0.418645\pi$
$557$	−16.7917	+	29.0841i	−0.711488	+	1.23233i	−0.964298	+	0.264818i	$0.914688\pi$
$558$	−7.20009	−	15.5984i	−0.304804	−	0.660333i
$559$	10.4356			0.441379
$560$		0			0
$561$	−3.40263	−	6.56747i	−0.143659	−	0.277279i
$562$	−36.6165			−1.54457
$563$	21.2396	+	36.7880i	0.895142	+	1.55043i	0.833629	+	0.552325i	$0.186259\pi$
$563$	21.2396	+	36.7880i	0.895142	+	1.55043i	0.0615128	+	0.998106i	$0.480407\pi$
$564$	−46.0261	+	71.9380i	−1.93805	+	3.02914i
$565$	−13.4720	+	23.3341i	−0.566770	+	0.981675i
$566$	49.2029			2.06815
$567$		0			0
$568$	−16.5438			−0.694161
$569$	−5.20175	+	9.00969i	−0.218069	+	0.377706i	−0.954217	−	0.299114i	$-0.903309\pi$
$569$	−5.20175	+	9.00969i	−0.218069	+	0.377706i	0.736149	+	0.676820i	$0.236642\pi$
$570$	24.1498	−	37.7458i	1.01152	−	1.58100i
$571$	−8.92480	−	15.4582i	−0.373491	−	0.646906i	0.616609	−	0.787270i	$-0.288506\pi$
$571$	−8.92480	−	15.4582i	−0.373491	−	0.646906i	−0.990100	+	0.140364i	$0.955173\pi$
$572$	−18.3025			−0.765267
$573$	0.559145	+	1.07922i	0.0233586	+	0.0450849i
$574$		0			0
$575$	−0.471974			−0.0196827
$576$	9.21274	+	19.9586i	0.383864	+	0.831609i
$577$	5.97150	−	10.3429i	0.248597	−	0.430582i	−0.714540	−	0.699595i	$-0.753364\pi$
$577$	5.97150	−	10.3429i	0.248597	−	0.430582i	0.963137	+	0.269013i	$0.0866973\pi$
$578$	39.6270			1.64827
$579$	21.0131	+	0.958305i	0.873276	+	0.0398258i
$580$	−12.9356	+	22.4051i	−0.537122	+	0.930322i
$581$		0			0
$582$	26.3894	−	41.2462i	1.09388	−	1.70971i
$583$	14.1608	−	24.5272i	0.586480	−	1.01581i
$584$	3.80924	−	6.59780i	0.157628	−	0.273019i
$585$	−7.74844	−	0.708209i	−0.320359	−	0.0292808i
$586$	−18.5344	−	32.1026i	−0.765650	−	1.32615i
$587$	11.9299	+	20.6631i	0.492398	+	0.852859i	0.999962	−	0.00875568i	$-0.00278706\pi$
$587$	11.9299	+	20.6631i	0.492398	+	0.852859i	−0.507563	+	0.861614i	$0.669454\pi$
$588$		0			0
$589$	4.71780	−	8.17147i	0.194394	−	0.336699i
$590$	−17.4002			−0.716354
$591$	15.3188	−	23.9430i	0.630130	−	0.984884i
$592$	7.70602			0.316715
$593$	9.79007	+	16.9569i	0.402030	+	0.696336i	0.993971	−	0.109645i	$-0.0349714\pi$
$593$	9.79007	+	16.9569i	0.402030	+	0.696336i	−0.591941	+	0.805981i	$0.701638\pi$
$594$	35.4035	−	45.5868i	1.45262	−	1.87045i
$595$		0			0
$596$	27.4538	+	47.5514i	1.12455	+	1.94778i
$597$	18.0919	+	34.9195i	0.740453	+	1.42916i
$598$	0.336285	+	0.582462i	0.0137517	+	0.0238187i
$599$	−9.27335	−	16.0619i	−0.378899	−	0.656272i	0.612004	−	0.790855i	$-0.290364\pi$
$599$	−9.27335	−	16.0619i	−0.378899	−	0.656272i	−0.990902	+	0.134583i	$0.957030\pi$
$600$	8.14601	−	12.7321i	0.332559	−	0.519785i
$601$	−9.09931	−	15.7605i	−0.371169	−	0.642883i	0.618577	−	0.785724i	$-0.287710\pi$
$601$	−9.09931	−	15.7605i	−0.371169	−	0.642883i	−0.989746	+	0.142841i	$0.954376\pi$
$602$		0			0
$603$	27.3676	−	38.7640i	1.11449	−	1.57859i
$604$	−20.1249	−	34.8573i	−0.818870	−	1.41832i
$605$	24.3317			0.989224
$606$	7.21420	+	13.9242i	0.293057	+	0.565634i
$607$	22.3097			0.905524			0.452762	−	0.891631i	$-0.350439\pi$
$607$	22.3097			0.905524			0.452762	+	0.891631i	$0.350439\pi$
$608$	1.09358	−	1.89413i	0.0443505	−	0.0768173i
$609$		0			0
$610$	7.25370	+	12.5638i	0.293694	+	0.508692i
$611$	6.08113	+	10.5328i	0.246016	+	0.426112i
$612$	−4.82150	−	10.4454i	−0.194898	−	0.422229i
$613$	−5.11849	+	8.86548i	−0.206734	+	0.358073i	−0.950684	−	0.310162i	$-0.899617\pi$
$613$	−5.11849	+	8.86548i	−0.206734	+	0.358073i	0.743950	+	0.668235i	$0.232950\pi$
$614$	33.5495	−	58.1094i	1.35395	−	2.34511i
$615$	−13.2391	−	25.5530i	−0.533852	−	1.03040i
$616$		0			0
$617$	5.66372	−	9.80984i	0.228013	−	0.394929i	−0.729206	−	0.684294i	$-0.760111\pi$
$617$	5.66372	−	9.80984i	0.228013	−	0.394929i	0.957219	+	0.289364i	$0.0934439\pi$
$618$	19.0692	+	36.8057i	0.767074	+	1.48054i
