LMFDB - Embedded newform 275.3.f.c.243.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(232,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.232"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			243.6
Character	$\chi$	$=$	275.243
Dual form			275.3.f.c.232.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.302824 + 0.302824i) q^{2} +(2.81582 + 2.81582i) q^{3} +3.81659i q^{4} -1.70540 q^{6} +(-3.80626 + 3.80626i) q^{7} +(-2.36706 - 2.36706i) q^{8} +6.85771i q^{9} +3.31662 q^{11} +(-10.7469 + 10.7469i) q^{12} +(7.59483 + 7.59483i) q^{13} -2.30526i q^{14} -13.8328 q^{16} +(-11.0798 + 11.0798i) q^{17} +(-2.07668 - 2.07668i) q^{18} -15.5505i q^{19} -21.4355 q^{21} +(-1.00435 + 1.00435i) q^{22} +(18.8856 + 18.8856i) q^{23} -13.3304i q^{24} -4.59980 q^{26} +(6.03230 - 6.03230i) q^{27} +(-14.5270 - 14.5270i) q^{28} -45.1044i q^{29} -19.2109 q^{31} +(13.6571 - 13.6571i) q^{32} +(9.33903 + 9.33903i) q^{33} -6.71047i q^{34} -26.1731 q^{36} +(-37.8254 + 37.8254i) q^{37} +(4.70908 + 4.70908i) q^{38} +42.7714i q^{39} +21.9625 q^{41} +(6.49119 - 6.49119i) q^{42} +(28.4432 + 28.4432i) q^{43} +12.6582i q^{44} -11.4380 q^{46} +(21.0651 - 21.0651i) q^{47} +(-38.9506 - 38.9506i) q^{48} +20.0248i q^{49} -62.3976 q^{51} +(-28.9864 + 28.9864i) q^{52} +(24.2334 + 24.2334i) q^{53} +3.65346i q^{54} +18.0193 q^{56} +(43.7876 - 43.7876i) q^{57} +(13.6587 + 13.6587i) q^{58} +84.9457i q^{59} +104.172 q^{61} +(5.81752 - 5.81752i) q^{62} +(-26.1022 - 26.1022i) q^{63} -47.0597i q^{64} -5.65617 q^{66} +(-58.0492 + 58.0492i) q^{67} +(-42.2871 - 42.2871i) q^{68} +106.357i q^{69} +80.1429 q^{71} +(16.2326 - 16.2326i) q^{72} +(-28.1783 - 28.1783i) q^{73} -22.9089i q^{74} +59.3501 q^{76} +(-12.6239 + 12.6239i) q^{77} +(-12.9522 - 12.9522i) q^{78} -155.067i q^{79} +95.6912 q^{81} +(-6.65079 + 6.65079i) q^{82} +(7.52080 + 7.52080i) q^{83} -81.8106i q^{84} -17.2266 q^{86} +(127.006 - 127.006i) q^{87} +(-7.85063 - 7.85063i) q^{88} +116.115i q^{89} -57.8158 q^{91} +(-72.0786 + 72.0786i) q^{92} +(-54.0944 - 54.0944i) q^{93} +12.7580i q^{94} +76.9121 q^{96} +(123.890 - 123.890i) q^{97} +(-6.06399 - 6.06399i) q^{98} +22.7445i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{6} - 128 q^{16} - 88 q^{21} + 96 q^{26} + 360 q^{31} + 176 q^{36} - 152 q^{41} + 56 q^{46} - 512 q^{51} - 1048 q^{56} + 784 q^{61} - 440 q^{66} + 728 q^{71} + 1704 q^{76} - 568 q^{81} - 328 q^{86}+ \cdots + 1568 q^{96}+O(q^{100}) $ 24 * q - 8 * q^6 - 128 * q^16 - 88 * q^21 + 96 * q^26 + 360 * q^31 + 176 * q^36 - 152 * q^41 + 56 * q^46 - 512 * q^51 - 1048 * q^56 + 784 * q^61 - 440 * q^66 + 728 * q^71 + 1704 * q^76 - 568 * q^81 - 328 * q^86 - 968 * q^91 + 1568 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.302824	+	0.302824i	−0.151412	+	0.151412i	−0.778748	−	0.627336i	$-0.784145\pi$
$2$	−0.302824	+	0.302824i	−0.151412	+	0.151412i	0.627336	+	0.778748i	$0.284145\pi$
$3$	2.81582	+	2.81582i	0.938607	+	0.938607i	0.998222	−	0.0596140i	$-0.0189870\pi$
$3$	2.81582	+	2.81582i	0.938607	+	0.938607i	−0.0596140	+	0.998222i	$0.518987\pi$
$4$			3.81659i			0.954149i
$5$		0			0
$5$		0			0
$6$	−1.70540			−0.284233
$7$	−3.80626	+	3.80626i	−0.543751	+	0.543751i	−0.924626	−	0.380875i	$-0.875623\pi$
$7$	−3.80626	+	3.80626i	−0.543751	+	0.543751i	0.380875	+	0.924626i	$0.375623\pi$
$8$	−2.36706	−	2.36706i	−0.295882	−	0.295882i
$9$			6.85771i			0.761968i
$10$		0			0
$11$	3.31662			0.301511
$11$	3.31662			0.301511
$12$	−10.7469	+	10.7469i	−0.895571	+	0.895571i
$13$	7.59483	+	7.59483i	0.584218	+	0.584218i	0.936060	−	0.351842i	$-0.114444\pi$
$13$	7.59483	+	7.59483i	0.584218	+	0.584218i	−0.351842	+	0.936060i	$0.614444\pi$
$14$		−	2.30526i		−	0.164661i
$15$		0			0
$16$	−13.8328			−0.864548
$17$	−11.0798	+	11.0798i	−0.651754	+	0.651754i	−0.953415	−	0.301661i	$-0.902459\pi$
$17$	−11.0798	+	11.0798i	−0.651754	+	0.651754i	0.301661	+	0.953415i	$0.402459\pi$
$18$	−2.07668	−	2.07668i	−0.115371	−	0.115371i
$19$		−	15.5505i		−	0.818449i	−0.912434	−	0.409225i	$-0.865799\pi$
$19$		−	15.5505i		−	0.818449i	0.912434	−	0.409225i	$-0.134201\pi$
$20$		0			0
$21$	−21.4355			−1.02074
$22$	−1.00435	+	1.00435i	−0.0456525	+	0.0456525i
$23$	18.8856	+	18.8856i	0.821112	+	0.821112i	0.986268	−	0.165155i	$-0.0528125\pi$
$23$	18.8856	+	18.8856i	0.821112	+	0.821112i	−0.165155	+	0.986268i	$0.552813\pi$
$24$		−	13.3304i		−	0.555434i
$25$		0			0
$26$	−4.59980			−0.176915
$27$	6.03230	−	6.03230i	0.223419	−	0.223419i
$28$	−14.5270	−	14.5270i	−0.518820	−	0.518820i
$29$		−	45.1044i		−	1.55532i	−0.628683	−	0.777661i	$-0.716406\pi$
$29$		−	45.1044i		−	1.55532i	0.628683	−	0.777661i	$-0.283594\pi$
$30$		0			0
$31$	−19.2109			−0.619706			−0.309853	−	0.950785i	$-0.600280\pi$
$31$	−19.2109			−0.619706			−0.309853	+	0.950785i	$0.600280\pi$
$32$	13.6571	−	13.6571i	0.426785	−	0.426785i
$33$	9.33903	+	9.33903i	0.283001	+	0.283001i
$34$		−	6.71047i		−	0.197367i
$35$		0			0
$36$	−26.1731			−0.727031
$37$	−37.8254	+	37.8254i	−1.02231	+	1.02231i	−0.0225640	+	0.999745i	$0.507183\pi$
$37$	−37.8254	+	37.8254i	−1.02231	+	1.02231i	−0.999745	+	0.0225640i	$0.992817\pi$
$38$	4.70908	+	4.70908i	0.123923	+	0.123923i
$39$			42.7714i			1.09670i
$40$		0			0
$41$	21.9625			0.535671			0.267836	−	0.963465i	$-0.413692\pi$
$41$	21.9625			0.535671			0.267836	+	0.963465i	$0.413692\pi$
$42$	6.49119	−	6.49119i	0.154552	−	0.154552i
$43$	28.4432	+	28.4432i	0.661470	+	0.661470i	0.955726	−	0.294257i	$-0.0950720\pi$
$43$	28.4432	+	28.4432i	0.661470	+	0.661470i	−0.294257	+	0.955726i	$0.595072\pi$
$44$			12.6582i			0.287687i
$45$		0			0
$46$	−11.4380			−0.248653
$47$	21.0651	−	21.0651i	0.448193	−	0.448193i	−0.446561	−	0.894753i	$-0.647351\pi$
$47$	21.0651	−	21.0651i	0.448193	−	0.448193i	0.894753	+	0.446561i	$0.147351\pi$
$48$	−38.9506	−	38.9506i	−0.811472	−	0.811472i
$49$			20.0248i			0.408669i
$50$		0			0
$51$	−62.3976			−1.22348
$52$	−28.9864	+	28.9864i	−0.557431	+	0.557431i
$53$	24.2334	+	24.2334i	0.457235	+	0.457235i	0.897747	−	0.440512i	$-0.145203\pi$
$53$	24.2334	+	24.2334i	0.457235	+	0.457235i	−0.440512	+	0.897747i	$0.645203\pi$
$54$			3.65346i			0.0676566i
$55$		0			0
$56$	18.0193			0.321772
$57$	43.7876	−	43.7876i	0.768203	−	0.768203i
$58$	13.6587	+	13.6587i	0.235495	+	0.235495i
$59$			84.9457i			1.43976i	0.694100	+	0.719878i	$0.255802\pi$
$59$			84.9457i			1.43976i	−0.694100	+	0.719878i	$0.744198\pi$
$60$		0			0
$61$	104.172			1.70774			0.853871	−	0.520485i	$-0.174249\pi$
$61$	104.172			1.70774			0.853871	+	0.520485i	$0.174249\pi$
$62$	5.81752	−	5.81752i	0.0938310	−	0.0938310i
$63$	−26.1022	−	26.1022i	−0.414321	−	0.414321i
$64$		−	47.0597i		−	0.735308i
$65$		0			0
$66$	−5.65617			−0.0856995
$67$	−58.0492	+	58.0492i	−0.866405	+	0.866405i	−0.992072	−	0.125667i	$-0.959893\pi$
$67$	−58.0492	+	58.0492i	−0.866405	+	0.866405i	0.125667	+	0.992072i	$0.459893\pi$
$68$	−42.2871	−	42.2871i	−0.621870	−	0.621870i
$69$			106.357i			1.54140i
$70$		0			0
$71$	80.1429			1.12877			0.564387	−	0.825511i	$-0.309113\pi$
$71$	80.1429			1.12877			0.564387	+	0.825511i	$0.309113\pi$
$72$	16.2326	−	16.2326i	0.225453	−	0.225453i
$73$	−28.1783	−	28.1783i	−0.386004	−	0.386004i	0.487255	−	0.873260i	$-0.337998\pi$
