LMFDB - Embedded newform 336.4.q.m.193.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,4,Mod(193,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("336.193");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.q (of order $3$, 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:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
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} + 173x^{6} + 9457x^{4} + 168048x^{2} + 746496 $ x^8 + 173x^6 + 9457x^4 + 168048*x^2 + 746496
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 7 $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.4
Root			$-4.63878i$ of defining polynomial
Character	$\chi$	$=$	336.193
Dual form			336.4.q.m.289.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 2.59808i) q^{3} +(7.90648 + 13.6944i) q^{5} +(-15.2050 - 10.5739i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(1.50000 - 2.59808i) q^{3} +(7.90648 + 13.6944i) q^{5} +(-15.2050 - 10.5739i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(-15.1240 + 26.1955i) q^{11} -61.6298 q^{13} +47.4389 q^{15} +(-28.0724 + 48.6228i) q^{17} +(-69.7002 - 120.724i) q^{19} +(-50.2793 + 23.6429i) q^{21} +(-4.07240 - 7.05360i) q^{23} +(-62.5247 + 108.296i) q^{25} -27.0000 q^{27} -0.217857 q^{29} +(88.2903 - 152.923i) q^{31} +(45.3719 + 78.5864i) q^{33} +(24.5855 - 291.826i) q^{35} +(-105.540 - 182.801i) q^{37} +(-92.4447 + 160.119i) q^{39} -293.305 q^{41} -434.591 q^{43} +(71.1583 - 123.250i) q^{45} +(241.698 + 418.633i) q^{47} +(119.385 + 321.553i) q^{49} +(84.2172 + 145.868i) q^{51} +(-10.2536 + 17.7598i) q^{53} -478.309 q^{55} -418.201 q^{57} +(-115.674 + 200.353i) q^{59} +(419.351 + 726.337i) q^{61} +(-13.9930 + 166.094i) q^{63} +(-487.274 - 843.984i) q^{65} +(-312.020 + 540.435i) q^{67} -24.4344 q^{69} -227.106 q^{71} +(-21.5247 + 37.2819i) q^{73} +(187.574 + 324.888i) q^{75} +(506.949 - 238.383i) q^{77} +(-154.530 - 267.654i) q^{79} +(-40.5000 + 70.1481i) q^{81} -1233.99 q^{83} -887.815 q^{85} +(-0.326785 + 0.566009i) q^{87} +(-572.179 - 991.042i) q^{89} +(937.082 + 651.668i) q^{91} +(-264.871 - 458.770i) q^{93} +(1102.17 - 1909.01i) q^{95} +1688.12 q^{97} +272.231 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{3} - 4 q^{5} - 18 q^{7} - 36 q^{9}+O(q^{10}) $ 8 * q + 12 * q^3 - 4 * q^5 - 18 * q^7 - 36 * q^9	$ 8 q + 12 q^{3} - 4 q^{5} - 18 q^{7} - 36 q^{9} + 14 q^{11} + 44 q^{13} - 24 q^{15} - 96 q^{17} - 26 q^{19} - 36 q^{21} + 96 q^{23} - 110 q^{25} - 216 q^{27} - 152 q^{29} + 238 q^{31} - 42 q^{33} - 152 q^{35} - 562 q^{37} + 66 q^{39} + 856 q^{41} + 516 q^{43} - 36 q^{45} - 80 q^{47} + 156 q^{49} + 288 q^{51} - 2952 q^{55} - 156 q^{57} + 262 q^{59} + 276 q^{61} + 54 q^{63} - 2196 q^{65} + 150 q^{67} + 576 q^{69} + 1696 q^{71} + 218 q^{73} + 330 q^{75} - 764 q^{77} + 1762 q^{79} - 324 q^{81} - 6900 q^{83} + 2904 q^{85} - 228 q^{87} + 344 q^{89} + 2806 q^{91} - 714 q^{93} + 2004 q^{95} - 1244 q^{97} - 252 q^{99}+O(q^{100}) $ 8 * q + 12 * q^3 - 4 * q^5 - 18 * q^7 - 36 * q^9 + 14 * q^11 + 44 * q^13 - 24 * q^15 - 96 * q^17 - 26 * q^19 - 36 * q^21 + 96 * q^23 - 110 * q^25 - 216 * q^27 - 152 * q^29 + 238 * q^31 - 42 * q^33 - 152 * q^35 - 562 * q^37 + 66 * q^39 + 856 * q^41 + 516 * q^43 - 36 * q^45 - 80 * q^47 + 156 * q^49 + 288 * q^51 - 2952 * q^55 - 156 * q^57 + 262 * q^59 + 276 * q^61 + 54 * q^63 - 2196 * q^65 + 150 * q^67 + 576 * q^69 + 1696 * q^71 + 218 * q^73 + 330 * q^75 - 764 * q^77 + 1762 * q^79 - 324 * q^81 - 6900 * q^83 + 2904 * q^85 - 228 * q^87 + 344 * q^89 + 2806 * q^91 - 714 * q^93 + 2004 * q^95 - 1244 * q^97 - 252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$4$		0			0
$5$	7.90648	+	13.6944i	0.707177	+	1.22487i	0.965900	+	0.258915i	$0.0833648\pi$
$5$	7.90648	+	13.6944i	0.707177	+	1.22487i	−0.258724	+	0.965951i	$0.583302\pi$
$6$		0			0
$7$	−15.2050	−	10.5739i	−0.820993	−	0.570938i
$7$	−15.2050	−	10.5739i	−0.820993	−	0.570938i
$8$		0			0
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$		0			0
$11$	−15.1240	+	26.1955i	−0.414550	+	0.718021i	−0.995381	−	0.0960028i	$-0.969394\pi$
$11$	−15.1240	+	26.1955i	−0.414550	+	0.718021i	0.580831	+	0.814024i	$0.302728\pi$
$12$		0			0
$13$	−61.6298			−1.31485			−0.657424	−	0.753521i	$-0.728354\pi$
$13$	−61.6298			−1.31485			−0.657424	+	0.753521i	$0.728354\pi$
$14$		0			0
$15$	47.4389			0.816577
$16$		0			0
$17$	−28.0724	+	48.6228i	−0.400503	+	0.693692i	−0.993787	−	0.111302i	$-0.964498\pi$
$17$	−28.0724	+	48.6228i	−0.400503	+	0.693692i	0.593283	+	0.804994i	$0.297831\pi$
$18$		0			0
$19$	−69.7002	−	120.724i	−0.841596	−	1.45769i	−0.888544	−	0.458790i	$-0.848283\pi$
$19$	−69.7002	−	120.724i	−0.841596	−	1.45769i	0.0469481	−	0.998897i	$-0.485050\pi$
$20$		0			0
$21$	−50.2793	+	23.6429i	−0.522469	+	0.245681i
$22$		0			0
$23$	−4.07240	−	7.05360i	−0.0369197	−	0.0639469i	0.846975	−	0.531633i	$-0.178421\pi$
$23$	−4.07240	−	7.05360i	−0.0369197	−	0.0639469i	−0.883895	+	0.467686i	$0.845088\pi$
$24$		0			0
$25$	−62.5247	+	108.296i	−0.500198	+	0.866368i
$26$		0			0
$27$	−27.0000			−0.192450
$28$		0			0
$29$	−0.217857			−0.00139500			−0.000697500	−	1.00000i	$-0.500222\pi$
$29$	−0.217857			−0.00139500			−0.000697500		1.00000i	$0.500222\pi$
$30$		0			0
$31$	88.2903	−	152.923i	0.511529	−	0.885994i	−0.488382	−	0.872630i	$-0.662413\pi$
$31$	88.2903	−	152.923i	0.511529	−	0.885994i	0.999911	−	0.0133642i	$-0.00425408\pi$
$32$		0			0
$33$	45.3719	+	78.5864i	0.239340	+	0.414550i
$34$		0			0
$35$	24.5855	−	291.826i	0.118735	−	1.40936i
$36$		0			0
$37$	−105.540	−	182.801i	−0.468937	−	0.812223i	0.530432	−	0.847727i	$-0.322030\pi$
$37$	−105.540	−	182.801i	−0.468937	−	0.812223i	−0.999370	+	0.0355042i	$0.988696\pi$
$38$		0			0
$39$	−92.4447	+	160.119i	−0.379564	+	0.657424i
$40$		0			0
$41$	−293.305			−1.11723			−0.558616	−	0.829427i	$-0.688667\pi$
$41$	−293.305			−1.11723			−0.558616	+	0.829427i	$0.688667\pi$
$42$		0			0
$43$	−434.591			−1.54127			−0.770634	−	0.637278i	$-0.780060\pi$
$43$	−434.591			−1.54127			−0.770634	+	0.637278i	$0.780060\pi$
$44$		0			0
$45$	71.1583	−	123.250i	0.235726	−	0.408289i
$46$		0			0
$47$	241.698	+	418.633i	0.750112	+	1.29923i	0.947768	+	0.318960i	$0.103334\pi$
$47$	241.698	+	418.633i	0.750112	+	1.29923i	−0.197657	+	0.980271i	$0.563333\pi$
$48$		0			0
$49$	119.385	+	321.553i	0.348060	+	0.937472i
$50$		0			0
$51$	84.2172	+	145.868i	0.231231	+	0.400503i
$52$		0			0
$53$	−10.2536	+	17.7598i	−0.0265745	+	0.0460283i	−0.879007	−	0.476809i	$-0.841793\pi$
$53$	−10.2536	+	17.7598i	−0.0265745	+	0.0460283i	0.852432	+	0.522838i	$0.175127\pi$
$54$		0			0
$55$	−478.309			−1.17264
$56$		0			0
$57$	−418.201			−0.971792
$58$		0			0
$59$	−115.674	+	200.353i	−0.255245	+	0.442097i	−0.964962	−	0.262390i	$-0.915489\pi$
