LMFDB - Embedded newform 380.2.k.c.343.6

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			343.6
Character	$\chi$	$=$	380.343
Dual form			380.2.k.c.267.6

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

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

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 $

$2$	−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	−0.518737	−	0.854934i	$-0.673598\pi$
$3$	0.582309	−	0.582309i	0.336196	−	0.336196i	0.854934	+	0.518737i	$0.173598\pi$
$4$	0.0796647	+	1.99841i	0.0398324	+	0.999206i
$5$	1.46731	−	1.68731i	0.656201	−	0.754586i
$5$	1.46731	−	1.68731i	0.656201	−	0.754586i
$6$	−1.16439	+	0.0231993i	−0.475359	+	0.00947109i
$7$	0.972933	+	0.972933i	0.367734	+	0.367734i	0.866650	−	0.498916i	$-0.166268\pi$
$7$	0.972933	+	0.972933i	0.367734	+	0.367734i	−0.498916	+	0.866650i	$0.666268\pi$
$8$	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	$-0.746800\pi$
$11$		−	4.73734i		−	1.42836i	0.699962	−	0.714180i	$-0.253200\pi$
$12$	1.21008	+	1.11730i	0.349321	+	0.322538i
$13$	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	$0.182532\pi$
$18$	2.27512	−	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	−0.871796	−	0.489869i	$-0.837045\pi$
$23$	−1.83166	+	1.83166i	−0.381928	+	0.381928i	0.489869	+	0.871796i	$0.337045\pi$
$24$	−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	$-0.793907\pi$
$29$		−	6.49625i		−	1.20632i	0.797619	−	0.603162i	$-0.206093\pi$
$30$	−1.66937	+	1.99872i	−0.304784	+	0.364914i
$31$		−	1.38349i		−	0.248483i	−0.992252	−	0.124241i	$-0.960350\pi$
$31$		−	1.38349i		−	0.248483i	0.992252	−	0.124241i	$-0.0396497\pi$
$32$	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	−0.361431	−	0.932399i	$-0.617712\pi$
$37$	3.47306	−	3.47306i	0.570968	−	0.570968i	0.932399	+	0.361431i	$0.117712\pi$
$38$	−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	−0.968751	−	0.248037i	$-0.920215\pi$
$43$	−4.72604	+	4.72604i	−0.720714	+	0.720714i	0.248037	+	0.968751i	$0.420215\pi$
$44$	9.46715	−	0.377398i	1.42723	−	0.0568950i
$45$	3.91764	+	3.40685i	0.584008	+	0.507863i
$46$	3.66259	−	0.0729738i	0.540020	−	0.0107594i
$47$	−6.12814	−	6.12814i	−0.893882	−	0.893882i	0.101004	−	0.994886i	$-0.467794\pi$
$47$	−6.12814	−	6.12814i	−0.893882	−	0.893882i	−0.994886	+	0.101004i	$0.967794\pi$
$48$	−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	0.911863	−	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
$58$	−6.36555	+	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	0.875073	−	0.483991i	$-0.160813\pi$
$67$	3.20114	+	3.20114i	0.391082	+	0.391082i	−0.483991	+	0.875073i	$0.660813\pi$
$68$	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	$0.342265\pi$
$71$			14.8252i			1.75942i	−0.475507	+	0.879712i	$0.657735\pi$
$72$	4.91273	+	4.35801i	0.578971	+	0.513597i
$73$	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
$78$	−4.75591	−	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	−0.906782	−	0.421600i	$-0.861469\pi$
$83$	−4.42022	+	4.42022i	−0.485183	+	0.485183i	0.421600	+	0.906782i	$0.361469\pi$
$84$	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	$0.152150\pi$
$89$			8.67923i			0.919997i	−0.887920	+	0.459998i	$0.847850\pi$
$90$	−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	−0.848439	−	0.529294i	$-0.822457\pi$
$97$	−3.14322	+	3.14322i	−0.319145	+	0.319145i	0.529294	+	0.848439i	$0.322457\pi$
$98$	−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	−0.915508	−	0.402299i	$-0.868211\pi$
$103$	−5.20851	+	5.20851i	−0.513209	+	0.513209i	0.402299	+	0.915508i	$0.368211\pi$
$104$	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	$0.159279\pi$
$107$	14.0386	+	14.0386i	1.35716	+	1.35716i	0.479767	+	0.877396i	$0.340721\pi$
$108$	−5.94611	+	6.43986i	−0.572164	+	0.619676i
$109$			13.0839i			1.25321i	0.779337	+	0.626605i	$0.215556\pi$
$109$			13.0839i			1.25321i	−0.779337	+	0.626605i	$0.784444\pi$
$110$	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	0.734316	−	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
$118$	0.294785	+	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	0.0125590	−	0.999921i	$-0.496002\pi$
$127$	−11.1270	−	11.1270i	−0.987362	−	0.987362i	−0.999921	+	0.0125590i	$0.996002\pi$