$73$	−28.1783	−	28.1783i	−0.386004	−	0.386004i	−0.873260	+	0.487255i	$0.837998\pi$
$74$		−	22.9089i		−	0.309580i
$75$		0			0
$76$	59.3501			0.780922
$77$	−12.6239	+	12.6239i	−0.163947	+	0.163947i
$78$	−12.9522	−	12.9522i	−0.166054	−	0.166054i
$79$		−	155.067i		−	1.96287i	−0.191793	−	0.981435i	$-0.561430\pi$
$79$		−	155.067i		−	1.96287i	0.191793	−	0.981435i	$-0.438570\pi$
$80$		0			0
$81$	95.6912			1.18137
$82$	−6.65079	+	6.65079i	−0.0811071	+	0.0811071i
$83$	7.52080	+	7.52080i	0.0906120	+	0.0906120i	0.750960	−	0.660348i	$-0.229591\pi$
$83$	7.52080	+	7.52080i	0.0906120	+	0.0906120i	−0.660348	+	0.750960i	$0.729591\pi$
$84$		−	81.8106i		−	0.973936i
$85$		0			0
$86$	−17.2266			−0.200309
$87$	127.006	−	127.006i	1.45984	−	1.45984i
$88$	−7.85063	−	7.85063i	−0.0892118	−	0.0892118i
$89$			116.115i			1.30466i	0.757935	+	0.652330i	$0.226208\pi$
$89$			116.115i			1.30466i	−0.757935	+	0.652330i	$0.773792\pi$
$90$		0			0
$91$	−57.8158			−0.635338
$92$	−72.0786	+	72.0786i	−0.783463	+	0.783463i
$93$	−54.0944	−	54.0944i	−0.581660	−	0.581660i
$94$			12.7580i			0.135724i
$95$		0			0
$96$	76.9121			0.801167
$97$	123.890	−	123.890i	1.27722	−	1.27722i	0.335002	−	0.942217i	$-0.391263\pi$
$97$	123.890	−	123.890i	1.27722	−	1.27722i	0.942217	−	0.335002i	$-0.108737\pi$
$98$	−6.06399	−	6.06399i	−0.0618775	−	0.0618775i
$99$			22.7445i			0.229742i
$100$		0			0
$101$	−30.0346			−0.297372			−0.148686	−	0.988884i	$-0.547504\pi$
$101$	−30.0346			−0.297372			−0.148686	+	0.988884i	$0.547504\pi$
$102$	18.8955	−	18.8955i	0.185250	−	0.185250i
$103$	−31.0226	−	31.0226i	−0.301191	−	0.301191i	0.540289	−	0.841480i	$-0.318315\pi$
$103$	−31.0226	−	31.0226i	−0.301191	−	0.301191i	−0.841480	+	0.540289i	$0.818315\pi$
$104$		−	35.9548i		−	0.345719i
$105$		0			0
$106$	−14.6770			−0.138462
$107$	131.590	−	131.590i	1.22981	−	1.22981i	0.265774	−	0.964035i	$-0.414373\pi$
$107$	131.590	−	131.590i	1.22981	−	1.22981i	0.964035	−	0.265774i	$-0.0856273\pi$
$108$	23.0229	+	23.0229i	0.213175	+	0.213175i
$109$		−	31.2375i		−	0.286583i	−0.989681	−	0.143291i	$-0.954231\pi$
$109$		−	31.2375i		−	0.286583i	0.989681	−	0.143291i	$-0.0457686\pi$
$110$		0			0
$111$	−213.019			−1.91909
$112$	52.6511	−	52.6511i	0.470099	−	0.470099i
$113$	66.4722	+	66.4722i	0.588249	+	0.588249i	0.937157	−	0.348908i	$-0.113447\pi$
$113$	66.4722	+	66.4722i	0.588249	+	0.588249i	−0.348908	+	0.937157i	$0.613447\pi$
$114$			26.5199i			0.232630i
$115$		0			0
$116$	172.145			1.48401
$117$	−52.0832	+	52.0832i	−0.445155	+	0.445155i
$118$	−25.7236	−	25.7236i	−0.217997	−	0.217997i
$119$		−	84.3453i		−	0.708784i
$120$		0			0
$121$	11.0000			0.0909091
$122$	−31.5459	+	31.5459i	−0.258573	+	0.258573i
$123$	61.8426	+	61.8426i	0.502785	+	0.502785i
$124$		−	73.3201i		−	0.591291i
$125$		0			0
$126$	15.8088			0.125467
$127$	−6.13057	+	6.13057i	−0.0482722	+	0.0482722i	−0.730831	−	0.682559i	$-0.760867\pi$
$127$	−6.13057	+	6.13057i	−0.0482722	+	0.0482722i	0.682559	+	0.730831i	$0.260867\pi$
$128$	68.8793	+	68.8793i	0.538120	+	0.538120i
$129$			160.182i			1.24172i
$130$		0			0
$131$	−44.4226			−0.339104			−0.169552	−	0.985521i	$-0.554232\pi$
$131$	−44.4226			−0.339104			−0.169552	+	0.985521i	$0.554232\pi$
$132$	−35.6433	+	35.6433i	−0.270025	+	0.270025i
$133$	59.1894	+	59.1894i	0.445033	+	0.445033i
$134$		−	35.1574i		−	0.262369i
$135$		0			0
$136$	52.4531			0.385684
$137$	51.1158	−	51.1158i	0.373108	−	0.373108i	−0.495500	−	0.868608i	$-0.665015\pi$
$137$	51.1158	−	51.1158i	0.373108	−	0.373108i	0.868608	+	0.495500i	$0.165015\pi$
$138$	−32.2075	−	32.2075i	−0.233387	−	0.233387i
$139$		−	62.2687i		−	0.447976i	−0.974592	−	0.223988i	$-0.928092\pi$
$139$		−	62.2687i		−	0.447976i	0.974592	−	0.223988i	$-0.0719077\pi$
$140$		0			0
$141$	118.631			0.841354
$142$	−24.2692	+	24.2692i	−0.170910	+	0.170910i
$143$	25.1892	+	25.1892i	0.176148	+	0.176148i
$144$		−	94.8612i		−	0.658758i
$145$		0			0
$146$	17.0662			0.116892
$147$	−56.3862	+	56.3862i	−0.383580	+	0.383580i
$148$	−144.364	−	144.364i	−0.975435	−	0.975435i
$149$			278.133i			1.86667i	0.359012	+	0.933333i	$0.383114\pi$
$149$			278.133i			1.86667i	−0.359012	+	0.933333i	$0.616886\pi$
$150$		0			0
$151$	−133.179			−0.881977			−0.440989	−	0.897513i	$-0.645372\pi$
$151$	−133.179			−0.881977			−0.440989	+	0.897513i	$0.645372\pi$
$152$	−36.8090	+	36.8090i	−0.242164	+	0.242164i
$153$	−75.9822	−	75.9822i	−0.496615	−	0.496615i
$154$		−	7.64567i		−	0.0496472i
$155$		0			0
$156$	−163.241			−1.04642
$157$	−112.036	+	112.036i	−0.713605	+	0.713605i	−0.967288	−	0.253682i	$-0.918358\pi$
$157$	−112.036	+	112.036i	−0.713605	+	0.713605i	0.253682	+	0.967288i	$0.418358\pi$
$158$	46.9580	+	46.9580i	0.297203	+	0.297203i
$159$			136.474i			0.858328i
$160$		0			0
$161$	−143.767			−0.892962
$162$	−28.9776	+	28.9776i	−0.178874	+	0.178874i
$163$	−17.6650	−	17.6650i	−0.108374	−	0.108374i	0.650840	−	0.759215i	$-0.274417\pi$
$163$	−17.6650	−	17.6650i	−0.108374	−	0.108374i	−0.759215	+	0.650840i	$0.774417\pi$
$164$			83.8220i			0.511110i
$165$		0			0
$166$	−4.55496			−0.0274395
$167$	−81.8301	+	81.8301i	−0.490001	+	0.490001i	−0.908306	−	0.418306i	$-0.862624\pi$
$167$	−81.8301	+	81.8301i	−0.490001	+	0.490001i	0.418306	+	0.908306i	$0.362624\pi$
$168$	50.7390	+	50.7390i	0.302018	+	0.302018i
$169$		−	53.6371i		−	0.317379i
$170$		0			0
$171$	106.641			0.623632
$172$	−108.556	+	108.556i	−0.631141	+	0.631141i
$173$	−157.646	−	157.646i	−0.911250	−	0.911250i	0.0851209	−	0.996371i	$-0.472872\pi$
$173$	−157.646	−	157.646i	−0.911250	−	0.911250i	−0.996371	+	0.0851209i	$0.972872\pi$
$174$			76.9209i			0.442074i
$175$		0			0
$176$	−45.8781			−0.260671
$177$	−239.192	+	239.192i	−1.35137	+	1.35137i
$178$	−35.1624	−	35.1624i	−0.197541	−	0.197541i
$179$		−	182.066i		−	1.01713i	−0.861024	−	0.508565i	$-0.830176\pi$
$179$		−	182.066i		−	1.01713i	0.861024	−	0.508565i	$-0.169824\pi$
$180$		0			0
$181$	157.842			0.872053			0.436027	−	0.899934i	$-0.356385\pi$
$181$	157.842			0.872053			0.436027	+	0.899934i	$0.356385\pi$
$182$	17.5080	−	17.5080i	0.0961980	−	0.0961980i
$183$	293.331	+	293.331i	1.60290	+	1.60290i
$184$		−	89.4064i		−	0.485905i
$185$		0			0
$186$	32.7622			0.176141
$187$	−36.7476	+	36.7476i	−0.196511	+	0.196511i
$188$	80.3968	+	80.3968i	0.427643	+	0.427643i
$189$			45.9210i			0.242968i
$190$		0			0
$191$	−223.392			−1.16959			−0.584796	−	0.811181i	$-0.698825\pi$
$191$	−223.392			−1.16959			−0.584796	+	0.811181i	$0.698825\pi$
$192$	132.512	−	132.512i	0.690165	−	0.690165i
$193$	−173.204	−	173.204i	−0.897431	−	0.897431i	0.0977771	−	0.995208i	$-0.468827\pi$
$193$	−173.204	−	173.204i	−0.897431	−	0.897431i	−0.995208	+	0.0977771i	$0.968827\pi$
$194$			75.0340i			0.386773i
$195$		0			0
$196$	−76.4265			−0.389931
$197$	60.4829	−	60.4829i	0.307020	−	0.307020i	−0.536733	−	0.843752i	$-0.680342\pi$
$197$	60.4829	−	60.4829i	0.307020	−	0.307020i	0.843752	+	0.536733i	$0.180342\pi$
$198$	−6.88758	−	6.88758i	−0.0347857	−	0.0347857i
$199$		−	147.632i		−	0.741867i	−0.928659	−	0.370934i	$-0.879038\pi$
$199$		−	147.632i		−	0.741867i	0.928659	−	0.370934i	$-0.120962\pi$
$200$		0			0
$201$	−326.912			−1.62643
$202$	9.09519	−	9.09519i	0.0450257	−	0.0450257i
