LMFDB - Embedded newform 225.2.q.a.121.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			121.19
Character	$\chi$	$=$	225.121
Dual form			225.2.q.a.106.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06328 - 0.226007i) q^{2} +(-1.68082 - 0.418155i) q^{3} +(-0.747608 + 0.332856i) q^{4} +(-2.22650 + 0.206637i) q^{5} +(-1.88168 - 0.0647394i) q^{6} +(1.73969 + 3.01324i) q^{7} +(-2.47854 + 1.80077i) q^{8} +(2.65029 + 1.40569i) q^{9} +O(q^{10})$	\(q+(1.06328 - 0.226007i) q^{2} +(-1.68082 - 0.418155i) q^{3} +(-0.747608 + 0.332856i) q^{4} +(-2.22650 + 0.206637i) q^{5} +(-1.88168 - 0.0647394i) q^{6} +(1.73969 + 3.01324i) q^{7} +(-2.47854 + 1.80077i) q^{8} +(2.65029 + 1.40569i) q^{9} +(-2.32069 + 0.722917i) q^{10} +(-3.44115 + 0.731439i) q^{11} +(1.39578 - 0.246855i) q^{12} +(-2.12159 - 0.450957i) q^{13} +(2.53079 + 2.81073i) q^{14} +(3.82875 + 0.583704i) q^{15} +(-1.13322 + 1.25857i) q^{16} +(-1.54674 + 1.12377i) q^{17} +(3.13570 + 0.895651i) q^{18} +(-0.970198 + 0.704890i) q^{19} +(1.59577 - 0.895588i) q^{20} +(-1.66410 - 5.79216i) q^{21} +(-3.49359 + 1.55545i) q^{22} +(1.34509 + 1.49387i) q^{23} +(4.91898 - 1.99035i) q^{24} +(4.91460 - 0.920154i) q^{25} -2.35776 q^{26} +(-3.86686 - 3.47093i) q^{27} +(-2.30358 - 1.67365i) q^{28} +(0.374039 - 3.55874i) q^{29} +(4.20295 - 0.244683i) q^{30} +(-0.663380 - 6.31164i) q^{31} +(2.14316 - 3.71207i) q^{32} +(6.08980 + 0.209520i) q^{33} +(-1.39064 + 1.54446i) q^{34} +(-4.49607 - 6.34948i) q^{35} +(-2.44927 - 0.168734i) q^{36} +(2.46324 + 7.58107i) q^{37} +(-0.872281 + 0.968766i) q^{38} +(3.37743 + 1.64513i) q^{39} +(5.14637 - 4.52157i) q^{40} +(-2.53573 - 0.538987i) q^{41} +(-3.07848 - 5.78258i) q^{42} +(5.34941 + 9.26545i) q^{43} +(2.32917 - 1.69224i) q^{44} +(-6.19134 - 2.58211i) q^{45} +(1.76783 + 1.28440i) q^{46} +(-1.37238 + 13.0573i) q^{47} +(2.43102 - 1.64156i) q^{48} +(-2.55306 + 4.42203i) q^{49} +(5.01763 - 2.08912i) q^{50} +(3.06970 - 1.24208i) q^{51} +(1.73622 - 0.369044i) q^{52} +(-11.2674 - 8.18624i) q^{53} +(-4.89601 - 2.81663i) q^{54} +(7.51058 - 2.33962i) q^{55} +(-9.73804 - 4.33566i) q^{56} +(1.92548 - 0.779098i) q^{57} +(-0.406593 - 3.86847i) q^{58} +(5.32898 + 1.13271i) q^{59} +(-3.05669 + 0.838041i) q^{60} +(-0.516362 + 0.109756i) q^{61} +(-2.13183 - 6.56111i) q^{62} +(0.375033 + 10.4314i) q^{63} +(2.48651 - 7.65270i) q^{64} +(4.81690 + 0.565658i) q^{65} +(6.52251 - 1.15356i) q^{66} +(1.12533 + 10.7068i) q^{67} +(0.782301 - 1.35499i) q^{68} +(-1.63618 - 3.07338i) q^{69} +(-6.21561 - 5.73513i) q^{70} +(6.38098 + 4.63605i) q^{71} +(-9.10018 + 1.28851i) q^{72} +(-2.75054 + 8.46529i) q^{73} +(4.33248 + 7.50408i) q^{74} +(-8.64532 - 0.508455i) q^{75} +(0.490700 - 0.849917i) q^{76} +(-8.19054 - 9.09652i) q^{77} +(3.96296 + 0.985909i) q^{78} +(-0.706394 + 6.72089i) q^{79} +(2.26305 - 3.03637i) q^{80} +(5.04810 + 7.45095i) q^{81} -2.81801 q^{82} +(-3.25148 - 1.44765i) q^{83} +(3.17205 + 3.77635i) q^{84} +(3.21161 - 2.82170i) q^{85} +(7.78197 + 8.64276i) q^{86} +(-2.11680 + 5.82519i) q^{87} +(7.21189 - 8.00962i) q^{88} +(2.71707 - 8.36227i) q^{89} +(-7.16670 - 1.34622i) q^{90} +(-2.33207 - 7.17736i) q^{91} +(-1.50284 - 0.669108i) q^{92} +(-1.52423 + 10.8861i) q^{93} +(1.49183 + 14.1938i) q^{94} +(2.01449 - 1.76992i) q^{95} +(-5.15449 + 5.34313i) q^{96} +(1.79542 - 17.0823i) q^{97} +(-1.71520 + 5.27886i) q^{98} +(-10.1482 - 2.89865i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	1.06328	−	0.226007i	0.751852	−	0.159811i	0.183982	−	0.982930i	$-0.441101\pi$
$2$	1.06328	−	0.226007i	0.751852	−	0.159811i	0.567870	+	0.823119i	$0.307768\pi$
$3$	−1.68082	−	0.418155i	−0.970420	−	0.241422i
$3$	−1.68082	−	0.418155i	−0.970420	−	0.241422i
$4$	−0.747608	+	0.332856i	−0.373804	+	0.166428i
$5$	−2.22650	+	0.206637i	−0.995721	+	0.0924109i
$5$	−2.22650	+	0.206637i	−0.995721	+	0.0924109i
$6$	−1.88168	−	0.0647394i	−0.768194	−	0.0264298i
$7$	1.73969	+	3.01324i	0.657542	+	1.13890i	0.981250	+	0.192739i	$0.0617370\pi$
$7$	1.73969	+	3.01324i	0.657542	+	1.13890i	−0.323708	+	0.946157i	$0.604930\pi$
$8$	−2.47854	+	1.80077i	−0.876298	+	0.636668i
$9$	2.65029	+	1.40569i	0.883431	+	0.468562i
$10$	−2.32069	+	0.722917i	−0.733866	+	0.228607i
$11$	−3.44115	+	0.731439i	−1.03755	+	0.220537i	−0.695034	−	0.718976i	$-0.744611\pi$
$11$	−3.44115	+	0.731439i	−1.03755	+	0.220537i	−0.342511	+	0.939514i	$0.611278\pi$
$12$	1.39578	−	0.246855i	0.402926	−	0.0712608i
$13$	−2.12159	−	0.450957i	−0.588422	−	0.125073i	−0.0959273	−	0.995388i	$-0.530582\pi$
$13$	−2.12159	−	0.450957i	−0.588422	−	0.125073i	−0.492495	+	0.870315i	$0.663915\pi$
$14$	2.53079	+	2.81073i	0.676382	+	0.751199i
$15$	3.82875	+	0.583704i	0.988578	+	0.150712i
$16$	−1.13322	+	1.25857i	−0.283305	+	0.314643i
$17$	−1.54674	+	1.12377i	−0.375140	+	0.272555i	−0.759339	−	0.650695i	$-0.774478\pi$
$17$	−1.54674	+	1.12377i	−0.375140	+	0.272555i	0.384199	+	0.923250i	$0.374478\pi$
$18$	3.13570	+	0.895651i	0.739090	+	0.211107i
$19$	−0.970198	+	0.704890i	−0.222579	+	0.161713i	−0.693487	−	0.720469i	$-0.743926\pi$
$19$	−0.970198	+	0.704890i	−0.222579	+	0.161713i	0.470908	+	0.882182i	$0.343926\pi$
$20$	1.59577	−	0.895588i	0.356824	−	0.200260i
$21$	−1.66410	−	5.79216i	−0.363137	−	1.26395i
$22$	−3.49359	+	1.55545i	−0.744837	+	0.331623i
$23$	1.34509	+	1.49387i	0.280470	+	0.311494i	0.866876	−	0.498524i	$-0.166124\pi$
$23$	1.34509	+	1.49387i	0.280470	+	0.311494i	−0.586406	+	0.810017i	$0.699458\pi$
$24$	4.91898	−	1.99035i	1.00408	−	0.406278i
$25$	4.91460	−	0.920154i	0.982920	−	0.184031i
$26$	−2.35776			−0.462394
$27$	−3.86686	−	3.47093i	−0.744178	−	0.667981i
$28$	−2.30358	−	1.67365i	−0.435336	−	0.316290i
$29$	0.374039	−	3.55874i	0.0694573	−	0.660842i	−0.903299	−	0.429012i	$-0.858862\pi$
$29$	0.374039	−	3.55874i	0.0694573	−	0.660842i	0.972756	−	0.231830i	$-0.0744714\pi$
$30$	4.20295	−	0.244683i	0.767349	−	0.0446728i
$31$	−0.663380	−	6.31164i	−0.119147	−	1.13360i	−0.876769	−	0.480911i	$-0.840306\pi$
$31$	−0.663380	−	6.31164i	−0.119147	−	1.13360i	0.757623	−	0.652693i	$-0.226361\pi$
$32$	2.14316	−	3.71207i	0.378862	−	0.656207i
$33$	6.08980	+	0.209520i	1.06010	+	0.0364727i
$34$	−1.39064	+	1.54446i	−0.238493	+	0.264873i
$35$	−4.49607	−	6.34948i	−0.759975	−	1.07326i
$36$	−2.44927	−	0.168734i	−0.408212	−	0.0281224i
$37$	2.46324	+	7.58107i	0.404954	+	1.24632i	0.920934	+	0.389719i	$0.127428\pi$
$37$	2.46324	+	7.58107i	0.404954	+	1.24632i	−0.515980	+	0.856601i	$0.672572\pi$
$38$	−0.872281	+	0.968766i	−0.141503	+	0.157155i
$39$	3.37743	+	1.64513i	0.540821	+	0.263431i
$40$	5.14637	−	4.52157i	0.813713	−	0.714923i
$41$	−2.53573	−	0.538987i	−0.396015	−	0.0841756i	0.00559964	−	0.999984i	$-0.498218\pi$
$41$	−2.53573	−	0.538987i	−0.396015	−	0.0841756i	−0.401615	+	0.915809i	$0.631551\pi$
$42$	−3.07848	−	5.78258i	−0.475019	−	0.892272i
$43$	5.34941	+	9.26545i	0.815778	+	1.41297i	0.908768	+	0.417301i	$0.137024\pi$
$43$	5.34941	+	9.26545i	0.815778	+	1.41297i	−0.0929908	+	0.995667i	$0.529643\pi$
$44$	2.32917	−	1.69224i	0.351135	−	0.255114i
$45$	−6.19134	−	2.58211i	−0.922951	−	0.384918i
$46$	1.76783	+	1.28440i	0.260652	+	0.189375i
$47$	−1.37238	+	13.0573i	−0.200183	+	1.90461i	0.186595	+	0.982437i	$0.440255\pi$
$47$	−1.37238	+	13.0573i	−0.200183	+	1.90461i	−0.386777	+	0.922173i	$0.626412\pi$
$48$	2.43102	−	1.64156i	0.350887	−	0.236939i
$49$	−2.55306	+	4.42203i	−0.364723	+	0.631718i
$50$	5.01763	−	2.08912i	0.709600	−	0.295446i
$51$	3.06970	−	1.24208i	0.429845	−	0.173926i
$52$	1.73622	−	0.369044i	0.240770	−	0.0511773i
$53$	−11.2674	−	8.18624i	−1.54770	−	1.12447i	−0.945269	−	0.326293i	$-0.894200\pi$
$53$	−11.2674	−	8.18624i	−1.54770	−	1.12447i	−0.602427	−	0.798174i	$-0.705800\pi$
$54$	−4.89601	−	2.81663i	−0.666262	−	0.383295i
$55$	7.51058	−	2.33962i	1.01273	−	0.315474i
$56$	−9.73804	−	4.33566i	−1.30130	−	0.579376i
$57$	1.92548	−	0.779098i	0.255036	−	0.103194i
$58$	−0.406593	−	3.86847i	−0.0533883	−	0.507956i
$59$	5.32898	+	1.13271i	0.693774	+	0.147466i	0.541285	−	0.840839i	$-0.317938\pi$
$59$	5.32898	+	1.13271i	0.693774	+	0.147466i	0.152488	+	0.988305i	$0.451271\pi$
$60$	−3.05669	+	0.838041i	−0.394617	+	0.108191i
$61$	−0.516362	+	0.109756i	−0.0661133	+	0.0140528i	−0.240850	−	0.970562i	$-0.577426\pi$
$61$	−0.516362	+	0.109756i	−0.0661133	+	0.0140528i	0.174736	+	0.984615i	$0.444093\pi$
$62$	−2.13183	−	6.56111i	−0.270743	−	0.833262i
$63$	0.375033	+	10.4314i	0.0472497	+	1.31423i
$64$	2.48651	−	7.65270i	0.310814	−	0.956588i
$65$	4.81690	+	0.565658i	0.597462	+	0.0701612i
$66$	6.52251	−	1.15356i	0.802865	−	0.141993i
$67$	1.12533	+	10.7068i	0.137482	+	1.30805i	0.817957	+	0.575279i	$0.195106\pi$
$67$	1.12533	+	10.7068i	0.137482	+	1.30805i	−0.680476	+	0.732771i	$0.738227\pi$
$68$	0.782301	−	1.35499i	0.0948680	−	0.164316i
$69$	−1.63618	−	3.07338i	−0.196972	−	0.369991i
$70$	−6.21561	−	5.73513i	−0.742907	−	0.685479i
$71$	6.38098	+	4.63605i	0.757283	+	0.550198i	0.898076	−	0.439841i	$-0.144965\pi$
$71$	6.38098	+	4.63605i	0.757283	+	0.550198i	−0.140793	+	0.990039i	$0.544965\pi$
$72$	−9.10018	+	1.28851i	−1.07247	+	0.151852i
$73$	−2.75054	+	8.46529i	−0.321926	+	0.990787i	0.650883	+	0.759178i	$0.274399\pi$
$73$	−2.75054	+	8.46529i	−0.321926	+	0.990787i	−0.972809	+	0.231609i	$0.925601\pi$
$74$	4.33248	+	7.50408i	0.503641	+	0.872332i
$75$	−8.64532	−	0.508455i	−0.998275	−	0.0587114i
$76$	0.490700	−	0.849917i	0.0562871	−	0.0974922i
