LMFDB - Embedded newform 930.2.bg.f.421.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(121,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	16.0.1669788916259765625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 16x^{14} + 90x^{12} + 239x^{10} + 329x^{8} + 239x^{6} + 90x^{4} + 16x^{2} + 1 $ x^16 + 16x^14 + 90x^12 + 239x^10 + 329x^8 + 239x^6 + 90x^4 + 16*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			421.2
Root			$1.28249i$ of defining polynomial
Character	$\chi$	$=$	930.421
Dual form			930.2.bg.f.391.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.913545 - 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.736831 + 0.818334i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.913545 - 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.736831 + 0.818334i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +(-0.913545 - 0.406737i) q^{10} +(3.09447 - 0.657750i) q^{11} +(-0.104528 - 0.994522i) q^{12} +(0.424121 - 4.03524i) q^{13} +(1.07711 + 0.228947i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-4.08139 - 0.867525i) q^{17} +(0.104528 - 0.994522i) q^{18} +(-0.190549 - 1.81295i) q^{19} +(-0.978148 + 0.207912i) q^{20} +(1.00597 + 0.447889i) q^{21} +(2.11686 - 2.35101i) q^{22} +(1.98108 + 6.09714i) q^{23} +(-0.669131 - 0.743145i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.02874 - 3.51387i) q^{26} +(0.309017 - 0.951057i) q^{27} +(1.00597 - 0.447889i) q^{28} +(8.38934 - 6.09521i) q^{29} -1.00000 q^{30} +(-5.49644 - 0.888362i) q^{31} -1.00000 q^{32} +(2.55941 - 1.85952i) q^{33} +(-3.81183 + 1.69714i) q^{34} +(0.340282 - 1.04728i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.56722 + 2.71450i) q^{37} +(-1.21978 - 1.35471i) q^{38} +(-1.25383 - 3.85888i) q^{39} +(-0.669131 + 0.743145i) q^{40} +(4.76896 + 2.12328i) q^{41} +(1.07711 - 0.228947i) q^{42} +(-0.0293865 - 0.279594i) q^{43} +(0.330686 - 3.14627i) q^{44} +(-0.978148 - 0.207912i) q^{45} +(5.18654 + 3.76824i) q^{46} +(0.876596 + 0.636884i) q^{47} +(-0.978148 - 0.207912i) q^{48} +(0.604949 - 5.75571i) q^{49} +(0.104528 + 0.994522i) q^{50} +(-4.08139 + 0.867525i) q^{51} +(-3.70668 - 1.65032i) q^{52} +(4.76216 - 5.28892i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-2.11686 - 2.35101i) q^{55} +(0.550588 - 0.953647i) q^{56} +(-0.911469 - 1.57871i) q^{57} +(3.20444 - 9.86226i) q^{58} +(-5.24682 + 2.33603i) q^{59} +(-0.809017 + 0.587785i) q^{60} -4.95380 q^{61} +(-4.96888 + 2.51202i) q^{62} +1.10118 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-3.70668 + 1.65032i) q^{65} +(0.977606 - 3.00876i) q^{66} +(0.937623 + 1.62401i) q^{67} +(-2.08628 + 3.61355i) q^{68} +(4.28974 + 4.76424i) q^{69} +(-0.340282 - 1.04728i) q^{70} +(-8.86211 + 9.84238i) q^{71} +(-0.913545 - 0.406737i) q^{72} +(-11.8104 + 2.51037i) q^{73} +(0.327638 + 3.11727i) q^{74} +(-0.104528 + 0.994522i) q^{75} +(-1.78310 - 0.379010i) q^{76} +(2.81836 + 2.04766i) q^{77} +(-3.28256 - 2.38492i) q^{78} +(11.6287 + 2.47176i) q^{79} +(-0.104528 + 0.994522i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(5.10620 - 1.08536i) q^{82} +(11.1697 + 4.97306i) q^{83} +(0.736831 - 0.818334i) q^{84} +(1.28939 + 3.96835i) q^{85} +(-0.188115 - 0.208923i) q^{86} +(5.18490 - 8.98051i) q^{87} +(-1.58180 - 2.73976i) q^{88} +(-4.83893 + 14.8927i) q^{89} +(-0.913545 + 0.406737i) q^{90} +(3.61468 - 2.62622i) q^{91} +6.41091 q^{92} +(-5.38257 + 1.42404i) q^{93} +1.08353 q^{94} +(-1.47479 + 1.07150i) q^{95} +(-0.913545 + 0.406737i) q^{96} +(-3.49674 + 10.7618i) q^{97} +(-2.89371 - 5.01204i) q^{98} +(1.58180 - 2.73976i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} - 13 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 - 13 * q^7 + 4 * q^8 + 2 * q^9	\( 16 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} - 13 q^{7} + 4 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{12} - 6 q^{13} - 2 q^{14} - 4 q^{15} - 4 q^{16} + 6 q^{17} - 2 q^{18} + 9 q^{19} + 2 q^{20} + 2 q^{21} - 13 q^{22} - 3 q^{23} - 2 q^{24} - 8 q^{25} + q^{26} - 4 q^{27} + 2 q^{28} - q^{29} - 16 q^{30} - 19 q^{31} - 16 q^{32} + 14 q^{33} + 4 q^{34} + 11 q^{35} - 8 q^{36} - 3 q^{37} + 6 q^{38} - 13 q^{39} - 2 q^{40} - 2 q^{42} + 2 q^{43} - 7 q^{44} + 2 q^{45} - 7 q^{46} - q^{47} + 2 q^{48} + 3 q^{49} - 2 q^{50} + 6 q^{51} - 6 q^{52} - 14 q^{53} + 4 q^{54} + 13 q^{55} - 7 q^{56} - 6 q^{57} - 4 q^{58} + 16 q^{59} - 4 q^{60} - 28 q^{61} - 21 q^{62} - 14 q^{63} - 4 q^{64} - 6 q^{65} + 11 q^{66} + 47 q^{67} - 4 q^{68} + 9 q^{69} - 11 q^{70} + 3 q^{71} - 2 q^{72} - 27 q^{73} + 8 q^{74} + 2 q^{75} - 6 q^{76} + 14 q^{77} - 12 q^{78} + 4 q^{79} + 2 q^{80} + 2 q^{81} + 30 q^{82} + 66 q^{83} - 13 q^{84} + 18 q^{85} + 13 q^{86} + 3 q^{87} - 3 q^{88} - 45 q^{89} - 2 q^{90} + 12 q^{91} - 8 q^{92} - 26 q^{93} + 36 q^{94} - 18 q^{95} - 2 q^{96} + 5 q^{97} - 13 q^{98} + 3 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 - 13 * q^7 + 4 * q^8 + 2 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^12 - 6 * q^13 - 2 * q^14 - 4 * q^15 - 4 * q^16 + 6 * q^17 - 2 * q^18 + 9 * q^19 + 2 * q^20 + 2 * q^21 - 13 * q^22 - 3 * q^23 - 2 * q^24 - 8 * q^25 + q^26 - 4 * q^27 + 2 * q^28 - q^29 - 16 * q^30 - 19 * q^31 - 16 * q^32 + 14 * q^33 + 4 * q^34 + 11 * q^35 - 8 * q^36 - 3 * q^37 + 6 * q^38 - 13 * q^39 - 2 * q^40 - 2 * q^42 + 2 * q^43 - 7 * q^44 + 2 * q^45 - 7 * q^46 - q^47 + 2 * q^48 + 3 * q^49 - 2 * q^50 + 6 * q^51 - 6 * q^52 - 14 * q^53 + 4 * q^54 + 13 * q^55 - 7 * q^56 - 6 * q^57 - 4 * q^58 + 16 * q^59 - 4 * q^60 - 28 * q^61 - 21 * q^62 - 14 * q^63 - 4 * q^64 - 6 * q^65 + 11 * q^66 + 47 * q^67 - 4 * q^68 + 9 * q^69 - 11 * q^70 + 3 * q^71 - 2 * q^72 - 27 * q^73 + 8 * q^74 + 2 * q^75 - 6 * q^76 + 14 * q^77 - 12 * q^78 + 4 * q^79 + 2 * q^80 + 2 * q^81 + 30 * q^82 + 66 * q^83 - 13 * q^84 + 18 * q^85 + 13 * q^86 + 3 * q^87 - 3 * q^88 - 45 * q^89 - 2 * q^90 + 12 * q^91 - 8 * q^92 - 26 * q^93 + 36 * q^94 - 18 * q^95 - 2 * q^96 + 5 * q^97 - 13 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{13}{15}\right)$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	0.913545	−	0.406737i	0.527436	−	0.234830i
$3$	0.913545	−	0.406737i	0.527436	−	0.234830i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	0.736831	+	0.818334i	0.278496	+	0.309301i	0.866123	−	0.499831i	$-0.166604\pi$
$7$	0.736831	+	0.818334i	0.278496	+	0.309301i	−0.587627	+	0.809132i	$0.699938\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	0.669131	−	0.743145i	0.223044	−	0.247715i
$10$	−0.913545	−	0.406737i	−0.288888	−	0.128621i
$11$	3.09447	−	0.657750i	0.933017	−	0.198319i	0.283767	−	0.958893i	$-0.408416\pi$
$11$	3.09447	−	0.657750i	0.933017	−	0.198319i	0.649251	+	0.760574i	$0.275083\pi$
$12$	−0.104528	−	0.994522i	−0.0301748	−	0.287094i
$13$	0.424121	−	4.03524i	0.117630	−	1.11918i	−0.763338	−	0.645999i	$-0.776441\pi$
$13$	0.424121	−	4.03524i	0.117630	−	1.11918i	0.880968	−	0.473176i	$-0.156893\pi$
$14$	1.07711	+	0.228947i	0.287871	+	0.0611888i
$15$	−0.809017	−	0.587785i	−0.208887	−	0.151765i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−4.08139	−	0.867525i	−0.989882	−	0.210406i	−0.315610	−	0.948889i	$-0.602209\pi$
$17$	−4.08139	−	0.867525i	−0.989882	−	0.210406i	−0.674272	+	0.738483i	$0.735542\pi$
$18$	0.104528	−	0.994522i	0.0246376	−	0.234411i
$19$	−0.190549	−	1.81295i	−0.0437149	−	0.415920i	−0.994394	−	0.105742i	$-0.966278\pi$
$19$	−0.190549	−	1.81295i	−0.0437149	−	0.415920i	0.950679	−	0.310177i	$-0.100388\pi$
$20$	−0.978148	+	0.207912i	−0.218720	+	0.0464905i
$21$	1.00597	+	0.447889i	0.219522	+	0.0977374i
$22$	2.11686	−	2.35101i	0.451316	−	0.501238i
$23$	1.98108	+	6.09714i	0.413084	+	1.27134i	0.913953	+	0.405819i	$0.133014\pi$
$23$	1.98108	+	6.09714i	0.413084	+	1.27134i	−0.500869	+	0.865523i	$0.666986\pi$
$24$	−0.669131	−	0.743145i	−0.136586	−	0.151694i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.02874	−	3.51387i	−0.397868	−	0.689127i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	1.00597	−	0.447889i	0.190111	−	0.0846430i
$29$	8.38934	−	6.09521i	1.55786	−	1.13185i	0.620127	−	0.784501i	$-0.287081\pi$
$29$	8.38934	−	6.09521i	1.55786	−	1.13185i	0.937735	−	0.347352i	$-0.112919\pi$
$30$	−1.00000			−0.182574
$31$	−5.49644	−	0.888362i	−0.987189	−	0.159554i
$31$	−5.49644	−	0.888362i	−0.987189	−	0.159554i
$32$	−1.00000			−0.176777
$33$	2.55941	−	1.85952i	0.445536	−	0.323701i
$34$	−3.81183	+	1.69714i	−0.653723	+	0.291056i
$35$	0.340282	−	1.04728i	0.0575182	−	0.177023i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−1.56722	+	2.71450i	−0.257649	+	0.446262i	−0.965612	−	0.259988i	$-0.916281\pi$
$37$	−1.56722	+	2.71450i	−0.257649	+	0.446262i	0.707962	+	0.706250i	$0.249615\pi$
$38$	−1.21978	−	1.35471i	−0.197875	−	0.219762i
$39$	−1.25383	−	3.85888i	−0.200773	−	0.617916i
$40$	−0.669131	+	0.743145i	−0.105799	+	0.117502i
$41$	4.76896	+	2.12328i	0.744786	+	0.331600i	0.743803	−	0.668399i	$-0.233020\pi$
$41$	4.76896	+	2.12328i	0.744786	+	0.331600i	0.000983702		1.00000i	$0.499687\pi$
$42$	1.07711	−	0.228947i	0.166202	−	0.0353274i
$43$	−0.0293865	−	0.279594i	−0.00448140	−	0.0426377i	0.992053	−	0.125823i	$-0.0401572\pi$
$43$	−0.0293865	−	0.279594i	−0.00448140	−	0.0426377i	−0.996534	+	0.0831856i	$0.973491\pi$
$44$	0.330686	−	3.14627i	0.0498528	−	0.474318i
$45$	−0.978148	−	0.207912i	−0.145814	−	0.0309936i
$46$	5.18654	+	3.76824i	0.764713	+	0.555597i
$47$	0.876596	+	0.636884i	0.127865	+	0.0928991i	0.649879	−	0.760037i	$-0.274819\pi$
$47$	0.876596	+	0.636884i	0.127865	+	0.0928991i	−0.522015	+	0.852936i	$0.674819\pi$
$48$	−0.978148	−	0.207912i	−0.141183	−	0.0300095i
$49$	0.604949	−	5.75571i	0.0864213	−	0.822244i
$50$	0.104528	+	0.994522i	0.0147826	+	0.140647i
$51$	−4.08139	+	0.867525i	−0.571508	+	0.121478i
$52$	−3.70668	−	1.65032i	−0.514025	−	0.228859i
$53$	4.76216	−	5.28892i	0.654134	−	0.726489i	−0.321252	−	0.946994i	$-0.604104\pi$
