LMFDB - Embedded newform 930.2.bg.e.421.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
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			421.2
Root			$-1.37050 + 0.406737i$ of defining polynomial
Character	$\chi$	$=$	930.421
Dual form			930.2.bg.e.391.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(-0.913545 + 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.16386 + 1.29260i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +O(q^{10})$	\(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} +(1.16386 + 1.29260i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +(0.913545 + 0.406737i) q^{10} +(1.59031 - 0.338031i) q^{11} +(0.104528 + 0.994522i) q^{12} +(-0.490830 + 4.66994i) q^{13} +(1.70136 + 0.361635i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.815119 - 0.173259i) q^{17} +(0.104528 - 0.994522i) q^{18} +(0.0546166 + 0.519642i) q^{19} +(0.978148 - 0.207912i) q^{20} +(-1.58899 - 0.707465i) q^{21} +(1.08790 - 1.20823i) q^{22} +(0.968545 + 2.98088i) q^{23} +(0.669131 + 0.743145i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.34783 + 4.06656i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.58899 - 0.707465i) q^{28} +(2.95103 - 2.14405i) q^{29} -1.00000 q^{30} +(1.68460 + 5.30680i) q^{31} -1.00000 q^{32} +(-1.31533 + 0.955645i) q^{33} +(-0.761284 + 0.338946i) q^{34} +(-0.537494 + 1.65424i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(1.09856 - 1.90277i) q^{37} +(0.349624 + 0.388297i) q^{38} +(-1.45104 - 4.46584i) q^{39} +(0.669131 - 0.743145i) q^{40} +(7.71048 + 3.43293i) q^{41} +(-1.70136 + 0.361635i) q^{42} +(0.0643697 + 0.612437i) q^{43} +(0.169947 - 1.61693i) q^{44} +(0.978148 + 0.207912i) q^{45} +(2.53568 + 1.84228i) q^{46} +(6.17486 + 4.48630i) q^{47} +(0.978148 + 0.207912i) q^{48} +(0.415459 - 3.95283i) q^{49} +(0.104528 + 0.994522i) q^{50} +(0.815119 - 0.173259i) q^{51} +(4.28970 + 1.90990i) q^{52} +(-2.01387 + 2.23663i) q^{53} +(0.309017 + 0.951057i) q^{54} +(1.08790 + 1.20823i) q^{55} +(0.869684 - 1.50634i) q^{56} +(-0.261252 - 0.452502i) q^{57} +(1.12719 - 3.46914i) q^{58} +(6.49304 - 2.89089i) q^{59} +(-0.809017 + 0.587785i) q^{60} -1.51373 q^{61} +(4.48213 + 3.30311i) q^{62} +1.73937 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-4.28970 + 1.90990i) q^{65} +(-0.502412 + 1.54627i) q^{66} +(1.48269 + 2.56810i) q^{67} +(-0.416665 + 0.721684i) q^{68} +(-2.09724 - 2.32922i) q^{69} +(0.537494 + 1.65424i) q^{70} +(-3.68314 + 4.09055i) q^{71} +(-0.913545 - 0.406737i) q^{72} +(1.03759 - 0.220546i) q^{73} +(-0.229662 - 2.18509i) q^{74} +(0.104528 - 0.994522i) q^{75} +(0.511087 + 0.108635i) q^{76} +(2.28785 + 1.66222i) q^{77} +(-3.79887 - 2.76004i) q^{78} +(-13.3328 - 2.83397i) q^{79} +(0.104528 - 0.994522i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(8.25573 - 1.75481i) q^{82} +(0.754311 + 0.335841i) q^{83} +(-1.16386 + 1.29260i) q^{84} +(-0.257513 - 0.792543i) q^{85} +(0.412058 + 0.457636i) q^{86} +(-1.82384 + 3.15898i) q^{87} +(-0.812920 - 1.40802i) q^{88} +(2.72937 - 8.40015i) q^{89} +(0.913545 - 0.406737i) q^{90} +(-6.60763 + 4.80073i) q^{91} +3.13428 q^{92} +(-3.69743 - 4.16281i) q^{93} +7.63255 q^{94} +(-0.422715 + 0.307120i) q^{95} +(0.913545 - 0.406737i) q^{96} +(2.36202 - 7.26954i) q^{97} +(-1.98730 - 3.44210i) q^{98} +(0.812920 - 1.40802i) 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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	−0.913545	+	0.406737i	−0.527436	+	0.234830i
$3$	−0.913545	+	0.406737i	−0.527436	+	0.234830i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	1.16386	+	1.29260i	0.439899	+	0.488558i	0.921799	−	0.387669i	$-0.126720\pi$
$7$	1.16386	+	1.29260i	0.439899	+	0.488558i	−0.481899	+	0.876227i	$0.660053\pi$
$8$	−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
$11$	1.59031	−	0.338031i	0.479497	−	0.101920i	0.0381789	−	0.999271i	$-0.487844\pi$
$11$	1.59031	−	0.338031i	0.479497	−	0.101920i	0.441318	+	0.897351i	$0.354511\pi$
$12$	0.104528	+	0.994522i	0.0301748	+	0.287094i
$13$	−0.490830	+	4.66994i	−0.136132	+	1.29521i	0.686707	+	0.726934i	$0.259055\pi$
$13$	−0.490830	+	4.66994i	−0.136132	+	1.29521i	−0.822839	+	0.568274i	$0.807611\pi$
$14$	1.70136	+	0.361635i	0.454707	+	0.0966510i
$15$	−0.809017	−	0.587785i	−0.208887	−	0.151765i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−0.815119	−	0.173259i	−0.197695	−	0.0420215i	0.108000	−	0.994151i	$-0.465555\pi$
$17$	−0.815119	−	0.173259i	−0.197695	−	0.0420215i	−0.305695	+	0.952129i	$0.598889\pi$
$18$	0.104528	−	0.994522i	0.0246376	−	0.234411i
$19$	0.0546166	+	0.519642i	0.0125299	+	0.119214i	0.998999	−	0.0447335i	$-0.0142439\pi$
$19$	0.0546166	+	0.519642i	0.0125299	+	0.119214i	−0.986469	+	0.163948i	$0.947577\pi$
$20$	0.978148	−	0.207912i	0.218720	−	0.0464905i
$21$	−1.58899	−	0.707465i	−0.346746	−	0.154381i
$22$	1.08790	−	1.20823i	0.231941	−	0.257597i
$23$	0.968545	+	2.98088i	0.201956	+	0.621556i	0.999825	+	0.0187248i	$0.00596062\pi$
$23$	0.968545	+	2.98088i	0.201956	+	0.621556i	−0.797869	+	0.602831i	$0.794039\pi$
$24$	0.669131	+	0.743145i	0.136586	+	0.151694i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.34783	+	4.06656i	0.460448	+	0.797519i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	1.58899	−	0.707465i	0.300291	−	0.133698i
$29$	2.95103	−	2.14405i	0.547992	−	0.398140i	−0.279052	−	0.960276i	$-0.590020\pi$
$29$	2.95103	−	2.14405i	0.547992	−	0.398140i	0.827045	+	0.562136i	$0.190020\pi$
$30$	−1.00000			−0.182574
$31$	1.68460	+	5.30680i	0.302563	+	0.953129i
$31$	1.68460	+	5.30680i	0.302563	+	0.953129i
$32$	−1.00000			−0.176777
$33$	−1.31533	+	0.955645i	−0.228970	+	0.166356i
$34$	−0.761284	+	0.338946i	−0.130559	+	0.0581287i
$35$	−0.537494	+	1.65424i	−0.0908531	+	0.279617i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	1.09856	−	1.90277i	0.180602	−	0.312813i	−0.761483	−	0.648184i	$-0.775529\pi$
$37$	1.09856	−	1.90277i	0.180602	−	0.312813i	0.942086	+	0.335372i	$0.108862\pi$
$38$	0.349624	+	0.388297i	0.0567165	+	0.0629900i
$39$	−1.45104	−	4.46584i	−0.232352	−	0.715107i
$40$	0.669131	−	0.743145i	0.105799	−	0.117502i
$41$	7.71048	+	3.43293i	1.20417	+	0.536133i	0.907988	−	0.418997i	$-0.137618\pi$
$41$	7.71048	+	3.43293i	1.20417	+	0.536133i	0.296187	+	0.955130i	$0.404285\pi$
$42$	−1.70136	+	0.361635i	−0.262525	+	0.0558015i
$43$	0.0643697	+	0.612437i	0.00981629	+	0.0933958i	0.998333	−	0.0577153i	$-0.0183816\pi$
$43$	0.0643697	+	0.612437i	0.00981629	+	0.0933958i	−0.988517	+	0.151111i	$0.951715\pi$
$44$	0.169947	−	1.61693i	0.0256204	−	0.243762i
$45$	0.978148	+	0.207912i	0.145814	+	0.0309936i
$46$	2.53568	+	1.84228i	0.373866	+	0.271630i
$47$	6.17486	+	4.48630i	0.900696	+	0.654394i	0.938645	−	0.344886i	$-0.112082\pi$
$47$	6.17486	+	4.48630i	0.900696	+	0.654394i	−0.0379488	+	0.999280i	$0.512082\pi$
$48$	0.978148	+	0.207912i	0.141183	+	0.0300095i
$49$	0.415459	−	3.95283i	0.0593513	−	0.564689i
$50$	0.104528	+	0.994522i	0.0147826	+	0.140647i
$51$	0.815119	−	0.173259i	0.114139	−	0.0242611i
$52$	4.28970	+	1.90990i	0.594875	+	0.264855i
$53$	−2.01387	+	2.23663i	−0.276626	+	0.307225i	−0.865408	−	0.501067i	$-0.832941\pi$
$53$	−2.01387	+	2.23663i	−0.276626	+	0.307225i	0.588782	+	0.808292i	$0.299608\pi$
$54$	0.309017	+	0.951057i	0.0420519	+	0.129422i
$55$	1.08790	+	1.20823i	0.146692	+	0.162918i
$56$	0.869684	−	1.50634i	0.116216	−	0.201293i
$57$	−0.261252	−	0.452502i	−0.0346037	−	0.0599354i
$58$	1.12719	−	3.46914i	0.148008	−	0.455521i
$59$	6.49304	−	2.89089i	0.845322	−	0.376362i	0.0620743	−	0.998072i	$-0.480228\pi$
$59$	6.49304	−	2.89089i	0.845322	−	0.376362i	0.783247	+	0.621710i	$0.213562\pi$
$60$	−0.809017	+	0.587785i	−0.104444	+	0.0758827i
$61$	−1.51373			−0.193813			−0.0969066	−	0.995293i	$-0.530895\pi$
$61$	−1.51373			−0.193813			−0.0969066	+	0.995293i	$0.530895\pi$
$62$	4.48213	+	3.30311i	0.569231	+	0.419495i
$63$	1.73937			0.219140
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−4.28970	+	1.90990i	−0.532072	+	0.236894i
$66$	−0.502412	+	1.54627i	−0.0618427	+	0.190332i
$67$	1.48269	+	2.56810i	0.181140	+	0.313743i	0.942269	−	0.334857i	$-0.108688\pi$
$67$	1.48269	+	2.56810i	0.181140	+	0.313743i	−0.761129	+	0.648600i	$0.775355\pi$
$68$	−0.416665	+	0.721684i	−0.0505280	+	0.0875171i
$69$	−2.09724	−	2.32922i	−0.252478	−	0.280405i
$70$	0.537494	+	1.65424i	0.0642428	+	0.197719i
$71$	−3.68314	+	4.09055i	−0.437109	+	0.485458i	−0.920941	−	0.389702i	$-0.872578\pi$
$71$	−3.68314	+	4.09055i	−0.437109	+	0.485458i	0.483832	+	0.875161i	$0.339245\pi$
$72$	−0.913545	−	0.406737i	−0.107662	−	0.0479344i
$73$	1.03759	−	0.220546i	0.121440	−	0.0258130i	−0.146791	−	0.989168i	$-0.546894\pi$
$73$	1.03759	−	0.220546i	0.121440	−	0.0258130i	0.268231	+	0.963355i	$0.413561\pi$
$74$	−0.229662	−	2.18509i	−0.0266977	−	0.254011i
$75$	0.104528	−	0.994522i	0.0120699	−	0.114837i
$76$	0.511087	+	0.108635i	0.0586256	+	0.0124613i
$77$	2.28785	+	1.66222i	0.260724	+	0.189427i
$78$	−3.79887	−	2.76004i	−0.430137	−	0.312513i
$79$	−13.3328	−	2.83397i	−1.50006	−	0.318847i	−0.616568	−	0.787302i	$-0.711477\pi$
$79$	−13.3328	−	2.83397i	−1.50006	−	0.318847i	−0.883487	+	0.468455i	$0.844811\pi$
$80$	0.104528	−	0.994522i	0.0116866	−	0.111191i
$81$	−0.104528	−	0.994522i	−0.0116143	−	0.110502i
