LMFDB - Embedded newform 380.2.k.d.267.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(267,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("380.267");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.k (of order $4$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			267.20
Character	$\chi$	$=$	380.267
Dual form			380.2.k.d.343.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.979881 - 1.01972i) q^{2} +(-0.582309 - 0.582309i) q^{3} +(-0.0796647 - 1.99841i) q^{4} +(1.46731 + 1.68731i) q^{5} +(-1.16439 + 0.0231993i) q^{6} +(-0.972933 + 0.972933i) q^{7} +(-2.11589 - 1.87697i) q^{8} -2.32183i q^{9} +O(q^{10})$	\(q+(0.979881 - 1.01972i) q^{2} +(-0.582309 - 0.582309i) q^{3} +(-0.0796647 - 1.99841i) q^{4} +(1.46731 + 1.68731i) q^{5} +(-1.16439 + 0.0231993i) q^{6} +(-0.972933 + 0.972933i) q^{7} +(-2.11589 - 1.87697i) q^{8} -2.32183i q^{9} +(3.15837 + 0.157113i) q^{10} -4.73734i q^{11} +(-1.11730 + 1.21008i) q^{12} +(4.00469 - 4.00469i) q^{13} +(0.0387619 + 1.94548i) q^{14} +(0.128106 - 1.83696i) q^{15} +(-3.98731 + 0.318406i) q^{16} +(1.22667 + 1.22667i) q^{17} +(-2.36762 - 2.27512i) q^{18} -1.00000 q^{19} +(3.25504 - 3.06671i) q^{20} +1.13310 q^{21} +(-4.83076 - 4.64203i) q^{22} +(1.83166 + 1.83166i) q^{23} +(0.139122 + 2.32508i) q^{24} +(-0.694006 + 4.95160i) q^{25} +(-0.159548 - 8.00779i) q^{26} +(-3.09895 + 3.09895i) q^{27} +(2.02183 + 1.86681i) q^{28} +6.49625i q^{29} +(-1.74766 - 1.93064i) q^{30} -1.38349i q^{31} +(-3.58240 + 4.37794i) q^{32} +(-2.75859 + 2.75859i) q^{33} +(2.45286 - 0.0488710i) q^{34} +(-3.06923 - 0.214042i) q^{35} +(-4.63998 + 0.184968i) q^{36} +(3.47306 + 3.47306i) q^{37} +(-0.979881 + 1.01972i) q^{38} -4.66393 q^{39} +(0.0623655 - 6.32425i) q^{40} -6.68423 q^{41} +(1.11030 - 1.15544i) q^{42} +(4.72604 + 4.72604i) q^{43} +(-9.46715 + 0.377398i) q^{44} +(3.91764 - 3.40685i) q^{45} +(3.66259 - 0.0729738i) q^{46} +(6.12814 - 6.12814i) q^{47} +(2.50726 + 2.13643i) q^{48} +5.10680i q^{49} +(4.36921 + 5.55967i) q^{50} -1.42861i q^{51} +(-8.32205 - 7.68399i) q^{52} +(3.65002 - 3.65002i) q^{53} +(0.123463 + 6.19667i) q^{54} +(7.99334 - 6.95114i) q^{55} +(3.88478 - 0.232448i) q^{56} +(0.582309 + 0.582309i) q^{57} +(6.62437 + 6.36555i) q^{58} +0.289084 q^{59} +(-3.68121 - 0.109668i) q^{60} -4.63716 q^{61} +(-1.41078 - 1.35566i) q^{62} +(2.25899 + 2.25899i) q^{63} +(0.953954 + 7.94292i) q^{64} +(12.6333 + 0.881019i) q^{65} +(0.109903 + 5.51609i) q^{66} +(-3.20114 + 3.20114i) q^{67} +(2.35368 - 2.54912i) q^{68} -2.13318i q^{69} +(-3.22574 + 2.92002i) q^{70} +14.8252i q^{71} +(-4.35801 + 4.91273i) q^{72} +(6.01054 - 6.01054i) q^{73} +(6.94475 - 0.138368i) q^{74} +(3.28749 - 2.47924i) q^{75} +(0.0796647 + 1.99841i) q^{76} +(4.60911 + 4.60911i) q^{77} +(-4.57010 + 4.75591i) q^{78} -5.24290 q^{79} +(-6.38786 - 6.26061i) q^{80} -3.35640 q^{81} +(-6.54976 + 6.81606i) q^{82} +(4.42022 + 4.42022i) q^{83} +(-0.0902677 - 2.26439i) q^{84} +(-0.269864 + 3.86968i) q^{85} +(9.45020 - 0.188287i) q^{86} +(3.78283 - 3.78283i) q^{87} +(-8.89184 + 10.0237i) q^{88} -8.67923i q^{89} +(0.364790 - 7.33321i) q^{90} +7.79259i q^{91} +(3.51449 - 3.80633i) q^{92} +(-0.805621 + 0.805621i) q^{93} +(-0.244147 - 12.2539i) q^{94} +(-1.46731 - 1.68731i) q^{95} +(4.63538 - 0.463251i) q^{96} +(-3.14322 - 3.14322i) q^{97} +(5.20752 + 5.00406i) q^{98} -10.9993 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) $ 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8	$ 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) $ 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.979881	−	1.01972i	0.692881	−	0.721052i
$2$	0.979881	−	1.01972i	0.692881	−	0.721052i
$3$	−0.582309	−	0.582309i	−0.336196	−	0.336196i	0.518737	−	0.854934i	$-0.326402\pi$
$3$	−0.582309	−	0.582309i	−0.336196	−	0.336196i	−0.854934	+	0.518737i	$0.826402\pi$
$4$	−0.0796647	−	1.99841i	−0.0398324	−	0.999206i
$5$	1.46731	+	1.68731i	0.656201	+	0.754586i
$5$	1.46731	+	1.68731i	0.656201	+	0.754586i
$6$	−1.16439	+	0.0231993i	−0.475359	+	0.00947109i
$7$	−0.972933	+	0.972933i	−0.367734	+	0.367734i	−0.866650	−	0.498916i	$-0.833732\pi$
$7$	−0.972933	+	0.972933i	−0.367734	+	0.367734i	0.498916	+	0.866650i	$0.333732\pi$
$8$	−2.11589	−	1.87697i	−0.748079	−	0.663610i
$9$		−	2.32183i		−	0.773944i
$10$	3.15837	+	0.157113i	0.998765	+	0.0496834i
$11$		−	4.73734i		−	1.42836i	−0.699962	−	0.714180i	$-0.746800\pi$
$11$		−	4.73734i		−	1.42836i	0.699962	−	0.714180i	$-0.253200\pi$
$12$	−1.11730	+	1.21008i	−0.322538	+	0.349321i
$13$	4.00469	−	4.00469i	1.11070	−	1.11070i	0.117645	−	0.993056i	$-0.462466\pi$
$13$	4.00469	−	4.00469i	1.11070	−	1.11070i	0.993056	−	0.117645i	$-0.0375345\pi$
$14$	0.0387619	+	1.94548i	0.0103596	+	0.519951i
$15$	0.128106	−	1.83696i	0.0330769	−	0.474301i
$16$	−3.98731	+	0.318406i	−0.996827	+	0.0796015i
$17$	1.22667	+	1.22667i	0.297512	+	0.297512i	0.840039	−	0.542527i	$-0.182532\pi$
$17$	1.22667	+	1.22667i	0.297512	+	0.297512i	−0.542527	+	0.840039i	$0.682532\pi$
$18$	−2.36762	−	2.27512i	−0.558054	−	0.536251i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	3.25504	−	3.06671i	0.727849	−	0.685737i
$21$	1.13310			0.247262
$22$	−4.83076	−	4.64203i	−1.02992	−	0.989683i
$23$	1.83166	+	1.83166i	0.381928	+	0.381928i	0.871796	−	0.489869i	$-0.162955\pi$
$23$	1.83166	+	1.83166i	0.381928	+	0.381928i	−0.489869	+	0.871796i	$0.662955\pi$
$24$	0.139122	+	2.32508i	0.0283983	+	0.474605i
$25$	−0.694006	+	4.95160i	−0.138801	+	0.990320i
$26$	−0.159548	−	8.00779i	−0.0312899	−	1.57046i
$27$	−3.09895	+	3.09895i	−0.596393	+	0.596393i
$28$	2.02183	+	1.86681i	0.382090	+	0.352795i
$29$			6.49625i			1.20632i	0.797619	+	0.603162i	$0.206093\pi$
$29$			6.49625i			1.20632i	−0.797619	+	0.603162i	$0.793907\pi$
$30$	−1.74766	−	1.93064i	−0.319078	−	0.352485i
$31$		−	1.38349i		−	0.248483i	−0.992252	−	0.124241i	$-0.960350\pi$
$31$		−	1.38349i		−	0.248483i	0.992252	−	0.124241i	$-0.0396497\pi$
$32$	−3.58240	+	4.37794i	−0.633285	+	0.773918i
$33$	−2.75859	+	2.75859i	−0.480209	+	0.480209i
$34$	2.45286	−	0.0488710i	0.420662	−	0.00838130i
$35$	−3.06923	−	0.214042i	−0.518795	−	0.0361797i
$36$	−4.63998	+	0.184968i	−0.773330	+	0.0308280i
$37$	3.47306	+	3.47306i	0.570968	+	0.570968i	0.932399	−	0.361431i	$-0.117712\pi$
$37$	3.47306	+	3.47306i	0.570968	+	0.570968i	−0.361431	+	0.932399i	$0.617712\pi$
$38$	−0.979881	+	1.01972i	−0.158958	+	0.165421i
$39$	−4.66393			−0.746827
$40$	0.0623655	−	6.32425i	0.00986085	−	0.999951i
$41$	−6.68423			−1.04390			−0.521951	−	0.852975i	$-0.674796\pi$
$41$	−6.68423			−1.04390			−0.521951	+	0.852975i	$0.674796\pi$
$42$	1.11030	−	1.15544i	0.171323	−	0.178289i
$43$	4.72604	+	4.72604i	0.720714	+	0.720714i	0.968751	−	0.248037i	$-0.0797853\pi$
$43$	4.72604	+	4.72604i	0.720714	+	0.720714i	−0.248037	+	0.968751i	$0.579785\pi$
$44$	−9.46715	+	0.377398i	−1.42723	+	0.0568950i
$45$	3.91764	−	3.40685i	0.584008	−	0.507863i
$46$	3.66259	−	0.0729738i	0.540020	−	0.0107594i
$47$	6.12814	−	6.12814i	0.893882	−	0.893882i	−0.101004	−	0.994886i	$-0.532206\pi$
