LMFDB - Embedded newform 930.2.bg.i.391.1

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:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			391.1
Character	$\chi$	$=$	930.391
Dual form			930.2.bg.i.421.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.913545 + 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-3.49940 + 3.88648i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})$	\(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} +(-3.49940 + 3.88648i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +(0.913545 - 0.406737i) q^{10} +(-2.07376 - 0.440792i) q^{11} +(-0.104528 + 0.994522i) q^{12} +(0.161270 + 1.53438i) q^{13} +(-5.11549 + 1.08733i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-3.29483 + 0.700338i) q^{17} +(0.104528 + 0.994522i) q^{18} +(-0.762974 + 7.25921i) q^{19} +(0.978148 + 0.207912i) q^{20} +(-4.77763 + 2.12714i) q^{21} +(-1.41862 - 1.57554i) q^{22} +(1.84914 - 5.69107i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.771415 + 1.33613i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-4.77763 - 2.12714i) q^{28} +(2.47503 + 1.79821i) q^{29} +1.00000 q^{30} +(3.07047 - 4.64459i) q^{31} -1.00000 q^{32} +(-1.71519 - 1.24616i) q^{33} +(-3.07722 - 1.37007i) q^{34} +(1.61609 + 4.97381i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(4.14083 + 7.17213i) q^{37} +(-4.88411 + 5.42436i) q^{38} +(-0.476761 + 1.46732i) q^{39} +(0.669131 + 0.743145i) q^{40} +(4.05309 - 1.80455i) q^{41} +(-5.11549 - 1.08733i) q^{42} +(-0.738649 + 7.02778i) q^{43} +(-0.221610 - 2.10848i) q^{44} +(0.978148 - 0.207912i) q^{45} +(4.84111 - 3.51728i) q^{46} +(-6.98769 + 5.07685i) q^{47} +(-0.978148 + 0.207912i) q^{48} +(-2.12721 - 20.2390i) q^{49} +(0.104528 - 0.994522i) q^{50} +(-3.29483 - 0.700338i) q^{51} +(-1.40945 + 0.627526i) q^{52} +(-5.52064 - 6.13129i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-1.41862 + 1.57554i) q^{55} +(-2.61489 - 4.52912i) q^{56} +(-3.64960 + 6.32129i) q^{57} +(0.945377 + 2.90957i) q^{58} +(8.71352 + 3.87951i) q^{59} +(0.809017 + 0.587785i) q^{60} +11.8850 q^{61} +(5.21408 - 1.95277i) q^{62} -5.22977 q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.40945 + 0.627526i) q^{65} +(-0.655144 - 2.01633i) q^{66} +(-0.991584 + 1.71747i) q^{67} +(-1.68422 - 2.91715i) q^{68} +(4.00404 - 4.44694i) q^{69} +(-1.61609 + 4.97381i) q^{70} +(9.35794 + 10.3930i) q^{71} +(-0.913545 + 0.406737i) q^{72} +(6.25865 + 1.33032i) q^{73} +(-0.865670 + 8.23630i) q^{74} +(-0.104528 - 0.994522i) q^{75} +(-7.13969 + 1.51759i) q^{76} +(8.97006 - 6.51713i) q^{77} +(-1.24818 + 0.906853i) q^{78} +(-4.12140 + 0.876030i) q^{79} +(0.104528 + 0.994522i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(4.33970 + 0.922432i) q^{82} +(14.3041 - 6.36857i) q^{83} +(-3.49940 - 3.88648i) q^{84} +(-1.04090 + 3.20357i) q^{85} +(-4.72840 + 5.25142i) q^{86} +(1.52965 + 2.64943i) q^{87} +(1.06005 - 1.83605i) q^{88} +(-4.11870 - 12.6761i) q^{89} +(0.913545 + 0.406737i) q^{90} +(-6.52767 - 4.74263i) q^{91} +5.98395 q^{92} +(4.69414 - 2.99417i) q^{93} -8.63726 q^{94} +(5.90517 + 4.29036i) q^{95} +(-0.913545 - 0.406737i) q^{96} +(-5.08286 - 15.6434i) q^{97} +(10.1753 - 17.6241i) q^{98} +(-1.06005 - 1.83605i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9} + 3 q^{10} - 13 q^{11} + 3 q^{12} + 11 q^{13} - 8 q^{14} + 6 q^{15} - 6 q^{16} - 29 q^{17} - 3 q^{18} + 9 q^{19} - 3 q^{20} - 2 q^{21} - 17 q^{22} - 5 q^{23} - 3 q^{24} - 12 q^{25} + 9 q^{26} - 6 q^{27} - 2 q^{28} + 13 q^{29} + 24 q^{30} + 57 q^{31} - 24 q^{32} + 16 q^{33} + 29 q^{34} + q^{35} - 12 q^{36} - 24 q^{37} + 6 q^{38} - 17 q^{39} + 3 q^{40} + 32 q^{41} - 8 q^{42} + 49 q^{43} - 8 q^{44} - 3 q^{45} + 28 q^{47} + 3 q^{48} + 12 q^{49} - 3 q^{50} - 29 q^{51} - 19 q^{52} - 36 q^{53} + 6 q^{54} - 17 q^{55} - 3 q^{56} - 6 q^{57} + 2 q^{58} + 6 q^{60} + 33 q^{62} - 6 q^{63} - 6 q^{64} + 19 q^{65} + 4 q^{66} - 5 q^{67} + 11 q^{68} + 10 q^{69} - q^{70} - 11 q^{71} - 3 q^{72} - 13 q^{73} + 9 q^{74} + 3 q^{75} - 6 q^{76} + 4 q^{77} - 8 q^{78} - 68 q^{79} - 3 q^{80} + 3 q^{81} - 2 q^{82} + 10 q^{83} - 7 q^{84} + 2 q^{85} - 34 q^{86} + 11 q^{87} - 12 q^{88} + 55 q^{89} + 3 q^{90} + 38 q^{91} + 10 q^{92} + 19 q^{93} + 42 q^{94} + 18 q^{95} - 3 q^{96} - q^{97} + 63 q^{98} + 12 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9 + 3 * q^10 - 13 * q^11 + 3 * q^12 + 11 * q^13 - 8 * q^14 + 6 * q^15 - 6 * q^16 - 29 * q^17 - 3 * q^18 + 9 * q^19 - 3 * q^20 - 2 * q^21 - 17 * q^22 - 5 * q^23 - 3 * q^24 - 12 * q^25 + 9 * q^26 - 6 * q^27 - 2 * q^28 + 13 * q^29 + 24 * q^30 + 57 * q^31 - 24 * q^32 + 16 * q^33 + 29 * q^34 + q^35 - 12 * q^36 - 24 * q^37 + 6 * q^38 - 17 * q^39 + 3 * q^40 + 32 * q^41 - 8 * q^42 + 49 * q^43 - 8 * q^44 - 3 * q^45 + 28 * q^47 + 3 * q^48 + 12 * q^49 - 3 * q^50 - 29 * q^51 - 19 * q^52 - 36 * q^53 + 6 * q^54 - 17 * q^55 - 3 * q^56 - 6 * q^57 + 2 * q^58 + 6 * q^60 + 33 * q^62 - 6 * q^63 - 6 * q^64 + 19 * q^65 + 4 * q^66 - 5 * q^67 + 11 * q^68 + 10 * q^69 - q^70 - 11 * q^71 - 3 * q^72 - 13 * q^73 + 9 * q^74 + 3 * q^75 - 6 * q^76 + 4 * q^77 - 8 * q^78 - 68 * q^79 - 3 * q^80 + 3 * q^81 - 2 * q^82 + 10 * q^83 - 7 * q^84 + 2 * q^85 - 34 * q^86 + 11 * q^87 - 12 * q^88 + 55 * q^89 + 3 * q^90 + 38 * q^91 + 10 * q^92 + 19 * q^93 + 42 * q^94 + 18 * q^95 - 3 * q^96 - q^97 + 63 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{15}\right)$

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
$7$	−3.49940	+	3.88648i	−1.32265	+	1.46895i	−0.548142	+	0.836385i	$0.684665\pi$
$7$	−3.49940	+	3.88648i	−1.32265	+	1.46895i	−0.774507	+	0.632565i	$0.782002\pi$
$8$	−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
$11$	−2.07376	−	0.440792i	−0.625263	−	0.132904i	−0.115625	−	0.993293i	$-0.536887\pi$
$11$	−2.07376	−	0.440792i	−0.625263	−	0.132904i	−0.509638	+	0.860389i	$0.670221\pi$
$12$	−0.104528	+	0.994522i	−0.0301748	+	0.287094i
$13$	0.161270	+	1.53438i	0.0447282	+	0.425560i	0.993857	+	0.110672i	$0.0353003\pi$
$13$	0.161270	+	1.53438i	0.0447282	+	0.425560i	−0.949129	+	0.314888i	$0.898033\pi$
$14$	−5.11549	+	1.08733i	−1.36717	+	0.290601i
$15$	0.809017	−	0.587785i	0.208887	−	0.151765i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−3.29483	+	0.700338i	−0.799114	+	0.169857i	−0.589331	−	0.807891i	$-0.700609\pi$
$17$	−3.29483	+	0.700338i	−0.799114	+	0.169857i	−0.209782	+	0.977748i	$0.567275\pi$
$18$	0.104528	+	0.994522i	0.0246376	+	0.234411i
$19$	−0.762974	+	7.25921i	−0.175038	+	1.66538i	0.456268	+	0.889843i	$0.349186\pi$
$19$	−0.762974	+	7.25921i	−0.175038	+	1.66538i	−0.631306	+	0.775534i	$0.717481\pi$
$20$	0.978148	+	0.207912i	0.218720	+	0.0464905i
$21$	−4.77763	+	2.12714i	−1.04257	+	0.464180i
$22$	−1.41862	−	1.57554i	−0.302450	−	0.335905i
$23$	1.84914	−	5.69107i	0.385573	−	1.18667i	−0.550491	−	0.834841i	$-0.685560\pi$
$23$	1.84914	−	5.69107i	0.385573	−	1.18667i	0.936064	−	0.351830i	$-0.114440\pi$
$24$	−0.669131	+	0.743145i	−0.136586	+	0.151694i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.771415	+	1.33613i	−0.151287	+	0.262037i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−4.77763	−	2.12714i	−0.902888	−	0.401992i
$29$	2.47503	+	1.79821i	0.459601	+	0.333920i	0.793375	−	0.608733i	$-0.208322\pi$
$29$	2.47503	+	1.79821i	0.459601	+	0.333920i	−0.333774	+	0.942653i	$0.608322\pi$
$30$	1.00000			0.182574
$31$	3.07047	−	4.64459i	0.551473	−	0.834193i
$31$	3.07047	−	4.64459i	0.551473	−	0.834193i
$32$	−1.00000			−0.176777
$33$	−1.71519	−	1.24616i	−0.298576	−	0.216928i
$34$	−3.07722	−	1.37007i	−0.527739	−	0.234965i
$35$	1.61609	+	4.97381i	0.273169	+	0.840727i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	4.14083	+	7.17213i	0.680749	+	1.17909i	0.974753	+	0.223287i	$0.0716787\pi$
$37$	4.14083	+	7.17213i	0.680749	+	1.17909i	−0.294004	+	0.955804i	$0.594988\pi$
$38$	−4.88411	+	5.42436i	−0.792308	+	0.879947i
$39$	−0.476761	+	1.46732i	−0.0763428	+	0.234959i
$40$	0.669131	+	0.743145i	0.105799	+	0.117502i
$41$	4.05309	−	1.80455i	0.632986	−	0.281823i	−0.0650549	−	0.997882i	$-0.520722\pi$
$41$	4.05309	−	1.80455i	0.632986	−	0.281823i	0.698040	+	0.716058i	$0.254056\pi$
$42$	−5.11549	−	1.08733i	−0.789337	−	0.167779i
$43$	−0.738649	+	7.02778i	−0.112643	+	1.07173i	0.781488	+	0.623920i	$0.214461\pi$
$43$	−0.738649	+	7.02778i	−0.112643	+	1.07173i	−0.894131	+	0.447806i	$0.852206\pi$
$44$	−0.221610	−	2.10848i	−0.0334090	−	0.317865i
$45$	0.978148	−	0.207912i	0.145814	−	0.0309936i
$46$	4.84111	−	3.51728i	0.713783	−	0.518594i
$47$	−6.98769	+	5.07685i	−1.01926	+	0.740535i	−0.966131	−	0.258052i	$-0.916919\pi$
$47$	−6.98769	+	5.07685i	−1.01926	+	0.740535i	−0.0531286	+	0.998588i	$0.516919\pi$
$48$	−0.978148	+	0.207912i	−0.141183	+	0.0300095i
$49$	−2.12721	−	20.2390i	−0.303887	−	2.89129i
$50$	0.104528	−	0.994522i	0.0147826	−	0.140647i
$51$	−3.29483	−	0.700338i	−0.461368	−	0.0980669i
$52$	−1.40945	+	0.627526i	−0.195455	+	0.0870221i
$53$	−5.52064	−	6.13129i	−0.758318	−	0.842197i	0.233165	−	0.972437i	$-0.425092\pi$
$53$	−5.52064	−	6.13129i	−0.758318	−	0.842197i	−0.991482	+	0.130240i	$0.958425\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	−1.41862	+	1.57554i	−0.191286	+	0.212445i
$56$	−2.61489	−	4.52912i	−0.349429	−	0.605228i
$57$	−3.64960	+	6.32129i	−0.483401	+	0.837275i
$58$	0.945377	+	2.90957i	0.124134	+	0.382045i
$59$	8.71352	+	3.87951i	1.13440	+	0.505069i	0.886045	−	0.463599i	$-0.153442\pi$
$59$	8.71352	+	3.87951i	1.13440	+	0.505069i	0.248359	+	0.968668i	$0.420109\pi$
$60$	0.809017	+	0.587785i	0.104444	+	0.0758827i
$61$	11.8850			1.52172			0.760858	−	0.648919i	$-0.224779\pi$
$61$	11.8850			1.52172			0.760858	+	0.648919i	$0.224779\pi$
