LMFDB - Embedded newform 1050.3.l.b.43.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(43,1050)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1050.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.l (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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.12745506816.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 23x^{4} + 1 $ x^8 + 23*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.3
Root			$-0.323042 + 0.323042i$ of defining polynomial
Character	$\chi$	$=$	1050.43
Dual form			1050.3.l.b.757.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} -2.44949 q^{6} +(-1.87083 + 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} -2.44949 q^{6} +(-1.87083 + 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} -12.4065 q^{11} +(2.44949 - 2.44949i) q^{12} +(-3.13309 - 3.13309i) q^{13} -3.74166i q^{14} -4.00000 q^{16} +(5.80341 - 5.80341i) q^{17} +(-3.00000 - 3.00000i) q^{18} -26.5813i q^{19} -4.58258 q^{21} +(12.4065 - 12.4065i) q^{22} +(10.4235 + 10.4235i) q^{23} +4.89898i q^{24} +6.26617 q^{26} +(-3.67423 + 3.67423i) q^{27} +(3.74166 + 3.74166i) q^{28} -14.5808i q^{29} +42.6563 q^{31} +(4.00000 - 4.00000i) q^{32} +(-15.1948 - 15.1948i) q^{33} +11.6068i q^{34} +6.00000 q^{36} +(-11.9306 + 11.9306i) q^{37} +(26.5813 + 26.5813i) q^{38} -7.67446i q^{39} +37.5226 q^{41} +(4.58258 - 4.58258i) q^{42} +(-24.0083 - 24.0083i) q^{43} +24.8131i q^{44} -20.8470 q^{46} +(-8.83609 + 8.83609i) q^{47} +(-4.89898 - 4.89898i) q^{48} -7.00000i q^{49} +14.2154 q^{51} +(-6.26617 + 6.26617i) q^{52} +(1.97883 + 1.97883i) q^{53} -7.34847i q^{54} -7.48331 q^{56} +(32.5553 - 32.5553i) q^{57} +(14.5808 + 14.5808i) q^{58} -88.2651i q^{59} +102.471 q^{61} +(-42.6563 + 42.6563i) q^{62} +(-5.61249 - 5.61249i) q^{63} +8.00000i q^{64} +30.3897 q^{66} +(22.8107 - 22.8107i) q^{67} +(-11.6068 - 11.6068i) q^{68} +25.5322i q^{69} -10.7950 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-80.4481 - 80.4481i) q^{73} -23.8612i q^{74} -53.1625 q^{76} +(23.2105 - 23.2105i) q^{77} +(7.67446 + 7.67446i) q^{78} -138.851i q^{79} -9.00000 q^{81} +(-37.5226 + 37.5226i) q^{82} +(96.0834 + 96.0834i) q^{83} +9.16515i q^{84} +48.0166 q^{86} +(17.8578 - 17.8578i) q^{87} +(-24.8131 - 24.8131i) q^{88} +3.29855i q^{89} +11.7229 q^{91} +(20.8470 - 20.8470i) q^{92} +(52.2431 + 52.2431i) q^{93} -17.6722i q^{94} +9.79796 q^{96} +(88.5219 - 88.5219i) q^{97} +(7.00000 + 7.00000i) q^{98} -37.2196i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 16 q^{8}+O(q^{10}) $ 8 * q - 8 * q^2 + 16 * q^8	$ 8 q - 8 q^{2} + 16 q^{8} - 8 q^{11} - 8 q^{13} - 32 q^{16} + 32 q^{17} - 24 q^{18} + 8 q^{22} + 40 q^{23} + 16 q^{26} + 144 q^{31} + 32 q^{32} - 120 q^{33} + 48 q^{36} - 160 q^{37} - 320 q^{41} + 32 q^{43} - 80 q^{46} + 144 q^{47} + 72 q^{51} - 16 q^{52} + 200 q^{53} + 24 q^{57} + 64 q^{58} + 288 q^{61} - 144 q^{62} + 240 q^{66} - 80 q^{67} - 64 q^{68} - 280 q^{71} - 48 q^{72} - 312 q^{73} + 56 q^{77} - 48 q^{78} - 72 q^{81} + 320 q^{82} + 320 q^{83} - 64 q^{86} + 48 q^{87} - 16 q^{88} + 80 q^{92} - 48 q^{93} + 24 q^{97} + 56 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 16 * q^8 - 8 * q^11 - 8 * q^13 - 32 * q^16 + 32 * q^17 - 24 * q^18 + 8 * q^22 + 40 * q^23 + 16 * q^26 + 144 * q^31 + 32 * q^32 - 120 * q^33 + 48 * q^36 - 160 * q^37 - 320 * q^41 + 32 * q^43 - 80 * q^46 + 144 * q^47 + 72 * q^51 - 16 * q^52 + 200 * q^53 + 24 * q^57 + 64 * q^58 + 288 * q^61 - 144 * q^62 + 240 * q^66 - 80 * q^67 - 64 * q^68 - 280 * q^71 - 48 * q^72 - 312 * q^73 + 56 * q^77 - 48 * q^78 - 72 * q^81 + 320 * q^82 + 320 * q^83 - 64 * q^86 + 48 * q^87 - 16 * q^88 + 80 * q^92 - 48 * q^93 + 24 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$4$		−	2.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	−2.44949			−0.408248
$7$	−1.87083	+	1.87083i	−0.267261	+	0.267261i
$7$	−1.87083	+	1.87083i	−0.267261	+	0.267261i
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$			3.00000i			0.333333i
$10$		0			0
$11$	−12.4065			−1.12787			−0.563933	−	0.825820i	$-0.690712\pi$
$11$	−12.4065			−1.12787			−0.563933	+	0.825820i	$0.690712\pi$
$12$	2.44949	−	2.44949i	0.204124	−	0.204124i
$13$	−3.13309	−	3.13309i	−0.241007	−	0.241007i	0.576260	−	0.817267i	$-0.304512\pi$
$13$	−3.13309	−	3.13309i	−0.241007	−	0.241007i	−0.817267	+	0.576260i	$0.804512\pi$
$14$		−	3.74166i		−	0.267261i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	5.80341	−	5.80341i	0.341377	−	0.341377i	−0.515508	−	0.856885i	$-0.672397\pi$
$17$	5.80341	−	5.80341i	0.341377	−	0.341377i	0.856885	+	0.515508i	$0.172397\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$		−	26.5813i		−	1.39901i	−0.714626	−	0.699507i	$-0.753403\pi$
$19$		−	26.5813i		−	1.39901i	0.714626	−	0.699507i	$-0.246597\pi$
$20$		0			0
$21$	−4.58258			−0.218218
$22$	12.4065	−	12.4065i	0.563933	−	0.563933i
$23$	10.4235	+	10.4235i	0.453195	+	0.453195i	0.896414	−	0.443218i	$-0.146163\pi$
$23$	10.4235	+	10.4235i	0.453195	+	0.453195i	−0.443218	+	0.896414i	$0.646163\pi$
$24$			4.89898i			0.204124i
$25$		0			0
$26$	6.26617			0.241007
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	3.74166	+	3.74166i	0.133631	+	0.133631i
$29$		−	14.5808i		−	0.502787i	−0.967885	−	0.251393i	$-0.919111\pi$
$29$		−	14.5808i		−	0.502787i	0.967885	−	0.251393i	$-0.0808888\pi$
$30$		0			0
$31$	42.6563			1.37601			0.688005	−	0.725706i	$-0.258487\pi$
$31$	42.6563			1.37601			0.688005	+	0.725706i	$0.258487\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	−15.1948	−	15.1948i	−0.460450	−	0.460450i
$34$			11.6068i			0.341377i
$35$		0			0
$36$	6.00000			0.166667
$37$	−11.9306	+	11.9306i	−0.322448	+	0.322448i	−0.849706	−	0.527257i	$-0.823220\pi$
$37$	−11.9306	+	11.9306i	−0.322448	+	0.322448i	0.527257	+	0.849706i	$0.323220\pi$
$38$	26.5813	+	26.5813i	0.699507	+	0.699507i
$39$		−	7.67446i		−	0.196781i
$40$		0			0
$41$	37.5226			0.915185			0.457593	−	0.889162i	$-0.348712\pi$
$41$	37.5226			0.915185			0.457593	+	0.889162i	$0.348712\pi$
$42$	4.58258	−	4.58258i	0.109109	−	0.109109i
$43$	−24.0083	−	24.0083i	−0.558332	−	0.558332i	0.370500	−	0.928832i	$-0.379186\pi$
$43$	−24.0083	−	24.0083i	−0.558332	−	0.558332i	−0.928832	+	0.370500i	$0.879186\pi$
$44$			24.8131i			0.563933i
$45$		0			0
$46$	−20.8470			−0.453195
$47$	−8.83609	+	8.83609i	−0.188002	+	0.188002i	−0.794832	−	0.606830i	$-0.792441\pi$
$47$	−8.83609	+	8.83609i	−0.188002	+	0.188002i	0.606830	+	0.794832i	$0.292441\pi$
$48$	−4.89898	−	4.89898i	−0.102062	−	0.102062i
$49$		−	7.00000i		−	0.142857i
$50$		0			0
$51$	14.2154			0.278733
$52$	−6.26617	+	6.26617i	−0.120503	+	0.120503i
$53$	1.97883	+	1.97883i	0.0373364	+	0.0373364i	0.725529	−	0.688192i	$-0.241595\pi$
$53$	1.97883	+	1.97883i	0.0373364	+	0.0373364i	−0.688192	+	0.725529i	$0.741595\pi$
$54$		−	7.34847i		−	0.136083i
$55$		0			0
$56$	−7.48331			−0.133631
$57$	32.5553	−	32.5553i	0.571145	−	0.571145i
$58$	14.5808	+	14.5808i	0.251393	+	0.251393i
$59$		−	88.2651i		−	1.49602i	−0.663688	−	0.748010i	$-0.731010\pi$
$59$		−	88.2651i		−	1.49602i	0.663688	−	0.748010i	$-0.268990\pi$
$60$		0			0
$61$	102.471			1.67985			0.839924	−	0.542704i	$-0.182600\pi$
$61$	102.471			1.67985			0.839924	+	0.542704i	$0.182600\pi$
$62$	−42.6563	+	42.6563i	−0.688005	+	0.688005i
$63$	−5.61249	−	5.61249i	−0.0890871	−	0.0890871i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	30.3897			0.460450
