LMFDB - Embedded newform 403.2.bl.a.256.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(16,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 6]))

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

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

chi := DirichletCharacter("403.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.bl (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:	$3.21797120146$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			256.1
Root			$0.669131 - 0.743145i$ of defining polynomial
Character	$\chi$	$=$	403.256
Dual form			403.2.bl.a.159.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.255585 - 0.283856i) q^{2} +(-2.18720 - 0.464905i) q^{3} +(0.193806 - 1.84395i) q^{4} -3.00000 q^{5} +(0.427051 + 0.739674i) q^{6} +(0.313585 - 2.98357i) q^{7} +(-1.19098 + 0.865300i) q^{8} +(1.82709 + 0.813473i) q^{9} +O(q^{10})$	\(q+(-0.255585 - 0.283856i) q^{2} +(-2.18720 - 0.464905i) q^{3} +(0.193806 - 1.84395i) q^{4} -3.00000 q^{5} +(0.427051 + 0.739674i) q^{6} +(0.313585 - 2.98357i) q^{7} +(-1.19098 + 0.865300i) q^{8} +(1.82709 + 0.813473i) q^{9} +(0.766755 + 0.851568i) q^{10} +(-2.04275 + 0.909491i) q^{11} +(-1.28115 + 3.94298i) q^{12} +(3.24346 + 1.57479i) q^{13} +(-0.927051 + 0.673542i) q^{14} +(6.56161 + 1.39471i) q^{15} +(-3.07715 - 0.654069i) q^{16} +(-3.30524 - 1.47159i) q^{17} +(-0.236068 - 0.726543i) q^{18} +(5.86889 - 1.24747i) q^{19} +(-0.581419 + 5.53184i) q^{20} +(-2.07295 + 6.37988i) q^{21} +(0.780261 + 0.347395i) q^{22} +(0.860904 + 8.19095i) q^{23} +(3.00721 - 1.33889i) q^{24} +4.00000 q^{25} +(-0.381966 - 1.32317i) q^{26} +(1.80902 + 1.31433i) q^{27} +(-5.44076 - 1.15647i) q^{28} +(-2.26298 - 2.51329i) q^{29} +(-1.28115 - 2.21902i) q^{30} +(-4.78115 + 2.85317i) q^{31} +(2.07295 + 3.59045i) q^{32} +(4.89074 - 1.03956i) q^{33} +(0.427051 + 1.31433i) q^{34} +(-0.940756 + 8.95070i) q^{35} +(1.85410 - 3.21140i) q^{36} +(-1.54508 + 2.67617i) q^{37} +(-1.85410 - 1.34708i) q^{38} +(-6.36198 - 4.95229i) q^{39} +(3.57295 - 2.59590i) q^{40} +(-5.57134 - 6.18760i) q^{41} +(2.34078 - 1.04218i) q^{42} +(-2.41811 + 0.513986i) q^{43} +(1.28115 + 3.94298i) q^{44} +(-5.48127 - 2.44042i) q^{45} +(2.10502 - 2.33786i) q^{46} +(-0.145898 - 0.449028i) q^{47} +(6.42628 + 2.86117i) q^{48} +(-1.95630 - 0.415823i) q^{49} +(-1.02234 - 1.13542i) q^{50} +(6.54508 + 4.75528i) q^{51} +(3.53243 - 5.67556i) q^{52} +(2.11803 - 1.53884i) q^{53} +(-0.0892780 - 0.849423i) q^{54} +(6.12825 - 2.72847i) q^{55} +(2.20820 + 3.82472i) q^{56} -13.4164 q^{57} +(-0.135029 + 1.28472i) q^{58} +(7.51840 - 8.35003i) q^{59} +(3.84346 - 11.8290i) q^{60} +(4.28115 + 7.41517i) q^{61} +(2.03188 + 0.627931i) q^{62} +(3.00000 - 5.19615i) q^{63} +(-1.45492 + 4.47777i) q^{64} +(-9.73038 - 4.72437i) q^{65} +(-1.54508 - 1.12257i) q^{66} +(-3.88197 + 6.72376i) q^{67} +(-3.35410 + 5.80948i) q^{68} +(1.92504 - 18.3155i) q^{69} +(2.78115 - 2.02063i) q^{70} +(-12.3074 - 5.47961i) q^{71} +(-2.87993 + 0.612149i) q^{72} +(-8.85410 - 6.43288i) q^{73} +(1.15455 - 0.245406i) q^{74} +(-8.74882 - 1.85962i) q^{75} +(-1.16284 - 11.0637i) q^{76} +(2.07295 + 6.37988i) q^{77} +(0.220290 + 3.07162i) q^{78} +(-8.42705 + 6.12261i) q^{79} +(9.23146 + 1.96221i) q^{80} +(-7.36044 - 8.17459i) q^{81} +(-0.332436 + 3.16292i) q^{82} +(-1.83688 + 5.65334i) q^{83} +(11.3624 + 5.05887i) q^{84} +(9.91572 + 4.41476i) q^{85} +(0.763932 + 0.555029i) q^{86} +(3.78115 + 6.54915i) q^{87} +(1.64590 - 2.85078i) q^{88} +(4.43444 - 1.97434i) q^{89} +(0.708204 + 2.17963i) q^{90} +(5.71560 - 9.18324i) q^{91} +15.2705 q^{92} +(11.7838 - 4.01769i) q^{93} +(-0.0901699 + 0.156179i) q^{94} +(-17.6067 + 3.74241i) q^{95} +(-2.86475 - 8.81678i) q^{96} +(0.169131 - 1.60917i) q^{97} +(0.381966 + 0.661585i) q^{98} -4.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 5 q^{3} - 6 q^{4} - 24 q^{5} - 10 q^{6} - 3 q^{7} - 14 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 5 * q^3 - 6 * q^4 - 24 * q^5 - 10 * q^6 - 3 * q^7 - 14 * q^8 + 2 * q^9	\( 8 q - 4 q^{2} - 5 q^{3} - 6 q^{4} - 24 q^{5} - 10 q^{6} - 3 q^{7} - 14 q^{8} + 2 q^{9} + 12 q^{10} - 5 q^{11} + 30 q^{12} - 5 q^{13} + 6 q^{14} + 15 q^{15} + 14 q^{16} - 5 q^{17} + 16 q^{18} - 6 q^{19} + 18 q^{20} - 30 q^{21} + 5 q^{22} - 11 q^{23} - 5 q^{24} + 32 q^{25} - 12 q^{26} + 10 q^{27} - 27 q^{28} - 7 q^{29} + 30 q^{30} + 2 q^{31} + 30 q^{32} - 5 q^{33} - 10 q^{34} + 9 q^{35} - 12 q^{36} + 10 q^{37} + 12 q^{38} - 10 q^{39} + 42 q^{40} + 17 q^{41} + 15 q^{42} - 12 q^{43} - 30 q^{44} - 6 q^{45} + 14 q^{46} - 28 q^{47} + 25 q^{48} + 2 q^{49} - 16 q^{50} + 30 q^{51} + 63 q^{52} + 8 q^{53} + 5 q^{54} + 15 q^{55} - 36 q^{56} - 7 q^{58} + 4 q^{59} - 90 q^{60} - 6 q^{61} - 16 q^{62} + 24 q^{63} - 34 q^{64} + 15 q^{65} + 10 q^{66} - 40 q^{67} - 35 q^{69} - 18 q^{70} - 19 q^{71} - 26 q^{72} - 44 q^{73} + 35 q^{74} - 20 q^{75} + 36 q^{76} + 30 q^{77} + 70 q^{78} - 54 q^{79} - 42 q^{80} - 11 q^{81} + 17 q^{82} - 46 q^{83} + 15 q^{85} + 24 q^{86} - 10 q^{87} + 40 q^{88} + 9 q^{89} - 48 q^{90} - 21 q^{91} - 12 q^{92} - 5 q^{93} + 44 q^{94} + 18 q^{95} - 90 q^{96} - 3 q^{97} + 12 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 - 5 * q^3 - 6 * q^4 - 24 * q^5 - 10 * q^6 - 3 * q^7 - 14 * q^8 + 2 * q^9 + 12 * q^10 - 5 * q^11 + 30 * q^12 - 5 * q^13 + 6 * q^14 + 15 * q^15 + 14 * q^16 - 5 * q^17 + 16 * q^18 - 6 * q^19 + 18 * q^20 - 30 * q^21 + 5 * q^22 - 11 * q^23 - 5 * q^24 + 32 * q^25 - 12 * q^26 + 10 * q^27 - 27 * q^28 - 7 * q^29 + 30 * q^30 + 2 * q^31 + 30 * q^32 - 5 * q^33 - 10 * q^34 + 9 * q^35 - 12 * q^36 + 10 * q^37 + 12 * q^38 - 10 * q^39 + 42 * q^40 + 17 * q^41 + 15 * q^42 - 12 * q^43 - 30 * q^44 - 6 * q^45 + 14 * q^46 - 28 * q^47 + 25 * q^48 + 2 * q^49 - 16 * q^50 + 30 * q^51 + 63 * q^52 + 8 * q^53 + 5 * q^54 + 15 * q^55 - 36 * q^56 - 7 * q^58 + 4 * q^59 - 90 * q^60 - 6 * q^61 - 16 * q^62 + 24 * q^63 - 34 * q^64 + 15 * q^65 + 10 * q^66 - 40 * q^67 - 35 * q^69 - 18 * q^70 - 19 * q^71 - 26 * q^72 - 44 * q^73 + 35 * q^74 - 20 * q^75 + 36 * q^76 + 30 * q^77 + 70 * q^78 - 54 * q^79 - 42 * q^80 - 11 * q^81 + 17 * q^82 - 46 * q^83 + 15 * q^85 + 24 * q^86 - 10 * q^87 + 40 * q^88 + 9 * q^89 - 48 * q^90 - 21 * q^91 - 12 * q^92 - 5 * q^93 + 44 * q^94 + 18 * q^95 - 90 * q^96 - 3 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.255585	−	0.283856i	−0.180726	−	0.200717i	0.645974	−	0.763359i	$-0.276451\pi$
$2$	−0.255585	−	0.283856i	−0.180726	−	0.200717i	−0.826700	+	0.562643i	$0.809785\pi$
$3$	−2.18720	−	0.464905i	−1.26278	−	0.268413i	−0.472596	−	0.881279i	$-0.656683\pi$
$3$	−2.18720	−	0.464905i	−1.26278	−	0.268413i	−0.790187	+	0.612866i	$0.790016\pi$
$4$	0.193806	−	1.84395i	0.0969032	−	0.921973i
$5$	−3.00000			−1.34164			−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000			−1.34164			−0.670820	+	0.741620i	$0.734058\pi$
$6$	0.427051	+	0.739674i	0.174343	+	0.301971i
$7$	0.313585	−	2.98357i	0.118524	−	1.12768i	−0.759980	−	0.649947i	$-0.774791\pi$
$7$	0.313585	−	2.98357i	0.118524	−	1.12768i	0.878504	−	0.477735i	$-0.158542\pi$
$8$	−1.19098	+	0.865300i	−0.421076	+	0.305930i
$9$	1.82709	+	0.813473i	0.609030	+	0.271158i
$10$	0.766755	+	0.851568i	0.242469	+	0.269290i
$11$	−2.04275	+	0.909491i	−0.615912	+	0.274222i	−0.690886	−	0.722964i	$-0.742779\pi$
$11$	−2.04275	+	0.909491i	−0.615912	+	0.274222i	0.0749738	+	0.997186i	$0.476113\pi$
$12$	−1.28115	+	3.94298i	−0.369837	+	1.13824i
$13$	3.24346	+	1.57479i	0.899574	+	0.436769i
$13$	3.24346	+	1.57479i	0.899574	+	0.436769i
$14$	−0.927051	+	0.673542i	−0.247765	+	0.180012i
$15$	6.56161	+	1.39471i	1.69420	+	0.360114i
$16$	−3.07715	−	0.654069i	−0.769288	−	0.163517i
$17$	−3.30524	−	1.47159i	−0.801638	−	0.356912i	−0.0353220	−	0.999376i	$-0.511246\pi$
$17$	−3.30524	−	1.47159i	−0.801638	−	0.356912i	−0.766316	+	0.642464i	$0.777912\pi$
$18$	−0.236068	−	0.726543i	−0.0556418	−	0.171248i
$19$	5.86889	−	1.24747i	1.34641	−	0.286189i	0.522372	−	0.852717i	$-0.325047\pi$
$19$	5.86889	−	1.24747i	1.34641	−	0.286189i	0.824042	+	0.566528i	$0.191714\pi$
$20$	−0.581419	+	5.53184i	−0.130009	+	1.23696i
$21$	−2.07295	+	6.37988i	−0.452355	+	1.39220i
$22$	0.780261	+	0.347395i	0.166352	+	0.0740648i
$23$	0.860904	+	8.19095i	0.179511	+	1.70793i	0.599477	+	0.800392i	$0.295375\pi$
$23$	0.860904	+	8.19095i	0.179511	+	1.70793i	−0.419967	+	0.907540i	$0.637958\pi$
$24$	3.00721	−	1.33889i	0.613843	−	0.273301i
$25$	4.00000			0.800000
$26$	−0.381966	−	1.32317i	−0.0749097	−	0.259495i
$27$	1.80902	+	1.31433i	0.348145	+	0.252942i
$28$	−5.44076	−	1.15647i	−1.02821	−	0.218552i
$29$	−2.26298	−	2.51329i	−0.420224	−	0.466706i	0.495445	−	0.868639i	$-0.335005\pi$
$29$	−2.26298	−	2.51329i	−0.420224	−	0.466706i	−0.915669	+	0.401933i	$0.868338\pi$
$30$	−1.28115	−	2.21902i	−0.233905	−	0.405136i
$31$	−4.78115	+	2.85317i	−0.858720	+	0.512444i
$31$	−4.78115	+	2.85317i	−0.858720	+	0.512444i
$32$	2.07295	+	3.59045i	0.366449	+	0.634708i
$33$	4.89074	−	1.03956i	0.851368	−	0.180964i
$34$	0.427051	+	1.31433i	0.0732386	+	0.225405i
$35$	−0.940756	+	8.95070i	−0.159017	+	1.51294i
$36$	1.85410	−	3.21140i	0.309017	−	0.535233i
$37$	−1.54508	+	2.67617i	−0.254010	+	0.439959i	−0.964626	−	0.263621i	$-0.915083\pi$
$37$	−1.54508	+	2.67617i	−0.254010	+	0.439959i	0.710616	+	0.703580i	$0.248416\pi$
$38$	−1.85410	−	1.34708i	−0.300775	−	0.218526i
$39$	−6.36198	−	4.95229i	−1.01873	−	0.793001i
$40$	3.57295	−	2.59590i	0.564933	−	0.410448i
$41$	−5.57134	−	6.18760i	−0.870097	−	0.966341i	0.129585	−	0.991568i	$-0.458636\pi$
$41$	−5.57134	−	6.18760i	−0.870097	−	0.966341i	−0.999682	+	0.0252275i	$0.991969\pi$
$42$	2.34078	−	1.04218i	0.361191	−	0.160812i
$43$	−2.41811	+	0.513986i	−0.368759	+	0.0783821i	−0.388564	−	0.921422i	$-0.627029\pi$
$43$	−2.41811	+	0.513986i	−0.368759	+	0.0783821i	0.0198051	+	0.999804i	$0.493695\pi$
$44$	1.28115	+	3.94298i	0.193141	+	0.594427i
$45$	−5.48127	−	2.44042i	−0.817100	−	0.363796i
$46$	2.10502	−	2.33786i	0.310368	−	0.344698i
