LMFDB - Embedded newform 380.2.k.d.343.11

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			343.11
Character	$\chi$	$=$	380.343
Dual form			380.2.k.d.267.11

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

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

Coefficient data

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

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

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

$2$	−0.283752	−	1.38545i	−0.200643	−	0.979664i
$2$	−0.283752	−	1.38545i	−0.200643	−	0.979664i
$3$	1.20015	−	1.20015i	0.692909	−	0.692909i	−0.269962	−	0.962871i	$-0.587011\pi$
$3$	1.20015	−	1.20015i	0.692909	−	0.692909i	0.962871	+	0.269962i	$0.0870111\pi$
$4$	−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	0.358541	−	0.933514i	$-0.383274\pi$
$7$	−1.52124	−	1.52124i	−0.574973	−	0.574973i	−0.933514	+	0.358541i	$0.883274\pi$
$8$	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	$-0.793132\pi$
$11$		−	4.01379i		−	1.21020i	0.796148	−	0.605102i	$-0.206868\pi$
$12$	−1.26342	+	3.15067i	−0.364719	+	0.909520i
$13$	−1.50202	−	1.50202i	−0.416585	−	0.416585i	0.467440	−	0.884025i	$-0.345176\pi$
$13$	−1.50202	−	1.50202i	−0.416585	−	0.416585i	−0.884025	+	0.467440i	$0.845176\pi$
$14$	−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	−0.999137	−	0.0415323i	$-0.986776\pi$
$17$	−3.94831	+	3.94831i	−0.957605	+	0.957605i	0.0415323	+	0.999137i	$0.486776\pi$
$18$	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	−0.999997	−	0.00254405i	$-0.999190\pi$
$23$	−4.78362	+	4.78362i	−0.997453	+	0.997453i	0.00254405	+	0.999997i	$0.499190\pi$
$24$	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	$-0.734460\pi$
$29$		−	7.97836i		−	1.48154i	0.671757	−	0.740772i	$-0.265540\pi$
$30$	3.00910	+	4.44440i	0.549383	+	0.811434i
$31$		−	10.3376i		−	1.85669i	−0.371719	−	0.928345i	$-0.621232\pi$
$31$		−	10.3376i		−	1.85669i	0.371719	−	0.928345i	$-0.378768\pi$
$32$	−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	−0.0111828	−	0.999937i	$-0.503560\pi$
$37$	6.01436	−	6.01436i	0.988755	−	0.988755i	0.999937	+	0.0111828i	$0.00355967\pi$
$38$	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	−0.840639	−	0.541597i	$-0.817820\pi$
$43$	−1.96095	+	1.96095i	−0.299042	+	0.299042i	0.541597	+	0.840639i	$0.317820\pi$
$44$	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	0.849952	−	0.526860i	$-0.176631\pi$
$47$	2.21501	+	2.21501i	0.323093	+	0.323093i	−0.526860	+	0.849952i	$0.676631\pi$
$48$	−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	0.244571	−	0.969631i	$-0.421353\pi$
$53$	−5.27852	−	5.27852i	−0.725060	−	0.725060i	−0.969631	+	0.244571i	$0.921353\pi$
$54$	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	0.667480	−	0.744627i	$-0.267373\pi$
$67$	−0.631476	−	0.631476i	−0.0771471	−	0.0771471i	−0.744627	+	0.667480i	$0.767373\pi$
$68$	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	$-0.875519\pi$
$71$		−	6.42369i		−	0.762352i	0.924502	−	0.381176i	$-0.124481\pi$
$72$	−0.277248	+	0.192146i	−0.0326740	+	0.0226446i
$73$	−2.26914	−	2.26914i	−0.265583	−	0.265583i	0.561735	−	0.827317i	$-0.310134\pi$
$73$	−2.26914	−	2.26914i	−0.265583	−	0.265583i	−0.827317	+	0.561735i	$0.810134\pi$
$74$	−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	−0.421081	−	0.907023i	$-0.638349\pi$
$83$	4.42714	−	4.42714i	0.485942	−	0.485942i	0.907023	+	0.421081i	$0.138349\pi$
$84$	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	$-0.845181\pi$
$89$		−	8.81939i		−	0.934854i	0.884032	−	0.467427i	$-0.154819\pi$
$90$	−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	−0.166998	−	0.985957i	$-0.553407\pi$
$97$	8.06581	−	8.06581i	0.818959	−	0.818959i	0.985957	+	0.166998i	$0.0534074\pi$
$98$	−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	−0.619673	−	0.784860i	$-0.712735\pi$
$103$	1.67647	−	1.67647i	0.165187	−	0.165187i	0.784860	+	0.619673i	$0.212735\pi$
$104$	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	0.915814	−	0.401602i	$-0.131546\pi$
$107$	5.31906	+	5.31906i	0.514212	+	0.514212i	−0.401602	+	0.915814i	$0.631546\pi$
