LMFDB - Embedded newform 126.5.n.a.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,5,Mod(19,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("126.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	126.n (of order $6$, degree $2$, 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:	$13.0246153486$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			73.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	126.73
Dual form			126.5.n.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41421 + 2.44949i) q^{2} +(-4.00000 + 6.92820i) q^{4} +(-21.9853 + 12.6932i) q^{5} +(-7.00000 - 48.4974i) q^{7} -22.6274 q^{8} +O(q^{10})$	\(q+(1.41421 + 2.44949i) q^{2} +(-4.00000 + 6.92820i) q^{4} +(-21.9853 + 12.6932i) q^{5} +(-7.00000 - 48.4974i) q^{7} -22.6274 q^{8} +(-62.1838 - 35.9018i) q^{10} +(21.9853 - 38.0796i) q^{11} -162.507i q^{13} +(108.894 - 85.7321i) q^{14} +(-32.0000 - 55.4256i) q^{16} +(-93.7355 - 54.1182i) q^{17} +(389.338 - 224.784i) q^{19} -203.091i q^{20} +124.368 q^{22} +(-217.911 - 377.433i) q^{23} +(9.73506 - 16.8616i) q^{25} +(398.059 - 229.819i) q^{26} +(364.000 + 145.492i) q^{28} -742.118 q^{29} +(-900.175 - 519.716i) q^{31} +(90.5097 - 156.767i) q^{32} -306.139i q^{34} +(769.485 + 977.377i) q^{35} +(-493.338 - 854.486i) q^{37} +(1101.21 + 635.786i) q^{38} +(497.470 - 287.215i) q^{40} -1143.70i q^{41} +2418.82 q^{43} +(175.882 + 304.637i) q^{44} +(616.346 - 1067.54i) q^{46} +(1165.17 - 672.714i) q^{47} +(-2303.00 + 678.964i) q^{49} +55.0698 q^{50} +(1125.88 + 650.027i) q^{52} +(-1783.10 + 3088.42i) q^{53} +1116.26i q^{55} +(158.392 + 1097.37i) q^{56} +(-1049.51 - 1817.81i) q^{58} +(-3710.93 - 2142.50i) q^{59} +(-1209.57 + 698.345i) q^{61} -2939.96i q^{62} +512.000 q^{64} +(2062.73 + 3572.76i) q^{65} +(-3632.89 + 6292.36i) q^{67} +(749.884 - 432.946i) q^{68} +(-1305.86 + 3267.07i) q^{70} -5987.76 q^{71} +(-500.123 - 288.746i) q^{73} +(1395.37 - 2416.85i) q^{74} +3596.55i q^{76} +(-2000.66 - 799.672i) q^{77} +(1573.12 + 2724.72i) q^{79} +(1407.06 + 812.365i) q^{80} +(2801.47 - 1617.43i) q^{82} -4729.96i q^{83} +2747.74 q^{85} +(3420.73 + 5924.88i) q^{86} +(-497.470 + 861.644i) q^{88} +(725.651 - 418.955i) q^{89} +(-7881.16 + 1137.55i) q^{91} +3486.58 q^{92} +(3295.61 + 1902.72i) q^{94} +(-5706.47 + 9883.89i) q^{95} -5622.23i q^{97} +(-4920.05 - 4680.97i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{4} - 54 q^{5} - 28 q^{7}+O(q^{10}) $ 4 * q - 16 * q^4 - 54 * q^5 - 28 * q^7	$ 4 q - 16 q^{4} - 54 q^{5} - 28 q^{7} - 96 q^{10} + 54 q^{11} - 128 q^{16} - 918 q^{17} + 30 q^{19} + 192 q^{22} + 486 q^{23} - 572 q^{25} + 1728 q^{26} + 1456 q^{28} - 3240 q^{29} - 546 q^{31} + 1890 q^{35} - 446 q^{37} + 4320 q^{38} + 768 q^{40} + 2344 q^{43} + 432 q^{44} + 3840 q^{46} - 702 q^{47} - 9212 q^{49} + 3456 q^{50} - 384 q^{52} - 2754 q^{53} + 384 q^{58} - 12366 q^{59} + 7686 q^{61} + 2048 q^{64} + 3024 q^{65} - 5062 q^{67} + 7344 q^{68} - 2016 q^{70} - 18792 q^{71} - 17274 q^{73} + 4320 q^{74} - 4914 q^{77} + 794 q^{79} + 3456 q^{80} + 9984 q^{82} + 10380 q^{85} + 10368 q^{86} - 768 q^{88} + 12474 q^{89} + 2688 q^{91} - 7776 q^{92} + 15168 q^{94} - 8910 q^{95}+O(q^{100}) $ 4 * q - 16 * q^4 - 54 * q^5 - 28 * q^7 - 96 * q^10 + 54 * q^11 - 128 * q^16 - 918 * q^17 + 30 * q^19 + 192 * q^22 + 486 * q^23 - 572 * q^25 + 1728 * q^26 + 1456 * q^28 - 3240 * q^29 - 546 * q^31 + 1890 * q^35 - 446 * q^37 + 4320 * q^38 + 768 * q^40 + 2344 * q^43 + 432 * q^44 + 3840 * q^46 - 702 * q^47 - 9212 * q^49 + 3456 * q^50 - 384 * q^52 - 2754 * q^53 + 384 * q^58 - 12366 * q^59 + 7686 * q^61 + 2048 * q^64 + 3024 * q^65 - 5062 * q^67 + 7344 * q^68 - 2016 * q^70 - 18792 * q^71 - 17274 * q^73 + 4320 * q^74 - 4914 * q^77 + 794 * q^79 + 3456 * q^80 + 9984 * q^82 + 10380 * q^85 + 10368 * q^86 - 768 * q^88 + 12474 * q^89 + 2688 * q^91 - 7776 * q^92 + 15168 * q^94 - 8910 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.41421	+	2.44949i	0.353553	+	0.612372i
$2$	1.41421	+	2.44949i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−4.00000	+	6.92820i	−0.250000	+	0.433013i
$5$	−21.9853	+	12.6932i	−0.879411	+	0.507728i	−0.870464	−	0.492232i	$-0.836181\pi$
$5$	−21.9853	+	12.6932i	−0.879411	+	0.507728i	−0.00894701	+	0.999960i	$0.502848\pi$
$6$		0			0
$7$	−7.00000	−	48.4974i	−0.142857	−	0.989743i
$7$	−7.00000	−	48.4974i	−0.142857	−	0.989743i
$8$	−22.6274			−0.353553
$9$		0			0
$10$	−62.1838	−	35.9018i	−0.621838	−	0.359018i
$11$	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	$-0.159650\pi$
$14$	108.894	−	85.7321i	0.555584	−	0.437409i
$15$		0			0
$16$	−32.0000	−	55.4256i	−0.125000	−	0.216506i
$17$	−93.7355	−	54.1182i	−0.324344	−	0.187260i	0.328983	−	0.944336i	$-0.393294\pi$
$17$	−93.7355	−	54.1182i	−0.324344	−	0.187260i	−0.653327	+	0.757076i	$0.726627\pi$
$18$		0			0
$19$	389.338	−	224.784i	1.07850	−	0.622671i	0.148007	−	0.988986i	$-0.452714\pi$
$19$	389.338	−	224.784i	1.07850	−	0.622671i	0.930491	+	0.366315i	$0.119381\pi$
$20$		−	203.091i		−	0.507728i
$21$		0			0
$22$	124.368			0.256958
$23$	−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
$26$	398.059	−	229.819i	0.588844	−	0.339970i
$27$		0			0
$28$	364.000	+	145.492i	0.464286	+	0.185577i
$29$	−742.118			−0.882423			−0.441212	−	0.897403i	$-0.645451\pi$
$29$	−742.118			−0.882423			−0.441212	+	0.897403i	$0.645451\pi$
$30$		0			0
$31$	−900.175	−	519.716i	−0.936707	−	0.540808i	−0.0477804	−	0.998858i	$-0.515215\pi$
$31$	−900.175	−	519.716i	−0.936707	−	0.540808i	−0.888926	+	0.458050i	$0.848548\pi$
$32$	90.5097	−	156.767i	0.0883883	−	0.153093i
$33$		0			0
$34$		−	306.139i		−	0.264826i
$35$	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	$0.950681\pi$
$38$	1101.21	+	635.786i	0.762613	+	0.440295i
$39$		0			0
$40$	497.470	−	287.215i	0.310919	−	0.179509i
$41$		−	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	$-0.273052\pi$
$43$	2418.82			1.30818			0.654089	+	0.756418i	$0.273052\pi$
$44$	175.882	+	304.637i	0.0908483	+	0.157354i
$45$		0			0
$46$	616.346	−	1067.54i	0.291279	−	0.504510i
$47$	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
$50$	55.0698			0.0220279
