LMFDB - Embedded newform 112.5.s.b.33.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [112,5,Mod(17,112)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 5, names="a")

//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);

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

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			33.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	112.33
Dual form			112.5.s.b.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(12.9853 - 7.49706i) q^{3} +(21.9853 + 12.6932i) q^{5} +(7.00000 - 48.4974i) q^{7} +(71.9117 - 124.555i) q^{9} +O(q^{10})$	\(q+(12.9853 - 7.49706i) q^{3} +(21.9853 + 12.6932i) q^{5} +(7.00000 - 48.4974i) q^{7} +(71.9117 - 124.555i) q^{9} +(21.9853 + 38.0796i) q^{11} +162.507i q^{13} +380.647 q^{15} +(93.7355 - 54.1182i) q^{17} +(-389.338 - 224.784i) q^{19} +(-272.691 - 682.232i) q^{21} +(-217.911 + 377.433i) q^{23} +(9.73506 + 16.8616i) q^{25} -941.981i q^{27} +742.118 q^{29} +(900.175 - 519.716i) q^{31} +(570.970 + 329.650i) q^{33} +(769.485 - 977.377i) q^{35} +(-493.338 + 854.486i) q^{37} +(1218.32 + 2110.20i) q^{39} -1143.70i q^{41} -2418.82 q^{43} +(3162.00 - 1825.58i) q^{45} +(1165.17 + 672.714i) q^{47} +(-2303.00 - 678.964i) q^{49} +(811.455 - 1405.48i) q^{51} +(1783.10 + 3088.42i) q^{53} +1116.26i q^{55} -6740.88 q^{57} +(-3710.93 + 2142.50i) q^{59} +(-1209.57 - 698.345i) q^{61} +(-5537.20 - 4359.41i) q^{63} +(-2062.73 + 3572.76i) q^{65} +(3632.89 + 6292.36i) q^{67} +6534.77i q^{69} -5987.76 q^{71} +(-500.123 + 288.746i) q^{73} +(252.825 + 145.969i) q^{75} +(2000.66 - 799.672i) q^{77} +(-1573.12 + 2724.72i) q^{79} +(-1237.24 - 2142.95i) q^{81} +4729.96i q^{83} +2747.74 q^{85} +(9636.61 - 5563.70i) q^{87} +(-725.651 - 418.955i) q^{89} +(7881.16 + 1137.55i) q^{91} +(7792.69 - 13497.3i) q^{93} +(-5706.47 - 9883.89i) q^{95} +5622.23i q^{97} +6323.99 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 18 q^{3} + 54 q^{5} + 28 q^{7} + 84 q^{9}+O(q^{10}) $ 4 * q + 18 * q^3 + 54 * q^5 + 28 * q^7 + 84 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	12.9853	−	7.49706i	1.44281	−	0.833006i	0.444773	−	0.895643i	$-0.353284\pi$
$3$	12.9853	−	7.49706i	1.44281	−	0.833006i	0.998036	+	0.0626373i	$0.0199511\pi$
$4$		0			0
$5$	21.9853	+	12.6932i	0.879411	+	0.507728i	0.870464	−	0.492232i	$-0.163819\pi$
$5$	21.9853	+	12.6932i	0.879411	+	0.507728i	0.00894701	+	0.999960i	$0.497152\pi$
$6$		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	0.942458	−	0.334324i	$-0.108508\pi$
$11$	21.9853	+	38.0796i	0.181697	+	0.314708i	−0.760762	+	0.649031i	$0.775174\pi$
$12$		0			0
$13$			162.507i			0.961579i	0.876836	+	0.480790i	$0.159650\pi$
$13$			162.507i			0.961579i	−0.876836	+	0.480790i	$0.840350\pi$
$14$		0			0
$15$	380.647			1.69176
$16$		0			0
$17$	93.7355	−	54.1182i	0.324344	−	0.187260i	−0.328983	−	0.944336i	$-0.606706\pi$
$17$	93.7355	−	54.1182i	0.324344	−	0.187260i	0.653327	+	0.757076i	$0.273373\pi$
$18$		0			0
$19$	−389.338	−	224.784i	−1.07850	−	0.622671i	−0.148007	−	0.988986i	$-0.547286\pi$
$19$	−389.338	−	224.784i	−1.07850	−	0.622671i	−0.930491	+	0.366315i	$0.880619\pi$
$20$		0			0
$21$	−272.691	−	682.232i	−0.618347	−	1.54701i
$22$		0			0
$23$	−217.911	+	377.433i	−0.411931	+	0.713485i	−0.995101	−	0.0988653i	$-0.968479\pi$
$23$	−217.911	+	377.433i	−0.411931	+	0.713485i	0.583170	+	0.812350i	$0.301812\pi$
$24$		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	0.0477804	−	0.998858i	$-0.484785\pi$
$31$	900.175	−	519.716i	0.936707	−	0.540808i	0.888926	+	0.458050i	$0.151452\pi$
$32$		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	−0.988021	−	0.154322i	$-0.950681\pi$
$37$	−493.338	+	854.486i	−0.360364	+	0.624168i	0.627657	+	0.778490i	$0.284014\pi$
$38$		0			0
$39$	1218.32	+	2110.20i	0.801001	+	1.38737i
$40$		0			0
$41$		−	1143.70i		−	0.680366i	−0.940359	−	0.340183i	$-0.889511\pi$