$108$	−9.82776	−	3.94095i	−0.945677	−	0.379218i
$109$			14.3543i			1.37489i	0.726237	+	0.687444i	$0.241267\pi$
$109$			14.3543i			1.37489i	−0.726237	+	0.687444i	$0.758733\pi$
$110$	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	0.793362	−	0.608750i	$-0.208329\pi$
$113$	1.96246	+	1.96246i	0.184613	+	0.184613i	−0.608750	+	0.793362i	$0.708329\pi$
$114$	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	0.962576	−	0.271012i	$-0.0873581\pi$
$127$	7.79354	+	7.79354i	0.691565	+	0.691565i	−0.271012	+	0.962576i	$0.587358\pi$
$128$	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	$-0.950101\pi$
$131$		−	3.57377i		−	0.312242i	0.987738	−	0.156121i	$-0.0498989\pi$
$132$	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	−0.426565	+	0.904457i	$0.640276\pi$
$137$	−15.5792	+	15.5792i	−1.33102	+	1.33102i	−0.904457	+	0.426565i	$0.859724\pi$
$138$	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	$0.0594247\pi$
$149$			4.53121i			0.371211i	−0.982624	+	0.185606i	$0.940575\pi$
$150$	−2.41849	−	11.7553i	−0.197469	−	0.959819i
$151$			14.4169i			1.17323i	0.809864	+	0.586617i	$0.199541\pi$
$151$			14.4169i			1.17323i	−0.809864	+	0.586617i	$0.800459\pi$
$152$	−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	−0.633629	−	0.773637i	$-0.718435\pi$
$157$	1.75431	−	1.75431i	0.140009	−	0.140009i	0.773637	+	0.633629i	$0.218435\pi$
$158$	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	−0.234648	−	0.972080i	$-0.575394\pi$
$163$	9.41490	−	9.41490i	0.737432	−	0.737432i	0.972080	+	0.234648i	$0.0753939\pi$
$164$	−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	0.270751	−	0.962649i	$-0.412728\pi$
$167$	−8.94130	−	8.94130i	−0.691899	−	0.691899i	−0.962649	+	0.270751i	$0.912728\pi$
$168$	−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	0.624290	−	0.781193i	$-0.285388\pi$
$173$	−2.06373	−	2.06373i	−0.156902	−	0.156902i	−0.781193	+	0.624290i	$0.785388\pi$
$174$	−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	$0.200020\pi$
$191$			16.2481i			1.17567i	−0.808980	+	0.587836i	$0.799980\pi$
$192$	5.61944	+	12.3608i	0.405548	+	0.892063i
$193$	6.47432	+	6.47432i	0.466031	+	0.466031i	0.900626	−	0.434595i	$-0.143108\pi$
$193$	6.47432	+	6.47432i	0.466031	+	0.466031i	−0.434595	+	0.900626i	$0.643108\pi$
$194$	−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	−0.839258	−	0.543734i	$-0.817010\pi$
$197$	−4.14788	+	4.14788i	−0.295524	+	0.295524i	0.543734	+	0.839258i	$0.317010\pi$
$198$	−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	$-0.813140\pi$
$211$		−	16.0916i		−	1.10779i	0.832585	−	0.553897i	$-0.186860\pi$
$212$	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	−0.977062	−	0.212957i	$-0.931691\pi$
$223$	−11.4105	+	11.4105i	−0.764105	+	0.764105i	0.212957	+	0.977062i	$0.431691\pi$
$224$	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	0.635096	−	0.772433i	$-0.280961\pi$
$227$	−2.06920	−	2.06920i	−0.137338	−	0.137338i	−0.772433	+	0.635096i	$0.780961\pi$
$228$	1.26342	−	3.15067i	0.0836723	−	0.208658i
$229$			21.9098i			1.44784i	0.689885	+	0.723919i	$0.257661\pi$
$229$			21.9098i			1.44784i	−0.689885	+	0.723919i	$0.742339\pi$
$230$	−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	0.938123	−	0.346302i	$-0.112563\pi$
$233$	9.03376	+	9.03376i	0.591821	+	0.591821i	−0.346302	+	0.938123i	$0.612563\pi$
$234$	−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	$0.211362\pi$
$251$			19.5275i			1.23256i	−0.787526	+	0.616282i	$0.788638\pi$
$252$	−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	−0.328788	−	0.944404i	$-0.606640\pi$
$257$	9.86907	−	9.86907i	0.615616	−	0.615616i	0.944404	+	0.328788i	$0.106640\pi$
$258$	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	−0.568324	−	0.822805i	$-0.692408\pi$
$263$	4.12699	−	4.12699i	0.254481	−	0.254481i	0.822805	+	0.568324i	$0.192408\pi$
$264$	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	$-0.824824\pi$
$269$		−	17.1547i		−	1.04594i	0.852351	−	0.522970i	$-0.175176\pi$
$270$	−13.8633	+	9.38615i	−0.843691	+	0.571223i
