LMFDB - Embedded newform 151.2.g.a.76.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [151,2,Mod(2,151)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(151, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([14]))

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

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

chi := DirichletCharacter("151.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	151.g (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:	$1.20574107052$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			76.6
Character	$\chi$	$=$	151.76
Dual form			151.2.g.a.2.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.183451 - 0.317746i) q^{2} +(0.0745133 + 0.0541371i) q^{3} +(0.932692 - 1.61547i) q^{4} +(0.164782 - 0.183009i) q^{5} +(0.00353232 - 0.0336078i) q^{6} +(0.250565 - 0.278280i) q^{7} -1.41821 q^{8} +(-0.924430 - 2.84510i) q^{9} +O(q^{10})$	\(q+(-0.183451 - 0.317746i) q^{2} +(0.0745133 + 0.0541371i) q^{3} +(0.932692 - 1.61547i) q^{4} +(0.164782 - 0.183009i) q^{5} +(0.00353232 - 0.0336078i) q^{6} +(0.250565 - 0.278280i) q^{7} -1.41821 q^{8} +(-0.924430 - 2.84510i) q^{9} +(-0.0883795 - 0.0187856i) q^{10} +(4.11086 + 1.83027i) q^{11} +(0.156955 - 0.0698807i) q^{12} +(-2.59806 + 1.15673i) q^{13} +(-0.134389 - 0.0285652i) q^{14} +(0.0221860 - 0.00471577i) q^{15} +(-1.60521 - 2.78031i) q^{16} +(7.33460 - 1.55902i) q^{17} +(-0.734432 + 0.815669i) q^{18} -5.82054 q^{19} +(-0.141954 - 0.436890i) q^{20} +(0.0337357 - 0.00717074i) q^{21} +(-0.172578 - 1.64197i) q^{22} +(2.90798 + 5.03677i) q^{23} +(-0.105676 - 0.0767779i) q^{24} +(0.516303 + 4.91230i) q^{25} +(0.844163 + 0.613320i) q^{26} +(0.170528 - 0.524831i) q^{27} +(-0.215854 - 0.664330i) q^{28} +(-5.61112 + 4.07672i) q^{29} +(-0.00556844 - 0.00618438i) q^{30} +(-1.74372 + 0.370639i) q^{31} +(-2.00717 + 3.47652i) q^{32} +(0.207228 + 0.358930i) q^{33} +(-1.84091 - 2.04454i) q^{34} +(-0.00963922 - 0.0917110i) q^{35} +(-5.45838 - 1.16022i) q^{36} +(-0.479030 + 4.55767i) q^{37} +(1.06778 + 1.84945i) q^{38} +(-0.256212 - 0.0544596i) q^{39} +(-0.233696 + 0.259545i) q^{40} +(-6.31752 - 4.58994i) q^{41} +(-0.00846731 - 0.00940390i) q^{42} +(4.03169 + 4.47765i) q^{43} +(6.79092 - 4.93389i) q^{44} +(-0.673007 - 0.299642i) q^{45} +(1.06694 - 1.84800i) q^{46} +(5.37631 - 2.39369i) q^{47} +(0.0309081 - 0.294071i) q^{48} +(0.717042 + 6.82220i) q^{49} +(1.46615 - 1.06522i) q^{50} +(0.630926 + 0.280906i) q^{51} +(-0.554526 + 5.27597i) q^{52} +(-8.67653 + 6.30387i) q^{53} +(-0.198046 + 0.0420960i) q^{54} +(1.01235 - 0.450728i) q^{55} +(-0.355355 + 0.394661i) q^{56} +(-0.433707 - 0.315107i) q^{57} +(2.32472 + 1.03503i) q^{58} +8.75756 q^{59} +(0.0130745 - 0.0402391i) q^{60} +(-1.46496 - 13.9382i) q^{61} +(0.437655 + 0.486065i) q^{62} +(-1.02337 - 0.455632i) q^{63} -4.94798 q^{64} +(-0.216421 + 0.666076i) q^{65} +(0.0760323 - 0.131692i) q^{66} +(4.29654 - 13.2234i) q^{67} +(4.32238 - 13.3029i) q^{68} +(-0.0559928 + 0.532736i) q^{69} +(-0.0273725 + 0.0198873i) q^{70} +(8.73189 + 1.85602i) q^{71} +(1.31104 + 4.03496i) q^{72} +(-3.78541 - 11.6503i) q^{73} +(1.53606 - 0.683897i) q^{74} +(-0.227466 + 0.393982i) q^{75} +(-5.42877 + 9.40290i) q^{76} +(1.53937 - 0.685371i) q^{77} +(0.0296980 + 0.0914010i) q^{78} +(0.608724 + 1.87346i) q^{79} +(-0.773329 - 0.164376i) q^{80} +(-7.21944 + 5.24523i) q^{81} +(-0.299483 + 2.84939i) q^{82} +(1.24078 - 3.81871i) q^{83} +(0.0198809 - 0.0611871i) q^{84} +(0.923294 - 1.59919i) q^{85} +(0.683137 - 2.10248i) q^{86} -0.638804 q^{87} +(-5.83008 - 2.59572i) q^{88} +(-2.38726 - 2.65133i) q^{89} +(0.0282536 + 0.268815i) q^{90} +(-0.329087 + 1.01283i) q^{91} +10.8490 q^{92} +(-0.149995 - 0.0667823i) q^{93} +(-1.74687 - 1.26918i) q^{94} +(-0.959117 + 1.06521i) q^{95} +(-0.337769 + 0.150384i) q^{96} +(5.86301 - 1.24622i) q^{97} +(2.03618 - 1.47937i) q^{98} +(1.40711 - 13.3878i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 3 q^{2} - 4 q^{3} - 49 q^{4} - 9 q^{5} + 7 q^{6} - 7 q^{7} + 12 q^{8} - 32 q^{9}+O(q^{10}) $ 96 * q - 3 * q^2 - 4 * q^3 - 49 * q^4 - 9 * q^5 + 7 * q^6 - 7 * q^7 + 12 * q^8 - 32 * q^9	\( 96 q - 3 q^{2} - 4 q^{3} - 49 q^{4} - 9 q^{5} + 7 q^{6} - 7 q^{7} + 12 q^{8} - 32 q^{9} + 11 q^{10} - 7 q^{11} + 7 q^{12} - 8 q^{13} + 5 q^{14} + 10 q^{15} - 47 q^{16} - 26 q^{17} - 40 q^{18} - 20 q^{19} + 23 q^{20} - 2 q^{21} - 32 q^{22} - q^{23} + 95 q^{24} - 51 q^{25} + 41 q^{26} + 5 q^{27} - 2 q^{28} + 13 q^{29} + 19 q^{30} - 24 q^{31} - 60 q^{32} + 39 q^{33} + 47 q^{34} - 54 q^{35} + 11 q^{36} + 5 q^{37} + 8 q^{38} - 13 q^{39} - 74 q^{40} + 8 q^{41} + 166 q^{42} - 8 q^{43} + 18 q^{44} - 33 q^{45} + 21 q^{46} - 5 q^{47} + 8 q^{48} + 21 q^{49} - 72 q^{50} - 6 q^{51} + 96 q^{52} + 41 q^{53} - 60 q^{54} - 116 q^{55} - 85 q^{56} - 8 q^{57} - 58 q^{58} + 32 q^{59} - 6 q^{60} - 18 q^{61} + 38 q^{62} - 129 q^{63} + 160 q^{64} + 53 q^{65} + 43 q^{66} + 4 q^{67} + 10 q^{68} + 81 q^{69} + 33 q^{70} - 41 q^{71} - 40 q^{72} - 58 q^{73} - 20 q^{74} + 32 q^{75} - q^{76} - 22 q^{77} - 10 q^{78} + 32 q^{79} + 71 q^{80} - 66 q^{81} - 10 q^{82} + 80 q^{83} - 58 q^{84} - 2 q^{85} - 72 q^{86} + 72 q^{87} + 89 q^{88} + 9 q^{89} + 121 q^{90} - 138 q^{91} - 72 q^{92} - 85 q^{93} + 11 q^{94} - 47 q^{95} - 201 q^{96} + 54 q^{97} - 92 q^{98} - 21 q^{99}+O(q^{100}) \) 96 * q - 3 * q^2 - 4 * q^3 - 49 * q^4 - 9 * q^5 + 7 * q^6 - 7 * q^7 + 12 * q^8 - 32 * q^9 + 11 * q^10 - 7 * q^11 + 7 * q^12 - 8 * q^13 + 5 * q^14 + 10 * q^15 - 47 * q^16 - 26 * q^17 - 40 * q^18 - 20 * q^19 + 23 * q^20 - 2 * q^21 - 32 * q^22 - q^23 + 95 * q^24 - 51 * q^25 + 41 * q^26 + 5 * q^27 - 2 * q^28 + 13 * q^29 + 19 * q^30 - 24 * q^31 - 60 * q^32 + 39 * q^33 + 47 * q^34 - 54 * q^35 + 11 * q^36 + 5 * q^37 + 8 * q^38 - 13 * q^39 - 74 * q^40 + 8 * q^41 + 166 * q^42 - 8 * q^43 + 18 * q^44 - 33 * q^45 + 21 * q^46 - 5 * q^47 + 8 * q^48 + 21 * q^49 - 72 * q^50 - 6 * q^51 + 96 * q^52 + 41 * q^53 - 60 * q^54 - 116 * q^55 - 85 * q^56 - 8 * q^57 - 58 * q^58 + 32 * q^59 - 6 * q^60 - 18 * q^61 + 38 * q^62 - 129 * q^63 + 160 * q^64 + 53 * q^65 + 43 * q^66 + 4 * q^67 + 10 * q^68 + 81 * q^69 + 33 * q^70 - 41 * q^71 - 40 * q^72 - 58 * q^73 - 20 * q^74 + 32 * q^75 - q^76 - 22 * q^77 - 10 * q^78 + 32 * q^79 + 71 * q^80 - 66 * q^81 - 10 * q^82 + 80 * q^83 - 58 * q^84 - 2 * q^85 - 72 * q^86 + 72 * q^87 + 89 * q^88 + 9 * q^89 + 121 * q^90 - 138 * q^91 - 72 * q^92 - 85 * q^93 + 11 * q^94 - 47 * q^95 - 201 * q^96 + 54 * q^97 - 92 * q^98 - 21 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/151\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{8}{15}\right)$

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 $

$2$	−0.183451	−	0.317746i	−0.129719	−	0.224680i	0.793849	−	0.608115i	$-0.208074\pi$
$2$	−0.183451	−	0.317746i	−0.129719	−	0.224680i	−0.923568	+	0.383435i	$0.874741\pi$
$3$	0.0745133	+	0.0541371i	0.0430203	+	0.0312560i	0.609088	−	0.793103i	$-0.291536\pi$
$3$	0.0745133	+	0.0541371i	0.0430203	+	0.0312560i	−0.566067	+	0.824359i	$0.691536\pi$
$4$	0.932692	−	1.61547i	0.466346	−	0.807735i
$5$	0.164782	−	0.183009i	0.0736926	−	0.0818439i	−0.705171	−	0.709037i	$-0.749130\pi$
$5$	0.164782	−	0.183009i	0.0736926	−	0.0818439i	0.778864	+	0.627193i	$0.215796\pi$
$6$	0.00353232	−	0.0336078i	0.00144206	−	0.0137203i
$7$	0.250565	−	0.278280i	0.0947046	−	0.105180i	−0.693929	−	0.720043i	$-0.744122\pi$
$7$	0.250565	−	0.278280i	0.0947046	−	0.105180i	0.788634	+	0.614863i	$0.210789\pi$
$8$	−1.41821			−0.501414
$9$	−0.924430	−	2.84510i	−0.308143	−	0.948367i
$10$	−0.0883795	−	0.0187856i	−0.0279480	−	0.00594054i
$11$	4.11086	+	1.83027i	1.23947	+	0.551849i	0.918568	−	0.395263i	$-0.129347\pi$
$11$	4.11086	+	1.83027i	1.23947	+	0.551849i	0.320904	+	0.947112i	$0.396013\pi$
$12$	0.156955	−	0.0698807i	0.0453089	−	0.0201728i
$13$	−2.59806	+	1.15673i	−0.720573	+	0.320820i	−0.734056	−	0.679089i	$-0.762375\pi$
$13$	−2.59806	+	1.15673i	−0.720573	+	0.320820i	0.0134827	+	0.999909i	$0.495708\pi$
$14$	−0.134389	−	0.0285652i	−0.0359169	−	0.00763437i
$15$	0.0221860	−	0.00471577i	0.00572839	−	0.00121761i
$16$	−1.60521	−	2.78031i	−0.401303	−	0.695077i
$17$	7.33460	−	1.55902i	1.77890	−	0.378117i	0.802941	−	0.596059i	$-0.203268\pi$
$17$	7.33460	−	1.55902i	1.77890	−	0.378117i	0.975962	+	0.217942i	$0.0699343\pi$
$18$	−0.734432	+	0.815669i	−0.173107	+	0.192255i
$19$	−5.82054			−1.33532			−0.667661	−	0.744465i	$-0.732704\pi$
$19$	−5.82054			−1.33532			−0.667661	+	0.744465i	$0.732704\pi$
$20$	−0.141954	−	0.436890i	−0.0317419	−	0.0976916i
$21$	0.0337357	−	0.00717074i	0.00736173	−	0.00156478i
$22$	−0.172578	−	1.64197i	−0.0367939	−	0.350070i
$23$	2.90798	+	5.03677i	0.606356	+	1.05024i	0.991836	+	0.127523i	$0.0407027\pi$
$23$	2.90798	+	5.03677i	0.606356	+	1.05024i	−0.385479	+	0.922716i	$0.625964\pi$
$24$	−0.105676	−	0.0767779i	−0.0215710	−	0.0156722i
$25$	0.516303	+	4.91230i	0.103261	+	0.982459i
$26$	0.844163	+	0.613320i	0.165554	+	0.120282i
$27$	0.170528	−	0.524831i	0.0328181	−	0.101004i
$28$	−0.215854	−	0.664330i	−0.0407925	−	0.125547i
$29$	−5.61112	+	4.07672i	−1.04196	+	0.757027i	−0.970667	−	0.240428i	$-0.922712\pi$
$29$	−5.61112	+	4.07672i	−1.04196	+	0.757027i	−0.0712919	+	0.997455i	$0.522712\pi$
$30$	−0.00556844	−	0.00618438i	−0.00101665	−	0.00112911i
$31$	−1.74372	+	0.370639i	−0.313181	+	0.0665687i	−0.361821	−	0.932248i	$-0.617845\pi$
$31$	−1.74372	+	0.370639i	−0.313181	+	0.0665687i	0.0486396	+	0.998816i	$0.484511\pi$
$32$	−2.00717	+	3.47652i	−0.354820	+	0.614567i
$33$	0.207228	+	0.358930i	0.0360738	+	0.0624817i
$34$	−1.84091	−	2.04454i	−0.315713	−	0.350635i
$35$	−0.00963922	−	0.0917110i	−0.00162932	−	0.0155020i
$36$	−5.45838	−	1.16022i	−0.909730	−	0.193369i
$37$	−0.479030	+	4.55767i	−0.0787521	+	0.749276i	0.881884	+	0.471466i	$0.156275\pi$
$37$	−0.479030	+	4.55767i	−0.0787521	+	0.749276i	−0.960636	+	0.277810i	$0.910392\pi$
$38$	1.06778	+	1.84945i	0.173217	+	0.300020i
$39$	−0.256212	−	0.0544596i	−0.0410268	−	0.00872051i
$40$	−0.233696	+	0.259545i	−0.0369505	+	0.0410377i
$41$	−6.31752	−	4.58994i	−0.986630	−	0.716829i	−0.0274496	−	0.999623i	$-0.508739\pi$
$41$	−6.31752	−	4.58994i	−0.986630	−	0.716829i	−0.959181	+	0.282794i	$0.908739\pi$
