LMFDB - Embedded newform 494.2.g.b.191.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [494,2,Mod(191,494)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(494, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("494.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 494 = 2 \cdot 13 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	494.g (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.94460985985$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.771147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} + 6x^{3} + 15x^{2} + 4x + 1 $ x^6 - x^5 + 5x^4 + 6x^3 + 15x^2 + 4x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			191.3
Root			$-0.688601 + 1.19269i$ of defining polynomial
Character	$\chi$	$=$	494.191
Dual form			494.2.g.b.419.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.18860 - 2.05872i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.65109 q^{5} +(1.18860 + 2.05872i) q^{6} +(-0.688601 - 1.19269i) q^{7} +1.00000 q^{8} +(-1.32555 - 2.29591i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.18860 - 2.05872i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.65109 q^{5} +(1.18860 + 2.05872i) q^{6} +(-0.688601 - 1.19269i) q^{7} +1.00000 q^{8} +(-1.32555 - 2.29591i) q^{9} +(0.825547 - 1.42989i) q^{10} +(0.174453 - 0.302162i) q^{11} -2.37720 q^{12} +(-2.56580 - 2.53311i) q^{13} +1.37720 q^{14} +(-1.96249 + 3.39914i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.37720 - 2.38539i) q^{17} +2.65109 q^{18} +(-0.500000 - 0.866025i) q^{19} +(0.825547 + 1.42989i) q^{20} -3.27389 q^{21} +(0.174453 + 0.302162i) q^{22} +(-0.0852891 + 0.147725i) q^{23} +(1.18860 - 2.05872i) q^{24} -2.27389 q^{25} +(3.47664 - 0.955496i) q^{26} +0.829422 q^{27} +(-0.688601 + 1.19269i) q^{28} +(4.09944 - 7.10043i) q^{29} +(-1.96249 - 3.39914i) q^{30} -10.3305 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.414711 - 0.718300i) q^{33} +2.75441 q^{34} +(1.13695 + 1.96925i) q^{35} +(-1.32555 + 2.29591i) q^{36} +(-2.92498 + 5.06622i) q^{37} +1.00000 q^{38} +(-8.26468 + 2.27141i) q^{39} -1.65109 q^{40} +(-1.03751 + 1.79702i) q^{41} +(1.63695 - 2.83527i) q^{42} +(-0.877203 - 1.51936i) q^{43} -0.348907 q^{44} +(2.18860 + 3.79077i) q^{45} +(-0.0852891 - 0.147725i) q^{46} +0.857718 q^{47} +(1.18860 + 2.05872i) q^{48} +(2.55166 - 4.41960i) q^{49} +(1.13695 - 1.96925i) q^{50} -6.54778 q^{51} +(-0.910836 + 3.48861i) q^{52} +10.3305 q^{53} +(-0.414711 + 0.718300i) q^{54} +(-0.288039 + 0.498898i) q^{55} +(-0.688601 - 1.19269i) q^{56} -2.37720 q^{57} +(4.09944 + 7.10043i) q^{58} +(0.00387504 + 0.00671177i) q^{59} +3.92498 q^{60} +(-1.74026 - 3.01421i) q^{61} +(5.16524 - 8.94646i) q^{62} +(-1.82555 + 3.16194i) q^{63} +1.00000 q^{64} +(4.23638 + 4.18240i) q^{65} +0.829422 q^{66} +(1.92498 - 3.33417i) q^{67} +(-1.37720 + 2.38539i) q^{68} +(0.202750 + 0.351173i) q^{69} -2.27389 q^{70} +(1.50000 + 2.59808i) q^{71} +(-1.32555 - 2.29591i) q^{72} +16.6999 q^{73} +(-2.92498 - 5.06622i) q^{74} +(-2.70275 + 4.68130i) q^{75} +(-0.500000 + 0.866025i) q^{76} -0.480515 q^{77} +(2.16524 - 8.29313i) q^{78} +7.88601 q^{79} +(0.825547 - 1.42989i) q^{80} +(4.96249 - 8.59529i) q^{81} +(-1.03751 - 1.79702i) q^{82} +13.9738 q^{83} +(1.63695 + 2.83527i) q^{84} +(2.27389 + 3.93849i) q^{85} +1.75441 q^{86} +(-9.74519 - 16.8792i) q^{87} +(0.174453 - 0.302162i) q^{88} +(5.41084 - 9.37184i) q^{89} -4.37720 q^{90} +(-1.25441 + 4.80452i) q^{91} +0.170578 q^{92} +(-12.2788 + 21.2676i) q^{93} +(-0.428859 + 0.742806i) q^{94} +(0.825547 + 1.42989i) q^{95} -2.37720 q^{96} +(1.62280 + 2.81077i) q^{97} +(2.55166 + 4.41960i) q^{98} -0.924984 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 2 q^{3} - 3 q^{4} + 4 q^{5} + 2 q^{6} + q^{7} + 6 q^{8} - q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 + 4 * q^5 + 2 * q^6 + q^7 + 6 * q^8 - q^9	\( 6 q - 3 q^{2} + 2 q^{3} - 3 q^{4} + 4 q^{5} + 2 q^{6} + q^{7} + 6 q^{8} - q^{9} - 2 q^{10} + 8 q^{11} - 4 q^{12} - 2 q^{14} - 3 q^{15} - 3 q^{16} + 2 q^{17} + 2 q^{18} - 3 q^{19} - 2 q^{20} - 16 q^{21} + 8 q^{22} - 2 q^{23} + 2 q^{24} - 10 q^{25} + 2 q^{27} + q^{28} + 14 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - q^{33} - 4 q^{34} + 5 q^{35} - q^{36} + 6 q^{38} - 13 q^{39} + 4 q^{40} - 15 q^{41} + 8 q^{42} + 5 q^{43} - 16 q^{44} + 8 q^{45} - 2 q^{46} - 22 q^{47} + 2 q^{48} + 12 q^{49} + 5 q^{50} - 32 q^{51} + 10 q^{53} - q^{54} + 14 q^{55} + q^{56} - 4 q^{57} + 14 q^{58} + 4 q^{59} + 6 q^{60} - 2 q^{61} + 5 q^{62} - 4 q^{63} + 6 q^{64} + 13 q^{65} + 2 q^{66} - 6 q^{67} + 2 q^{68} - 16 q^{69} - 10 q^{70} + 9 q^{71} - q^{72} + 30 q^{73} + q^{75} - 3 q^{76} + 14 q^{77} - 13 q^{78} - 4 q^{79} - 2 q^{80} + 21 q^{81} - 15 q^{82} + 10 q^{83} + 8 q^{84} + 10 q^{85} - 10 q^{86} - 5 q^{87} + 8 q^{88} + 27 q^{89} - 16 q^{90} + 13 q^{91} + 4 q^{92} - 25 q^{93} + 11 q^{94} - 2 q^{95} - 4 q^{96} + 20 q^{97} + 12 q^{98} + 12 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 + 4 * q^5 + 2 * q^6 + q^7 + 6 * q^8 - q^9 - 2 * q^10 + 8 * q^11 - 4 * q^12 - 2 * q^14 - 3 * q^15 - 3 * q^16 + 2 * q^17 + 2 * q^18 - 3 * q^19 - 2 * q^20 - 16 * q^21 + 8 * q^22 - 2 * q^23 + 2 * q^24 - 10 * q^25 + 2 * q^27 + q^28 + 14 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - q^33 - 4 * q^34 + 5 * q^35 - q^36 + 6 * q^38 - 13 * q^39 + 4 * q^40 - 15 * q^41 + 8 * q^42 + 5 * q^43 - 16 * q^44 + 8 * q^45 - 2 * q^46 - 22 * q^47 + 2 * q^48 + 12 * q^49 + 5 * q^50 - 32 * q^51 + 10 * q^53 - q^54 + 14 * q^55 + q^56 - 4 * q^57 + 14 * q^58 + 4 * q^59 + 6 * q^60 - 2 * q^61 + 5 * q^62 - 4 * q^63 + 6 * q^64 + 13 * q^65 + 2 * q^66 - 6 * q^67 + 2 * q^68 - 16 * q^69 - 10 * q^70 + 9 * q^71 - q^72 + 30 * q^73 + q^75 - 3 * q^76 + 14 * q^77 - 13 * q^78 - 4 * q^79 - 2 * q^80 + 21 * q^81 - 15 * q^82 + 10 * q^83 + 8 * q^84 + 10 * q^85 - 10 * q^86 - 5 * q^87 + 8 * q^88 + 27 * q^89 - 16 * q^90 + 13 * q^91 + 4 * q^92 - 25 * q^93 + 11 * q^94 - 2 * q^95 - 4 * q^96 + 20 * q^97 + 12 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/494\mathbb{Z}\right)^\times$.

$n$	$287$	$457$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.18860	−	2.05872i	0.686239	−	1.18860i	−0.286806	−	0.957989i	$-0.592594\pi$
$3$	1.18860	−	2.05872i	0.686239	−	1.18860i	0.973046	−	0.230613i	$-0.0740731\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.65109			−0.738391			−0.369196	−	0.929352i	$-0.620367\pi$
$5$	−1.65109			−0.738391			−0.369196	+	0.929352i	$0.620367\pi$
$6$	1.18860	+	2.05872i	0.485245	+	0.840468i
$7$	−0.688601	−	1.19269i	−0.260267	−	0.450795i	0.706046	−	0.708166i	$-0.250477\pi$
$7$	−0.688601	−	1.19269i	−0.260267	−	0.450795i	−0.966313	+	0.257371i	$0.917144\pi$
$8$	1.00000			0.353553
$9$	−1.32555	−	2.29591i	−0.441849	−	0.765305i
$10$	0.825547	−	1.42989i	0.261061	−	0.452171i
$11$	0.174453	−	0.302162i	0.0525996	−	0.0911053i	−0.838527	−	0.544860i	$-0.816583\pi$
$11$	0.174453	−	0.302162i	0.0525996	−	0.0911053i	0.891126	+	0.453755i	$0.149916\pi$
$12$	−2.37720			−0.686239
$13$	−2.56580	−	2.53311i	−0.711626	−	0.702558i
$13$	−2.56580	−	2.53311i	−0.711626	−	0.702558i
$14$	1.37720			0.368073
$15$	−1.96249	+	3.39914i	−0.506713	+	0.877653i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.37720	−	2.38539i	−0.334021	−	0.578541i	0.649275	−	0.760553i	$-0.275072\pi$
$17$	−1.37720	−	2.38539i	−0.334021	−	0.578541i	−0.983296	+	0.182012i	$0.941739\pi$
$18$	2.65109			0.624869
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i
$20$	0.825547	+	1.42989i	0.184598	+	0.319733i
$21$	−3.27389			−0.714421
$22$	0.174453	+	0.302162i	0.0371936	+	0.0644211i
$23$	−0.0852891	+	0.147725i	−0.0177840	+	0.0308028i	−0.874780	−	0.484520i	$-0.838994\pi$
$23$	−0.0852891	+	0.147725i	−0.0177840	+	0.0308028i	0.856996	+	0.515322i	$0.172328\pi$
$24$	1.18860	−	2.05872i	0.242622	−	0.420234i
$25$	−2.27389			−0.454778
$26$	3.47664	−	0.955496i	0.681825	−	0.187388i
$27$	0.829422			0.159622
$28$	−0.688601	+	1.19269i	−0.130133	+	0.225398i
$29$	4.09944	−	7.10043i	0.761246	−	1.31852i	−0.180962	−	0.983490i	$-0.557921\pi$
$29$	4.09944	−	7.10043i	0.761246	−	1.31852i	0.942208	−	0.335027i	$-0.108746\pi$
$30$	−1.96249	−	3.39914i	−0.358300	−	0.620594i
$31$	−10.3305			−1.85541			−0.927705	−	0.373315i	$-0.878221\pi$
$31$	−10.3305			−1.85541			−0.927705	+	0.373315i	$0.878221\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.414711	−	0.718300i	−0.0721919	−	0.125040i
$34$	2.75441			0.472377
$35$	1.13695	+	1.96925i	0.192179	+	0.332863i
$36$	−1.32555	+	2.29591i	−0.220924	+	0.382652i
$37$	−2.92498	+	5.06622i	−0.480864	+	0.832882i	−0.999759	−	0.0219567i	$-0.993010\pi$
$37$	−2.92498	+	5.06622i	−0.480864	+	0.832882i	0.518895	+	0.854838i	$0.326344\pi$
$38$	1.00000			0.162221
$39$	−8.26468	+	2.27141i	−1.32341	+	0.363717i
$40$	−1.65109			−0.261061
$41$	−1.03751	+	1.79702i	−0.162032	+	0.280647i	−0.935597	−	0.353069i	$-0.885138\pi$
$41$	−1.03751	+	1.79702i	−0.162032	+	0.280647i	0.773566	+	0.633716i	$0.218471\pi$
$42$	1.63695	−	2.83527i	0.252586	−	0.437492i
$43$	−0.877203	−	1.51936i	−0.133772	−	0.231700i	0.791356	−	0.611356i	$-0.209376\pi$
$43$	−0.877203	−	1.51936i	−0.133772	−	0.231700i	−0.925128	+	0.379656i	$0.876042\pi$
