LMFDB - Embedded newform 930.2.bg.e.661.1

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:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 27x^{14} + 345x^{12} - 2652x^{10} + 13244x^{8} - 43398x^{6} + 89940x^{4} - 107433x^{2} + 58081 $ x^16 - 27x^14 + 345x^12 - 2652x^10 + 13244x^8 - 43398x^6 + 89940x^4 - 107433*x^2 + 58081
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			661.1
Root			$-2.08547 + 0.994522i$ of defining polynomial
Character	$\chi$	$=$	930.661
Dual form			930.2.bg.e.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.104528 + 0.994522i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-4.44421 - 0.944645i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.978148 + 0.207912i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(0.104528 + 0.994522i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-4.44421 - 0.944645i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.978148 + 0.207912i) q^{9} +(-0.104528 + 0.994522i) q^{10} +(-1.58534 + 1.76070i) q^{11} +(-0.913545 + 0.406737i) q^{12} +(3.84167 + 1.71042i) q^{13} +(-3.04019 - 3.37647i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-2.60370 - 2.89170i) q^{17} +(-0.913545 - 0.406737i) q^{18} +(-4.22000 + 1.87886i) q^{19} +(-0.669131 + 0.743145i) q^{20} +(0.474924 - 4.51860i) q^{21} +(-2.31748 + 0.492596i) q^{22} +(-1.32510 + 4.07823i) q^{23} +(-0.978148 - 0.207912i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.10262 + 3.64184i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(-0.474924 - 4.51860i) q^{28} +(-4.30432 - 3.12727i) q^{29} -1.00000 q^{30} +(-1.99715 + 5.19725i) q^{31} -1.00000 q^{32} +(-1.91677 - 1.39261i) q^{33} +(-0.406738 - 3.86985i) q^{34} +(-1.40402 - 4.32112i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(2.08399 - 3.60957i) q^{37} +(-4.51842 - 0.960419i) q^{38} +(-1.29949 + 3.99941i) q^{39} +(-0.978148 + 0.207912i) q^{40} +(0.0225851 - 0.214883i) q^{41} +(3.04019 - 3.37647i) q^{42} +(-0.825040 + 0.367331i) q^{43} +(-2.16442 - 0.963663i) q^{44} +(-0.669131 - 0.743145i) q^{45} +(-3.46915 + 2.52049i) q^{46} +(0.677794 - 0.492446i) q^{47} +(-0.669131 - 0.743145i) q^{48} +(12.4638 + 5.54924i) q^{49} +(-0.913545 + 0.406737i) q^{50} +(2.60370 - 2.89170i) q^{51} +(-0.439566 + 4.18219i) q^{52} +(-4.37082 + 0.929046i) q^{53} +(0.309017 - 0.951057i) q^{54} +(-2.31748 - 0.492596i) q^{55} +(2.27175 - 3.93478i) q^{56} +(-2.30968 - 4.00048i) q^{57} +(-1.64410 - 5.06003i) q^{58} +(0.938086 + 8.92529i) q^{59} +(-0.809017 - 0.587785i) q^{60} -2.74622 q^{61} +(-4.67059 + 3.03077i) q^{62} +4.54349 q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.439566 + 4.18219i) q^{65} +(-0.732141 - 2.25330i) q^{66} +(3.57455 + 6.19131i) q^{67} +(1.94558 - 3.36985i) q^{68} +(-4.19440 - 0.891548i) q^{69} +(1.40402 - 4.32112i) q^{70} +(13.0351 - 2.77070i) q^{71} +(0.104528 - 0.994522i) q^{72} +(10.7385 - 11.9263i) q^{73} +(3.80763 - 1.69527i) q^{74} +(-0.913545 - 0.406737i) q^{75} +(-3.09096 - 3.43285i) q^{76} +(8.70883 - 6.32733i) q^{77} +(-3.40210 + 2.47177i) q^{78} +(7.56051 + 8.39679i) q^{79} +(-0.913545 - 0.406737i) q^{80} +(0.913545 - 0.406737i) q^{81} +(0.144577 - 0.160569i) q^{82} +(-1.09205 + 10.3901i) q^{83} +(4.44421 - 0.944645i) q^{84} +(1.20244 - 3.70072i) q^{85} +(-0.883383 - 0.187769i) q^{86} +(2.66022 - 4.60763i) q^{87} +(-1.18463 - 2.05184i) q^{88} +(2.45536 + 7.55681i) q^{89} +(-0.104528 - 0.994522i) q^{90} +(-15.4574 - 11.2305i) q^{91} -4.28811 q^{92} +(-5.37754 - 1.44295i) q^{93} +0.837799 q^{94} +(-3.73714 - 2.71519i) q^{95} +(-0.104528 - 0.994522i) q^{96} +(-4.48958 - 13.8175i) q^{97} +(6.82166 + 11.8155i) q^{98} +(1.18463 - 2.05184i) 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} - 5 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 - 5 * q^7 + 4 * q^8 + 2 * q^9	\( 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} - 5 q^{7} + 4 q^{8} + 2 q^{9} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 4 q^{13} - 10 q^{14} - 4 q^{15} - 4 q^{16} - 22 q^{17} - 2 q^{18} - 3 q^{19} - 2 q^{20} - 11 q^{22} + 9 q^{23} + 2 q^{24} - 8 q^{25} + 11 q^{26} + 4 q^{27} - 3 q^{29} - 16 q^{30} - 15 q^{31} - 16 q^{32} - 8 q^{33} - 8 q^{34} + 5 q^{35} - 8 q^{36} - 17 q^{37} - 2 q^{38} + 3 q^{39} + 2 q^{40} + 28 q^{41} + 10 q^{42} - 28 q^{43} - 19 q^{44} - 2 q^{45} - 9 q^{46} + 9 q^{47} - 2 q^{48} + 19 q^{49} - 2 q^{50} + 22 q^{51} + 4 q^{52} + 2 q^{53} - 4 q^{54} - 11 q^{55} + 5 q^{56} - 2 q^{57} - 12 q^{58} + 24 q^{59} - 4 q^{60} - 40 q^{61} - 25 q^{62} + 10 q^{63} - 4 q^{64} - 4 q^{65} - 7 q^{66} - q^{67} - 2 q^{68} - 3 q^{69} - 5 q^{70} + 39 q^{71} - 2 q^{72} + 81 q^{73} - 8 q^{74} - 2 q^{75} + 2 q^{76} + 28 q^{77} - 8 q^{78} + 64 q^{79} - 2 q^{80} + 2 q^{81} + 32 q^{82} - 40 q^{83} + 5 q^{84} - 14 q^{85} + 13 q^{86} - 9 q^{87} - q^{88} - 7 q^{89} + 2 q^{90} - 46 q^{91} - 36 q^{92} - 20 q^{93} - 4 q^{94} - 6 q^{95} + 2 q^{96} - 17 q^{97} - 9 q^{98} + q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 - 5 * q^7 + 4 * q^8 + 2 * q^9 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 4 * q^13 - 10 * q^14 - 4 * q^15 - 4 * q^16 - 22 * q^17 - 2 * q^18 - 3 * q^19 - 2 * q^20 - 11 * q^22 + 9 * q^23 + 2 * q^24 - 8 * q^25 + 11 * q^26 + 4 * q^27 - 3 * q^29 - 16 * q^30 - 15 * q^31 - 16 * q^32 - 8 * q^33 - 8 * q^34 + 5 * q^35 - 8 * q^36 - 17 * q^37 - 2 * q^38 + 3 * q^39 + 2 * q^40 + 28 * q^41 + 10 * q^42 - 28 * q^43 - 19 * q^44 - 2 * q^45 - 9 * q^46 + 9 * q^47 - 2 * q^48 + 19 * q^49 - 2 * q^50 + 22 * q^51 + 4 * q^52 + 2 * q^53 - 4 * q^54 - 11 * q^55 + 5 * q^56 - 2 * q^57 - 12 * q^58 + 24 * q^59 - 4 * q^60 - 40 * q^61 - 25 * q^62 + 10 * q^63 - 4 * q^64 - 4 * q^65 - 7 * q^66 - q^67 - 2 * q^68 - 3 * q^69 - 5 * q^70 + 39 * q^71 - 2 * q^72 + 81 * q^73 - 8 * q^74 - 2 * q^75 + 2 * q^76 + 28 * q^77 - 8 * q^78 + 64 * q^79 - 2 * q^80 + 2 * q^81 + 32 * q^82 - 40 * q^83 + 5 * q^84 - 14 * q^85 + 13 * q^86 - 9 * q^87 - q^88 - 7 * q^89 + 2 * q^90 - 46 * q^91 - 36 * q^92 - 20 * q^93 - 4 * q^94 - 6 * q^95 + 2 * q^96 - 17 * q^97 - 9 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{15}\right)$

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
$3$	0.104528	+	0.994522i	0.0603495	+	0.574187i
$3$	0.104528	+	0.994522i	0.0603495	+	0.574187i
$4$	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
$7$	−4.44421	−	0.944645i	−1.67975	−	0.357042i	−0.733305	−	0.679900i	$-0.762023\pi$
$7$	−4.44421	−	0.944645i	−1.67975	−	0.357042i	−0.946447	+	0.322858i	$0.895356\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−0.978148	+	0.207912i	−0.326049	+	0.0693039i
$10$	−0.104528	+	0.994522i	−0.0330548	+	0.314495i
$11$	−1.58534	+	1.76070i	−0.477999	+	0.530871i	−0.933123	−	0.359556i	$-0.882928\pi$
$11$	−1.58534	+	1.76070i	−0.477999	+	0.530871i	0.455125	+	0.890428i	$0.349595\pi$
$12$	−0.913545	+	0.406737i	−0.263718	+	0.117415i
$13$	3.84167	+	1.71042i	1.06549	+	0.474386i	0.863159	−	0.504932i	$-0.168482\pi$
$13$	3.84167	+	1.71042i	1.06549	+	0.474386i	0.202329	+	0.979318i	$0.435149\pi$
$14$	−3.04019	−	3.37647i	−0.812525	−	0.902400i
$15$	−0.809017	+	0.587785i	−0.208887	+	0.151765i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−2.60370	−	2.89170i	−0.631490	−	0.701341i	0.339461	−	0.940620i	$-0.389755\pi$
$17$	−2.60370	−	2.89170i	−0.631490	−	0.701341i	−0.970951	+	0.239280i	$0.923089\pi$
$18$	−0.913545	−	0.406737i	−0.215325	−	0.0958687i
$19$	−4.22000	+	1.87886i	−0.968134	+	0.431041i	−0.829010	−	0.559234i	$-0.811095\pi$
$19$	−4.22000	+	1.87886i	−0.968134	+	0.431041i	−0.139124	+	0.990275i	$0.544429\pi$
$20$	−0.669131	+	0.743145i	−0.149622	+	0.166172i
$21$	0.474924	−	4.51860i	0.103637	−	0.986040i
$22$	−2.31748	+	0.492596i	−0.494089	+	0.105022i
$23$	−1.32510	+	4.07823i	−0.276302	+	0.850371i	0.712570	+	0.701601i	$0.247531\pi$
$23$	−1.32510	+	4.07823i	−0.276302	+	0.850371i	−0.988872	+	0.148769i	$0.952469\pi$
$24$	−0.978148	−	0.207912i	−0.199664	−	0.0424398i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.10262	+	3.64184i	0.412357	+	0.714223i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	−0.474924	−	4.51860i	−0.0897523	−	0.853936i
$29$	−4.30432	−	3.12727i	−0.799292	−	0.580720i	0.111414	−	0.993774i	$-0.464462\pi$
$29$	−4.30432	−	3.12727i	−0.799292	−	0.580720i	−0.910706	+	0.413054i	$0.864462\pi$
$30$	−1.00000			−0.182574
$31$	−1.99715	+	5.19725i	−0.358699	+	0.933453i
$31$	−1.99715	+	5.19725i	−0.358699	+	0.933453i
$32$	−1.00000			−0.176777
$33$	−1.91677	−	1.39261i	−0.333667	−	0.242423i
$34$	−0.406738	−	3.86985i	−0.0697550	−	0.663674i
$35$	−1.40402	−	4.32112i	−0.237322	−	0.730402i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	2.08399	−	3.60957i	0.342605	−	0.593410i	−0.642310	−	0.766445i	$-0.722024\pi$
$37$	2.08399	−	3.60957i	0.342605	−	0.593410i	0.984916	+	0.173035i	$0.0553573\pi$
$38$	−4.51842	−	0.960419i	−0.732984	−	0.155801i
$39$	−1.29949	+	3.99941i	−0.208085	+	0.640419i
$40$	−0.978148	+	0.207912i	−0.154659	+	0.0328737i
$41$	0.0225851	−	0.214883i	0.00352720	−	0.0335591i	−0.992617	−	0.121293i	$-0.961296\pi$
$41$	0.0225851	−	0.214883i	0.00352720	−	0.0335591i	0.996144	+	0.0877340i	$0.0279626\pi$
$42$	3.04019	−	3.37647i	0.469112	−	0.521001i
$43$	−0.825040	+	0.367331i	−0.125817	+	0.0560175i	−0.468680	−	0.883368i	$-0.655270\pi$
$43$	−0.825040	+	0.367331i	−0.125817	+	0.0560175i	0.342862	+	0.939386i	$0.388604\pi$
$44$	−2.16442	−	0.963663i	−0.326299	−	0.145278i
$45$	−0.669131	−	0.743145i	−0.0997481	−	0.110781i
$46$	−3.46915	+	2.52049i	−0.511499	+	0.371626i
$47$	0.677794	−	0.492446i	0.0988664	−	0.0718306i	−0.537254	−	0.843421i	$-0.680538\pi$
$47$	0.677794	−	0.492446i	0.0988664	−	0.0718306i	0.636120	+	0.771590i	$0.280538\pi$
$48$	−0.669131	−	0.743145i	−0.0965807	−	0.107264i
$49$	12.4638	+	5.54924i	1.78054	+	0.792749i
$50$	−0.913545	+	0.406737i	−0.129195	+	0.0575212i
$51$	2.60370	−	2.89170i	0.364591	−	0.404919i