$51$		0			0
$52$	1125.88	+	650.027i	0.416376	+	0.240395i
$53$	−1783.10	+	3088.42i	−0.634782	+	1.09947i	0.351780	+	0.936083i	$0.385577\pi$
$53$	−1783.10	+	3088.42i	−0.634782	+	1.09947i	−0.986561	+	0.163391i	$0.947757\pi$
$54$		0			0
$55$			1116.26i			0.369010i
$56$	158.392	+	1097.37i	0.0505076	+	0.349927i
$57$		0			0
$58$	−1049.51	−	1817.81i	−0.311984	−	0.540372i
$59$	−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	$0.393429\pi$
$62$		−	2939.96i		−	0.764818i
$63$		0			0
$64$	512.000			0.125000
$65$	2062.73	+	3572.76i	0.488221	+	0.845623i
$66$		0			0
$67$	−3632.89	+	6292.36i	−0.809288	+	1.40173i	0.104070	+	0.994570i	$0.466813\pi$
$67$	−3632.89	+	6292.36i	−0.809288	+	1.40173i	−0.913358	+	0.407158i	$0.866520\pi$
$68$	749.884	−	432.946i	0.162172	−	0.0936301i
$69$		0			0
$70$	−1305.86	+	3267.07i	−0.266502	+	0.666748i
$71$	−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	$0.683922\pi$
$74$	1395.37	−	2416.85i	0.254815	−	0.441353i
$75$		0			0
$76$			3596.55i			0.622671i
$77$	−2000.66	−	799.672i	−0.337436	−	0.134875i
$78$		0			0
$79$	1573.12	+	2724.72i	0.252061	+	0.436583i	0.964093	−	0.265564i	$-0.0855582\pi$
$79$	1573.12	+	2724.72i	0.252061	+	0.436583i	−0.712032	+	0.702147i	$0.752225\pi$
$80$	1407.06	+	812.365i	0.219853	+	0.126932i
$81$		0			0
$82$	2801.47	−	1617.43i	0.416637	−	0.240546i
$83$		−	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
$86$	3420.73	+	5924.88i	0.462511	+	0.801092i
$87$		0			0
$88$	−497.470	+	861.644i	−0.0642394	+	0.111266i
$89$	725.651	−	418.955i	0.0916110	−	0.0528916i	−0.453495	−	0.891259i	$-0.649823\pi$
$89$	725.651	−	418.955i	0.0916110	−	0.0528916i	0.545106	+	0.838367i	$0.316490\pi$
$90$		0			0
$91$	−7881.16	+	1137.55i	−0.951716	+	0.137368i
$92$	3486.58			0.411931
$93$		0			0
$94$	3295.61	+	1902.72i	0.372975	+	0.215337i
$95$	−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	$-0.0965759\pi$
$98$	−4920.05	−	4680.97i	−0.512292	−	0.487398i
$99$		0			0
$100$	77.8805	+	134.893i	0.00778805	+	0.0134893i
$101$	5703.21	+	3292.75i	0.559083	+	0.322787i	0.752778	−	0.658275i	$-0.228714\pi$
$101$	5703.21	+	3292.75i	0.559083	+	0.322787i	−0.193694	+	0.981062i	$0.562047\pi$
$102$		0			0
$103$	1320.25	−	762.249i	0.124447	−	0.0718492i	−0.436484	−	0.899712i	$-0.643777\pi$
$103$	1320.25	−	762.249i	0.124447	−	0.0718492i	0.560931	+	0.827863i	$0.310443\pi$
$104$			3677.11i			0.339970i
$105$		0			0
$106$	−10086.7			−0.897717
$107$	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	$-0.0330902\pi$
$110$	−2734.26	+	1578.62i	−0.225972	+	0.130465i
$111$		0			0
$112$	−2464.00	+	1939.90i	−0.196429	+	0.154647i
$113$	8811.30			0.690054			0.345027	−	0.938593i	$-0.387870\pi$
$113$	8811.30			0.690054			0.345027	+	0.938593i	$0.387870\pi$
$114$		0			0
$115$	9581.68	+	5531.99i	0.724513	+	0.418298i
$116$	2968.47	−	5141.54i	0.220606	−	0.382100i
$117$		0			0
$118$		−	12119.8i		−	0.870427i
$119$	−1968.45	+	4924.76i	−0.139005	+	0.347769i
$120$		0			0
$121$	6353.79	+	11005.1i	0.433973	+	0.751663i
$122$	−3421.18	−	1975.22i	−0.229856	−	0.132707i
$123$		0			0
$124$	7201.40	−	4157.73i	0.468353	−	0.270404i
$125$		−	15372.2i		−	0.983823i
$126$		0			0
$127$	3992.70			0.247548			0.123774	−	0.992310i	$-0.460500\pi$
$127$	3992.70			0.247548			0.123774	+	0.992310i	$0.460500\pi$
$128$	724.077	+	1254.14i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−5834.29	+	10105.3i	−0.345224	+	0.597946i
$131$	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
$134$	−20550.7			−1.14451
$135$		0			0
$136$	2120.99	+	1224.56i	0.114673	+	0.0662065i
$137$	12528.9	−	21700.6i	0.667530	−	1.15620i	−0.311062	−	0.950389i	$-0.600685\pi$
$137$	12528.9	−	21700.6i	0.667530	−	1.15620i	0.978593	−	0.205807i	$-0.0659818\pi$
$138$		0			0
$139$		−	20070.1i		−	1.03877i	−0.854541	−	0.519385i	$-0.826161\pi$
$139$		−	20070.1i		−	1.03877i	0.854541	−	0.519385i	$-0.173839\pi$
$140$	−9849.41	+	1421.64i	−0.502521	+	0.0725326i
$141$		0			0
$142$	−8467.98	−	14667.0i	−0.419955	−	0.727384i
$143$	−6188.20	−	3572.76i	−0.302616	−	0.174716i
$144$		0			0
$145$	16315.7	−	9419.86i	0.776013	−	0.448031i
$146$		−	1633.40i		−	0.0766277i
$147$		0			0
$148$	7893.40			0.360364
$149$	−21353.9	−	36986.1i	−0.961846	−	1.66597i	−0.717860	−	0.696188i	$-0.754878\pi$
$149$	−21353.9	−	36986.1i	−0.961846	−	1.66597i	−0.243986	−	0.969779i	$-0.578455\pi$
$150$		0			0
$151$	−14803.7	+	25640.8i	−0.649258	+	1.12455i	0.334043	+	0.942558i	$0.391587\pi$
$151$	−14803.7	+	25640.8i	−0.649258	+	1.12455i	−0.983301	+	0.181989i	$0.941746\pi$
$152$	−8809.71	+	5086.29i	−0.381307	+	0.220147i
$153$		0			0
$154$	−870.573	−	6031.50i	−0.0367082	−	0.254322i
$155$	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	$0.586819\pi$
$158$	−4449.44	+	7706.66i	−0.178234	+	0.308711i
$159$		0			0
$160$			4595.43i			0.179509i
$161$	−16779.2	+	13210.2i	−0.647319	+	0.509632i
$162$		0			0
$163$	−10765.6	−	18646.5i	−0.405193	−	0.701814i	0.589151	−	0.808023i	$-0.299462\pi$
$163$	−10765.6	−	18646.5i	−0.405193	−	0.701814i	−0.994344	+	0.106209i	$0.966129\pi$
$164$	7923.75	+	4574.78i	0.294607	+	0.170092i
$165$		0			0
$166$	11586.0	−	6689.17i	0.420452	−	0.242748i
$167$			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
$170$	3885.88	+	6730.55i	0.134460	+	0.232891i
$171$		0			0
$172$	−9675.28	+	16758.1i	−0.327044	+	0.566458i
$173$	34972.8	−	20191.5i	1.16852	−	0.674648i	0.215192	−	0.976572i	$-0.430962\pi$
$173$	34972.8	−	20191.5i	1.16852	−	0.674648i	0.953332	+	0.301924i	$0.0976289\pi$
$174$		0			0
$175$	−885.891	−	354.094i	−0.0289270	−	0.0115623i
$176$	−2814.12			−0.0908483
$177$		0			0
$178$	2052.45	+	1184.98i	0.0647788	+	0.0374000i
$179$	−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	$-0.310087\pi$
$182$	−13932.1	−	17696.1i	−0.420603	−	0.534238i
$183$		0			0
$184$	4930.77	+	8540.34i	0.145639	+	0.252255i
$185$	21692.3	+	12524.1i	0.633815	+	0.365934i
$186$		0			0
$187$	−4121.60	+	2379.61i	−0.117864	+	0.0680491i
$188$			10763.4i			0.304533i
$189$		0			0
$190$	−32280.6			−0.894201
$191$	−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	$0.924812\pi$
$194$	13771.6	−	7951.03i	0.365915	−	0.211261i
$195$		0			0