$42$	−0.00846731	−	0.00940390i	−0.00130653	−	0.00145105i
$43$	4.03169	+	4.47765i	0.614827	+	0.682835i	0.967488	−	0.252916i	$-0.0813897\pi$
$43$	4.03169	+	4.47765i	0.614827	+	0.682835i	−0.352661	+	0.935751i	$0.614723\pi$
$44$	6.79092	−	4.93389i	1.02377	−	0.743812i
$45$	−0.673007	−	0.299642i	−0.100326	−	0.0446680i
$46$	1.06694	−	1.84800i	0.157312	−	0.272472i
$47$	5.37631	−	2.39369i	0.784215	−	0.349155i	0.0247421	−	0.999694i	$-0.492124\pi$
$47$	5.37631	−	2.39369i	0.784215	−	0.349155i	0.759473	+	0.650539i	$0.225457\pi$
$48$	0.0309081	−	0.294071i	0.00446121	−	0.0424455i
$49$	0.717042	+	6.82220i	0.102435	+	0.974600i
$50$	1.46615	−	1.06522i	0.207344	−	0.150644i
$51$	0.630926	+	0.280906i	0.0883473	+	0.0393348i
$52$	−0.554526	+	5.27597i	−0.0768990	+	0.731645i
$53$	−8.67653	+	6.30387i	−1.19181	+	0.865903i	−0.993455	−	0.114227i	$-0.963561\pi$
$53$	−8.67653	+	6.30387i	−1.19181	+	0.865903i	−0.198358	+	0.980130i	$0.563561\pi$
$54$	−0.198046	+	0.0420960i	−0.0269507	+	0.00572854i
$55$	1.01235	−	0.450728i	0.136505	−	0.0607761i
$56$	−0.355355	+	0.394661i	−0.0474862	+	0.0527388i
$57$	−0.433707	−	0.315107i	−0.0574459	−	0.0417369i
$58$	2.32472	+	1.03503i	0.305251	+	0.135907i
$59$	8.75756			1.14014			0.570068	−	0.821597i	$-0.306917\pi$
$59$	8.75756			1.14014			0.570068	+	0.821597i	$0.306917\pi$
$60$	0.0130745	−	0.0402391i	0.00168791	−	0.00519485i
$61$	−1.46496	−	13.9382i	−0.187569	−	1.78460i	−0.532958	−	0.846142i	$-0.678920\pi$
$61$	−1.46496	−	13.9382i	−0.187569	−	1.78460i	0.345389	−	0.938460i	$-0.387747\pi$
$62$	0.437655	+	0.486065i	0.0555823	+	0.0617303i
$63$	−1.02337	−	0.455632i	−0.128932	−	0.0574042i
$64$	−4.94798			−0.618498
$65$	−0.216421	+	0.666076i	−0.0268437	+	0.0826165i
$66$	0.0760323	−	0.131692i	0.00935893	−	0.0162101i
$67$	4.29654	−	13.2234i	0.524906	−	1.61549i	−0.239596	−	0.970873i	$-0.577015\pi$
$67$	4.29654	−	13.2234i	0.524906	−	1.61549i	0.764502	−	0.644621i	$-0.222985\pi$
$68$	4.32238	−	13.3029i	0.524165	−	1.61321i
$69$	−0.0559928	+	0.532736i	−0.00674074	+	0.0641339i
$70$	−0.0273725	+	0.0198873i	−0.00327164	+	0.00237698i
$71$	8.73189	+	1.85602i	1.03628	+	0.220269i	0.694488	−	0.719505i	$-0.255631\pi$
$71$	8.73189	+	1.85602i	1.03628	+	0.220269i	0.341797	+	0.939774i	$0.388964\pi$
$72$	1.31104	+	4.03496i	0.154507	+	0.475525i
$73$	−3.78541	−	11.6503i	−0.443049	−	1.36356i	−0.884610	−	0.466332i	$-0.845575\pi$
$73$	−3.78541	−	11.6503i	−0.443049	−	1.36356i	0.441561	−	0.897231i	$-0.354425\pi$
$74$	1.53606	−	0.683897i	0.178563	−	0.0795014i
$75$	−0.227466	+	0.393982i	−0.0262655	+	0.0454932i
$76$	−5.42877	+	9.40290i	−0.622722	+	1.07859i
$77$	1.53937	−	0.685371i	0.175427	−	0.0781052i
$78$	0.0296980	+	0.0914010i	0.00336263	+	0.0103491i
$79$	0.608724	+	1.87346i	0.0684868	+	0.210781i	0.979443	−	0.201724i	$-0.0646542\pi$
$79$	0.608724	+	1.87346i	0.0684868	+	0.210781i	−0.910956	+	0.412504i	$0.864654\pi$
$80$	−0.773329	−	0.164376i	−0.0864608	−	0.0183778i
$81$	−7.21944	+	5.24523i	−0.802161	+	0.582804i
$82$	−0.299483	+	2.84939i	−0.0330724	+	0.314663i
$83$	1.24078	−	3.81871i	0.136193	−	0.419158i	−0.859581	−	0.511000i	$-0.829275\pi$
$83$	1.24078	−	3.81871i	0.136193	−	0.419158i	0.995774	+	0.0918415i	$0.0292753\pi$
$84$	0.0198809	−	0.0611871i	0.00216918	−	0.00667606i
$85$	0.923294	−	1.59919i	0.100145	−	0.173457i
$86$	0.683137	−	2.10248i	0.0736646	−	0.226716i
$87$	−0.638804			−0.0684870
$88$	−5.83008	−	2.59572i	−0.621489	−	0.276705i
$89$	−2.38726	−	2.65133i	−0.253050	−	0.281040i	0.603214	−	0.797580i	$-0.293887\pi$
$89$	−2.38726	−	2.65133i	−0.253050	−	0.281040i	−0.856263	+	0.516540i	$0.827220\pi$
$90$	0.0282536	+	0.268815i	0.00297819	+	0.0283355i
$91$	−0.329087	+	1.01283i	−0.0344977	+	0.106173i
$92$	10.8490			1.13109
$93$	−0.149995	−	0.0667823i	−0.0155538	−	0.00692500i
$94$	−1.74687	−	1.26918i	−0.180176	−	0.130905i
$95$	−0.959117	+	1.06521i	−0.0984033	+	0.109288i
$96$	−0.337769	+	0.150384i	−0.0344734	+	0.0153486i
$97$	5.86301	−	1.24622i	0.595298	−	0.126535i	0.0995972	−	0.995028i	$-0.468245\pi$
$97$	5.86301	−	1.24622i	0.595298	−	0.126535i	0.495701	+	0.868493i	$0.334911\pi$
$98$	2.03618	−	1.47937i	0.205686	−	0.149439i
$99$	1.40711	−	13.3878i	0.141420	−	1.34552i
$100$	8.41722	+	3.74759i	0.841722	+	0.374759i
$101$	0.936385	−	0.680324i	0.0931738	−	0.0676948i	−0.540223	−	0.841522i	$-0.681660\pi$
$101$	0.936385	−	0.680324i	0.0931738	−	0.0676948i	0.633397	+	0.773827i	$0.281660\pi$
$102$	−0.0264869	−	0.252006i	−0.00262260	−	0.0249524i
$103$	−0.902553	+	8.58722i	−0.0889312	+	0.846124i	0.855586	+	0.517661i	$0.173197\pi$
$103$	−0.902553	+	8.58722i	−0.0889312	+	0.846124i	−0.944517	+	0.328463i	$0.893469\pi$
$104$	3.68461	−	1.64049i	0.361306	−	0.160864i
$105$	0.00424672	−	0.00735553i	0.000414437	−	0.000717826i
$106$	3.59474	+	1.60048i	0.349152	+	0.155453i
$107$	−11.8950	+	8.64222i	−1.14993	+	0.835475i	−0.988472	−	0.151404i	$-0.951621\pi$
$107$	−11.8950	+	8.64222i	−1.14993	+	0.835475i	−0.161461	+	0.986879i	$0.551621\pi$
$108$	−0.688798	−	0.764988i	−0.0662796	−	0.0736110i
$109$	−7.78503	−	8.64615i	−0.745671	−	0.828151i	0.244259	−	0.969710i	$-0.421455\pi$
$109$	−7.78503	−	8.64615i	−0.745671	−	0.828151i	−0.989930	+	0.141559i	$0.954789\pi$
$110$	−0.328933	−	0.238984i	−0.0313625	−	0.0227862i
$111$	−0.282433	+	0.313673i	−0.0268073	+	0.0297726i
$112$	−1.17591	−	0.249948i	−0.111114	−	0.0236179i
$113$	0.238179	+	0.412538i	0.0224060	+	0.0388083i	0.877011	−	0.480470i	$-0.159534\pi$
$113$	0.238179	+	0.412538i	0.0224060	+	0.0388083i	−0.854605	+	0.519279i	$0.826201\pi$
$114$	−0.0205600	+	0.195615i	−0.00192562	+	0.0183210i
$115$	1.40095	+	0.297782i	0.130640	+	0.0277683i
$116$	1.35237	+	12.8669i	0.125564	+	1.19466i
$117$	5.69275	+	6.32243i	0.526295	+	0.584509i
$118$	−1.60658	−	2.78268i	−0.147898	−	0.256166i
$119$	1.40395	−	2.43171i	0.128700	−	0.222915i
$120$	−0.0314644	+	0.00668797i	−0.00287230	+	0.000610526i
$121$	6.18886	+	6.87343i	0.562624	+	0.624857i
$122$	−4.16005	+	3.02245i	−0.376633	+	0.273640i
$123$	−0.222253	−	0.684023i	−0.0200399	−	0.0616763i
$124$	−1.02760	+	3.16262i	−0.0922809	+	0.284011i
$125$	1.98022	+	1.43871i	0.177116	+	0.128683i
$126$	0.0429620	+	0.408756i	0.00382736	+	0.0364149i
$127$	0.218431	+	0.158699i	0.0193826	+	0.0140823i	0.597434	−	0.801918i	$-0.296187\pi$
$127$	0.218431	+	0.158699i	0.0193826	+	0.0140823i	−0.578052	+	0.816000i	$0.696187\pi$
$128$	4.92205	+	8.52523i	0.435051	+	0.753531i
$129$	0.0580079	+	0.551908i	0.00510731	+	0.0485928i
$130$	0.251345	−	0.0534251i	0.0220444	−	0.00468569i
$131$	−1.08537	−	3.34043i	−0.0948293	−	0.291855i	0.892380	−	0.451285i	$-0.149034\pi$
$131$	−1.08537	−	3.34043i	−0.0948293	−	0.291855i	−0.987209	+	0.159430i	$0.949034\pi$
$132$	0.773120			0.0672915
$133$	−1.45842	+	1.61974i	−0.126461	+	0.140449i
$134$	−4.98988	+	1.06063i	−0.431060	+	0.0916246i
$135$	−0.0679486	−	0.117690i	−0.00584809	−	0.0101292i
$136$	−10.4020	+	2.21102i	−0.891967	+	0.189593i
$137$	−4.44075	−	0.943910i	−0.379399	−	0.0806437i	0.0142649	−	0.999898i	$-0.495459\pi$
$137$	−4.44075	−	0.943910i	−0.379399	−	0.0806437i	−0.393664	+	0.919255i	$0.628793\pi$
$138$	0.179547	−	0.0799393i	0.0152840	−	0.00680488i
$139$	−10.2616	+	4.56876i	−0.870377	+	0.387517i	−0.792809	−	0.609470i	$-0.791382\pi$
$139$	−10.2616	+	4.56876i	−0.870377	+	0.387517i	−0.0775683	+	0.996987i	$0.524716\pi$
$140$	−0.157147	−	0.0699662i	−0.0132813	−	0.00591323i
$141$	0.530193	+	0.112696i	0.0446503	+	0.00949072i
$142$	−1.01213	−	3.11501i	−0.0849359	−	0.261406i
$143$	−12.7974			−1.07017
$144$	−6.42635	+	7.13719i	−0.535529	+	0.594766i
$145$	−0.178535	+	1.69865i	−0.0148266	+	0.141065i
$146$	−3.00739	+	3.34005i	−0.248894	+	0.276425i
$147$	−0.315905	+	0.547163i	−0.0260554	+	0.0451292i
$148$	6.91598	+	5.02476i	0.568490	+	0.413032i
$149$	−1.37784	−	2.38648i	−0.112877	−	0.195508i	0.804052	−	0.594559i	$-0.202673\pi$
$149$	−1.37784	−	2.38648i	−0.112877	−	0.195508i	−0.916929	+	0.399050i	$0.869340\pi$
$150$	0.166915			0.0136286
$151$	1.73275	−	12.1654i	0.141009	−	0.990008i
$151$	1.73275	−	12.1654i	0.141009	−	0.990008i
$152$	8.25476			0.669550
$153$	−11.2159	−	19.4265i	−0.906751	−	1.57054i
$154$	−0.500172	−	0.363396i	−0.0403050	−	0.0292833i
$155$	−0.219503	+	0.380190i	−0.0176309	+	0.0305376i
$156$	−0.326945	+	0.363109i	−0.0261765	+	0.0290720i
$157$	−0.693240	+	6.59574i	−0.0553266	+	0.526398i	0.931399	+	0.364000i	$0.118589\pi$
$157$	−0.693240	+	6.59574i	−0.0553266	+	0.526398i	−0.986725	+	0.162397i	$0.948077\pi$
$158$	0.483613	−	0.537107i	0.0384742	−	0.0427299i
$159$	−0.987790			−0.0783368
$160$	0.305488	+	0.940195i	0.0241509	+	0.0743289i
$161$	2.13027	+	0.452804i	0.167889	+	0.0356859i
$162$	2.99106	+	1.33171i	0.235000	+	0.104629i
$163$	3.91572	−	1.74339i	0.306703	−	0.136553i	−0.247614	−	0.968859i	$-0.579646\pi$
$163$	3.91572	−	1.74339i	0.306703	−	0.136553i	0.554317	+	0.832306i	$0.312980\pi$
$164$	−13.3072	+	5.92475i	−1.03912	+	0.462645i
$165$	0.0998346	+	0.0212205i	0.00777212	+	0.00165201i
$166$	−1.44100	+	0.306294i	−0.111843	+	0.0237730i
$167$	7.79903	+	13.5083i	0.603507	+	1.04530i	0.992286	+	0.123973i	$0.0395638\pi$
$167$	7.79903	+	13.5083i	0.603507	+	1.04530i	−0.388779	+	0.921331i	$0.627103\pi$
$168$	−0.0478444	+	0.0101696i	−0.00369128	+	0.000784605i
$169$	−3.28680	+	3.65036i	−0.252831	+	0.280797i
$170$	−0.677515			−0.0519631
$171$	5.38067	+	16.5600i	0.411470	+	1.26638i
$172$	10.9938	−	2.33681i	0.838272	−	0.178180i
$173$	0.374934	+	3.56726i	0.0285057	+	0.271214i	0.999486	+	0.0320547i	$0.0102051\pi$
$173$	0.374934	+	3.56726i	0.0285057	+	0.271214i	−0.970980	+	0.239159i	$0.923128\pi$
$174$	0.117189	+	0.202977i	0.00888408	+	0.0153877i
$175$	1.49636	+	1.08717i	0.113114	+	0.0821825i
$176$	−1.51008	−	14.3674i	−0.113827	−	1.08299i
$177$	0.652554	+	0.474109i	0.0490490	+	0.0356362i
$178$	−0.404503	+	1.24493i	−0.0303187	+	0.0933115i
$179$	0.916924	+	2.82200i	0.0685341	+	0.210926i	0.979458	−	0.201648i	$-0.0646297\pi$
$179$	0.916924	+	2.82200i	0.0685341	+	0.210926i	−0.910924	+	0.412574i	$0.864630\pi$
$180$	−1.11177	+	0.807748i	−0.0828665	+	0.0602060i
$181$	−13.4727	−	14.9630i	−1.00142	−	1.11219i	−0.993684	−	0.112218i	$-0.964204\pi$
$181$	−13.4727	−	14.9630i	−1.00142	−	1.11219i	−0.00773529	−	0.999970i	$-0.502462\pi$
