LMFDB - Embedded newform 520.2.ca.b.101.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [520,2,Mod(101,520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 5]))

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

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

chi := DirichletCharacter("520.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 520 = 2^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	520.ca (of order $6$, degree $2$, 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:	$4.15222090511$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.5
Character	$\chi$	$=$	520.101
Dual form			520.2.ca.b.381.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30078 + 0.554941i) q^{2} +(0.176551 - 0.101932i) q^{3} +(1.38408 - 1.44372i) q^{4} +1.00000 q^{5} +(-0.173088 + 0.230566i) q^{6} +(0.820502 + 0.473717i) q^{7} +(-0.999213 + 2.64605i) q^{8} +(-1.47922 + 2.56208i) q^{9} +O(q^{10})$	\(q+(-1.30078 + 0.554941i) q^{2} +(0.176551 - 0.101932i) q^{3} +(1.38408 - 1.44372i) q^{4} +1.00000 q^{5} +(-0.173088 + 0.230566i) q^{6} +(0.820502 + 0.473717i) q^{7} +(-0.999213 + 2.64605i) q^{8} +(-1.47922 + 2.56208i) q^{9} +(-1.30078 + 0.554941i) q^{10} +(0.455050 + 0.788169i) q^{11} +(0.0972001 - 0.395971i) q^{12} +(-2.46575 + 2.63061i) q^{13} +(-1.33018 - 0.160874i) q^{14} +(0.176551 - 0.101932i) q^{15} +(-0.168640 - 3.99644i) q^{16} +(-1.02632 + 1.77763i) q^{17} +(0.502341 - 4.15360i) q^{18} +(0.975331 - 1.68932i) q^{19} +(1.38408 - 1.44372i) q^{20} +0.193147 q^{21} +(-1.02931 - 0.772713i) q^{22} +(3.80196 + 6.58518i) q^{23} +(0.0933042 + 0.569013i) q^{24} +1.00000 q^{25} +(1.74757 - 4.79020i) q^{26} +1.21471i q^{27} +(1.81955 - 0.528910i) q^{28} +(7.35427 - 4.24599i) q^{29} +(-0.173088 + 0.230566i) q^{30} +6.07035i q^{31} +(2.43715 + 5.10493i) q^{32} +(0.160679 + 0.0927679i) q^{33} +(0.348536 - 2.88187i) q^{34} +(0.820502 + 0.473717i) q^{35} +(1.65157 + 5.68171i) q^{36} +(-5.00013 - 8.66049i) q^{37} +(-0.331221 + 2.73869i) q^{38} +(-0.167187 + 0.715773i) q^{39} +(-0.999213 + 2.64605i) q^{40} +(-4.12069 + 2.37908i) q^{41} +(-0.251243 + 0.107185i) q^{42} +(4.14228 + 2.39155i) q^{43} +(1.76772 + 0.433927i) q^{44} +(-1.47922 + 2.56208i) q^{45} +(-8.59992 - 6.45604i) q^{46} +10.4185i q^{47} +(-0.437138 - 0.688385i) q^{48} +(-3.05118 - 5.28481i) q^{49} +(-1.30078 + 0.554941i) q^{50} +0.418457i q^{51} +(0.385062 + 7.20081i) q^{52} +11.4674i q^{53} +(-0.674091 - 1.58007i) q^{54} +(0.455050 + 0.788169i) q^{55} +(-2.07333 + 1.69774i) q^{56} -0.397668i q^{57} +(-7.21004 + 9.60430i) q^{58} +(4.67272 - 8.09338i) q^{59} +(0.0972001 - 0.395971i) q^{60} +(3.13747 + 1.81142i) q^{61} +(-3.36869 - 7.89622i) q^{62} +(-2.42741 + 1.40146i) q^{63} +(-6.00315 - 5.28793i) q^{64} +(-2.46575 + 2.63061i) q^{65} +(-0.260489 - 0.0315039i) q^{66} +(-0.283940 - 0.491798i) q^{67} +(1.14590 + 3.94210i) q^{68} +(1.34248 + 0.775080i) q^{69} +(-1.33018 - 0.160874i) q^{70} +(8.63801 + 4.98716i) q^{71} +(-5.30134 - 6.47416i) q^{72} +1.67947i q^{73} +(11.3102 + 8.49065i) q^{74} +(0.176551 - 0.101932i) q^{75} +(-1.08897 - 3.74626i) q^{76} +0.862259i q^{77} +(-0.179737 - 1.02385i) q^{78} +5.13825 q^{79} +(-0.168640 - 3.99644i) q^{80} +(-4.31384 - 7.47179i) q^{81} +(4.03988 - 5.38141i) q^{82} -15.0936 q^{83} +(0.267331 - 0.278850i) q^{84} +(-1.02632 + 1.77763i) q^{85} +(-6.71538 - 0.812165i) q^{86} +(0.865601 - 1.49926i) q^{87} +(-2.54023 + 0.416535i) q^{88} +(-1.09916 + 0.634602i) q^{89} +(0.502341 - 4.15360i) q^{90} +(-3.26931 + 0.990353i) q^{91} +(14.7694 + 3.62547i) q^{92} +(0.618761 + 1.07173i) q^{93} +(-5.78164 - 13.5522i) q^{94} +(0.975331 - 1.68932i) q^{95} +(0.950635 + 0.652855i) q^{96} +(-6.15706 - 3.55478i) q^{97} +(6.90169 + 5.18117i) q^{98} -2.69247 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9}+O(q^{10}) $ 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9	$ 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9} - 8 q^{11} + 6 q^{12} - 4 q^{14} + 14 q^{16} + 18 q^{18} - 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 22 q^{24} + 56 q^{25} - 37 q^{26} - 12 q^{28} - 13 q^{30} - 30 q^{32} - 16 q^{34} + 15 q^{36} + 4 q^{37} - 24 q^{39} - 61 q^{42} + 24 q^{44} + 28 q^{45} - 19 q^{46} - 51 q^{48} + 20 q^{49} - 64 q^{52} - 5 q^{54} - 8 q^{55} - 23 q^{56} - q^{58} - 16 q^{59} + 6 q^{60} + 10 q^{62} - 30 q^{64} + 14 q^{66} - 36 q^{67} - 51 q^{68} - 4 q^{70} - 81 q^{72} + 70 q^{74} - 60 q^{76} + 143 q^{78} + 14 q^{80} - 28 q^{81} + 21 q^{82} + 40 q^{83} + 31 q^{84} - 28 q^{86} - 36 q^{87} - 19 q^{88} + 18 q^{90} + 16 q^{91} - 18 q^{92} + 43 q^{94} - 16 q^{95} - 48 q^{96} + 24 q^{97} + 56 q^{98} - 48 q^{99}+O(q^{100}) $ 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9 - 8 * q^11 + 6 * q^12 - 4 * q^14 + 14 * q^16 + 18 * q^18 - 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 22 * q^24 + 56 * q^25 - 37 * q^26 - 12 * q^28 - 13 * q^30 - 30 * q^32 - 16 * q^34 + 15 * q^36 + 4 * q^37 - 24 * q^39 - 61 * q^42 + 24 * q^44 + 28 * q^45 - 19 * q^46 - 51 * q^48 + 20 * q^49 - 64 * q^52 - 5 * q^54 - 8 * q^55 - 23 * q^56 - q^58 - 16 * q^59 + 6 * q^60 + 10 * q^62 - 30 * q^64 + 14 * q^66 - 36 * q^67 - 51 * q^68 - 4 * q^70 - 81 * q^72 + 70 * q^74 - 60 * q^76 + 143 * q^78 + 14 * q^80 - 28 * q^81 + 21 * q^82 + 40 * q^83 + 31 * q^84 - 28 * q^86 - 36 * q^87 - 19 * q^88 + 18 * q^90 + 16 * q^91 - 18 * q^92 + 43 * q^94 - 16 * q^95 - 48 * q^96 + 24 * q^97 + 56 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$1$

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 $

$2$	−1.30078	+	0.554941i	−0.919794	+	0.392403i
$2$	−1.30078	+	0.554941i	−0.919794	+	0.392403i
$3$	0.176551	−	0.101932i	0.101932	−	0.0588503i	−0.448168	−	0.893950i	$-0.647923\pi$
$3$	0.176551	−	0.101932i	0.101932	−	0.0588503i	0.550099	+	0.835099i	$0.314590\pi$
$4$	1.38408	−	1.44372i	0.692040	−	0.721859i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−0.173088	+	0.230566i	−0.0706631	+	0.0941283i
$7$	0.820502	+	0.473717i	0.310121	+	0.179048i	0.646980	−	0.762507i	$-0.276032\pi$
$7$	0.820502	+	0.473717i	0.310121	+	0.179048i	−0.336860	+	0.941555i	$0.609365\pi$
$8$	−0.999213	+	2.64605i	−0.353275	+	0.935519i
$9$	−1.47922	+	2.56208i	−0.493073	+	0.854028i
$10$	−1.30078	+	0.554941i	−0.411344	+	0.175488i
$11$	0.455050	+	0.788169i	0.137203	+	0.237642i	0.926437	−	0.376450i	$-0.122856\pi$
$11$	0.455050	+	0.788169i	0.137203	+	0.237642i	−0.789234	+	0.614093i	$0.789522\pi$
$12$	0.0972001	−	0.395971i	0.0280592	−	0.114307i
$13$	−2.46575	+	2.63061i	−0.683875	+	0.729599i
$13$	−2.46575	+	2.63061i	−0.683875	+	0.729599i
$14$	−1.33018	−	0.160874i	−0.355506	−	0.0429953i
$15$	0.176551	−	0.101932i	0.0455852	−	0.0263186i
$16$	−0.168640	−	3.99644i	−0.0421600	−	0.999111i
$17$	−1.02632	+	1.77763i	−0.248919	+	0.431140i	−0.963226	−	0.268692i	$-0.913409\pi$
$17$	−1.02632	+	1.77763i	−0.248919	+	0.431140i	0.714307	+	0.699832i	$0.246742\pi$
$18$	0.502341	−	4.15360i	0.118403	−	0.979013i
$19$	0.975331	−	1.68932i	0.223756	−	0.387557i	−0.732189	−	0.681101i	$-0.761501\pi$
$19$	0.975331	−	1.68932i	0.223756	−	0.387557i	0.955946	+	0.293544i	$0.0948347\pi$
$20$	1.38408	−	1.44372i	0.309490	−	0.322825i
$21$	0.193147			0.0421481
$22$	−1.02931	−	0.772713i	−0.219449	−	0.164743i
$23$	3.80196	+	6.58518i	0.792763	+	1.37311i	0.924250	+	0.381788i	$0.124692\pi$
$23$	3.80196	+	6.58518i	0.792763	+	1.37311i	−0.131487	+	0.991318i	$0.541975\pi$
$24$	0.0933042	+	0.569013i	0.0190456	+	0.116149i
$25$	1.00000			0.200000
$26$	1.74757	−	4.79020i	0.342727	−	0.939435i
$27$			1.21471i			0.233770i
$28$	1.81955	−	0.528910i	0.343863	−	0.0999546i