$62$	5.21408	−	1.95277i	0.662189	−	0.248002i
$63$	−5.22977			−0.658889
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	1.40945	+	0.627526i	0.174820	+	0.0778350i
$66$	−0.655144	−	2.01633i	−0.0806427	−	0.248193i
$67$	−0.991584	+	1.71747i	−0.121141	+	0.209823i	−0.920218	−	0.391406i	$-0.871989\pi$
$67$	−0.991584	+	1.71747i	−0.121141	+	0.209823i	0.799077	+	0.601229i	$0.205322\pi$
$68$	−1.68422	−	2.91715i	−0.204242	−	0.353757i
$69$	4.00404	−	4.44694i	0.482030	−	0.535349i
$70$	−1.61609	+	4.97381i	−0.193160	+	0.594484i
$71$	9.35794	+	10.3930i	1.11058	+	1.23343i	0.969934	+	0.243368i	$0.0782523\pi$
$71$	9.35794	+	10.3930i	1.11058	+	1.23343i	0.140649	+	0.990059i	$0.455081\pi$
$72$	−0.913545	+	0.406737i	−0.107662	+	0.0479344i
$73$	6.25865	+	1.33032i	0.732520	+	0.155702i	0.559046	−	0.829137i	$-0.311167\pi$
$73$	6.25865	+	1.33032i	0.732520	+	0.155702i	0.173474	+	0.984838i	$0.444501\pi$
$74$	−0.865670	+	8.23630i	−0.100632	+	0.957450i
$75$	−0.104528	−	0.994522i	−0.0120699	−	0.114837i
$76$	−7.13969	+	1.51759i	−0.818979	+	0.174079i
$77$	8.97006	−	6.51713i	1.02223	−	0.742695i
$78$	−1.24818	+	0.906853i	−0.141328	+	0.102681i
$79$	−4.12140	+	0.876030i	−0.463694	+	0.0985611i	−0.433834	−	0.900993i	$-0.642839\pi$
$79$	−4.12140	+	0.876030i	−0.463694	+	0.0985611i	−0.0298599	+	0.999554i	$0.509506\pi$
$80$	0.104528	+	0.994522i	0.0116866	+	0.111191i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	4.33970	+	0.922432i	0.479240	+	0.101866i
$83$	14.3041	−	6.36857i	1.57007	−	0.699042i	0.577023	−	0.816728i	$-0.304214\pi$
$83$	14.3041	−	6.36857i	1.57007	−	0.699042i	0.993051	+	0.117686i	$0.0375477\pi$
$84$	−3.49940	−	3.88648i	−0.381816	−	0.424049i
$85$	−1.04090	+	3.20357i	−0.112902	+	0.347476i
$86$	−4.72840	+	5.25142i	−0.509877	+	0.566276i
$87$	1.52965	+	2.64943i	0.163996	+	0.284049i
$88$	1.06005	−	1.83605i	0.113001	−	0.195724i
$89$	−4.11870	−	12.6761i	−0.436581	−	1.34366i	−0.891457	−	0.453104i	$-0.850316\pi$
$89$	−4.11870	−	12.6761i	−0.436581	−	1.34366i	0.454876	−	0.890555i	$-0.349684\pi$
$90$	0.913545	+	0.406737i	0.0962961	+	0.0428738i
$91$	−6.52767	−	4.74263i	−0.684286	−	0.497163i
$92$	5.98395			0.623870
$93$	4.69414	−	2.99417i	0.486760	−	0.310481i
$94$	−8.63726			−0.890865
$95$	5.90517	+	4.29036i	0.605858	+	0.440182i
$96$	−0.913545	−	0.406737i	−0.0932383	−	0.0415124i
$97$	−5.08286	−	15.6434i	−0.516086	−	1.58835i	−0.781297	−	0.624159i	$-0.785442\pi$
$97$	−5.08286	−	15.6434i	−0.516086	−	1.58835i	0.265211	−	0.964190i	$-0.414558\pi$
$98$	10.1753	−	17.6241i	1.02786	−	1.78030i
$99$	−1.06005	−	1.83605i	−0.106539	−	0.184530i
$100$	0.669131	−	0.743145i	0.0669131	−	0.0743145i
$101$	−1.72110	+	5.29701i	−0.171256	+	0.527072i	−0.999443	−	0.0333804i	$-0.989373\pi$
$101$	−1.72110	+	5.29701i	−0.171256	+	0.527072i	0.828187	+	0.560452i	$0.189373\pi$
$102$	−2.25392	−	2.50324i	−0.223172	−	0.247857i
$103$	−15.8374	+	7.05125i	−1.56050	+	0.694780i	−0.991804	−	0.127767i	$-0.959219\pi$
$103$	−15.8374	+	7.05125i	−1.56050	+	0.694780i	−0.568697	+	0.822547i	$0.692552\pi$
$104$	−1.50912	−	0.320772i	−0.147981	−	0.0314543i
$105$	−0.546660	+	5.20112i	−0.0533486	+	0.507578i
$106$	−0.862408	−	8.20527i	−0.0837645	−	0.796966i
$107$	−11.2133	+	2.38346i	−1.08403	+	0.230418i	−0.715088	−	0.699035i	$-0.753613\pi$
$107$	−11.2133	+	2.38346i	−1.08403	+	0.230418i	−0.368942	+	0.929452i	$0.620280\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	−3.05219	+	2.21754i	−0.292346	+	0.212402i	−0.724285	−	0.689501i	$-0.757830\pi$
$109$	−3.05219	+	2.21754i	−0.292346	+	0.212402i	0.431938	+	0.901903i	$0.357830\pi$
$110$	−2.07376	+	0.440792i	−0.197726	+	0.0420279i
$111$	0.865670	+	8.23630i	0.0821657	+	0.781755i
$112$	0.546660	−	5.20112i	0.0516545	−	0.491460i
$113$	12.8186	+	2.72468i	1.20587	+	0.256316i	0.766652	−	0.642063i	$-0.221921\pi$
$113$	12.8186	+	2.72468i	1.20587	+	0.256316i	0.439221	+	0.898379i	$0.355254\pi$
$114$	−6.66815	+	2.96885i	−0.624529	+	0.278058i
$115$	−4.00404	−	4.44694i	−0.373379	−	0.414679i
$116$	−0.945377	+	2.90957i	−0.0877760	+	0.270147i
$117$	−1.03235	+	1.14655i	−0.0954412	+	0.105998i
$118$	4.76907	+	8.26027i	0.439028	+	0.760420i
$119$	8.80808	−	15.2560i	0.807435	−	1.39852i
$120$	0.309017	+	0.951057i	0.0282093	+	0.0868192i
$121$	−5.94280	−	2.64591i	−0.540255	−	0.240537i
$122$	9.61515	+	6.98581i	0.870515	+	0.632466i
$123$	4.43665			0.400040
$124$	5.36609	+	1.48494i	0.481889	+	0.133351i
$125$	−1.00000			−0.0894427
$126$	−4.23097	−	3.07398i	−0.376925	−	0.273852i
$127$	3.57067	+	1.58976i	0.316846	+	0.141069i	0.558997	−	0.829170i	$-0.311186\pi$
$127$	3.57067	+	1.58976i	0.316846	+	0.141069i	−0.242151	+	0.970239i	$0.577853\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−3.53324	+	6.11976i	−0.311085	+	0.538815i
$130$	0.771415	+	1.33613i	0.0676576	+	0.117186i
$131$	2.43524	−	2.70460i	0.212767	−	0.236302i	−0.627309	−	0.778771i	$-0.715844\pi$
$131$	2.43524	−	2.70460i	0.212767	−	0.236302i	0.840076	+	0.542468i	$0.182510\pi$
$132$	0.655144	−	2.01633i	0.0570230	−	0.175499i
$133$	−25.5428	−	28.3682i	−2.21484	−	2.45983i
$134$	−1.81171	+	0.806627i	−0.156508	+	0.0696820i
$135$	0.978148	+	0.207912i	0.0841855	+	0.0178942i
$136$	0.352098	−	3.34999i	0.0301921	−	0.287259i
$137$	1.09075	+	10.3778i	0.0931892	+	0.886636i	0.936843	+	0.349749i	$0.113733\pi$
$137$	1.09075	+	10.3778i	0.0931892	+	0.886636i	−0.843654	+	0.536887i	$0.819600\pi$
$138$	5.85318	−	1.24413i	0.498256	−	0.105908i
$139$	1.96965	−	1.43104i	0.167064	−	0.121379i	−0.501112	−	0.865383i	$-0.667075\pi$
$139$	1.96965	−	1.43104i	0.167064	−	0.121379i	0.668176	+	0.744004i	$0.267075\pi$
$140$	−4.23097	+	3.07398i	−0.357583	+	0.259799i
$141$	−8.44852	+	1.79579i	−0.711493	+	0.151233i
$142$	1.46185	+	13.9086i	0.122676	+	1.16718i
$143$	0.341907	−	3.25302i	0.0285917	−	0.272032i
$144$	−0.978148	−	0.207912i	−0.0815123	−	0.0173260i
$145$	2.79481	−	1.24433i	0.232097	−	0.103336i
$146$	4.28142	+	4.75499i	0.354333	+	0.393526i
$147$	6.28865	−	19.3545i	0.518679	−	1.59633i
$148$	−5.54151	+	6.15448i	−0.455510	+	0.505895i
$149$	2.83471	+	4.90986i	0.232228	+	0.402231i	0.958464	−	0.285215i	$-0.0920650\pi$
$149$	2.83471	+	4.90986i	0.232228	+	0.402231i	−0.726235	+	0.687446i	$0.758732\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	−0.926803	−	2.85241i	−0.0754222	−	0.232126i	0.906237	−	0.422770i	$-0.138942\pi$
$151$	−0.926803	−	2.85241i	−0.0754222	−	0.232126i	−0.981659	+	0.190644i	$0.938942\pi$
$152$	−6.66815	−	2.96885i	−0.540858	−	0.240806i
$153$	−2.72512	−	1.97992i	−0.220313	−	0.160067i
$154$	11.0876			0.893464
$155$	−2.48709	−	4.98140i	−0.199768	−	0.400116i
$156$	−1.54283			−0.123525
$157$	5.60930	+	4.07540i	0.447671	+	0.325252i	0.788676	−	0.614809i	$-0.210767\pi$
$157$	5.60930	+	4.07540i	0.447671	+	0.325252i	−0.341004	+	0.940062i	$0.610767\pi$
$158$	−3.84920	−	1.71377i	−0.306226	−	0.136341i
$159$	−2.54953	−	7.84666i	−0.202191	−	0.622280i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	15.6473	+	27.1020i	1.23318	+	2.13594i
$162$	−0.669131	+	0.743145i	−0.0525719	+	0.0583870i
$163$	−2.16852	+	6.67403i	−0.169852	+	0.522750i	−0.999361	−	0.0357429i	$-0.988620\pi$
$163$	−2.16852	+	6.67403i	−0.169852	+	0.522750i	0.829509	+	0.558493i	$0.188620\pi$
$164$	2.96870	+	3.29708i	0.231817	+	0.257458i
$165$	−1.93680	+	0.862319i	−0.150780	+	0.0671315i
$166$	15.3156	+	3.25543i	1.18872	+	0.252670i
$167$	−0.483317	+	4.59845i	−0.0374002	+	0.355839i	0.959778	+	0.280762i	$0.0905871\pi$
$167$	−0.483317	+	4.59845i	−0.0374002	+	0.355839i	−0.997178	+	0.0750774i	$0.976080\pi$
$168$	−0.546660	−	5.20112i	−0.0421757	−	0.401275i
$169$	10.3876	−	2.20795i	0.799047	−	0.169843i
$170$	−2.72512	+	1.97992i	−0.209007	+	0.151853i
$171$	−5.90517	+	4.29036i	−0.451580	+	0.328092i
$172$	−6.91207	+	1.46921i	−0.527040	+	0.112026i
$173$	−0.674214	−	6.41472i	−0.0512596	−	0.487702i	−0.989793	−	0.142513i	$-0.954482\pi$
$173$	−0.674214	−	6.41472i	−0.0512596	−	0.487702i	0.938533	−	0.345189i	$-0.112185\pi$
$174$	−0.319784	+	3.04254i	−0.0242428	+	0.230655i
$175$	5.11549	+	1.08733i	0.386695	+	0.0821945i
$176$	1.93680	−	0.862319i	0.145992	−	0.0649998i
$177$	6.38226	+	7.08822i	0.479720	+	0.532783i
$178$	4.11870	−	12.6761i	0.308710	−	0.950111i
$179$	14.4148	−	16.0093i	1.07742	−	1.19659i	0.0979049	−	0.995196i	$-0.468786\pi$
$179$	14.4148	−	16.0093i	1.07742	−	1.19659i	0.979510	−	0.201395i	$-0.0645474\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	−6.12307	+	10.6055i	−0.455124	+	0.788298i	−0.998695	−	0.0510649i	$-0.983738\pi$
$181$	−6.12307	+	10.6055i	−0.455124	+	0.788298i	0.543571	+	0.839363i	$0.317072\pi$
$182$	−2.49335	−	7.67374i	−0.184819	−	0.568816i
$183$	10.8575	+	4.83406i	0.802607	+	0.357344i
$184$	4.84111	+	3.51728i	0.356892	+	0.259297i
$185$	8.28166			0.608880
$186$	5.55757	+	0.336814i	0.407501	+	0.0246964i
$187$	7.14140			0.522231
$188$	−6.98769	−	5.07685i	−0.509630	−	0.370268i
$189$	−4.77763	−	2.12714i	−0.347522	−	0.154727i
$190$	2.25558	+	6.94195i	0.163637	+	0.503622i
$191$	0.00923565	−	0.0159966i	0.000668268	−	0.00115747i	−0.865691	−	0.500579i	$-0.833121\pi$
$191$	0.00923565	−	0.0159966i	0.000668268	−	0.00115747i	0.866359	+	0.499421i	$0.166454\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	7.39762	−	8.21588i	0.532492	−	0.591392i	−0.415537	−	0.909576i	$-0.636406\pi$
$193$	7.39762	−	8.21588i	0.532492	−	0.591392i	0.948029	+	0.318184i	$0.103073\pi$
$194$	5.08286	−	15.6434i	0.364928	−	1.12313i
$195$	1.03235	+	1.14655i	0.0739285	+	0.0821059i
$196$	18.5911	−	8.27730i	1.32794	−	0.591236i
$197$	3.65303	+	0.776476i	0.260268	+	0.0553216i	0.336197	−	0.941792i	$-0.390859\pi$
$197$	3.65303	+	0.776476i	0.260268	+	0.0553216i	−0.0759296	+	0.997113i	$0.524192\pi$
$198$	0.221610	−	2.10848i	0.0157491	−	0.149843i
