LMFDB - Embedded newform 637.2.e.n.79.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(79,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("637.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.e (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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 9 x^{10} - 6 x^{9} + 34 x^{8} - 18 x^{7} + 85 x^{6} - 2 x^{5} + 92 x^{4} - 26 x^{3} + \cdots + 1 $ x^12 - 2x^11 + 9x^10 - 6x^9 + 34x^8 - 18x^7 + 85x^6 - 2x^5 + 92x^4 - 26x^3 + 43x^2 + 6*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.3
Root			$0.954516 - 1.65327i$ of defining polynomial
Character	$\chi$	$=$	637.79
Dual form			637.2.e.n.508.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.132313 + 0.229173i) q^{2} +(-1.45452 - 2.51930i) q^{3} +(0.964986 + 1.67141i) q^{4} +(0.717577 - 1.24288i) q^{5} +0.769807 q^{6} -1.03998 q^{8} +(-2.73124 + 4.73064i) q^{9} +O(q^{10})$	\(q+(-0.132313 + 0.229173i) q^{2} +(-1.45452 - 2.51930i) q^{3} +(0.964986 + 1.67141i) q^{4} +(0.717577 - 1.24288i) q^{5} +0.769807 q^{6} -1.03998 q^{8} +(-2.73124 + 4.73064i) q^{9} +(0.189890 + 0.328899i) q^{10} +(-2.75237 - 4.76725i) q^{11} +(2.80718 - 4.86217i) q^{12} +1.00000 q^{13} -4.17491 q^{15} +(-1.79237 + 3.10448i) q^{16} +(-2.41536 - 4.18353i) q^{17} +(-0.722758 - 1.25185i) q^{18} +(-1.41018 + 2.44250i) q^{19} +2.76981 q^{20} +1.45670 q^{22} +(2.99978 - 5.19577i) q^{23} +(1.51266 + 2.62001i) q^{24} +(1.47017 + 2.54640i) q^{25} +(-0.132313 + 0.229173i) q^{26} +7.16341 q^{27} +1.04188 q^{29} +(0.552396 - 0.956778i) q^{30} +(-4.60448 - 7.97519i) q^{31} +(-1.51428 - 2.62282i) q^{32} +(-8.00674 + 13.8681i) q^{33} +1.27834 q^{34} -10.5424 q^{36} +(-0.306249 + 0.530438i) q^{37} +(-0.373171 - 0.646351i) q^{38} +(-1.45452 - 2.51930i) q^{39} +(-0.746262 + 1.29256i) q^{40} -10.6196 q^{41} -8.43685 q^{43} +(5.31200 - 9.20066i) q^{44} +(3.91974 + 6.78919i) q^{45} +(0.793822 + 1.37494i) q^{46} +(-1.20461 + 2.08645i) q^{47} +10.4281 q^{48} -0.778091 q^{50} +(-7.02636 + 12.1700i) q^{51} +(0.964986 + 1.67141i) q^{52} +(0.914793 + 1.58447i) q^{53} +(-0.947814 + 1.64166i) q^{54} -7.90015 q^{55} +8.20452 q^{57} +(-0.137855 + 0.238771i) q^{58} +(0.435457 + 0.754234i) q^{59} +(-4.02873 - 6.97797i) q^{60} +(1.66626 - 2.88605i) q^{61} +2.43693 q^{62} -6.36804 q^{64} +(0.717577 - 1.24288i) q^{65} +(-2.11880 - 3.66986i) q^{66} +(3.31370 + 5.73951i) q^{67} +(4.66158 - 8.07410i) q^{68} -17.4529 q^{69} -6.85856 q^{71} +(2.84042 - 4.91975i) q^{72} +(-1.57074 - 2.72060i) q^{73} +(-0.0810415 - 0.140368i) q^{74} +(4.27676 - 7.40757i) q^{75} -5.44322 q^{76} +0.769807 q^{78} +(8.78614 - 15.2180i) q^{79} +(2.57233 + 4.45540i) q^{80} +(-2.22559 - 3.85484i) q^{81} +(1.40511 - 2.43372i) q^{82} +11.4525 q^{83} -6.93283 q^{85} +(1.11631 - 1.93350i) q^{86} +(-1.51543 - 2.62480i) q^{87} +(2.86240 + 4.95782i) q^{88} +(0.497659 - 0.861970i) q^{89} -2.07454 q^{90} +11.5790 q^{92} +(-13.3946 + 23.2001i) q^{93} +(-0.318772 - 0.552130i) q^{94} +(2.02383 + 3.50537i) q^{95} +(-4.40510 + 7.62986i) q^{96} +13.5090 q^{97} +30.0695 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{3} - 4 q^{4} - 6 q^{5} + 8 q^{6} - 6 q^{9}+O(q^{10}) $ 12 * q - 8 * q^3 - 4 * q^4 - 6 * q^5 + 8 * q^6 - 6 * q^9	$ 12 q - 8 q^{3} - 4 q^{4} - 6 q^{5} + 8 q^{6} - 6 q^{9} - 4 q^{10} - 4 q^{11} + 4 q^{12} + 12 q^{13} + 24 q^{15} - 16 q^{17} + 4 q^{18} - 2 q^{19} + 32 q^{20} - 24 q^{22} + 6 q^{23} - 12 q^{24} + 4 q^{25} + 40 q^{27} - 12 q^{29} - 6 q^{31} + 20 q^{32} - 4 q^{33} - 48 q^{36} - 8 q^{38} - 8 q^{39} - 4 q^{40} - 16 q^{41} + 4 q^{43} + 4 q^{44} - 14 q^{45} - 8 q^{46} - 30 q^{47} - 16 q^{48} + 16 q^{50} + 4 q^{51} - 4 q^{52} + 14 q^{53} + 48 q^{54} - 16 q^{55} + 8 q^{57} + 8 q^{58} - 24 q^{59} - 12 q^{60} + 56 q^{62} - 40 q^{64} - 6 q^{65} + 4 q^{66} - 16 q^{67} - 28 q^{68} - 40 q^{69} + 16 q^{71} - 28 q^{72} + 6 q^{73} + 12 q^{74} - 12 q^{75} - 32 q^{76} + 8 q^{78} + 22 q^{79} + 28 q^{80} - 46 q^{81} + 40 q^{82} + 100 q^{83} - 16 q^{85} + 16 q^{86} + 16 q^{87} + 44 q^{88} - 26 q^{89} - 80 q^{90} + 40 q^{92} - 16 q^{93} + 32 q^{94} + 6 q^{95} + 20 q^{96} - 28 q^{97} + 24 q^{99}+O(q^{100}) $ 12 * q - 8 * q^3 - 4 * q^4 - 6 * q^5 + 8 * q^6 - 6 * q^9 - 4 * q^10 - 4 * q^11 + 4 * q^12 + 12 * q^13 + 24 * q^15 - 16 * q^17 + 4 * q^18 - 2 * q^19 + 32 * q^20 - 24 * q^22 + 6 * q^23 - 12 * q^24 + 4 * q^25 + 40 * q^27 - 12 * q^29 - 6 * q^31 + 20 * q^32 - 4 * q^33 - 48 * q^36 - 8 * q^38 - 8 * q^39 - 4 * q^40 - 16 * q^41 + 4 * q^43 + 4 * q^44 - 14 * q^45 - 8 * q^46 - 30 * q^47 - 16 * q^48 + 16 * q^50 + 4 * q^51 - 4 * q^52 + 14 * q^53 + 48 * q^54 - 16 * q^55 + 8 * q^57 + 8 * q^58 - 24 * q^59 - 12 * q^60 + 56 * q^62 - 40 * q^64 - 6 * q^65 + 4 * q^66 - 16 * q^67 - 28 * q^68 - 40 * q^69 + 16 * q^71 - 28 * q^72 + 6 * q^73 + 12 * q^74 - 12 * q^75 - 32 * q^76 + 8 * q^78 + 22 * q^79 + 28 * q^80 - 46 * q^81 + 40 * q^82 + 100 * q^83 - 16 * q^85 + 16 * q^86 + 16 * q^87 + 44 * q^88 - 26 * q^89 - 80 * q^90 + 40 * q^92 - 16 * q^93 + 32 * q^94 + 6 * q^95 + 20 * q^96 - 28 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.132313	+	0.229173i	−0.0935596	+	0.162050i	−0.909007	−	0.416782i	$-0.863158\pi$
$2$	−0.132313	+	0.229173i	−0.0935596	+	0.162050i	0.815447	+	0.578832i	$0.196491\pi$
$3$	−1.45452	−	2.51930i	−0.839765	−	1.45452i	−0.890091	−	0.455784i	$-0.849359\pi$
$3$	−1.45452	−	2.51930i	−0.839765	−	1.45452i	0.0503252	−	0.998733i	$-0.483974\pi$
$4$	0.964986	+	1.67141i	0.482493	+	0.835703i
$5$	0.717577	−	1.24288i	0.320910	−	0.555833i	−0.659766	−	0.751471i	$-0.729345\pi$
$5$	0.717577	−	1.24288i	0.320910	−	0.555833i	0.980676	+	0.195639i	$0.0626779\pi$
$6$	0.769807			0.314273
$7$		0			0
$7$		0			0
$8$	−1.03998			−0.367687
$9$	−2.73124	+	4.73064i	−0.910412	+	1.57688i
$10$	0.189890	+	0.328899i	0.0600484	+	0.104007i
$11$	−2.75237	−	4.76725i	−0.829871	−	1.43738i	−0.898139	−	0.439712i	$-0.855081\pi$
$11$	−2.75237	−	4.76725i	−0.829871	−	1.43738i	0.0682678	−	0.997667i	$-0.478253\pi$
$12$	2.80718	−	4.86217i	0.810362	−	1.40359i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$		0			0
$15$	−4.17491			−1.07796
$16$	−1.79237	+	3.10448i	−0.448093	+	0.776119i
$17$	−2.41536	−	4.18353i	−0.585811	−	1.01465i	−0.994774	−	0.102104i	$-0.967443\pi$
$17$	−2.41536	−	4.18353i	−0.585811	−	1.01465i	0.408963	−	0.912551i	$-0.365891\pi$
$18$	−0.722758	−	1.25185i	−0.170356	−	0.295065i
$19$	−1.41018	+	2.44250i	−0.323518	+	0.560349i	−0.981211	−	0.192937i	$-0.938199\pi$
$19$	−1.41018	+	2.44250i	−0.323518	+	0.560349i	0.657694	+	0.753286i	$0.271532\pi$
$20$	2.76981			0.619348
$21$		0			0
$22$	1.45670			0.310570
$23$	2.99978	−	5.19577i	0.625498	−	1.08339i	−0.362947	−	0.931810i	$-0.618229\pi$
$23$	2.99978	−	5.19577i	0.625498	−	1.08339i	0.988444	−	0.151584i	$-0.0484373\pi$