$53$	4.76216	−	5.28892i	0.654134	−	0.726489i	0.975386	+	0.220505i	$0.0707704\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$	−2.11686	−	2.35101i	−0.285438	−	0.317011i
$56$	0.550588	−	0.953647i	0.0735755	−	0.127436i
$57$	−0.911469	−	1.57871i	−0.120727	−	0.209105i
$58$	3.20444	−	9.86226i	0.420764	−	1.29498i
$59$	−5.24682	+	2.33603i	−0.683078	+	0.304126i	−0.718781	−	0.695237i	$-0.755300\pi$
$59$	−5.24682	+	2.33603i	−0.683078	+	0.304126i	0.0357032	+	0.999362i	$0.488633\pi$
$60$	−0.809017	+	0.587785i	−0.104444	+	0.0758827i
$61$	−4.95380			−0.634269			−0.317134	−	0.948381i	$-0.602721\pi$
$61$	−4.95380			−0.634269			−0.317134	+	0.948381i	$0.602721\pi$
$62$	−4.96888	+	2.51202i	−0.631048	+	0.319027i
$63$	1.10118			0.138735
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−3.70668	+	1.65032i	−0.459758	+	0.204697i
$66$	0.977606	−	3.00876i	0.120335	−	0.370353i
$67$	0.937623	+	1.62401i	0.114549	+	0.198404i	0.917599	−	0.397507i	$-0.130124\pi$
$67$	0.937623	+	1.62401i	0.114549	+	0.198404i	−0.803050	+	0.595911i	$0.796791\pi$
$68$	−2.08628	+	3.61355i	−0.252999	+	0.438207i
$69$	4.28974	+	4.76424i	0.516424	+	0.573547i
$70$	−0.340282	−	1.04728i	−0.0406715	−	0.125174i
$71$	−8.86211	+	9.84238i	−1.05174	+	1.16808i	−0.0663435	+	0.997797i	$0.521133\pi$
$71$	−8.86211	+	9.84238i	−1.05174	+	1.16808i	−0.985396	+	0.170278i	$0.945533\pi$
$72$	−0.913545	−	0.406737i	−0.107662	−	0.0479344i
$73$	−11.8104	+	2.51037i	−1.38230	+	0.293817i	−0.838273	−	0.545251i	$-0.816435\pi$
$73$	−11.8104	+	2.51037i	−1.38230	+	0.293817i	−0.544027	+	0.839068i	$0.683101\pi$
$74$	0.327638	+	3.11727i	0.0380872	+	0.362375i
$75$	−0.104528	+	0.994522i	−0.0120699	+	0.114837i
$76$	−1.78310	−	0.379010i	−0.204536	−	0.0434754i
$77$	2.81836	+	2.04766i	0.321182	+	0.233352i
$78$	−3.28256	−	2.38492i	−0.371677	−	0.270039i
$79$	11.6287	+	2.47176i	1.30833	+	0.278095i	0.808740	−	0.588166i	$-0.200150\pi$
$79$	11.6287	+	2.47176i	1.30833	+	0.278095i	0.499592	+	0.866261i	$0.333483\pi$
$80$	−0.104528	+	0.994522i	−0.0116866	+	0.111191i
$81$	−0.104528	−	0.994522i	−0.0116143	−	0.110502i
$82$	5.10620	−	1.08536i	0.563886	−	0.119858i
$83$	11.1697	+	4.97306i	1.22603	+	0.545864i	0.914583	−	0.404399i	$-0.132519\pi$
$83$	11.1697	+	4.97306i	1.22603	+	0.545864i	0.311449	+	0.950263i	$0.399186\pi$
$84$	0.736831	−	0.818334i	0.0803948	−	0.0892875i
$85$	1.28939	+	3.96835i	0.139854	+	0.430428i
$86$	−0.188115	−	0.208923i	−0.0202850	−	0.0225288i
$87$	5.18490	−	8.98051i	0.555880	−	0.962812i
$88$	−1.58180	−	2.73976i	−0.168620	−	0.292059i
$89$	−4.83893	+	14.8927i	−0.512925	+	1.57862i	0.274100	+	0.961701i	$0.411620\pi$
$89$	−4.83893	+	14.8927i	−0.512925	+	1.57862i	−0.787026	+	0.616920i	$0.788380\pi$
$90$	−0.913545	+	0.406737i	−0.0962961	+	0.0428738i
$91$	3.61468	−	2.62622i	0.378922	−	0.275303i
$92$	6.41091			0.668384
$93$	−5.38257	+	1.42404i	−0.558147	+	0.147666i
$94$	1.08353			0.111758
$95$	−1.47479	+	1.07150i	−0.151310	+	0.109933i
$96$	−0.913545	+	0.406737i	−0.0932383	+	0.0415124i
$97$	−3.49674	+	10.7618i	−0.355040	+	1.09270i	0.600947	+	0.799289i	$0.294790\pi$
$97$	−3.49674	+	10.7618i	−0.355040	+	1.09270i	−0.955986	+	0.293411i	$0.905210\pi$
$98$	−2.89371	−	5.01204i	−0.292308	−	0.506293i
$99$	1.58180	−	2.73976i	0.158977	−	0.275356i
$100$	0.669131	+	0.743145i	0.0669131	+	0.0743145i
$101$	−0.742094	−	2.28393i	−0.0738411	−	0.227260i	0.907323	−	0.420433i	$-0.138122\pi$
$101$	−0.742094	−	2.28393i	−0.0738411	−	0.227260i	−0.981165	+	0.193174i	$0.938122\pi$
$102$	−2.79199	+	3.10082i	−0.276448	+	0.307027i
$103$	0.104348	+	0.0464586i	0.0102817	+	0.00457770i	0.411871	−	0.911242i	$-0.364875\pi$
$103$	0.104348	+	0.0464586i	0.0102817	+	0.00457770i	−0.401589	+	0.915820i	$0.631542\pi$
$104$	−3.96881	+	0.843596i	−0.389173	+	0.0827214i
$105$	−0.115104	−	1.09514i	−0.0112330	−	0.106875i
$106$	0.743923	−	7.07796i	0.0722562	−	0.687472i
$107$	6.00347	+	1.27608i	0.580377	+	0.123363i	0.488740	−	0.872429i	$-0.337457\pi$
$107$	6.00347	+	1.27608i	0.580377	+	0.123363i	0.0916373	+	0.995792i	$0.470790\pi$
$108$	−0.809017	−	0.587785i	−0.0778477	−	0.0565597i
$109$	5.01310	+	3.64223i	0.480168	+	0.348863i	0.801391	−	0.598141i	$-0.204094\pi$
$109$	5.01310	+	3.64223i	0.480168	+	0.348863i	−0.321223	+	0.947004i	$0.604094\pi$
$110$	−3.09447	−	0.657750i	−0.295046	−	0.0627140i
$111$	−0.327638	+	3.11727i	−0.0310980	+	0.295878i
$112$	−0.115104	−	1.09514i	−0.0108763	−	0.103481i
$113$	16.1606	−	3.43505i	1.52026	−	0.323142i	0.629280	−	0.777179i	$-0.283350\pi$
$113$	16.1606	−	3.43505i	1.52026	−	0.323142i	0.890983	+	0.454037i	$0.150016\pi$
$114$	−1.66534	−	0.741456i	−0.155973	−	0.0694437i
$115$	4.28974	−	4.76424i	0.400020	−	0.444267i
$116$	−3.20444	−	9.86226i	−0.297525	−	0.915688i
$117$	−2.71498	−	3.01529i	−0.251000	−	0.278764i
$118$	−2.87168	+	4.97389i	−0.264360	+	0.457884i
$119$	−2.29737	−	3.97916i	−0.210599	−	0.364769i
$120$	−0.309017	+	0.951057i	−0.0282093	+	0.0868192i
$121$	−0.905900	+	0.403333i	−0.0823545	+	0.0366666i
$122$	−4.00771	+	2.91177i	−0.362841	+	0.263619i
$123$	5.22028			0.470696
$124$	−2.54337	+	4.95290i	−0.228402	+	0.444784i
$125$	1.00000			0.0894427
$126$	0.890871	−	0.647255i	0.0793651	−	0.0576621i
$127$	−7.13591	+	3.17711i	−0.633209	+	0.281923i	−0.698134	−	0.715967i	$-0.745986\pi$
$127$	−7.13591	+	3.17711i	−0.633209	+	0.281923i	0.0649245	+	0.997890i	$0.479319\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	−0.140567	−	0.243469i	−0.0123762	−	0.0214363i
$130$	−2.02874	+	3.51387i	−0.177932	+	0.308187i
$131$	1.86340	+	2.06951i	0.162806	+	0.180814i	0.819028	−	0.573754i	$-0.194513\pi$
$131$	1.86340	+	2.06951i	0.162806	+	0.180814i	−0.656222	+	0.754568i	$0.727847\pi$
$132$	−0.977606	−	3.00876i	−0.0850897	−	0.261879i
$133$	1.34320	−	1.49177i	0.116470	−	0.129353i
$134$	1.71312	+	0.762731i	0.147991	+	0.0658899i
$135$	−0.978148	+	0.207912i	−0.0841855	+	0.0178942i
$136$	0.436152	+	4.14971i	0.0373997	+	0.355835i
$137$	−2.06882	+	19.6835i	−0.176751	+	1.68168i	0.442723	+	0.896659i	$0.354013\pi$
$137$	−2.06882	+	19.6835i	−0.176751	+	1.68168i	−0.619474	+	0.785017i	$0.712654\pi$
$138$	6.27082	+	1.33290i	0.533808	+	0.113464i
$139$	4.89152	+	3.55389i	0.414893	+	0.301437i	0.775580	−	0.631250i	$-0.217458\pi$
$139$	4.89152	+	3.55389i	0.414893	+	0.301437i	−0.360687	+	0.932687i	$0.617458\pi$
$140$	−0.890871	−	0.647255i	−0.0752923	−	0.0547031i
$141$	1.05985	+	0.225279i	0.0892559	+	0.0189719i
$142$	−1.38440	+	13.1717i	−0.116176	+	1.10534i
$143$	−1.34175	−	12.7659i	−0.112203	−	1.06754i
$144$	−0.978148	+	0.207912i	−0.0815123	+	0.0173260i
$145$	−9.47328	−	4.21778i	−0.786713	−	0.350267i
$146$	−8.07924	+	8.97290i	−0.668642	+	0.742603i
$147$	−1.78841	−	5.50415i	−0.147505	−	0.453975i
$148$	2.09735	+	2.32934i	0.172401	+	0.191471i
$149$	9.44504	−	16.3593i	0.773768	−	1.34021i	−0.161716	−	0.986837i	$-0.551703\pi$
$149$	9.44504	−	16.3593i	0.773768	−	1.34021i	0.935484	−	0.353368i	$-0.114964\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	3.16211	−	9.73197i	0.257329	−	0.791976i	−0.736033	−	0.676945i	$-0.763303\pi$
$151$	3.16211	−	9.73197i	0.257329	−	0.791976i	0.993362	−	0.115031i	$-0.0366967\pi$
$152$	−1.66534	+	0.741456i	−0.135077	+	0.0601400i
$153$	−3.37568	+	2.45257i	−0.272907	+	0.198279i
$154$	3.48368			0.280723
$155$	1.97887	+	5.20423i	0.158947	+	0.418014i
$156$	−4.05747			−0.324858
$157$	−5.72981	+	4.16295i	−0.457289	+	0.332240i	−0.792467	−	0.609915i	$-0.791204\pi$
$157$	−5.72981	+	4.16295i	−0.457289	+	0.332240i	0.335178	+	0.942155i	$0.391204\pi$
$158$	10.8607	−	4.83549i	0.864030	−	0.384691i
$159$	2.19926	−	6.76862i	0.174412	−	0.536786i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−3.52977	+	6.11375i	−0.278185	+	0.481831i
$162$	−0.669131	−	0.743145i	−0.0525719	−	0.0583870i
$163$	3.42067	+	10.5278i	0.267928	+	0.824597i	0.991004	+	0.133829i	$0.0427274\pi$
$163$	3.42067	+	10.5278i	0.267928	+	0.824597i	−0.723076	+	0.690768i	$0.757273\pi$
$164$	3.49305	−	3.87942i	0.272761	−	0.302932i
$165$	−2.89009	−	1.28675i	−0.224993	−	0.100174i
$166$	11.9596	−	2.54208i	0.928241	−	0.197304i
$167$	2.16131	+	20.5635i	0.167247	+	1.59125i	0.680326	+	0.732910i	$0.261838\pi$
$167$	2.16131	+	20.5635i	0.167247	+	1.59125i	−0.513079	+	0.858341i	$0.671495\pi$
$168$	0.115104	−	1.09514i	0.00888049	−	0.0844922i
$169$	−3.38740	−	0.720014i	−0.260569	−	0.0553857i
$170$	3.37568	+	2.45257i	0.258903	+	0.188104i
$171$	−1.47479	−	1.07150i	−0.112780	−	0.0819393i
$172$	−0.274991	−	0.0584510i	−0.0209678	−	0.00445685i
$173$	−1.67394	+	15.9265i	−0.127267	+	1.21087i	0.725368	+	0.688362i	$0.241670\pi$
$173$	−1.67394	+	15.9265i	−0.127267	+	1.21087i	−0.852635	+	0.522507i	$0.824997\pi$
$174$	−1.08394	−	10.3130i	−0.0821732	−	0.781826i
$175$	−1.07711	+	0.228947i	−0.0814221	+	0.0173068i
$176$	−2.89009	−	1.28675i	−0.217849	−	0.0969926i
$177$	−3.84306	+	4.26815i	−0.288862	+	0.320814i
$178$	4.83893	+	14.8927i	0.362693	+	1.11625i
$179$	1.67762	+	1.86319i	0.125391	+	0.139261i	0.802571	−	0.596556i	$-0.203465\pi$
$179$	1.67762	+	1.86319i	0.125391	+	0.139261i	−0.677180	+	0.735818i	$0.736798\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	−4.43108	−	7.67486i	−0.329360	−	0.570468i	0.653025	−	0.757336i	$-0.273499\pi$
$181$	−4.43108	−	7.67486i	−0.329360	−	0.570468i	−0.982385	+	0.186869i	$0.940166\pi$
$182$	1.38069	−	4.24931i	0.102343	−	0.314980i
$183$	−4.52552	+	2.01489i	−0.334536	+	0.148945i
$184$	5.18654	−	3.76824i	0.382357	−	0.277798i
$185$	3.13444			0.230449
$186$	−3.51756	+	4.31587i	−0.257920	+	0.316455i
$187$	−13.2003			−0.965304
$188$	0.876596	−	0.636884i	0.0639324	−	0.0464496i
$189$	1.00597	−	0.447889i	0.0731739	−	0.0325791i
$190$	−0.563319	+	1.73372i	−0.0408674	+	0.125777i
$191$	3.69071	+	6.39250i	0.267050	+	0.462545i	0.968099	−	0.250569i	$-0.0806176\pi$
$191$	3.69071	+	6.39250i	0.267050	+	0.462545i	−0.701048	+	0.713114i	$0.747284\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−14.5338	−	16.1414i	−1.04617	−	1.16189i	−0.986516	−	0.163666i	$-0.947668\pi$