$619$	−8.63327			−0.347000			−0.173500	−	0.984834i	$-0.555508\pi$
$619$	−8.63327			−0.347000			−0.173500	+	0.984834i	$0.555508\pi$
$620$	12.2360	−	21.1934i	0.491409	−	0.851145i
$621$	−1.40709	−	0.193586i	−0.0564647	−	0.00776835i
$622$	−39.3245			−1.57677
$623$		0			0
$624$	−7.48755	−	0.341470i	−0.299742	−	0.0136697i
$625$	−30.6519			−1.22608
$626$	−14.2683	−	24.7134i	−0.570275	−	0.987746i
$627$	31.6680	+	1.44422i	1.26470	+	0.0576766i
$628$	12.2719	−	21.2555i	0.489701	−	0.848188i
$629$	1.68443			0.0671626
$630$		0			0
$631$	−14.8535			−0.591308			−0.295654	−	0.955295i	$-0.595538\pi$
$631$	−14.8535			−0.591308			−0.295654	+	0.955295i	$0.595538\pi$
$632$	37.1701	−	64.3805i	1.47855	−	2.56092i
$633$	−3.63454	−	7.01508i	−0.144460	−	0.278824i
$634$	−2.48229	−	4.29945i	−0.0985844	−	0.170753i
$635$	1.74436			0.0692229
$636$	23.7405	−	37.1060i	0.941370	−	1.47135i
$637$		0			0
$638$	−27.3317			−1.08207
$639$	−4.11556	−	8.91601i	−0.162809	−	0.352712i
$640$	−24.7793	+	42.9190i	−0.979487	+	1.69652i
$641$	−34.1593			−1.34921			−0.674606	−	0.738178i	$-0.735687\pi$
$641$	−34.1593			−1.34921			−0.674606	+	0.738178i	$0.735687\pi$
$642$	−3.15652	+	4.93359i	−0.124578	+	0.194713i
$643$	−5.41741	+	9.38323i	−0.213642	+	0.370039i	−0.952852	−	0.303437i	$-0.901866\pi$
$643$	−5.41741	+	9.38323i	−0.213642	+	0.370039i	0.739210	+	0.673475i	$0.235199\pi$
$644$		0			0
$645$	−46.8302	−	2.13570i	−1.84394	−	0.0840929i
$646$	4.71780	−	8.17147i	0.185619	−	0.321502i
$647$	16.4846	−	28.5522i	0.648077	−	1.12250i	−0.335504	−	0.942039i	$-0.608907\pi$
$647$	16.4846	−	28.5522i	0.648077	−	1.12250i	0.983582	−	0.180464i	$-0.0577600\pi$
$648$	29.5079	−	34.6169i	1.15918	−	1.35988i
$649$	−6.15486	−	10.6605i	−0.241599	−	0.418462i
$650$	−2.12422	−	3.67926i	−0.0833188	−	0.144312i
$651$		0			0
$652$	−36.1160	+	62.5548i	−1.41441	+	2.44984i
$653$	−3.93113			−0.153837			−0.0769185	−	0.997037i	$-0.524508\pi$
$653$	−3.93113			−0.153837			−0.0769185	+	0.997037i	$0.524508\pi$
$654$	14.4715	+	0.659973i	0.565880	+	0.0258070i
$655$	−20.5251			−0.801982
$656$	−13.8617	−	24.0091i	−0.541207	−	0.937399i
$657$	4.50340	+	0.411612i	0.175695	+	0.0160585i
$658$		0			0
$659$	−8.40856	−	14.5640i	−0.327551	−	0.567335i	0.654474	−	0.756084i	$-0.272890\pi$
$659$	−8.40856	−	14.5640i	−0.327551	−	0.567335i	−0.982025	+	0.188749i	$0.939557\pi$
$660$	82.1334	+	3.74570i	3.19704	+	0.145801i
$661$	−8.51080	−	14.7411i	−0.331032	−	0.573364i	0.651683	−	0.758492i	$-0.274063\pi$
$661$	−8.51080	−	14.7411i	−0.331032	−	0.573364i	−0.982714	+	0.185128i	$0.940730\pi$
$662$	−24.2470	−	41.9970i	−0.942386	−	1.63226i
$663$	−1.63667	−	0.0746406i	−0.0635631	−	0.00289880i
$664$	2.39037	+	4.14024i	0.0927643	+	0.160672i
$665$		0			0
$666$	5.50885	+	11.9345i	0.213464	+	0.462451i
$667$	0.336285	+	0.582462i	0.0130210	+	0.0225530i
$668$	34.3288			1.32822
$669$	−23.0548	−	1.05141i	−0.891348	−	0.0406500i
$670$	100.937			3.89954
$671$	−5.13161	+	8.88821i	−0.198104	+	0.343126i
$672$		0			0
$673$	−14.3727	−	24.8942i	−0.554025	−	0.959600i	−0.997979	−	0.0635501i	$-0.979758\pi$
$673$	−14.3727	−	24.8942i	−0.554025	−	0.959600i	0.443953	−	0.896050i	$-0.353576\pi$
$674$	−35.7403	−	61.9039i	−1.37666	−	2.38445i
$675$	8.88823	+	1.22283i	0.342108	+	0.0470668i
$676$	24.3245	−	42.1313i	0.935558	−	1.62043i
$677$	−3.01819	+	5.22765i	−0.115998	+	0.200915i	−0.918178	−	0.396167i	$-0.870340\pi$
$677$	−3.01819	+	5.22765i	−0.115998	+	0.200915i	0.802180	+	0.597082i	$0.203673\pi$
$678$	−44.2278	−	2.01701i	−1.69856	−	0.0774628i
$679$		0			0
$680$	6.19961	−	10.7380i	0.237744	−	0.411785i
$681$	1.28959	−	2.01561i	0.0494173	−	0.0772385i
$682$	25.8535			0.989981
$683$	−10.2556	+	17.7633i	−0.392421	+	0.679693i	−0.992768	−	0.120046i	$-0.961696\pi$