$24$	1.51266	+	2.62001i	0.308771	+	0.534806i
$25$	1.47017	+	2.54640i	0.294033	+	0.509281i
$26$	−0.132313	+	0.229173i	−0.0259488	+	0.0449446i
$27$	7.16341			1.37860
$28$		0			0
$29$	1.04188			0.193472			0.0967361	−	0.995310i	$-0.469160\pi$
$29$	1.04188			0.193472			0.0967361	+	0.995310i	$0.469160\pi$
$30$	0.552396	−	0.956778i	0.100853	−	0.174683i
$31$	−4.60448	−	7.97519i	−0.826988	−	1.43239i	−0.900390	−	0.435083i	$-0.856719\pi$
$31$	−4.60448	−	7.97519i	−0.826988	−	1.43239i	0.0734019	−	0.997302i	$-0.476614\pi$
$32$	−1.51428	−	2.62282i	−0.267690	−	0.463653i
$33$	−8.00674	+	13.8681i	−1.39379	+	2.41412i
$34$	1.27834			0.219233
$35$		0			0
$36$	−10.5424			−1.75707
$37$	−0.306249	+	0.530438i	−0.0503470	+	0.0872035i	−0.890101	−	0.455764i	$-0.849366\pi$
$37$	−0.306249	+	0.530438i	−0.0503470	+	0.0872035i	0.839754	+	0.542968i	$0.182699\pi$
$38$	−0.373171	−	0.646351i	−0.0605364	−	0.104852i
$39$	−1.45452	−	2.51930i	−0.232909	−	0.403410i
$40$	−0.746262	+	1.29256i	−0.117994	+	0.204372i
$41$	−10.6196			−1.65850			−0.829249	−	0.558879i	$-0.811232\pi$
$41$	−10.6196			−1.65850			−0.829249	+	0.558879i	$0.811232\pi$
$42$		0			0
$43$	−8.43685			−1.28661			−0.643304	−	0.765611i	$-0.722437\pi$
$43$	−8.43685			−1.28661			−0.643304	+	0.765611i	$0.722437\pi$
$44$	5.31200	−	9.20066i	0.800814	−	1.38705i
$45$	3.91974	+	6.78919i	0.584321	+	1.01207i
$46$	0.793822	+	1.37494i	0.117043	+	0.202724i
$47$	−1.20461	+	2.08645i	−0.175711	+	0.304340i	−0.940407	−	0.340051i	$-0.889556\pi$
$47$	−1.20461	+	2.08645i	−0.175711	+	0.304340i	0.764696	+	0.644391i	$0.222889\pi$
$48$	10.4281			1.50517
$49$		0			0
$50$	−0.778091			−0.110039
$51$	−7.02636	+	12.1700i	−0.983888	+	1.70414i
$52$	0.964986	+	1.67141i	0.133820	+	0.231782i
$53$	0.914793	+	1.58447i	0.125657	+	0.217643i	0.921989	−	0.387215i	$-0.126563\pi$
$53$	0.914793	+	1.58447i	0.125657	+	0.217643i	−0.796333	+	0.604859i	$0.793230\pi$
$54$	−0.947814	+	1.64166i	−0.128981	+	0.223402i
$55$	−7.90015			−1.06526
$56$		0			0
$57$	8.20452			1.08672
$58$	−0.137855	+	0.238771i	−0.0181012	+	0.0313522i
$59$	0.435457	+	0.754234i	0.0566917	+	0.0981929i	0.892978	−	0.450099i	$-0.148611\pi$
$59$	0.435457	+	0.754234i	0.0566917	+	0.0981929i	−0.836287	+	0.548292i	$0.815278\pi$
$60$	−4.02873	−	6.97797i	−0.520107	−	0.900851i
$61$	1.66626	−	2.88605i	0.213343	−	0.369521i	−0.739416	−	0.673249i	$-0.764898\pi$
$61$	1.66626	−	2.88605i	0.213343	−	0.369521i	0.952759	+	0.303728i	$0.0982314\pi$
$62$	2.43693			0.309491
$63$		0			0
$64$	−6.36804			−0.796005
$65$	0.717577	−	1.24288i	0.0890044	−	0.154160i
$66$	−2.11880	−	3.66986i	−0.260806	−	0.451729i
$67$	3.31370	+	5.73951i	0.404833	+	0.701192i	0.994302	−	0.106599i	$-0.0339962\pi$
$67$	3.31370	+	5.73951i	0.404833	+	0.701192i	−0.589469	+	0.807791i	$0.700663\pi$
$68$	4.66158	−	8.07410i	0.565300	−	0.979128i
$69$	−17.4529			−2.10108
$70$		0			0
$71$	−6.85856			−0.813961			−0.406980	−	0.913437i	$-0.633418\pi$
$71$	−6.85856			−0.813961			−0.406980	+	0.913437i	$0.633418\pi$
$72$	2.84042	−	4.91975i	0.334746	−	0.579798i
$73$	−1.57074	−	2.72060i	−0.183841	−	0.318422i	0.759345	−	0.650689i	$-0.225520\pi$
$73$	−1.57074	−	2.72060i	−0.183841	−	0.318422i	−0.943185	+	0.332267i	$0.892186\pi$
$74$	−0.0810415	−	0.140368i	−0.00942089	−	0.0163175i
$75$	4.27676	−	7.40757i	0.493838	−	0.855353i
$76$	−5.44322			−0.624380
$77$		0			0
$78$	0.769807			0.0871635
$79$	8.78614	−	15.2180i	0.988518	−	1.71216i	0.363402	−	0.931632i	$-0.381615\pi$
$79$	8.78614	−	15.2180i	0.988518	−	1.71216i	0.625116	−	0.780532i	$-0.285052\pi$
$80$	2.57233	+	4.45540i	0.287595	+	0.498129i
$81$	−2.22559	−	3.85484i	−0.247288	−	0.428315i
$82$	1.40511	−	2.43372i	0.155168	−	0.268760i
$83$	11.4525			1.25708			0.628538	−	0.777779i	$-0.283654\pi$
$83$	11.4525			1.25708			0.628538	+	0.777779i	$0.283654\pi$
$84$		0			0
$85$	−6.93283			−0.751971
$86$	1.11631	−	1.93350i	0.120374	−	0.208495i
$87$	−1.51543	−	2.62480i	−0.162471	−	0.281409i
$88$	2.86240	+	4.95782i	0.305133	+	0.528505i
$89$	0.497659	−	0.861970i	0.0527517	−	0.0913687i	−0.838444	−	0.544988i	$-0.816534\pi$
$89$	0.497659	−	0.861970i	0.0527517	−	0.0913687i	0.891195	+	0.453619i	$0.149867\pi$
$90$	−2.07454			−0.218675
$91$		0			0
$92$	11.5790			1.20719
$93$	−13.3946	+	23.2001i	−1.38895	+	2.40574i
$94$	−0.318772	−	0.552130i	−0.0328789	−	0.0569479i
$95$	2.02383	+	3.50537i	0.207640	+	0.359643i
$96$	−4.40510	+	7.62986i	−0.449594	+	0.778719i
$97$	13.5090			1.37163			0.685817	−	0.727774i	$-0.259445\pi$
$97$	13.5090			1.37163			0.685817	+	0.727774i	$0.259445\pi$
$98$		0			0
$99$	30.0695			3.02210
$100$	−2.83738	+	4.91449i	−0.283738	+	0.491449i
$101$	0.504033	+	0.873011i	0.0501532	+	0.0868678i	0.890012	−	0.455937i	$-0.150696\pi$
$101$	0.504033	+	0.873011i	0.0501532	+	0.0868678i	−0.839859	+	0.542805i	$0.817362\pi$
$102$	−1.85936	−	3.22051i	−0.184104	−	0.318878i
$103$	6.38772	−	11.0639i	0.629401	−	1.09015i	−0.358271	−	0.933618i	$-0.616634\pi$
$103$	6.38772	−	11.0639i	0.629401	−	1.09015i	0.987672	−	0.156537i	$-0.0500331\pi$
$104$	−1.03998			−0.101978
$105$		0			0
$106$	−0.484157			−0.0470255
$107$	0.342748	−	0.593656i	0.0331347	−	0.0573909i	−0.848983	−	0.528421i	$-0.822784\pi$
$107$	0.342748	−	0.593656i	0.0331347	−	0.0573909i	0.882117	+	0.471030i	$0.156118\pi$
$108$	6.91259	+	11.9730i	0.665165	+	1.15210i
$109$	1.45172	+	2.51446i	0.139050	+	0.240841i	0.927137	−	0.374722i	$-0.122262\pi$
$109$	1.45172	+	2.51446i	0.139050	+	0.240841i	−0.788087	+	0.615563i	$0.788929\pi$
$110$	1.04529	−	1.81050i	0.0996649	−	0.172625i
$111$	1.78177			0.169119
$112$		0			0
$113$	12.0315			1.13183			0.565915	−	0.824464i	$-0.308523\pi$
$113$	12.0315			1.13183			0.565915	+	0.824464i	$0.308523\pi$
$114$	−1.08557	+	1.88026i	−0.101673	+	0.176102i
$115$	−4.30515	−	7.45673i	−0.401457	−	0.695344i
$116$	1.00540	+	1.74140i	0.0933490	+	0.161685i
$117$	−2.73124	+	4.73064i	−0.252503	+	0.437348i
$118$	−0.230467			−0.0212162
$119$		0			0
$120$	4.34180			0.396350
$121$	−9.65109	+	16.7162i	−0.877372	+	1.51965i
$122$	0.440938	+	0.763726i	0.0399206	+	0.0691445i
$123$	15.4463	+	26.7539i	1.39275	+	2.41231i
$124$	8.88651	−	15.3919i	0.798032	−	1.38223i
$125$	11.3956			1.01925
$126$		0			0
$127$	15.6659			1.39012			0.695062	−	0.718950i	$-0.255377\pi$
$127$	15.6659			1.39012			0.695062	+	0.718950i	$0.255377\pi$
$128$	3.87114	−	6.70502i	0.342164	−	0.592645i
$129$	12.2715	+	21.2549i	1.08045	+	1.87139i
$130$	0.189890	+	0.328899i	0.0166544	+	0.0288463i
$131$	−6.06366	+	10.5026i	−0.529784	+	0.917613i	0.469612	+	0.882873i	$0.344394\pi$
$131$	−6.06366	+	10.5026i	−0.529784	+	0.917613i	−0.999396	+	0.0347403i	$0.988940\pi$
$132$	−30.9056			−2.68998
$133$		0			0
$134$	−1.75379			−0.151504
$135$	5.14030	−	8.90326i	0.442406	−	0.766270i
