LMFDB - Embedded newform 380.2.k.c.267.6

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			267.6
Character	$\chi$	$=$	380.267
Dual form			380.2.k.c.343.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.01972 + 0.979881i) q^{2} +(0.582309 + 0.582309i) q^{3} +(0.0796647 - 1.99841i) q^{4} +(1.46731 + 1.68731i) q^{5} +(-1.16439 - 0.0231993i) q^{6} +(0.972933 - 0.972933i) q^{7} +(1.87697 + 2.11589i) q^{8} -2.32183i q^{9} +O(q^{10})$	\(q+(-1.01972 + 0.979881i) 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} +(1.87697 + 2.11589i) q^{8} -2.32183i q^{9} +(-3.14961 - 0.282794i) q^{10} +4.73734i q^{11} +(1.21008 - 1.11730i) 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} +(2.27512 + 2.36762i) q^{18} +1.00000 q^{19} +(3.48883 - 2.79787i) q^{20} +1.13310 q^{21} +(-4.64203 - 4.83076i) 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} +(-1.86681 - 2.02183i) q^{28} +6.49625i q^{29} +(-1.66937 - 1.99872i) q^{30} +1.38349i q^{31} +(4.37794 - 3.58240i) 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} +(-1.01972 + 0.979881i) q^{38} +4.66393 q^{39} +(-0.816051 + 6.27169i) q^{40} -6.68423 q^{41} +(-1.15544 + 1.11030i) 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} +(-2.13643 - 2.50726i) q^{48} +5.10680i q^{49} +(-4.14429 - 5.72930i) q^{50} +1.42861i q^{51} +(-7.68399 - 8.32205i) 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} +(-6.36555 - 6.62437i) q^{58} -0.289084 q^{59} +(3.66080 + 0.402350i) q^{60} -4.63716 q^{61} +(-1.35566 - 1.41078i) 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} +(2.54912 - 2.35368i) q^{68} -2.13318i q^{69} +(-3.33950 + 2.78922i) q^{70} -14.8252i q^{71} +(4.91273 - 4.35801i) 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} +(-4.75591 + 4.57010i) q^{78} +5.24290 q^{79} +(-5.31337 - 7.19501i) q^{80} -3.35640 q^{81} +(6.81606 - 6.54976i) 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} +(-10.0237 + 8.89184i) q^{88} -8.67923i q^{89} +(-0.656599 + 7.31286i) q^{90} -7.79259i q^{91} +(-3.80633 + 3.51449i) 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} +(-5.00406 - 5.20752i) 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} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 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 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * 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 $

$2$	−1.01972	+	0.979881i	−0.721052	+	0.692881i
$2$	−1.01972	+	0.979881i	−0.721052	+	0.692881i
$3$	0.582309	+	0.582309i	0.336196	+	0.336196i	0.854934	−	0.518737i	$-0.173598\pi$
$3$	0.582309	+	0.582309i	0.336196	+	0.336196i	−0.518737	+	0.854934i	$0.673598\pi$
$4$	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	$-0.666268\pi$
$7$	0.972933	−	0.972933i	0.367734	−	0.367734i	0.866650	+	0.498916i	$0.166268\pi$
$8$	1.87697	+	2.11589i	0.663610	+	0.748079i
$9$		−	2.32183i		−	0.773944i
$10$	−3.14961	−	0.282794i	−0.995993	−	0.0894272i
$11$			4.73734i			1.42836i	0.699962	+	0.714180i	$0.253200\pi$
$11$			4.73734i			1.42836i	−0.699962	+	0.714180i	$0.746800\pi$
$12$	1.21008	−	1.11730i	0.349321	−	0.322538i
$13$	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	$0.682532\pi$
$18$	2.27512	+	2.36762i	0.536251	+	0.558054i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	3.48883	−	2.79787i	0.780126	−	0.625623i
$21$	1.13310			0.247262
$22$	−4.64203	−	4.83076i	−0.989683	−	1.02992i
$23$	−1.83166	−	1.83166i	−0.381928	−	0.381928i	0.489869	−	0.871796i	$-0.337045\pi$
$23$	−1.83166	−	1.83166i	−0.381928	−	0.381928i	−0.871796	+	0.489869i	$0.837045\pi$
$24$	−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
$28$	−1.86681	−	2.02183i	−0.352795	−	0.382090i
$29$			6.49625i			1.20632i	0.797619	+	0.603162i	$0.206093\pi$
$29$			6.49625i			1.20632i	−0.797619	+	0.603162i	$0.793907\pi$
$30$	−1.66937	−	1.99872i	−0.304784	−	0.364914i
$31$			1.38349i			0.248483i	0.992252	+	0.124241i	$0.0396497\pi$
$31$			1.38349i			0.248483i	−0.992252	+	0.124241i	$0.960350\pi$
$32$	4.37794	−	3.58240i	0.773918	−	0.633285i
$33$	−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	$0.617712\pi$
$38$	−1.01972	+	0.979881i	−0.165421	+	0.158958i
$39$	4.66393			0.746827
$40$	−0.816051	+	6.27169i	−0.129029	+	0.991641i
$41$	−6.68423			−1.04390			−0.521951	−	0.852975i	$-0.674796\pi$
$41$	−6.68423			−1.04390			−0.521951	+	0.852975i	$0.674796\pi$
$42$	−1.15544	+	1.11030i	−0.178289	+	0.171323i
$43$	−4.72604	−	4.72604i	−0.720714	−	0.720714i	0.248037	−	0.968751i	$-0.420215\pi$
$43$	−4.72604	−	4.72604i	−0.720714	−	0.720714i	−0.968751	+	0.248037i	$0.920215\pi$
$44$	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	$-0.967794\pi$
$47$	−6.12814	+	6.12814i	−0.893882	+	0.893882i	0.101004	+	0.994886i	$0.467794\pi$
$48$	−2.13643	−	2.50726i	−0.308368	−	0.361891i
$49$			5.10680i			0.729543i
$50$	−4.14429	−	5.72930i	−0.586091	−	0.810245i
$51$			1.42861i			0.200045i
$52$	−7.68399	−	8.32205i	−1.06558	−	1.15406i
$53$	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
$58$	−6.36555	−	6.62437i	−0.835838	−	0.869822i
$59$	−0.289084			−0.0376355			−0.0188178	−	0.999823i	$-0.505990\pi$
$59$	−0.289084			−0.0376355			−0.0188178	+	0.999823i	$0.505990\pi$
$60$	3.66080	+	0.402350i	0.472608	+	0.0519432i
$61$	−4.63716			−0.593728			−0.296864	−	0.954920i	$-0.595941\pi$
$61$	−4.63716			−0.593728			−0.296864	+	0.954920i	$0.595941\pi$
$62$	−1.35566	−	1.41078i	−0.172169	−	0.179169i
$63$	−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	$-0.660813\pi$
$67$	3.20114	−	3.20114i	0.391082	−	0.391082i	0.875073	+	0.483991i	$0.160813\pi$
$68$	2.54912	−	2.35368i	0.309126	−	0.285425i
$69$		−	2.13318i		−	0.256805i
$70$	−3.33950	+	2.78922i	−0.399146	+	0.333375i
$71$		−	14.8252i		−	1.75942i	−0.475507	−	0.879712i	$-0.657735\pi$
$71$		−	14.8252i		−	1.75942i	0.475507	−	0.879712i	$-0.342265\pi$
