LMFDB - Embedded newform 234.4.l.b.127.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,4,Mod(127,234)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(234, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("234.127"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	234.l (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,16,0,0,18] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$13.8064469413$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 122x^{6} + 5305x^{4} + 97056x^{2} + 627264 $ x^8 + 122x^6 + 5305x^4 + 97056*x^2 + 627264
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.4
Root			$4.95620i$ of defining polynomial
Character	$\chi$	$=$	234.127
Dual form			234.4.l.b.199.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73205 - 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} +13.0327i q^{5} +(-3.11419 - 1.79798i) q^{7} -8.00000i q^{8} +(13.0327 + 22.5733i) q^{10} +(24.2951 - 14.0268i) q^{11} +(40.6883 + 23.2693i) q^{13} -7.19192 q^{14} +(-8.00000 - 13.8564i) q^{16} +(-57.7378 + 100.005i) q^{17} +(112.111 + 64.7274i) q^{19} +(45.1465 + 26.0654i) q^{20} +(28.0536 - 48.5903i) q^{22} +(87.4123 + 151.403i) q^{23} -44.8507 q^{25} +(93.7435 - 0.384640i) q^{26} +(-12.4568 + 7.19192i) q^{28} +(-109.596 - 189.825i) q^{29} +53.3357i q^{31} +(-27.7128 - 16.0000i) q^{32} +230.951i q^{34} +(23.4325 - 40.5863i) q^{35} +(109.784 - 63.3839i) q^{37} +258.910 q^{38} +104.261 q^{40} +(222.786 - 128.625i) q^{41} +(-14.2476 + 24.6775i) q^{43} -112.214i q^{44} +(302.805 + 174.825i) q^{46} +108.626i q^{47} +(-165.035 - 285.848i) q^{49} +(-77.6837 + 44.8507i) q^{50} +(161.984 - 94.4098i) q^{52} -215.231 q^{53} +(182.807 + 316.631i) q^{55} +(-14.3838 + 24.9135i) q^{56} +(-379.651 - 219.191i) q^{58} +(-339.576 - 196.055i) q^{59} +(112.459 - 194.785i) q^{61} +(53.3357 + 92.3802i) q^{62} -64.0000 q^{64} +(-303.262 + 530.278i) q^{65} +(-120.801 + 69.7442i) q^{67} +(230.951 + 400.019i) q^{68} -93.7299i q^{70} +(-550.285 - 317.707i) q^{71} +946.887i q^{73} +(126.768 - 219.568i) q^{74} +(448.445 - 258.910i) q^{76} -100.880 q^{77} -198.927 q^{79} +(180.586 - 104.261i) q^{80} +(257.251 - 445.571i) q^{82} -692.956i q^{83} +(-1303.33 - 752.478i) q^{85} +56.9903i q^{86} +(-112.214 - 194.361i) q^{88} +(701.782 - 405.174i) q^{89} +(-84.8734 - 145.622i) q^{91} +699.298 q^{92} +(108.626 + 188.146i) q^{94} +(-843.572 + 1461.11i) q^{95} +(-996.265 - 575.194i) q^{97} +(-571.696 - 330.069i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{4} + 18 q^{7} - 8 q^{10} + 18 q^{11} - 130 q^{13} - 80 q^{14} - 64 q^{16} - 112 q^{17} + 594 q^{19} - 72 q^{20} - 72 q^{22} + 230 q^{23} - 180 q^{25} + 184 q^{26} + 72 q^{28} - 32 q^{29} + 128 q^{35}+ \cdots - 4272 q^{98}+O(q^{100}) $ 8 * q + 16 * q^4 + 18 * q^7 - 8 * q^10 + 18 * q^11 - 130 * q^13 - 80 * q^14 - 64 * q^16 - 112 * q^17 + 594 * q^19 - 72 * q^20 - 72 * q^22 + 230 * q^23 - 180 * q^25 + 184 * q^26 + 72 * q^28 - 32 * q^29 + 128 * q^35 - 768 * q^37 + 576 * q^38 - 64 * q^40 + 564 * q^41 - 114 * q^43 + 576 * q^46 - 110 * q^49 - 1968 * q^50 - 104 * q^52 - 36 * q^53 + 1248 * q^55 - 160 * q^56 - 1848 * q^58 + 1110 * q^59 + 900 * q^61 - 1064 * q^62 - 512 * q^64 - 1870 * q^65 + 510 * q^67 + 448 * q^68 + 1470 * q^71 + 680 * q^74 + 2376 * q^76 - 2340 * q^77 + 784 * q^79 - 288 * q^80 + 704 * q^82 - 2898 * q^85 + 288 * q^88 + 4434 * q^89 - 886 * q^91 + 1840 * q^92 - 2568 * q^94 + 816 * q^95 + 1854 * q^97 - 4272 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$			13.0327i			1.16568i	0.812588	+	0.582839i	$0.198058\pi$
$5$			13.0327i			1.16568i	−0.812588	+	0.582839i	$0.801942\pi$
$6$		0			0
$7$	−3.11419	−	1.79798i	−0.168151	−	0.0970817i	0.413563	−	0.910476i	$-0.364284\pi$
$7$	−3.11419	−	1.79798i	−0.168151	−	0.0970817i	−0.581713	+	0.813394i	$0.697617\pi$
$8$		−	8.00000i		−	0.353553i
$9$		0			0
$10$	13.0327	+	22.5733i	0.412129	+	0.713829i
$11$	24.2951	−	14.0268i	0.665933	−	0.384477i	−0.128601	−	0.991696i	$-0.541049\pi$
$11$	24.2951	−	14.0268i	0.665933	−	0.384477i	0.794534	+	0.607220i	$0.207715\pi$
$12$		0			0
$13$	40.6883	+	23.2693i	0.868070	+	0.496442i
$13$	40.6883	+	23.2693i	0.868070	+	0.496442i
$14$	−7.19192			−0.137294
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−57.7378	+	100.005i	−0.823733	+	1.42675i	0.0791507	+	0.996863i	$0.474779\pi$
$17$	−57.7378	+	100.005i	−0.823733	+	1.42675i	−0.902884	+	0.429885i	$0.858554\pi$
$18$		0			0
$19$	112.111	+	64.7274i	1.35369	+	0.781552i	0.988764	−	0.149485i	$-0.0477616\pi$
$19$	112.111	+	64.7274i	1.35369	+	0.781552i	0.364924	+	0.931037i	$0.381095\pi$
$20$	45.1465	+	26.0654i	0.504753	+	0.291420i
$21$		0			0
$22$	28.0536	−	48.5903i	0.271866	−	0.470886i
$23$	87.4123	+	151.403i	0.792466	+	1.37259i	0.924436	+	0.381338i	$0.124537\pi$
$23$	87.4123	+	151.403i	0.792466	+	1.37259i	−0.131970	+	0.991254i	$0.542130\pi$
$24$		0			0
$25$	−44.8507			−0.358806
$26$	93.7435	−	0.384640i	0.707101	−	0.00290131i
$27$		0			0
$28$	−12.4568	+	7.19192i	−0.0840753	+	0.0485409i
$29$	−109.596	−	189.825i	−0.701773	−	1.21551i	−0.967844	−	0.251553i	$-0.919059\pi$
$29$	−109.596	−	189.825i	−0.701773	−	1.21551i	0.266071	−	0.963953i	$-0.414274\pi$
$30$		0			0
$31$			53.3357i			0.309012i	0.987992	+	0.154506i	$0.0493786\pi$
$31$			53.3357i			0.309012i	−0.987992	+	0.154506i	$0.950621\pi$
$32$	−27.7128	−	16.0000i	−0.153093	−	0.0883883i
$33$		0			0
$34$			230.951i			1.16493i
$35$	23.4325	−	40.5863i	0.113166	−	0.196009i
$36$		0			0
$37$	109.784	−	63.3839i	0.487794	−	0.281628i	−0.235865	−	0.971786i	$-0.575792\pi$
$37$	109.784	−	63.3839i	0.487794	−	0.281628i	0.723659	+	0.690158i	$0.242459\pi$
$38$	258.910			1.10528
$39$		0			0
$40$	104.261			0.412129
$41$	222.786	−	128.625i	0.848616	−	0.489949i	−0.0115677	−	0.999933i	$-0.503682\pi$
$41$	222.786	−	128.625i	0.848616	−	0.489949i	0.860184	+	0.509984i	$0.170349\pi$
$42$		0			0
$43$	−14.2476	+	24.6775i	−0.0505287	+	0.0875183i	−0.890184	−	0.455602i	$-0.849424\pi$
$43$	−14.2476	+	24.6775i	−0.0505287	+	0.0875183i	0.839655	+	0.543120i	$0.182757\pi$
$44$		−	112.214i		−	0.384477i
$45$		0			0
$46$	302.805	+	174.825i	0.970569	+	0.560358i
$47$			108.626i			0.337122i	0.985691	+	0.168561i	$0.0539120\pi$
$47$			108.626i			0.337122i	−0.985691	+	0.168561i	$0.946088\pi$
$48$		0			0
$49$	−165.035	−	285.848i	−0.481150	−	0.833377i
$50$	−77.6837	+	44.8507i	−0.219723	+	0.126857i
$51$		0			0
$52$	161.984	−	94.4098i	0.431983	−	0.251775i
$53$	−215.231			−0.557817			−0.278908	−	0.960318i	$-0.589973\pi$
$53$	−215.231			−0.557817			−0.278908	+	0.960318i	$0.589973\pi$
$54$		0			0
$55$	182.807	+	316.631i	0.448176	+	0.776264i
$56$	−14.3838	+	24.9135i	−0.0343236	+	0.0594502i
$57$		0			0
$58$	−379.651	−	219.191i	−0.859493	−	0.496228i
$59$	−339.576	−	196.055i	−0.749306	−	0.432612i	0.0761368	−	0.997097i	$-0.475741\pi$
$59$	−339.576	−	196.055i	−0.749306	−	0.432612i	−0.825443	+	0.564485i	$0.809075\pi$
$60$		0			0
$61$	112.459	−	194.785i	0.236048	−	0.408848i	−0.723529	−	0.690294i	$-0.757481\pi$
$61$	112.459	−	194.785i	0.236048	−	0.408848i	0.959577	+	0.281447i	$0.0908143\pi$
$62$	53.3357	+	92.3802i	0.109252	+	0.189231i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	−303.262	+	530.278i	−0.578692	+	1.01189i
$66$		0			0
$67$	−120.801	+	69.7442i	−0.220271	+	0.127173i	−0.606076	−	0.795407i	$-0.707257\pi$
