LMFDB - Embedded newform 380.2.k.d.267.11

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			267.11
Character	$\chi$	$=$	380.267
Dual form			380.2.k.d.343.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.283752 + 1.38545i) q^{2} +(1.20015 + 1.20015i) q^{3} +(-1.83897 - 0.786251i) q^{4} +(-2.06624 + 0.854787i) q^{5} +(-2.00330 + 1.32221i) q^{6} +(-1.52124 + 1.52124i) q^{7} +(1.61113 - 2.32471i) q^{8} -0.119262i q^{9} +O(q^{10})$	\(q+(-0.283752 + 1.38545i) q^{2} +(1.20015 + 1.20015i) q^{3} +(-1.83897 - 0.786251i) q^{4} +(-2.06624 + 0.854787i) q^{5} +(-2.00330 + 1.32221i) q^{6} +(-1.52124 + 1.52124i) q^{7} +(1.61113 - 2.32471i) q^{8} -0.119262i q^{9} +(-0.597969 - 3.10523i) q^{10} +4.01379i q^{11} +(-1.26342 - 3.15067i) q^{12} +(-1.50202 + 1.50202i) q^{13} +(-1.67595 - 2.53926i) q^{14} +(-3.50568 - 1.45393i) q^{15} +(2.76362 + 2.89178i) q^{16} +(-3.94831 - 3.94831i) q^{17} +(0.165232 + 0.0338407i) q^{18} -1.00000 q^{19} +(4.47183 + 0.0526560i) q^{20} -3.65143 q^{21} +(-5.56092 - 1.13892i) q^{22} +(-4.78362 - 4.78362i) q^{23} +(4.72361 - 0.856407i) q^{24} +(3.53868 - 3.53239i) q^{25} +(-1.65478 - 2.50718i) q^{26} +(3.74359 - 3.74359i) q^{27} +(3.99358 - 1.60143i) q^{28} +7.97836i q^{29} +(3.00910 - 4.44440i) q^{30} +10.3376i q^{31} +(-4.79062 + 3.00832i) q^{32} +(-4.81717 + 4.81717i) q^{33} +(6.59054 - 4.34986i) q^{34} +(1.84290 - 4.44357i) q^{35} +(-0.0937696 + 0.219318i) q^{36} +(6.01436 + 6.01436i) q^{37} +(0.283752 - 1.38545i) q^{38} -3.60530 q^{39} +(-1.34184 + 6.18057i) q^{40} +4.47478 q^{41} +(1.03610 - 5.05889i) q^{42} +(-1.96095 - 1.96095i) q^{43} +(3.15585 - 7.38124i) q^{44} +(0.101943 + 0.246423i) q^{45} +(7.98484 - 5.27012i) q^{46} +(2.21501 - 2.21501i) q^{47} +(-0.153821 + 6.78735i) q^{48} +2.37169i q^{49} +(3.88985 + 5.90500i) q^{50} -9.47715i q^{51} +(3.94313 - 1.58120i) q^{52} +(-5.27852 + 5.27852i) q^{53} +(4.12433 + 6.24883i) q^{54} +(-3.43093 - 8.29345i) q^{55} +(1.08552 + 5.98733i) q^{56} +(-1.20015 - 1.20015i) q^{57} +(-11.0537 - 2.26388i) q^{58} -5.37196 q^{59} +(5.30368 + 5.43007i) q^{60} +12.0386 q^{61} +(-14.3223 - 2.93332i) q^{62} +(0.181425 + 0.181425i) q^{63} +(-2.80854 - 7.49080i) q^{64} +(1.81962 - 4.38743i) q^{65} +(-5.30708 - 8.04085i) q^{66} +(-0.631476 + 0.631476i) q^{67} +(4.15645 + 10.3652i) q^{68} -11.4821i q^{69} +(5.63343 + 3.81413i) q^{70} +6.42369i q^{71} +(-0.277248 - 0.192146i) q^{72} +(-2.26914 + 2.26914i) q^{73} +(-10.0392 + 6.62604i) q^{74} +(8.48637 + 0.00755284i) q^{75} +(1.83897 + 0.786251i) q^{76} +(-6.10592 - 6.10592i) q^{77} +(1.02301 - 4.99499i) q^{78} -4.54855 q^{79} +(-8.18215 - 3.61281i) q^{80} +8.62799 q^{81} +(-1.26973 + 6.19961i) q^{82} +(4.42714 + 4.42714i) q^{83} +(6.71487 + 2.87094i) q^{84} +(11.5331 + 4.78318i) q^{85} +(3.27323 - 2.16038i) q^{86} +(-9.57526 + 9.57526i) q^{87} +(9.33089 + 6.46673i) q^{88} +8.81939i q^{89} +(-0.370334 + 0.0713147i) q^{90} -4.56984i q^{91} +(5.03580 + 12.5580i) q^{92} +(-12.4067 + 12.4067i) q^{93} +(2.44029 + 3.69731i) q^{94} +(2.06624 - 0.854787i) q^{95} +(-9.35992 - 2.13904i) q^{96} +(8.06581 + 8.06581i) q^{97} +(-3.28586 - 0.672971i) q^{98} +0.478691 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) $ 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8	$ 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) $ 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.283752	+	1.38545i	−0.200643	+	0.979664i
$2$	−0.283752	+	1.38545i	−0.200643	+	0.979664i
$3$	1.20015	+	1.20015i	0.692909	+	0.692909i	0.962871	−	0.269962i	$-0.0870111\pi$
$3$	1.20015	+	1.20015i	0.692909	+	0.692909i	−0.269962	+	0.962871i	$0.587011\pi$
$4$	−1.83897	−	0.786251i	−0.919485	−	0.393126i
$5$	−2.06624	+	0.854787i	−0.924050	+	0.382272i
$5$	−2.06624	+	0.854787i	−0.924050	+	0.382272i
$6$	−2.00330	+	1.32221i	−0.817846	+	0.539791i
$7$	−1.52124	+	1.52124i	−0.574973	+	0.574973i	−0.933514	−	0.358541i	$-0.883274\pi$
$7$	−1.52124	+	1.52124i	−0.574973	+	0.574973i	0.358541	+	0.933514i	$0.383274\pi$
$8$	1.61113	−	2.32471i	0.569620	−	0.821908i
$9$		−	0.119262i		−	0.0397539i
$10$	−0.597969	−	3.10523i	−0.189094	−	0.981959i
$11$			4.01379i			1.21020i	0.796148	+	0.605102i	$0.206868\pi$
$11$			4.01379i			1.21020i	−0.796148	+	0.605102i	$0.793132\pi$
$12$	−1.26342	−	3.15067i	−0.364719	−	0.909520i
$13$	−1.50202	+	1.50202i	−0.416585	+	0.416585i	−0.884025	−	0.467440i	$-0.845176\pi$
$13$	−1.50202	+	1.50202i	−0.416585	+	0.416585i	0.467440	+	0.884025i	$0.345176\pi$
$14$	−1.67595	−	2.53926i	−0.447916	−	0.678645i
$15$	−3.50568	−	1.45393i	−0.905162	−	0.375403i
$16$	2.76362	+	2.89178i	0.690904	+	0.722946i
$17$	−3.94831	−	3.94831i	−0.957605	−	0.957605i	0.0415323	−	0.999137i	$-0.486776\pi$
$17$	−3.94831	−	3.94831i	−0.957605	−	0.957605i	−0.999137	+	0.0415323i	$0.986776\pi$
$18$	0.165232	+	0.0338407i	0.0389455	+	0.00797634i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	4.47183	+	0.0526560i	0.999931	+	0.0117742i
$21$	−3.65143			−0.796808
$22$	−5.56092	−	1.13892i	−1.18559	−	0.242819i
$23$	−4.78362	−	4.78362i	−0.997453	−	0.997453i	0.00254405	−	0.999997i	$-0.499190\pi$
$23$	−4.78362	−	4.78362i	−0.997453	−	0.997453i	−0.999997	+	0.00254405i	$0.999190\pi$
$24$	4.72361	−	0.856407i	0.964202	−	0.174813i
$25$	3.53868	−	3.53239i	0.707736	−	0.706477i
$26$	−1.65478	−	2.50718i	−0.324528	−	0.491698i
$27$	3.74359	−	3.74359i	0.720455	−	0.720455i
$28$	3.99358	−	1.60143i	0.754715	−	0.302642i
$29$			7.97836i			1.48154i	0.671757	+	0.740772i	$0.265540\pi$
$29$			7.97836i			1.48154i	−0.671757	+	0.740772i	$0.734460\pi$
$30$	3.00910	−	4.44440i	0.549383	−	0.811434i
$31$			10.3376i			1.85669i	0.371719	+	0.928345i	$0.378768\pi$
$31$			10.3376i			1.85669i	−0.371719	+	0.928345i	$0.621232\pi$
$32$	−4.79062	+	3.00832i	−0.846870	+	0.531800i
$33$	−4.81717	+	4.81717i	−0.838561	+	0.838561i
$34$	6.59054	−	4.34986i	1.13027	−	0.745995i
$35$	1.84290	−	4.44357i	0.311507	−	0.751100i
$36$	−0.0937696	+	0.219318i	−0.0156283	+	0.0365531i
$37$	6.01436	+	6.01436i	0.988755	+	0.988755i	0.999937	−	0.0111828i	$-0.00355967\pi$
$37$	6.01436	+	6.01436i	0.988755	+	0.988755i	−0.0111828	+	0.999937i	$0.503560\pi$
$38$	0.283752	−	1.38545i	0.0460307	−	0.224750i
$39$	−3.60530			−0.577311
$40$	−1.34184	+	6.18057i	−0.212164	+	0.977234i
$41$	4.47478			0.698844			0.349422	−	0.936965i	$-0.386378\pi$
$41$	4.47478			0.698844			0.349422	+	0.936965i	$0.386378\pi$
$42$	1.03610	−	5.05889i	0.159874	−	0.780604i
$43$	−1.96095	−	1.96095i	−0.299042	−	0.299042i	0.541597	−	0.840639i	$-0.317820\pi$
$43$	−1.96095	−	1.96095i	−0.299042	−	0.299042i	−0.840639	+	0.541597i	$0.817820\pi$
$44$	3.15585	−	7.38124i	0.475762	−	1.11276i
$45$	0.101943	+	0.246423i	0.0151968	+	0.0367346i
$46$	7.98484	−	5.27012i	1.17730	−	0.777037i
$47$	2.21501	−	2.21501i	0.323093	−	0.323093i	−0.526860	−	0.849952i	$-0.676631\pi$
$47$	2.21501	−	2.21501i	0.323093	−	0.323093i	0.849952	+	0.526860i	$0.176631\pi$
$48$	−0.153821	+	6.78735i	−0.0222022	+	0.979670i
