LMFDB - Embedded newform 380.2.k.c.267.25

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			267.25
Character	$\chi$	$=$	380.267
Dual form			380.2.k.c.343.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38545 - 0.283752i) q^{2} +(-1.20015 - 1.20015i) q^{3} +(1.83897 - 0.786251i) q^{4} +(-2.06624 + 0.854787i) q^{5} +(-2.00330 - 1.32221i) q^{6} +(1.52124 - 1.52124i) q^{7} +(2.32471 - 1.61113i) q^{8} -0.119262i q^{9} +O(q^{10})$	\(q+(1.38545 - 0.283752i) 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} +(2.32471 - 1.61113i) q^{8} -0.119262i q^{9} +(-2.62013 + 1.77057i) q^{10} -4.01379i q^{11} +(-3.15067 - 1.26342i) 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} +(-0.0338407 - 0.165232i) q^{18} +1.00000 q^{19} +(-3.12767 + 3.19651i) q^{20} -3.65143 q^{21} +(-1.13892 - 5.56092i) 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} +(1.60143 - 3.99358i) q^{28} +7.97836i q^{29} +(5.26951 + 1.01961i) q^{30} -10.3376i q^{31} +(3.00832 - 4.79062i) 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} +(1.38545 - 0.283752i) q^{38} +3.60530 q^{39} +(-3.42623 + 5.31610i) q^{40} +4.47478 q^{41} +(-5.05889 + 1.03610i) 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} +(-6.78735 + 0.153821i) q^{48} +2.37169i q^{49} +(3.90036 - 5.89807i) q^{50} +9.47715i q^{51} +(-1.58120 + 3.94313i) 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} +(2.26388 + 11.0537i) q^{58} +5.37196 q^{59} +(7.58999 - 0.0826166i) q^{60} +12.0386 q^{61} +(-2.93332 - 14.3223i) 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} +(-10.3652 - 4.15645i) q^{68} -11.4821i q^{69} +(-1.29239 + 6.67929i) q^{70} -6.42369i q^{71} +(-0.192146 - 0.277248i) 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} +(4.99499 - 1.02301i) q^{78} +4.54855 q^{79} +(-3.23843 + 8.33742i) q^{80} +8.62799 q^{81} +(6.19961 - 1.26973i) 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} +(-6.46673 - 9.33089i) q^{88} +8.81939i q^{89} +(0.211161 + 0.312481i) q^{90} +4.56984i q^{91} +(12.5580 + 5.03580i) 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} +(0.672971 + 3.28586i) 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} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) $ 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.38545	−	0.283752i	0.979664	−	0.200643i
$2$	1.38545	−	0.283752i	0.979664	−	0.200643i
$3$	−1.20015	−	1.20015i	−0.692909	−	0.692909i	0.269962	−	0.962871i	$-0.412989\pi$
$3$	−1.20015	−	1.20015i	−0.692909	−	0.692909i	−0.962871	+	0.269962i	$0.912989\pi$
$4$	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	$-0.616726\pi$
$7$	1.52124	−	1.52124i	0.574973	−	0.574973i	0.933514	+	0.358541i	$0.116726\pi$
$8$	2.32471	−	1.61113i	0.821908	−	0.569620i
$9$		−	0.119262i		−	0.0397539i
$10$	−2.62013	+	1.77057i	−0.828558	+	0.559903i
$11$		−	4.01379i		−	1.21020i	−0.796148	−	0.605102i	$-0.793132\pi$
$11$		−	4.01379i		−	1.21020i	0.796148	−	0.605102i	$-0.206868\pi$
$12$	−3.15067	−	1.26342i	−0.909520	−	0.364719i
$13$	−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	$0.986776\pi$
$18$	−0.0338407	−	0.165232i	−0.00797634	−	0.0389455i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	−3.12767	+	3.19651i	−0.699369	+	0.714761i
$21$	−3.65143			−0.796808
$22$	−1.13892	−	5.56092i	−0.242819	−	1.18559i
$23$	4.78362	+	4.78362i	0.997453	+	0.997453i	0.999997	−	0.00254405i	$-0.000809798\pi$
$23$	4.78362	+	4.78362i	0.997453	+	0.997453i	−0.00254405	+	0.999997i	$0.500810\pi$
$24$	−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
$28$	1.60143	−	3.99358i	0.302642	−	0.754715i
$29$			7.97836i			1.48154i	0.671757	+	0.740772i	$0.265540\pi$
$29$			7.97836i			1.48154i	−0.671757	+	0.740772i	$0.734460\pi$
$30$	5.26951	+	1.01961i	0.962077	+	0.186154i
$31$		−	10.3376i		−	1.85669i	−0.371719	−	0.928345i	$-0.621232\pi$
$31$		−	10.3376i		−	1.85669i	0.371719	−	0.928345i	$-0.378768\pi$
$32$	3.00832	−	4.79062i	0.531800	−	0.846870i
$33$	−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	$0.503560\pi$
$38$	1.38545	−	0.283752i	0.224750	−	0.0460307i
$39$	3.60530			0.577311
$40$	−3.42623	+	5.31610i	−0.541735	+	0.840550i
$41$	4.47478			0.698844			0.349422	−	0.936965i	$-0.386378\pi$
$41$	4.47478			0.698844			0.349422	+	0.936965i	$0.386378\pi$
$42$	−5.05889	+	1.03610i	−0.780604	+	0.159874i
$43$	1.96095	+	1.96095i	0.299042	+	0.299042i	0.840639	−	0.541597i	$-0.182180\pi$
$43$	1.96095	+	1.96095i	0.299042	+	0.299042i	−0.541597	+	0.840639i	$0.682180\pi$
$44$	−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	$-0.823369\pi$
