LMFDB - Embedded newform 430.2.q.c.111.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, degree $12$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			111.2
Character	$\chi$	$=$	430.111
Dual form			430.2.q.c.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.900969 + 0.433884i) q^{2} +(-0.889549 - 0.606484i) q^{3} +(0.623490 + 0.781831i) q^{4} +(-0.733052 + 0.680173i) q^{5} +(-0.538312 - 0.932384i) q^{6} +(2.53031 - 4.38263i) q^{7} +(0.222521 + 0.974928i) q^{8} +(-0.672549 - 1.71363i) q^{9} +O(q^{10})$	\(q+(0.900969 + 0.433884i) q^{2} +(-0.889549 - 0.606484i) q^{3} +(0.623490 + 0.781831i) q^{4} +(-0.733052 + 0.680173i) q^{5} +(-0.538312 - 0.932384i) q^{6} +(2.53031 - 4.38263i) q^{7} +(0.222521 + 0.974928i) q^{8} +(-0.672549 - 1.71363i) q^{9} +(-0.955573 + 0.294755i) q^{10} +(-0.488095 + 0.612052i) q^{11} +(-0.0804562 - 1.07361i) q^{12} +(1.07532 + 0.331693i) q^{13} +(4.18128 - 2.85075i) q^{14} +(1.06460 - 0.160463i) q^{15} +(-0.222521 + 0.974928i) q^{16} +(1.63553 + 1.51755i) q^{17} +(0.137569 - 1.83573i) q^{18} +(2.93443 - 7.47682i) q^{19} +(-0.988831 - 0.149042i) q^{20} +(-4.90883 + 2.36397i) q^{21} +(-0.705318 + 0.339663i) q^{22} +(4.37136 + 0.658876i) q^{23} +(0.393335 - 1.00220i) q^{24} +(0.0747301 - 0.997204i) q^{25} +(0.824915 + 0.765409i) q^{26} +(-1.15974 + 5.08114i) q^{27} +(5.00410 - 0.754246i) q^{28} +(-1.11229 + 0.758346i) q^{29} +(1.02879 + 0.317341i) q^{30} +(-0.00220136 - 0.0293751i) q^{31} +(-0.623490 + 0.781831i) q^{32} +(0.805384 - 0.248428i) q^{33} +(0.815119 + 2.07689i) q^{34} +(1.12609 + 4.93374i) q^{35} +(0.920440 - 1.59425i) q^{36} +(-1.20562 - 2.08819i) q^{37} +(5.88790 - 5.46318i) q^{38} +(-0.755384 - 0.947222i) q^{39} +(-0.826239 - 0.563320i) q^{40} +(3.88985 + 1.87325i) q^{41} -5.44839 q^{42} +(-1.12043 + 6.46101i) q^{43} -0.782843 q^{44} +(1.65858 + 0.798728i) q^{45} +(3.65258 + 2.49029i) q^{46} +(-1.27456 - 1.59824i) q^{47} +(0.789221 - 0.732291i) q^{48} +(-9.30494 - 16.1166i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-0.534512 - 2.34185i) q^{51} +(0.411124 + 1.04753i) q^{52} +(-9.64700 + 2.97571i) q^{53} +(-3.24951 + 4.07476i) q^{54} +(-0.0585020 - 0.780654i) q^{55} +(4.83579 + 1.49164i) q^{56} +(-7.14489 + 4.87131i) q^{57} +(-1.33117 + 0.200642i) q^{58} +(-0.663578 + 2.90733i) q^{59} +(0.789221 + 0.732291i) q^{60} +(-0.225097 + 3.00371i) q^{61} +(0.0107620 - 0.0274212i) q^{62} +(-9.21194 - 1.38848i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(-1.01387 + 0.488256i) q^{65} +(0.833415 + 0.125617i) q^{66} +(-3.94231 + 10.0448i) q^{67} +(-0.166732 + 2.22488i) q^{68} +(-3.48894 - 3.23726i) q^{69} +(-1.12609 + 4.93374i) q^{70} +(0.0568611 - 0.00857043i) q^{71} +(1.52101 - 1.03700i) q^{72} +(-5.82504 - 1.79679i) q^{73} +(-0.180192 - 2.40449i) q^{74} +(-0.671264 + 0.841739i) q^{75} +(7.67520 - 2.36749i) q^{76} +(1.44736 + 3.68782i) q^{77} +(-0.269593 - 1.18117i) q^{78} +(3.48037 - 6.02819i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(0.0648900 - 0.0602092i) q^{81} +(2.69186 + 3.37549i) q^{82} +(8.12225 + 5.53765i) q^{83} +(-4.90883 - 2.36397i) q^{84} -2.23112 q^{85} +(-3.81280 + 5.33503i) q^{86} +1.44936 q^{87} +(-0.705318 - 0.339663i) q^{88} +(8.44847 + 5.76007i) q^{89} +(1.14777 + 1.43926i) q^{90} +(4.17458 - 3.87344i) q^{91} +(2.21037 + 3.82847i) q^{92} +(-0.0158573 + 0.0274657i) q^{93} +(-0.454884 - 1.99298i) q^{94} +(2.93443 + 7.47682i) q^{95} +(1.02879 - 0.317341i) q^{96} +(-8.25602 + 10.3527i) q^{97} +(-1.39072 - 18.5578i) q^{98} +(1.37710 + 0.424778i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9}+O(q^{10}) $ 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9} - 4 q^{10} + q^{11} + 14 q^{12} - 23 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{17} - 20 q^{18} - 3 q^{19} + 4 q^{20} - 8 q^{21} - q^{22} + 7 q^{23} + 4 q^{25} - 19 q^{26} + 32 q^{27} + 4 q^{28} + 30 q^{29} + 9 q^{31} + 8 q^{32} + 39 q^{33} - 8 q^{34} - 22 q^{35} - 29 q^{36} - 37 q^{37} - 11 q^{38} - 52 q^{39} - 4 q^{40} - 28 q^{41} - 6 q^{42} + 41 q^{43} + 8 q^{44} + 2 q^{45} - 28 q^{46} + 3 q^{47} - 41 q^{49} + 24 q^{50} - 30 q^{51} - 9 q^{52} - 69 q^{53} + 3 q^{54} + 10 q^{55} - 11 q^{56} + 116 q^{57} + 5 q^{58} + 10 q^{59} - 19 q^{61} - 93 q^{62} + 34 q^{63} - 8 q^{64} - 3 q^{65} - 18 q^{66} + 3 q^{67} + 8 q^{68} + 42 q^{69} + 22 q^{70} - 36 q^{71} + 22 q^{72} - 56 q^{73} + 9 q^{74} - 10 q^{76} + 3 q^{77} + 45 q^{78} + 16 q^{79} - 24 q^{80} - 19 q^{81} + 14 q^{82} + 64 q^{83} - 8 q^{84} - 30 q^{85} + 36 q^{86} + 78 q^{87} - q^{88} - 75 q^{89} + 5 q^{90} + 5 q^{91} + 14 q^{92} - 10 q^{93} - 45 q^{94} - 3 q^{95} + 33 q^{97} - q^{98} - 11 q^{99}+O(q^{100}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9 - 4 * q^10 + q^11 + 14 * q^12 - 23 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^17 - 20 * q^18 - 3 * q^19 + 4 * q^20 - 8 * q^21 - q^22 + 7 * q^23 + 4 * q^25 - 19 * q^26 + 32 * q^27 + 4 * q^28 + 30 * q^29 + 9 * q^31 + 8 * q^32 + 39 * q^33 - 8 * q^34 - 22 * q^35 - 29 * q^36 - 37 * q^37 - 11 * q^38 - 52 * q^39 - 4 * q^40 - 28 * q^41 - 6 * q^42 + 41 * q^43 + 8 * q^44 + 2 * q^45 - 28 * q^46 + 3 * q^47 - 41 * q^49 + 24 * q^50 - 30 * q^51 - 9 * q^52 - 69 * q^53 + 3 * q^54 + 10 * q^55 - 11 * q^56 + 116 * q^57 + 5 * q^58 + 10 * q^59 - 19 * q^61 - 93 * q^62 + 34 * q^63 - 8 * q^64 - 3 * q^65 - 18 * q^66 + 3 * q^67 + 8 * q^68 + 42 * q^69 + 22 * q^70 - 36 * q^71 + 22 * q^72 - 56 * q^73 + 9 * q^74 - 10 * q^76 + 3 * q^77 + 45 * q^78 + 16 * q^79 - 24 * q^80 - 19 * q^81 + 14 * q^82 + 64 * q^83 - 8 * q^84 - 30 * q^85 + 36 * q^86 + 78 * q^87 - q^88 - 75 * q^89 + 5 * q^90 + 5 * q^91 + 14 * q^92 - 10 * q^93 - 45 * q^94 - 3 * q^95 + 33 * q^97 - q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{4}{21}\right)$

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 $

$2$	0.900969	+	0.433884i	0.637081	+	0.306802i
$2$	0.900969	+	0.433884i	0.637081	+	0.306802i
$3$	−0.889549	−	0.606484i	−0.513581	−	0.350154i	0.278632	−	0.960398i	$-0.410119\pi$
$3$	−0.889549	−	0.606484i	−0.513581	−	0.350154i	−0.792213	+	0.610244i	$0.791071\pi$
$4$	0.623490	+	0.781831i	0.311745	+	0.390916i
$5$	−0.733052	+	0.680173i	−0.327831	+	0.304182i
$5$	−0.733052	+	0.680173i	−0.327831	+	0.304182i
$6$	−0.538312	−	0.932384i	−0.219765	−	0.380644i
$7$	2.53031	−	4.38263i	0.956367	−	1.65648i	0.225159	−	0.974322i	$-0.427710\pi$
$7$	2.53031	−	4.38263i	0.956367	−	1.65648i	0.731208	−	0.682155i	$-0.238957\pi$
$8$	0.222521	+	0.974928i	0.0786730	+	0.344689i
$9$	−0.672549	−	1.71363i	−0.224183	−	0.571209i
$10$	−0.955573	+	0.294755i	−0.302179	+	0.0932098i
$11$	−0.488095	+	0.612052i	−0.147166	+	0.184541i	−0.849951	−	0.526862i	$-0.823368\pi$
$11$	−0.488095	+	0.612052i	−0.147166	+	0.184541i	0.702785	+	0.711403i	$0.251940\pi$
$12$	−0.0804562	−	1.07361i	−0.0232257	−	0.309926i
$13$	1.07532	+	0.331693i	0.298240	+	0.0919950i	0.440264	−	0.897868i	$-0.354885\pi$
$13$	1.07532	+	0.331693i	0.298240	+	0.0919950i	−0.142024	+	0.989863i	$0.545361\pi$
$14$	4.18128	−	2.85075i	1.11749	−	0.761895i
$15$	1.06460	−	0.160463i	0.274878	−	0.0414312i
$16$	−0.222521	+	0.974928i	−0.0556302	+	0.243732i
$17$	1.63553	+	1.51755i	0.396673	+	0.368059i	0.853140	−	0.521681i	$-0.174695\pi$
$17$	1.63553	+	1.51755i	0.396673	+	0.368059i	−0.456467	+	0.889740i	$0.650885\pi$
$18$	0.137569	−	1.83573i	0.0324254	−	0.432686i
$19$	2.93443	−	7.47682i	0.673206	−	1.71530i	−0.0252848	−	0.999680i	$-0.508049\pi$
$19$	2.93443	−	7.47682i	0.673206	−	1.71530i	0.698490	−	0.715619i	$-0.253855\pi$
$20$	−0.988831	−	0.149042i	−0.221109	−	0.0333269i
$21$	−4.90883	+	2.36397i	−1.07119	+	0.515860i
$22$	−0.705318	+	0.339663i	−0.150374	+	0.0724164i
$23$	4.37136	+	0.658876i	0.911492	+	0.137385i	0.588014	−	0.808851i	$-0.299910\pi$
$23$	4.37136	+	0.658876i	0.911492	+	0.137385i	0.323477	+	0.946236i	$0.395148\pi$
$24$	0.393335	−	1.00220i	0.0802892	−	0.204573i
$25$	0.0747301	−	0.997204i	0.0149460	−	0.199441i
$26$	0.824915	+	0.765409i	0.161779	+	0.150109i
$27$	−1.15974	+	5.08114i	−0.223191	+	0.977866i
$28$	5.00410	−	0.754246i	0.945685	−	0.142539i
$29$	−1.11229	+	0.758346i	−0.206547	+	0.140821i	−0.662176	−	0.749349i	$-0.730367\pi$
$29$	−1.11229	+	0.758346i	−0.206547	+	0.140821i	0.455629	+	0.890170i	$0.349414\pi$
$30$	1.02879	+	0.317341i	0.187831	+	0.0579382i
$31$	−0.00220136	−	0.0293751i	−0.000395376	−	0.00527592i	0.997003	−	0.0773678i	$-0.0246516\pi$
$31$	−0.00220136	−	0.0293751i	−0.000395376	−	0.00527592i	−0.997398	+	0.0720919i	$0.977033\pi$
$32$	−0.623490	+	0.781831i	−0.110218	+	0.138210i
$33$	0.805384	−	0.248428i	0.140199	−	0.0432458i
$34$	0.815119	+	2.07689i	0.139792	+	0.356184i
$35$	1.12609	+	4.93374i	0.190345	+	0.833954i
$36$	0.920440	−	1.59425i	0.153407	−	0.265708i
$37$	−1.20562	−	2.08819i	−0.198202	−	0.343297i	0.749743	−	0.661729i	$-0.230177\pi$
$37$	−1.20562	−	2.08819i	−0.198202	−	0.343297i	−0.947946	+	0.318432i	$0.896844\pi$
$38$	5.88790	−	5.46318i	0.955144	−	0.886244i
$39$	−0.755384	−	0.947222i	−0.120958	−	0.151677i
$40$	−0.826239	−	0.563320i	−0.130640	−	0.0890687i
$41$	3.88985	+	1.87325i	0.607493	+	0.292553i	0.712229	−	0.701947i	$-0.247686\pi$
$41$	3.88985	+	1.87325i	0.607493	+	0.292553i	−0.104736	+	0.994500i	$0.533400\pi$
$42$	−5.44839			−0.840704
$43$	−1.12043	+	6.46101i	−0.170865	+	0.985295i
$43$	−1.12043	+	6.46101i	−0.170865	+	0.985295i
$44$	−0.782843			−0.118018
$45$	1.65858	+	0.798728i	0.247246	+	0.119067i
$46$	3.65258	+	2.49029i	0.538544	+	0.367173i
$47$	−1.27456	−	1.59824i	−0.185913	−	0.233128i	0.680137	−	0.733085i	$-0.261920\pi$
$47$	−1.27456	−	1.59824i	−0.185913	−	0.233128i	−0.866050	+	0.499957i	$0.833349\pi$
$48$	0.789221	−	0.732291i	0.113914	−	0.105697i
$49$	−9.30494	−	16.1166i	−1.32928	−	2.30237i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−0.534512	−	2.34185i	−0.0748467	−	0.327925i
$52$	0.411124	+	1.04753i	0.0570126	+	0.145266i
$53$	−9.64700	+	2.97571i	−1.32512	+	0.408745i	−0.874956	−	0.484202i	$-0.839110\pi$