$67$	22.8107	−	22.8107i	0.340458	−	0.340458i	−0.516082	−	0.856539i	$-0.672610\pi$
$67$	22.8107	−	22.8107i	0.340458	−	0.340458i	0.856539	+	0.516082i	$0.172610\pi$
$68$	−11.6068	−	11.6068i	−0.170688	−	0.170688i
$69$			25.5322i			0.370032i
$70$		0			0
$71$	−10.7950			−0.152042			−0.0760208	−	0.997106i	$-0.524222\pi$
$71$	−10.7950			−0.152042			−0.0760208	+	0.997106i	$0.524222\pi$
$72$	−6.00000	+	6.00000i	−0.0833333	+	0.0833333i
$73$	−80.4481	−	80.4481i	−1.10203	−	1.10203i	−0.994166	−	0.107863i	$-0.965599\pi$
$73$	−80.4481	−	80.4481i	−1.10203	−	1.10203i	−0.107863	−	0.994166i	$-0.534401\pi$
$74$		−	23.8612i		−	0.322448i
$75$		0			0
$76$	−53.1625			−0.699507
$77$	23.2105	−	23.2105i	0.301435	−	0.301435i
$78$	7.67446	+	7.67446i	0.0983905	+	0.0983905i
$79$		−	138.851i		−	1.75761i	−0.477180	−	0.878806i	$-0.658341\pi$
$79$		−	138.851i		−	1.75761i	0.477180	−	0.878806i	$-0.341659\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	−37.5226	+	37.5226i	−0.457593	+	0.457593i
$83$	96.0834	+	96.0834i	1.15763	+	1.15763i	0.984984	+	0.172648i	$0.0552324\pi$
$83$	96.0834	+	96.0834i	1.15763	+	1.15763i	0.172648	+	0.984984i	$0.444768\pi$
$84$			9.16515i			0.109109i
$85$		0			0
$86$	48.0166			0.558332
$87$	17.8578	−	17.8578i	0.205262	−	0.205262i
$88$	−24.8131	−	24.8131i	−0.281967	−	0.281967i
$89$			3.29855i			0.0370623i	0.999828	+	0.0185312i	$0.00589899\pi$
$89$			3.29855i			0.0370623i	−0.999828	+	0.0185312i	$0.994101\pi$
$90$		0			0
$91$	11.7229			0.128823
$92$	20.8470	−	20.8470i	0.226598	−	0.226598i
$93$	52.2431	+	52.2431i	0.561754	+	0.561754i
$94$		−	17.6722i		−	0.188002i
$95$		0			0
$96$	9.79796			0.102062
$97$	88.5219	−	88.5219i	0.912597	−	0.912597i	−0.0838786	−	0.996476i	$-0.526731\pi$
$97$	88.5219	−	88.5219i	0.912597	−	0.912597i	0.996476	+	0.0838786i	$0.0267308\pi$
$98$	7.00000	+	7.00000i	0.0714286	+	0.0714286i
$99$		−	37.2196i		−	0.375955i
$100$		0			0
$101$	142.067			1.40661			0.703304	−	0.710889i	$-0.251707\pi$
$101$	142.067			1.40661			0.703304	+	0.710889i	$0.251707\pi$
$102$	−14.2154	+	14.2154i	−0.139367	+	0.139367i
$103$	−60.4386	−	60.4386i	−0.586782	−	0.586782i	0.349976	−	0.936759i	$-0.386190\pi$
$103$	−60.4386	−	60.4386i	−0.586782	−	0.586782i	−0.936759	+	0.349976i	$0.886190\pi$
$104$		−	12.5323i		−	0.120503i
$105$		0			0
$106$	−3.95766			−0.0373364
$107$	−78.7617	+	78.7617i	−0.736091	+	0.736091i	−0.971819	−	0.235728i	$-0.924253\pi$
$107$	−78.7617	+	78.7617i	−0.736091	+	0.736091i	0.235728	+	0.971819i	$0.424253\pi$
$108$	7.34847	+	7.34847i	0.0680414	+	0.0680414i
$109$			102.684i			0.942053i	0.882119	+	0.471026i	$0.156116\pi$
$109$			102.684i			0.942053i	−0.882119	+	0.471026i	$0.843884\pi$
$110$		0			0
$111$	−29.2239			−0.263278
$112$	7.48331	−	7.48331i	0.0668153	−	0.0668153i
$113$	34.2131	+	34.2131i	0.302771	+	0.302771i	0.842097	−	0.539326i	$-0.181321\pi$
$113$	34.2131	+	34.2131i	0.302771	+	0.302771i	−0.539326	+	0.842097i	$0.681321\pi$
$114$			65.1105i			0.571145i
$115$		0			0
$116$	−29.1616			−0.251393
$117$	9.39926	−	9.39926i	0.0803355	−	0.0803355i
$118$	88.2651	+	88.2651i	0.748010	+	0.748010i
$119$			21.7144i			0.182474i
$120$		0			0
$121$	32.9220			0.272083
$122$	−102.471	+	102.471i	−0.839924	+	0.839924i
$123$	45.9556	+	45.9556i	0.373623	+	0.373623i
$124$		−	85.3126i		−	0.688005i
$125$		0			0
$126$	11.2250			0.0890871
$127$	149.547	−	149.547i	1.17753	−	1.17753i	0.197161	−	0.980371i	$-0.436828\pi$
$127$	149.547	−	149.547i	1.17753	−	1.17753i	0.980371	−	0.197161i	$-0.0631721\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$		−	58.8080i		−	0.455876i
$130$		0			0
$131$	−93.4871			−0.713642			−0.356821	−	0.934173i	$-0.616139\pi$
$131$	−93.4871			−0.713642			−0.356821	+	0.934173i	$0.616139\pi$
$132$	−30.3897	+	30.3897i	−0.230225	+	0.230225i
$133$	49.7290	+	49.7290i	0.373902	+	0.373902i
$134$			45.6213i			0.340458i
$135$		0			0
$136$	23.2136			0.170688
$137$	66.0053	−	66.0053i	0.481790	−	0.481790i	−0.423913	−	0.905703i	$-0.639344\pi$
$137$	66.0053	−	66.0053i	0.481790	−	0.481790i	0.905703	+	0.423913i	$0.139344\pi$
$138$	−25.5322	−	25.5322i	−0.185016	−	0.185016i
$139$		−	111.764i		−	0.804059i	−0.915627	−	0.402029i	$-0.868305\pi$
$139$		−	111.764i		−	0.804059i	0.915627	−	0.402029i	$-0.131695\pi$
$140$		0			0
$141$	−21.6439			−0.153503
$142$	10.7950	−	10.7950i	0.0760208	−	0.0760208i
$143$	38.8707	+	38.8707i	0.271823	+	0.271823i
$144$		−	12.0000i		−	0.0833333i
$145$		0			0
$146$	160.896			1.10203
$147$	8.57321	−	8.57321i	0.0583212	−	0.0583212i
$148$	23.8612	+	23.8612i	0.161224	+	0.161224i
$149$			214.999i			1.44295i	0.692443	+	0.721473i	$0.256535\pi$
$149$			214.999i			1.44295i	−0.692443	+	0.721473i	$0.743465\pi$
$150$		0			0
$151$	−62.7527			−0.415581			−0.207790	−	0.978173i	$-0.566627\pi$
$151$	−62.7527			−0.415581			−0.207790	+	0.978173i	$0.566627\pi$
$152$	53.1625	−	53.1625i	0.349754	−	0.349754i
$153$	17.4102	+	17.4102i	0.113792	+	0.113792i
$154$			46.4210i			0.301435i
$155$		0			0
$156$	−15.3489			−0.0983905
$157$	−181.318	+	181.318i	−1.15489	+	1.15489i	−0.169329	+	0.985560i	$0.554160\pi$
$157$	−181.318	+	181.318i	−1.15489	+	1.15489i	−0.985560	+	0.169329i	$0.945840\pi$
$158$	138.851	+	138.851i	0.878806	+	0.878806i
$159$			4.84712i			0.0304850i
$160$		0			0
$161$	−39.0011			−0.242243
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	52.0026	+	52.0026i	0.319034	+	0.319034i	0.848396	−	0.529362i	$-0.177569\pi$
$163$	52.0026	+	52.0026i	0.319034	+	0.319034i	−0.529362	+	0.848396i	$0.677569\pi$
$164$		−	75.0452i		−	0.457593i
$165$		0			0
$166$	−192.167			−1.15763
$167$	153.475	−	153.475i	0.919013	−	0.919013i	−0.0779443	−	0.996958i	$-0.524836\pi$
$167$	153.475	−	153.475i	0.919013	−	0.919013i	0.996958	+	0.0779443i	$0.0248356\pi$
$168$	−9.16515	−	9.16515i	−0.0545545	−	0.0545545i
$169$		−	149.368i		−	0.883832i
$170$		0			0
$171$	79.7438			0.466338
$172$	−48.0166	+	48.0166i	−0.279166	+	0.279166i
$173$	86.7956	+	86.7956i	0.501708	+	0.501708i	0.911969	−	0.410260i	$-0.134562\pi$
$173$	86.7956	+	86.7956i	0.501708	+	0.501708i	−0.410260	+	0.911969i	$0.634562\pi$
$174$			35.7156i			0.205262i
$175$		0			0
$176$	49.6261			0.281967
$177$	108.102	−	108.102i	0.610747	−	0.610747i
$178$	−3.29855	−	3.29855i	−0.0185312	−	0.0185312i
$179$			203.414i			1.13639i	0.822893	+	0.568196i	$0.192359\pi$
$179$			203.414i			1.13639i	−0.822893	+	0.568196i	$0.807641\pi$
$180$		0			0
$181$	−251.290			−1.38834			−0.694172	−	0.719810i	$-0.744229\pi$
$181$	−251.290			−1.38834			−0.694172	+	0.719810i	$0.744229\pi$
$182$	−11.7229	+	11.7229i	−0.0644117	+	0.0644117i
$183$	125.500	+	125.500i	0.685795	+	0.685795i
$184$			41.6940i			0.226598i
$185$		0			0
$186$	−104.486			−0.561754
$187$	−72.0001	+	72.0001i	−0.385027	+	0.385027i
$188$	17.6722	+	17.6722i	0.0940010	+	0.0940010i
$189$		−	13.7477i		−	0.0727393i
$190$		0			0
$191$	367.604			1.92463			0.962315	−	0.271938i	$-0.0876646\pi$
$191$	367.604			1.92463			0.962315	+	0.271938i	$0.0876646\pi$
$192$	−9.79796	+	9.79796i	−0.0510310	+	0.0510310i
$193$	−95.7120	−	95.7120i	−0.495917	−	0.495917i	0.414247	−	0.910164i	$-0.364045\pi$
$193$	−95.7120	−	95.7120i	−0.495917	−	0.495917i	−0.910164	+	0.414247i	$0.864045\pi$
$194$			177.044i			0.912597i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	194.449	−	194.449i	0.987048	−	0.987048i	−0.0128689	−	0.999917i	$-0.504096\pi$
$197$	194.449	−	194.449i	0.987048	−	0.987048i	0.999917	+	0.0128689i	$0.00409643\pi$
