LMFDB - Embedded newform 112.5.s.b.17.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [112,5,Mod(17,112)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("112.17"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(112, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	112.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,18] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$11.5774358654$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	112.17
Dual form			112.5.s.b.33.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(12.9853 + 7.49706i) q^{3} +(21.9853 - 12.6932i) q^{5} +(7.00000 + 48.4974i) q^{7} +(71.9117 + 124.555i) q^{9} +(21.9853 - 38.0796i) q^{11} -162.507i q^{13} +380.647 q^{15} +(93.7355 + 54.1182i) q^{17} +(-389.338 + 224.784i) q^{19} +(-272.691 + 682.232i) q^{21} +(-217.911 - 377.433i) q^{23} +(9.73506 - 16.8616i) q^{25} +941.981i q^{27} +742.118 q^{29} +(900.175 + 519.716i) q^{31} +(570.970 - 329.650i) q^{33} +(769.485 + 977.377i) q^{35} +(-493.338 - 854.486i) q^{37} +(1218.32 - 2110.20i) q^{39} +1143.70i q^{41} -2418.82 q^{43} +(3162.00 + 1825.58i) q^{45} +(1165.17 - 672.714i) q^{47} +(-2303.00 + 678.964i) q^{49} +(811.455 + 1405.48i) q^{51} +(1783.10 - 3088.42i) q^{53} -1116.26i q^{55} -6740.88 q^{57} +(-3710.93 - 2142.50i) q^{59} +(-1209.57 + 698.345i) q^{61} +(-5537.20 + 4359.41i) q^{63} +(-2062.73 - 3572.76i) q^{65} +(3632.89 - 6292.36i) q^{67} -6534.77i q^{69} -5987.76 q^{71} +(-500.123 - 288.746i) q^{73} +(252.825 - 145.969i) q^{75} +(2000.66 + 799.672i) q^{77} +(-1573.12 - 2724.72i) q^{79} +(-1237.24 + 2142.95i) q^{81} -4729.96i q^{83} +2747.74 q^{85} +(9636.61 + 5563.70i) q^{87} +(-725.651 + 418.955i) q^{89} +(7881.16 - 1137.55i) q^{91} +(7792.69 + 13497.3i) q^{93} +(-5706.47 + 9883.89i) q^{95} -5622.23i q^{97} +6323.99 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 18 q^{3} + 54 q^{5} + 28 q^{7} + 84 q^{9} + 54 q^{11} + 708 q^{15} + 918 q^{17} - 30 q^{19} - 378 q^{21} + 486 q^{23} - 572 q^{25} + 3240 q^{29} + 546 q^{31} + 1062 q^{33} + 1890 q^{35} - 446 q^{37}+ \cdots + 11448 q^{99}+O(q^{100}) $ 4 * q + 18 * q^3 + 54 * q^5 + 28 * q^7 + 84 * q^9 + 54 * q^11 + 708 * q^15 + 918 * q^17 - 30 * q^19 - 378 * q^21 + 486 * q^23 - 572 * q^25 + 3240 * q^29 + 546 * q^31 + 1062 * q^33 + 1890 * q^35 - 446 * q^37 + 3312 * q^39 - 2344 * q^43 + 5724 * q^45 - 702 * q^47 - 9212 * q^49 - 318 * q^51 + 2754 * q^53 - 17460 * q^57 - 12366 * q^59 + 7686 * q^61 - 6468 * q^63 - 3024 * q^65 + 5062 * q^67 - 18792 * q^71 - 17274 * q^73 + 5220 * q^75 + 4914 * q^77 - 794 * q^79 - 4338 * q^81 + 10380 * q^85 + 12276 * q^87 - 12474 * q^89 - 2688 * q^91 + 18918 * q^93 - 8910 * q^95 + 11448 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	12.9853	+	7.49706i	1.44281	+	0.833006i	0.998036	−	0.0626373i	$-0.0199511\pi$
$3$	12.9853	+	7.49706i	1.44281	+	0.833006i	0.444773	+	0.895643i	$0.353284\pi$
$4$		0			0
$5$	21.9853	−	12.6932i	0.879411	−	0.507728i	0.00894701	−	0.999960i	$-0.497152\pi$
$5$	21.9853	−	12.6932i	0.879411	−	0.507728i	0.870464	+	0.492232i	$0.163819\pi$
$6$		0			0
$7$	7.00000	+	48.4974i	0.142857	+	0.989743i
$7$	7.00000	+	48.4974i	0.142857	+	0.989743i
$8$		0			0
$9$	71.9117	+	124.555i	0.887799	+	1.53771i
$10$		0			0
$11$	21.9853	−	38.0796i	0.181697	−	0.314708i	−0.760762	−	0.649031i	$-0.775174\pi$
$11$	21.9853	−	38.0796i	0.181697	−	0.314708i	0.942458	+	0.334324i	$0.108508\pi$
$12$		0			0
$13$		−	162.507i		−	0.961579i	−0.876836	−	0.480790i	$-0.840350\pi$
$13$		−	162.507i		−	0.961579i	0.876836	−	0.480790i	$-0.159650\pi$
$14$		0			0
$15$	380.647			1.69176
$16$		0			0
$17$	93.7355	+	54.1182i	0.324344	+	0.187260i	0.653327	−	0.757076i	$-0.273373\pi$
$17$	93.7355	+	54.1182i	0.324344	+	0.187260i	−0.328983	+	0.944336i	$0.606706\pi$
$18$		0			0
$19$	−389.338	+	224.784i	−1.07850	+	0.622671i	−0.930491	−	0.366315i	$-0.880619\pi$
$19$	−389.338	+	224.784i	−1.07850	+	0.622671i	−0.148007	+	0.988986i	$0.547286\pi$
$20$		0			0
$21$	−272.691	+	682.232i	−0.618347	+	1.54701i
$22$		0			0
$23$	−217.911	−	377.433i	−0.411931	−	0.713485i	0.583170	−	0.812350i	$-0.301812\pi$
$23$	−217.911	−	377.433i	−0.411931	−	0.713485i	−0.995101	+	0.0988653i	$0.968479\pi$
$24$		0			0
$25$	9.73506	−	16.8616i	0.0155761	−	0.0269786i
$26$		0			0
$27$			941.981i			1.29215i
$28$		0			0
$29$	742.118			0.882423			0.441212	−	0.897403i	$-0.354549\pi$
$29$	742.118			0.882423			0.441212	+	0.897403i	$0.354549\pi$
$30$		0			0
$31$	900.175	+	519.716i	0.936707	+	0.540808i	0.888926	−	0.458050i	$-0.151452\pi$
$31$	900.175	+	519.716i	0.936707	+	0.540808i	0.0477804	+	0.998858i	$0.484785\pi$
$32$		0			0
$33$	570.970	−	329.650i	0.524307	−	0.302709i
$34$		0			0
$35$	769.485	+	977.377i	0.628151	+	0.797859i
$36$		0			0
$37$	−493.338	−	854.486i	−0.360364	−	0.624168i	0.627657	−	0.778490i	$-0.284014\pi$
$37$	−493.338	−	854.486i	−0.360364	−	0.624168i	−0.988021	+	0.154322i	$0.950681\pi$
$38$		0			0
$39$	1218.32	−	2110.20i	0.801001	−	1.38737i
$40$		0			0
$41$			1143.70i			0.680366i	0.940359	+	0.340183i	$0.110489\pi$
$41$			1143.70i			0.680366i	−0.940359	+	0.340183i	$0.889511\pi$
$42$		0			0
$43$	−2418.82			−1.30818			−0.654089	−	0.756418i	$-0.726948\pi$
$43$	−2418.82			−1.30818			−0.654089	+	0.756418i	$0.726948\pi$
$44$		0			0
$45$	3162.00	+	1825.58i	1.56148	+	0.901521i
$46$		0			0
$47$	1165.17	−	672.714i	0.527467	−	0.304533i	−0.212517	−	0.977157i	$-0.568166\pi$
$47$	1165.17	−	672.714i	0.527467	−	0.304533i	0.739984	+	0.672624i	$0.234833\pi$
$48$		0			0
$49$	−2303.00	+	678.964i	−0.959184	+	0.282784i
$50$		0			0
$51$	811.455	+	1405.48i	0.311978	+	0.540362i
$52$		0			0
$53$	1783.10	−	3088.42i	0.634782	−	1.09947i	−0.351780	−	0.936083i	$-0.614423\pi$
$53$	1783.10	−	3088.42i	0.634782	−	1.09947i	0.986561	−	0.163391i	$-0.0522432\pi$
$54$		0			0
$55$		−	1116.26i		−	0.369010i
$56$		0			0
$57$	−6740.88			−2.07475
$58$		0			0
$59$	−3710.93	−	2142.50i	−1.06605	−	0.615485i	−0.138952	−	0.990299i	$-0.544373\pi$
$59$	−3710.93	−	2142.50i	−1.06605	−	0.615485i	−0.927100	+	0.374814i	$0.877707\pi$
$60$		0			0
$61$	−1209.57	+	698.345i	−0.325066	+	0.187677i	−0.653648	−	0.756799i	$-0.726762\pi$
$61$	−1209.57	+	698.345i	−0.325066	+	0.187677i	0.328583	+	0.944475i	$0.393429\pi$
$62$		0			0
$63$	−5537.20	+	4359.41i	−1.39511	+	1.09837i
$64$		0			0
$65$	−2062.73	−	3572.76i	−0.488221	−	0.845623i
$66$		0			0
$67$	3632.89	−	6292.36i	0.809288	−	1.40173i	−0.104070	−	0.994570i	$-0.533187\pi$
$67$	3632.89	−	6292.36i	0.809288	−	1.40173i	0.913358	−	0.407158i	$-0.133480\pi$
$68$		0			0
$69$		−	6534.77i		−	1.37256i
$70$		0			0
$71$	−5987.76			−1.18781			−0.593906	−	0.804534i	$-0.702415\pi$
