LMFDB - Embedded newform 1050.3.p.b.901.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(451,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1050.451");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.p (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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.3
Root			$-1.72286 - 0.178197i$ of defining polynomial
Character	$\chi$	$=$	1050.901
Dual form			1050.3.p.b.451.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-6.51658 - 2.55620i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(0.707107 - 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-6.51658 - 2.55620i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(-5.79240 - 10.0327i) q^{11} +(3.00000 + 1.73205i) q^{12} -7.86371i q^{13} +(-7.73861 + 6.17364i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-23.9080 + 13.8033i) q^{17} +(-2.12132 - 3.67423i) q^{18} +(27.2149 + 15.7125i) q^{19} +(11.9886 - 1.80922i) q^{21} -16.3834 q^{22} +(9.07959 - 15.7263i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-9.63104 - 5.56049i) q^{26} +5.19615i q^{27} +(2.08911 + 13.8433i) q^{28} -2.30331 q^{29} +(-4.55860 + 2.63191i) q^{31} +(2.82843 + 4.89898i) q^{32} +(17.3772 + 10.0327i) q^{33} +39.0416i q^{34} -6.00000 q^{36} +(0.993142 - 1.72017i) q^{37} +(38.4876 - 22.2208i) q^{38} +(6.81018 + 11.7956i) q^{39} +22.1905i q^{41} +(6.26139 - 15.9623i) q^{42} -49.8368 q^{43} +(-11.5848 + 20.0655i) q^{44} +(-12.8405 - 22.2404i) q^{46} +(66.3956 + 38.3335i) q^{47} -6.92820i q^{48} +(35.9317 + 33.3154i) q^{49} +(23.9080 - 41.4099i) q^{51} +(-13.6204 + 7.86371i) q^{52} +(28.5477 + 49.4461i) q^{53} +(6.36396 + 3.67423i) q^{54} +(18.4317 + 7.23003i) q^{56} -54.4297 q^{57} +(-1.62869 + 2.82097i) q^{58} +(-60.9245 + 35.1748i) q^{59} +(-58.5590 - 33.8091i) q^{61} +7.44416i q^{62} +(-16.4161 + 13.0963i) q^{63} +8.00000 q^{64} +(24.5751 - 14.1884i) q^{66} +(49.0823 + 85.0131i) q^{67} +(47.8160 + 27.6066i) q^{68} +31.4526i q^{69} -34.2597 q^{71} +(-4.24264 + 7.34847i) q^{72} +(-16.8801 + 9.74573i) q^{73} +(-1.40452 - 2.43269i) q^{74} -62.8501i q^{76} +(12.1010 + 80.1856i) q^{77} +19.2621 q^{78} +(-45.2142 + 78.3134i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(27.1777 + 15.6911i) q^{82} +133.803i q^{83} +(-15.1223 - 18.9557i) q^{84} +(-35.2400 + 61.0374i) q^{86} +(3.45496 - 1.99472i) q^{87} +(16.3834 + 28.3768i) q^{88} +(-9.58232 - 5.53235i) q^{89} +(-20.1012 + 51.2445i) q^{91} -36.3184 q^{92} +(4.55860 - 7.89573i) q^{93} +(93.8975 - 54.2118i) q^{94} +(-8.48528 - 4.89898i) q^{96} -72.3112i q^{97} +(66.2104 - 20.4496i) q^{98} -34.7544 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{3} - 8 q^{4} + 12 q^{9}+O(q^{10}) $ 8 * q - 12 * q^3 - 8 * q^4 + 12 * q^9	$ 8 q - 12 q^{3} - 8 q^{4} + 12 q^{9} - 4 q^{11} + 24 q^{12} - 40 q^{14} - 16 q^{16} - 84 q^{17} + 108 q^{19} + 48 q^{22} - 12 q^{23} - 96 q^{26} + 72 q^{29} - 132 q^{31} + 12 q^{33} - 48 q^{36} + 96 q^{37} + 168 q^{38} + 24 q^{39} + 72 q^{42} + 112 q^{43} - 8 q^{44} + 8 q^{46} + 24 q^{47} + 156 q^{49} + 84 q^{51} - 48 q^{52} - 32 q^{53} + 16 q^{56} - 216 q^{57} - 104 q^{58} + 132 q^{59} + 96 q^{61} + 64 q^{64} - 72 q^{66} + 120 q^{67} + 168 q^{68} + 8 q^{71} - 24 q^{73} - 16 q^{74} + 216 q^{77} + 192 q^{78} + 12 q^{79} - 36 q^{81} - 24 q^{82} - 40 q^{86} - 108 q^{87} - 48 q^{88} + 492 q^{89} - 308 q^{91} + 48 q^{92} + 132 q^{93} + 480 q^{94} - 24 q^{99}+O(q^{100}) $ 8 * q - 12 * q^3 - 8 * q^4 + 12 * q^9 - 4 * q^11 + 24 * q^12 - 40 * q^14 - 16 * q^16 - 84 * q^17 + 108 * q^19 + 48 * q^22 - 12 * q^23 - 96 * q^26 + 72 * q^29 - 132 * q^31 + 12 * q^33 - 48 * q^36 + 96 * q^37 + 168 * q^38 + 24 * q^39 + 72 * q^42 + 112 * q^43 - 8 * q^44 + 8 * q^46 + 24 * q^47 + 156 * q^49 + 84 * q^51 - 48 * q^52 - 32 * q^53 + 16 * q^56 - 216 * q^57 - 104 * q^58 + 132 * q^59 + 96 * q^61 + 64 * q^64 - 72 * q^66 + 120 * q^67 + 168 * q^68 + 8 * q^71 - 24 * q^73 - 16 * q^74 + 216 * q^77 + 192 * q^78 + 12 * q^79 - 36 * q^81 - 24 * q^82 - 40 * q^86 - 108 * q^87 - 48 * q^88 + 492 * q^89 - 308 * q^91 + 48 * q^92 + 132 * q^93 + 480 * q^94 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$			2.44949i			0.408248i
$7$	−6.51658	−	2.55620i	−0.930940	−	0.365172i
$7$	−6.51658	−	2.55620i	−0.930940	−	0.365172i
$8$	−2.82843			−0.353553
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	−5.79240	−	10.0327i	−0.526582	−	0.912066i	−0.999520	−	0.0309707i	$-0.990140\pi$
$11$	−5.79240	−	10.0327i	−0.526582	−	0.912066i	0.472939	−	0.881095i	$-0.343193\pi$
$12$	3.00000	+	1.73205i	0.250000	+	0.144338i
$13$		−	7.86371i		−	0.604901i	−0.953165	−	0.302451i	$-0.902195\pi$
$13$		−	7.86371i		−	0.604901i	0.953165	−	0.302451i	$-0.0978047\pi$
$14$	−7.73861	+	6.17364i	−0.552758	+	0.440975i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−23.9080	+	13.8033i	−1.40635	+	0.811959i	−0.995034	−	0.0995321i	$-0.968265\pi$
$17$	−23.9080	+	13.8033i	−1.40635	+	0.811959i	−0.411320	+	0.911491i	$0.634932\pi$
$18$	−2.12132	−	3.67423i	−0.117851	−	0.204124i
$19$	27.2149	+	15.7125i	1.43236	+	0.826974i	0.997301	−	0.0734266i	$-0.0233935\pi$
$19$	27.2149	+	15.7125i	1.43236	+	0.826974i	0.435061	+	0.900401i	$0.356727\pi$
$20$		0			0
$21$	11.9886	−	1.80922i	0.570886	−	0.0861535i
$22$	−16.3834			−0.744699
$23$	9.07959	−	15.7263i	0.394765	−	0.683753i	−0.598306	−	0.801268i	$-0.704159\pi$
$23$	9.07959	−	15.7263i	0.394765	−	0.683753i	0.993071	+	0.117515i	$0.0374927\pi$
$24$	4.24264	−	2.44949i	0.176777	−	0.102062i
$25$		0			0
$26$	−9.63104	−	5.56049i	−0.370425	−	0.213865i
$27$			5.19615i			0.192450i
$28$	2.08911	+	13.8433i	0.0746112	+	0.494402i
$29$	−2.30331			−0.0794244			−0.0397122	−	0.999211i	$-0.512644\pi$
$29$	−2.30331			−0.0794244			−0.0397122	+	0.999211i	$0.512644\pi$
$30$		0			0
$31$	−4.55860	+	2.63191i	−0.147052	+	0.0849003i	−0.571721	−	0.820448i	$-0.693724\pi$
$31$	−4.55860	+	2.63191i	−0.147052	+	0.0849003i	0.424669	+	0.905349i	$0.360391\pi$
$32$	2.82843	+	4.89898i	0.0883883	+	0.153093i
$33$	17.3772	+	10.0327i	0.526582	+	0.304022i
$34$			39.0416i			1.14828i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	0.993142	−	1.72017i	0.0268417	−	0.0464912i	−0.852293	−	0.523065i	$-0.824788\pi$
$37$	0.993142	−	1.72017i	0.0268417	−	0.0464912i	0.879134	+	0.476574i	$0.158122\pi$
$38$	38.4876	−	22.2208i	1.01283	−	0.584759i
$39$	6.81018	+	11.7956i	0.174620	+	0.302451i
$40$		0			0
$41$			22.1905i			0.541233i	0.962687	+	0.270616i	$0.0872275\pi$
$41$			22.1905i			0.541233i	−0.962687	+	0.270616i	$0.912773\pi$
$42$	6.26139	−	15.9623i	0.149081	−	0.380055i
$43$	−49.8368			−1.15900			−0.579498	−	0.814974i	$-0.696751\pi$
$43$	−49.8368			−1.15900			−0.579498	+	0.814974i	$0.696751\pi$
$44$	−11.5848	+	20.0655i	−0.263291	+	0.456033i
$45$		0			0
$46$	−12.8405	−	22.2404i	−0.279141	−	0.483486i
$47$	66.3956	+	38.3335i	1.41267	+	0.815606i	0.995639	−	0.0932854i	$-0.0297369\pi$
$47$	66.3956	+	38.3335i	1.41267	+	0.815606i	0.417032	+	0.908892i	$0.363070\pi$
$48$		−	6.92820i		−	0.144338i
$49$	35.9317	+	33.3154i	0.733300	+	0.679906i
$50$		0			0
$51$	23.9080	−	41.4099i	0.468785	−	0.811959i
$52$	−13.6204	+	7.86371i	−0.261930	+	0.151225i
$53$	28.5477	+	49.4461i	0.538636	+	0.932945i	0.998978	+	0.0452033i	$0.0143935\pi$
$53$	28.5477	+	49.4461i	0.538636	+	0.932945i	−0.460342	+	0.887742i	$0.652273\pi$
$54$	6.36396	+	3.67423i	0.117851	+	0.0680414i
$55$		0			0
$56$	18.4317	+	7.23003i	0.329137	+	0.129108i
$57$	−54.4297			−0.954908
$58$	−1.62869	+	2.82097i	−0.0280808	+	0.0486373i
$59$	−60.9245	+	35.1748i	−1.03262	+	0.596182i	−0.917734	−	0.397196i	$-0.869983\pi$
$59$	−60.9245	+	35.1748i	−1.03262	+	0.596182i	−0.114885	+	0.993379i	$0.536650\pi$
$60$		0			0
$61$	−58.5590	−	33.8091i	−0.959984	−	0.554247i	−0.0638160	−	0.997962i	$-0.520327\pi$
$61$	−58.5590	−	33.8091i	−0.959984	−	0.554247i	−0.896168	+	0.443715i	$0.853660\pi$
$62$			7.44416i			0.120067i
$63$	−16.4161	+	13.0963i	−0.260573	+	0.207877i
$64$	8.00000			0.125000
$65$		0			0
$66$	24.5751	−	14.1884i	0.372349	−	0.214976i