$47$	−0.145898	−	0.449028i	−0.0212814	−	0.0654975i	0.939852	−	0.341582i	$-0.110963\pi$
$47$	−0.145898	−	0.449028i	−0.0212814	−	0.0654975i	−0.961133	+	0.276085i	$0.910963\pi$
$48$	6.42628	+	2.86117i	0.927554	+	0.412974i
$49$	−1.95630	−	0.415823i	−0.279471	−	0.0594033i
$50$	−1.02234	−	1.13542i	−0.144581	−	0.160573i
$51$	6.54508	+	4.75528i	0.916495	+	0.665873i
$52$	3.53243	−	5.67556i	0.489860	−	0.787058i
$53$	2.11803	−	1.53884i	0.290934	−	0.211376i	−0.432738	−	0.901520i	$-0.642453\pi$
$53$	2.11803	−	1.53884i	0.290934	−	0.211376i	0.723673	+	0.690143i	$0.242453\pi$
$54$	−0.0892780	−	0.849423i	−0.0121492	−	0.115592i
$55$	6.12825	−	2.72847i	0.826333	−	0.367907i
$56$	2.20820	+	3.82472i	0.295084	+	0.511100i
$57$	−13.4164			−1.77705
$58$	−0.135029	+	1.28472i	−0.0177302	+	0.168692i
$59$	7.51840	−	8.35003i	0.978812	−	1.08708i	−0.0173761	−	0.999849i	$-0.505531\pi$
$59$	7.51840	−	8.35003i	0.978812	−	1.08708i	0.996188	−	0.0872317i	$-0.0278021\pi$
$60$	3.84346	−	11.8290i	0.496188	−	1.52711i
$61$	4.28115	+	7.41517i	0.548145	+	0.949416i	0.998402	+	0.0565164i	$0.0179993\pi$
$61$	4.28115	+	7.41517i	0.548145	+	0.949416i	−0.450256	+	0.892899i	$0.648667\pi$
$62$	2.03188	+	0.627931i	0.258049	+	0.0797474i
$63$	3.00000	−	5.19615i	0.377964	−	0.654654i
$64$	−1.45492	+	4.47777i	−0.181864	+	0.559721i
$65$	−9.73038	−	4.72437i	−1.20691	−	0.585987i
$66$	−1.54508	−	1.12257i	−0.190187	−	0.138179i
$67$	−3.88197	+	6.72376i	−0.474258	+	0.821438i	−0.999566	−	0.0294739i	$-0.990617\pi$
$67$	−3.88197	+	6.72376i	−0.474258	+	0.821438i	0.525308	+	0.850912i	$0.323950\pi$
$68$	−3.35410	+	5.80948i	−0.406745	+	0.704502i
$69$	1.92504	−	18.3155i	0.231747	−	2.20493i
$70$	2.78115	−	2.02063i	0.332411	−	0.241511i
$71$	−12.3074	−	5.47961i	−1.46062	−	0.650310i	−0.485956	−	0.873983i	$-0.661529\pi$
$71$	−12.3074	−	5.47961i	−1.46062	−	0.650310i	−0.974664	+	0.223673i	$0.928195\pi$
$72$	−2.87993	+	0.612149i	−0.339403	+	0.0721424i
$73$	−8.85410	−	6.43288i	−1.03629	−	0.752912i	−0.0667355	−	0.997771i	$-0.521258\pi$
$73$	−8.85410	−	6.43288i	−1.03629	−	0.752912i	−0.969559	+	0.244859i	$0.921258\pi$
$74$	1.15455	−	0.245406i	0.134213	−	0.0285279i
$75$	−8.74882	−	1.85962i	−1.01023	−	0.214730i
$76$	−1.16284	−	11.0637i	−0.133387	−	1.26909i
$77$	2.07295	+	6.37988i	0.236234	+	0.727055i
$78$	0.220290	+	3.07162i	0.0249430	+	0.347792i
$79$	−8.42705	+	6.12261i	−0.948117	+	0.688848i	−0.950361	−	0.311150i	$-0.899286\pi$
$79$	−8.42705	+	6.12261i	−0.948117	+	0.688848i	0.00224353	+	0.999997i	$0.499286\pi$
$80$	9.23146	+	1.96221i	1.03211	+	0.219381i
$81$	−7.36044	−	8.17459i	−0.817826	−	0.908288i
$82$	−0.332436	+	3.16292i	−0.0367114	+	0.349286i
$83$	−1.83688	+	5.65334i	−0.201624	+	0.620535i	0.798211	+	0.602378i	$0.205780\pi$
$83$	−1.83688	+	5.65334i	−0.201624	+	0.620535i	−0.999835	+	0.0181569i	$0.994220\pi$
$84$	11.3624	+	5.05887i	1.23974	+	0.551968i
$85$	9.91572	+	4.41476i	1.07551	+	0.478848i
$86$	0.763932	+	0.555029i	0.0823769	+	0.0598503i
$87$	3.78115	+	6.54915i	0.405382	+	0.702142i
$88$	1.64590	−	2.85078i	0.175453	−	0.303894i
$89$	4.43444	−	1.97434i	0.470050	−	0.209280i	−0.158021	−	0.987436i	$-0.550511\pi$
$89$	4.43444	−	1.97434i	0.470050	−	0.209280i	0.628071	+	0.778156i	$0.283845\pi$
$90$	0.708204	+	2.17963i	0.0746512	+	0.229753i
$91$	5.71560	−	9.18324i	0.599157	−	0.962666i
$92$	15.2705			1.59206
$93$	11.7838	−	4.01769i	1.22192	−	0.416615i
$94$	−0.0901699	+	0.156179i	−0.00930032	+	0.0161086i
$95$	−17.6067	+	3.74241i	−1.80640	+	0.383963i
$96$	−2.86475	−	8.81678i	−0.292382	−	0.899859i
$97$	0.169131	−	1.60917i	0.0171726	−	0.163386i	−0.982575	−	0.185868i	$-0.940490\pi$
$97$	0.169131	−	1.60917i	0.0171726	−	0.163386i	0.999747	+	0.0224820i	$0.00715684\pi$
$98$	0.381966	+	0.661585i	0.0385844	+	0.0668301i
$99$	−4.47214			−0.449467
$100$	0.775226	−	7.37578i	0.0775226	−	0.737578i
$101$	−0.959607	−	9.13005i	−0.0954844	−	0.908474i	−0.932470	−	0.361248i	$-0.882351\pi$
$101$	−0.959607	−	9.13005i	−0.0954844	−	0.908474i	0.836985	−	0.547226i	$-0.184316\pi$
$102$	−0.323011	−	3.07324i	−0.0319828	−	0.304296i
$103$	−1.21885	+	3.75123i	−0.120097	+	0.369619i	−0.992976	−	0.118317i	$-0.962250\pi$
$103$	−1.21885	+	3.75123i	−0.120097	+	0.369619i	0.872879	+	0.487936i	$0.162250\pi$
$104$	−5.22557	+	0.931015i	−0.512410	+	0.0912935i
$105$	6.21885	−	19.1396i	0.606897	−	1.86784i
$106$	−0.978148	−	0.207912i	−0.0950061	−	0.0201942i
$107$	1.89094	+	17.9911i	0.182804	+	1.73926i	0.573911	+	0.818917i	$0.305425\pi$
$107$	1.89094	+	17.9911i	0.182804	+	1.73926i	−0.391108	+	0.920345i	$0.627908\pi$
$108$	2.77415	−	3.08100i	0.266942	−	0.296470i
$109$	−0.954915	−	2.93893i	−0.0914643	−	0.281498i	0.894852	−	0.446363i	$-0.147281\pi$
$109$	−0.954915	−	2.93893i	−0.0914643	−	0.281498i	−0.986316	+	0.164865i	$0.947281\pi$
$110$	−2.34078	−	1.04218i	−0.223185	−	0.0993683i
$111$	4.62358	−	5.13500i	0.438851	−	0.487393i
$112$	−2.91641	+	8.97578i	−0.275575	+	0.848132i
$113$	1.12874	−	10.7392i	0.106183	−	1.01026i	−0.803598	−	0.595172i	$-0.797084\pi$
$113$	1.12874	−	10.7392i	0.106183	−	1.01026i	0.909781	−	0.415089i	$-0.136249\pi$
$114$	3.42903	+	3.80833i	0.321159	+	0.356683i
$115$	−2.58271	−	24.5728i	−0.240839	−	2.29143i
$116$	−5.07295	+	3.68571i	−0.471011	+	0.342210i
$117$	4.64505	+	5.51576i	0.429435	+	0.509932i
$118$	−4.29180			−0.395092
$119$	−5.42705	+	9.39993i	−0.497497	+	0.861690i
$120$	−9.02162	+	4.01668i	−0.823557	+	0.366671i
$121$	−4.01478	+	4.45887i	−0.364980	+	0.405352i
$122$	1.01064	−	3.11044i	0.0914993	−	0.281606i
$123$	9.30902	+	16.1237i	0.839366	+	1.45382i
$124$	4.33447	+	9.36915i	0.389247	+	0.841374i
$125$	3.00000			0.268328
$126$	−2.24171	+	0.476491i	−0.199708	+	0.0424492i
$127$	−2.27540	−	0.483652i	−0.201909	−	0.0429172i	0.105847	−	0.994382i	$-0.466245\pi$
$127$	−2.27540	−	0.483652i	−0.201909	−	0.0429172i	−0.307756	+	0.951465i	$0.599578\pi$
$128$	9.21783	−	4.10404i	0.814749	−	0.362749i
$129$	5.52786			0.486701
$130$	1.14590	+	3.96951i	0.100502	+	0.348149i
$131$	5.16312	+	3.75123i	0.451104	+	0.327746i	0.790031	−	0.613066i	$-0.210064\pi$
$131$	5.16312	+	3.75123i	0.451104	+	0.327746i	−0.338928	+	0.940812i	$0.610064\pi$
$132$	−0.969032	−	9.21973i	−0.0843434	−	0.802474i
$133$	−1.88151	−	17.9014i	−0.163148	−	1.55225i
$134$	2.90075	−	0.616574i	0.250587	−	0.0532639i
$135$	−5.42705	−	3.94298i	−0.467086	−	0.339358i
$136$	5.20985	−	1.10739i	0.446741	−	0.0949577i
$137$	−14.3677	+	15.9569i	−1.22751	+	1.36329i	−0.317743	+	0.948177i	$0.602925\pi$
$137$	−14.3677	+	15.9569i	−1.22751	+	1.36329i	−0.909770	+	0.415114i	$0.863742\pi$
$138$	−5.69098	+	4.13474i	−0.484449	+	0.351973i
$139$	−5.54829	+	6.16201i	−0.470600	+	0.522654i	−0.930981	−	0.365067i	$-0.881046\pi$
$139$	−5.54829	+	6.16201i	−0.470600	+	0.522654i	0.460381	+	0.887721i	$0.347713\pi$
$140$	16.3223	+	3.46941i	1.37948	+	0.293218i
$141$	0.110354	+	1.04994i	0.00929345	+	0.0884213i
$142$	1.59017	+	4.89404i	0.133444	+	0.410699i
$143$	−8.05784	−	0.267008i	−0.673830	−	0.0223284i
$144$	−5.09017	−	3.69822i	−0.424181	−	0.308185i
$145$	6.78893	+	7.53987i	0.563790	+	0.626152i
$146$	0.436965	+	4.15744i	0.0361634	+	0.344072i
$147$	4.08550	+	1.81898i	0.336966	+	0.150027i
$148$	4.63525	+	3.36771i	0.381016	+	0.276824i
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	0.798019	−	0.602632i	$-0.205881\pi$
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	−0.920904	+	0.389789i	$0.872548\pi$
$150$	1.70820	+	2.95870i	0.139474	+	0.241577i
$151$	−14.3262	−	10.4086i	−1.16585	−	0.847042i	−0.175346	−	0.984507i	$-0.556104\pi$
$151$	−14.3262	−	10.4086i	−1.16585	−	0.847042i	−0.990507	+	0.137465i	$0.956104\pi$
$152$	−5.91031	+	6.56406i	−0.479389	+	0.532416i
$153$	−4.84187	−	5.37745i	−0.391442	−	0.434741i
$154$	1.28115	−	2.21902i	0.103238	−	0.178814i
$155$	14.3435	−	8.55951i	1.15209	−	0.687516i
$156$	−10.3647	+	10.7714i	−0.829844	+	0.862399i
$157$	−5.83688	+	17.9641i	−0.465834	+	1.43369i	0.392097	+	0.919924i	$0.371750\pi$
$157$	−5.83688	+	17.9641i	−0.465834	+	1.43369i	−0.857931	+	0.513765i	$0.828250\pi$
$158$	3.89177	+	0.827221i	0.309613	+	0.0658102i
$159$	−5.34799	+	2.38108i	−0.424123	+	0.188832i
$160$	−6.21885	−	10.7714i	−0.491643	−	0.851551i
$161$	24.7082			1.94728
$162$	−0.439190	+	4.17861i	−0.0345060	+	0.328303i
$163$	−11.8252	−	5.26491i	−0.926220	−	0.412380i	−0.112510	−	0.993651i	$-0.535889\pi$
$163$	−11.8252	−	5.26491i	−0.926220	−	0.412380i	−0.813710	+	0.581271i	$0.802556\pi$
$164$	−12.4894	+	9.07405i	−0.975255	+	0.708564i
$165$	−14.6722	+	3.11868i	−1.14223	+	0.242789i
$166$	2.07421	−	0.923500i	0.160990	−	0.0716775i
$167$	9.48850	+	10.5380i	0.734242	+	0.815458i	0.988427	−	0.151697i	$-0.0484738\pi$
$167$	9.48850	+	10.5380i	0.734242	+	0.815458i	−0.254185	+	0.967156i	$0.581807\pi$
$168$	−3.05166	−	9.39205i	−0.235441	−	0.724613i
$169$	8.04006	+	10.2155i	0.618466	+	0.785811i
$170$	−1.28115	−	3.94298i	−0.0982599	−	0.302413i
$171$	11.7378	+	2.49494i	0.897610	+	0.190793i
$172$	0.479116	+	4.55848i	0.0365322	+	0.347581i
$173$	−5.72930	+	6.36303i	−0.435591	+	0.483772i	−0.920473	−	0.390807i	$-0.872196\pi$
$173$	−5.72930	+	6.36303i	−0.435591	+	0.483772i	0.484882	+	0.874580i	$0.338863\pi$
$174$	0.892609	−	2.74717i	0.0676685	−	0.208262i
$175$	1.25434	−	11.9343i	0.0948193	−	0.902145i
$176$	6.88072	−	1.46254i	0.518654	−	0.110243i
$177$	−20.3262	+	14.7679i	−1.52781	+	1.11002i
$178$	−1.69381	−	0.754131i	−0.126956	−	0.0565245i
$179$	0.298033	−	0.132693i	0.0222760	−	0.00991793i	−0.395568	−	0.918437i	$-0.629452\pi$
$179$	0.298033	−	0.132693i	0.0222760	−	0.00991793i	0.417844	+	0.908519i	$0.362786\pi$
$180$	−5.56231	+	9.63420i	−0.414590	+	0.718091i
$181$	−13.5623			−1.00808			−0.504039	−	0.863681i	$-0.668153\pi$
$181$	−13.5623			−1.00808			−0.504039	+	0.863681i	$0.668153\pi$
$182$	−4.06754	+	0.724694i	−0.301506	+	0.0537179i
$183$	−5.91641	−	18.2088i	−0.437353	−	1.34604i
$184$	−8.11295	−	9.01034i	−0.598095	−	0.664251i
$185$	4.63525	−	8.02850i	0.340791	−	0.590267i
$186$	−4.15221	−	2.31805i	−0.304455	−	0.169967i