$72$	4.91273	−	4.35801i	0.578971	−	0.513597i
$73$	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
$78$	−4.75591	+	4.57010i	−0.538501	+	0.517462i
$79$	5.24290			0.589873			0.294936	−	0.955517i	$-0.404702\pi$
$79$	5.24290			0.589873			0.294936	+	0.955517i	$0.404702\pi$
$80$	−5.31337	−	7.19501i	−0.594052	−	0.804426i
$81$	−3.35640			−0.372933
$82$	6.81606	−	6.54976i	0.752708	−	0.723300i
$83$	−4.42022	−	4.42022i	−0.485183	−	0.485183i	0.421600	−	0.906782i	$-0.361469\pi$
$83$	−4.42022	−	4.42022i	−0.485183	−	0.485183i	−0.906782	+	0.421600i	$0.861469\pi$
$84$	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
$88$	−10.0237	+	8.89184i	−1.06853	+	0.947874i
$89$		−	8.67923i		−	0.919997i	−0.887920	−	0.459998i	$-0.847850\pi$
$89$		−	8.67923i		−	0.919997i	0.887920	−	0.459998i	$-0.152150\pi$
$90$	−0.656599	+	7.31286i	−0.0692116	+	0.770843i
$91$		−	7.79259i		−	0.816885i
$92$	−3.80633	+	3.51449i	−0.396837	+	0.366411i
$93$	−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	$0.822457\pi$
$98$	−5.00406	−	5.20752i	−0.505487	−	0.526039i
$99$	10.9993			1.10547
$100$	9.84006	+	1.78138i	0.984006	+	0.178138i
$101$	−0.982880			−0.0978003			−0.0489001	−	0.998804i	$-0.515572\pi$
$101$	−0.982880			−0.0978003			−0.0489001	+	0.998804i	$0.515572\pi$
$102$	−1.39986	−	1.45678i	−0.138607	−	0.144243i
$103$	−5.20851	−	5.20851i	−0.513209	−	0.513209i	0.402299	−	0.915508i	$-0.368211\pi$
$103$	−5.20851	−	5.20851i	−0.513209	−	0.513209i	−0.915508	+	0.402299i	$0.868211\pi$
$104$	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	$-0.340721\pi$
$107$	14.0386	−	14.0386i	1.35716	−	1.35716i	0.877396	−	0.479767i	$-0.159279\pi$
$108$	−5.94611	−	6.43986i	−0.572164	−	0.619676i
$109$		−	13.0839i		−	1.25321i	−0.779337	−	0.626605i	$-0.784444\pi$
$109$		−	13.0839i		−	1.25321i	0.779337	−	0.626605i	$-0.215556\pi$
$110$	1.33969	−	14.9207i	0.127734	−	1.42264i
$111$			4.04479i			0.383915i
$112$	−4.18917	+	3.56959i	−0.395839	+	0.337295i
$113$	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
$118$	0.294785	−	0.283268i	0.0271372	−	0.0260769i
$119$	2.38694			0.218810
$120$	−4.12725	+	3.17687i	−0.376765	+	0.290007i
$121$	−11.4423			−1.04021
$122$	4.72861	−	4.54387i	0.428109	−	0.411383i
$123$	−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	$-0.996002\pi$
$127$	−11.1270	+	11.1270i	−0.987362	+	0.987362i	0.0125590	+	0.999921i	$0.496002\pi$
$128$	−6.81035	−	9.03433i	−0.601956	−	0.798529i
$129$		−	5.50403i		−	0.484603i
$130$	−13.7457	+	11.4807i	−1.20558	+	1.00692i
$131$			4.56983i			0.399268i	0.979871	+	0.199634i	$0.0639753\pi$
$131$			4.56983i			0.399268i	−0.979871	+	0.199634i	$0.936025\pi$
$132$	5.29305	+	5.73257i	0.460701	+	0.498956i
$133$	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	$0.905052\pi$
$138$	2.09027	+	2.17525i	0.177935	+	0.185170i
$139$	−22.2237			−1.88499			−0.942493	−	0.334225i	$-0.891525\pi$
$139$	−22.2237			−1.88499			−0.942493	+	0.334225i	$0.891525\pi$
$140$	0.672254	−	6.11654i	0.0568158	−	0.516942i
$141$	−7.13695			−0.601040
$142$	14.5269	+	15.1175i	1.21907	+	1.26864i
$143$	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
$148$	7.21729	−	6.66393i	0.593258	−	0.547772i
$149$			14.5547i			1.19237i	0.802848	+	0.596184i	$0.203317\pi$
$149$			14.5547i			1.19237i	−0.802848	+	0.596184i	$0.796683\pi$
$150$	0.922965	−	5.74948i	0.0753598	−	0.469443i
$151$			19.5609i			1.59185i	0.605397	+	0.795924i	$0.293014\pi$
$151$			19.5609i			1.59185i	−0.605397	+	0.795924i	$0.706986\pi$
$152$	1.87697	+	2.11589i	0.152243	+	0.171621i
$153$	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	$0.447001\pi$
$158$	−5.34630	+	5.13743i	−0.425329	+	0.408712i
$159$	4.25089			0.337117
$160$	12.4684	+	2.13044i	0.985714	+	0.168426i
$161$	−3.56416			−0.280896
$162$	3.42259	−	3.28887i	0.268904	−	0.258398i
$163$	−13.5096	−	13.5096i	−1.05816	−	1.05816i	−0.998201	−	0.0599555i	$-0.980904\pi$
$163$	−13.5096	−	13.5096i	−1.05816	−	1.05816i	−0.0599555	−	0.998201i	$-0.519096\pi$
$164$	−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	$-0.532285\pi$
$167$	11.5480	−	11.5480i	0.893610	−	0.893610i	0.994861	+	0.101251i	$0.0322846\pi$
$168$	2.12679	+	2.39750i	0.164085	+	0.184971i
$169$		−	19.0751i		−	1.46731i
$170$	−3.51664	−	4.21043i	−0.269714	−	0.322925i
$171$		−	2.32183i		−	0.177555i
$172$	−9.82107	+	9.06808i	−0.748850	+	0.691434i
$173$	−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
$178$	8.50462	+	8.85040i	0.637448	+	0.663366i
$179$	−4.60249			−0.344006			−0.172003	−	0.985096i	$-0.555024\pi$
$179$	−4.60249			−0.344006			−0.172003	+	0.985096i	$0.555024\pi$
$180$	−6.49619	−	8.10047i	−0.484197	−	0.603773i
$181$	−14.0226			−1.04229			−0.521147	−	0.853467i	$-0.674496\pi$
$181$	−14.0226			−1.04229			−0.521147	+	0.853467i	$0.674496\pi$
$182$	7.63581	+	7.94627i	0.566004	+	0.589017i
$183$	−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
$188$	11.7584	+	12.7348i	0.857567	+	0.928778i
$189$		−	6.03014i		−	0.438628i
$190$	−3.14961	−	0.282794i	−0.228497	−	0.0205160i
$191$		−	1.33503i		−	0.0965990i	−0.998833	−	0.0482995i	$-0.984620\pi$
$191$		−	1.33503i		−	0.0965990i	0.998833	−	0.0482995i	$-0.0153802\pi$
$192$	−5.18073	+	4.06974i	−0.373887	+	0.293708i
$193$	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	$0.772740\pi$
$198$	−11.2162	+	10.7780i	−0.797102	+	0.765960i
$199$	15.2147			1.07854			0.539270	−	0.842133i	$-0.318700\pi$
$199$	15.2147			1.07854			0.539270	+	0.842133i	$0.318700\pi$
$200$	−11.7797	+	7.82558i	−0.832948	+	0.553352i
$201$	3.72811			0.262960
$202$	1.00226	−	0.963106i	0.0705191	−	0.0677639i
$203$	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
$208$	−17.2430	+	14.6928i	−1.19559	+	1.01876i
$209$			4.73734i			0.327688i
$210$	−3.56881	−	0.320432i	−0.246271	−	0.0221119i
$211$			9.35082i			0.643737i	0.946784	+	0.321868i	$0.104311\pi$