$199$	−0.715730	−	6.80972i	−0.0507368	−	0.482728i	−0.990157	−	0.139961i	$-0.955302\pi$
$199$	−0.715730	−	6.80972i	−0.0507368	−	0.482728i	0.939420	−	0.342767i	$-0.111364\pi$
$200$	0.978148	−	0.207912i	0.0691655	−	0.0147016i
$201$	−1.60442	+	1.16568i	−0.113167	+	0.0822205i
$202$	−4.50590	+	3.27373i	−0.317034	+	0.230339i
$203$	−15.6498	+	3.32647i	−1.09840	+	0.233473i
$204$	−0.352098	−	3.34999i	−0.0246518	−	0.234546i
$205$	0.463757	−	4.41235i	0.0323902	−	0.308172i
$206$	−16.9573	−	3.60439i	−1.18147	−	0.251130i
$207$	5.46661	−	2.43389i	0.379955	−	0.169167i
$208$	−1.03235	−	1.14655i	−0.0715809	−	0.0794987i
$209$	4.78203	−	14.7176i	0.330780	−	1.01804i
$210$	−3.49940	+	3.88648i	−0.241482	+	0.268192i
$211$	−1.92209	−	3.32916i	−0.132322	−	0.229189i	0.792249	−	0.610198i	$-0.208910\pi$
$211$	−1.92209	−	3.32916i	−0.132322	−	0.229189i	−0.924571	+	0.381009i	$0.875577\pi$
$212$	4.12523	−	7.14511i	0.283322	−	0.490728i
$213$	4.32167	+	13.3007i	0.296116	+	0.911352i
$214$	−10.4727	−	4.66275i	−0.715899	−	0.318739i
$215$	5.71691	+	4.15358i	0.389890	+	0.283272i
$216$	−1.00000			−0.0680414
$217$	7.30627	+	28.1866i	0.495982	+	1.91343i
$218$	−3.77271			−0.255520
$219$	5.17648	+	3.76093i	0.349794	+	0.254140i
$220$	−1.93680	−	0.862319i	−0.130579	−	0.0581375i
$221$	−1.60594	−	4.94257i	−0.108027	−	0.332473i
$222$	−4.14083	+	7.17213i	−0.277914	+	0.481362i
$223$	12.6551	+	21.9194i	0.847451	+	1.46783i	0.883475	+	0.468477i	$0.155197\pi$
$223$	12.6551	+	21.9194i	0.847451	+	1.46783i	−0.0360243	+	0.999351i	$0.511469\pi$
$224$	3.49940	−	3.88648i	0.233814	−	0.259676i
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	8.76895	+	9.73890i	0.583302	+	0.647822i
$227$	2.40290	−	1.06984i	0.159486	−	0.0710077i	−0.325441	−	0.945562i	$-0.605513\pi$
$227$	2.40290	−	1.06984i	0.159486	−	0.0710077i	0.484927	+	0.874555i	$0.338846\pi$
$228$	−7.13969	−	1.51759i	−0.472838	−	0.100505i
$229$	1.78378	−	16.9715i	0.117876	−	1.12151i	−0.762419	−	0.647084i	$-0.775988\pi$
$229$	1.78378	−	16.9715i	0.117876	−	1.12151i	0.880295	−	0.474427i	$-0.157345\pi$
$230$	−0.625493	−	5.95117i	−0.0412438	−	0.392408i
$231$	10.8453	−	2.30524i	0.713569	−	0.151674i
$232$	−2.47503	+	1.79821i	−0.162494	+	0.118058i
$233$	14.6534	−	10.6463i	0.959978	−	0.697465i	0.00683262	−	0.999977i	$-0.497825\pi$
$233$	14.6534	−	10.6463i	0.959978	−	0.697465i	0.953146	+	0.302512i	$0.0978251\pi$
$234$	−1.50912	+	0.320772i	−0.0986540	+	0.0209696i
$235$	0.902840	+	8.58995i	0.0588948	+	0.560346i
$236$	−0.997007	+	9.48589i	−0.0648996	+	0.617479i
$237$	−4.12140	−	0.876030i	−0.267714	−	0.0569043i
$238$	16.0932	−	7.16514i	1.04316	−	0.464447i
$239$	−6.83452	−	7.59051i	−0.442089	−	0.490989i	0.480380	−	0.877060i	$-0.340499\pi$
$239$	−6.83452	−	7.59051i	−0.442089	−	0.490989i	−0.922469	+	0.386071i	$0.873832\pi$
$240$	−0.309017	+	0.951057i	−0.0199470	+	0.0613904i
$241$	8.36559	−	9.29093i	0.538875	−	0.598481i	−0.410797	−	0.911727i	$-0.634750\pi$
$241$	8.36559	−	9.29093i	0.538875	−	0.598481i	0.949672	+	0.313246i	$0.101416\pi$
$242$	−3.25260	−	5.63368i	−0.209085	−	0.362146i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	3.67266	+	11.3033i	0.235118	+	0.723619i
$245$	−18.5911	−	8.27730i	−1.18774	−	0.528817i
$246$	3.58933	+	2.60780i	0.228847	+	0.166267i
$247$	−11.2614			−0.716547
$248$	3.46844	+	4.35545i	0.220246	+	0.276571i
$249$	15.6577			0.992269
$250$	−0.809017	−	0.587785i	−0.0511667	−	0.0371748i
$251$	18.7221	+	8.33560i	1.18173	+	0.526138i	0.901071	−	0.433671i	$-0.142782\pi$
$251$	18.7221	+	8.33560i	1.18173	+	0.526138i	0.280654	+	0.959809i	$0.409449\pi$
$252$	−1.61609	−	4.97381i	−0.101804	−	0.313320i
$253$	−6.34326	+	10.9868i	−0.398797	+	0.690737i
$254$	1.95429	+	3.38493i	0.122623	+	0.212390i
$255$	−2.25392	+	2.50324i	−0.141146	+	0.156759i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	12.2118	+	13.5626i	0.761751	+	0.846010i	0.991884	−	0.127149i	$-0.0405828\pi$
$257$	12.2118	+	13.5626i	0.761751	+	0.846010i	−0.230133	+	0.973159i	$0.573916\pi$
$258$	−6.45556	+	2.87420i	−0.401905	+	0.178940i
$259$	−42.3648	−	9.00491i	−2.63242	−	0.559538i
$260$	−0.161270	+	1.53438i	−0.0100015	+	0.0951581i
$261$	0.319784	+	3.04254i	0.0197941	+	0.188329i
$262$	3.55987	−	0.756674i	0.219930	−	0.0467475i
$263$	−2.69802	+	1.96023i	−0.166367	+	0.120873i	−0.667854	−	0.744293i	$-0.732787\pi$
$263$	−2.69802	+	1.96023i	−0.166367	+	0.120873i	0.501486	+	0.865166i	$0.332787\pi$
$264$	1.71519	−	1.24616i	0.105563	−	0.0766958i
$265$	−8.07017	+	1.71537i	−0.495747	+	0.105374i
$266$	−3.99018	−	37.9640i	−0.244653	−	2.32772i
$267$	1.39320	−	13.2554i	0.0852622	−	0.811216i
$268$	−1.93983	−	0.412324i	−0.118494	−	0.0251867i
$269$	−22.6070	+	10.0653i	−1.37837	+	0.613691i	−0.956170	−	0.292811i	$-0.905409\pi$
$269$	−22.6070	+	10.0653i	−1.37837	+	0.613691i	−0.422202	+	0.906502i	$0.638743\pi$
$270$	0.669131	+	0.743145i	0.0407220	+	0.0452264i
$271$	2.25008	−	6.92504i	0.136683	−	0.420666i	−0.859165	−	0.511698i	$-0.829017\pi$
$271$	2.25008	−	6.92504i	0.136683	−	0.420666i	0.995848	+	0.0910322i	$0.0290166\pi$
$272$	2.25392	−	2.50324i	0.136664	−	0.151781i
$273$	−4.03432	−	6.98766i	−0.244168	−	0.422912i
$274$	−5.21748	+	9.03695i	−0.315200	+	0.545942i
$275$	0.655144	+	2.01633i	0.0395067	+	0.121589i
$276$	5.46661	+	2.43389i	0.329051	+	0.146503i
$277$	−7.18513	−	5.22030i	−0.431713	−	0.313658i	0.350621	−	0.936518i	$-0.385971\pi$
$277$	−7.18513	−	5.22030i	−0.431713	−	0.313658i	−0.782333	+	0.622860i	$0.785971\pi$
$278$	2.43463			0.146019
$279$	5.50615	−	0.826030i	0.329645	−	0.0494531i
$280$	−5.22977			−0.312539
$281$	9.23543	+	6.70993i	0.550939	+	0.400281i	0.828132	−	0.560534i	$-0.189404\pi$
$281$	9.23543	+	6.70993i	0.550939	+	0.400281i	−0.277192	+	0.960814i	$0.589404\pi$
$282$	−7.89053	−	3.51309i	−0.469874	−	0.209202i
$283$	−0.676701	−	2.08267i	−0.0402257	−	0.123802i	0.928927	−	0.370263i	$-0.120732\pi$
$283$	−0.676701	−	2.08267i	−0.0402257	−	0.123802i	−0.969153	+	0.246461i	$0.920732\pi$
$284$	−6.99261	+	12.1116i	−0.414935	+	0.718689i
$285$	3.64960	+	6.32129i	0.216183	+	0.374441i
$286$	2.18869	−	2.43078i	0.129420	−	0.143735i
$287$	−7.17002	+	22.0671i	−0.423233	+	1.30258i
$288$	−0.669131	−	0.743145i	−0.0394289	−	0.0437902i
$289$	−5.16484	+	2.29954i	−0.303814	+	0.135267i
$290$	2.99245	+	0.636065i	0.175723	+	0.0373510i
$291$	1.71933	−	16.3584i	0.100789	−	0.958945i
$292$	0.668823	+	6.36343i	0.0391399	+	0.372391i
$293$	−32.0713	+	6.81697i	−1.87363	+	0.398252i	−0.996614	−	0.0822167i	$-0.973800\pi$
$293$	−32.0713	+	6.81697i	−1.87363	+	0.398252i	−0.877012	+	0.480468i	$0.840467\pi$
$294$	16.4639	−	11.9617i	0.960195	−	0.697622i
$295$	7.71652	−	5.60638i	0.449273	−	0.326416i
$296$	−8.10069	+	1.72185i	−0.470843	+	0.100081i
$297$	−0.221610	−	2.10848i	−0.0128591	−	0.122346i
$298$	−0.592616	+	5.63836i	−0.0343293	+	0.326621i
$299$	9.03047	+	1.91949i	0.522245	+	0.111007i
$300$	0.913545	−	0.406737i	0.0527436	−	0.0234830i
$301$	−24.7285	−	27.4637i	−1.42533	−	1.58298i
$302$	0.926803	−	2.85241i	0.0533315	−	0.164138i
$303$	−3.72679	+	4.13902i	−0.214099	+	0.237781i
$304$	−3.64960	−	6.32129i	−0.209319	−	0.362551i
$305$	5.94249	−	10.2927i	0.340266	−	0.589358i
$306$	−1.04090	−	3.20357i	−0.0595046	−	0.183136i
$307$	6.46161	+	2.87690i	0.368784	+	0.164193i	0.582757	−	0.812646i	$-0.301974\pi$
$307$	6.46161	+	2.87690i	0.368784	+	0.164193i	−0.213973	+	0.976839i	$0.568641\pi$
$308$	8.97006	+	6.51713i	0.511116	+	0.371348i
$309$	−17.3361			−0.986219
$310$	0.915892	−	5.49192i	0.0520192	−	0.311920i
$311$	−7.97552			−0.452250			−0.226125	−	0.974098i	$-0.572606\pi$
$311$	−7.97552			−0.452250			−0.226125	+	0.974098i	$0.572606\pi$
$312$	−1.24818	−	0.906853i	−0.0706640	−	0.0513404i
$313$	−28.2047	−	12.5576i	−1.59423	−	0.709795i	−0.598411	−	0.801190i	$-0.704201\pi$
$313$	−28.2047	−	12.5576i	−1.59423	−	0.709795i	−0.995815	+	0.0913948i	$0.970867\pi$
$314$	2.14256	+	6.59413i	0.120912	+	0.372128i
$315$	−2.61489	+	4.52912i	−0.147332	+	0.255187i
$316$	−2.10674	−	3.64897i	−0.118513	−	0.205271i
$317$	20.3295	−	22.5781i	1.14182	−	1.26812i	0.183306	−	0.983056i	$-0.441320\pi$
$317$	20.3295	−	22.5781i	1.14182	−	1.26812i	0.958510	−	0.285059i	$-0.0920133\pi$
$318$	2.54953	−	7.84666i	0.142971	−	0.440019i
$319$	−4.33998	−	4.82004i	−0.242992	−	0.269870i
$320$	−0.913545	+	0.406737i	−0.0510687	+	0.0227373i
$321$	−11.2133	−	2.38346i	−0.625865	−	0.133032i
$322$	−3.27118	+	31.1232i	−0.182296	+	1.73443i
$323$	−2.57003	−	24.4522i	−0.143000	−	1.36056i
$324$	−0.978148	+	0.207912i	−0.0543415	+	0.0115506i
$325$	1.24818	−	0.906853i	0.0692363	−	0.0503031i
$326$	−5.67727	+	4.12478i	−0.314435	+	0.228450i
$327$	−3.69027	+	0.784390i	−0.204072	+	0.0433769i
$328$	0.463757	+	4.41235i	0.0256067	+	0.243631i
$329$	4.72165	−	44.9235i	0.260313	−	2.47671i
$330$	−2.07376	−	0.440792i	−0.114157	−	0.0242648i
$331$	11.0066	−	4.90043i	0.604975	−	0.269352i	−0.0813056	−	0.996689i	$-0.525909\pi$
$331$	11.0066	−	4.90043i	0.604975	−	0.269352i	0.686280	+	0.727337i	$0.259242\pi$
$332$	10.4771	+	11.6360i	0.575004	+	0.638607i
$333$	−2.55917	+	7.87633i	−0.140242	+	0.431620i
$334$	−3.09392	+	3.43614i	−0.169292	+	0.188017i
$335$	0.991584	+	1.71747i	0.0541760	+	0.0938356i
$336$	2.61489	−	4.52912i	0.142654	−	0.247083i
$337$	8.35962	+	25.7283i	0.455378	+	1.40151i	0.870691	+	0.491830i	$0.163672\pi$
$337$	8.35962	+	25.7283i	0.455378	+	1.40151i	−0.415314	+	0.909678i	$0.636328\pi$
$338$	9.70156	+	4.31941i	0.527695	+	0.234945i
$339$	10.6022	+	7.70292i	0.575830	+	0.418365i
$340$	−3.36844			−0.182679
$341$	−8.41473	+	8.27833i	−0.455683	+	0.448297i
$342$	−7.29919			−0.394695
$343$	56.4857	+	41.0392i	3.04994	+	2.21591i
$344$	−6.45556	−	2.87420i	−0.348060	−	0.154966i
$345$	−1.84914	−	5.69107i	−0.0995544	−	0.306397i