$196$	4508.00	−	18671.5i	0.117347	−	0.486035i
$197$	1456.28			0.0375242			0.0187621	−	0.999824i	$-0.494027\pi$
$197$	1456.28			0.0375242			0.0187621	+	0.999824i	$0.494027\pi$
$198$		0			0
$199$	59546.3	+	34379.1i	1.50366	+	0.868137i	0.999991	+	0.00423890i	$0.00134929\pi$
$199$	59546.3	+	34379.1i	1.50366	+	0.868137i	0.503667	+	0.863898i	$0.331984\pi$
$200$	−220.279	+	381.535i	−0.00550698	+	0.00953838i
$201$		0			0
$202$			18626.6i			0.456490i
$203$	5194.82	+	35990.8i	0.126060	+	0.873372i
$204$		0			0
$205$	14517.2	+	25144.5i	0.345441	+	0.598322i
$206$	3734.24	+	2155.96i	0.0879970	+	0.0508051i
$207$		0			0
$208$	−9007.04	+	5200.22i	−0.208188	+	0.120197i
$209$		−	19767.8i		−	0.452549i
$210$		0			0
$211$	−622.821			−0.0139894			−0.00699469	−	0.999976i	$-0.502226\pi$
$211$	−622.821			−0.0139894			−0.00699469	+	0.999976i	$0.502226\pi$
$212$	−14264.8	−	24707.4i	−0.317391	−	0.549737i
$213$		0			0
$214$	−15000.0	+	25980.8i	−0.327540	+	0.567316i
$215$	−53178.5	+	30702.6i	−1.15043	+	0.664199i
$216$		0			0
$217$	−18903.7	+	47294.2i	−0.401446	+	1.00436i
$218$	39463.0			0.830380
$219$		0			0
$220$	−7733.64	−	4465.02i	−0.159786	−	0.0922525i
$221$	−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	$-0.0369190\pi$
$224$	−8236.38	−	3292.11i	−0.164150	−	0.0656113i
$225$		0			0
$226$	12461.1	+	21583.2i	0.243971	+	0.422570i
$227$	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	$0.464905\pi$
$230$			31293.6i			0.591562i
$231$		0			0
$232$	16792.2			0.311984
$233$	−27550.9	−	47719.6i	−0.507486	−	0.878992i	−0.999962	−	0.00866633i	$-0.997241\pi$
$233$	−27550.9	−	47719.6i	−0.507486	−	0.878992i	0.492476	−	0.870326i	$-0.336092\pi$
$234$		0			0
$235$	−17077.8	+	29579.6i	−0.309240	+	0.535620i
$236$	29687.4	−	17140.0i	0.533026	−	0.307743i
$237$		0			0
$238$	−14846.9	+	2142.97i	−0.262110	+	0.0378323i
$239$	−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	$0.418854\pi$
$242$	−17971.2	+	31127.1i	−0.306865	+	0.531506i
$243$		0			0
$244$		−	11173.5i		−	0.187677i
$245$	42013.9	−	44159.7i	0.699940	−	0.735688i
$246$		0			0
$247$	−36529.0	−	63270.0i	−0.598747	−	1.03706i
$248$	20368.6	+	11759.8i	0.331176	+	0.191204i
$249$		0			0
$250$	37654.1	−	21739.6i	0.602466	−	0.347834i
$251$		−	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
$254$	5646.53	+	9780.08i	0.0875214	+	0.151592i
$255$		0			0
$256$	−2048.00	+	3547.24i	−0.0312500	+	0.0541266i
$257$	−93469.3	+	53964.5i	−1.41515	+	0.817038i	−0.995868	−	0.0908179i	$-0.971052\pi$
$257$	−93469.3	+	53964.5i	−1.41515	+	0.817038i	−0.419283	+	0.907856i	$0.637719\pi$
$258$		0			0
$259$	−37987.0	+	29907.0i	−0.566286	+	0.445834i
$260$	−33003.7			−0.488221
$261$		0			0
$262$	49540.9	+	28602.5i	0.721708	+	0.416678i
$263$	−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
$266$	23125.5	−	57856.5i	0.326834	−	0.817690i
$267$		0			0
$268$	−29063.1	−	50338.8i	−0.404644	−	0.700864i
$269$	−91239.0	−	52676.9i	−1.26089	−	0.727973i	−0.287641	−	0.957738i	$-0.592871\pi$
$269$	−91239.0	−	52676.9i	−1.26089	−	0.727973i	−0.973246	+	0.229765i	$0.926204\pi$
$270$		0			0
$271$	−13189.3	+	7614.84i	−0.179590	+	0.103687i	−0.587100	−	0.809514i	$-0.699731\pi$
$271$	−13189.3	+	7614.84i	−0.179590	+	0.103687i	0.407510	+	0.913201i	$0.366397\pi$
$272$			6927.13i			0.0936301i
$273$		0			0
$274$	70874.0			0.944030
$275$	−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	$0.146176\pi$
$278$	49161.4	−	28383.4i	0.636114	−	0.367260i
$279$		0			0
$280$	−17411.5	−	22115.5i	−0.222085	−	0.282086i
$281$	155117.			1.96448			0.982240	−	0.187631i	$-0.0600810\pi$
$281$	155117.			1.96448			0.982240	+	0.187631i	$0.0600810\pi$
$282$		0			0
$283$	−94970.0	−	54831.0i	−1.18581	−	0.684626i	−0.228456	−	0.973554i	$-0.573368\pi$
$283$	−94970.0	−	54831.0i	−1.18581	−	0.684626i	−0.957351	+	0.288929i	$0.906701\pi$
$284$	23951.1	−	41484.4i	0.296953	−	0.514338i
$285$		0			0
$286$		−	20210.6i		−	0.247085i
$287$	−55466.3	+	8005.87i	−0.673388	+	0.0971952i
$288$		0			0
$289$	−35902.9	−	62185.7i	−0.429867	−	0.744552i
$290$	46147.7	+	26643.4i	0.548724	+	0.316806i
$291$		0			0
$292$	4000.99	−	2309.97i	0.0469247	−	0.0270920i
$293$		−	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
$296$	11163.0	+	19334.8i	0.127408	+	0.220677i
$297$		0			0
$298$	60398.1	−	104613.i	0.680128	−	1.17802i
$299$	−61335.5	+	35412.1i	−0.686072	+	0.396104i
$300$		0			0
$301$	−16931.7	−	117307.i	−0.186883	−	1.29476i
$302$	−83742.5			−0.918189
$303$		0			0
$304$	−24917.6	−	14386.2i	−0.269624	−	0.155668i
$305$	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	$0.729267\pi$
$308$	13542.9	−	10662.3i	0.142762	−	0.112396i
$309$		0			0
$310$	37317.5	+	64635.9i	0.388320	+	0.672590i
$311$	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	$0.304325\pi$
$314$			34611.6i			0.351045i
$315$		0			0
$316$	−25169.8			−0.252061
$317$	40402.6	+	69979.4i	0.402060	+	0.696388i	0.993974	−	0.109613i	$-0.0349610\pi$
$317$	40402.6	+	69979.4i	0.402060	+	0.696388i	−0.591914	+	0.806001i	$0.701628\pi$
$318$		0			0
$319$	−16315.7	+	28259.6i	−0.160333	+	0.277705i
$320$	−11256.5	+	6498.92i	−0.109926	+	0.0634660i
$321$		0			0
$322$	−56087.5	−	22418.4i	−0.540946	−	0.216218i
$323$	−48659.7			−0.466406
$324$		0			0
$325$	−2740.13	−	1582.01i	−0.0259421	−	0.0149777i
$326$	30449.6	−	52740.3i	0.286514	−	0.496258i
$327$		0			0
$328$			25878.9i			0.240546i
$329$	−40781.1	−	51799.0i	−0.376762	−	0.478552i
$330$		0			0
$331$	−36402.1	−	63050.3i	−0.332254	−	0.575482i	0.650699	−	0.759336i	$-0.274476\pi$
$331$	−36402.1	−	63050.3i	−0.332254	−	0.575482i	−0.982954	+	0.183854i	$0.941143\pi$
$332$	32770.1	+	18919.8i	0.297305	+	0.171649i
$333$		0			0
$334$	−40609.9	+	23446.1i	−0.364031	+	0.210174i
$335$		−	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	$0.311916\pi$
$338$	3044.13	+	5272.58i	0.0266458	+	0.0461519i
$339$		0			0
$340$	−10990.9	+	19036.9i	−0.0950773	+	0.164679i
$341$	−39581.2	+	22852.2i	−0.340393	+	0.196526i
$342$		0			0
$343$	49049.0	+	106937.i	0.416910	+	0.908948i
$344$	−54731.7			−0.462511
$345$		0			0
$346$	98917.9	+	57110.3i	0.826271	+	0.477048i
$347$	−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	$-0.0334176\pi$