$128$	−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	$-0.936025\pi$
$131$		−	4.56983i		−	0.399268i	0.979871	−	0.199634i	$-0.0639753\pi$
$132$	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	−0.955841	−	0.293884i	$-0.905052\pi$
$137$	−7.74801	+	7.74801i	−0.661957	+	0.661957i	0.293884	+	0.955841i	$0.405052\pi$
$138$	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	$-0.796683\pi$
$149$		−	14.5547i		−	1.19237i	0.802848	−	0.596184i	$-0.203317\pi$
$150$	0.922965	+	5.74948i	0.0753598	+	0.469443i
$151$		−	19.5609i		−	1.59185i	−0.605397	−	0.795924i	$-0.706986\pi$
$151$		−	19.5609i		−	1.59185i	0.605397	−	0.795924i	$-0.293014\pi$
$152$	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	0.165734	−	0.986170i	$-0.447001\pi$
$157$	14.4333	−	14.4333i	1.15190	−	1.15190i	0.986170	−	0.165734i	$-0.0529994\pi$
$158$	−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	−0.0599555	+	0.998201i	$0.519096\pi$
$163$	−13.5096	+	13.5096i	−1.05816	+	1.05816i	−0.998201	+	0.0599555i	$0.980904\pi$
$164$	−0.532498	−	13.3579i	−0.0415811	−	1.04307i
$165$	−8.70230	+	0.606882i	−0.677473	+	0.0472457i
$166$	8.83869	−	0.176103i	0.686016	−	0.0136682i
$167$	11.5480	+	11.5480i	0.893610	+	0.893610i	0.994861	−	0.101251i	$-0.0322846\pi$
$167$	11.5480	+	11.5480i	0.893610	+	0.893610i	−0.101251	+	0.994861i	$0.532285\pi$
$168$	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	0.161919	−	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
$178$	8.50462	−	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	$0.0153802\pi$
$191$			1.33503i			0.0965990i	−0.998833	+	0.0482995i	$0.984620\pi$
$192$	−5.18073	−	4.06974i	−0.373887	−	0.293708i
$193$	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	$0.272740\pi$
$198$	−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	$-0.895689\pi$
$211$		−	9.35082i		−	0.643737i	0.946784	−	0.321868i	$-0.104311\pi$
$212$	−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	0.213058	−	0.977040i	$-0.431658\pi$
$223$	17.7719	−	17.7719i	1.19010	−	1.19010i	0.977040	−	0.213058i	$-0.0683424\pi$
$224$	0.774008	+	7.74488i	0.0517156	+	0.517477i
$225$	11.4968	−	1.61136i	0.766452	−	0.107424i
$226$	−0.0235078	−	1.17987i	−0.00156372	−	0.0784838i
$227$	6.78822	+	6.78822i	0.450550	+	0.450550i	0.895537	−	0.444987i	$-0.146792\pi$
$227$	6.78822	+	6.78822i	0.450550	+	0.450550i	−0.444987	+	0.895537i	$0.646792\pi$
$228$	1.21008	+	1.11730i	0.0801397	+	0.0739953i
$229$			22.4951i			1.48652i	0.669004	+	0.743259i	$0.266721\pi$
$229$			22.4951i			1.48652i	−0.669004	+	0.743259i	$0.733279\pi$
$230$	5.25103	−	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	−0.947407	−	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
$238$	−2.43401	−	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	$0.0355496\pi$
$251$			3.53141i			0.222900i	−0.993770	+	0.111450i	$0.964450\pi$
$252$	−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	−0.755819	−	0.654781i	$-0.772761\pi$
$257$	−1.61975	+	1.61975i	−0.101037	+	0.101037i	0.654781	+	0.755819i	$0.272761\pi$
$258$	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	−0.244222	−	0.969719i	$-0.578533\pi$
$263$	11.7656	−	11.7656i	0.725497	−	0.725497i	0.969719	+	0.244222i	$0.0785326\pi$
$264$	−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	$0.0566587\pi$
$269$			5.80800i			0.354120i	−0.984200	+	0.177060i	$0.943341\pi$
$270$	−10.6368	−	8.88412i	−0.647338	−	0.540670i
$271$		−	15.9470i		−	0.968709i	−0.874872	−	0.484354i	$-0.839055\pi$
$271$		−	15.9470i		−	0.968709i	0.874872	−	0.484354i	$-0.160945\pi$
$272$	−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	−0.141300	−	0.989967i	$-0.545128\pi$
$277$	14.1246	−	14.1246i	0.848667	−	0.848667i	0.989967	+	0.141300i	$0.0451282\pi$
$278$	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	−0.809009	−	0.587796i	$-0.799996\pi$
$283$	−3.72139	+	3.72139i	−0.221214	+	0.221214i	0.587796	+	0.809009i	$0.299996\pi$
$284$	−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	0.505213	−	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
$298$	−14.2619	+	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	0.817733	−	0.575597i	$-0.195230\pi$