$67$	49.0823	+	85.0131i	0.732572	+	1.26885i	0.955780	+	0.294081i	$0.0950137\pi$
$67$	49.0823	+	85.0131i	0.732572	+	1.26885i	−0.223208	+	0.974771i	$0.571653\pi$
$68$	47.8160	+	27.6066i	0.703177	+	0.405979i
$69$			31.4526i			0.455835i
$70$		0			0
$71$	−34.2597			−0.482531			−0.241266	−	0.970459i	$-0.577563\pi$
$71$	−34.2597			−0.482531			−0.241266	+	0.970459i	$0.577563\pi$
$72$	−4.24264	+	7.34847i	−0.0589256	+	0.102062i
$73$	−16.8801	+	9.74573i	−0.231234	+	0.133503i	−0.611141	−	0.791521i	$-0.709289\pi$
$73$	−16.8801	+	9.74573i	−0.231234	+	0.133503i	0.379907	+	0.925025i	$0.375956\pi$
$74$	−1.40452	−	2.43269i	−0.0189799	−	0.0328742i
$75$		0			0
$76$		−	62.8501i		−	0.826974i
$77$	12.1010	+	80.1856i	0.157155	+	1.04137i
$78$	19.2621			0.246950
$79$	−45.2142	+	78.3134i	−0.572332	+	0.991308i	0.423994	+	0.905665i	$0.360628\pi$
$79$	−45.2142	+	78.3134i	−0.572332	+	0.991308i	−0.996326	+	0.0856432i	$0.972705\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	27.1777	+	15.6911i	0.331436	+	0.191355i
$83$			133.803i			1.61209i	0.591854	+	0.806045i	$0.298396\pi$
$83$			133.803i			1.61209i	−0.591854	+	0.806045i	$0.701604\pi$
$84$	−15.1223	−	18.9557i	−0.180027	−	0.225663i
$85$		0			0
$86$	−35.2400	+	61.0374i	−0.409767	+	0.709737i
$87$	3.45496	−	1.99472i	0.0397122	−	0.0229279i
$88$	16.3834	+	28.3768i	0.186175	+	0.322464i
$89$	−9.58232	−	5.53235i	−0.107666	−	0.0621613i	0.445200	−	0.895431i	$-0.353133\pi$
$89$	−9.58232	−	5.53235i	−0.107666	−	0.0621613i	−0.552866	+	0.833270i	$0.686466\pi$
$90$		0			0
$91$	−20.1012	+	51.2445i	−0.220893	+	0.563127i
$92$	−36.3184			−0.394765
$93$	4.55860	−	7.89573i	0.0490172	−	0.0849003i
$94$	93.8975	−	54.2118i	0.998910	−	0.576721i
$95$		0			0
$96$	−8.48528	−	4.89898i	−0.0883883	−	0.0510310i
$97$		−	72.3112i		−	0.745476i	−0.927937	−	0.372738i	$-0.878419\pi$
$97$		−	72.3112i		−	0.745476i	0.927937	−	0.372738i	$-0.121581\pi$
$98$	66.2104	−	20.4496i	0.675616	−	0.208669i
$99$	−34.7544			−0.351054
$100$		0			0
$101$	43.8670	−	25.3266i	0.434327	−	0.250759i	−0.266861	−	0.963735i	$-0.585987\pi$
$101$	43.8670	−	25.3266i	0.434327	−	0.250759i	0.701188	+	0.712976i	$0.252653\pi$
$102$	−33.8110	−	58.5625i	−0.331481	−	0.574142i
$103$	171.442	+	98.9823i	1.66449	+	0.960993i	0.970531	+	0.240978i	$0.0774682\pi$
$103$	171.442	+	98.9823i	1.66449	+	0.960993i	0.693958	+	0.720015i	$0.255865\pi$
$104$			22.2419i			0.213865i
$105$		0			0
$106$	80.7451			0.761746
$107$	73.9679	−	128.116i	0.691289	−	1.19735i	−0.280127	−	0.959963i	$-0.590377\pi$
$107$	73.9679	−	128.116i	0.691289	−	1.19735i	0.971416	−	0.237384i	$-0.0762900\pi$
$108$	9.00000	−	5.19615i	0.0833333	−	0.0481125i
$109$	27.1610	+	47.0442i	0.249183	+	0.431598i	0.963299	−	0.268429i	$-0.0865046\pi$
$109$	27.1610	+	47.0442i	0.249183	+	0.431598i	−0.714116	+	0.700027i	$0.753171\pi$
$110$		0			0
$111$			3.44035i			0.0309941i
$112$	21.8881	−	17.4617i	0.195429	−	0.155908i
$113$	−47.7883			−0.422906			−0.211453	−	0.977388i	$-0.567819\pi$
$113$	−47.7883			−0.422906			−0.211453	+	0.977388i	$0.567819\pi$
$114$	−38.4876	+	66.6625i	−0.337611	+	0.584759i
$115$		0			0
$116$	2.30331	+	3.98945i	0.0198561	+	0.0343918i
$117$	−20.4305	−	11.7956i	−0.174620	−	0.100817i
$118$			99.4892i			0.843129i
$119$	191.083	−	28.8367i	1.60574	−	0.242325i
$120$		0			0
$121$	−6.60372	+	11.4380i	−0.0545762	+	0.0945288i
$122$	−82.8150	+	47.8132i	−0.678811	+	0.391912i
$123$	−19.2176	−	33.2858i	−0.156240	−	0.270616i
$124$	9.11720	+	5.26382i	0.0735258	+	0.0424501i
$125$		0			0
$126$	4.43168	+	29.3660i	0.0351720	+	0.233063i
$127$	101.973			0.802940			0.401470	−	0.915872i	$-0.368499\pi$
$127$	101.973			0.802940			0.401470	+	0.915872i	$0.368499\pi$
$128$	5.65685	−	9.79796i	0.0441942	−	0.0765466i
$129$	74.7552	−	43.1600i	0.579498	−	0.334573i
$130$		0			0
$131$	−64.6037	−	37.2990i	−0.493158	−	0.284725i	0.232726	−	0.972542i	$-0.425236\pi$
$131$	−64.6037	−	37.2990i	−0.493158	−	0.284725i	−0.725884	+	0.687817i	$0.758569\pi$
$132$		−	40.1309i		−	0.304022i
$133$	−137.184	−	171.959i	−1.03146	−	1.29292i
$134$	138.826			1.03601
$135$		0			0
$136$	67.6221	−	39.0416i	0.497221	−	0.287071i
$137$	−123.449	−	213.821i	−0.901091	−	1.56074i	−0.826080	−	0.563553i	$-0.809434\pi$
$137$	−123.449	−	213.821i	−0.901091	−	1.56074i	−0.0750109	−	0.997183i	$-0.523899\pi$
$138$	38.5215	+	22.2404i	0.279141	+	0.161162i
$139$			155.917i			1.12170i	0.827916	+	0.560852i	$0.189526\pi$
$139$			155.917i			1.12170i	−0.827916	+	0.560852i	$0.810474\pi$
$140$		0			0
$141$	−132.791			−0.941781
$142$	−24.2253	+	41.9594i	−0.170601	+	0.295489i
$143$	−78.8945	+	45.5498i	−0.551710	+	0.318530i
$144$	6.00000	+	10.3923i	0.0416667	+	0.0721688i
$145$		0			0
$146$			27.5651i			0.188802i
$147$	−82.7495	−	18.8553i	−0.562922	−	0.128268i
$148$	−3.97257			−0.0268417
$149$	−81.5452	+	141.240i	−0.547283	+	0.947922i	0.451176	+	0.892435i	$0.351005\pi$
$149$	−81.5452	+	141.240i	−0.547283	+	0.947922i	−0.998459	+	0.0554872i	$0.982329\pi$
$150$		0			0
$151$	37.5149	+	64.9778i	0.248443	+	0.430316i	0.963094	−	0.269165i	$-0.0867477\pi$
$151$	37.5149	+	64.9778i	0.248443	+	0.430316i	−0.714651	+	0.699481i	$0.753414\pi$
$152$	−76.9753	−	44.4417i	−0.506416	−	0.292380i
$153$			82.8198i			0.541306i
$154$	106.764	+	41.8792i	0.693270	+	0.271943i
$155$		0			0
$156$	13.6204	−	23.5911i	0.0873100	−	0.151225i
$157$	194.622	−	112.365i	1.23963	−	0.715702i	0.270614	−	0.962688i	$-0.412773\pi$
$157$	194.622	−	112.365i	1.23963	−	0.715702i	0.969019	+	0.246986i	$0.0794400\pi$
$158$	63.9426	+	110.752i	0.404700	+	0.700961i
$159$	−85.6431	−	49.4461i	−0.538636	−	0.310982i
$160$		0			0
$161$	−99.3675	+	79.2726i	−0.617190	+	0.492376i
$162$	−12.7279			−0.0785674
$163$	−115.059	+	199.288i	−0.705882	+	1.22262i	0.260491	+	0.965476i	$0.416116\pi$
$163$	−115.059	+	199.288i	−0.705882	+	1.22262i	−0.966372	+	0.257147i	$0.917218\pi$
$164$	38.4351	−	22.1905i	0.234361	−	0.135308i
$165$		0			0
$166$	163.875	+	94.6133i	0.987199	+	0.569960i
$167$			277.788i			1.66340i	0.555223	+	0.831702i	$0.312633\pi$
$167$			277.788i			1.66340i	−0.555223	+	0.831702i	$0.687367\pi$
$168$	−33.9089	+	5.11726i	−0.201839	+	0.0304599i
$169$	107.162			0.634095
$170$		0			0
$171$	81.6446	−	47.1375i	0.477454	−	0.275658i
$172$	49.8368	+	86.3199i	0.289749	+	0.501860i
$173$	−109.176	−	63.0327i	−0.631074	−	0.364351i	0.150094	−	0.988672i	$-0.452042\pi$
$173$	−109.176	−	63.0327i	−0.631074	−	0.364351i	−0.781168	+	0.624321i	$0.785376\pi$
$174$		−	5.64193i		−	0.0324249i
$175$		0			0
$176$	46.3392			0.263291
$177$	60.9245	−	105.524i	0.344206	−	0.596182i
$178$	−13.5514	+	7.82393i	−0.0761317	+	0.0439547i
$179$	−38.5535	−	66.7766i	−0.215382	−	0.373053i	0.738008	−	0.674792i	$-0.235766\pi$
$179$	−38.5535	−	66.7766i	−0.215382	−	0.373053i	−0.953391	+	0.301738i	$0.902433\pi$
$180$		0			0
$181$		−	212.012i		−	1.17134i	−0.810551	−	0.585668i	$-0.800832\pi$
$181$		−	212.012i		−	1.17134i	0.810551	−	0.585668i	$-0.199168\pi$
$182$	48.5478	+	60.8542i	0.266746	+	0.334364i
$183$	117.118			0.639989
$184$	−25.6810	+	44.4807i	−0.139570	+	0.241743i
$185$		0			0
$186$	−6.44683	−	11.1662i	−0.0346604	−	0.0600336i
$187$	276.969	+	159.908i	1.48112	+	0.855125i
$188$		−	153.334i		−	0.815606i
$189$	13.2824	−	33.8612i	0.0702773	−	0.179160i
$190$		0			0
$191$	−82.8480	+	143.497i	−0.433759	+	0.751293i	−0.997193	−	0.0748682i	$-0.976146\pi$
$191$	−82.8480	+	143.497i	−0.433759	+	0.751293i	0.563434	+	0.826161i	$0.309480\pi$
$192$	−12.0000	+	6.92820i	−0.0625000	+	0.0360844i
$193$	−52.6497	−	91.1920i	−0.272796	−	0.472497i	0.696780	−	0.717285i	$-0.254615\pi$
$193$	−52.6497	−	91.1920i	−0.272796	−	0.472497i	−0.969577	+	0.244787i	$0.921282\pi$
$194$	−88.5627	−	51.1317i	−0.456509	−	0.263566i
$195$		0			0
$196$	21.7723	−	95.5509i	0.111083	−	0.487504i
$197$	−244.736			−1.24231			−0.621156	−	0.783687i	$-0.713337\pi$
$197$	−244.736			−1.24231			−0.621156	+	0.783687i	$0.713337\pi$
$198$	−24.5751	+	42.5653i	−0.124116	+	0.214976i
$199$	84.8416	−	48.9833i	0.426340	−	0.246147i	−0.271446	−	0.962454i	$-0.587502\pi$
$199$	84.8416	−	48.9833i	0.426340	−	0.246147i	0.697786	+	0.716306i	$0.254169\pi$