$41$		−	1143.70i		−	0.680366i	0.940359	−	0.340183i	$-0.110489\pi$
$42$		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	0.739984	−	0.672624i	$-0.234833\pi$
$47$	1165.17	+	672.714i	0.527467	+	0.304533i	−0.212517	+	0.977157i	$0.568166\pi$
$48$		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	0.986561	+	0.163391i	$0.0522432\pi$
$53$	1783.10	+	3088.42i	0.634782	+	1.09947i	−0.351780	+	0.936083i	$0.614423\pi$
$54$		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	−0.927100	−	0.374814i	$-0.877707\pi$
$59$	−3710.93	+	2142.50i	−1.06605	+	0.615485i	−0.138952	+	0.990299i	$0.544373\pi$
$60$		0			0
$61$	−1209.57	−	698.345i	−0.325066	−	0.187677i	0.328583	−	0.944475i	$-0.393429\pi$
$61$	−1209.57	−	698.345i	−0.325066	−	0.187677i	−0.653648	+	0.756799i	$0.726762\pi$
$62$		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	0.913358	+	0.407158i	$0.133480\pi$
$67$	3632.89	+	6292.36i	0.809288	+	1.40173i	−0.104070	+	0.994570i	$0.533187\pi$
$68$		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	−0.546190	−	0.837661i	$-0.683922\pi$
$73$	−500.123	+	288.746i	−0.0938494	+	0.0541840i	0.452341	+	0.891845i	$0.350589\pi$
$74$		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	−0.964093	−	0.265564i	$-0.914442\pi$
$79$	−1573.12	+	2724.72i	−0.252061	+	0.436583i	0.712032	+	0.702147i	$0.247775\pi$
$80$		0			0
$81$	−1237.24	−	2142.95i	−0.188574	−	0.326620i
$82$		0			0
$83$			4729.96i			0.686596i	0.939227	+	0.343298i	$0.111544\pi$
$83$			4729.96i			0.686596i	−0.939227	+	0.343298i	$0.888456\pi$
$84$		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	0.453495	−	0.891259i	$-0.350177\pi$
$89$	−725.651	−	418.955i	−0.0916110	−	0.0528916i	−0.545106	+	0.838367i	$0.683510\pi$
$90$		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	$0.0965759\pi$
$97$			5622.23i			0.597537i	−0.954326	+	0.298769i	$0.903424\pi$
$98$		0			0
$99$	6323.99			0.645240
$100$		0			0
$101$	−5703.21	+	3292.75i	−0.559083	+	0.322787i	−0.752778	−	0.658275i	$-0.771286\pi$
$101$	−5703.21	+	3292.75i	−0.559083	+	0.322787i	0.193694	+	0.981062i	$0.437953\pi$
$102$		0			0
$103$	−1320.25	−	762.249i	−0.124447	−	0.0718492i	0.436484	−	0.899712i	$-0.356223\pi$
$103$	−1320.25	−	762.249i	−0.124447	−	0.0718492i	−0.560931	+	0.827863i	$0.689557\pi$
$104$		0			0
$105$	2664.53	−	18460.4i	0.241680	−	1.67441i
$106$		0			0
$107$	5303.31	−	9185.61i	0.463212	−	0.802306i	−0.535907	−	0.844277i	$-0.680030\pi$
$107$	5303.31	−	9185.61i	0.463212	−	0.802306i	0.999119	+	0.0419706i	$0.0133636\pi$
$108$		0			0
$109$	6976.13	+	12083.0i	0.587167	+	1.01700i	0.994601	+	0.103769i	$0.0330902\pi$
$109$	6976.13	+	12083.0i	0.587167	+	1.01700i	−0.407434	+	0.913235i	$0.633576\pi$
$110$		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	0.914292	−	0.405056i	$-0.132748\pi$
$131$	17515.4	+	10112.5i	1.02065	+	0.589272i	0.106357	+	0.994328i	$0.466081\pi$
$132$		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	−0.978593	−	0.205807i	$-0.934018\pi$
$137$	−12528.9	−	21700.6i	−0.667530	−	1.15620i	0.311062	−	0.950389i	$-0.399315\pi$
$138$		0			0
$139$		−	20070.1i		−	1.03877i	−0.854541	−	0.519385i	$-0.826161\pi$
$139$		−	20070.1i		−	1.03877i	0.854541	−	0.519385i	$-0.173839\pi$
$140$		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	0.243986	−	0.969779i	$-0.421545\pi$
$149$	21353.9	−	36986.1i	0.961846	−	1.66597i	0.717860	−	0.696188i	$-0.245122\pi$
$150$		0			0
$151$	14803.7	+	25640.8i	0.649258	+	1.12455i	0.983301	+	0.181989i	$0.0582536\pi$
$151$	14803.7	+	25640.8i	0.649258	+	1.12455i	−0.334043	+	0.942558i	$0.608413\pi$
$152$		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	−0.269381	−	0.963034i	$-0.586819\pi$
$157$	10597.6	−	6118.53i	0.429940	−	0.248226i	0.699321	+	0.714808i	$0.253486\pi$
$158$		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	−0.589151	−	0.808023i	$-0.700538\pi$
$163$	10765.6	−	18646.5i	0.405193	−	0.701814i	0.994344	+	0.106209i	$0.0338711\pi$
