LMFDB - Embedded newform 637.2.bl.a.534.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, 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:	$324$
Relative dimension:	$27$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			534.7
Character	$\chi$	$=$	637.534
Dual form			637.2.bl.a.235.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.64912 + 0.248565i) q^{2} +(0.245042 + 0.167067i) q^{3} +(0.746668 - 0.230317i) q^{4} +(0.200654 - 2.67754i) q^{5} +(-0.445631 - 0.214605i) q^{6} +(2.62546 - 0.327044i) q^{7} +(1.83108 - 0.881802i) q^{8} +(-1.06389 - 2.71074i) q^{9} +O(q^{10})$	\(q+(-1.64912 + 0.248565i) q^{2} +(0.245042 + 0.167067i) q^{3} +(0.746668 - 0.230317i) q^{4} +(0.200654 - 2.67754i) q^{5} +(-0.445631 - 0.214605i) q^{6} +(2.62546 - 0.327044i) q^{7} +(1.83108 - 0.881802i) q^{8} +(-1.06389 - 2.71074i) q^{9} +(0.334640 + 4.46546i) q^{10} +(0.884677 - 2.25412i) q^{11} +(0.221444 + 0.0683063i) q^{12} +(-0.623490 - 0.781831i) q^{13} +(-4.24841 + 1.19193i) q^{14} +(0.496497 - 0.622587i) q^{15} +(-4.09170 + 2.78968i) q^{16} +(-1.10025 + 1.02088i) q^{17} +(2.42828 + 4.20590i) q^{18} +(-1.62635 + 2.81692i) q^{19} +(-0.466859 - 2.04544i) q^{20} +(0.697987 + 0.358488i) q^{21} +(-0.898644 + 3.93722i) q^{22} +(-3.39278 - 3.14804i) q^{23} +(0.596013 + 0.0898344i) q^{24} +(-2.18479 - 0.329304i) q^{25} +(1.22255 + 1.13436i) q^{26} +(0.390161 - 1.70941i) q^{27} +(1.88502 - 0.848880i) q^{28} +(-0.0150067 - 0.0657485i) q^{29} +(-0.664030 + 1.15013i) q^{30} +(1.87054 + 3.23987i) q^{31} +(3.07467 - 2.85287i) q^{32} +(0.593373 - 0.404555i) q^{33} +(1.56068 - 1.95703i) q^{34} +(-0.348864 - 7.09539i) q^{35} +(-1.41870 - 1.77899i) q^{36} +(-10.3592 - 3.19538i) q^{37} +(1.98186 - 5.04970i) q^{38} +(-0.0221631 - 0.295746i) q^{39} +(-1.99364 - 5.07972i) q^{40} +(-1.25712 + 0.605399i) q^{41} +(-1.24017 - 0.417695i) q^{42} +(-3.12343 - 1.50417i) q^{43} +(0.141399 - 1.88684i) q^{44} +(-7.47159 + 2.30468i) q^{45} +(6.37759 + 4.34817i) q^{46} +(10.0620 - 1.51660i) q^{47} -1.46870 q^{48} +(6.78608 - 1.71728i) q^{49} +3.68483 q^{50} +(-0.440162 + 0.0663437i) q^{51} +(-0.645608 - 0.440168i) q^{52} +(1.67777 - 0.517523i) q^{53} +(-0.218524 + 2.91600i) q^{54} +(-5.85798 - 2.82105i) q^{55} +(4.51904 - 2.91398i) q^{56} +(-0.869139 + 0.418556i) q^{57} +(0.0410906 + 0.104697i) q^{58} +(-0.534977 - 7.13877i) q^{59} +(0.227326 - 0.579217i) q^{60} +(-3.00034 - 0.925482i) q^{61} +(-3.89006 - 4.87798i) q^{62} +(-3.67973 - 6.76901i) q^{63} +(1.81393 - 2.27459i) q^{64} +(-2.21849 + 1.51254i) q^{65} +(-0.877985 + 0.814651i) q^{66} +(0.497968 + 0.862506i) q^{67} +(-0.586393 + 1.01566i) q^{68} +(-0.305441 - 1.33822i) q^{69} +(2.33898 + 11.6144i) q^{70} +(0.0794855 - 0.348249i) q^{71} +(-4.33841 - 4.02545i) q^{72} +(3.93063 + 0.592447i) q^{73} +(17.8778 + 2.69464i) q^{74} +(-0.480350 - 0.445700i) q^{75} +(-0.565560 + 2.47788i) q^{76} +(1.58549 - 6.20743i) q^{77} +(0.110062 + 0.482213i) q^{78} +(3.62186 - 6.27324i) q^{79} +(6.64845 + 11.5155i) q^{80} +(-6.02284 + 5.58838i) q^{81} +(1.92267 - 1.31085i) q^{82} +(-2.69260 + 3.37641i) q^{83} +(0.603730 + 0.106914i) q^{84} +(2.51267 + 3.15079i) q^{85} +(5.52480 + 1.70417i) q^{86} +(0.00730714 - 0.0186183i) q^{87} +(-0.367773 - 4.90759i) q^{88} +(-5.05565 - 12.8816i) q^{89} +(11.7487 - 5.65787i) q^{90} +(-1.89264 - 1.84876i) q^{91} +(-3.25832 - 1.56913i) q^{92} +(-0.0829140 + 1.10641i) q^{93} +(-16.2165 + 5.00211i) q^{94} +(7.21608 + 4.91984i) q^{95} +(1.23004 - 0.185399i) q^{96} -9.44111 q^{97} +(-10.7642 + 4.51879i) q^{98} -7.05154 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) $ 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{4}{21}\right)$

Coefficient data

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

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

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

$2$	−1.64912	+	0.248565i	−1.16610	+	0.175762i	−0.703429	−	0.710766i	$-0.748349\pi$
$2$	−1.64912	+	0.248565i	−1.16610	+	0.175762i	−0.462675	+	0.886528i	$0.653110\pi$
$3$	0.245042	+	0.167067i	0.141475	+	0.0964562i	0.631989	−	0.774977i	$-0.282239\pi$
$3$	0.245042	+	0.167067i	0.141475	+	0.0964562i	−0.490514	+	0.871433i	$0.663191\pi$
$4$	0.746668	−	0.230317i	0.373334	−	0.115158i
$5$	0.200654	−	2.67754i	0.0897350	−	1.19743i	−0.752600	−	0.658477i	$-0.771201\pi$
$5$	0.200654	−	2.67754i	0.0897350	−	1.19743i	0.842335	−	0.538954i	$-0.181180\pi$
$6$	−0.445631	−	0.214605i	−0.181928	−	0.0876120i
$7$	2.62546	−	0.327044i	0.992331	−	0.123611i
$7$	2.62546	−	0.327044i	0.992331	−	0.123611i
$8$	1.83108	−	0.881802i	0.647385	−	0.311764i
$9$	−1.06389	−	2.71074i	−0.354630	−	0.903581i
$10$	0.334640	+	4.46546i	0.105822	+	1.41210i
$11$	0.884677	−	2.25412i	0.266740	−	0.679643i	−0.733260	−	0.679949i	$-0.762002\pi$
$11$	0.884677	−	2.25412i	0.266740	−	0.679643i	1.00000		0.000305690i	$9.73042e-5\pi$
$12$	0.221444	+	0.0683063i	0.0639252	+	0.0197183i
$13$	−0.623490	−	0.781831i	−0.172925	−	0.216841i
$13$	−0.623490	−	0.781831i	−0.172925	−	0.216841i
$14$	−4.24841	+	1.19193i	−1.13543	+	0.318557i
$15$	0.496497	−	0.622587i	0.128195	−	0.160751i
$16$	−4.09170	+	2.78968i	−1.02293	+	0.697419i
$17$	−1.10025	+	1.02088i	−0.266849	+	0.247599i	−0.802236	−	0.597007i	$-0.796356\pi$
$17$	−1.10025	+	1.02088i	−0.266849	+	0.247599i	0.535387	+	0.844607i	$0.320166\pi$
$18$	2.42828	+	4.20590i	0.572350	+	0.991340i
$19$	−1.62635	+	2.81692i	−0.373110	+	0.646246i	−0.990042	−	0.140770i	$-0.955042\pi$
$19$	−1.62635	+	2.81692i	−0.373110	+	0.646246i	0.616932	+	0.787017i	$0.288375\pi$
$20$	−0.466859	−	2.04544i	−0.104393	−	0.457375i
$21$	0.697987	+	0.358488i	0.152313	+	0.0782286i
$22$	−0.898644	+	3.93722i	−0.191592	+	0.839417i
$23$	−3.39278	−	3.14804i	−0.707443	−	0.656411i	0.242027	−	0.970270i	$-0.422188\pi$
$23$	−3.39278	−	3.14804i	−0.707443	−	0.656411i	−0.949470	+	0.313858i	$0.898378\pi$
$24$	0.596013	+	0.0898344i	0.121661	+	0.0183374i
$25$	−2.18479	−	0.329304i	−0.436958	−	0.0658608i
$26$	1.22255	+	1.13436i	0.239761	+	0.222466i
$27$	0.390161	−	1.70941i	0.0750866	−	0.328976i
$28$	1.88502	−	0.848880i	0.356236	−	0.160423i
$29$	−0.0150067	−	0.0657485i	−0.00278667	−	0.0122092i	0.973515	−	0.228621i	$-0.0734217\pi$
$29$	−0.0150067	−	0.0657485i	−0.00278667	−	0.0122092i	−0.976302	+	0.216412i	$0.930565\pi$
$30$	−0.664030	+	1.15013i	−0.121235	+	0.209985i
$31$	1.87054	+	3.23987i	0.335959	+	0.581898i	0.983669	−	0.179990i	$-0.0576064\pi$
$31$	1.87054	+	3.23987i	0.335959	+	0.581898i	−0.647710	+	0.761887i	$0.724273\pi$
$32$	3.07467	−	2.85287i	0.543529	−	0.504322i
$33$	0.593373	−	0.404555i	0.103293	−	0.0704239i
$34$	1.56068	−	1.95703i	0.267655	−	0.335629i
$35$	−0.348864	−	7.09539i	−0.0589687	−	1.19934i
$36$	−1.41870	−	1.77899i	−0.236450	−	0.296499i
$37$	−10.3592	−	3.19538i	−1.70304	−	0.525317i	−0.717760	−	0.696290i	$-0.754833\pi$
$37$	−10.3592	−	3.19538i	−1.70304	−	0.525317i	−0.985276	+	0.170973i	$0.945309\pi$
$38$	1.98186	−	5.04970i	0.321500	−	0.819169i
$39$	−0.0221631	−	0.295746i	−0.00354894	−	0.0473573i
$40$	−1.99364	−	5.07972i	−0.315223	−	0.803175i
$41$	−1.25712	+	0.605399i	−0.196330	+	0.0945474i	−0.529466	−	0.848331i	$-0.677608\pi$
$41$	−1.25712	+	0.605399i	−0.196330	+	0.0945474i	0.333136	+	0.942879i	$0.391893\pi$
$42$	−1.24017	−	0.417695i	−0.191363	−	0.0644518i
$43$	−3.12343	−	1.50417i	−0.476319	−	0.229383i	0.180291	−	0.983613i	$-0.442296\pi$
$43$	−3.12343	−	1.50417i	−0.476319	−	0.229383i	−0.656610	+	0.754230i	$0.728010\pi$
$44$	0.141399	−	1.88684i	0.0213167	−	0.284451i
$45$	−7.47159	+	2.30468i	−1.11380	+	0.343562i
$46$	6.37759	+	4.34817i	0.940325	+	0.641103i
$47$	10.0620	−	1.51660i	1.46769	−	0.221219i	0.633950	−	0.773374i	$-0.281432\pi$
$47$	10.0620	−	1.51660i	1.46769	−	0.221219i	0.833741	+	0.552155i	$0.186194\pi$
$48$	−1.46870			−0.211989
$49$	6.78608	−	1.71728i	0.969441	−	0.245326i
$50$	3.68483			0.521114
$51$	−0.440162	+	0.0663437i	−0.0616350	+	0.00928998i
$52$	−0.645608	−	0.440168i	−0.0895298	−	0.0610404i
$53$	1.67777	−	0.517523i	0.230459	−	0.0710872i	−0.177375	−	0.984143i	$-0.556760\pi$
$53$	1.67777	−	0.517523i	0.230459	−	0.0710872i	0.407834	+	0.913056i	$0.366284\pi$
$54$	−0.218524	+	2.91600i	−0.0297373	+	0.396817i
$55$	−5.85798	−	2.82105i	−0.789890	−	0.380391i
$56$	4.51904	−	2.91398i	0.603883	−	0.389397i
$57$	−0.869139	+	0.418556i	−0.115120	+	0.0554390i
$58$	0.0410906	+	0.104697i	0.00539546	+	0.0137474i
$59$	−0.534977	−	7.13877i	−0.0696481	−	0.929389i	−0.917136	−	0.398574i	$-0.869505\pi$
$59$	−0.534977	−	7.13877i	−0.0696481	−	0.929389i	0.847488	−	0.530815i	$-0.178114\pi$
$60$	0.227326	−	0.579217i	0.0293477	−	0.0747766i
$61$	−3.00034	−	0.925482i	−0.384154	−	0.118496i	0.0966621	−	0.995317i	$-0.469183\pi$
$61$	−3.00034	−	0.925482i	−0.384154	−	0.118496i	−0.480816	+	0.876821i	$0.659660\pi$
$62$	−3.89006	−	4.87798i	−0.494038	−	0.619504i
$63$	−3.67973	−	6.76901i	−0.463602	−	0.852816i
$64$	1.81393	−	2.27459i	0.226741	−	0.284324i
$65$	−2.21849	+	1.51254i	−0.275170	+	0.187607i
$66$	−0.877985	+	0.814651i	−0.108072	+	0.100277i
$67$	0.497968	+	0.862506i	0.0608365	+	0.105372i	0.894840	−	0.446388i	$-0.147290\pi$
$67$	0.497968	+	0.862506i	0.0608365	+	0.105372i	−0.834003	+	0.551760i	$0.813957\pi$
$68$	−0.586393	+	1.01566i	−0.0711106	+	0.123167i
$69$	−0.305441	−	1.33822i	−0.0367708	−	0.161103i
$70$	2.33898	+	11.6144i	0.279562	+	1.38819i
$71$	0.0794855	−	0.348249i	0.00943320	−	0.0413295i	−0.969992	−	0.243136i	$-0.921824\pi$
