LMFDB - Embedded newform 336.6.q.e.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,6,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, 6, names="a")

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

chi := DirichletCharacter("336.193");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
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:	$53.8889634572$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-83})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 20x^{2} - 21x + 441 $ x^4 - x^3 - 20x^2 - 21x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$-3.69493 + 2.71062i$ of defining polynomial
Character	$\chi$	$=$	336.289
Dual form			336.6.q.e.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.50000 - 7.79423i) q^{3} +(-19.3645 + 33.5404i) q^{5} +(87.5000 + 95.6596i) q^{7} +(-40.5000 + 70.1481i) q^{9} +(-288.195 - 499.168i) q^{11} +391.491 q^{13} +348.562 q^{15} +(664.850 + 1151.55i) q^{17} +(471.237 - 816.206i) q^{19} +(351.842 - 1112.46i) q^{21} +(-816.040 + 1413.42i) q^{23} +(812.530 + 1407.34i) q^{25} +729.000 q^{27} -1463.54 q^{29} +(-1956.21 - 3388.25i) q^{31} +(-2593.75 + 4492.51i) q^{33} +(-4902.85 + 1082.38i) q^{35} +(8150.17 - 14116.5i) q^{37} +(-1761.71 - 3051.37i) q^{39} -13103.8 q^{41} -14733.5 q^{43} +(-1568.53 - 2716.77i) q^{45} +(-3407.26 + 5901.55i) q^{47} +(-1494.50 + 16740.4i) q^{49} +(5983.65 - 10364.0i) q^{51} +(1005.67 + 1741.87i) q^{53} +22323.0 q^{55} -8482.26 q^{57} +(25726.6 + 44559.7i) q^{59} +(-20548.9 + 35591.8i) q^{61} +(-10254.1 + 2263.74i) q^{63} +(-7581.04 + 13130.8i) q^{65} +(25289.1 + 43802.0i) q^{67} +14688.7 q^{69} -39970.6 q^{71} +(27843.3 + 48226.0i) q^{73} +(7312.77 - 12666.1i) q^{75} +(22533.2 - 71245.8i) q^{77} +(-31575.7 + 54690.7i) q^{79} +(-3280.50 - 5681.99i) q^{81} -45572.4 q^{83} -51498.1 q^{85} +(6585.95 + 11407.2i) q^{87} +(-7843.34 + 13585.1i) q^{89} +(34255.5 + 37449.9i) q^{91} +(-17605.9 + 30494.3i) q^{93} +(18250.6 + 31610.9i) q^{95} +3128.49 q^{97} +46687.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 18 q^{3} + 33 q^{5} + 350 q^{7} - 162 q^{9} - 1137 q^{11} + 1850 q^{13} - 594 q^{15} + 324 q^{17} + 2311 q^{19} - 1575 q^{21} + 1596 q^{23} - 395 q^{25} + 2916 q^{27} - 4434 q^{29} + 4294 q^{31} - 10233 q^{33}+ \cdots + 184194 q^{99}+O(q^{100}) $ 4 * q - 18 * q^3 + 33 * q^5 + 350 * q^7 - 162 * q^9 - 1137 * q^11 + 1850 * q^13 - 594 * q^15 + 324 * q^17 + 2311 * q^19 - 1575 * q^21 + 1596 * q^23 - 395 * q^25 + 2916 * q^27 - 4434 * q^29 + 4294 * q^31 - 10233 * q^33 - 15414 * q^35 + 19109 * q^37 - 8325 * q^39 - 25716 * q^41 + 5542 * q^43 + 2673 * q^45 - 23160 * q^47 - 5978 * q^49 + 2916 * q^51 + 31653 * q^53 - 35778 * q^55 - 41598 * q^57 + 41097 * q^59 - 42052 * q^61 - 14175 * q^63 + 23106 * q^65 + 30763 * q^67 - 28728 * q^69 - 204192 * q^71 + 28577 * q^73 - 3555 * q^75 - 96873 * q^77 - 18464 * q^79 - 13122 * q^81 - 122358 * q^83 - 247272 * q^85 + 19953 * q^87 - 29322 * q^89 + 161875 * q^91 + 38646 * q^93 - 61662 * q^95 - 19582 * q^97 + 184194 * q^99

Character values

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

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

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
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$4$		0			0
$5$	−19.3645	+	33.5404i	−0.346403	+	0.599988i	−0.985608	−	0.169049i	$-0.945930\pi$
$5$	−19.3645	+	33.5404i	−0.346403	+	0.599988i	0.639204	+	0.769037i	$0.279264\pi$
$6$		0			0
$7$	87.5000	+	95.6596i	0.674937	+	0.737876i
$7$	87.5000	+	95.6596i	0.674937	+	0.737876i
$8$		0			0
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$		0			0
$11$	−288.195	−	499.168i	−0.718133	−	1.24384i	−0.961739	−	0.273968i	$-0.911664\pi$
$11$	−288.195	−	499.168i	−0.718133	−	1.24384i	0.243606	−	0.969874i	$-0.421670\pi$
$12$		0			0
$13$	391.491			0.642486			0.321243	−	0.946997i	$-0.395899\pi$
$13$	391.491			0.642486			0.321243	+	0.946997i	$0.395899\pi$
$14$		0			0
$15$	348.562			0.399992
$16$		0			0
$17$	664.850	+	1151.55i	0.557958	+	0.966412i	0.997667	+	0.0682711i	$0.0217483\pi$
$17$	664.850	+	1151.55i	0.557958	+	0.966412i	−0.439709	+	0.898140i	$0.644918\pi$
$18$		0			0
$19$	471.237	−	816.206i	0.299471	−	0.518699i	−0.676544	−	0.736402i	$-0.736523\pi$
$19$	471.237	−	816.206i	0.299471	−	0.518699i	0.976015	+	0.217703i	$0.0698564\pi$
$20$		0			0
$21$	351.842	−	1112.46i	0.174100	−	0.550475i
$22$		0			0
$23$	−816.040	+	1413.42i	−0.321656	+	0.557124i	−0.980830	−	0.194866i	$-0.937573\pi$
$23$	−816.040	+	1413.42i	−0.321656	+	0.557124i	0.659174	+	0.751991i	$0.270906\pi$
$24$		0			0
$25$	812.530	+	1407.34i	0.260009	+	0.450350i
$26$		0			0
$27$	729.000			0.192450
$28$		0			0
$29$	−1463.54			−0.323155			−0.161577	−	0.986860i	$-0.551658\pi$
$29$	−1463.54			−0.323155			−0.161577	+	0.986860i	$0.551658\pi$
$30$		0			0
$31$	−1956.21	−	3388.25i	−0.365604	−	0.633245i	0.623269	−	0.782008i	$-0.285804\pi$
$31$	−1956.21	−	3388.25i	−0.365604	−	0.633245i	−0.988873	+	0.148763i	$0.952471\pi$
$32$		0			0
$33$	−2593.75	+	4492.51i	−0.414614	+	0.718133i
$34$		0			0
$35$	−4902.85	+	1082.38i	−0.676517	+	0.149351i
$36$		0			0
$37$	8150.17	−	14116.5i	0.978729	−	1.69521i	0.311691	−	0.950184i	$-0.399105\pi$
$37$	8150.17	−	14116.5i	0.978729	−	1.69521i	0.667038	−	0.745024i	$-0.267562\pi$
$38$		0			0
$39$	−1761.71	−	3051.37i	−0.185470	−	0.321243i
$40$		0			0
$41$	−13103.8			−1.21741			−0.608707	−	0.793395i	$-0.708312\pi$
$41$	−13103.8			−1.21741			−0.608707	+	0.793395i	$0.708312\pi$
$42$		0			0
$43$	−14733.5			−1.21516			−0.607582	−	0.794257i	$-0.707860\pi$
$43$	−14733.5			−1.21516			−0.607582	+	0.794257i	$0.707860\pi$
$44$		0			0
$45$	−1568.53	−	2716.77i	−0.115468	−	0.199996i
$46$		0			0
$47$	−3407.26	+	5901.55i	−0.224989	+	0.389692i	−0.956316	−	0.292335i	$-0.905568\pi$
$47$	−3407.26	+	5901.55i	−0.224989	+	0.389692i	0.731327	+	0.682027i	$0.238901\pi$
$48$		0			0
$49$	−1494.50	+	16740.4i	−0.0889213	+	0.996039i
$50$		0			0
$51$	5983.65	−	10364.0i	0.322137	−	0.557958i
$52$		0			0
$53$	1005.67	+	1741.87i	0.0491775	+	0.0851779i	0.889566	−	0.456806i	$-0.151007\pi$
$53$	1005.67	+	1741.87i	0.0491775	+	0.0851779i	−0.840389	+	0.541984i	$0.817673\pi$
$54$		0			0
$55$	22323.0			0.995054
$56$		0			0
$57$	−8482.26			−0.345800
$58$		0			0
$59$	25726.6	+	44559.7i	0.962170	+	1.66653i	0.717035	+	0.697037i	$0.245499\pi$
$59$	25726.6	+	44559.7i	0.962170	+	1.66653i	0.245135	+	0.969489i	$0.421168\pi$
$60$		0			0
$61$	−20548.9	+	35591.8i	−0.707073	+	1.22469i	0.258865	+	0.965913i	$0.416651\pi$
$61$	−20548.9	+	35591.8i	−0.707073	+	1.22469i	−0.965938	+	0.258773i	$0.916682\pi$
$62$		0			0
$63$	−10254.1	+	2263.74i	−0.325496	+	0.0718581i
$64$		0			0
$65$	−7581.04	+	13130.8i	−0.222559	+	0.385484i
$66$		0			0
$67$	25289.1	+	43802.0i	0.688250	+	1.19208i	0.972404	+	0.233305i	$0.0749542\pi$