$67$	−120.801	+	69.7442i	−0.220271	+	0.127173i	0.385805	+	0.922580i	$0.373924\pi$
$68$	230.951	+	400.019i	0.411867	+	0.713374i
$69$		0			0
$70$		−	93.7299i		−	0.160041i
$71$	−550.285	−	317.707i	−0.919815	−	0.531055i	−0.0362388	−	0.999343i	$-0.511538\pi$
$71$	−550.285	−	317.707i	−0.919815	−	0.531055i	−0.883576	+	0.468288i	$0.844871\pi$
$72$		0			0
$73$			946.887i			1.51815i	0.651005	+	0.759073i	$0.274348\pi$
$73$			946.887i			1.51815i	−0.651005	+	0.759073i	$0.725652\pi$
$74$	126.768	−	219.568i	0.199141	−	0.344923i
$75$		0			0
$76$	448.445	−	258.910i	0.676844	−	0.390776i
$77$	−100.880			−0.149303
$78$		0			0
$79$	−198.927			−0.283305			−0.141652	−	0.989916i	$-0.545242\pi$
$79$	−198.927			−0.283305			−0.141652	+	0.989916i	$0.545242\pi$
$80$	180.586	−	104.261i	0.252377	−	0.145710i
$81$		0			0
$82$	257.251	−	445.571i	0.346446	−	0.600062i
$83$		−	692.956i		−	0.916408i	−0.888847	−	0.458204i	$-0.848493\pi$
$83$		−	692.956i		−	0.916408i	0.888847	−	0.458204i	$-0.151507\pi$
$84$		0			0
$85$	−1303.33	−	752.478i	−1.66313	−	0.960208i
$86$			56.9903i			0.0714584i
$87$		0			0
$88$	−112.214	−	194.361i	−0.135933	−	0.235443i
$89$	701.782	−	405.174i	0.835829	−	0.482566i	−0.0200152	−	0.999800i	$-0.506371\pi$
$89$	701.782	−	405.174i	0.835829	−	0.482566i	0.855844	+	0.517234i	$0.173038\pi$
$90$		0			0
$91$	−84.8734	−	145.622i	−0.0977709	−	0.167751i
$92$	699.298			0.792466
$93$		0			0
$94$	108.626	+	188.146i	0.119191	+	0.206444i
$95$	−843.572	+	1461.11i	−0.911038	+	1.57796i
$96$		0			0
$97$	−996.265	−	575.194i	−1.04284	−	0.602083i	−0.122203	−	0.992505i	$-0.538996\pi$
$97$	−996.265	−	575.194i	−1.04284	−	0.602083i	−0.920636	+	0.390422i	$0.872329\pi$
$98$	−571.696	−	330.069i	−0.589286	−	0.340225i
$99$		0			0
$100$	−89.7014	+	155.367i	−0.0897014	+	0.155367i
$101$	−90.5627	−	156.859i	−0.0892211	−	0.154535i	0.817961	−	0.575274i	$-0.195104\pi$
$101$	−90.5627	−	156.859i	−0.0892211	−	0.154535i	−0.907182	+	0.420738i	$0.861771\pi$
$102$		0			0
$103$	1767.21			1.69057			0.845284	−	0.534318i	$-0.179431\pi$
$103$	1767.21			1.69057			0.845284	+	0.534318i	$0.179431\pi$
$104$	186.155	−	325.506i	0.175519	−	0.306909i
$105$		0			0
$106$	−372.792	+	215.231i	−0.341592	+	0.197218i
$107$	145.226	+	251.538i	0.131210	+	0.227263i	0.924143	−	0.382046i	$-0.124780\pi$
$107$	145.226	+	251.538i	0.131210	+	0.227263i	−0.792933	+	0.609309i	$0.791447\pi$
$108$		0			0
$109$		−	903.654i		−	0.794077i	−0.917802	−	0.397039i	$-0.870038\pi$
$109$		−	903.654i		−	0.794077i	0.917802	−	0.397039i	$-0.129962\pi$
$110$	633.262	+	365.614i	0.548901	+	0.316908i
$111$		0			0
$112$			57.5353i			0.0485409i
$113$	446.360	−	773.119i	0.371593	−	0.643619i	−0.618217	−	0.786007i	$-0.712145\pi$
$113$	446.360	−	773.119i	0.371593	−	0.643619i	0.989811	+	0.142389i	$0.0454782\pi$
$114$		0			0
$115$	−1973.18	+	1139.22i	−1.60000	+	0.923761i
$116$	−876.766			−0.701773
$117$		0			0
$118$	−784.218			−0.611806
$119$	359.613	−	207.623i	0.277022	−	0.159939i
$120$		0			0
$121$	−271.997	+	471.113i	−0.204356	+	0.353954i
$122$		−	449.837i		−	0.333823i
$123$		0			0
$124$	184.760	+	106.671i	0.133806	+	0.0772531i
$125$			1044.56i			0.747426i
$126$		0			0
$127$	−283.278	−	490.652i	−0.197928	−	0.342821i	0.749929	−	0.661519i	$-0.230088\pi$
$127$	−283.278	−	490.652i	−0.197928	−	0.342821i	−0.947856	+	0.318698i	$0.896755\pi$
$128$	−110.851	+	64.0000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	5.01288	+	1221.73i	0.00338199	+	0.824252i
$131$	−1998.74			−1.33306			−0.666528	−	0.745480i	$-0.732221\pi$
$131$	−1998.74			−1.33306			−0.666528	+	0.745480i	$0.732221\pi$
$132$		0			0
$133$	−232.757	−	403.147i	−0.151749	−	0.262837i
$134$	−139.488	+	241.601i	−0.0899252	+	0.155755i
$135$		0			0
$136$	800.038	+	461.902i	0.504431	+	0.291234i
$137$	−857.379	−	495.008i	−0.534678	−	0.308696i	0.208241	−	0.978077i	$-0.433226\pi$
$137$	−857.379	−	495.008i	−0.534678	−	0.308696i	−0.742919	+	0.669381i	$0.766559\pi$
$138$		0			0
$139$	−898.616	+	1556.45i	−0.548343	+	0.949757i	0.450046	+	0.893005i	$0.351408\pi$
$139$	−898.616	+	1556.45i	−0.548343	+	0.949757i	−0.998388	+	0.0567517i	$0.981926\pi$
$140$	−93.7299	−	162.345i	−0.0565830	−	0.0980047i
$141$		0			0
$142$	−1270.83			−0.751026
$143$	1314.92	−	5.39527i	0.768947	−	0.00315507i
$144$		0			0
$145$	2473.93	−	1428.33i	1.41689	−	0.818041i
$146$	946.887	+	1640.06i	0.536746	+	0.929671i
$147$		0			0
$148$		−	507.071i		−	0.281628i
$149$	367.740	+	212.315i	0.202191	+	0.116735i	0.597677	−	0.801737i	$-0.296090\pi$
$149$	367.740	+	212.315i	0.202191	+	0.116735i	−0.395486	+	0.918472i	$0.629424\pi$
$150$		0			0
$151$		−	3045.16i		−	1.64114i	−0.571547	−	0.820569i	$-0.693657\pi$
$151$		−	3045.16i		−	1.64114i	0.571547	−	0.820569i	$-0.306343\pi$
$152$	517.820	−	896.890i	0.276320	−	0.478601i
$153$		0			0
$154$	−174.729	+	100.880i	−0.0914288	+	0.0527865i
$155$	−695.108			−0.360209
$156$		0			0
$157$	1349.62			0.686061			0.343031	−	0.939324i	$-0.388546\pi$
$157$	1349.62			0.686061			0.343031	+	0.939324i	$0.388546\pi$
$158$	−344.552	+	198.927i	−0.173488	+	0.100163i
$159$		0			0
$160$	208.523	−	361.172i	0.103032	−	0.178457i
$161$		−	628.662i		−	0.307736i
$162$		0			0
$163$	−937.821	−	541.451i	−0.450649	−	0.260182i	0.257455	−	0.966290i	$-0.417116\pi$
$163$	−937.821	−	541.451i	−0.450649	−	0.260182i	−0.708104	+	0.706108i	$0.750449\pi$
$164$		−	1029.00i		−	0.489949i
$165$		0			0
$166$	−692.956	−	1200.24i	−0.323999	−	0.561183i
$167$	−740.513	+	427.535i	−0.343129	+	0.198106i	−0.661655	−	0.749808i	$-0.730146\pi$
$167$	−740.513	+	427.535i	−0.343129	+	0.198106i	0.318526	+	0.947914i	$0.396812\pi$
$168$		0			0
$169$	1114.08	+	1893.58i	0.507090	+	0.861893i
$170$	−3009.91			−1.35794
$171$		0			0
$172$	56.9903	+	98.7101i	0.0252644	+	0.0437591i
$173$	1825.83	−	3162.43i	0.802401	−	1.38980i	−0.115631	−	0.993292i	$-0.536889\pi$
$173$	1825.83	−	3162.43i	0.802401	−	1.38980i	0.918032	−	0.396507i	$-0.129778\pi$
$174$		0			0
$175$	139.674	+	80.6407i	0.0603334	+	0.0348335i
$176$	−388.722	−	224.429i	−0.166483	−	0.0961191i
$177$		0			0
$178$	810.349	−	1403.56i	0.341226	−	0.591020i
$179$	951.190	+	1647.51i	0.397180	+	0.687936i	0.993377	−	0.114902i	$-0.0366555\pi$
$179$	951.190	+	1647.51i	0.397180	+	0.687936i	−0.596197	+	0.802838i	$0.703322\pi$
$180$		0			0
$181$	2019.38			0.829277			0.414639	−	0.909986i	$-0.363908\pi$
$181$	2019.38			0.829277			0.414639	+	0.909986i	$0.363908\pi$
$182$	−292.627	−	167.351i	−0.119181	−	0.0681587i
$183$		0			0
$184$	1211.22	−	699.298i	0.485284	−	0.280179i
$185$	826.062	+	1430.78i	0.328288	+	0.568611i
$186$		0			0
$187$			3239.51i			1.26682i
$188$	376.292	+	217.252i	0.145978	+	0.0842805i
$189$		0			0
$190$			3374.29i			1.28840i
$191$	776.636	−	1345.17i	0.294217	−	0.509599i	−0.680586	−	0.732669i	$-0.738275\pi$
$191$	776.636	−	1345.17i	0.294217	−	0.509599i	0.974802	+	0.223070i	$0.0716079\pi$
$192$		0			0
$193$	520.344	−	300.421i	0.194068	−	0.112045i	−0.399817	−	0.916595i	$-0.630926\pi$
$193$	520.344	−	300.421i	0.194068	−	0.112045i	0.593886	+	0.804549i	$0.297593\pi$
$194$	−2300.77			−0.851474
$195$		0			0
$196$	−1320.28			−0.481150
$197$	1525.58	−	880.793i	0.551741	−	0.318548i	−0.198083	−	0.980185i	$-0.563472\pi$
$197$	1525.58	−	880.793i	0.551741	−	0.318548i	0.749824	+	0.661638i	$0.230138\pi$
$198$		0			0
$199$	1708.66	−	2959.49i	0.608662	−	1.05423i	−0.382799	−	0.923832i	$-0.625040\pi$