$71$	0.0794855	−	0.348249i	0.00943320	−	0.0413295i	0.979425	+	0.201806i	$0.0646811\pi$
$72$	−4.33841	−	4.02545i	−0.511286	−	0.474404i
$73$	3.93063	+	0.592447i	0.460045	+	0.0693406i	0.374976	−	0.927034i	$-0.377651\pi$
$73$	3.93063	+	0.592447i	0.460045	+	0.0693406i	0.0850688	+	0.996375i	$0.472889\pi$
$74$	17.8778	+	2.69464i	2.07825	+	0.313245i
$75$	−0.480350	−	0.445700i	−0.0554660	−	0.0514650i
$76$	−0.565560	+	2.47788i	−0.0648742	+	0.284232i
$77$	1.58549	−	6.20743i	0.180683	−	0.707403i
$78$	0.110062	+	0.482213i	0.0124621	+	0.0545998i
$79$	3.62186	−	6.27324i	0.407491	−	0.705795i	−0.587117	−	0.809502i	$-0.699737\pi$
$79$	3.62186	−	6.27324i	0.407491	−	0.705795i	0.994608	+	0.103707i	$0.0330706\pi$
$80$	6.64845	+	11.5155i	0.743319	+	1.28747i
$81$	−6.02284	+	5.58838i	−0.669205	+	0.620931i
$82$	1.92267	−	1.31085i	0.212323	−	0.144759i
$83$	−2.69260	+	3.37641i	−0.295551	+	0.370610i	−0.907330	−	0.420420i	$-0.861883\pi$
$83$	−2.69260	+	3.37641i	−0.295551	+	0.370610i	0.611779	+	0.791029i	$0.290454\pi$
$84$	0.603730	+	0.106914i	0.0658724	+	0.0116652i
$85$	2.51267	+	3.15079i	0.272538	+	0.341751i
$86$	5.52480	+	1.70417i	0.595754	+	0.183766i
$87$	0.00730714	−	0.0186183i	0.000783408	−	0.00199609i
$88$	−0.367773	−	4.90759i	−0.0392047	−	0.523151i
$89$	−5.05565	−	12.8816i	−0.535897	−	1.36544i	−0.900733	−	0.434372i	$-0.856970\pi$
$89$	−5.05565	−	12.8816i	−0.535897	−	1.36544i	0.364836	−	0.931072i	$-0.381125\pi$
$90$	11.7487	−	5.65787i	1.23842	−	0.596392i
$91$	−1.89264	−	1.84876i	−0.198403	−	0.193803i
$92$	−3.25832	−	1.56913i	−0.339704	−	0.163593i
$93$	−0.0829140	+	1.10641i	−0.00859778	+	0.114729i
$94$	−16.2165	+	5.00211i	−1.67260	+	0.515929i
$95$	7.21608	+	4.91984i	0.740354	+	0.504765i
$96$	1.23004	−	0.185399i	0.125541	−	0.0189223i
$97$	−9.44111			−0.958600			−0.479300	−	0.877651i	$-0.659109\pi$
$97$	−9.44111			−0.958600			−0.479300	+	0.877651i	$0.659109\pi$
$98$	−10.7642	+	4.51879i	−1.08735	+	0.456466i
$99$	−7.05154			−0.708707
$100$	−1.70716	+	0.257312i	−0.170716	+	0.0257312i
$101$	−0.836329	−	0.570199i	−0.0832178	−	0.0567370i	0.520996	−	0.853559i	$-0.325560\pi$
$101$	−0.836329	−	0.570199i	−0.0832178	−	0.0567370i	−0.604214	+	0.796822i	$0.706513\pi$
$102$	0.709389	−	0.218818i	0.0702400	−	0.0216662i
$103$	1.32369	−	17.6635i	0.130427	−	1.74043i	−0.421755	−	0.906710i	$-0.638586\pi$
$103$	1.32369	−	17.6635i	0.130427	−	1.74043i	0.552182	−	0.833723i	$-0.313795\pi$
$104$	−1.83108	−	0.881802i	−0.179552	−	0.0864678i
$105$	1.09992	−	1.79695i	0.107341	−	0.175365i
$106$	−2.63820	+	1.27049i	−0.256245	+	0.123401i
$107$	3.34063	+	8.51179i	0.322951	+	0.822866i	0.996490	+	0.0837139i	$0.0266782\pi$
$107$	3.34063	+	8.51179i	0.322951	+	0.822866i	−0.673539	+	0.739152i	$0.735227\pi$
$108$	−0.102384	−	1.36622i	−0.00985191	−	0.131465i
$109$	−5.98048	+	15.2380i	−0.572826	+	1.45954i	0.291482	+	0.956576i	$0.405852\pi$
$109$	−5.98048	+	15.2380i	−0.572826	+	1.45954i	−0.864309	+	0.502962i	$0.832244\pi$
$110$	10.3617	+	3.19617i	0.987952	+	0.304743i
$111$	−2.00459	−	2.51368i	−0.190267	−	0.238588i
$112$	−9.83026	+	8.66235i	−0.928872	+	0.818516i
$113$	6.69432	−	8.39442i	0.629749	−	0.789680i	−0.359930	−	0.932979i	$-0.617200\pi$
$113$	6.69432	−	8.39442i	0.629749	−	0.789680i	0.989679	+	0.143299i	$0.0457710\pi$
$114$	1.32928	−	0.906286i	0.124498	−	0.0848815i
$115$	−9.10976	+	8.45263i	−0.849490	+	0.788211i
$116$	−0.0263480	−	0.0456360i	−0.00244635	−	0.00423720i
$117$	−1.45602	+	2.52190i	−0.134609	+	0.233150i
$118$	2.65669	+	11.6397i	0.244568	+	1.07152i
$119$	−2.55478	+	3.04011i	−0.234196	+	0.278686i
$120$	0.360127	−	1.57782i	0.0328750	−	0.144035i
$121$	3.76516	+	3.49356i	0.342288	+	0.317597i
$122$	5.17796	+	0.780452i	0.468791	+	0.0706588i
$123$	−0.409191	−	0.0616756i	−0.0368955	−	0.00556110i
$124$	2.14287	+	1.98829i	0.192435	+	0.178554i
$125$	1.66728	−	7.30485i	0.149126	−	0.653366i
$126$	7.75086	+	10.2483i	0.690501	+	0.912988i
$127$	1.52181	+	6.66747i	0.135039	+	0.591642i	0.996483	+	0.0837913i	$0.0267029\pi$
$127$	1.52181	+	6.66747i	0.135039	+	0.591642i	−0.861445	+	0.507851i	$0.830440\pi$
$128$	−6.62034	+	11.4668i	−0.585161	+	1.01353i
$129$	−0.514077	−	0.890407i	−0.0452619	−	0.0783960i
$130$	3.28259	−	3.04580i	0.287902	−	0.267134i
$131$	16.1063	−	10.9811i	1.40722	−	0.959424i	0.408302	−	0.912847i	$-0.366121\pi$
$131$	16.1063	−	10.9811i	1.40722	−	0.959424i	0.998915	−	0.0465774i	$-0.0148314\pi$
$132$	0.349877	−	0.438731i	0.0304529	−	0.0381867i
$133$	−3.34866	+	7.92760i	−0.290366	+	0.687410i
$134$	−1.03560	−	1.29860i	−0.0894620	−	0.112182i
$135$	−4.49872	−	1.38767i	−0.387188	−	0.119432i
$136$	−1.11443	+	2.83951i	−0.0955612	+	0.243486i
$137$	0.937455	+	12.5095i	0.0800922	+	1.06876i	0.881982	+	0.471284i	$0.156209\pi$
$137$	0.937455	+	12.5095i	0.0800922	+	1.06876i	−0.801889	+	0.597472i	$0.796172\pi$
$138$	0.836345	+	2.13097i	0.0711944	+	0.181400i
$139$	3.43490	−	1.65416i	0.291344	−	0.140304i	−0.282503	−	0.959266i	$-0.591165\pi$
$139$	3.43490	−	1.65416i	0.291344	−	0.140304i	0.573847	+	0.818963i	$0.305450\pi$
$140$	−1.89467	−	5.21755i	−0.160129	−	0.440963i
$141$	2.71899	+	1.30940i	0.228980	+	0.110271i
$142$	−0.0445188	+	0.594062i	−0.00373593	+	0.0498526i
$143$	−2.31393	+	0.713753i	−0.193501	+	0.0596870i
$144$	11.9152	+	8.12366i	0.992935	+	0.676972i
$145$	−0.179055	+	0.0269882i	−0.0148697	+	0.00224125i
$146$	−6.62934			−0.548648
$147$	1.94978	+	0.712925i	0.160815	+	0.0588010i
$148$	−8.47080			−0.696296
$149$	7.71403	−	1.16270i	0.631958	−	0.0952523i	0.174751	−	0.984613i	$-0.444088\pi$
$149$	7.71403	−	1.16270i	0.631958	−	0.0952523i	0.457207	+	0.889360i	$0.348850\pi$
$150$	0.902940	+	0.615614i	0.0737248	+	0.0502647i
$151$	−2.65856	+	0.820057i	−0.216351	+	0.0667353i	−0.401036	−	0.916062i	$-0.631350\pi$
$151$	−2.65856	+	0.820057i	−0.216351	+	0.0667353i	0.184685	+	0.982798i	$0.440873\pi$
$152$	−0.494012	+	6.59213i	−0.0400697	+	0.534692i
$153$	3.93788	+	1.89638i	0.318359	+	0.153313i
$154$	−1.07171	+	10.6309i	−0.0863610	+	0.856662i
$155$	9.05020	−	4.35835i	0.726929	−	0.350071i
$156$	−0.0846638	−	0.215720i	−0.00677853	−	0.0172714i
$157$	0.610226	+	8.14290i	0.0487013	+	0.649874i	0.967129	+	0.254285i	$0.0818403\pi$
$157$	0.610226	+	8.14290i	0.0487013	+	0.649874i	−0.918428	+	0.395588i	$0.870541\pi$
$158$	−4.41357	+	11.2456i	−0.351125	+	0.894651i
$159$	0.497585	+	0.153485i	0.0394611	+	0.0121721i
$160$	−7.02173	−	8.80497i	−0.555117	−	0.696094i
$161$	−9.93715	−	7.15546i	−0.783157	−	0.563930i
$162$	8.54332	−	10.7130i	0.671226	−	0.841691i
$163$	−12.7686	+	8.70552i	−1.00012	+	0.681869i	−0.948493	−	0.316798i	$-0.897392\pi$
$163$	−12.7686	+	8.70552i	−1.00012	+	0.681869i	−0.0516245	+	0.998667i	$0.516440\pi$
$164$	−0.799221	+	0.741568i	−0.0624086	+	0.0579068i
$165$	−0.964148	−	1.66995i	−0.0750588	−	0.130006i
$166$	3.60116	−	6.23740i	0.279504	−	0.484116i
$167$	5.28081	+	23.1367i	0.408641	+	1.79038i	0.590486	+	0.807048i	$0.298936\pi$
$167$	5.28081	+	23.1367i	0.408641	+	1.79038i	−0.181844	+	0.983327i	$0.558207\pi$
$168$	1.59419	+	0.0409345i	0.122994	+	0.00315817i
$169$	−0.222521	+	0.974928i	−0.0171170	+	0.0749945i
$170$	−4.92688	−	4.57147i	−0.377874	−	0.350616i
$171$	9.36621	+	1.41173i	0.716252	+	0.107958i
$172$	−2.67860	−	0.403734i	−0.204241	−	0.0307844i
$173$	5.13888	+	4.76819i	0.390702	+	0.362518i	0.850927	−	0.525284i	$-0.176041\pi$
$173$	5.13888	+	4.76819i	0.390702	+	0.362518i	−0.460225	+	0.887802i	$0.652231\pi$
$174$	−0.00742250	+	0.0325201i	−0.000562698	+	0.00246534i
$175$	−5.84377	−	0.150053i	−0.441748	−	0.0113429i
$176$	2.66843	+	11.6912i	0.201141	+	0.881254i
$177$	1.06156	−	1.83868i	0.0797919	−	0.138204i
$178$	11.5393	+	19.9866i	0.864905	+	1.49806i
$179$	11.6093	−	10.7718i	0.867719	−	0.805126i	−0.114391	−	0.993436i	$-0.536492\pi$
$179$	11.6093	−	10.7718i	0.867719	−	0.805126i	0.982110	+	0.188310i	$0.0603011\pi$
$180$	−5.04799	+	3.44166i	−0.376255	+	0.256526i
$181$	1.67505	−	2.10044i	0.124505	−	0.156125i	−0.715672	−	0.698437i	$-0.753879\pi$
$181$	1.67505	−	2.10044i	0.124505	−	0.156125i	0.840177	+	0.542312i	$0.182451\pi$
$182$	3.58073	+	2.57838i	0.265421	+	0.191122i
$183$	−0.580593	−	0.728040i	−0.0429187	−	0.0538183i
$184$	−8.98840	−	2.77255i	−0.662634	−	0.204395i
$185$	−10.6343	+	27.0959i	−0.781853	+	1.99213i
$186$	−0.138280	−	1.84521i	−0.0101392	−	0.135298i
$187$	1.32782	+	3.38323i	0.0970999	+	0.247407i
$188$	7.16366	−	3.44984i	0.522464	−	0.251605i
$189$	0.465301	−	4.61558i	0.0338457	−	0.335734i
$190$	−13.1231	−	6.31974i	−0.952048	−	0.458482i
$191$	1.24148	−	16.5664i	0.0898302	−	1.19870i	−0.752076	−	0.659077i	$-0.770947\pi$
$191$	1.24148	−	16.5664i	0.0898302	−	1.19870i	0.841906	−	0.539624i	$-0.181434\pi$
$192$	0.824499	−	0.254324i	0.0595031	−	0.0183543i
$193$	18.7513	+	12.7844i	1.34975	+	0.920244i	0.999863	−	0.0165487i	$-0.00526784\pi$
$193$	18.7513	+	12.7844i	1.34975	+	0.920244i	0.349886	+	0.936792i	$0.386220\pi$
$194$	15.5695	−	2.34673i	1.11783	−	0.168485i
$195$	−0.796319			−0.0570256
$196$	4.67143	−	2.84519i	0.333674	−	0.203228i
$197$	−0.688621			−0.0490622			−0.0245311	−	0.999699i	$-0.507809\pi$
$197$	−0.688621			−0.0490622			−0.0245311	+	0.999699i	$0.507809\pi$
$198$	11.6288	−	1.75277i	0.826426	−	0.124564i
$199$	−17.6884	−	12.0597i	−1.25389	−	0.854891i	−0.260041	−	0.965598i	$-0.583736\pi$
$199$	−17.6884	−	12.0597i	−1.25389	−	0.854891i	−0.993853	+	0.110707i	$0.964689\pi$
$200$	−4.29091	+	1.32357i	−0.303413	+	0.0935905i
$201$	−0.0220731	+	0.294544i	−0.00155691	+	0.0207756i
$202$	1.52094	+	0.732445i	0.107013	+	0.0515347i