$203$	171.679	+	171.679i	0.845709	+	0.845709i
$204$		−	238.146i		−	1.16738i
$205$		0			0
$206$	18.7888			0.0912079
$207$	−129.512	+	129.512i	−0.625661	+	0.625661i
$208$	−105.058	−	105.058i	−0.505085	−	0.505085i
$209$		−	51.5753i		−	0.246772i
$210$		0			0
$211$	104.789			0.496631			0.248315	−	0.968679i	$-0.420123\pi$
$211$	104.789			0.496631			0.248315	+	0.968679i	$0.420123\pi$
$212$	−92.4892	+	92.4892i	−0.436270	+	0.436270i
$213$	225.668	+	225.668i	1.05947	+	1.05947i
$214$			79.6971i			0.372416i
$215$		0			0
$216$	−28.5576			−0.132211
$217$	73.1216	−	73.1216i	0.336966	−	0.336966i
$218$	9.45948	+	9.45948i	0.0433921	+	0.0433921i
$219$		−	158.690i		−	0.724613i
$220$		0			0
$221$	−168.299			−0.761532
$222$	64.5075	−	64.5075i	0.290574	−	0.290574i
$223$	−223.013	−	223.013i	−1.00006	−	1.00006i	−1.00000		5.68023e-5i	$-0.999982\pi$
$223$	−223.013	−	223.013i	−1.00006	−	1.00006i	−5.68023e−5	−	1.00000i	$-0.500018\pi$
$224$			103.965i			0.464130i
$225$		0			0
$226$	−40.2588			−0.178136
$227$	−155.479	+	155.479i	−0.684928	+	0.684928i	−0.961106	−	0.276179i	$-0.910932\pi$
$227$	−155.479	+	155.479i	−0.684928	+	0.684928i	0.276179	+	0.961106i	$0.410932\pi$
$228$	167.119	+	167.119i	0.732980	+	0.732980i
$229$		−	184.113i		−	0.803986i	−0.915643	−	0.401993i	$-0.868318\pi$
$229$		−	184.113i		−	0.803986i	0.915643	−	0.401993i	$-0.131682\pi$
$230$		0			0
$231$	−71.0935			−0.307764
$232$	−106.765	+	106.765i	−0.460192	+	0.460192i
$233$	127.989	+	127.989i	0.549309	+	0.549309i	0.926241	−	0.376932i	$-0.123021\pi$
$233$	127.989	+	127.989i	0.549309	+	0.549309i	−0.376932	+	0.926241i	$0.623021\pi$
$234$		−	31.5441i		−	0.134804i
$235$		0			0
$236$	−324.203			−1.37374
$237$	436.641	−	436.641i	1.84237	−	1.84237i
$238$	25.5418	+	25.5418i	0.107319	+	0.107319i
$239$			132.757i			0.555467i	0.960658	+	0.277734i	$0.0895833\pi$
$239$			132.757i			0.555467i	−0.960658	+	0.277734i	$0.910417\pi$
$240$		0			0
$241$	448.287			1.86011			0.930056	−	0.367417i	$-0.119758\pi$
$241$	448.287			1.86011			0.930056	+	0.367417i	$0.119758\pi$
$242$	−3.33107	+	3.33107i	−0.0137647	+	0.0137647i
$243$	215.159	+	215.159i	0.885427	+	0.885427i
$244$			397.583i			1.62944i
$245$		0			0
$246$	−37.4549			−0.152256
$247$	118.104	−	118.104i	0.478153	−	0.478153i
$248$	45.4732	+	45.4732i	0.183360	+	0.183360i
$249$			42.3545i			0.170098i
$250$		0			0
$251$	177.874			0.708661			0.354331	−	0.935120i	$-0.384709\pi$
$251$	177.874			0.708661			0.354331	+	0.935120i	$0.384709\pi$
$252$	99.6217	−	99.6217i	0.395324	−	0.395324i
$253$	62.6364	+	62.6364i	0.247575	+	0.247575i
$254$		−	3.71297i		−	0.0146180i
$255$		0			0
$256$	146.522			0.572352
$257$	278.615	−	278.615i	1.08411	−	1.08411i	0.0879840	−	0.996122i	$-0.471958\pi$
$257$	278.615	−	278.615i	1.08411	−	1.08411i	0.996122	−	0.0879840i	$-0.0280424\pi$
$258$	−48.5070	−	48.5070i	−0.188012	−	0.188012i
$259$		−	287.947i		−	1.11176i
$260$		0			0
$261$	309.313			1.18511
$262$	13.4523	−	13.4523i	0.0513445	−	0.0513445i
$263$	−165.383	−	165.383i	−0.628832	−	0.628832i	0.318942	−	0.947774i	$-0.396672\pi$
$263$	−165.383	−	165.383i	−0.628832	−	0.628832i	−0.947774	+	0.318942i	$0.896672\pi$
$264$		−	44.2120i		−	0.167470i
$265$		0			0
$266$	−35.8480			−0.134767
$267$	−326.959	+	326.959i	−1.22456	+	1.22456i
$268$	−221.550	−	221.550i	−0.826680	−	0.826680i
$269$		−	243.522i		−	0.905286i	−0.891692	−	0.452643i	$-0.850481\pi$
$269$		−	243.522i		−	0.905286i	0.891692	−	0.452643i	$-0.149519\pi$
$270$		0			0
$271$	−505.046			−1.86364			−0.931820	−	0.362921i	$-0.881779\pi$
$271$	−505.046			−1.86364			−0.931820	+	0.362921i	$0.881779\pi$
$272$	153.265	−	153.265i	0.563473	−	0.563473i
$273$	−162.799	−	162.799i	−0.596333	−	0.596333i
$274$			30.9582i			0.112986i
$275$		0			0
$276$	−405.921			−1.47073
$277$	−193.183	+	193.183i	−0.697412	+	0.697412i	−0.963852	−	0.266440i	$-0.914153\pi$
$277$	−193.183	+	193.183i	−0.697412	+	0.697412i	0.266440	+	0.963852i	$0.414153\pi$
$278$	18.8565	+	18.8565i	0.0678291	+	0.0678291i
$279$		−	131.743i		−	0.472196i
$280$		0			0
$281$	304.004			1.08186			0.540932	−	0.841066i	$-0.318072\pi$
$281$	304.004			1.08186			0.540932	+	0.841066i	$0.318072\pi$
$282$	−35.9244	+	35.9244i	−0.127391	+	0.127391i
$283$	−18.6918	−	18.6918i	−0.0660487	−	0.0660487i	0.673311	−	0.739360i	$-0.264872\pi$
$283$	−18.6918	−	18.6918i	−0.0660487	−	0.0660487i	−0.739360	+	0.673311i	$0.764872\pi$
$284$			305.873i			1.07702i
$285$		0			0
$286$	−15.2558			−0.0533420
$287$	−83.5951	+	83.5951i	−0.291272	+	0.291272i
$288$	93.6566	+	93.6566i	0.325197	+	0.325197i
$289$			43.4756i			0.150434i
$290$		0			0
$291$	697.706			2.39762
$292$	107.545	−	107.545i	0.368306	−	0.368306i
$293$	−289.135	−	289.135i	−0.986810	−	0.986810i	0.0131043	−	0.999914i	$-0.495829\pi$
$293$	−289.135	−	289.135i	−0.986810	−	0.986810i	−0.999914	+	0.0131043i	$0.995829\pi$
$294$		−	34.1502i		−	0.116157i
$295$		0			0
$296$	179.070			0.604966
$297$	20.0069	−	20.0069i	0.0673632	−	0.0673632i
$298$	−84.2255	−	84.2255i	−0.282636	−	0.282636i
$299$			286.866i			0.959417i
$300$		0			0
$301$	−216.524			−0.719350
$302$	40.3297	−	40.3297i	0.133542	−	0.133542i
$303$	−84.5720	−	84.5720i	−0.279115	−	0.279115i
$304$			215.107i			0.707589i
$305$		0			0
$306$	46.0185			0.150387
$307$	−168.264	+	168.264i	−0.548090	+	0.548090i	−0.925888	−	0.377798i	$-0.876681\pi$
$307$	−168.264	+	168.264i	−0.548090	+	0.548090i	0.377798	+	0.925888i	$0.376681\pi$
$308$	−48.1804	−	48.1804i	−0.156430	−	0.156430i
$309$		−	174.708i		−	0.565400i
$310$		0			0
$311$	38.3017			0.123156			0.0615782	−	0.998102i	$-0.480387\pi$
$311$	38.3017			0.123156			0.0615782	+	0.998102i	$0.480387\pi$
$312$	101.242	−	101.242i	0.324494	−	0.324494i
$313$	−98.7720	−	98.7720i	−0.315565	−	0.315565i	0.531496	−	0.847061i	$-0.321630\pi$
$313$	−98.7720	−	98.7720i	−0.315565	−	0.315565i	−0.847061	+	0.531496i	$0.821630\pi$
$314$		−	67.8545i		−	0.216097i
$315$		0			0
$316$	591.827			1.87287
$317$	−71.0273	+	71.0273i	−0.224061	+	0.224061i	−0.810206	−	0.586145i	$-0.800645\pi$
$317$	−71.0273	+	71.0273i	−0.224061	+	0.224061i	0.586145	+	0.810206i	$0.300645\pi$
$318$	−41.3277	−	41.3277i	−0.129961	−	0.129961i
$319$		−	149.594i		−	0.468947i
$320$		0			0
$321$	741.066			2.30862
$322$	43.5361	−	43.5361i	0.135205	−	0.135205i
$323$	172.297	+	172.297i	0.533427	+	0.533427i
$324$			365.215i			1.12721i
$325$		0			0
$326$	10.6988			0.0328184
$327$	87.9593	−	87.9593i	0.268989	−	0.268989i
$328$	−51.9865	−	51.9865i	−0.158495	−	0.158495i
$329$			160.358i			0.487411i
$330$		0			0
$331$	−471.212			−1.42360			−0.711801	−	0.702381i	$-0.752120\pi$
$331$	−471.212			−1.42360			−0.711801	+	0.702381i	$0.752120\pi$
$332$	−28.7038	+	28.7038i	−0.0864574	+	0.0864574i
$333$	−259.396	−	259.396i	−0.778967	−	0.778967i
$334$		−	49.5603i		−	0.148384i
$335$		0			0
$336$	296.512			0.882478
$337$	−223.876	+	223.876i	−0.664320	+	0.664320i	−0.956395	−	0.292075i	$-0.905654\pi$
$337$	−223.876	+	223.876i	−0.664320	+	0.664320i	0.292075	+	0.956395i	$0.405654\pi$
$338$	16.2426	+	16.2426i	0.0480551	+	0.0480551i
$339$			374.348i			1.10427i
$340$		0			0
$341$	−63.7153			−0.186848
$342$	−32.2935	+	32.2935i	−0.0944255	+	0.0944255i
$343$	−262.726	−	262.726i	−0.765966	−	0.765966i
$344$		−	134.653i		−	0.391434i
