LMFDB - Embedded newform 637.2.e.o.508.3

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			508.3
Root			$0.954516 + 1.65327i$ of defining polynomial
Character	$\chi$	$=$	637.508
Dual form			637.2.e.o.79.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.132313 - 0.229173i) q^{2} +(1.45452 - 2.51930i) q^{3} +(0.964986 - 1.67141i) q^{4} +(-0.717577 - 1.24288i) q^{5} -0.769807 q^{6} -1.03998 q^{8} +(-2.73124 - 4.73064i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.132313	−	0.229173i	−0.0935596	−	0.162050i	0.815447	−	0.578832i	$-0.196491\pi$
$2$	−0.132313	−	0.229173i	−0.0935596	−	0.162050i	−0.909007	+	0.416782i	$0.863158\pi$
$3$	1.45452	−	2.51930i	0.839765	−	1.45452i	−0.0503252	−	0.998733i	$-0.516026\pi$
$3$	1.45452	−	2.51930i	0.839765	−	1.45452i	0.890091	−	0.455784i	$-0.150641\pi$
$4$	0.964986	−	1.67141i	0.482493	−	0.835703i
$5$	−0.717577	−	1.24288i	−0.320910	−	0.555833i	0.659766	−	0.751471i	$-0.270655\pi$
$5$	−0.717577	−	1.24288i	−0.320910	−	0.555833i	−0.980676	+	0.195639i	$0.937322\pi$
$6$	−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	0.0682678	+	0.997667i	$0.478253\pi$
$11$	−2.75237	+	4.76725i	−0.829871	+	1.43738i	−0.898139	+	0.439712i	$0.855081\pi$
$12$	−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	−0.408963	−	0.912551i	$-0.634109\pi$
$17$	2.41536	−	4.18353i	0.585811	−	1.01465i	0.994774	−	0.102104i	$-0.0325573\pi$
$18$	−0.722758	+	1.25185i	−0.170356	+	0.295065i
$19$	1.41018	+	2.44250i	0.323518	+	0.560349i	0.981211	−	0.192937i	$-0.0618012\pi$
$19$	1.41018	+	2.44250i	0.323518	+	0.560349i	−0.657694	+	0.753286i	$0.728468\pi$
$20$	−2.76981			−0.619348
$21$		0			0
$22$	1.45670			0.310570
$23$	2.99978	+	5.19577i	0.625498	+	1.08339i	0.988444	+	0.151584i	$0.0484373\pi$
$23$	2.99978	+	5.19577i	0.625498	+	1.08339i	−0.362947	+	0.931810i	$0.618229\pi$
$24$	−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	−0.0734019	−	0.997302i	$-0.523386\pi$
$31$	4.60448	−	7.97519i	0.826988	−	1.43239i	0.900390	−	0.435083i	$-0.143281\pi$
$32$	−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	0.839754	−	0.542968i	$-0.182699\pi$
$37$	−0.306249	−	0.530438i	−0.0503470	−	0.0872035i	−0.890101	+	0.455764i	$0.849366\pi$
$38$	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	$-0.188768\pi$
$41$	10.6196			1.65850			0.829249	+	0.558879i	$0.188768\pi$
$42$		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	$-0.110444\pi$
$47$	1.20461	+	2.08645i	0.175711	+	0.304340i	−0.764696	+	0.644391i	$0.777111\pi$
$48$	−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	−0.796333	−	0.604859i	$-0.793230\pi$
$53$	0.914793	−	1.58447i	0.125657	−	0.217643i	0.921989	+	0.387215i	$0.126563\pi$
$54$	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	$-0.851389\pi$
$59$	−0.435457	+	0.754234i	−0.0566917	+	0.0981929i	0.836287	+	0.548292i	$0.184722\pi$
$60$	−4.02873	+	6.97797i	−0.520107	+	0.900851i
$61$	−1.66626	−	2.88605i	−0.213343	−	0.369521i	0.739416	−	0.673249i	$-0.235102\pi$
$61$	−1.66626	−	2.88605i	−0.213343	−	0.369521i	−0.952759	+	0.303728i	$0.901769\pi$
$62$	−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	−0.589469	−	0.807791i	$-0.700663\pi$
$67$	3.31370	−	5.73951i	0.404833	−	0.701192i	0.994302	+	0.106599i	$0.0339962\pi$
$68$	−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	$-0.774480\pi$
$73$	1.57074	−	2.72060i	0.183841	−	0.318422i	0.943185	+	0.332267i	$0.107814\pi$
$74$	−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	0.625116	+	0.780532i	$0.285052\pi$
$79$	8.78614	+	15.2180i	0.988518	+	1.71216i	0.363402	+	0.931632i	$0.381615\pi$
$80$	−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	$-0.716346\pi$
$83$	−11.4525			−1.25708			−0.628538	+	0.777779i	$0.716346\pi$
$84$		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	$-0.183466\pi$
$89$	−0.497659	−	0.861970i	−0.0527517	−	0.0913687i	−0.891195	+	0.453619i	$0.850133\pi$
$90$	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	$-0.740555\pi$
$97$	−13.5090			−1.37163			−0.685817	+	0.727774i	$0.740555\pi$
$98$		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	$-0.849304\pi$
$101$	−0.504033	+	0.873011i	−0.0501532	+	0.0868678i	0.839859	+	0.542805i	$0.182638\pi$
