LMFDB - Embedded newform 71.2.g.a.15.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [71,2,Mod(2,71)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(71, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([6]))

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

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

chi := DirichletCharacter("71.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	71.g (of order $35$, degree $24$, 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:	$0.566937854351$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$5$ over $\Q(\zeta_{35})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{35}]$

Embedding invariants

Embedding label			15.4
Character	$\chi$	$=$	71.15
Dual form			71.2.g.a.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.682008 - 1.59564i) q^{2} +(-3.05466 - 0.554338i) q^{3} +(-0.698796 - 0.730883i) q^{4} +(0.984762 - 3.03079i) q^{5} +(-2.96782 + 4.49606i) q^{6} +(-1.95579 + 1.70872i) q^{7} +(1.60645 - 0.602910i) q^{8} +(6.21492 + 2.33250i) q^{9} +O(q^{10})$	\(q+(0.682008 - 1.59564i) q^{2} +(-3.05466 - 0.554338i) q^{3} +(-0.698796 - 0.730883i) q^{4} +(0.984762 - 3.03079i) q^{5} +(-2.96782 + 4.49606i) q^{6} +(-1.95579 + 1.70872i) q^{7} +(1.60645 - 0.602910i) q^{8} +(6.21492 + 2.33250i) q^{9} +(-4.16442 - 3.63834i) q^{10} +(2.87663 - 0.793900i) q^{11} +(1.72942 + 2.61997i) q^{12} +(1.82114 + 0.502604i) q^{13} +(1.39263 + 4.28609i) q^{14} +(-4.68819 + 8.71212i) q^{15} +(0.224319 - 4.99484i) q^{16} +(-4.31308 + 3.13364i) q^{17} +(7.96045 - 8.32598i) q^{18} +(0.616198 + 1.14509i) q^{19} +(-2.90330 + 1.39816i) q^{20} +(6.92147 - 4.13539i) q^{21} +(0.695110 - 5.13150i) q^{22} +(0.0673796 - 0.295209i) q^{23} +(-5.24136 + 0.951167i) q^{24} +(-4.17083 - 3.03028i) q^{25} +(2.04401 - 2.56310i) q^{26} +(-9.69617 - 5.79319i) q^{27} +(2.61557 + 0.235406i) q^{28} +(0.418132 + 3.08678i) q^{29} +(10.7040 + 13.4224i) q^{30} +(0.0495160 + 1.10256i) q^{31} +(-4.72509 - 2.27548i) q^{32} +(-9.22721 + 0.830464i) q^{33} +(2.05859 + 9.01928i) q^{34} +(3.25278 + 7.61026i) q^{35} +(-2.63818 - 6.17233i) q^{36} +(0.852397 + 3.73460i) q^{37} +(2.24739 - 0.202269i) q^{38} +(-5.28435 - 2.54481i) q^{39} +(-0.245322 - 5.46252i) q^{40} +(-1.29242 - 1.62064i) q^{41} +(-1.87808 - 13.8645i) q^{42} +(-4.77783 - 0.430012i) q^{43} +(-2.59043 - 1.54771i) q^{44} +(13.1895 - 16.5392i) q^{45} +(-0.425093 - 0.308848i) q^{46} +(8.29461 - 1.50525i) q^{47} +(-3.45405 + 15.1332i) q^{48} +(-0.0342515 + 0.252855i) q^{49} +(-7.67977 + 4.58845i) q^{50} +(14.9121 - 7.18128i) q^{51} +(-0.905263 - 1.68226i) q^{52} +(0.272330 - 0.284835i) q^{53} +(-15.8567 + 11.5206i) q^{54} +(0.426657 - 9.50026i) q^{55} +(-2.11167 + 3.92414i) q^{56} +(-1.24751 - 3.83943i) q^{57} +(5.21055 + 1.43802i) q^{58} +(6.26431 + 9.49003i) q^{59} +(9.64363 - 2.66147i) q^{60} +(-5.47002 - 4.77901i) q^{61} +(1.79305 + 0.672944i) q^{62} +(-16.1407 + 6.05769i) q^{63} +(0.677134 - 0.591594i) q^{64} +(3.31668 - 5.02455i) q^{65} +(-4.96791 + 15.2897i) q^{66} +(7.33409 + 7.67085i) q^{67} +(5.30429 + 0.962587i) q^{68} +(-0.369467 + 0.864412i) q^{69} +14.3616 q^{70} +(-3.28980 - 7.75740i) q^{71} +11.3902 q^{72} +(2.65610 - 6.21425i) q^{73} +(6.54040 + 1.18691i) q^{74} +(11.0606 + 11.5685i) q^{75} +(0.406329 - 1.25055i) q^{76} +(-4.26953 + 6.46806i) q^{77} +(-7.66456 + 6.69633i) q^{78} +(-16.0435 + 6.02123i) q^{79} +(-14.9174 - 5.59859i) q^{80} +(11.4099 + 9.96857i) q^{81} +(-3.46739 + 0.956940i) q^{82} +(-7.68728 - 11.6457i) q^{83} +(-7.85918 - 2.16900i) q^{84} +(5.25003 + 16.1579i) q^{85} +(-3.94466 + 7.33041i) q^{86} +(0.433868 - 9.66083i) q^{87} +(4.14251 - 3.00971i) q^{88} +(-6.19684 + 6.48139i) q^{89} +(-17.3951 - 32.3255i) q^{90} +(-4.42058 + 2.12884i) q^{91} +(-0.262848 + 0.157044i) q^{92} +(0.459936 - 3.39538i) q^{93} +(3.25516 - 14.2618i) q^{94} +(4.07732 - 0.739925i) q^{95} +(13.1721 + 9.57012i) q^{96} +(-2.79848 + 3.50918i) q^{97} +(0.380105 + 0.227102i) q^{98} +(19.7298 + 1.77572i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) $ 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/71\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{27}{35}\right)$

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 $

$2$	0.682008	−	1.59564i	0.482252	−	1.12829i	−0.485010	−	0.874508i	$-0.661184\pi$
$2$	0.682008	−	1.59564i	0.482252	−	1.12829i	0.967263	−	0.253777i	$-0.0816729\pi$
$3$	−3.05466	−	0.554338i	−1.76361	−	0.320047i	−0.802588	−	0.596533i	$-0.796544\pi$
$3$	−3.05466	−	0.554338i	−1.76361	−	0.320047i	−0.961018	+	0.276486i	$0.910830\pi$
$4$	−0.698796	−	0.730883i	−0.349398	−	0.365442i
$5$	0.984762	−	3.03079i	0.440399	−	1.35541i	−0.447052	−	0.894508i	$-0.647526\pi$
$5$	0.984762	−	3.03079i	0.440399	−	1.35541i	0.887451	−	0.460901i	$-0.152474\pi$
$6$	−2.96782	+	4.49606i	−1.21161	+	1.83551i
$7$	−1.95579	+	1.70872i	−0.739219	+	0.645836i	−0.942852	−	0.333211i	$-0.891868\pi$
$7$	−1.95579	+	1.70872i	−0.739219	+	0.645836i	0.203634	+	0.979047i	$0.434725\pi$
$8$	1.60645	−	0.602910i	0.567965	−	0.213161i
$9$	6.21492	+	2.33250i	2.07164	+	0.777500i
$10$	−4.16442	−	3.63834i	−1.31690	−	1.15054i
$11$	2.87663	−	0.793900i	0.867337	−	0.239370i	0.196074	−	0.980589i	$-0.437181\pi$
$11$	2.87663	−	0.793900i	0.867337	−	0.239370i	0.671263	+	0.741219i	$0.265752\pi$
$12$	1.72942	+	2.61997i	0.499242	+	0.756319i
$13$	1.82114	+	0.502604i	0.505094	+	0.139397i	0.509292	−	0.860594i	$-0.329907\pi$
$13$	1.82114	+	0.502604i	0.505094	+	0.139397i	−0.00419730	+	0.999991i	$0.501336\pi$
$14$	1.39263	+	4.28609i	0.372197	+	1.14551i
$15$	−4.68819	+	8.71212i	−1.21049	+	2.24946i
$16$	0.224319	−	4.99484i	0.0560796	−	1.24871i
$17$	−4.31308	+	3.13364i	−1.04608	+	0.760019i	−0.971462	−	0.237193i	$-0.923773\pi$
$17$	−4.31308	+	3.13364i	−1.04608	+	0.760019i	−0.0746142	+	0.997212i	$0.523773\pi$
$18$	7.96045	−	8.32598i	1.87630	−	1.96245i
$19$	0.616198	+	1.14509i	0.141365	+	0.262701i	0.941427	−	0.337217i	$-0.109486\pi$
$19$	0.616198	+	1.14509i	0.141365	+	0.262701i	−0.800062	+	0.599918i	$0.795200\pi$
$20$	−2.90330	+	1.39816i	−0.649197	+	0.312637i
$21$	6.92147	−	4.13539i	1.51039	−	0.902415i
$22$	0.695110	−	5.13150i	0.148198	−	1.09404i
$23$	0.0673796	−	0.295209i	0.0140496	−	0.0615554i	−0.967417	−	0.253188i	$-0.918521\pi$
$23$	0.0673796	−	0.295209i	0.0140496	−	0.0615554i	0.981467	+	0.191632i	$0.0613781\pi$
$24$	−5.24136	+	0.951167i	−1.06989	+	0.194156i
$25$	−4.17083	−	3.03028i	−0.834165	−	0.606057i
$26$	2.04401	−	2.56310i	0.400863	−	0.502666i
$27$	−9.69617	−	5.79319i	−1.86603	−	1.11490i
$28$	2.61557	+	0.235406i	0.494297	+	0.0444875i
$29$	0.418132	+	3.08678i	0.0776453	+	0.573200i	0.987423	+	0.158104i	$0.0505380\pi$
$29$	0.418132	+	3.08678i	0.0776453	+	0.573200i	−0.909777	+	0.415097i	$0.863748\pi$
$30$	10.7040	+	13.4224i	1.95427	+	2.45058i
$31$	0.0495160	+	1.10256i	0.00889333	+	0.198025i	0.998521	+	0.0543688i	$0.0173146\pi$
$31$	0.0495160	+	1.10256i	0.00889333	+	0.198025i	−0.989628	+	0.143657i	$0.954114\pi$
$32$	−4.72509	−	2.27548i	−0.835286	−	0.402252i
$33$	−9.22721	+	0.830464i	−1.60625	+	0.144565i
$34$	2.05859	+	9.01928i	0.353046	+	1.54679i
$35$	3.25278	+	7.61026i	0.549820	+	1.28637i
$36$	−2.63818	−	6.17233i	−0.439696	−	1.02872i
$37$	0.852397	+	3.73460i	0.140133	+	0.613964i	0.995403	+	0.0957801i	$0.0305346\pi$
$37$	0.852397	+	3.73460i	0.140133	+	0.613964i	−0.855269	+	0.518184i	$0.826608\pi$
$38$	2.24739	−	0.202269i	0.364575	−	0.0328124i
$39$	−5.28435	−	2.54481i	−0.846174	−	0.407496i
$40$	−0.245322	−	5.46252i	−0.0387888	−	0.863701i
$41$	−1.29242	−	1.62064i	−0.201842	−	0.253102i	0.670601	−	0.741819i	$-0.266036\pi$
$41$	−1.29242	−	1.62064i	−0.201842	−	0.253102i	−0.872442	+	0.488717i	$0.837465\pi$
$42$	−1.87808	−	13.8645i	−0.289793	−	2.13934i
$43$	−4.77783	−	0.430012i	−0.728612	−	0.0655763i	−0.280879	−	0.959743i	$-0.590626\pi$
$43$	−4.77783	−	0.430012i	−0.728612	−	0.0655763i	−0.447734	+	0.894167i	$0.647769\pi$
$44$	−2.59043	−	1.54771i	−0.390522	−	0.233326i
$45$	13.1895	−	16.5392i	1.96618	−	2.46551i
$46$	−0.425093	−	0.308848i	−0.0626766	−	0.0455372i
$47$	8.29461	−	1.50525i	1.20989	−	0.219563i	0.464126	−	0.885769i	$-0.346369\pi$
$47$	8.29461	−	1.50525i	1.20989	−	0.219563i	0.745768	+	0.666206i	$0.232083\pi$
$48$	−3.45405	+	15.1332i	−0.498549	+	2.18428i
$49$	−0.0342515	+	0.252855i	−0.00489308	+	0.0361221i
$50$	−7.67977	+	4.58845i	−1.08608	+	0.648904i
$51$	14.9121	−	7.18128i	2.08811	−	1.00558i
$52$	−0.905263	−	1.68226i	−0.125537	−	0.233288i
$53$	0.272330	−	0.284835i	0.0374075	−	0.0391251i	−0.703826	−	0.710372i	$-0.748527\pi$
$53$	0.272330	−	0.284835i	0.0374075	−	0.0391251i	0.741234	+	0.671247i	$0.234241\pi$
$54$	−15.8567	+	11.5206i	−2.15782	+	1.56775i
$55$	0.426657	−	9.50026i	0.0575304	−	1.28101i
$56$	−2.11167	+	3.92414i	−0.282183	+	0.524385i
$57$	−1.24751	−	3.83943i	−0.165236	−	0.508545i
$58$	5.21055	+	1.43802i	0.684178	+	0.188821i
$59$	6.26431	+	9.49003i	0.815544	+	1.23550i	0.968931	+	0.247330i	$0.0795532\pi$
$59$	6.26431	+	9.49003i	0.815544	+	1.23550i	−0.153387	+	0.988166i	$0.549018\pi$
$60$	9.64363	−	2.66147i	1.24499	−	0.343595i
$61$	−5.47002	−	4.77901i	−0.700364	−	0.611890i	0.232296	−	0.972645i	$-0.425376\pi$
$61$	−5.47002	−	4.77901i	−0.700364	−	0.611890i	−0.932661	+	0.360755i	$0.882519\pi$
$62$	1.79305	+	0.672944i	0.227718	+	0.0854640i
$63$	−16.1407	+	6.05769i	−2.03353	+	0.763198i
$64$	0.677134	−	0.591594i	0.0846417	−	0.0739492i
$65$	3.31668	−	5.02455i	0.411383	−	0.623219i
$66$	−4.96791	+	15.2897i	−0.611507	+	1.88203i