$59$	−115.674	+	200.353i	−0.255245	+	0.442097i	0.709717	+	0.704487i	$0.248823\pi$
$60$		0			0
$61$	419.351	+	726.337i	0.880203	+	1.52456i	0.851115	+	0.524979i	$0.175927\pi$
$61$	419.351	+	726.337i	0.880203	+	1.52456i	0.0290872	+	0.999577i	$0.490740\pi$
$62$		0			0
$63$	−13.9930	+	166.094i	−0.0279833	+	0.332157i
$64$		0			0
$65$	−487.274	−	843.984i	−0.929830	−	1.61051i
$66$		0			0
$67$	−312.020	+	540.435i	−0.568945	+	0.985442i	0.427726	+	0.903909i	$0.359315\pi$
$67$	−312.020	+	540.435i	−0.568945	+	0.985442i	−0.996671	+	0.0815332i	$0.974018\pi$
$68$		0			0
$69$	−24.4344			−0.0426312
$70$		0			0
$71$	−227.106			−0.379613			−0.189806	−	0.981822i	$-0.560786\pi$
$71$	−227.106			−0.379613			−0.189806	+	0.981822i	$0.560786\pi$
$72$		0			0
$73$	−21.5247	+	37.2819i	−0.0345107	+	0.0597742i	−0.882765	−	0.469815i	$-0.844321\pi$
$73$	−21.5247	+	37.2819i	−0.0345107	+	0.0597742i	0.848254	+	0.529589i	$0.177654\pi$
$74$		0			0
$75$	187.574	+	324.888i	0.288789	+	0.500198i
$76$		0			0
$77$	506.949	−	238.383i	0.750288	−	0.352809i
$78$		0			0
$79$	−154.530	−	267.654i	−0.220076	−	0.381183i	0.734755	−	0.678333i	$-0.237297\pi$
$79$	−154.530	−	267.654i	−0.220076	−	0.381183i	−0.954831	+	0.297150i	$0.903964\pi$
$80$		0			0
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−1233.99			−1.63190			−0.815951	−	0.578122i	$-0.803786\pi$
$83$	−1233.99			−1.63190			−0.815951	+	0.578122i	$0.803786\pi$
$84$		0			0
$85$	−887.815			−1.13291
$86$		0			0
$87$	−0.326785	+	0.566009i	−0.000402702	+	0.000697500i
$88$		0			0
$89$	−572.179	−	991.042i	−0.681470	−	1.18034i	−0.974532	−	0.224247i	$-0.928008\pi$
$89$	−572.179	−	991.042i	−0.681470	−	1.18034i	0.293063	−	0.956093i	$-0.405326\pi$
$90$		0			0
$91$	937.082	+	651.668i	1.07948	+	0.750696i
$92$		0			0
$93$	−264.871	−	458.770i	−0.295331	−	0.511529i
$94$		0			0
$95$	1102.17	−	1909.01i	1.19031	−	2.06169i
$96$		0			0
$97$	1688.12			1.76704			0.883520	−	0.468394i	$-0.155167\pi$
$97$	1688.12			1.76704			0.883520	+	0.468394i	$0.155167\pi$
$98$		0			0
$99$	272.231			0.276366
$100$		0			0
$101$	743.930	−	1288.52i	0.732909	−	1.26944i	−0.222726	−	0.974881i	$-0.571496\pi$
$101$	743.930	−	1288.52i	0.732909	−	1.26944i	0.955635	−	0.294554i	$-0.0951712\pi$
$102$		0			0
$103$	−389.204	−	674.121i	−0.372324	−	0.644884i	0.617598	−	0.786494i	$-0.288106\pi$
$103$	−389.204	−	674.121i	−0.372324	−	0.644884i	−0.989923	+	0.141609i	$0.954772\pi$
$104$		0			0
$105$	−721.308	−	501.614i	−0.670405	−	0.466215i
$106$		0			0
$107$	651.040	+	1127.63i	0.588209	+	1.01881i	0.994467	+	0.105050i	$0.0335001\pi$
$107$	651.040	+	1127.63i	0.588209	+	1.01881i	−0.406258	+	0.913758i	$0.633167\pi$
$108$		0			0
$109$	−234.541	+	406.237i	−0.206100	+	0.356976i	−0.950483	−	0.310777i	$-0.899411\pi$
$109$	−234.541	+	406.237i	−0.206100	+	0.356976i	0.744382	+	0.667754i	$0.232744\pi$
$110$		0			0
$111$	−633.240			−0.541482
$112$		0			0
$113$	1653.86			1.37684			0.688418	−	0.725314i	$-0.258306\pi$
$113$	1653.86			1.37684			0.688418	+	0.725314i	$0.258306\pi$
$114$		0			0
$115$	64.3966	−	111.538i	0.0522175	−	0.0904434i
$116$		0			0
$117$	277.334	+	480.357i	0.219141	+	0.379564i
$118$		0			0
$119$	940.975	−	442.475i	0.724866	−	0.340854i
$120$		0			0
$121$	208.032	+	360.321i	0.156297	+	0.270715i
$122$		0			0
$123$	−439.957	+	762.028i	−0.322517	+	0.558616i
$124$		0			0
$125$	−0.781685			−0.000559328
$126$		0			0
$127$	−163.760			−0.114420			−0.0572100	−	0.998362i	$-0.518220\pi$
$127$	−163.760			−0.114420			−0.0572100	+	0.998362i	$0.518220\pi$
$128$		0			0
$129$	−651.887	+	1129.10i	−0.444926	+	0.770634i
$130$		0			0
$131$	−260.947	−	451.973i	−0.174038	−	0.301443i	0.765790	−	0.643091i	$-0.222348\pi$
$131$	−260.947	−	451.973i	−0.174038	−	0.301443i	−0.939828	+	0.341648i	$0.889015\pi$
$132$		0			0
$133$	−216.736	+	2572.62i	−0.141304	+	1.67725i
$134$		0			0
$135$	−213.475	−	369.749i	−0.136096	−	0.235726i
$136$		0			0
$137$	−1338.44	+	2318.25i	−0.834679	+	1.44571i	0.0596120	+	0.998222i	$0.481014\pi$
$137$	−1338.44	+	2318.25i	−0.834679	+	1.44571i	−0.894291	+	0.447485i	$0.852320\pi$
$138$		0			0
$139$	−853.692			−0.520930			−0.260465	−	0.965483i	$-0.583876\pi$
$139$	−853.692			−0.520930			−0.260465	+	0.965483i	$0.583876\pi$
$140$		0			0
$141$	1450.19			0.866154
$142$		0			0
$143$	932.087	−	1614.42i	0.545070	−	0.944089i
$144$		0			0
$145$	−1.72248	−	2.98342i	−0.000986512	−	0.00170869i
$146$		0			0
$147$	1014.50	+	172.159i	0.569212	+	0.0965947i
$148$		0			0
$149$	−278.843	−	482.970i	−0.153313	−	0.265547i	0.779130	−	0.626862i	$-0.215661\pi$
$149$	−278.843	−	482.970i	−0.153313	−	0.265547i	−0.932444	+	0.361316i	$0.882328\pi$
$150$		0			0
$151$	884.674	−	1532.30i	0.476780	−	0.825807i	−0.522866	−	0.852415i	$-0.675137\pi$
$151$	884.674	−	1532.30i	0.476780	−	0.825807i	0.999646	+	0.0266077i	$0.00847049\pi$
$152$		0			0
$153$	505.303			0.267002
$154$		0			0
$155$	2792.26			1.44697
$156$		0			0
$157$	1202.45	−	2082.70i	0.611247	−	1.05871i	−0.379784	−	0.925075i	$-0.624002\pi$
$157$	1202.45	−	2082.70i	0.611247	−	1.05871i	0.991031	−	0.133635i	$-0.0426651\pi$
$158$		0			0
$159$	30.7609	+	53.2795i	0.0153428	+	0.0265745i
$160$		0			0
$161$	−12.6633	+	150.311i	−0.00619881	+	0.0735788i
$162$		0			0
$163$	1689.40	+	2926.12i	0.811802	+	1.40608i	0.911601	+	0.411075i	$0.134847\pi$
$163$	1689.40	+	2926.12i	0.811802	+	1.40608i	−0.0997991	+	0.995008i	$0.531820\pi$
$164$		0			0
$165$	−717.463	+	1242.68i	−0.338512	+	0.586320i
$166$		0			0
$167$	805.900			0.373428			0.186714	−	0.982414i	$-0.440216\pi$
$167$	805.900			0.373428			0.186714	+	0.982414i	$0.440216\pi$
$168$		0			0
$169$	1601.23			0.728826
$170$		0			0
$171$	−627.302	+	1086.52i	−0.280532	+	0.485896i
$172$		0			0
$173$	420.252	+	727.898i	0.184689	+	0.319890i	0.943472	−	0.331453i	$-0.107539\pi$
$173$	420.252	+	727.898i	0.184689	+	0.319890i	−0.758783	+	0.651344i	$0.774206\pi$
$174$		0			0
$175$	2095.80	−	985.511i	0.905301	−	0.425701i
$176$		0			0
$177$	347.021	+	601.059i	0.147366	+	0.255245i
$178$		0			0
$179$	802.305	−	1389.63i	0.335012	−	0.580258i	−0.648475	−	0.761236i	$-0.724593\pi$
$179$	802.305	−	1389.63i	0.335012	−	0.580258i	0.983487	+	0.180978i	$0.0579263\pi$
$180$		0			0
$181$	−3779.43			−1.55206			−0.776029	−	0.630697i	$-0.782769\pi$
$181$	−3779.43			−1.55206			−0.776029	+	0.630697i	$0.782769\pi$
$182$		0			0
$183$	2516.10			1.01637
$184$		0			0
$185$	1668.90	−	2890.62i	0.663243	−	1.14877i
$186$		0			0
$187$	−849.132	−	1470.74i	−0.332057	−	0.575140i
$188$		0			0
$189$	410.535	+	285.496i	0.158000	+	0.109877i
$190$		0			0
$191$	−924.798	−	1601.80i	−0.350346	−	0.606816i	0.635964	−	0.771718i	$-0.280603\pi$
$191$	−924.798	−	1601.80i	−0.350346	−	0.606816i	−0.986310	+	0.164902i	$0.947269\pi$
$192$		0			0
