LMFDB - Embedded newform 63.4.e.b.46.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(37,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("63.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.e (of order $3$, 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:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	63.46
Dual form			63.4.e.b.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(2.00000 - 3.46410i) q^{4} +(3.50000 + 6.06218i) q^{5} +(14.0000 + 12.1244i) q^{7} +24.0000 q^{8} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(2.00000 - 3.46410i) q^{4} +(3.50000 + 6.06218i) q^{5} +(14.0000 + 12.1244i) q^{7} +24.0000 q^{8} +(-7.00000 + 12.1244i) q^{10} +(-2.50000 + 4.33013i) q^{11} -14.0000 q^{13} +(-7.00000 + 36.3731i) q^{14} +(8.00000 + 13.8564i) q^{16} +(-10.5000 + 18.1865i) q^{17} +(-24.5000 - 42.4352i) q^{19} +28.0000 q^{20} -10.0000 q^{22} +(-79.5000 - 137.698i) q^{23} +(38.0000 - 65.8179i) q^{25} +(-14.0000 - 24.2487i) q^{26} +(70.0000 - 24.2487i) q^{28} -58.0000 q^{29} +(-73.5000 + 127.306i) q^{31} +(80.0000 - 138.564i) q^{32} -42.0000 q^{34} +(-24.5000 + 127.306i) q^{35} +(-109.500 - 189.660i) q^{37} +(49.0000 - 84.8705i) q^{38} +(84.0000 + 145.492i) q^{40} -350.000 q^{41} -124.000 q^{43} +(10.0000 + 17.3205i) q^{44} +(159.000 - 275.396i) q^{46} +(262.500 + 454.663i) q^{47} +(49.0000 + 339.482i) q^{49} +152.000 q^{50} +(-28.0000 + 48.4974i) q^{52} +(151.500 - 262.406i) q^{53} -35.0000 q^{55} +(336.000 + 290.985i) q^{56} +(-58.0000 - 100.459i) q^{58} +(-52.5000 + 90.9327i) q^{59} +(206.500 + 357.668i) q^{61} -294.000 q^{62} +448.000 q^{64} +(-49.0000 - 84.8705i) q^{65} +(-207.500 + 359.401i) q^{67} +(42.0000 + 72.7461i) q^{68} +(-245.000 + 84.8705i) q^{70} +432.000 q^{71} +(556.500 - 963.886i) q^{73} +(219.000 - 379.319i) q^{74} -196.000 q^{76} +(-87.5000 + 30.3109i) q^{77} +(51.5000 + 89.2006i) q^{79} +(-56.0000 + 96.9948i) q^{80} +(-350.000 - 606.218i) q^{82} -1092.00 q^{83} -147.000 q^{85} +(-124.000 - 214.774i) q^{86} +(-60.0000 + 103.923i) q^{88} +(-164.500 - 284.922i) q^{89} +(-196.000 - 169.741i) q^{91} -636.000 q^{92} +(-525.000 + 909.327i) q^{94} +(171.500 - 297.047i) q^{95} -882.000 q^{97} +(-539.000 + 424.352i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 4 q^{4} + 7 q^{5} + 28 q^{7} + 48 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 + 4 * q^4 + 7 * q^5 + 28 * q^7 + 48 * q^8	$ 2 q + 2 q^{2} + 4 q^{4} + 7 q^{5} + 28 q^{7} + 48 q^{8} - 14 q^{10} - 5 q^{11} - 28 q^{13} - 14 q^{14} + 16 q^{16} - 21 q^{17} - 49 q^{19} + 56 q^{20} - 20 q^{22} - 159 q^{23} + 76 q^{25} - 28 q^{26} + 140 q^{28} - 116 q^{29} - 147 q^{31} + 160 q^{32} - 84 q^{34} - 49 q^{35} - 219 q^{37} + 98 q^{38} + 168 q^{40} - 700 q^{41} - 248 q^{43} + 20 q^{44} + 318 q^{46} + 525 q^{47} + 98 q^{49} + 304 q^{50} - 56 q^{52} + 303 q^{53} - 70 q^{55} + 672 q^{56} - 116 q^{58} - 105 q^{59} + 413 q^{61} - 588 q^{62} + 896 q^{64} - 98 q^{65} - 415 q^{67} + 84 q^{68} - 490 q^{70} + 864 q^{71} + 1113 q^{73} + 438 q^{74} - 392 q^{76} - 175 q^{77} + 103 q^{79} - 112 q^{80} - 700 q^{82} - 2184 q^{83} - 294 q^{85} - 248 q^{86} - 120 q^{88} - 329 q^{89} - 392 q^{91} - 1272 q^{92} - 1050 q^{94} + 343 q^{95} - 1764 q^{97} - 1078 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + 4 * q^4 + 7 * q^5 + 28 * q^7 + 48 * q^8 - 14 * q^10 - 5 * q^11 - 28 * q^13 - 14 * q^14 + 16 * q^16 - 21 * q^17 - 49 * q^19 + 56 * q^20 - 20 * q^22 - 159 * q^23 + 76 * q^25 - 28 * q^26 + 140 * q^28 - 116 * q^29 - 147 * q^31 + 160 * q^32 - 84 * q^34 - 49 * q^35 - 219 * q^37 + 98 * q^38 + 168 * q^40 - 700 * q^41 - 248 * q^43 + 20 * q^44 + 318 * q^46 + 525 * q^47 + 98 * q^49 + 304 * q^50 - 56 * q^52 + 303 * q^53 - 70 * q^55 + 672 * q^56 - 116 * q^58 - 105 * q^59 + 413 * q^61 - 588 * q^62 + 896 * q^64 - 98 * q^65 - 415 * q^67 + 84 * q^68 - 490 * q^70 + 864 * q^71 + 1113 * q^73 + 438 * q^74 - 392 * q^76 - 175 * q^77 + 103 * q^79 - 112 * q^80 - 700 * q^82 - 2184 * q^83 - 294 * q^85 - 248 * q^86 - 120 * q^88 - 329 * q^89 - 392 * q^91 - 1272 * q^92 - 1050 * q^94 + 343 * q^95 - 1764 * q^97 - 1078 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.00000	+	1.73205i	0.353553	+	0.612372i	0.986869	−	0.161521i	$-0.0516399\pi$
$2$	1.00000	+	1.73205i	0.353553	+	0.612372i	−0.633316	+	0.773893i	$0.718307\pi$
$3$		0			0
$3$		0			0
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$	3.50000	+	6.06218i	0.313050	+	0.542218i	0.979021	−	0.203760i	$-0.0653161\pi$
$5$	3.50000	+	6.06218i	0.313050	+	0.542218i	−0.665971	+	0.745977i	$0.731983\pi$
$6$		0			0
$7$	14.0000	+	12.1244i	0.755929	+	0.654654i
$7$	14.0000	+	12.1244i	0.755929	+	0.654654i
$8$	24.0000			1.06066
$9$		0			0
$10$	−7.00000	+	12.1244i	−0.221359	+	0.383406i
$11$	−2.50000	+	4.33013i	−0.0685253	+	0.118689i	−0.898252	−	0.439480i	$-0.855163\pi$
$11$	−2.50000	+	4.33013i	−0.0685253	+	0.118689i	0.829727	+	0.558169i	$0.188496\pi$
$12$		0			0
$13$	−14.0000			−0.298685			−0.149342	−	0.988786i	$-0.547716\pi$
$13$	−14.0000			−0.298685			−0.149342	+	0.988786i	$0.547716\pi$
$14$	−7.00000	+	36.3731i	−0.133631	+	0.694365i
$15$		0			0
$16$	8.00000	+	13.8564i	0.125000	+	0.216506i
$17$	−10.5000	+	18.1865i	−0.149801	+	0.259464i	−0.931154	−	0.364626i	$-0.881197\pi$
$17$	−10.5000	+	18.1865i	−0.149801	+	0.259464i	0.781353	+	0.624090i	$0.214530\pi$
$18$		0			0
$19$	−24.5000	−	42.4352i	−0.295826	−	0.512385i	0.679351	−	0.733813i	$-0.262261\pi$
$19$	−24.5000	−	42.4352i	−0.295826	−	0.512385i	−0.975177	+	0.221429i	$0.928928\pi$
$20$	28.0000			0.313050
$21$		0			0
$22$	−10.0000			−0.0969094
$23$	−79.5000	−	137.698i	−0.720735	−	1.24835i	−0.960706	−	0.277569i	$-0.910471\pi$
$23$	−79.5000	−	137.698i	−0.720735	−	1.24835i	0.239971	−	0.970780i	$-0.422862\pi$
$24$		0			0
$25$	38.0000	−	65.8179i	0.304000	−	0.526543i
$26$	−14.0000	−	24.2487i	−0.105601	−	0.182906i
$27$		0			0
$28$	70.0000	−	24.2487i	0.472456	−	0.163663i
$29$	−58.0000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−58.0000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$	−73.5000	+	127.306i	−0.425838	+	0.737574i	−0.996498	−	0.0836128i	$-0.973354\pi$
$31$	−73.5000	+	127.306i	−0.425838	+	0.737574i	0.570660	+	0.821186i	$0.306687\pi$
$32$	80.0000	−	138.564i	0.441942	−	0.765466i
$33$		0			0
$34$	−42.0000			−0.211851
$35$	−24.5000	+	127.306i	−0.118322	+	0.614817i
$36$		0			0
$37$	−109.500	−	189.660i	−0.486532	−	0.842698i	0.513348	−	0.858181i	$-0.328405\pi$
$37$	−109.500	−	189.660i	−0.486532	−	0.842698i	−0.999880	+	0.0154821i	$0.995072\pi$
$38$	49.0000	−	84.8705i	0.209180	−	0.362311i
$39$		0			0
$40$	84.0000	+	145.492i	0.332039	+	0.575109i
$41$	−350.000			−1.33319			−0.666595	−	0.745420i	$-0.732249\pi$
$41$	−350.000			−1.33319			−0.666595	+	0.745420i	$0.732249\pi$
$42$		0			0
$43$	−124.000			−0.439763			−0.219882	−	0.975527i	$-0.570567\pi$
$43$	−124.000			−0.439763			−0.219882	+	0.975527i	$0.570567\pi$
$44$	10.0000	+	17.3205i	0.0342627	+	0.0593447i
$45$		0			0
$46$	159.000	−	275.396i	0.509636	−	0.882716i
$47$	262.500	+	454.663i	0.814671	+	1.41105i	0.909564	+	0.415565i	$0.136416\pi$
$47$	262.500	+	454.663i	0.814671	+	1.41105i	−0.0948921	+	0.995488i	$0.530251\pi$
$48$		0			0
$49$	49.0000	+	339.482i	0.142857	+	0.989743i
$50$	152.000			0.429921
$51$		0			0
$52$	−28.0000	+	48.4974i	−0.0746712	+	0.129334i
$53$	151.500	−	262.406i	0.392644	−	0.680079i	−0.600153	−	0.799885i	$-0.704894\pi$
$53$	151.500	−	262.406i	0.392644	−	0.680079i	0.992797	+	0.119806i	$0.0382272\pi$
$54$		0			0
$55$	−35.0000			−0.0858073
$56$	336.000	+	290.985i	0.801784	+	0.694365i
$57$		0			0
$58$	−58.0000	−	100.459i	−0.131306	−	0.227429i