$52$	−0.439566	+	4.18219i	−0.0609569	+	0.579966i
$53$	−4.37082	+	0.929046i	−0.600378	+	0.127614i	−0.498068	−	0.867138i	$-0.665957\pi$
$53$	−4.37082	+	0.929046i	−0.600378	+	0.127614i	−0.102311	+	0.994753i	$0.532624\pi$
$54$	0.309017	−	0.951057i	0.0420519	−	0.129422i
$55$	−2.31748	−	0.492596i	−0.312489	−	0.0664216i
$56$	2.27175	−	3.93478i	0.303575	−	0.525807i
$57$	−2.30968	−	4.00048i	−0.305925	−	0.529877i
$58$	−1.64410	−	5.06003i	−0.215881	−	0.664415i
$59$	0.938086	+	8.92529i	0.122128	+	1.16197i	0.868237	+	0.496150i	$0.165253\pi$
$59$	0.938086	+	8.92529i	0.122128	+	1.16197i	−0.746109	+	0.665824i	$0.768080\pi$
$60$	−0.809017	−	0.587785i	−0.104444	−	0.0758827i
$61$	−2.74622			−0.351618			−0.175809	−	0.984424i	$-0.556254\pi$
$61$	−2.74622			−0.351618			−0.175809	+	0.984424i	$0.556254\pi$
$62$	−4.67059	+	3.03077i	−0.593166	+	0.384908i
$63$	4.54349			0.572426
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.439566	+	4.18219i	0.0545215	+	0.518737i
$66$	−0.732141	−	2.25330i	−0.0901203	−	0.277362i
$67$	3.57455	+	6.19131i	0.436701	+	0.756389i	0.997433	−	0.0716089i	$-0.0228134\pi$
$67$	3.57455	+	6.19131i	0.436701	+	0.756389i	−0.560732	+	0.827998i	$0.689480\pi$
$68$	1.94558	−	3.36985i	0.235937	−	0.408654i
$69$	−4.19440	−	0.891548i	−0.504947	−	0.107330i
$70$	1.40402	−	4.32112i	0.167812	−	0.516472i
$71$	13.0351	−	2.77070i	1.54698	−	0.328822i	0.646227	−	0.763145i	$-0.276346\pi$
$71$	13.0351	−	2.77070i	1.54698	−	0.328822i	0.900757	+	0.434323i	$0.143012\pi$
$72$	0.104528	−	0.994522i	0.0123188	−	0.117206i
$73$	10.7385	−	11.9263i	1.25685	−	1.39587i	0.373173	−	0.927762i	$-0.378270\pi$
$73$	10.7385	−	11.9263i	1.25685	−	1.39587i	0.883672	−	0.468106i	$-0.155064\pi$
$74$	3.80763	−	1.69527i	0.442628	−	0.197071i
$75$	−0.913545	−	0.406737i	−0.105487	−	0.0469659i
$76$	−3.09096	−	3.43285i	−0.354557	−	0.393775i
$77$	8.70883	−	6.32733i	0.992463	−	0.721066i
$78$	−3.40210	+	2.47177i	−0.385212	+	0.279873i
$79$	7.56051	+	8.39679i	0.850624	+	0.944713i	0.999022	−	0.0442144i	$-0.0140785\pi$
$79$	7.56051	+	8.39679i	0.850624	+	0.944713i	−0.148398	+	0.988928i	$0.547412\pi$
$80$	−0.913545	−	0.406737i	−0.102137	−	0.0454745i
$81$	0.913545	−	0.406737i	0.101505	−	0.0451930i
$82$	0.144577	−	0.160569i	0.0159658	−	0.0177319i
$83$	−1.09205	+	10.3901i	−0.119868	+	1.14046i	0.754872	+	0.655872i	$0.227699\pi$
$83$	−1.09205	+	10.3901i	−0.119868	+	1.14046i	−0.874740	+	0.484593i	$0.838968\pi$
$84$	4.44421	−	0.944645i	0.484903	−	0.103069i
$85$	1.20244	−	3.70072i	0.130423	−	0.401400i
$86$	−0.883383	−	0.187769i	−0.0952576	−	0.0202476i
$87$	2.66022	−	4.60763i	0.285205	−	0.493990i
$88$	−1.18463	−	2.05184i	−0.126282	−	0.218726i
$89$	2.45536	+	7.55681i	0.260267	+	0.801020i	0.992746	+	0.120230i	$0.0383633\pi$
$89$	2.45536	+	7.55681i	0.260267	+	0.801020i	−0.732479	+	0.680790i	$0.761637\pi$
$90$	−0.104528	−	0.994522i	−0.0110183	−	0.104832i
$91$	−15.4574	−	11.2305i	−1.62038	−	1.17727i
$92$	−4.28811			−0.447066
$93$	−5.37754	−	1.44295i	−0.557625	−	0.149627i
$94$	0.837799			0.0864124
$95$	−3.73714	−	2.71519i	−0.383423	−	0.278573i
$96$	−0.104528	−	0.994522i	−0.0106684	−	0.101503i
$97$	−4.48958	−	13.8175i	−0.455848	−	1.40296i	−0.870137	−	0.492811i	$-0.835970\pi$
$97$	−4.48958	−	13.8175i	−0.455848	−	1.40296i	0.414289	−	0.910146i	$-0.364030\pi$
$98$	6.82166	+	11.8155i	0.689092	+	1.19354i
$99$	1.18463	−	2.05184i	0.119060	−	0.206217i
$100$	−0.978148	−	0.207912i	−0.0978148	−	0.0207912i
$101$	−3.30608	+	10.1751i	−0.328967	+	1.01246i	0.640651	+	0.767832i	$0.278665\pi$
$101$	−3.30608	+	10.1751i	−0.328967	+	1.01246i	−0.969618	+	0.244625i	$0.921335\pi$
$102$	3.80614	−	0.809019i	0.376864	−	0.0801049i
$103$	0.0278804	−	0.265264i	0.00274713	−	0.0261372i	−0.993062	−	0.117588i	$-0.962484\pi$
$103$	0.0278804	−	0.265264i	0.00274713	−	0.0261372i	0.995810	+	0.0914508i	$0.0291504\pi$
$104$	−2.81385	+	3.12510i	−0.275921	+	0.306441i
$105$	4.15069	−	1.84801i	0.405066	−	0.180347i
$106$	−4.08215	−	1.81749i	−0.396493	−	0.176530i
$107$	7.34664	+	8.15927i	0.710227	+	0.788787i	0.984969	−	0.172731i	$-0.0552592\pi$
$107$	7.34664	+	8.15927i	0.710227	+	0.788787i	−0.274742	+	0.961518i	$0.588593\pi$
$108$	0.809017	−	0.587785i	0.0778477	−	0.0565597i
$109$	−8.96166	+	6.51103i	−0.858372	+	0.623643i	−0.927441	−	0.373968i	$-0.877997\pi$
$109$	−8.96166	+	6.51103i	−0.858372	+	0.623643i	0.0690699	+	0.997612i	$0.477997\pi$
$110$	−1.58534	−	1.76070i	−0.151156	−	0.167876i
$111$	3.80763	+	1.69527i	0.361405	+	0.160908i
$112$	4.15069	−	1.84801i	0.392203	−	0.174620i
$113$	−8.25933	+	9.17292i	−0.776973	+	0.862916i	−0.993555	−	0.113349i	$-0.963842\pi$
$113$	−8.25933	+	9.17292i	−0.776973	+	0.862916i	0.216582	+	0.976264i	$0.430509\pi$
$114$	0.482855	−	4.59406i	0.0452235	−	0.430273i
$115$	−4.19440	+	0.891548i	−0.391130	+	0.0831373i
$116$	1.64410	−	5.06003i	0.152651	−	0.469812i
$117$	−4.11334	−	0.874317i	−0.380278	−	0.0808306i
$118$	−4.48723	+	7.77211i	−0.413083	+	0.715480i
$119$	8.83975	+	15.3109i	0.810338	+	1.40355i
$120$	−0.309017	−	0.951057i	−0.0282093	−	0.0868192i
$121$	0.563056	+	5.35712i	0.0511869	+	0.487010i
$122$	−2.22174	−	1.61419i	−0.201147	−	0.146142i
$123$	0.216067			0.0194821
$124$	−5.56003	−	0.293365i	−0.499305	−	0.0263449i
$125$	−1.00000			−0.0894427
$126$	3.67576	+	2.67060i	0.327463	+	0.237916i
$127$	−1.75888	−	16.7346i	−0.156075	−	1.48496i	−0.739702	−	0.672935i	$-0.765033\pi$
$127$	−1.75888	−	16.7346i	−0.156075	−	1.48496i	0.583627	−	0.812022i	$-0.301633\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−0.451559	−	0.782123i	−0.0397576	−	0.0688621i
$130$	−2.10262	+	3.64184i	−0.184412	+	0.319410i
$131$	−21.1834	−	4.50267i	−1.85080	−	0.393400i	−0.858047	−	0.513571i	$-0.828322\pi$
$131$	−21.1834	−	4.50267i	−1.85080	−	0.393400i	−0.992753	+	0.120171i	$0.961656\pi$
$132$	0.732141	−	2.25330i	0.0637247	−	0.196124i
$133$	20.5294	−	4.36366i	1.78012	−	0.378377i
$134$	−0.747285	+	7.10994i	−0.0645556	+	0.614206i
$135$	0.669131	−	0.743145i	0.0575896	−	0.0639597i
$136$	3.55476	−	1.58268i	0.304818	−	0.135714i
$137$	6.21981	+	2.76924i	0.531394	+	0.236592i	0.654851	−	0.755758i	$-0.272731\pi$
$137$	6.21981	+	2.76924i	0.531394	+	0.236592i	−0.123457	+	0.992350i	$0.539398\pi$
$138$	−2.86931	−	3.18669i	−0.244252	−	0.271269i
$139$	−3.55039	+	2.57951i	−0.301140	+	0.218791i	−0.728085	−	0.685486i	$-0.759590\pi$
$139$	−3.55039	+	2.57951i	−0.301140	+	0.218791i	0.426946	+	0.904277i	$0.359590\pi$
$140$	3.67576	−	2.67060i	0.310659	−	0.225707i
$141$	0.560597	+	0.622606i	0.0472108	+	0.0524329i
$142$	12.1742	+	5.42031i	1.02164	+	0.454862i
$143$	−9.10190	+	4.05243i	−0.761139	+	0.338881i
$144$	0.669131	−	0.743145i	0.0557609	−	0.0619287i
$145$	0.556137	−	5.29129i	0.0461846	−	0.439417i
$146$	15.6977	−	3.33665i	1.29915	−	0.276143i
$147$	−4.21602	+	12.9756i	−0.347731	+	1.07021i
$148$	4.07689	+	0.866570i	0.335119	+	0.0712316i
$149$	−7.97326	+	13.8101i	−0.653195	+	1.13137i	0.329149	+	0.944278i	$0.393238\pi$
$149$	−7.97326	+	13.8101i	−0.653195	+	1.13137i	−0.982343	+	0.187088i	$0.940095\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	0.253844	+	0.781253i	0.0206576	+	0.0635774i	0.960854	−	0.277056i	$-0.0893586\pi$
$151$	0.253844	+	0.781253i	0.0206576	+	0.0635774i	−0.940196	+	0.340633i	$0.889359\pi$
$152$	−0.482855	−	4.59406i	−0.0391647	−	0.372627i
$153$	3.14802	+	2.28717i	0.254502	+	0.184907i
$154$	10.7647			0.867444
$155$	−5.49952	+	0.869041i	−0.441732	+	0.0698031i
$156$	−4.20523			−0.336688
$157$	16.5040	+	11.9909i	1.31717	+	0.956977i	0.999963	+	0.00861870i	$0.00274345\pi$
$157$	16.5040	+	11.9909i	1.31717	+	0.956977i	0.317202	+	0.948358i	$0.397257\pi$
$158$	1.18107	+	11.2371i	0.0939607	+	0.893976i
$159$	−1.38083	−	4.24976i	−0.109507	−	0.337028i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	9.74150	−	16.8728i	0.767738	−	1.32976i
$162$	0.978148	+	0.207912i	0.0768505	+	0.0163351i
$163$	4.86429	−	14.9707i	0.381000	−	1.17260i	−0.558340	−	0.829612i	$-0.688561\pi$
$163$	4.86429	−	14.9707i	0.381000	−	1.17260i	0.939340	−	0.342987i	$-0.111439\pi$
$164$	0.211345	−	0.0449228i	0.0165033	−	0.00350788i
$165$	0.247655	−	2.35628i	0.0192799	−	0.183436i
$166$	−6.99065	+	7.76390i	−0.542579	+	0.602596i
$167$	2.67889	−	1.19272i	0.207299	−	0.0922954i	−0.300461	−	0.953794i	$-0.597140\pi$
$167$	2.67889	−	1.19272i	0.207299	−	0.0922954i	0.507760	+	0.861499i	$0.330474\pi$
$168$	4.15069	+	1.84801i	0.320232	+	0.142577i
$169$	3.13419	+	3.48087i	0.241092	+	0.267759i
$170$	3.14802	−	2.28717i	0.241442	−	0.175418i
$171$	3.73714	−	2.71519i	0.285786	−	0.207636i
$172$	−0.604304	−	0.671148i	−0.0460778	−	0.0511745i
$173$	8.94639	+	3.98319i	0.680181	+	0.302836i	0.717592	−	0.696464i	$-0.245244\pi$
$173$	8.94639	+	3.98319i	0.680181	+	0.302836i	−0.0374108	+	0.999300i	$0.511911\pi$
$174$	4.86046	−	2.16401i	0.368470	−	0.164054i
$175$	3.04019	−	3.37647i	0.229817	−	0.255237i
$176$	0.247655	−	2.35628i	0.0186677	−	0.177611i
$177$	−8.77834	+	1.86589i	−0.659821	+	0.140249i
$178$	−2.45536	+	7.55681i	−0.184037	+	0.566407i
$179$	9.41521	+	2.00127i	0.703726	+	0.149582i	0.545857	−	0.837878i	$-0.316204\pi$
$179$	9.41521	+	2.00127i	0.703726	+	0.149582i	0.157869	+	0.987460i	$0.449538\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	1.33476	+	2.31187i	0.0992117	+	0.171840i	0.911359	−	0.411613i	$-0.135035\pi$
$181$	1.33476	+	2.31187i	0.0992117	+	0.171840i	−0.812147	+	0.583453i	$0.801701\pi$
$182$	−5.90421	−	18.1713i	−0.437650	−	1.34695i
$183$	−0.287058	−	2.73118i	−0.0212200	−	0.201894i
$184$	−3.46915	−	2.52049i	−0.255749	−	0.185813i
$185$	4.16797			0.306435
$186$	−3.50237	−	4.32821i	−0.256807	−	0.317360i
$187$	9.21918			0.674173
$188$	0.677794	+	0.492446i	0.0494332	+	0.0359153i
$189$	0.474924	+	4.51860i	0.0345457	+	0.328680i
$190$	−1.42746	−	4.39327i	−0.103559	−	0.318722i
$191$	−7.99051	−	13.8400i	−0.578173	−	1.00143i	−0.995689	−	0.0927558i	$-0.970432\pi$