$193$	176.501	−	305.709i	0.0658282	−	0.114018i	−0.831233	−	0.555924i	$-0.812364\pi$
$193$	176.501	−	305.709i	0.0658282	−	0.114018i	0.897061	+	0.441907i	$0.145698\pi$
$194$		0			0
$195$	−2923.65			−1.07368
$196$		0			0
$197$	4448.22			1.60874			0.804372	−	0.594125i	$-0.202502\pi$
$197$	4448.22			1.60874			0.804372	+	0.594125i	$0.202502\pi$
$198$		0			0
$199$	−1120.08	+	1940.03i	−0.398995	+	0.691080i	−0.993602	−	0.112936i	$-0.963974\pi$
$199$	−1120.08	+	1940.03i	−0.398995	+	0.691080i	0.594607	+	0.804017i	$0.297308\pi$
$200$		0			0
$201$	936.060	+	1621.30i	0.328481	+	0.568945i
$202$		0			0
$203$	3.31252	+	2.30360i	0.00114529	+	0.000796458i
$204$		0			0
$205$	−2319.01	−	4016.64i	−0.790080	−	1.36846i
$206$		0			0
$207$	−36.6516	+	63.4824i	−0.0123066	+	0.0213156i
$208$		0			0
$209$	4216.58			1.39553
$210$		0			0
$211$	−1224.34			−0.399463			−0.199732	−	0.979851i	$-0.564007\pi$
$211$	−1224.34			−0.399463			−0.199732	+	0.979851i	$0.564007\pi$
$212$		0			0
$213$	−340.659	+	590.039i	−0.109585	+	0.189806i
$214$		0			0
$215$	−3436.08	−	5951.47i	−1.08995	−	1.88785i
$216$		0			0
$217$	−2959.45	+	1391.63i	−0.925810	+	0.435344i
$218$		0			0
$219$	64.5741	+	111.846i	0.0199247	+	0.0345107i
$220$		0			0
$221$	1730.10	−	2996.61i	0.526601	−	0.912100i
$222$		0			0
$223$	3457.37			1.03822			0.519108	−	0.854708i	$-0.326264\pi$
$223$	3457.37			1.03822			0.519108	+	0.854708i	$0.326264\pi$
$224$		0			0
$225$	1125.44			0.333465
$226$		0			0
$227$	−2589.11	+	4484.47i	−0.757027	+	1.31121i	0.187333	+	0.982296i	$0.440016\pi$
$227$	−2589.11	+	4484.47i	−0.757027	+	1.31121i	−0.944360	+	0.328913i	$0.893318\pi$
$228$		0			0
$229$	−1155.94	−	2002.15i	−0.333567	−	0.577755i	0.649642	−	0.760241i	$-0.274919\pi$
$229$	−1155.94	−	2002.15i	−0.333567	−	0.577755i	−0.983208	+	0.182486i	$0.941586\pi$
$230$		0			0
$231$	141.086	−	1674.67i	0.0401852	−	0.476991i
$232$		0			0
$233$	−2371.49	−	4107.54i	−0.666787	−	1.15491i	−0.978798	−	0.204830i	$-0.934336\pi$
$233$	−2371.49	−	4107.54i	−0.666787	−	1.15491i	0.312011	−	0.950078i	$-0.398997\pi$
$234$		0			0
$235$	−3821.95	+	6619.82i	−1.06092	+	1.83757i
$236$		0			0
$237$	−927.181			−0.254122
$238$		0			0
$239$	1412.59			0.382313			0.191157	−	0.981560i	$-0.438776\pi$
$239$	1412.59			0.382313			0.191157	+	0.981560i	$0.438776\pi$
$240$		0			0
$241$	940.577	−	1629.13i	0.251402	−	0.435441i	−0.712510	−	0.701662i	$-0.752442\pi$
$241$	940.577	−	1629.13i	0.251402	−	0.435441i	0.963912	+	0.266221i	$0.0857750\pi$
$242$		0			0
$243$	121.500	+	210.444i	0.0320750	+	0.0555556i
$244$		0			0
$245$	−3459.57	+	4177.25i	−0.902138	+	1.08929i
$246$		0			0
$247$	4295.61	+	7440.22i	1.10657	+	1.91664i
$248$		0			0
$249$	−1850.98	+	3206.00i	−0.471089	+	0.815951i
$250$		0			0
$251$	−4519.64			−1.13656			−0.568281	−	0.822834i	$-0.692391\pi$
$251$	−4519.64			−1.13656			−0.568281	+	0.822834i	$0.692391\pi$
$252$		0			0
$253$	246.363			0.0612202
$254$		0			0
$255$	−1331.72	+	2306.61i	−0.327042	+	0.566453i
$256$		0			0
$257$	−3956.33	−	6852.56i	−0.960268	−	1.66323i	−0.721824	−	0.692077i	$-0.756696\pi$
$257$	−3956.33	−	6852.56i	−0.960268	−	1.66323i	−0.238445	−	0.971156i	$-0.576638\pi$
$258$		0			0
$259$	−328.182	+	3895.46i	−0.0787344	+	0.934564i
$260$		0			0
$261$	0.980356	+	1.69803i	0.000232500	+	0.000402702i
$262$		0			0
$263$	−1715.58	+	2971.47i	−0.402233	+	0.696688i	−0.993995	−	0.109425i	$-0.965099\pi$
$263$	−1715.58	+	2971.47i	−0.402233	+	0.696688i	0.591762	+	0.806113i	$0.298432\pi$
$264$		0			0
$265$	−324.281			−0.0751714
$266$		0			0
$267$	−3433.07			−0.786894
$268$		0			0
$269$	−4149.60	+	7187.31i	−0.940540	+	1.62906i	−0.176097	+	0.984373i	$0.556347\pi$
$269$	−4149.60	+	7187.31i	−0.940540	+	1.62906i	−0.764443	+	0.644691i	$0.776986\pi$
$270$		0			0
$271$	−2962.24	−	5130.75i	−0.663998	−	1.15008i	−0.979556	−	0.201172i	$-0.935525\pi$
$271$	−2962.24	−	5130.75i	−0.663998	−	1.15008i	0.315558	−	0.948906i	$-0.397808\pi$
$272$		0			0
$273$	3098.71	−	1457.11i	0.686968	−	0.323033i
$274$		0			0
$275$	−1891.24	−	3275.73i	−0.414714	−	0.718305i
$276$		0			0
$277$	−760.300	+	1316.88i	−0.164917	+	0.285645i	−0.936626	−	0.350331i	$-0.886069\pi$
$277$	−760.300	+	1316.88i	−0.164917	+	0.285645i	0.771709	+	0.635976i	$0.219402\pi$
$278$		0			0
$279$	−1589.22			−0.341019
$280$		0			0
$281$	−352.333			−0.0747986			−0.0373993	−	0.999300i	$-0.511907\pi$
$281$	−352.333			−0.0747986			−0.0373993	+	0.999300i	$0.511907\pi$
$282$		0			0
$283$	2144.24	−	3713.94i	0.450396	−	0.780109i	−0.548014	−	0.836469i	$-0.684616\pi$
$283$	2144.24	−	3713.94i	0.450396	−	0.780109i	0.998411	+	0.0563599i	$0.0179494\pi$
$284$		0			0
$285$	−3306.50	−	5727.03i	−0.687229	−	1.19031i
$286$		0			0
$287$	4459.70	+	3101.38i	0.917239	+	0.637869i
$288$		0			0
$289$	880.381	+	1524.86i	0.179194	+	0.310373i
$290$		0			0
$291$	2532.18	−	4385.87i	0.510100	−	0.883520i
$292$		0			0
$293$	2661.99			0.530767			0.265384	−	0.964143i	$-0.414501\pi$
$293$	2661.99			0.530767			0.265384	+	0.964143i	$0.414501\pi$
$294$		0			0
$295$	−3658.29			−0.722013
$296$		0			0
$297$	408.347	−	707.278i	0.0797801	−	0.138183i
$298$		0			0
$299$	250.981	+	434.712i	0.0485438	+	0.0840804i
$300$		0			0
$301$	6607.96	+	4595.33i	1.26537	+	0.879968i
$302$		0			0
$303$	−2231.79	−	3865.57i	−0.423145	−	0.732909i
$304$		0			0
$305$	−6631.17	+	11485.5i	−1.24492	+	2.15626i
$306$		0			0
$307$	−145.970			−0.0271366			−0.0135683	−	0.999908i	$-0.504319\pi$
$307$	−145.970			−0.0271366			−0.0135683	+	0.999908i	$0.504319\pi$
$308$		0			0
$309$	−2335.22			−0.429923
$310$		0			0
$311$	1708.26	−	2958.79i	0.311467	−	0.539477i	−0.667213	−	0.744867i	$-0.732513\pi$
$311$	1708.26	−	2958.79i	0.311467	−	0.539477i	0.978680	+	0.205390i	$0.0658462\pi$
$312$		0			0
$313$	−1841.18	−	3189.01i	−0.332490	−	0.575890i	0.650509	−	0.759498i	$-0.274555\pi$
$313$	−1841.18	−	3189.01i	−0.332490	−	0.575890i	−0.982999	+	0.183608i	$0.941222\pi$
$314$		0			0
$315$	−2385.19	+	1121.59i	−0.426637	+	0.200618i
$316$		0			0
$317$	688.389	+	1192.32i	0.121968	+	0.211254i	0.920544	−	0.390640i	$-0.127746\pi$
$317$	688.389	+	1192.32i	0.121968	+	0.211254i	−0.798576	+	0.601894i	$0.794413\pi$
$318$		0			0
$319$	3.29486	−	5.70686i	0.000578297	−	0.00100164i
$320$		0			0
$321$	3906.24			0.679205
$322$		0			0
$323$	7826.61			1.34825
$324$		0			0
$325$	3853.38	−	6674.26i	0.657684	−	1.13914i
$326$		0			0
$327$	703.622	+	1218.71i	0.118992	+	0.206100i
$328$		0			0
$329$	751.570	−	8921.01i	0.125943	−	1.49493i
$330$		0			0
$331$	1087.46	+	1883.54i	0.180581	+	0.312776i	0.942079	−	0.335392i	$-0.108869\pi$
$331$	1087.46	+	1883.54i	0.180581	+	0.312776i	−0.761497	+	0.648168i	$0.775535\pi$
$332$		0			0
$333$	−949.860	+	1645.21i	−0.156312	+	0.270741i
$334$		0			0
$335$	−9867.92			−1.60938