$77$	−8.19054	−	9.09652i	−0.933399	−	1.03664i
$78$	3.96296	+	0.985909i	0.448717	+	0.111632i
$79$	−0.706394	+	6.72089i	−0.0794756	+	0.756160i	0.880115	+	0.474760i	$0.157465\pi$
$79$	−0.706394	+	6.72089i	−0.0794756	+	0.756160i	−0.959591	+	0.281399i	$0.909201\pi$
$80$	2.26305	−	3.03637i	0.253017	−	0.339477i
$81$	5.04810	+	7.45095i	0.560900	+	0.827884i
$82$	−2.81801			−0.311197
$83$	−3.25148	−	1.44765i	−0.356897	−	0.158901i	0.220453	−	0.975398i	$-0.429246\pi$
$83$	−3.25148	−	1.44765i	−0.356897	−	0.158901i	−0.577350	+	0.816497i	$0.695913\pi$
$84$	3.17205	+	3.77635i	0.346099	+	0.412034i
$85$	3.21161	−	2.82170i	0.348348	−	0.306056i
$86$	7.78197	+	8.64276i	0.839152	+	0.931972i
$87$	−2.11680	+	5.82519i	−0.226945	+	0.624526i
$88$	7.21189	−	8.00962i	0.768790	−	0.853828i
$89$	2.71707	−	8.36227i	0.288008	−	0.886399i	−0.697472	−	0.716612i	$-0.745692\pi$
$89$	2.71707	−	8.36227i	0.288008	−	0.886399i	0.985481	−	0.169787i	$-0.0543080\pi$
$90$	−7.16670	−	1.34622i	−0.755436	−	0.141904i
$91$	−2.33207	−	7.17736i	−0.244467	−	0.752392i
$92$	−1.50284	−	0.669108i	−0.156682	−	0.0697593i
$93$	−1.52423	+	10.8861i	−0.158055	+	1.12884i
$94$	1.49183	+	14.1938i	0.153870	+	1.46398i
$95$	2.01449	−	1.76992i	0.206682	−	0.181590i
$96$	−5.15449	+	5.34313i	−0.526078	+	0.545331i
$97$	1.79542	−	17.0823i	0.182298	−	1.73445i	−0.395676	−	0.918390i	$-0.629490\pi$
$97$	1.79542	−	17.0823i	0.182298	−	1.73445i	0.577974	−	0.816055i	$-0.303844\pi$
$98$	−1.71520	+	5.27886i	−0.173262	+	0.533245i
$99$	−10.1482	−	2.89865i	−1.01994	−	0.291325i
$100$	−3.36791	+	2.32377i	−0.336791	+	0.232377i
$101$	4.67773	+	8.10206i	0.465451	+	0.806185i	0.999222	−	0.0394441i	$-0.0125587\pi$
$101$	4.67773	+	8.10206i	0.465451	+	0.806185i	−0.533770	+	0.845629i	$0.679225\pi$
$102$	2.98323	−	2.01445i	0.295384	−	0.199461i
$103$	7.32153	−	3.25976i	0.721412	−	0.321193i	−0.0129830	−	0.999916i	$-0.504133\pi$
$103$	7.32153	−	3.25976i	0.721412	−	0.321193i	0.734395	+	0.678722i	$0.237466\pi$
$104$	6.07051	−	2.70277i	0.595263	−	0.265028i
$105$	4.90200	+	12.5524i	0.478386	+	1.22499i
$106$	−13.8305	−	6.15775i	−1.34334	−	0.598094i
$107$	5.04642			0.487855			0.243928	−	0.969793i	$-0.421564\pi$
$107$	5.04642			0.487855			0.243928	+	0.969793i	$0.421564\pi$
$108$	4.04622	+	1.30779i	0.389347	+	0.125842i
$109$	−1.49707	−	4.60752i	−0.143394	−	0.441320i	0.853407	−	0.521245i	$-0.174532\pi$
$109$	−1.49707	−	4.60752i	−0.143394	−	0.441320i	−0.996801	+	0.0799245i	$0.974532\pi$
$110$	7.45707	−	4.18511i	0.711004	−	0.399035i
$111$	−0.970190	−	13.7724i	−0.0920863	−	1.30722i
$112$	−5.76382	−	1.22514i	−0.544630	−	0.115765i
$113$	−2.15511	−	0.458084i	−0.202736	−	0.0430929i	0.105424	−	0.994427i	$-0.466380\pi$
$113$	−2.15511	−	0.458084i	−0.202736	−	0.0430929i	−0.308160	+	0.951334i	$0.599713\pi$
$114$	1.87124	−	1.26357i	0.175258	−	0.118344i
$115$	−3.30352	−	3.04816i	−0.308055	−	0.284242i
$116$	0.904916	+	2.78505i	0.0840193	+	0.258585i
$117$	−4.98892	−	4.17745i	−0.461226	−	0.386205i
$118$	5.92219			0.545182
$119$	−6.07705	−	2.70568i	−0.557083	−	0.248029i
$120$	−10.5408	+	5.44795i	−0.962242	+	0.497327i
$121$	1.25751	−	0.559881i	0.114319	−	0.0508982i
$122$	−0.524231	+	0.233403i	−0.0474616	+	0.0211313i
$123$	4.03672	+	1.96627i	0.363979	+	0.177292i
$124$	2.59682	+	4.49782i	0.233201	+	0.403916i
$125$	−10.7522	+	3.06426i	−0.961708	+	0.274076i
$126$	2.75634	+	11.0067i	0.245554	+	0.980559i
$127$	−5.91345	+	18.1997i	−0.524734	+	1.61497i	0.240106	+	0.970747i	$0.422818\pi$
$127$	−5.91345	+	18.1997i	−0.524734	+	1.61497i	−0.764841	+	0.644219i	$0.777182\pi$
$128$	0.0182077	−	0.173234i	0.00160934	−	0.0153119i
$129$	−5.11698	−	17.8104i	−0.450525	−	1.56812i
$130$	5.24955	−	0.487200i	0.460416	−	0.0427303i
$131$	0.806639	+	7.67466i	0.0704764	+	0.670538i	0.971544	+	0.236859i	$0.0761181\pi$
$131$	0.806639	+	7.67466i	0.0704764	+	0.670538i	−0.901068	+	0.433679i	$0.857215\pi$
$132$	−4.62252	+	1.87039i	−0.402339	+	0.162797i
$133$	−3.81184	−	1.69714i	−0.330529	−	0.147161i
$134$	3.61637	+	11.1300i	0.312407	+	0.961488i
$135$	9.32679	+	6.92900i	0.802722	+	0.596353i
$136$	1.81001	−	5.57065i	0.155207	−	0.477679i
$137$	4.19713	−	4.66138i	0.358585	−	0.398249i	−0.536678	−	0.843787i	$-0.680321\pi$
$137$	4.19713	−	4.66138i	0.358585	−	0.398249i	0.895263	+	0.445538i	$0.146988\pi$
$138$	−2.43432	−	2.89807i	−0.207223	−	0.246700i
$139$	−13.6446	−	15.1538i	−1.15732	−	1.28533i	−0.951814	−	0.306675i	$-0.900783\pi$
$139$	−13.6446	−	15.1538i	−1.15732	−	1.28533i	−0.205503	−	0.978656i	$-0.565883\pi$
$140$	5.47476	+	3.25038i	0.462702	+	0.274707i
$141$	7.76672	−	21.3731i	0.654076	−	1.79994i
$142$	7.83255	+	3.48727i	0.657293	+	0.292646i
$143$	7.63054			0.638098
$144$	−4.77252	+	1.74263i	−0.397710	+	0.145219i
$145$	−0.0974297	+	8.00083i	−0.00809110	+	0.664433i
$146$	−1.01138	+	9.62261i	−0.0837022	+	0.796373i
$147$	6.14032	−	6.36504i	0.506445	−	0.524980i
$148$	−4.36494	−	4.84776i	−0.358796	−	0.398483i
$149$	−3.52387	+	6.10353i	−0.288687	+	0.500021i	−0.973497	−	0.228701i	$-0.926552\pi$
$149$	−3.52387	+	6.10353i	−0.288687	+	0.500021i	0.684810	+	0.728722i	$0.259885\pi$
$150$	−9.30730	+	1.41327i	−0.759938	+	0.115393i
$151$	0.0155849	+	0.0269939i	0.00126828	+	0.00219673i	0.866659	−	0.498901i	$-0.166263\pi$
$151$	0.0155849	+	0.0269939i	0.00126828	+	0.00219673i	−0.865391	+	0.501098i	$0.832930\pi$
$152$	1.13533	−	3.49420i	0.0920878	−	0.283417i
$153$	−5.67899	+	0.804098i	−0.459119	+	0.0650074i
$154$	−10.7647	−	7.82102i	−0.867445	−	0.630236i
$155$	2.78123	+	13.9158i	0.223394	+	1.11774i
$156$	−3.07258	−	0.105712i	−0.246003	−	0.00846376i
$157$	−0.694083	+	1.20219i	−0.0553938	+	0.0959450i	−0.892393	−	0.451260i	$-0.850975\pi$
$157$	−0.694083	+	1.20219i	−0.0553938	+	0.0959450i	0.836999	+	0.547205i	$0.184308\pi$
$158$	0.767874	+	7.30584i	0.0610888	+	0.581221i
$159$	15.5153	+	18.4711i	1.23044	+	1.46485i
$160$	−4.00470	+	8.70778i	−0.316600	+	0.688410i
$161$	−2.16135	+	6.65194i	−0.170338	+	0.524246i
$162$	7.05151	+	6.78154i	0.554019	+	0.532808i
$163$	0.385069	+	1.18512i	0.0301609	+	0.0928258i	0.965004	−	0.262236i	$-0.0844598\pi$
$163$	0.385069	+	1.18512i	0.0301609	+	0.0928258i	−0.934843	+	0.355062i	$0.884460\pi$
$164$	2.07514	−	0.441084i	0.162041	−	0.0344429i
$165$	−13.6022	+	0.791882i	−1.05893	+	0.0616479i
$166$	−3.78441	−	0.804402i	−0.293727	−	0.0624337i
$167$	−0.0232635	−	0.221338i	−0.00180018	−	0.0171276i	0.993585	−	0.113088i	$-0.0360743\pi$
$167$	−0.0232635	−	0.221338i	−0.00180018	−	0.0171276i	−0.995385	+	0.0959608i	$0.969408\pi$
$168$	14.5549	+	11.3595i	1.12293	+	0.876401i
$169$	−7.57833	−	3.37409i	−0.582948	−	0.259545i
$170$	2.77711	−	3.72610i	0.212995	−	0.285779i
$171$	−3.56216	+	0.504372i	−0.272405	+	0.0385703i
$172$	−7.08332	−	5.14634i	−0.540098	−	0.392404i
$173$	−18.6996	+	3.97473i	−1.42171	+	0.302193i	−0.853672	−	0.520811i	$-0.825630\pi$
$173$	−18.6996	+	3.97473i	−1.42171	+	0.302193i	−0.568036	+	0.823004i	$0.692296\pi$
$174$	−0.934214	+	6.67222i	−0.0708226	+	0.505819i
$175$	11.3225	+	13.2081i	0.855903	+	0.998436i
$176$	2.97902	−	5.15981i	0.224552	−	0.388935i
$177$	−8.48339	−	4.13222i	−0.637650	−	0.310596i
$178$	0.999068	−	9.50550i	0.0748833	−	0.712467i
$179$	15.4208	+	11.2038i	1.15260	+	0.837415i	0.988825	−	0.149082i	$-0.0476320\pi$
$179$	15.4208	+	11.2038i	1.15260	+	0.837415i	0.163778	+	0.986497i	$0.447632\pi$
$180$	5.48816	−	0.130423i	0.409064	−	0.00972116i
$181$	9.13951	−	6.64024i	0.679335	−	0.493565i	−0.193802	−	0.981041i	$-0.562082\pi$
$181$	9.13951	−	6.64024i	0.679335	−	0.493565i	0.873137	+	0.487475i	$0.162082\pi$
$182$	−4.10177	−	7.10448i	−0.304044	−	0.526619i
$183$	0.913805	+	0.0314395i	0.0675504	+	0.00232407i
$184$	−6.02397	−	1.28043i	−0.444093	−	0.0943949i
$185$	−7.05093	−	16.3703i	−0.518395	−	1.20356i
$186$	0.839660	+	11.9195i	0.0615669	+	0.873977i
$187$	4.50060	−	4.99843i	0.329117	−	0.365521i
$188$	−3.32022	−	10.2186i	−0.242152	−	0.745266i
$189$	3.73159	−	17.6901i	0.271433	−	1.28677i
$190$	1.74195	−	2.33720i	0.126374	−	0.169559i
$191$	−1.50713	+	1.67384i	−0.109052	+	0.121114i	−0.795199	−	0.606348i	$-0.792634\pi$
$191$	−1.50713	+	1.67384i	−0.109052	+	0.121114i	0.686147	+	0.727463i	$0.259301\pi$
$192$	−7.37939	+	11.8230i	−0.532562	+	0.853255i
$193$	7.89562	−	13.6756i	0.568339	−	0.984393i	−0.428391	−	0.903593i	$-0.640919\pi$
$193$	7.89562	−	13.6756i	0.568339	−	0.984393i	0.996730	−	0.0807992i	$-0.0257472\pi$
$194$	−1.95168	−	18.5690i	−0.140123	−	1.33318i
$195$	−7.85979	−	2.96498i	−0.562851	−	0.212326i
$196$	0.436786	−	4.15574i	0.0311990	−	0.296839i
$197$	17.3982	+	12.6405i	1.23957	+	0.900601i	0.997570	−	0.0696750i	$-0.0221962\pi$
$197$	17.3982	+	12.6405i	1.23957	+	0.900601i	0.242001	+	0.970276i	$0.422196\pi$
$198$	−11.4455	−	0.788500i	−0.813397	−	0.0560363i
$199$	−17.1687			−1.21706			−0.608530	−	0.793531i	$-0.708240\pi$
$199$	−17.1687			−1.21706			−0.608530	+	0.793531i	$0.708240\pi$
$200$	−10.5241	+	11.1307i	−0.744165	+	0.787060i
$201$	2.58564	−	18.4668i	0.182377	−	1.30255i
$202$	6.80485	+	7.55755i	0.478788	+	0.531748i
$203$	11.3740	−	5.06405i	0.798302	−	0.355427i
$204$	−1.88150	+	1.95036i	−0.131731	+	0.136552i
$205$	5.75719	+	0.676078i	0.402099	+	0.0472193i
$206$	7.04810	−	5.12075i	0.491065	−	0.356779i
$207$	1.46496	+	5.84996i	0.101822	+	0.406600i
$208$	2.97179	−	2.15913i	0.206056	−	0.149709i
$209$	2.82301	−	3.13527i	0.195272	−	0.216871i
$210$	8.04912	+	12.2388i	0.555442	+	0.844557i