$182$	0.382193	−	0.0812375i	0.0283300	−	0.00602173i
$183$	0.645413	−	1.11789i	0.0477103	−	0.0826367i
$184$	−4.12414	−	7.14322i	−0.304036	−	0.526605i
$185$	0.755157	+	0.838686i	0.0555202	+	0.0616614i
$186$	0.00629697	+	0.0599117i	0.000461716	+	0.00439294i
$187$	33.0050	+	7.01543i	2.41356	+	0.513019i
$188$	1.14751	−	10.9178i	0.0836908	−	0.796265i
$189$	−0.103322	−	0.178959i	−0.00751556	−	0.0130173i
$190$	0.514416	+	0.109342i	0.0373196	+	0.00793254i
$191$	2.09545	−	2.32723i	0.151621	−	0.168393i	−0.662549	−	0.749018i	$-0.730525\pi$
$191$	2.09545	−	2.32723i	0.151621	−	0.168393i	0.814171	+	0.580626i	$0.197192\pi$
$192$	−0.368690	−	0.267869i	−0.0266079	−	0.0193318i
$193$	−4.38821	−	4.87360i	−0.315871	−	0.350810i	0.564212	−	0.825630i	$-0.309180\pi$
$193$	−4.38821	−	4.87360i	−0.315871	−	0.350810i	−0.880083	+	0.474820i	$0.842513\pi$
$194$	−1.47155	−	1.63433i	−0.105651	−	0.117338i
$195$	−0.0521856	+	0.0379151i	−0.00373709	+	0.00271516i
$196$	11.6898	+	5.20465i	0.834988	+	0.371761i
$197$	−2.93527	+	5.08404i	−0.209130	+	0.362223i	−0.951441	−	0.307832i	$-0.900396\pi$
$197$	−2.93527	+	5.08404i	−0.209130	+	0.362223i	0.742311	+	0.670056i	$0.233730\pi$
$198$	−4.51205	+	2.00889i	−0.320657	+	0.142766i
$199$	2.39962	−	22.8309i	0.170105	−	1.61844i	−0.493080	−	0.869984i	$-0.664129\pi$
$199$	2.39962	−	22.8309i	0.170105	−	1.61844i	0.663185	−	0.748456i	$-0.269204\pi$
$200$	−0.732228	−	6.96669i	−0.0517764	−	0.492619i
$201$	1.03602	−	0.752716i	0.0730755	−	0.0530925i
$202$	−0.387951	−	0.172727i	−0.0272961	−	0.0121530i
$203$	−0.271479	+	2.58295i	−0.0190541	+	0.181287i
$204$	1.04226	−	0.757243i	0.0729724	−	0.0530176i
$205$	−1.88101	+	0.399821i	−0.131375	+	0.0279247i
$206$	2.89413	−	1.28855i	0.201643	−	0.0897774i
$207$	11.6419	−	12.9296i	0.809168	−	0.898672i
$208$	7.38651	+	5.36661i	0.512162	+	0.372108i
$209$	−23.9274	−	10.6532i	−1.65509	−	0.736896i
$210$	−0.00311625			−0.000215042
$211$	−2.67572	+	8.23503i	−0.184204	+	0.566923i	−0.999934	−	0.0115111i	$-0.996336\pi$
$211$	−2.67572	+	8.23503i	−0.184204	+	0.566923i	0.815729	+	0.578434i	$0.196336\pi$
$212$	2.09118	+	19.8962i	0.143623	+	1.36648i
$213$	0.550162	+	0.611017i	0.0376965	+	0.0418662i
$214$	4.92817	+	2.19416i	0.336883	+	0.149990i
$215$	1.48380			0.101194
$216$	−0.241845	+	0.744322i	−0.0164555	+	0.0506447i
$217$	−0.333773	+	0.578112i	−0.0226580	+	0.0392448i
$218$	−1.31911	+	4.05980i	−0.0893414	+	0.274964i
$219$	0.348649	−	1.07303i	0.0235595	−	0.0725088i
$220$	0.216074	−	2.05581i	0.0145677	−	0.138603i
$221$	−17.2524	+	12.5346i	−1.16052	+	0.843168i
$222$	0.151481	+	0.0321983i	0.0101667	+	0.00216101i
$223$	−3.76929	−	11.6007i	−0.252410	−	0.776840i	−0.994329	−	0.106349i	$-0.966084\pi$
$223$	−3.76929	−	11.6007i	−0.252410	−	0.776840i	0.741918	−	0.670490i	$-0.233916\pi$
$224$	0.464521	+	1.42965i	0.0310371	+	0.0955224i
$225$	13.4987	−	6.01001i	0.899913	−	0.400667i
$226$	0.0873881	−	0.151361i	0.00581297	−	0.0100684i
$227$	7.18278	−	12.4409i	0.476738	−	0.825734i	−0.522907	−	0.852390i	$-0.675152\pi$
$227$	7.18278	−	12.4409i	0.476738	−	0.825734i	0.999645	+	0.0266559i	$0.00848583\pi$
$228$	−0.913560	+	0.406743i	−0.0605020	+	0.0269372i
$229$	7.05938	+	21.7265i	0.466497	+	1.43573i	0.857090	+	0.515166i	$0.172270\pi$
$229$	7.05938	+	21.7265i	0.466497	+	1.43573i	−0.390593	+	0.920563i	$0.627730\pi$
$230$	−0.162387	−	0.499776i	−0.0107075	−	0.0329542i
$231$	0.151807	+	0.0322676i	0.00998819	+	0.00212305i
$232$	7.95777	−	5.78166i	0.522453	−	0.379584i
$233$	1.98501	−	18.8861i	0.130042	−	1.23727i	−0.713673	−	0.700479i	$-0.752970\pi$
$233$	1.98501	−	18.8861i	0.130042	−	1.23727i	0.843715	−	0.536791i	$-0.180364\pi$
$234$	0.964589	−	2.96870i	0.0630572	−	0.194070i
$235$	0.447852	−	1.37835i	0.0292146	−	0.0899134i
$236$	8.16810	−	14.1476i	0.531698	−	0.920928i
$237$	−0.0560656	+	0.172552i	−0.00364185	+	0.0112085i
$238$	−1.03022			−0.0667793
$239$	6.48615	+	2.88782i	0.419554	+	0.186797i	0.605645	−	0.795735i	$-0.292915\pi$
$239$	6.48615	+	2.88782i	0.419554	+	0.186797i	−0.186091	+	0.982533i	$0.559582\pi$
$240$	−0.0487245	−	0.0541140i	−0.00314515	−	0.00349304i
$241$	−1.60090	−	15.2316i	−0.103123	−	0.981152i	−0.916668	−	0.399650i	$-0.869132\pi$
$241$	−1.60090	−	15.2316i	−0.103123	−	0.981152i	0.813545	−	0.581503i	$-0.197535\pi$
$242$	1.04865	−	3.22742i	0.0674099	−	0.207466i
$243$	−2.47742			−0.158927
$244$	−23.8831	−	10.6334i	−1.52896	−	0.680735i
$245$	1.36668	+	0.992948i	0.0873137	+	0.0634371i
$246$	−0.176573	+	0.196104i	−0.0112579	+	0.0125032i
$247$	15.1221	−	6.73280i	0.962197	−	0.428398i
$248$	2.47297	−	0.525645i	0.157033	−	0.0333785i
$249$	0.299188	−	0.217373i	0.0189603	−	0.0137755i
$250$	0.0938728	−	0.893140i	0.00593704	−	0.0564871i
$251$	−7.63089	−	3.39749i	−0.481657	−	0.214448i	0.151520	−	0.988454i	$-0.451583\pi$
$251$	−7.63089	−	3.39749i	−0.481657	−	0.214448i	−0.633178	+	0.774006i	$0.718250\pi$
$252$	−1.69054	+	1.22825i	−0.106494	+	0.0773726i
$253$	2.73564	+	26.0279i	0.171988	+	1.63636i
$254$	0.0103548	−	0.0985190i	0.000649716	−	0.00618163i
$255$	0.155373	−	0.0691766i	0.00972985	−	0.00433201i
$256$	−3.14208	+	5.44224i	−0.196380	+	0.340140i
$257$	6.28550	+	2.79848i	0.392079	+	0.174565i	0.593301	−	0.804981i	$-0.297825\pi$
$257$	6.28550	+	2.79848i	0.392079	+	0.174565i	−0.201222	+	0.979546i	$0.564491\pi$
$258$	0.164725	−	0.119680i	0.0102553	−	0.00745093i
$259$	1.14828	+	1.27530i	0.0713507	+	0.0792430i
$260$	0.874171	+	0.970865i	0.0542138	+	0.0602105i
$261$	16.7858	+	12.1956i	1.03901	+	0.754887i
$262$	−0.862295	+	0.957676i	−0.0532728	+	0.0591654i
$263$	−18.6426	−	3.96260i	−1.14955	−	0.244345i	−0.406546	−	0.913630i	$-0.633267\pi$
$263$	−18.6426	−	3.96260i	−1.14955	−	0.244345i	−0.743005	+	0.669286i	$0.766600\pi$
$264$	−0.293894	−	0.509039i	−0.0180879	−	0.0313292i
$265$	−0.276071	+	2.62664i	−0.0169589	+	0.161353i
$266$	0.782214	+	0.166265i	0.0479606	+	0.0101943i
$267$	−0.0343479	−	0.326799i	−0.00210206	−	0.0199997i
$268$	−17.3546	−	19.2743i	−1.06010	−	1.17736i
$269$	1.39008	+	2.40769i	0.0847546	+	0.146799i	0.905287	−	0.424801i	$-0.139656\pi$
$269$	1.39008	+	2.40769i	0.0847546	+	0.146799i	−0.820532	+	0.571601i	$0.806323\pi$
$270$	−0.0249304	+	0.0431808i	−0.00151722	+	0.00262790i
$271$	−9.12149	+	1.93883i	−0.554091	+	0.117776i	−0.476443	−	0.879205i	$-0.658074\pi$
$271$	−9.12149	+	1.93883i	−0.554091	+	0.117776i	−0.0776476	+	0.996981i	$0.524741\pi$
$272$	−16.1081	−	17.8899i	−0.976699	−	1.08473i
$273$	−0.0793528	+	0.0576532i	−0.00480265	+	0.00348933i
$274$	0.514735	+	1.58419i	0.0310963	+	0.0957044i
$275$	−6.86840	+	21.1388i	−0.414180	+	1.27472i
$276$	0.808395	+	0.587333i	0.0486596	+	0.0353533i
$277$	2.43180	+	23.1370i	0.146113	+	1.39017i	0.784345	+	0.620325i	$0.212999\pi$
$277$	2.43180	+	23.1370i	0.146113	+	1.39017i	−0.638233	+	0.769844i	$0.720334\pi$
$278$	3.33420	+	2.42244i	0.199972	+	0.145288i
$279$	2.66645	+	4.61843i	0.159636	+	0.276498i
$280$	0.0136705	+	0.130066i	0.000816967	+	0.00777292i
$281$	14.3424	−	3.04857i	0.855595	−	0.181862i	0.240825	−	0.970569i	$-0.422582\pi$
$281$	14.3424	−	3.04857i	0.855595	−	0.181862i	0.614770	+	0.788706i	$0.289249\pi$
$282$	−0.0614556	−	0.189141i	−0.00365963	−	0.0112632i
$283$	6.29446			0.374167			0.187083	−	0.982344i	$-0.440097\pi$
$283$	6.29446			0.374167			0.187083	+	0.982344i	$0.440097\pi$
$284$	11.1425	−	12.3750i	0.661186	−	0.734322i
$285$	−0.129134	+	0.0274483i	−0.00764925	+	0.00162590i
$286$	2.34769	+	4.06633i	0.138822	+	0.240447i
$287$	−2.86024	+	0.607963i	−0.168835	+	0.0358869i
$288$	11.7465	+	2.49680i	0.692171	+	0.147125i
$289$	35.8356	−	15.9550i	2.10798	−	0.938531i
$290$	0.572492	−	0.254890i	0.0336179	−	0.0149676i
$291$	0.504339	+	0.224546i	0.0295649	+	0.0131631i
$292$	−22.3513	−	4.75092i	−1.30801	−	0.278026i
$293$	−0.706217	−	2.17351i	−0.0412576	−	0.126978i	0.928306	−	0.371817i	$-0.121265\pi$
$293$	−0.706217	−	2.17351i	−0.0412576	−	0.126978i	−0.969564	+	0.244839i	$0.921265\pi$
$294$	0.231812			0.0135195
$295$	1.44308	−	1.60271i	0.0840196	−	0.0933133i
$296$	0.679367	−	6.46375i	0.0394874	−	0.375698i
$297$	1.66160	−	1.84539i	0.0964159	−	0.107081i
$298$	−0.505530	+	0.875604i	−0.0292846	+	0.0507224i
$299$	−13.3813	−	9.72209i	−0.773861	−	0.562243i
$300$	0.424311	+	0.734928i	0.0244976	+	0.0424311i
$301$	2.25624			0.130048
$302$	−4.18339	+	1.68118i	−0.240727	+	0.0967411i
$303$	0.106604			0.00612423
$304$	9.34319	+	16.1829i	0.535869	+	0.928152i
$305$	−2.79221	−	2.02866i	−0.159881	−	0.116161i
$306$	−4.11512	+	7.12760i	−0.235246	+	0.407458i
$307$	−16.5711	+	18.4041i	−0.945765	+	1.05038i	0.0528933	+	0.998600i	$0.483156\pi$
$307$	−16.5711	+	18.4041i	−0.945765	+	1.05038i	−0.998659	+	0.0517786i	$0.983511\pi$
$308$	0.328560	−	3.12604i	0.0187215	−	0.178123i
$309$	−0.532139	+	0.591000i	−0.0302723	+	0.0336208i
$310$	0.161072			0.00914825
$311$	7.38158	+	22.7182i	0.418571	+	1.28823i	0.909017	+	0.416758i	$0.136834\pi$
$311$	7.38158	+	22.7182i	0.418571	+	1.28823i	−0.490446	+	0.871472i	$0.663166\pi$
$312$	0.363364	+	0.0772353i	0.0205714	+	0.00437259i
$313$	2.63442	+	1.17292i	0.148906	+	0.0662973i	0.479837	−	0.877358i	$-0.340696\pi$
$313$	2.63442	+	1.17292i	0.148906	+	0.0662973i	−0.330930	+	0.943655i	$0.607363\pi$
$314$	2.22294	−	0.989719i	0.125448	−	0.0558531i
$315$	−0.252016	+	0.112205i	−0.0141995	+	0.00632203i
$316$	3.59427	+	0.763985i	0.202193	+	0.0429775i
$317$	−20.4520	+	4.34721i	−1.14870	+	0.244164i	−0.742645	−	0.669685i	$-0.766429\pi$
$317$	−20.4520	+	4.34721i	−1.14870	+	0.244164i	−0.406055	+	0.913849i	$0.633096\pi$
$318$	0.181211	+	0.313866i	0.0101618	+	0.0176007i
$319$	−30.5281	+	6.48894i	−1.70924	+	0.363311i
$320$	−0.815336	+	0.905523i	−0.0455787	+	0.0506203i
$321$	−1.35420			−0.0755841
$322$	−0.246924	−	0.759952i	−0.0137605	−	0.0423505i
$323$	−42.6913	+	9.07432i	−2.37541	+	0.504909i
$324$	1.74000	+	16.5550i	0.0966666	+	0.919721i
$325$	−7.02360	−	12.1652i	−0.389599	−	0.674806i
$326$	−1.27230	−	0.924378i	−0.0704660	−	0.0511966i
$327$	−0.112011	−	1.06571i	−0.00619421	−	0.0589340i
$328$	8.95959	+	6.50952i	0.494710	+	0.359428i
$329$	0.680998	−	2.09590i	0.0375446	−	0.115550i
$330$	−0.0115720	−	0.0356149i	−0.000637018	−	0.00196054i
$331$	14.6142	−	10.6178i	0.803268	−	0.583608i	−0.108603	−	0.994085i	$-0.534638\pi$
