LMFDB - Embedded newform 380.2.k.d.343.20

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			343.20
Character	$\chi$	$=$	380.343
Dual form			380.2.k.d.267.20

$q$-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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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	−0.854934	−	0.518737i	$-0.826402\pi$
$3$	−0.582309	+	0.582309i	−0.336196	+	0.336196i	0.518737	+	0.854934i	$0.326402\pi$
$4$	−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	0.498916	−	0.866650i	$-0.333732\pi$
$7$	−0.972933	−	0.972933i	−0.367734	−	0.367734i	−0.866650	+	0.498916i	$0.833732\pi$
$8$	−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	$0.253200\pi$
$11$			4.73734i			1.42836i	−0.699962	+	0.714180i	$0.746800\pi$
$12$	−1.11730	−	1.21008i	−0.322538	−	0.349321i
$13$	4.00469	+	4.00469i	1.11070	+	1.11070i	0.993056	+	0.117645i	$0.0375345\pi$
$13$	4.00469	+	4.00469i	1.11070	+	1.11070i	0.117645	+	0.993056i	$0.462466\pi$
$14$	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	−0.542527	−	0.840039i	$-0.682532\pi$
$17$	1.22667	−	1.22667i	0.297512	−	0.297512i	0.840039	+	0.542527i	$0.182532\pi$
$18$	−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	−0.489869	−	0.871796i	$-0.662955\pi$
$23$	1.83166	−	1.83166i	0.381928	−	0.381928i	0.871796	+	0.489869i	$0.162955\pi$
$24$	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	$-0.793907\pi$
$29$		−	6.49625i		−	1.20632i	0.797619	−	0.603162i	$-0.206093\pi$
$30$	−1.74766	+	1.93064i	−0.319078	+	0.352485i
$31$			1.38349i			0.248483i	0.992252	+	0.124241i	$0.0396497\pi$
$31$			1.38349i			0.248483i	−0.992252	+	0.124241i	$0.960350\pi$
$32$	−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	−0.361431	−	0.932399i	$-0.617712\pi$
$37$	3.47306	−	3.47306i	0.570968	−	0.570968i	0.932399	+	0.361431i	$0.117712\pi$
$38$	−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	−0.248037	−	0.968751i	$-0.579785\pi$
$43$	4.72604	−	4.72604i	0.720714	−	0.720714i	0.968751	+	0.248037i	$0.0797853\pi$
$44$	−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	0.994886	−	0.101004i	$-0.0322056\pi$
$47$	6.12814	+	6.12814i	0.893882	+	0.893882i	−0.101004	+	0.994886i	$0.532206\pi$
$48$	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	0.911863	−	0.410494i	$-0.134644\pi$
$53$	3.65002	+	3.65002i	0.501369	+	0.501369i	−0.410494	+	0.911863i	$0.634644\pi$
$54$	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	0.483991	−	0.875073i	$-0.339187\pi$
$67$	−3.20114	−	3.20114i	−0.391082	−	0.391082i	−0.875073	+	0.483991i	$0.839187\pi$
$68$	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	$-0.657735\pi$
$71$		−	14.8252i		−	1.75942i	0.475507	−	0.879712i	$-0.342265\pi$
$72$	−4.35801	−	4.91273i	−0.513597	−	0.578971i
$73$	6.01054	+	6.01054i	0.703480	+	0.703480i	0.965156	−	0.261676i	$-0.0842751\pi$
$73$	6.01054	+	6.01054i	0.703480	+	0.703480i	−0.261676	+	0.965156i	$0.584275\pi$
$74$	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	−0.421600	−	0.906782i	$-0.638531\pi$
$83$	4.42022	−	4.42022i	0.485183	−	0.485183i	0.906782	+	0.421600i	$0.138531\pi$
$84$	−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	$0.152150\pi$
$89$			8.67923i			0.919997i	−0.887920	+	0.459998i	$0.847850\pi$
$90$	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	−0.848439	−	0.529294i	$-0.822457\pi$
$97$	−3.14322	+	3.14322i	−0.319145	+	0.319145i	0.529294	+	0.848439i	$0.322457\pi$
$98$	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	−0.402299	−	0.915508i	$-0.631789\pi$
$103$	5.20851	−	5.20851i	0.513209	−	0.513209i	0.915508	+	0.402299i	$0.131789\pi$
$104$	−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	−0.877396	−	0.479767i	$-0.840721\pi$
$107$	−14.0386	−	14.0386i	−1.35716	−	1.35716i	−0.479767	−	0.877396i	$-0.659279\pi$
$108$	6.43986	−	5.94611i	0.619676	−	0.572164i
$109$			13.0839i			1.25321i	0.779337	+	0.626605i	$0.215556\pi$
$109$			13.0839i			1.25321i	−0.779337	+	0.626605i	$0.784444\pi$
$110$	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	0.734316	−	0.678808i	$-0.237503\pi$