$193$	−14.5338	−	16.1414i	−1.04617	−	1.16189i	−0.0596509	−	0.998219i	$-0.518999\pi$
$194$	3.49674	+	10.7618i	0.251051	+	0.772656i
$195$	−2.71498	+	3.01529i	−0.194424	+	0.215929i
$196$	−5.28706	−	2.35395i	−0.377647	−	0.168139i
$197$	−7.27400	+	1.54614i	−0.518251	+	0.110158i	−0.459609	−	0.888121i	$-0.652010\pi$
$197$	−7.27400	+	1.54614i	−0.518251	+	0.110158i	−0.0586420	+	0.998279i	$0.518677\pi$
$198$	−0.330686	−	3.14627i	−0.0235009	−	0.223596i
$199$	0.760944	−	7.23989i	0.0539419	−	0.513222i	−0.933875	−	0.357600i	$-0.883595\pi$
$199$	0.760944	−	7.23989i	0.0539419	−	0.513222i	0.987817	−	0.155622i	$-0.0497383\pi$
$200$	0.978148	+	0.207912i	0.0691655	+	0.0147016i
$201$	1.51711	+	1.10224i	0.107008	+	0.0777462i
$202$	−1.94283	−	1.41155i	−0.136697	−	0.0993161i
$203$	11.1694	+	2.37414i	0.783942	+	0.166632i
$204$	−0.436152	+	4.14971i	−0.0305367	+	0.290538i
$205$	−0.545667	−	5.19168i	−0.0381111	−	0.362603i
$206$	0.111727	−	0.0237482i	0.00778437	−	0.00165462i
$207$	5.85666	+	2.60755i	0.407066	+	0.181238i
$208$	−2.71498	+	3.01529i	−0.188250	+	0.209073i
$209$	−1.78212	−	5.48479i	−0.123272	−	0.379391i
$210$	−0.736831	−	0.818334i	−0.0508462	−	0.0564704i
$211$	5.95047	−	10.3065i	0.409648	−	0.709530i	−0.585203	−	0.810887i	$-0.698985\pi$
$211$	5.95047	−	10.3065i	0.409648	−	0.709530i	0.994850	+	0.101357i	$0.0323183\pi$
$212$	−3.55847	−	6.16345i	−0.244397	−	0.423308i
$213$	−4.09269	+	12.5960i	−0.280426	+	0.863064i
$214$	5.60697	−	2.49638i	0.383285	−	0.170649i
$215$	−0.227442	+	0.165246i	−0.0155114	+	0.0112697i
$216$	−1.00000			−0.0680414
$217$	−3.32297	−	5.15249i	−0.225578	−	0.349774i
$218$	6.19654			0.419682
$219$	−9.76826	+	7.09705i	−0.660078	+	0.479575i
$220$	−2.89009	+	1.28675i	−0.194850	+	0.0867528i
$221$	−5.23168	+	16.1015i	−0.351921	+	1.08310i
$222$	1.56722	+	2.71450i	0.105185	+	0.182186i
$223$	5.04752	−	8.74256i	0.338007	−	0.585445i	−0.646051	−	0.763294i	$-0.723581\pi$
$223$	5.04752	−	8.74256i	0.338007	−	0.585445i	0.984058	+	0.177849i	$0.0569139\pi$
$224$	−0.736831	−	0.818334i	−0.0492316	−	0.0546772i
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$	11.0551	−	12.2780i	0.735377	−	0.816719i
$227$	−1.52736	−	0.680024i	−0.101374	−	0.0451348i	0.355423	−	0.934706i	$-0.384337\pi$
$227$	−1.52736	−	0.680024i	−0.101374	−	0.0451348i	−0.456797	+	0.889571i	$0.651004\pi$
$228$	−1.78310	+	0.379010i	−0.118089	+	0.0251006i
$229$	−1.04396	−	9.93264i	−0.0689870	−	0.656367i	−0.973306	−	0.229510i	$-0.926288\pi$
$229$	−1.04396	−	9.93264i	−0.0689870	−	0.656367i	0.904319	−	0.426857i	$-0.140379\pi$
$230$	0.670123	−	6.37580i	0.0441866	−	0.420407i
$231$	3.40756	+	0.724298i	0.224201	+	0.0476553i
$232$	−8.38934	−	6.09521i	−0.550787	−	0.400170i
$233$	19.4670	+	14.1436i	1.27533	+	0.926580i	0.999401	−	0.0345987i	$-0.0110153\pi$
$233$	19.4670	+	14.1436i	1.27533	+	0.926580i	0.275927	+	0.961179i	$0.411015\pi$
$234$	−3.96881	−	0.843596i	−0.259449	−	0.0551476i
$235$	0.113260	−	1.07760i	0.00738827	−	0.0702947i
$236$	0.600344	+	5.71190i	0.0390791	+	0.371813i
$237$	11.6287	−	2.47176i	0.755366	−	0.160558i
$238$	−4.19750	−	1.86885i	−0.272083	−	0.121139i
$239$	17.7798	−	19.7465i	1.15008	−	1.27729i	0.195047	−	0.980794i	$-0.437514\pi$
$239$	17.7798	−	19.7465i	1.15008	−	1.27729i	0.955033	−	0.296500i	$-0.0958194\pi$
$240$	0.309017	+	0.951057i	0.0199470	+	0.0613904i
$241$	7.89964	+	8.77344i	0.508861	+	0.565147i	0.941756	−	0.336297i	$-0.109175\pi$
$241$	7.89964	+	8.77344i	0.508861	+	0.565147i	−0.432895	+	0.901444i	$0.642508\pi$
$242$	−0.495815	+	0.858778i	−0.0318722	+	0.0552043i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−1.53081	+	4.71134i	−0.0979999	+	0.301613i
$245$	−5.28706	+	2.35395i	−0.337778	+	0.150388i
$246$	4.22329	−	3.06840i	0.269267	−	0.195634i
$247$	−7.39652			−0.470629
$248$	0.853610	+	5.50194i	0.0542043	+	0.349374i
$249$	12.2267			0.774838
$250$	0.809017	−	0.587785i	0.0511667	−	0.0371748i
$251$	−11.4997	+	5.11998i	−0.725853	+	0.323170i	−0.736189	−	0.676776i	$-0.763376\pi$
$251$	−11.4997	+	5.11998i	−0.725853	+	0.323170i	0.0103363	+	0.999947i	$0.496710\pi$
$252$	0.340282	−	1.04728i	0.0214358	−	0.0659725i
$253$	10.1408	+	17.5644i	0.637546	+	1.10426i
$254$	−3.90561	+	6.76472i	−0.245060	+	0.424456i
$255$	2.79199	+	3.10082i	0.174841	+	0.194181i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	4.70136	−	5.22139i	0.293263	−	0.325701i	−0.578451	−	0.815717i	$-0.696342\pi$
$257$	4.70136	−	5.22139i	0.293263	−	0.325701i	0.871713	+	0.490016i	$0.163009\pi$
$258$	−0.256829	−	0.114347i	−0.0159895	−	0.00711896i
$259$	−3.37615	+	0.717622i	−0.209784	+	0.0445909i
$260$	0.424121	+	4.03524i	0.0263029	+	0.250255i
$261$	1.08394	−	10.3130i	0.0670941	−	0.638358i
$262$	2.72395	+	0.578994i	0.168286	+	0.0357703i
$263$	−18.3613	−	13.3403i	−1.13221	−	0.822598i	−0.146194	−	0.989256i	$-0.546702\pi$
$263$	−18.3613	−	13.3403i	−1.13221	−	0.822598i	−0.986015	+	0.166658i	$0.946702\pi$
$264$	−2.55941	−	1.85952i	−0.157521	−	0.114445i
$265$	−6.96142	−	1.47970i	−0.427637	−	0.0908970i
$266$	0.209828	−	1.99638i	0.0128654	−	0.122406i
$267$	1.63682	+	15.5733i	0.100172	+	0.953071i
$268$	1.83427	−	0.389886i	0.112046	−	0.0238161i
$269$	20.7080	+	9.21980i	1.26259	+	0.562141i	0.925292	−	0.379257i	$-0.123820\pi$
$269$	20.7080	+	9.21980i	1.26259	+	0.562141i	0.337298	+	0.941398i	$0.390487\pi$
$270$	−0.669131	+	0.743145i	−0.0407220	+	0.0452264i
$271$	−0.455727	−	1.40258i	−0.0276834	−	0.0852009i	0.936260	−	0.351307i	$-0.114263\pi$
$271$	−0.455727	−	1.40258i	−0.0276834	−	0.0852009i	−0.963944	+	0.266106i	$0.914263\pi$
$272$	2.79199	+	3.10082i	0.169289	+	0.188015i
$273$	2.23400	−	3.86940i	0.135208	−	0.234186i
$274$	9.89597	+	17.1403i	0.597837	+	1.03548i
$275$	−0.977606	+	3.00876i	−0.0589519	+	0.181435i
$276$	5.85666	−	2.60755i	0.352530	−	0.156956i
$277$	−19.3267	+	14.0417i	−1.16123	+	0.843683i	−0.989933	−	0.141536i	$-0.954796\pi$
$277$	−19.3267	+	14.0417i	−1.16123	+	0.843683i	−0.171297	+	0.985219i	$0.554796\pi$
$278$	6.04625			0.362630
$279$	−4.33802	+	3.49022i	−0.259710	+	0.208954i
$280$	−1.10118			−0.0658079
$281$	−22.3744	+	16.2559i	−1.33474	+	0.969748i	−0.335124	+	0.942174i	$0.608778\pi$
$281$	−22.3744	+	16.2559i	−1.33474	+	0.969748i	−0.999620	+	0.0275743i	$0.991222\pi$
$282$	0.989856	−	0.440712i	0.0589451	−	0.0262440i
$283$	1.45313	−	4.47227i	0.0863796	−	0.265849i	−0.898532	−	0.438908i	$-0.855365\pi$
$283$	1.45313	−	4.47227i	0.0863796	−	0.265849i	0.984911	+	0.173059i	$0.0553653\pi$
$284$	6.62211	+	11.4698i	0.392950	+	0.680609i
$285$	−0.911469	+	1.57871i	−0.0539908	+	0.0935147i
$286$	−8.58911	−	9.53917i	−0.507885	−	0.564063i
$287$	1.77637	+	5.46710i	0.104856	+	0.322713i
$288$	−0.669131	+	0.743145i	−0.0394289	+	0.0437902i
$289$	0.374840	+	0.166889i	0.0220494	+	0.00981703i
$290$	−10.1432	+	2.15600i	−0.595629	+	0.126605i
$291$	1.18281	+	11.2537i	0.0693376	+	0.659703i
$292$	−1.26210	+	12.0081i	−0.0738589	+	0.702720i
$293$	−19.2420	−	4.09002i	−1.12413	−	0.238942i	−0.391907	−	0.920005i	$-0.628184\pi$
$293$	−19.2420	−	4.09002i	−1.12413	−	0.238942i	−0.732225	+	0.681063i	$0.761518\pi$
$294$	−4.68211	−	3.40175i	−0.273066	−	0.198394i
$295$	4.64647	+	3.37586i	0.270528	+	0.196550i
$296$	3.06594	+	0.651687i	0.178204	+	0.0378785i
$297$	0.330686	−	3.14627i	0.0191884	−	0.182565i
$298$	−1.97455	−	18.7866i	−0.114383	−	1.08828i
$299$	25.4437	−	5.40822i	1.47145	−	0.312765i
$300$	0.913545	+	0.406737i	0.0527436	+	0.0234830i
$301$	0.207148	−	0.230061i	0.0119398	−	0.0132605i
$302$	−3.16211	−	9.73197i	−0.181959	−	0.560012i
$303$	−1.60690	−	1.78464i	−0.0923137	−	0.102525i
$304$	−0.911469	+	1.57871i	−0.0522763	+	0.0905453i
$305$	2.47690	+	4.29012i	0.141827	+	0.245651i
$306$	−1.28939	+	3.96835i	−0.0737098	+	0.226855i
$307$	5.51101	−	2.45366i	0.314530	−	0.140038i	−0.243399	−	0.969926i	$-0.578263\pi$
$307$	5.51101	−	2.45366i	0.314530	−	0.140038i	0.557930	+	0.829888i	$0.311596\pi$
$308$	2.81836	−	2.04766i	0.160591	−	0.116676i
$309$	0.114223			0.00649790
$310$	4.65992	+	3.04716i	0.264665	+	0.173067i
$311$	−5.53136			−0.313654			−0.156827	−	0.987626i	$-0.550127\pi$
$311$	−5.53136			−0.313654			−0.156827	+	0.987626i	$0.550127\pi$
$312$	−3.28256	+	2.38492i	−0.185839	+	0.135020i
$313$	−13.9085	+	6.19246i	−0.786154	+	0.350018i	−0.760237	−	0.649646i	$-0.774917\pi$
$313$	−13.9085	+	6.19246i	−0.786154	+	0.350018i	−0.0259171	+	0.999664i	$0.508251\pi$
$314$	−2.18859	+	6.73580i	−0.123509	+	0.380123i
$315$	−0.550588	−	0.953647i	−0.0310221	−	0.0537319i
$316$	5.94425	−	10.2957i	0.334390	−	0.579181i
$317$	−19.6101	−	21.7793i	−1.10142	−	1.22325i	−0.972823	−	0.231549i	$-0.925621\pi$
$317$	−19.6101	−	21.7793i	−1.10142	−	1.22325i	−0.128592	−	0.991698i	$-0.541046\pi$
$318$	−2.19926	−	6.76862i	−0.123328	−	0.379565i
$319$	21.9514	−	24.3795i	1.22904	−	1.36499i
$320$	0.913545	+	0.406737i	0.0510687	+	0.0227373i
$321$	6.00347	−	1.27608i	0.335081	−	0.0712237i
$322$	0.737924	+	7.02088i	0.0411229	+	0.391258i
$323$	−0.795078	+	7.56466i	−0.0442393	+	0.420909i
$324$	−0.978148	−	0.207912i	−0.0543415	−	0.0115506i
$325$	3.28256	+	2.38492i	0.182084	+	0.132292i
$326$	8.95544	+	6.50651i	0.495996	+	0.360362i
$327$	6.06113	+	1.28833i	0.335181	+	0.0712449i
$328$	0.545667	−	5.19168i	0.0301294	−	0.286663i
$329$	0.124719	+	1.18662i	0.00687600	+	0.0654207i
$330$	−3.09447	+	0.657750i	−0.170345	+	0.0362079i
$331$	−10.3375	−	4.60257i	−0.568203	−	0.252980i	0.102467	−	0.994736i	$-0.467326\pi$
$331$	−10.3375	−	4.60257i	−0.568203	−	0.252980i	−0.670669	+	0.741756i	$0.733993\pi$
$332$	8.18128	−	9.08623i	0.449006	−	0.498672i
$333$	0.968595	+	2.98103i	0.0530787	+	0.163359i
$334$	13.8355	+	15.3658i	0.757042	+	0.840781i
$335$	0.937623	−	1.62401i	0.0512278	−	0.0887292i
$336$	−0.550588	−	0.953647i	−0.0300371	−	0.0520257i
$337$	−4.67993	+	14.4033i	−0.254932	+	0.784600i	0.738911	+	0.673803i	$0.235340\pi$