$102$	−1.85936	+	3.22051i	−0.184104	+	0.318878i
$103$	−6.38772	−	11.0639i	−0.629401	−	1.09015i	−0.987672	−	0.156537i	$-0.949967\pi$
$103$	−6.38772	−	11.0639i	−0.629401	−	1.09015i	0.358271	−	0.933618i	$-0.383366\pi$
$104$	1.03998			0.101978
$105$		0			0
$106$	−0.484157			−0.0470255
$107$	0.342748	+	0.593656i	0.0331347	+	0.0573909i	0.882117	−	0.471030i	$-0.156118\pi$
$107$	0.342748	+	0.593656i	0.0331347	+	0.0573909i	−0.848983	+	0.528421i	$0.822784\pi$
$108$	−6.91259	+	11.9730i	−0.665165	+	1.15210i
$109$	1.45172	−	2.51446i	0.139050	−	0.240841i	−0.788087	−	0.615563i	$-0.788929\pi$
$109$	1.45172	−	2.51446i	0.139050	−	0.240841i	0.927137	+	0.374722i	$0.122262\pi$
$110$	−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	0.999396	+	0.0347403i	$0.0110604\pi$
$131$	6.06366	+	10.5026i	0.529784	+	0.917613i	−0.469612	+	0.882873i	$0.655606\pi$
$132$	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	0.293918	+	0.955831i	$0.405041\pi$
$137$	−7.96873	+	13.8022i	−0.680815	+	1.17921i	−0.974733	+	0.223375i	$0.928293\pi$
$138$	−2.30925	−	3.99974i	−0.196577	−	0.340481i
$139$	6.64088			0.563272			0.281636	−	0.959521i	$-0.409123\pi$
$139$	6.64088			0.563272			0.281636	+	0.959521i	$0.409123\pi$
$140$		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	0.919084	+	0.394061i	$0.128930\pi$
$149$	9.77512	+	16.9310i	0.800809	+	1.38704i	−0.118275	+	0.992981i	$0.537736\pi$
$150$	−1.13175	+	1.96024i	−0.0924066	+	0.160053i
$151$	−5.34401	+	9.25610i	−0.434890	+	0.753251i	−0.997287	−	0.0736163i	$-0.976546\pi$
$151$	−5.34401	+	9.25610i	−0.434890	+	0.753251i	0.562397	+	0.826867i	$0.309879\pi$
$152$	−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	0.391099	+	0.920349i	$0.372095\pi$
$157$	−7.53672	+	13.0540i	−0.601496	+	1.04182i	−0.992595	+	0.121473i	$0.961238\pi$
$158$	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	0.778847	+	0.627214i	$0.215805\pi$
$163$	11.9067	+	20.6231i	0.932607	+	1.61532i	0.153760	+	0.988108i	$0.450862\pi$
$164$	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	$-0.411115\pi$
$167$	7.12371			0.551249			0.275625	+	0.961265i	$0.411115\pi$
$168$		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	$-0.0261826\pi$
$173$	5.61834	+	9.73125i	0.427155	+	0.739854i	−0.569464	+	0.822016i	$0.692849\pi$
$174$	−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	−0.506867	−	0.862025i	$-0.669196\pi$
$179$	6.59725	−	11.4268i	0.493102	−	0.854078i	0.999968	+	0.00794701i	$0.00252964\pi$
$180$	7.56500	+	13.1030i	0.563862	+	0.976637i
$181$	13.7414			1.02139			0.510696	−	0.859761i	$-0.329388\pi$
$181$	13.7414			1.02139			0.510696	+	0.859761i	$0.329388\pi$
$182$		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	0.994122	+	0.108269i	$0.0345308\pi$
$191$	8.16536	+	14.1428i	0.590824	+	1.02334i	−0.403297	+	0.915069i	$0.632136\pi$
$192$	−9.26242	+	16.0430i	−0.668458	+	1.15780i
$193$	7.02666	−	12.1705i	0.505790	−	0.876054i	−0.494187	−	0.869355i	$-0.664534\pi$
$193$	7.02666	−	12.1705i	0.505790	−	0.876054i	0.999978	−	0.00669897i	$-0.00213237\pi$
$194$	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	$-0.990575\pi$
$199$	−6.68860	+	11.5850i	−0.474142	+	0.821239i	0.525419	+	0.850844i	$0.323909\pi$
$200$	−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	$-0.392304\pi$
$223$	9.91318			0.663836			0.331918	+	0.943308i	$0.392304\pi$
$224$		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	$-0.702119\pi$
$227$	6.03634	−	10.4552i	0.400646	−	0.693939i	0.993804	+	0.111147i	$0.0354524\pi$
$228$	7.91725	−	13.7131i	0.524333	−	0.908171i
$229$	2.02586	+	3.50888i	0.133872	+	0.231874i	0.925166	−	0.379563i	$-0.123925\pi$
$229$	2.02586	+	3.50888i	0.133872	+	0.231874i	−0.791294	+	0.611436i	$0.790592\pi$
$230$	−2.27851			−0.150241
$231$		0			0
$232$	−1.08353			−0.0711372
$233$	−6.27250	−	10.8643i	−0.410925	−	0.711743i	0.584066	−	0.811706i	$-0.301461\pi$
$233$	−6.27250	−	10.8643i	−0.410925	−	0.711743i	−0.994991	+	0.0999629i	$0.968128\pi$
$234$	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	−0.324930	−	0.945738i	$-0.605341\pi$
$241$	10.1927	−	17.6542i	0.656568	−	1.13721i	0.981498	−	0.191471i	$-0.0613259\pi$