$49$			2.37169i			0.338812i
$50$	3.88985	+	5.90500i	0.550108	+	0.835093i
$51$		−	9.47715i		−	1.32707i
$52$	3.94313	−	1.58120i	0.546813	−	0.219273i
$53$	−5.27852	+	5.27852i	−0.725060	+	0.725060i	−0.969631	−	0.244571i	$-0.921353\pi$
$53$	−5.27852	+	5.27852i	−0.725060	+	0.725060i	0.244571	+	0.969631i	$0.421353\pi$
$54$	4.12433	+	6.24883i	0.561250	+	0.850358i
$55$	−3.43093	−	8.29345i	−0.462627	−	1.11829i
$56$	1.08552	+	5.98733i	0.145059	+	0.800091i
$57$	−1.20015	−	1.20015i	−0.158964	−	0.158964i
$58$	−11.0537	−	2.26388i	−1.45142	−	0.297262i
$59$	−5.37196			−0.699370			−0.349685	−	0.936867i	$-0.613711\pi$
$59$	−5.37196			−0.699370			−0.349685	+	0.936867i	$0.613711\pi$
$60$	5.30368	+	5.43007i	0.684703	+	0.701020i
$61$	12.0386			1.54138			0.770692	−	0.637208i	$-0.219911\pi$
$61$	12.0386			1.54138			0.770692	+	0.637208i	$0.219911\pi$
$62$	−14.3223	−	2.93332i	−1.81893	−	0.372532i
$63$	0.181425	+	0.181425i	0.0228574	+	0.0228574i
$64$	−2.80854	−	7.49080i	−0.351067	−	0.936350i
$65$	1.81962	−	4.38743i	0.225696	−	0.544194i
$66$	−5.30708	−	8.04085i	−0.653257	−	0.989760i
$67$	−0.631476	+	0.631476i	−0.0771471	+	0.0771471i	−0.744627	−	0.667480i	$-0.767373\pi$
$67$	−0.631476	+	0.631476i	−0.0771471	+	0.0771471i	0.667480	+	0.744627i	$0.267373\pi$
$68$	4.15645	+	10.3652i	0.504044	+	1.25696i
$69$		−	11.4821i		−	1.38229i
$70$	5.63343	+	3.81413i	0.673324	+	0.455876i
$71$			6.42369i			0.762352i	0.924502	+	0.381176i	$0.124481\pi$
$71$			6.42369i			0.762352i	−0.924502	+	0.381176i	$0.875519\pi$
$72$	−0.277248	−	0.192146i	−0.0326740	−	0.0226446i
$73$	−2.26914	+	2.26914i	−0.265583	+	0.265583i	−0.827317	−	0.561735i	$-0.810134\pi$
$73$	−2.26914	+	2.26914i	−0.265583	+	0.265583i	0.561735	+	0.827317i	$0.310134\pi$
$74$	−10.0392	+	6.62604i	−1.16703	+	0.770261i
$75$	8.48637	+	0.00755284i	0.979921	+	0.000872127i
$76$	1.83897	+	0.786251i	0.210944	+	0.0901892i
$77$	−6.10592	−	6.10592i	−0.695834	−	0.695834i
$78$	1.02301	−	4.99499i	0.115833	−	0.565571i
$79$	−4.54855			−0.511751			−0.255876	−	0.966710i	$-0.582364\pi$
$79$	−4.54855			−0.511751			−0.255876	+	0.966710i	$0.582364\pi$
$80$	−8.18215	−	3.61281i	−0.914792	−	0.403925i
$81$	8.62799			0.958666
$82$	−1.26973	+	6.19961i	−0.140218	+	0.684632i
$83$	4.42714	+	4.42714i	0.485942	+	0.485942i	0.907023	−	0.421081i	$-0.138349\pi$
$83$	4.42714	+	4.42714i	0.485942	+	0.485942i	−0.421081	+	0.907023i	$0.638349\pi$
$84$	6.71487	+	2.87094i	0.732653	+	0.313246i
$85$	11.5331	+	4.78318i	1.25094	+	0.518809i
$86$	3.27323	−	2.16038i	0.352961	−	0.232960i
$87$	−9.57526	+	9.57526i	−1.02658	+	1.02658i
$88$	9.33089	+	6.46673i	0.994676	+	0.689355i
$89$			8.81939i			0.934854i	0.884032	+	0.467427i	$0.154819\pi$
$89$			8.81939i			0.934854i	−0.884032	+	0.467427i	$0.845181\pi$
$90$	−0.370334	+	0.0713147i	−0.0390367	+	0.00751723i
$91$		−	4.56984i		−	0.479050i
$92$	5.03580	+	12.5580i	0.525018	+	1.30927i
$93$	−12.4067	+	12.4067i	−1.28652	+	1.28652i
$94$	2.44029	+	3.69731i	0.251696	+	0.381349i
$95$	2.06624	−	0.854787i	0.211992	−	0.0876993i
$96$	−9.35992	−	2.13904i	−0.955293	−	0.218315i
$97$	8.06581	+	8.06581i	0.818959	+	0.818959i	0.985957	−	0.166998i	$-0.0534074\pi$
$97$	8.06581	+	8.06581i	0.818959	+	0.818959i	−0.166998	+	0.985957i	$0.553407\pi$
$98$	−3.28586	−	0.672971i	−0.331922	−	0.0679804i
$99$	0.478691			0.0481103
$100$	−9.28487	+	3.71366i	−0.928487	+	0.371366i
$101$	−12.2526			−1.21918			−0.609589	−	0.792718i	$-0.708666\pi$
$101$	−12.2526			−1.21918			−0.609589	+	0.792718i	$0.708666\pi$
$102$	13.1302	+	2.68916i	1.30008	+	0.266267i
$103$	1.67647	+	1.67647i	0.165187	+	0.165187i	0.784860	−	0.619673i	$-0.212735\pi$
$103$	1.67647	+	1.67647i	0.165187	+	0.165187i	−0.619673	+	0.784860i	$0.712735\pi$
$104$	1.07181	+	5.91169i	0.105100	+	0.579689i
$105$	7.54473	−	3.12120i	0.736290	−	0.304598i
$106$	−5.81536	−	8.81094i	−0.564837	−	0.855794i
$107$	5.31906	−	5.31906i	0.514212	−	0.514212i	−0.401602	−	0.915814i	$-0.631546\pi$
$107$	5.31906	−	5.31906i	0.514212	−	0.514212i	0.915814	+	0.401602i	$0.131546\pi$
$108$	−9.82776	+	3.94095i	−0.945677	+	0.379218i
$109$		−	14.3543i		−	1.37489i	−0.726237	−	0.687444i	$-0.758733\pi$
$109$		−	14.3543i		−	1.37489i	0.726237	−	0.687444i	$-0.241267\pi$
$110$	12.4637	−	2.40012i	1.18837	−	0.228843i
$111$			14.4363i			1.37023i
$112$	−8.60320	−	0.194973i	−0.812926	−	0.0184233i
$113$	1.96246	−	1.96246i	0.184613	−	0.184613i	−0.608750	−	0.793362i	$-0.708329\pi$
$113$	1.96246	−	1.96246i	0.184613	−	0.184613i	0.793362	+	0.608750i	$0.208329\pi$
$114$	2.00330	−	1.32221i	0.187627	−	0.123837i
$115$	13.9731	+	5.79512i	1.30299	+	0.540397i
$116$	6.27300	−	14.6720i	0.582433	−	1.36226i
$117$	0.179133	+	0.179133i	0.0165609	+	0.0165609i
$118$	1.52431	−	7.44261i	0.140324	−	0.685148i
$119$	12.0126			1.10119
$120$	−9.02805	+	5.80722i	−0.824145	+	0.530124i
$121$	−5.11051			−0.464592
$122$	−3.41598	+	16.6789i	−0.309268	+	1.51004i
$123$	5.37043	+	5.37043i	0.484235	+	0.484235i
$124$	8.12796	−	19.0106i	0.729913	−	1.70720i
$125$	−4.29232	+	10.3236i	−0.383916	+	0.923368i
$126$	−0.302836	+	0.199876i	−0.0269788	+	0.0178064i
$127$	7.79354	−	7.79354i	0.691565	−	0.691565i	−0.271012	−	0.962576i	$-0.587358\pi$
$127$	7.79354	−	7.79354i	0.691565	−	0.691565i	0.962576	+	0.271012i	$0.0873581\pi$
$128$	11.1751	−	1.76557i	0.987748	−	0.156056i
$129$		−	4.70688i		−	0.414418i
$130$	5.56226	+	3.76595i	0.487843	+	0.330295i
$131$			3.57377i			0.312242i	0.987738	+	0.156121i	$0.0498989\pi$
$131$			3.57377i			0.312242i	−0.987738	+	0.156121i	$0.950101\pi$
$132$	12.6461	−	5.07112i	1.10070	−	0.441384i
$133$	1.52124	−	1.52124i	0.131908	−	0.131908i
$134$	−0.695699	−	1.05406i	−0.0600992	−	0.0910573i
$135$	−4.53518	+	10.9351i	−0.390326	+	0.941146i
$136$	−15.5399	+	2.81744i	−1.33253	+	0.241593i
$137$	−15.5792	−	15.5792i	−1.33102	−	1.33102i	−0.904457	−	0.426565i	$-0.859724\pi$
$137$	−15.5792	−	15.5792i	−1.33102	−	1.33102i	−0.426565	−	0.904457i	$-0.640276\pi$
$138$	15.9080	+	3.25808i	1.35418	+	0.277347i
$139$	6.05603			0.513666			0.256833	−	0.966456i	$-0.417321\pi$
$139$	6.05603			0.513666			0.256833	+	0.966456i	$0.417321\pi$
$140$	−6.88280	+	6.72260i	−0.581703	+	0.568163i
$141$	5.31671			0.447748
$142$	−8.89973	−	1.82274i	−0.746849	−	0.152961i
$143$	−6.02878	−	6.02878i	−0.504152	−	0.504152i
$144$	0.344879	−	0.329593i	0.0287399	−	0.0274661i
$145$	−6.81979	−	16.4852i	−0.566353	−	1.36902i
$146$	−2.49992	−	3.78766i	−0.206895	−	0.313469i
$147$	−2.84639	+	2.84639i	−0.234766	+	0.234766i
$148$	−6.33142	−	15.7890i	−0.520440	−	1.29785i
$149$		−	4.53121i		−	0.371211i	−0.982624	−	0.185606i	$-0.940575\pi$
$149$		−	4.53121i		−	0.371211i	0.982624	−	0.185606i	$-0.0594247\pi$
$150$	−2.41849	+	11.7553i	−0.197469	+	0.959819i
$151$		−	14.4169i		−	1.17323i	−0.809864	−	0.586617i	$-0.800459\pi$
$151$		−	14.4169i		−	1.17323i	0.809864	−	0.586617i	$-0.199541\pi$
$152$	−1.61113	+	2.32471i	−0.130680	+	0.188559i
$153$	−0.470881	+	0.470881i	−0.0380685	+	0.0380685i
$154$	10.1920	−	6.72691i	0.821298	−	0.542070i