$203$	−0.0609021	−	0.167712i	−0.00427449	−	0.0117711i
$204$	−0.313375	+	0.150913i	−0.0219406	+	0.0105660i
$205$	1.36873	+	3.48747i	0.0955964	+	0.243576i
$206$	2.20759	+	29.4582i	0.153810	+	2.05245i
$207$	−4.92399	+	12.5461i	−0.342241	+	0.872015i
$208$	4.73219	+	1.45969i	0.328119	+	0.101211i
$209$	4.91089	+	6.15806i	0.339693	+	0.425962i
$210$	−1.36724	+	3.23680i	−0.0943485	+	0.223360i
$211$	−11.3946	+	14.2884i	−0.784436	+	0.983652i	0.215538	+	0.976495i	$0.430849\pi$
$211$	−11.3946	+	14.2884i	−0.784436	+	0.983652i	−0.999974	+	0.00715663i	$0.997722\pi$
$212$	1.13354	−	0.772835i	0.0778519	−	0.0530785i
$213$	0.0776583	−	0.0720563i	0.00532106	−	0.00493722i
$214$	−7.62484	−	13.2066i	−0.521223	−	0.902785i
$215$	−4.65419	+	8.06129i	−0.317413	+	0.549775i
$216$	−0.792943	−	3.47411i	−0.0539529	−	0.236383i
$217$	5.97061	+	7.89440i	0.405311	+	0.535907i
$218$	6.07490	−	26.6159i	0.411444	−	1.80265i
$219$	0.864192	+	0.801853i	0.0583967	+	0.0541842i
$220$	−5.02370	−	0.757201i	−0.338698	−	0.0510505i
$221$	1.48415	+	0.223699i	0.0998345	+	0.0150476i
$222$	3.93062	+	3.64709i	0.263806	+	0.244776i
$223$	3.04068	−	13.3221i	0.203619	−	0.892113i	−0.765092	−	0.643921i	$-0.777307\pi$
$223$	3.04068	−	13.3221i	0.203619	−	0.892113i	0.968711	−	0.248192i	$-0.0798363\pi$
$224$	7.13940	−	8.49566i	0.477021	−	0.567640i
$225$	1.43171	+	6.27275i	0.0954476	+	0.418183i
$226$	−8.95319	+	15.5074i	−0.595557	+	1.03154i
$227$	1.30025	+	2.25210i	0.0863005	+	0.149477i	0.905945	−	0.423396i	$-0.139162\pi$
$227$	1.30025	+	2.25210i	0.0863005	+	0.149477i	−0.819644	+	0.572873i	$0.805829\pi$
$228$	−0.552558	+	0.512699i	−0.0365941	+	0.0339543i
$229$	13.5214	−	9.21876i	0.893522	−	0.609193i	−0.0271068	−	0.999633i	$-0.508629\pi$
$229$	13.5214	−	9.21876i	0.893522	−	0.609193i	0.920628	+	0.390440i	$0.127677\pi$
$230$	12.9221	−	16.2038i	0.852056	−	1.06844i
$231$	1.42557	−	1.25620i	0.0937956	−	0.0826520i
$232$	−0.0854556	−	0.107158i	−0.00561044	−	0.00703526i
$233$	1.90695	+	0.588215i	0.124928	+	0.0385353i	0.356589	−	0.934261i	$-0.383940\pi$
$233$	1.90695	+	0.588215i	0.124928	+	0.0385353i	−0.231661	+	0.972797i	$0.574416\pi$
$234$	1.77430	−	4.52084i	0.115989	−	0.295536i
$235$	−2.04178	−	27.2457i	−0.133191	−	1.77731i
$236$	−2.04363	−	5.20708i	−0.133029	−	0.338952i
$237$	1.93556	−	0.932116i	0.125728	−	0.0605475i
$238$	3.45747	−	5.64853i	0.224115	−	0.366140i
$239$	−19.1059	−	9.20092i	−1.23586	−	0.595158i	−0.302173	−	0.953253i	$-0.597712\pi$
$239$	−19.1059	−	9.20092i	−1.23586	−	0.595158i	−0.933685	+	0.358095i	$0.883426\pi$
$240$	−0.294701	+	3.93251i	−0.0190229	+	0.253842i
$241$	25.3992	−	7.83461i	1.63610	−	0.504672i	0.665713	−	0.746208i	$-0.268127\pi$
$241$	25.3992	−	7.83461i	1.63610	−	0.504672i	0.970392	+	0.241536i	$0.0776513\pi$
$242$	−7.07759	−	4.82542i	−0.454964	−	0.310190i
$243$	−7.61084	+	1.14715i	−0.488236	+	0.0735897i
$244$	−2.45341			−0.157064
$245$	−3.23643	−	18.5146i	−0.206768	−	1.18285i
$246$	0.690135			0.0440014
$247$	3.21637	−	0.484790i	0.204653	−	0.0308464i
$248$	6.28203	+	4.28302i	0.398909	+	0.271972i
$249$	−1.22389	+	0.377520i	−0.0775608	+	0.0239243i
$250$	−0.933823	+	12.4610i	−0.0590602	+	0.788103i
$251$	−10.1650	−	4.89521i	−0.641609	−	0.308983i	0.0846426	−	0.996411i	$-0.473025\pi$
$251$	−10.1650	−	4.89521i	−0.641609	−	0.308983i	−0.726252	+	0.687429i	$0.758739\pi$
$252$	−4.30655	−	4.20670i	−0.271287	−	0.264997i
$253$	−10.0976	+	4.86273i	−0.634829	+	0.305718i
$254$	−4.16694	−	10.6172i	−0.261457	−	0.666182i
$255$	0.0893177	+	1.19186i	0.00559329	+	0.0746373i
$256$	5.94172	−	15.1392i	0.371357	−	0.946203i
$257$	8.15516	+	2.51553i	0.508705	+	0.156915i	0.538474	−	0.842642i	$-0.319001\pi$
$257$	8.15516	+	2.51553i	0.508705	+	0.156915i	−0.0297692	+	0.999557i	$0.509477\pi$
$258$	1.06910	+	1.34061i	0.0665591	+	0.0834625i
$259$	−28.2426	−	5.00144i	−1.75491	−	0.310774i
$260$	−1.30811	+	1.64032i	−0.0811256	+	0.101728i
$261$	−0.162262	+	0.110628i	−0.0100438	+	0.00684772i
$262$	−23.8318	+	22.1126i	−1.47233	+	1.36612i
$263$	−6.77545	−	11.7354i	−0.417792	−	0.723637i	0.577925	−	0.816090i	$-0.303863\pi$
$263$	−6.77545	−	11.7354i	−0.417792	−	0.723637i	−0.995717	+	0.0924528i	$0.970529\pi$
$264$	0.729776	−	1.26401i	0.0449146	−	0.0777944i
$265$	−1.04904	−	4.59613i	−0.0644418	−	0.282338i
$266$	3.55182	−	13.9059i	0.217776	−	0.852627i
$267$	0.913239	−	4.00116i	0.0558893	−	0.244867i
$268$	0.570466	+	0.529315i	0.0348468	+	0.0323331i
$269$	3.36161	+	0.506682i	0.204961	+	0.0308929i	0.250720	−	0.968060i	$-0.419333\pi$
$269$	3.36161	+	0.506682i	0.204961	+	0.0308929i	−0.0457591	+	0.998953i	$0.514571\pi$
$270$	7.76385	+	1.17021i	0.472493	+	0.0712168i
$271$	−8.74927	−	8.11813i	−0.531480	−	0.493141i	0.368167	−	0.929760i	$-0.379986\pi$
$271$	−8.74927	−	8.11813i	−0.531480	−	0.493141i	−0.899647	+	0.436618i	$0.856176\pi$
$272$	1.65396	−	7.24646i	0.100286	−	0.439381i
$273$	−0.154910	−	0.769222i	−0.00937561	−	0.0465555i
$274$	−4.65539	−	20.3966i	−0.281243	−	1.23220i
$275$	−2.67512	+	4.63345i	−0.161316	+	0.279408i
$276$	−0.536278	−	0.928861i	−0.0322802	−	0.0559109i
$277$	14.4610	−	13.4178i	0.868876	−	0.806199i	−0.113418	−	0.993547i	$-0.536180\pi$
$277$	14.4610	−	13.4178i	0.868876	−	0.806199i	0.982294	+	0.187348i	$0.0599893\pi$
$278$	−5.25339	+	3.58170i	−0.315078	+	0.214816i
$279$	6.79241	−	8.51741i	0.406651	−	0.509924i
$280$	−6.89553	−	12.6846i	−0.412087	−	0.758050i
$281$	−9.48376	−	11.8923i	−0.565754	−	0.709433i	0.413856	−	0.910342i	$-0.364182\pi$
$281$	−9.48376	−	11.8923i	−0.565754	−	0.709433i	−0.979610	+	0.200909i	$0.935610\pi$
$282$	−4.80941	−	1.48351i	−0.286396	−	0.0883415i
$283$	3.62090	−	9.22589i	0.215240	−	0.548422i	−0.781950	−	0.623342i	$-0.785775\pi$
$283$	3.62090	−	9.22589i	0.215240	−	0.548422i	0.997190	+	0.0749192i	$0.0238699\pi$
$284$	−0.0208582	−	0.278333i	−0.00123771	−	0.0165160i
$285$	0.946302	+	2.41114i	0.0560541	+	0.142823i
$286$	3.63853	−	1.75223i	0.215151	−	0.103611i
$287$	−3.10254	+	2.00059i	−0.183137	+	0.118091i
$288$	−11.0045	−	5.29950i	−0.648447	−	0.312276i
$289$	−1.10206	+	14.7060i	−0.0648273	+	0.865061i
$290$	0.288575	−	0.0890137i	0.0169457	−	0.00522706i
$291$	−2.31347	−	1.57730i	−0.135618	−	0.0924629i
$292$	3.07132	−	0.462927i	0.179736	−	0.0270908i
$293$	3.52034			0.205661			0.102830	−	0.994699i	$-0.467210\pi$
$293$	3.52034			0.205661			0.102830	+	0.994699i	$0.467210\pi$
$294$	−3.39263	−	0.691052i	−0.197862	−	0.0403029i
$295$	−19.2217			−1.11913
$296$	−21.7862	+	3.28374i	−1.26629	+	0.190863i
$297$	−3.50804	−	2.39174i	−0.203557	−	0.138783i
$298$	−12.4324	+	3.83487i	−0.720187	+	0.222148i
$299$	−0.345873	+	4.61535i	−0.0200023	+	0.266913i
$300$	−0.461314	−	0.222157i	−0.0266340	−	0.0128262i
$301$	−8.69238	−	2.92763i	−0.501020	−	0.168746i
$302$	4.18045	−	2.01320i	0.240558	−	0.115846i
$303$	−0.109674	−	0.279446i	−0.00630063	−	0.0160538i
$304$	−1.20376	−	16.0630i	−0.0690401	−	0.921276i
$305$	−3.08004	+	7.84782i	−0.176363	+	0.449365i
$306$	−6.96541	−	2.14855i	−0.398186	−	0.122824i
$307$	18.5001	+	23.1984i	1.05585	+	1.32400i	0.943880	+	0.330289i	$0.107146\pi$
$307$	18.5001	+	23.1984i	1.05585	+	1.32400i	0.111975	+	0.993711i	$0.464282\pi$
$308$	−0.245841	−	5.00005i	−0.0140081	−	0.284905i
$309$	3.27535	−	4.10715i	0.186328	−	0.233648i
$310$	−13.8415	+	9.43700i	−0.786146	+	0.535986i
$311$	18.1335	−	16.8254i	1.02826	−	0.954082i	0.0292913	−	0.999571i	$-0.490675\pi$
$311$	18.1335	−	16.8254i	1.02826	−	0.954082i	0.998965	+	0.0454887i	$0.0144845\pi$
$312$	−0.301372	−	0.521992i	−0.0170618	−	0.0295520i
$313$	0.495227	−	0.857759i	0.0279919	−	0.0484834i	−0.851690	−	0.524046i	$-0.824422\pi$
$313$	0.495227	−	0.857759i	0.0279919	−	0.0484834i	0.879682	+	0.475562i	$0.157755\pi$
$314$	−3.03037	−	13.2769i	−0.171014	−	0.749261i
$315$	−18.8626	+	8.49439i	−1.06279	+	0.478604i
$316$	1.25949	−	5.51820i	0.0708520	−	0.310423i
$317$	8.45602	+	7.84604i	0.474937	+	0.440677i	0.880964	−	0.473184i	$-0.156895\pi$
$317$	8.45602	+	7.84604i	0.474937	+	0.440677i	−0.406026	+	0.913861i	$0.633086\pi$
$318$	−0.858729	−	0.129433i	−0.0481551	−	0.00725822i
$319$	−0.161481	−	0.0243394i	−0.00904121	−	0.00136274i
$320$	−5.72634	−	5.31327i	−0.320112	−	0.297021i
$321$	−0.603443	+	2.64386i	−0.0336809	+	0.147566i
$322$	18.1662	+	9.33019i	1.01236	+	0.519951i
$323$	−1.08635	−	4.75961i	−0.0604461	−	0.264832i
$324$	−3.20997	+	5.55983i	−0.178331	+	0.308879i
$325$	1.10473	+	1.91345i	0.0612796	+	0.106139i
$326$	18.8931	−	17.5303i	1.04639	−	0.970912i
$327$	−4.01124	+	2.73482i	−0.221822	+	0.151236i
$328$	−1.76805	+	2.21707i	−0.0976244	+	0.122417i
$329$	25.9214	−	7.27249i	1.42909	−	0.400945i
$330$	2.00509	+	2.51430i	0.110376	+	0.138408i
$331$	10.2924	+	3.17479i	0.565723	+	0.174502i	0.564407	−	0.825497i	$-0.309105\pi$
$331$	10.2924	+	3.17479i	0.565723	+	0.174502i	0.00131590	+	0.999999i	$0.499581\pi$
$332$	−1.23283	+	3.14121i	−0.0676605	+	0.172396i
$333$	2.35914	+	31.4806i	0.129280	+	1.72512i
$334$	−14.4597	−	36.8427i	−0.791198	−	2.01594i
$335$	2.40931	−	1.16026i	0.131635	−	0.0633919i
$336$	−3.85602	+	0.480331i	−0.210363	+	0.0262042i
$337$	13.8102	+	6.65066i	0.752292	+	0.362285i	0.770408	−	0.637551i	$-0.220053\pi$
$337$	13.8102	+	6.65066i	0.752292	+	0.362285i	−0.0181161	+	0.999836i	$0.505767\pi$
$338$	0.124631	−	1.66308i	0.00677903	−	0.0904599i
$339$	3.04282	−	0.938587i	0.165263	−	0.0509770i
$340$	2.60181	+	1.77388i	0.141103	+	0.0962024i
$341$	8.95788	−	1.35018i	0.485096	−	0.0731165i
$342$	−15.7969			−0.854199
$343$	17.2550	−	6.72800i	0.931681	−	0.363278i