$53$	−9.64700	+	2.97571i	−1.32512	+	0.408745i	−0.450162	+	0.892947i	$0.648634\pi$
$54$	−3.24951	+	4.07476i	−0.442202	+	0.554504i
$55$	−0.0585020	−	0.780654i	−0.00788840	−	0.105263i
$56$	4.83579	+	1.49164i	0.646210	+	0.199329i
$57$	−7.14489	+	4.87131i	−0.946364	+	0.645220i
$58$	−1.33117	+	0.200642i	−0.174791	+	0.0263456i
$59$	−0.663578	+	2.90733i	−0.0863905	+	0.378502i	−0.999578	−	0.0290373i	$-0.990756\pi$
$59$	−0.663578	+	2.90733i	−0.0863905	+	0.378502i	0.913188	+	0.407539i	$0.133613\pi$
$60$	0.789221	+	0.732291i	0.101888	+	0.0945383i
$61$	−0.225097	+	3.00371i	−0.0288207	+	0.384586i	0.964078	+	0.265621i	$0.0855768\pi$
$61$	−0.225097	+	3.00371i	−0.0288207	+	0.384586i	−0.992898	+	0.118965i	$0.962042\pi$
$62$	0.0107620	−	0.0274212i	0.00136678	−	0.00348249i
$63$	−9.21194	−	1.38848i	−1.16060	−	0.174932i
$64$	−0.900969	+	0.433884i	−0.112621	+	0.0542355i
$65$	−1.01387	+	0.488256i	−0.125756	+	0.0605607i
$66$	0.833415	+	0.125617i	0.102586	+	0.0154624i
$67$	−3.94231	+	10.0448i	−0.481629	+	1.22717i	0.459213	+	0.888326i	$0.348132\pi$
$67$	−3.94231	+	10.0448i	−0.481629	+	1.22717i	−0.940842	+	0.338845i	$0.889964\pi$
$68$	−0.166732	+	2.22488i	−0.0202192	+	0.269806i
$69$	−3.48894	−	3.23726i	−0.420019	−	0.389721i
$70$	−1.12609	+	4.93374i	−0.134594	+	0.589695i
$71$	0.0568611	−	0.00857043i	0.00674817	−	0.00101712i	−0.145667	−	0.989334i	$-0.546533\pi$
$71$	0.0568611	−	0.00857043i	0.00674817	−	0.00101712i	0.152415	+	0.988317i	$0.451295\pi$
$72$	1.52101	−	1.03700i	0.179252	−	0.122212i
$73$	−5.82504	−	1.79679i	−0.681770	−	0.210298i	−0.0655226	−	0.997851i	$-0.520871\pi$
$73$	−5.82504	−	1.79679i	−0.681770	−	0.210298i	−0.616247	+	0.787553i	$0.711348\pi$
$74$	−0.180192	−	2.40449i	−0.0209469	−	0.279517i
$75$	−0.671264	+	0.841739i	−0.0775109	+	0.0971956i
$76$	7.67520	−	2.36749i	0.880406	−	0.271569i
$77$	1.44736	+	3.68782i	0.164942	+	0.420266i
$78$	−0.269593	−	1.18117i	−0.0305254	−	0.133741i
$79$	3.48037	−	6.02819i	0.391573	−	0.678224i	−0.601084	−	0.799186i	$-0.705264\pi$
$79$	3.48037	−	6.02819i	0.391573	−	0.678224i	0.992657	+	0.120962i	$0.0385978\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	0.0648900	−	0.0602092i	0.00721000	−	0.00668991i
$82$	2.69186	+	3.37549i	0.297266	+	0.372760i
$83$	8.12225	+	5.53765i	0.891532	+	0.607837i	0.920069	−	0.391756i	$-0.128132\pi$
$83$	8.12225	+	5.53765i	0.891532	+	0.607837i	−0.0285366	+	0.999593i	$0.509085\pi$
$84$	−4.90883	−	2.36397i	−0.535597	−	0.257930i
$85$	−2.23112			−0.241999
$86$	−3.81280	+	5.33503i	−0.411145	+	0.575291i
$87$	1.44936			0.155388
$88$	−0.705318	−	0.339663i	−0.0751871	−	0.0362082i
$89$	8.44847	+	5.76007i	0.895536	+	0.610566i	0.921194	−	0.389104i	$-0.127215\pi$
$89$	8.44847	+	5.76007i	0.895536	+	0.610566i	−0.0256573	+	0.999671i	$0.508168\pi$
$90$	1.14777	+	1.43926i	0.120986	+	0.151711i
$91$	4.17458	−	3.87344i	0.437615	−	0.406047i
$92$	2.21037	+	3.82847i	0.230447	+	0.399146i
$93$	−0.0158573	+	0.0274657i	−0.00164433	+	0.00284806i
$94$	−0.454884	−	1.99298i	−0.0469177	−	0.205560i
$95$	2.93443	+	7.47682i	0.301067	+	0.767105i
$96$	1.02879	−	0.317341i	0.105001	−	0.0323884i
$97$	−8.25602	+	10.3527i	−0.838272	+	1.05116i	0.159678	+	0.987169i	$0.448954\pi$
$97$	−8.25602	+	10.3527i	−0.838272	+	1.05116i	−0.997950	+	0.0639911i	$0.979617\pi$
$98$	−1.39072	−	18.5578i	−0.140484	−	1.87462i
$99$	1.37710	+	0.424778i	0.138403	+	0.0426918i
$100$	0.826239	−	0.563320i	0.0826239	−	0.0563320i
$101$	−1.30701	+	0.196999i	−0.130052	+	0.0196022i	−0.213746	−	0.976889i	$-0.568566\pi$
$101$	−1.30701	+	0.196999i	−0.130052	+	0.0196022i	0.0836937	+	0.996492i	$0.473328\pi$
$102$	0.534512	−	2.34185i	0.0529246	−	0.231878i
$103$	11.9857	+	11.1211i	1.18098	+	1.09579i	0.993536	+	0.113519i	$0.0362122\pi$
$103$	11.9857	+	11.1211i	1.18098	+	1.09579i	0.187448	+	0.982274i	$0.439978\pi$
$104$	−0.0840949	+	1.12217i	−0.00824619	+	0.110038i
$105$	1.99052	−	5.07176i	0.194255	−	0.494953i
$106$	−9.98276	−	1.50466i	−0.969611	−	0.146145i
$107$	−12.2718	+	5.90977i	−1.18636	+	0.571319i	−0.919757	−	0.392489i	$-0.871614\pi$
$107$	−12.2718	+	5.90977i	−1.18636	+	0.571319i	−0.266599	+	0.963808i	$0.585900\pi$
$108$	−4.69568	+	2.26132i	−0.451842	+	0.217596i
$109$	−1.48843	−	0.224344i	−0.142565	−	0.0214883i	0.0773718	−	0.997002i	$-0.475347\pi$
$109$	−1.48843	−	0.224344i	−0.142565	−	0.0214883i	−0.219937	+	0.975514i	$0.570585\pi$
$110$	0.286005	−	0.728728i	0.0272695	−	0.0694815i
$111$	−0.193999	+	2.58874i	−0.0184136	+	0.245712i
$112$	3.70970	+	3.44210i	0.350533	+	0.325247i
$113$	2.24298	−	9.82714i	0.211002	−	0.924460i	−0.752886	−	0.658151i	$-0.771339\pi$
$113$	2.24298	−	9.82714i	0.211002	−	0.924460i	0.963888	−	0.266309i	$-0.0858041\pi$
$114$	−8.55091	+	1.28884i	−0.800866	+	0.120711i
$115$	−3.65258	+	2.49029i	−0.340605	+	0.232221i
$116$	−1.28640	−	0.396802i	−0.119439	−	0.0368421i
$117$	−0.154809	−	2.06578i	−0.0143121	−	0.190981i
$118$	−1.85931	+	2.33150i	−0.171163	+	0.214632i
$119$	10.7892	−	3.32803i	0.989046	−	0.305080i
$120$	0.393335	+	1.00220i	0.0359064	+	0.0914880i
$121$	2.31136	+	10.1267i	0.210124	+	0.920612i
$122$	−1.50607	+	2.60859i	−0.136353	+	0.236170i
$123$	−2.32411	−	4.02548i	−0.209558	−	0.362966i
$124$	0.0215938	−	0.0200362i	0.00193918	−	0.00179930i
$125$	0.623490	+	0.781831i	0.0557666	+	0.0699291i
$126$	−7.69724	−	5.24789i	−0.685724	−	0.467519i
$127$	11.0004	+	5.29753i	0.976130	+	0.470080i	0.852772	−	0.522283i	$-0.174919\pi$
$127$	11.0004	+	5.29753i	0.976130	+	0.470080i	0.123358	+	0.992362i	$0.460634\pi$
$128$	−1.00000			−0.0883883
$129$	4.91518	−	5.06786i	0.432757	−	0.446200i
$130$	−1.12532			−0.0986967
$131$	−7.87202	−	3.79097i	−0.687782	−	0.331218i	0.0571437	−	0.998366i	$-0.481801\pi$
$131$	−7.87202	−	3.79097i	−0.687782	−	0.331218i	−0.744925	+	0.667148i	$0.767515\pi$
$132$	0.696377	+	0.474782i	0.0606119	+	0.0413245i
$133$	−25.3431	−	31.7792i	−2.19752	−	2.75561i
$134$	−7.91018	+	7.33958i	−0.683336	+	0.634043i
$135$	−2.60590	−	4.51356i	−0.224281	−	0.388465i
$136$	−1.11556	+	1.93221i	−0.0956584	+	0.165685i
$137$	−4.68641	−	20.5325i	−0.400387	−	1.75421i	−0.625835	−	0.779955i	$-0.715242\pi$
$137$	−4.68641	−	20.5325i	−0.400387	−	1.75421i	0.225448	−	0.974255i	$-0.427615\pi$
$138$	−1.73883	−	4.43047i	−0.148019	−	0.377146i
$139$	13.3510	−	4.11824i	1.13242	−	0.349305i	0.328771	−	0.944410i	$-0.393366\pi$
$139$	13.3510	−	4.11824i	1.13242	−	0.349305i	0.803648	+	0.595105i	$0.202889\pi$
$140$	−3.15524	+	3.95655i	−0.266667	+	0.334390i
$141$	0.164471	+	2.19471i	0.0138510	+	0.184828i
$142$	0.0549486	+	0.0169494i	0.00461119	+	0.00142236i
$143$	−0.727872	+	0.496254i	−0.0608677	+	0.0414989i
$144$	1.82032	−	0.274369i	0.151693	−	0.0228641i
$145$	0.299559	−	1.31245i	0.0248770	−	0.108993i
$146$	−4.46858	−	4.14624i	−0.369823	−	0.343145i
$147$	−1.49728	+	19.9798i	−0.123494	+	1.64791i
$148$	0.880923	−	2.24456i	0.0724114	−	0.184501i
$149$	−0.270236	−	0.0407315i	−0.0221386	−	0.00333685i	0.137964	−	0.990437i	$-0.455944\pi$
$149$	−0.270236	−	0.0407315i	−0.0221386	−	0.00333685i	−0.160102	+	0.987100i	$0.551182\pi$
$150$	−0.970005	+	0.467130i	−0.0792006	+	0.0381410i
$151$	−2.94336	+	1.41745i	−0.239527	+	0.115350i	−0.549797	−	0.835298i	$-0.685295\pi$
$151$	−2.94336	+	1.41745i	−0.239527	+	0.115350i	0.310270	+	0.950649i	$0.399581\pi$
$152$	7.94233	+	1.19711i	0.644208	+	0.0970988i
$153$	1.50054	−	3.82330i	0.121311	−	0.309096i
$154$	−0.296056	+	3.95060i	−0.0238569	+	0.318348i
$155$	0.0215938	+	0.0200362i	0.00173446	+	0.00160934i
$156$	0.269593	−	1.18117i	0.0215847	−	0.0945690i
$157$	11.6753	−	1.75977i	0.931791	−	0.140445i	0.334433	−	0.942420i	$-0.391455\pi$
$157$	11.6753	−	1.75977i	0.931791	−	0.140445i	0.597358	+	0.801975i	$0.296217\pi$
$158$	5.75124	−	3.92113i	0.457544	−	0.311948i
$159$	10.3862	+	3.20372i	0.823679	+	0.254071i
$160$	−0.0747301	−	0.997204i	−0.00590793	−	0.0788359i
$161$	13.9485	−	17.4909i	1.09930	−	1.37847i
$162$	0.0845877	−	0.0260918i	0.00664584	−	0.00204997i
$163$	9.06005	+	23.0846i	0.709638	+	1.80813i	0.576617	+	0.817014i	$0.304372\pi$
$163$	9.06005	+	23.0846i	0.709638	+	1.80813i	0.133021	+	0.991113i	$0.457532\pi$
$164$	0.960714	+	4.20916i	0.0750192	+	0.328681i
$165$	−0.421414	+	0.729911i	−0.0328070	+	0.0568235i
$166$	4.91519	+	8.51337i	0.381493	+	0.660765i
$167$	12.1135	−	11.2396i	0.937367	−	0.869750i	−0.0543067	−	0.998524i	$-0.517295\pi$
$167$	12.1135	−	11.2396i	0.937367	−	0.869750i	0.991674	+	0.128775i	$0.0411044\pi$
$168$	−3.39701	−	4.25972i	−0.262085	−	0.328645i
$169$	−9.69481	−	6.60981i	−0.745755	−	0.508447i
$170$	−2.01017	−	0.968046i	−0.154173	−	0.0742457i
$171$	−14.7860			−1.13072
$172$	−5.75000	+	3.15238i	−0.438433	+	0.240367i
$173$	11.7091			0.890227			0.445113	−	0.895474i	$-0.353163\pi$
$173$	11.7091			0.890227			0.445113	+	0.895474i	$0.353163\pi$
$174$	1.30583	+	0.628853i	0.0989945	+	0.0476733i
$175$	−4.18128	−	2.85075i	−0.316075	−	0.215496i
$176$	−0.488095	−	0.612052i	−0.0367915	−	0.0461351i
$177$	2.35353	−	2.18376i	0.176902	−	0.164141i
$178$	5.11261	+	8.85530i	0.383206	+	0.663733i
$179$	10.5602	−	18.2908i	0.789308	−	1.36712i	−0.137084	−	0.990559i	$-0.543773\pi$
$179$	10.5602	−	18.2908i	0.789308	−	1.36712i	0.926392	−	0.376561i	$-0.122894\pi$
$180$	0.409634	+	1.79473i	0.0305323	+	0.133771i
$181$	−3.05385	−	7.78108i	−0.226991	−	0.578363i	0.771321	−	0.636446i	$-0.219596\pi$
$181$	−3.05385	−	7.78108i	−0.226991	−	0.578363i	−0.998312	+	0.0580831i	$0.981501\pi$
$182$	5.44179	−	1.67857i	0.403372	−	0.124424i
$183$	2.02194	−	2.53543i	0.149466	−	0.187424i
$184$	0.330362	+	4.40837i	0.0243546	+	0.324990i
$185$	2.30411	+	0.710724i	0.169402	+	0.0522535i
$186$	−0.0262038	+	0.0178655i	−0.00192136	+	0.00130996i
$187$	−1.72711	+	0.260320i	−0.126299	+	0.0190365i
$188$	0.454884	−	1.99298i	0.0331758	−	0.145353i
$189$	19.3342	+	17.9395i	1.40636	+	1.30491i
$190$	−0.600235	+	8.00958i	−0.0435456	+	0.581076i
$191$	−9.14392	+	23.2983i	−0.661631	+	1.68581i	0.0642017	+	0.997937i	$0.479550\pi$
$191$	−9.14392	+	23.2983i	−0.661631	+	1.68581i	−0.725833	+	0.687871i	$0.758545\pi$