$155$	−8.83646	−	21.3600i	−0.709761	−	1.71567i
$156$	6.63004	+	2.83468i	0.530828	+	0.226956i
$157$	1.75431	+	1.75431i	0.140009	+	0.140009i	0.773637	−	0.633629i	$-0.218435\pi$
$157$	1.75431	+	1.75431i	0.140009	+	0.140009i	−0.633629	+	0.773637i	$0.718435\pi$
$158$	1.29066	−	6.30181i	0.102679	−	0.501345i
$159$	−12.6701			−1.00480
$160$	7.32709	−	10.3109i	0.579257	−	0.815145i
$161$	14.5540			1.14702
$162$	−2.44821	+	11.9537i	−0.192350	+	0.939171i
$163$	9.41490	+	9.41490i	0.737432	+	0.737432i	0.972080	−	0.234648i	$-0.0753939\pi$
$163$	9.41490	+	9.41490i	0.737432	+	0.737432i	−0.234648	+	0.972080i	$0.575394\pi$
$164$	−8.22899	−	3.51831i	−0.642576	−	0.274733i
$165$	5.83576	−	14.0711i	0.454313	−	1.09543i
$166$	−7.38981	+	4.87739i	−0.573561	+	0.378559i
$167$	−8.94130	+	8.94130i	−0.691899	+	0.691899i	−0.962649	−	0.270751i	$-0.912728\pi$
$167$	−8.94130	+	8.94130i	−0.691899	+	0.691899i	0.270751	+	0.962649i	$0.412728\pi$
$168$	−5.88292	+	8.48852i	−0.453877	+	0.654903i
$169$			8.48789i			0.652914i
$170$	−9.89942	+	14.6214i	−0.759251	+	1.12141i
$171$			0.119262i			0.00912016i
$172$	2.06433	+	5.14793i	0.157403	+	0.392526i
$173$	−2.06373	+	2.06373i	−0.156902	+	0.156902i	−0.781193	−	0.624290i	$-0.785388\pi$
$173$	−2.06373	+	2.06373i	−0.156902	+	0.156902i	0.624290	+	0.781193i	$0.285388\pi$
$174$	−10.5491	−	15.9831i	−0.799724	−	1.21167i
$175$	−0.00957348	+	10.7568i	−0.000723687	+	0.813134i
$176$	−11.6070	+	11.0926i	−0.874912	+	0.836135i
$177$	−6.44718	−	6.44718i	−0.484600	−	0.484600i
$178$	−12.2189	−	2.50252i	−0.915843	−	0.187572i
$179$	1.70622			0.127529			0.0637645	−	0.997965i	$-0.479689\pi$
$179$	1.70622			0.127529			0.0637645	+	0.997965i	$0.479689\pi$
$180$	0.00627984	−	0.533317i	0.000468071	−	0.0397511i
$181$	20.1290			1.49618			0.748089	−	0.663599i	$-0.230972\pi$
$181$	20.1290			1.49618			0.748089	+	0.663599i	$0.230972\pi$
$182$	6.33131	+	1.29670i	0.469308	+	0.0961180i
$183$	14.4482	+	14.4482i	1.06804	+	1.06804i
$184$	−18.8275	+	3.41350i	−1.38798	+	0.251646i
$185$	−17.5681	−	7.28610i	−1.29163	−	0.535685i
$186$	−13.6685	−	20.7094i	−1.00222	−	1.51849i
$187$	15.8477	−	15.8477i	1.15890	−	1.15890i
$188$	−5.81490	+	2.33178i	−0.424095	+	0.170063i
$189$			11.3898i			0.828484i
$190$	0.597969	+	3.10523i	0.0433812	+	0.225277i
$191$		−	16.2481i		−	1.17567i	−0.808980	−	0.587836i	$-0.799980\pi$
$191$		−	16.2481i		−	1.17567i	0.808980	−	0.587836i	$-0.200020\pi$
$192$	5.61944	−	12.3608i	0.405548	−	0.892063i
$193$	6.47432	−	6.47432i	0.466031	−	0.466031i	−0.434595	−	0.900626i	$-0.643108\pi$
$193$	6.47432	−	6.47432i	0.466031	−	0.466031i	0.900626	+	0.434595i	$0.143108\pi$
$194$	−13.4635	+	8.88612i	−0.966623	+	0.637987i
$195$	7.44942	−	3.08177i	0.533464	−	0.220690i
$196$	1.86474	−	4.36146i	0.133196	−	0.311533i
$197$	−4.14788	−	4.14788i	−0.295524	−	0.295524i	0.543734	−	0.839258i	$-0.317010\pi$
$197$	−4.14788	−	4.14788i	−0.295524	−	0.295524i	−0.839258	+	0.543734i	$0.817010\pi$
$198$	−0.135830	+	0.663205i	−0.00965299	+	0.0471319i
$199$	−10.4993			−0.744272			−0.372136	−	0.928178i	$-0.621375\pi$
$199$	−10.4993			−0.744272			−0.372136	+	0.928178i	$0.621375\pi$
$200$	−2.51050	−	13.9175i	−0.177519	−	0.984117i
$201$	−1.51574			−0.106912
$202$	3.47670	−	16.9754i	0.244620	−	1.19439i
$203$	−12.1370	−	12.1370i	−0.851847	−	0.851847i
$204$	−7.45142	+	17.4282i	−0.521704	+	1.22022i
$205$	−9.24597	+	3.82499i	−0.645766	+	0.267149i
$206$	−2.79837	+	1.84697i	−0.194972	+	0.128685i
$207$	−0.570502	+	0.570502i	−0.0396526	+	0.0396526i
$208$	−8.49451	−	0.192510i	−0.588989	−	0.0133482i
$209$		−	4.01379i		−	0.277640i
$210$	2.18344	+	11.3385i	0.150672	+	0.782433i
$211$			16.0916i			1.10779i	0.832585	+	0.553897i	$0.186860\pi$
$211$			16.0916i			1.10779i	−0.832585	+	0.553897i	$0.813140\pi$
$212$	13.8573	−	5.55679i	0.951721	−	0.381642i
$213$	−7.70942	+	7.70942i	−0.528241	+	0.528241i
$214$	5.86002	+	8.87860i	0.400583	+	0.606929i
$215$	5.72798	+	2.37559i	0.390645	+	0.162014i
$216$	−2.67136	−	14.7342i	−0.181763	−	1.00253i
$217$	−15.7259	−	15.7259i	−1.06755	−	1.06755i
$218$	19.8872	+	4.07305i	1.34693	+	0.275862i
$219$	−5.44663			−0.368049
$220$	−0.211350	+	17.9490i	−0.0142492	+	1.21012i
$221$	11.8609			0.797847
$222$	−20.0009	−	4.09634i	−1.34237	−	0.274928i
$223$	−11.4105	−	11.4105i	−0.764105	−	0.764105i	0.212957	−	0.977062i	$-0.431691\pi$
$223$	−11.4105	−	11.4105i	−0.764105	−	0.764105i	−0.977062	+	0.212957i	$0.931691\pi$
$224$	2.71130	−	11.8640i	0.181157	−	0.792698i
$225$	−0.421278	−	0.422029i	−0.0280852	−	0.0281352i
$226$	2.16205	+	3.27575i	0.143817	+	0.217900i
$227$	−2.06920	+	2.06920i	−0.137338	+	0.137338i	−0.772433	−	0.635096i	$-0.780961\pi$
$227$	−2.06920	+	2.06920i	−0.137338	+	0.137338i	0.635096	+	0.772433i	$0.280961\pi$
$228$	1.26342	+	3.15067i	0.0836723	+	0.208658i
$229$		−	21.9098i		−	1.44784i	−0.689885	−	0.723919i	$-0.742339\pi$
$229$		−	21.9098i		−	1.44784i	0.689885	−	0.723919i	$-0.257661\pi$
$230$	−11.9938	+	17.7147i	−0.790845	+	1.16807i
$231$		−	14.6561i		−	0.964299i
$232$	18.5474	+	12.8542i	1.21769	+	0.843916i
$233$	9.03376	−	9.03376i	0.591821	−	0.591821i	−0.346302	−	0.938123i	$-0.612563\pi$
$233$	9.03376	−	9.03376i	0.591821	−	0.591821i	0.938123	+	0.346302i	$0.112563\pi$
$234$	−0.299010	+	0.197351i	−0.0195469	+	0.0129013i
$235$	−2.68338	+	6.47011i	−0.175044	+	0.422063i
$236$	9.87887	+	4.22371i	0.643060	+	0.274940i
$237$	−5.45896	−	5.45896i	−0.354597	−	0.354597i
$238$	−3.40860	+	16.6429i	−0.220947	+	1.07880i
$239$	8.80262			0.569394			0.284697	−	0.958618i	$-0.408107\pi$
$239$	8.80262			0.569394			0.284697	+	0.958618i	$0.408107\pi$
$240$	−5.48391	−	14.1558i	−0.353985	−	0.913751i
$241$	−2.16116			−0.139212			−0.0696062	−	0.997575i	$-0.522174\pi$
$241$	−2.16116			−0.139212			−0.0696062	+	0.997575i	$0.522174\pi$
$242$	1.45012	−	7.08038i	0.0932171	−	0.455144i
$243$	−0.875864	−	0.875864i	−0.0561867	−	0.0561867i
$244$	−22.1386	−	9.46536i	−1.41728	−	0.605958i
$245$	−2.02729	−	4.90047i	−0.129519	−	0.313080i
$246$	−8.96436	+	5.91661i	−0.571546	+	0.377230i
$247$	1.50202	−	1.50202i	0.0955711	−	0.0955711i
$248$	24.0319	+	16.6552i	1.52603	+	1.05761i
$249$			10.6265i			0.673427i
$250$	−13.0849	−	8.87614i	−0.827560	−	0.561377i
$251$		−	19.5275i		−	1.23256i	−0.787526	−	0.616282i	$-0.788638\pi$
$251$		−	19.5275i		−	1.23256i	0.787526	−	0.616282i	$-0.211362\pi$
$252$	−0.190989	−	0.476281i	−0.0120312	−	0.0300029i
$253$	19.2004	−	19.2004i	1.20712	−	1.20712i
$254$	8.58616	+	13.0090i	0.538744	+	0.816259i
$255$	8.10094	+	19.5820i	0.507301	+	1.22628i
$256$	−0.724840	+	15.9836i	−0.0453025	+	0.998973i
$257$	9.86907	+	9.86907i	0.615616	+	0.615616i	0.944404	−	0.328788i	$-0.106640\pi$
$257$	9.86907	+	9.86907i	0.615616	+	0.615616i	−0.328788	+	0.944404i	$0.606640\pi$
$258$	6.52117	+	1.33559i	0.405990	+	0.0831501i
$259$	−18.2985			−1.13701
$260$	−6.79585	+	6.63767i	−0.421461	+	0.411651i
$261$	0.951512			0.0588971
$262$	−4.95129	−	1.01406i	−0.305892	−	0.0626491i