$44$	−0.348907			−0.0525996
$45$	2.18860	+	3.79077i	0.326257	+	0.565094i
$46$	−0.0852891	−	0.147725i	−0.0125752	−	0.0217809i
$47$	0.857718			0.125111			0.0625555	−	0.998041i	$-0.480075\pi$
$47$	0.857718			0.125111			0.0625555	+	0.998041i	$0.480075\pi$
$48$	1.18860	+	2.05872i	0.171560	+	0.297150i
$49$	2.55166	−	4.41960i	0.364522	−	0.631371i
$50$	1.13695	−	1.96925i	0.160788	−	0.278494i
$51$	−6.54778			−0.916873
$52$	−0.910836	+	3.48861i	−0.126310	+	0.483783i
$53$	10.3305			1.41900			0.709500	−	0.704705i	$-0.248921\pi$
$53$	10.3305			1.41900			0.709500	+	0.704705i	$0.248921\pi$
$54$	−0.414711	+	0.718300i	−0.0564350	+	0.0977483i
$55$	−0.288039	+	0.498898i	−0.0388391	+	0.0672713i
$56$	−0.688601	−	1.19269i	−0.0920182	−	0.159380i
$57$	−2.37720			−0.314868
$58$	4.09944	+	7.10043i	0.538282	+	0.932333i
$59$	0.00387504	+	0.00671177i	0.000504487	+	0.000873797i	0.866278	−	0.499563i	$-0.166506\pi$
$59$	0.00387504	+	0.00671177i	0.000504487	+	0.000873797i	−0.865773	+	0.500437i	$0.833173\pi$
$60$	3.92498			0.506713
$61$	−1.74026	−	3.01421i	−0.222817	−	0.385931i	0.732845	−	0.680395i	$-0.238192\pi$
$61$	−1.74026	−	3.01421i	−0.222817	−	0.385931i	−0.955662	+	0.294465i	$0.904859\pi$
$62$	5.16524	−	8.94646i	0.655986	−	1.13620i
$63$	−1.82555	+	3.16194i	−0.229997	+	0.398367i
$64$	1.00000			0.125000
$65$	4.23638	+	4.18240i	0.525459	+	0.518763i
$66$	0.829422			0.102095
$67$	1.92498	−	3.33417i	0.235174	−	0.407334i	−0.724149	−	0.689643i	$-0.757767\pi$
$67$	1.92498	−	3.33417i	0.235174	−	0.407334i	0.959323	+	0.282310i	$0.0911006\pi$
$68$	−1.37720	+	2.38539i	−0.167010	+	0.289270i
$69$	0.202750	+	0.351173i	0.0244082	+	0.0422762i
$70$	−2.27389			−0.271782
$71$	1.50000	+	2.59808i	0.178017	+	0.308335i	0.941201	−	0.337846i	$-0.109698\pi$
$71$	1.50000	+	2.59808i	0.178017	+	0.308335i	−0.763184	+	0.646181i	$0.776365\pi$
$72$	−1.32555	−	2.29591i	−0.156217	−	0.270576i
$73$	16.6999			1.95458			0.977290	−	0.211907i	$-0.0679674\pi$
$73$	16.6999			1.95458			0.977290	+	0.211907i	$0.0679674\pi$
$74$	−2.92498	−	5.06622i	−0.340022	−	0.588936i
$75$	−2.70275	+	4.68130i	−0.312087	+	0.540550i
$76$	−0.500000	+	0.866025i	−0.0573539	+	0.0993399i
$77$	−0.480515			−0.0547598
$78$	2.16524	−	8.29313i	0.245165	−	0.939012i
$79$	7.88601			0.887246			0.443623	−	0.896214i	$-0.353693\pi$
$79$	7.88601			0.887246			0.443623	+	0.896214i	$0.353693\pi$
$80$	0.825547	−	1.42989i	0.0922989	−	0.159866i
$81$	4.96249	−	8.59529i	0.551388	−	0.955032i
$82$	−1.03751	−	1.79702i	−0.114574	−	0.198447i
$83$	13.9738			1.53383			0.766913	−	0.641751i	$-0.221792\pi$
$83$	13.9738			1.53383			0.766913	+	0.641751i	$0.221792\pi$
$84$	1.63695	+	2.83527i	0.178605	+	0.309354i
$85$	2.27389	+	3.93849i	0.246638	+	0.427190i
$86$	1.75441			0.189182
$87$	−9.74519	−	16.8792i	−1.04479	−	1.80964i
$88$	0.174453	−	0.302162i	0.0185968	−	0.0322106i
$89$	5.41084	−	9.37184i	0.573547	−	0.993413i	−0.422650	−	0.906293i	$-0.638900\pi$
$89$	5.41084	−	9.37184i	0.573547	−	0.993413i	0.996198	−	0.0871205i	$-0.0277665\pi$
$90$	−4.37720			−0.461398
$91$	−1.25441	+	4.80452i	−0.131497	+	0.503650i
$92$	0.170578			0.0177840
$93$	−12.2788	+	21.2676i	−1.27326	+	2.20534i
$94$	−0.428859	+	0.742806i	−0.0442334	+	0.0766145i
$95$	0.825547	+	1.42989i	0.0846993	+	0.146703i
$96$	−2.37720			−0.242622
$97$	1.62280	+	2.81077i	0.164770	+	0.285390i	0.936574	−	0.350471i	$-0.113978\pi$
$97$	1.62280	+	2.81077i	0.164770	+	0.285390i	−0.771804	+	0.635861i	$0.780645\pi$
$98$	2.55166	+	4.41960i	0.257756	+	0.446447i
$99$	−0.924984			−0.0929644
$100$	1.13695	+	1.96925i	0.113695	+	0.196925i
$101$	0.670578	−	1.16148i	0.0667250	−	0.115571i	−0.830733	−	0.556671i	$-0.812078\pi$
$101$	0.670578	−	1.16148i	0.0667250	−	0.115571i	0.897458	+	0.441100i	$0.145412\pi$
$102$	3.27389	−	5.67054i	0.324163	−	0.561468i
$103$	−6.13936			−0.604929			−0.302464	−	0.953161i	$-0.597809\pi$
$103$	−6.13936			−0.604929			−0.302464	+	0.953161i	$0.597809\pi$
$104$	−2.56580	−	2.53311i	−0.251598	−	0.248392i
$105$	5.40550			0.527523
$106$	−5.16524	+	8.94646i	−0.501693	+	0.868957i
$107$	0.0375080	−	0.0649658i	0.00362604	−	0.00628048i	−0.864207	−	0.503137i	$-0.832179\pi$
$107$	0.0375080	−	0.0649658i	0.00362604	−	0.00628048i	0.867833	+	0.496856i	$0.165512\pi$
$108$	−0.414711	−	0.718300i	−0.0399056	−	0.0691185i
$109$	−11.2632			−1.07882			−0.539410	−	0.842043i	$-0.681353\pi$
$109$	−11.2632			−1.07882			−0.539410	+	0.842043i	$0.681353\pi$
$110$	−0.288039	−	0.498898i	−0.0274634	−	0.0475680i
$111$	6.95328	+	12.0434i	0.659976	+	1.14311i
$112$	1.37720			0.130133
$113$	0.905499	+	1.56837i	0.0851822	+	0.147540i	0.905469	−	0.424413i	$-0.139519\pi$
$113$	0.905499	+	1.56837i	0.0851822	+	0.147540i	−0.820287	+	0.571953i	$0.806186\pi$
$114$	1.18860	−	2.05872i	0.111323	−	0.192817i
$115$	0.140820	−	0.243908i	0.0131316	−	0.0227445i
$116$	−8.19887			−0.761246
$117$	−2.41471	+	9.24862i	−0.223240	+	0.855035i
$118$	−0.00775008			−0.000713453
$119$	−1.89669	+	3.28516i	−0.173869	+	0.301150i
$120$	−1.96249	+	3.39914i	−0.179150	+	0.310297i
$121$	5.43913	+	9.42085i	0.494467	+	0.856441i
$122$	3.48052			0.315111
$123$	2.46637	+	4.27187i	0.222385	+	0.385182i
$124$	5.16524	+	8.94646i	0.463852	+	0.803416i
$125$	12.0099			1.07420
$126$	−1.82555	−	3.16194i	−0.162633	−	0.281688i
$127$	−1.43913	+	2.49265i	−0.127702	+	0.221187i	−0.922786	−	0.385313i	$-0.874094\pi$
$127$	−1.43913	+	2.49265i	−0.127702	+	0.221187i	0.795084	+	0.606500i	$0.207427\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−4.17058			−0.367199
$130$	−5.74026	+	1.57761i	−0.503454	+	0.138366i
$131$	−14.1033			−1.23221			−0.616106	−	0.787663i	$-0.711291\pi$
$131$	−14.1033			−1.23221			−0.616106	+	0.787663i	$0.711291\pi$
$132$	−0.414711	+	0.718300i	−0.0360959	+	0.0625200i
$133$	−0.688601	+	1.19269i	−0.0597093	+	0.103420i
$134$	1.92498	+	3.33417i	0.166293	+	0.288028i
$135$	−1.36945			−0.117864
$136$	−1.37720	−	2.38539i	−0.118094	−	0.204545i
$137$	−1.63307	−	2.82856i	−0.139523	−	0.241660i	0.787793	−	0.615940i	$-0.211223\pi$
$137$	−1.63307	−	2.82856i	−0.139523	−	0.241660i	−0.927316	+	0.374279i	$0.877890\pi$
$138$	−0.405499			−0.0345184
$139$	2.03363	+	3.52236i	0.172490	+	0.298762i	0.939290	−	0.343124i	$-0.111485\pi$
$139$	2.03363	+	3.52236i	0.172490	+	0.298762i	−0.766799	+	0.641887i	$0.778152\pi$
$140$	1.13695	−	1.96925i	0.0960894	−	0.166432i
$141$	1.01948	−	1.76580i	0.0858561	−	0.148707i
$142$	−3.00000			−0.251754
$143$	−1.21302	+	0.333379i	−0.101438	+	0.0278786i
$144$	2.65109			0.220924
$145$	−6.76855	+	11.7235i	−0.562098	+	0.973582i
$146$	−8.34997	+	14.4626i	−0.691048	+	1.19693i
$147$	−6.06580	−	10.5063i	−0.500299	−	0.866543i
$148$	5.84997			0.480864
$149$	7.08529	+	12.2721i	0.580450	+	1.00537i	0.995426	+	0.0955359i	$0.0304565\pi$
$149$	7.08529	+	12.2721i	0.580450	+	1.00537i	−0.414976	+	0.909832i	$0.636210\pi$
$150$	−2.70275	−	4.68130i	−0.220679	−	0.382227i
$151$	−15.1316			−1.23139			−0.615696	−	0.787983i	$-0.711125\pi$
$151$	−15.1316			−1.23139			−0.615696	+	0.787983i	$0.711125\pi$
$152$	−0.500000	−	0.866025i	−0.0405554	−	0.0702439i
$153$	−3.65109	+	6.32388i	−0.295173	+	0.511255i
$154$	0.240258	−	0.416138i	0.0193605	−	0.0335334i
$155$	17.0566			1.37002
$156$	6.09944	+	6.02172i	0.488346	+	0.482123i
$157$	−10.9533			−0.874167			−0.437083	−	0.899421i	$-0.643989\pi$
$157$	−10.9533			−0.874167			−0.437083	+	0.899421i	$0.643989\pi$
$158$	−3.94301	+	6.82949i	−0.313689	+	0.543325i
$159$	12.2788	−	21.2676i	0.973774	−	1.68663i
$160$	0.825547	+	1.42989i	0.0652652	+	0.113043i
$161$	0.234921			0.0185144
$162$	4.96249	+	8.59529i	0.389890	+	0.675310i
$163$	1.32555	+	2.29591i	0.103825	+	0.179830i	0.913257	−	0.407383i	$-0.133559\pi$
$163$	1.32555	+	2.29591i	0.103825	+	0.179830i	−0.809433	+	0.587213i	$0.800225\pi$
$164$	2.07502			0.162032
$165$	0.684726	+	1.18598i	0.0533059	+	0.0923285i
$166$	−6.98691	+	12.1017i	−0.542290	+	0.939273i
$167$	7.35384	−	12.7372i	0.569057	−	0.985636i	−0.427602	−	0.903967i	$-0.640642\pi$
$167$	7.35384	−	12.7372i	0.569057	−	0.985636i	0.996659	−	0.0816693i	$-0.0260251\pi$
$168$	−3.27389			−0.252586
$169$	0.166703	+	12.9989i	0.0128233	+	0.999918i
$170$	−4.54778			−0.348799
$171$	−1.32555	+	2.29591i	−0.101367	+	0.175573i
$172$	−0.877203	+	1.51936i	−0.0668861	+	0.115850i
$173$	3.04632	+	5.27638i	0.231607	+	0.401156i	0.958281	−	0.285827i	$-0.0922682\pi$
$173$	3.04632	+	5.27638i	0.231607	+	0.401156i	−0.726674	+	0.686983i	$0.758935\pi$
$174$	19.4904			1.47756
$175$	1.56580	+	2.71205i	0.118364	+	0.205012i
$176$	0.174453	+	0.302162i	0.0131499	+	0.0227763i
$177$	0.0184235			0.00138480
$178$	5.41084	+	9.37184i	0.405559	+	0.702449i
$179$	3.09023	−	5.35243i	0.230974	−	0.400059i	−0.727121	−	0.686510i	$-0.759142\pi$
$179$	3.09023	−	5.35243i	0.230974	−	0.400059i	0.958095	+	0.286450i	$0.0924753\pi$
$180$	2.18860	−	3.79077i	0.163129	−	0.282547i
$181$	5.81875			0.432504			0.216252	−	0.976338i	$-0.430617\pi$
$181$	5.81875			0.432504			0.216252	+	0.976338i	$0.430617\pi$
$182$	−3.53363	−	3.48861i	−0.261930	−	0.258593i
$183$	−8.27389			−0.611624
$184$	−0.0852891	+	0.147725i	−0.00628760	+	0.0108904i