$211$	−9.14241	−	10.1537i	−0.629389	−	0.699008i	0.341134	−	0.940015i	$-0.389189\pi$
$211$	−9.14241	−	10.1537i	−0.629389	−	0.699008i	−0.970523	+	0.241007i	$0.922522\pi$
$212$	11.1484	+	2.36967i	0.765677	+	0.162750i
$213$	−8.78667	−	10.4606i	−0.602053	−	0.716749i
$214$	5.36575	−	1.14053i	0.366795	−	0.0779647i
$215$	−13.8250	−	19.5241i	−0.942860	−	1.33154i
$216$	15.8345	+	1.63954i	1.07740	+	0.111557i
$217$	17.8644	−	12.9792i	1.21271	−	0.881088i
$218$	−2.63314	−	4.56073i	−0.178339	−	0.308892i
$219$	8.16296	−	13.0785i	0.551602	−	0.883760i
$220$	−4.83621	+	4.24906i	−0.326057	+	0.286472i
$221$	3.78832	−	1.68667i	0.254830	−	0.113458i
$222$	−4.14424	−	14.4246i	−0.278143	−	0.968119i
$223$	−21.4185	+	4.55265i	−1.43429	+	0.304868i	−0.858536	−	0.512754i	$-0.828625\pi$
$223$	−21.4185	+	4.55265i	−1.43429	+	0.304868i	−0.575756	+	0.817622i	$0.695292\pi$
$224$	14.9138			0.996469
$225$	14.3186	+	4.46970i	0.954572	+	0.297980i
$226$	−2.39502			−0.159314
$227$	25.3190	−	5.38172i	1.68048	−	0.357197i	0.733799	−	0.679366i	$-0.237745\pi$
$227$	25.3190	−	5.38172i	1.68048	−	0.357197i	0.946682	+	0.322169i	$0.104412\pi$
$228$	−1.18017	+	1.22337i	−0.0781589	+	0.0810194i
$229$	20.9924	−	9.34642i	1.38722	−	0.617629i	0.428904	−	0.903350i	$-0.358900\pi$
$229$	20.9924	−	9.34642i	1.38722	−	0.617629i	0.958313	+	0.285721i	$0.0922331\pi$
$230$	−4.20147	−	2.49442i	−0.277037	−	0.164477i
$231$	9.96304	+	18.7145i	0.655520	+	1.23132i
$232$	5.48140	+	9.49406i	0.359872	+	0.623316i
$233$	−7.19284	+	5.22590i	−0.471219	+	0.342360i	−0.797916	−	0.602769i	$-0.794064\pi$
$233$	−7.19284	+	5.22590i	−0.471219	+	0.342360i	0.326697	+	0.945129i	$0.394064\pi$
$234$	−6.24875	−	3.31426i	−0.408493	−	0.216660i
$235$	0.357478	−	29.3558i	0.0233193	−	1.91496i
$236$	−4.36101	+	0.926962i	−0.283878	+	0.0603401i
$237$	3.99770	−	11.0012i	0.259678	−	0.714605i
$238$	−7.07311	−	1.50344i	−0.458481	−	0.0974532i
$239$	−3.46656	−	3.85001i	−0.224233	−	0.249036i	0.620522	−	0.784189i	$-0.286921\pi$
$239$	−3.46656	−	3.85001i	−0.224233	−	0.249036i	−0.844755	+	0.535153i	$0.820254\pi$
$240$	−5.07345	+	4.15728i	−0.327490	+	0.268351i
$241$	−4.38633	+	4.87152i	−0.282549	+	0.313802i	−0.867667	−	0.497146i	$-0.834381\pi$
$241$	−4.38633	+	4.87152i	−0.282549	+	0.313802i	0.585118	+	0.810948i	$0.301048\pi$
$242$	1.21055	−	0.879516i	0.0778171	−	0.0565374i
$243$	−5.36928	−	14.6346i	−0.344439	−	0.938809i
$244$	0.349503	−	0.253929i	0.0223746	−	0.0162561i
$245$	4.77063	−	10.3732i	0.304784	−	0.662719i
$246$	4.73656	+	1.17836i	0.301992	+	0.0751298i
$247$	2.37623	−	1.05797i	0.151196	−	0.0673168i
$248$	13.0100	+	14.4491i	0.826137	+	0.917518i
$249$	4.85980	+	3.79287i	0.307978	+	0.240363i
$250$	−10.7401	+	5.68824i	−0.679262	+	0.359756i
$251$	−7.14839			−0.451202			−0.225601	−	0.974220i	$-0.572435\pi$
$251$	−7.14839			−0.451202			−0.225601	+	0.974220i	$0.572435\pi$
$252$	−3.75254	−	7.67377i	−0.236388	−	0.483402i
$253$	−5.72132	−	4.15678i	−0.359696	−	0.261335i
$254$	−2.17438	+	20.6879i	−0.136433	+	1.29807i
$255$	−6.57804	+	3.39981i	−0.411933	+	0.212904i
$256$	1.66239	+	15.8166i	0.103899	+	0.988537i
$257$	2.06283	−	3.57292i	0.128676	−	0.222873i	−0.794488	−	0.607280i	$-0.792261\pi$
$257$	2.06283	−	3.57292i	0.128676	−	0.222873i	0.923164	+	0.384407i	$0.125594\pi$
$258$	−9.46606	−	17.7810i	−0.589331	−	1.10699i
$259$	−18.5583	+	20.6110i	−1.15315	+	1.28071i
$260$	−3.78943	+	1.18044i	−0.235010	+	0.0732080i
$261$	5.99379	−	8.90593i	0.371006	−	0.551263i
$262$	2.59221	+	7.97800i	0.160147	+	0.492883i
$263$	11.8078	−	13.1139i	0.728102	−	0.808639i	−0.259479	−	0.965749i	$-0.583551\pi$
$263$	11.8078	−	13.1139i	0.728102	−	0.808639i	0.987581	+	0.157109i	$0.0502175\pi$
$264$	−15.4711	+	10.4470i	−0.952183	+	0.642969i
$265$	26.7784	+	15.8984i	1.64499	+	0.976631i
$266$	−4.43662	−	0.943033i	−0.272027	−	0.0578210i
$267$	−8.06362	+	12.9193i	−0.493485	+	0.790648i
$268$	−4.40515	−	7.62994i	−0.269087	−	0.466073i
$269$	−21.6298	+	15.7150i	−1.31879	+	0.958158i	−0.318845	+	0.947807i	$0.603295\pi$
$269$	−21.6298	+	15.7150i	−1.31879	+	0.958158i	−0.999946	+	0.0103508i	$0.996705\pi$
$270$	11.4830	+	5.25954i	0.698832	+	0.320085i
$271$	17.6749	+	12.8416i	1.07367	+	0.780069i	0.976569	−	0.215205i	$-0.0690419\pi$
$271$	17.6749	+	12.8416i	1.07367	+	0.780069i	0.0971044	+	0.995274i	$0.469042\pi$
$272$	0.338454	−	3.22017i	0.0205218	−	0.195251i
$273$	0.918525	+	13.0390i	0.0555917	+	0.789156i
$274$	3.40921	−	5.90493i	0.205958	−	0.356730i
$275$	−16.2388	+	6.76112i	−0.979239	+	0.407711i
$276$	2.24621	+	1.75307i	0.135206	+	0.105522i
$277$	13.9125	−	2.95719i	0.835919	−	0.177680i	0.229984	−	0.973194i	$-0.426133\pi$
$277$	13.9125	−	2.95719i	0.835919	−	0.177680i	0.605935	+	0.795514i	$0.292799\pi$
$278$	−17.9329	−	13.0290i	−1.07554	−	0.781427i
$279$	7.11403	−	17.6602i	0.425906	−	1.05729i
$280$	22.5777	+	7.64110i	1.34927	+	0.456643i
$281$	−6.56257	−	2.92184i	−0.391490	−	0.174303i	0.201545	−	0.979479i	$-0.435404\pi$
$281$	−6.56257	−	2.92184i	−0.391490	−	0.174303i	−0.593035	+	0.805177i	$0.702070\pi$
$282$	3.42772	−	24.4810i	0.204117	−	1.45782i
$283$	−1.41160	−	13.4305i	−0.0839108	−	0.798357i	−0.952851	−	0.303440i	$-0.901865\pi$
$283$	−1.41160	−	13.4305i	−0.0839108	−	0.798357i	0.868940	−	0.494918i	$-0.164802\pi$
$284$	−6.31361	−	1.34200i	−0.374644	−	0.0796330i
$285$	−4.12609	+	2.13254i	−0.244408	+	0.126321i
$286$	8.11340	−	1.72456i	0.479755	−	0.101975i
$287$	−2.78730	−	8.57843i	−0.164529	−	0.506369i
$288$	10.8980	−	6.82546i	0.642172	−	0.402194i
$289$	−4.12374	+	12.6916i	−0.242573	+	0.746564i
$290$	1.70465	+	8.52914i	0.100100	+	0.500848i
$291$	−10.1608	+	27.9615i	−0.595639	+	1.63913i
$292$	−0.761401	−	7.24425i	−0.0445576	−	0.423938i
$293$	−0.157560	+	0.272902i	−0.00920475	+	0.0159431i	−0.870591	−	0.492007i	$-0.836263\pi$
$293$	−0.157560	+	0.272902i	−0.00920475	+	0.0159431i	0.861386	+	0.507950i	$0.169597\pi$
$294$	5.09033	−	8.15557i	0.296874	−	0.475643i
$295$	−12.0990	−	1.42081i	−0.704432	−	0.0827229i
$296$	−19.7570	−	14.3543i	−1.14835	−	0.834327i
$297$	15.8452	+	9.11563i	0.919433	+	0.528942i
$298$	−2.36742	+	7.28617i	−0.137141	+	0.422077i
$299$	−2.18005	−	3.77595i	−0.126075	−	0.218369i
$300$	6.63255	−	2.49752i	0.382930	−	0.144195i
$301$	−18.6127	+	32.2381i	−1.07282	+	1.85817i
$302$	0.0226720	+	0.0251798i	0.00130462	+	0.00144893i
$303$	−4.47448	−	15.5741i	−0.257052	−	0.894709i
$304$	0.212296	−	2.01986i	0.0121760	−	0.115847i
$305$	1.12700	−	0.351071i	0.0645318	−	0.0201023i
$306$	−5.85662	+	2.13847i	−0.334801	+	0.122248i
$307$	−8.35636			−0.476923			−0.238461	−	0.971152i	$-0.576643\pi$
$307$	−8.35636			−0.476923			−0.238461	+	0.971152i	$0.576643\pi$
$308$	9.15114	+	4.07435i	0.521435	+	0.232158i
$309$	−13.6692	+	2.41752i	−0.777616	+	0.137528i
$310$	6.10229	+	14.1678i	0.346587	+	0.804676i
$311$	13.6693	+	15.1813i	0.775113	+	0.860851i	0.993361	−	0.115043i	$-0.0367005\pi$
$311$	13.6693	+	15.1813i	0.775113	+	0.860851i	−0.218247	+	0.975894i	$0.570034\pi$
$312$	−11.3336	+	2.00444i	−0.641639	+	0.113479i
$313$	10.5424	−	11.7085i	0.595890	−	0.661803i	−0.367464	−	0.930038i	$-0.619774\pi$
$313$	10.5424	−	11.7085i	0.595890	−	0.661803i	0.963353	+	0.268235i	$0.0864404\pi$
$314$	−0.466301	+	1.43513i	−0.0263149	+	0.0809889i
$315$	−2.99053	−	23.1480i	−0.168497	−	1.30424i
$316$	−1.70899	−	5.25972i	−0.0961380	−	0.295882i
$317$	11.6877	+	5.20368i	0.656444	+	0.292268i	0.707800	−	0.706413i	$-0.249688\pi$
$317$	11.6877	+	5.20368i	0.656444	+	0.292268i	−0.0513561	+	0.998680i	$0.516354\pi$
$318$	20.6717	+	16.1334i	1.15921	+	0.904714i
$319$	1.31588	+	12.5198i	0.0736751	+	0.700972i
$320$	−3.95489	+	17.5525i	−0.221085	+	0.981217i
$321$	−8.48210	−	2.11019i	−0.473425	−	0.117779i
$322$	−0.794730	+	7.56135i	−0.0442885	+	0.421377i
$323$	0.708509	−	2.18057i	0.0394225	−	0.121330i
$324$	−6.25409	−	3.89010i	−0.347450	−	0.216116i
$325$	−10.8417	−	0.264088i	−0.601389	−	0.0146489i
$326$	0.677282	+	1.17309i	0.0375112	+	0.0649712i
$327$	0.589649	+	8.37040i	0.0326076	+	0.462884i
$328$	7.25552	−	3.23037i	0.400619	−	0.178367i
$329$	−41.7324	+	18.5805i	−2.30078	+	1.02437i
$330$	−14.2840	+	3.91619i	−0.786308	+	0.215579i
$331$	22.9601	+	10.2225i	1.26200	+	0.561879i	0.925122	−	0.379669i	$-0.123962\pi$
$331$	22.9601	+	10.2225i	1.26200	+	0.561879i	0.336879	+	0.941548i	$0.390629\pi$
$332$	2.91269			0.159855
$333$	−4.12829	+	23.5546i	−0.226229	+	1.29078i
$334$	−0.0747594	−	0.230086i	−0.00409065	−	0.0125897i
$335$	−4.71799	−	23.6063i	−0.257771	−	1.28975i
$336$	9.17564	+	4.46941i	0.500572	+	0.243826i
$337$	−18.4734	−	3.92664i	−1.00631	−	0.213898i	−0.324859	−	0.945762i	$-0.605317\pi$
$337$	−18.4734	−	3.92664i	−1.00631	−	0.213898i	−0.681450	+	0.731865i	$0.738650\pi$
$338$	−8.82044	−	1.87484i	−0.479769	−	0.101978i
$339$	3.43080	+	1.67113i	0.186336	+	0.0907632i
$340$	−1.46180	+	3.17853i	−0.0792774	+	0.172380i
$341$	6.89937	+	21.2341i	0.373622	+	1.14989i
$342$	−3.67358	+	1.34136i	−0.198644	+	0.0725325i
$343$	6.58955			0.355802
$344$	−29.9437	−	13.3318i	−1.61446	−	0.718802i
$345$	4.27802	+	6.50478i	0.230321	+	0.350206i
$346$	−18.9846	+	8.45250i	−1.02062	+	0.454409i
$347$	−25.7819	+	11.4789i	−1.38405	+	0.616217i	−0.957549	−	0.288271i	$-0.906920\pi$
$347$	−25.7819	+	11.4789i	−1.38405	+	0.616217i	−0.426498	+	0.904488i	$0.640253\pi$
$348$	−0.356417	−	5.05955i	−0.0191060	−	0.271220i
$349$	10.1548	+	17.5887i	0.543575	+	0.941500i	0.998695	+	0.0510695i	$0.0162630\pi$
$349$	10.1548	+	17.5887i	0.543575	+	0.941500i	−0.455120	+	0.890430i	$0.650404\pi$