$191$	−7.99051	−	13.8400i	−0.578173	−	1.00143i	0.417516	−	0.908670i	$-0.362901\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	18.4973	+	3.93172i	1.33146	+	0.283011i	0.818059	−	0.575135i	$-0.195050\pi$
$193$	18.4973	+	3.93172i	1.33146	+	0.283011i	0.513405	+	0.858146i	$0.328384\pi$
$194$	4.48958	−	13.8175i	0.322333	−	0.992040i
$195$	−4.11334	+	0.874317i	−0.294562	+	0.0626111i
$196$	−1.42612	+	13.5686i	−0.101865	+	0.969185i
$197$	−18.0635	+	20.0615i	−1.28697	+	1.42932i	−0.439710	+	0.898140i	$0.644919\pi$
$197$	−18.0635	+	20.0615i	−1.28697	+	1.42932i	−0.847257	+	0.531183i	$0.821748\pi$
$198$	2.16442	−	0.963663i	0.153819	−	0.0684846i
$199$	7.69368	+	3.42545i	0.545390	+	0.242823i	0.660888	−	0.750484i	$-0.270180\pi$
$199$	7.69368	+	3.42545i	0.545390	+	0.242823i	−0.115498	+	0.993308i	$0.536846\pi$
$200$	−0.669131	−	0.743145i	−0.0473147	−	0.0525483i
$201$	−5.78375	+	4.20214i	−0.407954	+	0.296396i
$202$	−8.65543	+	6.28854i	−0.608994	+	0.442460i
$203$	16.1751	+	17.9643i	1.13527	+	1.26085i
$204$	3.55476	+	1.58268i	0.248883	+	0.110810i
$205$	0.197387	−	0.0878822i	0.0137861	−	0.00613796i
$206$	0.178474	−	0.198215i	0.0124349	−	0.0138103i
$207$	0.448230	−	4.26462i	0.0311541	−	0.296412i
$208$	−4.11334	+	0.874317i	−0.285209	+	0.0606230i
$209$	3.38202	−	10.4088i	0.233939	−	0.719991i
$210$	4.44421	+	0.944645i	0.306679	+	0.0651867i
$211$	−2.04828	+	3.54772i	−0.141009	+	0.244235i	−0.927877	−	0.372887i	$-0.878368\pi$
$211$	−2.04828	+	3.54772i	−0.141009	+	0.244235i	0.786868	+	0.617122i	$0.211701\pi$
$212$	−2.23423	−	3.86980i	−0.153448	−	0.265779i
$213$	4.11806	+	12.6741i	0.282165	+	0.868415i
$214$	1.14766	+	10.9192i	0.0784523	+	0.746424i
$215$	−0.730638	−	0.530840i	−0.0498291	−	0.0362030i
$216$	1.00000			0.0680414
$217$	13.7853	−	21.2110i	0.935807	−	1.43990i
$218$	−11.0772			−0.750244
$219$	12.9834	+	9.43303i	0.877340	+	0.637425i
$220$	−0.247655	−	2.35628i	−0.0166969	−	0.158860i
$221$	−5.05653	−	15.5624i	−0.340139	−	1.04684i
$222$	2.08399	+	3.60957i	0.139868	+	0.242259i
$223$	3.36729	−	5.83232i	0.225491	−	0.390561i	−0.730976	−	0.682403i	$-0.760935\pi$
$223$	3.36729	−	5.83232i	0.225491	−	0.390561i	0.956467	+	0.291842i	$0.0942682\pi$
$224$	4.44421	+	0.944645i	0.296941	+	0.0631168i
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	−12.0736	+	2.56633i	−0.803127	+	0.170710i
$227$	1.34545	−	12.8011i	0.0893007	−	0.849639i	−0.854573	−	0.519332i	$-0.826181\pi$
$227$	1.34545	−	12.8011i	0.0893007	−	0.849639i	0.943873	−	0.330308i	$-0.107152\pi$
$228$	3.09096	−	3.43285i	0.204704	−	0.227346i
$229$	14.6827	−	6.53718i	0.970263	−	0.431989i	0.140485	−	0.990083i	$-0.455134\pi$
$229$	14.6827	−	6.53718i	0.970263	−	0.431989i	0.829778	+	0.558094i	$0.188467\pi$
$230$	−3.91738	−	1.74413i	−0.258305	−	0.115005i
$231$	7.20299	+	7.99973i	0.473922	+	0.526344i
$232$	4.30432	−	3.12727i	0.282592	−	0.205315i
$233$	22.4192	−	16.2885i	1.46873	−	1.06710i	0.487752	−	0.872982i	$-0.337817\pi$
$233$	22.4192	−	16.2885i	1.46873	−	1.06710i	0.980979	−	0.194113i	$-0.0621830\pi$
$234$	−2.81385	−	3.12510i	−0.183947	−	0.204294i
$235$	0.765368	+	0.340764i	0.0499271	+	0.0222290i
$236$	−8.19857	+	3.65024i	−0.533682	+	0.237610i
$237$	−7.56051	+	8.39679i	−0.491108	+	0.545430i
$238$	−1.84801	+	17.5826i	−0.119789	+	1.13971i
$239$	−1.54390	+	0.328166i	−0.0998665	+	0.0212273i	−0.257574	−	0.966259i	$-0.582923\pi$
$239$	−1.54390	+	0.328166i	−0.0998665	+	0.0212273i	0.157707	+	0.987486i	$0.449590\pi$
$240$	0.309017	−	0.951057i	0.0199470	−	0.0613904i
$241$	−2.67150	−	0.567844i	−0.172086	−	0.0365781i	0.121063	−	0.992645i	$-0.461370\pi$
$241$	−2.67150	−	0.567844i	−0.172086	−	0.0365781i	−0.293149	+	0.956067i	$0.594703\pi$
$242$	−2.69331	+	4.66495i	−0.173133	+	0.299875i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−0.848629	−	2.61181i	−0.0543279	−	0.167204i
$245$	1.42612	+	13.5686i	0.0911112	+	0.866865i
$246$	0.174802	+	0.127001i	0.0111449	+	0.00809728i
$247$	−19.4255			−1.23601
$248$	−4.32572	−	3.50544i	−0.274684	−	0.222596i
$249$	−10.4474			−0.662074
$250$	−0.809017	−	0.587785i	−0.0511667	−	0.0371748i
$251$	3.17829	+	30.2394i	0.200612	+	1.90870i	0.380114	+	0.924939i	$0.375885\pi$
$251$	3.17829	+	30.2394i	0.200612	+	1.90870i	−0.179502	+	0.983758i	$0.557449\pi$
$252$	1.40402	+	4.32112i	0.0884447	+	0.272205i
$253$	−5.07982	−	8.79850i	−0.319365	−	0.553157i
$254$	8.41340	−	14.5724i	0.527903	−	0.914356i
$255$	3.80614	+	0.809019i	0.238350	+	0.0506628i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	15.8892	−	3.37734i	0.991138	−	0.210673i	0.316316	−	0.948654i	$-0.397554\pi$
$257$	15.8892	−	3.37734i	0.991138	−	0.210673i	0.674822	+	0.737981i	$0.264221\pi$
$258$	0.0944016	−	0.898171i	0.00587718	−	0.0559177i
$259$	−12.6714	+	14.0731i	−0.787364	+	0.874457i
$260$	−3.84167	+	1.71042i	−0.238250	+	0.106076i
$261$	4.86046	+	2.16401i	0.300855	+	0.133949i
$262$	−14.4911	−	16.0940i	−0.895264	−	0.994291i
$263$	−15.6712	+	11.3858i	−0.966327	+	0.702078i	−0.954612	−	0.297853i	$-0.903729\pi$
$263$	−15.6712	+	11.3858i	−0.966327	+	0.702078i	−0.0117157	+	0.999931i	$0.503729\pi$
$264$	1.91677	−	1.39261i	0.117969	−	0.0857095i
$265$	−2.98999	−	3.32072i	−0.183673	−	0.203990i
$266$	19.1735	+	8.53660i	1.17560	+	0.523413i
$267$	−7.25876	+	3.23181i	−0.444229	+	0.197783i
$268$	−4.78369	+	5.31282i	−0.292210	+	0.324532i
$269$	−1.09039	+	10.3744i	−0.0664823	+	0.632536i	0.909652	+	0.415370i	$0.136348\pi$
$269$	−1.09039	+	10.3744i	−0.0664823	+	0.632536i	−0.976135	+	0.217166i	$0.930319\pi$
$270$	0.978148	−	0.207912i	0.0595282	−	0.0126531i
$271$	−1.08622	+	3.34303i	−0.0659829	+	0.203074i	−0.978612	−	0.205714i	$-0.934048\pi$
$271$	−1.08622	+	3.34303i	−0.0659829	+	0.203074i	0.912629	+	0.408788i	$0.134048\pi$
$272$	3.80614	+	0.809019i	0.230781	+	0.0490540i
$273$	9.55322	−	16.5467i	0.578187	−	1.00145i
$274$	3.40421	+	5.89627i	0.205656	+	0.356207i
$275$	−0.732141	−	2.25330i	−0.0441497	−	0.135879i
$276$	−0.448230	−	4.26462i	−0.0269802	−	0.256700i
$277$	−16.1452	−	11.7301i	−0.970068	−	0.704796i	−0.0146011	−	0.999893i	$-0.504648\pi$
$277$	−16.1452	−	11.7301i	−0.970068	−	0.704796i	−0.955467	+	0.295098i	$0.904648\pi$
$278$	−4.38852			−0.263206
$279$	0.872939	−	5.49891i	0.0522615	−	0.329211i
$280$	4.54349			0.271526
$281$	3.22083	+	2.34007i	0.192139	+	0.139597i	0.679696	−	0.733494i	$-0.262112\pi$
$281$	3.22083	+	2.34007i	0.192139	+	0.139597i	−0.487557	+	0.873091i	$0.662112\pi$
$282$	0.0875739	+	0.833210i	0.00521495	+	0.0496169i
$283$	−6.20966	−	19.1114i	−0.369126	−	1.13605i	−0.947357	−	0.320180i	$-0.896257\pi$
$283$	−6.20966	−	19.1114i	−0.369126	−	1.13605i	0.578231	−	0.815873i	$-0.303743\pi$
$284$	6.66317	+	11.5409i	0.395386	+	0.684829i
$285$	2.30968	−	4.00048i	0.136814	−	0.236968i
$286$	−9.74555	−	2.07148i	−0.576266	−	0.122489i
$287$	−0.303361	+	0.933650i	−0.0179068	+	0.0551116i
$288$	0.978148	−	0.207912i	0.0576379	−	0.0122513i
$289$	0.194298	−	1.84863i	0.0114293	−	0.108743i
$290$	3.56006	−	3.95385i	0.209054	−	0.232178i
$291$	13.2725	−	5.90931i	0.778050	−	0.346410i
$292$	14.6610	+	6.52748i	0.857968	+	0.381992i
$293$	−12.7066	−	14.1121i	−0.742326	−	0.824436i	0.247174	−	0.968971i	$-0.420498\pi$
$293$	−12.7066	−	14.1121i	−0.742326	−	0.824436i	−0.989500	+	0.144535i	$0.953831\pi$
$294$	−11.0377	+	8.01935i	−0.643731	+	0.467698i
$295$	−7.26049	+	5.27505i	−0.422722	+	0.307125i
$296$	2.78892	+	3.09741i	0.162103	+	0.180033i
$297$	2.16442	+	0.963663i	0.125593	+	0.0559174i
$298$	−14.5679	+	6.48603i	−0.843894	+	0.375726i
$299$	−12.0661	+	13.4008i	−0.697800	+	0.774986i
$300$	0.104528	−	0.994522i	0.00603495	−	0.0574187i
$301$	4.01364	−	0.853126i	0.231343	−	0.0491734i
$302$	−0.253844	+	0.781253i	−0.0146071	+	0.0449560i
$303$	−10.4649	−	2.22438i	−0.601193	−	0.127788i
$304$	2.30968	−	4.00048i	0.132469	−	0.229444i
$305$	−1.37311	−	2.37830i	−0.0786241	−	0.136181i
$306$	1.20244	+	3.70072i	0.0687388	+	0.211556i
$307$	−3.54182	−	33.6982i	−0.202143	−	1.92326i	−0.354731	−	0.934969i	$-0.615427\pi$
$307$	−3.54182	−	33.6982i	−0.202143	−	1.92326i	0.152588	−	0.988290i	$-0.451239\pi$
$308$	8.70883	+	6.32733i	0.496231	+	0.360533i
$309$	0.266725			0.0151735
$310$	−4.96002	−	2.52947i	−0.281710	−	0.143664i
$311$	−8.80148			−0.499086			−0.249543	−	0.968364i	$-0.580280\pi$
$311$	−8.80148			−0.499086			−0.249543	+	0.968364i	$0.580280\pi$
$312$	−3.40210	−	2.47177i	−0.192606	−	0.139937i
$313$	2.53041	+	24.0753i	0.143027	+	1.36081i	0.796855	+	0.604171i	$0.206496\pi$
$313$	2.53041	+	24.0753i	0.143027	+	1.36081i	−0.653827	+	0.756644i	$0.726838\pi$
$314$	6.30398	+	19.4017i	0.355754	+	1.09490i
$315$	2.27175	+	3.93478i	0.127998	+	0.221700i
$316$	−5.64950	+	9.78522i	−0.317809	+	0.550462i
$317$	−16.9157	−	3.59555i	−0.950082	−	0.201946i	−0.293294	−	0.956022i	$-0.594752\pi$
$317$	−16.9157	−	3.59555i	−0.950082	−	0.201946i	−0.656787	+	0.754076i	$0.728085\pi$
$318$	1.38083	−	4.24976i	0.0774332	−	0.238315i
$319$	12.3300	−	2.62082i	0.690348	−	0.146738i
$320$	0.104528	−	0.994522i	0.00584332	−	0.0555955i
$321$	−7.34664	+	8.15927i	−0.410050	+	0.455406i
$322$	17.7986	−	7.92445i	0.991877	−	0.441612i
$323$	16.4207	+	7.31097i	0.913673	+	0.406793i
$324$	0.669131	+	0.743145i	0.0371739	+	0.0412858i
$325$	−3.40210	+	2.47177i	−0.188715	+	0.137109i
$326$	12.7349	−	9.25243i	0.705319	−	0.512445i
$327$	−7.41211	−	8.23198i	−0.409891	−	0.455230i
$328$	0.197387	+	0.0878822i	0.0108989	+	0.00485249i
$329$	−3.47744	+	1.54826i	−0.191718	+	0.0853582i
$330$	1.58534	−	1.76070i	0.0872702	−	0.0969234i
$331$	0.983336	−	9.35582i	0.0540490	−	0.514242i	−0.933685	−	0.358096i	$-0.883426\pi$
$331$	0.983336	−	9.35582i	0.0540490	−	0.514242i	0.987734	−	0.156147i	$-0.0499072\pi$
$332$	−10.2191	+	2.17213i	−0.560844	+	0.119211i
$333$	−1.28797	+	3.96398i	−0.0705806	+	0.217225i
$334$	2.86833	+	0.609683i	0.156948	+	0.0333604i
$335$	−3.57455	+	6.19131i	−0.195299	+	0.338267i
$336$	2.27175	+	3.93478i	0.123934	+	0.214660i