$47$	6.12814	−	6.12814i	0.893882	−	0.893882i	0.994886	+	0.101004i	$0.0322056\pi$
$48$	2.50726	+	2.13643i	0.361891	+	0.308368i
$49$			5.10680i			0.729543i
$50$	4.36921	+	5.55967i	0.617900	+	0.786257i
$51$		−	1.42861i		−	0.200045i
$52$	−8.32205	−	7.68399i	−1.15406	−	1.06558i
$53$	3.65002	−	3.65002i	0.501369	−	0.501369i	−0.410494	−	0.911863i	$-0.634644\pi$
$53$	3.65002	−	3.65002i	0.501369	−	0.501369i	0.911863	+	0.410494i	$0.134644\pi$
$54$	0.123463	+	6.19667i	0.0168012	+	0.843260i
$55$	7.99334	−	6.95114i	1.07782	−	0.937291i
$56$	3.88478	−	0.232448i	0.519126	−	0.0310622i
$57$	0.582309	+	0.582309i	0.0771287	+	0.0771287i
$58$	6.62437	+	6.36555i	0.869822	+	0.835838i
$59$	0.289084			0.0376355			0.0188178	−	0.999823i	$-0.494010\pi$
$59$	0.289084			0.0376355			0.0188178	+	0.999823i	$0.494010\pi$
$60$	−3.68121	−	0.109668i	−0.475243	−	0.0141581i
$61$	−4.63716			−0.593728			−0.296864	−	0.954920i	$-0.595941\pi$
$61$	−4.63716			−0.593728			−0.296864	+	0.954920i	$0.595941\pi$
$62$	−1.41078	−	1.35566i	−0.179169	−	0.172169i
$63$	2.25899	+	2.25899i	0.284606	+	0.284606i
$64$	0.953954	+	7.94292i	0.119244	+	0.992865i
$65$	12.6333	+	0.881019i	1.56696	+	0.109277i
$66$	0.109903	+	5.51609i	0.0135281	+	0.678984i
$67$	−3.20114	+	3.20114i	−0.391082	+	0.391082i	−0.875073	−	0.483991i	$-0.839187\pi$
$67$	−3.20114	+	3.20114i	−0.391082	+	0.391082i	0.483991	+	0.875073i	$0.339187\pi$
$68$	2.35368	−	2.54912i	0.285425	−	0.309126i
$69$		−	2.13318i		−	0.256805i
$70$	−3.22574	+	2.92002i	−0.385550	+	0.349010i
$71$			14.8252i			1.75942i	0.475507	+	0.879712i	$0.342265\pi$
$71$			14.8252i			1.75942i	−0.475507	+	0.879712i	$0.657735\pi$
$72$	−4.35801	+	4.91273i	−0.513597	+	0.578971i
$73$	6.01054	−	6.01054i	0.703480	−	0.703480i	−0.261676	−	0.965156i	$-0.584275\pi$
$73$	6.01054	−	6.01054i	0.703480	−	0.703480i	0.965156	+	0.261676i	$0.0842751\pi$
$74$	6.94475	−	0.138368i	0.807311	−	0.0160849i
$75$	3.28749	−	2.47924i	0.379606	−	0.286278i
$76$	0.0796647	+	1.99841i	0.00913817	+	0.229234i
$77$	4.60911	+	4.60911i	0.525257	+	0.525257i
$78$	−4.57010	+	4.75591i	−0.517462	+	0.538501i
$79$	−5.24290			−0.589873			−0.294936	−	0.955517i	$-0.595298\pi$
$79$	−5.24290			−0.589873			−0.294936	+	0.955517i	$0.595298\pi$
$80$	−6.38786	−	6.26061i	−0.714185	−	0.699957i
$81$	−3.35640			−0.372933
$82$	−6.54976	+	6.81606i	−0.723300	+	0.752708i
$83$	4.42022	+	4.42022i	0.485183	+	0.485183i	0.906782	−	0.421600i	$-0.138531\pi$
$83$	4.42022	+	4.42022i	0.485183	+	0.485183i	−0.421600	+	0.906782i	$0.638531\pi$
$84$	−0.0902677	−	2.26439i	−0.00984902	−	0.247065i
$85$	−0.269864	+	3.86968i	−0.0292709	+	0.419726i
$86$	9.45020	−	0.188287i	1.01904	−	0.0203035i
$87$	3.78283	−	3.78283i	0.405561	−	0.405561i
$88$	−8.89184	+	10.0237i	−0.947874	+	1.06853i
$89$		−	8.67923i		−	0.919997i	−0.887920	−	0.459998i	$-0.847850\pi$
$89$		−	8.67923i		−	0.919997i	0.887920	−	0.459998i	$-0.152150\pi$
$90$	0.364790	−	7.33321i	0.0384522	−	0.772988i
$91$			7.79259i			0.816885i
$92$	3.51449	−	3.80633i	0.366411	−	0.396837i
$93$	−0.805621	+	0.805621i	−0.0835391	+	0.0835391i
$94$	−0.244147	−	12.2539i	−0.0251818	−	1.26389i
$95$	−1.46731	−	1.68731i	−0.150543	−	0.173114i
$96$	4.63538	−	0.463251i	0.473097	−	0.0472803i
$97$	−3.14322	−	3.14322i	−0.319145	−	0.319145i	0.529294	−	0.848439i	$-0.322457\pi$
$97$	−3.14322	−	3.14322i	−0.319145	−	0.319145i	−0.848439	+	0.529294i	$0.822457\pi$
$98$	5.20752	+	5.00406i	0.526039	+	0.505487i
$99$	−10.9993			−1.10547
$100$	9.95063	+	0.992442i	0.995063	+	0.0992442i
$101$	−0.982880			−0.0978003			−0.0489001	−	0.998804i	$-0.515572\pi$
$101$	−0.982880			−0.0978003			−0.0489001	+	0.998804i	$0.515572\pi$
$102$	−1.45678	−	1.39986i	−0.144243	−	0.138607i
$103$	5.20851	+	5.20851i	0.513209	+	0.513209i	0.915508	−	0.402299i	$-0.131789\pi$
$103$	5.20851	+	5.20851i	0.513209	+	0.513209i	−0.402299	+	0.915508i	$0.631789\pi$
$104$	−15.9902	+	0.956780i	−1.56796	+	0.0938200i
$105$	1.66260	+	1.91188i	0.162253	+	0.186580i
$106$	−0.145418	−	7.29860i	−0.0141242	−	0.708903i
$107$	−14.0386	+	14.0386i	−1.35716	+	1.35716i	−0.479767	+	0.877396i	$0.659279\pi$
$107$	−14.0386	+	14.0386i	−1.35716	+	1.35716i	−0.877396	+	0.479767i	$0.840721\pi$
$108$	6.43986	+	5.94611i	0.619676	+	0.572164i
$109$		−	13.0839i		−	1.25321i	−0.779337	−	0.626605i	$-0.784444\pi$
$109$		−	13.0839i		−	1.25321i	0.779337	−	0.626605i	$-0.215556\pi$
$110$	0.744296	−	14.9623i	0.0709659	−	1.42660i
$111$		−	4.04479i		−	0.383915i
$112$	3.56959	−	4.18917i	0.337295	−	0.395839i
$113$	0.590052	−	0.590052i	0.0555074	−	0.0555074i	−0.678808	−	0.734316i	$-0.737503\pi$
$113$	0.590052	−	0.590052i	0.0555074	−	0.0555074i	0.734316	+	0.678808i	$0.237503\pi$
$114$	1.16439	−	0.0231993i	0.109055	−	0.00217282i
$115$	−0.402959	+	5.77818i	−0.0375762	+	0.538818i
$116$	12.9822	−	0.517522i	1.20537	−	0.0480507i
$117$	−9.29821	−	9.29821i	−0.859620	−	0.859620i
$118$	0.283268	−	0.294785i	0.0260769	−	0.0271372i
$119$	−2.38694			−0.218810
$120$	−3.71898	+	3.64635i	−0.339495	+	0.332865i
$121$	−11.4423			−1.04021
$122$	−4.54387	+	4.72861i	−0.411383	+	0.428109i
$123$	3.89229	+	3.89229i	0.350956	+	0.350956i
$124$	−2.76479	+	0.110216i	−0.248286	+	0.00989766i
$125$	−9.37319	+	6.09453i	−0.838364	+	0.545111i
$126$	4.51708	−	0.0899986i	0.402413	−	0.00801772i
$127$	11.1270	−	11.1270i	0.987362	−	0.987362i	−0.0125590	−	0.999921i	$-0.503998\pi$
$127$	11.1270	−	11.1270i	0.987362	−	0.987362i	0.999921	+	0.0125590i	$0.00399777\pi$
$128$	9.03433	+	6.81035i	0.798529	+	0.601956i
$129$		−	5.50403i		−	0.484603i
$130$	13.2775	−	12.0191i	1.16451	−	1.05415i
$131$		−	4.56983i		−	0.399268i	−0.979871	−	0.199634i	$-0.936025\pi$
$131$		−	4.56983i		−	0.399268i	0.979871	−	0.199634i	$-0.0639753\pi$
$132$	5.73257	+	5.29305i	0.498956	+	0.460701i
$133$	0.972933	−	0.972933i	0.0843640	−	0.0843640i
$134$	0.127534	+	6.40101i	0.0110173	+	0.552963i
$135$	−9.77600	−	0.681760i	−0.841384	−	0.0586765i
$136$	−0.293071	−	4.89793i	−0.0251306	−	0.419994i
$137$	−7.74801	−	7.74801i	−0.661957	−	0.661957i	0.293884	−	0.955841i	$-0.405052\pi$
$137$	−7.74801	−	7.74801i	−0.661957	−	0.661957i	−0.955841	+	0.293884i	$0.905052\pi$
$138$	−2.17525	−	2.09027i	−0.185170	−	0.177935i
$139$	22.2237			1.88499			0.942493	−	0.334225i	$-0.108475\pi$
$139$	22.2237			1.88499			0.942493	+	0.334225i	$0.108475\pi$
$140$	−0.183235	+	6.15064i	−0.0154862	+	0.519824i
$141$	−7.13695			−0.601040
$142$	15.1175	+	14.5269i	1.26864	+	1.21907i
$143$	−18.9715	−	18.9715i	−1.58648	−	1.58648i
$144$	0.739285	+	9.25786i	0.0616071	+	0.771488i
$145$	−10.9612	+	9.53201i	−0.910275	+	0.791590i
$146$	−0.239461	−	12.0187i	−0.0198180	−	0.994674i
$147$	2.97374	−	2.97374i	0.245270	−	0.245270i
$148$	6.66393	−	7.21729i	0.547772	−	0.593258i
$149$			14.5547i			1.19237i	0.802848	+	0.596184i	$0.203317\pi$
$149$			14.5547i			1.19237i	−0.802848	+	0.596184i	$0.796683\pi$
$150$	0.693217	−	5.78168i	0.0566010	−	0.472072i
$151$		−	19.5609i		−	1.59185i	−0.605397	−	0.795924i	$-0.706986\pi$
$151$		−	19.5609i		−	1.59185i	0.605397	−	0.795924i	$-0.293014\pi$