$67$	7.33409	+	7.67085i	0.896001	+	0.937144i	0.998339	−	0.0576060i	$-0.0183467\pi$
$67$	7.33409	+	7.67085i	0.896001	+	0.937144i	−0.102338	+	0.994750i	$0.532632\pi$
$68$	5.30429	+	0.962587i	0.643240	+	0.116731i
$69$	−0.369467	+	0.864412i	−0.0444786	+	0.104063i
$70$	14.3616			1.71654
$71$	−3.28980	−	7.75740i	−0.390427	−	0.920634i
$71$	−3.28980	−	7.75740i	−0.390427	−	0.920634i
$72$	11.3902			1.34235
$73$	2.65610	−	6.21425i	0.310873	−	0.727323i	−0.689124	−	0.724644i	$-0.742004\pi$
$73$	2.65610	−	6.21425i	0.310873	−	0.727323i	0.999996	−	0.00267905i	$-0.000852769\pi$
$74$	6.54040	+	1.18691i	0.760306	+	0.137975i
$75$	11.0606	+	11.5685i	1.27717	+	1.33582i
$76$	0.406329	−	1.25055i	0.0466091	−	0.143448i
$77$	−4.26953	+	6.46806i	−0.486558	+	0.737104i
$78$	−7.66456	+	6.69633i	−0.867841	+	0.758210i
$79$	−16.0435	+	6.02123i	−1.80504	+	0.677441i	−0.809069	+	0.587713i	$0.800028\pi$
$79$	−16.0435	+	6.02123i	−1.80504	+	0.677441i	−0.995966	+	0.0897278i	$0.971400\pi$
$80$	−14.9174	−	5.59859i	−1.66782	−	0.625942i
$81$	11.4099	+	9.96857i	1.26777	+	1.10762i
$82$	−3.46739	+	0.956940i	−0.382910	+	0.105676i
$83$	−7.68728	−	11.6457i	−0.843789	−	1.27829i	−0.958559	−	0.284893i	$-0.908042\pi$
$83$	−7.68728	−	11.6457i	−0.843789	−	1.27829i	0.114771	−	0.993392i	$-0.463387\pi$
$84$	−7.85918	−	2.16900i	−0.857507	−	0.236657i
$85$	5.25003	+	16.1579i	0.569446	+	1.75257i
$86$	−3.94466	+	7.33041i	−0.425364	+	0.790458i
$87$	0.433868	−	9.66083i	0.0465156	−	1.03575i
$88$	4.14251	−	3.00971i	0.441593	−	0.320836i
$89$	−6.19684	+	6.48139i	−0.656864	+	0.687026i	−0.964381	−	0.264517i	$-0.914788\pi$
$89$	−6.19684	+	6.48139i	−0.656864	+	0.687026i	0.307517	+	0.951543i	$0.400502\pi$
$90$	−17.3951	−	32.3255i	−1.83361	−	3.40741i
$91$	−4.42058	+	2.12884i	−0.463403	+	0.223163i
$92$	−0.262848	+	0.157044i	−0.0274038	+	0.0163730i
$93$	0.459936	−	3.39538i	0.0476932	−	0.352085i
$94$	3.25516	−	14.2618i	0.335744	−	1.47099i
$95$	4.07732	−	0.739925i	0.418324	−	0.0759147i
$96$	13.1721	+	9.57012i	1.34438	+	0.976746i
$97$	−2.79848	+	3.50918i	−0.284142	+	0.356303i	−0.903335	−	0.428936i	$-0.858889\pi$
$97$	−2.79848	+	3.50918i	−0.284142	+	0.356303i	0.619193	+	0.785239i	$0.287460\pi$
$98$	0.380105	+	0.227102i	0.0383964	+	0.0229408i
$99$	19.7298	+	1.77572i	1.98292	+	0.178466i
$100$	0.699774	+	5.16594i	0.0699774	+	0.516594i
$101$	1.77909	+	2.23091i	0.177026	+	0.221984i	0.862426	−	0.506183i	$-0.168944\pi$
$101$	1.77909	+	2.23091i	0.177026	+	0.221984i	−0.685400	+	0.728167i	$0.740373\pi$
$102$	−1.28856	−	28.6920i	−0.127586	−	2.84093i
$103$	0.439739	+	0.211767i	0.0433287	+	0.0208660i	0.455423	−	0.890275i	$-0.349488\pi$
$103$	0.439739	+	0.211767i	0.0433287	+	0.0208660i	−0.412094	+	0.911141i	$0.635202\pi$
$104$	3.22860	−	0.290579i	0.316590	−	0.0284936i
$105$	−5.71747	−	25.0499i	−0.557968	−	2.44462i
$106$	−0.268762	−	0.628800i	−0.0261045	−	0.0610745i
$107$	−6.84660	−	16.0184i	−0.661885	−	1.54856i	−0.826950	−	0.562275i	$-0.809926\pi$
$107$	−6.84660	−	16.0184i	−0.661885	−	1.54856i	0.165065	−	0.986283i	$-0.447217\pi$
$108$	2.54150	+	11.1350i	0.244556	+	1.07147i
$109$	−10.4692	+	0.942248i	−1.00277	+	0.0902510i	−0.578838	−	0.815443i	$-0.696494\pi$
$109$	−10.4692	+	0.942248i	−1.00277	+	0.0902510i	−0.423933	+	0.905694i	$0.639351\pi$
$110$	−14.8680	−	7.16004i	−1.41761	−	0.682683i
$111$	−0.533550	−	11.8804i	−0.0506424	−	1.12764i
$112$	8.09607	+	10.1521i	0.765007	+	0.959288i
$113$	2.76895	+	20.4412i	0.260481	+	1.92295i	0.370132	+	0.928979i	$0.379313\pi$
$113$	2.76895	+	20.4412i	0.260481	+	1.92295i	−0.109651	+	0.993970i	$0.534973\pi$
$114$	−6.97714	−	0.627954i	−0.653469	−	0.0588133i
$115$	−0.828364	−	0.494924i	−0.0772453	−	0.0461519i
$116$	1.96389	−	2.46263i	0.182342	−	0.228650i
$117$	10.1459	+	7.37146i	0.937993	+	0.681492i
$118$	19.4149	−	3.52329i	1.78729	−	0.324345i
$119$	3.08097	−	13.4986i	0.282432	−	1.23741i
$120$	−2.27871	+	16.8221i	−0.208017	+	1.53564i
$121$	−1.79820	+	1.07438i	−0.163473	+	0.0976706i
$122$	−11.3562	+	5.46884i	−1.02814	+	0.495125i
$123$	3.04951	+	5.66694i	0.274965	+	0.510971i
$124$	0.771240	−	0.806654i	0.0692594	−	0.0724396i
$125$	−0.400707	+	0.291131i	−0.0358403	+	0.0260395i
$126$	−1.34218	+	29.8860i	−0.119571	+	2.66246i
$127$	−2.57161	+	4.77886i	−0.228194	+	0.424055i	−0.968786	−	0.247900i	$-0.920260\pi$
$127$	−2.57161	+	4.77886i	−0.228194	+	0.424055i	0.740592	+	0.671955i	$0.234545\pi$
$128$	−3.72341	−	11.4595i	−0.329106	−	1.01288i
$129$	14.3562	+	3.96207i	1.26400	+	0.348841i
$130$	−5.75536	−	8.71900i	−0.504778	−	0.764707i
$131$	1.40273	−	0.387129i	0.122557	−	0.0338236i	−0.204220	−	0.978925i	$-0.565466\pi$
$131$	1.40273	−	0.387129i	0.122557	−	0.0338236i	0.326777	+	0.945101i	$0.394037\pi$
$132$	7.05491	+	6.16369i	0.614051	+	0.536480i
$133$	−3.16179	−	1.18664i	−0.274162	−	0.102895i
$134$	17.2418	−	6.47095i	1.48946	−	0.559005i
$135$	−27.1064	+	23.6821i	−2.33294	+	2.03823i
$136$	−5.03944	+	7.63443i	−0.432129	+	0.654647i
$137$	−0.276187	+	0.850016i	−0.0235962	+	0.0726217i	−0.962161	−	0.272481i	$-0.912156\pi$
$137$	−0.276187	+	0.850016i	−0.0235962	+	0.0726217i	0.938565	+	0.345103i	$0.112156\pi$
$138$	1.12731	+	1.17907i	0.0959628	+	0.100369i
$139$	−10.4043	−	1.88809i	−0.882477	−	0.160146i	−0.281643	−	0.959519i	$-0.590879\pi$
$139$	−10.4043	−	1.88809i	−0.882477	−	0.160146i	−0.600835	+	0.799373i	$0.705165\pi$
$140$	3.28918	−	7.69542i	0.277987	−	0.650382i
$141$	−26.1716			−2.20405
$142$	−14.6217	−	0.0412797i	−1.22702	−	0.00346411i
$143$	5.63778			0.471455
$144$	13.0446	−	30.5193i	1.08705	−	2.54328i
$145$	9.76713	+	1.77247i	0.811116	+	0.147196i
$146$	−8.10420	−	8.47633i	−0.670709	−	0.701506i
$147$	0.244794	−	0.753398i	0.0201903	−	0.0621392i
$148$	2.13390	−	3.23272i	0.175406	−	0.265728i
$149$	16.3489	−	14.2836i	1.33936	−	1.17016i	0.368737	−	0.929534i	$-0.379790\pi$
$149$	16.3489	−	14.2836i	1.33936	−	1.17016i	0.970618	−	0.240626i	$-0.0773527\pi$
$150$	26.0026	−	9.75893i	2.12310	−	0.796814i
$151$	8.43652	+	3.16628i	0.686555	+	0.257668i	0.670181	−	0.742198i	$-0.266216\pi$
$151$	8.43652	+	3.16628i	0.686555	+	0.257668i	0.0163735	+	0.999866i	$0.494788\pi$
$152$	1.68027	+	1.46801i	0.136288	+	0.119071i
$153$	−34.1147	+	9.41506i	−2.75801	+	0.761163i
$154$	7.40882	+	11.2239i	0.597020	+	0.904446i
$155$	3.39038	+	0.935686i	0.272322	+	0.0751561i
$156$	1.83273	+	5.64055i	0.146735	+	0.451605i
$157$	−0.409058	+	0.760157i	−0.0326464	+	0.0606671i	−0.896396	−	0.443254i	$-0.853824\pi$
$157$	−0.409058	+	0.760157i	−0.0326464	+	0.0606671i	0.863750	+	0.503921i	$0.168110\pi$
$158$	−1.33410	+	29.7061i	−0.106136	+	2.36329i
$159$	−0.989771	+	0.719111i	−0.0784939	+	0.0570292i
$160$	−11.5496	+	12.0799i	−0.913076	+	0.955002i
$161$	0.372650	+	0.692500i	0.0293689	+	0.0545766i
$162$	23.6879	−	11.4075i	1.86110	−	0.896256i
$163$	4.11173	−	2.45665i	0.322056	−	0.192419i	−0.342767	−	0.939420i	$-0.611364\pi$
$163$	4.11173	−	2.45665i	0.322056	−	0.192419i	0.664823	+	0.747001i	$0.268507\pi$
$164$	−0.281363	+	2.07710i	−0.0219708	+	0.162195i
$165$	−6.56965	+	28.7835i	−0.511446	+	2.24079i
$166$	−23.8251	+	4.32362i	−1.84919	+	0.335578i
$167$	9.53134	+	6.92493i	0.737557	+	0.535867i	0.891945	−	0.452143i	$-0.149340\pi$
$167$	9.53134	+	6.92493i	0.737557	+	0.535867i	−0.154388	+	0.988010i	$0.549340\pi$
$168$	8.62571	−	10.8163i	0.665488	−	0.834496i
$169$	−8.09588	−	4.83706i	−0.622760	−	0.372082i
$170$	29.3627	+	2.64269i	2.25202	+	0.202685i
$171$	1.15871	+	8.55391i	0.0886084	+	0.654134i
$172$	3.02444	+	3.79253i	0.230611	+	0.289177i
$173$	−0.736632	−	16.4024i	−0.0560051	−	1.24705i	−0.808518	−	0.588472i	$-0.799730\pi$
$173$	−0.736632	−	16.4024i	−0.0560051	−	1.24705i	0.752513	−	0.658578i	$-0.228842\pi$
$174$	−15.1193	−	7.28106i	−1.14619	−	0.551976i
$175$	13.3352	−	1.20019i	1.00804	−	0.0907256i
$176$	−3.32012	−	14.5464i	−0.250264	−	1.09648i
$177$	−13.8746	−	32.4613i	−1.04288	−	2.43994i
$178$	6.11565	+	14.3083i	0.458387	+	1.07245i
$179$	−2.41342	−	10.5739i	−0.180387	−	0.790328i	−0.981445	−	0.191742i	$-0.938586\pi$
$179$	−2.41342	−	10.5739i	−0.180387	−	0.790328i	0.801058	−	0.598587i	$-0.204271\pi$
$180$	−21.3050	+	1.91748i	−1.58798	+	0.142921i
$181$	19.5171	+	9.39895i	1.45070	+	0.698618i	0.982716	−	0.185121i	$-0.0592676\pi$
$181$	19.5171	+	9.39895i	1.45070	+	0.698618i	0.467980	+	0.883739i	$0.344982\pi$
$182$	0.381984	+	8.50552i	0.0283145	+	0.630471i
$183$	14.0598	+	17.6305i	1.03933	+	1.30328i
$184$	−0.0697428	−	0.514862i	−0.00514151	−	0.0379561i
$185$	12.1582	+	1.09426i	0.893887	+	0.0804513i
$186$	−5.10412	−	3.04957i	−0.374252	−	0.223605i
$187$	−9.91936	+	12.4385i	−0.725375	+	0.909592i
$188$	−6.89640	−	5.01053i	−0.502972	−	0.365430i
$189$	28.8626	−	5.23779i	2.09945	−	0.380993i
$190$	1.60011	−	7.01056i	0.116084	−	0.508599i
$191$	2.00601	−	14.8090i	0.145150	−	1.07154i	−0.761051	−	0.648692i	$-0.775316\pi$
$191$	2.00601	−	14.8090i	0.145150	−	1.07154i	0.906201	−	0.422848i	$-0.138970\pi$
$192$	−2.39635	+	1.43175i	−0.172942	+	0.103328i
$193$	13.0207	−	6.27043i	0.937250	−	0.451356i	0.0980516	−	0.995181i	$-0.468739\pi$
$193$	13.0207	−	6.27043i	0.937250	−	0.451356i	0.839198	+	0.543826i	$0.183025\pi$
$194$	3.69079	+	6.85864i	0.264983	+	0.492422i
$195$	−12.9166	+	13.5097i	−0.924978	+	0.967451i
$196$	0.208742	−	0.151660i	0.0149102	−	0.0108329i
$197$	0.102441	−	2.28102i	0.00729860	−	0.162516i	−0.992034	−	0.125974i	$-0.959794\pi$
$197$	0.102441	−	2.28102i	0.00729860	−	0.162516i	0.999332	−	0.0365418i	$-0.0116342\pi$
$198$	16.2893	−	30.2706i	1.15763	−	2.15124i