$29$	7.35427	−	4.24599i	1.36565	−	0.788460i	0.375283	−	0.926910i	$-0.377545\pi$
$29$	7.35427	−	4.24599i	1.36565	−	0.788460i	0.990369	+	0.138450i	$0.0442120\pi$
$30$	−0.173088	+	0.230566i	−0.0316015	+	0.0420955i
$31$			6.07035i			1.09027i	0.838349	+	0.545134i	$0.183521\pi$
$31$			6.07035i			1.09027i	−0.838349	+	0.545134i	$0.816479\pi$
$32$	2.43715	+	5.10493i	0.430832	+	0.902432i
$33$	0.160679	+	0.0927679i	0.0279706	+	0.0161488i
$34$	0.348536	−	2.88187i	0.0597734	−	0.494236i
$35$	0.820502	+	0.473717i	0.138690	+	0.0800728i
$36$	1.65157	+	5.68171i	0.275261	+	0.946951i
$37$	−5.00013	−	8.66049i	−0.822017	−	1.42378i	−0.904178	−	0.427156i	$-0.859515\pi$
$37$	−5.00013	−	8.66049i	−0.822017	−	1.42378i	0.0821607	−	0.996619i	$-0.473818\pi$
$38$	−0.331221	+	2.73869i	−0.0537311	+	0.444275i
$39$	−0.167187	+	0.715773i	−0.0267714	+	0.114615i
$40$	−0.999213	+	2.64605i	−0.157989	+	0.418377i
$41$	−4.12069	+	2.37908i	−0.643544	+	0.371550i	−0.785978	−	0.618254i	$-0.787840\pi$
$41$	−4.12069	+	2.37908i	−0.643544	+	0.371550i	0.142434	+	0.989804i	$0.454507\pi$
$42$	−0.251243	+	0.107185i	−0.0387676	+	0.0165390i
$43$	4.14228	+	2.39155i	0.631692	+	0.364707i	0.781407	−	0.624022i	$-0.214502\pi$
$43$	4.14228	+	2.39155i	0.631692	+	0.364707i	−0.149715	+	0.988729i	$0.547836\pi$
$44$	1.76772	+	0.433927i	0.266494	+	0.0654169i
$45$	−1.47922	+	2.56208i	−0.220509	+	0.381933i
$46$	−8.59992	−	6.45604i	−1.26799	−	0.951892i
$47$			10.4185i			1.51969i	0.650104	+	0.759846i	$0.274725\pi$
$47$			10.4185i			1.51969i	−0.650104	+	0.759846i	$0.725275\pi$
$48$	−0.437138	−	0.688385i	−0.0630954	−	0.0993599i
$49$	−3.05118	−	5.28481i	−0.435883	−	0.754972i
$50$	−1.30078	+	0.554941i	−0.183959	+	0.0784805i
$51$			0.418457i			0.0585957i
$52$	0.385062	+	7.20081i	0.0533985	+	0.998573i
$53$			11.4674i			1.57516i	0.616209	+	0.787582i	$0.288667\pi$
$53$			11.4674i			1.57516i	−0.616209	+	0.787582i	$0.711333\pi$
$54$	−0.674091	−	1.58007i	−0.0917321	−	0.215021i
$55$	0.455050	+	0.788169i	0.0613589	+	0.106277i
$56$	−2.07333	+	1.69774i	−0.277061	+	0.226871i
$57$		−	0.397668i		−	0.0526724i
$58$	−7.21004	+	9.60430i	−0.946725	+	1.26111i
$59$	4.67272	−	8.09338i	0.608336	−	1.05367i	−0.383179	−	0.923674i	$-0.625171\pi$
$59$	4.67272	−	8.09338i	0.608336	−	1.05367i	0.991515	−	0.129995i	$-0.0414960\pi$
$60$	0.0972001	−	0.395971i	0.0125485	−	0.0511196i
$61$	3.13747	+	1.81142i	0.401711	+	0.231928i	0.687222	−	0.726447i	$-0.258830\pi$
$61$	3.13747	+	1.81142i	0.401711	+	0.231928i	−0.285511	+	0.958376i	$0.592163\pi$
$62$	−3.36869	−	7.89622i	−0.427824	−	1.00282i
$63$	−2.42741	+	1.40146i	−0.305824	+	0.176568i
$64$	−6.00315	−	5.28793i	−0.750393	−	0.660992i
$65$	−2.46575	+	2.63061i	−0.305838	+	0.326287i
$66$	−0.260489	−	0.0315039i	−0.0320640	−	0.00387786i
$67$	−0.283940	−	0.491798i	−0.0346888	−	0.0600827i	0.848160	−	0.529740i	$-0.177711\pi$
$67$	−0.283940	−	0.491798i	−0.0346888	−	0.0600827i	−0.882849	+	0.469658i	$0.844377\pi$
$68$	1.14590	+	3.94210i	0.138960	+	0.478050i
$69$	1.34248	+	0.775080i	0.161615	+	0.0933086i
$70$	−1.33018	−	0.160874i	−0.158987	−	0.0192281i
$71$	8.63801	+	4.98716i	1.02514	+	0.591867i	0.915590	−	0.402114i	$-0.131725\pi$
$71$	8.63801	+	4.98716i	1.02514	+	0.591867i	0.109554	+	0.993981i	$0.465058\pi$
$72$	−5.30134	−	6.47416i	−0.624769	−	0.762987i
$73$			1.67947i			0.196567i	0.995158	+	0.0982837i	$0.0313352\pi$
$73$			1.67947i			0.196567i	−0.995158	+	0.0982837i	$0.968665\pi$
$74$	11.3102	+	8.49065i	1.31478	+	0.987018i
$75$	0.176551	−	0.101932i	0.0203863	−	0.0117701i
$76$	−1.08897	−	3.74626i	−0.124913	−	0.429725i
$77$			0.862259i			0.0982636i
$78$	−0.179737	−	1.02385i	−0.0203512	−	0.115928i
$79$	5.13825			0.578099			0.289049	−	0.957314i	$-0.406661\pi$
$79$	5.13825			0.578099			0.289049	+	0.957314i	$0.406661\pi$
$80$	−0.168640	−	3.99644i	−0.0188545	−	0.446816i
$81$	−4.31384	−	7.47179i	−0.479316	−	0.830199i
$82$	4.03988	−	5.38141i	0.446130	−	0.594278i
$83$	−15.0936			−1.65674			−0.828369	−	0.560183i	$-0.810731\pi$
$83$	−15.0936			−1.65674			−0.828369	+	0.560183i	$0.810731\pi$
$84$	0.267331	−	0.278850i	0.0291682	−	0.0304250i
$85$	−1.02632	+	1.77763i	−0.111320	+	0.192812i
$86$	−6.71538	−	0.812165i	−0.724138	−	0.0875780i
$87$	0.865601	−	1.49926i	0.0928021	−	0.160738i
$88$	−2.54023	+	0.416535i	−0.270789	+	0.0444028i
$89$	−1.09916	+	0.634602i	−0.116511	+	0.0672677i	−0.557123	−	0.830430i	$-0.688095\pi$
$89$	−1.09916	+	0.634602i	−0.116511	+	0.0672677i	0.440612	+	0.897698i	$0.354761\pi$
$90$	0.502341	−	4.15360i	0.0529514	−	0.437828i
$91$	−3.26931	+	0.990353i	−0.342717	+	0.103817i
$92$	14.7694	+	3.62547i	1.53981	+	0.377982i
$93$	0.618761	+	1.07173i	0.0641625	+	0.111133i
$94$	−5.78164	−	13.5522i	−0.596331	−	1.39780i
$95$	0.975331	−	1.68932i	0.100067	−	0.173321i
$96$	0.950635	+	0.652855i	0.0970238	+	0.0666318i
$97$	−6.15706	−	3.55478i	−0.625154	−	0.360933i	0.153719	−	0.988115i	$-0.450875\pi$
$97$	−6.15706	−	3.55478i	−0.625154	−	0.360933i	−0.778873	+	0.627182i	$0.784208\pi$
$98$	6.90169	+	5.18117i	0.697176	+	0.523377i
$99$	−2.69247			−0.270604
$100$	1.38408	−	1.44372i	0.138408	−	0.144372i
$101$	5.94485	−	3.43226i	0.591535	−	0.341523i	−0.174169	−	0.984716i	$-0.555724\pi$
$101$	5.94485	−	3.43226i	0.591535	−	0.341523i	0.765704	+	0.643193i	$0.222391\pi$
$102$	−0.232219	−	0.544322i	−0.0229931	−	0.0538960i
$103$	13.7687			1.35667			0.678335	−	0.734753i	$-0.262702\pi$
$103$	13.7687			1.35667			0.678335	+	0.734753i	$0.262702\pi$
$104$	−4.49691	−	9.15302i	−0.440958	−	0.897528i
$105$	0.193147			0.0188492
$106$	−6.36372	−	14.9166i	−0.618099	−	1.44883i
$107$	15.9543	−	9.21122i	1.54236	−	0.890483i	0.543672	−	0.839298i	$-0.317034\pi$
$107$	15.9543	−	9.21122i	1.54236	−	0.890483i	0.998689	−	0.0511847i	$-0.0162997\pi$
$108$	1.75369	+	1.68125i	0.168749	+	0.161779i
$109$	−9.34839			−0.895414			−0.447707	−	0.894180i	$-0.647759\pi$
$109$	−9.34839			−0.895414			−0.447707	+	0.894180i	$0.647759\pi$
$110$	−1.02931	−	0.772713i	−0.0981408	−	0.0736753i
$111$	−1.76556	−	1.01934i	−0.167579	−	0.0967518i
$112$	1.75481	−	3.35898i	0.165814	−	0.317394i
$113$	4.37276	−	7.57384i	0.411355	−	0.712487i	−0.583683	−	0.811981i	$-0.698389\pi$
$113$	4.37276	−	7.57384i	0.411355	−	0.712487i	0.995038	+	0.0994941i	$0.0317224\pi$
$114$	0.220682	+	0.517281i	0.0206688	+	0.0484478i
$115$	3.80196	+	6.58518i	0.354534	+	0.614072i
$116$	4.04889	−	16.4943i	0.375930	−	1.53145i
$117$	−3.09246	−	10.2087i	−0.285898	−	0.943794i
$118$	−1.58685	+	13.1208i	−0.146081	+	1.20787i
$119$	−1.68419	+	0.972369i	−0.154390	+	0.0891369i
$120$	0.0933042	+	0.569013i	0.00851747	+	0.0519436i
$121$	5.08586	−	8.80897i	0.462351	−	0.800815i
$122$	−5.08640	−	0.615154i	−0.460501	−	0.0556935i
$123$	−0.485008	+	0.840058i	−0.0437317	+	0.0757454i
$124$	8.76387	+	8.40186i	0.787019	+	0.754509i
$125$	1.00000			0.0894427
$126$	2.37980	−	3.17007i	0.212010	−	0.282412i
$127$	−2.83054	−	4.90264i	−0.251170	−	0.435039i	0.712678	−	0.701491i	$-0.247482\pi$
$127$	−2.83054	−	4.90264i	−0.251170	−	0.435039i	−0.963848	+	0.266452i	$0.914149\pi$
$128$	10.7433	+	3.54707i	0.949582	+	0.313520i
$129$	0.975097			0.0858525
$130$	1.74757	−	4.79020i	0.153272	−	0.420128i
$131$			5.99225i			0.523545i	0.965130	+	0.261773i	$0.0843071\pi$
$131$			5.99225i			0.523545i	−0.965130	+	0.261773i	$0.915693\pi$
$132$	0.356323	−	0.103576i	0.0310139	−	0.00901517i
$133$	1.60052	−	0.924061i	0.138783	−	0.0801263i
$134$	0.642264	+	0.482154i	0.0554832	+	0.0416518i
$135$			1.21471i			0.104545i
$136$	−3.67820	−	4.49192i	−0.315403	−	0.385179i
$137$	−6.90871	−	3.98874i	−0.590251	−	0.340781i	0.174946	−	0.984578i	$-0.444025\pi$
$137$	−6.90871	−	3.98874i	−0.590251	−	0.340781i	−0.765197	+	0.643797i	$0.777358\pi$