$346$	3.22503	−	5.58591i	0.173379	−	0.300300i
$347$	11.0350	+	19.1132i	0.592390	+	1.02605i	0.993909	+	0.110200i	$0.0351490\pi$
$347$	11.0350	+	19.1132i	0.592390	+	1.02605i	−0.401519	+	0.915851i	$0.631518\pi$
$348$	−2.04707	+	2.27351i	−0.109735	+	0.121873i
$349$	−9.70281	+	29.8622i	−0.519379	+	1.59849i	0.255790	+	0.966732i	$0.417664\pi$
$349$	−9.70281	+	29.8622i	−0.519379	+	1.59849i	−0.775170	+	0.631753i	$0.782336\pi$
$350$	3.49940	+	3.88648i	0.187051	+	0.207741i
$351$	−1.40945	+	0.627526i	−0.0752306	+	0.0334948i
$352$	2.07376	+	0.440792i	0.110532	+	0.0234943i
$353$	−0.511235	+	4.86408i	−0.0272103	+	0.258889i	0.972457	+	0.233084i	$0.0748816\pi$
$353$	−0.511235	+	4.86408i	−0.0272103	+	0.258889i	−0.999667	+	0.0258051i	$0.991785\pi$
$354$	0.997007	+	9.48589i	0.0529903	+	0.504169i
$355$	13.6796	−	2.90769i	0.726038	−	0.154324i
$356$	10.7829	−	7.83423i	0.571492	−	0.415214i
$357$	14.2518	−	10.3545i	0.754284	−	0.548019i
$358$	21.0719	−	4.47896i	1.11368	−	0.236721i
$359$	0.123239	+	1.17254i	0.00650432	+	0.0618845i	0.997293	−	0.0735356i	$-0.0234283\pi$
$359$	0.123239	+	1.17254i	0.00650432	+	0.0618845i	−0.990788	+	0.135420i	$0.956762\pi$
$360$	−0.104528	+	0.994522i	−0.00550913	+	0.0524159i
$361$	−33.5292	−	7.12685i	−1.76469	−	0.375097i
$362$	−11.1874	+	4.98095i	−0.587997	+	0.261793i
$363$	−4.35283	−	4.83431i	−0.228465	−	0.253736i
$364$	2.49335	−	7.67374i	0.130687	−	0.402213i
$365$	4.28142	−	4.75499i	0.224100	−	0.248888i
$366$	5.94249	+	10.2927i	0.310619	+	0.538008i
$367$	−14.2307	+	24.6483i	−0.742836	+	1.28663i	0.208363	+	0.978051i	$0.433186\pi$
$367$	−14.2307	+	24.6483i	−0.742836	+	1.28663i	−0.951199	+	0.308578i	$0.900147\pi$
$368$	1.84914	+	5.69107i	0.0963931	+	0.296668i
$369$	4.05309	+	1.80455i	0.210995	+	0.0939411i
$370$	6.70001	+	4.86784i	0.348317	+	0.253067i
$371$	43.1480			2.24013
$372$	4.29819	+	3.53914i	0.222851	+	0.183496i
$373$	8.45795			0.437936			0.218968	−	0.975732i	$-0.429731\pi$
$373$	8.45795			0.437936			0.218968	+	0.975732i	$0.429731\pi$
$374$	5.77751	+	4.19761i	0.298748	+	0.217053i
$375$	−0.913545	−	0.406737i	−0.0471753	−	0.0210038i
$376$	−2.66906	−	8.21452i	−0.137646	−	0.423632i
$377$	−2.35999	+	4.08763i	−0.121546	+	0.210524i
$378$	−2.61489	−	4.52912i	−0.134495	−	0.232953i
$379$	6.67000	−	7.40778i	0.342615	−	0.380512i	−0.547071	−	0.837087i	$-0.684257\pi$
$379$	6.67000	−	7.40778i	0.342615	−	0.380512i	0.889685	+	0.456574i	$0.150924\pi$
$380$	−2.25558	+	6.94195i	−0.115709	+	0.356114i
$381$	2.61535	+	2.90464i	0.133989	+	0.148809i
$382$	0.0168744	−	0.00751295i	0.000863368	−	0.000384396i
$383$	−19.0020	−	4.03900i	−0.970958	−	0.206383i	−0.304983	−	0.952358i	$-0.598651\pi$
$383$	−19.0020	−	4.03900i	−0.970958	−	0.206383i	−0.665975	+	0.745974i	$0.731984\pi$
$384$	0.104528	−	0.994522i	0.00533420	−	0.0507515i
$385$	−1.15897	−	11.0269i	−0.0590666	−	0.561981i
$386$	10.8140	−	2.29858i	0.550417	−	0.116995i
$387$	−5.71691	+	4.15358i	−0.290607	+	0.211138i
$388$	13.3071	−	9.66817i	0.675565	−	0.490827i
$389$	−10.8415	+	2.30442i	−0.549683	+	0.116839i	−0.474377	−	0.880322i	$-0.657327\pi$
$389$	−10.8415	+	2.30442i	−0.549683	+	0.116839i	−0.0753061	+	0.997160i	$0.523993\pi$
$390$	0.161270	+	1.53438i	0.00816621	+	0.0776963i
$391$	−2.10693	+	20.0461i	−0.106552	+	1.01378i
$392$	19.9058	+	4.23111i	1.00539	+	0.213703i
$393$	3.32476	−	1.48028i	0.167712	−	0.0746702i
$394$	2.49896	+	2.77538i	0.125896	+	0.139822i
$395$	−1.30203	+	4.00725i	−0.0655125	+	0.201627i
$396$	1.41862	−	1.57554i	0.0712883	−	0.0791736i
$397$	−6.12285	−	10.6051i	−0.307297	−	0.532254i	0.670473	−	0.741934i	$-0.266091\pi$
$397$	−6.12285	−	10.6051i	−0.307297	−	0.532254i	−0.977770	+	0.209680i	$0.932758\pi$
$398$	3.42361	−	5.92987i	0.171610	−	0.297238i
$399$	−11.7961	−	36.3048i	−0.590546	−	1.81751i
$400$	0.913545	+	0.406737i	0.0456773	+	0.0203368i
$401$	1.86883	+	1.35778i	0.0933247	+	0.0678044i	0.633469	−	0.773768i	$-0.281630\pi$
$401$	1.86883	+	1.35778i	0.0933247	+	0.0678044i	−0.540144	+	0.841572i	$0.681630\pi$
$402$	−1.98317			−0.0989114
$403$	7.62173	+	3.96224i	0.379665	+	0.197373i
$404$	−5.56960			−0.277098
$405$	0.809017	+	0.587785i	0.0402004	+	0.0292073i
$406$	−14.6162	−	6.50757i	−0.725391	−	0.322965i
$407$	−5.42569	−	16.6985i	−0.268941	−	0.827716i
$408$	1.68422	−	2.91715i	0.0833813	−	0.144421i
$409$	7.22116	+	12.5074i	0.357063	+	0.618452i	0.987469	−	0.157814i	$-0.0504447\pi$
$409$	7.22116	+	12.5074i	0.357063	+	0.618452i	−0.630405	+	0.776266i	$0.717111\pi$
$410$	2.96870	−	3.29708i	0.146614	−	0.162831i
$411$	−3.22458	+	9.92424i	−0.159057	+	0.489527i
$412$	−11.6001	−	12.8833i	−0.571498	−	0.634713i
$413$	−45.5697	+	20.2890i	−2.24234	+	0.998354i
$414$	5.85318	+	1.24413i	0.287668	+	0.0611458i
$415$	1.63668	−	15.5720i	0.0803414	−	0.764397i
$416$	−0.161270	−	1.53438i	−0.00790690	−	0.0752291i
$417$	2.38142	−	0.506188i	0.116619	−	0.0247881i
$418$	12.5195	−	9.09596i	0.612349	−	0.444898i
$419$	0.00483104	−	0.00350995i	0.000236012	−	0.000171472i	−0.587667	−	0.809103i	$-0.699954\pi$
$419$	0.00483104	−	0.00350995i	0.000236012	−	0.000171472i	0.587903	+	0.808931i	$0.299954\pi$
$420$	−5.11549	+	1.08733i	−0.249610	+	0.0530563i
$421$	−2.77230	−	26.3767i	−0.135114	−	1.28552i	−0.826459	−	0.562997i	$-0.809648\pi$
$421$	−2.77230	−	26.3767i	−0.135114	−	1.28552i	0.691345	−	0.722525i	$-0.257019\pi$
$422$	0.401827	−	3.82312i	0.0195606	−	0.186107i
$423$	−8.44852	−	1.79579i	−0.410781	−	0.0873142i
$424$	7.53717	−	3.35577i	0.366037	−	0.162970i
$425$	2.25392	+	2.50324i	0.109331	+	0.121425i
$426$	−4.32167	+	13.3007i	−0.209386	+	0.644423i
$427$	−41.5903	+	46.1907i	−2.01270	+	2.23532i
$428$	−5.73190	−	9.92794i	−0.277062	−	0.479885i
$429$	1.63547	−	2.83272i	0.0789613	−	0.136765i
$430$	2.18366	+	6.72063i	0.105306	+	0.324098i
$431$	−29.9775	−	13.3468i	−1.44396	−	0.642894i	−0.472770	−	0.881186i	$-0.656746\pi$
$431$	−29.9775	−	13.3468i	−1.44396	−	0.642894i	−0.971194	+	0.238292i	$0.923412\pi$
$432$	−0.809017	−	0.587785i	−0.0389238	−	0.0282798i
$433$	−17.5371			−0.842781			−0.421390	−	0.906879i	$-0.638458\pi$
$433$	−17.5371			−0.842781			−0.421390	+	0.906879i	$0.638458\pi$
$434$	−10.6568	+	27.0980i	−0.511541	+	1.30074i
$435$	3.05930			0.146682
$436$	−3.05219	−	2.21754i	−0.146173	−	0.106201i
$437$	39.9018	+	17.7654i	1.90876	+	0.849836i
$438$	1.97724	+	6.08531i	0.0944761	+	0.290767i
$439$	3.12753	−	5.41703i	0.149269	−	0.258541i	−0.781689	−	0.623669i	$-0.785641\pi$
$439$	3.12753	−	5.41703i	0.149269	−	0.258541i	0.930957	+	0.365128i	$0.118975\pi$
$440$	−1.06005	−	1.83605i	−0.0505357	−	0.0875304i
$441$	13.6172	−	15.1234i	0.648436	−	0.720161i
$442$	1.60594	−	4.94257i	0.0763867	−	0.235094i
$443$	4.74062	+	5.26499i	0.225234	+	0.250147i	0.845161	−	0.534512i	$-0.179505\pi$
$443$	4.74062	+	5.26499i	0.225234	+	0.250147i	−0.619927	+	0.784659i	$0.712838\pi$
$444$	−7.56568	+	3.36846i	−0.359051	+	0.159860i
$445$	−13.0371	−	2.77113i	−0.618020	−	0.131364i
$446$	−2.64565	+	25.1716i	−0.125275	+	1.19191i
$447$	0.592616	+	5.63836i	0.0280298	+	0.266685i
$448$	5.11549	−	1.08733i	0.241684	−	0.0513715i
$449$	−4.07060	+	2.95746i	−0.192103	+	0.139571i	−0.679680	−	0.733509i	$-0.737881\pi$
$449$	−4.07060	+	2.95746i	−0.192103	+	0.139571i	0.487576	+	0.873080i	$0.337881\pi$
$450$	0.809017	−	0.587785i	0.0381374	−	0.0277085i
$451$	−9.20057	+	1.95564i	−0.433238	+	0.0920876i
$452$	1.36984	+	13.0332i	0.0644320	+	0.613030i
$453$	0.313502	−	2.98277i	0.0147296	−	0.140143i
$454$	2.57282	+	0.546870i	0.120748	+	0.0256659i
$455$	−7.37108	+	3.28182i	−0.345561	+	0.153854i
$456$	−4.88411	−	5.42436i	−0.228720	−	0.254019i
$457$	5.17551	−	15.9286i	0.242100	−	0.745108i	−0.754000	−	0.656875i	$-0.771878\pi$
$457$	5.17551	−	15.9286i	0.242100	−	0.745108i	0.996100	−	0.0882330i	$-0.0281220\pi$
$458$	11.4187	−	12.6818i	0.533562	−	0.592581i
$459$	−1.68422	−	2.91715i	−0.0786126	−	0.136161i
$460$	2.99197	−	5.18225i	0.139501	−	0.241624i
$461$	−3.77448	−	11.6167i	−0.175795	−	0.541042i	0.823874	−	0.566773i	$-0.191809\pi$
$461$	−3.77448	−	11.6167i	−0.175795	−	0.541042i	−0.999669	+	0.0257315i	$0.991809\pi$
$462$	10.1290	+	4.50973i	0.471245	+	0.209812i
$463$	−7.86877	−	5.71699i	−0.365693	−	0.265691i	0.389730	−	0.920929i	$-0.372568\pi$
$463$	−7.86877	−	5.71699i	−0.365693	−	0.265691i	−0.755423	+	0.655238i	$0.772568\pi$
$464$	−3.05930			−0.142025
$465$	−0.245956	−	5.56233i	−0.0114059	−	0.257947i
$466$	18.1126			0.839052
$467$	−5.19989	−	3.77794i	−0.240622	−	0.174822i	0.460938	−	0.887432i	$-0.347513\pi$
$467$	−5.19989	−	3.77794i	−0.240622	−	0.174822i	−0.701560	+	0.712610i	$0.747513\pi$
$468$	−1.40945	−	0.627526i	−0.0651516	−	0.0290074i
$469$	−3.20497	−	9.86390i	−0.147992	−	0.455472i
$470$	−4.31863	+	7.48009i	−0.199204	+	0.345031i
$471$	3.46674	+	6.00457i	0.159739	+	0.276676i
$472$	−6.38226	+	7.08822i	−0.293767	+	0.326262i
$473$	4.62957	−	14.2484i	0.212868	−	0.655140i
$474$	−2.81936	−	3.13122i	−0.129498	−	0.143822i
$475$	6.66815	−	2.96885i	0.305956	−	0.136220i
$476$	17.2312	+	3.66261i	0.789791	+	0.167875i
$477$	0.862408	−	8.20527i	0.0394870	−	0.375693i
$478$	−1.06766	−	10.1581i	−0.0488335	−	0.464620i
$479$	−13.1099	+	2.78660i	−0.599007	+	0.127323i	−0.497429	−	0.867505i	$-0.665722\pi$
$479$	−13.1099	+	2.78660i	−0.599007	+	0.127323i	−0.101578	+	0.994828i	$0.532389\pi$
$480$	−0.809017	+	0.587785i	−0.0369264	+	0.0268286i
$481$	−10.3370	+	7.51025i	−0.471325	+	0.342438i
$482$	12.2290	−	2.59935i	0.557014	−	0.118397i
$483$	3.27118	+	31.1232i	0.148844	+	1.41616i
$484$	0.679980	−	6.46957i	0.0309082	−	0.294072i
$485$	−16.0890	−	3.41983i	−0.730566	−	0.155287i
$486$	−0.913545	+	0.406737i	−0.0414393	+	0.0184499i
$487$	26.8546	+	29.8250i	1.21690	+	1.35150i	0.917682	+	0.397315i	$0.130058\pi$