$344$	−7.04563			−0.379875
$345$	−3.64443	+	0.549310i	−0.196210	+	0.0295739i
$346$	−9.65984	−	6.58597i	−0.519316	−	0.354064i
$347$	−26.0185	+	8.02563i	−1.39674	+	0.430839i	−0.899556	−	0.436804i	$-0.856110\pi$
$347$	−26.0185	+	8.02563i	−1.39674	+	0.430839i	−0.497188	+	0.867643i	$0.665634\pi$
$348$	0.00116791	−	0.0155846i	6.26064e−5	−	0.000835424i
$349$	−1.97896	−	0.953019i	−0.105932	−	0.0510139i	0.380168	−	0.924918i	$-0.375866\pi$
$349$	−1.97896	−	0.953019i	−0.105932	−	0.0510139i	−0.486099	+	0.873904i	$0.661581\pi$
$350$	9.67438	−	1.20510i	0.517118	−	0.0644154i
$351$	−1.57973	+	0.760758i	−0.0843198	+	0.0406063i
$352$	−3.71063	−	9.45454i	−0.197777	−	0.503929i
$353$	−1.93627	−	25.8377i	−0.103057	−	1.37520i	−0.773761	−	0.633477i	$-0.781627\pi$
$353$	−1.93627	−	25.8377i	−0.103057	−	1.37520i	0.670704	−	0.741725i	$-0.265992\pi$
$354$	−1.29361	+	3.29607i	−0.0687547	+	0.175184i
$355$	−0.916500	−	0.282703i	−0.0486428	−	0.0150043i
$356$	−6.74173	−	8.45386i	−0.357311	−	0.448054i
$357$	−1.13393	+	0.318135i	−0.0600140	+	0.0168375i
$358$	−16.4676	+	20.6497i	−0.870340	+	1.09137i
$359$	6.98076	−	4.75940i	0.368430	−	0.251191i	−0.364925	−	0.931037i	$-0.618905\pi$
$359$	6.98076	−	4.75940i	0.368430	−	0.251191i	0.733356	+	0.679845i	$0.237953\pi$
$360$	−11.6488	+	10.8085i	−0.613947	+	0.569659i
$361$	4.20997	+	7.29188i	0.221577	+	0.383783i
$362$	−2.24026	+	3.88024i	−0.117745	+	0.203941i
$363$	0.338966	+	1.48511i	0.0177911	+	0.0779478i
$364$	−1.83897	−	0.944502i	−0.0963884	−	0.0495054i
$365$	2.37499	−	10.4055i	0.124313	−	0.544650i
$366$	1.13843	+	1.05631i	0.0595068	+	0.0552143i
$367$	25.4404	+	3.83452i	1.32798	+	0.200160i	0.774431	−	0.632659i	$-0.218036\pi$
$367$	25.4404	+	3.83452i	1.32798	+	0.200160i	0.553546	+	0.832819i	$0.313274\pi$
$368$	22.6643	+	3.41609i	1.18146	+	0.178076i
$369$	2.97852	+	2.76366i	0.155056	+	0.143871i
$370$	10.8022	−	47.3277i	0.561582	−	2.46045i
$371$	4.23566	−	1.90744i	0.219904	−	0.0990293i
$372$	0.192915	+	0.845218i	0.0100022	+	0.0438225i
$373$	10.0785	−	17.4565i	0.521846	−	0.903864i	−0.477831	−	0.878452i	$-0.658577\pi$
$373$	10.0785	−	17.4565i	0.521846	−	0.903864i	0.999677	−	0.0254119i	$-0.00808972\pi$
$374$	−3.03069	−	5.24931i	−0.156713	−	0.271435i
$375$	1.62896	−	1.51145i	0.0841189	−	0.0780509i
$376$	17.0870	−	11.6497i	0.881193	−	0.600787i
$377$	−0.0420478	+	0.0527262i	−0.00216557	+	0.00271554i
$378$	0.379934	+	7.72731i	0.0195417	+	0.397450i
$379$	7.51747	+	9.42661i	0.386146	+	0.484212i	0.936474	−	0.350736i	$-0.114069\pi$
$379$	7.51747	+	9.42661i	0.386146	+	0.484212i	−0.550328	+	0.834949i	$0.685497\pi$
$380$	6.52113	+	2.01150i	0.334527	+	0.103188i
$381$	−0.741008	+	1.88806i	−0.0379630	+	0.0967281i
$382$	2.07047	+	27.6285i	0.105935	+	1.41360i
$383$	6.52339	+	16.6213i	0.333330	+	0.849310i	0.995033	+	0.0995446i	$0.0317386\pi$
$383$	6.52339	+	16.6213i	0.333330	+	0.849310i	−0.661703	+	0.749766i	$0.730166\pi$
$384$	−3.53798	+	1.70380i	−0.180547	+	0.0869468i
$385$	−16.3025	−	5.49075i	−0.830852	−	0.279834i
$386$	−34.1009	−	16.4221i	−1.73569	−	0.835865i
$387$	−0.754424	+	10.0671i	−0.0383495	+	0.511739i
$388$	−7.04937	+	2.17444i	−0.357878	+	0.110391i
$389$	−7.38279	−	5.03350i	−0.374323	−	0.255209i	0.361516	−	0.932366i	$-0.382259\pi$
$389$	−7.38279	−	5.03350i	−0.374323	−	0.255209i	−0.735838	+	0.677157i	$0.763212\pi$
$390$	1.31323	−	0.197937i	0.0664978	−	0.0100229i
$391$	6.94666			0.351307
$392$	10.9116	−	9.12847i	0.551117	−	0.461057i
$393$	5.78132			0.291629
$394$	1.13562	−	0.171167i	0.0572117	−	0.00862327i
$395$	−16.0701	−	10.9564i	−0.808574	−	0.551276i
$396$	−5.26516	+	1.62409i	−0.264584	+	0.0816134i
$397$	−0.467489	+	6.23820i	−0.0234626	+	0.313087i	0.973109	+	0.230347i	$0.0739861\pi$
$397$	−0.467489	+	6.23820i	−0.0234626	+	0.313087i	−0.996571	+	0.0827397i	$0.973633\pi$
$398$	32.1679	+	15.4912i	1.61243	+	0.776505i
$399$	−2.14501	+	1.38315i	−0.107385	+	0.0692440i
$400$	9.85816	−	4.74744i	0.492908	−	0.237372i
$401$	7.38554	+	18.8181i	0.368816	+	0.939729i	0.987996	+	0.154479i	$0.0493700\pi$
$401$	7.38554	+	18.8181i	0.368816	+	0.939729i	−0.619180	+	0.785249i	$0.712535\pi$
$402$	−0.0368123	−	0.491226i	−0.00183603	−	0.0245001i
$403$	1.36677	−	3.48247i	0.0680836	−	0.173474i
$404$	−0.755786	−	0.233129i	−0.0376018	−	0.0115986i
$405$	13.7546	+	17.2477i	0.683471	+	0.857046i
$406$	0.142122	+	0.261440i	0.00705341	+	0.0129750i
$407$	−16.3673	+	20.5239i	−0.811296	+	1.01733i
$408$	−0.747470	+	0.509617i	−0.0370053	+	0.0252298i
$409$	17.3561	−	16.1041i	0.858205	−	0.796298i	−0.122361	−	0.992486i	$-0.539047\pi$
$409$	17.3561	−	16.1041i	0.858205	−	0.796298i	0.980566	+	0.196187i	$0.0628561\pi$
$410$	−3.12407	−	5.41104i	−0.154287	−	0.267232i
$411$	−1.86020	+	3.22197i	−0.0917571	+	0.158928i
$412$	−3.07983	−	13.4936i	−0.151732	−	0.664783i
$413$	−3.73925	−	18.5676i	−0.183997	−	0.913652i
$414$	5.00173	−	21.9140i	0.245821	−	1.07701i
$415$	8.50019	+	7.88703i	0.417258	+	0.387159i
$416$	−4.14749	−	0.625134i	−0.203347	−	0.0306497i
$417$	1.11805	+	0.168519i	0.0547512	+	0.00825241i
$418$	−9.62932	−	8.93470i	−0.470985	−	0.437010i
$419$	2.34829	−	10.2885i	0.114722	−	0.502628i	−0.884619	−	0.466315i	$-0.845581\pi$
$419$	2.34829	−	10.2885i	0.114722	−	0.502628i	0.999340	−	0.0363132i	$-0.0115614\pi$
$420$	0.407406	−	1.59506i	0.0198794	−	0.0778309i
$421$	8.55595	+	37.4861i	0.416992	+	1.82696i	0.549141	+	0.835730i	$0.314955\pi$
$421$	8.55595	+	37.4861i	0.416992	+	1.82696i	−0.132149	+	0.991230i	$0.542188\pi$
$422$	15.2395	−	26.3955i	0.741846	−	1.28491i
$423$	−14.8159	−	25.6620i	−0.720376	−	1.24773i
$424$	2.61578	−	2.42709i	0.127033	−	0.117870i
$425$	2.73998	−	1.86809i	0.132909	−	0.0906156i
$426$	−0.110157	+	0.138133i	−0.00533713	+	0.00669255i
$427$	−8.17995	−	1.44857i	−0.395855	−	0.0701014i
$428$	4.45475	+	5.58608i	0.215328	+	0.270013i
$429$	−0.686255	−	0.211682i	−0.0331327	−	0.0102201i
$430$	5.67156	−	14.4509i	0.273507	−	0.696884i
$431$	0.837595	+	11.1769i	0.0403455	+	0.538373i	0.980357	+	0.197231i	$0.0631949\pi$
$431$	0.837595	+	11.1769i	0.0403455	+	0.538373i	−0.940012	+	0.341143i	$0.889186\pi$
$432$	3.17227	+	8.08282i	0.152626	+	0.388885i
$433$	−0.429584	+	0.206877i	−0.0206445	+	0.00994186i	−0.444178	−	0.895939i	$-0.646504\pi$
$433$	−0.429584	+	0.206877i	−0.0206445	+	0.00994186i	0.423533	+	0.905881i	$0.360790\pi$
$434$	−11.8085	−	11.5347i	−0.566827	−	0.553685i
$435$	−0.0483850	−	0.0233010i	−0.00231988	−	0.00111720i
$436$	−0.955866	+	12.7551i	−0.0457777	+	0.610861i
$437$	14.3856	−	4.43738i	0.688158	−	0.212269i
$438$	−1.62447	−	1.10754i	−0.0776201	−	0.0529205i
$439$	17.3079	−	2.60874i	0.826059	−	0.124508i	0.277612	−	0.960693i	$-0.410457\pi$
$439$	17.3079	−	2.60874i	0.826059	−	0.124508i	0.548448	+	0.836185i	$0.315219\pi$
$440$	−13.2140			−0.629955
$441$	−11.8747	−	16.5683i	−0.565464	−	0.788969i
$442$	−2.50314			−0.119062
$443$	−33.3998	+	5.03422i	−1.58687	+	0.239183i	−0.882384	−	0.470531i	$-0.844063\pi$
$443$	−33.3998	+	5.03422i	−1.58687	+	0.239183i	−0.704490	+	0.709713i	$0.748824\pi$
$444$	−2.07571	−	1.41519i	−0.0985086	−	0.0671620i
$445$	−35.5053	+	10.9519i	−1.68311	+	0.519172i
$446$	−1.70304	+	22.7255i	−0.0806414	+	1.07608i
$447$	2.08451	+	1.00385i	0.0985941	+	0.0474804i
$448$	4.01851	−	6.56509i	0.189857	−	0.310171i
$449$	32.2881	−	15.5491i	1.52377	−	0.733808i	0.530289	−	0.847817i	$-0.322083\pi$
$449$	32.2881	−	15.5491i	1.52377	−	0.733808i	0.993480	+	0.114008i	$0.0363691\pi$
$450$	−3.92025	−	9.98864i	−0.184802	−	0.470869i
$451$	0.252494	+	3.36929i	0.0118895	+	0.158654i
$452$	3.06506	−	7.80965i	0.144168	−	0.367335i
$453$	−0.788464	−	0.243209i	−0.0370453	−	0.0114270i
$454$	−2.70406	−	3.39078i	−0.126908	−	0.159137i
$455$	−5.32989	+	4.69666i	−0.249869	+	0.220183i
$456$	−1.22238	+	1.53282i	−0.0572433	+	0.0717808i
$457$	−21.6374	+	14.7521i	−1.01216	+	0.690076i	−0.951362	−	0.308075i	$-0.900315\pi$
$457$	−21.6374	+	14.7521i	−1.01216	+	0.690076i	−0.0607931	+	0.998150i	$0.519363\pi$
$458$	−20.0070	+	18.5638i	−0.934866	+	0.867429i
$459$	1.31582	+	2.27908i	0.0614175	+	0.106378i
$460$	−4.85519	+	8.40943i	−0.226374	+	0.392092i
$461$	2.59037	+	11.3492i	0.120646	+	0.528583i	0.998744	+	0.0501031i	$0.0159550\pi$
$461$	2.59037	+	11.3492i	0.120646	+	0.528583i	−0.878098	+	0.478480i	$0.841188\pi$
$462$	−2.03869	+	2.42597i	−0.0948483	+	0.112866i
$463$	−7.61745	+	33.3742i	−0.354013	+	1.55103i	0.413806	+	0.910365i	$0.364199\pi$
$463$	−7.61745	+	33.3742i	−0.354013	+	1.55103i	−0.767819	+	0.640667i	$0.778658\pi$
$464$	0.244820	+	0.227160i	0.0113655	+	0.0105456i
$465$	2.94582	+	0.444011i	0.136609	+	0.0205905i
$466$	−3.29100	−	0.496038i	−0.152452	−	0.0229785i
$467$	12.9869	+	12.0501i	0.600963	+	0.557613i	0.920886	−	0.389831i	$-0.127467\pi$
$467$	12.9869	+	12.0501i	0.600963	+	0.557613i	−0.319923	+	0.947444i	$0.603657\pi$
$468$	−0.506328	+	2.21837i	−0.0234050	+	0.102544i
$469$	1.58947	+	2.10162i	0.0733950	+	0.0970437i
$470$	10.1395	+	44.4238i	0.467698	+	2.04912i
$471$	−1.21088	+	2.09730i	−0.0557943	+	0.0966386i
$472$	−7.27457	−	12.5999i	−0.334839	−	0.579959i
$473$	−6.15380	+	5.70989i	−0.282952	+	0.262541i
$474$	−2.96028	+	2.01828i	−0.135970	+	0.0927029i
$475$	4.48086	−	5.61881i	0.205596	−	0.257809i
$476$	−1.20738	+	2.85836i	−0.0553404	+	0.131013i
$477$	−3.18783	−	3.99741i	−0.145961	−	0.183029i
$478$	33.7950	+	10.4244i	1.54575	+	0.476799i
$479$	10.9056	−	27.7869i	0.498287	−	1.26962i	−0.431698	−	0.902018i	$-0.642085\pi$
$479$	10.9056	−	27.7869i	0.498287	−	1.26962i	0.929985	−	0.367597i	$-0.119819\pi$