$67$	25289.1	+	43802.0i	0.688250	+	1.19208i	−0.284153	+	0.958779i	$0.591712\pi$
$68$		0			0
$69$	14688.7			0.371416
$70$		0			0
$71$	−39970.6			−0.941012			−0.470506	−	0.882397i	$-0.655929\pi$
$71$	−39970.6			−0.941012			−0.470506	+	0.882397i	$0.655929\pi$
$72$		0			0
$73$	27843.3	+	48226.0i	0.611524	+	1.05919i	0.990984	+	0.133983i	$0.0427767\pi$
$73$	27843.3	+	48226.0i	0.611524	+	1.05919i	−0.379459	+	0.925208i	$0.623890\pi$
$74$		0			0
$75$	7312.77	−	12666.1i	0.150117	−	0.260009i
$76$		0			0
$77$	22533.2	−	71245.8i	0.433107	−	1.36941i
$78$		0			0
$79$	−31575.7	+	54690.7i	−0.569226	+	0.985929i	0.427416	+	0.904055i	$0.359424\pi$
$79$	−31575.7	+	54690.7i	−0.569226	+	0.985929i	−0.996643	+	0.0818739i	$0.973910\pi$
$80$		0			0
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−45572.4			−0.726116			−0.363058	−	0.931766i	$-0.618267\pi$
$83$	−45572.4			−0.726116			−0.363058	+	0.931766i	$0.618267\pi$
$84$		0			0
$85$	−51498.1			−0.773114
$86$		0			0
$87$	6585.95	+	11407.2i	0.0932868	+	0.161577i
$88$		0			0
$89$	−7843.34	+	13585.1i	−0.104961	+	0.181797i	−0.913722	−	0.406340i	$-0.866805\pi$
$89$	−7843.34	+	13585.1i	−0.104961	+	0.181797i	0.808762	+	0.588137i	$0.200138\pi$
$90$		0			0
$91$	34255.5	+	37449.9i	0.433637	+	0.474075i
$92$		0			0
$93$	−17605.9	+	30494.3i	−0.211082	+	0.365604i
$94$		0			0
$95$	18250.6	+	31610.9i	0.207476	+	0.359358i
$96$		0			0
$97$	3128.49			0.0337603			0.0168801	−	0.999858i	$-0.494627\pi$
$97$	3128.49			0.0337603			0.0168801	+	0.999858i	$0.494627\pi$
$98$		0			0
$99$	46687.6			0.478755
$100$		0			0
$101$	84505.5	+	146368.i	0.824292	+	1.42772i	0.902459	+	0.430776i	$0.141760\pi$
$101$	84505.5	+	146368.i	0.824292	+	1.42772i	−0.0781663	+	0.996940i	$0.524907\pi$
$102$		0			0
$103$	56410.1	−	97705.1i	0.523918	−	0.907453i	−0.475694	−	0.879611i	$-0.657803\pi$
$103$	56410.1	−	97705.1i	0.523918	−	0.907453i	0.999612	−	0.0278422i	$-0.00886360\pi$
$104$		0			0
$105$	30499.1	+	33343.2i	0.269969	+	0.295144i
$106$		0			0
$107$	−11154.7	+	19320.6i	−0.0941890	+	0.163140i	−0.909270	−	0.416207i	$-0.863359\pi$
$107$	−11154.7	+	19320.6i	−0.0941890	+	0.163140i	0.815081	+	0.579347i	$0.196692\pi$
$108$		0			0
$109$	41909.8	+	72589.8i	0.337869	+	0.585207i	0.984032	−	0.177993i	$-0.0569604\pi$
$109$	41909.8	+	72589.8i	0.337869	+	0.585207i	−0.646162	+	0.763200i	$0.723627\pi$
$110$		0			0
$111$	−146703.			−1.13014
$112$		0			0
$113$	−40928.4			−0.301529			−0.150764	−	0.988570i	$-0.548174\pi$
$113$	−40928.4			−0.301529			−0.150764	+	0.988570i	$0.548174\pi$
$114$		0			0
$115$	−31604.4	−	54740.5i	−0.222845	−	0.385980i
$116$		0			0
$117$	−15855.4	+	27462.3i	−0.107081	+	0.185470i
$118$		0			0
$119$	−51982.8	+	164360.i	−0.336505	+	1.06397i
$120$		0			0
$121$	−85587.1	+	148241.i	−0.531429	+	0.920462i
$122$		0			0
$123$	58967.2	+	102134.i	0.351437	+	0.608707i
$124$		0			0
$125$	−183965.			−1.05308
$126$		0			0
$127$	−83270.1			−0.458120			−0.229060	−	0.973412i	$-0.573565\pi$
$127$	−83270.1			−0.458120			−0.229060	+	0.973412i	$0.573565\pi$
$128$		0			0
$129$	66300.7	+	114836.i	0.350788	+	0.607582i
$130$		0			0
$131$	−83437.4	+	144518.i	−0.424798	+	0.735772i	−0.996402	−	0.0847580i	$-0.972988\pi$
$131$	−83437.4	+	144518.i	−0.424798	+	0.735772i	0.571603	+	0.820530i	$0.306322\pi$
$132$		0			0
$133$	119311.	−	26339.7i	0.584860	−	0.129117i
$134$		0			0
$135$	−14116.7	+	24450.9i	−0.0666653	+	0.115468i
$136$		0			0
$137$	−19111.9	−	33102.9i	−0.0869969	−	0.150683i	0.819244	−	0.573446i	$-0.194394\pi$
$137$	−19111.9	−	33102.9i	−0.0869969	−	0.150683i	−0.906240	+	0.422763i	$0.861060\pi$
$138$		0			0
$139$	−106263.			−0.466492			−0.233246	−	0.972418i	$-0.574935\pi$
$139$	−106263.			−0.466492			−0.233246	+	0.972418i	$0.574935\pi$
$140$		0			0
$141$	61330.7			0.259795
$142$		0			0
$143$	−112826.	−	195420.i	−0.461390	−	0.799151i
$144$		0			0
$145$	28340.8	−	49087.8i	0.111942	−	0.193889i
$146$		0			0
$147$	137204.	−	63683.4i	0.523689	−	0.243071i
$148$		0			0
$149$	−96277.8	+	166758.i	−0.355271	+	0.615348i	−0.987164	−	0.159708i	$-0.948945\pi$
$149$	−96277.8	+	166758.i	−0.355271	+	0.615348i	0.631893	+	0.775056i	$0.282278\pi$
$150$		0			0
$151$	70849.3	+	122715.i	0.252868	+	0.437980i	0.964314	−	0.264761i	$-0.0852929\pi$
$151$	70849.3	+	122715.i	0.252868	+	0.437980i	−0.711447	+	0.702740i	$0.751960\pi$
$152$		0			0
$153$	−107706.			−0.371972
$154$		0			0
$155$	151524.			0.506586
$156$		0			0
$157$	−282885.	−	489972.i	−0.915928	−	1.58643i	−0.805536	−	0.592546i	$-0.798123\pi$
$157$	−282885.	−	489972.i	−0.915928	−	1.58643i	−0.110392	−	0.993888i	$-0.535211\pi$
$158$		0			0
$159$	9051.04	−	15676.9i	0.0283926	−	0.0491775i
$160$		0			0
$161$	−206611.	+	45612.4i	−0.628186	+	0.138682i
$162$		0			0
$163$	−215101.	+	372565.i	−0.634121	+	1.09833i	0.352579	+	0.935782i	$0.385305\pi$
$163$	−215101.	+	372565.i	−0.634121	+	1.09833i	−0.986701	+	0.162549i	$0.948029\pi$
$164$		0			0
$165$	−100454.	−	173991.i	−0.287247	−	0.497527i
$166$		0			0
$167$	240265.			0.666653			0.333327	−	0.942811i	$-0.391829\pi$
$167$	240265.			0.666653			0.333327	+	0.942811i	$0.391829\pi$
$168$		0			0
$169$	−218028.			−0.587212
$170$		0			0
$171$	38170.2	+	66112.7i	0.0998238	+	0.172900i
$172$		0			0
$173$	89650.1	−	155279.i	0.227738	−	0.394454i	−0.729399	−	0.684088i	$-0.760200\pi$
$173$	89650.1	−	155279.i	0.227738	−	0.394454i	0.957137	+	0.289634i	$0.0935337\pi$
$174$		0			0
$175$	−63529.4	+	200869.i	−0.156812	+	0.495812i
$176$		0			0
$177$	231539.	−	401037.i	0.555509	−	0.962170i
$178$		0			0
$179$	−287780.	−	498449.i	−0.671317	−	1.16275i	−0.977531	−	0.210792i	$-0.932396\pi$
$179$	−287780.	−	498449.i	−0.671317	−	1.16275i	0.306214	−	0.951963i	$-0.400938\pi$
$180$		0			0
$181$	581006.			1.31821			0.659105	−	0.752051i	$-0.270935\pi$
$181$	581006.			1.31821			0.659105	+	0.752051i	$0.270935\pi$
$182$		0			0
$183$	369880.			0.816458
$184$		0			0
$185$	315648.	+	546719.i	0.678070	+	1.17445i
$186$		0			0
$187$	383213.	−	663744.i	0.801376	−	1.38802i
$188$		0			0
$189$	63787.5	+	69735.8i	0.129892	+	0.142004i
$190$		0			0
$191$	−330280.	+	572062.i	−0.655087	+	1.13464i	0.326785	+	0.945099i	$0.394035\pi$
$191$	−330280.	+	572062.i	−0.655087	+	1.13464i	−0.981872	+	0.189545i	$0.939299\pi$
$192$		0			0
$193$	278655.	+	482645.i	0.538485	+	0.932684i	0.998986	+	0.0450243i	$0.0143365\pi$
$193$	278655.	+	482645.i	0.538485	+	0.932684i	−0.460501	+	0.887659i	$0.652330\pi$
$194$		0			0
$195$	136459.			0.256989
$196$		0			0
$197$	−761400.			−1.39781			−0.698904	−	0.715216i	$-0.746328\pi$
$197$	−761400.			−1.39781			−0.698904	+	0.715216i	$0.746328\pi$
$198$		0			0
$199$	−67929.9	−	117658.i	−0.121598	−	0.210615i	0.798800	−	0.601597i	$-0.205469\pi$
$199$	−67929.9	−	117658.i	−0.121598	−	0.210615i	−0.920398	+	0.390982i	$0.872135\pi$
$200$		0			0