$307$	4.24256	+	4.24256i	0.242136	+	0.242136i	−0.575597	+	0.817733i	$0.695230\pi$
$308$	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	$-0.970318\pi$
$311$		−	3.28417i		−	0.186228i	0.995655	−	0.0931141i	$-0.0296821\pi$
$312$	8.75407	−	9.86835i	0.495602	−	0.558686i
$313$	−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	$0.319599\pi$
$318$	−4.33472	−	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	$0.266978\pi$
$331$			27.0645i			1.48760i	−0.668403	+	0.743799i	$0.733022\pi$
$332$	−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	−0.872558	−	0.488510i	$-0.837541\pi$
$337$	−7.05018	+	7.05018i	−0.384048	+	0.384048i	0.488510	+	0.872558i	$0.337541\pi$
$338$	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	0.857141	−	0.515083i	$-0.172239\pi$
$347$	6.37184	+	6.37184i	0.342058	+	0.342058i	−0.515083	+	0.857141i	$0.672239\pi$
$348$	7.25829	−	7.86100i	0.389085	−	0.421394i
$349$			2.28416i			0.122268i	0.998130	+	0.0611342i	$0.0194718\pi$
$349$			2.28416i			0.122268i	−0.998130	+	0.0611342i	$0.980528\pi$
$350$	−9.60634	+	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	0.996552	−	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
$358$	4.69325	+	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	0.669310	−	0.742984i	$-0.266590\pi$
$367$	−1.41139	−	1.41139i	−0.0736740	−	0.0736740i	−0.742984	+	0.669310i	$0.766590\pi$
$368$	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	0.920259	−	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
$378$	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	−0.536076	−	0.844169i	$-0.680094\pi$
$383$	6.02950	−	6.02950i	0.308093	−	0.308093i	0.844169	+	0.536076i	$0.180094\pi$
$384$	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	$-0.679179\pi$
$389$		−	33.3599i		−	1.69141i	0.533647	−	0.845707i	$-0.320821\pi$
$390$	−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	−0.942168	−	0.335141i	$-0.891216\pi$
$397$	−12.0949	+	12.0949i	−0.607027	+	0.607027i	0.335141	+	0.942168i	$0.391216\pi$
$398$	−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	$-0.893594\pi$
$409$		−	13.2705i		−	0.656186i	0.944645	−	0.328093i	$-0.106406\pi$
$410$	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	$-0.867547\pi$
$431$		−	16.7831i		−	0.808415i	0.914667	−	0.404208i	$-0.132453\pi$
$432$	−13.3432	−	11.3697i	−0.641975	−	0.547027i
$433$	−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
$438$	−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	−0.974037	−	0.226387i	$-0.927309\pi$
$443$	−15.7362	+	15.7362i	−0.747651	+	0.747651i	0.226387	+	0.974037i	$0.427309\pi$
$444$	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	$-0.675515\pi$
$449$		−	36.0983i		−	1.70359i	0.523878	−	0.851793i	$-0.324485\pi$
$450$	−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	0.186773	−	0.982403i	$-0.440197\pi$
$457$	24.9941	−	24.9941i	1.16918	−	1.16918i	0.982403	−	0.186773i	$-0.0598028\pi$
$458$	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	−0.992159	−	0.124983i	$-0.960112\pi$
$463$	−18.6594	+	18.6594i	−0.867175	+	0.867175i	0.124983	+	0.992159i	$0.460112\pi$
$464$	2.06844	+	25.9025i	0.0960251	+	1.20250i
$465$	−2.54143	+	0.177234i	−0.117856	+	0.00821904i
$466$	0.770773	+	38.6855i	0.0357054	+	1.79207i
$467$	−3.14547	−	3.14547i	−0.145555	−	0.145555i	0.630574	−	0.776129i	$-0.282819\pi$
$467$	−3.14547	−	3.14547i	−0.145555	−	0.145555i	−0.776129	+	0.630574i	$0.782819\pi$
$468$	−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	0.284167	−	0.958775i	$-0.408283\pi$
$487$	−14.8873	−	14.8873i	−0.674607	−	0.674607i	−0.958775	+	0.284167i	$0.908283\pi$
$488$	−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	$-0.892160\pi$
$491$		−	14.7286i		−	0.664692i	0.943158	−	0.332346i	$-0.107840\pi$
$492$	−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	−0.302874	−	0.953031i	$-0.597946\pi$
$503$	14.5815	−	14.5815i	0.650157	−	0.650157i	0.953031	+	0.302874i	$0.0979461\pi$
$504$	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	$0.239522\pi$
$509$			30.8387i			1.36690i	−0.729996	+	0.683452i	$0.760478\pi$
$510$	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	0.0638230	−	0.997961i	$-0.479671\pi$
$523$	24.2821	−	24.2821i	1.06178	−	1.06178i	0.997961	−	0.0638230i	$-0.0203293\pi$