$71$	−5987.76			−1.18781			−0.593906	+	0.804534i	$0.702415\pi$
$72$		0			0
$73$	−500.123	−	288.746i	−0.0938494	−	0.0541840i	0.452341	−	0.891845i	$-0.350589\pi$
$73$	−500.123	−	288.746i	−0.0938494	−	0.0541840i	−0.546190	+	0.837661i	$0.683922\pi$
$74$		0			0
$75$	252.825	−	145.969i	0.0449467	−	0.0259500i
$76$		0			0
$77$	2000.66	+	799.672i	0.337436	+	0.134875i
$78$		0			0
$79$	−1573.12	−	2724.72i	−0.252061	−	0.436583i	0.712032	−	0.702147i	$-0.247775\pi$
$79$	−1573.12	−	2724.72i	−0.252061	−	0.436583i	−0.964093	+	0.265564i	$0.914442\pi$
$80$		0			0
$81$	−1237.24	+	2142.95i	−0.188574	+	0.326620i
$82$		0			0
$83$		−	4729.96i		−	0.686596i	−0.939227	−	0.343298i	$-0.888456\pi$
$83$		−	4729.96i		−	0.686596i	0.939227	−	0.343298i	$-0.111544\pi$
$84$		0			0
$85$	2747.74			0.380309
$86$		0			0
$87$	9636.61	+	5563.70i	1.27317	+	0.735064i
$88$		0			0
$89$	−725.651	+	418.955i	−0.0916110	+	0.0528916i	−0.545106	−	0.838367i	$-0.683510\pi$
$89$	−725.651	+	418.955i	−0.0916110	+	0.0528916i	0.453495	+	0.891259i	$0.350177\pi$
$90$		0			0
$91$	7881.16	−	1137.55i	0.951716	−	0.137368i
$92$		0			0
$93$	7792.69	+	13497.3i	0.900993	+	1.56057i
$94$		0			0
$95$	−5706.47	+	9883.89i	−0.632295	+	1.09517i
$96$		0			0
$97$		−	5622.23i		−	0.597537i	−0.954326	−	0.298769i	$-0.903424\pi$
$97$		−	5622.23i		−	0.597537i	0.954326	−	0.298769i	$-0.0965759\pi$
$98$		0			0
$99$	6323.99			0.645240
$100$		0			0
$101$	−5703.21	−	3292.75i	−0.559083	−	0.322787i	0.193694	−	0.981062i	$-0.437953\pi$
$101$	−5703.21	−	3292.75i	−0.559083	−	0.322787i	−0.752778	+	0.658275i	$0.771286\pi$
$102$		0			0
$103$	−1320.25	+	762.249i	−0.124447	+	0.0718492i	−0.560931	−	0.827863i	$-0.689557\pi$
$103$	−1320.25	+	762.249i	−0.124447	+	0.0718492i	0.436484	+	0.899712i	$0.356223\pi$
$104$		0			0
$105$	2664.53	+	18460.4i	0.241680	+	1.67441i
$106$		0			0
$107$	5303.31	+	9185.61i	0.463212	+	0.802306i	0.999119	−	0.0419706i	$-0.0133636\pi$
$107$	5303.31	+	9185.61i	0.463212	+	0.802306i	−0.535907	+	0.844277i	$0.680030\pi$
$108$		0			0
$109$	6976.13	−	12083.0i	0.587167	−	1.01700i	−0.407434	−	0.913235i	$-0.633576\pi$
$109$	6976.13	−	12083.0i	0.587167	−	1.01700i	0.994601	−	0.103769i	$-0.0330902\pi$
$110$		0			0
$111$		−	14794.3i		−	1.20074i
$112$		0			0
$113$	−8811.30			−0.690054			−0.345027	−	0.938593i	$-0.612130\pi$
$113$	−8811.30			−0.690054			−0.345027	+	0.938593i	$0.612130\pi$
$114$		0			0
$115$	−9581.68	−	5531.99i	−0.724513	−	0.418298i
$116$		0			0
$117$	20241.0	−	11686.1i	1.47863	−	0.853689i
$118$		0			0
$119$	−1968.45	+	4924.76i	−0.139005	+	0.347769i
$120$		0			0
$121$	6353.79	+	11005.1i	0.433973	+	0.751663i
$122$		0			0
$123$	−8574.35	+	14851.2i	−0.566749	+	0.981638i
$124$		0			0
$125$			15372.2i			0.983823i
$126$		0			0
$127$	−3992.70			−0.247548			−0.123774	−	0.992310i	$-0.539500\pi$
$127$	−3992.70			−0.247548			−0.123774	+	0.992310i	$0.539500\pi$
$128$		0			0
$129$	−31409.1	−	18134.0i	−1.88745	−	1.08972i
$130$		0			0
$131$	17515.4	−	10112.5i	1.02065	−	0.589272i	0.106357	−	0.994328i	$-0.466081\pi$
$131$	17515.4	−	10112.5i	1.02065	−	0.589272i	0.914292	+	0.405056i	$0.132748\pi$
$132$		0			0
$133$	−13626.8	−	17308.4i	−0.770355	−	0.978483i
$134$		0			0
$135$	11956.8	+	20709.7i	0.656063	+	1.13634i
$136$		0			0
$137$	−12528.9	+	21700.6i	−0.667530	+	1.15620i	0.311062	+	0.950389i	$0.399315\pi$
$137$	−12528.9	+	21700.6i	−0.667530	+	1.15620i	−0.978593	+	0.205807i	$0.934018\pi$
$138$		0			0
$139$			20070.1i			1.03877i	0.854541	+	0.519385i	$0.173839\pi$
$139$			20070.1i			1.03877i	−0.854541	+	0.519385i	$0.826161\pi$
$140$		0			0
$141$	20173.5			1.01471
$142$		0			0
$143$	−6188.20	−	3572.76i	−0.302616	−	0.174716i
$144$		0			0
$145$	16315.7	−	9419.86i	0.776013	−	0.448031i
$146$		0			0
$147$	−34995.3	−	8449.18i	−1.61948	−	0.391003i
$148$		0			0
$149$	21353.9	+	36986.1i	0.961846	+	1.66597i	0.717860	+	0.696188i	$0.245122\pi$
$149$	21353.9	+	36986.1i	0.961846	+	1.66597i	0.243986	+	0.969779i	$0.421545\pi$
$150$		0			0
$151$	14803.7	−	25640.8i	0.649258	−	1.12455i	−0.334043	−	0.942558i	$-0.608413\pi$
$151$	14803.7	−	25640.8i	0.649258	−	1.12455i	0.983301	−	0.181989i	$-0.0582536\pi$
$152$		0			0
$153$			15566.9i			0.664998i
$154$		0			0
$155$	26387.5			1.09833
$156$		0			0
$157$	10597.6	+	6118.53i	0.429940	+	0.248226i	0.699321	−	0.714808i	$-0.253486\pi$
$157$	10597.6	+	6118.53i	0.429940	+	0.248226i	−0.269381	+	0.963034i	$0.586819\pi$
$158$		0			0
$159$	46308.1	−	26736.0i	1.83174	−	1.05755i
$160$		0			0
$161$	16779.2	−	13210.2i	0.647319	−	0.509632i
$162$		0			0
$163$	10765.6	+	18646.5i	0.405193	+	0.701814i	0.994344	−	0.106209i	$-0.0338711\pi$
$163$	10765.6	+	18646.5i	0.405193	+	0.701814i	−0.589151	+	0.808023i	$0.700538\pi$
$164$		0			0
$165$	8368.63	−	14494.9i	0.307388	−	0.532411i
$166$		0			0
$167$			16578.9i			0.594461i	0.954806	+	0.297230i	$0.0960629\pi$
$167$			16578.9i			0.594461i	−0.954806	+	0.297230i	$0.903937\pi$
$168$		0			0
$169$	2152.52			0.0753658
$170$		0			0
$171$	−55995.9	−	32329.2i	−1.91498	−	1.10561i
$172$		0			0
$173$	−34972.8	+	20191.5i	−1.16852	+	0.674648i	−0.953332	−	0.301924i	$-0.902371\pi$
$173$	−34972.8	+	20191.5i	−1.16852	+	0.674648i	−0.215192	+	0.976572i	$0.569038\pi$
$174$		0			0
$175$	885.891	+	354.094i	0.0289270	+	0.0115623i
$176$		0			0
$177$	−32124.9	−	55642.0i	−1.02541	−	1.77606i
$178$		0			0
$179$	−26747.2	+	46327.5i	−0.834780	+	1.44588i	0.0594290	+	0.998233i	$0.481072\pi$
$179$	−26747.2	+	46327.5i	−0.834780	+	1.44588i	−0.894209	+	0.447649i	$0.852261\pi$
$180$		0			0
$181$		−	54202.1i		−	1.65447i	−0.561857	−	0.827235i	$-0.689913\pi$
$181$		−	54202.1i		−	1.65447i	0.561857	−	0.827235i	$-0.310087\pi$
$182$		0			0
$183$	−20942.1			−0.625343
$184$		0			0
$185$	−21692.3	−	12524.1i	−0.633815	−	0.365934i
$186$		0			0
$187$	4121.60	−	2379.61i	0.117864	−	0.0680491i
$188$		0			0
$189$	−45683.6	+	6593.86i	−1.27890	+	0.184594i
$190$		0			0
$191$	−601.936	−	1042.58i	−0.0165000	−	0.0285788i	0.857658	−	0.514221i	$-0.171919\pi$
$191$	−601.936	−	1042.58i	−0.0165000	−	0.0285788i	−0.874158	+	0.485643i	$0.838586\pi$
$192$		0			0
$193$	−25656.5	+	44438.3i	−0.688783	+	1.19301i	0.283449	+	0.958987i	$0.408521\pi$
$193$	−25656.5	+	44438.3i	−0.688783	+	1.19301i	−0.972232	+	0.234019i	$0.924812\pi$
$194$		0			0
$195$		−	61857.7i		−	1.62676i
$196$		0			0
$197$	−1456.28			−0.0375242			−0.0187621	−	0.999824i	$-0.505973\pi$
$197$	−1456.28			−0.0375242			−0.0187621	+	0.999824i	$0.505973\pi$
$198$		0			0
$199$	−59546.3	−	34379.1i	−1.50366	−	0.868137i	−0.999991	−	0.00423890i	$-0.998651\pi$
$199$	−59546.3	−	34379.1i	−1.50366	−	0.868137i	−0.503667	−	0.863898i	$-0.668016\pi$
$200$		0			0
$201$	94348.3	−	54472.0i	2.33530	−	1.34828i
$202$		0			0