$201$	227602.	−	394218.i	0.397361	−	0.688250i
$202$		0			0
$203$	−128060.	−	140002.i	−0.218109	−	0.238448i
$204$		0			0
$205$	253750.	−	439507.i	0.421716	−	0.730434i
$206$		0			0
$207$	−66099.2	−	114487.i	−0.107219	−	0.185708i
$208$		0			0
$209$	−543232.			−0.860240
$210$		0			0
$211$	991157.			1.53263			0.766313	−	0.642467i	$-0.222089\pi$
$211$	991157.			1.53263			0.766313	+	0.642467i	$0.222089\pi$
$212$		0			0
$213$	179868.	+	311540.i	0.271647	+	0.470506i
$214$		0			0
$215$	285307.	−	494167.i	0.420937	−	0.729084i
$216$		0			0
$217$	152951.	−	483602.i	0.220496	−	0.697170i
$218$		0			0
$219$	250590.	−	434034.i	0.353064	−	0.611524i
$220$		0			0
$221$	260283.	+	450823.i	0.358480	+	0.620906i
$222$		0			0
$223$	−543344.			−0.731666			−0.365833	−	0.930681i	$-0.619216\pi$
$223$	−543344.			−0.731666			−0.365833	+	0.930681i	$0.619216\pi$
$224$		0			0
$225$	−131630.			−0.173340
$226$		0			0
$227$	8.16704	+	14.1457i	1.05196e−5	+	1.82205e-5i	0.866031	−	0.499991i	$-0.166663\pi$
$227$	8.16704	+	14.1457i	1.05196e−5	+	1.82205e-5i	−0.866020	+	0.500009i	$0.833330\pi$
$228$		0			0
$229$	38689.5	−	67012.2i	0.0487534	−	0.0844433i	−0.840619	−	0.541627i	$-0.817808\pi$
$229$	38689.5	−	67012.2i	0.0487534	−	0.0844433i	0.889372	+	0.457184i	$0.151142\pi$
$230$		0			0
$231$	−656705.	+	144978.i	−0.809731	+	0.178760i
$232$		0			0
$233$	51828.6	−	89769.9i	0.0625432	−	0.108328i	−0.833058	−	0.553185i	$-0.813412\pi$
$233$	51828.6	−	89769.9i	0.0625432	−	0.108328i	0.895602	+	0.444857i	$0.146746\pi$
$234$		0			0
$235$	−131960.	−	228561.i	−0.155874	−	0.269981i
$236$		0			0
$237$	568362.			0.657286
$238$		0			0
$239$	−689109.			−0.780356			−0.390178	−	0.920739i	$-0.627587\pi$
$239$	−689109.			−0.780356			−0.390178	+	0.920739i	$0.627587\pi$
$240$		0			0
$241$	−110148.	−	190782.i	−0.122161	−	0.211590i	0.798458	−	0.602050i	$-0.205649\pi$
$241$	−110148.	−	190782.i	−0.122161	−	0.211590i	−0.920620	+	0.390460i	$0.872316\pi$
$242$		0			0
$243$	−29524.5	+	51137.9i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	−532539.	−	374297.i	−0.566809	−	0.398383i
$246$		0			0
$247$	184485.	−	319537.i	0.192406	−	0.333257i
$248$		0			0
$249$	205076.	+	355201.i	0.209612	+	0.363058i
$250$		0			0
$251$	−1.43641e6			−1.43912			−0.719558	−	0.694433i	$-0.755655\pi$
$251$	−1.43641e6			−1.43912			−0.719558	+	0.694433i	$0.755655\pi$
$252$		0			0
$253$	940714.			0.923966
$254$		0			0
$255$	231741.	+	401388.i	0.223179	+	0.386557i
$256$		0			0
$257$	454598.	−	787388.i	0.429334	−	0.743628i	−0.567480	−	0.823387i	$-0.692082\pi$
$257$	454598.	−	787388.i	0.429334	−	0.743628i	0.996814	+	0.0797589i	$0.0254151\pi$
$258$		0			0
$259$	2.06352e6	−	455553.i	1.91143	−	0.421977i
$260$		0			0
$261$	59273.5	−	102665.i	0.0538592	−	0.0932868i
$262$		0			0
$263$	374528.	+	648702.i	0.333884	+	0.578304i	0.983270	−	0.182155i	$-0.0583073\pi$
$263$	374528.	+	648702.i	0.333884	+	0.578304i	−0.649386	+	0.760459i	$0.724974\pi$
$264$		0			0
$265$	−77897.4			−0.0681410
$266$		0			0
$267$	141180.			0.121198
$268$		0			0
$269$	−334972.	−	580189.i	−0.282246	−	0.488865i	0.689691	−	0.724104i	$-0.257746\pi$
$269$	−334972.	−	580189.i	−0.282246	−	0.488865i	−0.971938	+	0.235238i	$0.924413\pi$
$270$		0			0
$271$	270330.	−	468225.i	0.223599	−	0.387285i	−0.732299	−	0.680983i	$-0.761553\pi$
$271$	270330.	−	468225.i	0.223599	−	0.387285i	0.955898	+	0.293698i	$0.0948860\pi$
$272$		0			0
$273$	137743.	−	435519.i	0.111857	−	0.353672i
$274$		0			0
$275$	468334.	−	811178.i	0.373443	−	0.646821i
$276$		0			0
$277$	200955.	+	348064.i	0.157362	+	0.272558i	0.933916	−	0.357491i	$-0.116368\pi$
$277$	200955.	+	348064.i	0.157362	+	0.272558i	−0.776555	+	0.630050i	$0.783035\pi$
$278$		0			0
$279$	316906.			0.243736
$280$		0			0
$281$	−429139.			−0.324214			−0.162107	−	0.986773i	$-0.551829\pi$
$281$	−429139.			−0.324214			−0.162107	+	0.986773i	$0.551829\pi$
$282$		0			0
$283$	−170463.	−	295251.i	−0.126522	−	0.219142i	0.795805	−	0.605553i	$-0.207048\pi$
$283$	−170463.	−	295251.i	−0.126522	−	0.219142i	−0.922327	+	0.386411i	$0.873715\pi$
$284$		0			0
$285$	164255.	−	284498.i	0.119786	−	0.207476i
$286$		0			0
$287$	−1.14658e6	−	1.25351e6i	−0.821678	−	0.898301i
$288$		0			0
$289$	−174123.	+	301590.i	−0.122634	+	0.212409i
$290$		0			0
$291$	−14078.2	−	24384.2i	−0.00974575	−	0.0168801i
$292$		0			0
$293$	−388847.			−0.264612			−0.132306	−	0.991209i	$-0.542238\pi$
$293$	−388847.			−0.264612			−0.132306	+	0.991209i	$0.542238\pi$
$294$		0			0
$295$	−1.99273e6			−1.33319
$296$		0			0
$297$	−210094.	−	363894.i	−0.138205	−	0.239378i
$298$		0			0
$299$	−319472.	+	553342.i	−0.206659	+	0.357945i
$300$		0			0
$301$	−1.28918e6	−	1.40940e6i	−0.820158	−	0.896640i
$302$		0			0
$303$	760549.	−	1.31731e6i	0.475905	−	0.824292i
$304$		0			0
$305$	−795840.	−	1.37844e6i	−0.489865	−	0.848471i
$306$		0			0
$307$	2.35747e6			1.42758			0.713789	−	0.700361i	$-0.246978\pi$
$307$	2.35747e6			1.42758			0.713789	+	0.700361i	$0.246978\pi$
$308$		0			0
$309$	−1.01538e6			−0.604969
$310$		0			0
$311$	−718314.	−	1.24416e6i	−0.421127	−	0.729414i	0.574923	−	0.818208i	$-0.305032\pi$
$311$	−718314.	−	1.24416e6i	−0.421127	−	0.729414i	−0.996050	+	0.0887939i	$0.971699\pi$
$312$		0			0
$313$	411400.	−	712566.i	0.237358	−	0.411116i	−0.722598	−	0.691269i	$-0.757052\pi$
$313$	411400.	−	712566.i	0.237358	−	0.411116i	0.959955	+	0.280153i	$0.0903853\pi$
$314$		0			0
$315$	122639.	−	387762.i	0.0696388	−	0.220186i
$316$		0			0
$317$	883467.	−	1.53021e6i	0.493790	−	0.855269i	−0.506184	−	0.862425i	$-0.668944\pi$
$317$	883467.	−	1.53021e6i	0.493790	−	0.855269i	0.999974	+	0.00715584i	$0.00227779\pi$
$318$		0			0
$319$	421786.	+	730555.i	0.232068	+	0.401954i
$320$		0			0
$321$	200785.			0.108760
$322$		0			0
$323$	1.25321e6			0.668370
$324$		0			0
$325$	318098.	+	550962.i	0.167052	+	0.289343i
$326$		0			0
$327$	377188.	−	653309.i	0.195069	−	0.337869i
$328$		0			0
$329$	−862675.	+	190448.i	−0.439397	+	0.0970036i
$330$		0			0
$331$	−1526.14	+	2643.35i	−0.000765638	+	0.00132612i	−0.866408	−	0.499337i	$-0.833577\pi$
$331$	−1526.14	+	2643.35i	−0.000765638	+	0.00132612i	0.865642	+	0.500663i	$0.166910\pi$
$332$		0			0
$333$	660164.	+	1.14344e6i	0.326243	+	0.565069i
$334$		0			0
$335$	−1.95885e6			−0.953649
$336$		0			0
$337$	2.02939e6			0.973398			0.486699	−	0.873570i	$-0.338201\pi$
$337$	2.02939e6			0.973398			0.486699	+	0.873570i	$0.338201\pi$
$338$		0			0
$339$	184178.	+	319006.i	0.0870439	+	0.150764i
$340$		0			0
$341$	−1.12754e6	+	1.95295e6i	−0.525104	+	0.909507i
$342$		0			0
$343$	−1.73215e6	+	1.32182e6i	−0.794969	+	0.606650i
$344$		0			0
$345$	−284440.	+	492665.i	−0.128660	+	0.222845i
$346$		0			0
$347$	1.89109e6	+	3.27547e6i	0.843119	+	1.46033i	0.887245	+	0.461299i	$0.152617\pi$
$347$	1.89109e6	+	3.27547e6i	0.843119	+	1.46033i	−0.0441252	+	0.999026i	$0.514050\pi$