$336$		0			0
$337$	−6321.14			−1.02176			−0.510882	−	0.859651i	$-0.670681\pi$
$337$	−6321.14			−1.02176			−0.510882	+	0.859651i	$0.670681\pi$
$338$		0			0
$339$	2480.80	−	4296.86i	0.397458	−	0.688418i
$340$		0			0
$341$	2670.60	+	4625.61i	0.424108	+	0.734577i
$342$		0			0
$343$	1584.83	−	6151.58i	0.249483	−	0.968379i
$344$		0			0
$345$	−193.190	−	334.615i	−0.0301478	−	0.0522175i
$346$		0			0
$347$	−5812.21	+	10067.0i	−0.899181	+	1.55743i	−0.0706381	+	0.997502i	$0.522504\pi$
$347$	−5812.21	+	10067.0i	−0.899181	+	1.55743i	−0.828543	+	0.559925i	$0.810830\pi$
$348$		0			0
$349$	−9841.79			−1.50951			−0.754755	−	0.656007i	$-0.772244\pi$
$349$	−9841.79			−1.50951			−0.754755	+	0.656007i	$0.772244\pi$
$350$		0			0
$351$	1664.00			0.253043
$352$		0			0
$353$	−2265.94	+	3924.73i	−0.341654	+	0.591762i	−0.984740	−	0.174032i	$-0.944320\pi$
$353$	−2265.94	+	3924.73i	−0.341654	+	0.591762i	0.643086	+	0.765794i	$0.277654\pi$
$354$		0			0
$355$	−1795.61	−	3110.08i	−0.268453	−	0.464975i
$356$		0			0
$357$	261.877	−	3108.44i	0.0388236	−	0.460829i
$358$		0			0
$359$	−1140.05	−	1974.63i	−0.167603	−	0.290298i	0.769973	−	0.638076i	$-0.220269\pi$
$359$	−1140.05	−	1974.63i	−0.167603	−	0.290298i	−0.937577	+	0.347779i	$0.886936\pi$
$360$		0			0
$361$	−6286.75	+	10889.0i	−0.916569	+	1.58754i
$362$		0			0
$363$	1248.19			0.180476
$364$		0			0
$365$	−680.739			−0.0976205
$366$		0			0
$367$	3168.76	−	5488.45i	0.450702	−	0.780639i	−0.547728	−	0.836657i	$-0.684507\pi$
$367$	3168.76	−	5488.45i	0.450702	−	0.780639i	0.998430	+	0.0560176i	$0.0178403\pi$
$368$		0			0
$369$	1319.87	+	2286.08i	0.186205	+	0.322517i
$370$		0			0
$371$	343.698	−	161.617i	0.0480968	−	0.0226166i
$372$		0			0
$373$	1812.48	+	3139.31i	0.251600	+	0.435783i	0.963966	−	0.266024i	$-0.0857100\pi$
$373$	1812.48	+	3139.31i	0.251600	+	0.435783i	−0.712367	+	0.701807i	$0.752377\pi$
$374$		0			0
$375$	−1.17253	+	2.03088i	−0.000161464	+	0.000279664i
$376$		0			0
$377$	13.4265			0.00183421
$378$		0			0
$379$	−268.622			−0.0364068			−0.0182034	−	0.999834i	$-0.505795\pi$
$379$	−268.622			−0.0364068			−0.0182034	+	0.999834i	$0.505795\pi$
$380$		0			0
$381$	−245.640	+	425.461i	−0.0330302	+	0.0572100i
$382$		0			0
$383$	−1068.70	−	1851.03i	−0.142579	−	0.246954i	0.785888	−	0.618369i	$-0.212206\pi$
$383$	−1068.70	−	1851.03i	−0.142579	−	0.246954i	−0.928467	+	0.371415i	$0.878873\pi$
$384$		0			0
$385$	7272.69	+	5057.60i	0.962729	+	0.669504i
$386$		0			0
$387$	1955.66	+	3387.30i	0.256878	+	0.444926i
$388$		0			0
$389$	−731.615	+	1267.19i	−0.0953583	+	0.165165i	−0.909758	−	0.415139i	$-0.863733\pi$
$389$	−731.615	+	1267.19i	−0.0953583	+	0.165165i	0.814400	+	0.580304i	$0.197066\pi$
$390$		0			0
$391$	457.288			0.0591459
$392$		0			0
$393$	−1565.68			−0.200962
$394$		0			0
$395$	2443.58	−	4232.40i	0.311265	−	0.539127i
$396$		0			0
$397$	618.718	+	1071.65i	0.0782180	+	0.135478i	0.902481	−	0.430729i	$-0.141744\pi$
$397$	618.718	+	1071.65i	0.0782180	+	0.135478i	−0.824263	+	0.566207i	$0.808410\pi$
$398$		0			0
$399$	6358.76	+	4422.03i	0.797835	+	0.554833i
$400$		0			0
$401$	3089.94	+	5351.94i	0.384799	+	0.666492i	0.991741	−	0.128254i	$-0.0409374\pi$
$401$	3089.94	+	5351.94i	0.384799	+	0.666492i	−0.606942	+	0.794746i	$0.707604\pi$
$402$		0			0
$403$	−5441.31	+	9424.63i	−0.672583	+	1.16495i
$404$		0			0
$405$	−1280.85			−0.157150
$406$		0			0
$407$	6384.73			0.777591
$408$		0			0
$409$	1127.49	−	1952.87i	0.136310	−	0.236096i	−0.789787	−	0.613381i	$-0.789809\pi$
$409$	1127.49	−	1952.87i	0.136310	−	0.236096i	0.926097	+	0.377285i	$0.123142\pi$
$410$		0			0
$411$	4015.33	+	6954.76i	0.481902	+	0.834679i
$412$		0			0
$413$	3877.34	−	1823.24i	0.461964	−	0.217230i
$414$		0			0
$415$	−9756.50	−	16898.7i	−1.15404	−	1.99886i
$416$		0			0
$417$	−1280.54	+	2217.96i	−0.150379	+	0.260465i
$418$		0			0
$419$	1404.53			0.163761			0.0818806	−	0.996642i	$-0.473907\pi$
$419$	1404.53			0.163761			0.0818806	+	0.996642i	$0.473907\pi$
$420$		0			0
$421$	13068.1			1.51283			0.756414	−	0.654094i	$-0.226950\pi$
$421$	13068.1			1.51283			0.756414	+	0.654094i	$0.226950\pi$
$422$		0			0
$423$	2175.28	−	3767.70i	0.250037	−	0.433077i
$424$		0			0
$425$	−3510.44	−	6080.26i	−0.400662	−	0.693966i
$426$		0			0
$427$	1303.99	−	15478.1i	0.147786	−	1.75419i
$428$		0			0
$429$	−2796.26	−	4843.26i	−0.314696	−	0.545070i
$430$		0			0
$431$	−2681.39	+	4644.31i	−0.299671	+	0.519046i	−0.976061	−	0.217499i	$-0.930210\pi$
$431$	−2681.39	+	4644.31i	−0.299671	+	0.519046i	0.676390	+	0.736544i	$0.263544\pi$
$432$		0			0
$433$	−2495.82			−0.277001			−0.138501	−	0.990362i	$-0.544228\pi$
$433$	−2495.82			−0.277001			−0.138501	+	0.990362i	$0.544228\pi$
$434$		0			0
$435$	−10.3349			−0.00113913
$436$		0			0
$437$	−567.694	+	983.275i	−0.0621430	+	0.107635i
$438$		0			0
$439$	1881.06	+	3258.09i	0.204506	+	0.354215i	0.949975	−	0.312325i	$-0.101108\pi$
$439$	1881.06	+	3258.09i	0.204506	+	0.354215i	−0.745469	+	0.666540i	$0.767775\pi$
$440$		0			0
$441$	1969.03	−	2377.50i	0.212615	−	0.256722i
$442$		0			0
$443$	5722.63	+	9911.88i	0.613748	+	1.06304i	0.990603	+	0.136770i	$0.0436721\pi$
$443$	5722.63	+	9911.88i	0.613748	+	1.06304i	−0.376855	+	0.926272i	$0.622995\pi$
$444$		0			0
$445$	9047.83	−	15671.3i	0.963839	−	1.66942i
$446$		0			0
$447$	−1673.06			−0.177031
$448$		0			0
$449$	−9420.02			−0.990107			−0.495054	−	0.868862i	$-0.664852\pi$
$449$	−9420.02			−0.990107			−0.495054	+	0.868862i	$0.664852\pi$
$450$		0			0
$451$	4435.93	−	7683.25i	0.463148	−	0.802196i
$452$		0			0
$453$	−2654.02	−	4596.90i	−0.275269	−	0.476780i
$454$		0			0
$455$	−1515.20	+	17985.2i	−0.156118	+	1.85310i
$456$		0			0
$457$	−5731.98	−	9928.08i	−0.586719	−	1.01623i	−0.994659	−	0.103219i	$-0.967086\pi$
$457$	−5731.98	−	9928.08i	−0.586719	−	1.01623i	0.407939	−	0.913009i	$-0.366247\pi$
$458$		0			0
$459$	757.955	−	1312.82i	0.0770769	−	0.133501i
$460$		0			0
$461$	−9751.10			−0.985149			−0.492575	−	0.870270i	$-0.663944\pi$
$461$	−9751.10			−0.985149			−0.492575	+	0.870270i	$0.663944\pi$
$462$		0			0
$463$	−2182.03			−0.219023			−0.109512	−	0.993986i	$-0.534929\pi$
$463$	−2182.03			−0.219023			−0.109512	+	0.993986i	$0.534929\pi$
$464$		0			0
$465$	4188.39	−	7254.50i	0.417703	−	0.723483i
$466$		0			0
$467$	1598.17	+	2768.11i	0.158361	+	0.274289i	0.934278	−	0.356546i	$-0.116046\pi$
$467$	1598.17	+	2768.11i	0.158361	+	0.274289i	−0.775917	+	0.630835i	$0.782712\pi$
$468$		0			0
$469$	10458.8	−	4918.04i	1.02973	−	0.484209i
$470$		0			0
$471$	−3607.34	−	6248.10i	−0.352904	−	0.611247i
$472$		0			0
$473$	6572.74	−	11384.3i	0.638932	−	1.10666i
$474$		0			0
$475$	17432.0			1.68386
$476$		0			0
$477$	184.566			0.0177163
$478$		0			0
$479$	−6071.79	+	10516.7i	−0.579180	+	1.00317i	0.416394	+	0.909184i	$0.363294\pi$