$185$	4.82942	−	8.36480i	0.355066	−	0.614993i
$186$	−12.2788	−	21.2676i	−0.900327	−	1.55941i
$187$	−0.961030			−0.0702775
$188$	−0.428859	−	0.742806i	−0.0312778	−	0.0541747i
$189$	−0.571141	−	0.989245i	−0.0415444	−	0.0719570i
$190$	−1.65109			−0.119783
$191$	0.236383	+	0.409427i	0.0171040	+	0.0296251i	0.874451	−	0.485114i	$-0.161222\pi$
$191$	0.236383	+	0.409427i	0.0171040	+	0.0296251i	−0.857347	+	0.514739i	$0.827889\pi$
$192$	1.18860	−	2.05872i	0.0857799	−	0.148575i
$193$	4.10971	−	7.11823i	0.295823	−	0.512381i	−0.679353	−	0.733812i	$-0.737739\pi$
$193$	4.10971	−	7.11823i	0.295823	−	0.512381i	0.975176	+	0.221431i	$0.0710727\pi$
$194$	−3.24559			−0.233020
$195$	13.6458	−	3.75031i	0.977193	−	0.268565i
$196$	−5.10331			−0.364522
$197$	−2.11252	+	3.65900i	−0.150511	+	0.260693i	−0.931415	−	0.363958i	$-0.881425\pi$
$197$	−2.11252	+	3.65900i	−0.150511	+	0.260693i	0.780904	+	0.624651i	$0.214759\pi$
$198$	0.462492	−	0.801060i	0.0328679	−	0.0569288i
$199$	−12.0722	−	20.9097i	−0.855776	−	1.48225i	−0.875923	−	0.482450i	$-0.839747\pi$
$199$	−12.0722	−	20.9097i	−0.855776	−	1.48225i	0.0201478	−	0.999797i	$-0.493586\pi$
$200$	−2.27389			−0.160788
$201$	−4.57608	−	7.92600i	−0.322772	−	0.559057i
$202$	0.670578	+	1.16148i	0.0471817	+	0.0817211i
$203$	−11.2915			−0.792509
$204$	3.27389	+	5.67054i	0.229218	+	0.397018i
$205$	1.71302	−	2.96704i	0.119643	−	0.207227i
$206$	3.06968	−	5.31684i	0.213875	−	0.370442i
$207$	0.452219			0.0314314
$208$	3.47664	−	0.955496i	0.241062	−	0.0662518i
$209$	−0.348907			−0.0241344
$210$	−2.70275	+	4.68130i	−0.186507	+	0.323040i
$211$	13.1082	−	22.7042i	0.902409	−	1.56302i	0.0780512	−	0.996949i	$-0.475130\pi$
$211$	13.1082	−	22.7042i	0.902409	−	1.56302i	0.824358	−	0.566069i	$-0.191536\pi$
$212$	−5.16524	−	8.94646i	−0.354750	−	0.614445i
$213$	7.13161			0.488650
$214$	0.0375080	+	0.0649658i	0.00256400	+	0.00444097i
$215$	1.44834	+	2.50861i	0.0987762	+	0.171085i
$216$	0.829422			0.0564350
$217$	7.11359	+	12.3211i	0.482902	+	0.836410i
$218$	5.63161	−	9.75423i	0.381421	−	0.660640i
$219$	19.8496	−	34.3805i	1.34131	−	2.32322i
$220$	0.576077			0.0388391
$221$	−2.50881	+	9.60904i	−0.168761	+	0.646374i
$222$	−13.9066			−0.933347
$223$	2.39669	−	4.15118i	0.160494	−	0.277984i	−0.774552	−	0.632510i	$-0.782025\pi$
$223$	2.39669	−	4.15118i	0.160494	−	0.277984i	0.935046	+	0.354526i	$0.115358\pi$
$224$	−0.688601	+	1.19269i	−0.0460091	+	0.0796901i
$225$	3.01415	+	5.22066i	0.200943	+	0.348044i
$226$	−1.81100			−0.120466
$227$	1.12667	+	1.95145i	0.0747799	+	0.129523i	0.900991	−	0.433839i	$-0.142841\pi$
$227$	1.12667	+	1.95145i	0.0747799	+	0.129523i	−0.826211	+	0.563361i	$0.809508\pi$
$228$	1.18860	+	2.05872i	0.0787171	+	0.136342i
$229$	−16.5860			−1.09603			−0.548015	−	0.836468i	$-0.684616\pi$
$229$	−16.5860			−1.09603			−0.548015	+	0.836468i	$0.684616\pi$
$230$	0.140820	+	0.243908i	0.00928542	+	0.0160828i
$231$	−0.571141	+	0.989245i	−0.0375783	+	0.0650876i
$232$	4.09944	−	7.10043i	0.269141	−	0.466166i
$233$	1.23492			0.0809024			0.0404512	−	0.999182i	$-0.487120\pi$
$233$	1.23492			0.0809024			0.0404512	+	0.999182i	$0.487120\pi$
$234$	−6.80219	−	6.71551i	−0.444673	−	0.439007i
$235$	−1.41617			−0.0923809
$236$	0.00387504	−	0.00671177i	0.000252244	−	0.000436899i
$237$	9.37333	−	16.2351i	0.608863	−	1.05458i
$238$	−1.89669	−	3.28516i	−0.122944	−	0.212945i
$239$	−28.9837			−1.87480			−0.937400	−	0.348255i	$-0.886774\pi$
$239$	−28.9837			−1.87480			−0.937400	+	0.348255i	$0.886774\pi$
$240$	−1.96249	−	3.39914i	−0.126678	−	0.219413i
$241$	−1.94834	−	3.37463i	−0.125504	−	0.217379i	0.796426	−	0.604736i	$-0.206721\pi$
$241$	−1.94834	−	3.37463i	−0.125504	−	0.217379i	−0.921930	+	0.387357i	$0.873388\pi$
$242$	−10.8783			−0.699281
$243$	−10.5527	−	18.2778i	−0.676957	−	1.17252i
$244$	−1.74026	+	3.01421i	−0.111409	+	0.192965i
$245$	−4.21302	+	7.29717i	−0.269160	+	0.466199i
$246$	−4.93273			−0.314500
$247$	−0.910836	+	3.48861i	−0.0579551	+	0.221975i
$248$	−10.3305			−0.655986
$249$	16.6093	−	28.7682i	1.05257	−	1.82311i
$250$	−6.00494	+	10.4009i	−0.379786	+	0.657808i
$251$	1.41471	+	2.45035i	0.0892958	+	0.154665i	0.907214	−	0.420670i	$-0.138205\pi$
$251$	1.41471	+	2.45035i	0.0892958	+	0.154665i	−0.817918	+	0.575335i	$0.804872\pi$
$252$	3.65109			0.229997
$253$	0.0297579	+	0.0515423i	0.00187087	+	0.00324043i
$254$	−1.43913	−	2.49265i	−0.0902992	−	0.156403i
$255$	10.8110			0.677011
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.69354	−	13.3256i	0.479910	−	0.831228i	−0.519825	−	0.854273i	$-0.674003\pi$
$257$	7.69354	−	13.3256i	0.479910	−	0.831228i	0.999734	+	0.0230450i	$0.00733608\pi$
$258$	2.08529	−	3.61183i	0.129824	−	0.224863i
$259$	8.05659			0.500612
$260$	1.50388	−	5.76002i	0.0932664	−	0.357221i
$261$	−21.7360			−1.34542
$262$	7.05166	−	12.2138i	0.435653	−	0.754573i
$263$	3.23145	−	5.59703i	0.199260	−	0.345128i	−0.749029	−	0.662537i	$-0.769480\pi$
$263$	3.23145	−	5.59703i	0.199260	−	0.345128i	0.948289	+	0.317410i	$0.102813\pi$
$264$	−0.414711	−	0.718300i	−0.0255237	−	0.0442083i
$265$	−17.0566			−1.04778
$266$	−0.688601	−	1.19269i	−0.0422209	−	0.0731287i
$267$	−12.8627	−	22.2788i	−0.787182	−	1.36344i
$268$	−3.84997			−0.235174
$269$	−8.43526	−	14.6103i	−0.514307	−	0.890805i	−0.999862	−	0.0165995i	$-0.994716\pi$
$269$	−8.43526	−	14.6103i	−0.514307	−	0.890805i	0.485556	−	0.874206i	$-0.338617\pi$
$270$	0.684726	−	1.18598i	0.0416711	−	0.0721765i
$271$	2.10719	−	3.64976i	0.128003	−	0.221707i	−0.794900	−	0.606740i	$-0.792477\pi$
$271$	2.10719	−	3.64976i	0.128003	−	0.221707i	0.922903	+	0.385033i	$0.125810\pi$
$272$	2.75441			0.167010
$273$	8.40016	+	8.29313i	0.508401	+	0.501923i
$274$	3.26614			0.197315
$275$	−0.396688	+	0.687083i	−0.0239212	+	0.0414327i
$276$	0.202750	−	0.351173i	0.0122041	−	0.0211381i
$277$	11.9908	+	20.7687i	0.720457	+	1.24787i	0.960817	+	0.277184i	$0.0894011\pi$
$277$	11.9908	+	20.7687i	0.720457	+	1.24787i	−0.240360	+	0.970684i	$0.577266\pi$
$278$	−4.06727			−0.243938
$279$	13.6935	+	23.7179i	0.819811	+	1.41995i
$280$	1.13695	+	1.96925i	0.0679455	+	0.117685i
$281$	22.0643			1.31625			0.658124	−	0.752909i	$-0.271350\pi$
$281$	22.0643			1.31625			0.658124	+	0.752909i	$0.271350\pi$
$282$	1.01948	+	1.76580i	0.0607094	+	0.105152i
$283$	−6.89629	+	11.9447i	−0.409942	+	0.710040i	−0.994883	−	0.101036i	$-0.967784\pi$
$283$	−6.89629	+	11.9447i	−0.409942	+	0.710040i	0.584941	+	0.811076i	$0.301118\pi$
$284$	1.50000	−	2.59808i	0.0890086	−	0.154167i
$285$	3.92498			0.232496
$286$	0.317797	−	1.21720i	0.0187917	−	0.0719744i
$287$	2.85772			0.168686
$288$	−1.32555	+	2.29591i	−0.0781086	+	0.135288i
$289$	4.70662	−	8.15211i	0.276860	−	0.479536i
$290$	−6.76855	−	11.7235i	−0.397463	−	0.688426i
$291$	7.71544			0.452287
$292$	−8.34997	−	14.4626i	−0.488645	−	0.846358i
$293$	10.2516	+	17.7563i	0.598904	+	1.03733i	0.992983	+	0.118256i	$0.0377304\pi$
$293$	10.2516	+	17.7563i	0.598904	+	1.03733i	−0.394079	+	0.919077i	$0.628936\pi$
$294$	12.1316			0.707530
$295$	−0.00639805	−	0.0110818i	−0.000372509	−	0.000645205i
$296$	−2.92498	+	5.06622i	−0.170011	+	0.294468i
$297$	0.144695	−	0.250620i	0.00839608	−	0.0145424i
$298$	−14.1706			−0.820880
$299$	0.593039	−	0.162987i	0.0342963	−	0.00942578i
$300$	5.40550			0.312087
$301$	−1.20809	+	2.09247i	−0.0696329	+	0.120608i
$302$	7.56580	−	13.1044i	0.435363	−	0.754071i
$303$	−1.59410	−	2.76106i	−0.0915787	−	0.158619i
$304$	1.00000			0.0573539
$305$	2.87333	+	4.97675i	0.164526	+	0.284968i
$306$	−3.65109	−	6.32388i	−0.208719	−	0.361512i
$307$	−3.81100			−0.217505			−0.108753	−	0.994069i	$-0.534686\pi$
$307$	−3.81100			−0.217505			−0.108753	+	0.994069i	$0.534686\pi$
$308$	0.240258	+	0.416138i	0.0136899	+	0.0237117i
$309$	−7.29725	+	12.6392i	−0.415126	+	0.719019i
$310$	−8.52830	+	14.7714i	−0.484375	+	0.838962i
$311$	−2.43380			−0.138008			−0.0690039	−	0.997616i	$-0.521982\pi$
$311$	−2.43380			−0.138008			−0.0690039	+	0.997616i	$0.521982\pi$
$312$	−8.26468	+	2.27141i	−0.467895	+	0.128593i
$313$	−25.1882			−1.42372			−0.711861	−	0.702321i	$-0.752147\pi$
$313$	−25.1882			−1.42372			−0.711861	+	0.702321i	$0.752147\pi$
$314$	5.47664	−	9.48582i	0.309065	−	0.535316i
$315$	3.01415	−	5.22066i	0.169828	−	0.294151i
$316$	−3.94301	−	6.82949i	−0.221811	−	0.384189i
$317$	17.5139			0.983676			0.491838	−	0.870687i	$-0.336325\pi$
$317$	17.5139			0.983676			0.491838	+	0.870687i	$0.336325\pi$
$318$	12.2788	+	21.2676i	0.688562	+	1.19263i
$319$	−1.43032	−	2.47739i	−0.0800826	−	0.138707i
$320$	−1.65109			−0.0922989
$321$	−0.0891642	−	0.154437i	−0.00497666	−	0.00861983i
$322$	−0.117460	+	0.203447i	−0.00654581	+	0.0113377i
$323$	−1.37720	+	2.38539i	−0.0766296	+	0.132726i
$324$	−9.92498			−0.551388
$325$	5.83436	+	5.76002i	0.323632	+	0.319508i
$326$	−2.65109			−0.146830
$327$	−13.3875	+	23.1878i	−0.740329	+	1.28229i
$328$	−1.03751	+	1.79702i	−0.0572868	+	0.0992236i
$329$	−0.590626	−	1.02299i	−0.0325623	−	0.0563995i
$330$	−1.36945			−0.0753859
$331$	7.50494	+	12.9989i	0.412509	+	0.714486i	0.995163	−	0.0982339i	$-0.0313193\pi$
$331$	7.50494	+	12.9989i	0.412509	+	0.714486i	−0.582655	+	0.812720i	$0.697986\pi$