$152$	2.11589	+	1.87697i	0.171621	+	0.152243i
$153$	2.84813	−	2.84813i	0.230257	−	0.230257i
$154$	9.21639	−	0.183628i	0.742678	−	0.0147972i
$155$	2.33438	−	2.03001i	0.187502	−	0.163055i
$156$	0.371551	+	9.32046i	0.0297479	+	0.746234i
$157$	14.4333	+	14.4333i	1.15190	+	1.15190i	0.986170	+	0.165734i	$0.0529994\pi$
$157$	14.4333	+	14.4333i	1.15190	+	1.15190i	0.165734	+	0.986170i	$0.447001\pi$
$158$	−5.13743	+	5.34630i	−0.408712	+	0.425329i
$159$	−4.25089			−0.337117
$160$	−12.6434	+	0.379187i	−0.999551	+	0.0299774i
$161$	−3.56416			−0.280896
$162$	−3.28887	+	3.42259i	−0.258398	+	0.268904i
$163$	13.5096	+	13.5096i	1.05816	+	1.05816i	0.998201	+	0.0599555i	$0.0190959\pi$
$163$	13.5096	+	13.5096i	1.05816	+	1.05816i	0.0599555	+	0.998201i	$0.480904\pi$
$164$	0.532498	+	13.3579i	0.0415811	+	1.04307i
$165$	−8.70230	−	0.606882i	−0.677473	−	0.0472457i
$166$	8.83869	−	0.176103i	0.686016	−	0.0136682i
$167$	−11.5480	+	11.5480i	−0.893610	+	0.893610i	−0.994861	−	0.101251i	$-0.967715\pi$
$167$	−11.5480	+	11.5480i	−0.893610	+	0.893610i	0.101251	+	0.994861i	$0.467715\pi$
$168$	−2.39750	−	2.12679i	−0.184971	−	0.164085i
$169$		−	19.0751i		−	1.46731i
$170$	3.68156	+	4.06701i	0.282363	+	0.311926i
$171$			2.32183i			0.177555i
$172$	9.06808	−	9.82107i	0.691434	−	0.748850i
$173$	−10.8497	+	10.8497i	−0.824885	+	0.824885i	−0.986804	−	0.161919i	$-0.948232\pi$
$173$	−10.8497	+	10.8497i	−0.824885	+	0.824885i	0.161919	+	0.986804i	$0.448232\pi$
$174$	−0.150709	−	7.56415i	−0.0114252	−	0.573437i
$175$	−4.14236	−	5.49280i	−0.313133	−	0.415216i
$176$	1.50840	+	18.8892i	0.113700	+	1.42383i
$177$	−0.168336	−	0.168336i	−0.0126529	−	0.0126529i
$178$	−8.85040	−	8.50462i	−0.663366	−	0.637448i
$179$	4.60249			0.344006			0.172003	−	0.985096i	$-0.444976\pi$
$179$	4.60249			0.344006			0.172003	+	0.985096i	$0.444976\pi$
$180$	−7.12038	−	7.55766i	−0.530722	−	0.563315i
$181$	−14.0226			−1.04229			−0.521147	−	0.853467i	$-0.674496\pi$
$181$	−14.0226			−1.04229			−0.521147	+	0.853467i	$0.674496\pi$
$182$	7.94627	+	7.63581i	0.589017	+	0.566004i
$183$	2.70026	+	2.70026i	0.199609	+	0.199609i
$184$	−0.437611	−	7.31356i	−0.0322611	−	0.539163i
$185$	−0.764063	+	10.9562i	−0.0561750	+	0.805514i
$186$	0.0320962	+	1.61092i	0.00235341	+	0.118119i
$187$	5.81116	−	5.81116i	0.424954	−	0.424954i
$188$	−12.7348	−	11.7584i	−0.928778	−	0.857567i
$189$		−	6.03014i		−	0.438628i
$190$	−3.15837	−	0.157113i	−0.229132	−	0.0113982i
$191$			1.33503i			0.0965990i	0.998833	+	0.0482995i	$0.0153802\pi$
$191$			1.33503i			0.0965990i	−0.998833	+	0.0482995i	$0.984620\pi$
$192$	4.06974	−	5.18073i	0.293708	−	0.373887i
$193$	10.3291	−	10.3291i	0.743504	−	0.743504i	−0.229747	−	0.973250i	$-0.573790\pi$
$193$	10.3291	−	10.3291i	0.743504	−	0.743504i	0.973250	+	0.229747i	$0.0737897\pi$
$194$	−6.28518	+	0.125227i	−0.451250	+	0.00899074i
$195$	−6.84343	−	7.86948i	−0.490068	−	0.563545i
$196$	10.2055	−	0.406832i	0.728964	−	0.0290594i
$197$	−1.41685	−	1.41685i	−0.100947	−	0.100947i	0.654830	−	0.755776i	$-0.272740\pi$
$197$	−1.41685	−	1.41685i	−0.100947	−	0.100947i	−0.755776	+	0.654830i	$0.772740\pi$
$198$	−10.7780	+	11.2162i	−0.765960	+	0.797102i
$199$	−15.2147			−1.07854			−0.539270	−	0.842133i	$-0.681300\pi$
$199$	−15.2147			−1.07854			−0.539270	+	0.842133i	$0.681300\pi$
$200$	10.7625	−	9.17440i	0.761020	−	0.648728i
$201$	3.72811			0.262960
$202$	−0.963106	+	1.00226i	−0.0677639	+	0.0705191i
$203$	−6.32042	−	6.32042i	−0.443606	−	0.443606i
$204$	−2.85494	+	0.113809i	−0.199886	+	0.00796825i
$205$	−9.80784	−	11.2784i	−0.685009	−	0.787714i
$206$	10.4149	−	0.207508i	0.725644	−	0.0144578i
$207$	4.25281	−	4.25281i	0.295591	−	0.295591i
$208$	−14.6928	+	17.2430i	−1.01876	+	1.19559i
$209$			4.73734i			0.327688i
$210$	3.57874	+	0.178024i	0.246956	+	0.0122848i
$211$		−	9.35082i		−	0.643737i	−0.946784	−	0.321868i	$-0.895689\pi$
$211$		−	9.35082i		−	0.643737i	0.946784	−	0.321868i	$-0.104311\pi$
$212$	−7.58503	−	7.00348i	−0.520942	−	0.481001i
$213$	8.63283	−	8.63283i	0.591512	−	0.591512i
$214$	0.559302	+	28.0716i	0.0382331	+	1.91894i
$215$	−1.03971	+	14.9088i	−0.0709079	+	1.01677i
$216$	12.3737	−	0.740386i	0.841922	−	0.0503769i
$217$	1.34605	+	1.34605i	0.0913757	+	0.0913757i
$218$	−13.3419	−	12.8207i	−0.903629	−	0.868325i
$219$	−6.99998			−0.473015
$220$	−14.5280	−	15.4202i	−0.979479	−	1.03963i
$221$	9.82488			0.660893
$222$	−4.12456	−	3.96342i	−0.276823	−	0.266007i
$223$	−17.7719	−	17.7719i	−1.19010	−	1.19010i	−0.977040	−	0.213058i	$-0.931658\pi$
$223$	−17.7719	−	17.7719i	−1.19010	−	1.19010i	−0.213058	−	0.977040i	$-0.568342\pi$
$224$	−0.774008	−	7.74488i	−0.0517156	−	0.517477i
$225$	11.4968	+	1.61136i	0.766452	+	0.107424i
$226$	−0.0235078	−	1.17987i	−0.00156372	−	0.0784838i
$227$	−6.78822	+	6.78822i	−0.450550	+	0.450550i	−0.895537	−	0.444987i	$-0.853208\pi$
$227$	−6.78822	+	6.78822i	−0.450550	+	0.450550i	0.444987	+	0.895537i	$0.353208\pi$
$228$	1.11730	−	1.21008i	0.0739953	−	0.0801397i
$229$		−	22.4951i		−	1.48652i	−0.669004	−	0.743259i	$-0.733279\pi$
$229$		−	22.4951i		−	1.48652i	0.669004	−	0.743259i	$-0.266721\pi$
$230$	5.49729	+	6.07284i	0.362480	+	0.400431i
$231$		−	5.36785i		−	0.353179i
$232$	12.1933	−	13.7453i	0.800528	−	0.902425i
$233$	−19.3466	+	19.3466i	−1.26744	+	1.26744i	−0.320030	+	0.947407i	$0.603693\pi$
$233$	−19.3466	+	19.3466i	−1.26744	+	1.26744i	−0.947407	+	0.320030i	$0.896307\pi$
$234$	−18.5927	+	0.370443i	−1.21545	+	0.0242166i
$235$	19.3319	+	1.34817i	1.26108	+	0.0879451i
$236$	−0.0230298	−	0.577709i	−0.00149911	−	0.0376057i
$237$	3.05299	+	3.05299i	0.198313	+	0.198313i
$238$	−2.33892	+	2.43401i	−0.151610	+	0.157774i
$239$	25.6419			1.65864			0.829320	−	0.558774i	$-0.188728\pi$
$239$	25.6419			1.65864			0.829320	+	0.558774i	$0.188728\pi$
$240$	0.0741008	+	7.36532i	0.00478319	+	0.475429i
$241$	−1.95779			−0.126112			−0.0630561	−	0.998010i	$-0.520085\pi$
$241$	−1.95779			−0.126112			−0.0630561	+	0.998010i	$0.520085\pi$
$242$	−11.2121	+	11.6680i	−0.720744	+	0.750048i
$243$	11.2513	+	11.2513i	0.721772	+	0.721772i
$244$	0.369418	+	9.26696i	0.0236496	+	0.593256i
$245$	−8.61674	+	7.49326i	−0.550503	+	0.478727i
$246$	7.78304	−	0.155070i	0.496228	−	0.00988689i
$247$	−4.00469	+	4.00469i	−0.254812	+	0.254812i
$248$	−2.59678	+	2.92732i	−0.164896	+	0.185885i
$249$		−	5.14787i		−	0.326233i
$250$	−2.96989	+	15.5300i	−0.187832	+	0.982201i
$251$			3.53141i			0.222900i	0.993770	+	0.111450i	$0.0355496\pi$
$251$			3.53141i			0.222900i	−0.993770	+	0.111450i	$0.964450\pi$
$252$	4.33443	−	4.69435i	0.273043	−	0.295716i
$253$	8.67719	−	8.67719i	0.545530	−	0.545530i
$254$	−0.443303	−	22.2496i	−0.0278153	−	1.39606i
$255$	2.41049	−	2.09621i	0.150951	−	0.131270i
$256$	15.7972	−	2.53916i	0.987327	−	0.158698i
$257$	−1.61975	−	1.61975i	−0.101037	−	0.101037i	0.654781	−	0.755819i	$-0.272761\pi$
$257$	−1.61975	−	1.61975i	−0.101037	−	0.101037i	−0.755819	+	0.654781i	$0.772761\pi$
$258$	−5.61258	−	5.39330i	−0.349424	−	0.335772i
$259$	−6.75811			−0.419929
$260$	0.754215	−	25.3166i	0.0467744	−	1.57007i
$261$	15.0832			0.933627