$47$	−2.21501	+	2.21501i	−0.323093	+	0.323093i	0.526860	+	0.849952i	$0.323369\pi$
$48$	−6.78735	+	0.153821i	−0.979670	+	0.0222022i
$49$			2.37169i			0.338812i
$50$	3.90036	−	5.89807i	0.551594	−	0.834113i
$51$			9.47715i			1.32707i
$52$	−1.58120	+	3.94313i	−0.219273	+	0.546813i
$53$	−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
$58$	2.26388	+	11.0537i	0.297262	+	1.45142i
$59$	5.37196			0.699370			0.349685	−	0.936867i	$-0.386289\pi$
$59$	5.37196			0.699370			0.349685	+	0.936867i	$0.386289\pi$
$60$	7.58999	−	0.0826166i	0.979863	−	0.0106658i
$61$	12.0386			1.54138			0.770692	−	0.637208i	$-0.219911\pi$
$61$	12.0386			1.54138			0.770692	+	0.637208i	$0.219911\pi$
$62$	−2.93332	−	14.3223i	−0.372532	−	1.81893i
$63$	−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	$-0.732627\pi$
$67$	0.631476	−	0.631476i	0.0771471	−	0.0771471i	0.744627	+	0.667480i	$0.232627\pi$
$68$	−10.3652	−	4.15645i	−1.25696	−	0.504044i
$69$		−	11.4821i		−	1.38229i
$70$	−1.29239	+	6.67929i	−0.154470	+	0.798327i
$71$		−	6.42369i		−	0.762352i	−0.924502	−	0.381176i	$-0.875519\pi$
$71$		−	6.42369i		−	0.762352i	0.924502	−	0.381176i	$-0.124481\pi$
$72$	−0.192146	−	0.277248i	−0.0226446	−	0.0326740i
$73$	−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
$78$	4.99499	−	1.02301i	0.565571	−	0.115833i
$79$	4.54855			0.511751			0.255876	−	0.966710i	$-0.417636\pi$
$79$	4.54855			0.511751			0.255876	+	0.966710i	$0.417636\pi$
$80$	−3.23843	+	8.33742i	−0.362068	+	0.932152i
$81$	8.62799			0.958666
$82$	6.19961	−	1.26973i	0.684632	−	0.140218i
$83$	−4.42714	−	4.42714i	−0.485942	−	0.485942i	0.421081	−	0.907023i	$-0.361651\pi$
$83$	−4.42714	−	4.42714i	−0.485942	−	0.485942i	−0.907023	+	0.421081i	$0.861651\pi$
$84$	−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
$88$	−6.46673	−	9.33089i	−0.689355	−	0.994676i
$89$			8.81939i			0.934854i	0.884032	+	0.467427i	$0.154819\pi$
$89$			8.81939i			0.934854i	−0.884032	+	0.467427i	$0.845181\pi$
$90$	0.211161	+	0.312481i	0.0222583	+	0.0329384i
$91$			4.56984i			0.479050i
$92$	12.5580	+	5.03580i	1.30927	+	0.525018i
$93$	−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	$0.553407\pi$
$98$	0.672971	+	3.28586i	0.0679804	+	0.331922i
$99$	−0.478691			−0.0481103
$100$	3.73018	−	9.27824i	0.373018	−	0.927824i
$101$	−12.2526			−1.21918			−0.609589	−	0.792718i	$-0.708666\pi$
$101$	−12.2526			−1.21918			−0.609589	+	0.792718i	$0.708666\pi$
$102$	2.68916	+	13.1302i	0.266267	+	1.30008i
$103$	−1.67647	−	1.67647i	−0.165187	−	0.165187i	0.619673	−	0.784860i	$-0.287265\pi$
$103$	−1.67647	−	1.67647i	−0.165187	−	0.165187i	−0.784860	+	0.619673i	$0.787265\pi$
$104$	−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	$-0.868454\pi$
$107$	−5.31906	+	5.31906i	−0.514212	+	0.514212i	0.401602	+	0.915814i	$0.368454\pi$
$108$	−3.94095	+	9.82776i	−0.379218	+	0.945677i
$109$		−	14.3543i		−	1.37489i	−0.726237	−	0.687444i	$-0.758733\pi$
$109$		−	14.3543i		−	1.37489i	0.726237	−	0.687444i	$-0.241267\pi$
$110$	7.10669	+	10.5167i	0.677596	+	1.00272i
$111$		−	14.4363i		−	1.37023i
$112$	−0.194973	−	8.60320i	−0.0184233	−	0.812926i
$113$	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
$118$	7.44261	−	1.52431i	0.685148	−	0.140324i
$119$	−12.0126			−1.10119
$120$	10.4921	−	2.26814i	0.957797	−	0.207052i
$121$	−5.11051			−0.464592
$122$	16.6789	−	3.41598i	1.51004	−	0.309268i
$123$	−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	$-0.912642\pi$
$127$	−7.79354	+	7.79354i	−0.691565	+	0.691565i	0.271012	+	0.962576i	$0.412642\pi$
$128$	1.76557	−	11.1751i	0.156056	−	0.987748i
$129$		−	4.70688i		−	0.414418i
$130$	1.27606	−	6.59491i	0.111918	−	0.578412i
$131$		−	3.57377i		−	0.312242i	−0.987738	−	0.156121i	$-0.950101\pi$
$131$		−	3.57377i		−	0.312242i	0.987738	−	0.156121i	$-0.0498989\pi$
$132$	−5.07112	+	12.6461i	−0.441384	+	1.10070i
$133$	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	$-0.640276\pi$
$138$	−3.25808	−	15.9080i	−0.277347	−	1.35418i
$139$	−6.05603			−0.513666			−0.256833	−	0.966456i	$-0.582679\pi$
$139$	−6.05603			−0.513666			−0.256833	+	0.966456i	$0.582679\pi$
$140$	0.104719	+	9.62057i	0.00885040	+	0.813086i
$141$	5.31671			0.447748
$142$	−1.82274	−	8.89973i	−0.152961	−	0.746849i
$143$	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
$148$	15.7890	+	6.33142i	1.29785	+	0.520440i
$149$		−	4.53121i		−	0.371211i	−0.982624	−	0.185606i	$-0.940575\pi$
$149$		−	4.53121i		−	0.371211i	0.982624	−	0.185606i	$-0.0594247\pi$
$150$	−11.7596	+	2.39756i	−0.960169	+	0.195760i
$151$			14.4169i			1.17323i	0.809864	+	0.586617i	$0.199541\pi$