$192$	1.06460	+	0.160463i	0.0768308	+	0.0115804i
$193$	−3.34969	+	1.61313i	−0.241116	+	0.116115i	−0.550540	−	0.834809i	$-0.685578\pi$
$193$	−3.34969	+	1.61313i	−0.241116	+	0.116115i	0.309424	+	0.950924i	$0.399864\pi$
$194$	−11.9303	+	5.74533i	−0.856546	+	0.412491i
$195$	1.19801	+	0.180571i	0.0857913	+	0.0129310i
$196$	6.79895	−	17.3234i	0.485639	−	1.23739i
$197$	−1.28064	+	17.0889i	−0.0912415	+	1.21753i	0.744201	+	0.667956i	$0.232830\pi$
$197$	−1.28064	+	17.0889i	−0.0912415	+	1.21753i	−0.835443	+	0.549578i	$0.814789\pi$
$198$	1.05642	+	0.980211i	0.0750762	+	0.0696606i
$199$	3.31144	−	14.5083i	0.234741	−	1.02847i	−0.710909	−	0.703284i	$-0.751716\pi$
$199$	3.31144	−	14.5083i	0.234741	−	1.02847i	0.945650	−	0.325185i	$-0.105427\pi$
$200$	0.988831	−	0.149042i	0.0699209	−	0.0105389i
$201$	9.59890	−	6.54442i	0.677054	−	0.461608i
$202$	−1.26305	−	0.389598i	−0.0888676	−	0.0274120i
$203$	0.509109	+	6.79359i	0.0357325	+	0.476817i
$204$	1.49767	−	1.87802i	0.104858	−	0.131488i
$205$	−4.12560	+	1.27258i	−0.288144	+	0.0888808i
$206$	5.97347	+	15.2201i	0.416191	+	1.06044i
$207$	−1.81089	−	7.93401i	−0.125865	−	0.551452i
$208$	−0.562658	+	0.974552i	−0.0390133	+	0.0675730i
$209$	3.14392	+	5.44542i	0.217469	+	0.376668i
$210$	3.99395	−	3.70584i	0.275609	−	0.255728i
$211$	−8.37661	−	10.5039i	−0.576669	−	0.723120i	0.404871	−	0.914374i	$-0.367316\pi$
$211$	−8.37661	−	10.5039i	−0.576669	−	0.723120i	−0.981541	+	0.191253i	$0.938745\pi$
$212$	−8.34131	−	5.68701i	−0.572883	−	0.390585i
$213$	−0.0557785	−	0.0268615i	−0.00382188	−	0.00184052i
$214$	−13.6206			−0.931087
$215$	−3.57326	−	5.49834i	−0.243695	−	0.374984i
$216$	−5.21181			−0.354619
$217$	−0.134310	−	0.0646803i	−0.00911756	−	0.00439079i
$218$	−1.24369	−	0.847931i	−0.0842331	−	0.0574292i
$219$	4.09194	+	5.13112i	0.276507	+	0.346729i
$220$	0.573865	−	0.532469i	0.0386900	−	0.0358990i
$221$	1.25536	+	2.17434i	0.0844444	+	0.146262i
$222$	−1.29800	+	2.24820i	−0.0871159	+	0.150889i
$223$	0.724649	+	3.17489i	0.0485261	+	0.212607i	0.993378	−	0.114891i	$-0.0366518\pi$
$223$	0.724649	+	3.17489i	0.0485261	+	0.212607i	−0.944852	+	0.327498i	$0.893795\pi$
$224$	1.84885	+	4.71080i	0.123532	+	0.314753i
$225$	−1.75909	+	0.542609i	−0.117273	+	0.0361739i
$226$	6.28469	−	7.88076i	0.418052	−	0.524220i
$227$	1.61088	+	21.4957i	0.106918	+	1.42672i	0.750260	+	0.661142i	$0.229928\pi$
$227$	1.61088	+	21.4957i	0.106918	+	1.42672i	−0.643342	+	0.765579i	$0.722453\pi$
$228$	−8.26331	−	2.54889i	−0.547251	−	0.168805i
$229$	5.53635	−	3.77462i	0.365852	−	0.249434i	−0.366415	−	0.930452i	$-0.619415\pi$
$229$	5.53635	−	3.77462i	0.365852	−	0.249434i	0.732267	+	0.681018i	$0.238462\pi$
$230$	−4.37136	+	0.658876i	−0.288239	+	0.0434450i
$231$	0.949104	−	4.15830i	0.0624464	−	0.273596i
$232$	−0.986840	−	0.915653i	−0.0647892	−	0.0601156i
$233$	−0.794140	+	10.5971i	−0.0520258	+	0.694237i	0.908826	+	0.417175i	$0.136980\pi$
$233$	−0.794140	+	10.5971i	−0.0520258	+	0.694237i	−0.960852	+	0.277062i	$0.910639\pi$
$234$	0.756830	−	1.92837i	0.0494755	−	0.126062i
$235$	2.02140	+	0.304677i	0.131862	+	0.0198749i
$236$	−2.68677	+	1.29388i	−0.174894	+	0.0842246i
$237$	−6.75196	+	3.25157i	−0.438587	+	0.211212i
$238$	11.1647	+	1.68281i	0.723702	+	0.109081i
$239$	−2.82263	+	7.19195i	−0.182581	+	0.465209i	−0.992635	−	0.121147i	$-0.961343\pi$
$239$	−2.82263	+	7.19195i	−0.182581	+	0.465209i	0.810054	+	0.586356i	$0.199438\pi$
$240$	−0.0804562	+	1.07361i	−0.00519343	+	0.0693015i
$241$	4.48789	+	4.16416i	0.289091	+	0.268237i	0.811364	−	0.584541i	$-0.198725\pi$
$241$	4.48789	+	4.16416i	0.289091	+	0.268237i	−0.522273	+	0.852778i	$0.674916\pi$
$242$	−2.31136	+	10.1267i	−0.148580	+	0.650971i
$243$	15.3666	−	2.31614i	0.985765	−	0.148580i
$244$	−2.48874	+	1.69680i	−0.159325	+	0.108626i
$245$	17.7831	+	5.48536i	1.13612	+	0.350447i
$246$	−0.347363	−	4.63523i	−0.0221470	−	0.295532i
$247$	5.63546	−	7.06665i	0.358576	−	0.449640i
$248$	0.0281487	−	0.00868274i	0.00178745	−	0.000551354i
$249$	−3.86664	−	9.85203i	−0.245038	−	0.624347i
$250$	0.222521	+	0.974928i	0.0140735	+	0.0616599i
$251$	11.8532	−	20.5304i	0.748170	−	1.29587i	−0.200529	−	0.979688i	$-0.564266\pi$
$251$	11.8532	−	20.5304i	0.748170	−	1.29587i	0.948699	−	0.316180i	$-0.102400\pi$
$252$	−4.65800	−	8.06789i	−0.293426	−	0.508229i
$253$	−2.53690	+	2.35390i	−0.159494	+	0.147989i
$254$	7.61253	+	9.54581i	0.477653	+	0.598958i
$255$	1.98469	+	1.35314i	0.124286	+	0.0847368i
$256$	−0.900969	−	0.433884i	−0.0563106	−	0.0271177i
$257$	3.47028			0.216470			0.108235	−	0.994125i	$-0.465480\pi$
$257$	3.47028			0.216470			0.108235	+	0.994125i	$0.465480\pi$
$258$	6.62728	−	2.43336i	0.412597	−	0.151495i
$259$	−12.2023			−0.758217
$260$	−1.01387	−	0.488256i	−0.0628778	−	0.0302804i
$261$	2.04759	+	1.39602i	0.126743	+	0.0864117i
$262$	−5.44761	−	6.83108i	−0.336554	−	0.422026i
$263$	−1.13012	+	1.04859i	−0.0696859	+	0.0646591i	−0.714247	−	0.699894i	$-0.753231\pi$
$263$	−1.13012	+	1.04859i	−0.0696859	+	0.0646591i	0.644561	+	0.764553i	$0.277040\pi$
$264$	0.421414	+	0.729911i	0.0259362	+	0.0449229i
$265$	5.04776	−	8.74298i	0.310081	−	0.537077i
$266$	−9.04483	−	39.6280i	−0.554574	−	2.42975i
$267$	−4.02194	−	10.2477i	−0.246139	−	0.627151i
$268$	−10.3114	+	3.18063i	−0.629866	+	0.194288i
$269$	−19.4252	+	24.3584i	−1.18438	+	1.48516i	−0.347576	+	0.937652i	$0.612995\pi$
$269$	−19.4252	+	24.3584i	−1.18438	+	1.48516i	−0.836800	+	0.547509i	$0.815576\pi$
$270$	−0.389479	−	5.19724i	−0.0237029	−	0.316294i
$271$	−9.00498	−	2.77767i	−0.547013	−	0.168731i	0.00891688	−	0.999960i	$-0.497162\pi$
$271$	−9.00498	−	2.77767i	−0.547013	−	0.168731i	−0.555930	+	0.831229i	$0.687638\pi$
$272$	−1.84344	+	1.25683i	−0.111775	+	0.0762067i
$273$	−6.06267	+	0.913801i	−0.366930	+	0.0553057i
$274$	4.68641	−	20.5325i	0.283116	−	1.24041i
$275$	0.573865	+	0.532469i	0.0346054	+	0.0321091i
$276$	0.355676	−	4.74616i	0.0214092	−	0.285685i
$277$	−4.87925	+	12.4321i	−0.293166	+	0.746974i	0.706080	+	0.708132i	$0.250462\pi$
$277$	−4.87925	+	12.4321i	−0.293166	+	0.746974i	−0.999245	+	0.0388416i	$0.987633\pi$
$278$	13.8157	+	2.08238i	0.828610	+	0.124893i
$279$	−0.0488574	+	0.0235285i	−0.00292502	+	0.00140861i
$280$	−4.55946	+	2.19572i	−0.272480	+	0.131219i
$281$	−18.5392	−	2.79434i	−1.10596	−	0.166696i	−0.429421	−	0.903105i	$-0.641282\pi$
$281$	−18.5392	−	2.79434i	−1.10596	−	0.166696i	−0.676537	+	0.736408i	$0.736520\pi$
$282$	−0.804068	+	2.04873i	−0.0478815	+	0.122000i
$283$	2.27181	−	30.3151i	0.135045	−	1.80205i	−0.359760	−	0.933045i	$-0.617142\pi$
$283$	2.27181	−	30.3151i	0.135045	−	1.80205i	0.494805	−	0.869004i	$-0.335239\pi$
$284$	0.0421529	+	0.0391122i	0.00250132	+	0.00232088i
$285$	1.92425	−	8.43068i	0.113983	−	0.499391i
$286$	−0.871106	+	0.131298i	−0.0515096	+	0.00776382i
$287$	18.0523	−	12.3079i	1.06559	−	0.726510i
$288$	1.75909	+	0.542609i	0.103656	+	0.0319735i
$289$	−0.898414	−	11.9885i	−0.0528479	−	0.705206i
$290$	0.839346	−	1.05251i	0.0492881	−	0.0618053i
$291$	13.6229	−	4.20211i	0.798589	−	0.246332i
$292$	−2.22707	−	5.67448i	−0.130329	−	0.332074i
$293$	6.56902	+	28.7807i	0.383766	+	1.68139i	0.685560	+	0.728016i	$0.259557\pi$
$293$	6.56902	+	28.7807i	0.383766	+	1.68139i	−0.301794	+	0.953373i	$0.597585\pi$
$294$	−10.0179	+	17.3515i	−0.584257	+	1.01196i
$295$	−1.49105	−	2.58257i	−0.0868121	−	0.150363i
$296$	1.76756	−	1.64006i	0.102737	−	0.0953264i
$297$	−2.54386	−	3.18990i	−0.147610	−	0.185097i
$298$	−0.225801	−	0.153949i	−0.0130803	−	0.00891801i
$299$	4.48207	+	2.15845i	0.259205	+	0.124826i
$300$	−1.07662			−0.0621589
$301$	25.4811	+	21.2588i	1.46871	+	1.22534i
$302$	−3.26688			−0.187988
$303$	1.28212	+	0.617438i	0.0736560	+	0.0354709i
$304$	6.63639	+	4.52461i	0.380623	+	0.259504i
$305$	−1.87804	−	2.35498i	−0.107536	−	0.134846i
$306$	3.01081	−	2.79362i	0.172116	−	0.159701i
$307$	1.99652	+	3.45808i	0.113948	+	0.197363i	0.917359	−	0.398062i	$-0.130317\pi$
$307$	1.99652	+	3.45808i	0.113948	+	0.197363i	−0.803411	+	0.595425i	$0.796984\pi$
$308$	−1.98084	+	3.43091i	−0.112869	+	0.195494i
$309$	−3.91709	−	17.1619i	−0.222835	−	0.976305i
$310$	0.0107620	+	0.0274212i	0.000611241	+	0.00155742i
$311$	12.0288	−	3.71041i	0.682093	−	0.210398i	0.0657034	−	0.997839i	$-0.479071\pi$
$311$	12.0288	−	3.71041i	0.682093	−	0.210398i	0.616390	+	0.787441i	$0.288595\pi$
$312$	0.755384	−	0.947222i	0.0427652	−	0.0536259i
$313$	0.220983	+	2.94882i	0.0124907	+	0.166677i	0.999961	+	0.00886978i	$0.00282338\pi$
$313$	0.220983	+	2.94882i	0.0124907	+	0.166677i	−0.987470	+	0.157807i	$0.949558\pi$
$314$	11.2826	+	3.48023i	0.636715	+	0.196401i
$315$	7.69724	−	5.24789i	0.433690	−	0.295685i
$316$	6.88300	−	1.03745i	0.387199	−	0.0583609i
$317$	1.80934	−	7.92722i	0.101623	−	0.445237i	−0.898360	−	0.439261i	$-0.855240\pi$
$317$	1.80934	−	7.92722i	0.101623	−	0.445237i	0.999982	−	0.00597658i	$-0.00190241\pi$
$318$	7.96760	+	7.39285i	0.446801	+	0.414571i
$319$	0.0787558	−	1.05092i	0.00440948	−	0.0588404i
$320$	0.365341	−	0.930874i	0.0204232	−	0.0520374i
$321$	14.5005	+	2.18560i	0.809340	+	0.121988i
$322$	20.1562	−	9.70670i	1.12326	−	0.540933i
$323$	16.1458	−	7.77539i	0.898374	−	0.432634i
$324$	0.0875317	+	0.0131933i	0.00486287	+	0.000732960i
$325$	0.411124	−	1.04753i	0.0228050	−	0.0581063i
$326$	−1.85322	+	24.7295i	−0.102641	+	1.36964i
$327$	1.18797	+	1.10227i	0.0656947	+	0.0609558i
$328$	−0.960714	+	4.20916i	−0.0530466	+	0.232412i
$329$	−10.2295	+	1.54185i	−0.563972	+	0.0850051i
$330$	−0.696377	+	0.474782i	−0.0383343	+	0.0261359i
$331$	−2.96129	−	0.913438i	−0.162767	−	0.0502071i	0.212301	−	0.977204i	$-0.431904\pi$
$331$	−2.96129	−	0.913438i	−0.162767	−	0.0502071i	−0.375068	+	0.926997i	$0.622381\pi$
$332$	0.734626	+	9.80290i	0.0403178	+	0.538004i
$333$	−2.76754	+	3.47039i	−0.151660	+	0.190176i
$334$	15.7905	−	4.87074i	0.864020	−	0.266515i
$335$	−3.94231	−	10.0448i	−0.215391	−	0.548808i
$336$	−1.21238	−	5.31178i	−0.0661408	−	0.289782i
$337$	9.94003	−	17.2166i	0.541468	−	0.937850i	−0.457352	−	0.889286i	$-0.651202\pi$