$138$	−2.17640	−	0.263216i	−0.185267	−	0.0224064i
$139$	−16.6654	−	9.62177i	−1.41354	−	0.816107i	−0.417820	−	0.908530i	$-0.637206\pi$
$139$	−16.6654	−	9.62177i	−1.41354	−	0.816107i	−0.995720	+	0.0924224i	$0.970539\pi$
$140$	1.81955	−	0.528910i	0.153780	−	0.0447011i
$141$	1.06197	+	1.83939i	0.0894342	+	0.154905i
$142$	−14.0038	−	1.69363i	−1.17517	−	0.142126i
$143$	−3.19540	−	0.746368i	−0.267213	−	0.0624144i
$144$	10.4887	+	5.47955i	0.874057	+	0.456629i
$145$	7.35427	−	4.24599i	0.610739	−	0.352610i
$146$	−0.932008	−	2.18463i	−0.0771335	−	0.180801i
$147$	−1.07738	−	0.622024i	−0.0888606	−	0.0513037i
$148$	−19.4239	−	4.76803i	−1.59663	−	0.391930i
$149$	−5.12408	+	8.87516i	−0.419781	+	0.727082i	−0.995917	−	0.0902718i	$-0.971226\pi$
$149$	−5.12408	+	8.87516i	−0.419781	+	0.727082i	0.576136	+	0.817354i	$0.304560\pi$
$150$	−0.173088	+	0.230566i	−0.0141326	+	0.0188257i
$151$		−	19.3244i		−	1.57260i	−0.617845	−	0.786300i	$-0.711994\pi$
$151$		−	19.3244i		−	1.57260i	0.617845	−	0.786300i	$-0.288006\pi$
$152$	3.49547	+	4.26876i	0.283520	+	0.346243i
$153$	−3.03630	−	5.25903i	−0.245470	−	0.425167i
$154$	−0.478503	−	1.12161i	−0.0385589	−	0.0903822i
$155$			6.07035i			0.487582i
$156$	0.801974	+	1.23206i	0.0642093	+	0.0986437i
$157$		−	8.86549i		−	0.707543i	−0.935332	−	0.353772i	$-0.884899\pi$
$157$		−	8.86549i		−	0.707543i	0.935332	−	0.353772i	$-0.115101\pi$
$158$	−6.68376	+	2.85143i	−0.531731	+	0.226847i
$159$	1.16889	+	2.02457i	0.0926988	+	0.160559i
$160$	2.43715	+	5.10493i	0.192674	+	0.403580i
$161$			7.20421i			0.567771i
$162$	9.75779	+	7.32527i	0.766644	+	0.575527i
$163$	−0.149213	+	0.258444i	−0.0116873	+	0.0202429i	−0.871810	−	0.489844i	$-0.837054\pi$
$163$	−0.149213	+	0.258444i	−0.0116873	+	0.0202429i	0.860123	+	0.510087i	$0.170387\pi$
$164$	−2.26865	+	9.24196i	−0.177152	+	0.721676i
$165$	0.160679	+	0.0927679i	0.0125088	+	0.00722197i
$166$	19.6335	−	8.37606i	1.52386	−	0.650108i
$167$	19.1340	−	11.0470i	1.48063	−	0.854842i	0.480871	−	0.876791i	$-0.340320\pi$
$167$	19.1340	−	11.0470i	1.48063	−	0.854842i	0.999759	+	0.0219487i	$0.00698705\pi$
$168$	−0.192995	+	0.511076i	−0.0148899	+	0.0394304i
$169$	−0.840192	−	12.9728i	−0.0646302	−	0.997909i
$170$	0.348536	−	2.88187i	0.0267315	−	0.221029i
$171$	2.88546	+	4.99776i	0.220656	+	0.382188i
$172$	9.18597	−	2.67019i	0.700423	−	0.203600i
$173$	−4.64831	−	2.68370i	−0.353405	−	0.204038i	0.312779	−	0.949826i	$-0.398740\pi$
$173$	−4.64831	−	2.68370i	−0.353405	−	0.204038i	−0.666184	+	0.745788i	$0.732073\pi$
$174$	−0.293957	+	2.43058i	−0.0222848	+	0.184262i
$175$	0.820502	+	0.473717i	0.0620241	+	0.0358096i
$176$	3.07313	−	1.95150i	0.231646	−	0.147100i
$177$		−	1.90519i		−	0.143203i
$178$	1.07761	−	1.43545i	0.0807701	−	0.107592i
$179$	−2.41643	+	1.39512i	−0.180612	+	0.104276i	−0.587580	−	0.809166i	$-0.699919\pi$
$179$	−2.41643	+	1.39512i	−0.180612	+	0.104276i	0.406968	+	0.913442i	$0.366586\pi$
$180$	1.65157	+	5.68171i	0.123100	+	0.423489i
$181$			17.0340i			1.26613i	0.774100	+	0.633063i	$0.218203\pi$
$181$			17.0340i			1.26613i	−0.774100	+	0.633063i	$0.781797\pi$
$182$	3.70308	−	3.10251i	0.274491	−	0.229973i
$183$	0.738563			0.0545961
$184$	−21.2237	+	3.48016i	−1.56463	+	0.256561i
$185$	−5.00013	−	8.66049i	−0.367617	−	0.636732i
$186$	−1.39962	−	1.05071i	−0.102625	−	0.0770416i
$187$	−1.86810			−0.136609
$188$	15.0413	+	14.4200i	1.09700	+	1.05169i
$189$	−0.575427	+	0.996669i	−0.0418562	+	0.0724970i
$190$	−0.331221	+	2.73869i	−0.0240293	+	0.198686i
$191$	−3.03214	+	5.25182i	−0.219398	+	0.380008i	−0.954624	−	0.297814i	$-0.903743\pi$
$191$	−3.03214	+	5.25182i	−0.219398	+	0.380008i	0.735226	+	0.677822i	$0.237076\pi$
$192$	−1.59887	−	0.321678i	−0.115388	−	0.0232151i
$193$	−6.53284	+	3.77174i	−0.470244	+	0.271495i	−0.716342	−	0.697750i	$-0.754185\pi$
$193$	−6.53284	+	3.77174i	−0.470244	+	0.271495i	0.246098	+	0.969245i	$0.420852\pi$
$194$	9.98170	+	1.20720i	0.716644	+	0.0866717i
$195$	−0.167187	+	0.715773i	−0.0119725	+	0.0512576i
$196$	−11.8529	−	2.90955i	−0.846632	−	0.207825i
$197$	−10.9228	−	18.9188i	−0.778214	−	1.34791i	−0.932970	−	0.359954i	$-0.882792\pi$
$197$	−10.9228	−	18.9188i	−0.778214	−	1.34791i	0.154756	−	0.987953i	$-0.450541\pi$
$198$	3.50233	−	1.49416i	0.248900	−	0.106186i
$199$	−5.17919	+	8.97062i	−0.367143	+	0.635910i	−0.989118	−	0.147127i	$-0.952997\pi$
$199$	−5.17919	+	8.97062i	−0.367143	+	0.635910i	0.621975	+	0.783037i	$0.286331\pi$
$200$	−0.999213	+	2.64605i	−0.0706550	+	0.187104i
$201$	−0.100260	−	0.0578849i	−0.00707177	−	0.00408289i
$202$	−5.82827	+	7.76368i	−0.410076	+	0.546250i
$203$	8.04559			0.564689
$204$	0.604134	+	0.579178i	0.0422978	+	0.0405506i
$205$	−4.12069	+	2.37908i	−0.287802	+	0.166162i
$206$	−17.9101	+	7.64081i	−1.24786	+	0.532361i
$207$	−22.4957			−1.56356
$208$	10.9289	+	9.41059i	0.757783	+	0.652507i
$209$	1.77530			0.122800
$210$	−0.251243	+	0.107185i	−0.0173374	+	0.00739648i
$211$	15.4851	−	8.94031i	1.06604	−	0.615477i	0.138941	−	0.990301i	$-0.455630\pi$
$211$	15.4851	−	8.94031i	1.06604	−	0.615477i	0.927096	+	0.374824i	$0.122297\pi$
$212$	16.5556	+	15.8718i	1.13705	+	1.09008i
$213$	2.03340			0.139326
$214$	−15.6414	+	20.8355i	−1.06923	+	1.42429i
$215$	4.14228	+	2.39155i	0.282501	+	0.163102i
$216$	−3.21417	−	1.21375i	−0.218697	−	0.0825853i
$217$	−2.87563	+	4.98074i	−0.195210	+	0.338114i
$218$	12.1602	−	5.18781i	0.823596	−	0.351363i
$219$	0.171191	+	0.296512i	0.0115680	+	0.0200364i
$220$	1.76772	+	0.433927i	0.119180	+	0.0292553i
$221$	−2.14562	−	7.08304i	−0.144330	−	0.476457i
$222$	2.86228	+	0.346168i	0.192104	+	0.0232332i
$223$	−8.20409	+	4.73663i	−0.549386	+	0.317188i	−0.748874	−	0.662712i	$-0.769405\pi$
$223$	−8.20409	+	4.73663i	−0.549386	+	0.317188i	0.199488	+	0.979900i	$0.436072\pi$
$224$	−0.418600	+	5.34312i	−0.0279689	+	0.357002i
$225$	−1.47922	+	2.56208i	−0.0986147	+	0.170806i
$226$	−1.48498	+	12.2786i	−0.0987796	+	0.816758i
$227$	−3.15175	+	5.45899i	−0.209189	+	0.362326i	−0.951459	−	0.307775i	$-0.900416\pi$
$227$	−3.15175	+	5.45899i	−0.209189	+	0.362326i	0.742270	+	0.670101i	$0.233749\pi$
$228$	−0.574120	−	0.550405i	−0.0380221	−	0.0364515i
$229$	18.3896			1.21522			0.607610	−	0.794235i	$-0.292128\pi$
$229$	18.3896			1.21522			0.607610	+	0.794235i	$0.292128\pi$
$230$	−8.59992	−	6.45604i	−0.567062	−	0.425699i
$231$	0.0878915	+	0.152233i	0.00578284	+	0.0100162i
$232$	3.88661	+	23.7024i	0.255169	+	1.55614i
$233$	−5.13679			−0.336523			−0.168261	−	0.985742i	$-0.553815\pi$
$233$	−5.13679			−0.336523			−0.168261	+	0.985742i	$0.553815\pi$
$234$	9.68784	+	11.5632i	0.633314	+	0.755909i
$235$			10.4185i			0.679627i
$236$	−5.21714	−	17.9480i	−0.339607	−	1.16831i
$237$	0.907162	−	0.523750i	0.0589265	−	0.0340212i
$238$	1.65116	−	2.19947i	0.107029	−	0.142570i
$239$			6.33273i			0.409630i	0.978801	+	0.204815i	$0.0656594\pi$
$239$			6.33273i			0.409630i	−0.978801	+	0.204815i	$0.934341\pi$
$240$	−0.437138	−	0.688385i	−0.0282171	−	0.0444351i
$241$	−1.02250	−	0.590343i	−0.0658653	−	0.0380273i	0.466706	−	0.884413i	$-0.345441\pi$
$241$	−1.02250	−	0.590343i	−0.0658653	−	0.0380273i	−0.532571	+	0.846385i	$0.678774\pi$
$242$	−1.72715	+	14.2809i	−0.111025	+	0.918012i
$243$	−4.67913	−	2.70149i	−0.300166	−	0.173301i
$244$	6.95768	−	2.02247i	0.445420	−	0.129475i
$245$	−3.05118	−	5.28481i	−0.194933	−	0.337634i
$246$	0.164708	−	1.36188i	0.0105014	−	0.0868306i
$247$	2.03903	+	6.73115i	0.129740	+	0.428293i
$248$	−16.0624	−	6.06558i	−1.01997	−	0.385164i
$249$	−2.66479	+	1.53852i	−0.168874	+	0.0974994i
$250$	−1.30078	+	0.554941i	−0.0822688	+	0.0350976i
$251$	4.69876	+	2.71283i	0.296583	+	0.171232i	0.640907	−	0.767619i	$-0.278558\pi$