$187$	8.09017			0.591612
$188$	−0.856259	+	0.182003i	−0.0624491	+	0.0132740i
$189$	4.48866	−	4.98517i	0.326502	−	0.362618i
$190$	5.56231	+	4.04125i	0.403532	+	0.293183i
$191$	3.57295	+	6.18853i	0.258530	+	0.447786i	0.965848	−	0.259109i	$-0.0834287\pi$
$191$	3.57295	+	6.18853i	0.258530	+	0.447786i	−0.707319	+	0.706895i	$0.750095\pi$
$192$	5.26393	−	9.11740i	0.379892	−	0.657992i
$193$	−2.34078	+	1.04218i	−0.168493	+	0.0750180i	−0.489250	−	0.872144i	$-0.662729\pi$
$193$	−2.34078	+	1.04218i	−0.168493	+	0.0750180i	0.320757	+	0.947162i	$0.396063\pi$
$194$	−0.500000	+	0.363271i	−0.0358979	+	0.0260814i
$195$	19.0859	+	14.8569i	1.36677	+	1.06392i
$196$	−1.14590	+	3.52671i	−0.0818499	+	0.251908i
$197$	7.25745	−	3.23123i	0.517072	−	0.230215i	−0.131573	−	0.991307i	$-0.542003\pi$
$197$	7.25745	−	3.23123i	0.517072	−	0.230215i	0.648645	+	0.761091i	$0.275336\pi$
$198$	1.14301	+	1.26944i	0.0812303	+	0.0902154i
$199$	12.2023	−	13.5520i	0.864999	−	0.960679i	−0.134544	−	0.990908i	$-0.542957\pi$
$199$	12.2023	−	13.5520i	0.864999	−	0.960679i	0.999543	+	0.0302290i	$0.00962365\pi$
$200$	−4.76393	+	3.46120i	−0.336861	+	0.244744i
$201$	11.6166	−	12.9015i	0.819369	−	0.910002i
$202$	−2.34636	+	2.60590i	−0.165089	+	0.183350i
$203$	−8.20820	+	5.96361i	−0.576103	+	0.418563i
$204$	10.0370	−	11.1472i	0.702728	−	0.780458i
$205$	16.7140	+	18.5628i	1.16736	+	1.29648i
$206$	1.37633	−	0.612780i	0.0958933	−	0.0426944i
$207$	−5.09017	+	15.6659i	−0.353791	+	1.08886i
$208$	−8.95060	−	6.96732i	−0.620612	−	0.483097i
$209$	−10.8541	+	7.88597i	−0.750794	+	0.545484i
$210$	−7.02235	+	3.12655i	−0.484588	+	0.215753i
$211$	−13.3541	+	23.1300i	−0.919334	+	1.59233i	−0.118906	+	0.992906i	$0.537939\pi$
$211$	−13.3541	+	23.1300i	−0.919334	+	1.59233i	−0.800429	+	0.599428i	$0.795395\pi$
$212$	−2.42705	−	4.20378i	−0.166691	−	0.288716i
$213$	24.3713	+	17.7068i	1.66990	+	1.21325i
$214$	4.62358	−	5.13500i	0.316061	−	0.351022i
$215$	7.25434	−	1.54196i	0.494742	−	0.105161i
$216$	−3.29180			−0.223978
$217$	7.01332	+	15.1596i	0.476095	+	1.02910i
$218$	−0.590170	+	1.02220i	−0.0399714	+	0.0692324i
$219$	16.3751	+	18.1863i	1.10652	+	1.22892i
$220$	−3.84346	−	11.8290i	−0.259126	−	0.797508i
$221$	−8.40297	−	9.97810i	−0.565245	−	0.671199i
$222$	−2.63932			−0.177140
$223$	−7.59017	+	13.1466i	−0.508275	+	0.880359i	0.491679	+	0.870777i	$0.336383\pi$
$223$	−7.59017	+	13.1466i	−0.508275	+	0.880359i	−0.999954	+	0.00958208i	$0.996950\pi$
$224$	11.3624	−	5.05887i	0.759182	−	0.338010i
$225$	7.30836	+	3.25389i	0.487224	+	0.216926i
$226$	−3.33688	+	2.42439i	−0.221966	+	0.161268i
$227$	−13.9250	+	2.95984i	−0.924233	+	0.196452i	−0.645362	−	0.763877i	$-0.723294\pi$
$227$	−13.9250	+	2.95984i	−0.924233	+	0.196452i	−0.278871	+	0.960329i	$0.589960\pi$
$228$	−2.60019	+	24.7391i	−0.172202	+	1.63839i
$229$	7.85410	−	24.1724i	0.519014	−	1.59736i	−0.256845	−	0.966453i	$-0.582683\pi$
$229$	7.85410	−	24.1724i	0.519014	−	1.59736i	0.775858	−	0.630907i	$-0.217317\pi$
$230$	−6.31505	+	7.01357i	−0.416402	+	0.462461i
$231$	−1.56793	−	14.9178i	−0.103162	−	0.981521i
$232$	4.86992	+	1.03513i	0.319726	+	0.0679598i
$233$	−3.82624	−	11.7759i	−0.250665	−	0.771468i	−0.994653	−	0.103275i	$-0.967068\pi$
$233$	−3.82624	−	11.7759i	−0.250665	−	0.771468i	0.743988	−	0.668193i	$-0.232932\pi$
$234$	0.378476	−	2.72827i	0.0247418	−	0.178353i
$235$	0.437694	+	1.34708i	0.0285520	+	0.0878741i
$236$	−13.9399	−	15.4818i	−0.907409	−	1.00778i
$237$	21.2781	−	9.47363i	1.38216	−	0.615378i
$238$	4.05530	−	0.861981i	0.262866	−	0.0558739i
$239$	−9.78115	+	7.10642i	−0.632690	+	0.459676i	−0.857331	−	0.514765i	$-0.827879\pi$
$239$	−9.78115	+	7.10642i	−0.632690	+	0.459676i	0.224641	+	0.974442i	$0.427879\pi$
$240$	−19.2788	−	8.58350i	−1.24444	−	0.554062i
$241$	1.08521	−	10.3251i	0.0699046	−	0.665098i	−0.902323	−	0.431060i	$-0.858140\pi$
$241$	1.08521	−	10.3251i	0.0699046	−	0.665098i	0.972228	−	0.234037i	$-0.0751938\pi$
$242$	2.29180			0.147322
$243$	8.94427	+	15.4919i	0.573775	+	0.993808i
$244$	14.5029	−	6.45710i	0.928452	−	0.413374i
$245$	5.86889	+	1.24747i	0.374949	+	0.0796979i
$246$	2.19756	−	6.76340i	0.140111	−	0.431218i
$247$	21.0000	+	5.19615i	1.33620	+	0.330623i
$248$	3.22542	−	7.53521i	0.204815	−	0.478486i
$249$	6.64590	−	11.5110i	0.421167	−	0.729482i
$250$	−0.766755	−	0.851568i	−0.0484939	−	0.0538579i
$251$	2.22569	−	2.47188i	0.140484	−	0.156023i	−0.668797	−	0.743445i	$-0.733190\pi$
$251$	2.22569	−	2.47188i	0.140484	−	0.156023i	0.809281	+	0.587422i	$0.199857\pi$
$252$	−9.00000	−	6.53888i	−0.566947	−	0.411911i
$253$	−9.20820	−	15.9491i	−0.578915	−	1.00271i
$254$	0.444272	+	0.769502i	0.0278761	+	0.0482828i
$255$	−19.6353	−	14.2658i	−1.22961	−	0.893362i
$256$	5.08142	+	2.26239i	0.317589	+	0.141400i
$257$	−0.488541	−	4.64816i	−0.0304744	−	0.289944i	−0.999136	−	0.0415602i	$-0.986767\pi$
$257$	−0.488541	−	4.64816i	−0.0304744	−	0.289944i	0.968662	−	0.248384i	$-0.0798995\pi$
$258$	−1.41284	−	1.56912i	−0.0879596	−	0.0976890i
$259$	7.50000	+	5.44907i	0.466027	+	0.338589i
$260$	−10.5973	+	17.0267i	−0.657216	+	1.05595i
$261$	−2.09017	−	6.43288i	−0.129378	−	0.398185i
$262$	−0.254808	−	2.42434i	−0.0157421	−	0.149776i
$263$	17.5185	+	3.72366i	1.08023	+	0.229611i	0.713458	−	0.700698i	$-0.247128\pi$
$263$	17.5185	+	3.72366i	1.08023	+	0.229611i	0.366777	+	0.930309i	$0.380461\pi$
$264$	−4.92526	+	5.47005i	−0.303129	+	0.336658i
$265$	−6.35410	+	4.61653i	−0.390329	+	0.283591i
$266$	−4.60053	+	5.10941i	−0.282077	+	0.313278i
$267$	−10.6169	+	2.25669i	−0.649745	+	0.138107i
$268$	11.6459	+	8.46124i	0.711386	+	0.516853i
$269$	−0.230909	+	0.0490813i	−0.0140788	+	0.00299254i	−0.214946	−	0.976626i	$-0.568957\pi$
$269$	−0.230909	+	0.0490813i	−0.0140788	+	0.00299254i	0.200867	+	0.979619i	$0.435624\pi$
$270$	0.267834	+	2.54827i	0.0162999	+	0.155083i
$271$	−2.48761	−	23.6680i	−0.151111	−	1.43773i	−0.762802	−	0.646632i	$-0.776177\pi$
$271$	−2.48761	−	23.6680i	−0.151111	−	1.43773i	0.611691	−	0.791097i	$-0.290490\pi$
$272$	9.20820	+	6.69015i	0.558329	+	0.405650i
$273$	−16.7705	+	17.4284i	−1.01500	+	1.05482i
$274$	8.20163			0.495478
$275$	−8.17100	+	3.63796i	−0.492730	+	0.219377i
$276$	−33.3997	−	7.09933i	−2.01043	−	0.427330i
$277$	29.0045	−	6.16510i	1.74271	−	0.370425i	0.776891	−	0.629636i	$-0.216796\pi$
$277$	29.0045	−	6.16510i	1.74271	−	0.370425i	0.965821	+	0.259211i	$0.0834624\pi$
$278$	3.16718			0.189955
$279$	−11.0566	+	1.32366i	−0.661940	+	0.0792454i
$280$	−6.62461	−	11.4742i	−0.395896	−	0.685712i
$281$	−0.690983	+	2.12663i	−0.0412206	+	0.126864i	−0.969549	−	0.244897i	$-0.921246\pi$
$281$	−0.690983	+	2.12663i	−0.0412206	+	0.126864i	0.928329	+	0.371761i	$0.121246\pi$
$282$	0.269828	−	0.299675i	0.0160680	−	0.0178454i
$283$	0.729351	−	0.324728i	0.0433554	−	0.0193031i	−0.384944	−	0.922940i	$-0.625779\pi$
$283$	0.729351	−	0.324728i	0.0433554	−	0.0193031i	0.428300	+	0.903637i	$0.359113\pi$
$284$	−12.4894	+	21.6322i	−0.741107	+	1.28363i
$285$	40.2492			2.38416
$286$	1.98367	+	2.35551i	0.117297	+	0.139284i
$287$	−20.2082	+	14.6821i	−1.19285	+	0.866658i
$288$	0.866729	+	8.24637i	0.0510725	+	0.485922i
$289$	−2.61619	−	2.90557i	−0.153893	−	0.170916i
$290$	0.405088	−	3.85416i	0.0237876	−	0.226324i
$291$	−1.11803	+	3.44095i	−0.0655403	+	0.201712i
$292$	−13.5779	+	15.0797i	−0.794584	+	0.882475i
$293$	−14.9462	−	6.65449i	−0.873168	−	0.388759i	−0.0793007	−	0.996851i	$-0.525269\pi$
$293$	−14.9462	−	6.65449i	−0.873168	−	0.388759i	−0.793867	+	0.608091i	$0.791935\pi$
$294$	−0.527864	−	1.62460i	−0.0307857	−	0.0947485i
$295$	−22.5552	+	25.0501i	−1.31321	+	1.45847i
$296$	−0.475516	−	4.52423i	−0.0276388	−	0.262966i
$297$	−4.89074	−	1.03956i	−0.283789	−	0.0603213i
$298$	−0.354102	+	1.08981i	−0.0205126	+	0.0631312i
$299$	−10.1067	+	27.9228i	−0.584487	+	1.61481i
$300$	−5.12461	+	15.7719i	−0.295870	+	0.910593i
$301$	0.775226	+	7.37578i	0.0446833	+	0.425133i
$302$	0.707023	+	6.72688i	0.0406846	+	0.387088i
$303$	−2.14575	+	20.4154i	−0.123270	+	1.17283i
$304$	−18.8754			−1.08258
$305$	−12.8435	−	22.2455i	−0.735414	−	1.27377i
$306$	−0.288910	+	2.74879i	−0.0165159	+	0.157138i
$307$	−2.69098	−	8.28199i	−0.153583	−	0.472678i	0.844432	−	0.535663i	$-0.179938\pi$
$307$	−2.69098	−	8.28199i	−0.153583	−	0.472678i	−0.998015	+	0.0629844i	$0.979938\pi$
$308$	12.1659	−	2.58594i	0.693217	−	0.147348i
$309$	4.40983	−	7.63805i	0.250866	−	0.434513i
$310$	−6.09564	−	1.88379i	−0.346209	−	0.106992i
$311$	33.0689			1.87516			0.937582	−	0.347764i	$-0.113059\pi$
$311$	33.0689			1.87516			0.937582	+	0.347764i	$0.113059\pi$
$312$	11.8622	+	0.393073i	0.671566	+	0.0222534i
$313$	−0.708204	−	2.17963i	−0.0400301	−	0.123200i	0.929044	−	0.369968i	$-0.120631\pi$
$313$	−0.708204	−	2.17963i	−0.0400301	−	0.123200i	−0.969075	+	0.246768i	$0.920631\pi$
$314$	6.59103	−	2.93452i	0.371953	−	0.165604i
$315$	−9.00000	+	15.5885i	−0.507093	+	0.878310i
$316$	9.65654	+	16.7256i	0.543223	+	0.940890i
$317$	−9.92705	−	7.21242i	−0.557559	−	0.405090i	0.273006	−	0.962012i	$-0.411982\pi$
$317$	−9.92705	−	7.21242i	−0.557559	−	0.405090i	−0.830565	+	0.556922i	$0.811982\pi$
$318$	2.04275	+	0.909491i	0.114552	+	0.0510017i
$319$	6.90851	+	3.07587i	0.386802	+	0.172215i
$320$	4.36475	−	13.4333i	0.243997	−	0.750945i
$321$	4.22827	−	40.2293i	0.235999	−	2.24538i
$322$	−6.31505	−	7.01357i	−0.351924	−	0.390851i
$323$	−21.2338	−	4.51339i	−1.18148	−	0.251132i
$324$	−16.5000	+	11.9880i	−0.916667	+	0.665997i
$325$	12.9738	+	6.29917i	0.719659	+	0.349415i
$326$	1.52786	+	4.70228i	0.0846206	+	0.260435i
$327$	0.722274	+	6.87198i	0.0399418	+	0.380021i
$328$	11.9895	+	2.54845i	0.662009	+	0.140714i
$329$	−1.38546	+	0.294488i	−0.0763827	+	0.0162356i
$330$	4.63525	+	3.36771i	0.255162	+	0.185386i
$331$	1.03266	−	0.219498i	0.0567600	−	0.0120647i	−0.179444	−	0.983768i	$-0.557430\pi$
$331$	1.03266	−	0.219498i	0.0567600	−	0.0120647i	0.236204	+	0.971703i	$0.424097\pi$
$332$	10.0684	+	4.48276i	0.552578	+	0.246023i
$333$	−5.00000	+	3.63271i	−0.273998	+	0.199071i
