LMFDB - Embedded newform 112.3.s.b.33.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [112,3,Mod(17,112)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(112, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("112.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	112.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.05177896084$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			33.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	112.33
Dual form			112.3.s.b.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.621320 + 0.358719i) q^{3} +(-5.74264 - 3.31552i) q^{5} +(-6.24264 - 3.16693i) q^{7} +(-4.24264 + 7.34847i) q^{9} +O(q^{10})$	\(q+(-0.621320 + 0.358719i) q^{3} +(-5.74264 - 3.31552i) q^{5} +(-6.24264 - 3.16693i) q^{7} +(-4.24264 + 7.34847i) q^{9} +(-2.37868 - 4.11999i) q^{11} -15.2913i q^{13} +4.75736 q^{15} +(-3.25736 + 1.88064i) q^{17} +(-3.62132 - 2.09077i) q^{19} +(5.01472 - 0.271680i) q^{21} +(-13.8640 + 24.0131i) q^{23} +(9.48528 + 16.4290i) q^{25} -12.5446i q^{27} +3.51472 q^{29} +(42.3198 - 24.4334i) q^{31} +(2.95584 + 1.70656i) q^{33} +(25.3492 + 38.8841i) q^{35} +(1.47056 - 2.54709i) q^{37} +(5.48528 + 9.50079i) q^{39} +27.9590i q^{41} +10.4853 q^{43} +(48.7279 - 28.1331i) q^{45} +(-45.6213 - 26.3395i) q^{47} +(28.9411 + 39.5400i) q^{49} +(1.34924 - 2.33696i) q^{51} +(-27.9853 - 48.4719i) q^{53} +31.5462i q^{55} +3.00000 q^{57} +(-33.5330 + 19.3603i) q^{59} +(-78.3823 - 45.2540i) q^{61} +(49.7574 - 32.4377i) q^{63} +(-50.6985 + 87.8124i) q^{65} +(-17.3198 - 29.9988i) q^{67} -19.8931i q^{69} -36.4264 q^{71} +(45.5589 - 26.3034i) q^{73} +(-11.7868 - 6.80511i) q^{75} +(1.80152 + 33.2528i) q^{77} +(-16.8934 + 29.2602i) q^{79} +(-33.6838 - 58.3420i) q^{81} -127.577i q^{83} +24.9411 q^{85} +(-2.18377 + 1.26080i) q^{87} +(-43.5883 - 25.1657i) q^{89} +(-48.4264 + 95.4580i) q^{91} +(-17.5294 + 30.3619i) q^{93} +(13.8640 + 24.0131i) q^{95} -101.792i q^{97} +40.3675 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} - 6 q^{5} - 8 q^{7}+O(q^{10}) $ 4 * q + 6 * q^3 - 6 * q^5 - 8 * q^7	$ 4 q + 6 q^{3} - 6 q^{5} - 8 q^{7} - 18 q^{11} + 36 q^{15} - 30 q^{17} - 6 q^{19} + 54 q^{21} - 30 q^{23} + 4 q^{25} + 48 q^{29} + 42 q^{31} - 90 q^{33} + 42 q^{35} - 62 q^{37} - 12 q^{39} + 8 q^{43} + 144 q^{45} - 174 q^{47} - 20 q^{49} - 54 q^{51} - 78 q^{53} + 12 q^{57} + 78 q^{59} - 42 q^{61} + 216 q^{63} - 84 q^{65} + 58 q^{67} + 24 q^{71} + 318 q^{73} - 132 q^{75} + 126 q^{77} - 110 q^{79} + 18 q^{81} - 36 q^{85} + 144 q^{87} - 378 q^{89} - 24 q^{91} - 138 q^{93} + 30 q^{95} - 144 q^{99}+O(q^{100}) $ 4 * q + 6 * q^3 - 6 * q^5 - 8 * q^7 - 18 * q^11 + 36 * q^15 - 30 * q^17 - 6 * q^19 + 54 * q^21 - 30 * q^23 + 4 * q^25 + 48 * q^29 + 42 * q^31 - 90 * q^33 + 42 * q^35 - 62 * q^37 - 12 * q^39 + 8 * q^43 + 144 * q^45 - 174 * q^47 - 20 * q^49 - 54 * q^51 - 78 * q^53 + 12 * q^57 + 78 * q^59 - 42 * q^61 + 216 * q^63 - 84 * q^65 + 58 * q^67 + 24 * q^71 + 318 * q^73 - 132 * q^75 + 126 * q^77 - 110 * q^79 + 18 * q^81 - 36 * q^85 + 144 * q^87 - 378 * q^89 - 24 * q^91 - 138 * q^93 + 30 * q^95 - 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.621320	+	0.358719i	−0.207107	+	0.119573i	−0.599966	−	0.800025i	$-0.704819\pi$
$3$	−0.621320	+	0.358719i	−0.207107	+	0.119573i	0.392859	+	0.919599i	$0.371486\pi$
$4$		0			0
$5$	−5.74264	−	3.31552i	−1.14853	−	0.663103i	−0.200000	−	0.979796i	$-0.564094\pi$
$5$	−5.74264	−	3.31552i	−1.14853	−	0.663103i	−0.948528	+	0.316693i	$0.897428\pi$
$6$		0			0
$7$	−6.24264	−	3.16693i	−0.891806	−	0.452418i
$7$	−6.24264	−	3.16693i	−0.891806	−	0.452418i
$8$		0			0
$9$	−4.24264	+	7.34847i	−0.471405	+	0.816497i
$10$		0			0
$11$	−2.37868	−	4.11999i	−0.216244	−	0.374545i	0.737413	−	0.675442i	$-0.236047\pi$
$11$	−2.37868	−	4.11999i	−0.216244	−	0.374545i	−0.953657	+	0.300897i	$0.902714\pi$
$12$		0			0
$13$		−	15.2913i		−	1.17625i	−0.808769	−	0.588126i	$-0.799866\pi$
$13$		−	15.2913i		−	1.17625i	0.808769	−	0.588126i	$-0.200134\pi$
$14$		0			0
$15$	4.75736			0.317157
$16$		0			0
$17$	−3.25736	+	1.88064i	−0.191609	+	0.110626i	−0.592736	−	0.805397i	$-0.701952\pi$
$17$	−3.25736	+	1.88064i	−0.191609	+	0.110626i	0.401126	+	0.916023i	$0.368619\pi$
$18$		0			0
$19$	−3.62132	−	2.09077i	−0.190596	−	0.110041i	0.401666	−	0.915786i	$-0.368431\pi$
$19$	−3.62132	−	2.09077i	−0.190596	−	0.110041i	−0.592261	+	0.805746i	$0.701765\pi$
$20$		0			0
$21$	5.01472	−	0.271680i	0.238796	−	0.0129371i
$22$		0			0
$23$	−13.8640	+	24.0131i	−0.602781	+	1.04405i	0.389617	+	0.920977i	$0.372607\pi$
$23$	−13.8640	+	24.0131i	−0.602781	+	1.04405i	−0.992398	+	0.123070i	$0.960726\pi$
$24$		0			0
$25$	9.48528	+	16.4290i	0.379411	+	0.657160i
$26$		0			0
$27$		−	12.5446i		−	0.464616i
$28$		0			0
$29$	3.51472			0.121197			0.0605986	−	0.998162i	$-0.480699\pi$
$29$	3.51472			0.121197			0.0605986	+	0.998162i	$0.480699\pi$
$30$		0			0
$31$	42.3198	−	24.4334i	1.36516	−	0.788173i	0.374850	−	0.927085i	$-0.377694\pi$
$31$	42.3198	−	24.4334i	1.36516	−	0.788173i	0.990305	+	0.138913i	$0.0443607\pi$
$32$		0			0
$33$	2.95584	+	1.70656i	0.0895710	+	0.0517139i
$34$		0			0
$35$	25.3492	+	38.8841i	0.724264	+	1.11097i
$36$		0			0
$37$	1.47056	−	2.54709i	0.0397449	−	0.0688403i	−0.845469	−	0.534025i	$-0.820679\pi$
$37$	1.47056	−	2.54709i	0.0397449	−	0.0688403i	0.885214	+	0.465185i	$0.154012\pi$
$38$		0			0
$39$	5.48528	+	9.50079i	0.140648	+	0.243610i
$40$		0			0
$41$			27.9590i			0.681927i	0.940077	+	0.340963i	$0.110753\pi$
$41$			27.9590i			0.681927i	−0.940077	+	0.340963i	$0.889247\pi$
$42$		0			0
$43$	10.4853			0.243844			0.121922	−	0.992540i	$-0.461094\pi$
$43$	10.4853			0.243844			0.121922	+	0.992540i	$0.461094\pi$
$44$		0			0
$45$	48.7279	−	28.1331i	1.08284	−	0.625180i
$46$		0			0
$47$	−45.6213	−	26.3395i	−0.970666	−	0.560415i	−0.0712271	−	0.997460i	$-0.522691\pi$
$47$	−45.6213	−	26.3395i	−0.970666	−	0.560415i	−0.899439	+	0.437046i	$0.856025\pi$
$48$		0			0
$49$	28.9411	+	39.5400i	0.590635	+	0.806939i
$50$		0			0
$51$	1.34924	−	2.33696i	0.0264557	−	0.0458227i
$52$		0			0
$53$	−27.9853	−	48.4719i	−0.528024	−	0.914565i	−0.999466	−	0.0326677i	$-0.989600\pi$
$53$	−27.9853	−	48.4719i	−0.528024	−	0.914565i	0.471442	−	0.881897i	$-0.343734\pi$
$54$		0			0
$55$			31.5462i			0.573567i
$56$		0			0
$57$	3.00000			0.0526316
$58$		0			0
$59$	−33.5330	+	19.3603i	−0.568356	+	0.328141i	−0.756492	−	0.654002i	$-0.773089\pi$
$59$	−33.5330	+	19.3603i	−0.568356	+	0.328141i	0.188136	+	0.982143i	$0.439755\pi$
$60$		0			0
$61$	−78.3823	−	45.2540i	−1.28495	−	0.741869i	−0.307205	−	0.951643i	$-0.599394\pi$
$61$	−78.3823	−	45.2540i	−1.28495	−	0.741869i	−0.977750	+	0.209774i	$0.932727\pi$
$62$		0			0
$63$	49.7574	−	32.4377i	0.789799	−	0.514884i
$64$		0			0
$65$	−50.6985	+	87.8124i	−0.779977	+	1.35096i
$66$		0			0
$67$	−17.3198	−	29.9988i	−0.258505	−	0.447743i	0.707337	−	0.706877i	$-0.249896\pi$