$242$	−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	$-0.682551\pi$
$251$	−17.1921			−1.08515			−0.542577	+	0.840006i	$0.682551\pi$
$252$		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	$-0.243323\pi$
$257$	−3.82348	−	6.62245i	−0.238502	−	0.413097i	−0.960285	+	0.279022i	$0.909990\pi$
$258$	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	−0.864464	−	0.502695i	$-0.832342\pi$
$263$	0.0505186	−	0.0875008i	0.00311511	−	0.00539553i	0.867579	+	0.497300i	$0.165675\pi$
$264$	−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	$-0.907445\pi$
$269$	−3.78426	+	6.55453i	−0.230730	+	0.399637i	0.727293	+	0.686327i	$0.240778\pi$
$270$	1.36026	−	2.35604i	0.0827827	−	0.143384i
$271$	−6.92768	−	11.9991i	−0.420826	−	0.728893i	0.575194	−	0.818017i	$-0.304927\pi$
$271$	−6.92768	−	11.9991i	−0.420826	−	0.728893i	−0.996021	+	0.0891242i	$0.971593\pi$
$272$	−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	−0.874212	−	0.485545i	$-0.838621\pi$
$277$	−0.276468	+	0.478856i	−0.0166113	+	0.0287717i	0.857600	+	0.514317i	$0.171954\pi$
$278$	−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	$-0.871780\pi$
$283$	−2.02698	+	3.51083i	−0.120491	+	0.208697i	0.799470	+	0.600706i	$0.205114\pi$
$284$	−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	$-0.645040\pi$
$293$	−15.0649			−0.880102			−0.440051	+	0.897973i	$0.645040\pi$
$294$		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	$-0.307315\pi$
$307$	19.9408			1.13808			0.569040	+	0.822310i	$0.307315\pi$
$308$		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	$-0.933300\pi$
$311$	−5.44780	+	9.43587i	−0.308916	+	0.535059i	0.669209	+	0.743074i	$0.266633\pi$
$312$	1.51266	−	2.62001i	0.0856376	−	0.148329i
$313$	−0.0259595	−	0.0449632i	−0.00146732	−	0.00254147i	0.865291	−	0.501270i	$-0.167134\pi$
$313$	−0.0259595	−	0.0449632i	−0.00146732	−	0.00254147i	−0.866758	+	0.498729i	$0.833800\pi$
$314$	3.98883			0.225103
$315$		0			0
$316$	33.9140			1.90781
$317$	−8.05049	−	13.9439i	−0.452161	−	0.783165i	0.546359	−	0.837551i	$-0.316013\pi$
$317$	−8.05049	−	13.9439i	−0.452161	−	0.783165i	−0.998520	+	0.0543857i	$0.982680\pi$
$318$	−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	−0.884679	−	0.466201i	$-0.845622\pi$
$331$	−15.3931	−	26.6616i	−0.846081	−	1.46546i	0.0385973	−	0.999255i	$-0.487711\pi$
$332$	−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	−0.859340	−	0.511405i	$-0.829125\pi$
$347$	0.246264	−	0.426541i	0.0132201	−	0.0228979i	0.872560	+	0.488507i	$0.162458\pi$
$348$	−2.92474	−	5.06580i	−0.156783	−	0.271555i
$349$	11.9442			0.639356			0.319678	−	0.947526i	$-0.396425\pi$
$349$	11.9442			0.639356			0.319678	+	0.947526i	$0.396425\pi$
$350$		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	$-0.697714\pi$
$353$	7.76497	−	13.4493i	0.413288	−	0.715835i	0.995247	+	0.0973828i	$0.0310471\pi$
$354$	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	0.956167	−	0.292821i	$-0.0945939\pi$
$359$	4.25354	+	7.36735i	0.224493	+	0.388834i	−0.731674	+	0.681655i	$0.761261\pi$
$360$	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	$-0.790076\pi$
$367$	2.59542	−	4.49540i	0.135480	−	0.234658i	0.925781	+	0.378061i	$0.123409\pi$
$368$	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	0.966928	−	0.255049i	$-0.0820918\pi$
$373$	5.07135	+	8.78384i	0.262585	+	0.454810i	−0.704343	+	0.709859i	$0.748758\pi$
$374$	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	$-0.129148\pi$
$383$	2.30140	+	3.98615i	0.117596	+	0.203683i	−0.801218	+	0.598372i	$0.795814\pi$
$384$	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	−0.999995	−	0.00329604i	$-0.998951\pi$
$389$	−9.80519	+	16.9831i	−0.497143	+	0.861077i	0.502852	+	0.864373i	$0.332284\pi$
$390$	−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	$-0.332767\pi$
$397$	−9.93173	−	17.2023i	−0.498459	−	0.863357i	−0.999998	+	0.00177809i	$0.999434\pi$
$398$	3.53996			0.177442
$399$		0			0
$400$	−10.5403			−0.527017
$401$	7.55587	+	13.0872i	0.377322	+	0.653541i	0.990672	−	0.136270i	$-0.0435116\pi$
$401$	7.55587	+	13.0872i	0.377322	+	0.653541i	−0.613350	+	0.789812i	$0.710178\pi$
$402$	−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	−0.0107701	+	0.999942i	$0.503428\pi$