$337$	9.94003	−	17.2166i	0.541468	−	0.937850i	0.998820	−	0.0485641i	$-0.0154645\pi$
$338$	−5.86683	−	10.1617i	−0.319114	−	0.552721i
$339$	−7.95525	+	7.38139i	−0.432070	+	0.400902i
$340$	−1.39108	−	1.74436i	−0.0754419	−	0.0946011i
$341$	0.0190535	+	0.0129905i	0.00103181	+	0.000703474i
$342$	−13.3218	−	6.41542i	−0.720358	−	0.346906i
$343$	−58.7531			−3.17237
$344$	−6.54834	+	0.345367i	−0.353063	+	0.0186209i
$345$	4.75947			0.256241
$346$	10.5495	+	5.08039i	0.567147	+	0.273124i
$347$	21.4739	+	14.6407i	1.15278	+	0.785952i	0.979998	−	0.199008i	$-0.0637721\pi$
$347$	21.4739	+	14.6407i	1.15278	+	0.785952i	0.172782	+	0.984960i	$0.444725\pi$
$348$	0.903661	+	1.13315i	0.0484413	+	0.0607435i
$349$	−1.49786	+	1.38981i	−0.0801788	+	0.0743951i	−0.719244	−	0.694757i	$-0.755512\pi$
$349$	−1.49786	+	1.38981i	−0.0801788	+	0.0743951i	0.639065	+	0.769152i	$0.279321\pi$
$350$	−2.53031	−	4.38263i	−0.135251	−	0.234261i
$351$	−2.93246	+	5.07918i	−0.156523	+	0.271106i
$352$	−0.174199	−	0.763216i	−0.00928484	−	0.0406795i
$353$	3.58143	+	9.12533i	0.190620	+	0.485693i	0.993949	−	0.109843i	$-0.0350349\pi$
$353$	3.58143	+	9.12533i	0.190620	+	0.485693i	−0.803329	+	0.595536i	$0.796940\pi$
$354$	3.06796	−	0.946339i	0.163060	−	0.0502974i
$355$	−0.0358527	+	0.0449579i	−0.00190287	+	0.00238612i
$356$	0.764132	+	10.1966i	0.0404989	+	0.540420i
$357$	−11.6159	−	3.58304i	−0.614781	−	0.189635i
$358$	17.4505	−	11.8976i	0.922289	−	0.628806i
$359$	−33.8244	+	5.09821i	−1.78518	+	0.269073i	−0.956729	−	0.290981i	$-0.906018\pi$
$359$	−33.8244	+	5.09821i	−1.78518	+	0.269073i	−0.828456	+	0.560054i	$0.810780\pi$
$360$	−0.409634	+	1.79473i	−0.0215896	+	0.0945903i
$361$	−33.3639	−	30.9572i	−1.75600	−	1.62933i
$362$	0.624662	−	8.33553i	0.0328315	−	0.438106i
$363$	4.08563	−	10.4100i	0.214440	−	0.546384i
$364$	5.63119	+	0.848765i	0.295154	+	0.0444874i
$365$	5.49218	−	2.64490i	0.287474	−	0.138440i
$366$	2.92179	−	1.40706i	0.152724	−	0.0735481i
$367$	−36.4910	−	5.50014i	−1.90482	−	0.287105i	−0.912329	−	0.409457i	$-0.865718\pi$
$367$	−36.4910	−	5.50014i	−1.90482	−	0.287105i	−0.992487	+	0.122352i	$0.960956\pi$
$368$	−1.61508	+	4.11515i	−0.0841917	+	0.214517i
$369$	0.593943	−	7.92561i	0.0309194	−	0.412591i
$370$	1.76756	+	1.64006i	0.0918911	+	0.0852625i
$371$	−11.3685	+	49.8087i	−0.590223	+	2.58594i
$372$	−0.0313604	+	0.00472682i	−0.00162596	+	0.000245074i
$373$	−29.1294	+	19.8601i	−1.50826	+	1.02832i	−0.523977	+	0.851732i	$0.675552\pi$
$373$	−29.1294	+	19.8601i	−1.50826	+	1.02832i	−0.984286	+	0.176584i	$0.943495\pi$
$374$	−1.66902	−	0.514824i	−0.0863029	−	0.0266209i
$375$	−0.0804562	−	1.07361i	−0.00415474	−	0.0554412i
$376$	1.27456	−	1.59824i	0.0657303	−	0.0824232i
$377$	−1.44760	+	0.446527i	−0.0745554	+	0.0229973i
$378$	9.63586	+	24.5518i	0.495615	+	1.26281i
$379$	−2.25313	−	9.87159i	−0.115735	−	0.507069i	−0.999252	−	0.0386699i	$-0.987688\pi$
$379$	−2.25313	−	9.87159i	−0.115735	−	0.507069i	0.883517	−	0.468400i	$-0.155169\pi$
$380$	−4.01602	+	6.95595i	−0.206018	+	0.356833i
$381$	−6.57255	−	11.3840i	−0.336722	−	0.583220i
$382$	−18.3472	+	17.0237i	−0.938722	+	0.871007i
$383$	−5.36625	−	6.72907i	−0.274203	−	0.343839i	0.625594	−	0.780149i	$-0.284857\pi$
$383$	−5.36625	−	6.72907i	−0.274203	−	0.343839i	−0.899797	+	0.436310i	$0.856285\pi$
$384$	0.889549	+	0.606484i	0.0453946	+	0.0309495i
$385$	−3.56934	−	1.71891i	−0.181911	−	0.0876035i
$386$	−3.71788			−0.189235
$387$	11.8253	−	2.42534i	0.601114	−	0.123287i
$388$	−13.2416			−0.672242
$389$	−23.1580	−	11.1523i	−1.17416	−	0.565445i	−0.257955	−	0.966157i	$-0.583048\pi$
$389$	−23.1580	−	11.1523i	−1.17416	−	0.565445i	−0.916204	+	0.400712i	$0.868763\pi$
$390$	1.00102	+	0.682486i	0.0506888	+	0.0345590i
$391$	6.14959	+	7.71135i	0.310998	+	0.389980i
$392$	13.6420	−	12.6579i	0.689025	−	0.639322i
$393$	4.70339	+	8.14650i	0.237254	+	0.410937i
$394$	−8.56841	+	14.8409i	−0.431670	+	0.747675i
$395$	1.54891	+	6.78623i	0.0779342	+	0.341452i
$396$	0.526501	+	1.34150i	0.0264576	+	0.0674130i
$397$	−15.1773	+	4.68158i	−0.761727	+	0.234962i	−0.651195	−	0.758911i	$-0.725732\pi$
$397$	−15.1773	+	4.68158i	−0.761727	+	0.234962i	−0.110533	+	0.993873i	$0.535256\pi$
$398$	9.27843	−	11.6348i	0.465086	−	0.583199i
$399$	3.27031	+	43.6393i	0.163720	+	2.18470i
$400$	0.955573	+	0.294755i	0.0477786	+	0.0147378i
$401$	12.3570	−	8.42489i	0.617081	−	0.420719i	−0.214028	−	0.976827i	$-0.568658\pi$
$401$	12.3570	−	8.42489i	0.617081	−	0.420719i	0.831110	+	0.556109i	$0.187706\pi$
$402$	11.4878	−	1.73151i	0.572961	−	0.0863600i
$403$	0.00737633	−	0.0323178i	0.000367441	−	0.00160986i
$404$	−0.968925	−	0.899031i	−0.0482058	−	0.0447285i
$405$	−0.00661514	+	0.0882729i	−0.000328709	+	0.00438631i
$406$	−2.48894	+	6.34171i	−0.123524	+	0.314734i
$407$	1.86654	+	0.281335i	0.0925208	+	0.0139453i
$408$	2.16420	−	1.04222i	0.107144	−	0.0515977i
$409$	−0.458262	+	0.220688i	−0.0226596	+	0.0109123i	−0.445179	−	0.895441i	$-0.646860\pi$
$409$	−0.458262	+	0.220688i	−0.0226596	+	0.0109123i	0.422520	+	0.906354i	$0.361146\pi$
$410$	−4.26919	−	0.643477i	−0.210840	−	0.0317790i
$411$	−8.28385	+	21.1069i	−0.408612	+	1.04113i
$412$	−1.22187	+	16.3047i	−0.0601970	+	0.803273i
$413$	11.0627	+	10.2647i	0.544358	+	0.505091i
$414$	1.81089	−	7.93401i	0.0890002	−	0.389935i
$415$	−9.72059	+	1.46514i	−0.477165	+	0.0719210i
$416$	−0.929779	+	0.633913i	−0.0455862	+	0.0310801i
$417$	−14.3740	−	4.43380i	−0.703900	−	0.217124i
$418$	0.469890	+	6.27025i	0.0229831	+	0.306688i
$419$	23.5464	−	29.5263i	1.15032	−	1.44245i	0.273342	−	0.961917i	$-0.411871\pi$
$419$	23.5464	−	29.5263i	1.15032	−	1.44245i	0.876976	−	0.480535i	$-0.159558\pi$
$420$	5.20633	−	1.60594i	0.254043	−	0.0783619i
$421$	2.69430	+	6.86495i	0.131312	+	0.334577i	0.981375	−	0.192104i	$-0.0615312\pi$
$421$	2.69430	+	6.86495i	0.131312	+	0.334577i	−0.850063	+	0.526682i	$0.823436\pi$
$422$	−2.98958	−	13.0982i	−0.145530	−	0.637610i
$423$	−1.88159	+	3.25901i	−0.0914861	+	0.158459i
$424$	−5.04776	−	8.74298i	−0.245141	−	0.424596i
$425$	1.63553	−	1.51755i	0.0793346	−	0.0736118i
$426$	−0.0385999	−	0.0484028i	−0.00187017	−	0.00234512i
$427$	12.5946	+	8.58684i	0.609495	+	0.415546i
$428$	−12.2718	−	5.90977i	−0.593178	−	0.285659i
$429$	0.948448			0.0457915
$430$	−0.833759	−	6.50422i	−0.0402074	−	0.313661i
$431$	−27.2776			−1.31392			−0.656959	−	0.753927i	$-0.728157\pi$
$431$	−27.2776			−1.31392			−0.656959	+	0.753927i	$0.728157\pi$
$432$	−4.69568	−	2.26132i	−0.225921	−	0.108798i
$433$	7.82966	+	5.33817i	0.376270	+	0.256536i	0.736657	−	0.676266i	$-0.236403\pi$
$433$	7.82966	+	5.33817i	0.376270	+	0.256536i	−0.360388	+	0.932803i	$0.617356\pi$
$434$	−0.0929455	−	0.116550i	−0.00446153	−	0.00559458i
$435$	−1.06246	+	0.985815i	−0.0509408	+	0.0472662i
$436$	−0.752620	−	1.30358i	−0.0360439	−	0.0624299i
$437$	17.7538	−	30.7504i	0.849278	−	1.47099i
$438$	1.46039	+	6.39841i	0.0697804	+	0.305728i
$439$	11.3827	+	29.0026i	0.543265	+	1.38422i	0.894137	+	0.447793i	$0.147790\pi$
$439$	11.3827	+	29.0026i	0.543265	+	1.38422i	−0.350872	+	0.936423i	$0.614115\pi$
$440$	0.748064	−	0.230747i	0.0356625	−	0.0110004i
$441$	−21.3599	+	26.7844i	−1.01714	+	1.27545i
$442$	0.187626	+	2.50369i	0.00892444	+	0.119088i
$443$	2.01117	+	0.620362i	0.0955534	+	0.0294743i	0.342163	−	0.939641i	$-0.388840\pi$
$443$	2.01117	+	0.620362i	0.0955534	+	0.0294743i	−0.246610	+	0.969115i	$0.579317\pi$
$444$	−2.14491	+	1.46238i	−0.101793	+	0.0694013i
$445$	−10.1110	+	1.52399i	−0.479308	+	0.0722441i
$446$	−0.724649	+	3.17489i	−0.0343131	+	0.150336i
$447$	0.215685	+	0.200126i	0.0102015	+	0.00946565i
$448$	−0.378181	+	5.04647i	−0.0178674	+	0.238423i
$449$	−6.82097	+	17.3796i	−0.321902	+	0.820192i	0.674721	+	0.738073i	$0.264264\pi$
$449$	−6.82097	+	17.3796i	−0.321902	+	0.820192i	−0.996623	+	0.0821188i	$0.973831\pi$
$450$	−1.82032	−	0.274369i	−0.0858107	−	0.0129339i
$451$	−3.04515	+	1.46646i	−0.143390	+	0.0690531i
$452$	9.08165	−	4.37349i	0.427165	−	0.205712i
$453$	3.47792	+	0.524212i	0.163407	+	0.0246296i
$454$	−7.87529	+	20.0659i	−0.369606	+	0.941740i
$455$	−0.425572	+	5.67887i	−0.0199511	+	0.266229i
$456$	−6.33906	−	5.88179i	−0.296854	−	0.275440i
$457$	4.93220	−	21.6094i	0.230718	−	1.01084i	−0.718327	−	0.695705i	$-0.755092\pi$
$457$	4.93220	−	21.6094i	0.230718	−	1.01084i	0.949046	−	0.315138i	$-0.102051\pi$
$458$	6.62583	−	0.998682i	0.309604	−	0.0466654i
$459$	−9.60764	+	6.55038i	−0.448446	+	0.305745i
$460$	−4.22433	−	1.30303i	−0.196961	−	0.0607543i
$461$	2.51988	+	33.6255i	0.117363	+	1.56609i	0.676138	+	0.736775i	$0.263652\pi$
$461$	2.51988	+	33.6255i	0.117363	+	1.56609i	−0.558775	+	0.829319i	$0.688729\pi$
$462$	2.65933	−	3.33469i	0.123723	−	0.155144i
$463$	−37.0611	+	11.4318i	−1.72237	+	0.531282i	−0.988919	−	0.148456i	$-0.952570\pi$
$463$	−37.0611	+	11.4318i	−1.72237	+	0.531282i	−0.733455	+	0.679738i	$0.762093\pi$
$464$	−0.491825	−	1.25315i	−0.0228324	−	0.0581760i
$465$	−0.00705716	−	0.0309195i	−0.000327268	−	0.00143386i
$466$	−5.31339	+	9.20306i	−0.246138	+	0.426323i
$467$	−15.5987	−	27.0178i	−0.721823	−	1.25023i	−0.960268	−	0.279078i	$-0.909971\pi$
$467$	−15.5987	−	27.0178i	−0.721823	−	1.25023i	0.238446	−	0.971156i	$-0.423362\pi$
$468$	1.51857	−	1.40903i	0.0701959	−	0.0651322i
$469$	34.0475	+	42.6942i	1.57217	+	1.97143i
$470$	1.68902	+	1.15156i	0.0779088	+	0.0531173i
$471$	−11.4530	−	5.51549i	−0.527727	−	0.254140i
$472$	−2.98209			−0.137262
$473$	−3.40759	−	3.83935i	−0.156681	−	0.176533i
$474$	−7.49411			−0.344216
$475$	−7.23662	−	3.48497i	−0.332039	−	0.159902i
$476$	9.32893	+	6.36036i	0.427591	+	0.291526i
$477$	11.5873	+	14.5301i	0.530547	+	0.665286i
$478$	−5.66358	+	5.25503i	−0.259046	+	0.240360i
$479$	−5.48420	−	9.49891i	−0.250579	−	0.434016i	0.713106	−	0.701056i	$-0.247288\pi$
$479$	−5.48420	−	9.49891i	−0.250579	−	0.434016i	−0.963685	+	0.267040i	$0.913954\pi$
$480$	−0.538312	+	0.932384i	−0.0245705	+	0.0425573i
$481$	−0.603788	−	2.64537i	−0.0275304	−	0.120618i
$482$	2.23669	+	5.69900i	0.101879	+	0.259582i