$332$	−6.98691	−	12.1017i	−0.383457	−	0.664166i
$333$	15.5088			0.849878
$334$	7.35384	+	12.7372i	0.402384	+	0.696950i
$335$	−3.17833	+	5.50503i	−0.173651	+	0.300772i
$336$	1.63695	−	2.83527i	0.0893027	−	0.154677i
$337$	−5.67939			−0.309376			−0.154688	−	0.987963i	$-0.549437\pi$
$337$	−5.67939			−0.309376			−0.154688	+	0.987963i	$0.549437\pi$
$338$	−11.3408	−	6.35510i	−0.616856	−	0.345672i
$339$	4.30511			0.233821
$340$	2.27389	−	3.93849i	0.123319	−	0.213595i
$341$	−1.80219	+	3.12148i	−0.0975939	+	0.169038i
$342$	−1.32555	−	2.29591i	−0.0716774	−	0.124149i
$343$	−16.6687			−0.900026
$344$	−0.877203	−	1.51936i	−0.0472956	−	0.0819184i
$345$	−0.334758	−	0.579819i	−0.0180228	−	0.0312164i
$346$	−6.09264			−0.327542
$347$	14.0152	+	24.2751i	0.752376	+	1.30315i	0.946668	+	0.322210i	$0.104426\pi$
$347$	14.0152	+	24.2751i	0.752376	+	1.30315i	−0.194292	+	0.980944i	$0.562241\pi$
$348$	−9.74519	+	16.8792i	−0.522397	+	0.904819i
$349$	−17.2126	+	29.8131i	−0.921371	+	1.59586i	−0.124074	+	0.992273i	$0.539596\pi$
$349$	−17.2126	+	29.8131i	−0.921371	+	1.59586i	−0.797297	+	0.603588i	$0.793737\pi$
$350$	−3.13161			−0.167392
$351$	−2.12813	−	2.10102i	−0.113591	−	0.112144i
$352$	−0.348907			−0.0185968
$353$	2.01908	−	3.49716i	0.107465	−	0.186135i	−0.807278	−	0.590172i	$-0.799060\pi$
$353$	2.01908	−	3.49716i	0.107465	−	0.186135i	0.914743	+	0.404037i	$0.132393\pi$
$354$	−0.00921176	+	0.0159552i	−0.000489599	+	0.000848011i
$355$	−2.47664	−	4.28967i	−0.131446	−	0.227672i
$356$	−10.8217			−0.573547
$357$	4.50881	+	7.80949i	0.238632	+	0.413322i
$358$	3.09023	+	5.35243i	0.163323	+	0.282885i
$359$	−8.80113			−0.464506			−0.232253	−	0.972655i	$-0.574610\pi$
$359$	−8.80113			−0.464506			−0.232253	+	0.972655i	$0.574610\pi$
$360$	2.18860	+	3.79077i	0.115349	+	0.199791i
$361$	−0.500000	+	0.866025i	−0.0263158	+	0.0455803i
$362$	−2.90937	+	5.03918i	−0.152913	+	0.264854i
$363$	25.8598			1.35729
$364$	4.78804	−	1.31591i	0.250961	−	0.0689726i
$365$	−27.5732			−1.44324
$366$	4.13695	−	7.16540i	0.216242	−	0.374541i
$367$	10.4805	−	18.1528i	0.547078	−	0.947568i	−0.451394	−	0.892324i	$-0.649073\pi$
$367$	10.4805	−	18.1528i	0.547078	−	0.947568i	0.998473	−	0.0552432i	$-0.0175934\pi$
$368$	−0.0852891	−	0.147725i	−0.00444600	−	0.00770070i
$369$	5.50106			0.286374
$370$	4.82942	+	8.36480i	0.251070	+	0.434865i
$371$	−7.11359	−	12.3211i	−0.369319	−	0.639679i
$372$	24.5577			1.27326
$373$	10.6093	+	18.3759i	0.549329	+	0.951466i	0.998321	+	0.0579301i	$0.0184500\pi$
$373$	10.6093	+	18.3759i	0.549329	+	0.951466i	−0.448991	+	0.893536i	$0.648217\pi$
$374$	0.480515	−	0.832277i	0.0248468	−	0.0430360i
$375$	14.2750	−	24.7249i	0.737155	−	1.27679i
$376$	0.857718			0.0442334
$377$	−28.5045	+	7.83400i	−1.46806	+	0.403471i
$378$	1.14228			0.0587526
$379$	1.16272	−	2.01389i	0.0597248	−	0.103446i	−0.834617	−	0.550831i	$-0.814311\pi$
$379$	1.16272	−	2.01389i	0.0597248	−	0.103446i	0.894342	+	0.447384i	$0.147644\pi$
$380$	0.825547	−	1.42989i	0.0423497	−	0.0733517i
$381$	3.42111	+	5.92553i	0.175269	+	0.303574i
$382$	−0.472765			−0.0241888
$383$	−18.2774	−	31.6573i	−0.933930	−	1.61761i	−0.776531	−	0.630079i	$-0.783023\pi$
$383$	−18.2774	−	31.6573i	−0.933930	−	1.61761i	−0.157398	−	0.987535i	$-0.550311\pi$
$384$	1.18860	+	2.05872i	0.0606556	+	0.105059i
$385$	0.793375			0.0404342
$386$	4.10971	+	7.11823i	0.209179	+	0.362308i
$387$	−2.32555	+	4.02797i	−0.118214	+	0.204753i
$388$	1.62280	−	2.81077i	0.0823850	−	0.142695i
$389$	19.1628			0.971594			0.485797	−	0.874072i	$-0.338529\pi$
$389$	19.1628			0.971594			0.485797	+	0.874072i	$0.338529\pi$
$390$	−3.57502	+	13.6927i	−0.181028	+	0.693358i
$391$	0.469842			0.0237609
$392$	2.55166	−	4.41960i	0.128878	−	0.223223i
$393$	−16.7632	+	29.0347i	−0.845592	+	1.46461i
$394$	−2.11252	−	3.65900i	−0.106427	−	0.184338i
$395$	−13.0205			−0.655135
$396$	0.462492	+	0.801060i	0.0232411	+	0.0402548i
$397$	−10.4649	−	18.1257i	−0.525219	−	0.909705i	−0.999569	−	0.0293689i	$-0.990650\pi$
$397$	−10.4649	−	18.1257i	−0.525219	−	0.909705i	0.474350	−	0.880336i	$-0.342683\pi$
$398$	24.1444			1.21025
$399$	1.63695	+	2.83527i	0.0819498	+	0.141941i
$400$	1.13695	−	1.96925i	0.0568473	−	0.0984623i
$401$	−5.60331	+	9.70522i	−0.279816	+	0.484656i	−0.971339	−	0.237699i	$-0.923607\pi$
$401$	−5.60331	+	9.70522i	−0.279816	+	0.484656i	0.691523	+	0.722355i	$0.256940\pi$
$402$	9.15215			0.456468
$403$	26.5060	+	26.1683i	1.32036	+	1.30353i
$404$	−1.34116			−0.0667250
$405$	−8.19354	+	14.1916i	−0.407140	+	0.705187i
$406$	5.64576	−	9.77874i	0.280194	−	0.485311i
$407$	1.02055	+	1.76764i	0.0505866	+	0.0876186i
$408$	−6.54778			−0.324163
$409$	−14.7657	−	25.5750i	−0.730119	−	1.26460i	−0.956832	−	0.290641i	$-0.906131\pi$
$409$	−14.7657	−	25.5750i	−0.730119	−	1.26460i	0.226713	−	0.973962i	$-0.427202\pi$
$410$	1.71302	+	2.96704i	0.0846002	+	0.146532i
$411$	−7.76428			−0.382984
$412$	3.06968	+	5.31684i	0.151232	+	0.261942i
$413$	0.00533672	−	0.00924346i	0.000262603	−	0.000454841i
$414$	−0.226109	+	0.391633i	−0.0111127	+	0.0192477i
$415$	−23.0721			−1.13256
$416$	−0.910836	+	3.48861i	−0.0446574	+	0.171043i
$417$	9.66872			0.473479
$418$	0.174453	−	0.302162i	0.00853279	−	0.0147792i
$419$	−5.85878	+	10.1477i	−0.286220	+	0.495748i	−0.972904	−	0.231208i	$-0.925732\pi$
$419$	−5.85878	+	10.1477i	−0.286220	+	0.495748i	0.686684	+	0.726956i	$0.259066\pi$
$420$	−2.70275	−	4.68130i	−0.131881	−	0.228424i
$421$	15.7184			0.766066			0.383033	−	0.923735i	$-0.374880\pi$
$421$	15.7184			0.766066			0.383033	+	0.923735i	$0.374880\pi$
$422$	13.1082	+	22.7042i	0.638100	+	1.10522i
$423$	−1.13695	−	1.96925i	−0.0552802	−	0.0957481i
$424$	10.3305			0.501693
$425$	3.13161	+	5.42411i	0.151905	+	0.263108i
$426$	−3.56580	+	6.17615i	−0.172764	+	0.299236i
$427$	−2.39669	+	4.15118i	−0.115984	+	0.200890i
$428$	−0.0750160			−0.00362604
$429$	−0.755467	+	2.89353i	−0.0364743	+	0.139701i
$430$	−2.89669			−0.139691
$431$	4.10971	−	7.11823i	0.197958	−	0.342873i	−0.749908	−	0.661542i	$-0.769902\pi$
$431$	4.10971	−	7.11823i	0.197958	−	0.342873i	0.947866	+	0.318669i	$0.103236\pi$
$432$	−0.414711	+	0.718300i	−0.0199528	+	0.0345592i
$433$	13.4094	+	23.2257i	0.644413	+	1.11616i	0.984437	+	0.175740i	$0.0562317\pi$
$433$	13.4094	+	23.2257i	0.644413	+	1.11616i	−0.340023	+	0.940417i	$0.610435\pi$
$434$	−14.2272			−0.682926
$435$	16.0902	+	27.8691i	0.771467	+	1.33622i
$436$	5.63161	+	9.75423i	0.269705	+	0.467143i
$437$	0.170578			0.00815986
$438$	19.8496	+	34.3805i	0.948449	+	1.64276i
$439$	−0.560468	+	0.970758i	−0.0267497	+	0.0463318i	−0.879090	−	0.476655i	$-0.841849\pi$
$439$	−0.560468	+	0.970758i	−0.0267497	+	0.0463318i	0.852341	+	0.522987i	$0.175182\pi$
$440$	−0.288039	+	0.498898i	−0.0137317	+	0.0237840i
$441$	−13.5294			−0.644255
$442$	−7.06727	−	6.97721i	−0.336156	−	0.331872i
$443$	−38.0459			−1.80762			−0.903808	−	0.427938i	$-0.859240\pi$
$443$	−38.0459			−1.80762			−0.903808	+	0.427938i	$0.859240\pi$
$444$	6.95328	−	12.0434i	0.329988	−	0.571556i
$445$	−8.93380	+	15.4738i	−0.423503	+	0.733528i
$446$	2.39669	+	4.15118i	0.113486	+	0.196564i
$447$	33.6863			1.59331
$448$	−0.688601	−	1.19269i	−0.0325334	−	0.0563494i
$449$	−13.6985	−	23.7265i	−0.646471	−	1.11972i	−0.983960	−	0.178391i	$-0.942911\pi$
$449$	−13.6985	−	23.7265i	−0.646471	−	1.11972i	0.337489	−	0.941330i	$-0.390423\pi$
$450$	−6.02830			−0.284177
$451$	0.361993	+	0.626991i	0.0170456	+	0.0295239i
$452$	0.905499	−	1.56837i	0.0425911	−	0.0737699i
$453$	−17.9855	+	31.1517i	−0.845030	+	1.46364i
$454$	−2.25334			−0.105755
$455$	2.07114	−	7.93271i	0.0970966	−	0.371891i
$456$	−2.37720			−0.111323
$457$	19.9762	−	34.5999i	0.934449	−	1.61851i	0.158836	−	0.987305i	$-0.449226\pi$
$457$	19.9762	−	34.5999i	0.934449	−	1.61851i	0.775613	−	0.631208i	$-0.217441\pi$
$458$	8.29298	−	14.3639i	0.387505	−	0.671179i
$459$	−1.14228	−	1.97849i	−0.0533172	−	0.0923480i
$460$	−0.281641			−0.0131316
$461$	−16.0825	−	27.8557i	−0.749036	−	1.29737i	−0.948285	−	0.317419i	$-0.897184\pi$
$461$	−16.0825	−	27.8557i	−0.749036	−	1.29737i	0.199250	−	0.979949i	$-0.436149\pi$
$462$	−0.571141	−	0.989245i	−0.0265719	−	0.0460239i
$463$	−26.5860			−1.23555			−0.617777	−	0.786353i	$-0.711967\pi$
$463$	−26.5860			−1.23555			−0.617777	+	0.786353i	$0.711967\pi$
$464$	4.09944	+	7.10043i	0.190312	+	0.329629i
$465$	20.2735	−	35.1147i	0.940161	−	1.62841i
$466$	−0.617460	+	1.06947i	−0.0286033	+	0.0495424i
$467$	13.4776			0.623669			0.311834	−	0.950137i	$-0.399057\pi$
$467$	13.4776			0.623669			0.311834	+	0.950137i	$0.399057\pi$
$468$	9.21690	−	2.53311i	0.426051	−	0.117093i
$469$	−5.30219			−0.244832
$470$	0.708086	−	1.22644i	0.0326616	−	0.0565715i
$471$	−13.0191	+	22.5497i	−0.599888	+	1.03904i
$472$	0.00387504	+	0.00671177i	0.000178363	+	0.000308934i
$473$	−0.612124			−0.0281455
$474$	9.37333	+	16.2351i	0.430531	+	0.745702i
$475$	1.13695	+	1.96925i	0.0521666	+	0.0903552i
$476$	3.79338			0.173869
$477$	−13.6935	−	23.7179i	−0.626984	−	1.08597i
$478$	14.4918	−	25.1006i	0.662842	−	1.14808i
$479$	1.97170	−	3.41509i	0.0900894	−	0.156039i	−0.817459	−	0.575987i	$-0.804618\pi$