$211$			9.35082i			0.643737i	−0.946784	+	0.321868i	$0.895689\pi$
$212$	−7.00348	−	7.58503i	−0.481001	−	0.520942i
$213$	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
$218$	12.8207	+	13.3419i	0.868325	+	0.903629i
$219$	6.99998			0.473015
$220$	13.2545	+	16.5277i	0.893615	+	1.11430i
$221$	9.82488			0.660893
$222$	−3.96342	−	4.12456i	−0.266007	−	0.276823i
$223$	17.7719	+	17.7719i	1.19010	+	1.19010i	0.977040	+	0.213058i	$0.0683424\pi$
$223$	17.7719	+	17.7719i	1.19010	+	1.19010i	0.213058	+	0.977040i	$0.431658\pi$
$224$	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	$-0.646792\pi$
$227$	6.78822	−	6.78822i	0.450550	−	0.450550i	0.895537	+	0.444987i	$0.146792\pi$
$228$	1.21008	−	1.11730i	0.0801397	−	0.0739953i
$229$		−	22.4951i		−	1.48652i	−0.669004	−	0.743259i	$-0.733279\pi$
$229$		−	22.4951i		−	1.48652i	0.669004	−	0.743259i	$-0.266721\pi$
$230$	5.25103	+	6.28699i	0.346243	+	0.414552i
$231$			5.36785i			0.353179i
$232$	−13.7453	+	12.1933i	−0.902425	+	0.800528i
$233$	−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
$238$	−2.43401	+	2.33892i	−0.157774	+	0.151610i
$239$	−25.6419			−1.65864			−0.829320	−	0.558774i	$-0.811272\pi$
$239$	−25.6419			−1.65864			−0.829320	+	0.558774i	$0.811272\pi$
$240$	1.09570	−	7.28374i	0.0707270	−	0.470163i
$241$	−1.95779			−0.126112			−0.0630561	−	0.998010i	$-0.520085\pi$
$241$	−1.95779			−0.126112			−0.0630561	+	0.998010i	$0.520085\pi$
$242$	11.6680	−	11.2121i	0.750048	−	0.720744i
$243$	−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
$248$	−2.92732	+	2.59678i	−0.185885	+	0.164896i
$249$		−	5.14787i		−	0.326233i
$250$	3.58613	−	15.3993i	0.226807	−	0.973940i
$251$		−	3.53141i		−	0.222900i	−0.993770	−	0.111450i	$-0.964450\pi$
$251$		−	3.53141i		−	0.222900i	0.993770	−	0.111450i	$-0.0355496\pi$
$252$	−4.69435	+	4.33443i	−0.295716	+	0.273043i
$253$	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	$0.772761\pi$
$258$	5.39330	+	5.61258i	0.335772	+	0.349424i
$259$	6.75811			0.419929
$260$	2.76706	−	25.1763i	0.171606	−	1.56137i
$261$	15.0832			0.933627
$262$	−4.47789	−	4.65996i	−0.276645	−	0.287893i
$263$	11.7656	+	11.7656i	0.725497	+	0.725497i	0.969719	−	0.244222i	$-0.0785326\pi$
$263$	11.7656	+	11.7656i	0.725497	+	0.725497i	−0.244222	+	0.969719i	$0.578533\pi$
$264$	−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
$268$	−6.14218	−	6.65222i	−0.375194	−	0.406349i
$269$		−	5.80800i		−	0.354120i	−0.984200	−	0.177060i	$-0.943341\pi$
$269$		−	5.80800i		−	0.354120i	0.984200	−	0.177060i	$-0.0566587\pi$
$270$	−10.6368	+	8.88412i	−0.647338	+	0.540670i
$271$			15.9470i			0.968709i	0.874872	+	0.484354i	$0.160945\pi$
$271$			15.9470i			0.968709i	−0.874872	+	0.484354i	$0.839055\pi$
$272$	−4.50054	−	5.28170i	−0.272885	−	0.320250i
$273$	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	$0.545128\pi$
$278$	22.6620	−	21.7766i	1.35917	−	1.30607i
$279$	3.21224			0.192312
$280$	5.30797	+	6.89589i	0.317212	+	0.412109i
$281$	−31.6384			−1.88739			−0.943693	−	0.330821i	$-0.892674\pi$
$281$	−31.6384			−1.88739			−0.943693	+	0.330821i	$0.892674\pi$
$282$	7.27770	−	6.99336i	0.433381	−	0.416449i
$283$	−3.72139	−	3.72139i	−0.221214	−	0.221214i	0.587796	−	0.809009i	$-0.299996\pi$
$283$	−3.72139	−	3.72139i	−0.221214	−	0.221214i	−0.809009	+	0.587796i	$0.799996\pi$
$284$	−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
$288$	−8.31774	−	10.1649i	−0.490127	−	0.598970i
$289$		−	13.9905i		−	0.822973i
$290$	1.83710	−	20.4606i	0.107878	−	1.20149i
$291$		−	3.66065i		−	0.214591i
$292$	−11.5327	−	12.4904i	−0.674901	−	0.730943i
$293$	−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
$298$	−14.2619	−	14.8417i	−0.826169	−	0.859759i
$299$	−14.6705			−0.848414
$300$	4.69264	+	6.76727i	0.270930	+	0.390708i
$301$	−9.19624			−0.530062
$302$	−19.1674	−	19.9467i	−1.10296	−	1.14781i
$303$	−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	$-0.695230\pi$
$307$	4.24256	−	4.24256i	0.242136	−	0.242136i	0.817733	+	0.575597i	$0.195230\pi$
$308$	9.57809	−	8.84372i	0.545762	−	0.503918i
$309$		−	6.06592i		−	0.345078i
$310$	0.391243	−	4.35746i	0.0222211	−	0.247487i
$311$			3.28417i			0.186228i	0.995655	+	0.0931141i	$0.0296821\pi$
$311$			3.28417i			0.186228i	−0.995655	+	0.0931141i	$0.970318\pi$
$312$	8.75407	+	9.86835i	0.495602	+	0.558686i
$313$	−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	$0.819599\pi$
$318$	−4.33472	+	4.16536i	−0.243079	+	0.233582i
$319$	−30.7749			−1.72306
$320$	−14.8019	+	10.0451i	−0.827451	+	0.561539i
$321$	16.3496			0.912546
$322$	3.63446	−	3.49246i	0.202540	−	0.194627i
$323$	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
$328$	−12.5461	−	14.1431i	−0.692743	−	0.780921i
$329$			11.9245i			0.657422i
$330$	9.46860	−	7.90837i	0.521229	−	0.435342i
$331$		−	27.0645i		−	1.48760i	−0.668403	−	0.743799i	$-0.733022\pi$
$331$		−	27.0645i		−	1.48760i	0.668403	−	0.743799i	$-0.266978\pi$
$332$	−9.18557	+	8.48130i	−0.504124	+	0.465472i
$333$	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	$0.837541\pi$
$338$	18.6913	+	19.4512i	1.01667	+	1.05801i
$339$	0.687185			0.0373228
$340$	7.71172	+	0.847577i	0.418227	+	0.0459663i
$341$	−6.55408			−0.354923
$342$	2.27512	+	2.36762i	0.123024	+	0.128026i
$343$	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	$-0.672239\pi$
$347$	6.37184	−	6.37184i	0.342058	−	0.342058i	0.857141	+	0.515083i	$0.172239\pi$
$348$	7.25829	+	7.86100i	0.389085	+	0.421394i
$349$		−	2.28416i		−	0.122268i	−0.998130	−	0.0611342i	$-0.980528\pi$
$349$		−	2.28416i		−	0.122268i	0.998130	−	0.0611342i	$-0.0194718\pi$
$350$	−9.60634	−	1.54211i	−0.513480	−	0.0824291i
$351$		−	24.8207i		−	1.32483i
$352$	16.9710	+	20.7398i	0.904560	+	1.10543i
$353$	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
$358$	4.69325	−	4.50989i	0.248046	−	0.238355i