$200$		0			0
$201$	−147.247	−	85.0131i	−0.732572	−	0.422951i
$202$		−	71.6346i		−	0.354627i
$203$	15.0097	+	5.88772i	0.0739394	+	0.0290035i
$204$	−95.6321			−0.468785
$205$		0			0
$206$	242.456	−	139.982i	1.17697	−	0.679525i
$207$	−27.2388	−	47.1790i	−0.131588	−	0.227918i
$208$	27.2407	+	15.7274i	0.130965	+	0.0756126i
$209$		−	364.052i		−	1.74188i
$210$		0			0
$211$	−388.914			−1.84319			−0.921597	−	0.388149i	$-0.873114\pi$
$211$	−388.914			−1.84319			−0.921597	+	0.388149i	$0.873114\pi$
$212$	57.0954	−	98.8922i	0.269318	−	0.466473i
$213$	51.3896	−	29.6698i	0.241266	−	0.139295i
$214$	−104.606	−	181.184i	−0.488815	−	0.846652i
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	36.4342	−	5.49835i	0.167899	−	0.0253380i
$218$	76.8228			0.352398
$219$	16.8801	−	29.2372i	0.0770781	−	0.133503i
$220$		0			0
$221$	108.545	+	188.006i	0.491155	+	0.850705i
$222$	4.21355	+	2.43269i	0.0189799	+	0.0109581i
$223$		−	251.913i		−	1.12965i	−0.825210	−	0.564827i	$-0.808943\pi$
$223$		−	251.913i		−	1.12965i	0.825210	−	0.564827i	$-0.191057\pi$
$224$	−5.90890	−	39.1546i	−0.0263790	−	0.174797i
$225$		0			0
$226$	−33.7915	+	58.5285i	−0.149520	+	0.258976i
$227$	−231.941	+	133.911i	−1.02176	+	0.589916i	−0.914615	−	0.404327i	$-0.867506\pi$
$227$	−231.941	+	133.911i	−1.02176	+	0.589916i	−0.107150	+	0.994243i	$0.534173\pi$
$228$	54.4297	+	94.2751i	0.238727	+	0.413487i
$229$	299.237	+	172.765i	1.30671	+	0.754431i	0.981546	−	0.191226i	$-0.0612463\pi$
$229$	299.237	+	172.765i	1.30671	+	0.754431i	0.325167	+	0.945657i	$0.394580\pi$
$230$		0			0
$231$	−87.5942	−	109.799i	−0.379196	−	0.475319i
$232$	6.51474			0.0280808
$233$	−144.032	+	249.471i	−0.618164	+	1.07069i	0.371656	+	0.928370i	$0.378790\pi$
$233$	−144.032	+	249.471i	−0.618164	+	1.07069i	−0.989821	+	0.142321i	$0.954543\pi$
$234$	−28.8931	+	16.6815i	−0.123475	+	0.0712883i
$235$		0			0
$236$	121.849	+	70.3495i	0.516309	+	0.298091i
$237$		−	156.627i		−	0.660872i
$238$	99.7983	−	254.418i	0.419320	−	1.06898i
$239$	−188.810			−0.789999			−0.395000	−	0.918681i	$-0.629255\pi$
$239$	−188.810			−0.789999			−0.395000	+	0.918681i	$0.629255\pi$
$240$		0			0
$241$	84.7389	−	48.9240i	0.351614	−	0.203004i	−0.313782	−	0.949495i	$-0.601596\pi$
$241$	84.7389	−	48.9240i	0.351614	−	0.203004i	0.665396	+	0.746491i	$0.268263\pi$
$242$	9.33908	+	16.1758i	0.0385912	+	0.0668420i
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$			135.236i			0.554247i
$245$		0			0
$246$	−54.3555			−0.220957
$247$	123.559	−	214.010i	0.500238	−	0.866437i
$248$	12.8937	−	7.44416i	0.0519906	−	0.0300168i
$249$	−115.877	−	200.705i	−0.465370	−	0.806045i
$250$		0			0
$251$		−	241.345i		−	0.961533i	−0.876849	−	0.480767i	$-0.840358\pi$
$251$		−	241.345i		−	0.961533i	0.876849	−	0.480767i	$-0.159642\pi$
$252$	39.0995	+	15.3372i	0.155157	+	0.0608619i
$253$	−210.370			−0.831504
$254$	72.1061	−	124.891i	0.283882	−	0.491698i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	10.8807	+	6.28197i	0.0423373	+	0.0244435i	0.521019	−	0.853545i	$-0.325552\pi$
$257$	10.8807	+	6.28197i	0.0423373	+	0.0244435i	−0.478682	+	0.877988i	$0.658885\pi$
$258$		−	122.075i		−	0.473158i
$259$	−10.8690	+	8.67098i	−0.0419653	+	0.0334787i
$260$		0			0
$261$	−3.45496	+	5.98417i	−0.0132374	+	0.0229279i
$262$	−91.3635	+	52.7487i	−0.348716	+	0.201331i
$263$	−106.240	−	184.014i	−0.403956	−	0.699672i	0.590244	−	0.807225i	$-0.299032\pi$
$263$	−106.240	−	184.014i	−0.403956	−	0.699672i	−0.994199	+	0.107554i	$0.965698\pi$
$264$	−49.1501	−	28.3768i	−0.186175	−	0.107488i
$265$		0			0
$266$	−307.609	+	46.4219i	−1.15642	+	0.174518i
$267$	19.1646			0.0717777
$268$	98.1647	−	170.026i	0.366286	−	0.634426i
$269$	−289.769	+	167.298i	−1.07721	+	0.621927i	−0.930142	−	0.367200i	$-0.880317\pi$
$269$	−289.769	+	167.298i	−1.07721	+	0.621927i	−0.147067	+	0.989127i	$0.546983\pi$
$270$		0			0
$271$	−157.920	−	91.1752i	−0.582731	−	0.336440i	0.179487	−	0.983760i	$-0.442556\pi$
$271$	−157.920	−	91.1752i	−0.582731	−	0.336440i	−0.762218	+	0.647321i	$0.775889\pi$
$272$		−	110.426i		−	0.405979i
$273$	−14.2272	−	94.2750i	−0.0521144	−	0.345330i
$274$	−349.168			−1.27434
$275$		0			0
$276$	54.4776	−	31.4526i	0.197382	−	0.113959i
$277$	83.3807	+	144.420i	0.301013	+	0.521370i	0.976366	−	0.216125i	$-0.0693418\pi$
$277$	83.3807	+	144.420i	0.301013	+	0.521370i	−0.675353	+	0.737495i	$0.736009\pi$
$278$	190.958	+	110.250i	0.686900	+	0.396582i
$279$			15.7915i			0.0566002i
$280$		0			0
$281$	38.3085			0.136329			0.0681647	−	0.997674i	$-0.478286\pi$
$281$	38.3085			0.136329			0.0681647	+	0.997674i	$0.478286\pi$
$282$	−93.8975	+	162.635i	−0.332970	+	0.576721i
$283$	333.849	−	192.748i	1.17968	−	0.681088i	0.223739	−	0.974649i	$-0.428174\pi$
$283$	333.849	−	192.748i	1.17968	−	0.681088i	0.955940	+	0.293561i	$0.0948404\pi$
$284$	34.2597	+	59.3396i	0.120633	+	0.208942i
$285$		0			0
$286$			128.834i			0.450469i
$287$	56.7235	−	144.606i	0.197643	−	0.503855i
$288$	16.9706			0.0589256
$289$	236.562	−	409.738i	0.818555	−	1.41778i
$290$		0			0
$291$	62.6233	+	108.467i	0.215200	+	0.372738i
$292$	33.7602	+	19.4915i	0.115617	+	0.0667516i
$293$		−	90.9844i		−	0.310527i	−0.987873	−	0.155264i	$-0.950377\pi$
$293$		−	90.9844i		−	0.310527i	0.987873	−	0.155264i	$-0.0496227\pi$
$294$	−81.6057	+	88.0143i	−0.277570	+	0.299368i
$295$		0			0
$296$	−2.80903	+	4.86538i	−0.00948997	+	0.0164371i
$297$	52.1316	−	30.0982i	0.175527	−	0.101341i
$298$	115.322	+	199.744i	0.386988	+	0.670282i
$299$	−123.667	−	71.3993i	−0.413603	−	0.238794i
$300$		0			0
$301$	324.766	+	127.393i	1.07896	+	0.423232i
$302$	106.108			0.351352
$303$	−43.8670	+	75.9799i	−0.144776	+	0.250759i
$304$	−108.859	+	62.8501i	−0.358090	+	0.206744i
$305$		0			0
$306$	101.433	+	58.5625i	0.331481	+	0.191381i
$307$			508.077i			1.65497i	0.561485	+	0.827487i	$0.310230\pi$
$307$			508.077i			1.65497i	−0.561485	+	0.827487i	$0.689770\pi$
$308$	126.785	−	101.145i	0.411638	−	0.328393i
$309$	−342.885			−1.10966
$310$		0			0
$311$	90.3447	−	52.1605i	0.290497	−	0.167719i	−0.347669	−	0.937617i	$-0.613027\pi$
$311$	90.3447	−	52.1605i	0.290497	−	0.167719i	0.638166	+	0.769899i	$0.279693\pi$
$312$	−19.2621	−	33.3629i	−0.0617375	−	0.106932i
$313$	−230.249	−	132.934i	−0.735619	−	0.424710i	0.0848550	−	0.996393i	$-0.472957\pi$
$313$	−230.249	−	132.934i	−0.735619	−	0.424710i	−0.820474	+	0.571683i	$0.806291\pi$
$314$		−	317.817i		−	1.01216i
$315$		0			0
$316$	180.857			0.572332
$317$	−5.36113	+	9.28575i	−0.0169121	+	0.0292926i	−0.874358	−	0.485282i	$-0.838717\pi$
$317$	−5.36113	+	9.28575i	−0.0169121	+	0.0292926i	0.857446	+	0.514575i	$0.172050\pi$
$318$	−121.118	+	69.9273i	−0.380873	+	0.219897i
$319$	13.3417	+	23.1085i	0.0418234	+	0.0724403i
$320$		0			0
$321$			256.232i			0.798231i
$322$	26.8252	+	177.754i	0.0833081	+	0.552031i
$323$	−867.538			−2.68588
$324$	−9.00000	+	15.5885i	−0.0277778	+	0.0481125i
$325$		0			0
$326$	162.718	+	281.835i	0.499134	+	0.864525i
$327$	−81.4829	−	47.0442i	−0.249183	−	0.143866i
$328$		−	62.7643i		−	0.191355i
$329$	−334.684	−	419.524i	−1.01728	−	1.27515i
$330$		0			0
$331$	176.460	−	305.638i	0.533113	−	0.923379i	−0.466139	−	0.884711i	$-0.654355\pi$
$331$	176.460	−	305.638i	0.533113	−	0.923379i	0.999252	−	0.0386675i	$-0.0123113\pi$
$332$	231.754	−	133.803i	0.698055	−	0.403022i
$333$	−2.97943	−	5.16052i	−0.00894723	−	0.0154971i
$334$	340.220	+	196.426i	1.01862	+	0.588102i
$335$		0			0
$336$	−17.7099	+	45.1482i	−0.0527080	+	0.134370i
$337$	−220.634			−0.654699			−0.327349	−	0.944903i	$-0.606155\pi$
$337$	−220.634			−0.654699			−0.327349	+	0.944903i	$0.606155\pi$
$338$	75.7750	−	131.246i	0.224186	−	0.388302i
$339$	71.6825	−	41.3859i	0.211453	−	0.122082i
$340$		0			0
$341$	52.8104	+	30.4901i	0.154869	+	0.0894138i
$342$		−	133.325i		−	0.389839i
$343$	−148.991	−	308.951i	−0.434376	−	0.900732i
$344$	140.960			0.409767
$345$		0			0
$346$	−154.398	+	89.1417i	−0.446237	+	0.257635i
$347$	−128.004	−	221.710i	−0.368888	−	0.638933i	0.620504	−	0.784204i	$-0.286928\pi$