$331$	14.6142	−	10.6178i	0.803268	−	0.583608i	0.911871	+	0.410477i	$0.134638\pi$
$332$	−5.01175	−	5.56612i	−0.275056	−	0.305480i
$333$	13.4099	−	2.85035i	0.734856	−	0.156198i
$334$	2.86147	−	4.95622i	0.156573	−	0.271192i
$335$	−1.71200	−	2.96527i	−0.0935367	−	0.162010i
$336$	−0.0740898	−	0.0822851i	−0.00404193	−	0.00448902i
$337$	2.28846	+	21.7732i	0.124660	+	1.18606i	0.860696	+	0.509120i	$0.170029\pi$
$337$	2.28846	+	21.7732i	0.124660	+	1.18606i	−0.736035	+	0.676943i	$0.763304\pi$
$338$	1.76285	+	0.374706i	0.0958865	+	0.0203813i
$339$	−0.00458610	+	0.0436338i	−0.000249083	+	0.00236986i
$340$	−1.72230	−	2.98311i	−0.0934047	−	0.161782i
$341$	−7.84656	−	1.66784i	−0.424915	−	0.0903185i
$342$	4.27479	−	4.74763i	0.231154	−	0.256723i
$343$	4.19878	+	3.05059i	0.226713	+	0.164717i
$344$	−5.71780	−	6.35026i	−0.308283	−	0.342383i
$345$	0.0882686	+	0.0980323i	0.00475222	+	0.00527788i
$346$	1.06470	−	0.773550i	0.0572386	−	0.0415863i
$347$	−7.89717	−	3.51605i	−0.423942	−	0.188751i	0.183665	−	0.982989i	$-0.441204\pi$
$347$	−7.89717	−	3.51605i	−0.423942	−	0.188751i	−0.607607	+	0.794238i	$0.707871\pi$
$348$	−0.595808	+	1.03197i	−0.0319386	+	0.0553194i
$349$	−26.5981	+	11.8422i	−1.42376	+	0.633901i	−0.966788	−	0.255578i	$-0.917734\pi$
$349$	−26.5981	+	11.8422i	−1.42376	+	0.633901i	−0.456976	+	0.889479i	$0.651067\pi$
$350$	0.0709354	−	0.674905i	0.00379166	−	0.0360752i
$351$	0.164046	+	1.56080i	0.00875615	+	0.0833092i
$352$	−14.6142	+	10.6178i	−0.778938	+	0.565932i
$353$	9.04413	+	4.02671i	0.481371	+	0.214320i	0.633052	−	0.774109i	$-0.281802\pi$
$353$	9.04413	+	4.02671i	0.481371	+	0.214320i	−0.151681	+	0.988429i	$0.548469\pi$
$354$	0.0309345	−	0.294322i	0.00164415	−	0.0156430i
$355$	1.77852	−	1.29217i	0.0943942	−	0.0685814i
$356$	−6.50972	+	1.38368i	−0.345014	+	0.0733351i
$357$	0.236259	−	0.105189i	0.0125041	−	0.00556720i
$358$	0.728469	−	0.809047i	0.0385008	−	0.0427594i
$359$	12.0346	+	8.74365i	0.635162	+	0.461472i	0.858185	−	0.513341i	$-0.171592\pi$
$359$	12.0346	+	8.74365i	0.635162	+	0.461472i	−0.223023	+	0.974813i	$0.571592\pi$
$360$	0.954468	+	0.424956i	0.0503049	+	0.0223972i
$361$	14.8786			0.783086
$362$	−2.28284	+	7.02586i	−0.119983	+	0.369271i
$363$	0.0890452	+	0.847208i	0.00467366	+	0.0444669i
$364$	1.32925	+	1.47629i	0.0696718	+	0.0773784i
$365$	−2.75587	−	1.22699i	−0.144249	−	0.0642237i
$366$	−0.473606			−0.0247558
$367$	−4.08607	+	12.5756i	−0.213291	+	0.656442i	0.785980	+	0.618252i	$0.212159\pi$
$367$	−4.08607	+	12.5756i	−0.213291	+	0.656442i	−0.999271	+	0.0381895i	$0.987841\pi$
$368$	9.33585	−	16.1702i	0.486665	−	0.842928i
$369$	−7.21876	+	22.2171i	−0.375794	+	1.15657i
$370$	0.127955	−	0.393805i	0.00665207	−	0.0204730i
$371$	−0.419790	+	3.99404i	−0.0217944	+	0.207360i
$372$	−0.247784	+	0.180026i	−0.0128470	+	0.00933390i
$373$	24.4347	+	5.19375i	1.26518	+	0.268922i	0.791170	−	0.611597i	$-0.209472\pi$
$373$	24.4347	+	5.19375i	1.26518	+	0.268922i	0.474011	+	0.880519i	$0.342806\pi$
$374$	−3.82566	−	11.7742i	−0.197820	−	0.608828i
$375$	0.0696650	+	0.214407i	0.00359748	+	0.0110719i
$376$	−7.62475	+	3.39476i	−0.393217	+	0.175071i
$377$	9.86237	−	17.0821i	0.507938	−	0.879774i
$378$	−0.0379089	+	0.0656601i	−0.00194982	+	0.00337719i
$379$	15.9762	−	7.11304i	0.820640	−	0.365373i	0.0469189	−	0.998899i	$-0.485060\pi$
$379$	15.9762	−	7.11304i	0.820640	−	0.365373i	0.773721	+	0.633526i	$0.218393\pi$
$380$	0.826250	+	2.54293i	0.0423857	+	0.130450i
$381$	0.00768449	+	0.0236504i	0.000393688	+	0.00121165i
$382$	−1.12388	−	0.238888i	−0.0575027	−	0.0122226i
$383$	−0.751352	+	0.545889i	−0.0383923	+	0.0278936i	−0.606816	−	0.794842i	$-0.707553\pi$
$383$	−0.751352	+	0.545889i	−0.0383923	+	0.0278936i	0.568424	+	0.822736i	$0.307553\pi$
$384$	−0.0947734	+	0.901708i	−0.00483638	+	0.0460151i
$385$	0.128231	−	0.394654i	0.00653525	−	0.0201134i
$386$	−0.743547	+	2.28840i	−0.0378455	+	0.116477i
$387$	9.01235	−	15.6098i	0.458124	−	0.793493i
$388$	3.45515	−	10.6338i	0.175408	−	0.539852i
$389$	−18.3041			−0.928053			−0.464026	−	0.885821i	$-0.653596\pi$
$389$	−18.3041			−0.928053			−0.464026	+	0.885821i	$0.653596\pi$
$390$	0.0216208	+	0.00962622i	0.00109481	+	0.000487443i
$391$	29.1813	+	32.4091i	1.47576	+	1.63900i
$392$	−1.01692	−	9.67534i	−0.0513622	−	0.488678i
$393$	0.0999665	−	0.307665i	0.00504264	−	0.0155197i
$394$	2.15391			0.108512
$395$	0.443165	+	0.197310i	0.0222981	+	0.00992774i
$396$	−20.3152	−	14.7598i	−1.02088	−	0.741709i
$397$	13.9553	−	15.4989i	0.700396	−	0.777869i	−0.283043	−	0.959107i	$-0.591344\pi$
$397$	13.9553	−	15.4989i	0.700396	−	0.777869i	0.983439	+	0.181238i	$0.0580105\pi$
$398$	−7.69464	+	3.42587i	−0.385697	+	0.171723i
$399$	−0.196360	+	0.0417376i	−0.00983029	+	0.00208949i
$400$	12.8289	−	9.32076i	0.641446	−	0.466038i
$401$	1.91201	−	18.1915i	0.0954810	−	0.908441i	−0.836995	−	0.547210i	$-0.815690\pi$
$401$	1.91201	−	18.1915i	0.0954810	−	0.908441i	0.932476	−	0.361231i	$-0.117643\pi$
$402$	−0.429232	−	0.191106i	−0.0214081	−	0.00953151i
$403$	4.10156	−	2.97996i	0.204313	−	0.148442i
$404$	−0.225683	−	2.14723i	−0.0112282	−	0.106829i
$405$	−0.229709	+	2.18554i	−0.0114143	+	0.108600i
$406$	0.870523	−	0.387582i	0.0432034	−	0.0192354i
$407$	−10.3110	+	17.8592i	−0.511098	+	0.885247i
$408$	−0.894788	−	0.398385i	−0.0442986	−	0.0197230i
$409$	15.3322	−	11.1395i	0.758129	−	0.550813i	−0.140207	−	0.990122i	$-0.544777\pi$
$409$	15.3322	−	11.1395i	0.758129	−	0.550813i	0.898336	+	0.439309i	$0.144777\pi$
$410$	0.472114	+	0.524335i	0.0233160	+	0.0258951i
$411$	−0.279794	−	0.310743i	−0.0138012	−	0.0153278i
$412$	13.0306	+	9.46728i	0.641971	+	0.466419i
$413$	2.19434	−	2.43706i	0.107976	−	0.119920i
$414$	−6.24405	−	1.32721i	−0.306879	−	0.0652290i
$415$	−0.494400	−	0.856326i	−0.0242692	−	0.0420354i
$416$	1.19335	−	11.3540i	0.0585088	−	0.556674i
$417$	−1.01196	−	0.215100i	−0.0495561	−	0.0105335i
$418$	1.00450	+	9.55717i	0.0491317	+	0.467457i
$419$	6.88119	+	7.64234i	0.336168	+	0.373353i	0.887401	−	0.460999i	$-0.152509\pi$
$419$	6.88119	+	7.64234i	0.336168	+	0.373353i	−0.551232	+	0.834352i	$0.685842\pi$
$420$	−0.00792175	−	0.0137209i	−0.000386542	−	0.000669510i
$421$	−8.17869	+	14.1659i	−0.398605	+	0.690404i	−0.993554	−	0.113359i	$-0.963839\pi$
$421$	−8.17869	+	14.1659i	−0.398605	+	0.690404i	0.594949	+	0.803763i	$0.297172\pi$
$422$	3.10751	−	0.660521i	0.151271	−	0.0321537i
$423$	−11.7803	−	13.0833i	−0.572778	−	0.636134i
$424$	12.3052	−	8.94023i	0.597592	−	0.434176i
$425$	11.4452	+	35.2248i	0.555176	+	1.70865i
$426$	0.0932205	−	0.286903i	0.00451655	−	0.0139005i
$427$	−4.24579	−	3.08475i	−0.205468	−	0.149281i
$428$	2.86688	+	27.2765i	0.138576	+	1.31846i
$429$	−0.953578	−	0.692815i	−0.0460392	−	0.0334494i
$430$	−0.272203	−	0.471470i	−0.0131268	−	0.0227363i
$431$	−2.44709	−	23.2825i	−0.117872	−	1.12148i	−0.880304	−	0.474410i	$-0.842661\pi$
$431$	−2.44709	−	23.2825i	−0.117872	−	1.12148i	0.762432	−	0.647068i	$-0.224005\pi$
$432$	−1.73292	+	0.368344i	−0.0833753	+	0.0177220i
$433$	−10.5615	−	32.5049i	−0.507553	−	1.56209i	−0.796436	−	0.604722i	$-0.793284\pi$
$433$	−10.5615	−	32.5049i	−0.507553	−	1.56209i	0.288884	−	0.957364i	$-0.406716\pi$
$434$	0.244923			0.0117567
$435$	−0.105263	+	0.116907i	−0.00504699	+	0.00560525i
$436$	−21.2286	+	4.51228i	−1.01667	+	0.216099i
$437$	−16.9260	−	29.3167i	−0.809681	−	1.40241i
$438$	−0.404911	+	0.0860666i	−0.0193474	+	0.00411242i
$439$	−25.2950	−	5.37662i	−1.20727	−	0.256612i	−0.440033	−	0.897981i	$-0.645033\pi$
$439$	−25.2950	−	5.37662i	−1.20727	−	0.256612i	−0.767232	+	0.641369i	$0.778367\pi$
$440$	−1.43573	+	0.639228i	−0.0684457	+	0.0304740i
$441$	18.7470	−	8.34670i	0.892714	−	0.397462i
$442$	7.14778	+	3.18239i	0.339985	+	0.151371i
$443$	37.9060	+	8.05717i	1.80097	+	0.382807i	0.981674	−	0.190567i	$-0.0610326\pi$
$443$	37.9060	+	8.05717i	1.80097	+	0.382807i	0.819293	+	0.573374i	$0.194366\pi$
$444$	0.243307	+	0.748822i	0.0115468	+	0.0355375i
$445$	−0.878593			−0.0416493
$446$	−2.99459	+	3.32583i	−0.141798	+	0.157483i
$447$	0.0265301	−	0.252417i	0.00125483	−	0.0119389i
$448$	−1.23979	+	1.37693i	−0.0585746	+	0.0650537i
$449$	14.8075	−	25.6473i	0.698809	−	1.21037i	−0.270071	−	0.962840i	$-0.587047\pi$
$449$	14.8075	−	25.6473i	0.698809	−	1.21037i	0.968880	−	0.247532i	$-0.0796194\pi$
$450$	−4.38600	−	3.18661i	−0.206758	−	0.150218i
$451$	−17.5696	−	30.4314i	−0.827320	−	1.43296i
$452$	0.888590			0.0417957
$453$	0.787713	−	0.812680i	0.0370100	−	0.0381830i
$454$	−5.27074			−0.247368
$455$	0.131128	+	0.227121i	0.00614739	+	0.0106476i
$456$	0.615090	+	0.446889i	0.0288042	+	0.0209275i
$457$	3.62340	−	6.27591i	0.169495	−	0.293575i	−0.768747	−	0.639553i	$-0.779120\pi$
$457$	3.62340	−	6.27591i	0.169495	−	0.293575i	0.938243	+	0.345978i	$0.112453\pi$
$458$	5.60847	−	6.22883i	0.262066	−	0.291054i
$459$	0.432533	−	4.11528i	0.0201889	−	0.192085i
$460$	1.78772	−	1.98546i	0.0833527	−	0.0925726i
$461$	−9.42361			−0.438901			−0.219451	−	0.975624i	$-0.570426\pi$
$461$	−9.42361			−0.438901			−0.219451	+	0.975624i	$0.570426\pi$
$462$	−0.0175962	−	0.0541556i	−0.000818651	−	0.00251955i
$463$	−11.3282	−	2.40788i	−0.526466	−	0.111904i	−0.0629918	−	0.998014i	$-0.520064\pi$
$463$	−11.3282	−	2.40788i	−0.526466	−	0.111904i	−0.463475	+	0.886110i	$0.653398\pi$
$464$	20.3416	+	9.05665i	0.944333	+	0.420444i
$465$	−0.0369382	+	0.0164460i	−0.00171297	+	0.000762663i
$466$	−6.36514	+	2.83394i	−0.294859	+	0.131280i
$467$	1.17835	+	0.250466i	0.0545276	+	0.0115902i	0.235095	−	0.971972i	$-0.424460\pi$
$467$	1.17835	+	0.250466i	0.0545276	+	0.0115902i	−0.180567	+	0.983563i	$0.557793\pi$
$468$	15.5233	−	3.29957i	0.717564	−	0.152523i
$469$	−2.60325	−	4.50896i	−0.120207	−	0.208204i
$470$	−0.520122	+	0.110555i	−0.0239914	+	0.00509954i
$471$	−0.408730	+	0.453940i	−0.0188333	+	0.0209165i
$472$	−12.4201			−0.571681
$473$	8.37842	+	25.7861i	0.385240	+	1.18565i
$474$	0.0651130	−	0.0138402i	0.00299074	−	0.000635701i
$475$	−3.00516	−	28.5922i	−0.137886	−	1.31190i
$476$	−2.61890	−	4.53607i	−0.120037	−	0.207911i
$477$	25.9560	+	18.8581i	1.18844	+	0.863454i
$478$	−0.272295	−	2.59072i	−0.0124545	−	0.118497i
$479$	27.8884	+	20.2621i	1.27425	+	0.925800i	0.999363	−	0.0356753i	$-0.0113582\pi$