$164$		0			0
$165$	8368.63	+	14494.9i	0.307388	+	0.532411i
$166$		0			0
$167$		−	16578.9i		−	0.594461i	−0.954806	−	0.297230i	$-0.903937\pi$
$167$		−	16578.9i		−	0.594461i	0.954806	−	0.297230i	$-0.0960629\pi$
$168$		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	−0.215192	−	0.976572i	$-0.569038\pi$
$173$	−34972.8	−	20191.5i	−1.16852	−	0.674648i	−0.953332	+	0.301924i	$0.902371\pi$
$174$		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	−0.894209	−	0.447649i	$-0.852261\pi$
$179$	−26747.2	−	46327.5i	−0.834780	−	1.44588i	0.0594290	−	0.998233i	$-0.481072\pi$
$180$		0			0
$181$			54202.1i			1.65447i	0.561857	+	0.827235i	$0.310087\pi$
$181$			54202.1i			1.65447i	−0.561857	+	0.827235i	$0.689913\pi$
$182$		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	−0.874158	−	0.485643i	$-0.838586\pi$
$191$	−601.936	+	1042.58i	−0.0165000	+	0.0285788i	0.857658	+	0.514221i	$0.171919\pi$
$192$		0			0
$193$	−25656.5	−	44438.3i	−0.688783	−	1.19301i	−0.972232	−	0.234019i	$-0.924812\pi$
$193$	−25656.5	−	44438.3i	−0.688783	−	1.19301i	0.283449	−	0.958987i	$-0.408521\pi$
$194$		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	−0.503667	+	0.863898i	$0.668016\pi$
$199$	−59546.3	+	34379.1i	−1.50366	+	0.868137i	−0.999991	+	0.00423890i	$0.998651\pi$
$200$		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	$-0.963081\pi$
$223$		−	11509.7i		−	0.231449i	0.993281	−	0.115725i	$-0.0369190\pi$
$224$		0			0
$225$	2800.26			0.0553138
$226$		0			0
$227$	48815.4	−	28183.6i	0.947339	−	0.546946i	0.0550855	−	0.998482i	$-0.482457\pi$
$227$	48815.4	−	28183.6i	0.947339	−	0.546946i	0.892253	+	0.451535i	$0.149124\pi$
$228$		0			0
$229$	−36484.4	−	21064.3i	−0.695722	−	0.401675i	0.110030	−	0.993928i	$-0.464905\pi$
$229$	−36484.4	−	21064.3i	−0.695722	−	0.401675i	−0.805752	+	0.592253i	$0.798239\pi$
$230$		0			0
$231$	19984.0	−	25383.0i	0.374505	−	0.475685i
$232$		0			0
$233$	27550.9	−	47719.6i	0.507486	−	0.878992i	−0.492476	−	0.870326i	$-0.663908\pi$
$233$	27550.9	−	47719.6i	0.507486	−	0.878992i	0.999962	−	0.00866633i	$-0.00275861\pi$
$234$		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	0.252175	−	0.967682i	$-0.418854\pi$
$241$	70643.9	−	40786.3i	1.21630	−	0.702231i	0.964124	+	0.265451i	$0.0855209\pi$
$242$		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	$0.0692782\pi$
$251$			27207.6i			0.431859i	−0.976409	+	0.215930i	$0.930722\pi$
$252$		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	0.995868	−	0.0908179i	$-0.0289481\pi$
$257$	93469.3	+	53964.5i	1.41515	+	0.817038i	0.419283	+	0.907856i	$0.362281\pi$
$258$		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	0.683666	−	0.729795i	$-0.260385\pi$
$263$	−20072.0	−	34765.8i	−0.290188	−	0.502621i	−0.973854	+	0.227174i	$0.927051\pi$
$264$		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	0.287641	−	0.957738i	$-0.407129\pi$
$269$	91239.0	−	52676.9i	1.26089	−	0.727973i	0.973246	+	0.229765i	$0.0737958\pi$
$270$		0			0
$271$	13189.3	+	7614.84i	0.179590	+	0.103687i	0.587100	−	0.809514i	$-0.300269\pi$
$271$	13189.3	+	7614.84i	0.179590	+	0.103687i	−0.407510	+	0.913201i	$0.633603\pi$
$272$		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	0.896396	−	0.443255i	$-0.146176\pi$
$277$	4935.81	+	8549.07i	0.0643278	+	0.111419i	−0.832068	+	0.554674i	$0.812843\pi$
$278$		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	0.228456	−	0.973554i	$-0.426632\pi$
$283$	94970.0	−	54831.0i	1.18581	−	0.684626i	0.957351	+	0.288929i	$0.0932990\pi$
$284$		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	$-0.824564\pi$
$293$		−	89912.4i		−	1.04733i	0.851924	−	0.523666i	$-0.175436\pi$
$294$		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	$0.270733\pi$
$307$			141681.i			1.50327i	−0.659582	+	0.751633i	$0.729267\pi$
$308$		0			0
$309$	−22858.5			−0.239403
$310$		0			0
$311$	74171.3	−	42822.8i	0.766858	−	0.442746i	−0.0648948	−	0.997892i	$-0.520671\pi$