$345$		0			0
$346$	95.4782			0.275949
$347$	454.589	−	454.589i	1.31005	−	1.31005i	0.388682	−	0.921372i	$-0.372930\pi$
$347$	454.589	−	454.589i	1.31005	−	1.31005i	0.921372	−	0.388682i	$-0.127070\pi$
$348$	484.730	+	484.730i	1.39290	+	1.39290i
$349$			46.4703i			0.133153i	0.997781	+	0.0665764i	$0.0212076\pi$
$349$			46.4703i			0.133153i	−0.997781	+	0.0665764i	$0.978792\pi$
$350$		0			0
$351$	91.6286			0.261050
$352$	45.2956	−	45.2956i	0.128681	−	0.128681i
$353$	175.728	+	175.728i	0.497812	+	0.497812i	0.910756	−	0.412944i	$-0.135500\pi$
$353$	175.728	+	175.728i	0.497812	+	0.497812i	−0.412944	+	0.910756i	$0.635500\pi$
$354$		−	144.866i		−	0.409227i
$355$		0			0
$356$	−443.163			−1.24484
$357$	237.501	−	237.501i	0.665270	−	0.665270i
$358$	55.1341	+	55.1341i	0.154006	+	0.154006i
$359$			379.365i			1.05673i	0.849019	+	0.528363i	$0.177194\pi$
$359$			379.365i			1.05673i	−0.849019	+	0.528363i	$0.822806\pi$
$360$		0			0
$361$	119.181			0.330141
$362$	−47.7983	+	47.7983i	−0.132039	+	0.132039i
$363$	30.9740	+	30.9740i	0.0853280	+	0.0853280i
$364$		−	220.659i		−	0.606207i
$365$		0			0
$366$	−177.655			−0.485397
$367$	167.560	−	167.560i	0.456567	−	0.456567i	−0.440960	−	0.897527i	$-0.645362\pi$
$367$	167.560	−	167.560i	0.456567	−	0.456567i	0.897527	+	0.440960i	$0.145362\pi$
$368$	−261.240	−	261.240i	−0.709891	−	0.709891i
$369$			150.613i			0.408164i
$370$		0			0
$371$	−184.478			−0.497244
$372$	206.456	−	206.456i	0.554990	−	0.554990i
$373$	−158.449	−	158.449i	−0.424797	−	0.424797i	0.462055	−	0.886851i	$-0.347112\pi$
$373$	−158.449	−	158.449i	−0.424797	−	0.424797i	−0.886851	+	0.462055i	$0.847112\pi$
$374$		−	22.2561i		−	0.0595084i
$375$		0			0
$376$	−99.7244			−0.265224
$377$	342.560	−	342.560i	0.908647	−	0.908647i
$378$	−13.9060	−	13.9060i	−0.0367884	−	0.0367884i
$379$		−	432.559i		−	1.14132i	−0.821187	−	0.570659i	$-0.806688\pi$
$379$		−	432.559i		−	1.14132i	0.821187	−	0.570659i	$-0.193312\pi$
$380$		0			0
$381$	−34.5252			−0.0906173
$382$	67.6485	−	67.6485i	0.177090	−	0.177090i
$383$	−181.171	−	181.171i	−0.473031	−	0.473031i	0.429863	−	0.902894i	$-0.358562\pi$
$383$	−181.171	−	181.171i	−0.473031	−	0.473031i	−0.902894	+	0.429863i	$0.858562\pi$
$384$			387.904i			1.01017i
$385$		0			0
$386$	104.901			0.271764
$387$	−195.055	+	195.055i	−0.504019	+	0.504019i
$388$	472.839	+	472.839i	1.21866	+	1.21866i
$389$		−	629.098i		−	1.61722i	−0.588345	−	0.808610i	$-0.700220\pi$
$389$		−	629.098i		−	1.61722i	0.588345	−	0.808610i	$-0.299780\pi$
$390$		0			0
$391$	−418.497			−1.07033
$392$	47.3998	−	47.3998i	0.120918	−	0.120918i
$393$	−125.086	−	125.086i	−0.318286	−	0.318286i
$394$			36.6314i			0.0929730i
$395$		0			0
$396$	−86.8064			−0.219208
$397$	−116.971	+	116.971i	−0.294638	+	0.294638i	−0.838909	−	0.544271i	$-0.816806\pi$
$397$	−116.971	+	116.971i	−0.294638	+	0.294638i	0.544271	+	0.838909i	$0.316806\pi$
$398$	44.7064	+	44.7064i	0.112328	+	0.112328i
$399$			333.334i			0.835422i
$400$		0			0
$401$	−131.703			−0.328438			−0.164219	−	0.986424i	$-0.552510\pi$
$401$	−131.703			−0.328438			−0.164219	+	0.986424i	$0.552510\pi$
$402$	98.9970	−	98.9970i	0.246261	−	0.246261i
$403$	−145.903	−	145.903i	−0.362043	−	0.362043i
$404$		−	114.630i		−	0.283737i
$405$		0			0
$406$	−103.977			−0.256101
$407$	−125.453	+	125.453i	−0.308238	+	0.308238i
$408$	147.698	+	147.698i	0.362006	+	0.362006i
$409$		−	133.599i		−	0.326648i	−0.986572	−	0.163324i	$-0.947778\pi$
$409$		−	133.599i		−	0.326648i	0.986572	−	0.163324i	$-0.0522216\pi$
$410$		0			0
$411$	287.866			0.700404
$412$	118.401	−	118.401i	0.287381	−	0.287381i
$413$	−323.325	−	323.325i	−0.782870	−	0.782870i
$414$		−	78.4387i		−	0.189466i
$415$		0			0
$416$	207.447			0.498671
$417$	175.338	−	175.338i	0.420474	−	0.420474i
$418$	15.6183	+	15.6183i	0.0373642	+	0.0373642i
$419$		−	273.075i		−	0.651731i	−0.945416	−	0.325865i	$-0.894344\pi$
$419$		−	273.075i		−	0.651731i	0.945416	−	0.325865i	$-0.105656\pi$
$420$		0			0
$421$	−56.6994			−0.134678			−0.0673390	−	0.997730i	$-0.521451\pi$
$421$	−56.6994			−0.134678			−0.0673390	+	0.997730i	$0.521451\pi$
$422$	−31.7327	+	31.7327i	−0.0751960	+	0.0751960i
$423$	144.458	+	144.458i	0.341509	+	0.341509i
$424$		−	114.724i		−	0.270575i
$425$		0			0
$426$	−136.676			−0.320835
$427$	−396.507	+	396.507i	−0.928587	+	0.928587i
$428$	502.224	+	502.224i	1.17342	+	1.17342i
$429$			141.857i			0.330668i
$430$		0			0
$431$	−342.678			−0.795076			−0.397538	−	0.917586i	$-0.630135\pi$
$431$	−342.678			−0.795076			−0.397538	+	0.917586i	$0.630135\pi$
$432$	−83.4435	+	83.4435i	−0.193156	+	0.193156i
$433$	55.7092	+	55.7092i	0.128659	+	0.128659i	0.768504	−	0.639845i	$-0.221002\pi$
$433$	55.7092	+	55.7092i	0.128659	+	0.128659i	−0.639845	+	0.768504i	$0.721002\pi$
$434$			44.2860i			0.102041i
$435$		0			0
$436$	119.221			0.273443
$437$	293.681	−	293.681i	0.672039	−	0.672039i
$438$	48.0553	+	48.0553i	0.109715	+	0.109715i
$439$		−	86.0559i		−	0.196027i	−0.995185	−	0.0980136i	$-0.968751\pi$
$439$		−	86.0559i		−	0.196027i	0.995185	−	0.0980136i	$-0.0312489\pi$
$440$		0			0
$441$	−137.324			−0.311393
$442$	50.9649	−	50.9649i	0.115305	−	0.115305i
$443$	364.933	+	364.933i	0.823776	+	0.823776i	0.986647	−	0.162871i	$-0.0520756\pi$
$443$	364.933	+	364.933i	0.823776	+	0.823776i	−0.162871	+	0.986647i	$0.552076\pi$
$444$		−	813.009i		−	1.83110i
$445$		0			0
$446$	135.067			0.302842
$447$	−783.174	+	783.174i	−1.75207	+	1.75207i
$448$	179.121	+	179.121i	0.399824	+	0.399824i
$449$		−	400.375i		−	0.891704i	−0.895107	−	0.445852i	$-0.852901\pi$
$449$		−	400.375i		−	0.891704i	0.895107	−	0.445852i	$-0.147099\pi$
$450$		0			0
$451$	72.8414			0.161511
$452$	−253.697	+	253.697i	−0.561277	+	0.561277i
$453$	−375.007	−	375.007i	−0.827830	−	0.827830i
$454$		−	94.1654i		−	0.207413i
$455$		0			0
$456$	−207.295			−0.454595
$457$	107.160	−	107.160i	0.234486	−	0.234486i	−0.580076	−	0.814562i	$-0.696977\pi$
$457$	107.160	−	107.160i	0.234486	−	0.234486i	0.814562	+	0.580076i	$0.196977\pi$
$458$	55.7539	+	55.7539i	0.121733	+	0.121733i
$459$			133.674i			0.291228i
$460$		0			0
$461$	432.605			0.938405			0.469202	−	0.883091i	$-0.344542\pi$
$461$	432.605			0.938405			0.469202	+	0.883091i	$0.344542\pi$
$462$	21.5289	−	21.5289i	0.0465992	−	0.0465992i
$463$	279.700	+	279.700i	0.604103	+	0.604103i	0.941399	−	0.337295i	$-0.109512\pi$
$463$	279.700	+	279.700i	0.604103	+	0.604103i	−0.337295	+	0.941399i	$0.609512\pi$
$464$			623.918i			1.34465i
$465$		0			0
$466$	−77.5164			−0.166344
$467$	−455.242	+	455.242i	−0.974823	+	0.974823i	−0.999691	−	0.0248681i	$-0.992083\pi$
$467$	−455.242	+	455.242i	−0.974823	+	0.974823i	0.0248681	+	0.999691i	$0.492083\pi$
$468$	−198.780	−	198.780i	−0.424744	−	0.424744i
$469$		−	441.900i		−	0.942218i
$470$		0			0
$471$	−630.947			−1.33959
$472$	201.071	−	201.071i	0.425998	−	0.425998i
$473$	94.3354	+	94.3354i	0.199441	+	0.199441i
$474$			264.451i			0.557913i
$475$		0			0
$476$	321.912			0.676285
$477$	−166.186	+	166.186i	−0.348398	+	0.348398i
$478$	−40.2020	−	40.2020i	−0.0841045	−	0.0841045i
$479$			535.339i			1.11762i	0.829297	+	0.558809i	$0.188741\pi$
$479$			535.339i			1.11762i	−0.829297	+	0.558809i	$0.811259\pi$
$480$		0			0