$359$	28.3972			1.49875			0.749373	−	0.662148i	$-0.230355\pi$
$359$	28.3972			1.49875			0.749373	+	0.662148i	$0.230355\pi$
$360$	14.5618	+	1.89473i	0.767475	+	0.0998612i
$361$	1.00000			0.0526316
$362$	14.2992	−	13.7405i	0.751548	−	0.722186i
$363$	−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	$-0.766590\pi$
$367$	−1.41139	+	1.41139i	−0.0736740	+	0.0736740i	0.669310	+	0.742984i	$0.266590\pi$
$368$	6.72018	+	7.88660i	0.350314	+	0.411118i
$369$			15.5197i			0.807922i
$370$	−9.95663	−	11.9209i	−0.517620	−	0.619740i
$371$		−	7.10246i		−	0.368741i
$372$	1.54578	+	1.67414i	0.0801452	+	0.0868003i
$373$	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
$378$	5.90883	+	6.14907i	0.303917	+	0.316274i
$379$	16.8864			0.867397			0.433699	−	0.901058i	$-0.357208\pi$
$379$	16.8864			0.867397			0.433699	+	0.901058i	$0.357208\pi$
$380$	3.48883	−	2.79787i	0.178973	−	0.143528i
$381$	−12.9587			−0.663895
$382$	1.30817	+	1.36135i	0.0669316	+	0.0696529i
$383$	6.02950	+	6.02950i	0.308093	+	0.308093i	0.844169	−	0.536076i	$-0.180094\pi$
$383$	6.02950	+	6.02950i	0.308093	+	0.308093i	−0.536076	+	0.844169i	$0.680094\pi$
$384$	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
$388$	−6.53185	+	6.03104i	−0.331604	+	0.306180i
$389$			33.3599i			1.69141i	0.533647	+	0.845707i	$0.320821\pi$
$389$			33.3599i			1.69141i	−0.533647	+	0.845707i	$0.679179\pi$
$390$	−14.6896	−	1.31893i	−0.743835	−	0.0667866i
$391$		−	4.49369i		−	0.227256i
$392$	−10.8054	+	9.58532i	−0.545756	+	0.484132i
$393$	−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	$0.891216\pi$
$398$	−15.5147	+	14.9086i	−0.777683	+	0.747299i
$399$	1.13310			0.0567257
$400$	4.34383	−	19.5226i	0.217192	−	0.976129i
$401$	−8.90471			−0.444680			−0.222340	−	0.974969i	$-0.571369\pi$
$401$	−8.90471			−0.444680			−0.222340	+	0.974969i	$0.571369\pi$
$402$	−3.80163	+	3.65310i	−0.189608	+	0.182200i
$403$	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
$408$	−3.02277	+	2.68145i	−0.149649	+	0.132752i
$409$			13.2705i			0.656186i	0.944645	+	0.328093i	$0.106406\pi$
$409$			13.2705i			0.656186i	−0.944645	+	0.328093i	$0.893594\pi$
$410$	21.0527	+	1.89026i	1.03972	+	0.0933532i
$411$		−	9.02348i		−	0.445095i
$412$	−10.8237	+	9.99381i	−0.533244	+	0.492360i
$413$	−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
$418$	−4.64203	−	4.83076i	−0.227049	−	0.236280i
$419$	−11.4136			−0.557592			−0.278796	−	0.960350i	$-0.589935\pi$
$419$	−11.4136			−0.557592			−0.278796	+	0.960350i	$0.589935\pi$
$420$	3.95317	−	3.17026i	0.192895	−	0.154693i
$421$	16.0960			0.784472			0.392236	−	0.919865i	$-0.371702\pi$
$421$	16.0960			0.784472			0.392236	+	0.919865i	$0.371702\pi$
$422$	−9.16269	−	9.53523i	−0.446033	−	0.464168i
$423$	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
$428$	−26.9365	−	29.1733i	−1.30203	−	1.41014i
$429$			22.0946i			1.06674i
$430$	13.5487	+	16.2217i	0.653375	+	0.782278i
$431$			16.7831i			0.808415i	0.914667	+	0.404208i	$0.132453\pi$
$431$			16.7831i			0.808415i	−0.914667	+	0.404208i	$0.867547\pi$
$432$	−13.3432	+	11.3697i	−0.641975	+	0.547027i
$433$	−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
$438$	−7.13803	+	6.85915i	−0.341068	+	0.327743i
$439$	−15.6404			−0.746477			−0.373239	−	0.927735i	$-0.621753\pi$
$439$	−15.6404			−0.746477			−0.373239	+	0.927735i	$0.621753\pi$
$440$	−29.7111	−	3.86591i	−1.41642	−	0.184300i
$441$	11.8571			0.564626
$442$	−10.0186	+	9.62722i	−0.476538	+	0.457920i
$443$	−15.7362	−	15.7362i	−0.747651	−	0.747651i	0.226387	−	0.974037i	$-0.427309\pi$
$443$	−15.7362	−	15.7362i	−0.747651	−	0.747651i	−0.974037	+	0.226387i	$0.927309\pi$
$444$	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
$448$	6.79979	+	8.65606i	0.321260	+	0.408960i
$449$			36.0983i			1.70359i	0.523878	+	0.851793i	$0.324485\pi$
$449$			36.0983i			1.70359i	−0.523878	+	0.851793i	$0.675515\pi$
$450$	−13.3025	+	9.62234i	−0.627084	+	0.453602i
$451$		−	31.6655i		−	1.49107i
$452$	−1.13216	−	1.22617i	−0.0532524	−	0.0576744i
$453$	−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	$0.440197\pi$
$458$	22.0425	+	22.9387i	1.02998	+	1.07186i
$459$	7.60280			0.354868
$460$	−11.5151	−	1.26560i	−0.536894	−	0.0590088i
$461$	33.6026			1.56503			0.782514	−	0.622633i	$-0.213937\pi$
$461$	33.6026			1.56503			0.782514	+	0.622633i	$0.213937\pi$
$462$	−5.25986	−	5.47372i	−0.244711	−	0.254660i
$463$	−18.6594	−	18.6594i	−0.867175	−	0.867175i	0.124983	−	0.992159i	$-0.460112\pi$
$463$	−18.6594	−	18.6594i	−0.867175	−	0.867175i	−0.992159	+	0.124983i	$0.960112\pi$
$464$	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	$-0.782819\pi$
$467$	−3.14547	+	3.14547i	−0.145555	+	0.145555i	0.630574	+	0.776129i	$0.282819\pi$
$468$	−19.3224	+	17.8409i	−0.893179	+	0.824697i
$469$		−	6.22899i		−	0.287628i
$470$	21.0342	−	17.5682i	0.970238	−	0.810363i
$471$			16.8093i			0.774532i
$472$	−0.542603	−	0.611669i	−0.0249753	−	0.0281544i
$473$	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
$478$	26.1477	−	25.1261i	1.19597	−	1.14924i
$479$	−34.5022			−1.57645			−0.788223	−	0.615389i	$-0.788999\pi$
$479$	−34.5022			−1.57645			−0.788223	+	0.615389i	$0.788999\pi$
$480$	6.01989	+	8.50104i	0.274769	+	0.388018i
$481$	27.8171			1.26835
$482$	1.99640	−	1.91840i	0.0909335	−	0.0873808i
$483$	−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	$-0.908283\pi$
$487$	−14.8873	+	14.8873i	−0.674607	+	0.674607i	0.284167	+	0.958775i	$0.408283\pi$
$488$	−8.70382	−	9.81171i	−0.394003	−	0.444155i
$489$		−	15.7336i		−	0.711497i
$490$	1.44417	−	16.0844i	0.0652410	−	0.726620i
$491$			14.7286i			0.664692i	0.943158	+	0.332346i	$0.107840\pi$
$491$			14.7286i			0.664692i	−0.943158	+	0.332346i	$0.892160\pi$
$492$	−8.08848	+	7.46832i	−0.364657	+	0.336698i
$493$	−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