$348$		0			0
$349$	291147.			0.127953			0.0639763	−	0.997951i	$-0.479622\pi$
$349$	291147.			0.127953			0.0639763	+	0.997951i	$0.479622\pi$
$350$		0			0
$351$	285397.			0.123646
$352$		0			0
$353$	−192538.	−	333486.i	−0.0822394	−	0.142443i	0.821972	−	0.569528i	$-0.192874\pi$
$353$	−192538.	−	333486.i	−0.0822394	−	0.142443i	−0.904212	+	0.427085i	$0.859541\pi$
$354$		0			0
$355$	774013.	−	1.34063e6i	0.325970	−	0.564596i
$356$		0			0
$357$	1.51498e6	−	334456.i	0.629126	−	0.138889i
$358$		0			0
$359$	−1.61507e6	+	2.79738e6i	−0.661385	+	1.14555i	0.318866	+	0.947800i	$0.396698\pi$
$359$	−1.61507e6	+	2.79738e6i	−0.661385	+	1.14555i	−0.980252	+	0.197753i	$0.936635\pi$
$360$		0			0
$361$	793921.	+	1.37511e6i	0.320634	+	0.555354i
$362$		0			0
$363$	1.54057e6			0.613641
$364$		0			0
$365$	−2.15669e6			−0.847336
$366$		0			0
$367$	−239779.	−	415310.i	−0.0929280	−	0.160956i	0.815814	−	0.578314i	$-0.196289\pi$
$367$	−239779.	−	415310.i	−0.0929280	−	0.160956i	−0.908742	+	0.417358i	$0.862956\pi$
$368$		0			0
$369$	530705.	−	919208.i	0.202902	−	0.351437i
$370$		0			0
$371$	−78630.6	+	248616.i	−0.0296590	+	0.0937766i
$372$		0			0
$373$	−436333.	+	755751.i	−0.162385	+	0.281259i	−0.935724	−	0.352734i	$-0.885252\pi$
$373$	−436333.	+	755751.i	−0.162385	+	0.281259i	0.773339	+	0.633993i	$0.218585\pi$
$374$		0			0
$375$	827844.	+	1.43387e6i	0.303998	+	0.526540i
$376$		0			0
$377$	−572965.			−0.207622
$378$		0			0
$379$	2.43493e6			0.870742			0.435371	−	0.900251i	$-0.356617\pi$
$379$	2.43493e6			0.870742			0.435371	+	0.900251i	$0.356617\pi$
$380$		0			0
$381$	374715.	+	649026.i	0.132248	+	0.229060i
$382$		0			0
$383$	−1.80584e6	+	3.12781e6i	−0.629047	+	1.08954i	0.358696	+	0.933454i	$0.383222\pi$
$383$	−1.80584e6	+	3.12781e6i	−0.629047	+	1.08954i	−0.987743	+	0.156087i	$0.950112\pi$
$384$		0			0
$385$	1.95327e6	+	2.13541e6i	0.671598	+	0.734226i
$386$		0			0
$387$	596707.	−	1.03353e6i	0.202527	−	0.350788i
$388$		0			0
$389$	87616.2	+	151756.i	0.0293569	+	0.0508477i	0.880331	−	0.474361i	$-0.157321\pi$
$389$	87616.2	+	151756.i	0.0293569	+	0.0508477i	−0.850974	+	0.525208i	$0.823987\pi$
$390$		0			0
$391$	−2.17018e6			−0.717882
$392$		0			0
$393$	1.50187e6			0.490515
$394$		0			0
$395$	−1.22290e6	−	2.11812e6i	−0.394364	−	0.683058i
$396$		0			0
$397$	−942577.	+	1.63259e6i	−0.300152	+	0.519878i	−0.976170	−	0.217007i	$-0.930371\pi$
$397$	−942577.	+	1.63259e6i	−0.300152	+	0.519878i	0.676019	+	0.736885i	$0.263704\pi$
$398$		0			0
$399$	−742198.	−	811409.i	−0.233393	−	0.255157i
$400$		0			0
$401$	−669915.	+	1.16033e6i	−0.208046	+	0.360346i	−0.951099	−	0.308887i	$-0.900044\pi$
$401$	−669915.	+	1.16033e6i	−0.208046	+	0.360346i	0.743053	+	0.669232i	$0.233377\pi$
$402$		0			0
$403$	−765839.	−	1.32647e6i	−0.234895	−	0.406851i
$404$		0			0
$405$	254101.			0.0769785
$406$		0			0
$407$	−9.39535e6			−2.81143
$408$		0			0
$409$	−3.29314e6	−	5.70388e6i	−0.973423	−	1.68602i	−0.685043	−	0.728503i	$-0.740217\pi$
$409$	−3.29314e6	−	5.70388e6i	−0.973423	−	1.68602i	−0.288381	−	0.957516i	$-0.593117\pi$
$410$		0			0
$411$	−172008.	+	297926.i	−0.0502277	+	0.0869969i
$412$		0			0
$413$	−2.01149e6	+	6.35996e6i	−0.580286	+	1.83476i
$414$		0			0
$415$	882487.	−	1.52851e6i	0.251529	−	0.435661i
$416$		0			0
$417$	478182.	+	828236.i	0.134665	+	0.233246i
$418$		0			0
$419$	6.96869e6			1.93917			0.969585	−	0.244754i	$-0.0787071\pi$
$419$	6.96869e6			1.93917			0.969585	+	0.244754i	$0.0787071\pi$
$420$		0			0
$421$	3.84041e6			1.05602			0.528010	−	0.849238i	$-0.322938\pi$
$421$	3.84041e6			1.05602			0.528010	+	0.849238i	$0.322938\pi$
$422$		0			0
$423$	−275988.	−	478025.i	−0.0749962	−	0.129897i
$424$		0			0
$425$	−1.08042e6	+	1.87134e6i	−0.290149	+	0.502552i
$426$		0			0
$427$	−5.20272e6	+	1.14858e6i	−1.38090	+	0.304854i
$428$		0			0
$429$	−1.01543e6	+	1.75878e6i	−0.266384	+	0.461390i
$430$		0			0
$431$	1.51818e6	+	2.62957e6i	0.393668	+	0.681854i	0.992930	−	0.118699i	$-0.0378725\pi$
$431$	1.51818e6	+	2.62957e6i	0.393668	+	0.681854i	−0.599262	+	0.800553i	$0.704539\pi$
$432$		0			0
$433$	−941529.			−0.241332			−0.120666	−	0.992693i	$-0.538503\pi$
$433$	−941529.			−0.241332			−0.120666	+	0.992693i	$0.538503\pi$
$434$		0			0
$435$	−510135.			−0.129259
$436$		0			0
$437$	769096.	+	1.33211e6i	0.192653	+	0.333686i
$438$		0			0
$439$	670546.	−	1.16142e6i	0.166061	−	0.287626i	−0.770971	−	0.636871i	$-0.780229\pi$
$439$	670546.	−	1.16142e6i	0.166061	−	0.287626i	0.937031	+	0.349245i	$0.113562\pi$
$440$		0			0
$441$	−1.11378e6	−	782823.i	−0.272711	−	0.191676i
$442$		0			0
$443$	−386171.	+	668867.i	−0.0934910	+	0.161931i	−0.908978	−	0.416844i	$-0.863136\pi$
$443$	−386171.	+	668867.i	−0.0934910	+	0.161931i	0.815487	+	0.578776i	$0.196469\pi$
$444$		0			0
$445$	−303765.	−	526137.i	−0.0727174	−	0.125950i
$446$		0			0
$447$	1.73300e6			0.410232
$448$		0			0
$449$	2.25684e6			0.528304			0.264152	−	0.964481i	$-0.414908\pi$
$449$	2.25684e6			0.528304			0.264152	+	0.964481i	$0.414908\pi$
$450$		0			0
$451$	3.77646e6	+	6.54101e6i	0.874265	+	1.51427i
$452$		0			0
$453$	637644.	−	1.10443e6i	0.145993	−	0.252868i
$454$		0			0
$455$	−1.91942e6	+	423742.i	−0.434653	+	0.0959561i
$456$		0			0
$457$	−2.14235e6	+	3.71066e6i	−0.479844	+	0.831114i	−0.999733	−	0.0231196i	$-0.992640\pi$
$457$	−2.14235e6	+	3.71066e6i	−0.479844	+	0.831114i	0.519889	+	0.854234i	$0.325973\pi$
$458$		0			0
$459$	484676.	+	839483.i	0.107379	+	0.185986i
$460$		0			0
$461$	−3.10462e6			−0.680387			−0.340193	−	0.940355i	$-0.610493\pi$
$461$	−3.10462e6			−0.680387			−0.340193	+	0.940355i	$0.610493\pi$
$462$		0			0
$463$	3.53386e6			0.766121			0.383060	−	0.923723i	$-0.374870\pi$
$463$	3.53386e6			0.766121			0.383060	+	0.923723i	$0.374870\pi$
$464$		0			0
$465$	−681859.	−	1.18102e6i	−0.146239	−	0.253293i
$466$		0			0
$467$	1.36230e6	−	2.35957e6i	0.289054	−	0.500657i	−0.684530	−	0.728985i	$-0.739993\pi$
$467$	1.36230e6	−	2.35957e6i	0.289054	−	0.500657i	0.973584	+	0.228328i	$0.0733258\pi$
$468$		0			0
$469$	−1.97728e6	+	6.25182e6i	−0.415085	+	1.31242i
$470$		0			0
$471$	−2.54597e6	+	4.40975e6i	−0.528812	+	0.915928i
$472$		0			0
$473$	4.24612e6	+	7.35449e6i	0.872649	+	1.51147i
$474$		0			0
$475$	1.53158e6			0.311461
$476$		0			0
$477$	−162919.			−0.0327850
$478$		0			0
$479$	489342.	+	847566.i	0.0974482	+	0.168785i	0.910628	−	0.413228i	$-0.135599\pi$
$479$	489342.	+	847566.i	0.0974482	+	0.168785i	−0.813180	+	0.582013i	$0.802265\pi$
$480$		0			0
$481$	3.19072e6	−	5.52649e6i	0.628819	−	1.08915i
$482$		0			0
$483$	1.28526e6	+	1.40512e6i	0.250682	+	0.274059i
$484$		0			0
$485$	−60581.8	+	104931.i	−0.0116947	+	0.0202558i
$486$		0			0
$487$	1.96372e6	+	3.40126e6i	0.375195	+	0.649857i	0.990356	−	0.138544i	$-0.0442423\pi$
$487$	1.96372e6	+	3.40126e6i	0.375195	+	0.649857i	−0.615161	+	0.788401i	$0.710909\pi$