$262$	−4.65996	−	4.47789i	−0.287893	−	0.276645i
$263$	−11.7656	−	11.7656i	−0.725497	−	0.725497i	0.244222	−	0.969719i	$-0.421467\pi$
$263$	−11.7656	−	11.7656i	−0.725497	−	0.725497i	−0.969719	+	0.244222i	$0.921467\pi$
$264$	11.0147	−	0.659070i	0.677906	−	0.0405629i
$265$	11.5144	+	0.802994i	0.707326	+	0.0493275i
$266$	−0.0387619	−	1.94548i	−0.00237664	−	0.119285i
$267$	−5.05400	+	5.05400i	−0.309300	+	0.309300i
$268$	6.65222	+	6.14218i	0.406349	+	0.375194i
$269$		−	5.80800i		−	0.354120i	−0.984200	−	0.177060i	$-0.943341\pi$
$269$		−	5.80800i		−	0.354120i	0.984200	−	0.177060i	$-0.0566587\pi$
$270$	−10.2745	+	9.30076i	−0.625288	+	0.566026i
$271$		−	15.9470i		−	0.968709i	−0.874872	−	0.484354i	$-0.839055\pi$
$271$		−	15.9470i		−	0.968709i	0.874872	−	0.484354i	$-0.160945\pi$
$272$	−5.28170	−	4.50054i	−0.320250	−	0.272885i
$273$	4.53769	−	4.53769i	0.274634	−	0.274634i
$274$	−15.4930	+	0.308683i	−0.935963	+	0.0186482i
$275$	23.4574	+	3.28774i	1.41453	+	0.198258i
$276$	−4.26298	+	0.169940i	−0.256601	+	0.0102292i
$277$	14.1246	+	14.1246i	0.848667	+	0.848667i	0.989967	−	0.141300i	$-0.0451282\pi$
$277$	14.1246	+	14.1246i	0.848667	+	0.848667i	−0.141300	+	0.989967i	$0.545128\pi$
$278$	21.7766	−	22.6620i	1.30607	−	1.35917i
$279$	−3.21224			−0.192312
$280$	6.09239	+	6.21375i	0.364090	+	0.371342i
$281$	−31.6384			−1.88739			−0.943693	−	0.330821i	$-0.892674\pi$
$281$	−31.6384			−1.88739			−0.943693	+	0.330821i	$0.892674\pi$
$282$	−6.99336	+	7.27770i	−0.416449	+	0.433381i
$283$	3.72139	+	3.72139i	0.221214	+	0.221214i	0.809009	−	0.587796i	$-0.200004\pi$
$283$	3.72139	+	3.72139i	0.221214	+	0.221214i	−0.587796	+	0.809009i	$0.700004\pi$
$284$	29.6268	−	1.18104i	1.75803	−	0.0700820i
$285$	−0.128106	+	1.83696i	−0.00758836	+	0.108812i
$286$	−37.9356	+	0.755831i	−2.24318	+	0.0446933i
$287$	6.50331	−	6.50331i	0.383878	−	0.383878i
$288$	10.1649	+	8.31774i	0.598970	+	0.490127i
$289$		−	13.9905i		−	0.822973i
$290$	−1.02064	+	20.5176i	−0.0599343	+	1.20483i
$291$			3.66065i			0.214591i
$292$	−12.4904	−	11.5327i	−0.730943	−	0.674901i
$293$	−6.12424	+	6.12424i	−0.357782	+	0.357782i	−0.862995	−	0.505213i	$-0.831414\pi$
$293$	−6.12424	+	6.12424i	−0.357782	+	0.357782i	0.505213	+	0.862995i	$0.331414\pi$
$294$	−0.118475	−	5.94630i	−0.00690957	−	0.346795i
$295$	0.424176	+	0.487773i	0.0246965	+	0.0283993i
$296$	−0.829767	−	13.8674i	−0.0482292	−	0.806029i
$297$	14.6808	+	14.6808i	0.851865	+	0.851865i
$298$	14.8417	+	14.2619i	0.859759	+	0.826169i
$299$	14.6705			0.848414
$300$	−5.21644	−	6.37225i	−0.301171	−	0.367902i
$301$	−9.19624			−0.530062
$302$	−19.9467	−	19.1674i	−1.14781	−	1.10296i
$303$	0.572340	+	0.572340i	0.0328801	+	0.0328801i
$304$	3.98731	−	0.318406i	0.228688	−	0.0182618i
$305$	−6.80415	−	7.82431i	−0.389605	−	0.448019i
$306$	−0.113470	−	5.69512i	−0.00648666	−	0.325569i
$307$	−4.24256	+	4.24256i	−0.242136	+	0.242136i	−0.817733	−	0.575597i	$-0.804770\pi$
$307$	−4.24256	+	4.24256i	−0.242136	+	0.242136i	0.575597	+	0.817733i	$0.304770\pi$
$308$	8.84372	−	9.57809i	0.503918	−	0.545762i
$309$		−	6.06592i		−	0.345078i
$310$	0.217365	−	4.36959i	0.0123455	−	0.248176i
$311$		−	3.28417i		−	0.186228i	−0.995655	−	0.0931141i	$-0.970318\pi$
$311$		−	3.28417i		−	0.186228i	0.995655	−	0.0931141i	$-0.0296821\pi$
$312$	9.86835	+	8.75407i	0.558686	+	0.495602i
$313$	−2.98777	+	2.98777i	−0.168879	+	0.168879i	−0.786486	−	0.617608i	$-0.788102\pi$
$313$	−2.98777	+	2.98777i	−0.168879	+	0.168879i	0.617608	+	0.786486i	$0.288102\pi$
$314$	28.8609	−	0.575027i	1.62872	−	0.0324507i
$315$	−0.496970	+	7.12624i	−0.0280011	+	0.401518i
$316$	0.417675	+	10.4775i	0.0234960	+	0.589405i
$317$	−5.46173	−	5.46173i	−0.306761	−	0.306761i	0.536891	−	0.843652i	$-0.319599\pi$
$317$	−5.46173	−	5.46173i	−0.306761	−	0.306761i	−0.843652	+	0.536891i	$0.819599\pi$
$318$	−4.16536	+	4.33472i	−0.233582	+	0.243079i
$319$	30.7749			1.72306
$320$	−12.0024	+	13.2643i	−0.670954	+	0.741499i
$321$	16.3496			0.912546
$322$	−3.49246	+	3.63446i	−0.194627	+	0.202540i
$323$	−1.22667	−	1.22667i	−0.0682539	−	0.0682539i
$324$	0.267387	+	6.70747i	0.0148548	+	0.372637i
$325$	17.0503	+	22.6089i	0.945783	+	1.25412i
$326$	27.0139	−	0.538228i	1.49616	−	0.0298097i
$327$	−7.61887	+	7.61887i	−0.421324	+	0.421324i
$328$	14.1431	+	12.5461i	0.780921	+	0.692743i
$329$			11.9245i			0.657422i
$330$	−9.14608	+	8.27925i	−0.503475	+	0.455758i
$331$			27.0645i			1.48760i	0.668403	+	0.743799i	$0.266978\pi$
$331$			27.0645i			1.48760i	−0.668403	+	0.743799i	$0.733022\pi$
$332$	8.48130	−	9.18557i	0.465472	−	0.504124i
$333$	8.06387	−	8.06387i	0.441897	−	0.441897i
$334$	0.460075	+	23.0914i	0.0251742	+	1.26350i
$335$	−10.0984	−	0.704241i	−0.551733	−	0.0384768i
$336$	−4.51800	+	0.360784i	−0.246477	+	0.0196824i
$337$	−7.05018	−	7.05018i	−0.384048	−	0.384048i	0.488510	−	0.872558i	$-0.337541\pi$
$337$	−7.05018	−	7.05018i	−0.384048	−	0.384048i	−0.872558	+	0.488510i	$0.837541\pi$
$338$	−19.4512	−	18.6913i	−1.05801	−	1.01667i
$339$	−0.687185			−0.0373228
$340$	7.75472	+	0.231023i	0.420559	+	0.0125290i
$341$	−6.55408			−0.354923
$342$	2.36762	+	2.27512i	0.128026	+	0.123024i
$343$	−11.7791	−	11.7791i	−0.636012	−	0.636012i
$344$	−1.12912	−	18.8704i	−0.0608782	−	1.01742i
$345$	3.59934	−	3.13004i	0.193782	−	0.168516i
$346$	0.432254	+	21.6950i	0.0232381	+	1.16633i
$347$	−6.37184	+	6.37184i	−0.342058	+	0.342058i	−0.857141	−	0.515083i	$-0.827761\pi$
$347$	−6.37184	+	6.37184i	−0.342058	+	0.342058i	0.515083	+	0.857141i	$0.327761\pi$
$348$	−7.86100	−	7.25829i	−0.421394	−	0.389085i
$349$		−	2.28416i		−	0.122268i	−0.998130	−	0.0611342i	$-0.980528\pi$
$349$		−	2.28416i		−	0.122268i	0.998130	−	0.0611342i	$-0.0194718\pi$
$350$	−9.66014	−	1.15824i	−0.516356	−	0.0619106i
$351$			24.8207i			1.32483i
$352$	20.7398	+	16.9710i	1.10543	+	0.904560i
$353$	17.1646	−	17.1646i	0.913578	−	0.913578i	−0.0829741	−	0.996552i	$-0.526442\pi$
$353$	17.1646	−	17.1646i	0.913578	−	0.913578i	0.996552	+	0.0829741i	$0.0264419\pi$
$354$	−0.336606	+	0.00670656i	−0.0178904	+	0.000356450i
$355$	−25.0146	+	21.7531i	−1.32764	+	1.15454i
$356$	−17.3447	+	0.691429i	−0.919267	+	0.0366456i
$357$	1.38994	+	1.38994i	0.0735633	+	0.0735633i
$358$	4.50989	−	4.69325i	0.238355	−	0.248046i
$359$	−28.3972			−1.49875			−0.749373	−	0.662148i	$-0.769645\pi$
$359$	−28.3972			−1.49875			−0.749373	+	0.662148i	$0.769645\pi$
$360$	−14.6838	−	0.144802i	−0.773906	−	0.00763175i
$361$	1.00000			0.0526316
$362$	−13.7405	+	14.2992i	−0.722186	+	0.751548i
$363$	6.66298	+	6.66298i	0.349716	+	0.349716i
$364$	15.5728	−	0.620794i	0.816237	−	0.0325385i
$365$	18.9609	+	1.32230i	0.992461	+	0.0692123i
$366$	5.39945	−	0.107579i	0.282234	−	0.00562325i
$367$	1.41139	−	1.41139i	0.0736740	−	0.0736740i	−0.669310	−	0.742984i	$-0.733410\pi$
$367$	1.41139	−	1.41139i	0.0736740	−	0.0736740i	0.742984	+	0.669310i	$0.233410\pi$
$368$	−7.88660	−	6.72018i	−0.411118	−	0.350314i
$369$			15.5197i			0.807922i
$370$	10.4236	+	11.5149i	0.541895	+	0.598631i
$371$			7.10246i			0.368741i