$498$	5.04431	+	5.24940i	0.226041	+	0.235231i
$499$	32.1745			1.44033			0.720165	−	0.693803i	$-0.244066\pi$
$499$	32.1745			1.44033			0.720165	+	0.693803i	$0.244066\pi$
$500$	11.4327	+	19.2170i	0.511285	+	0.859411i
$501$	13.4490			0.600857
$502$	3.46036	+	3.60105i	0.154443	+	0.160723i
$503$	14.5815	+	14.5815i	0.650157	+	0.650157i	0.953031	−	0.302874i	$-0.0979461\pi$
$503$	14.5815	+	14.5815i	0.650157	+	0.650157i	−0.302874	+	0.953031i	$0.597946\pi$
$504$	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
$508$	21.3499	+	23.1228i	0.947250	+	1.02591i
$509$		−	30.8387i		−	1.36690i	−0.729996	−	0.683452i	$-0.760478\pi$
$509$		−	30.8387i		−	1.36690i	0.729996	−	0.683452i	$-0.239522\pi$
$510$	0.404000	−	4.49955i	0.0178894	−	0.199243i
$511$		−	11.6957i		−	0.517387i
$512$	−18.5969	+	12.8902i	−0.821873	+	0.569671i
$513$	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
$518$	−6.89140	+	6.62215i	−0.302791	+	0.290961i
$519$	−12.6357			−0.554647
$520$	21.8481	+	28.3842i	0.958104	+	1.24473i
$521$	−15.7674			−0.690782			−0.345391	−	0.938459i	$-0.612254\pi$
$521$	−15.7674			−0.690782			−0.345391	+	0.938459i	$0.612254\pi$
$522$	−15.3807	+	14.7797i	−0.673193	+	0.646892i
$523$	24.2821	+	24.2821i	1.06178	+	1.06178i	0.997961	+	0.0638230i	$0.0203293\pi$
$523$	24.2821	+	24.2821i	1.06178	+	1.06178i	0.0638230	+	0.997961i	$0.479671\pi$
$524$	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
$528$	11.8777	−	10.1210i	0.516911	−	0.440460i
$529$		−	16.2900i		−	0.708263i
$530$	−12.5283	+	10.4639i	−0.544197	+	0.454525i
$531$			0.671205i			0.0291278i
$532$	−1.86681	−	2.02183i	−0.0809366	−	0.0876575i
$533$	−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
$538$	5.69115	+	5.92255i	0.245363	+	0.255339i
$539$	−24.1926			−1.04205
$540$	2.14124	−	19.4822i	0.0921443	−	0.838379i
$541$	−13.1301			−0.564506			−0.282253	−	0.959340i	$-0.591082\pi$
$541$	−13.1301			−0.564506			−0.282253	+	0.959340i	$0.591082\pi$
$542$	−15.6261	−	16.2615i	−0.671200	−	0.698490i
$543$	−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	$-0.814676\pi$
$547$	−6.67431	+	6.67431i	−0.285373	+	0.285373i	0.549875	+	0.835247i	$0.314676\pi$
$548$	−16.1010	+	14.8665i	−0.687799	+	0.635065i
$549$			10.7667i			0.459512i
$550$	27.1416	−	19.6329i	1.15732	−	0.837149i
$551$			6.49625i			0.276750i
$552$	4.51358	−	4.00393i	0.192111	−	0.170418i
$553$	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	$0.852538\pi$
$558$	−3.27559	+	3.14762i	−0.138667	+	0.133249i
$559$	−37.8526			−1.60100
$560$	−12.1698	−	1.83071i	−0.514268	−	0.0773617i
$561$	−6.76778			−0.285736
$562$	32.2623	−	31.0019i	1.36090	−	1.30773i
$563$	18.7352	+	18.7352i	0.789595	+	0.789595i	0.981428	−	0.191833i	$-0.0614431\pi$
$563$	18.7352	+	18.7352i	0.789595	+	0.789595i	−0.191833	+	0.981428i	$0.561443\pi$
$564$	−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
$568$	31.3684	−	27.8264i	1.31619	−	1.16757i
$569$			33.1004i			1.38764i	0.720147	+	0.693821i	$0.244074\pi$
$569$			33.1004i			1.38764i	−0.720147	+	0.693821i	$0.755926\pi$
$570$	−1.66937	−	1.99872i	−0.0699223	−	0.0837171i
$571$			17.4026i			0.728277i	0.931345	+	0.364138i	$0.118636\pi$
$571$			17.4026i			0.728277i	−0.931345	+	0.364138i	$0.881364\pi$
$572$	39.4243	−	36.4016i	1.64841	−	1.52203i
$573$	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	$0.707639\pi$
$578$	13.7091	+	14.2665i	0.570223	+	0.593407i
$579$	12.0294			0.499927
$580$	18.1757	+	22.6643i	0.754704	+	0.941084i
$581$	−8.60116			−0.356836
$582$	3.58700	+	3.73284i	0.148686	+	0.154731i
$583$	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	$-0.814942\pi$
$587$	−6.94211	+	6.94211i	−0.286531	+	0.286531i	0.549176	+	0.835707i	$0.314942\pi$
$588$	5.70585	+	6.17966i	0.235305	+	0.254845i
$589$			1.38349i			0.0570059i
$590$	0.910501	+	0.0817511i	0.0374847	+	0.00336564i
$591$		−	1.65009i		−	0.0678757i
$592$	−12.7423	−	14.9540i	−0.523706	−	0.614606i
$593$	−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
$598$	14.9598	−	14.3753i	0.611751	−	0.587850i
$599$	41.8628			1.71047			0.855233	−	0.518243i	$-0.173414\pi$
$599$	41.8628			1.71047			0.855233	+	0.518243i	$0.173414\pi$
$600$	−11.4163	−	2.30250i	−0.466069	−	0.0939990i
$601$	9.08392			0.370541			0.185270	−	0.982688i	$-0.440684\pi$
$601$	9.08392			0.370541			0.185270	+	0.982688i	$0.440684\pi$
$602$	9.37760	−	9.01122i	0.382203	−	0.367270i
$603$	−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	$-0.793925\pi$
$607$	−4.79286	+	4.79286i	−0.194536	+	0.194536i	0.603117	+	0.797653i	$0.293925\pi$
$608$	4.37794	−	3.58240i	0.177549	−	0.145286i
$609$			7.36087i			0.298278i
$610$	14.6052	+	1.31136i	0.591349	+	0.0530954i
$611$			49.0826i			1.98567i
$612$	−5.46484	−	5.91863i	−0.220903	−	0.239246i
$613$	−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	$0.701555\pi$
$618$	5.94388	+	6.18555i	0.239098	+	0.248819i
$619$	4.51100			0.181312			0.0906562	−	0.995882i	$-0.471104\pi$
$619$	4.51100			0.181312			0.0906562	+	0.995882i	$0.471104\pi$
$620$	3.87084	+	4.82677i	0.155457	+	0.193848i
$621$	−11.3525			−0.455558
$622$	−3.21810	−	3.34894i	−0.129034	−	0.134280i
$623$	−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
$628$	29.9936	−	27.6939i	1.19687	−	1.10511i
$629$			8.52062i			0.339739i
$630$	6.47610	+	7.75375i	0.258014	+	0.308917i
$631$			5.20294i			0.207126i	0.994623	+	0.103563i	$0.0330243\pi$
$631$			5.20294i			0.207126i	−0.994623	+	0.103563i	$0.966976\pi$
$632$	9.84078	+	11.0934i	0.391445	+	0.441271i
$633$	−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
$638$	31.3818	−	30.1558i	1.24242	−	1.19388i
$639$	−34.4216			−1.36170
$640$	5.25079	−	24.7473i	0.207556	−	0.978223i
$641$	−3.06495			−0.121058			−0.0605290	−	0.998166i	$-0.519279\pi$
$641$	−3.06495			−0.121058			−0.0605290	+	0.998166i	$0.519279\pi$
$642$	−16.6721	+	16.0207i	−0.657993	+	0.632286i