$59$	−52.5000	+	90.9327i	−0.115846	+	0.200651i	−0.918118	−	0.396308i	$-0.870291\pi$
$59$	−52.5000	+	90.9327i	−0.115846	+	0.200651i	0.802272	+	0.596959i	$0.203625\pi$
$60$		0			0
$61$	206.500	+	357.668i	0.433436	+	0.750734i	0.997167	−	0.0752252i	$-0.0239676\pi$
$61$	206.500	+	357.668i	0.433436	+	0.750734i	−0.563730	+	0.825959i	$0.690634\pi$
$62$	−294.000			−0.602226
$63$		0			0
$64$	448.000			0.875000
$65$	−49.0000	−	84.8705i	−0.0935031	−	0.161952i
$66$		0			0
$67$	−207.500	+	359.401i	−0.378361	+	0.655340i	−0.990824	−	0.135159i	$-0.956845\pi$
$67$	−207.500	+	359.401i	−0.378361	+	0.655340i	0.612463	+	0.790499i	$0.290179\pi$
$68$	42.0000	+	72.7461i	0.0749007	+	0.129732i
$69$		0			0
$70$	−245.000	+	84.8705i	−0.418330	+	0.144914i
$71$	432.000			0.722098			0.361049	−	0.932547i	$-0.382419\pi$
$71$	432.000			0.722098			0.361049	+	0.932547i	$0.382419\pi$
$72$		0			0
$73$	556.500	−	963.886i	0.892238	−	1.54540i	0.0550526	−	0.998483i	$-0.482467\pi$
$73$	556.500	−	963.886i	0.892238	−	1.54540i	0.837186	−	0.546919i	$-0.184199\pi$
$74$	219.000	−	379.319i	0.344030	−	0.595878i
$75$		0			0
$76$	−196.000			−0.295826
$77$	−87.5000	+	30.3109i	−0.129501	+	0.0448603i
$78$		0			0
$79$	51.5000	+	89.2006i	0.0733443	+	0.127036i	0.900365	−	0.435135i	$-0.143299\pi$
$79$	51.5000	+	89.2006i	0.0733443	+	0.127036i	−0.827021	+	0.562171i	$0.809966\pi$
$80$	−56.0000	+	96.9948i	−0.0782624	+	0.135554i
$81$		0			0
$82$	−350.000	−	606.218i	−0.471354	−	0.816409i
$83$	−1092.00			−1.44413			−0.722064	−	0.691827i	$-0.756806\pi$
$83$	−1092.00			−1.44413			−0.722064	+	0.691827i	$0.756806\pi$
$84$		0			0
$85$	−147.000			−0.187581
$86$	−124.000	−	214.774i	−0.155480	−	0.269299i
$87$		0			0
$88$	−60.0000	+	103.923i	−0.0726821	+	0.125889i
$89$	−164.500	−	284.922i	−0.195921	−	0.339345i	0.751281	−	0.659982i	$-0.229436\pi$
$89$	−164.500	−	284.922i	−0.195921	−	0.339345i	−0.947202	+	0.320637i	$0.896103\pi$
$90$		0			0
$91$	−196.000	−	169.741i	−0.225784	−	0.195535i
$92$	−636.000			−0.720735
$93$		0			0
$94$	−525.000	+	909.327i	−0.576060	+	0.997765i
$95$	171.500	−	297.047i	0.185216	−	0.320804i
$96$		0			0
$97$	−882.000			−0.923232			−0.461616	−	0.887080i	$-0.652730\pi$
$97$	−882.000			−0.923232			−0.461616	+	0.887080i	$0.652730\pi$
$98$	−539.000	+	424.352i	−0.555584	+	0.437409i
$99$		0			0
$100$	−152.000	−	263.272i	−0.152000	−	0.263272i
$101$	689.500	−	1194.25i	0.679285	−	1.17656i	−0.295911	−	0.955215i	$-0.595623\pi$
$101$	689.500	−	1194.25i	0.679285	−	1.17656i	0.975196	−	0.221341i	$-0.0710434\pi$
$102$		0			0
$103$	339.500	+	588.031i	0.324776	+	0.562529i	0.981467	−	0.191631i	$-0.0613777\pi$
$103$	339.500	+	588.031i	0.324776	+	0.562529i	−0.656691	+	0.754160i	$0.728044\pi$
$104$	−336.000			−0.316803
$105$		0			0
$106$	606.000			0.555282
$107$	228.500	+	395.774i	0.206448	+	0.357578i	0.950593	−	0.310440i	$-0.100476\pi$
$107$	228.500	+	395.774i	0.206448	+	0.357578i	−0.744145	+	0.668018i	$0.767143\pi$
$108$		0			0
$109$	562.500	−	974.279i	0.494291	−	0.856137i	−0.505687	−	0.862717i	$-0.668761\pi$
$109$	562.500	−	974.279i	0.494291	−	0.856137i	0.999978	+	0.00657959i	$0.00209436\pi$
$110$	−35.0000	−	60.6218i	−0.0303374	−	0.0525460i
$111$		0			0
$112$	−56.0000	+	290.985i	−0.0472456	+	0.245495i
$113$	1538.00			1.28038			0.640190	−	0.768217i	$-0.278856\pi$
$113$	1538.00			1.28038			0.640190	+	0.768217i	$0.278856\pi$
$114$		0			0
$115$	556.500	−	963.886i	0.451251	−	0.781590i
$116$	−116.000	+	200.918i	−0.0928477	+	0.160817i
$117$		0			0
$118$	−210.000			−0.163831
$119$	−367.500	+	127.306i	−0.283098	+	0.0980680i
$120$		0			0
$121$	653.000	+	1131.03i	0.490609	+	0.849759i
$122$	−413.000	+	715.337i	−0.306486	+	0.530849i
$123$		0			0
$124$	294.000	+	509.223i	0.212919	+	0.368787i
$125$	1407.00			1.00677
$126$		0			0
$127$	72.0000			0.0503068			0.0251534	−	0.999684i	$-0.491993\pi$
$127$	72.0000			0.0503068			0.0251534	+	0.999684i	$0.491993\pi$
$128$	−192.000	−	332.554i	−0.132583	−	0.229640i
$129$		0			0
$130$	98.0000	−	169.741i	0.0661167	−	0.114517i
$131$	1074.50	+	1861.09i	0.716637	+	1.24125i	0.962325	+	0.271903i	$0.0876531\pi$
$131$	1074.50	+	1861.09i	0.716637	+	1.24125i	−0.245687	+	0.969349i	$0.579014\pi$
$132$		0			0
$133$	171.500	−	891.140i	0.111812	−	0.580990i
$134$	−830.000			−0.535083
$135$		0			0
$136$	−252.000	+	436.477i	−0.158888	+	0.275203i
$137$	−562.500	+	974.279i	−0.350786	+	0.607578i	−0.986387	−	0.164439i	$-0.947419\pi$
$137$	−562.500	+	974.279i	−0.350786	+	0.607578i	0.635602	+	0.772017i	$0.280752\pi$
$138$		0			0
$139$	252.000			0.153772			0.0768862	−	0.997040i	$-0.475502\pi$
$139$	252.000			0.153772			0.0768862	+	0.997040i	$0.475502\pi$
$140$	392.000	+	339.482i	0.236643	+	0.204939i
$141$		0			0
$142$	432.000	+	748.246i	0.255300	+	0.442193i
$143$	35.0000	−	60.6218i	0.0204675	−	0.0354507i
$144$		0			0
$145$	−203.000	−	351.606i	−0.116264	−	0.201375i
$146$	2226.00			1.26182
$147$		0			0
$148$	−876.000			−0.486532
$149$	−100.500	−	174.071i	−0.0552569	−	0.0957078i	0.837074	−	0.547090i	$-0.184264\pi$
$149$	−100.500	−	174.071i	−0.0552569	−	0.0957078i	−0.892331	+	0.451382i	$0.850931\pi$
$150$		0			0
$151$	−809.500	+	1402.10i	−0.436266	+	0.755635i	−0.997398	−	0.0720914i	$-0.977033\pi$
$151$	−809.500	+	1402.10i	−0.436266	+	0.755635i	0.561132	+	0.827726i	$0.310366\pi$
$152$	−588.000	−	1018.45i	−0.313770	−	0.543466i
$153$		0			0
$154$	−140.000	−	121.244i	−0.0732566	−	0.0634421i
$155$	−1029.00			−0.533234
$156$		0			0
$157$	−339.500	+	588.031i	−0.172580	+	0.298917i	−0.939321	−	0.343039i	$-0.888544\pi$
$157$	−339.500	+	588.031i	−0.172580	+	0.298917i	0.766741	+	0.641956i	$0.221877\pi$
$158$	−103.000	+	178.401i	−0.0518623	+	0.0898281i
$159$		0			0
$160$	1120.00			0.553399
$161$	556.500	−	2891.66i	0.272412	−	1.41549i
$162$		0			0
$163$	233.500	+	404.434i	0.112203	+	0.194342i	0.916658	−	0.399672i	$-0.130876\pi$
$163$	233.500	+	404.434i	0.112203	+	0.194342i	−0.804455	+	0.594014i	$0.797543\pi$
$164$	−700.000	+	1212.44i	−0.333298	+	0.577288i
$165$		0			0
$166$	−1092.00	−	1891.40i	−0.510576	−	0.884344i
$167$	−1204.00			−0.557894			−0.278947	−	0.960306i	$-0.589985\pi$
$167$	−1204.00			−0.557894			−0.278947	+	0.960306i	$0.589985\pi$
$168$		0			0
$169$	−2001.00			−0.910787
$170$	−147.000	−	254.611i	−0.0663199	−	0.114869i
$171$		0			0
$172$	−248.000	+	429.549i	−0.109941	+	0.190423i
$173$	−1410.50	−	2443.06i	−0.619875	−	1.07365i	−0.989508	−	0.144477i	$-0.953850\pi$
$173$	−1410.50	−	2443.06i	−0.619875	−	1.07365i	0.369633	−	0.929178i	$-0.379483\pi$
$174$		0			0
$175$	1330.00	−	460.726i	0.574506	−	0.199015i
$176$	−80.0000			−0.0342627
$177$		0			0
$178$	329.000	−	569.845i	0.138537	−	0.239953i
$179$	−1626.50	+	2817.18i	−0.679164	+	1.17635i	0.296069	+	0.955166i	$0.404324\pi$
$179$	−1626.50	+	2817.18i	−0.679164	+	1.17635i	−0.975233	+	0.221180i	$0.929009\pi$
$180$		0			0
$181$	1582.00			0.649664			0.324832	−	0.945772i	$-0.394692\pi$
$181$	1582.00			0.649664			0.324832	+	0.945772i	$0.394692\pi$
$182$	98.0000	−	509.223i	0.0399134	−	0.207396i
$183$		0			0
$184$	−1908.00	−	3304.75i	−0.764454	−	1.32407i
$185$	766.500	−	1327.62i	0.304617	−	0.527613i
$186$		0			0
$187$	−52.5000	−	90.9327i	−0.0205304	−	0.0355597i
$188$	2100.00			0.814671
$189$		0			0
$190$	686.000			0.261935
$191$	1278.50	+	2214.43i	0.484340	+	0.838902i	0.999838	−	0.0179887i	$-0.00572630\pi$
$191$	1278.50	+	2214.43i	0.484340	+	0.838902i	−0.515498	+	0.856891i	$0.672393\pi$
$192$		0			0
$193$	198.500	−	343.812i	0.0740329	−	0.128229i	−0.826632	−	0.562742i	$-0.809746\pi$
$193$	198.500	−	343.812i	0.0740329	−	0.128229i	0.900665	+	0.434514i	$0.143080\pi$
$194$	−882.000	−	1527.67i	−0.326412	−	0.565362i
$195$		0			0
$196$	1274.00	+	509.223i	0.464286	+	0.185577i