$151$			14.4169i			1.17323i	−0.809864	+	0.586617i	$0.800459\pi$
$152$	2.32471	−	1.61113i	0.188559	−	0.130680i
$153$	−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	$0.718435\pi$
$158$	6.30181	−	1.29066i	0.501345	−	0.102679i
$159$	12.6701			1.00480
$160$	−2.12094	+	12.4700i	−0.167675	+	0.985842i
$161$	14.5540			1.14702
$162$	11.9537	−	2.44821i	0.939171	−	0.192350i
$163$	−9.41490	−	9.41490i	−0.737432	−	0.737432i	0.234648	−	0.972080i	$-0.424606\pi$
$163$	−9.41490	−	9.41490i	−0.737432	−	0.737432i	−0.972080	+	0.234648i	$0.924606\pi$
$164$	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	$-0.587272\pi$
$167$	8.94130	−	8.94130i	0.691899	−	0.691899i	0.962649	+	0.270751i	$0.0872719\pi$
$168$	−8.48852	+	5.88292i	−0.654903	+	0.453877i
$169$			8.48789i			0.652914i
$170$	17.3358	+	3.35434i	1.32960	+	0.257266i
$171$		−	0.119262i		−	0.00912016i
$172$	5.14793	+	2.06433i	0.392526	+	0.157403i
$173$	−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
$178$	2.50252	+	12.2189i	0.187572	+	0.915843i
$179$	−1.70622			−0.127529			−0.0637645	−	0.997965i	$-0.520311\pi$
$179$	−1.70622			−0.127529			−0.0637645	+	0.997965i	$0.520311\pi$
$180$	0.381221	+	0.373011i	0.0284145	+	0.0278026i
$181$	20.1290			1.49618			0.748089	−	0.663599i	$-0.230972\pi$
$181$	20.1290			1.49618			0.748089	+	0.663599i	$0.230972\pi$
$182$	1.29670	+	6.33131i	0.0961180	+	0.469308i
$183$	−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
$188$	−2.33178	+	5.81490i	−0.170063	+	0.424095i
$189$			11.3898i			0.828484i
$190$	−2.62013	+	1.77057i	−0.190084	+	0.128450i
$191$			16.2481i			1.17567i	0.808980	+	0.587836i	$0.200020\pi$
$191$			16.2481i			1.17567i	−0.808980	+	0.587836i	$0.799980\pi$
$192$	−12.3608	+	5.61944i	−0.892063	+	0.405548i
$193$	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	$0.817010\pi$
$198$	−0.663205	+	0.135830i	−0.0471319	+	0.00965299i
$199$	10.4993			0.744272			0.372136	−	0.928178i	$-0.378625\pi$
$199$	10.4993			0.744272			0.372136	+	0.928178i	$0.378625\pi$
$200$	2.53527	−	13.9130i	0.179271	−	0.983800i
$201$	−1.51574			−0.106912
$202$	−16.9754	+	3.47670i	−1.19439	+	0.244620i
$203$	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
$208$	0.192510	+	8.49451i	0.0133482	+	0.588989i
$209$		−	4.01379i		−	0.277640i
$210$	9.56723	−	6.46511i	0.660202	−	0.446135i
$211$		−	16.0916i		−	1.10779i	−0.832585	−	0.553897i	$-0.813140\pi$
$211$		−	16.0916i		−	1.10779i	0.832585	−	0.553897i	$-0.186860\pi$
$212$	−5.55679	+	13.8573i	−0.381642	+	0.951721i
$213$	−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
$218$	−4.07305	−	19.8872i	−0.275862	−	1.34693i
$219$	5.44663			0.368049
$220$	12.8301	+	12.5538i	0.865006	+	0.846378i
$221$	11.8609			0.797847
$222$	−4.09634	−	20.0009i	−0.274928	−	1.34237i
$223$	11.4105	+	11.4105i	0.764105	+	0.764105i	0.977062	−	0.212957i	$-0.0683094\pi$
$223$	11.4105	+	11.4105i	0.764105	+	0.764105i	−0.212957	+	0.977062i	$0.568309\pi$
$224$	−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	$-0.719039\pi$
$227$	2.06920	−	2.06920i	0.137338	−	0.137338i	0.772433	+	0.635096i	$0.219039\pi$
$228$	−3.15067	−	1.26342i	−0.208658	−	0.0836723i
$229$		−	21.9098i		−	1.44784i	−0.689885	−	0.723919i	$-0.742339\pi$
$229$		−	21.9098i		−	1.44784i	0.689885	−	0.723919i	$-0.257661\pi$
$230$	−21.0034	−	4.06399i	−1.38492	−	0.267971i
$231$			14.6561i			0.964299i
$232$	12.8542	+	18.5474i	0.843916	+	1.21769i
$233$	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
$238$	−16.6429	+	3.40860i	−1.07880	+	0.220947i
$239$	−8.80262			−0.569394			−0.284697	−	0.958618i	$-0.591893\pi$
$239$	−8.80262			−0.569394			−0.284697	+	0.958618i	$0.591893\pi$
$240$	13.8928	−	6.11957i	0.896776	−	0.395017i
$241$	−2.16116			−0.139212			−0.0696062	−	0.997575i	$-0.522174\pi$
$241$	−2.16116			−0.139212			−0.0696062	+	0.997575i	$0.522174\pi$
$242$	−7.08038	+	1.45012i	−0.455144	+	0.0932171i
$243$	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
$248$	−16.6552	−	24.0319i	−1.05761	−	1.52603i
$249$			10.6265i			0.673427i
$250$	−3.01748	+	15.5208i	−0.190842	+	0.981621i
$251$			19.5275i			1.23256i	0.787526	+	0.616282i	$0.211362\pi$
$251$			19.5275i			1.23256i	−0.787526	+	0.616282i	$0.788638\pi$
$252$	−0.476281	−	0.190989i	−0.0300029	−	0.0120312i
$253$	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	$0.606640\pi$
$258$	−1.33559	−	6.52117i	−0.0831501	−	0.405990i
$259$	18.2985			1.13701
$260$	−0.103396	−	9.49903i	−0.00641237	−	0.589105i
$261$	0.951512			0.0588971
$262$	−1.01406	−	4.95129i	−0.0626491	−	0.305892i