$198$	37.2196	+	37.2196i	0.187978	+	0.187978i
$199$		−	91.9043i		−	0.461831i	−0.972974	−	0.230915i	$-0.925828\pi$
$199$		−	91.9043i		−	0.461831i	0.972974	−	0.230915i	$-0.0741720\pi$
$200$		0			0
$201$	55.8745			0.277982
$202$	−142.067	+	142.067i	−0.703304	+	0.703304i
$203$	27.2782	+	27.2782i	0.134375	+	0.134375i
$204$		−	28.4308i		−	0.139367i
$205$		0			0
$206$	120.877			0.586782
$207$	−31.2705	+	31.2705i	−0.151065	+	0.151065i
$208$	12.5323	+	12.5323i	0.0602517	+	0.0602517i
$209$			329.781i			1.57790i
$210$		0			0
$211$	296.539			1.40540			0.702700	−	0.711486i	$-0.251978\pi$
$211$	296.539			1.40540			0.702700	+	0.711486i	$0.251978\pi$
$212$	3.95766	−	3.95766i	0.0186682	−	0.0186682i
$213$	−13.2211	−	13.2211i	−0.0620707	−	0.0620707i
$214$		−	157.523i		−	0.736091i
$215$		0			0
$216$	−14.6969			−0.0680414
$217$	−79.8026	+	79.8026i	−0.367754	+	0.367754i
$218$	−102.684	−	102.684i	−0.471026	−	0.471026i
$219$		−	197.057i		−	0.899803i
$220$		0			0
$221$	−36.3651			−0.164548
$222$	29.2239	−	29.2239i	0.131639	−	0.131639i
$223$	−99.7016	−	99.7016i	−0.447092	−	0.447092i	0.447295	−	0.894387i	$-0.352388\pi$
$223$	−99.7016	−	99.7016i	−0.447092	−	0.447092i	−0.894387	+	0.447295i	$0.852388\pi$
$224$			14.9666i			0.0668153i
$225$		0			0
$226$	−68.4262			−0.302771
$227$	45.7570	−	45.7570i	0.201573	−	0.201573i	−0.599101	−	0.800674i	$-0.704475\pi$
$227$	45.7570	−	45.7570i	0.201573	−	0.201573i	0.800674	+	0.599101i	$0.204475\pi$
$228$	−65.1105	−	65.1105i	−0.285573	−	0.285573i
$229$		−	248.102i		−	1.08342i	−0.840567	−	0.541708i	$-0.817778\pi$
$229$		−	248.102i		−	1.08342i	0.840567	−	0.541708i	$-0.182222\pi$
$230$		0			0
$231$	56.8539			0.246121
$232$	29.1616	−	29.1616i	0.125697	−	0.125697i
$233$	−306.481	−	306.481i	−1.31537	−	1.31537i	−0.917399	−	0.397968i	$-0.869716\pi$
$233$	−306.481	−	306.481i	−1.31537	−	1.31537i	−0.397968	−	0.917399i	$-0.630284\pi$
$234$			18.7985i			0.0803355i
$235$		0			0
$236$	−176.530			−0.748010
$237$	170.057	−	170.057i	0.717542	−	0.717542i
$238$	−21.7144	−	21.7144i	−0.0912368	−	0.0912368i
$239$		−	136.398i		−	0.570702i	−0.958423	−	0.285351i	$-0.907890\pi$
$239$		−	136.398i		−	0.570702i	0.958423	−	0.285351i	$-0.0921102\pi$
$240$		0			0
$241$	332.727			1.38061			0.690305	−	0.723519i	$-0.257477\pi$
$241$	332.727			1.38061			0.690305	+	0.723519i	$0.257477\pi$
$242$	−32.9220	+	32.9220i	−0.136041	+	0.136041i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$		−	204.941i		−	0.839924i
$245$		0			0
$246$	−91.9112			−0.373623
$247$	−83.2814	+	83.2814i	−0.337172	+	0.337172i
$248$	85.3126	+	85.3126i	0.344002	+	0.344002i
$249$			235.355i			0.945202i
$250$		0			0
$251$	244.521			0.974186			0.487093	−	0.873350i	$-0.338057\pi$
$251$	244.521			0.974186			0.487093	+	0.873350i	$0.338057\pi$
$252$	−11.2250	+	11.2250i	−0.0445435	+	0.0445435i
$253$	−129.319	−	129.319i	−0.511144	−	0.511144i
$254$			299.093i			1.17753i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−102.592	+	102.592i	−0.399191	+	0.399191i	−0.877948	−	0.478756i	$-0.841088\pi$
$257$	−102.592	+	102.592i	−0.399191	+	0.399191i	0.478756	+	0.877948i	$0.341088\pi$
$258$	58.8080	+	58.8080i	0.227938	+	0.227938i
$259$		−	44.6402i		−	0.172356i
$260$		0			0
$261$	43.7424			0.167596
$262$	93.4871	−	93.4871i	0.356821	−	0.356821i
$263$	−253.841	−	253.841i	−0.965174	−	0.965174i	0.0342400	−	0.999414i	$-0.489099\pi$
$263$	−253.841	−	253.841i	−0.965174	−	0.965174i	−0.999414	+	0.0342400i	$0.989099\pi$
$264$		−	60.7793i		−	0.230225i
$265$		0			0
$266$	−99.4580			−0.373902
$267$	−4.03988	+	4.03988i	−0.0151306	+	0.0151306i
$268$	−45.6213	−	45.6213i	−0.170229	−	0.170229i
$269$			207.747i			0.772295i	0.922437	+	0.386147i	$0.126194\pi$
$269$			207.747i			0.772295i	−0.922437	+	0.386147i	$0.873806\pi$
$270$		0			0
$271$	−476.286			−1.75751			−0.878756	−	0.477270i	$-0.841626\pi$
$271$	−476.286			−1.75751			−0.878756	+	0.477270i	$0.841626\pi$
$272$	−23.2136	+	23.2136i	−0.0853442	+	0.0853442i
$273$	14.3576	+	14.3576i	0.0525920	+	0.0525920i
$274$			132.011i			0.481790i
$275$		0			0
$276$	51.0645			0.185016
$277$	9.67870	−	9.67870i	0.0349412	−	0.0349412i	−0.689420	−	0.724362i	$-0.742135\pi$
$277$	9.67870	−	9.67870i	0.0349412	−	0.0349412i	0.724362	+	0.689420i	$0.242135\pi$
$278$	111.764	+	111.764i	0.402029	+	0.402029i
$279$			127.969i			0.458670i
$280$		0			0
$281$	101.463			0.361079			0.180540	−	0.983568i	$-0.442216\pi$
$281$	101.463			0.361079			0.180540	+	0.983568i	$0.442216\pi$
$282$	21.6439	−	21.6439i	0.0767515	−	0.0767515i
$283$	−276.026	−	276.026i	−0.975358	−	0.975358i	0.0243452	−	0.999704i	$-0.492250\pi$
$283$	−276.026	−	276.026i	−0.975358	−	0.975358i	−0.999704	+	0.0243452i	$0.992250\pi$
$284$			21.5899i			0.0760208i
$285$		0			0
$286$	−77.7415			−0.271823
$287$	−70.1983	+	70.1983i	−0.244594	+	0.244594i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$			221.641i			0.766924i
$290$		0			0
$291$	216.834			0.745133
$292$	−160.896	+	160.896i	−0.551014	+	0.551014i
$293$	−104.873	−	104.873i	−0.357928	−	0.357928i	0.505121	−	0.863049i	$-0.331448\pi$
$293$	−104.873	−	104.873i	−0.357928	−	0.357928i	−0.863049	+	0.505121i	$0.831448\pi$
$294$			17.1464i			0.0583212i
$295$		0			0
$296$	−47.7224			−0.161224
$297$	45.5845	−	45.5845i	0.153483	−	0.153483i
$298$	−214.999	−	214.999i	−0.721473	−	0.721473i
$299$		−	65.3154i		−	0.218446i
$300$		0			0
$301$	89.8308			0.298441
$302$	62.7527	−	62.7527i	0.207790	−	0.207790i
$303$	173.996	+	173.996i	0.574245	+	0.574245i
$304$			106.325i			0.349754i
$305$		0			0
$306$	−34.8204			−0.113792
$307$	−158.138	+	158.138i	−0.515108	+	0.515108i	−0.916087	−	0.400979i	$-0.868670\pi$
$307$	−158.138	+	158.138i	−0.515108	+	0.515108i	0.400979	+	0.916087i	$0.368670\pi$
$308$	−46.4210	−	46.4210i	−0.150717	−	0.150717i
$309$		−	148.044i		−	0.479106i
$310$		0			0
$311$	−519.537			−1.67054			−0.835269	−	0.549842i	$-0.814688\pi$
$311$	−519.537			−1.67054			−0.835269	+	0.549842i	$0.814688\pi$
$312$	15.3489	−	15.3489i	0.0491953	−	0.0491953i
$313$	−73.0852	−	73.0852i	−0.233499	−	0.233499i	0.580653	−	0.814152i	$-0.302798\pi$
$313$	−73.0852	−	73.0852i	−0.233499	−	0.233499i	−0.814152	+	0.580653i	$0.802798\pi$
$314$		−	362.635i		−	1.15489i
$315$		0			0
$316$	−277.703			−0.878806
$317$	−279.849	+	279.849i	−0.882805	+	0.882805i	−0.993819	−	0.111014i	$-0.964590\pi$
$317$	−279.849	+	279.849i	−0.882805	+	0.882805i	0.111014	+	0.993819i	$0.464590\pi$
$318$	−4.84712	−	4.84712i	−0.0152425	−	0.0152425i
$319$			180.897i			0.567076i
$320$		0			0
$321$	−192.926			−0.601016
$322$	39.0011	−	39.0011i	0.121122	−	0.121122i
$323$	−154.262	−	154.262i	−0.477591	−	0.477591i
$324$			18.0000i			0.0555556i
$325$		0			0
$326$	−104.005			−0.319034
$327$	−125.761	+	125.761i	−0.384592	+	0.384592i
$328$	75.0452	+	75.0452i	0.228796	+	0.228796i
$329$		−	33.0616i		−	0.100491i
$330$		0			0
$331$	−601.834			−1.81823			−0.909115	−	0.416546i	$-0.863241\pi$
$331$	−601.834			−1.81823			−0.909115	+	0.416546i	$0.863241\pi$
$332$	192.167	−	192.167i	0.578816	−	0.578816i
$333$	−35.7918	−	35.7918i	−0.107483	−	0.107483i
$334$			306.950i			0.919013i
$335$		0			0
$336$	18.3303			0.0545545
$337$	−17.0969	+	17.0969i	−0.0507325	+	0.0507325i	−0.732018	−	0.681285i	$-0.761421\pi$
$337$	−17.0969	+	17.0969i	−0.0507325	+	0.0507325i	0.681285	+	0.732018i	$0.261421\pi$
$338$	149.368	+	149.368i	0.441916	+	0.441916i
$339$			83.8046i			0.247211i
$340$		0			0
$341$	−529.217			−1.55195