$197$	−2914.00			−1.05388			−0.526939	−	0.849903i	$-0.676660\pi$
$197$	−2914.00			−1.05388			−0.526939	+	0.849903i	$0.676660\pi$
$198$		0			0
$199$	−1669.50	+	2891.66i	−0.594712	+	1.03007i	0.398875	+	0.917005i	$0.369401\pi$
$199$	−1669.50	+	2891.66i	−0.594712	+	1.03007i	−0.993587	+	0.113066i	$0.963933\pi$
$200$	912.000	−	1579.63i	0.322441	−	0.558484i
$201$		0			0
$202$	2758.00			0.960654
$203$	−812.000	−	703.213i	−0.280745	−	0.243132i
$204$		0			0
$205$	−1225.00	−	2121.76i	−0.417355	−	0.722880i
$206$	−679.000	+	1176.06i	−0.229651	+	0.397768i
$207$		0			0
$208$	−112.000	−	193.990i	−0.0373356	−	0.0646671i
$209$	245.000			0.0810861
$210$		0			0
$211$	1780.00			0.580759			0.290380	−	0.956911i	$-0.406218\pi$
$211$	1780.00			0.580759			0.290380	+	0.956911i	$0.406218\pi$
$212$	−606.000	−	1049.62i	−0.196322	−	0.340040i
$213$		0			0
$214$	−457.000	+	791.547i	−0.145981	+	0.252846i
$215$	−434.000	−	751.710i	−0.137668	−	0.238447i
$216$		0			0
$217$	−2572.50	+	891.140i	−0.804759	+	0.278777i
$218$	2250.00			0.699033
$219$		0			0
$220$	−70.0000	+	121.244i	−0.0214518	+	0.0371556i
$221$	147.000	−	254.611i	0.0447434	−	0.0774978i
$222$		0			0
$223$	−1400.00			−0.420408			−0.210204	−	0.977658i	$-0.567413\pi$
$223$	−1400.00			−0.420408			−0.210204	+	0.977658i	$0.567413\pi$
$224$	2800.00	−	969.948i	0.835191	−	0.289319i
$225$		0			0
$226$	1538.00	+	2663.89i	0.452682	+	0.784069i
$227$	−1102.50	+	1909.59i	−0.322359	+	0.558342i	−0.980974	−	0.194138i	$-0.937809\pi$
$227$	−1102.50	+	1909.59i	−0.322359	+	0.558342i	0.658615	+	0.752480i	$0.271142\pi$
$228$		0			0
$229$	−143.500	−	248.549i	−0.0414094	−	0.0717231i	0.844578	−	0.535433i	$-0.179851\pi$
$229$	−143.500	−	248.549i	−0.0414094	−	0.0717231i	−0.885987	+	0.463710i	$0.846518\pi$
$230$	2226.00			0.638166
$231$		0			0
$232$	−1392.00			−0.393919
$233$	2293.50	+	3972.46i	0.644859	+	1.11693i	0.984334	+	0.176314i	$0.0564173\pi$
$233$	2293.50	+	3972.46i	0.644859	+	1.11693i	−0.339475	+	0.940615i	$0.610249\pi$
$234$		0			0
$235$	−1837.50	+	3182.64i	−0.510065	+	0.883459i
$236$	210.000	+	363.731i	0.0579230	+	0.100326i
$237$		0			0
$238$	−588.000	−	509.223i	−0.160144	−	0.138689i
$239$	−1668.00			−0.451439			−0.225720	−	0.974192i	$-0.572473\pi$
$239$	−1668.00			−0.451439			−0.225720	+	0.974192i	$0.572473\pi$
$240$		0			0
$241$	1704.50	−	2952.28i	0.455587	−	0.789100i	−0.543135	−	0.839646i	$-0.682763\pi$
$241$	1704.50	−	2952.28i	0.455587	−	0.789100i	0.998722	+	0.0505456i	$0.0160960\pi$
$242$	−1306.00	+	2262.06i	−0.346913	+	0.600870i
$243$		0			0
$244$	1652.00			0.433436
$245$	−1886.50	+	1485.23i	−0.491935	+	0.387298i
$246$		0			0
$247$	343.000	+	594.093i	0.0883586	+	0.153042i
$248$	−1764.00	+	3055.34i	−0.451670	+	0.782315i
$249$		0			0
$250$	1407.00	+	2437.00i	0.355946	+	0.616517i
$251$	4760.00			1.19701			0.598503	−	0.801121i	$-0.295762\pi$
$251$	4760.00			1.19701			0.598503	+	0.801121i	$0.295762\pi$
$252$		0			0
$253$	795.000			0.197554
$254$	72.0000	+	124.708i	0.0177861	+	0.0308065i
$255$		0			0
$256$	2176.00	−	3768.94i	0.531250	−	0.920152i
$257$	−402.500	−	697.150i	−0.0976936	−	0.169210i	0.813036	−	0.582213i	$-0.197813\pi$
$257$	−402.500	−	697.150i	−0.0976936	−	0.169210i	−0.910730	+	0.413003i	$0.864480\pi$
$258$		0			0
$259$	766.500	−	3982.85i	0.183892	−	0.955530i
$260$	−392.000			−0.0935031
$261$		0			0
$262$	−2149.00	+	3722.18i	−0.506739	+	0.877698i
$263$	−128.500	+	222.569i	−0.0301279	+	0.0521831i	−0.880696	−	0.473681i	$-0.842925\pi$
$263$	−128.500	+	222.569i	−0.0301279	+	0.0521831i	0.850568	+	0.525865i	$0.176258\pi$
$264$		0			0
$265$	2121.00			0.491668
$266$	1715.00	−	594.093i	0.395314	−	0.136941i
$267$		0			0
$268$	830.000	+	1437.60i	0.189180	+	0.327670i
$269$	1795.50	−	3109.90i	0.406965	−	0.704884i	−0.587583	−	0.809164i	$-0.699920\pi$
$269$	1795.50	−	3109.90i	0.406965	−	0.704884i	0.994548	+	0.104280i	$0.0332538\pi$
$270$		0			0
$271$	−696.500	−	1206.37i	−0.156123	−	0.270413i	0.777344	−	0.629075i	$-0.216566\pi$
$271$	−696.500	−	1206.37i	−0.156123	−	0.270413i	−0.933467	+	0.358662i	$0.883233\pi$
$272$	−336.000			−0.0749007
$273$		0			0
$274$	−2250.00			−0.496086
$275$	190.000	+	329.090i	0.0416634	+	0.0721631i
$276$		0			0
$277$	−207.500	+	359.401i	−0.0450089	+	0.0779577i	−0.887652	−	0.460514i	$-0.847665\pi$
$277$	−207.500	+	359.401i	−0.0450089	+	0.0779577i	0.842643	+	0.538472i	$0.180998\pi$
$278$	252.000	+	436.477i	0.0543667	+	0.0941660i
$279$		0			0
$280$	−588.000	+	3055.34i	−0.125499	+	0.652112i
$281$	4954.00			1.05171			0.525856	−	0.850574i	$-0.323745\pi$
$281$	4954.00			1.05171			0.525856	+	0.850574i	$0.323745\pi$
$282$		0			0
$283$	2138.50	−	3703.99i	0.449190	−	0.778019i	−0.549144	−	0.835728i	$-0.685046\pi$
$283$	2138.50	−	3703.99i	0.449190	−	0.778019i	0.998333	+	0.0577087i	$0.0183795\pi$
$284$	864.000	−	1496.49i	0.180525	−	0.312678i
$285$		0			0
$286$	140.000			0.0289454
$287$	−4900.00	−	4243.52i	−1.00780	−	0.872778i
$288$		0			0
$289$	2236.00	+	3872.87i	0.455119	+	0.788289i
$290$	406.000	−	703.213i	0.0822108	−	0.142393i
$291$		0			0
$292$	−2226.00	−	3855.55i	−0.446119	−	0.772701i
$293$	−7742.00			−1.54366			−0.771830	−	0.635829i	$-0.780658\pi$
$293$	−7742.00			−1.54366			−0.771830	+	0.635829i	$0.780658\pi$
$294$		0			0
$295$	−735.000			−0.145062
$296$	−2628.00	−	4551.83i	−0.516045	−	0.893817i
$297$		0			0
$298$	201.000	−	348.142i	0.0390725	−	0.0676756i
$299$	1113.00	+	1927.77i	0.215272	+	0.372863i
$300$		0			0
$301$	−1736.00	−	1503.42i	−0.332430	−	0.287893i
$302$	−3238.00			−0.616973
$303$		0			0
$304$	392.000	−	678.964i	0.0739564	−	0.128096i
$305$	−1445.50	+	2503.68i	−0.271374	+	0.470034i
$306$		0			0
$307$	−7364.00			−1.36901			−0.684504	−	0.729009i	$-0.739981\pi$
$307$	−7364.00			−1.36901			−0.684504	+	0.729009i	$0.739981\pi$
$308$	−70.0000	+	363.731i	−0.0129501	+	0.0672905i
$309$		0			0
$310$	−1029.00	−	1782.28i	−0.188527	−	0.326538i
$311$	4987.50	−	8638.60i	0.909374	−	1.57508i	0.0944372	−	0.995531i	$-0.469895\pi$
$311$	4987.50	−	8638.60i	0.909374	−	1.57508i	0.814936	−	0.579550i	$-0.196772\pi$
$312$		0			0
$313$	2376.50	+	4116.22i	0.429162	+	0.743330i	0.996799	−	0.0799485i	$-0.0254756\pi$
$313$	2376.50	+	4116.22i	0.429162	+	0.743330i	−0.567637	+	0.823279i	$0.692142\pi$
$314$	−1358.00			−0.244065
$315$		0			0
$316$	412.000			0.0733443
$317$	−1738.50	−	3011.17i	−0.308025	−	0.533515i	0.669905	−	0.742447i	$-0.266335\pi$
$317$	−1738.50	−	3011.17i	−0.308025	−	0.533515i	−0.977930	+	0.208932i	$0.933001\pi$
$318$		0			0
$319$	145.000	−	251.147i	0.0254497	−	0.0440801i
$320$	1568.00	+	2715.86i	0.273918	+	0.474440i
$321$		0			0
$322$	5565.00	−	1927.77i	0.963122	−	0.333635i
$323$	1029.00			0.177260
$324$		0			0
$325$	−532.000	+	921.451i	−0.0908002	+	0.157270i
$326$	−467.000	+	808.868i	−0.0793397	+	0.137420i
$327$		0			0
$328$	−8400.00			−1.41406
$329$	−1837.50	+	9547.93i	−0.307917	+	1.59998i
$330$		0			0
$331$	−1670.50	−	2893.39i	−0.277399	−	0.480469i	0.693339	−	0.720612i	$-0.256139\pi$
$331$	−1670.50	−	2893.39i	−0.277399	−	0.480469i	−0.970738	+	0.240143i	$0.922806\pi$
$332$	−2184.00	+	3782.80i	−0.361032	+	0.625325i
$333$		0			0
$334$	−1204.00	−	2085.39i	−0.197245	−	0.341639i
$335$	−2905.00			−0.473782
$336$		0			0
$337$	7366.00			1.19066			0.595329	−	0.803482i	$-0.297022\pi$
$337$	7366.00			1.19066			0.595329	+	0.803482i	$0.297022\pi$
$338$	−2001.00	−	3465.83i	−0.322012	−	0.557741i
$339$		0			0
$340$	−294.000	+	509.223i	−0.0468953	+	0.0812250i
$341$	−367.500	−	636.529i	−0.0583614	−	0.101085i
$342$		0			0
$343$	−3430.00	+	5346.84i	−0.539949	+	0.841698i
$344$	−2976.00			−0.466439
$345$		0			0
$346$	2821.00	−	4886.12i	0.438318	−	0.759188i
$347$	3707.50	−	6421.58i	0.573571	−	0.993454i	−0.422625	−	0.906305i	$-0.638891\pi$