$82$	8.25573	−	1.75481i	0.911693	−	0.193786i
$83$	0.754311	+	0.335841i	0.0827964	+	0.0368634i	0.447717	−	0.894175i	$-0.352237\pi$
$83$	0.754311	+	0.335841i	0.0827964	+	0.0368634i	−0.364921	+	0.931039i	$0.618904\pi$
$84$	−1.16386	+	1.29260i	−0.126988	+	0.141034i
$85$	−0.257513	−	0.792543i	−0.0279312	−	0.0859634i
$86$	0.412058	+	0.457636i	0.0444333	+	0.0493482i
$87$	−1.82384	+	3.15898i	−0.195536	+	0.338678i
$88$	−0.812920	−	1.40802i	−0.0866576	−	0.150095i
$89$	2.72937	−	8.40015i	0.289313	−	0.890414i	−0.695759	−	0.718275i	$-0.744932\pi$
$89$	2.72937	−	8.40015i	0.289313	−	0.890414i	0.985073	−	0.172139i	$-0.0550680\pi$
$90$	0.913545	−	0.406737i	0.0962961	−	0.0428738i
$91$	−6.60763	+	4.80073i	−0.692668	+	0.503253i
$92$	3.13428			0.326771
$93$	−3.69743	−	4.16281i	−0.383406	−	0.431664i
$94$	7.63255			0.787237
$95$	−0.422715	+	0.307120i	−0.0433696	+	0.0315099i
$96$	0.913545	−	0.406737i	0.0932383	−	0.0415124i
$97$	2.36202	−	7.26954i	0.239827	−	0.738110i	−0.756618	−	0.653857i	$-0.773150\pi$
$97$	2.36202	−	7.26954i	0.239827	−	0.738110i	0.996444	−	0.0842529i	$-0.0268504\pi$
$98$	−1.98730	−	3.44210i	−0.200748	−	0.347705i
$99$	0.812920	−	1.40802i	0.0817016	−	0.141511i
$100$	0.669131	+	0.743145i	0.0669131	+	0.0743145i
$101$	−3.97281	−	12.2271i	−0.395310	−	1.21664i	−0.928720	−	0.370782i	$-0.879090\pi$
$101$	−3.97281	−	12.2271i	−0.395310	−	1.21664i	0.533410	−	0.845857i	$-0.320910\pi$
$102$	0.557606	−	0.619284i	0.0552112	−	0.0613183i
$103$	5.32281	+	2.36987i	0.524472	+	0.233510i	0.651855	−	0.758344i	$-0.273991\pi$
$103$	5.32281	+	2.36987i	0.524472	+	0.233510i	−0.127383	+	0.991854i	$0.540658\pi$
$104$	4.59305	−	0.976283i	0.450386	−	0.0957324i
$105$	−0.181813	−	1.72984i	−0.0177432	−	0.168815i
$106$	−0.314597	+	2.99319i	−0.0305564	+	0.290725i
$107$	−4.27621	−	0.908936i	−0.413397	−	0.0878702i	−0.00348179	−	0.999994i	$-0.501108\pi$
$107$	−4.27621	−	0.908936i	−0.413397	−	0.0878702i	−0.409915	+	0.912124i	$0.634442\pi$
$108$	0.809017	+	0.587785i	0.0778477	+	0.0565597i
$109$	−2.18856	−	1.59008i	−0.209626	−	0.152302i	0.478019	−	0.878350i	$-0.341355\pi$
$109$	−2.18856	−	1.59008i	−0.209626	−	0.152302i	−0.687644	+	0.726048i	$0.741355\pi$
$110$	1.59031	+	0.338031i	0.151630	+	0.0322300i
$111$	−0.229662	+	2.18509i	−0.0217986	+	0.207399i
$112$	−0.181813	−	1.72984i	−0.0171798	−	0.163454i
$113$	9.79239	−	2.08144i	0.921191	−	0.195805i	0.277177	−	0.960819i	$-0.410601\pi$
$113$	9.79239	−	2.08144i	0.921191	−	0.195805i	0.644014	+	0.765014i	$0.277268\pi$
$114$	−0.477332	−	0.212522i	−0.0447062	−	0.0199045i
$115$	−2.09724	+	2.32922i	−0.195569	+	0.217201i
$116$	−1.12719	−	3.46914i	−0.104657	−	0.322102i
$117$	3.14201	+	3.48956i	0.290479	+	0.322610i
$118$	3.55376	−	6.15529i	0.327150	−	0.566640i
$119$	−0.724733	−	1.25527i	−0.0664362	−	0.115071i
$120$	−0.309017	+	0.951057i	−0.0282093	+	0.0868192i
$121$	−7.63417	+	3.39895i	−0.694016	+	0.308996i
$122$	−1.22463	+	0.889748i	−0.110873	+	0.0805540i
$123$	−8.44017			−0.761024
$124$	5.56764	+	0.0377395i	0.499989	+	0.00338911i
$125$	−1.00000			−0.0894427
$126$	1.40718	−	1.02237i	0.125361	−	0.0910804i
$127$	−19.5319	+	8.69615i	−1.73317	+	0.771659i	−0.737860	+	0.674953i	$0.764164\pi$
$127$	−19.5319	+	8.69615i	−1.73317	+	0.771659i	−0.995313	+	0.0967050i	$0.969170\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	−0.307905	−	0.533307i	−0.0271095	−	0.0469551i
$130$	−2.34783	+	4.06656i	−0.205918	+	0.356661i
$131$	−5.85990	−	6.50808i	−0.511982	−	0.568613i	0.430620	−	0.902534i	$-0.358295\pi$
$131$	−5.85990	−	6.50808i	−0.511982	−	0.568613i	−0.942601	+	0.333920i	$0.891628\pi$
$132$	0.502412	+	1.54627i	0.0437294	+	0.134585i
$133$	−0.608124	+	0.675390i	−0.0527311	+	0.0585638i
$134$	2.70901	+	1.20613i	0.234023	+	0.104194i
$135$	−0.978148	+	0.207912i	−0.0841855	+	0.0178942i
$136$	0.0871066	+	0.828764i	0.00746933	+	0.0710659i
$137$	1.35872	−	12.9273i	0.116083	−	1.10445i	−0.769073	−	0.639161i	$-0.779282\pi$
$137$	1.35872	−	12.9273i	0.116083	−	1.10445i	0.885156	−	0.465294i	$-0.154051\pi$
$138$	−3.06579	−	0.651653i	−0.260977	−	0.0554724i
$139$	−8.17764	−	5.94141i	−0.693619	−	0.503943i	0.184229	−	0.982883i	$-0.441021\pi$
$139$	−8.17764	−	5.94141i	−0.693619	−	0.503943i	−0.877848	+	0.478940i	$0.841021\pi$
$140$	1.40718	+	1.02237i	0.118928	+	0.0864064i
$141$	−7.46576	−	1.58690i	−0.628730	−	0.133641i
$142$	−0.575364	+	5.47422i	−0.0482834	+	0.459386i
$143$	0.798012	+	7.59258i	0.0667331	+	0.634923i
$144$	−0.978148	+	0.207912i	−0.0815123	+	0.0173260i
$145$	3.33231	+	1.48364i	0.276734	+	0.123210i
$146$	0.709792	−	0.788304i	0.0587428	−	0.0652405i
$147$	1.22822	+	3.78007i	0.101302	+	0.311775i
$148$	−1.47016	−	1.63278i	−0.120847	−	0.134214i
$149$	7.95396	−	13.7767i	0.651614	−	1.12863i	−0.331118	−	0.943589i	$-0.607426\pi$
$149$	7.95396	−	13.7767i	0.651614	−	1.12863i	0.982731	−	0.185038i	$-0.0592410\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	−4.94043	+	15.2051i	−0.402046	+	1.23737i	0.521290	+	0.853379i	$0.325451\pi$
$151$	−4.94043	+	15.2051i	−0.402046	+	1.23737i	−0.923337	+	0.383992i	$0.874549\pi$
$152$	0.477332	−	0.212522i	0.0387167	−	0.0172378i
$153$	−0.674178	+	0.489819i	−0.0545040	+	0.0395995i
$154$	2.82793			0.227881
$155$	−3.75352	+	4.11231i	−0.301490	+	0.330308i
$156$	−4.69566			−0.375954
$157$	−10.5588	+	7.67141i	−0.842684	+	0.612245i	−0.923119	−	0.384514i	$-0.874369\pi$
$157$	−10.5588	+	7.67141i	−0.842684	+	0.612245i	0.0804355	+	0.996760i	$0.474369\pi$
$158$	−12.4522	+	5.54408i	−0.990645	+	0.441064i
$159$	0.930042	−	2.86238i	0.0737572	−	0.227001i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−2.72583	+	4.72128i	−0.214826	+	0.372089i
$162$	−0.669131	−	0.743145i	−0.0525719	−	0.0583870i
$163$	−4.34800	−	13.3818i	−0.340561	−	1.04814i	−0.963917	−	0.266202i	$-0.914231\pi$
$163$	−4.34800	−	13.3818i	−0.340561	−	1.04814i	0.623356	−	0.781938i	$-0.285769\pi$
$164$	5.64758	−	6.27227i	0.441002	−	0.489782i
$165$	−1.48528	−	0.661289i	−0.115629	−	0.0514813i
$166$	0.807653	−	0.171672i	0.0626860	−	0.0133243i
$167$	1.98049	+	18.8431i	0.153255	+	1.45812i	0.753048	+	0.657965i	$0.228583\pi$
$167$	1.98049	+	18.8431i	0.153255	+	1.45812i	−0.599794	+	0.800155i	$0.704751\pi$
$168$	−0.181813	+	1.72984i	−0.0140272	+	0.133460i
$169$	−8.85150	−	1.88145i	−0.680885	−	0.144727i
$170$	−0.674178	−	0.489819i	−0.0517071	−	0.0375674i
$171$	0.422715	+	0.307120i	0.0323258	+	0.0234861i
$172$	0.602354	+	0.128034i	0.0459290	+	0.00976252i
$173$	0.233376	−	2.22042i	0.0177433	−	0.168816i	−0.982062	−	0.188559i	$-0.939618\pi$
$173$	0.233376	−	2.22042i	0.0177433	−	0.168816i	0.999805	+	0.0197434i	$0.00628493\pi$
$174$	0.381286	+	3.62769i	0.0289052	+	0.275014i
$175$	−1.70136	+	0.361635i	−0.128611	+	0.0273370i
$176$	−1.48528	−	0.661289i	−0.111957	−	0.0498465i
$177$	−4.75586	+	5.28191i	−0.357472	+	0.397013i
$178$	−2.72937	−	8.40015i	−0.204575	−	0.629618i
$179$	−1.84474	−	2.04880i	−0.137883	−	0.153134i	0.670249	−	0.742137i	$-0.266187\pi$
$179$	−1.84474	−	2.04880i	−0.137883	−	0.153134i	−0.808131	+	0.589003i	$0.799521\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	−1.64776	−	2.85401i	−0.122477	−	0.212137i	0.798267	−	0.602304i	$-0.205751\pi$
$181$	−1.64776	−	2.85401i	−0.122477	−	0.212137i	−0.920744	+	0.390167i	$0.872417\pi$
$182$	−2.52389	+	7.76774i	−0.187083	+	0.575783i
$183$	1.38286	−	0.615689i	0.102224	−	0.0455130i
$184$	2.53568	−	1.84228i	0.186933	−	0.135815i
$185$	2.19712			0.161536
$186$	−5.43812	−	1.19449i	−0.398743	−	0.0875844i
$187$	−1.35486			−0.0990772
$188$	6.17486	−	4.48630i	0.450348	−	0.327197i
$189$	−1.58899	+	0.707465i	−0.115582	+	0.0514605i
$190$	−0.161463	+	0.496931i	−0.0117137	+	0.0360512i
$191$	−5.67984	−	9.83777i	−0.410979	−	0.711836i	0.584018	−	0.811740i	$-0.301480\pi$
$191$	−5.67984	−	9.83777i	−0.410979	−	0.711836i	−0.994997	+	0.0999046i	$0.968146\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−9.67950	−	10.7502i	−0.696746	−	0.773815i	0.286109	−	0.958197i	$-0.407638\pi$
$193$	−9.67950	−	10.7502i	−0.696746	−	0.773815i	−0.982855	+	0.184383i	$0.940971\pi$
$194$	−2.36202	−	7.26954i	−0.169583	−	0.521923i
$195$	3.14201	−	3.48956i	0.225004	−	0.249892i
$196$	−3.63098	−	1.61662i	−0.259356	−	0.115473i
$197$	7.36934	−	1.56640i	0.525044	−	0.111602i	0.0622382	−	0.998061i	$-0.480176\pi$
$197$	7.36934	−	1.56640i	0.525044	−	0.111602i	0.462806	+	0.886460i	$0.346843\pi$
$198$	−0.169947	−	1.61693i	−0.0120776	−	0.114910i
$199$	1.14150	−	10.8606i	0.0809185	−	0.769888i	−0.876542	−	0.481325i	$-0.840156\pi$
$199$	1.14150	−	10.8606i	0.0809185	−	0.769888i	0.957461	−	0.288563i	$-0.0931775\pi$
$200$	0.978148	+	0.207912i	0.0691655	+	0.0147016i
$201$	−2.39904	−	1.74301i	−0.169216	−	0.122942i
$202$	−10.4010	−	7.55674i	−0.731809	−	0.531691i
$203$	6.20600	+	1.31913i	0.435576	+	0.0925845i
$204$	0.0871066	−	0.828764i	0.00609868	−	0.0580251i
$205$	0.882238	+	8.39393i	0.0616182	+	0.586258i
$206$	5.69922	−	1.21141i	0.397083	−	0.0844026i
$207$	2.86331	+	1.27483i	0.199014	+	0.0886065i
$208$	3.14201	−	3.48956i	0.217859	−	0.241957i
$209$	0.262513	+	0.807931i	0.0181584	+	0.0558858i
$210$	−1.16386	−	1.29260i	−0.0803143	−	0.0891980i
$211$	3.59361	−	6.22431i	0.247394	−	0.428499i	−0.715408	−	0.698707i	$-0.753759\pi$
$211$	3.59361	−	6.22431i	0.247394	−	0.428499i	0.962802	+	0.270208i	$0.0870924\pi$