$251$	4.69876	+	2.71283i	0.296583	+	0.171232i	−0.344324	+	0.938851i	$0.611892\pi$
$252$	−1.33641	+	5.44423i	−0.0841858	+	0.342954i
$253$	−3.46016	+	5.99317i	−0.217538	+	0.376788i
$254$	6.40260	+	4.80650i	0.401735	+	0.301587i
$255$			0.418457i			0.0262048i
$256$	−15.9431	+	1.34792i	−0.996445	+	0.0842451i
$257$	−2.83044	−	4.90246i	−0.176558	−	0.305807i	0.764141	−	0.645049i	$-0.223163\pi$
$257$	−2.83044	−	4.90246i	−0.176558	−	0.305807i	−0.940699	+	0.339242i	$0.889830\pi$
$258$	−1.26839	+	0.541121i	−0.0789665	+	0.0336887i
$259$		−	9.47460i		−	0.588723i
$260$	0.385062	+	7.20081i	0.0238805	+	0.446576i
$261$			25.1230i			1.55507i
$262$	−3.32535	−	7.79463i	−0.205441	−	0.481554i
$263$	−7.55918	−	13.0929i	−0.466119	−	0.807341i	0.533132	−	0.846032i	$-0.321015\pi$
$263$	−7.55918	−	13.0929i	−0.466119	−	0.807341i	−0.999251	+	0.0386904i	$0.987681\pi$
$264$	−0.406021	+	0.332469i	−0.0249889	+	0.0204620i
$265$			11.4674i			0.704435i
$266$	−1.56913	+	2.09020i	−0.0962098	+	0.128158i
$267$	−0.129372	+	0.224079i	−0.00791744	+	0.0137134i
$268$	−1.10301	−	0.270760i	−0.0673773	−	0.0165393i
$269$	20.6859	+	11.9430i	1.26124	+	0.728177i	0.973314	−	0.229476i	$-0.0737014\pi$
$269$	20.6859	+	11.9430i	1.26124	+	0.728177i	0.287925	+	0.957653i	$0.407035\pi$
$270$	−0.674091	−	1.58007i	−0.0410239	−	0.0961601i
$271$	−4.13463	+	2.38713i	−0.251161	+	0.145008i	−0.620296	−	0.784368i	$-0.712987\pi$
$271$	−4.13463	+	2.38713i	−0.251161	+	0.145008i	0.369135	+	0.929376i	$0.379654\pi$
$272$	7.27730	+	3.80184i	0.441251	+	0.230520i
$273$	−0.476251	+	0.508094i	−0.0288240	+	0.0307512i
$274$	11.2003	+	1.35457i	0.676632	+	0.0818326i
$275$	0.455050	+	0.788169i	0.0274405	+	0.0475284i
$276$	2.97709	−	0.865385i	0.179200	−	0.0520900i
$277$	−13.8603	−	8.00227i	−0.832787	−	0.480810i	0.0220192	−	0.999758i	$-0.492991\pi$
$277$	−13.8603	−	8.00227i	−0.832787	−	0.480810i	−0.854806	+	0.518948i	$0.826324\pi$
$278$	27.0176	+	3.26754i	1.62041	+	0.195974i
$279$	−15.5528	−	8.97939i	−0.931119	−	0.537582i
$280$	−2.07333	+	1.69774i	−0.123905	+	0.101460i
$281$		−	7.56569i		−	0.451331i	−0.974205	−	0.225666i	$-0.927544\pi$
$281$		−	7.56569i		−	0.451331i	0.974205	−	0.225666i	$-0.0724557\pi$
$282$	−2.40215	−	1.80332i	−0.143046	−	0.107386i
$283$	−5.23546	+	3.02269i	−0.311216	+	0.179680i	−0.647470	−	0.762091i	$-0.724173\pi$
$283$	−5.23546	+	3.02269i	−0.311216	+	0.179680i	0.336255	+	0.941771i	$0.390840\pi$
$284$	19.1558	−	5.56822i	1.13668	−	0.330413i
$285$		−	0.397668i		−	0.0235558i
$286$	4.57072	−	0.802395i	0.270272	−	0.0474466i
$287$	−4.50805			−0.266102
$288$	−16.6843	−	1.30711i	−0.983134	−	0.0770224i
$289$	6.39334	+	11.0736i	0.376079	+	0.651388i
$290$	−7.21004	+	9.60430i	−0.423388	+	0.563984i
$291$	−1.44938			−0.0849640
$292$	2.42468	+	2.32453i	0.141894	+	0.136033i
$293$	7.04335	−	12.1994i	0.411477	−	0.712699i	−0.583575	−	0.812059i	$-0.698346\pi$
$293$	7.04335	−	12.1994i	0.411477	−	0.712699i	0.995051	+	0.0993608i	$0.0316798\pi$
$294$	1.74662	+	0.211239i	0.101865	+	0.0123197i
$295$	4.67272	−	8.09338i	0.272056	−	0.471215i
$296$	27.9123	−	4.57693i	1.62237	−	0.266029i
$297$	−0.957395	+	0.552752i	−0.0555537	+	0.0320739i
$298$	1.74013	−	14.3882i	0.100803	−	0.833488i
$299$	−26.6977	−	6.23593i	−1.54397	−	0.360633i
$300$	0.0972001	−	0.395971i	0.00561185	−	0.0228614i
$301$	2.26583	+	3.92454i	0.130600	+	0.226206i
$302$	10.7239	+	25.1369i	0.617092	+	1.44647i
$303$	0.699712	−	1.21194i	0.0401974	−	0.0696240i
$304$	−6.91576	−	3.61297i	−0.396646	−	0.207218i
$305$	3.13747	+	1.81142i	0.179651	+	0.103721i
$306$	6.86802	+	5.15589i	0.392619	+	0.294743i
$307$	28.3105			1.61577			0.807883	−	0.589343i	$-0.200613\pi$
$307$	28.3105			1.61577			0.807883	+	0.589343i	$0.200613\pi$
$308$	1.24486	+	1.19344i	0.0709324	+	0.0680024i
$309$	2.43087	−	1.40346i	0.138288	−	0.0798403i
$310$	−3.36869	−	7.89622i	−0.191329	−	0.448475i
$311$	12.3778			0.701880			0.350940	−	0.936398i	$-0.385862\pi$
$311$	12.3778			0.701880			0.350940	+	0.936398i	$0.385862\pi$
$312$	−1.72692	−	1.15760i	−0.0977673	−	0.0655359i
$313$	24.2462			1.37048			0.685239	−	0.728318i	$-0.259698\pi$
$313$	24.2462			1.37048			0.685239	+	0.728318i	$0.259698\pi$
$314$	4.91983	+	11.5321i	0.277642	+	0.650794i
$315$	−2.42741	+	1.40146i	−0.136769	+	0.0789635i
$316$	7.11176	−	7.41818i	0.400068	−	0.417305i
$317$	−21.7910			−1.22391			−0.611953	−	0.790894i	$-0.709616\pi$
$317$	−21.7910			−1.22391			−0.611953	+	0.790894i	$0.709616\pi$
$318$	−2.64399	−	1.98487i	−0.148268	−	0.111306i
$319$	6.69311	+	3.86427i	0.374742	+	0.216358i
$320$	−6.00315	−	5.28793i	−0.335586	−	0.295604i
$321$	1.87783	−	3.25250i	0.104810	−	0.181537i
$322$	−3.99791	−	9.37112i	−0.222795	−	0.522232i
$323$	2.00200	+	3.46756i	0.111394	+	0.192940i
$324$	−16.7579	−	4.11360i	−0.930993	−	0.228533i
$325$	−2.46575	+	2.63061i	−0.136775	+	0.145920i
$326$	0.0506725	−	0.418985i	0.00280649	−	0.0232054i
$327$	−1.65047	+	0.952897i	−0.0912710	+	0.0526953i
$328$	−2.17772	−	13.2808i	−0.120244	−	0.733307i
$329$	−4.93541	+	8.54838i	−0.272098	+	0.471287i
$330$	−0.260489	−	0.0315039i	−0.0143395	−	0.00173423i
$331$	−4.90658	+	8.49845i	−0.269690	+	0.467117i	−0.968782	−	0.247915i	$-0.920255\pi$
$331$	−4.90658	+	8.49845i	−0.269690	+	0.467117i	0.699092	+	0.715032i	$0.253588\pi$
$332$	−20.8908	+	21.7909i	−1.14653	+	1.19593i
$333$	29.5852			1.62126
$334$	−18.7587	+	24.9880i	−1.02643	+	1.36728i
$335$	−0.283940	−	0.491798i	−0.0155133	−	0.0268698i
$336$	−0.0325723	−	0.771901i	−0.00177697	−	0.0421106i
$337$	12.3215			0.671193			0.335597	−	0.942006i	$-0.391062\pi$
$337$	12.3215			0.671193			0.335597	+	0.942006i	$0.391062\pi$
$338$	8.29206	+	16.4086i	0.451029	+	0.892510i
$339$		−	1.78289i		−	0.0968333i
$340$	1.14590	+	3.94210i	0.0621449	+	0.213791i
$341$	−4.78447	+	2.76231i	−0.259093	+	0.149588i
$342$	−6.52682	−	4.89975i	−0.352930	−	0.264948i
$343$		−	12.4136i		−	0.670273i
$344$	−10.4672	+	8.57101i	−0.564352	+	0.462118i
$345$	1.34248	+	0.775080i	0.0722765	+	0.0417289i
$346$	7.53575	+	0.911382i	0.405125	+	0.0489962i
$347$	−1.88100	−	1.08599i	−0.100977	−	0.0582993i	0.448661	−	0.893702i	$-0.351901\pi$
$347$	−1.88100	−	1.08599i	−0.100977	−	0.0582993i	−0.549638	+	0.835403i	$0.685234\pi$
$348$	−0.966453	−	3.32479i	−0.0518073	−	0.178227i
$349$	−9.73002	−	16.8529i	−0.520836	−	0.902114i	−0.999706	−	0.0242286i	$-0.992287\pi$
$349$	−9.73002	−	16.8529i	−0.520836	−	0.902114i	0.478871	−	0.877885i	$-0.341046\pi$
$350$	−1.33018	−	0.160874i	−0.0711012	−	0.00859905i
$351$	−3.19542	−	2.99516i	−0.170559	−	0.159870i
$352$	−2.91452	+	4.24389i	−0.155344	+	0.226200i
$353$	−17.6089	+	10.1665i	−0.937228	+	0.541109i	−0.889090	−	0.457732i	$-0.848662\pi$
$353$	−17.6089	+	10.1665i	−0.937228	+	0.541109i	−0.0481380	+	0.998841i	$0.515329\pi$
$354$	1.05727	+	2.47824i	0.0561932	+	0.131717i
$355$	8.63801	+	4.98716i	0.458458	+	0.264691i
$356$	−0.605144	+	2.46522i	−0.0320726	+	0.130656i
$357$	−0.198230	+	0.343345i	−0.0104915	+	0.0181717i
$358$	2.36904	−	3.15573i	0.125208	−	0.166786i
$359$		−	36.4015i		−	1.92120i	−0.277934	−	0.960600i	$-0.589650\pi$
$359$		−	36.4015i		−	1.92120i	0.277934	−	0.960600i	$-0.410350\pi$
$360$	−5.30134	−	6.47416i	−0.279405	−	0.341218i
$361$	7.59746	+	13.1592i	0.399866	+	0.692589i
$362$	−9.45286	−	22.1576i	−0.496831	−	1.16458i
$363$		−	2.07364i		−	0.108838i
$364$	−3.09520	+	6.09069i	−0.162233	+	0.319239i
$365$			1.67947i			0.0879076i
$366$	−0.960711	+	0.409859i	−0.0502172	+	0.0214237i
$367$	−3.86297	−	6.69086i	−0.201645	−	0.349260i	0.747413	−	0.664359i	$-0.231296\pi$
$367$	−3.86297	−	6.69086i	−0.201645	−	0.349260i	−0.949059	+	0.315099i	$0.897962\pi$