$337$	−6.49904	−	20.0020i	−0.354025	−	1.08958i	−0.956572	−	0.291495i	$-0.905847\pi$
$337$	−6.49904	−	20.0020i	−0.354025	−	1.08958i	0.602547	−	0.798083i	$-0.294153\pi$
$338$	0.489609	+	4.65831i	0.0266312	+	0.253379i
$339$	−9.98600	−	7.25526i	−0.542365	−	0.394051i
$340$	3.89117			0.211028
$341$	−5.98463	−	11.7558i	−0.324086	−	0.636612i
$342$	4.61936			0.249786
$343$	−24.4193	−	17.7417i	−1.31852	−	0.957959i
$344$	−0.0944016	−	0.898171i	−0.00508979	−	0.0484261i
$345$	−1.32510	−	4.07823i	−0.0713409	−	0.219565i
$346$	4.89652	+	8.48102i	0.263238	+	0.455942i
$347$	7.40869	−	12.8322i	0.397719	−	0.688870i	−0.595725	−	0.803189i	$-0.703135\pi$
$347$	7.40869	−	12.8322i	0.397719	−	0.688870i	0.993444	+	0.114318i	$0.0364684\pi$
$348$	5.20417	+	1.10618i	0.278973	+	0.0592975i
$349$	3.29683	−	10.1466i	0.176476	−	0.543136i	−0.823222	−	0.567719i	$-0.807826\pi$
$349$	3.29683	−	10.1466i	0.176476	−	0.543136i	0.999698	+	0.0245834i	$0.00782593\pi$
$350$	4.44421	−	0.944645i	0.237553	−	0.0504934i
$351$	0.439566	−	4.18219i	0.0234623	−	0.223229i
$352$	1.58534	−	1.76070i	0.0844990	−	0.0938457i
$353$	−8.05029	+	3.58422i	−0.428474	+	0.190769i	−0.609631	−	0.792685i	$-0.708682\pi$
$353$	−8.05029	+	3.58422i	−0.428474	+	0.190769i	0.181157	+	0.983454i	$0.442016\pi$
$354$	−8.19857	−	3.65024i	−0.435749	−	0.194008i
$355$	8.91706	+	9.90340i	0.473268	+	0.525618i
$356$	−6.42821	+	4.67037i	−0.340694	+	0.247529i
$357$	−14.3030	+	10.3917i	−0.756996	+	0.549990i
$358$	6.44075	+	7.15318i	0.340404	+	0.378057i
$359$	−25.1743	−	11.2083i	−1.32865	−	0.591553i	−0.385128	−	0.922863i	$-0.625843\pi$
$359$	−25.1743	−	11.2083i	−1.32865	−	0.591553i	−0.943522	+	0.331310i	$0.892509\pi$
$360$	0.913545	−	0.406737i	0.0481481	−	0.0214369i
$361$	1.56476	−	1.73784i	0.0823558	−	0.0914654i
$362$	−0.279040	+	2.65489i	−0.0146660	+	0.139538i
$363$	−5.26891	+	1.11994i	−0.276546	+	0.0587817i
$364$	5.90421	−	18.1713i	0.309465	−	0.952435i
$365$	15.6977	+	3.33665i	0.821656	+	0.174648i
$366$	1.37311	−	2.37830i	0.0717737	−	0.124316i
$367$	5.40543	+	9.36248i	0.282161	+	0.488717i	0.971917	−	0.235325i	$-0.0756154\pi$
$367$	5.40543	+	9.36248i	0.282161	+	0.488717i	−0.689756	+	0.724042i	$0.742282\pi$
$368$	−1.32510	−	4.07823i	−0.0690756	−	0.212593i
$369$	0.0225851	+	0.214883i	0.00117573	+	0.0111864i
$370$	3.37196	+	2.44987i	0.175300	+	0.127363i
$371$	20.3024			1.05405
$372$	−0.289424	−	5.56024i	−0.0150059	−	0.288285i
$373$	−25.1342			−1.30140			−0.650700	−	0.759335i	$-0.725524\pi$
$373$	−25.1342			−1.30140			−0.650700	+	0.759335i	$0.725524\pi$
$374$	7.45847	+	5.41890i	0.385668	+	0.280204i
$375$	−0.104528	−	0.994522i	−0.00539783	−	0.0513569i
$376$	0.258894	+	0.796794i	0.0133514	+	0.0410915i
$377$	−11.1868	−	19.3761i	−0.576151	−	0.997922i
$378$	−2.27175	+	3.93478i	−0.116846	+	0.202383i
$379$	16.8178	+	3.57474i	0.863873	+	0.183622i	0.618479	−	0.785801i	$-0.287749\pi$
$379$	16.8178	+	3.57474i	0.863873	+	0.183622i	0.245394	+	0.969423i	$0.421083\pi$
$380$	1.42746	−	4.39327i	0.0732272	−	0.225370i
$381$	16.4591	−	3.49849i	0.843225	−	0.179233i
$382$	1.67047	−	15.8935i	0.0854688	−	0.813181i
$383$	−8.35306	+	9.27701i	−0.426821	+	0.474033i	−0.917745	−	0.397169i	$-0.869993\pi$
$383$	−8.35306	+	9.27701i	−0.426821	+	0.474033i	0.490924	+	0.871202i	$0.336659\pi$
$384$	0.913545	−	0.406737i	0.0466192	−	0.0207562i
$385$	9.83404	+	4.37840i	0.501189	+	0.223144i
$386$	12.6536	+	14.0533i	0.644052	+	0.715292i
$387$	0.730638	−	0.530840i	0.0371404	−	0.0269841i
$388$	11.7539	−	8.53969i	0.596713	−	0.433537i
$389$	6.04402	+	6.71256i	0.306444	+	0.340340i	0.876621	−	0.481181i	$-0.159792\pi$
$389$	6.04402	+	6.71256i	0.306444	+	0.340340i	−0.570177	+	0.821522i	$0.693125\pi$
$390$	−3.84167	−	1.71042i	−0.194531	−	0.0866106i
$391$	15.2432	−	6.78671i	0.770882	−	0.343219i
$392$	−9.12917	+	10.1390i	−0.461093	+	0.512095i
$393$	2.26373	−	21.5380i	0.114190	−	1.08645i
$394$	−26.4055	+	5.61266i	−1.33029	+	0.282762i
$395$	−3.49158	+	10.7460i	−0.175681	+	0.540689i
$396$	2.31748	+	0.492596i	0.116458	+	0.0247539i
$397$	−0.539543	+	0.934516i	−0.0270789	+	0.0469020i	−0.879247	−	0.476366i	$-0.841954\pi$
$397$	−0.539543	+	0.934516i	−0.0270789	+	0.0469020i	0.852168	+	0.523268i	$0.175287\pi$
$398$	4.21089	+	7.29348i	0.211073	+	0.365589i
$399$	6.48566	+	19.9608i	0.324689	+	0.999290i
$400$	−0.104528	−	0.994522i	−0.00522642	−	0.0497261i
$401$	22.2873	+	16.1927i	1.11298	+	0.808624i	0.983130	−	0.182910i	$-0.0585518\pi$
$401$	22.2873	+	16.1927i	1.11298	+	0.808624i	0.129846	+	0.991534i	$0.458552\pi$
$402$	−7.14911			−0.356565
$403$	−16.5619	+	16.5501i	−0.825006	+	0.824421i
$404$	−10.6987			−0.532280
$405$	0.809017	+	0.587785i	0.0402004	+	0.0292073i
$406$	2.52680	+	24.0409i	0.125403	+	1.19313i
$407$	3.05154	+	9.39168i	0.151259	+	0.465528i
$408$	1.94558	+	3.36985i	0.0963208	+	0.166832i
$409$	−6.94234	+	12.0245i	−0.343277	+	0.594573i	−0.985039	−	0.172331i	$-0.944870\pi$
$409$	−6.94234	+	12.0245i	−0.343277	+	0.594573i	0.641762	+	0.766904i	$0.278204\pi$
$410$	0.211345	+	0.0449228i	0.0104376	+	0.00221858i
$411$	−2.10392	+	6.47520i	−0.103779	+	0.319398i
$412$	0.260896	−	0.0554553i	0.0128534	−	0.00273208i
$413$	4.26219	−	40.5520i	0.209729	−	1.99543i
$414$	2.86931	−	3.18669i	0.141019	−	0.156617i
$415$	−9.54414	+	4.24932i	−0.468503	+	0.208591i
$416$	−3.84167	−	1.71042i	−0.188353	−	0.0838603i
$417$	−2.93649	−	3.26131i	−0.143801	−	0.159707i
$418$	8.85425	−	6.43299i	0.433075	−	0.314648i
$419$	7.32473	−	5.32173i	0.357837	−	0.259984i	−0.394313	−	0.918976i	$-0.629017\pi$
$419$	7.32473	−	5.32173i	0.357837	−	0.259984i	0.752149	+	0.658993i	$0.229017\pi$
$420$	3.04019	+	3.37647i	0.148346	+	0.164755i
$421$	−27.3642	−	12.1833i	−1.33365	−	0.593779i	−0.388811	−	0.921317i	$-0.627114\pi$
$421$	−27.3642	−	12.1833i	−1.33365	−	0.593779i	−0.944838	+	0.327539i	$0.893781\pi$
$422$	−3.74239	+	1.66622i	−0.182177	+	0.0811103i
$423$	−0.560597	+	0.622606i	−0.0272572	+	0.0302721i
$424$	0.467082	−	4.44399i	0.0226835	−	0.215819i
$425$	3.80614	−	0.809019i	0.184625	−	0.0392432i
$426$	−4.11806	+	12.6741i	−0.199521	+	0.614062i
$427$	12.2048	+	2.59421i	0.590631	+	0.125542i
$428$	−5.48969	+	9.50842i	−0.265354	+	0.459607i
$429$	−4.98164	−	8.62845i	−0.240516	−	0.416585i
$430$	−0.279079	−	0.858917i	−0.0134584	−	0.0414206i
$431$	0.106796	+	1.01610i	0.00514420	+	0.0489438i	0.996793	−	0.0800249i	$-0.0255000\pi$
$431$	0.106796	+	1.01610i	0.00514420	+	0.0489438i	−0.991649	+	0.128969i	$0.958833\pi$
$432$	0.809017	+	0.587785i	0.0389238	+	0.0282798i
$433$	11.5364			0.554402			0.277201	−	0.960812i	$-0.410593\pi$
$433$	11.5364			0.554402			0.277201	+	0.960812i	$0.410593\pi$
$434$	23.6201	−	9.05730i	1.13380	−	0.434764i
$435$	5.32043			0.255095
$436$	−8.96166	−	6.51103i	−0.429186	−	0.311822i
$437$	−2.07053	−	19.6998i	−0.0990471	−	0.942370i
$438$	4.95923	+	15.2630i	0.236961	+	0.729292i
$439$	15.7929	+	27.3541i	0.753753	+	1.30554i	0.945992	+	0.324191i	$0.105092\pi$
$439$	15.7929	+	27.3541i	0.753753	+	1.30554i	−0.192238	+	0.981348i	$0.561575\pi$
$440$	1.18463	−	2.05184i	0.0564749	−	0.0978175i
$441$	−13.3452	−	2.83661i	−0.635485	−	0.135077i
$442$	5.05653	−	15.5624i	0.240514	−	0.740227i
$443$	−4.63244	+	0.984656i	−0.220094	+	0.0467824i	−0.316639	−	0.948546i	$-0.602554\pi$
$443$	−4.63244	+	0.984656i	−0.220094	+	0.0467824i	0.0965447	+	0.995329i	$0.469221\pi$
$444$	−0.435672	+	4.14514i	−0.0206761	+	0.196720i
$445$	−5.31671	+	5.90481i	−0.252036	+	0.279915i
$446$	6.15235	−	2.73920i	0.291322	−	0.129705i
$447$	−14.5679	−	6.48603i	−0.689036	−	0.306779i
$448$	3.04019	+	3.37647i	0.143635	+	0.159523i
$449$	23.9578	−	17.4064i	1.13064	−	0.821458i	0.144852	−	0.989453i	$-0.453729\pi$
$449$	23.9578	−	17.4064i	1.13064	−	0.821458i	0.985788	+	0.167995i	$0.0537294\pi$
$450$	0.809017	−	0.587785i	0.0381374	−	0.0277085i
$451$	0.342540	+	0.380429i	0.0161296	+	0.0179137i
$452$	−11.2762	−	5.02051i	−0.530390	−	0.236145i
$453$	−0.750439	+	0.334117i	−0.0352587	+	0.0156982i
$454$	8.61280	−	9.56548i	0.404219	−	0.448930i
$455$	1.99717	−	19.0018i	0.0936286	−	0.890817i
$456$	4.51842	−	0.960419i	0.211594	−	0.0449758i
$457$	−10.2450	+	31.5307i	−0.479239	+	1.47494i	0.360916	+	0.932598i	$0.382464\pi$
$457$	−10.2450	+	31.5307i	−0.479239	+	1.47494i	−0.840155	+	0.542347i	$0.817536\pi$
$458$	15.7210	+	3.34161i	0.734596	+	0.156143i
$459$	−1.94558	+	3.36985i	−0.0908121	+	0.157291i
$460$	−2.14405	−	3.71361i	−0.0999671	−	0.173148i
$461$	−3.87472	−	11.9252i	−0.180464	−	0.555411i	0.819377	−	0.573255i	$-0.194320\pi$
$461$	−3.87472	−	11.9252i	−0.180464	−	0.555411i	−0.999841	+	0.0178445i	$0.994320\pi$
$462$	1.12522	+	10.7057i	0.0523499	+	0.498076i
$463$	−30.8740	−	22.4313i	−1.43484	−	1.04247i	−0.989090	−	0.147310i	$-0.952938\pi$
$463$	−30.8740	−	22.4313i	−1.43484	−	1.04247i	−0.445746	−	0.895159i	$-0.647062\pi$
$464$	5.32043			0.246995
$465$	−1.43914	−	5.37856i	−0.0667384	−	0.249425i
$466$	27.7117			1.28372
$467$	3.32314	+	2.41440i	0.153777	+	0.111725i	0.662013	−	0.749492i	$-0.269702\pi$
$467$	3.32314	+	2.41440i	0.153777	+	0.111725i	−0.508236	+	0.861218i	$0.669702\pi$
$468$	−0.439566	−	4.18219i	−0.0203190	−	0.193322i
$469$	−10.0375	−	30.8921i	−0.463487	−	1.42647i
$470$	0.418900	+	0.725555i	0.0193224	+	0.0334674i
$471$	−10.2001	+	17.6670i	−0.469994	+	0.814053i
$472$	−8.77834	−	1.86589i	−0.404056	−	0.0858847i
$473$	0.661209	−	2.03499i	0.0304024	−	0.0935691i
$474$	−11.0521	+	2.34919i	−0.507639	+	0.107902i
$475$	0.482855	−	4.59406i	0.0221549	−	0.210790i
$476$	−11.8299	+	13.1384i	−0.542222	+	0.602199i
$477$	4.08215	−	1.81749i	0.186909	−	0.0832171i
$478$	−1.44193	−	0.641989i	−0.0659524	−	0.0293639i
$479$	−15.7308	−	17.4708i	−0.718758	−	0.798262i	0.267485	−	0.963562i	$-0.413807\pi$
$479$	−15.7308	−	17.4708i	−0.718758	−	0.798262i	−0.986243	+	0.165300i	$0.947141\pi$
$480$	0.809017	−	0.587785i	0.0369264	−	0.0268286i
$481$	14.1799	−	10.3023i	0.646547	−	0.469744i