$337$	−4.67993	+	14.4033i	−0.254932	+	0.784600i	−0.993843	+	0.110797i	$0.964660\pi$
$338$	−3.16368	+	1.40856i	−0.172081	+	0.0766156i
$339$	13.3663	−	9.71119i	0.725958	−	0.527439i
$340$	4.17257			0.226289
$341$	−17.5929	+	0.866271i	−0.952707	+	0.0469112i
$342$	−1.82294			−0.0985732
$343$	11.3919	−	8.27672i	0.615106	−	0.446901i
$344$	−0.256829	+	0.114347i	−0.0138473	+	0.00616520i
$345$	1.98108	−	6.09714i	0.106658	−	0.328259i
$346$	8.00711	+	13.8687i	0.430465	+	0.745587i
$347$	−14.0106	+	24.2671i	−0.752129	+	1.30273i	0.194660	+	0.980871i	$0.437640\pi$
$347$	−14.0106	+	24.2671i	−0.752129	+	1.30273i	−0.946789	+	0.321855i	$0.895694\pi$
$348$	−6.93875	−	7.70626i	−0.371956	−	0.413099i
$349$	−7.49110	−	23.0552i	−0.400989	−	1.23412i	−0.924198	−	0.381914i	$-0.875265\pi$
$349$	−7.49110	−	23.0552i	−0.400989	−	1.23412i	0.523209	−	0.852205i	$-0.324735\pi$
$350$	−0.736831	+	0.818334i	−0.0393853	+	0.0437418i
$351$	−3.70668	−	1.65032i	−0.197848	−	0.0880877i
$352$	−3.09447	+	0.657750i	−0.164936	+	0.0350582i
$353$	0.149546	+	1.42283i	0.00795952	+	0.0757298i	0.997781	−	0.0665878i	$-0.0212112\pi$
$353$	0.149546	+	1.42283i	0.00795952	+	0.0757298i	−0.989821	+	0.142318i	$0.954545\pi$
$354$	−0.600344	+	5.71190i	−0.0319079	+	0.303584i
$355$	12.9548	+	2.75363i	0.687570	+	0.146147i
$356$	12.6685	+	9.20418i	0.671428	+	0.487821i
$357$	−3.71722	−	2.70072i	−0.196736	−	0.142937i
$358$	2.45238	+	0.521270i	0.129612	+	0.0275500i
$359$	1.84967	−	17.5985i	0.0976220	−	0.928811i	−0.830621	−	0.556838i	$-0.812014\pi$
$359$	1.84967	−	17.5985i	0.0976220	−	0.928811i	0.928243	−	0.371974i	$-0.121319\pi$
$360$	0.104528	+	0.994522i	0.00550913	+	0.0524159i
$361$	15.3343	−	3.25941i	0.807069	−	0.171548i
$362$	−8.09599	−	3.60457i	−0.425516	−	0.189452i
$363$	−0.663531	+	0.736925i	−0.0348263	+	0.0386786i
$364$	−1.38069	−	4.24931i	−0.0723676	−	0.222725i
$365$	8.07924	+	8.97290i	0.422887	+	0.469663i
$366$	−2.47690	+	4.29012i	−0.129470	+	0.224248i
$367$	−11.5936	−	20.0806i	−0.605179	−	1.04820i	−0.992023	−	0.126056i	$-0.959768\pi$
$367$	−11.5936	−	20.0806i	−0.605179	−	1.04820i	0.386844	−	0.922145i	$-0.373565\pi$
$368$	1.98108	−	6.09714i	0.103271	−	0.317836i
$369$	4.76896	−	2.12328i	0.248262	−	0.110533i
$370$	2.53582	−	1.84238i	0.131831	−	0.0957806i
$371$	7.83701			0.406877
$372$	−0.308961	+	5.55919i	−0.0160189	+	0.288230i
$373$	7.41940			0.384162			0.192081	−	0.981379i	$-0.438476\pi$
$373$	7.41940			0.384162			0.192081	+	0.981379i	$0.438476\pi$
$374$	−10.6793	+	7.75896i	−0.552213	+	0.401206i
$375$	0.913545	−	0.406737i	0.0471753	−	0.0210038i
$376$	0.334830	−	1.03050i	0.0172675	−	0.0531440i
$377$	−21.0376	−	36.4382i	−1.08349	−	1.87666i
$378$	0.550588	−	0.953647i	0.0283192	−	0.0490503i
$379$	13.1559	+	14.6111i	0.675773	+	0.750522i	0.979325	−	0.202293i	$-0.0648393\pi$
$379$	13.1559	+	14.6111i	0.675773	+	0.750522i	−0.303552	+	0.952815i	$0.598173\pi$
$380$	0.563319	+	1.73372i	0.0288976	+	0.0889378i
$381$	−5.22673	+	5.80487i	−0.267773	+	0.297392i
$382$	6.74326	+	3.00229i	0.345015	+	0.153611i
$383$	28.8210	−	6.12609i	1.47268	−	0.313028i	0.599482	−	0.800388i	$-0.295373\pi$
$383$	28.8210	−	6.12609i	1.47268	−	0.313028i	0.873201	+	0.487360i	$0.162040\pi$
$384$	0.104528	+	0.994522i	0.00533420	+	0.0507515i
$385$	0.364144	−	3.46460i	0.0185585	−	0.176572i
$386$	−21.2458	−	4.51593i	−1.08138	−	0.229855i
$387$	−0.227442	−	0.165246i	−0.0115615	−	0.00839995i
$388$	9.15458	+	6.65119i	0.464753	+	0.337663i
$389$	−29.6777	−	6.30820i	−1.50472	−	0.319838i	−0.619495	−	0.785000i	$-0.712663\pi$
$389$	−29.6777	−	6.30820i	−1.50472	−	0.319838i	−0.885226	+	0.465162i	$0.845996\pi$
$390$	−0.424121	+	4.03524i	−0.0214762	+	0.204333i
$391$	−2.79613	−	26.6034i	−0.141407	−	1.34539i
$392$	−5.66094	+	1.20327i	−0.285921	+	0.0607743i
$393$	2.54405	+	1.13268i	0.128330	+	0.0571363i
$394$	−4.97599	+	5.52640i	−0.250687	+	0.278416i
$395$	−3.67375	−	11.3066i	−0.184846	−	0.568899i
$396$	−2.11686	−	2.35101i	−0.106376	−	0.118143i
$397$	−6.59261	+	11.4187i	−0.330874	+	0.573090i	−0.982683	−	0.185293i	$-0.940677\pi$
$397$	−6.59261	+	11.4187i	−0.330874	+	0.573090i	0.651810	+	0.758382i	$0.274010\pi$
$398$	−3.63989	−	6.30447i	−0.182451	−	0.316014i
$399$	0.620313	−	1.90913i	0.0310545	−	0.0955760i
$400$	0.913545	−	0.406737i	0.0456773	−	0.0203368i
$401$	−3.31374	+	2.40757i	−0.165480	+	0.120228i	−0.667443	−	0.744661i	$-0.732611\pi$
$401$	−3.31374	+	2.40757i	−0.165480	+	0.120228i	0.501963	+	0.864889i	$0.332611\pi$
$402$	1.87525			0.0935288
$403$	−5.91591	+	21.8027i	−0.294693	+	1.08607i
$404$	−2.40147			−0.119477
$405$	−0.809017	+	0.587785i	−0.0402004	+	0.0292073i
$406$	10.4318	−	4.64452i	0.517719	−	0.230504i
$407$	−3.06425	+	9.43079i	−0.151889	+	0.467467i
$408$	2.08628	+	3.61355i	0.103286	+	0.178897i
$409$	−16.5248	+	28.6218i	−0.817098	+	1.41525i	0.0907144	+	0.995877i	$0.471085\pi$
$409$	−16.5248	+	28.6218i	−0.817098	+	1.41525i	−0.907812	+	0.419378i	$0.862248\pi$
$410$	−3.49305	−	3.87942i	−0.172509	−	0.191591i
$411$	6.11604	+	18.8232i	0.301682	+	0.928482i
$412$	0.0764299	−	0.0848840i	0.00376543	−	0.00418193i
$413$	−5.77767	−	2.57239i	−0.284301	−	0.126579i
$414$	6.27082	−	1.33290i	0.308194	−	0.0655087i
$415$	−1.27804	−	12.1598i	−0.0627366	−	0.596899i
$416$	−0.424121	+	4.03524i	−0.0207943	+	0.197844i
$417$	5.91412	+	1.25709i	0.289616	+	0.0615597i
$418$	−4.66564	−	3.38979i	−0.228204	−	0.165800i
$419$	−9.69256	−	7.04206i	−0.473512	−	0.344027i	0.325296	−	0.945612i	$-0.394536\pi$
$419$	−9.69256	−	7.04206i	−0.473512	−	0.344027i	−0.798809	+	0.601585i	$0.794536\pi$
$420$	−1.07711	−	0.228947i	−0.0525577	−	0.0111715i
$421$	2.71598	−	25.8408i	0.132369	−	1.25941i	−0.703587	−	0.710609i	$-0.748419\pi$
$421$	2.71598	−	25.8408i	0.132369	−	1.25941i	0.835956	−	0.548797i	$-0.184914\pi$
$422$	−1.24399	−	11.8358i	−0.0605564	−	0.576156i
$423$	1.05985	−	0.225279i	0.0515319	−	0.0109534i
$424$	−6.50165	−	2.89472i	−0.315748	−	0.140580i
$425$	2.79199	−	3.10082i	0.135432	−	0.150412i
$426$	4.09269	+	12.5960i	0.198291	+	0.610278i
$427$	−3.65011	−	4.05386i	−0.176641	−	0.196180i
$428$	3.06880	−	5.31531i	0.148336	−	0.256925i
$429$	−6.41811	−	11.1165i	−0.309869	−	0.536709i
$430$	−0.0868752	+	0.267374i	−0.00418949	+	0.0128939i
$431$	19.7225	−	8.78100i	0.949997	−	0.422966i	0.127566	−	0.991830i	$-0.459284\pi$
$431$	19.7225	−	8.78100i	0.949997	−	0.422966i	0.822432	+	0.568864i	$0.192617\pi$
$432$	−0.809017	+	0.587785i	−0.0389238	+	0.0282798i
$433$	−29.0728			−1.39715			−0.698574	−	0.715538i	$-0.746182\pi$
$433$	−29.0728			−1.39715			−0.698574	+	0.715538i	$0.746182\pi$
$434$	−5.71690	−	2.21526i	−0.274420	−	0.106336i
$435$	−10.3698			−0.497194
$436$	5.01310	−	3.64223i	0.240084	−	0.174431i
$437$	10.6763	−	4.75341i	0.510718	−	0.227386i
$438$	−3.73114	+	11.4833i	−0.178281	+	0.548692i
$439$	−15.2405	−	26.3973i	−0.727388	−	1.25987i	−0.957984	−	0.286823i	$-0.907401\pi$
$439$	−15.2405	−	26.3973i	−0.727388	−	1.25987i	0.230596	−	0.973050i	$-0.425933\pi$
$440$	−1.58180	+	2.73976i	−0.0754094	+	0.130613i
$441$	−3.87253	−	4.30088i	−0.184406	−	0.204804i
$442$	5.23168	+	16.1015i	0.248846	+	0.765868i
$443$	−6.38194	+	7.08786i	−0.303215	+	0.336754i	−0.875426	−	0.483352i	$-0.839419\pi$
$443$	−6.38194	+	7.08786i	−0.303215	+	0.336754i	0.572211	+	0.820106i	$0.306086\pi$
$444$	2.86345	+	1.27489i	0.135893	+	0.0605037i
$445$	15.3169	−	3.25571i	0.726091	−	0.154335i
$446$	−1.05522	−	10.0397i	−0.0499661	−	0.475395i
$447$	1.97455	−	18.7866i	0.0933931	−	0.888576i
$448$	−1.07711	−	0.228947i	−0.0508888	−	0.0108168i
$449$	−21.9852	−	15.9731i	−1.03754	−	0.753819i	−0.0677390	−	0.997703i	$-0.521579\pi$
$449$	−21.9852	−	15.9731i	−1.03754	−	0.753819i	−0.969805	+	0.243884i	$0.921579\pi$
$450$	0.809017	+	0.587785i	0.0381374	+	0.0277085i
$451$	16.1540	+	3.43363i	0.760661	+	0.161684i
$452$	1.72698	−	16.4311i	0.0812305	−	0.772856i
$453$	−1.06962	−	10.1767i	−0.0502551	−	0.478145i
$454$	−1.63537	+	0.347608i	−0.0767516	+	0.0163141i
$455$	−4.08171	−	1.81730i	−0.191354	−	0.0851962i
$456$	−1.21978	+	1.35471i	−0.0571216	+	0.0634400i
$457$	−8.90540	−	27.4080i	−0.416577	−	1.28209i	−0.910833	−	0.412776i	$-0.864559\pi$
$457$	−8.90540	−	27.4080i	−0.416577	−	1.28209i	0.494255	−	0.869317i	$-0.335441\pi$
$458$	−6.68284	−	7.42205i	−0.312269	−	0.346809i
$459$	−2.08628	+	3.61355i	−0.0973794	+	0.168666i
$460$	−3.20546	−	5.55202i	−0.149455	−	0.258864i
$461$	2.52562	−	7.77307i	0.117630	−	0.362028i	−0.874857	−	0.484382i	$-0.839044\pi$
$461$	2.52562	−	7.77307i	0.117630	−	0.362028i	0.992486	+	0.122354i	$0.0390444\pi$
$462$	3.18250	−	1.41694i	0.148063	−	0.0659221i
$463$	−14.8180	+	10.7659i	−0.688653	+	0.500336i	−0.876217	−	0.481917i	$-0.839941\pi$
$463$	−14.8180	+	10.7659i	−0.688653	+	0.500336i	0.187564	+	0.982252i	$0.439941\pi$
$464$	−10.3698			−0.481406
$465$	3.92454	+	3.94942i	0.181996	+	0.183150i
$466$	24.0626			1.11468
$467$	9.80105	−	7.12088i	0.453539	−	0.329515i	−0.337453	−	0.941343i	$-0.609565\pi$
$467$	9.80105	−	7.12088i	0.453539	−	0.329515i	0.790991	+	0.611827i	$0.209565\pi$
$468$	−3.70668	+	1.65032i	−0.171342	+	0.0762862i
$469$	−0.638113	+	1.96391i	−0.0294653	+	0.0906849i
$470$	−0.541766	−	0.938367i	−0.0249898	−	0.0432836i
$471$	−3.54122	+	6.13357i	−0.163171	+	0.282620i
$472$	3.84306	+	4.26815i	0.176891	+	0.196457i
$473$	−0.274838	−	0.845865i	−0.0126371	−	0.0388929i
$474$	7.95496	−	8.83488i	0.365383	−	0.405799i
$475$	1.66534	+	0.741456i	0.0764109	+	0.0340203i
$476$	−4.49433	+	0.955299i	−0.205997	+	0.0437860i
$477$	−0.743923	−	7.07796i	−0.0340619	−	0.324077i
$478$	2.77748	−	26.4259i	0.127039	−	1.20869i
$479$	38.1397	+	8.10685i	1.74265	+	0.370412i	0.965803	−	0.259278i	$-0.0834847\pi$
$479$	38.1397	+	8.10685i	1.74265	+	0.370412i	0.776847	+	0.629690i	$0.216818\pi$
$480$	0.809017	+	0.587785i	0.0369264	+	0.0268286i
$481$	10.2890	+	7.47539i	0.469138	+	0.340849i
$482$	11.5478	+	2.45457i	0.525990	+	0.111803i