$483$	−23.0158	+	7.09944i	−1.04726	+	0.323036i
$484$	−6.47629	+	8.12101i	−0.294377	+	0.369137i
$485$	−0.989549	−	13.2046i	−0.0449331	−	0.599590i
$486$	14.8497	+	4.58053i	0.673597	+	0.207777i
$487$	20.9410	−	14.2773i	0.948925	−	0.646966i	0.0132812	−	0.999912i	$-0.495772\pi$
$487$	20.9410	−	14.2773i	0.948925	−	0.646966i	0.935644	+	0.352946i	$0.114820\pi$
$488$	−2.97849	+	0.448936i	−0.134830	+	0.0203224i
$489$	5.94110	−	26.0297i	0.268666	−	1.17710i
$490$	13.6420	+	12.6579i	0.616283	+	0.571827i
$491$	2.30393	−	30.7439i	0.103975	−	1.38745i	−0.664364	−	0.747409i	$-0.731298\pi$
$491$	2.30393	−	30.7439i	0.103975	−	1.38745i	0.768339	−	0.640043i	$-0.221083\pi$
$492$	1.69819	−	4.32691i	0.0765603	−	0.195072i
$493$	−2.97000	−	0.447656i	−0.133762	−	0.0201614i
$494$	8.14348	−	3.92169i	0.366393	−	0.176445i
$495$	−1.29841	+	0.625279i	−0.0583590	+	0.0281042i
$496$	0.0291284	+	0.00439041i	0.00130791	+	0.000197135i
$497$	0.106315	−	0.270887i	0.00476889	−	0.0121509i
$498$	0.790916	−	10.5540i	0.0354418	−	0.472938i
$499$	24.1909	+	22.4459i	1.08293	+	1.00482i	0.999966	+	0.00826351i	$0.00263039\pi$
$499$	24.1909	+	22.4459i	1.08293	+	1.00482i	0.0829679	+	0.996552i	$0.473560\pi$
$500$	−0.222521	+	0.974928i	−0.00995144	+	0.0436001i
$501$	−17.5922	+	2.65159i	−0.785960	+	0.118464i
$502$	19.5872	−	13.3543i	0.874220	−	0.596033i
$503$	36.2012	+	11.1666i	1.61413	+	0.497894i	0.964882	−	0.262682i	$-0.0846070\pi$
$503$	36.2012	+	11.1666i	1.61413	+	0.497894i	0.649249	+	0.760576i	$0.275083\pi$
$504$	−0.696185	−	9.28994i	−0.0310105	−	0.413807i
$505$	0.824109	−	1.03340i	0.0366724	−	0.0459857i
$506$	−3.30699	+	1.02007i	−0.147014	+	0.0453477i
$507$	4.61526	+	11.7595i	0.204971	+	0.522258i
$508$	2.71688	+	11.9034i	0.120542	+	0.528130i
$509$	−7.13328	+	12.3552i	−0.316177	+	0.547635i	−0.979687	−	0.200533i	$-0.935733\pi$
$509$	−7.13328	+	12.3552i	−0.316177	+	0.547635i	0.663510	+	0.748168i	$0.269066\pi$
$510$	1.20104	+	2.08026i	0.0531829	+	0.0921154i
$511$	−22.6138	+	20.9825i	−1.00038	+	0.928213i
$512$	−0.623490	−	0.781831i	−0.0275546	−	0.0345524i
$513$	34.5876	+	23.5814i	1.52708	+	1.04114i
$514$	3.12662	+	1.50570i	0.137909	+	0.0664135i
$515$	−16.3504			−0.720484
$516$	7.02677	+	0.683086i	0.309336	+	0.0300712i
$517$	1.60031			0.0703817
$518$	−10.9939	−	5.29440i	−0.483046	−	0.232623i
$519$	−10.4158	−	7.10139i	−0.457204	−	0.311716i
$520$	−0.701623	−	0.879807i	−0.0307682	−	0.0385821i
$521$	5.93784	−	5.50951i	0.260141	−	0.241376i	−0.539309	−	0.842108i	$-0.681315\pi$
$521$	5.93784	−	5.50951i	0.260141	−	0.241376i	0.799451	+	0.600732i	$0.205124\pi$
$522$	1.23910	+	2.14619i	0.0542341	+	0.0939362i
$523$	7.16315	−	12.4069i	0.313223	−	0.542518i	−0.665835	−	0.746099i	$-0.731925\pi$
$523$	7.16315	−	12.4069i	0.313223	−	0.542518i	0.979058	+	0.203581i	$0.0652580\pi$
$524$	−1.94423	−	8.51822i	−0.0849340	−	0.372120i
$525$	1.99052	+	5.07176i	0.0868734	+	0.221350i
$526$	−1.47317	+	0.454412i	−0.0642331	+	0.0198133i
$527$	0.0409777	−	0.0513844i	0.00178501	−	0.00223834i
$528$	0.0629846	+	0.840472i	0.00274105	+	0.0365768i
$529$	−3.30351	−	1.01900i	−0.143631	−	0.0443042i
$530$	8.34131	−	5.68701i	0.362323	−	0.247028i
$531$	5.42836	−	0.818194i	0.235571	−	0.0355066i
$532$	9.04483	−	39.6280i	0.392143	−	1.71809i
$533$	3.56149	+	3.30458i	0.154265	+	0.143137i
$534$	0.822683	−	10.9779i	0.0356010	−	0.475062i
$535$	4.97617	−	12.6791i	0.215139	−	0.548165i
$536$	−10.6702	−	1.60828i	−0.460884	−	0.0694671i
$537$	−20.4869	+	9.86598i	−0.884076	+	0.425749i
$538$	−28.0702	+	13.5179i	−1.21019	+	0.582799i
$539$	14.4059	+	2.17134i	0.620506	+	0.0935262i
$540$	1.90409	−	4.85154i	0.0819389	−	0.208777i
$541$	1.72437	−	23.0102i	0.0741366	−	0.989284i	−0.828810	−	0.559531i	$-0.810981\pi$
$541$	1.72437	−	23.0102i	0.0741366	−	0.989284i	0.902946	−	0.429753i	$-0.141400\pi$
$542$	−6.90802	−	6.40970i	−0.296725	−	0.275320i
$543$	−2.00255	+	8.77376i	−0.0859378	+	0.376518i
$544$	−2.20620	+	0.332531i	−0.0945900	+	0.0142571i
$545$	1.24369	−	0.847931i	0.0532737	−	0.0363214i
$546$	−5.85876	−	1.80719i	−0.250732	−	0.0773405i
$547$	−2.35909	−	31.4798i	−0.100867	−	1.34598i	−0.786300	−	0.617844i	$-0.788006\pi$
$547$	−2.35909	−	31.4798i	−0.100867	−	1.34598i	0.685433	−	0.728136i	$-0.259613\pi$
$548$	13.1310	−	16.4658i	0.560930	−	0.703384i
$549$	5.29863	−	1.63441i	0.226140	−	0.0697550i
$550$	0.286005	+	0.728728i	0.0121953	+	0.0310731i
$551$	2.40607	+	10.5417i	0.102502	+	0.449091i
$552$	2.37974	−	4.12182i	0.101288	−	0.175436i
$553$	−17.6129	−	30.5064i	−0.748975	−	1.29726i
$554$	−9.79015	+	9.08393i	−0.415944	+	0.385939i
$555$	−1.61858	−	2.02963i	−0.0687047	−	0.0861530i
$556$	11.5440	+	7.87057i	0.489575	+	0.333786i
$557$	−16.9811	−	8.17765i	−0.719511	−	0.346498i	0.0380385	−	0.999276i	$-0.487889\pi$
$557$	−16.9811	−	8.17765i	−0.719511	−	0.346498i	−0.757549	+	0.652778i	$0.773603\pi$
$558$	−0.0542276			−0.00229564
$559$	−3.34789	+	6.57602i	−0.141601	+	0.278136i
$560$	−5.06062			−0.213850
$561$	1.69423	+	0.815896i	0.0715303	+	0.0344472i
$562$	−15.4909	−	10.5615i	−0.653442	−	0.445509i
$563$	−25.4102	−	31.8633i	−1.07091	−	1.34288i	−0.935991	−	0.352023i	$-0.885494\pi$
$563$	−25.4102	−	31.8633i	−1.07091	−	1.34288i	−0.134920	−	0.990857i	$-0.543078\pi$
$564$	−1.61335	+	1.49697i	−0.0679343	+	0.0630339i
$565$	5.03993	+	8.72942i	0.212032	+	0.367250i
$566$	15.2001	−	26.3273i	0.638907	−	1.10662i
$567$	−0.0996823	−	0.436737i	−0.00418626	−	0.0183412i
$568$	0.0210083	+	0.0535283i	0.000881490	+	0.00224600i
$569$	−36.3848	+	11.2232i	−1.52533	+	0.470502i	−0.940253	−	0.340476i	$-0.889412\pi$
$569$	−36.3848	+	11.2232i	−1.52533	+	0.470502i	−0.585077	+	0.810978i	$0.698936\pi$
$570$	5.39162	−	6.76088i	0.225830	−	0.283182i
$571$	2.31444	+	30.8840i	0.0968561	+	1.29246i	0.807905	+	0.589313i	$0.200601\pi$
$571$	2.31444	+	30.8840i	0.0968561	+	1.29246i	−0.711049	+	0.703143i	$0.751780\pi$
$572$	−0.841808	−	0.259663i	−0.0351978	−	0.0108571i
$573$	22.2640	−	15.1794i	0.930093	−	0.634127i
$574$	21.6047	−	3.25639i	0.901765	−	0.135919i
$575$	0.983706	−	4.30990i	0.0410234	−	0.179735i
$576$	1.34946	+	1.25212i	0.0562275	+	0.0521715i
$577$	3.03957	−	40.5603i	0.126539	−	1.68855i	−0.467407	−	0.884042i	$-0.654812\pi$
$577$	3.03957	−	40.5603i	0.126539	−	1.68855i	0.593946	−	0.804505i	$-0.297569\pi$
$578$	4.39217	−	11.1911i	0.182690	−	0.465487i
$579$	3.95805	+	0.596581i	0.164491	+	0.0247930i
$580$	1.21289	−	0.584097i	0.0503625	−	0.0242533i
$581$	44.8213	−	21.5848i	1.85950	−	0.895488i
$582$	14.0970	+	2.12479i	0.584341	+	0.0880752i
$583$	2.88737	−	7.35689i	0.119583	−	0.304691i
$584$	0.455544	−	6.07882i	0.0188506	−	0.251543i
$585$	1.51857	+	1.40903i	0.0627851	+	0.0582560i
$586$	−6.56902	+	28.7807i	−0.271364	+	1.18892i
$587$	0.971675	−	0.146456i	0.0401053	−	0.00604491i	−0.128959	−	0.991650i	$-0.541164\pi$
$587$	0.971675	−	0.146456i	0.0401053	−	0.00604491i	0.169064	+	0.985605i	$0.445925\pi$
$588$	−16.5544	+	11.2866i	−0.682691	+	0.465451i
$589$	−0.226092	−	0.0697401i	−0.00931595	−	0.00287359i
$590$	−0.222852	−	2.97376i	−0.00917468	−	0.122428i
$591$	11.5033	−	14.4247i	0.473184	−	0.593354i
$592$	2.30411	−	0.710724i	0.0946984	−	0.0292106i
$593$	−3.16117	−	8.05453i	−0.129814	−	0.330760i	0.851158	−	0.524909i	$-0.175901\pi$
$593$	−3.16117	−	8.05453i	−0.129814	−	0.330760i	−0.980972	+	0.194149i	$0.937805\pi$
$594$	−0.907892	−	3.97774i	−0.0372513	−	0.163208i
$595$	−5.64542	+	9.77815i	−0.231440	+	0.400865i
$596$	−0.136644	−	0.236674i	−0.00559716	−	0.00969456i
$597$	−11.7448	+	10.8975i	−0.480681	+	0.446007i
$598$	3.10169	+	3.88939i	0.126837	+	0.159049i
$599$	−4.11253	−	2.80388i	−0.168034	−	0.114563i	0.476383	−	0.879238i	$-0.341947\pi$
$599$	−4.11253	−	2.80388i	−0.168034	−	0.114563i	−0.644417	+	0.764674i	$0.722900\pi$
$600$	−0.970005	−	0.467130i	−0.0396003	−	0.0190705i
$601$	30.0644			1.22635			0.613176	−	0.789946i	$-0.289892\pi$
$601$	30.0644			1.22635			0.613176	+	0.789946i	$0.289892\pi$
$602$	13.7339	+	30.2094i	0.559750	+	1.23124i
$603$	19.8645			0.808944
$604$	−2.94336	−	1.41745i	−0.119764	−	0.0576751i
$605$	−8.58227	−	5.85129i	−0.348919	−	0.237889i
$606$	0.887256	+	1.11258i	0.0360423	+	0.0451956i
$607$	23.8391	−	22.1194i	0.967598	−	0.897800i	−0.0272036	−	0.999630i	$-0.508660\pi$
$607$	23.8391	−	22.1194i	0.967598	−	0.897800i	0.994802	+	0.101830i	$0.0324698\pi$
$608$	4.01602	+	6.95595i	0.162871	+	0.282101i
$609$	3.66733	−	6.35200i	0.148608	−	0.257396i
$610$	−0.670263	−	2.93661i	−0.0271382	−	0.118900i
$611$	−0.840432	−	2.14139i	−0.0340002	−	0.0866312i
$612$	3.92475	−	1.21062i	0.158649	−	0.0489366i
$613$	4.27379	−	5.35917i	0.172617	−	0.216455i	−0.687996	−	0.725715i	$-0.741509\pi$
$613$	4.27379	−	5.35917i	0.172617	−	0.216455i	0.860613	+	0.509260i	$0.170081\pi$
$614$	0.298401	+	3.98188i	0.0120425	+	0.160696i
$615$	4.44172	+	1.37009i	0.179108	+	0.0552474i
$616$	−3.27329	+	2.23169i	−0.131885	+	0.0899173i
$617$	−43.4034	+	6.54201i	−1.74736	+	0.263371i	−0.943481	−	0.331428i	$-0.892470\pi$
$617$	−43.4034	+	6.54201i	−1.74736	+	0.263371i	−0.803874	+	0.594799i	$0.797232\pi$
$618$	3.91709	−	17.1619i	0.157568	−	0.690352i
$619$	−13.4670	−	12.4956i	−0.541285	−	0.502239i	0.361476	−	0.932381i	$-0.382273\pi$
$619$	−13.4670	−	12.4956i	−0.541285	−	0.502239i	−0.902761	+	0.430142i	$0.858463\pi$
$620$	−0.00220136	+	0.0293751i	−8.84087e−5	+	0.00117973i
$621$	−8.41747	+	21.4474i	−0.337781	+	0.860653i
$622$	12.4475	+	1.87616i	0.499099	+	0.0752271i
$623$	46.6215	−	22.4517i	1.86785	−	0.899509i
$624$	1.09156	−	0.525668i	0.0436974	−	0.0210436i
$625$	−0.988831	−	0.149042i	−0.0395532	−	0.00596169i
$626$	−1.08034	+	2.75267i	−0.0431792	+	0.110019i
$627$	0.505895	−	6.75070i	0.0202035	−	0.269597i
$628$	8.65528	+	8.03092i	0.345383	+	0.320469i
$629$	1.19711	−	5.24487i	0.0477318	−	0.209127i
$630$	9.21194	−	1.38848i	0.367013	−	0.0553182i
$631$	40.0116	−	27.2795i	1.59284	−	1.08598i	0.646446	−	0.762960i	$-0.276255\pi$
$631$	40.0116	−	27.2795i	1.59284	−	1.08598i	0.946392	−	0.323019i	$-0.104698\pi$