$350$	15.0241	+	11.4849i	0.803074	+	0.613893i
$351$	6.63864	+	9.10767i	0.354344	+	0.486132i
$352$	−4.65980	+	14.3414i	−0.248368	+	0.764398i
$353$	−0.942606	+	8.96830i	−0.0501699	+	0.477334i	0.940374	+	0.340141i	$0.110475\pi$
$353$	−0.942606	+	8.96830i	−0.0501699	+	0.477334i	−0.990544	+	0.137193i	$0.956192\pi$
$354$	−9.95412	−	2.47639i	−0.529055	−	0.131619i
$355$	−15.1652	−	9.00363i	−0.804887	−	0.477863i
$356$	0.752135	+	7.15609i	0.0398631	+	0.379272i
$357$	9.08302	+	7.08890i	0.480725	+	0.375185i
$358$	18.9287	+	8.42761i	1.00041	+	0.445413i
$359$	2.84427	+	8.75376i	0.150115	+	0.462006i	0.997633	−	0.0687601i	$-0.0219043\pi$
$359$	2.84427	+	8.75376i	0.150115	+	0.462006i	−0.847518	+	0.530766i	$0.821904\pi$
$360$	19.9953	−	4.74930i	1.05384	−	0.250310i
$361$	−5.42691	+	16.7023i	−0.285627	+	0.879069i
$362$	8.21711	−	9.12603i	0.431882	−	0.479653i
$363$	−2.34777	+	0.415221i	−0.123226	+	0.0217935i
$364$	4.13250	+	4.58961i	0.216602	+	0.240561i
$365$	4.37483	−	19.4163i	0.228989	−	1.01630i
$366$	0.978735	−	0.173097i	0.0511593	−	0.00904794i
$367$	−17.3961	−	7.74523i	−0.908067	−	0.404298i	−0.101088	−	0.994877i	$-0.532232\pi$
$367$	−17.3961	−	7.74523i	−0.908067	−	0.404298i	−0.806979	+	0.590580i	$0.798899\pi$
$368$	−3.40442			−0.177468
$369$	−5.96279	−	4.99292i	−0.310410	−	0.259921i
$370$	−11.1969	−	15.8126i	−0.582099	−	0.822057i
$371$	5.06527	−	48.1929i	0.262976	−	2.50205i
$372$	−2.48399	−	8.64589i	−0.128789	−	0.448268i
$373$	2.86875	+	3.18607i	0.148538	+	0.164968i	0.812822	−	0.582512i	$-0.197930\pi$
$373$	2.86875	+	3.18607i	0.148538	+	0.164968i	−0.664284	+	0.747480i	$0.731263\pi$
$374$	3.65572	−	6.33189i	0.189033	−	0.327414i
$375$	19.3539	−	0.654366i	0.999429	−	0.0337913i
$376$	−20.1117	−	34.8346i	−1.03718	−	1.79646i
$377$	−2.39840	+	7.38151i	−0.123524	+	0.380167i
$378$	−0.0303698	−	19.6529i	−0.00156206	−	1.01084i
$379$	−7.81297	−	5.67645i	−0.401325	−	0.291580i	0.368755	−	0.929526i	$-0.379784\pi$
$379$	−7.81297	−	5.67645i	−0.401325	−	0.291580i	−0.770081	+	0.637947i	$0.779784\pi$
$380$	−0.916919	+	1.99374i	−0.0470370	+	0.102277i
$381$	17.5498	−	28.1177i	0.899101	−	1.44051i
$382$	−1.22420	+	2.12038i	−0.0626355	+	0.108488i
$383$	−0.976200	−	9.28793i	−0.0498815	−	0.474591i	−0.990738	−	0.135786i	$-0.956644\pi$
$383$	−0.976200	−	9.28793i	−0.0498815	−	0.474591i	0.940857	−	0.338805i	$-0.110023\pi$
$384$	−0.103043	+	0.283561i	−0.00525837	+	0.0144704i
$385$	20.1159	+	18.5609i	1.02520	+	0.945952i
$386$	5.30447	−	16.3255i	0.269990	−	0.830944i
$387$	1.15320	+	32.0757i	0.0586202	+	1.63050i
$388$	4.34368	+	13.3685i	0.220517	+	0.678682i
$389$	25.4190	−	5.40297i	1.28879	−	0.273942i	0.487980	−	0.872855i	$-0.337734\pi$
$389$	25.4190	−	5.40297i	1.28879	−	0.273942i	0.800814	+	0.598913i	$0.204400\pi$
$390$	−9.02725	−	1.37623i	−0.457113	−	0.0696882i
$391$	−3.75928	−	0.799059i	−0.190115	−	0.0404102i
$392$	−1.63518	−	15.5577i	−0.0825888	−	0.785780i
$393$	1.85339	−	13.2370i	0.0934910	−	0.667718i
$394$	21.3560	+	9.50830i	1.07590	+	0.479021i
$395$	0.184002	−	15.1100i	0.00925812	−	0.760268i
$396$	8.55172	−	1.21085i	0.429740	−	0.0608476i
$397$	10.9374	+	7.94651i	0.548934	+	0.398824i	0.827392	−	0.561624i	$-0.189823\pi$
$397$	10.9374	+	7.94651i	0.548934	+	0.398824i	−0.278458	+	0.960448i	$0.589823\pi$
$398$	−18.2552	+	3.88025i	−0.915048	+	0.194500i
$399$	5.69734	+	4.44653i	0.285224	+	0.222605i
$400$	−4.41125	+	7.22811i	−0.220563	+	0.361406i
$401$	3.70665	−	6.42010i	0.185101	−	0.320604i	−0.758509	−	0.651662i	$-0.774072\pi$
$401$	3.70665	−	6.42010i	0.185101	−	0.320604i	0.943611	+	0.331057i	$0.107405\pi$
$402$	−1.42437	−	20.2198i	−0.0710411	−	1.00847i
$403$	−1.43886	+	13.6898i	−0.0716748	+	0.681940i
$404$	−6.19393	−	4.50015i	−0.308159	−	0.223891i
$405$	−12.7792	−	15.5464i	−0.635005	−	0.772508i
$406$	10.9493	−	7.95511i	0.543403	−	0.394806i
$407$	−14.0215	−	24.2859i	−0.695018	−	1.20381i
$408$	−5.37170	+	8.60638i	−0.265939	+	0.426079i
$409$	−10.4862	−	2.22891i	−0.518509	−	0.110212i	−0.0587786	−	0.998271i	$-0.518721\pi$
$409$	−10.4862	−	2.22891i	−0.518509	−	0.110212i	−0.459730	+	0.888059i	$0.652054\pi$
$410$	6.27429	−	0.582305i	0.309865	−	0.0287580i
$411$	−9.00379	+	6.07988i	−0.444124	+	0.299898i
$412$	−4.38860	+	4.87404i	−0.216211	+	0.240126i
$413$	5.85766	+	18.0280i	0.288237	+	0.887101i
$414$	2.87980	+	5.88905i	0.141534	+	0.289431i
$415$	7.53857	+	2.55132i	0.370054	+	0.125240i
$416$	−6.22089	+	6.90900i	−0.305004	+	0.338742i
$417$	16.5974	+	31.1764i	0.812777	+	1.52671i
$418$	2.29306	−	3.97169i	0.112157	−	0.194262i
$419$	1.24999	+	11.8928i	0.0610659	+	0.581003i	0.981681	+	0.190532i	$0.0610213\pi$
$419$	1.24999	+	11.8928i	0.0610659	+	0.581003i	−0.920615	+	0.390471i	$0.872312\pi$
$420$	−7.84291	−	7.75259i	−0.382695	−	0.378288i
$421$	0.924308	−	8.79420i	0.0450480	−	0.428603i	−0.948634	−	0.316374i	$-0.897534\pi$
$421$	0.924308	−	8.79420i	0.0450480	−	0.428603i	0.993682	−	0.112229i	$-0.0357989\pi$
$422$	−12.0157	−	8.72994i	−0.584917	−	0.424967i
$423$	−21.9917	+	32.6767i	−1.06927	+	1.58879i
$424$	42.6683			2.07215
$425$	−6.56758	+	6.94615i	−0.318574	+	0.336938i
$426$	−11.7069	−	9.13669i	−0.567199	−	0.442674i
$427$	−1.22903	−	1.36498i	−0.0594770	−	0.0660559i
$428$	−3.77274	+	1.67973i	−0.182362	+	0.0811929i
$429$	−12.8255	−	3.19075i	−0.619223	−	0.154051i
$430$	−19.1125	−	17.6351i	−0.921685	−	0.850438i
$431$	−2.85794	+	2.07642i	−0.137662	+	0.100017i	−0.654485	−	0.756075i	$-0.727115\pi$
$431$	−2.85794	+	2.07642i	−0.137662	+	0.100017i	0.516823	+	0.856092i	$0.327115\pi$
$432$	8.75042	−	0.933380i	0.421005	−	0.0449073i
$433$	−2.00164	+	1.45427i	−0.0961924	+	0.0698879i	−0.634842	−	0.772642i	$-0.718935\pi$
$433$	−2.00164	+	1.45427i	−0.0961924	+	0.0698879i	0.538649	+	0.842530i	$0.318935\pi$
$434$	16.0614	−	17.8380i	0.770973	−	0.856253i
$435$	3.50935	−	13.4072i	0.168261	−	0.642826i
$436$	2.65286	+	2.94630i	0.127049	+	0.141102i
$437$	−2.35801	−	0.501211i	−0.112799	−	0.0239762i
$438$	5.72368	−	15.7509i	0.273488	−	0.752609i
$439$	8.13001	−	1.72809i	0.388024	−	0.0824771i	−0.00976881	−	0.999952i	$-0.503110\pi$
$439$	8.13001	−	1.72809i	0.388024	−	0.0824771i	0.397793	+	0.917475i	$0.369776\pi$
$440$	−14.4022	+	19.3237i	−0.686598	+	0.921219i
$441$	−12.9823	+	8.13087i	−0.618206	+	0.387184i
$442$	3.64685	−	2.64959i	0.173463	−	0.126028i
$443$	11.6123	+	20.1132i	0.551719	+	0.955606i	0.998151	+	0.0607879i	$0.0193613\pi$
$443$	11.6123	+	20.1132i	0.551719	+	0.955606i	−0.446432	+	0.894818i	$0.647305\pi$
$444$	5.30955	+	9.97342i	0.251980	+	0.473318i
$445$	−4.32159	+	19.1800i	−0.204863	+	0.909221i
$446$	−21.7450	+	9.68148i	−1.02965	+	0.458431i
$447$	8.47521	−	8.78539i	0.400864	−	0.415535i
$448$	27.3852	−	5.82090i	1.29383	−	0.275012i
$449$	18.8212			0.888227			0.444114	−	0.895970i	$-0.353519\pi$
$449$	18.8212			0.888227			0.444114	+	0.895970i	$0.353519\pi$
$450$	16.2348	+	1.51645i	0.765317	+	0.0714859i
$451$	9.12008			0.429448
$452$	1.76366	−	0.374877i	0.0829554	−	0.0176327i
$453$	−0.0149078	−	0.0518888i	−0.000700429	−	0.00243795i
$454$	25.7049	−	11.4445i	1.20639	−	0.537119i
$455$	6.67546	+	15.4985i	0.312950	+	0.726581i
$456$	−3.36941	+	5.39837i	−0.157787	+	0.252802i
$457$	−1.31514	−	2.27788i	−0.0615194	−	0.106555i	0.833625	−	0.552330i	$-0.186261\pi$
$457$	−1.31514	−	2.27788i	−0.0615194	−	0.106555i	−0.895145	+	0.445776i	$0.852928\pi$
$458$	20.2084	−	14.6823i	0.944278	−	0.686058i
$459$	9.88159	+	1.02316i	0.461233	+	0.0477570i
$460$	3.48434	+	1.17923i	0.162458	+	0.0549817i
$461$	19.0870	−	4.05707i	0.888970	−	0.188956i	0.259279	−	0.965802i	$-0.416515\pi$
$461$	19.0870	−	4.05707i	0.888970	−	0.188956i	0.629691	+	0.776846i	$0.283182\pi$
$462$	14.8231	+	17.6470i	0.689633	+	0.821014i
$463$	−1.50059	−	0.318960i	−0.0697382	−	0.0148233i	0.172910	−	0.984938i	$-0.444683\pi$
$463$	−1.50059	−	0.318960i	−0.0697382	−	0.0148233i	−0.242649	+	0.970114i	$0.578016\pi$
$464$	4.05506	+	4.50360i	0.188251	+	0.209074i
$465$	1.14421	−	24.5529i	0.0530617	−	1.13861i
$466$	−6.46691	+	7.18223i	−0.299574	+	0.332710i
$467$	−5.25538	+	3.81826i	−0.243190	+	0.176688i	−0.702703	−	0.711483i	$-0.748024\pi$
$467$	−5.25538	+	3.81826i	−0.243190	+	0.176688i	0.459513	+	0.888171i	$0.348024\pi$
$468$	5.12024	+	1.46250i	0.236683	+	0.0676041i
$469$	−30.3045	+	22.0175i	−1.39933	+	1.01667i
$470$	−6.25451	−	31.2942i	−0.288499	−	1.44349i
$471$	1.66933	−	1.73042i	0.0769185	−	0.0797336i
$472$	−15.2479	+	6.78878i	−0.701839	+	0.312479i
$473$	−25.1852	−	27.9710i	−1.15802	−	1.28611i
$474$	1.76432	−	12.6009i	0.0810378	−	0.578777i
$475$	−4.11953	+	4.35698i	−0.189017	+	0.199912i
$476$	5.44385			0.249519
$477$	−18.3546	−	37.5343i	−0.840400	−	1.71858i
$478$	−4.55605	−	3.31017i	−0.208389	−	0.151403i
$479$	−0.572460	+	5.44660i	−0.0261564	+	0.248861i	0.973629	+	0.228138i	$0.0732637\pi$
$479$	−0.572460	+	5.44660i	−0.0261564	+	0.248861i	−0.999785	+	0.0207236i	$0.993403\pi$
$480$	10.3724	−	12.9616i	0.473432	−	0.591613i
$481$	−1.80724	−	17.1947i	−0.0824029	−	0.784011i
$482$	−3.56290	+	6.17113i	−0.162286	+	0.281087i
$483$	6.41437	−	10.2769i	0.291864	−	0.467616i
$484$	−0.753766	+	0.837142i	−0.0342621	+	0.0380519i
$485$	−0.467672	+	38.4047i	−0.0212359	+	1.74387i
$486$	−9.01656	−	14.3471i	−0.408999	−	0.650800i
$487$	−10.8960	−	33.5344i	−0.493744	−	1.51959i	−0.818905	−	0.573929i	$-0.805419\pi$
$487$	−10.8960	−	33.5344i	−0.493744	−	1.51959i	0.325162	−	0.945658i	$-0.394581\pi$