$488$		0			0
$489$	3.87181e6			0.732220
$490$		0			0
$491$	−2.63241e6			−0.492777			−0.246388	−	0.969171i	$-0.579244\pi$
$491$	−2.63241e6			−0.492777			−0.246388	+	0.969171i	$0.579244\pi$
$492$		0			0
$493$	−973037.	−	1.68535e6i	−0.180307	−	0.312301i
$494$		0			0
$495$	−904083.	+	1.56592e6i	−0.165842	+	0.287247i
$496$		0			0
$497$	−3.49743e6	−	3.82357e6i	−0.635123	−	0.694350i
$498$		0			0
$499$	1.06272e6	−	1.84069e6i	0.191059	−	0.330924i	−0.754542	−	0.656251i	$-0.772141\pi$
$499$	1.06272e6	−	1.84069e6i	0.191059	−	0.330924i	0.945601	+	0.325327i	$0.105474\pi$
$500$		0			0
$501$	−1.08119e6	−	1.87268e6i	−0.192446	−	0.333327i
$502$		0			0
$503$	−2.60929e6			−0.459835			−0.229917	−	0.973210i	$-0.573846\pi$
$503$	−2.60929e6			−0.459835			−0.229917	+	0.973210i	$0.573846\pi$
$504$		0			0
$505$	−6.54564e6			−1.14215
$506$		0			0
$507$	981124.	+	1.69936e6i	0.169513	+	0.293606i
$508$		0			0
$509$	5.00911e6	−	8.67603e6i	0.856970	−	1.48432i	−0.0178348	−	0.999841i	$-0.505677\pi$
$509$	5.00911e6	−	8.67603e6i	0.856970	−	1.48432i	0.874805	−	0.484475i	$-0.160989\pi$
$510$		0			0
$511$	−2.17699e6	+	6.88326e6i	−0.368811	+	1.16612i
$512$		0			0
$513$	343532.	−	595014.i	0.0576333	−	0.0998238i
$514$		0			0
$515$	2.18471e6	+	3.78403e6i	0.362974	+	0.628689i
$516$		0			0
$517$	3.92782e6			0.646287
$518$		0			0
$519$	−1.61370e6			−0.262969
$520$		0			0
$521$	2.08970e6	+	3.61947e6i	0.337280	+	0.584186i	0.983920	−	0.178609i	$-0.0571598\pi$
$521$	2.08970e6	+	3.61947e6i	0.337280	+	0.584186i	−0.646640	+	0.762795i	$0.723826\pi$
$522$		0			0
$523$	1.80263e6	−	3.12224e6i	0.288172	−	0.499128i	−0.685202	−	0.728353i	$-0.740286\pi$
$523$	1.80263e6	−	3.12224e6i	0.288172	−	0.499128i	0.973373	+	0.229225i	$0.0736193\pi$
$524$		0			0
$525$	1.85150e6	−	408746.i	0.293174	−	0.0647225i
$526$		0			0
$527$	2.60117e6	−	4.50536e6i	0.407983	−	0.706648i
$528$		0			0
$529$	1.88633e6	+	3.26722e6i	0.293075	+	0.507621i
$530$		0			0
$531$	−4.16770e6			−0.641446
$532$		0			0
$533$	−5.13003e6			−0.782172
$534$		0			0
$535$	−432013.	−	748268.i	−0.0652547	−	0.113025i
$536$		0			0
$537$	−2.59002e6	+	4.48604e6i	−0.387585	+	0.671317i
$538$		0			0
$539$	8.78699e6	−	4.07850e6i	1.30277	−	0.604684i
$540$		0			0
$541$	3.34083e6	−	5.78648e6i	0.490751	−	0.850005i	−0.509193	−	0.860653i	$-0.670056\pi$
$541$	3.34083e6	−	5.78648e6i	0.490751	−	0.850005i	0.999943	+	0.0106475i	$0.00338926\pi$
$542$		0			0
$543$	−2.61453e6	−	4.52850e6i	−0.380534	−	0.659105i
$544$		0			0
$545$	−3.24625e6			−0.468156
$546$		0			0
$547$	−8.69076e6			−1.24191			−0.620954	−	0.783847i	$-0.713255\pi$
$547$	−8.69076e6			−1.24191			−0.620954	+	0.783847i	$0.713255\pi$
$548$		0			0
$549$	−1.66446e6	−	2.88293e6i	−0.235691	−	0.408229i
$550$		0			0
$551$	−689676.	+	1.19455e6i	−0.0967756	+	0.167620i
$552$		0			0
$553$	−7.99456e6	+	1.76492e6i	−1.11168	+	0.245421i
$554$		0			0
$555$	2.84084e6	−	4.92047e6i	0.391484	−	0.678070i
$556$		0			0
$557$	−3.12371e6	−	5.41042e6i	−0.426612	−	0.738913i	0.569958	−	0.821674i	$-0.306960\pi$
$557$	−3.12371e6	−	5.41042e6i	−0.426612	−	0.738913i	−0.996569	+	0.0827611i	$0.973626\pi$
$558$		0			0
$559$	−5.76803e6			−0.780725
$560$		0			0
$561$	−6.89783e6			−0.925349
$562$		0			0
$563$	−5.95223e6	−	1.03096e7i	−0.791423	−	1.37078i	−0.925086	−	0.379758i	$-0.876007\pi$
$563$	−5.95223e6	−	1.03096e7i	−0.791423	−	1.37078i	0.133663	−	0.991027i	$-0.457326\pi$
$564$		0			0
$565$	792560.	−	1.37275e6i	0.104451	−	0.180914i
$566$		0			0
$567$	256493.	−	810986.i	0.0335057	−	0.105939i
$568$		0			0
$569$	−10707.2	+	18545.4i	−0.00138642	+	0.00240135i	−0.866718	−	0.498799i	$-0.833775\pi$
$569$	−10707.2	+	18545.4i	−0.00138642	+	0.00240135i	0.865331	+	0.501200i	$0.167108\pi$
$570$		0			0
$571$	3.55823e6	+	6.16304e6i	0.456714	+	0.791051i	0.998785	−	0.0492811i	$-0.0156930\pi$
$571$	3.55823e6	+	6.16304e6i	0.456714	+	0.791051i	−0.542071	+	0.840333i	$0.682360\pi$
$572$		0			0
$573$	5.94504e6			0.756429
$574$		0			0
$575$	−2.65223e6			−0.334534
$576$		0			0
$577$	5.33259e6	+	9.23632e6i	0.666805	+	1.15494i	0.978793	+	0.204854i	$0.0656719\pi$
$577$	5.33259e6	+	9.23632e6i	0.666805	+	1.15494i	−0.311988	+	0.950086i	$0.600995\pi$
$578$		0			0
$579$	2.50790e6	−	4.34380e6i	0.310895	−	0.538485i
$580$		0			0
$581$	−3.98758e6	−	4.35943e6i	−0.490083	−	0.535784i
$582$		0			0
$583$	579659.	−	1.00400e6i	0.0706319	−	0.122338i
$584$		0			0
$585$	−614065.	−	1.06359e6i	−0.0741864	−	0.128495i
$586$		0			0
$587$	1.30101e7			1.55843			0.779213	−	0.626759i	$-0.215619\pi$
$587$	1.30101e7			1.55843			0.779213	+	0.626759i	$0.215619\pi$
$588$		0			0
$589$	−3.68735e6			−0.437952
$590$		0			0
$591$	3.42630e6	+	5.93453e6i	0.403512	+	0.698904i
$592$		0			0
$593$	−2.13043e6	+	3.69002e6i	−0.248789	+	0.430915i	−0.963190	−	0.268821i	$-0.913366\pi$
$593$	−2.13043e6	+	3.69002e6i	−0.248789	+	0.430915i	0.714401	+	0.699736i	$0.246699\pi$
$594$		0			0
$595$	−4.50608e6	−	4.92628e6i	−0.521803	−	0.570462i
$596$		0			0
$597$	−611369.	+	1.05892e6i	−0.0702049	+	0.121598i
$598$		0			0
$599$	−6.89790e6	−	1.19475e7i	−0.785507	−	1.36054i	−0.928696	−	0.370842i	$-0.879069\pi$
$599$	−6.89790e6	−	1.19475e7i	−0.785507	−	1.36054i	0.143189	−	0.989695i	$-0.454264\pi$
$600$		0			0
$601$	4.99695e6			0.564311			0.282155	−	0.959369i	$-0.408951\pi$
$601$	4.99695e6			0.564311			0.282155	+	0.959369i	$0.408951\pi$
$602$		0			0
$603$	−4.09683e6			−0.458833
$604$		0			0
$605$	−3.31471e6	−	5.74125e6i	−0.368177	−	0.637702i
$606$		0			0
$607$	−1.52473e6	+	2.64091e6i	−0.167966	+	0.290926i	−0.937705	−	0.347434i	$-0.887053\pi$
$607$	−1.52473e6	+	2.64091e6i	−0.167966	+	0.290926i	0.769739	+	0.638359i	$0.220387\pi$
$608$		0			0
$609$	−514937.	+	1.62814e6i	−0.0562614	+	0.177889i
$610$		0			0
$611$	−1.33391e6	+	2.31040e6i	−0.144552	+	0.250372i
$612$		0			0
$613$	3.51813e6	+	6.09357e6i	0.378147	+	0.654969i	0.990793	−	0.135388i	$-0.0432282\pi$
$613$	3.51813e6	+	6.09357e6i	0.378147	+	0.654969i	−0.612646	+	0.790357i	$0.709895\pi$
$614$		0			0
$615$	−4.56749e6			−0.486956
$616$		0			0
$617$	1.00066e7			1.05822			0.529108	−	0.848554i	$-0.322527\pi$
$617$	1.00066e7			1.05822			0.529108	+	0.848554i	$0.322527\pi$
$618$		0			0
$619$	−3.27533e6	−	5.67304e6i	−0.343581	−	0.595099i	0.641514	−	0.767111i	$-0.278307\pi$
$619$	−3.27533e6	−	5.67304e6i	−0.343581	−	0.595099i	−0.985095	+	0.172012i	$0.944973\pi$
$620$		0			0
$621$	−594893.	+	1.03038e6i	−0.0619027	+	0.107219i
$622$		0			0
$623$	−1.98583e6	+	438403.i	−0.204985	+	0.0452536i
$624$		0			0
$625$	1.02325e6	−	1.77232e6i	0.104781	−	0.181485i
$626$		0			0
$627$	2.44455e6	+	4.23408e6i	0.248330	+	0.430120i
$628$		0			0
$629$	2.16746e7			2.18436
$630$		0			0
$631$	−2.22672e6			−0.222635			−0.111317	−	0.993785i	$-0.535507\pi$
$631$	−2.22672e6			−0.222635			−0.111317	+	0.993785i	$0.535507\pi$