$632$	6.65150	+	2.05172i	0.264583	+	0.0816129i
$633$	1.08093	+	14.4240i	0.0429632	+	0.573304i
$634$	5.06965	−	6.35714i	0.201342	−	0.252474i
$635$	−11.6671	+	3.59883i	−0.462995	+	0.142815i
$636$	3.97092	+	10.1177i	0.157457	+	0.401195i
$637$	−4.66003	−	20.4169i	−0.184637	−	0.808948i
$638$	0.526935	−	0.912678i	0.0208615	−	0.0361333i
$639$	−0.0529284	−	0.0916746i	−0.00209381	−	0.00362659i
$640$	0.733052	−	0.680173i	0.0289764	−	0.0268862i
$641$	24.3613	+	30.5481i	0.962213	+	1.20658i	0.978403	+	0.206708i	$0.0662751\pi$
$641$	24.3613	+	30.5481i	0.962213	+	1.20658i	−0.0161894	+	0.999869i	$0.505153\pi$
$642$	12.1162	+	8.26069i	0.478189	+	0.326024i
$643$	−25.1620	−	12.1174i	−0.992291	−	0.477862i	−0.133975	−	0.990985i	$-0.542774\pi$
$643$	−25.1620	−	12.1174i	−0.992291	−	0.477862i	−0.858315	+	0.513123i	$0.828489\pi$
$644$	22.3717			0.881567
$645$	−0.156064	+	7.05817i	−0.00614502	+	0.277915i
$646$	17.9204			0.705070
$647$	−23.5725	−	11.3519i	−0.926732	−	0.446290i	−0.0912618	−	0.995827i	$-0.529090\pi$
$647$	−23.5725	−	11.3519i	−0.926732	−	0.446290i	−0.835470	+	0.549537i	$0.814804\pi$
$648$	0.0731390	+	0.0498653i	0.00287317	+	0.00195889i
$649$	−1.45554	−	1.82520i	−0.0571351	−	0.0716452i
$650$	0.824915	−	0.765409i	0.0323558	−	0.0300218i
$651$	0.0802478	+	0.138993i	0.00314516	+	0.00544757i
$652$	−12.3994	+	21.4765i	−0.485600	+	0.841083i
$653$	6.61260	+	28.9717i	0.258771	+	1.13375i	0.922567	+	0.385836i	$0.126087\pi$
$653$	6.61260	+	28.9717i	0.258771	+	1.13375i	−0.663796	+	0.747913i	$0.731056\pi$
$654$	0.592063	+	1.50855i	0.0231515	+	0.0589891i
$655$	8.34911	−	2.57536i	0.326227	−	0.100628i
$656$	−2.69186	+	3.37549i	−0.105100	+	0.131791i
$657$	0.838603	+	11.1904i	0.0327170	+	0.436578i
$658$	−9.88547	−	3.04926i	−0.385376	−	0.118873i
$659$	−8.69034	+	5.92497i	−0.338527	+	0.230804i	−0.720636	−	0.693313i	$-0.756150\pi$
$659$	−8.69034	+	5.92497i	−0.338527	+	0.230804i	0.382109	+	0.924117i	$0.375198\pi$
$660$	−0.833415	+	0.125617i	−0.0324406	+	0.00488964i
$661$	1.52873	−	6.69779i	0.0594606	−	0.260514i	−0.936457	−	0.350783i	$-0.885916\pi$
$661$	1.52873	−	6.69779i	0.0594606	−	0.260514i	0.995917	+	0.0902690i	$0.0287727\pi$
$662$	−2.27171	−	2.10784i	−0.0882924	−	0.0819234i
$663$	0.202002	−	2.69553i	0.00784512	−	0.104686i
$664$	−3.59144	+	9.15085i	−0.139375	+	0.355122i
$665$	40.1931	+	6.05814i	1.55862	+	0.234925i
$666$	−3.99922	+	1.92592i	−0.154966	+	0.0746279i
$667$	−5.36187	+	2.58214i	−0.207612	+	0.0999809i
$668$	16.3401	+	2.46288i	0.632218	+	0.0952916i
$669$	1.28091	−	3.26371i	0.0495229	−	0.126182i
$670$	0.806394	−	10.7606i	0.0311537	−	0.415718i
$671$	−1.72856	−	1.60387i	−0.0667303	−	0.0619166i
$672$	1.21238	−	5.31178i	0.0467686	−	0.204907i
$673$	2.42442	−	0.365422i	0.0934544	−	0.0140860i	−0.102149	−	0.994769i	$-0.532572\pi$
$673$	2.42442	−	0.365422i	0.0934544	−	0.0140860i	0.195603	+	0.980683i	$0.437334\pi$
$674$	16.4257	−	11.1988i	0.632693	−	0.431363i
$675$	4.98026	+	1.53621i	0.191690	+	0.0591287i
$676$	−0.876858	−	11.7009i	−0.0337253	−	0.450033i
$677$	5.06057	−	6.34575i	0.194493	−	0.243887i	−0.675016	−	0.737803i	$-0.735863\pi$
$677$	5.06057	−	6.34575i	0.194493	−	0.243887i	0.869510	+	0.493916i	$0.164435\pi$
$678$	−10.3701	+	3.19875i	−0.398261	+	0.122847i
$679$	24.4818	+	62.3787i	0.939526	+	2.39387i
$680$	−0.496471	−	2.17518i	−0.0190388	−	0.0834143i
$681$	11.6039	−	20.0985i	0.444661	−	0.770175i
$682$	0.0115303	+	0.0199710i	0.000441517	+	0.000764731i
$683$	10.0544	−	9.32916i	0.384723	−	0.356970i	−0.463975	−	0.885848i	$-0.653577\pi$
$683$	10.0544	−	9.32916i	0.384723	−	0.356970i	0.848698	+	0.528878i	$0.177387\pi$
$684$	−9.21894	−	11.5602i	−0.352495	−	0.442015i
$685$	17.4010	+	11.8638i	0.664859	+	0.453293i
$686$	−52.9348	−	25.4920i	−2.02106	−	0.973290i
$687$	−7.21410			−0.275235
$688$	−6.04970	−	2.53005i	−0.230643	−	0.0964573i
$689$	−11.3606			−0.432806
$690$	4.28814	+	2.06506i	0.163247	+	0.0786154i
$691$	−21.8497	−	14.8969i	−0.831201	−	0.566703i	0.0712686	−	0.997457i	$-0.477295\pi$
$691$	−21.8497	−	14.8969i	−0.831201	−	0.566703i	−0.902469	+	0.430754i	$0.858248\pi$
$692$	7.30051	+	9.15455i	0.277524	+	0.348004i
$693$	5.34612	−	4.96048i	0.203082	−	0.188433i
$694$	12.9950	+	22.5080i	0.493282	+	0.854390i
$695$	−6.98587	+	12.0999i	−0.264989	+	0.458975i
$696$	0.322513	+	1.41302i	0.0122248	+	0.0535604i
$697$	3.51920	+	8.96678i	0.133299	+	0.339641i
$698$	−1.95255	+	0.602281i	−0.0739050	+	0.0227967i
$699$	7.13337	−	8.94497i	0.269809	−	0.338330i
$700$	−0.378181	−	5.04647i	−0.0142939	−	0.190739i
$701$	−13.7387	−	4.23781i	−0.518902	−	0.160060i	0.0242316	−	0.999706i	$-0.492286\pi$
$701$	−13.7387	−	4.23781i	−0.518902	−	0.160060i	−0.543134	+	0.839646i	$0.682762\pi$
$702$	−4.84583	+	3.30383i	−0.182894	+	0.124695i
$703$	−19.1508	+	2.88652i	−0.722287	+	0.108867i
$704$	0.174199	−	0.763216i	0.00656537	−	0.0287648i
$705$	−1.61335	−	1.49697i	−0.0607623	−	0.0563792i
$706$	−0.732577	+	9.77557i	−0.0275709	+	0.367908i
$707$	−2.44375	+	6.22659i	−0.0919069	+	0.234175i
$708$	3.17474	+	0.478514i	0.119314	+	0.0179837i
$709$	18.0576	−	8.69609i	0.678168	−	0.326588i	−0.0628989	−	0.998020i	$-0.520035\pi$
$709$	18.0576	−	8.69609i	0.678168	−	0.326588i	0.741067	+	0.671432i	$0.234320\pi$
$710$	−0.0518087	+	0.0249498i	−0.00194435	+	0.000936348i
$711$	−12.6708	−	1.90981i	−0.475192	−	0.0716236i
$712$	−3.73569	+	9.51839i	−0.140001	+	0.356717i
$713$	0.00973162	−	0.129859i	0.000364452	−	0.00486328i
$714$	−8.91097	−	8.26818i	−0.333485	−	0.309429i
$715$	0.196029	−	0.858859i	0.00733106	−	0.0321195i
$716$	20.8845	−	3.14784i	0.780492	−	0.117640i
$717$	6.87268	−	4.68571i	0.256665	−	0.174991i
$718$	−32.6868	−	10.0825i	−1.21986	−	0.376277i
$719$	−1.61542	−	21.5563i	−0.0602452	−	0.803916i	−0.942726	−	0.333568i	$-0.891747\pi$
$719$	−1.61542	−	21.5563i	−0.0602452	−	0.803916i	0.882481	−	0.470348i	$-0.155872\pi$
$720$	−1.14777	+	1.43926i	−0.0427749	+	0.0536380i
$721$	79.0670	−	24.3890i	2.94461	−	0.908292i
$722$	−16.6280	−	42.3675i	−0.618831	−	1.57676i
$723$	−1.46671	−	6.42606i	−0.0545474	−	0.238988i
$724$	4.17945	−	7.23902i	0.155328	−	0.269036i
$725$	0.673104	+	1.16585i	0.0249984	+	0.0432986i
$726$	8.19777	−	7.60642i	0.304248	−	0.282301i
$727$	6.31595	+	7.91996i	0.234246	+	0.293735i	0.885036	−	0.465523i	$-0.154134\pi$
$727$	6.31595	+	7.91996i	0.234246	+	0.293735i	−0.650790	+	0.759258i	$0.725562\pi$
$728$	4.70526	+	3.20799i	0.174388	+	0.118896i
$729$	−15.3133	−	7.37448i	−0.567158	−	0.273129i
$730$	6.09586			0.225618
$731$	−11.6374	+	8.86683i	−0.430424	+	0.327952i
$732$	3.24294			0.119862
$733$	22.9834	+	11.0682i	0.848910	+	0.408814i	0.807173	−	0.590315i	$-0.200996\pi$
$733$	22.9834	+	11.0682i	0.848910	+	0.408814i	0.0417373	+	0.999129i	$0.486711\pi$
$734$	−30.4909	−	20.7883i	−1.12544	−	0.767311i
$735$	−12.4921	−	15.6647i	−0.460780	−	0.577799i
$736$	−3.24063	+	3.00686i	−0.119451	+	0.110834i
$737$	−4.22374	−	7.31573i	−0.155583	−	0.269478i
$738$	3.97392	−	6.88303i	0.146282	−	0.253368i
$739$	−1.04442	−	4.57591i	−0.0384196	−	0.168327i	0.952078	−	0.305854i	$-0.0989419\pi$
$739$	−1.04442	−	4.57591i	−0.0384196	−	0.168327i	−0.990498	+	0.137526i	$0.956085\pi$
$740$	0.880923	+	2.24456i	0.0323834	+	0.0825115i
$741$	−9.29883	+	2.86831i	−0.341601	+	0.105370i
$742$	−31.8538	+	39.9434i	−1.16939	+	1.46637i
$743$	0.0825635	+	1.10173i	0.00302896	+	0.0404187i	0.998513	−	0.0545054i	$-0.0173582\pi$
$743$	0.0825635	+	1.10173i	0.00302896	+	0.0404187i	−0.995485	+	0.0949241i	$0.969739\pi$
$744$	−0.0303056	−	0.00934804i	−0.00111106	−	0.000342716i
$745$	0.225801	−	0.153949i	0.00827272	−	0.00564024i
$746$	−34.8616	+	5.25455i	−1.27638	+	0.192383i
$747$	4.02686	−	17.6428i	0.147335	−	0.645518i
$748$	−1.28036	−	1.18800i	−0.0468146	−	0.0434376i
$749$	−5.15106	+	68.7361i	−0.188216	+	2.51156i
$750$	0.393335	−	1.00220i	0.0143626	−	0.0365952i
$751$	33.4786	+	5.04609i	1.22165	+	0.184134i	0.728032	−	0.685544i	$-0.240435\pi$
$751$	33.4786	+	5.04609i	1.22165	+	0.184134i	0.493620	+	0.869678i	$0.335673\pi$
$752$	1.84179	−	0.886959i	0.0671631	−	0.0323441i
$753$	−22.9954	+	11.0740i	−0.837999	+	0.403559i
$754$	−1.49799	−	0.225785i	−0.0545535	−	0.00822261i
$755$	1.19353	−	3.04106i	0.0434369	−	0.110675i
$756$	−1.97101	+	26.3012i	−0.0716848	+	0.956567i
$757$	2.45263	+	2.27571i	0.0891424	+	0.0827121i	0.723485	−	0.690340i	$-0.242539\pi$
$757$	2.45263	+	2.27571i	0.0891424	+	0.0827121i	−0.634343	+	0.773052i	$0.718729\pi$
$758$	2.25313	−	9.87159i	0.0818372	−	0.358552i
$759$	3.68431	−	0.555320i	0.133732	−	0.0201568i
$760$	−6.63639	+	4.52461i	−0.240727	+	0.164125i
$761$	7.29518	+	2.25026i	0.264450	+	0.0815720i	0.424145	−	0.905594i	$-0.360575\pi$
$761$	7.29518	+	2.25026i	0.264450	+	0.0815720i	−0.159695	+	0.987166i	$0.551051\pi$
$762$	−0.982335	−	13.1083i	−0.0355862	−	0.474865i
$763$	−4.74940	+	5.95556i	−0.171940	+	0.215606i
$764$	−23.9165	+	7.37727i	−0.865269	+	0.266900i
$765$	1.50054	+	3.82330i	0.0542520	+	0.138232i
$766$	−1.91519	−	8.39101i	−0.0691988	−	0.303180i
$767$	−1.67790	+	2.90620i	−0.0605854	+	0.104937i
$768$	0.538312	+	0.932384i	0.0194247	+	0.0336445i
$769$	−10.3985	+	9.64837i	−0.374978	+	0.347929i	−0.845039	−	0.534705i	$-0.820423\pi$
$769$	−10.3985	+	9.64837i	−0.374978	+	0.347929i	0.470060	+	0.882634i	$0.344232\pi$
$770$	−2.47006	−	3.09736i	−0.0890149	−	0.111621i
$771$	−3.08698	−	2.10467i	−0.111175	−	0.0757979i
$772$	−3.34969	−	1.61313i	−0.120558	−	0.0580577i
$773$	−20.3971			−0.733633			−0.366816	−	0.930293i	$-0.619552\pi$
$773$	−20.3971			−0.733633			−0.366816	+	0.930293i	$0.619552\pi$
$774$	11.7065	+	2.94565i	0.420783	+	0.105879i
$775$	−0.0294575			−0.00105814
$776$	−11.9303	−	5.74533i	−0.428273	−	0.206245i
$777$	10.8546	+	7.40053i	0.389406	+	0.265492i
$778$	−16.0259	−	20.0958i	−0.574555	−	0.720469i
$779$	25.4205	−	23.5868i	0.910784	−	0.845084i
$780$	0.605771	+	1.04923i	0.0216901	+	0.0375683i
$781$	−0.0225081	+	0.0389851i	−0.000805401	+	0.00139500i
$782$	2.19476	+	9.61589i	0.0784846	+	0.343864i
$783$	−2.56330	−	6.53117i	−0.0916047	−	0.233405i