$683$	−10.2556	+	17.7633i	−0.392421	+	0.679693i	0.600347	+	0.799739i	$0.295029\pi$
$684$	49.1021	+	4.48794i	1.87747	+	0.171601i
$685$	−9.52510			−0.363935
$686$		0			0
$687$	−16.7831	+	26.2317i	−0.640314	+	1.00080i
$688$	−45.1593			−1.72168
$689$	−3.13667	−	5.43288i	−0.119498	−	0.206976i
$690$	−1.38989	−	2.68265i	−0.0529122	−	0.102127i
$691$	−7.50146	+	12.9929i	−0.285369	+	0.494274i	−0.972699	−	0.232072i	$-0.925450\pi$
$691$	−7.50146	+	12.9929i	−0.285369	+	0.494274i	0.687330	+	0.726346i	$0.258783\pi$
$692$	−70.3652			−2.67488
$693$		0			0
$694$	−71.5595			−2.71636
$695$	−2.66372	+	4.61369i	−0.101040	+	0.175007i
$696$	−21.5167	−	0.981271i	−0.815589	−	0.0371950i
$697$	−3.02997	−	5.24806i	−0.114768	−	0.198784i
$698$	60.9296			2.30622
$699$	−32.8442	−	1.49786i	−1.24228	−	0.0566542i
$700$		0			0
$701$	38.5113			1.45455			0.727275	−	0.686346i	$-0.240786\pi$
$701$	38.5113			1.45455			0.727275	+	0.686346i	$0.240786\pi$
$702$	−4.82383	−	11.8402i	−0.182064	−	0.446880i
$703$	−3.60963	+	6.25206i	−0.136140	+	0.235801i
$704$	−33.0803			−1.24676
$705$	−25.1337	−	48.5111i	−0.946592	−	1.82703i
$706$	40.9705	−	70.9630i	1.54195	−	2.67073i
$707$		0			0
$708$	−8.80778	−	17.0000i	−0.331017	−	0.638901i
$709$	−3.82004	+	6.61650i	−0.143465	+	0.248488i	−0.928799	−	0.370584i	$-0.879158\pi$
$709$	−3.82004	+	6.61650i	−0.143465	+	0.248488i	0.785334	+	0.619072i	$0.212491\pi$
$710$	10.4445	−	18.0903i	0.391973	−	0.678918i
$711$	43.9437	+	4.01646i	1.64802	+	0.150629i
$712$	36.2798	+	62.8384i	1.35964	+	2.35497i
$713$	−0.318097	−	0.550960i	−0.0119128	−	0.0206336i
$714$		0			0
$715$	5.85447	−	10.1402i	0.218945	−	0.379224i
$716$	−46.0115			−1.71953
$717$	−3.89776	−	7.52313i	−0.145565	−	0.280956i
$718$	−62.8329			−2.34490
$719$	−15.0182	−	26.0123i	−0.560084	−	0.970094i	−0.997488	−	0.0708289i	$-0.977436\pi$
$719$	−15.0182	−	26.0123i	−0.560084	−	0.970094i	0.437405	−	0.899265i	$-0.355898\pi$
$720$	33.5308	+	3.06472i	1.24962	+	0.114216i
$721$		0			0
$722$	−3.15486	−	5.46438i	−0.117412	−	0.203363i
$723$	−24.4188	+	38.1662i	−0.908143	+	1.41941i
$724$	44.3697	+	76.8506i	1.64899	+	2.85613i
$725$	−2.12422	−	3.67926i	−0.0788916	−	0.136644i
$726$	18.3925	+	35.4997i	0.682610	+	1.31752i
$727$	1.72812	+	2.99319i	0.0640923	+	0.111011i	0.896291	−	0.443466i	$-0.146251\pi$
$727$	1.72812	+	2.99319i	0.0640923	+	0.111011i	−0.832199	+	0.554478i	$0.812918\pi$
$728$		0			0
$729$	25.9969	+	7.29124i	0.962847	+	0.270046i
$730$	4.80972	+	8.33068i	0.178016	+	0.308332i
$731$	−9.87120			−0.365099
$732$	−8.60311	+	13.4465i	−0.317980	+	0.496998i
$733$	−38.5261			−1.42299			−0.711496	−	0.702690i	$-0.751982\pi$
$733$	−38.5261			−1.42299			−0.711496	+	0.702690i	$0.751982\pi$
$734$	−33.7709	+	58.4929i	−1.24651	+	2.15901i
$735$		0			0
$736$	−0.0737345	−	0.127712i	−0.00271789	−	0.00470752i
$737$	35.7039	+	61.8409i	1.31517	+	2.27794i
$738$	27.2740	−	38.6314i	1.00397	−	1.42204i
$739$	−22.5620	+	39.0785i	−0.829955	+	1.43752i	0.0681179	+	0.997677i	$0.478301\pi$
$739$	−22.5620	+	39.0785i	−0.829955	+	1.43752i	−0.898073	+	0.439847i	$0.855033\pi$
$740$	−9.36186	+	16.2152i	−0.344149	+	0.596084i
$741$	3.78434	−	5.91486i	0.139021	−	0.217288i
$742$		0			0
$743$	−4.74338	+	8.21577i	−0.174018	+	0.301407i	−0.939821	−	0.341668i	$-0.889008\pi$
$743$	−4.74338	+	8.21577i	−0.174018	+	0.301407i	0.765803	+	0.643075i	$0.222342\pi$
$744$	20.3530	+	0.928200i	0.746178	+	0.0340295i
$745$	−35.1268			−1.28695
$746$	20.0869	−	34.7915i	0.735432	−	1.27381i
$747$	−1.63667	+	2.31821i	−0.0598827	+	0.0848190i
$748$	17.3126			0.633013
$749$		0			0
$750$	−16.6441	−	32.1250i	−0.607755	−	1.17304i
$751$	−9.83190			−0.358771			−0.179386	−	0.983779i	$-0.557411\pi$
$751$	−9.83190			−0.358771			−0.179386	+	0.983779i	$0.557411\pi$