$483$	−0.737924	+	7.02088i	−0.0335767	+	0.319461i
$484$	0.103654	+	0.986199i	0.00471153	+	0.0448272i
$485$	11.0684	−	2.35266i	0.502590	−	0.106829i
$486$	−0.913545	−	0.406737i	−0.0414393	−	0.0184499i
$487$	−19.2078	+	21.3324i	−0.870386	+	0.966662i	−0.999689	−	0.0249431i	$-0.992060\pi$
$487$	−19.2078	+	21.3324i	−0.870386	+	0.966662i	0.129302	+	0.991605i	$0.458726\pi$
$488$	1.53081	+	4.71134i	0.0692964	+	0.213272i
$489$	7.40697	+	8.22627i	0.334955	+	0.372005i
$490$	−2.89371	+	5.01204i	−0.130724	+	0.226421i
$491$	−7.57775	−	13.1251i	−0.341979	−	0.592326i	0.642821	−	0.766016i	$-0.277764\pi$
$491$	−7.57775	−	13.1251i	−0.341979	−	0.592326i	−0.984800	+	0.173691i	$0.944431\pi$
$492$	1.61315	−	4.96478i	0.0727266	−	0.223829i
$493$	−39.5279	+	17.5990i	−1.78025	+	0.792617i
$494$	−5.98391	+	4.34756i	−0.269229	+	0.195606i
$495$	−3.16360			−0.142193
$496$	3.92454	+	3.94942i	0.176217	+	0.177334i
$497$	−14.5842			−0.654192
$498$	9.89164	−	7.18669i	0.443255	−	0.322043i
$499$	6.87160	−	3.05943i	0.307615	−	0.136959i	−0.247123	−	0.968984i	$-0.579485\pi$
$499$	6.87160	−	3.05943i	0.307615	−	0.136959i	0.554738	+	0.832025i	$0.312819\pi$
$500$	0.309017	−	0.951057i	0.0138197	−	0.0425325i
$501$	10.3384	+	17.9066i	0.461885	+	0.800008i
$502$	−6.29398	+	10.9015i	−0.280914	+	0.486557i
$503$	−8.19180	−	9.09791i	−0.365254	−	0.405656i	0.532303	−	0.846554i	$-0.321327\pi$
$503$	−8.19180	−	9.09791i	−0.365254	−	0.405656i	−0.897557	+	0.440898i	$0.854660\pi$
$504$	−0.340282	−	1.04728i	−0.0151574	−	0.0466496i
$505$	−1.60690	+	1.78464i	−0.0715059	+	0.0794153i
$506$	18.5281	+	8.24926i	0.823676	+	0.366724i
$507$	−3.38740	+	0.720014i	−0.150440	+	0.0319770i
$508$	0.816495	+	7.76843i	0.0362261	+	0.344668i
$509$	2.58301	−	24.5757i	0.114490	−	1.08930i	−0.774879	−	0.632109i	$-0.782189\pi$
$509$	2.58301	−	24.5757i	0.114490	−	1.08930i	0.889369	−	0.457190i	$-0.151144\pi$
$510$	4.08139	+	0.867525i	0.180727	+	0.0384147i
$511$	−10.7566	−	7.81511i	−0.475843	−	0.345720i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−1.78310	−	0.379010i	−0.0787259	−	0.0167337i
$514$	0.734425	−	6.98758i	0.0323941	−	0.308209i
$515$	−0.0119395	−	0.113597i	−0.000526118	−	0.00500568i
$516$	−0.274991	+	0.0584510i	−0.0121058	+	0.00257316i
$517$	3.13151	+	1.39424i	0.137724	+	0.0613185i
$518$	−2.30955	+	2.56502i	−0.101476	+	0.112700i
$519$	4.94866	+	15.2304i	0.217222	+	0.668541i
$520$	2.71498	+	3.01529i	0.119060	+	0.132229i
$521$	6.93247	−	12.0074i	0.303717	−	0.526053i	−0.673258	−	0.739408i	$-0.735106\pi$
$521$	6.93247	−	12.0074i	0.303717	−	0.526053i	0.976975	+	0.213354i	$0.0684389\pi$
$522$	−5.18490	−	8.98051i	−0.226937	−	0.393066i
$523$	1.25721	−	3.86930i	0.0549740	−	0.169193i	−0.919800	−	0.392388i	$-0.871649\pi$
$523$	1.25721	−	3.86930i	0.0549740	−	0.169193i	0.974774	+	0.223196i	$0.0716489\pi$
$524$	2.54405	−	1.13268i	0.111137	−	0.0494815i
$525$	−0.890871	+	0.647255i	−0.0388808	+	0.0282485i
$526$	−22.6959			−0.989587
$527$	21.6624	+	8.39405i	0.943629	+	0.365650i
$528$	−3.16360			−0.137678
$529$	−14.6431	+	10.6388i	−0.636655	+	0.462557i
$530$	−6.50165	+	2.89472i	−0.282414	+	0.125739i
$531$	−1.77480	+	5.46226i	−0.0770196	+	0.237042i
$532$	−1.00369	−	1.73844i	−0.0435154	−	0.0753709i
$533$	10.5906	−	18.3434i	0.458728	−	0.794540i
$534$	10.4780	+	11.6370i	0.453427	+	0.503581i
$535$	−1.89662	−	5.83720i	−0.0819980	−	0.252364i
$536$	1.25478	−	1.39358i	0.0541984	−	0.0601935i
$537$	2.29041	+	1.01976i	0.0988386	+	0.0440058i
$538$	22.1724	−	4.71289i	0.955920	−	0.203187i
$539$	−1.91382	−	18.2088i	−0.0824339	−	0.784307i
$540$	−0.104528	+	0.994522i	−0.00449819	+	0.0427974i
$541$	33.3286	+	7.08422i	1.43291	+	0.304575i	0.858003	−	0.513644i	$-0.171705\pi$
$541$	33.3286	+	7.08422i	1.43291	+	0.304575i	0.574907	+	0.818219i	$0.305038\pi$
$542$	−1.19311	−	0.866844i	−0.0512484	−	0.0372341i
$543$	−7.16964	−	5.20905i	−0.307679	−	0.223542i
$544$	4.08139	+	0.867525i	0.174988	+	0.0371948i
$545$	0.647714	−	6.16259i	0.0277450	−	0.263976i
$546$	−0.467032	−	4.44352i	−0.0199871	−	0.190165i
$547$	25.3665	−	5.39181i	1.08459	−	0.230537i	0.369263	−	0.929325i	$-0.379610\pi$
$547$	25.3665	−	5.39181i	1.08459	−	0.230537i	0.715329	+	0.698788i	$0.246277\pi$
$548$	18.0808	+	8.05010i	0.772375	+	0.343883i
$549$	−3.31474	+	3.68139i	−0.141470	+	0.157118i
$550$	0.977606	+	3.00876i	0.0416853	+	0.128294i
$551$	−12.6489	−	14.0480i	−0.538862	−	0.598466i
$552$	3.20546	−	5.55202i	0.136433	−	0.236309i
$553$	6.54567	+	11.3374i	0.278350	+	0.482117i
$554$	−7.38215	+	22.7199i	−0.313638	+	0.965277i
$555$	2.86345	−	1.27489i	0.121547	−	0.0541161i
$556$	4.89152	−	3.55389i	0.207446	−	0.150719i
$557$	−28.9512			−1.22670			−0.613351	−	0.789811i	$-0.710179\pi$
$557$	−28.9512			−1.22670			−0.613351	+	0.789811i	$0.710179\pi$
$558$	−1.45803	+	5.37347i	−0.0617233	+	0.227477i
$559$	−1.14069			−0.0482462
$560$	−0.890871	+	0.647255i	−0.0376462	+	0.0273515i
$561$	−12.0591	+	5.36906i	−0.509136	+	0.226682i
$562$	−8.54625	+	26.3027i	−0.360502	+	1.10951i
$563$	−7.11340	−	12.3208i	−0.299794	−	0.519259i	0.676295	−	0.736631i	$-0.263585\pi$
$563$	−7.11340	−	12.3208i	−0.299794	−	0.519259i	−0.976089	+	0.217373i	$0.930251\pi$
$564$	0.541766	−	0.938367i	0.0228125	−	0.0395124i
$565$	−11.0551	−	12.2780i	−0.465093	−	0.516539i
$566$	−1.45313	−	4.47227i	−0.0610796	−	0.187984i
$567$	0.736831	−	0.818334i	0.0309440	−	0.0343668i
$568$	12.0992	+	5.38691i	0.507671	+	0.226030i
$569$	17.0106	−	3.61572i	0.713122	−	0.151579i	0.162955	−	0.986633i	$-0.447897\pi$
$569$	17.0106	−	3.61572i	0.713122	−	0.151579i	0.550167	+	0.835055i	$0.314564\pi$
$570$	0.190549	+	1.81295i	0.00798121	+	0.0759362i
$571$	4.18230	−	39.7919i	0.175024	−	1.66524i	−0.456380	−	0.889785i	$-0.650854\pi$
$571$	4.18230	−	39.7919i	0.175024	−	1.66524i	0.631404	−	0.775454i	$-0.282479\pi$
$572$	−12.5557	−	2.66880i	−0.524981	−	0.111588i
$573$	5.97170	+	4.33869i	0.249471	+	0.181251i
$574$	4.65059	+	3.37885i	0.194112	+	0.141031i
$575$	−6.27082	−	1.33290i	−0.261511	−	0.0555859i
$576$	−0.104528	+	0.994522i	−0.00435535	+	0.0414384i
$577$	−2.14169	−	20.3768i	−0.0891596	−	0.848297i	−0.944120	−	0.329603i	$-0.893085\pi$
$577$	−2.14169	−	20.3768i	−0.0891596	−	0.848297i	0.854960	−	0.518694i	$-0.173582\pi$
$578$	0.401347	−	0.0853089i	0.0166938	−	0.00354838i
$579$	−19.8426	−	8.83450i	−0.824631	−	0.367149i
$580$	−6.93875	+	7.70626i	−0.288116	+	0.319985i
$581$	4.16054	+	12.8048i	0.172608	+	0.531234i
$582$	7.57167	+	8.40919i	0.313856	+	0.348572i
$583$	11.2576	−	19.4987i	0.466241	−	0.807554i
$584$	6.03712	+	10.4566i	0.249818	+	0.432697i
$585$	−1.25383	+	3.85888i	−0.0518394	+	0.159545i
$586$	−17.9712	+	8.00129i	−0.742383	+	0.330530i
$587$	2.76868	−	2.01156i	0.114276	−	0.0830261i	−0.529180	−	0.848510i	$-0.677500\pi$
$587$	2.76868	−	2.01156i	0.114276	−	0.0830261i	0.643455	+	0.765484i	$0.277500\pi$
$588$	−5.78741			−0.238669
$589$	−0.563217	+	10.1340i	−0.0232069	+	0.417566i
$590$	5.74336			0.236450
$591$	−6.01626	+	4.37107i	−0.247476	+	0.179802i
$592$	2.86345	−	1.27489i	0.117687	−	0.0523977i
$593$	5.72456	−	17.6184i	0.235079	−	0.723500i	−0.762031	−	0.647540i	$-0.775798\pi$
$593$	5.72456	−	17.6184i	0.235079	−	0.723500i	0.997111	−	0.0759600i	$-0.0242021\pi$
$594$	−1.58180	−	2.73976i	−0.0649021	−	0.112414i
$595$	−2.29737	+	3.97916i	−0.0941828	+	0.163129i
$596$	−12.6399	−	14.0381i	−0.517752	−	0.575022i
$597$	−2.24957	−	6.92348i	−0.0920689	−	0.283359i
$598$	17.4055	−	19.3308i	0.711764	−	0.790494i
$599$	−7.95346	−	3.54111i	−0.324969	−	0.144686i	0.237767	−	0.971322i	$-0.423585\pi$
$599$	−7.95346	−	3.54111i	−0.324969	−	0.144686i	−0.562736	+	0.826637i	$0.690251\pi$
$600$	0.978148	−	0.207912i	0.0399327	−	0.00848796i
$601$	3.72063	+	35.3994i	0.151767	+	1.44397i	0.759851	+	0.650098i	$0.225272\pi$
$601$	3.72063	+	35.3994i	0.151767	+	1.44397i	−0.608083	+	0.793873i	$0.708061\pi$
$602$	0.0323597	−	0.307882i	0.00131888	−	0.0125483i
$603$	1.83427	+	0.389886i	0.0746971	+	0.0158774i
$604$	−8.27851	−	6.01469i	−0.336848	−	0.244734i
$605$	0.802246	+	0.582866i	0.0326160	+	0.0236969i
$606$	−2.34899	−	0.499293i	−0.0954212	−	0.0202824i
$607$	0.289002	−	2.74967i	0.0117302	−	0.111606i	−0.987090	−	0.160167i	$-0.948797\pi$
$607$	0.289002	−	2.74967i	0.0117302	−	0.111606i	0.998820	+	0.0485609i	$0.0154635\pi$
$608$	0.190549	+	1.81295i	0.00772778	+	0.0735249i
$609$	11.1694	−	2.37414i	0.452609	−	0.0962050i
$610$	4.52552	+	2.01489i	0.183233	+	0.0815806i
$611$	2.94177	−	3.26716i	0.119011	−	0.132175i
$612$	1.28939	+	3.96835i	0.0521207	+	0.160411i
$613$	10.5000	+	11.6615i	0.424092	+	0.471002i	0.916889	−	0.399142i	$-0.130692\pi$
$613$	10.5000	+	11.6615i	0.424092	+	0.471002i	−0.492797	+	0.870144i	$0.664025\pi$
$614$	3.01628	−	5.22435i	0.121727	−	0.210837i
$615$	−2.61014	−	4.52089i	−0.105251	−	0.182300i
$616$	1.07652	−	3.31318i	0.0433741	−	0.133492i
$617$	14.7430	−	6.56400i	0.593530	−	0.264257i	−0.0879124	−	0.996128i	$-0.528020\pi$
$617$	14.7430	−	6.56400i	0.593530	−	0.264257i	0.681443	+	0.731872i	$0.261353\pi$
$618$	0.0924081	−	0.0671384i	0.00371720	−	0.00270070i
$619$	−16.2581			−0.653466			−0.326733	−	0.945117i	$-0.605948\pi$
$619$	−16.2581			−0.653466			−0.326733	+	0.945117i	$0.605948\pi$
$620$	5.56103	−	0.273825i	0.223336	−	0.0109971i
$621$	6.41091			0.257261
$622$	−4.47496	+	3.25125i	−0.179430	+	0.130363i
$623$	−15.7527	+	7.01353i	−0.631117	+	0.280991i
$624$	−1.25383	+	3.85888i	−0.0501933	+	0.154479i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−7.61237	+	13.1850i	−0.304251	+	0.526979i
$627$	−3.85891	−	4.28575i	−0.154110	−	0.171156i
$628$	2.18859	+	6.73580i	0.0873344	+	0.268788i
$629$	8.75133	−	9.71934i	0.348938	−	0.387535i
$630$	−1.00597	−	0.447889i	−0.0400790	−	0.0178443i
$631$	39.4980	−	8.39557i	1.57239	−	0.334222i	0.662498	−	0.749064i	$-0.269496\pi$
$631$	39.4980	−	8.39557i	1.57239	−	0.334222i	0.909894	+	0.414842i	$0.136163\pi$