$212$	1.50484	+	2.60646i	0.103353	+	0.179012i
$213$	1.70094	−	5.23497i	0.116547	−	0.358694i
$214$	−3.99379	+	1.77815i	−0.273010	+	0.121552i
$215$	−0.498201	+	0.361964i	−0.0339770	+	0.0246858i
$216$	1.00000			0.0680414
$217$	−4.89893	+	8.35391i	−0.332561	+	0.567101i
$218$	−2.70521			−0.183220
$219$	−0.858179	+	0.623504i	−0.0579904	+	0.0421325i
$220$	1.48528	−	0.661289i	0.100138	−	0.0445841i
$221$	1.20919	−	3.72152i	0.0813392	−	0.250336i
$222$	1.09856	+	1.90277i	0.0737307	+	0.127705i
$223$	−4.46962	+	7.74161i	−0.299308	+	0.518417i	−0.975978	−	0.217870i	$-0.930089\pi$
$223$	−4.46962	+	7.74161i	−0.299308	+	0.518417i	0.676670	+	0.736287i	$0.263422\pi$
$224$	−1.16386	−	1.29260i	−0.0777640	−	0.0863656i
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$	6.69877	−	7.43974i	0.445596	−	0.494884i
$227$	6.83217	+	3.04188i	0.453467	+	0.201897i	0.620744	−	0.784013i	$-0.286831\pi$
$227$	6.83217	+	3.04188i	0.453467	+	0.201897i	−0.167277	+	0.985910i	$0.553497\pi$
$228$	−0.511087	+	0.108635i	−0.0338475	+	0.00719451i
$229$	−1.84950	−	17.5968i	−0.122218	−	1.16283i	−0.867973	−	0.496611i	$-0.834578\pi$
$229$	−1.84950	−	17.5968i	−0.122218	−	1.16283i	0.745755	−	0.666220i	$-0.232089\pi$
$230$	−0.327621	+	3.11711i	−0.0216027	+	0.205536i
$231$	−2.76614	−	0.587961i	−0.181998	−	0.0386850i
$232$	−2.95103	−	2.14405i	−0.193745	−	0.140764i
$233$	1.08727	+	0.789946i	0.0712292	+	0.0517511i	0.622830	−	0.782357i	$-0.285983\pi$
$233$	1.08727	+	0.789946i	0.0712292	+	0.0517511i	−0.551601	+	0.834108i	$0.685983\pi$
$234$	4.59305	+	0.976283i	0.300257	+	0.0638216i
$235$	−0.797818	+	7.59073i	−0.0520439	+	0.495165i
$236$	−0.742938	−	7.06858i	−0.0483611	−	0.460125i
$237$	13.3328	−	2.83397i	0.866057	−	0.184086i
$238$	−1.32415	−	0.589551i	−0.0858321	−	0.0382149i
$239$	5.23201	−	5.81074i	0.338431	−	0.375865i	−0.549774	−	0.835314i	$-0.685286\pi$
$239$	5.23201	−	5.81074i	0.338431	−	0.375865i	0.888205	+	0.459448i	$0.151953\pi$
$240$	0.309017	+	0.951057i	0.0199470	+	0.0613904i
$241$	−1.39797	−	1.55260i	−0.0900512	−	0.100012i	0.696435	−	0.717620i	$-0.254769\pi$
$241$	−1.39797	−	1.55260i	−0.0900512	−	0.100012i	−0.786486	+	0.617608i	$0.788102\pi$
$242$	−4.17832	+	7.23706i	−0.268593	+	0.465216i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−0.467768	+	1.43964i	−0.0299458	+	0.0921636i
$245$	3.63098	−	1.61662i	0.231975	−	0.103282i
$246$	−6.82824	+	4.96101i	−0.435353	+	0.316302i
$247$	−2.45351			−0.156113
$248$	4.52650	−	3.24204i	0.287433	−	0.205870i
$249$	−0.825697			−0.0523264
$250$	−0.809017	+	0.587785i	−0.0511667	+	0.0371748i
$251$	−3.99789	+	1.77997i	−0.252344	+	0.112351i	−0.529011	−	0.848615i	$-0.677437\pi$
$251$	−3.99789	+	1.77997i	−0.252344	+	0.112351i	0.276667	+	0.960966i	$0.410770\pi$
$252$	0.537494	−	1.65424i	0.0338590	−	0.104207i
$253$	2.54792	+	4.41312i	0.160186	+	0.277451i
$254$	−10.6901	+	18.5159i	−0.670760	+	1.16179i
$255$	0.557606	+	0.619284i	0.0349187	+	0.0387811i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	5.86493	−	6.51366i	0.365844	−	0.406311i	−0.531915	−	0.846798i	$-0.678527\pi$
$257$	5.86493	−	6.51366i	0.365844	−	0.406311i	0.897759	+	0.440487i	$0.145194\pi$
$258$	−0.562571	−	0.250473i	−0.0350241	−	0.0155937i
$259$	3.73810	−	0.794557i	0.232274	−	0.0493714i
$260$	0.490830	+	4.66994i	0.0304400	+	0.289617i
$261$	0.381286	−	3.62769i	0.0236010	−	0.224548i
$262$	−8.56611	−	1.82078i	−0.529216	−	0.112488i
$263$	11.8789	+	8.63055i	0.732487	+	0.532183i	0.890349	−	0.455278i	$-0.150460\pi$
$263$	11.8789	+	8.63055i	0.732487	+	0.532183i	−0.157863	+	0.987461i	$0.550460\pi$
$264$	1.31533	+	0.955645i	0.0809531	+	0.0588159i
$265$	−2.94391	−	0.625748i	−0.180843	−	0.0384394i
$266$	−0.0949983	+	0.903849i	−0.00582472	+	0.0554185i
$267$	0.923242	+	8.78406i	0.0565015	+	0.537576i
$268$	2.90058	−	0.616537i	0.177181	−	0.0376610i
$269$	−12.4883	−	5.56014i	−0.761424	−	0.339008i	−0.0109782	−	0.999940i	$-0.503495\pi$
$269$	−12.4883	−	5.56014i	−0.761424	−	0.339008i	−0.750446	+	0.660932i	$0.770161\pi$
$270$	−0.669131	+	0.743145i	−0.0407220	+	0.0452264i
$271$	9.29677	+	28.6125i	0.564738	+	1.73809i	0.668727	+	0.743508i	$0.266839\pi$
$271$	9.29677	+	28.6125i	0.564738	+	1.73809i	−0.103989	+	0.994578i	$0.533161\pi$
$272$	0.557606	+	0.619284i	0.0338098	+	0.0375496i
$273$	4.08374	−	7.07325i	0.247159	−	0.428093i
$274$	−6.49926	−	11.2570i	−0.392635	−	0.680063i
$275$	−0.502412	+	1.54627i	−0.0302966	+	0.0932434i
$276$	−2.86331	+	1.27483i	−0.172351	+	0.0767355i
$277$	−13.8802	+	10.0846i	−0.833980	+	0.605922i	−0.920683	−	0.390312i	$-0.872367\pi$
$277$	−13.8802	+	10.0846i	−0.833980	+	0.605922i	0.0867025	+	0.996234i	$0.472367\pi$
$278$	−10.1081			−0.606245
$279$	5.07094	+	2.29904i	0.303589	+	0.137640i
$280$	1.73937			0.103947
$281$	26.2843	−	19.0967i	1.56799	−	1.13921i	0.638940	−	0.769256i	$-0.279373\pi$
$281$	26.2843	−	19.0967i	1.56799	−	1.13921i	0.929050	−	0.369955i	$-0.120627\pi$
$282$	−6.97268	+	3.10444i	−0.415217	+	0.184866i
$283$	4.12697	−	12.7015i	0.245323	−	0.755027i	−0.750260	−	0.661143i	$-0.770072\pi$
$283$	4.12697	−	12.7015i	0.245323	−	0.755027i	0.995583	−	0.0938838i	$-0.0299282\pi$
$284$	2.75219	+	4.76693i	0.163312	+	0.282865i
$285$	0.261252	−	0.452502i	0.0154752	−	0.0268039i
$286$	5.10841	+	5.67346i	0.302067	+	0.335479i
$287$	4.53654	+	13.9620i	0.267784	+	0.824153i
$288$	−0.669131	+	0.743145i	−0.0394289	+	0.0437902i
$289$	−14.8959	−	6.63207i	−0.876228	−	0.390122i
$290$	3.56796	−	0.758394i	0.209518	−	0.0445344i
$291$	0.798979	+	7.60178i	0.0468370	+	0.445624i
$292$	0.110880	−	1.05496i	0.00648879	−	0.0617367i
$293$	−12.8410	−	2.72944i	−0.750179	−	0.159455i	−0.183072	−	0.983100i	$-0.558604\pi$
$293$	−12.8410	−	2.72944i	−0.750179	−	0.159455i	−0.567107	+	0.823644i	$0.691937\pi$
$294$	3.21552	+	2.33621i	0.187533	+	0.136251i
$295$	5.75010	+	4.17769i	0.334784	+	0.243235i
$296$	−2.14911	−	0.456808i	−0.124915	−	0.0265514i
$297$	−0.169947	+	1.61693i	−0.00986130	+	0.0938240i
$298$	−1.66283	−	15.8208i	−0.0963252	−	0.916473i
$299$	−14.3959	+	3.05994i	−0.832537	+	0.176961i
$300$	−0.913545	−	0.406737i	−0.0527436	−	0.0234830i
$301$	−0.716720	+	0.795998i	−0.0413110	+	0.0458806i
$302$	4.94043	+	15.2051i	0.284290	+	0.874953i
$303$	8.60254	+	9.55409i	0.494203	+	0.548868i
$304$	0.261252	−	0.452502i	0.0149838	−	0.0259528i
$305$	−0.756864	−	1.31093i	−0.0433379	−	0.0750635i
$306$	−0.257513	+	0.792543i	−0.0147210	+	0.0453067i
$307$	12.0499	−	5.36496i	0.687724	−	0.306195i	−0.0329612	−	0.999457i	$-0.510494\pi$
$307$	12.0499	−	5.36496i	0.687724	−	0.306195i	0.720686	+	0.693262i	$0.243827\pi$
$308$	2.28785	−	1.66222i	0.130362	−	0.0947137i
$309$	−5.82654			−0.331460
$310$	−0.619509	+	5.53319i	−0.0351858	+	0.314264i
$311$	−4.24104			−0.240487			−0.120244	−	0.992744i	$-0.538368\pi$
$311$	−4.24104			−0.240487			−0.120244	+	0.992744i	$0.538368\pi$
$312$	−3.79887	+	2.76004i	−0.215069	+	0.156257i
$313$	7.68087	−	3.41974i	0.434149	−	0.193295i	−0.178013	−	0.984028i	$-0.556967\pi$
$313$	7.68087	−	3.41974i	0.434149	−	0.193295i	0.612162	+	0.790733i	$0.290300\pi$
$314$	−4.03310	+	12.4126i	−0.227601	+	0.700484i
$315$	0.869684	+	1.50634i	0.0490011	+	0.0848725i
$316$	−6.81532	+	11.8045i	−0.383392	+	0.664054i
$317$	−0.246217	−	0.273452i	−0.0138290	−	0.0153586i	0.736191	−	0.676774i	$-0.236623\pi$
$317$	−0.246217	−	0.273452i	−0.0138290	−	0.0153586i	−0.750020	+	0.661416i	$0.769956\pi$
$318$	−0.930042	−	2.86238i	−0.0521542	−	0.160514i
$319$	3.96830	−	4.40725i	0.222182	−	0.246758i
$320$	−0.913545	−	0.406737i	−0.0510687	−	0.0227373i
$321$	4.27621	−	0.908936i	0.238675	−	0.0507319i
$322$	0.569854	+	5.42180i	0.0317567	+	0.302145i
$323$	0.0455136	−	0.433033i	0.00253244	−	0.0240946i
$324$	−0.978148	−	0.207912i	−0.0543415	−	0.0115506i
$325$	−3.79887	−	2.76004i	−0.210723	−	0.153100i
$326$	−11.3832	−	8.27038i	−0.630457	−	0.458054i
$327$	2.64609	+	0.562444i	0.146329	+	0.0311032i
$328$	0.882238	−	8.39393i	0.0487134	−	0.463477i
$329$	1.38770	+	13.2031i	0.0765064	+	0.727909i
$330$	−1.59031	+	0.338031i	−0.0875438	+	0.0186080i
$331$	15.8490	+	7.05642i	0.871138	+	0.387856i	0.793098	−	0.609095i	$-0.208467\pi$
$331$	15.8490	+	7.05642i	0.871138	+	0.387856i	0.0780405	+	0.996950i	$0.475134\pi$
$332$	0.552499	−	0.613612i	0.0303223	−	0.0336763i
$333$	−0.678949	−	2.08959i	−0.0372062	−	0.114509i
$334$	12.6779	+	14.0803i	0.693705	+	0.770437i
$335$	−1.48269	+	2.56810i	−0.0810080	+	0.140310i
$336$	0.869684	+	1.50634i	0.0474451	+	0.0821774i
$337$	1.80138	−	5.54408i	0.0981275	−	0.302005i	−0.889929	−	0.456100i	$-0.849246\pi$
$337$	1.80138	−	5.54408i	0.0981275	−	0.302005i	0.988056	+	0.154094i	$0.0492460\pi$
$338$	−8.26690	+	3.68066i	−0.449660	+	0.200202i
$339$	−8.09920	+	5.88441i	−0.439888	+	0.319597i
$340$	−0.833329			−0.0451936
$341$	4.47291	+	7.87002i	0.242221	+	0.426185i
$342$	0.522504			0.0282538
$343$	15.4432	−	11.2202i	0.833855	−	0.605831i
$344$	0.562571	−	0.250473i	0.0303318	−	0.0135046i
$345$	0.968545	−	2.98088i	0.0521447	−	0.160485i
$346$	−1.11633	−	1.93354i	−0.0600142	−	0.103948i
$347$	−1.11548	+	1.93206i	−0.0598819	+	0.103718i	−0.894412	−	0.447244i	$-0.852406\pi$
$347$	−1.11548	+	1.93206i	−0.0598819	+	0.103718i	0.834530	+	0.550962i	$0.185739\pi$
$348$	2.44077	+	2.71075i	0.130839	+	0.145311i
$349$	−1.16212	−	3.57662i	−0.0622066	−	0.191452i	0.915123	−	0.403174i	$-0.132093\pi$