$342$	−79.7438	+	79.7438i	−0.233169	+	0.233169i
$343$	13.0958	+	13.0958i	0.0381802	+	0.0381802i
$344$		−	96.0331i		−	0.279166i
$345$		0			0
$346$	−173.591			−0.501708
$347$	−233.692	+	233.692i	−0.673465	+	0.673465i	−0.958513	−	0.285048i	$-0.907990\pi$
$347$	−233.692	+	233.692i	−0.673465	+	0.673465i	0.285048	+	0.958513i	$0.407990\pi$
$348$	−35.7156	−	35.7156i	−0.102631	−	0.102631i
$349$		−	399.184i		−	1.14379i	−0.820326	−	0.571896i	$-0.806208\pi$
$349$		−	399.184i		−	1.14379i	0.820326	−	0.571896i	$-0.193792\pi$
$350$		0			0
$351$	23.0234			0.0655937
$352$	−49.6261	+	49.6261i	−0.140983	+	0.140983i
$353$	137.005	+	137.005i	0.388117	+	0.388117i	0.874015	−	0.485898i	$-0.161507\pi$
$353$	137.005	+	137.005i	0.388117	+	0.388117i	−0.485898	+	0.874015i	$0.661507\pi$
$354$			216.205i			0.610747i
$355$		0			0
$356$	6.59709			0.0185312
$357$	−26.5945	+	26.5945i	−0.0744945	+	0.0744945i
$358$	−203.414	−	203.414i	−0.568196	−	0.568196i
$359$		−	473.333i		−	1.31848i	−0.751934	−	0.659239i	$-0.770879\pi$
$359$		−	473.333i		−	1.31848i	0.751934	−	0.659239i	$-0.229121\pi$
$360$		0			0
$361$	−345.564			−0.957241
$362$	251.290	−	251.290i	0.694172	−	0.694172i
$363$	40.3210	+	40.3210i	0.111077	+	0.111077i
$364$		−	23.4459i		−	0.0644117i
$365$		0			0
$366$	−251.001			−0.685795
$367$	256.657	−	256.657i	0.699338	−	0.699338i	−0.264930	−	0.964268i	$-0.585349\pi$
$367$	256.657	−	256.657i	0.699338	−	0.699338i	0.964268	+	0.264930i	$0.0853487\pi$
$368$	−41.6940	−	41.6940i	−0.113299	−	0.113299i
$369$			112.568i			0.305062i
$370$		0			0
$371$	−7.40410			−0.0199571
$372$	104.486	−	104.486i	0.280877	−	0.280877i
$373$	278.764	+	278.764i	0.747355	+	0.747355i	0.973982	−	0.226627i	$-0.0727697\pi$
$373$	278.764	+	278.764i	0.747355	+	0.747355i	−0.226627	+	0.973982i	$0.572770\pi$
$374$		−	144.000i		−	0.385027i
$375$		0			0
$376$	−35.3444			−0.0940010
$377$	−45.6830	+	45.6830i	−0.121175	+	0.121175i
$378$	13.7477	+	13.7477i	0.0363696	+	0.0363696i
$379$		−	168.579i		−	0.444800i	−0.974955	−	0.222400i	$-0.928611\pi$
$379$		−	168.579i		−	0.444800i	0.974955	−	0.222400i	$-0.0713891\pi$
$380$		0			0
$381$	366.313			0.961451
$382$	−367.604	+	367.604i	−0.962315	+	0.962315i
$383$	166.588	+	166.588i	0.434956	+	0.434956i	0.890310	−	0.455354i	$-0.150487\pi$
$383$	166.588	+	166.588i	0.434956	+	0.434956i	−0.455354	+	0.890310i	$0.650487\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	191.424			0.495917
$387$	72.0249	−	72.0249i	0.186111	−	0.186111i
$388$	−177.044	−	177.044i	−0.456299	−	0.456299i
$389$		−	73.9237i		−	0.190035i	−0.995476	−	0.0950176i	$-0.969709\pi$
$389$		−	73.9237i		−	0.190035i	0.995476	−	0.0950176i	$-0.0302907\pi$
$390$		0			0
$391$	120.984			0.309421
$392$	14.0000	−	14.0000i	0.0357143	−	0.0357143i
$393$	−114.498	−	114.498i	−0.291343	−	0.291343i
$394$			388.897i			0.987048i
$395$		0			0
$396$	−74.4392			−0.187978
$397$	−73.4533	+	73.4533i	−0.185021	+	0.185021i	−0.793540	−	0.608519i	$-0.791764\pi$
$397$	−73.4533	+	73.4533i	−0.185021	+	0.185021i	0.608519	+	0.793540i	$0.291764\pi$
$398$	91.9043	+	91.9043i	0.230915	+	0.230915i
$399$			121.811i			0.305290i
$400$		0			0
$401$	−534.615			−1.33321			−0.666603	−	0.745413i	$-0.732252\pi$
$401$	−534.615			−1.33321			−0.666603	+	0.745413i	$0.732252\pi$
$402$	−55.8745	+	55.8745i	−0.138991	+	0.138991i
$403$	−133.646	−	133.646i	−0.331627	−	0.331627i
$404$		−	284.135i		−	0.703304i
$405$		0			0
$406$	−54.5564			−0.134375
$407$	148.017	−	148.017i	0.363679	−	0.363679i
$408$	28.4308	+	28.4308i	0.0696833	+	0.0696833i
$409$		−	14.4205i		−	0.0352578i	−0.999845	−	0.0176289i	$-0.994388\pi$
$409$		−	14.4205i		−	0.0352578i	0.999845	−	0.0176289i	$-0.00561175\pi$
$410$		0			0
$411$	161.679			0.393380
$412$	−120.877	+	120.877i	−0.293391	+	0.293391i
$413$	165.129	+	165.129i	0.399828	+	0.399828i
$414$		−	62.5410i		−	0.151065i
$415$		0			0
$416$	−25.0647			−0.0602517
$417$	136.883	−	136.883i	0.328256	−	0.328256i
$418$	−329.781	−	329.781i	−0.788951	−	0.788951i
$419$			337.860i			0.806349i	0.915123	+	0.403174i	$0.132093\pi$
$419$			337.860i			0.806349i	−0.915123	+	0.403174i	$0.867907\pi$
$420$		0			0
$421$	372.730			0.885345			0.442672	−	0.896683i	$-0.354031\pi$
$421$	372.730			0.885345			0.442672	+	0.896683i	$0.354031\pi$
$422$	−296.539	+	296.539i	−0.702700	+	0.702700i
$423$	−26.5083	−	26.5083i	−0.0626673	−	0.0626673i
$424$			7.91531i			0.0186682i
$425$		0			0
$426$	26.4421			0.0620707
$427$	−191.705	+	191.705i	−0.448958	+	0.448958i
$428$	157.523	+	157.523i	0.368046	+	0.368046i
$429$			95.2134i			0.221943i
$430$		0			0
$431$	−591.932			−1.37339			−0.686696	−	0.726944i	$-0.740940\pi$
$431$	−591.932			−1.37339			−0.686696	+	0.726944i	$0.740940\pi$
$432$	14.6969	−	14.6969i	0.0340207	−	0.0340207i
$433$	239.916	+	239.916i	0.554079	+	0.554079i	0.927615	−	0.373537i	$-0.121855\pi$
$433$	239.916	+	239.916i	0.554079	+	0.554079i	−0.373537	+	0.927615i	$0.621855\pi$
$434$		−	159.605i		−	0.367754i
$435$		0			0
$436$	205.368			0.471026
$437$	277.070	−	277.070i	0.634027	−	0.634027i
$438$	197.057	+	197.057i	0.449901	+	0.449901i
$439$			243.928i			0.555644i	0.960633	+	0.277822i	$0.0896125\pi$
$439$			243.928i			0.555644i	−0.960633	+	0.277822i	$0.910388\pi$
$440$		0			0
$441$	21.0000			0.0476190
$442$	36.3651	−	36.3651i	0.0822741	−	0.0822741i
$443$	−459.426	−	459.426i	−1.03708	−	1.03708i	−0.999286	−	0.0377942i	$-0.987967\pi$
$443$	−459.426	−	459.426i	−1.03708	−	1.03708i	−0.0377942	−	0.999286i	$-0.512033\pi$
$444$			58.4477i			0.131639i
$445$		0			0
$446$	199.403			0.447092
$447$	−263.319	+	263.319i	−0.589080	+	0.589080i
$448$	−14.9666	−	14.9666i	−0.0334077	−	0.0334077i
$449$			136.444i			0.303885i	0.988389	+	0.151943i	$0.0485529\pi$
$449$			136.444i			0.303885i	−0.988389	+	0.151943i	$0.951447\pi$
$450$		0			0
$451$	−465.525			−1.03221
$452$	68.4262	−	68.4262i	0.151385	−	0.151385i
$453$	−76.8561	−	76.8561i	−0.169660	−	0.169660i
$454$			91.5140i			0.201573i
$455$		0			0
$456$	130.221			0.285573
$457$	−269.807	+	269.807i	−0.590388	+	0.590388i	−0.937736	−	0.347348i	$-0.887082\pi$
$457$	−269.807	+	269.807i	−0.590388	+	0.590388i	0.347348	+	0.937736i	$0.387082\pi$
$458$	248.102	+	248.102i	0.541708	+	0.541708i
$459$			42.6461i			0.0929110i
$460$		0			0
$461$	−238.818			−0.518043			−0.259022	−	0.965872i	$-0.583400\pi$
$461$	−238.818			−0.518043			−0.259022	+	0.965872i	$0.583400\pi$
$462$	−56.8539	+	56.8539i	−0.123060	+	0.123060i
$463$	−308.280	−	308.280i	−0.665831	−	0.665831i	0.290917	−	0.956748i	$-0.406040\pi$
$463$	−308.280	−	308.280i	−0.665831	−	0.665831i	−0.956748	+	0.290917i	$0.906040\pi$
$464$			58.3233i			0.125697i
$465$		0			0
$466$	612.961			1.31537
$467$	−228.918	+	228.918i	−0.490188	+	0.490188i	−0.908365	−	0.418177i	$-0.862669\pi$
$467$	−228.918	+	228.918i	−0.490188	+	0.490188i	0.418177	+	0.908365i	$0.362669\pi$
$468$	−18.7985	−	18.7985i	−0.0401678	−	0.0401678i
$469$			85.3497i			0.181982i
$470$		0			0
$471$	−444.135			−0.942963
$472$	176.530	−	176.530i	0.374005	−	0.374005i
$473$	297.860	+	297.860i	0.629724	+	0.629724i
$474$			340.115i			0.717542i
$475$		0			0
$476$	43.4287			0.0912368
$477$	−5.93649	+	5.93649i	−0.0124455	+	0.0124455i
$478$	136.398	+	136.398i	0.285351	+	0.285351i
$479$		−	342.177i		−	0.714357i	−0.934036	−	0.357178i	$-0.883739\pi$
$479$		−	342.177i		−	0.714357i	0.934036	−	0.357178i	$-0.116261\pi$
$480$		0			0
$481$	74.7591			0.155424