$199$	0.0399363	+	0.122911i	0.00283101	+	0.00871296i	0.952462	−	0.304657i	$-0.0985419\pi$
$199$	0.0399363	+	0.122911i	0.00283101	+	0.00871296i	−0.949631	+	0.313370i	$0.898542\pi$
$200$	−8.52720	−	2.35336i	−0.602964	−	0.166408i
$201$	−18.1509	−	27.4974i	−1.28026	−	1.93952i
$202$	4.77308	−	1.31729i	0.335833	−	0.0926839i
$203$	−6.09222	−	5.32261i	−0.427590	−	0.373574i
$204$	−15.6692	−	5.88074i	−1.09706	−	0.411734i
$205$	−6.18454	+	2.32110i	−0.431947	+	0.162112i
$206$	0.637808	−	0.557236i	0.0444382	−	0.0388245i
$207$	1.10733	−	1.67754i	0.0769651	−	0.116597i
$208$	2.91894	−	8.98358i	0.202392	−	0.622899i
$209$	2.68166	+	2.80479i	0.185494	+	0.194012i
$210$	−43.8698	−	7.96120i	−3.02731	−	0.549375i
$211$	2.85481	−	6.67915i	0.196533	−	0.459812i	−0.792056	−	0.610448i	$-0.790989\pi$
$211$	2.85481	−	6.67915i	0.196533	−	0.459812i	0.988589	+	0.150636i	$0.0481322\pi$
$212$	−0.398485			−0.0273680
$213$	5.74898	+	25.5198i	0.393914	+	1.74859i
$214$	−30.2290			−2.06641
$215$	−6.00830	+	14.0571i	−0.409763	+	0.958688i
$216$	−19.0692	−	3.46054i	−1.29749	−	0.235460i
$217$	−1.98081	−	2.07176i	−0.134466	−	0.140640i
$218$	−5.63661	+	17.3477i	−0.381760	+	1.17494i
$219$	−11.5583	+	17.5100i	−0.781035	+	1.18322i
$220$	−7.24173	+	6.32691i	−0.488237	+	0.426560i
$221$	−9.42972	+	3.53903i	−0.634312	+	0.238061i
$222$	−19.3207	−	7.25119i	−1.29672	−	0.486668i
$223$	16.5665	+	14.4737i	1.10938	+	0.969234i	0.999694	−	0.0247326i	$-0.00787344\pi$
$223$	16.5665	+	14.4737i	1.10938	+	0.969234i	0.109683	+	0.993967i	$0.465016\pi$
$224$	13.1294	−	3.62350i	0.877248	−	0.242105i
$225$	−18.8532	−	28.5614i	−1.25688	−	1.90410i
$226$	34.5052	+	9.52284i	2.29525	+	0.633450i
$227$	3.53209	+	10.8706i	0.234433	+	0.721510i	0.997196	+	0.0748322i	$0.0238421\pi$
$227$	3.53209	+	10.8706i	0.234433	+	0.721510i	−0.762763	+	0.646678i	$0.776158\pi$
$228$	−1.93442	+	3.59476i	−0.128110	+	0.238069i
$229$	−0.766335	+	17.0638i	−0.0506408	+	1.12761i	0.799369	+	0.600840i	$0.205167\pi$
$229$	−0.766335	+	17.0638i	−0.0506408	+	1.12761i	−0.850010	+	0.526766i	$0.823404\pi$
$230$	−1.35467	+	0.984225i	−0.0893243	+	0.0648979i
$231$	16.6274	−	17.3909i	1.09400	−	1.14424i
$232$	2.53276	+	4.70665i	0.166284	+	0.309007i
$233$	−6.78032	+	3.26523i	−0.444194	+	0.213912i	−0.642591	−	0.766209i	$-0.722141\pi$
$233$	−6.78032	+	3.26523i	−0.444194	+	0.213912i	0.198398	+	0.980122i	$0.436426\pi$
$234$	18.6818	−	11.1618i	1.22127	−	0.729673i
$235$	3.60613	−	26.6215i	0.235238	−	1.73660i
$236$	2.55863	−	11.2101i	0.166552	−	0.729714i
$237$	52.3452	−	9.49925i	3.40018	−	0.617043i
$238$	−19.4376	−	14.1222i	−1.25995	−	0.915409i
$239$	−14.5780	+	18.2803i	−0.942975	+	1.18245i	0.0400898	+	0.999196i	$0.487236\pi$
$239$	−14.5780	+	18.2803i	−0.942975	+	1.18245i	−0.983065	+	0.183257i	$0.941336\pi$
$240$	42.4640	+	25.3711i	2.74104	+	1.63769i
$241$	−21.8000	−	1.96204i	−1.40426	−	0.126386i	−0.638556	−	0.769575i	$-0.720468\pi$
$241$	−21.8000	−	1.96204i	−1.40426	−	0.126386i	−0.765707	+	0.643189i	$0.777611\pi$
$242$	0.487926	+	3.60201i	0.0313650	+	0.231546i
$243$	−8.20054	−	10.2832i	−0.526065	−	0.659665i
$244$	0.329528	+	7.33750i	0.0210958	+	0.469735i
$245$	0.732620	+	0.352811i	0.0468054	+	0.0225403i
$246$	11.1222	−	1.00101i	0.709123	−	0.0638222i
$247$	0.546659	+	2.39507i	0.0347831	+	0.152395i
$248$	0.744288	+	1.74135i	0.0472624	+	0.110576i
$249$	17.0263	+	39.8350i	1.07900	+	2.52444i
$250$	0.191254	+	0.837937i	0.0120959	+	0.0529958i
$251$	9.23919	−	0.831543i	0.583173	−	0.0524865i	0.205875	−	0.978578i	$-0.433996\pi$
$251$	9.23919	−	0.831543i	0.583173	−	0.0524865i	0.377298	+	0.926092i	$0.376853\pi$
$252$	15.7065	+	7.56385i	0.989417	+	0.476478i
$253$	−0.0405404	−	0.902701i	−0.00254875	−	0.0567523i
$254$	5.87146	+	7.36258i	0.368408	+	0.461969i
$255$	−7.08007	−	52.2672i	−0.443371	−	3.27310i
$256$	−19.0335	−	1.71304i	−1.18959	−	0.107065i
$257$	−18.6898	−	11.1666i	−1.16584	−	0.696556i	−0.206398	−	0.978468i	$-0.566174\pi$
$257$	−18.6898	−	11.1666i	−1.16584	−	0.696556i	−0.959440	+	0.281913i	$0.909031\pi$
$258$	16.1131	−	20.2052i	1.00316	−	1.25792i
$259$	−8.04849	−	5.84757i	−0.500109	−	0.363350i
$260$	−5.99004	+	1.08703i	−0.371487	+	0.0674149i
$261$	−4.60125	+	20.1594i	−0.284810	+	1.24783i
$262$	0.338956	−	2.50227i	0.0209408	−	0.154591i
$263$	3.33901	−	1.99496i	0.205892	−	0.123015i	−0.406252	−	0.913761i	$-0.633164\pi$
$263$	3.33901	−	1.99496i	0.205892	−	0.123015i	0.612144	+	0.790746i	$0.290307\pi$
$264$	−14.3223	+	6.89727i	−0.881479	+	0.424498i
$265$	−0.595094	−	1.10587i	−0.0365564	−	0.0679331i
$266$	−4.04981	+	4.23576i	−0.248310	+	0.259711i
$267$	22.5221	−	16.3633i	1.37833	−	1.00142i
$268$	0.481468	−	10.7207i	0.0294103	−	0.654872i
$269$	4.45577	−	8.28020i	0.271673	−	0.504853i	−0.707804	−	0.706409i	$-0.750314\pi$
$269$	4.45577	−	8.28020i	0.271673	−	0.504853i	0.979477	+	0.201556i	$0.0645998\pi$
$270$	19.3013	+	59.4033i	1.17464	+	3.61517i
$271$	−2.11331	−	0.583237i	−0.128375	−	0.0354291i	0.201259	−	0.979538i	$-0.435497\pi$
$271$	−2.11331	−	0.583237i	−0.128375	−	0.0354291i	−0.329634	+	0.944109i	$0.606925\pi$
$272$	14.6845	+	22.2461i	0.890380	+	1.34887i
$273$	14.6834	−	4.05237i	0.888683	−	0.245261i
$274$	1.16795	+	1.02041i	0.0705587	+	0.0616453i
$275$	−14.4037	−	5.40579i	−0.868574	−	0.325981i
$276$	0.889966	−	0.334010i	0.0535697	−	0.0201050i
$277$	10.6742	−	9.32574i	0.641348	−	0.560329i	−0.274633	−	0.961549i	$-0.588557\pi$
$277$	10.6742	−	9.32574i	0.641348	−	0.560329i	0.915982	+	0.401220i	$0.131414\pi$
$278$	−10.1085	+	15.3137i	−0.606267	+	0.918455i
$279$	−2.26398	+	6.96781i	−0.135541	+	0.417152i
$280$	9.81373	+	10.2644i	0.586482	+	0.613412i
$281$	−25.1087	−	4.55656i	−1.49786	−	0.271821i	−0.633125	−	0.774050i	$-0.718228\pi$
$281$	−25.1087	−	4.55656i	−1.49786	−	0.271821i	−0.864735	+	0.502228i	$0.832514\pi$
$282$	−17.8492	+	41.7604i	−1.06291	+	2.48679i
$283$	8.08615			0.480672			0.240336	−	0.970690i	$-0.422742\pi$
$283$	8.08615			0.480672			0.240336	+	0.970690i	$0.422742\pi$
$284$	−3.37085	+	7.82530i	−0.200023	+	0.464346i
$285$	−12.8650			−0.762056
$286$	3.84501	−	8.99584i	0.227360	−	0.531935i
$287$	5.29692	+	0.961249i	0.312667	+	0.0567408i
$288$	−24.0585	−	25.1632i	−1.41766	−	1.48276i
$289$	3.52971	−	10.8633i	0.207630	−	0.639020i
$290$	9.48948	−	14.3759i	0.557241	−	0.844185i
$291$	10.4937	−	9.16803i	0.615149	−	0.537440i
$292$	−6.39796	+	2.40119i	−0.374412	+	0.140519i
$293$	−14.8862	−	5.58690i	−0.869663	−	0.326390i	−0.123654	−	0.992325i	$-0.539461\pi$
$293$	−14.8862	−	5.58690i	−0.869663	−	0.326390i	−0.746009	+	0.665935i	$0.768033\pi$
$294$	−1.03520	−	0.904425i	−0.0603740	−	0.0527471i
$295$	34.9311	−	9.64037i	2.03377	−	0.561284i
$296$	3.62096	+	5.48552i	0.210464	+	0.318839i
$297$	−32.4915	−	8.96710i	−1.88535	−	0.520324i
$298$	−11.6414	−	35.8285i	−0.674367	−	2.07549i
$299$	0.271081	−	0.503753i	0.0156770	−	0.0291328i
$300$	0.726109	−	16.1681i	0.0419219	−	0.933464i
$301$	10.0792	−	7.32296i	0.580955	−	0.422089i
$302$	10.8060	−	11.3022i	0.621816	−	0.650368i
$303$	−4.19784	−	7.80089i	−0.241159	−	0.448149i
$304$	5.85775	−	2.82094i	0.335965	−	0.161792i
$305$	−19.8708	+	11.8723i	−1.13780	+	0.679804i
$306$	−8.24348	+	60.8558i	−0.471248	+	3.47890i
$307$	0.141279	−	0.618982i	0.00806320	−	0.0353272i	−0.970736	−	0.240148i	$-0.922804\pi$
$307$	0.141279	−	0.618982i	0.00806320	−	0.0353272i	0.978799	+	0.204821i	$0.0656612\pi$
$308$	7.71093	−	1.39933i	0.439371	−	0.0797341i
$309$	−1.22586	−	0.890639i	−0.0697367	−	0.0506667i
$310$	3.80528	−	4.77167i	0.216125	−	0.271013i
$311$	0.453540	+	0.270978i	0.0257179	+	0.0153657i	0.525701	−	0.850670i	$-0.323803\pi$
$311$	0.453540	+	0.270978i	0.0257179	+	0.0153657i	−0.499983	+	0.866035i	$0.666660\pi$
$312$	−10.0233	−	0.902116i	−0.567459	−	0.0510723i
$313$	−1.05660	−	7.80010i	−0.0597223	−	0.440888i	−0.995980	−	0.0895741i	$-0.971449\pi$
$313$	−1.05660	−	7.80010i	−0.0597223	−	0.440888i	0.936258	−	0.351314i	$-0.114265\pi$
$314$	0.933954	+	1.17114i	0.0527060	+	0.0660913i
$315$	2.46486	+	54.8843i	0.138879	+	3.09238i
$316$	15.6120	+	7.51832i	0.878241	+	0.422939i
$317$	−11.2986	+	1.01689i	−0.634593	+	0.0571144i	−0.402265	−	0.915523i	$-0.631777\pi$
$317$	−11.2986	+	1.01689i	−0.634593	+	0.0571144i	−0.232328	+	0.972638i	$0.574634\pi$
$318$	0.472408	+	2.06975i	0.0264913	+	0.116066i
$319$	3.65341	+	8.54757i	0.204551	+	0.478572i
$320$	−1.12618	−	2.63483i	−0.0629553	−	0.147291i
$321$	12.0344	+	52.7260i	0.671693	+	2.94288i
$322$	1.35913	−	0.122324i	0.0757413	−	0.00681684i
$323$	−6.24600	−	3.00792i	−0.347537	−	0.167365i
$324$	−0.687363	−	15.3053i	−0.0381868	−	0.850296i
$325$	−6.07264	−	7.61485i	−0.336850	−	0.422396i
$326$	−1.11568	−	8.23628i	−0.0617918	−	0.456166i
$327$	32.5022	+	2.92525i	1.79738	+	0.161767i
$328$	−3.05330	−	1.82426i	−0.168590	−	0.100728i
$329$	−13.6505	+	17.1171i	−0.752574	+	0.943698i
$330$	41.4475	+	30.1133i	2.28161	+	1.65769i
$331$	−17.2903	+	3.13773i	−0.950362	+	0.172465i	−0.631535	−	0.775347i	$-0.717575\pi$
$331$	−17.2903	+	3.13773i	−0.950362	+	0.172465i	−0.318827	+	0.947813i	$0.603289\pi$
$332$	−3.13983	+	13.7565i	−0.172321	+	0.754986i
$333$	−3.41336	+	25.1985i	−0.187051	+	1.38087i
$334$	17.5501	−	10.4857i	0.960300	−	0.573752i
$335$	30.4710	−	14.6741i	1.66481	−	0.801731i
$336$	−19.1030	−	35.4993i	−1.04215	−	1.93664i
$337$	−9.04172	+	9.45689i	−0.492534	+	0.515150i	−0.921609	−	0.388119i	$-0.873125\pi$
$337$	−9.04172	+	9.45689i	−0.492534	+	0.515150i	0.429076	+	0.903268i	$0.358839\pi$
$338$	−13.2396	+	9.61917i	−0.720142	+	0.523214i
$339$	2.87316	−	63.9759i	0.156049	−	3.47469i
$340$	8.14086	−	15.1283i	0.441500	−	0.820445i