$643$	−14.6071	−	14.6071i	−0.576047	−	0.576047i	0.357764	−	0.933812i	$-0.383539\pi$
$643$	−14.6071	−	14.6071i	−0.576047	−	0.576047i	−0.933812	+	0.357764i	$0.883539\pi$
$644$	−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	$-0.744806\pi$
$647$	0.586994	−	0.586994i	0.0230771	−	0.0230771i	0.718551	+	0.695474i	$0.244806\pi$
$648$	−6.29987	−	7.10176i	−0.247482	−	0.278984i
$649$		−	1.36949i		−	0.0537571i
$650$	−39.5406	−	6.34747i	−1.55091	−	0.248968i
$651$			1.56763i			0.0614403i
$652$	−28.0741	+	25.9216i	−1.09947	+	1.01517i
$653$	−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
$658$	−11.6846	−	12.1597i	−0.455515	−	0.474035i
$659$	33.1760			1.29235			0.646177	−	0.763188i	$-0.276367\pi$
$659$	33.1760			1.29235			0.646177	+	0.763188i	$0.276367\pi$
$660$	−1.90607	+	17.3424i	−0.0741936	+	0.675054i
$661$	14.2978			0.556121			0.278060	−	0.960564i	$-0.410308\pi$
$661$	14.2978			0.556121			0.278060	+	0.960564i	$0.410308\pi$
$662$	26.5200	+	27.5982i	1.03073	+	1.07264i
$663$	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
$668$	−22.1577	−	23.9976i	−0.857306	−	0.928495i
$669$			20.6975i			0.800213i
$670$	−10.9876	+	9.17708i	−0.424488	+	0.354541i
$671$		−	21.9678i		−	0.848057i
$672$	4.96063	−	4.05920i	0.191360	−	0.156587i
$673$	−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	$-0.521352\pi$
$678$	−0.700738	+	0.673360i	−0.0269117	+	0.0258602i
$679$	−6.11628			−0.234721
$680$	−8.69433	+	6.69228i	−0.333412	+	0.256637i
$681$	7.90569			0.302947
$682$	6.68333	−	6.42222i	0.255918	−	0.245919i
$683$	−17.0782	−	17.0782i	−0.653480	−	0.653480i	0.300349	−	0.953829i	$-0.402897\pi$
$683$	−17.0782	−	17.0782i	−0.653480	−	0.653480i	−0.953829	+	0.300349i	$0.902897\pi$
$684$	−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
$688$	17.3394	+	20.3490i	0.661057	+	0.775797i
$689$		−	29.2344i		−	1.11374i
$690$	−0.603251	+	6.71869i	−0.0229654	+	0.255776i
$691$		−	40.9903i		−	1.55934i	−0.626188	−	0.779672i	$-0.715386\pi$
$691$		−	40.9903i		−	1.55934i	0.626188	−	0.779672i	$-0.284614\pi$
$692$	20.8178	+	22.5465i	0.791373	+	0.857088i
$693$	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
$698$	2.23821	+	2.32921i	0.0847175	+	0.0881619i
$699$	−22.5314			−0.852216
$700$	11.3069	−	7.84055i	0.427360	−	0.296345i
$701$	−14.1506			−0.534461			−0.267231	−	0.963633i	$-0.586109\pi$
$701$	−14.1506			−0.534461			−0.267231	+	0.963633i	$0.586109\pi$
$702$	24.3213	+	25.3102i	0.917949	+	0.955271i
$703$	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
$708$	−0.349816	+	0.322995i	−0.0131469	+	0.0121389i
$709$			12.9874i			0.487753i	0.969806	+	0.243877i	$0.0784192\pi$
$709$			12.9874i			0.487753i	−0.969806	+	0.243877i	$0.921581\pi$
$710$	−4.19246	+	46.6935i	−0.157340	+	1.75237i
$711$		−	12.1731i		−	0.456529i
$712$	18.3643	−	16.2907i	0.688230	−	0.610519i
$713$	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
$718$	−28.9572	+	27.8259i	−1.08067	+	1.03845i
$719$	45.7262			1.70530			0.852649	−	0.522484i	$-0.174995\pi$
$719$	45.7262			1.70530			0.852649	+	0.522484i	$0.174995\pi$
$720$	−16.7056	+	12.3367i	−0.622581	+	0.459763i
$721$	−10.1351			−0.377449
$722$	−1.01972	+	0.979881i	−0.0379501	+	0.0364674i
$723$	−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	$-0.583534\pi$
$727$	19.0449	−	19.0449i	0.706336	−	0.706336i	0.965763	+	0.259427i	$0.0835337\pi$
$728$	16.4882	−	14.6265i	0.611094	−	0.542093i
$729$		−	3.03429i		−	0.112381i
$730$	−20.6306	+	17.2311i	−0.763572	+	0.637751i
$731$		−	11.5946i		−	0.428842i
$732$	−5.61135	+	5.18112i	−0.207402	+	0.191500i
$733$	−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
$738$	−15.2074	−	15.8257i	−0.559793	−	0.582554i
$739$	53.0093			1.94998			0.974989	−	0.222254i	$-0.0713416\pi$
$739$	53.0093			1.94998			0.974989	+	0.222254i	$0.0713416\pi$
$740$	21.8341	+	2.39973i	0.802637	+	0.0882160i
$741$	4.66393			0.171334
$742$	6.95957	+	7.24253i	0.255494	+	0.265882i
$743$	−18.7441	−	18.7441i	−0.687655	−	0.687655i	0.274058	−	0.961713i	$-0.411634\pi$
$743$	−18.7441	−	18.7441i	−0.687655	−	0.687655i	−0.961713	+	0.274058i	$0.911634\pi$
$744$	−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
$748$	11.1501	+	12.0760i	0.407690	+	0.441544i
$749$		−	27.3172i		−	0.998150i
$750$	11.0554	−	6.87894i	0.403687	−	0.251183i
$751$		−	12.1326i		−	0.442724i	−0.975192	−	0.221362i	$-0.928950\pi$
$751$		−	12.1326i		−	0.442724i	0.975192	−	0.221362i	$-0.0710502\pi$
$752$	26.3860	−	22.4836i	0.962200	−	0.819891i
$753$	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	$0.865247\pi$
$758$	−17.2195	+	16.5467i	−0.625439	+	0.601003i
$759$	10.1056			0.366810
$760$	−0.816051	+	6.27169i	−0.0296013	+	0.227498i
$761$	6.65971			0.241414			0.120707	−	0.992688i	$-0.461484\pi$
$761$	6.65971			0.241414			0.120707	+	0.992688i	$0.461484\pi$
$762$	13.2143	−	12.6980i	0.478703	−	0.460000i
$763$	−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
$768$	7.72030	+	10.6775i	0.278582	+	0.385289i
$769$		−	39.7893i		−	1.43484i	−0.696641	−	0.717420i	$-0.745323\pi$
$769$		−	39.7893i		−	1.43484i	0.696641	−	0.717420i	$-0.254677\pi$
$770$	−13.2135	−	15.8203i	−0.476180	−	0.570124i
$771$		−	1.88639i		−	0.0679368i
$772$	−19.8189	−	21.4646i	−0.713298	−	0.772529i
$773$	7.50151	−	7.50151i	0.269811	−	0.269811i	−0.559213	−	0.829024i	$-0.688897\pi$
$773$	7.50151	−	7.50151i	0.269811	−	0.269811i	0.829024	+	0.559213i	$0.188897\pi$
$774$	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
$778$	−32.6887	−	34.0178i	−1.17195	−	1.21960i
$779$	−6.68423			−0.239488
$780$	16.2717	−	13.0491i	0.582619	−	0.467232i
$781$	70.2318			2.51309
$782$	4.40329	+	4.58232i	0.157461	+	0.163863i
$783$	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	$-0.547865\pi$
$787$	23.5343	−	23.5343i	0.838908	−	0.838908i	0.988715	+	0.149807i	$0.0478653\pi$