$350$	−385.489	−	2670.75i	−0.00314685	−	0.0218020i
$351$		0			0
$352$	−3979.76	−	6893.15i	−0.0321197	−	0.0556330i
$353$	48995.9	+	28287.8i	0.393197	+	0.227013i	0.683545	−	0.729909i	$-0.260437\pi$
$353$	48995.9	+	28287.8i	0.393197	+	0.227013i	−0.290347	+	0.956921i	$0.593771\pi$
$354$		0			0
$355$	131643.	−	76003.9i	1.04458	−	0.603086i
$356$			6703.27i			0.0528916i
$357$		0			0
$358$	−151305.			−1.18056
$359$	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
$362$	132767.	−	76653.3i	1.01315	−	0.584943i
$363$		0			0
$364$	23643.5	−	59152.5i	0.178447	−	0.446447i
$365$	14660.5			0.110043
$366$		0			0
$367$	9367.27	+	5408.20i	0.0695474	+	0.0401532i	0.534370	−	0.845250i	$-0.320549\pi$
$367$	9367.27	+	5408.20i	0.0695474	+	0.0401532i	−0.464823	+	0.885404i	$0.653882\pi$
$368$	−13946.3	+	24155.7i	−0.102983	+	0.178371i
$369$		0			0
$370$			70846.9i			0.517508i
$371$	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	$0.797771\pi$
$374$	−11657.7	−	6730.55i	−0.0833428	−	0.0481180i
$375$		0			0
$376$	−26364.9	+	15221.8i	−0.186488	+	0.107669i
$377$			120599.i			0.848519i
$378$		0			0
$379$	−98527.5			−0.685929			−0.342964	−	0.939348i	$-0.611431\pi$
$379$	−98527.5			−0.685929			−0.342964	+	0.939348i	$0.611431\pi$
$380$	−45651.7	−	79071.1i	−0.316148	−	0.547584i
$381$		0			0
$382$	1702.53	−	2948.87i	0.0116673	−	0.0202083i
$383$	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
$386$	−145135.			−0.974086
$387$		0			0
$388$	38951.9	+	22488.9i	0.258741	+	0.149384i
$389$	43141.0	−	74722.4i	0.285096	−	0.493801i	−0.687537	−	0.726150i	$-0.741308\pi$
$389$	43141.0	−	74722.4i	0.285096	−	0.493801i	0.972632	+	0.232349i	$0.0746412\pi$
$390$		0			0
$391$			47171.9i			0.308553i
$392$	52110.9	−	15363.2i	0.339123	−	0.0999792i
$393$		0			0
$394$	2059.48	+	3567.13i	0.0132668	+	0.0229788i
$395$	−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	$0.498041\pi$
$398$			194478.i			1.22773i
$399$		0			0
$400$	−1246.09			−0.00778805
$401$	17307.2	+	29977.0i	0.107631	+	0.186423i	0.914810	−	0.403884i	$-0.132340\pi$
$401$	17307.2	+	29977.0i	0.107631	+	0.186423i	−0.807179	+	0.590307i	$0.799007\pi$
$402$		0			0
$403$	−84457.5	+	146285.i	−0.520030	+	0.900718i
$404$	−45625.7	+	26342.0i	−0.279542	+	0.161393i
$405$		0			0
$406$	−80812.5	+	63623.3i	−0.490260	+	0.385980i
$407$	−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	$-0.720572\pi$
$410$	−41060.7	+	71119.3i	−0.244264	+	0.423077i
$411$		0			0
$412$			12196.0i			0.0718492i
$413$	−77929.4	+	194968.i	−0.456879	+	1.14304i
$414$		0			0
$415$	60038.3	+	103989.i	0.348604	+	0.603800i
$416$	−25475.8	−	14708.4i	−0.147211	−	0.0849924i
$417$		0			0
$418$	48421.0	−	27955.9i	0.277128	−	0.160000i
$419$		−	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	$0.522628\pi$
$422$	−880.802	−	1525.59i	−0.00494599	−	0.00856671i
$423$		0			0
$424$	40347.0	−	69883.0i	0.224429	−	0.388723i
$425$	−1825.04	+	1053.69i	−0.0101040	+	0.00583357i
$426$		0			0
$427$	42334.9	+	53772.6i	0.232190	+	0.294920i
$428$	−84853.0			−0.463212
$429$		0			0
$430$	−150411.	−	86840.1i	−0.813474	−	0.469660i
$431$	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	$0.959622\pi$
$434$	−142580.	+	20579.7i	−0.756973	+	0.109260i
$435$		0			0
$436$	55809.1	+	96664.1i	0.293584	+	0.508502i
$437$	−169682.	−	97966.0i	−0.888532	−	0.512994i
$438$		0			0
$439$	95101.7	−	54907.0i	0.493469	−	0.284904i	−0.232544	−	0.972586i	$-0.574705\pi$
$439$	95101.7	−	54907.0i	0.493469	−	0.284904i	0.726012	+	0.687682i	$0.241372\pi$
$440$		−	25258.0i		−	0.130465i
$441$		0			0
$442$	−49749.7			−0.254651
$443$	−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
$446$	28193.0	−	16277.2i	0.141733	−	0.0818297i
$447$		0			0
$448$	−3584.00	−	24830.7i	−0.0178571	−	0.123718i
$449$	330438.			1.63907			0.819534	−	0.573030i	$-0.194232\pi$
$449$	330438.			1.63907			0.819534	+	0.573030i	$0.194232\pi$
$450$		0			0
$451$	−43551.5	−	25144.5i	−0.214116	−	0.123620i
$452$	−35245.2	+	61046.4i	−0.172513	+	0.298802i
$453$		0			0
$454$			159430.i			0.773499i
$455$	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	$0.481450\pi$
$458$	−103193.	−	59578.7i	−0.491950	−	0.284027i
$459$		0			0
$460$	−76653.4	+	44255.9i	−0.362256	+	0.209149i
$461$		−	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	$-0.523447\pi$
$463$	−31552.7			−0.147189			−0.0735944	+	0.997288i	$0.523447\pi$
$464$	23747.8	+	41132.3i	0.110303	+	0.191050i
$465$		0			0
$466$	77925.8	−	134971.i	0.358847	−	0.621541i
$467$	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
$470$	−96606.6			−0.437332
$471$		0			0
$472$	83968.7	+	48479.3i	0.376906	+	0.217607i
$473$	53178.5	−	92107.8i	0.237691	−	0.411694i
$474$		0			0
$475$		−	8753.16i		−	0.0387951i
$476$	−26245.9	−	33336.8i	−0.115837	−	0.147133i
$477$		0			0
$478$	−32643.5	−	56540.3i	−0.142870	−	0.247458i
$479$	−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
$482$			230722.i			0.993104i
$483$		0			0
$484$	−101661.			−0.433973
$485$	71364.1	+	123606.i	0.303387	+	0.525481i
$486$		0			0
$487$	203873.	−	353119.i	0.859611	−	1.48889i	−0.0126891	−	0.999919i	$-0.504039\pi$
$487$	203873.	−	353119.i	0.859611	−	1.48889i	0.872300	−	0.488971i	$-0.162628\pi$
$488$	27369.4	−	15801.7i	0.114928	−	0.0663537i
$489$		0			0
$490$	167585.	+	40461.3i	0.697981	+	0.168519i
$491$	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
$494$	103320.	−	178955.i	0.423378	−	0.733313i
$495$		0			0
$496$			66523.7i			0.270404i
$497$	41914.3	+	290391.i	0.169687	+	1.17563i
$498$		0			0
$499$	−175718.	−	304352.i	−0.705690	−	1.22229i	−0.966442	−	0.256886i	$-0.917304\pi$
$499$	−175718.	−	304352.i	−0.705690	−	1.22229i	0.260751	−	0.965406i	$-0.416030\pi$
$500$	106502.	+	61488.9i	0.426008	+	0.245956i
$501$		0			0
$502$	66644.7	−	38477.3i	0.264459	−	0.152685i
$503$		−	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
$506$	−27101.1	−	46940.5i	−0.105849	−	0.183335i
$507$		0			0
$508$	−15970.8	+	27662.2i	−0.0618870	+	0.107191i
$509$	−72030.7	+	41586.9i	−0.278024	+	0.160517i	−0.632528	−	0.774537i	$-0.717983\pi$
$509$	−72030.7	+	41586.9i	−0.278024	+	0.160517i	0.354505	+	0.935054i	$0.384649\pi$