$263$	4.12699	+	4.12699i	0.254481	+	0.254481i	0.822805	−	0.568324i	$-0.192408\pi$
$263$	4.12699	+	4.12699i	0.254481	+	0.254481i	−0.568324	+	0.822805i	$0.692408\pi$
$264$	3.43744	+	18.9596i	0.211560	+	1.16688i
$265$	6.39467	−	15.4187i	0.392821	−	0.947162i
$266$	1.67595	+	2.53926i	0.102759	+	0.155692i
$267$	−10.5846	+	10.5846i	−0.647769	+	0.647769i
$268$	1.65776	−	0.664766i	0.101264	−	0.0406070i
$269$			17.1547i			1.04594i	0.852351	+	0.522970i	$0.175176\pi$
$269$			17.1547i			1.04594i	−0.852351	+	0.522970i	$0.824824\pi$
$270$	−13.8633	−	9.38615i	−0.843691	−	0.571223i
$271$			24.3506i			1.47919i	0.673050	+	0.739597i	$0.264984\pi$
$271$			24.3506i			1.47919i	−0.673050	+	0.739597i	$0.735016\pi$
$272$	0.506046	−	22.3293i	0.0306835	−	1.35391i
$273$	5.48452	−	5.48452i	0.331938	−	0.331938i
$274$	26.0049	−	17.1637i	1.57101	−	1.03689i
$275$	14.1783	+	14.2035i	0.854981	+	0.856504i
$276$	−9.02786	+	21.1153i	−0.543413	+	1.27099i
$277$	−10.5003	−	10.5003i	−0.630902	−	0.630902i	0.317393	−	0.948294i	$-0.397193\pi$
$277$	−10.5003	−	10.5003i	−0.630902	−	0.630902i	−0.948294	+	0.317393i	$0.897193\pi$
$278$	−1.71841	+	8.39035i	−0.103063	+	0.503220i
$279$	1.23288			0.0738106
$280$	−7.36084	−	11.4434i	−0.439895	−	0.683872i
$281$	−1.50845			−0.0899866			−0.0449933	−	0.998987i	$-0.514327\pi$
$281$	−1.50845			−0.0899866			−0.0449933	+	0.998987i	$0.514327\pi$
$282$	−1.50863	+	7.36606i	−0.0898375	+	0.438643i
$283$	−12.4817	−	12.4817i	−0.741959	−	0.741959i	0.230996	−	0.972955i	$-0.425802\pi$
$283$	−12.4817	−	12.4817i	−0.741959	−	0.741959i	−0.972955	+	0.230996i	$0.925802\pi$
$284$	5.05064	−	11.8130i	0.299700	−	0.700971i
$285$	3.50568	+	1.45393i	0.207659	+	0.0861233i
$286$	10.0633	−	6.64193i	0.595055	−	0.392745i
$287$	−6.80720	+	6.80720i	−0.401816	+	0.401816i
$288$	0.358777	+	0.571337i	0.0211411	+	0.0336664i
$289$			14.1782i			0.834014i
$290$	24.7746	−	4.77081i	1.45482	−	0.280152i
$291$			19.3604i			1.13493i
$292$	5.95699	−	2.38876i	0.348607	−	0.139792i
$293$	−0.143152	+	0.143152i	−0.00836306	+	0.00836306i	−0.711276	−	0.702913i	$-0.751882\pi$
$293$	−0.143152	+	0.143152i	−0.00836306	+	0.00836306i	0.702913	+	0.711276i	$0.251882\pi$
$294$	−3.13587	−	4.75121i	−0.182888	−	0.277096i
$295$	11.0997	−	4.59188i	0.646252	−	0.267350i
$296$	23.6715	−	4.29173i	1.37588	−	0.249452i
$297$	15.0260	+	15.0260i	0.871897	+	0.871897i
$298$	6.27779	+	1.28574i	0.363662	+	0.0744809i
$299$	14.3701			0.831047
$300$	−15.6002	−	6.68631i	−0.900680	−	0.386034i
$301$	5.96613			0.343882
$302$	19.9740	+	4.09084i	1.14938	+	0.235401i
$303$	−14.7050	−	14.7050i	−0.844780	−	0.844780i
$304$	−2.76362	−	2.89178i	−0.158504	−	0.165855i
$305$	−24.8746	+	10.2904i	−1.42432	+	0.589228i
$306$	−0.518771	−	0.785999i	−0.0296562	−	0.0449325i
$307$	22.5165	−	22.5165i	1.28508	−	1.28508i	0.347348	−	0.937736i	$-0.387082\pi$
$307$	22.5165	−	22.5165i	1.28508	−	1.28508i	0.937736	−	0.347348i	$-0.112918\pi$
$308$	6.42781	+	16.0294i	0.366258	+	0.913359i
$309$			4.02404i			0.228920i
$310$	32.1006	−	6.18157i	1.82319	−	0.351090i
$311$			10.0019i			0.567158i	0.958949	+	0.283579i	$0.0915219\pi$
$311$			10.0019i			0.567158i	−0.958949	+	0.283579i	$0.908478\pi$
$312$	−5.80860	+	8.38128i	−0.328847	+	0.474497i
$313$	−19.1644	+	19.1644i	−1.08324	+	1.08324i	−0.0870306	+	0.996206i	$0.527738\pi$
$313$	−19.1644	+	19.1644i	−1.08324	+	1.08324i	−0.996206	+	0.0870306i	$0.972262\pi$
$314$	−2.92830	+	1.93272i	−0.165253	+	0.109070i
$315$	−0.529947	−	0.219788i	−0.0298591	−	0.0123836i
$316$	8.36464	+	3.57630i	0.470548	+	0.201183i
$317$	9.07885	+	9.07885i	0.509919	+	0.509919i	0.914501	−	0.404583i	$-0.132583\pi$
$317$	9.07885	+	9.07885i	0.509919	+	0.509919i	−0.404583	+	0.914501i	$0.632583\pi$
$318$	3.59516	−	17.5538i	0.201606	−	0.984368i
$319$	−32.0235			−1.79297
$320$	12.2061	+	13.0771i	0.682344	+	0.731031i
$321$	12.7674			0.712605
$322$	−4.12973	+	20.1639i	−0.230141	+	1.12369i
$323$	3.94831	+	3.94831i	0.219690	+	0.219690i
$324$	−15.8666	−	6.78377i	−0.881479	−	0.376876i
$325$	−0.00945254	+	10.6209i	−0.000524332	+	0.589140i
$326$	−15.7154	+	10.3724i	−0.870396	+	0.574475i
$327$	17.2273	−	17.2273i	0.952673	−	0.952673i
$328$	7.20945	−	10.4026i	0.398075	−	0.574386i
$329$			6.73911i			0.371539i
$330$	17.8389	+	12.0779i	0.981999	+	0.664865i
$331$			7.53646i			0.414242i	0.978315	+	0.207121i	$0.0664093\pi$
$331$			7.53646i			0.414242i	−0.978315	+	0.207121i	$0.933591\pi$
$332$	−4.66053	−	11.6222i	−0.255780	−	0.637852i
$333$	0.717282	−	0.717282i	0.0393068	−	0.0393068i
$334$	−9.85066	−	14.9249i	−0.539004	−	0.816653i
$335$	0.765002	−	1.84456i	0.0417965	−	0.100779i
$336$	−10.0912	−	10.5592i	−0.550518	−	0.576049i
$337$	7.14595	+	7.14595i	0.389264	+	0.389264i	0.874425	−	0.485161i	$-0.161239\pi$
$337$	7.14595	+	7.14595i	0.389264	+	0.389264i	−0.485161	+	0.874425i	$0.661239\pi$
$338$	−11.7596	−	2.40846i	−0.639637	−	0.131003i
$339$	4.71051			0.255840
$340$	−17.4482	−	17.8640i	−0.946263	−	0.968814i
$341$	−41.4930			−2.24697
$342$	−0.165232	−	0.0338407i	−0.00893470	−	0.00182990i
$343$	−14.2565	−	14.2565i	−0.769781	−	0.769781i
$344$	−7.71797	+	1.39930i	−0.416125	+	0.0754450i
$345$	9.81479	+	23.7249i	0.528410	+	1.27730i
$346$	−2.27362	−	3.44479i	−0.122230	−	0.185193i
$347$	2.43847	−	2.43847i	0.130904	−	0.130904i	−0.638619	−	0.769523i	$-0.720494\pi$
$347$	2.43847	−	2.43847i	0.130904	−	0.130904i	0.769523	+	0.638619i	$0.220494\pi$
$348$	25.1372	−	10.0800i	1.34749	−	0.540347i
$349$			25.9387i			1.38847i	0.719750	+	0.694233i	$0.244256\pi$
$349$			25.9387i			1.38847i	−0.719750	+	0.694233i	$0.755744\pi$
$350$	−14.9003	−	3.06552i	−0.796453	−	0.163859i
$351$			11.2459i			0.600261i
$352$	−12.0747	−	19.2285i	−0.643586	−	1.02488i
$353$	−15.6893	+	15.6893i	−0.835056	+	0.835056i	−0.988203	−	0.153148i	$-0.951059\pi$
$353$	−15.6893	+	15.6893i	−0.835056	+	0.835056i	0.153148	+	0.988203i	$0.451059\pi$
$354$	10.7617	−	7.10287i	0.571977	−	0.377513i
$355$	−5.49089	−	13.2729i	−0.291426	−	0.704451i
$356$	6.93426	−	16.2186i	0.367515	−	0.859584i
$357$	14.4170	+	14.4170i	0.763027	+	0.763027i
$358$	−0.484144	+	2.36389i	−0.0255878	+	0.124936i
$359$	15.8725			0.837718			0.418859	−	0.908051i	$-0.362430\pi$
$359$	15.8725			0.837718			0.418859	+	0.908051i	$0.362430\pi$
$360$	0.737105	+	0.160030i	0.0388488	+	0.00843434i
$361$	1.00000			0.0526316
$362$	−5.71165	+	27.8878i	−0.300198	+	1.46575i
$363$	−6.13340	−	6.13340i	−0.321920	−	0.321920i
$364$	−3.59305	+	8.40380i	−0.188327	+	0.440479i
$365$	2.74895	−	6.62821i	0.143887	−	0.346937i
$366$	−24.1170	+	15.9176i	−1.26061	+	0.832025i
$367$	−9.08519	+	9.08519i	−0.474243	+	0.474243i	−0.903285	−	0.429042i	$-0.858851\pi$
$367$	−9.08519	+	9.08519i	−0.474243	+	0.474243i	0.429042	+	0.903285i	$0.358851\pi$
$368$	0.613105	−	27.0533i	0.0319603	−	1.41025i
$369$		−	0.533670i		−	0.0277817i
$370$	15.0796	−	22.2724i	0.783949	−	1.15788i
$371$		−	16.0597i		−	0.833780i
$372$	32.5704	−	13.0608i	1.68870	−	0.677170i
$373$	−3.81246	+	3.81246i	−0.197402	+	0.197402i	−0.798885	−	0.601483i	$-0.794577\pi$