$481$	−574.556			−1.19450
$482$	−135.752	+	135.752i	−0.281644	+	0.281644i
$483$	−404.822	−	404.822i	−0.838141	−	0.838141i
$484$			41.9825i			0.0867408i
$485$		0			0
$486$	−130.311			−0.268129
$487$	−465.777	+	465.777i	−0.956421	+	0.956421i	−0.999089	−	0.0426682i	$-0.986414\pi$
$487$	−465.777	+	465.777i	−0.956421	+	0.956421i	0.0426682	+	0.999089i	$0.486414\pi$
$488$	−246.582	−	246.582i	−0.505290	−	0.505290i
$489$		−	99.4831i		−	0.203442i
$490$		0			0
$491$	271.139			0.552217			0.276109	−	0.961126i	$-0.410955\pi$
$491$	271.139			0.552217			0.276109	+	0.961126i	$0.410955\pi$
$492$	−236.028	+	236.028i	−0.479732	+	0.479732i
$493$	499.748	+	499.748i	1.01369	+	1.01369i
$494$			71.5294i			0.144796i
$495$		0			0
$496$	265.740			0.535766
$497$	−305.045	+	305.045i	−0.613772	+	0.613772i
$498$	−12.8260	−	12.8260i	−0.0257550	−	0.0257550i
$499$			791.002i			1.58517i	0.609759	+	0.792587i	$0.291266\pi$
$499$			791.002i			1.58517i	−0.609759	+	0.792587i	$0.708734\pi$
$500$		0			0
$501$	−460.838			−0.919837
$502$	−53.8646	+	53.8646i	−0.107300	+	0.107300i
$503$	−555.020	−	555.020i	−1.10342	−	1.10342i	−0.993995	−	0.109424i	$-0.965099\pi$
$503$	−555.020	−	555.020i	−1.10342	−	1.10342i	−0.109424	−	0.993995i	$-0.534901\pi$
$504$			123.571i			0.245180i
$505$		0			0
$506$	−37.9357			−0.0749716
$507$	151.032	−	151.032i	0.297894	−	0.297894i
$508$	−23.3979	−	23.3979i	−0.0460589	−	0.0460589i
$509$		−	55.1248i		−	0.108300i	−0.998533	−	0.0541501i	$-0.982755\pi$
$509$		−	55.1248i		−	0.108300i	0.998533	−	0.0541501i	$-0.0172449\pi$
$510$		0			0
$511$	214.508			0.419781
$512$	−319.888	+	319.888i	−0.624781	+	0.624781i
$513$	−93.8055	−	93.8055i	−0.182857	−	0.182857i
$514$			168.743i			0.328294i
$515$		0			0
$516$	−611.350			−1.18479
$517$	69.8649	−	69.8649i	0.135135	−	0.135135i
$518$	87.1974	+	87.1974i	0.168335	+	0.168335i
$519$		−	887.807i		−	1.71061i
$520$		0			0
$521$	504.150			0.967659			0.483829	−	0.875162i	$-0.339246\pi$
$521$	504.150			0.967659			0.483829	+	0.875162i	$0.339246\pi$
$522$	−93.6674	+	93.6674i	−0.179440	+	0.179440i
$523$	267.008	+	267.008i	0.510531	+	0.510531i	0.914689	−	0.404158i	$-0.132435\pi$
$523$	267.008	+	267.008i	0.510531	+	0.510531i	−0.404158	+	0.914689i	$0.632435\pi$
$524$		−	169.543i		−	0.323556i
$525$		0			0
$526$	100.164			0.190426
$527$	212.853	−	212.853i	0.403895	−	0.403895i
$528$	−129.185	−	129.185i	−0.244668	−	0.244668i
$529$			184.331i			0.348451i
$530$		0			0
$531$	−582.533			−1.09705
$532$	−225.902	+	225.902i	−0.424628	+	0.424628i
$533$	166.802	+	166.802i	0.312949	+	0.312949i
$534$		−	198.022i		−	0.370828i
$535$		0			0
$536$	274.811			0.512707
$537$	512.666	−	512.666i	0.954686	−	0.954686i
$538$	73.7444	+	73.7444i	0.137071	+	0.137071i
$539$			66.4147i			0.123218i
$540$		0			0
$541$	268.056			0.495482			0.247741	−	0.968826i	$-0.420312\pi$
$541$	268.056			0.495482			0.247741	+	0.968826i	$0.420312\pi$
$542$	152.940	−	152.940i	0.282178	−	0.282178i
$543$	444.454	+	444.454i	0.818516	+	0.818516i
$544$			302.637i			0.556317i
$545$		0			0
$546$	98.5990			0.180584
$547$	−644.962	+	644.962i	−1.17909	+	1.17909i	−0.199112	+	0.979977i	$0.563806\pi$
$547$	−644.962	+	644.962i	−1.17909	+	1.17909i	−0.979977	+	0.199112i	$0.936194\pi$
$548$	195.088	+	195.088i	0.356000	+	0.356000i
$549$			714.383i			1.30124i
$550$		0			0
$551$	−701.397			−1.27295
$552$	251.753	−	251.753i	0.456074	−	0.456074i
$553$	590.225	+	590.225i	1.06731	+	1.06731i
$554$		−	117.001i		−	0.211193i
$555$		0			0
$556$	237.654			0.427436
$557$	371.791	−	371.791i	0.667488	−	0.667488i	−0.289646	−	0.957134i	$-0.593537\pi$
$557$	371.791	−	371.791i	0.667488	−	0.667488i	0.957134	+	0.289646i	$0.0935374\pi$
$558$	39.8949	+	39.8949i	0.0714962	+	0.0714962i
$559$			432.043i			0.772885i
$560$		0			0
$561$	−206.949			−0.368894
$562$	−92.0597	+	92.0597i	−0.163807	+	0.163807i
$563$	432.918	+	432.918i	0.768949	+	0.768949i	0.977921	−	0.208973i	$-0.0670120\pi$
$563$	432.918	+	432.918i	0.768949	+	0.768949i	−0.208973	+	0.977921i	$0.567012\pi$
$564$			452.766i			0.802777i
$565$		0			0
$566$	11.3207			0.0200012
$567$	−364.226	+	364.226i	−0.642373	+	0.642373i
$568$	−189.703	−	189.703i	−0.333984	−	0.333984i
$569$		−	659.519i		−	1.15908i	−0.814942	−	0.579542i	$-0.803231\pi$
$569$		−	659.519i		−	1.15908i	0.814942	−	0.579542i	$-0.196769\pi$
$570$		0			0
$571$	1.31160			0.00229702			0.00114851	−	0.999999i	$-0.499634\pi$
$571$	1.31160			0.00229702			0.00114851	+	0.999999i	$0.499634\pi$
$572$	−96.1370	+	96.1370i	−0.168072	+	0.168072i
$573$	−629.032	−	629.032i	−1.09779	−	1.09779i
$574$		−	50.6292i		−	0.0882042i
$575$		0			0
$576$	322.722			0.560281
$577$	336.434	−	336.434i	0.583075	−	0.583075i	−0.352672	−	0.935747i	$-0.614727\pi$
$577$	336.434	−	336.434i	0.583075	−	0.583075i	0.935747	+	0.352672i	$0.114727\pi$
$578$	−13.1655	−	13.1655i	−0.0227776	−	0.0227776i
$579$		−	975.425i		−	1.68467i
$580$		0			0
$581$	−57.2522			−0.0985409
$582$	−211.282	+	211.282i	−0.363028	+	0.363028i
$583$	80.3732	+	80.3732i	0.137861	+	0.137861i
$584$			133.399i			0.228423i
$585$		0			0
$586$	175.114			0.298830
$587$	−352.414	+	352.414i	−0.600365	+	0.600365i	−0.940409	−	0.340045i	$-0.889558\pi$
$587$	−352.414	+	352.414i	−0.600365	+	0.600365i	0.340045	+	0.940409i	$0.389558\pi$
$588$	−215.203	−	215.203i	−0.365992	−	0.365992i
$589$			298.739i			0.507198i
$590$		0			0
$591$	340.618			0.576342
$592$	523.231	−	523.231i	0.883836	−	0.883836i
$593$	632.485	+	632.485i	1.06659	+	1.06659i	0.997619	+	0.0689668i	$0.0219702\pi$
$593$	632.485	+	632.485i	1.06659	+	1.06659i	0.0689668	+	0.997619i	$0.478030\pi$
$594$			12.1171i			0.0203992i
$595$		0			0
$596$	−1061.52			−1.78108
$597$	415.704	−	415.704i	0.696322	−	0.696322i
$598$	−86.8699	−	86.8699i	−0.145267	−	0.145267i
$599$			99.4952i			0.166102i	0.996545	+	0.0830511i	$0.0264665\pi$
$599$			99.4952i			0.166102i	−0.996545	+	0.0830511i	$0.973534\pi$
$600$		0			0
$601$	−876.575			−1.45853			−0.729264	−	0.684233i	$-0.760137\pi$
$601$	−876.575			−1.45853			−0.729264	+	0.684233i	$0.760137\pi$
$602$	65.5689	−	65.5689i	0.108918	−	0.108918i
$603$	−398.084	−	398.084i	−0.660173	−	0.660173i
$604$		−	508.289i		−	0.841537i
$605$		0			0
$606$	51.2209			0.0845229
$607$	556.411	−	556.411i	0.916658	−	0.916658i	−0.0801271	−	0.996785i	$-0.525533\pi$
$607$	556.411	−	556.411i	0.916658	−	0.916658i	0.996785	+	0.0801271i	$0.0255326\pi$
$608$	−212.376	−	212.376i	−0.349302	−	0.349302i
$609$			966.835i			1.58758i
$610$		0			0
$611$	319.971			0.523685
$612$	289.993	−	289.993i	0.473845	−	0.473845i
$613$	−105.303	−	105.303i	−0.171783	−	0.171783i	0.615979	−	0.787762i	$-0.288760\pi$
$613$	−105.303	−	105.303i	−0.171783	−	0.171783i	−0.787762	+	0.615979i	$0.788760\pi$
$614$		−	101.909i		−	0.165975i
$615$		0			0
$616$	59.7631			0.0970180
$617$	582.669	−	582.669i	0.944359	−	0.944359i	−0.0541727	−	0.998532i	$-0.517252\pi$
$617$	582.669	−	582.669i	0.944359	−	0.944359i	0.998532	+	0.0541727i	$0.0172521\pi$
$618$	52.9060	+	52.9060i	0.0856084	+	0.0856084i
$619$		−	217.773i		−	0.351814i	−0.984407	−	0.175907i	$-0.943714\pi$
$619$		−	217.773i		−	0.351814i	0.984407	−	0.175907i	$-0.0562859\pi$
$620$		0			0
$621$	227.847			0.366903
$622$	−11.5987	+	11.5987i	−0.0186474	+	0.0186474i