$271$		−	24.3506i		−	1.47919i	−0.673050	−	0.739597i	$-0.735016\pi$
$271$		−	24.3506i		−	1.47919i	0.673050	−	0.739597i	$-0.264984\pi$
$272$	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	−0.948294	−	0.317393i	$-0.897193\pi$
$277$	−10.5003	+	10.5003i	−0.630902	+	0.630902i	0.317393	+	0.948294i	$0.397193\pi$
$278$	−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	−0.972955	−	0.230996i	$-0.925802\pi$
$283$	−12.4817	+	12.4817i	−0.741959	+	0.741959i	0.230996	+	0.972955i	$0.425802\pi$
$284$	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	0.702913	−	0.711276i	$-0.251882\pi$
$293$	−0.143152	−	0.143152i	−0.00836306	−	0.00836306i	−0.711276	+	0.702913i	$0.751882\pi$
$294$	−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	0.937736	+	0.347348i	$0.112918\pi$
$307$	22.5165	+	22.5165i	1.28508	+	1.28508i	0.347348	+	0.937736i	$0.387082\pi$
$308$	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	$-0.908478\pi$
$311$		−	10.0019i		−	0.567158i	0.958949	−	0.283579i	$-0.0915219\pi$
$312$	−5.80860	−	8.38128i	−0.328847	−	0.474497i
$313$	−19.1644	−	19.1644i	−1.08324	−	1.08324i	−0.996206	−	0.0870306i	$-0.972262\pi$
$313$	−19.1644	−	19.1644i	−1.08324	−	1.08324i	−0.0870306	−	0.996206i	$-0.527738\pi$
$314$	−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	−0.404583	−	0.914501i	$-0.632583\pi$
$317$	9.07885	−	9.07885i	0.509919	−	0.509919i	0.914501	+	0.404583i	$0.132583\pi$
$318$	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	$-0.933591\pi$
$331$		−	7.53646i		−	0.414242i	0.978315	−	0.207121i	$-0.0664093\pi$
$332$	−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	−0.485161	−	0.874425i	$-0.661239\pi$
$337$	7.14595	−	7.14595i	0.389264	−	0.389264i	0.874425	+	0.485161i	$0.161239\pi$
$338$	−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	0.769523	−	0.638619i	$-0.220494\pi$
$347$	2.43847	+	2.43847i	0.130904	+	0.130904i	−0.638619	+	0.769523i	$0.720494\pi$
$348$	25.1372	+	10.0800i	1.34749	+	0.540347i
$349$		−	25.9387i		−	1.38847i	−0.719750	−	0.694233i	$-0.755744\pi$
$349$		−	25.9387i		−	1.38847i	0.719750	−	0.694233i	$-0.244256\pi$
$350$	−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	0.153148	−	0.988203i	$-0.451059\pi$
$353$	−15.6893	−	15.6893i	−0.835056	−	0.835056i	−0.988203	+	0.153148i	$0.951059\pi$
$354$	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	0.429042	−	0.903285i	$-0.358851\pi$
$367$	−9.08519	−	9.08519i	−0.474243	−	0.474243i	−0.903285	+	0.429042i	$0.858851\pi$
$368$	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	0.601483	−	0.798885i	$-0.294577\pi$
$373$	−3.81246	−	3.81246i	−0.197402	−	0.197402i	−0.798885	+	0.601483i	$0.794577\pi$
$374$	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	−0.972913	−	0.231170i	$-0.925745\pi$
$383$	−14.5162	+	14.5162i	−0.741744	+	0.741744i	0.231170	+	0.972913i	$0.425745\pi$
$384$	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	$-0.870237\pi$
$389$		−	15.6390i		−	0.792929i	0.918050	−	0.396465i	$-0.129763\pi$
$390$	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	−0.587262	−	0.809397i	$-0.699794\pi$
$397$	4.42602	−	4.42602i	0.222136	−	0.222136i	0.809397	+	0.587262i	$0.199794\pi$
$398$	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	$-0.798579\pi$
$409$		−	23.9203i		−	1.18278i	0.806385	−	0.591391i	$-0.201421\pi$
$410$	−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	$0.0910142\pi$
$431$			11.7110i			0.564099i	−0.959400	+	0.282049i	$0.908986\pi$
$432$	21.1715	−	0.479808i	1.01862	−	0.0230848i
$433$	−4.06976	−	4.06976i	−0.195580	−	0.195580i	0.602522	−	0.798102i	$-0.294163\pi$
$433$	−4.06976	−	4.06976i	−0.195580	−	0.195580i	−0.798102	+	0.602522i	$0.794163\pi$
$434$	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	−0.146561	−	0.989202i	$-0.546821\pi$
$443$	17.7355	−	17.7355i	0.842640	−	0.842640i	0.989202	+	0.146561i	$0.0468205\pi$
$444$	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	$0.0426652\pi$
$449$			5.66338i			0.267272i	−0.991031	+	0.133636i	$0.957335\pi$
$450$	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	−0.0730444	−	0.997329i	$-0.523271\pi$