$136$	2.51192	+	4.35077i	0.215395	+	0.373075i
$137$	−7.96873	−	13.8022i	−0.680815	−	1.17921i	−0.974733	−	0.223375i	$-0.928293\pi$
$137$	−7.96873	−	13.8022i	−0.680815	−	1.17921i	0.293918	−	0.955831i	$-0.405041\pi$
$138$	2.30925	−	3.99974i	0.196577	−	0.340481i
$139$	−6.64088			−0.563272			−0.281636	−	0.959521i	$-0.590877\pi$
$139$	−6.64088			−0.563272			−0.281636	+	0.959521i	$0.590877\pi$
$140$		0			0
$141$	7.00851			0.590223
$142$	0.907478	−	1.57180i	0.0761539	−	0.131902i
$143$	−2.75237	−	4.76725i	−0.230165	−	0.398657i
$144$	−9.79077	−	16.9581i	−0.815898	−	1.41318i
$145$	0.747629	−	1.29493i	0.0620872	−	0.107538i
$146$	0.831317			0.0688003
$147$		0			0
$148$	−1.18210			−0.0971683
$149$	9.77512	−	16.9310i	0.800809	−	1.38704i	−0.118275	−	0.992981i	$-0.537736\pi$
$149$	9.77512	−	16.9310i	0.800809	−	1.38704i	0.919084	−	0.394061i	$-0.128930\pi$
$150$	1.13175	+	1.96024i	0.0924066	+	0.160053i
$151$	−5.34401	−	9.25610i	−0.434890	−	0.753251i	0.562397	−	0.826867i	$-0.309879\pi$
$151$	−5.34401	−	9.25610i	−0.434890	−	0.753251i	−0.997287	+	0.0736163i	$0.976546\pi$
$152$	1.46655	−	2.54014i	0.118953	−	0.206033i
$153$	26.3877			2.13332
$154$		0			0
$155$	−13.2163			−1.06156
$156$	2.80718	−	4.86217i	0.224754	−	0.389285i
$157$	7.53672	+	13.0540i	0.601496	+	1.04182i	0.992595	+	0.121473i	$0.0387617\pi$
$157$	7.53672	+	13.0540i	0.601496	+	1.04182i	−0.391099	+	0.920349i	$0.627905\pi$
$158$	2.32505	+	4.02710i	0.184971	+	0.320379i
$159$	2.66116	−	4.60927i	0.211044	−	0.365539i
$160$	−4.34646			−0.343618
$161$		0			0
$162$	1.17790			0.0925447
$163$	11.9067	−	20.6231i	0.932607	−	1.61532i	0.153760	−	0.988108i	$-0.450862\pi$
$163$	11.9067	−	20.6231i	0.932607	−	1.61532i	0.778847	−	0.627214i	$-0.215805\pi$
$164$	−10.2477	−	17.7496i	−0.800214	−	1.38601i
$165$	11.4909	+	19.9028i	0.894565	+	1.54943i
$166$	−1.51532	+	2.62461i	−0.117611	+	0.203709i
$167$	−7.12371			−0.551249			−0.275625	−	0.961265i	$-0.588885\pi$
$167$	−7.12371			−0.551249			−0.275625	+	0.961265i	$0.588885\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	0.917305	−	1.58882i	0.0703541	−	0.121857i
$171$	−7.70307	−	13.3421i	−0.589069	−	1.02030i
$172$	−8.14145	−	14.1014i	−0.620779	−	1.07522i
$173$	−5.61834	+	9.73125i	−0.427155	+	0.739854i	−0.996619	−	0.0821625i	$-0.973817\pi$
$173$	−5.61834	+	9.73125i	−0.427155	+	0.739854i	0.569464	+	0.822016i	$0.307151\pi$
$174$	0.802047			0.0608030
$175$		0			0
$176$	19.7331			1.48744
$177$	1.26676	−	2.19409i	0.0952155	−	0.164918i
$178$	0.131694	+	0.228100i	0.00987086	+	0.0170968i
$179$	6.59725	+	11.4268i	0.493102	+	0.854078i	0.999968	−	0.00794701i	$-0.00252964\pi$
$179$	6.59725	+	11.4268i	0.493102	+	0.854078i	−0.506867	+	0.862025i	$0.669196\pi$
$180$	−7.56500	+	13.1030i	−0.563862	+	0.976637i
$181$	−13.7414			−1.02139			−0.510696	−	0.859761i	$-0.670612\pi$
$181$	−13.7414			−1.02139			−0.510696	+	0.859761i	$0.670612\pi$
$182$		0			0
$183$	−9.69443			−0.716633
$184$	−3.11970	+	5.40347i	−0.229987	+	0.398349i
$185$	0.439514	+	0.761260i	0.0323137	+	0.0559690i
$186$	−3.54456	−	6.13936i	−0.259900	−	0.450159i
$187$	−13.2959	+	23.0292i	−0.972295	+	1.68407i
$188$	−4.64974			−0.339117
$189$		0			0
$190$	−1.07112			−0.0777069
$191$	8.16536	−	14.1428i	0.590824	−	1.02334i	−0.403297	−	0.915069i	$-0.632136\pi$
$191$	8.16536	−	14.1428i	0.590824	−	1.02334i	0.994122	−	0.108269i	$-0.0345308\pi$
$192$	9.26242	+	16.0430i	0.668458	+	1.15780i
$193$	7.02666	+	12.1705i	0.505790	+	0.876054i	0.999978	+	0.00669897i	$0.00213237\pi$
$193$	7.02666	+	12.1705i	0.505790	+	0.876054i	−0.494187	+	0.869355i	$0.664534\pi$
$194$	−1.78742	+	3.09591i	−0.128330	+	0.222273i
$195$	−4.17491			−0.298971
$196$		0			0
$197$	−1.46898			−0.104660			−0.0523302	−	0.998630i	$-0.516665\pi$
$197$	−1.46898			−0.104660			−0.0523302	+	0.998630i	$0.516665\pi$
$198$	−3.97859	+	6.89113i	−0.282746	+	0.489731i
$199$	6.68860	+	11.5850i	0.474142	+	0.821239i	0.999562	−	0.0296046i	$-0.00942482\pi$
$199$	6.68860	+	11.5850i	0.474142	+	0.821239i	−0.525419	+	0.850844i	$0.676091\pi$
$200$	−1.52894	−	2.64820i	−0.108112	−	0.187256i
$201$	9.63968	−	16.6964i	0.679930	−	1.17767i
$202$	−0.266761			−0.0187692
$203$		0			0
$204$	−27.1214			−1.89888
$205$	−7.62036	+	13.1988i	−0.532229	+	0.921848i
$206$	1.69036	+	2.92779i	0.117773	+	0.203989i
$207$	16.3862	+	28.3818i	1.13892	+	1.97267i
$208$	−1.79237	+	3.10448i	−0.124279	+	0.215257i
$209$	15.5254			1.07391
$210$		0			0
$211$	3.47044			0.238915			0.119457	−	0.992839i	$-0.461885\pi$
$211$	3.47044			0.238915			0.119457	+	0.992839i	$0.461885\pi$
$212$	−1.76553	+	3.05798i	−0.121257	+	0.210023i
$213$	9.97588	+	17.2787i	0.683536	+	1.18392i
$214$	0.0907001	+	0.157097i	0.00620013	+	0.0107389i
$215$	−6.05409	+	10.4860i	−0.412885	+	0.715138i
$216$	−7.44977			−0.506893
$217$		0			0
$218$	−0.768328			−0.0520378
$219$	−4.56932	+	7.91430i	−0.308766	+	0.534799i
$220$	−7.62354	−	13.2044i	−0.513979	−	0.890237i
$221$	−2.41536	−	4.18353i	−0.162475	−	0.281415i
$222$	−0.235752	+	0.408335i	−0.0158227	+	0.0274057i
$223$	−9.91318			−0.663836			−0.331918	−	0.943308i	$-0.607696\pi$
$223$	−9.91318			−0.663836			−0.331918	+	0.943308i	$0.607696\pi$
$224$		0			0
$225$	−16.0615			−1.07077
$226$	−1.59193	+	2.75730i	−0.105894	+	0.183413i
$227$	−6.03634	−	10.4552i	−0.400646	−	0.693939i	0.593158	−	0.805086i	$-0.297881\pi$
$227$	−6.03634	−	10.4552i	−0.400646	−	0.693939i	−0.993804	+	0.111147i	$0.964548\pi$
$228$	7.91725	+	13.7131i	0.524333	+	0.908171i
$229$	−2.02586	+	3.50888i	−0.133872	+	0.231874i	−0.925166	−	0.379563i	$-0.876075\pi$
$229$	−2.02586	+	3.50888i	−0.133872	+	0.231874i	0.791294	+	0.611436i	$0.209408\pi$
$230$	2.27851			0.150241
$231$		0			0
$232$	−1.08353			−0.0711372
$233$	−6.27250	+	10.8643i	−0.410925	+	0.711743i	−0.994991	−	0.0999629i	$-0.968128\pi$
$233$	−6.27250	+	10.8643i	−0.410925	+	0.711743i	0.584066	+	0.811706i	$0.301461\pi$
$234$	−0.722758	−	1.25185i	−0.0472481	−	0.0818362i
$235$	1.72880	+	2.99438i	0.112775	+	0.195332i
$236$	−0.840421	+	1.45565i	−0.0547067	+	0.0947548i
$237$	−51.1184			−3.32049
$238$		0			0
$239$	13.3463			0.863299			0.431649	−	0.902042i	$-0.357932\pi$
$239$	13.3463			0.863299			0.431649	+	0.902042i	$0.357932\pi$
$240$	7.48298	−	12.9609i	0.483024	−	0.836623i
$241$	−10.1927	−	17.6542i	−0.656568	−	1.13721i	−0.981498	−	0.191471i	$-0.938674\pi$
$241$	−10.1927	−	17.6542i	−0.656568	−	1.13721i	0.324930	−	0.945738i	$-0.394659\pi$
$242$	−2.55394	−	4.42355i	−0.164173	−	0.284356i
$243$	4.27080	−	7.39724i	0.273972	−	0.474533i
$244$	6.43169			0.411747
$245$		0			0
$246$	−8.17502			−0.521221
$247$	−1.41018	+	2.44250i	−0.0897276	+	0.155413i
$248$	4.78854	+	8.29400i	0.304073	+	0.526669i
$249$	−16.6579	−	28.8522i	−1.05565	−	1.82844i
$250$	−1.50779	+	2.61157i	−0.0953609	+	0.165170i