$784$	17.7831	−	5.48536i	0.635110	−	0.195906i
$785$	−7.36166	+	9.23123i	−0.262749	+	0.329477i
$786$	0.702969	+	9.38047i	0.0250741	+	0.334590i
$787$	26.9200	+	8.30371i	0.959593	+	0.295995i	0.734703	−	0.678389i	$-0.237322\pi$
$787$	26.9200	+	8.30371i	0.959593	+	0.295995i	0.224890	+	0.974384i	$0.427798\pi$
$788$	−14.1591	+	9.65351i	−0.504397	+	0.343892i
$789$	1.64125	−	0.247378i	0.0584300	−	0.00880691i
$790$	−1.54891	+	6.78623i	−0.0551078	+	0.241443i
$791$	−37.3933	−	34.6959i	−1.32955	−	1.23364i
$792$	−0.107695	+	1.43709i	−0.00382678	+	0.0510648i
$793$	−1.23836	+	3.15529i	−0.0439755	+	0.112048i
$794$	−15.7055	−	2.36723i	−0.557369	−	0.0840098i
$795$	−9.79270	+	4.71592i	−0.347311	+	0.167256i
$796$	13.4077	−	6.45682i	0.475224	−	0.228856i
$797$	−19.9806	−	3.01159i	−0.707749	−	0.106676i	−0.214703	−	0.976679i	$-0.568878\pi$
$797$	−19.9806	−	3.01159i	−0.707749	−	0.106676i	−0.493046	+	0.870003i	$0.664117\pi$
$798$	−15.9879	+	40.7366i	−0.565967	+	1.44206i
$799$	0.340838	−	4.54817i	0.0120580	−	0.160903i
$800$	0.733052	+	0.680173i	0.0259173	+	0.0240477i
$801$	4.18860	−	18.3515i	0.147997	−	0.648417i
$802$	14.7887	−	2.22904i	0.522208	−	0.0787102i
$803$	3.94290	−	2.68822i	0.139142	−	0.0948653i
$804$	11.1015	+	3.42434i	0.391518	+	0.120767i
$805$	1.67184	+	22.3091i	0.0589245	+	0.786293i
$806$	0.0206680	−	0.0259169i	0.000728000	−	0.000912883i
$807$	32.0527	−	9.88694i	1.12831	−	0.348037i
$808$	−0.482896	−	1.23040i	−0.0169882	−	0.0432853i
$809$	9.47196	+	41.4994i	0.333017	+	1.45904i	0.813257	+	0.581904i	$0.197692\pi$
$809$	9.47196	+	41.4994i	0.333017	+	1.45904i	−0.480241	+	0.877137i	$0.659451\pi$
$810$	−0.0442602	+	0.0766609i	−0.00155514	+	0.00269359i
$811$	−11.9216	−	20.6488i	−0.418624	−	0.725079i	0.577177	−	0.816619i	$-0.304154\pi$
$811$	−11.9216	−	20.6488i	−0.418624	−	0.725079i	−0.995801	+	0.0915405i	$0.970821\pi$
$812$	−4.99402	+	4.63377i	−0.175256	+	0.162614i
$813$	6.32575	+	7.93224i	0.221854	+	0.278196i
$814$	1.55962	+	1.06333i	0.0546648	+	0.0372698i
$815$	−22.3430	−	10.7598i	−0.782642	−	0.376900i
$816$	2.40208			0.0840895
$817$	45.0199	+	27.3367i	1.57505	+	0.956390i
$818$	−0.508633			−0.0177839
$819$	−9.44524	−	4.54859i	−0.330044	−	0.158941i
$820$	−3.56721	−	2.43208i	−0.124572	−	0.0849321i
$821$	−0.0295805	−	0.0370928i	−0.00103237	−	0.00129455i	0.781315	−	0.624137i	$-0.214549\pi$
$821$	−0.0295805	−	0.0370928i	−0.00103237	−	0.00129455i	−0.782347	+	0.622842i	$0.785978\pi$
$822$	−16.6214	+	15.4224i	−0.579739	+	0.537919i
$823$	−4.71796	−	8.17174i	−0.164458	−	0.284849i	0.772005	−	0.635617i	$-0.219254\pi$
$823$	−4.71796	−	8.17174i	−0.164458	−	0.284849i	−0.936463	+	0.350768i	$0.885921\pi$
$824$	−8.17519	+	14.1598i	−0.284796	+	0.493282i
$825$	−0.187547	−	0.821697i	−0.00652955	−	0.0286078i
$826$	5.51345	+	14.0480i	0.191837	+	0.488794i
$827$	−22.4297	+	6.91865i	−0.779957	+	0.240585i	−0.659070	−	0.752081i	$-0.729050\pi$
$827$	−22.4297	+	6.91865i	−0.779957	+	0.240585i	−0.120887	+	0.992666i	$0.538574\pi$
$828$	5.07399	−	6.36258i	0.176333	−	0.221115i
$829$	−1.69463	−	22.6133i	−0.0588570	−	0.785392i	−0.946056	−	0.324004i	$-0.894971\pi$
$829$	−1.69463	−	22.6133i	−0.0588570	−	0.785392i	0.887199	−	0.461388i	$-0.152648\pi$
$830$	−9.39365	−	2.89756i	−0.326058	−	0.100576i
$831$	11.8802	−	8.09979i	0.412120	−	0.280979i
$832$	−1.11275	+	0.167720i	−0.0385775	+	0.00581463i
$833$	9.23925	−	40.4798i	0.320121	−	1.40254i
$834$	−11.0268	−	10.2314i	−0.381827	−	0.354284i
$835$	−1.23489	+	16.4785i	−0.0427352	+	0.570261i
$836$	−2.29720	+	5.85318i	−0.0794504	+	0.202436i
$837$	0.151812	+	0.0228820i	0.00524739	+	0.000790916i
$838$	34.0255	−	16.3858i	1.17539	−	0.566039i
$839$	38.4912	−	18.5364i	1.32886	−	0.639946i	0.371392	−	0.928476i	$-0.378881\pi$
$839$	38.4912	−	18.5364i	1.32886	−	0.639946i	0.957471	+	0.288530i	$0.0931664\pi$
$840$	5.38753	+	0.812040i	0.185888	+	0.0280180i
$841$	−9.93279	+	25.3083i	−0.342510	+	0.872701i
$842$	−0.551115	+	7.35412i	−0.0189927	+	0.253440i
$843$	14.7968	+	13.7295i	0.509630	+	0.472867i
$844$	2.98958	−	13.0982i	0.102905	−	0.450858i
$845$	11.6026	−	1.74881i	0.399142	−	0.0601610i
$846$	−3.10929	+	2.11988i	−0.106900	+	0.0728829i
$847$	50.2301	+	15.4939i	1.72593	+	0.532378i
$848$	−0.754439	−	10.0673i	−0.0259075	−	0.345712i
$849$	−20.4065	+	25.5890i	−0.700351	+	0.878212i
$850$	2.13200	−	0.657634i	0.0731269	−	0.0225566i
$851$	−3.89433	−	9.92259i	−0.133496	−	0.340142i
$852$	−0.0137762	−	0.0603573i	−0.000471963	−	0.00206781i
$853$	−20.5070	+	35.5192i	−0.702147	+	1.21615i	0.265565	+	0.964093i	$0.414442\pi$
$853$	−20.5070	+	35.5192i	−0.702147	+	1.21615i	−0.967711	+	0.252061i	$0.918892\pi$
$854$	7.62164	+	13.2011i	0.260807	+	0.451731i
$855$	10.8389	−	10.0571i	0.370683	−	0.343944i
$856$	−8.49232	−	10.6490i	−0.290262	−	0.363977i
$857$	−8.90874	−	6.07387i	−0.304317	−	0.207480i	0.401527	−	0.915847i	$-0.368480\pi$
$857$	−8.90874	−	6.07387i	−0.304317	−	0.207480i	−0.705844	+	0.708368i	$0.749432\pi$
$858$	0.854522	+	0.411516i	0.0291729	+	0.0140489i
$859$	−56.2246			−1.91836			−0.959180	−	0.282797i	$-0.908738\pi$
$859$	−56.2246			−1.91836			−0.959180	+	0.282797i	$0.908738\pi$
$860$	2.07088	−	6.22185i	0.0706165	−	0.212163i
$861$	−23.5229			−0.801659
$862$	−24.5763	−	11.8353i	−0.837072	−	0.403113i
$863$	12.9028	+	8.79697i	0.439216	+	0.299452i	0.762666	−	0.646793i	$-0.223890\pi$
$863$	12.9028	+	8.79697i	0.439216	+	0.299452i	−0.323450	+	0.946245i	$0.604843\pi$
$864$	−3.24951	−	4.07476i	−0.110551	−	0.138626i
$865$	−8.58338	+	7.96422i	−0.291844	+	0.270791i
$866$	4.73814	+	8.20669i	0.161008	+	0.278875i
$867$	−6.47165	+	11.2092i	−0.219789	+	0.380685i
$868$	−0.0331719	−	0.145335i	−0.00112593	−	0.00493300i
$869$	1.99081	+	5.07250i	0.0675335	+	0.172073i
$870$	−1.38497	+	0.427206i	−0.0469548	+	0.0144836i
$871$	−7.57104	+	9.49378i	−0.256535	+	0.321685i
$872$	−0.112487	−	1.50103i	−0.00380928	−	0.0508313i
$873$	23.2933	+	7.18503i	0.788359	+	0.243176i
$874$	29.3377	−	20.0021i	0.992363	−	0.676581i
$875$	5.00410	−	0.754246i	0.169169	−	0.0254982i
$876$	−1.46039	+	6.39841i	−0.0493422	+	0.216182i
$877$	22.4662	+	20.8456i	0.758631	+	0.703907i	0.961350	−	0.275330i	$-0.0887873\pi$
$877$	22.4662	+	20.8456i	0.758631	+	0.703907i	−0.202719	+	0.979237i	$0.564978\pi$
$878$	−2.32831	+	31.0692i	−0.0785767	+	1.04853i
$879$	11.6116	−	29.5859i	0.391650	−	0.997907i
$880$	0.774100	+	0.116677i	0.0260949	+	0.00393317i
$881$	4.92273	−	2.37066i	0.165851	−	0.0798697i	−0.349116	−	0.937079i	$-0.613518\pi$
$881$	4.92273	−	2.37066i	0.165851	−	0.0798697i	0.514968	+	0.857210i	$0.327804\pi$
$882$	−30.8659	+	14.8642i	−1.03931	+	0.500504i
$883$	21.7799	+	3.28279i	0.732951	+	0.110475i	0.504904	−	0.863176i	$-0.331528\pi$
$883$	21.7799	+	3.28279i	0.732951	+	0.110475i	0.228047	+	0.973650i	$0.426766\pi$
$884$	−0.917266	+	2.33716i	−0.0308510	+	0.0786070i
$885$	−0.239928	+	3.20162i	−0.00806509	+	0.107621i
$886$	1.54283	+	1.43154i	0.0518325	+	0.0480935i
$887$	−8.75877	+	38.3747i	−0.294091	+	1.28850i	0.584685	+	0.811261i	$0.301218\pi$
$887$	−8.75877	+	38.3747i	−0.294091	+	1.28850i	−0.878776	+	0.477235i	$0.841639\pi$
$888$	−2.56700	+	0.386913i	−0.0861429	+	0.0129839i
$889$	51.0516	−	34.8064i	1.71221	−	1.16737i
$890$	−9.77094	−	3.01394i	−0.327523	−	0.101027i
$891$	0.00517862	+	0.0691038i	0.000173490	+	0.00231507i
$892$	−2.03042	+	2.54607i	−0.0679835	+	0.0852486i
$893$	−15.6899	+	4.83969i	−0.525042	+	0.161954i
$894$	0.107494	+	0.273890i	0.00359513	+	0.00916024i
$895$	4.69974	+	20.5909i	0.157095	+	0.688278i
$896$	−2.53031	+	4.38263i	−0.0845317	+	0.146413i
$897$	−2.67795	−	4.63835i	−0.0894143	−	0.154870i
$898$	−13.6862	+	12.6989i	−0.456714	+	0.423769i
$899$	0.0247250	+	0.0310042i	0.000824625	+	0.00103405i
$900$	−1.52101	−	1.03700i	−0.0507002	−	0.0345668i
$901$	−20.2937	−	9.77292i	−0.676081	−	0.325583i
$902$	−3.37986			−0.112537
$903$	−9.77359	−	34.3646i	−0.325245	−	1.14358i
$904$	10.0799			0.335251
$905$	7.53111	+	3.62679i	0.250343	+	0.120559i
$906$	2.90605	+	1.98131i	0.0965471	+	0.0658247i
$907$	−1.94630	−	2.44058i	−0.0646258	−	0.0810381i	0.748468	−	0.663171i	$-0.230790\pi$
$907$	−1.94630	−	2.44058i	−0.0646258	−	0.0810381i	−0.813094	+	0.582133i	$0.802218\pi$
$908$	−15.8017	+	14.6618i	−0.524397	+	0.486569i
$909$	1.21661	+	2.10723i	0.0403524	+	0.0698924i
$910$	−2.84740	+	4.93184i	−0.0943903	+	0.163489i
$911$	−4.03703	−	17.6874i	−0.133753	−	0.586009i	−0.996733	−	0.0807711i	$-0.974262\pi$
$911$	−4.03703	−	17.6874i	−0.133753	−	0.586009i	0.862980	−	0.505238i	$-0.168595\pi$
$912$	−3.15928	−	8.04972i	−0.104614	−	0.266553i
$913$	−7.35376	+	2.26833i	−0.243374	+	0.0750709i
$914$	13.8197	−	17.3294i	0.457115	−	0.573205i
$915$	0.242345	+	3.23387i	0.00801168	+	0.106908i
$916$	6.40297	+	1.97506i	0.211560	+	0.0652577i
$917$	−36.5330	+	24.9078i	−1.20643	+	0.822528i
$918$	−11.4983	+	1.73309i	−0.379500	+	0.0572004i
$919$	−2.55815	+	11.2080i	−0.0843857	+	0.369718i	−0.999435	−	0.0336253i	$-0.989295\pi$
$919$	−2.55815	+	11.2080i	−0.0843857	+	0.369718i	0.915049	+	0.403343i	$0.132152\pi$
$920$	−3.24063	−	3.00686i	−0.106840	−	0.0991334i
$921$	0.321266	−	4.28699i	0.0105861	−	0.141261i
$922$	−12.3192	+	31.3888i	−0.405712	+	1.03374i
$923$	0.0639866	+	0.00964443i	0.00210615	+	0.000317450i
$924$	3.84284	−	1.85062i	0.126420	−	0.0608808i
$925$	−2.17245	+	1.04620i	−0.0714297	+	0.0343987i
$926$	−38.3510	−	5.78048i	−1.26029	−	0.189958i
$927$	10.9964	−	28.0185i	0.361170	−	0.920247i
$928$	0.100602	−	1.34244i	0.00330243	−	0.0440678i
$929$	−10.8687	−	10.0847i	−0.356591	−	0.330868i	0.481452	−	0.876473i	$-0.340110\pi$
$929$	−10.8687	−	10.0847i	−0.356591	−	0.330868i	−0.838043	+	0.545604i	$0.816300\pi$
$930$	0.00705716	−	0.0309195i	0.000231414	−	0.00101389i
$931$	−147.806	+	22.2781i	−4.84414	+	0.730136i
$932$	−8.78025	+	5.98628i	−0.287607	+	0.196087i
$933$	−12.9505	−	3.99471i	−0.423982	−	0.130781i
$934$	−2.33139	−	31.1102i	−0.0762854	−	1.01796i
$935$	1.08900	−	1.36556i	0.0356140	−	0.0446586i
$936$	1.97954	−	0.610606i	0.0647032	−	0.0199583i