$480$	−0.249601	−	3.33069i	−0.0113927	−	0.152025i
$481$	3.96058	+	10.0914i	0.180587	+	0.460128i
$482$	−39.9389	+	19.2336i	−1.81917	+	0.876065i
$483$	−1.23958	−	3.41356i	−0.0564029	−	0.155322i
$484$	3.61595	+	1.74135i	0.164361	+	0.0791523i
$485$	−1.89439	+	25.2789i	−0.0860200	+	1.14786i
$486$	12.2661	−	3.78358i	0.556399	−	0.171626i
$487$	18.6270	+	12.6996i	0.844068	+	0.575476i	0.906324	−	0.422584i	$-0.138877\pi$
$487$	18.6270	+	12.6996i	0.844068	+	0.575476i	−0.0622555	+	0.998060i	$0.519829\pi$
$488$	−6.30996	+	0.951073i	−0.285638	+	0.0430531i
$489$	−4.58326			−0.207262
$490$	9.93934	+	29.7283i	0.449014	+	1.34299i
$491$	−32.3306			−1.45906			−0.729530	−	0.683949i	$-0.760261\pi$
$491$	−32.3306			−1.45906			−0.729530	+	0.683949i	$0.760261\pi$
$492$	−0.319735	+	0.0481922i	−0.0144147	+	0.00217267i
$493$	0.0836323	+	0.0570195i	0.00376661	+	0.00256803i
$494$	−5.18368	+	1.59895i	−0.233225	+	0.0719403i
$495$	−1.41492	+	18.8808i	−0.0635958	+	0.848627i
$496$	−16.6919	−	8.03839i	−0.749488	−	0.360934i
$497$	0.0947935	−	0.940309i	0.00425207	−	0.0421786i
$498$	1.92450	−	0.926791i	0.0862390	−	0.0415305i
$499$	−2.11041	−	5.37723i	−0.0944747	−	0.240718i	0.875823	−	0.482633i	$-0.160320\pi$
$499$	−2.11041	−	5.37723i	−0.0944747	−	0.240718i	−0.970297	+	0.241916i	$0.922224\pi$
$500$	−0.437520	−	5.83830i	−0.0195665	−	0.261097i
$501$	−2.57137	+	6.55173i	−0.114880	+	0.292710i
$502$	17.9801	+	5.54612i	0.802491	+	0.247536i
$503$	13.4356	+	16.8477i	0.599062	+	0.751200i	0.985231	−	0.171228i	$-0.0547734\pi$
$503$	13.4356	+	16.8477i	0.599062	+	0.751200i	−0.386169	+	0.922428i	$0.626202\pi$
$504$	−12.7068	−	9.14982i	−0.566007	−	0.407565i
$505$	−1.69454	+	2.12489i	−0.0754062	+	0.0945563i
$506$	15.4434	−	10.5291i	0.686543	−	0.468077i
$507$	−0.217405	+	0.201723i	−0.00965531	+	0.00895882i
$508$	2.67191	+	4.62789i	0.118547	+	0.205329i
$509$	−11.5701	+	20.0400i	−0.512835	+	0.888257i	0.487054	+	0.873372i	$0.338072\pi$
$509$	−11.5701	+	20.0400i	−0.512835	+	0.888257i	−0.999889	+	0.0148849i	$0.995262\pi$
$510$	−0.443551	−	1.94332i	−0.0196408	−	0.0860518i
$511$	10.5135	+	0.269958i	0.465088	+	0.0119422i
$512$	−0.142864	+	0.625928i	−0.00631375	+	0.0276624i
$513$	4.18073	+	3.87915i	0.184584	+	0.171269i
$514$	−14.0741	−	2.12133i	−0.620782	−	0.0935679i
$515$	−47.0290	−	7.08848i	−2.07234	−	0.312356i
$516$	−0.588920	−	0.546438i	−0.0259258	−	0.0240556i
$517$	5.48301	−	24.0226i	0.241142	−	1.05651i
$518$	47.8186	+	1.22786i	2.10103	+	0.0539489i
$519$	0.462637	+	2.02695i	0.0203075	+	0.0889730i
$520$	−2.72847	+	4.72585i	−0.119651	+	0.207242i
$521$	−0.817245	−	1.41551i	−0.0358041	−	0.0620146i	0.847568	−	0.530687i	$-0.178066\pi$
$521$	−0.817245	−	1.41551i	−0.0358041	−	0.0620146i	−0.883372	+	0.468672i	$0.844733\pi$
$522$	0.240091	−	0.222772i	0.0105085	−	0.00975047i
$523$	−26.7912	+	18.2659i	−1.17150	+	0.798712i	−0.983044	−	0.183370i	$-0.941299\pi$
$523$	−26.7912	+	18.2659i	−1.17150	+	0.798712i	−0.188452	+	0.982082i	$0.560347\pi$
$524$	9.49695	−	11.9088i	0.414876	−	0.520238i
$525$	−1.40690	−	1.01307i	−0.0614023	−	0.0442141i
$526$	14.0905	+	17.6690i	0.614377	+	0.770404i
$527$	−5.36557	−	1.65506i	−0.233728	−	0.0720954i
$528$	−1.29933	+	3.31064i	−0.0565460	+	0.144077i
$529$	−0.117992	−	1.57449i	−0.00513008	−	0.0684561i
$530$	2.87242	+	7.31881i	0.124770	+	0.317909i
$531$	−18.7822	+	9.04505i	−0.815079	+	0.392522i
$532$	−0.674480	+	6.69054i	−0.0292424	+	0.290072i
$533$	1.25712	+	0.605399i	0.0544521	+	0.0262227i
$534$	−0.511493	+	6.82540i	−0.0221345	+	0.295364i
$535$	23.4609	−	7.23674i	1.01430	−	0.312872i
$536$	1.67238	+	1.14021i	0.0722358	+	0.0492495i
$537$	4.64439	−	0.700029i	0.200420	−	0.0302085i
$538$	−5.66965			−0.244436
$539$	2.13253	−	16.8159i	0.0918548	−	0.724312i
$540$	−3.67865			−0.158304
$541$	29.7221	−	4.47989i	1.27785	−	0.192605i	0.525175	−	0.850994i	$-0.324000\pi$
$541$	29.7221	−	4.47989i	1.27785	−	0.192605i	0.752678	+	0.658389i	$0.228762\pi$
$542$	16.4465	+	11.2130i	0.706437	+	0.481640i
$543$	0.761372	−	0.234852i	0.0326736	−	0.0100785i
$544$	−0.470450	+	6.27772i	−0.0201704	+	0.269155i
$545$	39.6004	+	19.0705i	1.69629	+	0.816892i
$546$	0.446668	+	1.23003i	0.0191156	+	0.0526406i
$547$	−14.4974	+	6.98159i	−0.619865	+	0.298511i	−0.717336	−	0.696727i	$-0.754639\pi$
$547$	−14.4974	+	6.98159i	−0.619865	+	0.298511i	0.0974711	+	0.995238i	$0.468925\pi$
$548$	3.58111	+	9.12451i	0.152977	+	0.389780i
$549$	0.683282	+	9.11776i	0.0291618	+	0.389137i
$550$	3.25989	−	8.30606i	0.139002	−	0.354172i
$551$	0.209614	+	0.0646575i	0.00892988	+	0.00275450i
$552$	−1.73934	−	2.18106i	−0.0740311	−	0.0928320i
$553$	7.45742	−	17.6546i	0.317122	−	0.750752i
$554$	−20.5127	+	25.7221i	−0.871501	+	1.09283i
$555$	−7.13269	+	4.86299i	−0.302766	+	0.206422i
$556$	2.18375	−	2.02622i	0.0926115	−	0.0859309i
$557$	−3.88595	−	6.73067i	−0.164653	−	0.285187i	0.771879	−	0.635770i	$-0.219317\pi$
$557$	−3.88595	−	6.73067i	−0.164653	−	0.285187i	−0.936532	+	0.350582i	$0.885984\pi$
$558$	−9.08437	+	15.7346i	−0.384572	+	0.666098i
$559$	0.771424	+	3.37983i	0.0326278	+	0.142952i
$560$	21.2213	+	28.0590i	0.896763	+	1.18571i
$561$	−0.239854	+	1.05087i	−0.0101267	+	0.0443678i
$562$	18.5959	+	17.2544i	0.784419	+	0.727835i
$563$	11.6210	+	1.75158i	0.489765	+	0.0738202i	0.389282	−	0.921119i	$-0.372723\pi$
$563$	11.6210	+	1.75158i	0.489765	+	0.0738202i	0.100483	+	0.994939i	$0.467961\pi$
$564$	2.33176	+	0.351456i	0.0981846	+	0.0147989i
$565$	−21.1331	−	19.6087i	−0.889077	−	0.824943i
$566$	−3.67806	+	16.1146i	−0.154600	+	0.677349i
$567$	−13.9851	+	16.6418i	−0.587319	+	0.698890i
$568$	−0.161542	−	0.707763i	−0.00677816	−	0.0296971i
$569$	12.2821	−	21.2732i	0.514891	−	0.891818i	−0.484960	−	0.874537i	$-0.661166\pi$
$569$	12.2821	−	21.2732i	0.514891	−	0.891818i	0.999851	−	0.0172811i	$-0.00550100\pi$
$570$	−2.15989	−	3.74104i	−0.0904678	−	0.156695i
$571$	23.8819	−	22.1592i	0.999428	−	0.927334i	0.00207183	−	0.999998i	$-0.499341\pi$
$571$	23.8819	−	22.1592i	0.999428	−	0.927334i	0.997356	+	0.0726639i	$0.0231500\pi$
$572$	−1.56335	+	1.06587i	−0.0653669	+	0.0445664i
$573$	3.07191	−	3.85205i	0.128331	−	0.160922i
$574$	4.61918	−	4.07039i	0.192801	−	0.169895i
$575$	6.37584	+	7.99505i	0.265891	+	0.333417i
$576$	−8.09566	−	2.49718i	−0.337319	−	0.104049i
$577$	−4.34397	+	11.0683i	−0.180842	+	0.460778i	−0.992334	−	0.123586i	$-0.960561\pi$
$577$	−4.34397	+	11.0683i	−0.180842	+	0.460778i	0.811492	+	0.584364i	$0.198656\pi$
$578$	−1.83797	−	24.5259i	−0.0764493	−	1.02014i
$579$	2.45901	+	6.26545i	0.102193	+	0.260383i
$580$	−0.127479	+	0.0613906i	−0.00529327	+	0.00254911i
$581$	−5.96508	+	9.74524i	−0.247473	+	0.404301i
$582$	4.20726	+	2.02611i	0.174396	+	0.0839848i
$583$	0.317724	−	4.23973i	0.0131588	−	0.175592i
$584$	7.71972	−	2.38122i	0.319444	−	0.0985355i
$585$	6.46033	+	4.40458i	0.267102	+	0.182107i
$586$	−5.80547	+	0.875034i	−0.239822	+	0.0361473i
$587$	−14.9999			−0.619111			−0.309556	−	0.950881i	$-0.600180\pi$
$587$	−14.9999			−0.619111			−0.309556	+	0.950881i	$0.600180\pi$
$588$	1.62004	+	0.0832514i	0.0668092	+	0.00343323i
$589$	−12.1686			−0.501399
$590$	31.6989	−	4.77783i	1.30502	−	0.196700i
$591$	−0.168741	−	0.115046i	−0.00694109	−	0.00473236i
$592$	51.3007	−	15.8242i	2.10845	−	0.650370i
$593$	−0.821509	+	10.9623i	−0.0337353	+	0.450167i	0.954602	+	0.297885i	$0.0962812\pi$
$593$	−0.821509	+	10.9623i	−0.0337353	+	0.450167i	−0.988337	+	0.152282i	$0.951338\pi$
$594$	6.37969	+	3.07230i	0.261762	+	0.126058i
$595$	7.62737	+	7.45052i	0.312692	+	0.305442i
$596$	5.49203	−	2.64482i	0.224962	−	0.108336i
$597$	−2.31962	−	5.91028i	−0.0949355	−	0.241892i
$598$	−0.576828	−	7.69724i	−0.0235883	−	0.314764i
$599$	0.105205	−	0.268059i	0.00429857	−	0.0109526i	−0.928708	−	0.370811i	$-0.879080\pi$
$599$	0.105205	−	0.268059i	0.00429857	−	0.0109526i	0.933007	+	0.359858i	$0.117175\pi$
$600$	−1.27258	−	0.392539i	−0.0519528	−	0.0160253i
$601$	12.7881	+	16.0357i	0.521637	+	0.654112i	0.970956	−	0.239260i	$-0.0769048\pi$
$601$	12.7881	+	16.0357i	0.521637	+	0.654112i	−0.449319	+	0.893371i	$0.648333\pi$
$602$	15.0625	+	2.66739i	0.613901	+	0.108715i
$603$	1.80825	−	2.26747i	0.0736376	−	0.0923387i
$604$	−1.79619	+	1.22462i	−0.0730859	+	0.0498291i
$605$	10.1096	−	9.38037i	0.411015	−	0.381366i
$606$	0.250327	+	0.433579i	0.0101688	+	0.0176129i
$607$	8.16240	−	14.1377i	0.331302	−	0.573831i	−0.651466	−	0.758678i	$-0.725846\pi$
$607$	8.16240	−	14.1377i	0.331302	−	0.573831i	0.982767	+	0.184847i	$0.0591789\pi$
$608$	3.03584	+	13.3009i	0.123119	+	0.539421i
$609$	0.0130956	−	0.0512713i	0.000530661	−	0.00207762i
$610$	3.12867	−	13.7076i	0.126676	−	0.555004i
$611$	−7.45927	−	6.92119i	−0.301770	−	0.280001i
$612$	3.37706	+	0.509009i	0.136509	+	0.0205755i
$613$	−42.6561	−	6.42937i	−1.72286	−	0.259680i	−0.788253	−	0.615351i	$-0.789014\pi$
$613$	−42.6561	−	6.42937i	−1.72286	−	0.259680i	−0.934611	+	0.355671i	$0.884252\pi$
$614$	−36.2751	−	33.6584i	−1.46395	−	1.35834i
$615$	−0.247244	+	1.08325i	−0.00996985	+	0.0436808i
$616$	−2.57057	−	12.7644i	−0.103571	−	0.514292i
$617$	8.67360	+	38.0015i	0.349186	+	1.52988i	0.779033	+	0.626982i	$0.215710\pi$
$617$	8.67360	+	38.0015i	0.349186	+	1.52988i	−0.429847	+	0.902902i	$0.641433\pi$
$618$	−4.38054	+	7.58733i	−0.176211	+	0.305207i
$619$	−11.7283	−	20.3140i	−0.471400	−	0.816489i	0.528064	−	0.849204i	$-0.322918\pi$
$619$	−11.7283	−	20.3140i	−0.471400	−	0.816489i	−0.999465	+	0.0327150i	$0.989585\pi$
$620$	5.75369	−	5.33865i	0.231074	−	0.214405i
