LMFDB - Embedded newform 1050.3.p.i.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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 92 x^{14} - 112 x^{13} + 5846 x^{12} - 7728 x^{11} + 197216 x^{10} - 298200 x^{9} + \cdots + 101626561 $ x^16 + 92x^14 - 112x^13 + 5846x^12 - 7728x^11 + 197216x^10 - 298200x^9 + 4836403x^8 - 6808704x^7 + 64376800x^6 - 91953512x^5 + 595763862x^4 - 630430976x^3 + 1087013404x^2 + 294123256x + 101626561
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{4}\cdot 7 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.3
Root			$-2.10711 - 3.64962i$ of defining polynomial
Character	$\chi$	$=$	1050.901
Dual form			1050.3.p.i.451.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(5.26304 - 4.61524i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(5.26304 - 4.61524i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(5.41099 + 9.37211i) q^{11} +(-3.00000 - 1.73205i) q^{12} -19.2715i q^{13} +(1.93096 + 9.70935i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(8.89730 - 5.13686i) q^{17} +(2.12132 + 3.67423i) q^{18} +(-18.0756 - 10.4359i) q^{19} +(3.89764 - 11.4808i) q^{21} -15.3046 q^{22} +(10.5373 - 18.2511i) q^{23} +(4.24264 - 2.44949i) q^{24} +(23.6026 + 13.6270i) q^{26} -5.19615i q^{27} +(-13.2569 - 4.50061i) q^{28} +19.0888 q^{29} +(-34.6556 + 20.0084i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(16.2330 + 9.37211i) q^{33} +14.5292i q^{34} -6.00000 q^{36} +(-25.1827 + 43.6177i) q^{37} +(25.5627 - 14.7586i) q^{38} +(-16.6896 - 28.9072i) q^{39} -22.7706i q^{41} +(11.3050 + 12.8918i) q^{42} +48.4307 q^{43} +(10.8220 - 18.7442i) q^{44} +(14.9020 + 25.8110i) q^{46} +(-57.6236 - 33.2690i) q^{47} +6.92820i q^{48} +(6.39913 - 48.5804i) q^{49} +(8.89730 - 15.4106i) q^{51} +(-33.3792 + 19.2715i) q^{52} +(2.47531 + 4.28736i) q^{53} +(6.36396 + 3.67423i) q^{54} +(14.8861 - 13.0539i) q^{56} -36.1511 q^{57} +(-13.4978 + 23.3789i) q^{58} +(-24.4105 + 14.0934i) q^{59} +(-60.6988 - 35.0445i) q^{61} -56.5924i q^{62} +(-4.09619 - 20.5966i) q^{63} +8.00000 q^{64} +(-22.9569 + 13.2542i) q^{66} +(9.65287 + 16.7193i) q^{67} +(-17.7946 - 10.2737i) q^{68} -36.5023i q^{69} +49.4968 q^{71} +(4.24264 - 7.34847i) q^{72} +(115.159 - 66.4872i) q^{73} +(-35.6137 - 61.6848i) q^{74} +41.7437i q^{76} +(71.7328 + 24.3527i) q^{77} +47.2053 q^{78} +(45.0404 - 78.0122i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(27.8882 + 16.1013i) q^{82} -101.045i q^{83} +(-23.7829 + 4.72987i) q^{84} +(-34.2456 + 59.3152i) q^{86} +(28.6332 - 16.5314i) q^{87} +(15.3046 + 26.5083i) q^{88} +(34.3077 + 19.8075i) q^{89} +(-88.9425 - 101.427i) q^{91} -42.1492 q^{92} +(-34.6556 + 60.0253i) q^{93} +(81.4920 - 47.0495i) q^{94} +(-8.48528 - 4.89898i) q^{96} +68.6944i q^{97} +(54.9737 + 42.1888i) q^{98} +32.4659 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 24 q^{3} - 16 q^{4} - 4 q^{7} + 24 