$341$	1.01776	+	3.13234i	0.0551148	+	0.169626i
$342$	14.4392	+	3.98496i	0.780781	+	0.215482i
$343$	−10.3801	−	15.7252i	−0.560475	−	0.849083i
$344$	−7.93459	+	2.18981i	−0.427804	+	0.118067i
$345$	2.25601	+	1.97102i	0.121459	+	0.106116i
$346$	−26.6746	−	10.0112i	−1.43404	−	0.538203i
$347$	−7.00905	+	2.63054i	−0.376266	+	0.141215i	−0.532340	−	0.846530i	$-0.678687\pi$
$347$	−7.00905	+	2.63054i	−0.376266	+	0.141215i	0.156075	+	0.987745i	$0.450116\pi$
$348$	−7.36412	+	6.43384i	−0.394758	+	0.344890i
$349$	10.9873	−	16.6451i	0.588139	−	0.890992i	−0.411654	−	0.911340i	$-0.635049\pi$
$349$	10.9873	−	16.6451i	0.588139	−	0.890992i	0.999793	+	0.0203478i	$0.00647736\pi$
$350$	7.17962	−	22.0966i	0.383767	−	1.18111i
$351$	−14.7464	−	15.4236i	−0.787107	−	0.823249i
$352$	−15.3989	−	2.79448i	−0.820761	−	0.148946i
$353$	−2.32328	+	5.43558i	−0.123656	+	0.289307i	−0.969906	−	0.243478i	$-0.921712\pi$
$353$	−2.32328	+	5.43558i	−0.123656	+	0.289307i	0.846251	+	0.532785i	$0.178854\pi$
$354$	−61.2590			−3.25588
$355$	−26.7507	+	2.33149i	−1.41978	+	0.123743i
$356$	9.06747			0.480575
$357$	−16.8941	+	39.5257i	−0.894129	+	2.09192i
$358$	−18.5180	−	3.36053i	−0.978708	−	0.177609i
$359$	12.4398	+	13.0110i	0.656547	+	0.686694i	0.964312	−	0.264768i	$-0.0852954\pi$
$359$	12.4398	+	13.0110i	0.656547	+	0.686694i	−0.307765	+	0.951462i	$0.599581\pi$
$360$	11.2167	−	34.5214i	0.591171	−	1.81944i
$361$	9.53552	−	14.4457i	0.501869	−	0.760300i
$362$	28.3081	−	24.7321i	1.48784	−	1.29989i
$363$	6.08846	−	2.28504i	0.319561	−	0.119933i
$364$	4.64502	+	1.74330i	0.243465	+	0.0913740i
$365$	−16.2184	−	14.1696i	−0.848912	−	0.741672i
$366$	37.7208	−	10.4103i	1.97170	−	0.544153i
$367$	3.74989	+	5.68083i	0.195742	+	0.296537i	0.919168	−	0.393865i	$-0.128862\pi$
$367$	3.74989	+	5.68083i	0.195742	+	0.296537i	−0.723426	+	0.690402i	$0.757434\pi$
$368$	−1.45941	−	0.402771i	−0.0760769	−	0.0209959i
$369$	−4.25214	−	13.0867i	−0.221357	−	0.681268i
$370$	10.0380	−	18.6537i	0.521851	−	0.969762i
$371$	−0.0459167	+	1.02241i	−0.00238388	+	0.0530811i
$372$	−2.80303	+	2.03652i	−0.145330	+	0.105589i
$373$	12.8311	−	13.4203i	0.664371	−	0.694878i	−0.301627	−	0.953426i	$-0.597530\pi$
$373$	12.8311	−	13.4203i	0.664371	−	0.694878i	0.965998	+	0.258548i	$0.0832441\pi$
$374$	13.0822	+	24.3108i	0.676465	+	1.25708i
$375$	1.38541	−	0.667177i	0.0715421	−	0.0344529i
$376$	12.4173	−	7.41901i	0.640375	−	0.382606i
$377$	−0.789947	+	5.83162i	−0.0406843	+	0.300344i
$378$	11.3269	−	49.6265i	0.582594	−	2.55251i
$379$	−35.6116	+	6.46255i	−1.82924	+	0.331959i	−0.980450	−	0.196766i	$-0.936956\pi$
$379$	−35.6116	+	6.46255i	−1.82924	+	0.331959i	−0.848793	+	0.528725i	$0.822670\pi$
$380$	−3.39002	−	2.46299i	−0.173904	−	0.126349i
$381$	10.5045	−	13.1722i	0.538161	−	0.674833i
$382$	−22.2616	−	13.3007i	−1.13900	−	0.680523i
$383$	11.7096	+	1.05389i	0.598334	+	0.0538510i	0.384667	−	0.923056i	$-0.374316\pi$
$383$	11.7096	+	1.05389i	0.598334	+	0.0538510i	0.213667	+	0.976907i	$0.431459\pi$
$384$	5.02131	+	37.0688i	0.256242	+	1.89166i
$385$	15.3988	+	19.3095i	0.784798	+	0.984105i
$386$	−1.12512	−	25.0528i	−0.0572672	−	1.27515i
$387$	−28.6908	−	13.8168i	−1.45844	−	0.702346i
$388$	4.52037	−	0.406840i	0.229487	−	0.0206542i
$389$	−1.42100	−	6.22580i	−0.0720475	−	0.315661i	0.926044	−	0.377416i	$-0.123187\pi$
$389$	−1.42100	−	6.22580i	−0.0720475	−	0.315661i	−0.998091	+	0.0617554i	$0.980330\pi$
$390$	12.7474	+	29.8239i	0.645488	+	1.51019i
$391$	0.634466	+	1.48441i	0.0320863	+	0.0750696i
$392$	0.0974255	+	0.426849i	0.00492073	+	0.0215591i
$393$	−4.49946	+	0.404958i	−0.226968	+	0.0204274i
$394$	−3.56981	−	1.71913i	−0.179845	−	0.0866086i
$395$	2.45002	+	54.5539i	0.123274	+	2.74491i
$396$	−12.4893	−	15.6611i	−0.627610	−	0.786998i
$397$	4.97690	+	36.7410i	0.249784	+	1.84398i	0.488098	+	0.872789i	$0.337691\pi$
$397$	4.97690	+	36.7410i	0.249784	+	1.84398i	−0.238314	+	0.971188i	$0.576595\pi$
$398$	0.223359	+	0.0201027i	0.0111960	+	0.00100765i
$399$	9.00037	+	5.37747i	0.450582	+	0.269210i
$400$	−16.0714	+	20.1529i	−0.803569	+	1.00764i
$401$	21.3045	+	15.4786i	1.06389	+	0.772964i	0.974805	−	0.223059i	$-0.0716044\pi$
$401$	21.3045	+	15.4786i	1.06389	+	0.772964i	0.0890893	+	0.996024i	$0.471604\pi$
$402$	−56.2548	+	10.2087i	−2.80574	+	0.509166i
$403$	−0.463974	+	2.03280i	−0.0231122	+	0.101261i
$404$	0.387313	−	2.85926i	0.0192696	−	0.142254i
$405$	41.4487	−	24.7644i	2.05960	−	1.23055i
$406$	−12.6479	+	6.09091i	−0.627705	+	0.302287i
$407$	5.41693	+	10.0663i	0.268507	+	0.498970i
$408$	19.6258	−	20.5270i	0.971623	−	1.01624i
$409$	16.5702	−	12.0389i	0.819342	−	0.595286i	−0.0971823	−	0.995267i	$-0.530983\pi$
$409$	16.5702	−	12.0389i	0.819342	−	0.595286i	0.916524	+	0.399980i	$0.130983\pi$
$410$	−0.514278	+	11.4513i	−0.0253984	+	0.565539i
$411$	1.31485	−	2.44340i	0.0648568	−	0.120524i
$412$	−0.152511	−	0.469379i	−0.00751366	−	0.0231247i
$413$	−28.4675	−	7.85652i	−1.40079	−	0.386594i
$414$	−1.92153	−	2.91100i	−0.0944382	−	0.143068i
$415$	−42.8659	+	11.8302i	−2.10420	+	0.580723i
$416$	−7.46140	−	6.51883i	−0.365825	−	0.319612i
$417$	30.7348	+	11.5350i	1.50509	+	0.564869i
$418$	6.30434	−	2.36606i	0.308356	−	0.115728i
$419$	22.4114	−	19.5803i	1.09487	−	0.956559i	0.0956257	−	0.995417i	$-0.469515\pi$
$419$	22.4114	−	19.5803i	1.09487	−	0.956559i	0.999245	+	0.0388579i	$0.0123720\pi$
$420$	−14.3132	+	21.6835i	−0.698412	+	1.05805i
$421$	5.02628	−	15.4693i	0.244966	−	0.753927i	−0.750676	−	0.660670i	$-0.770272\pi$
$421$	5.02628	−	15.4693i	0.244966	−	0.753927i	0.995642	−	0.0932569i	$-0.0297278\pi$
$422$	−8.71050	−	9.11047i	−0.424021	−	0.443491i
$423$	55.0614	+	9.99217i	2.67718	+	0.485836i
$424$	0.265755	−	0.621764i	0.0129062	−	0.0301955i
$425$	27.4849			1.33322
$426$	44.6412	+	8.23144i	2.16287	+	0.398814i
$427$	18.8642			0.912903
$428$	−6.92321	+	16.1977i	−0.334646	+	0.782943i
$429$	−17.2215	−	3.12523i	−0.831460	−	0.150888i
$430$	18.3323	+	19.1741i	0.884064	+	0.924659i
$431$	−1.23459	+	3.79968i	−0.0594681	+	0.183024i	−0.976378	−	0.216071i	$-0.930676\pi$
$431$	−1.23459	+	3.79968i	−0.0594681	+	0.183024i	0.916910	+	0.399095i	$0.130676\pi$
$432$	−31.1111	+	47.1313i	−1.49683	+	2.26761i
$433$	−29.0241	+	25.3576i	−1.39481	+	1.21861i	−0.449143	+	0.893460i	$0.648271\pi$
$433$	−29.0241	+	25.3576i	−1.39481	+	1.21861i	−0.945664	+	0.325146i	$0.894586\pi$
$434$	−4.65671	+	1.74769i	−0.223529	+	0.0838918i
$435$	−28.8527	−	10.8286i	−1.38338	−	0.519191i
$436$	8.00453	+	6.99335i	0.383348	+	0.334921i
$437$	0.379559	−	0.104752i	0.0181568	−	0.00501096i
$438$	20.0568	+	30.3847i	0.958351	+	1.45184i
$439$	5.60096	+	1.54577i	0.267319	+	0.0737754i	0.397127	−	0.917764i	$-0.370007\pi$
$439$	5.60096	+	1.54577i	0.267319	+	0.0737754i	−0.129807	+	0.991539i	$0.541436\pi$
$440$	−5.04240	−	15.5189i	−0.240387	−	0.739835i
$441$	−0.802655	+	1.49158i	−0.0382217	+	0.0710277i
$442$	−0.784132	+	17.4601i	−0.0372974	+	0.830490i
$443$	−9.92712	+	7.21247i	−0.471652	+	0.342675i	−0.798085	−	0.602545i	$-0.794153\pi$
$443$	−9.92712	+	7.21247i	−0.471652	+	0.342675i	0.326433	+	0.945220i	$0.394153\pi$
$444$	−8.31036	+	8.69195i	−0.394392	+	0.412502i
$445$	13.5413	+	25.1639i	0.641919	+	1.19288i
$446$	34.3934	−	16.5630i	1.62857	−	0.784279i
$447$	−57.8583	+	34.5687i	−2.73660	+	1.63504i
$448$	−0.313461	+	2.31406i	−0.0148097	+	0.109329i
$449$	6.07927	−	26.6350i	0.286899	−	1.25698i	−0.601857	−	0.798604i	$-0.705572\pi$
$449$	6.07927	−	26.6350i	0.286899	−	1.25698i	0.888756	−	0.458381i	$-0.151570\pi$
$450$	−58.4317	+	10.6038i	−2.75450	+	0.499868i
$451$	−5.00444	−	3.63594i	−0.235650	−	0.171210i
$452$	13.0052	−	16.3080i	0.611714	−	0.767065i
$453$	−24.0155	−	14.3486i	−1.12835	−	0.674155i
$454$	19.7545	+	1.77794i	0.927125	+	0.0834427i
$455$	2.09884	+	15.4942i	0.0983950	+	0.726381i
$456$	−4.31888	−	5.41571i	−0.202250	−	0.253614i
$457$	−1.04249	−	23.2129i	−0.0487657	−	1.08585i	−0.862964	−	0.505266i	$-0.831394\pi$
$457$	−1.04249	−	23.2129i	−0.0487657	−	1.08585i	0.814198	−	0.580588i	$-0.197177\pi$
$458$	26.7049	+	12.8604i	1.24784	+	0.600928i
$459$	59.9742	−	5.39778i	2.79936	−	0.251947i
$460$	0.217125	+	0.951288i	0.0101235	+	0.0443540i
$461$	0.478426	+	1.11933i	0.0222825	+	0.0521325i	0.930299	−	0.366801i	$-0.119547\pi$
$461$	0.478426	+	1.11933i	0.0222825	+	0.0521325i	−0.908017	+	0.418933i	$0.862404\pi$
$462$	−16.4096	−	38.3921i	−0.763442	−	1.78616i
$463$	5.20919	+	22.8229i	0.242092	+	1.06067i	0.939109	+	0.343619i	$0.111653\pi$
$463$	5.20919	+	22.8229i	0.242092	+	1.06067i	−0.697018	+	0.717054i	$0.745490\pi$
$464$	15.5118	−	1.39608i	0.720115	−	0.0648115i
$465$	−9.83776	−	4.73762i	−0.456215	−	0.219702i
$466$	0.585889	+	13.0458i	0.0271408	+	0.604337i
$467$	−21.6557	−	27.1554i	−1.00210	−	1.25660i	−0.966348	−	0.257239i	$-0.917187\pi$
$467$	−21.6557	−	27.1554i	−1.00210	−	1.25660i	−0.0357572	−	0.999361i	$-0.511384\pi$
$468$	−1.70227	−	12.5666i	−0.0786874	−	0.580894i
$469$	−27.4513	−	2.47066i	−1.26758	−	0.114084i
$470$	−40.0188	−	23.9101i	−1.84593	−	1.10289i
$471$	1.67092	−	2.09526i	0.0769917	−	0.0965445i
$472$	15.7849	+	11.4684i	0.726560	+	0.527877i
$473$	−14.0854	+	2.55613i	−0.647649	+	0.117531i
$474$	20.5425	−	90.0024i	0.943547	−	4.13395i
$475$	0.899884	−	6.64321i	0.0412895	−	0.304811i
$476$	−12.0189	+	7.18094i	−0.550884	+	0.329138i
$477$	2.35689	−	1.13502i	0.107915	−	0.0519690i
$478$	19.2264	+	35.7286i	0.879393	+	1.63419i
$479$	10.7701	−	11.2646i	0.492096	−	0.514693i	−0.429381	−	0.903123i	$-0.641268\pi$
$479$	10.7701	−	11.2646i	0.492096	−	0.514693i	0.921478	+	0.388431i	$0.126983\pi$