$113$	0.590052	+	0.590052i	0.0555074	+	0.0555074i	−0.678808	+	0.734316i	$0.737503\pi$
$114$	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	0.999921	−	0.0125590i	$-0.00399777\pi$
$127$	11.1270	+	11.1270i	0.987362	+	0.987362i	−0.0125590	+	0.999921i	$0.503998\pi$
$128$	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	$0.0639753\pi$
$131$			4.56983i			0.399268i	−0.979871	+	0.199634i	$0.936025\pi$
$132$	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	−0.955841	−	0.293884i	$-0.905052\pi$
$137$	−7.74801	+	7.74801i	−0.661957	+	0.661957i	0.293884	+	0.955841i	$0.405052\pi$
$138$	−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	$-0.796683\pi$
$149$		−	14.5547i		−	1.19237i	0.802848	−	0.596184i	$-0.203317\pi$
$150$	0.693217	+	5.78168i	0.0566010	+	0.472072i
$151$			19.5609i			1.59185i	0.605397	+	0.795924i	$0.293014\pi$
$151$			19.5609i			1.59185i	−0.605397	+	0.795924i	$0.706986\pi$
$152$	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	0.165734	−	0.986170i	$-0.447001\pi$
$157$	14.4333	−	14.4333i	1.15190	−	1.15190i	0.986170	−	0.165734i	$-0.0529994\pi$
$158$	−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	0.0599555	−	0.998201i	$-0.480904\pi$
$163$	13.5096	−	13.5096i	1.05816	−	1.05816i	0.998201	−	0.0599555i	$-0.0190959\pi$
$164$	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	0.101251	−	0.994861i	$-0.467715\pi$
$167$	−11.5480	−	11.5480i	−0.893610	−	0.893610i	−0.994861	+	0.101251i	$0.967715\pi$
$168$	−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	0.161919	−	0.986804i	$-0.448232\pi$
$173$	−10.8497	−	10.8497i	−0.824885	−	0.824885i	−0.986804	+	0.161919i	$0.948232\pi$
$174$	−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	$-0.984620\pi$
$191$		−	1.33503i		−	0.0965990i	0.998833	−	0.0482995i	$-0.0153802\pi$
$192$	4.06974	+	5.18073i	0.293708	+	0.373887i
$193$	10.3291	+	10.3291i	0.743504	+	0.743504i	0.973250	−	0.229747i	$-0.0737897\pi$
$193$	10.3291	+	10.3291i	0.743504	+	0.743504i	−0.229747	+	0.973250i	$0.573790\pi$
$194$	−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	−0.755776	−	0.654830i	$-0.772740\pi$
$197$	−1.41685	+	1.41685i	−0.100947	+	0.100947i	0.654830	+	0.755776i	$0.272740\pi$
$198$	−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	$0.104311\pi$
$211$			9.35082i			0.643737i	−0.946784	+	0.321868i	$0.895689\pi$
$212$	−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	−0.213058	+	0.977040i	$0.568342\pi$
$223$	−17.7719	+	17.7719i	−1.19010	+	1.19010i	−0.977040	+	0.213058i	$0.931658\pi$
$224$	−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	0.444987	−	0.895537i	$-0.353208\pi$
$227$	−6.78822	−	6.78822i	−0.450550	−	0.450550i	−0.895537	+	0.444987i	$0.853208\pi$
$228$	1.11730	+	1.21008i	0.0739953	+	0.0801397i
$229$			22.4951i			1.48652i	0.669004	+	0.743259i	$0.266721\pi$
$229$			22.4951i			1.48652i	−0.669004	+	0.743259i	$0.733279\pi$
$230$	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	−0.947407	−	0.320030i	$-0.896307\pi$
$233$	−19.3466	−	19.3466i	−1.26744	−	1.26744i	−0.320030	−	0.947407i	$-0.603693\pi$
$234$	−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	$-0.964450\pi$
$251$		−	3.53141i		−	0.222900i	0.993770	−	0.111450i	$-0.0355496\pi$
$252$	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	−0.755819	−	0.654781i	$-0.772761\pi$
$257$	−1.61975	+	1.61975i	−0.101037	+	0.101037i	0.654781	+	0.755819i	$0.272761\pi$
$258$	−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	−0.969719	−	0.244222i	$-0.921467\pi$
$263$	−11.7656	+	11.7656i	−0.725497	+	0.725497i	0.244222	+	0.969719i	$0.421467\pi$
$264$	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	$0.0566587\pi$
$269$			5.80800i			0.354120i	−0.984200	+	0.177060i	$0.943341\pi$
$270$	−10.2745	−	9.30076i	−0.625288	−	0.566026i
$271$			15.9470i			0.968709i	0.874872	+	0.484354i	$0.160945\pi$
$271$			15.9470i			0.968709i	−0.874872	+	0.484354i	$0.839055\pi$
$272$	−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	−0.141300	−	0.989967i	$-0.545128\pi$