$334$	0.566169	−	5.38674i	0.0309794	−	0.294749i
$335$	11.6459	−	20.1713i	0.636283	−	1.10208i
$336$	10.5517	−	18.2760i	0.575640	−	0.997038i
$337$	−21.0623	−	15.3027i	−1.14734	−	0.833589i	−0.159212	−	0.987244i	$-0.550895\pi$
$337$	−21.0623	−	15.3027i	−1.14734	−	0.833589i	−0.988125	+	0.153655i	$0.950895\pi$
$338$	0.844824	−	4.89316i	0.0459524	−	0.266153i
$339$	−7.46149	+	22.9641i	−0.405253	+	1.24724i
$340$	10.0623	−	17.4284i	0.545705	−	0.945189i
$341$	7.17177	−	10.1767i	0.388373	−	0.551101i
$342$	−2.29180	−	3.96951i	−0.123926	−	0.214646i
$343$	4.63525	−	14.2658i	0.250280	−	0.770283i
$344$	2.43518	−	2.70454i	0.131296	−	0.145819i
$345$	−5.77512	+	54.9466i	−0.310922	+	2.95822i
$346$	3.27051			0.175824
$347$	−5.32624	−	9.22531i	−0.285927	−	0.495241i	0.686906	−	0.726746i	$-0.258968\pi$
$347$	−5.32624	−	9.22531i	−0.285927	−	0.495241i	−0.972834	+	0.231505i	$0.925635\pi$
$348$	12.8091	−	5.70297i	0.686639	−	0.305711i
$349$	−0.830403	−	7.90075i	−0.0444504	−	0.422918i	−0.994007	−	0.109320i	$-0.965133\pi$
$349$	−0.830403	−	7.90075i	−0.0444504	−	0.422918i	0.949556	−	0.313597i	$-0.101534\pi$
$350$	−3.70820	+	2.69417i	−0.198212	+	0.144009i
$351$	3.79768	+	7.11179i	0.202705	+	0.379599i
$352$	−7.50000	−	5.44907i	−0.399751	−	0.290436i
$353$	−8.66141	−	9.61947i	−0.461000	−	0.511993i	0.467160	−	0.884173i	$-0.345277\pi$
$353$	−8.66141	−	9.61947i	−0.461000	−	0.511993i	−0.928161	+	0.372180i	$0.878610\pi$
$354$	9.38704	+	1.99528i	0.498915	+	0.106048i
$355$	36.9222	+	16.4388i	1.95963	+	0.872483i
$356$	−2.78115	−	8.55951i	−0.147401	−	0.453653i
$357$	16.2401	−	18.0365i	0.859519	−	0.954593i
$358$	−0.113839	−	0.0506842i	−0.00601655	−	0.00267874i
$359$	−10.4271	−	32.0912i	−0.550319	−	1.69371i	−0.707996	−	0.706216i	$-0.750401\pi$
$359$	−10.4271	−	32.0912i	−0.550319	−	1.69371i	0.157678	−	0.987491i	$-0.449599\pi$
$360$	8.63980	−	1.83645i	0.455357	−	0.0967892i
$361$	15.5303	−	6.91452i	0.817383	−	0.363922i
$362$	3.46632	+	3.84974i	0.182186	+	0.202338i
$363$	10.8541	−	7.88597i	0.569693	−	0.413906i
$364$	−15.8257	−	12.3190i	−0.829491	−	0.645692i
$365$	26.5623	+	19.2986i	1.39033	+	1.01014i
$366$	−3.65654	+	6.33332i	−0.191130	+	0.331048i
$367$	2.50000	−	4.33013i	0.130499	−	0.226031i	−0.793370	−	0.608740i	$-0.791675\pi$
$367$	2.50000	−	4.33013i	0.130499	−	0.226031i	0.923869	+	0.382709i	$0.125009\pi$
$368$	2.70831	−	25.7679i	0.141181	−	1.34324i
$369$	−5.14590	−	15.8374i	−0.267885	−	0.824464i
$370$	−3.46364	+	0.736219i	−0.180066	+	0.0382742i
$371$	−3.92705	−	6.80185i	−0.203882	−	0.353135i
$372$	−5.12461	−	22.5074i	−0.265699	−	1.16695i
$373$	7.70820	+	13.3510i	0.399116	+	0.691289i	0.993617	−	0.112806i	$-0.0359839\pi$
$373$	7.70820	+	13.3510i	0.399116	+	0.691289i	−0.594501	+	0.804095i	$0.702651\pi$
$374$	−2.06773	−	2.29644i	−0.106920	−	0.118746i
$375$	−6.56161	−	1.39471i	−0.338840	−	0.0720227i
$376$	0.562306	+	0.408539i	0.0289987	+	0.0210688i
$377$	−3.38197	−	11.7155i	−0.174180	−	0.603378i
$378$	−2.56231			−0.131791
$379$	1.69381	−	0.754131i	0.0870050	−	0.0387371i	−0.362773	−	0.931878i	$-0.618170\pi$
$379$	1.69381	−	0.754131i	0.0870050	−	0.0387371i	0.449778	+	0.893141i	$0.351503\pi$
$380$	3.48852	+	33.1910i	0.178957	+	1.70266i
$381$	4.75192	+	2.11569i	0.243448	+	0.108390i
$382$	0.843459	−	2.59590i	0.0431551	−	0.132818i
$383$	−0.273659	+	2.60369i	−0.0139833	+	0.133042i	−0.999286	−	0.0377731i	$-0.987974\pi$
$383$	−0.273659	+	2.60369i	−0.0139833	+	0.133042i	0.985303	+	0.170816i	$0.0546402\pi$
$384$	−22.0693	+	4.69097i	−1.12622	+	0.239385i
$385$	−6.21885	−	19.1396i	−0.316942	−	0.975447i
$386$	0.894100	+	0.398079i	0.0455085	+	0.0202617i
$387$	−4.83623	−	1.02797i	−0.245839	−	0.0522548i
$388$	−2.93444	−	0.623735i	−0.148974	−	0.0316654i
$389$	18.2082	−	13.2290i	0.923193	−	0.670739i	−0.0211240	−	0.999777i	$-0.506724\pi$
$389$	18.2082	−	13.2290i	0.923193	−	0.670739i	0.944317	+	0.329038i	$0.106724\pi$
$390$	−0.660871	−	9.21486i	−0.0334645	−	0.466612i
$391$	9.20820	−	28.3399i	0.465679	−	1.43321i
$392$	2.68973	−	1.19754i	0.135852	−	0.0604851i
$393$	−9.54883	−	10.6051i	−0.481675	−	0.534954i
$394$	−2.77210	−	1.23422i	−0.139656	−	0.0621790i
$395$	25.2812	−	18.3678i	1.27203	−	0.924186i
$396$	−0.866729	+	8.24637i	−0.0435548	+	0.414396i
$397$	−16.6353	−	28.8131i	−0.834900	−	1.44609i	−0.894112	−	0.447843i	$-0.852192\pi$
$397$	−16.6353	−	28.8131i	−0.834900	−	1.44609i	0.0592127	−	0.998245i	$-0.481141\pi$
$398$	−6.96556			−0.349152
$399$	−4.20719	+	40.0287i	−0.210623	+	2.00394i
$400$	−12.3086	−	2.61628i	−0.615431	−	0.130814i
$401$	−0.315921	−	0.350865i	−0.0157763	−	0.0175214i	0.735205	−	0.677845i	$-0.237086\pi$
$401$	−0.315921	−	0.350865i	−0.0157763	−	0.0175214i	−0.750981	+	0.660323i	$0.770419\pi$
$402$	−6.63119			−0.330734
$403$	−20.0006	+	1.72482i	−0.996302	+	0.0859195i
$404$	−17.0213			−0.846841
$405$	22.0813	+	24.5238i	1.09723	+	1.21860i
$406$	3.79070	+	0.805739i	0.188129	+	0.0399881i
$407$	0.722274	−	6.87198i	0.0358018	−	0.340631i
$408$	−11.9098			−0.589624
$409$	−10.5172	−	18.2164i	−0.520043	−	0.900741i	−0.999729	−	0.0233005i	$-0.992583\pi$
$409$	−10.5172	−	18.2164i	−0.520043	−	0.900741i	0.479685	−	0.877441i	$-0.340751\pi$
$410$	0.997308	−	9.48875i	0.0492535	−	0.468616i
$411$	38.8435	−	28.2214i	1.91601	−	1.39206i
$412$	6.68083	+	2.97450i	0.329141	+	0.146543i
$413$	−22.5552	−	25.0501i	−1.10987	−	1.23263i
$414$	5.74784	−	2.55910i	0.282491	−	0.125773i
$415$	5.51064	−	16.9600i	0.270507	−	0.832534i
$416$	1.06931	+	14.9100i	0.0524273	+	0.731021i
$417$	15.0000	−	10.8981i	0.734553	−	0.533684i
$418$	5.01263	+	1.06547i	0.245176	+	0.0521137i
$419$	−17.8713	−	3.79865i	−0.873068	−	0.185576i	−0.250476	−	0.968123i	$-0.580587\pi$
$419$	−17.8713	−	3.79865i	−0.873068	−	0.185576i	−0.622592	+	0.782547i	$0.713920\pi$
$420$	−34.0872	−	15.1766i	−1.66328	−	0.740542i
$421$	−1.82624	−	5.62058i	−0.0890054	−	0.273930i	0.896640	−	0.442761i	$-0.146001\pi$
$421$	−1.82624	−	5.62058i	−0.0890054	−	0.273930i	−0.985645	+	0.168830i	$0.946001\pi$
$422$	9.97870	−	2.12104i	0.485755	−	0.103250i
$423$	0.0987033	−	0.939099i	0.00479912	−	0.0456606i
$424$	−1.19098	+	3.66547i	−0.0578392	+	0.178011i
$425$	−13.2210	−	5.88635i	−0.641310	−	0.285530i
$426$	−1.20276	−	11.4435i	−0.0582741	−	0.554441i
$427$	23.4662	−	10.4478i	1.13561	−	0.505605i
$428$	33.5410			1.62127
$429$	17.5000	+	4.33013i	0.844908	+	0.209061i
$430$	−2.29180	−	1.66509i	−0.110520	−	0.0802976i
$431$	13.3541	+	2.83851i	0.643246	+	0.136726i	0.517974	−	0.855396i	$-0.326686\pi$
$431$	13.3541	+	2.83851i	0.643246	+	0.136726i	0.125272	+	0.992122i	$0.460020\pi$
$432$	−4.70696	−	5.22761i	−0.226464	−	0.251513i
$433$	−15.3541	−	26.5941i	−0.737871	−	1.27803i	−0.953452	−	0.301544i	$-0.902498\pi$
$433$	−15.3541	−	26.5941i	−0.737871	−	1.27803i	0.215581	−	0.976486i	$-0.430835\pi$
$434$	2.51064	−	5.86534i	0.120515	−	0.281545i
$435$	−11.3435	−	19.6474i	−0.543877	−	0.942023i
$436$	−5.60429	+	1.19123i	−0.268397	+	0.0570495i
$437$	15.2705	+	46.9978i	0.730488	+	2.24821i
$438$	0.977082	−	9.29632i	0.0466868	−	0.444195i
$439$	−16.9721	+	29.3966i	−0.810036	+	1.40302i	0.102802	+	0.994702i	$0.467219\pi$
$439$	−16.9721	+	29.3966i	−0.810036	+	1.40302i	−0.912838	+	0.408321i	$0.866114\pi$
$440$	−4.93769	+	8.55234i	−0.235395	+	0.407717i
$441$	−3.23607	−	2.35114i	−0.154098	−	0.111959i
$442$	−0.684670	+	4.93549i	−0.0325664	+	0.234757i
$443$	−24.1353	+	17.5353i	−1.14670	+	0.833127i	−0.988039	−	0.154206i	$-0.950718\pi$
$443$	−24.1353	+	17.5353i	−1.14670	+	0.833127i	−0.158662	+	0.987333i	$0.550718\pi$
$444$	−8.57259	−	9.52082i	−0.406837	−	0.451838i
$445$	−13.3033	+	5.92302i	−0.630638	+	0.280778i
$446$	5.67167	−	1.20555i	0.268561	−	0.0570844i
$447$	2.07295	+	6.37988i	0.0980471	+	0.301758i
$448$	12.9035	+	5.74500i	0.609632	+	0.271426i
$449$	6.02218	−	6.68830i	0.284204	−	0.315641i	−0.584091	−	0.811688i	$-0.698549\pi$
$449$	6.02218	−	6.68830i	0.284204	−	0.315641i	0.868296	+	0.496047i	$0.165216\pi$
$450$	−0.944272	−	2.90617i	−0.0445134	−	0.136998i
$451$	17.0084	+	7.57264i	0.800895	+	0.356582i
$452$	−19.5838	−	4.16266i	−0.921143	−	0.195795i
$453$	26.4954	+	29.4261i	1.24486	+	1.38256i
$454$	4.39919	+	3.19620i	0.206464	+	0.150005i
$455$	−17.1468	+	27.5497i	−0.803854	+	1.29155i
$456$	15.9787	−	11.6092i	0.748272	−	0.543651i
$457$	1.98022	+	18.8405i	0.0926306	+	0.881321i	0.937882	+	0.346953i	$0.112784\pi$
$457$	1.98022	+	18.8405i	0.0926306	+	0.881321i	−0.845252	+	0.534368i	$0.820550\pi$
$458$	−8.86889	+	3.94868i	−0.414416	+	0.184510i
$459$	−4.04508	−	7.00629i	−0.188808	−	0.327026i
$460$	−45.8115			−2.13597
$461$	−2.07892	+	19.7796i	−0.0968249	+	0.921227i	0.833012	+	0.553255i	$0.186615\pi$
$461$	−2.07892	+	19.7796i	−0.0968249	+	0.921227i	−0.929837	+	0.367972i	$0.880052\pi$
$462$	−3.83378	+	4.25784i	−0.178363	+	0.198093i
$463$	−5.78115	+	17.7926i	−0.268673	+	0.826890i	0.722151	+	0.691735i	$0.243153\pi$
$463$	−5.78115	+	17.7926i	−0.268673	+	0.826890i	−0.990824	+	0.135155i	$0.956847\pi$
$464$	5.31966	+	9.21392i	0.246959	+	0.427746i
$465$	−35.3514	+	12.0531i	−1.63938	+	0.558947i
$466$	−2.36475	+	4.09586i	−0.109545	+	0.189737i
$467$	12.1697	−	37.4545i	0.563146	−	1.73319i	−0.110249	−	0.993904i	$-0.535165\pi$
$467$	12.1697	−	37.4545i	0.563146	−	1.73319i	0.673395	−	0.739282i	$-0.264835\pi$
$468$	11.0710	−	7.49622i	0.511757	−	0.346513i
$469$	18.8435	+	13.6906i	0.870110	+	0.632172i
$470$	0.270510	−	0.468537i	0.0124777	−	0.0216120i
$471$	21.1180	−	36.5775i	0.973068	−	1.68540i
$472$	−1.72901	+	16.4504i	−0.0795840	+	0.757191i
$473$	4.47214	−	3.24920i	0.205629	−	0.149398i
$474$	−8.12752	−	3.61860i	−0.373309	−	0.166208i
$475$	23.4755	−	4.98988i	1.07713	−	0.228951i
$476$	16.2812	+	11.8290i	0.746245	+	0.542179i
$477$	5.12165	−	1.08864i	0.234504	−	0.0498454i
$478$	4.51712	+	0.960143i	0.206608	+	0.0439159i
$479$	2.10942	+	20.0698i	0.0963819	+	0.917012i	0.930713	+	0.365749i	$0.119187\pi$
$479$	2.10942	+	20.0698i	0.0963819	+	0.917012i	−0.834332	+	0.551263i	$0.814146\pi$
$480$	8.59424	+	26.4503i	0.392271	+	1.20729i