$752$	−26.3157	−	45.5800i	−0.959633	−	1.66213i
$753$	17.2295	−	26.9294i	0.627877	−	0.981362i
$754$	−3.02704	+	5.24299i	−0.110238	+	0.190938i
$755$	25.7496			0.937124
$756$		0			0
$757$	−41.8171			−1.51987			−0.759934	−	0.650000i	$-0.774769\pi$
$757$	−41.8171			−1.51987			−0.759934	+	0.650000i	$0.774769\pi$
$758$	14.8078	−	25.6478i	0.537843	−	0.931571i
$759$	1.15194	−	1.80046i	0.0418126	−	0.0653525i
$760$	26.5708	+	46.0220i	0.963825	+	1.66939i
$761$	−22.9794			−0.833001			−0.416501	−	0.909135i	$-0.636744\pi$
$761$	−22.9794			−0.833001			−0.416501	+	0.909135i	$0.636744\pi$
$762$	1.31858	+	2.54500i	0.0477670	+	0.0921958i
$763$		0			0
$764$	−2.84494			−0.102926
$765$	7.32937	+	0.669906i	0.264994	+	0.0242205i
$766$	15.2989	−	26.4985i	0.552773	−	0.957430i
$767$	−2.72665			−0.0984538
$768$	−55.9925	−	2.55354i	−2.02046	−	0.0921429i
$769$	3.04329	−	5.27113i	0.109744	−	0.190082i	−0.805923	−	0.592021i	$-0.798330\pi$
$769$	3.04329	−	5.27113i	0.109744	−	0.190082i	0.915666	+	0.401939i	$0.131664\pi$
$770$		0			0
$771$	−10.9531	+	17.1196i	−0.394467	+	0.616546i
$772$	−24.6175	+	42.6388i	−0.886003	+	1.53460i
$773$	−20.9107	+	36.2184i	−0.752105	+	1.30268i	0.194695	+	0.980864i	$0.437628\pi$
$773$	−20.9107	+	36.2184i	−0.752105	+	1.30268i	−0.946801	+	0.321821i	$0.895705\pi$
$774$	−32.2834	−	69.9392i	−1.16040	−	2.51391i
$775$	2.00933	+	3.48027i	0.0721774	+	0.125015i
$776$	29.0349	+	50.2899i	1.04229	+	1.80530i
$777$		0			0
$778$	25.3442	−	43.8974i	0.908632	−	1.57380i
$779$	25.9722			0.930550
$780$	9.81498	−	15.3407i	0.351433	−	0.549284i
$781$	14.7778			0.528792
$782$	−0.318097	−	0.550960i	−0.0113751	−	0.0197023i
$783$	−4.82383	−	11.8402i	−0.172390	−	0.423135i
$784$		0			0
$785$	7.85087	+	13.5981i	0.280210	+	0.485337i
$786$	−15.5151	−	29.9459i	−0.553404	−	1.06813i
$787$	16.1460	+	27.9657i	0.575543	+	0.996870i	0.995982	+	0.0895491i	$0.0285426\pi$
$787$	16.1460	+	27.9657i	0.575543	+	0.996870i	−0.420439	+	0.907321i	$0.638124\pi$
$788$	33.2652	+	57.6170i	1.18502	+	2.05252i
$789$	7.02131	−	10.9742i	0.249965	−	0.390692i
$790$	46.9327	+	81.2898i	1.66979	+	2.89216i
$791$		0			0
$792$	28.6878	+	62.1498i	1.01938	+	2.20840i
$793$	1.13667	+	1.96878i	0.0403644	+	0.0699133i
$794$	−58.1593			−2.06400
$795$	12.9641	+	25.0222i	0.459789	+	0.887447i
$796$	−92.0521			−3.26270
$797$	23.2829	−	40.3271i	0.824722	−	1.42846i	−0.0774101	−	0.996999i	$-0.524665\pi$
$797$	23.2829	−	40.3271i	0.824722	−	1.42846i	0.902132	−	0.431461i	$-0.142002\pi$
$798$		0			0
$799$	−5.75223	−	9.96316i	−0.203499	−	0.352471i
$800$	0.465761	+	0.806721i	0.0164671	+	0.0285219i
$801$	−24.8406	+	35.1846i	−0.877698	+	1.24319i
$802$	−3.15486	+	5.46438i	−0.111402	+	0.192954i
$803$	−3.40263	+	5.89352i	−0.120076	+	0.207978i
$804$	51.0933	+	98.6159i	1.80192	+	3.47792i
$805$		0			0
$806$	2.86333	−	4.95943i	0.100856	−	0.174688i
$807$	−15.0074	−	28.9660i	−0.528285	−	1.01965i
$808$	−18.5979			−0.654270
$809$	5.40116	−	9.35509i	0.189895	−	0.328908i	−0.755320	−	0.655356i	$-0.772519\pi$
$809$	5.40116	−	9.35509i	0.189895	−	0.328908i	0.945215	+	0.326448i	$0.105852\pi$
$810$	19.2240	+	54.1208i	0.675463	+	1.90161i
$811$	−5.58307			−0.196048			−0.0980240	−	0.995184i	$-0.531252\pi$
$811$	−5.58307			−0.196048			−0.0980240	+	0.995184i	$0.531252\pi$
$812$		0			0
$813$	41.4954	+	1.89240i	1.45531	+	0.0663694i
$814$	−19.7807			−0.693315
$815$	−23.1050	−	40.0191i	−0.809335	−	1.40181i
$816$	7.08259	+	0.323002i	0.247940	+	0.0113073i
$817$	21.1534	−	36.6388i	0.740064	−	1.28183i
$818$	−84.4556			−2.95292
$819$		0			0
$820$	67.3609			2.35234
$821$	15.8940	−	27.5292i	0.554703	−	0.960774i	−0.443223	−	0.896411i	$-0.646165\pi$
$821$	15.8940	−	27.5292i	0.554703	−	0.960774i	0.997927	−	0.0643630i	$-0.0205016\pi$