$263$	−4.12699	−	4.12699i	−0.254481	−	0.254481i	0.568324	−	0.822805i	$-0.307592\pi$
$263$	−4.12699	−	4.12699i	−0.254481	−	0.254481i	−0.822805	+	0.568324i	$0.807592\pi$
$264$	−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
$268$	0.664766	−	1.65776i	0.0406070	−	0.101264i
$269$			17.1547i			1.04594i	0.852351	+	0.522970i	$0.175176\pi$
$269$			17.1547i			1.04594i	−0.852351	+	0.522970i	$0.824824\pi$
$270$	3.18042	−	16.4370i	0.193554	−	1.00032i
$271$		−	24.3506i		−	1.47919i	−0.673050	−	0.739597i	$-0.735016\pi$
$271$		−	24.3506i		−	1.47919i	0.673050	−	0.739597i	$-0.264984\pi$
$272$	−22.3293	+	0.506046i	−1.35391	+	0.0306835i
$273$	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	$0.897193\pi$
$278$	−8.39035	+	1.71841i	−0.503220	+	0.103063i
$279$	−1.23288			−0.0738106
$280$	2.87494	+	13.2991i	0.171811	+	0.794776i
$281$	−1.50845			−0.0899866			−0.0449933	−	0.998987i	$-0.514327\pi$
$281$	−1.50845			−0.0899866			−0.0449933	+	0.998987i	$0.514327\pi$
$282$	7.36606	−	1.50863i	0.438643	−	0.0898375i
$283$	12.4817	+	12.4817i	0.741959	+	0.741959i	0.972955	−	0.230996i	$-0.0741985\pi$
$283$	12.4817	+	12.4817i	0.741959	+	0.741959i	−0.230996	+	0.972955i	$0.574198\pi$
$284$	−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
$288$	−0.571337	−	0.358777i	−0.0336664	−	0.0211411i
$289$			14.1782i			0.834014i
$290$	−14.1262	−	20.9043i	−0.829520	−	1.22755i
$291$		−	19.3604i		−	1.13493i
$292$	−2.38876	+	5.95699i	−0.139792	+	0.348607i
$293$	−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
$298$	−1.28574	−	6.27779i	−0.0744809	−	0.363662i
$299$	−14.3701			−0.831047
$300$	−15.6121	+	6.65853i	−0.901365	+	0.384430i
$301$	5.96613			0.343882
$302$	4.09084	+	19.9740i	0.235401	+	1.14938i
$303$	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	$0.612918\pi$
$307$	−22.5165	+	22.5165i	−1.28508	+	1.28508i	−0.937736	+	0.347348i	$0.887082\pi$
$308$	−16.0294	−	6.42781i	−0.913359	−	0.366258i
$309$			4.02404i			0.228920i
$310$	18.3034	+	27.0859i	1.03957	+	1.53838i
$311$		−	10.0019i		−	0.567158i	−0.958949	−	0.283579i	$-0.908478\pi$
$311$		−	10.0019i		−	0.567158i	0.958949	−	0.283579i	$-0.0915219\pi$
$312$	8.38128	−	5.80860i	0.474497	−	0.328847i
$313$	−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	$0.632583\pi$
$318$	17.5538	−	3.59516i	0.984368	−	0.201606i
$319$	32.0235			1.79297
$320$	0.599932	+	17.8785i	0.0335372	+	0.999437i
$321$	12.7674			0.712605
$322$	20.1639	−	4.12973i	1.12369	−	0.230141i
$323$	−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
$328$	10.4026	−	7.20945i	0.574386	−	0.398075i
$329$			6.73911i			0.371539i
$330$	4.09249	−	21.1507i	0.225284	−	1.16431i
$331$		−	7.53646i		−	0.414242i	−0.978315	−	0.207121i	$-0.933591\pi$
$331$		−	7.53646i		−	0.414242i	0.978315	−	0.207121i	$-0.0664093\pi$
$332$	−11.6222	−	4.66053i	−0.637852	−	0.255780i
$333$	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	$0.661239\pi$
$338$	2.40846	+	11.7596i	0.131003	+	0.639637i
$339$	−4.71051			−0.255840
$340$	24.9698	−	0.271795i	1.35418	−	0.0147401i
$341$	−41.4930			−2.24697
$342$	−0.0338407	−	0.165232i	−0.00182990	−	0.00893470i
$343$	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	$-0.779506\pi$
$347$	−2.43847	+	2.43847i	−0.130904	+	0.130904i	0.638619	+	0.769523i	$0.279506\pi$
$348$	10.0800	−	25.1372i	0.540347	−	1.34749i
$349$			25.9387i			1.38847i	0.719750	+	0.694233i	$0.244256\pi$
$349$			25.9387i			1.38847i	−0.719750	+	0.694233i	$0.755744\pi$
$350$	−3.03899	−	14.9057i	−0.162441	−	0.796744i
$351$		−	11.2459i		−	0.600261i
$352$	−19.2285	−	12.0747i	−1.02488	−	0.643586i
$353$	−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
$358$	−2.36389	+	0.484144i	−0.124936	+	0.0255878i
$359$	−15.8725			−0.837718			−0.418859	−	0.908051i	$-0.637570\pi$
$359$	−15.8725			−0.837718			−0.418859	+	0.908051i	$0.637570\pi$
$360$	0.634007	+	0.408618i	0.0334151	+	0.0215360i
$361$	1.00000			0.0526316
$362$	27.8878	−	5.71165i	1.46575	−	0.300198i
$363$	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	$-0.641149\pi$
$367$	9.08519	−	9.08519i	0.474243	−	0.474243i	0.903285	+	0.429042i	$0.141149\pi$
$368$	27.0533	−	0.613105i	1.41025	−	0.0319603i
$369$		−	0.533670i		−	0.0277817i
$370$	−26.4072	−	5.10958i	−1.37285	−	0.265635i
$371$			16.0597i			0.833780i
$372$	−13.0608	+	32.5704i	−0.677170	+	1.68870i
$373$	−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
$378$	3.23187	+	15.7800i	0.166230	+	0.811636i
$379$	−10.9007			−0.559930			−0.279965	−	0.960010i	$-0.590323\pi$
$379$	−10.9007			−0.559930			−0.279965	+	0.960010i	$0.590323\pi$