$277$	14.1246	−	14.1246i	0.848667	−	0.848667i	0.989967	+	0.141300i	$0.0451282\pi$
$278$	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	−0.587796	−	0.809009i	$-0.700004\pi$
$283$	3.72139	−	3.72139i	0.221214	−	0.221214i	0.809009	+	0.587796i	$0.200004\pi$
$284$	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	0.505213	−	0.862995i	$-0.331414\pi$
$293$	−6.12424	−	6.12424i	−0.357782	−	0.357782i	−0.862995	+	0.505213i	$0.831414\pi$
$294$	−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	0.575597	−	0.817733i	$-0.304770\pi$
$307$	−4.24256	−	4.24256i	−0.242136	−	0.242136i	−0.817733	+	0.575597i	$0.804770\pi$
$308$	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	$0.0296821\pi$
$311$			3.28417i			0.186228i	−0.995655	+	0.0931141i	$0.970318\pi$
$312$	9.86835	−	8.75407i	0.558686	−	0.495602i
$313$	−2.98777	−	2.98777i	−0.168879	−	0.168879i	0.617608	−	0.786486i	$-0.288102\pi$
$313$	−2.98777	−	2.98777i	−0.168879	−	0.168879i	−0.786486	+	0.617608i	$0.788102\pi$
$314$	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	−0.843652	−	0.536891i	$-0.819599\pi$
$317$	−5.46173	+	5.46173i	−0.306761	+	0.306761i	0.536891	+	0.843652i	$0.319599\pi$
$318$	−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	$-0.733022\pi$
$331$		−	27.0645i		−	1.48760i	0.668403	−	0.743799i	$-0.266978\pi$
$332$	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	−0.872558	−	0.488510i	$-0.837541\pi$
$337$	−7.05018	+	7.05018i	−0.384048	+	0.384048i	0.488510	+	0.872558i	$0.337541\pi$
$338$	−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	0.515083	−	0.857141i	$-0.327761\pi$
$347$	−6.37184	−	6.37184i	−0.342058	−	0.342058i	−0.857141	+	0.515083i	$0.827761\pi$
$348$	−7.86100	+	7.25829i	−0.421394	+	0.389085i
$349$			2.28416i			0.122268i	0.998130	+	0.0611342i	$0.0194718\pi$
$349$			2.28416i			0.122268i	−0.998130	+	0.0611342i	$0.980528\pi$
$350$	−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	0.996552	−	0.0829741i	$-0.0264419\pi$
$353$	17.1646	+	17.1646i	0.913578	+	0.913578i	−0.0829741	+	0.996552i	$0.526442\pi$
$354$	−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	0.742984	−	0.669310i	$-0.233410\pi$
$367$	1.41139	+	1.41139i	0.0736740	+	0.0736740i	−0.669310	+	0.742984i	$0.733410\pi$
$368$	−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	0.920259	−	0.391310i	$-0.127978\pi$
$373$	10.2157	+	10.2157i	0.528949	+	0.528949i	−0.391310	+	0.920259i	$0.627978\pi$
$374$	−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	−0.844169	−	0.536076i	$-0.819906\pi$
$383$	−6.02950	+	6.02950i	−0.308093	+	0.308093i	0.536076	+	0.844169i	$0.319906\pi$
$384$	−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	$-0.679179\pi$
$389$		−	33.3599i		−	1.69141i	0.533647	−	0.845707i	$-0.320821\pi$
$390$	−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	−0.942168	−	0.335141i	$-0.891216\pi$
$397$	−12.0949	+	12.0949i	−0.607027	+	0.607027i	0.335141	+	0.942168i	$0.391216\pi$
$398$	−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	$-0.893594\pi$
$409$		−	13.2705i		−	0.656186i	0.944645	−	0.328093i	$-0.106406\pi$
$410$	−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	$0.132453\pi$
$431$			16.7831i			0.808415i	−0.914667	+	0.404208i	$0.867547\pi$
$432$	11.3697	+	13.3432i	0.547027	+	0.641975i
$433$	−0.362193	−	0.362193i	−0.0174059	−	0.0174059i	0.698350	−	0.715756i	$-0.253918\pi$
$433$	−0.362193	−	0.362193i	−0.0174059	−	0.0174059i	−0.715756	+	0.698350i	$0.753918\pi$
$434$	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	−0.226387	−	0.974037i	$-0.572691\pi$
$443$	15.7362	−	15.7362i	0.747651	−	0.747651i	0.974037	+	0.226387i	$0.0726913\pi$
$444$	−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	$-0.675515\pi$
$449$		−	36.0983i		−	1.70359i	0.523878	−	0.851793i	$-0.324485\pi$
$450$	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	0.186773	−	0.982403i	$-0.440197\pi$
$457$	24.9941	−	24.9941i	1.16918	−	1.16918i	0.982403	−	0.186773i	$-0.0598028\pi$