$822$	−7.20009	−	13.8970i	−0.251132	−	0.484714i
$823$	18.0000	+	31.1769i	0.627441	+	1.08676i	0.988063	+	0.154047i	$0.0492308\pi$
$823$	18.0000	+	31.1769i	0.627441	+	1.08676i	−0.360623	+	0.932712i	$0.617436\pi$
$824$	−49.1593			−1.71255
$825$	−7.27647	+	11.3730i	−0.253334	+	0.395957i
$826$		0			0
$827$	15.9224			0.553675			0.276837	−	0.960917i	$-0.410714\pi$
$827$	15.9224			0.553675			0.276837	+	0.960917i	$0.410714\pi$
$828$	1.91741	−	2.71586i	0.0666346	−	0.0943825i
$829$	17.7360	−	30.7196i	0.615996	−	1.06694i	−0.374213	−	0.927343i	$-0.622087\pi$
$829$	17.7360	−	30.7196i	0.615996	−	1.06694i	0.990209	−	0.139594i	$-0.0445797\pi$
$830$	−6.03638			−0.209526
$831$	−6.68570	+	10.4496i	−0.231924	+	0.362494i
$832$	−3.66372	+	6.34574i	−0.127016	+	0.219999i
$833$		0			0
$834$	−8.74484	−	0.398809i	−0.302809	−	0.0138096i
$835$	−10.9808	+	19.0194i	−0.380007	+	0.658192i
$836$	−37.1000	+	64.2591i	−1.28313	+	2.22245i
$837$	4.56294	+	11.1999i	0.157718	+	0.387124i
$838$	−4.99115	−	8.64492i	−0.172416	−	0.298634i
$839$	−27.3391	−	47.3527i	−0.943850	−	1.63480i	−0.758037	−	0.652212i	$-0.773841\pi$
$839$	−27.3391	−	47.3527i	−0.943850	−	1.63480i	−0.185814	−	0.982585i	$-0.559492\pi$
$840$		0			0
$841$	11.4730	−	19.8717i	0.395619	−	0.685233i
$842$	51.8401			1.78653
$843$	25.7491	+	1.17429i	0.886847	+	0.0404447i
$844$	18.4926			0.636542
$845$	15.5615	+	26.9533i	0.535331	+	0.927221i
$846$	51.7783	−	73.3397i	1.78017	−	2.52147i
$847$		0			0
$848$	13.5737	+	23.5104i	0.466124	+	0.807350i
$849$	−34.6000	−	1.57793i	−1.18747	−	0.0541546i
$850$	2.00933	+	3.48027i	0.0689196	+	0.119372i
$851$	0.243379	+	0.421545i	0.00834292	+	0.0144504i
$852$	22.9612	+	1.04715i	0.786637	+	0.0358746i
$853$	−1.09884	−	1.90324i	−0.0376234	−	0.0651656i	0.846601	−	0.532229i	$-0.178645\pi$
$853$	−1.09884	−	1.90324i	−0.0376234	−	0.0651656i	−0.884224	+	0.467063i	$0.845312\pi$
$854$		0			0
$855$	−18.1929	+	25.7687i	−0.622184	+	0.881272i
$856$	−3.47296	−	6.01534i	−0.118703	−	0.205600i
$857$	15.7765			0.538914			0.269457	−	0.963012i	$-0.413156\pi$
$857$	15.7765			0.538914			0.269457	+	0.963012i	$0.413156\pi$
$858$	19.2199	+	0.876526i	0.656158	+	0.0299241i
$859$	−5.57626			−0.190260			−0.0951298	−	0.995465i	$-0.530327\pi$
$859$	−5.57626			−0.190260			−0.0951298	+	0.995465i	$0.530327\pi$
$860$	54.8630	−	95.0255i	1.87081	−	3.24034i
$861$		0			0
$862$	27.8264	+	48.1968i	0.947773	+	1.64159i
$863$	−11.5634	−	20.0284i	−0.393623	−	0.681776i	0.599301	−	0.800524i	$-0.295445\pi$
$863$	−11.5634	−	20.0284i	−0.393623	−	0.681776i	−0.992924	+	0.118748i	$0.962112\pi$
$864$	1.05768	+	2.59611i	0.0359831	+	0.0883215i
$865$	22.5079	−	38.9848i	0.765291	−	1.32552i
$866$	−2.97462	+	5.15218i	−0.101082	+	0.175078i
$867$	−27.8661	−	1.27084i	−0.946384	−	0.0431599i
$868$		0			0
$869$	−33.2024	+	57.5083i	−1.12631	+	1.95083i
$870$	14.6570	−	22.9087i	0.496919	−	0.776677i
$871$	15.8171			0.535942
$872$	−8.58998	+	14.8783i	−0.290893	+	0.503842i
$873$	−19.8801	+	28.1585i	−0.672838	+	0.953019i
$874$	2.72665			0.0922304
$875$		0			0
$876$	−5.70448	+	8.91601i	−0.192736	+	0.301244i
$877$	3.92528			0.132547			0.0662737	−	0.997801i	$-0.478889\pi$
$877$	3.92528			0.132547			0.0662737	+	0.997801i	$0.478889\pi$
$878$	28.8982	+	50.0532i	0.975268	+	1.68921i
$879$	12.0041	+	23.1693i	0.404887	+	0.781480i
$880$	−25.3348	+	43.8812i	−0.854037	+	1.47923i
$881$	−27.1986			−0.916345			−0.458173	−	0.888863i	$-0.651496\pi$
$881$	−27.1986			−0.916345			−0.458173	+	0.888863i	$0.651496\pi$
$882$		0			0
$883$	8.21341			0.276403			0.138202	−	0.990404i	$-0.455868\pi$
$883$	8.21341			0.276403			0.138202	+	0.990404i	$0.455868\pi$
$884$	1.91741	−	3.32105i	0.0644895	−	0.111699i
$885$	12.2360	+	0.558023i	0.411308	+	0.0187577i
$886$	−16.5074	−	28.5916i	−0.554577	−	0.960555i