$67$	−17.3198	−	29.9988i	−0.258505	−	0.447743i	−0.965842	+	0.259134i	$0.916563\pi$
$68$		0			0
$69$		−	19.8931i		−	0.288306i
$70$		0			0
$71$	−36.4264			−0.513048			−0.256524	−	0.966538i	$-0.582577\pi$
$71$	−36.4264			−0.513048			−0.256524	+	0.966538i	$0.582577\pi$
$72$		0			0
$73$	45.5589	−	26.3034i	0.624094	−	0.360321i	−0.154367	−	0.988014i	$-0.549334\pi$
$73$	45.5589	−	26.3034i	0.624094	−	0.360321i	0.778461	+	0.627693i	$0.216001\pi$
$74$		0			0
$75$	−11.7868	−	6.80511i	−0.157157	−	0.0907348i
$76$		0			0
$77$	1.80152	+	33.2528i	0.0233963	+	0.431854i
$78$		0			0
$79$	−16.8934	+	29.2602i	−0.213840	+	0.370383i	−0.952913	−	0.303243i	$-0.901931\pi$
$79$	−16.8934	+	29.2602i	−0.213840	+	0.370383i	0.739073	+	0.673626i	$0.235264\pi$
$80$		0			0
$81$	−33.6838	−	58.3420i	−0.415849	−	0.720272i
$82$		0			0
$83$		−	127.577i		−	1.53708i	−0.639803	−	0.768539i	$-0.720984\pi$
$83$		−	127.577i		−	1.53708i	0.639803	−	0.768539i	$-0.279016\pi$
$84$		0			0
$85$	24.9411			0.293425
$86$		0			0
$87$	−2.18377	+	1.26080i	−0.0251008	+	0.0144919i
$88$		0			0
$89$	−43.5883	−	25.1657i	−0.489756	−	0.282761i	0.234717	−	0.972064i	$-0.424584\pi$
$89$	−43.5883	−	25.1657i	−0.489756	−	0.282761i	−0.724473	+	0.689303i	$0.757917\pi$
$90$		0			0
$91$	−48.4264	+	95.4580i	−0.532158	+	1.04899i
$92$		0			0
$93$	−17.5294	+	30.3619i	−0.188489	+	0.326472i
$94$		0			0
$95$	13.8640	+	24.0131i	0.145936	+	0.252769i
$96$		0			0
$97$		−	101.792i		−	1.04940i	−0.851287	−	0.524700i	$-0.824177\pi$
$97$		−	101.792i		−	1.04940i	0.851287	−	0.524700i	$-0.175823\pi$
$98$		0			0
$99$	40.3675			0.407753
$100$		0			0
$101$	−51.6838	+	29.8396i	−0.511720	+	0.295442i	−0.733541	−	0.679646i	$-0.762134\pi$
$101$	−51.6838	+	29.8396i	−0.511720	+	0.295442i	0.221820	+	0.975088i	$0.428800\pi$
$102$		0			0
$103$	−104.077	−	60.0890i	−1.01046	−	0.583388i	−0.0991322	−	0.995074i	$-0.531607\pi$
$103$	−104.077	−	60.0890i	−1.01046	−	0.583388i	−0.911326	+	0.411686i	$0.864940\pi$
$104$		0			0
$105$	−29.6985	−	15.0662i	−0.282843	−	0.143488i
$106$		0			0
$107$	−56.8051	+	98.3893i	−0.530889	+	0.919526i	0.468462	+	0.883484i	$0.344808\pi$
$107$	−56.8051	+	98.3893i	−0.530889	+	0.919526i	−0.999350	+	0.0360423i	$0.988525\pi$
$108$		0			0
$109$	72.6543	+	125.841i	0.666553	+	1.15450i	0.978862	+	0.204524i	$0.0655645\pi$
$109$	72.6543	+	125.841i	0.666553	+	1.15450i	−0.312308	+	0.949981i	$0.601102\pi$
$110$		0			0
$111$			2.11008i			0.0190097i
$112$		0			0
$113$	34.5442			0.305700			0.152850	−	0.988249i	$-0.451155\pi$
$113$	34.5442			0.305700			0.152850	+	0.988249i	$0.451155\pi$
$114$		0			0
$115$	159.231	−	91.9323i	1.38462	−	0.799412i
$116$		0			0
$117$	112.368	+	64.8754i	0.960406	+	0.554491i
$118$		0			0
$119$	26.2904	−	1.42432i	0.220927	−	0.0119691i
$120$		0			0
$121$	49.1838	−	85.1888i	0.406477	−	0.704040i
$122$		0			0
$123$	−10.0294	−	17.3715i	−0.0815401	−	0.141232i
$124$		0			0
$125$			39.9814i			0.319851i
$126$		0			0
$127$	247.338			1.94754			0.973772	−	0.227526i	$-0.0730636\pi$
$127$	247.338			1.94754			0.973772	+	0.227526i	$0.0730636\pi$
$128$		0			0
$129$	−6.51472	+	3.76127i	−0.0505017	+	0.0291572i
$130$		0			0
$131$	127.864	+	73.8223i	0.976061	+	0.563529i	0.901079	−	0.433656i	$-0.142777\pi$
$131$	127.864	+	73.8223i	0.976061	+	0.563529i	0.0749822	+	0.997185i	$0.476110\pi$
$132$		0			0
$133$	15.9853	+	24.5204i	0.120190	+	0.184364i
$134$		0			0
$135$	−41.5919	+	72.0393i	−0.308088	+	0.533624i
$136$		0			0
$137$	16.2868	+	28.2096i	0.118882	+	0.205909i	0.919325	−	0.393500i	$-0.128736\pi$
$137$	16.2868	+	28.2096i	0.118882	+	0.205909i	−0.800443	+	0.599409i	$0.795402\pi$
$138$		0			0
$139$			68.5857i			0.493422i	0.969089	+	0.246711i	$0.0793499\pi$
$139$			68.5857i			0.493422i	−0.969089	+	0.246711i	$0.920650\pi$
$140$		0			0
$141$	37.7939			0.268042
$142$		0			0
$143$	−63.0000	+	36.3731i	−0.440559	+	0.254357i
$144$		0			0
$145$	−20.1838	−	11.6531i	−0.139198	−	0.0803662i
$146$		0			0
$147$	−32.1655	−	14.1853i	−0.218813	−	0.0964984i
$148$		0			0
$149$	−46.1985	+	80.0181i	−0.310057	+	0.537034i	−0.978374	−	0.206842i	$-0.933681\pi$
$149$	−46.1985	+	80.0181i	−0.310057	+	0.537034i	0.668317	+	0.743876i	$0.267015\pi$
$150$		0			0
$151$	−45.8934	−	79.4897i	−0.303930	−	0.526422i	0.673093	−	0.739558i	$-0.264965\pi$
$151$	−45.8934	−	79.4897i	−0.303930	−	0.526422i	−0.977022	+	0.213136i	$0.931632\pi$
$152$		0			0
$153$		−	31.9155i		−	0.208598i
$154$		0			0
$155$	−324.037			−2.09056
$156$		0			0
$157$	7.32338	−	4.22815i	0.0466457	−	0.0269309i	−0.476496	−	0.879177i	$-0.658093\pi$
$157$	7.32338	−	4.22815i	0.0466457	−	0.0269309i	0.523142	+	0.852246i	$0.324760\pi$
$158$		0			0
$159$	34.7756	+	20.0777i	0.218715	+	0.126275i
$160$		0			0
$161$	162.595	−	105.999i	1.00991	−	0.658378i
$162$		0			0
$163$	110.989	−	192.238i	0.680913	−	1.17938i	−0.293789	−	0.955870i	$-0.594916\pi$
$163$	110.989	−	192.238i	0.680913	−	1.17938i	0.974703	−	0.223506i	$-0.0717503\pi$
$164$		0			0
$165$	−11.3162	−	19.6003i	−0.0685832	−	0.118790i
$166$		0			0
$167$			168.841i			1.01102i	0.862820	+	0.505511i	$0.168696\pi$
$167$			168.841i			1.01102i	−0.862820	+	0.505511i	$0.831304\pi$
$168$		0			0
$169$	−64.8234			−0.383570
$170$		0			0
$171$	30.7279	−	17.7408i	0.179695	−	0.103747i
$172$		0			0
$173$	−142.323	−	82.1704i	−0.822678	−	0.474974i	0.0286608	−	0.999589i	$-0.490876\pi$
$173$	−142.323	−	82.1704i	−0.822678	−	0.474974i	−0.851339	+	0.524616i	$0.824209\pi$
$174$		0			0
$175$	−7.18377	−	132.599i	−0.0410501	−	0.757711i
$176$		0			0
$177$	13.8898	−	24.0579i	0.0784736	−	0.135920i
$178$		0			0
$179$	92.5919	+	160.374i	0.517273	+	0.895943i	0.999799	+	0.0200614i	$0.00638618\pi$
$179$	92.5919	+	160.374i	0.517273	+	0.895943i	−0.482526	+	0.875882i	$0.660280\pi$
$180$		0			0
$181$			155.086i			0.856830i	0.903582	+	0.428415i	$0.140928\pi$
$181$			155.086i			0.856830i	−0.903582	+	0.428415i	$0.859072\pi$
$182$		0			0
$183$	64.9340			0.354831
$184$		0			0
$185$	−16.8898	+	9.75135i	−0.0912964	+	0.0527100i
$186$		0			0
$187$	15.4964	+	8.94687i	0.0828686	+	0.0478442i
$188$		0			0
$189$	−39.7279	+	78.3116i	−0.210201	+	0.414347i
$190$		0			0
$191$	124.048	−	214.857i	0.649465	−	1.12491i	−0.333786	−	0.942649i	$-0.608326\pi$
$191$	124.048	−	214.857i	0.649465	−	1.12491i	0.983251	−	0.182257i	$-0.0583402\pi$
$192$		0			0
$193$	−77.1690	−	133.661i	−0.399840	−	0.692543i	0.593866	−	0.804564i	$-0.297601\pi$
$193$	−77.1690	−	133.661i	−0.399840	−	0.692543i	−0.993706	+	0.112021i	$0.964268\pi$
$194$		0			0
$195$		−	72.7461i		−	0.373057i
$196$		0			0
$197$	−181.103			−0.919303			−0.459651	−	0.888099i	$-0.652026\pi$
$197$	−181.103			−0.919303			−0.459651	+	0.888099i	$0.652026\pi$
$198$		0			0
$199$	−301.989	+	174.353i	−1.51753	+	0.876147i	−0.517744	+	0.855535i	$0.673228\pi$
$199$	−301.989	+	174.353i	−1.51753	+	0.876147i	−0.999788	+	0.0206121i	$0.993439\pi$
$200$		0			0
$201$	21.5223	+	12.4259i	0.107076	+	0.0618204i