$457$	19.7589	−	19.7589i	0.924284	−	0.924284i	0.997329	+	0.0730444i	$0.0232715\pi$
$458$	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	−0.449560	−	0.893250i	$-0.648419\pi$
$463$	9.54706	−	9.54706i	0.443689	−	0.443689i	0.893250	+	0.449560i	$0.148419\pi$
$464$	−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	0.168520	−	0.985698i	$-0.446101\pi$
$467$	−17.6594	−	17.6594i	−0.817178	−	0.817178i	−0.985698	+	0.168520i	$0.946101\pi$
$468$	−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	0.915127	−	0.403165i	$-0.132090\pi$
$487$	11.2980	+	11.2980i	0.511962	+	0.511962i	−0.403165	+	0.915127i	$0.632090\pi$
$488$	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	$0.158446\pi$
$491$			21.1601i			0.954942i	−0.878647	+	0.477471i	$0.841554\pi$
$492$	−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	−0.996118	−	0.0880249i	$-0.971944\pi$
$503$	−20.3664	+	20.3664i	−0.908093	+	0.908093i	0.0880249	+	0.996118i	$0.471944\pi$
$504$	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	$0.218583\pi$
$509$			28.6068i			1.26798i	−0.773343	+	0.633988i	$0.781417\pi$
$510$	−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	−0.424521	−	0.905418i	$-0.639558\pi$
$523$	10.9977	−	10.9977i	0.480897	−	0.480897i	0.905418	+	0.424521i	$0.139558\pi$
$524$	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	0.308377	−	0.951264i	$-0.400214\pi$
$547$	−15.0359	−	15.0359i	−0.642887	−	0.642887i	−0.951264	+	0.308377i	$0.900214\pi$
$548$	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	−0.818191	−	0.574946i	$-0.805023\pi$
$557$	−5.74079	+	5.74079i	−0.243245	+	0.243245i	0.574946	+	0.818191i	$0.305023\pi$
$558$	−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	−0.0759053	−	0.997115i	$-0.524185\pi$
$563$	21.8581	−	21.8581i	0.921210	−	0.921210i	0.997115	+	0.0759053i	$0.0241847\pi$
$564$	−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	$0.0237495\pi$
$569$			3.55621i			0.149084i	−0.997218	+	0.0745421i	$0.976250\pi$
$570$	−3.00910	−	4.44440i	−0.126037	−	0.186156i
$571$			33.7698i			1.41322i	0.707602	+	0.706611i	$0.249777\pi$
$571$			33.7698i			1.41322i	−0.707602	+	0.706611i	$0.750223\pi$
$572$	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	−0.655765	−	0.754965i	$-0.727654\pi$
$577$	2.38287	−	2.38287i	0.0992004	−	0.0992004i	0.754965	+	0.655765i	$0.227654\pi$
$578$	−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	0.214870	−	0.976643i	$-0.431067\pi$
$587$	−18.4563	−	18.4563i	−0.761773	−	0.761773i	−0.976643	+	0.214870i	$0.931067\pi$
$588$	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	0.102807	−	0.994701i	$-0.467218\pi$
$593$	−21.7190	−	21.7190i	−0.891894	−	0.891894i	−0.994701	+	0.102807i	$0.967218\pi$
$594$	−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	−0.969389	−	0.245532i	$-0.921037\pi$
$607$	−29.9324	−	29.9324i	−1.21492	−	1.21492i	−0.245532	−	0.969389i	$-0.578963\pi$
$608$	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	0.822861	−	0.568243i	$-0.192377\pi$
$613$	6.30403	+	6.30403i	0.254617	+	0.254617i	−0.568243	+	0.822861i	$0.692377\pi$
$614$	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	−0.878620	−	0.477521i	$-0.841535\pi$
$617$	−9.96310	+	9.96310i	−0.401099	+	0.401099i	0.477521	+	0.878620i	$0.341535\pi$
$618$	−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	$-0.832951\pi$
$631$		−	25.1719i		−	1.00208i	0.865425	−	0.501039i	$-0.167049\pi$
$632$	−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	−0.0929271	−	0.995673i	$-0.529622\pi$
$643$	22.8913	−	22.8913i	0.902746	−	0.902746i	0.995673	+	0.0929271i	$0.0296224\pi$
$644$	−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	0.830305	−	0.557309i	$-0.188166\pi$
$647$	6.94398	+	6.94398i	0.272996	+	0.272996i	−0.557309	+	0.830305i	$0.688166\pi$
$648$	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	0.772050	−	0.635562i	$-0.219231\pi$
$653$	3.48781	+	3.48781i	0.136489	+	0.136489i	−0.635562	+	0.772050i	$0.719231\pi$
$654$	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	0.118492	−	0.992955i	$-0.462194\pi$