$481$	−9.22582	+	6.24685i	−0.420661	+	0.284832i
$482$	−3.20820	+	2.33090i	−0.146130	+	0.106169i
$483$	−54.0419	−	11.4870i	−2.45899	−	0.522675i
$484$	7.44382	+	8.26720i	0.338355	+	0.375782i
$485$	−0.507392	+	4.82751i	−0.0230395	+	0.219206i
$486$	2.11146	−	6.49839i	0.0957776	−	0.294773i
$487$	27.0889	+	12.0607i	1.22751	+	0.546525i	0.915025	−	0.403397i	$-0.132170\pi$
$487$	27.0889	+	12.0607i	1.22751	+	0.546525i	0.312489	+	0.949921i	$0.398837\pi$
$488$	−11.5151	−	5.12687i	−0.521265	−	0.232082i
$489$	23.4164	+	17.0130i	1.05893	+	0.769355i
$490$	−1.14590	−	1.98475i	−0.0517664	−	0.0896620i
$491$	−13.6074	+	23.5687i	−0.614093	+	1.06364i	0.376450	+	0.926437i	$0.377145\pi$
$491$	−13.6074	+	23.5687i	−0.614093	+	1.06364i	−0.990543	+	0.137203i	$0.956189\pi$
$492$	31.5353	−	14.0404i	1.42172	−	0.632992i
$493$	3.78115	+	11.6372i	0.170295	+	0.524113i
$494$	−3.89233	−	7.28904i	−0.175124	−	0.327949i
$495$	13.4164			0.603023
$496$	16.5785	−	5.65243i	0.744397	−	0.253802i
$497$	−20.2082	+	35.0016i	−0.906462	+	1.57004i
$498$	−4.96607	+	1.05557i	−0.222535	+	0.0473013i
$499$	12.6180	+	38.8343i	0.564861	+	1.73846i	0.668365	+	0.743834i	$0.266995\pi$
$499$	12.6180	+	38.8343i	0.564861	+	1.73846i	−0.103504	+	0.994629i	$0.533005\pi$
$500$	0.581419	−	5.53184i	0.0260019	−	0.247391i
$501$	−15.8541	−	27.4601i	−0.708309	−	1.22683i
$502$	−1.27051			−0.0567056
$503$	−1.93669	+	18.4264i	−0.0863527	+	0.821591i	0.862539	+	0.505990i	$0.168873\pi$
$503$	−1.93669	+	18.4264i	−0.0863527	+	0.821591i	−0.948892	+	0.315601i	$0.897794\pi$
$504$	0.923281	+	8.78443i	0.0411262	+	0.391290i
$505$	2.87882	+	27.3901i	0.128106	+	1.21885i
$506$	−2.17376	+	6.69015i	−0.0966355	+	0.297414i
$507$	−12.8360	−	26.0814i	−0.570067	−	1.15831i
$508$	−1.33282	+	4.10199i	−0.0591341	+	0.181996i
$509$	−14.2778	−	3.03483i	−0.632851	−	0.134517i	−0.119693	−	0.992811i	$-0.538191\pi$
$509$	−14.2778	−	3.03483i	−0.632851	−	0.134517i	−0.513158	+	0.858294i	$0.671524\pi$
$510$	0.969032	+	9.21973i	0.0429095	+	0.408256i
$511$	−21.9694	+	24.3995i	−0.971871	+	1.07937i
$512$	−6.89261	−	21.2133i	−0.304613	−	0.937503i
$513$	12.2565	+	5.45694i	0.541138	+	0.240930i
$514$	−1.19454	+	1.32668i	−0.0526891	+	0.0585172i
$515$	3.65654	−	11.2537i	0.161126	−	0.495896i
$516$	1.07134	−	10.1931i	0.0471629	−	0.448725i
$517$	0.706420	+	0.784559i	0.0310683	+	0.0345049i
$518$	−0.370137	−	3.52162i	−0.0162629	−	0.154731i
$519$	15.4894	−	11.2537i	0.679907	−	0.493982i
$520$	15.6767	−	2.79305i	0.687470	−	0.122483i
$521$	−32.8885			−1.44087			−0.720437	−	0.693521i	$-0.756059\pi$
$521$	−32.8885			−1.44087			−0.720437	+	0.693521i	$0.756059\pi$
$522$	−1.29180	+	2.23746i	−0.0565404	+	0.0979308i
$523$	31.9232	−	14.2131i	1.39590	−	0.621496i	0.435520	−	0.900179i	$-0.356564\pi$
$523$	31.9232	−	14.2131i	1.39590	−	0.621496i	0.960383	+	0.278683i	$0.0898978\pi$
$524$	7.91770	−	8.79350i	0.345886	−	0.384146i
$525$	−8.29180	+	25.5195i	−0.361884	+	1.11376i
$526$	−3.42047	−	5.92443i	−0.149140	−	0.258318i
$527$	20.0015	−	2.39452i	0.871281	−	0.104307i
$528$	−15.7295			−0.684538
$529$	−43.8531	+	9.32127i	−1.90666	+	0.405272i
$530$	2.93444	+	0.623735i	0.127464	+	0.0270933i
$531$	20.5293	−	9.14024i	0.890897	−	0.396653i
$532$	−33.3738			−1.44694
$533$	−8.32624	−	28.8429i	−0.360649	−	1.24933i
$534$	3.35410	+	2.43690i	0.145146	+	0.105455i
$535$	−5.67281	−	53.9732i	−0.245257	−	2.33347i
$536$	−1.19471	−	11.3670i	−0.0516038	−	0.490978i
$537$	−0.713549	+	0.151670i	−0.0307919	+	0.00654502i
$538$	0.0729490	+	0.0530006i	0.00314506	+	0.00228502i
$539$	4.37441	−	0.929809i	0.188419	−	0.0400497i
$540$	−8.32244	+	9.24301i	−0.358141	+	0.397756i
$541$	−16.0902	+	11.6902i	−0.691770	+	0.502601i	−0.877242	−	0.480049i	$-0.840619\pi$
$541$	−16.0902	+	11.6902i	−0.691770	+	0.502601i	0.185471	+	0.982650i	$0.440619\pi$
$542$	−6.08251	+	6.75531i	−0.261266	+	0.290166i
$543$	29.6635	+	6.30518i	1.27298	+	0.270581i
$544$	−1.56793	−	14.9178i	−0.0672243	−	0.639597i
$545$	2.86475	+	8.81678i	0.122712	+	0.377669i
$546$	9.23346	+	0.305964i	0.395155	+	0.0130941i
$547$	25.8262	+	18.7639i	1.10425	+	0.802285i	0.981749	−	0.190184i	$-0.0609083\pi$
$547$	25.8262	+	18.7639i	1.10425	+	0.802285i	0.122502	+	0.992468i	$0.460908\pi$
$548$	26.6391	+	29.5857i	1.13797	+	1.26384i
$549$	1.79001	+	17.0308i	0.0763957	+	0.726857i
$550$	3.12104	+	1.38958i	0.133082	+	0.0592518i
$551$	−16.4164	−	11.9272i	−0.699362	−	0.508117i
$552$	13.5557	+	23.4792i	0.576970	+	0.999342i
$553$	15.6246	+	27.0626i	0.664426	+	1.15082i
$554$	−9.16312	−	6.65740i	−0.389304	−	0.282846i
$555$	−13.8707	+	15.4050i	−0.588780	+	0.653906i
$556$	10.2871	+	11.4250i	0.436270	+	0.484527i
$557$	3.92705	−	6.80185i	0.166394	−	0.288204i	−0.770755	−	0.637131i	$-0.780121\pi$
$557$	3.92705	−	6.80185i	0.166394	−	0.288204i	0.937150	+	0.348928i	$0.113454\pi$
$558$	3.20163	+	2.80017i	0.135536	+	0.118541i
$559$	−8.65248	−	2.14093i	−0.365961	−	0.0905518i
$560$	8.74922	−	26.9273i	0.369722	−	1.13789i
$561$	−17.6949	−	3.76116i	−0.747077	−	0.158796i
$562$	0.780261	−	0.347395i	0.0329133	−	0.0146540i
$563$	1.25329	+	2.17076i	0.0528198	+	0.0914866i	0.891226	−	0.453559i	$-0.149846\pi$
$563$	1.25329	+	2.17076i	0.0528198	+	0.0914866i	−0.838407	+	0.545045i	$0.816512\pi$
$564$	1.95743			0.0824226
$565$	−3.38621	+	32.2177i	−0.142459	+	1.35541i
$566$	−0.278587	−	0.124035i	−0.0117099	−	0.00521358i
$567$	−26.6976	+	19.3969i	−1.12119	+	0.814594i
$568$	19.3994	−	4.12347i	0.813982	−	0.173017i
$569$	−18.4866	+	8.23075i	−0.774997	+	0.345051i	−0.755832	−	0.654765i	$-0.772767\pi$
$569$	−18.4866	+	8.23075i	−0.774997	+	0.345051i	−0.0191650	+	0.999816i	$0.506101\pi$
$570$	−10.2871	−	11.4250i	−0.430879	−	0.478540i
$571$	−11.4271	−	35.1688i	−0.478207	−	1.47177i	−0.841583	−	0.540128i	$-0.818376\pi$
$571$	−11.4271	−	35.1688i	−0.478207	−	1.47177i	0.363376	−	0.931643i	$-0.381624\pi$
$572$	−2.05401	+	14.8065i	−0.0858824	+	0.619089i
$573$	−4.93769	−	15.1967i	−0.206275	−	0.634850i
$574$	9.33253	+	1.98369i	0.389532	+	0.0827976i
$575$	3.44361	+	32.7638i	0.143609	+	1.36634i
$576$	−6.30081	+	6.99775i	−0.262534	+	0.291573i
$577$	−7.77051	+	23.9152i	−0.323491	+	0.995602i	0.648627	+	0.761107i	$0.275344\pi$
$577$	−7.77051	+	23.9152i	−0.323491	+	0.995602i	−0.972117	+	0.234495i	$0.924656\pi$
$578$	−0.156105	+	1.48524i	−0.00649312	+	0.0617779i
$579$	5.60429	−	1.19123i	0.232906	−	0.0495057i
$580$	15.2188	−	11.0571i	0.631928	−	0.459123i
$581$	16.2911	+	7.25326i	0.675868	+	0.300916i
$582$	1.26249	−	0.562096i	0.0523318	−	0.0232996i
$583$	−2.92705	+	5.06980i	−0.121226	+	0.209970i
$584$	16.1115			0.666697
$585$	−13.9351	−	16.5473i	−0.576147	−	0.684145i
$586$	1.93112	+	5.94336i	0.0797737	+	0.245518i
$587$	−15.0741	−	16.7415i	−0.622174	−	0.690994i	0.346861	−	0.937916i	$-0.387247\pi$
$587$	−15.0741	−	16.7415i	−0.622174	−	0.690994i	−0.969035	+	0.246922i	$0.920581\pi$
$588$	4.14590	−	7.18091i	0.170974	−	0.296136i
$589$	−24.5008	+	22.7093i	−1.00954	+	0.935719i
$590$	12.8754			0.530071
$591$	−17.3757	+	3.69333i	−0.714743	+	0.151923i
$592$	6.50486	−	7.22438i	0.267348	−	0.296920i
$593$	28.9443	+	21.0292i	1.18860	+	0.863568i	0.993115	−	0.117139i	$-0.0373725\pi$
$593$	28.9443	+	21.0292i	1.18860	+	0.863568i	0.195483	+	0.980707i	$0.437372\pi$
$594$	0.954915	+	1.65396i	0.0391806	+	0.0678629i
$595$	16.2812	−	28.1998i	0.667462	−	1.15608i
$596$	−5.08142	+	2.26239i	−0.208143	+	0.0926713i
$597$	−32.9894	+	23.9682i	−1.35016	+	0.980952i
$598$	10.5092	−	4.26779i	0.429752	−	0.174523i
$599$	4.71885	−	14.5231i	0.192807	−	0.593399i	−0.807188	−	0.590294i	$-0.799012\pi$
$599$	4.71885	−	14.5231i	0.192807	−	0.593399i	0.999995	−	0.00310450i	$-0.000988194\pi$
$600$	12.0288	−	5.35558i	0.491075	−	0.218640i
$601$	0.743709	+	0.825973i	0.0303365	+	0.0336921i	0.758122	−	0.652113i	$-0.226117\pi$
$601$	0.743709	+	0.825973i	0.0303365	+	0.0336921i	−0.727786	+	0.685805i	$0.759450\pi$
$602$	1.89552	−	2.10519i	0.0772558	−	0.0858012i
$603$	−12.5623	+	9.12705i	−0.511577	+	0.371682i
$604$	−21.9694	+	24.3995i	−0.893924	+	0.992803i
$605$	12.0444	−	13.3766i	0.489672	−	0.543836i
$606$	6.34346	−	4.60879i	0.257685	−	0.187219i
$607$	−11.8118	+	13.1183i	−0.479427	+	0.532457i	−0.933534	−	0.358490i	$-0.883292\pi$
$607$	−11.8118	+	13.1183i	−0.479427	+	0.532457i	0.454107	+	0.890947i	$0.349958\pi$
$608$	16.6449	+	18.4860i	0.675039	+	0.749707i
$609$	20.7255	−	9.22760i	0.839841	−	0.373921i
$610$	−3.03193	+	9.33132i	−0.122759	+	0.377814i
$611$	0.233911	−	1.68616i	0.00946303	−	0.0682149i
$612$	−10.8541	+	7.88597i	−0.438751	+	0.318771i
$613$	−23.8975	+	10.6398i	−0.965210	+	0.429739i	−0.827954	−	0.560796i	$-0.810495\pi$
$613$	−23.8975	+	10.6398i	−0.965210	+	0.429739i	−0.137256	+	0.990536i	$0.543828\pi$
$614$	−1.66312	+	2.88061i	−0.0671180	+	0.116252i
$615$	−27.9271	−	48.3711i	−1.12613	−	1.95051i
$616$	−7.98936	−	5.80461i	−0.321900	−	0.233874i
$617$	10.5481	−	11.7149i	0.424652	−	0.471623i	−0.492413	−	0.870362i	$-0.663885\pi$
$617$	10.5481	−	11.7149i	0.424652	−	0.471623i	0.917065	+	0.398738i	$0.130552\pi$
$618$	−3.29519	+	0.700415i	−0.132552	+	0.0281748i
$619$	−4.27051			−0.171646			−0.0858231	−	0.996310i	$-0.527352\pi$
$619$	−4.27051			−0.171646			−0.0858231	+	0.996310i	$0.527352\pi$
$620$	−13.0034	−	28.1074i	−0.522229	−	1.12882i
$621$	−9.20820	+	15.9491i	−0.369512	+	0.640014i
$622$	−8.45192	−	9.38680i	−0.338891	−	0.376377i
$623$	−4.50000	−	13.8496i	−0.180289	−	0.554872i
$624$	16.3376	+	19.4001i	0.654029	+	0.776627i
$625$	−29.0000			−1.16000
$626$	−0.437694	+	0.758108i	−0.0174938	+	0.0303001i
$627$	27.4064	−	12.2021i	1.09450	−	0.487305i
$628$	31.9935	+	14.2444i	1.27668	+	0.568415i
$629$	9.04508	−	6.57164i	0.360651	−	0.262028i
$630$	6.72514	−	1.42947i	0.267936	−	0.0569516i
$631$	−2.29740	+	21.8583i	−0.0914581	+	0.870166i	0.848573	+	0.529078i	$0.177462\pi$
$631$	−2.29740	+	21.8583i	−0.0914581	+	0.870166i	−0.940031	+	0.341088i	$0.889205\pi$
$632$	4.73858	−	14.5839i	0.188491	−	0.580114i
$633$	39.9614	−	44.3816i	1.58832	−	1.76401i