$488$	1.08218	−	1.20188i	0.0489880	−	0.0544067i
$489$	−0.151666	−	2.15299i	−0.00685858	−	0.0973616i
$490$	2.72810	−	12.1078i	0.123243	−	0.546975i
$491$	−2.79851	−	0.594842i	−0.126295	−	0.0268448i	0.144330	−	0.989530i	$-0.453897\pi$
$491$	−2.79851	−	0.594842i	−0.126295	−	0.0268448i	−0.270625	+	0.962685i	$0.587231\pi$
$492$	−3.67237	−	0.126348i	−0.165563	−	0.00569621i
$493$	3.42068	+	5.92480i	0.154060	+	0.266839i
$494$	2.28749	−	1.66196i	0.102919	−	0.0747751i
$495$	23.1940	+	4.35684i	1.04249	+	0.195825i
$496$	8.69540	+	6.31758i	0.390435	+	0.283668i
$497$	−2.86858	+	27.2927i	−0.128673	+	1.22425i
$498$	6.02454	+	2.93453i	0.269966	+	0.131499i
$499$	18.3438	−	31.7725i	0.821183	−	1.42233i	−0.0836188	−	0.996498i	$-0.526648\pi$
$499$	18.3438	−	31.7725i	0.821183	−	1.42233i	0.904802	−	0.425833i	$-0.140019\pi$
$500$	7.01848	−	5.86981i	0.313876	−	0.262506i
$501$	−0.0534517	+	0.381756i	−0.00238805	+	0.0170556i
$502$	−7.60073	+	1.61558i	−0.339237	+	0.0721071i
$503$	14.2611	+	10.3613i	0.635873	+	0.461989i	0.858430	−	0.512931i	$-0.171440\pi$
$503$	14.2611	+	10.3613i	0.635873	+	0.461989i	−0.222557	+	0.974920i	$0.571440\pi$
$504$	−19.7141	−	25.1794i	−0.878136	−	1.12158i
$505$	−12.0891	−	17.0726i	−0.537960	−	0.759723i
$506$	−7.02282	−	3.12676i	−0.312203	−	0.139002i
$507$	11.3269	+	8.84014i	0.503045	+	0.392604i
$508$	−1.63696	−	15.5746i	−0.0726282	−	0.691011i
$509$	14.7522	+	3.13568i	0.653881	+	0.138987i	0.522894	−	0.852398i	$-0.324852\pi$
$509$	14.7522	+	3.13568i	0.653881	+	0.138987i	0.130986	+	0.991384i	$0.458186\pi$
$510$	−6.22591	+	5.10163i	−0.275688	+	0.225904i
$511$	−30.2930	+	6.43898i	−1.34008	+	0.284844i
$512$	5.44990	+	16.7731i	0.240854	+	0.741272i
$513$	6.19825	+	0.641779i	0.273659	+	0.0283353i
$514$	1.38585	−	4.26522i	0.0611274	−	0.188131i
$515$	−15.6278	+	8.77074i	−0.688643	+	0.386485i
$516$	9.75380	+	11.6120i	0.429387	+	0.511189i
$517$	−4.82808	−	45.9361i	−0.212339	−	2.02027i
$518$	−15.0744	+	26.1096i	−0.662330	+	1.14719i
$519$	33.0927	+	1.13856i	1.45261	+	0.0499771i
$520$	−12.9575	+	7.27210i	−0.568224	+	0.318903i
$521$	29.3467	+	21.3216i	1.28570	+	0.934118i	0.999709	−	0.0241133i	$-0.00767623\pi$
$521$	29.3467	+	21.3216i	1.28570	+	0.934118i	0.285994	+	0.958231i	$0.407676\pi$
$522$	4.36027	−	10.8241i	0.190844	−	0.473759i
$523$	−2.83321	+	8.71972i	−0.123888	+	0.381287i	−0.993697	−	0.112102i	$-0.964242\pi$
$523$	−2.83321	+	8.71972i	−0.123888	+	0.381287i	0.869809	+	0.493388i	$0.164242\pi$
$524$	−3.15761	−	5.46914i	−0.137941	−	0.238920i
$525$	−13.5081	−	26.9349i	−0.589541	−	1.17554i
$526$	9.59118	−	16.6124i	0.418195	−	0.724336i
$527$	8.11894	+	9.01700i	0.353667	+	0.392787i
$528$	−7.16479	+	7.42701i	−0.311807	+	0.323219i
$529$	1.98176	−	18.8552i	0.0861637	−	0.819793i
$530$	32.0661	+	10.8523i	1.39286	+	0.471395i
$531$	12.5311	+	10.4929i	0.543804	+	0.455352i
$532$	3.41467			0.148045
$533$	5.13672	+	2.28701i	0.222496	+	0.0990616i
$534$	−5.65403	+	15.5592i	−0.244674	+	0.673314i
$535$	−11.2358	+	1.04278i	−0.485768	+	0.0450832i
$536$	−22.0697	−	24.5109i	−0.953268	−	1.05871i
$537$	−21.2345	−	25.2799i	−0.916338	−	1.09091i
$538$	−19.4468	+	21.5979i	−0.838411	+	0.931150i
$539$	5.55101	−	17.0843i	0.239099	−	0.735871i
$540$	−9.27914	−	2.07569i	−0.399311	−	0.0893234i
$541$	−4.66886	−	14.3693i	−0.200730	−	0.617784i	−0.999862	−	0.0166277i	$-0.994707\pi$
$541$	−4.66886	−	14.3693i	−0.200730	−	0.617784i	0.799132	−	0.601156i	$-0.205293\pi$
$542$	21.6956	+	9.65952i	0.931907	+	0.414912i
$543$	−18.1385	+	7.33930i	−0.778398	+	0.314960i
$544$	0.856605	+	8.15005i	0.0367266	+	0.349431i
$545$	4.28532	+	9.94929i	0.183563	+	0.426181i
$546$	3.92355	+	13.6565i	0.167913	+	0.584445i
$547$	4.04017	−	38.4396i	0.172745	−	1.64356i	−0.473763	−	0.880652i	$-0.657105\pi$
$547$	4.04017	−	38.4396i	0.172745	−	1.64356i	0.646508	−	0.762907i	$-0.276229\pi$
$548$	−1.58623	+	4.88193i	−0.0677606	+	0.208546i
$549$	−1.52279	−	0.434956i	−0.0649912	−	0.0185635i
$550$	−15.7384	+	10.8591i	−0.671086	+	0.463032i
$551$	2.14563	+	3.71634i	0.0914069	+	0.158321i
$552$	9.58977	+	4.67113i	0.408168	+	0.198817i
$553$	−21.4805	+	9.56375i	−0.913446	+	0.406692i
$554$	14.1245	−	6.28863i	0.600092	−	0.267178i
$555$	5.00602	+	30.4638i	0.212494	+	1.29312i
$556$	15.2448	+	6.78744i	0.646525	+	0.287851i
$557$	−16.9105			−0.716522			−0.358261	−	0.933621i	$-0.616630\pi$
$557$	−16.9105			−0.716522			−0.358261	+	0.933621i	$0.616630\pi$
$558$	3.57287	−	20.3855i	0.151252	−	0.862989i
$559$	−7.17092	−	22.0698i	−0.303297	−	0.933453i
$560$	13.0863	+	1.53675i	0.552998	+	0.0649396i
$561$	−9.65481	+	6.51949i	−0.407626	+	0.275253i
$562$	−7.63820	−	1.62355i	−0.322198	−	0.0684853i
$563$	22.1504	+	4.70822i	0.933530	+	0.198428i	0.649477	−	0.760381i	$-0.274988\pi$
$563$	22.1504	+	4.70822i	0.933530	+	0.198428i	0.284052	+	0.958809i	$0.408321\pi$
$564$	1.30773	+	18.5639i	0.0550652	+	0.781682i
$565$	4.89302	+	0.574597i	0.205851	+	0.0241735i
$566$	−4.53630	−	13.9613i	−0.190675	−	0.586837i
$567$	−13.6693	+	28.1735i	−0.574058	+	1.18317i
$568$	−24.1640			−1.01390
$569$	−16.4211	−	7.31117i	−0.688410	−	0.306500i	0.0325562	−	0.999470i	$-0.489635\pi$
$569$	−16.4211	−	7.31117i	−0.688410	−	0.306500i	−0.720967	+	0.692970i	$0.756302\pi$
$570$	−3.90521	+	3.20000i	−0.163571	+	0.134033i
$571$	−13.6141	+	6.06140i	−0.569734	+	0.253662i	−0.671323	−	0.741165i	$-0.734274\pi$
$571$	−13.6141	+	6.06140i	−0.569734	+	0.253662i	0.101590	+	0.994826i	$0.467607\pi$
$572$	−5.70465	+	2.53987i	−0.238523	+	0.106197i
$573$	3.23313	−	2.18320i	0.135066	−	0.0912044i
$574$	−4.90247	−	8.49132i	−0.204625	−	0.354421i
$575$	7.98516	+	6.10409i	0.333004	+	0.254558i
$576$	17.3473	−	16.7866i	0.722803	−	0.699444i
$577$	−7.48625	+	23.0403i	−0.311657	+	0.959181i	0.665452	+	0.746441i	$0.268239\pi$
$577$	−7.48625	+	23.0403i	−0.311657	+	0.959181i	−0.977109	+	0.212740i	$0.931761\pi$
$578$	−1.51631	+	14.4267i	−0.0630700	+	0.600071i
$579$	−18.9896	+	19.6846i	−0.789182	+	0.818065i
$580$	−2.59029	−	6.01391i	−0.107556	−	0.249714i
$581$	−1.29446	−	12.3160i	−0.0537032	−	0.510952i
$582$	−4.48432	+	32.0273i	−0.185881	+	1.32757i
$583$	44.7605	+	19.9287i	1.85379	+	0.825361i
$584$	−8.42669	−	25.9347i	−0.348699	−	1.07319i
$585$	11.9710	+	8.27020i	0.494942	+	0.341931i
$586$	−0.105852	+	0.325780i	−0.00437272	+	0.0134579i
$587$	−6.78580	+	7.53640i	−0.280080	+	0.311060i	−0.866727	−	0.498782i	$-0.833781\pi$
$587$	−6.78580	+	7.53640i	−0.280080	+	0.311060i	0.586647	+	0.809843i	$0.300447\pi$
$588$	−2.47190	+	6.80240i	−0.101940	+	0.280526i
$589$	5.09262	+	5.65593i	0.209838	+	0.233049i
$590$	−13.1858	+	1.22374i	−0.542849	+	0.0503807i
$591$	−23.9575	−	28.5216i	−0.985480	−	1.17322i
$592$	−12.3327	−	5.49087i	−0.506871	−	0.225673i
$593$	28.7337			1.17995			0.589975	−	0.807422i	$-0.299138\pi$
$593$	28.7337			1.17995			0.589975	+	0.807422i	$0.299138\pi$
$594$	18.9081	+	6.11133i	0.775809	+	0.250751i
$595$	14.0897	+	4.76845i	0.577619	+	0.195487i
$596$	0.602877	−	5.73599i	0.0246948	−	0.234955i
$597$	28.8575	+	7.17920i	1.18106	+	0.293825i
$598$	−3.17139	−	3.52218i	−0.129688	−	0.144033i
$599$	−0.738992	+	1.27997i	−0.0301944	+	0.0522982i	−0.880728	−	0.473623i	$-0.842946\pi$
$599$	−0.738992	+	1.27997i	−0.0301944	+	0.0522982i	0.850533	+	0.525921i	$0.176279\pi$
$600$	22.3434	−	14.3080i	0.912166	−	0.584121i
$601$	−9.97465	−	17.2766i	−0.406874	−	0.704727i	0.587663	−	0.809106i	$-0.300048\pi$
$601$	−9.97465	−	17.2766i	−0.406874	−	0.704727i	−0.994538	+	0.104378i	$0.966715\pi$
$602$	−12.5044	+	38.4847i	−0.509642	+	1.56852i
$603$	−12.0680	+	29.9581i	−0.491446	+	1.21999i
$604$	−0.0206365	−	0.0149933i	−0.000839688	−	0.000610069i
$605$	−2.68416	+	1.50642i	−0.109127	+	0.0612448i
$606$	−8.27748	−	15.5484i	−0.336250	−	0.631609i
$607$	−11.5351	+	19.9793i	−0.468194	+	0.810935i	−0.999339	−	0.0363452i	$-0.988428\pi$
$607$	−11.5351	+	19.9793i	−0.468194	+	0.810935i	0.531146	+	0.847281i	$0.321762\pi$
$608$	0.537307	+	5.11214i	0.0217907	+	0.207324i
$609$	−21.2353	+	3.75563i	−0.860496	+	0.152186i
$610$	1.11897	−	0.627997i	0.0453058	−	0.0254268i
$611$	8.79993	−	27.0834i	0.356007	−	1.09568i
$612$	3.97801	−	2.49144i	0.160802	−	0.100710i
$613$	−7.36834	−	22.6774i	−0.297605	−	0.915932i	−0.982334	−	0.187135i	$-0.940080\pi$
$613$	−7.36834	−	22.6774i	−0.297605	−	0.915932i	0.684730	−	0.728797i	$-0.259920\pi$
$614$	−8.88515	+	1.88860i	−0.358575	+	0.0762175i
$615$	−9.39407	−	3.54376i	−0.378805	−	0.142898i
$616$	36.6813	+	7.79686i	1.47793	+	0.314144i
$617$	−0.0931604	−	0.886362i	−0.00375050	−	0.0356836i	0.992487	−	0.122353i	$-0.0390441\pi$
$617$	−0.0931604	−	0.886362i	−0.00375050	−	0.0356836i	−0.996237	+	0.0866698i	$0.972377\pi$
$618$	−13.9878	+	5.65984i	−0.562673	+	0.227672i
$619$	−0.275213	−	0.122533i	−0.0110617	−	0.00492500i	0.401198	−	0.915991i	$-0.368594\pi$
$619$	−0.275213	−	0.122533i	−0.0110617	−	0.00492500i	−0.412260	+	0.911066i	$0.635260\pi$
$620$	−6.71123	−	9.47780i	−0.269529	−	0.380638i
$621$	−0.0161412	−	10.4453i	−0.000647725	−	0.419155i
$622$	17.9653	+	13.0526i	0.720344	+	0.523361i
$623$	29.9243	−	6.36061i	1.19889	−	0.254833i
$624$	−5.89788	+	2.38643i	−0.236104	+	0.0955338i
$625$	23.3066	−	9.04439i	0.932265	−	0.361775i
$626$	8.56328	−	14.8320i	0.342258	−	0.592808i
$627$	−6.05600	+	4.08936i	−0.241853	+	0.163313i
$628$	0.118746	−	1.12979i	0.00473849	−	0.0450837i
$629$	−12.3294	−	8.95784i	−0.491606	−	0.357173i
$630$	−8.41138	−	23.9370i	−0.335118	−	0.953671i