$311$	74171.3	−	42822.8i	0.766858	−	0.442746i	0.831753	+	0.555147i	$0.187338\pi$
$312$		0			0
$313$	15442.6	+	8915.78i	0.157627	+	0.0910061i	0.576739	−	0.816929i	$-0.304325\pi$
$313$	15442.6	+	8915.78i	0.157627	+	0.0910061i	−0.419112	+	0.907935i	$0.637658\pi$
$314$		0			0
$315$	−66401.9	−	166128.i	−0.669206	−	1.67425i
$316$		0			0
$317$	−40402.6	+	69979.4i	−0.402060	+	0.696388i	−0.993974	−	0.109613i	$-0.965039\pi$
$317$	−40402.6	+	69979.4i	−0.402060	+	0.696388i	0.591914	+	0.806001i	$0.298372\pi$
$318$		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	−0.650699	−	0.759336i	$-0.725524\pi$
$331$	36402.1	−	63050.3i	0.332254	−	0.575482i	0.982954	+	0.183854i	$0.0588574\pi$
$332$		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	0.692882	−	0.721051i	$-0.256341\pi$
$347$	−33474.6	−	57979.8i	−0.278008	−	0.481524i	−0.970890	+	0.239528i	$0.923007\pi$
$348$		0			0
$349$			25527.5i			0.209583i	0.994494	+	0.104792i	$0.0334176\pi$
$349$			25527.5i			0.209583i	−0.994494	+	0.104792i	$0.966582\pi$
$350$		0			0
$351$	153078.			1.24251
$352$		0			0
$353$	−48995.9	+	28287.8i	−0.393197	+	0.227013i	−0.683545	−	0.729909i	$-0.739563\pi$
$353$	−48995.9	+	28287.8i	−0.393197	+	0.227013i	0.290347	+	0.956921i	$0.406229\pi$
$354$		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	−0.783328	−	0.621609i	$-0.786479\pi$
$359$	18902.4	−	32739.9i	0.146665	−	0.254032i	0.929993	+	0.367577i	$0.119813\pi$
$360$		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	−0.534370	−	0.845250i	$-0.679451\pi$
$367$	−9367.27	+	5408.20i	−0.0695474	+	0.0401532i	0.464823	+	0.885404i	$0.346118\pi$
$368$		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	−0.804880	−	0.593437i	$-0.797771\pi$
$373$	15511.7	−	26867.0i	0.111491	−	0.193109i	0.916372	+	0.400328i	$0.131104\pi$
$374$		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	0.515106	−	0.857127i	$-0.327753\pi$
$383$	4454.26	+	2571.67i	0.0303653	+	0.0175314i	−0.484741	+	0.874658i	$0.661086\pi$
$384$		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	0.687537	−	0.726150i	$-0.258692\pi$
$389$	−43141.0	−	74722.4i	−0.285096	−	0.493801i	−0.972632	+	0.232349i	$0.925359\pi$
$390$		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	0.00615368	−	0.999981i	$-0.498041\pi$
$397$	−135036.	−	77963.1i	−0.856778	−	0.494661i	−0.862932	+	0.505320i	$0.831375\pi$
$398$		0			0
$399$	−47186.2	+	326915.i	−0.296394	+	2.05347i
$400$		0			0
$401$	−17307.2	+	29977.0i	−0.107631	+	0.186423i	−0.914810	−	0.403884i	$-0.867660\pi$
$401$	−17307.2	+	29977.0i	−0.107631	+	0.186423i	0.807179	+	0.590307i	$0.200993\pi$
$402$		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	−0.638809	+	0.769366i	$0.720572\pi$
$409$	−271749.	+	156894.i	−1.62450	+	0.937907i	−0.985695	+	0.168542i	$0.946094\pi$
$410$		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	$0.00664073\pi$
$419$			7324.74i			0.0417219i	−0.999782	+	0.0208609i	$0.993359\pi$
$420$		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	0.884034	−	0.467422i	$-0.154817\pi$
$431$	6913.59	+	11974.7i	0.0372176	+	0.0644629i	−0.846817	+	0.531885i	$0.821484\pi$
$432$		0			0
$433$		−	47438.8i		−	0.253022i	−0.991965	−	0.126511i	$-0.959622\pi$
$433$		−	47438.8i		−	0.253022i	0.991965	−	0.126511i	$-0.0403779\pi$
$434$		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	0.232544	−	0.972586i	$-0.425295\pi$
$439$	−95101.7	−	54907.0i	−0.493469	−	0.284904i	−0.726012	+	0.687682i	$0.758628\pi$
$440$		0			0
$441$	−250181.	+	238024.i	−1.28640	+	1.22389i
$442$		0			0
$443$	−41280.4	+	71499.7i	−0.210347	+	0.364331i	−0.951823	−	0.306648i	$-0.900793\pi$
$443$	−41280.4	+	71499.7i	−0.210347	+	0.364331i	0.741476	+	0.670979i	$0.234126\pi$
$444$		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	0.0582431	−	0.998302i	$-0.481450\pi$
$457$	186644.	−	323276.i	0.893677	−	1.54789i	0.835434	−	0.549591i	$-0.185217\pi$
$458$		0			0