$480$	41.9764	−	30.4976i	1.91595	−	1.39202i
$481$	−0.324684	+	7.22965i	−0.0148043	+	0.329644i
$482$	−17.9985	+	33.4468i	−0.819809	+	1.52346i
$483$	−0.754438	−	2.32192i	−0.0343281	−	0.105651i
$484$	2.04182	+	0.563507i	0.0928100	+	0.0256139i
$485$	7.87974	+	11.9373i	0.357801	+	0.542045i
$486$	−22.0010	+	6.07189i	−0.997986	+	0.275427i
$487$	−4.71595	−	4.12020i	−0.213700	−	0.186704i	0.544432	−	0.838805i	$-0.316745\pi$
$487$	−4.71595	−	4.12020i	−0.213700	−	0.186704i	−0.758133	+	0.652101i	$0.773888\pi$
$488$	−11.6686	−	4.37930i	−0.528213	−	0.198242i
$489$	−13.9217	+	5.22492i	−0.629563	+	0.236279i
$490$	1.06261	−	0.928375i	0.0480039	−	0.0419397i
$491$	3.03712	−	4.60104i	0.137063	−	0.207642i	−0.759559	−	0.650439i	$-0.774585\pi$
$491$	3.03712	−	4.60104i	0.137063	−	0.207642i	0.896622	+	0.442797i	$0.146014\pi$
$492$	2.01089	−	6.18887i	0.0906577	−	0.279016i
$493$	−11.4763	−	12.0033i	−0.516866	−	0.540600i
$494$	4.19449	+	0.761187i	0.188719	+	0.0342474i
$495$	24.8110	−	58.0482i	1.11517	−	2.60907i
$496$	5.51821			0.247775
$497$	19.6894	+	9.55048i	0.883189	+	0.428397i
$498$	75.1743			3.36864
$499$	9.71823	−	22.7369i	0.435048	−	1.01784i	−0.548328	−	0.836263i	$-0.684736\pi$
$499$	9.71823	−	22.7369i	0.435048	−	1.01784i	0.983376	−	0.181581i	$-0.0581216\pi$
$500$	0.492795	+	0.0894292i	0.0220385	+	0.00399939i
$501$	−25.2762	−	26.4369i	−1.12926	−	1.18111i
$502$	4.97436	−	15.3095i	0.222017	−	0.683297i
$503$	−5.50528	+	8.34014i	−0.245468	+	0.371869i	−0.936332	−	0.351117i	$-0.885802\pi$
$503$	−5.50528	+	8.34014i	−0.245468	+	0.371869i	0.690863	+	0.722985i	$0.257231\pi$
$504$	−22.2769	+	19.4627i	−0.992292	+	0.866939i
$505$	8.51340	−	3.19513i	0.378841	−	0.142182i
$506$	−1.46803	−	0.550962i	−0.0652620	−	0.0244932i
$507$	22.0488	+	19.2634i	0.979220	+	0.855519i
$508$	5.28982	−	1.45990i	0.234698	−	0.0647725i
$509$	−11.6983	−	17.7222i	−0.518520	−	0.785524i	0.477117	−	0.878840i	$-0.341682\pi$
$509$	−11.6983	−	17.7222i	−0.518520	−	0.785524i	−0.995637	+	0.0933163i	$0.970253\pi$
$510$	−88.2281	−	24.3494i	−3.90681	−	1.07821i
$511$	5.42365	+	16.6923i	0.239928	+	0.738423i
$512$	−4.29488	+	7.98123i	−0.189809	+	0.352724i
$513$	0.658952	−	14.6727i	0.0290935	−	0.647816i
$514$	−30.5645	+	22.2064i	−1.34814	+	0.979482i
$515$	1.07486	−	1.12421i	0.0473639	−	0.0495388i
$516$	−7.13628	−	13.2614i	−0.314157	−	0.583802i
$517$	22.6655	−	10.9151i	0.996829	−	0.480047i
$518$	−14.8197	+	8.85438i	−0.651142	+	0.389039i
$519$	−6.84231	+	50.5120i	−0.300344	+	2.21723i
$520$	2.29872	−	10.0713i	0.100805	−	0.441657i
$521$	25.3625	−	4.60262i	1.11115	−	0.201644i	0.408208	−	0.912889i	$-0.366154\pi$
$521$	25.3625	−	4.60262i	1.11115	−	0.201644i	0.702945	+	0.711245i	$0.251868\pi$
$522$	29.0290	+	21.0908i	1.27056	+	0.923118i
$523$	15.5014	−	19.4382i	0.677830	−	0.849971i	−0.317323	−	0.948318i	$-0.602784\pi$
$523$	15.5014	−	19.4382i	0.677830	−	0.849971i	0.995152	+	0.0983462i	$0.0313552\pi$
$524$	−1.26317	−	0.754708i	−0.0551817	−	0.0329696i
$525$	−41.3996	−	3.72603i	−1.80683	−	0.162617i
$526$	−0.906009	−	6.68842i	−0.0395038	−	0.291629i
$527$	−3.66859	−	4.60026i	−0.159806	−	0.200391i
$528$	2.07820	+	46.2747i	0.0904420	+	2.01385i
$529$	20.6397	+	9.93954i	0.897377	+	0.432154i
$530$	−2.17043	+	0.195342i	−0.0942773	+	0.00848511i
$531$	16.7967	+	73.5913i	0.728916	+	3.19359i
$532$	1.34215	+	3.14011i	0.0581896	+	0.136141i
$533$	−1.53914	−	3.60099i	−0.0666675	−	0.155976i
$534$	−10.7496	−	47.0970i	−0.465179	−	2.03808i
$535$	−55.2906	+	4.97625i	−2.39042	+	0.215142i
$536$	16.4067	+	7.90103i	0.708660	+	0.341272i
$537$	1.51066	+	33.6374i	0.0651896	+	1.45156i
$538$	−10.1733	−	12.7569i	−0.438603	−	0.549991i
$539$	0.102212	+	0.754563i	0.00440260	+	0.0325013i
$540$	36.2507	+	3.26262i	1.55998	+	0.140401i
$541$	11.5537	+	6.90302i	0.496733	+	0.296784i	0.739330	−	0.673343i	$-0.235142\pi$
$541$	11.5537	+	6.90302i	0.496733	+	0.296784i	−0.242597	+	0.970127i	$0.577999\pi$
$542$	−2.37193	+	2.97431i	−0.101883	+	0.127757i
$543$	−54.4079	−	39.5296i	−2.33486	−	1.69638i
$544$	27.5103	−	4.99238i	1.17949	−	0.214046i
$545$	−7.45396	+	32.6579i	−0.319292	+	1.39891i
$546$	3.54811	−	26.1932i	0.151845	−	1.12097i
$547$	−18.3569	+	10.9677i	−0.784884	+	0.468946i	−0.848608	−	0.529021i	$-0.822559\pi$
$547$	−18.3569	+	10.9677i	−0.784884	+	0.468946i	0.0637249	+	0.997968i	$0.479702\pi$
$548$	0.814260	−	0.392127i	0.0347835	−	0.0167508i
$549$	−22.8487	−	42.4600i	−0.975159	−	1.81215i
$550$	−18.4491	+	19.2962i	−0.786672	+	0.822794i
$551$	−3.27698	+	2.38086i	−0.139604	+	0.101428i
$552$	−0.0723675	+	1.61139i	−0.00308017	+	0.0685852i
$553$	21.0891	−	39.1901i	0.896800	−	1.66653i
$554$	−7.60062	−	23.3923i	−0.322919	−	0.993844i
$555$	−36.5324	−	10.0823i	−1.55072	−	0.427970i
$556$	5.89047	+	8.92369i	0.249812	+	0.378449i
$557$	35.5051	−	9.79879i	1.50440	−	0.415188i	0.585826	−	0.810437i	$-0.300770\pi$
$557$	35.5051	−	9.79879i	1.50440	−	0.415188i	0.918574	+	0.395249i	$0.129342\pi$
$558$	9.57405	+	8.36459i	0.405302	+	0.354101i
$559$	−8.48499	−	3.18447i	−0.358877	−	0.134689i
$560$	38.7417	−	14.5400i	1.63714	−	0.614427i
$561$	37.1954	−	32.4966i	1.57039	−	1.37201i
$562$	−24.3949	+	36.9568i	−1.02904	+	1.55893i
$563$	−7.39121	+	22.7478i	−0.311502	+	0.958706i	0.665668	+	0.746248i	$0.268147\pi$
$563$	−7.39121	+	22.7478i	−0.311502	+	0.958706i	−0.977170	+	0.212458i	$0.931853\pi$
$564$	18.2886	+	19.1284i	0.770089	+	0.805450i
$565$	64.6798	+	11.7376i	2.72110	+	0.493807i
$566$	5.51482	−	12.9026i	0.231805	−	0.542335i
$567$	−39.3489			−1.65250
$568$	−9.96190	−	10.4784i	−0.417992	−	0.439664i
$569$	−8.58042			−0.359710			−0.179855	−	0.983693i	$-0.557563\pi$
$569$	−8.58042			−0.359710			−0.179855	+	0.983693i	$0.557563\pi$
$570$	−8.77402	+	20.5278i	−0.367503	+	0.859817i
$571$	2.48207	+	0.450430i	0.103872	+	0.0188499i	0.230244	−	0.973133i	$-0.426048\pi$
$571$	2.48207	+	0.450430i	0.103872	+	0.0188499i	−0.126372	+	0.991983i	$0.540333\pi$
$572$	−3.93965	−	4.12056i	−0.164725	−	0.172289i
$573$	−14.3369	+	44.1243i	−0.598931	+	1.84332i
$574$	5.14635	−	7.79638i	0.214804	−	0.325415i
$575$	−1.17560	+	1.02709i	−0.0490258	+	0.0428325i
$576$	5.58823	−	2.09730i	0.232843	−	0.0873873i
$577$	−21.1497	−	7.93762i	−0.880474	−	0.330448i	−0.130132	−	0.991497i	$-0.541540\pi$
$577$	−21.1497	−	7.93762i	−0.880474	−	0.330448i	−0.750343	+	0.661049i	$0.770111\pi$
$578$	−14.9267	−	13.0410i	−0.620867	−	0.542435i
$579$	−43.2497	+	11.9361i	−1.79739	+	0.496049i
$580$	−5.52976	−	8.37723i	−0.229611	−	0.347845i
$581$	34.9340	+	9.64117i	1.44931	+	0.399983i
$582$	−7.47209	−	22.9967i	−0.309728	−	0.953245i
$583$	0.557264	−	1.03557i	0.0230795	−	0.0428889i
$584$	0.520249	−	11.5843i	0.0215281	−	0.479360i
$585$	32.3327	−	23.4911i	1.33679	−	0.971236i
$586$	−19.0672	+	19.9427i	−0.787658	+	0.823826i
$587$	−10.1924	−	18.9407i	−0.420685	−	0.781764i	0.578745	−	0.815508i	$-0.303543\pi$
$587$	−10.1924	−	18.9407i	−0.420685	−	0.781764i	−0.999431	+	0.0337441i	$0.989257\pi$
$588$	−0.721707	+	0.347556i	−0.0297627	+	0.0143330i
$589$	−1.23201	+	0.736094i	−0.0507642	+	0.0303302i
$590$	8.44075	−	62.3121i	0.347500	−	2.56535i
$591$	−1.57738	+	6.91095i	−0.0648847	+	0.284278i
$592$	18.8449	−	3.41985i	0.774522	−	0.140555i
$593$	−18.2978	−	13.2941i	−0.751400	−	0.545924i	0.144860	−	0.989452i	$-0.453727\pi$
$593$	−18.2978	−	13.2941i	−0.751400	−	0.545924i	−0.896261	+	0.443528i	$0.853727\pi$
$594$	−36.4677	+	45.7291i	−1.49629	+	1.87629i
$595$	−37.8773	−	22.6307i	−1.55282	−	0.927766i
$596$	−21.8642	−	1.96781i	−0.895593	−	0.0806048i
$597$	−0.0538572	−	0.397590i	−0.00220423	−	0.0162723i
$598$	−0.618928	−	0.776111i	−0.0253098	−	0.0317375i
$599$	1.81631	+	40.4432i	0.0742122	+	1.65246i	0.598647	+	0.801013i	$0.295705\pi$
$599$	1.81631	+	40.4432i	0.0742122	+	1.65246i	−0.524435	+	0.851450i	$0.675723\pi$
$600$	24.7431	+	11.9157i	1.01013	+	0.486454i
$601$	13.3199	−	1.19881i	0.543330	−	0.0489006i	0.185425	−	0.982658i	$-0.440634\pi$
$601$	13.3199	−	1.19881i	0.543330	−	0.0489006i	0.357905	+	0.933758i	$0.383491\pi$
$602$	−4.81070	−	21.0770i	−0.196069	−	0.859036i
$603$	27.6885	+	64.7805i	1.12756	+	2.63807i
$604$	−3.58123	−	8.37870i	−0.145718	−	0.340924i
$605$	1.48540	+	6.50798i	0.0603902	+	0.264587i
$606$	−15.3103	+	1.37796i	−0.621940	+	0.0559756i
$607$	10.9552	+	5.27573i	0.444657	+	0.214135i	0.642794	−	0.766039i	$-0.277775\pi$
$607$	10.9552	+	5.27573i	0.444657	+	0.214135i	−0.198138	+	0.980174i	$0.563489\pi$
$608$	−0.305963	−	6.81279i	−0.0124084	−	0.276295i
$609$	15.6591	+	19.6359i	0.634539	+	0.795687i
$610$	5.39177	+	39.8036i	0.218306	+	1.61160i
$611$	15.8622	+	1.42763i	0.641717	+	0.0577556i
$612$	30.7205	+	18.3547i	1.24180	+	0.741943i
$613$	4.54225	−	5.69580i	0.183460	−	0.230051i	−0.681594	−	0.731731i	$-0.738713\pi$
$613$	4.54225	−	5.69580i	0.183460	−	0.230051i	0.865054	+	0.501679i	$0.167284\pi$
$614$	−0.891317	−	0.647580i	−0.0359706	−	0.0261342i
$615$	20.1783	−	3.66183i	0.813668	−	0.147659i
$616$	−2.95912	+	12.9647i	−0.119226	+	0.522364i
$617$	4.40005	−	32.4824i	0.177139	−	1.30769i	−0.656055	−	0.754713i	$-0.727776\pi$
$617$	4.40005	−	32.4824i	0.177139	−	1.30769i	0.833194	−	0.552981i	$-0.186510\pi$
$618$	−2.25718	+	1.34860i	−0.0907972	+	0.0542488i
$619$	−17.4427	+	8.39997i	−0.701082	+	0.337623i	−0.750238	−	0.661168i	$-0.770061\pi$
$619$	−17.4427	+	8.39997i	−0.701082	+	0.337623i	0.0491562	+	0.998791i	$0.484347\pi$
$620$	−1.68531	−	3.13183i	−0.0676836	−	0.125777i
$621$	−2.36353	+	2.47206i	−0.0948452	+	0.0992003i
$622$	0.741700	−	0.538877i	0.0297395	−	0.0216070i