$487$	26.8546	+	29.8250i	1.21690	+	1.35150i	0.299215	+	0.954186i	$0.403275\pi$
$488$	−3.67266	+	11.3033i	−0.166253	+	0.511676i
$489$	−4.69562	+	5.21501i	−0.212343	+	0.235831i
$490$	−10.1753	−	17.6241i	−0.459671	−	0.796174i
$491$	0.291565	−	0.505005i	0.0131581	−	0.0227906i	−0.859371	−	0.511352i	$-0.829145\pi$
$491$	0.291565	−	0.505005i	0.0131581	−	0.0227906i	0.872529	+	0.488561i	$0.162478\pi$
$492$	1.37100	+	4.21951i	0.0618095	+	0.190230i
$493$	−9.41415	−	4.19145i	−0.423992	−	0.188773i
$494$	−9.11068	−	6.61930i	−0.409909	−	0.297816i
$495$	−2.12009			−0.0952911
$496$	0.245956	+	5.56233i	0.0110437	+	0.249756i
$497$	−73.1395			−3.28076
$498$	12.6674	+	9.20339i	0.567639	+	0.412414i
$499$	0.0555633	+	0.0247384i	0.00248735	+	0.00110744i	0.407980	−	0.912991i	$-0.366233\pi$
$499$	0.0555633	+	0.0247384i	0.00248735	+	0.00110744i	−0.405493	+	0.914098i	$0.632900\pi$
$500$	−0.309017	−	0.951057i	−0.0138197	−	0.0425325i
$501$	−2.31189	+	4.00431i	−0.103288	+	0.178900i
$502$	10.2469	+	17.7482i	0.457342	+	0.792140i
$503$	−20.4015	+	22.6582i	−0.909660	+	1.01028i	0.0902374	+	0.995920i	$0.471237\pi$
$503$	−20.4015	+	22.6582i	−0.909660	+	1.01028i	−0.999897	+	0.0143590i	$0.995429\pi$
$504$	1.61609	−	4.97381i	0.0719863	−	0.221551i
$505$	3.72679	+	4.13902i	0.165840	+	0.184184i
$506$	−11.5897	+	5.16007i	−0.515226	+	0.229393i
$507$	10.3876	+	2.20795i	0.461330	+	0.0980587i
$508$	−0.408558	+	3.88717i	−0.0181268	+	0.172465i
$509$	−1.21375	−	11.5480i	−0.0537984	−	0.511857i	−0.987927	−	0.154921i	$-0.950488\pi$
$509$	−1.21375	−	11.5480i	−0.0537984	−	0.511857i	0.934129	−	0.356937i	$-0.116179\pi$
$510$	−3.29483	+	0.700338i	−0.145898	+	0.0310115i
$511$	−27.0718	+	19.6688i	−1.19759	+	0.870097i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−7.13969	+	1.51759i	−0.315225	+	0.0670031i
$514$	1.90767	+	18.1503i	0.0841437	+	0.800574i
$515$	−1.81212	+	17.2412i	−0.0798516	+	0.759737i
$516$	−6.91207	−	1.46921i	−0.304287	−	0.0646782i
$517$	16.7287	−	7.44808i	0.735725	−	0.327566i
$518$	−28.9809	−	32.1865i	−1.27335	−	1.41419i
$519$	1.99318	−	6.13437i	0.0874907	−	0.269269i
$520$	−1.03235	+	1.14655i	−0.0452718	+	0.0502794i
$521$	−15.3576	−	26.6002i	−0.672830	−	1.16537i	−0.977098	−	0.212789i	$-0.931745\pi$
$521$	−15.3576	−	26.6002i	−0.672830	−	1.16537i	0.304269	−	0.952586i	$-0.401588\pi$
$522$	−1.52965	+	2.64943i	−0.0669510	+	0.115963i
$523$	−1.14349	−	3.51930i	−0.0500013	−	0.153888i	0.922938	−	0.384948i	$-0.125781\pi$
$523$	−1.14349	−	3.51930i	−0.0500013	−	0.153888i	−0.972940	+	0.231060i	$0.925781\pi$
$524$	3.32476	+	1.48028i	0.145243	+	0.0646663i
$525$	4.23097	+	3.07398i	0.184655	+	0.134160i
$526$	−3.33494			−0.145410
$527$	−6.86390	+	17.4535i	−0.298996	+	0.760286i
$528$	2.12009			0.0922652
$529$	−10.3616	−	7.52813i	−0.450504	−	0.327310i
$530$	−7.53717	−	3.35577i	−0.327394	−	0.145765i
$531$	2.94745	+	9.07131i	0.127908	+	0.393661i
$532$	19.0866	−	33.0589i	0.827507	−	1.43328i
$533$	3.42250	+	5.92795i	0.148245	+	0.256768i
$534$	8.91844	−	9.90493i	0.385938	−	0.428628i
$535$	−3.54251	+	10.9027i	−0.153156	+	0.471366i
$536$	−1.32700	−	1.47378i	−0.0573176	−	0.0636576i
$537$	19.6802	−	8.76218i	0.849262	−	0.378116i
$538$	−24.2057	−	5.14507i	−1.04358	−	0.221820i
$539$	−4.50988	+	42.9086i	−0.194254	+	1.84820i
$540$	0.104528	+	0.994522i	0.00449819	+	0.0427974i
$541$	3.35178	−	0.712443i	0.144104	−	0.0306303i	−0.135295	−	0.990805i	$-0.543198\pi$
$541$	3.35178	−	0.712443i	0.144104	−	0.0306303i	0.279399	+	0.960175i	$0.409865\pi$
$542$	5.89079	−	4.27991i	0.253031	−	0.183838i
$543$	−9.90733	+	7.19810i	−0.425164	+	0.308900i
$544$	3.29483	−	0.700338i	0.141265	−	0.0300267i
$545$	0.394355	+	3.75204i	0.0168923	+	0.160720i
$546$	0.843404	−	8.02445i	0.0360943	−	0.343415i
$547$	−24.1786	−	5.13931i	−1.03380	−	0.219741i	−0.340391	−	0.940284i	$-0.610559\pi$
$547$	−24.1786	−	5.13931i	−1.03380	−	0.219741i	−0.693410	+	0.720543i	$0.743893\pi$
$548$	−9.53282	+	4.24428i	−0.407222	+	0.181307i
$549$	7.95260	+	8.83226i	0.339409	+	0.376952i
$550$	−0.655144	+	2.01633i	−0.0279355	+	0.0859765i
$551$	−14.9420	+	16.5948i	−0.636550	+	0.706960i
$552$	2.99197	+	5.18225i	0.127347	+	0.220571i
$553$	11.0178	−	19.0833i	0.468522	−	0.811505i
$554$	−2.74448	−	8.44663i	−0.116602	−	0.358863i
$555$	7.56568	+	3.36846i	0.321145	+	0.142983i
$556$	1.96965	+	1.43104i	0.0835320	+	0.0606895i
$557$	−23.1665			−0.981595			−0.490797	−	0.871274i	$-0.663294\pi$
$557$	−23.1665			−0.981595			−0.490797	+	0.871274i	$0.663294\pi$
$558$	4.94010	+	2.56816i	0.209131	+	0.108719i
$559$	−10.9024			−0.461122
$560$	−4.23097	−	3.07398i	−0.178791	−	0.129899i
$561$	6.52399	+	2.90467i	0.275443	+	0.122635i
$562$	3.52762	+	10.8569i	0.148804	+	0.457971i
$563$	11.7725	−	20.3905i	0.496151	−	0.859359i	−0.503839	−	0.863797i	$-0.668080\pi$
$563$	11.7725	−	20.3905i	0.496151	−	0.859359i	0.999990	+	0.00443890i	$0.00141295\pi$
$564$	−4.31863	−	7.48009i	−0.181847	−	0.314969i
$565$	8.76895	−	9.73890i	0.368912	−	0.409719i
$566$	0.676701	−	2.08267i	0.0284439	−	0.0875413i
$567$	−3.49940	−	3.88648i	−0.146961	−	0.163217i
$568$	−12.7761	+	5.68830i	−0.536075	+	0.238676i
$569$	34.2413	+	7.27821i	1.43547	+	0.305118i	0.858990	−	0.511993i	$-0.171093\pi$
$569$	34.2413	+	7.27821i	1.43547	+	0.305118i	0.576480	+	0.817111i	$0.304426\pi$
$570$	−0.762974	+	7.25921i	−0.0319574	+	0.304055i
$571$	−1.31586	−	12.5196i	−0.0550671	−	0.523929i	−0.986934	−	0.161127i	$-0.948487\pi$
$571$	−1.31586	−	12.5196i	−0.0550671	−	0.523929i	0.931866	−	0.362801i	$-0.118180\pi$
$572$	3.19946	−	0.680067i	0.133776	−	0.0284350i
$573$	0.0149436	−	0.0108572i	0.000624278	−	0.000453564i
$574$	−18.7714	+	13.6382i	−0.783502	+	0.569247i
$575$	−5.85318	+	1.24413i	−0.244095	+	0.0518839i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	2.73168	−	25.9902i	0.113721	−	1.08199i	−0.777645	−	0.628704i	$-0.783586\pi$
$577$	2.73168	−	25.9902i	0.113721	−	1.08199i	0.891366	−	0.453284i	$-0.149748\pi$
$578$	−5.53008	−	1.17545i	−0.230021	−	0.0488925i
$579$	10.0998	−	4.49670i	0.419732	−	0.186877i
$580$	2.04707	+	2.27351i	0.0850001	+	0.0944022i
$581$	−25.3043	+	77.8786i	−1.04980	+	3.23095i
$582$	11.0062	−	12.2236i	0.456221	−	0.506685i
$583$	8.74587	+	15.1483i	0.362217	+	0.627378i
$584$	−3.19924	+	5.54124i	−0.132385	+	0.229298i
$585$	0.476761	+	1.46732i	0.0197116	+	0.0606662i
$586$	−29.9532	−	13.3360i	−1.23735	−	0.550905i
$587$	−31.9456	−	23.2098i	−1.31854	−	0.957972i	−0.999949	−	0.0100780i	$-0.996792\pi$
$587$	−31.9456	−	23.2098i	−1.31854	−	0.957972i	−0.318586	−	0.947894i	$-0.603208\pi$
$588$	20.3505			0.839241
$589$	31.3733	+	25.8329i	1.29272	+	1.06443i
$590$	9.53814			0.392679
$591$	3.02139	+	2.19517i	0.124283	+	0.0902971i
$592$	−7.56568	−	3.36846i	−0.310947	−	0.138443i
$593$	2.70763	+	8.33322i	0.111189	+	0.342204i	0.991133	−	0.132873i	$-0.0424202\pi$
$593$	2.70763	+	8.33322i	0.111189	+	0.342204i	−0.879944	+	0.475077i	$0.842420\pi$
$594$	1.06005	−	1.83605i	0.0434942	−	0.0753342i
$595$	−8.80808	−	15.2560i	−0.361096	−	0.625437i
$596$	−3.79358	+	4.21320i	−0.155391	+	0.172579i
$597$	2.11591	−	6.51210i	0.0865984	−	0.266522i
$598$	6.17756	+	6.86087i	0.252619	+	0.280562i
$599$	−5.71322	+	2.54369i	−0.233436	+	0.103932i	−0.520121	−	0.854093i	$-0.674113\pi$
$599$	−5.71322	+	2.54369i	−0.233436	+	0.103932i	0.286685	+	0.958025i	$0.407447\pi$
$600$	0.978148	+	0.207912i	0.0399327	+	0.00848796i
$601$	−0.0700924	+	0.666885i	−0.00285913	+	0.0272028i	−0.995858	−	0.0909173i	$-0.971020\pi$
$601$	−0.0700924	+	0.666885i	−0.00285913	+	0.0272028i	0.992999	+	0.118120i	$0.0376868\pi$
$602$	−3.86297	−	36.7537i	−0.157443	−	1.49797i
$603$	−1.93983	+	0.412324i	−0.0789960	+	0.0167911i
$604$	2.42640	−	1.76288i	0.0987289	−	0.0717308i
$605$	−5.26282	+	3.82367i	−0.213964	+	0.155454i
$606$	−5.44789	+	1.15799i	−0.221306	+	0.0470399i
$607$	−0.841159	−	8.00309i	−0.0341416	−	0.324836i	−0.998241	−	0.0592926i	$-0.981115\pi$
$607$	−0.841159	−	8.00309i	−0.0341416	−	0.324836i	0.964099	−	0.265543i	$-0.0855512\pi$
$608$	0.762974	−	7.25921i	0.0309427	−	0.294400i
$609$	−15.6498	−	3.32647i	−0.634163	−	0.134796i
$610$	10.8575	−	4.83406i	0.439606	−	0.195725i
$611$	−8.91672	−	9.90302i	−0.360732	−	0.400633i
$612$	1.04090	−	3.20357i	0.0420761	−	0.129497i
$613$	27.5078	−	30.5505i	1.11103	−	1.23392i	0.141239	−	0.989975i	$-0.454891\pi$
$613$	27.5078	−	30.5505i	1.11103	−	1.23392i	0.969789	−	0.243946i	$-0.0784420\pi$
$614$	3.53656	+	6.12550i	0.142724	+	0.247205i
$615$	2.21833	−	3.84226i	0.0894516	−	0.154935i
$616$	3.42626	+	10.5449i	0.138048	+	0.424867i
$617$	16.6998	+	7.43525i	0.672310	+	0.299332i	0.714355	−	0.699784i	$-0.246720\pi$
$617$	16.6998	+	7.43525i	0.672310	+	0.299332i	−0.0420444	+	0.999116i	$0.513387\pi$
$618$	−14.0252	−	10.1899i	−0.564178	−	0.409899i
$619$	4.23927			0.170390			0.0851952	−	0.996364i	$-0.472849\pi$
$619$	4.23927			0.170390			0.0851952	+	0.996364i	$0.472849\pi$
$620$	3.96904	−	3.90471i	0.159400	−	0.156817i
$621$	5.98395			0.240128
$622$	−6.45233	−	4.68789i	−0.258715	−	0.187967i
$623$	63.6782	+	28.3514i	2.55121	+	1.13587i
$624$	−0.476761	−	1.46732i	−0.0190857	−	0.0587398i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−15.4370	−	26.7376i	−0.616985	−	1.06865i
$627$	10.3548	−	11.5001i	0.413530	−	0.459271i
$628$	−2.14256	+	6.59413i	−0.0854976	+	0.263135i
$629$	−18.6662	−	20.7310i	−0.744272	−	0.826598i
$630$	−4.77763	+	2.12714i	−0.190346	+	0.0847473i
$631$	36.1770	+	7.68967i	1.44018	+	0.306121i	0.860804	−	0.508936i	$-0.169961\pi$
$631$	36.1770	+	7.68967i	1.44018	+	0.306121i	0.579381	+	0.815057i	$0.303294\pi$
$632$	0.440428	−	4.19039i	0.0175193	−	0.166685i
$633$	−0.401827	−	3.82312i	−0.0159712	−	0.151956i
$634$	29.7180	−	6.31675i	1.18025	−	0.250870i