$631$	−11.5670	+	8.40394i	−0.460476	+	0.334556i	−0.793718	−	0.608286i	$-0.791857\pi$
$631$	−11.5670	+	8.40394i	−0.460476	+	0.334556i	0.333242	+	0.942841i	$0.391857\pi$
$632$	−10.3519	−	17.9301i	−0.411778	−	0.713221i
$633$	11.1209	+	20.8894i	0.442016	+	0.830280i
$634$	13.6033	+	2.89147i	0.540256	+	0.114835i
$635$	9.40557	−	41.7437i	0.373248	−	1.65655i
$636$	−17.7476	−	8.64476i	−0.703738	−	0.342787i
$637$	7.41068	−	8.23039i	0.293622	−	0.326100i
$638$	4.22870	+	13.0146i	0.167416	+	0.515253i
$639$	10.3946	+	21.2566i	0.411205	+	0.840896i
$640$	−0.00474273	+	0.389468i	−0.000187473	+	0.0153951i
$641$	0.809085	−	0.898580i	0.0319569	−	0.0354918i	−0.726954	−	0.686686i	$-0.759065\pi$
$641$	0.809085	−	0.898580i	0.0319569	−	0.0354918i	0.758911	+	0.651194i	$0.225732\pi$
$642$	−9.49576	−	0.326702i	−0.374768	−	0.0128939i
$643$	−12.3127	+	21.3262i	−0.485566	+	0.841025i	−0.999862	−	0.0165876i	$-0.994720\pi$
$643$	−12.3127	+	21.3262i	−0.485566	+	0.841025i	0.514297	+	0.857612i	$0.328053\pi$
$644$	−0.598301	−	5.69246i	−0.0235764	−	0.224314i
$645$	15.0733	+	38.5975i	0.593509	+	1.51978i
$646$	0.260520	−	2.47868i	0.0102500	−	0.0975223i
$647$	5.45922	+	3.96635i	0.214624	+	0.155933i	0.689903	−	0.723901i	$-0.257653\pi$
$647$	5.45922	+	3.96635i	0.214624	+	0.155933i	−0.475279	+	0.879835i	$0.657653\pi$
$648$	−25.9294	−	9.37706i	−1.01860	−	0.368366i
$649$	−19.1663			−0.752344
$650$	−11.5874	+	2.16950i	−0.454497	+	0.0850948i
$651$	−35.4541	+	14.3456i	−1.38956	+	0.562250i
$652$	−0.682356	−	0.757833i	−0.0267231	−	0.0296790i
$653$	−1.59205	+	0.708826i	−0.0623017	+	0.0277385i	−0.437651	−	0.899145i	$-0.644189\pi$
$653$	−1.59205	+	0.708826i	−0.0623017	+	0.0277385i	0.375349	+	0.926883i	$0.377523\pi$
$654$	2.51873	+	8.76681i	0.0984902	+	0.342809i
$655$	−3.38185	−	16.9210i	−0.132140	−	0.661156i
$656$	3.55190	−	2.58061i	0.138678	−	0.100756i
$657$	−19.1893	+	18.5691i	−0.748645	+	0.724450i
$658$	−40.1739	+	29.1880i	−1.56614	+	1.13787i
$659$	21.8980	−	24.3202i	0.853026	−	0.947381i	−0.146096	−	0.989270i	$-0.546671\pi$
$659$	21.8980	−	24.3202i	0.853026	−	0.947381i	0.999122	+	0.0418891i	$0.0133376\pi$
$660$	9.90555	−	5.11961i	0.385573	−	0.199280i
$661$	29.5406	+	32.8081i	1.14900	+	1.27609i	0.955501	+	0.294987i	$0.0953152\pi$
$661$	29.5406	+	32.8081i	1.14900	+	1.27609i	0.193494	+	0.981102i	$0.438018\pi$
$662$	26.7233	+	5.68022i	1.03863	+	0.220768i
$663$	−7.07277	+	1.25088i	−0.274684	+	0.0485800i
$664$	10.6658	−	2.26709i	0.413915	−	0.0879803i
$665$	8.83776	+	2.99102i	0.342714	+	0.115987i
$666$	0.933973	+	25.9781i	0.0361907	+	1.00663i
$667$	5.81942	−	4.22805i	0.225329	−	0.163711i
$668$	0.0910656	+	0.157730i	0.00352343	+	0.00610276i
$669$	37.9044	+	1.30410i	1.46547	+	0.0504195i
$670$	−10.3517	−	24.0337i	−0.399922	−	0.928504i
$671$	1.69660	−	0.755374i	0.0654965	−	0.0291609i
$672$	−25.0673	−	6.23628i	−0.966994	−	0.240570i
$673$	−6.18540	+	1.31475i	−0.238430	+	0.0506798i	−0.325577	−	0.945516i	$-0.605558\pi$
$673$	−6.18540	+	1.31475i	−0.238430	+	0.0506798i	0.0871469	+	0.996195i	$0.472225\pi$
$674$	−20.5298			−0.790779
$675$	−22.1979	−	13.5001i	−0.854397	−	0.519621i
$676$	6.78870			0.261104
$677$	−49.0316	+	10.4220i	−1.88444	+	0.400550i	−0.998051	−	0.0623959i	$-0.980126\pi$
$677$	−49.0316	+	10.4220i	−1.88444	+	0.400550i	−0.886387	+	0.462946i	$0.846793\pi$
$678$	4.02559	+	1.00149i	0.154602	+	0.0384620i
$679$	54.5965	−	24.3079i	2.09522	−	0.932852i
$680$	−2.87889	+	12.7771i	−0.110401	+	0.489978i
$681$	−44.8070	−	1.54159i	−1.71701	−	0.0590738i
$682$	12.1350	+	21.0185i	0.464674	+	0.804838i
$683$	15.2867	−	11.1065i	0.584931	−	0.424977i	−0.255568	−	0.966791i	$-0.582262\pi$
$683$	15.2867	−	11.1065i	0.584931	−	0.424977i	0.840498	+	0.541814i	$0.182262\pi$
$684$	2.49521	−	1.56276i	0.0954069	−	0.0597536i
$685$	−8.38169	+	11.2459i	−0.320248	+	0.429682i
$686$	7.00653	−	1.48928i	0.267511	−	0.0568611i
$687$	−39.1926	+	6.93154i	−1.49529	+	0.264455i
$688$	−17.7233	−	3.76720i	−0.675694	−	0.143623i
$689$	20.2131	+	22.4489i	0.770058	+	0.855236i
$690$	6.01885	+	5.94954i	0.229134	+	0.226495i
$691$	18.6879	−	20.7550i	0.710922	−	0.789559i	−0.274153	−	0.961686i	$-0.588397\pi$
$691$	18.6879	−	20.7550i	0.710922	−	0.789559i	0.985075	+	0.172128i	$0.0550641\pi$
$692$	12.6570	−	9.19584i	0.481146	−	0.349573i
$693$	−8.92049	−	35.6217i	−0.338861	−	1.35316i
$694$	−24.8191	+	18.0321i	−0.942120	+	0.684490i
$695$	33.5110	+	30.9205i	1.27114	+	1.17288i
$696$	−5.24324	−	18.2499i	−0.198744	−	0.691759i
$697$	4.52783	−	2.01592i	0.171504	−	0.0763584i
$698$	14.7726	+	16.4066i	0.559150	+	0.620999i
$699$	14.2751	−	5.77606i	0.539933	−	0.218471i
$700$	−12.8612	−	6.10567i	−0.486108	−	0.230773i
$701$	−14.8415			−0.560556			−0.280278	−	0.959919i	$-0.590427\pi$
$701$	−14.8415			−0.560556			−0.280278	+	0.959919i	$0.590427\pi$
$702$	9.11712	+	8.18362i	0.344104	+	0.308871i
$703$	−7.73365	−	5.61882i	−0.291680	−	0.211918i
$704$	−2.95898	+	28.1528i	−0.111521	+	1.06105i
$705$	−12.8761	+	49.1922i	−0.484943	+	1.85269i
$706$	1.02464	+	9.74884i	0.0385630	+	0.366902i
$707$	−16.2756	+	28.1902i	−0.612107	+	1.06020i
$708$	7.71768	+	0.265527i	0.290048	+	0.00997912i
$709$	1.07027	−	1.18866i	0.0401949	−	0.0446410i	−0.722712	−	0.691149i	$-0.757105\pi$
$709$	1.07027	−	1.18866i	0.0401949	−	0.0446410i	0.762907	+	0.646508i	$0.223771\pi$
$710$	−18.1598	−	6.14592i	−0.681524	−	0.230652i
$711$	−11.3196	+	16.8194i	−0.424519	+	0.630775i
$712$	8.32414	+	25.6191i	0.311960	+	0.960115i
$713$	8.53647	−	9.48071i	0.319693	−	0.355055i
$714$	11.2599	+	5.48466i	0.421392	+	0.205258i
$715$	−16.9894	+	1.57675i	−0.635368	+	0.0589672i
$716$	−15.2580	−	3.24318i	−0.570217	−	0.121203i
$717$	4.21676	+	7.92072i	0.157478	+	0.295805i
$718$	5.00266	+	8.66487i	0.186698	+	0.323370i
$719$	−19.6770	+	14.2962i	−0.733830	+	0.533159i	−0.890773	−	0.454449i	$-0.849836\pi$
$719$	−19.6770	+	14.2962i	−0.733830	+	0.533159i	0.156943	+	0.987608i	$0.449836\pi$
$720$	10.2659	−	4.86614i	0.382589	−	0.181350i
$721$	22.5596	+	16.3905i	0.840164	+	0.610415i
$722$	−1.99548	+	18.9857i	−0.0742641	+	0.706576i
$723$	9.40968	−	6.35396i	0.349950	−	0.236306i
$724$	−4.62252	+	8.00644i	−0.171795	+	0.297557i
$725$	−1.43634	−	17.8340i	−0.0533444	−	0.662338i
$726$	−2.40249	+	0.972108i	−0.0891646	+	0.0360783i
$727$	11.7113	−	2.48930i	0.434346	−	0.0923232i	0.0144508	−	0.999896i	$-0.495400\pi$
$727$	11.7113	−	2.48930i	0.434346	−	0.0923232i	0.419896	+	0.907572i	$0.362067\pi$
$728$	18.7049	+	13.5899i	0.693250	+	0.503675i
$729$	2.90524	+	26.8432i	0.107602	+	0.994194i
$730$	0.263443	−	21.6337i	0.00975048	−	0.800700i
$731$	−18.6864	−	8.31974i	−0.691143	−	0.307717i
$732$	−0.693632	+	0.280661i	−0.0256374	+	0.0103735i
$733$	1.09056	+	10.3760i	0.0402808	+	0.383247i	0.996027	+	0.0890535i	$0.0283842\pi$
$733$	1.09056	+	10.3760i	0.0402808	+	0.383247i	−0.955746	+	0.294193i	$0.904949\pi$
$734$	−20.2474	−	4.30371i	−0.747343	−	0.158853i
$735$	−12.3562	+	15.4406i	−0.455764	+	0.569534i
$736$	8.42809	−	1.79145i	0.310664	−	0.0660336i
$737$	−11.7039	−	36.0208i	−0.431117	−	1.32684i
$738$	−7.46854	−	3.96123i	−0.274921	−	0.145815i
$739$	9.63830	−	29.6636i	0.354551	−	1.09119i	−0.601719	−	0.798708i	$-0.705517\pi$
$739$	9.63830	−	29.6636i	0.354551	−	1.09119i	0.956270	−	0.292487i	$-0.0944827\pi$
$740$	10.7203	+	9.89158i	0.394085	+	0.363622i
$741$	−4.43641	+	0.784615i	−0.162975	+	0.0288235i
$742$	−5.50612	−	52.3872i	−0.202136	−	1.92320i
$743$	17.4838	−	30.2828i	0.641418	−	1.11097i	−0.343698	−	0.939080i	$-0.611680\pi$
$743$	17.4838	−	30.2828i	0.641418	−	1.11097i	0.985116	−	0.171889i	$-0.0549870\pi$
$744$	−15.8255	−	29.7265i	−0.580191	−	1.08983i
$745$	6.58469	−	14.3177i	0.241244	−	0.524559i
$746$	3.77035	+	2.73932i	0.138042	+	0.100294i
$747$	−6.58244	−	8.40727i	−0.240839	−	0.307606i
$748$	−1.70093	+	5.23491i	−0.0621920	+	0.191407i
$749$	8.77921	+	15.2060i	0.320785	+	0.555617i
$750$	20.4307	−	5.06988i	0.746022	−	0.185126i
$751$	−13.7941	+	23.8921i	−0.503354	+	0.871835i	0.496638	+	0.867958i	$0.334568\pi$
$751$	−13.7941	+	23.8921i	−0.503354	+	0.871835i	−0.999992	+	0.00387741i	$0.998766\pi$
$752$	−14.8784	−	16.5241i	−0.542559	−	0.602572i
$753$	12.0151	+	2.98913i	0.437856	+	0.108930i
$754$	−0.881894	+	8.39066i	−0.0321167	+	0.305570i
$755$	−0.0402778	−	0.0568815i	−0.00146586	−	0.00207013i
$756$	3.09850	+	14.4673i	0.112692	+	0.526172i
$757$	31.2879			1.13718			0.568589	−	0.822622i	$-0.307489\pi$
$757$	31.2879			1.13718			0.568589	+	0.822622i	$0.307489\pi$
$758$	−9.59028	−	4.26987i	−0.348335	−	0.155089i
$759$	7.87831	+	9.37919i	0.285965	+	0.340443i
$760$	−1.80579	+	8.01444i	−0.0655029	+	0.290714i
$761$	−12.5311	−	13.9172i	−0.454251	−	0.504497i	0.471899	−	0.881653i	$-0.343569\pi$
$761$	−12.5311	−	13.9172i	−0.454251	−	0.504497i	−0.926150	+	0.377156i	$0.876902\pi$
$762$	12.3055	−	33.8633i	0.445781	−	1.22674i
$763$	11.2791	−	12.5267i	0.408330	−	0.453497i
$764$	0.569594	−	1.75303i	0.0206072	−	0.0634224i
$765$	12.4781	−	2.96381i	0.451147	−	0.107157i
$766$	−3.13711	−	9.65503i	−0.113348	−	0.348850i
$767$	−10.7951	−	4.80628i	−0.389788	−	0.173545i
$768$	3.81962	−	27.2799i	0.137828	−	0.984380i
$769$	2.43743	+	23.1906i	0.0878960	+	0.836274i	0.946298	+	0.323296i	$0.104791\pi$
$769$	2.43743	+	23.1906i	0.0878960	+	0.836274i	−0.858402	+	0.512978i	$0.828542\pi$
$770$	25.5837	+	15.1891i	0.921974	+	0.547377i
$771$	−4.96127	+	5.14284i	−0.178676	+	0.185215i
$772$	−1.35081	+	12.8521i	−0.0486167	+	0.462557i