$202$		0			0
$203$	−21.9411	−	11.1309i	−0.108084	−	0.0548318i
$204$		0			0
$205$	92.6985	−	160.558i	0.452188	−	0.783212i
$206$		0			0
$207$	−117.640	−	203.758i	−0.568307	−	0.984337i
$208$		0			0
$209$			19.8931i			0.0951823i
$210$		0			0
$211$	−364.073			−1.72547			−0.862733	−	0.505660i	$-0.831249\pi$
$211$	−364.073			−1.72547			−0.862733	+	0.505660i	$0.831249\pi$
$212$		0			0
$213$	22.6325	−	13.0669i	0.106256	−	0.0613468i
$214$		0			0
$215$	−60.2132	−	34.7641i	−0.280061	−	0.161694i
$216$		0			0
$217$	−341.566	+	18.5048i	−1.57404	+	0.0852757i
$218$		0			0
$219$	−18.8711	+	32.6857i	−0.0861694	+	0.149250i
$220$		0			0
$221$	28.7574	+	49.8092i	0.130124	+	0.225381i
$222$		0			0
$223$			123.231i			0.552603i	0.961071	+	0.276302i	$0.0891089\pi$
$223$			123.231i			0.552603i	−0.961071	+	0.276302i	$0.910891\pi$
$224$		0			0
$225$	−160.971			−0.715425
$226$		0			0
$227$	66.1432	−	38.1878i	0.291380	−	0.168228i	−0.347184	−	0.937797i	$-0.612862\pi$
$227$	66.1432	−	38.1878i	0.291380	−	0.168228i	0.638564	+	0.769569i	$0.279529\pi$
$228$		0			0
$229$	309.419	+	178.643i	1.35117	+	0.780101i	0.988414	−	0.151782i	$-0.0485012\pi$
$229$	309.419	+	178.643i	1.35117	+	0.780101i	0.362760	+	0.931883i	$0.381834\pi$
$230$		0			0
$231$	−13.0477	−	20.0144i	−0.0564837	−	0.0866423i
$232$		0			0
$233$	136.537	−	236.488i	0.585994	−	1.01497i	−0.408757	−	0.912643i	$-0.634038\pi$
$233$	136.537	−	236.488i	0.585994	−	1.01497i	0.994751	−	0.102328i	$-0.0326291\pi$
$234$		0			0
$235$	174.658	+	302.516i	0.743225	+	1.28730i
$236$		0			0
$237$		−	24.2400i		−	0.102278i
$238$		0			0
$239$	265.103			1.10922			0.554608	−	0.832112i	$-0.312868\pi$
$239$	265.103			1.10922			0.554608	+	0.832112i	$0.312868\pi$
$240$		0			0
$241$	−75.8970	+	43.8191i	−0.314925	+	0.181822i	−0.649128	−	0.760679i	$-0.724866\pi$
$241$	−75.8970	+	43.8191i	−0.314925	+	0.181822i	0.334203	+	0.942501i	$0.391533\pi$
$242$		0			0
$243$	139.632	+	80.6168i	0.574619	+	0.331757i
$244$		0			0
$245$	−35.1030	−	323.019i	−0.143278	−	1.31844i
$246$		0			0
$247$	−31.9706	+	55.3746i	−0.129435	+	0.224189i
$248$		0			0
$249$	45.7645	+	79.2664i	0.183793	+	0.318339i
$250$		0			0
$251$		−	495.655i		−	1.97472i	−0.158491	−	0.987360i	$-0.550663\pi$
$251$		−	495.655i		−	1.97472i	0.158491	−	0.987360i	$-0.449337\pi$
$252$		0			0
$253$	131.912			0.521390
$254$		0			0
$255$	−15.4964	+	8.94687i	−0.0607703	+	0.0350858i
$256$		0			0
$257$	346.875	+	200.268i	1.34971	+	0.779254i	0.988208	−	0.153119i	$-0.0489317\pi$
$257$	346.875	+	200.268i	1.34971	+	0.779254i	0.361499	+	0.932372i	$0.382265\pi$
$258$		0			0
$259$	−17.2466	+	11.2434i	−0.0665894	+	0.0434108i
$260$		0			0
$261$	−14.9117	+	25.8278i	−0.0571329	+	0.0989571i
$262$		0			0
$263$	−16.1726	−	28.0118i	−0.0614928	−	0.106509i	0.833640	−	0.552308i	$-0.186253\pi$
$263$	−16.1726	−	28.0118i	−0.0614928	−	0.106509i	−0.895133	+	0.445799i	$0.852919\pi$
$264$		0			0
$265$			371.142i			1.40054i
$266$		0			0
$267$	36.1097			0.135242
$268$		0			0
$269$	−265.838	+	153.482i	−0.988246	+	0.570564i	−0.904749	−	0.425944i	$-0.859942\pi$
$269$	−265.838	+	153.482i	−0.988246	+	0.570564i	−0.0834963	+	0.996508i	$0.526609\pi$
$270$		0			0
$271$	65.8051	+	37.9926i	0.242823	+	0.140194i	0.616474	−	0.787376i	$-0.288561\pi$
$271$	65.8051	+	37.9926i	0.242823	+	0.140194i	−0.373650	+	0.927570i	$0.621894\pi$
$272$		0			0
$273$	−4.15433	−	76.6815i	−0.0152173	−	0.280885i
$274$		0			0
$275$	45.1249	−	78.1586i	0.164091	−	0.284213i
$276$		0			0
$277$	−139.206	−	241.111i	−0.502547	−	0.870438i	−0.999996	−	0.00294398i	$-0.999063\pi$
$277$	−139.206	−	241.111i	−0.502547	−	0.870438i	0.497448	−	0.867494i	$-0.334270\pi$
$278$		0			0
$279$			414.648i			1.48619i
$280$		0			0
$281$	394.690			1.40459			0.702296	−	0.711885i	$-0.252158\pi$
$281$	394.690			1.40459			0.702296	+	0.711885i	$0.252158\pi$
$282$		0			0
$283$	−126.783	+	73.1981i	−0.447996	+	0.258650i	−0.706983	−	0.707230i	$-0.749944\pi$
$283$	−126.783	+	73.1981i	−0.447996	+	0.258650i	0.258988	+	0.965881i	$0.416611\pi$
$284$		0			0
$285$	−17.2279	−	9.94655i	−0.0604488	−	0.0349002i
$286$		0			0
$287$	88.5442	−	174.538i	0.308516	−	0.608146i
$288$		0			0
$289$	−137.426	+	238.030i	−0.475524	+	0.823632i
$290$		0			0
$291$	36.5147	+	63.2453i	0.125480	+	0.217338i
$292$		0			0
$293$		−	299.678i		−	1.02279i	−0.859345	−	0.511396i	$-0.829128\pi$
$293$		−	299.678i		−	1.02279i	0.859345	−	0.511396i	$-0.170872\pi$
$294$		0			0
$295$	256.757			0.870364
$296$		0			0
$297$	−51.6838	+	29.8396i	−0.174019	+	0.100470i
$298$		0			0
$299$	367.191	+	211.998i	1.22806	+	0.709023i
$300$		0			0
$301$	−65.4558	−	33.2061i	−0.217461	−	0.110319i
$302$		0			0
$303$	21.4081	−	37.0799i	0.0706539	−	0.122376i
$304$		0			0
$305$	300.081	+	519.755i	0.983871	+	1.70412i
$306$		0			0
$307$		−	20.9886i		−	0.0683666i	−0.999416	−	0.0341833i	$-0.989117\pi$
$307$		−	20.9886i		−	0.0683666i	0.999416	−	0.0341833i	$-0.0108830\pi$
$308$		0			0
$309$	86.2203			0.279030
$310$		0			0
$311$	−157.651	+	91.0197i	−0.506916	+	0.292668i	−0.731565	−	0.681772i	$-0.761210\pi$
$311$	−157.651	+	91.0197i	−0.506916	+	0.292668i	0.224649	+	0.974440i	$0.427876\pi$
$312$		0			0
$313$	−84.8087	−	48.9643i	−0.270954	−	0.156435i	0.358367	−	0.933581i	$-0.383334\pi$
$313$	−84.8087	−	48.9643i	−0.270954	−	0.156435i	−0.629321	+	0.777145i	$0.716667\pi$
$314$		0			0
$315$	−393.286	+	21.3068i	−1.24853	+	0.0676408i
$316$		0			0
$317$	240.985	−	417.399i	0.760206	−	1.31672i	−0.182538	−	0.983199i	$-0.558431\pi$
$317$	240.985	−	417.399i	0.760206	−	1.31672i	0.942744	−	0.333517i	$-0.108235\pi$
$318$		0			0
$319$	−8.36039	−	14.4806i	−0.0262081	−	0.0453938i
$320$		0			0
$321$		−	81.5084i		−	0.253920i
$322$		0			0
$323$	15.7279			0.0486933
$324$		0			0
$325$	251.220	−	145.042i	0.772986	−	0.446283i
$326$		0			0
$327$	−90.2832	−	52.1250i	−0.276095	−	0.159404i
$328$		0			0
$329$	201.382	+	308.907i	0.612104	+	0.938928i
$330$		0			0
$331$	112.504	−	194.862i	0.339890	−	0.588707i	−0.644522	−	0.764586i	$-0.722944\pi$
$331$	112.504	−	194.862i	0.339890	−	0.588707i	0.984412	+	0.175879i	$0.0562768\pi$
$332$		0			0
$333$	12.4781	+	21.6128i	0.0374719	+	0.0649032i
$334$		0			0
$335$			229.696i			0.685661i
$336$		0			0
$337$	−264.368			−0.784473			−0.392237	−	0.919864i	$-0.628299\pi$
$337$	−264.368			−0.784473			−0.392237	+	0.919864i	$0.628299\pi$
$338$		0			0
$339$	−21.4630	+	12.3917i	−0.0633126	+	0.0365536i
$340$		0			0
$341$	−201.331	−	116.238i	−0.590412	−	0.340875i
$342$		0			0
$343$	−55.4487	−	338.488i	−0.161658	−	0.986847i
$344$		0			0
$345$	−65.9558	+	114.239i	−0.191176	+	0.331127i
$346$		0			0
$347$	−95.6285	−	165.633i	−0.275586	−	0.477330i	0.694697	−	0.719303i	$-0.255539\pi$
$347$	−95.6285	−	165.633i	−0.275586	−	0.477330i	−0.970283	+	0.241973i	$0.922205\pi$
$348$		0			0
$349$		−	135.448i		−	0.388104i	−0.980991	−	0.194052i	$-0.937837\pi$