$458$	−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	−0.124983	−	0.992159i	$-0.539888\pi$
$463$	18.6594	−	18.6594i	0.867175	−	0.867175i	0.992159	+	0.124983i	$0.0398878\pi$
$464$	−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	0.776129	−	0.630574i	$-0.217181\pi$
$467$	3.14547	+	3.14547i	0.145555	+	0.145555i	−0.630574	+	0.776129i	$0.717181\pi$
$468$	−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	0.958775	−	0.284167i	$-0.0917171\pi$
$487$	14.8873	+	14.8873i	0.674607	+	0.674607i	−0.284167	+	0.958775i	$0.591717\pi$
$488$	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	$0.107840\pi$
$491$			14.7286i			0.664692i	−0.943158	+	0.332346i	$0.892160\pi$
$492$	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	−0.953031	−	0.302874i	$-0.902054\pi$
$503$	−14.5815	+	14.5815i	−0.650157	+	0.650157i	0.302874	+	0.953031i	$0.402054\pi$
$504$	−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	$0.239522\pi$
$509$			30.8387i			1.36690i	−0.729996	+	0.683452i	$0.760478\pi$
$510$	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	−0.0638230	+	0.997961i	$0.520329\pi$
$523$	−24.2821	+	24.2821i	−1.06178	+	1.06178i	−0.997961	+	0.0638230i	$0.979671\pi$
$524$	−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	0.835247	−	0.549875i	$-0.185324\pi$
$547$	6.67431	+	6.67431i	0.285373	+	0.285373i	−0.549875	+	0.835247i	$0.685324\pi$
$548$	−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	−0.894598	−	0.446873i	$-0.852538\pi$
$557$	−10.5667	+	10.5667i	−0.447725	+	0.447725i	0.446873	+	0.894598i	$0.352538\pi$
$558$	−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	−0.981428	−	0.191833i	$-0.938557\pi$
$563$	−18.7352	+	18.7352i	−0.789595	+	0.789595i	0.191833	+	0.981428i	$0.438557\pi$
$564$	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	$-0.755926\pi$
$569$		−	33.1004i		−	1.38764i	0.720147	−	0.693821i	$-0.244074\pi$
$570$	1.74766	−	1.93064i	0.0732015	−	0.0808655i
$571$			17.4026i			0.728277i	0.931345	+	0.364138i	$0.118636\pi$
$571$			17.4026i			0.728277i	−0.931345	+	0.364138i	$0.881364\pi$
$572$	−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	−0.607030	−	0.794679i	$-0.707639\pi$
$577$	4.50750	−	4.50750i	0.187650	−	0.187650i	0.794679	+	0.607030i	$0.207639\pi$
$578$	−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	0.835707	−	0.549176i	$-0.185058\pi$
$587$	6.94211	+	6.94211i	0.286531	+	0.286531i	−0.549176	+	0.835707i	$0.685058\pi$
$588$	−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	0.549793	−	0.835301i	$-0.314706\pi$
$593$	−6.95256	−	6.95256i	−0.285507	−	0.285507i	−0.835301	+	0.549793i	$0.814706\pi$
$594$	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	0.797653	−	0.603117i	$-0.206075\pi$
$607$	4.79286	+	4.79286i	0.194536	+	0.194536i	−0.603117	+	0.797653i	$0.706075\pi$
$608$	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	0.259677	−	0.965696i	$-0.416384\pi$
$613$	−17.4802	−	17.4802i	−0.706018	−	0.706018i	−0.965696	+	0.259677i	$0.916384\pi$
$614$	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	−0.591730	−	0.806136i	$-0.701555\pi$
$617$	5.32574	−	5.32574i	0.214406	−	0.214406i	0.806136	+	0.591730i	$0.201555\pi$
$618$	−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	$0.0330243\pi$
$631$			5.20294i			0.207126i	−0.994623	+	0.103563i	$0.966976\pi$
$632$	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	−0.357764	−	0.933812i	$-0.616461\pi$
$643$	14.6071	−	14.6071i	0.576047	−	0.576047i	0.933812	+	0.357764i	$0.116461\pi$
$644$	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	0.695474	−	0.718551i	$-0.255194\pi$
$647$	−0.586994	−	0.586994i	−0.0230771	−	0.0230771i	−0.718551	+	0.695474i	$0.755194\pi$
$648$	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	0.632507	−	0.774555i	$-0.282026\pi$
$653$	−3.62988	−	3.62988i	−0.142048	−	0.142048i	−0.774555	+	0.632507i	$0.782026\pi$
$654$	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	0.445127	−	0.895468i	$-0.353159\pi$
$673$	−11.6828	−	11.6828i	−0.450341	−	0.450341i	−0.895468	+	0.445127i	$0.853159\pi$