$479$	1.97170	−	3.41509i	0.0900894	−	0.156039i	0.907549	+	0.419947i	$0.137951\pi$
$480$	3.92498			0.179150
$481$	20.3382	−	5.58962i	0.927344	−	0.254865i
$482$	3.89669			0.177489
$483$	0.279227	−	0.483636i	0.0127053	−	0.0220062i
$484$	5.43913	−	9.42085i	0.247233	−	0.428221i
$485$	−2.67939	−	4.64084i	−0.121665	−	0.210730i
$486$	21.1054			0.957362
$487$	0.567266	+	0.982533i	0.0257053	+	0.0445228i	0.878592	−	0.477573i	$-0.158484\pi$
$487$	0.567266	+	0.982533i	0.0257053	+	0.0445228i	−0.852887	+	0.522096i	$0.825150\pi$
$488$	−1.74026	−	3.01421i	−0.0787778	−	0.136447i
$489$	6.30219			0.284995
$490$	−4.21302	−	7.29717i	−0.190325	−	0.329653i
$491$	−15.2657	+	26.4410i	−0.688933	+	1.19327i	0.283250	+	0.959046i	$0.408587\pi$
$491$	−15.2657	+	26.4410i	−0.688933	+	1.19327i	−0.972183	+	0.234221i	$0.924746\pi$
$492$	2.46637	−	4.27187i	0.111192	−	0.192591i
$493$	−22.5830			−1.01709
$494$	−2.56580	−	2.53311i	−0.115441	−	0.113970i
$495$	1.52723			0.0686441
$496$	5.16524	−	8.94646i	0.231926	−	0.401708i
$497$	2.06580	−	3.57808i	0.0926640	−	0.160499i
$498$	16.6093	+	28.7682i	0.744281	+	1.28913i
$499$	−1.75441			−0.0785380			−0.0392690	−	0.999229i	$-0.512503\pi$
$499$	−1.75441			−0.0785380			−0.0392690	+	0.999229i	$0.512503\pi$
$500$	−6.00494	−	10.4009i	−0.268549	−	0.465140i
$501$	−17.4816	−	30.2790i	−0.781019	−	1.35277i
$502$	−2.82942			−0.126283
$503$	20.5937	+	35.6693i	0.918228	+	1.59042i	0.802106	+	0.597182i	$0.203713\pi$
$503$	20.5937	+	35.6693i	0.918228	+	1.59042i	0.116122	+	0.993235i	$0.462954\pi$
$504$	−1.82555	+	3.16194i	−0.0813163	+	0.140844i
$505$	−1.10719	+	1.91770i	−0.0492692	+	0.0853367i
$506$	−0.0595159			−0.00264580
$507$	26.9593	+	15.1074i	1.19730	+	0.670941i
$508$	2.87826			0.127702
$509$	14.5785	−	25.2507i	0.646180	−	1.11922i	−0.337847	−	0.941201i	$-0.609699\pi$
$509$	14.5785	−	25.2507i	0.646180	−	1.11922i	0.984028	−	0.178016i	$-0.0569679\pi$
$510$	−5.40550	+	9.36260i	−0.239360	+	0.414583i
$511$	−11.4996	−	19.9179i	−0.508712	−	0.881116i
$512$	1.00000			0.0441942
$513$	−0.414711	−	0.718300i	−0.0183099	−	0.0317137i
$514$	7.69354	+	13.3256i	0.339347	+	0.587767i
$515$	10.1367			0.446674
$516$	2.08529	+	3.61183i	0.0917997	+	0.159002i
$517$	0.149632	−	0.259170i	0.00658080	−	0.0113983i
$518$	−4.02830	+	6.97721i	−0.176993	+	0.306561i
$519$	14.4834			0.635752
$520$	4.23638	+	4.18240i	0.185778	+	0.183410i
$521$	−10.5761			−0.463346			−0.231673	−	0.972794i	$-0.574420\pi$
$521$	−10.5761			−0.463346			−0.231673	+	0.972794i	$0.574420\pi$
$522$	10.8680	−	18.8239i	0.475679	−	0.823900i
$523$	19.5279	−	33.8233i	0.853895	−	1.47899i	−0.0237708	−	0.999717i	$-0.507567\pi$
$523$	19.5279	−	33.8233i	0.853895	−	1.47899i	0.877666	−	0.479273i	$-0.159099\pi$
$524$	7.05166	+	12.2138i	0.308053	+	0.533563i
$525$	7.44447			0.324903
$526$	3.23145	+	5.59703i	0.140898	+	0.244042i
$527$	14.2272	+	24.6422i	0.619745	+	1.07343i
$528$	0.829422			0.0360959
$529$	11.4855	+	19.8934i	0.499367	+	0.864930i
$530$	8.52830	−	14.7714i	0.370446	−	0.641630i
$531$	0.0102731	−	0.0177935i	0.000445814	−	0.000772173i
$532$	1.37720			0.0597093
$533$	7.21408	−	1.98267i	0.312477	−	0.0858790i
$534$	25.7253			1.11324
$535$	−0.0619292	+	0.107265i	−0.00267743	+	0.00463745i
$536$	1.92498	−	3.33417i	0.0831466	−	0.144014i
$537$	−7.34609	−	12.7238i	−0.317007	−	0.549073i
$538$	16.8705			0.727340
$539$	−0.890290	−	1.54203i	−0.0383475	−	0.0664198i
$540$	0.684726	+	1.18598i	0.0294659	+	0.0510365i
$541$	36.1492			1.55418			0.777088	−	0.629391i	$-0.216696\pi$
$541$	36.1492			1.55418			0.777088	+	0.629391i	$0.216696\pi$
$542$	2.10719	+	3.64976i	0.0905114	+	0.156770i
$543$	6.91617	−	11.9792i	0.296801	−	0.514075i
$544$	−1.37720	+	2.38539i	−0.0590471	+	0.102273i
$545$	18.5966			0.796592
$546$	−11.3821	+	3.12819i	−0.487111	+	0.133874i
$547$	6.19032			0.264679			0.132340	−	0.991204i	$-0.457751\pi$
$547$	6.19032			0.264679			0.132340	+	0.991204i	$0.457751\pi$
$548$	−1.63307	+	2.82856i	−0.0697613	+	0.120830i
$549$	−4.61359	+	7.99096i	−0.196903	+	0.341046i
$550$	−0.396688	−	0.687083i	−0.0169148	−	0.0292973i
$551$	−8.19887			−0.349284
$552$	0.202750	+	0.351173i	0.00862959	+	0.0149469i
$553$	−5.43032	−	9.40559i	−0.230921	−	0.399966i
$554$	−23.9816			−1.01888
$555$	−11.4805	−	19.8848i	−0.487321	−	0.844064i
$556$	2.03363	−	3.52236i	0.0862452	−	0.149381i
$557$	−3.61252	+	6.25708i	−0.153068	+	0.265121i	−0.932354	−	0.361547i	$-0.882249\pi$
$557$	−3.61252	+	6.25708i	−0.153068	+	0.265121i	0.779286	+	0.626668i	$0.215582\pi$
$558$	−27.3871			−1.15939
$559$	−1.59798	+	6.12043i	−0.0675872	+	0.258867i
$560$	−2.27389			−0.0960894
$561$	−1.14228	+	1.97849i	−0.0482272	+	0.0835319i
$562$	−11.0322	+	19.1083i	−0.465364	+	0.806034i
$563$	20.6854	+	35.8281i	0.871785	+	1.50998i	0.860148	+	0.510044i	$0.170371\pi$
$563$	20.6854	+	35.8281i	0.871785	+	1.50998i	0.0116367	+	0.999932i	$0.496296\pi$
$564$	−2.03897			−0.0858561
$565$	−1.49506	−	2.58953i	−0.0628978	−	0.108942i
$566$	−6.89629	−	11.9447i	−0.289873	−	0.502074i
$567$	−13.6687			−0.574032
$568$	1.50000	+	2.59808i	0.0629386	+	0.109013i
$569$	14.4752	−	25.0717i	0.606831	−	1.05106i	−0.384928	−	0.922947i	$-0.625774\pi$
$569$	14.4752	−	25.0717i	0.606831	−	1.05106i	0.991759	−	0.128116i	$-0.0408929\pi$
$570$	−1.96249	+	3.39914i	−0.0821997	+	0.142374i
$571$	−7.80325			−0.326556			−0.163278	−	0.986580i	$-0.552207\pi$
$571$	−7.80325			−0.326556			−0.163278	+	0.986580i	$0.552207\pi$
$572$	0.895226	+	0.883819i	0.0374313	+	0.0369543i
$573$	1.12386			0.0469499
$574$	−1.42886	+	2.47486i	−0.0596394	+	0.103299i
$575$	0.193938	−	0.335911i	0.00808778	−	0.0140084i
$576$	−1.32555	−	2.29591i	−0.0552311	−	0.0956631i
$577$	−4.29736			−0.178901			−0.0894507	−	0.995991i	$-0.528511\pi$
$577$	−4.29736			−0.178901			−0.0894507	+	0.995991i	$0.528511\pi$
$578$	4.70662	+	8.15211i	0.195770	+	0.339083i
$579$	−9.76962	−	16.9215i	−0.406011	−	0.703232i
$580$	13.5371			0.562098
$581$	−9.62240	−	16.6665i	−0.399204	−	0.691442i
$582$	−3.85772	+	6.68176i	−0.159908	+	0.276968i
$583$	1.80219	−	3.12148i	0.0746390	−	0.129278i
$584$	16.6999			0.691048
$585$	3.98691	−	15.2703i	0.164839	−	0.631351i
$586$	−20.5032			−0.846979
$587$	−20.4801	+	35.4726i	−0.845305	+	1.46411i	0.0400514	+	0.999198i	$0.487248\pi$
$587$	−20.4801	+	35.4726i	−0.845305	+	1.46411i	−0.885356	+	0.464913i	$0.846086\pi$
$588$	−6.06580	+	10.5063i	−0.250150	+	0.433272i
$589$	5.16524	+	8.94646i	0.212830	+	0.368632i
$590$	0.0127961			0.000526807
$591$	5.02190	+	8.69818i	0.206573	+	0.357795i
$592$	−2.92498	−	5.06622i	−0.120216	−	0.208220i
$593$	23.8655			0.980037			0.490019	−	0.871712i	$-0.336990\pi$
$593$	23.8655			0.980037			0.490019	+	0.871712i	$0.336990\pi$
$594$	0.144695	+	0.250620i	0.00593692	+	0.0102831i
$595$	3.13161	−	5.42411i	0.128383	−	0.222367i
$596$	7.08529	−	12.2721i	0.290225	−	0.502684i
$597$	−57.3961			−2.34907
$598$	−0.155369	+	0.595080i	−0.00635350	+	0.0243347i
$599$	−44.6631			−1.82488			−0.912442	−	0.409206i	$-0.865806\pi$
$599$	−44.6631			−1.82488			−0.912442	+	0.409206i	$0.865806\pi$
$600$	−2.70275	+	4.68130i	−0.110339	+	0.191113i
$601$	20.3740	−	35.2888i	0.831072	−	1.43946i	−0.0661163	−	0.997812i	$-0.521061\pi$
$601$	20.3740	−	35.2888i	0.831072	−	1.43946i	0.897189	−	0.441648i	$-0.145606\pi$
$602$	−1.20809	−	2.09247i	−0.0492379	−	0.0852826i
$603$	−10.2066			−0.415646
$604$	7.56580	+	13.1044i	0.307848	+	0.533209i
$605$	−8.98052	−	15.5547i	−0.365110	−	0.632389i
$606$	3.18820			0.129512
$607$	14.0141	+	24.2732i	0.568817	+	0.985219i	0.996683	+	0.0813776i	$0.0259320\pi$
$607$	14.0141	+	24.2732i	0.568817	+	0.985219i	−0.427867	+	0.903842i	$0.640735\pi$
$608$	−0.500000	+	0.866025i	−0.0202777	+	0.0351220i
$609$	−13.4211	+	23.2460i	−0.543851	+	0.941977i
$610$	−5.74666			−0.232675
$611$	−2.20074	−	2.17269i	−0.0890323	−	0.0878978i
$612$	7.30219			0.295173
$613$	−18.5007	+	32.0441i	−0.747235	+	1.29425i	0.201909	+	0.979404i	$0.435286\pi$
$613$	−18.5007	+	32.0441i	−0.747235	+	1.29425i	−0.949143	+	0.314844i	$0.898048\pi$
$614$	1.90550	−	3.30042i	0.0768997	−	0.133194i
$615$	−4.07220	−	7.05326i	−0.164207	−	0.284415i
$616$	−0.480515			−0.0193605
$617$	19.7735	+	34.2487i	0.796051	+	1.37880i	0.922170	+	0.386785i	$0.126415\pi$
$617$	19.7735	+	34.2487i	0.796051	+	1.37880i	−0.126119	+	0.992015i	$0.540252\pi$
$618$	−7.29725	−	12.6392i	−0.293538	−	0.508424i
$619$	−37.8422			−1.52101			−0.760504	−	0.649334i	$-0.775048\pi$
$619$	−37.8422			−1.52101			−0.760504	+	0.649334i	$0.775048\pi$
$620$	−8.52830	−	14.7714i	−0.342505	−	0.593235i
$621$	−0.0707407	+	0.122526i	−0.00283872	+	0.00491682i
$622$	1.21690	−	2.10773i	0.0487932	−	0.0845122i
$623$	−14.9036			−0.597102
$624$	2.16524	−	8.29313i	0.0866790	−	0.331991i
$625$	−8.45997			−0.338399
$626$	12.5941	−	21.8136i	0.503361	−	0.871848i
$627$	−0.414711	+	0.718300i	−0.0165620	+	0.0286862i
$628$	5.47664	+	9.48582i	0.218542	+	0.378525i
$629$	16.1132			0.642475
$630$	3.01415	+	5.22066i	0.120087	+	0.207996i
$631$	−12.6033	−	21.8296i	−0.501730	−	0.869022i	−0.999998	−	0.00199872i	$-0.999364\pi$
$631$	−12.6033	−	21.8296i	−0.501730	−	0.869022i	0.498268	−	0.867023i	$-0.333970\pi$
$632$	7.88601			0.313689
$633$	−31.1610	−	53.9724i	−1.23854	−	2.14521i