$482$	−332.727	+	332.727i	−0.690305	+	0.690305i
$483$	−47.7665	−	47.7665i	−0.0988953	−	0.0988953i
$484$		−	65.8440i		−	0.136041i
$485$		0			0
$486$	22.0454			0.0453609
$487$	456.499	−	456.499i	0.937370	−	0.937370i	−0.0607814	−	0.998151i	$-0.519359\pi$
$487$	456.499	−	456.499i	0.937370	−	0.937370i	0.998151	+	0.0607814i	$0.0193593\pi$
$488$	204.941	+	204.941i	0.419962	+	0.419962i
$489$			127.380i			0.260491i
$490$		0			0
$491$	795.504			1.62017			0.810085	−	0.586312i	$-0.199421\pi$
$491$	795.504			1.62017			0.810085	+	0.586312i	$0.199421\pi$
$492$	91.9112	−	91.9112i	0.186811	−	0.186811i
$493$	−84.6184	−	84.6184i	−0.171640	−	0.171640i
$494$		−	166.563i		−	0.337172i
$495$		0			0
$496$	−170.625			−0.344002
$497$	20.1955	−	20.1955i	0.0406348	−	0.0406348i
$498$	−235.355	−	235.355i	−0.472601	−	0.472601i
$499$			145.240i			0.291062i	0.989354	+	0.145531i	$0.0464890\pi$
$499$			145.240i			0.291062i	−0.989354	+	0.145531i	$0.953511\pi$
$500$		0			0
$501$	375.936			0.750371
$502$	−244.521	+	244.521i	−0.487093	+	0.487093i
$503$	−169.609	−	169.609i	−0.337195	−	0.337195i	0.518115	−	0.855311i	$-0.326634\pi$
$503$	−169.609	−	169.609i	−0.337195	−	0.337195i	−0.855311	+	0.518115i	$0.826634\pi$
$504$		−	22.4499i		−	0.0445435i
$505$		0			0
$506$	258.639			0.511144
$507$	182.937	−	182.937i	0.360823	−	0.360823i
$508$	−299.093	−	299.093i	−0.588766	−	0.588766i
$509$			734.035i			1.44211i	0.692877	+	0.721056i	$0.256343\pi$
$509$			734.035i			1.44211i	−0.692877	+	0.721056i	$0.743657\pi$
$510$		0			0
$511$	301.009			0.589059
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	97.6658	+	97.6658i	0.190382	+	0.190382i
$514$		−	205.184i		−	0.399191i
$515$		0			0
$516$	−117.616			−0.227938
$517$	109.625	−	109.625i	0.212041	−	0.212041i
$518$	44.6402	+	44.6402i	0.0861780	+	0.0861780i
$519$			212.605i			0.409643i
$520$		0			0
$521$	96.5998			0.185412			0.0927061	−	0.995694i	$-0.470448\pi$
$521$	96.5998			0.185412			0.0927061	+	0.995694i	$0.470448\pi$
$522$	−43.7424	+	43.7424i	−0.0837978	+	0.0837978i
$523$	−256.326	−	256.326i	−0.490108	−	0.490108i	0.418232	−	0.908340i	$-0.362650\pi$
$523$	−256.326	−	256.326i	−0.490108	−	0.490108i	−0.908340	+	0.418232i	$0.862650\pi$
$524$			186.974i			0.356821i
$525$		0			0
$526$	507.681			0.965174
$527$	247.552	−	247.552i	0.469738	−	0.469738i
$528$	60.7793	+	60.7793i	0.115112	+	0.115112i
$529$		−	311.702i		−	0.589228i
$530$		0			0
$531$	264.795			0.498673
$532$	99.4580	−	99.4580i	0.186951	−	0.186951i
$533$	−117.562	−	117.562i	−0.220566	−	0.220566i
$534$		−	8.07976i		−	0.0151306i
$535$		0			0
$536$	91.2426			0.170229
$537$	−249.131	+	249.131i	−0.463930	+	0.463930i
$538$	−207.747	−	207.747i	−0.386147	−	0.386147i
$539$			86.8457i			0.161124i
$540$		0			0
$541$	−967.814			−1.78894			−0.894468	−	0.447133i	$-0.852445\pi$
$541$	−967.814			−1.78894			−0.894468	+	0.447133i	$0.852445\pi$
$542$	476.286	−	476.286i	0.878756	−	0.878756i
$543$	−307.766	−	307.766i	−0.566789	−	0.566789i
$544$		−	46.4272i		−	0.0853442i
$545$		0			0
$546$	−28.7152			−0.0525920
$547$	−107.907	+	107.907i	−0.197271	+	0.197271i	−0.798829	−	0.601558i	$-0.794547\pi$
$547$	−107.907	+	107.907i	−0.197271	+	0.197271i	0.601558	+	0.798829i	$0.294547\pi$
$548$	−132.011	−	132.011i	−0.240895	−	0.240895i
$549$			307.412i			0.559949i
$550$		0			0
$551$	−387.577			−0.703406
$552$	−51.0645	+	51.0645i	−0.0925081	+	0.0925081i
$553$	259.767	+	259.767i	0.469741	+	0.469741i
$554$			19.3574i			0.0349412i
$555$		0			0
$556$	−223.528			−0.402029
$557$	−106.902	+	106.902i	−0.191925	+	0.191925i	−0.796527	−	0.604603i	$-0.793332\pi$
$557$	−106.902	+	106.902i	−0.191925	+	0.191925i	0.604603	+	0.796527i	$0.293332\pi$
$558$	−127.969	−	127.969i	−0.229335	−	0.229335i
$559$			150.440i			0.269123i
$560$		0			0
$561$	−176.364			−0.314374
$562$	−101.463	+	101.463i	−0.180540	+	0.180540i
$563$	290.841	+	290.841i	0.516592	+	0.516592i	0.916539	−	0.399946i	$-0.130971\pi$
$563$	290.841	+	290.841i	0.516592	+	0.516592i	−0.399946	+	0.916539i	$0.630971\pi$
$564$			43.2878i			0.0767515i
$565$		0			0
$566$	552.053			0.975358
$567$	16.8375	−	16.8375i	0.0296957	−	0.0296957i
$568$	−21.5899	−	21.5899i	−0.0380104	−	0.0380104i
$569$			53.2185i			0.0935299i	0.998906	+	0.0467649i	$0.0148912\pi$
$569$			53.2185i			0.0935299i	−0.998906	+	0.0467649i	$0.985109\pi$
$570$		0			0
$571$	437.943			0.766976			0.383488	−	0.923546i	$-0.374723\pi$
$571$	437.943			0.766976			0.383488	+	0.923546i	$0.374723\pi$
$572$	77.7415	−	77.7415i	0.135912	−	0.135912i
$573$	450.221	+	450.221i	0.785727	+	0.785727i
$574$		−	140.397i		−	0.244594i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$	219.701	−	219.701i	0.380764	−	0.380764i	−0.490613	−	0.871377i	$-0.663227\pi$
$577$	219.701	−	219.701i	0.380764	−	0.380764i	0.871377	+	0.490613i	$0.163227\pi$
$578$	−221.641	−	221.641i	−0.383462	−	0.383462i
$579$		−	234.446i		−	0.404915i
$580$		0			0
$581$	−359.511			−0.618780
$582$	−216.834	+	216.834i	−0.372566	+	0.372566i
$583$	−24.5504	−	24.5504i	−0.0421105	−	0.0421105i
$584$		−	321.792i		−	0.551014i
$585$		0			0
$586$	209.746			0.357928
$587$	−677.250	+	677.250i	−1.15375	+	1.15375i	−0.167952	+	0.985795i	$0.553715\pi$
$587$	−677.250	+	677.250i	−1.15375	+	1.15375i	−0.985795	+	0.167952i	$0.946285\pi$
$588$	−17.1464	−	17.1464i	−0.0291606	−	0.0291606i
$589$		−	1133.86i		−	1.92506i
$590$		0			0
$591$	476.300			0.805922
$592$	47.7224	−	47.7224i	0.0806121	−	0.0806121i
$593$	558.797	+	558.797i	0.942322	+	0.942322i	0.998425	−	0.0561035i	$-0.0178677\pi$
$593$	558.797	+	558.797i	0.942322	+	0.942322i	−0.0561035	+	0.998425i	$0.517868\pi$
$594$			91.1690i			0.153483i
$595$		0			0
$596$	429.998			0.721473
$597$	112.559	−	112.559i	0.188542	−	0.188542i
$598$	65.3154	+	65.3154i	0.109223	+	0.109223i
$599$		−	538.111i		−	0.898349i	−0.893444	−	0.449175i	$-0.851718\pi$
$599$		−	538.111i		−	0.898349i	0.893444	−	0.449175i	$-0.148282\pi$
$600$		0			0
$601$	573.831			0.954793			0.477397	−	0.878688i	$-0.341580\pi$
$601$	573.831			0.954793			0.477397	+	0.878688i	$0.341580\pi$
$602$	−89.8308	+	89.8308i	−0.149221	+	0.149221i
$603$	68.4320	+	68.4320i	0.113486	+	0.113486i
$604$			125.505i			0.207790i
$605$		0			0
$606$	−347.993			−0.574245
$607$	−409.542	+	409.542i	−0.674699	+	0.674699i	−0.958796	−	0.284097i	$-0.908306\pi$
$607$	−409.542	+	409.542i	−0.674699	+	0.674699i	0.284097	+	0.958796i	$0.408306\pi$
$608$	−106.325	−	106.325i	−0.174877	−	0.174877i
$609$			66.8177i			0.109717i
$610$		0			0
$611$	55.3685			0.0906195
$612$	34.8204	−	34.8204i	0.0568961	−	0.0568961i
$613$	571.915	+	571.915i	0.932977	+	0.932977i	0.997891	−	0.0649138i	$-0.0206773\pi$
$613$	571.915	+	571.915i	0.932977	+	0.932977i	−0.0649138	+	0.997891i	$0.520677\pi$
$614$		−	316.277i		−	0.515108i
$615$		0			0
$616$	92.8420			0.150717
$617$	479.790	−	479.790i	0.777617	−	0.777617i	−0.201808	−	0.979425i	$-0.564682\pi$
$617$	479.790	−	479.790i	0.777617	−	0.777617i	0.979425	+	0.201808i	$0.0646817\pi$
$618$	148.044	+	148.044i	0.239553	+	0.239553i
$619$			308.772i			0.498824i	0.968398	+	0.249412i	$0.0802373\pi$
$619$			308.772i			0.498824i	−0.968398	+	0.249412i	$0.919763\pi$
$620$		0			0
$621$	−76.5967			−0.123344
$622$	519.537	−	519.537i	0.835269	−	0.835269i
$623$	−6.17102	−	6.17102i	−0.00990532	−	0.00990532i
$624$			30.6978i			0.0491953i
$625$		0			0
$626$	146.170			0.233499
$627$	−403.898	+	403.898i	−0.644175	+	0.644175i
$628$	362.635	+	362.635i	0.577444	+	0.577444i