$349$		−	135.448i		−	0.388104i	0.980991	−	0.194052i	$-0.0621630\pi$
$350$		0			0
$351$	−191.823			−0.546505
$352$		0			0
$353$	−301.802	+	174.245i	−0.854962	+	0.493612i	−0.862322	−	0.506360i	$-0.830991\pi$
$353$	−301.802	+	174.245i	−0.854962	+	0.493612i	0.00736010	+	0.999973i	$0.497657\pi$
$354$		0			0
$355$	209.184	+	120.772i	0.589250	+	0.340204i
$356$		0			0
$357$	−15.8238	+	10.3158i	−0.0443244	+	0.0288959i
$358$		0			0
$359$	152.415	−	263.991i	0.424555	−	0.735351i	−0.571824	−	0.820377i	$-0.693764\pi$
$359$	152.415	−	263.991i	0.424555	−	0.735351i	0.996379	+	0.0850256i	$0.0270972\pi$
$360$		0			0
$361$	−171.757	−	297.492i	−0.475782	−	0.824079i
$362$		0			0
$363$			70.5727i			0.194415i
$364$		0			0
$365$	−348.838			−0.955720
$366$		0			0
$367$	82.2761	−	47.5021i	0.224186	−	0.129434i	−0.383701	−	0.923457i	$-0.625351\pi$
$367$	82.2761	−	47.5021i	0.224186	−	0.129434i	0.607887	+	0.794024i	$0.292017\pi$
$368$		0			0
$369$	−205.456	−	118.620i	−0.556791	−	0.321463i
$370$		0			0
$371$	21.1949	+	391.220i	0.0571291	+	1.05450i
$372$		0			0
$373$	−126.779	+	219.588i	−0.339891	+	0.588708i	−0.984412	−	0.175879i	$-0.943723\pi$
$373$	−126.779	+	219.588i	−0.339891	+	0.588708i	0.644521	+	0.764586i	$0.277057\pi$
$374$		0			0
$375$	−14.3421	−	24.8412i	−0.0382456	−	0.0662433i
$376$		0			0
$377$		−	53.7446i		−	0.142559i
$378$		0			0
$379$	−508.250			−1.34103			−0.670514	−	0.741897i	$-0.733926\pi$
$379$	−508.250			−1.34103			−0.670514	+	0.741897i	$0.733926\pi$
$380$		0			0
$381$	−153.676	+	88.7250i	−0.403350	+	0.232874i
$382$		0			0
$383$	−413.753	−	238.881i	−1.08030	−	0.623709i	−0.149320	−	0.988789i	$-0.547708\pi$
$383$	−413.753	−	238.881i	−1.08030	−	0.623709i	−0.930976	+	0.365080i	$0.881042\pi$
$384$		0			0
$385$	99.9045	−	196.932i	0.259492	−	0.511511i
$386$		0			0
$387$	−44.4853	+	77.0508i	−0.114949	+	0.199098i
$388$		0			0
$389$	−85.1102	−	147.415i	−0.218792	−	0.378959i	0.735647	−	0.677365i	$-0.236878\pi$
$389$	−85.1102	−	147.415i	−0.218792	−	0.378959i	−0.954439	+	0.298406i	$0.903545\pi$
$390$		0			0
$391$		−	104.292i		−	0.266732i
$392$		0			0
$393$	−105.926			−0.269532
$394$		0			0
$395$	194.025	−	112.021i	0.491204	−	0.283597i
$396$		0			0
$397$	211.786	+	122.275i	0.533467	+	0.307997i	0.742427	−	0.669927i	$-0.233675\pi$
$397$	211.786	+	122.275i	0.533467	+	0.307997i	−0.208960	+	0.977924i	$0.567008\pi$
$398$		0			0
$399$	−18.7279	−	9.50079i	−0.0469371	−	0.0238115i
$400$		0			0
$401$	208.786	−	361.629i	0.520664	−	0.901817i	−0.479047	−	0.877789i	$-0.659018\pi$
$401$	208.786	−	361.629i	0.520664	−	0.901817i	0.999711	−	0.0240277i	$-0.00764899\pi$
$402$		0			0
$403$	−373.617	−	647.124i	−0.927090	−	1.60577i
$404$		0			0
$405$			446.716i			1.10300i
$406$		0			0
$407$	−13.9920			−0.0343784
$408$		0			0
$409$	266.919	−	154.106i	0.652614	−	0.376787i	−0.136843	−	0.990593i	$-0.543696\pi$
$409$	266.919	−	154.106i	0.652614	−	0.376787i	0.789457	+	0.613806i	$0.210362\pi$
$410$		0			0
$411$	−20.2386	−	11.6848i	−0.0492424	−	0.0284301i
$412$		0			0
$413$	270.647	−	14.6627i	0.655320	−	0.0355029i
$414$		0			0
$415$	−422.985	+	732.631i	−1.01924	+	1.76538i
$416$		0			0
$417$	−24.6030	−	42.6137i	−0.0590001	−	0.102191i
$418$		0			0
$419$		−	103.142i		−	0.246163i	−0.992397	−	0.123081i	$-0.960722\pi$
$419$		−	103.142i		−	0.246163i	0.992397	−	0.123081i	$-0.0392776\pi$
$420$		0			0
$421$	−165.220			−0.392447			−0.196224	−	0.980559i	$-0.562868\pi$
$421$	−165.220			−0.392447			−0.196224	+	0.980559i	$0.562868\pi$
$422$		0			0
$423$	387.110	−	223.498i	0.915153	−	0.528364i
$424$		0			0
$425$	−61.7939	−	35.6767i	−0.145398	−	0.0839453i
$426$		0			0
$427$	345.996	+	530.736i	0.810295	+	1.24294i
$428$		0			0
$429$	26.0955	−	45.1987i	0.0608286	−	0.105358i
$430$		0			0
$431$	297.268	+	514.883i	0.689717	+	1.19463i	0.971929	+	0.235273i	$0.0755984\pi$
$431$	297.268	+	514.883i	0.689717	+	1.19463i	−0.282212	+	0.959352i	$0.591068\pi$
$432$		0			0
$433$			40.6267i			0.0938261i	0.998899	+	0.0469131i	$0.0149384\pi$
$433$			40.6267i			0.0938261i	−0.998899	+	0.0469131i	$0.985062\pi$
$434$		0			0
$435$	16.7208			0.0384386
$436$		0			0
$437$	100.412	−	57.9727i	0.229775	−	0.132661i
$438$		0			0
$439$	−126.959	−	73.3001i	−0.289201	−	0.166971i	0.348380	−	0.937353i	$-0.386732\pi$
$439$	−126.959	−	73.3001i	−0.289201	−	0.166971i	−0.637582	+	0.770383i	$0.720065\pi$
$440$		0			0
$441$	−413.345	+	44.9190i	−0.937291	+	0.101857i
$442$		0			0
$443$	53.6802	−	92.9768i	0.121174	−	0.209880i	−0.799057	−	0.601256i	$-0.794667\pi$
$443$	53.6802	−	92.9768i	0.121174	−	0.209880i	0.920231	+	0.391376i	$0.128001\pi$
$444$		0			0
$445$	166.875	+	289.035i	0.374999	+	0.649518i
$446$		0			0
$447$		−	66.2892i		−	0.148298i
$448$		0			0
$449$	135.161			0.301028			0.150514	−	0.988608i	$-0.451907\pi$
$449$	135.161			0.301028			0.150514	+	0.988608i	$0.451907\pi$
$450$		0			0
$451$	115.191	−	66.5055i	0.255412	−	0.147462i
$452$		0			0
$453$	57.0290	+	32.9257i	0.125892	+	0.0726837i
$454$		0			0
$455$	594.588	−	387.622i	1.30679	−	0.851918i
$456$		0			0
$457$	−79.8675	+	138.335i	−0.174765	+	0.302702i	−0.940080	−	0.340954i	$-0.889250\pi$
$457$	−79.8675	+	138.335i	−0.174765	+	0.302702i	0.765315	+	0.643656i	$0.222583\pi$
$458$		0			0
$459$	23.5919	+	40.8623i	0.0513984	+	0.0890247i
$460$		0			0
$461$		−	310.250i		−	0.672993i	−0.941685	−	0.336497i	$-0.890758\pi$
$461$		−	310.250i		−	0.672993i	0.941685	−	0.336497i	$-0.109242\pi$
$462$		0			0
$463$	326.014			0.704135			0.352067	−	0.935975i	$-0.385479\pi$
$463$	326.014			0.704135			0.352067	+	0.935975i	$0.385479\pi$
$464$		0			0
$465$	201.331	−	116.238i	0.432969	−	0.249975i
$466$		0			0
$467$	−515.769	−	297.779i	−1.10443	−	0.637643i	−0.167048	−	0.985949i	$-0.553424\pi$
$467$	−515.769	−	297.779i	−1.10443	−	0.637643i	−0.937381	+	0.348306i	$0.886757\pi$
$468$		0			0
$469$	13.1173	+	242.122i	0.0279687	+	0.516252i
$470$		0			0
$471$	−3.03344	+	5.25408i	−0.00644043	+	0.0111551i
$472$		0			0
$473$	−24.9411	−	43.1993i	−0.0527297	−	0.0913304i
$474$		0			0
$475$		−	79.3262i		−	0.167002i
$476$		0			0
$477$	474.926			0.995652
$478$		0			0
$479$	−438.798	+	253.340i	−0.916071	+	0.528894i	−0.882379	−	0.470539i	$-0.844060\pi$
$479$	−438.798	+	253.340i	−0.916071	+	0.528894i	−0.0336914	+	0.999432i	$0.510726\pi$
$480$		0			0
$481$	−38.9483	−	22.4868i	−0.0809735	−	0.0467501i
$482$		0			0
$483$	−63.0000	+	124.185i	−0.130435	+	0.257113i
$484$		0			0
$485$	−337.492	+	584.554i	−0.695861	+	1.20527i
$486$		0			0
$487$	105.651	+	182.992i	0.216942	+	0.375755i	0.953872	−	0.300215i	$-0.0970584\pi$
$487$	105.651	+	182.992i	0.216942	+	0.375755i	−0.736930	+	0.675970i	$0.763725\pi$
$488$		0			0
$489$			159.255i			0.325676i
$490$		0			0
$491$	784.161			1.59707			0.798534	−	0.601949i	$-0.205609\pi$
$491$	784.161			1.59707			0.798534	+	0.601949i	$0.205609\pi$
$492$		0			0
$493$	−11.4487	+	6.60991i	−0.0232225	+	0.0134075i
$494$		0			0