$887$	6.48114			0.217615			0.108808	−	0.994063i	$-0.465297\pi$
$887$	6.48114			0.217615			0.108808	+	0.994063i	$0.465297\pi$
$888$	−15.5723	−	0.710174i	−0.522571	−	0.0238319i
$889$		0			0
$890$	−91.6169			−3.07101
$891$	−26.3581	+	30.9218i	−0.883029	+	1.03592i
$892$	27.0093	−	46.7815i	0.904339	−	1.56636i
$893$	49.3068			1.64999
$894$	−26.5526	−	51.2496i	−0.888053	−	1.71404i
$895$	14.7178	−	25.4920i	0.491962	−	0.852103i
$896$		0			0
$897$	−0.217799	−	0.420378i	−0.00727211	−	0.0140360i
$898$	−11.2719	+	19.5235i	−0.376148	+	0.651507i
$899$	2.86333	−	4.95943i	0.0954973	−	0.165406i
$900$	−12.1118	+	17.1553i	−0.403726	+	0.571844i
$901$	2.96703	+	5.13904i	0.0988461	+	0.171206i
$902$	35.5818	+	61.6295i	1.18474	+	2.05204i
$903$		0			0
$904$	26.2527	−	45.4710i	0.873152	−	1.51234i
$905$	−56.7706			−1.88712
$906$	19.4643	+	37.5684i	0.646658	+	1.24813i
$907$	10.1288			0.336321			0.168161	−	0.985760i	$-0.446217\pi$
$907$	10.1288			0.336321			0.168161	+	0.985760i	$0.446217\pi$
$908$	2.80039	+	4.85041i	0.0929341	+	0.160967i
$909$	−4.62655	−	10.0230i	−0.153453	−	0.332443i
$910$		0			0
$911$	−22.9612	−	39.7699i	−0.760738	−	1.31764i	−0.942471	−	0.334289i	$-0.891504\pi$
$911$	−22.9612	−	39.7699i	−0.760738	−	1.31764i	0.181733	−	0.983348i	$-0.441829\pi$
$912$	−16.3765	+	25.5962i	−0.542279	+	0.847573i
$913$	−2.13521	−	3.69829i	−0.0706652	−	0.122396i
$914$	10.8473	+	18.7880i	0.358796	+	0.621453i
$915$	−4.69795	−	9.06760i	−0.155310	−	0.299766i
$916$	−36.4449	−	63.1245i	−1.20417	−	2.08569i
$917$		0			0
$918$	4.56294	+	11.1999i	0.150599	+	0.369650i
$919$	2.46216	+	4.26459i	0.0812192	+	0.140676i	0.903774	−	0.428010i	$-0.140785\pi$
$919$	2.46216	+	4.26459i	0.0812192	+	0.140676i	−0.822555	+	0.568686i	$0.807452\pi$
$920$	3.58307			0.118130
$921$	−25.4559	+	39.7872i	−0.838801	+	1.31103i
$922$	−13.9243			−0.458573
$923$	1.63667	−	2.83480i	0.0538718	−	0.0933086i
$924$		0			0
$925$	−1.53736	−	2.66278i	−0.0505481	−	0.0875518i
$926$	19.3478	+	33.5113i	0.635807	+	1.10125i
$927$	−12.2293	−	26.4937i	−0.401662	−	0.870167i
$928$	0.663715	−	1.14959i	0.0217875	−	0.0377371i
$929$	0.00379324	−	0.00657009i	0.000124452	−	0.000215558i	−0.865963	−	0.500108i	$-0.833294\pi$
$929$	0.00379324	−	0.00657009i	0.000124452	−	0.000215558i	0.866088	+	0.499892i	$0.166627\pi$
$930$	−13.8643	+	21.6697i	−0.454628	+	0.710577i
$931$		0			0
$932$	38.4779	−	66.6457i	1.26039	−	2.18305i
$933$	27.6534	+	1.26113i	0.905332	+	0.0412877i
$934$	−54.1239			−1.77099
$935$	−5.53784	+	9.59182i	−0.181107	+	0.313686i
$936$	15.0993	+	1.38008i	0.493537	+	0.0451093i
$937$	−21.1623			−0.691341			−0.345670	−	0.938356i	$-0.612348\pi$
$937$	−21.1623			−0.691341			−0.345670	+	0.938356i	$0.612348\pi$
$938$		0			0
$939$	9.24105	+	17.8363i	0.301570	+	0.582066i
$940$	127.881			4.17102
$941$	2.27908	+	3.94748i	0.0742959	+	0.128684i	0.900780	−	0.434276i	$-0.142996\pi$
$941$	2.27908	+	3.94748i	0.0742959	+	0.128684i	−0.826484	+	0.562960i	$0.809662\pi$
$942$	−13.9050	+	21.7332i	−0.453048	+	0.708107i
$943$	0.875585	−	1.51656i	0.0285130	−	0.0493859i
$944$	11.7994			0.384038
$945$		0			0
$946$	115.920			3.76890
$947$	−6.86760	+	11.8950i	−0.223167	+	0.386537i	−0.955768	−	0.294122i	$-0.904973\pi$
$947$	−6.86760	+	11.8950i	−0.223167	+	0.386537i	0.732601	+	0.680658i	$0.238306\pi$
$948$	−55.6636	+	87.0014i	−1.80787	+	2.82567i
$949$	0.753696	+	1.30544i	0.0244660	+	0.0423764i
$950$	−17.2235			−0.558805
$951$	1.60769	+	3.10303i	0.0521329	+	0.100623i
$952$		0			0
$953$	8.80699			0.285286			0.142643	−	0.989774i	$-0.454440\pi$
$953$	8.80699			0.285286			0.142643	+	0.989774i	$0.454440\pi$
$954$	−26.7075	+	37.8290i	−0.864687	+	1.22476i
$955$	0.910019	−	1.57620i	0.0294475	−	0.0510046i
$956$	19.8319			0.641409