$635$	3.16211	−	2.29741i	0.125485	−	0.0911699i
$636$	6.67476	−	4.84950i	0.264672	−	0.192295i
$637$	30.7113	−	6.52788i	1.21683	−	0.258644i
$638$	−0.677972	−	6.45047i	−0.0268412	−	0.255377i
$639$	−1.46185	+	13.9086i	−0.0578300	+	0.550216i
$640$	−0.978148	−	0.207912i	−0.0386647	−	0.00821843i
$641$	−21.2450	+	9.45889i	−0.839128	+	0.373604i	−0.780867	−	0.624698i	$-0.785222\pi$
$641$	−21.2450	+	9.45889i	−0.839128	+	0.373604i	−0.0582610	+	0.998301i	$0.518556\pi$
$642$	−7.67078	−	8.51926i	−0.302741	−	0.336228i
$643$	−6.18003	+	19.0202i	−0.243717	+	0.750083i	0.752128	+	0.659017i	$0.229027\pi$
$643$	−6.18003	+	19.0202i	−0.243717	+	0.750083i	−0.995845	+	0.0910661i	$0.970973\pi$
$644$	−20.9402	+	23.2565i	−0.825160	+	0.916434i
$645$	3.53324	+	6.11976i	0.139121	+	0.240965i
$646$	12.2934	−	21.2929i	0.483679	−	0.837757i
$647$	−1.58291	−	4.87168i	−0.0622304	−	0.191526i	0.915108	−	0.403209i	$-0.132105\pi$
$647$	−1.58291	−	4.87168i	−0.0622304	−	0.191526i	−0.977338	+	0.211684i	$0.932105\pi$
$648$	−0.913545	−	0.406737i	−0.0358875	−	0.0159781i
$649$	−16.3597	−	11.8860i	−0.642175	−	0.466568i
$650$	1.54283			0.0605148
$651$	−4.78991	+	28.7215i	−0.187731	+	1.12568i
$652$	−7.01749			−0.274826
$653$	21.5304	+	15.6427i	0.842549	+	0.612148i	0.923082	−	0.384604i	$-0.125662\pi$
$653$	21.5304	+	15.6427i	0.842549	+	0.612148i	−0.0805326	+	0.996752i	$0.525662\pi$
$654$	−3.44654	−	1.53450i	−0.134770	−	0.0600036i
$655$	−1.12464	−	3.46128i	−0.0439432	−	0.135243i
$656$	−2.21833	+	3.84226i	−0.0866111	+	0.150015i
$657$	3.19924	+	5.54124i	0.124814	+	0.216184i
$658$	30.2252	−	33.5685i	1.17830	−	1.30864i
$659$	4.51684	−	13.9014i	0.175951	−	0.541522i	−0.823725	−	0.566990i	$-0.808108\pi$
$659$	4.51684	−	13.9014i	0.175951	−	0.541522i	0.999676	+	0.0254685i	$0.00810775\pi$
$660$	−1.41862	−	1.57554i	−0.0552197	−	0.0613276i
$661$	7.16161	−	3.18856i	0.278555	−	0.124020i	−0.262705	−	0.964876i	$-0.584614\pi$
$661$	7.16161	−	3.18856i	0.278555	−	0.124020i	0.541259	+	0.840856i	$0.317948\pi$
$662$	11.7849	+	2.50496i	0.458033	+	0.0973579i
$663$	0.543227	−	5.16846i	0.0210972	−	0.200726i
$664$	1.63668	+	15.5720i	0.0635155	+	0.604309i
$665$	−37.3389	+	7.93664i	−1.44794	+	0.307770i
$666$	−6.70001	+	4.86784i	−0.259620	+	0.188625i
$667$	14.8104	−	10.7604i	0.573462	−	0.416645i
$668$	−4.52274	+	0.961339i	−0.174990	+	0.0371953i
$669$	2.64565	+	25.1716i	0.102287	+	0.973192i
$670$	−0.207297	+	1.97230i	−0.00800860	+	0.0761967i
$671$	−24.6466	−	5.23880i	−0.951472	−	0.202242i
$672$	4.77763	−	2.12714i	0.184301	−	0.0820562i
$673$	21.3229	+	23.6815i	0.821938	+	0.912855i	0.997432	−	0.0716255i	$-0.0228186\pi$
$673$	21.3229	+	23.6815i	0.821938	+	0.912855i	−0.175493	+	0.984481i	$0.556152\pi$
$674$	−8.35962	+	25.7283i	−0.322001	+	0.991016i
$675$	0.669131	−	0.743145i	0.0257548	−	0.0286037i
$676$	5.30984	+	9.19691i	0.204225	+	0.353727i
$677$	19.2489	−	33.3401i	0.739795	−	1.28136i	−0.212793	−	0.977097i	$-0.568256\pi$
$677$	19.2489	−	33.3401i	0.739795	−	1.28136i	0.952587	−	0.304265i	$-0.0984108\pi$
$678$	4.04966	+	12.4636i	0.155526	+	0.478661i
$679$	78.5848	+	34.9882i	3.01581	+	1.34272i
$680$	−2.72512	−	1.97992i	−0.104504	−	0.0759264i
$681$	2.63030			0.100793
$682$	−11.6735	+	1.75126i	−0.447003	+	0.0670592i
$683$	3.33339			0.127549			0.0637744	−	0.997964i	$-0.479686\pi$
$683$	3.33339			0.127549			0.0637744	+	0.997964i	$0.479686\pi$
$684$	−5.90517	−	4.29036i	−0.225790	−	0.164046i
$685$	9.53282	+	4.24428i	0.364230	+	0.162166i
$686$	21.5756	+	66.4029i	0.823761	+	2.53527i
$687$	8.53251	−	14.7787i	0.325536	−	0.563844i
$688$	−3.53324	−	6.11976i	−0.134704	−	0.233314i
$689$	8.51741	−	9.45954i	0.324487	−	0.360380i
$690$	1.84914	−	5.69107i	0.0703956	−	0.216655i
$691$	−18.0119	−	20.0043i	−0.685207	−	0.760999i	0.295742	−	0.955268i	$-0.404433\pi$
$691$	−18.0119	−	20.0043i	−0.685207	−	0.760999i	−0.980948	+	0.194269i	$0.937767\pi$
$692$	5.89242	−	2.62347i	0.223996	−	0.0997295i
$693$	10.8453	+	2.30524i	0.411979	+	0.0875689i
$694$	−2.30695	+	21.9491i	−0.0875705	+	0.833177i
$695$	−0.254488	−	2.42129i	−0.00965327	−	0.0918448i
$696$	−2.99245	+	0.636065i	−0.113429	+	0.0241100i
$697$	−12.0904	+	8.78421i	−0.457958	+	0.332726i
$698$	−25.4023	+	18.4558i	−0.961491	+	0.698564i
$699$	17.7168	−	3.76583i	0.670112	−	0.142437i
$700$	0.546660	+	5.20112i	0.0206618	+	0.196584i
$701$	−1.37339	+	13.0669i	−0.0518723	+	0.493532i	0.937485	+	0.348025i	$0.113148\pi$
$701$	−1.37339	+	13.0669i	−0.0518723	+	0.493532i	−0.989357	+	0.145506i	$0.953519\pi$
$702$	−1.50912	−	0.320772i	−0.0569579	−	0.0121068i
$703$	−55.2233	+	24.5870i	−2.08279	+	0.927317i
$704$	1.41862	+	1.57554i	0.0534662	+	0.0593802i
$705$	−2.66906	+	8.21452i	−0.100523	+	0.309377i
$706$	−3.27263	+	3.63463i	−0.123167	+	0.136791i
$707$	−14.5639	−	25.2254i	−0.547731	−	0.948698i
$708$	−4.76907	+	8.26027i	−0.179233	+	0.310440i
$709$	14.8728	+	45.7739i	0.558561	+	1.71907i	0.686349	+	0.727272i	$0.259212\pi$
$709$	14.8728	+	45.7739i	0.558561	+	1.71907i	−0.127788	+	0.991802i	$0.540788\pi$
$710$	12.7761	+	5.68830i	0.479480	+	0.213478i
$711$	−3.40877	−	2.47662i	−0.127839	−	0.0928804i
$712$	13.3284			0.499503
$713$	−20.7549	−	26.0628i	−0.777279	−	0.976059i
$714$	17.6162			0.659268
$715$	−2.64625	−	1.92261i	−0.0989641	−	0.0719016i
$716$	19.6802	+	8.76218i	0.735482	+	0.327458i
$717$	−3.15631	−	9.71412i	−0.117875	−	0.362781i
$718$	−0.589501	+	1.02105i	−0.0220000	+	0.0381051i
$719$	1.01105	+	1.75119i	0.0377058	+	0.0653084i	0.884262	−	0.466990i	$-0.154662\pi$
$719$	1.01105	+	1.75119i	0.0377058	+	0.0653084i	−0.846557	+	0.532299i	$0.821328\pi$
$720$	−0.669131	+	0.743145i	−0.0249370	+	0.0276954i
$721$	28.0167	−	86.2267i	1.04340	−	3.21125i
$722$	−22.9366	−	25.4737i	−0.853613	−	0.948033i
$723$	11.4213	−	5.08509i	0.424763	−	0.189117i
$724$	−11.9785	−	2.54612i	−0.445179	−	0.0946256i
$725$	0.319784	−	3.04254i	0.0118765	−	0.112997i
$726$	−0.679980	−	6.46957i	−0.0252364	−	0.240108i
$727$	−32.5558	+	6.91996i	−1.20743	+	0.256647i	−0.767301	−	0.641288i	$-0.778401\pi$
$727$	−32.5558	+	6.91996i	−1.20743	+	0.256647i	−0.440129	+	0.897935i	$0.645067\pi$
$728$	6.52767	−	4.74263i	0.241932	−	0.175774i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	6.25865	−	1.33032i	0.231643	−	0.0492373i
$731$	−2.48809	−	23.6726i	−0.0920255	−	0.875564i
$732$	−1.24232	+	11.8199i	−0.0459174	+	0.436875i
$733$	13.4383	+	2.85640i	0.496355	+	0.105504i	0.449286	−	0.893388i	$-0.351678\pi$
$733$	13.4383	+	2.85640i	0.496355	+	0.105504i	0.0470694	+	0.998892i	$0.485012\pi$
$734$	−26.0008	+	11.5763i	−0.959705	+	0.427288i
$735$	−13.6172	−	15.1234i	−0.502276	−	0.557834i
$736$	−1.84914	+	5.69107i	−0.0681602	+	0.209776i
$737$	2.81336	−	3.12455i	0.103631	−	0.115094i
$738$	2.21833	+	3.84226i	0.0816577	+	0.141435i
$739$	12.9521	−	22.4337i	0.476452	−	0.825239i	−0.523184	−	0.852220i	$-0.675256\pi$
$739$	12.9521	−	22.4337i	0.476452	−	0.825239i	0.999636	+	0.0269810i	$0.00858936\pi$
$740$	2.55917	+	7.87633i	0.0940771	+	0.289540i
$741$	−10.2878	−	4.58043i	−0.377932	−	0.168266i
$742$	34.9075	+	25.3618i	1.28149	+	0.931060i
$743$	−3.22212			−0.118208			−0.0591040	−	0.998252i	$-0.518824\pi$
$743$	−3.22212			−0.118208			−0.0591040	+	0.998252i	$0.518824\pi$
$744$	1.39705	+	5.38964i	0.0512185	+	0.197594i
$745$	5.66942			0.207711
$746$	6.84262	+	4.97146i	0.250526	+	0.182018i
$747$	14.3041	+	6.36857i	0.523358	+	0.233014i
$748$	2.20681	+	6.79187i	0.0806891	+	0.248335i
$749$	29.9765	−	51.9209i	1.09532	−	1.89715i
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	15.3597	−	17.0586i	0.560482	−	0.622479i	−0.394588	−	0.918858i	$-0.629113\pi$
$751$	15.3597	−	17.0586i	0.560482	−	0.622479i	0.955070	+	0.296380i	$0.0957793\pi$
$752$	2.66906	−	8.21452i	0.0973306	−	0.299553i
$753$	13.7131	+	15.2299i	0.499732	+	0.555008i
$754$	−4.31192	+	1.91979i	−0.157031	+	0.0699147i
$755$	−2.93366	−	0.623569i	−0.106767	−	0.0226940i
$756$	0.546660	−	5.20112i	0.0198818	−	0.189163i
$757$	1.50057	+	14.2770i	0.0545391	+	0.518905i	0.987352	+	0.158544i	$0.0506799\pi$
$757$	1.50057	+	14.2770i	0.0545391	+	0.518905i	−0.932813	+	0.360361i	$0.882653\pi$
$758$	9.75033	−	2.07250i	0.354148	−	0.0752764i
$759$	−10.2636	+	7.45695i	−0.372545	+	0.270670i
$760$	−5.90517	+	4.29036i	−0.214203	+	0.155628i
$761$	−24.7637	+	5.26368i	−0.897682	+	0.190808i	−0.633571	−	0.773684i	$-0.718412\pi$
$761$	−24.7637	+	5.26368i	−0.897682	+	0.190808i	−0.264111	+	0.964492i	$0.585078\pi$
$762$	0.408558	+	3.88717i	0.0148005	+	0.140817i
$763$	2.06239	−	19.6223i	0.0746635	−	0.710376i
$764$	0.0180677	+	0.00384040i	0.000653665	+	0.000138941i
$765$	−3.07722	+	1.37007i	−0.111257	+	0.0495349i
$766$	−12.9989	−	14.4367i	−0.469669	−	0.521620i
$767$	−4.54741	+	13.9955i	−0.164197	+	0.505348i
$768$	0.669131	−	0.743145i	0.0241452	−	0.0268159i
$769$	−15.0077	−	25.9941i	−0.541192	−	0.937372i	−0.998836	−	0.0482368i	$-0.984640\pi$
$769$	−15.0077	−	25.9941i	−0.541192	−	0.937372i	0.457644	−	0.889136i	$-0.348694\pi$
$770$	5.54380	−	9.60214i	0.199785	−	0.346037i
$771$	5.63963	+	17.3570i	0.203106	+	0.625097i
$772$	10.0998	+	4.49670i	0.363498	+	0.161840i
$773$	27.5276	+	20.0000i	0.990099	+	0.719349i	0.959943	−	0.280196i	$-0.0903994\pi$
$773$	27.5276	+	20.0000i	0.990099	+	0.719349i	0.0301565	+	0.999545i	$0.490399\pi$
$774$	−7.06649			−0.254000
$775$	−5.55757	−	0.336814i	−0.199634	−	0.0120987i
$776$	16.4485			0.590466
$777$	−35.0395	−	25.4577i	−1.25704	−	0.913290i
$778$	−10.1254	−	4.50813i	−0.363014	−	0.161624i
$779$	10.0072	+	30.7990i	0.358545	+	1.10349i
$780$	−0.771415	+	1.33613i	−0.0276211	+	0.0478411i
$781$	−14.8250	−	25.6776i	−0.530480	−	0.918817i
$782$	−13.4874	+	14.9792i	−0.482307	+	0.535656i
$783$	−0.945377	+	2.90957i	−0.0337850	+	0.103980i