$349$	−1.16212	−	3.57662i	−0.0622066	−	0.191452i	−0.977330	+	0.211722i	$0.932093\pi$
$350$	−1.16386	+	1.29260i	−0.0622112	+	0.0690925i
$351$	−4.28970	−	1.90990i	−0.228967	−	0.101943i
$352$	−1.59031	+	0.338031i	−0.0847639	+	0.0180171i
$353$	3.19592	+	30.4072i	0.170102	+	1.61841i	0.663204	+	0.748439i	$0.269196\pi$
$353$	3.19592	+	30.4072i	0.170102	+	1.61841i	−0.493102	+	0.869972i	$0.664137\pi$
$354$	−0.742938	+	7.06858i	−0.0394867	+	0.375691i
$355$	−5.38409	−	1.14442i	−0.285758	−	0.0607397i
$356$	−7.14560	−	5.19158i	−0.378716	−	0.275153i
$357$	1.17264	+	0.851975i	0.0620628	+	0.0450913i
$358$	−2.69668	−	0.573197i	−0.142524	−	0.0302944i
$359$	0.713600	−	6.78945i	0.0376624	−	0.358334i	−0.959419	−	0.281985i	$-0.909007\pi$
$359$	0.713600	−	6.78945i	0.0376624	−	0.358334i	0.997081	−	0.0763486i	$-0.0243262\pi$
$360$	−0.104528	−	0.994522i	−0.00550913	−	0.0524159i
$361$	18.3178	−	3.89356i	0.964093	−	0.204924i
$362$	−3.01062	−	1.34041i	−0.158234	−	0.0704505i
$363$	5.59169	−	6.21020i	0.293487	−	0.325951i
$364$	2.52389	+	7.76774i	0.132288	+	0.407140i
$365$	0.709792	+	0.788304i	0.0371522	+	0.0412617i
$366$	0.756864	−	1.31093i	0.0395619	−	0.0685233i
$367$	−4.47175	−	7.74529i	−0.233423	−	0.404301i	0.725390	−	0.688338i	$-0.241659\pi$
$367$	−4.47175	−	7.74529i	−0.233423	−	0.404301i	−0.958813	+	0.284037i	$0.908326\pi$
$368$	0.968545	−	2.98088i	0.0504889	−	0.155389i
$369$	7.71048	−	3.43293i	0.401391	−	0.178711i
$370$	1.77751	−	1.29144i	0.0924084	−	0.0671386i
$371$	−5.23494			−0.271785
$372$	−5.10164	+	2.23008i	−0.264508	+	0.115625i
$373$	9.34115			0.483667			0.241833	−	0.970318i	$-0.422251\pi$
$373$	9.34115			0.483667			0.241833	+	0.970318i	$0.422251\pi$
$374$	−1.09611	+	0.796367i	−0.0566782	+	0.0411792i
$375$	0.913545	−	0.406737i	0.0471753	−	0.0210038i
$376$	2.35859	−	7.25898i	0.121635	−	0.374353i
$377$	8.56412	+	14.8335i	0.441075	+	0.763964i
$378$	−0.869684	+	1.50634i	−0.0447317	+	0.0774776i
$379$	−12.9696	−	14.4043i	−0.666206	−	0.739897i	0.311414	−	0.950274i	$-0.399197\pi$
$379$	−12.9696	−	14.4043i	−0.666206	−	0.739897i	−0.977620	+	0.210378i	$0.932531\pi$
$380$	0.161463	+	0.496931i	0.00828287	+	0.0254920i
$381$	14.3062	−	15.8887i	0.732929	−	0.814001i
$382$	−10.3776	−	4.62040i	−0.530963	−	0.236400i
$383$	30.6464	−	6.51409i	1.56596	−	0.332854i	0.658362	−	0.752701i	$-0.271250\pi$
$383$	30.6464	−	6.51409i	1.56596	−	0.332854i	0.907595	+	0.419847i	$0.137916\pi$
$384$	−0.104528	−	0.994522i	−0.00533420	−	0.0507515i
$385$	−0.295600	+	2.81244i	−0.0150652	+	0.143335i
$386$	−14.1497	−	3.00761i	−0.720200	−	0.153083i
$387$	0.498201	+	0.361964i	0.0253250	+	0.0183997i
$388$	−6.18384	−	4.49282i	−0.313937	−	0.228089i
$389$	−17.0595	−	3.62610i	−0.864950	−	0.183851i	−0.245989	−	0.969273i	$-0.579113\pi$
$389$	−17.0595	−	3.62610i	−0.864950	−	0.183851i	−0.618961	+	0.785422i	$0.712446\pi$
$390$	0.490830	−	4.66994i	0.0248542	−	0.236472i
$391$	−0.273016	−	2.59758i	−0.0138070	−	0.131365i
$392$	−3.88774	+	0.826366i	−0.196361	+	0.0417378i
$393$	8.00036	+	3.56199i	0.403565	+	0.179679i
$394$	5.04121	−	5.59884i	0.253973	−	0.282065i
$395$	−4.21210	−	12.9635i	−0.211934	−	0.652265i
$396$	−1.08790	−	1.20823i	−0.0546690	−	0.0607161i
$397$	7.93036	−	13.7358i	0.398013	−	0.689379i	−0.595467	−	0.803380i	$-0.703033\pi$
$397$	7.93036	−	13.7358i	0.398013	−	0.689379i	0.993481	+	0.114000i	$0.0363664\pi$
$398$	−5.46021	−	9.45737i	−0.273696	−	0.474055i
$399$	0.280843	−	0.864346i	0.0140597	−	0.0432714i
$400$	0.913545	−	0.406737i	0.0456773	−	0.0203368i
$401$	18.6071	−	13.5188i	0.929193	−	0.675098i	−0.0166022	−	0.999862i	$-0.505285\pi$
$401$	18.6071	−	13.5188i	0.929193	−	0.675098i	0.945795	+	0.324764i	$0.105285\pi$
$402$	−2.96538			−0.147900
$403$	−25.6093	+	5.26225i	−1.27569	+	0.262131i
$404$	−12.8563			−0.639625
$405$	0.809017	−	0.587785i	0.0402004	−	0.0292073i
$406$	5.79612	−	2.58060i	0.287657	−	0.128073i
$407$	1.10386	−	3.39734i	0.0547164	−	0.168400i
$408$	−0.416665	−	0.721684i	−0.0206280	−	0.0357287i
$409$	−13.8213	+	23.9393i	−0.683421	+	1.18372i	0.290509	+	0.956872i	$0.406175\pi$
$409$	−13.8213	+	23.9393i	−0.683421	+	1.18372i	−0.973930	+	0.226848i	$0.927158\pi$
$410$	5.64758	+	6.27227i	0.278914	+	0.309765i
$411$	4.01676	+	12.3623i	0.198132	+	0.609789i
$412$	3.89872	−	4.32996i	0.192076	−	0.213322i
$413$	11.2938	+	5.02832i	0.555731	+	0.247427i
$414$	3.06579	−	0.651653i	0.150675	−	0.0320270i
$415$	0.0863088	+	0.821173i	0.00423673	+	0.0403098i
$416$	0.490830	−	4.66994i	0.0240649	−	0.228963i
$417$	9.88724	+	2.10160i	0.484180	+	0.102916i
$418$	0.687267	+	0.499329i	0.0336153	+	0.0244230i
$419$	29.4370	+	21.3872i	1.43809	+	1.04483i	0.988437	+	0.151630i	$0.0484521\pi$
$419$	29.4370	+	21.3872i	1.43809	+	1.04483i	0.449652	+	0.893204i	$0.351548\pi$
$420$	−1.70136	−	0.361635i	−0.0830178	−	0.0176460i
$421$	−1.40649	+	13.3819i	−0.0685484	+	0.652194i	0.905265	+	0.424847i	$0.139672\pi$
$421$	−1.40649	+	13.3819i	−0.0685484	+	0.652194i	−0.973814	+	0.227347i	$0.926995\pi$
$422$	−0.751268	−	7.14784i	−0.0365712	−	0.347951i
$423$	7.46576	−	1.58690i	0.362998	−	0.0771575i
$424$	2.74948	+	1.22415i	0.133527	+	0.0594499i
$425$	0.557606	−	0.619284i	0.0270479	−	0.0300397i
$426$	−1.70094	−	5.23497i	−0.0824110	−	0.253635i
$427$	−1.76177	−	1.95665i	−0.0852583	−	0.0946889i
$428$	−2.18587	+	3.78604i	−0.105658	+	0.183005i
$429$	−3.81720	−	6.61158i	−0.184296	−	0.319210i
$430$	−0.190296	+	0.585671i	−0.00917688	+	0.0282435i
$431$	−8.22733	+	3.66304i	−0.396296	+	0.176443i	−0.595202	−	0.803576i	$-0.702928\pi$
$431$	−8.22733	+	3.66304i	−0.396296	+	0.176443i	0.198906	+	0.980019i	$0.436261\pi$
$432$	0.809017	−	0.587785i	0.0389238	−	0.0282798i
$433$	9.59495			0.461104			0.230552	−	0.973060i	$-0.425947\pi$
$433$	9.59495			0.461104			0.230552	+	0.973060i	$0.425947\pi$
$434$	0.946988	+	9.63798i	0.0454569	+	0.462638i
$435$	−3.64767			−0.174893
$436$	−2.18856	+	1.59008i	−0.104813	+	0.0761510i
$437$	−1.49609	+	0.666102i	−0.0715677	+	0.0318640i
$438$	−0.327795	+	1.00885i	−0.0156627	+	0.0482047i
$439$	−3.51439	−	6.08709i	−0.167732	−	0.290521i	0.769890	−	0.638177i	$-0.220311\pi$
$439$	−3.51439	−	6.08709i	−0.167732	−	0.290521i	−0.937622	+	0.347656i	$0.886978\pi$
$440$	0.812920	−	1.40802i	0.0387545	−	0.0671247i
$441$	−2.65953	−	2.95370i	−0.126644	−	0.140653i
$442$	−1.20919	−	3.72152i	−0.0575155	−	0.177014i
$443$	−12.6594	+	14.0597i	−0.601465	+	0.667995i	−0.964592	−	0.263745i	$-0.915042\pi$
$443$	−12.6594	+	14.0597i	−0.601465	+	0.667995i	0.363127	+	0.931740i	$0.381709\pi$
$444$	2.00717	+	0.893651i	0.0952562	+	0.0424108i
$445$	8.63943	−	1.83637i	0.409548	−	0.0870522i
$446$	0.934405	+	8.89027i	0.0442454	+	0.420967i
$447$	−1.66283	+	15.8208i	−0.0786492	+	0.748297i
$448$	−1.70136	−	0.361635i	−0.0803816	−	0.0170856i
$449$	−15.1197	−	10.9851i	−0.713544	−	0.518420i	0.170771	−	0.985311i	$-0.445374\pi$
$449$	−15.1197	−	10.9851i	−0.713544	−	0.518420i	−0.884315	+	0.466890i	$0.845374\pi$
$450$	0.809017	+	0.587785i	0.0381374	+	0.0277085i
$451$	13.4225	+	2.85304i	0.632041	+	0.134344i
$452$	1.04645	−	9.95632i	0.0492209	−	0.468306i
$453$	−1.67115	−	15.9000i	−0.0785177	−	0.747046i
$454$	7.31531	−	1.55492i	0.343325	−	0.0729759i
$455$	−7.46137	−	3.32202i	−0.349794	−	0.155738i
$456$	−0.349624	+	0.388297i	−0.0163726	+	0.0181836i
$457$	6.74555	+	20.7607i	0.315543	+	0.971143i	0.975530	+	0.219866i	$0.0705619\pi$
$457$	6.74555	+	20.7607i	0.315543	+	0.971143i	−0.659987	+	0.751277i	$0.729438\pi$
$458$	−11.8394	−	13.1490i	−0.553220	−	0.614413i
$459$	0.416665	−	0.721684i	0.0194482	−	0.0336853i
$460$	1.56714	+	2.71436i	0.0730682	+	0.126558i
$461$	5.22104	−	16.0687i	0.243168	−	0.748395i	−0.752764	−	0.658290i	$-0.771280\pi$
$461$	5.22104	−	16.0687i	0.243168	−	0.748395i	0.995932	−	0.0901043i	$-0.0287200\pi$
$462$	−2.58345	+	1.15022i	−0.120193	+	0.0535133i
$463$	−11.9150	+	8.65677i	−0.553738	+	0.402314i	−0.829162	−	0.559009i	$-0.811182\pi$
$463$	−11.9150	+	8.65677i	−0.553738	+	0.402314i	0.275424	+	0.961323i	$0.411182\pi$
$464$	−3.64767			−0.169339
$465$	1.75639	−	5.28347i	0.0814505	−	0.245015i
$466$	1.34394			0.0622566
$467$	−13.2104	+	9.59790i	−0.611303	+	0.444138i	−0.849873	−	0.526988i	$-0.823321\pi$
$467$	−13.2104	+	9.59790i	−0.611303	+	0.444138i	0.238570	+	0.971125i	$0.423321\pi$
$468$	4.28970	−	1.90990i	0.198292	−	0.0882851i
$469$	−1.59388	+	4.90544i	−0.0735983	+	0.226512i
$470$	3.81627	+	6.60998i	0.176032	+	0.304896i
$471$	6.52569	−	11.3028i	0.300688	−	0.520807i
$472$	−4.75586	−	5.28191i	−0.218906	−	0.243120i
$473$	0.309391	+	0.952207i	0.0142258	+	0.0437825i
$474$	9.12068	−	10.1295i	0.418927	−	0.465265i
$475$	−0.477332	−	0.212522i	−0.0219015	−	0.00975117i
$476$	−1.41779	+	0.301361i	−0.0649844	+	0.0138129i
$477$	0.314597	+	2.99319i	0.0144044	+	0.137049i
$478$	0.817321	−	7.77629i	0.0373834	−	0.355679i
$479$	17.1891	+	3.65366i	0.785392	+	0.166940i	0.583116	−	0.812389i	$-0.301833\pi$
$479$	17.1891	+	3.65366i	0.785392	+	0.166940i	0.202275	+	0.979329i	$0.435166\pi$
$480$	0.809017	+	0.587785i	0.0369264	+	0.0268286i
$481$	8.34659	+	6.06415i	0.380572	+	0.276502i
$482$	−2.04358	−	0.434376i	−0.0930825	−	0.0197853i
$483$	0.569854	−	5.42180i	0.0259293	−	0.246700i
$484$	0.873507	+	8.31086i	0.0397049	+	0.377767i
$485$	7.47662	−	1.58920i	0.339496	−	0.0721620i