$372$	1.67414	+	1.54578i	0.0868003	+	0.0801452i
$373$	10.2157	−	10.2157i	0.528949	−	0.528949i	−0.391310	−	0.920259i	$-0.627978\pi$
$373$	10.2157	−	10.2157i	0.528949	−	0.528949i	0.920259	+	0.391310i	$0.127978\pi$
$374$	−0.231518	−	11.6200i	−0.0119715	−	0.600856i
$375$	9.00700	+	1.90919i	0.465119	+	0.0985903i
$376$	−24.4688	+	1.46411i	−1.26188	+	0.0755055i
$377$	26.0155	+	26.0155i	1.33986	+	1.33986i
$378$	−6.14907	−	5.90883i	−0.316274	−	0.303917i
$379$	−16.8864			−0.867397			−0.433699	−	0.901058i	$-0.642792\pi$
$379$	−16.8864			−0.867397			−0.433699	+	0.901058i	$0.642792\pi$
$380$	−3.25504	+	3.06671i	−0.166980	+	0.157319i
$381$	−12.9587			−0.663895
$382$	1.36135	+	1.30817i	0.0696529	+	0.0669316i
$383$	−6.02950	−	6.02950i	−0.308093	−	0.308093i	0.536076	−	0.844169i	$-0.319906\pi$
$383$	−6.02950	−	6.02950i	−0.308093	−	0.308093i	−0.844169	+	0.536076i	$0.819906\pi$
$384$	−1.29504	−	9.22650i	−0.0660874	−	0.470838i
$385$	−1.01399	+	14.5400i	−0.0516777	+	0.741025i
$386$	−0.411513	−	20.6541i	−0.0209455	−	1.05126i
$387$	10.9731	−	10.9731i	0.557792	−	0.557792i
$388$	−6.03104	+	6.53185i	−0.306180	+	0.331604i
$389$			33.3599i			1.69141i	0.533647	+	0.845707i	$0.320821\pi$
$389$			33.3599i			1.69141i	−0.533647	+	0.845707i	$0.679179\pi$
$390$	−14.7304	−	0.732764i	−0.745905	−	0.0371049i
$391$			4.49369i			0.227256i
$392$	9.58532	−	10.8054i	0.484132	−	0.545756i
$393$	−2.66105	+	2.66105i	−0.134232	+	0.134232i
$394$	−2.83314	+	0.0564477i	−0.142732	+	0.00284380i
$395$	−7.69296	−	8.84639i	−0.387075	−	0.445110i
$396$	0.876256	+	21.9811i	0.0440335	+	1.10459i
$397$	−12.0949	−	12.0949i	−0.607027	−	0.607027i	0.335141	−	0.942168i	$-0.391216\pi$
$397$	−12.0949	−	12.0949i	−0.607027	−	0.607027i	−0.942168	+	0.335141i	$0.891216\pi$
$398$	−14.9086	+	15.5147i	−0.747299	+	0.777683i
$399$	−1.13310			−0.0567257
$400$	1.19059	−	19.9645i	0.0595297	−	0.998227i
$401$	−8.90471			−0.444680			−0.222340	−	0.974969i	$-0.571369\pi$
$401$	−8.90471			−0.444680			−0.222340	+	0.974969i	$0.571369\pi$
$402$	3.65310	−	3.80163i	0.182200	−	0.189608i
$403$	−5.54046	−	5.54046i	−0.275990	−	0.275990i
$404$	0.0783009	+	1.96420i	0.00389561	+	0.0977226i
$405$	−4.92488	−	5.66328i	−0.244719	−	0.281410i
$406$	−12.6383	+	0.251807i	−0.627229	+	0.0124970i
$407$	16.4531	−	16.4531i	0.815548	−	0.815548i
$408$	−2.68145	+	3.02277i	−0.132752	+	0.149649i
$409$			13.2705i			0.656186i	0.944645	+	0.328093i	$0.106406\pi$
$409$			13.2705i			0.656186i	−0.944645	+	0.328093i	$0.893594\pi$
$410$	−21.1113	−	1.05018i	−1.04261	−	0.0518646i
$411$			9.02348i			0.445095i
$412$	9.99381	−	10.8237i	0.492360	−	0.533244i
$413$	−0.281259	+	0.281259i	−0.0138399	+	0.0138399i
$414$	−0.169433	−	8.50393i	−0.00832718	−	0.417945i
$415$	−0.972435	+	13.9441i	−0.0477350	+	0.684489i
$416$	3.18589	+	31.8787i	0.156201	+	1.56298i
$417$	−12.9410	−	12.9410i	−0.633726	−	0.633726i
$418$	4.83076	+	4.64203i	0.236280	+	0.227049i
$419$	11.4136			0.557592			0.278796	−	0.960350i	$-0.410065\pi$
$419$	11.4136			0.557592			0.278796	+	0.960350i	$0.410065\pi$
$420$	3.68827	−	3.47487i	0.179969	−	0.169556i
$421$	16.0960			0.784472			0.392236	−	0.919865i	$-0.371702\pi$
$421$	16.0960			0.784472			0.392236	+	0.919865i	$0.371702\pi$
$422$	−9.53523	−	9.16269i	−0.464168	−	0.446033i
$423$	−14.2285	−	14.2285i	−0.691814	−	0.691814i
$424$	−14.5740	+	0.872046i	−0.707778	+	0.0423503i
$425$	−6.92531	+	5.22268i	−0.335927	+	0.253337i
$426$	−0.343934	−	17.2622i	−0.0166637	−	0.836358i
$427$	4.51165	−	4.51165i	0.218334	−	0.218334i
$428$	29.1733	+	26.9365i	1.41014	+	1.30203i
$429$			22.0946i			1.06674i
$430$	14.1841	+	15.6691i	0.684016	+	0.755631i
$431$		−	16.7831i		−	0.808415i	−0.914667	−	0.404208i	$-0.867547\pi$
$431$		−	16.7831i		−	0.808415i	0.914667	−	0.404208i	$-0.132453\pi$
$432$	11.3697	−	13.3432i	0.547027	−	0.641975i
$433$	−0.362193	+	0.362193i	−0.0174059	+	0.0174059i	−0.715756	−	0.698350i	$-0.753918\pi$
$433$	−0.362193	+	0.362193i	−0.0174059	+	0.0174059i	0.698350	+	0.715756i	$0.253918\pi$
$434$	2.69156	−	0.0536269i	0.129199	−	0.00257417i
$435$	11.9334	+	0.832210i	0.572161	+	0.0399014i
$436$	−26.1470	+	1.04232i	−1.25221	+	0.0499183i
$437$	−1.83166	−	1.83166i	−0.0876202	−	0.0876202i
$438$	−6.85915	+	7.13803i	−0.327743	+	0.341068i
$439$	15.6404			0.746477			0.373239	−	0.927735i	$-0.378247\pi$
$439$	15.6404			0.746477			0.373239	+	0.927735i	$0.378247\pi$
$440$	−29.9601	−	0.295446i	−1.42829	−	0.0140848i
$441$	11.8571			0.564626
$442$	9.62722	−	10.0186i	0.457920	−	0.476538i
$443$	15.7362	+	15.7362i	0.747651	+	0.747651i	0.974037	−	0.226387i	$-0.0726913\pi$
$443$	15.7362	+	15.7362i	0.747651	+	0.747651i	−0.226387	+	0.974037i	$0.572691\pi$
$444$	−8.08317	+	0.322227i	−0.383610	+	0.0152922i
$445$	14.6445	−	12.7351i	0.694217	−	0.603703i
$446$	−35.5368	+	0.708039i	−1.68272	+	0.0335266i
$447$	8.47534	−	8.47534i	0.400870	−	0.400870i
$448$	−8.65606	−	6.79979i	−0.408960	−	0.321260i
$449$			36.0983i			1.70359i	0.523878	+	0.851793i	$0.324485\pi$
$449$			36.0983i			1.70359i	−0.523878	+	0.851793i	$0.675515\pi$
$450$	12.9086	−	10.1446i	0.608519	−	0.478220i
$451$			31.6655i			1.49107i
$452$	−1.22617	−	1.13216i	−0.0576744	−	0.0532524i
$453$	−11.3905	+	11.3905i	−0.535173	+	0.535173i
$454$	0.270445	+	13.5738i	0.0126926	+	0.637048i
$455$	−13.1485	+	11.4341i	−0.616410	+	0.536041i
$456$	−0.139122	−	2.32508i	−0.00651501	−	0.108882i
$457$	24.9941	+	24.9941i	1.16918	+	1.16918i	0.982403	+	0.186773i	$0.0598028\pi$
$457$	24.9941	+	24.9941i	1.16918	+	1.16918i	0.186773	+	0.982403i	$0.440197\pi$
$458$	−22.9387	−	22.0425i	−1.07186	−	1.02998i
$459$	−7.60280			−0.354868
$460$	11.5793	+	0.344962i	0.539888	+	0.0160839i
$461$	33.6026			1.56503			0.782514	−	0.622633i	$-0.213937\pi$
$461$	33.6026			1.56503			0.782514	+	0.622633i	$0.213937\pi$
$462$	−5.47372	−	5.25986i	−0.254660	−	0.244711i
$463$	18.6594	+	18.6594i	0.867175	+	0.867175i	0.992159	−	0.124983i	$-0.0398878\pi$
$463$	18.6594	+	18.6594i	0.867175	+	0.867175i	−0.124983	+	0.992159i	$0.539888\pi$
$464$	−2.06844	−	25.9025i	−0.0960251	−	1.20250i
$465$	−2.54143	−	0.177234i	−0.117856	−	0.00821904i
$466$	0.770773	+	38.6855i	0.0357054	+	1.79207i
$467$	3.14547	−	3.14547i	0.145555	−	0.145555i	−0.630574	−	0.776129i	$-0.717181\pi$
$467$	3.14547	−	3.14547i	0.145555	−	0.145555i	0.776129	+	0.630574i	$0.217181\pi$
$468$	−17.8409	+	19.3224i	−0.824697	+	0.893179i
$469$		−	6.22899i		−	0.287628i
$470$	20.3178	−	18.3922i	0.937189	−	0.848367i
$471$		−	16.8093i		−	0.774532i
$472$	−0.611669	−	0.542603i	−0.0281544	−	0.0249753i
$473$	22.3888	−	22.3888i	1.02944	−	1.02944i
$474$	6.10477	−	0.121632i	0.280401	−	0.00558674i
$475$	0.694006	−	4.95160i	0.0318432	−	0.227195i
$476$	0.190155	+	4.77009i	0.00871574	+	0.218637i
$477$	−8.47474	−	8.47474i	−0.388032	−	0.388032i
$478$	25.1261	−	26.1477i	1.14924	−	1.19597i
$479$	34.5022			1.57645			0.788223	−	0.615389i	$-0.211001\pi$
$479$	34.5022			1.57645			0.788223	+	0.615389i	$0.211001\pi$
$480$	7.58319	+	7.14158i	0.346124	+	0.325967i
$481$	27.8171			1.26835
$482$	−1.91840	+	1.99640i	−0.0873808	+	0.0909335i