$784$	13.6172	+	15.1234i	0.486327	+	0.540121i
$785$	6.33405	−	2.82010i	0.226072	−	0.100654i
$786$	3.55987	+	0.756674i	0.126976	+	0.0269897i
$787$	−0.545917	+	5.19406i	−0.0194598	+	0.185148i	−0.999934	−	0.0115006i	$-0.996339\pi$
$787$	−0.545917	+	5.19406i	−0.0194598	+	0.185148i	0.980474	+	0.196649i	$0.0630058\pi$
$788$	0.390376	+	3.71418i	0.0139066	+	0.132312i
$789$	−3.26206	+	0.693373i	−0.116133	+	0.0246847i
$790$	−3.40877	+	2.47662i	−0.121279	+	0.0881141i
$791$	−55.4468	+	40.2845i	−1.97146	+	1.43235i
$792$	2.07376	−	0.440792i	0.0736880	−	0.0156629i
$793$	1.91669	+	18.2361i	0.0680635	+	0.647581i
$794$	1.28002	−	12.1786i	0.0454264	−	0.432203i
$795$	−8.07017	−	1.71537i	−0.286219	−	0.0608378i
$796$	6.25525	−	2.78502i	0.221712	−	0.0987123i
$797$	20.4696	+	22.7338i	0.725070	+	0.805271i	0.987154	−	0.159774i	$-0.0510765\pi$
$797$	20.4696	+	22.7338i	0.725070	+	0.805271i	−0.262084	+	0.965045i	$0.584410\pi$
$798$	11.7961	−	36.3048i	0.417579	−	1.28518i
$799$	19.4677	−	21.6211i	0.688719	−	0.764900i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	6.66420	−	11.5427i	0.235468	−	0.407842i
$802$	0.713828	+	2.19694i	0.0252061	+	0.0775765i
$803$	−12.3926	−	5.51753i	−0.437324	−	0.194709i
$804$	−1.60442	−	1.16568i	−0.0565834	−	0.0411102i
$805$	31.2947			1.10299
$806$	3.83716	+	7.68546i	0.135158	+	0.270709i
$807$	−24.7464			−0.871115
$808$	−4.50590	−	3.27373i	−0.158517	−	0.115169i
$809$	18.7087	+	8.32963i	0.657761	+	0.292854i	0.708346	−	0.705866i	$-0.249442\pi$
$809$	18.7087	+	8.32963i	0.657761	+	0.292854i	−0.0505846	+	0.998720i	$0.516108\pi$
$810$	0.309017	+	0.951057i	0.0108578	+	0.0334167i
$811$	−2.38404	+	4.12928i	−0.0837151	+	0.144999i	−0.904843	−	0.425746i	$-0.860012\pi$
$811$	−2.38404	+	4.12928i	−0.0837151	+	0.144999i	0.821128	+	0.570744i	$0.193345\pi$
$812$	−7.99973	−	13.8559i	−0.280735	−	0.486248i
$813$	4.87222	−	5.41114i	0.170876	−	0.189777i
$814$	5.42569	−	16.6985i	0.190170	−	0.585284i
$815$	4.69562	+	5.21501i	0.164480	+	0.182674i
$816$	3.07722	−	1.37007i	0.107724	−	0.0479619i
$817$	−50.4525	−	10.7240i	−1.76511	−	0.375186i
$818$	−1.50963	+	14.3632i	−0.0527831	+	0.502198i
$819$	−0.843404	−	8.02445i	−0.0294709	−	0.280397i
$820$	4.33970	−	0.922432i	0.151549	−	0.0322127i
$821$	−20.6960	+	15.0365i	−0.722294	+	0.524777i	−0.887116	−	0.461546i	$-0.847295\pi$
$821$	−20.6960	+	15.0365i	−0.722294	+	0.524777i	0.164822	+	0.986323i	$0.447295\pi$
$822$	−8.44207	+	6.13352i	−0.294451	+	0.213931i
$823$	−9.23750	+	1.96349i	−0.321999	+	0.0684430i	−0.366076	−	0.930585i	$-0.619299\pi$
$823$	−9.23750	+	1.96349i	−0.321999	+	0.0684430i	0.0440765	+	0.999028i	$0.485965\pi$
$824$	−1.81212	−	17.2412i	−0.0631282	−	0.600625i
$825$	−0.221610	+	2.10848i	−0.00771547	+	0.0734078i
$826$	−48.7922	−	10.3711i	−1.69770	−	0.360857i
$827$	−16.1572	+	7.19367i	−0.561843	+	0.250148i	−0.667950	−	0.744206i	$-0.732828\pi$
$827$	−16.1572	+	7.19367i	−0.561843	+	0.250148i	0.106107	+	0.994355i	$0.466161\pi$
$828$	4.00404	+	4.44694i	0.139150	+	0.154542i
$829$	2.33723	−	7.19325i	0.0811753	−	0.249832i	−0.902230	−	0.431256i	$-0.858071\pi$
$829$	2.33723	−	7.19325i	0.0811753	−	0.249832i	0.983405	+	0.181424i	$0.0580706\pi$
$830$	10.4771	−	11.6360i	0.363664	−	0.403890i
$831$	−4.44065	−	7.69144i	−0.154045	−	0.266813i
$832$	0.771415	−	1.33613i	0.0267440	−	0.0463220i
$833$	21.1829	+	65.1944i	0.733945	+	2.25885i
$834$	2.22414	+	0.990252i	0.0770158	+	0.0342896i
$835$	3.74072	+	2.71779i	0.129453	+	0.0940531i
$836$	15.4750			0.535213
$837$	5.36609	+	1.48494i	0.185479	+	0.0513269i
$838$	0.00597149			0.000206282
$839$	37.4527	+	27.2110i	1.29301	+	0.939427i	0.999862	−	0.0166398i	$-0.00529686\pi$
$839$	37.4527	+	27.2110i	1.29301	+	0.939427i	0.293149	+	0.956067i	$0.405297\pi$
$840$	−4.77763	−	2.12714i	−0.164844	−	0.0733933i
$841$	−6.06930	−	18.6794i	−0.209286	−	0.644117i
$842$	13.2610	−	22.9687i	0.457004	−	0.791555i
$843$	5.70781	+	9.88621i	0.196587	+	0.340499i
$844$	2.57226	−	2.85678i	0.0885409	−	0.0983346i
$845$	3.28166	−	10.0999i	0.112893	−	0.347448i
$846$	−5.77946	−	6.41874i	−0.198702	−	0.220681i
$847$	31.0795	−	13.8375i	1.06790	−	0.475462i
$848$	8.07017	+	1.71537i	0.277131	+	0.0589060i
$849$	0.228902	−	2.17786i	0.00785589	−	0.0747438i
$850$	0.352098	+	3.34999i	0.0120768	+	0.114904i
$851$	48.4741	−	10.3035i	1.66167	−	0.353199i
$852$	−11.3143	+	8.22031i	−0.387621	+	0.281623i
$853$	−29.4505	+	21.3971i	−1.00837	+	0.732622i	−0.963866	−	0.266388i	$-0.914170\pi$
$853$	−29.4505	+	21.3971i	−1.00837	+	0.732622i	−0.0445013	+	0.999009i	$0.514170\pi$
$854$	−60.7975	+	12.9229i	−2.08045	+	0.442212i
$855$	0.762974	+	7.25921i	0.0260931	+	0.248260i
$856$	1.19829	−	11.4010i	0.0409568	−	0.389678i
$857$	14.9032	+	3.16777i	0.509083	+	0.108209i	0.455290	−	0.890343i	$-0.349536\pi$
$857$	14.9032	+	3.16777i	0.509083	+	0.108209i	0.0537929	+	0.998552i	$0.482869\pi$
$858$	2.98815	−	1.33041i	0.102014	−	0.0454195i
$859$	19.9658	+	22.1742i	0.681224	+	0.756575i	0.980270	−	0.197663i	$-0.0633352\pi$
$859$	19.9658	+	22.1742i	0.681224	+	0.756575i	−0.299046	+	0.954239i	$0.596669\pi$
$860$	−2.18366	+	6.72063i	−0.0744623	+	0.229172i
$861$	−15.5256	+	17.2430i	−0.529112	+	0.587638i
$862$	−16.4072	−	28.4181i	−0.558832	−	0.967925i
$863$	20.8964	−	36.1936i	0.711321	−	1.23204i	−0.253040	−	0.967456i	$-0.581430\pi$
$863$	20.8964	−	36.1936i	0.711321	−	1.23204i	0.964361	−	0.264589i	$-0.0852362\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	−5.89242	−	2.62347i	−0.200348	−	0.0892008i
$866$	−14.1878	−	10.3081i	−0.482122	−	0.350282i
$867$	−5.65363			−0.192007
$868$	−24.5493	+	15.6588i	−0.833257	+	0.531495i
$869$	8.93295			0.303030
$870$	2.47503	+	1.79821i	0.0839113	+	0.0609651i
$871$	−2.79517	−	1.24449i	−0.0947106	−	0.0421679i
$872$	−1.16583	−	3.58806i	−0.0394800	−	0.121507i
$873$	8.22424	−	14.2448i	0.278348	−	0.482113i
$874$	21.8390	+	37.8263i	0.738715	+	1.27949i
$875$	3.49940	−	3.88648i	0.118301	−	0.131387i
$876$	−1.97724	+	6.08531i	−0.0668047	+	0.205604i
$877$	−17.5759	−	19.5200i	−0.593496	−	0.659144i	0.369320	−	0.929302i	$-0.379591\pi$
$877$	−17.5759	−	19.5200i	−0.593496	−	0.659144i	−0.962816	+	0.270158i	$0.912924\pi$
$878$	5.71427	−	2.54416i	0.192847	−	0.0858612i
$879$	−32.0713	−	6.81697i	−1.08174	−	0.229931i
$880$	0.221610	−	2.10848i	0.00747047	−	0.0710768i
$881$	−3.88151	−	36.9301i	−0.130771	−	1.24421i	−0.841312	−	0.540550i	$-0.818216\pi$
$881$	−3.88151	−	36.9301i	−0.130771	−	1.24421i	0.710540	−	0.703656i	$-0.248451\pi$
$882$	19.9058	−	4.23111i	0.670263	−	0.142469i
$883$	35.6983	−	25.9364i	1.20134	−	0.872828i	0.206929	−	0.978356i	$-0.433653\pi$
$883$	35.6983	−	25.9364i	1.20134	−	0.872828i	0.994416	+	0.105528i	$0.0336532\pi$
$884$	4.20440	−	3.05468i	0.141409	−	0.102740i
$885$	9.32971	−	1.98309i	0.313615	−	0.0666609i
$886$	0.740557	+	7.04593i	0.0248795	+	0.236713i
$887$	3.45294	−	32.8525i	0.115938	−	1.10308i	−0.769604	−	0.638521i	$-0.779546\pi$
$887$	3.45294	−	32.8525i	0.115938	−	1.10308i	0.885543	−	0.464558i	$-0.153787\pi$
$888$	−8.10069	−	1.72185i	−0.271841	−	0.0577817i
$889$	−18.6738	+	8.31411i	−0.626299	+	0.278846i
$890$	−8.91844	−	9.90493i	−0.298947	−	0.332014i
$891$	0.655144	−	2.01633i	0.0219482	−	0.0675495i
$892$	−16.9359	+	18.8092i	−0.567055	+	0.629779i
$893$	−31.5225	−	54.5986i	−1.05486	−	1.82707i
$894$	−2.83471	+	4.90986i	−0.0948069	+	0.164210i
$895$	−6.65704	−	20.4883i	−0.222520	−	0.684847i
$896$	4.77763	+	2.12714i	0.159610	+	0.0710628i
$897$	7.46902	+	5.42656i	0.249383	+	0.181188i
$898$	−5.03153			−0.167904
$899$	15.9515	−	5.97412i	0.532011	−	0.199248i
$900$	1.00000			0.0333333
$901$	22.4835	+	16.3352i	0.749035	+	0.544206i
$902$	−8.59291	−	3.82581i	−0.286113	−	0.127386i
$903$	−11.4201	−	35.1474i	−0.380036	−	1.16963i
$904$	−6.55249	+	11.3492i	−0.217933	+	0.377470i
$905$	6.12307	+	10.6055i	0.203538	+	0.352538i
$906$	2.00686	−	2.22884i	0.0666733	−	0.0740482i
$907$	13.7346	−	42.2707i	0.456049	−	1.40357i	−0.413851	−	0.910345i	$-0.635816\pi$
$907$	13.7346	−	42.2707i	0.456049	−	1.40357i	0.869899	−	0.493229i	$-0.164184\pi$
$908$	1.76001	+	1.95469i	0.0584081	+	0.0648687i
$909$	−5.08809	+	2.26536i	−0.168761	+	0.0751373i
$910$	−7.89233	−	1.67757i	−0.261628	−	0.0556108i
$911$	0.135483	−	1.28903i	0.00448874	−	0.0427075i	−0.992048	−	0.125858i	$-0.959832\pi$
$911$	0.135483	−	1.28903i	0.00448874	−	0.0427075i	0.996537	+	0.0831506i	$0.0264983\pi$
$912$	−0.762974	−	7.25921i	−0.0252646	−	0.240376i
$913$	−32.4704	+	6.90180i	−1.07461	+	0.228416i
$914$	13.5497	−	9.84441i	0.448183	−	0.325624i
$915$	9.61515	−	6.98581i	0.317867	−	0.230944i
$916$	16.6921	−	3.54802i	0.551523	−	0.117230i
$917$	1.98952	+	18.9290i	0.0656996	+	0.625090i
$918$	0.352098	−	3.34999i	0.0116210	−	0.110566i
$919$	1.94889	+	0.414250i	0.0642880	+	0.0136648i	0.239943	−	0.970787i	$-0.422871\pi$
$919$	1.94889	+	0.414250i	0.0642880	+	0.0136648i	−0.175655	+	0.984452i	$0.556204\pi$
$920$	5.46661	−	2.43389i	0.180229	−	0.0802430i
$921$	4.73284	+	5.25635i	0.155952	+	0.173203i
$922$	3.77448	−	11.6167i	0.124306	−	0.382574i
$923$	−14.4377	+	16.0347i	−0.475223	+	0.527789i
$924$	5.54380	+	9.60214i	0.182378	+	0.315887i
$925$	4.14083	−	7.17213i	0.136150	−	0.235818i
$926$	−3.00560	−	9.25029i	−0.0987702	−	0.303983i
$927$	−15.8374	−	7.05125i	−0.520167	−	0.231593i
$928$	−2.47503	−	1.79821i	−0.0812468	−	0.0590292i
$929$	−6.20727			−0.203654			−0.101827	−	0.994802i	$-0.532469\pi$
$929$	−6.20727			−0.203654			−0.101827	+	0.994802i	$0.532469\pi$
$930$	3.07047	−	4.64459i	0.100685	−	0.152302i
$931$	148.542			4.86828
$932$	14.6534	+	10.6463i	0.479989	+	0.348733i
$933$	−7.28600	−	3.24394i	−0.238533	−	0.106202i
$934$	−1.98618	−	6.11284i	−0.0649899	−	0.200018i
$935$	3.57070	−	6.18463i	0.116774	−	0.202259i