$347$	−128.004	−	221.710i	−0.368888	−	0.638933i	−0.989392	+	0.145270i	$0.953595\pi$
$348$	−6.90993	−	3.98945i	−0.0198561	−	0.0114639i
$349$		−	407.250i		−	1.16691i	−0.812147	−	0.583453i	$-0.801701\pi$
$349$		−	407.250i		−	1.16691i	0.812147	−	0.583453i	$-0.198299\pi$
$350$		0			0
$351$	40.8611			0.116413
$352$	32.7667	−	56.7537i	0.0930873	−	0.161232i
$353$	505.099	−	291.619i	1.43087	−	0.826116i	0.433687	−	0.901064i	$-0.357212\pi$
$353$	505.099	−	291.619i	1.43087	−	0.826116i	0.997187	+	0.0749482i	$0.0238791\pi$
$354$	−86.1602	−	149.234i	−0.243390	−	0.421565i
$355$		0			0
$356$			22.1294i			0.0621613i
$357$	−261.651	+	208.737i	−0.732915	+	0.584698i
$358$	−109.046			−0.304597
$359$	−345.764	+	598.881i	−0.963131	+	1.66819i	−0.248577	+	0.968612i	$0.579963\pi$
$359$	−345.764	+	598.881i	−0.963131	+	1.66819i	−0.714554	+	0.699580i	$0.753370\pi$
$360$		0			0
$361$	313.266	+	542.593i	0.867773	+	1.50303i
$362$	−259.660	−	149.915i	−0.717294	−	0.414130i
$363$		−	22.8760i		−	0.0630192i
$364$	108.859	−	16.4282i	0.299064	−	0.0451324i
$365$		0			0
$366$	82.8150	−	143.440i	0.226270	−	0.391912i
$367$	−198.949	+	114.863i	−0.542096	+	0.312980i	−0.745928	−	0.666026i	$-0.767994\pi$
$367$	−198.949	+	114.863i	−0.542096	+	0.312980i	0.203832	+	0.979006i	$0.434660\pi$
$368$	36.3184	+	62.9053i	0.0986912	+	0.170938i
$369$	57.6527	+	33.2858i	0.156240	+	0.0902054i
$370$		0			0
$371$	−59.6394	−	395.193i	−0.160753	−	1.06521i
$372$	−18.2344			−0.0490172
$373$	−202.304	+	350.401i	−0.542371	+	0.939414i	0.456397	+	0.889776i	$0.349140\pi$
$373$	−202.304	+	350.401i	−0.542371	+	0.939414i	−0.998767	+	0.0496372i	$0.984193\pi$
$374$	391.694	−	226.145i	1.04731	−	0.604665i
$375$		0			0
$376$	−187.795	−	108.424i	−0.499455	−	0.288360i
$377$			18.1126i			0.0480439i
$378$	−32.0792	−	40.2110i	−0.0848656	−	0.106378i
$379$	265.866			0.701493			0.350746	−	0.936471i	$-0.385928\pi$
$379$	265.866			0.701493			0.350746	+	0.936471i	$0.385928\pi$
$380$		0			0
$381$	−152.960	+	88.3115i	−0.401470	+	0.231789i
$382$	117.165	+	202.935i	0.306714	+	0.531244i
$383$	−265.353	−	153.202i	−0.692829	−	0.400005i	0.111842	−	0.993726i	$-0.464325\pi$
$383$	−265.353	−	153.202i	−0.692829	−	0.400005i	−0.804671	+	0.593721i	$0.797658\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	−148.916			−0.385792
$387$	−74.7552	+	129.480i	−0.193166	+	0.334573i
$388$	−125.247	+	72.3112i	−0.322801	+	0.186369i
$389$	−53.1772	−	92.1056i	−0.136702	−	0.236775i	0.789544	−	0.613694i	$-0.210317\pi$
$389$	−53.1772	−	92.1056i	−0.136702	−	0.236775i	−0.926246	+	0.376918i	$0.876984\pi$
$390$		0			0
$391$			501.314i			1.28213i
$392$	−101.630	−	94.2301i	−0.259261	−	0.240383i
$393$	129.207			0.328772
$394$	−173.054	+	299.739i	−0.439224	+	0.760758i
$395$		0			0
$396$	34.7544	+	60.1964i	0.0877636	+	0.152011i
$397$	188.643	+	108.913i	0.475172	+	0.274341i	0.718402	−	0.695628i	$-0.244874\pi$
$397$	188.643	+	108.913i	0.475172	+	0.274341i	−0.243230	+	0.969969i	$0.578207\pi$
$398$		−	138.546i		−	0.348105i
$399$	354.696	+	139.133i	0.888962	+	0.348705i
$400$		0			0
$401$	−30.9907	+	53.6775i	−0.0772836	+	0.133859i	−0.902077	−	0.431575i	$-0.857958\pi$
$401$	−30.9907	+	53.6775i	−0.0772836	+	0.133859i	0.824793	+	0.565434i	$0.191291\pi$
$402$	−208.239	+	120.227i	−0.518007	+	0.299071i
$403$	20.6966	+	35.8475i	0.0513563	+	0.0889517i
$404$	−87.7341	−	50.6533i	−0.217164	−	0.125379i
$405$		0			0
$406$	17.8244	−	14.2198i	0.0439025	−	0.0350242i
$407$	−23.0107			−0.0565373
$408$	−67.6221	+	117.125i	−0.165740	+	0.287071i
$409$	−376.167	+	217.180i	−0.919724	+	0.531003i	−0.883547	−	0.468342i	$-0.844851\pi$
$409$	−376.167	+	217.180i	−0.919724	+	0.531003i	−0.0361772	+	0.999345i	$0.511518\pi$
$410$		0			0
$411$	370.348	+	213.821i	0.901091	+	0.520245i
$412$		−	395.929i		−	0.960993i
$413$	486.933	−	73.4840i	1.17901	−	0.177927i
$414$	−77.0429			−0.186094
$415$		0			0
$416$	38.5242	−	22.2419i	0.0926062	−	0.0534662i
$417$	−135.028	−	233.875i	−0.323808	−	0.560852i
$418$	−445.871	−	257.424i	−1.06668	−	0.615847i
$419$			457.221i			1.09122i	0.838040	+	0.545609i	$0.183702\pi$
$419$			457.221i			1.09122i	−0.838040	+	0.545609i	$0.816298\pi$
$420$		0			0
$421$	−653.149			−1.55142			−0.775712	−	0.631088i	$-0.782609\pi$
$421$	−653.149			−1.55142			−0.775712	+	0.631088i	$0.782609\pi$
$422$	−275.004	+	476.320i	−0.651667	+	1.12872i
$423$	199.187	−	115.000i	0.470891	−	0.271869i
$424$	−80.7451	−	139.855i	−0.190437	−	0.329846i
$425$		0			0
$426$		−	83.9188i		−	0.196993i
$427$	295.182	+	370.008i	0.691293	+	0.866530i
$428$	−295.872			−0.691289
$429$	78.8945	−	136.649i	0.183903	−	0.318530i
$430$		0			0
$431$	235.128	+	407.253i	0.545540	+	0.944904i	0.998573	+	0.0534095i	$0.0170089\pi$
$431$	235.128	+	407.253i	0.545540	+	0.944904i	−0.453032	+	0.891494i	$0.649658\pi$
$432$	−18.0000	−	10.3923i	−0.0416667	−	0.0240563i
$433$		−	32.0299i		−	0.0739719i	−0.999316	−	0.0369860i	$-0.988224\pi$
$433$		−	32.0299i		−	0.0739719i	0.999316	−	0.0369860i	$-0.0117757\pi$
$434$	19.0288	−	48.5105i	0.0438451	−	0.111775i
$435$		0			0
$436$	54.3219	−	94.0883i	0.124592	−	0.215799i
$437$	494.200	−	285.326i	1.13089	−	0.652921i
$438$	−23.8721	−	41.3476i	−0.0545024	−	0.0944010i
$439$	331.028	+	191.119i	0.754051	+	0.435352i	0.827156	−	0.561973i	$-0.189957\pi$
$439$	331.028	+	191.119i	0.754051	+	0.435352i	−0.0731046	+	0.997324i	$0.523291\pi$
$440$		0			0
$441$	140.453	−	43.3802i	0.318488	−	0.0983677i
$442$	307.012			0.694598
$443$	61.8708	−	107.163i	0.139663	−	0.241904i	−0.787706	−	0.616051i	$-0.788731\pi$
$443$	61.8708	−	107.163i	0.139663	−	0.241904i	0.927369	+	0.374148i	$0.122065\pi$
$444$	5.95885	−	3.44035i	0.0134208	−	0.00774853i
$445$		0			0
$446$	−308.529	−	178.129i	−0.691769	−	0.399393i
$447$		−	282.481i		−	0.631948i
$448$	−52.1327	−	20.4496i	−0.116368	−	0.0456464i
$449$	−266.985			−0.594622			−0.297311	−	0.954781i	$-0.596090\pi$
$449$	−266.985			−0.594622			−0.297311	+	0.954781i	$0.596090\pi$
$450$		0			0
$451$	222.632	−	128.536i	0.493640	−	0.285003i
$452$	47.7883	+	82.7718i	0.105726	+	0.183124i
$453$	−112.545	−	64.9778i	−0.248443	−	0.143439i
$454$			378.757i			0.834267i
$455$		0			0
$456$	153.951			0.337611
$457$	−224.670	+	389.140i	−0.491619	+	0.851509i	−0.999953	−	0.00965069i	$-0.996928\pi$
$457$	−224.670	+	389.140i	−0.491619	+	0.851509i	0.508334	+	0.861160i	$0.330261\pi$
$458$	423.185	−	244.326i	0.923985	−	0.533463i
$459$	−71.7241	−	124.230i	−0.156262	−	0.270653i
$460$		0			0
$461$		−	105.528i		−	0.228912i	−0.993428	−	0.114456i	$-0.963487\pi$
$461$		−	105.528i		−	0.228912i	0.993428	−	0.114456i	$-0.0365125\pi$
$462$	−196.414	+	29.6412i	−0.425138	+	0.0641584i
$463$	−588.555			−1.27118			−0.635588	−	0.772028i	$-0.719242\pi$
$463$	−588.555			−1.27118			−0.635588	+	0.772028i	$0.719242\pi$
$464$	4.60662	−	7.97889i	0.00992805	−	0.0171959i
$465$		0			0
$466$	203.692	+	352.805i	0.437108	+	0.757093i
$467$	−316.668	−	182.829i	−0.678091	−	0.391496i	0.121044	−	0.992647i	$-0.461376\pi$
$467$	−316.668	−	182.829i	−0.678091	−	0.391496i	−0.799135	+	0.601151i	$0.794709\pi$
$468$			47.1823i			0.100817i
$469$	−102.539	−	679.459i	−0.218632	−	1.44874i
$470$		0			0
$471$	−194.622	+	337.096i	−0.413211	+	0.715702i
$472$	172.320	−	99.4892i	0.365086	−	0.210782i
$473$	288.675	+	499.999i	0.610306	+	1.05708i
$474$	−191.828	−	110.752i	−0.404700	−	0.233654i
$475$		0			0
$476$	−241.029	−	302.128i	−0.506364	−	0.634723i
$477$	171.286			0.359091
$478$	−133.509	+	231.244i	−0.279307	+	0.483774i
$479$	−421.907	+	243.588i	−0.880808	+	0.508535i	−0.870925	−	0.491416i	$-0.836479\pi$
$479$	−421.907	+	243.588i	−0.880808	+	0.508535i	−0.00988318	+	0.999951i	$0.503146\pi$
$480$		0			0
$481$	−13.5270	−	7.80979i	−0.0281226	−	0.0162366i
$482$		−	138.378i		−	0.287091i
$483$	80.3992	−	204.964i	0.166458	−	0.424355i
$484$	26.4149			0.0545762
$485$		0			0
$486$	19.0919	−	11.0227i	0.0392837	−	0.0226805i
$487$	−97.8870	−	169.545i	−0.201000	−	0.348142i	0.747851	−	0.663867i	$-0.231086\pi$
$487$	−97.8870	−	169.545i	−0.201000	−	0.348142i	−0.948851	+	0.315725i	$0.897752\pi$