$368$	25.6762	−	16.3048i	1.33846	−	0.849948i
$369$		−	14.0767i		−	0.732806i
$370$	11.3102	+	8.49065i	0.587987	+	0.441408i
$371$	−5.43229	+	9.40900i	−0.282030	+	0.488491i
$372$	2.40368	+	0.590039i	0.124625	+	0.0305921i
$373$	−3.34521	−	1.93136i	−0.173208	−	0.100002i	0.410889	−	0.911685i	$-0.365218\pi$
$373$	−3.34521	−	1.93136i	−0.173208	−	0.100002i	−0.584098	+	0.811683i	$0.698552\pi$
$374$	2.43000	−	1.03669i	0.125652	−	0.0536058i
$375$	0.176551	−	0.101932i	0.00911704	−	0.00526373i
$376$	−27.5678	−	10.4103i	−1.42170	−	0.536869i
$377$	−6.96423	+	29.8157i	−0.358676	+	1.53559i
$378$	0.195414	−	1.61578i	0.0100510	−	0.0831068i
$379$	−6.76637	−	11.7197i	−0.347565	−	0.602000i	0.638251	−	0.769828i	$-0.279658\pi$
$379$	−6.76637	−	11.7197i	−0.347565	−	0.602000i	−0.985816	+	0.167828i	$0.946325\pi$
$380$	−1.08897	−	3.74626i	−0.0558628	−	0.192179i
$381$	−0.999469	−	0.577044i	−0.0512043	−	0.0295628i
$382$	1.02971	−	8.51414i	0.0526845	−	0.435622i
$383$	9.70246	+	5.60172i	0.495773	+	0.286234i	0.726966	−	0.686673i	$-0.240930\pi$
$383$	9.70246	+	5.60172i	0.495773	+	0.286234i	−0.231193	+	0.972908i	$0.574263\pi$
$384$	2.25829	−	0.468843i	0.115243	−	0.0239256i
$385$			0.862259i			0.0439448i
$386$	6.40472	−	8.53155i	0.325992	−	0.434245i
$387$	−12.2547	+	7.07524i	−0.622940	+	0.359655i
$388$	−13.6540	+	3.96895i	−0.693175	+	0.201493i
$389$			24.7818i			1.25649i	0.778017	+	0.628243i	$0.216225\pi$
$389$			24.7818i			1.25649i	−0.778017	+	0.628243i	$0.783775\pi$
$390$	−0.179737	−	1.02385i	−0.00910136	−	0.0518444i
$391$	−15.6081			−0.789334
$392$	17.0326	−	2.79293i	0.860278	−	0.141065i
$393$	0.610800	+	1.05794i	0.0308108	+	0.0533658i
$394$	24.7070	+	18.5478i	1.24472	+	0.934423i
$395$	5.13825			0.258534
$396$	−3.72660	+	3.88717i	−0.187269	+	0.195338i
$397$	11.1940	−	19.3886i	0.561813	−	0.973088i	−0.435526	−	0.900176i	$-0.643437\pi$
$397$	11.1940	−	19.3886i	0.561813	−	0.973088i	0.997338	−	0.0729119i	$-0.0232292\pi$
$398$	1.75884	−	14.5430i	0.0881629	−	0.728974i
$399$	0.188382	−	0.326287i	0.00943090	−	0.0163348i
$400$	−0.168640	−	3.99644i	−0.00843200	−	0.199822i
$401$	−3.99466	+	2.30632i	−0.199484	+	0.115172i	−0.596415	−	0.802677i	$-0.703409\pi$
$401$	−3.99466	+	2.30632i	−0.199484	+	0.115172i	0.396931	+	0.917848i	$0.370075\pi$
$402$	0.162539	+	0.0196576i	0.00810670	+	0.000980434i
$403$	−15.9687	−	14.9679i	−0.795458	−	0.745607i
$404$	3.27294	−	13.3332i	0.162835	−	0.663352i
$405$	−4.31384	−	7.47179i	−0.214357	−	0.371276i
$406$	−10.4656	+	4.46483i	−0.519398	+	0.221586i
$407$	4.55062	−	7.88191i	0.225566	−	0.390692i
$408$	−1.10726	−	0.418128i	−0.0548174	−	0.0207004i
$409$	16.1251	+	9.30986i	0.797337	+	0.460343i	0.842539	−	0.538635i	$-0.181060\pi$
$409$	16.1251	+	9.30986i	0.797337	+	0.460343i	−0.0452019	+	0.998978i	$0.514393\pi$
$410$	4.03988	−	5.38141i	0.199516	−	0.265769i
$411$	−1.62632			−0.0802203
$412$	19.0570	−	19.8781i	0.938870	−	0.979324i
$413$	7.66795	−	4.42709i	0.377315	−	0.217843i
$414$	29.2621	−	12.4838i	1.43815	−	0.613545i
$415$	−15.0936			−0.740916
$416$	−19.4385	−	6.17626i	−0.953049	−	0.302816i
$417$	−3.92305			−0.192113
$418$	−2.30928	+	0.985185i	−0.112950	+	0.0481869i
$419$	19.5563	−	11.2909i	0.955389	−	0.551594i	0.0606385	−	0.998160i	$-0.480686\pi$
$419$	19.5563	−	11.2909i	0.955389	−	0.551594i	0.894751	+	0.446565i	$0.147353\pi$
$420$	0.267331	−	0.278850i	0.0130444	−	0.0136065i
$421$	10.0032			0.487528			0.243764	−	0.969835i	$-0.421618\pi$
$421$	10.0032			0.487528			0.243764	+	0.969835i	$0.421618\pi$
$422$	−15.1814	+	20.2227i	−0.739019	+	0.984427i
$423$	−26.6930	−	15.4112i	−1.29786	−	0.749319i
$424$	−30.3432	−	11.4583i	−1.47360	−	0.556467i
$425$	−1.02632	+	1.77763i	−0.0497837	+	0.0862280i
$426$	−2.64501	+	1.12842i	−0.128151	+	0.0546719i
$427$	1.71620	+	2.97254i	0.0830526	+	0.143851i
$428$	8.78365	−	35.7826i	0.424574	−	1.72962i
$429$	−0.640229	+	0.193941i	−0.0309106	+	0.00936354i
$430$	−6.71538	−	0.812165i	−0.323844	−	0.0391661i
$431$	3.75891	−	2.17021i	0.181061	−	0.104535i	−0.406730	−	0.913548i	$-0.633331\pi$
$431$	3.75891	−	2.17021i	0.181061	−	0.104535i	0.587791	+	0.809013i	$0.299998\pi$
$432$	4.85451	−	0.204848i	0.233563	−	0.00985577i
$433$	10.4081	−	18.0274i	0.500181	−	0.866340i	−0.499819	−	0.866130i	$-0.666600\pi$
$433$	10.4081	−	18.0274i	0.500181	−	0.866340i	1.00000		0.000209462i	$-6.66737e-5\pi$
$434$	0.976559	−	8.07467i	0.0468763	−	0.387596i
$435$	0.865601	−	1.49926i	0.0415024	−	0.0718842i
$436$	−12.9389	+	13.4964i	−0.619662	+	0.646362i
$437$	14.8327			0.709542
$438$	−0.387230	−	0.290697i	−0.0185026	−	0.0138900i
$439$	3.70929	+	6.42467i	0.177035	+	0.306633i	0.940863	−	0.338786i	$-0.110016\pi$
$439$	3.70929	+	6.42467i	0.177035	+	0.306633i	−0.763829	+	0.645419i	$0.776683\pi$
$440$	−2.54023	+	0.416535i	−0.121101	+	0.0198575i
$441$	18.0535			0.859690
$442$	6.72166	+	8.02281i	0.319717	+	0.381606i
$443$		−	25.6118i		−	1.21686i	−0.793609	−	0.608428i	$-0.791801\pi$
$443$		−	25.6118i		−	1.21686i	0.793609	−	0.608428i	$-0.208199\pi$
$444$	−3.91532	+	1.13811i	−0.185813	+	0.0540122i
$445$	−1.09916	+	0.634602i	−0.0521053	+	0.0300830i
$446$	8.04320	−	10.7141i	0.380856	−	0.507328i
$447$			2.08922i			0.0988168i
$448$	−2.42061	−	7.18255i	−0.114363	−	0.339344i
$449$	20.0446	+	11.5728i	0.945963	+	0.546152i	0.891825	−	0.452381i	$-0.149425\pi$
$449$	20.0446	+	11.5728i	0.945963	+	0.546152i	0.0541386	+	0.998533i	$0.482759\pi$
$450$	0.502341	−	4.15360i	0.0236806	−	0.195803i
$451$	−3.75024	−	2.16520i	−0.176592	−	0.101955i
$452$	−4.88224	−	16.7958i	−0.229641	−	0.790010i
$453$	−1.96977	−	3.41174i	−0.0925478	−	0.160298i
$454$	1.07033	−	8.85001i	0.0502331	−	0.415351i
$455$	−3.26931	+	0.990353i	−0.153268	+	0.0464284i
$456$	1.05225	+	0.397355i	0.0492761	+	0.0186079i
$457$	24.5250	−	14.1595i	1.14723	−	0.662355i	0.199021	−	0.979995i	$-0.436224\pi$
$457$	24.5250	−	14.1595i	1.14723	−	0.662355i	0.948211	+	0.317640i	$0.102890\pi$
$458$	−23.9209	+	10.2052i	−1.11775	+	0.476856i
$459$	−2.15931	−	1.24668i	−0.100788	−	0.0581898i
$460$	14.7694	+	3.62547i	0.688625	+	0.169039i
$461$	−11.8155	+	20.4650i	−0.550302	+	0.953150i	0.447951	+	0.894058i	$0.352154\pi$
$461$	−11.8155	+	20.4650i	−0.550302	+	0.953150i	−0.998253	+	0.0590923i	$0.981179\pi$
$462$	−0.198808	−	0.149247i	−0.00924938	−	0.00694360i
$463$			26.1046i			1.21318i	0.795014	+	0.606592i	$0.207464\pi$
$463$			26.1046i			1.21318i	−0.795014	+	0.606592i	$0.792536\pi$
$464$	−18.2091	−	28.6749i	−0.845335	−	1.33120i
$465$	0.618761	+	1.07173i	0.0286943	+	0.0497001i
$466$	6.68186	−	2.85062i	0.309531	−	0.132052i
$467$			18.7238i			0.866434i	0.901290	+	0.433217i	$0.142622\pi$
$467$			18.7238i			0.866434i	−0.901290	+	0.433217i	$0.857378\pi$
$468$	−19.0187	−	9.66503i	−0.879139	−	0.446766i
$469$		−	0.538029i		−	0.0248439i
$470$	−5.78164	−	13.5522i	−0.266687	−	0.625116i
$471$	−0.903674	−	1.56521i	−0.0416391	−	0.0721210i
$472$	16.7464	+	20.4513i	0.770818	+	0.941345i
$473$			4.35309i			0.200155i
$474$	−0.889372	+	1.18471i	−0.0408502	+	0.0544154i
$475$	0.975331	−	1.68932i	0.0447512	−	0.0775114i
$476$	−0.927232	+	3.77733i	−0.0424996	+	0.173134i
$477$	−29.3804	−	16.9628i	−1.34523	−	0.776672i
$478$	−3.51429	−	8.23752i	−0.160740	−	0.376776i
$479$	−10.7411	+	6.20137i	−0.490772	+	0.283348i	−0.724895	−	0.688860i	$-0.758112\pi$
$479$	−10.7411	+	6.20137i	−0.490772	+	0.283348i	0.234122	+	0.972207i	$0.424778\pi$
$480$	0.950635	+	0.652855i	0.0433904	+	0.0297986i
$481$	35.1114	+	8.20117i	1.60094	+	0.373941i
$482$	1.65766	+	0.200480i	0.0755045	+	0.00913159i
$483$	0.734337	+	1.27191i	0.0334135	+	0.0578738i
$484$	−5.67842	−	19.5349i	−0.258110	−	0.887948i
$485$	−6.15706	−	3.55478i	−0.279578	−	0.161414i