$486$	0.913545	+	0.406737i	0.0414393	+	0.0184499i
$487$	25.8833	−	28.7463i	1.17288	−	1.30262i	0.228587	−	0.973524i	$-0.426590\pi$
$487$	25.8833	−	28.7463i	1.17288	−	1.30262i	0.944297	−	0.329095i	$-0.106744\pi$
$488$	0.467768	+	1.43964i	0.0211749	+	0.0651695i
$489$	9.41495	+	10.4564i	0.425759	+	0.472853i
$490$	1.98730	−	3.44210i	0.0897770	−	0.155498i
$491$	−14.0457	−	24.3279i	−0.633875	−	1.09790i	−0.986752	−	0.162234i	$-0.948130\pi$
$491$	−14.0457	−	24.3279i	−0.633875	−	1.09790i	0.352877	−	0.935670i	$-0.385203\pi$
$492$	−2.60816	+	8.02708i	−0.117585	+	0.361889i
$493$	−2.77692	+	1.23636i	−0.125066	+	0.0556830i
$494$	−1.98493	+	1.44213i	−0.0893061	+	0.0648847i
$495$	1.62584			0.0730761
$496$	1.75639	−	5.28347i	0.0788641	−	0.237235i
$497$	−9.57413			−0.429458
$498$	−0.668003	+	0.485332i	−0.0299339	+	0.0217483i
$499$	−11.0701	+	4.92872i	−0.495565	+	0.220640i	−0.639272	−	0.768980i	$-0.720764\pi$
$499$	−11.0701	+	4.92872i	−0.495565	+	0.220640i	0.143707	+	0.989620i	$0.454098\pi$
$500$	−0.309017	+	0.951057i	−0.0138197	+	0.0425325i
$501$	−9.47343	−	16.4085i	−0.423241	−	0.733076i
$502$	−2.18812	+	3.78993i	−0.0976604	+	0.169153i
$503$	−0.891634	−	0.990260i	−0.0397560	−	0.0441535i	0.722939	−	0.690912i	$-0.242791\pi$
$503$	−0.891634	−	0.990260i	−0.0397560	−	0.0441535i	−0.762695	+	0.646759i	$0.776124\pi$
$504$	−0.537494	−	1.65424i	−0.0239419	−	0.0736856i
$505$	8.60254	−	9.55409i	0.382808	−	0.425151i
$506$	4.65528	+	2.07266i	0.206952	+	0.0921411i
$507$	8.85150	−	1.88145i	0.393109	−	0.0835579i
$508$	2.23485	+	21.2632i	0.0991554	+	0.943401i
$509$	3.21830	−	30.6201i	0.142649	−	1.35721i	−0.655702	−	0.755020i	$-0.727627\pi$
$509$	3.21830	−	30.6201i	0.142649	−	1.35721i	0.798351	−	0.602192i	$-0.205706\pi$
$510$	0.815119	+	0.173259i	0.0360941	+	0.00767203i
$511$	1.49269	+	1.08450i	0.0660327	+	0.0479755i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−0.511087	−	0.108635i	−0.0225650	−	0.00479634i
$514$	0.916191	−	8.71698i	0.0404115	−	0.384489i
$515$	0.609039	+	5.79462i	0.0268375	+	0.255341i
$516$	−0.602354	+	0.128034i	−0.0265171	+	0.00563639i
$517$	11.3365	+	5.04732i	0.498577	+	0.221981i
$518$	2.55715	−	2.84001i	0.112355	−	0.124783i
$519$	0.689929	+	2.12338i	0.0302845	+	0.0932061i
$520$	3.14201	+	3.48956i	0.137786	+	0.153027i
$521$	12.6176	−	21.8543i	0.552786	−	0.957453i	−0.445286	−	0.895388i	$-0.646898\pi$
$521$	12.6176	−	21.8543i	0.552786	−	0.957453i	0.998072	−	0.0620648i	$-0.0197686\pi$
$522$	−1.82384	−	3.15898i	−0.0798271	−	0.138265i
$523$	0.0312539	−	0.0961895i	0.00136664	−	0.00420607i	−0.950371	−	0.311119i	$-0.899296\pi$
$523$	0.0312539	−	0.0961895i	0.00136664	−	0.00420607i	0.951738	+	0.306913i	$0.0992961\pi$
$524$	−8.00036	+	3.56199i	−0.349497	+	0.155606i
$525$	1.40718	−	1.02237i	0.0614143	−	0.0446201i
$526$	14.6832			0.640217
$527$	−0.453701	−	4.61755i	−0.0197635	−	0.201143i
$528$	1.62584			0.0707556
$529$	10.6598	−	7.74483i	0.463472	−	0.336732i
$530$	−2.74948	+	1.22415i	−0.119430	+	0.0531736i
$531$	2.19634	−	6.75965i	0.0953132	−	0.293344i
$532$	0.454414	+	0.787068i	0.0197013	+	0.0341237i
$533$	−19.8161	+	34.3225i	−0.858330	+	1.48667i
$534$	5.91006	+	6.56378i	0.255753	+	0.284043i
$535$	−1.35094	−	4.15777i	−0.0584063	−	0.179756i
$536$	1.98423	−	2.20371i	0.0857056	−	0.0951857i
$537$	2.51858	+	1.12134i	0.108685	+	0.0483895i
$538$	−13.3714	+	2.84218i	−0.576482	+	0.122535i
$539$	−0.675470	−	6.42666i	−0.0290945	−	0.276816i
$540$	−0.104528	+	0.994522i	−0.00449819	+	0.0427974i
$541$	19.4970	+	4.14421i	0.838241	+	0.178174i	0.606979	−	0.794718i	$-0.292381\pi$
$541$	19.4970	+	4.14421i	0.838241	+	0.178174i	0.231262	+	0.972892i	$0.425715\pi$
$542$	24.3393	+	17.6835i	1.04546	+	0.759572i
$543$	2.66614	+	1.93706i	0.114415	+	0.0831273i
$544$	0.815119	+	0.173259i	0.0349479	+	0.00742841i
$545$	0.282771	−	2.69039i	0.0121126	−	0.115243i
$546$	−0.853735	−	8.12274i	−0.0365365	−	0.347621i
$547$	−9.51332	+	2.02212i	−0.406760	+	0.0864595i	−0.406748	−	0.913540i	$-0.633337\pi$
$547$	−9.51332	+	2.02212i	−0.406760	+	0.0864595i	−1.22035e−5		1.00000i	$0.500004\pi$
$548$	−11.8747	−	5.28697i	−0.507264	−	0.225848i
$549$	−1.01288	+	1.12492i	−0.0432288	+	0.0480104i
$550$	0.502412	+	1.54627i	0.0214229	+	0.0659330i
$551$	1.27531	+	1.41638i	0.0543302	+	0.0603397i
$552$	−1.56714	+	2.71436i	−0.0667019	+	0.115531i
$553$	−11.8544	−	20.5323i	−0.504098	−	0.873124i
$554$	−5.30176	+	16.3171i	−0.225250	+	0.693249i
$555$	−2.00717	+	0.893651i	−0.0851997	+	0.0379334i
$556$	−8.17764	+	5.94141i	−0.346809	+	0.251972i
$557$	−20.5430			−0.870434			−0.435217	−	0.900326i	$-0.643328\pi$
$557$	−20.5430			−0.870434			−0.435217	+	0.900326i	$0.643328\pi$
$558$	5.45382	−	1.12066i	0.230878	−	0.0474414i
$559$	−2.89164			−0.122303
$560$	1.40718	−	1.02237i	0.0594641	−	0.0432032i
$561$	1.23773	−	0.551071i	0.0522569	−	0.0232663i
$562$	10.0397	−	30.8990i	0.423500	−	1.30340i
$563$	−2.86745	−	4.96656i	−0.120848	−	0.209316i	0.799254	−	0.600993i	$-0.205228\pi$
$563$	−2.86745	−	4.96656i	−0.120848	−	0.209316i	−0.920103	+	0.391678i	$0.871895\pi$
$564$	−3.81627	+	6.60998i	−0.160694	+	0.278330i
$565$	6.69877	+	7.43974i	0.281820	+	0.312992i
$566$	−4.12697	−	12.7015i	−0.173470	−	0.533884i
$567$	1.16386	−	1.29260i	0.0488777	−	0.0542842i
$568$	5.02849	+	2.23883i	0.210991	+	0.0939392i
$569$	23.9582	−	5.09248i	1.00438	−	0.213488i	0.323773	−	0.946135i	$-0.395049\pi$
$569$	23.9582	−	5.09248i	1.00438	−	0.213488i	0.680609	+	0.732647i	$0.261715\pi$
$570$	−0.0546166	−	0.519642i	−0.00228764	−	0.0217654i
$571$	−0.435244	+	4.14107i	−0.0182144	+	0.173298i	−0.999847	−	0.0174819i	$-0.994435\pi$
$571$	−0.435244	+	4.14107i	−0.0182144	+	0.173298i	0.981633	+	0.190780i	$0.0611017\pi$
$572$	7.46757	+	1.58728i	0.312235	+	0.0663675i
$573$	9.19017	+	6.67705i	0.383925	+	0.278938i
$574$	11.8768	+	8.62902i	0.495729	+	0.360168i
$575$	−3.06579	−	0.651653i	−0.127852	−	0.0271758i
$576$	−0.104528	+	0.994522i	−0.00435535	+	0.0414384i
$577$	2.81572	+	26.7898i	0.117220	+	1.11527i	0.882087	+	0.471086i	$0.156138\pi$
$577$	2.81572	+	26.7898i	0.117220	+	1.11527i	−0.764867	+	0.644188i	$0.777195\pi$
$578$	−15.9492	+	3.39012i	−0.663401	+	0.141010i
$579$	13.2152	+	5.88377i	0.549203	+	0.244521i
$580$	2.44077	−	2.71075i	0.101347	−	0.112558i
$581$	0.443807	+	1.36590i	0.0184122	+	0.0566670i
$582$	5.11460	+	5.68034i	0.212007	+	0.235458i
$583$	−2.44663	+	4.23769i	−0.101329	+	0.175507i
$584$	−0.530384	−	0.918652i	−0.0219474	−	0.0380141i
$585$	−1.45104	+	4.46584i	−0.0599931	+	0.184640i
$586$	−11.9929	+	5.33958i	−0.495422	+	0.220576i
$587$	−13.6635	+	9.92710i	−0.563952	+	0.409735i	−0.832903	−	0.553419i	$-0.813323\pi$
$587$	−13.6635	+	9.92710i	−0.563952	+	0.409735i	0.268951	+	0.963154i	$0.413323\pi$
$588$	3.97460			0.163910
$589$	−2.66563	+	1.16523i	−0.109835	+	0.0480124i
$590$	7.10752			0.292612
$591$	−6.09511	+	4.42836i	−0.250720	+	0.182158i
$592$	−2.00717	+	0.893651i	−0.0824943	+	0.0367288i
$593$	9.37991	−	28.8684i	0.385187	−	1.18548i	−0.551158	−	0.834401i	$-0.685814\pi$
$593$	9.37991	−	28.8684i	0.385187	−	1.18548i	0.936345	−	0.351082i	$-0.114186\pi$
$594$	0.812920	+	1.40802i	0.0333545	+	0.0577717i
$595$	0.724733	−	1.25527i	0.0297112	−	0.0514612i
$596$	−10.6445	−	11.8219i	−0.436015	−	0.484243i
$597$	3.37460	+	10.3859i	0.138113	+	0.425068i
$598$	−9.84794	+	10.9372i	−0.402712	+	0.447257i
$599$	20.0724	+	8.93682i	0.820137	+	0.365149i	0.773526	−	0.633765i	$-0.218491\pi$
$599$	20.0724	+	8.93682i	0.820137	+	0.365149i	0.0466111	+	0.998913i	$0.485158\pi$
$600$	−0.978148	+	0.207912i	−0.0399327	+	0.00848796i
$601$	3.99819	+	38.0402i	0.163089	+	1.55169i	0.703748	+	0.710450i	$0.251508\pi$
$601$	3.99819	+	38.0402i	0.163089	+	1.55169i	−0.540659	+	0.841242i	$0.681825\pi$
$602$	−0.111963	+	1.06525i	−0.00456326	+	0.0434165i
$603$	2.90058	+	0.616537i	0.118121	+	0.0251073i
$604$	12.9342	+	9.39725i	0.526285	+	0.382369i
$605$	−6.76067	−	4.91191i	−0.274860	−	0.199698i
$606$	12.5754	+	2.67297i	0.510839	+	0.108582i
$607$	0.577832	−	5.49771i	0.0234535	−	0.223145i	−0.976517	−	0.215441i	$-0.930881\pi$
$607$	0.577832	−	5.49771i	0.0234535	−	0.223145i	0.999970	−	0.00770395i	$-0.00245227\pi$
$608$	−0.0546166	−	0.519642i	−0.00221500	−	0.0210743i
$609$	−6.20600	+	1.31913i	−0.251480	+	0.0534537i
$610$	−1.38286	−	0.615689i	−0.0559904	−	0.0249285i
$611$	−23.9816	+	26.6342i	−0.970190	+	1.07750i
$612$	0.257513	+	0.792543i	0.0104093	+	0.0320367i
$613$	−1.69067	−	1.87768i	−0.0682854	−	0.0758387i	0.708034	−	0.706178i	$-0.249582\pi$
$613$	−1.69067	−	1.87768i	−0.0682854	−	0.0758387i	−0.776319	+	0.630340i	$0.782916\pi$
$614$	6.59513	−	11.4231i	0.266158	−	0.460999i
$615$	−4.22008	−	7.30940i	−0.170170	−	0.294743i
$616$	0.873880	−	2.68953i	0.0352096	−	0.108364i
$617$	−34.6300	+	15.4183i	−1.39415	+	0.620717i	−0.959969	−	0.280108i	$-0.909630\pi$
$617$	−34.6300	+	15.4183i	−1.39415	+	0.620717i	−0.434184	+	0.900824i	$0.642963\pi$
$618$	−4.71377	+	3.42475i	−0.189616	+	0.137764i
$619$	22.6595			0.910761			0.455381	−	0.890297i	$-0.349503\pi$
$619$	22.6595			0.910761			0.455381	+	0.890297i	$0.349503\pi$
$620$	2.75113	+	4.84058i	0.110488	+	0.194403i
$621$	−3.13428			−0.125774
$622$	−3.43107	+	2.49282i	−0.137574	+	0.0999530i
$623$	14.0347	−	6.24864i	0.562287	−	0.250347i