$380$	−3.12767	+	3.19651i	−0.160446	+	0.163977i
$381$	18.7069			0.958383
$382$	4.61044	+	22.5110i	0.235891	+	1.15176i
$383$	14.5162	+	14.5162i	0.741744	+	0.741744i	0.972913	−	0.231170i	$-0.0742553\pi$
$383$	14.5162	+	14.5162i	0.741744	+	0.741744i	−0.231170	+	0.972913i	$0.574255\pi$
$384$	−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
$388$	21.1745	+	8.49102i	1.07497	+	0.431066i
$389$			15.6390i			0.792929i	0.918050	+	0.396465i	$0.129763\pi$
$389$			15.6390i			0.792929i	−0.918050	+	0.396465i	$0.870237\pi$
$390$	−9.44637	+	6.38344i	−0.478336	+	0.323238i
$391$		−	37.7744i		−	1.91033i
$392$	3.82109	+	5.51348i	0.192994	+	0.278473i
$393$	−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	$0.699794\pi$
$398$	14.5462	−	2.97919i	0.729137	−	0.149333i
$399$	−3.65143			−0.182800
$400$	−0.435346	−	19.9953i	−0.0217673	−	0.999763i
$401$	11.7922			0.588875			0.294438	−	0.955671i	$-0.404868\pi$
$401$	11.7922			0.588875			0.294438	+	0.955671i	$0.404868\pi$
$402$	−2.09998	+	0.430093i	−0.104738	+	0.0214511i
$403$	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
$408$	15.2689	+	22.0316i	0.755923	+	1.09073i
$409$			23.9203i			1.18278i	0.806385	+	0.591391i	$0.201421\pi$
$409$			23.9203i			1.18278i	−0.806385	+	0.591391i	$0.798579\pi$
$410$	−11.7245	+	7.92291i	−0.579033	+	0.391285i
$411$			37.3949i			1.84455i
$412$	−4.40110	−	1.76485i	−0.216827	−	0.0869479i
$413$	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
$418$	−1.13892	−	5.56092i	−0.0557065	−	0.271994i
$419$	−23.7000			−1.15782			−0.578910	−	0.815391i	$-0.696522\pi$
$419$	−23.7000			−1.15782			−0.578910	+	0.815391i	$0.696522\pi$
$420$	11.4205	−	11.6718i	0.557262	−	0.569527i
$421$	−27.6593			−1.34803			−0.674015	−	0.738718i	$-0.735432\pi$
$421$	−27.6593			−1.34803			−0.674015	+	0.738718i	$0.735432\pi$
$422$	−4.56604	−	22.2942i	−0.222271	−	1.08527i
$423$	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
$428$	−5.59946	+	13.9637i	−0.270660	+	0.674961i
$429$		−	14.4709i		−	0.698663i
$430$	−8.60994	−	1.66595i	−0.415208	−	0.0803393i
$431$			11.7110i			0.564099i	0.959400	+	0.282049i	$0.0910142\pi$
$431$			11.7110i			0.564099i	−0.959400	+	0.282049i	$0.908986\pi$
$432$	0.479808	+	21.1715i	0.0230848	+	1.01862i
$433$	−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
$438$	7.54607	−	1.54549i	0.360565	−	0.0738466i
$439$	−25.7007			−1.22663			−0.613313	−	0.789840i	$-0.710164\pi$
$439$	−25.7007			−1.22663			−0.613313	+	0.789840i	$0.710164\pi$
$440$	21.3377	+	13.7522i	1.01724	+	0.655609i
$441$	0.282851			0.0134691
$442$	16.4327	−	3.36554i	0.781622	−	0.160082i
$443$	−17.7355	−	17.7355i	−0.842640	−	0.842640i	0.146561	−	0.989202i	$-0.453179\pi$
$443$	−17.7355	−	17.7355i	−0.842640	−	0.842640i	−0.989202	+	0.146561i	$0.953179\pi$
$444$	−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
$448$	−7.12283	−	15.6677i	−0.336522	−	0.740230i
$449$		−	5.66338i		−	0.267272i	−0.991031	−	0.133636i	$-0.957335\pi$
$449$		−	5.66338i		−	0.267272i	0.991031	−	0.133636i	$-0.0426652\pi$
$450$	−0.703413	−	0.465163i	−0.0331592	−	0.0219280i
$451$		−	17.9608i		−	0.845743i
$452$	2.06592	−	5.15189i	0.0971726	−	0.242325i
$453$	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	$0.523271\pi$
$458$	−6.21694	−	30.3550i	−0.290499	−	1.41840i
$459$	29.5617			1.37982
$460$	−30.2524	+	0.329296i	−1.41053	+	0.0153535i
$461$	31.3335			1.45935			0.729674	−	0.683795i	$-0.239672\pi$
$461$	31.3335			1.45935			0.729674	+	0.683795i	$0.239672\pi$
$462$	4.15870	+	20.3053i	0.193480	+	0.944690i
$463$	−9.54706	−	9.54706i	−0.443689	−	0.443689i	0.449560	−	0.893250i	$-0.351581\pi$
$463$	−9.54706	−	9.54706i	−0.443689	−	0.443689i	−0.893250	+	0.449560i	$0.851581\pi$
$464$	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	$-0.553899\pi$
$467$	17.6594	−	17.6594i	0.817178	−	0.817178i	0.985698	+	0.168520i	$0.0538989\pi$
$468$	0.470264	+	0.188577i	0.0217380	+	0.00871696i
$469$		−	1.92125i		−	0.0887149i
$470$	1.88179	−	9.72546i	0.0868007	−	0.448602i
$471$		−	4.21087i		−	0.194027i
$472$	12.4882	−	8.65491i	0.574818	−	0.398375i
$473$	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
$478$	−12.1956	+	2.49776i	−0.557815	+	0.114245i
$479$	21.7112			0.992010			0.496005	−	0.868320i	$-0.334800\pi$
$479$	21.7112			0.992010			0.496005	+	0.868320i	$0.334800\pi$
$480$	17.5114	−	12.4205i	0.799283	−	0.566916i
$481$	−18.0673			−0.823800
$482$	−2.99418	+	0.613233i	−0.136381	+	0.0279320i
$483$	−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	$-0.867910\pi$