$773$	−0.276069	+	0.849654i	−0.00992952	+	0.0305599i	−0.955899	−	0.293697i	$-0.905114\pi$
$773$	−0.276069	+	0.849654i	−0.00992952	+	0.0305599i	0.945969	+	0.324257i	$0.105114\pi$
$774$	8.47551	+	33.8448i	0.304646	+	1.21653i
$775$	−9.06794	−	30.4088i	−0.325730	−	1.09232i
$776$	26.3112	+	45.5724i	0.944518	+	1.63595i
$777$	39.8117	−	26.8832i	1.42824	−	0.964428i
$778$	25.8064	−	11.4897i	0.925204	−	0.411927i
$779$	2.84009	−	1.26449i	0.101757	−	0.0453050i
$780$	6.86295	−	0.399541i	0.245733	−	0.0143059i
$781$	−25.3489	−	11.2861i	−0.907055	−	0.403847i
$782$	−4.17775			−0.149396
$783$	−13.7985	+	12.4629i	−0.493119	+	0.445388i
$784$	−2.67225	−	8.22434i	−0.0954375	−	0.293726i
$785$	1.29696	−	2.82009i	0.0462905	−	0.100653i
$786$	−1.02099	−	14.4935i	−0.0364174	−	0.516966i
$787$	−30.9822	−	6.58548i	−1.10440	−	0.234747i	−0.380587	−	0.924745i	$-0.624278\pi$
$787$	−30.9822	−	6.58548i	−1.10440	−	0.234747i	−0.723811	+	0.689998i	$0.757611\pi$
$788$	−17.2145	−	3.65906i	−0.613242	−	0.130349i
$789$	−25.3305	+	17.1046i	−0.901788	+	0.608940i
$790$	−3.21933	−	16.1078i	−0.114539	−	0.573089i
$791$	−2.36892	−	7.29079i	−0.0842292	−	0.259231i
$792$	30.3726	−	11.0902i	1.07924	−	0.394072i
$793$	1.14500			0.0406602
$794$	13.4255	+	5.97742i	0.476454	+	0.212131i
$795$	−38.3617	−	37.9199i	−1.36055	−	1.34488i
$796$	12.8355	−	5.71472i	0.454941	−	0.202553i
$797$	31.0674	−	13.8321i	1.10046	−	0.489958i	0.225547	−	0.974232i	$-0.427583\pi$
$797$	31.0674	−	13.8321i	1.10046	−	0.489958i	0.874916	+	0.484275i	$0.160916\pi$
$798$	7.06281	+	3.44026i	0.250021	+	0.121784i
$799$	−12.5508	−	21.7386i	−0.444015	−	0.769057i
$800$	7.11712	−	20.2154i	0.251628	−	0.714722i
$801$	18.9557	−	18.3431i	0.669768	−	0.648122i
$802$	2.49021	−	7.66409i	0.0879325	−	0.270628i
$803$	3.27318	−	31.1422i	0.115508	−	1.09898i
$804$	4.21375	+	14.6666i	0.148608	+	0.517250i
$805$	3.43770	−	15.2572i	0.121163	−	0.537744i
$806$	1.56409	+	14.8813i	0.0550927	+	0.524172i
$807$	42.9270	−	17.3694i	1.51110	−	0.611430i
$808$	−26.1839	−	11.6578i	−0.921146	−	0.410121i
$809$	−9.52295	−	29.3086i	−0.334809	−	1.03044i	−0.966816	−	0.255474i	$-0.917769\pi$
$809$	−9.52295	−	29.3086i	−0.334809	−	1.03044i	0.632007	−	0.774963i	$-0.282231\pi$
$810$	−17.1015	−	13.6420i	−0.600885	−	0.479331i
$811$	−2.77389	+	8.53714i	−0.0974043	+	0.299780i	−0.987873	−	0.155265i	$-0.950377\pi$
$811$	−2.77389	+	8.53714i	−0.0974043	+	0.299780i	0.890469	+	0.455045i	$0.150377\pi$
$812$	−6.81772	+	7.57185i	−0.239255	+	0.265720i
$813$	−24.3385	−	28.9752i	−0.853588	−	1.01620i
$814$	−20.3975	−	22.6537i	−0.714932	−	0.794013i
$815$	−1.10225	−	2.55910i	−0.0386100	−	0.0896414i
$816$	−1.91541	+	5.27099i	−0.0670527	+	0.184522i
$817$	−11.7211	−	5.21857i	−0.410070	−	0.182575i
$818$	−11.6535			−0.407455
$819$	3.90845	−	22.3003i	0.136572	−	0.779234i
$820$	−4.52915	+	1.41087i	−0.158165	+	0.0492699i
$821$	−0.729457	+	6.94032i	−0.0254582	+	0.242219i	0.974391	+	0.224860i	$0.0721924\pi$
$821$	−0.729457	+	6.94032i	−0.0254582	+	0.242219i	−0.999849	+	0.0173588i	$0.994474\pi$
$822$	−8.19944	+	8.49953i	−0.285988	+	0.296455i
$823$	20.1113	+	22.3358i	0.701035	+	0.778579i	0.983541	−	0.180687i	$-0.0578321\pi$
$823$	20.1113	+	22.3358i	0.701035	+	0.778579i	−0.282505	+	0.959266i	$0.591165\pi$
$824$	−12.2767	+	21.2638i	−0.427678	+	0.740761i
$825$	30.1217	−	4.57385i	1.04870	−	0.159241i
$826$	10.3028	+	17.8449i	0.358480	+	0.620905i
$827$	−2.38874	+	7.35179i	−0.0830647	+	0.255647i	−0.983960	−	0.178390i	$-0.942911\pi$
$827$	−2.38874	+	7.35179i	−0.0830647	+	0.255647i	0.900895	+	0.434037i	$0.142911\pi$
$828$	−3.04241	−	3.88585i	−0.105731	−	0.135043i
$829$	40.9296	+	29.7371i	1.42155	+	1.03281i	0.991514	+	0.129999i	$0.0414973\pi$
$829$	40.9296	+	29.7371i	1.42155	+	1.03281i	0.430031	+	0.902814i	$0.358503\pi$
$830$	8.59222	+	1.00900i	0.298240	+	0.0350229i
$831$	−24.6209	−	0.847082i	−0.854089	−	0.0293850i
$832$	−8.72639	+	15.1146i	−0.302533	+	0.524003i
$833$	−1.02044	−	9.70880i	−0.0353560	−	0.336390i
$834$	24.6937	+	29.3981i	0.855074	+	1.01797i
$835$	0.0975327	+	0.488001i	0.00337526	+	0.0168880i
$836$	−1.06691	+	3.28361i	−0.0368998	+	0.113566i
$837$	−19.3421	+	26.7088i	−0.668560	+	0.923191i
$838$	4.01695	+	12.3629i	0.138763	+	0.427070i
$839$	−3.27066	+	0.695201i	−0.112916	+	0.0240010i	−0.264023	−	0.964516i	$-0.585049\pi$
$839$	−3.27066	+	0.695201i	−0.112916	+	0.0240010i	0.151107	+	0.988517i	$0.451716\pi$
$840$	−34.7537	−	22.2843i	−1.19912	−	0.768880i
$841$	15.8415	+	3.36722i	0.546260	+	0.116111i
$842$	−1.00475	−	9.55959i	−0.0346261	−	0.329445i
$843$	9.80869	+	7.65526i	0.337829	+	0.263661i
$844$	10.2146	+	4.54785i	0.351603	+	0.156544i
$845$	17.5704	+	5.94644i	0.604438	+	0.204564i
$846$	−15.9982	+	39.7147i	−0.550030	+	1.36542i
$847$	3.87474	+	2.81516i	0.133138	+	0.0967301i
$848$	23.0714	−	4.90398i	0.792276	−	0.168403i
$849$	−3.24338	+	23.1644i	−0.111312	+	0.795000i
$850$	−5.41329	+	8.87001i	−0.185674	+	0.304239i
$851$	−8.01186	+	13.8770i	−0.274643	+	0.475696i
$852$	10.0509	+	4.89572i	0.344337	+	0.167725i
$853$	−5.28710	+	50.3034i	−0.181027	+	1.72236i	0.406926	+	0.913461i	$0.366601\pi$
$853$	−5.28710	+	50.3034i	−0.181027	+	1.72236i	−0.587953	+	0.808895i	$0.700066\pi$
$854$	−1.61530	−	1.17358i	−0.0552743	−	0.0401592i
$855$	7.82693	−	1.85906i	0.267675	−	0.0635784i
$856$	−12.5078	+	9.08743i	−0.427507	+	0.310602i
$857$	−24.3694	−	42.2090i	−0.832443	−	1.44183i	−0.896096	−	0.443861i	$-0.853608\pi$
$857$	−24.3694	−	42.2090i	−0.832443	−	1.44183i	0.0636526	−	0.997972i	$-0.479725\pi$
$858$	−14.3583	−	0.493997i	−0.490183	−	0.0168648i
$859$	−50.1025	−	10.6496i	−1.70947	−	0.363360i	−0.753645	−	0.657282i	$-0.771706\pi$
$859$	−50.1025	−	10.6496i	−1.70947	−	0.363360i	−0.955829	+	0.293922i	$0.905039\pi$
$860$	16.8344	+	9.99464i	0.574050	+	0.340814i
$861$	1.09783	+	15.5843i	0.0374139	+	0.531112i
$862$	−2.56951	+	2.85373i	−0.0875177	+	0.0971983i
$863$	−3.13109	−	9.63651i	−0.106584	−	0.328031i	0.883515	−	0.468402i	$-0.155170\pi$
$863$	−3.13109	−	9.63651i	−0.106584	−	0.328031i	−0.990099	+	0.140372i	$0.955170\pi$
$864$	−21.1717	+	6.91528i	−0.720275	+	0.235263i
$865$	40.8134	−	12.7138i	1.38770	−	0.432281i
$866$	−1.79962	+	1.99868i	−0.0611536	+	0.0679180i
$867$	12.2383	−	19.6079i	0.415635	−	0.665918i
$868$	−9.03533	+	15.6496i	−0.306679	+	0.531184i
$869$	−2.48511	−	23.6443i	−0.0843017	−	0.802078i
$870$	0.701301	−	15.0487i	0.0237763	−	0.510200i
$871$	2.44083	−	23.2230i	0.0827045	−	0.786880i
$872$	12.0076	+	8.72406i	0.406630	+	0.295434i
$873$	28.7707	−	42.7493i	0.973742	−	1.44684i
$874$	−2.62050			−0.0886399
$875$	−27.9389	−	27.0681i	−0.944507	−	0.915069i
$876$	−1.74944	+	12.4946i	−0.0591083	+	0.422155i
$877$	18.2099	+	20.2242i	0.614905	+	0.682921i	0.967505	−	0.252853i	$-0.0813689\pi$
$877$	18.2099	+	20.2242i	0.614905	+	0.682921i	−0.352600	+	0.935774i	$0.614702\pi$
$878$	8.25391	−	3.67488i	0.278556	−	0.124021i
$879$	0.378945	−	0.392813i	0.0127815	−	0.0132493i
$880$	−5.56658	+	12.1039i	−0.187649	+	0.408022i
$881$	26.5743	−	19.3074i	0.895312	−	0.650482i	−0.0419459	−	0.999120i	$-0.513356\pi$
$881$	26.5743	−	19.3074i	0.895312	−	0.650482i	0.937257	+	0.348638i	$0.113356\pi$
$882$	−11.9662	+	11.5795i	−0.402923	+	0.389901i
$883$	−28.3821	+	20.6208i	−0.955134	+	0.693946i	−0.952016	−	0.306050i	$-0.900993\pi$
$883$	−28.3821	+	20.6208i	−0.955134	+	0.693946i	−0.00311854	+	0.999995i	$0.500993\pi$
$884$	−2.27076	+	2.52193i	−0.0763739	+	0.0848218i
$885$	19.7421	+	7.44740i	0.663624	+	0.250341i
$886$	16.8929	+	18.7614i	0.567527	+	0.630303i
$887$	14.4331	+	3.06784i	0.484615	+	0.103008i	0.443739	−	0.896156i	$-0.353652\pi$
$887$	14.4331	+	3.06784i	0.484615	+	0.103008i	0.0408760	+	0.999164i	$0.486985\pi$
$888$	27.2056	+	32.3884i	0.912959	+	1.08688i
$889$	−65.1277	+	13.8433i	−2.18431	+	0.464290i
$890$	−0.260237	+	21.3704i	−0.00872317	+	0.716339i
$891$	−22.8212	−	21.9475i	−0.764538	−	0.735268i
$892$	14.4973	−	10.5329i	0.485405	−	0.352667i
$893$	−7.87251	−	13.6356i	−0.263444	−	0.456298i
$894$	7.02596	−	11.2568i	0.234983	−	0.376483i
$895$	−36.6495	−	21.7589i	−1.22506	−	0.727318i
$896$	0.553671	−	0.246510i	0.0184969	−	0.00823533i
$897$	2.08533	+	7.25828i	0.0696270	+	0.242347i
$898$	20.0122	−	4.25372i	0.667815	−	0.141949i
$899$	−22.7096			−0.757409
$900$	−12.1924	+	1.42444i	−0.406415	+	0.0474815i
$901$	26.6273			0.887083
$902$	9.69719	−	2.06120i	0.322881	−	0.0686305i
$903$	44.7650	−	46.4033i	1.48969	−	1.54421i
$904$	6.16645	−	2.74548i	0.205093	−	0.0913133i
$905$	−18.9770	+	16.6731i	−0.630817	+	0.554231i
$906$	−0.0275784	−	0.0518030i	−0.000916230	−	0.00172104i
$907$	−28.4907	−	49.3473i	−0.946018	−	1.63855i	−0.753700	−	0.657219i	$-0.771733\pi$
$907$	−28.4907	−	49.3473i	−0.946018	−	1.63855i	−0.192318	−	0.981333i	$-0.561601\pi$
$908$	−17.1373	+	12.4510i	−0.568723	+	0.413201i
$909$	1.00840	+	28.0482i	0.0334465	+	0.930302i
$910$	10.6006	+	14.9705i	0.351408	+	0.496269i
$911$	24.4628	−	5.19972i	0.810487	−	0.172274i	0.216015	−	0.976390i	$-0.430694\pi$
$911$	24.4628	−	5.19972i	0.810487	−	0.172274i	0.594473	+	0.804116i	$0.297361\pi$
$912$	−1.20144	+	3.30624i	−0.0397838	+	0.109481i
$913$	12.2477	+	2.60333i	0.405340	+	0.0861577i
$914$	−1.91317	−	2.12479i	−0.0632821	−	0.0702819i
$915$	−2.04108	+	0.118826i	−0.0674761	+	0.00392826i
$916$	−12.5831	+	13.9749i	−0.415756	+	0.461744i
$917$	−21.7223	+	15.7821i	−0.717332	+	0.521172i
$918$	10.7381	−	1.14540i	0.354411	−	0.0378039i