$347$	3707.50	−	6421.58i	0.573571	−	0.993454i	0.996195	−	0.0871487i	$-0.0277755\pi$
$348$		0			0
$349$	−3878.00			−0.594798			−0.297399	−	0.954753i	$-0.596119\pi$
$349$	−3878.00			−0.594798			−0.297399	+	0.954753i	$0.596119\pi$
$350$	2128.00	+	1842.90i	0.324990	+	0.281449i
$351$		0			0
$352$	400.000	+	692.820i	0.0605684	+	0.104908i
$353$	633.500	−	1097.25i	0.0955179	−	0.165442i	−0.814307	−	0.580435i	$-0.802883\pi$
$353$	633.500	−	1097.25i	0.0955179	−	0.165442i	0.909825	+	0.414993i	$0.136216\pi$
$354$		0			0
$355$	1512.00	+	2618.86i	0.226052	+	0.391534i
$356$	−1316.00			−0.195921
$357$		0			0
$358$	−6506.00			−0.960483
$359$	2342.50	+	4057.33i	0.344380	+	0.596484i	0.985241	−	0.171173i	$-0.0547558\pi$
$359$	2342.50	+	4057.33i	0.344380	+	0.596484i	−0.640861	+	0.767657i	$0.721422\pi$
$360$		0			0
$361$	2229.00	−	3860.74i	0.324974	−	0.562872i
$362$	1582.00	+	2740.10i	0.229691	+	0.397836i
$363$		0			0
$364$	−980.000	+	339.482i	−0.141115	+	0.0488838i
$365$	7791.00			1.11726
$366$		0			0
$367$	2320.50	−	4019.22i	0.330052	−	0.571667i	−0.652470	−	0.757815i	$-0.726267\pi$
$367$	2320.50	−	4019.22i	0.330052	−	0.571667i	0.982522	+	0.186148i	$0.0596004\pi$
$368$	1272.00	−	2203.17i	0.180184	−	0.312087i
$369$		0			0
$370$	3066.00			0.430794
$371$	5302.50	−	1836.84i	0.742027	−	0.257046i
$372$		0			0
$373$	4398.50	+	7618.43i	0.610578	+	1.05755i	0.991143	+	0.132798i	$0.0423963\pi$
$373$	4398.50	+	7618.43i	0.610578	+	1.05755i	−0.380565	+	0.924754i	$0.624270\pi$
$374$	105.000	−	181.865i	0.0145172	−	0.0251445i
$375$		0			0
$376$	6300.00	+	10911.9i	0.864090	+	1.49665i
$377$	812.000			0.110929
$378$		0			0
$379$	13680.0			1.85407			0.927037	−	0.374969i	$-0.122347\pi$
$379$	13680.0			1.85407			0.927037	+	0.374969i	$0.122347\pi$
$380$	−686.000	−	1188.19i	−0.0926080	−	0.160402i
$381$		0			0
$382$	−2557.00	+	4428.85i	−0.342480	+	0.593193i
$383$	4882.50	+	8456.74i	0.651395	+	1.12825i	0.982785	+	0.184755i	$0.0591490\pi$
$383$	4882.50	+	8456.74i	0.651395	+	1.12825i	−0.331390	+	0.943494i	$0.607518\pi$
$384$		0			0
$385$	−490.000	−	424.352i	−0.0648642	−	0.0561740i
$386$	794.000			0.104698
$387$		0			0
$388$	−1764.00	+	3055.34i	−0.230808	+	0.399771i
$389$	865.500	−	1499.09i	0.112809	−	0.195390i	−0.804093	−	0.594504i	$-0.797349\pi$
$389$	865.500	−	1499.09i	0.112809	−	0.195390i	0.916902	+	0.399113i	$0.130682\pi$
$390$		0			0
$391$	3339.00			0.431868
$392$	1176.00	+	8147.57i	0.151523	+	1.04978i
$393$		0			0
$394$	−2914.00	−	5047.20i	−0.372602	−	0.645366i
$395$	−360.500	+	624.404i	−0.0459208	+	0.0795372i
$396$		0			0
$397$	−5491.50	−	9511.56i	−0.694233	−	1.20245i	−0.970439	−	0.241348i	$-0.922410\pi$
$397$	−5491.50	−	9511.56i	−0.694233	−	1.20245i	0.276206	−	0.961099i	$-0.410923\pi$
$398$	−6678.00			−0.841050
$399$		0			0
$400$	1216.00			0.152000
$401$	3301.50	+	5718.37i	0.411145	+	0.712124i	0.995015	−	0.0997232i	$-0.0317957\pi$
$401$	3301.50	+	5718.37i	0.411145	+	0.712124i	−0.583870	+	0.811847i	$0.698462\pi$
$402$		0			0
$403$	1029.00	−	1782.28i	0.127191	−	0.220302i
$404$	−2758.00	−	4777.00i	−0.339643	−	0.588278i
$405$		0			0
$406$	406.000	−	2109.64i	0.0496292	−	0.257881i
$407$	1095.00			0.133359
$408$		0			0
$409$	−5477.50	+	9487.31i	−0.662213	+	1.14699i	0.317820	+	0.948151i	$0.397049\pi$
$409$	−5477.50	+	9487.31i	−0.662213	+	1.14699i	−0.980033	+	0.198835i	$0.936284\pi$
$410$	2450.00	−	4243.52i	0.295114	−	0.511153i
$411$		0			0
$412$	2716.00			0.324776
$413$	−1837.50	+	636.529i	−0.218928	+	0.0758391i
$414$		0			0
$415$	−3822.00	−	6619.90i	−0.452083	−	0.783031i
$416$	−1120.00	+	1939.90i	−0.132001	+	0.228633i
$417$		0			0
$418$	245.000	+	424.352i	0.0286683	+	0.0496549i
$419$	−6636.00			−0.773723			−0.386861	−	0.922138i	$-0.626441\pi$
$419$	−6636.00			−0.773723			−0.386861	+	0.922138i	$0.626441\pi$
$420$		0			0
$421$	−16630.0			−1.92517			−0.962585	−	0.270980i	$-0.912652\pi$
$421$	−16630.0			−1.92517			−0.962585	+	0.270980i	$0.912652\pi$
$422$	1780.00	+	3083.05i	0.205329	+	0.355641i
$423$		0			0
$424$	3636.00	−	6297.74i	0.416462	−	0.721333i
$425$	798.000	+	1382.18i	0.0910793	+	0.157754i
$426$		0			0
$427$	−1445.50	+	7511.04i	−0.163824	+	0.851252i
$428$	1828.00			0.206448
$429$		0			0
$430$	868.000	−	1503.42i	0.0973458	−	0.168608i
$431$	2461.50	−	4263.44i	0.275096	−	0.476480i	−0.695064	−	0.718948i	$-0.744624\pi$
$431$	2461.50	−	4263.44i	0.275096	−	0.476480i	0.970159	+	0.242468i	$0.0779571\pi$
$432$		0			0
$433$	8974.00			0.995988			0.497994	−	0.867180i	$-0.334070\pi$
$433$	8974.00			0.995988			0.497994	+	0.867180i	$0.334070\pi$
$434$	−4116.00	−	3564.56i	−0.455240	−	0.394250i
$435$		0			0
$436$	−2250.00	−	3897.11i	−0.247146	−	0.428069i
$437$	−3895.50	+	6747.20i	−0.426423	+	0.738587i
$438$		0			0
$439$	2089.50	+	3619.12i	0.227167	+	0.393465i	0.956967	−	0.290195i	$-0.0937203\pi$
$439$	2089.50	+	3619.12i	0.227167	+	0.393465i	−0.729800	+	0.683660i	$0.760387\pi$
$440$	−840.000			−0.0910123
$441$		0			0
$442$	588.000			0.0632767
$443$	−6463.50	−	11195.1i	−0.693206	−	1.20067i	−0.970782	−	0.239964i	$-0.922864\pi$
$443$	−6463.50	−	11195.1i	−0.693206	−	1.20067i	0.277576	−	0.960704i	$-0.410469\pi$
$444$		0			0
$445$	1151.50	−	1994.46i	0.122666	−	0.212464i
$446$	−1400.00	−	2424.87i	−0.148637	−	0.257446i
$447$		0			0
$448$	6272.00	+	5431.71i	0.661438	+	0.572822i
$449$	2826.00			0.297032			0.148516	−	0.988910i	$-0.452550\pi$
$449$	2826.00			0.297032			0.148516	+	0.988910i	$0.452550\pi$
$450$		0			0
$451$	875.000	−	1515.54i	0.0913573	−	0.158235i
$452$	3076.00	−	5327.79i	0.320095	−	0.554421i
$453$		0			0
$454$	−4410.00			−0.455884
$455$	343.000	−	1782.28i	0.0353409	−	0.183636i
$456$		0			0
$457$	−4239.50	−	7343.03i	−0.433951	−	0.751625i	0.563259	−	0.826281i	$-0.309547\pi$
$457$	−4239.50	−	7343.03i	−0.433951	−	0.751625i	−0.997209	+	0.0746560i	$0.976214\pi$
$458$	287.000	−	497.099i	0.0292808	−	0.0507159i
$459$		0			0
$460$	−2226.00	−	3855.55i	−0.225626	−	0.390795i
$461$	−9338.00			−0.943414			−0.471707	−	0.881755i	$-0.656362\pi$
$461$	−9338.00			−0.943414			−0.471707	+	0.881755i	$0.656362\pi$
$462$		0			0
$463$	−4016.00			−0.403109			−0.201554	−	0.979477i	$-0.564599\pi$
$463$	−4016.00			−0.403109			−0.201554	+	0.979477i	$0.564599\pi$
$464$	−464.000	−	803.672i	−0.0464238	−	0.0804084i
$465$		0			0
$466$	−4587.00	+	7944.92i	−0.455984	+	0.789788i
$467$	−2929.50	−	5074.04i	−0.290281	−	0.502781i	0.683595	−	0.729861i	$-0.260415\pi$
$467$	−2929.50	−	5074.04i	−0.290281	−	0.502781i	−0.973876	+	0.227080i	$0.927082\pi$
$468$		0			0
$469$	−7262.50	+	2515.80i	−0.715034	+	0.247695i
$470$	−7350.00			−0.721341
$471$		0			0
$472$	−1260.00	+	2182.38i	−0.122873	+	0.212823i
$473$	310.000	−	536.936i	0.0301349	−	0.0521952i
$474$		0			0
$475$	−3724.00			−0.359724
$476$	−294.000	+	1527.67i	−0.0283098	+	0.147102i
$477$		0			0
$478$	−1668.00	−	2889.06i	−0.159608	−	0.276449i
$479$	3251.50	−	5631.76i	0.310156	−	0.537206i	−0.668240	−	0.743946i	$-0.732952\pi$
$479$	3251.50	−	5631.76i	0.310156	−	0.537206i	0.978396	+	0.206740i	$0.0662853\pi$
$480$		0			0
$481$	1533.00	+	2655.23i	0.145320	+	0.251701i
$482$	6818.00			0.644297
$483$		0			0
$484$	5224.00			0.490609
$485$	−3087.00	−	5346.84i	−0.289017	−	0.500593i
$486$		0			0
$487$	8024.50	−	13898.8i	0.746663	−	1.29326i	−0.202751	−	0.979230i	$-0.564988\pi$
$487$	8024.50	−	13898.8i	0.746663	−	1.29326i	0.949414	−	0.314028i	$-0.101678\pi$
$488$	4956.00	+	8584.04i	0.459729	+	0.796273i
$489$		0			0
$490$	−4459.00	−	1782.28i	−0.411096	−	0.164317i
$491$	−8864.00			−0.814718			−0.407359	−	0.913268i	$-0.633550\pi$
$491$	−8864.00			−0.814718			−0.407359	+	0.913268i	$0.633550\pi$
$492$		0			0