$373$	−3.81246	+	3.81246i	−0.197402	+	0.197402i	0.601483	+	0.798885i	$0.294577\pi$
$374$	17.4594	+	26.4530i	0.902805	+	1.36785i
$375$	−17.5413	+	7.23843i	−0.905829	+	0.373791i
$376$	−1.58059	−	8.71793i	−0.0815128	−	0.449593i
$377$	−11.9836	−	11.9836i	−0.617189	−	0.617189i
$378$	−15.7800	−	3.23187i	−0.811636	−	0.166230i
$379$	10.9007			0.559930			0.279965	−	0.960010i	$-0.409677\pi$
$379$	10.9007			0.559930			0.279965	+	0.960010i	$0.409677\pi$
$380$	−4.47183	−	0.0526560i	−0.229400	−	0.00270119i
$381$	18.7069			0.958383
$382$	22.5110	+	4.61044i	1.15176	+	0.235891i
$383$	−14.5162	−	14.5162i	−0.741744	−	0.741744i	0.231170	−	0.972913i	$-0.425745\pi$
$383$	−14.5162	−	14.5162i	−0.741744	−	0.741744i	−0.972913	+	0.231170i	$0.925745\pi$
$384$	15.5308	+	11.2929i	0.792552	+	0.576287i
$385$	17.8355	+	7.39702i	0.908983	+	0.376987i
$386$	7.13277	+	10.8070i	0.363048	+	0.550060i
$387$	−0.233866	+	0.233866i	−0.0118881	+	0.0118881i
$388$	−8.49102	−	21.1745i	−0.431066	−	1.07497i
$389$			15.6390i			0.792929i	0.918050	+	0.396465i	$0.129763\pi$
$389$			15.6390i			0.792929i	−0.918050	+	0.396465i	$0.870237\pi$
$390$	2.15586	+	11.1953i	0.109166	+	0.566895i
$391$			37.7744i			1.91033i
$392$	5.51348	+	3.82109i	0.278473	+	0.192994i
$393$	−4.28907	+	4.28907i	−0.216355	+	0.216355i
$394$	6.92367	−	4.56973i	0.348810	−	0.230220i
$395$	9.39838	−	3.88804i	0.472884	−	0.195628i
$396$	−0.880298	−	0.376372i	−0.0442367	−	0.0189134i
$397$	4.42602	+	4.42602i	0.222136	+	0.222136i	0.809397	−	0.587262i	$-0.199794\pi$
$397$	4.42602	+	4.42602i	0.222136	+	0.222136i	−0.587262	+	0.809397i	$0.699794\pi$
$398$	2.97919	−	14.5462i	0.149333	−	0.729137i
$399$	3.65143			0.182800
$400$	19.9945	+	0.470937i	0.999723	+	0.0235468i
$401$	11.7922			0.588875			0.294438	−	0.955671i	$-0.404868\pi$
$401$	11.7922			0.588875			0.294438	+	0.955671i	$0.404868\pi$
$402$	0.430093	−	2.09998i	0.0214511	−	0.104738i
$403$	−15.5273	−	15.5273i	−0.773469	−	0.773469i
$404$	22.5321	+	9.63362i	1.12102	+	0.479290i
$405$	−17.8275	+	7.37509i	−0.885855	+	0.366471i
$406$	20.2591	−	13.3713i	1.00544	−	0.663607i
$407$	−24.1404	+	24.1404i	−1.19659	+	1.19659i
$408$	−22.0316	−	15.2689i	−1.09073	−	0.755923i
$409$			23.9203i			1.18278i	0.806385	+	0.591391i	$0.201421\pi$
$409$			23.9203i			1.18278i	−0.806385	+	0.591391i	$0.798579\pi$
$410$	−2.67578	−	13.8952i	−0.132147	−	0.686236i
$411$		−	37.3949i		−	1.84455i
$412$	−1.76485	−	4.40110i	−0.0869479	−	0.216827i
$413$	8.17202	−	8.17202i	0.402119	−	0.402119i
$414$	−0.628523	−	0.952285i	−0.0308902	−	0.0468023i
$415$	−12.9318	−	5.36326i	−0.634796	−	0.263272i
$416$	2.67705	−	11.7141i	0.131253	−	0.574333i
$417$	7.26816	+	7.26816i	0.355924	+	0.355924i
$418$	5.56092	+	1.13892i	0.271994	+	0.0557065i
$419$	23.7000			1.15782			0.578910	−	0.815391i	$-0.303478\pi$
$419$	23.7000			1.15782			0.578910	+	0.815391i	$0.303478\pi$
$420$	−16.3286	−	0.192270i	−0.796753	−	0.00938180i
$421$	−27.6593			−1.34803			−0.674015	−	0.738718i	$-0.735432\pi$
$421$	−27.6593			−1.34803			−0.674015	+	0.738718i	$0.735432\pi$
$422$	−22.2942	−	4.56604i	−1.08527	−	0.222271i
$423$	−0.264166	−	0.264166i	−0.0128442	−	0.0128442i
$424$	3.76665	+	20.7754i	0.182925	+	1.00894i
$425$	−27.9187	−	0.0248476i	−1.35426	−	0.00120528i
$426$	−8.49349	−	12.8686i	−0.411511	−	0.623486i
$427$	−18.3135	+	18.3135i	−0.886254	+	0.886254i
$428$	−13.9637	+	5.59946i	−0.674961	+	0.270660i
$429$		−	14.4709i		−	0.698663i
$430$	−4.91661	+	7.26178i	−0.237100	+	0.350194i
$431$		−	11.7110i		−	0.564099i	−0.959400	−	0.282049i	$-0.908986\pi$
$431$		−	11.7110i		−	0.564099i	0.959400	−	0.282049i	$-0.0910142\pi$
$432$	21.1715	+	0.479808i	1.01862	+	0.0230848i
$433$	−4.06976	+	4.06976i	−0.195580	+	0.195580i	−0.798102	−	0.602522i	$-0.794163\pi$
$433$	−4.06976	+	4.06976i	−0.195580	+	0.195580i	0.602522	+	0.798102i	$0.294163\pi$
$434$	26.2498	−	17.3253i	1.26003	−	0.831641i
$435$	11.6000	−	27.9696i	0.556175	−	1.34104i
$436$	−11.2861	+	26.3970i	−0.540504	+	1.26419i
$437$	4.78362	+	4.78362i	0.228831	+	0.228831i
$438$	1.54549	−	7.54607i	0.0738466	−	0.360565i
$439$	25.7007			1.22663			0.613313	−	0.789840i	$-0.289836\pi$
$439$	25.7007			1.22663			0.613313	+	0.789840i	$0.289836\pi$
$440$	−24.8075	−	5.38587i	−1.18265	−	0.256762i
$441$	0.282851			0.0134691
$442$	−3.36554	+	16.4327i	−0.160082	+	0.781622i
$443$	17.7355	+	17.7355i	0.842640	+	0.842640i	0.989202	−	0.146561i	$-0.0468205\pi$
$443$	17.7355	+	17.7355i	0.842640	+	0.842640i	−0.146561	+	0.989202i	$0.546821\pi$
$444$	11.3506	−	26.5479i	0.538674	−	1.25991i
$445$	−7.53870	−	18.2230i	−0.357369	−	0.863851i
$446$	19.0465	−	12.5710i	0.901878	−	0.595254i
$447$	5.43815	−	5.43815i	0.257216	−	0.257216i
$448$	15.6677	+	7.12283i	0.740230	+	0.336522i
$449$		−	5.66338i		−	0.267272i	−0.991031	−	0.133636i	$-0.957335\pi$
$449$		−	5.66338i		−	0.267272i	0.991031	−	0.133636i	$-0.0426652\pi$
$450$	0.704240	−	0.463910i	0.0331982	−	0.0218689i
$451$			17.9608i			0.845743i
$452$	−5.15189	+	2.06592i	−0.242325	+	0.0971726i
$453$	17.3025	−	17.3025i	0.812945	−	0.812945i
$454$	−2.27964	−	3.45392i	−0.106989	−	0.162101i
$455$	3.90624	+	9.44239i	0.183127	+	0.442666i
$456$	−4.72361	+	0.856407i	−0.221203	+	0.0401049i
$457$	19.7589	+	19.7589i	0.924284	+	0.924284i	0.997329	−	0.0730444i	$-0.0232715\pi$
$457$	19.7589	+	19.7589i	0.924284	+	0.924284i	−0.0730444	+	0.997329i	$0.523271\pi$
$458$	30.3550	+	6.21694i	1.41840	+	0.290499i
$459$	−29.5617			−1.37982
$460$	−21.1396	−	21.6434i	−0.985639	−	1.00913i
$461$	31.3335			1.45935			0.729674	−	0.683795i	$-0.239672\pi$
$461$	31.3335			1.45935			0.729674	+	0.683795i	$0.239672\pi$
$462$	20.3053	+	4.15870i	0.944690	+	0.193480i
$463$	9.54706	+	9.54706i	0.443689	+	0.443689i	0.893250	−	0.449560i	$-0.148419\pi$
$463$	9.54706	+	9.54706i	0.443689	+	0.443689i	−0.449560	+	0.893250i	$0.648419\pi$
$464$	−23.0717	+	22.0491i	−1.07108	+	1.02360i
$465$	15.0301	−	36.2404i	0.697006	−	1.68061i
$466$	9.95251	+	15.0792i	0.461041	+	0.698531i
$467$	−17.6594	+	17.6594i	−0.817178	+	0.817178i	−0.985698	−	0.168520i	$-0.946101\pi$
$467$	−17.6594	+	17.6594i	−0.817178	+	0.817178i	0.168520	+	0.985698i	$0.446101\pi$
$468$	−0.188577	−	0.470264i	−0.00871696	−	0.0217380i
$469$		−	1.92125i		−	0.0887149i
$470$	−8.20263	−	5.55361i	−0.378359	−	0.256169i
$471$			4.21087i			0.194027i
$472$	−8.65491	+	12.4882i	−0.398375	+	0.574818i
$473$	7.87084	−	7.87084i	0.361902	−	0.361902i
$474$	9.11213	−	6.01415i	0.418534	−	0.276239i
$475$	−3.53868	+	3.53239i	−0.162366	+	0.162077i
$476$	−22.0908	−	9.44493i	−1.01253	−	0.432908i
$477$	0.629525	+	0.629525i	0.0288239	+	0.0288239i
$478$	−2.49776	+	12.1956i	−0.114245	+	0.557815i
$479$	−21.7112			−0.992010			−0.496005	−	0.868320i	$-0.665200\pi$
$479$	−21.7112			−0.992010			−0.496005	+	0.868320i	$0.665200\pi$
$480$	21.1682	−	3.58098i	0.966194	−	0.163448i
$481$	−18.0673			−0.823800
$482$	0.613233	−	2.99418i	0.0279320	−	0.136381i
$483$	17.4670	+	17.4670i	0.794778	+	0.794778i