$459$	−50978.3	−	88297.0i	−0.241969	−	0.419103i
$460$		0			0
$461$		−	20355.2i		−	0.0957798i	−0.998853	−	0.0478899i	$-0.984750\pi$
$461$		−	20355.2i		−	0.0957798i	0.998853	−	0.0478899i	$-0.0152497\pi$
$462$		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	0.896295	−	0.443458i	$-0.146248\pi$
$467$	209452.	+	120927.i	0.960397	+	0.554486i	0.0641019	+	0.997943i	$0.479582\pi$
$468$		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	−0.916117	−	0.400910i	$-0.868694\pi$
$479$	−235631.	+	136042.i	−1.02698	+	0.592926i	−0.110861	+	0.993836i	$0.535361\pi$
$480$		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	−0.872300	−	0.488971i	$-0.837372\pi$
$487$	−203873.	−	353119.i	−0.859611	−	1.48889i	0.0126891	−	0.999919i	$-0.495961\pi$
$488$		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	−0.260751	−	0.965406i	$-0.583970\pi$
$499$	175718.	−	304352.i	0.705690	−	1.22229i	0.966442	−	0.256886i	$-0.0826964\pi$
$500$		0			0
$501$	−124293.	−	215282.i	−0.495189	−	0.857693i
$502$		0			0
$503$			116045.i			0.458660i	0.973349	+	0.229330i	$0.0736535\pi$
$503$			116045.i			0.458660i	−0.973349	+	0.229330i	$0.926347\pi$
$504$		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	0.632528	−	0.774537i	$-0.282017\pi$
$509$	72030.7	+	41586.9i	0.278024	+	0.160517i	−0.354505	+	0.935054i	$0.615351\pi$
$510$		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	−0.141835	−	0.989890i	$-0.545300\pi$
$521$	174948.	−	101006.i	0.644517	−	0.372112i	0.786352	+	0.617778i	$0.211967\pi$
$522$		0			0
$523$	24134.0	+	13933.8i	0.0882321	+	0.0509408i	0.543467	−	0.839431i	$-0.317111\pi$
$523$	24134.0	+	13933.8i	0.0882321	+	0.0509408i	−0.455235	+	0.890371i	$0.650445\pi$
$524$		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	−0.831746	−	0.555156i	$-0.812659\pi$
$541$	18996.8	−	32903.4i	0.0649062	−	0.112421i	0.896652	+	0.442735i	$0.145992\pi$
$542$		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	−1.00000		0.000547960i	$-0.999826\pi$
$557$	−155272.	−	268938.i	−0.500474	−	0.866847i	0.499525	−	0.866299i	$-0.333508\pi$
$558$		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	−0.522626	−	0.852562i	$-0.675048\pi$
$563$	−14453.4	+	8344.68i	−0.0455988	+	0.0263265i	0.477027	+	0.878888i	$0.341714\pi$
$564$		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	−0.747736	−	0.663997i	$-0.768859\pi$
$569$	65131.1	−	112810.i	0.201170	−	0.348437i	0.948906	+	0.315560i	$0.102192\pi$
$570$		0			0
$571$	−249119.	−	431487.i	−0.764073	−	1.32341i	−0.940735	−	0.339142i	$-0.889863\pi$
$571$	−249119.	−	431487.i	−0.764073	−	1.32341i	0.176662	−	0.984272i	$-0.443470\pi$
$572$		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	−0.543210	−	0.839597i	$-0.682791\pi$
$577$	−29199.1	+	16858.1i	−0.0877035	+	0.0506357i	0.455507	+	0.890232i	$0.349458\pi$
$578$		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	$0.173235\pi$
$587$			356809.i			1.03552i	−0.855525	+	0.517762i	$0.826765\pi$
$588$		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	0.458385	−	0.888754i	$-0.348428\pi$
$593$	−28872.6	−	16669.6i	−0.0821063	−	0.0474041i	−0.540491	+	0.841350i	$0.681762\pi$
$594$		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	0.998508	−	0.0546064i	$-0.0173904\pi$
$599$	162165.	+	280878.i	0.451963	+	0.782824i	−0.546545	+	0.837430i	$0.684057\pi$
$600$		0			0
$601$		−	66322.0i		−	0.183615i	−0.995777	−	0.0918076i	$-0.970736\pi$
$601$		−	66322.0i		−	0.183615i	0.995777	−	0.0918076i	$-0.0292645\pi$
$602$		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	0.947962	−	0.318383i	$-0.103140\pi$
$607$	422322.	+	243828.i	1.14622	+	0.661768i	0.198253	+	0.980151i	$0.436473\pi$
$608$		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	0.998654	−	0.0518597i	$-0.0165149\pi$
$613$	170755.	+	295757.i	0.454415	+	0.787070i	−0.544239	+	0.838930i	$0.683182\pi$
$614$		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	−0.315340	−	0.948979i	$-0.602119\pi$