$203$	5194.82	+	35990.8i	0.126060	+	0.873372i
$204$		0			0
$205$	14517.2	+	25144.5i	0.345441	+	0.598322i
$206$		0			0
$207$	31340.7	−	54283.7i	0.731423	−	1.26686i
$208$		0			0
$209$			19767.8i			0.452549i
$210$		0			0
$211$	622.821			0.0139894			0.00699469	−	0.999976i	$-0.497774\pi$
$211$	622.821			0.0139894			0.00699469	+	0.999976i	$0.497774\pi$
$212$		0			0
$213$	−77752.8	−	44890.6i	−1.71379	−	0.989455i
$214$		0			0
$215$	−53178.5	+	30702.6i	−1.15043	+	0.664199i
$216$		0			0
$217$	−18903.7	+	47294.2i	−0.401446	+	1.00436i
$218$		0			0
$219$	−4329.50	−	7498.91i	−0.0902712	−	0.156354i
$220$		0			0
$221$	8794.58	−	15232.7i	0.180066	−	0.311883i
$222$		0			0
$223$			11509.7i			0.231449i	0.993281	+	0.115725i	$0.0369190\pi$
$223$			11509.7i			0.231449i	−0.993281	+	0.115725i	$0.963081\pi$
$224$		0			0
$225$	2800.26			0.0553138
$226$		0			0
$227$	48815.4	+	28183.6i	0.947339	+	0.546946i	0.892253	−	0.451535i	$-0.149124\pi$
$227$	48815.4	+	28183.6i	0.947339	+	0.546946i	0.0550855	+	0.998482i	$0.482457\pi$
$228$		0			0
$229$	−36484.4	+	21064.3i	−0.695722	+	0.401675i	−0.805752	−	0.592253i	$-0.798239\pi$
$229$	−36484.4	+	21064.3i	−0.695722	+	0.401675i	0.110030	+	0.993928i	$0.464905\pi$
$230$		0			0
$231$	19984.0	+	25383.0i	0.374505	+	0.475685i
$232$		0			0
$233$	27550.9	+	47719.6i	0.507486	+	0.878992i	0.999962	+	0.00866633i	$0.00275861\pi$
$233$	27550.9	+	47719.6i	0.507486	+	0.878992i	−0.492476	+	0.870326i	$0.663908\pi$
$234$		0			0
$235$	17077.8	−	29579.6i	0.309240	−	0.535620i
$236$		0			0
$237$		−	47174.9i		−	0.839875i
$238$		0			0
$239$	−23082.5			−0.404098			−0.202049	−	0.979375i	$-0.564760\pi$
$239$	−23082.5			−0.404098			−0.202049	+	0.979375i	$0.564760\pi$
$240$		0			0
$241$	70643.9	+	40786.3i	1.21630	+	0.702231i	0.964124	−	0.265451i	$-0.0855209\pi$
$241$	70643.9	+	40786.3i	1.21630	+	0.702231i	0.252175	+	0.967682i	$0.418854\pi$
$242$		0			0
$243$	33946.4	−	19599.0i	0.574886	−	0.331910i
$244$		0			0
$245$	−42013.9	+	44159.7i	−0.699940	+	0.735688i
$246$		0			0
$247$	36529.0	+	63270.0i	0.598747	+	1.03706i
$248$		0			0
$249$	35460.8	−	61419.8i	0.571939	−	0.990627i
$250$		0			0
$251$		−	27207.6i		−	0.431859i	−0.976409	−	0.215930i	$-0.930722\pi$
$251$		−	27207.6i		−	0.431859i	0.976409	−	0.215930i	$-0.0692782\pi$
$252$		0			0
$253$	−19163.4			−0.299385
$254$		0			0
$255$	35680.1	+	20599.9i	0.548714	+	0.316800i
$256$		0			0
$257$	93469.3	−	53964.5i	1.41515	−	0.817038i	0.419283	−	0.907856i	$-0.362281\pi$
$257$	93469.3	−	53964.5i	1.41515	−	0.817038i	0.995868	+	0.0908179i	$0.0289481\pi$
$258$		0			0
$259$	37987.0	−	29907.0i	0.566286	−	0.445834i
$260$		0			0
$261$	53366.9	+	92434.3i	0.783414	+	1.35691i
$262$		0			0
$263$	−20072.0	+	34765.8i	−0.290188	+	0.502621i	−0.973854	−	0.227174i	$-0.927051\pi$
$263$	−20072.0	+	34765.8i	−0.290188	+	0.502621i	0.683666	+	0.729795i	$0.260385\pi$
$264$		0			0
$265$		−	90533.1i		−	1.28919i
$266$		0			0
$267$	−12563.7			−0.176236
$268$		0			0
$269$	91239.0	+	52676.9i	1.26089	+	0.727973i	0.973246	−	0.229765i	$-0.0737958\pi$
$269$	91239.0	+	52676.9i	1.26089	+	0.727973i	0.287641	+	0.957738i	$0.407129\pi$
$270$		0			0
$271$	13189.3	−	7614.84i	0.179590	−	0.103687i	−0.407510	−	0.913201i	$-0.633603\pi$
$271$	13189.3	−	7614.84i	0.179590	−	0.103687i	0.587100	+	0.809514i	$0.300269\pi$
$272$		0			0
$273$	110867.	+	44314.1i	1.48757	+	0.594589i
$274$		0			0
$275$	−428.056	−	741.415i	−0.00566025	−	0.00980384i
$276$		0			0
$277$	4935.81	−	8549.07i	0.0643278	−	0.111419i	−0.832068	−	0.554674i	$-0.812843\pi$
$277$	4935.81	−	8549.07i	0.0643278	−	0.111419i	0.896396	+	0.443255i	$0.146176\pi$
$278$		0			0
$279$			149495.i			1.92051i
$280$		0			0
$281$	−155117.			−1.96448			−0.982240	−	0.187631i	$-0.939919\pi$
$281$	−155117.			−1.96448			−0.982240	+	0.187631i	$0.939919\pi$
$282$		0			0
$283$	94970.0	+	54831.0i	1.18581	+	0.684626i	0.957351	−	0.288929i	$-0.0932990\pi$
$283$	94970.0	+	54831.0i	1.18581	+	0.684626i	0.228456	+	0.973554i	$0.426632\pi$
$284$		0			0
$285$	−148200.	+	85563.4i	−1.82456	+	1.05341i
$286$		0			0
$287$	−55466.3	+	8005.87i	−0.673388	+	0.0971952i
$288$		0			0
$289$	−35902.9	−	62185.7i	−0.429867	−	0.744552i
$290$		0			0
$291$	42150.2	−	73006.2i	0.497752	−	0.862132i
$292$		0			0
$293$			89912.4i			1.04733i	0.851924	+	0.523666i	$0.175436\pi$
$293$			89912.4i			1.04733i	−0.851924	+	0.523666i	$0.824564\pi$
$294$		0			0
$295$	−108781.			−1.25000
$296$		0			0
$297$	35870.3	+	20709.7i	0.406651	+	0.234780i
$298$		0			0
$299$	−61335.5	+	35412.1i	−0.686072	+	0.396104i
$300$		0			0
$301$	−16931.7	−	117307.i	−0.186883	−	1.29476i
$302$		0			0
$303$	−49371.9	−	85514.6i	−0.537767	−	0.931440i
$304$		0			0
$305$	−17728.5	+	30706.6i	−0.190578	+	0.330090i
$306$		0			0
$307$		−	141681.i		−	1.50327i	−0.659582	−	0.751633i	$-0.729267\pi$
$307$		−	141681.i		−	1.50327i	0.659582	−	0.751633i	$-0.270733\pi$
$308$		0			0
$309$	−22858.5			−0.239403
$310$		0			0
$311$	74171.3	+	42822.8i	0.766858	+	0.442746i	0.831753	−	0.555147i	$-0.187338\pi$
$311$	74171.3	+	42822.8i	0.766858	+	0.442746i	−0.0648948	+	0.997892i	$0.520671\pi$
$312$		0			0
$313$	15442.6	−	8915.78i	0.157627	−	0.0910061i	−0.419112	−	0.907935i	$-0.637658\pi$
$313$	15442.6	−	8915.78i	0.157627	−	0.0910061i	0.576739	+	0.816929i	$0.304325\pi$
$314$		0			0
$315$	−66401.9	+	166128.i	−0.669206	+	1.67425i
$316$		0			0
$317$	−40402.6	−	69979.4i	−0.402060	−	0.696388i	0.591914	−	0.806001i	$-0.298372\pi$
$317$	−40402.6	−	69979.4i	−0.402060	−	0.696388i	−0.993974	+	0.109613i	$0.965039\pi$
$318$		0			0
$319$	16315.7	−	28259.6i	0.160333	−	0.277705i
$320$		0			0
$321$			159037.i			1.54343i
$322$		0			0
$323$	−48659.7			−0.466406
$324$		0			0
$325$	−2740.13	−	1582.01i	−0.0259421	−	0.0149777i
$326$		0			0
$327$	181174.	−	104601.i	1.69434	−	0.978228i
$328$		0			0
$329$	40781.1	+	51799.0i	0.376762	+	0.478552i
$330$		0			0
$331$	36402.1	+	63050.3i	0.332254	+	0.575482i	0.982954	−	0.183854i	$-0.0588574\pi$
$331$	36402.1	+	63050.3i	0.332254	+	0.575482i	−0.650699	+	0.759336i	$0.725524\pi$
$332$		0			0
$333$	70953.5	−	122895.i	0.639860	−	1.10827i
$334$		0			0
$335$		−	184452.i		−	1.64359i
$336$		0			0
$337$	126538.			1.11419			0.557095	−	0.830449i	$-0.311916\pi$
$337$	126538.			1.11419			0.557095	+	0.830449i	$0.311916\pi$
$338$		0			0
$339$	−114417.	−	66058.8i	−0.995616	−	0.574819i
$340$		0			0
$341$	39581.2	−	22852.2i	0.340393	−	0.196526i
$342$		0			0
$343$	−49049.0	−	106937.i	−0.416910	−	0.908948i
$344$		0			0
$345$	−82947.2	−	143669.i	−0.696889	−	1.20705i
$346$		0			0
$347$	−33474.6	+	57979.8i	−0.278008	+	0.481524i	−0.970890	−	0.239528i	$-0.923007\pi$
$347$	−33474.6	+	57979.8i	−0.278008	+	0.481524i	0.692882	+	0.721051i	$0.256341\pi$