$937$	10.1850	+	25.9509i	0.332729	+	0.847780i	0.995125	+	0.0986257i	$0.0314446\pi$
$937$	10.1850	+	25.9509i	0.332729	+	0.847780i	−0.662395	+	0.749154i	$0.730460\pi$
$938$	12.1514	+	53.2388i	0.396757	+	1.73831i
$939$	1.59183	−	2.75714i	0.0519475	−	0.0899758i
$940$	1.02212	+	1.77036i	0.0333377	+	0.0577426i
$941$	−15.4850	+	14.3679i	−0.504795	+	0.468381i	−0.890982	−	0.454039i	$-0.849983\pi$
$941$	−15.4850	+	14.3679i	−0.504795	+	0.468381i	0.386187	+	0.922421i	$0.373792\pi$
$942$	−7.92574	−	9.93856i	−0.258235	−	0.323816i
$943$	15.7697	+	10.7516i	0.513532	+	0.350120i
$944$	−2.68677	−	1.29388i	−0.0874470	−	0.0421123i
$945$	−26.3750			−0.857978
$946$	−1.40430	−	4.93763i	−0.0456578	−	0.160536i
$947$	35.1939			1.14365			0.571824	−	0.820376i	$-0.306236\pi$
$947$	35.1939			1.14365			0.571824	+	0.820376i	$0.306236\pi$
$948$	−6.75196	−	3.25157i	−0.219294	−	0.105606i
$949$	−5.66781	−	3.86425i	−0.183985	−	0.125439i
$950$	−5.00790	−	6.27970i	−0.162478	−	0.203741i
$951$	−6.41723	+	5.95432i	−0.208093	+	0.193082i
$952$	5.64542	+	9.77815i	0.182969	+	0.316912i
$953$	25.2231	−	43.6876i	0.817055	−	1.41518i	−0.0907871	−	0.995870i	$-0.528938\pi$
$953$	25.2231	−	43.6876i	0.817055	−	1.41518i	0.907843	−	0.419311i	$-0.137728\pi$
$954$	4.13547	+	18.1187i	0.133891	+	0.586614i
$955$	−9.14392	−	23.2983i	−0.295890	−	0.753916i
$956$	−7.38278	+	2.27729i	−0.238776	+	0.0736527i
$957$	−0.707425	+	0.887083i	−0.0228678	+	0.0286753i
$958$	−0.819669	−	10.9377i	−0.0264823	−	0.353382i
$959$	−101.844	−	31.4148i	−3.28873	−	1.01444i
$960$	−0.889549	+	0.606484i	−0.0287101	+	0.0195742i
$961$	30.6529	−	4.62018i	0.988803	−	0.149038i
$962$	0.603788	−	2.64537i	0.0194669	−	0.0852901i
$963$	18.3805	+	17.0546i	0.592303	+	0.549577i
$964$	−0.457513	+	6.10509i	−0.0147355	+	0.196632i
$965$	1.35829	−	3.46088i	0.0437250	−	0.111410i
$966$	−23.8169	−	3.58981i	−0.766295	−	0.115500i
$967$	5.82933	−	2.80726i	0.187459	−	0.0902753i	−0.337800	−	0.941218i	$-0.609683\pi$
$967$	5.82933	−	2.80726i	0.187459	−	0.0902753i	0.525259	+	0.850943i	$0.323969\pi$
$968$	−9.35850	+	4.50682i	−0.300794	+	0.144855i
$969$	−19.0781	−	2.87556i	−0.612876	−	0.0923763i
$970$	4.83771	−	12.3263i	0.155330	−	0.395773i
$971$	−1.09751	+	14.6452i	−0.0352207	+	0.469987i	0.951510	+	0.307619i	$0.0995323\pi$
$971$	−1.09751	+	14.6452i	−0.0352207	+	0.469987i	−0.986730	+	0.162368i	$0.948087\pi$
$972$	11.3917	+	10.5700i	0.365390	+	0.339032i
$973$	15.7335	−	68.9330i	0.504393	−	2.20989i
$974$	25.0618	−	3.77746i	0.803033	−	0.121038i
$975$	−1.00102	+	0.682486i	−0.0320584	+	0.0218570i
$976$	−2.87831	−	0.887843i	−0.0921326	−	0.0284191i
$977$	−1.82548	−	24.3593i	−0.0584022	−	0.779323i	−0.947122	−	0.320873i	$-0.896024\pi$
$977$	−1.82548	−	24.3593i	−0.0584022	−	0.779323i	0.888720	−	0.458450i	$-0.151595\pi$
$978$	16.6466	−	20.8742i	0.532300	−	0.667483i
$979$	−7.64912	+	2.35944i	−0.244467	+	0.0754080i
$980$	6.79895	+	17.3234i	0.217184	+	0.553377i
$981$	0.616598	+	2.70149i	0.0196864	+	0.0862520i
$982$	15.4150	−	26.6996i	0.491914	−	0.852019i
$983$	−1.29673	−	2.24600i	−0.0413592	−	0.0716363i	0.844605	−	0.535390i	$-0.179835\pi$
$983$	−1.29673	−	2.24600i	−0.0413592	−	0.0716363i	−0.885964	+	0.463754i	$0.846502\pi$
$984$	3.40739	−	3.16160i	0.108624	−	0.100788i
$985$	−10.6846	−	13.3981i	−0.340441	−	0.426899i
$986$	−2.48165	−	1.69196i	−0.0790318	−	0.0538829i
$987$	10.0348	+	4.83249i	0.319410	+	0.153820i
$988$	9.03858			0.287556
$989$	−9.15483	+	27.5052i	−0.291107	+	0.874613i
$990$	−1.44112			−0.0458018
$991$	17.6610	+	8.50511i	0.561022	+	0.270174i	0.692829	−	0.721101i	$-0.256364\pi$
$991$	17.6610	+	8.50511i	0.561022	+	0.270174i	−0.131808	+	0.991275i	$0.542078\pi$
$992$	0.0243389	+	0.0165940i	0.000772760	+	0.000526859i
$993$	2.08023	+	2.60853i	0.0660141	+	0.0827790i
$994$	0.213320	−	0.197932i	0.00676610	−	0.00627802i
$995$	7.44073	+	12.8877i	0.235887	+	0.408568i
$996$	5.29182	−	9.16570i	0.167678	−	0.290426i
$997$	8.38667	+	36.7444i	0.265608	+	1.16371i	0.915065	+	0.403307i	$0.132139\pi$
$997$	8.38667	+	36.7444i	0.265608	+	1.16371i	−0.649456	+	0.760399i	$0.725003\pi$
$998$	12.0564	+	30.7191i	0.381637	+	0.972396i
$999$	12.0086	−	3.70416i	0.379935	−	0.117194i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.c.111.2	yes	48
43.31	even	21	inner	430.2.q.c.31.2	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.c.31.2	✓	48	43.31	even	21	inner
430.2.q.c.111.2	yes	48	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.900969 + 0.433884i) q^{2} +(-0.889549 - 0.606484i) q^{3} +(0.623490 + 0.781831i) q^{4} +(-0.733052 + 0.680173i) q^{5} +(-0.538312 - 0.932384i) q^{6} +(2.53031 - 4.38263i) q^{7} +(0.222521 + 0.974928i) q^{8} +(-0.672549 - 1.71363i) q^{9} +O(q^{10})\)	\(q+(0.900969 + 0.433884i) q^{2} +(-0.889549 - 0.606484i) q^{3} +(0.623490 + 0.781831i) q^{4} +(-0.733052 + 0.680173i) q^{5} +(-0.538312 - 0.932384i) q^{6} +(2.53031 - 4.38263i) q^{7} +(0.222521 + 0.974928i) q^{8} +(-0.672549 - 1.71363i) q^{9} +(-0.955573 + 0.294755i) q^{10} +(-0.488095 + 0.612052i) q^{11} +(-0.0804562 - 1.07361i) q^{12} +(1.07532 + 0.331693i) q^{13} +(4.18128 - 2.85075i) q^{14} +(1.06460 - 0.160463i) q^{15} +(-0.222521 + 0.974928i) q^{16} +(1.63553 + 1.51755i) q^{17} +(0.137569 - 1.83573i) q^{18} +(2.93443 - 7.47682i) q^{19} +(-0.988831 - 0.149042i) q^{20} +(-4.90883 + 2.36397i) q^{21} +(-0.705318 + 0.339663i) q^{22} +(4.37136 + 0.658876i) q^{23} +(0.393335 - 1.00220i) q^{24} +(0.0747301 - 0.997204i) q^{25} +(0.824915 + 0.765409i) q^{26} +(-1.15974 + 5.08114i) q^{27} +(5.00410 - 0.754246i) q^{28} +(-1.11229 + 0.758346i) q^{29} +(1.02879 + 0.317341i) q^{30} +(-0.00220136 - 0.0293751i) q^{31} +(-0.623490 + 0.781831i) q^{32} +(0.805384 - 0.248428i) q^{33} +(0.815119 + 2.07689i) q^{34} +(1.12609 + 4.93374i) q^{35} +(0.920440 - 1.59425i) q^{36} +(-1.20562 - 2.08819i) q^{37} +(5.88790 - 5.46318i) q^{38} +(-0.755384 - 0.947222i) q^{39} +(-0.826239 - 0.563320i) q^{40} +(3.88985 + 1.87325i) q^{41} -5.44839 q^{42} +(-1.12043 + 6.46101i) q^{43} -0.782843 q^{44} +(1.65858 + 0.798728i) q^{45} +(3.65258 + 2.49029i) q^{46} +(-1.27456 - 1.59824i) q^{47} +(0.789221 - 0.732291i) q^{48} +(-9.30494 - 16.1166i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-0.534512 - 2.34185i) q^{51} +(0.411124 + 1.04753i) q^{52} +(-9.64700 + 2.97571i) q^{53} +(-3.24951 + 4.07476i) q^{54} +(-0.0585020 - 0.780654i) q^{55} +(4.83579 + 1.49164i) q^{56} +(-7.14489 + 4.87131i) q^{57} +(-1.33117 + 0.200642i) q^{58} +(-0.663578 + 2.90733i) q^{59} +(0.789221 + 0.732291i) q^{60} +(-0.225097 + 3.00371i) q^{61} +(0.0107620 - 0.0274212i) q^{62} +(-9.21194 - 1.38848i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(-1.01387 + 0.488256i) q^{65} +(0.833415 + 0.125617i) q^{66} +(-3.94231 + 10.0448i) q^{67} +(-0.166732 + 2.22488i) q^{68} +(-3.48894 - 3.23726i) q^{69} +(-1.12609 + 4.93374i) q^{70} +(0.0568611 - 0.00857043i) q^{71} +(1.52101 - 1.03700i) q^{72} +(-5.82504 - 1.79679i) q^{73} +(-0.180192 - 2.40449i) q^{74} +(-0.671264 + 0.841739i) q^{75} +(7.67520 - 2.36749i) q^{76} +(1.44736 + 3.68782i) q^{77} +(-0.269593 - 1.18117i) q^{78} +(3.48037 - 6.02819i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(0.0648900 - 0.0602092i) q^{81} +(2.69186 + 3.37549i) q^{82} +(8.12225 + 5.53765i) q^{83} +(-4.90883 - 2.36397i) q^{84} -2.23112 q^{85} +(-3.81280 + 5.33503i) q^{86} +1.44936 q^{87} +(-0.705318 - 0.339663i) q^{88} +(8.44847 + 5.76007i) q^{89} +(1.14777 + 1.43926i) q^{90} +(4.17458 - 3.87344i) q^{91} +(2.21037 + 3.82847i) q^{92} +(-0.0158573 + 0.0274657i) q^{93} +(-0.454884 - 1.99298i) q^{94} +(2.93443 + 7.47682i) q^{95} +(1.02879 - 0.317341i) q^{96} +(-8.25602 + 10.3527i) q^{97} +(-1.39072 - 18.5578i) q^{98} +(1.37710 + 0.424778i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9}+O(q^{10}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9} - 4 q^{10} + q^{11} + 14 q^{12} - 23 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{17} - 20 q^{18} - 3 q^{19} + 4 q^{20} - 8 q^{21} - q^{22} + 7 q^{23} + 4 q^{25} - 19 q^{26} + 32 q^{27} + 4 q^{28} + 30 q^{29} + 9 q^{31} + 8 q^{32} + 39 q^{33} - 8 q^{34} - 22 q^{35} - 29 q^{36} - 37 q^{37} - 11 q^{38} - 52 q^{39} - 4 q^{40} - 28 q^{41} - 6 q^{42} + 41 q^{43} + 8 q^{44} + 2 q^{45} - 28 q^{46} + 3 q^{47} - 41 q^{49} + 24 q^{50} - 30 q^{51} - 9 q^{52} - 69 q^{53} + 3 q^{54} + 10 q^{55} - 11 q^{56} + 116 q^{57} + 5 q^{58} + 10 q^{59} - 19 q^{61} - 93 q^{62} + 34 q^{63} - 8 q^{64} - 3 q^{65} - 18 q^{66} + 3 q^{67} + 8 q^{68} + 42 q^{69} + 22 q^{70} - 36 q^{71} + 22 q^{72} - 56 q^{73} + 9 q^{74} - 10 q^{76} + 3 q^{77} + 45 q^{78} + 16 q^{79} - 24 q^{80} - 19 q^{81} + 14 q^{82} + 64 q^{83} - 8 q^{84} - 30 q^{85} + 36 q^{86} + 78 q^{87} - q^{88} - 75 q^{89} + 5 q^{90} + 5 q^{91} + 14 q^{92} - 10 q^{93} - 45 q^{94} - 3 q^{95} + 33 q^{97} - q^{98} - 11 q^{99}+O(q^{100}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9 - 4 * q^10 + q^11 + 14 * q^12 - 23 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^17 - 20 * q^18 - 3 * q^19 + 4 * q^20 - 8 * q^21 - q^22 + 7 * q^23 + 4 * q^25 - 19 * q^26 + 32 * q^27 + 4 * q^28 + 30 * q^29 + 9 * q^31 + 8 * q^32 + 39 * q^33 - 8 * q^34 - 22 * q^35 - 29 * q^36 - 37 * q^37 - 11 * q^38 - 52 * q^39 - 4 * q^40 - 28 * q^41 - 6 * q^42 + 41 * q^43 + 8 * q^44 + 2 * q^45 - 28 * q^46 + 3 * q^47 - 41 * q^49 + 24 * q^50 - 30 * q^51 - 9 * q^52 - 69 * q^53 + 3 * q^54 + 10 * q^55 - 11 * q^56 + 116 * q^57 + 5 * q^58 + 10 * q^59 - 19 * q^61 - 93 * q^62 + 34 * q^63 - 8 * q^64 - 3 * q^65 - 18 * q^66 + 3 * q^67 + 8 * q^68 + 42 * q^69 + 22 * q^70 - 36 * q^71 + 22 * q^72 - 56 * q^73 + 9 * q^74 - 10 * q^76 + 3 * q^77 + 45 * q^78 + 16 * q^79 - 24 * q^80 - 19 * q^81 + 14 * q^82 + 64 * q^83 - 8 * q^84 - 30 * q^85 + 36 * q^86 + 78 * q^87 - q^88 - 75 * q^89 + 5 * q^90 + 5 * q^91 + 14 * q^92 - 10 * q^93 - 45 * q^94 - 3 * q^95 + 33 * q^97 - q^98 - 11 * q^99

Introduction

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