$634$	−8.75693	+	15.1674i	−0.347782	+	0.602376i
$635$	2.37614	−	4.11560i	0.0942943	−	0.163323i
$636$	−24.5577			−0.973774
$637$	−17.7424	+	4.87620i	−0.702979	+	0.193202i
$638$	2.86064			0.113254
$639$	3.97664	−	6.88774i	0.157313	−	0.272475i
$640$	0.825547	−	1.42989i	0.0326326	−	0.0565213i
$641$	8.35918	+	14.4785i	0.330168	+	0.571867i	0.982545	−	0.186027i	$-0.0595613\pi$
$641$	8.35918	+	14.4785i	0.330168	+	0.571867i	−0.652377	+	0.757895i	$0.726228\pi$
$642$	0.178328			0.00703806
$643$	−10.7314	−	18.5874i	−0.423207	−	0.733016i	0.573044	−	0.819524i	$-0.305762\pi$
$643$	−10.7314	−	18.5874i	−0.423207	−	0.733016i	−0.996251	+	0.0865086i	$0.972429\pi$
$644$	−0.117460	−	0.203447i	−0.00462859	−	0.00801695i
$645$	6.88601			0.271137
$646$	−1.37720	−	2.38539i	−0.0541853	−	0.0938517i
$647$	−15.9685	+	27.6582i	−0.627786	+	1.08736i	0.360209	+	0.932872i	$0.382705\pi$
$647$	−15.9685	+	27.6582i	−0.627786	+	1.08736i	−0.987995	+	0.154486i	$0.950628\pi$
$648$	4.96249	−	8.59529i	0.194945	−	0.337655i
$649$	0.00270405			0.000106143
$650$	−7.90550	+	2.17269i	−0.310079	+	0.0852201i
$651$	33.8209			1.32554
$652$	1.32555	−	2.29591i	0.0519124	−	0.0899149i
$653$	−17.7657	+	30.7712i	−0.695227	+	1.20417i	0.274877	+	0.961479i	$0.411363\pi$
$653$	−17.7657	+	30.7712i	−0.695227	+	1.20417i	−0.970104	+	0.242689i	$0.921970\pi$
$654$	−13.3875	−	23.1878i	−0.523492	−	0.906714i
$655$	23.2859			0.909855
$656$	−1.03751	−	1.79702i	−0.0405079	−	0.0701617i
$657$	−22.1365	−	38.3416i	−0.863629	−	1.49585i
$658$	1.18125			0.0460500
$659$	11.5990	+	20.0901i	0.451834	+	0.782600i	0.998500	−	0.0547509i	$-0.0174365\pi$
$659$	11.5990	+	20.0901i	0.451834	+	0.782600i	−0.546666	+	0.837351i	$0.684103\pi$
$660$	0.684726	−	1.18598i	0.0266529	−	0.0461642i
$661$	10.5718	−	18.3109i	0.411195	−	0.712211i	−0.583825	−	0.811879i	$-0.698445\pi$
$661$	10.5718	−	18.3109i	0.411195	−	0.712211i	0.995021	+	0.0996679i	$0.0317780\pi$
$662$	−15.0099			−0.583375
$663$	16.8003	+	16.5863i	0.652471	+	0.644157i
$664$	13.9738			0.542290
$665$	1.13695	−	1.96925i	0.0440888	−	0.0763641i
$666$	−7.75441	+	13.4310i	−0.300477	+	0.520442i
$667$	0.699275	+	1.21118i	0.0270760	+	0.0468971i
$668$	−14.7077			−0.569057
$669$	−5.69741	−	9.86821i	−0.220275	−	0.381527i
$670$	−3.17833	−	5.50503i	−0.122790	−	0.212678i
$671$	−1.21437			−0.0468804
$672$	1.63695	+	2.83527i	0.0631465	+	0.109373i
$673$	−17.2750	+	29.9211i	−0.665900	+	1.15337i	0.313140	+	0.949707i	$0.398619\pi$
$673$	−17.2750	+	29.9211i	−0.665900	+	1.15337i	−0.979040	+	0.203666i	$0.934714\pi$
$674$	2.83969	−	4.91850i	0.109381	−	0.189453i
$675$	−1.88601			−0.0725927
$676$	11.1741	−	6.64383i	0.429771	−	0.255532i
$677$	19.3043			0.741925			0.370962	−	0.928648i	$-0.379028\pi$
$677$	19.3043			0.741925			0.370962	+	0.928648i	$0.379028\pi$
$678$	−2.15256	+	3.72833i	−0.0826684	+	0.143186i
$679$	2.23492	−	3.87100i	0.0857684	−	0.148555i
$680$	2.27389	+	3.93849i	0.0871997	+	0.151034i
$681$	5.35666			0.205268
$682$	−1.80219	−	3.12148i	−0.0690093	−	0.119528i
$683$	18.7169	+	32.4186i	0.716182	+	1.24046i	0.962502	+	0.271275i	$0.0874454\pi$
$683$	18.7169	+	32.4186i	0.716182	+	1.24046i	−0.246320	+	0.969189i	$0.579221\pi$
$684$	2.65109			0.101367
$685$	2.69635	+	4.67022i	0.103022	+	0.178440i
$686$	8.33436	−	14.4355i	0.318207	−	0.551151i
$687$	−19.7141	+	34.1458i	−0.752139	+	1.30274i
$688$	1.75441			0.0668861
$689$	−26.5060	−	26.1683i	−1.00980	−	0.996931i
$690$	0.669517			0.0254881
$691$	0.887476	−	1.53715i	0.0337612	−	0.0584761i	−0.848651	−	0.528953i	$-0.822585\pi$
$691$	0.887476	−	1.53715i	0.0337612	−	0.0584761i	0.882412	+	0.470477i	$0.155918\pi$
$692$	3.04632	−	5.27638i	0.115804	−	0.200578i
$693$	0.636945	+	1.10322i	0.0241956	+	0.0419079i
$694$	−28.0304			−1.06402
$695$	−3.35772	−	5.81574i	−0.127366	−	0.220604i
$696$	−9.74519	−	16.8792i	−0.369391	−	0.639803i
$697$	5.71544			0.216488
$698$	−17.2126	−	29.8131i	−0.651507	−	1.12844i
$699$	1.46783	−	2.54235i	0.0555184	−	0.0961607i
$700$	1.56580	−	2.71205i	0.0591818	−	0.102506i
$701$	41.5547			1.56950			0.784750	−	0.619812i	$-0.212791\pi$
$701$	41.5547			1.56950			0.784750	+	0.619812i	$0.212791\pi$
$702$	2.88360	−	0.792510i	0.108835	−	0.0299113i
$703$	5.84997			0.220636
$704$	0.174453	−	0.302162i	0.00657496	−	0.0113882i
$705$	−1.68326	+	2.91550i	−0.0633954	+	0.109804i
$706$	2.01908	+	3.49716i	0.0759892	+	0.131617i
$707$	−1.84704			−0.0694653
$708$	−0.00921176	−	0.0159552i	−0.000346199	−	0.000599634i
$709$	8.07220	+	13.9815i	0.303158	+	0.525085i	0.976849	−	0.213928i	$-0.0686257\pi$
$709$	8.07220	+	13.9815i	0.303158	+	0.525085i	−0.673692	+	0.739013i	$0.735292\pi$
$710$	4.95328			0.185893
$711$	−10.4533	−	18.1056i	−0.392029	−	0.679014i
$712$	5.41084	−	9.37184i	0.202780	−	0.351225i
$713$	0.881078	−	1.52607i	0.0329966	−	0.0571518i
$714$	−9.01762			−0.337476
$715$	2.00281	−	0.550440i	0.0749010	−	0.0205853i
$716$	−6.18045			−0.230974
$717$	−34.4501	+	59.6693i	−1.28656	+	2.22839i
$718$	4.40056	−	7.62200i	0.164228	−	0.284450i
$719$	9.59809	+	16.6244i	0.357948	+	0.619984i	0.987618	−	0.156879i	$-0.0501431\pi$
$719$	9.59809	+	16.6244i	0.357948	+	0.619984i	−0.629670	+	0.776863i	$0.716810\pi$
$720$	−4.37720			−0.163129
$721$	4.22757	+	7.32237i	0.157443	+	0.272699i
$722$	−0.500000	−	0.866025i	−0.0186081	−	0.0322301i
$723$	−9.26322			−0.344503
$724$	−2.90937	−	5.03918i	−0.108126	−	0.187280i
$725$	−9.32167	+	16.1456i	−0.346198	+	0.599633i
$726$	−12.9299	+	22.3953i	−0.479874	+	0.831167i
$727$	−10.6540			−0.395136			−0.197568	−	0.980289i	$-0.563304\pi$
$727$	−10.6540			−0.395136			−0.197568	+	0.980289i	$0.563304\pi$
$728$	−1.25441	+	4.80452i	−0.0464914	+	0.178067i
$729$	−20.3969			−0.755443
$730$	13.7866	−	23.8791i	0.510264	−	0.883803i
$731$	−2.41617	+	4.18493i	−0.0893654	+	0.154785i
$732$	4.13695	+	7.16540i	0.152906	+	0.264841i
$733$	50.6220			1.86977			0.934883	−	0.354956i	$-0.115504\pi$
$733$	50.6220			1.86977			0.934883	+	0.354956i	$0.115504\pi$
$734$	10.4805	+	18.1528i	0.386843	+	0.670032i
$735$	10.0152	+	17.3469i	0.369417	+	0.639848i
$736$	0.170578			0.00628760
$737$	−0.671640	−	1.16331i	−0.0247402	−	0.0428512i
$738$	−2.75053	+	4.76406i	−0.101248	+	0.175367i
$739$	−1.47412	+	2.55325i	−0.0542263	+	0.0939227i	−0.891864	−	0.452303i	$-0.850603\pi$
$739$	−1.47412	+	2.55325i	−0.0542263	+	0.0939227i	0.837638	+	0.546226i	$0.183936\pi$
$740$	−9.65884			−0.355066
$741$	6.09944	+	6.02172i	0.224068	+	0.221213i
$742$	14.2272			0.522296
$743$	−9.20662	+	15.9463i	−0.337758	+	0.585015i	−0.984011	−	0.178109i	$-0.943002\pi$
$743$	−9.20662	+	15.9463i	−0.337758	+	0.585015i	0.646252	+	0.763124i	$0.276335\pi$
$744$	−12.2788	+	21.2676i	−0.450164	+	0.779706i
$745$	−11.6985	−	20.2624i	−0.428599	−	0.742355i
$746$	−21.2186			−0.776869
$747$	−18.5230	−	32.0827i	−0.677720	−	1.17384i
$748$	0.480515	+	0.832277i	0.0175694	+	0.0304310i
$749$	−0.103312			−0.00377495
$750$	14.2750	+	24.7249i	0.521248	+	0.902827i
$751$	10.1964	−	17.6606i	0.372070	−	0.644444i	−0.617814	−	0.786325i	$-0.711981\pi$
$751$	10.1964	−	17.6606i	0.372070	−	0.644444i	0.989884	+	0.141880i	$0.0453147\pi$
$752$	−0.428859	+	0.742806i	−0.0156389	+	0.0270873i
$753$	6.72611			0.245113
$754$	7.46783	−	28.6027i	0.271962	−	1.04165i
$755$	24.9837			0.909250
$756$	−0.571141	+	0.989245i	−0.0207722	+	0.0359785i
$757$	12.8631	−	22.2795i	0.467516	−	0.809761i	−0.531795	−	0.846873i	$-0.678482\pi$
$757$	12.8631	−	22.2795i	0.467516	−	0.809761i	0.999311	+	0.0371119i	$0.0118158\pi$
$758$	1.16272	+	2.01389i	0.0422318	+	0.0731477i
$759$	0.141481			0.00513545
$760$	0.825547	+	1.42989i	0.0299457	+	0.0518675i
$761$	−4.42458	−	7.66360i	−0.160391	−	0.277805i	0.774618	−	0.632429i	$-0.217942\pi$
$761$	−4.42458	−	7.66360i	−0.160391	−	0.277805i	−0.935009	+	0.354624i	$0.884609\pi$
$762$	−6.84222			−0.247867
$763$	7.75587	+	13.4336i	0.280781	+	0.486327i
$764$	0.236383	−	0.409427i	0.00855202	−	0.0148125i
$765$	6.02830	−	10.4413i	0.217954	−	0.377507i
$766$	36.5547			1.32078
$767$	0.00705905	−	0.0270370i	0.000254888	−	0.000976249i
$768$	−2.37720			−0.0857799
$769$	25.6387	−	44.4075i	0.924554	−	1.60137i	0.132277	−	0.991213i	$-0.457771\pi$
$769$	25.6387	−	44.4075i	0.924554	−	1.60137i	0.792277	−	0.610162i	$-0.208896\pi$
$770$	−0.396688	+	0.687083i	−0.0142956	+	0.0247608i
$771$	−18.2891	−	31.6777i	−0.658666	−	1.14084i
$772$	−8.21942			−0.295823
$773$	−14.0371	−	24.3130i	−0.504880	−	0.874477i	−0.999984	−	0.00564375i	$-0.998204\pi$
$773$	−14.0371	−	24.3130i	−0.504880	−	0.874477i	0.495104	−	0.868833i	$-0.335130\pi$
$774$	−2.32555	−	4.02797i	−0.0835901	−	0.144782i
$775$	23.4904			0.843800
$776$	1.62280	+	2.81077i	0.0582550	+	0.100901i
$777$	9.57608	−	16.5863i	0.343540	−	0.595028i
$778$	−9.58141	+	16.5955i	−0.343510	+	0.594977i
$779$	2.07502			0.0743452
$780$	−10.0707	−	9.94242i	−0.360590	−	0.355996i
$781$	1.04672			0.0374546
$782$	−0.234921	+	0.406895i	−0.00840075	+	0.0145505i
$783$	3.40016	−	5.88925i	0.121512	−	0.210465i
$784$	2.55166	+	4.41960i	0.0911306	+	0.157843i
$785$	18.0849			0.645477
$786$	−16.7632	−	29.0347i	−0.597924	−	1.03564i
$787$	−8.86558	−	15.3556i	−0.316024	−	0.547369i	0.663631	−	0.748060i	$-0.269015\pi$