$199$	1708.66	−	2959.49i	0.608662	−	1.05423i	0.991461	−	0.130402i	$-0.0416269\pi$
$200$			358.806i			0.126857i
$201$		0			0
$202$	−313.718	−	181.125i	−0.109273	−	0.0630888i
$203$			788.203i			0.272517i
$204$		0			0
$205$	1676.33	+	2903.49i	0.571122	+	0.989213i
$206$	3060.90	−	1767.21i	1.03526	−	0.597706i
$207$		0			0
$208$	−3.07712	−	749.948i	−0.00102577	−	0.249998i
$209$	3631.68			1.20195
$210$		0			0
$211$	1314.36	+	2276.54i	0.428836	+	0.742766i	0.996770	−	0.0803079i	$-0.0255904\pi$
$211$	1314.36	+	2276.54i	0.428836	+	0.742766i	−0.567934	+	0.823074i	$0.692257\pi$
$212$	−430.463	+	745.583i	−0.139454	+	0.241542i
$213$		0			0
$214$	503.076	+	290.451i	0.160699	+	0.0927796i
$215$	−321.614	−	185.684i	−0.102018	−	0.0589002i
$216$		0			0
$217$	95.8965	−	166.098i	0.0299995	−	0.0519606i
$218$	−903.654	−	1565.18i	−0.280749	−	0.486271i
$219$		0			0
$220$	1462.46			0.448176
$221$	−4676.29	+	2725.50i	−1.42336	+	0.829580i
$222$		0			0
$223$	−2105.52	+	1215.62i	−0.632269	+	0.365040i	−0.781630	−	0.623742i	$-0.785612\pi$
$223$	−2105.52	+	1215.62i	−0.632269	+	0.365040i	0.149361	+	0.988783i	$0.452278\pi$
$224$	57.5353	+	99.6541i	0.0171618	+	0.0297251i
$225$		0			0
$226$		−	1785.44i		−	0.525512i
$227$	5662.09	+	3269.01i	1.65553	+	0.955823i	0.974738	+	0.223351i	$0.0716997\pi$
$227$	5662.09	+	3269.01i	1.65553	+	0.955823i	0.680797	+	0.732472i	$0.261634\pi$
$228$		0			0
$229$			2167.38i			0.625434i	0.949846	+	0.312717i	$0.101239\pi$
$229$			2167.38i			0.625434i	−0.949846	+	0.312717i	$0.898761\pi$
$230$	−2278.43	+	3946.36i	−0.653197	+	1.13137i
$231$		0			0
$232$	−1518.60	+	876.766i	−0.429746	+	0.248114i
$233$	3040.55			0.854906			0.427453	−	0.904038i	$-0.359411\pi$
$233$	3040.55			0.854906			0.427453	+	0.904038i	$0.359411\pi$
$234$		0			0
$235$	−1415.69			−0.392976
$236$	−1358.31	+	784.218i	−0.374653	+	0.216306i
$237$		0			0
$238$	415.245	−	719.226i	0.113094	−	0.195884i
$239$			4747.31i			1.28485i	0.766351	+	0.642423i	$0.222071\pi$
$239$			4747.31i			1.28485i	−0.766351	+	0.642423i	$0.777929\pi$
$240$		0			0
$241$	−2367.90	−	1367.11i	−0.632904	−	0.365408i	0.148972	−	0.988841i	$-0.452404\pi$
$241$	−2367.90	−	1367.11i	−0.632904	−	0.365408i	−0.781876	+	0.623434i	$0.785737\pi$
$242$			1087.99i			0.289002i
$243$		0			0
$244$	−449.837	−	779.141i	−0.118024	−	0.204424i
$245$	3725.37	−	2150.84i	0.971449	−	0.560866i
$246$		0			0
$247$	3055.45	+	5242.40i	0.787100	+	1.35047i
$248$	426.686			0.109252
$249$		0			0
$250$	1044.56	+	1809.23i	0.264255	+	0.457703i
$251$	−210.392	+	364.410i	−0.0529077	+	0.0916389i	−0.891266	−	0.453480i	$-0.850182\pi$
$251$	−210.392	+	364.410i	−0.0529077	+	0.0916389i	0.838359	+	0.545119i	$0.183516\pi$
$252$		0			0
$253$	4247.39	+	2452.23i	1.05546	+	0.609369i
$254$	−981.303	−	566.556i	−0.242411	−	0.139956i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−1744.07	−	3020.82i	−0.423316	−	0.733205i	0.572945	−	0.819594i	$-0.305801\pi$
$257$	−1744.07	−	3020.82i	−0.423316	−	0.733205i	−0.996262	+	0.0863885i	$0.972467\pi$
$258$		0			0
$259$	−455.852			−0.109364
$260$	1230.41	+	2111.08i	0.293488	+	0.503554i
$261$		0			0
$262$	−3461.91	+	1998.74i	−0.816327	+	0.471307i
$263$	−1664.65	−	2883.26i	−0.390291	−	0.676005i	0.602196	−	0.798348i	$-0.294292\pi$
$263$	−1664.65	−	2883.26i	−0.390291	−	0.676005i	−0.992488	+	0.122343i	$0.960959\pi$
$264$		0			0
$265$		−	2805.04i		−	0.650235i
$266$	−806.294	−	465.514i	−0.185854	−	0.107303i
$267$		0			0
$268$			557.954i			0.127173i
$269$	2898.78	−	5020.84i	0.657033	−	1.13801i	−0.324347	−	0.945938i	$-0.605145\pi$
$269$	2898.78	−	5020.84i	0.657033	−	1.13801i	0.981380	−	0.192076i	$-0.0615220\pi$
$270$		0			0
$271$	195.689	−	112.981i	0.0438645	−	0.0253252i	−0.477907	−	0.878410i	$-0.658605\pi$
$271$	195.689	−	112.981i	0.0438645	−	0.0253252i	0.521772	+	0.853085i	$0.325271\pi$
$272$	1847.61			0.411867
$273$		0			0
$274$	−1980.03			−0.436563
$275$	−1089.65	+	629.113i	−0.238941	+	0.137952i
$276$		0			0
$277$	3071.46	−	5319.92i	0.666232	−	1.15395i	−0.312718	−	0.949846i	$-0.601240\pi$
$277$	3071.46	−	5319.92i	0.666232	−	1.15395i	0.978950	−	0.204101i	$-0.0654271\pi$
$278$			3594.46i			0.775473i
$279$		0			0
$280$	−324.690	−	187.460i	−0.0692998	−	0.0400103i
$281$		−	2631.82i		−	0.558724i	−0.960186	−	0.279362i	$-0.909877\pi$
$281$		−	2631.82i		−	0.558724i	0.960186	−	0.279362i	$-0.0901229\pi$
$282$		0			0
$283$	−1634.26	−	2830.62i	−0.343275	−	0.594569i	0.641764	−	0.766902i	$-0.278203\pi$
$283$	−1634.26	−	2830.62i	−0.343275	−	0.594569i	−0.985039	+	0.172333i	$0.944870\pi$
$284$	−2201.14	+	1270.83i	−0.459907	+	0.265528i
$285$		0			0
$286$	2272.12	−	1324.27i	0.469766	−	0.273796i
$287$	−925.062			−0.190260
$288$		0			0
$289$	−4210.80	−	7293.31i	−0.857072	−	1.48449i
$290$	2856.65	−	4947.86i	0.578443	−	1.00189i
$291$		0			0
$292$	3280.11	+	1893.77i	0.657377	+	0.379537i
$293$	−6160.79	−	3556.93i	−1.22839	−	0.709209i	−0.261694	−	0.965151i	$-0.584281\pi$
$293$	−6160.79	−	3556.93i	−1.22839	−	0.709209i	−0.966692	+	0.255942i	$0.917614\pi$
$294$		0			0
$295$	2555.12	−	4425.59i	0.504287	−	0.873450i
$296$	−507.071	−	878.273i	−0.0995706	−	0.172461i
$297$		0			0
$298$	849.260			0.165088
$299$	33.6222	+	8194.34i	0.00650309	+	1.58492i
$300$		0			0
$301$	88.7393	−	51.2337i	0.0169929	−	0.00981083i
$302$	−3045.16	−	5274.38i	−0.580230	−	1.00499i
$303$		0			0
$304$		−	2071.28i		−	0.390776i
$305$	2538.57	+	1465.65i	0.476585	+	0.275156i
$306$		0			0
$307$			5015.75i			0.932456i	0.884665	+	0.466228i	$0.154387\pi$
$307$			5015.75i			0.932456i	−0.884665	+	0.466228i	$0.845613\pi$
$308$	−201.759	+	349.457i	−0.0373257	+	0.0646499i
$309$		0			0
$310$	−1203.96	+	695.108i	−0.220582	+	0.127353i
$311$	−563.698			−0.102779			−0.0513897	−	0.998679i	$-0.516365\pi$
$311$	−563.698			−0.102779			−0.0513897	+	0.998679i	$0.516365\pi$
$312$		0			0
$313$	−1516.36			−0.273832			−0.136916	−	0.990583i	$-0.543719\pi$
$313$	−1516.36			−0.273832			−0.136916	+	0.990583i	$0.543719\pi$
$314$	2337.62	−	1349.62i	0.420125	−	0.242559i
$315$		0			0
$316$	−397.855	+	689.105i	−0.0708262	+	0.122675i
$317$		−	2358.19i		−	0.417820i	−0.977935	−	0.208910i	$-0.933008\pi$
$317$		−	2358.19i		−	0.417820i	0.977935	−	0.208910i	$-0.0669915\pi$
$318$		0			0
$319$	−5325.29	−	3074.56i	−0.934667	−	0.539630i
$320$		−	834.091i		−	0.145710i
$321$		0			0
$322$	−628.662	−	1088.87i	−0.108801	−	0.188449i
$323$	−12946.1	+	7474.43i	−2.23016	+	1.28758i
$324$		0			0
$325$	−1824.90	−	1043.65i	−0.311468	−	0.178126i
$326$	−2165.80			−0.367953
$327$		0			0
$328$	−1029.00	−	1782.28i	−0.173223	−	0.300031i
$329$	195.307	−	338.282i	0.0327284	−	0.0566873i
$330$		0			0
$331$	−1472.43	−	850.110i	−0.244508	−	0.141167i	0.372739	−	0.927936i	$-0.378419\pi$
$331$	−1472.43	−	850.110i	−0.244508	−	0.141167i	−0.617247	+	0.786769i	$0.711752\pi$
$332$	−2400.47	−	1385.91i	−0.396816	−	0.229102i
$333$		0			0
$334$	−855.071	+	1481.03i	−0.140082	+	0.242629i
$335$	−908.954	−	1574.36i	−0.148243	−	0.256765i
$336$		0			0
$337$	−11512.3			−1.86087			−0.930437	−	0.366453i	$-0.880572\pi$
$337$	−11512.3			−1.86087			−0.930437	+	0.366453i	$0.880572\pi$
$338$	3823.22	+	2165.70i	0.615253	+	0.348516i
$339$		0			0
$340$	−5213.32	+	3009.91i	−0.831564	+	0.480104i
$341$	748.130	+	1295.80i	0.118808	+	0.205781i
$342$		0			0
$343$			2420.33i			0.381007i
$344$	197.420	+	113.981i	0.0309424	+	0.0178646i
$345$		0			0
$346$		−	7303.32i		−	1.13477i