$936$	−0.771415	−	1.33613i	−0.0252145	−	0.0436728i
$937$	−3.12802	+	3.47402i	−0.102188	+	0.113491i	−0.792069	−	0.610431i	$-0.790996\pi$
$937$	−3.12802	+	3.47402i	−0.102188	+	0.113491i	0.689881	+	0.723923i	$0.257663\pi$
$938$	3.20497	−	9.86390i	0.104646	−	0.322068i
$939$	−20.6587	−	22.9438i	−0.674171	−	0.748742i
$940$	−7.89053	+	3.51309i	−0.257361	+	0.114584i
$941$	42.8283	+	9.10344i	1.39616	+	0.296764i	0.843719	−	0.536786i	$-0.180362\pi$
$941$	42.8283	+	9.10344i	1.39616	+	0.296764i	0.552445	+	0.833549i	$0.313695\pi$
$942$	−0.724746	+	6.89550i	−0.0236135	+	0.224668i
$943$	−2.77509	−	26.4033i	−0.0903695	−	0.859809i
$944$	−9.32971	+	1.98309i	−0.303656	+	0.0645441i
$945$	−4.23097	+	3.07398i	−0.137634	+	0.0999967i
$946$	12.1204	−	8.80597i	0.394067	−	0.286307i
$947$	15.4838	−	3.29119i	0.503156	−	0.106949i	0.0506609	−	0.998716i	$-0.483867\pi$
$947$	15.4838	−	3.29119i	0.503156	−	0.106949i	0.452495	+	0.891767i	$0.350534\pi$
$948$	−0.440428	−	4.19039i	−0.0143044	−	0.136098i
$949$	−1.03188	+	9.81768i	−0.0334962	+	0.318696i
$950$	7.13969	+	1.51759i	0.231642	+	0.0492371i
$951$	27.7552	−	12.3574i	0.900025	−	0.400717i
$952$	11.7875	+	13.0914i	0.382035	+	0.424293i
$953$	−10.8768	+	33.4755i	−0.352335	+	1.08438i	0.605203	+	0.796071i	$0.293092\pi$
$953$	−10.8768	+	33.4755i	−0.352335	+	1.08438i	−0.957538	+	0.288305i	$0.906908\pi$
$954$	5.52064	−	6.13129i	0.178737	−	0.198508i
$955$	−0.00923565	−	0.0159966i	−0.000298859	−	0.000517638i
$956$	5.10702	−	8.84561i	0.165173	−	0.286088i
$957$	−2.00429	−	6.16856i	−0.0647894	−	0.199401i
$958$	−12.2441	−	5.45140i	−0.395587	−	0.176127i
$959$	−44.1501	−	32.0769i	−1.42568	−	1.03582i
$960$	−1.00000			−0.0322749
$961$	−12.1444	−	28.5222i	−0.391755	−	0.920070i
$962$	−12.7772			−0.411953
$963$	−9.27441	−	6.73825i	−0.298864	−	0.217137i
$964$	11.4213	+	5.08509i	0.367855	+	0.163780i
$965$	−3.41636	−	10.5145i	−0.109976	−	0.338473i
$966$	−15.6473	+	27.1020i	−0.503445	+	0.871992i
$967$	8.38639	+	14.5257i	0.269688	+	0.467114i	0.968781	−	0.247917i	$-0.0797460\pi$
$967$	8.38639	+	14.5257i	0.269688	+	0.467114i	−0.699093	+	0.715031i	$0.746413\pi$
$968$	4.35283	−	4.83431i	0.139905	−	0.155381i
$969$	7.59777	−	23.3835i	0.244075	−	0.751187i
$970$	−11.0062	−	12.2236i	−0.353387	−	0.392476i
$971$	53.6760	−	23.8981i	1.72255	−	0.766927i	0.725661	−	0.688052i	$-0.241534\pi$
$971$	53.6760	−	23.8981i	1.72255	−	0.766927i	0.996885	−	0.0788749i	$-0.0251328\pi$
$972$	−0.978148	−	0.207912i	−0.0313741	−	0.00666877i
$973$	−1.33091	+	12.6628i	−0.0426671	+	0.405951i
$974$	4.19510	+	39.9137i	0.134420	+	1.27892i
$975$	1.50912	−	0.320772i	0.0483304	−	0.0102729i
$976$	−9.61515	+	6.98581i	−0.307773	+	0.223610i
$977$	4.96957	−	3.61060i	0.158991	−	0.115513i	−0.505445	−	0.862859i	$-0.668672\pi$
$977$	4.96957	−	3.61060i	0.158991	−	0.115513i	0.664436	+	0.747345i	$0.268672\pi$
$978$	−6.86414	+	1.45902i	−0.219491	+	0.0466542i
$979$	2.95370	+	28.1026i	0.0944008	+	0.898164i
$980$	2.12721	−	20.2390i	0.0679512	−	0.646512i
$981$	−3.69027	−	0.784390i	−0.117821	−	0.0250436i
$982$	0.532715	−	0.237180i	0.0169996	−	0.00756872i
$983$	−3.86896	−	4.29692i	−0.123401	−	0.137050i	0.678278	−	0.734805i	$-0.262726\pi$
$983$	−3.86896	−	4.29692i	−0.123401	−	0.137050i	−0.801679	+	0.597755i	$0.796060\pi$
$984$	−1.37100	+	4.21951i	−0.0437059	+	0.134513i
$985$	2.49896	−	2.77538i	0.0796236	−	0.0884310i
$986$	−5.15254	−	8.92446i	−0.164090	−	0.284213i
$987$	22.5855	−	39.1192i	0.718903	−	1.24518i
$988$	−3.47997	−	10.7102i	−0.110713	−	0.340738i
$989$	38.6297	+	17.1991i	1.22835	+	0.546898i
$990$	−1.71519	−	1.24616i	−0.0545123	−	0.0396055i
$991$	56.9300			1.80844			0.904220	−	0.427067i	$-0.140453\pi$
$991$	56.9300			1.80844			0.904220	+	0.427067i	$0.140453\pi$
$992$	−3.07047	+	4.64459i	−0.0974876	+	0.147466i
$993$	12.0482			0.382337
$994$	−59.1711	−	42.9903i	−1.87679	−	1.36357i
$995$	−6.25525	−	2.78502i	−0.198305	−	0.0882910i
$996$	4.83851	+	14.8914i	0.153314	+	0.471852i
$997$	7.35746	−	12.7435i	0.233013	−	0.403590i	−0.725680	−	0.688032i	$-0.758475\pi$
$997$	7.35746	−	12.7435i	0.233013	−	0.403590i	0.958693	+	0.284442i	$0.0918082\pi$
$998$	0.0304108	+	0.0526731i	0.000962637	+	0.00166734i
$999$	−5.54151	+	6.15448i	−0.175326	+	0.194719i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.i.391.1	✓	24
31.18	even	15	inner	930.2.bg.i.421.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.i.391.1	✓	24	1.1	even	1	trivial
930.2.bg.i.421.1	yes	24	31.18	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.913545 + 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-3.49940 + 3.88648i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})\)	\(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} +(-3.49940 + 3.88648i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +(0.913545 - 0.406737i) q^{10} +(-2.07376 - 0.440792i) q^{11} +(-0.104528 + 0.994522i) q^{12} +(0.161270 + 1.53438i) q^{13} +(-5.11549 + 1.08733i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-3.29483 + 0.700338i) q^{17} +(0.104528 + 0.994522i) q^{18} +(-0.762974 + 7.25921i) q^{19} +(0.978148 + 0.207912i) q^{20} +(-4.77763 + 2.12714i) q^{21} +(-1.41862 - 1.57554i) q^{22} +(1.84914 - 5.69107i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.771415 + 1.33613i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-4.77763 - 2.12714i) q^{28} +(2.47503 + 1.79821i) q^{29} +1.00000 q^{30} +(3.07047 - 4.64459i) q^{31} -1.00000 q^{32} +(-1.71519 - 1.24616i) q^{33} +(-3.07722 - 1.37007i) q^{34} +(1.61609 + 4.97381i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(4.14083 + 7.17213i) q^{37} +(-4.88411 + 5.42436i) q^{38} +(-0.476761 + 1.46732i) q^{39} +(0.669131 + 0.743145i) q^{40} +(4.05309 - 1.80455i) q^{41} +(-5.11549 - 1.08733i) q^{42} +(-0.738649 + 7.02778i) q^{43} +(-0.221610 - 2.10848i) q^{44} +(0.978148 - 0.207912i) q^{45} +(4.84111 - 3.51728i) q^{46} +(-6.98769 + 5.07685i) q^{47} +(-0.978148 + 0.207912i) q^{48} +(-2.12721 - 20.2390i) q^{49} +(0.104528 - 0.994522i) q^{50} +(-3.29483 - 0.700338i) q^{51} +(-1.40945 + 0.627526i) q^{52} +(-5.52064 - 6.13129i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-1.41862 + 1.57554i) q^{55} +(-2.61489 - 4.52912i) q^{56} +(-3.64960 + 6.32129i) q^{57} +(0.945377 + 2.90957i) q^{58} +(8.71352 + 3.87951i) q^{59} +(0.809017 + 0.587785i) q^{60} +11.8850 q^{61} +(5.21408 - 1.95277i) q^{62} -5.22977 q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.40945 + 0.627526i) q^{65} +(-0.655144 - 2.01633i) q^{66} +(-0.991584 + 1.71747i) q^{67} +(-1.68422 - 2.91715i) q^{68} +(4.00404 - 4.44694i) q^{69} +(-1.61609 + 4.97381i) q^{70} +(9.35794 + 10.3930i) q^{71} +(-0.913545 + 0.406737i) q^{72} +(6.25865 + 1.33032i) q^{73} +(-0.865670 + 8.23630i) q^{74} +(-0.104528 - 0.994522i) q^{75} +(-7.13969 + 1.51759i) q^{76} +(8.97006 - 6.51713i) q^{77} +(-1.24818 + 0.906853i) q^{78} +(-4.12140 + 0.876030i) q^{79} +(0.104528 + 0.994522i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(4.33970 + 0.922432i) q^{82} +(14.3041 - 6.36857i) q^{83} +(-3.49940 - 3.88648i) q^{84} +(-1.04090 + 3.20357i) q^{85} +(-4.72840 + 5.25142i) q^{86} +(1.52965 + 2.64943i) q^{87} +(1.06005 - 1.83605i) q^{88} +(-4.11870 - 12.6761i) q^{89} +(0.913545 + 0.406737i) q^{90} +(-6.52767 - 4.74263i) q^{91} +5.98395 q^{92} +(4.69414 - 2.99417i) q^{93} -8.63726 q^{94} +(5.90517 + 4.29036i) q^{95} +(-0.913545 - 0.406737i) q^{96} +(-5.08286 - 15.6434i) q^{97} +(10.1753 - 17.6241i) q^{98} +(-1.06005 - 1.83605i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9} + 3 q^{10} - 13 q^{11} + 3 q^{12} + 11 q^{13} - 8 q^{14} + 6 q^{15} - 6 q^{16} - 29 q^{17} - 3 q^{18} + 9 q^{19} - 3 q^{20} - 2 q^{21} - 17 q^{22} - 5 q^{23} - 3 q^{24} - 12 q^{25} + 9 q^{26} - 6 q^{27} - 2 q^{28} + 13 q^{29} + 24 q^{30} + 57 q^{31} - 24 q^{32} + 16 q^{33} + 29 q^{34} + q^{35} - 12 q^{36} - 24 q^{37} + 6 q^{38} - 17 q^{39} + 3 q^{40} + 32 q^{41} - 8 q^{42} + 49 q^{43} - 8 q^{44} - 3 q^{45} + 28 q^{47} + 3 q^{48} + 12 q^{49} - 3 q^{50} - 29 q^{51} - 19 q^{52} - 36 q^{53} + 6 q^{54} - 17 q^{55} - 3 q^{56} - 6 q^{57} + 2 q^{58} + 6 q^{60} + 33 q^{62} - 6 q^{63} - 6 q^{64} + 19 q^{65} + 4 q^{66} - 5 q^{67} + 11 q^{68} + 10 q^{69} - q^{70} - 11 q^{71} - 3 q^{72} - 13 q^{73} + 9 q^{74} + 3 q^{75} - 6 q^{76} + 4 q^{77} - 8 q^{78} - 68 q^{79} - 3 q^{80} + 3 q^{81} - 2 q^{82} + 10 q^{83} - 7 q^{84} + 2 q^{85} - 34 q^{86} + 11 q^{87} - 12 q^{88} + 55 q^{89} + 3 q^{90} + 38 q^{91} + 10 q^{92} + 19 q^{93} + 42 q^{94} + 18 q^{95} - 3 q^{96} - q^{97} + 63 q^{98} + 12 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9 + 3 * q^10 - 13 * q^11 + 3 * q^12 + 11 * q^13 - 8 * q^14 + 6 * q^15 - 6 * q^16 - 29 * q^17 - 3 * q^18 + 9 * q^19 - 3 * q^20 - 2 * q^21 - 17 * q^22 - 5 * q^23 - 3 * q^24 - 12 * q^25 + 9 * q^26 - 6 * q^27 - 2 * q^28 + 13 * q^29 + 24 * q^30 + 57 * q^31 - 24 * q^32 + 16 * q^33 + 29 * q^34 + q^35 - 12 * q^36 - 24 * q^37 + 6 * q^38 - 17 * q^39 + 3 * q^40 + 32 * q^41 - 8 * q^42 + 49 * q^43 - 8 * q^44 - 3 * q^45 + 28 * q^47 + 3 * q^48 + 12 * q^49 - 3 * q^50 - 29 * q^51 - 19 * q^52 - 36 * q^53 + 6 * q^54 - 17 * q^55 - 3 * q^56 - 6 * q^57 + 2 * q^58 + 6 * q^60 + 33 * q^62 - 6 * q^63 - 6 * q^64 + 19 * q^65 + 4 * q^66 - 5 * q^67 + 11 * q^68 + 10 * q^69 - q^70 - 11 * q^71 - 3 * q^72 - 13 * q^73 + 9 * q^74 + 3 * q^75 - 6 * q^76 + 4 * q^77 - 8 * q^78 - 68 * q^79 - 3 * q^80 + 3 * q^81 - 2 * q^82 + 10 * q^83 - 7 * q^84 + 2 * q^85 - 34 * q^86 + 11 * q^87 - 12 * q^88 + 55 * q^89 + 3 * q^90 + 38 * q^91 + 10 * q^92 + 19 * q^93 + 42 * q^94 + 18 * q^95 - 3 * q^96 - q^97 + 63 * q^98 + 12 * q^99

Introduction

L-functions

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