$787$	−8.86558	−	15.3556i	−0.316024	−	0.547369i	−0.979655	+	0.200691i	$0.935681\pi$
$788$	4.22505			0.150511
$789$	−7.68180	−	13.3053i	−0.273479	−	0.473680i
$790$	6.51027	−	11.2761i	0.231625	−	0.401186i
$791$	1.24706	−	2.15996i	0.0443402	−	0.0767995i
$792$	−0.924984			−0.0328679
$793$	−3.17018	+	12.1421i	−0.112576	+	0.431180i
$794$	20.9298			0.742771
$795$	−20.2735	+	35.1147i	−0.719027	+	1.24539i
$796$	−12.0722	+	20.9097i	−0.427888	+	0.741124i
$797$	−22.1040	−	38.2852i	−0.782963	−	1.35613i	−0.930208	−	0.367032i	$-0.880374\pi$
$797$	−22.1040	−	38.2852i	−0.782963	−	1.35613i	0.147246	−	0.989100i	$-0.452959\pi$
$798$	−3.27389			−0.115894
$799$	−1.18125	−	2.04599i	−0.0417897	−	0.0723819i
$800$	1.13695	+	1.96925i	0.0401971	+	0.0696234i
$801$	−28.6893			−1.01369
$802$	−5.60331	−	9.70522i	−0.197860	−	0.342703i
$803$	2.91336	−	5.04609i	0.102810	−	0.178072i
$804$	−4.57608	+	7.92600i	−0.161386	+	0.279528i
$805$	−0.387876			−0.0136708
$806$	−35.9154	+	9.87074i	−1.26507	+	0.347682i
$807$	−40.1046			−1.41175
$808$	0.670578	−	1.16148i	0.0235909	−	0.0408606i
$809$	−7.97664	+	13.8159i	−0.280444	+	0.485743i	−0.971494	−	0.237064i	$-0.923815\pi$
$809$	−7.97664	+	13.8159i	−0.280444	+	0.485743i	0.691050	+	0.722807i	$0.257148\pi$
$810$	−8.19354	−	14.1916i	−0.287892	−	0.498643i
$811$	23.2349			0.815888			0.407944	−	0.913007i	$-0.366246\pi$
$811$	23.2349			0.815888			0.407944	+	0.913007i	$0.366246\pi$
$812$	5.64576	+	9.77874i	0.198127	+	0.343166i
$813$	−5.00921	−	8.67621i	−0.175681	−	0.304288i
$814$	−2.04109			−0.0715403
$815$	−2.18860	−	3.79077i	−0.0766634	−	0.132785i
$816$	3.27389	−	5.67054i	0.114609	−	0.198509i
$817$	−0.877203	+	1.51936i	−0.0306894	+	0.0531557i
$818$	29.5315			1.03254
$819$	12.6935	−	3.48861i	0.443548	−	0.121902i
$820$	−3.42605			−0.119643
$821$	4.24278	−	7.34871i	0.148074	−	0.256472i	−0.782442	−	0.622724i	$-0.786026\pi$
$821$	4.24278	−	7.34871i	0.148074	−	0.256472i	0.930516	+	0.366252i	$0.119359\pi$
$822$	3.88214	−	6.72406i	0.135405	−	0.234529i
$823$	20.1794	+	34.9517i	0.703409	+	1.21834i	0.967263	+	0.253778i	$0.0816732\pi$
$823$	20.1794	+	34.9517i	0.703409	+	1.21834i	−0.263853	+	0.964563i	$0.584993\pi$
$824$	−6.13936			−0.213875
$825$	0.943007	+	1.63334i	0.0328313	+	0.0568655i
$826$	0.00533672	+	0.00924346i	0.000185688	+	0.000321621i
$827$	−30.3227			−1.05442			−0.527212	−	0.849734i	$-0.676763\pi$
$827$	−30.3227			−1.05442			−0.527212	+	0.849734i	$0.676763\pi$
$828$	−0.226109	−	0.391633i	−0.00785785	−	0.0136102i
$829$	6.45716	−	11.1841i	0.224266	−	0.388441i	−0.731833	−	0.681484i	$-0.761335\pi$
$829$	6.45716	−	11.1841i	0.224266	−	0.388441i	0.956099	+	0.293044i	$0.0946681\pi$
$830$	11.5360	−	19.9810i	0.400422	−	0.693551i
$831$	57.0091			1.97762
$832$	−2.56580	−	2.53311i	−0.0889533	−	0.0878198i
$833$	−14.0566			−0.487032
$834$	−4.83436	+	8.37335i	−0.167400	+	0.289946i
$835$	−12.1419	+	21.0304i	−0.420187	+	0.727785i
$836$	0.174453	+	0.302162i	0.00603359	+	0.0104505i
$837$	−8.56833			−0.296165
$838$	−5.85878	−	10.1477i	−0.202388	−	0.350547i
$839$	−6.85143	−	11.8670i	−0.236538	−	0.409695i	0.723181	−	0.690659i	$-0.242679\pi$
$839$	−6.85143	−	11.8670i	−0.236538	−	0.409695i	−0.959718	+	0.280964i	$0.909346\pi$
$840$	5.40550			0.186507
$841$	−19.1108	−	33.1008i	−0.658992	−	1.14141i
$842$	−7.85918	+	13.6125i	−0.270845	+	0.469118i
$843$	26.2257	−	45.4243i	0.903261	−	1.56449i
$844$	−26.2165			−0.902409
$845$	−0.275243	−	21.4624i	−0.00946863	−	0.738331i
$846$	2.27389			0.0781780
$847$	7.49079	−	12.9744i	0.257387	−	0.445807i
$848$	−5.16524	+	8.94646i	−0.177375	+	0.307223i
$849$	16.3939	+	28.3950i	0.562636	+	0.974515i
$850$	−6.26322			−0.214827
$851$	−0.498939	−	0.864187i	−0.0171034	−	0.0296240i
$852$	−3.56580	−	6.17615i	−0.122162	−	0.211592i
$853$	48.1174			1.64751			0.823755	−	0.566946i	$-0.191875\pi$
$853$	48.1174			1.64751			0.823755	+	0.566946i	$0.191875\pi$
$854$	−2.39669	−	4.15118i	−0.0820130	−	0.142051i
$855$	2.18860	−	3.79077i	0.0748486	−	0.129642i
$856$	0.0375080	−	0.0649658i	0.00128200	−	0.00222049i
$857$	37.6941			1.28761			0.643803	−	0.765191i	$-0.277356\pi$
$857$	37.6941			1.28761			0.643803	+	0.765191i	$0.277356\pi$
$858$	−2.12813	−	2.10102i	−0.0726533	−	0.0717275i
$859$	−34.1153			−1.16400			−0.582000	−	0.813189i	$-0.697729\pi$
$859$	−34.1153			−1.16400			−0.582000	+	0.813189i	$0.697729\pi$
$860$	1.44834	−	2.50861i	0.0493881	−	0.0855427i
$861$	3.39669	−	5.88324i	0.115759	−	0.200500i
$862$	4.10971	+	7.11823i	0.139977	+	0.242448i
$863$	−0.518684			−0.0176562			−0.00882811	−	0.999961i	$-0.502810\pi$
$863$	−0.518684			−0.0176562			−0.00882811	+	0.999961i	$0.502810\pi$
$864$	−0.414711	−	0.718300i	−0.0141088	−	0.0244371i
$865$	−5.02976	−	8.71180i	−0.171017	−	0.296210i
$866$	−26.8187			−0.911338
$867$	−11.1886	−	19.3792i	−0.379985	−	0.658153i
$868$	7.11359	−	12.3211i	0.241451	−	0.418205i
$869$	1.37574	−	2.38285i	0.0466688	−	0.0808328i
$870$	−32.1805			−1.09102
$871$	−13.3850	+	3.67863i	−0.453532	+	0.124646i
$872$	−11.2632			−0.381421
$873$	4.30219	−	7.45161i	0.145607	−	0.252199i
$874$	−0.0852891	+	0.147725i	−0.00288495	+	0.00499688i
$875$	−8.27002	−	14.3241i	−0.279578	−	0.484243i
$876$	−39.6991			−1.34131
$877$	−19.8899	−	34.4503i	−0.671634	−	1.16330i	−0.977441	−	0.211210i	$-0.932259\pi$
$877$	−19.8899	−	34.4503i	−0.671634	−	1.16330i	0.305807	−	0.952094i	$-0.401074\pi$
$878$	−0.560468	−	0.970758i	−0.0189149	−	0.0327615i
$879$	48.7402			1.64397
$880$	−0.288039	−	0.498898i	−0.00970978	−	0.0168178i
$881$	−8.84211	+	15.3150i	−0.297898	+	0.515975i	−0.975655	−	0.219311i	$-0.929619\pi$
$881$	−8.84211	+	15.3150i	−0.297898	+	0.515975i	0.677757	+	0.735286i	$0.262952\pi$
$882$	6.76468	−	11.7168i	0.227779	−	0.394524i
$883$	−8.21942			−0.276606			−0.138303	−	0.990390i	$-0.544165\pi$
$883$	−8.21942			−0.276606			−0.138303	+	0.990390i	$0.544165\pi$
$884$	9.57608	−	2.63182i	0.322078	−	0.0885179i
$885$	−0.0304189			−0.00102252
$886$	19.0230	−	32.9487i	0.639089	−	1.10693i
$887$	−11.0414	+	19.1242i	−0.370733	+	0.642129i	−0.989679	−	0.143305i	$-0.954227\pi$
$887$	−11.0414	+	19.1242i	−0.370733	+	0.642129i	0.618945	+	0.785434i	$0.287560\pi$
$888$	6.95328	+	12.0434i	0.233337	+	0.404151i
$889$	3.96395			0.132947
$890$	−8.93380	−	15.4738i	−0.299462	−	0.518683i
$891$	−1.73145	−	2.99895i	−0.0580056	−	0.100469i
$892$	−4.79338			−0.160494
$893$	−0.428859	−	0.742806i	−0.0143512	−	0.0248570i
$894$	−16.8432	+	29.1732i	−0.563320	+	0.975699i
$895$	−5.10225	+	8.83736i	−0.170549	+	0.295400i
$896$	1.37720			0.0460091
$897$	0.369343	−	1.41463i	0.0123320	−	0.0472330i
$898$	27.3969			0.914248
$899$	−42.3492	+	73.3509i	−1.41242	+	2.44639i
$900$	3.01415	−	5.22066i	0.100472	−	0.174022i
$901$	−14.2272	−	24.6422i	−0.473976	−	0.820950i
$902$	−0.723987			−0.0241061
$903$	2.87187	+	4.97422i	0.0955697	+	0.165532i
$904$	0.905499	+	1.56837i	0.0301165	+	0.0521632i
$905$	−9.60730			−0.319357
$906$	−17.9855	−	31.1517i	−0.597527	−	1.03495i
$907$	17.7555	−	30.7534i	0.589561	−	1.02115i	−0.404729	−	0.914437i	$-0.632634\pi$
$907$	17.7555	−	30.7534i	0.589561	−	1.02115i	0.994290	−	0.106712i	$-0.0340324\pi$
$908$	1.12667	−	1.95145i	0.0373899	−	0.0647613i
$909$	−3.55553			−0.117930
$910$	5.83436	+	5.76002i	0.193407	+	0.190943i
$911$	55.1690			1.82783			0.913915	−	0.405906i	$-0.133044\pi$
$911$	55.1690			1.82783			0.913915	+	0.405906i	$0.133044\pi$
$912$	1.18860	−	2.05872i	0.0393585	−	0.0681710i
$913$	2.43778	−	4.22236i	0.0806787	−	0.139740i
$914$	19.9762	+	34.5999i	0.660755	+	1.14446i
$915$	13.6610			0.451618
$916$	8.29298	+	14.3639i	0.274008	+	0.474595i
$917$	9.71156	+	16.8209i	0.320704	+	0.555476i
$918$	2.28456			0.0754018
$919$	15.3139	+	26.5245i	0.505160	+	0.874962i	0.999982	+	0.00596815i	$0.00189973\pi$
$919$	15.3139	+	26.5245i	0.505160	+	0.874962i	−0.494823	+	0.868994i	$0.664767\pi$
$920$	0.140820	−	0.243908i	0.00464271	−	0.00804141i
$921$	−4.52976	+	7.84577i	−0.149261	+	0.258527i
$922$	32.1650			1.05930
$923$	2.73251	−	10.4658i	0.0899416	−	0.344487i
$924$	1.14228			0.0375783
$925$	6.65109	−	11.5200i	0.218687	−	0.378776i
$926$	13.2930	−	23.0241i	0.436834	−	0.756619i
$927$	8.13801	+	14.0954i	0.267287	+	0.462955i
$928$	−8.19887			−0.269141
$929$	3.32302	+	5.75565i	0.109025	+	0.188837i	0.915375	−	0.402601i	$-0.131894\pi$
$929$	3.32302	+	5.75565i	0.109025	+	0.188837i	−0.806351	+	0.591438i	$0.798561\pi$
$930$	20.2735	+	35.1147i	0.664794	+	1.15146i
$931$	−5.10331			−0.167254
$932$	−0.617460	−	1.06947i	−0.0202256	−	0.0350317i
$933$	−2.89281	+	5.01050i	−0.0947064	+	0.164036i
$934$	−6.73880	+	11.6719i	−0.220500	+	0.381917i
$935$	1.58675			0.0518923
$936$	−2.41471	+	9.24862i	−0.0789273	+	0.302301i
$937$	−23.3638			−0.763263			−0.381631	−	0.924315i	$-0.624638\pi$
$937$	−23.3638			−0.763263			−0.381631	+	0.924315i	$0.624638\pi$
$938$	2.65109	−	4.59183i	0.0865613	−	0.149929i
$939$	−29.9387	+	51.8554i	−0.977014	+	1.69224i
$940$	0.708086	+	1.22644i	0.0230952	+	0.0400021i
$941$	17.0262			0.555037			0.277519	−	0.960720i	$-0.410488\pi$
$941$	17.0262			0.555037			0.277519	+	0.960720i	$0.410488\pi$
$942$	−13.0191	−	22.5497i	−0.424185	−	0.734709i