$788$	−2.94433	+	2.71858i	−0.104887	+	0.0968454i
$789$			13.7024i			0.487819i
$790$	−16.5131	−	1.48266i	−0.587509	−	0.0527507i
$791$		−	1.14816i		−	0.0408239i
$792$	20.6454	+	23.2733i	0.733601	+	0.826980i
$793$	−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	0.876441	−	0.481510i	$-0.159911\pi$
$797$	11.1494	+	11.1494i	0.394931	+	0.394931i	−0.481510	+	0.876441i	$0.659911\pi$
$798$	−1.15544	+	1.11030i	−0.0409022	+	0.0393042i
$799$	−15.0345			−0.531881
$800$	14.7003	+	24.1640i	0.519735	+	0.854328i
$801$	−20.1517			−0.712026
$802$	9.08033	−	8.72556i	0.320637	−	0.308110i
$803$	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
$808$	−1.84484	−	2.07966i	−0.0649012	−	0.0731623i
$809$		−	6.48790i		−	0.228103i	−0.993475	−	0.114051i	$-0.963617\pi$
$809$		−	6.48790i		−	0.228103i	0.993475	−	0.114051i	$-0.0363828\pi$
$810$	10.5713	+	0.949169i	0.371439	+	0.0333504i
$811$			32.9698i			1.15773i	0.815424	+	0.578864i	$0.196504\pi$
$811$			32.9698i			1.15773i	−0.815424	+	0.578864i	$0.803496\pi$
$812$	13.1343	−	12.1273i	0.460924	−	0.425584i
$813$	−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
$818$	−13.0036	−	13.5323i	−0.454659	−	0.473145i
$819$	−18.0931			−0.632223
$820$	−23.3201	+	18.7016i	−0.814375	+	0.653089i
$821$	16.0339			0.559587			0.279794	−	0.960060i	$-0.409734\pi$
$821$	16.0339			0.559587			0.279794	+	0.960060i	$0.409734\pi$
$822$	8.84194	+	9.20144i	0.308398	+	0.320937i
$823$	−24.5540	−	24.5540i	−0.855899	−	0.855899i	0.134953	−	0.990852i	$-0.456912\pi$
$823$	−24.5540	−	24.5540i	−0.855899	−	0.855899i	−0.990852	+	0.134953i	$0.956912\pi$
$824$	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	$-0.792049\pi$
$827$	−5.35688	+	5.35688i	−0.186277	+	0.186277i	0.607808	+	0.794084i	$0.292049\pi$
$828$	8.16007	+	8.83766i	0.283582	+	0.307130i
$829$		−	3.90562i		−	0.135648i	−0.997697	−	0.0678240i	$-0.978394\pi$
$829$		−	3.90562i		−	0.135648i	0.997697	−	0.0678240i	$-0.0216056\pi$
$830$	12.6720	+	15.1720i	0.439850	+	0.526627i
$831$			16.4498i			0.570637i
$832$	27.9886	+	35.6292i	0.970331	+	1.23522i
$833$	−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
$838$	11.6387	−	11.1840i	0.402053	−	0.386345i
$839$	−3.17730			−0.109692			−0.0548462	−	0.998495i	$-0.517467\pi$
$839$	−3.17730			−0.109692			−0.0548462	+	0.998495i	$0.517467\pi$
$840$	−0.924664	+	7.10642i	−0.0319039	+	0.245195i
$841$	−13.2013			−0.455216
$842$	−16.4135	+	15.7722i	−0.565645	+	0.543545i
$843$	−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
$848$	−15.7160	+	13.3916i	−0.539688	+	0.459869i
$849$		−	4.33400i		−	0.148742i
$850$	1.94429	−	12.1117i	0.0666885	−	0.415426i
$851$		−	12.7229i		−	0.436137i
$852$	−16.5642	−	17.9397i	−0.567481	−	0.614604i
$853$	2.55407	−	2.55407i	0.0874497	−	0.0874497i	−0.662029	−	0.749478i	$-0.730304\pi$
$853$	2.55407	−	2.55407i	0.0874497	−	0.0874497i	0.749478	+	0.662029i	$0.230304\pi$
$854$	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	−0.987204	−	0.159465i	$-0.949023\pi$
$857$	−33.5682	−	33.5682i	−1.14667	−	1.14667i	−0.159465	−	0.987204i	$-0.550977\pi$
$858$	−21.6501	−	22.5304i	−0.739122	−	0.769174i
$859$	39.6086			1.35143			0.675714	−	0.737164i	$-0.263835\pi$
$859$	39.6086			1.35143			0.675714	+	0.737164i	$0.263835\pi$
$860$	−29.7112	−	3.26548i	−1.01314	−	0.111352i
$861$	−7.57388			−0.258117
$862$	−16.4455	−	17.1141i	−0.560135	−	0.582910i
$863$	0.501749	+	0.501749i	0.0170797	+	0.0170797i	0.715595	−	0.698515i	$-0.246156\pi$
$863$	0.501749	+	0.501749i	0.0170797	+	0.0170797i	−0.698515	+	0.715595i	$0.746156\pi$
$864$	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
$868$	2.79719	−	2.58273i	0.0949428	−	0.0876634i
$869$			24.8374i			0.842551i
$870$	12.9842	−	10.8447i	0.440205	−	0.367668i
$871$		−	25.6391i		−	0.868749i
$872$	27.6840	−	24.5581i	0.937500	−	0.831642i
$873$	−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	0.909159	−	0.416450i	$-0.136726\pi$
$877$	14.5912	+	14.5912i	0.492709	+	0.492709i	−0.416450	+	0.909159i	$0.636726\pi$
$878$	15.9489	−	15.3258i	0.538249	−	0.517220i
$879$	−7.13241			−0.240570
$880$	34.0852	−	25.1712i	1.14901	−	0.848521i
$881$	23.8812			0.804578			0.402289	−	0.915513i	$-0.368215\pi$
$881$	23.8812			0.804578			0.402289	+	0.915513i	$0.368215\pi$
$882$	−12.0910	+	11.6186i	−0.407125	+	0.391218i
$883$	0.694415	+	0.694415i	0.0233689	+	0.0233689i	0.718695	−	0.695326i	$-0.244740\pi$
$883$	0.694415	+	0.694415i	0.0233689	+	0.0233689i	−0.695326	+	0.718695i	$0.744740\pi$
$884$	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	$-0.530692\pi$
$887$	26.7770	−	26.7770i	0.899084	−	0.899084i	0.995355	+	0.0962716i	$0.0306917\pi$
$888$	−8.55832	+	7.59196i	−0.287199	+	0.254770i
$889$			21.6517i			0.726173i
$890$	−2.45443	+	27.3362i	−0.0822727	+	0.916311i
$891$		−	15.9004i		−	0.532683i
$892$	36.9315	−	34.0999i	1.23656	−	1.14175i
$893$	−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
$898$	−35.3721	−	36.8103i	−1.18038	−	1.22837i
$899$	−8.98752			−0.299751
$900$	4.13606	−	22.8470i	0.137869	−	0.761565i
$901$	8.95477			0.298327
$902$	31.0284	+	32.2900i	1.03313	+	1.07514i
$903$	−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	$-0.884283\pi$
$907$	−17.4394	+	17.4394i	−0.579066	+	0.579066i	0.355580	+	0.934646i	$0.384283\pi$
$908$	−13.0249	−	14.1065i	−0.432246	−	0.468139i
$909$			2.28208i			0.0756919i
$910$	−2.20369	+	24.5436i	−0.0730517	+	0.813612i
$911$			15.9437i			0.528237i	0.964490	+	0.264119i	$0.0850810\pi$
$911$			15.9437i			0.528237i	−0.964490	+	0.264119i	$0.914919\pi$
$912$	−2.13643	−	2.50726i	−0.0707444	−	0.0830235i
$913$	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
$918$	−7.75274	+	7.44984i	−0.255878	+	0.245881i
$919$	−26.2087			−0.864546			−0.432273	−	0.901743i	$-0.642288\pi$
$919$	−26.2087			−0.864546			−0.432273	+	0.901743i	$0.642288\pi$