q^{9}+O(q^{10}) $ 16 * q + 24 * q^3 - 16 * q^4 - 4 * q^7 + 24 * q^9	$ 16 q + 24 q^{3} - 16 q^{4} - 4 q^{7} + 24 q^{9} - 4 q^{11} - 48 q^{12} + 8 q^{14} - 32 q^{16} - 12 q^{17} - 72 q^{19} - 24 q^{21} + 48 q^{22} + 12 q^{23} - 32 q^{28} + 72 q^{29} + 120 q^{31} - 12 q^{33} - 96 q^{36} - 44 q^{37} + 72 q^{38} + 36 q^{39} + 24 q^{42} + 56 q^{43} - 8 q^{44} + 8 q^{46} + 24 q^{47} - 40 q^{49} - 12 q^{51} + 72 q^{52} - 32 q^{53} + 16 q^{56} - 144 q^{57} + 88 q^{58} + 132 q^{59} + 96 q^{61} - 60 q^{63} + 128 q^{64} + 72 q^{66} + 164 q^{67} + 24 q^{68} - 136 q^{71} + 348 q^{73} - 112 q^{74} - 96 q^{77} + 280 q^{79} - 72 q^{81} - 264 q^{82} - 24 q^{84} - 88 q^{86} + 108 q^{87} - 48 q^{88} - 300 q^{89} - 272 q^{91} - 48 q^{92} + 120 q^{93} - 384 q^{98} - 24 q^{99}+O(q^{100}) $ 16 * q + 24 * q^3 - 16 * q^4 - 4 * q^7 + 24 * q^9 - 4 * q^11 - 48 * q^12 + 8 * q^14 - 32 * q^16 - 12 * q^17 - 72 * q^19 - 24 * q^21 + 48 * q^22 + 12 * q^23 - 32 * q^28 + 72 * q^29 + 120 * q^31 - 12 * q^33 - 96 * q^36 - 44 * q^37 + 72 * q^38 + 36 * q^39 + 24 * q^42 + 56 * q^43 - 8 * q^44 + 8 * q^46 + 24 * q^47 - 40 * q^49 - 12 * q^51 + 72 * q^52 - 32 * q^53 + 16 * q^56 - 144 * q^57 + 88 * q^58 + 132 * q^59 + 96 * q^61 - 60 * q^63 + 128 * q^64 + 72 * q^66 + 164 * q^67 + 24 * q^68 - 136 * q^71 + 348 * q^73 - 112 * q^74 - 96 * q^77 + 280 * q^79 - 72 * q^81 - 264 * q^82 - 24 * q^84 - 88 * q^86 + 108 * q^87 - 48 * q^88 - 300 * q^89 - 272 * q^91 - 48 * q^92 + 120 * q^93 - 384 * q^98 - 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
$7$	5.26304	−	4.61524i	0.751863	−	0.659320i
$7$	5.26304	−	4.61524i	0.751863	−	0.659320i
$8$	2.82843			0.353553
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	5.41099	+	9.37211i	0.491908	+	0.852010i	0.999957	−	0.00931868i	$-0.00296627\pi$
$11$	5.41099	+	9.37211i	0.491908	+	0.852010i	−0.508049	+	0.861328i	$0.669633\pi$
$12$	−3.00000	−	1.73205i	−0.250000	−	0.144338i
$13$		−	19.2715i		−	1.48242i	−0.671273	−	0.741211i	$-0.734252\pi$
$13$		−	19.2715i		−	1.48242i	0.671273	−	0.741211i	$-0.265748\pi$
$14$	1.93096	+	9.70935i	0.137926	+	0.693525i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	8.89730	−	5.13686i	0.523371	−	0.302168i	−0.214942	−	0.976627i	$-0.568956\pi$
$17$	8.89730	−	5.13686i	0.523371	−	0.302168i	0.738313	+	0.674459i	$0.235623\pi$
$18$	2.12132	+	3.67423i	0.117851	+	0.204124i
$19$	−18.0756	−	10.4359i	−0.951346	−	0.549260i	−0.0578471	−	0.998325i	$-0.518424\pi$
$19$	−18.0756	−	10.4359i	−0.951346	−	0.549260i	−0.893499	+	0.449066i	$0.851757\pi$
$20$		0			0
$21$	3.89764	−	11.4808i	0.185602	−	0.546704i
$22$	−15.3046			−0.695663
$23$	10.5373	−	18.2511i	0.458143	−	0.793527i	−0.540720	−	0.841203i	$-0.681848\pi$
$23$	10.5373	−	18.2511i	0.458143	−	0.793527i	0.998863	+	0.0476755i	$0.0151813\pi$
$24$	4.24264	−	2.44949i	0.176777	−	0.102062i
$25$		0			0
$26$	23.6026	+	13.6270i	0.907794	+	0.524115i
$27$		−	5.19615i		−	0.192450i