$488$	165.630	+	95.6265i	0.339406	+	0.195956i
$489$		−	398.575i		−	0.815082i
$490$		0			0
$491$	−349.221			−0.711244			−0.355622	−	0.934630i	$-0.615731\pi$
$491$	−349.221			−0.711244			−0.355622	+	0.934630i	$0.615731\pi$
$492$	−38.4351	+	66.5716i	−0.0781202	+	0.135308i
$493$	55.0675	−	31.7933i	0.111699	−	0.0644894i
$494$	−174.738	−	302.656i	−0.353722	−	0.612664i
$495$		0			0
$496$		−	21.0553i		−	0.0424501i
$497$	223.256	+	87.5747i	0.449208	+	0.176207i
$498$	−327.750			−0.658133
$499$	167.719	−	290.498i	0.336111	−	0.582161i	−0.647587	−	0.761992i	$-0.724222\pi$
$499$	167.719	−	290.498i	0.336111	−	0.582161i	0.983698	+	0.179831i	$0.0575550\pi$
$500$		0			0
$501$	−240.572	−	416.683i	−0.480183	−	0.831702i
$502$	−295.586	−	170.657i	−0.588817	−	0.339953i
$503$			523.663i			1.04108i	0.853837	+	0.520540i	$0.174269\pi$
$503$			523.663i			1.04108i	−0.853837	+	0.520540i	$0.825731\pi$
$504$	46.4317	−	37.0419i	0.0921263	−	0.0734958i
$505$		0			0
$506$	−148.754	+	257.650i	−0.293981	+	0.509190i
$507$	−160.743	+	92.8050i	−0.317047	+	0.183047i
$508$	−101.973	−	176.623i	−0.200735	−	0.347683i
$509$	−417.731	−	241.177i	−0.820690	−	0.473825i	0.0299645	−	0.999551i	$-0.490461\pi$
$509$	−417.731	−	241.177i	−0.820690	−	0.473825i	−0.850654	+	0.525726i	$0.823794\pi$
$510$		0			0
$511$	134.913	−	20.3599i	0.264017	−	0.0398433i
$512$	−22.6274			−0.0441942
$513$	−81.6446	+	141.413i	−0.159151	+	0.275658i
$514$	15.3876	−	8.88405i	0.0299370	−	0.0172841i
$515$		0			0
$516$	−149.510	−	86.3199i	−0.289749	−	0.167287i
$517$		−	888.171i		−	1.71793i
$518$	2.93419	+	19.4431i	0.00566446	+	0.0375349i
$519$	218.352			0.420716
$520$		0			0
$521$	−61.7509	+	35.6519i	−0.118524	+	0.0684298i	−0.558090	−	0.829780i	$-0.688466\pi$
$521$	−61.7509	+	35.6519i	−0.118524	+	0.0684298i	0.439566	+	0.898210i	$0.355132\pi$
$522$	4.88606	+	8.46290i	0.00936026	+	0.0162124i
$523$	521.458	+	301.064i	0.997052	+	0.575648i	0.907375	−	0.420323i	$-0.138083\pi$
$523$	521.458	+	301.064i	0.997052	+	0.575648i	0.0896773	+	0.995971i	$0.471416\pi$
$524$			149.196i			0.284725i
$525$		0			0
$526$	−300.493			−0.571279
$527$	72.6581	−	125.847i	0.137871	−	0.238800i
$528$	−69.5088	+	40.1309i	−0.131645	+	0.0760055i
$529$	99.6220	+	172.550i	0.188321	+	0.326182i
$530$		0			0
$531$			211.049i			0.397455i
$532$	−160.657	+	409.568i	−0.301987	+	0.769864i
$533$	174.500			0.327392
$534$	13.5514	−	23.4718i	0.0253772	−	0.0439547i
$535$		0			0
$536$	−138.826	−	240.453i	−0.259003	−	0.448607i
$537$	115.660	+	66.7766i	0.215382	+	0.124351i
$538$			473.191i			0.879537i
$539$	126.114	−	553.469i	0.233977	−	1.02684i
$540$		0			0
$541$	301.657	−	522.485i	0.557591	−	0.965776i	−0.440106	−	0.897946i	$-0.645059\pi$
$541$	301.657	−	522.485i	0.557591	−	0.965776i	0.997697	−	0.0678303i	$-0.0216077\pi$
$542$	−223.333	+	128.941i	−0.412053	+	0.237899i
$543$	183.608	+	318.018i	0.338136	+	0.585668i
$544$	−135.244	−	78.0833i	−0.248611	−	0.143535i
$545$		0			0
$546$	−125.523	−	49.2378i	−0.229896	−	0.0901791i
$547$	879.935			1.60866			0.804328	−	0.594185i	$-0.202525\pi$
$547$	879.935			1.60866			0.804328	+	0.594185i	$0.202525\pi$
$548$	−246.899	+	427.642i	−0.450546	+	0.780368i
$549$	−175.677	+	101.427i	−0.319995	+	0.184749i
$550$		0			0
$551$	−62.6842	−	36.1908i	−0.113765	−	0.0656820i
$552$		−	88.9615i		−	0.161162i
$553$	494.827	−	394.759i	0.894805	−	0.713849i
$554$	235.836			0.425697
$555$		0			0
$556$	270.056	−	155.917i	0.485712	−	0.280426i
$557$	−441.404	−	764.533i	−0.792466	−	1.37259i	−0.924436	−	0.381338i	$-0.875464\pi$
$557$	−441.404	−	764.533i	−0.792466	−	1.37259i	0.131970	−	0.991254i	$-0.457870\pi$
$558$	19.3405	+	11.1662i	0.0346604	+	0.0200112i
$559$			391.903i			0.701078i
$560$		0			0
$561$	−553.939			−0.987414
$562$	27.0882	−	46.9182i	0.0481997	−	0.0834843i
$563$	451.334	−	260.578i	0.801659	−	0.462838i	−0.0423920	−	0.999101i	$-0.513498\pi$
$563$	451.334	−	260.578i	0.801659	−	0.462838i	0.844051	+	0.536263i	$0.180165\pi$
$564$	132.791	+	230.001i	0.235445	+	0.407803i
$565$		0			0
$566$		−	545.174i		−	0.963204i
$567$	9.40101	+	62.2946i	0.0165803	+	0.109867i
$568$	96.9011			0.170601
$569$	−122.400	+	212.004i	−0.215115	+	0.372590i	−0.953308	−	0.301999i	$-0.902346\pi$
$569$	−122.400	+	212.004i	−0.215115	+	0.372590i	0.738193	+	0.674589i	$0.235679\pi$
$570$		0			0
$571$	208.126	+	360.486i	0.364495	+	0.631323i	0.988695	−	0.149941i	$-0.0479084\pi$
$571$	208.126	+	360.486i	0.364495	+	0.631323i	−0.624200	+	0.781264i	$0.714575\pi$
$572$	157.789	+	91.0995i	0.275855	+	0.159265i
$573$		−	286.994i		−	0.500862i
$574$	−136.996	−	171.724i	−0.238670	−	0.299171i
$575$		0			0
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	−669.929	+	386.784i	−1.16106	+	0.670336i	−0.951557	−	0.307473i	$-0.900517\pi$
$577$	−669.929	+	386.784i	−1.16106	+	0.670336i	−0.209499	+	0.977809i	$0.567183\pi$
$578$	−334.550	−	579.457i	−0.578806	−	1.00252i
$579$	157.949	+	91.1920i	0.272796	+	0.157499i
$580$		0			0
$581$	342.028	−	871.941i	0.588689	−	1.50076i
$582$	177.125			0.304339
$583$	330.719	−	572.823i	0.567272	−	0.982543i
$584$	47.7441	−	27.5651i	0.0817537	−	0.0472005i
$585$		0			0
$586$	−111.433	−	64.3357i	−0.190158	−	0.109788i
$587$			633.860i			1.07983i	0.841720	+	0.539915i	$0.181544\pi$
$587$			633.860i			1.07983i	−0.841720	+	0.539915i	$0.818456\pi$
$588$	50.0911	+	162.182i	0.0851889	+	0.275819i
$589$	−165.416			−0.280841
$590$		0			0
$591$	367.103	−	211.947i	0.621156	−	0.358625i
$592$	3.97257	+	6.88069i	0.00671042	+	0.0116228i
$593$	−80.4028	−	46.4206i	−0.135587	−	0.0782809i	0.430672	−	0.902508i	$-0.358276\pi$
$593$	−80.4028	−	46.4206i	−0.135587	−	0.0782809i	−0.566259	+	0.824227i	$0.691610\pi$
$594$		−	85.1305i		−	0.143317i
$595$		0			0
$596$	326.181			0.547283
$597$	−84.8416	+	146.950i	−0.142113	+	0.246147i
$598$	−174.892	+	100.974i	−0.292461	+	0.168853i
$599$	307.680	+	532.918i	0.513657	+	0.889679i	0.999875	+	0.0158418i	$0.00504280\pi$
$599$	307.680	+	532.918i	0.513657	+	0.889679i	−0.486218	+	0.873838i	$0.661624\pi$
$600$		0			0
$601$			821.399i			1.36672i	0.730081	+	0.683360i	$0.239482\pi$
$601$			821.399i			1.36672i	−0.730081	+	0.683360i	$0.760518\pi$
$602$	385.668	−	307.675i	0.640644	−	0.511088i
$603$	294.494			0.488381
$604$	75.0299	−	129.956i	0.124222	−	0.215158i
$605$		0			0
$606$	62.0374	+	107.452i	0.102372	+	0.177313i
$607$	869.979	+	502.282i	1.43324	+	0.827483i	0.997367	−	0.0725231i	$-0.0231051\pi$
$607$	869.979	+	502.282i	1.43324	+	0.827483i	0.435876	+	0.900006i	$0.356438\pi$
$608$			177.767i			0.292380i
$609$	−27.6135	+	4.16720i	−0.0453423	+	0.00684270i
$610$		0			0
$611$	301.444	−	522.116i	0.493361	−	0.854527i
$612$	143.448	−	82.8198i	0.234392	−	0.135326i
$613$	556.873	+	964.532i	0.908438	+	1.57346i	0.816234	+	0.577721i	$0.196058\pi$
$613$	556.873	+	964.532i	0.908438	+	1.57346i	0.0922038	+	0.995740i	$0.470609\pi$
$614$	622.264	+	359.265i	1.01346	+	0.585121i
$615$		0			0
$616$	−34.2267	−	226.799i	−0.0555628	−	0.368180i
$617$	463.256			0.750820			0.375410	−	0.926859i	$-0.377502\pi$
$617$	463.256			0.750820			0.375410	+	0.926859i	$0.377502\pi$
$618$	−242.456	+	419.946i	−0.392324	+	0.679525i
$619$	486.109	−	280.655i	0.785314	−	0.453401i	−0.0529963	−	0.998595i	$-0.516877\pi$
$619$	486.109	−	280.655i	0.785314	−	0.453401i	0.838310	+	0.545193i	$0.183544\pi$
$620$		0			0
$621$	81.7163	+	47.1790i	0.131588	+	0.0759725i
$622$		−	147.532i		−	0.237190i
$623$	48.3021	+	60.5464i	0.0775315	+	0.0971852i
$624$	−54.4814			−0.0873100
$625$		0			0
$626$	−325.621	+	187.997i	−0.520161	+	0.300315i
$627$	315.279	+	546.079i	0.502837	+	0.870939i
$628$	−389.245	−	224.731i	−0.619816	−	0.357851i
$629$			54.8346i			0.0871774i
$630$		0			0
$631$	244.533			0.387533			0.193767	−	0.981048i	$-0.437930\pi$
$631$	244.533			0.387533			0.193767	+	0.981048i	$0.437930\pi$
$632$	127.885	−	221.504i	0.202350	−	0.350480i
$633$	583.371	−	336.809i	0.921597	−	0.532084i
$634$	7.58178	+	13.1320i	0.0119587	+	0.0207130i
$635$		0			0
$636$			197.784i			0.310982i
$637$	261.983	−	282.556i	0.411276	−	0.443574i
$638$	37.7360			0.0591473