$482$	−1.82752	−	2.02966i	−0.0832411	−	0.0924486i
$483$	17.7986	+	7.92445i	0.809864	+	0.360575i
$484$	−4.92093	+	2.19094i	−0.223678	+	0.0995881i
$485$	9.72153	−	10.7969i	0.441432	−	0.490260i
$486$	−0.104528	+	0.994522i	−0.00474151	+	0.0451124i
$487$	−11.0266	+	2.34377i	−0.499661	+	0.106206i	−0.450846	−	0.892602i	$-0.648878\pi$
$487$	−11.0266	+	2.34377i	−0.499661	+	0.106206i	−0.0488149	+	0.998808i	$0.515544\pi$
$488$	0.848629	−	2.61181i	0.0384156	−	0.118231i
$489$	15.3972	+	3.27277i	0.696285	+	0.148000i
$490$	−6.82166	+	11.8155i	−0.308171	+	0.533768i
$491$	−9.30784	−	16.1216i	−0.420057	−	0.727560i	0.575888	−	0.817529i	$-0.304656\pi$
$491$	−9.30784	−	16.1216i	−0.420057	−	0.727560i	−0.995945	+	0.0899691i	$0.971323\pi$
$492$	0.0667683	+	0.205492i	0.00301015	+	0.00926428i
$493$	2.16402	+	20.5893i	0.0974626	+	0.927295i
$494$	−15.7155	−	11.4180i	−0.707076	−	0.513721i
$495$	2.36926			0.106490
$496$	−1.43914	−	5.37856i	−0.0646192	−	0.241504i
$497$	−60.5481			−2.71595
$498$	−8.45209	−	6.14080i	−0.378747	−	0.275176i
$499$	−4.07668	−	38.7870i	−0.182497	−	1.73635i	−0.576377	−	0.817184i	$-0.695534\pi$
$499$	−4.07668	−	38.7870i	−0.182497	−	1.73635i	0.393879	−	0.919162i	$-0.371133\pi$
$500$	−0.309017	−	0.951057i	−0.0138197	−	0.0425325i
$501$	1.46621	+	2.53954i	0.0655052	+	0.113458i
$502$	−15.2030	+	26.3324i	−0.678543	+	1.17527i
$503$	−3.79006	−	0.805603i	−0.168991	−	0.0359200i	0.122639	−	0.992451i	$-0.460864\pi$
$503$	−3.79006	−	0.805603i	−0.168991	−	0.0359200i	−0.291630	+	0.956531i	$0.594198\pi$
$504$	−1.40402	+	4.32112i	−0.0625399	+	0.192478i
$505$	−10.4649	+	2.22438i	−0.465682	+	0.0989838i
$506$	1.06197	−	10.1040i	0.0472104	−	0.449177i
$507$	−3.13419	+	3.48087i	−0.139194	+	0.154591i
$508$	15.3720	−	6.84407i	0.682024	−	0.303657i
$509$	−11.0059	−	4.90013i	−0.487827	−	0.217195i	0.148058	−	0.988979i	$-0.452698\pi$
$509$	−11.0059	−	4.90013i	−0.487827	−	0.217195i	−0.635885	+	0.771784i	$0.719365\pi$
$510$	2.60370	+	2.89170i	0.115294	+	0.128047i
$511$	−58.9902	+	42.8589i	−2.60957	+	1.89597i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	3.09096	+	3.43285i	0.136469	+	0.151564i
$514$	14.8397	+	6.60708i	0.654553	+	0.291426i
$515$	0.243665	−	0.108487i	0.0107372	−	0.00478050i
$516$	0.604304	−	0.671148i	0.0266030	−	0.0295456i
$517$	−0.207485	+	1.97409i	−0.00912518	+	0.0868203i
$518$	−18.5233	+	3.93726i	−0.813869	+	0.172993i
$519$	−3.02622	+	9.31373i	−0.132836	+	0.408827i
$520$	−4.11334	−	0.874317i	−0.180382	−	0.0383413i
$521$	−3.27900	+	5.67939i	−0.143655	+	0.248818i	−0.928870	−	0.370405i	$-0.879219\pi$
$521$	−3.27900	+	5.67939i	−0.143655	+	0.248818i	0.785215	+	0.619223i	$0.212552\pi$
$522$	2.66022	+	4.60763i	0.116434	+	0.201670i
$523$	12.1472	+	37.3851i	0.531158	+	1.63474i	0.751806	+	0.659384i	$0.229183\pi$
$523$	12.1472	+	37.3851i	0.531158	+	1.63474i	−0.220648	+	0.975354i	$0.570817\pi$
$524$	−2.26373	−	21.5380i	−0.0988917	−	0.940891i
$525$	3.67576	+	2.67060i	0.160423	+	0.116554i
$526$	−19.3707			−0.844601
$527$	20.2289	−	7.75691i	0.881183	−	0.337896i
$528$	2.36926			0.103109
$529$	3.73128	+	2.71093i	0.162229	+	0.117867i
$530$	−0.467082	−	4.44399i	−0.0202887	−	0.193034i
$531$	−2.77326	−	8.53521i	−0.120349	−	0.370397i
$532$	10.4940	+	18.1762i	0.454973	+	0.788037i
$533$	0.454305	−	0.786880i	0.0196781	−	0.0340835i
$534$	−7.77207	−	1.65200i	−0.336330	−	0.0714892i
$535$	−3.39282	+	10.4420i	−0.146684	+	0.451448i
$536$	−6.99288	+	1.48638i	−0.302047	+	0.0642020i
$537$	−1.00614	+	9.57283i	−0.0434183	+	0.413098i
$538$	−6.98005	+	7.75213i	−0.300931	+	0.334218i
$539$	−29.5299	+	13.1476i	−1.27194	+	0.566306i
$540$	0.913545	+	0.406737i	0.0393127	+	0.0175032i
$541$	18.2678	+	20.2885i	0.785394	+	0.872269i	0.994404	−	0.105645i	$-0.0336907\pi$
$541$	18.2678	+	20.2885i	0.785394	+	0.872269i	−0.209010	+	0.977914i	$0.567024\pi$
$542$	−2.84375	+	2.06610i	−0.122149	+	0.0887468i
$543$	−2.15968	+	1.56910i	−0.0926808	+	0.0673365i
$544$	2.60370	+	2.89170i	0.111633	+	0.123981i
$545$	−10.1195	−	4.50551i	−0.433474	−	0.192995i
$546$	17.4546	−	7.77129i	0.746988	−	0.332580i
$547$	9.81624	−	10.9020i	0.419712	−	0.466138i	−0.495795	−	0.868440i	$-0.665123\pi$
$547$	9.81624	−	10.9020i	0.419712	−	0.466138i	0.915507	+	0.402302i	$0.131790\pi$
$548$	−0.711674	+	6.77113i	−0.0304012	+	0.289248i
$549$	2.68621	−	0.570972i	0.114645	−	0.0243685i
$550$	0.732141	−	2.25330i	0.0312186	−	0.0960809i
$551$	24.0399	+	5.10985i	1.02414	+	0.217687i
$552$	2.14405	−	3.71361i	0.0912570	−	0.158062i
$553$	−25.6685	−	44.4591i	−1.09153	−	1.89059i
$554$	−6.16690	−	18.9798i	−0.262006	−	0.806373i
$555$	0.435672	+	4.14514i	0.0184932	+	0.175951i
$556$	−3.55039	−	2.57951i	−0.150570	−	0.109395i
$557$	1.73530			0.0735269			0.0367635	−	0.999324i	$-0.488295\pi$
$557$	1.73530			0.0735269			0.0367635	+	0.999324i	$0.488295\pi$
$558$	3.93840	−	3.93561i	0.166726	−	0.166608i
$559$	−3.79782			−0.160631
$560$	3.67576	+	2.67060i	0.155329	+	0.112853i
$561$	0.963666	+	9.16867i	0.0406860	+	0.387102i
$562$	1.23025	+	3.78631i	0.0518949	+	0.159716i
$563$	−4.69555	−	8.13293i	−0.197894	−	0.342762i	0.749951	−	0.661493i	$-0.230077\pi$
$563$	−4.69555	−	8.13293i	−0.197894	−	0.342762i	−0.947845	+	0.318731i	$0.896743\pi$
$564$	−0.418900	+	0.725555i	−0.0176389	+	0.0305514i
$565$	−12.0736	−	2.56633i	−0.507942	−	0.107966i
$566$	6.20966	−	19.1114i	0.261011	−	0.803311i
$567$	−4.44421	+	0.944645i	−0.186639	+	0.0396714i
$568$	−1.39298	+	13.2533i	−0.0584482	+	0.556098i
$569$	−25.8593	+	28.7197i	−1.08408	+	1.20399i	−0.106305	+	0.994334i	$0.533902\pi$
$569$	−25.8593	+	28.7197i	−1.08408	+	1.20399i	−0.977775	+	0.209659i	$0.932765\pi$
$570$	4.22000	−	1.87886i	0.176756	−	0.0786969i
$571$	−6.47270	−	2.88183i	−0.270874	−	0.120601i	0.266805	−	0.963751i	$-0.414032\pi$
$571$	−6.47270	−	2.88183i	−0.270874	−	0.120601i	−0.537679	+	0.843150i	$0.680699\pi$
$572$	−6.66673	−	7.40415i	−0.278750	−	0.309583i
$573$	12.9289	−	9.39341i	0.540114	−	0.392415i
$574$	−0.794210	+	0.577027i	−0.0331497	+	0.0240847i
$575$	−2.86931	−	3.18669i	−0.119658	−	0.132894i
$576$	0.913545	+	0.406737i	0.0380644	+	0.0169474i
$577$	8.65811	−	3.85484i	0.360442	−	0.160479i	−0.218523	−	0.975832i	$-0.570124\pi$
$577$	8.65811	−	3.85484i	0.360442	−	0.160479i	0.578964	+	0.815353i	$0.303457\pi$
$578$	1.24379	−	1.38136i	0.0517347	−	0.0574572i
$579$	−1.97669	+	18.8069i	−0.0821484	+	0.781589i
$580$	5.20417	−	1.10618i	0.216091	−	0.0459316i
$581$	14.6683	−	45.1443i	0.608542	−	1.87290i
$582$	14.2111	+	3.02066i	0.589070	+	0.125211i
$583$	5.29347	−	9.16856i	0.219233	−	0.379723i
$584$	8.02421	+	13.8983i	0.332044	+	0.575117i
$585$	−1.29949	−	3.99941i	−0.0537272	−	0.165355i
$586$	−1.98496	−	18.8856i	−0.0819980	−	0.780159i
$587$	8.96518	+	6.51358i	0.370032	+	0.268844i	0.757224	−	0.653155i	$-0.226555\pi$
$587$	8.96518	+	6.51358i	0.370032	+	0.268844i	−0.387192	+	0.921999i	$0.626555\pi$
$588$	−13.6433			−0.562641
$589$	−1.33695	−	25.6847i	−0.0550882	−	1.05832i
$590$	−8.97446			−0.369472
$591$	−21.8397	−	15.8675i	−0.898367	−	0.652702i
$592$	0.435672	+	4.14514i	0.0179060	+	0.170364i
$593$	3.10388	+	9.55275i	0.127461	+	0.392284i	0.994341	−	0.106232i	$-0.0338785\pi$
$593$	3.10388	+	9.55275i	0.127461	+	0.392284i	−0.866881	+	0.498516i	$0.833879\pi$
$594$	1.18463	+	2.05184i	0.0486059	+	0.0841879i
$595$	−8.83975	+	15.3109i	−0.362394	+	0.627685i
$596$	−15.5980	−	3.31547i	−0.638921	−	0.135807i
$597$	−2.60247	+	8.00959i	−0.106512	+	0.327811i
$598$	−17.6384	+	3.74917i	−0.721290	+	0.153315i
$599$	−1.79830	+	17.1097i	−0.0734766	+	0.699084i	0.894333	+	0.447401i	$0.147650\pi$
$599$	−1.79830	+	17.1097i	−0.0734766	+	0.699084i	−0.967810	+	0.251682i	$0.919016\pi$
$600$	0.669131	−	0.743145i	0.0273171	−	0.0303388i
$601$	27.5911	−	12.2844i	1.12547	−	0.501090i	0.242324	−	0.970195i	$-0.422090\pi$
$601$	27.5911	−	12.2844i	1.12547	−	0.501090i	0.883142	+	0.469106i	$0.155424\pi$
$602$	3.74856	+	1.66897i	0.152780	+	0.0680220i
$603$	−4.78369	−	5.31282i	−0.194807	−	0.216355i
$604$	−0.664573	+	0.482841i	−0.0270411	+	0.0196465i
$605$	−4.35787	+	3.16618i	−0.177173	+	0.128723i
$606$	−7.15883	−	7.95068i	−0.290807	−	0.322974i
$607$	20.2594	+	9.02008i	0.822305	+	0.366114i	0.774367	−	0.632737i	$-0.218068\pi$
$607$	20.2594	+	9.02008i	0.822305	+	0.366114i	0.0479378	+	0.998850i	$0.484735\pi$
$608$	4.22000	−	1.87886i	0.171143	−	0.0761980i
$609$	−16.1751	+	17.9643i	−0.655449	+	0.727950i
$610$	0.287058	−	2.73118i	0.0116227	−	0.110582i
$611$	3.44615	−	0.732502i	0.139416	−	0.0296339i
$612$	−1.20244	+	3.70072i	−0.0486056	+	0.149593i
$613$	12.2929	+	2.61294i	0.496507	+	0.105536i	0.449357	−	0.893352i	$-0.351653\pi$
$613$	12.2929	+	2.61294i	0.496507	+	0.105536i	0.0471494	+	0.998888i	$0.484986\pi$
$614$	16.9419	−	29.3443i	0.683720	−	1.18424i
$615$	0.108033	+	0.187119i	0.00435633	+	0.00754538i
$616$	3.32648	+	10.2378i	0.134028	+	0.412494i
$617$	−3.79866	−	36.1418i	−0.152928	−	1.45501i	−0.754555	−	0.656237i	$-0.772147\pi$
$617$	−3.79866	−	36.1418i	−0.152928	−	1.45501i	0.601627	−	0.798777i	$-0.294519\pi$
$618$	0.215785	+	0.156777i	0.00868015	+	0.00630650i
$619$	4.49909			0.180834			0.0904168	−	0.995904i	$-0.471180\pi$
$619$	4.49909			0.180834			0.0904168	+	0.995904i	$0.471180\pi$
$620$	−2.52595	−	4.96181i	−0.101445	−	0.199271i
$621$	4.28811			0.172076
$622$	−7.12054	−	5.17338i	−0.285508	−	0.207434i
$623$	−3.77361	−	35.9035i	−0.151186	−	1.43844i
$624$	−1.29949	−	3.99941i	−0.0520212	−	0.160105i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−12.1039	+	20.9646i	−0.483771	+	0.837916i
$627$	10.7053	+	2.27548i	0.427528	+	0.0908739i
$628$	−6.30398	+	19.4017i	−0.251556	+	0.774210i
$629$	−15.8639	+	3.37197i	−0.632534	+	0.134449i
$630$	−0.474924	+	4.51860i	−0.0189214	+	0.180025i
$631$	−10.5951	+	11.7671i	−0.421785	+	0.468439i	−0.916162	−	0.400808i	$-0.868729\pi$
$631$	−10.5951	+	11.7671i	−0.421785	+	0.468439i	0.494377	+	0.869247i	$0.335396\pi$