$495$	−231.816	−	133.839i	−0.468316	−	0.270382i
$496$		0			0
$497$	227.397	+	115.360i	0.457539	+	0.232112i
$498$		0			0
$499$	−85.7462	+	148.517i	−0.171836	+	0.297629i	−0.939062	−	0.343748i	$-0.888303\pi$
$499$	−85.7462	+	148.517i	−0.171836	+	0.297629i	0.767226	+	0.641377i	$0.221637\pi$
$500$		0			0
$501$	−60.5665	−	104.904i	−0.120891	−	0.209390i
$502$		0			0
$503$		−	20.0883i		−	0.0399370i	−0.999801	−	0.0199685i	$-0.993643\pi$
$503$		−	20.0883i		−	0.0399370i	0.999801	−	0.0199685i	$-0.00635659\pi$
$504$		0			0
$505$	395.735			0.783634
$506$		0			0
$507$	40.2761	−	23.2534i	0.0794400	−	0.0458647i
$508$		0			0
$509$	−412.890	−	238.382i	−0.811178	−	0.468334i	0.0361865	−	0.999345i	$-0.488479\pi$
$509$	−412.890	−	238.382i	−0.811178	−	0.468334i	−0.847365	+	0.531011i	$0.821812\pi$
$510$		0			0
$511$	−367.709	+	19.9211i	−0.719587	+	0.0389846i
$512$		0			0
$513$	−26.2279	+	45.4281i	−0.0511266	+	0.0885538i
$514$		0			0
$515$	398.452	+	690.139i	0.773693	+	1.34008i
$516$		0			0
$517$			250.613i			0.484744i
$518$		0			0
$519$	117.905			0.227176
$520$		0			0
$521$	739.823	−	427.137i	1.42001	−	0.819841i	0.423707	−	0.905799i	$-0.360729\pi$
$521$	739.823	−	427.137i	1.42001	−	0.819841i	0.996299	+	0.0859587i	$0.0273953\pi$
$522$		0			0
$523$	513.554	+	296.501i	0.981940	+	0.566923i	0.902855	−	0.429945i	$-0.141467\pi$
$523$	513.554	+	296.501i	0.981940	+	0.566923i	0.0790845	+	0.996868i	$0.474800\pi$
$524$		0			0
$525$	52.0294	+	79.8098i	0.0991037	+	0.152019i
$526$		0			0
$527$	−91.9005	+	159.176i	−0.174384	+	0.302043i
$528$		0			0
$529$	−119.919	−	207.706i	−0.226690	−	0.392638i
$530$		0			0
$531$		−	328.555i		−	0.618748i
$532$		0			0
$533$	427.529			0.802118
$534$		0			0
$535$	652.422	−	376.676i	1.21948	−	0.704068i
$536$		0			0
$537$	−115.058	−	66.4290i	−0.214262	−	0.123704i
$538$		0			0
$539$	94.0629	−	213.290i	0.174514	−	0.395715i
$540$		0			0
$541$	−427.595	+	740.617i	−0.790380	+	1.36898i	0.135352	+	0.990798i	$0.456783\pi$
$541$	−427.595	+	740.617i	−0.790380	+	1.36898i	−0.925732	+	0.378180i	$0.876550\pi$
$542$		0			0
$543$	−55.6325	−	96.3583i	−0.102454	−	0.177455i
$544$		0			0
$545$		−	963.546i		−	1.76797i
$546$		0			0
$547$	−415.897			−0.760323			−0.380161	−	0.924920i	$-0.624132\pi$
$547$	−415.897			−0.760323			−0.380161	+	0.924920i	$0.624132\pi$
$548$		0			0
$549$	665.095	−	383.993i	1.21147	−	0.699441i
$550$		0			0
$551$	−12.7279	−	7.34847i	−0.0230997	−	0.0133366i
$552$		0			0
$553$	198.124	−	129.161i	0.358272	−	0.233564i
$554$		0			0
$555$	6.99600	−	12.1174i	0.0126054	−	0.0218332i
$556$		0			0
$557$	292.110	+	505.950i	0.524435	+	0.908348i	0.999595	+	0.0284485i	$0.00905667\pi$
$557$	292.110	+	505.950i	0.524435	+	0.908348i	−0.475160	+	0.879899i	$0.657610\pi$
$558$		0			0
$559$		−	160.333i		−	0.286822i
$560$		0			0
$561$	−12.8377			−0.0228835
$562$		0			0
$563$	−789.076	+	455.573i	−1.40156	+	0.809189i	−0.994552	−	0.104237i	$-0.966760\pi$
$563$	−789.076	+	455.573i	−1.40156	+	0.809189i	−0.407004	+	0.913426i	$0.633427\pi$
$564$		0			0
$565$	−198.375	−	114.532i	−0.351106	−	0.202711i
$566$		0			0
$567$	25.5107	+	470.882i	0.0449924	+	0.830480i
$568$		0			0
$569$	−350.000	+	606.217i	−0.615113	+	1.06541i	0.375251	+	0.926923i	$0.377556\pi$
$569$	−350.000	+	606.217i	−0.615113	+	1.06541i	−0.990365	+	0.138485i	$0.955777\pi$
$570$		0			0
$571$	−281.231	−	487.107i	−0.492525	−	0.853077i	0.507438	−	0.861688i	$-0.330592\pi$
$571$	−281.231	−	487.107i	−0.492525	−	0.853077i	−0.999963	+	0.00861055i	$0.997259\pi$
$572$		0			0
$573$			177.993i			0.310634i
$574$		0			0
$575$	−526.014			−0.914807
$576$		0			0
$577$	−573.014	+	330.830i	−0.993092	+	0.573362i	−0.906197	−	0.422856i	$-0.861028\pi$
$577$	−573.014	+	330.830i	−0.993092	+	0.573362i	−0.0868946	+	0.996218i	$0.527694\pi$
$578$		0			0
$579$	95.8934	+	55.3641i	0.165619	+	0.0956202i
$580$		0			0
$581$	−404.029	+	796.420i	−0.695402	+	1.37077i
$582$		0			0
$583$	−133.136	+	230.598i	−0.228364	+	0.395538i
$584$		0			0
$585$	−430.191	−	745.113i	−0.735369	−	1.27370i
$586$		0			0
$587$		−	823.029i		−	1.40209i	−0.713116	−	0.701046i	$-0.752717\pi$
$587$		−	823.029i		−	1.40209i	0.713116	−	0.701046i	$-0.247283\pi$
$588$		0			0
$589$	−204.338			−0.346924
$590$		0			0
$591$	112.523	−	64.9650i	0.190394	−	0.109924i
$592$		0			0
$593$	−538.890	−	311.128i	−0.908752	−	0.524668i	−0.0287225	−	0.999587i	$-0.509144\pi$
$593$	−538.890	−	311.128i	−0.908752	−	0.524668i	−0.880029	+	0.474919i	$0.842477\pi$
$594$		0			0
$595$	−155.698	−	78.9868i	−0.261678	−	0.132751i
$596$		0			0
$597$	125.088	−	216.659i	0.209527	−	0.362912i
$598$		0			0
$599$	−256.422	−	444.137i	−0.428084	−	0.741463i	0.568619	−	0.822601i	$-0.307478\pi$
$599$	−256.422	−	444.137i	−0.428084	−	0.741463i	−0.996703	+	0.0811377i	$0.974145\pi$
$600$		0			0
$601$		−	680.160i		−	1.13171i	−0.824504	−	0.565857i	$-0.808546\pi$
$601$		−	680.160i		−	1.13171i	0.824504	−	0.565857i	$-0.191454\pi$
$602$		0			0
$603$	293.927			0.487441
$604$		0			0
$605$	−564.889	+	326.139i	−0.933701	+	0.539073i
$606$		0			0
$607$	−33.5482	−	19.3690i	−0.0552688	−	0.0319095i	0.472111	−	0.881539i	$-0.343492\pi$
$607$	−33.5482	−	19.3690i	−0.0552688	−	0.0319095i	−0.527380	+	0.849630i	$0.676825\pi$
$608$		0			0
$609$	17.6253	−	0.954877i	0.0289414	−	0.00156794i
$610$		0			0
$611$	−402.765	+	697.609i	−0.659189	+	1.14175i
$612$		0			0
$613$	−200.552	−	347.366i	−0.327164	−	0.566665i	0.654784	−	0.755816i	$-0.272760\pi$
$613$	−200.552	−	347.366i	−0.327164	−	0.566665i	−0.981948	+	0.189151i	$0.939426\pi$
$614$		0			0
$615$			133.011i			0.216278i
$616$		0			0
$617$	−959.044			−1.55437			−0.777183	−	0.629275i	$-0.783352\pi$
$617$	−959.044			−1.55437			−0.777183	+	0.629275i	$0.783352\pi$
$618$		0			0
$619$	869.951	−	502.267i	1.40541	−	0.811416i	0.410473	−	0.911873i	$-0.365364\pi$
$619$	869.951	−	502.267i	1.40541	−	0.811416i	0.994941	+	0.100457i	$0.0320303\pi$
$620$		0			0
$621$	301.235	+	173.918i	0.485081	+	0.280061i
$622$		0			0
$623$	192.408	+	295.142i	0.308841	+	0.473743i
$624$		0			0
$625$	369.691	−	640.323i	0.591505	−	1.02452i
$626$		0			0
$627$	−7.13604	−	12.3600i	−0.0113812	−	0.0197129i
$628$		0			0
$629$			11.0624i			0.0175873i
$630$		0			0
$631$	386.514			0.612542			0.306271	−	0.951944i	$-0.400919\pi$
$631$	386.514			0.612542			0.306271	+	0.951944i	$0.400919\pi$
$632$		0			0
$633$	226.206	−	130.600i	0.357356	−	0.206319i
$634$		0			0
$635$	−1420.37	−	820.053i	−2.23681	−	1.29142i
$636$		0			0
$637$	604.617	−	442.547i	0.949164	−	0.694736i
$638$		0			0
$639$	154.544	−	267.678i	0.241853	−	0.418902i
$640$		0			0
$641$	496.074	+	859.225i	0.773906	+	1.34044i	0.935407	+	0.353572i	$0.115033\pi$
$641$	496.074	+	859.225i	0.773906	+	1.34044i	−0.161502	+	0.986872i	$0.551634\pi$
$642$		0			0
$643$			944.986i			1.46965i	0.678256	+	0.734826i	$0.262736\pi$
$643$			944.986i			1.46965i	−0.678256	+	0.734826i	$0.737264\pi$
$644$		0			0
$645$	49.8823			0.0773368