$629$			138.476i			0.220153i
$630$		0			0
$631$	876.945			1.38977			0.694885	−	0.719121i	$-0.255455\pi$
$631$	876.945			1.38977			0.694885	+	0.719121i	$0.255455\pi$
$632$	277.703	−	277.703i	0.439403	−	0.439403i
$633$	363.185	+	363.185i	0.573752	+	0.573752i
$634$		−	559.698i		−	0.882805i
$635$		0			0
$636$	9.69424			0.0152425
$637$	−21.9316	+	21.9316i	−0.0344295	+	0.0344295i
$638$	−180.897	−	180.897i	−0.283538	−	0.283538i
$639$		−	32.3849i		−	0.0506805i
$640$		0			0
$641$	492.966			0.769057			0.384529	−	0.923113i	$-0.374364\pi$
$641$	492.966			0.769057			0.384529	+	0.923113i	$0.374364\pi$
$642$	192.926	−	192.926i	0.300508	−	0.300508i
$643$	30.0997	+	30.0997i	0.0468114	+	0.0468114i	0.730125	−	0.683314i	$-0.239462\pi$
$643$	30.0997	+	30.0997i	0.0468114	+	0.0468114i	−0.683314	+	0.730125i	$0.739462\pi$
$644$			78.0023i			0.121122i
$645$		0			0
$646$	308.524			0.477591
$647$	484.636	−	484.636i	0.749051	−	0.749051i	−0.225250	−	0.974301i	$-0.572320\pi$
$647$	484.636	−	484.636i	0.749051	−	0.749051i	0.974301	+	0.225250i	$0.0723198\pi$
$648$	−18.0000	−	18.0000i	−0.0277778	−	0.0277778i
$649$			1095.06i			1.68731i
$650$		0			0
$651$	−195.476			−0.300270
$652$	104.005	−	104.005i	0.159517	−	0.159517i
$653$	113.485	+	113.485i	0.173791	+	0.173791i	0.788643	−	0.614852i	$-0.210784\pi$
$653$	113.485	+	113.485i	0.173791	+	0.173791i	−0.614852	+	0.788643i	$0.710784\pi$
$654$		−	251.523i		−	0.384592i
$655$		0			0
$656$	−150.090			−0.228796
$657$	241.344	−	241.344i	0.367343	−	0.367343i
$658$	33.0616	+	33.0616i	0.0502456	+	0.0502456i
$659$		−	625.067i		−	0.948509i	−0.880388	−	0.474254i	$-0.842718\pi$
$659$		−	625.067i		−	0.948509i	0.880388	−	0.474254i	$-0.157282\pi$
$660$		0			0
$661$	608.913			0.921200			0.460600	−	0.887608i	$-0.347634\pi$
$661$	608.913			0.921200			0.460600	+	0.887608i	$0.347634\pi$
$662$	601.834	−	601.834i	0.909115	−	0.909115i
$663$	−44.5380	−	44.5380i	−0.0671765	−	0.0671765i
$664$			384.334i			0.578816i
$665$		0			0
$666$	71.5835			0.107483
$667$	151.983	−	151.983i	0.227861	−	0.227861i
$668$	−306.950	−	306.950i	−0.459507	−	0.459507i
$669$		−	244.218i		−	0.365049i
$670$		0			0
$671$	−1271.31			−1.89464
$672$	−18.3303	+	18.3303i	−0.0272772	+	0.0272772i
$673$	884.941	+	884.941i	1.31492	+	1.31492i	0.917741	+	0.397179i	$0.130011\pi$
$673$	884.941	+	884.941i	1.31492	+	1.31492i	0.397179	+	0.917741i	$0.369989\pi$
$674$		−	34.1937i		−	0.0507325i
$675$		0			0
$676$	−298.735			−0.441916
$677$	390.548	−	390.548i	0.576881	−	0.576881i	−0.357162	−	0.934043i	$-0.616255\pi$
$677$	390.548	−	390.548i	0.576881	−	0.576881i	0.934043	+	0.357162i	$0.116255\pi$
$678$	−83.8046	−	83.8046i	−0.123606	−	0.123606i
$679$			331.219i			0.487804i
$680$		0			0
$681$	112.081			0.164583
$682$	529.217	−	529.217i	0.775977	−	0.775977i
$683$	−869.027	−	869.027i	−1.27237	−	1.27237i	−0.944842	−	0.327526i	$-0.893785\pi$
$683$	−869.027	−	869.027i	−1.27237	−	1.27237i	−0.327526	−	0.944842i	$-0.606215\pi$
$684$		−	159.488i		−	0.233169i
$685$		0			0
$686$	−26.1916			−0.0381802
$687$	303.862	−	303.862i	0.442303	−	0.442303i
$688$	96.0331	+	96.0331i	0.139583	+	0.139583i
$689$		−	12.3997i		−	0.0179966i
$690$		0			0
$691$	−148.448			−0.214831			−0.107415	−	0.994214i	$-0.534257\pi$
$691$	−148.448			−0.214831			−0.107415	+	0.994214i	$0.534257\pi$
$692$	173.591	−	173.591i	0.250854	−	0.250854i
$693$	69.6315	+	69.6315i	0.100478	+	0.100478i
$694$		−	467.385i		−	0.673465i
$695$		0			0
$696$	71.4311			0.102631
$697$	217.759	−	217.759i	0.312423	−	0.312423i
$698$	399.184	+	399.184i	0.571896	+	0.571896i
$699$		−	750.721i		−	1.07399i
$700$		0			0
$701$	65.2652			0.0931029			0.0465515	−	0.998916i	$-0.485177\pi$
$701$	65.2652			0.0931029			0.0465515	+	0.998916i	$0.485177\pi$
$702$	−23.0234	+	23.0234i	−0.0327968	+	0.0327968i
$703$	317.130	+	317.130i	0.451110	+	0.451110i
$704$		−	99.2522i		−	0.140983i
$705$		0			0
$706$	−274.011			−0.388117
$707$	−265.784	+	265.784i	−0.375932	+	0.375932i
$708$	−216.205	−	216.205i	−0.305374	−	0.305374i
$709$		−	817.389i		−	1.15288i	−0.817141	−	0.576438i	$-0.804442\pi$
$709$		−	817.389i		−	1.15288i	0.817141	−	0.576438i	$-0.195558\pi$
$710$		0			0
$711$	416.554			0.585870
$712$	−6.59709	+	6.59709i	−0.00926558	+	0.00926558i
$713$	444.628	+	444.628i	0.623601	+	0.623601i
$714$		−	53.1891i		−	0.0744945i
$715$		0			0
$716$	406.828			0.568196
$717$	167.052	−	167.052i	0.232988	−	0.232988i
$718$	473.333	+	473.333i	0.659239	+	0.659239i
$719$			1151.64i			1.60173i	0.598846	+	0.800864i	$0.295626\pi$
$719$			1151.64i			1.60173i	−0.598846	+	0.800864i	$0.704374\pi$
$720$		0			0
$721$	226.141			0.313648
$722$	345.564	−	345.564i	0.478620	−	0.478620i
$723$	407.505	+	407.505i	0.563631	+	0.563631i
$724$			502.580i			0.694172i
$725$		0			0
$726$	−80.6421			−0.111077
$727$	82.3587	−	82.3587i	0.113286	−	0.113286i	−0.648192	−	0.761477i	$-0.724474\pi$
$727$	82.3587	−	82.3587i	0.113286	−	0.113286i	0.761477	+	0.648192i	$0.224474\pi$
$728$	23.4459	+	23.4459i	0.0322059	+	0.0322059i
$729$		−	27.0000i		−	0.0370370i
$730$		0			0
$731$	−278.660			−0.381203
$732$	251.001	−	251.001i	0.342897	−	0.342897i
$733$	482.749	+	482.749i	0.658593	+	0.658593i	0.955047	−	0.296454i	$-0.0958041\pi$
$733$	482.749	+	482.749i	0.658593	+	0.658593i	−0.296454	+	0.955047i	$0.595804\pi$
$734$			513.314i			0.699338i
$735$		0			0
$736$	83.3880			0.113299
$737$	−283.001	+	283.001i	−0.383991	+	0.383991i
$738$	−112.568	−	112.568i	−0.152531	−	0.152531i
$739$			430.657i			0.582757i	0.956608	+	0.291379i	$0.0941139\pi$
$739$			430.657i			0.582757i	−0.956608	+	0.291379i	$0.905886\pi$
$740$		0			0
$741$	−203.997			−0.275300
$742$	7.40410	−	7.40410i	0.00997857	−	0.00997857i
$743$	−902.316	−	902.316i	−1.21442	−	1.21442i	−0.969557	−	0.244866i	$-0.921256\pi$
$743$	−902.316	−	902.316i	−1.21442	−	1.21442i	−0.244866	−	0.969557i	$-0.578744\pi$
$744$			208.972i			0.280877i
$745$		0			0
$746$	−557.527			−0.747355
$747$	−288.250	+	288.250i	−0.385877	+	0.385877i
$748$	144.000	+	144.000i	0.192514	+	0.192514i
$749$		−	294.699i		−	0.393457i
$750$		0			0
$751$	−262.783			−0.349910			−0.174955	−	0.984576i	$-0.555978\pi$
$751$	−262.783			−0.349910			−0.174955	+	0.984576i	$0.555978\pi$
$752$	35.3444	−	35.3444i	0.0470005	−	0.0470005i
$753$	299.475	+	299.475i	0.397710	+	0.397710i
$754$		−	91.3659i		−	0.121175i
$755$		0			0
$756$	−27.4955			−0.0363696
$757$	786.569	−	786.569i	1.03906	−	1.03906i	0.0398555	−	0.999205i	$-0.487310\pi$
$757$	786.569	−	786.569i	1.03906	−	1.03906i	0.999205	−	0.0398555i	$-0.0126897\pi$
$758$	168.579	+	168.579i	0.222400	+	0.222400i
$759$		−	316.767i		−	0.417347i
$760$		0			0
$761$	1469.36			1.93082			0.965412	−	0.260728i	$-0.0839627\pi$
$761$	1469.36			1.93082			0.965412	+	0.260728i	$0.0839627\pi$
$762$	−366.313	+	366.313i	−0.480725	+	0.480725i
$763$	−192.104	−	192.104i	−0.251774	−	0.251774i
$764$		−	735.208i		−	0.962315i
$765$		0			0
$766$	−333.177			−0.434956
$767$	−276.542	+	276.542i	−0.360551	+	0.360551i
$768$	19.5959	+	19.5959i	0.0255155	+	0.0255155i
$769$		−	1018.45i		−	1.32439i	−0.749333	−	0.662193i	$-0.769626\pi$
$769$		−	1018.45i		−	1.32439i	0.749333	−	0.662193i	$-0.230374\pi$
$770$		0			0
$771$	−251.299			−0.325938
$772$	−191.424	+	191.424i	−0.247958	+	0.247958i
$773$	−570.658	−	570.658i	−0.738238	−	0.738238i	0.233999	−	0.972237i	$-0.424819\pi$
$773$	−570.658	−	570.658i	−0.738238	−	0.738238i	−0.972237	+	0.233999i	$0.924819\pi$