$409$	−17.6222	+	30.5225i	−0.871360	+	1.50924i	−0.860590	+	0.509298i	$0.829905\pi$
$410$	−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	$-0.511702\pi$
$419$	−1.50468			−0.0735084			−0.0367542	+	0.999324i	$0.511702\pi$
$420$		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	−0.366574	+	0.930389i	$0.619469\pi$
$431$	−20.5327	+	35.5638i	−0.989027	+	1.71305i	−0.622454	+	0.782657i	$0.713864\pi$
$432$	12.8395	+	22.2386i	0.617740	+	1.06996i
$433$	−6.65603			−0.319869			−0.159934	−	0.987128i	$-0.551128\pi$
$433$	−6.65603			−0.319869			−0.159934	+	0.987128i	$0.551128\pi$
$434$		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	$-0.103743\pi$
$439$	4.11495	+	7.12730i	0.196396	+	0.340168i	−0.750961	+	0.660346i	$0.770410\pi$
$440$	−8.21596			−0.391681
$441$		0			0
$442$	1.27834			0.0608043
$443$	−8.84278	−	15.3161i	−0.420133	−	0.727692i	0.575819	−	0.817577i	$-0.304683\pi$
$443$	−8.84278	−	15.3161i	−0.420133	−	0.727692i	−0.995952	+	0.0898854i	$0.971350\pi$
$444$	−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	0.818305	−	0.574784i	$-0.194914\pi$
$457$	−1.89460	−	3.28154i	−0.0886255	−	0.153504i	−0.906930	+	0.421281i	$0.861581\pi$
$458$	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	$-0.598761\pi$
$461$	−13.1107			−0.610627			−0.305314	+	0.952252i	$0.598761\pi$
$462$		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	0.964097	+	0.265550i	$0.0855536\pi$
$467$	15.3869	+	26.6509i	0.712022	+	1.23326i	−0.252075	+	0.967708i	$0.581113\pi$
$468$	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	$-0.845825\pi$
$479$	−0.858699	+	1.48731i	−0.0392350	+	0.0679569i	0.845741	+	0.533593i	$0.179159\pi$
$480$	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	0.485994	+	0.873962i	$0.338458\pi$
$487$	−11.3403	+	19.6419i	−0.513877	+	0.890060i	−0.999870	+	0.0160982i	$0.994876\pi$
$488$	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	0.665030	−	0.746817i	$-0.268419\pi$
$499$	−7.01976	−	12.1586i	−0.314248	−	0.544293i	−0.979277	+	0.202524i	$0.935086\pi$
$500$	−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	$-0.502611\pi$
$503$	−0.367865			−0.0164023			−0.00820114	+	0.999966i	$0.502611\pi$
$504$		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	0.808668	+	0.588266i	$0.200189\pi$
$509$	20.6160	+	35.7079i	0.913787	+	1.58273i	0.105119	+	0.994460i	$0.466478\pi$
$510$	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	$-0.826074\pi$
$521$	0.520493	−	0.901521i	0.0228032	−	0.0394963i	0.877202	+	0.480122i	$0.159408\pi$
$522$	−0.753027	+	1.30428i	−0.0329591	+	0.0570868i
$523$	−10.0104	−	17.3386i	−0.437726	−	0.758163i	0.559788	−	0.828636i	$-0.310883\pi$
$523$	−10.0104	−	17.3386i	−0.437726	−	0.758163i	−0.997514	+	0.0704727i	$0.977549\pi$
$524$	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	0.951839	−	0.306597i	$-0.0991905\pi$
$541$	4.89375	+	8.47622i	0.210399	+	0.364421i	−0.741441	+	0.671018i	$0.765857\pi$
$542$	−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	−0.413887	−	0.910328i	$-0.635829\pi$
$557$	13.7221	−	23.7674i	0.581424	−	1.00706i	0.995311	−	0.0967277i	$-0.0308376\pi$
$558$	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	$-0.832242\pi$
$563$	0.0813542	−	0.140910i	0.00342867	−	0.00593863i	0.867735	+	0.497028i	$0.165575\pi$
$564$	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	0.966164	−	0.257929i	$-0.0830399\pi$
$569$	6.19503	+	10.7301i	0.259709	+	0.449830i	−0.706455	+	0.707758i	$0.749707\pi$
$570$	−1.55796	+	2.69846i	−0.0652556	+	0.113026i
$571$	10.9061	−	18.8899i	0.456405	−	0.790517i	−0.542363	−	0.840145i	$-0.682470\pi$
$571$	10.9061	−	18.8899i	0.456405	−	0.790517i	0.998768	+	0.0496275i	$0.0158034\pi$
$572$	−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	$-0.793035\pi$
$577$	3.03292	−	5.25316i	0.126262	−	0.218692i	0.922226	+	0.386652i	$0.126369\pi$
$578$	−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	$-0.639640\pi$
$587$	−20.5820			−0.849510			−0.424755	+	0.905308i	$0.639640\pi$
$588$		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	$-0.330984\pi$
$593$	−12.0198	−	20.8189i	−0.493595	−	0.854932i	−0.999973	+	0.00738005i	$0.997651\pi$