$486$	7.58570	+	0.917423i	0.344095	+	0.0416152i
$487$	11.0900	+	6.40279i	0.502534	+	0.290138i	0.729759	−	0.683704i	$-0.239632\pi$
$487$	11.0900	+	6.40279i	0.502534	+	0.290138i	−0.227225	+	0.973842i	$0.572965\pi$
$488$	−7.92809	+	6.49190i	−0.358888	+	0.293874i
$489$			0.0608381i			0.00275119i
$490$	6.90169	+	5.18117i	0.311787	+	0.234061i
$491$	−4.12069	+	2.37908i	−0.185964	+	0.107366i	−0.590092	−	0.807336i	$-0.700908\pi$
$491$	−4.12069	+	2.37908i	−0.185964	+	0.107366i	0.404128	+	0.914703i	$0.367575\pi$
$492$	0.541516	+	1.86292i	0.0244134	+	0.0839870i
$493$			17.4309i			0.785050i
$494$	−6.38773	−	7.62424i	−0.287397	−	0.343031i
$495$	−2.69247			−0.121018
$496$	24.2598	−	1.02370i	1.08930	−	0.0459657i
$497$	4.72500	+	8.18394i	0.211945	+	0.367100i
$498$	2.61253	−	3.48008i	0.117070	−	0.155946i
$499$	−30.2817			−1.35559			−0.677797	−	0.735249i	$-0.737065\pi$
$499$	−30.2817			−1.35559			−0.677797	+	0.735249i	$0.737065\pi$
$500$	1.38408	−	1.44372i	0.0618980	−	0.0645650i
$501$	2.25208	−	3.90071i	0.100615	−	0.174271i
$502$	−7.61754	−	0.921273i	−0.339987	−	0.0411184i
$503$	−1.02393	+	1.77350i	−0.0456548	+	0.0790764i	−0.887950	−	0.459940i	$-0.847871\pi$
$503$	−1.02393	+	1.77350i	−0.0456548	+	0.0790764i	0.842295	+	0.539017i	$0.181204\pi$
$504$	−1.28284	−	7.82339i	−0.0571424	−	0.348482i
$505$	5.94485	−	3.43226i	0.264543	−	0.152734i
$506$	1.17507	−	9.71601i	0.0522380	−	0.431929i
$507$	−1.47068	−	2.20472i	−0.0653151	−	0.0979150i
$508$	−10.9957	−	2.69915i	−0.487857	−	0.119755i
$509$	14.0474	+	24.3308i	0.622640	+	1.07844i	0.988992	+	0.147967i	$0.0472731\pi$
$509$	14.0474	+	24.3308i	0.622640	+	1.07844i	−0.366353	+	0.930476i	$0.619394\pi$
$510$	−0.232219	−	0.544322i	−0.0102828	−	0.0241030i
$511$	−0.795594	+	1.37801i	−0.0351950	+	0.0609596i
$512$	19.9905	−	10.6008i	0.883466	−	0.468496i
$513$	2.05203	+	1.18474i	0.0905994	+	0.0523076i
$514$	6.40237	+	4.80632i	0.282396	+	0.211998i
$515$	13.7687			0.606721
$516$	1.34961	−	1.40776i	0.0594134	−	0.0619734i
$517$	−8.21152	+	4.74093i	−0.361142	+	0.208506i
$518$	5.25784	+	12.3244i	0.231016	+	0.541503i
$519$	−1.09422			−0.0480308
$520$	−4.49691	−	9.15302i	−0.197203	−	0.401387i
$521$	−23.8519			−1.04497			−0.522484	−	0.852649i	$-0.674995\pi$
$521$	−23.8519			−1.04497			−0.522484	+	0.852649i	$0.674995\pi$
$522$	−13.9418	−	32.6796i	−0.610215	−	1.43035i
$523$	30.2270	−	17.4516i	1.32174	−	0.763105i	0.337731	−	0.941243i	$-0.390341\pi$
$523$	30.2270	−	17.4516i	1.32174	−	0.763105i	0.984006	+	0.178138i	$0.0570074\pi$
$524$	8.65112	+	8.29376i	0.377926	+	0.362315i
$525$	0.193147			0.00842962
$526$	17.0986	+	12.8361i	0.745536	+	0.559681i
$527$	−10.7909	−	6.23011i	−0.470058	−	0.271388i
$528$	0.343645	−	0.657788i	0.0149552	−	0.0286265i
$529$	−17.4098	+	30.1546i	−0.756946	+	1.31107i
$530$	−6.36372	−	14.9166i	−0.276422	−	0.647935i
$531$	13.8240	+	23.9438i	0.599908	+	1.03907i
$532$	0.881167	−	3.58968i	0.0382034	−	0.155632i
$533$	3.90215	−	16.7061i	0.169021	−	0.723623i
$534$	0.0439345	−	0.363272i	0.00190123	−	0.0157203i
$535$	15.9543	−	9.21122i	0.689765	−	0.398236i
$536$	1.58504	−	0.259908i	0.0684633	−	0.0112263i
$537$	−0.284415	+	0.492620i	−0.0122734	+	0.0212581i
$538$	−33.5355	−	4.05582i	−1.44582	−	0.174859i
$539$	2.77688	−	4.80970i	0.119609	−	0.207168i
$540$	1.75369	+	1.68125i	0.0754670	+	0.0723496i
$541$	36.1168			1.55278			0.776391	−	0.630251i	$-0.217048\pi$
$541$	36.1168			1.55278			0.776391	+	0.630251i	$0.217048\pi$
$542$	4.05355	−	5.39962i	0.174115	−	0.231933i
$543$	1.73630	+	3.00736i	0.0745119	+	0.129058i
$544$	−11.5760	−	0.906906i	−0.496317	−	0.0388833i
$545$	−9.34839			−0.400441
$546$	0.337538	−	0.925212i	0.0144453	−	0.0395954i
$547$			7.44775i			0.318443i	0.987243	+	0.159221i	$0.0508984\pi$
$547$			7.44775i			0.318443i	−0.987243	+	0.159221i	$0.949102\pi$
$548$	−15.3208	+	4.45348i	−0.654473	+	0.190243i
$549$	−9.28201	+	5.35897i	−0.396146	+	0.228715i
$550$	−1.02931	−	0.772713i	−0.0438899	−	0.0329486i
$551$		−	16.5650i		−	0.705691i
$552$	−3.39232	+	2.77779i	−0.144387	+	0.118231i
$553$	4.21595	+	2.43408i	0.179280	+	0.103507i
$554$	22.4701	+	2.71756i	0.954663	+	0.115458i
$555$	−1.76556	−	1.01934i	−0.0749436	−	0.0432687i
$556$	−36.9574	+	10.7428i	−1.56734	+	0.455597i
$557$	−19.3137	−	33.4523i	−0.818347	−	1.41742i	−0.906899	−	0.421348i	$-0.861557\pi$
$557$	−19.3137	−	33.4523i	−0.818347	−	1.41742i	0.0885520	−	0.996072i	$-0.471776\pi$
$558$	25.2138	+	3.04939i	1.06739	+	0.129091i
$559$	−16.5050	+	4.99976i	−0.698088	+	0.211468i
$560$	1.75481	−	3.35898i	0.0741544	−	0.141943i
$561$	−0.329815	+	0.190419i	−0.0139248	+	0.00803949i
$562$	4.19851	+	9.84133i	0.177104	+	0.415132i
$563$	−23.1968	−	13.3927i	−0.977627	−	0.564433i	−0.0760739	−	0.997102i	$-0.524238\pi$
$563$	−23.1968	−	13.3927i	−0.977627	−	0.564433i	−0.901553	+	0.432669i	$0.857572\pi$
$564$	4.12541	+	1.01268i	0.173711	+	0.0426414i
$565$	4.37276	−	7.57384i	0.183963	−	0.318634i
$566$	5.13279	−	6.83724i	0.215747	−	0.287391i
$567$		−	8.17416i		−	0.343283i
$568$	−21.8275	+	17.8734i	−0.915860	+	0.749950i
$569$	−2.22781	−	3.85869i	−0.0933948	−	0.161765i	0.815543	−	0.578697i	$-0.196439\pi$
$569$	−2.22781	−	3.85869i	−0.0933948	−	0.161765i	−0.908938	+	0.416932i	$0.863105\pi$
$570$	0.220682	+	0.517281i	0.00924337	+	0.0216665i
$571$			35.6563i			1.49217i	0.665852	+	0.746084i	$0.268068\pi$
$571$			35.6563i			1.49217i	−0.665852	+	0.746084i	$0.731932\pi$
$572$	−5.50024	+	3.58022i	−0.229977	+	0.149697i
$573$			1.23628i			0.0516465i
$574$	5.86400	−	2.50170i	0.244759	−	0.104419i
$575$	3.80196	+	6.58518i	0.158553	+	0.274621i
$576$	22.4281	−	7.55855i	0.934504	−	0.314940i
$577$			18.4920i			0.769832i	0.922952	+	0.384916i	$0.125770\pi$
$577$			18.4920i			0.769832i	−0.922952	+	0.384916i	$0.874230\pi$
$578$	−14.4616	−	10.8564i	−0.601521	−	0.451568i
$579$	−0.768918	+	1.33181i	−0.0319552	+	0.0553479i
$580$	4.04889	−	16.4943i	0.168121	−	0.684887i
$581$	−12.3843	−	7.15009i	−0.513788	−	0.296636i
$582$	1.88533	−	0.804319i	0.0781493	−	0.0333401i
$583$	−9.03823	+	5.21823i	−0.374325	+	0.216117i
$584$	−4.44396	−	1.67815i	−0.183893	−	0.0694424i
$585$	−3.09246	−	10.2087i	−0.127857	−	0.422078i
$586$	−2.39191	+	19.7775i	−0.0988089	+	0.817000i
$587$	19.1108	+	33.1009i	0.788788	+	1.36622i	0.926710	+	0.375778i	$0.122624\pi$
$587$	19.1108	+	33.1009i	0.788788	+	1.36622i	−0.137922	+	0.990443i	$0.544042\pi$
$588$	−2.38921	+	0.694497i	−0.0985292	+	0.0286406i
$589$	10.2548	+	5.92060i	0.422541	+	0.243954i
$590$	−1.58685	+	13.1208i	−0.0653295	+	0.540176i
$591$	−3.85684	−	2.22675i	−0.158649	−	0.0915962i
$592$	−33.7679	+	21.4433i	−1.38785	+	0.881313i
$593$			2.58816i			0.106283i	0.998587	+	0.0531415i	$0.0169234\pi$
$593$			2.58816i			0.106283i	−0.998587	+	0.0531415i	$0.983077\pi$
$594$	0.938620	−	1.25031i	0.0385120	−	0.0513008i
$595$	−1.68419	+	0.972369i	−0.0690451	+	0.0398632i
$596$	5.72109	+	19.6817i	0.234345	+	0.806193i
$597$			2.11169i			0.0864258i
$598$	38.1885	−	6.70404i	1.56165	−	0.274149i
$599$	43.0158			1.75758			0.878788	−	0.477212i	$-0.158353\pi$
$599$	43.0158			1.75758			0.878788	+	0.477212i	$0.158353\pi$
$600$	0.0933042	+	0.569013i	0.00380913	+	0.0232299i
$601$	5.80881	+	10.0612i	0.236946	+	0.410403i	0.959837	−	0.280560i	$-0.0905201\pi$
$601$	5.80881	+	10.0612i	0.236946	+	0.410403i	−0.722890	+	0.690963i	$0.757187\pi$
$602$	−5.12524	−	3.84757i	−0.208889	−	0.156815i
$603$	1.68004			0.0684165
$604$	−27.8990	−	26.7466i	−1.13519	−	1.08830i
$605$	5.08586	−	8.80897i	0.206770	−	0.358135i
$606$	−0.237621	+	1.96477i	−0.00965270	+	0.0798133i
$607$	−6.25095	+	10.8270i	−0.253718	+	0.439453i	−0.964547	−	0.263913i	$-0.914987\pi$