$646$		0			0
$647$	−2.50357	+	1.44544i	−0.00386951	+	0.00223406i	−0.501934	−	0.864906i	$-0.667378\pi$
$647$	−2.50357	+	1.44544i	−0.00386951	+	0.00223406i	0.498064	+	0.867140i	$0.334044\pi$
$648$		0			0
$649$	159.529	+	92.1039i	0.245807	+	0.141917i
$650$		0			0
$651$	205.584	−	134.024i	0.315797	−	0.205874i
$652$		0			0
$653$	161.529	−	279.777i	0.247365	−	0.428449i	−0.715429	−	0.698686i	$-0.753769\pi$
$653$	161.529	−	279.777i	0.247365	−	0.428449i	0.962794	+	0.270237i	$0.0871019\pi$
$654$		0			0
$655$	−489.518	−	847.870i	−0.747356	−	1.29446i
$656$		0			0
$657$			446.384i			0.679428i
$658$		0			0
$659$	−295.955			−0.449098			−0.224549	−	0.974463i	$-0.572091\pi$
$659$	−295.955			−0.449098			−0.224549	+	0.974463i	$0.572091\pi$
$660$		0			0
$661$	17.9710	−	10.3756i	0.0271876	−	0.0156968i	−0.486345	−	0.873767i	$-0.661670\pi$
$661$	17.9710	−	10.3756i	0.0271876	−	0.0156968i	0.513532	+	0.858070i	$0.328337\pi$
$662$		0			0
$663$	−35.7351	−	20.6316i	−0.0538990	−	0.0311186i
$664$		0			0
$665$	−10.5000	−	193.811i	−0.0157895	−	0.291445i
$666$		0			0
$667$	−48.7279	+	84.3992i	−0.0730554	+	0.126536i
$668$		0			0
$669$	−44.2052	−	76.5656i	−0.0660765	−	0.114448i
$670$		0			0
$671$			430.579i			0.641698i
$672$		0			0
$673$	627.044			0.931714			0.465857	−	0.884860i	$-0.345746\pi$
$673$	627.044			0.931714			0.465857	+	0.884860i	$0.345746\pi$
$674$		0			0
$675$	206.095	−	118.989i	0.305327	−	0.176280i
$676$		0			0
$677$	−94.6097	−	54.6230i	−0.139749	−	0.0806838i	0.428496	−	0.903544i	$-0.359044\pi$
$677$	−94.6097	−	54.6230i	−0.139749	−	0.0806838i	−0.568244	+	0.822860i	$0.692377\pi$
$678$		0			0
$679$	−322.368	+	635.450i	−0.474768	+	0.935861i
$680$		0			0
$681$	−27.3974	+	47.4537i	−0.0402311	+	0.0696824i
$682$		0			0
$683$	396.783	+	687.248i	0.580941	+	1.00622i	0.995368	+	0.0961370i	$0.0306487\pi$
$683$	396.783	+	687.248i	0.580941	+	1.00622i	−0.414427	+	0.910083i	$0.636018\pi$
$684$		0			0
$685$		−	215.996i		−	0.315323i
$686$		0			0
$687$	−256.331			−0.373116
$688$		0			0
$689$	−741.198	+	427.931i	−1.07576	+	0.621090i
$690$		0			0
$691$	−159.253	−	91.9447i	−0.230467	−	0.133060i	0.380320	−	0.924855i	$-0.375814\pi$
$691$	−159.253	−	91.9447i	−0.230467	−	0.133060i	−0.610788	+	0.791794i	$0.709147\pi$
$692$		0			0
$693$	−252.000	−	127.841i	−0.363636	−	0.184475i
$694$		0			0
$695$	227.397	−	393.863i	0.327190	−	0.566710i
$696$		0			0
$697$	−52.5807	−	91.0725i	−0.0754386	−	0.130664i
$698$		0			0
$699$			195.913i			0.280277i
$700$		0			0
$701$	−1043.82			−1.48905			−0.744525	−	0.667595i	$-0.767324\pi$
$701$	−1043.82			−1.48905			−0.744525	+	0.667595i	$0.767324\pi$
$702$		0			0
$703$	−10.6508	+	6.14922i	−0.0151504	+	0.00874711i
$704$		0			0
$705$	−217.037	−	125.306i	−0.307854	−	0.177740i
$706$		0			0
$707$	417.143	−	22.5993i	0.590019	−	0.0319651i
$708$		0			0
$709$	490.279	−	849.188i	0.691507	−	1.19773i	−0.279836	−	0.960048i	$-0.590280\pi$
$709$	490.279	−	849.188i	0.691507	−	1.19773i	0.971344	−	0.237678i	$-0.0763864\pi$
$710$		0			0
$711$	−143.345	−	248.281i	−0.201611	−	0.349200i
$712$		0			0
$713$			1354.97i			1.90038i
$714$		0			0
$715$	482.382			0.674660
$716$		0			0
$717$	−164.714	+	95.0975i	−0.229726	+	0.132632i
$718$		0			0
$719$	674.187	+	389.242i	0.937673	+	0.541366i	0.889230	−	0.457460i	$-0.151241\pi$
$719$	674.187	+	389.242i	0.937673	+	0.541366i	0.0484429	+	0.998826i	$0.484574\pi$
$720$		0			0
$721$	459.419	+	704.719i	0.637197	+	0.977419i
$722$		0			0
$723$	31.4376	−	54.4514i	0.0434821	−	0.0753132i
$724$		0			0
$725$	33.3381	+	57.7433i	0.0459836	+	0.0796459i
$726$		0			0
$727$		−	735.255i		−	1.01135i	−0.862723	−	0.505677i	$-0.831243\pi$
$727$		−	735.255i		−	1.01135i	0.862723	−	0.505677i	$-0.168757\pi$
$728$		0			0
$729$	490.632			0.673021
$730$		0			0
$731$	−34.1543	+	19.7190i	−0.0467227	+	0.0269754i
$732$		0			0
$733$	−414.705	−	239.430i	−0.565764	−	0.326644i	0.189692	−	0.981844i	$-0.439251\pi$
$733$	−414.705	−	239.430i	−0.565764	−	0.326644i	−0.755456	+	0.655200i	$0.772585\pi$
$734$		0			0
$735$	137.683	+	188.106i	0.187324	+	0.255926i
$736$		0			0
$737$	−82.3965	+	142.715i	−0.111800	+	0.193643i
$738$		0			0
$739$	−9.95227	−	17.2378i	−0.0134672	−	0.0233259i	0.859213	−	0.511618i	$-0.170954\pi$
$739$	−9.95227	−	17.2378i	−0.0134672	−	0.0233259i	−0.872680	+	0.488292i	$0.837620\pi$
$740$		0			0
$741$		−	45.8739i		−	0.0619080i
$742$		0			0
$743$	−43.3095			−0.0582901			−0.0291450	−	0.999575i	$-0.509278\pi$
$743$	−43.3095			−0.0582901			−0.0291450	+	0.999575i	$0.509278\pi$
$744$		0			0
$745$	530.603	−	306.344i	0.712218	−	0.411199i
$746$		0			0
$747$	937.499	+	541.265i	1.25502	+	0.724585i
$748$		0			0
$749$	666.206	−	434.311i	0.889460	−	0.579855i
$750$		0			0
$751$	112.665	−	195.142i	0.150020	−	0.259842i	−0.781215	−	0.624263i	$-0.785400\pi$
$751$	112.665	−	195.142i	0.150020	−	0.259842i	0.931235	+	0.364420i	$0.118733\pi$
$752$		0			0
$753$	177.801	+	307.961i	0.236124	+	0.408978i
$754$		0			0
$755$			608.641i			0.806147i
$756$		0			0
$757$	935.779			1.23617			0.618084	−	0.786112i	$-0.287909\pi$
$757$	935.779			1.23617			0.618084	+	0.786112i	$0.287909\pi$
$758$		0			0
$759$	−81.9594	+	47.3193i	−0.107983	+	0.0623443i
$760$		0			0
$761$	1214.79	+	701.357i	1.59630	+	0.921625i	0.992191	+	0.124724i	$0.0398046\pi$
$761$	1214.79	+	701.357i	1.59630	+	0.921625i	0.604110	+	0.796901i	$0.293529\pi$
$762$		0			0
$763$	−55.0254	−	1015.67i	−0.0721172	−	1.33115i
$764$		0			0
$765$	−105.816	+	183.279i	−0.138322	+	0.239581i
$766$		0			0
$767$	296.044	+	512.763i	0.385976	+	0.668530i
$768$		0			0
$769$		−	1.72330i		−	0.00224097i	−0.999999	−	0.00112048i	$-0.999643\pi$
$769$		−	1.72330i		−	0.00224097i	0.999999	−	0.00112048i	$-0.000356661\pi$
$770$		0			0
$771$	−287.360			−0.372711
$772$		0			0
$773$	194.213	−	112.129i	0.251245	−	0.145057i	−0.369089	−	0.929394i	$-0.620330\pi$
$773$	194.213	−	112.129i	0.251245	−	0.145057i	0.620334	+	0.784337i	$0.286997\pi$
$774$		0			0
$775$	802.831	+	463.514i	1.03591	+	0.598083i
$776$		0			0
$777$	6.68247	−	13.1725i	0.00860034	−	0.0169530i
$778$		0			0
$779$	58.4558	−	101.248i	0.0750396	−	0.129972i
$780$		0			0
$781$	86.6468	+	150.077i	0.110943	+	0.192160i
$782$		0			0
$783$		−	44.0908i		−	0.0563101i
$784$		0			0
$785$	−56.0740			−0.0714319
$786$		0			0
$787$	−60.7979	+	35.1017i	−0.0772528	+	0.0446019i	−0.538129	−	0.842863i	$-0.680869\pi$
$787$	−60.7979	+	35.1017i	−0.0772528	+	0.0446019i	0.460876	+	0.887465i	$0.347535\pi$
$788$		0			0
$789$	20.0968	+	11.6029i	0.0254712	+	0.0147058i
$790$		0			0
$791$	−215.647	−	109.399i	−0.272625	−	0.138305i
$792$		0			0
$793$	−691.992	+	1198.57i	−0.872625	+	1.51143i
$794$		0			0
$795$	−133.136	−	230.598i	−0.167467	−	0.290061i
$796$		0			0
$797$		−	1305.38i		−	1.63787i	−0.573889	−	0.818933i	$-0.694566\pi$
$797$		−	1305.38i		−	1.63787i	0.573889	−	0.818933i	$-0.305434\pi$
$798$		0			0
$799$	198.140			0.247985
$800$		0			0