$594$	−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	0.322005	+	0.946738i	$0.395643\pi$
$599$	−16.1261	+	27.9313i	−0.658896	+	1.14124i	−0.980902	+	0.194504i	$0.937690\pi$
$600$	4.44773	+	7.70369i	0.181578	+	0.314502i
$601$	−5.21454			−0.212705			−0.106353	−	0.994328i	$-0.533917\pi$
$601$	−5.21454			−0.212705			−0.106353	+	0.994328i	$0.533917\pi$
$602$		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	$-0.107736\pi$
$607$	4.53524	+	7.85527i	0.184080	+	0.318836i	−0.759186	+	0.650873i	$0.774403\pi$
$608$	−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	−0.994409	−	0.105598i	$-0.966324\pi$
$613$	−10.0460	+	17.4002i	−0.405754	+	0.702786i	0.588655	+	0.808384i	$0.299658\pi$
$614$	−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	−0.0535955	+	0.998563i	$0.517068\pi$
$619$	−22.1822	+	38.4207i	−0.891578	+	1.54426i	−0.837983	+	0.545696i	$0.816265\pi$
$620$	−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	−0.990233	−	0.139424i	$-0.955475\pi$
$641$	−9.47834	+	16.4170i	−0.374372	+	0.648432i	0.615861	+	0.787855i	$0.288808\pi$
$642$	−0.263850	−	0.457001i	−0.0104133	−	0.0180364i
$643$	−13.4019			−0.528517			−0.264259	−	0.964452i	$-0.585127\pi$
$643$	−13.4019			−0.528517			−0.264259	+	0.964452i	$0.585127\pi$
$644$		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	−0.0489522	−	0.998801i	$-0.515588\pi$
$647$	21.3794	−	37.0302i	0.840511	−	1.45581i	0.889463	−	0.457007i	$-0.151078\pi$
$648$	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	0.738313	−	0.674459i	$-0.235623\pi$
$653$	−5.49260	−	9.51346i	−0.214942	−	0.372290i	−0.953255	+	0.302168i	$0.902290\pi$
$654$	−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	$-0.782464\pi$
$661$	4.09127	−	7.08629i	0.159132	−	0.275625i	0.934556	+	0.355816i	$0.115797\pi$
$662$	−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	−0.925434	−	0.378909i	$-0.876299\pi$
$677$	−20.5776	−	35.6415i	−0.790862	−	1.36981i	0.134572	−	0.990904i	$-0.457034\pi$
$678$	−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	0.195472	+	0.980709i	$0.437376\pi$
$683$	−19.6421	+	34.0211i	−0.751583	+	1.30178i	−0.947055	+	0.321071i	$0.895957\pi$
$684$	−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	$-0.185044\pi$
$691$	−1.51678	−	2.62713i	−0.0577009	−	0.0999409i	−0.893433	+	0.449197i	$0.851710\pi$
$692$	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	0.930461	−	0.366391i	$-0.119407\pi$
$709$	3.93885	+	6.82229i	0.147927	+	0.256216i	−0.782534	+	0.622607i	$0.786073\pi$
$710$	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	0.879837	+	0.475276i	$0.157652\pi$
$719$	22.8328	+	39.5476i	0.851519	+	1.47487i	−0.0283174	+	0.999599i	$0.509015\pi$
$720$	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	$-0.745551\pi$
$727$	−37.5947			−1.39431			−0.697155	+	0.716921i	$0.745551\pi$
$728$		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	0.654003	+	0.756492i	$0.273088\pi$
$733$	26.5905	+	46.0561i	0.982143	+	1.70112i	0.328139	+	0.944629i	$0.393578\pi$
$734$	−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	0.164742	+	0.986337i	$0.447321\pi$
$739$	−20.9816	+	36.3412i	−0.771822	+	1.33683i	−0.936564	+	0.350498i	$0.886012\pi$
$740$	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	−0.980282	−	0.197602i	$-0.936685\pi$
$751$	−18.1217	−	31.3877i	−0.661270	−	1.14535i	0.319013	−	0.947750i	$-0.396649\pi$
$752$	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	−0.763963	−	0.645261i	$-0.776749\pi$
$761$	−25.9529	−	44.9518i	−0.940793	−	1.62950i	−0.176831	−	0.984241i	$-0.556585\pi$
$762$	−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	$-0.457902\pi$
$769$	7.31376			0.263741			0.131870	+	0.991267i	$0.457902\pi$
$770$		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	$-0.915438\pi$
$773$	−7.09220	+	12.2841i	−0.255089	+	0.441827i	0.709831	+	0.704372i	$0.248771\pi$
$774$	6.09780	−	10.5617i	0.219181	−	0.379632i
$775$	−13.5387	−	23.4497i	−0.486324	−	0.842339i
$776$	14.0491			0.504332
$777$		0			0
$778$	5.18943			0.186050
$779$	14.9755	+	25.9384i	0.536553	+	0.929338i
$780$	4.02873	−	6.97797i	0.144252	−	0.249851i
$781$	18.8773	−	32.6964i	0.675483	−	1.16997i