$510$		0			0
$511$	−10502.6	+	26275.9i	−0.0402212	+	0.100627i
$512$	−11585.2			−0.0441942
$513$		0			0
$514$	−264371.	−	152635.i	−1.00066	−	0.577733i
$515$	−19350.8	+	33516.5i	−0.0729598	+	0.126370i
$516$		0			0
$517$		−	59159.2i		−	0.221330i
$518$	−126979.	−	50753.9i	−0.473229	−	0.189151i
$519$		0			0
$520$	−46674.3	−	80842.3i	−0.172612	−	0.298973i
$521$	−174948.	−	101006.i	−0.644517	−	0.372112i	0.141835	−	0.989890i	$-0.454700\pi$
$521$	−174948.	−	101006.i	−0.644517	−	0.372112i	−0.786352	+	0.617778i	$0.788033\pi$
$522$		0			0
$523$	−24134.0	+	13933.8i	−0.0882321	+	0.0509408i	−0.543467	−	0.839431i	$-0.682889\pi$
$523$	−24134.0	+	13933.8i	−0.0882321	+	0.0509408i	0.455235	+	0.890371i	$0.349555\pi$
$524$			161800.i			0.589272i
$525$		0			0
$526$	−113545.			−0.410389
$527$	56252.3	+	97431.8i	0.202544	+	0.350816i
$528$		0			0
$529$	44949.9	−	77855.5i	0.160626	−	0.278213i
$530$	221760.	−	128033.i	0.789462	−	0.455796i
$531$		0			0
$532$	174423.	−	25175.8i	0.616284	−	0.0889530i
$533$	−185858.			−0.654226
$534$		0			0
$535$	−233190.	−	134632.i	−0.814707	−	0.470372i
$536$	82203.0	−	142380.i	0.286126	−	0.495586i
$537$		0			0
$538$		−	297985.i		−	1.02951i
$539$	−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	$0.812659\pi$
$542$	−37305.0	−	21538.0i	−0.126990	−	0.0733175i
$543$		0			0
$544$	−16967.9	+	9796.44i	−0.0573365	+	0.0331032i
$545$			354198.i			1.19249i
$546$		0			0
$547$	360160.			1.20371			0.601854	−	0.798606i	$-0.294429\pi$
$547$	360160.			1.20371			0.601854	+	0.798606i	$0.294429\pi$
$548$	100231.	+	173605.i	0.333765	+	0.578098i
$549$		0			0
$550$	1210.73	−	2097.04i	0.00400240	−	0.00693236i
$551$	−288934.	+	166816.i	−0.951691	+	0.549459i
$552$		0			0
$553$	121130.	−	95365.1i	0.396097	−	0.311845i
$554$	27921.1			0.0909732
$555$		0			0
$556$	139049.	+	80280.2i	0.449800	+	0.259692i
$557$	155272.	−	268938.i	0.500474	−	0.866847i	−0.499525	−	0.866299i	$-0.666492\pi$
$557$	155272.	−	268938.i	0.500474	−	0.866847i	1.00000		0.000547960i	$-0.000174421\pi$
$558$		0			0
$559$		−	393075.i		−	1.25792i
$560$	29548.2	−	73925.2i	0.0942226	−	0.235731i
$561$		0			0
$562$	219369.	+	379958.i	0.694548	+	1.20299i
$563$	−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
$566$		−	310171.i		−	0.968207i
$567$		0			0
$568$	135488.			0.419955
$569$	−65131.1	−	112810.i	−0.201170	−	0.348437i	0.747736	−	0.663997i	$-0.231141\pi$
$569$	−65131.1	−	112810.i	−0.201170	−	0.348437i	−0.948906	+	0.315560i	$0.897808\pi$
$570$		0			0
$571$	249119.	−	431487.i	0.764073	−	1.32341i	−0.176662	−	0.984272i	$-0.556530\pi$
$571$	249119.	−	431487.i	0.764073	−	1.32341i	0.940735	−	0.339142i	$-0.110137\pi$
$572$	49505.6	−	28582.1i	0.151308	−	0.0873578i
$573$		0			0
$574$	−98051.5	−	124542.i	−0.297598	−	0.378000i
$575$	−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	$0.682791\pi$
$578$	101549.	−	175888.i	0.303962	−	0.526478i
$579$		0			0
$580$			150718.i			0.448031i
$581$	−229391.	+	33109.7i	−0.679554	+	0.0980851i
$582$		0			0
$583$	78404.0	+	135800.i	0.230675	+	0.399541i
$584$	11316.5	+	6533.58i	0.0331808	+	0.0191569i
$585$		0			0
$586$	220240.	−	127155.i	0.641357	−	0.370288i
$587$		−	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
$590$	153840.	+	266458.i	0.441941	+	0.765464i
$591$		0			0
$592$	−31573.6	+	54687.1i	−0.0900909	+	0.156042i
$593$	28872.6	−	16669.6i	0.0821063	−	0.0474041i	−0.458385	−	0.888754i	$-0.651572\pi$
$593$	28872.6	−	16669.6i	0.0821063	−	0.0474041i	0.540491	+	0.841350i	$0.318238\pi$
$594$		0			0
$595$	−19234.1	−	133258.i	−0.0543299	−	0.376409i
$596$	341663.			0.961846
$597$		0			0
$598$	−173483.	−	100160.i	−0.485126	−	0.280088i
$599$	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	$0.970736\pi$
$602$	263396.	−	207371.i	0.726803	−	0.572209i
$603$		0			0
$604$	−118430.	−	205126.i	−0.324629	−	0.562274i
$605$	−279380.	−	161300.i	−0.763281	−	0.440680i
$606$		0			0
$607$	−422322.	+	243828.i	−1.14622	+	0.661768i	−0.947962	−	0.318383i	$-0.896860\pi$
$607$	−422322.	+	243828.i	−1.14622	+	0.661768i	−0.198253	+	0.980151i	$0.563527\pi$
$608$		−	81380.6i		−	0.220147i
$609$		0			0
$610$	100287.			0.269517
$611$	−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	$0.0165149\pi$
$614$	−347047.	+	200368.i	−0.920558	+	0.531484i
$615$		0			0
$616$	45269.8	+	18094.5i	0.119302	+	0.0476854i
$617$	−240873.			−0.632728			−0.316364	−	0.948638i	$-0.602462\pi$
$617$	−240873.			−0.632728			−0.316364	+	0.948638i	$0.602462\pi$
$618$		0			0
$619$	−133658.	−	77167.4i	−0.348830	−	0.201397i	0.315340	−	0.948979i	$-0.397881\pi$
$619$	−133658.	−	77167.4i	−0.348830	−	0.201397i	−0.664170	+	0.747582i	$0.731215\pi$
$620$	−105550.	+	182818.i	−0.274584	+	0.475593i
$621$		0			0
$622$			242242.i			0.626137i
$623$	−25397.8	−	32259.5i	−0.0654364	−	0.0831154i
$624$		0			0
$625$	201207.	+	348501.i	0.515091	+	0.892164i
$626$	43678.2	+	25217.6i	0.111459	+	0.0643510i
$627$		0			0
$628$	−84780.8	+	48948.2i	−0.214970	+	0.124113i
$629$			106794.i			0.269927i
$630$		0			0
$631$	220248.			0.553164			0.276582	−	0.960990i	$-0.410798\pi$
$631$	220248.			0.553164			0.276582	+	0.960990i	$0.410798\pi$
$632$	−35595.5	−	61653.3i	−0.0891172	−	0.154355i
$633$		0			0
$634$	−114276.	+	197932.i	−0.284299	+	0.492421i
$635$	−87780.7	+	50680.2i	−0.217696	+	0.125687i
$636$		0			0
$637$	110336.	+	374253.i	0.271919	+	0.922331i
$638$	−92295.4			−0.226745
$639$		0			0
$640$	−31838.1	−	18381.7i	−0.0777297	−	0.0448773i
$641$	−340604.	+	589943.i	−0.828960	+	1.43580i	0.0698947	+	0.997554i	$0.477734\pi$
$641$	−340604.	+	589943.i	−0.828960	+	1.43580i	−0.898855	+	0.438247i	$0.855600\pi$
$642$		0			0
$643$			572102.i			1.38373i	0.722027	+	0.691865i	$0.243211\pi$
$643$			572102.i			1.38373i	−0.722027	+	0.691865i	$0.756789\pi$
$644$	−24406.1	−	169090.i	−0.0588472	−	0.407705i
$645$		0			0
$646$	−68815.2	−	119191.i	−0.164899	−	0.285614i
$647$	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
$650$		−	8949.23i		−	0.0211816i
$651$		0			0
$652$	172249.			0.405193
$653$	−242335.	−	419737.i	−0.568316	−	0.984353i	−0.996733	−	0.0807713i	$-0.974262\pi$
$653$	−242335.	−	419737.i	−0.568316	−	0.984353i	0.428416	−	0.903581i	$-0.359072\pi$