$774$			144.050i			0.186111i
$775$		0			0
$776$	354.088			0.456299
$777$	54.6728	−	54.6728i	0.0703640	−	0.0703640i
$778$	73.9237	+	73.9237i	0.0950176	+	0.0950176i
$779$		−	997.398i		−	1.28036i
$780$		0			0
$781$	133.928			0.171483
$782$	−120.984	+	120.984i	−0.154710	+	0.154710i
$783$	53.5733	+	53.5733i	0.0684206	+	0.0684206i
$784$			28.0000i			0.0357143i
$785$		0			0
$786$	228.996			0.291343
$787$	−1053.50	+	1053.50i	−1.33862	+	1.33862i	−0.441227	+	0.897395i	$0.645457\pi$
$787$	−1053.50	+	1053.50i	−1.33862	+	1.33862i	−0.897395	+	0.441227i	$0.854543\pi$
$788$	−388.897	−	388.897i	−0.493524	−	0.493524i
$789$		−	621.780i		−	0.788061i
$790$		0			0
$791$	−128.014			−0.161838
$792$	74.4392	−	74.4392i	0.0939889	−	0.0939889i
$793$	−321.050	−	321.050i	−0.404854	−	0.404854i
$794$		−	146.907i		−	0.185021i
$795$		0			0
$796$	−183.809			−0.230915
$797$	−874.260	+	874.260i	−1.09694	+	1.09694i	−0.102172	+	0.994767i	$0.532579\pi$
$797$	−874.260	+	874.260i	−1.09694	+	1.09694i	−0.994767	+	0.102172i	$0.967421\pi$
$798$	−121.811	−	121.811i	−0.152645	−	0.152645i
$799$			102.559i			0.128359i
$800$		0			0
$801$	−9.89564			−0.0123541
$802$	534.615	−	534.615i	0.666603	−	0.666603i
$803$	998.082	+	998.082i	1.24294	+	1.24294i
$804$		−	111.749i		−	0.138991i
$805$		0			0
$806$	267.292			0.331627
$807$	−254.437	+	254.437i	−0.315288	+	0.315288i
$808$	284.135	+	284.135i	0.351652	+	0.351652i
$809$			938.860i			1.16052i	0.814432	+	0.580260i	$0.197049\pi$
$809$			938.860i			1.16052i	−0.814432	+	0.580260i	$0.802951\pi$
$810$		0			0
$811$	422.265			0.520672			0.260336	−	0.965518i	$-0.416167\pi$
$811$	422.265			0.520672			0.260336	+	0.965518i	$0.416167\pi$
$812$	54.5564	−	54.5564i	0.0671877	−	0.0671877i
$813$	−583.329	−	583.329i	−0.717502	−	0.717502i
$814$			296.034i			0.363679i
$815$		0			0
$816$	−56.8615			−0.0696833
$817$	−638.171	+	638.171i	−0.781115	+	0.781115i
$818$	14.4205	+	14.4205i	0.0176289	+	0.0176289i
$819$			35.1688i			0.0429412i
$820$		0			0
$821$	750.531			0.914167			0.457083	−	0.889424i	$-0.348894\pi$
$821$	750.531			0.914167			0.457083	+	0.889424i	$0.348894\pi$
$822$	−161.679	+	161.679i	−0.196690	+	0.196690i
$823$	755.539	+	755.539i	0.918031	+	0.918031i	0.996886	−	0.0788552i	$-0.0251265\pi$
$823$	755.539	+	755.539i	0.918031	+	0.918031i	−0.0788552	+	0.996886i	$0.525126\pi$
$824$		−	241.754i		−	0.293391i
$825$		0			0
$826$	−330.258			−0.399828
$827$	578.780	−	578.780i	0.699854	−	0.699854i	−0.264525	−	0.964379i	$-0.585215\pi$
$827$	578.780	−	578.780i	0.699854	−	0.699854i	0.964379	+	0.264525i	$0.0852150\pi$
$828$	62.5410	+	62.5410i	0.0755326	+	0.0755326i
$829$			318.623i			0.384346i	0.981361	+	0.192173i	$0.0615534\pi$
$829$			318.623i			0.384346i	−0.981361	+	0.192173i	$0.938447\pi$
$830$		0			0
$831$	23.7079			0.0285293
$832$	25.0647	−	25.0647i	0.0301258	−	0.0301258i
$833$	−40.6238	−	40.6238i	−0.0487681	−	0.0487681i
$834$			273.765i			0.328256i
$835$		0			0
$836$	659.563			0.788951
$837$	−156.729	+	156.729i	−0.187251	+	0.187251i
$838$	−337.860	−	337.860i	−0.403174	−	0.403174i
$839$		−	264.028i		−	0.314694i	−0.987543	−	0.157347i	$-0.949706\pi$
$839$		−	264.028i		−	0.314694i	0.987543	−	0.157347i	$-0.0502940\pi$
$840$		0			0
$841$	628.400			0.747205
$842$	−372.730	+	372.730i	−0.442672	+	0.442672i
$843$	124.267	+	124.267i	0.147410	+	0.147410i
$844$		−	593.079i		−	0.702700i
$845$		0			0
$846$	53.0166			0.0626673
$847$	−61.5914	+	61.5914i	−0.0727171	+	0.0727171i
$848$	−7.91531	−	7.91531i	−0.00933410	−	0.00933410i
$849$		−	676.124i		−	0.796377i
$850$		0			0
$851$	−248.717			−0.292264
$852$	−26.4421	+	26.4421i	−0.0310354	+	0.0310354i
$853$	426.618	+	426.618i	0.500138	+	0.500138i	0.911481	−	0.411343i	$-0.134940\pi$
$853$	426.618	+	426.618i	0.500138	+	0.500138i	−0.411343	+	0.911481i	$0.634940\pi$
$854$		−	383.410i		−	0.448958i
$855$		0			0
$856$	−315.047			−0.368046
$857$	−670.381	+	670.381i	−0.782242	+	0.782242i	−0.980209	−	0.197967i	$-0.936566\pi$
$857$	−670.381	+	670.381i	−0.782242	+	0.782242i	0.197967	+	0.980209i	$0.436566\pi$
$858$	−95.2134	−	95.2134i	−0.110971	−	0.110971i
$859$			383.866i			0.446875i	0.974718	+	0.223437i	$0.0717278\pi$
$859$			383.866i			0.446875i	−0.974718	+	0.223437i	$0.928272\pi$
$860$		0			0
$861$	−171.950			−0.199710
$862$	591.932	−	591.932i	0.686696	−	0.686696i
$863$	−563.290	−	563.290i	−0.652711	−	0.652711i	0.300934	−	0.953645i	$-0.402702\pi$
$863$	−563.290	−	563.290i	−0.652711	−	0.652711i	−0.953645	+	0.300934i	$0.902702\pi$
$864$			29.3939i			0.0340207i
$865$		0			0
$866$	−479.832			−0.554079
$867$	−271.454	+	271.454i	−0.313095	+	0.313095i
$868$	159.605	+	159.605i	0.183877	+	0.183877i
$869$			1722.66i			1.98235i
$870$		0			0
$871$	−142.935			−0.164105
$872$	−205.368	+	205.368i	−0.235513	+	0.235513i
$873$	265.566	+	265.566i	0.304199	+	0.304199i
$874$			554.139i			0.634027i
$875$		0			0
$876$	−394.114			−0.449901
$877$	617.434	−	617.434i	0.704029	−	0.704029i	−0.261244	−	0.965273i	$-0.584133\pi$
$877$	617.434	−	617.434i	0.704029	−	0.704029i	0.965273	+	0.261244i	$0.0841326\pi$
$878$	−243.928	−	243.928i	−0.277822	−	0.277822i
$879$		−	256.885i		−	0.292247i
$880$		0			0
$881$	−456.278			−0.517910			−0.258955	−	0.965889i	$-0.583378\pi$
$881$	−456.278			−0.517910			−0.258955	+	0.965889i	$0.583378\pi$
$882$	−21.0000	+	21.0000i	−0.0238095	+	0.0238095i
$883$	161.141	+	161.141i	0.182493	+	0.182493i	0.792441	−	0.609948i	$-0.208810\pi$
$883$	161.141	+	161.141i	0.182493	+	0.182493i	−0.609948	+	0.792441i	$0.708810\pi$
$884$			72.7303i			0.0822741i
$885$		0			0
$886$	918.853			1.03708
$887$	−701.018	+	701.018i	−0.790324	+	0.790324i	−0.981547	−	0.191222i	$-0.938755\pi$
$887$	−701.018	+	701.018i	−0.790324	+	0.790324i	0.191222	+	0.981547i	$0.438755\pi$
$888$	−58.4477	−	58.4477i	−0.0658195	−	0.0658195i
$889$			559.552i			0.629417i
$890$		0			0
$891$	111.659			0.125318
$892$	−199.403	+	199.403i	−0.223546	+	0.223546i
$893$	234.875	+	234.875i	0.263017	+	0.263017i
$894$		−	526.638i		−	0.589080i
$895$		0			0
$896$	29.9333			0.0334077
$897$	79.9947	−	79.9947i	0.0891803	−	0.0891803i
$898$	−136.444	−	136.444i	−0.151943	−	0.151943i
$899$		−	621.964i		−	0.691839i
$900$		0			0
$901$	22.9679			0.0254916
$902$	465.525	−	465.525i	0.516103	−	0.516103i
$903$	110.020	+	110.020i	0.121838	+	0.121838i
$904$			136.852i			0.151385i
$905$		0			0
$906$	153.712			0.169660
$907$	126.915	−	126.915i	0.139928	−	0.139928i	−0.633673	−	0.773601i	$-0.718454\pi$
$907$	126.915	−	126.915i	0.139928	−	0.139928i	0.773601	+	0.633673i	$0.218454\pi$
$908$	−91.5140	−	91.5140i	−0.100786	−	0.100786i
$909$			426.202i			0.468869i
$910$		0			0
$911$	−508.167			−0.557813			−0.278906	−	0.960318i	$-0.589972\pi$
$911$	−508.167			−0.557813			−0.278906	+	0.960318i	$0.589972\pi$
$912$	−130.221	+	130.221i	−0.142786	+	0.142786i
$913$	−1192.06	−	1192.06i	−1.30565	−	1.30565i
$914$		−	539.614i		−	0.590388i
$915$		0			0
$916$	−496.205			−0.541708
$917$	174.898	−	174.898i	0.190729	−	0.190729i
$918$	−42.6461	−	42.6461i	−0.0464555	−	0.0464555i
$919$			671.030i			0.730174i	0.930973	+	0.365087i	$0.118961\pi$
$919$			671.030i			0.730174i	−0.930973	+	0.365087i	$0.881039\pi$
$920$		0			0
$921$	−387.358			−0.420584
$922$	238.818	−	238.818i	0.259022	−	0.259022i
$923$	33.8215	+	33.8215i	0.0366430	+	0.0366430i
$924$		−	113.708i		−	0.123060i
$925$		0			0
$926$	616.560			0.665831
$927$	181.316	−	181.316i	0.195594	−	0.195594i
$928$	−58.3233	−	58.3233i	−0.0628483	−	0.0628483i