$479$	−6071.79	+	10516.7i	−0.579180	+	1.00317i	−0.995574	+	0.0939849i	$0.970039\pi$
$480$		0			0
$481$	6504.41	+	11266.0i	0.616581	+	1.06795i
$482$		0			0
$483$	371.525	+	258.367i	0.0350000	+	0.0243398i
$484$		0			0
$485$	13347.1	+	23117.9i	1.24961	+	2.16439i
$486$		0			0
$487$	−10151.2	+	17582.5i	−0.944551	+	1.63601i	−0.187905	+	0.982187i	$0.560170\pi$
$487$	−10151.2	+	17582.5i	−0.944551	+	1.63601i	−0.756647	+	0.653824i	$0.773164\pi$
$488$		0			0
$489$	10136.4			0.937389
$490$		0			0
$491$	−2562.41			−0.235519			−0.117760	−	0.993042i	$-0.537571\pi$
$491$	−2562.41			−0.235519			−0.117760	+	0.993042i	$0.537571\pi$
$492$		0			0
$493$	6.11577	−	10.5928i	0.000558702	−	0.000967701i
$494$		0			0
$495$	2152.39	+	3728.05i	0.195440	+	0.338512i
$496$		0			0
$497$	3453.15	+	2401.40i	0.311660	+	0.216735i
$498$		0			0
$499$	−5828.05	−	10094.5i	−0.522844	−	0.905592i	−0.999647	−	0.0265820i	$-0.991538\pi$
$499$	−5828.05	−	10094.5i	−0.522844	−	0.905592i	0.476803	−	0.879010i	$-0.341796\pi$
$500$		0			0
$501$	1208.85	−	2093.79i	0.107799	−	0.186714i
$502$		0			0
$503$	18532.8			1.64281			0.821407	−	0.570342i	$-0.193189\pi$
$503$	18532.8			1.64281			0.821407	+	0.570342i	$0.193189\pi$
$504$		0			0
$505$	23527.5			2.07318
$506$		0			0
$507$	2401.85	−	4160.12i	0.210394	−	0.364413i
$508$		0			0
$509$	−9366.05	−	16222.5i	−0.815605	−	1.41267i	−0.908893	−	0.417030i	$-0.863071\pi$
$509$	−9366.05	−	16222.5i	−0.815605	−	1.41267i	0.0932881	−	0.995639i	$-0.470262\pi$
$510$		0			0
$511$	721.499	−	339.271i	0.0624604	−	0.0293708i
$512$		0			0
$513$	1881.91	+	3259.56i	0.161965	+	0.280532i
$514$		0			0
$515$	6154.46	−	10659.8i	0.526598	−	0.912094i
$516$		0			0
$517$	−14621.7			−1.24383
$518$		0			0
$519$	2521.51			0.213260
$520$		0			0
$521$	1661.63	−	2878.02i	0.139726	−	0.242012i	−0.787667	−	0.616101i	$-0.788711\pi$
$521$	1661.63	−	2878.02i	0.139726	−	0.242012i	0.927393	+	0.374089i	$0.122045\pi$
$522$		0			0
$523$	−11648.7	−	20176.2i	−0.973925	−	1.68689i	−0.683437	−	0.730010i	$-0.739516\pi$
$523$	−11648.7	−	20176.2i	−0.973925	−	1.68689i	−0.290489	−	0.956878i	$-0.593818\pi$
$524$		0			0
$525$	583.270	−	6923.32i	0.0484876	−	0.575540i
$526$		0			0
$527$	4957.04	+	8585.84i	0.409738	+	0.709687i
$528$		0			0
$529$	6050.33	−	10479.5i	0.497274	−	0.861304i
$530$		0			0
$531$	2082.13			0.170163
$532$		0			0
$533$	18076.3			1.46899
$534$		0			0
$535$	−10294.9	+	17831.2i	−0.831936	+	1.44095i
$536$		0			0
$537$	−2406.92	−	4168.90i	−0.193419	−	0.335012i
$538$		0			0
$539$	−10228.8	−	1735.82i	−0.817413	−	0.138714i
$540$		0			0
$541$	−4525.01	−	7837.54i	−0.359603	−	0.622851i	0.628292	−	0.777978i	$-0.283755\pi$
$541$	−4525.01	−	7837.54i	−0.359603	−	0.622851i	−0.987894	+	0.155127i	$0.950421\pi$
$542$		0			0
$543$	−5669.14	+	9819.24i	−0.448041	+	0.776029i
$544$		0			0
$545$	−7417.56			−0.582997
$546$		0			0
$547$	12316.7			0.962749			0.481374	−	0.876515i	$-0.340138\pi$
$547$	12316.7			0.962749			0.481374	+	0.876515i	$0.340138\pi$
$548$		0			0
$549$	3774.16	−	6537.03i	0.293401	−	0.508185i
$550$		0			0
$551$	15.1847	+	26.3006i	0.00117403	+	0.00203347i
$552$		0			0
$553$	−480.518	+	5703.67i	−0.0369507	+	0.438598i
$554$		0			0
$555$	−5006.70	−	8671.86i	−0.382923	−	0.663243i
$556$		0			0
$557$	−12452.0	+	21567.6i	−0.947236	+	1.64066i	−0.196024	+	0.980599i	$0.562803\pi$
$557$	−12452.0	+	21567.6i	−0.947236	+	1.64066i	−0.751212	+	0.660061i	$0.770530\pi$
$558$		0			0
$559$	26783.8			2.02653
$560$		0			0
$561$	−5094.79			−0.383426
$562$		0			0
$563$	−2073.30	+	3591.06i	−0.155203	+	0.268819i	−0.933133	−	0.359532i	$-0.882936\pi$
$563$	−2073.30	+	3591.06i	−0.155203	+	0.268819i	0.777930	+	0.628351i	$0.216270\pi$
$564$		0			0
$565$	13076.2	+	22648.7i	0.973666	+	1.68644i
$566$		0			0
$567$	1357.54	−	638.358i	0.100549	−	0.0472814i
$568$		0			0
$569$	−3648.74	−	6319.80i	−0.268828	−	0.465624i	0.699731	−	0.714406i	$-0.253303\pi$
$569$	−3648.74	−	6319.80i	−0.268828	−	0.465624i	−0.968559	+	0.248782i	$0.919970\pi$
$570$		0			0
$571$	−5782.45	+	10015.5i	−0.423797	+	0.734037i	−0.996307	−	0.0858600i	$-0.972636\pi$
$571$	−5782.45	+	10015.5i	−0.423797	+	0.734037i	0.572511	+	0.819897i	$0.305970\pi$
$572$		0			0
$573$	−5548.79			−0.404544
$574$		0			0
$575$	1018.50			0.0738687
$576$		0			0
$577$	−4736.72	+	8204.25i	−0.341755	+	0.591936i	−0.984759	−	0.173926i	$-0.944354\pi$
$577$	−4736.72	+	8204.25i	−0.341755	+	0.591936i	0.643004	+	0.765863i	$0.277688\pi$
$578$		0			0
$579$	−529.504	−	917.128i	−0.0380059	−	0.0658282i
$580$		0			0
$581$	18762.8	+	13048.1i	1.33978	+	0.931714i
$582$		0			0
$583$	−310.152	−	537.198i	−0.0220329	−	0.0381620i
$584$		0			0
$585$	−4385.47	+	7595.86i	−0.309943	+	0.536838i
$586$		0			0
$587$	−7336.02			−0.515826			−0.257913	−	0.966168i	$-0.583035\pi$
$587$	−7336.02			−0.515826			−0.257913	+	0.966168i	$0.583035\pi$
$588$		0			0
$589$	−24615.4			−1.72200
$590$		0			0
$591$	6672.33	−	11556.8i	0.464405	−	0.804372i
$592$		0			0
$593$	−9040.73	−	15659.0i	−0.626068	−	1.08438i	−0.988333	−	0.152307i	$-0.951330\pi$
$593$	−9040.73	−	15659.0i	−0.626068	−	1.08438i	0.362265	−	0.932075i	$-0.382004\pi$
$594$		0			0
$595$	13499.2	+	9387.68i	0.930109	+	0.646819i
$596$		0			0
$597$	3360.23	+	5820.08i	0.230360	+	0.398995i
$598$		0			0
$599$	−96.2165	+	166.652i	−0.00656310	+	0.0113676i	−0.869288	−	0.494305i	$-0.835422\pi$
$599$	−96.2165	+	166.652i	−0.00656310	+	0.0113676i	0.862725	+	0.505673i	$0.168756\pi$
$600$		0			0
$601$	−5055.76			−0.343143			−0.171571	−	0.985172i	$-0.554884\pi$
$601$	−5055.76			−0.343143			−0.171571	+	0.985172i	$0.554884\pi$
$602$		0			0
$603$	5616.36			0.379297
$604$		0			0
$605$	−3289.59	+	5697.74i	−0.221059	+	0.382886i
$606$		0			0
$607$	10117.9	+	17524.7i	0.676560	+	1.17184i	0.976010	+	0.217724i	$0.0698633\pi$
$607$	10117.9	+	17524.7i	0.676560	+	1.17184i	−0.299451	+	0.954112i	$0.596803\pi$
$608$		0			0
$609$	10.9537	−	5.15077i	0.000728845	−	0.000342725i
$610$		0			0
$611$	−14895.8	−	25800.2i	−0.986283	−	1.70829i
$612$		0			0
$613$	1920.25	−	3325.98i	0.126523	−	0.219143i	−0.795805	−	0.605554i	$-0.792952\pi$
$613$	1920.25	−	3325.98i	0.126523	−	0.219143i	0.922327	+	0.386410i	$0.126285\pi$
$614$		0			0
$615$	−13914.0			−0.912306
$616$		0			0
$617$	−5720.89			−0.373281			−0.186641	−	0.982428i	$-0.559760\pi$
$617$	−5720.89			−0.373281			−0.186641	+	0.982428i	$0.559760\pi$
$618$		0			0
$619$	11470.1	−	19866.8i	0.744787	−	1.29001i	−0.205507	−	0.978656i	$-0.565884\pi$
$619$	11470.1	−	19866.8i	0.744787	−	1.29001i	0.950294	−	0.311354i	$-0.100782\pi$
$620$		0			0
$621$	109.955	+	190.447i	0.00710521	+	0.0123066i
$622$		0			0
$623$	−1779.22	+	21119.0i	−0.114419	+	1.35813i
$624$		0			0
$625$	7809.41	+	13526.3i	0.499802	+	0.865683i