$623$	1.04483	−	23.2649i	0.0418601	−	0.932088i
$624$	−13.8963	+	25.8237i	−0.556297	+	1.03377i
$625$	−7.47782	−	23.0143i	−0.299113	−	0.920574i
$626$	−13.1667	−	3.63379i	−0.526248	−	0.145235i
$627$	−6.63674	−	10.0542i	−0.265046	−	0.401527i
$628$	0.841434	−	0.232221i	0.0335769	−	0.00926663i
$629$	−15.3793	−	13.4365i	−0.613214	−	0.535749i
$630$	89.2565	+	33.4985i	3.55606	+	1.33461i
$631$	12.0336	−	4.51628i	0.479049	−	0.179790i	−0.100156	−	0.994972i	$-0.531934\pi$
$631$	12.0336	−	4.51628i	0.479049	−	0.179790i	0.579206	+	0.815182i	$0.303363\pi$
$632$	−22.1428	+	19.3456i	−0.880793	+	0.769526i
$633$	−12.4230	+	18.8200i	−0.493768	+	0.748027i
$634$	−6.08315	+	18.7220i	−0.241593	+	0.743546i
$635$	11.9513	+	12.5000i	0.474272	+	0.496049i
$636$	1.21723	+	0.220895i	0.0482665	+	0.00875907i
$637$	−0.189463	+	0.443270i	−0.00750679	+	0.0175630i
$638$	16.1305			0.638611
$639$	−2.35173	−	55.8851i	−0.0930330	−	2.21078i
$640$	−38.3979			−1.51781
$641$	−1.14528	+	2.67953i	−0.0452360	+	0.105835i	−0.940622	−	0.339456i	$-0.889757\pi$
$641$	−1.14528	+	2.67953i	−0.0452360	+	0.105835i	0.895386	+	0.445291i	$0.146900\pi$
$642$	92.3391	+	16.7571i	3.64433	+	0.661349i
$643$	−2.44425	−	2.55649i	−0.0963920	−	0.100818i	0.672839	−	0.739789i	$-0.265075\pi$
$643$	−2.44425	−	2.55649i	−0.0963920	−	0.100818i	−0.769231	+	0.638971i	$0.779360\pi$
$644$	0.245730	−	0.756280i	0.00968313	−	0.0298016i
$645$	26.1457	−	39.6090i	1.02949	−	1.55960i
$646$	−9.05936	+	7.91493i	−0.356436	+	0.311409i
$647$	−0.0530828	+	0.0199223i	−0.00208690	+	0.000783227i	−0.352418	−	0.935843i	$-0.614640\pi$
$647$	−0.0530828	+	0.0199223i	−0.00208690	+	0.000783227i	0.350331	+	0.936626i	$0.386069\pi$
$648$	24.3396	+	9.13481i	0.956151	+	0.358849i
$649$	25.5542	+	22.3261i	1.00309	+	0.876375i
$650$	−16.2921	+	4.49634i	−0.639030	+	0.176361i
$651$	4.90223	+	7.42656i	0.192133	+	0.291070i
$652$	−4.66878	−	1.28850i	−0.182844	−	0.0504617i
$653$	−3.33406	−	10.2612i	−0.130472	−	0.401551i	0.864386	−	0.502828i	$-0.167707\pi$
$653$	−3.33406	−	10.2612i	−0.130472	−	0.401551i	−0.994858	+	0.101277i	$0.967707\pi$
$654$	26.8344	−	49.8667i	1.04931	−	1.94994i
$655$	0.208050	−	4.63260i	0.00812920	−	0.181011i
$656$	−8.38476	+	6.09188i	−0.327370	+	0.237848i
$657$	31.0022	−	32.4257i	1.20951	−	1.26505i
$658$	18.0030	+	33.4552i	0.701830	+	1.30422i
$659$	−29.8696	+	14.3844i	−1.16355	+	0.560337i	−0.913078	−	0.407786i	$-0.866301\pi$
$659$	−29.8696	+	14.3844i	−1.16355	+	0.560337i	−0.250475	+	0.968123i	$0.580587\pi$
$660$	25.6282	−	15.3122i	0.997577	−	0.596025i
$661$	−4.54281	+	33.5364i	−0.176695	+	1.30441i	0.657714	+	0.753268i	$0.271524\pi$
$661$	−4.54281	+	33.5364i	−0.176695	+	1.30441i	−0.834409	+	0.551146i	$0.814191\pi$
$662$	−6.78546	+	29.7290i	−0.263724	+	1.15545i
$663$	30.7664	−	5.58327i	1.19487	−	0.216836i
$664$	−19.3705	−	14.0735i	−0.751723	−	0.546159i
$665$	−6.71006	+	8.41414i	−0.260205	+	0.326286i
$666$	37.8796	+	22.6320i	1.46781	+	0.876973i
$667$	0.939419	+	0.0845493i	0.0363745	+	0.00327376i
$668$	−1.59915	−	11.8054i	−0.0618730	−	0.456765i
$669$	−42.5817	−	53.3958i	−1.64630	−	2.06440i
$670$	−2.63301	−	58.6286i	−0.101722	−	2.26502i
$671$	−19.5293	−	9.40481i	−0.753920	−	0.363069i
$672$	−42.1146	+	3.79038i	−1.62460	+	0.146217i
$673$	6.00505	+	26.3099i	0.231478	+	1.01417i	0.948415	+	0.317032i	$0.102686\pi$
$673$	6.00505	+	26.3099i	0.231478	+	1.01417i	−0.716937	+	0.697138i	$0.754457\pi$
$674$	8.92324	+	20.8770i	0.343710	+	0.804151i
$675$	22.8860	+	53.5446i	0.880884	+	2.06093i
$676$	2.12204	+	9.29726i	0.0816169	+	0.357587i
$677$	32.4142	−	2.91733i	1.24578	−	0.112122i	0.552944	−	0.833219i	$-0.313505\pi$
$677$	32.4142	−	2.91733i	1.24578	−	0.112122i	0.692834	+	0.721097i	$0.256362\pi$
$678$	−100.123	−	48.2166i	−3.84519	−	1.85175i
$679$	−0.522979	−	11.6450i	−0.0200701	−	0.446895i
$680$	18.1757	+	22.7916i	0.697005	+	0.874017i
$681$	−4.76329	−	35.1640i	−0.182530	−	1.34749i
$682$	5.69220	+	0.512308i	0.217966	+	0.0196173i
$683$	18.0799	+	10.8022i	0.691808	+	0.413336i	0.815323	−	0.579007i	$-0.196560\pi$
$683$	18.0799	+	10.8022i	0.691808	+	0.413336i	−0.123515	+	0.992343i	$0.539417\pi$
$684$	5.44221	−	6.82432i	0.208088	−	0.260934i
$685$	2.30424	+	1.67413i	0.0880404	+	0.0639651i
$686$	−32.1711	+	5.83820i	−1.22830	+	0.222903i
$687$	11.8000	−	51.6991i	0.450198	−	1.97245i
$688$	−3.21960	+	23.7680i	−0.122746	+	0.906148i
$689$	0.639112	−	0.381852i	0.0243482	−	0.0145474i
$690$	4.68364	−	2.25552i	0.178303	−	0.0858663i
$691$	5.60161	+	10.4095i	0.213095	+	0.395997i	0.964595	−	0.263736i	$-0.0849549\pi$
$691$	5.60161	+	10.4095i	0.213095	+	0.395997i	−0.751500	+	0.659733i	$0.770669\pi$
$692$	−11.4735	+	12.0003i	−0.436156	+	0.456183i
$693$	−41.6216	+	30.2398i	−1.58107	+	1.14872i
$694$	−0.582840	+	12.9780i	−0.0221243	+	0.492636i
$695$	−15.9681	+	29.6738i	−0.605706	+	1.12559i
$696$	−5.12762	−	15.7812i	−0.194362	−	0.598185i
$697$	10.6528	+	2.93999i	0.403504	+	0.111360i
$698$	−19.0661	−	28.8839i	−0.721662	−	1.09327i
$699$	22.5216	−	6.21556i	0.851845	−	0.235094i
$700$	−10.1958	−	8.90776i	−0.385363	−	0.336682i
$701$	−39.9645	−	14.9989i	−1.50944	−	0.566502i	−0.546794	−	0.837267i	$-0.684152\pi$
$701$	−39.9645	−	14.9989i	−1.50944	−	0.566502i	−0.962645	+	0.270765i	$0.912723\pi$
$702$	−34.6676	+	13.0110i	−1.30844	+	0.491067i
$703$	−3.75119	+	3.27732i	−0.141479	+	0.123606i
$704$	1.47820	−	2.23937i	0.0557117	−	0.0843996i
$705$	−25.7728	+	79.3205i	−0.970660	+	2.98738i
$706$	7.08872	+	7.41422i	0.266787	+	0.279038i
$707$	−7.29153	−	1.32322i	−0.274226	−	0.0497648i
$708$	−14.0299	+	32.8246i	−0.527276	+	1.23362i
$709$	36.1333			1.35702			0.678508	−	0.734593i	$-0.262627\pi$
$709$	36.1333			1.35702			0.678508	+	0.734593i	$0.262627\pi$
$710$	−14.5240	+	44.2745i	−0.545075	+	1.66159i
$711$	−113.754			−4.26610
$712$	−6.04721	+	14.1481i	−0.226629	+	0.530224i
$713$	0.328822	+	0.0596724i	0.0123145	+	0.00223475i
$714$	51.5467	+	53.9136i	1.92909	+	2.01767i
$715$	5.55187	−	17.0869i	0.207628	−	0.639014i
$716$	−6.04178	+	9.15291i	−0.225792	+	0.342060i
$717$	54.6644	−	47.7588i	2.04148	−	1.78359i
$718$	29.2449	−	10.9758i	1.09141	−	0.409612i
$719$	10.4002	+	3.90326i	0.387862	+	0.145567i	0.537685	−	0.843146i	$-0.319299\pi$
$719$	10.4002	+	3.90326i	0.387862	+	0.145567i	−0.149823	+	0.988713i	$0.547870\pi$
$720$	−79.6518	−	69.5896i	−2.96845	−	2.59345i
$721$	−1.22189	+	0.337219i	−0.0455054	+	0.0125587i
$722$	−16.5468	−	25.0673i	−0.615807	−	0.932908i
$723$	65.5039	+	18.0779i	2.43612	+	0.672326i
$724$	−6.76895	−	20.8327i	−0.251566	−	0.774240i
$725$	7.60985	−	14.1415i	0.282623	−	0.525201i
$726$	0.506288	−	11.2734i	0.0187901	−	0.418394i
$727$	16.8023	−	12.2076i	0.623162	−	0.452754i	−0.230863	−	0.972986i	$-0.574155\pi$
$727$	16.8023	−	12.2076i	0.623162	−	0.452754i	0.854024	+	0.520233i	$0.174155\pi$
$728$	−5.81793	+	6.08508i	−0.215627	+	0.225528i
$729$	−2.18956	−	4.06889i	−0.0810950	−	0.150700i
$730$	−33.6707	+	16.2149i	−1.24621	+	0.600142i
$731$	21.9547	−	13.1173i	0.812023	−	0.485161i
$732$	3.06086	−	22.5962i	0.113133	−	0.835180i
$733$	0.945777	−	4.14372i	0.0349331	−	0.153052i	−0.954453	−	0.298360i	$-0.903560\pi$
$733$	0.945777	−	4.14372i	0.0349331	−	0.153052i	0.989386	+	0.145308i	$0.0464175\pi$
$734$	11.6220	−	2.10908i	0.428976	−	0.0778476i
$735$	−2.04232	−	1.48384i	−0.0753323	−	0.0547321i
$736$	−0.990119	+	1.24157i	−0.0364963	+	0.0457649i
$737$	27.1874	+	16.2437i	1.00146	+	0.598344i
$738$	−23.7817	−	2.14039i	−0.875415	−	0.0787887i
$739$	−4.75763	−	35.1222i	−0.175012	−	1.29199i	−0.838951	−	0.544206i	$-0.816831\pi$
$739$	−4.75763	−	35.1222i	−0.175012	−	1.29199i	0.663939	−	0.747787i	$-0.268883\pi$
$740$	−7.69631	−	9.65087i	−0.282922	−	0.354773i
$741$	−0.342176	−	7.61915i	−0.0125702	−	0.279896i
$742$	1.60009	+	0.770561i	0.0587410	+	0.0282882i
$743$	9.79422	−	0.881496i	0.359315	−	0.0323390i	0.0914887	−	0.995806i	$-0.470837\pi$
$743$	9.79422	−	0.881496i	0.359315	−	0.0323390i	0.267826	+	0.963467i	$0.413695\pi$
$744$	−1.30825	−	5.73181i	−0.0479627	−	0.210138i
$745$	−27.1908	−	63.6160i	−0.996194	−	2.33071i
$746$	−12.6630	−	29.6266i	−0.463626	−	1.08471i
$747$	−20.6122	−	90.3079i	−0.754161	−	3.30419i
$748$	16.0227	−	1.44207i	0.585848	−	0.0527272i
$749$	40.7615	+	19.6297i	1.48939	+	0.717253i
$750$	−0.119713	−	2.66563i	−0.00437132	−	0.0973349i
$751$	−1.41711	−	1.77699i	−0.0517109	−	0.0648434i	0.755303	−	0.655375i	$-0.227489\pi$
$751$	−1.41711	−	1.77699i	−0.0517109	−	0.0648434i	−0.807014	+	0.590532i	$0.798918\pi$
$752$	−5.65785	−	41.7679i	−0.206321	−	1.52312i
$753$	−28.6835	−	2.58156i	−1.04529	−	0.0940774i
$754$	8.76640	+	5.23768i	0.319253	+	0.190745i
$755$	17.9043	−	22.4513i	0.651604	−	0.817085i
$756$	−23.9973	−	17.4351i	−0.872773	−	0.634107i
$757$	−11.1502	+	2.02347i	−0.405262	+	0.0735442i	−0.377360	−	0.926066i	$-0.623168\pi$
$757$	−11.1502	+	2.02347i	−0.405262	+	0.0735442i	−0.0279015	+	0.999611i	$0.508882\pi$
$758$	−13.9755	+	61.2306i	−0.507613	+	2.22400i
$759$	−0.376565	+	2.77991i	−0.0136684	+	0.100904i
$760$	6.10390	−	3.64691i	0.221412	−	0.132287i
$761$	−22.5690	+	10.8686i	−0.818125	+	0.393988i	−0.795648	−	0.605759i	$-0.792869\pi$
$761$	−22.5690	+	10.8686i	−0.818125	+	0.393988i	−0.0224768	+	0.999747i	$0.507155\pi$
$762$	−13.8539	−	25.7449i	−0.501875	−	0.932639i
$763$	18.8656	−	19.7318i	0.682980	−	0.714341i
$764$	−12.2254	+	8.88229i	−0.442300	+	0.321350i
$765$	−5.05984	+	112.666i	−0.182939	+	4.07345i
$766$	9.66767	−	17.9655i	0.349307	−	0.649121i
$767$	6.63849	+	20.4312i	0.239702	+	0.737727i
$768$	57.1911	+	15.7837i	2.06371	+	0.569546i