$782$	−3.83473	−	6.64195i	−0.137130	−	0.237516i
$783$	−7.46341			−0.266721
$784$		0			0
$785$	21.6327			0.772104
$786$	−4.66785	−	8.08495i	−0.166497	−	0.288381i
$787$	15.6389	−	27.0873i	0.557465	−	0.965557i	−0.440242	−	0.897879i	$-0.645107\pi$
$787$	15.6389	−	27.0873i	0.557465	−	0.965557i	0.997707	−	0.0676785i	$-0.0215592\pi$
$788$	−1.41755	+	2.45526i	−0.0504980	+	0.0874651i
$789$	−0.146960	−	0.254543i	−0.00523193	−	0.00906196i
$790$	−6.67360			−0.237436
$791$		0			0
$792$	−31.2715			−1.11119
$793$	1.66626	+	2.88605i	0.0591708	+	0.102487i
$794$	−2.62820	+	4.55218i	−0.0932713	+	0.161551i
$795$	−3.81918	+	6.61501i	−0.135452	+	0.234610i
$796$	12.9088	+	22.3587i	0.457541	+	0.792484i
$797$	−20.2422			−0.717017			−0.358509	−	0.933526i	$-0.616715\pi$
$797$	−20.2422			−0.717017			−0.358509	+	0.933526i	$0.616715\pi$
$798$		0			0
$799$	11.6383			0.411733
$800$	4.45250	+	7.71196i	0.157420	+	0.272659i
$801$	−2.71845	+	4.70849i	−0.0960516	+	0.166366i
$802$	1.99948	−	3.46321i	0.0706042	−	0.122290i
$803$	8.64650	+	14.9762i	0.305128	+	0.528498i
$804$	−37.2086			−1.31225
$805$		0			0
$806$	2.43693			0.0858373
$807$	11.0085	+	19.0673i	0.387519	+	0.671202i
$808$	0.524182	−	0.907910i	0.0184407	−	0.0319402i
$809$	−3.94133	+	6.82658i	−0.138570	+	0.240010i	−0.926955	−	0.375171i	$-0.877584\pi$
$809$	−3.94133	+	6.82658i	−0.138570	+	0.240010i	0.788386	+	0.615181i	$0.210917\pi$
$810$	−0.845235	−	1.46399i	−0.0296985	−	0.0514393i
$811$	5.99962			0.210675			0.105338	−	0.994437i	$-0.466408\pi$
$811$	5.99962			0.210675			0.105338	+	0.994437i	$0.466408\pi$
$812$		0			0
$813$	−40.3057			−1.41358
$814$	−0.446113	−	0.772690i	−0.0156362	−	0.0270828i
$815$	17.0880	−	29.5973i	0.598566	−	1.03675i
$816$	−25.1877	+	43.6264i	−0.881746	+	1.52723i
$817$	−11.8975	−	20.6070i	−0.416240	−	0.720949i
$818$	9.32659			0.326096
$819$		0			0
$820$	−29.4142			−1.02719
$821$	9.58461	+	16.6010i	0.334505	+	0.579380i	0.983390	−	0.181507i	$-0.0580974\pi$
$821$	9.58461	+	16.6010i	0.334505	+	0.579380i	−0.648884	+	0.760887i	$0.724764\pi$
$822$	6.13439	−	10.6251i	0.213961	−	0.370592i
$823$	15.1867	−	26.3042i	0.529376	−	0.916907i	−0.470037	−	0.882647i	$-0.655759\pi$
$823$	15.1867	−	26.3042i	0.529376	−	0.916907i	0.999413	−	0.0342597i	$-0.0109073\pi$
$824$	6.64307	+	11.5061i	0.231422	+	0.400835i
$825$	47.0850			1.63929
$826$		0			0
$827$	−14.6870			−0.510717			−0.255359	−	0.966846i	$-0.582193\pi$
$827$	−14.6870			−0.510717			−0.255359	+	0.966846i	$0.582193\pi$
$828$	−31.6250	−	54.7760i	−1.09904	−	1.90360i
$829$	−17.4993	+	30.3096i	−0.607774	+	1.05270i	0.383832	+	0.923403i	$0.374604\pi$
$829$	−17.4993	+	30.3096i	−0.607774	+	1.05270i	−0.991606	+	0.129293i	$0.958729\pi$
$830$	2.17471	−	3.76671i	0.0754854	−	0.130745i
$831$	0.804253	+	1.39301i	0.0278992	+	0.0483229i
$832$	6.36804			0.220772
$833$		0			0
$834$	−5.11220			−0.177021
$835$	−5.11181	−	8.85391i	−0.176901	−	0.306402i
$836$	−14.9818	+	25.9492i	−0.518155	+	0.897471i
$837$	−32.9838	+	57.1295i	−1.14009	+	1.97469i
$838$	0.199089	+	0.344832i	0.00687742	+	0.0119120i
$839$	−27.6333			−0.954008			−0.477004	−	0.878901i	$-0.658277\pi$
$839$	−27.6333			−0.954008			−0.477004	+	0.878901i	$0.658277\pi$
$840$		0			0
$841$	−27.9145			−0.962568
$842$	3.24272	+	5.61656i	0.111752	+	0.193559i
$843$	1.66784	−	2.88879i	0.0574436	−	0.0994952i
$844$	3.34893	−	5.80051i	0.115275	−	0.199662i
$845$	−0.717577	−	1.24288i	−0.0246854	−	0.0427564i
$846$	−3.48257			−0.119733
$847$		0			0
$848$	−6.55859			−0.225223
$849$	5.89655	+	10.2131i	0.202369	+	0.350513i
$850$	−1.87937	+	3.25516i	−0.0644618	+	0.111651i
$851$	1.83736	−	3.18240i	0.0629838	−	0.109091i
$852$	19.2532	+	33.3475i	0.659603	+	1.14247i
$853$	−32.6336			−1.11735			−0.558676	−	0.829386i	$-0.688690\pi$
$853$	−32.6336			−1.11735			−0.558676	+	0.829386i	$0.688690\pi$
$854$		0			0
$855$	−22.1102			−0.756152
$856$	−0.356449	−	0.617388i	−0.0121832	−	0.0211019i
$857$	−9.43709	+	16.3455i	−0.322365	+	0.558352i	−0.980975	−	0.194132i	$-0.937811\pi$
$857$	−9.43709	+	16.3455i	−0.322365	+	0.558352i	0.658611	+	0.752484i	$0.271144\pi$
$858$	−2.11880	+	3.66986i	−0.0723345	+	0.125287i
$859$	7.91210	+	13.7042i	0.269957	+	0.467580i	0.968851	−	0.247646i	$-0.0796571\pi$