$347$	−90.7510	+	157.185i	−0.0140397	+	0.0243174i	−0.872960	−	0.487792i	$-0.837802\pi$
$347$	−90.7510	+	157.185i	−0.0140397	+	0.0243174i	0.858920	+	0.512109i	$0.171136\pi$
$348$		0			0
$349$	−4504.64	+	2600.76i	−0.690911	+	0.398898i	−0.803953	−	0.594693i	$-0.797274\pi$
$349$	−4504.64	+	2600.76i	−0.690911	+	0.398898i	0.113042	+	0.993590i	$0.463940\pi$
$350$	322.563			0.0492620
$351$		0			0
$352$	−897.716			−0.135933
$353$	4190.52	−	2419.40i	0.631839	−	0.364792i	−0.149625	−	0.988743i	$-0.547807\pi$
$353$	4190.52	−	2419.40i	0.631839	−	0.364792i	0.781464	+	0.623951i	$0.214473\pi$
$354$		0			0
$355$	4140.58	−	7171.69i	0.619040	−	1.07221i
$356$		−	3241.39i		−	0.482566i
$357$		0			0
$358$	3295.02	+	1902.38i	0.486444	+	0.280849i
$359$		−	2374.12i		−	0.349029i	−0.984655	−	0.174514i	$-0.944164\pi$
$359$		−	2374.12i		−	0.349029i	0.984655	−	0.174514i	$-0.0558356\pi$
$360$		0			0
$361$	4949.78	+	8573.27i	0.721648	+	1.24993i
$362$	3497.67	−	2019.38i	0.507827	−	0.293194i
$363$		0			0
$364$	−674.196	+	2.76630i	−0.0970809	+	0.000398333i
$365$	−12340.5			−1.76967
$366$		0			0
$367$	3241.30	+	5614.10i	0.461021	+	0.798512i	0.999012	−	0.0444389i	$-0.0141500\pi$
$367$	3241.30	+	5614.10i	0.461021	+	0.798512i	−0.537991	+	0.842950i	$0.680817\pi$
$368$	1398.60	−	2422.44i	0.198117	−	0.343148i
$369$		0			0
$370$	2861.56	+	1652.12i	0.402069	+	0.232135i
$371$	670.272	+	386.981i	0.0937972	+	0.0541538i
$372$		0			0
$373$	156.532	−	271.121i	0.0217290	−	0.0376357i	−0.854956	−	0.518700i	$-0.826416\pi$
$373$	156.532	−	271.121i	0.0217290	−	0.0376357i	0.876685	+	0.481064i	$0.159750\pi$
$374$	3239.51	+	5610.99i	0.447890	+	0.775768i
$375$		0			0
$376$	869.009			0.119191
$377$	−42.1548	−	10273.9i	−0.00575885	−	1.40353i
$378$		0			0
$379$	2093.43	−	1208.64i	0.283727	−	0.163810i	−0.351383	−	0.936232i	$-0.614288\pi$
$379$	2093.43	−	1208.64i	0.283727	−	0.163810i	0.635109	+	0.772422i	$0.280955\pi$
$380$	3374.29	+	5844.44i	0.455519	+	0.788982i
$381$		0			0
$382$		−	3106.54i		−	0.416085i
$383$	−1031.33	−	595.441i	−0.137595	−	0.0794402i	0.429623	−	0.903009i	$-0.358647\pi$
$383$	−1031.33	−	595.441i	−0.137595	−	0.0794402i	−0.567217	+	0.823568i	$0.691980\pi$
$384$		0			0
$385$		−	1314.73i		−	0.174039i
$386$	600.841	−	1040.69i	0.0792280	−	0.137227i
$387$		0			0
$388$	−3985.06	+	2300.77i	−0.521419	+	0.301042i
$389$	2337.99			0.304732			0.152366	−	0.988324i	$-0.451311\pi$
$389$	2337.99			0.304732			0.152366	+	0.988324i	$0.451311\pi$
$390$		0			0
$391$	−20188.0			−2.61112
$392$	−2286.79	+	1320.28i	−0.294643	+	0.170112i
$393$		0			0
$394$	1761.59	−	3051.16i	0.225247	−	0.390140i
$395$		−	2592.56i		−	0.330242i
$396$		0			0
$397$	−12017.7	−	6938.45i	−1.51928	−	0.877156i	−0.999742	−	0.0227072i	$-0.992771\pi$
$397$	−12017.7	−	6938.45i	−1.51928	−	0.877156i	−0.519536	−	0.854448i	$-0.673895\pi$
$398$		−	6834.64i		−	0.860778i
$399$		0			0
$400$	358.806	+	621.470i	0.0448507	+	0.0776837i
$401$	−7850.46	+	4532.46i	−0.977639	+	0.564440i	−0.901556	−	0.432661i	$-0.857575\pi$
$401$	−7850.46	+	4532.46i	−0.977639	+	0.564440i	−0.0760824	+	0.997102i	$0.524241\pi$
$402$		0			0
$403$	−1241.09	+	2170.14i	−0.153407	+	0.268244i
$404$	−724.502			−0.0892211
$405$		0			0
$406$	788.203	+	1365.21i	0.0963494	+	0.166882i
$407$	1778.15	−	3079.84i	0.216559	−	0.375091i
$408$		0			0
$409$	12316.6	+	7111.00i	1.48904	+	0.859698i	0.999922	−	0.0125189i	$-0.00398500\pi$
$409$	12316.6	+	7111.00i	1.48904	+	0.859698i	0.489119	+	0.872217i	$0.337318\pi$
$410$	5806.98	+	3352.66i	0.699479	+	0.403845i
$411$		0			0
$412$	3534.42	−	6121.80i	0.422642	−	0.732037i
$413$	705.004	+	1221.10i	0.0839975	+	0.145488i
$414$		0			0
$415$	9031.08			1.06824
$416$	−755.278	−	1295.87i	−0.0890158	−	0.152729i
$417$		0			0
$418$	6290.25	−	3631.68i	0.736044	−	0.424955i
$419$	−143.734	−	248.955i	−0.0167587	−	0.0290269i	0.857524	−	0.514443i	$-0.172001\pi$
$419$	−143.734	−	248.955i	−0.0167587	−	0.0290269i	−0.874283	+	0.485416i	$0.838668\pi$
$420$		0			0
$421$		−	12089.3i		−	1.39952i	−0.714380	−	0.699758i	$-0.753291\pi$
$421$		−	12089.3i		−	1.39952i	0.714380	−	0.699758i	$-0.246709\pi$
$422$	4553.09	+	2628.73i	0.525215	+	0.303233i
$423$		0			0
$424$			1721.85i			0.197218i
$425$	2589.58	−	4485.28i	0.295560	−	0.511925i
$426$		0			0
$427$	−700.440	+	404.399i	−0.0793833	+	0.0458319i
$428$	1161.80			0.131210
$429$		0			0
$430$	−742.736			−0.0832975
$431$	132.526	−	76.5139i	0.0148110	−	0.00855115i	−0.492576	−	0.870269i	$-0.663945\pi$
$431$	132.526	−	76.5139i	0.0148110	−	0.00855115i	0.507387	+	0.861718i	$0.330611\pi$
$432$		0			0
$433$	4806.82	−	8325.66i	0.533490	−	0.924032i	−0.465745	−	0.884919i	$-0.654213\pi$
$433$	4806.82	−	8325.66i	0.533490	−	0.924032i	0.999235	−	0.0391128i	$-0.0124532\pi$
$434$		−	383.586i		−	0.0424256i
$435$		0			0
$436$	−3130.35	−	1807.31i	−0.343845	−	0.198519i
$437$			22631.9i			2.47741i
$438$		0			0
$439$	6582.62	+	11401.4i	0.715652	+	1.23955i	0.962708	+	0.270544i	$0.0872036\pi$
$439$	6582.62	+	11401.4i	0.715652	+	1.23955i	−0.247056	+	0.969001i	$0.579463\pi$
$440$	2533.05	−	1462.46i	0.274451	−	0.158454i
$441$		0			0
$442$	−5374.08	+	9397.01i	−0.578323	+	1.01124i
$443$	15445.0			1.65647			0.828235	−	0.560382i	$-0.189346\pi$
$443$	15445.0			1.65647			0.828235	+	0.560382i	$0.189346\pi$
$444$		0			0
$445$	5280.51	+	9146.11i	0.562517	+	0.974308i
$446$	−2431.24	+	4211.04i	−0.258123	+	0.447081i
$447$		0			0
$448$	199.308	+	115.071i	0.0210188	+	0.0121352i
$449$	1831.13	+	1057.20i	0.192464	+	0.111119i	0.593136	−	0.805103i	$-0.297890\pi$
$449$	1831.13	+	1057.20i	0.192464	+	0.111119i	−0.400671	+	0.916222i	$0.631223\pi$
$450$		0			0
$451$	3608.41	−	6249.94i	0.376748	−	0.652546i
$452$	−1785.44	−	3092.48i	−0.185797	−	0.321809i
$453$		0			0
$454$	13076.0			1.35174
$455$	1897.84	−	1106.13i	0.195543	−	0.113969i
$456$		0			0
$457$	−7359.07	+	4248.76i	−0.753267	+	0.434899i	−0.826873	−	0.562389i	$-0.809882\pi$
$457$	−7359.07	+	4248.76i	−0.753267	+	0.434899i	0.0736064	+	0.997287i	$0.476549\pi$
$458$	2167.38	+	3754.01i	0.221124	+	0.382999i
$459$		0			0
$460$			9113.73i			0.923761i
$461$	−6756.14	−	3900.66i	−0.682570	−	0.394082i	0.118253	−	0.992984i	$-0.462271\pi$
$461$	−6756.14	−	3900.66i	−0.682570	−	0.394082i	−0.800823	+	0.598902i	$0.795604\pi$
$462$		0			0
$463$			9734.48i			0.977105i	0.872535	+	0.488552i	$0.162475\pi$
$463$			9734.48i			0.977105i	−0.872535	+	0.488552i	$0.837525\pi$
$464$	−1753.53	+	3037.21i	−0.175443	+	0.303877i
$465$		0			0
$466$	5266.39	−	3040.55i	0.523521	−	0.302255i
$467$	−9446.38			−0.936031			−0.468015	−	0.883720i	$-0.655031\pi$
$467$	−9446.38			−0.936031			−0.468015	+	0.883720i	$0.655031\pi$
$468$		0			0
$469$	501.595			0.0493849
$470$	−2452.05	+	1415.69i	−0.240648	+	0.138938i
$471$		0			0
$472$	−1568.44	+	2716.61i	−0.152952	+	0.264920i
$473$			799.392i			0.0777084i
$474$		0			0
$475$	−5028.27	−	2903.07i	−0.485711	−	0.280425i
$476$		−	1660.98i		−	0.159939i
$477$		0			0
$478$	4747.31	+	8222.58i	0.454261	+	0.786804i
$479$	−2926.17	+	1689.43i	−0.279124	+	0.161152i	−0.633027	−	0.774130i	$-0.718188\pi$
$479$	−2926.17	+	1689.43i	−0.279124	+	0.161152i	0.353903	+	0.935282i	$0.384854\pi$
$480$		0			0
$481$	5941.83	−	24.3799i	0.563252	−	0.00231108i
$482$	−5468.44			−0.516764
$483$		0			0
$484$	1087.99	+	1884.45i	0.102178	+	0.176977i
$485$	7496.31	−	12984.0i	0.701835	−	1.21561i
$486$		0			0