$654$		0			0
$655$	−256720.	+	444652.i	−0.598380	+	1.03642i
$656$	−63390.0	+	36598.3i	−0.147304	+	0.0850458i
$657$		0			0
$658$	69207.8	−	173148.i	0.159847	−	0.399912i
$659$	−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	$0.744147\pi$
$662$	102961.	−	178333.i	0.234939	−	0.406927i
$663$		0			0
$664$			107027.i			0.242748i
$665$	519288.	+	207562.i	1.17426	+	0.469358i
$666$		0			0
$667$	161716.	+	280100.i	0.363497	+	0.629595i
$668$	−114862.	−	66315.7i	−0.257409	−	0.148615i
$669$		0			0
$670$	451814.	−	260855.i	1.00649	−	0.581098i
$671$			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	$0.466659\pi$
$674$	178951.	+	309952.i	0.393926	+	0.682300i
$675$		0			0
$676$	−8610.09	+	14913.1i	−0.0188414	+	0.0326343i
$677$	−466400.	+	269276.i	−1.01761	+	0.587517i	−0.913411	−	0.407039i	$-0.866561\pi$
$677$	−466400.	+	269276.i	−1.01761	+	0.587517i	−0.104199	+	0.994556i	$0.533228\pi$
$678$		0			0
$679$	−272664.	+	39355.6i	−0.591408	+	0.0853625i
$680$	−62174.1			−0.134460
$681$		0			0
$682$	−111953.	−	64635.9i	−0.240694	−	0.138965i
$683$	−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
$686$	−192575.	+	271377.i	−0.409215	+	0.576666i
$687$		0			0
$688$	−77402.3	−	134065.i	−0.163522	−	0.283229i
$689$	501890.	+	289766.i	1.05723	+	0.610393i
$690$		0			0
$691$	113201.	−	65356.6i	0.237079	−	0.136878i	−0.376754	−	0.926313i	$-0.622960\pi$
$691$	113201.	−	65356.6i	0.237079	−	0.136878i	0.613834	+	0.789435i	$0.289627\pi$
$692$			323064.i			0.674648i
$693$		0			0
$694$	−189361.			−0.393162
$695$	254753.	+	441246.i	0.527413	+	0.913505i
$696$		0			0
$697$	−61894.8	+	107205.i	−0.127406	+	0.220673i
$698$	62529.3	−	36101.3i	0.128343	−	0.0740989i
$699$		0			0
$700$	5996.80	−	4721.26i	0.0122384	−	0.00963522i
$701$	182501.			0.371389			0.185694	−	0.982608i	$-0.440547\pi$
$701$	182501.			0.371389			0.185694	+	0.982608i	$0.440547\pi$
$702$		0			0
$703$	−384150.	−	221789.i	−0.777302	−	0.448776i
$704$	11256.5	−	19496.8i	0.0227121	−	0.0393385i
$705$		0			0
$706$			160020.i			0.321044i
$707$	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	$-0.466905\pi$
$710$	372342.	+	214972.i	0.738627	+	0.426446i
$711$		0			0
$712$	−16419.6	+	9479.86i	−0.0323894	+	0.0187000i
$713$			453008.i			0.891101i
$714$		0			0
$715$	181399.			0.354832
$716$	−213978.	−	370620.i	−0.417390	−	0.722941i
$717$		0			0
$718$	−53464.0	+	92602.4i	−0.103708	+	0.179628i
$719$	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
$722$	203055.			0.389528
$723$		0			0
$724$	375523.	+	216808.i	0.716406	+	0.413617i
$725$	−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	$0.947685\pi$
$728$	178330.	−	25739.8i	0.336483	−	0.0485671i
$729$		0			0
$730$	20733.0	+	35910.7i	0.0389061	+	0.0673873i
$731$	−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	$0.294264\pi$
$734$			30593.4i			0.0567852i
$735$		0			0
$736$	−78892.3			−0.145639
$737$	159740.	+	276678.i	0.294090	+	0.509378i
$738$		0			0
$739$	244884.	−	424151.i	0.448406	−	0.776662i	−0.549877	−	0.835246i	$-0.685325\pi$
$739$	244884.	−	424151.i	0.448406	−	0.776662i	0.998282	+	0.0585842i	$0.0186586\pi$
$740$	−173539.	+	100193.i	−0.316908	+	0.182967i
$741$		0			0
$742$	70607.2	+	489181.i	0.128245	+	0.888509i
$743$	−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
$746$	−43873.7	+	75991.5i	−0.0788364	+	0.136549i
$747$		0			0
$748$		−	38073.7i		−	0.0680491i
$749$	408355.	−	321496.i	0.727904	−	0.573076i
$750$		0			0
$751$	−218698.	−	378797.i	−0.387763	−	0.671624i	0.604386	−	0.796692i	$-0.293419\pi$
$751$	−218698.	−	378797.i	−0.387763	−	0.671624i	−0.992148	+	0.125067i	$0.960085\pi$
$752$	−74571.2	−	43053.7i	−0.131867	−	0.0761333i
$753$		0			0
$754$	−295407.	+	170553.i	−0.519610	+	0.299997i
$755$		−	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	$0.506714\pi$
$758$	−139339.	−	241342.i	−0.242512	−	0.420044i
$759$		0			0
$760$	129123.	−	223647.i	0.223550	−	0.387200i
$761$	561376.	−	324111.i	0.969359	−	0.559659i	0.0703180	−	0.997525i	$-0.477599\pi$
$761$	561376.	−	324111.i	0.969359	−	0.559659i	0.899041	+	0.437865i	$0.144265\pi$
$762$		0			0
$763$	−634828.	−	253743.i	−1.09045	−	0.435859i
$764$	9630.98			0.0165000
$765$		0			0
$766$	12598.5	+	7273.77i	0.0214715	+	0.0123966i
$767$	−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	$-0.0485143\pi$
$770$	95698.9	+	121554.i	0.161408	+	0.205016i
$771$		0			0
$772$	−205252.	−	355506.i	−0.344391	−	0.596503i
$773$	−529068.	−	305457.i	−0.885426	−	0.511201i	−0.0129823	−	0.999916i	$-0.504133\pi$
$773$	−529068.	−	305457.i	−0.885426	−	0.511201i	−0.872444	+	0.488715i	$0.837466\pi$
$774$		0			0
$775$	−17526.5	+	10118.9i	−0.0291805	+	0.0168474i
$776$			127216.i			0.211261i
$777$		0			0
$778$	244042.			0.403186
$779$	−257085.	−	445284.i	−0.423644	−	0.733773i
$780$		0			0
$781$	−131643.	+	228012.i	−0.215821	+	0.373814i
$782$	−115547.	+	66711.1i	−0.188949	+	0.109090i
$783$		0			0
$784$	111328.	+	105918.i	0.181122	+	0.172321i
$785$	−310655.			−0.504126
$786$		0			0
$787$	1.03191e6	+	595774.i	1.66607	+	0.961905i	0.969726	+	0.244195i	$0.0785236\pi$
$787$	1.03191e6	+	595774.i	1.66607	+	0.961905i	0.696342	+	0.717710i	$0.254810\pi$
$788$	−5825.10	+	10089.4i	−0.00938104	+	0.0162484i
$789$		0			0
$790$		−	225911.i		−	0.361979i
$791$	−61679.1	−	427325.i	−0.0985791	−	0.682976i
$792$		0			0
$793$	113486.	+	196563.i	0.180466	+	0.312576i
$794$	−381939.	−	220513.i	−0.605834	−	0.349778i
$795$		0			0
$796$	−476371.	+	275033.i	−0.751829	+	0.434069i
$797$			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
$800$	−1762.23	−	3052.28i	−0.00275349	−	0.00476919i
$801$		0			0
$802$	−48952.2	+	84787.8i	−0.0761069	+	0.131821i
$803$	−21990.7	+	12696.3i	−0.0341042	+	0.0196901i
$804$		0			0
$805$	201215.	−	503411.i	0.310505	−	0.776838i
$806$	−477764.			−0.735433
$807$		0			0
$808$	−129049.	−	74506.4i	−0.197666	−	0.114122i
$809$	277882.	−	481306.i	0.424584	−	0.735401i	−0.571798	−	0.820395i	$-0.693754\pi$
$809$	277882.	−	481306.i	0.424584	−	0.735401i	0.996381	+	0.0849939i	$0.0270871\pi$
$810$		0			0
$811$			70954.2i			0.107879i	0.998544	+	0.0539395i	$0.0171778\pi$