$251$	17.1921			1.08515			0.542577	−	0.840006i	$-0.317449\pi$
$251$	17.1921			1.08515			0.542577	+	0.840006i	$0.317449\pi$
$252$		0			0
$253$	−33.0260			−2.07633
$254$	−2.07281	+	3.59021i	−0.130059	+	0.225270i
$255$	10.0839	+	17.4658i	0.631479	+	1.09375i
$256$	−5.34363	−	9.25545i	−0.333977	−	0.578465i
$257$	3.82348	−	6.62245i	0.238502	−	0.413097i	−0.721783	−	0.692120i	$-0.756677\pi$
$257$	3.82348	−	6.62245i	0.238502	−	0.413097i	0.960285	+	0.279022i	$0.0900104\pi$
$258$	−6.49475			−0.404345
$259$		0			0
$260$	2.76981			0.171776
$261$	−2.84562	+	4.92876i	−0.176139	+	0.305082i
$262$	−1.60460	−	2.77926i	−0.0991328	−	0.171703i
$263$	0.0505186	+	0.0875008i	0.00311511	+	0.00539553i	0.867579	−	0.497300i	$-0.165675\pi$
$263$	0.0505186	+	0.0875008i	0.00311511	+	0.00539553i	−0.864464	+	0.502695i	$0.832342\pi$
$264$	8.32681	−	14.4225i	0.512480	−	0.887641i
$265$	2.62574			0.161298
$266$		0			0
$267$	−2.89541			−0.177196
$268$	−6.39536	+	11.0771i	−0.390659	+	0.676641i
$269$	3.78426	+	6.55453i	0.230730	+	0.399637i	0.958023	−	0.286691i	$-0.0925552\pi$
$269$	3.78426	+	6.55453i	0.230730	+	0.399637i	−0.727293	+	0.686327i	$0.759222\pi$
$270$	1.36026	+	2.35604i	0.0827827	+	0.143384i
$271$	6.92768	−	11.9991i	0.420826	−	0.728893i	−0.575194	−	0.818017i	$-0.695073\pi$
$271$	6.92768	−	11.9991i	0.420826	−	0.728893i	0.996021	+	0.0891242i	$0.0284068\pi$
$272$	17.3169			1.04999
$273$		0			0
$274$	4.21748			0.254787
$275$	8.09289	−	14.0173i	0.488020	−	0.845275i
$276$	−16.8418	−	29.1709i	−1.01376	−	1.75588i
$277$	−0.276468	−	0.478856i	−0.0166113	−	0.0287717i	0.857600	−	0.514317i	$-0.171954\pi$
$277$	−0.276468	−	0.478856i	−0.0166113	−	0.0287717i	−0.874212	+	0.485545i	$0.838621\pi$
$278$	0.878677	−	1.52191i	0.0526995	−	0.0912783i
$279$	50.3036			3.01160
$280$		0			0
$281$	1.14667			0.0684043			0.0342022	−	0.999415i	$-0.489111\pi$
$281$	1.14667			0.0684043			0.0342022	+	0.999415i	$0.489111\pi$
$282$	−0.927319	+	1.60616i	−0.0552211	+	0.0956457i
$283$	2.02698	+	3.51083i	0.120491	+	0.208697i	0.919962	−	0.392009i	$-0.128220\pi$
$283$	2.02698	+	3.51083i	0.120491	+	0.208697i	−0.799470	+	0.600706i	$0.794886\pi$
$284$	−6.61841	−	11.4634i	−0.392731	−	0.680229i
$285$	5.88737	−	10.1972i	0.348738	−	0.604032i
$286$	1.45670			0.0861365
$287$		0			0
$288$	16.5435			0.974833
$289$	−3.16794	+	5.48703i	−0.186349	+	0.322767i
$290$	0.197842	+	0.342673i	0.0116177	+	0.0201225i
$291$	−19.6491	−	34.0332i	−1.15185	−	1.99506i
$292$	3.03148	−	5.25067i	0.177404	−	0.307272i
$293$	15.0649			0.880102			0.440051	−	0.897973i	$-0.354960\pi$
$293$	15.0649			0.880102			0.440051	+	0.897973i	$0.354960\pi$
$294$		0			0
$295$	1.24990			0.0727718
$296$	0.318491	−	0.551643i	0.0185119	−	0.0320636i
$297$	−19.7164	−	34.1497i	−1.14406	−	1.98157i
$298$	2.58676	+	4.48039i	0.149847	+	0.259542i
$299$	2.99978	−	5.19577i	0.173482	−	0.300479i
$300$	16.5081			0.953094
$301$		0			0
$302$	2.82834			0.162752
$303$	1.46625	−	2.53962i	0.0842338	−	0.145897i
$304$	−5.05513	−	8.75574i	−0.289932	−	0.502176i
$305$	−2.39134	−	4.14193i	−0.136928	−	0.237166i
$306$	−3.49144	+	6.04735i	−0.199592	+	0.345704i
$307$	−19.9408			−1.13808			−0.569040	−	0.822310i	$-0.692685\pi$
$307$	−19.9408			−1.13808			−0.569040	+	0.822310i	$0.692685\pi$
$308$		0			0
$309$	−37.1642			−2.11420
$310$	1.74869	−	3.02881i	0.0993187	−	0.172025i
$311$	5.44780	+	9.43587i	0.308916	+	0.535059i	0.978126	−	0.208015i	$-0.0667003\pi$
$311$	5.44780	+	9.43587i	0.308916	+	0.535059i	−0.669209	+	0.743074i	$0.733367\pi$
$312$	1.51266	+	2.62001i	0.0856376	+	0.148329i
$313$	0.0259595	−	0.0449632i	0.00146732	−	0.00254147i	−0.865291	−	0.501270i	$-0.832866\pi$
$313$	0.0259595	−	0.0449632i	0.00146732	−	0.00254147i	0.866758	+	0.498729i	$0.166200\pi$
$314$	−3.98883			−0.225103
$315$		0			0
$316$	33.9140			1.90781
$317$	−8.05049	+	13.9439i	−0.452161	+	0.783165i	−0.998520	−	0.0543857i	$-0.982680\pi$
$317$	−8.05049	+	13.9439i	−0.452161	+	0.783165i	0.546359	+	0.837551i	$0.316013\pi$
$318$	0.704215	+	1.21974i	0.0394904	+	0.0683994i
$319$	−2.86764	−	4.96690i	−0.160557	−	0.278093i
$320$	−4.56956	+	7.91471i	−0.255446	+	0.442446i
$321$	−1.99413			−0.111301
$322$		0			0
$323$	13.6244			0.758081
$324$	4.29533	−	7.43973i	0.238630	−	0.413318i
$325$	1.47017	+	2.54640i	0.0815502	+	0.141249i
$326$	3.15084	+	5.45741i	0.174509	+	0.302258i
$327$	4.22311	−	7.31463i	0.233538	−	0.404500i
$328$	11.0441			0.609808
$329$		0			0
$330$	−6.08159			−0.334781
$331$	−15.3931	+	26.6616i	−0.846081	+	1.46546i	0.0385973	+	0.999255i	$0.487711\pi$
$331$	−15.3931	+	26.6616i	−0.846081	+	1.46546i	−0.884679	+	0.466201i	$0.845622\pi$
$332$	11.0515	+	19.1418i	0.606530	+	1.05054i
$333$	−1.67287	−	2.89750i	−0.0916730	−	0.158782i
$334$	0.942561	−	1.63256i	0.0515746	−	0.0893299i
$335$	9.51135			0.519661
$336$		0			0
$337$	−2.41842			−0.131740			−0.0658700	−	0.997828i	$-0.520982\pi$
$337$	−2.41842			−0.131740			−0.0658700	+	0.997828i	$0.520982\pi$
$338$	−0.132313	+	0.229173i	−0.00719689	+	0.0124654i
$339$	−17.5000	−	30.3109i	−0.950471	−	1.64626i
$340$	−6.69009	−	11.5876i	−0.362821	−	0.628424i
$341$	−25.3465	+	43.9013i	−1.37259	+	2.37739i
$342$	4.07687			0.220452
$343$		0			0
$344$	8.77411			0.473069
$345$	−12.5238	+	21.6919i	−0.674259	+	1.16785i
$346$	−1.48676	−	2.57515i	−0.0799289	−	0.138441i
$347$	0.246264	+	0.426541i	0.0132201	+	0.0228979i	0.872560	−	0.488507i	$-0.162458\pi$
$347$	0.246264	+	0.426541i	0.0132201	+	0.0228979i	−0.859340	+	0.511405i	$0.829125\pi$
$348$	2.92474	−	5.06580i	0.156783	−	0.271555i
$349$	−11.9442			−0.639356			−0.319678	−	0.947526i	$-0.603575\pi$
$349$	−11.9442			−0.639356			−0.319678	+	0.947526i	$0.603575\pi$
$350$		0			0
$351$	7.16341			0.382355
$352$	−8.33574	+	14.4379i	−0.444297	+	0.769544i
$353$	−7.76497	−	13.4493i	−0.413288	−	0.715835i	0.581959	−	0.813218i	$-0.302286\pi$
$353$	−7.76497	−	13.4493i	−0.413288	−	0.715835i	−0.995247	+	0.0973828i	$0.968953\pi$
$354$	0.335218	+	0.580615i	0.0178166	+	0.0308593i
$355$	−4.92154	+	8.52436i	−0.261208	+	0.452426i
$356$	1.92094			0.101809
$357$		0			0
$358$	−3.49162			−0.184538
$359$	4.25354	−	7.36735i	0.224493	−	0.388834i	−0.731674	−	0.681655i	$-0.761261\pi$
$359$	4.25354	−	7.36735i	0.224493	−	0.388834i	0.956167	+	0.292821i	$0.0945939\pi$
$360$	−4.07644	−	7.06059i	−0.214847	−	0.372126i
$361$	5.52278	+	9.56574i	0.290673	+	0.503460i
$362$	1.81817	−	3.14917i	0.0955611	−	0.165517i
$363$	56.1507			2.94715
$364$		0			0
$365$	−4.50850			−0.235985
$366$	1.28270	−	2.22170i	0.0670479	−	0.116130i
$367$	−2.59542	−	4.49540i	−0.135480	−	0.234658i	0.790301	−	0.612719i	$-0.209924\pi$
$367$	−2.59542	−	4.49540i	−0.135480	−	0.234658i	−0.925781	+	0.378061i	$0.876591\pi$
$368$	10.7534	+	18.6255i	0.560562	+	0.970921i