$634$	0.489916	+	4.66124i	0.0194571	+	0.185122i
$635$	6.82621	+	1.45096i	0.270890	+	0.0575794i
$636$	3.35410	+	10.3229i	0.132999	+	0.409328i
$637$	−5.69033	−	4.42946i	−0.225459	−	0.175502i
$638$	−0.892609	−	2.74717i	−0.0353387	−	0.108761i
$639$	−18.0292	−	20.0235i	−0.713226	−	0.792117i
$640$	−27.6535	+	12.3121i	−1.09310	+	0.486679i
$641$	35.8515	−	7.62048i	1.41605	−	0.300991i	0.564573	−	0.825383i	$-0.309041\pi$
$641$	35.8515	−	7.62048i	1.41605	−	0.300991i	0.851477	+	0.524392i	$0.175707\pi$
$642$	−12.5000	+	9.08178i	−0.493336	+	0.358429i
$643$	−22.7877	−	10.1457i	−0.898660	−	0.400109i	−0.0951934	−	0.995459i	$-0.530347\pi$
$643$	−22.7877	−	10.1457i	−0.898660	−	0.400109i	−0.803467	+	0.595350i	$0.797014\pi$
$644$	4.78861	−	45.5606i	0.188698	−	1.79534i
$645$	−16.5836			−0.652978
$646$	4.14590	+	7.18091i	0.163118	+	0.282529i
$647$	17.4906	−	7.78734i	0.687628	−	0.306152i	−0.0330180	−	0.999455i	$-0.510512\pi$
$647$	17.4906	−	7.78734i	0.687628	−	0.306152i	0.720646	+	0.693303i	$0.243845\pi$
$648$	15.8396	+	3.36682i	0.622239	+	0.132261i
$649$	−7.76393	+	23.8949i	−0.304761	+	0.937958i
$650$	−1.52786	−	5.29268i	−0.0599278	−	0.207596i
$651$	−8.29180	−	36.4177i	−0.324981	−	1.42732i
$652$	−12.0000	+	20.7846i	−0.469956	+	0.813988i
$653$	−3.75920	−	4.17501i	−0.147109	−	0.163381i	0.665087	−	0.746766i	$-0.268395\pi$
$653$	−3.75920	−	4.17501i	−0.147109	−	0.163381i	−0.812196	+	0.583385i	$0.801728\pi$
$654$	1.76605	−	1.96140i	0.0690580	−	0.0766967i
$655$	−15.4894	−	11.2537i	−0.605219	−	0.439718i
$656$	13.0967	+	22.6842i	0.511342	+	0.885670i
$657$	−10.9443	−	18.9560i	−0.426977	−	0.739545i
$658$	0.437694	+	0.318003i	0.0170631	+	0.0123971i
$659$	−8.25337	−	3.67464i	−0.321506	−	0.143144i	0.239637	−	0.970863i	$-0.422972\pi$
$659$	−8.25337	−	3.67464i	−0.321506	−	0.143144i	−0.561143	+	0.827719i	$0.689638\pi$
$660$	2.90710	+	27.6592i	0.113159	+	1.07663i
$661$	−1.82639	−	2.02841i	−0.0710382	−	0.0788959i	0.706578	−	0.707635i	$-0.250238\pi$
$661$	−1.82639	−	2.02841i	−0.0710382	−	0.0788959i	−0.777616	+	0.628739i	$0.783571\pi$
$662$	−0.326238	−	0.237026i	−0.0126796	−	0.00921227i
$663$	13.7401	+	25.7307i	0.533623	+	0.999298i
$664$	−2.70414	−	8.32248i	−0.104941	−	0.322975i
$665$	5.64454	+	53.7042i	0.218886	+	2.08256i
$666$	2.30909	+	0.490813i	0.0894755	+	0.0190186i
$667$	18.6380	−	20.6996i	0.721667	−	0.801493i
$668$	21.2705	−	15.4539i	0.822981	−	0.597931i
$669$	22.7132	−	25.2255i	0.878141	−	0.975275i
$670$	−8.70226	+	1.84972i	−0.336198	+	0.0714610i
$671$	−15.4894	−	11.2537i	−0.597960	−	0.434443i
$672$	−27.2038	+	5.78234i	−1.04941	+	0.223059i
$673$	−1.03946	−	9.88980i	−0.0400682	−	0.381224i	−0.996119	−	0.0880212i	$-0.971946\pi$
$673$	−1.03946	−	9.88980i	−0.0400682	−	0.381224i	0.956050	−	0.293202i	$-0.0947210\pi$
$674$	1.03946	+	9.88980i	0.0400385	+	0.380941i
$675$	7.23607	+	5.25731i	0.278516	+	0.202354i
$676$	20.3951	−	12.8456i	0.784428	−	0.494061i
$677$	−1.49342			−0.0573969			−0.0286984	−	0.999588i	$-0.509136\pi$
$677$	−1.49342			−0.0573969			−0.0286984	+	0.999588i	$0.509136\pi$
$678$	8.42555	−	3.75130i	0.323581	−	0.144068i
$679$	−4.74803	−	1.00922i	−0.182213	−	0.0387305i
$680$	−15.6295	+	3.32216i	−0.599366	+	0.127399i
$681$	31.8328			1.21984
$682$	−4.72172	+	0.565270i	−0.180804	+	0.0216453i
$683$	−17.9443	−	31.0804i	−0.686618	−	1.18926i	−0.972925	−	0.231120i	$-0.925761\pi$
$683$	−17.9443	−	31.0804i	−0.686618	−	1.18926i	0.286307	−	0.958138i	$-0.407572\pi$
$684$	6.87539	−	21.1603i	0.262887	−	0.809083i
$685$	43.1030	−	47.8707i	1.64688	−	1.82905i
$686$	−5.23415	+	2.33039i	−0.199841	+	0.0889748i
$687$	−28.4164	+	49.2187i	−1.08415	+	1.87781i
$688$	7.77709			0.296499
$689$	9.29311	−	1.65571i	0.354039	−	0.0630775i
$690$	17.0729	−	12.4042i	0.649956	−	0.472221i
$691$	−0.879754	−	8.37030i	−0.0334674	−	0.318421i	−0.998429	−	0.0560303i	$-0.982156\pi$
$691$	−0.879754	−	8.37030i	−0.0334674	−	0.318421i	0.964962	−	0.262391i	$-0.0845110\pi$
$692$	10.6227	+	11.7977i	0.403815	+	0.448482i
$693$	−1.40240	+	13.3429i	−0.0532726	+	0.506855i
$694$	−1.25735	+	3.86974i	−0.0477285	+	0.146893i
$695$	16.6449	−	18.4860i	0.631376	−	0.701215i
$696$	−10.1703	−	4.52809i	−0.385503	−	0.171637i
$697$	9.30902	+	28.6502i	0.352604	+	1.08520i
$698$	−2.03044	+	2.25503i	−0.0768532	+	0.0853541i
$699$	2.89407	+	27.5352i	0.109464	+	1.04148i
$700$	−21.7630	−	4.62587i	−0.822565	−	0.174842i
$701$	−15.0000	+	46.1653i	−0.566542	+	1.74364i	0.0967822	+	0.995306i	$0.469145\pi$
$701$	−15.0000	+	46.1653i	−0.566542	+	1.74364i	−0.663324	+	0.748332i	$0.730855\pi$
$702$	1.04809	−	2.89566i	0.0395578	−	0.109290i
$703$	−5.72949	+	17.6336i	−0.216092	+	0.665062i
$704$	−1.10046	−	10.4702i	−0.0414752	−	0.394610i
$705$	−0.331061	−	3.14983i	−0.0124685	−	0.118630i
$706$	−0.516817	+	4.91719i	−0.0194507	+	0.185061i
$707$	−27.5410			−1.03579
$708$	23.2918	+	40.3426i	0.875359	+	1.51617i
$709$	−4.86126	+	46.2518i	−0.182568	+	1.73702i	0.393238	+	0.919437i	$0.371355\pi$
$709$	−4.86126	+	46.2518i	−0.182568	+	1.73702i	−0.575806	+	0.817586i	$0.695312\pi$
$710$	−4.77051	−	14.6821i	−0.179034	−	0.551010i
$711$	−20.3776	+	4.33139i	−0.764219	+	0.162440i
$712$	−3.57295	+	6.18853i	−0.133902	+	0.231925i
$713$	−27.4863	−	36.7059i	−1.02937	−	1.37465i
$714$	−9.27051			−0.346940
$715$	24.1735	+	0.801025i	0.904038	+	0.0299566i
$716$	−0.186918	−	0.575274i	−0.00698544	−	0.0214990i
$717$	24.6972	−	10.9959i	0.922334	−	0.410649i
$718$	−6.44427	+	11.1618i	−0.240498	+	0.416555i
$719$	4.47214	+	7.74597i	0.166783	+	0.288876i	0.937287	−	0.348559i	$-0.113329\pi$
$719$	4.47214	+	7.74597i	0.166783	+	0.288876i	−0.770504	+	0.637435i	$0.779996\pi$
$720$	15.2705	+	11.0947i	0.569098	+	0.413474i
$721$	10.8098	+	4.81284i	0.402579	+	0.179240i
$722$	−5.93204	−	2.64111i	−0.220768	−	0.0982920i
$723$	−7.17376	+	22.0786i	−0.266795	+	0.821111i
$724$	−2.62846	+	25.0081i	−0.0976860	+	0.929420i
$725$	−9.05191	−	10.0532i	−0.336179	−	0.373365i
$726$	−5.01263	−	1.06547i	−0.186036	−	0.0395432i
$727$	−0.809017	+	0.587785i	−0.0300048	+	0.0217997i	−0.602687	−	0.797978i	$-0.705903\pi$
$727$	−0.809017	+	0.587785i	−0.0300048	+	0.0217997i	0.572682	+	0.819778i	$0.305903\pi$
$728$	1.13908	+	15.8828i	0.0422172	+	0.588655i
$729$	−2.16312	−	6.65740i	−0.0801155	−	0.246570i
$730$	−1.31089	−	12.4723i	−0.0485183	−	0.461621i
$731$	8.74882	+	1.85962i	0.323587	+	0.0687805i
$732$	−34.7227	+	7.38054i	−1.28339	+	0.272793i
$733$	9.68034	+	7.03318i	0.357552	+	0.259776i	0.752030	−	0.659129i	$-0.229075\pi$
$733$	9.68034	+	7.03318i	0.357552	+	0.259776i	−0.394479	+	0.918905i	$0.629075\pi$
$734$	−1.86810	+	0.397076i	−0.0689527	+	0.0146563i
$735$	−12.2565	−	5.45694i	−0.452088	−	0.201282i
$736$	−27.6246	+	20.0705i	−1.01826	+	0.739807i
$737$	1.81469	−	17.2656i	0.0668448	−	0.635986i
$738$	−3.18034	+	5.50851i	−0.117070	+	0.202771i
$739$	23.5172	−	40.7330i	0.865095	−	1.49839i	−0.00185791	−	0.999998i	$-0.500591\pi$
$739$	23.5172	−	40.7330i	0.865095	−	1.49839i	0.866953	−	0.498390i	$-0.166075\pi$
$740$	−13.9058	−	10.1031i	−0.511186	−	0.371398i
$741$	−43.5156	−	21.1280i	−1.59858	−	0.776158i
$742$	−0.927051	+	2.85317i	−0.0340331	+	0.104743i
$743$	6.23607	−	10.8012i	0.228779	−	0.396257i	−0.728667	−	0.684868i	$-0.759860\pi$
$743$	6.23607	−	10.8012i	0.228779	−	0.396257i	0.957447	+	0.288611i	$0.0931933\pi$
$744$	−10.5578	+	14.9815i	−0.387068	+	0.549249i
$745$	4.50000	+	7.79423i	0.164867	+	0.285558i
$746$	1.81966	−	5.60034i	0.0666225	−	0.205043i
$747$	−7.95499	+	8.83491i	−0.291058	+	0.323252i
$748$	1.56793	−	14.9178i	0.0573291	−	0.545450i
$749$	54.2705			1.98300
$750$	1.28115	+	2.21902i	0.0467811	+	0.0810272i
$751$	5.34799	−	2.38108i	0.195151	−	0.0868868i	−0.306834	−	0.951763i	$-0.599270\pi$
$751$	5.34799	−	2.38108i	0.195151	−	0.0868868i	0.501985	+	0.864876i	$0.332603\pi$
$752$	0.155255	+	1.47715i	0.00566158	+	0.0538663i
$753$	−6.01722	+	4.37177i	−0.219280	+	0.159316i
$754$	−2.46113	+	3.95429i	−0.0896290	+	0.144007i
$755$	42.9787	+	31.2259i	1.56416	+	1.13643i
$756$	−8.32244	−	9.24301i	−0.302684	−	0.336165i
$757$	−1.84727	−	0.392650i	−0.0671403	−	0.0142711i	0.174219	−	0.984707i	$-0.444260\pi$
$757$	−1.84727	−	0.392650i	−0.0671403	−	0.0142711i	−0.241359	+	0.970436i	$0.577593\pi$
$758$	−0.646976	−	0.288052i	−0.0234992	−	0.0104625i
$759$	12.7254	+	39.1648i	0.461904	+	1.42159i
$760$	17.7309	−	19.6922i	0.643168	−	0.714311i
$761$	−13.7032	−	6.10105i	−0.496740	−	0.221163i	0.143046	−	0.989716i	$-0.454310\pi$
$761$	−13.7032	−	6.10105i	−0.496740	−	0.221163i	−0.639786	+	0.768553i	$0.720977\pi$
$762$	−0.613969	−	1.88960i	−0.0222417	−	0.0684530i
$763$	−9.06793	+	1.92745i	−0.328281	+	0.0697783i
$764$	12.1038	−	5.38894i	0.437899	−	0.194965i
$765$	14.5256	+	16.1323i	0.525175	+	0.583266i
$766$	0.809017	−	0.587785i	0.0292310	−	0.0212375i
$767$	37.5352	−	15.2431i	1.35532	−	0.550395i
$768$	−10.0623	−	7.31069i	−0.363092	−	0.263802i
$769$	−0.791796	+	1.37143i	−0.0285529	+	0.0494551i	−0.879949	−	0.475069i	$-0.842423\pi$
$769$	−0.791796	+	1.37143i	−0.0285529	+	0.0494551i	0.851396	+	0.524524i	$0.175757\pi$
$770$	−3.84346	+	6.65707i	−0.138509	+	0.239904i
$771$	−1.09241	+	10.3936i	−0.0393422	+	0.374316i
$772$	1.46807	+	4.51826i	0.0528370	+	0.162616i
$773$	7.16614	−	1.52321i	0.257748	−	0.0547861i	−0.0772251	−	0.997014i	$-0.524606\pi$
$773$	7.16614	−	1.52321i	0.257748	−	0.0547861i	0.334973	+	0.942228i	$0.391273\pi$
$774$	0.944272	+	1.63553i	0.0339412	+	0.0587878i
$775$	−19.1246	+	11.4127i	−0.686976	+	0.409956i
$776$	1.19098	+	2.06284i	0.0427538	+	0.0740518i
$777$	−13.8707	−	15.4050i	−0.497610	−	0.552652i
$778$	−8.40889	−	1.78736i	−0.301473	−	0.0640801i
$779$	−40.4164	−	29.3642i	−1.44807	−	1.05208i
$780$	31.0942	−	32.3141i	1.11335	−	1.15703i
$781$	30.1246			1.07794
$782$	−10.3979	+	4.62946i	−0.371830	+	0.165549i
$783$	−0.790476	−	7.52088i	−0.0282493	−	0.268774i
$784$	5.74784	+	2.55910i	0.205280	+	0.0913966i
$785$	17.5106	−	53.8922i	0.624982	−	1.92350i
$786$	−0.569769	+	5.42099i	−0.0203230	+	0.193360i