$957$	19.2199	+	0.876526i	0.621292	+	0.0283341i
$958$	−30.7257	+	53.2184i	−0.992701	+	1.71941i
$959$		0			0
$960$	17.7398	−	27.7270i	0.572549	−	0.894886i
$961$	12.7915	−	22.1556i	0.412630	−	0.714696i
$962$	−2.19076	+	3.79450i	−0.0706329	+	0.122340i
$963$	2.37792	−	3.36812i	0.0766273	−	0.108536i
$964$	−53.0261	−	91.8438i	−1.70785	−	2.95809i
$965$	−15.7489	−	27.2779i	−0.506976	−	0.878108i
$966$		0			0
$967$	−19.1642	+	33.1934i	−0.616279	+	1.06743i	0.373880	+	0.927477i	$0.378027\pi$
$967$	−19.1642	+	33.1934i	−0.616279	+	1.06743i	−0.990159	+	0.139949i	$0.955306\pi$
$968$	−47.4150			−1.52397
$969$	−3.57966	+	5.59496i	−0.114995	+	0.179736i
$970$	−73.3216			−2.35421
$971$	−15.5093	−	26.8630i	−0.497718	−	0.862073i	0.502278	−	0.864706i	$-0.332495\pi$
$971$	−15.5093	−	26.8630i	−0.497718	−	0.862073i	−0.999997	+	0.00263281i	$0.999162\pi$
$972$	−43.1452	+	46.1773i	−1.38388	+	1.48114i
$973$		0			0
$974$	−21.6498	−	37.4986i	−0.693704	−	1.20153i
$975$	1.37578	+	2.65542i	0.0440602	+	0.0850413i
$976$	−4.91887	−	8.51974i	−0.157449	−	0.272710i
$977$	26.3712	+	45.6763i	0.843689	+	1.46131i	0.886755	+	0.462241i	$0.152954\pi$
$977$	26.3712	+	45.6763i	0.843689	+	1.46131i	−0.0430652	+	0.999072i	$0.513712\pi$
$978$	40.9222	−	63.9607i	1.30855	−	2.04524i
$979$	−32.4071	−	56.1307i	−1.03574	−	1.79395i
$980$		0			0
$981$	−10.1553	−	0.928200i	−0.324235	−	0.0296351i
$982$	16.9715	+	29.3955i	0.541582	+	0.938048i
$983$	18.3029			0.583772			0.291886	−	0.956453i	$-0.405717\pi$
$983$	18.3029			0.583772			0.291886	+	0.956453i	$0.405717\pi$
$984$	25.7989	+	49.7949i	0.822440	+	1.58740i
$985$	−42.5624			−1.35615
$986$	2.86333	−	4.95943i	0.0911869	−	0.157940i
$987$		0			0
$988$	8.21780	+	14.2336i	0.261443	+	0.452833i
$989$	−1.42627	−	2.47036i	−0.0453526	−	0.0785530i
$990$	−86.0710	−	7.86690i	−2.73552	−	0.250027i
$991$	6.30039	−	10.9126i	0.200138	−	0.346650i	−0.748434	−	0.663209i	$-0.769194\pi$
$991$	6.30039	−	10.9126i	0.200138	−	0.346650i	0.948573	+	0.316559i	$0.102527\pi$
$992$	−0.627819	+	1.08741i	−0.0199333	+	0.0345254i
$993$	15.7039	+	30.3103i	0.498348	+	0.961869i
$994$		0			0
$995$	29.4449	−	51.0001i	0.933467	−	1.61681i
$996$	−3.05555	−	5.89756i	−0.0968187	−	0.186871i
$997$	−11.7424			−0.371885			−0.185943	−	0.982561i	$-0.559534\pi$
$997$	−11.7424			−0.371885			−0.185943	+	0.982561i	$0.559534\pi$
$998$	16.1010	−	27.8877i	0.509667	−	0.882770i
$999$	−3.49115	−	8.56911i	−0.110455	−	0.271115i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.g.d.67.3		6
3.2	odd	2		1323.2.g.b.361.1		6
7.2	even	3		441.2.h.b.373.1		6
7.3	odd	6		63.2.f.b.22.3	✓	6
7.4	even	3		441.2.f.d.148.3		6
7.5	odd	6		441.2.h.c.373.1		6
7.6	odd	2		441.2.g.e.67.3		6
9.2	odd	6		1323.2.h.e.802.3		6
9.7	even	3		441.2.h.b.214.1		6
21.2	odd	6		1323.2.h.e.226.3		6
21.5	even	6		1323.2.h.d.226.3		6
21.11	odd	6		1323.2.f.c.442.1		6
21.17	even	6		189.2.f.a.64.1		6
21.20	even	2		1323.2.g.c.361.1		6
28.3	even	6		1008.2.r.k.337.3		6
63.2	odd	6		1323.2.g.b.667.1		6
63.4	even	3		3969.2.a.m.1.1		3
63.11	odd	6		1323.2.f.c.883.1		6
63.16	even	3	inner	441.2.g.d.79.3		6
63.20	even	6		1323.2.h.d.802.3		6
63.25	even	3		441.2.f.d.295.3		6
63.31	odd	6		567.2.a.d.1.1		3
63.32	odd	6		3969.2.a.p.1.3		3
63.34	odd	6		441.2.h.c.214.1		6
63.38	even	6		189.2.f.a.127.1		6
63.47	even	6		1323.2.g.c.667.1		6
63.52	odd	6		63.2.f.b.43.3	yes	6
63.59	even	6		567.2.a.g.1.3		3
63.61	odd	6		441.2.g.e.79.3		6
84.59	odd	6		3024.2.r.g.1009.2		6
252.31	even	6		9072.2.a.bq.1.2		3
252.59	odd	6		9072.2.a.cd.1.2		3
252.115	even	6		1008.2.r.k.673.3		6
252.227	odd	6		3024.2.r.g.2017.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.b.22.3	✓	6	7.3	odd	6
63.2.f.b.43.3	yes	6	63.52	odd	6
189.2.f.a.64.1		6	21.17	even	6
189.2.f.a.127.1		6	63.38	even	6