$673$	−22.6855	−	22.6855i	−0.874464	−	0.874464i	−0.992955	+	0.118492i	$0.962194\pi$
$674$	−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	−0.210902	−	0.977507i	$-0.567640\pi$
$677$	19.9465	−	19.9465i	0.766605	−	0.766605i	0.977507	+	0.210902i	$0.0676401\pi$
$678$	−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	−0.571991	−	0.820260i	$-0.693829\pi$
$683$	6.48834	−	6.48834i	0.248270	−	0.248270i	0.820260	+	0.571991i	$0.193829\pi$
$684$	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	$-0.750681\pi$
$691$		−	37.0957i		−	1.41119i	0.708617	−	0.705593i	$-0.249319\pi$
$692$	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	$-0.913954\pi$
$709$		−	14.2210i		−	0.534080i	0.963685	−	0.267040i	$-0.0860455\pi$
$710$	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	0.962587	−	0.270973i	$-0.0873455\pi$
$727$	18.6479	+	18.6479i	0.691613	+	0.691613i	−0.270973	+	0.962587i	$0.587346\pi$
$728$	−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	0.778748	−	0.627336i	$-0.215855\pi$
$733$	4.09933	+	4.09933i	0.151412	+	0.151412i	−0.627336	+	0.778748i	$0.715855\pi$
$734$	−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	−0.870857	−	0.491536i	$-0.836435\pi$
$743$	−10.3395	+	10.3395i	−0.379321	+	0.379321i	0.491536	+	0.870857i	$0.336435\pi$
$744$	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	$0.196951\pi$
$751$			31.7895i			1.16002i	−0.814611	+	0.580008i	$0.803049\pi$
$752$	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	−0.764919	−	0.644127i	$-0.777221\pi$
$757$	−3.32343	+	3.32343i	−0.120792	+	0.120792i	0.644127	+	0.764919i	$0.277221\pi$
$758$	−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	$-0.984296\pi$
$769$		−	2.73507i		−	0.0986291i	0.998783	−	0.0493145i	$-0.0157037\pi$
$770$	−15.3091	−	22.6114i	−0.551702	−	0.814859i
$771$		−	23.6888i		−	0.853132i
$772$	−16.9965	−	6.81563i	−0.611718	−	0.245300i
$773$	22.8002	+	22.8002i	0.820068	+	0.820068i	0.986117	−	0.166050i	$-0.0531012\pi$
$773$	22.8002	+	22.8002i	0.820068	+	0.820068i	−0.166050	+	0.986117i	$0.553101\pi$
$774$	−0.257651	+	0.390371i	−0.00926107	+	0.0140316i
$775$	36.5164	−	36.5815i	1.31171	−	1.31405i
$776$	31.7457	+	5.75561i	1.13960	+	0.206614i
$777$	−21.9610	+	21.9610i	−0.787848	+	0.787848i
$778$	−21.6671	+	4.43760i	−0.776805	+	0.159096i
$779$	−4.47478			−0.160326
$780$	−16.1223	+	0.189841i	−0.577271	+	0.00679739i
$781$	−25.7834			−0.922601
$782$	−52.3347	+	10.7186i	−1.87148	+	0.383295i
$783$	29.8677	−	29.8677i	1.06739	−	1.06739i
$784$	−6.85841	−	6.55443i	−0.244943	−	0.234087i
$785$	−5.12437	+	2.12526i	−0.182897	+	0.0758536i
$786$	−4.72528	+	7.15935i	−0.168545	+	0.255365i
$787$	7.21929	+	7.21929i	0.257340	+	0.257340i	0.823971	−	0.566632i	$-0.191754\pi$
$787$	7.21929	+	7.21929i	0.257340	+	0.257340i	−0.566632	+	0.823971i	$0.691754\pi$
$788$	4.36655	−	10.8891i	0.155552	−	0.387908i
$789$		−	9.90604i		−	0.352664i
$790$	2.71989	−	14.1243i	0.0967693	−	0.502519i
$791$		−	5.97073i		−	0.212295i
$792$	0.771232	+	1.11282i	0.0274045	+	0.0395422i
$793$	−18.0822	−	18.0822i	−0.642117	−	0.642117i
$794$	−7.38795	−	4.87616i	−0.262189	−	0.173048i
$795$	26.1794	+	10.8302i	0.928487	+	0.384108i
$796$	19.3078	−	8.25505i	0.684347	−	0.292593i
$797$	24.0462	−	24.0462i	0.851760	−	0.851760i	−0.138590	−	0.990350i	$-0.544257\pi$
$797$	24.0462	−	24.0462i	0.851760	−	0.851760i	0.990350	+	0.138590i	$0.0442569\pi$
$798$	−1.03610	−	5.05889i	−0.0366776	−	0.179083i
$799$	−17.4911			−0.618791
$800$	−6.32593	−	27.5678i	−0.223655	−	0.974668i
$801$	1.05182			0.0371641
$802$	−3.34607	−	16.3376i	−0.118154	−	0.576900i
$803$	−9.10785	+	9.10785i	−0.321409	+	0.321409i
$804$	2.78739	−	1.19175i	0.0983038	−	0.0420298i
$805$	−30.0720	−	12.4406i	−1.05990	−	0.438473i
$806$	25.9182	+	17.1064i	0.912931	+	0.602549i
$807$	−20.5883	−	20.5883i	−0.724742	−	0.724742i
$808$	−19.7405	−	28.4837i	−0.694468	−	1.00205i
$809$			49.8101i			1.75123i	0.483009	+	0.875615i	$0.339544\pi$
$809$			49.8101i			1.75123i	−0.483009	+	0.875615i	$0.660456\pi$
$810$	−5.15927	+	26.7919i	−0.181278	+	0.941370i
$811$			21.6879i			0.761564i	0.924665	+	0.380782i	$0.124345\pi$