$483$	2.07545	+	2.07545i	0.0944361	+	0.0944361i
$484$	0.911551	+	22.8665i	0.0414341	+	1.03939i
$485$	0.691498	−	9.91564i	0.0313993	−	0.450246i
$486$	22.4982	−	0.448255i	1.02054	−	0.0203333i
$487$	14.8873	−	14.8873i	0.674607	−	0.674607i	−0.284167	−	0.958775i	$-0.591717\pi$
$487$	14.8873	−	14.8873i	0.674607	−	0.674607i	0.958775	+	0.284167i	$0.0917171\pi$
$488$	9.81171	+	8.70382i	0.444155	+	0.394003i
$489$		−	15.7336i		−	0.711497i
$490$	−0.802344	+	16.1292i	−0.0362462	+	0.728642i
$491$		−	14.7286i		−	0.664692i	−0.943158	−	0.332346i	$-0.892160\pi$
$491$		−	14.7286i		−	0.664692i	0.943158	−	0.332346i	$-0.107840\pi$
$492$	7.46832	−	8.08848i	0.336698	−	0.364657i
$493$	−7.96877	+	7.96877i	−0.358895	+	0.358895i
$494$	0.159548	+	8.00779i	0.00717840	+	0.360287i
$495$	−16.1394	−	18.5592i	−0.725411	−	0.834173i
$496$	0.440513	+	5.51642i	0.0197796	+	0.247694i
$497$	−14.4239	−	14.4239i	−0.647000	−	0.647000i
$498$	−5.24940	−	5.04431i	−0.235231	−	0.226041i
$499$	−32.1745			−1.44033			−0.720165	−	0.693803i	$-0.755934\pi$
$499$	−32.1745			−1.44033			−0.720165	+	0.693803i	$0.755934\pi$
$500$	12.9261	+	18.2460i	0.578073	+	0.815985i
$501$	13.4490			0.600857
$502$	3.60105	+	3.46036i	0.160723	+	0.154443i
$503$	−14.5815	−	14.5815i	−0.650157	−	0.650157i	0.302874	−	0.953031i	$-0.402054\pi$
$503$	−14.5815	−	14.5815i	−0.650157	−	0.650157i	−0.953031	+	0.302874i	$0.902054\pi$
$504$	−0.539706	−	9.01982i	−0.0240404	−	0.401775i
$505$	−1.44219	−	1.65842i	−0.0641766	−	0.0737987i
$506$	−0.345701	−	17.3509i	−0.0153683	−	0.771343i
$507$	−11.1076	+	11.1076i	−0.493305	+	0.493305i
$508$	−23.1228	−	21.3499i	−1.02591	−	0.947250i
$509$		−	30.8387i		−	1.36690i	−0.729996	−	0.683452i	$-0.760478\pi$
$509$		−	30.8387i		−	1.36690i	0.729996	−	0.683452i	$-0.239522\pi$
$510$	0.224452	−	4.51207i	0.00993891	−	0.199798i
$511$			11.6957i			0.517387i
$512$	12.8902	−	18.5969i	0.569671	−	0.821873i
$513$	3.09895	−	3.09895i	0.136822	−	0.136822i
$514$	−3.23886	+	0.0645314i	−0.142860	+	0.00284636i
$515$	−1.14586	+	16.4308i	−0.0504924	+	0.724029i
$516$	−10.9993	+	0.438477i	−0.484218	+	0.0193029i
$517$	−29.0311	−	29.0311i	−1.27679	−	1.27679i
$518$	−6.62215	+	6.89140i	−0.290961	+	0.302791i
$519$	12.6357			0.554647
$520$	−25.0769	−	25.5764i	−1.09969	−	1.12160i
$521$	−15.7674			−0.690782			−0.345391	−	0.938459i	$-0.612254\pi$
$521$	−15.7674			−0.690782			−0.345391	+	0.938459i	$0.612254\pi$
$522$	14.7797	−	15.3807i	0.646892	−	0.673193i
$523$	−24.2821	−	24.2821i	−1.06178	−	1.06178i	−0.997961	−	0.0638230i	$-0.979671\pi$
$523$	−24.2821	−	24.2821i	−1.06178	−	1.06178i	−0.0638230	−	0.997961i	$-0.520329\pi$
$524$	−9.13241	+	0.364054i	−0.398951	+	0.0159038i
$525$	−0.786375	+	5.61064i	−0.0343202	+	0.244868i
$526$	−23.5265	+	0.468744i	−1.02580	+	0.0204382i
$527$	1.69709	−	1.69709i	0.0739266	−	0.0739266i
$528$	10.1210	−	11.8777i	0.440460	−	0.516911i
$529$		−	16.2900i		−	0.708263i
$530$	12.1016	−	10.9547i	0.525660	−	0.475840i
$531$		−	0.671205i		−	0.0291278i
$532$	−2.02183	−	1.86681i	−0.0876575	−	0.0809366i
$533$	−26.7683	+	26.7683i	−1.15946	+	1.15946i
$534$	0.201353	+	10.1060i	0.00871338	+	0.437329i
$535$	−44.2864	−	3.08845i	−1.91467	−	0.133525i
$536$	12.7817	−	0.764801i	0.552086	−	0.0330344i
$537$	−2.68007	−	2.68007i	−0.115654	−	0.115654i
$538$	−5.92255	−	5.69115i	−0.255339	−	0.245363i
$539$	24.1926			1.04205
$540$	−0.583635	+	19.5908i	−0.0251156	+	0.843054i
$541$	−13.1301			−0.564506			−0.282253	−	0.959340i	$-0.591082\pi$
$541$	−13.1301			−0.564506			−0.282253	+	0.959340i	$0.591082\pi$
$542$	−16.2615	−	15.6261i	−0.698490	−	0.671200i
$543$	8.16551	+	8.16551i	0.350415	+	0.350415i
$544$	−9.76474	+	0.975868i	−0.418660	+	0.0418400i
$545$	22.0765	−	19.1981i	0.945655	−	0.822357i
$546$	−0.180783	−	9.07359i	−0.00773680	−	0.388314i
$547$	6.67431	−	6.67431i	0.285373	−	0.285373i	−0.549875	−	0.835247i	$-0.685324\pi$
$547$	6.67431	−	6.67431i	0.285373	−	0.285373i	0.835247	+	0.549875i	$0.185324\pi$
$548$	−14.8665	+	16.1010i	−0.635065	+	0.687799i
$549$			10.7667i			0.459512i
$550$	26.3380	−	20.6984i	1.12306	−	0.882584i
$551$		−	6.49625i		−	0.276750i
$552$	−4.00393	+	4.51358i	−0.170418	+	0.192111i
$553$	5.10100	−	5.10100i	0.216916	−	0.216916i
$554$	28.2437	−	0.562729i	1.19996	−	0.0239081i
$555$	6.82480	−	5.93496i	0.289697	−	0.251925i
$556$	−1.77044	−	44.4121i	−0.0750835	−	1.88349i
$557$	−10.5667	−	10.5667i	−0.447725	−	0.447725i	0.446873	−	0.894598i	$-0.352538\pi$
$557$	−10.5667	−	10.5667i	−0.447725	−	0.447725i	−0.894598	+	0.446873i	$0.852538\pi$
$558$	−3.14762	+	3.27559i	−0.133249	+	0.138667i
$559$	37.8526			1.60100
$560$	12.3061	−	0.123809i	0.520028	−	0.00523189i
$561$	−6.76778			−0.285736
$562$	−31.0019	+	32.2623i	−1.30773	+	1.36090i
$563$	−18.7352	−	18.7352i	−0.789595	−	0.789595i	0.191833	−	0.981428i	$-0.438557\pi$
$563$	−18.7352	−	18.7352i	−0.789595	−	0.789595i	−0.981428	+	0.191833i	$0.938557\pi$
$564$	0.568563	+	14.2626i	0.0239408	+	0.600563i
$565$	1.86139	+	0.129810i	0.0783091	+	0.00546113i
$566$	7.44130	−	0.148261i	0.312781	−	0.00623188i
$567$	3.26555	−	3.26555i	0.137140	−	0.137140i
$568$	27.8264	−	31.3684i	1.16757	−	1.31619i
$569$			33.1004i			1.38764i	0.720147	+	0.693821i	$0.244074\pi$
$569$			33.1004i			1.38764i	−0.720147	+	0.693821i	$0.755926\pi$
$570$	1.74766	+	1.93064i	0.0732015	+	0.0808655i
$571$		−	17.4026i		−	0.728277i	−0.931345	−	0.364138i	$-0.881364\pi$
$571$		−	17.4026i		−	0.728277i	0.931345	−	0.364138i	$-0.118636\pi$
$572$	−36.4016	+	39.4243i	−1.52203	+	1.64841i
$573$	0.777397	−	0.777397i	0.0324762	−	0.0324762i
$574$	−0.259094	−	13.0040i	−0.0108144	−	0.542778i
$575$	−10.3408	+	7.79847i	−0.431243	+	0.325219i
$576$	18.4421	−	2.21492i	0.768422	−	0.0922884i
$577$	4.50750	+	4.50750i	0.187650	+	0.187650i	0.794679	−	0.607030i	$-0.207639\pi$
$577$	4.50750	+	4.50750i	0.187650	+	0.187650i	−0.607030	+	0.794679i	$0.707639\pi$
$578$	−14.2665	−	13.7091i	−0.593407	−	0.570223i
$579$	−12.0294			−0.499927
$580$	19.9221	+	21.1456i	0.827220	+	0.878022i
$581$	−8.60116			−0.356836
$582$	3.73284	+	3.58700i	0.154731	+	0.148686i
$583$	−17.2914	−	17.2914i	−0.716136	−	0.716136i
$584$	−23.9992	+	1.43601i	−0.993095	+	0.0594224i
$585$	2.04558	−	29.3323i	0.0845742	−	1.21274i
$586$	0.243991	+	12.2461i	0.0100792	+	0.505880i
$587$	6.94211	−	6.94211i	0.286531	−	0.286531i	−0.549176	−	0.835707i	$-0.685058\pi$
$587$	6.94211	−	6.94211i	0.286531	−	0.286531i	0.835707	+	0.549176i	$0.185058\pi$
$588$	−6.17966	−	5.70585i	−0.254845	−	0.235305i
$589$			1.38349i			0.0570059i
$590$	0.913035	+	0.0454188i	0.0375891	+	0.00186986i
$591$			1.65009i			0.0678757i
$592$	−14.9540	−	12.7423i	−0.614606	−	0.523706i
$593$	−6.95256	+	6.95256i	−0.285507	+	0.285507i	−0.835301	−	0.549793i	$-0.814706\pi$
$593$	−6.95256	+	6.95256i	−0.285507	+	0.285507i	0.549793	+	0.835301i	$0.314706\pi$
$594$	29.3557	−	0.584886i	1.20448	−	0.0239982i
$595$	−3.50238	−	4.02750i	−0.143584	−	0.165111i
$596$	29.0863	−	1.15950i	1.19142	−	0.0474948i
$597$	8.85964	+	8.85964i	0.362601	+	0.362601i
$598$	14.3753	−	14.9598i	0.587850	−	0.611751i