$787$	5.90257	−	1.25463i	0.210404	−	0.0447228i	−0.101504	−	0.994835i	$-0.532365\pi$
$787$	5.90257	−	1.25463i	0.210404	−	0.0447228i	0.311908	+	0.950112i	$0.399032\pi$
$788$	−4.55166	−	14.0086i	−0.162146	−	0.499035i
$789$	−36.5853	−	16.2888i	−1.30247	−	0.579898i
$790$	−11.6753	−	2.48166i	−0.415389	−	0.0882936i
$791$	−31.6872	−	6.73532i	−1.12667	−	0.239481i
$792$	5.32624	−	3.86974i	0.189260	−	0.137505i
$793$	2.20839	+	30.7927i	0.0784223	+	1.09348i
$794$	−3.92705	+	12.0862i	−0.139366	+	0.428924i
$795$	16.0440	−	7.14323i	0.569021	−	0.253344i
$796$	−22.6243	−	25.1269i	−0.801898	−	0.890598i
$797$	−6.52810	−	2.90650i	−0.231237	−	0.102953i	0.287847	−	0.957676i	$-0.407060\pi$
$797$	−6.52810	−	2.90650i	−0.231237	−	0.102953i	−0.519085	+	0.854723i	$0.673727\pi$
$798$	12.4377	−	9.03651i	0.440290	−	0.319889i
$799$	−0.178556	+	1.69885i	−0.00631685	+	0.0601009i
$800$	8.29180	+	14.3618i	0.293159	+	0.507767i
$801$	9.70820			0.343023
$802$	−0.0188507	+	0.179352i	−0.000665640	+	0.00633314i
$803$	23.9374	+	5.08804i	0.844731	+	0.179553i
$804$	−21.5383	−	23.9207i	−0.759597	−	0.843618i
$805$	−74.1246			−2.61255
$806$	5.60146	+	5.23646i	0.197303	+	0.184446i
$807$	0.527864			0.0185817
$808$	9.04311	+	10.0434i	0.318135	+	0.353325i
$809$	−40.2805	−	8.56187i	−1.41619	−	0.301019i	−0.564656	−	0.825326i	$-0.690991\pi$
$809$	−40.2805	−	8.56187i	−1.41619	−	0.301019i	−0.851529	+	0.524307i	$0.824324\pi$
$810$	1.31757	−	12.5358i	0.0462946	−	0.440464i
$811$	33.2705			1.16829			0.584143	−	0.811651i	$-0.301431\pi$
$811$	33.2705			1.16829			0.584143	+	0.811651i	$0.301431\pi$
$812$	9.40576	+	16.2913i	0.330078	+	0.571711i
$813$	−5.56246	+	52.9233i	−0.195084	+	1.85610i
$814$	−2.13525	+	1.55135i	−0.0748406	+	0.0543749i
$815$	35.4755	+	15.7947i	1.24265	+	0.553265i
$816$	−17.0299	−	18.9137i	−0.596167	−	0.662111i
$817$	−13.5505	+	6.03305i	−0.474070	+	0.211070i
$818$	−2.48278	+	7.64121i	−0.0868083	+	0.267169i
$819$	17.9132	−	12.1291i	0.625939	−	0.423826i
$820$	37.4681	−	27.2221i	1.30844	−	0.950639i
$821$	−20.9147	−	4.44556i	−0.729929	−	0.155151i	−0.172067	−	0.985085i	$-0.555045\pi$
$821$	−20.9147	−	4.44556i	−0.729929	−	0.155151i	−0.557861	+	0.829934i	$0.688378\pi$
$822$	−17.9386	−	3.81297i	−0.625682	−	0.132993i
$823$	−19.1021	−	8.50479i	−0.665857	−	0.296458i	0.0458365	−	0.998949i	$-0.485405\pi$
$823$	−19.1021	−	8.50479i	−0.665857	−	0.296458i	−0.711693	+	0.702490i	$0.752071\pi$
$824$	−1.79431	−	5.52231i	−0.0625077	−	0.192379i
$825$	19.5630	−	4.15823i	0.681095	−	0.144771i
$826$	−1.34584	+	12.8049i	−0.0468279	+	0.445538i
$827$	9.12461	−	28.0827i	0.317294	−	0.976530i	−0.657506	−	0.753449i	$-0.728389\pi$
$827$	9.12461	−	28.0827i	0.317294	−	0.976530i	0.974800	−	0.223081i	$-0.0716114\pi$
$828$	27.9006	+	12.4222i	0.969613	+	0.431700i
$829$	3.24038	+	30.8302i	0.112543	+	1.07078i	0.894385	+	0.447299i	$0.147614\pi$
$829$	3.24038	+	30.8302i	0.112543	+	1.07078i	−0.781841	+	0.623477i	$0.785719\pi$
$830$	−6.22264	+	2.77050i	−0.215991	+	0.0961654i
$831$	−66.3050			−2.30009
$832$	−11.7705	+	12.2323i	−0.408069	+	0.424078i
$833$	5.85410	+	4.25325i	0.202833	+	0.147367i
$834$	−6.92728	−	1.47244i	−0.239872	−	0.0509864i
$835$	−28.4655	−	31.6141i	−0.985089	−	1.09405i
$836$	12.4377	+	21.5427i	0.430167	+	0.745070i
$837$	−12.3992	−	1.12257i	−0.428579	−	0.0388017i
$838$	3.48936	+	6.04374i	0.120538	+	0.208778i
$839$	11.6496	−	2.47619i	0.402188	−	0.0854877i	−0.00237654	−	0.999997i	$-0.500756\pi$
$839$	11.6496	−	2.47619i	0.402188	−	0.0854877i	0.404564	+	0.914510i	$0.367423\pi$
$840$	9.15499	+	28.1762i	0.315877	+	0.972170i
$841$	1.83576	−	17.4661i	0.0633021	−	0.602279i
$842$	−1.12868	+	1.95493i	−0.0388968	+	0.0673712i
$843$	2.50000	−	4.33013i	0.0861046	−	0.149137i
$844$	40.0623	+	29.1070i	1.37900	+	1.00190i
$845$	−24.1202	−	30.6466i	−0.829760	−	1.05428i
$846$	−0.291796	+	0.212002i	−0.0100322	+	0.00728879i
$847$	12.0444	+	13.3766i	0.413849	+	0.459626i
$848$	−7.52402	+	3.34991i	−0.258376	+	0.115036i
$849$	−1.74621	+	0.371168i	−0.0599297	+	0.0127384i
$850$	1.70820	+	5.25731i	0.0585909	+	0.180324i
$851$	−23.2505	−	10.3518i	−0.797017	−	0.354855i
$852$	37.3737	−	41.5077i	1.28040	−	1.42203i
$853$	4.05573	+	12.4822i	0.138865	+	0.427384i	0.996171	−	0.0874236i	$-0.0278634\pi$
$853$	4.05573	+	12.4822i	0.138865	+	0.427384i	−0.857306	+	0.514808i	$0.827863\pi$
$854$	−8.96328	−	3.99071i	−0.306717	−	0.136559i
$855$	−35.2133	−	7.48482i	−1.20427	−	0.255975i
$856$	−17.8197	−	19.7908i	−0.609066	−	0.676437i
$857$	2.71885	+	1.97536i	0.0928740	+	0.0674769i	0.633253	−	0.773945i	$-0.281719\pi$
$857$	2.71885	+	1.97536i	0.0928740	+	0.0674769i	−0.540379	+	0.841422i	$0.681719\pi$
$858$	−3.24361	−	6.07420i	−0.110735	−	0.207370i
$859$	−44.2705	+	32.1644i	−1.51049	+	1.09744i	−0.544531	+	0.838741i	$0.683292\pi$
$859$	−44.2705	+	32.1644i	−1.51049	+	1.09744i	−0.965959	+	0.258695i	$0.916708\pi$
$860$	−1.43735	−	13.6754i	−0.0490131	−	0.466329i
$861$	51.0253	−	22.7179i	1.73894	−	0.774224i
$862$	−2.60739	−	4.51613i	−0.0888081	−	0.153820i
$863$	8.32624			0.283428			0.141714	−	0.989908i	$-0.454739\pi$
$863$	8.32624			0.283428			0.141714	+	0.989908i	$0.454739\pi$
$864$	−0.969032	+	9.21973i	−0.0329671	+	0.313661i
$865$	17.1879	−	19.0891i	0.584406	−	0.649049i
$866$	−3.62461	+	11.1554i	−0.123169	+	0.379076i
$867$	4.37132	+	7.57135i	0.148458	+	0.257137i
$868$	29.3127	−	9.99415i	0.994937	−	0.339223i
$869$	11.6459	−	20.1713i	0.395060	−	0.684264i
$870$	−2.67783	+	8.24151i	−0.0907869	+	0.279413i
$871$	−23.1795	+	15.6950i	−0.785408	+	0.531804i
$872$	3.68034	+	2.67392i	0.124632	+	0.0905505i
$873$	1.61803	−	2.80252i	0.0547622	−	0.0948508i
$874$	9.43769	−	16.3466i	0.319235	−	0.552931i
$875$	0.940756	−	8.95070i	0.0318034	−	0.302589i
$876$	36.7082	−	26.6701i	1.24026	−	0.901098i
$877$	15.3146	+	6.81851i	0.517138	+	0.230245i	0.648673	−	0.761067i	$-0.275324\pi$
$877$	15.3146	+	6.81851i	0.517138	+	0.230245i	−0.131536	+	0.991311i	$0.541991\pi$
$878$	12.6822	−	2.69569i	0.428005	−	0.0909752i
$879$	29.5967	+	21.5033i	0.998274	+	0.725288i
$880$	−20.6422	+	4.38763i	−0.695847	+	0.147907i
$881$	−9.17695	−	1.95062i	−0.309179	−	0.0657181i	0.0507091	−	0.998713i	$-0.483852\pi$
$881$	−9.17695	−	1.95062i	−0.309179	−	0.0657181i	−0.359888	+	0.932995i	$0.617185\pi$
$882$	0.159705	+	1.51949i	0.00537756	+	0.0511640i
$883$	9.57295	+	29.4625i	0.322155	+	0.991492i	0.972708	+	0.232031i	$0.0745372\pi$
$883$	9.57295	+	29.4625i	0.322155	+	0.991492i	−0.650553	+	0.759461i	$0.725463\pi$
$884$	−20.0276	+	13.5608i	−0.673601	+	0.456099i
$885$	60.9787	−	44.3036i	2.04978	−	1.48925i
$886$	11.1461	+	2.36918i	0.374461	+	0.0795941i
$887$	6.63977	+	7.37422i	0.222942	+	0.247602i	0.844231	−	0.535979i	$-0.180058\pi$
$887$	6.63977	+	7.37422i	0.222942	+	0.247602i	−0.621289	+	0.783581i	$0.713391\pi$
$888$	−1.06329	+	10.1165i	−0.0356815	+	0.339487i
$889$	−2.15654	+	6.63715i	−0.0723281	+	0.222603i
$890$	5.08142	+	2.26239i	0.170330	+	0.0758356i
$891$	22.4702	+	10.0044i	0.752782	+	0.335160i
$892$	22.7705	+	16.5437i	0.762413	+	0.553926i
$893$	−1.41641	−	2.45329i	−0.0473983	−	0.0820962i
$894$	1.28115	−	2.21902i	0.0428482	−	0.0742152i
$895$	−0.894100	+	0.398079i	−0.0298865	+	0.0133063i
$896$	−9.35410	−	28.7890i	−0.312499	−	0.961772i
$897$	35.0869	−	56.3741i	1.17152	−	1.88228i
$898$	−3.43769			−0.114717
$899$	17.9905	+	5.55977i	0.600016	+	0.185429i
$900$	7.41641	−	12.8456i	0.247214	−	0.428187i
$901$	−9.26515	+	1.96937i	−0.308667	+	0.0656092i
$902$	−2.19756	−	6.76340i	−0.0731708	−	0.225196i
$903$	1.73346	−	16.4927i	0.0576859	−	0.548844i
$904$	7.94834	+	13.7669i	0.264358	+	0.457881i
$905$	40.6869			1.35248
$906$	1.58095	−	15.0418i	0.0525236	−	0.499729i
$907$	−3.25563	−	30.9753i	−0.108102	−	1.02852i	−0.905292	−	0.424790i	$-0.860348\pi$
$907$	−3.25563	−	30.9753i	−0.108102	−	1.02852i	0.797191	−	0.603728i	$-0.206319\pi$
$908$	2.75904	+	26.2505i	0.0915620	+	0.871154i
$909$	5.67376	−	17.4620i	0.188187	−	0.579179i
$910$	12.2026	−	2.17408i	0.404513	−	0.0720701i
$911$	−3.06637	+	9.43732i	−0.101593	+	0.312672i	−0.988916	−	0.148477i	$-0.952563\pi$
$911$	−3.06637	+	9.43732i	−0.101593	+	0.312672i	0.887322	+	0.461150i	$0.152563\pi$
$912$	41.2843	+	8.77526i	1.36706	+	0.290578i
$913$	−1.38937	−	13.2190i	−0.0459815	−	0.437484i
$914$	4.84187	−	5.37745i	0.160155	−	0.177870i
$915$	17.7492	+	54.6265i	0.586771	+	1.80590i
$916$	−43.0505	−	19.1673i	−1.42243	−	0.633306i
$917$	12.8111	−	14.2282i	0.423060	−	0.469856i
$918$	−0.954915	+	2.93893i	−0.0315169	+	0.0969990i
$919$	6.04740	−	57.5372i	0.199485	−	1.89798i	−0.197739	−	0.980255i	$-0.563360\pi$
$919$	6.04740	−	57.5372i	0.199485	−	1.89798i	0.397224	−	0.917721i	$-0.369973\pi$
$920$	24.3388	+	27.0310i	0.802428	+	0.891187i
$921$	2.03539	+	19.3655i	0.0670685	+	0.638114i
$922$	6.14590	−	4.46526i	0.202404	−	0.147055i
$923$	−31.2893	−	37.1545i	−1.02990	−	1.22296i
$924$	−27.8115			−0.914932
$925$	−6.18034	+	10.7047i	−0.203208	+	0.351967i
$926$	6.52810	−	2.90650i	0.214527	−	0.0955135i
$927$	−5.27847	+	5.86233i	−0.173368	+	0.192544i
$928$	4.33282	−	13.3350i	0.142232	−	0.437744i
$929$	9.53444	+	16.5141i	0.312815	+	0.541811i	0.978971	−	0.204001i	$-0.0653947\pi$
$929$	9.53444	+	16.5141i	0.312815	+	0.541811i	−0.666156	+	0.745813i	$0.732061\pi$
$930$	12.4566	+	6.95414i	0.408469	+	0.228035i
$931$	−12.0000			−0.393284
$932$	−22.4558	+	4.77312i	−0.735563	+	0.156349i
$933$	−72.3284	−	15.3739i	−2.36793	−	0.503318i
$934$	−13.7421	+	6.11837i	−0.449654	+	0.200199i
$935$	−24.2705			−0.793731
$936$	−10.3050	−	2.54981i	−0.336828	−	0.0833433i
$937$	−0.218847	−	0.159002i	−0.00714942	−	0.00519436i	0.584205	−	0.811606i	$-0.301406\pi$
$937$	−0.218847	−	0.159002i	−0.00714942	−	0.00519436i	−0.591354	+	0.806412i	$0.701406\pi$
$938$	−0.929956	−	8.84794i	−0.0303641	−	0.288895i
$939$	0.535668	+	5.09654i	0.0174809	+	0.166319i
$940$	2.56878	−	0.546010i	0.0837843	−	0.0178089i
$941$	−8.59017	−	6.24112i	−0.280032	−	0.203455i	0.438900	−	0.898536i	$-0.355368\pi$
$941$	−8.59017	−	6.24112i	−0.280032	−	0.203455i	−0.718931	+	0.695081i	$0.755368\pi$