$28$	−13.2569	−	4.50061i	−0.473460	−	0.160736i
$29$	19.0888			0.658235			0.329118	−	0.944289i	$-0.393249\pi$
$29$	19.0888			0.658235			0.329118	+	0.944289i	$0.393249\pi$
$30$		0			0
$31$	−34.6556	+	20.0084i	−1.11792	+	0.645434i	−0.940870	−	0.338768i	$-0.889990\pi$
$31$	−34.6556	+	20.0084i	−1.11792	+	0.645434i	−0.177054	+	0.984201i	$0.556657\pi$
$32$	−2.82843	−	4.89898i	−0.0883883	−	0.153093i
$33$	16.2330	+	9.37211i	0.491908	+	0.284003i
$34$			14.5292i			0.427330i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	−25.1827	+	43.6177i	−0.680614	+	1.17886i	0.294180	+	0.955750i	$0.404953\pi$
$37$	−25.1827	+	43.6177i	−0.680614	+	1.17886i	−0.974794	+	0.223107i	$0.928380\pi$
$38$	25.5627	−	14.7586i	0.672703	−	0.388385i
$39$	−16.6896	−	28.9072i	−0.427938	−	0.741211i
$40$		0			0
$41$		−	22.7706i		−	0.555382i	−0.960671	−	0.277691i	$-0.910431\pi$
$41$		−	22.7706i		−	0.555382i	0.960671	−	0.277691i	$-0.0895691\pi$
$42$	11.3050	+	12.8918i	0.269166	+	0.306947i
$43$	48.4307			1.12629			0.563147	−	0.826357i	$-0.309590\pi$
$43$	48.4307			1.12629			0.563147	+	0.826357i	$0.309590\pi$
$44$	10.8220	−	18.7442i	0.245954	−	0.426005i
$45$		0			0
$46$	14.9020	+	25.8110i	0.323956	+	0.561109i
$47$	−57.6236	−	33.2690i	−1.22603	−	0.707851i	−0.259836	−	0.965653i	$-0.583668\pi$
$47$	−57.6236	−	33.2690i	−1.22603	−	0.707851i	−0.966198	+	0.257802i	$0.917002\pi$
$48$			6.92820i			0.144338i
$49$	6.39913	−	48.5804i	0.130595	−	0.991436i
$50$		0			0
$51$	8.89730	−	15.4106i	0.174457	−	0.302168i
$52$	−33.3792	+	19.2715i	−0.641907	+	0.370605i
$53$	2.47531	+	4.28736i	0.0467040	+	0.0808937i	0.888432	−	0.459008i	$-0.151795\pi$
$53$	2.47531	+	4.28736i	0.0467040	+	0.0808937i	−0.841728	+	0.539901i	$0.818462\pi$
$54$	6.36396	+	3.67423i	0.117851	+	0.0680414i
$55$		0			0
$56$	14.8861	−	13.0539i	0.265824	−	0.233105i
$57$	−36.1511			−0.634231
$58$	−13.4978	+	23.3789i	−0.232721	+	0.403085i
$59$	−24.4105	+	14.0934i	−0.413737	+	0.238871i	−0.692394	−	0.721520i	$-0.743444\pi$
$59$	−24.4105	+	14.0934i	−0.413737	+	0.238871i	0.278657	+	0.960391i	$0.410111\pi$
$60$		0			0
$61$	−60.6988	−	35.0445i	−0.995062	−	0.574499i	−0.0882785	−	0.996096i	$-0.528137\pi$
$61$	−60.6988	−	35.0445i	−0.995062	−	0.574499i	−0.906784	+	0.421596i	$0.861470\pi$
$62$		−	56.5924i		−	0.912781i
$63$	−4.09619	−	20.5966i	−0.0650188	−	0.326931i
$64$	8.00000			0.125000
$65$		0			0
$66$	−22.9569	+	13.2542i	−0.347832	+	0.200821i
$67$	9.65287	+	16.7193i	0.144073	+	0.249541i	0.929027	−	0.370013i	$-0.120647\pi$
$67$	9.65287	+	16.7193i	0.144073	+	0.249541i	−0.784954	+	0.619554i	$0.787313\pi$
$68$	−17.7946	−	10.2737i	−0.261685	−	0.151084i
$69$		−	36.5023i		−	0.529018i
$70$		0			0
$71$	49.4968			0.697138			0.348569	−	0.937283i	$-0.386668\pi$
$71$	49.4968			0.697138			0.348569	+	0.937283i	$0.386668\pi$
$72$	4.24264	−	7.34847i	0.0589256	−	0.102062i
$73$	115.159	−	66.4872i	1.57752	−	0.910783i	0.582318	−	0.812961i	$-0.302146\pi$