$369$	29.0046	−	50.2374i	1.50992	−	2.61525i
$370$	−0.232614			−0.0120930
$371$		0			0
$372$	−51.7023			−2.68064
$373$	5.07135	−	8.78384i	0.262585	−	0.454810i	−0.704343	−	0.709859i	$-0.748758\pi$
$373$	5.07135	−	8.78384i	0.262585	−	0.454810i	0.966928	+	0.255049i	$0.0820918\pi$
$374$	−3.51846	−	6.09415i	−0.181935	−	0.315121i
$375$	−16.5751	−	28.7089i	−0.855934	−	1.48252i
$376$	1.25277	−	2.16986i	0.0646065	−	0.111902i
$377$	1.04188			0.0536595
$378$		0			0
$379$	−3.63670			−0.186805			−0.0934024	−	0.995628i	$-0.529774\pi$
$379$	−3.63670			−0.186805			−0.0934024	+	0.995628i	$0.529774\pi$
$380$	−3.90593	+	6.76527i	−0.200370	+	0.347051i
$381$	−22.7863	−	39.4670i	−1.16738	−	2.02196i
$382$	2.16077	+	3.74256i	0.110555	+	0.191486i
$383$	−2.30140	+	3.98615i	−0.117596	+	0.203683i	−0.918815	−	0.394689i	$-0.870852\pi$
$383$	−2.30140	+	3.98615i	−0.117596	+	0.203683i	0.801218	+	0.598372i	$0.204186\pi$
$384$	−22.5226			−1.14935
$385$		0			0
$386$	−3.71888			−0.189286
$387$	23.0430	−	39.9117i	1.17134	−	2.02883i
$388$	13.0360	+	22.5791i	0.661804	+	1.14628i
$389$	−9.80519	−	16.9831i	−0.497143	−	0.861077i	0.502852	−	0.864373i	$-0.332284\pi$
$389$	−9.80519	−	16.9831i	−0.497143	−	0.861077i	−0.999995	+	0.00329604i	$0.998951\pi$
$390$	0.552396	−	0.956778i	0.0279717	−	0.0484483i
$391$	−28.9822			−1.46569
$392$		0			0
$393$	35.2788			1.77958
$394$	0.194366	−	0.336651i	0.00979199	−	0.0169602i
$395$	−12.6095	−	21.8402i	−0.634451	−	1.09890i
$396$	29.0167	+	50.2583i	1.45814	+	2.52558i
$397$	9.93173	−	17.2023i	0.498459	−	0.863357i	−0.501539	−	0.865135i	$-0.667233\pi$
$397$	9.93173	−	17.2023i	0.498459	−	0.863357i	0.999998	+	0.00177809i	$0.000565985\pi$
$398$	−3.53996			−0.177442
$399$		0			0
$400$	−10.5403			−0.527017
$401$	7.55587	−	13.0872i	0.377322	−	0.653541i	−0.613350	−	0.789812i	$-0.710178\pi$
$401$	7.55587	−	13.0872i	0.377322	−	0.653541i	0.990672	+	0.136270i	$0.0435116\pi$
$402$	2.55091	+	4.41831i	0.127228	+	0.220365i
$403$	−4.60448	−	7.97519i	−0.229365	−	0.397272i
$404$	−0.972770	+	1.68489i	−0.0483971	+	0.0838263i
$405$	−6.38813			−0.317429
$406$		0			0
$407$	3.37164			0.167126
$408$	7.30724	−	12.6565i	0.361763	−	0.626591i
$409$	17.6222	+	30.5225i	0.871360	+	1.50924i	0.860590	+	0.509298i	$0.170095\pi$
$409$	17.6222	+	30.5225i	0.871360	+	1.50924i	0.0107701	+	0.999942i	$0.496572\pi$
$410$	−2.01655	−	3.49277i	−0.0995903	−	0.172495i
$411$	−23.1813	+	40.1512i	−1.14345	+	1.98051i
$412$	24.6563			1.21473
$413$		0			0
$414$	−8.67246			−0.426228
$415$	8.21805	−	14.2341i	0.403408	−	0.698723i
$416$	−1.51428	−	2.62282i	−0.0742439	−	0.128594i
$417$	9.65927	+	16.7304i	0.473017	+	0.819289i
$418$	−2.05421	+	3.55800i	−0.100475	+	0.174027i
$419$	1.50468			0.0735084			0.0367542	−	0.999324i	$-0.488298\pi$
$419$	1.50468			0.0735084			0.0367542	+	0.999324i	$0.488298\pi$
$420$		0			0
$421$	−24.5079			−1.19444			−0.597221	−	0.802077i	$-0.703728\pi$
$421$	−24.5079			−1.19444			−0.597221	+	0.802077i	$0.703728\pi$
$422$	−0.459185	+	0.795332i	−0.0223528	+	0.0387161i
$423$	−6.58016	−	11.3972i	−0.319938	−	0.554149i
$424$	−0.951362	−	1.64781i	−0.0462022	−	0.0800246i
$425$	7.10197	−	12.3010i	0.344496	−	0.596685i
$426$	−5.27977			−0.255806
$427$		0			0
$428$	1.32299			0.0639490
$429$	−8.00674	+	13.8681i	−0.386569	+	0.669557i
$430$	−1.60207	−	2.77487i	−0.0772588	−	0.133816i
$431$	−20.5327	−	35.5638i	−0.989027	−	1.71305i	−0.622454	−	0.782657i	$-0.713864\pi$
$431$	−20.5327	−	35.5638i	−0.989027	−	1.71305i	−0.366574	−	0.930389i	$-0.619469\pi$
$432$	−12.8395	+	22.2386i	−0.617740	+	1.06996i
$433$	6.65603			0.319869			0.159934	−	0.987128i	$-0.448872\pi$
$433$	6.65603			0.319869			0.159934	+	0.987128i	$0.448872\pi$
$434$		0			0
$435$	−4.34975			−0.208555
$436$	−2.80178	+	4.85283i	−0.134181	+	0.232408i
$437$	8.46046	+	14.6540i	0.404719	+	0.700994i
$438$	−1.20916	−	2.09433i	−0.0577761	−	0.100071i
$439$	−4.11495	+	7.12730i	−0.196396	+	0.340168i	−0.947357	−	0.320179i	$-0.896257\pi$
$439$	−4.11495	+	7.12730i	−0.196396	+	0.340168i	0.750961	+	0.660346i	$0.229590\pi$
$440$	8.21596			0.391681
$441$		0			0
$442$	1.27834			0.0608043
$443$	−8.84278	+	15.3161i	−0.420133	+	0.727692i	−0.995952	−	0.0898854i	$-0.971350\pi$
$443$	−8.84278	+	15.3161i	−0.420133	+	0.727692i	0.575819	+	0.817577i	$0.304683\pi$
$444$	1.71939	+	2.97807i	0.0815986	+	0.141333i
$445$	−0.714217	−	1.23706i	−0.0338571	−	0.0586423i
$446$	1.31165	−	2.27184i	0.0621082	−	0.107575i
$447$	−56.8723			−2.68997
$448$		0			0
$449$	−14.5250			−0.685477			−0.342738	−	0.939431i	$-0.611354\pi$
$449$	−14.5250			−0.685477			−0.342738	+	0.939431i	$0.611354\pi$
$450$	2.12515	−	3.68087i	0.100180	−	0.173518i
$451$	29.2290	+	50.6261i	1.37634	+	2.38389i
$452$	11.6102	+	20.1095i	0.546100	+	0.945873i
$453$	−15.5459	+	26.9263i	−0.730411	+	1.26511i
$454$	3.19475			0.149937
$455$		0			0
$456$	−8.53250			−0.399571
$457$	−1.89460	+	3.28154i	−0.0886255	+	0.153504i	−0.906930	−	0.421281i	$-0.861581\pi$
$457$	−1.89460	+	3.28154i	−0.0886255	+	0.153504i	0.818305	+	0.574784i	$0.194914\pi$
$458$	−0.536095	−	0.928544i	−0.0250501	−	0.0433880i
$459$	−17.3022	−	29.9683i	−0.807599	−	1.39880i
$460$	8.30881	−	14.3913i	0.387400	−	0.670997i
$461$	13.1107			0.610627			0.305314	−	0.952252i	$-0.401239\pi$
$461$	13.1107			0.610627			0.305314	+	0.952252i	$0.401239\pi$
$462$		0			0
$463$	15.3027			0.711176			0.355588	−	0.934643i	$-0.384281\pi$
$463$	15.3027			0.711176			0.355588	+	0.934643i	$0.384281\pi$
$464$	−1.86743	+	3.23449i	−0.0866935	+	0.150158i
$465$	19.2233	+	33.2957i	0.891458	+	1.54405i
$466$	−1.65987	−	2.87498i	−0.0768920	−	0.133181i
$467$	−15.3869	+	26.6509i	−0.712022	+	1.23326i	0.252075	+	0.967708i	$0.418887\pi$
$467$	−15.3869	+	26.6509i	−0.712022	+	1.23326i	−0.964097	+	0.265550i	$0.914446\pi$
$468$	−10.5424			−0.487324
$469$		0			0
$470$	−0.914975			−0.0422046
$471$	21.9246	−	37.9745i	1.01023	−	1.74977i
$472$	−0.452865	−	0.784385i	−0.0208448	−	0.0361042i
$473$	23.2213	+	40.2205i	1.06772	+	1.84934i
$474$	6.76364	−	11.7150i	0.310664	−	0.538086i
$475$	−8.29280			−0.380500
$476$		0			0
$477$	−9.99407			−0.457597
$478$	−1.76589	+	3.05861i	−0.0807699	+	0.139898i
$479$	0.858699	+	1.48731i	0.0392350	+	0.0679569i	0.884976	−	0.465637i	$-0.154175\pi$
$479$	0.858699	+	1.48731i	0.0392350	+	0.0679569i	−0.845741	+	0.533593i	$0.820841\pi$
$480$	6.32200	+	10.9500i	0.288558	+	0.499798i
$481$	−0.306249	+	0.530438i	−0.0139637	+	0.0241859i
$482$	5.39451			0.245713
$483$		0			0
$484$	−37.2527			−1.69330
$485$	9.69377	−	16.7901i	0.440171	−	0.762399i
$486$	1.13017	+	1.95751i	0.0512654	+	0.0887943i
$487$	−11.3403	−	19.6419i	−0.513877	−	0.890060i	−0.999870	−	0.0160982i	$-0.994876\pi$
$487$	−11.3403	−	19.6419i	−0.513877	−	0.890060i	0.485994	−	0.873962i	$-0.338458\pi$