$348$		0			0
$349$		−	25527.5i		−	0.209583i	−0.994494	−	0.104792i	$-0.966582\pi$
$349$		−	25527.5i		−	0.209583i	0.994494	−	0.104792i	$-0.0334176\pi$
$350$		0			0
$351$	153078.			1.24251
$352$		0			0
$353$	−48995.9	−	28287.8i	−0.393197	−	0.227013i	0.290347	−	0.956921i	$-0.406229\pi$
$353$	−48995.9	−	28287.8i	−0.393197	−	0.227013i	−0.683545	+	0.729909i	$0.739563\pi$
$354$		0			0
$355$	−131643.	+	76003.9i	−1.04458	+	0.603086i
$356$		0			0
$357$	−62482.0	+	49191.8i	−0.490251	+	0.385973i
$358$		0			0
$359$	18902.4	+	32739.9i	0.146665	+	0.254032i	0.929993	−	0.367577i	$-0.119813\pi$
$359$	18902.4	+	32739.9i	0.146665	+	0.254032i	−0.783328	+	0.621609i	$0.786479\pi$
$360$		0			0
$361$	35895.4	−	62172.6i	0.275438	−	0.477073i
$362$		0			0
$363$			190539.i			1.44601i
$364$		0			0
$365$	−14660.5			−0.110043
$366$		0			0
$367$	−9367.27	−	5408.20i	−0.0695474	−	0.0401532i	0.464823	−	0.885404i	$-0.346118\pi$
$367$	−9367.27	−	5408.20i	−0.0695474	−	0.0401532i	−0.534370	+	0.845250i	$0.679451\pi$
$368$		0			0
$369$	−142453.	+	82245.1i	−1.04621	+	0.604028i
$370$		0			0
$371$	162262.	+	64856.9i	1.17888	+	0.471203i
$372$		0			0
$373$	15511.7	+	26867.0i	0.111491	+	0.193109i	0.916372	−	0.400328i	$-0.131104\pi$
$373$	15511.7	+	26867.0i	0.111491	+	0.193109i	−0.804880	+	0.593437i	$0.797771\pi$
$374$		0			0
$375$	−115246.	+	199613.i	−0.819531	+	1.41947i
$376$		0			0
$377$		−	120599.i		−	0.848519i
$378$		0			0
$379$	98527.5			0.685929			0.342964	−	0.939348i	$-0.388569\pi$
$379$	98527.5			0.685929			0.342964	+	0.939348i	$0.388569\pi$
$380$		0			0
$381$	−51846.3	−	29933.5i	−0.357164	−	0.206209i
$382$		0			0
$383$	4454.26	−	2571.67i	0.0303653	−	0.0175314i	−0.484741	−	0.874658i	$-0.661086\pi$
$383$	4454.26	−	2571.67i	0.0303653	−	0.0175314i	0.515106	+	0.857127i	$0.327753\pi$
$384$		0			0
$385$	54135.5	−	7813.79i	0.365225	−	0.0527157i
$386$		0			0
$387$	−173941.	−	301275.i	−1.16140	−	2.01160i
$388$		0			0
$389$	−43141.0	+	74722.4i	−0.285096	+	0.493801i	−0.972632	−	0.232349i	$-0.925359\pi$
$389$	−43141.0	+	74722.4i	−0.285096	+	0.493801i	0.687537	+	0.726150i	$0.258692\pi$
$390$		0			0
$391$		−	47171.9i		−	0.308553i
$392$		0			0
$393$	303256.			1.96347
$394$		0			0
$395$	−69170.8	−	39935.8i	−0.443331	−	0.255957i
$396$		0			0
$397$	−135036.	+	77963.1i	−0.856778	+	0.494661i	−0.862932	−	0.505320i	$-0.831375\pi$
$397$	−135036.	+	77963.1i	−0.856778	+	0.494661i	0.00615368	+	0.999981i	$0.498041\pi$
$398$		0			0
$399$	−47186.2	−	326915.i	−0.296394	−	2.05347i
$400$		0			0
$401$	−17307.2	−	29977.0i	−0.107631	−	0.186423i	0.807179	−	0.590307i	$-0.200993\pi$
$401$	−17307.2	−	29977.0i	−0.107631	−	0.186423i	−0.914810	+	0.403884i	$0.867660\pi$
$402$		0			0
$403$	84457.5	−	146285.i	0.520030	−	0.900718i
$404$		0			0
$405$			62817.9i			0.382978i
$406$		0			0
$407$	−43384.7			−0.261907
$408$		0			0
$409$	−271749.	−	156894.i	−1.62450	−	0.937907i	−0.985695	−	0.168542i	$-0.946094\pi$
$409$	−271749.	−	156894.i	−1.62450	−	0.937907i	−0.638809	−	0.769366i	$-0.720572\pi$
$410$		0			0
$411$	−325382.	+	187859.i	−1.92624	+	1.11211i
$412$		0			0
$413$	77929.4	−	194968.i	0.456879	−	1.14304i
$414$		0			0
$415$	−60038.3	−	103989.i	−0.348604	−	0.603800i
$416$		0			0
$417$	−150466.	+	260615.i	−0.865301	+	1.49875i
$418$		0			0
$419$		−	7324.74i		−	0.0417219i	−0.999782	−	0.0208609i	$-0.993359\pi$
$419$		−	7324.74i		−	0.0417219i	0.999782	−	0.0208609i	$-0.00664073\pi$
$420$		0			0
$421$	−25178.3			−0.142057			−0.0710285	−	0.997474i	$-0.522628\pi$
$421$	−25178.3			−0.142057			−0.0710285	+	0.997474i	$0.522628\pi$
$422$		0			0
$423$	167579.	+	96752.0i	0.936569	+	0.540728i
$424$		0			0
$425$	1825.04	−	1053.69i	0.0101040	−	0.00583357i
$426$		0			0
$427$	−42334.9	−	53772.6i	−0.232190	−	0.294920i
$428$		0			0
$429$	−53570.3	−	92786.6i	−0.291078	−	0.504162i
$430$		0			0
$431$	6913.59	−	11974.7i	0.0372176	−	0.0644629i	−0.846817	−	0.531885i	$-0.821484\pi$
$431$	6913.59	−	11974.7i	0.0372176	−	0.0644629i	0.884034	+	0.467422i	$0.154817\pi$
$432$		0			0
$433$			47438.8i			0.253022i	0.991965	+	0.126511i	$0.0403779\pi$
$433$			47438.8i			0.253022i	−0.991965	+	0.126511i	$0.959622\pi$
$434$		0			0
$435$	282485.			1.49285
$436$		0			0
$437$	169682.	+	97966.0i	0.888532	+	0.512994i
$438$		0			0
$439$	−95101.7	+	54907.0i	−0.493469	+	0.284904i	−0.726012	−	0.687682i	$-0.758628\pi$
$439$	−95101.7	+	54907.0i	−0.493469	+	0.284904i	0.232544	+	0.972586i	$0.425295\pi$
$440$		0			0
$441$	−250181.	−	238024.i	−1.28640	−	1.22389i
$442$		0			0
$443$	−41280.4	−	71499.7i	−0.210347	−	0.364331i	0.741476	−	0.670979i	$-0.234126\pi$
$443$	−41280.4	−	71499.7i	−0.210347	−	0.364331i	−0.951823	+	0.306648i	$0.900793\pi$
$444$		0			0
$445$	−10635.8	+	18421.7i	−0.0537092	+	0.0930270i
$446$		0			0
$447$			640367.i			3.20490i
$448$		0			0
$449$	−330438.			−1.63907			−0.819534	−	0.573030i	$-0.805768\pi$
$449$	−330438.			−1.63907			−0.819534	+	0.573030i	$0.805768\pi$
$450$		0			0
$451$	43551.5	+	25144.5i	0.214116	+	0.123620i
$452$		0			0
$453$	384461.	−	221969.i	1.87351	−	1.08167i
$454$		0			0
$455$	158830.	−	125047.i	0.767204	−	0.604017i
$456$		0			0
$457$	186644.	+	323276.i	0.893677	+	1.54789i	0.835434	+	0.549591i	$0.185217\pi$
$457$	186644.	+	323276.i	0.893677	+	1.54789i	0.0582431	+	0.998302i	$0.481450\pi$
$458$		0			0
$459$	−50978.3	+	88297.0i	−0.241969	+	0.419103i
$460$		0			0
$461$			20355.2i			0.0957798i	0.998853	+	0.0478899i	$0.0152497\pi$
$461$			20355.2i			0.0957798i	−0.998853	+	0.0478899i	$0.984750\pi$
$462$		0			0
$463$	31552.7			0.147189			0.0735944	−	0.997288i	$-0.476553\pi$
$463$	31552.7			0.147189			0.0735944	+	0.997288i	$0.476553\pi$
$464$		0			0
$465$	342649.	+	197828.i	1.58469	+	0.914919i
$466$		0			0
$467$	209452.	−	120927.i	0.960397	−	0.554486i	0.0641019	−	0.997943i	$-0.479582\pi$
$467$	209452.	−	120927.i	0.960397	−	0.554486i	0.896295	+	0.443458i	$0.146248\pi$
$468$		0			0
$469$	330593.	+	132139.i	1.50296	+	0.600740i
$470$		0			0
$471$	91741.9	+	158902.i	0.413548	+	0.716286i
$472$		0			0
$473$	−53178.5	+	92107.8i	−0.237691	+	0.411694i
$474$		0			0
$475$			8753.16i			0.0387951i
$476$		0			0
$477$	512903.			2.25423
$478$		0			0
$479$	−235631.	−	136042.i	−1.02698	−	0.592926i	−0.110861	−	0.993836i	$-0.535361\pi$
$479$	−235631.	−	136042.i	−1.02698	−	0.592926i	−0.916117	+	0.400910i	$0.868694\pi$
$480$		0			0
$481$	−138860.	+	80170.8i	−0.600187	+	0.346518i
$482$		0			0
$483$	316920.	−	45743.4i	1.35848	−	0.196080i
$484$		0			0
$485$	−71364.1	−	123606.i	−0.303387	−	0.525481i
$486$		0			0
$487$	−203873.	+	353119.i	−0.859611	+	1.48889i	0.0126891	+	0.999919i	$0.495961\pi$
$487$	−203873.	+	353119.i	−0.859611	+	1.48889i	−0.872300	+	0.488971i	$0.837372\pi$