$479$	27.8884	+	20.2621i	1.27425	+	0.925800i	0.274891	+	0.961475i	$0.411358\pi$
$480$	−0.0281365	+	0.0865952i	−0.00128425	+	0.00395251i
$481$	−4.02745	−	12.3952i	−0.183636	−	0.565173i
$482$	−4.54608	+	3.30292i	−0.207068	+	0.150444i
$483$	0.134220	+	0.149067i	0.00610723	+	0.00678277i
$484$	16.8761	−	3.58713i	0.767096	−	0.163051i
$485$	0.738047	−	1.27833i	0.0335130	−	0.0580462i
$486$	0.454485	+	0.787191i	0.0206159	+	0.0357077i
$487$	−16.0346	−	17.8082i	−0.726596	−	0.806966i	0.260774	−	0.965400i	$-0.416022\pi$
$487$	−16.0346	−	17.8082i	−0.726596	−	0.806966i	−0.987370	+	0.158434i	$0.949356\pi$
$488$	2.07763	+	19.7673i	0.0940499	+	0.894825i
$489$	0.386156	+	0.0820799i	0.0174626	+	0.00371178i
$490$	0.0647876	−	0.616412i	0.00292680	−	0.0278467i
$491$	−20.1277	−	34.8622i	−0.908350	−	1.57331i	−0.816356	−	0.577549i	$-0.804009\pi$
$491$	−20.1277	−	34.8622i	−0.908350	−	1.57331i	−0.0919939	−	0.995760i	$-0.529324\pi$
$492$	−1.31231	−	0.278941i	−0.0591636	−	0.0125756i
$493$	−34.7997	+	38.6489i	−1.56730	+	1.74066i
$494$	−4.91348	−	3.56985i	−0.221068	−	0.160615i
$495$	−2.21821	−	2.46357i	−0.0997012	−	0.110729i
$496$	3.82953	+	4.25312i	0.171951	+	0.190971i
$497$	2.70440	−	1.96486i	0.121309	−	0.0881361i
$498$	−0.123956	−	0.0551886i	−0.00555458	−	0.00247306i
$499$	0.298160	−	0.516429i	0.0133475	−	0.0231185i	−0.859275	−	0.511515i	$-0.829085\pi$
$499$	0.298160	−	0.516429i	0.0133475	−	0.0231185i	0.872622	+	0.488396i	$0.162418\pi$
$500$	4.17114	−	1.85711i	0.186539	−	0.0830525i
$501$	−0.150169	+	1.42877i	−0.00670907	+	0.0638325i
$502$	0.320353	+	3.04795i	0.0142980	+	0.136037i
$503$	−28.9401	+	21.0262i	−1.29038	+	0.937513i	−0.999813	−	0.0193433i	$-0.993842\pi$
$503$	−28.9401	+	21.0262i	−1.29038	+	0.937513i	−0.290563	+	0.956856i	$0.593842\pi$
$504$	1.45135	+	0.646183i	0.0646483	+	0.0287833i
$505$	0.0297940	−	0.283471i	0.00132582	−	0.0126143i
$506$	7.76840	−	5.64407i	0.345347	−	0.250910i
$507$	−0.442530	+	0.0940626i	−0.0196534	+	0.00417747i
$508$	0.460103	−	0.204851i	0.0204138	−	0.00908879i
$509$	13.5392	−	15.0368i	0.600116	−	0.666496i	−0.364178	−	0.931329i	$-0.618650\pi$
$509$	13.5392	−	15.0368i	0.600116	−	0.666496i	0.964294	+	0.264833i	$0.0853168\pi$
$510$	−0.0504839	−	0.0366787i	−0.00223546	−	0.00162416i
$511$	−4.19054	−	1.86575i	−0.185378	−	0.0825358i
$512$	21.9938			0.972000
$513$	−0.992563	+	3.05479i	−0.0438227	+	0.134872i
$514$	−0.263872	−	2.51057i	−0.0116389	−	0.110737i
$515$	1.42281	+	1.58019i	0.0626965	+	0.0696315i
$516$	0.945695	+	0.421050i	0.0416319	+	0.0185357i
$517$	26.4824			1.16469
$518$	0.194567	−	0.598815i	0.00854878	−	0.0263104i
$519$	−0.165183	+	0.286106i	−0.00725075	+	0.0125587i
$520$	0.306931	−	0.944638i	0.0134598	−	0.0414251i
$521$	4.00324	−	12.3207i	0.175385	−	0.539780i	−0.824266	−	0.566203i	$-0.808412\pi$
$521$	4.00324	−	12.3207i	0.175385	−	0.539780i	0.999651	+	0.0264232i	$0.00841173\pi$
$522$	0.795733	−	7.57089i	0.0348283	−	0.331369i
$523$	8.87265	−	6.44636i	0.387974	−	0.281880i	−0.376651	−	0.926355i	$-0.622924\pi$
$523$	8.87265	−	6.44636i	0.387974	−	0.281880i	0.764625	+	0.644476i	$0.222924\pi$
$524$	−6.40868	−	1.36221i	−0.279964	−	0.0595083i
$525$	0.0526427	+	0.162017i	0.00229751	+	0.00707102i
$526$	2.16089	+	6.65055i	0.0942194	+	0.289978i
$527$	−12.2116	+	5.43698i	−0.531948	+	0.236838i
$528$	0.665290	−	1.15232i	0.0289530	−	0.0501481i
$529$	−5.41272	+	9.37510i	−0.235336	+	0.407613i
$530$	0.885249	−	0.394138i	0.0384528	−	0.0171203i
$531$	−8.09575	−	24.9161i	−0.351325	−	1.08127i
$532$	1.25638	+	3.86675i	0.0544712	+	0.167645i
$533$	21.7226	+	4.61729i	0.940912	+	0.199997i
$534$	−0.0975377	+	0.0708653i	−0.00422087	+	0.00306664i
$535$	−0.378477	+	3.60097i	−0.0163630	+	0.155683i
$536$	−6.09341	+	18.7536i	−0.263195	+	0.810032i
$537$	−0.0844519	+	0.259916i	−0.00364437	+	0.0112162i
$538$	0.510022	−	0.883384i	0.0219886	−	0.0380854i
$539$	−9.53883	+	29.3575i	−0.410867	+	1.26452i
$540$	−0.253501			−0.0109089
$541$	14.2607	+	6.34926i	0.613114	+	0.272976i	0.689709	−	0.724086i	$-0.257738\pi$
$541$	14.2607	+	6.34926i	0.613114	+	0.272976i	−0.0765954	+	0.997062i	$0.524405\pi$
$542$	2.28940	+	2.54263i	0.0983381	+	0.109215i
$543$	−0.193845	−	1.84431i	−0.00831869	−	0.0791470i
$544$	−9.30183	+	28.6281i	−0.398813	+	1.22742i
$545$	−2.86515			−0.122730
$546$	0.0328764	+	0.0146375i	0.00140698	+	0.000626428i
$547$	−8.46392	−	6.14940i	−0.361891	−	0.262929i	0.391949	−	0.919987i	$-0.371801\pi$
$547$	−8.46392	−	6.14940i	−0.361891	−	0.262929i	−0.753840	+	0.657058i	$0.771801\pi$
$548$	−5.66671	+	6.29352i	−0.242070	+	0.268846i
$549$	−38.3013	+	17.0528i	−1.63466	+	0.727797i
$550$	7.97676	−	1.69551i	0.340130	−	0.0722969i
$551$	32.6597	−	23.7287i	1.39135	−	1.01088i
$552$	0.0794098	−	0.755534i	0.00337990	−	0.0321576i
$553$	0.673872	+	0.300027i	0.0286559	+	0.0127584i
$554$	6.90557	−	5.01719i	0.293390	−	0.213160i
$555$	0.0108652	+	0.103375i	0.000461201	+	0.00438803i
$556$	−2.19022	+	20.8385i	−0.0928860	+	0.883751i
$557$	14.6167	−	6.50776i	0.619328	−	0.275743i	−0.0729925	−	0.997332i	$-0.523255\pi$
$557$	14.6167	−	6.50776i	0.619328	−	0.275743i	0.692321	+	0.721590i	$0.256588\pi$
$558$	0.978324	−	1.69451i	0.0414157	−	0.0717342i
$559$	−15.6540	−	6.96962i	−0.662095	−	0.294784i
$560$	−0.239512	+	0.174016i	−0.0101212	+	0.00735350i
$561$	2.07952	+	2.30954i	0.0877972	+	0.0975087i
$562$	−3.59979	−	3.99797i	−0.151848	−	0.168644i
$563$	4.83883	+	3.51561i	0.203932	+	0.148166i	0.685064	−	0.728483i	$-0.259774\pi$
$563$	4.83883	+	3.51561i	0.203932	+	0.148166i	−0.481132	+	0.876648i	$0.659774\pi$
$564$	0.676564	−	0.751401i	0.0284885	−	0.0316397i
$565$	0.114745	+	0.0243899i	0.00482738	+	0.00102609i
$566$	−1.15472	−	2.00004i	−0.0485366	−	0.0840678i
$567$	−0.349293	+	3.32330i	−0.0146689	+	0.139566i
$568$	−12.3837	−	2.63223i	−0.519608	−	0.110446i
$569$	1.15577	+	10.9964i	0.0484524	+	0.460993i	0.991669	+	0.128814i	$0.0411171\pi$
$569$	1.15577	+	10.9964i	0.0484524	+	0.460993i	−0.943216	+	0.332179i	$0.892216\pi$
$570$	0.0324113	+	0.0359964i	0.00135756	+	0.00150772i
$571$	19.2696	+	33.3758i	0.806406	+	1.39674i	0.915338	+	0.402687i	$0.131924\pi$
$571$	19.2696	+	33.3758i	0.806406	+	1.39674i	−0.108932	+	0.994049i	$0.534743\pi$
$572$	−11.9360	+	20.6738i	−0.499071	+	0.864417i
$573$	0.282128	−	0.0599682i	0.0117861	−	0.00250521i
$574$	0.717890	+	0.797298i	0.0299642	+	0.0332786i
$575$	−23.2407	+	16.8854i	−0.969205	+	0.704169i
$576$	4.57406	+	14.0775i	0.190586	+	0.586563i
$577$	11.6531	−	35.8645i	0.485124	−	1.49306i	−0.346678	−	0.937984i	$-0.612690\pi$
$577$	11.6531	−	35.8645i	0.485124	−	1.49306i	0.831802	−	0.555073i	$-0.187310\pi$
$578$	−11.6437	−	8.45965i	−0.484314	−	0.351875i
$579$	−0.0631375	−	0.600713i	−0.00262391	−	0.0249648i
$580$	2.57760	+	1.87274i	0.107029	+	0.0777611i
$581$	−0.751779	−	1.30212i	−0.0311890	−	0.0540210i
$582$	−0.0211727	−	0.201445i	−0.000877636	−	0.00835015i
$583$	−47.2058	+	10.0339i	−1.95507	+	0.415562i
$584$	5.36852	+	16.5226i	0.222151	+	0.683710i
$585$	2.09512			0.0866225
$586$	−0.561068	+	0.623130i	−0.0231775	+	0.0257413i
$587$	−43.4095	+	9.22697i	−1.79170	+	0.380838i	−0.979325	−	0.202296i	$-0.935160\pi$
$587$	−43.4095	+	9.22697i	−1.79170	+	0.380838i	−0.812376	+	0.583133i	$0.801827\pi$
$588$	0.589283	+	1.02067i	0.0243016	+	0.0420917i
$589$	10.1494	−	2.15732i	0.418198	−	0.0888907i
$590$	−0.773988	−	0.164516i	−0.0318646	−	0.00677303i
$591$	−0.493952	+	0.219922i	−0.0203185	+	0.00904637i
$592$	13.4407	−	5.98417i	0.552408	−	0.245948i
$593$	16.3651	+	7.28621i	0.672034	+	0.299209i	0.714241	−	0.699900i	$-0.246772\pi$
$593$	16.3651	+	7.28621i	0.672034	+	0.299209i	−0.0422069	+	0.999109i	$0.513439\pi$
$594$	−0.891188	−	0.189428i	−0.0365659	−	0.00777232i
$595$	−0.213679	−	0.657636i	−0.00875998	−	0.0269605i
$596$	−5.14039			−0.210559
$597$	1.41480	−	1.57130i	0.0579040	−	0.0643089i
$598$	−0.634344	+	6.03538i	−0.0259403	+	0.246805i
$599$	7.77379	−	8.63367i	0.317628	−	0.352762i	−0.563096	−	0.826392i	$-0.690390\pi$
$599$	7.77379	−	8.63367i	0.317628	−	0.352762i	0.880724	+	0.473630i	$0.157056\pi$
$600$	0.322595	−	0.558751i	0.0131699	−	0.0228109i
$601$	6.84883	+	4.97596i	0.279369	+	0.202974i	0.718642	−	0.695380i	$-0.244764\pi$
$601$	6.84883	+	4.97596i	0.279369	+	0.202974i	−0.439273	+	0.898354i	$0.644764\pi$
$602$	−0.413909	−	0.716912i	−0.0168697	−	0.0292191i
$603$	−41.5937			−1.69383
$604$	−18.0368	−	14.1458i	−0.733905	−	0.575584i
$605$	2.27771			0.0926019
$606$	−0.0195565	−	0.0338729i	−0.000794430	−	0.00137599i
$607$	21.3409	+	15.5050i	0.866199	+	0.629330i	0.929564	−	0.368660i	$-0.120183\pi$
$607$	21.3409	+	15.5050i	0.866199	+	0.629330i	−0.0633654	+	0.997990i	$0.520183\pi$
$608$	11.6828	−	20.2352i	0.473800	−	0.820645i
$609$	−0.160062	+	0.177767i	−0.00648604	+	0.00720347i
$610$	−0.132365	+	1.25937i	−0.00535931	+	0.0509904i
$611$	−11.1991	+	12.4379i	−0.453068	+	0.503183i
$612$	−41.8439			−1.69144
$613$	−6.63004	−	20.4052i	−0.267785	−	0.824157i	−0.991039	−	0.133575i	$-0.957354\pi$
$613$	−6.63004	−	20.4052i	−0.267785	−	0.824157i	0.723254	−	0.690582i	$-0.242646\pi$
$614$	8.88782	+	1.88916i	0.358683	+	0.0762405i
$615$	−0.161805	−	0.0720404i	−0.00652462	−	0.00290495i
$616$	−2.18315	+	0.972002i	−0.0879617	+	0.0391631i
$617$	−18.8854	+	8.40832i	−0.760298	+	0.338506i	−0.749998	−	0.661441i	$-0.769945\pi$
$617$	−18.8854	+	8.40832i	−0.760298	+	0.338506i	−0.0103001	+	0.999947i	$0.503279\pi$
$618$	0.285409	+	0.0606656i	0.0114808	+	0.00244033i
$619$	−2.56859	+	0.545970i	−0.103240	+	0.0219444i	−0.259242	−	0.965812i	$-0.583473\pi$
$619$	−2.56859	+	0.545970i	−0.103240	+	0.0219444i	0.156002	+	0.987757i	$0.450139\pi$
$620$	0.409457	+	0.709200i	0.0164442	+	0.0284821i
$621$	3.13934	−	0.667288i	0.125978	−	0.0267774i
$622$	5.86445	−	6.51313i	0.235143	−	0.261153i
$623$	−1.33598			−0.0535248
$624$	0.259860	+	0.799768i	0.0104027	+	0.0320163i
$625$	−23.5675	+	5.00942i	−0.942700	+	0.200377i
$626$	−0.110596	−	1.05225i	−0.00442030	−	0.0420563i
$627$	−1.20618	−	2.08916i	−0.0481702	−	0.0834332i
$628$	10.0086	+	7.27170i	0.399388	+	0.290173i
$629$	3.59199	+	34.1755i	0.143222	+	1.36267i
$630$	0.0818852	+	0.0594931i	0.00326238	+	0.00237026i
$631$	11.6132	−	35.7416i	0.462313	−	1.42285i	−0.400019	−	0.916507i	$-0.630996\pi$