$484$	9.39807	+	4.01815i	0.427185	+	0.182643i
$485$	−23.5604	−	9.77134i	−1.06982	−	0.443694i
$486$	1.46200	−	0.964942i	0.0663176	−	0.0437706i
$487$	11.2980	−	11.2980i	0.511962	−	0.511962i	−0.403165	−	0.915127i	$-0.632090\pi$
$487$	11.2980	−	11.2980i	0.511962	−	0.511962i	0.915127	+	0.403165i	$0.132090\pi$
$488$	19.3957	−	27.9862i	0.878002	−	1.26688i
$489$			22.5987i			1.02195i
$490$	7.36463	−	1.41819i	0.332700	−	0.0640675i
$491$		−	21.1601i		−	0.954942i	−0.878647	−	0.477471i	$-0.841554\pi$
$491$		−	21.1601i		−	0.954942i	0.878647	−	0.477471i	$-0.158446\pi$
$492$	−5.65355	−	14.0986i	−0.254882	−	0.635612i
$493$	31.5010	−	31.5010i	1.41873	−	1.41873i
$494$	1.65478	+	2.50718i	0.0744519	+	0.112803i
$495$	−0.989090	+	0.409179i	−0.0444563	+	0.0183912i
$496$	−29.8942	+	28.5692i	−1.34229	+	1.28280i
$497$	−9.77195	−	9.77195i	−0.438332	−	0.438332i
$498$	−14.7225	−	3.01529i	−0.659732	−	0.135118i
$499$	24.0759			1.07778			0.538892	−	0.842375i	$-0.318843\pi$
$499$	24.0759			1.07778			0.538892	+	0.842375i	$0.318843\pi$
$500$	16.0104	−	15.6099i	0.716005	−	0.698095i
$501$	−21.4619			−0.958846
$502$	27.0544	+	5.54097i	1.20750	+	0.247305i
$503$	−20.3664	−	20.3664i	−0.908093	−	0.908093i	0.0880249	−	0.996118i	$-0.471944\pi$
$503$	−20.3664	−	20.3664i	−0.908093	−	0.908093i	−0.996118	+	0.0880249i	$0.971944\pi$
$504$	0.714059	−	0.129461i	0.0318067	−	0.00576667i
$505$	25.3168	−	10.4734i	1.12658	−	0.466058i
$506$	21.1532	+	32.0495i	0.940373	+	1.42477i
$507$	−10.1868	+	10.1868i	−0.452410	+	0.452410i
$508$	−20.4598	+	8.20440i	−0.907755	+	0.364011i
$509$		−	28.6068i		−	1.26798i	−0.773343	−	0.633988i	$-0.781417\pi$
$509$		−	28.6068i		−	1.26798i	0.773343	−	0.633988i	$-0.218583\pi$
$510$	−29.4287	+	5.66704i	−1.30312	+	0.250941i
$511$		−	6.90379i		−	0.305406i
$512$	−21.9388	−	5.53961i	−0.969569	−	0.244818i
$513$	−3.74359	+	3.74359i	−0.165284	+	0.165284i
$514$	−16.4735	+	10.8728i	−0.726616	+	0.479578i
$515$	−4.89701	−	2.03096i	−0.215788	−	0.0894948i
$516$	−3.70079	+	8.65581i	−0.162918	+	0.381051i
$517$	8.89060	+	8.89060i	0.391008	+	0.391008i
$518$	5.19224	−	25.3518i	0.228134	−	1.11389i
$519$	−4.95359			−0.217438
$520$	−7.26785	−	11.2988i	−0.318717	−	0.495485i
$521$	−33.7509			−1.47866			−0.739328	−	0.673346i	$-0.764857\pi$
$521$	−33.7509			−1.47866			−0.739328	+	0.673346i	$0.764857\pi$
$522$	−0.269994	+	1.31828i	−0.0118173	+	0.0576994i
$523$	10.9977	+	10.9977i	0.480897	+	0.480897i	0.905418	−	0.424521i	$-0.139558\pi$
$523$	10.9977	+	10.9977i	0.480897	+	0.480897i	−0.424521	+	0.905418i	$0.639558\pi$
$524$	2.80988	−	6.57205i	0.122750	−	0.287101i
$525$	−12.9212	+	12.8983i	−0.563929	+	0.562927i
$526$	−6.88880	+	4.54671i	−0.300366	+	0.198246i
$527$	40.8161	−	40.8161i	1.77798	−	1.77798i
$528$	−27.2430	−	0.617405i	−1.18560	−	0.0268691i
$529$			22.7659i			0.989824i
$530$	19.5474	+	13.2346i	0.849084	+	0.574874i
$531$			0.640669i			0.0278027i
$532$	−3.99358	+	1.60143i	−0.173144	+	0.0694309i
$533$	−6.72120	+	6.72120i	−0.291128	+	0.291128i
$534$	−11.6611	−	17.6679i	−0.504626	−	0.764566i
$535$	−6.44378	+	15.5371i	−0.278589	+	0.671727i
$536$	0.450609	+	2.48539i	0.0194634	+	0.107352i
$537$	2.04773	+	2.04773i	0.0883660	+	0.0883660i
$538$	−23.7671	−	4.86768i	−1.02467	−	0.209861i
$539$	−9.51945			−0.410032
$540$	16.9378	−	16.5436i	0.728888	−	0.711922i
$541$	−44.1197			−1.89685			−0.948427	−	0.316995i	$-0.897326\pi$
$541$	−44.1197			−1.89685			−0.948427	+	0.316995i	$0.897326\pi$
$542$	−33.7367	−	6.90954i	−1.44911	−	0.296790i
$543$	24.1579	+	24.1579i	1.03671	+	1.03671i
$544$	30.7926	+	7.03708i	1.32022	+	0.301712i
$545$	12.2698	+	29.6593i	0.525582	+	1.27047i
$546$	6.04230	+	9.15479i	0.258587	+	0.391789i
$547$	−15.0359	+	15.0359i	−0.642887	+	0.642887i	−0.951264	−	0.308377i	$-0.900214\pi$
$547$	−15.0359	+	15.0359i	−0.642887	+	0.642887i	0.308377	+	0.951264i	$0.400214\pi$
$548$	16.4005	+	40.8989i	0.700595	+	1.74711i
$549$		−	1.43574i		−	0.0612760i
$550$	−23.7014	+	15.6131i	−1.01063	+	0.665743i
$551$		−	7.97836i		−	0.339889i
$552$	−26.6926	−	18.4992i	−1.13611	−	0.787378i
$553$	6.91941	−	6.91941i	0.294243	−	0.294243i
$554$	17.5272	−	11.5682i	0.744658	−	0.491486i
$555$	−12.3400	−	29.8289i	−0.523803	−	1.26616i
$556$	−11.1368	−	4.76156i	−0.472308	−	0.201935i
$557$	−5.74079	−	5.74079i	−0.243245	−	0.243245i	0.574946	−	0.818191i	$-0.305023\pi$
$557$	−5.74079	−	5.74079i	−0.243245	−	0.243245i	−0.818191	+	0.574946i	$0.805023\pi$
$558$	−0.349833	+	1.70810i	−0.0148096	+	0.0723096i
$559$	5.89076			0.249153
$560$	17.9429	−	6.95104i	0.758226	−	0.293735i
$561$	38.0393			1.60602
$562$	0.428026	−	2.08989i	0.0180552	−	0.0881567i
$563$	21.8581	+	21.8581i	0.921210	+	0.921210i	0.997115	−	0.0759053i	$-0.0241847\pi$
$563$	21.8581	+	21.8581i	0.921210	+	0.921210i	−0.0759053	+	0.997115i	$0.524185\pi$
$564$	−9.77727	−	4.18027i	−0.411697	−	0.176021i
$565$	−2.37742	+	5.73239i	−0.100019	+	0.241164i
$566$	20.8345	−	13.7511i	0.875739	−	0.578002i
$567$	−13.1252	+	13.1252i	−0.551207	+	0.551207i
$568$	14.9332	+	10.3494i	0.626584	+	0.434251i
$569$		−	3.55621i		−	0.149084i	−0.997218	−	0.0745421i	$-0.976250\pi$
$569$		−	3.55621i		−	0.149084i	0.997218	−	0.0745421i	$-0.0237495\pi$
$570$	−3.00910	+	4.44440i	−0.126037	+	0.186156i
$571$		−	33.7698i		−	1.41322i	−0.707602	−	0.706611i	$-0.750223\pi$
$571$		−	33.7698i		−	1.41322i	0.707602	−	0.706611i	$-0.249777\pi$
$572$	6.34661	+	15.8269i	0.265365	+	0.661755i
$573$	19.5002	−	19.5002i	0.814634	−	0.814634i
$574$	−7.49951	−	11.3626i	−0.313023	−	0.474267i
$575$	−33.8253	−	0.0301044i	−1.41061	−	0.00125544i
$576$	−0.893365	+	0.334951i	−0.0372236	+	0.0139563i
$577$	2.38287	+	2.38287i	0.0992004	+	0.0992004i	0.754965	−	0.655765i	$-0.227654\pi$
$577$	2.38287	+	2.38287i	0.0992004	+	0.0992004i	−0.655765	+	0.754965i	$0.727654\pi$
$578$	−19.6433	−	4.02311i	−0.817054	−	0.167339i
$579$	15.5403			0.645835
$580$	−0.420108	+	35.6778i	−0.0174440	+	1.48144i
$581$	−13.4694			−0.558806
$582$	−26.8230	−	5.49356i	−1.11185	−	0.227716i
$583$	−21.1869	−	21.1869i	−0.877470	−	0.877470i
$584$	1.61922	+	8.93096i	0.0670036	+	0.369566i
$585$	−0.523252	−	0.217011i	−0.0216338	−	0.00897230i
$586$	−0.157711	−	0.238951i	−0.00651500	−	0.00987098i
$587$	−18.4563	+	18.4563i	−0.761773	+	0.761773i	−0.976643	−	0.214870i	$-0.931067\pi$
$587$	−18.4563	+	18.4563i	−0.761773	+	0.761773i	0.214870	+	0.976643i	$0.431067\pi$
$588$	7.47240	−	2.99644i	0.308157	−	0.123571i
$589$		−	10.3376i		−	0.425954i
$590$	3.21226	+	16.6812i	0.132247	+	0.686752i
$591$		−	9.95619i		−	0.409543i
$592$	−0.770847	+	34.0136i	−0.0316816	+	1.39795i
$593$	−21.7190	+	21.7190i	−0.891894	+	0.891894i	−0.994701	−	0.102807i	$-0.967218\pi$
$593$	−21.7190	+	21.7190i	−0.891894	+	0.891894i	0.102807	+	0.994701i	$0.467218\pi$
$594$	−25.0815	+	16.5542i	−1.02911	+	0.679226i
$595$	−24.8209	+	10.2682i	−1.01756	+	0.420956i
$596$	−3.56267	+	8.33276i	−0.145933	+	0.341323i
$597$	−12.6007	−	12.6007i	−0.515713	−	0.515713i
$598$	−4.07756	+	19.9092i	−0.166744	+	0.814147i