$488$	−1.73287	+	3.00142i	−0.0784435	+	0.135868i
$489$	−69.2741			−3.13268
$490$		0			0
$491$	−13.1366			−0.592846			−0.296423	−	0.955057i	$-0.595794\pi$
$491$	−13.1366			−0.592846			−0.296423	+	0.955057i	$0.595794\pi$
$492$	−29.8110	+	51.6342i	−1.34398	+	2.32785i
$493$	−2.51652	−	4.35873i	−0.113338	−	0.196308i
$494$	−0.373171	−	0.646351i	−0.0167898	−	0.0290807i
$495$	21.5772	−	37.3728i	0.969822	−	1.67978i
$496$	33.0117			1.48227
$497$		0			0
$498$	8.81622			0.395064
$499$	−7.01976	+	12.1586i	−0.314248	+	0.544293i	−0.979277	−	0.202524i	$-0.935086\pi$
$499$	−7.01976	+	12.1586i	−0.314248	+	0.544293i	0.665030	+	0.746817i	$0.268419\pi$
$500$	10.9966	+	19.0467i	0.491783	+	0.851793i
$501$	10.3615	+	17.9467i	0.462920	+	0.801801i
$502$	−2.27474	+	3.93996i	−0.101527	+	0.175849i
$503$	0.367865			0.0164023			0.00820114	−	0.999966i	$-0.497389\pi$
$503$	0.367865			0.0164023			0.00820114	+	0.999966i	$0.497389\pi$
$504$		0			0
$505$	1.44673			0.0643786
$506$	4.36978	−	7.56869i	0.194261	−	0.336469i
$507$	−1.45452	−	2.51930i	−0.0645973	−	0.111886i
$508$	15.1174	+	26.1841i	0.670725	+	1.16173i
$509$	−20.6160	+	35.7079i	−0.913787	+	1.58273i	−0.105119	+	0.994460i	$0.533522\pi$
$509$	−20.6160	+	35.7079i	−0.913787	+	1.58273i	−0.808668	+	0.588266i	$0.799811\pi$
$510$	−5.33694			−0.236324
$511$		0			0
$512$	18.3127			0.809315
$513$	−10.1017	+	17.4967i	−0.446001	+	0.772497i
$514$	1.01179	+	1.75248i	0.0446283	+	0.0772985i
$515$	−9.16736	−	15.8783i	−0.403962	−	0.699683i
$516$	−23.6837	+	41.0214i	−1.04262	+	1.80587i
$517$	13.2622			0.583269
$518$		0			0
$519$	32.6879			1.43484
$520$	−0.746262	+	1.29256i	−0.0327258	+	0.0566827i
$521$	−0.520493	−	0.901521i	−0.0228032	−	0.0394963i	0.854399	−	0.519618i	$-0.173926\pi$
$521$	−0.520493	−	0.901521i	−0.0228032	−	0.0394963i	−0.877202	+	0.480122i	$0.840592\pi$
$522$	−0.753027	−	1.30428i	−0.0329591	−	0.0570868i
$523$	10.0104	−	17.3386i	0.437726	−	0.758163i	−0.559788	−	0.828636i	$-0.689117\pi$
$523$	10.0104	−	17.3386i	0.437726	−	0.758163i	0.997514	+	0.0704727i	$0.0224508\pi$
$524$	−23.4054			−1.02247
$525$		0			0
$526$	−0.0267371			−0.00116579
$527$	−22.2429	+	38.5259i	−0.968918	+	1.67822i
$528$	−28.7021	−	49.7135i	−1.24910	−	2.16350i
$529$	−6.49737	−	11.2538i	−0.282494	−	0.489295i
$530$	−0.347420	+	0.601749i	−0.0150910	+	0.0261383i
$531$	−4.75735			−0.206451
$532$		0			0
$533$	−10.6196			−0.459985
$534$	0.383101	−	0.663551i	0.0165784	−	0.0287147i
$535$	−0.491895	−	0.851988i	−0.0212665	−	0.0368346i
$536$	−3.44617	−	5.96894i	−0.148852	−	0.257819i
$537$	19.1916	−	33.2409i	0.828180	−	1.43445i
$538$	−2.00283			−0.0863481
$539$		0			0
$540$	19.8413			0.853832
$541$	4.89375	−	8.47622i	0.210399	−	0.364421i	−0.741441	−	0.671018i	$-0.765857\pi$
$541$	4.89375	−	8.47622i	0.210399	−	0.364421i	0.951839	+	0.306597i	$0.0991905\pi$
$542$	1.83325	+	3.17528i	0.0787447	+	0.136390i
$543$	19.9871	+	34.6187i	0.857730	+	1.48563i
$544$	−7.31508	+	12.6701i	−0.313632	+	0.543226i
$545$	4.16689			0.178490
$546$		0			0
$547$	−2.56174			−0.109532			−0.0547660	−	0.998499i	$-0.517441\pi$
$547$	−2.56174			−0.109532			−0.0547660	+	0.998499i	$0.517441\pi$
$548$	15.3794	−	26.6380i	0.656977	−	1.13792i
$549$	9.10192	+	15.7650i	0.388460	+	0.672833i
$550$	2.14159	+	3.70935i	0.0913179	+	0.158167i
$551$	−1.46924	+	2.54480i	−0.0625917	+	0.108412i
$552$	18.1506			0.772541
$553$		0			0
$554$	0.146321			0.00621660
$555$	1.27856	−	2.21453i	0.0542719	−	0.0940016i
$556$	−6.40836	−	11.0996i	−0.271775	−	0.470728i
$557$	13.7221	+	23.7674i	0.581424	+	1.00706i	0.995311	+	0.0967277i	$0.0308376\pi$
$557$	13.7221	+	23.7674i	0.581424	+	1.00706i	−0.413887	+	0.910328i	$0.635829\pi$
$558$	−6.65584	+	11.5283i	−0.281764	+	0.488030i
$559$	−8.43685			−0.356841
$560$		0			0
$561$	77.3567			3.26600
$562$	−0.151719	+	0.262785i	−0.00639988	+	0.0110849i
$563$	−0.0813542	−	0.140910i	−0.00342867	−	0.00593863i	0.864306	−	0.502966i	$-0.167758\pi$
$563$	−0.0813542	−	0.140910i	−0.00342867	−	0.00593863i	−0.867735	+	0.497028i	$0.834425\pi$
$564$	6.76312	+	11.7141i	0.284779	+	0.493251i
$565$	8.63353	−	14.9537i	0.363216	−	0.629108i
$566$	−1.07278			−0.0450925
$567$		0			0
$568$	7.13273			0.299283
$569$	6.19503	−	10.7301i	0.259709	−	0.449830i	−0.706455	−	0.707758i	$-0.749707\pi$
$569$	6.19503	−	10.7301i	0.259709	−	0.449830i	0.966164	+	0.257929i	$0.0830399\pi$
$570$	1.55796	+	2.69846i	0.0652556	+	0.113026i
$571$	10.9061	+	18.8899i	0.456405	+	0.790517i	0.998768	−	0.0496275i	$-0.0158034\pi$
$571$	10.9061	+	18.8899i	0.456405	+	0.790517i	−0.542363	+	0.840145i	$0.682470\pi$
$572$	5.31200	−	9.20066i	0.222106	−	0.384699i
$573$	−47.5066			−1.98462
$574$		0			0
$575$	17.6407			0.735669
$576$	17.3926	−	30.1249i	0.724693	−	1.25520i
$577$	−3.03292	−	5.25316i	−0.126262	−	0.218692i	0.795964	−	0.605345i	$-0.206965\pi$
$577$	−3.03292	−	5.25316i	−0.126262	−	0.218692i	−0.922226	+	0.386652i	$0.873631\pi$
$578$	−0.838321	−	1.45201i	−0.0348696	−	0.0603958i
$579$	20.4408	−	35.4045i	0.849490	−	1.47136i
$580$	2.88581			0.119827
$581$		0			0
$582$	10.3993			0.431067
$583$	5.03570	−	8.72209i	0.208557	−	0.361232i
$584$	1.63353	+	2.82935i	0.0675958	+	0.117079i
$585$	3.91974	+	6.78919i	0.162061	+	0.280699i
$586$	−1.99329	+	3.45248i	−0.0823420	+	0.142620i
$587$	20.5820			0.849510			0.424755	−	0.905308i	$-0.360360\pi$
$587$	20.5820			0.849510			0.424755	+	0.905308i	$0.360360\pi$
$588$		0			0
$589$	25.9726			1.07018
$590$	−0.165378	+	0.286443i	−0.00680850	+	0.0117927i
$591$	2.13666	+	3.70080i	0.0878903	+	0.152230i
$592$	−1.09782	−	1.90148i	−0.0451202	−	0.0781505i
$593$	12.0198	−	20.8189i	0.493595	−	0.854932i	−0.506378	−	0.862312i	$-0.669016\pi$
$593$	12.0198	−	20.8189i	0.493595	−	0.854932i	0.999973	+	0.00738005i	$0.00234917\pi$
$594$	10.4349			0.428151
$595$		0			0
$596$	37.7314			1.54554
$597$	19.4574	−	33.7011i	0.796337	−	1.37930i
$598$	0.793822	+	1.37494i	0.0324618	+	0.0562255i
$599$	−16.1261	−	27.9313i	−0.658896	−	1.14124i	−0.980902	−	0.194504i	$-0.937690\pi$
$599$	−16.1261	−	27.9313i	−0.658896	−	1.14124i	0.322005	−	0.946738i	$-0.395643\pi$
$600$	−4.44773	+	7.70369i	−0.181578	+	0.314502i
$601$	5.21454			0.212705			0.106353	−	0.994328i	$-0.466083\pi$
$601$	5.21454			0.212705			0.106353	+	0.994328i	$0.466083\pi$
$602$		0			0
$603$	−36.2020			−1.47426
$604$	10.3138	−	17.8640i	0.419663	−	0.726877i
$605$	13.8508	+	23.9903i	0.563115	+	0.975344i
$606$	0.388008	+	0.672050i	0.0157618	+	0.0273002i
$607$	−4.53524	+	7.85527i	−0.184080	+	0.318836i	−0.943266	−	0.332038i	$-0.892264\pi$
$607$	−4.53524	+	7.85527i	−0.184080	+	0.318836i	0.759186	+	0.650873i	$0.225597\pi$
$608$	8.54165			0.346410
$609$		0			0
$610$	1.26563			0.0512437
$611$	−1.20461	+	2.08645i	−0.0487334	+	0.0844087i
$612$	25.4638	+	44.1045i	1.02931	+	1.78282i