$674$	−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	−0.0670286	+	0.997751i	$0.521352\pi$
$677$	−27.7047	+	27.7047i	−1.06478	+	1.06478i	−0.997751	+	0.0670286i	$0.978648\pi$
$678$	−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	−0.300349	−	0.953829i	$-0.597103\pi$
$683$	17.0782	−	17.0782i	0.653480	−	0.653480i	0.953829	+	0.300349i	$0.0971032\pi$
$684$	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	$-0.715386\pi$
$691$		−	40.9903i		−	1.55934i	0.626188	−	0.779672i	$-0.284614\pi$
$692$	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	$-0.921581\pi$
$709$		−	12.9874i		−	0.487753i	0.969806	−	0.243877i	$-0.0784192\pi$
$710$	−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	0.259427	−	0.965763i	$-0.416466\pi$
$727$	−19.0449	−	19.0449i	−0.706336	−	0.706336i	−0.965763	+	0.259427i	$0.916466\pi$
$728$	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	−0.983900	−	0.178718i	$-0.942805\pi$
$733$	−31.4767	−	31.4767i	−1.16262	−	1.16262i	−0.178718	−	0.983900i	$-0.557195\pi$
$734$	−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	−0.274058	−	0.961713i	$-0.588366\pi$
$743$	18.7441	−	18.7441i	0.687655	−	0.687655i	0.961713	+	0.274058i	$0.0883661\pi$
$744$	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	$-0.928950\pi$
$751$		−	12.1326i		−	0.442724i	0.975192	−	0.221362i	$-0.0710502\pi$
$752$	−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	−0.911722	−	0.410808i	$-0.865247\pi$
$757$	−13.7820	+	13.7820i	−0.500914	+	0.500914i	0.410808	+	0.911722i	$0.365247\pi$
$758$	−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	$0.254677\pi$
$769$			39.7893i			1.43484i	−0.696641	+	0.717420i	$0.745323\pi$
$770$	13.8331	−	15.2814i	0.498512	−	0.550705i
$771$		−	1.88639i		−	0.0679368i
$772$	−21.4646	+	19.8189i	−0.772529	+	0.713298i
$773$	7.50151	+	7.50151i	0.269811	+	0.269811i	0.829024	−	0.559213i	$-0.188897\pi$
$773$	7.50151	+	7.50151i	0.269811	+	0.269811i	−0.559213	+	0.829024i	$0.688897\pi$
$774$	−0.437170	+	21.9418i	−0.0157137	+	0.788681i
$775$	6.85051	−	0.960153i	0.246078	−	0.0344897i
$776$	0.750962	−	12.5504i	0.0269580	−	0.450534i
$777$	3.93531	−	3.93531i	0.141179	−	0.141179i
$778$	34.0178	−	32.6887i	1.21960	−	1.17195i
$779$	6.68423			0.239488
$780$	−15.1813	−	14.3029i	−0.543578	−	0.512127i
$781$	70.2318			2.51309
$782$	4.58232	−	4.40329i	0.163863	−	0.157461i
$783$	−20.1316	+	20.1316i	−0.719443	+	0.719443i
$784$	−1.62604	+	20.3624i	−0.0580727	+	0.727228i
$785$	−3.17529	−	45.5316i	−0.113331	−	1.62509i
$786$	0.106017	−	5.32105i	0.00378150	−	0.189796i
$787$	−23.5343	−	23.5343i	−0.838908	−	0.838908i	0.149807	−	0.988715i	$-0.452135\pi$
$787$	−23.5343	−	23.5343i	−0.838908	−	0.838908i	−0.988715	+	0.149807i	$0.952135\pi$
$788$	−2.71858	−	2.94433i	−0.0968454	−	0.104887i
$789$		−	13.7024i		−	0.487819i
$790$	−16.5590	+	0.823728i	−0.589144	+	0.0293069i
$791$		−	1.14816i		−	0.0408239i
$792$	23.2733	−	20.6454i	0.826980	−	0.733601i
$793$	−18.5704	−	18.5704i	−0.659454	−	0.659454i
$794$	−24.1851	−	0.481865i	−0.858296	−	0.0171008i
$795$	−6.23736	+	7.17255i	−0.221217	+	0.254384i
$796$	1.21207	−	30.4052i	0.0429608	−	1.07768i
$797$	11.1494	−	11.1494i	0.394931	−	0.394931i	−0.481510	−	0.876441i	$-0.659911\pi$
$797$	11.1494	−	11.1494i	0.394931	−	0.394931i	0.876441	+	0.481510i	$0.159911\pi$
$798$	−1.11030	−	1.15544i	−0.0393042	−	0.0409022i
$799$	15.0345			0.531881
$800$	−19.1916	+	20.7769i	−0.678526	+	0.734576i
$801$	−20.1517			−0.712026
$802$	−8.72556	−	9.08033i	−0.308110	−	0.320637i
$803$	−28.4739	+	28.4739i	−1.00482	+	1.00482i
$804$	−0.296999	+	7.45030i	−0.0104743	+	0.262752i
$805$	−5.22973	+	6.01384i	−0.184324	+	0.211960i
$806$	−11.0787	−	0.220734i	−0.390232	−	0.00777501i
$807$	−3.38205	−	3.38205i	−0.119054	−	0.119054i
$808$	2.07966	−	1.84484i	0.0731623	−	0.0649012i
$809$			6.48790i			0.228103i	0.993475	+	0.114051i	$0.0363828\pi$
$809$			6.48790i			0.228103i	−0.993475	+	0.114051i	$0.963617\pi$
$810$	−10.6008	+	0.527334i	−0.372473	+	0.0185286i
$811$			32.9698i			1.15773i	0.815424	+	0.578864i	$0.196504\pi$