$624$	−1.45104	+	4.46584i	−0.0580881	+	0.178777i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	4.20388	−	7.28134i	0.168021	−	0.291021i
$627$	−0.568432	−	0.631308i	−0.0227010	−	0.0252120i
$628$	4.03310	+	12.4126i	0.160938	+	0.495317i
$629$	−1.22513	+	1.36064i	−0.0488491	+	0.0542524i
$630$	1.58899	+	0.707465i	0.0633069	+	0.0281861i
$631$	7.73546	−	1.64422i	0.307944	−	0.0654555i	−0.0513477	−	0.998681i	$-0.516352\pi$
$631$	7.73546	−	1.64422i	0.307944	−	0.0654555i	0.359292	+	0.933225i	$0.383018\pi$
$632$	1.42479	+	13.5560i	0.0566751	+	0.539228i
$633$	−0.751268	+	7.14784i	−0.0298602	+	0.284101i
$634$	−0.359925	−	0.0765045i	−0.0142945	−	0.00303838i
$635$	−17.2970	−	12.5670i	−0.686411	−	0.498707i
$636$	−2.43488	−	1.76905i	−0.0965494	−	0.0701472i
$637$	18.2555	+	3.88033i	0.723311	+	0.153744i
$638$	0.619910	−	5.89805i	0.0245425	−	0.233506i
$639$	0.575364	+	5.47422i	0.0227610	+	0.216557i
$640$	−0.978148	+	0.207912i	−0.0386647	+	0.00821843i
$641$	−6.34187	−	2.82358i	−0.250489	−	0.111525i	0.277652	−	0.960682i	$-0.410444\pi$
$641$	−6.34187	−	2.82358i	−0.250489	−	0.111525i	−0.528140	+	0.849157i	$0.677111\pi$
$642$	2.92527	−	3.24884i	0.115451	−	0.128221i
$643$	13.3662	+	41.1371i	0.527113	+	1.62229i	0.760099	+	0.649807i	$0.225150\pi$
$643$	13.3662	+	41.1371i	0.527113	+	1.62229i	−0.232986	+	0.972480i	$0.574850\pi$
$644$	3.64787	+	4.05138i	0.143746	+	0.159647i
$645$	0.307905	−	0.533307i	0.0121238	−	0.0209990i
$646$	−0.217709	−	0.377083i	−0.00856565	−	0.0148361i
$647$	3.62333	−	11.1515i	0.142448	−	0.438410i	−0.854226	−	0.519902i	$-0.825969\pi$
$647$	3.62333	−	11.1515i	0.142448	−	0.438410i	0.996674	+	0.0814921i	$0.0259686\pi$
$648$	−0.913545	+	0.406737i	−0.0358875	+	0.0159781i
$649$	9.34875	−	6.79226i	0.366970	−	0.266620i
$650$	−4.69566			−0.184179
$651$	1.07755	−	9.62426i	0.0422327	−	0.377204i
$652$	−14.0704			−0.551040
$653$	−17.3822	+	12.6289i	−0.680219	+	0.494208i	−0.873430	−	0.486949i	$-0.838110\pi$
$653$	−17.3822	+	12.6289i	−0.680219	+	0.494208i	0.193211	+	0.981157i	$0.438110\pi$
$654$	2.47133	−	1.10031i	0.0966366	−	0.0430254i
$655$	2.70621	−	8.32886i	0.105740	−	0.325436i
$656$	−4.22008	−	7.30940i	−0.164767	−	0.285384i
$657$	0.530384	−	0.918652i	0.0206922	−	0.0358400i
$658$	8.88325	+	9.86585i	0.346305	+	0.384611i
$659$	10.0526	+	30.9389i	0.391596	+	1.20521i	0.931581	+	0.363533i	$0.118430\pi$
$659$	10.0526	+	30.9389i	0.391596	+	1.20521i	−0.539986	+	0.841674i	$0.681570\pi$
$660$	−1.08790	+	1.20823i	−0.0423464	+	0.0470305i
$661$	42.8455	+	19.0760i	1.66650	+	0.741972i	0.999994	−	0.00353040i	$-0.00112376\pi$
$661$	42.8455	+	19.0760i	1.66650	+	0.741972i	0.666503	+	0.745502i	$0.267790\pi$
$662$	16.9697	−	3.60703i	0.659548	−	0.140191i
$663$	0.409023	+	3.89160i	0.0158852	+	0.151137i
$664$	0.0863088	−	0.821173i	0.00334943	−	0.0318677i
$665$	−0.888967	−	0.188956i	−0.0344727	−	0.00732739i
$666$	−1.77751	−	1.29144i	−0.0688771	−	0.0500422i
$667$	9.24935	+	6.72004i	0.358136	+	0.260201i
$668$	18.5328	+	3.93927i	0.717056	+	0.152415i
$669$	0.934405	−	8.89027i	0.0361262	−	0.343718i
$670$	0.309967	+	2.94914i	0.0119751	+	0.113935i
$671$	−2.40730	+	0.511688i	−0.0929328	+	0.0197535i
$672$	1.58899	+	0.707465i	0.0612967	+	0.0272910i
$673$	−6.52902	+	7.25121i	−0.251675	+	0.279513i	−0.855723	−	0.517435i	$-0.826887\pi$
$673$	−6.52902	+	7.25121i	−0.251675	+	0.279513i	0.604048	+	0.796948i	$0.293554\pi$
$674$	−1.80138	−	5.54408i	−0.0693866	−	0.213550i
$675$	−0.669131	−	0.743145i	−0.0257548	−	0.0286037i
$676$	−4.52463	+	7.83688i	−0.174024	+	0.301419i
$677$	−24.3590	−	42.1911i	−0.936194	−	1.62154i	−0.772491	−	0.635026i	$-0.780989\pi$
$677$	−24.3590	−	42.1911i	−0.936194	−	1.62154i	−0.163703	−	0.986510i	$-0.552344\pi$
$678$	−3.09362	+	9.52118i	−0.118810	+	0.365659i
$679$	12.1457	−	5.40761i	0.466109	−	0.207525i
$680$	−0.674178	+	0.489819i	−0.0258535	+	0.0187837i
$681$	−7.47874			−0.286586
$682$	8.24454	+	3.73787i	0.315700	+	0.143130i
$683$	−3.84194			−0.147008			−0.0735039	−	0.997295i	$-0.523418\pi$
$683$	−3.84194			−0.147008			−0.0735039	+	0.997295i	$0.523418\pi$
$684$	0.422715	−	0.307120i	0.0161629	−	0.0117430i
$685$	11.8747	−	5.28697i	0.453710	−	0.202005i
$686$	5.89878	−	18.1546i	0.225217	−	0.693145i
$687$	8.84688	+	15.3232i	0.337529	+	0.584618i
$688$	0.307905	−	0.533307i	0.0117388	−	0.0203322i
$689$	−9.45645	−	10.5025i	−0.360262	−	0.400112i
$690$	−0.968545	−	2.98088i	−0.0368719	−	0.113480i
$691$	−2.74183	+	3.04511i	−0.104304	+	0.115842i	−0.793036	−	0.609174i	$-0.791501\pi$
$691$	−2.74183	+	3.04511i	−0.104304	+	0.115842i	0.688732	+	0.725016i	$0.258168\pi$
$692$	−2.03963	−	0.908103i	−0.0775352	−	0.0345209i
$693$	2.76614	−	0.587961i	0.105077	−	0.0223348i
$694$	0.233198	+	2.21873i	0.00885207	+	0.0842218i
$695$	1.05659	−	10.0527i	0.0400786	−	0.381323i
$696$	3.56796	+	0.758394i	0.135243	+	0.0287468i
$697$	−5.69017	−	4.13415i	−0.215531	−	0.156592i
$698$	−3.04246	−	2.21048i	−0.115159	−	0.0836677i
$699$	−1.31457	−	0.279420i	−0.0497215	−	0.0105686i
$700$	−0.181813	+	1.72984i	−0.00687190	+	0.0653818i
$701$	0.758744	+	7.21896i	0.0286574	+	0.272656i	0.999462	+	0.0327865i	$0.0104381\pi$
$701$	0.758744	+	7.21896i	0.0286574	+	0.272656i	−0.970805	+	0.239870i	$0.922895\pi$
$702$	−4.59305	+	0.976283i	−0.173354	+	0.0368474i
$703$	1.04876	+	0.466937i	0.0395546	+	0.0176108i
$704$	−1.08790	+	1.20823i	−0.0410018	+	0.0455371i
$705$	−2.35859	−	7.25898i	−0.0888295	−	0.273389i
$706$	20.4584	+	22.7214i	0.769964	+	0.855131i
$707$	11.1809	−	19.3659i	0.420502	−	0.728330i
$708$	3.55376	+	6.15529i	0.133558	+	0.231330i
$709$	−13.1747	+	40.5477i	−0.494788	+	1.52280i	0.322499	+	0.946570i	$0.395477\pi$
$709$	−13.1747	+	40.5477i	−0.494788	+	1.52280i	−0.817287	+	0.576230i	$0.804523\pi$
$710$	−5.02849	+	2.23883i	−0.188716	+	0.0840218i
$711$	−11.0274	+	8.01189i	−0.413561	+	0.300469i
$712$	−8.83244			−0.331010
$713$	−14.1873	+	10.1615i	−0.531318	+	0.380550i
$714$	1.44947			0.0542449
$715$	−6.17636	+	4.48739i	−0.230983	+	0.167819i
$716$	−2.51858	+	1.12134i	−0.0941236	+	0.0419065i
$717$	−2.41624	+	7.43642i	−0.0902362	+	0.277718i
$718$	−3.41343	−	5.91223i	−0.127388	−	0.220642i
$719$	−20.1630	+	34.9234i	−0.751955	+	1.30242i	0.194919	+	0.980819i	$0.437555\pi$
$719$	−20.1630	+	34.9234i	−0.751955	+	1.30242i	−0.946874	+	0.321604i	$0.895778\pi$
$720$	−0.669131	−	0.743145i	−0.0249370	−	0.0276954i
$721$	3.13173	+	9.63848i	0.116632	+	0.358956i
$722$	12.5308	−	13.9169i	0.466348	−	0.517932i
$723$	1.90861	+	0.849768i	0.0709820	+	0.0316032i
$724$	−3.22351	+	0.685179i	−0.119801	+	0.0254645i
$725$	0.381286	+	3.62769i	0.0141606	+	0.134729i
$726$	0.873507	−	8.31086i	0.0324189	−	0.308445i
$727$	−8.37358	−	1.77986i	−0.310559	−	0.0660113i	0.0499957	−	0.998749i	$-0.484079\pi$
$727$	−8.37358	−	1.77986i	−0.310559	−	0.0660113i	−0.360555	+	0.932738i	$0.617413\pi$
$728$	6.60763	+	4.80073i	0.244895	+	0.177927i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	1.03759	+	0.220546i	0.0384028	+	0.00816277i
$731$	0.0536412	−	0.510362i	0.00198399	−	0.0188764i
$732$	−0.158228	−	1.50544i	−0.00584827	−	0.0556425i
$733$	22.7812	−	4.84229i	0.841442	−	0.178854i	0.233024	−	0.972471i	$-0.425138\pi$
$733$	22.7812	−	4.84229i	0.841442	−	0.178854i	0.608418	+	0.793617i	$0.291804\pi$
$734$	−8.17029	−	3.63765i	−0.301571	−	0.134268i
$735$	−2.65953	+	2.95370i	−0.0980981	+	0.108949i
$736$	−0.968545	−	2.98088i	−0.0357011	−	0.109877i
$737$	3.22604	+	3.58288i	0.118833	+	0.131977i
$738$	4.22008	−	7.30940i	0.155343	−	0.269063i
$739$	−21.6371	−	37.4765i	−0.795932	−	1.37859i	−0.922246	−	0.386604i	$-0.873648\pi$
$739$	−21.6371	−	37.4765i	−0.795932	−	1.37859i	0.126314	−	0.991990i	$-0.459685\pi$
$740$	0.678949	−	2.08959i	0.0249586	−	0.0768148i
$741$	2.24139	−	0.997930i	0.0823395	−	0.0366599i
$742$	−4.23516	+	3.07702i	−0.155477	+	0.112961i
$743$	3.79068			0.139067			0.0695333	−	0.997580i	$-0.477849\pi$
$743$	3.79068			0.139067			0.0695333	+	0.997580i	$0.477849\pi$
$744$	−2.81650	+	4.80284i	−0.103258	+	0.176081i
$745$	15.9079			0.582821
$746$	7.55715	−	5.49059i	0.276687	−	0.201025i
$747$	0.754311	−	0.335841i	0.0275988	−	0.0122878i
$748$	−0.418675	+	1.28855i	−0.0153083	+	0.0471140i
$749$	−3.80203	−	6.58532i	−0.138923	−	0.240622i
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	−4.78284	−	5.31188i	−0.174528	−	0.193833i	0.649534	−	0.760333i	$-0.274964\pi$
$751$	−4.78284	−	5.31188i	−0.174528	−	0.193833i	−0.824062	+	0.566499i	$0.808297\pi$
$752$	−2.35859	−	7.25898i	−0.0860088	−	0.264708i
$753$	2.92827	−	3.25217i	0.106712	−	0.118516i
$754$	15.6474	+	6.96668i	0.569846	+	0.253712i
$755$	−15.6382	+	3.32400i	−0.569132	+	0.120973i
$756$	0.181813	+	1.72984i	0.00661249	+	0.0629137i
$757$	1.64401	−	15.6417i	0.0597525	−	0.568507i	−0.923158	−	0.384421i	$-0.874401\pi$
$757$	1.64401	−	15.6417i	0.0597525	−	0.568507i	0.982910	−	0.184086i	$-0.0589324\pi$
$758$	−18.9593	−	4.02992i	−0.688632	−	0.146373i
$759$	−4.12262	−	2.99526i	−0.149642	−	0.108721i
$760$	0.422715	+	0.307120i	0.0153335	+	0.0111404i
$761$	−1.45671	−	0.309633i	−0.0528057	−	0.0112242i	0.181433	−	0.983403i	$-0.441926\pi$
$761$	−1.45671	−	0.309633i	−0.0528057	−	0.0112242i	−0.234239	+	0.972179i	$0.575260\pi$
$762$	2.23485	−	21.2632i	0.0809601	−	0.770283i
$763$	−0.491843	−	4.67957i	−0.0178059	−	0.169412i
$764$	−11.1114	+	2.36181i	−0.401998	+	0.0854473i