$811$			21.6879i			0.761564i	−0.924665	+	0.380782i	$0.875655\pi$
$812$	12.7768	−	31.8622i	0.448378	−	1.11814i
$813$	−29.2245	−	29.2245i	−1.02495	−	1.02495i
$814$	−26.5955	+	40.2953i	−0.932172	+	1.41235i
$815$	−27.5012	+	11.4057i	−0.963324	+	0.399524i
$816$	27.4059	+	26.1912i	0.959398	+	0.916876i
$817$	1.96095	−	1.96095i	0.0686049	−	0.0686049i
$818$	−33.1405	+	6.78743i	−1.15873	+	0.237317i
$819$	−0.545007			−0.0190441
$820$	20.0105	−	0.235624i	0.698795	−	0.00822835i
$821$	33.5950			1.17247			0.586236	−	0.810140i	$-0.300609\pi$
$821$	33.5950			1.17247			0.586236	+	0.810140i	$0.300609\pi$
$822$	51.8089	−	10.6109i	1.80704	−	0.370097i
$823$	33.8797	−	33.8797i	1.18097	−	1.18097i	0.201479	−	0.979493i	$-0.435425\pi$
$823$	33.8797	−	33.8797i	1.18097	−	1.18097i	0.979493	−	0.201479i	$-0.0645747\pi$
$824$	6.59831	+	1.19630i	0.229863	+	0.0416750i
$825$	−0.0303155	−	34.0625i	−0.00105545	−	1.18590i
$826$	9.00313	−	13.6408i	0.313259	−	0.474624i
$827$	25.8243	+	25.8243i	0.897997	+	0.897997i	0.995259	−	0.0972616i	$-0.0310084\pi$
$827$	25.8243	+	25.8243i	0.897997	+	0.897997i	−0.0972616	+	0.995259i	$0.531008\pi$
$828$	1.49769	+	0.600577i	0.0520484	+	0.0208715i
$829$		−	38.9493i		−	1.35276i	−0.736551	−	0.676382i	$-0.763547\pi$
$829$		−	38.9493i		−	1.35276i	0.736551	−	0.676382i	$-0.236453\pi$
$830$	11.1000	+	16.3946i	0.385286	+	0.569064i
$831$			25.2039i			0.874315i
$832$	15.4698	−	7.03284i	0.536318	−	0.243820i
$833$	9.36415	+	9.36415i	0.324448	+	0.324448i
$834$	−12.1321	−	8.00735i	−0.420099	−	0.277272i
$835$	10.8320	+	26.1178i	0.374855	+	0.903843i
$836$	−3.15585	−	7.38124i	−0.109147	−	0.255285i
$837$	38.6998	−	38.6998i	1.33766	−	1.33766i
$838$	−6.72493	−	32.8353i	−0.232309	−	1.13428i
$839$	16.6669			0.575406			0.287703	−	0.957720i	$-0.407108\pi$
$839$	16.6669			0.575406			0.287703	+	0.957720i	$0.407108\pi$
$840$	4.89965	+	22.5679i	0.169054	+	0.778668i
$841$	−34.6542			−1.19497
$842$	7.84838	+	38.3207i	0.270473	+	1.32062i
$843$	−1.81037	+	1.81037i	−0.0623526	+	0.0623526i
$844$	12.6521	+	29.5920i	0.435502	+	1.01860i
$845$	−7.25533	+	17.5380i	−0.249591	+	0.603325i
$846$	0.440948	+	0.291032i	0.0151601	+	0.0100059i
$847$	7.77429	+	7.77429i	0.267128	+	0.267128i
$848$	−29.8521	+	0.676536i	−1.02513	+	0.0232323i
$849$			29.9599i			1.02822i
$850$	7.95642	+	38.6731i	0.272903	+	1.32648i
$851$			57.5408i			1.97247i
$852$	20.2389	+	8.11584i	0.693374	+	0.278044i
$853$	23.5705	+	23.5705i	0.807039	+	0.807039i	0.984185	−	0.177145i	$-0.0566863\pi$
$853$	23.5705	+	23.5705i	0.807039	+	0.807039i	−0.177145	+	0.984185i	$0.556686\pi$
$854$	−20.1761	+	30.5691i	−0.690411	+	1.04605i
$855$	−0.101943	+	0.246423i	−0.00348639	+	0.00842749i
$856$	−3.79558	+	20.9349i	−0.129730	+	0.715541i
$857$	−5.00669	+	5.00669i	−0.171025	+	0.171025i	−0.787430	−	0.616404i	$-0.788589\pi$
$857$	−5.00669	+	5.00669i	−0.171025	+	0.171025i	0.616404	+	0.787430i	$0.288589\pi$
$858$	20.0488	−	4.10616i	0.684456	−	0.140182i
$859$	−10.6947			−0.364898			−0.182449	−	0.983215i	$-0.558402\pi$
$859$	−10.6947			−0.364898			−0.182449	+	0.983215i	$0.558402\pi$
$860$	−8.66577	+	8.87228i	−0.295500	+	0.302542i
$861$	−16.3394			−0.556844
$862$	16.2251	−	3.32302i	0.552627	−	0.113182i
$863$	−30.2137	+	30.2137i	−1.02849	+	1.02849i	−0.0289054	+	0.999582i	$0.509202\pi$
$863$	−30.2137	+	30.2137i	−1.02849	+	1.02849i	−0.999582	+	0.0289054i	$0.990798\pi$
$864$	−6.67222	−	29.1960i	−0.226994	−	0.993270i
$865$	2.50011	+	6.02820i	0.0850062	+	0.204965i
$866$	−4.48366	+	6.79327i	−0.152361	+	0.230845i
$867$	−17.0161	−	17.0161i	−0.577896	−	0.577896i
$868$	16.5550	−	41.2841i	0.561913	−	1.40127i
$869$			18.2569i			0.619323i
$870$	35.4590	−	24.0076i	1.20217	−	0.813935i
$871$			1.89698i			0.0642766i
$872$	−33.3695	+	23.1265i	−1.13003	+	0.783163i
$873$	0.961942	+	0.961942i	0.0325568	+	0.0325568i
$874$	−7.98484	−	5.27012i	−0.270091	−	0.178265i
$875$	−9.17495	+	22.2342i	−0.310170	+	0.751653i
$876$	10.0162	−	4.28242i	0.338416	−	0.144690i
$877$	6.44438	−	6.44438i	0.217611	−	0.217611i	−0.589880	−	0.807491i	$-0.700825\pi$