$632$		0			0
$633$	−4.46021e6	−	7.72531e6i	−0.442431	−	0.766313i
$634$		0			0
$635$	1.61249e6	−	2.79291e6i	0.158694	−	0.274867i
$636$		0			0
$637$	−585084.	+	6.55373e6i	−0.0571307	+	0.639941i
$638$		0			0
$639$	1.61881e6	−	2.80386e6i	0.156835	−	0.271647i
$640$		0			0
$641$	7.96698e6	+	1.37992e7i	0.765859	+	1.32651i	0.939791	+	0.341749i	$0.111019\pi$
$641$	7.96698e6	+	1.37992e7i	0.765859	+	1.32651i	−0.173932	+	0.984758i	$0.555647\pi$
$642$		0			0
$643$	1.49933e7			1.43011			0.715056	−	0.699067i	$-0.246401\pi$
$643$	1.49933e7			1.43011			0.715056	+	0.699067i	$0.246401\pi$
$644$		0			0
$645$	−5.13553e6			−0.486056
$646$		0			0
$647$	6.49027e6	+	1.12415e7i	0.609540	+	1.05575i	0.991316	+	0.131500i	$0.0419792\pi$
$647$	6.49027e6	+	1.12415e7i	0.609540	+	1.05575i	−0.381776	+	0.924255i	$0.624687\pi$
$648$		0			0
$649$	1.48285e7	−	2.56838e7i	1.38193	−	2.39357i
$650$		0			0
$651$	−4.45758e6	+	984079.i	−0.412237	+	0.0910075i
$652$		0			0
$653$	8.27460e6	−	1.43320e7i	0.759389	−	1.31530i	−0.183774	−	0.982969i	$-0.558831\pi$
$653$	8.27460e6	−	1.43320e7i	0.759389	−	1.31530i	0.943163	−	0.332332i	$-0.107835\pi$
$654$		0			0
$655$	−3.23145e6	−	5.59704e6i	−0.294303	−	0.509748i
$656$		0			0
$657$	−4.51062e6			−0.407683
$658$		0			0
$659$	−5.86879e6			−0.526423			−0.263212	−	0.964738i	$-0.584782\pi$
$659$	−5.86879e6			−0.526423			−0.263212	+	0.964738i	$0.584782\pi$
$660$		0			0
$661$	−3.63843e6	−	6.30195e6i	−0.323900	−	0.561011i	0.657389	−	0.753551i	$-0.271661\pi$
$661$	−3.63843e6	−	6.30195e6i	−0.323900	−	0.561011i	−0.981289	+	0.192540i	$0.938327\pi$
$662$		0			0
$663$	2.34255e6	−	4.05741e6i	0.206969	−	0.358480i
$664$		0			0
$665$	−1.42696e6	+	4.51179e6i	−0.125129	+	0.395635i
$666$		0			0
$667$	1.19431e6	−	2.06861e6i	0.103945	−	0.180038i
$668$		0			0
$669$	2.44505e6	+	4.23495e6i	0.211214	+	0.365833i
$670$		0			0
$671$	2.36884e7			2.03109
$672$		0			0
$673$	−1.82417e7			−1.55248			−0.776241	−	0.630437i	$-0.782876\pi$
$673$	−1.82417e7			−1.55248			−0.776241	+	0.630437i	$0.782876\pi$
$674$		0			0
$675$	592334.	+	1.02595e6i	0.0500388	+	0.0866698i
$676$		0			0
$677$	3.88203e6	−	6.72387e6i	0.325527	−	0.563829i	−0.656092	−	0.754681i	$-0.727792\pi$
$677$	3.88203e6	−	6.72387e6i	0.325527	−	0.563829i	0.981619	+	0.190852i	$0.0611250\pi$
$678$		0			0
$679$	273743.	+	299270.i	0.0227860	+	0.0249109i
$680$		0			0
$681$	73.5034	−	127.312i	6.07351e−6	−	1.05196e-5i
$682$		0			0
$683$	4.28162e6	+	7.41598e6i	0.351201	+	0.608299i	0.986460	−	0.164001i	$-0.0524399\pi$
$683$	4.28162e6	+	7.41598e6i	0.351201	+	0.608299i	−0.635259	+	0.772299i	$0.719107\pi$
$684$		0			0
$685$	1.48038e6			0.120544
$686$		0			0
$687$	−696411.			−0.0562955
$688$		0			0
$689$	393712.	+	681928.i	0.0315959	+	0.0547256i
$690$		0			0
$691$	8.22547e6	−	1.42469e7i	0.655338	−	1.13508i	−0.326471	−	0.945207i	$-0.605860\pi$
$691$	8.22547e6	−	1.42469e7i	0.655338	−	1.13508i	0.981809	−	0.189872i	$-0.0608071\pi$
$692$		0			0
$693$	4.08516e6	+	4.46611e6i	0.323129	+	0.353262i
$694$		0			0
$695$	2.05773e6	−	3.56409e6i	0.161594	−	0.279890i
$696$		0			0
$697$	−8.71208e6	−	1.50898e7i	−0.679266	−	1.17652i
$698$		0			0
$699$	−932916.			−0.0722187
$700$		0			0
$701$	−1.66928e7			−1.28302			−0.641512	−	0.767113i	$-0.721693\pi$
$701$	−1.66928e7			−1.28302			−0.641512	+	0.767113i	$0.721693\pi$
$702$		0			0
$703$	−7.68132e6	−	1.33044e7i	−0.586202	−	1.01533i
$704$		0			0
$705$	−1.18764e6	+	2.05705e6i	−0.0899937	+	0.155874i
$706$		0			0
$707$	−6.60725e6	+	2.08909e7i	−0.497132	+	1.57184i
$708$		0			0
$709$	−2.80890e6	+	4.86515e6i	−0.209855	+	0.363480i	−0.951669	−	0.307126i	$-0.900633\pi$
$709$	−2.80890e6	+	4.86515e6i	−0.209855	+	0.363480i	0.741813	+	0.670606i	$0.233966\pi$
$710$		0			0
$711$	−2.55763e6	−	4.42994e6i	−0.189742	−	0.328643i
$712$		0			0
$713$	6.38537e6			0.470395
$714$		0			0
$715$	8.73927e6			0.639308
$716$		0			0
$717$	3.10099e6	+	5.37107e6i	0.225269	+	0.390178i
$718$		0			0
$719$	5.18592e6	−	8.98227e6i	0.374113	−	0.647983i	−0.616081	−	0.787683i	$-0.711280\pi$
$719$	5.18592e6	−	8.98227e6i	0.374113	−	0.647983i	0.990194	+	0.139700i	$0.0446138\pi$
$720$		0			0
$721$	1.42823e7	−	3.15303e6i	1.02320	−	0.225887i
$722$		0			0
$723$	−991332.	+	1.71704e6i	−0.0705299	+	0.122161i
$724$		0			0
$725$	−1.18917e6	−	2.05971e6i	−0.0840233	−	0.145533i
$726$		0			0
$727$	−1.15369e7			−0.809565			−0.404783	−	0.914413i	$-0.632653\pi$
$727$	−1.15369e7			−0.809565			−0.404783	+	0.914413i	$0.632653\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$		0			0
$731$	−9.79557e6	−	1.69664e7i	−0.678010	−	1.17435i
$732$		0			0
$733$	−7.47349e6	+	1.29445e7i	−0.513764	+	0.889865i	0.486109	+	0.873898i	$0.338416\pi$
$733$	−7.47349e6	+	1.29445e7i	−0.513764	+	0.889865i	−0.999873	+	0.0159667i	$0.994917\pi$
$734$		0			0
$735$	−520925.	+	5.83507e6i	−0.0355678	+	0.398408i
$736$		0			0
$737$	1.45764e7	−	2.52470e7i	0.988510	−	1.71215i
$738$		0			0
$739$	4.50682e6	+	7.80604e6i	0.303570	+	0.525799i	0.976942	−	0.213505i	$-0.0684880\pi$
$739$	4.50682e6	+	7.80604e6i	0.303570	+	0.525799i	−0.673372	+	0.739304i	$0.735155\pi$
$740$		0			0
$741$	−3.32073e6			−0.222171
$742$		0			0
$743$	2.10239e7			1.39714			0.698571	−	0.715541i	$-0.253820\pi$
$743$	2.10239e7			1.39714			0.698571	+	0.715541i	$0.253820\pi$
$744$		0			0
$745$	−3.72875e6	−	6.45838e6i	−0.246134	−	0.426317i
$746$		0			0
$747$	1.84568e6	−	3.19681e6i	0.121019	−	0.209612i
$748$		0			0
$749$	−2.82424e6	+	623493.i	−0.183949	+	0.0406094i
$750$		0			0
$751$	2.02110e6	−	3.50064e6i	0.130764	−	0.226489i	−0.793207	−	0.608952i	$-0.791590\pi$
$751$	2.02110e6	−	3.50064e6i	0.130764	−	0.226489i	0.923971	+	0.382462i	$0.124924\pi$
$752$		0			0
$753$	6.46387e6	+	1.11957e7i	0.415437	+	0.719558i
$754$		0			0
$755$	−5.48786e6			−0.350377
$756$		0			0
$757$	−1.82059e7			−1.15471			−0.577353	−	0.816495i	$-0.695914\pi$
$757$	−1.82059e7			−1.15471			−0.577353	+	0.816495i	$0.695914\pi$
$758$		0			0
$759$	−4.23321e6	−	7.33214e6i	−0.266726	−	0.461983i
$760$		0			0
$761$	9.45999e6	−	1.63852e7i	0.592146	−	1.02563i	−0.401797	−	0.915729i	$-0.631614\pi$
$761$	9.45999e6	−	1.63852e7i	0.592146	−	1.02563i	0.993943	−	0.109898i	$-0.0350526\pi$
$762$		0			0
$763$	−3.27681e6	+	1.03607e7i	−0.203770	+	0.644283i
$764$		0			0
$765$	2.08567e6	−	3.61249e6i	0.128852	−	0.223179i
$766$		0			0
$767$	1.00717e7	+	1.74447e7i	0.618180	+	1.07072i
$768$		0			0
$769$	−1.12831e7			−0.688037			−0.344019	−	0.938963i	$-0.611788\pi$
$769$	−1.12831e7			−0.688037			−0.344019	+	0.938963i	$0.611788\pi$
$770$		0			0
$771$	−8.18277e6			−0.495752
$772$		0			0
$773$	1.84282e6	+	3.19186e6i	0.110926	+	0.192130i	0.916144	−	0.400849i	$-0.131285\pi$
$773$	1.84282e6	+	3.19186e6i	0.110926	+	0.192130i	−0.805218	+	0.592979i	$0.797952\pi$
$774$		0			0
$775$	3.17896e6	−	5.50611e6i	0.190121	−	0.329299i