$599$	8.38180			0.342471			0.171236	−	0.985230i	$-0.445224\pi$
$599$	8.38180			0.342471			0.171236	+	0.985230i	$0.445224\pi$
$600$	13.6902	−	19.7162i	0.558899	−	0.804909i
$601$	12.0065			0.489754			0.244877	−	0.969554i	$-0.421252\pi$
$601$	12.0065			0.489754			0.244877	+	0.969554i	$0.421252\pi$
$602$	−1.69290	+	8.26580i	−0.0689976	+	0.336889i
$603$	0.0753108	+	0.0753108i	0.00306689	+	0.00306689i
$604$	−11.3353	+	26.5123i	−0.461229	+	1.07877i
$605$	10.5595	−	4.36840i	0.429306	−	0.177601i
$606$	24.5457	−	16.2005i	0.997100	−	0.658101i
$607$	−29.9324	+	29.9324i	−1.21492	+	1.21492i	−0.245532	+	0.969389i	$0.578963\pi$
$607$	−29.9324	+	29.9324i	−1.21492	+	1.21492i	−0.969389	+	0.245532i	$0.921037\pi$
$608$	4.79062	−	3.00832i	0.194285	−	0.122003i
$609$		−	29.1324i		−	1.18051i
$610$	−7.19870	−	37.3826i	−0.291467	−	1.51358i
$611$			6.65398i			0.269191i
$612$	1.23617	−	0.495705i	0.0499691	−	0.0200377i
$613$	6.30403	−	6.30403i	0.254617	−	0.254617i	−0.568243	−	0.822861i	$-0.692377\pi$
$613$	6.30403	−	6.30403i	0.254617	−	0.254617i	0.822861	+	0.568243i	$0.192377\pi$
$614$	24.8065	+	37.5847i	1.00111	+	1.51679i
$615$	−15.6872	−	6.50601i	−0.632567	−	0.262348i
$616$	−24.0319	+	4.35707i	−0.968273	+	0.175551i
$617$	−9.96310	−	9.96310i	−0.401099	−	0.401099i	0.477521	−	0.878620i	$-0.341535\pi$
$617$	−9.96310	−	9.96310i	−0.401099	−	0.401099i	−0.878620	+	0.477521i	$0.841535\pi$
$618$	−5.57513	−	1.14183i	−0.224264	−	0.0459312i
$619$	−8.56649			−0.344316			−0.172158	−	0.985069i	$-0.555074\pi$
$619$	−8.56649			−0.344316			−0.172158	+	0.985069i	$0.555074\pi$
$620$	−0.544337	+	46.2280i	−0.0218611	+	1.85656i
$621$	−35.8158			−1.43724
$622$	−13.8572	−	2.83807i	−0.555625	−	0.113796i
$623$	−13.4164	−	13.4164i	−0.537516	−	0.537516i
$624$	−9.96368	−	10.4258i	−0.398866	−	0.417365i
$625$	0.0444998	−	25.0000i	0.00177999	−	0.999998i
$626$	−21.1135	−	31.9894i	−0.843864	−	1.27855i
$627$	4.81717	−	4.81717i	0.192379	−	0.192379i
$628$	−1.84679	−	4.60544i	−0.0736949	−	0.183777i
$629$		−	47.4931i		−	1.89367i
$630$	0.454879	−	0.671852i	0.0181228	−	0.0267672i
$631$			25.1719i			1.00208i	0.865425	+	0.501039i	$0.167049\pi$
$631$			25.1719i			1.00208i	−0.865425	+	0.501039i	$0.832951\pi$
$632$	−7.32829	+	10.5740i	−0.291504	+	0.420613i
$633$	−19.3124	+	19.3124i	−0.767601	+	0.767601i
$634$	−15.1545	+	10.0022i	−0.601861	+	0.397238i
$635$	−9.44149	+	22.7651i	−0.374674	+	0.903406i
$636$	23.2999	+	9.96186i	0.923900	+	0.395013i
$637$	−3.56232	−	3.56232i	−0.141144	−	0.141144i
$638$	9.08672	−	44.3670i	0.359747	−	1.75651i
$639$	0.766100			0.0303064
$640$	−21.5812	+	13.2004i	−0.853073	+	0.521792i
$641$	21.8637			0.863565			0.431783	−	0.901978i	$-0.357885\pi$
$641$	21.8637			0.863565			0.431783	+	0.901978i	$0.357885\pi$
$642$	−3.62277	+	17.6886i	−0.142979	+	0.698114i
$643$	22.8913	+	22.8913i	0.902746	+	0.902746i	0.995673	−	0.0929271i	$-0.0296224\pi$
$643$	22.8913	+	22.8913i	0.902746	+	0.902746i	−0.0929271	+	0.995673i	$0.529622\pi$
$644$	−26.7644	−	11.4431i	−1.05466	−	0.450922i
$645$	4.02338	+	9.72554i	0.158420	+	0.382943i
$646$	−6.59054	+	4.34986i	−0.259301	+	0.171143i
$647$	6.94398	−	6.94398i	0.272996	−	0.272996i	−0.557309	−	0.830305i	$-0.688166\pi$
$647$	6.94398	−	6.94398i	0.272996	−	0.272996i	0.830305	+	0.557309i	$0.188166\pi$
$648$	13.9008	−	20.0576i	0.546075	−	0.787936i
$649$		−	21.5619i		−	0.846379i
$650$	−14.7120	−	3.02679i	−0.577054	−	0.118720i
$651$		−	37.7471i		−	1.47943i
$652$	−9.91123	−	24.7162i	−0.388154	−	0.967961i
$653$	3.48781	−	3.48781i	0.136489	−	0.136489i	−0.635562	−	0.772050i	$-0.719231\pi$
$653$	3.48781	−	3.48781i	0.136489	−	0.136489i	0.772050	+	0.635562i	$0.219231\pi$
$654$	18.9794	+	28.7560i	0.742153	+	1.12445i
$655$	−3.05481	−	7.38425i	−0.119361	−	0.288527i
$656$	12.3666	+	12.9401i	0.482834	+	0.505226i
$657$	0.270621	+	0.270621i	0.0105579	+	0.0105579i
$658$	−9.33673	−	1.91224i	−0.363984	−	0.0745468i
$659$	20.3040			0.790932			0.395466	−	0.918481i	$-0.370583\pi$
$659$	20.3040			0.790932			0.395466	+	0.918481i	$0.370583\pi$
$660$	−21.7952	+	21.2879i	−0.848376	+	0.828629i
$661$	−29.3931			−1.14326			−0.571629	−	0.820512i	$-0.693688\pi$
$661$	−29.3931			−1.14326			−0.571629	+	0.820512i	$0.693688\pi$
$662$	−10.4414	−	2.13849i	−0.405818	−	0.0831147i
$663$	14.2348	+	14.2348i	0.552836	+	0.552836i
$664$	17.4245	−	3.15912i	0.676201	−	0.122598i
$665$	−1.84290	+	4.44357i	−0.0714647	+	0.172314i
$666$	0.790232	+	1.19729i	0.0306209	+	0.0463941i
$667$	38.1654	−	38.1654i	1.47777	−	1.47777i
$668$	23.4729	−	9.41267i	0.908194	−	0.364187i
$669$		−	27.3887i		−	1.05891i
$670$	2.33848	+	1.58327i	0.0903433	+	0.0611672i
$671$			48.3204i			1.86539i
$672$	17.4926	−	10.9847i	0.674793	−	0.423743i
$673$	−22.6855	+	22.6855i	−0.874464	+	0.874464i	−0.992955	−	0.118492i	$-0.962194\pi$
$673$	−22.6855	+	22.6855i	−0.874464	+	0.874464i	0.118492	+	0.992955i	$0.462194\pi$
$674$	−11.9281	+	7.87271i	−0.459452	+	0.303245i
$675$	0.0235593	−	26.4712i	0.000906797	−	1.01888i
$676$	6.67361	−	15.6090i	0.256677	−	0.600345i
$677$	19.9465	+	19.9465i	0.766605	+	0.766605i	0.977507	−	0.210902i	$-0.0676401\pi$
$677$	19.9465	+	19.9465i	0.766605	+	0.766605i	−0.210902	+	0.977507i	$0.567640\pi$
$678$	−1.33662	+	6.52620i	−0.0513325	+	0.250637i
$679$	−24.5400			−0.941758
$680$	29.7008	−	19.1048i	1.13897	−	0.732635i
$681$	−4.96672			−0.190325
$682$	11.7737	−	57.4867i	0.450839	−	2.20128i
$683$	6.48834	+	6.48834i	0.248270	+	0.248270i	0.820260	−	0.571991i	$-0.193829\pi$
$683$	6.48834	+	6.48834i	0.248270	+	0.248270i	−0.571991	+	0.820260i	$0.693829\pi$
$684$	0.0937696	−	0.219318i	0.00358537	−	0.00838585i
$685$	45.5073	+	18.8735i	1.73874	+	0.721118i
$686$	23.7971	−	15.7065i	0.908578	−	0.599676i
$687$	26.2951	−	26.2951i	1.00322	−	1.00322i
$688$	0.251331	−	11.0900i	0.00958189	−	0.422801i
$689$		−	15.8569i		−	0.604098i
$690$	−35.6547	+	6.86597i	−1.35735	+	0.261383i
$691$			37.0957i			1.41119i	0.708617	+	0.705593i	$0.249319\pi$
$691$			37.0957i			1.41119i	−0.708617	+	0.705593i	$0.750681\pi$
$692$	5.41775	−	2.17252i	0.205952	−	0.0825870i
$693$	−0.728202	+	0.728202i	−0.0276621	+	0.0276621i
$694$	2.68647	+	4.07032i	0.101977	+	0.154507i
$695$	−12.5132	+	5.17661i	−0.474652	+	0.196360i
$696$	6.83272	+	37.6866i	0.258994	+	1.42851i
$697$	−17.6678	−	17.6678i	−0.669216	−	0.669216i
$698$	−35.9369	−	7.36016i	−1.36023	−	0.278586i
$699$	21.6838			0.820157
$700$	8.47512	−	19.7738i	0.320329	−	0.747380i
$701$	11.2588			0.425239			0.212619	−	0.977135i	$-0.431801\pi$
$701$	11.2588			0.425239			0.212619	+	0.977135i	$0.431801\pi$
$702$	−15.5807	−	3.19104i	−0.588054	−	0.120438i
$703$	−6.01436	−	6.01436i	−0.226836	−	0.226836i
$704$	30.0665	−	11.2729i	1.13317	−	0.424863i
$705$	−10.9856	+	4.54466i	−0.413741	+	0.171162i
$706$	−17.2849	−	26.1886i	−0.650526	−	0.985622i
$707$	18.6391	−	18.6391i	0.700994	−	0.700994i
$708$	6.78706	+	16.9253i	0.255073	+	0.636091i
$709$			14.2210i			0.534080i	0.963685	+	0.267040i	$0.0860455\pi$