$607$	−6.25095	+	10.8270i	−0.253718	+	0.439453i	0.710828	+	0.703365i	$0.248320\pi$
$608$	11.0009	+	0.861851i	0.446145	+	0.0349527i
$609$	1.42045	−	0.820100i	0.0575597	−	0.0332321i
$610$	−5.08640	−	0.615154i	−0.205942	−	0.0249069i
$611$	−27.4069	−	25.6893i	−1.10877	−	1.03928i
$612$	−11.7950	−	2.89536i	−0.476786	−	0.117038i
$613$	5.66362	+	9.80969i	0.228752	+	0.396209i	0.957438	−	0.288638i	$-0.0932023\pi$
$613$	5.66362	+	9.80969i	0.228752	+	0.396209i	−0.728687	+	0.684847i	$0.759869\pi$
$614$	−36.8259	+	15.7107i	−1.48617	+	0.634031i
$615$	−0.485008	+	0.840058i	−0.0195574	+	0.0338744i
$616$	−2.28158	−	0.861581i	−0.0919275	−	0.0347141i
$617$	6.40877	+	3.70011i	0.258008	+	0.148961i	0.623425	−	0.781883i	$-0.285741\pi$
$617$	6.40877	+	3.70011i	0.258008	+	0.148961i	−0.365418	+	0.930844i	$0.619074\pi$
$618$	−2.38320	+	3.17460i	−0.0958664	+	0.127701i
$619$	−8.97939			−0.360912			−0.180456	−	0.983583i	$-0.557757\pi$
$619$	−8.97939			−0.360912			−0.180456	+	0.983583i	$0.557757\pi$
$620$	8.76387	+	8.40186i	0.351966	+	0.337427i
$621$	−7.99907	+	4.61826i	−0.320992	+	0.185325i
$622$	−16.1008	+	6.86895i	−0.645585	+	0.275420i
$623$	−1.20249			−0.0481766
$624$	2.88874	+	0.547446i	0.115642	+	0.0219154i
$625$	1.00000			0.0400000
$626$	−31.5391	+	13.4552i	−1.26056	+	0.537779i
$627$	0.313430	−	0.180959i	0.0125172	−	0.00722680i
$628$	−12.7993	−	12.2706i	−0.510746	−	0.489649i
$629$	20.5269			0.818462
$630$	2.37980	−	3.17007i	0.0948136	−	0.126299i
$631$	25.9248	+	14.9677i	1.03205	+	0.595854i	0.917571	−	0.397571i	$-0.130147\pi$
$631$	25.9248	+	14.9677i	1.03205	+	0.595854i	0.114479	+	0.993426i	$0.463480\pi$
$632$	−5.13421	+	13.5961i	−0.204228	+	0.540822i
$633$	1.82260	−	3.15684i	0.0724419	−	0.125473i
$634$	28.3454	−	12.0927i	1.12574	−	0.480264i
$635$	−2.83054	−	4.90264i	−0.112327	−	0.194555i
$636$	4.54075	+	1.11463i	0.180052	+	0.0441979i
$637$	21.4257	+	5.00452i	0.848917	+	0.198286i
$638$	−10.8507	−	1.31230i	−0.429585	−	0.0519545i
$639$	−25.5550	+	14.7542i	−1.01094	+	0.583667i
$640$	10.7433	+	3.54707i	0.424666	+	0.140210i
$641$	−18.5886	+	32.1965i	−0.734207	+	1.27168i	0.220864	+	0.975305i	$0.429112\pi$
$641$	−18.5886	+	32.1965i	−0.734207	+	1.27168i	−0.955070	+	0.296379i	$0.904221\pi$
$642$	−0.637708	+	5.27288i	−0.0251683	+	0.208104i
$643$	14.1618	−	24.5290i	0.558488	−	0.967330i	−0.439135	−	0.898421i	$-0.644715\pi$
$643$	14.1618	−	24.5290i	0.558488	−	0.967330i	0.997623	−	0.0689088i	$-0.0219517\pi$
$644$	10.4008	+	9.97121i	0.409851	+	0.392921i
$645$	0.975097			0.0383944
$646$	−4.52846	−	3.39956i	−0.178170	−	0.133754i
$647$	−16.1098	−	27.9029i	−0.633341	−	1.09698i	−0.986864	−	0.161552i	$-0.948350\pi$
$647$	−16.1098	−	27.9029i	−0.633341	−	1.09698i	0.353523	−	0.935426i	$-0.384983\pi$
$648$	24.0812	−	3.94872i	0.945998	−	0.155120i
$649$	8.50528			0.333861
$650$	1.74757	−	4.79020i	0.0685454	−	0.187887i
$651$			1.17247i			0.0459527i
$652$	0.166598	+	0.573129i	0.00652448	+	0.0224455i
$653$	−15.6423	+	9.03111i	−0.612132	+	0.353415i	−0.773799	−	0.633431i	$-0.781646\pi$
$653$	−15.6423	+	9.03111i	−0.612132	+	0.353415i	0.161667	+	0.986845i	$0.448313\pi$
$654$	1.61810	−	2.15542i	0.0632727	−	0.0842838i
$655$			5.99225i			0.234137i
$656$	10.2028	+	16.0669i	0.398352	+	0.627307i
$657$	−4.30295	−	2.48431i	−0.167874	−	0.0969221i
$658$	1.67606	−	13.8585i	0.0653395	−	0.540259i
$659$	6.57871	+	3.79822i	0.256270	+	0.147958i	0.622632	−	0.782515i	$-0.286063\pi$
$659$	6.57871	+	3.79822i	0.256270	+	0.147958i	−0.366362	+	0.930472i	$0.619397\pi$
$660$	0.356323	−	0.103576i	0.0138699	−	0.00403171i
$661$	−16.8080	−	29.1123i	−0.653755	−	1.13234i	−0.982204	−	0.187816i	$-0.939859\pi$
$661$	−16.8080	−	29.1123i	−0.653755	−	1.13234i	0.328449	−	0.944522i	$-0.393474\pi$
$662$	1.66627	−	13.7775i	0.0647614	−	0.535479i
$663$	−1.10080	−	1.03181i	−0.0427514	−	0.0400721i
$664$	15.0817	−	39.9384i	0.585284	−	1.54991i
$665$	1.60052	−	0.924061i	0.0620655	−	0.0358336i
$666$	−38.4840	+	16.4180i	−1.49122	+	0.636186i
$667$	55.9212	+	32.2861i	2.16528	+	1.25012i
$668$	10.5342	−	42.9140i	0.407581	−	1.66039i
$669$	−0.965625	+	1.67251i	−0.0373332	+	0.0646630i
$670$	0.642264	+	0.482154i	0.0248128	+	0.0186272i
$671$			3.29714i			0.127285i
$672$	0.470729	+	0.986001i	0.0181588	+	0.0380358i
$673$	21.7955	+	37.7509i	0.840156	+	1.45519i	0.889763	+	0.456423i	$0.150870\pi$
$673$	21.7955	+	37.7509i	0.840156	+	1.45519i	−0.0496072	+	0.998769i	$0.515797\pi$
$674$	−16.0276	+	6.83769i	−0.617359	+	0.263378i
$675$			1.21471i			0.0467541i
$676$	−19.8920	−	16.7424i	−0.765076	−	0.643940i
$677$			33.4500i			1.28559i	0.766040	+	0.642793i	$0.222225\pi$
$677$			33.4500i			1.28559i	−0.766040	+	0.642793i	$0.777775\pi$
$678$	0.989399	+	2.31916i	0.0379976	+	0.0890667i
$679$	−3.36792	−	5.83340i	−0.129249	−	0.223866i
$680$	−3.67820	−	4.49192i	−0.141052	−	0.172257i
$681$			1.28505i			0.0492433i
$682$	4.69064	−	6.24827i	0.179614	−	0.239259i
$683$	−13.1705	+	22.8120i	−0.503955	+	0.872876i	0.496035	+	0.868303i	$0.334789\pi$
$683$	−13.1705	+	22.8120i	−0.503955	+	0.872876i	−0.999990	+	0.00457291i	$0.998544\pi$
$684$	11.2091	+	2.75152i	0.428589	+	0.105207i
$685$	−6.90871	−	3.98874i	−0.263968	−	0.152402i
$686$	6.88883	+	16.1475i	0.263017	+	0.616513i
$687$	3.24670	−	1.87448i	0.123869	−	0.0715160i
$688$	8.85912	−	16.9577i	0.337751	−	0.646506i
$689$	−30.1662	−	28.2756i	−1.14924	−	1.07722i
$690$	−2.17640	−	0.263216i	−0.0828540	−	0.0100205i
$691$	2.33735	+	4.04842i	0.0889171	+	0.154009i	0.907054	−	0.421015i	$-0.138326\pi$
$691$	2.33735	+	4.04842i	0.0889171	+	0.154009i	−0.818137	+	0.575024i	$0.804993\pi$
$692$	−10.3082	+	2.99639i	−0.391857	+	0.113906i
$693$	−2.20918	−	1.27547i	−0.0839198	−	0.0484511i
$694$	3.04944	+	0.368802i	0.115755	+	0.0139995i
$695$	−16.6654	−	9.62177i	−0.632154	−	0.364974i
$696$	3.10221	+	3.78851i	0.117589	+	0.143603i
$697$		−	9.76678i		−	0.369943i
$698$	22.0090	+	16.5224i	0.833053	+	0.625381i
$699$	−0.906905	+	0.523602i	−0.0343023	+	0.0198044i
$700$	1.81955	−	0.528910i	0.0687727	−	0.0199909i
$701$		−	5.91052i		−	0.223237i	−0.993751	−	0.111619i	$-0.964396\pi$
$701$		−	5.91052i		−	0.223237i	0.993751	−	0.111619i	$-0.0356035\pi$
$702$	5.81869	+	2.12279i	0.219612	+	0.0801195i
$703$	−19.5071			−0.735726
$704$	1.43606	−	7.13777i	0.0541234	−	0.269015i
$705$	1.06197	+	1.83939i	0.0399962	+	0.0692754i
$706$	17.2636	−	22.9964i	0.649724	−	0.865479i
$707$	6.50369			0.244596
$708$	−2.75056	−	2.63694i	−0.103372	−	0.0991022i
$709$	15.6266	−	27.0660i	0.586868	−	1.01649i	−0.407772	−	0.913084i	$-0.633694\pi$
$709$	15.6266	−	27.0660i	0.586868	−	1.01649i	0.994640	−	0.103401i	$-0.0329726\pi$
$710$	−14.0038	−	1.69363i	−0.525552	−	0.0635608i
$711$	−7.60060	+	13.1646i	−0.285045	+	0.493712i
$712$	−0.580890	−	3.54254i	−0.0217698	−	0.132762i
$713$	−39.9744	+	23.0792i	−1.49705	+	0.864324i
$714$	0.0673187	−	0.556624i	0.00251934	−	0.0208311i
$715$	−3.19540	−	0.746368i	−0.119501	−	0.0279126i
$716$	−1.33036	+	5.41960i	−0.0497180	+	0.202540i
$717$	0.645506	+	1.11805i	0.0241069	+	0.0417543i
$718$	20.2007	+	47.3506i	0.753884	+	1.76711i
$719$	−9.15518	+	15.8572i	−0.341431	+	0.591375i	−0.984699	−	0.174266i	$-0.944245\pi$
$719$	−9.15518	+	15.8572i	−0.341431	+	0.591375i	0.643268	+	0.765641i	$0.277578\pi$
$720$	10.4887	+	5.47955i	0.390890	+	0.204211i
$721$	11.2972	+	6.52246i	0.420731	+	0.242909i
$722$	−17.1852	−	12.9011i	−0.639568	−	0.480130i
$723$	−0.240698			−0.00895167
$724$	24.5923	+	23.5764i	0.913965	+	0.876211i
$725$	7.35427	−	4.24599i	0.273131	−	0.157692i
$726$	1.15075	+	2.69736i	0.0427083	+	0.100108i
$727$	34.1329			1.26592			0.632960	−	0.774184i	$-0.281840\pi$
$727$	34.1329			1.26592			0.632960	+	0.774184i	$0.281840\pi$