$623$	−441.963	−	441.963i	−0.709411	−	0.709411i
$624$		−	591.647i		−	0.948152i
$625$		0			0
$626$	59.8211			0.0955609
$627$	145.227	−	145.227i	0.231622	−	0.231622i
$628$	−427.596	−	427.596i	−0.680885	−	0.680885i
$629$		−	838.198i		−	1.33259i
$630$		0			0
$631$	38.3765			0.0608186			0.0304093	−	0.999538i	$-0.490319\pi$
$631$	38.3765			0.0608186			0.0304093	+	0.999538i	$0.490319\pi$
$632$	−367.052	+	367.052i	−0.580778	+	0.580778i
$633$	295.068	+	295.068i	0.466142	+	0.466142i
$634$		−	43.0176i		−	0.0678511i
$635$		0			0
$636$	−520.867			−0.818973
$637$	−152.085	+	152.085i	−0.238752	+	0.238752i
$638$	45.3008	+	45.3008i	0.0710044	+	0.0710044i
$639$			549.597i			0.860089i
$640$		0			0
$641$	964.429			1.50457			0.752285	−	0.658838i	$-0.228952\pi$
$641$	964.429			1.50457			0.752285	+	0.658838i	$0.228952\pi$
$642$	−224.413	+	224.413i	−0.349553	+	0.349553i
$643$	346.789	+	346.789i	0.539330	+	0.539330i	0.923332	−	0.384002i	$-0.125454\pi$
$643$	346.789	+	346.789i	0.539330	+	0.539330i	−0.384002	+	0.923332i	$0.625454\pi$
$644$		−	548.700i		−	0.852018i
$645$		0			0
$646$	−104.351			−0.161535
$647$	−63.5374	+	63.5374i	−0.0982030	+	0.0982030i	−0.754501	−	0.656298i	$-0.772121\pi$
$647$	−63.5374	+	63.5374i	−0.0982030	+	0.0982030i	0.656298	+	0.754501i	$0.272121\pi$
$648$	−226.506	−	226.506i	−0.349547	−	0.349547i
$649$			281.733i			0.434103i
$650$		0			0
$651$	411.795			0.632557
$652$	67.4202	−	67.4202i	0.103405	−	0.103405i
$653$	−164.479	−	164.479i	−0.251881	−	0.251881i	0.569860	−	0.821742i	$-0.306997\pi$
$653$	−164.479	−	164.479i	−0.251881	−	0.251881i	−0.821742	+	0.569860i	$0.806997\pi$
$654$			53.2725i			0.0814564i
$655$		0			0
$656$	−303.803			−0.463114
$657$	193.239	−	193.239i	0.294123	−	0.294123i
$658$	−48.5604	−	48.5604i	−0.0738000	−	0.0738000i
$659$		−	1213.42i		−	1.84131i	−0.390375	−	0.920656i	$-0.627655\pi$
$659$		−	1213.42i		−	1.84131i	0.390375	−	0.920656i	$-0.372345\pi$
$660$		0			0
$661$	908.585			1.37456			0.687281	−	0.726392i	$-0.258804\pi$
$661$	908.585			1.37456			0.687281	+	0.726392i	$0.258804\pi$
$662$	142.695	−	142.695i	0.215551	−	0.215551i
$663$	−473.899	−	473.899i	−0.714780	−	0.714780i
$664$		−	35.6043i		−	0.0536209i
$665$		0			0
$666$	157.103			0.235890
$667$	851.822	−	851.822i	1.27709	−	1.27709i
$668$	−312.312	−	312.312i	−0.467534	−	0.467534i
$669$		−	1255.93i		−	1.87732i
$670$		0			0
$671$	345.500			0.514904
$672$	−292.747	+	292.747i	−0.435636	+	0.435636i
$673$	−1.17454	−	1.17454i	−0.00174523	−	0.00174523i	0.706234	−	0.707979i	$-0.250393\pi$
$673$	−1.17454	−	1.17454i	−0.00174523	−	0.00174523i	−0.707979	+	0.706234i	$0.750393\pi$
$674$		−	135.590i		−	0.201172i
$675$		0			0
$676$	204.711			0.302827
$677$	−199.496	+	199.496i	−0.294677	+	0.294677i	−0.838924	−	0.544248i	$-0.816815\pi$
$677$	−199.496	+	199.496i	−0.294677	+	0.294677i	0.544248	+	0.838924i	$0.316815\pi$
$678$	−113.362	−	113.362i	−0.167200	−	0.167200i
$679$			943.117i			1.38898i
$680$		0			0
$681$	−875.600			−1.28576
$682$	19.2945	−	19.2945i	0.0282911	−	0.0282911i
$683$	−246.276	−	246.276i	−0.360580	−	0.360580i	0.503446	−	0.864027i	$-0.332065\pi$
$683$	−246.276	−	246.276i	−0.360580	−	0.360580i	−0.864027	+	0.503446i	$0.832065\pi$
$684$			407.006i			0.595038i
$685$		0			0
$686$	159.120			0.231953
$687$	518.429	−	518.429i	0.754628	−	0.754628i
$688$	−393.448	−	393.448i	−0.571873	−	0.571873i
$689$			368.098i			0.534249i
$690$		0			0
$691$	686.637			0.993685			0.496843	−	0.867841i	$-0.334493\pi$
$691$	686.637			0.993685			0.496843	+	0.867841i	$0.334493\pi$
$692$	601.672	−	601.672i	0.869468	−	0.869468i
$693$	−86.5713	−	86.5713i	−0.124923	−	0.124923i
$694$			275.321i			0.396716i
$695$		0			0
$696$	−601.260			−0.863879
$697$	−243.341	+	243.341i	−0.349126	+	0.349126i
$698$	−14.0724	−	14.0724i	−0.0201610	−	0.0201610i
$699$			720.789i			1.03117i
$700$		0			0
$701$	599.940			0.855834			0.427917	−	0.903818i	$-0.359248\pi$
$701$	599.940			0.855834			0.427917	+	0.903818i	$0.359248\pi$
$702$	−27.7474	+	27.7474i	−0.0395262	+	0.0395262i
$703$	588.206	+	588.206i	0.836708	+	0.836708i
$704$		−	156.079i		−	0.221704i
$705$		0			0
$706$	−106.429			−0.150750
$707$	114.319	−	114.319i	0.161696	−	0.161696i
$708$	−912.899	−	912.899i	−1.28940	−	1.28940i
$709$			292.288i			0.412254i	0.978525	+	0.206127i	$0.0660859\pi$
$709$			292.288i			0.412254i	−0.978525	+	0.206127i	$0.933914\pi$
$710$		0			0
$711$	1063.40			1.49564
$712$	274.850	−	274.850i	0.386025	−	0.386025i
$713$	−362.809	−	362.809i	−0.508848	−	0.508848i
$714$			143.842i			0.201460i
$715$		0			0
$716$	694.873			0.970493
$717$	−373.819	+	373.819i	−0.521366	+	0.521366i
$718$	−114.881	−	114.881i	−0.160001	−	0.160001i
$719$			1112.74i			1.54762i	0.633416	+	0.773812i	$0.281652\pi$
$719$			1112.74i			1.54762i	−0.633416	+	0.773812i	$0.718348\pi$
$720$		0			0
$721$	236.160			0.327546
$722$	−36.0909	+	36.0909i	−0.0499873	+	0.0499873i
$723$	1262.30	+	1262.30i	1.74592	+	1.74592i
$724$			602.418i			0.832068i
$725$		0			0
$726$	−18.7594			−0.0258394
$727$	240.222	−	240.222i	0.330429	−	0.330429i	−0.522320	−	0.852749i	$-0.674933\pi$
$727$	240.222	−	240.222i	0.330429	−	0.330429i	0.852749	+	0.522320i	$0.174933\pi$
$728$	136.853	+	136.853i	0.187985	+	0.187985i
$729$			350.477i			0.480764i
$730$		0			0
$731$	−630.291			−0.862231
$732$	−1119.52	+	1119.52i	−1.52940	+	1.52940i
$733$	−149.864	−	149.864i	−0.204453	−	0.204453i	0.597452	−	0.801905i	$-0.296180\pi$
$733$	−149.864	−	149.864i	−0.204453	−	0.204453i	−0.801905	+	0.597452i	$0.796180\pi$
$734$			101.483i			0.138260i
$735$		0			0
$736$	515.845			0.700877
$737$	−192.527	+	192.527i	−0.261231	+	0.261231i
$738$	−45.6092	−	45.6092i	−0.0618011	−	0.0618011i
$739$		−	397.130i		−	0.537389i	−0.963225	−	0.268694i	$-0.913408\pi$
$739$		−	397.130i		−	0.537389i	0.963225	−	0.268694i	$-0.0865922\pi$
$740$		0			0
$741$	665.118			0.897595
$742$	55.8643	−	55.8643i	0.0752888	−	0.0752888i
$743$	194.137	+	194.137i	0.261288	+	0.261288i	0.825577	−	0.564289i	$-0.190850\pi$
$743$	194.137	+	194.137i	0.261288	+	0.261288i	−0.564289	+	0.825577i	$0.690850\pi$
$744$			256.089i			0.344206i
$745$		0			0
$746$	95.9645			0.128639
$747$	−51.5755	+	51.5755i	−0.0690435	+	0.0690435i
$748$	−140.251	−	140.251i	−0.187501	−	0.187501i
$749$			1001.73i			1.33742i
$750$		0			0
$751$	35.7328			0.0475803			0.0237901	−	0.999717i	$-0.492427\pi$
$751$	35.7328			0.0475803			0.0237901	+	0.999717i	$0.492427\pi$
$752$	−291.388	+	291.388i	−0.387485	+	0.387485i
$753$	500.861	+	500.861i	0.665155	+	0.665155i
$754$			207.471i			0.275161i
$755$		0			0
$756$	−175.262			−0.231828
$757$	301.624	−	301.624i	0.398447	−	0.398447i	−0.479238	−	0.877685i	$-0.659087\pi$
$757$	301.624	−	301.624i	0.398447	−	0.398447i	0.877685	+	0.479238i	$0.159087\pi$
$758$	130.990	+	130.990i	0.172809	+	0.172809i
$759$			352.746i			0.464751i
$760$		0			0
$761$	−249.741			−0.328175			−0.164087	−	0.986446i	$-0.552468\pi$
$761$	−249.741			−0.328175			−0.164087	+	0.986446i	$0.552468\pi$
$762$	10.4551	−	10.4551i	0.0137206	−	0.0137206i
$763$	118.898	+	118.898i	0.155830	+	0.155830i
$764$		−	852.597i		−	1.11596i
$765$		0			0
$766$	109.726			0.143245
$767$	−645.148	+	645.148i	−0.841132	+	0.841132i