$632$	−1.24269	−	11.8234i	−0.0494314	−	0.470309i
$633$	1.24399	−	11.8358i	0.0494441	−	0.470429i
$634$	−28.6665	−	6.09325i	−1.13849	−	0.241994i
$635$	6.31941	+	4.59132i	0.250778	+	0.182201i
$636$	−5.75773	−	4.18323i	−0.228309	−	0.165876i
$637$	−22.9691	−	4.88224i	−0.910069	−	0.193441i
$638$	3.42915	−	32.6262i	0.135761	−	1.29168i
$639$	1.38440	+	13.1717i	0.0547659	+	0.521063i
$640$	0.978148	−	0.207912i	0.0386647	−	0.00821843i
$641$	−12.2696	−	5.46279i	−0.484621	−	0.215767i	0.149858	−	0.988708i	$-0.452118\pi$
$641$	−12.2696	−	5.46279i	−0.484621	−	0.215767i	−0.634479	+	0.772940i	$0.718785\pi$
$642$	4.10685	−	4.56112i	0.162084	−	0.180013i
$643$	−0.0794397	−	0.244490i	−0.00313280	−	0.00964176i	0.949478	−	0.313834i	$-0.101614\pi$
$643$	−0.0794397	−	0.244490i	−0.00313280	−	0.00964176i	−0.952611	+	0.304192i	$0.901614\pi$
$644$	4.72376	+	5.24627i	0.186142	+	0.206732i
$645$	−0.140567	+	0.243469i	−0.00553482	+	0.00958659i
$646$	3.80316	+	6.58727i	0.149634	+	0.259173i
$647$	−6.48257	+	19.9513i	−0.254856	+	0.784366i	0.739002	+	0.673703i	$0.235297\pi$
$647$	−6.48257	+	19.9513i	−0.254856	+	0.784366i	−0.993858	+	0.110663i	$0.964703\pi$
$648$	−0.913545	+	0.406737i	−0.0358875	+	0.0159781i
$649$	−14.6996	+	10.6799i	−0.577009	+	0.419222i
$650$	4.05747			0.159147
$651$	−5.13139	−	3.35546i	−0.201115	−	0.131511i
$652$	11.0695			0.433516
$653$	−23.5265	+	17.0930i	−0.920662	+	0.668900i	−0.943689	−	0.330835i	$-0.892670\pi$
$653$	−23.5265	+	17.0930i	−0.920662	+	0.668900i	0.0230270	+	0.999735i	$0.492670\pi$
$654$	5.66082	−	2.52036i	0.221355	−	0.0985538i
$655$	0.860552	−	2.64851i	0.0336246	−	0.103486i
$656$	−2.61014	−	4.52089i	−0.101909	−	0.176511i
$657$	−6.03712	+	10.4566i	−0.235530	+	0.407950i
$658$	0.798380	+	0.886691i	0.0311241	+	0.0345668i
$659$	−6.14188	−	18.9028i	−0.239254	−	0.736347i	−0.996529	−	0.0832510i	$-0.973470\pi$
$659$	−6.14188	−	18.9028i	−0.239254	−	0.736347i	0.757275	−	0.653096i	$-0.226530\pi$
$660$	−2.11686	+	2.35101i	−0.0823987	+	0.0915131i
$661$	18.6262	+	8.29290i	0.724473	+	0.322556i	0.735632	−	0.677381i	$-0.236885\pi$
$661$	18.6262	+	8.29290i	0.724473	+	0.322556i	−0.0111586	+	0.999938i	$0.503552\pi$
$662$	−11.0686	+	2.35270i	−0.430192	+	0.0914402i
$663$	1.76967	+	16.8373i	0.0687285	+	0.653908i
$664$	1.27804	−	12.1598i	0.0495976	−	0.471890i
$665$	−1.96351	−	0.417357i	−0.0761417	−	0.0161844i
$666$	2.53582	+	1.84238i	0.0982608	+	0.0713907i
$667$	53.7834	+	39.0759i	2.08250	+	1.51303i
$668$	20.2249	+	4.29894i	0.782526	+	0.166331i
$669$	1.05522	−	10.0397i	0.0407971	−	0.388159i
$670$	−0.196017	−	1.86497i	−0.00757278	−	0.0720502i
$671$	−15.3294	+	3.25836i	−0.591784	+	0.125788i
$672$	−1.00597	−	0.447889i	−0.0388063	−	0.0172777i
$673$	−20.3295	+	22.5782i	−0.783646	+	0.870327i	−0.994232	−	0.107249i	$-0.965796\pi$
$673$	−20.3295	+	22.5782i	−0.783646	+	0.870327i	0.210587	+	0.977575i	$0.432463\pi$
$674$	4.67993	+	14.4033i	0.180264	+	0.554796i
$675$	0.669131	+	0.743145i	0.0257548	+	0.0286037i
$676$	−1.73154	+	2.99911i	−0.0665976	+	0.115350i
$677$	−3.52433	−	6.10432i	−0.135451	−	0.234608i	0.790319	−	0.612696i	$-0.209915\pi$
$677$	−3.52433	−	6.10432i	−0.135451	−	0.234608i	−0.925770	+	0.378088i	$0.876582\pi$
$678$	5.10547	−	15.7130i	0.196074	−	0.603455i
$679$	−11.3833	+	5.06817i	−0.436850	+	0.194498i
$680$	3.37568	−	2.45257i	0.129451	−	0.0940519i
$681$	−1.67190			−0.0640675
$682$	−13.7237	+	11.0417i	−0.525509	+	0.422807i
$683$	−20.1370			−0.770522			−0.385261	−	0.922808i	$-0.625889\pi$
$683$	−20.1370			−0.770522			−0.385261	+	0.922808i	$0.625889\pi$
$684$	−1.47479	+	1.07150i	−0.0563899	+	0.0409697i
$685$	18.0808	−	8.05010i	0.690833	−	0.307579i
$686$	4.35133	−	13.3920i	0.166135	−	0.511309i
$687$	−4.99367	−	8.64930i	−0.190521	−	0.329991i
$688$	−0.140567	+	0.243469i	−0.00535907	+	0.00928217i
$689$	−19.3223	−	21.4596i	−0.736123	−	0.817547i
$690$	−1.98108	−	6.09714i	−0.0754185	−	0.232114i
$691$	−4.02907	+	4.47473i	−0.153273	+	0.170227i	−0.814891	−	0.579614i	$-0.803203\pi$
$691$	−4.02907	+	4.47473i	−0.153273	+	0.170227i	0.661618	+	0.749841i	$0.269870\pi$
$692$	14.6297	+	6.51357i	0.556138	+	0.247609i
$693$	3.40756	−	0.724298i	0.129442	−	0.0275138i
$694$	2.92902	+	27.8677i	0.111184	+	1.05784i
$695$	0.632005	−	6.01312i	0.0239733	−	0.228091i
$696$	−10.1432	−	2.15600i	−0.384477	−	0.0817231i
$697$	−17.6220	−	12.8031i	−0.667480	−	0.484952i
$698$	−19.6119	−	14.2489i	−0.742323	−	0.539329i
$699$	23.5368	+	5.00289i	0.890242	+	0.189227i
$700$	−0.115104	+	1.09514i	−0.00435053	+	0.0413926i
$701$	−0.171642	−	1.63307i	−0.00648284	−	0.0616801i	0.990802	−	0.135318i	$-0.0432057\pi$
$701$	−0.171642	−	1.63307i	−0.00648284	−	0.0616801i	−0.997285	+	0.0736382i	$0.976539\pi$
$702$	−3.96881	+	0.843596i	−0.149793	+	0.0318395i
$703$	5.21990	+	2.32405i	0.196872	+	0.0876531i
$704$	−2.11686	+	2.35101i	−0.0797822	+	0.0886072i
$705$	−0.334830	−	1.03050i	−0.0126104	−	0.0388109i
$706$	0.957306	+	1.06320i	0.0360287	+	0.0400139i
$707$	1.32222	−	2.29015i	0.0497272	−	0.0861300i
$708$	2.87168	+	4.97389i	0.107924	+	0.186930i
$709$	−11.1788	+	34.4047i	−0.419827	+	1.29209i	0.488034	+	0.872824i	$0.337714\pi$
$709$	−11.1788	+	34.4047i	−0.419827	+	1.29209i	−0.907861	+	0.419270i	$0.862286\pi$
$710$	12.0992	−	5.38691i	0.454075	−	0.202167i
$711$	9.61800	−	6.98788i	0.360703	−	0.262066i
$712$	15.6591			0.586849
$713$	−5.47242	−	35.2725i	−0.204944	−	1.32096i
$714$	−4.59473			−0.171954
$715$	−10.3847	+	7.54494i	−0.388367	+	0.282165i
$716$	2.29041	−	1.01976i	0.0855968	−	0.0381101i
$717$	8.21105	−	25.2710i	0.306647	−	0.943763i
$718$	−8.84770	−	15.3247i	−0.330193	−	0.571912i
$719$	6.00415	−	10.3995i	0.223917	−	0.387836i	−0.732077	−	0.681222i	$-0.761449\pi$
$719$	6.00415	−	10.3995i	0.223917	−	0.387836i	0.955994	+	0.293386i	$0.0947822\pi$
$720$	0.669131	+	0.743145i	0.0249370	+	0.0276954i
$721$	0.0388680	+	0.119623i	0.00144752	+	0.00445500i
$722$	10.4899	−	11.6502i	0.390393	−	0.433576i
$723$	10.7852	+	4.80186i	0.401105	+	0.178583i
$724$	−8.66850	+	1.84255i	−0.322162	+	0.0684777i
$725$	1.08394	+	10.3130i	0.0402565	+	0.383015i
$726$	−0.103654	+	0.986199i	−0.00384695	+	0.0366013i
$727$	48.4748	+	10.3036i	1.79783	+	0.382141i	0.980887	−	0.194577i	$-0.0623333\pi$
$727$	48.4748	+	10.3036i	1.79783	+	0.382141i	0.816944	+	0.576717i	$0.195667\pi$
$728$	−3.61468	−	2.62622i	−0.133969	−	0.0973342i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	11.8104	+	2.51037i	0.437122	+	0.0929131i
$731$	−0.122617	+	1.16662i	−0.00453516	+	0.0431492i
$732$	0.517813	+	4.92666i	0.0191389	+	0.182095i
$733$	−0.375834	+	0.0798859i	−0.0138817	+	0.00295065i	−0.214847	−	0.976648i	$-0.568925\pi$
$733$	−0.375834	+	0.0798859i	−0.0138817	+	0.00295065i	0.200966	+	0.979598i	$0.435592\pi$
$734$	−21.1825	−	9.43105i	−0.781860	−	0.348106i
$735$	−3.87253	+	4.30088i	−0.142841	+	0.158640i
$736$	−1.98108	−	6.09714i	−0.0730236	−	0.224744i
$737$	3.96964	+	4.40873i	0.146223	+	0.162398i
$738$	2.61014	−	4.52089i	0.0960805	−	0.166416i
$739$	8.36145	+	14.4825i	0.307581	+	0.532746i	0.977833	−	0.209388i	$-0.0671472\pi$
$739$	8.36145	+	14.4825i	0.307581	+	0.532746i	−0.670252	+	0.742134i	$0.733814\pi$
$740$	0.968595	−	2.98103i	0.0356063	−	0.109585i
$741$	−6.75706	+	3.00844i	−0.248227	+	0.110518i
$742$	6.34028	−	4.60648i	0.232759	−	0.169109i
$743$	4.21671			0.154696			0.0773481	−	0.997004i	$-0.475355\pi$
$743$	4.21671			0.154696			0.0773481	+	0.997004i	$0.475355\pi$
$744$	3.01765	+	4.67908i	0.110633	+	0.171543i
$745$	−18.8901			−0.692079
$746$	6.00242	−	4.36101i	0.219764	−	0.159668i
$747$	11.1697	−	4.97306i	0.408677	−	0.181955i
$748$	−4.07913	+	12.5543i	−0.149148	+	0.459029i
$749$	3.37929	+	5.85310i	0.123476	+	0.213867i
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	5.36126	+	5.95428i	0.195635	+	0.217275i	0.832979	−	0.553305i	$-0.186634\pi$
$751$	5.36126	+	5.95428i	0.195635	+	0.217275i	−0.637344	+	0.770580i	$0.719967\pi$
$752$	−0.334830	−	1.03050i	−0.0122100	−	0.0375785i
$753$	−8.42298	+	9.35467i	−0.306951	+	0.340903i
$754$	−38.4376	−	17.1135i	−1.39981	−	0.623237i
$755$	−10.0092	+	2.12752i	−0.364272	+	0.0774283i
$756$	−0.115104	−	1.09514i	−0.00418630	−	0.0398300i
$757$	2.10811	−	20.0574i	0.0766207	−	0.728997i	−0.887008	−	0.461754i	$-0.847220\pi$
$757$	2.10811	−	20.0574i	0.0766207	−	0.728997i	0.963629	−	0.267244i	$-0.0861129\pi$
$758$	19.2315	+	4.08779i	0.698521	+	0.148475i
$759$	16.4081	+	11.9212i	0.595578	+	0.432713i
$760$	1.47479	+	1.07150i	0.0534962	+	0.0388672i
$761$	40.0288	+	8.50838i	1.45104	+	0.308428i	0.864967	−	0.501829i	$-0.167339\pi$
$761$	40.0288	+	8.50838i	1.45104	+	0.308428i	0.586075	+	0.810257i	$0.300673\pi$
$762$	−0.816495	+	7.76843i	−0.0295785	+	0.281421i
$763$	0.713248	+	6.78610i	0.0258213	+	0.245673i
$764$	7.22012	−	1.53468i	0.261215	−	0.0555229i
$765$	3.81183	+	1.69714i	0.137817	+	0.0613601i
$766$	19.7158	−	21.8967i	0.712362	−	0.791158i
$767$	7.20118	+	22.1630i	0.260020	+	0.800258i
$768$	0.669131	+	0.743145i	0.0241452	+	0.0268159i
$769$	−5.42556	+	9.39735i	−0.195651	+	0.338877i	−0.947114	−	0.320898i	$-0.896015\pi$
$769$	−5.42556	+	9.39735i	−0.195651	+	0.338877i	0.751463	+	0.659775i	$0.229349\pi$
$770$	−1.74184	−	3.01696i	−0.0627716	−	0.108724i
$771$	2.17118	−	6.68219i	0.0781930	−	0.240653i
$772$	−19.8426	+	8.83450i	−0.714151	+	0.317961i
$773$	31.8751	−	23.1586i	1.14647	−	0.832958i	0.158461	−	0.987365i	$-0.449347\pi$
$773$	31.8751	−	23.1586i	1.14647	−	0.832958i	0.988007	+	0.154407i	$0.0493467\pi$
$774$	−0.281134			−0.0101052
$775$	3.51756	−	4.31587i	0.126355	−	0.155031i
$776$	11.3157			0.406209
$777$	−2.79238	+	2.02878i	−0.100176	+	0.0727822i
$778$	−27.7177	+	12.3407i	−0.993726	+	0.442435i
$779$	2.94068	−	9.05048i	0.105361	−	0.324267i
$780$	2.02874	+	3.51387i	0.0726404	+	0.125817i
$781$	−20.9497	+	36.2860i	−0.749640	+	1.29841i
$782$	−17.8992	−	19.8791i	−0.640075	−	0.710875i
$783$	−3.20444	−	9.86226i	−0.114517	−	0.352449i