$709$			14.2210i			0.534080i	−0.963685	+	0.267040i	$0.913954\pi$
$710$	19.9470	−	3.84117i	0.748598	−	0.144156i
$711$			0.542467i			0.0203441i
$712$	20.5025	+	14.2092i	0.768364	+	0.532511i
$713$	49.4512	−	49.4512i	1.85196	−	1.85196i
$714$	−24.0649	+	15.8832i	−0.900607	+	0.594414i
$715$	17.6102	+	7.30358i	0.658585	+	0.273138i
$716$	−3.13769	−	1.34152i	−0.117261	−	0.0501349i
$717$	10.5645	+	10.5645i	0.394538	+	0.394538i
$718$	−4.50385	+	21.9906i	−0.168082	+	0.820682i
$719$	14.7950			0.551761			0.275880	−	0.961192i	$-0.411031\pi$
$719$	14.7950			0.551761			0.275880	+	0.961192i	$0.411031\pi$
$720$	−0.430870	+	0.975817i	−0.0160576	+	0.0363665i
$721$	−5.10061			−0.189957
$722$	−0.283752	+	1.38545i	−0.0105602	+	0.0515613i
$723$	−2.59372	−	2.59372i	−0.0964615	−	0.0964615i
$724$	−37.0166	−	15.8265i	−1.37571	−	0.588186i
$725$	28.1826	+	28.2328i	1.04668	+	1.04854i
$726$	10.2379	−	6.75718i	0.379964	−	0.250782i
$727$	18.6479	−	18.6479i	0.691613	−	0.691613i	−0.270973	−	0.962587i	$-0.587346\pi$
$727$	18.6479	−	18.6479i	0.691613	−	0.691613i	0.962587	+	0.270973i	$0.0873455\pi$
$728$	−10.6236	−	7.36260i	−0.393735	−	0.272876i
$729$		−	27.9863i		−	1.03653i
$730$	8.40307	+	5.68932i	0.311012	+	0.210571i
$731$			15.4849i			0.572728i
$732$	−15.2098	−	37.9296i	−0.562172	−	1.40192i
$733$	4.09933	−	4.09933i	0.151412	−	0.151412i	−0.627336	−	0.778748i	$-0.715855\pi$
$733$	4.09933	−	4.09933i	0.151412	−	0.151412i	0.778748	+	0.627336i	$0.215855\pi$
$734$	−10.0092	−	15.1651i	−0.369446	−	0.559753i
$735$	3.44826	−	8.31437i	0.127191	−	0.306680i
$736$	37.3071	+	8.52585i	1.37516	+	0.314267i
$737$	−2.53461	−	2.53461i	−0.0933636	−	0.0933636i
$738$	0.739376	+	0.151430i	0.0272168	+	0.00557422i
$739$	−14.1367			−0.520025			−0.260013	−	0.965605i	$-0.583727\pi$
$739$	−14.1367			−0.520025			−0.260013	+	0.965605i	$0.583727\pi$
$740$	26.5785	+	27.2119i	0.977044	+	1.00033i
$741$	3.60530			0.132444
$742$	22.2500	+	4.55698i	0.816824	+	0.167292i
$743$	−10.3395	−	10.3395i	−0.379321	−	0.379321i	0.491536	−	0.870857i	$-0.336435\pi$
$743$	−10.3395	−	10.3395i	−0.379321	−	0.379321i	−0.870857	+	0.491536i	$0.836435\pi$
$744$	8.85320	+	48.8308i	0.324574	+	1.79023i
$745$	3.87322	+	9.36256i	0.141904	+	0.343018i
$746$	−4.20020	−	6.36379i	−0.153780	−	0.232995i
$747$	0.527988	−	0.527988i	0.0193181	−	0.0193181i
$748$	−41.6036	+	16.6831i	−1.52118	+	0.609996i
$749$			16.1831i			0.591316i
$750$	−5.05113	−	26.3566i	−0.184441	−	0.962407i
$751$		−	31.7895i		−	1.16002i	−0.814611	−	0.580008i	$-0.803049\pi$
$751$		−	31.7895i		−	1.16002i	0.814611	−	0.580008i	$-0.196951\pi$
$752$	12.5268	+	0.283893i	0.456805	+	0.0103525i
$753$	23.4360	−	23.4360i	0.854055	−	0.854055i
$754$	20.0032	−	13.2024i	0.728472	−	0.480803i
$755$	12.3234	+	29.7888i	0.448495	+	1.08413i
$756$	8.95523	−	20.9454i	0.325698	−	0.761778i
$757$	−3.32343	−	3.32343i	−0.120792	−	0.120792i	0.644127	−	0.764919i	$-0.277221\pi$
$757$	−3.32343	−	3.32343i	−0.120792	−	0.120792i	−0.764919	+	0.644127i	$0.777221\pi$
$758$	−3.09309	+	15.1024i	−0.112346	+	0.548543i
$759$	46.0869			1.67285
$760$	1.34184	−	6.18057i	0.0486738	−	0.224193i
$761$	−7.45399			−0.270207			−0.135103	−	0.990831i	$-0.543137\pi$
$761$	−7.45399			−0.270207			−0.135103	+	0.990831i	$0.543137\pi$
$762$	−5.30812	+	25.9175i	−0.192293	+	0.938894i
$763$	21.8362	+	21.8362i	0.790524	+	0.790524i
$764$	−12.7751	+	29.8798i	−0.462187	+	1.08101i
$765$	0.570450	−	1.37546i	0.0206247	−	0.0497297i
$766$	24.2306	−	15.9925i	0.875486	−	0.577834i
$767$	8.06878	−	8.06878i	0.291347	−	0.291347i
$768$	−20.0527	+	18.3128i	−0.723588	+	0.660807i
$769$			2.73507i			0.0986291i	0.998783	+	0.0493145i	$0.0157037\pi$
$769$			2.73507i			0.0986291i	−0.998783	+	0.0493145i	$0.984296\pi$
$770$	−15.3091	+	22.6114i	−0.551702	+	0.814859i
$771$			23.6888i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.283752 + 1.38545i) q^{2} +(1.20015 + 1.20015i) q^{3} +(-1.83897 - 0.786251i) q^{4} +(-2.06624 + 0.854787i) q^{5} +(-2.00330 + 1.32221i) q^{6} +(-1.52124 + 1.52124i) q^{7} +(1.61113 - 2.32471i) q^{8} -0.119262i q^{9} +O(q^{10})\)	\(q+(-0.283752 + 1.38545i) q^{2} +(1.20015 + 1.20015i) q^{3} +(-1.83897 - 0.786251i) q^{4} +(-2.06624 + 0.854787i) q^{5} +(-2.00330 + 1.32221i) q^{6} +(-1.52124 + 1.52124i) q^{7} +(1.61113 - 2.32471i) q^{8} -0.119262i q^{9} +(-0.597969 - 3.10523i) q^{10} +4.01379i q^{11} +(-1.26342 - 3.15067i) q^{12} +(-1.50202 + 1.50202i) q^{13} +(-1.67595 - 2.53926i) q^{14} +(-3.50568 - 1.45393i) q^{15} +(2.76362 + 2.89178i) q^{16} +(-3.94831 - 3.94831i) q^{17} +(0.165232 + 0.0338407i) q^{18} -1.00000 q^{19} +(4.47183 + 0.0526560i) q^{20} -3.65143 q^{21} +(-5.56092 - 1.13892i) q^{22} +(-4.78362 - 4.78362i) q^{23} +(4.72361 - 0.856407i) q^{24} +(3.53868 - 3.53239i) q^{25} +(-1.65478 - 2.50718i) q^{26} +(3.74359 - 3.74359i) q^{27} +(3.99358 - 1.60143i) q^{28} +7.97836i q^{29} +(3.00910 - 4.44440i) q^{30} +10.3376i q^{31} +(-4.79062 + 3.00832i) q^{32} +(-4.81717 + 4.81717i) q^{33} +(6.59054 - 4.34986i) q^{34} +(1.84290 - 4.44357i) q^{35} +(-0.0937696 + 0.219318i) q^{36} +(6.01436 + 6.01436i) q^{37} +(0.283752 - 1.38545i) q^{38} -3.60530 q^{39} +(-1.34184 + 6.18057i) q^{40} +4.47478 q^{41} +(1.03610 - 5.05889i) q^{42} +(-1.96095 - 1.96095i) q^{43} +(3.15585 - 7.38124i) q^{44} +(0.101943 + 0.246423i) q^{45} +(7.98484 - 5.27012i) q^{46} +(2.21501 - 2.21501i) q^{47} +(-0.153821 + 6.78735i) q^{48} +2.37169i q^{49} +(3.88985 + 5.90500i) q^{50} -9.47715i q^{51} +(3.94313 - 1.58120i) q^{52} +(-5.27852 + 5.27852i) q^{53} +(4.12433 + 6.24883i) q^{54} +(-3.43093 - 8.29345i) q^{55} +(1.08552 + 5.98733i) q^{56} +(-1.20015 - 1.20015i) q^{57} +(-11.0537 - 2.26388i) q^{58} -5.37196 q^{59} +(5.30368 + 5.43007i) q^{60} +12.0386 q^{61} +(-14.3223 - 2.93332i) q^{62} +(0.181425 + 0.181425i) q^{63} +(-2.80854 - 7.49080i) q^{64} +(1.81962 - 4.38743i) q^{65} +(-5.30708 - 8.04085i) q^{66} +(-0.631476 + 0.631476i) q^{67} +(4.15645 + 10.3652i) q^{68} -11.4821i q^{69} +(5.63343 + 3.81413i) q^{70} +6.42369i q^{71} +(-0.277248 - 0.192146i) q^{72} +(-2.26914 + 2.26914i) q^{73} +(-10.0392 + 6.62604i) q^{74} +(8.48637 + 0.00755284i) q^{75} +(1.83897 + 0.786251i) q^{76} +(-6.10592 - 6.10592i) q^{77} +(1.02301 - 4.99499i) q^{78} -4.54855 q^{79} +(-8.18215 - 3.61281i) q^{80} +8.62799 q^{81} +(-1.26973 + 6.19961i) q^{82} +(4.42714 + 4.42714i) q^{83} +(6.71487 + 2.87094i) q^{84} +(11.5331 + 4.78318i) q^{85} +(3.27323 - 2.16038i) q^{86} +(-9.57526 + 9.57526i) q^{87} +(9.33089 + 6.46673i) q^{88} +8.81939i q^{89} +(-0.370334 + 0.0713147i) q^{90} -4.56984i q^{91} +(5.03580 + 12.5580i) q^{92} +(-12.4067 + 12.4067i) q^{93} +(2.44029 + 3.69731i) q^{94} +(2.06624 - 0.854787i) q^{95} +(-9.35992 - 2.13904i) q^{96} +(8.06581 + 8.06581i) q^{97} +(-3.28586 - 0.672971i) q^{98} +0.478691 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) \) 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) \) 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more