$613$	−10.0460	−	17.4002i	−0.405754	−	0.702786i	0.588655	−	0.808384i	$-0.299658\pi$
$613$	−10.0460	−	17.4002i	−0.405754	−	0.702786i	−0.994409	+	0.105598i	$0.966324\pi$
$614$	2.63843	−	4.56990i	0.106478	−	0.184426i
$615$	44.3357			1.78779
$616$		0			0
$617$	−12.9556			−0.521572			−0.260786	−	0.965397i	$-0.583982\pi$
$617$	−12.9556			−0.521572			−0.260786	+	0.965397i	$0.583982\pi$
$618$	4.91732	−	8.51704i	0.197803	−	0.342606i
$619$	22.1822	+	38.4207i	0.891578	+	1.54426i	0.837983	+	0.545696i	$0.183735\pi$
$619$	22.1822	+	38.4207i	0.891578	+	1.54426i	0.0535955	+	0.998563i	$0.482932\pi$
$620$	−12.7535	−	22.0897i	−0.512193	−	0.887145i
$621$	21.4887	−	37.2195i	0.862310	−	1.49357i
$622$	−2.88327			−0.115608
$623$		0			0
$624$	10.4281			0.417459
$625$	0.826381	−	1.43133i	0.0330553	−	0.0572534i
$626$	0.00686958	+	0.0118985i	0.000274563	+	0.000475558i
$627$	−22.5819	−	39.1130i	−0.901834	−	1.56202i
$628$	−14.5457	+	25.1938i	−0.580435	+	1.00534i
$629$	2.95880			0.117975
$630$		0			0
$631$	6.61717			0.263426			0.131713	−	0.991288i	$-0.457952\pi$
$631$	6.61717			0.263426			0.131713	+	0.991288i	$0.457952\pi$
$632$	−9.13737	+	15.8264i	−0.363465	+	0.629540i
$633$	−5.04781	−	8.74306i	−0.200632	−	0.347506i
$634$	−2.13037	−	3.68991i	−0.0846079	−	0.146545i
$635$	11.2415	−	19.4708i	0.446105	−	0.772676i
$636$	10.2719			0.407309
$637$		0			0
$638$	1.51771			0.0600866
$639$	18.7323	−	32.4454i	0.741040	−	1.28352i
$640$	−5.55569	−	9.62273i	−0.219608	−	0.380372i
$641$	−9.47834	−	16.4170i	−0.374372	−	0.648432i	0.615861	−	0.787855i	$-0.288808\pi$
$641$	−9.47834	−	16.4170i	−0.374372	−	0.648432i	−0.990233	+	0.139424i	$0.955475\pi$
$642$	0.263850	−	0.457001i	0.0104133	−	0.0180364i
$643$	13.4019			0.528517			0.264259	−	0.964452i	$-0.414873\pi$
$643$	13.4019			0.528517			0.264259	+	0.964452i	$0.414873\pi$
$644$		0			0
$645$	35.2231			1.38691
$646$	−1.80269	+	3.12234i	−0.0709257	+	0.122847i
$647$	−21.3794	−	37.0302i	−0.840511	−	1.45581i	−0.889463	−	0.457007i	$-0.848922\pi$
$647$	−21.3794	−	37.0302i	−0.840511	−	1.45581i	0.0489522	−	0.998801i	$-0.484412\pi$
$648$	2.31456	+	4.00894i	0.0909245	+	0.157486i
$649$	2.39708	−	4.15186i	0.0940936	−	0.162975i
$650$	−0.778091			−0.0305192
$651$		0			0
$652$	45.9593			1.79991
$653$	−5.49260	+	9.51346i	−0.214942	+	0.372290i	−0.953255	−	0.302168i	$-0.902290\pi$
$653$	−5.49260	+	9.51346i	−0.214942	+	0.372290i	0.738313	+	0.674459i	$0.235623\pi$
$654$	1.11755	+	1.93565i	0.0436995	+	0.0756898i
$655$	8.70228	+	15.0728i	0.340026	+	0.588943i
$656$	19.0342	−	32.9682i	0.743161	−	1.28719i
$657$	17.1602			0.669483
$658$		0			0
$659$	−17.7614			−0.691884			−0.345942	−	0.938256i	$-0.612441\pi$
$659$	−17.7614			−0.691884			−0.345942	+	0.938256i	$0.612441\pi$
$660$	−22.1771	+	38.4119i	−0.863243	+	1.49518i
$661$	−4.09127	−	7.08629i	−0.159132	−	0.275625i	0.775424	−	0.631441i	$-0.217536\pi$
$661$	−4.09127	−	7.08629i	−0.159132	−	0.275625i	−0.934556	+	0.355816i	$0.884203\pi$
$662$	−4.07342	−	7.05538i	−0.158318	−	0.274215i
$663$	−7.02636	+	12.1700i	−0.272881	+	0.472644i
$664$	−11.9103			−0.462210
$665$		0			0
$666$	0.885374			0.0343076
$667$	3.12541	−	5.41337i	0.121016	−	0.209607i
$668$	−6.87428	−	11.9066i	−0.265974	−	0.460680i
$669$	14.4189	+	24.9742i	0.557466	+	0.965560i
$670$	−1.25848	+	2.17975i	−0.0486192	+	0.0842110i
$671$	−18.3447			−0.708189
$672$		0			0
$673$	9.30129			0.358539			0.179269	−	0.983800i	$-0.442627\pi$
$673$	9.30129			0.358539			0.179269	+	0.983800i	$0.442627\pi$
$674$	0.319990	−	0.554238i	0.0123255	−	0.0213485i
$675$	10.5314	+	18.2409i	0.405354	+	0.702094i
$676$	0.964986	+	1.67141i	0.0371149	+	0.0642848i
$677$	20.5776	−	35.6415i	0.790862	−	1.36981i	−0.134572	−	0.990904i	$-0.542966\pi$
$677$	20.5776	−	35.6415i	0.790862	−	1.36981i	0.925434	−	0.378909i	$-0.123701\pi$
$678$	9.26195			0.355703
$679$		0			0
$680$	7.20997			0.276490
$681$	−17.5599	+	30.4147i	−0.672897	+	1.16549i
$682$	−6.70734	−	11.6175i	−0.256837	−	0.444856i
$683$	−19.6421	−	34.0211i	−0.751583	−	1.30178i	−0.947055	−	0.321071i	$-0.895957\pi$
$683$	−19.6421	−	34.0211i	−0.751583	−	1.30178i	0.195472	−	0.980709i	$-0.437376\pi$
$684$	14.8667	−	25.7499i	0.568443	−	0.984572i
$685$	−22.8727			−0.873921
$686$		0			0
$687$	11.7866			0.449685
$688$	15.1220	−	26.1920i	0.576519	−	0.998561i
$689$	0.914793	+	1.58447i	0.0348509	+	0.0603634i
$690$	−3.31413	−	5.74025i	−0.126167	−	0.218527i
$691$	1.51678	−	2.62713i	0.0577009	−	0.0999409i	−0.835732	−	0.549137i	$-0.814956\pi$
$691$	1.51678	−	2.62713i	0.0577009	−	0.0999409i	0.893433	+	0.449197i	$0.148290\pi$
$692$	−21.6865			−0.824397
$693$		0			0
$694$	−0.130336			−0.00494748
$695$	−4.76534	+	8.25382i	−0.180760	+	0.313085i
$696$	1.57601	+	2.72973i	0.0597385	+	0.103470i
$697$	25.6501	+	44.4273i	0.971567	+	1.68280i
$698$	1.58037	−	2.73728i	0.0598179	−	0.103608i
$699$	36.4938			1.38032
$700$		0			0
$701$	−26.2320			−0.990767			−0.495384	−	0.868674i	$-0.664972\pi$
$701$	−26.2320			−0.990767			−0.495384	+	0.868674i	$0.664972\pi$
$702$	−0.947814	+	1.64166i	−0.0357729	+	0.0619606i
$703$	−0.863732	−	1.49603i	−0.0325763	−	0.0564237i
$704$	17.5272	+	30.3580i	0.660582	+	1.14416i
$705$	5.02915	−	8.71074i	0.189409	−	0.328065i
$706$	4.10963			0.154668
$707$		0			0
$708$	4.88962			0.183763
$709$	3.93885	−	6.82229i	0.147927	−	0.256216i	−0.782534	−	0.622607i	$-0.786073\pi$
$709$	3.93885	−	6.82229i	0.147927	−	0.256216i	0.930461	+	0.366391i	$0.119407\pi$
$710$	−1.30237	−	2.25577i	−0.0488771	−	0.0846576i
$711$	47.9941	+	83.1282i	1.79992	+	3.11755i
$712$	−0.517553	+	0.896428i	−0.0193961	+	0.0335951i
$713$	−55.2497			−2.06912
$714$		0			0
$715$	−7.90015			−0.295449
$716$	−12.7325	+	22.0534i	−0.475837	+	0.824173i
$717$	−19.4124	−	33.6232i	−0.724968	−	1.25568i
$718$	1.12560	+	1.94960i	0.0420070	+	0.0727583i
$719$	−22.8328	+	39.5476i	−0.851519	+	1.47487i	0.0283174	+	0.999599i	$0.490985\pi$
$719$	−22.8328	+	39.5476i	−0.851519	+	1.47487i	−0.879837	+	0.475276i	$0.842348\pi$
$720$	−28.1025			−1.04732
$721$		0			0
$722$	−2.92295			−0.108781
$723$	−29.6508	+	51.3568i	−1.10273	+	1.90998i
$724$	−13.2603	−	22.9675i	−0.492815	−	0.853580i
$725$	1.53174	+	2.65305i	0.0568873	+	0.0985317i
$726$	−7.42948	+	12.8682i	−0.275734	+	0.477585i
$727$	37.5947			1.39431			0.697155	−	0.716921i	$-0.254449\pi$
$727$	37.5947			1.39431			0.697155	+	0.716921i	$0.254449\pi$
$728$		0			0
$729$	−38.2013			−1.41486
$730$	0.596534	−	1.03323i	0.0220787	−	0.0382414i
$731$	20.3780	+	35.2958i	0.753709	+	1.30546i
$732$	−9.35499	−	16.2033i	−0.345771	−	0.598892i
$733$	−26.5905	+	46.0561i	−0.982143	+	1.70112i	−0.328139	+	0.944629i	$0.606422\pi$
$733$	−26.5905	+	46.0561i	−0.982143	+	1.70112i	−0.654003	+	0.756492i	$0.726912\pi$
$734$	1.37363			0.0507018
$735$		0			0
$736$	−18.1701			−0.669758