$493$	609.000	−	1054.82i	0.0556348	−	0.0963624i
$494$	−686.000	+	1188.19i	−0.0624789	+	0.108217i
$495$		0			0
$496$	−2352.00			−0.212919
$497$	6048.00	+	5237.72i	0.545855	+	0.472724i
$498$		0			0
$499$	5105.50	+	8842.99i	0.458023	+	0.793319i	0.998856	−	0.0478104i	$-0.0152243\pi$
$499$	5105.50	+	8842.99i	0.458023	+	0.793319i	−0.540833	+	0.841130i	$0.681891\pi$
$500$	2814.00	−	4873.99i	0.251692	−	0.435943i
$501$		0			0
$502$	4760.00	+	8244.56i	0.423206	+	0.733014i
$503$	1680.00			0.148921			0.0744607	−	0.997224i	$-0.476276\pi$
$503$	1680.00			0.148921			0.0744607	+	0.997224i	$0.476276\pi$
$504$		0			0
$505$	9653.00			0.850600
$506$	795.000	+	1376.98i	0.0698460	+	0.120977i
$507$		0			0
$508$	144.000	−	249.415i	0.0125767	−	0.0217835i
$509$	−4728.50	−	8190.00i	−0.411762	−	0.713193i	0.583320	−	0.812242i	$-0.301753\pi$
$509$	−4728.50	−	8190.00i	−0.411762	−	0.713193i	−0.995083	+	0.0990489i	$0.968420\pi$
$510$		0			0
$511$	19477.5	−	6747.20i	1.68617	−	0.584107i
$512$	5632.00			0.486136
$513$		0			0
$514$	805.000	−	1394.30i	0.0690798	−	0.119650i
$515$	−2376.50	+	4116.22i	−0.203342	+	0.352199i
$516$		0			0
$517$	−2625.00			−0.223302
$518$	7665.00	−	2655.23i	0.650156	−	0.225221i
$519$		0			0
$520$	−1176.00	−	2036.89i	−0.0991750	−	0.171776i
$521$	−9040.50	+	15658.6i	−0.760214	+	1.31673i	0.182526	+	0.983201i	$0.441573\pi$
$521$	−9040.50	+	15658.6i	−0.760214	+	1.31673i	−0.942740	+	0.333528i	$0.891761\pi$
$522$		0			0
$523$	−10188.5	−	17647.0i	−0.851839	−	1.47543i	−0.879546	−	0.475813i	$-0.842154\pi$
$523$	−10188.5	−	17647.0i	−0.851839	−	1.47543i	0.0277071	−	0.999616i	$-0.491179\pi$
$524$	8596.00			0.716637
$525$		0			0
$526$	−514.000			−0.0426073
$527$	−1543.50	−	2673.42i	−0.127582	−	0.220979i
$528$		0			0
$529$	−6557.00	+	11357.1i	−0.538917	+	0.933431i
$530$	2121.00	+	3673.68i	0.173831	+	0.301084i
$531$		0			0
$532$	−2744.00	−	2376.37i	−0.223623	−	0.193663i
$533$	4900.00			0.398204
$534$		0			0
$535$	−1599.50	+	2770.42i	−0.129257	+	0.223879i
$536$	−4980.00	+	8625.61i	−0.401312	+	0.695093i
$537$		0			0
$538$	7182.00			0.575535
$539$	−1592.50	−	636.529i	−0.127261	−	0.0508668i
$540$		0			0
$541$	3096.50	+	5363.30i	0.246079	+	0.426222i	0.962435	−	0.271514i	$-0.0875243\pi$
$541$	3096.50	+	5363.30i	0.246079	+	0.426222i	−0.716355	+	0.697736i	$0.754191\pi$
$542$	1393.00	−	2412.75i	0.110396	−	0.191211i
$543$		0			0
$544$	1680.00	+	2909.85i	0.132407	+	0.229336i
$545$	7875.00			0.618950
$546$		0			0
$547$	−18464.0			−1.44326			−0.721630	−	0.692279i	$-0.756607\pi$
$547$	−18464.0			−1.44326			−0.721630	+	0.692279i	$0.756607\pi$
$548$	2250.00	+	3897.11i	0.175393	+	0.303789i
$549$		0			0
$550$	−380.000	+	658.179i	−0.0294605	+	0.0510270i
$551$	1421.00	+	2461.24i	0.109867	+	0.190295i
$552$		0			0
$553$	−360.500	+	1873.21i	−0.0277216	+	0.144045i
$554$	−830.000			−0.0636522
$555$		0			0
$556$	504.000	−	872.954i	0.0384431	−	0.0665854i
$557$	−4706.50	+	8151.90i	−0.358027	+	0.620120i	−0.987631	−	0.156796i	$-0.949884\pi$
$557$	−4706.50	+	8151.90i	−0.358027	+	0.620120i	0.629604	+	0.776916i	$0.283217\pi$
$558$		0			0
$559$	1736.00			0.131351
$560$	−1960.00	+	678.964i	−0.147902	+	0.0512348i
$561$		0			0
$562$	4954.00	+	8580.58i	0.371836	+	0.644039i
$563$	1599.50	−	2770.42i	0.119735	−	0.207387i	−0.799928	−	0.600097i	$-0.795129\pi$
$563$	1599.50	−	2770.42i	0.119735	−	0.207387i	0.919663	+	0.392709i	$0.128462\pi$
$564$		0			0
$565$	5383.00	+	9323.63i	0.400822	+	0.694244i
$566$	8554.00			0.635250
$567$		0			0
$568$	10368.0			0.765901
$569$	10791.5	+	18691.4i	0.795085	+	1.37713i	0.922785	+	0.385314i	$0.125907\pi$
$569$	10791.5	+	18691.4i	0.795085	+	1.37713i	−0.127701	+	0.991813i	$0.540760\pi$
$570$		0			0
$571$	−10133.5	+	17551.7i	−0.742686	+	1.28637i	0.208582	+	0.978005i	$0.433115\pi$
$571$	−10133.5	+	17551.7i	−0.742686	+	1.28637i	−0.951268	+	0.308365i	$0.900218\pi$
$572$	−140.000	−	242.487i	−0.0102337	−	0.0177253i
$573$		0			0
$574$	2450.00	−	12730.6i	0.178155	−	0.925721i
$575$	−12084.0			−0.876413
$576$		0			0
$577$	−6975.50	+	12081.9i	−0.503282	+	0.871710i	0.496711	+	0.867916i	$0.334541\pi$
$577$	−6975.50	+	12081.9i	−0.503282	+	0.871710i	−0.999993	+	0.00379418i	$0.998792\pi$
$578$	−4472.00	+	7745.73i	−0.321818	+	0.557405i
$579$		0			0
$580$	−1624.00			−0.116264
$581$	−15288.0	−	13239.8i	−1.09166	−	0.945403i
$582$		0			0
$583$	757.500	+	1312.03i	0.0538121	+	0.0932053i
$584$	13356.0	−	23133.3i	0.946362	−	1.63915i
$585$		0			0
$586$	−7742.00	−	13409.5i	−0.545766	−	0.945295i
$587$	20972.0			1.47463			0.737314	−	0.675550i	$-0.236094\pi$
$587$	20972.0			1.47463			0.737314	+	0.675550i	$0.236094\pi$
$588$		0			0
$589$	7203.00			0.503895
$590$	−735.000	−	1273.06i	−0.0512872	−	0.0888321i
$591$		0			0
$592$	1752.00	−	3034.55i	0.121633	−	0.210675i
$593$	−94.5000	−	163.679i	−0.00654410	−	0.0113347i	0.862735	−	0.505657i	$-0.168750\pi$
$593$	−94.5000	−	163.679i	−0.00654410	−	0.0113347i	−0.869279	+	0.494322i	$0.835416\pi$
$594$		0			0
$595$	−2058.00	−	1782.28i	−0.141798	−	0.122801i
$596$	−804.000			−0.0552569
$597$		0			0
$598$	−2226.00	+	3855.55i	−0.152221	+	0.263654i
$599$	−5140.50	+	8903.61i	−0.350643	+	0.607331i	−0.986362	−	0.164589i	$-0.947370\pi$
$599$	−5140.50	+	8903.61i	−0.350643	+	0.607331i	0.635719	+	0.771920i	$0.280704\pi$
$600$		0			0
$601$	−6090.00			−0.413338			−0.206669	−	0.978411i	$-0.566262\pi$
$601$	−6090.00			−0.413338			−0.206669	+	0.978411i	$0.566262\pi$
$602$	868.000	−	4510.26i	0.0587658	−	0.305356i
$603$		0			0
$604$	3238.00	+	5608.38i	0.218133	+	0.377817i
$605$	−4571.00	+	7917.20i	−0.307170	+	0.532033i
$606$		0			0
$607$	−2474.50	−	4285.96i	−0.165464	−	0.286593i	0.771356	−	0.636404i	$-0.219579\pi$
$607$	−2474.50	−	4285.96i	−0.165464	−	0.286593i	−0.936820	+	0.349812i	$0.886246\pi$
$608$	−7840.00			−0.522951
$609$		0			0
$610$	−5782.00			−0.383781
$611$	−3675.00	−	6365.29i	−0.243330	−	0.421460i
$612$		0			0
$613$	7898.50	−	13680.6i	0.520420	−	0.901394i	−0.479298	−	0.877652i	$-0.659109\pi$
$613$	7898.50	−	13680.6i	0.520420	−	0.901394i	0.999718	−	0.0237416i	$-0.00755791\pi$
$614$	−7364.00	−	12754.8i	−0.484018	−	0.838343i
$615$		0			0
$616$	−2100.00	+	727.461i	−0.137356	+	0.0475816i
$617$	9378.00			0.611903			0.305951	−	0.952047i	$-0.401025\pi$
$617$	9378.00			0.611903			0.305951	+	0.952047i	$0.401025\pi$
$618$		0			0
$619$	12176.5	−	21090.3i	0.790654	−	1.36945i	−0.134908	−	0.990858i	$-0.543074\pi$
$619$	12176.5	−	21090.3i	0.790654	−	1.36945i	0.925562	−	0.378595i	$-0.123593\pi$
$620$	−2058.00	+	3564.56i	−0.133308	+	0.230897i
$621$		0			0
$622$	19950.0			1.28605
$623$	1151.50	−	5983.37i	0.0740512	−	0.384781i
$624$		0			0
$625$	174.500	+	302.243i	0.0111680	+	0.0193435i
$626$	−4753.00	+	8232.44i	−0.303463	+	0.525614i
$627$		0			0
$628$	1358.00	+	2352.12i	0.0862900	+	0.149459i
$629$	4599.00			0.291533
$630$		0			0
$631$	−12640.0			−0.797449			−0.398725	−	0.917071i	$-0.630547\pi$
$631$	−12640.0			−0.797449			−0.398725	+	0.917071i	$0.630547\pi$
$632$	1236.00	+	2140.81i	0.0777934	+	0.134742i
$633$		0			0
$634$	3477.00	−	6022.34i	0.217806	−	0.377252i
$635$	252.000	+	436.477i	0.0157485	+	0.0272772i
$636$		0			0
$637$	−686.000	−	4752.75i	−0.0426692	−	0.295621i
$638$	580.000			0.0359913
$639$		0			0
$640$	1344.00	−	2327.88i	0.0830098	−	0.143777i
$641$	−520.500	+	901.532i	−0.0320726	+	0.0555513i	−0.881616	−	0.471967i	$-0.843544\pi$
$641$	−520.500	+	901.532i	−0.0320726	+	0.0555513i	0.849544	+	0.527518i	$0.176877\pi$
$642$		0			0
$643$	9548.00			0.585593			0.292797	−	0.956175i	$-0.405414\pi$
$643$	9548.00			0.585593			0.292797	+	0.956175i	$0.405414\pi$
$644$	−8904.00	−	7711.09i	−0.544824	−	0.471832i
$645$		0			0
$646$	1029.00	+	1782.28i	0.0626710	+	0.108549i