$631$	11.6132	−	35.7416i	0.462313	−	1.42285i	0.862331	−	0.506345i	$-0.169004\pi$
$632$	−0.863300	−	2.65697i	−0.0343402	−	0.105688i
$633$	−0.645197	+	0.468763i	−0.0256443	+	0.0186317i
$634$	5.13324	+	5.70104i	0.203867	+	0.226417i
$635$	0.0650367	−	0.0138240i	0.00258090	−	0.000548588i
$636$	−0.921303	+	1.59574i	−0.0365320	+	0.0632754i
$637$	−9.75438	−	16.8951i	−0.386482	−	0.669407i
$638$	7.66223	+	8.50976i	0.303350	+	0.336905i
$639$	−2.79145	−	26.5589i	−0.110428	−	1.05065i
$640$	2.37125	+	0.504025i	0.0937320	+	0.0199234i
$641$	−2.20459	+	20.9753i	−0.0870761	+	0.828474i	0.860609	+	0.509267i	$0.170083\pi$
$641$	−2.20459	+	20.9753i	−0.0870761	+	0.828474i	−0.947685	+	0.319207i	$0.896583\pi$
$642$	0.248429	+	0.430291i	0.00980470	+	0.0169822i
$643$	8.16166	+	1.73481i	0.321864	+	0.0684144i	0.366011	−	0.930611i	$-0.380723\pi$
$643$	8.16166	+	1.73481i	0.321864	+	0.0684144i	−0.0441461	+	0.999025i	$0.514057\pi$
$644$	2.71838	−	3.01907i	0.107119	−	0.118968i
$645$	0.110563	+	0.0803284i	0.00435340	+	0.00316293i
$646$	10.7151	+	11.9003i	0.421579	+	0.468211i
$647$	14.1391	+	15.7031i	0.555867	+	0.617353i	0.953939	−	0.300002i	$-0.0969872\pi$
$647$	14.1391	+	15.7031i	0.555867	+	0.617353i	−0.398072	+	0.917354i	$0.630321\pi$
$648$	10.2387	−	7.43886i	0.402215	−	0.292226i
$649$	36.0011	+	16.0287i	1.41317	+	0.629183i
$650$	−2.57697	+	4.46344i	−0.101077	+	0.175070i
$651$	−0.0561678	+	0.0250075i	−0.00220139	+	0.000980122i
$652$	0.835766	−	7.95178i	0.0327311	−	0.311416i
$653$	0.593118	+	5.64314i	0.0232105	+	0.220833i	0.999979	+	0.00653437i	$0.00207997\pi$
$653$	0.593118	+	5.64314i	0.0232105	+	0.220833i	−0.976768	+	0.214299i	$0.931253\pi$
$654$	−0.318077	+	0.231096i	−0.0124378	+	0.00903659i
$655$	−0.790176	−	0.351809i	−0.0308747	−	0.0137463i
$656$	−2.62051	+	24.9325i	−0.102314	+	0.973449i
$657$	−29.6469	+	21.5397i	−1.15664	+	0.840345i
$658$	−0.790891	+	0.168109i	−0.0308321	+	0.00655358i
$659$	30.9314	−	13.7715i	1.20491	−	0.536463i	0.296701	−	0.954970i	$-0.404113\pi$
$659$	30.9314	−	13.7715i	1.20491	−	0.536463i	0.908213	+	0.418508i	$0.137447\pi$
$660$	0.127396	−	0.141488i	0.00495888	−	0.00550740i
$661$	6.02721	+	4.37902i	0.234431	+	0.170324i	0.698799	−	0.715318i	$-0.253718\pi$
$661$	6.02721	+	4.37902i	0.234431	+	0.170324i	−0.464367	+	0.885643i	$0.653718\pi$
$662$	−6.05475	−	2.69575i	−0.235325	−	0.104773i
$663$	−1.96412			−0.0762800
$664$	−1.75968	+	5.41575i	−0.0682890	+	0.210172i
$665$	0.0561054	+	0.533807i	0.00217567	+	0.0207002i
$666$	−3.36573	−	3.73803i	−0.130420	−	0.144846i
$667$	−36.8505	−	16.4069i	−1.42686	−	0.635278i
$668$	29.0964			1.12577
$669$	0.347165	−	1.06846i	0.0134222	−	0.0413092i
$670$	−0.628136	+	1.08796i	−0.0242670	+	0.0420317i
$671$	19.4884	−	59.9793i	0.752343	−	2.31547i
$672$	−0.0427840	+	0.131676i	−0.00165043	+	0.00507950i
$673$	−1.17604	+	11.1892i	−0.0453328	+	0.431313i	0.948192	+	0.317698i	$0.102910\pi$
$673$	−1.17604	+	11.1892i	−0.0453328	+	0.431313i	−0.993525	+	0.113615i	$0.963757\pi$
$674$	6.49853	−	4.72146i	0.250314	−	0.181864i
$675$	2.66617	+	0.566711i	0.102621	+	0.0218127i
$676$	2.83147	+	8.71438i	0.108903	+	0.335169i
$677$	−14.6046	−	44.9485i	−0.561302	−	1.72751i	−0.678691	−	0.734424i	$-0.737453\pi$
$677$	−14.6046	−	44.9485i	−0.561302	−	1.72751i	0.117389	−	0.993086i	$-0.462547\pi$
$678$	0.0147058	−	0.00654744i	0.000564773	−	0.000251453i
$679$	1.12226	−	1.94382i	0.0430686	−	0.0745969i
$680$	−1.30943	+	2.26800i	−0.0502143	+	0.0869737i
$681$	1.20873	−	0.538160i	0.0463186	−	0.0206224i
$682$	0.909508	+	2.79918i	0.0348269	+	0.107186i
$683$	12.9998	+	40.0093i	0.497423	+	1.53091i	0.813146	+	0.582060i	$0.197753\pi$
$683$	12.9998	+	40.0093i	0.497423	+	1.53091i	−0.315722	+	0.948852i	$0.602247\pi$
$684$	31.7707	+	6.75307i	1.21478	+	0.258210i
$685$	−0.904497	+	0.657156i	−0.0345591	+	0.0251086i
$686$	0.199044	−	1.89378i	0.00759954	−	0.0723048i
$687$	−0.650193	+	2.00109i	−0.0248064	+	0.0763463i
$688$	5.97752	−	18.3969i	0.227891	−	0.701376i
$689$	15.2503	−	26.4143i	0.580989	−	1.00630i
$690$	0.0149564	−	0.0460311i	0.000569380	−	0.00175237i
$691$	−4.82147			−0.183417			−0.0917087	−	0.995786i	$-0.529233\pi$
$691$	−4.82147			−0.183417			−0.0917087	+	0.995786i	$0.529233\pi$
$692$	6.11250	+	2.72146i	0.232362	+	0.103454i
$693$	−3.37299	−	3.74608i	−0.128129	−	0.142302i
$694$	0.331532	+	3.15431i	0.0125848	+	0.119736i
$695$	−0.854801	+	2.63081i	−0.0324245	+	0.0997922i
$696$	0.905961			0.0343404
$697$	−53.4923	−	23.8163i	−2.02616	−	0.902106i
$698$	8.64226	+	6.27897i	0.327114	+	0.237663i
$699$	1.17035	−	1.29980i	0.0442667	−	0.0491631i
$700$	3.15194	−	1.40333i	0.119132	−	0.0530410i
$701$	13.9703	−	2.96948i	0.527651	−	0.112156i	0.0636192	−	0.997974i	$-0.479736\pi$
$701$	13.9703	−	2.96948i	0.527651	−	0.112156i	0.464032	+	0.885819i	$0.346402\pi$
$702$	0.465842	−	0.338454i	0.0175821	−	0.0127741i
$703$	2.78821	−	26.5281i	0.105159	−	1.00052i
$704$	−20.3405	−	9.05616i	−0.766611	−	0.341317i
$705$	0.107990	−	0.0784597i	0.00406716	−	0.00295496i
$706$	−0.379682	−	3.61244i	−0.0142895	−	0.135956i
$707$	0.0453044	−	0.431043i	0.00170385	−	0.0162110i
$708$	1.37454	−	0.611985i	0.0516584	−	0.0229998i
$709$	9.84722	−	17.0559i	0.369820	−	0.640547i	−0.619717	−	0.784825i	$-0.712753\pi$
$709$	9.84722	−	17.0559i	0.369820	−	0.640547i	0.989537	+	0.144278i	$0.0460860\pi$
$710$	−0.736853	−	0.328068i	−0.0276536	−	0.0123122i
$711$	4.76746	−	3.46376i	0.178794	−	0.129901i
$712$	3.38565	+	3.76015i	0.126883	+	0.140917i
$713$	−6.93752	−	7.70490i	−0.259812	−	0.288551i
$714$	−0.0767652	−	0.0557732i	−0.00287286	−	0.00208726i
$715$	−2.10878	+	2.34204i	−0.0788639	+	0.0875872i
$716$	5.41406	+	1.15079i	0.202333	+	0.0430072i
$717$	0.326966	+	0.566322i	0.0122108	+	0.0211497i
$718$	0.570503	−	5.42797i	0.0212910	−	0.202570i
$719$	−8.87896	−	1.88728i	−0.331130	−	0.0703837i	0.0393469	−	0.999226i	$-0.487472\pi$
$719$	−8.87896	−	1.88728i	−0.331130	−	0.0703837i	−0.370476	+	0.928842i	$0.620806\pi$
$720$	0.247221	+	2.35215i	0.00921340	+	0.0876596i
$721$	2.16351	+	2.40282i	0.0805732	+	0.0894856i
$722$	−2.72949	−	4.72762i	−0.101581	−	0.175944i
$723$	0.705305	−	1.22162i	0.0262306	−	0.0454327i
$724$	−36.7381	+	7.80892i	−1.36536	+	0.290216i
$725$	−22.9231	−	25.4587i	−0.851342	−	0.945511i
$726$	0.252861	−	0.183715i	0.00938457	−	0.00681829i
$727$	7.01470	+	21.5890i	0.260161	+	0.800693i	0.992769	+	0.120042i	$0.0383029\pi$
$727$	7.01470	+	21.5890i	0.260161	+	0.800693i	−0.732608	+	0.680651i	$0.761697\pi$
$728$	0.466716	−	1.43640i	0.0172976	−	0.0532367i
$729$	21.4737	+	15.6016i	0.795323	+	0.577836i
$730$	0.115694	+	1.10076i	0.00428204	+	0.0407409i
$731$	36.5516	+	26.5563i	1.35191	+	0.982220i
$732$	−1.20394	−	2.08529i	−0.0444990	−	0.0770746i
$733$	2.52192	+	23.9945i	0.0931493	+	0.886256i	0.936918	+	0.349549i	$0.113665\pi$
$733$	2.52192	+	23.9945i	0.0931493	+	0.886256i	−0.843769	+	0.536707i	$0.819668\pi$
$734$	4.74544	−	1.00867i	0.175157	−	0.0372309i
$735$	0.0480802	+	0.147976i	0.00177346	+	0.00545816i
$736$	−23.3472			−0.860590
$737$	41.8649	−	46.4957i	1.54211	−	1.71269i
$738$	8.38366	−	1.78200i	0.308607	−	0.0655964i
$739$	7.83480	+	13.5703i	0.288208	+	0.499190i	0.973382	−	0.229189i	$-0.0736073\pi$
$739$	7.83480	+	13.5703i	0.288208	+	0.499190i	−0.685174	+	0.728379i	$0.740274\pi$
$740$	2.05920	−	0.437697i	0.0756977	−	0.0160900i
$741$	1.49129	+	0.316984i	0.0547840	+	0.0116447i
$742$	1.34610	−	0.599322i	0.0494168	−	0.0220018i
$743$	14.3421	−	6.38551i	0.526160	−	0.234262i	−0.126426	−	0.991976i	$-0.540351\pi$
$743$	14.3421	−	6.38551i	0.526160	−	0.234262i	0.652586	+	0.757714i	$0.273684\pi$
$744$	0.212726	+	0.0947116i	0.00779890	+	0.00347229i
$745$	−0.663789	−	0.141093i	−0.0243193	−	0.00516924i
$746$	−2.83227	−	8.71682i	−0.103697	−	0.319145i
$747$	−12.0116			−0.439483
$748$	42.1167	−	46.7753i	1.53994	−	1.71027i
$749$	−0.575507	+	5.47558i	−0.0210286	+	0.200073i
$750$	0.0553468	−	0.0614688i	0.00202098	−	0.00224452i
$751$	−23.8921	+	41.3823i	−0.871834	+	1.51006i	−0.0117373	+	0.999931i	$0.503736\pi$
$751$	−23.8921	+	41.3823i	−0.871834	+	1.51006i	−0.860097	+	0.510130i	$0.829597\pi$
$752$	−15.2853	−	11.1054i	−0.557397	−	0.404973i
$753$	−0.384672	−	0.666272i	−0.0140182	−	0.0242803i
$754$	−7.23703			−0.263557
$755$	−1.94085	−	2.32175i	−0.0706348	−	0.0844970i
$756$	−0.385470			−0.0140194
$757$	−6.05793	−	10.4926i	−0.220179	−	0.381361i	0.734683	−	0.678410i	$-0.237331\pi$
$757$	−6.05793	−	10.4926i	−0.220179	−	0.381361i	−0.954862	+	0.297049i	$0.903997\pi$
$758$	−5.19098	−	3.77146i	−0.188545	−	0.136986i
$759$	−1.20523	+	2.08752i	−0.0437472	+	0.0757723i
$760$	1.36023	−	1.51069i	0.0493408	−	0.0547986i
$761$	4.59466	−	43.7152i	0.166556	−	1.58468i	−0.517783	−	0.855512i	$-0.673242\pi$
$761$	4.59466	−	43.7152i	0.166556	−	1.58468i	0.684339	−	0.729164i	$-0.260091\pi$
$762$	0.00610510	−	0.00678040i	0.000221164	−	0.000245628i
$763$	−4.35671			−0.157723
$764$	−1.80516	−	5.55573i	−0.0653086	−	0.200999i
$765$	−5.40339	−	1.14852i	−0.195360	−	0.0415250i
$766$	0.311290	+	0.138595i	0.0112474	+	0.00500765i
$767$	−22.7527	+	10.1301i	−0.821552	+	0.365778i
$768$	−0.528753	+	0.235416i	−0.0190797	+	0.00849484i
$769$	−8.40701	−	1.78697i	−0.303165	−	0.0644396i	0.0538177	−	0.998551i	$-0.482861\pi$
$769$	−8.40701	−	1.78697i	−0.303165	−	0.0644396i	−0.356982	+	0.934111i	$0.616194\pi$
$770$	−0.148924	+	0.0316547i	−0.00536683	+	0.00114076i
$771$	0.316851	+	0.548803i	0.0114111	+	0.0197647i
$772$	−11.9660	+	2.54345i	−0.430666	+	0.0915409i
$773$	−10.4160	+	11.5682i	−0.374639	+	0.416079i	−0.900751	−	0.434337i	$-0.856983\pi$
$773$	−10.4160	+	11.5682i	−0.374639	+	0.416079i	0.526111	+	0.850416i	$0.323649\pi$
$774$	−6.61328			−0.237710
$775$	−2.72098	−	8.37430i	−0.0977403	−	0.300814i
$776$	−8.31500	+	1.76741i	−0.298491	+	0.0634462i
$777$	0.0165214	+	0.157191i	0.000592704	+	0.00563920i
$778$	3.35789	+	5.81604i	0.120386	+	0.208515i
$779$	36.7713	+	26.7159i	1.31747	+	0.957197i
$780$	0.0125775	+	0.119667i	0.000450349	+	0.00428478i
$781$	32.4986	+	23.6116i	1.16289	+	0.844890i
$782$	4.94453	−	15.2177i	0.176816	−	0.544184i
$783$	1.18273	+	3.64008i	0.0422675	+	0.130086i
$784$	17.8168	−	12.9447i	0.636315	−	0.462310i
$785$	1.09284	+	1.21373i	0.0390053	+	0.0433197i