$487$	−11.2980	+	11.2980i	−0.511962	+	0.511962i	0.403165	+	0.915127i	$0.367910\pi$
$488$	27.9862	−	19.3957i	1.26688	−	0.878002i
$489$			22.5987i			1.02195i
$490$	−4.19923	−	6.21413i	−0.189702	−	0.280726i
$491$			21.1601i			0.954942i	0.878647	+	0.477471i	$0.158446\pi$
$491$			21.1601i			0.954942i	−0.878647	+	0.477471i	$0.841554\pi$
$492$	−14.0986	−	5.65355i	−0.635612	−	0.254882i
$493$	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
$498$	3.01529	+	14.7225i	0.135118	+	0.659732i
$499$	−24.0759			−1.07778			−0.538892	−	0.842375i	$-0.681157\pi$
$499$	−24.0759			−1.07778			−0.538892	+	0.842375i	$0.681157\pi$
$500$	0.223480	+	22.3596i	0.00999435	+	0.999950i
$501$	−21.4619			−0.958846
$502$	5.54097	+	27.0544i	0.247305	+	1.20750i
$503$	20.3664	+	20.3664i	0.908093	+	0.908093i	0.996118	−	0.0880249i	$-0.0280555\pi$
$503$	20.3664	+	20.3664i	0.908093	+	0.908093i	−0.0880249	+	0.996118i	$0.528056\pi$
$504$	−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
$508$	−8.20440	+	20.4598i	−0.364011	+	0.907755i
$509$		−	28.6068i		−	1.26798i	−0.773343	−	0.633988i	$-0.781417\pi$
$509$		−	28.6068i		−	1.26798i	0.773343	−	0.633988i	$-0.218583\pi$
$510$	−16.7799	−	24.8314i	−0.743028	−	1.09955i
$511$			6.90379i			0.305406i
$512$	−5.53961	−	21.9388i	−0.244818	−	0.969569i
$513$	−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
$518$	25.3518	−	5.19224i	1.11389	−	0.228134i
$519$	4.95359			0.217438
$520$	−2.83862	−	13.1311i	−0.124482	−	0.575838i
$521$	−33.7509			−1.47866			−0.739328	−	0.673346i	$-0.764857\pi$
$521$	−33.7509			−1.47866			−0.739328	+	0.673346i	$0.764857\pi$
$522$	1.31828	−	0.269994i	0.0576994	−	0.0118173i
$523$	−10.9977	−	10.9977i	−0.480897	−	0.480897i	0.424521	−	0.905418i	$-0.360442\pi$
$523$	−10.9977	−	10.9977i	−0.480897	−	0.480897i	−0.905418	+	0.424521i	$0.860442\pi$
$524$	−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
$528$	0.617405	+	27.2430i	0.0268691	+	1.18560i
$529$			22.7659i			0.989824i
$530$	4.48444	−	23.1764i	0.194791	−	1.00672i
$531$		−	0.640669i		−	0.0278027i
$532$	1.60143	−	3.99358i	0.0694309	−	0.173144i
$533$	−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
$538$	4.86768	+	23.7671i	0.209861	+	1.02467i
$539$	9.51945			0.410032
$540$	−0.257703	−	23.6752i	−0.0110898	−	1.01882i
$541$	−44.1197			−1.89685			−0.948427	−	0.316995i	$-0.897326\pi$
$541$	−44.1197			−1.89685			−0.948427	+	0.316995i	$0.897326\pi$
$542$	−6.90954	−	33.7367i	−0.296790	−	1.44911i
$543$	−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	$-0.599786\pi$
$547$	15.0359	−	15.0359i	0.642887	−	0.642887i	0.951264	+	0.308377i	$0.0997858\pi$
$548$	−40.8989	−	16.4005i	−1.74711	−	0.700595i
$549$		−	1.43574i		−	0.0612760i
$550$	−23.6736	−	15.6552i	−1.00945	−	0.667541i
$551$			7.97836i			0.339889i
$552$	−18.4992	−	26.6926i	−0.787378	−	1.13611i
$553$	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	$0.805023\pi$
$558$	−1.70810	+	0.349833i	−0.0723096	+	0.0148096i
$559$	−5.89076			−0.249153
$560$	7.75676	+	17.6096i	0.327783	+	0.744141i
$561$	38.0393			1.60602
$562$	−2.08989	+	0.428026i	−0.0881567	+	0.0180552i
$563$	−21.8581	−	21.8581i	−0.921210	−	0.921210i	0.0759053	−	0.997115i	$-0.475815\pi$
$563$	−21.8581	−	21.8581i	−0.921210	−	0.921210i	−0.997115	+	0.0759053i	$0.975815\pi$
$564$	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
$568$	−10.3494	−	14.9332i	−0.434251	−	0.626584i
$569$		−	3.55621i		−	0.149084i	−0.997218	−	0.0745421i	$-0.976250\pi$
$569$		−	3.55621i		−	0.149084i	0.997218	−	0.0745421i	$-0.0237495\pi$
$570$	5.26951	+	1.01961i	0.220716	+	0.0427066i
$571$			33.7698i			1.41322i	0.707602	+	0.706611i	$0.249777\pi$
$571$			33.7698i			1.41322i	−0.707602	+	0.706611i	$0.750223\pi$
$572$	15.8269	+	6.34661i	0.661755	+	0.265365i
$573$	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	$0.727654\pi$
$578$	4.02311	+	19.6433i	0.167339	+	0.817054i
$579$	−15.5403			−0.645835
$580$	−25.5029	−	24.9537i	−1.05895	−	1.03615i
$581$	−13.4694			−0.558806
$582$	−5.49356	−	26.8230i	−0.227716	−	1.11185i
$583$	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	$-0.568933\pi$
$587$	18.4563	−	18.4563i	0.761773	−	0.761773i	0.976643	+	0.214870i	$0.0689327\pi$
$588$	2.99644	−	7.47240i	0.123571	−	0.308157i
$589$		−	10.3376i		−	0.425954i
$590$	−14.0752	+	9.51142i	−0.579469	+	0.391579i
$591$			9.95619i			0.409543i
$592$	34.0136	−	0.770847i	1.39795	−	0.0316816i
$593$	−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
$598$	−19.9092	+	4.07756i	−0.814147	+	0.166744i
$599$	−8.38180			−0.342471			−0.171236	−	0.985230i	$-0.554776\pi$