$488$		0			0
$489$			322840.i			1.35011i
$490$		0			0
$491$	286772.			1.18953			0.594763	−	0.803901i	$-0.297246\pi$
$491$	286772.			1.18953			0.594763	+	0.803901i	$0.297246\pi$
$492$		0			0
$493$	69562.8	+	40162.1i	0.286209	+	0.165243i
$494$		0			0
$495$	139035.	−	80271.8i	0.567431	−	0.327606i
$496$		0			0
$497$	−41914.3	−	290391.i	−0.169687	−	1.17563i
$498$		0			0
$499$	175718.	+	304352.i	0.705690	+	1.22229i	0.966442	+	0.256886i	$0.0826964\pi$
$499$	175718.	+	304352.i	0.705690	+	1.22229i	−0.260751	+	0.965406i	$0.583970\pi$
$500$		0			0
$501$	−124293.	+	215282.i	−0.495189	+	0.857693i
$502$		0			0
$503$		−	116045.i		−	0.458660i	−0.973349	−	0.229330i	$-0.926347\pi$
$503$		−	116045.i		−	0.458660i	0.973349	−	0.229330i	$-0.0736535\pi$
$504$		0			0
$505$	−167182.			−0.655552
$506$		0			0
$507$	27951.1	+	16137.6i	0.108738	+	0.0627802i
$508$		0			0
$509$	72030.7	−	41586.9i	0.278024	−	0.160517i	−0.354505	−	0.935054i	$-0.615351\pi$
$509$	72030.7	−	41586.9i	0.278024	−	0.160517i	0.632528	+	0.774537i	$0.282017\pi$
$510$		0			0
$511$	10502.6	−	26275.9i	0.0402212	−	0.100627i
$512$		0			0
$513$	−211742.	−	366749.i	−0.804587	−	1.39359i
$514$		0			0
$515$	−19350.8	+	33516.5i	−0.0729598	+	0.126370i
$516$		0			0
$517$		−	59159.2i		−	0.221330i
$518$		0			0
$519$	−605508.			−2.24794
$520$		0			0
$521$	174948.	+	101006.i	0.644517	+	0.372112i	0.786352	−	0.617778i	$-0.211967\pi$
$521$	174948.	+	101006.i	0.644517	+	0.372112i	−0.141835	+	0.989890i	$0.545300\pi$
$522$		0			0
$523$	24134.0	−	13933.8i	0.0882321	−	0.0509408i	−0.455235	−	0.890371i	$-0.650445\pi$
$523$	24134.0	−	13933.8i	0.0882321	−	0.0509408i	0.543467	+	0.839431i	$0.317111\pi$
$524$		0			0
$525$	8848.88	+	11239.6i	0.0321048	+	0.0407785i
$526$		0			0
$527$	56252.3	+	97431.8i	0.202544	+	0.350816i
$528$		0			0
$529$	44949.9	−	77855.5i	0.160626	−	0.278213i
$530$		0			0
$531$		−	616284.i		−	2.18571i
$532$		0			0
$533$	185858.			0.654226
$534$		0			0
$535$	233190.	+	134632.i	0.814707	+	0.470372i
$536$		0			0
$537$	−694640.	+	401050.i	−2.40886	+	1.39075i
$538$		0			0
$539$	−24777.4	+	102625.i	−0.0852861	+	0.353243i
$540$		0			0
$541$	18996.8	+	32903.4i	0.0649062	+	0.112421i	0.896652	−	0.442735i	$-0.145992\pi$
$541$	18996.8	+	32903.4i	0.0649062	+	0.112421i	−0.831746	+	0.555156i	$0.812659\pi$
$542$		0			0
$543$	406356.	−	703829.i	1.37818	−	2.38708i
$544$		0			0
$545$		−	354198.i		−	1.19249i
$546$		0			0
$547$	−360160.			−1.20371			−0.601854	−	0.798606i	$-0.705571\pi$
$547$	−360160.			−1.20371			−0.601854	+	0.798606i	$0.705571\pi$
$548$		0			0
$549$	−173964.	−	100438.i	−0.577185	−	0.333238i
$550$		0			0
$551$	−288934.	+	166816.i	−0.951691	+	0.549459i
$552$		0			0
$553$	121130.	−	95365.1i	0.396097	−	0.311845i
$554$		0			0
$555$	−187787.	−	325257.i	−0.609650	−	1.05594i
$556$		0			0
$557$	−155272.	+	268938.i	−0.500474	+	0.866847i	0.499525	+	0.866299i	$0.333508\pi$
$557$	−155272.	+	268938.i	−0.500474	+	0.866847i	−1.00000		0.000547960i	$0.999826\pi$
$558$		0			0
$559$			393075.i			1.25792i
$560$		0			0
$561$	71360.2			0.226741
$562$		0			0
$563$	−14453.4	−	8344.68i	−0.0455988	−	0.0263265i	0.477027	−	0.878888i	$-0.341714\pi$
$563$	−14453.4	−	8344.68i	−0.0455988	−	0.0263265i	−0.522626	+	0.852562i	$0.675048\pi$
$564$		0			0
$565$	−193719.	+	111844.i	−0.606841	+	0.350360i
$566$		0			0
$567$	−112588.	−	45002.0i	−0.350209	−	0.139980i
$568$		0			0
$569$	65131.1	+	112810.i	0.201170	+	0.348437i	0.948906	−	0.315560i	$-0.102192\pi$
$569$	65131.1	+	112810.i	0.201170	+	0.348437i	−0.747736	+	0.663997i	$0.768859\pi$
$570$		0			0
$571$	−249119.	+	431487.i	−0.764073	+	1.32341i	0.176662	+	0.984272i	$0.443470\pi$
$571$	−249119.	+	431487.i	−0.764073	+	1.32341i	−0.940735	+	0.339142i	$0.889863\pi$
$572$		0			0
$573$		−	18051.0i		−	0.0549784i
$574$		0			0
$575$	−8485.52			−0.0256651
$576$		0			0
$577$	−29199.1	−	16858.1i	−0.0877035	−	0.0506357i	0.455507	−	0.890232i	$-0.349458\pi$
$577$	−29199.1	−	16858.1i	−0.0877035	−	0.0506357i	−0.543210	+	0.839597i	$0.682791\pi$
$578$		0			0
$579$	−666313.	+	384696.i	−1.98756	+	1.14752i
$580$		0			0
$581$	229391.	−	33109.7i	0.679554	−	0.0980851i
$582$		0			0
$583$	−78404.0	−	135800.i	−0.230675	−	0.399541i
$584$		0			0
$585$	296669.	−	513846.i	0.866884	−	1.50149i
$586$		0			0
$587$		−	356809.i		−	1.03552i	−0.855525	−	0.517762i	$-0.826765\pi$
$587$		−	356809.i		−	1.03552i	0.855525	−	0.517762i	$-0.173235\pi$
$588$		0			0
$589$	−467296.			−1.34698
$590$		0			0
$591$	−18910.1	−	10917.8i	−0.0541402	−	0.0312579i
$592$		0			0
$593$	−28872.6	+	16669.6i	−0.0821063	+	0.0474041i	−0.540491	−	0.841350i	$-0.681762\pi$
$593$	−28872.6	+	16669.6i	−0.0821063	+	0.0474041i	0.458385	+	0.888754i	$0.348428\pi$
$594$		0			0
$595$	19234.1	+	133258.i	0.0543299	+	0.376409i
$596$		0			0
$597$	−515484.	−	892844.i	−1.44633	−	2.50511i
$598$		0			0
$599$	162165.	−	280878.i	0.451963	−	0.782824i	−0.546545	−	0.837430i	$-0.684057\pi$
$599$	162165.	−	280878.i	0.451963	−	0.782824i	0.998508	+	0.0546064i	$0.0173904\pi$
$600$		0			0
$601$			66322.0i			0.183615i	0.995777	+	0.0918076i	$0.0292645\pi$
$601$			66322.0i			0.183615i	−0.995777	+	0.0918076i	$0.970736\pi$
$602$		0			0
$603$	1.04499e6			2.87394
$604$		0			0
$605$	279380.	+	161300.i	0.763281	+	0.440680i
$606$		0			0
$607$	422322.	−	243828.i	1.14622	−	0.661768i	0.198253	−	0.980151i	$-0.436473\pi$
$607$	422322.	−	243828.i	1.14622	−	0.661768i	0.947962	+	0.318383i	$0.103140\pi$
$608$		0			0
$609$	−202369.	+	506297.i	−0.545643	+	1.36512i
$610$		0			0
$611$	−109321.	−	189349.i	−0.292833	−	0.507201i
$612$		0			0
$613$	170755.	−	295757.i	0.454415	−	0.787070i	−0.544239	−	0.838930i	$-0.683182\pi$
$613$	170755.	−	295757.i	0.454415	−	0.787070i	0.998654	+	0.0518597i	$0.0165149\pi$
$614$		0			0
$615$			435344.i			1.15102i
$616$		0			0
$617$	240873.			0.632728			0.316364	−	0.948638i	$-0.397538\pi$
$617$	240873.			0.632728			0.316364	+	0.948638i	$0.397538\pi$
$618$		0			0
$619$	133658.	+	77167.4i	0.348830	+	0.201397i	0.664170	−	0.747582i	$-0.268785\pi$
$619$	133658.	+	77167.4i	0.348830	+	0.201397i	−0.315340	+	0.948979i	$0.602119\pi$
$620$		0			0
$621$	355535.	−	205268.i	0.921932	−	0.532278i
$622$		0			0
$623$	−25397.8	−	32259.5i	−0.0654364	−	0.0831154i
$624$		0			0
$625$	201207.	+	348501.i	0.515091	+	0.892164i
$626$		0			0
$627$	−148200.	+	256690.i	−0.376976	+	0.652941i
$628$		0			0
$629$		−	106794.i		−	0.269927i
$630$		0			0
$631$	−220248.			−0.553164			−0.276582	−	0.960990i	$-0.589202\pi$
$631$	−220248.			−0.553164			−0.276582	+	0.960990i	$0.589202\pi$
$632$		0			0
$633$	8087.50	+	4669.32i	0.0201840	+	0.0116532i
$634$		0			0
$635$	−87780.7	+	50680.2i	−0.217696	+	0.125687i