$639$	−51.3896	+	89.0094i	−0.0804219	+	0.139295i
$640$		0			0
$641$	−325.885	−	564.449i	−0.508400	−	0.880575i	−0.999953	−	0.00972698i	$-0.996904\pi$
$641$	−325.885	−	564.449i	−0.508400	−	0.880575i	0.491553	−	0.870848i	$-0.336430\pi$
$642$	313.819	+	181.184i	0.488815	+	0.282217i
$643$			76.4894i			0.118957i	0.998230	+	0.0594786i	$0.0189438\pi$
$643$			76.4894i			0.118957i	−0.998230	+	0.0594786i	$0.981056\pi$
$644$	236.672	+	92.8371i	0.367503	+	0.144157i
$645$		0			0
$646$	−613.442	+	1062.51i	−0.949601	+	1.64476i
$647$	−141.933	+	81.9453i	−0.219372	+	0.126654i	−0.605659	−	0.795724i	$-0.707091\pi$
$647$	−141.933	+	81.9453i	−0.219372	+	0.126654i	0.386288	+	0.922378i	$0.373757\pi$
$648$	12.7279	+	22.0454i	0.0196419	+	0.0340207i
$649$	705.797	+	407.492i	1.08752	+	0.627877i
$650$		0			0
$651$	−49.8895	+	39.8004i	−0.0766352	+	0.0611374i
$652$	460.235			0.705882
$653$	−557.431	+	965.499i	−0.853647	+	1.47856i	0.0242480	+	0.999706i	$0.492281\pi$
$653$	−557.431	+	965.499i	−0.853647	+	1.47856i	−0.877895	+	0.478854i	$0.841052\pi$
$654$	−115.234	+	66.5305i	−0.176199	+	0.101729i
$655$		0			0
$656$	−76.8703	−	44.3811i	−0.117180	−	0.0676541i
$657$			58.4744i			0.0890021i
$658$	−750.467	+	113.254i	−1.14053	+	0.172119i
$659$	1164.66			1.76732			0.883660	−	0.468130i	$-0.155072\pi$
$659$	1164.66			1.76732			0.883660	+	0.468130i	$0.155072\pi$
$660$		0			0
$661$	542.087	−	312.974i	0.820101	−	0.473485i	−0.0303505	−	0.999539i	$-0.509662\pi$
$661$	542.087	−	312.974i	0.820101	−	0.473485i	0.850451	+	0.526054i	$0.176329\pi$
$662$	−249.553	−	432.238i	−0.376968	−	0.652928i
$663$	−325.636	−	188.006i	−0.491155	−	0.283568i
$664$		−	378.453i		−	0.569960i
$665$		0			0
$666$	−8.42709			−0.0126533
$667$	−20.9131	+	36.2226i	−0.0313540	+	0.0543067i
$668$	481.144	−	277.788i	0.720275	−	0.415851i
$669$	218.163	+	377.869i	0.326103	+	0.564827i
$670$		0			0
$671$			783.342i			1.16743i
$672$	42.7723	+	53.6147i	0.0636492	+	0.0797838i
$673$	38.0207			0.0564943			0.0282471	−	0.999601i	$-0.491007\pi$
$673$	38.0207			0.0564943			0.0282471	+	0.999601i	$0.491007\pi$
$674$	−156.011	+	270.220i	−0.231471	+	0.400920i
$675$		0			0
$676$	−107.162	−	185.610i	−0.158524	−	0.274571i
$677$	−676.984	−	390.857i	−0.999976	−	0.577336i	−0.0917347	−	0.995783i	$-0.529241\pi$
$677$	−676.984	−	390.857i	−0.999976	−	0.577336i	−0.908241	+	0.418447i	$0.862574\pi$
$678$		−	117.057i		−	0.172651i
$679$	−184.842	+	471.222i	−0.272227	+	0.693994i
$680$		0			0
$681$	231.941	−	401.733i	0.340588	−	0.589916i
$682$	74.6852	−	43.1195i	0.109509	−	0.0632251i
$683$	−67.2190	−	116.427i	−0.0984172	−	0.170464i	0.812612	−	0.582804i	$-0.198045\pi$
$683$	−67.2190	−	116.427i	−0.0984172	−	0.170464i	−0.911030	+	0.412341i	$0.864711\pi$
$684$	−163.289	−	94.2751i	−0.238727	−	0.137829i
$685$		0			0
$686$	−483.739	−	35.9855i	−0.705158	−	0.0524570i
$687$	−598.474			−0.871142
$688$	99.6736	−	172.640i	0.144874	−	0.250930i
$689$	388.830	−	224.491i	0.564340	−	0.325822i
$690$		0			0
$691$	−393.253	−	227.045i	−0.569107	−	0.328574i	0.187686	−	0.982229i	$-0.439901\pi$
$691$	−393.253	−	227.045i	−0.569107	−	0.328574i	−0.756792	+	0.653655i	$0.773235\pi$
$692$			252.131i			0.364351i
$693$	226.480	+	88.8392i	0.326811	+	0.128195i
$694$	−362.051			−0.521687
$695$		0			0
$696$	−9.77211	+	5.64193i	−0.0140404	+	0.00810622i
$697$	−306.303	−	530.532i	−0.439459	−	0.761165i
$698$	−498.778	−	287.969i	−0.714581	−	0.412564i
$699$		−	498.942i		−	0.713794i
$700$		0			0
$701$	982.015			1.40088			0.700439	−	0.713713i	$-0.252988\pi$
$701$	982.015			1.40088			0.700439	+	0.713713i	$0.252988\pi$
$702$	28.8931	−	50.0444i	0.0411583	−	0.0712883i
$703$	54.0565	−	31.2095i	0.0768940	−	0.0443948i
$704$	−46.3392	−	80.2618i	−0.0658227	−	0.114008i
$705$		0			0
$706$		−	824.822i		−	1.16830i
$707$	−350.603	+	52.9102i	−0.495903	+	0.0748376i
$708$	−243.698			−0.344206
$709$	166.536	−	288.449i	0.234889	−	0.406839i	−0.724352	−	0.689431i	$-0.757861\pi$
$709$	166.536	−	288.449i	0.234889	−	0.406839i	0.959240	+	0.282591i	$0.0911940\pi$
$710$		0			0
$711$	135.643	+	234.940i	0.190777	+	0.330436i
$712$	27.1029	+	15.6479i	0.0380658	+	0.0219773i
$713$			95.5866i			0.134063i
$714$	70.6351	+	468.055i	0.0989287	+	0.655539i
$715$		0			0
$716$	−77.1069	+	133.553i	−0.107691	+	0.186527i
$717$	283.215	−	163.514i	0.395000	−	0.228053i
$718$	488.984	+	846.946i	0.681037	+	1.17959i
$719$	1055.73	+	609.523i	1.46832	+	0.847737i	0.999370	−	0.0354852i	$-0.0112977\pi$
$719$	1055.73	+	609.523i	1.46832	+	0.847737i	0.468954	+	0.883223i	$0.344631\pi$
$720$		0			0
$721$	−864.200	−	1083.27i	−1.19861	−	1.50245i
$722$	886.051			1.22722
$723$	−84.7389	+	146.772i	−0.117205	+	0.203004i
$724$	−367.215	+	212.012i	−0.507203	+	0.292834i
$725$		0			0
$726$	−28.0172	−	16.1758i	−0.0385912	−	0.0222807i
$727$		−	215.108i		−	0.295885i	−0.988996	−	0.147942i	$-0.952735\pi$
$727$		−	215.108i		−	0.295885i	0.988996	−	0.147942i	$-0.0472650\pi$
$728$	56.8549	−	144.941i	0.0780974	−	0.199095i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	1191.50	−	687.913i	1.62996	−	0.941057i
$732$	−117.118	−	202.854i	−0.159997	−	0.277124i
$733$	649.047	+	374.728i	0.885467	+	0.511225i	0.872457	−	0.488691i	$-0.162525\pi$
$733$	649.047	+	374.728i	0.885467	+	0.511225i	0.0130099	+	0.999915i	$0.495859\pi$
$734$			324.883i			0.442620i
$735$		0			0
$736$	102.724			0.139570
$737$	568.609	−	984.859i	0.771518	−	1.33631i
$738$	81.5332	−	47.0732i	0.110479	−	0.0637849i
$739$	467.102	+	809.045i	0.632073	+	1.09478i	0.987127	+	0.159937i	$0.0511291\pi$
$739$	467.102	+	809.045i	0.632073	+	1.09478i	−0.355054	+	0.934846i	$0.615538\pi$
$740$		0			0
$741$			428.020i			0.577625i
$742$	−526.182	−	206.401i	−0.709140	−	0.278168i
$743$	−1232.47			−1.65878			−0.829389	−	0.558671i	$-0.811311\pi$
$743$	−1232.47			−1.65878			−0.829389	+	0.558671i	$0.811311\pi$
$744$	−12.8937	+	22.3325i	−0.0173302	+	0.0300168i
$745$		0			0
$746$	286.101	+	495.542i	0.383514	+	0.664266i
$747$	347.632	+	200.705i	0.465370	+	0.268682i
$748$		−	639.634i		−	0.855125i
$749$	−809.508	+	645.803i	−1.08079	+	0.862220i
$750$		0			0
$751$	−393.353	+	681.307i	−0.523772	+	0.907200i	0.475845	+	0.879529i	$0.342142\pi$
$751$	−393.353	+	681.307i	−0.523772	+	0.907200i	−0.999617	+	0.0276709i	$0.991191\pi$
$752$	−265.582	+	153.334i	−0.353168	+	0.203902i
$753$	209.011	+	362.017i	0.277571	+	0.480767i
$754$	22.1833	+	12.8075i	0.0294208	+	0.0169861i
$755$		0			0
$756$	−71.9316	+	10.8553i	−0.0951477	+	0.0143589i
$757$	−1303.18			−1.72151			−0.860753	−	0.509023i	$-0.830007\pi$
$757$	−1303.18			−1.72151			−0.860753	+	0.509023i	$0.830007\pi$
$758$	187.995	−	325.618i	0.248015	−	0.429575i
$759$	315.556	−	182.186i	0.415752	−	0.240034i
$760$		0			0
$761$	601.784	+	347.440i	0.790780	+	0.456557i	0.840237	−	0.542219i	$-0.182416\pi$
$761$	601.784	+	347.440i	0.790780	+	0.456557i	−0.0494571	+	0.998776i	$0.515749\pi$
$762$			249.783i			0.327799i
$763$	−56.7423	−	375.996i	−0.0743674	−	0.492786i
$764$	331.392			0.433759
$765$		0			0
$766$	−375.266	+	216.660i	−0.489904	+	0.282846i
$767$	276.604	+	479.093i	0.360631	+	0.624632i
$768$	24.0000	+	13.8564i	0.0312500	+	0.0180422i
$769$			263.988i			0.343287i	0.985159	+	0.171644i	$0.0549077\pi$
$769$			263.988i			0.343287i	−0.985159	+	0.171644i	$0.945092\pi$
$770$		0			0
$771$	−21.7614			−0.0282249
$772$	−105.299	+	182.384i	−0.136398	+	0.236249i
$773$	136.278	−	78.6802i	0.176298	−	0.101786i	−0.409254	−	0.912420i	$-0.634211\pi$
$773$	136.278	−	78.6802i	0.176298	−	0.101786i	0.585552	+	0.810635i	$0.300878\pi$
$774$	105.720	+	183.112i	0.136589	+	0.236579i
$775$		0			0
$776$			204.527i			0.263566i
$777$	8.79422	−	22.4193i	0.0113182	−	0.0288537i
$778$	−150.408			−0.193326
$779$	−348.669	+	603.913i	−0.447586	+	0.775241i
$780$		0			0
$781$	198.446	+	343.718i	0.254092	+	0.440100i
$782$	613.981	+	354.482i	0.785142	+	0.453302i
$783$		−	11.9683i		−	0.0152852i
$784$	−187.271	+	57.8402i	−0.238866	+	0.0737758i
$785$		0			0
$786$	91.3635	−	158.246i	0.116239	−	0.201331i
$787$	−850.660	+	491.129i	−1.08089	+	0.624052i	−0.931136	−	0.364671i	$-0.881181\pi$