$929$		−	198.819i		−	0.214014i	−0.994258	−	0.107007i	$-0.965873\pi$
$929$		−	198.819i		−	0.214014i	0.994258	−	0.107007i	$-0.0341267\pi$
$930$		0			0
$931$	−186.069			−0.199859
$932$	−612.961	+	612.961i	−0.657684	+	0.657684i
$933$	−636.300	−	636.300i	−0.681994	−	0.681994i
$934$		−	457.836i		−	0.490188i
$935$		0			0
$936$	37.5970			0.0401678
$937$	−691.159	+	691.159i	−0.737630	+	0.737630i	−0.972119	−	0.234489i	$-0.924658\pi$
$937$	−691.159	+	691.159i	−0.737630	+	0.737630i	0.234489	+	0.972119i	$0.424658\pi$
$938$	−85.3497	−	85.3497i	−0.0909911	−	0.0909911i
$939$		−	179.021i		−	0.190651i
$940$		0			0
$941$	1460.09			1.55164			0.775819	−	0.630956i	$-0.217337\pi$
$941$	1460.09			1.55164			0.775819	+	0.630956i	$0.217337\pi$
$942$	444.135	−	444.135i	0.471481	−	0.471481i
$943$	391.117	+	391.117i	0.414758	+	0.414758i
$944$			353.061i			0.374005i
$945$		0			0
$946$	−595.719			−0.629724
$947$	332.380	−	332.380i	0.350982	−	0.350982i	−0.509493	−	0.860475i	$-0.670167\pi$
$947$	332.380	−	332.380i	0.350982	−	0.350982i	0.860475	+	0.509493i	$0.170167\pi$
$948$	−340.115	−	340.115i	−0.358771	−	0.358771i
$949$			504.102i			0.531192i
$950$		0			0
$951$	−685.488			−0.720807
$952$	−43.4287	+	43.4287i	−0.0456184	+	0.0456184i
$953$	473.427	+	473.427i	0.496776	+	0.496776i	0.910433	−	0.413657i	$-0.135749\pi$
$953$	473.427	+	473.427i	0.496776	+	0.496776i	−0.413657	+	0.910433i	$0.635749\pi$
$954$		−	11.8730i		−	0.0124455i
$955$		0			0
$956$	−272.796			−0.285351
$957$	−221.553	+	221.553i	−0.231508	+	0.231508i
$958$	342.177	+	342.177i	0.357178	+	0.357178i
$959$			246.969i			0.257528i
$960$		0			0
$961$	858.560			0.893402
$962$	−74.7591	+	74.7591i	−0.0777122	+	0.0777122i
$963$	−236.285	−	236.285i	−0.245364	−	0.245364i
$964$		−	665.454i		−	0.690305i
$965$		0			0
$966$	95.5329			0.0988953
$967$	696.942	−	696.942i	0.720726	−	0.720726i	−0.248027	−	0.968753i	$-0.579782\pi$
$967$	696.942	−	696.942i	0.720726	−	0.720726i	0.968753	+	0.248027i	$0.0797823\pi$
$968$	65.8440	+	65.8440i	0.0680207	+	0.0680207i
$969$		−	377.863i		−	0.389951i
$970$		0			0
$971$	−262.031			−0.269857			−0.134929	−	0.990855i	$-0.543081\pi$
$971$	−262.031			−0.269857			−0.134929	+	0.990855i	$0.543081\pi$
$972$	−22.0454	+	22.0454i	−0.0226805	+	0.0226805i
$973$	209.092	+	209.092i	0.214894	+	0.214894i
$974$			912.998i			0.937370i
$975$		0			0
$976$	−409.883			−0.419962
$977$	−363.414	+	363.414i	−0.371969	+	0.371969i	−0.868194	−	0.496225i	$-0.834719\pi$
$977$	−363.414	+	363.414i	−0.371969	+	0.371969i	0.496225	+	0.868194i	$0.334719\pi$
$978$	−127.380	−	127.380i	−0.130245	−	0.130245i
$979$		−	40.9235i		−	0.0418014i
$980$		0			0
$981$	−308.051			−0.314018
$982$	−795.504	+	795.504i	−0.810085	+	0.810085i
$983$	−589.265	−	589.265i	−0.599456	−	0.599456i	0.340712	−	0.940168i	$-0.389332\pi$
$983$	−589.265	−	589.265i	−0.599456	−	0.599456i	−0.940168	+	0.340712i	$0.889332\pi$
$984$			183.822i			0.186811i
$985$		0			0
$986$	169.237			0.171640
$987$	40.4921	−	40.4921i	0.0410254	−	0.0410254i
$988$	166.563	+	166.563i	0.168586	+	0.168586i
$989$		−	500.500i		−	0.506067i
$990$		0			0
$991$	1470.51			1.48386			0.741931	−	0.670476i	$-0.233910\pi$
$991$	1470.51			1.48386			0.741931	+	0.670476i	$0.233910\pi$
$992$	170.625	−	170.625i	0.172001	−	0.172001i
$993$	−737.093	−	737.093i	−0.742289	−	0.742289i
$994$			40.3910i			0.0406348i
$995$		0			0
$996$	470.711			0.472601
$997$	−639.149	+	639.149i	−0.641073	+	0.641073i	−0.950819	−	0.309747i	$-0.899756\pi$
$997$	−639.149	+	639.149i	−0.641073	+	0.641073i	0.309747	+	0.950819i	$0.399756\pi$
$998$	−145.240	−	145.240i	−0.145531	−	0.145531i
$999$		−	87.6716i		−	0.0877593i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.l.b.43.3		8
5.2	odd	4	inner	1050.3.l.b.757.3		8
5.3	odd	4		210.3.l.a.127.2	yes	8
5.4	even	2		210.3.l.a.43.2	✓	8
15.8	even	4		630.3.o.b.127.3		8
15.14	odd	2		630.3.o.b.253.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.a.43.2	✓	8	5.4	even	2
210.3.l.a.127.2	yes	8	5.3	odd	4
630.3.o.b.127.3		8	15.8	even	4
630.3.o.b.253.3		8	15.14	odd	2
1050.3.l.b.43.3		8	1.1	even	1	trivial
1050.3.l.b.757.3		8	5.2	odd	4	inner

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} -2.44949 q^{6} +(-1.87083 + 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} -2.44949 q^{6} +(-1.87083 + 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} -12.4065 q^{11} +(2.44949 - 2.44949i) q^{12} +(-3.13309 - 3.13309i) q^{13} -3.74166i q^{14} -4.00000 q^{16} +(5.80341 - 5.80341i) q^{17} +(-3.00000 - 3.00000i) q^{18} -26.5813i q^{19} -4.58258 q^{21} +(12.4065 - 12.4065i) q^{22} +(10.4235 + 10.4235i) q^{23} +4.89898i q^{24} +6.26617 q^{26} +(-3.67423 + 3.67423i) q^{27} +(3.74166 + 3.74166i) q^{28} -14.5808i q^{29} +42.6563 q^{31} +(4.00000 - 4.00000i) q^{32} +(-15.1948 - 15.1948i) q^{33} +11.6068i q^{34} +6.00000 q^{36} +(-11.9306 + 11.9306i) q^{37} +(26.5813 + 26.5813i) q^{38} -7.67446i q^{39} +37.5226 q^{41} +(4.58258 - 4.58258i) q^{42} +(-24.0083 - 24.0083i) q^{43} +24.8131i q^{44} -20.8470 q^{46} +(-8.83609 + 8.83609i) q^{47} +(-4.89898 - 4.89898i) q^{48} -7.00000i q^{49} +14.2154 q^{51} +(-6.26617 + 6.26617i) q^{52} +(1.97883 + 1.97883i) q^{53} -7.34847i q^{54} -7.48331 q^{56} +(32.5553 - 32.5553i) q^{57} +(14.5808 + 14.5808i) q^{58} -88.2651i q^{59} +102.471 q^{61} +(-42.6563 + 42.6563i) q^{62} +(-5.61249 - 5.61249i) q^{63} +8.00000i q^{64} +30.3897 q^{66} +(22.8107 - 22.8107i) q^{67} +(-11.6068 - 11.6068i) q^{68} +25.5322i q^{69} -10.7950 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-80.4481 - 80.4481i) q^{73} -23.8612i q^{74} -53.1625 q^{76} +(23.2105 - 23.2105i) q^{77} +(7.67446 + 7.67446i) q^{78} -138.851i q^{79} -9.00000 q^{81} +(-37.5226 + 37.5226i) q^{82} +(96.0834 + 96.0834i) q^{83} +9.16515i q^{84} +48.0166 q^{86} +(17.8578 - 17.8578i) q^{87} +(-24.8131 - 24.8131i) q^{88} +3.29855i q^{89} +11.7229 q^{91} +(20.8470 - 20.8470i) q^{92} +(52.2431 + 52.2431i) q^{93} -17.6722i q^{94} +9.79796 q^{96} +(88.5219 - 88.5219i) q^{97} +(7.00000 + 7.00000i) q^{98} -37.2196i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 16 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 16 * q^8	\( 8 q - 8 q^{2} + 16 q^{8} - 8 q^{11} - 8 q^{13} - 32 q^{16} + 32 q^{17} - 24 q^{18} + 8 q^{22} + 40 q^{23} + 16 q^{26} + 144 q^{31} + 32 q^{32} - 120 q^{33} + 48 q^{36} - 160 q^{37} - 320 q^{41} + 32 q^{43} - 80 q^{46} + 144 q^{47} + 72 q^{51} - 16 q^{52} + 200 q^{53} + 24 q^{57} + 64 q^{58} + 288 q^{61} - 144 q^{62} + 240 q^{66} - 80 q^{67} - 64 q^{68} - 280 q^{71} - 48 q^{72} - 312 q^{73} + 56 q^{77} - 48 q^{78} - 72 q^{81} + 320 q^{82} + 320 q^{83} - 64 q^{86} + 48 q^{87} - 16 q^{88} + 80 q^{92} - 48 q^{93} + 24 q^{97} + 56 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 16 * q^8 - 8 * q^11 - 8 * q^13 - 32 * q^16 + 32 * q^17 - 24 * q^18 + 8 * q^22 + 40 * q^23 + 16 * q^26 + 144 * q^31 + 32 * q^32 - 120 * q^33 + 48 * q^36 - 160 * q^37 - 320 * q^41 + 32 * q^43 - 80 * q^46 + 144 * q^47 + 72 * q^51 - 16 * q^52 + 200 * q^53 + 24 * q^57 + 64 * q^58 + 288 * q^61 - 144 * q^62 + 240 * q^66 - 80 * q^67 - 64 * q^68 - 280 * q^71 - 48 * q^72 - 312 * q^73 + 56 * q^77 - 48 * q^78 - 72 * q^81 + 320 * q^82 + 320 * q^83 - 64 * q^86 + 48 * q^87 - 16 * q^88 + 80 * q^92 - 48 * q^93 + 24 * q^97 + 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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