$487$	−15593.2	−	9002.76i	−1.45092	−	0.837688i	−0.452384	−	0.891823i	$-0.649426\pi$
$487$	−15593.2	−	9002.76i	−1.45092	−	0.837688i	−0.998534	+	0.0541352i	$0.982760\pi$
$488$	−1558.28	−	899.675i	−0.144549	−	0.0834556i
$489$		0			0
$490$	4301.68	−	7450.74i	0.396592	−	0.686918i
$491$	1353.21	+	2343.83i	0.124378	+	0.215429i	0.921490	−	0.388403i	$-0.126973\pi$
$491$	1353.21	+	2343.83i	0.124378	+	0.215429i	−0.797112	+	0.603832i	$0.793640\pi$
$492$		0			0
$493$	25311.2			2.31229
$494$	10534.6	+	6024.66i	0.959462	+	0.548709i
$495$		0			0
$496$	739.042	−	426.686i	0.0669031	−	0.0386265i
$497$	1142.46	+	1978.80i	0.103112	+	0.178594i
$498$		0			0
$499$			8991.30i			0.806625i	0.915062	+	0.403313i	$0.132141\pi$
$499$			8991.30i			0.806625i	−0.915062	+	0.403313i	$0.867859\pi$
$500$	3618.46	+	2089.12i	0.323645	+	0.186857i
$501$		0			0
$502$			841.569i			0.0748228i
$503$	−6204.92	+	10747.2i	−0.550028	+	0.952676i	0.448244	+	0.893911i	$0.352049\pi$
$503$	−6204.92	+	10747.2i	−0.550028	+	0.952676i	−0.998272	+	0.0587647i	$0.981284\pi$
$504$		0			0
$505$	2044.30	−	1180.27i	0.180139	−	0.104003i
$506$	9808.92			0.861778
$507$		0			0
$508$	−2266.22			−0.197928
$509$	−2670.76	+	1541.96i	−0.232572	+	0.134276i	−0.611758	−	0.791045i	$-0.709537\pi$
$509$	−2670.76	+	1541.96i	−0.232572	+	0.134276i	0.379186	+	0.925321i	$0.376204\pi$
$510$		0			0
$511$	1702.48	−	2948.79i	0.147384	−	0.255277i
$512$			512.000i			0.0441942i
$513$		0			0
$514$	−6041.64	−	3488.14i	−0.518454	−	0.299330i
$515$			23031.5i			1.97066i
$516$		0			0
$517$	1523.68	+	2639.09i	0.129616	+	0.224501i
$518$	−789.558	+	455.852i	−0.0669714	+	0.0386660i
$519$		0			0
$520$	4242.22	+	2426.09i	0.357757	+	0.204599i
$521$	−3824.30			−0.321584			−0.160792	−	0.986988i	$-0.551405\pi$
$521$	−3824.30			−0.321584			−0.160792	+	0.986988i	$0.551405\pi$
$522$		0			0
$523$	2012.17	+	3485.19i	0.168234	+	0.291389i	0.937799	−	0.347179i	$-0.112860\pi$
$523$	2012.17	+	3485.19i	0.168234	+	0.291389i	−0.769565	+	0.638568i	$0.779527\pi$
$524$	−3997.47	+	6923.83i	−0.333264	+	0.577231i
$525$		0			0
$526$	−5766.51	−	3329.30i	−0.478007	−	0.275978i
$527$	−5333.83	−	3079.49i	−0.440883	−	0.254544i
$528$		0			0
$529$	−9198.32	+	15932.0i	−0.756005	+	1.30944i
$530$	−2805.04	−	4858.47i	−0.229893	−	0.398186i
$531$		0			0
$532$	−1862.06			−0.151749
$533$	12057.8	−	49.4744i	0.979889	−	0.00402059i
$534$		0			0
$535$	−3278.21	+	1892.68i	−0.264915	+	0.152949i
$536$	557.954	+	966.405i	0.0449626	+	0.0778775i
$537$		0			0
$538$		−	11595.1i		−	0.929184i
$539$	−8019.08	−	4629.82i	−0.640828	−	0.369982i
$540$		0			0
$541$		−	2764.37i		−	0.219685i	−0.993949	−	0.109842i	$-0.964965\pi$
$541$		−	2764.37i		−	0.219685i	0.993949	−	0.109842i	$-0.0350346\pi$
$542$	225.962	−	391.379i	0.0179076	−	0.0310169i
$543$		0			0
$544$	3200.15	−	1847.61i	0.252216	−	0.145617i
$545$	11777.0			0.925638
$546$		0			0
$547$	24620.8			1.92451			0.962255	−	0.272148i	$-0.0877341\pi$
$547$	24620.8			1.92451			0.962255	+	0.272148i	$0.0877341\pi$
$548$	−3429.52	+	1980.03i	−0.267339	+	0.154348i
$549$		0			0
$550$	−1258.23	+	2179.31i	−0.0975471	+	0.168957i
$551$		−	28375.4i		−	2.19389i
$552$		0			0
$553$	619.498	+	357.667i	0.0476379	+	0.0275037i
$554$		−	12285.8i		−	0.942194i
$555$		0			0
$556$	3594.46	+	6225.79i	0.274171	+	0.474879i
$557$	8405.82	−	4853.10i	0.639437	−	0.369179i	−0.144961	−	0.989437i	$-0.546306\pi$
$557$	8405.82	−	4853.10i	0.639437	−	0.369179i	0.784397	+	0.620259i	$0.212972\pi$
$558$		0			0
$559$	−1153.94	+	672.555i	−0.0873102	+	0.0508874i
$560$	−749.840			−0.0565830
$561$		0			0
$562$	−2631.82	−	4558.45i	−0.197539	−	0.342147i
$563$	9984.31	−	17293.3i	0.747404	−	1.29454i	−0.201659	−	0.979456i	$-0.564633\pi$
$563$	9984.31	−	17293.3i	0.747404	−	1.29454i	0.949063	−	0.315087i	$-0.102034\pi$
$564$		0			0
$565$	10075.8	+	5817.27i	0.750252	+	0.433158i
$566$	−5661.25	−	3268.52i	−0.420424	−	0.242732i
$567$		0			0
$568$	−2541.66	+	4402.28i	−0.187756	+	0.325204i
$569$	5753.03	+	9964.54i	0.423865	+	0.734156i	0.996314	−	0.0857843i	$-0.0273396\pi$
$569$	5753.03	+	9964.54i	0.423865	+	0.734156i	−0.572448	+	0.819941i	$0.694006\pi$
$570$		0			0
$571$	−16173.1			−1.18533			−0.592666	−	0.805448i	$-0.701925\pi$
$571$	−16173.1			−1.18533			−0.592666	+	0.805448i	$0.701925\pi$
$572$	2611.16	−	4565.82i	0.190870	−	0.333752i
$573$		0			0
$574$	−1602.25	+	925.062i	−0.116510	+	0.0672672i
$575$	−3920.50	−	6790.51i	−0.284341	−	0.492494i
$576$		0			0
$577$		−	23233.2i		−	1.67627i	−0.545462	−	0.838136i	$-0.683646\pi$
$577$		−	23233.2i		−	1.67627i	0.545462	−	0.838136i	$-0.316354\pi$
$578$	−14586.6	−	8421.59i	−1.04969	−	0.606042i
$579$		0			0
$580$		−	11426.6i		−	0.818041i
$581$	−1245.92	+	2158.00i	−0.0889665	+	0.154094i
$582$		0			0
$583$	−5229.08	+	3019.01i	−0.371469	+	0.214468i
$584$	7575.09			0.536746
$585$		0			0
$586$	−14227.7			−1.00297
$587$	−3663.35	+	2115.04i	−0.257585	+	0.148717i	−0.623233	−	0.782037i	$-0.714181\pi$
$587$	−3663.35	+	2115.04i	−0.257585	+	0.148717i	0.365647	+	0.930754i	$0.380848\pi$
$588$		0			0
$589$	−3452.29	+	5979.53i	−0.241509	+	0.418306i
$590$		−	10220.5i		−	0.713169i
$591$		0			0
$592$	−1756.55	−	1014.14i	−0.121949	−	0.0704071i
$593$			2252.09i			0.155956i	0.996955	+	0.0779782i	$0.0248465\pi$
$593$			2252.09i			0.155956i	−0.996955	+	0.0779782i	$0.975154\pi$
$594$		0			0
$595$	2705.88	+	4686.72i	0.186437	+	0.322919i
$596$	1470.96	−	849.260i	0.101096	−	0.0583675i
$597$		0			0
$598$	8252.57	+	14159.4i	0.564336	+	0.968262i
$599$	−2097.38			−0.143066			−0.0715331	−	0.997438i	$-0.522789\pi$
$599$	−2097.38			−0.143066			−0.0715331	+	0.997438i	$0.522789\pi$
$600$		0			0
$601$	−6187.67	−	10717.4i	−0.419967	−	0.727405i	0.575968	−	0.817472i	$-0.304625\pi$
$601$	−6187.67	−	10717.4i	−0.419967	−	0.727405i	−0.995936	+	0.0900673i	$0.971292\pi$
$602$	102.467	−	177.479i	0.00693731	−	0.0120158i
$603$		0			0
$604$	−10548.8	−	6090.33i	−0.710634	−	0.410285i
$605$	−6139.86	−	3544.85i	−0.412597	−	0.238213i
$606$		0			0
$607$	12164.8	−	21070.1i	0.813435	−	1.40891i	−0.0970120	−	0.995283i	$-0.530929\pi$
$607$	12164.8	−	21070.1i	0.813435	−	1.40891i	0.910447	−	0.413627i	$-0.135738\pi$
$608$	−2071.28	−	3587.56i	−0.138160	−	0.239301i
$609$		0			0
$610$	5862.59			0.389130
$611$	−2527.66	+	4419.81i	−0.167362	+	0.292646i
$612$		0			0
$613$	−12595.5	+	7272.00i	−0.829896	+	0.479141i	−0.853817	−	0.520573i	$-0.825718\pi$
$613$	−12595.5	+	7272.00i	−0.829896	+	0.479141i	0.0239210	+	0.999714i	$0.492385\pi$
$614$	5015.75	+	8687.54i	0.329673	+	0.571010i
$615$		0			0
$616$			807.037i			0.0527865i
$617$	5213.40	+	3009.96i	0.340168	+	0.196396i	0.660346	−	0.750961i	$-0.270410\pi$
$617$	5213.40	+	3009.96i	0.340168	+	0.196396i	−0.320178	+	0.947357i	$0.603743\pi$
$618$		0			0
$619$			11663.1i			0.757320i	0.925536	+	0.378660i	$0.123615\pi$
$619$			11663.1i			0.757320i	−0.925536	+	0.378660i	$0.876385\pi$
$620$	−1390.22	+	2407.92i	−0.0900522	+	0.155975i
$621$		0			0
$622$	−976.354	+	563.698i	−0.0629393	+	0.0363380i
$623$	−2913.98			−0.187393
$624$		0			0
$625$	−19219.8			−1.23006
$626$	−2626.41	+	1516.36i	−0.167687	+	0.0968144i
$627$		0			0
$628$	2699.25	−	4675.23i	0.171515	−	0.297073i
$629$			14638.6i			0.927946i
$630$		0			0
$631$	−4828.46	−	2787.71i	−0.304624	−	0.175875i	0.339894	−	0.940464i	$-0.389609\pi$
$631$	−4828.46	−	2787.71i	−0.304624	−	0.175875i	−0.644518	+	0.764589i	$0.722942\pi$