$786$	−0.116098	+	0.0246774i	−0.00414109	+	0.000880215i
$787$	−15.9211	+	27.5761i	−0.567526	+	0.982983i	0.429284	+	0.903170i	$0.358766\pi$
$787$	−15.9211	+	27.5761i	−0.567526	+	0.982983i	−0.996810	+	0.0798138i	$0.974567\pi$
$788$	5.47541	+	9.48369i	0.195053	+	0.337843i
$789$	−1.17460	−	1.30452i	−0.0418167	−	0.0464422i
$790$	−0.0186046	−	0.177011i	−0.000661921	−	0.00629775i
$791$	0.174480	+	0.0370870i	0.00620381	+	0.00131866i
$792$	−1.99559	+	18.9867i	−0.0709101	+	0.674665i
$793$	19.9288	+	34.5177i	0.707693	+	1.22576i
$794$	−7.48483	−	1.59095i	−0.265627	−	0.0564607i
$795$	−0.162770	+	0.180774i	−0.00577284	+	0.00641139i
$796$	−34.6445	−	25.1707i	−1.22794	−	0.892152i
$797$	15.4867	+	17.1997i	0.548566	+	0.609245i	0.952125	−	0.305709i	$-0.0988935\pi$
$797$	15.4867	+	17.1997i	0.548566	+	0.609245i	−0.403559	+	0.914954i	$0.632227\pi$
$798$	0.0492843	+	0.0547357i	0.00174464	+	0.00193762i
$799$	35.7013	−	25.9385i	1.26302	−	0.917638i
$800$	−18.1140	−	8.06487i	−0.640426	−	0.285136i
$801$	−5.33643	+	9.24298i	−0.188554	+	0.326584i
$802$	−6.13104	+	2.72971i	−0.216494	+	0.0963895i
$803$	5.76193	−	54.8211i	0.203334	−	1.93459i
$804$	−0.249698	−	2.37572i	−0.00880617	−	0.0837851i
$805$	0.433897	−	0.315244i	0.0152929	−	0.0111109i
$806$	−1.69930	−	0.756578i	−0.0598554	−	0.0266493i
$807$	−0.0267658	+	0.254660i	−0.000942201	+	0.00896444i
$808$	−1.32799	+	0.964845i	−0.0467187	+	0.0339431i
$809$	28.5727	−	6.07332i	1.00456	−	0.213526i	0.323875	−	0.946100i	$-0.395014\pi$
$809$	28.5727	−	6.07332i	1.00456	−	0.213526i	0.680688	+	0.732573i	$0.261681\pi$
$810$	0.736586	−	0.327949i	0.0258810	−	0.0115230i
$811$	−12.6590	+	14.0592i	−0.444516	+	0.493686i	−0.923210	−	0.384297i	$-0.874444\pi$
$811$	−12.6590	+	14.0592i	−0.444516	+	0.493686i	0.478693	+	0.877982i	$0.341111\pi$
$812$	3.91947	+	2.84766i	0.137546	+	0.0999332i
$813$	−0.784635	−	0.349342i	−0.0275183	−	0.0122520i
$814$	7.56624			0.265197
$815$	0.326184	−	1.00389i	0.0114257	−	0.0351647i
$816$	−0.231763	−	2.20508i	−0.00811334	−	0.0771933i
$817$	−23.4666	−	26.0623i	−0.820993	−	0.911805i
$818$	−6.35224	−	2.82820i	−0.222101	−	0.0988856i
$819$	3.18581			0.111321
$820$	−1.10850	+	3.41162i	−0.0387106	+	0.119139i
$821$	6.09951	−	10.5647i	0.212874	−	0.368709i	−0.739739	−	0.672894i	$-0.765051\pi$
$821$	6.09951	−	10.5647i	0.212874	−	0.368709i	0.952613	+	0.304185i	$0.0983841\pi$
$822$	−0.0474088	+	0.145909i	−0.00165357	+	0.00508918i
$823$	8.90779	−	27.4154i	0.310506	−	0.955640i	−0.667059	−	0.745005i	$-0.732447\pi$
$823$	8.90779	−	27.4154i	0.310506	−	0.955640i	0.977565	−	0.210635i	$-0.0675530\pi$
$824$	1.28001	−	12.1785i	0.0445914	−	0.424259i
$825$	−1.65618	+	1.20328i	−0.0576607	+	0.0418929i
$826$	−1.17692	−	0.250161i	−0.0409502	−	0.00870423i
$827$	−2.46844	−	7.59707i	−0.0858360	−	0.264176i	0.898921	−	0.438110i	$-0.144352\pi$
$827$	−2.46844	−	7.59707i	−0.0858360	−	0.264176i	−0.984757	+	0.173934i	$0.944352\pi$
$828$	−10.0291	−	30.8665i	−0.348537	−	1.07269i
$829$	18.0498	−	8.03627i	0.626894	−	0.279111i	−0.0685986	−	0.997644i	$-0.521853\pi$
$829$	18.0498	−	8.03627i	0.626894	−	0.279111i	0.695493	+	0.718533i	$0.255186\pi$
$830$	−0.181396	+	0.314187i	−0.00629635	+	0.0109056i
$831$	−1.07137	+	1.85566i	−0.0371654	+	0.0643723i
$832$	12.8552	−	5.72349i	0.445673	−	0.198426i
$833$	15.8951	+	48.9202i	0.550734	+	1.69499i
$834$	0.117298	+	0.361008i	0.00406171	+	0.0125007i
$835$	3.75727	+	0.798633i	0.130026	+	0.0276378i
$836$	−39.5268	+	28.7179i	−1.36706	+	0.993229i
$837$	−0.102830	+	0.978361i	−0.00355432	+	0.0338171i
$838$	1.16596	−	3.58846i	0.0402775	−	0.123961i
$839$	−3.34597	+	10.2979i	−0.115516	+	0.355521i	−0.992054	−	0.125811i	$-0.959847\pi$
$839$	−3.34597	+	10.2979i	−0.115516	+	0.355521i	0.876538	+	0.481332i	$0.159847\pi$
$840$	−0.00602275	+	0.0104317i	−0.000207805	+	0.000359928i
$841$	5.90355	−	18.1693i	0.203571	−	0.626526i
$842$	6.00154			0.206827
$843$	1.23374	+	0.549296i	0.0424922	+	0.0189188i
$844$	10.8078	+	12.0033i	0.372020	+	0.413170i
$845$	0.126443	+	1.20302i	0.00434977	+	0.0413853i
$846$	−1.99608	+	6.14329i	−0.0686265	+	0.211211i
$847$	3.46345			0.119006
$848$	31.4544	+	14.0044i	1.08015	+	0.480912i
$849$	0.469021	+	0.340763i	0.0160967	+	0.0116950i
$850$	9.09290	−	10.0987i	0.311884	−	0.346382i
$851$	−24.3489	+	10.8408i	−0.834671	+	0.371619i
$852$	1.50021	−	0.318880i	0.0513964	−	0.0109246i
$853$	−13.8097	+	10.0333i	−0.472836	+	0.343535i	−0.798545	−	0.601935i	$-0.794397\pi$
$853$	−13.8097	+	10.0333i	−0.472836	+	0.343535i	0.325710	+	0.945470i	$0.394397\pi$
$854$	−0.201273	+	1.91498i	−0.00688741	+	0.0655293i
$855$	3.91726	+	1.74408i	0.133967	+	0.0596462i
$856$	16.8697	−	12.2565i	0.576593	−	0.418919i
$857$	−0.630123	−	5.99522i	−0.0215246	−	0.204793i	0.978474	−	0.206369i	$-0.0661649\pi$
$857$	−0.630123	−	5.99522i	−0.0215246	−	0.204793i	−0.999999	+	0.00157646i	$0.999498\pi$
$858$	−0.0452045	+	0.430093i	−0.00154326	+	0.0146831i
$859$	−14.7417	+	6.56342i	−0.502980	+	0.223941i	−0.642511	−	0.766277i	$-0.722107\pi$
$859$	−14.7417	+	6.56342i	−0.502980	+	0.223941i	0.139531	+	0.990218i	$0.455441\pi$
$860$	1.38393	−	2.39703i	0.0471915	−	0.0817380i
$861$	−0.246039	−	0.109544i	−0.00838499	−	0.00373324i
$862$	−6.94899	+	5.04874i	−0.236684	+	0.171961i
$863$	21.0813	+	23.4132i	0.717616	+	0.796993i	0.986076	−	0.166298i	$-0.0531813\pi$
$863$	21.0813	+	23.4132i	0.717616	+	0.796993i	−0.268460	+	0.963291i	$0.586515\pi$
$864$	1.48230	+	1.64627i	0.0504290	+	0.0560071i
$865$	0.714621	+	0.519203i	0.0242978	+	0.0176534i
$866$	−8.39079	+	9.31891i	−0.285131	+	0.316670i
$867$	3.53399	+	0.751172i	0.120020	+	0.0255111i
$868$	0.622615	+	1.07840i	0.0211329	+	0.0366033i
$869$	−0.926564	+	8.81567i	−0.0314315	+	0.299051i
$870$	0.0564572	+	0.0120003i	0.00191408	+	0.000406850i
$871$	4.13324	+	39.3251i	0.140049	+	1.33248i
$872$	11.0408	+	12.2621i	0.373890	+	0.415247i
$873$	−8.96556	−	15.5288i	−0.303438	−	0.525570i
$874$	−6.21017	+	10.7563i	−0.210062	+	0.363839i
$875$	0.896540	−	0.190565i	0.0303086	−	0.00644229i
$876$	−1.40827	−	1.56404i	−0.0475810	−	0.0528440i
$877$	−3.95070	+	2.87035i	−0.133406	+	0.0969249i	−0.652487	−	0.757800i	$-0.726274\pi$
$877$	−3.95070	+	2.87035i	−0.133406	+	0.0969249i	0.519081	+	0.854725i	$0.326274\pi$
$878$	2.93199	+	9.02373i	0.0989498	+	0.304536i
$879$	0.0650450	−	0.200188i	0.00219392	−	0.00675218i
$880$	−2.87820	−	2.09113i	−0.0970240	−	0.0704921i
$881$	−0.499146	−	4.74906i	−0.0168167	−	0.160000i	0.982891	−	0.184190i	$-0.0589661\pi$
$881$	−0.499146	−	4.74906i	−0.0168167	−	0.160000i	−0.999707	+	0.0241898i	$0.992299\pi$
$882$	−6.09128	−	4.42557i	−0.205104	−	0.149017i
$883$	7.79204	+	13.4962i	0.262223	+	0.454183i	0.966832	−	0.255412i	$-0.0822111\pi$
$883$	7.79204	+	13.4962i	0.262223	+	0.454183i	−0.704609	+	0.709595i	$0.748878\pi$
$884$	4.15809	+	39.5616i	0.139852	+	1.33060i
$885$	0.194295	−	0.0412986i	0.00653115	−	0.00138824i
$886$	−4.39375	−	13.5226i	−0.147611	−	0.454299i
$887$	−11.7848			−0.395695			−0.197848	−	0.980233i	$-0.563395\pi$
$887$	−11.7848			−0.395695			−0.197848	+	0.980233i	$0.563395\pi$
$888$	0.400550	−	0.444856i	0.0134416	−	0.0149284i
$889$	0.0988940	−	0.0210206i	0.00331680	−	0.000705007i
$890$	0.161178	+	0.279169i	0.00540271	+	0.00935777i
$891$	−39.2784	+	8.34888i	−1.31588	+	0.279698i
$892$	−22.2561	−	4.73069i	−0.745191	−	0.158395i
$893$	−31.2930	+	13.9325i	−1.04718	+	0.466235i
$894$	−0.0850713	+	0.0378762i	−0.00284521	+	0.00126677i
$895$	0.667543	+	0.297209i	0.0223135	+	0.00993460i
$896$	3.60570	+	0.766415i	0.120458	+	0.0256041i
$897$	−0.470760	−	1.44885i	−0.0157182	−	0.0483757i
$898$	−10.8658			−0.362596
$899$	8.27322	−	9.18835i	0.275927	−	0.306449i
$900$	2.88114	−	27.4122i	0.0960380	−	0.913741i
$901$	−53.8111	+	59.7632i	−1.79271	+	1.99100i
$902$	−6.44630	+	11.1653i	−0.214638	+	0.371765i
$903$	0.168120	+	0.122146i	0.00559468	+	0.00406478i
$904$	−0.337788	−	0.585067i	−0.0112347	−	0.0194590i
$905$	−4.95841			−0.164823
$906$	−0.402732	−	0.101206i	−0.0133799	−	0.00336234i
$907$	8.85780			0.294118			0.147059	−	0.989128i	$-0.453019\pi$
$907$	8.85780			0.294118			0.147059	+	0.989128i	$0.453019\pi$
$908$	−13.3986	−	23.2071i	−0.444649	−	0.770155i
$909$	−2.80121	−	2.03520i	−0.0929104	−	0.0675033i
$910$	0.0481111	−	0.0833309i	0.00159487	−	0.00276239i
$911$	32.0824	−	35.6311i	1.06294	−	1.18051i	0.0799569	−	0.996798i	$-0.474522\pi$
$911$	32.0824	−	35.6311i	1.06294	−	1.18051i	0.982980	−	0.183713i	$-0.0588116\pi$
$912$	−0.179902	+	1.71165i	−0.00595715	+	0.0566785i
$913$	12.0900	−	13.4273i	0.400119	−	0.444377i
$914$	−2.65886			−0.0879472
$915$	−0.0982309	−	0.302324i	−0.00324741	−	0.00999451i
$916$	41.6828	+	8.85995i	1.37724	+	0.292741i
$917$	−1.20153	−	0.534957i	−0.0396781	−	0.0176658i
$918$	−1.38696	+	0.617515i	−0.0457765	+	0.0203810i
$919$	−42.6736	+	18.9995i	−1.40767	+	0.626737i	−0.963134	−	0.269023i	$-0.913299\pi$
$919$	−42.6736	+	18.9995i	−1.40767	+	0.626737i	−0.444540	+	0.895759i	$0.646633\pi$
$920$	−1.98685	−	0.422319i	−0.0655046	−	0.0139234i
$921$	−2.23112	+	0.474238i	−0.0735178	+	0.0156267i
$922$	1.72877	+	2.99431i	0.0569339	+	0.0986124i
$923$	−24.8329	+	5.27840i	−0.817386	+	0.173741i
$924$	0.193717	−	0.215144i	0.00637281	−	0.00707773i
$925$	−22.6359			−0.744265
$926$	1.31307	+	4.04122i	0.0431502	+	0.132803i
$927$	25.2659	−	5.37042i	0.829840	−	0.176388i
$928$	−2.91032	−	27.6898i	−0.0955358	−	0.908963i
$929$	12.6458	+	21.9031i	0.414894	+	0.718618i	0.995417	−	0.0956259i	$-0.0304852\pi$
$929$	12.6458	+	21.9031i	0.414894	+	0.718618i	−0.580523	+	0.814244i	$0.697152\pi$
$930$	0.0120020	+	0.00871994i	0.000393560	+	0.000285938i
$931$	−4.17357	−	39.7088i	−0.136783	−	1.30140i
$932$	−28.6585	−	20.8217i	−0.938742	−	0.682036i
$933$	−0.679870	+	2.09242i	−0.0222579	+	0.0685029i
$934$	−0.136585	−	0.420365i	−0.00446919	−	0.0137547i
$935$	6.72250	−	4.88418i	0.219849	−	0.159730i
$936$	−8.07353	−	8.96656i	−0.263892	−	0.293081i
$937$	−3.15640	+	0.670913i	−0.103115	+	0.0219178i	−0.259180	−	0.965829i	$-0.583452\pi$
$937$	−3.15640	+	0.670913i	−0.103115	+	0.0219178i	0.156065	+	0.987747i	$0.450119\pi$
$938$	−0.955135	+	1.65434i	−0.0311863	+	0.0540162i
$939$	0.132801	+	0.230018i	0.00433379	+	0.00750635i
$940$	−1.80897	−	2.00906i	−0.0590020	−	0.0655284i