$776$		0			0
$777$	−1.28365e7	−	1.40335e7i	−0.762772	−	0.833902i
$778$		0			0
$779$	−6.17501e6	+	1.06954e7i	−0.364581	+	0.631472i
$780$		0			0
$781$	1.15193e7	+	1.99521e7i	0.675771	+	1.17047i
$782$		0			0
$783$	−1.06692e6			−0.0621912
$784$		0			0
$785$	2.19118e7			1.26912
$786$		0			0
$787$	−7.03741e6	−	1.21891e7i	−0.405019	−	0.701514i	0.589304	−	0.807911i	$-0.299402\pi$
$787$	−7.03741e6	−	1.21891e7i	−0.405019	−	0.701514i	−0.994324	+	0.106397i	$0.966069\pi$
$788$		0			0
$789$	3.37076e6	−	5.83832e6i	0.192768	−	0.333884i
$790$		0			0
$791$	−3.58124e6	−	3.91519e6i	−0.203513	−	0.222491i
$792$		0			0
$793$	−8.04472e6	+	1.39339e7i	−0.454284	+	0.786844i
$794$		0			0
$795$	350538.	+	607150.i	0.0196706	+	0.0340705i
$796$		0			0
$797$	−1.75191e7			−0.976937			−0.488469	−	0.872582i	$-0.662444\pi$
$797$	−1.75191e7			−0.976937			−0.488469	+	0.872582i	$0.662444\pi$
$798$		0			0
$799$	−9.06127e6			−0.502137
$800$		0			0
$801$	−635311.	−	1.10039e6i	−0.0349869	−	0.0605990i
$802$		0			0
$803$	1.60486e7	−	2.77970e7i	0.878311	−	1.52128i
$804$		0			0
$805$	2.47106e6	−	7.81306e6i	0.134398	−	0.424944i
$806$		0			0
$807$	−3.01475e6	+	5.22170e6i	−0.162955	+	0.282246i
$808$		0			0
$809$	−407261.	−	705396.i	−0.0218777	−	0.0378932i	0.854879	−	0.518827i	$-0.173631\pi$
$809$	−407261.	−	705396.i	−0.0218777	−	0.0378932i	−0.876757	+	0.480934i	$0.840298\pi$
$810$		0			0
$811$	−1.26533e7			−0.675540			−0.337770	−	0.941229i	$-0.609673\pi$
$811$	−1.26533e7			−0.675540			−0.337770	+	0.941229i	$0.609673\pi$
$812$		0			0
$813$	−4.86593e6			−0.258190
$814$		0			0
$815$	−8.33064e6	−	1.44291e7i	−0.439324	−	0.760931i
$816$		0			0
$817$	−6.94297e6	+	1.20256e7i	−0.363907	+	0.630305i
$818$		0			0
$819$	−4.01438e6	+	886236.i	−0.209126	+	0.0461678i
$820$		0			0
$821$	−2.13697e6	+	3.70133e6i	−0.110647	+	0.191646i	−0.916031	−	0.401107i	$-0.868626\pi$
$821$	−2.13697e6	+	3.70133e6i	−0.110647	+	0.191646i	0.805384	+	0.592753i	$0.201959\pi$
$822$		0			0
$823$	8.52317e6	+	1.47626e7i	0.438633	+	0.759735i	0.997584	−	0.0694656i	$-0.0221294\pi$
$823$	8.52317e6	+	1.47626e7i	0.438633	+	0.759735i	−0.558951	+	0.829201i	$0.688796\pi$
$824$		0			0
$825$	−8.43001e6			−0.431214
$826$		0			0
$827$	−2.60828e6			−0.132614			−0.0663071	−	0.997799i	$-0.521122\pi$
$827$	−2.60828e6			−0.132614			−0.0663071	+	0.997799i	$0.521122\pi$
$828$		0			0
$829$	−1.06932e7	−	1.85212e7i	−0.540409	−	0.936016i	−0.998880	−	0.0473066i	$-0.984936\pi$
$829$	−1.06932e7	−	1.85212e7i	−0.540409	−	0.936016i	0.458471	−	0.888709i	$-0.348397\pi$
$830$		0			0
$831$	1.80859e6	−	3.13257e6i	0.0908528	−	0.157362i
$832$		0			0
$833$	−2.02711e7	+	9.40887e6i	−1.01220	+	0.469813i
$834$		0			0
$835$	−4.65263e6	+	8.05859e6i	−0.230931	+	0.399984i
$836$		0			0
$837$	−1.42608e6	−	2.47004e6i	−0.0703605	−	0.121868i
$838$		0			0
$839$	−771393.			−0.0378330			−0.0189165	−	0.999821i	$-0.506022\pi$
$839$	−771393.			−0.0378330			−0.0189165	+	0.999821i	$0.506022\pi$
$840$		0			0
$841$	−1.83692e7			−0.895571
$842$		0			0
$843$	1.93112e6	+	3.34480e6i	0.0935925	+	0.162107i
$844$		0			0
$845$	4.22200e6	−	7.31272e6i	0.203412	−	0.352320i
$846$		0			0
$847$	−2.16696e7	+	4.78388e6i	−1.03787	+	0.229125i
$848$		0			0
$849$	−1.53417e6	+	2.65726e6i	−0.0730474	+	0.126522i
$850$		0			0
$851$	1.33017e7	+	2.30393e7i	0.629628	+	1.09055i
$852$		0			0
$853$	2.94032e7			1.38364			0.691818	−	0.722072i	$-0.256810\pi$
$853$	2.94032e7			1.38364			0.691818	+	0.722072i	$0.256810\pi$
$854$		0			0
$855$	−2.95659e6			−0.138317
$856$		0			0
$857$	1.32505e7	+	2.29505e7i	0.616283	+	1.06743i	0.990158	+	0.139954i	$0.0446955\pi$
$857$	1.32505e7	+	2.29505e7i	0.616283	+	1.06743i	−0.373875	+	0.927479i	$0.621971\pi$
$858$		0			0
$859$	−1.83759e7	+	3.18281e7i	−0.849702	+	1.47173i	0.0317727	+	0.999495i	$0.489885\pi$
$859$	−1.83759e7	+	3.18281e7i	−0.849702	+	1.47173i	−0.881475	+	0.472232i	$0.843449\pi$
$860$		0			0
$861$	−4.61048e6	+	1.45775e7i	−0.211952	+	0.670156i
$862$		0			0
$863$	5.90946e6	−	1.02355e7i	0.270098	−	0.467823i	−0.698789	−	0.715328i	$-0.746277\pi$
$863$	5.90946e6	−	1.02355e7i	0.270098	−	0.467823i	0.968887	+	0.247505i	$0.0796106\pi$
$864$		0			0
$865$	3.47207e6	+	6.01379e6i	0.157778	+	0.273280i
$866$		0			0
$867$	3.13421e6			0.141606
$868$		0			0
$869$	3.63998e7			1.63512
$870$		0			0
$871$	9.90046e6	+	1.71481e7i	0.442191	+	0.765897i
$872$		0			0
$873$	−126704.	+	219458.i	−0.00562671	+	0.00974575i
$874$		0			0
$875$	−1.60970e7	−	1.75980e7i	−0.710762	−	0.777042i
$876$		0			0
$877$	−3.96754e6	+	6.87199e6i	−0.174190	+	0.301706i	−0.939881	−	0.341503i	$-0.889064\pi$
$877$	−3.96754e6	+	6.87199e6i	−0.174190	+	0.301706i	0.765691	+	0.643209i	$0.222397\pi$
$878$		0			0
$879$	1.74981e6	+	3.03077e6i	0.0763870	+	0.132306i
$880$		0			0
$881$	4.20152e7			1.82375			0.911877	−	0.410464i	$-0.134633\pi$
$881$	4.20152e7			1.82375			0.911877	+	0.410464i	$0.134633\pi$
$882$		0			0
$883$	−2.12461e7			−0.917016			−0.458508	−	0.888690i	$-0.651616\pi$
$883$	−2.12461e7			−0.917016			−0.458508	+	0.888690i	$0.651616\pi$
$884$		0			0
$885$	8.96729e6	+	1.55318e7i	0.384860	+	0.666597i
$886$		0			0
$887$	9.42452e6	−	1.63238e7i	0.402208	−	0.696644i	−0.591784	−	0.806096i	$-0.701576\pi$
$887$	9.42452e6	−	1.63238e7i	0.402208	−	0.696644i	0.993992	+	0.109452i	$0.0349097\pi$
$888$		0			0
$889$	−7.28613e6	−	7.96558e6i	−0.309202	−	0.338036i
$890$		0			0
$891$	−1.89085e6	+	3.27504e6i	−0.0797925	+	0.138205i
$892$		0			0
$893$	3.21125e6	+	5.56205e6i	0.134755	+	0.233403i
$894$		0			0
$895$	2.22909e7			0.930186
$896$		0			0
$897$	5.75050e6			0.238630
$898$		0			0
$899$	2.86300e6	+	4.95886e6i	0.118147	+	0.204636i
$900$		0			0
$901$	−1.33724e6	+	2.31617e6i	−0.0548780	+	0.0950514i
$902$		0			0
$903$	−5.18387e6	+	1.63905e7i	−0.211561	+	0.668917i
$904$		0			0
$905$	−1.12509e7	+	1.94872e7i	−0.456632	+	0.790910i
$906$		0			0
$907$	−3.09723e6	−	5.36456e6i	−0.125013	−	0.216529i	0.796725	−	0.604342i	$-0.206564\pi$
$907$	−3.09723e6	−	5.36456e6i	−0.125013	−	0.216529i	−0.921738	+	0.387813i	$0.873231\pi$
$908$		0			0
$909$	−1.36899e7			−0.549528
$910$		0			0
$911$	2.50171e7			0.998712			0.499356	−	0.866397i	$-0.333570\pi$
$911$	2.50171e7			0.998712			0.499356	+	0.866397i	$0.333570\pi$
$912$		0			0
$913$	1.31337e7	+	2.27483e7i	0.521448	+	0.903174i
$914$		0			0
$915$	−7.16256e6	+	1.24059e7i	−0.282824	+	0.489865i
$916$		0			0
$917$	−2.11253e7	+	4.66373e6i	−0.829620	+	0.183151i
$918$		0			0
$919$	7.74961e6	−	1.34227e7i	0.302685	−	0.524266i	−0.674058	−	0.738678i	$-0.735450\pi$
$919$	7.74961e6	−	1.34227e7i	0.302685	−	0.524266i	0.976743	+	0.214412i	$0.0687836\pi$
$920$		0			0
$921$	−1.06086e7	−	1.83746e7i	−0.412106	−	0.713789i
$922$		0			0
$923$	−1.56481e7			−0.604587
$924$		0			0
$925$	2.64890e7			1.01791
$926$		0			0
$927$	4.56921e6	+	7.91411e6i	0.174639	+	0.302484i