$859$	7.91210	+	13.7042i	0.269957	+	0.467580i	−0.698893	+	0.715226i	$0.746324\pi$
$860$	23.3684			0.796857
$861$		0			0
$862$	10.8670			0.370132
$863$	−26.1606	−	45.3115i	−0.890518	−	1.54242i	−0.839256	−	0.543737i	$-0.817009\pi$
$863$	−26.1606	−	45.3115i	−0.890518	−	1.54242i	−0.0512621	−	0.998685i	$-0.516324\pi$
$864$	10.8474	−	18.7883i	0.369037	−	0.639191i
$865$	8.06318	−	13.9658i	0.274156	−	0.474853i
$866$	0.880682	+	1.52539i	0.0299268	+	0.0518347i
$867$	−18.4313			−0.625959
$868$		0			0
$869$	−96.7309			−3.28137
$870$	0.575530	+	0.996847i	0.0195123	+	0.0337963i
$871$	−3.31370	+	5.73951i	−0.112281	+	0.194476i
$872$	−1.50975	+	2.61497i	−0.0511267	+	0.0885541i
$873$	36.8963	+	63.9063i	1.24875	+	2.16290i
$874$	4.47773			0.151461
$875$		0			0
$876$	−17.6373			−0.595911
$877$	27.0081	+	46.7794i	0.911999	+	1.57963i	0.811237	+	0.584717i	$0.198795\pi$
$877$	27.0081	+	46.7794i	0.911999	+	1.57963i	0.100762	+	0.994911i	$0.467872\pi$
$878$	1.08893	−	1.88607i	0.0367494	−	0.0636519i
$879$	−21.9122	+	37.9530i	−0.739079	+	1.28012i
$880$	−14.1600	−	24.5258i	−0.477333	−	0.826766i
$881$	42.0823			1.41779			0.708895	−	0.705314i	$-0.249194\pi$
$881$	42.0823			1.41779			0.708895	+	0.705314i	$0.249194\pi$
$882$		0			0
$883$	36.5314			1.22938			0.614689	−	0.788769i	$-0.289281\pi$
$883$	36.5314			1.22938			0.614689	+	0.788769i	$0.289281\pi$
$884$	4.66158	+	8.07410i	0.156786	+	0.271561i
$885$	1.81799	−	3.14886i	0.0611112	−	0.105848i
$886$	−2.34003	+	4.05306i	−0.0786150	+	0.136165i
$887$	−5.73240	−	9.92880i	−0.192475	−	0.333376i	0.753595	−	0.657339i	$-0.228318\pi$
$887$	−5.73240	−	9.92880i	−0.192475	−	0.333376i	−0.946070	+	0.323963i	$0.894985\pi$
$888$	1.85300			0.0621827
$889$		0			0
$890$	0.378001			0.0126706
$891$	−12.2513	−	21.2199i	−0.410434	−	0.710893i
$892$	9.56609	−	16.5689i	0.320296	−	0.554769i
$893$	−3.39744	+	5.88454i	−0.113691	+	0.196919i
$894$	−7.52496	−	13.0336i	−0.251672	−	0.435909i
$895$	−18.9361			−0.632965
$896$		0			0
$897$	−17.4529			−0.582736
$898$	1.92185	+	3.32874i	0.0641329	+	0.111082i
$899$	4.79731	−	8.30919i	0.159999	−	0.277127i
$900$	−15.4991	+	26.8453i	−0.516637	+	0.894842i
$901$	−4.41911	−	7.65413i	−0.147222	−	0.254996i
$902$	15.4695			0.515079
$903$		0			0
$904$	−12.5125			−0.416159
$905$	−9.86053	−	17.0789i	−0.327775	−	0.567723i
$906$	4.11386	−	7.12542i	0.136674	−	0.236726i
$907$	2.52332	−	4.37052i	0.0837856	−	0.145121i	−0.821087	−	0.570802i	$-0.806632\pi$
$907$	2.52332	−	4.37052i	0.0837856	−	0.145121i	0.904873	+	0.425681i	$0.139966\pi$
$908$	−11.6500	−	20.1783i	−0.386618	−	0.669642i
$909$	5.50653			0.182640
$910$		0			0
$911$	47.5236			1.57453			0.787263	−	0.616618i	$-0.211497\pi$
$911$	47.5236			1.57453			0.787263	+	0.616618i	$0.211497\pi$
$912$	−14.7055	−	25.4707i	−0.486949	−	0.843421i
$913$	31.5215	−	54.5969i	1.04321	−	1.80689i
$914$	−0.501361	+	0.868382i	−0.0165835	+	0.0287235i
$915$	6.95650	+	12.0490i	0.229975	+	0.398328i
$916$	7.81969			0.258370
$917$		0			0
$918$	9.15726			0.302235
$919$	22.8349	+	39.5512i	0.753254	+	1.30467i	0.946238	+	0.323472i	$0.104850\pi$
$919$	22.8349	+	39.5512i	0.753254	+	1.30467i	−0.192984	+	0.981202i	$0.561817\pi$
$920$	−4.47724	+	7.75482i	−0.147610	+	0.255669i
$921$	29.0042	−	50.2367i	0.955721	−	1.65536i
$922$	1.73472	+	3.00463i	0.0571301	+	0.0989522i
$923$	6.85856			0.225752
$924$		0			0
$925$	−1.80095			−0.0592148
$926$	−2.02475	−	3.50697i	−0.0665374	−	0.115246i
$927$	−34.8928	+	60.4360i	−1.14603	+	1.98498i
$928$	−1.57770	+	2.73266i	−0.0517906	+	0.0897040i
$929$	−22.2225	−	38.4904i	−0.729095	−	1.26283i	−0.957266	−	0.289209i	$-0.906608\pi$
$929$	−22.2225	−	38.4904i	−0.729095	−	1.26283i	0.228171	−	0.973621i	$-0.426725\pi$
$930$	10.1740			0.333618
$931$		0			0
$932$	−24.2115			−0.793074
$933$	15.8478	+	27.4492i	0.518835	+	0.898648i
$934$	4.07179	−	7.05254i	0.133233	−	0.230766i
$935$	19.0817	−	33.0505i	0.624039	−	1.08087i
$936$	−2.84042	−	4.91975i	−0.0928419	−	0.160807i
$937$	−46.9796			−1.53476			−0.767379	−	0.641194i	$-0.778439\pi$
$937$	−46.9796			−1.53476			−0.767379	+	0.641194i	$0.778439\pi$
$938$		0			0
$939$	−0.151034			−0.00492881