$811$			70954.2i			0.107879i	−0.998544	+	0.0539395i	$0.982822\pi$
$812$	−270131.	−	107972.i	−0.409696	−	0.163757i
$813$		0			0
$814$	−61355.2	−	106270.i	−0.0925982	−	0.160385i
$815$	473368.	+	273299.i	0.712662	+	0.411455i
$816$		0			0
$817$	941738.	−	543713.i	1.41087	−	0.814564i
$818$		−	887527.i		−	1.32640i
$819$		0			0
$820$	−232275.			−0.345441
$821$	−312356.	−	541016.i	−0.463408	−	0.802646i	0.535720	−	0.844396i	$-0.320040\pi$
$821$	−312356.	−	541016.i	−0.463408	−	0.802646i	−0.999128	+	0.0417495i	$0.986707\pi$
$822$		0			0
$823$	105029.	−	181916.i	0.155064	−	0.268579i	−0.778018	−	0.628242i	$-0.783775\pi$
$823$	105029.	−	181916.i	0.155064	−	0.268579i	0.933082	+	0.359663i	$0.117108\pi$
$824$	−29873.9	+	17247.7i	−0.0439985	+	0.0254025i
$825$		0			0
$826$	−587781.	+	84838.8i	−0.861500	+	0.124347i
$827$	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	$-0.722974\pi$
$830$	−169814.	+	294127.i	−0.246500	+	0.426951i
$831$		0			0
$832$		−	83203.5i		−	0.120197i
$833$	252617.	+	60991.2i	0.364060	+	0.0878977i
$834$		0			0
$835$	−210440.	−	364492.i	−0.301825	−	0.522775i
$836$	136955.	+	79071.1i	0.195959	+	0.113137i
$837$		0			0
$838$	17941.9	−	10358.7i	0.0255493	−	0.0147509i
$839$		−	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
$842$	−35607.5	−	61674.1i	−0.0502247	−	0.0869918i
$843$		0			0
$844$	2491.28	−	4315.03i	0.00349734	−	0.00605758i
$845$	−47323.8	+	27322.4i	−0.0662775	+	0.0382653i
$846$		0			0
$847$	489242.	−	385178.i	0.681957	−	0.536902i
$848$	228237.			0.317391
$849$		0			0
$850$	−5162.00	−	2980.28i	−0.00714464	−	0.00412496i
$851$	−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	$-0.346650\pi$
$854$	−71844.7	+	179745.i	−0.0985097	+	0.246457i
$855$		0			0
$856$	−120000.	−	207847.i	−0.163770	−	0.283658i
$857$	566854.	+	327273.i	0.771809	+	0.445604i	0.833519	−	0.552490i	$-0.186322\pi$
$857$	566854.	+	327273.i	0.771809	+	0.445604i	−0.0617109	+	0.998094i	$0.519656\pi$
$858$		0			0
$859$	211796.	−	122281.i	0.287033	−	0.165718i	−0.349570	−	0.936910i	$-0.613672\pi$
$859$	211796.	−	122281.i	0.287033	−	0.165718i	0.636603	+	0.771192i	$0.280339\pi$
$860$		−	491242.i		−	0.664199i
$861$		0			0
$862$	39109.2			0.0526337
$863$	−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
$866$	−116201.	+	67088.6i	−0.154944	+	0.0894567i
$867$		0			0
$868$	−252049.	−	320145.i	−0.334538	−	0.424921i
$869$	138342.			0.183195
$870$		0			0
$871$	1.02255e6	+	590370.i	1.34787	+	0.778194i
$872$	−157852.	+	273407.i	−0.207595	+	0.359565i
$873$		0			0
$874$		−	554179.i		−	0.725484i
$875$	−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	$0.896693\pi$
$878$	268988.	+	155301.i	0.348935	+	0.201458i
$879$		0			0
$880$	61869.1	−	35720.2i	0.0798930	−	0.0461262i
$881$			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	$-0.306215\pi$
$883$	891773.			1.14375			0.571877	+	0.820339i	$0.306215\pi$
$884$	−70356.6	−	121861.i	−0.0900328	−	0.155941i
$885$		0			0
$886$	116758.	−	202232.i	0.148738	−	0.257621i
$887$	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
$890$	−60164.9			−0.0759562
$891$		0			0
$892$	79741.8	+	46039.0i	0.100220	+	0.0578623i
$893$	302431.	−	523826.i	0.379248	−	0.656877i
$894$		0			0
$895$		−	1.35803e6i		−	1.69537i
$896$	55754.0	−	43894.9i	0.0694480	−	0.0546761i
$897$		0			0
$898$	467310.	+	809404.i	0.579498	+	1.00372i
$899$	668036.	+	385691.i	0.826572	+	0.477221i
$900$		0			0
$901$	334280.	−	192997.i	0.411776	−	0.237739i
$902$		−	142239.i		−	0.174825i
$903$		0			0
$904$	−199377.			−0.243971
$905$	687998.	+	1.19165e6i	0.840021	+	1.45496i
$906$		0			0
$907$	−475990.	+	824439.i	−0.578607	+	1.00218i	0.417033	+	0.908891i	$0.363070\pi$
$907$	−475990.	+	824439.i	−0.578607	+	1.00218i	−0.995639	+	0.0932848i	$0.970263\pi$
$908$	−390523.	+	225469.i	−0.473669	+	0.273473i
$909$		0			0
$910$	530920.	+	212211.i	0.641131	+	0.256263i
$911$	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
$914$	−527908.	+	914363.i	−0.631925	+	1.09453i
$915$		0			0
$916$		−	337028.i		−	0.401675i
$917$	−613038.	−	778662.i	−0.729035	−	0.925999i
$918$		0			0
$919$	262150.	+	454057.i	0.310398	+	0.537625i	0.978449	−	0.206491i	$-0.0662043\pi$
$919$	262150.	+	454057.i	0.310398	+	0.537625i	−0.668050	+	0.744116i	$0.732871\pi$
$920$	−216809.	−	125175.i	−0.256154	−	0.147891i
$921$		0			0
$922$	49859.9	−	28786.6i	0.0586529	−	0.0338633i
$923$			973052.i			1.14218i
$924$		0			0
$925$	−19210.7			−0.0224522
$926$	−44622.3	−	77288.1i	−0.0520391	−	0.0901344i
$927$		0			0
$928$	−67168.8	+	116340.i	−0.0779959	+	0.135093i
$929$	−848178.	+	489696.i	−0.982779	+	0.567408i	−0.903108	−	0.429414i	$-0.858720\pi$
$929$	−848178.	+	489696.i	−0.982779	+	0.567408i	−0.0796709	+	0.996821i	$0.525387\pi$
$930$		0			0
$931$	−744024.	+	782024.i	−0.858396	+	0.902237i
$932$	440815.			0.507486
$933$		0			0
$934$	592420.	+	342034.i	0.679103	+	0.392081i
$935$	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	$0.775123\pi$
$938$	143855.	+	996658.i	0.163501	+	1.13277i
$939$		0			0
$940$	−136622.	−	236637.i	−0.154620	−	0.267810i
$941$	−693791.	−	400561.i	−0.783519	−	0.452365i	0.0541569	−	0.998532i	$-0.482753\pi$
$941$	−693791.	−	400561.i	−0.783519	−	0.452365i	−0.837676	+	0.546167i	$0.816086\pi$
$942$		0			0
$943$	−431669.	+	249224.i	−0.485431	+	0.280264i
$944$			274240.i			0.307743i
$945$		0			0
$946$	300823.			0.336146
$947$	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
$950$	21440.8	−	12378.8i	0.0237571	−	0.0137162i
$951$		0			0
$952$	44540.8	−	111435.i	0.0491456	−	0.122955i
$953$	394774.			0.434673			0.217337	−	0.976097i	$-0.430263\pi$
$953$	394774.			0.434673			0.217337	+	0.976097i	$0.430263\pi$
$954$		0			0
$955$	26467.5	+	15281.0i	0.0290206	+	0.0167550i
$956$	92329.9	−	159920.i	0.101024	−	0.174979i
$957$		0			0
$958$		−	769567.i		−	0.838524i
$959$	−1.14013e6	−	455714.i	−1.23970	−	0.495513i
$960$		0			0
$961$	78449.9	+	135879.i	0.0849465	+	0.147132i
$962$	−392755.	−	226757.i	−0.424396	−	0.245025i
$963$		0			0
$964$	−565151.	+	326290.i	−0.608150	+	0.351115i
$965$		−	1.30265e6i		−	1.39886i
$966$		0			0
$967$	−604328.			−0.646279			−0.323140	−	0.946351i	$-0.604738\pi$