$877$	6.44438	−	6.44438i	0.217611	−	0.217611i	0.807491	+	0.589880i	$0.200825\pi$
$878$	−7.29262	−	35.6071i	−0.246114	−	1.20168i
$879$	−0.343610			−0.0115897
$880$	14.5011	+	32.8414i	0.488831	+	1.10708i
$881$	27.9286			0.940938			0.470469	−	0.882417i	$-0.344085\pi$
$881$	27.9286			0.940938			0.470469	+	0.882417i	$0.344085\pi$
$882$	−0.0802596	−	0.391878i	−0.00270248	−	0.0131952i
$883$	24.6095	−	24.6095i	0.828175	−	0.828175i	−0.159089	−	0.987264i	$-0.550856\pi$
$883$	24.6095	−	24.6095i	0.828175	−	0.828175i	0.987264	+	0.159089i	$0.0508556\pi$
$884$	−21.8117	+	9.32561i	−0.733608	+	0.313654i
$885$	18.8324	−	7.81044i	0.633043	−	0.262545i
$886$	−29.6043	−	19.5393i	−0.994575	−	0.656435i
$887$	−12.1805	−	12.1805i	−0.408980	−	0.408980i	0.472403	−	0.881383i	$-0.343387\pi$
$887$	−12.1805	−	12.1805i	−0.408980	−	0.408980i	−0.881383	+	0.472403i	$0.843387\pi$
$888$	33.5602	−	23.2587i	1.12621	−	0.780512i
$889$		−	23.7116i		−	0.795262i
$890$	27.3862	+	5.27372i	0.917988	+	0.176776i
$891$		−	34.6309i		−	1.16018i
$892$	12.0121	−	29.9551i	0.402193	−	1.00297i
$893$	−2.21501	−	2.21501i	−0.0741226	−	0.0741226i
$894$	5.99122	−	9.07739i	0.200376	−	0.303593i
$895$	−3.52546	−	1.45846i	−0.117843	−	0.0487508i
$896$	−14.3141	−	19.6858i	−0.478201	−	0.657656i
$897$	17.2464	−	17.2464i	0.575840	−	0.575840i
$898$	7.84636	−	1.60700i	0.261836	−	0.0536262i
$899$	−82.4772			−2.75077
$900$	0.442897	−	1.10733i	0.0147632	−	0.0369109i
$901$	41.6824			1.38864
$902$	−24.8839	+	5.09643i	−0.828544	+	0.169692i
$903$	7.16027	−	7.16027i	0.238279	−	0.238279i
$904$	−1.40037	+	7.72392i	−0.0465757	+	0.256894i
$905$	−41.5913	−	17.2060i	−1.38254	−	0.571947i
$906$	19.0623	−	28.8815i	0.633301	−	0.959525i
$907$	−37.7176	−	37.7176i	−1.25239	−	1.25239i	−0.954644	−	0.297749i	$-0.903764\pi$
$907$	−37.7176	−	37.7176i	−1.25239	−	1.25239i	−0.297749	−	0.954644i	$-0.596236\pi$
$908$	5.43211	+	2.17828i	0.180271	+	0.0722889i
$909$		−	1.46126i		−	0.0484671i
$910$	−14.1904	−	2.73262i	−0.470407	−	0.0905856i
$911$			47.4298i			1.57142i	0.618596	+	0.785709i	$0.287702\pi$
$911$			47.4298i			1.57142i	−0.618596	+	0.785709i	$0.712298\pi$
$912$	0.153821	+	6.78735i	0.00509352	+	0.224752i
$913$	−17.7696	−	17.7696i	−0.588088	−	0.588088i
$914$	−32.9818	−	21.7685i	−1.09094	−	0.720037i
$915$	−42.2034	+	17.5032i	−1.39520	+	0.578639i
$916$	−17.2266	−	40.2914i	−0.569183	−	1.33127i
$917$	−5.43654	+	5.43654i	−0.179530	+	0.179530i
$918$	8.38820	+	40.9564i	0.276852	+	1.35176i
$919$	24.1651			0.797132			0.398566	−	0.917140i	$-0.369508\pi$
$919$	24.1651			0.797132			0.398566	+	0.917140i	$0.369508\pi$
$920$	35.9843	+	23.1466i	1.18637	+	0.763121i
$921$	54.0465			1.78089
$922$	−8.89096	−	43.4112i	−0.292808	−	1.42967i
$923$	−9.64850	+	9.64850i	−0.317584	+	0.317584i
$924$	−11.5234	−	26.9521i	−0.379091	−	0.886659i
$925$	42.5279	−	0.0378497i	1.39831	−	0.00124449i
$926$	−15.9360	−	10.5180i	−0.523690	−	0.345644i
$927$	0.199938	+	0.199938i	0.00656684	+	0.00656684i
$928$	−24.0014	+	38.2213i	−0.787885	+	1.25467i
$929$		−	52.8659i		−	1.73447i	−0.497896	−	0.867237i	$-0.665894\pi$
$929$		−	52.8659i		−	1.73447i	0.497896	−	0.867237i	$-0.334106\pi$
$930$	45.9445	−	31.1069i	1.50658	−	1.02003i
$931$			2.37169i			0.0777289i
$932$	−23.7156	−	9.51000i	−0.776831	−	0.311510i
$933$	−12.0039	−	12.0039i	−0.392989	−	0.392989i
$934$	−19.4554	+	29.4771i	−0.636599	+	0.964521i
$935$	−19.1987	−	46.2914i	−0.627864	−	1.51389i
$936$	0.705038	+	0.127826i	0.0230449	+	0.00417812i
$937$	−19.2914	+	19.2914i	−0.630222	+	0.630222i	−0.948124	−	0.317902i	$-0.897022\pi$
$937$	−19.2914	+	19.2914i	−0.630222	+	0.630222i	0.317902	+	0.948124i	$0.397022\pi$
$938$	2.66180	−	0.545158i	0.0869109	−	0.0178000i
$939$	−46.0005			−1.50117
$940$	10.0218	+	9.78852i	0.326875	+	0.319266i
$941$	−57.1900			−1.86434			−0.932170	−	0.362020i	$-0.882087\pi$
$941$	−57.1900			−1.86434			−0.932170	+	0.362020i	$0.882087\pi$
$942$	−5.83397	+	1.19484i	−0.190081	+	0.0389301i
$943$	−21.4056	+	21.4056i	−0.697064	+	0.697064i
$944$	−14.8460	+	15.5346i	−0.483197	+	0.505607i
$945$	−9.73583	+	23.5340i	−0.316706	+	0.765561i