$636$		0			0
$637$	110336.	+	374253.i	0.271919	+	0.922331i
$638$		0			0
$639$	−430590.	−	745804.i	−1.05454	−	1.82651i
$640$		0			0
$641$	340604.	−	589943.i	0.828960	−	1.43580i	−0.0698947	−	0.997554i	$-0.522266\pi$
$641$	340604.	−	589943.i	0.828960	−	1.43580i	0.898855	−	0.438247i	$-0.144400\pi$
$642$		0			0
$643$		−	572102.i		−	1.38373i	−0.722027	−	0.691865i	$-0.756789\pi$
$643$		−	572102.i		−	1.38373i	0.722027	−	0.691865i	$-0.243211\pi$
$644$		0			0
$645$	−920716.			−2.21313
$646$		0			0
$647$	525915.	+	303637.i	1.25634	+	0.725348i	0.972361	−	0.233482i	$-0.0750120\pi$
$647$	525915.	+	303637.i	1.25634	+	0.725348i	0.283979	+	0.958830i	$0.408345\pi$
$648$		0			0
$649$	−163171.	+	94207.1i	−0.387396	+	0.223663i
$650$		0			0
$651$	−600037.	+	472407.i	−1.41585	+	1.11469i
$652$		0			0
$653$	242335.	+	419737.i	0.568316	+	0.984353i	0.996733	+	0.0807713i	$0.0257383\pi$
$653$	242335.	+	419737.i	0.568316	+	0.984353i	−0.428416	+	0.903581i	$0.640928\pi$
$654$		0			0
$655$	256720.	−	444652.i	0.598380	−	1.03642i
$656$		0			0
$657$		−	83057.0i		−	0.192418i
$658$		0			0
$659$	−329627.			−0.759017			−0.379509	−	0.925188i	$-0.623907\pi$
$659$	−329627.			−0.759017			−0.379509	+	0.925188i	$0.623907\pi$
$660$		0			0
$661$	−182392.	−	105304.i	−0.417449	−	0.241014i	0.276536	−	0.961003i	$-0.410813\pi$
$661$	−182392.	−	105304.i	−0.417449	−	0.241014i	−0.693985	+	0.719989i	$0.744147\pi$
$662$		0			0
$663$	228400.	−	131867.i	0.519600	−	0.299991i
$664$		0			0
$665$	−519288.	−	207562.i	−1.17426	−	0.469358i
$666$		0			0
$667$	−161716.	−	280100.i	−0.363497	−	0.629595i
$668$		0			0
$669$	−86289.2	+	149457.i	−0.192799	+	0.333937i
$670$		0			0
$671$			61413.2i			0.136401i
$672$		0			0
$673$	94709.8			0.209105			0.104553	−	0.994519i	$-0.466659\pi$
$673$	94709.8			0.209105			0.104553	+	0.994519i	$0.466659\pi$
$674$		0			0
$675$	15883.3	+	9170.24i	0.0348605	+	0.0201267i
$676$		0			0
$677$	466400.	−	269276.i	1.01761	−	0.587517i	0.104199	−	0.994556i	$-0.466772\pi$
$677$	466400.	−	269276.i	1.01761	−	0.587517i	0.913411	+	0.407039i	$0.133439\pi$
$678$		0			0
$679$	272664.	−	39355.6i	0.591408	−	0.0853625i
$680$		0			0
$681$	422588.	+	731944.i	0.911219	+	1.57828i
$682$		0			0
$683$	−64535.9	+	111779.i	−0.138344	+	0.239618i	−0.926870	−	0.375383i	$-0.877511\pi$
$683$	−64535.9	+	111779.i	−0.138344	+	0.239618i	0.788526	+	0.615001i	$0.210845\pi$
$684$		0			0
$685$			636126.i			1.35570i
$686$		0			0
$687$	−631680.			−1.33839
$688$		0			0
$689$	−501890.	−	289766.i	−1.05723	−	0.610393i
$690$		0			0
$691$	−113201.	+	65356.6i	−0.237079	+	0.136878i	−0.613834	−	0.789435i	$-0.710373\pi$
$691$	−113201.	+	65356.6i	−0.237079	+	0.136878i	0.376754	+	0.926313i	$0.377040\pi$
$692$		0			0
$693$	44268.0	+	306697.i	0.0921771	+	0.638622i
$694$		0			0
$695$	254753.	+	441246.i	0.527413	+	0.913505i
$696$		0			0
$697$	−61894.8	+	107205.i	−0.127406	+	0.220673i
$698$		0			0
$699$			826204.i			1.69096i
$700$		0			0
$701$	−182501.			−0.371389			−0.185694	−	0.982608i	$-0.559453\pi$
$701$	−182501.			−0.371389			−0.185694	+	0.982608i	$0.559453\pi$
$702$		0			0
$703$	384150.	+	221789.i	0.777302	+	0.448776i
$704$		0			0
$705$	443520.	−	256066.i	0.892349	−	0.515198i
$706$		0			0
$707$	119767.	−	299640.i	0.239607	−	0.599462i
$708$		0			0
$709$	−406899.	−	704770.i	−0.809458	−	1.40202i	−0.913240	−	0.407422i	$-0.866428\pi$
$709$	−406899.	−	704770.i	−0.809458	−	1.40202i	0.103783	−	0.994600i	$-0.466905\pi$
$710$		0			0
$711$	226251.	−	391878.i	0.447560	−	0.775196i
$712$		0			0
$713$		−	453008.i		−	0.891101i
$714$		0			0
$715$	−181399.			−0.354832
$716$		0			0
$717$	−299732.	−	173051.i	−0.583036	−	0.336616i
$718$		0			0
$719$	364222.	−	210283.i	0.704544	−	0.406769i	−0.104494	−	0.994526i	$-0.533322\pi$
$719$	364222.	−	210283.i	0.704544	−	0.406769i	0.809038	+	0.587757i	$0.199989\pi$
$720$		0			0
$721$	−46208.9	−	58693.1i	−0.0888904	−	0.112906i
$722$		0			0
$723$	611554.	+	1.05924e6i	1.16992	+	2.02637i
$724$		0			0
$725$	7224.56	−	12513.3i	0.0137447	−	0.0238065i
$726$		0			0
$727$		−	172948.i		−	0.327225i	−0.986525	−	0.163613i	$-0.947685\pi$
$727$		−	172948.i		−	0.327225i	0.986525	−	0.163613i	$-0.0523147\pi$
$728$		0			0
$729$	788171.			1.48308
$730$		0			0
$731$	−226729.	−	130902.i	−0.424300	−	0.244970i
$732$		0			0
$733$	113936.	−	65780.9i	0.212057	−	0.122431i	−0.390210	−	0.920726i	$-0.627598\pi$
$733$	113936.	−	65780.9i	0.212057	−	0.122431i	0.602267	+	0.798295i	$0.294264\pi$
$734$		0			0
$735$	−876629.	+	258445.i	−1.62271	+	0.478403i
$736$		0			0
$737$	−159740.	−	276678.i	−0.294090	−	0.509378i
$738$		0			0
$739$	−244884.	+	424151.i	−0.448406	+	0.776662i	−0.998282	−	0.0585842i	$-0.981341\pi$
$739$	−244884.	+	424151.i	−0.448406	+	0.776662i	0.549877	+	0.835246i	$0.314675\pi$
$740$		0			0
$741$			1.09544e6i			1.99504i
$742$		0			0
$743$	−580258.			−1.05110			−0.525549	−	0.850763i	$-0.676140\pi$
$743$	−580258.			−1.05110			−0.525549	+	0.850763i	$0.676140\pi$
$744$		0			0
$745$	938945.	+	542100.i	1.69172	+	0.976713i
$746$		0			0
$747$	589139.	−	340139.i	1.05579	−	0.609559i
$748$		0			0
$749$	−408355.	+	321496.i	−0.727904	+	0.573076i
$750$		0			0
$751$	218698.	+	378797.i	0.387763	+	0.671624i	0.992148	−	0.125067i	$-0.0399147\pi$
$751$	218698.	+	378797.i	0.387763	+	0.671624i	−0.604386	+	0.796692i	$0.706581\pi$
$752$		0			0
$753$	203977.	−	353298.i	0.359742	−	0.623091i
$754$		0			0
$755$		−	751627.i		−	1.31859i
$756$		0			0
$757$	−24171.7			−0.0421809			−0.0210905	−	0.999778i	$-0.506714\pi$
$757$	−24171.7			−0.0421809			−0.0210905	+	0.999778i	$0.506714\pi$
$758$		0			0
$759$	−248842.	−	143669.i	−0.431956	−	0.249390i
$760$		0			0
$761$	−561376.	+	324111.i	−0.969359	+	0.559659i	−0.899041	−	0.437865i	$-0.855735\pi$
$761$	−561376.	+	324111.i	−0.969359	+	0.559659i	−0.0703180	+	0.997525i	$0.522401\pi$
$762$		0			0
$763$	634828.	+	253743.i	1.09045	+	0.435859i
$764$		0			0
$765$	197594.	+	342243.i	0.337638	+	0.584806i
$766$		0			0
$767$	−348172.	+	603051.i	−0.591838	+	1.02509i
$768$		0			0
$769$		−	179564.i		−	0.303646i	−0.988408	−	0.151823i	$-0.951486\pi$
$769$		−	179564.i		−	0.303646i	0.988408	−	0.151823i	$-0.0485143\pi$
$770$		0			0
$771$	1.61830e6			2.72239
$772$		0			0
$773$	529068.	+	305457.i	0.885426	+	0.511201i	0.872444	−	0.488715i	$-0.162534\pi$
$773$	529068.	+	305457.i	0.885426	+	0.511201i	0.0129823	+	0.999916i	$0.495867\pi$
$774$		0			0
$775$	17526.5	−	10118.9i	0.0291805	−	0.0168474i
$776$		0			0
$777$	717486.	−	103560.i	1.18842	−	0.171534i
$778$		0			0
$779$	−257085.	−	445284.i	−0.423644	−	0.733773i
$780$		0			0
$781$	−131643.	+	228012.i	−0.215821	+	0.373814i
$782$		0			0
$783$			699061.i			1.14023i