$647$	−1620.50	+	2806.79i	−0.0984674	+	0.170551i	−0.911050	−	0.412295i	$-0.864727\pi$
$647$	−1620.50	+	2806.79i	−0.0984674	+	0.170551i	0.812583	+	0.582845i	$0.198061\pi$
$648$		0			0
$649$	−262.500	−	454.663i	−0.0158768	−	0.0274994i
$650$	−2128.00			−0.128411
$651$		0			0
$652$	1868.00			0.112203
$653$	−4426.50	−	7666.92i	−0.265272	−	0.459464i	0.702363	−	0.711819i	$-0.252128\pi$
$653$	−4426.50	−	7666.92i	−0.265272	−	0.459464i	−0.967635	+	0.252355i	$0.918795\pi$
$654$		0			0
$655$	−7521.50	+	13027.6i	−0.448686	+	0.777147i
$656$	−2800.00	−	4849.74i	−0.166649	−	0.288644i
$657$		0			0
$658$	−18375.0	+	6365.29i	−1.08865	+	0.377120i
$659$	−7044.00			−0.416381			−0.208191	−	0.978088i	$-0.566757\pi$
$659$	−7044.00			−0.416381			−0.208191	+	0.978088i	$0.566757\pi$
$660$		0			0
$661$	6044.50	−	10469.4i	0.355679	−	0.616054i	−0.631555	−	0.775331i	$-0.717583\pi$
$661$	6044.50	−	10469.4i	0.355679	−	0.616054i	0.987234	+	0.159277i	$0.0509163\pi$
$662$	3341.00	−	5786.78i	0.196151	−	0.339743i
$663$		0			0
$664$	−26208.0			−1.53173
$665$	6002.50	−	2079.33i	0.350026	−	0.121252i
$666$		0			0
$667$	4611.00	+	7986.49i	0.267674	+	0.463625i
$668$	−2408.00	+	4170.78i	−0.139474	+	0.241575i
$669$		0			0
$670$	−2905.00	−	5031.61i	−0.167507	−	0.290131i
$671$	−2065.00			−0.118805
$672$		0			0
$673$	982.000			0.0562456			0.0281228	−	0.999604i	$-0.491047\pi$
$673$	982.000			0.0562456			0.0281228	+	0.999604i	$0.491047\pi$
$674$	7366.00	+	12758.3i	0.420961	+	0.729126i
$675$		0			0
$676$	−4002.00	+	6931.67i	−0.227697	+	0.394383i
$677$	−15256.5	−	26425.0i	−0.866108	−	1.50014i	−0.865943	−	0.500143i	$-0.833281\pi$
$677$	−15256.5	−	26425.0i	−0.866108	−	1.50014i	−0.000164659	−	1.00000i	$-0.500052\pi$
$678$		0			0
$679$	−12348.0	−	10693.7i	−0.697898	−	0.604397i
$680$	−3528.00			−0.198960
$681$		0			0
$682$	735.000	−	1273.06i	0.0412677	−	0.0714778i
$683$	5737.50	−	9937.64i	0.321434	−	0.556740i	−0.659350	−	0.751836i	$-0.729169\pi$
$683$	5737.50	−	9937.64i	0.321434	−	0.556740i	0.980784	+	0.195096i	$0.0625019\pi$
$684$		0			0
$685$	−7875.00			−0.439253
$686$	−12691.0	−	594.093i	−0.706333	−	0.0330650i
$687$		0			0
$688$	−992.000	−	1718.19i	−0.0549704	−	0.0952116i
$689$	−2121.00	+	3673.68i	−0.117277	+	0.203129i
$690$		0			0
$691$	14157.5	+	24521.5i	0.779416	+	1.34999i	0.932279	+	0.361741i	$0.117818\pi$
$691$	14157.5	+	24521.5i	0.779416	+	1.34999i	−0.152862	+	0.988248i	$0.548849\pi$
$692$	−11284.0			−0.619875
$693$		0			0
$694$	14830.0			0.811151
$695$	882.000	+	1527.67i	0.0481384	+	0.0833781i
$696$		0			0
$697$	3675.00	−	6365.29i	0.199714	−	0.345915i
$698$	−3878.00	−	6716.89i	−0.210293	−	0.364238i
$699$		0			0
$700$	1064.00	−	5528.71i	0.0574506	−	0.298522i
$701$	−10614.0			−0.571876			−0.285938	−	0.958248i	$-0.592305\pi$
$701$	−10614.0			−0.571876			−0.285938	+	0.958248i	$0.592305\pi$
$702$		0			0
$703$	−5365.50	+	9293.32i	−0.287857	+	0.498583i
$704$	−1120.00	+	1939.90i	−0.0599596	+	0.103853i
$705$		0			0
$706$	2534.00			0.135083
$707$	24132.5	−	8359.74i	1.28373	−	0.444697i
$708$		0			0
$709$	−5149.50	−	8919.20i	−0.272769	−	0.472451i	0.696801	−	0.717265i	$-0.254606\pi$
$709$	−5149.50	−	8919.20i	−0.272769	−	0.472451i	−0.969570	+	0.244814i	$0.921273\pi$
$710$	−3024.00	+	5237.72i	−0.159843	+	0.276857i
$711$		0			0
$712$	−3948.00	−	6838.14i	−0.207806	−	0.359930i
$713$	23373.0			1.22767
$714$		0			0
$715$	490.000			0.0256293
$716$	6506.00	+	11268.7i	0.339582	+	0.588173i
$717$		0			0
$718$	−4685.00	+	8114.66i	−0.243513	+	0.421778i
$719$	16264.5	+	28170.9i	0.843621	+	1.46119i	0.886813	+	0.462128i	$0.152914\pi$
$719$	16264.5	+	28170.9i	0.843621	+	1.46119i	−0.0431924	+	0.999067i	$0.513753\pi$
$720$		0			0
$721$	−2376.50	+	12348.7i	−0.122754	+	0.637847i
$722$	8916.00			0.459583
$723$		0			0
$724$	3164.00	−	5480.21i	0.162416	−	0.281313i
$725$	−2204.00	+	3817.44i	−0.112903	+	0.195553i
$726$		0			0
$727$	29456.0			1.50270			0.751350	−	0.659904i	$-0.229403\pi$
$727$	29456.0			1.50270			0.751350	+	0.659904i	$0.229403\pi$
$728$	−4704.00	−	4073.78i	−0.239481	−	0.207396i
$729$		0			0
$730$	7791.00	+	13494.4i	0.395011	+	0.684179i
$731$	1302.00	−	2255.13i	0.0658772	−	0.114103i
$732$		0			0
$733$	−13933.5	−	24133.5i	−0.702109	−	1.21609i	−0.967725	−	0.252009i	$-0.918909\pi$
$733$	−13933.5	−	24133.5i	−0.702109	−	1.21609i	0.265616	−	0.964079i	$-0.414425\pi$
$734$	9282.00			0.466764
$735$		0			0
$736$	−25440.0			−1.27409
$737$	−1037.50	−	1797.00i	−0.0518546	−	0.0898147i
$738$		0			0
$739$	−9769.50	+	16921.3i	−0.486302	+	0.842299i	−0.999876	−	0.0157460i	$-0.994988\pi$
$739$	−9769.50	+	16921.3i	−0.486302	+	0.842299i	0.513574	+	0.858045i	$0.328321\pi$
$740$	−3066.00	−	5310.47i	−0.152309	−	0.263806i
$741$		0			0
$742$	8484.00	+	7347.36i	0.419754	+	0.363518i
$743$	−1248.00			−0.0616214			−0.0308107	−	0.999525i	$-0.509809\pi$
$743$	−1248.00			−0.0616214			−0.0308107	+	0.999525i	$0.509809\pi$
$744$		0			0
$745$	703.500	−	1218.50i	0.0345963	−	0.0599226i
$746$	−8797.00	+	15236.9i	−0.431744	+	0.747803i
$747$		0			0
$748$	−420.000			−0.0205304
$749$	−1599.50	+	8311.25i	−0.0780300	+	0.405456i
$750$		0			0
$751$	−14046.5	−	24329.3i	−0.682509	−	1.18214i	−0.974213	−	0.225631i	$-0.927556\pi$
$751$	−14046.5	−	24329.3i	−0.682509	−	1.18214i	0.291704	−	0.956509i	$-0.405778\pi$
$752$	−4200.00	+	7274.61i	−0.203668	+	0.352763i
$753$		0			0
$754$	812.000	+	1406.43i	0.0392192	+	0.0679297i
$755$	−11333.0			−0.546292
$756$		0			0
$757$	35954.0			1.72625			0.863124	−	0.504991i	$-0.168504\pi$
$757$	35954.0			1.72625			0.863124	+	0.504991i	$0.168504\pi$
$758$	13680.0	+	23694.5i	0.655514	+	1.13538i
$759$		0			0
$760$	4116.00	−	7129.12i	0.196451	−	0.340264i
$761$	−430.500	−	745.648i	−0.0205067	−	0.0355187i	0.855590	−	0.517654i	$-0.173195\pi$
$761$	−430.500	−	745.648i	−0.0205067	−	0.0355187i	−0.876097	+	0.482136i	$0.839861\pi$
$762$		0			0
$763$	19687.5	−	6819.95i	0.934122	−	0.323589i
$764$	10228.0			0.484340
$765$		0			0
$766$	−9765.00	+	16913.5i	−0.460605	+	0.797792i
$767$	735.000	−	1273.06i	0.0346014	−	0.0599315i
$768$		0			0
$769$	24710.0			1.15873			0.579366	−	0.815067i	$-0.303300\pi$
$769$	24710.0			1.15873			0.579366	+	0.815067i	$0.303300\pi$
$770$	245.000	−	1273.06i	0.0114665	−	0.0595816i
$771$		0			0
$772$	−794.000	−	1375.25i	−0.0370164	−	0.0641143i
$773$	8249.50	−	14288.6i	0.383847	−	0.664843i	−0.607761	−	0.794120i	$-0.707932\pi$
$773$	8249.50	−	14288.6i	0.383847	−	0.664843i	0.991609	+	0.129277i	$0.0412656\pi$
$774$		0			0
$775$	5586.00	+	9675.24i	0.258910	+	0.448445i
$776$	−21168.0			−0.979236
$777$		0			0
$778$	3462.00			0.159536
$779$	8575.00	+	14852.3i	0.394392	+	0.683107i
$780$		0			0
$781$	−1080.00	+	1870.61i	−0.0494820	+	0.0857053i
$782$	3339.00	+	5783.32i	0.152688	+	0.264464i
$783$		0			0
$784$	−4312.00	+	3394.82i	−0.196429	+	0.154647i
$785$	−4753.00			−0.216104
$786$		0			0
$787$	−8235.50	+	14264.3i	−0.373016	+	0.646083i	−0.990028	−	0.140871i	$-0.955010\pi$
$787$	−8235.50	+	14264.3i	−0.373016	+	0.646083i	0.617012	+	0.786954i	$0.288343\pi$
$788$	−5828.00	+	10094.4i	−0.263469	+	0.456342i
$789$		0			0
$790$	−1442.00			−0.0649418
$791$	21532.0	+	18647.3i	0.967876	+	0.838205i
$792$		0			0
$793$	−2891.00	−	5007.36i	−0.129461	−	0.224233i
$794$	10983.0	−	19023.1i	0.490897	−	0.850258i
$795$		0			0
$796$	6678.00	+	11566.6i	0.297356	+	0.515036i
$797$	36470.0			1.62087			0.810435	−	0.585828i	$-0.199231\pi$
$797$	36470.0			1.62087			0.810435	+	0.585828i	$0.199231\pi$
$798$		0			0
$799$	−11025.0			−0.488156
$800$	−6080.00	−	10530.9i	−0.268701	−	0.465403i
$801$		0			0
$802$	−6603.00	+	11436.7i	−0.290723	+	0.503547i
$803$	2782.50	+	4819.43i	0.122282	+	0.211798i
$804$		0			0