$784$	−3.87253	+	4.30088i	−0.138305	+	0.153603i
$785$	6.47013	+	2.88069i	0.230929	+	0.102816i
$786$	2.72395	−	0.578994i	0.0971601	−	0.0206520i
$787$	5.49181	+	52.2510i	0.195762	+	1.86255i	0.446882	+	0.894593i	$0.352534\pi$
$787$	5.49181	+	52.2510i	0.195762	+	1.86255i	−0.251121	+	0.967956i	$0.580799\pi$
$788$	−0.777326	+	7.39576i	−0.0276911	+	0.263463i
$789$	−22.1999	−	4.71873i	−0.790337	−	0.167991i
$790$	−9.61800	−	6.98788i	−0.342193	−	0.248618i
$791$	14.7187	+	10.6937i	0.523335	+	0.380225i
$792$	−3.09447	−	0.657750i	−0.109957	−	0.0233721i
$793$	−2.10101	+	19.9898i	−0.0746091	+	0.709858i
$794$	1.37823	+	13.1130i	0.0489116	+	0.465363i
$795$	−6.96142	+	1.47970i	−0.246896	+	0.0524794i
$796$	−6.65040	−	2.96095i	−0.235717	−	0.104948i
$797$	29.5450	−	32.8130i	1.04654	−	1.16230i	0.0600935	−	0.998193i	$-0.480860\pi$
$797$	29.5450	−	32.8130i	1.04654	−	1.16230i	0.986443	−	0.164104i	$-0.0524732\pi$
$798$	−0.620313	−	1.90913i	−0.0219589	−	0.0675824i
$799$	−3.02521	−	3.35984i	−0.107024	−	0.118863i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	7.82955	+	13.5612i	0.276643	+	0.479161i
$802$	−1.26574	+	3.89553i	−0.0446947	+	0.137556i
$803$	−34.8957	+	15.5365i	−1.23144	+	0.548273i
$804$	1.51711	−	1.10224i	0.0535042	−	0.0388731i
$805$	7.05955			0.248816
$806$	8.02923	+	21.1160i	0.282817	+	0.743781i
$807$	22.6677			0.797942
$808$	−1.94283	+	1.41155i	−0.0683484	+	0.0496581i
$809$	−30.8780	+	13.7478i	−1.08561	+	0.483346i	−0.869959	−	0.493124i	$-0.835855\pi$
$809$	−30.8780	+	13.7478i	−1.08561	+	0.483346i	−0.215654	+	0.976470i	$0.569188\pi$
$810$	−0.309017	+	0.951057i	−0.0108578	+	0.0334167i
$811$	6.12501	+	10.6088i	0.215078	+	0.372526i	0.953297	−	0.302035i	$-0.0976661\pi$
$811$	6.12501	+	10.6088i	0.215078	+	0.372526i	−0.738219	+	0.674561i	$0.764333\pi$
$812$	5.70949	−	9.88913i	0.200364	−	0.347040i
$813$	−0.986809	−	1.09596i	−0.0346089	−	0.0384371i
$814$	3.06425	+	9.43079i	0.107402	+	0.330549i
$815$	7.40697	−	8.22627i	0.259455	−	0.288154i
$816$	3.81183	+	1.69714i	0.133441	+	0.0594116i
$817$	−0.501291	+	0.106553i	−0.0175379	+	0.00372780i
$818$	3.45462	+	32.8685i	0.120788	+	1.14922i
$819$	0.467032	−	4.44352i	0.0163194	−	0.155269i
$820$	−5.10620	−	1.08536i	−0.178316	−	0.0379023i
$821$	31.9467	+	23.2107i	1.11495	+	0.810058i	0.983436	−	0.181257i	$-0.0580166\pi$
$821$	31.9467	+	23.2107i	1.11495	+	0.810058i	0.131513	+	0.991314i	$0.458017\pi$
$822$	16.0120	+	11.6334i	0.558483	+	0.405762i
$823$	27.0885	+	5.75783i	0.944245	+	0.200705i	0.654212	−	0.756311i	$-0.273000\pi$
$823$	27.0885	+	5.75783i	0.944245	+	0.200705i	0.290033	+	0.957017i	$0.406334\pi$
$824$	0.0119395	−	0.113597i	0.000415933	−	0.00395734i
$825$	0.330686	+	3.14627i	0.0115130	+	0.109539i
$826$	−6.18625	+	1.31493i	−0.215247	+	0.0457522i
$827$	19.8450	+	8.83555i	0.690077	+	0.307242i	0.721649	−	0.692259i	$-0.243385\pi$
$827$	19.8450	+	8.83555i	0.690077	+	0.307242i	−0.0315715	+	0.999501i	$0.510051\pi$
$828$	4.28974	−	4.76424i	0.149079	−	0.165569i
$829$	6.22273	+	19.1516i	0.216124	+	0.665162i	0.999072	+	0.0430745i	$0.0137153\pi$
$829$	6.22273	+	19.1516i	0.216124	+	0.665162i	−0.782948	+	0.622088i	$0.786285\pi$
$830$	−8.18128	−	9.08623i	−0.283976	−	0.315388i
$831$	−11.9446	+	20.6886i	−0.414353	+	0.717680i
$832$	2.02874	+	3.51387i	0.0703338	+	0.121822i
$833$	−7.46225	+	22.9665i	−0.258552	+	0.795740i
$834$	5.52352	−	2.45923i	0.191264	−	0.0851562i
$835$	16.7279	−	12.1535i	0.578891	−	0.420589i
$836$	−5.76705			−0.199457
$837$	−2.54337	+	4.95290i	−0.0879119	+	0.171197i
$838$	−11.9807			−0.413865
$839$	−23.8678	+	17.3410i	−0.824007	+	0.598676i	−0.917858	−	0.396910i	$-0.870083\pi$
$839$	−23.8678	+	17.3410i	−0.824007	+	0.598676i	0.0938501	+	0.995586i	$0.470083\pi$
$840$	−1.00597	+	0.447889i	−0.0347094	+	0.0154536i
$841$	24.2679	−	74.6891i	0.836826	−	2.57549i
$842$	−12.9916	−	22.5021i	−0.447720	−	0.775473i
$843$	−13.8281	+	23.9510i	−0.476266	+	0.824917i
$844$	−7.96329	−	8.84413i	−0.274108	−	0.304427i
$845$	1.07015	+	3.29358i	0.0368143	+	0.113303i
$846$	0.725025	−	0.805222i	0.0249269	−	0.0276841i
$847$	−0.997556	−	0.444140i	−0.0342764	−	0.0152608i
$848$	−6.96142	+	1.47970i	−0.239056	+	0.0508130i
$849$	−0.491537	−	4.67666i	−0.0168695	−	0.160503i
$850$	0.436152	−	4.14971i	0.0149599	−	0.142334i
$851$	−19.6555	−	4.17791i	−0.673782	−	0.143217i
$852$	10.7148	+	7.78476i	0.367083	+	0.266701i
$853$	−0.636820	−	0.462677i	−0.0218043	−	0.0158417i	0.576830	−	0.816864i	$-0.304290\pi$
$853$	−0.636820	−	0.462677i	−0.0218043	−	0.0158417i	−0.598634	+	0.801023i	$0.704290\pi$
$854$	−5.33580	−	1.13416i	−0.182587	−	0.0388101i
$855$	−0.190549	+	1.81295i	−0.00651663	+	0.0620016i
$856$	−0.641553	−	6.10397i	−0.0219278	−	0.208629i
$857$	17.5450	−	3.72931i	0.599326	−	0.127391i	0.101748	−	0.994810i	$-0.467556\pi$
$857$	17.5450	−	3.72931i	0.599326	−	0.127391i	0.497578	+	0.867420i	$0.334223\pi$
$858$	−11.7265	−	5.22096i	−0.400335	−	0.178241i
$859$	−14.5927	+	16.2068i	−0.497895	+	0.552968i	−0.938745	−	0.344612i	$-0.888010\pi$
$859$	−14.5927	+	16.2068i	−0.497895	+	0.552968i	0.440850	+	0.897581i	$0.354677\pi$
$860$	0.0868752	+	0.267374i	0.00296242	+	0.00911739i
$861$	3.84646	+	4.27193i	0.131087	+	0.145587i
$862$	10.7945	−	18.6965i	0.367661	−	0.636807i
$863$	−28.2826	−	48.9868i	−0.962749	−	1.66753i	−0.715544	−	0.698567i	$-0.753821\pi$
$863$	−28.2826	−	48.9868i	−0.962749	−	1.66753i	−0.247205	−	0.968963i	$-0.579512\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$	14.6297	−	6.51357i	0.497425	−	0.221468i
$866$	−23.5204	+	17.0885i	−0.799254	+	0.580692i
$867$	0.410313			0.0139350
$868$	−5.92716	+	1.56812i	−0.201181	+	0.0532256i
$869$	37.6105			1.27585
$870$	−8.38934	+	6.09521i	−0.284425	+	0.206647i
$871$	6.95095	−	3.09476i	0.235524	−	0.104862i
$872$	1.91483	−	5.89326i	0.0648445	−	0.199571i
$873$	5.65784	+	9.79966i	0.191489	+	0.331668i
$874$	5.84335	−	10.1210i	0.197654	−	0.342347i
$875$	0.736831	+	0.818334i	0.0249094	+	0.0276647i
$876$	3.73114	+	11.4833i	0.126064	+	0.387984i
$877$	−25.9374	+	28.8064i	−0.875845	+	0.972724i	−0.999809	−	0.0195624i	$-0.993773\pi$
$877$	−25.9374	+	28.8064i	−0.875845	+	0.972724i	0.123964	+	0.992287i	$0.460439\pi$
$878$	−27.8457	−	12.3977i	−0.939748	−	0.418403i
$879$	−19.2420	+	4.09002i	−0.649018	+	0.137953i
$880$	0.330686	+	3.14627i	0.0111474	+	0.106061i
$881$	−2.35104	+	22.3687i	−0.0792086	+	0.753620i	0.880770	+	0.473545i	$0.157026\pi$
$881$	−2.35104	+	22.3687i	−0.0792086	+	0.753620i	−0.959978	+	0.280075i	$0.909641\pi$
$882$	−5.66094	−	1.20327i	−0.190614	−	0.0405162i
$883$	29.1819	+	21.2019i	0.982050	+	0.713501i	0.958166	−	0.286214i	$-0.0923967\pi$
$883$	29.1819	+	21.2019i	0.982050	+	0.713501i	0.0238842	+	0.999715i	$0.492397\pi$
$884$	13.6967	+	9.95125i	0.460670	+	0.334697i
$885$	5.61785	+	1.19411i	0.188842	+	0.0401396i
$886$	−0.996956	+	9.48540i	−0.0334934	+	0.318668i
$887$	−3.34007	−	31.7786i	−0.112148	−	1.06702i	−0.895384	−	0.445296i	$-0.853099\pi$
$887$	−3.34007	−	31.7786i	−0.112148	−	1.06702i	0.783235	−	0.621726i	$-0.213568\pi$
$888$	3.06594	−	0.651687i	0.102886	−	0.0218692i
$889$	−7.85789	−	3.49856i	−0.263545	−	0.117338i
$890$	10.4780	−	11.6370i	0.351223	−	0.390072i
$891$	−0.977606	−	3.00876i	−0.0327510	−	0.100797i
$892$	−6.75490	−	7.50208i	−0.226171	−	0.251188i
$893$	0.987606	−	1.71058i	0.0330490	−	0.0572425i
$894$	−9.44504	−	16.3593i	−0.315890	−	0.547137i
$895$	0.774758	−	2.38446i	0.0258973	−	0.0797037i
$896$	−1.00597	+	0.447889i	−0.0336073	+	0.0149629i
$897$	21.0442	−	15.2895i	0.702647	−	0.510503i
$898$	−27.1751			−0.906846
$899$	−51.5262	+	26.0492i	−1.71850	+	0.868789i
$900$	1.00000			0.0333333
$901$	−24.0245	+	17.4548i	−0.800372	+	0.581505i
$902$	15.0871	−	6.71720i	0.502345	−	0.223658i
$903$	0.0956649	−	0.294426i	0.00318353	−	0.00979789i
$904$	−8.26083	−	14.3082i	−0.274751	−	0.475883i
$905$	−4.43108	+	7.67486i	−0.147294	+	0.255121i
$906$	−6.84708	−	7.60445i	−0.227479	−	0.252641i
$907$	−6.45288	−	19.8599i	−0.214264	−	0.659438i	−0.999205	−	0.0398669i	$-0.987307\pi$
$907$	−6.45288	−	19.8599i	−0.214264	−	0.659438i	0.784941	−	0.619571i	$-0.212693\pi$
$908$	−1.11872	+	1.24247i	−0.0371261	+	0.0412327i
$909$	−2.19385	−	0.976765i	−0.0727654	−	0.0323972i
$910$	−4.37036	+	0.928948i	−0.144876	+	0.0307943i
$911$	−1.86698	−	17.7632i	−0.0618559	−	0.588520i	−0.980920	−	0.194412i	$-0.937720\pi$
$911$	−1.86698	−	17.7632i	−0.0618559	−	0.588520i	0.919064	−	0.394108i	$-0.128946\pi$
$912$	−0.190549	+	1.81295i	−0.00630970	+	0.0600328i
$913$	37.8352	+	8.04213i	1.25216	+	0.266156i
$914$	−23.3147	−	16.9391i	−0.771180	−	0.560295i
$915$	4.00771	+	2.91177i	0.132491	+	0.0962601i
$916$	−9.76910	−	2.07649i	−0.322780	−	0.0686090i
$917$	−0.320543	+	3.04976i	−0.0105853	+	0.100712i
$918$	0.436152	+	4.14971i	0.0143952	+	0.136961i
$919$	7.35899	−	1.56420i	0.242751	−	0.0515983i	−0.0849294	−	0.996387i	$-0.527066\pi$
$919$	7.35899	−	1.56420i	0.242751	−	0.0515983i	0.327680	+	0.944789i	$0.393733\pi$
$920$	−5.85666	−	2.60755i	−0.193088	−	0.0859685i
$921$	4.03657	−	4.48306i	0.133009	−	0.147722i
$922$	−2.52562	−	7.77307i	−0.0831770	−	0.255992i
$923$	35.9578	+	39.9352i	1.18356	+	1.31448i
$924$	1.74184	−	3.01696i	0.0573024	−	0.0992506i
$925$	−1.56722	−	2.71450i	−0.0515299	−	0.0892524i
$926$	−5.65999	+	17.4197i	−0.185999	+	0.572446i
$927$	0.104348	−	0.0464586i	0.00342723	−	0.00152590i
$928$	−8.38934	+	6.09521i	−0.275394	+	0.200085i
$929$	−6.82901			−0.224053			−0.112026	−	0.993705i	$-0.535734\pi$
$929$	−6.82901			−0.224053			−0.112026	+	0.993705i	$0.535734\pi$
$930$	5.49644	+	0.888362i	0.180235	+	0.0291305i
$931$	−10.5501			−0.345765
$932$	19.4670	−	14.1436i	0.637664	−	0.463290i
$933$	−5.05315	+	2.24981i	−0.165433	+	0.0736553i
$934$	3.74367	−	11.5218i	0.122497	−	0.377006i
$935$	6.60017	+	11.4318i	0.215849	+	0.373861i
$936$	−2.02874	+	3.51387i	−0.0663113	+	0.114855i
$937$	10.5311	+	11.6960i	0.344035	+	0.382090i	0.890186	−	0.455597i	$-0.150574\pi$