441.2.f.d.148.3		6	7.4	even	3
441.2.f.d.295.3		6	63.25	even	3
441.2.g.d.67.3		6	1.1	even	1	trivial
441.2.g.d.79.3		6	63.16	even	3	inner
441.2.g.e.67.3		6	7.6	odd	2
441.2.g.e.79.3		6	63.61	odd	6
441.2.h.b.214.1		6	9.7	even	3
441.2.h.b.373.1		6	7.2	even	3
441.2.h.c.214.1		6	63.34	odd	6
441.2.h.c.373.1		6	7.5	odd	6
567.2.a.d.1.1		3	63.31	odd	6
567.2.a.g.1.3		3	63.59	even	6
1008.2.r.k.337.3		6	28.3	even	6
1008.2.r.k.673.3		6	252.115	even	6
1323.2.f.c.442.1		6	21.11	odd	6
1323.2.f.c.883.1		6	63.11	odd	6
1323.2.g.b.361.1		6	3.2	odd	2
1323.2.g.b.667.1		6	63.2	odd	6
1323.2.g.c.361.1		6	21.20	even	2
1323.2.g.c.667.1		6	63.47	even	6
1323.2.h.d.226.3		6	21.5	even	6
1323.2.h.d.802.3		6	63.20	even	6
1323.2.h.e.226.3		6	21.2	odd	6
1323.2.h.e.802.3		6	9.2	odd	6
3024.2.r.g.1009.2		6	84.59	odd	6
3024.2.r.g.2017.2		6	252.227	odd	6
3969.2.a.m.1.1		3	63.4	even	3
3969.2.a.p.1.3		3	63.32	odd	6
9072.2.a.bq.1.2		3	252.31	even	6
9072.2.a.cd.1.2		3	252.59	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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.23025 - 2.13086i) q^{2} +(-0.933463 + 1.45899i) q^{3} +(-2.02704 - 3.51094i) q^{4} +2.59358 q^{5} +(1.96050 + 3.78400i) q^{6} -5.05408 q^{8} +(-1.25729 - 2.72382i) q^{9} +O(q^{10})\)	\(q+(1.23025 - 2.13086i) q^{2} +(-0.933463 + 1.45899i) q^{3} +(-2.02704 - 3.51094i) q^{4} +2.59358 q^{5} +(1.96050 + 3.78400i) q^{6} -5.05408 q^{8} +(-1.25729 - 2.72382i) q^{9} +(3.19076 - 5.52655i) q^{10} +4.51459 q^{11} +(7.01459 + 0.319901i) q^{12} +(0.500000 - 0.866025i) q^{13} +(-2.42101 + 3.78400i) q^{15} +(-2.16372 + 3.74766i) q^{16} +(-0.472958 + 0.819187i) q^{17} +(-7.35087 - 0.671871i) q^{18} +(-2.02704 - 3.51094i) q^{19} +(-5.25729 - 9.10590i) q^{20} +(5.55408 - 9.61996i) q^{22} -0.273346 q^{23} +(4.71780 - 7.37385i) q^{24} +1.72665 q^{25} +(-1.23025 - 2.13086i) q^{26} +(5.14766 + 0.708209i) q^{27} +(-1.23025 - 2.13086i) q^{29} +(5.08472 + 9.81411i) q^{30} +(1.16372 + 2.01561i) q^{31} +(0.269748 + 0.467216i) q^{32} +(-4.21420 + 6.58673i) q^{33} +(1.16372 + 2.01561i) q^{34} +(-7.01459 + 9.93559i) q^{36} +(-0.890369 - 1.54216i) q^{37} -9.97509 q^{38} +(0.796790 + 1.53790i) q^{39} -13.1082 q^{40} +(-3.20321 + 5.54812i) q^{41} +(5.21780 + 9.03749i) q^{43} +(-9.15126 - 15.8505i) q^{44} +(-3.26089 - 7.06445i) q^{45} +(-0.336285 + 0.582462i) q^{46} +(-6.08113 + 10.5328i) q^{47} +(-3.44805 - 6.65514i) q^{48} +(2.12422 - 3.67926i) q^{50} +(-0.753696 - 1.45472i) q^{51} -4.05408 q^{52} +(3.13667 - 5.43288i) q^{53} +(7.84202 - 10.0977i) q^{54} +11.7089 q^{55} +(7.01459 + 0.319901i) q^{57} -6.05408 q^{58} +(-1.36333 - 2.36135i) q^{59} +(18.1929 + 0.829688i) q^{60} +(-1.13667 + 1.96878i) q^{61} +5.72665 q^{62} -7.32743 q^{64} +(1.29679 - 2.24611i) q^{65} +(8.85087 + 17.0832i) q^{66} +(7.90856 + 13.6980i) q^{67} +3.83482 q^{68} +(0.255158 - 0.398809i) q^{69} +3.27335 q^{71} +(6.35447 + 13.7664i) q^{72} +(-0.753696 + 1.30544i) q^{73} -4.38151 q^{74} +(-1.61177 + 2.51917i) q^{75} +(-8.21780 + 14.2336i) q^{76} +(4.25729 + 0.194154i) q^{78} +(-7.35447 + 12.7383i) q^{79} +(-5.61177 + 9.71987i) q^{80} +(-5.83842 + 6.84929i) q^{81} +(7.88151 + 13.6512i) q^{82} +(-0.472958 - 0.819187i) q^{83} +(-1.22665 + 2.12463i) q^{85} +25.6768 q^{86} +(4.25729 + 0.194154i) q^{87} -22.8171 q^{88} +(-7.17830 - 12.4332i) q^{89} +(-19.0651 - 1.74255i) q^{90} +(0.554084 + 0.959702i) q^{92} +(-4.02704 - 0.183653i) q^{93} +(14.9626 + 25.9161i) q^{94} +(-5.25729 - 9.10590i) q^{95} +(-0.933463 - 0.0425706i) q^{96} +(-5.74484 - 9.95036i) q^{97} +(-5.67617 - 12.2969i) 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

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Database

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