$769$	17.1281	+	25.9479i	0.617654	+	0.935705i	0.999932	+	0.0116582i	$0.00371100\pi$
$769$	17.1281	+	25.9479i	0.617654	+	0.935705i	−0.382278	+	0.924047i	$0.624860\pi$
$770$	41.3131	−	11.4017i	1.48882	−	0.410889i
$771$	50.9008	+	44.4707i	1.83315	+	1.60157i
$772$	−13.6818	−	5.13485i	−0.492417	−	0.184807i
$773$	−29.6525	+	11.1288i	−1.06652	+	0.400273i	−0.822069	−	0.569387i	$-0.807181\pi$
$773$	−29.6525	+	11.1288i	−1.06652	+	0.400273i	−0.244455	+	0.969661i	$0.578609\pi$
$774$	−41.6139	+	36.3570i	−1.49578	+	1.30683i
$775$	3.13454	−	4.74863i	0.112596	−	0.170576i
$776$	−2.37989	+	7.32455i	−0.0854330	+	0.262936i
$777$	21.3438	+	22.3239i	0.765706	+	0.800866i
$778$	−10.9032	−	1.97865i	−0.390900	−	0.0709379i
$779$	1.05939	−	2.47857i	0.0379566	−	0.0888039i
$780$	18.9001			0.676732
$781$	−15.6221	−	19.7034i	−0.559004	−	0.705043i
$782$	2.80128			0.100174
$783$	13.8280	−	32.3523i	0.494173	−	1.15618i
$784$	1.25529	+	0.227801i	0.0448317	+	0.00813575i
$785$	1.90105	+	1.98834i	0.0678513	+	0.0709669i
$786$	−2.42250	+	7.45568i	−0.0864076	+	0.265935i
$787$	−7.88684	+	11.9480i	−0.281135	+	0.425902i	−0.947515	−	0.319710i	$-0.896414\pi$
$787$	−7.88684	+	11.9480i	−0.281135	+	0.425902i	0.666380	+	0.745612i	$0.267843\pi$
$788$	−1.73875	+	1.51910i	−0.0619402	+	0.0541156i
$789$	−11.3054	+	4.24299i	−0.402483	+	0.151054i
$790$	88.7192	+	33.2969i	3.15649	+	1.18465i
$791$	−40.3438	−	35.2474i	−1.43446	−	1.25325i
$792$	32.7655	−	9.04271i	1.16427	−	0.321319i
$793$	−7.55974	−	11.4525i	−0.268454	−	0.406691i
$794$	62.0195	+	17.1163i	2.20099	+	0.607435i
$795$	1.20478	+	3.70794i	0.0427292	+	0.131507i
$796$	0.0619265	−	0.115079i	0.00219493	−	0.00407886i
$797$	−0.123002	+	2.73886i	−0.00435697	+	0.0970155i	0.995636	+	0.0933196i	$0.0297478\pi$
$797$	−0.123002	+	2.73886i	−0.00435697	+	0.0970155i	−0.999993	+	0.00369583i	$0.998824\pi$
$798$	14.7188	−	10.6938i	0.521040	−	0.378558i
$799$	−31.0585	+	32.4846i	−1.09877	+	1.14922i
$800$	12.8122	+	23.8090i	0.452979	+	0.841775i
$801$	−53.6307	+	25.8272i	−1.89495	+	0.912559i
$802$	39.2280	−	23.4377i	1.38519	−	0.827612i
$803$	2.70712	−	19.9848i	0.0955323	−	0.705248i
$804$	−7.41362	+	32.4812i	−0.261458	+	1.14552i
$805$	2.46579	−	0.447475i	0.0869077	−	0.0157714i
$806$	2.92718	+	2.12672i	0.103106	+	0.0749106i
$807$	−18.2009	+	22.8232i	−0.640701	+	0.803413i
$808$	4.20306	+	2.51121i	0.147863	+	0.0883441i
$809$	−17.5363	−	1.57829i	−0.616543	−	0.0554898i	−0.223034	−	0.974811i	$-0.571596\pi$
$809$	−17.5363	−	1.57829i	−0.616543	−	0.0554898i	−0.393509	+	0.919321i	$0.628739\pi$
$810$	−11.2467	−	83.0266i	−0.395169	−	2.91726i
$811$	0.719170	+	0.901811i	0.0252535	+	0.0316669i	0.794298	−	0.607528i	$-0.207839\pi$
$811$	0.719170	+	0.901811i	0.0252535	+	0.0316669i	−0.769044	+	0.639195i	$0.779268\pi$
$812$	0.367010	+	8.17212i	0.0128795	+	0.286785i
$813$	6.13213	+	2.95308i	0.215063	+	0.103569i
$814$	19.7566	−	1.77813i	0.692469	−	0.0623233i
$815$	−3.39649	−	14.8810i	−0.118974	−	0.521259i
$816$	−32.5243	−	76.0944i	−1.13858	−	2.66384i
$817$	−2.45168	−	5.73600i	−0.0857736	−	0.200677i
$818$	−7.90877	−	34.6506i	−0.276524	−	1.21153i
$819$	−32.4391	+	2.91957i	−1.13351	+	0.102018i
$820$	6.01818	+	2.89820i	0.210164	+	0.101210i
$821$	0.933970	+	20.7965i	0.0325958	+	0.725801i	0.947045	+	0.321101i	$0.104053\pi$
$821$	0.933970	+	20.7965i	0.0325958	+	0.725801i	−0.914449	+	0.404701i	$0.867376\pi$
$822$	−3.00205	−	3.76445i	−0.104708	−	0.131300i
$823$	4.45278	+	32.8717i	0.155214	+	1.14584i	0.886153	+	0.463394i	$0.153368\pi$
$823$	4.45278	+	32.8717i	0.155214	+	1.14584i	−0.730938	+	0.682443i	$0.760917\pi$
$824$	0.834094	+	0.0750698i	0.0290570	+	0.00261518i
$825$	41.0016	+	24.4973i	1.42749	+	0.852888i
$826$	−31.9512	+	40.0655i	−1.11172	+	1.39406i
$827$	−27.7940	−	20.1935i	−0.966491	−	0.702197i	−0.0118415	−	0.999930i	$-0.503769\pi$
$827$	−27.7940	−	20.1935i	−0.966491	−	0.702197i	−0.954649	+	0.297733i	$0.903769\pi$
$828$	−1.99989	+	0.362926i	−0.0695009	+	0.0126126i
$829$	−10.2518	+	44.9161i	−0.356060	+	1.56000i	0.406850	+	0.913495i	$0.366627\pi$
$829$	−10.2518	+	44.9161i	−0.356060	+	1.56000i	−0.762909	+	0.646505i	$0.776230\pi$
$830$	−10.3581	+	76.4667i	−0.359535	+	2.65420i
$831$	−37.7755	+	22.5698i	−1.31042	+	0.782938i
$832$	1.53049	−	0.737047i	0.0530603	−	0.0255525i
$833$	−0.644626	−	1.19792i	−0.0223350	−	0.0415054i
$834$	39.3669	−	41.1746i	1.36317	−	1.42576i
$835$	30.3741	−	22.0681i	1.05114	−	0.763697i
$836$	0.176046	−	3.91996i	0.00608866	−	0.135575i
$837$	5.90722	−	10.9775i	0.204183	−	0.379436i
$838$	−15.9582	−	49.1144i	−0.551268	−	1.69663i
$839$	−3.44340	−	0.950317i	−0.118879	−	0.0328086i	0.206091	−	0.978533i	$-0.433926\pi$
$839$	−3.44340	−	0.950317i	−0.118879	−	0.0328086i	−0.324970	+	0.945724i	$0.605354\pi$
$840$	−24.2876	−	36.7942i	−0.838003	−	1.26952i
$841$	18.6016	−	5.13370i	0.641433	−	0.177024i
$842$	−21.2554	−	18.5703i	−0.732510	−	0.639974i
$843$	74.1726	+	27.8374i	2.55464	+	0.958772i
$844$	−6.87661	+	2.58083i	−0.236703	+	0.0888360i
$845$	−22.6326	+	19.7735i	−0.778586	+	0.680230i
$846$	53.4962	−	81.0432i	1.83924	−	2.78632i
$847$	1.68110	−	5.17388i	0.0577631	−	0.177777i
$848$	−1.36162	−	1.42414i	−0.0467582	−	0.0489052i
$849$	−24.7004	−	4.48246i	−0.847716	−	0.153838i
$850$	18.7449	−	43.8560i	0.642946	−	1.50425i
$851$	1.15992			0.0397616
$852$	14.6347	−	22.0350i	0.501375	−	0.754907i
$853$	12.1584			0.416297			0.208148	−	0.978097i	$-0.433256\pi$
$853$	12.1584			0.416297			0.208148	+	0.978097i	$0.433256\pi$
$854$	12.8655	−	30.1004i	0.440249	−	1.03001i
$855$	27.0661	+	4.91178i	0.925642	+	0.167979i
$856$	−20.6564	−	21.6049i	−0.706020	−	0.738439i
$857$	−2.37526	+	7.31031i	−0.0811375	+	0.249716i	−0.983394	−	0.181485i	$-0.941910\pi$
$857$	−2.37526	+	7.31031i	−0.0811375	+	0.249716i	0.902256	+	0.431200i	$0.141910\pi$
$858$	−16.7319	+	25.3478i	−0.571218	+	0.865358i
$859$	−18.1256	+	15.8358i	−0.618437	+	0.540312i	−0.909134	−	0.416503i	$-0.863256\pi$
$859$	−18.1256	+	15.8358i	−0.618437	+	0.540312i	0.290697	+	0.956815i	$0.406113\pi$
$860$	14.4727	−	5.43169i	0.493515	−	0.185219i
$861$	−15.6474	−	5.87257i	−0.533262	−	0.200137i
$862$	5.22090	+	4.56137i	0.177825	+	0.155361i
$863$	33.3680	−	9.20897i	1.13586	−	0.313477i	0.352967	−	0.935636i	$-0.385173\pi$
$863$	33.3680	−	9.20897i	1.13586	−	0.313477i	0.782891	+	0.622159i	$0.213744\pi$
$864$	32.6330	+	49.4369i	1.11020	+	1.68188i
$865$	−50.4375	−	13.9199i	−1.71493	−	0.473290i
$866$	20.6668	+	63.6059i	0.702287	+	2.16142i
$867$	−16.8040	+	31.2271i	−0.570695	+	1.06053i
$868$	−0.130036	+	2.89548i	−0.00441371	+	0.0982789i
$869$	−41.3710	+	30.0578i	−1.40342	+	1.01964i
$870$	−36.9562	+	38.6532i	−1.25293	+	1.31047i
$871$	9.50102	+	17.6559i	0.321930	+	0.598246i
$872$	−16.2502	+	7.82568i	−0.550301	+	0.265011i
$873$	−25.5775	+	15.2818i	−0.865667	+	0.517212i
$874$	0.0917168	−	0.677080i	0.00310237	−	0.0229026i
$875$	0.286237	−	1.25409i	0.00967658	−	0.0423959i
$876$	20.8746	−	3.78819i	0.705289	−	0.127991i
$877$	34.5337	+	25.0902i	1.16612	+	0.847237i	0.990539	−	0.137228i	$-0.0438194\pi$
$877$	34.5337	+	25.0902i	1.16612	+	0.847237i	0.175582	+	0.984465i	$0.443819\pi$
$878$	6.28638	−	7.88287i	0.212155	−	0.266034i
$879$	42.3753	+	25.3181i	1.42928	+	0.853957i
$880$	−47.3566	−	4.26217i	−1.59639	−	0.143678i
$881$	1.23422	+	9.11140i	0.0415820	+	0.306971i	0.999782	+	0.0208721i	$0.00664427\pi$
$881$	1.23422	+	9.11140i	0.0415820	+	0.306971i	−0.958200	+	0.286099i	$0.907641\pi$
$882$	1.83261	+	2.29802i	0.0617071	+	0.0773782i
$883$	0.0396267	+	0.882357i	0.00133354	+	0.0296937i	0.999550	−	0.0300130i	$-0.00955488\pi$
$883$	0.0396267	+	0.882357i	0.00133354	+	0.0296937i	−0.998216	+	0.0597067i	$0.980983\pi$
$884$	9.17607	+	4.41896i	0.308625	+	0.148626i
$885$	−112.047	+	10.0844i	−3.76640	+	0.338982i
$886$	4.73812	+	20.7590i	0.159180	+	0.697414i
$887$	−9.15354	−	21.4158i	−0.307346	−	0.719071i	0.692652	−	0.721272i	$-0.256442\pi$
$887$	−9.15354	−	21.4158i	−0.307346	−	0.719071i	−0.999998	+	0.00220105i	$0.999299\pi$
$888$	−8.01994	−	18.7636i	−0.269132	−	0.629665i
$889$	−3.13620	−	13.7406i	−0.105185	−	0.460845i
$890$	49.3878	−	4.44498i	1.65548	−	0.148996i
$891$	40.7362	+	19.6175i	1.36472	+	0.657212i
$892$	−0.998009	−	22.2224i	−0.0334158	−	0.744061i
$893$	6.83476	+	8.57052i	0.228717	+	0.286802i
$894$	15.6993	+	115.897i	0.525063	+	3.87617i
$895$	−34.4238	−	3.09820i	−1.15066	−	0.103561i
$896$	26.8632	+	16.0500i	0.897438	+	0.536194i
$897$	−1.10731	+	1.38852i	−0.0369720	+	0.0463614i
$898$	−38.3537	−	27.8656i	−1.27988	−	0.929887i
$899$	−3.38265	+	0.613860i	−0.112818	+	0.0204734i
$900$	−7.70051	+	33.7381i	−0.256684	+	1.12460i
$901$	−0.282013	+	2.08190i	−0.00939522	+	0.0693583i
$902$	−9.21470	+	5.50553i	−0.306816	+	0.183314i
$903$	−34.8479	+	16.7818i	−1.15966	+	0.558465i
$904$	16.7724	+	31.1683i	0.557842	+	1.03664i
$905$	47.7059	−	49.8965i	1.58580	−	1.65862i
$906$	−39.2739	+	28.5341i	−1.30479	+	0.947983i
$907$	−1.53521	+	34.1840i	−0.0509757	+	1.13506i	0.796641	+	0.604453i	$0.206608\pi$
$907$	−1.53521	+	34.1840i	−0.0509757	+	1.13506i	−0.847617	+	0.530609i	$0.821963\pi$
$908$	5.47696	−	10.1779i	0.181759	−	0.337766i
$909$	5.85332	+	18.0147i	0.194143	+	0.597509i
$910$	26.1546	+	7.21821i	0.867016	+	0.239281i
$911$	8.26039	+	12.5140i	0.273679	+	0.414606i	0.945256	−	0.326328i	$-0.105812\pi$
$911$	8.26039	+	12.5140i	0.273679	+	0.414606i	−0.671577	+	0.740934i	$0.734383\pi$
$912$	−19.4572	+	5.36984i	−0.644291	+	0.177813i
$913$	−31.3590	−	27.3975i	−1.03783	−	0.906727i
$914$	−37.7503	−	14.1679i	−1.24867	−	0.468634i