$801$	369.859	−	213.538i	0.461747	−	0.266590i
$802$		0			0
$803$	−216.740	−	125.135i	−0.269913	−	0.155834i
$804$		0			0
$805$	−1285.17	+	69.6258i	−1.59648	+	0.0864917i
$806$		0			0
$807$	110.114	−	190.723i	0.136448	−	0.236335i
$808$		0			0
$809$	−381.382	−	660.573i	−0.471424	−	0.816531i	0.528041	−	0.849219i	$-0.322927\pi$
$809$	−381.382	−	660.573i	−0.471424	−	0.816531i	−0.999466	+	0.0326879i	$0.989593\pi$
$810$		0			0
$811$			1214.98i			1.49813i	0.662498	+	0.749064i	$0.269496\pi$
$811$			1214.98i			1.49813i	−0.662498	+	0.749064i	$0.730504\pi$
$812$		0			0
$813$	−54.5147			−0.0670538
$814$		0			0
$815$	−1274.74	+	735.970i	−1.56410	+	0.903031i
$816$		0			0
$817$	−37.9706	−	21.9223i	−0.0464756	−	0.0268327i
$818$		0			0
$819$	−496.014	−	760.854i	−0.605634	−	0.929004i
$820$		0			0
$821$	291.684	−	505.211i	0.355279	−	0.615361i	−0.631887	−	0.775061i	$-0.717719\pi$
$821$	291.684	−	505.211i	0.355279	−	0.615361i	0.987166	+	0.159700i	$0.0510527\pi$
$822$		0			0
$823$	515.371	+	892.648i	0.626210	+	1.08463i	0.988306	+	0.152486i	$0.0487280\pi$
$823$	515.371	+	892.648i	0.626210	+	1.08463i	−0.362096	+	0.932141i	$0.617939\pi$
$824$		0			0
$825$			64.7487i			0.0784833i
$826$		0			0
$827$	−152.102			−0.183920			−0.0919599	−	0.995763i	$-0.529313\pi$
$827$	−152.102			−0.183920			−0.0919599	+	0.995763i	$0.529313\pi$
$828$		0			0
$829$	532.095	−	307.205i	0.641852	−	0.370573i	−0.143476	−	0.989654i	$-0.545828\pi$
$829$	532.095	−	307.205i	0.641852	−	0.370573i	0.785327	+	0.619081i	$0.212495\pi$
$830$		0			0
$831$	172.983	+	99.8715i	0.208162	+	0.120182i
$832$		0			0
$833$	−168.632	−	74.3682i	−0.202439	−	0.0892776i
$834$		0			0
$835$	559.794	−	969.592i	0.670412	−	1.16119i
$836$		0			0
$837$	−306.507	−	530.886i	−0.366197	−	0.634272i
$838$		0			0
$839$		−	1546.14i		−	1.84284i	−0.388568	−	0.921420i	$-0.627030\pi$
$839$		−	1546.14i		−	1.84284i	0.388568	−	0.921420i	$-0.372970\pi$
$840$		0			0
$841$	−828.647			−0.985311
$842$		0			0
$843$	−245.229	+	141.583i	−0.290901	+	0.167952i
$844$		0			0
$845$	372.257	+	214.923i	0.440541	+	0.254347i
$846$		0			0
$847$	−576.823	+	376.041i	−0.681019	+	0.443969i
$848$		0			0
$849$	52.5152	−	90.9589i	0.0618553	−	0.107137i
$850$		0			0
$851$	40.7756	+	70.6255i	0.0479150	+	0.0829912i
$852$		0			0
$853$			1235.15i			1.44800i	0.689798	+	0.724002i	$0.257699\pi$
$853$			1235.15i			1.44800i	−0.689798	+	0.724002i	$0.742301\pi$
$854$		0			0
$855$	−235.279			−0.275180
$856$		0			0
$857$	−953.219	+	550.341i	−1.11227	+	0.642172i	−0.939417	−	0.342775i	$-0.888633\pi$
$857$	−953.219	+	550.341i	−1.11227	+	0.642172i	−0.172857	+	0.984947i	$0.555300\pi$
$858$		0			0
$859$	−512.488	−	295.885i	−0.596610	−	0.344453i	0.171096	−	0.985254i	$-0.445269\pi$
$859$	−512.488	−	295.885i	−0.596610	−	0.344453i	−0.767707	+	0.640801i	$0.778602\pi$
$860$		0			0
$861$	7.59589	+	140.207i	0.00882217	+	0.162841i
$862$		0			0
$863$	−32.3635	+	56.0553i	−0.0375012	+	0.0649540i	−0.884167	−	0.467171i	$-0.845273\pi$
$863$	−32.3635	+	56.0553i	−0.0375012	+	0.0649540i	0.846666	+	0.532125i	$0.178606\pi$
$864$		0			0
$865$	544.875	+	943.751i	0.629913	+	1.09104i
$866$		0			0
$867$		−	197.190i		−	0.227440i
$868$		0			0
$869$	160.736			0.184967
$870$		0			0
$871$	−458.720	+	264.842i	−0.526659	+	0.304067i
$872$		0			0
$873$	748.014	+	431.866i	0.856832	+	0.494692i
$874$		0			0
$875$	126.618	−	249.589i	0.144706	−	0.285245i
$876$		0			0
$877$	152.096	−	263.438i	0.173427	−	0.300385i	−0.766188	−	0.642616i	$-0.777849\pi$
$877$	152.096	−	263.438i	0.173427	−	0.300385i	0.939616	+	0.342231i	$0.111182\pi$
$878$		0			0
$879$	107.500	+	186.196i	0.122299	+	0.211827i
$880$		0			0
$881$		−	863.732i		−	0.980400i	−0.871610	−	0.490200i	$-0.836924\pi$
$881$		−	863.732i		−	0.980400i	0.871610	−	0.490200i	$-0.163076\pi$
$882$		0			0
$883$	567.456			0.642645			0.321323	−	0.946970i	$-0.395873\pi$
$883$	567.456			0.642645			0.321323	+	0.946970i	$0.395873\pi$
$884$		0			0
$885$	−159.529	+	92.1039i	−0.180258	+	0.104072i
$886$		0			0
$887$	770.555	+	444.880i	0.868721	+	0.501556i	0.866923	−	0.498442i	$-0.166094\pi$
$887$	770.555	+	444.880i	0.868721	+	0.501556i	0.00179783	+	0.999998i	$0.499428\pi$
$888$		0			0
$889$	−1544.04	−	783.302i	−1.73683	−	0.881105i
$890$		0			0
$891$	−160.246	+	277.554i	−0.179849	+	0.311508i
$892$		0			0
$893$	110.140	+	190.767i	0.123337	+	0.213625i
$894$		0			0
$895$		−	1227.96i		−	1.37202i
$896$		0			0
$897$	−304.191			−0.339120
$898$		0			0
$899$	148.742	−	85.8764i	0.165453	−	0.0955243i
$900$		0			0
$901$	182.316	+	105.260i	0.202349	+	0.116826i
$902$		0			0
$903$	52.5807	−	2.84864i	0.0582289	−	0.00315464i
$904$		0			0
$905$	514.191	−	890.605i	0.568167	−	0.984094i
$906$		0			0
$907$	186.989	+	323.874i	0.206162	+	0.357083i	0.950502	−	0.310717i	$-0.100569\pi$
$907$	186.989	+	323.874i	0.206162	+	0.357083i	−0.744340	+	0.667800i	$0.767236\pi$
$908$		0			0
$909$		−	506.395i		−	0.557091i
$910$		0			0
$911$	−1133.75			−1.24451			−0.622256	−	0.782814i	$-0.713784\pi$
$911$	−1133.75			−1.24451			−0.622256	+	0.782814i	$0.713784\pi$
$912$		0			0
$913$	−525.618	+	303.466i	−0.575704	+	0.332383i
$914$		0			0
$915$	−372.893	−	215.290i	−0.407533	−	0.235289i
$916$		0			0
$917$	−564.419	−	865.782i	−0.615506	−	0.944146i
$918$		0			0
$919$	228.151	−	395.169i	0.248260	−	0.429999i	−0.714783	−	0.699346i	$-0.753475\pi$
$919$	228.151	−	395.169i	0.248260	−	0.429999i	0.963043	+	0.269347i	$0.0868078\pi$
$920$		0			0
$921$	7.52900	+	13.0406i	0.00817481	+	0.0141592i
$922$		0			0
$923$			557.007i			0.603474i
$924$		0			0
$925$	55.7948			0.0603187
$926$		0			0
$927$	883.124	−	509.872i	0.952669	−	0.550024i
$928$		0			0
$929$	−824.058	−	475.770i	−0.887037	−	0.512131i	−0.0140650	−	0.999901i	$-0.504477\pi$
$929$	−824.058	−	475.770i	−0.887037	−	0.512131i	−0.872972	+	0.487770i	$0.837811\pi$
$930$		0			0
$931$	−22.1360	−	203.696i	−0.0237766	−	0.218793i
$932$		0			0
$933$	65.3011	−	113.105i	0.0699904	−	0.121227i
$934$		0			0
$935$	−59.3269	−	102.757i	−0.0634513	−	0.109901i
$936$		0			0
$937$			1295.71i			1.38283i	0.722460	+	0.691413i	$0.243011\pi$
$937$			1295.71i			1.38283i	−0.722460	+	0.691413i	$0.756989\pi$
$938$		0			0
$939$	70.2578			0.0748219
$940$		0			0
$941$	−1175.10	+	678.446i	−1.24878	+	0.720984i	−0.970866	−	0.239622i	$-0.922977\pi$
$941$	−1175.10	+	678.446i	−1.24878	+	0.720984i	−0.277915	+	0.960606i	$0.589643\pi$
$942$		0			0
$943$	−671.382	−	387.622i	−0.711964	−	0.411052i
$944$		0			0
$945$	487.786	−	317.997i	0.516176	−	0.336504i
$946$		0			0
$947$	−354.731	+	614.412i	−0.374584	+	0.648799i	−0.990265	−	0.139197i	$-0.955548\pi$
$947$	−354.731	+	614.412i	−0.374584	+	0.648799i	0.615681	+	0.787996i	$0.288881\pi$
$948$		0			0
$949$	−402.213	−	696.654i	−0.423828	−	0.734092i
$950$		0			0
$951$			345.784i			0.363601i
$952$		0			0
$953$	936.603			0.982794			0.491397	−	0.870936i	$-0.336486\pi$