$632$	−10.3222	+	4.59572i	−0.410593	+	0.182808i
$633$	−3.74239	−	1.66622i	−0.148747	−	0.0662263i
$634$	−11.5717	−	12.8517i	−0.459571	−	0.510405i
$635$	13.6132	−	9.89054i	0.540222	−	0.392494i
$636$	3.61506	−	2.62650i	0.143347	−	0.104147i
$637$	38.3903	+	42.6367i	1.52108	+	1.68933i
$638$	11.5157	+	5.12711i	0.455910	+	0.202984i
$639$	−12.1742	+	5.42031i	−0.481604	+	0.214424i
$640$	0.669131	−	0.743145i	0.0264497	−	0.0293754i
$641$	2.26977	−	21.5955i	0.0896507	−	0.852969i	−0.853609	−	0.520914i	$-0.825591\pi$
$641$	2.26977	−	21.5955i	0.0896507	−	0.852969i	0.943260	−	0.332055i	$-0.107742\pi$
$642$	−10.7395	+	2.28274i	−0.423853	+	0.0900926i
$643$	−10.9152	+	33.5936i	−0.430454	+	1.32480i	0.467220	+	0.884141i	$0.345255\pi$
$643$	−10.9152	+	33.5936i	−0.430454	+	1.32480i	−0.897674	+	0.440660i	$0.854745\pi$
$644$	19.0572	+	4.05074i	0.750961	+	0.159622i
$645$	0.451559	−	0.782123i	0.0177801	−	0.0307961i
$646$	8.98736	+	15.5666i	0.353603	+	0.612458i
$647$	4.15553	+	12.7894i	0.163371	+	0.502803i	0.998913	−	0.0466235i	$-0.0148461\pi$
$647$	4.15553	+	12.7894i	0.163371	+	0.502803i	−0.835542	+	0.549427i	$0.814846\pi$
$648$	0.104528	+	0.994522i	0.00410627	+	0.0390685i
$649$	−17.2020	−	12.4980i	−0.675236	−	0.490588i
$650$	−4.20523			−0.164943
$651$	22.5358	+	11.4926i	0.883248	+	0.450432i
$652$	15.7412			0.616472
$653$	−17.4696	−	12.6924i	−0.683637	−	0.496692i	0.190925	−	0.981605i	$-0.438851\pi$
$653$	−17.4696	−	12.6924i	−0.683637	−	0.496692i	−0.874562	+	0.484913i	$0.838851\pi$
$654$	−1.15789	−	11.0165i	−0.0452769	−	0.430781i
$655$	−6.69227	−	20.5967i	−0.261488	−	0.804779i
$656$	0.108033	+	0.187119i	0.00421799	+	0.00730578i
$657$	−8.02421	+	13.8983i	−0.313054	+	0.542226i
$658$	−3.72335	−	0.791423i	−0.145151	−	0.0308529i
$659$	1.35177	−	4.16033i	0.0526576	−	0.162064i	−0.921269	−	0.388925i	$-0.872846\pi$
$659$	1.35177	−	4.16033i	0.0526576	−	0.162064i	0.973927	+	0.226862i	$0.0728465\pi$
$660$	2.31748	−	0.492596i	0.0902079	−	0.0191743i
$661$	−2.82784	+	26.9051i	−0.109990	+	1.04649i	0.790754	+	0.612134i	$0.209689\pi$
$661$	−2.82784	+	26.9051i	−0.109990	+	1.04649i	−0.900744	+	0.434351i	$0.856978\pi$
$662$	6.29475	−	6.99103i	0.244652	−	0.271714i
$663$	14.9486	−	6.65554i	0.580555	−	0.258480i
$664$	−9.54414	−	4.24932i	−0.370384	−	0.164906i
$665$	14.0437	+	15.5971i	0.544593	+	0.604832i
$666$	−3.37196	+	2.44987i	−0.130661	+	0.0949307i
$667$	18.4574	−	13.4101i	0.714673	−	0.519241i
$668$	1.96217	+	2.17921i	0.0759185	+	0.0843160i
$669$	6.15235	+	2.73920i	0.237864	+	0.105904i
$670$	−6.53103	+	2.90780i	−0.252316	+	0.112338i
$671$	4.35370	−	4.83527i	0.168073	−	0.186664i
$672$	−0.474924	+	4.51860i	−0.0183206	+	0.174309i
$673$	33.7914	−	7.18259i	1.30256	−	0.276868i	0.496158	−	0.868232i	$-0.334744\pi$
$673$	33.7914	−	7.18259i	1.30256	−	0.276868i	0.806405	+	0.591364i	$0.201410\pi$
$674$	6.49904	−	20.0020i	0.250334	−	0.770448i
$675$	0.978148	+	0.207912i	0.0376489	+	0.00800252i
$676$	−2.34199	+	4.05644i	−0.0900764	+	0.156017i
$677$	16.2229	+	28.0989i	0.623496	+	1.07993i	0.988830	+	0.149050i	$0.0476216\pi$
$677$	16.2229	+	28.0989i	0.623496	+	1.07993i	−0.365334	+	0.930877i	$0.619045\pi$
$678$	−3.81431	−	11.7393i	−0.146488	−	0.450843i
$679$	6.89998	+	65.6490i	0.264797	+	2.51938i
$680$	3.14802	+	2.28717i	0.120721	+	0.0877090i
$681$	12.8716			0.493242
$682$	2.06822	−	13.0283i	0.0791961	−	0.498880i
$683$	−25.1102			−0.960816			−0.480408	−	0.877045i	$-0.659511\pi$
$683$	−25.1102			−0.960816			−0.480408	+	0.877045i	$0.659511\pi$
$684$	3.73714	+	2.71519i	0.142893	+	0.103818i
$685$	0.711674	+	6.77113i	0.0271917	+	0.258711i
$686$	−9.32734	−	28.7066i	−0.356120	−	1.09602i
$687$	8.03613	+	13.9190i	0.306598	+	0.531043i
$688$	0.451559	−	0.782123i	0.0172155	−	0.0298182i
$689$	−18.3803	−	3.90685i	−0.700234	−	0.148839i
$690$	1.32510	−	4.07823i	0.0504456	−	0.155256i
$691$	30.0354	−	6.38423i	1.14260	−	0.242868i	0.402537	−	0.915404i	$-0.368128\pi$
$691$	30.0354	−	6.38423i	1.14260	−	0.242868i	0.740064	+	0.672536i	$0.234795\pi$
$692$	−1.02365	+	9.73939i	−0.0389134	+	0.370236i
$693$	−7.20299	+	7.99973i	−0.273619	+	0.303885i
$694$	13.5364	−	6.02677i	0.513833	−	0.228773i
$695$	−4.00911	−	1.78497i	−0.152074	−	0.0677078i
$696$	3.56006	+	3.95385i	0.134944	+	0.149870i
$697$	−0.680183	+	0.494182i	−0.0257638	+	0.0187185i
$698$	8.63123	−	6.27095i	0.326697	−	0.237359i
$699$	18.5427	+	20.5938i	0.701350	+	0.778928i
$700$	4.15069	+	1.84801i	0.156881	+	0.0698480i
$701$	11.6201	−	5.17359i	0.438884	−	0.195404i	−0.175386	−	0.984500i	$-0.556117\pi$
$701$	11.6201	−	5.17359i	0.438884	−	0.195404i	0.614270	+	0.789096i	$0.289451\pi$
$702$	2.81385	−	3.12510i	0.106202	−	0.117949i
$703$	−2.01253	+	19.1479i	−0.0759038	+	0.722177i
$704$	2.31748	−	0.492596i	0.0873434	−	0.0185654i
$705$	−0.258894	+	0.796794i	−0.00975052	+	0.0300090i
$706$	−8.61957	−	1.83215i	−0.324402	−	0.0689537i
$707$	24.3047	−	42.0970i	0.914073	−	1.58322i
$708$	−4.48723	−	7.77211i	−0.168640	−	0.292094i
$709$	3.18665	+	9.80750i	0.119677	+	0.368328i	0.992894	−	0.119004i	$-0.0379701\pi$
$709$	3.18665	+	9.80750i	0.119677	+	0.368328i	−0.873217	+	0.487332i	$0.837970\pi$
$710$	1.39298	+	13.2533i	0.0522777	+	0.497389i
$711$	−9.14108	−	6.64139i	−0.342817	−	0.249071i
$712$	−7.94570			−0.297778
$713$	−18.5492	−	15.0317i	−0.694672	−	0.562942i
$714$	−17.6795			−0.661638
$715$	−8.06046	−	5.85626i	−0.301444	−	0.219012i
$716$	1.00614	+	9.57283i	0.0376014	+	0.357753i
$717$	−0.487750	−	1.50114i	−0.0182153	−	0.0560611i
$718$	−13.7784	−	23.8648i	−0.514204	−	0.890628i
$719$	3.94232	−	6.82830i	0.147024	−	0.254653i	−0.783102	−	0.621893i	$-0.786364\pi$
$719$	3.94232	−	6.82830i	0.147024	−	0.254653i	0.930126	+	0.367240i	$0.119697\pi$
$720$	0.978148	+	0.207912i	0.0364534	+	0.00774841i
$721$	−0.374486	+	1.15255i	−0.0139466	+	0.0429232i
$722$	2.28740	−	0.486201i	0.0851281	−	0.0180945i
$723$	0.285486	−	2.71622i	0.0106173	−	0.101017i
$724$	−1.78625	+	1.98383i	−0.0663856	+	0.0737286i
$725$	4.86046	−	2.16401i	0.180513	−	0.0803695i
$726$	−4.92093	−	2.19094i	−0.182633	−	0.0813133i
$727$	−4.28285	−	4.75658i	−0.158842	−	0.176412i	0.658471	−	0.752607i	$-0.271204\pi$
$727$	−4.28285	−	4.75658i	−0.158842	−	0.176412i	−0.817313	+	0.576195i	$0.804537\pi$
$728$	15.4574	−	11.2305i	0.572891	−	0.416229i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	10.7385	+	11.9263i	0.397449	+	0.441412i
$731$	3.21037	+	1.42935i	0.118740	+	0.0528663i
$732$	2.50880	−	1.11699i	0.0927279	−	0.0412851i
$733$	13.3306	−	14.8051i	0.492377	−	0.546840i	−0.444829	−	0.895615i	$-0.646736\pi$
$733$	13.3306	−	14.8051i	0.492377	−	0.546840i	0.937206	+	0.348775i	$0.113402\pi$
$734$	−1.13004	+	10.7516i	−0.0417106	+	0.396850i
$735$	−13.3452	+	2.83661i	−0.492245	+	0.104630i
$736$	1.32510	−	4.07823i	0.0488438	−	0.150326i
$737$	−16.5679	−	3.52162i	−0.610288	−	0.129721i
$738$	−0.108033	+	0.187119i	−0.00397676	+	0.00688796i
$739$	−0.746376	−	1.29276i	−0.0274559	−	0.0475550i	0.851971	−	0.523589i	$-0.175407\pi$
$739$	−0.746376	−	1.29276i	−0.0274559	−	0.0475550i	−0.879427	+	0.476034i	$0.842074\pi$
$740$	1.28797	+	3.96398i	0.0473469	+	0.145719i
$741$	−2.03052	−	19.3191i	−0.0745929	−	0.709704i
$742$	16.4250	+	11.9335i	0.602981	+	0.438092i
$743$	−29.4614			−1.08084			−0.540418	−	0.841397i	$-0.681734\pi$
$743$	−29.4614			−1.08084			−0.540418	+	0.841397i	$0.681734\pi$
$744$	3.03408	−	4.66845i	0.111235	−	0.171154i
$745$	−15.9465			−0.584235
$746$	−20.3340	−	14.7735i	−0.744480	−	0.540897i
$747$	−1.09205	−	10.3901i	−0.0399559	−	0.380155i
$748$	2.84888	+	8.76796i	0.104165	+	0.320588i
$749$	−24.9424	−	43.2015i	−0.911375	−	1.57855i
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	−45.6655	−	9.70650i	−1.66636	−	0.354195i	−0.724258	−	0.689529i	$-0.757818\pi$
$751$	−45.6655	−	9.70650i	−1.66636	−	0.354195i	−0.942100	+	0.335333i	$0.891151\pi$
$752$	−0.258894	+	0.796794i	−0.00944090	+	0.0290561i
$753$	−29.7416	+	6.32177i	−1.08384	+	0.230378i
$754$	2.33868	−	22.2511i	0.0851698	−	0.810337i
$755$	−0.549662	+	0.610462i	−0.0200043	+	0.0222170i
$756$	−4.15069	+	1.84801i	−0.150959	+	0.0672113i
$757$	28.1156	+	12.5179i	1.02188	+	0.454969i	0.848111	−	0.529818i	$-0.177740\pi$
$757$	28.1156	+	12.5179i	1.02188	+	0.454969i	0.173766	+	0.984787i	$0.444406\pi$
$758$	11.5047	+	12.7773i	0.417870	+	0.464092i
$759$	8.21931	−	5.97168i	0.298342	−	0.216758i
$760$	3.73714	−	2.71519i	0.135560	−	0.0984904i
$761$	8.39313	+	9.32151i	0.304251	+	0.337905i	0.875810	−	0.482656i	$-0.160328\pi$
$761$	8.39313	+	9.32151i	0.304251	+	0.337905i	−0.571559	+	0.820561i	$0.693661\pi$
$762$	15.3720	+	6.84407i	0.556870	+	0.247935i
$763$	45.9781	−	20.4708i	1.66452	−	0.741091i
$764$	10.6934	−	11.8762i	0.386873	−	0.429666i
$765$	−0.406738	+	3.86985i	−0.0147056	+	0.139915i
$766$	−12.2107	+	2.59546i	−0.441189	+	0.0937776i
$767$	−11.6622	+	35.8926i	−0.421098	+	1.29600i
$768$	0.978148	+	0.207912i	0.0352959	+	0.00750237i
$769$	20.4417	−	35.4061i	0.737148	−	1.27678i	−0.216627	−	0.976254i	$-0.569506\pi$
$769$	20.4417	−	35.4061i	0.737148	−	1.27678i	0.953775	−	0.300523i	$-0.0971611\pi$
$770$	5.38235	+	9.32250i	0.193966	+	0.335960i
$771$	5.01971	+	15.4491i	0.180780	+	0.556385i
$772$	1.97669	+	18.8069i	0.0711426	+	0.676876i
$773$	15.3284	+	11.1368i	0.551325	+	0.400561i	0.828274	−	0.560323i	$-0.189323\pi$
$773$	15.3284	+	11.1368i	0.551325	+	0.400561i	−0.276948	+	0.960885i	$0.589323\pi$
$774$	0.903118			0.0324619
$775$	−3.50237	−	4.32821i	−0.125809	−	0.155474i
$776$	14.5286			0.521546
$777$	−15.3205	−	11.1310i	−0.549619	−	0.399322i
$778$	0.944169	+	8.98316i	0.0338501	+	0.322062i
$779$	0.308427	+	0.949240i	0.0110505	+	0.0340101i
$780$	−2.10262	−	3.64184i	−0.0752857	−	0.130399i
$781$	−15.7868	+	27.3435i	−0.564894	+	0.978426i
$782$	16.3211	+	3.46916i	0.583643	+	0.124057i
$783$	−1.64410	+	5.06003i	−0.0587555	+	0.180831i
$784$	−13.3452	+	2.83661i	−0.476614	+	0.101307i
$785$	−2.13239	+	20.2884i	−0.0761083	+	0.724122i