$632$			1591.42i			0.100163i
$633$		0			0
$634$	−2358.19	−	4084.50i	−0.147722	−	0.255861i
$635$	6394.50	−	3691.87i	0.399619	−	0.230720i
$636$		0			0
$637$	−63.4788	−	15470.9i	−0.00394839	−	0.962292i
$638$	−12298.2			−0.763153
$639$		0			0
$640$	−834.091	−	1444.69i	−0.0515162	−	0.0892287i
$641$	−9908.76	+	17162.5i	−0.610566	+	1.05753i	0.380580	+	0.924748i	$0.375725\pi$
$641$	−9908.76	+	17162.5i	−0.610566	+	1.05753i	−0.991145	+	0.132782i	$0.957609\pi$
$642$		0			0
$643$	17250.8	+	9959.77i	1.05802	+	0.610848i	0.924884	−	0.380250i	$-0.124162\pi$
$643$	17250.8	+	9959.77i	1.05802	+	0.610848i	0.133135	+	0.991098i	$0.457495\pi$
$644$	−2177.75	−	1257.32i	−0.133254	−	0.0769340i
$645$		0			0
$646$	−14948.9	+	25892.2i	−0.910457	+	1.57696i
$647$	12381.7	+	21445.7i	0.752356	+	1.30312i	0.946678	+	0.322180i	$0.104416\pi$
$647$	12381.7	+	21445.7i	0.752356	+	1.30312i	−0.194323	+	0.980938i	$0.562251\pi$
$648$		0			0
$649$	−11000.1			−0.665317
$650$	−4204.47	+	17.2514i	−0.253712	+	0.00104101i
$651$		0			0
$652$	−3751.28	+	2165.80i	−0.225324	+	0.130091i
$653$	−3230.41	−	5595.23i	−0.193592	−	0.335311i	0.752846	−	0.658197i	$-0.228680\pi$
$653$	−3230.41	−	5595.23i	−0.193592	−	0.335311i	−0.946438	+	0.322885i	$0.895347\pi$
$654$		0			0
$655$		−	26048.9i		−	1.55392i
$656$	−3564.57	−	2058.00i	−0.212154	−	0.122487i
$657$		0			0
$658$		−	781.230i		−	0.0462850i
$659$	9995.68	−	17313.0i	0.590860	−	1.02340i	−0.403257	−	0.915087i	$-0.632122\pi$
$659$	9995.68	−	17313.0i	0.590860	−	1.02340i	0.994117	−	0.108312i	$-0.0345446\pi$
$660$		0			0
$661$	−11657.5	+	6730.43i	−0.685964	+	0.396042i	−0.802098	−	0.597192i	$-0.796283\pi$
$661$	−11657.5	+	6730.43i	−0.685964	+	0.396042i	0.116134	+	0.993234i	$0.462950\pi$
$662$	−3400.44			−0.199640
$663$		0			0
$664$	−5543.65			−0.323999
$665$	5254.09	−	3033.45i	0.306383	−	0.176890i
$666$		0			0
$667$	19160.0	−	33186.1i	1.11226	−	1.92649i
$668$			3420.28i			0.198106i
$669$		0			0
$670$	−3148.71	−	1817.91i	−0.181560	−	0.104824i
$671$		−	6309.78i		−	0.363020i
$672$		0			0
$673$	2099.82	+	3636.99i	0.120271	+	0.208315i	0.919874	−	0.392213i	$-0.128290\pi$
$673$	2099.82	+	3636.99i	0.120271	+	0.208315i	−0.799604	+	0.600528i	$0.794957\pi$
$674$	−19939.9	+	11512.3i	−1.13955	+	0.657918i
$675$		0			0
$676$	8787.70	−	72.1149i	0.499983	−	0.00410304i
$677$	−7849.62			−0.445621			−0.222811	−	0.974862i	$-0.571523\pi$
$677$	−7849.62			−0.445621			−0.222811	+	0.974862i	$0.571523\pi$
$678$		0			0
$679$	2068.37	+	3582.53i	0.116903	+	0.202481i
$680$	−6019.82	+	10426.6i	−0.339485	+	0.588005i
$681$		0			0
$682$	2591.60	+	1496.26i	0.145509	+	0.0840099i
$683$	11924.1	+	6884.39i	0.668028	+	0.385686i	0.795329	−	0.606178i	$-0.207298\pi$
$683$	11924.1	+	6884.39i	0.668028	+	0.385686i	−0.127301	+	0.991864i	$0.540631\pi$
$684$		0			0
$685$	6451.28	−	11174.0i	0.359841	−	0.623262i
$686$	2420.33	+	4192.13i	0.134706	+	0.233318i
$687$		0			0
$688$	455.922			0.0252644
$689$	−8757.40	−	5008.29i	−0.484224	−	0.276924i
$690$		0			0
$691$	−19812.4	+	11438.7i	−1.09074	+	0.629738i	−0.933773	−	0.357866i	$-0.883504\pi$
$691$	−19812.4	+	11438.7i	−1.09074	+	0.629738i	−0.156965	+	0.987604i	$0.550171\pi$
$692$	−7303.32	−	12649.7i	−0.401200	−	0.694900i
$693$		0			0
$694$			363.004i			0.0198551i
$695$	−20284.7	−	11711.4i	−1.10711	−	0.639191i
$696$		0			0
$697$			29706.1i			1.61435i
$698$	−5201.51	+	9009.28i	−0.282063	+	0.488548i
$699$		0			0
$700$	558.695	−	322.563i	0.0301667	−	0.0174167i
$701$	3514.23			0.189345			0.0946724	−	0.995508i	$-0.469820\pi$
$701$	3514.23			0.189345			0.0946724	+	0.995508i	$0.469820\pi$
$702$		0			0
$703$	16410.7			0.880429
$704$	−1554.89	+	897.716i	−0.0832416	+	0.0480596i
$705$		0			0
$706$	4838.80	−	8381.05i	0.257947	−	0.446777i
$707$			651.320i			0.0346469i
$708$		0			0
$709$	−6139.10	−	3544.41i	−0.325189	−	0.187748i	0.328514	−	0.944499i	$-0.393452\pi$
$709$	−6139.10	−	3544.41i	−0.325189	−	0.187748i	−0.653703	+	0.756751i	$0.726785\pi$
$710$		−	16562.3i		−	0.875454i
$711$		0			0
$712$	−3241.39	−	5614.26i	−0.170613	−	0.295510i
$713$	−8075.17	+	4662.20i	−0.424148	+	0.244882i
$714$		0			0
$715$	70.3148	+	17137.0i	0.00367779	+	0.896344i
$716$	7609.52			0.397180
$717$		0			0
$718$	−2374.12	−	4112.10i	−0.123400	−	0.213736i
$719$	7572.65	−	13116.2i	0.392785	−	0.680323i	−0.600031	−	0.799977i	$-0.704845\pi$
$719$	7572.65	−	13116.2i	0.392785	−	0.680323i	0.992816	+	0.119654i	$0.0381784\pi$
$720$		0			0
$721$	−5503.43	−	3177.41i	−0.284270	−	0.164123i
$722$	17146.5	+	9899.56i	0.883834	+	0.510282i
$723$		0			0
$724$	4038.76	−	6995.33i	0.207319	−	0.359088i
$725$	4915.45	+	8513.80i	0.251800	+	0.436131i
$726$		0			0
$727$	−3785.73			−0.193129			−0.0965645	−	0.995327i	$-0.530785\pi$
$727$	−3785.73			−0.193129			−0.0965645	+	0.995327i	$0.530785\pi$
$728$	−1164.97	+	678.987i	−0.0593089	+	0.0345672i
$729$		0			0
$730$	−21374.3	+	12340.5i	−1.08370	+	0.625673i
$731$	−1645.25	−	2849.65i	−0.0832443	−	0.144183i
$732$		0			0
$733$			1412.04i			0.0711528i	0.999367	+	0.0355764i	$0.0113267\pi$
$733$			1412.04i			0.0711528i	−0.999367	+	0.0355764i	$0.988673\pi$
$734$	11228.2	+	6482.61i	0.564633	+	0.325991i
$735$		0			0
$736$		−	5594.39i		−	0.280179i
$737$	−1956.58	+	3388.89i	−0.0977904	+	0.169378i
$738$		0			0
$739$	761.097	−	439.420i	0.0378855	−	0.0218732i	−0.480938	−	0.876755i	$-0.659704\pi$
$739$	761.097	−	439.420i	0.0378855	−	0.0218732i	0.518823	+	0.854882i	$0.326370\pi$
$740$	6608.49			0.328288
$741$		0			0
$742$	1547.93			0.0765851
$743$	−3375.21	+	1948.68i	−0.166655	+	0.0962181i	−0.581007	−	0.813898i	$-0.697341\pi$
$743$	−3375.21	+	1948.68i	−0.166655	+	0.0962181i	0.414353	+	0.910116i	$0.364008\pi$
$744$		0			0
$745$	−2767.03	+	4792.64i	−0.136076	+	0.235690i
$746$		−	626.128i		−	0.0307294i
$747$		0			0
$748$	11222.0	+	6479.01i	0.548551	+	0.316706i
$749$		−	1044.45i		−	0.0509524i
$750$		0			0
$751$	−10476.9	−	18146.5i	−0.509064	−	0.881724i	−0.999945	−	0.0104978i	$-0.996658\pi$
$751$	−10476.9	−	18146.5i	−0.509064	−	0.881724i	0.490881	−	0.871227i	$-0.336675\pi$
$752$	1505.17	−	869.009i	0.0729891	−	0.0421403i
$753$		0			0
$754$	−10346.9	−	17752.7i	−0.499751	−	0.857449i
$755$	39686.6			1.91304
$756$		0			0
$757$	10219.6	+	17700.8i	0.490669	+	0.849863i	0.999942	−	0.0107414i	$-0.00341914\pi$
$757$	10219.6	+	17700.8i	0.490669	+	0.849863i	−0.509273	+	0.860605i	$0.670086\pi$
$758$	2417.29	−	4186.87i	0.115831	−	0.200625i
$759$		0			0
$760$	11688.9	+	6748.58i	0.557895	+	0.322101i
$761$	−16771.2	−	9682.87i	−0.798892	−	0.461240i	0.0441918	−	0.999023i	$-0.485929\pi$
$761$	−16771.2	−	9682.87i	−0.798892	−	0.461240i	−0.843083	+	0.537783i	$0.819262\pi$
$762$		0			0
$763$	−1624.75	+	2814.15i	−0.0770904	+	0.133524i
$764$	−3106.54	−	5380.69i	−0.147108	−	0.254799i
$765$		0			0
$766$	−2381.76			−0.112345
$767$	−9254.73	−	15878.8i	−0.435683	−	0.747525i
$768$		0			0
$769$	32141.9	−	18557.1i	1.50724	−	0.870203i	0.507272	−	0.861786i	$-0.330654\pi$
$769$	32141.9	−	18557.1i	1.50724	−	0.870203i	0.999965	−	0.00841718i	$-0.00267930\pi$
$770$	−1314.73	−	2277.18i	−0.0615320	−	0.106577i
$771$		0			0
$772$		−	2403.36i		−	0.112045i
$773$	8387.78	+	4842.69i	0.390281	+	0.225329i	0.682282	−	0.731089i	$-0.260988\pi$
$773$	8387.78	+	4842.69i	0.390281	+	0.225329i	−0.292001	+	0.956418i	$0.594321\pi$
$774$		0			0
$775$		−	2392.15i		−	0.110875i
$776$	−4601.55	+	7970.12i	−0.212869	+	0.368699i