$811$			32.9698i			1.15773i	−0.815424	+	0.578864i	$0.803496\pi$
$812$	−12.1273	−	13.1343i	−0.425584	−	0.460924i
$813$	−9.28606	−	9.28606i	−0.325676	−	0.325676i
$814$	−0.655494	+	32.8996i	−0.0229751	+	1.15313i
$815$	−2.97208	−	42.6177i	−0.104107	−	1.49283i
$816$	0.454876	−	5.69629i	0.0159239	−	0.199410i
$817$	−4.72604	+	4.72604i	−0.165343	+	0.165343i
$818$	13.5323	−	13.0036i	0.473145	−	0.454659i
$819$	18.0931			0.632223
$820$	−21.7575	−	20.4986i	−0.759803	−	0.715842i
$821$	16.0339			0.559587			0.279794	−	0.960060i	$-0.409734\pi$
$821$	16.0339			0.559587			0.279794	+	0.960060i	$0.409734\pi$
$822$	9.20144	−	8.84194i	0.320937	−	0.308398i
$823$	24.5540	−	24.5540i	0.855899	−	0.855899i	−0.134953	−	0.990852i	$-0.543088\pi$
$823$	24.5540	−	24.5540i	0.855899	−	0.855899i	0.990852	+	0.134953i	$0.0430884\pi$
$824$	−1.24439	+	20.7968i	−0.0433504	+	0.724492i
$825$	−11.7450	+	15.5739i	−0.408908	+	0.542215i
$826$	0.0112054	−	0.562407i	0.000389887	−	0.0195686i
$827$	5.35688	+	5.35688i	0.186277	+	0.186277i	0.794084	−	0.607808i	$-0.207951\pi$
$827$	5.35688	+	5.35688i	0.186277	+	0.186277i	−0.607808	+	0.794084i	$0.707951\pi$
$828$	−8.83766	+	8.16007i	−0.307130	+	0.283582i
$829$			3.90562i			0.135648i	0.997697	+	0.0678240i	$0.0216056\pi$
$829$			3.90562i			0.135648i	−0.997697	+	0.0678240i	$0.978394\pi$
$830$	13.2662	−	14.6552i	0.460478	−	0.508689i
$831$			16.4498i			0.570637i
$832$	35.6292	−	27.9886i	1.23522	−	0.970331i
$833$	−6.26437	−	6.26437i	−0.217048	−	0.217048i
$834$	−25.8769	−	0.515575i	−0.896045	−	0.0178529i
$835$	−36.4294	+	2.54052i	−1.26069	+	0.0879183i
$836$	9.46715	+	0.377398i	0.327428	+	0.0130526i
$837$	4.28738	−	4.28738i	0.148194	−	0.148194i
$838$	11.1840	+	11.6387i	0.386345	+	0.402053i
$839$	3.17730			0.109692			0.0548462	−	0.998495i	$-0.482533\pi$
$839$	3.17730			0.109692			0.0548462	+	0.998495i	$0.482533\pi$
$840$	0.0706661	+	7.16598i	0.00243821	+	0.247250i
$841$	−13.2013			−0.455216
$842$	15.7722	+	16.4135i	0.543545	+	0.565645i
$843$	18.4233	−	18.4233i	0.634533	−	0.634533i
$844$	−18.6868	−	0.744930i	−0.643226	−	0.0256416i
$845$	32.1855	+	27.9890i	1.10721	+	0.962851i
$846$	−28.4514	−	0.566868i	−0.978179	−	0.0194893i
$847$	11.1326	+	11.1326i	0.382522	+	0.382522i
$848$	−13.3916	−	15.7160i	−0.459869	−	0.539688i
$849$			4.33400i			0.148742i
$850$	−1.46031	−	12.1795i	−0.0500881	−	0.417753i
$851$		−	12.7229i		−	0.436137i
$852$	−17.9397	+	16.5642i	−0.614604	+	0.567481i
$853$	2.55407	+	2.55407i	0.0874497	+	0.0874497i	0.749478	−	0.662029i	$-0.230304\pi$
$853$	2.55407	+	2.55407i	0.0874497	+	0.0874497i	−0.662029	+	0.749478i	$0.730304\pi$
$854$	−0.179745	+	9.02150i	−0.00615075	+	0.308710i
$855$	−3.91764	−	3.40685i	−0.133981	−	0.116512i
$856$	56.0541	+	3.35403i	1.91589	+	0.114639i
$857$	−33.5682	+	33.5682i	−1.14667	+	1.14667i	−0.159465	+	0.987204i	$0.550977\pi$
$857$	−33.5682	+	33.5682i	−1.14667	+	1.14667i	−0.987204	+	0.159465i	$0.949023\pi$
$858$	22.5304	−	21.6501i	0.769174	−	0.739122i
$859$	−39.6086			−1.35143			−0.675714	−	0.737164i	$-0.736165\pi$
$859$	−39.6086			−1.35143			−0.675714	+	0.737164i	$0.736165\pi$
$860$	29.8768	−	0.890069i	1.01879	−	0.0303511i
$861$	−7.57388			−0.258117
$862$	−17.1141	+	16.4455i	−0.582910	+	0.560135i
$863$	−0.501749	+	0.501749i	−0.0170797	+	0.0170797i	−0.715595	−	0.698515i	$-0.753844\pi$
$863$	−0.501749	+	0.501749i	−0.0170797	+	0.0170797i	0.698515	+	0.715595i	$0.253844\pi$
$864$	−2.46534	+	24.6687i	−0.0838727	+	0.839247i
$865$	−34.2265	+	2.38689i	−1.16374	+	0.0811568i
$866$	0.0144299	−	0.724243i	0.000490347	−	0.0246108i
$867$	−8.14682	−	8.14682i	−0.276681	−	0.276681i
$868$	2.58273	+	2.79719i	0.0876634	+	0.0949428i
$869$		−	24.8374i		−	0.842551i
$870$	12.5419	+	11.3532i	0.425210	+	0.384911i
$871$		−	25.6391i		−	0.868749i
$872$	−24.5581	−	27.6840i	−0.831642	−	0.937500i
$873$	−7.29802	−	7.29802i	−0.247001	−	0.247001i
$874$	−3.66259	−	0.0729738i	−0.123889	−	0.00246838i
$875$	3.18991	+	15.0491i	0.107839	+	0.508751i
$876$	0.557652	−	13.9889i	0.0188413	−	0.472640i