$737$	18.2411	−	31.5945i	0.671919	−	1.16380i
$738$	7.67538	+	13.2941i	0.282535	+	0.489364i
$739$	−20.9816	−	36.3412i	−0.771822	−	1.33683i	−0.936564	−	0.350498i	$-0.886012\pi$
$739$	−20.9816	−	36.3412i	−0.771822	−	1.33683i	0.164742	−	0.986337i	$-0.447321\pi$
$740$	−0.848250	+	1.46921i	−0.0311823	+	0.0540093i
$741$	8.20452			0.301401
$742$		0			0
$743$	−38.5424			−1.41398			−0.706991	−	0.707222i	$-0.749948\pi$
$743$	−38.5424			−1.41398			−0.706991	+	0.707222i	$0.749948\pi$
$744$	13.9300	−	24.1275i	0.510699	−	0.884557i
$745$	−14.0288	−	24.2986i	−0.513975	−	0.890232i
$746$	1.34201	+	2.32444i	0.0491346	+	0.0851037i
$747$	−31.2795	+	54.1777i	−1.14446	+	1.98226i
$748$	−51.3216			−1.87650
$749$		0			0
$750$	8.77242			0.320323
$751$	−18.1217	+	31.3877i	−0.661270	+	1.14535i	0.319013	+	0.947750i	$0.396649\pi$
$751$	−18.1217	+	31.3877i	−0.661270	+	1.14535i	−0.980282	+	0.197602i	$0.936685\pi$
$752$	−4.31822	−	7.47938i	−0.157469	−	0.272745i
$753$	−25.0062	−	43.3119i	−0.911275	−	1.57837i
$754$	−0.137855	+	0.238771i	−0.00502037	+	0.00869553i
$755$	−15.3390			−0.558242
$756$		0			0
$757$	19.4752			0.707837			0.353919	−	0.935276i	$-0.384849\pi$
$757$	19.4752			0.707837			0.353919	+	0.935276i	$0.384849\pi$
$758$	0.481184	−	0.833435i	0.0174774	−	0.0302717i
$759$	48.0369	+	83.2024i	1.74363	+	3.02006i
$760$	−2.10473	−	3.64550i	−0.0763465	−	0.132236i
$761$	25.9529	−	44.9518i	0.940793	−	1.62950i	0.176831	−	0.984241i	$-0.443415\pi$
$761$	25.9529	−	44.9518i	0.940793	−	1.62950i	0.763963	−	0.645261i	$-0.223251\pi$
$762$	12.0597			0.436878
$763$		0			0
$764$	31.5178			1.14028
$765$	18.9352	−	32.7967i	0.684603	−	1.18577i
$766$	−0.609013	−	1.05484i	−0.0220045	−	0.0381129i
$767$	0.435457	+	0.754234i	0.0157234	+	0.0272338i
$768$	−15.5448	+	26.9244i	−0.560925	+	0.971550i
$769$	−7.31376			−0.263741			−0.131870	−	0.991267i	$-0.542098\pi$
$769$	−7.31376			−0.263741			−0.131870	+	0.991267i	$0.542098\pi$
$770$		0			0
$771$	−22.2452			−0.801142
$772$	−13.5613	+	23.4888i	−0.488081	+	0.845381i
$773$	7.09220	+	12.2841i	0.255089	+	0.441827i	0.964920	−	0.262545i	$-0.0845620\pi$
$773$	7.09220	+	12.2841i	0.255089	+	0.441827i	−0.709831	+	0.704372i	$0.751229\pi$
$774$	6.09780	+	10.5617i	0.219181	+	0.379632i
$775$	13.5387	−	23.4497i	0.486324	−	0.842339i

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.132313 + 0.229173i) q^{2} +(-1.45452 - 2.51930i) q^{3} +(0.964986 + 1.67141i) q^{4} +(0.717577 - 1.24288i) q^{5} +0.769807 q^{6} -1.03998 q^{8} +(-2.73124 + 4.73064i) q^{9} +O(q^{10})\)	\(q+(-0.132313 + 0.229173i) q^{2} +(-1.45452 - 2.51930i) q^{3} +(0.964986 + 1.67141i) q^{4} +(0.717577 - 1.24288i) q^{5} +0.769807 q^{6} -1.03998 q^{8} +(-2.73124 + 4.73064i) q^{9} +(0.189890 + 0.328899i) q^{10} +(-2.75237 - 4.76725i) q^{11} +(2.80718 - 4.86217i) q^{12} +1.00000 q^{13} -4.17491 q^{15} +(-1.79237 + 3.10448i) q^{16} +(-2.41536 - 4.18353i) q^{17} +(-0.722758 - 1.25185i) q^{18} +(-1.41018 + 2.44250i) q^{19} +2.76981 q^{20} +1.45670 q^{22} +(2.99978 - 5.19577i) q^{23} +(1.51266 + 2.62001i) q^{24} +(1.47017 + 2.54640i) q^{25} +(-0.132313 + 0.229173i) q^{26} +7.16341 q^{27} +1.04188 q^{29} +(0.552396 - 0.956778i) q^{30} +(-4.60448 - 7.97519i) q^{31} +(-1.51428 - 2.62282i) q^{32} +(-8.00674 + 13.8681i) q^{33} +1.27834 q^{34} -10.5424 q^{36} +(-0.306249 + 0.530438i) q^{37} +(-0.373171 - 0.646351i) q^{38} +(-1.45452 - 2.51930i) q^{39} +(-0.746262 + 1.29256i) q^{40} -10.6196 q^{41} -8.43685 q^{43} +(5.31200 - 9.20066i) q^{44} +(3.91974 + 6.78919i) q^{45} +(0.793822 + 1.37494i) q^{46} +(-1.20461 + 2.08645i) q^{47} +10.4281 q^{48} -0.778091 q^{50} +(-7.02636 + 12.1700i) q^{51} +(0.964986 + 1.67141i) q^{52} +(0.914793 + 1.58447i) q^{53} +(-0.947814 + 1.64166i) q^{54} -7.90015 q^{55} +8.20452 q^{57} +(-0.137855 + 0.238771i) q^{58} +(0.435457 + 0.754234i) q^{59} +(-4.02873 - 6.97797i) q^{60} +(1.66626 - 2.88605i) q^{61} +2.43693 q^{62} -6.36804 q^{64} +(0.717577 - 1.24288i) q^{65} +(-2.11880 - 3.66986i) q^{66} +(3.31370 + 5.73951i) q^{67} +(4.66158 - 8.07410i) q^{68} -17.4529 q^{69} -6.85856 q^{71} +(2.84042 - 4.91975i) q^{72} +(-1.57074 - 2.72060i) q^{73} +(-0.0810415 - 0.140368i) q^{74} +(4.27676 - 7.40757i) q^{75} -5.44322 q^{76} +0.769807 q^{78} +(8.78614 - 15.2180i) q^{79} +(2.57233 + 4.45540i) q^{80} +(-2.22559 - 3.85484i) q^{81} +(1.40511 - 2.43372i) q^{82} +11.4525 q^{83} -6.93283 q^{85} +(1.11631 - 1.93350i) q^{86} +(-1.51543 - 2.62480i) q^{87} +(2.86240 + 4.95782i) q^{88} +(0.497659 - 0.861970i) q^{89} -2.07454 q^{90} +11.5790 q^{92} +(-13.3946 + 23.2001i) q^{93} +(-0.318772 - 0.552130i) q^{94} +(2.02383 + 3.50537i) q^{95} +(-4.40510 + 7.62986i) q^{96} +13.5090 q^{97} +30.0695 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{3} - 4 q^{4} - 6 q^{5} + 8 q^{6} - 6 q^{9}+O(q^{10}) \) 12 * q - 8 * q^3 - 4 * q^4 - 6 * q^5 + 8 * q^6 - 6 * q^9	\( 12 q - 8 q^{3} - 4 q^{4} - 6 q^{5} + 8 q^{6} - 6 q^{9} - 4 q^{10} - 4 q^{11} + 4 q^{12} + 12 q^{13} + 24 q^{15} - 16 q^{17} + 4 q^{18} - 2 q^{19} + 32 q^{20} - 24 q^{22} + 6 q^{23} - 12 q^{24} + 4 q^{25} + 40 q^{27} - 12 q^{29} - 6 q^{31} + 20 q^{32} - 4 q^{33} - 48 q^{36} - 8 q^{38} - 8 q^{39} - 4 q^{40} - 16 q^{41} + 4 q^{43} + 4 q^{44} - 14 q^{45} - 8 q^{46} - 30 q^{47} - 16 q^{48} + 16 q^{50} + 4 q^{51} - 4 q^{52} + 14 q^{53} + 48 q^{54} - 16 q^{55} + 8 q^{57} + 8 q^{58} - 24 q^{59} - 12 q^{60} + 56 q^{62} - 40 q^{64} - 6 q^{65} + 4 q^{66} - 16 q^{67} - 28 q^{68} - 40 q^{69} + 16 q^{71} - 28 q^{72} + 6 q^{73} + 12 q^{74} - 12 q^{75} - 32 q^{76} + 8 q^{78} + 22 q^{79} + 28 q^{80} - 46 q^{81} + 40 q^{82} + 100 q^{83} - 16 q^{85} + 16 q^{86} + 16 q^{87} + 44 q^{88} - 26 q^{89} - 80 q^{90} + 40 q^{92} - 16 q^{93} + 32 q^{94} + 6 q^{95} + 20 q^{96} - 28 q^{97} + 24 q^{99}+O(q^{100}) \) 12 * q - 8 * q^3 - 4 * q^4 - 6 * q^5 + 8 * q^6 - 6 * q^9 - 4 * q^10 - 4 * q^11 + 4 * q^12 + 12 * q^13 + 24 * q^15 - 16 * q^17 + 4 * q^18 - 2 * q^19 + 32 * q^20 - 24 * q^22 + 6 * q^23 - 12 * q^24 + 4 * q^25 + 40 * q^27 - 12 * q^29 - 6 * q^31 + 20 * q^32 - 4 * q^33 - 48 * q^36 - 8 * q^38 - 8 * q^39 - 4 * q^40 - 16 * q^41 + 4 * q^43 + 4 * q^44 - 14 * q^45 - 8 * q^46 - 30 * q^47 - 16 * q^48 + 16 * q^50 + 4 * q^51 - 4 * q^52 + 14 * q^53 + 48 * q^54 - 16 * q^55 + 8 * q^57 + 8 * q^58 - 24 * q^59 - 12 * q^60 + 56 * q^62 - 40 * q^64 - 6 * q^65 + 4 * q^66 - 16 * q^67 - 28 * q^68 - 40 * q^69 + 16 * q^71 - 28 * q^72 + 6 * q^73 + 12 * q^74 - 12 * q^75 - 32 * q^76 + 8 * q^78 + 22 * q^79 + 28 * q^80 - 46 * q^81 + 40 * q^82 + 100 * q^83 - 16 * q^85 + 16 * q^86 + 16 * q^87 + 44 * q^88 - 26 * q^89 - 80 * q^90 + 40 * q^92 - 16 * q^93 + 32 * q^94 + 6 * q^95 + 20 * q^96 - 28 * q^97 + 24 * q^99

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