$943$	−0.176976	−	0.306532i	−0.00576314	−	0.00998205i
$944$	−0.00775008			−0.000252244
$945$	0.943007	+	1.63334i	0.0306760	+	0.0531324i
$946$	0.306062	−	0.530115i	0.00995093	−	0.0172355i
$947$	−11.5459	+	19.9981i	−0.375192	+	0.649852i	−0.990356	−	0.138548i	$-0.955757\pi$
$947$	−11.5459	+	19.9981i	−0.375192	+	0.649852i	0.615164	+	0.788399i	$0.289090\pi$
$948$	−18.7467			−0.608863
$949$	−42.8488	−	42.3028i	−1.39093	−	1.37321i
$950$	−2.27389			−0.0737748
$951$	20.8170	−	36.0561i	0.675037	−	1.16920i
$952$	−1.89669	+	3.28516i	−0.0614720	+	0.106473i
$953$	16.3474	+	28.3146i	0.529546	+	0.917200i	0.999406	+	0.0344593i	$0.0109709\pi$
$953$	16.3474	+	28.3146i	0.529546	+	0.917200i	−0.469860	+	0.882741i	$0.655696\pi$
$954$	27.3871			0.886689
$955$	−0.390290	−	0.676002i	−0.0126295	−	0.0218749i
$956$	14.4918	+	25.1006i	0.468700	+	0.811812i
$957$	−6.80032			−0.219823
$958$	1.97170	+	3.41509i	0.0637029	+	0.110337i
$959$	−2.24907	+	3.89550i	−0.0726262	+	0.125792i
$960$	−1.96249	+	3.39914i	−0.0633392	+	0.109707i
$961$	75.7189			2.44254
$962$	−5.32836	+	20.4082i	−0.171793	+	0.657988i
$963$	−0.198875			−0.00640864
$964$	−1.94834	+	3.37463i	−0.0627519	+	0.108690i
$965$	−6.78552	+	11.7529i	−0.218433	+	0.378338i
$966$	0.279227	+	0.483636i	0.00898399	+	0.0155607i
$967$	13.6305			0.438329			0.219164	−	0.975688i	$-0.429667\pi$
$967$	13.6305			0.438329			0.219164	+	0.975688i	$0.429667\pi$
$968$	5.43913	+	9.42085i	0.174820	+	0.302798i
$969$	3.27389	+	5.67054i	0.105173	+	0.182164i
$970$	5.35878			0.172060
$971$	−13.4430	−	23.2840i	−0.431407	−	0.747218i	0.565588	−	0.824688i	$-0.308649\pi$
$971$	−13.4430	−	23.2840i	−0.431407	−	0.747218i	−0.996995	+	0.0774697i	$0.975316\pi$
$972$	−10.5527	+	18.2778i	−0.338479	+	0.586262i
$973$	2.80073	−	4.85100i	0.0897871	−	0.155516i
$974$	−1.13453			−0.0363527
$975$	18.7930	−	5.16494i	0.601857	−	0.165410i
$976$	3.48052			0.111409
$977$	−4.94699	+	8.56844i	−0.158268	+	0.274129i	−0.934244	−	0.356634i	$-0.883924\pi$
$977$	−4.94699	+	8.56844i	−0.158268	+	0.274129i	0.775976	+	0.630762i	$0.217258\pi$
$978$	−3.15109	+	5.45785i	−0.100761	+	0.174523i
$979$	−1.88788	−	3.26990i	−0.0603368	−	0.104506i
$980$	8.42605			0.269160
$981$	14.9299	+	25.8594i	0.476676	+	0.825626i
$982$	−15.2657	−	26.4410i	−0.487149	−	0.843767i
$983$	24.8492			0.792565			0.396283	−	0.918129i	$-0.370300\pi$
$983$	24.8492			0.792565			0.396283	+	0.918129i	$0.370300\pi$
$984$	2.46637	+	4.27187i	0.0786249	+	0.136182i
$985$	3.48797	−	6.04135i	0.111136	−	0.192493i
$986$	11.2915	−	19.5575i	0.359595	−	0.622837i
$987$	−2.80807			−0.0893820
$988$	3.47664	−	0.955496i	0.110607	−	0.0303984i
$989$	0.299263			0.00951602
$990$	−0.763617	+	1.32262i	−0.0242694	+	0.0420358i
$991$	14.8744	−	25.7632i	0.472501	−	0.818395i	−0.527004	−	0.849863i	$-0.676685\pi$
$991$	14.8744	−	25.7632i	0.472501	−	0.818395i	0.999505	+	0.0314677i	$0.0100181\pi$
$992$	5.16524	+	8.94646i	0.163997	+	0.284050i
$993$	35.6815			1.13232
$994$	2.06580	+	3.57808i	0.0655233	+	0.113490i
$995$	19.9323	+	34.5238i	0.631897	+	1.09448i
$996$	−33.2186			−1.05257
$997$	16.1794	+	28.0235i	0.512406	+	0.887514i	0.999897	+	0.0143854i	$0.00457918\pi$
$997$	16.1794	+	28.0235i	0.512406	+	0.887514i	−0.487490	+	0.873129i	$0.662087\pi$
$998$	0.877203	−	1.51936i	0.0277674	−	0.0480945i
$999$	−2.42605	+	4.20203i	−0.0767567	+	0.132946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	494.2.g.b.191.3	✓	6
13.3	even	3	inner	494.2.g.b.419.3	yes	6
13.4	even	6		6422.2.a.m.1.1		3
13.9	even	3		6422.2.a.u.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.g.b.191.3	✓	6	1.1	even	1	trivial
494.2.g.b.419.3	yes	6	13.3	even	3	inner
6422.2.a.m.1.1		3	13.4	even	6
6422.2.a.u.1.1		3	13.9	even	3

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:	\( N \)	\(=\)	\( 494 = 2 \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	494.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.18860 - 2.05872i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.65109 q^{5} +(1.18860 + 2.05872i) q^{6} +(-0.688601 - 1.19269i) q^{7} +1.00000 q^{8} +(-1.32555 - 2.29591i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.18860 - 2.05872i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.65109 q^{5} +(1.18860 + 2.05872i) q^{6} +(-0.688601 - 1.19269i) q^{7} +1.00000 q^{8} +(-1.32555 - 2.29591i) q^{9} +(0.825547 - 1.42989i) q^{10} +(0.174453 - 0.302162i) q^{11} -2.37720 q^{12} +(-2.56580 - 2.53311i) q^{13} +1.37720 q^{14} +(-1.96249 + 3.39914i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.37720 - 2.38539i) q^{17} +2.65109 q^{18} +(-0.500000 - 0.866025i) q^{19} +(0.825547 + 1.42989i) q^{20} -3.27389 q^{21} +(0.174453 + 0.302162i) q^{22} +(-0.0852891 + 0.147725i) q^{23} +(1.18860 - 2.05872i) q^{24} -2.27389 q^{25} +(3.47664 - 0.955496i) q^{26} +0.829422 q^{27} +(-0.688601 + 1.19269i) q^{28} +(4.09944 - 7.10043i) q^{29} +(-1.96249 - 3.39914i) q^{30} -10.3305 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.414711 - 0.718300i) q^{33} +2.75441 q^{34} +(1.13695 + 1.96925i) q^{35} +(-1.32555 + 2.29591i) q^{36} +(-2.92498 + 5.06622i) q^{37} +1.00000 q^{38} +(-8.26468 + 2.27141i) q^{39} -1.65109 q^{40} +(-1.03751 + 1.79702i) q^{41} +(1.63695 - 2.83527i) q^{42} +(-0.877203 - 1.51936i) q^{43} -0.348907 q^{44} +(2.18860 + 3.79077i) q^{45} +(-0.0852891 - 0.147725i) q^{46} +0.857718 q^{47} +(1.18860 + 2.05872i) q^{48} +(2.55166 - 4.41960i) q^{49} +(1.13695 - 1.96925i) q^{50} -6.54778 q^{51} +(-0.910836 + 3.48861i) q^{52} +10.3305 q^{53} +(-0.414711 + 0.718300i) q^{54} +(-0.288039 + 0.498898i) q^{55} +(-0.688601 - 1.19269i) q^{56} -2.37720 q^{57} +(4.09944 + 7.10043i) q^{58} +(0.00387504 + 0.00671177i) q^{59} +3.92498 q^{60} +(-1.74026 - 3.01421i) q^{61} +(5.16524 - 8.94646i) q^{62} +(-1.82555 + 3.16194i) q^{63} +1.00000 q^{64} +(4.23638 + 4.18240i) q^{65} +0.829422 q^{66} +(1.92498 - 3.33417i) q^{67} +(-1.37720 + 2.38539i) q^{68} +(0.202750 + 0.351173i) q^{69} -2.27389 q^{70} +(1.50000 + 2.59808i) q^{71} +(-1.32555 - 2.29591i) q^{72} +16.6999 q^{73} +(-2.92498 - 5.06622i) q^{74} +(-2.70275 + 4.68130i) q^{75} +(-0.500000 + 0.866025i) q^{76} -0.480515 q^{77} +(2.16524 - 8.29313i) q^{78} +7.88601 q^{79} +(0.825547 - 1.42989i) q^{80} +(4.96249 - 8.59529i) q^{81} +(-1.03751 - 1.79702i) q^{82} +13.9738 q^{83} +(1.63695 + 2.83527i) q^{84} +(2.27389 + 3.93849i) q^{85} +1.75441 q^{86} +(-9.74519 - 16.8792i) q^{87} +(0.174453 - 0.302162i) q^{88} +(5.41084 - 9.37184i) q^{89} -4.37720 q^{90} +(-1.25441 + 4.80452i) q^{91} +0.170578 q^{92} +(-12.2788 + 21.2676i) q^{93} +(-0.428859 + 0.742806i) q^{94} +(0.825547 + 1.42989i) q^{95} -2.37720 q^{96} +(1.62280 + 2.81077i) q^{97} +(2.55166 + 4.41960i) q^{98} -0.924984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 2 q^{3} - 3 q^{4} + 4 q^{5} + 2 q^{6} + q^{7} + 6 q^{8} - q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 + 4 * q^5 + 2 * q^6 + q^7 + 6 * q^8 - q^9	\( 6 q - 3 q^{2} + 2 q^{3} - 3 q^{4} + 4 q^{5} + 2 q^{6} + q^{7} + 6 q^{8} - q^{9} - 2 q^{10} + 8 q^{11} - 4 q^{12} - 2 q^{14} - 3 q^{15} - 3 q^{16} + 2 q^{17} + 2 q^{18} - 3 q^{19} - 2 q^{20} - 16 q^{21} + 8 q^{22} - 2 q^{23} + 2 q^{24} - 10 q^{25} + 2 q^{27} + q^{28} + 14 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - q^{33} - 4 q^{34} + 5 q^{35} - q^{36} + 6 q^{38} - 13 q^{39} + 4 q^{40} - 15 q^{41} + 8 q^{42} + 5 q^{43} - 16 q^{44} + 8 q^{45} - 2 q^{46} - 22 q^{47} + 2 q^{48} + 12 q^{49} + 5 q^{50} - 32 q^{51} + 10 q^{53} - q^{54} + 14 q^{55} + q^{56} - 4 q^{57} + 14 q^{58} + 4 q^{59} + 6 q^{60} - 2 q^{61} + 5 q^{62} - 4 q^{63} + 6 q^{64} + 13 q^{65} + 2 q^{66} - 6 q^{67} + 2 q^{68} - 16 q^{69} - 10 q^{70} + 9 q^{71} - q^{72} + 30 q^{73} + q^{75} - 3 q^{76} + 14 q^{77} - 13 q^{78} - 4 q^{79} - 2 q^{80} + 21 q^{81} - 15 q^{82} + 10 q^{83} + 8 q^{84} + 10 q^{85} - 10 q^{86} - 5 q^{87} + 8 q^{88} + 27 q^{89} - 16 q^{90} + 13 q^{91} + 4 q^{92} - 25 q^{93} + 11 q^{94} - 2 q^{95} - 4 q^{96} + 20 q^{97} + 12 q^{98} + 12 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 + 4 * q^5 + 2 * q^6 + q^7 + 6 * q^8 - q^9 - 2 * q^10 + 8 * q^11 - 4 * q^12 - 2 * q^14 - 3 * q^15 - 3 * q^16 + 2 * q^17 + 2 * q^18 - 3 * q^19 - 2 * q^20 - 16 * q^21 + 8 * q^22 - 2 * q^23 + 2 * q^24 - 10 * q^25 + 2 * q^27 + q^28 + 14 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - q^33 - 4 * q^34 + 5 * q^35 - q^36 + 6 * q^38 - 13 * q^39 + 4 * q^40 - 15 * q^41 + 8 * q^42 + 5 * q^43 - 16 * q^44 + 8 * q^45 - 2 * q^46 - 22 * q^47 + 2 * q^48 + 12 * q^49 + 5 * q^50 - 32 * q^51 + 10 * q^53 - q^54 + 14 * q^55 + q^56 - 4 * q^57 + 14 * q^58 + 4 * q^59 + 6 * q^60 - 2 * q^61 + 5 * q^62 - 4 * q^63 + 6 * q^64 + 13 * q^65 + 2 * q^66 - 6 * q^67 + 2 * q^68 - 16 * q^69 - 10 * q^70 + 9 * q^71 - q^72 + 30 * q^73 + q^75 - 3 * q^76 + 14 * q^77 - 13 * q^78 - 4 * q^79 - 2 * q^80 + 21 * q^81 - 15 * q^82 + 10 * q^83 + 8 * q^84 + 10 * q^85 - 10 * q^86 - 5 * q^87 + 8 * q^88 + 27 * q^89 - 16 * q^90 + 13 * q^91 + 4 * q^92 - 25 * q^93 + 11 * q^94 - 2 * q^95 - 4 * q^96 + 20 * q^97 + 12 * q^98 + 12 * q^99

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