$768$	412.580	+	412.580i	0.537214	+	0.537214i
$769$		−	44.3983i		−	0.0577351i	−0.999583	−	0.0288676i	$-0.990810\pi$
$769$		−	44.3983i		−	0.0577351i	0.999583	−	0.0288676i	$-0.00919011\pi$
$770$		0			0
$771$	1569.06			2.03510
$772$	661.050	−	661.050i	0.856283	−	0.856283i
$773$	−396.644	−	396.644i	−0.513122	−	0.513122i	0.402359	−	0.915482i	$-0.368190\pi$
$773$	−396.644	−	396.644i	−0.513122	−	0.513122i	−0.915482	+	0.402359i	$0.868190\pi$
$774$		−	118.135i		−	0.152629i
$775$		0			0
$776$	−586.510			−0.755812
$777$	810.807	−	810.807i	1.04351	−	1.04351i
$778$	190.506	+	190.506i	0.244867	+	0.244867i
$779$		−	341.529i		−	0.438420i
$780$		0			0
$781$	265.804			0.340338
$782$	126.731	−	126.731i	0.162060	−	0.162060i
$783$	−272.083	−	272.083i	−0.347488	−	0.347488i
$784$		−	276.998i		−	0.353314i
$785$		0			0
$786$	75.7583			0.0963847
$787$	−195.722	+	195.722i	−0.248693	+	0.248693i	−0.820434	−	0.571741i	$-0.806268\pi$
$787$	−195.722	+	195.722i	−0.248693	+	0.248693i	0.571741	+	0.820434i	$0.306268\pi$
$788$	230.839	+	230.839i	0.292942	+	0.292942i
$789$		−	931.378i		−	1.18045i
$790$		0			0
$791$	−506.021			−0.639723
$792$	53.8374	−	53.8374i	0.0679765	−	0.0679765i
$793$	791.171	+	791.171i	0.997693	+	0.997693i
$794$		−	70.8435i		−	0.0892236i
$795$		0			0
$796$	563.450			0.707851
$797$	−814.020	+	814.020i	−1.02136	+	1.02136i	−0.0215887	+	0.999767i	$0.506872\pi$
$797$	−814.020	+	814.020i	−1.02136	+	1.02136i	−0.999767	+	0.0215887i	$0.993128\pi$
$798$	−100.942	−	100.942i	−0.126493	−	0.126493i
$799$			466.794i			0.584223i
$800$		0			0
$801$	−796.282			−0.994109
$802$	39.8830	−	39.8830i	0.0497294	−	0.0497294i
$803$	−93.4569	−	93.4569i	−0.116385	−	0.116385i
$804$		−	1247.69i		−	1.55186i
$805$		0			0
$806$	88.3662			0.109635
$807$	685.714	−	685.714i	0.849708	−	0.849708i
$808$	71.0934	+	71.0934i	0.0879869	+	0.0879869i
$809$			1202.81i			1.48679i	0.668855	+	0.743393i	$0.266785\pi$
$809$			1202.81i			1.48679i	−0.668855	+	0.743393i	$0.733215\pi$
$810$		0			0
$811$	−1088.36			−1.34199			−0.670996	−	0.741461i	$-0.734133\pi$
$811$	−1088.36			−1.34199			−0.670996	+	0.741461i	$0.734133\pi$
$812$	−655.229	+	655.229i	−0.806932	+	0.806932i
$813$	−1422.12	−	1422.12i	−1.74923	−	1.74923i
$814$		−	75.9803i		−	0.0933419i
$815$		0			0
$816$	863.131			1.05776
$817$	442.307	−	442.307i	0.541379	−	0.541379i
$818$	40.4571	+	40.4571i	0.0494585	+	0.0494585i
$819$		−	396.484i		−	0.484108i
$820$		0			0
$821$	123.965			0.150993			0.0754964	−	0.997146i	$-0.475946\pi$
$821$	123.965			0.150993			0.0754964	+	0.997146i	$0.475946\pi$
$822$	−87.1728	+	87.1728i	−0.106050	+	0.106050i
$823$	1.88916	+	1.88916i	0.00229546	+	0.00229546i	0.708254	−	0.705958i	$-0.249483\pi$
$823$	1.88916	+	1.88916i	0.00229546	+	0.00229546i	−0.705958	+	0.708254i	$0.749483\pi$
$824$			146.865i			0.178234i
$825$		0			0
$826$	195.822			0.237072
$827$	717.551	−	717.551i	0.867656	−	0.867656i	−0.124557	−	0.992213i	$-0.539751\pi$
$827$	717.551	−	717.551i	0.867656	−	0.867656i	0.992213	+	0.124557i	$0.0397508\pi$
$828$	−494.294	−	494.294i	−0.596974	−	0.596974i
$829$			1275.35i			1.53842i	0.638997	+	0.769209i	$0.279350\pi$
$829$			1275.35i			1.53842i	−0.638997	+	0.769209i	$0.720650\pi$
$830$		0			0
$831$	−1087.94			−1.30919
$832$	357.410	−	357.410i	0.429580	−	0.429580i
$833$	−221.871	−	221.871i	−0.266351	−	0.266351i
$834$			106.193i			0.127330i
$835$		0			0
$836$	196.842			0.235457
$837$	−115.886	+	115.886i	−0.138454	+	0.138454i
$838$	82.6938	+	82.6938i	0.0986799	+	0.0986799i
$839$		−	509.291i		−	0.607022i	−0.952828	−	0.303511i	$-0.901841\pi$
$839$		−	509.291i		−	0.607022i	0.952828	−	0.303511i	$-0.0981588\pi$
$840$		0			0
$841$	−1193.40			−1.41903
$842$	17.1700	−	17.1700i	0.0203919	−	0.0203919i
$843$	856.021	+	856.021i	1.01545	+	1.01545i
$844$			399.938i			0.473860i
$845$		0			0
$846$	−87.4909			−0.103417
$847$	−41.8689	+	41.8689i	−0.0494319	+	0.0494319i
$848$	−335.216	−	335.216i	−0.395302	−	0.395302i
$849$		−	105.265i		−	0.123988i
$850$		0			0
$851$	−1428.71			−1.67886
$852$	−861.284	+	861.284i	−1.01090	+	1.01090i
$853$	933.655	+	933.655i	1.09455	+	1.09455i	0.995036	+	0.0995185i	$0.0317302\pi$
$853$	933.655	+	933.655i	1.09455	+	1.09455i	0.0995185	+	0.995036i	$0.468270\pi$
$854$		−	240.144i		−	0.281199i
$855$		0			0
$856$	−622.960			−0.727757
$857$	−934.650	+	934.650i	−1.09061	+	1.09061i	−0.0951436	+	0.995464i	$0.530331\pi$
$857$	−934.650	+	934.650i	−1.09061	+	1.09061i	−0.995464	+	0.0951436i	$0.969669\pi$
$858$	−42.9577	−	42.9577i	−0.0500672	−	0.0500672i
$859$		−	709.345i		−	0.825780i	−0.910781	−	0.412890i	$-0.864519\pi$
$859$		−	709.345i		−	0.825780i	0.910781	−	0.412890i	$-0.135481\pi$
$860$		0			0
$861$	−470.778			−0.546780
$862$	103.771	−	103.771i	0.120384	−	0.120384i
$863$	−835.152	−	835.152i	−0.967731	−	0.967731i	0.0317640	−	0.999495i	$-0.489888\pi$
$863$	−835.152	−	835.152i	−0.967731	−	0.967731i	−0.999495	+	0.0317640i	$0.989888\pi$
$864$		−	164.768i		−	0.190703i
$865$		0			0
$866$	−33.7402			−0.0389610
$867$	−122.419	+	122.419i	−0.141199	+	0.141199i
$868$	279.075	+	279.075i	0.321515	+	0.321515i
$869$		−	514.298i		−	0.591828i
$870$		0			0
$871$	−881.747			−1.01234
$872$	−73.9410	+	73.9410i	−0.0847947	+	0.0847947i
$873$	849.604	+	849.604i	0.973201	+	0.973201i
$874$			177.868i			0.203510i
$875$		0			0
$876$	605.656			0.691389
$877$	356.418	−	356.418i	0.406406	−	0.406406i	−0.474077	−	0.880483i	$-0.657218\pi$
$877$	356.418	−	356.418i	0.406406	−	0.406406i	0.880483	+	0.474077i	$0.157218\pi$
$878$	26.0598	+	26.0598i	0.0296809	+	0.0296809i
$879$		−	1628.31i		−	1.85245i
$880$		0			0
$881$	886.405			1.00613			0.503067	−	0.864247i	$-0.332205\pi$
$881$	886.405			1.00613			0.503067	+	0.864247i	$0.332205\pi$
$882$	41.5851	−	41.5851i	0.0471486	−	0.0471486i
$883$	205.857	+	205.857i	0.233134	+	0.233134i	0.814000	−	0.580866i	$-0.197286\pi$
$883$	205.857	+	205.857i	0.233134	+	0.233134i	−0.580866	+	0.814000i	$0.697286\pi$
$884$		−	642.328i		−	0.726615i
$885$		0			0
$886$	−221.021			−0.249459
$887$	332.542	−	332.542i	0.374906	−	0.374906i	−0.494354	−	0.869261i	$-0.664595\pi$
$887$	332.542	−	332.542i	0.374906	−	0.374906i	0.869261	+	0.494354i	$0.164595\pi$
$888$	504.229	+	504.229i	0.567825	+	0.567825i
$889$		−	46.6691i		−	0.0524962i
$890$		0			0
$891$	317.372			0.356197
$892$	851.149	−	851.149i	0.954203	−	0.954203i
$893$	−327.573	−	327.573i	−0.366823	−	0.366823i
$894$		−	474.328i		−	0.530568i
$895$		0			0
$896$	−524.345			−0.585207
$897$	−807.763	+	807.763i	−0.900516	+	0.900516i
$898$	121.243	+	121.243i	0.135015	+	0.135015i
$899$			866.494i			0.963842i
$900$		0			0
$901$	−537.004			−0.596009
$902$	−22.0582	+	22.0582i	−0.0244547	+	0.0244547i
$903$	−609.694	−	609.694i	−0.675187	−	0.675187i
$904$		−	314.687i		−	0.348105i
$905$		0			0
$906$	227.123			0.250687
$907$	−400.864	+	400.864i	−0.441967	+	0.441967i	−0.892673	−	0.450706i	$-0.851172\pi$
$907$	−400.864	+	400.864i	−0.441967	+	0.441967i	0.450706	+	0.892673i	$0.351172\pi$
$908$	−593.399	−	593.399i	−0.653523	−	0.653523i
$909$		−	205.968i		−	0.226588i
$910$		0			0
$911$	−16.0995			−0.0176723			−0.00883614	−	0.999961i	$-0.502813\pi$
$911$	−16.0995			−0.0176723			−0.00883614	+	0.999961i	$0.502813\pi$