$599$	−8.38180			−0.342471			−0.171236	+	0.985230i	$0.554776\pi$
$600$	−19.7405	+	13.6551i	−0.805902	+	0.557465i
$601$	12.0065			0.489754			0.244877	−	0.969554i	$-0.421252\pi$
$601$	12.0065			0.489754			0.244877	+	0.969554i	$0.421252\pi$
$602$	8.26580	−	1.69290i	0.336889	−	0.0689976i
$603$	−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	$-0.421037\pi$
$607$	29.9324	−	29.9324i	1.21492	−	1.21492i	0.969389	−	0.245532i	$-0.0789626\pi$
$608$	3.00832	−	4.79062i	0.122003	−	0.194285i
$609$		−	29.1324i		−	1.18051i
$610$	−31.5427	+	21.3151i	−1.27713	+	0.863025i
$611$		−	6.65398i		−	0.269191i
$612$	−0.495705	+	1.23617i	−0.0200377	+	0.0499691i
$613$	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	$0.841535\pi$
$618$	1.14183	+	5.57513i	0.0459312	+	0.224264i
$619$	8.56649			0.344316			0.172158	−	0.985069i	$-0.444926\pi$
$619$	8.56649			0.344316			0.172158	+	0.985069i	$0.444926\pi$
$620$	33.0443	+	32.3327i	1.32709	+	1.29851i
$621$	−35.8158			−1.43724
$622$	−2.83807	−	13.8572i	−0.113796	−	0.555625i
$623$	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
$628$	4.60544	+	1.84679i	0.183777	+	0.0736949i
$629$		−	47.4931i		−	1.89367i
$630$	0.796583	+	0.154132i	0.0317366	+	0.00614077i
$631$		−	25.1719i		−	1.00208i	−0.865425	−	0.501039i	$-0.832951\pi$
$631$		−	25.1719i		−	1.00208i	0.865425	−	0.501039i	$-0.167049\pi$
$632$	10.5740	−	7.32829i	0.420613	−	0.291504i
$633$	−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
$638$	44.3670	−	9.08672i	1.75651	−	0.359747i
$639$	−0.766100			−0.0303064
$640$	5.90424	+	24.5996i	0.233385	+	0.972384i
$641$	21.8637			0.863565			0.431783	−	0.901978i	$-0.357885\pi$
$641$	21.8637			0.863565			0.431783	+	0.901978i	$0.357885\pi$
$642$	17.6886	−	3.62277i	0.698114	−	0.142979i
$643$	−22.8913	−	22.8913i	−0.902746	−	0.902746i	0.0929271	−	0.995673i	$-0.470378\pi$
$643$	−22.8913	−	22.8913i	−0.902746	−	0.902746i	−0.995673	+	0.0929271i	$0.970378\pi$
$644$	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	$-0.811834\pi$
$647$	−6.94398	+	6.94398i	−0.272996	+	0.272996i	0.557309	+	0.830305i	$0.311834\pi$
$648$	20.0576	−	13.9008i	0.787936	−	0.546075i
$649$		−	21.5619i		−	0.846379i
$650$	3.00060	+	14.7174i	0.117693	+	0.577264i
$651$			37.7471i			1.47943i
$652$	−24.7162	−	9.91123i	−0.967961	−	0.388154i
$653$	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
$658$	1.91224	+	9.33673i	0.0745468	+	0.363984i
$659$	−20.3040			−0.790932			−0.395466	−	0.918481i	$-0.629417\pi$
$659$	−20.3040			−0.790932			−0.395466	+	0.918481i	$0.629417\pi$
$660$	−0.331606	−	30.4646i	−0.0129077	−	1.18583i
$661$	−29.3931			−1.14326			−0.571629	−	0.820512i	$-0.693688\pi$
$661$	−29.3931			−1.14326			−0.571629	+	0.820512i	$0.693688\pi$
$662$	−2.13849	−	10.4414i	−0.0831147	−	0.405818i
$663$	−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
$668$	9.41267	−	23.4729i	0.364187	−	0.908194i
$669$		−	27.3887i		−	1.05891i
$670$	−0.536479	+	2.77262i	−0.0207260	+	0.107116i
$671$		−	48.3204i		−	1.86539i
$672$	−10.9847	+	17.4926i	−0.423743	+	0.674793i
$673$	−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	$0.567640\pi$
$678$	−6.52620	+	1.33662i	−0.250637	+	0.0513325i
$679$	24.5400			0.941758
$680$	34.5174	−	7.46179i	1.32368	−	0.286147i
$681$	−4.96672			−0.190325
$682$	−57.4867	+	11.7737i	−2.20128	+	0.450839i
$683$	−6.48834	−	6.48834i	−0.248270	−	0.248270i	0.571991	−	0.820260i	$-0.306171\pi$
$683$	−6.48834	−	6.48834i	−0.248270	−	0.248270i	−0.820260	+	0.571991i	$0.806171\pi$
$684$	−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
$688$	11.0900	−	0.251331i	0.422801	−	0.00958189i
$689$		−	15.8569i		−	0.604098i
$690$	20.3299	+	30.0847i	0.773947	+	1.14531i
$691$		−	37.0957i		−	1.41119i	−0.708617	−	0.705593i	$-0.750681\pi$
$691$		−	37.0957i		−	1.41119i	0.708617	−	0.705593i	$-0.249319\pi$
$692$	−2.17252	+	5.41775i	−0.0825870	+	0.205952i
$693$	−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
$698$	7.36016	+	35.9369i	0.278586	+	1.36023i
$699$	−21.6838			−0.820157
$700$	−8.43991	−	19.7889i	−0.318999	−	0.747949i
$701$	11.2588			0.425239			0.212619	−	0.977135i	$-0.431801\pi$
$701$	11.2588			0.425239			0.212619	+	0.977135i	$0.431801\pi$
$702$	−3.19104	−	15.5807i	−0.120438	−	0.588054i
$703$	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
$708$	−16.9253	−	6.78706i	−0.636091	−	0.255073i
$709$			14.2210i			0.534080i	0.963685	+	0.267040i	$0.0860455\pi$
$709$			14.2210i			0.534080i	−0.963685	+	0.267040i	$0.913954\pi$
$710$	11.3736	+	16.8309i	0.426843	+	0.631653i
$711$		−	0.542467i		−	0.0203441i