$928$		0			0
$929$	−1.87643e7	+	3.25007e7i	−0.713333	+	1.23553i	0.250266	+	0.968177i	$0.419482\pi$
$929$	−1.87643e7	+	3.25007e7i	−0.713333	+	1.23553i	−0.963599	+	0.267352i	$0.913852\pi$
$930$		0			0
$931$	1.29594e7	+	9.10852e6i	0.490015	+	0.344408i
$932$		0			0
$933$	−6.46483e6	+	1.11974e7i	−0.243138	+	0.421127i
$934$		0			0
$935$	1.48415e7	+	2.57062e7i	0.555198	+	0.961632i
$936$		0			0
$937$	−1.08298e7			−0.402969			−0.201485	−	0.979492i	$-0.564577\pi$
$937$	−1.08298e7			−0.402969			−0.201485	+	0.979492i	$0.564577\pi$
$938$		0			0
$939$	−7.40520e6			−0.274077
$940$		0			0
$941$	−1.62295e7	−	2.81104e7i	−0.597492	−	1.03489i	−0.993190	−	0.116505i	$-0.962831\pi$
$941$	−1.62295e7	−	2.81104e7i	−0.597492	−	1.03489i	0.395699	−	0.918380i	$-0.370503\pi$
$942$		0			0
$943$	1.06932e7	−	1.85212e7i	0.391589	−	0.678251i
$944$		0			0
$945$	−3.57418e6	+	789054.i	−0.130196	+	0.0287427i
$946$		0			0
$947$	3.76939e6	−	6.52877e6i	0.136583	−	0.236568i	−0.789618	−	0.613598i	$-0.789721\pi$
$947$	3.76939e6	−	6.52877e6i	0.136583	−	0.236568i	0.926201	+	0.377030i	$0.123055\pi$
$948$		0			0
$949$	1.09004e7	+	1.88801e7i	0.392896	+	0.680516i
$950$		0			0
$951$	−1.59024e7			−0.570180
$952$		0			0
$953$	−3.01356e7			−1.07485			−0.537424	−	0.843312i	$-0.680602\pi$
$953$	−3.01356e7			−1.07485			−0.537424	+	0.843312i	$0.680602\pi$
$954$		0			0
$955$	−1.27914e7	−	2.21554e7i	−0.453848	−	0.786089i
$956$		0			0
$957$	3.79607e6	−	6.57499e6i	0.133985	−	0.232068i
$958$		0			0
$959$	1.49431e6	−	4.72474e6i	0.0524680	−	0.165894i
$960$		0			0
$961$	6.66107e6	−	1.15373e7i	0.232667	−	0.402992i
$962$		0			0
$963$	−903534.	−	1.56497e6i	−0.0313963	−	0.0543800i
$964$		0			0
$965$	−2.15841e7			−0.746132
$966$		0			0
$967$	−2.88021e6			−0.0990509			−0.0495255	−	0.998773i	$-0.515771\pi$
$967$	−2.88021e6			−0.0990509			−0.0495255	+	0.998773i	$0.515771\pi$
$968$		0			0
$969$	−5.63943e6	−	9.76779e6i	−0.192942	−	0.334185i
$970$		0			0
$971$	−1.37245e7	+	2.37715e7i	−0.467142	+	0.809113i	−0.999295	−	0.0375347i	$-0.988050\pi$
$971$	−1.37245e7	+	2.37715e7i	−0.467142	+	0.809113i	0.532154	+	0.846648i	$0.321383\pi$
$972$		0			0
$973$	−9.29799e6	−	1.01650e7i	−0.314852	−	0.344213i
$974$		0			0
$975$	2.86288e6	−	4.95866e6i	0.0964478	−	0.167052i
$976$		0			0
$977$	2.94262e7	+	5.09676e7i	0.986274	+	1.70828i	0.636133	+	0.771579i	$0.280533\pi$
$977$	2.94262e7	+	5.09676e7i	0.986274	+	1.70828i	0.350141	+	0.936697i	$0.386134\pi$
$978$		0			0
$979$	9.04164e6			0.301502
$980$		0			0
$981$	−6.78938e6			−0.225246
$982$		0			0
$983$	9.30384e6	+	1.61147e7i	0.307099	+	0.531911i	0.977726	−	0.209883i	$-0.0673084\pi$
$983$	9.30384e6	+	1.61147e7i	0.307099	+	0.531911i	−0.670627	+	0.741794i	$0.733975\pi$
$984$		0			0
$985$	1.47442e7	−	2.55376e7i	0.484205	−	0.838668i
$986$		0			0
$987$	5.36643e6	+	5.86687e6i	0.175345	+	0.191696i
$988$		0			0
$989$	1.20231e7	−	2.08246e7i	0.390865	−	0.676997i
$990$		0			0
$991$	1.23577e7	+	2.14041e7i	0.399718	+	0.692331i	0.993691	−	0.112154i	$-0.0357749\pi$
$991$	1.23577e7	+	2.14041e7i	0.399718	+	0.692331i	−0.593973	+	0.804485i	$0.702442\pi$
$992$		0			0
$993$	27470.5			0.000884083
$994$		0			0
$995$	5.26172e6			0.168488
$996$		0			0
$997$	8.97906e6	+	1.55522e7i	0.286084	+	0.495511i	0.972871	−	0.231347i	$-0.0743131\pi$
$997$	8.97906e6	+	1.55522e7i	0.286084	+	0.495511i	−0.686788	+	0.726858i	$0.740980\pi$
$998$		0			0
$999$	5.94147e6	−	1.02909e7i	0.188356	−	0.326243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.6.q.e.289.1		4
4.3	odd	2		21.6.e.b.16.1	yes	4
7.4	even	3	inner	336.6.q.e.193.1		4
12.11	even	2		63.6.e.c.37.2		4
28.3	even	6		147.6.e.l.67.1		4
28.11	odd	6		21.6.e.b.4.1	✓	4
28.19	even	6		147.6.a.k.1.2		2
28.23	odd	6		147.6.a.i.1.2		2
28.27	even	2		147.6.e.l.79.1		4
84.11	even	6		63.6.e.c.46.2		4
84.23	even	6		441.6.a.t.1.1		2
84.47	odd	6		441.6.a.s.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.e.b.4.1	✓	4	28.11	odd	6
21.6.e.b.16.1	yes	4	4.3	odd	2
63.6.e.c.37.2		4	12.11	even	2
63.6.e.c.46.2		4	84.11	even	6
147.6.a.i.1.2		2	28.23	odd	6
147.6.a.k.1.2		2	28.19	even	6
147.6.e.l.67.1		4	28.3	even	6
147.6.e.l.79.1		4	28.27	even	2
336.6.q.e.193.1		4	7.4	even	3	inner
336.6.q.e.289.1		4	1.1	even	1	trivial
441.6.a.s.1.1		2	84.47	odd	6
441.6.a.t.1.1		2	84.23	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	336.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.50000 - 7.79423i) q^{3} +(-19.3645 + 33.5404i) q^{5} +(87.5000 + 95.6596i) q^{7} +(-40.5000 + 70.1481i) q^{9} +(-288.195 - 499.168i) q^{11} +391.491 q^{13} +348.562 q^{15} +(664.850 + 1151.55i) q^{17} +(471.237 - 816.206i) q^{19} +(351.842 - 1112.46i) q^{21} +(-816.040 + 1413.42i) q^{23} +(812.530 + 1407.34i) q^{25} +729.000 q^{27} -1463.54 q^{29} +(-1956.21 - 3388.25i) q^{31} +(-2593.75 + 4492.51i) q^{33} +(-4902.85 + 1082.38i) q^{35} +(8150.17 - 14116.5i) q^{37} +(-1761.71 - 3051.37i) q^{39} -13103.8 q^{41} -14733.5 q^{43} +(-1568.53 - 2716.77i) q^{45} +(-3407.26 + 5901.55i) q^{47} +(-1494.50 + 16740.4i) q^{49} +(5983.65 - 10364.0i) q^{51} +(1005.67 + 1741.87i) q^{53} +22323.0 q^{55} -8482.26 q^{57} +(25726.6 + 44559.7i) q^{59} +(-20548.9 + 35591.8i) q^{61} +(-10254.1 + 2263.74i) q^{63} +(-7581.04 + 13130.8i) q^{65} +(25289.1 + 43802.0i) q^{67} +14688.7 q^{69} -39970.6 q^{71} +(27843.3 + 48226.0i) q^{73} +(7312.77 - 12666.1i) q^{75} +(22533.2 - 71245.8i) q^{77} +(-31575.7 + 54690.7i) q^{79} +(-3280.50 - 5681.99i) q^{81} -45572.4 q^{83} -51498.1 q^{85} +(6585.95 + 11407.2i) q^{87} +(-7843.34 + 13585.1i) q^{89} +(34255.5 + 37449.9i) q^{91} +(-17605.9 + 30494.3i) q^{93} +(18250.6 + 31610.9i) q^{95} +3128.49 q^{97} +46687.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 18 q^{3} + 33 q^{5} + 350 q^{7} - 162 q^{9} - 1137 q^{11} + 1850 q^{13} - 594 q^{15} + 324 q^{17} + 2311 q^{19} - 1575 q^{21} + 1596 q^{23} - 395 q^{25} + 2916 q^{27} - 4434 q^{29} + 4294 q^{31} - 10233 q^{33}+ \cdots + 184194 q^{99}+O(q^{100}) \) 4 * q - 18 * q^3 + 33 * q^5 + 350 * q^7 - 162 * q^9 - 1137 * q^11 + 1850 * q^13 - 594 * q^15 + 324 * q^17 + 2311 * q^19 - 1575 * q^21 + 1596 * q^23 - 395 * q^25 + 2916 * q^27 - 4434 * q^29 + 4294 * q^31 - 10233 * q^33 - 15414 * q^35 + 19109 * q^37 - 8325 * q^39 - 25716 * q^41 + 5542 * q^43 + 2673 * q^45 - 23160 * q^47 - 5978 * q^49 + 2916 * q^51 + 31653 * q^53 - 35778 * q^55 - 41598 * q^57 + 41097 * q^59 - 42052 * q^61 - 14175 * q^63 + 23106 * q^65 + 30763 * q^67 - 28728 * q^69 - 204192 * q^71 + 28577 * q^73 - 3555 * q^75 - 96873 * q^77 - 18464 * q^79 - 13122 * q^81 - 122358 * q^83 - 247272 * q^85 + 19953 * q^87 - 29322 * q^89 + 161875 * q^91 + 38646 * q^93 - 61662 * q^95 - 19582 * q^97 + 184194 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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