$621$	−6.70501	+	4.57140i	−0.269063	+	0.183444i
$622$	−25.7221	+	32.2545i	−1.03136	+	1.29329i
$623$	−17.4862	−	32.1666i	−0.700571	−	1.28873i
$624$	0.915722	+	1.14828i	0.0366582	+	0.0459680i
$625$	−29.7810	−	9.18622i	−1.19124	−	0.367449i
$626$	−0.603481	+	1.53764i	−0.0241199	+	0.0614566i
$627$	0.174567	+	2.32943i	0.00697153	+	0.0930285i
$628$	2.33108	+	5.93949i	0.0930202	+	0.237012i
$629$	14.6597	−	7.05975i	0.584521	−	0.281491i
$630$	28.9953	−	18.6969i	1.15520	−	0.744900i
$631$	32.9753	+	15.8800i	1.31272	+	0.632175i	0.953589	−	0.301111i	$-0.0973575\pi$
$631$	32.9753	+	15.8800i	1.31272	+	0.632175i	0.359135	+	0.933286i	$0.383072\pi$
$632$	1.10016	−	14.6806i	0.0437619	−	0.583962i
$633$	−5.17928	+	1.59759i	−0.205858	+	0.0634987i
$634$	−15.8952	−	10.8372i	−0.631281	−	0.430400i
$635$	18.1578	−	2.73684i	0.720569	−	0.108608i
$636$	0.406881			0.0161339
$637$	−5.57368	−	4.23487i	−0.220837	−	0.167792i
$638$	0.272352			0.0107825
$639$	−1.02858	+	0.155033i	−0.0406899	+	0.00613302i
$640$	29.3743	+	20.0271i	1.16112	+	0.791639i
$641$	−32.9242	+	10.1558i	−1.30043	+	0.401129i	−0.866211	−	0.499679i	$-0.833451\pi$
$641$	−32.9242	+	10.1558i	−1.30043	+	0.401129i	−0.434218	+	0.900808i	$0.642975\pi$
$642$	0.337980	−	4.51004i	0.0133390	−	0.177997i
$643$	−6.33571	−	3.05112i	−0.249856	−	0.120324i	0.304764	−	0.952428i	$-0.401422\pi$
$643$	−6.33571	−	3.05112i	−0.249856	−	0.120324i	−0.554620	+	0.832103i	$0.687137\pi$
$644$	−9.06777	−	3.05406i	−0.357320	−	0.120347i
$645$	−2.48725	+	1.19780i	−0.0979353	+	0.0471632i
$646$	2.97459	+	7.57914i	0.117034	+	0.298197i
$647$	2.38712	+	31.8539i	0.0938473	+	1.25230i	0.823035	+	0.567991i	$0.192279\pi$
$647$	2.38712	+	31.8539i	0.0938473	+	1.25230i	−0.729188	+	0.684314i	$0.760102\pi$
$648$	−6.10047	+	15.5437i	−0.239649	+	0.610616i
$649$	−16.5649	−	5.10961i	−0.650231	−	0.200570i
$650$	−2.29746	−	2.88092i	−0.0901136	−	0.112999i
$651$	0.144157	+	2.93195i	0.00564997	+	0.114912i
$652$	−7.52891	+	9.44096i	−0.294855	+	0.369736i
$653$	4.08282	−	2.78362i	0.159773	−	0.108932i	−0.480794	−	0.876833i	$-0.659652\pi$
$653$	4.08282	−	2.78362i	0.159773	−	0.108932i	0.640567	+	0.767902i	$0.278699\pi$
$654$	5.93524	−	5.50710i	0.232086	−	0.215345i
$655$	−26.1705	−	45.3287i	−1.02257	−	1.77114i
$656$	3.45491	−	5.98408i	0.134892	−	0.233639i
$657$	−2.57578	−	11.2852i	−0.100491	−	0.440278i
$658$	−40.9397	+	18.4363i	−1.59600	+	0.718723i
$659$	8.29821	−	36.3569i	0.323253	−	1.41626i	−0.508474	−	0.861077i	$-0.669790\pi$
$659$	8.29821	−	36.3569i	0.323253	−	1.41626i	0.831727	−	0.555185i	$-0.187352\pi$
$660$	−1.10452	−	1.02484i	−0.0429932	−	0.0398919i
$661$	42.4647	+	6.40052i	1.65168	+	0.248951i	0.907814	−	0.419373i	$-0.137750\pi$
$661$	42.4647	+	6.40052i	1.65168	+	0.248951i	0.743870	+	0.668325i	$0.232988\pi$
$662$	−17.7626	−	2.67728i	−0.690362	−	0.104055i
$663$	0.326306	+	0.302768i	0.0126727	+	0.0117585i
$664$	−1.95304	+	8.55683i	−0.0757927	+	0.332069i
$665$	20.5545	+	10.5569i	0.797070	+	0.409378i
$666$	−11.7155	−	51.3288i	−0.453965	−	1.98895i
$667$	−0.156065	+	0.270312i	−0.00604284	+	0.0104665i
$668$	9.27179	+	16.0592i	0.358736	+	0.621349i
$669$	2.97078	−	2.75648i	0.114857	−	0.106572i
$670$	−3.68484	+	2.51228i	−0.142358	+	0.0970579i
$671$	−4.74048	+	5.94437i	−0.183004	+	0.229480i
$672$	3.16880	−	0.889038i	0.122239	−	0.0342954i
$673$	8.03830	+	10.0797i	0.309854	+	0.388544i	0.912237	−	0.409663i	$-0.134354\pi$
$673$	8.03830	+	10.0797i	0.309854	+	0.388544i	−0.602383	+	0.798207i	$0.705782\pi$
$674$	−24.4279	−	7.53500i	−0.940926	−	0.290237i
$675$	−1.41533	+	3.60621i	−0.0544763	+	0.138803i
$676$	0.0583928	+	0.779198i	0.00224588	+	0.0299691i
$677$	4.82062	+	12.2827i	0.185272	+	0.472064i	0.993088	−	0.117369i	$-0.0374461\pi$
$677$	4.82062	+	12.2827i	0.185272	+	0.472064i	−0.807817	+	0.589434i	$0.799351\pi$
$678$	−4.78468	+	2.30418i	−0.183755	+	0.0884916i
$679$	−24.7873	+	3.08766i	−0.951248	+	0.118493i
$680$	7.37928	+	3.55367i	0.282983	+	0.136277i
$681$	−0.0576352	+	0.769088i	−0.00220858	+	0.0294715i
$682$	−14.4370	+	4.45323i	−0.552822	+	0.170523i
$683$	−13.3017	−	9.06898i	−0.508977	−	0.347015i	0.281445	−	0.959577i	$-0.409186\pi$
$683$	−13.3017	−	9.06898i	−0.508977	−	0.347015i	−0.790422	+	0.612563i	$0.790139\pi$
$684$	7.31859	−	1.10310i	0.279833	−	0.0421781i
$685$	33.6827			1.28695
$686$	−26.7832	+	15.3843i	−1.02259	+	0.587374i
$687$	4.85348			0.185172
$688$	16.9763	−	2.55877i	0.647215	−	0.0975520i
$689$	−1.45069	−	0.989061i	−0.0552668	−	0.0376802i
$690$	5.87357	−	1.81176i	0.223603	−	0.0689724i
$691$	−2.59205	+	34.5885i	−0.0986061	+	1.31581i	0.700082	+	0.714062i	$0.253147\pi$
$691$	−2.59205	+	34.5885i	−0.0986061	+	1.31581i	−0.798688	+	0.601745i	$0.794472\pi$
$692$	4.93523	+	2.37668i	0.187609	+	0.0903479i
$693$	−18.5135	+	2.30616i	−0.703271	+	0.0876039i
$694$	40.9127	−	19.7025i	1.55302	−	0.747897i
$695$	−3.73985	−	9.52898i	−0.141861	−	0.361455i
$696$	−0.00303768	−	0.0405351i	−0.000115143	−	0.00153648i
$697$	0.765106	−	1.94946i	0.0289805	−	0.0738410i
$698$	3.50044	+	1.07974i	0.132493	+	0.0408688i
$699$	0.369012	+	0.462726i	0.0139573	+	0.0175019i
$700$	−4.39792	+	1.23388i	−0.166226	+	0.0466362i
$701$	−18.6472	+	23.3828i	−0.704295	+	0.883158i	−0.997336	−	0.0729421i	$-0.976761\pi$
$701$	−18.6472	+	23.3828i	−0.704295	+	0.883158i	0.293041	+	0.956100i	$0.405333\pi$
$702$	2.41607	−	1.64725i	0.0911886	−	0.0621713i
$703$	25.8488	−	23.9841i	0.974904	−	0.904579i
$704$	−3.52247	−	6.10110i	−0.132758	−	0.229944i
$705$	4.05153	−	7.01745i	0.152589	−	0.264293i
$706$	9.61549	+	42.1282i	0.361884	+	1.58552i
$707$	−2.38223	−	1.22352i	−0.0895929	−	0.0460152i
$708$	0.369156	−	1.61738i	0.0138737	−	0.0607848i
$709$	5.18786	+	4.81363i	0.194834	+	0.180780i	0.771557	−	0.636160i	$-0.219478\pi$
$709$	5.18786	+	4.81363i	0.194834	+	0.180780i	−0.576723	+	0.816940i	$0.695669\pi$
$710$	1.58169	+	0.238401i	0.0593597	+	0.00894704i
$711$	−20.8584	−	3.14390i	−0.782251	−	0.117905i
$712$	−20.6163	−	19.1291i	−0.772628	−	0.716894i
$713$	3.85291	−	16.8807i	0.144292	−	0.632187i
$714$	1.79091	−	0.806499i	0.0670232	−	0.0301824i
$715$	1.44680	+	6.33885i	0.0541073	+	0.237060i
$716$	6.18735	−	10.7168i	0.231232	−	0.400506i
$717$	−3.14459	−	5.44658i	−0.117437	−	0.203406i
$718$	−10.3291	+	9.58399i	−0.385478	+	0.357671i
$719$	−16.7707	+	11.4341i	−0.625443	+	0.426420i	−0.834134	−	0.551562i	$-0.814032\pi$
$719$	−16.7707	+	11.4341i	−0.625443	+	0.426420i	0.208691	+	0.977982i	$0.433080\pi$
$720$	24.1422	−	30.2734i	0.899728	−	1.12822i
$721$	−2.30142	−	46.8076i	−0.0857095	−	1.74321i
$722$	−8.75525	−	10.9787i	−0.325837	−	0.408586i
$723$	7.53278	+	2.32356i	0.280147	+	0.0864139i
$724$	0.766937	−	1.95412i	0.0285030	−	0.0726245i
$725$	0.0111352	+	0.148588i	0.000413549	+	0.00551843i
$726$	−0.928140	−	2.36486i	−0.0344465	−	0.0877683i
$727$	23.6836	−	11.4054i	0.878375	−	0.423003i	0.0603445	−	0.998178i	$-0.480780\pi$
$727$	23.6836	−	11.4054i	0.878375	−	0.423003i	0.818031	+	0.575174i	$0.195066\pi$
$728$	−5.09582	−	1.71629i	−0.188864	−	0.0636100i
$729$	20.1508	+	9.70410i	0.746325	+	0.359411i
$730$	−1.33020	+	17.7503i	−0.0492329	+	0.656968i
$731$	4.97211	−	1.53369i	0.183900	−	0.0567257i
$732$	−0.601190	−	0.409884i	−0.0222206	−	0.0151498i
$733$	13.6539	−	2.05799i	0.504318	−	0.0760137i	0.108044	−	0.994146i	$-0.465541\pi$
$733$	13.6539	−	2.05799i	0.504318	−	0.0760137i	0.396274	+	0.918132i	$0.370303\pi$
$734$	−42.9074			−1.58374
$735$	2.30011	−	5.07756i	0.0848409	−	0.187288i
$736$	−19.4126			−0.715559
$737$	2.38473	−	0.359441i	0.0878428	−	0.0132402i
$738$	−5.59889	−	3.81726i	−0.206098	−	0.140515i
$739$	37.6294	−	11.6071i	1.38422	−	0.426975i	0.488877	−	0.872353i	$-0.337407\pi$
$739$	37.6294	−	11.6071i	1.38422	−	0.426975i	0.895343	+	0.445377i	$0.146930\pi$
$740$	−1.69970	+	22.6809i	−0.0624821	+	0.833766i
$741$	0.869139	+	0.418556i	0.0319286	+	0.0153760i
$742$	−6.51099	+	4.19843i	−0.239026	+	0.154129i
$743$	40.4062	−	19.4586i	1.48236	−	0.713867i	0.494494	−	0.869181i	$-0.335353\pi$
$743$	40.4062	−	19.4586i	1.48236	−	0.713867i	0.987865	+	0.155315i	$0.0496391\pi$
$744$	0.823813	+	2.09904i	0.0302024	+	0.0769546i
$745$	−1.56533	−	20.8879i	−0.0573493	−	0.765273i
$746$	−12.2816	+	31.2930i	−0.449662	+	1.14572i
$747$	12.0172	+	3.70682i	0.439687	+	0.135626i
$748$	1.77066	+	2.22033i	0.0647416	+	0.0811834i
$749$	11.5544	+	21.2548i	0.422189	+	0.776635i
$750$	−2.31065	+	2.89746i	−0.0843730	+	0.105800i
$751$	−2.65822	+	1.81234i	−0.0969999	+	0.0661334i	−0.610849	−	0.791747i	$-0.709172\pi$
$751$	−2.65822	+	1.81234i	−0.0969999	+	0.0661334i	0.513849	+	0.857881i	$0.328219\pi$
$752$	−36.9399	+	34.2752i	−1.34706	+	1.24989i
$753$	−1.67303	−	2.89777i	−0.0609686	−	0.105601i
$754$	0.0562359	−	0.0974035i	0.00204799	−	0.00354723i
$755$	1.66228	+	7.28294i	0.0604967	+	0.265053i
$756$	−0.715619	−	3.55347i	−0.0260268	−	0.129239i
$757$	9.92475	−	43.4832i	0.360721	−	1.58042i	−0.390648	−	0.920540i	$-0.627749\pi$
$757$	9.92475	−	43.4832i	0.360721	−	1.58042i	0.751369	−	0.659883i	$-0.229394\pi$
$758$	−14.7403	−	13.6770i	−0.535393	−	0.496772i
$759$	−3.28674	−	0.495396i	−0.119301	−	0.0179817i
$760$	17.5515	+	2.64547i	0.636662	+	0.0959613i
$761$	4.73929	+	4.39742i	0.171799	+	0.159406i	0.761386	−	0.648298i	$-0.224519\pi$
$761$	4.73929	+	4.39742i	0.171799	+	0.159406i	−0.589587	+	0.807705i	$0.700710\pi$
$762$	0.752706	−	3.29782i	0.0272677	−	0.119467i
$763$	−10.7180	+	41.9627i	−0.388018	+	1.51915i
$764$	−2.88854	−	12.6555i	−0.104504	−	0.457860i