$619$	133658.	−	77167.4i	0.348830	−	0.201397i	0.664170	+	0.747582i	$0.268785\pi$
$620$		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	0.898855	+	0.438247i	$0.144400\pi$
$641$	340604.	+	589943.i	0.828960	+	1.43580i	−0.0698947	+	0.997554i	$0.522266\pi$
$642$		0			0
$643$			572102.i			1.38373i	0.722027	+	0.691865i	$0.243211\pi$
$643$			572102.i			1.38373i	−0.722027	+	0.691865i	$0.756789\pi$
$644$		0			0
$645$	−920716.			−2.21313
$646$		0			0
$647$	525915.	−	303637.i	1.25634	−	0.725348i	0.283979	−	0.958830i	$-0.408345\pi$
$647$	525915.	−	303637.i	1.25634	−	0.725348i	0.972361	+	0.233482i	$0.0750120\pi$
$648$		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	−0.428416	−	0.903581i	$-0.640928\pi$
$653$	242335.	−	419737.i	0.568316	−	0.984353i	0.996733	−	0.0807713i	$-0.0257383\pi$
$654$		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	−0.693985	−	0.719989i	$-0.744147\pi$
$661$	−182392.	+	105304.i	−0.417449	+	0.241014i	0.276536	+	0.961003i	$0.410813\pi$
$662$		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	0.913411	−	0.407039i	$-0.133439\pi$
$677$	466400.	+	269276.i	1.01761	+	0.587517i	0.104199	+	0.994556i	$0.466772\pi$
$678$		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	0.788526	−	0.615001i	$-0.210845\pi$
$683$	−64535.9	−	111779.i	−0.138344	−	0.239618i	−0.926870	+	0.375383i	$0.877511\pi$
$684$		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	0.376754	−	0.926313i	$-0.377040\pi$
$691$	−113201.	−	65356.6i	−0.237079	−	0.136878i	−0.613834	+	0.789435i	$0.710373\pi$
$692$		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	0.103783	+	0.994600i	$0.466905\pi$
$709$	−406899.	+	704770.i	−0.809458	+	1.40202i	−0.913240	+	0.407422i	$0.866428\pi$
$710$		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	0.809038	−	0.587757i	$-0.199989\pi$
$719$	364222.	+	210283.i	0.704544	+	0.406769i	−0.104494	+	0.994526i	$0.533322\pi$
$720$		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	$0.0523147\pi$
$727$			172948.i			0.327225i	−0.986525	+	0.163613i	$0.947685\pi$
$728$		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	0.602267	−	0.798295i	$-0.294264\pi$
$733$	113936.	+	65780.9i	0.212057	+	0.122431i	−0.390210	+	0.920726i	$0.627598\pi$
$734$		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	0.549877	−	0.835246i	$-0.314675\pi$
$739$	−244884.	−	424151.i	−0.448406	−	0.776662i	−0.998282	+	0.0585842i	$0.981341\pi$
$740$		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	−0.604386	−	0.796692i	$-0.706581\pi$
$751$	218698.	−	378797.i	0.387763	−	0.671624i	0.992148	+	0.125067i	$0.0399147\pi$
$752$		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	−0.0703180	−	0.997525i	$-0.522401\pi$
$761$	−561376.	−	324111.i	−0.969359	−	0.559659i	−0.899041	+	0.437865i	$0.855735\pi$
$762$		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	$0.0485143\pi$
$769$			179564.i			0.303646i	−0.988408	+	0.151823i	$0.951486\pi$
$770$		0			0
$771$	1.61830e6			2.72239
$772$		0			0
$773$	529068.	−	305457.i	0.885426	−	0.511201i	0.0129823	−	0.999916i	$-0.495867\pi$
$773$	529068.	−	305457.i	0.885426	−	0.511201i	0.872444	+	0.488715i	$0.162534\pi$
$774$		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	−0.696342	+	0.717710i	$0.745190\pi$
$787$	−1.03191e6	+	595774.i	−1.66607	+	0.961905i	−0.969726	+	0.244195i	$0.921476\pi$
$788$		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	$0.250771\pi$
$797$			900495.i			1.41764i	−0.705392	+	0.708818i	$0.749229\pi$
$798$		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	0.571798	−	0.820395i	$-0.306246\pi$
$809$	−277882.	−	481306.i	−0.424584	−	0.735401i	−0.996381	+	0.0849939i	$0.972913\pi$
$810$		0			0
$811$			70954.2i			0.107879i	0.998544	+	0.0539395i	$0.0171778\pi$
$811$			70954.2i			0.107879i	−0.998544	+	0.0539395i	$0.982822\pi$
$812$		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	−0.535720	−	0.844396i	$-0.679960\pi$