$912$	−605.703	+	605.703i	−0.664148	+	0.664148i
$913$	24.9437	+	24.9437i	0.0273206	+	0.0273206i
$914$			64.9015i			0.0710082i
$915$		0			0
$916$	702.684			0.767123
$917$	169.084	−	169.084i	0.184388	−	0.184388i
$918$	−40.4796	−	40.4796i	−0.0440954	−	0.0440954i
$919$		−	641.788i		−	0.698355i	−0.937057	−	0.349178i	$-0.886461\pi$
$919$		−	641.788i		−	0.698355i	0.937057	−	0.349178i	$-0.113539\pi$
$920$		0			0
$921$	−947.601			−1.02888
$922$	−131.003	+	131.003i	−0.142086	+	0.142086i
$923$	608.672	+	608.672i	0.659449	+	0.659449i
$924$		−	271.335i		−	0.293653i
$925$		0			0
$926$	−169.400			−0.182937
$927$	212.744	−	212.744i	0.229498	−	0.229498i
$928$	−615.996	−	615.996i	−0.663789	−	0.663789i
$929$			553.220i			0.595500i	0.954644	+	0.297750i	$0.0962363\pi$
$929$			553.220i			0.595500i	−0.954644	+	0.297750i	$0.903764\pi$
$930$		0			0
$931$	311.396			0.334475
$932$	−488.482	+	488.482i	−0.524123	+	0.524123i
$933$	107.851	+	107.851i	0.115596	+	0.115596i
$934$		−	275.717i		−	0.295200i
$935$		0			0
$936$	246.568			0.263427
$937$	−868.178	+	868.178i	−0.926550	+	0.926550i	−0.997481	−	0.0709308i	$-0.977403\pi$
$937$	−868.178	+	868.178i	−0.926550	+	0.926550i	0.0709308	+	0.997481i	$0.477403\pi$
$938$	133.818	+	133.818i	0.142663	+	0.142663i
$939$		−	556.249i		−	0.592384i
$940$		0			0
$941$	−452.091			−0.480437			−0.240218	−	0.970719i	$-0.577219\pi$
$941$	−452.091			−0.480437			−0.240218	+	0.970719i	$0.577219\pi$
$942$	191.066	−	191.066i	0.202830	−	0.202830i
$943$	414.775	+	414.775i	0.439846	+	0.439846i
$944$		−	1175.03i		−	1.24474i
$945$		0			0
$946$	−57.1341			−0.0603955
$947$	871.051	−	871.051i	0.919801	−	0.919801i	−0.0772137	−	0.997015i	$-0.524602\pi$
$947$	871.051	−	871.051i	0.919801	−	0.919801i	0.997015	+	0.0772137i	$0.0246024\pi$
$948$	1666.48	+	1666.48i	1.75789	+	1.75789i
$949$		−	428.019i		−	0.451021i
$950$		0			0
$951$	−400.000			−0.420610
$952$	−199.650	+	199.650i	−0.209716	+	0.209716i
$953$	−1145.59	−	1145.59i	−1.20209	−	1.20209i	−0.973529	−	0.228564i	$-0.926597\pi$
$953$	−1145.59	−	1145.59i	−1.20209	−	1.20209i	−0.228564	−	0.973529i	$-0.573403\pi$
$954$		−	100.650i		−	0.105504i
$955$		0			0
$956$	−506.678			−0.529998
$957$	421.231	−	421.231i	0.440158	−	0.440158i
$958$	−162.114	−	162.114i	−0.169221	−	0.169221i
$959$			389.120i			0.405756i
$960$		0			0
$961$	−591.942			−0.615965
$962$	173.989	−	173.989i	0.180862	−	0.180862i
$963$	902.403	+	902.403i	0.937075	+	0.937075i
$964$			1710.93i			1.77482i
$965$		0			0
$966$	245.180			0.253809
$967$	−891.448	+	891.448i	−0.921870	+	0.921870i	−0.997162	−	0.0752914i	$-0.976011\pi$
$967$	−891.448	+	891.448i	−0.921870	+	0.921870i	0.0752914	+	0.997162i	$0.476011\pi$
$968$	−26.0376	−	26.0376i	−0.0268984	−	0.0268984i
$969$			970.316i			1.00136i
$970$		0			0
$971$	1424.02			1.46655			0.733276	−	0.679931i	$-0.237990\pi$
$971$	1424.02			1.46655			0.733276	+	0.679931i	$0.237990\pi$
$972$	−821.174	+	821.174i	−0.844829	+	0.844829i
$973$	237.011	+	237.011i	0.243588	+	0.243588i
$974$		−	282.097i		−	0.289628i
$975$		0			0
$976$	−1440.99			−1.47643
$977$	−362.424	+	362.424i	−0.370956	+	0.370956i	−0.867825	−	0.496869i	$-0.834483\pi$
$977$	−362.424	+	362.424i	−0.370956	+	0.370956i	0.496869	+	0.867825i	$0.334483\pi$
$978$	30.1259	+	30.1259i	0.0308036	+	0.0308036i
$979$			385.109i			0.393370i
$980$		0			0
$981$	214.218			0.218367
$982$	−82.1074	+	82.1074i	−0.0836124	+	0.0836124i
$983$	497.627	+	497.627i	0.506233	+	0.506233i	0.913368	−	0.407135i	$-0.133472\pi$
$983$	497.627	+	497.627i	0.506233	+	0.506233i	−0.407135	+	0.913368i	$0.633472\pi$
$984$		−	292.770i		−	0.297530i
$985$		0			0
$986$	−302.672			−0.306969
$987$	−451.540	+	451.540i	−0.457488	+	0.457488i
$988$	450.754	+	450.754i	0.456229	+	0.456229i
$989$			1074.33i			1.08628i
$990$		0			0
$991$	−1243.98			−1.25528			−0.627640	−	0.778504i	$-0.715979\pi$
$991$	−1243.98			−1.25528			−0.627640	+	0.778504i	$0.715979\pi$
$992$	−262.365	+	262.365i	−0.264481	+	0.264481i
$993$	−1326.85	−	1326.85i	−1.33620	−	1.33620i
$994$		−	184.750i		−	0.185865i
$995$		0			0
$996$	−161.650			−0.162299
$997$	−647.206	+	647.206i	−0.649153	+	0.649153i	−0.952788	−	0.303635i	$-0.901800\pi$
$997$	−647.206	+	647.206i	−0.649153	+	0.649153i	0.303635	+	0.952788i	$0.401800\pi$
$998$	−239.535	−	239.535i	−0.240015	−	0.240015i
$999$			456.349i			0.456806i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.f.c.243.6	yes	24
5.2	odd	4	inner	275.3.f.c.232.6	✓	24
5.3	odd	4	inner	275.3.f.c.232.7	yes	24
5.4	even	2	inner	275.3.f.c.243.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.f.c.232.6	✓	24	5.2	odd	4	inner
275.3.f.c.232.7	yes	24	5.3	odd	4	inner
275.3.f.c.243.6	yes	24	1.1	even	1	trivial
275.3.f.c.243.7	yes	24	5.4	even	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.302824 + 0.302824i) q^{2} +(2.81582 + 2.81582i) q^{3} +3.81659i q^{4} -1.70540 q^{6} +(-3.80626 + 3.80626i) q^{7} +(-2.36706 - 2.36706i) q^{8} +6.85771i q^{9} +3.31662 q^{11} +(-10.7469 + 10.7469i) q^{12} +(7.59483 + 7.59483i) q^{13} -2.30526i q^{14} -13.8328 q^{16} +(-11.0798 + 11.0798i) q^{17} +(-2.07668 - 2.07668i) q^{18} -15.5505i q^{19} -21.4355 q^{21} +(-1.00435 + 1.00435i) q^{22} +(18.8856 + 18.8856i) q^{23} -13.3304i q^{24} -4.59980 q^{26} +(6.03230 - 6.03230i) q^{27} +(-14.5270 - 14.5270i) q^{28} -45.1044i q^{29} -19.2109 q^{31} +(13.6571 - 13.6571i) q^{32} +(9.33903 + 9.33903i) q^{33} -6.71047i q^{34} -26.1731 q^{36} +(-37.8254 + 37.8254i) q^{37} +(4.70908 + 4.70908i) q^{38} +42.7714i q^{39} +21.9625 q^{41} +(6.49119 - 6.49119i) q^{42} +(28.4432 + 28.4432i) q^{43} +12.6582i q^{44} -11.4380 q^{46} +(21.0651 - 21.0651i) q^{47} +(-38.9506 - 38.9506i) q^{48} +20.0248i q^{49} -62.3976 q^{51} +(-28.9864 + 28.9864i) q^{52} +(24.2334 + 24.2334i) q^{53} +3.65346i q^{54} +18.0193 q^{56} +(43.7876 - 43.7876i) q^{57} +(13.6587 + 13.6587i) q^{58} +84.9457i q^{59} +104.172 q^{61} +(5.81752 - 5.81752i) q^{62} +(-26.1022 - 26.1022i) q^{63} -47.0597i q^{64} -5.65617 q^{66} +(-58.0492 + 58.0492i) q^{67} +(-42.2871 - 42.2871i) q^{68} +106.357i q^{69} +80.1429 q^{71} +(16.2326 - 16.2326i) q^{72} +(-28.1783 - 28.1783i) q^{73} -22.9089i q^{74} +59.3501 q^{76} +(-12.6239 + 12.6239i) q^{77} +(-12.9522 - 12.9522i) q^{78} -155.067i q^{79} +95.6912 q^{81} +(-6.65079 + 6.65079i) q^{82} +(7.52080 + 7.52080i) q^{83} -81.8106i q^{84} -17.2266 q^{86} +(127.006 - 127.006i) q^{87} +(-7.85063 - 7.85063i) q^{88} +116.115i q^{89} -57.8158 q^{91} +(-72.0786 + 72.0786i) q^{92} +(-54.0944 - 54.0944i) q^{93} +12.7580i q^{94} +76.9121 q^{96} +(123.890 - 123.890i) q^{97} +(-6.06399 - 6.06399i) q^{98} +22.7445i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{6} - 128 q^{16} - 88 q^{21} + 96 q^{26} + 360 q^{31} + 176 q^{36} - 152 q^{41} + 56 q^{46} - 512 q^{51} - 1048 q^{56} + 784 q^{61} - 440 q^{66} + 728 q^{71} + 1704 q^{76} - 568 q^{81} - 328 q^{86}+ \cdots + 1568 q^{96}+O(q^{100}) \) 24 * q - 8 * q^6 - 128 * q^16 - 88 * q^21 + 96 * q^26 + 360 * q^31 + 176 * q^36 - 152 * q^41 + 56 * q^46 - 512 * q^51 - 1048 * q^56 + 784 * q^61 - 440 * q^66 + 728 * q^71 + 1704 * q^76 - 568 * q^81 - 328 * q^86 - 968 * q^91 + 1568 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more