$765$	5.86779	−	10.1633i	0.212150	−	0.367455i
$766$	−14.8893	−	25.7891i	−0.537974	−	0.931798i
$767$	−5.24776	+	4.86921i	−0.189486	+	0.175817i
$768$	3.98524	−	2.71709i	0.143805	−	0.0980446i
$769$	11.2035	−	14.0487i	0.404007	−	0.506609i	−0.537657	−	0.843164i	$-0.680690\pi$
$769$	11.2035	−	14.0487i	0.404007	−	0.506609i	0.941664	+	0.336555i	$0.109262\pi$
$770$	28.2496	+	5.00268i	1.01804	+	0.180284i
$771$	1.57810	+	1.97887i	0.0568338	+	0.0712673i
$772$	16.9455	+	5.22699i	0.609881	+	0.188123i
$773$	10.1691	−	25.9105i	0.365758	−	0.931936i	−0.622975	−	0.782242i	$-0.714076\pi$
$773$	10.1691	−	25.9105i	0.365758	−	0.931936i	0.988732	−	0.149694i	$-0.0478287\pi$
$774$	−1.25819	−	16.7894i	−0.0452247	−	0.603481i
$775$	−3.01983	−	7.69440i	−0.108476	−	0.276391i
$776$	−17.2874	+	8.32519i	−0.620583	+	0.298857i
$777$	−6.08506	−	5.94397i	−0.218300	−	0.213239i
$778$	13.4263	+	6.46575i	0.481355	+	0.231808i
$779$	0.339163	−	4.52581i	0.0121518	−	0.162154i
$780$	−0.594586	+	0.183405i	−0.0212896	+	0.00656697i
$781$	−0.714676	−	0.487258i	−0.0255731	−	0.0174355i
$782$	−11.4559	+	1.72669i	−0.409661	+	0.0617465i
$783$	−0.118246			−0.00422577
$784$	−22.9760	+	25.9576i	−0.820571	+	0.927057i
$785$	21.9254			0.782549
$786$	−9.53409	+	1.43703i	−0.340070	+	0.0512572i
$787$	−0.529467	−	0.360984i	−0.0188735	−	0.0128677i	0.553847	−	0.832619i	$-0.313159\pi$
$787$	−0.529467	−	0.360984i	−0.0188735	−	0.0128677i	−0.572720	+	0.819751i	$0.694112\pi$
$788$	−0.514171	+	0.158601i	−0.0183166	+	0.00564992i
$789$	0.300330	−	4.00763i	0.0106920	−	0.142675i
$790$	29.2249	+	14.0740i	1.03977	+	0.500729i
$791$	14.8303	−	24.2285i	0.527306	−	0.861468i
$792$	−12.9119	+	6.21807i	−0.458806	+	0.220949i
$793$	1.14711	+	2.92279i	0.0407351	+	0.103791i
$794$	−0.779653	−	10.4038i	−0.0276689	−	0.369215i
$795$	0.510803	−	1.30151i	0.0181163	−	0.0461596i
$796$	−15.9849	−	4.93068i	−0.566569	−	0.174763i
$797$	18.7802	+	23.5496i	0.665227	+	0.834168i	0.993901	−	0.110275i	$-0.0351732\pi$
$797$	18.7802	+	23.5496i	0.665227	+	0.834168i	−0.328674	+	0.944443i	$0.606602\pi$
$798$	3.19357	−	2.81415i	0.113051	−	0.0996198i
$799$	−9.52239	+	11.9407i	−0.336878	+	0.422432i
$800$	−7.65696	+	5.22043i	−0.270714	+	0.184570i
$801$	−29.5400	+	27.4091i	−1.04374	+	0.968454i
$802$	−16.8572	−	29.1974i	−0.595247	−	1.03100i
$803$	4.81278	−	8.33598i	0.169839	−	0.294170i
$804$	0.0513572	+	0.225011i	0.00181123	+	0.00793551i
$805$	−21.1529	+	25.1713i	−0.745543	+	0.887173i
$806$	−1.38835	+	6.08275i	−0.0489024	+	0.214256i
$807$	0.739088	+	0.685773i	0.0260171	+	0.0241404i
$808$	−2.03419	−	0.306605i	−0.0715625	−	0.0107863i
$809$	−24.8548	−	3.74626i	−0.873849	−	0.131712i	−0.303221	−	0.952920i	$-0.598062\pi$
$809$	−24.8548	−	3.74626i	−0.873849	−	0.131712i	−0.570628	+	0.821209i	$0.693300\pi$
$810$	−26.9702	−	25.0247i	−0.947635	−	0.879277i
$811$	3.78300	−	16.5744i	0.132839	−	0.582006i	−0.864065	−	0.503380i	$-0.832090\pi$
$811$	3.78300	−	16.5744i	0.132839	−	0.582006i	0.996904	−	0.0786260i	$-0.0250533\pi$
$812$	−0.0841005	−	0.111199i	−0.00295135	−	0.00390231i
$813$	−0.787668	−	3.45100i	−0.0276247	−	0.121032i
$814$	21.8901	−	37.9148i	0.767247	−	1.32891i
$815$	20.7473	+	35.9353i	0.726745	+	1.25876i
$816$	1.61594	−	1.49937i	0.0565691	−	0.0524884i
$817$	9.31691	−	6.35216i	0.325957	−	0.222234i
$818$	−24.6194	+	30.8718i	−0.860798	+	1.07941i
$819$	−2.99795	+	7.09734i	−0.104757	+	0.248001i
$820$	1.82521	+	2.28874i	0.0637391	+	0.0799263i
$821$	−43.8042	−	13.5118i	−1.52878	−	0.471565i	−0.587506	−	0.809220i	$-0.699890\pi$
$821$	−43.8042	−	13.5118i	−1.52878	−	0.471565i	−0.941270	+	0.337655i	$0.890366\pi$
$822$	2.26683	−	5.77579i	0.0790649	−	0.201454i
$823$	1.04670	+	13.9673i	0.0364857	+	0.486868i	0.985277	+	0.170965i	$0.0546885\pi$
$823$	1.04670	+	13.9673i	0.0364857	+	0.486868i	−0.948791	+	0.315903i	$0.897692\pi$
$824$	−13.1519	−	33.5105i	−0.458168	−	1.16739i
$825$	−1.42962	+	0.688467i	−0.0497728	+	0.0239693i
$826$	10.7817	+	29.6908i	0.375144	+	1.03307i
$827$	−42.8053	−	20.6140i	−1.48849	−	0.716817i	−0.499706	−	0.866195i	$-0.666559\pi$
$827$	−42.8053	−	20.6140i	−1.48849	−	0.716817i	−0.988780	+	0.149377i	$0.952273\pi$
$828$	−0.787005	+	10.5019i	−0.0273503	+	0.364965i
$829$	21.2749	−	6.56242i	0.738906	−	0.227922i	0.0976195	−	0.995224i	$-0.468877\pi$
$829$	21.2749	−	6.56242i	0.738906	−	0.227922i	0.641287	+	0.767301i	$0.278401\pi$
$830$	−15.9783	−	10.8938i	−0.554614	−	0.378130i
$831$	5.78523	−	0.871983i	0.200687	−	0.0302488i
$832$	−2.90932			−0.100862
$833$	−5.71322	+	8.81720i	−0.197951	+	0.305498i
$834$	−1.88569			−0.0652960
$835$	63.0091	−	9.49710i	2.18052	−	0.328661i
$836$	5.08510	+	3.46696i	0.175872	+	0.119907i
$837$	6.26807	−	1.93344i	0.216656	−	0.0668296i
$838$	−1.31525	+	17.5507i	−0.0454344	+	0.606280i
$839$	−32.7501	−	15.7716i	−1.13066	−	0.544497i	−0.227491	−	0.973780i	$-0.573052\pi$
$839$	−32.7501	−	15.7716i	−1.13066	−	0.544497i	−0.903170	+	0.429283i	$0.858766\pi$
$840$	0.429483	−	4.26028i	0.0148186	−	0.146994i
$841$	26.1240	−	12.5807i	0.900828	−	0.433816i
$842$	−23.4275	−	59.6923i	−0.807366	−	2.05713i
$843$	−0.337118	−	4.49853i	−0.0116110	−	0.154938i
$844$	−5.21713	+	13.2930i	−0.179581	+	0.457565i
$845$	2.56576	+	0.791431i	0.0882647	+	0.0272261i
$846$	30.8120	+	38.6370i	1.05934	+	1.32837i
$847$	11.0278	+	7.94084i	0.378921	+	0.272850i
$848$	−5.42121	+	6.79798i	−0.186165	+	0.233444i
$849$	2.42862	−	1.65580i	0.0833499	−	0.0568270i
$850$	−4.05422	+	3.76177i	−0.139059	+	0.129028i
$851$	25.0872	+	43.4523i	0.859977	+	1.48952i
$852$	0.0413892	−	0.0716881i	0.00141797	−	0.00245599i
$853$	5.53527	+	24.2516i	0.189524	+	0.830359i	0.976868	+	0.213845i	$0.0685986\pi$
$853$	5.53527	+	24.2516i	0.189524	+	0.830359i	−0.787344	+	0.616514i	$0.788544\pi$
$854$	13.8498	+	0.355626i	0.473930	+	0.0121693i
$855$	5.65932	−	24.7951i	0.193545	−	0.847975i
$856$	13.6227	+	12.6400i	0.465614	+	0.432026i
$857$	−49.4257	−	7.44973i	−1.68835	−	0.254478i	−0.766562	−	0.642171i	$-0.778034\pi$
$857$	−49.4257	−	7.44973i	−1.68835	−	0.254478i	−0.921789	+	0.387693i	$0.873272\pi$
$858$	1.18433	+	0.178510i	0.0404325	+	0.00609422i
$859$	−26.5303	−	24.6165i	−0.905202	−	0.839905i	0.0824457	−	0.996596i	$-0.473727\pi$
$859$	−26.5303	−	24.6165i	−0.905202	−	0.839905i	−0.987648	+	0.156691i	$0.949917\pi$
$860$	−1.61848	+	7.09104i	−0.0551898	+	0.241802i
$861$	−1.09449	−	0.0281035i	−0.0373000	−	0.000957764i
$862$	−4.15949	−	18.2239i	−0.141673	−	0.620708i
$863$	18.2940	−	31.6862i	0.622735	−	1.07861i	−0.366239	−	0.930521i	$-0.619355\pi$
$863$	18.2940	−	31.6862i	0.622735	−	1.07861i	0.988974	−	0.148088i	$-0.0473120\pi$
$864$	−3.67711	−	6.36894i	−0.125098	−	0.216676i
$865$	13.7981	−	12.8028i	0.469150	−	0.435308i
$866$	0.657013	−	0.447944i	0.0223262	−	0.0152218i
$867$	−2.72695	+	3.41948i	−0.0926119	+	0.116132i
$868$	6.27627	+	4.51936i	0.213030	+	0.153397i
$869$	−10.9365	−	13.7139i	−0.370994	−	0.465212i
$870$	0.0855844	+	0.0263993i	0.00290158	+	0.000895020i
$871$	0.363856	−	0.927091i	0.0123288	−	0.0314133i
$872$	2.48617	+	33.1757i	0.0841924	+	1.12347i
$873$	10.0443	+	25.5924i	0.339948	+	0.866173i
$874$	−22.6206	+	10.8935i	−0.765155	+	0.368479i
$875$	1.98838	−	19.7239i	0.0672196	−	0.666788i
$876$	0.829944	+	0.399680i	0.0280412	+	0.0135039i
$877$	−3.85067	+	51.3836i	−0.130028	+	1.73510i	0.426687	+	0.904399i	$0.359680\pi$
$877$	−3.85067	+	51.3836i	−0.130028	+	1.73510i	−0.556715	+	0.830703i	$0.687939\pi$
$878$	−27.8943	+	8.60425i	−0.941387	+	0.290380i
$879$	0.862634	+	0.588134i	0.0290959	+	0.0198373i
$880$	31.8389	−	4.79895i	1.07329	−	0.161773i
$881$	−34.7598			−1.17109			−0.585544	−	0.810641i	$-0.699119\pi$
$881$	−34.7598			−1.17109			−0.585544	+	0.810641i	$0.699119\pi$
$882$	23.7012	+	24.3715i	0.798061	+	0.820633i
$883$	−33.7958			−1.13732			−0.568660	−	0.822573i	$-0.692538\pi$
$883$	−33.7958			−1.13732			−0.568660	+	0.822573i	$0.692538\pi$
$884$	1.15969	−	0.174795i	0.0390045	−	0.00587898i
$885$	−4.71012	−	3.21131i	−0.158329	−	0.107947i
$886$	53.8290	−	16.6041i	1.80842	−	0.557824i
$887$	3.37902	−	45.0899i	0.113456	−	1.51397i	−0.592416	−	0.805632i	$-0.701826\pi$
$887$	3.37902	−	45.0899i	0.113456	−	1.51397i	0.705873	−	0.708339i	$-0.250555\pi$
$888$	−5.88714	−	2.83510i	−0.197559	−	0.0951396i
$889$	6.17600	+	17.0075i	0.207136	+	0.570413i
$890$	55.8303	−	26.8865i	1.87144	−	0.901236i
$891$	7.26862	+	18.5201i	0.243508	+	0.620448i
$892$	−0.797919	−	10.6475i	−0.0267163	−	0.356504i
$893$	−12.0922	+	30.8103i	−0.404649	+	1.03103i
$894$	−3.68713	−	1.13733i	−0.123316	−	0.0380380i
$895$	−26.5126	−	33.2457i	−0.886217	−	1.11128i
$896$	−13.6313	+	32.2707i	−0.455390	+	1.07809i
$897$	−0.855827	+	1.07317i	−0.0285752	+	0.0358322i
$898$	−49.3820	+	33.6681i	−1.64790	+	1.12352i
$899$	0.184946	−	0.171605i	0.00616829	−	0.00572334i
$900$	2.51373	+	4.35391i	0.0837910	+	0.145130i
$901$	−1.31763	+	2.28220i	−0.0438966	+	0.0760311i
$902$	−1.25388	−	5.49361i	−0.0417496	−	0.182917i
$903$	−1.64089	−	2.16960i	−0.0546054	−	0.0721999i
$904$	4.85563	−	21.2739i	0.161496	−	0.707560i
$905$	−5.28791	−	4.90646i	−0.175776	−	0.163096i
$906$	1.36073	+	0.205096i	0.0452071	+	0.00681387i
$907$	−28.3647	−	4.27529i	−0.941833	−	0.141959i	−0.339861	−	0.940476i	$-0.610380\pi$
$907$	−28.3647	−	4.27529i	−0.941833	−	0.141959i	−0.601972	+	0.798517i	$0.705618\pi$
$908$	1.48955	+	1.38210i	0.0494324	+	0.0458666i
$909$	−0.655904	+	2.87370i	−0.0217550	+	0.0953147i
$910$	7.62220	−	9.07017i	0.252673	−	0.300673i
$911$	−2.36366	−	10.3559i	−0.0783115	−	0.343105i	0.920560	−	0.390601i	$-0.127733\pi$