$728$	0.646219	−	9.64033i	0.0239505	−	0.357295i
$729$	24.7816			0.917836
$730$	−0.932008	−	2.18463i	−0.0344952	−	0.0808568i
$731$	−8.50259	+	4.90897i	−0.314480	+	0.181565i
$732$	1.02223	−	1.06628i	0.0377827	−	0.0394107i
$733$	−21.7917			−0.804895			−0.402447	−	0.915443i	$-0.631840\pi$
$733$	−21.7917			−0.804895			−0.402447	+	0.915443i	$0.631840\pi$
$734$	8.73793	+	6.55965i	0.322523	+	0.242121i
$735$	−1.07738	−	0.622024i	−0.0397397	−	0.0229437i
$736$	−24.3509	+	35.4578i	−0.897587	+	1.30699i
$737$	0.258414	−	0.447586i	0.00951879	−	0.0164870i
$738$	7.81176	+	18.3108i	0.287555	+	0.674030i
$739$	−7.01484	−	12.1501i	−0.258045	−	0.446947i	0.707673	−	0.706540i	$-0.249745\pi$
$739$	−7.01484	−	12.1501i	−0.258045	−	0.446947i	−0.965718	+	0.259593i	$0.916412\pi$
$740$	−19.4239	−	4.76803i	−0.714036	−	0.175276i
$741$	1.04611	+	0.980549i	0.0384298	+	0.0360214i
$742$	1.84480	−	15.2537i	0.0677246	−	0.559980i
$743$	27.2452	−	15.7300i	0.999530	−	0.577079i	0.0914205	−	0.995812i	$-0.470859\pi$
$743$	27.2452	−	15.7300i	0.999530	−	0.577079i	0.908109	+	0.418734i	$0.137526\pi$
$744$	−3.45411	+	0.566390i	−0.126634	+	0.0207648i
$745$	−5.12408	+	8.87516i	−0.187732	+	0.325161i
$746$	5.42319	+	0.655886i	0.198557	+	0.0240137i
$747$	22.3268	−	38.6711i	0.816893	−	1.41490i
$748$	−2.58561	+	2.69701i	−0.0945391	+	0.0986126i
$749$	17.4541			0.637757
$750$	−0.173088	+	0.230566i	−0.00632030	+	0.00841909i
$751$	6.02077	+	10.4283i	0.219701	+	0.380533i	0.954717	−	0.297517i	$-0.0961585\pi$
$751$	6.02077	+	10.4283i	0.219701	+	0.380533i	−0.735016	+	0.678050i	$0.762825\pi$
$752$	41.6369	−	1.75697i	1.51834	−	0.0640702i
$753$	1.10609			0.0403083
$754$	−7.48701	−	42.6486i	−0.272661	−	1.55317i
$755$		−	19.3244i		−	0.703288i
$756$	0.642471	+	2.21023i	0.0233664	+	0.0803851i
$757$	−12.2994	+	7.10108i	−0.447031	+	0.258093i	−0.706575	−	0.707638i	$-0.749761\pi$
$757$	−12.2994	+	7.10108i	−0.447031	+	0.258093i	0.259545	+	0.965731i	$0.416427\pi$
$758$	15.3053	+	11.4899i	0.555915	+	0.417331i
$759$			1.41080i			0.0512088i
$760$	3.49547	+	4.26876i	0.126794	+	0.154844i
$761$	−9.71814	−	5.61077i	−0.352282	−	0.203390i	0.313408	−	0.949619i	$-0.398529\pi$
$761$	−9.71814	−	5.61077i	−0.352282	−	0.203390i	−0.665690	+	0.746228i	$0.731863\pi$
$762$	1.62032	+	0.195963i	0.0586980	+	0.00709899i
$763$	−7.67037	−	4.42849i	−0.277686	−	0.160322i
$764$	3.38542	+	11.6465i	0.122480	+	0.421355i
$765$	−3.03630	−	5.25903i	−0.109778	−	0.190140i
$766$	−15.7294	−	1.90234i	−0.568328	−	0.0687342i
$767$	9.76878	+	32.2483i	0.352730	+	1.16442i
$768$	−2.67737	+	1.86308i	−0.0966114	+	0.0672283i
$769$	19.8028	−	11.4331i	0.714107

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:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.ca (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30078 + 0.554941i) q^{2} +(0.176551 - 0.101932i) q^{3} +(1.38408 - 1.44372i) q^{4} +1.00000 q^{5} +(-0.173088 + 0.230566i) q^{6} +(0.820502 + 0.473717i) q^{7} +(-0.999213 + 2.64605i) q^{8} +(-1.47922 + 2.56208i) q^{9} +O(q^{10})\)	\(q+(-1.30078 + 0.554941i) q^{2} +(0.176551 - 0.101932i) q^{3} +(1.38408 - 1.44372i) q^{4} +1.00000 q^{5} +(-0.173088 + 0.230566i) q^{6} +(0.820502 + 0.473717i) q^{7} +(-0.999213 + 2.64605i) q^{8} +(-1.47922 + 2.56208i) q^{9} +(-1.30078 + 0.554941i) q^{10} +(0.455050 + 0.788169i) q^{11} +(0.0972001 - 0.395971i) q^{12} +(-2.46575 + 2.63061i) q^{13} +(-1.33018 - 0.160874i) q^{14} +(0.176551 - 0.101932i) q^{15} +(-0.168640 - 3.99644i) q^{16} +(-1.02632 + 1.77763i) q^{17} +(0.502341 - 4.15360i) q^{18} +(0.975331 - 1.68932i) q^{19} +(1.38408 - 1.44372i) q^{20} +0.193147 q^{21} +(-1.02931 - 0.772713i) q^{22} +(3.80196 + 6.58518i) q^{23} +(0.0933042 + 0.569013i) q^{24} +1.00000 q^{25} +(1.74757 - 4.79020i) q^{26} +1.21471i q^{27} +(1.81955 - 0.528910i) q^{28} +(7.35427 - 4.24599i) q^{29} +(-0.173088 + 0.230566i) q^{30} +6.07035i q^{31} +(2.43715 + 5.10493i) q^{32} +(0.160679 + 0.0927679i) q^{33} +(0.348536 - 2.88187i) q^{34} +(0.820502 + 0.473717i) q^{35} +(1.65157 + 5.68171i) q^{36} +(-5.00013 - 8.66049i) q^{37} +(-0.331221 + 2.73869i) q^{38} +(-0.167187 + 0.715773i) q^{39} +(-0.999213 + 2.64605i) q^{40} +(-4.12069 + 2.37908i) q^{41} +(-0.251243 + 0.107185i) q^{42} +(4.14228 + 2.39155i) q^{43} +(1.76772 + 0.433927i) q^{44} +(-1.47922 + 2.56208i) q^{45} +(-8.59992 - 6.45604i) q^{46} +10.4185i q^{47} +(-0.437138 - 0.688385i) q^{48} +(-3.05118 - 5.28481i) q^{49} +(-1.30078 + 0.554941i) q^{50} +0.418457i q^{51} +(0.385062 + 7.20081i) q^{52} +11.4674i q^{53} +(-0.674091 - 1.58007i) q^{54} +(0.455050 + 0.788169i) q^{55} +(-2.07333 + 1.69774i) q^{56} -0.397668i q^{57} +(-7.21004 + 9.60430i) q^{58} +(4.67272 - 8.09338i) q^{59} +(0.0972001 - 0.395971i) q^{60} +(3.13747 + 1.81142i) q^{61} +(-3.36869 - 7.89622i) q^{62} +(-2.42741 + 1.40146i) q^{63} +(-6.00315 - 5.28793i) q^{64} +(-2.46575 + 2.63061i) q^{65} +(-0.260489 - 0.0315039i) q^{66} +(-0.283940 - 0.491798i) q^{67} +(1.14590 + 3.94210i) q^{68} +(1.34248 + 0.775080i) q^{69} +(-1.33018 - 0.160874i) q^{70} +(8.63801 + 4.98716i) q^{71} +(-5.30134 - 6.47416i) q^{72} +1.67947i q^{73} +(11.3102 + 8.49065i) q^{74} +(0.176551 - 0.101932i) q^{75} +(-1.08897 - 3.74626i) q^{76} +0.862259i q^{77} +(-0.179737 - 1.02385i) q^{78} +5.13825 q^{79} +(-0.168640 - 3.99644i) q^{80} +(-4.31384 - 7.47179i) q^{81} +(4.03988 - 5.38141i) q^{82} -15.0936 q^{83} +(0.267331 - 0.278850i) q^{84} +(-1.02632 + 1.77763i) q^{85} +(-6.71538 - 0.812165i) q^{86} +(0.865601 - 1.49926i) q^{87} +(-2.54023 + 0.416535i) q^{88} +(-1.09916 + 0.634602i) q^{89} +(0.502341 - 4.15360i) q^{90} +(-3.26931 + 0.990353i) q^{91} +(14.7694 + 3.62547i) q^{92} +(0.618761 + 1.07173i) q^{93} +(-5.78164 - 13.5522i) q^{94} +(0.975331 - 1.68932i) q^{95} +(0.950635 + 0.652855i) q^{96} +(-6.15706 - 3.55478i) q^{97} +(6.90169 + 5.18117i) q^{98} -2.69247 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9}+O(q^{10}) \) 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9	\( 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9} - 8 q^{11} + 6 q^{12} - 4 q^{14} + 14 q^{16} + 18 q^{18} - 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 22 q^{24} + 56 q^{25} - 37 q^{26} - 12 q^{28} - 13 q^{30} - 30 q^{32} - 16 q^{34} + 15 q^{36} + 4 q^{37} - 24 q^{39} - 61 q^{42} + 24 q^{44} + 28 q^{45} - 19 q^{46} - 51 q^{48} + 20 q^{49} - 64 q^{52} - 5 q^{54} - 8 q^{55} - 23 q^{56} - q^{58} - 16 q^{59} + 6 q^{60} + 10 q^{62} - 30 q^{64} + 14 q^{66} - 36 q^{67} - 51 q^{68} - 4 q^{70} - 81 q^{72} + 70 q^{74} - 60 q^{76} + 143 q^{78} + 14 q^{80} - 28 q^{81} + 21 q^{82} + 40 q^{83} + 31 q^{84} - 28 q^{86} - 36 q^{87} - 19 q^{88} + 18 q^{90} + 16 q^{91} - 18 q^{92} + 43 q^{94} - 16 q^{95} - 48 q^{96} + 24 q^{97} + 56 q^{98} - 48 q^{99}+O(q^{100}) \) 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9 - 8 * q^11 + 6 * q^12 - 4 * q^14 + 14 * q^16 + 18 * q^18 - 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 22 * q^24 + 56 * q^25 - 37 * q^26 - 12 * q^28 - 13 * q^30 - 30 * q^32 - 16 * q^34 + 15 * q^36 + 4 * q^37 - 24 * q^39 - 61 * q^42 + 24 * q^44 + 28 * q^45 - 19 * q^46 - 51 * q^48 + 20 * q^49 - 64 * q^52 - 5 * q^54 - 8 * q^55 - 23 * q^56 - q^58 - 16 * q^59 + 6 * q^60 + 10 * q^62 - 30 * q^64 + 14 * q^66 - 36 * q^67 - 51 * q^68 - 4 * q^70 - 81 * q^72 + 70 * q^74 - 60 * q^76 + 143 * q^78 + 14 * q^80 - 28 * q^81 + 21 * q^82 + 40 * q^83 + 31 * q^84 - 28 * q^86 - 36 * q^87 - 19 * q^88 + 18 * q^90 + 16 * q^91 - 18 * q^92 + 43 * q^94 - 16 * q^95 - 48 * q^96 + 24 * q^97 + 56 * q^98 - 48 * q^99

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