$953$	936.603			0.982794			0.491397	+	0.870936i	$0.336486\pi$
$954$		0			0
$955$	−1424.72	+	822.564i	−1.49186	+	0.861324i
$956$		0			0
$957$	10.3890	+	5.99807i	0.0108558	+	0.00626757i
$958$		0			0
$959$	−12.3350	−	227.681i	−0.0128623	−	0.237415i
$960$		0			0
$961$	713.477	−	1235.78i	0.742432	−	1.28593i
$962$		0			0
$963$	−482.007	−	834.861i	−0.500527	−	0.866938i
$964$		0			0
$965$			1023.42i			1.06054i
$966$		0			0
$967$	−1374.37			−1.42127			−0.710635	−	0.703561i	$-0.751592\pi$
$967$	−1374.37			−1.42127			−0.710635	+	0.703561i	$0.751592\pi$
$968$		0			0
$969$	−9.77208	+	5.64191i	−0.0100847	+	0.00582241i
$970$		0			0
$971$	27.2466	+	15.7309i	0.0280604	+	0.0162007i	0.513965	−	0.857811i	$-0.328176\pi$
$971$	27.2466	+	15.7309i	0.0280604	+	0.0162007i	−0.485904	+	0.874012i	$0.661510\pi$
$972$		0			0
$973$	217.206	−	428.156i	0.223233	−	0.440037i
$974$		0			0
$975$	−104.059	+	180.235i	−0.106727	+	0.184857i
$976$		0			0
$977$	270.949	+	469.297i	0.277327	+	0.480345i	0.970720	−	0.240215i	$-0.0772181\pi$
$977$	270.949	+	469.297i	0.277327	+	0.480345i	−0.693392	+	0.720560i	$0.743885\pi$
$978$		0			0
$979$			239.445i			0.244581i
$980$		0			0
$981$	−1232.98			−1.25687
$982$		0			0
$983$	−19.4161	+	11.2099i	−0.0197519	+	0.0114038i	−0.509843	−	0.860267i	$-0.670297\pi$
$983$	−19.4161	+	11.2099i	−0.0197519	+	0.0114038i	0.490092	+	0.871671i	$0.336963\pi$
$984$		0			0
$985$	1040.01	+	600.448i	1.05584	+	0.609592i
$986$		0			0
$987$	−235.934	−	119.691i	−0.239042	−	0.121267i
$988$		0			0
$989$	−145.368	+	251.784i	−0.146984	+	0.254584i
$990$		0			0
$991$	339.017	+	587.195i	0.342096	+	0.592528i	0.984822	−	0.173568i	$-0.0555298\pi$
$991$	339.017	+	587.195i	0.342096	+	0.592528i	−0.642726	+	0.766097i	$0.722196\pi$
$992$		0			0
$993$			161.429i			0.162567i
$994$		0			0
$995$	2312.28			2.32390
$996$		0			0
$997$	758.779	−	438.081i	0.761062	−	0.439400i	−0.0686147	−	0.997643i	$-0.521858\pi$
$997$	758.779	−	438.081i	0.761062	−	0.439400i	0.829677	+	0.558244i	$0.188525\pi$
$998$		0			0
$999$	−31.9523	−	18.4477i	−0.0319843	−	0.0184661i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.3.s.b.33.1		4
3.2	odd	2		1008.3.cg.l.145.2		4
4.3	odd	2		14.3.d.a.5.1	yes	4
7.2	even	3		784.3.c.e.97.2		4
7.3	odd	6	inner	112.3.s.b.17.1		4
7.4	even	3		784.3.s.c.129.2		4
7.5	odd	6		784.3.c.e.97.3		4
7.6	odd	2		784.3.s.c.705.2		4
8.3	odd	2		448.3.s.d.257.1		4
8.5	even	2		448.3.s.c.257.2		4
12.11	even	2		126.3.n.c.19.2		4
20.3	even	4		350.3.i.a.299.3		8
20.7	even	4		350.3.i.a.299.2		8
20.19	odd	2		350.3.k.a.201.2		4
21.17	even	6		1008.3.cg.l.577.2		4
28.3	even	6		14.3.d.a.3.1	✓	4
28.11	odd	6		98.3.d.a.31.1		4
28.19	even	6		98.3.b.b.97.3		4
28.23	odd	6		98.3.b.b.97.4		4
28.27	even	2		98.3.d.a.19.1		4
56.3	even	6		448.3.s.d.129.1		4
56.45	odd	6		448.3.s.c.129.2		4
84.11	even	6		882.3.n.b.325.2		4
84.23	even	6		882.3.c.f.685.1		4
84.47	odd	6		882.3.c.f.685.2		4
84.59	odd	6		126.3.n.c.73.2		4
84.83	odd	2		882.3.n.b.19.2		4
140.3	odd	12		350.3.i.a.199.2		8
140.59	even	6		350.3.k.a.101.2		4
140.87	odd	12		350.3.i.a.199.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.3.d.a.3.1	✓	4	28.3	even	6
14.3.d.a.5.1	yes	4	4.3	odd	2
98.3.b.b.97.3		4	28.19	even	6
98.3.b.b.97.4		4	28.23	odd	6
98.3.d.a.19.1		4	28.27	even	2
98.3.d.a.31.1		4	28.11	odd	6
112.3.s.b.17.1		4	7.3	odd	6	inner
112.3.s.b.33.1		4	1.1	even	1	trivial
126.3.n.c.19.2		4	12.11	even	2
126.3.n.c.73.2		4	84.59	odd	6
350.3.i.a.199.2		8	140.3	odd	12
350.3.i.a.199.3		8	140.87	odd	12
350.3.i.a.299.2		8	20.7	even	4
350.3.i.a.299.3		8	20.3	even	4
350.3.k.a.101.2		4	140.59	even	6
350.3.k.a.201.2		4	20.19	odd	2
448.3.s.c.129.2		4	56.45	odd	6
448.3.s.c.257.2		4	8.5	even	2
448.3.s.d.129.1		4	56.3	even	6
448.3.s.d.257.1		4	8.3	odd	2
784.3.c.e.97.2		4	7.2	even	3
784.3.c.e.97.3		4	7.5	odd	6
784.3.s.c.129.2		4	7.4	even	3
784.3.s.c.705.2		4	7.6	odd	2
882.3.c.f.685.1		4	84.23	even	6
882.3.c.f.685.2		4	84.47	odd	6
882.3.n.b.19.2		4	84.83	odd	2
882.3.n.b.325.2		4	84.11	even	6
1008.3.cg.l.145.2		4	3.2	odd	2
1008.3.cg.l.577.2		4	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	112.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.621320 + 0.358719i) q^{3} +(-5.74264 - 3.31552i) q^{5} +(-6.24264 - 3.16693i) q^{7} +(-4.24264 + 7.34847i) q^{9} +O(q^{10})\)	\(q+(-0.621320 + 0.358719i) q^{3} +(-5.74264 - 3.31552i) q^{5} +(-6.24264 - 3.16693i) q^{7} +(-4.24264 + 7.34847i) q^{9} +(-2.37868 - 4.11999i) q^{11} -15.2913i q^{13} +4.75736 q^{15} +(-3.25736 + 1.88064i) q^{17} +(-3.62132 - 2.09077i) q^{19} +(5.01472 - 0.271680i) q^{21} +(-13.8640 + 24.0131i) q^{23} +(9.48528 + 16.4290i) q^{25} -12.5446i q^{27} +3.51472 q^{29} +(42.3198 - 24.4334i) q^{31} +(2.95584 + 1.70656i) q^{33} +(25.3492 + 38.8841i) q^{35} +(1.47056 - 2.54709i) q^{37} +(5.48528 + 9.50079i) q^{39} +27.9590i q^{41} +10.4853 q^{43} +(48.7279 - 28.1331i) q^{45} +(-45.6213 - 26.3395i) q^{47} +(28.9411 + 39.5400i) q^{49} +(1.34924 - 2.33696i) q^{51} +(-27.9853 - 48.4719i) q^{53} +31.5462i q^{55} +3.00000 q^{57} +(-33.5330 + 19.3603i) q^{59} +(-78.3823 - 45.2540i) q^{61} +(49.7574 - 32.4377i) q^{63} +(-50.6985 + 87.8124i) q^{65} +(-17.3198 - 29.9988i) q^{67} -19.8931i q^{69} -36.4264 q^{71} +(45.5589 - 26.3034i) q^{73} +(-11.7868 - 6.80511i) q^{75} +(1.80152 + 33.2528i) q^{77} +(-16.8934 + 29.2602i) q^{79} +(-33.6838 - 58.3420i) q^{81} -127.577i q^{83} +24.9411 q^{85} +(-2.18377 + 1.26080i) q^{87} +(-43.5883 - 25.1657i) q^{89} +(-48.4264 + 95.4580i) q^{91} +(-17.5294 + 30.3619i) q^{93} +(13.8640 + 24.0131i) q^{95} -101.792i q^{97} +40.3675 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} - 6 q^{5} - 8 q^{7}+O(q^{10}) \) 4 * q + 6 * q^3 - 6 * q^5 - 8 * q^7	\( 4 q + 6 q^{3} - 6 q^{5} - 8 q^{7} - 18 q^{11} + 36 q^{15} - 30 q^{17} - 6 q^{19} + 54 q^{21} - 30 q^{23} + 4 q^{25} + 48 q^{29} + 42 q^{31} - 90 q^{33} + 42 q^{35} - 62 q^{37} - 12 q^{39} + 8 q^{43} + 144 q^{45} - 174 q^{47} - 20 q^{49} - 54 q^{51} - 78 q^{53} + 12 q^{57} + 78 q^{59} - 42 q^{61} + 216 q^{63} - 84 q^{65} + 58 q^{67} + 24 q^{71} + 318 q^{73} - 132 q^{75} + 126 q^{77} - 110 q^{79} + 18 q^{81} - 36 q^{85} + 144 q^{87} - 378 q^{89} - 24 q^{91} - 138 q^{93} + 30 q^{95} - 144 q^{99}+O(q^{100}) \) 4 * q + 6 * q^3 - 6 * q^5 - 8 * q^7 - 18 * q^11 + 36 * q^15 - 30 * q^17 - 6 * q^19 + 54 * q^21 - 30 * q^23 + 4 * q^25 + 48 * q^29 + 42 * q^31 - 90 * q^33 + 42 * q^35 - 62 * q^37 - 12 * q^39 + 8 * q^43 + 144 * q^45 - 174 * q^47 - 20 * q^49 - 54 * q^51 - 78 * q^53 + 12 * q^57 + 78 * q^59 - 42 * q^61 + 216 * q^63 - 84 * q^65 + 58 * q^67 + 24 * q^71 + 318 * q^73 - 132 * q^75 + 126 * q^77 - 110 * q^79 + 18 * q^81 - 36 * q^85 + 144 * q^87 - 378 * q^89 - 24 * q^91 - 138 * q^93 + 30 * q^95 - 144 * q^99

Introduction

L-functions

Modular forms

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Database

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