$784$		0			0
$785$	310655.			0.504126
$786$		0			0
$787$	−1.03191e6	−	595774.i	−1.66607	−	0.961905i	−0.969726	−	0.244195i	$-0.921476\pi$
$787$	−1.03191e6	−	595774.i	−1.66607	−	0.961905i	−0.696342	−	0.717710i	$-0.745190\pi$
$788$		0			0
$789$	−521282.	+	300963.i	−0.837373	+	0.483458i
$790$		0			0
$791$	−61679.1	−	427325.i	−0.0985791	−	0.682976i
$792$		0			0
$793$	113486.	+	196563.i	0.180466	+	0.312576i
$794$		0			0
$795$	678732.	−	1.17560e6i	1.07390	−	1.86005i
$796$		0			0
$797$		−	900495.i		−	1.41764i	−0.705392	−	0.708818i	$-0.749229\pi$
$797$		−	900495.i		−	1.41764i	0.705392	−	0.708818i	$-0.250771\pi$
$798$		0			0
$799$	145624.			0.228108
$800$		0			0
$801$	−104366.	−	60255.5i	−0.162664	−	0.0939142i
$802$		0			0
$803$	−21990.7	+	12696.3i	−0.0341042	+	0.0196901i
$804$		0			0
$805$	201215.	−	503411.i	0.310505	−	0.776838i
$806$		0			0
$807$	789843.	+	1.36805e6i	1.21281	+	2.10065i
$808$		0			0
$809$	−277882.	+	481306.i	−0.424584	+	0.735401i	−0.996381	−	0.0849939i	$-0.972913\pi$
$809$	−277882.	+	481306.i	−0.424584	+	0.735401i	0.571798	+	0.820395i	$0.306246\pi$
$810$		0			0
$811$		−	70954.2i		−	0.107879i	−0.998544	−	0.0539395i	$-0.982822\pi$
$811$		−	70954.2i		−	0.107879i	0.998544	−	0.0539395i	$-0.0171778\pi$
$812$		0			0
$813$	228356.			0.345486
$814$		0			0
$815$	473368.	+	273299.i	0.712662	+	0.411455i
$816$		0			0
$817$	941738.	−	543713.i	1.41087	−	0.814564i
$818$		0			0
$819$	708435.	+	899833.i	1.05617	+	1.34151i
$820$		0			0
$821$	312356.	+	541016.i	0.463408	+	0.802646i	0.999128	−	0.0417495i	$-0.0132931\pi$
$821$	312356.	+	541016.i	0.463408	+	0.802646i	−0.535720	+	0.844396i	$0.679960\pi$
$822$		0			0
$823$	−105029.	+	181916.i	−0.155064	+	0.268579i	−0.933082	−	0.359663i	$-0.882892\pi$
$823$	−105029.	+	181916.i	−0.155064	+	0.268579i	0.778018	+	0.628242i	$0.216225\pi$
$824$		0			0
$825$		−	12836.6i		−	0.0188601i
$826$		0			0
$827$	880910.			1.28801			0.644007	−	0.765020i	$-0.277271\pi$
$827$	880910.			1.28801			0.644007	+	0.765020i	$0.277271\pi$
$828$		0			0
$829$	−1.11951e6	−	646349.i	−1.62899	−	0.940498i	−0.984395	−	0.175974i	$-0.943692\pi$
$829$	−1.11951e6	−	646349.i	−1.62899	−	0.940498i	−0.644595	−	0.764524i	$-0.722974\pi$
$830$		0			0
$831$	128186.	−	74008.1i	0.185625	−	0.107171i
$832$		0			0
$833$	−252617.	−	60991.2i	−0.364060	−	0.0878977i
$834$		0			0
$835$	210440.	+	364492.i	0.301825	+	0.522775i
$836$		0			0
$837$	−489563.	+	847948.i	−0.698808	+	1.21037i
$838$		0			0
$839$		−	1.11586e6i		−	1.58520i	−0.609741	−	0.792601i	$-0.708726\pi$
$839$		−	1.11586e6i		−	1.58520i	0.609741	−	0.792601i	$-0.291274\pi$
$840$		0			0
$841$	−156542.			−0.221330
$842$		0			0
$843$	−2.01424e6	−	1.16292e6i	−2.83437	−	1.63642i
$844$		0			0
$845$	47323.8	−	27322.4i	0.0662775	−	0.0382653i
$846$		0			0
$847$	−489242.	+	385178.i	−0.681957	+	0.536902i
$848$		0			0
$849$	822142.	+	1.42399e6i	1.14059	+	1.97557i
$850$		0			0
$851$	−215008.	+	372404.i	−0.296889	+	0.514228i
$852$		0			0
$853$		−	1.28959e6i		−	1.77236i	−0.463341	−	0.886180i	$-0.653350\pi$
$853$		−	1.28959e6i		−	1.77236i	0.463341	−	0.886180i	$-0.346650\pi$
$854$		0			0
$855$	−1.64145e6			−2.24540
$856$		0			0
$857$	−566854.	−	327273.i	−0.771809	−	0.445604i	0.0617109	−	0.998094i	$-0.480344\pi$
$857$	−566854.	−	327273.i	−0.771809	−	0.445604i	−0.833519	+	0.552490i	$0.813678\pi$
$858$		0			0
$859$	−211796.	+	122281.i	−0.287033	+	0.165718i	−0.636603	−	0.771192i	$-0.719661\pi$
$859$	−211796.	+	122281.i	−0.287033	+	0.165718i	0.349570	+	0.936910i	$0.386328\pi$
$860$		0			0
$861$	−780266.	−	311875.i	−1.05253	−	0.420702i
$862$		0			0
$863$	−232638.	−	402942.i	−0.312363	−	0.541029i	0.666510	−	0.745496i	$-0.267787\pi$
$863$	−232638.	−	402942.i	−0.312363	−	0.541029i	−0.978873	+	0.204467i	$0.934454\pi$
$864$		0			0
$865$	−512591.	+	887833.i	−0.685075	+	1.18659i
$866$		0			0
$867$		−	1.07667e6i		−	1.43233i
$868$		0			0
$869$	−138342.			−0.183195
$870$		0			0
$871$	−1.02255e6	−	590370.i	−1.34787	−	0.778194i
$872$		0			0
$873$	700275.	−	404304.i	0.918840	−	0.530493i
$874$		0			0
$875$	−745514.	+	107606.i	−0.973732	+	0.140546i
$876$		0			0
$877$	−152086.	−	263420.i	−0.197738	−	0.342492i	0.750057	−	0.661373i	$-0.230026\pi$
$877$	−152086.	−	263420.i	−0.197738	−	0.342492i	−0.947795	+	0.318882i	$0.896693\pi$
$878$		0			0
$879$	−674078.	+	1.16754e6i	−0.872434	+	1.51110i
$880$		0			0
$881$		−	697876.i		−	0.899138i	−0.893246	−	0.449569i	$-0.851578\pi$
$881$		−	697876.i		−	0.899138i	0.893246	−	0.449569i	$-0.148422\pi$
$882$		0			0
$883$	−891773.			−1.14375			−0.571877	−	0.820339i	$-0.693785\pi$
$883$	−891773.			−1.14375			−0.571877	+	0.820339i	$0.693785\pi$
$884$		0			0
$885$	−1.41255e6	−	815537.i	−1.80351	−	1.04126i
$886$		0			0
$887$	1.09340e6	−	631278.i	1.38974	−	0.802367i	0.396455	−	0.918054i	$-0.370240\pi$
$887$	1.09340e6	−	631278.i	1.38974	−	0.802367i	0.993286	+	0.115687i	$0.0369070\pi$
$888$		0			0
$889$	−27948.9	−	193636.i	−0.0353640	−	0.245009i
$890$		0			0
$891$	54401.9	+	94226.9i	0.0685265	+	0.118691i
$892$		0			0
$893$	−302431.	+	523826.i	−0.379248	+	0.656877i
$894$		0			0
$895$			1.35803e6i			1.69537i
$896$		0			0
$897$	−1.06195e6			−1.31983
$898$		0			0
$899$	668036.	+	385691.i	0.826572	+	0.477221i
$900$		0			0
$901$	334280.	−	192997.i	0.411776	−	0.237739i
$902$		0			0
$903$	659590.	−	1.65020e6i	0.808907	−	2.02377i
$904$		0			0
$905$	−687998.	−	1.19165e6i	−0.840021	−	1.45496i
$906$		0			0
$907$	475990.	−	824439.i	0.578607	−	1.00218i	−0.417033	−	0.908891i	$-0.636930\pi$
$907$	475990.	−	824439.i	0.578607	−	1.00218i	0.995639	−	0.0932848i	$-0.0297367\pi$
$908$		0			0
$909$		−	947149.i		−	1.14628i
$910$		0			0
$911$	743243.			0.895559			0.447779	−	0.894144i	$-0.352215\pi$
$911$	743243.			0.895559			0.447779	+	0.894144i	$0.352215\pi$
$912$		0			0
$913$	−180115.	−	103989.i	−0.216077	−	0.124752i
$914$		0			0
$915$	−460418.	+	265823.i	−0.549934	+	0.317505i
$916$		0			0
$917$	613038.	+	778662.i	0.729035	+	0.925999i
$918$		0			0
$919$	−262150.	−	454057.i	−0.310398	−	0.537625i	0.668050	−	0.744116i	$-0.267129\pi$
$919$	−262150.	−	454057.i	−0.310398	−	0.537625i	−0.978449	+	0.206491i	$0.933796\pi$
$920$		0			0
$921$	1.06219e6	−	1.83977e6i	1.25223	−	2.16892i
$922$		0			0
$923$			973052.i			1.14218i
$924$		0			0
$925$	−19210.7			−0.0224522
$926$		0			0
$927$	−189883.	−	109629.i	−0.220967	−	0.127575i
$928$		0			0
$929$	848178.	−	489696.i	0.982779	−	0.567408i	0.0796709	−	0.996821i	$-0.474613\pi$
$929$	848178.	−	489696.i	0.982779	−	0.567408i	0.903108	+	0.429414i	$0.141280\pi$
$930$		0			0
$931$	744024.	−	782024.i	0.858396	−	0.902237i
$932$		0			0
$933$	642090.	+	1.11213e6i	0.737620	+	1.27759i
$934$		0			0