$765$	−0.761284	−	0.338946i	−0.0275243	−	0.0122546i
$766$	20.9646	−	23.2835i	0.757480	−	0.841267i
$767$	10.3133	+	31.7410i	0.372391	+	1.14610i
$768$	−0.669131	−	0.743145i	−0.0241452	−	0.0268159i
$769$	−1.43160	+	2.47961i	−0.0516249	+	0.0894170i	−0.890683	−	0.454625i	$-0.849773\pi$
$769$	−1.43160	+	2.47961i	−0.0516249	+	0.0894170i	0.839058	+	0.544042i	$0.183107\pi$
$770$	1.41397	+	2.44906i	0.0509558	+	0.0882581i
$771$	−2.70853	+	8.33600i	−0.0975454	+	0.300214i
$772$	−13.2152	+	5.88377i	−0.475624	+	0.211761i
$773$	−9.61330	+	6.98447i	−0.345766	+	0.251214i	−0.747091	−	0.664722i	$-0.768550\pi$
$773$	−9.61330	+	6.98447i	−0.345766	+	0.251214i	0.401324	+	0.915936i	$0.368550\pi$
$774$	0.615810			0.0221348
$775$	−5.43812	−	1.19449i	−0.195343	−	0.0429074i
$776$	−7.64365			−0.274391
$777$	−3.09174	+	2.24628i	−0.110916	+	0.0805850i
$778$	−15.9328	+	7.09373i	−0.571218	+	0.254323i
$779$	−1.36277	+	4.19418i	−0.0488264	+	0.150272i
$780$	−2.34783	−	4.06656i	−0.0840659	−	0.145606i
$781$	−4.47462	+	7.75026i	−0.160114	+	0.277326i
$782$	−1.74769	−	1.94101i	−0.0624974	−	0.0694104i
$783$	1.12719	+	3.46914i	0.0402826	+	0.123977i
$784$	−2.65953	+	2.95370i	−0.0949831	+	0.105489i
$785$	−11.9230	−	5.30848i	−0.425551	−	0.189468i
$786$	8.56611	−	1.82078i	0.305543	−	0.0649452i
$787$	−4.19730	−	39.9346i	−0.149617	−	1.42352i	−0.769413	−	0.638752i	$-0.779451\pi$
$787$	−4.19730	−	39.9346i	−0.149617	−	1.42352i	0.619795	−	0.784763i	$-0.287216\pi$
$788$	0.787515	−	7.49270i	0.0280541	−	0.266917i
$789$	−14.3623	−	3.05280i	−0.511312	−	0.108683i
$790$	−11.0274	−	8.01189i	−0.392338	−	0.285050i
$791$	14.0875	+	10.2352i	0.500893	+	0.363920i
$792$	−1.59031	−	0.338031i	−0.0565093	−	0.0120114i
$793$	0.742984	−	7.06902i	0.0263841	−	0.251028i
$794$	−1.65790	−	15.7738i	−0.0588366	−	0.559792i
$795$	2.94391	−	0.625748i	0.104410	−	0.0221930i
$796$	−9.97630	−	4.44174i	−0.353601	−	0.157433i
$797$	−28.7273	+	31.9049i	−1.01757	+	1.13013i	−0.0261225	+	0.999659i	$0.508316\pi$
$797$	−28.7273	+	31.9049i	−1.01757	+	1.13013i	−0.991452	+	0.130472i	$0.958351\pi$
$798$	−0.280843	−	0.864346i	−0.00994174	−	0.0305975i
$799$	−4.25595	−	4.72672i	−0.150565	−	0.167219i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−4.41622	−	7.64912i	−0.156040	−	0.270268i
$802$	7.10727	−	21.8739i	0.250966	−	0.772395i
$803$	1.57554	−	0.701474i	0.0555995	−	0.0247545i
$804$	−2.39904	+	1.74301i	−0.0846078	+	0.0614711i
$805$	−5.45166			−0.192146
$806$	−17.6253	+	19.3100i	−0.620824	+	0.680166i
$807$	13.6701			0.481211
$808$	−10.4010	+	7.55674i	−0.365905	+	0.265845i
$809$	−30.3100	+	13.4949i	−1.06564	+	0.474455i	−0.863212	−	0.504842i	$-0.831551\pi$
$809$	−30.3100	+	13.4949i	−1.06564	+	0.474455i	−0.202431	+	0.979297i	$0.564884\pi$
$810$	0.309017	−	0.951057i	0.0108578	−	0.0334167i
$811$	−9.98018	−	17.2862i	−0.350451	−	0.607000i	0.635877	−	0.771790i	$-0.280638\pi$
$811$	−9.98018	−	17.2862i	−0.350451	−	0.607000i	−0.986329	+	0.164791i	$0.947305\pi$
$812$	3.17232	−	5.49462i	0.111327	−	0.192823i
$813$	−20.1308	−	22.3575i	−0.706017	−	0.784112i
$814$	−1.10386	−	3.39734i	−0.0386903	−	0.119077i
$815$	9.41495	−	10.4564i	0.329791	−	0.366270i
$816$	−0.761284	−	0.338946i	−0.0266503	−	0.0118655i
$817$	−0.314732	+	0.0668984i	−0.0110111	+	0.00234048i
$818$	2.88945	+	27.4912i	0.101027	+	0.961209i
$819$	−0.853735	+	8.12274i	−0.0298319	+	0.283832i
$820$	8.25573	+	1.75481i	0.288303	+	0.0612806i
$821$	−38.4388	−	27.9274i	−1.34152	−	0.974674i	−0.999386	−	0.0350237i	$-0.988849\pi$
$821$	−38.4388	−	27.9274i	−1.34152	−	0.974674i	−0.342137	−	0.939650i	$-0.611151\pi$
$822$	10.5160	+	7.64034i	0.366788	+	0.266487i
$823$	21.0600	+	4.47645i	0.734107	+	0.156039i	0.559771	−	0.828647i	$-0.310889\pi$
$823$	21.0600	+	4.47645i	0.734107	+	0.156039i	0.174336	+	0.984686i	$0.444222\pi$
$824$	0.609039	−	5.79462i	0.0212169	−	0.201865i
$825$	−0.169947	−	1.61693i	−0.00591678	−	0.0562944i
$826$	12.0924	−	2.57033i	0.420750	−	0.0894331i
$827$	−49.0803	−	21.8520i	−1.70669	−	0.759867i	−0.998552	−	0.0537934i	$-0.982869\pi$
$827$	−49.0803	−	21.8520i	−1.70669	−	0.759867i	−0.708138	−	0.706074i	$-0.750465\pi$
$828$	2.09724	−	2.32922i	0.0728842	−	0.0809461i
$829$	−7.48641	−	23.0408i	−0.260014	−	0.800240i	−0.992800	−	0.119782i	$-0.961781\pi$
$829$	−7.48641	−	23.0408i	−0.260014	−	0.800240i	0.732786	−	0.680459i	$-0.238219\pi$
$830$	0.552499	+	0.613612i	0.0191775	+	0.0212988i
$831$	8.57843	−	14.8583i	0.297583	−	0.515428i
$832$	−2.34783	−	4.06656i	−0.0813964	−	0.140983i
$833$	−1.02351	+	3.15004i	−0.0354625	+	0.109142i
$834$	9.23423	−	4.11134i	0.319755	−	0.142364i
$835$	−15.3283	+	11.1367i	−0.530459	+	0.385401i
$836$	0.849509			0.0293809
$837$	−5.56764	−	0.0377395i	−0.192446	−	0.00130447i
$838$	36.3861			1.25694
$839$	−30.5063	+	22.1641i	−1.05320	+	0.765191i	−0.972817	−	0.231573i	$-0.925613\pi$
$839$	−30.5063	+	22.1641i	−1.05320	+	0.765191i	−0.0803776	+	0.996764i	$0.525613\pi$
$840$	−1.58899	+	0.707465i	−0.0548254	+	0.0244098i
$841$	−4.84986	+	14.9263i	−0.167237	+	0.514702i
$842$	6.72781	+	11.6529i	0.231856	+	0.401586i
$843$	−16.2446	+	28.1365i	−0.559493	+	0.969071i
$844$	−4.80918	−	5.34114i	−0.165539	−	0.183850i
$845$	−2.79637	−	8.60635i	−0.0961981	−	0.296067i
$846$	5.10717	−	5.67209i	0.175588	−	0.195010i
$847$	−13.2786	−	5.91203i	−0.456259	−	0.203140i
$848$	2.94391	−	0.625748i	0.101094	−	0.0214883i
$849$	1.39599	+	13.2820i	0.0479104	+	0.455837i
$850$	0.0871066	−	0.828764i	0.00298773	−	0.0284264i
$851$	6.73591	+	1.43176i	0.230904	+	0.0490802i
$852$	−4.45313	−	3.23539i	−0.152562	−	0.110843i
$853$	−0.323492	−	0.235031i	−0.0110761	−	0.00804729i	0.582233	−	0.813022i	$-0.302179\pi$
$853$	−0.323492	−	0.235031i	−0.0110761	−	0.00804729i	−0.593310	+	0.804974i	$0.702179\pi$
$854$	−2.57540	−	0.547417i	−0.0881282	−	0.0187322i
$855$	−0.0546166	+	0.519642i	−0.00186785	+	0.0177714i
$856$	0.456972	+	4.34779i	0.0156190	+	0.148605i
$857$	14.4839	−	3.07865i	0.494761	−	0.105165i	0.0462277	−	0.998931i	$-0.485280\pi$
$857$	14.4839	−	3.07865i	0.494761	−	0.105165i	0.448533	+	0.893766i	$0.351947\pi$
$858$	−6.97437	−	3.10519i	−0.238101	−	0.106009i
$859$	6.46800	−	7.18344i	0.220685	−	0.245096i	−0.622628	−	0.782518i	$-0.713935\pi$
$859$	6.46800	−	7.18344i	0.220685	−	0.245096i	0.843313	+	0.537422i	$0.180602\pi$
$860$	0.190296	+	0.585671i	0.00648904	+	0.0199712i
$861$	−9.82321	−	10.9098i	−0.334774	−	0.371804i
$862$	−4.50297	+	7.79937i	−0.153372	+	0.265647i
$863$	8.59730	+	14.8910i	0.292656	+	0.506894i	0.974437	−	0.224662i	$-0.0721277\pi$
$863$	8.59730	+	14.8910i	0.292656	+	0.506894i	−0.681781	+	0.731556i	$0.738794\pi$
$864$	0.309017	−	0.951057i	0.0105130	−	0.0323556i
$865$	2.03963	−	0.908103i	0.0693496	−	0.0308764i
$866$	7.76248	−	5.63977i	0.263780	−	0.191647i
$867$	16.3056			0.553766
$868$	6.43119	+	7.24066i	0.218289	+	0.245764i
$869$	−22.1613			−0.751769
$870$	−2.95103	+	2.14405i	−0.100049	+	0.0726900i
$871$	−12.7206	+	5.66358i	−0.431021	+	0.191903i
$872$	−0.835954	+	2.57280i	−0.0283090	+	0.0871261i
$873$	−3.82183	−	6.61960i	−0.129349	−	0.224039i
$874$	−0.818837	+	1.41827i	−0.0276976	+	0.0479736i
$875$	−1.16386	−	1.29260i	−0.0393458	−	0.0436979i
$876$	0.327795	+	1.00885i	0.0110752	+	0.0340859i
$877$	7.94858	−	8.82779i	0.268405	−	0.298093i	−0.593843	−	0.804581i	$-0.702390\pi$
$877$	7.94858	−	8.82779i	0.268405	−	0.298093i	0.862247	+	0.506488i	$0.169056\pi$
$878$	−6.42110	−	2.85886i	−0.216702	−	0.0964818i
$879$	12.8410	−	2.72944i	0.433116	−	0.0920616i
$880$	−0.169947	−	1.61693i	−0.00572890	−	0.0545068i
$881$	0.149161	−	1.41917i	0.00502535	−	0.0478130i	−0.991722	−	0.128405i	$-0.959014\pi$
$881$	0.149161	−	1.41917i	0.00502535	−	0.0478130i	0.996747	+	0.0805918i	$0.0256810\pi$
$882$	−3.88774	−	0.826366i	−0.130907	−	0.0278252i
$883$	−20.7718	−	15.0916i	−0.699027	−	0.507873i	0.180588	−	0.983559i	$-0.442200\pi$
$883$	−20.7718	−	15.0916i	−0.699027	−	0.507873i	−0.879615	+	0.475686i	$0.842200\pi$
$884$	−3.16571	−	2.30002i	−0.106474	−	0.0773582i
$885$	−6.95220	−	1.47774i	−0.233696	−	0.0496735i
$886$	−1.97759	+	18.8155i	−0.0664384	+	0.632119i
$887$	−4.49214	−	42.7399i	−0.150831	−	1.43506i	−0.764053	−	0.645154i	$-0.776793\pi$
$887$	−4.49214	−	42.7399i	−0.150831	−	1.43506i	0.613222	−	0.789911i	$-0.289873\pi$
$888$	2.14911	−	0.456808i	0.0721195	−	0.0153295i
$889$	−33.9731	−	15.1258i	−1.13942	−	0.507303i
$890$	5.91006	−	6.56378i	0.198106	−	0.220019i
$891$	−0.502412	−	1.54627i	−0.0168314	−	0.0518019i
$892$	5.98152	+	6.64315i	0.200276	+	0.222429i
$893$	−1.99402	+	3.45374i	−0.0667273	+	0.115575i
$894$	7.95396	+	13.7767i	0.266020	+	0.460760i
$895$	0.851937	−	2.62199i	0.0284771	−	0.0876435i
$896$	−1.58899	+	0.707465i	−0.0530845	+	0.0236347i
$897$	11.9067	−	8.65074i	0.397554	−	0.288840i
$898$	−18.6890			−0.623661
$899$	16.3493	+	12.0487i	0.545281	+	0.401845i
$900$	1.00000			0.0333333
$901$	2.02906	−	1.47420i	0.0675978	−	0.0491126i
$902$	12.5360	−	5.58139i	0.417403	−	0.185840i
$903$	0.330995	−	1.01870i	0.0110148	−	0.0339001i
$904$	−5.00558	−	8.66992i	−0.166483	−	0.288357i
$905$	1.64776	−	2.85401i	0.0547735	−	0.0948706i
$906$	−10.6978	−	11.8811i	−0.355409	−	0.394722i
$907$	−12.0946	−	37.2234i	−0.401595	−	1.23598i	−0.923705	−	0.383104i	$-0.874855\pi$
$907$	−12.0946	−	37.2234i	−0.401595	−	1.23598i	0.522111	−	0.852878i	$-0.325145\pi$