$940$	−3.33654	−	5.77906i	−0.108826	−	0.188492i
$941$	17.7827	−	30.8005i	0.579699	−	1.00407i	−0.415814	−	0.909450i	$-0.636503\pi$
$941$	17.7827	−	30.8005i	0.579699	−	1.00407i	0.995514	−	0.0946191i	$-0.0301633\pi$
$942$	5.80182	−	10.0491i	0.189034	−	0.327416i
$943$	31.8564	+	55.1769i	1.03739	+	1.79681i
$944$	3.12200			0.101613
$945$		0			0
$946$	−12.2900			−0.399581
$947$	11.1796	+	19.3636i	0.363288	+	0.629234i	0.988500	−	0.151222i	$-0.0483207\pi$
$947$	11.1796	+	19.3636i	0.363288	+	0.629234i	−0.625212	+	0.780455i	$0.714987\pi$
$948$	49.3285	−	85.4395i	1.60212	−	2.77495i
$949$	−1.57074	+	2.72060i	−0.0509883	+	0.0883143i
$950$	−1.09725	−	1.90049i	−0.0355994	−	0.0616600i
$951$	−46.8383			−1.51884
$952$		0			0
$953$	−46.7684			−1.51498			−0.757488	−	0.652849i	$-0.773574\pi$
$953$	−46.7684			−1.51498			−0.757488	+	0.652849i	$0.773574\pi$
$954$	1.32235	+	2.29037i	0.0428126	+	0.0741536i
$955$	11.7185	−	20.2971i	0.379203	−	0.656799i
$956$	12.8790	−	22.3070i	0.416536	−	0.721461i
$957$	8.34206	+	14.4489i	0.269660	+	0.467066i
$958$	0.454469			0.0146832
$959$		0			0
$960$	26.5860			0.858059
$961$	−26.9024	−	46.5963i	−0.867819	−	1.50311i
$962$	0.0810415	−	0.140368i	0.00261288	−	0.00452565i
$963$	1.87225	−	3.24283i	0.0603324	−	0.104499i
$964$	−19.6716	−	34.0722i	−0.633579	−	1.09739i
$965$	−20.1687			−0.649253
$966$		0			0
$967$	8.22976			0.264651			0.132326	−	0.991206i	$-0.457756\pi$
$967$	8.22976			0.264651			0.132326	+	0.991206i	$0.457756\pi$
$968$	10.0369	+	17.3844i	0.322598	+	0.558756i
$969$	19.8169	−	34.3239i	0.636610	−	1.10264i
$970$	2.56523	−	4.44310i	0.0823645	−	0.142659i
$971$	−11.8163	−	20.4665i	−0.379204	−	0.656800i	0.611743	−	0.791057i	$-0.290469\pi$
$971$	−11.8163	−	20.4665i	−0.379204	−	0.656800i	−0.990947	+	0.134257i	$0.957135\pi$
$972$	−16.4850			−0.528758
$973$		0			0
$974$	6.00187			0.192312
$975$	4.27676	+	7.40757i	0.136966	+	0.237232i
$976$	−5.97312	+	10.3458i	−0.191195	+	0.331159i
$977$	13.3214	−	23.0734i	0.426190	−	0.738182i	−0.570341	−	0.821408i	$-0.693189\pi$
$977$	13.3214	−	23.0734i	0.426190	−	0.738182i	0.996531	+	0.0832258i	$0.0265223\pi$
$978$	−9.16589	−	15.8758i	−0.293093	−	0.507652i
$979$	5.47897			0.175109
$980$		0			0
$981$	−15.8600			−0.506370
$982$	1.73815	+	3.01056i	0.0554665	+	0.0960707i
$983$	21.8151	−	37.7848i	0.695793	−	1.20515i	−0.274119	−	0.961696i	$-0.588386\pi$
$983$	21.8151	−	37.7848i	0.695793	−	1.20515i	0.969913	−	0.243453i	$-0.0782803\pi$
$984$	−16.0638	+	27.8233i	−0.512096	+	0.886976i
$985$	1.05411	+	1.82577i	0.0335866	+	0.0581737i
$986$	−1.33187			−0.0424155
$987$		0			0
$988$	−5.44322			−0.173172
$989$	−25.3087	−	43.8360i	−0.804770	−	1.39390i
$990$	−5.70989	+	9.88983i	−0.181472	+	0.314319i
$991$	3.80408	−	6.58886i	0.120841	−	0.209302i	−0.799259	−	0.600987i	$-0.794774\pi$
$991$	3.80408	−	6.58886i	0.120841	−	0.209302i	0.920099	+	0.391685i	$0.128108\pi$
$992$	13.9450	+	24.1534i	0.442753	+	0.766871i
$993$	−89.5581			−2.84204
$994$		0			0
$995$	19.1983			0.608628
$996$	32.1492	+	55.6840i	1.01869	+	1.76442i
$997$	9.71781	−	16.8317i	0.307766	−	0.533066i	−0.670107	−	0.742264i	$-0.733752\pi$
$997$	9.71781	−	16.8317i	0.307766	−	0.533066i	0.977873	+	0.209198i	$0.0670852\pi$
$998$	−1.85762	+	3.21748i	−0.0588018	+	0.101848i
$999$	2.19379	+	3.79975i	0.0694083	+	0.120219i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.e.o.508.3		12
7.2	even	3	inner	637.2.e.o.79.3		12
7.3	odd	6		637.2.a.n.1.4	yes	6
7.4	even	3		637.2.a.m.1.4	✓	6
7.5	odd	6		637.2.e.n.79.3		12
7.6	odd	2		637.2.e.n.508.3		12
21.11	odd	6		5733.2.a.bu.1.3		6
21.17	even	6		5733.2.a.br.1.3		6
91.25	even	6		8281.2.a.cc.1.3		6
91.38	odd	6		8281.2.a.cd.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.a.m.1.4	✓	6	7.4	even	3
637.2.a.n.1.4	yes	6	7.3	odd	6
637.2.e.n.79.3		12	7.5	odd	6
637.2.e.n.508.3		12	7.6	odd	2
637.2.e.o.79.3		12	7.2	even	3	inner
637.2.e.o.508.3		12	1.1	even	1	trivial
5733.2.a.br.1.3		6	21.17	even	6
5733.2.a.bu.1.3		6	21.11	odd	6
8281.2.a.cc.1.3		6	91.25	even	6
8281.2.a.cd.1.3		6	91.38	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
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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