$821$	312356.	−	541016.i	0.463408	−	0.802646i	0.999128	+	0.0417495i	$0.0132931\pi$
$822$		0			0
$823$	−105029.	−	181916.i	−0.155064	−	0.268579i	0.778018	−	0.628242i	$-0.216225\pi$
$823$	−105029.	−	181916.i	−0.155064	−	0.268579i	−0.933082	+	0.359663i	$0.882892\pi$
$824$		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	−0.644595	+	0.764524i	$0.722974\pi$
$829$	−1.11951e6	+	646349.i	−1.62899	+	0.940498i	−0.984395	+	0.175974i	$0.943692\pi$
$830$		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	$0.291274\pi$
$839$			1.11586e6i			1.58520i	−0.609741	+	0.792601i	$0.708726\pi$
$840$		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	$0.346650\pi$
$853$			1.28959e6i			1.77236i	−0.463341	+	0.886180i	$0.653350\pi$
$854$		0			0
$855$	−1.64145e6			−2.24540
$856$		0			0
$857$	−566854.	+	327273.i	−0.771809	+	0.445604i	−0.833519	−	0.552490i	$-0.813678\pi$
$857$	−566854.	+	327273.i	−0.771809	+	0.445604i	0.0617109	+	0.998094i	$0.480344\pi$
$858$		0			0
$859$	−211796.	−	122281.i	−0.287033	−	0.165718i	0.349570	−	0.936910i	$-0.386328\pi$
$859$	−211796.	−	122281.i	−0.287033	−	0.165718i	−0.636603	+	0.771192i	$0.719661\pi$
$860$		0			0
$861$	−780266.	+	311875.i	−1.05253	+	0.420702i
$862$		0			0
$863$	−232638.	+	402942.i	−0.312363	+	0.541029i	−0.978873	−	0.204467i	$-0.934454\pi$
$863$	−232638.	+	402942.i	−0.312363	+	0.541029i	0.666510	+	0.745496i	$0.267787\pi$
$864$		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	−0.947795	−	0.318882i	$-0.896693\pi$
$877$	−152086.	+	263420.i	−0.197738	+	0.342492i	0.750057	+	0.661373i	$0.230026\pi$
$878$		0			0
$879$	−674078.	−	1.16754e6i	−0.872434	−	1.51110i
$880$		0			0
$881$			697876.i			0.899138i	0.893246	+	0.449569i	$0.148422\pi$
$881$			697876.i			0.899138i	−0.893246	+	0.449569i	$0.851578\pi$
$882$		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	0.993286	−	0.115687i	$-0.0369070\pi$
$887$	1.09340e6	+	631278.i	1.38974	+	0.802367i	0.396455	+	0.918054i	$0.370240\pi$
$888$		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	0.995639	+	0.0932848i	$0.0297367\pi$
$907$	475990.	+	824439.i	0.578607	+	1.00218i	−0.417033	+	0.908891i	$0.636930\pi$
$908$		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	−0.978449	−	0.206491i	$-0.933796\pi$
$919$	−262150.	+	454057.i	−0.310398	+	0.537625i	0.668050	+	0.744116i	$0.267129\pi$
$920$		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	0.903108	−	0.429414i	$-0.141280\pi$
$929$	848178.	+	489696.i	0.982779	+	0.567408i	0.0796709	+	0.996821i	$0.474613\pi$
$930$		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	$-0.775123\pi$
$937$		−	1.13988e6i		−	1.29831i	0.760656	−	0.649155i	$-0.224877\pi$
$938$		0			0
$939$	267368.			0.303235
$940$		0			0
$941$	693791.	−	400561.i	0.783519	−	0.452365i	−0.0541569	−	0.998532i	$-0.517247\pi$
$941$	693791.	−	400561.i	0.783519	−	0.452365i	0.837676	+	0.546167i	$0.183914\pi$
$942$		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	−0.611676	−	0.791108i	$-0.709504\pi$
$947$	340143.	−	589145.i	0.379282	−	0.656935i	0.990958	+	0.134173i	$0.0428378\pi$
$948$		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	0.109136	−	0.994027i	$-0.465192\pi$
$971$	−657301.	−	379493.i	−0.697149	−	0.402499i	−0.806285	+	0.591528i	$0.798525\pi$
$972$		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	−0.985037	−	0.172345i	$-0.944866\pi$
$977$	−612591.	−	1.06104e6i	−0.641773	−	1.11158i	0.343263	−	0.939239i	$-0.388468\pi$
$978$		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	0.146120	−	0.989267i	$-0.453322\pi$
$983$	1.03964e6	−	600236.i	1.07591	−	0.621177i	0.929790	+	0.368090i	$0.119988\pi$
$984$		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	0.797134	+	0.603802i	$0.206348\pi$
$991$	904963.	+	1.56744e6i	0.921475	+	1.59604i	0.124340	+	0.992240i	$0.460318\pi$
$992$		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	−0.136719	−	0.990610i	$-0.543656\pi$