$777$		0			0
$778$	4049.51	−	2337.99i	0.186609	−	0.107739i
$779$	33302.3			1.53168
$780$		0			0
$781$	−17825.7			−0.816713
$782$	−34966.6	+	20188.0i	−1.59898	+	0.923171i
$783$		0			0
$784$	−2640.55	+	4573.57i	−0.120288	+	0.208344i
$785$			17589.2i			0.799727i
$786$		0			0
$787$	−17642.7	−	10186.0i	−0.799103	−	0.461362i	0.0440543	−	0.999029i	$-0.485973\pi$
$787$	−17642.7	−	10186.0i	−0.799103	−	0.461362i	−0.843157	+	0.537667i	$0.819306\pi$
$788$		−	7046.34i		−	0.318548i
$789$		0			0
$790$	−2592.56	−	4490.44i	−0.116758	−	0.202231i
$791$	−2780.10	+	1605.09i	−0.124967	+	0.0721499i
$792$		0			0
$793$	9108.30	−	5308.63i	0.407876	−	0.237724i
$794$	−27753.8			−1.24049
$795$		0			0
$796$	−6834.64	−	11838.0i	−0.304331	−	0.527117i
$797$	12703.7	−	22003.5i	0.564603	−	0.977921i	−0.432484	−	0.901642i	$-0.642363\pi$
$797$	12703.7	−	22003.5i	0.564603	−	0.977921i	0.997087	−	0.0762789i	$-0.0243039\pi$
$798$		0			0
$799$	−10863.1	−	6271.83i	−0.480988	−	0.277699i
$800$	1242.94	+	717.611i	0.0549307	+	0.0317142i
$801$		0			0
$802$	−9064.93	+	15700.9i	−0.399119	+	0.691295i
$803$	13281.8	+	23004.8i	0.583692	+	1.01098i
$804$		0			0
$805$	8193.15			0.358721
$806$	20.5150	+	4999.88i	0.000896540	+	0.218503i
$807$		0			0
$808$	−1254.87	+	724.502i	−0.0546365	+	0.0315444i
$809$	−3240.16	−	5612.12i	−0.140813	−	0.243896i	0.786990	−	0.616966i	$-0.211638\pi$
$809$	−3240.16	−	5612.12i	−0.140813	−	0.243896i	−0.927803	+	0.373070i	$0.878305\pi$
$810$		0			0
$811$			30651.9i			1.32717i	0.748102	+	0.663584i	$0.230966\pi$
$811$			30651.9i			1.32717i	−0.748102	+	0.663584i	$0.769034\pi$
$812$	2730.42	+	1576.41i	0.118003	+	0.0681293i
$813$		0			0
$814$		−	7112.59i		−	0.306261i
$815$	7056.56	−	12222.3i	0.303289	−	0.525312i
$816$		0			0
$817$	−3194.63	+	1844.42i	−0.136800	+	0.0789817i
$818$	28444.0			1.21580
$819$		0			0
$820$	13410.7			0.571122
$821$	−29694.2	+	17144.0i	−1.26228	+	0.728780i	−0.973516	−	0.228619i	$-0.926579\pi$
$821$	−29694.2	+	17144.0i	−1.26228	+	0.728780i	−0.288768	+	0.957399i	$0.593246\pi$
$822$		0			0
$823$	−10447.4	+	18095.5i	−0.442496	+	0.766426i	−0.997874	−	0.0651720i	$-0.979240\pi$
$823$	−10447.4	+	18095.5i	−0.442496	+	0.766426i	0.555378	+	0.831598i	$0.312574\pi$
$824$		−	14137.7i		−	0.597706i
$825$		0			0
$826$	2442.21	+	1410.01i	0.102876	+	0.0593952i
$827$		−	8158.74i		−	0.343056i	−0.985179	−	0.171528i	$-0.945130\pi$
$827$		−	8158.74i		−	0.343056i	0.985179	−	0.171528i	$-0.0548704\pi$
$828$		0			0
$829$	−5080.52	−	8799.72i	−0.212851	−	0.368669i	0.739754	−	0.672877i	$-0.234942\pi$
$829$	−5080.52	−	8799.72i	−0.212851	−	0.368669i	−0.952606	+	0.304208i	$0.901608\pi$
$830$	15642.3	−	9031.08i	0.654159	−	0.377679i
$831$		0			0
$832$	−2604.05	−	1489.24i	−0.108509	−	0.0620553i
$833$	38114.9			1.58536
$834$		0			0
$835$	−5571.93	−	9650.87i	−0.230928	−	0.399979i
$836$	7263.36	−	12580.5i	0.300489	−	0.520461i
$837$		0			0
$838$	−497.910	−	287.469i	−0.0205251	−	0.0118502i
$839$	−26886.9	−	15523.2i	−1.10636	−	0.638759i	−0.168478	−	0.985705i	$-0.553885\pi$
$839$	−26886.9	−	15523.2i	−1.10636	−	0.638759i	−0.937885	+	0.346946i	$0.887219\pi$
$840$		0			0
$841$	−11827.9	+	20486.6i	−0.484970	+	0.839993i
$842$	−12089.3	−	20939.3i	−0.494803	−	0.857024i
$843$		0			0
$844$	10514.9			0.428836
$845$	−24678.4	+	14519.4i	−1.00469	+	0.591104i
$846$		0			0
$847$	1694.10	−	978.091i	0.0687250	−	0.0396784i
$848$	1721.85	+	2982.33i	0.0697271	+	0.120771i
$849$		0			0
$850$		−	10358.3i		−	0.417985i
$851$	19193.0	+	11081.1i	0.773121	+	0.446362i
$852$		0			0
$853$			15549.5i			0.624155i	0.950057	+	0.312077i	$0.101025\pi$
$853$			15549.5i			0.624155i	−0.950057	+	0.312077i	$0.898975\pi$
$854$	−808.798	+	1400.88i	−0.0324081	+	0.0561324i
$855$		0			0
$856$	2012.30	−	1161.80i	0.0803495	−	0.0463898i
$857$	−44590.9			−1.77736			−0.888678	−	0.458531i	$-0.848376\pi$
$857$	−44590.9			−1.77736			−0.888678	+	0.458531i	$0.848376\pi$
$858$		0			0
$859$	41540.7			1.65000			0.825001	−	0.565131i	$-0.191174\pi$
$859$	41540.7			1.65000			0.825001	+	0.565131i	$0.191174\pi$
$860$	−1286.46	+	742.736i	−0.0510091	+	0.0294501i
$861$		0			0
$862$	153.028	−	265.052i	0.00604657	−	0.0104730i
$863$			6952.24i			0.274226i	0.990555	+	0.137113i	$0.0437823\pi$
$863$			6952.24i			0.274226i	−0.990555	+	0.137113i	$0.956218\pi$
$864$		0			0
$865$	41215.0	+	23795.5i	1.62006	+	0.935341i
$866$		−	19227.3i		−	0.754469i
$867$		0			0
$868$	−383.586	−	664.391i	−0.0149997	−	0.0259803i
$869$	−4832.97	+	2790.32i	−0.188662	+	0.108924i
$870$		0			0
$871$	−6538.07	+	26.8264i	−0.254345	+	0.00104360i
$872$	−7229.24			−0.280749
$873$		0			0
$874$	22631.9	+	39199.6i	0.875898	+	1.51710i
$875$	1878.10	−	3252.96i	0.0725614	−	0.125680i
$876$		0			0
$877$	−20404.4	−	11780.5i	−0.785643	−	0.453591i	0.0527837	−	0.998606i	$-0.483191\pi$
$877$	−20404.4	−	11780.5i	−0.785643	−	0.453591i	−0.838426	+	0.545015i	$0.816524\pi$
$878$	22802.9	+	13165.2i	0.876491	+	0.506042i
$879$		0			0
$880$	2924.91	−	5066.09i	0.112044	−	0.194066i
$881$	−15950.6	−	27627.3i	−0.609978	−	1.05651i	−0.991243	−	0.132047i	$-0.957845\pi$
$881$	−15950.6	−	27627.3i	−0.609978	−	1.05651i	0.381266	−	0.924465i	$-0.375488\pi$
$882$		0			0
$883$	20282.6			0.773004			0.386502	−	0.922288i	$-0.373683\pi$
$883$	20282.6			0.773004			0.386502	+	0.922288i	$0.373683\pi$
$884$	88.8329	+	21650.2i	0.00337983	+	0.823726i
$885$		0			0
$886$	26751.6	−	15445.0i	1.01438	−	0.585650i
$887$	4916.10	+	8514.94i	0.186095	+	0.322327i	0.943945	−	0.330103i	$-0.107083\pi$
$887$	4916.10	+	8514.94i	0.186095	+	0.322327i	−0.757850	+	0.652429i	$0.773750\pi$
$888$		0			0
$889$			2037.31i			0.0768607i
$890$	18292.2	+	10561.0i	0.688940	+	0.397759i
$891$		0			0
$892$			9724.97i			0.365040i
$893$	−7031.09	+	12178.2i	−0.263479	+	0.456358i
$894$		0			0
$895$	−21471.5	+	12396.5i	−0.801912	+	0.462984i
$896$	460.283			0.0171618
$897$		0			0
$898$	4228.82			0.157146
$899$	10124.5	−	5845.37i	0.375606	−	0.216856i
$900$		0			0
$901$	12427.0	−	21524.1i	0.459492	−	0.795864i
$902$		−	14433.6i		−	0.532802i
$903$		0			0
$904$	−6184.95	−	3570.88i	−0.227554	−	0.131378i
$905$			26317.9i			0.966670i
$906$		0			0
$907$	8271.94	+	14327.4i	0.302828	+	0.524514i	0.976775	−	0.214265i	$-0.0687357\pi$
$907$	8271.94	+	14327.4i	0.302828	+	0.524514i	−0.673947	+	0.738780i	$0.735402\pi$
$908$	22648.4	−	13076.0i	0.827767	−	0.477912i
$909$		0			0
$910$	2181.03	−	3813.71i	0.0794511	−	0.138927i
$911$	24198.4			0.880053			0.440027	−	0.897985i	$-0.354969\pi$
$911$	24198.4			0.880053			0.440027	+	0.897985i	$0.354969\pi$
$912$		0			0
$913$	−9719.97	−	16835.5i	−0.352337	−	0.610266i
$914$	−8497.52	+	14718.1i	−0.307520	+	0.532640i
$915$		0			0
$916$	7508.02	+	4334.76i	0.270821	+	0.156359i
$917$	6224.45	+	3593.69i	0.224154	+	0.129415i
$918$		0			0
$919$	15554.9	−	26941.8i	0.558332	−	0.967060i	−0.439303	−	0.898339i	$-0.644775\pi$
$919$	15554.9	−	26941.8i	0.558332	−	0.967060i	0.997636	−	0.0687214i	$-0.0218920\pi$
$920$	9113.73	+	15785.4i	0.326599	+	0.565686i
$921$		0			0
$922$	−15602.6			−0.557316
$923$	−14997.3	−	25731.7i	−0.534825	−	0.917628i
$924$		0			0
$925$	−4923.90	+	2842.81i	−0.175023	+	0.101050i
$926$	9734.48	+	16860.6i	0.345459	+	0.598352i
$927$		0			0
$928$			7014.12i			0.248114i
$929$	18504.8	+	10683.7i	0.653521	+	0.377311i	0.789804	−	0.613359i	$-0.210182\pi$
$929$	18504.8	+	10683.7i	0.653521	+	0.377311i	−0.136283	+	0.990670i	$0.543516\pi$