$626$		0			0
$627$	6324.86	−	10955.0i	0.402856	−	0.697767i
$628$		0			0
$629$	11851.0			0.751244
$630$		0			0
$631$	−7634.81			−0.481675			−0.240837	−	0.970565i	$-0.577422\pi$
$631$	−7634.81			−0.481675			−0.240837	+	0.970565i	$0.577422\pi$
$632$		0			0
$633$	−1836.50	+	3180.92i	−0.115315	+	0.199732i
$634$		0			0
$635$	−1294.76	−	2242.60i	−0.0809152	−	0.140149i
$636$		0			0
$637$	−7357.65	−	19817.2i	−0.457646	−	1.23263i
$638$		0			0
$639$	1021.98	+	1770.12i	0.0632688	+	0.109585i
$640$		0			0
$641$	1389.80	−	2407.20i	0.0856376	−	0.148329i	−0.820025	−	0.572328i	$-0.806041\pi$
$641$	1389.80	−	2407.20i	0.0856376	−	0.148329i	0.905663	+	0.423999i	$0.139374\pi$
$642$		0			0
$643$	−18304.5			−1.12264			−0.561322	−	0.827598i	$-0.689707\pi$
$643$	−18304.5			−1.12264			−0.561322	+	0.827598i	$0.689707\pi$
$644$		0			0
$645$	−20616.5			−1.25856
$646$		0			0
$647$	3276.27	−	5674.66i	0.199078	−	0.344813i	−0.749152	−	0.662398i	$-0.769539\pi$
$647$	3276.27	−	5674.66i	0.199078	−	0.344813i	0.948230	+	0.317585i	$0.102872\pi$
$648$		0			0
$649$	−3498.89	−	6060.26i	−0.211623	−	0.366542i
$650$		0			0
$651$	−823.628	+	9776.32i	−0.0495861	+	0.588578i
$652$		0			0
$653$	15993.0	+	27700.8i	0.958432	+	1.66005i	0.726312	+	0.687365i	$0.241233\pi$
$653$	15993.0	+	27700.8i	0.958432	+	1.66005i	0.232120	+	0.972687i	$0.425434\pi$
$654$		0			0
$655$	4126.34	−	7147.03i	0.246152	−	0.426348i
$656$		0			0
$657$	387.445			0.0230071
$658$		0			0
$659$	−517.327			−0.0305799			−0.0152900	−	0.999883i	$-0.504867\pi$
$659$	−517.327			−0.0305799			−0.0152900	+	0.999883i	$0.504867\pi$
$660$		0			0
$661$	−9828.40	+	17023.3i	−0.578336	+	1.00171i	0.417334	+	0.908753i	$0.362965\pi$
$661$	−9828.40	+	17023.3i	−0.578336	+	1.00171i	−0.995670	+	0.0929549i	$0.970369\pi$
$662$		0			0
$663$	−5190.29	−	8989.84i	−0.304033	−	0.526601i
$664$		0			0
$665$	−36944.1	+	17372.3i	−2.15433	+	1.01303i
$666$		0			0
$667$	0.887200	+	1.53668i	5.15030e−5	+	8.92059e-5i
$668$		0			0
$669$	5186.05	−	8982.50i	0.299707	−	0.519108i
$670$		0			0
$671$	−25369.0			−1.45955
$672$		0			0
$673$	25836.1			1.47981			0.739904	−	0.672713i	$-0.234871\pi$
$673$	25836.1			1.47981			0.739904	+	0.672713i	$0.234871\pi$
$674$		0			0
$675$	1688.17	−	2923.99i	0.0962631	−	0.166733i
$676$		0			0
$677$	−13263.1	−	22972.4i	−0.752944	−	1.30414i	−0.946390	−	0.323026i	$-0.895300\pi$
$677$	−13263.1	−	22972.4i	−0.752944	−	1.30414i	0.193447	−	0.981111i	$-0.438033\pi$
$678$		0			0
$679$	−25667.9	−	17850.1i	−1.45073	−	1.00887i
$680$		0			0
$681$	7767.33	+	13453.4i	0.437070	+	0.757027i
$682$		0			0
$683$	16939.4	−	29339.9i	0.949002	−	1.64372i	0.201470	−	0.979495i	$-0.435428\pi$
$683$	16939.4	−	29339.9i	0.949002	−	1.64372i	0.747532	−	0.664225i	$-0.231239\pi$
$684$		0			0
$685$	−42329.5			−2.36106
$686$		0			0
$687$	−6935.65			−0.385170
$688$		0			0
$689$	631.930	−	1094.53i	0.0349414	−	0.0605203i
$690$		0			0
$691$	−500.631	−	867.119i	−0.0275614	−	0.0477377i	0.851916	−	0.523679i	$-0.175441\pi$
$691$	−500.631	−	867.119i	−0.0275614	−	0.0477377i	−0.879477	+	0.475941i	$0.842108\pi$
$692$		0			0
$693$	−4139.28	−	2878.55i	−0.226895	−	0.157788i
$694$		0			0
$695$	−6749.70	−	11690.8i	−0.368389	−	0.638069i
$696$		0			0
$697$	8233.76	−	14261.3i	0.447455	−	0.775015i
$698$		0			0
$699$	−14228.9			−0.769939
$700$		0			0
$701$	7713.38			0.415592			0.207796	−	0.978172i	$-0.433371\pi$
$701$	7713.38			0.415592			0.207796	+	0.978172i	$0.433371\pi$
$702$		0			0
$703$	−14712.3	+	25482.5i	−0.789312	+	1.36713i
$704$		0			0
$705$	11465.9	+	19859.5i	0.612524	+	1.06092i
$706$		0			0
$707$	−24936.2	+	11725.8i	−1.32648	+	0.623753i
$708$		0			0
$709$	−5017.56	−	8690.67i	−0.265781	−	0.460346i	0.701987	−	0.712190i	$-0.252296\pi$
$709$	−5017.56	−	8690.67i	−0.265781	−	0.460346i	−0.967768	+	0.251844i	$0.918963\pi$
$710$		0			0
$711$	−1390.77	+	2408.89i	−0.0733586	+	0.127061i
$712$		0			0
$713$	−1438.21			−0.0755421
$714$		0			0
$715$	29478.1			1.54184
$716$		0			0
$717$	2118.89	−	3670.02i	0.110364	−	0.191157i
$718$		0			0
$719$	−10059.7	−	17423.9i	−0.521785	−	0.903758i	−0.999679	−	0.0253401i	$-0.991933\pi$
$719$	−10059.7	−	17423.9i	−0.521785	−	0.903758i	0.477894	−	0.878417i	$-0.341400\pi$
$720$		0			0
$721$	−1210.25	+	14365.4i	−0.0625131	+	0.742020i
$722$		0			0
$723$	−2821.73	−	4887.38i	−0.145147	−	0.251402i
$724$		0			0
$725$	13.6214	−	23.5930i	0.000697776	−	0.00120858i
$726$		0			0
$727$	7567.09			0.386035			0.193018	−	0.981195i	$-0.438173\pi$
$727$	7567.09			0.386035			0.193018	+	0.981195i	$0.438173\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	12200.0	−	21131.0i	0.617283	−	1.06917i
$732$		0			0
$733$	−15400.0	−	26673.6i	−0.776006	−	1.34408i	−0.934228	−	0.356678i	$-0.883909\pi$
$733$	−15400.0	−	26673.6i	−0.776006	−	1.34408i	0.158222	−	0.987404i	$-0.449424\pi$
$734$		0			0
$735$	5663.47	+	15254.1i	0.284218	+	0.765518i
$736$		0			0
$737$	−9437.96	−	16347.0i	−0.471712	−	0.817029i
$738$		0			0
$739$	−6659.66	+	11534.9i	−0.331501	+	0.574177i	−0.982806	−	0.184639i	$-0.940889\pi$
$739$	−6659.66	+	11534.9i	−0.331501	+	0.574177i	0.651305	+	0.758816i	$0.274222\pi$
$740$		0			0
$741$	25773.7			1.27776
$742$		0			0
$743$	10747.7			0.530682			0.265341	−	0.964155i	$-0.414516\pi$
$743$	10747.7			0.530682			0.265341	+	0.964155i	$0.414516\pi$
$744$		0			0
$745$	4409.33	−	7637.18i	0.216839	−	0.375577i
$746$		0			0
$747$	5552.95	+	9617.99i	0.271984	+	0.471089i
$748$		0			0
$749$	2024.44	−	24029.7i	0.0987601	−	1.17227i
$750$		0			0
$751$	6106.70	+	10577.1i	0.296720	+	0.513934i	0.975383	−	0.220515i	$-0.0707739\pi$
$751$	6106.70	+	10577.1i	0.296720	+	0.513934i	−0.678664	+	0.734449i	$0.737441\pi$
$752$		0			0
$753$	−6779.46	+	11742.4i	−0.328097	+	0.568281i
$754$		0			0
$755$	27978.6			1.34867
$756$		0			0
$757$	−30173.2			−1.44870			−0.724349	−	0.689434i	$-0.757860\pi$
$757$	−30173.2			−1.44870			−0.724349	+	0.689434i	$0.757860\pi$
$758$		0			0
$759$	369.545	−	640.070i	0.0176728	−	0.0306101i
$760$		0			0
$761$	−7603.67	−	13169.9i	−0.362198	−	0.627346i	0.626124	−	0.779723i	$-0.284640\pi$
$761$	−7603.67	−	13169.9i	−0.362198	−	0.627346i	−0.988322	+	0.152378i	$0.951307\pi$
$762$		0			0
$763$	7861.71	−	3696.82i	0.373018	−	0.175405i
$764$		0			0
$765$	3995.17	+	6919.83i	0.188818	+	0.327042i
$766$		0			0
$767$	7128.95	−	12347.7i	0.335608	−	0.581290i
$768$		0			0
$769$	−9368.65			−0.439327			−0.219663	−	0.975576i	$-0.570496\pi$
$769$	−9368.65			−0.439327			−0.219663	+	0.975576i	$0.570496\pi$
$770$		0			0
$771$	−23738.0			−1.10882
$772$		0			0
$773$	−16258.2	+	28159.9i	−0.756488	+	1.31028i	0.188143	+	0.982142i	$0.439753\pi$
$773$	−16258.2	+	28159.9i	−0.756488	+	1.31028i	−0.944631	+	0.328134i	$0.893580\pi$
$774$		0			0
$775$	11040.6	+	19123.0i	0.511731	+	0.886345i