$805$	19477.5	−	6747.20i	0.852785	−	0.295413i
$806$	4116.00			0.179876
$807$		0			0
$808$	16548.0	−	28662.0i	0.720491	−	1.24793i
$809$	17875.5	−	30961.3i	0.776847	−	1.34554i	−0.156904	−	0.987614i	$-0.550151\pi$
$809$	17875.5	−	30961.3i	0.776847	−	1.34554i	0.933751	−	0.357924i	$-0.116515\pi$
$810$		0			0
$811$	−16492.0			−0.714072			−0.357036	−	0.934091i	$-0.616213\pi$
$811$	−16492.0			−0.714072			−0.357036	+	0.934091i	$0.616213\pi$
$812$	−4060.00	+	1406.43i	−0.175466	+	0.0607831i
$813$		0			0
$814$	1095.00	+	1896.60i	0.0471495	+	0.0816654i
$815$	−1634.50	+	2831.04i	−0.0702504	+	0.121677i
$816$		0			0
$817$	3038.00	+	5261.97i	0.130093	+	0.225328i
$818$	−21910.0			−0.936510
$819$		0			0
$820$	−9800.00			−0.417355
$821$	−20736.5	−	35916.7i	−0.881497	−	1.52680i	−0.849677	−	0.527304i	$-0.823203\pi$
$821$	−20736.5	−	35916.7i	−0.881497	−	1.52680i	−0.0318198	−	0.999494i	$-0.510130\pi$
$822$		0			0
$823$	12532.5	−	21706.9i	0.530809	−	0.919387i	−0.468545	−	0.883440i	$-0.655222\pi$
$823$	12532.5	−	21706.9i	0.530809	−	0.919387i	0.999354	−	0.0359479i	$-0.0114450\pi$
$824$	8148.00	+	14112.7i	0.344477	+	0.596652i
$825$		0			0
$826$	−2940.00	−	2546.11i	−0.123845	−	0.107253i
$827$	−9732.00			−0.409208			−0.204604	−	0.978845i	$-0.565591\pi$
$827$	−9732.00			−0.409208			−0.204604	+	0.978845i	$0.565591\pi$
$828$		0			0
$829$	−13877.5	+	24036.5i	−0.581406	+	1.00702i	0.413907	+	0.910319i	$0.364164\pi$
$829$	−13877.5	+	24036.5i	−0.581406	+	1.00702i	−0.995313	+	0.0967055i	$0.969170\pi$
$830$	7644.00	−	13239.8i	0.319671	−	0.553687i
$831$		0			0
$832$	−6272.00			−0.261349
$833$	−6688.50	−	2673.42i	−0.278203	−	0.111199i
$834$		0			0
$835$	−4214.00	−	7298.86i	−0.174648	−	0.302500i
$836$	490.000	−	848.705i	0.0202715	−	0.0351113i
$837$		0			0
$838$	−6636.00	−	11493.9i	−0.273552	−	0.473806i
$839$	−21112.0			−0.868733			−0.434367	−	0.900736i	$-0.643028\pi$
$839$	−21112.0			−0.868733			−0.434367	+	0.900736i	$0.643028\pi$
$840$		0			0
$841$	−21025.0			−0.862069
$842$	−16630.0	−	28804.0i	−0.680650	−	1.17892i
$843$		0			0
$844$	3560.00	−	6166.10i	0.145190	−	0.251476i
$845$	−7003.50	−	12130.4i	−0.285122	−	0.493845i
$846$		0			0
$847$	−4571.00	+	23751.6i	−0.185433	+	0.963536i
$848$	4848.00			0.196322
$849$		0			0
$850$	−1596.00	+	2764.35i	−0.0644028	+	0.111549i
$851$	−17410.5	+	30155.9i	−0.701321	+	1.21472i
$852$		0			0
$853$	−21238.0			−0.852492			−0.426246	−	0.904607i	$-0.640164\pi$
$853$	−21238.0			−0.852492			−0.426246	+	0.904607i	$0.640164\pi$
$854$	−14455.0	+	5007.36i	−0.579204	+	0.200642i
$855$		0			0
$856$	5484.00	+	9498.57i	0.218971	+	0.379269i
$857$	−17804.5	+	30838.3i	−0.709673	+	1.22919i	0.255305	+	0.966861i	$0.417824\pi$
$857$	−17804.5	+	30838.3i	−0.709673	+	1.22919i	−0.964978	+	0.262330i	$0.915509\pi$
$858$		0			0
$859$	−1088.50	−	1885.34i	−0.0432353	−	0.0748858i	0.843598	−	0.536975i	$-0.180433\pi$
$859$	−1088.50	−	1885.34i	−0.0432353	−	0.0748858i	−0.886833	+	0.462090i	$0.847100\pi$
$860$	−3472.00			−0.137668
$861$		0			0
$862$	9846.00			0.389044
$863$	−16123.5	−	27926.7i	−0.635980	−	1.10155i	−0.986307	−	0.164921i	$-0.947263\pi$
$863$	−16123.5	−	27926.7i	−0.635980	−	1.10155i	0.350327	−	0.936627i	$-0.386070\pi$
$864$		0			0
$865$	9873.50	−	17101.4i	0.388103	−	0.672214i
$866$	8974.00	+	15543.4i	0.352135	+	0.609916i
$867$		0			0
$868$	−2058.00	+	10693.7i	−0.0804759	+	0.418165i
$869$	−515.000			−0.0201038
$870$		0			0
$871$	2905.00	−	5031.61i	0.113011	−	0.195740i
$872$	13500.0	−	23382.7i	0.524275	−	0.908071i
$873$		0			0
$874$	−15582.0			−0.603054
$875$	19698.0	+	17059.0i	0.761045	+	0.659084i
$876$		0			0
$877$	−13815.5	−	23929.1i	−0.531946	−	0.921357i	−0.999305	−	0.0372891i	$-0.988128\pi$
$877$	−13815.5	−	23929.1i	−0.531946	−	0.921357i	0.467359	−	0.884068i	$-0.345206\pi$
$878$	−4179.00	+	7238.24i	−0.160631	+	0.278222i
$879$		0			0
$880$	−280.000	−	484.974i	−0.0107259	−	0.0185778i
$881$	−24402.0			−0.933172			−0.466586	−	0.884476i	$-0.654516\pi$
$881$	−24402.0			−0.933172			−0.466586	+	0.884476i	$0.654516\pi$
$882$		0			0
$883$	−19612.0			−0.747448			−0.373724	−	0.927540i	$-0.621919\pi$
$883$	−19612.0			−0.747448			−0.373724	+	0.927540i	$0.621919\pi$
$884$	−588.000	−	1018.45i	−0.0223717	−	0.0387489i
$885$		0			0
$886$	12927.0	−	22390.2i	0.490170	−	0.849000i
$887$	1130.50	+	1958.08i	0.0427942	+	0.0741218i	0.886629	−	0.462481i	$-0.153041\pi$
$887$	1130.50	+	1958.08i	0.0427942	+	0.0741218i	−0.843835	+	0.536603i	$0.819707\pi$
$888$		0			0
$889$	1008.00	+	872.954i	0.0380284	+	0.0329335i
$890$	4606.00			0.173476
$891$		0			0
$892$	−2800.00	+	4849.74i	−0.105102	+	0.182042i
$893$	12862.5	−	22278.5i	0.482001	−	0.834851i
$894$		0			0
$895$	−22771.0			−0.850448
$896$	1344.00	−	6983.63i	0.0501115	−	0.260387i
$897$		0			0
$898$	2826.00	+	4894.78i	0.105017	+	0.181894i
$899$	4263.00	−	7383.73i	0.158152	−	0.273928i
$900$		0			0
$901$	3181.50	+	5510.52i	0.117637	+	0.203754i
$902$	3500.00			0.129199
$903$		0			0
$904$	36912.0			1.35805
$905$	5537.00	+	9590.37i	0.203377	+	0.352259i
$906$		0			0
$907$	11916.5	−	20640.0i	0.436252	−	0.755611i	−0.561145	−	0.827718i	$-0.689639\pi$
$907$	11916.5	−	20640.0i	0.436252	−	0.755611i	0.997397	+	0.0721066i	$0.0229722\pi$
$908$	4410.00	+	7638.34i	0.161180	+	0.279171i
$909$		0			0
$910$	3430.00	−	1188.19i	0.124949	−	0.0432835i
$911$	−31824.0			−1.15738			−0.578692	−	0.815546i	$-0.696437\pi$
$911$	−31824.0			−1.15738			−0.578692	+	0.815546i	$0.696437\pi$
$912$		0			0
$913$	2730.00	−	4728.50i	0.0989593	−	0.171402i
$914$	8479.00	−	14686.1i	0.306849	−	0.531479i
$915$		0			0
$916$	−1148.00			−0.0414094
$917$	−7521.50	+	39082.9i	−0.270863	+	1.40745i
$918$		0			0
$919$	8409.50	+	14565.7i	0.301854	+	0.522826i	0.976556	−	0.215264i	$-0.0690612\pi$
$919$	8409.50	+	14565.7i	0.301854	+	0.522826i	−0.674702	+	0.738090i	$0.735728\pi$
$920$	13356.0	−	23133.3i	0.478624	−	0.829001i
$921$		0			0
$922$	−9338.00	−	16173.9i	−0.333547	−	0.577721i
$923$	−6048.00			−0.215680
$924$		0			0
$925$	−16644.0			−0.591623
$926$	−4016.00	−	6955.92i	−0.142520	−	0.246853i
$927$		0			0
$928$	−4640.00	+	8036.72i	−0.164133	+	0.284287i
$929$	899.500	+	1557.98i	0.0317671	+	0.0550222i	0.881472	−	0.472237i	$-0.156553\pi$
$929$	899.500	+	1557.98i	0.0317671	+	0.0550222i	−0.849705	+	0.527259i	$0.823220\pi$
$930$		0			0
$931$	13205.5	−	10396.6i	0.464869	−	0.365989i
$932$	18348.0			0.644859
$933$		0			0
$934$	5859.00	−	10148.1i	0.205259	−	0.355520i
$935$	367.500	−	636.529i	0.0128540	−	0.0222639i
$936$		0			0
$937$	14154.0			0.493480			0.246740	−	0.969082i	$-0.420641\pi$
$937$	14154.0			0.493480			0.246740	+	0.969082i	$0.420641\pi$
$938$	−11620.0	−	10063.2i	−0.404484	−	0.350294i
$939$		0			0
$940$	7350.00	+	12730.6i	0.255033	+	0.441729i
$941$	6023.50	−	10433.0i	0.208672	−	0.361431i	−0.742624	−	0.669708i	$-0.766419\pi$
$941$	6023.50	−	10433.0i	0.208672	−	0.361431i	0.951296	+	0.308277i	$0.0997525\pi$
$942$		0			0
$943$	27825.0	+	48194.3i	0.960877	+	1.66429i
$944$	−1680.00			−0.0579230
$945$		0			0
$946$	1240.00			0.0426172
$947$	−12189.5	−	21112.8i	−0.418274	−	0.724472i	0.577492	−	0.816396i	$-0.304031\pi$
$947$	−12189.5	−	21112.8i	−0.418274	−	0.724472i	−0.995766	+	0.0919245i	$0.970698\pi$
$948$		0			0
$949$	−7791.00	+	13494.4i	−0.266498	+	0.461588i
$950$	−3724.00	−	6450.16i	−0.127182	−	0.220285i
$951$		0			0
$952$	−8820.00	+	3055.34i	−0.300271	+	0.104017i
$953$	52330.0			1.77874			0.889368	−	0.457192i	$-0.151145\pi$
$953$	52330.0			1.77874			0.889368	+	0.457192i	$0.151145\pi$
$954$		0			0
$955$	−8949.50	+	15501.0i	−0.303245	+	0.525236i
$956$	−3336.00	+	5778.12i	−0.112860	+	0.195479i
$957$		0			0
$958$	13006.0			0.438627
$959$	−19687.5	+	6819.95i	−0.662922	+	0.229643i