$915$	67.2798	−	25.2505i	2.22420	−	0.834757i
$916$	13.0071	−	11.3640i	0.429768	−	0.375477i
$917$	−2.08195	+	3.15402i	−0.0687520	+	0.104155i
$918$	32.2900	−	99.3784i	1.06573	−	3.27997i
$919$	30.1263	+	31.5096i	0.993774	+	1.03941i	0.999223	+	0.0394211i	$0.0125514\pi$
$919$	30.1263	+	31.5096i	0.993774	+	1.03941i	−0.00544856	+	0.999985i	$0.501734\pi$
$920$	−1.62912	−	0.295641i	−0.0537104	−	0.00974700i
$921$	−0.774683	+	1.81246i	−0.0255267	+	0.0597226i
$922$	2.11234			0.0695662
$923$	−2.09230	−	15.7808i	−0.0688690	−	0.519431i
$924$	−24.3299			−0.800396
$925$	7.76168	−	18.1594i	0.255203	−	0.597076i
$926$	39.9698	+	7.25346i	1.31349	+	0.238363i
$927$	2.23900	+	2.34181i	0.0735383	+	0.0769150i
$928$	5.04820	−	15.5368i	0.165715	−	0.510019i
$929$	20.1310	−	30.4972i	0.660478	−	1.00058i	−0.337759	−	0.941232i	$-0.609669\pi$
$929$	20.1310	−	30.4972i	0.660478	−	1.00058i	0.998237	−	0.0593487i	$-0.0189024\pi$
$930$	−14.2689	+	12.4664i	−0.467897	+	0.408789i
$931$	−0.310647	+	0.116588i	−0.0101810	+	0.00382101i
$932$	7.12456	+	2.67389i	0.233373	+	0.0875863i
$933$	−1.23520	−	1.07916i	−0.0404385	−	0.0353301i
$934$	−58.0994	+	16.0344i	−1.90107	+	0.524662i
$935$	27.9302	+	42.3124i	0.913415	+	1.38376i
$936$	20.7433	+	5.72478i	0.678015	+	0.187120i
$937$	2.01751	+	6.20927i	0.0659093	+	0.202848i	0.978588	−	0.205831i	$-0.0659896\pi$
$937$	2.01751	+	6.20927i	0.0659093	+	0.202848i	−0.912678	+	0.408679i	$0.865990\pi$
$938$	−22.6642	+	42.1172i	−0.740014	+	1.37518i
$939$	−1.09636	+	24.4123i	−0.0357783	+	0.796666i
$940$	−21.9772	+	15.9673i	−0.716816	+	0.520797i
$941$	23.1583	−	24.2217i	0.754938	−	0.789604i	−0.227976	−	0.973667i	$-0.573211\pi$
$941$	23.1583	−	24.2217i	0.754938	−	0.789604i	0.982914	+	0.184063i	$0.0589251\pi$
$942$	−2.20370	−	4.09516i	−0.0718004	−	0.133427i
$943$	−0.565511	+	0.272336i	−0.0184156	+	0.00886847i
$944$	48.8064	−	29.1604i	1.58851	−	0.949092i
$945$	12.5482	−	92.6344i	0.408192	−	3.01340i
$946$	−5.52772	+	24.2185i	−0.179722	+	0.787413i
$947$	−5.33901	+	0.968888i	−0.173495	+	0.0314846i	−0.264609	−	0.964356i	$-0.585243\pi$
$947$	−5.33901	+	0.968888i	−0.173495	+	0.0314846i	0.0911143	+	0.995840i	$0.470957\pi$
$948$	−43.5214	−	31.6202i	−1.41351	−	1.02698i
$949$	7.96044	−	9.98207i	0.258407	−	0.324032i
$950$	−9.98642	−	5.96661i	−0.324002	−	0.193582i
$951$	35.0771	+	3.15699i	1.13745	+	0.102372i
$952$	−3.18903	−	23.5423i	−0.103357	−	0.763011i
$953$	15.9369	+	19.9843i	0.516248	+	0.647355i	0.969808	−	0.243871i	$-0.0784174\pi$
$953$	15.9369	+	19.9843i	0.516248	+	0.647355i	−0.453559	+	0.891226i	$0.649846\pi$
$954$	−0.203660	−	4.53483i	−0.00659372	−	0.146821i
$955$	−42.9074	−	20.6631i	−1.38845	−	0.668643i
$956$	23.5478	−	2.11934i	0.761591	−	0.0685445i
$957$	−6.42165	−	28.1351i	−0.207583	−	0.909479i
$958$	−10.6289	−	24.8676i	−0.343405	−	0.803437i
$959$	−0.912276	−	2.13438i	−0.0294589	−	0.0689226i
$960$	1.97950	+	8.67277i	0.0638882	+	0.279912i
$961$	29.6620	−	2.66963i	0.956839	−	0.0861171i
$962$	11.3145	+	5.44876i	0.364793	+	0.175675i
$963$	−5.18814	−	115.523i	−0.167185	−	3.72267i
$964$	13.7997	+	17.3043i	0.444460	+	0.557335i
$965$	−6.18206	−	45.6378i	−0.199008	−	1.46913i
$966$	−4.21948	−	0.379760i	−0.135759	−	0.0122186i
$967$	−41.0614	−	24.5330i	−1.32045	−	0.788930i	−0.332407	−	0.943136i	$-0.607861\pi$
$967$	−41.0614	−	24.5330i	−1.32045	−	0.788930i	−0.988039	+	0.154206i	$0.950718\pi$
$968$	−2.24097	+	2.81008i	−0.0720274	+	0.0903195i
$969$	17.4120	+	12.6505i	0.559353	+	0.406394i
$970$	24.4216	−	4.43187i	0.784131	−	0.142299i
$971$	−1.54162	+	6.75430i	−0.0494731	+	0.216756i	−0.993622	−	0.112764i	$-0.964030\pi$
$971$	−1.54162	+	6.75430i	−0.0494731	+	0.216756i	0.944149	+	0.329520i	$0.106887\pi$
$972$	−1.78528	+	13.1795i	−0.0572629	+	0.422732i
$973$	23.5747	−	14.0853i	0.755772	−	0.451553i
$974$	−9.79066	+	4.71494i	−0.313713	+	0.151076i
$975$	14.3286	+	26.6270i	0.458883	+	0.852748i
$976$	−25.0974	+	26.2499i	−0.803349	+	0.840237i
$977$	33.1377	−	24.0760i	1.06017	−	0.770259i	0.0860504	−	0.996291i	$-0.472575\pi$
$977$	33.1377	−	24.0760i	1.06017	−	0.770259i	0.974120	+	0.226032i	$0.0725754\pi$
$978$	−1.15767	+	25.7775i	−0.0370181	+	0.824273i
$979$	−12.6805	+	23.5642i	−0.405269	+	0.753116i
$980$	−0.254088	−	0.782003i	−0.00811654	−	0.0249802i
$981$	−67.2633	−	18.5635i	−2.14755	−	0.592687i
$982$	−5.27025	−	7.98409i	−0.168181	−	0.254783i
$983$	−4.33613	+	1.19669i	−0.138301	+	0.0381686i	−0.334502	−	0.942395i	$-0.608568\pi$
$983$	−4.33613	+	1.19669i	−0.138301	+	0.0381686i	0.196201	+	0.980564i	$0.437139\pi$
$984$	8.31553	+	7.26506i	0.265089	+	0.231602i
$985$	−6.81241	−	2.55674i	−0.217061	−	0.0814645i
$986$	−26.9798	+	10.1257i	−0.859210	+	0.322467i
$987$	51.1861	−	44.7200i	1.62927	−	1.42345i
$988$	1.36851	−	2.07321i	0.0435382	−	0.0659576i
$989$	−0.448872	+	1.38149i	−0.0142733	+	0.0439287i
$990$	−75.7026	−	79.1787i	−2.40599	−	2.51646i
$991$	11.7575	+	2.13368i	0.373491	+	0.0677786i	0.362057	−	0.932156i	$-0.382075\pi$
$991$	11.7575	+	2.13368i	0.373491	+	0.0677786i	0.0114339	+	0.999935i	$0.496360\pi$
$992$	2.27489	−	5.32236i	0.0722277	−	0.168985i
$993$	54.5554			1.73126
$994$	28.6674	−	24.9036i	0.909275	−	0.789894i
$995$	0.411846			0.0130564
$996$	17.2168	−	40.2808i	0.545537	−	1.27635i
$997$	−33.7729	−	6.12889i	−1.06960	−	0.194104i	−0.384922	−	0.922949i	$-0.625772\pi$
$997$	−33.7729	−	6.12889i	−1.06960	−	0.194104i	−0.684678	+	0.728845i	$0.740057\pi$
$998$	−29.6520	−	31.0135i	−0.938616	−	0.981716i
$999$	13.3703	−	41.1494i	0.423016	−	1.30191i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.2.g.a.15.4	✓	120
3.2	odd	2		639.2.v.a.370.2		120
71.19	even	35	inner	71.2.g.a.19.4	yes	120
71.27	even	35		5041.2.a.s.1.12		60
71.44	odd	70		5041.2.a.t.1.12		60
213.161	odd	70		639.2.v.a.19.2		120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.2.g.a.15.4	✓	120	1.1	even	1	trivial
71.2.g.a.19.4	yes	120	71.19	even	35	inner
639.2.v.a.19.2		120	213.161	odd	70
639.2.v.a.370.2		120	3.2	odd	2
5041.2.a.s.1.12		60	71.27	even	35
5041.2.a.t.1.12		60	71.44	odd	70

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:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	71.g (of order \(35\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.682008 - 1.59564i) q^{2} +(-3.05466 - 0.554338i) q^{3} +(-0.698796 - 0.730883i) q^{4} +(0.984762 - 3.03079i) q^{5} +(-2.96782 + 4.49606i) q^{6} +(-1.95579 + 1.70872i) q^{7} +(1.60645 - 0.602910i) q^{8} +(6.21492 + 2.33250i) q^{9} +O(q^{10})\)	\(q+(0.682008 - 1.59564i) q^{2} +(-3.05466 - 0.554338i) q^{3} +(-0.698796 - 0.730883i) q^{4} +(0.984762 - 3.03079i) q^{5} +(-2.96782 + 4.49606i) q^{6} +(-1.95579 + 1.70872i) q^{7} +(1.60645 - 0.602910i) q^{8} +(6.21492 + 2.33250i) q^{9} +(-4.16442 - 3.63834i) q^{10} +(2.87663 - 0.793900i) q^{11} +(1.72942 + 2.61997i) q^{12} +(1.82114 + 0.502604i) q^{13} +(1.39263 + 4.28609i) q^{14} +(-4.68819 + 8.71212i) q^{15} +(0.224319 - 4.99484i) q^{16} +(-4.31308 + 3.13364i) q^{17} +(7.96045 - 8.32598i) q^{18} +(0.616198 + 1.14509i) q^{19} +(-2.90330 + 1.39816i) q^{20} +(6.92147 - 4.13539i) q^{21} +(0.695110 - 5.13150i) q^{22} +(0.0673796 - 0.295209i) q^{23} +(-5.24136 + 0.951167i) q^{24} +(-4.17083 - 3.03028i) q^{25} +(2.04401 - 2.56310i) q^{26} +(-9.69617 - 5.79319i) q^{27} +(2.61557 + 0.235406i) q^{28} +(0.418132 + 3.08678i) q^{29} +(10.7040 + 13.4224i) q^{30} +(0.0495160 + 1.10256i) q^{31} +(-4.72509 - 2.27548i) q^{32} +(-9.22721 + 0.830464i) q^{33} +(2.05859 + 9.01928i) q^{34} +(3.25278 + 7.61026i) q^{35} +(-2.63818 - 6.17233i) q^{36} +(0.852397 + 3.73460i) q^{37} +(2.24739 - 0.202269i) q^{38} +(-5.28435 - 2.54481i) q^{39} +(-0.245322 - 5.46252i) q^{40} +(-1.29242 - 1.62064i) q^{41} +(-1.87808 - 13.8645i) q^{42} +(-4.77783 - 0.430012i) q^{43} +(-2.59043 - 1.54771i) q^{44} +(13.1895 - 16.5392i) q^{45} +(-0.425093 - 0.308848i) q^{46} +(8.29461 - 1.50525i) q^{47} +(-3.45405 + 15.1332i) q^{48} +(-0.0342515 + 0.252855i) q^{49} +(-7.67977 + 4.58845i) q^{50} +(14.9121 - 7.18128i) q^{51} +(-0.905263 - 1.68226i) q^{52} +(0.272330 - 0.284835i) q^{53} +(-15.8567 + 11.5206i) q^{54} +(0.426657 - 9.50026i) q^{55} +(-2.11167 + 3.92414i) q^{56} +(-1.24751 - 3.83943i) q^{57} +(5.21055 + 1.43802i) q^{58} +(6.26431 + 9.49003i) q^{59} +(9.64363 - 2.66147i) q^{60} +(-5.47002 - 4.77901i) q^{61} +(1.79305 + 0.672944i) q^{62} +(-16.1407 + 6.05769i) q^{63} +(0.677134 - 0.591594i) q^{64} +(3.31668 - 5.02455i) q^{65} +(-4.96791 + 15.2897i) q^{66} +(7.33409 + 7.67085i) q^{67} +(5.30429 + 0.962587i) q^{68} +(-0.369467 + 0.864412i) q^{69} +14.3616 q^{70} +(-3.28980 - 7.75740i) q^{71} +11.3902 q^{72} +(2.65610 - 6.21425i) q^{73} +(6.54040 + 1.18691i) q^{74} +(11.0606 + 11.5685i) q^{75} +(0.406329 - 1.25055i) q^{76} +(-4.26953 + 6.46806i) q^{77} +(-7.66456 + 6.69633i) q^{78} +(-16.0435 + 6.02123i) q^{79} +(-14.9174 - 5.59859i) q^{80} +(11.4099 + 9.96857i) q^{81} +(-3.46739 + 0.956940i) q^{82} +(-7.68728 - 11.6457i) q^{83} +(-7.85918 - 2.16900i) q^{84} +(5.25003 + 16.1579i) q^{85} +(-3.94466 + 7.33041i) q^{86} +(0.433868 - 9.66083i) q^{87} +(4.14251 - 3.00971i) q^{88} +(-6.19684 + 6.48139i) q^{89} +(-17.3951 - 32.3255i) q^{90} +(-4.42058 + 2.12884i) q^{91} +(-0.262848 + 0.157044i) q^{92} +(0.459936 - 3.39538i) q^{93} +(3.25516 - 14.2618i) q^{94} +(4.07732 - 0.739925i) q^{95} +(13.1721 + 9.57012i) q^{96} +(-2.79848 + 3.50918i) q^{97} +(0.380105 + 0.227102i) q^{98} +(19.7298 + 1.77572i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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