$942$	−15.7802	+	3.35419i	−0.514147	+	0.109285i
$943$	45.8859	−	50.9615i	1.49425	−	1.65953i
$944$	−28.5967	+	20.7768i	−0.930745	+	0.676226i
$945$	−13.4660	+	14.9555i	−0.438049	+	0.486502i
$946$	−2.06532	−	0.438996i	−0.0671492	−	0.0142730i
$947$	1.71598	+	16.3265i	0.0557619	+	0.530539i	0.986372	+	0.164528i	$0.0526101\pi$
$947$	1.71598	+	16.3265i	0.0557619	+	0.530539i	−0.930610	+	0.366011i	$0.880723\pi$
$948$	−13.3450	−	41.0717i	−0.433426	−	1.33395i
$949$	−18.5875	−	34.8082i	−0.603375	−	1.12992i
$950$	−7.41641	−	5.38834i	−0.240620	−	0.174821i
$951$	18.3594	+	20.3902i	0.595344	+	0.661197i
$952$	−1.67023	−	15.8912i	−0.0541325	−	0.515036i
$953$	13.9188	+	6.19707i	0.450875	+	0.200743i	0.619595	−	0.784921i	$-0.287297\pi$
$953$	13.9188	+	6.19707i	0.450875	+	0.200743i	−0.168720	+	0.985664i	$0.553963\pi$
$954$	−1.61803	−	1.17557i	−0.0523858	−	0.0380605i
$955$	−10.7188	−	18.5656i	−0.346854	−	0.600768i
$956$	11.2082	+	19.4132i	0.362499	+	0.627867i
$957$	−13.6803	−	9.93935i	−0.442223	−	0.321294i
$958$	5.15780	−	5.72831i	0.166641	−	0.185073i
$959$	43.1030	+	47.8707i	1.39187	+	1.54583i
$960$	−15.7918	+	27.3522i	−0.509678	+	0.882788i
$961$	14.7188	−	27.2829i	0.474802	−	0.880093i
$962$	4.13119	+	1.02220i	0.133195	+	0.0329572i
$963$	−11.1803	+	34.4095i	−0.360281	+	1.10883i
$964$	−18.8286	−	4.00214i	−0.606428	−	0.128900i
$965$	7.02235	−	3.12655i	0.226057	−	0.100647i
$966$	10.5517	+	18.2760i	0.339494	+	0.588021i
$967$	−54.1033			−1.73985			−0.869923	−	0.493188i	$-0.835832\pi$
$967$	−54.1033			−1.73985			−0.869923	+	0.493188i	$0.835832\pi$
$968$	0.923281	−	8.78443i	0.0296754	−	0.282342i
$969$	44.3444	+	19.7434i	1.42455	+	0.634250i
$970$	1.50000	−	1.08981i	0.0481621	−	0.0349918i
$971$	42.5013	−	9.03394i	1.36393	−	0.289913i	0.532920	−	0.846166i	$-0.321095\pi$
$971$	42.5013	−	9.03394i	1.36393	−	0.289913i	0.831013	+	0.556253i	$0.187761\pi$
$972$	30.2997	−	13.4903i	0.971864	−	0.432702i
$973$	16.6449	+	18.4860i	0.533610	+	0.592634i
$974$	−3.50000	−	10.7719i	−0.112147	−	0.345154i
$975$	−25.4479	−	19.8092i	−0.814986	−	0.634401i
$976$	−8.32373	−	25.6178i	−0.266436	−	0.820006i
$977$	18.2994	+	3.88965i	0.585449	+	0.124441i	0.491108	−	0.871099i	$-0.336592\pi$
$977$	18.2994	+	3.88965i	0.585449	+	0.124441i	0.0943414	+	0.995540i	$0.469925\pi$
$978$	−1.15564	−	10.9952i	−0.0369532	−	0.351587i
$979$	−7.26281	+	8.06617i	−0.232120	+	0.257796i
$980$	3.43769	−	10.5801i	0.109813	−	0.337970i
$981$	0.646021	−	6.14648i	0.0206259	−	0.196242i
$982$	10.1680	−	2.16127i	0.324473	−	0.0689688i
$983$	−26.9164	+	19.5559i	−0.858500	+	0.623737i	−0.927476	−	0.373881i	$-0.878027\pi$
$983$	−26.9164	+	19.5559i	−0.858500	+	0.623737i	0.0689764	+	0.997618i	$0.478027\pi$
$984$	−25.0387	−	11.1480i	−0.798205	−	0.355384i
$985$	−21.7724	+	9.69368i	−0.693725	+	0.308866i
$986$	2.33688	−	4.04760i	0.0744215	−	0.128902i
$987$	3.16718			0.100813
$988$	13.6514	−	37.7158i	0.434307	−	1.19990i
$989$	−6.29180	−	19.3642i	−0.200067	−	0.615744i
$990$	−3.42903	−	3.80833i	−0.108982	−	0.121037i
$991$	18.3156	−	31.7235i	0.581814	−	1.00773i	−0.413450	−	0.910527i	$-0.635676\pi$
$991$	18.3156	−	31.7235i	0.581814	−	1.00773i	0.995264	−	0.0972048i	$-0.0309902\pi$
$992$	−20.1553	−	11.2520i	−0.639930	−	0.357252i
$993$	−2.36068			−0.0749139
$994$	15.1003	−	3.20968i	0.478954	−	0.101805i
$995$	−36.6069	+	40.6561i	−1.16052	+	1.28889i
$996$	−19.9377	−	14.4856i	−0.631750	−	0.458993i
$997$	−14.3435	−	24.8436i	−0.454262	−	0.786805i	0.544384	−	0.838836i	$-0.316764\pi$
$997$	−14.3435	−	24.8436i	−0.454262	−	0.786805i	−0.998645	+	0.0520317i	$0.983430\pi$
$998$	7.79837	−	13.5072i	0.246853	−	0.427562i
$999$	−6.31244	+	2.81048i	−0.199717	+	0.0889197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.bl.a.256.1	yes	8
13.3	even	3	inner	403.2.bl.a.380.1	yes	8
31.4	even	5	inner	403.2.bl.a.35.1	✓	8
403.159	even	15	inner	403.2.bl.a.159.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.bl.a.35.1	✓	8	31.4	even	5	inner
403.2.bl.a.159.1	yes	8	403.159	even	15	inner
403.2.bl.a.256.1	yes	8	1.1	even	1	trivial
403.2.bl.a.380.1	yes	8	13.3	even	3	inner

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.bl (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.255585 - 0.283856i) q^{2} +(-2.18720 - 0.464905i) q^{3} +(0.193806 - 1.84395i) q^{4} -3.00000 q^{5} +(0.427051 + 0.739674i) q^{6} +(0.313585 - 2.98357i) q^{7} +(-1.19098 + 0.865300i) q^{8} +(1.82709 + 0.813473i) q^{9} +O(q^{10})\)	\(q+(-0.255585 - 0.283856i) q^{2} +(-2.18720 - 0.464905i) q^{3} +(0.193806 - 1.84395i) q^{4} -3.00000 q^{5} +(0.427051 + 0.739674i) q^{6} +(0.313585 - 2.98357i) q^{7} +(-1.19098 + 0.865300i) q^{8} +(1.82709 + 0.813473i) q^{9} +(0.766755 + 0.851568i) q^{10} +(-2.04275 + 0.909491i) q^{11} +(-1.28115 + 3.94298i) q^{12} +(3.24346 + 1.57479i) q^{13} +(-0.927051 + 0.673542i) q^{14} +(6.56161 + 1.39471i) q^{15} +(-3.07715 - 0.654069i) q^{16} +(-3.30524 - 1.47159i) q^{17} +(-0.236068 - 0.726543i) q^{18} +(5.86889 - 1.24747i) q^{19} +(-0.581419 + 5.53184i) q^{20} +(-2.07295 + 6.37988i) q^{21} +(0.780261 + 0.347395i) q^{22} +(0.860904 + 8.19095i) q^{23} +(3.00721 - 1.33889i) q^{24} +4.00000 q^{25} +(-0.381966 - 1.32317i) q^{26} +(1.80902 + 1.31433i) q^{27} +(-5.44076 - 1.15647i) q^{28} +(-2.26298 - 2.51329i) q^{29} +(-1.28115 - 2.21902i) q^{30} +(-4.78115 + 2.85317i) q^{31} +(2.07295 + 3.59045i) q^{32} +(4.89074 - 1.03956i) q^{33} +(0.427051 + 1.31433i) q^{34} +(-0.940756 + 8.95070i) q^{35} +(1.85410 - 3.21140i) q^{36} +(-1.54508 + 2.67617i) q^{37} +(-1.85410 - 1.34708i) q^{38} +(-6.36198 - 4.95229i) q^{39} +(3.57295 - 2.59590i) q^{40} +(-5.57134 - 6.18760i) q^{41} +(2.34078 - 1.04218i) q^{42} +(-2.41811 + 0.513986i) q^{43} +(1.28115 + 3.94298i) q^{44} +(-5.48127 - 2.44042i) q^{45} +(2.10502 - 2.33786i) q^{46} +(-0.145898 - 0.449028i) q^{47} +(6.42628 + 2.86117i) q^{48} +(-1.95630 - 0.415823i) q^{49} +(-1.02234 - 1.13542i) q^{50} +(6.54508 + 4.75528i) q^{51} +(3.53243 - 5.67556i) q^{52} +(2.11803 - 1.53884i) q^{53} +(-0.0892780 - 0.849423i) q^{54} +(6.12825 - 2.72847i) q^{55} +(2.20820 + 3.82472i) q^{56} -13.4164 q^{57} +(-0.135029 + 1.28472i) q^{58} +(7.51840 - 8.35003i) q^{59} +(3.84346 - 11.8290i) q^{60} +(4.28115 + 7.41517i) q^{61} +(2.03188 + 0.627931i) q^{62} +(3.00000 - 5.19615i) q^{63} +(-1.45492 + 4.47777i) q^{64} +(-9.73038 - 4.72437i) q^{65} +(-1.54508 - 1.12257i) q^{66} +(-3.88197 + 6.72376i) q^{67} +(-3.35410 + 5.80948i) q^{68} +(1.92504 - 18.3155i) q^{69} +(2.78115 - 2.02063i) q^{70} +(-12.3074 - 5.47961i) q^{71} +(-2.87993 + 0.612149i) q^{72} +(-8.85410 - 6.43288i) q^{73} +(1.15455 - 0.245406i) q^{74} +(-8.74882 - 1.85962i) q^{75} +(-1.16284 - 11.0637i) q^{76} +(2.07295 + 6.37988i) q^{77} +(0.220290 + 3.07162i) q^{78} +(-8.42705 + 6.12261i) q^{79} +(9.23146 + 1.96221i) q^{80} +(-7.36044 - 8.17459i) q^{81} +(-0.332436 + 3.16292i) q^{82} +(-1.83688 + 5.65334i) q^{83} +(11.3624 + 5.05887i) q^{84} +(9.91572 + 4.41476i) q^{85} +(0.763932 + 0.555029i) q^{86} +(3.78115 + 6.54915i) q^{87} +(1.64590 - 2.85078i) q^{88} +(4.43444 - 1.97434i) q^{89} +(0.708204 + 2.17963i) q^{90} +(5.71560 - 9.18324i) q^{91} +15.2705 q^{92} +(11.7838 - 4.01769i) q^{93} +(-0.0901699 + 0.156179i) q^{94} +(-17.6067 + 3.74241i) q^{95} +(-2.86475 - 8.81678i) q^{96} +(0.169131 - 1.60917i) q^{97} +(0.381966 + 0.661585i) q^{98} -4.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 5 q^{3} - 6 q^{4} - 24 q^{5} - 10 q^{6} - 3 q^{7} - 14 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 5 * q^3 - 6 * q^4 - 24 * q^5 - 10 * q^6 - 3 * q^7 - 14 * q^8 + 2 * q^9	\( 8 q - 4 q^{2} - 5 q^{3} - 6 q^{4} - 24 q^{5} - 10 q^{6} - 3 q^{7} - 14 q^{8} + 2 q^{9} + 12 q^{10} - 5 q^{11} + 30 q^{12} - 5 q^{13} + 6 q^{14} + 15 q^{15} + 14 q^{16} - 5 q^{17} + 16 q^{18} - 6 q^{19} + 18 q^{20} - 30 q^{21} + 5 q^{22} - 11 q^{23} - 5 q^{24} + 32 q^{25} - 12 q^{26} + 10 q^{27} - 27 q^{28} - 7 q^{29} + 30 q^{30} + 2 q^{31} + 30 q^{32} - 5 q^{33} - 10 q^{34} + 9 q^{35} - 12 q^{36} + 10 q^{37} + 12 q^{38} - 10 q^{39} + 42 q^{40} + 17 q^{41} + 15 q^{42} - 12 q^{43} - 30 q^{44} - 6 q^{45} + 14 q^{46} - 28 q^{47} + 25 q^{48} + 2 q^{49} - 16 q^{50} + 30 q^{51} + 63 q^{52} + 8 q^{53} + 5 q^{54} + 15 q^{55} - 36 q^{56} - 7 q^{58} + 4 q^{59} - 90 q^{60} - 6 q^{61} - 16 q^{62} + 24 q^{63} - 34 q^{64} + 15 q^{65} + 10 q^{66} - 40 q^{67} - 35 q^{69} - 18 q^{70} - 19 q^{71} - 26 q^{72} - 44 q^{73} + 35 q^{74} - 20 q^{75} + 36 q^{76} + 30 q^{77} + 70 q^{78} - 54 q^{79} - 42 q^{80} - 11 q^{81} + 17 q^{82} - 46 q^{83} + 15 q^{85} + 24 q^{86} - 10 q^{87} + 40 q^{88} + 9 q^{89} - 48 q^{90} - 21 q^{91} - 12 q^{92} - 5 q^{93} + 44 q^{94} + 18 q^{95} - 90 q^{96} - 3 q^{97} + 12 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 - 5 * q^3 - 6 * q^4 - 24 * q^5 - 10 * q^6 - 3 * q^7 - 14 * q^8 + 2 * q^9 + 12 * q^10 - 5 * q^11 + 30 * q^12 - 5 * q^13 + 6 * q^14 + 15 * q^15 + 14 * q^16 - 5 * q^17 + 16 * q^18 - 6 * q^19 + 18 * q^20 - 30 * q^21 + 5 * q^22 - 11 * q^23 - 5 * q^24 + 32 * q^25 - 12 * q^26 + 10 * q^27 - 27 * q^28 - 7 * q^29 + 30 * q^30 + 2 * q^31 + 30 * q^32 - 5 * q^33 - 10 * q^34 + 9 * q^35 - 12 * q^36 + 10 * q^37 + 12 * q^38 - 10 * q^39 + 42 * q^40 + 17 * q^41 + 15 * q^42 - 12 * q^43 - 30 * q^44 - 6 * q^45 + 14 * q^46 - 28 * q^47 + 25 * q^48 + 2 * q^49 - 16 * q^50 + 30 * q^51 + 63 * q^52 + 8 * q^53 + 5 * q^54 + 15 * q^55 - 36 * q^56 - 7 * q^58 + 4 * q^59 - 90 * q^60 - 6 * q^61 - 16 * q^62 + 24 * q^63 - 34 * q^64 + 15 * q^65 + 10 * q^66 - 40 * q^67 - 35 * q^69 - 18 * q^70 - 19 * q^71 - 26 * q^72 - 44 * q^73 + 35 * q^74 - 20 * q^75 + 36 * q^76 + 30 * q^77 + 70 * q^78 - 54 * q^79 - 42 * q^80 - 11 * q^81 + 17 * q^82 - 46 * q^83 + 15 * q^85 + 24 * q^86 - 10 * q^87 + 40 * q^88 + 9 * q^89 - 48 * q^90 - 21 * q^91 - 12 * q^92 - 5 * q^93 + 44 * q^94 + 18 * q^95 - 90 * q^96 - 3 * q^97 + 12 * q^98

Introduction

L-functions

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