$960$		0			0
$961$	4091.00	+	7085.82i	0.137323	+	0.237851i
$962$	−3066.00	+	5310.47i	−0.102757	+	0.177980i
$963$		0			0
$964$	−6818.00	−	11809.1i	−0.227794	−	0.394550i
$965$	2779.00			0.0927038
$966$		0			0
$967$	−12416.0			−0.412897			−0.206449	−	0.978457i	$-0.566191\pi$
$967$	−12416.0			−0.412897			−0.206449	+	0.978457i	$0.566191\pi$
$968$	15672.0	+	27144.7i	0.520369	+	0.901305i
$969$		0			0
$970$	6174.00	−	10693.7i	0.204366	−	0.353973i
$971$	18406.5	+	31881.0i	0.608334	+	1.05367i	0.991515	+	0.129993i	$0.0414954\pi$
$971$	18406.5	+	31881.0i	0.608334	+	1.05367i	−0.383181	+	0.923673i	$0.625171\pi$
$972$		0			0
$973$	3528.00	+	3055.34i	0.116241	+	0.100668i
$974$	32098.0			1.05594
$975$		0			0
$976$	−3304.00	+	5722.70i	−0.108359	+	0.187683i
$977$	17497.5	−	30306.6i	0.572973	−	0.992418i	−0.423286	−	0.905996i	$-0.639123\pi$
$977$	17497.5	−	30306.6i	0.572973	−	0.992418i	0.996259	−	0.0864221i	$-0.0275434\pi$
$978$		0			0
$979$	1645.00			0.0537022
$980$	1372.00	+	9505.49i	0.0447214	+	0.309839i
$981$		0			0
$982$	−8864.00	−	15352.9i	−0.288046	−	0.498911i
$983$	−7150.50	+	12385.0i	−0.232010	+	0.401853i	−0.958399	−	0.285430i	$-0.907863\pi$
$983$	−7150.50	+	12385.0i	−0.232010	+	0.401853i	0.726390	+	0.687283i	$0.241197\pi$
$984$		0			0
$985$	−10199.0	−	17665.2i	−0.329916	−	0.571431i
$986$	2436.00			0.0786796
$987$		0			0
$988$	2744.00			0.0883586
$989$	9858.00	+	17074.6i	0.316953	+	0.548978i
$990$		0			0
$991$	1332.50	−	2307.96i	0.0427127	−	0.0739805i	−0.843879	−	0.536534i	$-0.819733\pi$
$991$	1332.50	−	2307.96i	0.0427127	−	0.0739805i	0.886591	+	0.462553i	$0.153067\pi$
$992$	11760.0	+	20368.9i	0.376392	+	0.651929i
$993$		0			0
$994$	−3024.00	+	15713.2i	−0.0964944	+	0.501400i
$995$	−23373.0			−0.744697
$996$		0			0
$997$	−12435.5	+	21538.9i	−0.395021	+	0.684197i	−0.993104	−	0.117237i	$-0.962596\pi$
$997$	−12435.5	+	21538.9i	−0.395021	+	0.684197i	0.598083	+	0.801434i	$0.295929\pi$
$998$	−10211.0	+	17686.0i	−0.323871	+	0.560962i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.e.b.46.1		2
3.2	odd	2		7.4.c.a.4.1	yes	2
7.2	even	3	inner	63.4.e.b.37.1		2
7.3	odd	6		441.4.a.e.1.1		1
7.4	even	3		441.4.a.d.1.1		1
7.5	odd	6		441.4.e.k.226.1		2
7.6	odd	2		441.4.e.k.361.1		2
12.11	even	2		112.4.i.c.81.1		2
15.2	even	4		175.4.k.a.74.2		4
15.8	even	4		175.4.k.a.74.1		4
15.14	odd	2		175.4.e.a.151.1		2
21.2	odd	6		7.4.c.a.2.1	✓	2
21.5	even	6		49.4.c.a.30.1		2
21.11	odd	6		49.4.a.d.1.1		1
21.17	even	6		49.4.a.c.1.1		1
21.20	even	2		49.4.c.a.18.1		2
24.5	odd	2		448.4.i.f.193.1		2
24.11	even	2		448.4.i.a.193.1		2
84.11	even	6		784.4.a.b.1.1		1
84.23	even	6		112.4.i.c.65.1		2
84.59	odd	6		784.4.a.r.1.1		1
105.2	even	12		175.4.k.a.149.1		4
105.23	even	12		175.4.k.a.149.2		4
105.44	odd	6		175.4.e.a.51.1		2
105.59	even	6		1225.4.a.d.1.1		1
105.74	odd	6		1225.4.a.c.1.1		1
168.107	even	6		448.4.i.a.65.1		2
168.149	odd	6		448.4.i.f.65.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.4.c.a.2.1	✓	2	21.2	odd	6
7.4.c.a.4.1	yes	2	3.2	odd	2
49.4.a.c.1.1		1	21.17	even	6
49.4.a.d.1.1		1	21.11	odd	6
49.4.c.a.18.1		2	21.20	even	2
49.4.c.a.30.1		2	21.5	even	6
63.4.e.b.37.1		2	7.2	even	3	inner
63.4.e.b.46.1		2	1.1	even	1	trivial
112.4.i.c.65.1		2	84.23	even	6
112.4.i.c.81.1		2	12.11	even	2
175.4.e.a.51.1		2	105.44	odd	6
175.4.e.a.151.1		2	15.14	odd	2
175.4.k.a.74.1		4	15.8	even	4
175.4.k.a.74.2		4	15.2	even	4
175.4.k.a.149.1		4	105.2	even	12
175.4.k.a.149.2		4	105.23	even	12
441.4.a.d.1.1		1	7.4	even	3
441.4.a.e.1.1		1	7.3	odd	6
441.4.e.k.226.1		2	7.5	odd	6
441.4.e.k.361.1		2	7.6	odd	2
448.4.i.a.65.1		2	168.107	even	6
448.4.i.a.193.1		2	24.11	even	2
448.4.i.f.65.1		2	168.149	odd	6
448.4.i.f.193.1		2	24.5	odd	2
784.4.a.b.1.1		1	84.11	even	6
784.4.a.r.1.1		1	84.59	odd	6
1225.4.a.c.1.1		1	105.74	odd	6
1225.4.a.d.1.1		1	105.59	even	6

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(2.00000 - 3.46410i) q^{4} +(3.50000 + 6.06218i) q^{5} +(14.0000 + 12.1244i) q^{7} +24.0000 q^{8} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(2.00000 - 3.46410i) q^{4} +(3.50000 + 6.06218i) q^{5} +(14.0000 + 12.1244i) q^{7} +24.0000 q^{8} +(-7.00000 + 12.1244i) q^{10} +(-2.50000 + 4.33013i) q^{11} -14.0000 q^{13} +(-7.00000 + 36.3731i) q^{14} +(8.00000 + 13.8564i) q^{16} +(-10.5000 + 18.1865i) q^{17} +(-24.5000 - 42.4352i) q^{19} +28.0000 q^{20} -10.0000 q^{22} +(-79.5000 - 137.698i) q^{23} +(38.0000 - 65.8179i) q^{25} +(-14.0000 - 24.2487i) q^{26} +(70.0000 - 24.2487i) q^{28} -58.0000 q^{29} +(-73.5000 + 127.306i) q^{31} +(80.0000 - 138.564i) q^{32} -42.0000 q^{34} +(-24.5000 + 127.306i) q^{35} +(-109.500 - 189.660i) q^{37} +(49.0000 - 84.8705i) q^{38} +(84.0000 + 145.492i) q^{40} -350.000 q^{41} -124.000 q^{43} +(10.0000 + 17.3205i) q^{44} +(159.000 - 275.396i) q^{46} +(262.500 + 454.663i) q^{47} +(49.0000 + 339.482i) q^{49} +152.000 q^{50} +(-28.0000 + 48.4974i) q^{52} +(151.500 - 262.406i) q^{53} -35.0000 q^{55} +(336.000 + 290.985i) q^{56} +(-58.0000 - 100.459i) q^{58} +(-52.5000 + 90.9327i) q^{59} +(206.500 + 357.668i) q^{61} -294.000 q^{62} +448.000 q^{64} +(-49.0000 - 84.8705i) q^{65} +(-207.500 + 359.401i) q^{67} +(42.0000 + 72.7461i) q^{68} +(-245.000 + 84.8705i) q^{70} +432.000 q^{71} +(556.500 - 963.886i) q^{73} +(219.000 - 379.319i) q^{74} -196.000 q^{76} +(-87.5000 + 30.3109i) q^{77} +(51.5000 + 89.2006i) q^{79} +(-56.0000 + 96.9948i) q^{80} +(-350.000 - 606.218i) q^{82} -1092.00 q^{83} -147.000 q^{85} +(-124.000 - 214.774i) q^{86} +(-60.0000 + 103.923i) q^{88} +(-164.500 - 284.922i) q^{89} +(-196.000 - 169.741i) q^{91} -636.000 q^{92} +(-525.000 + 909.327i) q^{94} +(171.500 - 297.047i) q^{95} -882.000 q^{97} +(-539.000 + 424.352i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 4 q^{4} + 7 q^{5} + 28 q^{7} + 48 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 + 4 * q^4 + 7 * q^5 + 28 * q^7 + 48 * q^8	\( 2 q + 2 q^{2} + 4 q^{4} + 7 q^{5} + 28 q^{7} + 48 q^{8} - 14 q^{10} - 5 q^{11} - 28 q^{13} - 14 q^{14} + 16 q^{16} - 21 q^{17} - 49 q^{19} + 56 q^{20} - 20 q^{22} - 159 q^{23} + 76 q^{25} - 28 q^{26} + 140 q^{28} - 116 q^{29} - 147 q^{31} + 160 q^{32} - 84 q^{34} - 49 q^{35} - 219 q^{37} + 98 q^{38} + 168 q^{40} - 700 q^{41} - 248 q^{43} + 20 q^{44} + 318 q^{46} + 525 q^{47} + 98 q^{49} + 304 q^{50} - 56 q^{52} + 303 q^{53} - 70 q^{55} + 672 q^{56} - 116 q^{58} - 105 q^{59} + 413 q^{61} - 588 q^{62} + 896 q^{64} - 98 q^{65} - 415 q^{67} + 84 q^{68} - 490 q^{70} + 864 q^{71} + 1113 q^{73} + 438 q^{74} - 392 q^{76} - 175 q^{77} + 103 q^{79} - 112 q^{80} - 700 q^{82} - 2184 q^{83} - 294 q^{85} - 248 q^{86} - 120 q^{88} - 329 q^{89} - 392 q^{91} - 1272 q^{92} - 1050 q^{94} + 343 q^{95} - 1764 q^{97} - 1078 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + 4 * q^4 + 7 * q^5 + 28 * q^7 + 48 * q^8 - 14 * q^10 - 5 * q^11 - 28 * q^13 - 14 * q^14 + 16 * q^16 - 21 * q^17 - 49 * q^19 + 56 * q^20 - 20 * q^22 - 159 * q^23 + 76 * q^25 - 28 * q^26 + 140 * q^28 - 116 * q^29 - 147 * q^31 + 160 * q^32 - 84 * q^34 - 49 * q^35 - 219 * q^37 + 98 * q^38 + 168 * q^40 - 700 * q^41 - 248 * q^43 + 20 * q^44 + 318 * q^46 + 525 * q^47 + 98 * q^49 + 304 * q^50 - 56 * q^52 + 303 * q^53 - 70 * q^55 + 672 * q^56 - 116 * q^58 - 105 * q^59 + 413 * q^61 - 588 * q^62 + 896 * q^64 - 98 * q^65 - 415 * q^67 + 84 * q^68 - 490 * q^70 + 864 * q^71 + 1113 * q^73 + 438 * q^74 - 392 * q^76 - 175 * q^77 + 103 * q^79 - 112 * q^80 - 700 * q^82 - 2184 * q^83 - 294 * q^85 - 248 * q^86 - 120 * q^88 - 329 * q^89 - 392 * q^91 - 1272 * q^92 - 1050 * q^94 + 343 * q^95 - 1764 * q^97 - 1078 * q^98

Introduction

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