$930$		0			0
$931$		−	42729.1i		−	1.50418i
$932$	6081.10	−	10532.8i	0.213727	−	0.370185i
$933$		0			0
$934$	−16361.6	+	9446.38i	−0.573199	+	0.330937i
$935$	−42219.4			−1.47671
$936$		0			0
$937$	−955.004			−0.0332963			−0.0166481	−	0.999861i	$-0.505300\pi$
$937$	−955.004			−0.0332963			−0.0166481	+	0.999861i	$0.505300\pi$
$938$	868.788	−	501.595i	0.0302419	−	0.0174602i
$939$		0			0
$940$	−2831.38	+	4904.09i	−0.0982440	+	0.170164i
$941$		−	41533.1i		−	1.43883i	−0.694580	−	0.719416i	$-0.744410\pi$
$941$		−	41533.1i		−	1.43883i	0.694580	−	0.719416i	$-0.255590\pi$
$942$		0			0
$943$	38948.4	+	22486.9i	1.34500	+	0.776535i
$944$			6273.75i			0.216306i
$945$		0			0
$946$	799.392	+	1384.59i	0.0274741	+	0.0475865i
$947$	−27485.3	+	15868.7i	−0.943139	+	0.544522i	−0.890943	−	0.454115i	$-0.849955\pi$
$947$	−27485.3	+	15868.7i	−0.943139	+	0.544522i	−0.0521963	+	0.998637i	$0.516622\pi$
$948$		0			0
$949$	−22033.4	+	38527.2i	−0.753672	+	1.31786i
$950$	−11612.3			−0.396581
$951$		0			0
$952$	−1660.98	−	2876.90i	−0.0565469	−	0.0979422i
$953$	−16032.6	+	27769.2i	−0.544959	+	0.943896i	0.453651	+	0.891180i	$0.350121\pi$
$953$	−16032.6	+	27769.2i	−0.544959	+	0.943896i	−0.998610	+	0.0527168i	$0.983212\pi$
$954$		0			0
$955$	17531.2	+	10121.6i	0.594028	+	0.342962i
$956$	16445.2	+	9494.62i	0.556354	+	0.321211i
$957$		0			0
$958$	−3378.85	+	5852.34i	−0.113952	+	0.197370i
$959$	1780.03	+	3083.10i	0.0599376	+	0.103815i
$960$		0			0
$961$	26946.3			0.904511
$962$	10267.2	−	5984.06i	0.344103	−	0.200555i
$963$		0			0
$964$	−9471.61	+	5468.44i	−0.316452	+	0.182704i
$965$	3915.29	+	6781.47i	0.130609	+	0.226221i
$966$		0			0
$967$		−	11821.6i		−	0.393131i	−0.980491	−	0.196565i	$-0.937021\pi$
$967$		−	11821.6i		−	0.393131i	0.980491	−	0.196565i	$-0.0629788\pi$
$968$	3768.90	+	2175.98i	0.125142	+	0.0722506i
$969$		0			0
$970$		−	29985.3i		−	0.992545i
$971$	−7792.48	+	13497.0i	−0.257541	+	0.446075i	−0.965583	−	0.260096i	$-0.916246\pi$
$971$	−7792.48	+	13497.0i	−0.257541	+	0.446075i	0.708041	+	0.706171i	$0.249579\pi$
$972$		0			0
$973$	5596.92	−	3231.39i	0.184408	−	0.106468i
$974$	−36011.0			−1.18467
$975$		0			0
$976$	−3598.70			−0.118024
$977$	46550.1	−	26875.7i	1.52433	−	0.880072i	0.524744	−	0.851260i	$-0.324161\pi$
$977$	46550.1	−	26875.7i	1.52433	−	0.880072i	0.999585	−	0.0288119i	$-0.00917240\pi$
$978$		0			0
$979$	11366.6	−	19687.5i	0.371071	−	0.642713i
$980$		−	17206.7i		−	0.560866i
$981$		0			0
$982$	4687.65	+	2706.42i	0.152331	+	0.0879483i
$983$		−	30852.0i		−	1.00104i	−0.865724	−	0.500521i	$-0.833142\pi$
$983$		−	30852.0i		−	1.00104i	0.865724	−	0.500521i	$-0.166858\pi$
$984$		0			0
$985$	11479.1	+	19882.4i	0.371324	+	0.643152i
$986$	43840.3	−	25311.2i	1.41598	−	0.817519i
$987$		0			0
$988$	24271.1	−	99.5869i	0.781546	−	0.00320676i
$989$	−4981.65			−0.160169
$990$		0			0
$991$	−22122.8	−	38317.8i	−0.709136	−	1.22826i	−0.965178	−	0.261594i	$-0.915752\pi$
$991$	−22122.8	−	38317.8i	−0.709136	−	1.22826i	0.256042	−	0.966666i	$-0.417581\pi$
$992$	853.372	−	1478.08i	0.0273131	−	0.0473077i
$993$		0			0
$994$	3957.61	+	2284.92i	0.126285	+	0.0729109i
$995$	38570.1	+	22268.4i	1.22890	+	0.709504i
$996$		0			0
$997$	−27178.8	+	47075.1i	−0.863352	+	1.49537i	0.00532306	+	0.999986i	$0.498306\pi$
$997$	−27178.8	+	47075.1i	−0.863352	+	1.49537i	−0.868675	+	0.495383i	$0.835028\pi$
$998$	8991.30	+	15573.4i	0.285185	+	0.493955i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.4.l.b.127.4		8
3.2	odd	2		26.4.e.a.23.1	yes	8
12.11	even	2		208.4.w.d.49.3		8
13.4	even	6	inner	234.4.l.b.199.3		8
39.2	even	12		338.4.a.l.1.3		4
39.5	even	4		338.4.c.n.315.2		8
39.8	even	4		338.4.c.m.315.2		8
39.11	even	12		338.4.a.m.1.3		4
39.17	odd	6		26.4.e.a.17.1	✓	8
39.20	even	12		338.4.c.m.191.2		8
39.23	odd	6		338.4.b.g.337.7		8
39.29	odd	6		338.4.b.g.337.3		8
39.32	even	12		338.4.c.n.191.2		8
39.35	odd	6		338.4.e.e.147.3		8
39.38	odd	2		338.4.e.e.23.3		8
156.95	even	6		208.4.w.d.17.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.4.e.a.17.1	✓	8	39.17	odd	6
26.4.e.a.23.1	yes	8	3.2	odd	2
208.4.w.d.17.3		8	156.95	even	6
208.4.w.d.49.3		8	12.11	even	2
234.4.l.b.127.4		8	1.1	even	1	trivial
234.4.l.b.199.3		8	13.4	even	6	inner
338.4.a.l.1.3		4	39.2	even	12
338.4.a.m.1.3		4	39.11	even	12
338.4.b.g.337.3		8	39.29	odd	6
338.4.b.g.337.7		8	39.23	odd	6
338.4.c.m.191.2		8	39.20	even	12
338.4.c.m.315.2		8	39.8	even	4
338.4.c.n.191.2		8	39.32	even	12
338.4.c.n.315.2		8	39.5	even	4
338.4.e.e.23.3		8	39.38	odd	2
338.4.e.e.147.3		8	39.35	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	234.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} +13.0327i q^{5} +(-3.11419 - 1.79798i) q^{7} -8.00000i q^{8} +(13.0327 + 22.5733i) q^{10} +(24.2951 - 14.0268i) q^{11} +(40.6883 + 23.2693i) q^{13} -7.19192 q^{14} +(-8.00000 - 13.8564i) q^{16} +(-57.7378 + 100.005i) q^{17} +(112.111 + 64.7274i) q^{19} +(45.1465 + 26.0654i) q^{20} +(28.0536 - 48.5903i) q^{22} +(87.4123 + 151.403i) q^{23} -44.8507 q^{25} +(93.7435 - 0.384640i) q^{26} +(-12.4568 + 7.19192i) q^{28} +(-109.596 - 189.825i) q^{29} +53.3357i q^{31} +(-27.7128 - 16.0000i) q^{32} +230.951i q^{34} +(23.4325 - 40.5863i) q^{35} +(109.784 - 63.3839i) q^{37} +258.910 q^{38} +104.261 q^{40} +(222.786 - 128.625i) q^{41} +(-14.2476 + 24.6775i) q^{43} -112.214i q^{44} +(302.805 + 174.825i) q^{46} +108.626i q^{47} +(-165.035 - 285.848i) q^{49} +(-77.6837 + 44.8507i) q^{50} +(161.984 - 94.4098i) q^{52} -215.231 q^{53} +(182.807 + 316.631i) q^{55} +(-14.3838 + 24.9135i) q^{56} +(-379.651 - 219.191i) q^{58} +(-339.576 - 196.055i) q^{59} +(112.459 - 194.785i) q^{61} +(53.3357 + 92.3802i) q^{62} -64.0000 q^{64} +(-303.262 + 530.278i) q^{65} +(-120.801 + 69.7442i) q^{67} +(230.951 + 400.019i) q^{68} -93.7299i q^{70} +(-550.285 - 317.707i) q^{71} +946.887i q^{73} +(126.768 - 219.568i) q^{74} +(448.445 - 258.910i) q^{76} -100.880 q^{77} -198.927 q^{79} +(180.586 - 104.261i) q^{80} +(257.251 - 445.571i) q^{82} -692.956i q^{83} +(-1303.33 - 752.478i) q^{85} +56.9903i q^{86} +(-112.214 - 194.361i) q^{88} +(701.782 - 405.174i) q^{89} +(-84.8734 - 145.622i) q^{91} +699.298 q^{92} +(108.626 + 188.146i) q^{94} +(-843.572 + 1461.11i) q^{95} +(-996.265 - 575.194i) q^{97} +(-571.696 - 330.069i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{4} + 18 q^{7} - 8 q^{10} + 18 q^{11} - 130 q^{13} - 80 q^{14} - 64 q^{16} - 112 q^{17} + 594 q^{19} - 72 q^{20} - 72 q^{22} + 230 q^{23} - 180 q^{25} + 184 q^{26} + 72 q^{28} - 32 q^{29} + 128 q^{35}+ \cdots - 4272 q^{98}+O(q^{100}) \) 8 * q + 16 * q^4 + 18 * q^7 - 8 * q^10 + 18 * q^11 - 130 * q^13 - 80 * q^14 - 64 * q^16 - 112 * q^17 + 594 * q^19 - 72 * q^20 - 72 * q^22 + 230 * q^23 - 180 * q^25 + 184 * q^26 + 72 * q^28 - 32 * q^29 + 128 * q^35 - 768 * q^37 + 576 * q^38 - 64 * q^40 + 564 * q^41 - 114 * q^43 + 576 * q^46 - 110 * q^49 - 1968 * q^50 - 104 * q^52 - 36 * q^53 + 1248 * q^55 - 160 * q^56 - 1848 * q^58 + 1110 * q^59 + 900 * q^61 - 1064 * q^62 - 512 * q^64 - 1870 * q^65 + 510 * q^67 + 448 * q^68 + 1470 * q^71 + 680 * q^74 + 2376 * q^76 - 2340 * q^77 + 784 * q^79 - 288 * q^80 + 704 * q^82 - 2898 * q^85 + 288 * q^88 + 4434 * q^89 - 886 * q^91 + 1840 * q^92 - 2568 * q^94 + 816 * q^95 + 1854 * q^97 - 4272 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more