$997$	648903.	−	374644.i	0.652814	−	0.376902i	0.789534	+	0.613707i	$0.210323\pi$
$998$		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.33.2		4
4.3	odd	2		14.5.d.a.5.1	yes	4
7.2	even	3		784.5.c.b.97.4		4
7.3	odd	6	inner	112.5.s.b.17.2		4
7.5	odd	6		784.5.c.b.97.1		4
12.11	even	2		126.5.n.a.19.2		4
20.3	even	4		350.5.i.a.299.3		8
20.7	even	4		350.5.i.a.299.2		8
20.19	odd	2		350.5.k.a.201.2		4
28.3	even	6		14.5.d.a.3.1	✓	4
28.11	odd	6		98.5.d.a.31.1		4
28.19	even	6		98.5.b.b.97.4		4
28.23	odd	6		98.5.b.b.97.3		4
28.27	even	2		98.5.d.a.19.1		4
84.23	even	6		882.5.c.b.685.2		4
84.47	odd	6		882.5.c.b.685.1		4
84.59	odd	6		126.5.n.a.73.2		4
140.3	odd	12		350.5.i.a.199.2		8
140.59	even	6		350.5.k.a.101.2		4
140.87	odd	12		350.5.i.a.199.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.5.d.a.3.1	✓	4	28.3	even	6
14.5.d.a.5.1	yes	4	4.3	odd	2
98.5.b.b.97.3		4	28.23	odd	6
98.5.b.b.97.4		4	28.19	even	6
98.5.d.a.19.1		4	28.27	even	2
98.5.d.a.31.1		4	28.11	odd	6
112.5.s.b.17.2		4	7.3	odd	6	inner
112.5.s.b.33.2		4	1.1	even	1	trivial
126.5.n.a.19.2		4	12.11	even	2
126.5.n.a.73.2		4	84.59	odd	6
350.5.i.a.199.2		8	140.3	odd	12
350.5.i.a.199.3		8	140.87	odd	12
350.5.i.a.299.2		8	20.7	even	4
350.5.i.a.299.3		8	20.3	even	4
350.5.k.a.101.2		4	140.59	even	6
350.5.k.a.201.2		4	20.19	odd	2
784.5.c.b.97.1		4	7.5	odd	6
784.5.c.b.97.4		4	7.2	even	3
882.5.c.b.685.1		4	84.47	odd	6
882.5.c.b.685.2		4	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:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	112.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(12.9853 - 7.49706i) q^{3} +(21.9853 + 12.6932i) q^{5} +(7.00000 - 48.4974i) q^{7} +(71.9117 - 124.555i) q^{9} +O(q^{10})\)	\(q+(12.9853 - 7.49706i) q^{3} +(21.9853 + 12.6932i) q^{5} +(7.00000 - 48.4974i) q^{7} +(71.9117 - 124.555i) q^{9} +(21.9853 + 38.0796i) q^{11} +162.507i q^{13} +380.647 q^{15} +(93.7355 - 54.1182i) q^{17} +(-389.338 - 224.784i) q^{19} +(-272.691 - 682.232i) q^{21} +(-217.911 + 377.433i) q^{23} +(9.73506 + 16.8616i) q^{25} -941.981i q^{27} +742.118 q^{29} +(900.175 - 519.716i) q^{31} +(570.970 + 329.650i) q^{33} +(769.485 - 977.377i) q^{35} +(-493.338 + 854.486i) q^{37} +(1218.32 + 2110.20i) q^{39} -1143.70i q^{41} -2418.82 q^{43} +(3162.00 - 1825.58i) q^{45} +(1165.17 + 672.714i) q^{47} +(-2303.00 - 678.964i) q^{49} +(811.455 - 1405.48i) q^{51} +(1783.10 + 3088.42i) q^{53} +1116.26i q^{55} -6740.88 q^{57} +(-3710.93 + 2142.50i) q^{59} +(-1209.57 - 698.345i) q^{61} +(-5537.20 - 4359.41i) q^{63} +(-2062.73 + 3572.76i) q^{65} +(3632.89 + 6292.36i) q^{67} +6534.77i q^{69} -5987.76 q^{71} +(-500.123 + 288.746i) q^{73} +(252.825 + 145.969i) q^{75} +(2000.66 - 799.672i) q^{77} +(-1573.12 + 2724.72i) q^{79} +(-1237.24 - 2142.95i) q^{81} +4729.96i q^{83} +2747.74 q^{85} +(9636.61 - 5563.70i) q^{87} +(-725.651 - 418.955i) q^{89} +(7881.16 + 1137.55i) q^{91} +(7792.69 - 13497.3i) q^{93} +(-5706.47 - 9883.89i) q^{95} +5622.23i q^{97} +6323.99 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 18 q^{3} + 54 q^{5} + 28 q^{7} + 84 q^{9}+O(q^{10}) \) 4 * q + 18 * q^3 + 54 * q^5 + 28 * q^7 + 84 * q^9	\( 4 q + 18 q^{3} + 54 q^{5} + 28 q^{7} + 84 q^{9} + 54 q^{11} + 708 q^{15} + 918 q^{17} - 30 q^{19} - 378 q^{21} + 486 q^{23} - 572 q^{25} + 3240 q^{29} + 546 q^{31} + 1062 q^{33} + 1890 q^{35} - 446 q^{37} + 3312 q^{39} - 2344 q^{43} + 5724 q^{45} - 702 q^{47} - 9212 q^{49} - 318 q^{51} + 2754 q^{53} - 17460 q^{57} - 12366 q^{59} + 7686 q^{61} - 6468 q^{63} - 3024 q^{65} + 5062 q^{67} - 18792 q^{71} - 17274 q^{73} + 5220 q^{75} + 4914 q^{77} - 794 q^{79} - 4338 q^{81} + 10380 q^{85} + 12276 q^{87} - 12474 q^{89} - 2688 q^{91} + 18918 q^{93} - 8910 q^{95} + 11448 q^{99}+O(q^{100}) \) 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

L-functions

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