$911$	−2.36366	−	10.3559i	−0.0783115	−	0.343105i	−0.998871	+	0.0474964i	$0.984876\pi$
$912$	2.38863	−	4.13722i	0.0790954	−	0.136997i
$913$	5.22876	+	9.05648i	0.173047	+	0.299726i
$914$	32.0158	−	29.7063i	1.05899	−	0.982599i
$915$	−2.06585	+	1.40847i	−0.0682950	+	0.0465627i
$916$	7.97279	−	9.99756i	0.263428	−	0.330329i
$917$	38.6952	−	34.0980i	1.27783	−	1.12601i
$918$	−2.73645	−	3.43140i	−0.0903164	−	0.113253i
$919$	55.5707	+	17.1413i	1.83311	+	0.565439i	0.999923	+	0.0124449i	$0.00396143\pi$
$919$	55.5707	+	17.1413i	1.83311	+	0.565439i	0.833185	+	0.552994i	$0.186515\pi$
$920$	−9.22717	+	23.5105i	−0.304211	+	0.775117i
$921$	0.657620	+	8.77533i	0.0216693	+	0.289157i
$922$	−7.09284	−	18.0723i	−0.233590	−	0.595178i
$923$	−0.321830	+	0.154985i	−0.0105932	+	0.00510141i
$924$	0.775103	−	1.26630i	0.0254990	−	0.0416581i
$925$	21.5803	+	10.3925i	0.709557	+	0.341705i
$926$	4.26643	−	56.9315i	0.140204	−	1.87089i
$927$	−49.2894	+	15.2038i	−1.61888	+	0.499357i
$928$	−0.233713	−	0.159343i	−0.00767200	−	0.00523068i
$929$	−37.6340	+	5.67242i	−1.23473	+	0.186106i	−0.733791	−	0.679375i	$-0.762251\pi$
$929$	−37.6340	+	5.67242i	−1.23473	+	0.186106i	−0.500942	+	0.865481i	$0.667013\pi$
$930$	−4.96837			−0.162919
$931$	−6.19910	+	21.9088i	−0.203167	+	0.718031i
$932$	1.55933			0.0510776
$933$	7.25445	−	1.09343i	0.237500	−	0.0357974i
$934$	−24.4122	−	16.6440i	−0.798793	−	0.544608i
$935$	9.32517	−	2.87643i	0.304966	−	0.0940694i
$936$	−0.442274	+	5.90173i	−0.0144562	+	0.192904i
$937$	−49.0266	−	23.6100i	−1.60163	−	0.771304i	−0.601998	−	0.798497i	$-0.705629\pi$
$937$	−49.0266	−	23.6100i	−1.60163	−	0.771304i	−0.999630	+	0.0271939i	$0.991343\pi$
$938$	−3.14362	−	3.07073i	−0.102643	−	0.100263i
$939$	0.264655	−	0.127451i	0.00863669	−	0.00415921i
$940$	−7.79965	−	19.8732i	−0.254397	−	0.648192i
$941$	2.10320	+	28.0652i	0.0685622	+	0.914900i	0.920371	+	0.391047i	$0.127887\pi$
$941$	2.10320	+	28.0652i	0.0685622	+	0.914900i	−0.851809	+	0.523853i	$0.824494\pi$
$942$	1.47557	−	3.75969i	0.0480766	−	0.122497i
$943$	6.17096	+	1.90349i	0.200954	+	0.0619862i
$944$	22.1038	+	27.7173i	0.719419	+	0.902122i
$945$	−12.2650	−	2.17200i	−0.398981	−	0.0706550i
$946$	8.72908	−	10.9459i	0.283807	−	0.355882i
$947$	3.74322	−	2.55208i	0.121638	−	0.0829316i	−0.500973	−	0.865463i	$-0.667024\pi$
$947$	3.74322	−	2.55208i	0.121638	−	0.0829316i	0.622611	+	0.782531i	$0.286072\pi$
$948$	1.23054	−	1.14177i	0.0399660	−	0.0370831i
$949$	−1.98751	−	3.44247i	−0.0645174	−	0.111747i
$950$	−5.99283	+	10.3799i	−0.194433	+	0.336768i
$951$	0.761268	+	3.33533i	0.0246858	+	0.108156i
$952$	−1.99724	+	7.81949i	−0.0647308	+	0.253431i
$953$	−12.8175	+	56.1571i	−0.415200	+	1.81911i	0.143393	+	0.989666i	$0.454199\pi$
$953$	−12.8175	+	56.1571i	−0.415200	+	1.81911i	−0.558592	+	0.829442i	$0.688658\pi$
$954$	6.25073	+	5.79983i	0.202375	+	0.187776i
$955$	−44.1080	−	6.64821i	−1.42730	−	0.215131i
$956$	−16.3849	−	2.46962i	−0.529925	−	0.0798734i
$957$	−0.0355034	−	0.0329424i	−0.00114766	−	0.00106488i
$958$	−11.0777	+	48.5347i	−0.357905	+	1.56808i
$959$	6.55240	+	32.5365i	0.211588	+	1.05066i
$960$	−0.515524	−	2.25866i	−0.0166385	−	0.0728979i
$961$	8.50217	−	14.7262i	0.274263	−	0.475038i
$962$	−9.03985	−	15.6575i	−0.291456	−	0.504817i
$963$	19.5192	−	18.1112i	0.628998	−	0.583625i
$964$	17.1603	−	11.6997i	0.552696	−	0.376822i
$965$	37.9933	−	47.6421i	1.22305	−	1.53365i
$966$	2.89271	+	5.32126i	0.0930714	+	0.171209i
$967$	1.32564	+	1.66230i	0.0426297	+	0.0534560i	0.802689	−	0.596397i	$-0.203402\pi$
$967$	1.32564	+	1.66230i	0.0426297	+	0.0534560i	−0.760060	+	0.649853i	$0.774830\pi$
$968$	9.97495	+	3.07687i	0.320607	+	0.0988942i
$969$	0.528972	−	1.34780i	0.0169930	−	0.0432976i
$970$	−3.15937	−	42.1589i	−0.101441	−	1.35364i
$971$	−8.13556	−	20.7291i	−0.261082	−	0.665227i	0.738880	−	0.673837i	$-0.235355\pi$
$971$	−8.13556	−	20.7291i	−0.261082	−	0.665227i	−0.999963	+	0.00860923i	$0.997260\pi$
$972$	−5.41856	+	2.60944i	−0.173800	+	0.0836979i
$973$	8.47720	−	5.46629i	0.271767	−	0.175241i
$974$	−33.8748	−	16.3132i	−1.08542	−	0.522710i
$975$	−0.0489687	+	0.653442i	−0.00156825	+	0.0209269i
$976$	14.8583	−	4.58318i	0.475603	−	0.146704i
$977$	25.7164	+	17.5331i	0.822739	+	0.560934i	0.899906	−	0.436084i	$-0.143635\pi$
$977$	25.7164	+	17.5331i	0.822739	+	0.560934i	−0.0771668	+	0.997018i	$0.524587\pi$
$978$	7.55835	−	1.13924i	0.241690	−	0.0364288i
$979$	−33.5092			−1.07096
$980$	−6.68075	−	13.0788i	−0.213409	−	0.417788i
$981$	47.6689			1.52195
$982$	53.3171	−	8.03625i	1.70142	−	0.256447i
$983$	26.3678	+	17.9773i	0.841002	+	0.573386i	0.905410	−	0.424538i	$-0.139563\pi$
$983$	26.3678	+	17.9773i	0.841002	+	0.573386i	−0.0644077	+	0.997924i	$0.520516\pi$
$984$	−0.803647	+	0.247892i	−0.0256193	+	0.00790252i
$985$	−0.138174	+	1.84381i	−0.00440260	+	0.0587487i
$986$	−0.152093	−	0.0732440i	−0.00484362	−	0.00233256i
$987$	7.56682	+	2.54854i	0.240855	+	0.0811208i
$988$	2.28991	−	1.10276i	0.0728516	−	0.0350835i
$989$	5.86194	+	14.9360i	0.186399	+	0.474937i
$990$	−2.35973	−	31.4884i	−0.0749970	−	1.00077i
$991$	11.0480	−	28.1498i	0.350950	−	0.894207i	−0.640996	−	0.767544i	$-0.721478\pi$
$991$	11.0480	−	28.1498i	0.350950	−	0.894207i	0.991946	−	0.126662i	$-0.0404264\pi$
$992$	14.9942	+	4.62510i	0.476067	+	0.146847i
$993$	1.99168	+	2.49748i	0.0632039	+	0.0792552i
$994$	0.0774020	+	1.57425i	0.00245504	+	0.0499320i
$995$	−35.8396	+	44.9414i	−1.13619	+	1.42474i
$996$	−0.826889	+	0.563763i	−0.0262010	+	0.0178635i
$997$	28.1711	−	26.1390i	0.892189	−	0.827830i	−0.0936362	−	0.995606i	$-0.529849\pi$
$997$	28.1711	−	26.1390i	0.892189	−	0.827830i	0.985825	+	0.167776i	$0.0536586\pi$
$998$	4.81690	+	8.34312i	0.152476	+	0.264097i
$999$	−9.50395	+	16.4613i	−0.300692	+	0.520813i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.a.534.7	yes	324
49.39	even	21	inner	637.2.bl.a.235.7	✓	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.a.235.7	✓	324	49.39	even	21	inner
637.2.bl.a.534.7	yes	324	1.1	even	1	trivial

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.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.64912 + 0.248565i) q^{2} +(0.245042 + 0.167067i) q^{3} +(0.746668 - 0.230317i) q^{4} +(0.200654 - 2.67754i) q^{5} +(-0.445631 - 0.214605i) q^{6} +(2.62546 - 0.327044i) q^{7} +(1.83108 - 0.881802i) q^{8} +(-1.06389 - 2.71074i) q^{9} +O(q^{10})\)	\(q+(-1.64912 + 0.248565i) q^{2} +(0.245042 + 0.167067i) q^{3} +(0.746668 - 0.230317i) q^{4} +(0.200654 - 2.67754i) q^{5} +(-0.445631 - 0.214605i) q^{6} +(2.62546 - 0.327044i) q^{7} +(1.83108 - 0.881802i) q^{8} +(-1.06389 - 2.71074i) q^{9} +(0.334640 + 4.46546i) q^{10} +(0.884677 - 2.25412i) q^{11} +(0.221444 + 0.0683063i) q^{12} +(-0.623490 - 0.781831i) q^{13} +(-4.24841 + 1.19193i) q^{14} +(0.496497 - 0.622587i) q^{15} +(-4.09170 + 2.78968i) q^{16} +(-1.10025 + 1.02088i) q^{17} +(2.42828 + 4.20590i) q^{18} +(-1.62635 + 2.81692i) q^{19} +(-0.466859 - 2.04544i) q^{20} +(0.697987 + 0.358488i) q^{21} +(-0.898644 + 3.93722i) q^{22} +(-3.39278 - 3.14804i) q^{23} +(0.596013 + 0.0898344i) q^{24} +(-2.18479 - 0.329304i) q^{25} +(1.22255 + 1.13436i) q^{26} +(0.390161 - 1.70941i) q^{27} +(1.88502 - 0.848880i) q^{28} +(-0.0150067 - 0.0657485i) q^{29} +(-0.664030 + 1.15013i) q^{30} +(1.87054 + 3.23987i) q^{31} +(3.07467 - 2.85287i) q^{32} +(0.593373 - 0.404555i) q^{33} +(1.56068 - 1.95703i) q^{34} +(-0.348864 - 7.09539i) q^{35} +(-1.41870 - 1.77899i) q^{36} +(-10.3592 - 3.19538i) q^{37} +(1.98186 - 5.04970i) q^{38} +(-0.0221631 - 0.295746i) q^{39} +(-1.99364 - 5.07972i) q^{40} +(-1.25712 + 0.605399i) q^{41} +(-1.24017 - 0.417695i) q^{42} +(-3.12343 - 1.50417i) q^{43} +(0.141399 - 1.88684i) q^{44} +(-7.47159 + 2.30468i) q^{45} +(6.37759 + 4.34817i) q^{46} +(10.0620 - 1.51660i) q^{47} -1.46870 q^{48} +(6.78608 - 1.71728i) q^{49} +3.68483 q^{50} +(-0.440162 + 0.0663437i) q^{51} +(-0.645608 - 0.440168i) q^{52} +(1.67777 - 0.517523i) q^{53} +(-0.218524 + 2.91600i) q^{54} +(-5.85798 - 2.82105i) q^{55} +(4.51904 - 2.91398i) q^{56} +(-0.869139 + 0.418556i) q^{57} +(0.0410906 + 0.104697i) q^{58} +(-0.534977 - 7.13877i) q^{59} +(0.227326 - 0.579217i) q^{60} +(-3.00034 - 0.925482i) q^{61} +(-3.89006 - 4.87798i) q^{62} +(-3.67973 - 6.76901i) q^{63} +(1.81393 - 2.27459i) q^{64} +(-2.21849 + 1.51254i) q^{65} +(-0.877985 + 0.814651i) q^{66} +(0.497968 + 0.862506i) q^{67} +(-0.586393 + 1.01566i) q^{68} +(-0.305441 - 1.33822i) q^{69} +(2.33898 + 11.6144i) q^{70} +(0.0794855 - 0.348249i) q^{71} +(-4.33841 - 4.02545i) q^{72} +(3.93063 + 0.592447i) q^{73} +(17.8778 + 2.69464i) q^{74} +(-0.480350 - 0.445700i) q^{75} +(-0.565560 + 2.47788i) q^{76} +(1.58549 - 6.20743i) q^{77} +(0.110062 + 0.482213i) q^{78} +(3.62186 - 6.27324i) q^{79} +(6.64845 + 11.5155i) q^{80} +(-6.02284 + 5.58838i) q^{81} +(1.92267 - 1.31085i) q^{82} +(-2.69260 + 3.37641i) q^{83} +(0.603730 + 0.106914i) q^{84} +(2.51267 + 3.15079i) q^{85} +(5.52480 + 1.70417i) q^{86} +(0.00730714 - 0.0186183i) q^{87} +(-0.367773 - 4.90759i) q^{88} +(-5.05565 - 12.8816i) q^{89} +(11.7487 - 5.65787i) q^{90} +(-1.89264 - 1.84876i) q^{91} +(-3.25832 - 1.56913i) q^{92} +(-0.0829140 + 1.10641i) q^{93} +(-16.2165 + 5.00211i) q^{94} +(7.21608 + 4.91984i) q^{95} +(1.23004 - 0.185399i) q^{96} -9.44111 q^{97} +(-10.7642 + 4.51879i) q^{98} -7.05154 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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