$946$	8.67132	−	13.1381i	0.281929	−	0.427155i
$947$	−26.9305	−	26.9305i	−0.875124	−	0.875124i	0.117901	−	0.993025i	$-0.462383\pi$
$947$	−26.9305	−	26.9305i	−0.875124	−	0.875124i	−0.993025	+	0.117901i	$0.962383\pi$
$948$	5.74674	−	14.3310i	0.186645	−	0.465448i
$949$			6.81658i			0.221275i
$950$	−3.88985	+	5.90500i	−0.126203	+	0.191584i
$951$		−	21.7920i		−	0.706655i
$952$	19.3538	+	27.9258i	0.627261	+	0.905080i
$953$	−10.7214	−	10.7214i	−0.347301	−	0.347301i	0.511802	−	0.859103i	$-0.328978\pi$
$953$	−10.7214	−	10.7214i	−0.347301	−	0.347301i	−0.859103	+	0.511802i	$0.828978\pi$
$954$	−1.05081	−	0.693549i	−0.0340211	−	0.0224545i
$955$	13.8887	−	33.5725i	0.449427	−	1.08638i
$956$	−16.1877	+	6.92107i	−0.523549	+	0.223843i
$957$	−38.4331	+	38.4331i	−1.24236	+	1.24236i
$958$	6.16060	+	30.0799i	0.199040	+	0.971837i
$959$	47.3993			1.53060
$960$	−1.04526	−	30.3438i	−0.0337355	−	0.979341i
$961$	−75.8663			−2.44730
$962$	5.12665	+	25.0315i	0.165290	+	0.807048i
$963$	−0.634359	+	0.634359i	−0.0204419	+	0.0204419i
$964$	3.97430	−	1.69921i	0.128004	−	0.0547280i
$965$	−7.84332	−	18.9116i	−0.252485	−	0.608787i
$966$	−29.1561	−	19.2435i	−0.938083	−	0.619149i
$967$	28.2118	+	28.2118i	0.907231	+	0.907231i	0.996048	−	0.0888168i	$-0.0283086\pi$
$967$	28.2118	+	28.2118i	0.907231	+	0.907231i	−0.0888168	+	0.996048i	$0.528309\pi$
$968$	−8.23368	−	11.8804i	−0.264641	−	0.381852i
$969$		−	9.47715i		−	0.304450i
$970$	20.2231	+	29.8693i	0.649324	+	0.959045i
$971$		−	15.3403i		−	0.492294i	−0.969232	−	0.246147i	$-0.920835\pi$
$971$		−	15.3403i		−	0.492294i	0.969232	−	0.246147i	$-0.0791646\pi$
$972$	0.922038	−	2.29934i	0.0295744	−	0.0737513i
$973$	−9.21264	−	9.21264i	−0.295344	−	0.295344i
$974$	12.4470	−	18.8587i	0.398829	−	0.604272i
$975$	−12.7580	−	12.7353i	−0.408583	−	0.407857i
$976$	33.2701	−	34.8130i	1.06495	−	1.11434i
$977$	43.0518	−	43.0518i	1.37735	−	1.37735i	0.528276	−	0.849073i	$-0.322839\pi$
$977$	43.0518	−	43.0518i	1.37735	−	1.37735i	0.849073	−	0.528276i	$-0.177161\pi$
$978$	−31.3094	+	6.41242i	−1.00116	+	0.205047i
$979$	−35.3992			−1.13136
$980$	−0.124883	−	10.6058i	−0.00398926	−	0.338789i
$981$	−1.71191			−0.0546572
$982$	29.3164	−	6.00423i	0.935523	−	0.191603i
$983$	19.7481	−	19.7481i	0.629867	−	0.629867i	−0.318168	−	0.948034i	$-0.603068\pi$
$983$	19.7481	−	19.7481i	0.629867	−	0.629867i	0.948034	+	0.318168i	$0.103068\pi$
$984$	21.1371	+	3.83224i	0.673827	+	0.122167i
$985$	12.1161	−	5.02496i	0.386050	−	0.160108i
$986$	34.7047	−	52.5817i	1.10522	−	1.67454i
$987$	−8.08797	−	8.08797i	−0.257443	−	0.257443i
$988$	−3.94313	−	1.58120i	−0.125448	−	0.0503047i
$989$		−	18.7609i		−	0.596560i
$990$	−0.286242	+	1.48644i	−0.00909738	+	0.0472423i
$991$			34.3112i			1.08993i	0.838458	+	0.544966i	$0.183457\pi$
$991$			34.3112i			1.08993i	−0.838458	+	0.544966i	$0.816543\pi$
$992$	−31.0988	+	49.5236i	−0.987388	+	1.57237i
$993$	−9.04492	−	9.04492i	−0.287032	−	0.287032i
$994$	16.3114	+	10.7658i	0.517366	+	0.341470i
$995$	21.6940	+	8.97462i	0.687745	+	0.284515i
$996$	8.35510	+	19.5418i	0.264741	+	0.619206i
$997$	−5.61418	+	5.61418i	−0.177803	+	0.177803i	−0.790397	−	0.612594i	$-0.790126\pi$
$997$	−5.61418	+	5.61418i	−0.177803	+	0.177803i	0.612594	+	0.790397i	$0.290126\pi$
$998$	−6.83159	−	33.3561i	−0.216250	−	1.05587i
$999$	45.0306			1.42471

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.k.d.343.11	yes	52
4.3	odd	2		380.2.k.c.343.25	yes	52
5.2	odd	4		380.2.k.c.267.25	✓	52
20.7	even	4	inner	380.2.k.d.267.11	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.k.c.267.25	✓	52	5.2	odd	4
380.2.k.c.343.25	yes	52	4.3	odd	2
380.2.k.d.267.11	yes	52	20.7	even	4	inner
380.2.k.d.343.11	yes	52	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.283752 - 1.38545i) q^{2} +(1.20015 - 1.20015i) q^{3} +(-1.83897 + 0.786251i) q^{4} +(-2.06624 - 0.854787i) q^{5} +(-2.00330 - 1.32221i) q^{6} +(-1.52124 - 1.52124i) q^{7} +(1.61113 + 2.32471i) q^{8} +0.119262i q^{9} +O(q^{10})\)	\(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

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