$877$	14.5912	−	14.5912i	0.492709	−	0.492709i	−0.416450	−	0.909159i	$-0.636726\pi$
$877$	14.5912	−	14.5912i	0.492709	−	0.492709i	0.909159	+	0.416450i	$0.136726\pi$
$878$	15.3258	+	15.9489i	0.517220	+	0.538249i
$879$	7.13241			0.240570
$880$	−29.6586	−	30.2614i	−0.999791	−	1.02011i
$881$	23.8812			0.804578			0.402289	−	0.915513i	$-0.368215\pi$
$881$	23.8812			0.804578			0.402289	+	0.915513i	$0.368215\pi$
$882$	11.6186	+	12.0910i	0.391218	+	0.407125i
$883$	−0.694415	+	0.694415i	−0.0233689	+	0.0233689i	−0.718695	−	0.695326i	$-0.755260\pi$
$883$	−0.694415	+	0.694415i	−0.0233689	+	0.0233689i	0.695326	+	0.718695i	$0.255260\pi$
$884$	−0.782696	+	19.6342i	−0.0263249	+	0.660369i
$885$	0.0370335	+	0.531036i	0.00124487	+	0.0178506i
$886$	31.4662	+	0.626935i	1.05713	+	0.0210623i
$887$	−26.7770	−	26.7770i	−0.899084	−	0.899084i	0.0962716	−	0.995355i	$-0.469308\pi$
$887$	−26.7770	−	26.7770i	−0.899084	−	0.899084i	−0.995355	+	0.0962716i	$0.969308\pi$
$888$	−7.59196	−	8.55832i	−0.254770	−	0.287199i
$889$		−	21.6517i		−	0.726173i
$890$	1.36362	+	27.4122i	0.0457086	+	0.918861i
$891$		−	15.9004i		−	0.532683i
$892$	−34.0999	−	36.9315i	−1.14175	−	1.23656i
$893$	−6.12814	−	6.12814i	−0.205071	−	0.205071i
$894$	−0.337660	+	16.9473i	−0.0112930	+	0.566803i
$895$	6.75327	−	7.76580i	0.225737	−	0.259582i
$896$	−15.4158	−	2.16378i	−0.515006	−	0.0722869i
$897$	−8.54274	+	8.54274i	−0.285234	+	0.285234i
$898$	36.8103	−	35.3721i	1.22837	−	1.18038i
$899$	8.98752			0.299751
$900$	2.30428	+	23.1037i	0.0768094	+	0.770123i
$901$	8.95477			0.298327
$902$	32.2900	−	31.0284i	1.07514	−	1.03313i
$903$	5.35505	−	5.35505i	0.178205	−	0.178205i
$904$	−2.35599	−	0.140972i	−0.0783592	−	0.00468867i
$905$	−20.5755	+	23.6605i	−0.683954	+	0.786501i
$906$	0.453801	−	22.7765i	0.0150765	−	0.756699i
$907$	17.4394	+	17.4394i	0.579066	+	0.579066i	0.934646	−	0.355580i	$-0.115717\pi$
$907$	17.4394	+	17.4394i	0.579066	+	0.579066i	−0.355580	+	0.934646i	$0.615717\pi$
$908$	14.1065	−	13.0249i	0.468139	−	0.432246i
$909$		−	2.28208i		−	0.0756919i
$910$	−1.22432	−	24.6119i	−0.0405857	−	0.815876i
$911$			15.9437i			0.528237i	0.964490	+	0.264119i	$0.0850810\pi$
$911$			15.9437i			0.528237i	−0.964490	+	0.264119i	$0.914919\pi$
$912$	−2.50726	+	2.13643i	−0.0830235	+	0.0707444i
$913$	20.9401	+	20.9401i	0.693016	+	0.693016i
$914$	49.9783	+	0.995773i	1.65314	+	0.0329372i
$915$	−0.594049	−	8.51829i	−0.0196387	−	0.281606i
$916$	−44.9545	−	1.79207i	−1.48534	−	0.0592115i
$917$	4.44614	−	4.44614i	0.146824	−	0.146824i
$918$	−7.44984	−	7.75274i	−0.245881	−	0.255878i
$919$	26.2087			0.864546			0.432273	−	0.901743i	$-0.357712\pi$
$919$	26.2087			0.864546			0.432273	+	0.901743i	$0.357712\pi$
$920$	11.6981	+	11.4696i	0.385675	+	0.378143i
$921$	4.94096			0.162810
$922$	32.9265	+	34.2653i	1.08438	+	1.12847i
$923$	59.3702	−	59.3702i	1.95419	−	1.95419i
$924$	−10.7272	−	0.427628i	−0.352899	−	0.0140679i
$925$	−19.6075	−	14.7869i	−0.644692	−	0.486190i
$926$	37.3114	+	0.743395i	1.22613	+	0.0244295i
$927$	12.0933	+	12.0933i	0.397195	+	0.397195i
$928$	−28.4402	+	23.2722i	−0.933596	+	0.763947i
$929$		−	49.0636i		−	1.60972i	−0.593462	−	0.804862i	$-0.702239\pi$
$929$		−	49.0636i		−	1.60972i	0.593462	−	0.804862i	$-0.297761\pi$
$930$	−2.67103	−	2.41788i	−0.0875864	−	0.0792854i
$931$			5.10680i			0.167369i
$932$	40.2037	−	37.1212i	1.31692	−	1.21595i
$933$	−1.91240	−	1.91240i	−0.0626092	−	0.0626092i
$934$	−0.125316	+	6.28969i	−0.00410047	+	0.205805i
$935$	18.3320	−	1.27844i	0.599520	−	0.0418094i
$936$	2.22148	−	37.1265i	0.0726115	−	1.21352i
$937$	−33.3125	+	33.3125i	−1.08827	+	1.08827i	−0.0925647	+	0.995707i	$0.529507\pi$
$937$	−33.3125	+	33.3125i	−1.08827	+	1.08827i	−0.995707	+	0.0925647i	$0.970493\pi$
$938$	−6.35184	+	6.10367i	−0.207395	+	0.199292i
$939$	3.47961			0.113553
$940$	1.15413	+	38.7406i	0.0376436	+	1.26358i
$941$	37.9053			1.23568			0.617839	−	0.786305i	$-0.288008\pi$
$941$	37.9053			1.23568			0.617839	+	0.786305i	$0.288008\pi$
$942$	−17.1408	+	16.4711i	−0.558478	+	0.536659i