$937$	10.5311	+	11.6960i	0.344035	+	0.382090i	−0.546151	+	0.837687i	$0.683907\pi$
$938$	0.638113	+	1.96391i	0.0208351	+	0.0641239i
$939$	−10.1873	+	11.3142i	−0.332451	+	0.369224i
$940$	−0.989856	−	0.440712i	−0.0322856	−	0.0143745i
$941$	−38.2709	+	8.13473i	−1.24760	+	0.265185i	−0.783943	−	0.620832i	$-0.786795\pi$
$941$	−38.2709	+	8.13473i	−1.24760	+	0.265185i	−0.463653	+	0.886017i	$0.653461\pi$
$942$	0.740316	+	7.04364i	0.0241208	+	0.229494i
$943$	−3.49823	+	33.2834i	−0.113918	+	1.08386i
$944$	5.61785	+	1.19411i	0.182846	+	0.0388650i
$945$	−0.890871	−	0.647255i	−0.0289800	−	0.0210552i
$946$	−0.719536	−	0.522774i	−0.0233941	−	0.0169968i
$947$	41.9942	+	8.92614i	1.36463	+	0.290061i	0.831289	−	0.555841i	$-0.187604\pi$
$947$	41.9942	+	8.92614i	1.36463	+	0.290061i	0.533339	+	0.845902i	$0.320937\pi$
$948$	1.24269	−	11.8234i	0.0403606	−	0.384005i
$949$	5.12094	+	48.7225i	0.166233	+	1.58160i
$950$	1.78310	−	0.379010i	0.0578515	−	0.0122967i
$951$	−26.7732	−	11.9202i	−0.868180	−	0.386539i
$952$	−3.07448	+	3.41455i	−0.0996443	+	0.110666i
$953$	4.68924	+	14.4320i	0.151899	+	0.467498i	0.997834	−	0.0657893i	$-0.0209565\pi$
$953$	4.68924	+	14.4320i	0.151899	+	0.467498i	−0.845934	+	0.533287i	$0.820957\pi$
$954$	−4.76216	−	5.28892i	−0.154181	−	0.171235i
$955$	3.69071	−	6.39250i	0.119429	−	0.206856i
$956$	−13.2858	−	23.0116i	−0.429692	−	0.744248i
$957$	10.1376	−	31.2003i	0.327701	−	1.00856i
$958$	35.6208	−	15.8594i	1.15086	−	0.512394i
$959$	−17.6321	+	12.8104i	−0.569369	+	0.413671i
$960$	1.00000			0.0322749
$961$	29.4216	+	9.76565i	0.949085	+	0.315021i
$962$	12.7179			0.410042
$963$	4.96542	−	3.60759i	0.160008	−	0.116253i
$964$	10.7852	−	4.80186i	0.347367	−	0.154658i
$965$	−6.71198	+	20.6574i	−0.216066	+	0.664984i
$966$	3.52977	+	6.11375i	0.113569	+	0.196707i
$967$	−26.5296	+	45.9506i	−0.853135	+	1.47767i	0.0252302	+	0.999682i	$0.491968\pi$
$967$	−26.5296	+	45.9506i	−0.853135	+	1.47767i	−0.878365	+	0.477991i	$0.841365\pi$
$968$	0.663531	+	0.736925i	0.0213267	+	0.0236857i
$969$	2.35049	+	7.23405i	0.0755085	+	0.232391i
$970$	7.57167	−	8.40919i	0.243112	−	0.270003i
$971$	−39.7553	−	17.7002i	−1.27581	−	0.568027i	−0.346750	−	0.937958i	$-0.612715\pi$
$971$	−39.7553	−	17.7002i	−1.27581	−	0.568027i	−0.929059	+	0.369931i	$0.879381\pi$
$972$	−0.978148	+	0.207912i	−0.0313741	+	0.00666877i
$973$	0.695949	+	6.62151i	0.0223111	+	0.212276i
$974$	−3.00055	+	28.5483i	−0.0961437	+	0.914746i
$975$	3.96881	+	0.843596i	0.127104	+	0.0270167i
$976$	4.00771	+	2.91177i	0.128284	+	0.0932035i
$977$	11.2015	+	8.13837i	0.358368	+	0.260369i	0.752371	−	0.658740i	$-0.228910\pi$
$977$	11.2015	+	8.13837i	0.358368	+	0.260369i	−0.394003	+	0.919109i	$0.628910\pi$
$978$	10.8276	+	2.30149i	0.346230	+	0.0735934i
$979$	−5.17825	+	49.2677i	−0.165498	+	1.57460i
$980$	0.604949	+	5.75571i	0.0193244	+	0.183859i
$981$	6.06113	−	1.28833i	0.193517	−	0.0411333i
$982$	−13.8452	−	6.16430i	−0.441820	−	0.196711i
$983$	−19.1052	+	21.2185i	−0.609362	+	0.676765i	−0.966317	−	0.257357i	$-0.917149\pi$
$983$	−19.1052	+	21.2185i	−0.609362	+	0.676765i	0.356954	+	0.934122i	$0.383815\pi$
$984$	−1.61315	−	4.96478i	−0.0514255	−	0.158271i
$985$	4.97599	+	5.52640i	0.158548	+	0.176086i
$986$	−21.6343	+	37.4718i	−0.688978	+	1.19334i
$987$	0.596580	+	1.03331i	0.0189894	+	0.0328905i
$988$	−2.28565	+	7.03451i	−0.0727162	+	0.223797i
$989$	1.64651	−	0.733072i	0.0523559	−	0.0233103i
$990$	−2.55941	+	1.85952i	−0.0813433	+	0.0590994i
$991$	−14.6113			−0.464142			−0.232071	−	0.972699i	$-0.574550\pi$
$991$	−14.6113			−0.464142			−0.232071	+	0.972699i	$0.574550\pi$
$992$	5.49644	+	0.888362i	0.174512	+	0.0282055i
$993$	−11.3158			−0.359098
$994$	−11.7989	+	8.57239i	−0.374238	+	0.271900i
$995$	−6.65040	+	2.96095i	−0.210832	+	0.0938684i
$996$	3.77827	−	11.6283i	0.119719	−	0.368457i
$997$	3.33452	+	5.77555i	0.105605	+	0.182914i	0.913985	−	0.405747i	$-0.132989\pi$
$997$	3.33452	+	5.77555i	0.105605	+	0.182914i	−0.808380	+	0.588661i	$0.799655\pi$
$998$	3.76095	−	6.51415i	0.119051	−	0.206202i
$999$	2.09735	+	2.32934i	0.0663572	+	0.0736971i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.f.421.2	yes	16
31.19	even	15	inner	930.2.bg.f.391.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.f.391.2	✓	16	31.19	even	15	inner
930.2.bg.f.421.2	yes	16	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.913545 - 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.736831 + 0.818334i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.913545 - 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.736831 + 0.818334i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +(-0.913545 - 0.406737i) q^{10} +(3.09447 - 0.657750i) q^{11} +(-0.104528 - 0.994522i) q^{12} +(0.424121 - 4.03524i) q^{13} +(1.07711 + 0.228947i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-4.08139 - 0.867525i) q^{17} +(0.104528 - 0.994522i) q^{18} +(-0.190549 - 1.81295i) q^{19} +(-0.978148 + 0.207912i) q^{20} +(1.00597 + 0.447889i) q^{21} +(2.11686 - 2.35101i) q^{22} +(1.98108 + 6.09714i) q^{23} +(-0.669131 - 0.743145i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.02874 - 3.51387i) q^{26} +(0.309017 - 0.951057i) q^{27} +(1.00597 - 0.447889i) q^{28} +(8.38934 - 6.09521i) q^{29} -1.00000 q^{30} +(-5.49644 - 0.888362i) q^{31} -1.00000 q^{32} +(2.55941 - 1.85952i) q^{33} +(-3.81183 + 1.69714i) q^{34} +(0.340282 - 1.04728i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.56722 + 2.71450i) q^{37} +(-1.21978 - 1.35471i) q^{38} +(-1.25383 - 3.85888i) q^{39} +(-0.669131 + 0.743145i) q^{40} +(4.76896 + 2.12328i) q^{41} +(1.07711 - 0.228947i) q^{42} +(-0.0293865 - 0.279594i) q^{43} +(0.330686 - 3.14627i) q^{44} +(-0.978148 - 0.207912i) q^{45} +(5.18654 + 3.76824i) q^{46} +(0.876596 + 0.636884i) q^{47} +(-0.978148 - 0.207912i) q^{48} +(0.604949 - 5.75571i) q^{49} +(0.104528 + 0.994522i) q^{50} +(-4.08139 + 0.867525i) q^{51} +(-3.70668 - 1.65032i) q^{52} +(4.76216 - 5.28892i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-2.11686 - 2.35101i) q^{55} +(0.550588 - 0.953647i) q^{56} +(-0.911469 - 1.57871i) q^{57} +(3.20444 - 9.86226i) q^{58} +(-5.24682 + 2.33603i) q^{59} +(-0.809017 + 0.587785i) q^{60} -4.95380 q^{61} +(-4.96888 + 2.51202i) q^{62} +1.10118 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-3.70668 + 1.65032i) q^{65} +(0.977606 - 3.00876i) q^{66} +(0.937623 + 1.62401i) q^{67} +(-2.08628 + 3.61355i) q^{68} +(4.28974 + 4.76424i) q^{69} +(-0.340282 - 1.04728i) q^{70} +(-8.86211 + 9.84238i) q^{71} +(-0.913545 - 0.406737i) q^{72} +(-11.8104 + 2.51037i) q^{73} +(0.327638 + 3.11727i) q^{74} +(-0.104528 + 0.994522i) q^{75} +(-1.78310 - 0.379010i) q^{76} +(2.81836 + 2.04766i) q^{77} +(-3.28256 - 2.38492i) q^{78} +(11.6287 + 2.47176i) q^{79} +(-0.104528 + 0.994522i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(5.10620 - 1.08536i) q^{82} +(11.1697 + 4.97306i) q^{83} +(0.736831 - 0.818334i) q^{84} +(1.28939 + 3.96835i) q^{85} +(-0.188115 - 0.208923i) q^{86} +(5.18490 - 8.98051i) q^{87} +(-1.58180 - 2.73976i) q^{88} +(-4.83893 + 14.8927i) q^{89} +(-0.913545 + 0.406737i) q^{90} +(3.61468 - 2.62622i) q^{91} +6.41091 q^{92} +(-5.38257 + 1.42404i) q^{93} +1.08353 q^{94} +(-1.47479 + 1.07150i) q^{95} +(-0.913545 + 0.406737i) q^{96} +(-3.49674 + 10.7618i) q^{97} +(-2.89371 - 5.01204i) q^{98} +(1.58180 - 2.73976i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} - 13 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 - 13 * q^7 + 4 * q^8 + 2 * q^9	\( 16 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} - 13 q^{7} + 4 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{12} - 6 q^{13} - 2 q^{14} - 4 q^{15} - 4 q^{16} + 6 q^{17} - 2 q^{18} + 9 q^{19} + 2 q^{20} + 2 q^{21} - 13 q^{22} - 3 q^{23} - 2 q^{24} - 8 q^{25} + q^{26} - 4 q^{27} + 2 q^{28} - q^{29} - 16 q^{30} - 19 q^{31} - 16 q^{32} + 14 q^{33} + 4 q^{34} + 11 q^{35} - 8 q^{36} - 3 q^{37} + 6 q^{38} - 13 q^{39} - 2 q^{40} - 2 q^{42} + 2 q^{43} - 7 q^{44} + 2 q^{45} - 7 q^{46} - q^{47} + 2 q^{48} + 3 q^{49} - 2 q^{50} + 6 q^{51} - 6 q^{52} - 14 q^{53} + 4 q^{54} + 13 q^{55} - 7 q^{56} - 6 q^{57} - 4 q^{58} + 16 q^{59} - 4 q^{60} - 28 q^{61} - 21 q^{62} - 14 q^{63} - 4 q^{64} - 6 q^{65} + 11 q^{66} + 47 q^{67} - 4 q^{68} + 9 q^{69} - 11 q^{70} + 3 q^{71} - 2 q^{72} - 27 q^{73} + 8 q^{74} + 2 q^{75} - 6 q^{76} + 14 q^{77} - 12 q^{78} + 4 q^{79} + 2 q^{80} + 2 q^{81} + 30 q^{82} + 66 q^{83} - 13 q^{84} + 18 q^{85} + 13 q^{86} + 3 q^{87} - 3 q^{88} - 45 q^{89} - 2 q^{90} + 12 q^{91} - 8 q^{92} - 26 q^{93} + 36 q^{94} - 18 q^{95} - 2 q^{96} + 5 q^{97} - 13 q^{98} + 3 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 - 13 * q^7 + 4 * q^8 + 2 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^12 - 6 * q^13 - 2 * q^14 - 4 * q^15 - 4 * q^16 + 6 * q^17 - 2 * q^18 + 9 * q^19 + 2 * q^20 + 2 * q^21 - 13 * q^22 - 3 * q^23 - 2 * q^24 - 8 * q^25 + q^26 - 4 * q^27 + 2 * q^28 - q^29 - 16 * q^30 - 19 * q^31 - 16 * q^32 + 14 * q^33 + 4 * q^34 + 11 * q^35 - 8 * q^36 - 3 * q^37 + 6 * q^38 - 13 * q^39 - 2 * q^40 - 2 * q^42 + 2 * q^43 - 7 * q^44 + 2 * q^45 - 7 * q^46 - q^47 + 2 * q^48 + 3 * q^49 - 2 * q^50 + 6 * q^51 - 6 * q^52 - 14 * q^53 + 4 * q^54 + 13 * q^55 - 7 * q^56 - 6 * q^57 - 4 * q^58 + 16 * q^59 - 4 * q^60 - 28 * q^61 - 21 * q^62 - 14 * q^63 - 4 * q^64 - 6 * q^65 + 11 * q^66 + 47 * q^67 - 4 * q^68 + 9 * q^69 - 11 * q^70 + 3 * q^71 - 2 * q^72 - 27 * q^73 + 8 * q^74 + 2 * q^75 - 6 * q^76 + 14 * q^77 - 12 * q^78 + 4 * q^79 + 2 * q^80 + 2 * q^81 + 30 * q^82 + 66 * q^83 - 13 * q^84 + 18 * q^85 + 13 * q^86 + 3 * q^87 - 3 * q^88 - 45 * q^89 - 2 * q^90 + 12 * q^91 - 8 * q^92 - 26 * q^93 + 36 * q^94 - 18 * q^95 - 2 * q^96 + 5 * q^97 - 13 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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