$712$	14.2092	+	20.5025i	0.532511	+	0.768364i
$713$	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
$718$	−21.9906	+	4.50385i	−0.820682	+	0.168082i
$719$	−14.7950			−0.551761			−0.275880	−	0.961192i	$-0.588969\pi$
$719$	−14.7950			−0.551761			−0.275880	+	0.961192i	$0.588969\pi$
$720$	0.994334	+	0.386221i	0.0370566	+	0.0143936i
$721$	−5.10061			−0.189957
$722$	1.38545	−	0.283752i	0.0515613	−	0.0105602i
$723$	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	$-0.912654\pi$
$727$	−18.6479	+	18.6479i	−0.691613	+	0.691613i	0.270973	+	0.962587i	$0.412654\pi$
$728$	7.36260	+	10.6236i	0.272876	+	0.393735i
$729$		−	27.9863i		−	1.03653i
$730$	1.92778	−	9.96311i	0.0713503	−	0.368751i
$731$		−	15.4849i		−	0.572728i
$732$	−37.9296	−	15.2098i	−1.40192	−	0.562172i
$733$	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
$738$	−0.151430	−	0.739376i	−0.00557422	−	0.0272168i
$739$	14.1367			0.520025			0.260013	−	0.965605i	$-0.416273\pi$
$739$	14.1367			0.520025			0.260013	+	0.965605i	$0.416273\pi$
$740$	−38.0359	+	0.414018i	−1.39823	+	0.0152196i
$741$	3.60530			0.132444
$742$	4.55698	+	22.2500i	0.167292	+	0.816824i
$743$	10.3395	+	10.3395i	0.379321	+	0.379321i	0.870857	−	0.491536i	$-0.163565\pi$
$743$	10.3395	+	10.3395i	0.379321	+	0.379321i	−0.491536	+	0.870857i	$0.663565\pi$
$744$	−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
$748$	−16.6831	+	41.6036i	−0.609996	+	1.52118i
$749$			16.1831i			0.591316i
$750$	22.2488	−	15.0059i	0.812410	−	0.547938i
$751$			31.7895i			1.16002i	0.814611	+	0.580008i	$0.196951\pi$
$751$			31.7895i			1.16002i	−0.814611	+	0.580008i	$0.803049\pi$
$752$	0.283893	+	12.5268i	0.0103525	+	0.456805i
$753$	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	$0.777221\pi$
$758$	−15.1024	+	3.09309i	−0.548543	+	0.112346i
$759$	−46.0869			−1.67285
$760$	−3.42623	+	5.31610i	−0.124282	+	0.192835i
$761$	−7.45399			−0.270207			−0.135103	−	0.990831i	$-0.543137\pi$
$761$	−7.45399			−0.270207			−0.135103	+	0.990831i	$0.543137\pi$
$762$	25.9175	−	5.30812i	0.938894	−	0.192293i
$763$	−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
$768$	−18.3128	+	20.0527i	−0.660807	+	0.723588i
$769$			2.73507i			0.0986291i	0.998783	+	0.0493145i	$0.0157037\pi$
$769$			2.73507i			0.0986291i	−0.998783	+	0.0493145i	$0.984296\pi$
$770$	26.8093	+	5.18737i	0.966138	+	0.186940i
$771$		−

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.38545 - 0.283752i) q^{2} +(-1.20015 - 1.20015i) q^{3} +(1.83897 - 0.786251i) q^{4} +(-2.06624 + 0.854787i) q^{5} +(-2.00330 - 1.32221i) q^{6} +(1.52124 - 1.52124i) q^{7} +(2.32471 - 1.61113i) q^{8} -0.119262i q^{9} +O(q^{10})\)	\(q+(1.38545 - 0.283752i) 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} +(2.32471 - 1.61113i) q^{8} -0.119262i q^{9} +(-2.62013 + 1.77057i) q^{10} -4.01379i q^{11} +(-3.15067 - 1.26342i) 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} +(-0.0338407 - 0.165232i) q^{18} +1.00000 q^{19} +(-3.12767 + 3.19651i) q^{20} -3.65143 q^{21} +(-1.13892 - 5.56092i) 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} +(1.60143 - 3.99358i) q^{28} +7.97836i q^{29} +(5.26951 + 1.01961i) q^{30} -10.3376i q^{31} +(3.00832 - 4.79062i) 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} +(1.38545 - 0.283752i) q^{38} +3.60530 q^{39} +(-3.42623 + 5.31610i) q^{40} +4.47478 q^{41} +(-5.05889 + 1.03610i) 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} +(-6.78735 + 0.153821i) q^{48} +2.37169i q^{49} +(3.90036 - 5.89807i) q^{50} +9.47715i q^{51} +(-1.58120 + 3.94313i) 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} +(2.26388 + 11.0537i) q^{58} +5.37196 q^{59} +(7.58999 - 0.0826166i) q^{60} +12.0386 q^{61} +(-2.93332 - 14.3223i) 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} +(-10.3652 - 4.15645i) q^{68} -11.4821i q^{69} +(-1.29239 + 6.67929i) q^{70} -6.42369i q^{71} +(-0.192146 - 0.277248i) 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} +(4.99499 - 1.02301i) q^{78} +4.54855 q^{79} +(-3.23843 + 8.33742i) q^{80} +8.62799 q^{81} +(6.19961 - 1.26973i) 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} +(-6.46673 - 9.33089i) q^{88} +8.81939i q^{89} +(0.211161 + 0.312481i) q^{90} +4.56984i q^{91} +(12.5580 + 5.03580i) 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} +(0.672971 + 3.28586i) 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	\( 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) \) 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

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