$943$	−12.2432	+	12.2432i	−0.398695	+	0.398695i
$944$	−1.15267	−	0.0920461i	−0.0375161	−	0.00299584i
$945$	10.1747	+	8.84809i	0.330983	+	0.287828i
$946$	−0.891977	+	44.7688i	−0.0290007	+	1.45556i
$947$	−27.1241	−	27.1241i	−0.881415	−	0.881415i	0.112263	−	0.993678i	$-0.464190\pi$
$947$	−27.1241	−	27.1241i	−0.881415	−	0.881415i	−0.993678	+	0.112263i	$0.964190\pi$
$948$	5.85792	+	6.34435i	0.190256	+	0.206055i
$949$			48.1407i			1.56271i
$950$	−4.36921	+	5.55967i	−0.141756	+	0.180380i
$951$		−	6.36083i		−	0.206264i
$952$	5.05050	−	4.48022i	0.163687	−	0.145205i
$953$	−2.24190	−	2.24190i	−0.0726223	−	0.0726223i	0.669863	−	0.742485i	$-0.266353\pi$
$953$	−2.24190	−	2.24190i	−0.0726223	−	0.0726223i	−0.742485	+	0.669863i	$0.766353\pi$
$954$	−16.9461	−	0.337636i	−0.548651	−	0.0109314i
$955$	−2.25260	−	1.95890i	−0.0728923	−	0.0633884i
$956$	−2.04276	+	51.2432i	−0.0660675	+	1.65732i
$957$	−17.9205	+	17.9205i	−0.579288	+	0.579288i
$958$	33.8081	+	35.1827i	1.09229	+	1.13670i
$959$	15.0766			0.486849
$960$	14.7130	+	0.734840i	0.474862	+	0.0237169i
$961$	29.0859			0.938256
$962$	27.2574	+	28.3657i	0.878815	+	0.914546i
$963$	32.5953	−	32.5953i	1.05037	−	1.05037i
$964$	0.155967	−	3.91247i	0.00502335	−	0.126012i
$965$	32.5843	−	2.27237i	1.04893	−	0.0731501i
$966$	4.15007	+	0.0826863i	0.133526	+	0.00266039i
$967$	21.0580	+	21.0580i	0.677179	+	0.677179i	0.959361	−	0.282182i	$-0.0910583\pi$
$967$	21.0580	+	21.0580i	0.677179	+	0.677179i	−0.282182	+	0.959361i	$0.591058\pi$
$968$	24.2107	−	21.4770i	0.778161	−	0.690295i
$969$		−	1.42861i		−	0.0458934i
$970$	−9.43361	+	10.4213i	−0.302895	+	0.334607i
$971$			51.7396i			1.66040i	0.557463	+	0.830202i	$0.311775\pi$
$971$			51.7396i			1.66040i	−0.557463	+	0.830202i	$0.688225\pi$
$972$	21.5884	+	23.3811i	0.692450	+	0.749949i
$973$	−21.6221	−	21.6221i	−0.693174	−	0.693174i
$974$	−0.593114	+	29.7687i	−0.0190046	+	0.953850i
$975$	3.23680	+	23.0939i	0.103660	+	0.739598i
$976$	18.4898	+	1.47650i	0.591844	+	0.0472616i
$977$	35.1350	−	35.1350i	1.12407	−	1.12407i	0.132944	−	0.991123i	$-0.457557\pi$
$977$	35.1350	−	35.1350i	1.12407	−	1.12407i	0.991123	−	0.132944i	$-0.0424432\pi$
$978$	−16.0439	+	15.4170i	−0.513026	+	0.492982i
$979$	−41.1164			−1.31409
$980$	15.6611	−	16.6229i	0.500275	−	0.530998i
$981$	−30.3786			−0.969914
$982$	−15.0191	+	14.4323i	−0.479277	+	0.460552i
$983$	−3.13196	+	3.13196i	−0.0998941	+	0.0998941i	−0.755288	−	0.655393i	$-0.772503\pi$
$983$	−3.13196	+	3.13196i	−0.0998941	+	0.0998941i	0.655393	+	0.755288i	$0.272503\pi$
$984$	−0.929927	+	15.5414i	−0.0296450	+	0.495441i
$985$	0.311703	+	4.46962i	0.00993168	+	0.142414i
$986$	0.317478	−	15.9344i	0.0101106	−	0.507454i
$987$	6.94377	+	6.94377i	0.221023	+	0.221023i
$988$	8.32205	−	7.68399i	0.264760	−	0.244460i
$989$		−	17.3130i		−	0.550521i
$990$	−34.7399	+	1.72813i	−1.10411	+	0.0549236i
$991$		−	14.2396i		−	0.452334i	−0.974089	−	0.226167i	$-0.927380\pi$
$991$		−	14.2396i		−	0.452334i	0.974089	−	0.226167i	$-0.0726196\pi$
$992$	6.05686	−	4.95623i	0.192306	−	0.157361i
$993$	15.7599	+	15.7599i	0.500125	+	0.500125i
$994$	−28.8421	−	0.574652i	−0.914815	−	0.0182269i
$995$	−22.3246	+	25.6718i	−0.707738	+	0.813851i
$996$	−10.2876	−	0.410104i	−0.325974	−	0.0129946i
$997$	13.3738	−	13.3738i	0.423552	−	0.423552i	−0.462873	−	0.886425i	$-0.653181\pi$
$997$	13.3738	−	13.3738i	0.423552	−	0.423552i	0.886425	+	0.462873i	$0.153181\pi$
$998$	−31.5272	−	32.8091i	−0.997976	−	1.03855i
$999$	−21.5257			−0.681043

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.k.d.343.20	yes	52
4.3	odd	2		380.2.k.c.343.6	yes	52
5.2	odd	4		380.2.k.c.267.6	✓	52
20.7	even	4	inner	380.2.k.d.267.20	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.k.c.267.6	✓	52	5.2	odd	4
380.2.k.c.343.6	yes	52	4.3	odd	2
380.2.k.d.267.20	yes	52	20.7	even	4	inner
380.2.k.d.343.20	yes	52	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
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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