$73$	115.159	−	66.4872i	1.57752	−	0.910783i	0.995204	−	0.0978221i	$-0.0311876\pi$
$74$	−35.6137	−	61.6848i	−0.481266	−	0.833578i
$75$		0			0
$76$			41.7437i			0.549260i
$77$	71.7328	+	24.3527i	0.931594	+	0.316269i
$78$	47.2053			0.605196
$79$	45.0404	−	78.0122i	0.570132	−	0.987497i	−0.426420	−	0.904525i	$-0.640226\pi$
$79$	45.0404	−	78.0122i	0.570132	−	0.987497i	0.996552	−	0.0829717i	$-0.0264411\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	27.8882	+	16.1013i	0.340100	+	0.196357i
$83$		−	101.045i		−	1.21741i	−0.793396	−	0.608706i	$-0.791689\pi$
$83$		−	101.045i		−	1.21741i	0.793396	−	0.608706i	$-0.208311\pi$
$84$	−23.7829	+	4.72987i	−0.283130	+	0.0563080i
$85$		0			0
$86$	−34.2456	+	59.3152i	−0.398205	+	0.689712i
$87$	28.6332	−	16.5314i	0.329118	−	0.190016i
$88$	15.3046	+	26.5083i	0.173916	+	0.301231i
$89$	34.3077	+	19.8075i	0.385479	+	0.222557i	0.680200	−	0.733027i	$-0.261893\pi$
$89$	34.3077	+	19.8075i	0.385479	+	0.222557i	−0.294720	+	0.955584i	$0.595226\pi$
$90$		0			0
$91$	−88.9425	−	101.427i	−0.977390	−	1.11458i
$92$	−42.1492			−0.458143
$93$	−34.6556	+	60.0253i	−0.372641	+	0.645434i
$94$	81.4920	−	47.0495i	0.866937	−	0.500526i
$95$		0			0
$96$	−8.48528	−	4.89898i	−0.0883883	−	0.0510310i
$97$			68.6944i			0.708190i	0.935210	+	0.354095i	$0.115211\pi$
$97$			68.6944i			0.708190i	−0.935210	+	0.354095i	$0.884789\pi$
$98$	54.9737	+	42.1888i	0.560956	+	0.430498i
$99$	32.4659			0.327939
$100$		0			0
$101$	−6.96199	+	4.01951i	−0.0689306	+	0.0397971i	−0.534069	−	0.845441i	$-0.679338\pi$
$101$	−6.96199	+	4.01951i	−0.0689306	+	0.0397971i	0.465139	+	0.885238i	$0.346004\pi$
$102$	12.5827	+	21.7939i	0.123360	+	0.213665i
$103$	−177.158	−	102.282i	−1.71998	−	0.993033i	−0.918911	−	0.394465i	$-0.870930\pi$
$103$	−177.158	−	102.282i	−1.71998	−	0.993033i	−0.801072	−	0.598568i	$-0.795737\pi$
$104$		−	54.5080i		−	0.524115i
$105$		0			0
$106$	−7.00124			−0.0660494
$107$	82.2769	−	142.508i	0.768943	−	1.33185i	−0.169193	−	0.985583i	$-0.554116\pi$
$107$	82.2769	−	142.508i	0.768943	−	1.33185i	0.938136	−	0.346266i	$-0.112551\pi$
$108$	−9.00000	+	5.19615i	−0.0833333	+	0.0481125i
$109$	39.5050	+	68.4247i	0.362432	+	0.627750i	0.988360	−	0.152130i	$-0.0486133\pi$
$109$	39.5050	+	68.4247i	0.362432	+	0.627750i	−0.625929	+	0.779880i	$0.715280\pi$
$110$		0			0
$111$			87.2354i			0.785905i
$112$	5.46158	+	27.4622i	0.0487641	+	0.245198i
$113$	−84.5690			−0.748398			−0.374199	−	0.927348i	$-0.622082\pi$
$113$	−84.5690			−0.748398			−0.374199	+	0.927348i	$0.622082\pi$
$114$	25.5627	−	44.2759i	0.224234	−	0.388385i
$115$		0			0
$116$	−19.0888	−	33.0628i	−0.164559	−	0.285024i
$117$	−50.0688	−	28.9072i	−0.427938	−	0.247070i
$118$		−	39.8621i		−	0.337815i
$119$	23.1190	−	68.0987i	0.194277	−	0.572258i
$120$		0			0
$121$	1.94240	−	3.36434i	0.0160529	−	0.0278044i
$122$	85.8410	−	49.5603i	0.703615	−	0.406232i