$967$	−604328.			−0.646279			−0.323140	+	0.946351i	$0.604738\pi$
$968$	−143770.	−	249017.i	−0.153433	−	0.265753i
$969$		0			0
$970$	−201848.	+	349611.i	−0.214527	+	0.371571i
$971$	−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
$974$	1.15328e6			1.21567
$975$		0			0
$976$	77412.4	+	44694.1i	0.0812664	+	0.0469192i
$977$	612591.	−	1.06104e6i	0.641773	−	1.11158i	−0.343263	−	0.939239i	$-0.611532\pi$
$977$	612591.	−	1.06104e6i	0.641773	−	1.11158i	0.985037	−	0.172345i	$-0.0551344\pi$
$978$		0			0
$979$		−	36843.3i		−	0.0384409i
$980$	137892.	+	467719.i	0.143577	+	0.487005i
$981$		0			0
$982$	405557.	+	702446.i	0.420561	+	0.728434i
$983$	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
$986$			227191.i			0.233689i
$987$		0			0
$988$	584464.			0.598747
$989$	−527088.	−	912944.i	−0.538878	−	0.933365i
$990$		0			0
$991$	−904963.	+	1.56744e6i	−0.921475	+	1.59604i	−0.124340	+	0.992240i	$0.539682\pi$
$991$	−904963.	+	1.56744e6i	−0.921475	+	1.59604i	−0.797134	+	0.603802i	$0.793652\pi$
$992$	−162949.	+	94078.7i	−0.165588	+	0.0956022i
$993$		0			0
$994$	−652034.	+	513344.i	−0.659929	+	0.519560i
$995$	−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	$0.543656\pi$
$998$	497004.	−	860837.i	0.498998	−	0.864291i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.5.n.a.73.2		4
3.2	odd	2		14.5.d.a.3.1	✓	4
7.3	odd	6		882.5.c.b.685.2		4
7.4	even	3		882.5.c.b.685.1		4
7.5	odd	6	inner	126.5.n.a.19.2		4
12.11	even	2		112.5.s.b.17.2		4
15.2	even	4		350.5.i.a.199.3		8
15.8	even	4		350.5.i.a.199.2		8
15.14	odd	2		350.5.k.a.101.2		4
21.2	odd	6		98.5.d.a.19.1		4
21.5	even	6		14.5.d.a.5.1	yes	4
21.11	odd	6		98.5.b.b.97.4		4
21.17	even	6		98.5.b.b.97.3		4
21.20	even	2		98.5.d.a.31.1		4
84.11	even	6		784.5.c.b.97.1		4
84.47	odd	6		112.5.s.b.33.2		4
84.59	odd	6		784.5.c.b.97.4		4
105.47	odd	12		350.5.i.a.299.2		8
105.68	odd	12		350.5.i.a.299.3		8
105.89	even	6		350.5.k.a.201.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.5.d.a.3.1	✓	4	3.2	odd	2
14.5.d.a.5.1	yes	4	21.5	even	6
98.5.b.b.97.3		4	21.17	even	6
98.5.b.b.97.4		4	21.11	odd	6
98.5.d.a.19.1		4	21.2	odd	6
98.5.d.a.31.1		4	21.20	even	2
112.5.s.b.17.2		4	12.11	even	2
112.5.s.b.33.2		4	84.47	odd	6
126.5.n.a.19.2		4	7.5	odd	6	inner
126.5.n.a.73.2		4	1.1	even	1	trivial
350.5.i.a.199.2		8	15.8	even	4
350.5.i.a.199.3		8	15.2	even	4
350.5.i.a.299.2		8	105.47	odd	12
350.5.i.a.299.3		8	105.68	odd	12
350.5.k.a.101.2		4	15.14	odd	2
350.5.k.a.201.2		4	105.89	even	6
784.5.c.b.97.1		4	84.11	even	6
784.5.c.b.97.4		4	84.59	odd	6
882.5.c.b.685.1		4	7.4	even	3
882.5.c.b.685.2		4	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	126.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41421 + 2.44949i) q^{2} +(-4.00000 + 6.92820i) q^{4} +(-21.9853 + 12.6932i) q^{5} +(-7.00000 - 48.4974i) q^{7} -22.6274 q^{8} +O(q^{10})\)	\(q+(1.41421 + 2.44949i) q^{2} +(-4.00000 + 6.92820i) q^{4} +(-21.9853 + 12.6932i) q^{5} +(-7.00000 - 48.4974i) q^{7} -22.6274 q^{8} +(-62.1838 - 35.9018i) q^{10} +(21.9853 - 38.0796i) q^{11} -162.507i q^{13} +(108.894 - 85.7321i) q^{14} +(-32.0000 - 55.4256i) q^{16} +(-93.7355 - 54.1182i) q^{17} +(389.338 - 224.784i) q^{19} -203.091i q^{20} +124.368 q^{22} +(-217.911 - 377.433i) q^{23} +(9.73506 - 16.8616i) q^{25} +(398.059 - 229.819i) q^{26} +(364.000 + 145.492i) q^{28} -742.118 q^{29} +(-900.175 - 519.716i) q^{31} +(90.5097 - 156.767i) q^{32} -306.139i q^{34} +(769.485 + 977.377i) q^{35} +(-493.338 - 854.486i) q^{37} +(1101.21 + 635.786i) q^{38} +(497.470 - 287.215i) q^{40} -1143.70i q^{41} +2418.82 q^{43} +(175.882 + 304.637i) q^{44} +(616.346 - 1067.54i) q^{46} +(1165.17 - 672.714i) q^{47} +(-2303.00 + 678.964i) q^{49} +55.0698 q^{50} +(1125.88 + 650.027i) q^{52} +(-1783.10 + 3088.42i) q^{53} +1116.26i q^{55} +(158.392 + 1097.37i) q^{56} +(-1049.51 - 1817.81i) q^{58} +(-3710.93 - 2142.50i) q^{59} +(-1209.57 + 698.345i) q^{61} -2939.96i q^{62} +512.000 q^{64} +(2062.73 + 3572.76i) q^{65} +(-3632.89 + 6292.36i) q^{67} +(749.884 - 432.946i) q^{68} +(-1305.86 + 3267.07i) q^{70} -5987.76 q^{71} +(-500.123 - 288.746i) q^{73} +(1395.37 - 2416.85i) q^{74} +3596.55i q^{76} +(-2000.66 - 799.672i) q^{77} +(1573.12 + 2724.72i) q^{79} +(1407.06 + 812.365i) q^{80} +(2801.47 - 1617.43i) q^{82} -4729.96i q^{83} +2747.74 q^{85} +(3420.73 + 5924.88i) q^{86} +(-497.470 + 861.644i) q^{88} +(725.651 - 418.955i) q^{89} +(-7881.16 + 1137.55i) q^{91} +3486.58 q^{92} +(3295.61 + 1902.72i) q^{94} +(-5706.47 + 9883.89i) q^{95} -5622.23i q^{97} +(-4920.05 - 4680.97i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{4} - 54 q^{5} - 28 q^{7}+O(q^{10}) \) 4 * q - 16 * q^4 - 54 * q^5 - 28 * q^7	\( 4 q - 16 q^{4} - 54 q^{5} - 28 q^{7} - 96 q^{10} + 54 q^{11} - 128 q^{16} - 918 q^{17} + 30 q^{19} + 192 q^{22} + 486 q^{23} - 572 q^{25} + 1728 q^{26} + 1456 q^{28} - 3240 q^{29} - 546 q^{31} + 1890 q^{35} - 446 q^{37} + 4320 q^{38} + 768 q^{40} + 2344 q^{43} + 432 q^{44} + 3840 q^{46} - 702 q^{47} - 9212 q^{49} + 3456 q^{50} - 384 q^{52} - 2754 q^{53} + 384 q^{58} - 12366 q^{59} + 7686 q^{61} + 2048 q^{64} + 3024 q^{65} - 5062 q^{67} + 7344 q^{68} - 2016 q^{70} - 18792 q^{71} - 17274 q^{73} + 4320 q^{74} - 4914 q^{77} + 794 q^{79} + 3456 q^{80} + 9984 q^{82} + 10380 q^{85} + 10368 q^{86} - 768 q^{88} + 12474 q^{89} + 2688 q^{91} - 7776 q^{92} + 15168 q^{94} - 8910 q^{95}+O(q^{100}) \) 4 * q - 16 * q^4 - 54 * q^5 - 28 * q^7 - 96 * q^10 + 54 * q^11 - 128 * q^16 - 918 * q^17 + 30 * q^19 + 192 * q^22 + 486 * q^23 - 572 * q^25 + 1728 * q^26 + 1456 * q^28 - 3240 * q^29 - 546 * q^31 + 1890 * q^35 - 446 * q^37 + 4320 * q^38 + 768 * q^40 + 2344 * q^43 + 432 * q^44 + 3840 * q^46 - 702 * q^47 - 9212 * q^49 + 3456 * q^50 - 384 * q^52 - 2754 * q^53 + 384 * q^58 - 12366 * q^59 + 7686 * q^61 + 2048 * q^64 + 3024 * q^65 - 5062 * q^67 + 7344 * q^68 - 2016 * q^70 - 18792 * q^71 - 17274 * q^73 + 4320 * q^74 - 4914 * q^77 + 794 * q^79 + 3456 * q^80 + 9984 * q^82 + 10380 * q^85 + 10368 * q^86 - 768 * q^88 + 12474 * q^89 + 2688 * q^91 - 7776 * q^92 + 15168 * q^94 - 8910 * q^95

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