$941$	3.43563	+	32.6879i	0.111998	+	1.06559i	0.895762	+	0.444534i	$0.146631\pi$
$941$	3.43563	+	32.6879i	0.111998	+	1.06559i	−0.783763	+	0.621059i	$0.786703\pi$
$942$	0.219219	+	0.0465965i	0.00714255	+	0.00151820i
$943$	4.74728	−	45.1674i	0.154593	−	1.47085i
$944$	−14.0577	−	24.3487i	−0.457540	−	0.792483i
$945$	−0.0497765	−	0.0105803i	−0.00161923	−	0.000344178i
$946$	6.65640	−	7.39268i	0.216418	−	0.240357i
$947$	20.6075	+	14.9722i	0.669655	+	0.486533i	0.869910	−	0.493211i	$-0.164177\pi$
$947$	20.6075	+	14.9722i	0.669655	+	0.486533i	−0.200255	+	0.979744i	$0.564177\pi$
$948$	0.226461	+	0.251510i	0.00735510	+	0.00816867i
$949$	23.3110	+	25.8895i	0.756707	+	0.840408i
$950$	−8.53375	+	6.20013i	−0.276871	+	0.201159i
$951$	−1.75929	−	0.783287i	−0.0570490	−	0.0253998i
$952$	−1.99110	+	3.44869i	−0.0645319	+	0.111773i
$953$	−11.7394	+	5.22672i	−0.380277	+	0.169310i	−0.587968	−	0.808884i	$-0.700072\pi$
$953$	−11.7394	+	5.22672i	−0.380277	+	0.169310i	0.207691	+	0.978194i	$0.433405\pi$
$954$	1.23045	−	11.7069i	0.0398373	−	0.379026i
$955$	−0.0806118	−	0.766970i	−0.00260854	−	0.0248186i
$956$	10.7148	−	7.78473i	0.346540	−	0.251776i
$957$	−2.62604	−	1.16919i	−0.0848878	−	0.0377945i
$958$	1.32206	−	12.5785i	0.0427137	−	0.406394i
$959$	−1.37537	+	0.999263i	−0.0444129	+	0.0322679i
$960$	−0.109776	+	0.0233335i	−0.00354300	+	0.000753087i
$961$	−25.4167	+	11.3163i	−0.819894	+	0.365041i
$962$	−3.19969	+	3.55361i	−0.103162	+	0.114573i
$963$	35.5841	+	25.8534i	1.14668	+	0.833113i
$964$	−26.0993	−	11.6202i	−0.840602	−	0.374260i
$965$	−1.61501			−0.0519890
$966$	0.0227425	−	0.0699943i	0.000731728	−	0.00225203i
$967$	5.73418	+	54.5571i	0.184399	+	1.75444i	0.560772	+	0.827970i	$0.310505\pi$
$967$	5.73418	+	54.5571i	0.184399	+	1.75444i	−0.376373	+	0.926468i	$0.622829\pi$
$968$	−8.77713	−	9.74799i	−0.282108	−	0.313312i
$969$	−3.67233	−	1.63503i	−0.117972	−	0.0525246i
$970$	−0.541580			−0.0173891
$971$	−7.72103	+	23.7629i	−0.247780	+	0.762588i	0.747387	+	0.664389i	$0.231308\pi$
$971$	−7.72103	+	23.7629i	−0.247780	+	0.762588i	−0.995167	+	0.0981988i	$0.968692\pi$
$972$	−2.31067	+	4.00220i	−0.0741149	+	0.128371i
$973$	−1.29980	+	4.00037i	−0.0416697	+	0.128246i
$974$	−2.71693	+	8.36184i	−0.0870559	+	0.267931i
$975$	0.135238	−	1.28671i	0.00433110	−	0.0412076i
$976$	−36.4009	+	26.4468i	−1.16516	+	0.846541i
$977$	19.4274	+	4.12942i	0.621538	+	0.132112i	0.507908	−	0.861411i	$-0.330419\pi$
$977$	19.4274	+	4.12942i	0.621538	+	0.132112i	0.113630	+	0.993523i	$0.463752\pi$
$978$	−0.0447599	−	0.137757i	−0.00143126	−	0.00440498i
$979$	−4.96107	−	15.2686i	−0.158556	−	0.487986i
$980$	2.87876	−	1.28171i	0.0919588	−	0.0409427i
$981$	−17.4025	+	30.1420i	−0.555618	+	0.962359i
$982$	−7.38487	+	12.7910i	−0.235661	+	0.408177i
$983$	−51.4906	+	22.9251i	−1.64229	+	0.731196i	−0.999396	−	0.0347558i	$-0.988935\pi$
$983$	−51.4906	+	22.9251i	−1.64229	+	0.731196i	−0.642898	+	0.765952i	$0.722268\pi$
$984$	0.315202	+	0.970092i	0.0100483	+	0.0309254i
$985$	0.446744	+	1.37494i	0.0142345	+	0.0438091i
$986$	18.6646	+	3.96727i	0.594401	+	0.126344i
$987$	0.164209	−	0.119305i	0.00522683	−	0.00379751i
$988$	3.22764	−	30.7089i	0.102685	−	0.976982i
$989$	−10.8288	+	33.3276i	−0.344336	+	1.05976i
$990$	−0.375858	+	1.15677i	−0.0119456	+	0.0367646i
$991$	0.618400	−	1.07110i	0.0196441	−	0.0340246i	−0.856036	−	0.516916i	$-0.827080\pi$
$991$	0.618400	−	1.07110i	0.0196441	−	0.0340246i	0.875680	+	0.482891i	$0.160413\pi$
$992$	2.21140	−	6.80600i	0.0702121	−	0.216091i
$993$	1.66377			0.0527981
$994$	−1.12045	−	0.498857i	−0.0355385	−	0.0158228i
$995$	−3.78284	−	4.20127i	−0.119924	−	0.133189i
$996$	−0.0721090	−	0.686071i	−0.00228486	−	0.0217390i
$997$	−1.52035	+	4.67917i	−0.0481501	+	0.148191i	−0.972241	−	0.233982i	$-0.924824\pi$
$997$	−1.52035	+	4.67917i	−0.0481501	+	0.148191i	0.924091	+	0.382173i	$0.124824\pi$
$998$	−0.218791			−0.00692570
$999$	2.31032	+	1.02862i	0.0730951	+	0.0325441i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.2.g.a.76.6	yes	96
151.2	even	15	inner	151.2.g.a.2.6	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.2.g.a.2.6	✓	96	151.2	even	15	inner
151.2.g.a.76.6	yes	96	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	151.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.183451 - 0.317746i) q^{2} +(0.0745133 + 0.0541371i) q^{3} +(0.932692 - 1.61547i) q^{4} +(0.164782 - 0.183009i) q^{5} +(0.00353232 - 0.0336078i) q^{6} +(0.250565 - 0.278280i) q^{7} -1.41821 q^{8} +(-0.924430 - 2.84510i) q^{9} +O(q^{10})\)	\(q+(-0.183451 - 0.317746i) q^{2} +(0.0745133 + 0.0541371i) q^{3} +(0.932692 - 1.61547i) q^{4} +(0.164782 - 0.183009i) q^{5} +(0.00353232 - 0.0336078i) q^{6} +(0.250565 - 0.278280i) q^{7} -1.41821 q^{8} +(-0.924430 - 2.84510i) q^{9} +(-0.0883795 - 0.0187856i) q^{10} +(4.11086 + 1.83027i) q^{11} +(0.156955 - 0.0698807i) q^{12} +(-2.59806 + 1.15673i) q^{13} +(-0.134389 - 0.0285652i) q^{14} +(0.0221860 - 0.00471577i) q^{15} +(-1.60521 - 2.78031i) q^{16} +(7.33460 - 1.55902i) q^{17} +(-0.734432 + 0.815669i) q^{18} -5.82054 q^{19} +(-0.141954 - 0.436890i) q^{20} +(0.0337357 - 0.00717074i) q^{21} +(-0.172578 - 1.64197i) q^{22} +(2.90798 + 5.03677i) q^{23} +(-0.105676 - 0.0767779i) q^{24} +(0.516303 + 4.91230i) q^{25} +(0.844163 + 0.613320i) q^{26} +(0.170528 - 0.524831i) q^{27} +(-0.215854 - 0.664330i) q^{28} +(-5.61112 + 4.07672i) q^{29} +(-0.00556844 - 0.00618438i) q^{30} +(-1.74372 + 0.370639i) q^{31} +(-2.00717 + 3.47652i) q^{32} +(0.207228 + 0.358930i) q^{33} +(-1.84091 - 2.04454i) q^{34} +(-0.00963922 - 0.0917110i) q^{35} +(-5.45838 - 1.16022i) q^{36} +(-0.479030 + 4.55767i) q^{37} +(1.06778 + 1.84945i) q^{38} +(-0.256212 - 0.0544596i) q^{39} +(-0.233696 + 0.259545i) q^{40} +(-6.31752 - 4.58994i) q^{41} +(-0.00846731 - 0.00940390i) q^{42} +(4.03169 + 4.47765i) q^{43} +(6.79092 - 4.93389i) q^{44} +(-0.673007 - 0.299642i) q^{45} +(1.06694 - 1.84800i) q^{46} +(5.37631 - 2.39369i) q^{47} +(0.0309081 - 0.294071i) q^{48} +(0.717042 + 6.82220i) q^{49} +(1.46615 - 1.06522i) q^{50} +(0.630926 + 0.280906i) q^{51} +(-0.554526 + 5.27597i) q^{52} +(-8.67653 + 6.30387i) q^{53} +(-0.198046 + 0.0420960i) q^{54} +(1.01235 - 0.450728i) q^{55} +(-0.355355 + 0.394661i) q^{56} +(-0.433707 - 0.315107i) q^{57} +(2.32472 + 1.03503i) q^{58} +8.75756 q^{59} +(0.0130745 - 0.0402391i) q^{60} +(-1.46496 - 13.9382i) q^{61} +(0.437655 + 0.486065i) q^{62} +(-1.02337 - 0.455632i) q^{63} -4.94798 q^{64} +(-0.216421 + 0.666076i) q^{65} +(0.0760323 - 0.131692i) q^{66} +(4.29654 - 13.2234i) q^{67} +(4.32238 - 13.3029i) q^{68} +(-0.0559928 + 0.532736i) q^{69} +(-0.0273725 + 0.0198873i) q^{70} +(8.73189 + 1.85602i) q^{71} +(1.31104 + 4.03496i) q^{72} +(-3.78541 - 11.6503i) q^{73} +(1.53606 - 0.683897i) q^{74} +(-0.227466 + 0.393982i) q^{75} +(-5.42877 + 9.40290i) q^{76} +(1.53937 - 0.685371i) q^{77} +(0.0296980 + 0.0914010i) q^{78} +(0.608724 + 1.87346i) q^{79} +(-0.773329 - 0.164376i) q^{80} +(-7.21944 + 5.24523i) q^{81} +(-0.299483 + 2.84939i) q^{82} +(1.24078 - 3.81871i) q^{83} +(0.0198809 - 0.0611871i) q^{84} +(0.923294 - 1.59919i) q^{85} +(0.683137 - 2.10248i) q^{86} -0.638804 q^{87} +(-5.83008 - 2.59572i) q^{88} +(-2.38726 - 2.65133i) q^{89} +(0.0282536 + 0.268815i) q^{90} +(-0.329087 + 1.01283i) q^{91} +10.8490 q^{92} +(-0.149995 - 0.0667823i) q^{93} +(-1.74687 - 1.26918i) q^{94} +(-0.959117 + 1.06521i) q^{95} +(-0.337769 + 0.150384i) q^{96} +(5.86301 - 1.24622i) q^{97} +(2.03618 - 1.47937i) q^{98} +(1.40711 - 13.3878i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 3 q^{2} - 4 q^{3} - 49 q^{4} - 9 q^{5} + 7 q^{6} - 7 q^{7} + 12 q^{8} - 32 q^{9}+O(q^{10}) \) 96 * q - 3 * q^2 - 4 * q^3 - 49 * q^4 - 9 * q^5 + 7 * q^6 - 7 * q^7 + 12 * q^8 - 32 * q^9	\( 96 q - 3 q^{2} - 4 q^{3} - 49 q^{4} - 9 q^{5} + 7 q^{6} - 7 q^{7} + 12 q^{8} - 32 q^{9} + 11 q^{10} - 7 q^{11} + 7 q^{12} - 8 q^{13} + 5 q^{14} + 10 q^{15} - 47 q^{16} - 26 q^{17} - 40 q^{18} - 20 q^{19} + 23 q^{20} - 2 q^{21} - 32 q^{22} - q^{23} + 95 q^{24} - 51 q^{25} + 41 q^{26} + 5 q^{27} - 2 q^{28} + 13 q^{29} + 19 q^{30} - 24 q^{31} - 60 q^{32} + 39 q^{33} + 47 q^{34} - 54 q^{35} + 11 q^{36} + 5 q^{37} + 8 q^{38} - 13 q^{39} - 74 q^{40} + 8 q^{41} + 166 q^{42} - 8 q^{43} + 18 q^{44} - 33 q^{45} + 21 q^{46} - 5 q^{47} + 8 q^{48} + 21 q^{49} - 72 q^{50} - 6 q^{51} + 96 q^{52} + 41 q^{53} - 60 q^{54} - 116 q^{55} - 85 q^{56} - 8 q^{57} - 58 q^{58} + 32 q^{59} - 6 q^{60} - 18 q^{61} + 38 q^{62} - 129 q^{63} + 160 q^{64} + 53 q^{65} + 43 q^{66} + 4 q^{67} + 10 q^{68} + 81 q^{69} + 33 q^{70} - 41 q^{71} - 40 q^{72} - 58 q^{73} - 20 q^{74} + 32 q^{75} - q^{76} - 22 q^{77} - 10 q^{78} + 32 q^{79} + 71 q^{80} - 66 q^{81} - 10 q^{82} + 80 q^{83} - 58 q^{84} - 2 q^{85} - 72 q^{86} + 72 q^{87} + 89 q^{88} + 9 q^{89} + 121 q^{90} - 138 q^{91} - 72 q^{92} - 85 q^{93} + 11 q^{94} - 47 q^{95} - 201 q^{96} + 54 q^{97} - 92 q^{98} - 21 q^{99}+O(q^{100}) \) 96 * q - 3 * q^2 - 4 * q^3 - 49 * q^4 - 9 * q^5 + 7 * q^6 - 7 * q^7 + 12 * q^8 - 32 * q^9 + 11 * q^10 - 7 * q^11 + 7 * q^12 - 8 * q^13 + 5 * q^14 + 10 * q^15 - 47 * q^16 - 26 * q^17 - 40 * q^18 - 20 * q^19 + 23 * q^20 - 2 * q^21 - 32 * q^22 - q^23 + 95 * q^24 - 51 * q^25 + 41 * q^26 + 5 * q^27 - 2 * q^28 + 13 * q^29 + 19 * q^30 - 24 * q^31 - 60 * q^32 + 39 * q^33 + 47 * q^34 - 54 * q^35 + 11 * q^36 + 5 * q^37 + 8 * q^38 - 13 * q^39 - 74 * q^40 + 8 * q^41 + 166 * q^42 - 8 * q^43 + 18 * q^44 - 33 * q^45 + 21 * q^46 - 5 * q^47 + 8 * q^48 + 21 * q^49 - 72 * q^50 - 6 * q^51 + 96 * q^52 + 41 * q^53 - 60 * q^54 - 116 * q^55 - 85 * q^56 - 8 * q^57 - 58 * q^58 + 32 * q^59 - 6 * q^60 - 18 * q^61 + 38 * q^62 - 129 * q^63 + 160 * q^64 + 53 * q^65 + 43 * q^66 + 4 * q^67 + 10 * q^68 + 81 * q^69 + 33 * q^70 - 41 * q^71 - 40 * q^72 - 58 * q^73 - 20 * q^74 + 32 * q^75 - q^76 - 22 * q^77 - 10 * q^78 + 32 * q^79 + 71 * q^80 - 66 * q^81 - 10 * q^82 + 80 * q^83 - 58 * q^84 - 2 * q^85 - 72 * q^86 + 72 * q^87 + 89 * q^88 + 9 * q^89 + 121 * q^90 - 138 * q^91 - 72 * q^92 - 85 * q^93 + 11 * q^94 - 47 * q^95 - 201 * q^96 + 54 * q^97 - 92 * q^98 - 21 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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