$920$	12.9823	−	9.99287i	0.428015	−	0.329455i
$921$	4.94096			0.162810
$922$	−34.2653	+	32.9265i	−1.12847	+	1.08438i
$923$	−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
$928$	23.2722	+	28.4402i	0.763947	+	0.933596i
$929$			49.0636i			1.60972i	0.593462	+	0.804862i	$0.297761\pi$
$929$			49.0636i			1.60972i	−0.593462	+	0.804862i	$0.702239\pi$
$930$	2.76522	−	2.30957i	0.0906750	−	0.0757337i
$931$			5.10680i			0.167369i
$932$	37.1212	+	40.2037i	1.21595	+	1.31692i
$933$	−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	−0.995707	−	0.0925647i	$-0.970493\pi$
$937$	−33.3125	−	33.3125i	−1.08827	−	1.08827i	−0.0925647	−	0.995707i	$-0.529507\pi$
$938$	6.10367	+	6.35184i	0.199292	+	0.207395i
$939$	−3.47961			−0.113553
$940$	−4.23428	+	38.5258i	−0.138107	+	1.25657i
$941$	37.9053			1.23568			0.617839	−	0.786305i	$-0.288008\pi$
$941$	37.9053			1.23568			0.617839	+	0.786305i	$0.288008\pi$
$942$	−16.4711	−	17.1408i	−0.536659	−	0.558478i
$943$	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	$-0.535810\pi$
$947$	27.1241	−	27.1241i	0.881415	−	0.881415i	0.993678	+	0.112263i	$0.0358100\pi$
$948$	6.34435	−	5.85792i	0.206055	−	0.190256i
$949$		−	48.1407i		−	1.56271i
$950$	−4.14429	−	5.72930i	−0.134459	−	0.185883i
$951$		−	6.36083i		−	0.206264i
$952$	4.48022	+	5.05050i	0.145205	+	0.163687i
$953$	−2.24190	+	2.24190i	−0.0726223	+	0.0726223i	−0.742485	−	0.669863i	$-0.766353\pi$
$953$	−2.24190	+	2.24190i	−0.0726223	+	0.0726223i	0.669863	+	0.742485i	$0.266353\pi$
$954$	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
$958$	35.1827	−	33.8081i	1.13670	−	1.09229i
$959$	−15.0766			−0.486849
$960$	−14.4686	−	2.76991i	−0.466973	−	0.0893986i
$961$	29.0859			0.938256
$962$	−28.3657	+	27.2574i	−0.914546	+	0.878815i
$963$	−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	$-0.908942\pi$
$967$	−21.0580	+	21.0580i	−0.677179	+	0.677179i	0.282182	+	0.959361i	$0.408942\pi$
$968$	−21.4770	−	24.2107i	−0.690295	−	0.778161i
$969$			1.42861i			0.0458934i
$970$	9.01101	+	10.7888i	0.289326	+	0.346407i
$971$			51.7396i			1.66040i	0.557463	+	0.830202i	$0.311775\pi$
$971$			51.7396i			1.66040i	−0.557463	+	0.830202i	$0.688225\pi$
$972$	−23.3811	+	21.5884i	−0.749949	+	0.692450i
$973$	−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	0.991123	+	0.132944i	$0.0424432\pi$
$977$	35.1350	+	35.1350i	1.12407	+	1.12407i	0.132944	+	0.991123i	$0.457557\pi$
$978$	15.4170	+	16.0439i	0.492982	+	0.513026i
$979$	41.1164			1.31409
$980$	14.2882	+	17.8168i	0.456419	+	0.569135i
$981$	−30.3786			−0.969914
$982$	−14.4323	−	15.0191i	−0.460552	−	0.479277i
$983$	3.13196	+	3.13196i	0.0998941	+	0.0998941i	0.755288	−	0.655393i	$-0.227497\pi$
$983$	3.13196	+	3.13196i	0.0998941	+	0.0998941i	−0.655393	+	0.755288i	$0.727497\pi$
$984$	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
$988$	−7.68399	−	8.32205i	−0.244460	−	0.264760i
$989$			17.3130i			0.550521i
$990$	−34.6435	−	3.11053i	−1.10104	−	0.0988591i
$991$		−	14.2396i		−	0.452334i	−0.974089	−	0.226167i	$-0.927380\pi$
$991$		−	14.2396i		−	0.452334i	0.974089	−	0.226167i	$-0.0726196\pi$
$992$	4.95623	+	6.05686i	0.157361	+	0.192306i
$993$	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	0.886425	−	0.462873i	$-0.153181\pi$
$997$	13.3738	+	13.3738i	0.423552	+	0.423552i	−0.462873	+	0.886425i	$0.653181\pi$
$998$	−32.8091	+	31.5272i	−1.03855	+	0.997976i
$999$	21.5257			0.681043

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.k.c.267.6	✓	52	1.1	even	1	trivial
380.2.k.c.343.6	yes	52	20.3	even	4	inner
380.2.k.d.267.20	yes	52	4.3	odd	2
380.2.k.d.343.20	yes	52	5.3	odd	4

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)

\(f(q)\)	\(=\)	\(q+(-1.01972 + 0.979881i) q^{2} +(0.582309 + 0.582309i) q^{3} +(0.0796647 - 1.99841i) q^{4} +(1.46731 + 1.68731i) q^{5} +(-1.16439 - 0.0231993i) q^{6} +(0.972933 - 0.972933i) q^{7} +(1.87697 + 2.11589i) q^{8} -2.32183i q^{9} +O(q^{10})\)	\(q+(-1.01972 + 0.979881i) 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} +(1.87697 + 2.11589i) q^{8} -2.32183i q^{9} +(-3.14961 - 0.282794i) q^{10} +4.73734i q^{11} +(1.21008 - 1.11730i) 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} +(2.27512 + 2.36762i) q^{18} +1.00000 q^{19} +(3.48883 - 2.79787i) q^{20} +1.13310 q^{21} +(-4.64203 - 4.83076i) 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} +(-1.86681 - 2.02183i) q^{28} +6.49625i q^{29} +(-1.66937 - 1.99872i) q^{30} +1.38349i q^{31} +(4.37794 - 3.58240i) 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} +(-1.01972 + 0.979881i) q^{38} +4.66393 q^{39} +(-0.816051 + 6.27169i) q^{40} -6.68423 q^{41} +(-1.15544 + 1.11030i) 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} +(-2.13643 - 2.50726i) q^{48} +5.10680i q^{49} +(-4.14429 - 5.72930i) q^{50} +1.42861i q^{51} +(-7.68399 - 8.32205i) 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} +(-6.36555 - 6.62437i) q^{58} -0.289084 q^{59} +(3.66080 + 0.402350i) q^{60} -4.63716 q^{61} +(-1.35566 - 1.41078i) 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} +(2.54912 - 2.35368i) q^{68} -2.13318i q^{69} +(-3.33950 + 2.78922i) q^{70} -14.8252i q^{71} +(4.91273 - 4.35801i) 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} +(-4.75591 + 4.57010i) q^{78} +5.24290 q^{79} +(-5.31337 - 7.19501i) q^{80} -3.35640 q^{81} +(6.81606 - 6.54976i) 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} +(-10.0237 + 8.89184i) q^{88} -8.67923i q^{89} +(-0.656599 + 7.31286i) q^{90} -7.79259i q^{91} +(-3.80633 + 3.51449i) 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} +(-5.00406 - 5.20752i) 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	\( 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) \) 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

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