$919$	42.0477	−	30.5494i	1.38703	−	1.00773i	0.390841	−	0.920458i	$-0.372184\pi$
$919$	42.0477	−	30.5494i	1.38703	−	1.00773i	0.996184	−	0.0872745i	$-0.0278157\pi$
$920$	13.6770	+	1.60611i	0.450916	+	0.0529520i
$921$	14.0455	+	3.49426i	0.462816	+	0.115140i
$922$	19.3779	−	8.62759i	0.638176	−	0.284134i
$923$	−11.4471	−	12.7133i	−0.376787	−	0.418465i
$924$	−13.6777	−	10.6748i	−0.449963	−	0.351176i
$925$	19.0816	+	34.9914i	0.627399	+	1.15051i
$926$	−1.66763			−0.0548017
$927$	23.9864	+	1.65246i	0.787816	+	0.0542740i
$928$	−12.4087	−	9.01543i	−0.407335	−	0.295946i
$929$	−0.496757	+	4.72633i	−0.0162981	+	0.155066i	−0.999644	−	0.0266774i	$-0.991507\pi$
$929$	−0.496757	+	4.72633i	−0.0162981	+	0.155066i	0.983346	+	0.181743i	$0.0581740\pi$
$930$	−4.33250	−	26.3652i	−0.142068	−	0.864548i
$931$	−0.640070	−	6.08986i	−0.0209775	−	0.199587i
$932$	3.63795	−	6.30111i	0.119165	−	0.206400i
$933$	−16.6274	−	31.2328i	−0.544357	−	1.02252i
$934$	−4.72498	+	5.24762i	−0.154606	+	0.171707i
$935$	−8.98773	+	12.0590i	−0.293930	+	0.394371i
$936$	19.8879	+	1.37011i	0.650056	+	0.0447834i
$937$	−1.81033	−	5.57164i	−0.0591410	−	0.182017i	0.917122	−	0.398608i	$-0.130506\pi$
$937$	−1.81033	−	5.57164i	−0.0591410	−	0.182017i	−0.976263	+	0.216590i	$0.930506\pi$
$938$	−27.2460	+	30.2598i	−0.889615	+	0.988017i
$939$	−22.6158	+	15.2715i	−0.738037	+	0.498366i
$940$	9.50400	+	22.0656i	0.309986	+	0.719700i
$941$	34.5561	+	7.34512i	1.12650	+	0.239444i	0.733230	−	0.679981i	$-0.238012\pi$
$941$	34.5561	+	7.34512i	1.12650	+	0.239444i	0.393266	+	0.919425i	$0.371345\pi$
$942$	1.38387	−	2.21720i	0.0450890	−	0.0722403i
$943$	−2.60561	−	4.51304i	−0.0848502	−	0.146965i
$944$	−7.46450	+	5.42328i	−0.242949	+	0.176513i
$945$	−4.65295	+	40.1581i	−0.151360	+	1.30634i
$946$	−33.1006	−	24.0490i	−1.07619	−	0.781900i
$947$	−3.92521	+	37.3459i	−0.127552	+	1.21358i	0.724184	+	0.689607i	$0.242217\pi$
$947$	−3.92521	+	37.3459i	−0.127552	+	1.21358i	−0.851736	+	0.523971i	$0.824450\pi$
$948$	0.673114	+	9.55525i	0.0218617	+	0.310340i
$949$	9.65299	−	16.7195i	0.313349	−	0.542737i
$950$	−3.39550	+	5.56373i	−0.110165	+	0.180511i
$951$	−17.4689	−	13.6337i	−0.566467	−	0.442103i
$952$	19.9346	−	4.23722i	0.646082	−	0.137329i
$953$	1.17391	+	0.852898i	0.0380268	+	0.0276281i	0.606636	−	0.794979i	$-0.292518\pi$
$953$	1.17391	+	0.852898i	0.0380268	+	0.0276281i	−0.568609	+	0.822608i	$0.692518\pi$
$954$	−27.9991	−	35.7612i	−0.906504	−	1.15781i
$955$	3.00974	−	4.03822i	0.0973930	−	0.130674i
$956$	3.87313	+	1.72443i	0.125266	+	0.0557720i
$957$	3.02345	−	21.5937i	0.0977343	−	0.698024i
$958$	0.622284	+	5.92063i	0.0201051	+	0.191287i
$959$	21.3476	+	4.53756i	0.689349	+	0.146526i
$960$	13.9871	−	27.8489i	0.451433	−	0.898818i
$961$	−9.07417	+	1.92877i	−0.292715	+	0.0622185i
$962$	−5.80772	−	17.8743i	−0.187248	−	0.576291i
$963$	13.3745	+	7.09367i	0.430987	+	0.228590i
$964$	1.65774	−	5.10200i	0.0533922	−	0.164324i
$965$	−14.7537	+	32.0803i	−0.474939	+	1.03270i
$966$	4.49761	−	12.3769i	0.144708	−	0.398221i
$967$	4.98183	+	47.3990i	0.160205	+	1.52425i	0.719039	+	0.694969i	$0.244582\pi$
$967$	4.98183	+	47.3990i	0.160205	+	1.52425i	−0.558834	+	0.829279i	$0.688751\pi$
$968$	−2.10859	+	3.65218i	−0.0677725	+	0.117385i
$969$	−2.10269	+	3.36887i	−0.0675481	+	0.108224i
$970$	8.18248	+	40.9407i	0.262723	+	1.31453i
$971$	−14.0919	−	10.2383i	−0.452229	−	0.328564i	0.338246	−	0.941058i	$-0.390166\pi$
$971$	−14.0919	−	10.2383i	−0.452229	−	0.328564i	−0.790475	+	0.612494i	$0.790166\pi$
$972$	8.88532	+	9.15372i	0.284997	+	0.293606i
$973$	21.9247	−	67.4773i	0.702874	−	2.16322i
$974$	−19.1645	−	33.1938i	−0.614069	−	1.06360i
$975$	18.1125	+	4.97740i	0.580064	+	0.159404i
$976$	0.447017	−	0.774255i	0.0143086	−	0.0247833i
$977$	−1.38895	−	1.54259i	−0.0444365	−	0.0493517i	0.720517	−	0.693437i	$-0.243905\pi$
$977$	−1.38895	−	1.54259i	−0.0444365	−	0.0493517i	−0.764953	+	0.644086i	$0.777238\pi$
$978$	−0.647854	−	2.25495i	−0.0207161	−	0.0721054i
$979$	−3.23334	+	30.7632i	−0.103338	+	0.983196i
$980$	−0.113774	+	9.34301i	−0.00363438	+	0.298452i
$981$	2.50904	−	14.3157i	0.0801074	−	0.457065i
$982$	−3.11004			−0.0992453
$983$	−27.3233	−	12.1651i	−0.871477	−	0.388007i	−0.0782508	−	0.996934i	$-0.524933\pi$
$983$	−27.3233	−	12.1651i	−0.871477	−	0.388007i	−0.793226	+	0.608927i	$0.791600\pi$
$984$	−13.5460	+	2.39572i	−0.431831	+	0.0763728i
$985$	−41.3491	−	24.5490i	−1.31749	−	0.782197i
$986$	4.97619	+	5.52662i	0.158474	+	0.176003i
$987$	77.9140	−	13.7797i	2.48003	−	0.438614i
$988$	−1.42434	+	1.58189i	−0.0453142	+	0.0503266i
$989$	−6.64596	+	20.4542i	−0.211329	+	0.650405i
$990$	25.6464	−	0.609471i	0.815095	−	0.0193703i
$991$	3.05364	+	9.39812i	0.0970019	+	0.298541i	0.987770	−	0.155916i	$-0.0498331\pi$
$991$	3.05364	+	9.39812i	0.0970019	+	0.298541i	−0.890768	+	0.454458i	$0.849833\pi$
$992$	−24.8510	−	11.0644i	−0.789020	−	0.351294i
$993$	−34.3171	−	26.7830i	−1.08902	−	0.849934i
$994$	3.11824	+	29.6681i	0.0989046	+	0.941015i
$995$	38.2262	−	3.54770i	1.21185	−	0.112470i
$996$	−4.89571	−	1.21796i	−0.155126	−	0.0385925i
$997$	1.61725	−	15.3872i	0.0512190	−	0.487316i	−0.938602	−	0.345001i	$-0.887879\pi$
$997$	1.61725	−	15.3872i	0.0512190	−	0.487316i	0.989821	−	0.142315i	$-0.0454547\pi$
$998$	12.3238	−	37.9288i	0.390104	−	1.20062i
$999$	16.7884	−	37.8647i	0.531161	−	1.19799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.121.19	yes	224
3.2	odd	2		675.2.r.a.496.10		224
9.2	odd	6		675.2.r.a.46.19		224
9.7	even	3	inner	225.2.q.a.196.10	yes	224
25.6	even	5	inner	225.2.q.a.31.10	✓	224
75.56	odd	10		675.2.r.a.631.19		224
225.56	odd	30		675.2.r.a.181.10		224
225.106	even	15	inner	225.2.q.a.106.19	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.10	✓	224	25.6	even	5	inner
225.2.q.a.106.19	yes	224	225.106	even	15	inner
225.2.q.a.121.19	yes	224	1.1	even	1	trivial
225.2.q.a.196.10	yes	224	9.7	even	3	inner
675.2.r.a.46.19		224	9.2	odd	6
675.2.r.a.181.10		224	225.56	odd	30
675.2.r.a.496.10		224	3.2	odd	2
675.2.r.a.631.19		224	75.56	odd	10

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06328 - 0.226007i) q^{2} +(-1.68082 - 0.418155i) q^{3} +(-0.747608 + 0.332856i) q^{4} +(-2.22650 + 0.206637i) q^{5} +(-1.88168 - 0.0647394i) q^{6} +(1.73969 + 3.01324i) q^{7} +(-2.47854 + 1.80077i) q^{8} +(2.65029 + 1.40569i) q^{9} +O(q^{10})\)	\(q+(1.06328 - 0.226007i) q^{2} +(-1.68082 - 0.418155i) q^{3} +(-0.747608 + 0.332856i) q^{4} +(-2.22650 + 0.206637i) q^{5} +(-1.88168 - 0.0647394i) q^{6} +(1.73969 + 3.01324i) q^{7} +(-2.47854 + 1.80077i) q^{8} +(2.65029 + 1.40569i) q^{9} +(-2.32069 + 0.722917i) q^{10} +(-3.44115 + 0.731439i) q^{11} +(1.39578 - 0.246855i) q^{12} +(-2.12159 - 0.450957i) q^{13} +(2.53079 + 2.81073i) q^{14} +(3.82875 + 0.583704i) q^{15} +(-1.13322 + 1.25857i) q^{16} +(-1.54674 + 1.12377i) q^{17} +(3.13570 + 0.895651i) q^{18} +(-0.970198 + 0.704890i) q^{19} +(1.59577 - 0.895588i) q^{20} +(-1.66410 - 5.79216i) q^{21} +(-3.49359 + 1.55545i) q^{22} +(1.34509 + 1.49387i) q^{23} +(4.91898 - 1.99035i) q^{24} +(4.91460 - 0.920154i) q^{25} -2.35776 q^{26} +(-3.86686 - 3.47093i) q^{27} +(-2.30358 - 1.67365i) q^{28} +(0.374039 - 3.55874i) q^{29} +(4.20295 - 0.244683i) q^{30} +(-0.663380 - 6.31164i) q^{31} +(2.14316 - 3.71207i) q^{32} +(6.08980 + 0.209520i) q^{33} +(-1.39064 + 1.54446i) q^{34} +(-4.49607 - 6.34948i) q^{35} +(-2.44927 - 0.168734i) q^{36} +(2.46324 + 7.58107i) q^{37} +(-0.872281 + 0.968766i) q^{38} +(3.37743 + 1.64513i) q^{39} +(5.14637 - 4.52157i) q^{40} +(-2.53573 - 0.538987i) q^{41} +(-3.07848 - 5.78258i) q^{42} +(5.34941 + 9.26545i) q^{43} +(2.32917 - 1.69224i) q^{44} +(-6.19134 - 2.58211i) q^{45} +(1.76783 + 1.28440i) q^{46} +(-1.37238 + 13.0573i) q^{47} +(2.43102 - 1.64156i) q^{48} +(-2.55306 + 4.42203i) q^{49} +(5.01763 - 2.08912i) q^{50} +(3.06970 - 1.24208i) q^{51} +(1.73622 - 0.369044i) q^{52} +(-11.2674 - 8.18624i) q^{53} +(-4.89601 - 2.81663i) q^{54} +(7.51058 - 2.33962i) q^{55} +(-9.73804 - 4.33566i) q^{56} +(1.92548 - 0.779098i) q^{57} +(-0.406593 - 3.86847i) q^{58} +(5.32898 + 1.13271i) q^{59} +(-3.05669 + 0.838041i) q^{60} +(-0.516362 + 0.109756i) q^{61} +(-2.13183 - 6.56111i) q^{62} +(0.375033 + 10.4314i) q^{63} +(2.48651 - 7.65270i) q^{64} +(4.81690 + 0.565658i) q^{65} +(6.52251 - 1.15356i) q^{66} +(1.12533 + 10.7068i) q^{67} +(0.782301 - 1.35499i) q^{68} +(-1.63618 - 3.07338i) q^{69} +(-6.21561 - 5.73513i) q^{70} +(6.38098 + 4.63605i) q^{71} +(-9.10018 + 1.28851i) q^{72} +(-2.75054 + 8.46529i) q^{73} +(4.33248 + 7.50408i) q^{74} +(-8.64532 - 0.508455i) q^{75} +(0.490700 - 0.849917i) q^{76} +(-8.19054 - 9.09652i) q^{77} +(3.96296 + 0.985909i) q^{78} +(-0.706394 + 6.72089i) q^{79} +(2.26305 - 3.03637i) q^{80} +(5.04810 + 7.45095i) q^{81} -2.81801 q^{82} +(-3.25148 - 1.44765i) q^{83} +(3.17205 + 3.77635i) q^{84} +(3.21161 - 2.82170i) q^{85} +(7.78197 + 8.64276i) q^{86} +(-2.11680 + 5.82519i) q^{87} +(7.21189 - 8.00962i) q^{88} +(2.71707 - 8.36227i) q^{89} +(-7.16670 - 1.34622i) q^{90} +(-2.33207 - 7.17736i) q^{91} +(-1.50284 - 0.669108i) q^{92} +(-1.52423 + 10.8861i) q^{93} +(1.49183 + 14.1938i) q^{94} +(2.01449 - 1.76992i) q^{95} +(-5.15449 + 5.34313i) q^{96} +(1.79542 - 17.0823i) q^{97} +(-1.71520 + 5.27886i) q^{98} +(-10.1482 - 2.89865i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

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