$787$	−850.660	+	491.129i	−1.08089	+	0.624052i	−0.149754	+	0.988723i	$0.547848\pi$
$788$	244.736	+	423.894i	0.310578	+	0.537937i
$789$	318.721	+	184.014i	0.403956	+	0.233224i
$790$		0			0
$791$	311.417	+	122.157i	0.393700	+	0.154433i
$792$	98.3002			0.124116
$793$	−265.865	+	460.492i	−0.335265	+	0.580695i
$794$	266.782	−	154.027i	0.335998	−	0.193988i
$795$		0			0
$796$	−169.683	−	97.9667i	−0.213170	−	0.123074i
$797$			946.927i			1.18811i	0.804423	+	0.594057i	$0.202475\pi$
$797$			946.927i			1.18811i	−0.804423	+	0.594057i	$0.797525\pi$
$798$	421.211	−	336.030i	0.527833	−	0.421090i
$799$	−2116.52			−2.64896
$800$		0			0
$801$	−28.7470	+	16.5971i	−0.0358888	+	0.0207204i
$802$	43.8275	+	75.9114i	0.0546477	+	0.0946526i
$803$	195.553	+	112.902i	0.243527	+	0.140601i
$804$			340.052i			0.422951i
$805$		0			0
$806$	58.5388			0.0726287
$807$	289.769	−	501.895i	0.359070	−	0.621927i
$808$	−124.075	+	71.6346i	−0.153558	+	0.0886567i
$809$	−214.568	−	371.642i	−0.265226	−	0.459385i	0.702397	−	0.711786i	$-0.252113\pi$
$809$	−214.568	−	371.642i	−0.265226	−	0.459385i	−0.967623	+	0.252401i	$0.918780\pi$
$810$		0			0
$811$		−	948.404i		−	1.16943i	−0.811241	−	0.584713i	$-0.801207\pi$
$811$		−	948.404i		−	1.16943i	0.811241	−	0.584713i	$-0.198793\pi$
$812$	−4.81187	−	31.8853i	−0.00592595	−	0.0392676i
$813$	315.840			0.388487
$814$	−16.2710	+	28.1822i	−0.0199890	+	0.0346219i
$815$		0			0
$816$	95.6321	+	165.640i	0.117196	+	0.202990i
$817$	−1356.30	−	783.062i	−1.66010	−	0.958460i
$818$			614.278i			0.750952i
$819$	102.985	+	129.091i	0.125745	+	0.157621i
$820$		0			0
$821$	201.884	−	349.673i	0.245900	−	0.425911i	−0.716484	−	0.697603i	$-0.754250\pi$
$821$	201.884	−	349.673i	0.245900	−	0.425911i	0.962384	+	0.271692i	$0.0875832\pi$
$822$	523.752	−	302.388i	0.637168	−	0.367869i
$823$	433.014	+	750.003i	0.526141	+	0.911303i	0.999536	+	0.0304530i	$0.00969501\pi$
$823$	433.014	+	750.003i	0.526141	+	0.911303i	−0.473395	+	0.880850i	$0.656972\pi$
$824$	−484.912	−	279.964i	−0.588486	−	0.339762i
$825$		0			0
$826$	254.314	−	648.330i	0.307887	−	0.784903i
$827$	363.528			0.439574			0.219787	−	0.975548i	$-0.429464\pi$
$827$	363.528			0.439574			0.219787	+	0.975548i	$0.429464\pi$
$828$	−54.4776	+	94.3579i	−0.0657942	+	0.113959i
$829$	208.617	−	120.445i	0.251649	−	0.145290i	−0.368870	−	0.929481i	$-0.620255\pi$
$829$	208.617	−	120.445i	0.251649	−	0.145290i	0.620519	+	0.784191i	$0.286922\pi$
$830$		0			0
$831$	−250.142	−	144.420i	−0.301013	−	0.173790i
$832$		−	62.9097i		−	0.0756126i
$833$	−1318.92	−	300.529i	−1.58333	−	0.360779i
$834$	−381.917			−0.457934
$835$		0			0
$836$	−630.557	+	364.052i	−0.754255	+	0.435469i
$837$	−13.6758	−	23.6872i	−0.0163391	−	0.0283001i
$838$	559.979	+	323.304i	0.668232	+	0.385804i
$839$		−	214.638i		−	0.255826i	−0.991785	−	0.127913i	$-0.959172\pi$
$839$		−	214.638i		−	0.255826i	0.991785	−	0.127913i	$-0.0408278\pi$
$840$		0			0
$841$	−835.695			−0.993692
$842$	−461.846	+	799.941i	−0.548511	+	0.950049i
$843$	−57.4628	+	33.1762i	−0.0681647	+	0.0393549i
$844$	388.914	+	673.618i	0.460798	+	0.798126i
$845$		0			0
$846$		−	325.271i		−	0.384481i
$847$	72.2715	−	57.6561i	0.0853264	−	0.0680710i
$848$	−228.382			−0.269318
$849$	−333.849	+	578.244i	−0.393226	+	0.681088i
$850$		0			0
$851$	−18.0347	−	31.2369i	−0.0211923	−	0.0367062i
$852$	−102.779	−	59.3396i	−0.120633	−	0.0696474i
$853$			1388.39i			1.62765i	0.581110	+	0.813825i	$0.302618\pi$
$853$			1388.39i			1.62765i	−0.581110	+	0.813825i	$0.697382\pi$
$854$	661.891	−	99.8873i	0.775048	−	0.116964i
$855$		0			0
$856$	−209.213	+	362.367i	−0.244407	+	0.423326i
$857$	−950.012	+	548.489i	−1.10853	+	0.640011i	−0.938449	−	0.345419i	$-0.887737\pi$
$857$	−950.012	+	548.489i	−1.10853	+	0.640011i	−0.170083	+	0.985430i	$0.554404\pi$
$858$	−111.574	−	193.251i	−0.130039	−	0.225235i
$859$	−234.305	−	135.276i	−0.272764	−	0.157481i	0.357379	−	0.933959i	$-0.383670\pi$
$859$	−234.305	−	135.276i	−0.272764	−	0.157481i	−0.630143	+	0.776479i	$0.717004\pi$
$860$		0			0
$861$	40.1477	+	266.034i	0.0466291	+	0.308982i
$862$	665.042			0.771511
$863$	134.107	−	232.280i	0.155396	−	0.269154i	−0.777807	−	0.628503i	$-0.783668\pi$
$863$	134.107	−	232.280i	0.155396	−	0.269154i	0.933203	+	0.359349i	$0.117001\pi$
$864$	−25.4558	+	14.6969i	−0.0294628	+	0.0170103i
$865$		0			0
$866$	−39.2284	−	22.6485i	−0.0452984	−	0.0261530i
$867$			819.476i			0.945186i
$868$	−45.9576	−	57.6075i	−0.0529465	−	0.0663681i
$869$	1047.60			1.20552
$870$		0			0
$871$	668.519	−	385.970i	0.767530	−	0.443134i
$872$	−76.8228	−	133.061i	−0.0880995	−	0.152593i
$873$	−187.870	−	108.467i	−0.215200	−	0.124246i
$874$		−	807.025i		−	0.923370i
$875$		0			0
$876$	−67.5204			−0.0770781
$877$	253.705	−	439.430i	0.289288	−	0.501061i	−0.684352	−	0.729152i	$-0.739915\pi$
$877$	253.705	−	439.430i	0.289288	−	0.501061i	0.973640	+	0.228091i	$0.0732482\pi$
$878$	468.145	−	270.284i	0.533195	−	0.307840i
$879$	78.7948	+	136.477i	0.0896414	+	0.155264i
$880$		0			0
$881$			833.545i			0.946135i	0.881026	+	0.473067i	$0.156853\pi$
$881$			833.545i			0.946135i	−0.881026	+	0.473067i	$0.843147\pi$
$882$	46.1859	−	202.694i	0.0523650	−	0.229812i
$883$	1350.99			1.53000			0.765002	−	0.644028i	$-0.222738\pi$
$883$	1350.99			1.53000			0.765002	+	0.644028i	$0.222738\pi$
$884$	217.090	−	376.012i	0.245577	−	0.425353i
$885$		0			0
$886$	−87.4985	−	151.552i	−0.0987568	−	0.171052i
$887$	−324.005	−	187.065i	−0.365282	−	0.210896i	0.306113	−	0.951995i	$-0.400971\pi$
$887$	−324.005	−	187.065i	−0.365282	−	0.210896i	−0.671395	+	0.741099i	$0.734305\pi$
$888$		−	9.73077i		−	0.0109581i
$889$	−664.518	−	260.664i	−0.747489	−	0.293211i
$890$		0			0
$891$	−52.1316	+	90.2945i	−0.0585091	+	0.101341i
$892$	−436.326	+	251.913i	−0.489154	+	0.282413i
$893$	1204.63	+	2086.48i	1.34897	+	2.33649i
$894$	−345.967	−	199.744i	−0.386988	−	0.223427i
$895$		0			0
$896$	−61.9089	+	49.3891i	−0.0690948	+	0.0551218i
$897$	247.335			0.275735
$898$	−188.787	+	326.989i	−0.210230	+	0.364130i
$899$	10.4999	−	6.06210i	0.0116795	−	0.00674316i
$900$		0			0
$901$	−1365.04	−	788.105i	−1.51503	−	0.874701i
$902$		−	363.556i		−	0.403055i
$903$	−597.474	+	90.1660i	−0.661655	+	0.0998516i
$904$	135.166			0.149520
$905$		0			0
$906$	−159.162	+	91.8925i	−0.175676	+	0.101427i
$907$	−178.758	−	309.618i	−0.197087	−	0.341365i	0.750496	−	0.660875i	$-0.229815\pi$
$907$	−178.758	−	309.618i	−0.197087	−	0.341365i	−0.947583	+	0.319510i	$0.896482\pi$
$908$	463.881	+	267.822i	0.510882	+	0.294958i
$909$		−	151.960i		−	0.167173i
$910$		0			0
$911$	−1503.55			−1.65044			−0.825219	−	0.564813i	$-0.808948\pi$
$911$	−1503.55			−1.65044			−0.825219	+	0.564813i	$0.808948\pi$
$912$	108.859	−	188.550i	0.119363	−	0.206744i
$913$	1342.41	−	775.043i	1.47033	−	0.848897i
$914$	317.731	+	550.327i	0.347627	+	0.602108i
$915$		0			0
$916$		−	691.059i		−	0.754431i
$917$	325.652	+	408.202i	0.355127	+	0.445149i
$918$	−202.866			−0.220987
$919$	312.499	−	541.265i	0.340043	−	0.588971i	−0.644398	−	0.764691i	$-0.722892\pi$
$919$	312.499	−	541.265i	0.340043	−	0.588971i	0.984440	+	0.175719i	$0.0562251\pi$
$920$		0			0
$921$	−440.007	−	762.115i	−0.477750	−	0.827487i
$922$	−129.245	−	74.6199i	−0.140179	−	0.0809327i
$923$			269.409i			0.291884i
$924$	−102.583	+	261.516i	−0.111020	+	0.283026i
$925$		0			0
$926$	−416.171	+	720.829i	−0.449429	+	0.778433i
$927$	514.327	−	296.947i	0.554830	−	0.320331i
$928$	−6.51474	−	11.2839i	−0.00702019	−	0.0121593i
$929$	−942.883	−	544.374i	−1.01494	−	0.585978i	−0.102309	−	0.994753i	$-0.532623\pi$
$929$	−942.883	−	544.374i	−1.01494	−	0.585978i	−0.912636	+	0.408774i	$0.865956\pi$
$930$		0			0
$931$	454.408	+	1471.25i	0.488086	+	1.58029i
$932$	576.129			0.618164
$933$	−90.3447	+	156.482i	−0.0968325	+	0.167719i
$934$	−447.837	+	258.559i	−0.479483	+	0.276829i
$935$		0			0
$936$	57.7863	+	33.3629i	0.0617375	+	0.0356441i
$937$		−	252.836i		−	0.269835i	−0.990857	−	0.134918i	$-0.956923\pi$
$937$		−	252.836i		−	0.269835i	0.990857	−	0.134918i	$-0.0430770\pi$