$776$		0			0
$777$	9628.42	+	6695.83i	0.444553	+	0.309152i
$778$		0			0
$779$	20443.4	+	35409.0i	0.940258	+	1.62857i
$780$		0			0
$781$	3434.74	−	5949.15i	0.157368	−	0.272570i
$782$		0			0
$783$	5.88214			0.000268468
$784$		0			0
$785$	38028.5			1.72904
$786$		0			0
$787$	−20125.1	+	34857.8i	−0.911542	+	1.57884i	−0.0996552	+	0.995022i	$0.531774\pi$
$787$	−20125.1	+	34857.8i	−0.911542	+	1.57884i	−0.811887	+	0.583815i	$0.801559\pi$
$788$		0			0
$789$	5146.74	+	8914.42i	0.232229	+	0.402233i
$790$		0			0
$791$	−25147.0	−	17487.8i	−1.13037	−	0.786087i
$792$		0			0
$793$	−25844.5	−	44764.0i	−1.15733	−	2.00456i
$794$		0			0
$795$	−486.421	+	842.506i	−0.0217001	+	0.0375857i
$796$		0			0
$797$	21387.5			0.950544			0.475272	−	0.879839i	$-0.342350\pi$
$797$	21387.5			0.950544			0.475272	+	0.879839i	$0.342350\pi$
$798$		0			0
$799$	−27140.1			−1.20169
$800$		0			0
$801$	−5149.61	+	8919.38i	−0.227157	+	0.393447i
$802$		0			0
$803$	−651.078	−	1127.70i	−0.0286128	−	0.0495587i
$804$		0			0
$805$	−2158.55	+	1015.02i	−0.0945078	+	0.0444405i
$806$		0			0
$807$	12448.8	+	21561.9i	0.543021	+	0.940540i
$808$		0			0
$809$	9817.06	−	17003.6i	0.426637	−	0.738957i	−0.569935	−	0.821690i	$-0.693032\pi$
$809$	9817.06	−	17003.6i	0.426637	−	0.738957i	0.996572	+	0.0827330i	$0.0263649\pi$
$810$		0			0
$811$	−35238.1			−1.52574			−0.762872	−	0.646549i	$-0.776211\pi$
$811$	−35238.1			−1.52574			−0.762872	+	0.646549i	$0.776211\pi$
$812$		0			0
$813$	−17773.5			−0.766719
$814$		0			0
$815$	−26714.4	+	46270.6i	−1.14818	+	1.98870i
$816$		0			0
$817$	30291.1	+	52465.7i	1.29713	+	2.24669i
$818$		0			0
$819$	862.383	−	10236.3i	0.0367938	−	0.436736i
$820$		0			0
$821$	3527.40	+	6109.63i	0.149948	+	0.259717i	0.931208	−	0.364488i	$-0.118756\pi$
$821$	3527.40	+	6109.63i	0.149948	+	0.259717i	−0.781260	+	0.624205i	$0.785423\pi$
$822$		0			0
$823$	3094.16	−	5359.25i	0.131052	−	0.226989i	−0.793030	−	0.609182i	$-0.791498\pi$
$823$	3094.16	−	5359.25i	0.131052	−	0.226989i	0.924082	+	0.382193i	$0.124831\pi$
$824$		0			0
$825$	−11347.5			−0.478870
$826$		0			0
$827$	24000.0			1.00915			0.504573	−	0.863369i	$-0.331650\pi$
$827$	24000.0			1.00915			0.504573	+	0.863369i	$0.331650\pi$
$828$		0			0
$829$	4354.43	−	7542.09i	0.182431	−	0.315980i	−0.760277	−	0.649599i	$-0.774937\pi$
$829$	4354.43	−	7542.09i	0.182431	−	0.315980i	0.942708	+	0.333619i	$0.108270\pi$
$830$		0			0
$831$	2280.90	+	3950.63i	0.0952149	+	0.164917i
$832$		0			0
$833$	−18986.2	−	3221.94i	−0.789716	−	0.134014i
$834$		0			0
$835$	6371.83	+	11036.3i	0.264079	+	0.457399i
$836$		0			0
$837$	−2383.84	+	4128.93i	−0.0984438	+	0.170510i
$838$		0			0
$839$	−7820.46			−0.321802			−0.160901	−	0.986971i	$-0.551440\pi$
$839$	−7820.46			−0.321802			−0.160901	+	0.986971i	$0.551440\pi$
$840$		0			0
$841$	−24389.0			−0.999998
$842$		0			0
$843$	−528.499	+	915.388i	−0.0215925	+	0.0373993i
$844$		0			0
$845$	12660.1	+	21927.9i	0.515409	+	0.892714i
$846$		0			0
$847$	646.884	−	7678.39i	0.0262422	−	0.311491i
$848$		0			0
$849$	−6432.73	−	11141.8i	−0.260036	−	0.450396i
$850$		0			0
$851$	−859.602	+	1488.87i	−0.0346261	+	0.0599741i
$852$		0			0
$853$	31176.8			1.25143			0.625717	−	0.780050i	$-0.284807\pi$
$853$	31176.8			1.25143			0.625717	+	0.780050i	$0.284807\pi$
$854$		0			0
$855$	−19839.0			−0.793543
$856$		0			0
$857$	−447.864	+	775.724i	−0.0178515	+	0.0309197i	−0.874813	−	0.484460i	$-0.839016\pi$
$857$	−447.864	+	775.724i	−0.0178515	+	0.0309197i	0.856962	+	0.515380i	$0.172349\pi$
$858$		0			0
$859$	4557.51	+	7893.83i	0.181025	+	0.313544i	0.942230	−	0.334967i	$-0.108725\pi$
$859$	4557.51	+	7893.83i	0.181025	+	0.313544i	−0.761205	+	0.648511i	$0.775392\pi$
$860$		0			0
$861$	14747.2	−	6934.57i	0.583719	−	0.274483i
$862$		0			0
$863$	−10563.3	−	18296.2i	−0.416662	−	0.721680i	0.578939	−	0.815371i	$-0.303467\pi$
$863$	−10563.3	−	18296.2i	−0.416662	−	0.721680i	−0.995601	+	0.0936906i	$0.970134\pi$
$864$		0			0
$865$	−6645.42	+	11510.2i	−0.261215	+	0.452438i
$866$		0			0
$867$	5282.29			0.206916
$868$		0			0
$869$	9348.43			0.364930
$870$		0			0
$871$	19229.7	−	33306.9i	0.748076	−	1.29571i
$872$		0			0
$873$	−7596.55	−	13157.6i	−0.294507	−	0.510100i
$874$		0			0
$875$	11.8855	+	8.26547i	0.000459205	+	0.000319342i
$876$		0			0
$877$	9374.72	+	16237.5i	0.360960	+	0.625201i	0.988119	−	0.153690i	$-0.0491158\pi$
$877$	9374.72	+	16237.5i	0.360960	+	0.625201i	−0.627159	+	0.778891i	$0.715782\pi$
$878$		0			0
$879$	3992.98	−	6916.04i	0.153219	−	0.265384i
$880$		0			0
$881$	37000.3			1.41495			0.707475	−	0.706739i	$-0.249834\pi$
$881$	37000.3			1.41495			0.707475	+	0.706739i	$0.249834\pi$
$882$		0			0
$883$	−21618.3			−0.823913			−0.411956	−	0.911204i	$-0.635154\pi$
$883$	−21618.3			−0.823913			−0.411956	+	0.911204i	$0.635154\pi$
$884$		0			0
$885$	−5487.43	+	9504.51i	−0.208427	+	0.361006i
$886$		0			0
$887$	4151.85	+	7191.21i	0.157165	+	0.272218i	0.933845	−	0.357677i	$-0.116431\pi$
$887$	4151.85	+	7191.21i	0.157165	+	0.272218i	−0.776680	+	0.629895i	$0.783098\pi$
$888$		0			0
$889$	2489.97	+	1731.58i	0.0939381	+	0.0653267i
$890$		0			0
$891$	−1225.04	−	2121.83i	−0.0460611	−	0.0797801i
$892$		0			0
$893$	33692.8	−	58357.6i	1.26258	−	2.18686i
$894$		0			0
$895$	25373.6			0.947650
$896$		0			0
$897$	1505.89			0.0560536
$898$		0			0
$899$	−19.2346	+	33.3154i	−0.000713583	+	0.00123596i
$900$		0			0
$901$	−575.689	−	997.122i	−0.0212863	−	0.0368690i
$902$		0			0
$903$	21851.0	−	10275.0i	0.805265	−	0.378661i
$904$		0			0
$905$	−29881.9	−	51757.0i	−1.09758	−	1.90106i
$906$		0			0
$907$	−17272.2	+	29916.4i	−0.632321	+	1.09521i	0.354755	+	0.934959i	$0.384564\pi$
$907$	−17272.2	+	29916.4i	−0.632321	+	1.09521i	−0.987076	+	0.160253i	$0.948769\pi$
$908$		0			0
$909$	−13390.7			−0.488606
$910$		0			0
$911$	10505.3			0.382059			0.191030	−	0.981584i	$-0.438817\pi$
$911$	10505.3			0.382059			0.191030	+	0.981584i	$0.438817\pi$
$912$		0			0
$913$	18662.8	−	32324.9i	0.676504	−	1.17174i
$914$		0			0
$915$	19893.5	+	34456.6i	0.718753	+	1.24492i
$916$		0			0
$917$	−811.426	+	9631.49i	−0.0292210	+	0.346848i
$918$		0			0
$919$	16100.8	+	27887.4i	0.577929	+	1.00100i	0.995717	+	0.0924578i	$0.0294723\pi$
$919$	16100.8	+	27887.4i	0.577929	+	1.00100i	−0.417787	+	0.908545i	$0.637194\pi$
$920$		0			0
$921$	−218.955	+	379.241i	−0.00783366	+	0.0135683i
$922$		0			0
$923$	13996.5			0.499133
$924$		0			0
$925$	26395.4			0.938245
$926$		0			0
$927$	−3502.83	+	6067.09i	−0.124108	+	0.214961i
$928$		0			0
$929$	18517.4	+	32073.1i	0.653968	+	1.13271i	0.982151	+	0.188092i	$0.0602303\pi$
$929$	18517.4	+	32073.1i	0.653968	+	1.13271i	−0.328183	+	0.944614i	$0.606436\pi$
$930$		0			0
$931$	30498.1	−	36825.0i	1.07362	−	1.29634i
$932$		0			0