$935$	60409.7	−	104633.i	0.0691009	−	0.119686i
$936$		0			0
$937$			1.13988e6i			1.29831i	0.760656	+	0.649155i	$0.224877\pi$
$937$			1.13988e6i			1.29831i	−0.760656	+	0.649155i	$0.775123\pi$
$938$		0			0
$939$	267368.			0.303235
$940$		0			0
$941$	693791.	+	400561.i	0.783519	+	0.452365i	0.837676	−	0.546167i	$-0.183914\pi$
$941$	693791.	+	400561.i	0.783519	+	0.452365i	−0.0541569	+	0.998532i	$0.517247\pi$
$942$		0			0
$943$	431669.	−	249224.i	0.485431	−	0.280264i
$944$		0			0
$945$	−920670.	+	724840.i	−1.03096	+	0.811668i
$946$		0			0
$947$	340143.	+	589145.i	0.379282	+	0.656935i	0.990958	−	0.134173i	$-0.0428378\pi$
$947$	340143.	+	589145.i	0.379282	+	0.656935i	−0.611676	+	0.791108i	$0.709504\pi$
$948$		0			0
$949$	−46923.3	+	81273.5i	−0.0521022	+	0.0902436i
$950$		0			0
$951$		−	1.21160e6i		−	1.33967i
$952$		0			0
$953$	−394774.			−0.434673			−0.217337	−	0.976097i	$-0.569737\pi$
$953$	−394774.			−0.434673			−0.217337	+	0.976097i	$0.569737\pi$
$954$		0			0
$955$	−26467.5	−	15281.0i	−0.0290206	−	0.0167550i
$956$		0			0
$957$	423727.	−	244639.i	0.462660	−	0.267117i
$958$		0			0
$959$	−1.14013e6	−	455714.i	−1.23970	−	0.495513i
$960$		0			0
$961$	78449.9	+	135879.i	0.0849465	+	0.147132i
$962$		0			0
$963$	−762740.	+	1.32110e6i	−0.822478	+	1.42457i
$964$		0			0
$965$			1.30265e6i			1.39886i
$966$		0			0
$967$	604328.			0.646279			0.323140	−	0.946351i	$-0.395262\pi$
$967$	604328.			0.646279			0.323140	+	0.946351i	$0.395262\pi$
$968$		0			0
$969$	−631860.	−	364804.i	−0.672935	−	0.388519i
$970$		0			0
$971$	−657301.	+	379493.i	−0.697149	+	0.402499i	−0.806285	−	0.591528i	$-0.798525\pi$
$971$	−657301.	+	379493.i	−0.697149	+	0.402499i	0.109136	+	0.994027i	$0.465192\pi$
$972$		0			0
$973$	−973346.	+	140490.i	−1.02811	+	0.148396i
$974$		0			0
$975$	−23720.9	−	41085.8i	−0.0249530	−	0.0432198i
$976$		0			0
$977$	−612591.	+	1.06104e6i	−0.641773	+	1.11158i	0.343263	+	0.939239i	$0.388468\pi$
$977$	−612591.	+	1.06104e6i	−0.641773	+	1.11158i	−0.985037	+	0.172345i	$0.944866\pi$
$978$		0			0
$979$			36843.3i			0.0384409i
$980$		0			0
$981$	2.00666e6			2.08514
$982$		0			0
$983$	1.03964e6	+	600236.i	1.07591	+	0.621177i	0.929790	−	0.368090i	$-0.119988\pi$
$983$	1.03964e6	+	600236.i	1.07591	+	0.621177i	0.146120	+	0.989267i	$0.453322\pi$
$984$		0			0
$985$	−32016.6	+	18484.8i	−0.0329992	+	0.0190521i
$986$		0			0
$987$	141214.	+	978362.i	0.144959	+	1.00430i
$988$		0			0
$989$	527088.	+	912944.i	0.538878	+	0.933365i
$990$		0			0
$991$	904963.	−	1.56744e6i	0.921475	−	1.59604i	0.124340	−	0.992240i	$-0.460318\pi$
$991$	904963.	−	1.56744e6i	0.921475	−	1.59604i	0.797134	−	0.603802i	$-0.206348\pi$
$992$		0			0
$993$			1.09164e6i			1.10708i
$994$		0			0
$995$	−1.74552e6			−1.76311
$996$		0			0
$997$	648903.	+	374644.i	0.652814	+	0.376902i	0.789534	−	0.613707i	$-0.210323\pi$
$997$	648903.	+	374644.i	0.652814	+	0.376902i	−0.136719	+	0.990610i	$0.543656\pi$
$998$		0			0
$999$	804909.	−	464715.i	0.806521	−	0.465645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.5.s.b.17.2		4
4.3	odd	2		14.5.d.a.3.1	✓	4
7.3	odd	6		784.5.c.b.97.4		4
7.4	even	3		784.5.c.b.97.1		4
7.5	odd	6	inner	112.5.s.b.33.2		4
12.11	even	2		126.5.n.a.73.2		4
20.3	even	4		350.5.i.a.199.2		8
20.7	even	4		350.5.i.a.199.3		8
20.19	odd	2		350.5.k.a.101.2		4
28.3	even	6		98.5.b.b.97.3		4
28.11	odd	6		98.5.b.b.97.4		4
28.19	even	6		14.5.d.a.5.1	yes	4
28.23	odd	6		98.5.d.a.19.1		4
28.27	even	2		98.5.d.a.31.1		4
84.11	even	6		882.5.c.b.685.1		4
84.47	odd	6		126.5.n.a.19.2		4
84.59	odd	6		882.5.c.b.685.2		4
140.19	even	6		350.5.k.a.201.2		4
140.47	odd	12		350.5.i.a.299.2		8
140.103	odd	12		350.5.i.a.299.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.5.d.a.3.1	✓	4	4.3	odd	2
14.5.d.a.5.1	yes	4	28.19	even	6
98.5.b.b.97.3		4	28.3	even	6
98.5.b.b.97.4		4	28.11	odd	6
98.5.d.a.19.1		4	28.23	odd	6
98.5.d.a.31.1		4	28.27	even	2
112.5.s.b.17.2		4	1.1	even	1	trivial
112.5.s.b.33.2		4	7.5	odd	6	inner
126.5.n.a.19.2		4	84.47	odd	6
126.5.n.a.73.2		4	12.11	even	2
350.5.i.a.199.2		8	20.3	even	4
350.5.i.a.199.3		8	20.7	even	4
350.5.i.a.299.2		8	140.47	odd	12
350.5.i.a.299.3		8	140.103	odd	12
350.5.k.a.101.2		4	20.19	odd	2
350.5.k.a.201.2		4	140.19	even	6
784.5.c.b.97.1		4	7.4	even	3
784.5.c.b.97.4		4	7.3	odd	6
882.5.c.b.685.1		4	84.11	even	6
882.5.c.b.685.2		4	84.59	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	112.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(12.9853 + 7.49706i) q^{3} +(21.9853 - 12.6932i) q^{5} +(7.00000 + 48.4974i) q^{7} +(71.9117 + 124.555i) q^{9} +(21.9853 - 38.0796i) q^{11} -162.507i q^{13} +380.647 q^{15} +(93.7355 + 54.1182i) q^{17} +(-389.338 + 224.784i) q^{19} +(-272.691 + 682.232i) q^{21} +(-217.911 - 377.433i) q^{23} +(9.73506 - 16.8616i) q^{25} +941.981i q^{27} +742.118 q^{29} +(900.175 + 519.716i) q^{31} +(570.970 - 329.650i) q^{33} +(769.485 + 977.377i) q^{35} +(-493.338 - 854.486i) q^{37} +(1218.32 - 2110.20i) q^{39} +1143.70i q^{41} -2418.82 q^{43} +(3162.00 + 1825.58i) q^{45} +(1165.17 - 672.714i) q^{47} +(-2303.00 + 678.964i) q^{49} +(811.455 + 1405.48i) q^{51} +(1783.10 - 3088.42i) q^{53} -1116.26i q^{55} -6740.88 q^{57} +(-3710.93 - 2142.50i) q^{59} +(-1209.57 + 698.345i) q^{61} +(-5537.20 + 4359.41i) q^{63} +(-2062.73 - 3572.76i) q^{65} +(3632.89 - 6292.36i) q^{67} -6534.77i q^{69} -5987.76 q^{71} +(-500.123 - 288.746i) q^{73} +(252.825 - 145.969i) q^{75} +(2000.66 + 799.672i) q^{77} +(-1573.12 - 2724.72i) q^{79} +(-1237.24 + 2142.95i) q^{81} -4729.96i q^{83} +2747.74 q^{85} +(9636.61 + 5563.70i) q^{87} +(-725.651 + 418.955i) q^{89} +(7881.16 - 1137.55i) q^{91} +(7792.69 + 13497.3i) q^{93} +(-5706.47 + 9883.89i) q^{95} -5622.23i q^{97} +6323.99 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 18 q^{3} + 54 q^{5} + 28 q^{7} + 84 q^{9} + 54 q^{11} + 708 q^{15} + 918 q^{17} - 30 q^{19} - 378 q^{21} + 486 q^{23} - 572 q^{25} + 3240 q^{29} + 546 q^{31} + 1062 q^{33} + 1890 q^{35} - 446 q^{37}+ \cdots + 11448 q^{99}+O(q^{100}) \) 4 * q + 18 * q^3 + 54 * q^5 + 28 * q^7 + 84 * q^9 + 54 * q^11 + 708 * q^15 + 918 * q^17 - 30 * q^19 - 378 * q^21 + 486 * q^23 - 572 * q^25 + 3240 * q^29 + 546 * q^31 + 1062 * q^33 + 1890 * q^35 - 446 * q^37 + 3312 * q^39 - 2344 * q^43 + 5724 * q^45 - 702 * q^47 - 9212 * q^49 - 318 * q^51 + 2754 * q^53 - 17460 * q^57 - 12366 * q^59 + 7686 * q^61 - 6468 * q^63 - 3024 * q^65 + 5062 * q^67 - 18792 * q^71 - 17274 * q^73 + 5220 * q^75 + 4914 * q^77 - 794 * q^79 - 4338 * q^81 + 10380 * q^85 + 12276 * q^87 - 12474 * q^89 - 2688 * q^91 + 18918 * q^93 - 8910 * q^95 + 11448 * q^99

Introduction

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