$938$	−904.670	−	354.867i	−0.964467	−	0.378323i
$939$	460.498			0.490413
$940$		0			0
$941$	−332.262	+	191.832i	−0.353095	+	0.203859i	−0.666048	−	0.745909i	$-0.732015\pi$
$941$	−332.262	+	191.832i	−0.353095	+	0.203859i	0.312953	+	0.949769i	$0.398682\pi$
$942$	275.238	+	476.726i	0.292184	+	0.506078i
$943$	348.975	+	201.481i	0.370069	+	0.213660i
$944$		−	281.398i		−	0.298091i
$945$		0			0
$946$	816.495			0.863103
$947$	−140.892	+	244.032i	−0.148777	+	0.257690i	−0.930776	−	0.365591i	$-0.880867\pi$
$947$	−140.892	+	244.032i	−0.148777	+	0.257690i	0.781999	+	0.623280i	$0.214200\pi$
$948$	−271.285	+	156.627i	−0.286166	+	0.165218i
$949$	76.6377	+	132.740i	0.0807562	+	0.139874i
$950$		0			0
$951$		−	18.5715i		−	0.0195284i
$952$	−540.463	+	81.5624i	−0.567713	+	0.0856748i
$953$	332.322			0.348711			0.174356	−	0.984683i	$-0.444216\pi$
$953$	332.322			0.348711			0.174356	+	0.984683i	$0.444216\pi$
$954$	121.118	−	209.782i	0.126958	−	0.219897i
$955$		0			0
$956$	188.810	+	327.028i	0.197500	+	0.342080i
$957$	−40.0250	−	23.1085i	−0.0418234	−	0.0241468i
$958$			688.971i			0.719177i
$959$	257.900	+	1708.94i	0.268926	+	1.78200i
$960$		0			0
$961$	−466.646	+	808.255i	−0.485584	+	0.841056i
$962$	−19.1300	+	11.0447i	−0.0198857	+	0.0114810i
$963$	−221.904	−	384.348i	−0.230430	−	0.399116i
$964$	−169.478	−	97.8480i	−0.175807	−	0.101502i
$965$		0			0
$966$	−194.177	−	243.400i	−0.201012	−	0.251967i
$967$	−1155.53			−1.19496			−0.597482	−	0.801882i	$-0.703832\pi$
$967$	−1155.53			−1.19496			−0.597482	+	0.801882i	$0.703832\pi$
$968$	18.6782	−	32.3515i	0.0192956	−	0.0334210i
$969$	1301.31	−	751.310i	1.34294	−	0.775346i
$970$		0			0
$971$	−1307.94	−	755.140i	−1.34700	−	0.777693i	−0.359179	−	0.933269i	$-0.616943\pi$
$971$	−1307.94	−	755.140i	−1.34700	−	0.777693i	−0.987824	+	0.155576i	$0.950277\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	398.555	−	1016.04i	0.409614	−	1.04424i
$974$	−276.866			−0.284257
$975$		0			0
$976$	234.236	−	135.236i	0.239996	−	0.138562i
$977$	400.808	+	694.220i	0.410244	+	0.710563i	0.994916	−	0.100706i	$-0.0321103\pi$
$977$	400.808	+	694.220i	0.410244	+	0.710563i	−0.584672	+	0.811269i	$0.698777\pi$
$978$	−488.153	−	281.835i	−0.499134	−	0.288175i
$979$			128.182i			0.130932i
$980$		0			0
$981$	162.966			0.166122
$982$	−246.937	+	427.707i	−0.251463	+	0.435547i
$983$	948.116	−	547.395i	0.964513	−	0.556862i	0.0669540	−	0.997756i	$-0.478672\pi$
$983$	948.116	−	547.395i	0.964513	−	0.556862i	0.897559	+	0.440894i	$0.145339\pi$
$984$	54.3555	+	94.1465i	0.0552393	+	0.0956773i
$985$		0			0
$986$		−	89.9249i		−	0.0912018i
$987$	865.344	+	339.441i	0.876742	+	0.343912i
$988$	−494.235			−0.500238
$989$	−452.498	+	783.750i	−0.457531	+	0.792467i
$990$		0			0
$991$	−21.9962	−	38.0986i	−0.0221960	−	0.0384446i	0.854714	−	0.519099i	$-0.173732\pi$
$991$	−21.9962	−	38.0986i	−0.0221960	−	0.0384446i	−0.876910	+	0.480655i	$0.840399\pi$
$992$	−25.7873	−	14.8883i	−0.0259953	−	0.0150084i
$993$			611.277i			0.615586i
$994$	265.123	−	211.507i	0.266723	−	0.212784i
$995$		0			0
$996$	−231.754	+	401.410i	−0.232685	+	0.403022i
$997$	−10.6141	+	6.12803i	−0.0106460	+	0.00614647i	−0.505314	−	0.862936i	$-0.668623\pi$
$997$	−10.6141	+	6.12803i	−0.0106460	+	0.00614647i	0.494668	+	0.869082i	$0.335290\pi$
$998$	−237.191	−	410.827i	−0.237666	−	0.411650i
$999$	8.93828	+	5.16052i	0.00894723	+	0.00516569i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.p.b.901.3		8
5.2	odd	4		1050.3.q.c.649.7		16
5.3	odd	4		1050.3.q.c.649.2		16
5.4	even	2		210.3.o.a.61.2	yes	8
7.3	odd	6	inner	1050.3.p.b.451.3		8
15.14	odd	2		630.3.v.b.271.3		8
35.3	even	12		1050.3.q.c.199.7		16
35.9	even	6		1470.3.f.a.391.7		8
35.17	even	12		1050.3.q.c.199.2		16
35.19	odd	6		1470.3.f.a.391.6		8
35.24	odd	6		210.3.o.a.31.2	✓	8
105.59	even	6		630.3.v.b.451.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.a.31.2	✓	8	35.24	odd	6
210.3.o.a.61.2	yes	8	5.4	even	2
630.3.v.b.271.3		8	15.14	odd	2
630.3.v.b.451.3		8	105.59	even	6
1050.3.p.b.451.3		8	7.3	odd	6	inner
1050.3.p.b.901.3		8	1.1	even	1	trivial
1050.3.q.c.199.2		16	35.17	even	12
1050.3.q.c.199.7		16	35.3	even	12
1050.3.q.c.649.2		16	5.3	odd	4
1050.3.q.c.649.7		16	5.2	odd	4
1470.3.f.a.391.6		8	35.19	odd	6
1470.3.f.a.391.7		8	35.9	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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-6.51658 - 2.55620i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-6.51658 - 2.55620i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(-5.79240 - 10.0327i) q^{11} +(3.00000 + 1.73205i) q^{12} -7.86371i q^{13} +(-7.73861 + 6.17364i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-23.9080 + 13.8033i) q^{17} +(-2.12132 - 3.67423i) q^{18} +(27.2149 + 15.7125i) q^{19} +(11.9886 - 1.80922i) q^{21} -16.3834 q^{22} +(9.07959 - 15.7263i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-9.63104 - 5.56049i) q^{26} +5.19615i q^{27} +(2.08911 + 13.8433i) q^{28} -2.30331 q^{29} +(-4.55860 + 2.63191i) q^{31} +(2.82843 + 4.89898i) q^{32} +(17.3772 + 10.0327i) q^{33} +39.0416i q^{34} -6.00000 q^{36} +(0.993142 - 1.72017i) q^{37} +(38.4876 - 22.2208i) q^{38} +(6.81018 + 11.7956i) q^{39} +22.1905i q^{41} +(6.26139 - 15.9623i) q^{42} -49.8368 q^{43} +(-11.5848 + 20.0655i) q^{44} +(-12.8405 - 22.2404i) q^{46} +(66.3956 + 38.3335i) q^{47} -6.92820i q^{48} +(35.9317 + 33.3154i) q^{49} +(23.9080 - 41.4099i) q^{51} +(-13.6204 + 7.86371i) q^{52} +(28.5477 + 49.4461i) q^{53} +(6.36396 + 3.67423i) q^{54} +(18.4317 + 7.23003i) q^{56} -54.4297 q^{57} +(-1.62869 + 2.82097i) q^{58} +(-60.9245 + 35.1748i) q^{59} +(-58.5590 - 33.8091i) q^{61} +7.44416i q^{62} +(-16.4161 + 13.0963i) q^{63} +8.00000 q^{64} +(24.5751 - 14.1884i) q^{66} +(49.0823 + 85.0131i) q^{67} +(47.8160 + 27.6066i) q^{68} +31.4526i q^{69} -34.2597 q^{71} +(-4.24264 + 7.34847i) q^{72} +(-16.8801 + 9.74573i) q^{73} +(-1.40452 - 2.43269i) q^{74} -62.8501i q^{76} +(12.1010 + 80.1856i) q^{77} +19.2621 q^{78} +(-45.2142 + 78.3134i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(27.1777 + 15.6911i) q^{82} +133.803i q^{83} +(-15.1223 - 18.9557i) q^{84} +(-35.2400 + 61.0374i) q^{86} +(3.45496 - 1.99472i) q^{87} +(16.3834 + 28.3768i) q^{88} +(-9.58232 - 5.53235i) q^{89} +(-20.1012 + 51.2445i) q^{91} -36.3184 q^{92} +(4.55860 - 7.89573i) q^{93} +(93.8975 - 54.2118i) q^{94} +(-8.48528 - 4.89898i) q^{96} -72.3112i q^{97} +(66.2104 - 20.4496i) q^{98} -34.7544 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{3} - 8 q^{4} + 12 q^{9}+O(q^{10}) \) 8 * q - 12 * q^3 - 8 * q^4 + 12 * q^9	\( 8 q - 12 q^{3} - 8 q^{4} + 12 q^{9} - 4 q^{11} + 24 q^{12} - 40 q^{14} - 16 q^{16} - 84 q^{17} + 108 q^{19} + 48 q^{22} - 12 q^{23} - 96 q^{26} + 72 q^{29} - 132 q^{31} + 12 q^{33} - 48 q^{36} + 96 q^{37} + 168 q^{38} + 24 q^{39} + 72 q^{42} + 112 q^{43} - 8 q^{44} + 8 q^{46} + 24 q^{47} + 156 q^{49} + 84 q^{51} - 48 q^{52} - 32 q^{53} + 16 q^{56} - 216 q^{57} - 104 q^{58} + 132 q^{59} + 96 q^{61} + 64 q^{64} - 72 q^{66} + 120 q^{67} + 168 q^{68} + 8 q^{71} - 24 q^{73} - 16 q^{74} + 216 q^{77} + 192 q^{78} + 12 q^{79} - 36 q^{81} - 24 q^{82} - 40 q^{86} - 108 q^{87} - 48 q^{88} + 492 q^{89} - 308 q^{91} + 48 q^{92} + 132 q^{93} + 480 q^{94} - 24 q^{99}+O(q^{100}) \) 8 * q - 12 * q^3 - 8 * q^4 + 12 * q^9 - 4 * q^11 + 24 * q^12 - 40 * q^14 - 16 * q^16 - 84 * q^17 + 108 * q^19 + 48 * q^22 - 12 * q^23 - 96 * q^26 + 72 * q^29 - 132 * q^31 + 12 * q^33 - 48 * q^36 + 96 * q^37 + 168 * q^38 + 24 * q^39 + 72 * q^42 + 112 * q^43 - 8 * q^44 + 8 * q^46 + 24 * q^47 + 156 * q^49 + 84 * q^51 - 48 * q^52 - 32 * q^53 + 16 * q^56 - 216 * q^57 - 104 * q^58 + 132 * q^59 + 96 * q^61 + 64 * q^64 - 72 * q^66 + 120 * q^67 + 168 * q^68 + 8 * q^71 - 24 * q^73 - 16 * q^74 + 216 * q^77 + 192 * q^78 + 12 * q^79 - 36 * q^81 - 24 * q^82 - 40 * q^86 - 108 * q^87 - 48 * q^88 + 492 * q^89 - 308 * q^91 + 48 * q^92 + 132 * q^93 + 480 * q^94 - 24 * q^99

Introduction

L-functions

Modular forms

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