$599$	−41.8628			−1.71047			−0.855233	−	0.518243i	$-0.826586\pi$
$599$	−41.8628			−1.71047			−0.855233	+	0.518243i	$0.826586\pi$
$600$	−11.6094	−	0.924738i	−0.473952	−	0.0377523i
$601$	9.08392			0.370541			0.185270	−	0.982688i	$-0.440684\pi$
$601$	9.08392			0.370541			0.185270	+	0.982688i	$0.440684\pi$
$602$	−9.01122	+	9.37760i	−0.367270	+	0.382203i
$603$	7.43251	+	7.43251i	0.302675	+	0.302675i
$604$	−39.0909	+	1.55832i	−1.59058	+	0.0634070i
$605$	−16.7895	−	19.3067i	−0.682589	−	0.784931i
$606$	1.14445	−	0.0228022i	0.0464902	−	0.000926275i
$607$	4.79286	−	4.79286i	0.194536	−	0.194536i	−0.603117	−	0.797653i	$-0.706075\pi$
$607$	4.79286	−	4.79286i	0.194536	−	0.194536i	0.797653	+	0.603117i	$0.206075\pi$
$608$	3.58240	−	4.37794i	0.145286	−	0.177549i
$609$			7.36087i			0.298278i
$610$	−14.6459	−	0.728558i	−0.592994	−	0.0294984i
$611$		−	49.0826i		−	1.98567i
$612$	−5.91863	−	5.46484i	−0.239246	−	0.220903i
$613$	−17.4802	+	17.4802i	−0.706018	+	0.706018i	−0.965696	−	0.259677i	$-0.916384\pi$
$613$	−17.4802	+	17.4802i	−0.706018	+	0.706018i	0.259677	+	0.965696i	$0.416384\pi$
$614$	0.169025	+	8.48344i	0.00682128	+	0.342364i
$615$	−0.856292	+	12.2787i	−0.0345290	+	0.495124i
$616$	−1.10119	−	18.4035i	−0.0443680	−	0.741499i
$617$	5.32574	+	5.32574i	0.214406	+	0.214406i	0.806136	−	0.591730i	$-0.201555\pi$
$617$	5.32574	+	5.32574i	0.214406	+	0.214406i	−0.591730	+	0.806136i	$0.701555\pi$
$618$	−6.18555	−	5.94388i	−0.248819	−	0.239098i
$619$	−4.51100			−0.181312			−0.0906562	−	0.995882i	$-0.528896\pi$
$619$	−4.51100			−0.181312			−0.0906562	+	0.995882i	$0.528896\pi$
$620$	−4.24277	−	4.50333i	−0.170394	−	0.180858i
$621$	−11.3525			−0.455558
$622$	−3.34894	−	3.21810i	−0.134280	−	0.129034i
$623$	8.44431	+	8.44431i	0.338314	+	0.338314i
$624$	18.5965	−	1.48502i	0.744457	−	0.0594485i
$625$	−24.0367	−	6.87288i	−0.961468	−	0.274915i
$626$	0.119033	+	5.97435i	0.00475753	+	0.238783i
$627$	2.75859	−	2.75859i	0.110168	−	0.110168i
$628$	27.6939	−	29.9936i	1.10511	−	1.19687i
$629$			8.52062i			0.339739i
$630$	6.77981	+	7.48964i	0.270114	+	0.298394i
$631$		−	5.20294i		−	0.207126i	−0.994623	−	0.103563i	$-0.966976\pi$
$631$		−	5.20294i		−	0.207126i	0.994623	−	0.103563i	$-0.0330243\pi$
$632$	11.0934	+	9.84078i	0.441271	+	0.391445i
$633$	−5.44507	+	5.44507i	−0.216422	+	0.216422i
$634$	−10.9213	+	0.217597i	−0.433740	+	0.00864186i
$635$	35.1014	+	2.44791i	1.39296	+	0.0971422i
$636$	0.338646	+	8.49502i	0.0134282	+	0.336850i
$637$	20.4512	+	20.4512i	0.810304	+	0.810304i
$638$	30.1558	−	31.3818i	1.19388	−	1.24242i
$639$	34.4216			1.36170
$640$	1.76501	+	25.2366i	0.0697681	+	0.997563i
$641$	−3.06495			−0.121058			−0.0605290	−	0.998166i	$-0.519279\pi$
$641$	−3.06495			−0.121058			−0.0605290	+	0.998166i	$0.519279\pi$
$642$	16.0207	−	16.6721i	0.632286	−	0.657993i
$643$	14.6071	+	14.6071i	0.576047	+	0.576047i	0.933812	−	0.357764i	$-0.116461\pi$
$643$	14.6071	+	14.6071i	0.576047	+	0.576047i	−0.357764	+	0.933812i	$0.616461\pi$
$644$	0.283938	+	7.12267i	0.0111887	+	0.280673i
$645$	9.28699	−	8.07612i	0.365675	−	0.317997i
$646$	−2.45286	+	0.0488710i	−0.0965064	+	0.00192280i
$647$	−0.586994	+	0.586994i	−0.0230771	+	0.0230771i	−0.718551	−	0.695474i	$-0.755194\pi$
$647$	−0.586994	+	0.586994i	−0.0230771	+	0.0230771i	0.695474	+	0.718551i	$0.255194\pi$
$648$	7.10176	+	6.29987i	0.278984	+	0.247482i
$649$		−	1.36949i		−	0.0537571i
$650$	39.7621	+	4.76743i	1.55960	+	0.186994i
$651$		−	1.56763i		−	0.0614403i
$652$	25.9216	−	28.0741i	1.01517	−	1.09947i
$653$	−3.62988	+	3.62988i	−0.142048	+	0.142048i	−0.774555	−	0.632507i	$-0.782026\pi$
$653$	−3.62988	+	3.62988i	−0.142048	+	0.142048i	0.632507	+	0.774555i	$0.282026\pi$
$654$	0.303538	+	15.2347i	0.0118693	+	0.595724i
$655$	7.71070	−	6.70536i	0.301282	−	0.262000i
$656$	26.6521	−	2.12830i	1.04059	−	0.0830962i
$657$	−13.9555	−	13.9555i	−0.544454	−	0.544454i
$658$	12.1597	+	11.6846i	0.474035	+	0.455515i
$659$	−33.1760			−1.29235			−0.646177	−	0.763188i	$-0.723633\pi$
$659$	−33.1760			−1.29235			−0.646177	+	0.763188i	$0.723633\pi$
$660$	−0.519534	+	17.4391i	−0.0202228	+	0.678818i
$661$	14.2978			0.556121			0.278060	−	0.960564i	$-0.410308\pi$
$661$	14.2978			0.556121			0.278060	+	0.960564i	$0.410308\pi$
$662$	27.5982	+	26.5200i	1.07264	+	1.03073i
$663$	−5.72112	−	5.72112i	−0.222190	−	0.222190i
$664$	−1.05606	−	17.6493i	−0.0409830	−	0.684927i
$665$	3.06923	+	0.214042i	0.119020	+	0.00830020i
$666$	−0.321267	−	16.1245i	−0.0124488	−	0.624813i
$667$	−11.8989	+	11.8989i	−0.460728	+	0.460728i
$668$	23.9976	+	22.1577i	0.928495	+	0.857306i
$669$			20.6975i			0.800213i
$670$	−10.6133	+	9.60746i	−0.410029	+	0.371168i
$671$			21.9678i			0.848057i
$672$	−4.05920	+	4.96063i	−0.156587	+	0.191360i
$673$	−11.6828	+	11.6828i	−0.450341	+	0.450341i	−0.895468	−	0.445127i	$-0.853159\pi$
$673$	−11.6828	+	11.6828i	−0.450341	+	0.450341i	0.445127	+	0.895468i	$0.353159\pi$
$674$	−14.0976	+	0.280881i	−0.543018	+	0.0108191i
$675$	−13.1941	−	17.4955i	−0.507840	−	0.673401i
$676$	−38.1198	+	1.51961i	−1.46615	+	0.0584465i
$677$	−27.7047	−	27.7047i	−1.06478	−	1.06478i	−0.997751	−	0.0670286i	$-0.978648\pi$
$677$	−27.7047	−	27.7047i	−1.06478	−	1.06478i	−0.0670286	−	0.997751i	$-0.521352\pi$
$678$	−0.673360	+	0.700738i	−0.0258602	+	0.0269117i
$679$	6.11628			0.234721
$680$	7.83428	−	7.68128i	0.300431	−	0.294564i
$681$	7.90569			0.302947
$682$	−6.42222	+	6.68333i	−0.245919	+	0.255918i
$683$	17.0782	+	17.0782i	0.653480	+	0.653480i	0.953829	−	0.300349i	$-0.0971032\pi$
$683$	17.0782	+	17.0782i	0.653480	+	0.653480i	−0.300349	+	0.953829i	$0.597103\pi$
$684$	4.63998	−	0.184968i	0.177414	−	0.00707243i
$685$	1.70454	−	24.4420i	0.0651271	−	0.933881i
$686$	−23.5535	+	0.469283i	−0.899278	+	0.0179173i
$687$	−13.0991	+	13.0991i	−0.499762	+	0.499762i
$688$	−20.3490	−	17.3394i	−0.775797	−	0.661057i
$689$		−	29.2344i		−	1.11374i
$690$	0.335151	−	6.73739i	0.0127590	−	0.256488i
$691$			40.9903i			1.55934i	0.626188	+	0.779672i	$0.284614\pi$
$691$			40.9903i			1.55934i	−0.626188	+	0.779672i	$0.715386\pi$
$692$	22.5465	+	20.8178i	0.857088	+	0.791373i
$693$	10.7016	−	10.7016i	0.406519	−	0.406519i
$694$	0.253856	+	12.7411i	0.00963623	+	0.483647i
$695$	32.6090	+	37.4981i	1.23693	+	1.42239i
$696$	−15.1043	+	0.903774i	−0.572527	+	0.0342575i
$697$	−8.19937	−	8.19937i	−0.310573	−	0.310573i
$698$	−2.32921	−	2.23821i	−0.0881619	−	0.0847175i
$699$	22.5314			0.852216
$700$	−10.6469	+	8.71572i	−0.402414	+	0.329423i
$701$	−14.1506			−0.534461			−0.267231	−	0.963633i	$-0.586109\pi$
$701$	−14.1506			−0.534461			−0.267231	+	0.963633i	$0.586109\pi$
$702$	25.3102	+	24.3213i	0.955271	+	0.917949i
$703$	−3.47306	−	3.47306i	−0.130989	−	0.130989i
$704$	37.6283	−	4.51920i	1.41817	−	0.170324i
$705$	−10.4721	−	12.0422i	−0.394403	−	0.453536i
$706$	−0.683841	−	34.3223i	−0.0257367	−	1.29174i
$707$	0.956277	−	0.956277i	0.0359645	−	0.0359645i
$708$	−0.322995	+	0.349816i	−0.0121389	+	0.0131469i
$709$			12.9874i			0.487753i	0.969806	+	0.243877i	$0.0784192\pi$