$786$	14.4911	−	16.0940i	0.516881	−	0.574054i
$787$	−11.7370	+	5.22563i	−0.418377	+	0.186274i	−0.605118	−	0.796136i	$-0.706874\pi$
$787$	−11.7370	+	5.22563i	−0.418377	+	0.186274i	0.186741	+	0.982409i	$0.440208\pi$
$788$	−24.6615	−	10.9800i	−0.878531	−	0.391147i
$789$	−12.9615	−	14.3952i	−0.461442	−	0.512483i
$790$	−9.14108	+	6.64139i	−0.325225	+	0.236290i
$791$	45.3713	−	32.9642i	1.61322	−	1.17207i
$792$	1.58534	+	1.76070i	0.0563327	+	0.0625638i
$793$	−10.5501	−	4.69720i	−0.374644	−	0.166802i
$794$	−0.985794	+	0.438904i	−0.0349845	+	0.0155761i
$795$	2.98999	−	3.32072i	0.106044	−	0.117774i
$796$	−0.880316	+	8.37565i	−0.0312020	+	0.296867i
$797$	−43.1360	+	9.16884i	−1.52796	+	0.324777i	−0.893813	−	0.448440i	$-0.851980\pi$
$797$	−43.1360	+	9.16884i	−1.52796	+	0.324777i	−0.634142	+	0.773217i	$0.718647\pi$
$798$	−6.48566	+	19.9608i	−0.229590	+	0.706605i
$799$	−3.18878	−	0.677796i	−0.112811	−	0.0239787i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−3.97285	−	6.88118i	−0.140374	−	0.243134i
$802$	8.51300	+	26.2003i	0.300604	+	0.925165i
$803$	3.97447	+	37.8145i	0.140256	+	1.33445i
$804$	−5.78375	−	4.20214i	−0.203977	−	0.148198i
$805$	19.4830			0.686685
$806$	−23.1268	+	3.65452i	−0.814606	+	0.128725i
$807$	−10.4315			−0.367207
$808$	−8.65543	−	6.28854i	−0.304497	−	0.221230i
$809$	4.36930	+	41.5711i	0.153616	+	1.46156i	0.751369	+	0.659882i	$0.229394\pi$
$809$	4.36930	+	41.5711i	0.153616	+	1.46156i	−0.597753	+	0.801680i	$0.703940\pi$
$810$	0.309017	+	0.951057i	0.0108578	+	0.0334167i
$811$	3.91191	+	6.77562i	0.137366	+	0.237924i	0.926499	−	0.376298i	$-0.122803\pi$
$811$	3.91191	+	6.77562i	0.137366	+	0.237924i	−0.789133	+	0.614222i	$0.789470\pi$
$812$	−12.0867	+	20.9347i	−0.424159	+	0.734665i
$813$	−3.43825	−	0.730823i	−0.120585	−	0.0256311i
$814$	−3.05154	+	9.39168i	−0.106956	+	0.329178i
$815$	15.3972	−	3.27277i	0.539340	−	0.114640i
$816$	−0.406738	+	3.86985i	−0.0142387	+	0.135472i
$817$	2.79150	−	3.10027i	0.0976622	−	0.108465i
$818$	−12.6843	+	5.64741i	−0.443496	+	0.197457i
$819$	17.4546	+	7.77129i	0.609913	+	0.271551i
$820$	0.144577	+	0.160569i	0.00504884	+	0.00560731i
$821$	26.5803	−	19.3117i	0.927660	−	0.673984i	−0.0177589	−	0.999842i	$-0.505653\pi$
$821$	26.5803	−	19.3117i	0.927660	−	0.673984i	0.945419	+	0.325858i	$0.105653\pi$
$822$	−5.50813	+	4.00189i	−0.192118	+	0.139582i
$823$	27.9830	+	31.0782i	0.975425	+	1.08332i	0.996504	+	0.0835410i	$0.0266229\pi$
$823$	27.9830	+	31.0782i	0.975425	+	1.08332i	−0.0210797	+	0.999778i	$0.506710\pi$
$824$	0.243665	+	0.108487i	0.00848849	+	0.00377932i
$825$	2.16442	−	0.963663i	0.0753556	−	0.0335505i
$826$	27.2841	−	30.3020i	0.949334	−	1.05434i
$827$	−5.80717	+	55.2515i	−0.201935	+	1.92128i	0.156405	+	0.987693i	$0.450009\pi$
$827$	−5.80717	+	55.2515i	−0.201935	+	1.92128i	−0.358340	+	0.933591i	$0.616657\pi$
$828$	4.19440	−	0.891548i	0.145766	−	0.0309834i
$829$	−11.6525	+	35.8627i	−0.404708	+	1.24556i	0.516431	+	0.856329i	$0.327260\pi$
$829$	−11.6525	+	35.8627i	−0.404708	+	1.24556i	−0.921139	+	0.389234i	$0.872740\pi$
$830$	−10.2191	−	2.17213i	−0.354709	−	0.0753957i
$831$	9.97825	−	17.2828i	0.346142	−	0.599535i
$832$	−2.10262	−	3.64184i	−0.0728951	−	0.126258i
$833$	−16.4052	−	50.4901i	−0.568408	−	1.74938i
$834$	−0.458725	−	4.36448i	−0.0158844	−	0.151130i
$835$	2.37237	+	1.72363i	0.0820993	+	0.0596486i
$836$	10.9445			0.378522
$837$	5.56003	+	0.293365i	0.192183	+	0.0101402i
$838$	9.05387			0.312761
$839$	−18.5264	−	13.4602i	−0.639601	−	0.464697i	0.220112	−	0.975475i	$-0.429358\pi$
$839$	−18.5264	−	13.4602i	−0.639601	−	0.464697i	−0.859713	+	0.510777i	$0.829358\pi$
$840$	0.474924	+	4.51860i	0.0163864	+	0.155907i
$841$	−0.214148	−	0.659081i	−0.00738443	−	0.0227269i
$842$	−14.9769	−	25.9408i	−0.516139	−	0.893978i
$843$	−1.99058	+	3.44779i	−0.0685593	+	0.118748i
$844$	−4.00704	−	0.851722i	−0.137928	−	0.0293175i
$845$	−1.44743	+	4.45472i	−0.0497930	+	0.153247i
$846$	−0.819491	+	0.174188i	−0.0281747	+	0.00598871i
$847$	2.55824	−	24.3400i	0.0879021	−	0.836333i
$848$	2.98999	−	3.32072i	0.102677	−	0.114034i
$849$	18.3576	−	8.17332i	0.630031	−	0.280508i
$850$	3.55476	+	1.58268i	0.121927	+	0.0542855i
$851$	11.9592	+	13.2820i	0.409956	+	0.455302i
$852$	−10.7812	+	7.83302i	−0.369359	+	0.268355i
$853$	−3.49705	+	2.54076i	−0.119737	+	0.0869939i	−0.646042	−	0.763302i	$-0.723577\pi$
$853$	−3.49705	+	2.54076i	−0.119737	+	0.0869939i	0.526305	+	0.850296i	$0.323577\pi$
$854$	8.34904	+	9.27254i	0.285698	+	0.317300i
$855$	4.22000	+	1.87886i	0.144321	+	0.0642558i
$856$	−10.0302	+	4.46572i	−0.342824	+	0.152635i
$857$	17.0654	−	18.9530i	0.582942	−	0.647422i	−0.377465	−	0.926024i	$-0.623204\pi$
$857$	17.0654	−	18.9530i	0.582942	−	0.647422i	0.960407	+	0.278602i	$0.0898709\pi$
$858$	1.04145	−	9.90869i	0.0355544	−	0.338277i
$859$	9.29005	−	1.97466i	0.316972	−	0.0673746i	−0.0466782	−	0.998910i	$-0.514864\pi$
$859$	9.29005	−	1.97466i	0.316972	−	0.0673746i	0.363651	+	0.931535i	$0.381530\pi$
$860$	0.279079	−	0.858917i	0.00951651	−	0.0292888i
$861$	−0.960245	−	0.204106i	−0.0327251	−	0.00695593i
$862$	−0.510848	+	0.884815i	−0.0173996	+	0.0301369i
$863$	−16.7464	−	29.0056i	−0.570053	−	0.987362i	−0.996560	−	0.0828770i	$-0.973589\pi$
$863$	−16.7464	−	29.0056i	−0.570053	−	0.987362i	0.426506	−	0.904485i	$-0.359744\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	1.02365	+	9.73939i	0.0348052	+	0.331149i
$866$	9.33311	+	6.78090i	0.317152	+	0.230424i
$867$	1.85881			0.0631285
$868$	24.4328	+	6.55603i	0.829303	+	0.222526i
$869$	−26.7702			−0.908118
$870$	4.30432	+	3.12727i	0.145930	+	0.106024i
$871$	3.14251	+	29.8990i	0.106480	+	1.01309i
$872$	−3.42305	−	10.5351i	−0.115919	−	0.356762i
$873$	7.26430	+	12.5821i	0.245859	+	0.425841i
$874$	9.90416	−	17.1545i	0.335013	−	0.580260i
$875$	4.44421	+	0.944645i	0.150242	+	0.0319348i
$876$	−4.95923	+	15.2630i	−0.167557	+	0.515687i
$877$	−30.1302	+	6.40437i	−1.01742	+	0.216260i	−0.686293	−	0.727325i	$-0.740763\pi$
$877$	−30.1302	+	6.40437i	−1.01742	+	0.216260i	−0.331131	+	0.943585i	$0.607430\pi$
$878$	−3.30161	+	31.4127i	−0.111424	+	1.06013i
$879$	12.7066	−	14.1121i	0.428582	−	0.475988i
$880$	2.16442	−	0.963663i	0.0729627	−	0.0324851i
$881$	30.1624	+	13.4292i	1.01620	+	0.452441i	0.846121	−	0.532990i	$-0.178932\pi$
$881$	30.1624	+	13.4292i	1.01620	+	0.452441i	0.170077	+	0.985431i	$0.445598\pi$
$882$	−9.12917	−	10.1390i	−0.307395	−	0.341397i
$883$	33.7056	−	24.4885i	1.13428	−	0.824105i	0.147970	−	0.988992i	$-0.452726\pi$
$883$	33.7056	−	24.4885i	1.13428	−	0.824105i	0.986312	+	0.164887i	$0.0527260\pi$
$884$	13.2382	−	9.61809i	0.445247	−	0.323491i
$885$	−6.00508	−	6.66932i	−0.201859	−	0.224187i
$886$	−4.32649	−	1.92628i	−0.145351	−	0.0647146i
$887$	27.4765	−	12.2333i	0.922571	−	0.410755i	0.110209	−	0.993908i	$-0.464848\pi$
$887$	27.4765	−	12.2333i	0.922571	−	0.410755i	0.812362	+	0.583153i	$0.198181\pi$
$888$	−2.78892	+	3.09741i	−0.0935900	+	0.103942i
$889$	−7.99145	+	76.0336i	−0.268025	+	2.55009i
$890$	−7.77207	+	1.65200i	−0.260520	+	0.0553753i
$891$	−0.732141	+	2.25330i	−0.0245276	+	0.0754883i
$892$	6.58742	+	1.40020i	0.220563	+	0.0468821i
$893$	−1.93505	+	3.35160i	−0.0647539	+	0.112157i
$894$	−7.97326	−	13.8101i	−0.266666	−	0.461878i
$895$	2.97446	+	9.15445i	0.0994252	+	0.305999i
$896$	0.474924	+	4.51860i	0.0158661	+	0.150956i
$897$	−14.5886	−	10.5992i	−0.487099	−	0.353898i
$898$	29.6135			0.988215
$899$	24.8496	−	16.1250i	0.828780	−	0.537799i
$900$	1.00000			0.0333333
$901$	14.0668	+	10.2201i	0.468634	+	0.340482i
$902$	0.0535099	+	0.509113i	0.00178169	+	0.0169516i
$903$	1.26799	+	3.90248i	0.0421962	+	0.129866i
$904$	−6.17169	−	10.6897i	−0.205267	−	0.355534i
$905$	−1.33476	+	2.31187i	−0.0443688	+	0.0768490i
$906$	−0.803507	−	0.170791i	−0.0266947	−	0.00567414i
$907$	13.1822	−	40.5708i	0.437709	−	1.34713i	−0.452575	−	0.891726i	$-0.649495\pi$
$907$	13.1822	−	40.5708i	0.437709	−	1.34713i	0.890285	−	0.455405i	$-0.150505\pi$
$908$	12.5903	−	2.67616i	0.417825	−	0.0888115i
$909$	1.11832	−	10.6401i	0.0370923	−	0.352910i
$910$	12.7847	−	14.1989i	0.423809	−	0.470687i
$911$	−3.15240	+	1.40354i	−0.104444	+	0.0465014i	−0.458293	−	0.888801i	$-0.651539\pi$
$911$	−3.15240	+	1.40354i	−0.104444	+	0.0465014i	0.353850	+	0.935302i	$0.384872\pi$
$912$	4.22000	+	1.87886i	0.139738	+	0.0622154i
$913$	−16.5626	−	18.3947i	−0.548143	−	0.608775i
$914$	−26.8216	+	19.4871i	−0.887181	+	0.644574i
$915$	2.22174	−	1.61419i	0.0734485	−	0.0533634i
$916$	10.7544	+	11.9440i	0.355337	+	0.394642i
$917$	89.8899	+	40.0216i	2.96843	+	1.32163i
$918$	−3.55476	+	1.58268i	−0.117325	+	0.0522362i
$919$	−3.86418	+	4.29161i	−0.127468	+	0.141567i	−0.803500	−	0.595305i	$-0.797031\pi$
$919$	−3.86418	+	4.29161i	−0.127468	+	0.141567i	0.676032	+	0.736872i	$0.263698\pi$
$920$	0.448230	−	4.26462i	0.0147777	−	0.140600i
$921$	33.1434	−	7.04484i	1.09211	−	0.232136i
$922$	3.87472	−	11.9252i	0.127607	−	0.392735i
$923$	54.8157	+	11.6514i	1.80428	+	0.383512i
$924$	−5.38235	+	9.32250i	−0.177066	+	0.306688i
$925$	2.08399	+	3.60957i	0.0685211	+	0.118682i
$926$	−11.7928	−	36.2946i	−0.387536	−	1.19271i
$927$	0.0278804	+	0.265264i	0.000915711	+	0.00871241i
$928$	4.30432	+	3.12727i	0.141296	+	0.102658i
$929$	36.6580			1.20271			0.601355	−	0.798982i	$-0.294628\pi$
$929$	36.6580			1.20271			0.601355	+	0.798982i	$0.294628\pi$
$930$	1.99715	−	5.19725i	0.0654891	−	0.170424i
$931$	−63.0235			−2.06551
$932$	22.4192	+	16.2885i	0.734366	+	0.533548i
$933$	−0.920005	−	8.75326i	−0.0301196	−	0.286569i
$934$	1.26933	+	3.90659i	0.0415337	+	0.127827i
$935$	4.60959	+	7.98404i	0.150750	+	0.261106i
$936$	2.10262	−	3.64184i	0.0687261	−	0.119037i
$937$	30.3624	+	6.45372i	0.991896	+	0.210834i	0.675153	−	0.737678i	$-0.264078\pi$
$937$	30.3624	+	6.45372i	0.991896	+	0.210834i	0.316742	+	0.948512i	$0.397411\pi$
$938$	10.0375	−	30.8921i	0.327735	−	1.00866i