$933$	−5124.77	−	8876.36i	−0.179826	−	0.311467i
$934$		0			0
$935$	13427.3	−	23256.7i	0.469646	−	0.813451i
$936$		0			0
$937$	−7207.18			−0.251279			−0.125639	−	0.992076i	$-0.540098\pi$
$937$	−7207.18			−0.251279			−0.125639	+	0.992076i	$0.540098\pi$
$938$		0			0
$939$	−11047.1			−0.383927
$940$		0			0
$941$	10859.4	−	18809.1i	0.376203	−	0.651603i	−0.614303	−	0.789070i	$-0.710563\pi$
$941$	10859.4	−	18809.1i	0.376203	−	0.651603i	0.990506	+	0.137467i	$0.0438961\pi$
$942$		0			0
$943$	1194.45	+	2068.85i	0.0412479	+	0.0714434i
$944$		0			0
$945$	−663.810	+	7879.31i	−0.0228505	+	0.271232i
$946$		0			0
$947$	−65.6714	−	113.746i	−0.00225347	−	0.00390312i	0.864896	−	0.501950i	$-0.167384\pi$
$947$	−65.6714	−	113.746i	−0.00225347	−	0.00390312i	−0.867150	+	0.498047i	$0.834051\pi$
$948$		0			0
$949$	1326.56	−	2297.68i	0.0453763	−	0.0785940i
$950$		0			0
$951$	4130.33			0.140836
$952$		0			0
$953$	−39810.0			−1.35317			−0.676586	−	0.736363i	$-0.736541\pi$
$953$	−39810.0			−1.35317			−0.676586	+	0.736363i	$0.736541\pi$
$954$		0			0
$955$	14623.8	−	25329.1i	0.495512	−	0.858253i
$956$		0			0
$957$	−9.88458	−	17.1206i	−0.000333880	−	0.000578297i
$958$		0			0
$959$	44864.1	−	21096.5i	1.51067	−	0.710366i
$960$		0			0
$961$	−694.846	−	1203.51i	−0.0233240	−	0.0403984i
$962$		0			0
$963$	5859.36	−	10148.7i	0.196070	−	0.339603i
$964$		0			0
$965$	5582.01			0.186209
$966$		0			0
$967$	−18858.5			−0.627145			−0.313573	−	0.949564i	$-0.601526\pi$
$967$	−18858.5			−0.627145			−0.313573	+	0.949564i	$0.601526\pi$
$968$		0			0
$969$	11739.9	−	20334.1i	0.389206	−	0.674124i
$970$		0			0
$971$	−24177.5	−	41876.7i	−0.799067	−	1.38402i	−0.920225	−	0.391391i	$-0.871994\pi$
$971$	−24177.5	−	41876.7i	−0.799067	−	1.38402i	0.121158	−	0.992633i	$-0.461339\pi$
$972$		0			0
$973$	12980.4	+	9026.87i	0.427680	+	0.297418i
$974$		0			0
$975$	−11560.2	−	20022.8i	−0.379714	−	0.657684i
$976$		0			0
$977$	2542.86	−	4404.36i	0.0832685	−	0.144225i	−0.821384	−	0.570376i	$-0.806797\pi$
$977$	2542.86	−	4404.36i	0.0832685	−	0.144225i	0.904652	+	0.426151i	$0.140131\pi$
$978$		0			0
$979$	34614.4			1.13001
$980$		0			0
$981$	4221.73			0.137400
$982$		0			0
$983$	24308.9	−	42104.2i	0.788741	−	1.36614i	−0.137998	−	0.990433i	$-0.544067\pi$
$983$	24308.9	−	42104.2i	0.788741	−	1.36614i	0.926739	−	0.375707i	$-0.122600\pi$
$984$		0			0
$985$	35169.8	+	60915.8i	1.13767	+	1.97050i
$986$		0			0
$987$	−22050.1	−	15334.1i	−0.711107	−	0.494520i
$988$		0			0
$989$	1769.83	+	3065.43i	0.0569032	+	0.0985592i
$990$		0			0
$991$	17500.0	−	30310.9i	0.560955	−	0.971603i	−0.436458	−	0.899725i	$-0.643767\pi$
$991$	17500.0	−	30310.9i	0.560955	−	0.971603i	0.997413	−	0.0718786i	$-0.0228994\pi$
$992$		0			0
$993$	6524.79			0.208517
$994$		0			0
$995$	−35423.4			−1.12864
$996$		0			0
$997$	−16403.9	+	28412.4i	−0.521081	+	0.902539i	0.478618	+	0.878023i	$0.341138\pi$
$997$	−16403.9	+	28412.4i	−0.521081	+	0.902539i	−0.999699	+	0.0245157i	$0.992196\pi$
$998$		0			0
$999$	2849.58	+	4935.62i	0.0902470	+	0.156312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.q.m.193.4		8
4.3	odd	2		168.4.q.f.25.4	✓	8
7.2	even	3	inner	336.4.q.m.289.4		8
7.3	odd	6		2352.4.a.cp.1.4		4
7.4	even	3		2352.4.a.cm.1.1		4
12.11	even	2		504.4.s.j.361.1		8
28.3	even	6		1176.4.a.ba.1.4		4
28.11	odd	6		1176.4.a.bd.1.1		4
28.23	odd	6		168.4.q.f.121.4	yes	8
84.23	even	6		504.4.s.j.289.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.q.f.25.4	✓	8	4.3	odd	2
168.4.q.f.121.4	yes	8	28.23	odd	6
336.4.q.m.193.4		8	1.1	even	1	trivial
336.4.q.m.289.4		8	7.2	even	3	inner
504.4.s.j.289.1		8	84.23	even	6
504.4.s.j.361.1		8	12.11	even	2
1176.4.a.ba.1.4		4	28.3	even	6
1176.4.a.bd.1.1		4	28.11	odd	6
2352.4.a.cm.1.1		4	7.4	even	3
2352.4.a.cp.1.4		4	7.3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 2.59808i) q^{3} +(7.90648 + 13.6944i) q^{5} +(-15.2050 - 10.5739i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 2.59808i) q^{3} +(7.90648 + 13.6944i) q^{5} +(-15.2050 - 10.5739i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(-15.1240 + 26.1955i) q^{11} -61.6298 q^{13} +47.4389 q^{15} +(-28.0724 + 48.6228i) q^{17} +(-69.7002 - 120.724i) q^{19} +(-50.2793 + 23.6429i) q^{21} +(-4.07240 - 7.05360i) q^{23} +(-62.5247 + 108.296i) q^{25} -27.0000 q^{27} -0.217857 q^{29} +(88.2903 - 152.923i) q^{31} +(45.3719 + 78.5864i) q^{33} +(24.5855 - 291.826i) q^{35} +(-105.540 - 182.801i) q^{37} +(-92.4447 + 160.119i) q^{39} -293.305 q^{41} -434.591 q^{43} +(71.1583 - 123.250i) q^{45} +(241.698 + 418.633i) q^{47} +(119.385 + 321.553i) q^{49} +(84.2172 + 145.868i) q^{51} +(-10.2536 + 17.7598i) q^{53} -478.309 q^{55} -418.201 q^{57} +(-115.674 + 200.353i) q^{59} +(419.351 + 726.337i) q^{61} +(-13.9930 + 166.094i) q^{63} +(-487.274 - 843.984i) q^{65} +(-312.020 + 540.435i) q^{67} -24.4344 q^{69} -227.106 q^{71} +(-21.5247 + 37.2819i) q^{73} +(187.574 + 324.888i) q^{75} +(506.949 - 238.383i) q^{77} +(-154.530 - 267.654i) q^{79} +(-40.5000 + 70.1481i) q^{81} -1233.99 q^{83} -887.815 q^{85} +(-0.326785 + 0.566009i) q^{87} +(-572.179 - 991.042i) q^{89} +(937.082 + 651.668i) q^{91} +(-264.871 - 458.770i) q^{93} +(1102.17 - 1909.01i) q^{95} +1688.12 q^{97} +272.231 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{3} - 4 q^{5} - 18 q^{7} - 36 q^{9}+O(q^{10}) \) 8 * q + 12 * q^3 - 4 * q^5 - 18 * q^7 - 36 * q^9	\( 8 q + 12 q^{3} - 4 q^{5} - 18 q^{7} - 36 q^{9} + 14 q^{11} + 44 q^{13} - 24 q^{15} - 96 q^{17} - 26 q^{19} - 36 q^{21} + 96 q^{23} - 110 q^{25} - 216 q^{27} - 152 q^{29} + 238 q^{31} - 42 q^{33} - 152 q^{35} - 562 q^{37} + 66 q^{39} + 856 q^{41} + 516 q^{43} - 36 q^{45} - 80 q^{47} + 156 q^{49} + 288 q^{51} - 2952 q^{55} - 156 q^{57} + 262 q^{59} + 276 q^{61} + 54 q^{63} - 2196 q^{65} + 150 q^{67} + 576 q^{69} + 1696 q^{71} + 218 q^{73} + 330 q^{75} - 764 q^{77} + 1762 q^{79} - 324 q^{81} - 6900 q^{83} + 2904 q^{85} - 228 q^{87} + 344 q^{89} + 2806 q^{91} - 714 q^{93} + 2004 q^{95} - 1244 q^{97} - 252 q^{99}+O(q^{100}) \) 8 * q + 12 * q^3 - 4 * q^5 - 18 * q^7 - 36 * q^9 + 14 * q^11 + 44 * q^13 - 24 * q^15 - 96 * q^17 - 26 * q^19 - 36 * q^21 + 96 * q^23 - 110 * q^25 - 216 * q^27 - 152 * q^29 + 238 * q^31 - 42 * q^33 - 152 * q^35 - 562 * q^37 + 66 * q^39 + 856 * q^41 + 516 * q^43 - 36 * q^45 - 80 * q^47 + 156 * q^49 + 288 * q^51 - 2952 * q^55 - 156 * q^57 + 262 * q^59 + 276 * q^61 + 54 * q^63 - 2196 * q^65 + 150 * q^67 + 576 * q^69 + 1696 * q^71 + 218 * q^73 + 330 * q^75 - 764 * q^77 + 1762 * q^79 - 324 * q^81 - 6900 * q^83 + 2904 * q^85 - 228 * q^87 + 344 * q^89 + 2806 * q^91 - 714 * q^93 + 2004 * q^95 - 1244 * q^97 - 252 * q^99

Introduction

L-functions

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