$709$			12.9874i			0.487753i	−0.969806	+	0.243877i	$0.921581\pi$
$710$	−2.32922	+	46.8234i	−0.0874143	+	1.75725i
$711$			12.1731i			0.456529i
$712$	−16.2907	+	18.3643i	−0.610519	+	0.688230i
$713$	2.53409	−	2.53409i	0.0949025	−	0.0949025i
$714$	2.77932	−	0.0553755i	0.104014	−	0.00207237i
$715$	4.17368	−	59.8480i	0.156087	−	2.23819i
$716$	−0.366656	−	9.19766i	−0.0137026	−	0.343733i
$717$	−14.9315	−	14.9315i	−0.557629	−	0.557629i
$718$	−27.8259	+	28.9572i	−1.03845	+	1.08067i
$719$	−45.7262			−1.70530			−0.852649	−	0.522484i	$-0.825005\pi$
$719$	−45.7262			−1.70530			−0.852649	+	0.522484i	$0.825005\pi$
$720$	−14.5361	+	14.8315i	−0.541728	+	0.552739i
$721$	−10.1351			−0.377449
$722$	0.979881	−	1.01972i	0.0364674	−	0.0379501i
$723$	1.14004	+	1.14004i	0.0423985	+	0.0423985i
$724$	1.11711	+	28.0230i	0.0415170	+	1.04147i
$725$	−32.1668	−	4.50843i	−1.19465	−	0.167439i
$726$	13.3233	−	0.265455i	0.494475	−	0.00985196i
$727$	−19.0449	+	19.0449i	−0.706336	+	0.706336i	−0.965763	−	0.259427i	$-0.916466\pi$
$727$	−19.0449	+	19.0449i	−0.706336	+	0.706336i	0.259427	+	0.965763i	$0.416466\pi$
$728$	14.6265	−	16.4882i	0.542093	−	0.611094i
$729$		−	3.03429i		−	0.112381i
$730$	19.9279	−	18.0392i	0.737563	−	0.667660i
$731$			11.5946i			0.428842i
$732$	5.18112	−	5.61135i	0.191500	−	0.207402i
$733$	−31.4767	+	31.4767i	−1.16262	+	1.16262i	−0.178718	+	0.983900i	$0.557195\pi$
$733$	−31.4767	+	31.4767i	−1.16262	+	1.16262i	−0.983900	+	0.178718i	$0.942805\pi$
$734$	−0.0562302	−	2.82222i	−0.00207549	−	0.104170i
$735$	9.38100	+	0.654213i	0.346023	+	0.0241310i
$736$	−14.5806	+	1.45716i	−0.537450	+	0.0537116i
$737$	15.1649	+	15.1649i	0.558606	+	0.558606i
$738$	15.8257	+	15.2074i	0.582554	+	0.559793i
$739$	−53.0093			−1.94998			−0.974989	−	0.222254i	$-0.928658\pi$
$739$	−53.0093			−1.94998			−0.974989	+	0.222254i	$0.928658\pi$
$740$	21.9558	+	0.654092i	0.807113	+	0.0240449i
$741$	4.66393			0.171334
$742$	7.24253	+	6.95957i	0.265882	+	0.255494i
$743$	18.7441	+	18.7441i	0.687655	+	0.687655i	0.961713	−	0.274058i	$-0.0883661\pi$
$743$	18.7441	+	18.7441i	0.687655	+	0.687655i	−0.274058	+	0.961713i	$0.588366\pi$
$744$	3.21673	−	0.192475i	0.117931	−	0.00705648i
$745$	−24.5582	+	21.3563i	−0.899744	+	0.782433i
$746$	−0.406996	−	20.4273i	−0.0149012	−	0.747898i
$747$	10.2630	−	10.2630i	0.375504	−	0.375504i
$748$	−12.0760	−	11.1501i	−0.441544	−	0.407690i
$749$		−	27.3172i		−	0.998150i
$750$	10.7726	−	7.31385i	0.393361	−	0.267064i
$751$			12.1326i			0.442724i	0.975192	+	0.221362i	$0.0710502\pi$
$751$			12.1326i			0.442724i	−0.975192	+	0.221362i	$0.928950\pi$
$752$	−22.4836	+	26.3860i	−0.819891	+	0.962200i
$753$	2.05637	−	2.05637i	0.0749383	−	0.0749383i
$754$	52.0206	−	1.03646i	1.89448	−	0.0377457i
$755$	33.0053	−	28.7020i	1.20119	−	1.04457i
$756$	−12.0507	+	0.480390i	−0.438280	+	0.0174716i
$757$	−13.7820	−	13.7820i	−0.500914	−	0.500914i	0.410808	−	0.911722i	$-0.365247\pi$
$757$	−13.7820	−	13.7820i	−0.500914	−	0.500914i	−0.911722	+	0.410808i	$0.865247\pi$
$758$	−16.5467	+	17.2195i	−0.601003	+	0.625439i
$759$	−10.1056			−0.366810
$760$	−0.0623655	+	6.32425i	−0.00226223	+	0.229405i
$761$	6.65971			0.241414			0.120707	−	0.992688i	$-0.461484\pi$
$761$	6.65971			0.241414			0.120707	+	0.992688i	$0.461484\pi$
$762$	−12.6980	+	13.2143i	−0.460000	+	0.478703i
$763$	12.7297	+	12.7297i	0.460848	+	0.460848i
$764$	2.66793	−	0.106354i	0.0965224	−	0.00384777i
$765$	8.98475	+	0.626579i	0.324844	+	0.0226540i
$766$	−12.0566	+	0.240217i	−0.435623	+	0.00867938i
$767$	1.15769	−	1.15769i	0.0418018	−	0.0418018i
$768$	−10.6775	−	7.72030i	−0.385289	−	0.278582i
$769$		−	39.7893i		−	1.43484i	−0.696641	−	0.717420i	$-0.745323\pi$
$769$		−	39.7893i		−	1.43484i	0.696641	−	0.717420i	$-0.254677\pi$
$770$	13.8331	+	15.2814i	0.498512	+	0.550705i
$771$

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.979881 - 1.01972i) q^{2} +(-0.582309 - 0.582309i) q^{3} +(-0.0796647 - 1.99841i) q^{4} +(1.46731 + 1.68731i) q^{5} +(-1.16439 + 0.0231993i) q^{6} +(-0.972933 + 0.972933i) q^{7} +(-2.11589 - 1.87697i) q^{8} -2.32183i q^{9} +O(q^{10})\)	\(q+(0.979881 - 1.01972i) q^{2} +(-0.582309 - 0.582309i) q^{3} +(-0.0796647 - 1.99841i) q^{4} +(1.46731 + 1.68731i) q^{5} +(-1.16439 + 0.0231993i) q^{6} +(-0.972933 + 0.972933i) q^{7} +(-2.11589 - 1.87697i) q^{8} -2.32183i q^{9} +(3.15837 + 0.157113i) q^{10} -4.73734i q^{11} +(-1.11730 + 1.21008i) q^{12} +(4.00469 - 4.00469i) q^{13} +(0.0387619 + 1.94548i) q^{14} +(0.128106 - 1.83696i) q^{15} +(-3.98731 + 0.318406i) q^{16} +(1.22667 + 1.22667i) q^{17} +(-2.36762 - 2.27512i) q^{18} -1.00000 q^{19} +(3.25504 - 3.06671i) q^{20} +1.13310 q^{21} +(-4.83076 - 4.64203i) q^{22} +(1.83166 + 1.83166i) q^{23} +(0.139122 + 2.32508i) q^{24} +(-0.694006 + 4.95160i) q^{25} +(-0.159548 - 8.00779i) q^{26} +(-3.09895 + 3.09895i) q^{27} +(2.02183 + 1.86681i) q^{28} +6.49625i q^{29} +(-1.74766 - 1.93064i) q^{30} -1.38349i q^{31} +(-3.58240 + 4.37794i) q^{32} +(-2.75859 + 2.75859i) q^{33} +(2.45286 - 0.0488710i) q^{34} +(-3.06923 - 0.214042i) q^{35} +(-4.63998 + 0.184968i) q^{36} +(3.47306 + 3.47306i) q^{37} +(-0.979881 + 1.01972i) q^{38} -4.66393 q^{39} +(0.0623655 - 6.32425i) q^{40} -6.68423 q^{41} +(1.11030 - 1.15544i) q^{42} +(4.72604 + 4.72604i) q^{43} +(-9.46715 + 0.377398i) q^{44} +(3.91764 - 3.40685i) q^{45} +(3.66259 - 0.0729738i) q^{46} +(6.12814 - 6.12814i) q^{47} +(2.50726 + 2.13643i) q^{48} +5.10680i q^{49} +(4.36921 + 5.55967i) q^{50} -1.42861i q^{51} +(-8.32205 - 7.68399i) q^{52} +(3.65002 - 3.65002i) q^{53} +(0.123463 + 6.19667i) q^{54} +(7.99334 - 6.95114i) q^{55} +(3.88478 - 0.232448i) q^{56} +(0.582309 + 0.582309i) q^{57} +(6.62437 + 6.36555i) q^{58} +0.289084 q^{59} +(-3.68121 - 0.109668i) q^{60} -4.63716 q^{61} +(-1.41078 - 1.35566i) q^{62} +(2.25899 + 2.25899i) q^{63} +(0.953954 + 7.94292i) q^{64} +(12.6333 + 0.881019i) q^{65} +(0.109903 + 5.51609i) q^{66} +(-3.20114 + 3.20114i) q^{67} +(2.35368 - 2.54912i) q^{68} -2.13318i q^{69} +(-3.22574 + 2.92002i) q^{70} +14.8252i q^{71} +(-4.35801 + 4.91273i) q^{72} +(6.01054 - 6.01054i) q^{73} +(6.94475 - 0.138368i) q^{74} +(3.28749 - 2.47924i) q^{75} +(0.0796647 + 1.99841i) q^{76} +(4.60911 + 4.60911i) q^{77} +(-4.57010 + 4.75591i) q^{78} -5.24290 q^{79} +(-6.38786 - 6.26061i) q^{80} -3.35640 q^{81} +(-6.54976 + 6.81606i) q^{82} +(4.42022 + 4.42022i) q^{83} +(-0.0902677 - 2.26439i) q^{84} +(-0.269864 + 3.86968i) q^{85} +(9.45020 - 0.188287i) q^{86} +(3.78283 - 3.78283i) q^{87} +(-8.89184 + 10.0237i) q^{88} -8.67923i q^{89} +(0.364790 - 7.33321i) q^{90} +7.79259i q^{91} +(3.51449 - 3.80633i) q^{92} +(-0.805621 + 0.805621i) q^{93} +(-0.244147 - 12.2539i) q^{94} +(-1.46731 - 1.68731i) q^{95} +(4.63538 - 0.463251i) q^{96} +(-3.14322 - 3.14322i) q^{97} +(5.20752 + 5.00406i) q^{98} -10.9993 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) \) 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) \) 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

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