$939$	−23.6789	+	5.03310i	−0.772731	+	0.164249i
$940$	−0.0875739	+	0.833210i	−0.00285634	+	0.0271763i
$941$	−12.9542	+	14.3871i	−0.422294	+	0.469005i	−0.916323	−	0.400440i	$-0.868857\pi$
$941$	−12.9542	+	14.3871i	−0.422294	+	0.469005i	0.494029	+	0.869446i	$0.335524\pi$
$942$	−18.6364	+	8.29747i	−0.607208	+	0.270346i
$943$	0.846416	+	0.376849i	0.0275631	+	0.0122719i
$944$	−6.00508	−	6.66932i	−0.195449	−	0.217068i
$945$	−3.67576	+	2.67060i	−0.119573	+	0.0868746i
$946$	1.73107	−	1.25770i	0.0562819	−	0.0408912i
$947$	6.84412	+	7.60117i	0.222404	+	0.247005i	0.844013	−	0.536323i	$-0.180187\pi$
$947$	6.84412	+	7.60117i	0.222404	+	0.247005i	−0.621609	+	0.783328i	$0.713521\pi$
$948$	−10.3222	−	4.59572i	−0.335248	−	0.149262i
$949$	61.6527	−	27.4496i	2.00133	−	0.891051i
$950$	3.09096	−	3.43285i	0.100284	−	0.111377i
$951$	1.80768	−	17.1989i	0.0586179	−	0.557712i
$952$	−17.2932	+	3.67577i	−0.560474	+	0.119133i
$953$	−12.2367	+	37.6606i	−0.396385	+	1.21995i	0.531493	+	0.847063i	$0.321631\pi$
$953$	−12.2367	+	37.6606i	−0.396385	+	1.21995i	−0.927878	+	0.372885i	$0.878369\pi$
$954$	4.37082	+	0.929046i	0.141510	+	0.0300790i
$955$	7.99051	−	13.8400i	0.258567	−	0.447851i
$956$	−0.789195	−	1.36693i	−0.0255244	−	0.0442096i
$957$	3.89530	+	11.9885i	0.125917	+	0.387534i
$958$	−2.45739	−	23.3805i	−0.0793947	−	0.755390i
$959$	−25.0262	−	18.1826i	−0.808137	−	0.587146i
$960$	1.00000			0.0322749
$961$	−23.0228	−	20.7594i	−0.742670	−	0.669657i
$962$	17.5273			0.565103
$963$	−8.88251	−	6.45352i	−0.286235	−	0.207962i
$964$	−0.285486	−	2.71622i	−0.00919489	−	0.0874835i
$965$	5.84367	+	17.9850i	0.188115	+	0.578957i
$966$	9.74150	+	16.8728i	0.313428	+	0.542872i
$967$	5.57241	−	9.65169i	0.179197	−	0.310378i	−0.762409	−	0.647095i	$-0.775984\pi$
$967$	5.57241	−	9.65169i	0.179197	−	0.310378i	0.941606	+	0.336718i	$0.109317\pi$
$968$	−5.26891	−	1.11994i	−0.169349	−	0.0359963i
$969$	−5.55449	+	17.0950i	−0.178436	+	0.549169i
$970$	14.2111	−	3.02066i	0.456291	−	0.0969877i
$971$	−5.87624	+	55.9087i	−0.188578	+	1.79420i	0.335000	+	0.942218i	$0.391264\pi$
$971$	−5.87624	+	55.9087i	−0.188578	+	1.79420i	−0.523578	+	0.851978i	$0.675403\pi$
$972$	−0.669131	+	0.743145i	−0.0214624	+	0.0238364i
$973$	18.2154	−	8.11001i	0.583958	−	0.259995i
$974$	−10.2983	−	4.58510i	−0.329979	−	0.146916i
$975$	−2.81385	−	3.12510i	−0.0901153	−	0.100083i
$976$	2.22174	−	1.61419i	0.0711162	−	0.0516689i
$977$	−13.2627	+	9.63595i	−0.424313	+	0.308281i	−0.779371	−	0.626563i	$-0.784461\pi$
$977$	−13.2627	+	9.63595i	−0.424313	+	0.308281i	0.355058	+	0.934844i	$0.384461\pi$
$978$	10.5329	+	11.6980i	0.336805	+	0.374060i
$979$	−17.1979	−	7.65698i	−0.549646	−	0.244718i
$980$	−12.4638	+	5.54924i	−0.398141	+	0.177264i
$981$	7.41211	−	8.23198i	0.236650	−	0.262827i
$982$	1.94587	−	18.5137i	0.0620951	−	0.590796i
$983$	39.4414	−	8.38354i	1.25799	−	0.267393i	0.469769	−	0.882789i	$-0.344337\pi$
$983$	39.4414	−	8.38354i	1.25799	−	0.267393i	0.788218	+	0.615396i	$0.211004\pi$
$984$	−0.0667683	+	0.205492i	−0.00212850	+	0.00655083i
$985$	−26.4055	−	5.61266i	−0.841349	−	0.178834i
$986$	−10.3513	+	17.9291i	−0.329654	+	0.570978i
$987$	−1.90327	−	3.29656i	−0.0605817	−	0.104931i
$988$	−6.00280	−	18.4747i	−0.190975	−	0.587760i
$989$	−0.404804	−	3.85146i	−0.0128720	−	0.122469i
$990$	1.91677	+	1.39261i	0.0609189	+	0.0442602i
$991$	−59.0685			−1.87637			−0.938186	−	0.346131i	$-0.887495\pi$
$991$	−59.0685			−1.87637			−0.938186	+	0.346131i	$0.887495\pi$
$992$	1.99715	−	5.19725i	0.0634096	−	0.165013i
$993$	9.40735			0.298533
$994$	−48.9845	−	35.5893i	−1.55369	−	1.12882i
$995$	0.880316	+	8.37565i	0.0279079	+	0.265526i
$996$	−3.22841	−	9.93603i	−0.102296	−	0.314835i
$997$	16.8504	+	29.1857i	0.533656	+	0.924319i	0.999227	+	0.0393088i	$0.0125156\pi$
$997$	16.8504	+	29.1857i	0.533656	+	0.924319i	−0.465571	+	0.885010i	$0.654151\pi$
$998$	19.5003	−	33.7756i	0.617273	−	1.06915i
$999$	−4.07689	−	0.866570i	−0.128987	−	0.0274171i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.e.661.1	yes	16
31.28	even	15	inner	930.2.bg.e.121.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.e.121.1	✓	16	31.28	even	15	inner
930.2.bg.e.661.1	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)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.104528 + 0.994522i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-4.44421 - 0.944645i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.978148 + 0.207912i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.104528 + 0.994522i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-4.44421 - 0.944645i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.978148 + 0.207912i) q^{9} +(-0.104528 + 0.994522i) q^{10} +(-1.58534 + 1.76070i) q^{11} +(-0.913545 + 0.406737i) q^{12} +(3.84167 + 1.71042i) q^{13} +(-3.04019 - 3.37647i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-2.60370 - 2.89170i) q^{17} +(-0.913545 - 0.406737i) q^{18} +(-4.22000 + 1.87886i) q^{19} +(-0.669131 + 0.743145i) q^{20} +(0.474924 - 4.51860i) q^{21} +(-2.31748 + 0.492596i) q^{22} +(-1.32510 + 4.07823i) q^{23} +(-0.978148 - 0.207912i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.10262 + 3.64184i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(-0.474924 - 4.51860i) q^{28} +(-4.30432 - 3.12727i) q^{29} -1.00000 q^{30} +(-1.99715 + 5.19725i) q^{31} -1.00000 q^{32} +(-1.91677 - 1.39261i) q^{33} +(-0.406738 - 3.86985i) q^{34} +(-1.40402 - 4.32112i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(2.08399 - 3.60957i) q^{37} +(-4.51842 - 0.960419i) q^{38} +(-1.29949 + 3.99941i) q^{39} +(-0.978148 + 0.207912i) q^{40} +(0.0225851 - 0.214883i) q^{41} +(3.04019 - 3.37647i) q^{42} +(-0.825040 + 0.367331i) q^{43} +(-2.16442 - 0.963663i) q^{44} +(-0.669131 - 0.743145i) q^{45} +(-3.46915 + 2.52049i) q^{46} +(0.677794 - 0.492446i) q^{47} +(-0.669131 - 0.743145i) q^{48} +(12.4638 + 5.54924i) q^{49} +(-0.913545 + 0.406737i) q^{50} +(2.60370 - 2.89170i) q^{51} +(-0.439566 + 4.18219i) q^{52} +(-4.37082 + 0.929046i) q^{53} +(0.309017 - 0.951057i) q^{54} +(-2.31748 - 0.492596i) q^{55} +(2.27175 - 3.93478i) q^{56} +(-2.30968 - 4.00048i) q^{57} +(-1.64410 - 5.06003i) q^{58} +(0.938086 + 8.92529i) q^{59} +(-0.809017 - 0.587785i) q^{60} -2.74622 q^{61} +(-4.67059 + 3.03077i) q^{62} +4.54349 q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.439566 + 4.18219i) q^{65} +(-0.732141 - 2.25330i) q^{66} +(3.57455 + 6.19131i) q^{67} +(1.94558 - 3.36985i) q^{68} +(-4.19440 - 0.891548i) q^{69} +(1.40402 - 4.32112i) q^{70} +(13.0351 - 2.77070i) q^{71} +(0.104528 - 0.994522i) q^{72} +(10.7385 - 11.9263i) q^{73} +(3.80763 - 1.69527i) q^{74} +(-0.913545 - 0.406737i) q^{75} +(-3.09096 - 3.43285i) q^{76} +(8.70883 - 6.32733i) q^{77} +(-3.40210 + 2.47177i) q^{78} +(7.56051 + 8.39679i) q^{79} +(-0.913545 - 0.406737i) q^{80} +(0.913545 - 0.406737i) q^{81} +(0.144577 - 0.160569i) q^{82} +(-1.09205 + 10.3901i) q^{83} +(4.44421 - 0.944645i) q^{84} +(1.20244 - 3.70072i) q^{85} +(-0.883383 - 0.187769i) q^{86} +(2.66022 - 4.60763i) q^{87} +(-1.18463 - 2.05184i) q^{88} +(2.45536 + 7.55681i) q^{89} +(-0.104528 - 0.994522i) q^{90} +(-15.4574 - 11.2305i) q^{91} -4.28811 q^{92} +(-5.37754 - 1.44295i) q^{93} +0.837799 q^{94} +(-3.73714 - 2.71519i) q^{95} +(-0.104528 - 0.994522i) q^{96} +(-4.48958 - 13.8175i) q^{97} +(6.82166 + 11.8155i) q^{98} +(1.18463 - 2.05184i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} - 5 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 - 5 * q^7 + 4 * q^8 + 2 * q^9	\( 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} - 5 q^{7} + 4 q^{8} + 2 q^{9} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 4 q^{13} - 10 q^{14} - 4 q^{15} - 4 q^{16} - 22 q^{17} - 2 q^{18} - 3 q^{19} - 2 q^{20} - 11 q^{22} + 9 q^{23} + 2 q^{24} - 8 q^{25} + 11 q^{26} + 4 q^{27} - 3 q^{29} - 16 q^{30} - 15 q^{31} - 16 q^{32} - 8 q^{33} - 8 q^{34} + 5 q^{35} - 8 q^{36} - 17 q^{37} - 2 q^{38} + 3 q^{39} + 2 q^{40} + 28 q^{41} + 10 q^{42} - 28 q^{43} - 19 q^{44} - 2 q^{45} - 9 q^{46} + 9 q^{47} - 2 q^{48} + 19 q^{49} - 2 q^{50} + 22 q^{51} + 4 q^{52} + 2 q^{53} - 4 q^{54} - 11 q^{55} + 5 q^{56} - 2 q^{57} - 12 q^{58} + 24 q^{59} - 4 q^{60} - 40 q^{61} - 25 q^{62} + 10 q^{63} - 4 q^{64} - 4 q^{65} - 7 q^{66} - q^{67} - 2 q^{68} - 3 q^{69} - 5 q^{70} + 39 q^{71} - 2 q^{72} + 81 q^{73} - 8 q^{74} - 2 q^{75} + 2 q^{76} + 28 q^{77} - 8 q^{78} + 64 q^{79} - 2 q^{80} + 2 q^{81} + 32 q^{82} - 40 q^{83} + 5 q^{84} - 14 q^{85} + 13 q^{86} - 9 q^{87} - q^{88} - 7 q^{89} + 2 q^{90} - 46 q^{91} - 36 q^{92} - 20 q^{93} - 4 q^{94} - 6 q^{95} + 2 q^{96} - 17 q^{97} - 9 q^{98} + q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 - 5 * q^7 + 4 * q^8 + 2 * q^9 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 4 * q^13 - 10 * q^14 - 4 * q^15 - 4 * q^16 - 22 * q^17 - 2 * q^18 - 3 * q^19 - 2 * q^20 - 11 * q^22 + 9 * q^23 + 2 * q^24 - 8 * q^25 + 11 * q^26 + 4 * q^27 - 3 * q^29 - 16 * q^30 - 15 * q^31 - 16 * q^32 - 8 * q^33 - 8 * q^34 + 5 * q^35 - 8 * q^36 - 17 * q^37 - 2 * q^38 + 3 * q^39 + 2 * q^40 + 28 * q^41 + 10 * q^42 - 28 * q^43 - 19 * q^44 - 2 * q^45 - 9 * q^46 + 9 * q^47 - 2 * q^48 + 19 * q^49 - 2 * q^50 + 22 * q^51 + 4 * q^52 + 2 * q^53 - 4 * q^54 - 11 * q^55 + 5 * q^56 - 2 * q^57 - 12 * q^58 + 24 * q^59 - 4 * q^60 - 40 * q^61 - 25 * q^62 + 10 * q^63 - 4 * q^64 - 4 * q^65 - 7 * q^66 - q^67 - 2 * q^68 - 3 * q^69 - 5 * q^70 + 39 * q^71 - 2 * q^72 + 81 * q^73 - 8 * q^74 - 2 * q^75 + 2 * q^76 + 28 * q^77 - 8 * q^78 + 64 * q^79 - 2 * q^80 + 2 * q^81 + 32 * q^82 - 40 * q^83 + 5 * q^84 - 14 * q^85 + 13 * q^86 - 9 * q^87 - q^88 - 7 * q^89 + 2 * q^90 - 46 * q^91 - 36 * q^92 - 20 * q^93 - 4 * q^94 - 6 * q^95 + 2 * q^96 - 17 * q^97 - 9 * q^98 + q^99

Introduction

L-functions

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