$908$	5.00425	−	5.55779i	0.166072	−	0.184442i
$909$	−11.7448	−	5.22913i	−0.389551	−	0.173439i
$910$	−7.98901	+	1.69812i	−0.264833	+	0.0562920i
$911$	3.39591	+	32.3099i	0.112511	+	1.07048i	0.894465	+	0.447138i	$0.147557\pi$
$911$	3.39591	+	32.3099i	0.112511	+	1.07048i	−0.781953	+	0.623337i	$0.785776\pi$
$912$	−0.0546166	+	0.519642i	−0.00180854	+	0.0172071i
$913$	1.31312	+	0.279111i	0.0434578	+	0.00923724i
$914$	17.6601	+	12.8308i	0.584143	+	0.424405i
$915$	1.22463	+	0.889748i	0.0404851	+	0.0294141i
$916$	−17.3071	−	3.67874i	−0.571843	−	0.121549i
$917$	1.59223	−	15.1490i	0.0525800	−	0.500265i
$918$	−0.0871066	−	0.828764i	−0.00287495	−	0.0273533i
$919$	59.0670	−	12.5551i	1.94844	−	0.414154i	0.955606	−	0.294649i	$-0.0952026\pi$
$919$	59.0670	−	12.5551i	1.94844	−	0.414154i	0.992834	−	0.119505i	$-0.0381307\pi$
$920$	2.86331	+	1.27483i	0.0944004	+	0.0420298i
$921$	−8.82601	+	9.80228i	−0.290827	+	0.322996i
$922$	−5.22104	−	16.0687i	−0.171946	−	0.529195i
$923$	−17.2948	−	19.2078i	−0.569265	−	0.632233i
$924$	−1.41397	+	2.44906i	−0.0465161	+	0.0805683i
$925$	1.09856	+	1.90277i	0.0361205	+	0.0625625i
$926$	−4.55113	+	14.0070i	−0.149560	+	0.460297i
$927$	5.32281	−	2.36987i	0.174824	−	0.0778366i
$928$	−2.95103	+	2.14405i	−0.0968723	+	0.0703818i
$929$	−11.7497			−0.385495			−0.192747	−	0.981248i	$-0.561740\pi$
$929$	−11.7497			−0.385495			−0.192747	+	0.981248i	$0.561740\pi$
$930$	−1.68460	−	5.30680i	−0.0552403	−	0.174017i
$931$	2.07675			0.0680626
$932$	1.08727	−	0.789946i	0.0356146	−	0.0258755i
$933$	3.87438	−	1.72499i	0.126842	−	0.0564735i
$934$	−5.04591	+	15.5297i	−0.165107	+	0.508148i
$935$	−0.677430	−	1.17334i	−0.0221543	−	0.0383724i
$936$	2.34783	−	4.06656i	0.0767413	−	0.132920i
$937$	−31.2369	−	34.6921i	−1.02046	−	1.13334i	−0.991012	−	0.133774i	$-0.957290\pi$
$937$	−31.2369	−	34.6921i	−1.02046	−	1.13334i	−0.0294527	−	0.999566i	$-0.509376\pi$
$938$	1.59388	+	4.90544i	0.0520419	+	0.160168i
$939$	−5.62589	+	6.24818i	−0.183594	+	0.203902i
$940$	6.97268	+	3.10444i	0.227424	+	0.101256i
$941$	22.5307	−	4.78906i	0.734481	−	0.156119i	0.174539	−	0.984650i	$-0.444157\pi$
$941$	22.5307	−	4.78906i	0.734481	−	0.156119i	0.559943	+	0.828531i	$0.310823\pi$
$942$	−1.36424	−	12.9799i	−0.0444494	−	0.422908i
$943$	−2.76518	+	26.3089i	−0.0900466	+	0.856736i
$944$	−6.95220	−	1.47774i	−0.226275	−	0.0480962i
$945$	−1.40718	−	1.02237i	−0.0457755	−	0.0332579i
$946$	0.809996	+	0.588496i	0.0263352	+	0.0191337i
$947$	12.5370	+	2.66481i	0.407396	+	0.0865948i	0.407052	−	0.913405i	$-0.366557\pi$
$947$	12.5370	+	2.66481i	0.407396	+	0.0865948i	0.000344792		1.00000i	$0.499890\pi$
$948$	1.42479	−	13.5560i	0.0462750	−	0.440278i
$949$	0.520657	+	4.95372i	0.0169012	+	0.160805i
$950$	−0.511087	+	0.108635i	−0.0165818	+	0.00352458i
$951$	0.336154	+	0.149665i	0.0109005	+	0.00485323i
$952$	−0.969882	+	1.07716i	−0.0314341	+	0.0349111i
$953$	−1.15872	−	3.56617i	−0.0375346	−	0.115520i	0.930534	−	0.366206i	$-0.119344\pi$
$953$	−1.15872	−	3.56617i	−0.0375346	−	0.115520i	−0.968068	+	0.250687i	$0.919344\pi$
$954$	2.01387	+	2.23663i	0.0652014	+	0.0724135i
$955$	5.67984	−	9.83777i	0.183795	−	0.318343i
$956$	−3.90956	−	6.77156i	−0.126444	−	0.219008i
$957$	−1.83264	+	5.64027i	−0.0592407	+	0.182324i
$958$	16.0539	−	7.14764i	0.518677	−	0.230930i
$959$	18.2912	−	13.2894i	0.590655	−	0.429136i
$960$	1.00000			0.0322749
$961$	−25.3242	+	17.8797i	−0.816911	+	0.576764i
$962$	10.3170			0.332632
$963$	−3.53681	+	2.56965i	−0.113972	+	0.0828057i
$964$	−1.90861	+	0.849768i	−0.0614722	+	0.0273692i
$965$	4.47017	−	13.7578i	0.143900	−	0.442879i
$966$	−2.72583	−	4.72128i	−0.0877022	−	0.151905i
$967$	8.10033	−	14.0302i	0.260489	−	0.451181i	−0.705883	−	0.708329i	$-0.749449\pi$
$967$	8.10033	−	14.0302i	0.260489	−	0.451181i	0.966372	+	0.257148i	$0.0827828\pi$
$968$	5.59169	+	6.21020i	0.179724	+	0.199603i
$969$	0.134552	+	0.414107i	0.00432242	+	0.0133030i
$970$	5.11460	−	5.68034i	0.164220	−	0.182385i
$971$	−33.9541	−	15.1173i	−1.08964	−	0.485139i	−0.218331	−	0.975875i	$-0.570061\pi$
$971$	−33.9541	−	15.1173i	−1.08964	−	0.485139i	−0.871308	+	0.490736i	$0.836728\pi$
$972$	0.978148	−	0.207912i	0.0313741	−	0.00666877i
$973$	−1.83779	−	17.4854i	−0.0589169	−	0.560557i
$974$	4.04337	−	38.4701i	0.129558	−	1.23266i
$975$	4.59305	+	0.976283i	0.147095	+	0.0312661i
$976$	1.22463	+	0.889748i	0.0391995	+	0.0284801i
$977$	−45.4307	−	33.0073i	−1.45346	−	1.05600i	−0.985008	−	0.172508i	$-0.944813\pi$
$977$	−45.4307	−	33.0073i	−1.45346	−	1.05600i	−0.468449	−	0.883491i	$-0.655187\pi$
$978$	13.7629	+	2.92540i	0.440090	+	0.0935441i
$979$	1.50104	−	14.2815i	0.0479736	−	0.456438i
$980$	−0.415459	−	3.95283i	−0.0132713	−	0.126268i
$981$	−2.64609	+	0.562444i	−0.0844832	+	0.0179574i
$982$	−25.6628	−	11.4258i	−0.818934	−	0.364613i
$983$	1.31809	−	1.46389i	0.0420406	−	0.0466908i	−0.721758	−	0.692146i	$-0.756666\pi$
$983$	1.31809	−	1.46389i	0.0420406	−	0.0466908i	0.763798	+	0.645455i	$0.223332\pi$
$984$	2.60816	+	8.02708i	0.0831450	+	0.255894i
$985$	5.04121	+	5.59884i	0.160626	+	0.178394i
$986$	−1.51986	+	2.63247i	−0.0484021	+	0.0838349i
$987$	−6.63790	−	11.4972i	−0.211287	−	0.365959i
$988$	−0.758175	+	2.33342i	−0.0241208	+	0.0742360i
$989$	−1.76325	+	0.785051i	−0.0560682	+	0.0249632i
$990$	1.31533	−	0.955645i	0.0418040	−	0.0303724i
$991$	−7.78796			−0.247393			−0.123696	−	0.992320i	$-0.539475\pi$
$991$	−7.78796			−0.247393			−0.123696	+	0.992320i	$0.539475\pi$
$992$	−1.68460	−	5.30680i	−0.0534862	−	0.168491i
$993$	−17.3489			−0.550549
$994$	−7.74563	+	5.62753i	−0.245677	+	0.178494i
$995$	9.97630	−	4.44174i	0.316270	−	0.140813i
$996$	−0.255154	+	0.785284i	−0.00808487	+	0.0248827i
$997$	−7.03492	−	12.1848i	−0.222798	−	0.385898i	0.732858	−	0.680381i	$-0.238186\pi$
$997$	−7.03492	−	12.1848i	−0.222798	−	0.385898i	−0.955657	+	0.294483i	$0.904852\pi$
$998$	−6.05886	+	10.4943i	−0.191790	+	0.332190i
$999$	1.47016	+	1.63278i	0.0465139	+	0.0516589i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.e.391.2	✓	16	31.19	even	15	inner
930.2.bg.e.421.2	yes	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.913545 + 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.16386 + 1.29260i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +O(q^{10})\)	\(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} +(1.16386 + 1.29260i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +(0.913545 + 0.406737i) q^{10} +(1.59031 - 0.338031i) q^{11} +(0.104528 + 0.994522i) q^{12} +(-0.490830 + 4.66994i) q^{13} +(1.70136 + 0.361635i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.815119 - 0.173259i) q^{17} +(0.104528 - 0.994522i) q^{18} +(0.0546166 + 0.519642i) q^{19} +(0.978148 - 0.207912i) q^{20} +(-1.58899 - 0.707465i) q^{21} +(1.08790 - 1.20823i) q^{22} +(0.968545 + 2.98088i) q^{23} +(0.669131 + 0.743145i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.34783 + 4.06656i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.58899 - 0.707465i) q^{28} +(2.95103 - 2.14405i) q^{29} -1.00000 q^{30} +(1.68460 + 5.30680i) q^{31} -1.00000 q^{32} +(-1.31533 + 0.955645i) q^{33} +(-0.761284 + 0.338946i) q^{34} +(-0.537494 + 1.65424i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(1.09856 - 1.90277i) q^{37} +(0.349624 + 0.388297i) q^{38} +(-1.45104 - 4.46584i) q^{39} +(0.669131 - 0.743145i) q^{40} +(7.71048 + 3.43293i) q^{41} +(-1.70136 + 0.361635i) q^{42} +(0.0643697 + 0.612437i) q^{43} +(0.169947 - 1.61693i) q^{44} +(0.978148 + 0.207912i) q^{45} +(2.53568 + 1.84228i) q^{46} +(6.17486 + 4.48630i) q^{47} +(0.978148 + 0.207912i) q^{48} +(0.415459 - 3.95283i) q^{49} +(0.104528 + 0.994522i) q^{50} +(0.815119 - 0.173259i) q^{51} +(4.28970 + 1.90990i) q^{52} +(-2.01387 + 2.23663i) q^{53} +(0.309017 + 0.951057i) q^{54} +(1.08790 + 1.20823i) q^{55} +(0.869684 - 1.50634i) q^{56} +(-0.261252 - 0.452502i) q^{57} +(1.12719 - 3.46914i) q^{58} +(6.49304 - 2.89089i) q^{59} +(-0.809017 + 0.587785i) q^{60} -1.51373 q^{61} +(4.48213 + 3.30311i) q^{62} +1.73937 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-4.28970 + 1.90990i) q^{65} +(-0.502412 + 1.54627i) q^{66} +(1.48269 + 2.56810i) q^{67} +(-0.416665 + 0.721684i) q^{68} +(-2.09724 - 2.32922i) q^{69} +(0.537494 + 1.65424i) q^{70} +(-3.68314 + 4.09055i) q^{71} +(-0.913545 - 0.406737i) q^{72} +(1.03759 - 0.220546i) q^{73} +(-0.229662 - 2.18509i) q^{74} +(0.104528 - 0.994522i) q^{75} +(0.511087 + 0.108635i) q^{76} +(2.28785 + 1.66222i) q^{77} +(-3.79887 - 2.76004i) q^{78} +(-13.3328 - 2.83397i) q^{79} +(0.104528 - 0.994522i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(8.25573 - 1.75481i) q^{82} +(0.754311 + 0.335841i) q^{83} +(-1.16386 + 1.29260i) q^{84} +(-0.257513 - 0.792543i) q^{85} +(0.412058 + 0.457636i) q^{86} +(-1.82384 + 3.15898i) q^{87} +(-0.812920 - 1.40802i) q^{88} +(2.72937 - 8.40015i) q^{89} +(0.913545 - 0.406737i) q^{90} +(-6.60763 + 4.80073i) q^{91} +3.13428 q^{92} +(-3.69743 - 4.16281i) q^{93} +7.63255 q^{94} +(-0.422715 + 0.307120i) q^{95} +(0.913545 - 0.406737i) q^{96} +(2.36202 - 7.26954i) q^{97} +(-1.98730 - 3.44210i) q^{98} +(0.812920 - 1.40802i) 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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