$524$	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	0.549875	−	0.835247i	$-0.314676\pi$
$547$	−6.67431	−	6.67431i	−0.285373	−	0.285373i	−0.835247	+	0.549875i	$0.814676\pi$
$548$	−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	−0.894598	−	0.446873i	$-0.852538\pi$
$557$	−10.5667	+	10.5667i	−0.447725	+	0.447725i	0.446873	+	0.894598i	$0.352538\pi$
$558$	−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	−0.191833	−	0.981428i	$-0.561443\pi$
$563$	18.7352	−	18.7352i	0.789595	−	0.789595i	0.981428	+	0.191833i	$0.0614431\pi$
$564$	−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	$-0.755926\pi$
$569$		−	33.1004i		−	1.38764i	0.720147	−	0.693821i	$-0.244074\pi$
$570$	−1.66937	+	1.99872i	−0.0699223	+	0.0837171i
$571$		−	17.4026i		−	0.728277i	−0.931345	−	0.364138i	$-0.881364\pi$
$571$		−	17.4026i		−	0.728277i	0.931345	−	0.364138i	$-0.118636\pi$
$572$	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	−0.607030	−	0.794679i	$-0.707639\pi$
$577$	4.50750	−	4.50750i	0.187650	−	0.187650i	0.794679	+	0.607030i	$0.207639\pi$
$578$	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	0.549176	−	0.835707i	$-0.314942\pi$
$587$	−6.94211	−	6.94211i	−0.286531	−	0.286531i	−0.835707	+	0.549176i	$0.814942\pi$
$588$	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	0.549793	−	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
$598$	14.9598	+	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	0.603117	−	0.797653i	$-0.293925\pi$
$607$	−4.79286	−	4.79286i	−0.194536	−	0.194536i	−0.797653	+	0.603117i	$0.793925\pi$
$608$	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	0.259677	−	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	$0.201555\pi$
$618$	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	$-0.966976\pi$
$631$		−	5.20294i		−	0.207126i	0.994623	−	0.103563i	$-0.0330243\pi$
$632$	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	−0.933812	−	0.357764i	$-0.883539\pi$
$643$	−14.6071	+	14.6071i	−0.576047	+	0.576047i	0.357764	+	0.933812i	$0.383539\pi$
$644$	−0.283938	−	7.12267i	−0.0111887	−	0.280673i
$645$	9.28699	+	8.07612i	0.365675	+	0.317997i
$646$	−2.45286	+	0.0488710i	−0.0965064	+	0.00192280i
$647$	0.586994	+	0.586994i	0.0230771	+	0.0230771i	0.718551	−	0.695474i	$-0.244806\pi$
$647$	0.586994	+	0.586994i	0.0230771	+	0.0230771i	−0.695474	+	0.718551i	$0.744806\pi$
$648$	−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	0.632507	−	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
$658$	−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	0.445127	−	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	$0.978648\pi$
$678$	−0.700738	−	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	−0.953829	−	0.300349i	$-0.902897\pi$
$683$	−17.0782	+	17.0782i	−0.653480	+	0.653480i	0.300349	+	0.953829i	$0.402897\pi$
$684$	−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	$0.284614\pi$
$691$			40.9903i			1.55934i	−0.626188	+	0.779672i	$0.715386\pi$
$692$	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	$-0.921581\pi$
$709$		−	12.9874i		−	0.487753i	0.969806	−	0.243877i	$-0.0784192\pi$
$710$	−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	0.965763	−	0.259427i	$-0.0835337\pi$
$727$	19.0449	+	19.0449i	0.706336	+	0.706336i	−0.259427	+	0.965763i	$0.583534\pi$
$728$	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	−0.983900	−	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
$738$	−15.2074	+	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	−0.961713	−	0.274058i	$-0.911634\pi$
$743$	−18.7441	+	18.7441i	−0.687655	+	0.687655i	0.274058	+	0.961713i	$0.411634\pi$
$744$	−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	$0.0710502\pi$
$751$			12.1326i			0.442724i	−0.975192	+	0.221362i	$0.928950\pi$
$752$	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	−0.911722	−	0.410808i	$-0.865247\pi$
$757$	−13.7820	+	13.7820i	−0.500914	+	0.500914i	0.410808	+	0.911722i	$0.365247\pi$
$758$	−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	$0.254677\pi$
$769$			39.7893i			1.43484i	−0.696641

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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