$123$	−19.7200	−	34.1560i	−0.160325	−	0.277691i
$124$	69.3113	+	40.0169i	0.558962	+	0.322717i
$125$		0			0
$126$	28.1221	+	9.54723i	0.223191	+	0.0757717i
$127$	101.777			0.801393			0.400697	−	0.916211i	$-0.368768\pi$
$127$	101.777			0.801393			0.400697	+	0.916211i	$0.368768\pi$
$128$	−5.65685	+	9.79796i	−0.0441942	+	0.0765466i
$129$	72.6460	−	41.9422i	0.563147	−	0.325133i
$130$		0			0
$131$	61.2264	+	35.3491i	0.467377	+	0.269840i	0.715141	−	0.698980i	$-0.246362\pi$
$131$	61.2264	+	35.3491i	0.467377	+	0.269840i	−0.247764	+	0.968820i	$0.579696\pi$
$132$		−	37.4884i		−	0.284003i
$133$	−143.297	+	28.4984i	−1.07742	+	0.214273i
$134$	−27.3024			−0.203750
$135$		0			0
$136$	25.1654	−	14.5292i	0.185039	−	0.106833i
$137$	−58.9138	−	102.042i	−0.430027	−	0.744829i	0.566848	−	0.823823i	$-0.308163\pi$
$137$	−58.9138	−	102.042i	−0.430027	−	0.744829i	−0.996875	+	0.0789932i	$0.974829\pi$
$138$	44.7060	+	25.8110i	0.323956	+	0.187036i
$139$			158.507i			1.14034i	0.821528	+	0.570168i	$0.193122\pi$
$139$			158.507i			1.14034i	−0.821528	+	0.570168i	$0.806878\pi$
$140$		0			0
$141$	−115.247			−0.817356
$142$	−34.9995	+	60.6209i	−0.246475	+	0.426908i
$143$	180.614	−	104.278i	1.26304	−	0.729215i
$144$	6.00000	+	10.3923i	0.0416667	+	0.0721688i
$145$		0			0
$146$			188.054i			1.28804i
$147$	−32.4731	−	78.4123i	−0.220906	−	0.533417i
$148$	100.731			0.680614
$149$	147.948	−	256.254i	0.992940	−	1.71982i	0.393747	−	0.919219i	$-0.371179\pi$
$149$	147.948	−	256.254i	0.992940	−	1.71982i	0.599193	−	0.800604i	$-0.295488\pi$
$150$		0			0
$151$	62.6478	+	108.509i	0.414886	+	0.718604i	0.995417	−	0.0956344i	$-0.0304880\pi$
$151$	62.6478	+	108.509i	0.414886	+	0.718604i	−0.580530	+	0.814239i	$0.697155\pi$
$152$	−51.1254	−	29.5173i	−0.336352	−	0.194193i
$153$		−	30.8212i		−	0.201445i
$154$	−80.5486	+	70.6343i	−0.523043	+	0.458665i
$155$		0			0
$156$	−33.3792	+	57.8144i	−0.213969	+	0.370605i
$157$	−4.61909	+	2.66684i	−0.0294210	+	0.0169862i	−0.514638	−	0.857407i	$-0.672074\pi$
$157$	−4.61909	+	2.66684i	−0.0294210	+	0.0169862i	0.485217	+	0.874394i	$0.338740\pi$
$158$	63.6967	+	110.326i	0.403144	+	0.698266i
$159$	7.42593	+	4.28736i	0.0467040	+	0.0269646i
$160$		0			0
$161$	−28.7752	−	144.689i	−0.178728	−	0.898686i
$162$	12.7279			0.0785674
$163$	119.623	−	207.193i	0.733883	−	1.27112i	−0.221329	−	0.975199i	$-0.571039\pi$
$163$	119.623	−	207.193i	0.733883	−	1.27112i	0.955212	−	0.295923i	$-0.0956273\pi$
$164$	−39.4399	+	22.7706i	−0.240487	+	0.138845i
$165$		0			0
$166$	123.754	+	71.4497i	0.745509	+	0.430420i
$167$			310.440i			1.85892i	0.368918	+	0.929462i	$0.379728\pi$
$167$			310.440i			1.85892i	−0.368918	+	0.929462i	$0.620272\pi$
$168$	11.0242	−	32.4726i	0.0656202	−	0.193289i
$169$	−202.390			−1.19757
$170$		0			0
$171$	−54.2267	+	31.3078i	−0.317115	+	0.183087i
$172$	−48.4307	−	83.8844i	−0.281574	−	0.487700i
$173$	−78.7285	−	45.4539i	−0.455078	−	0.262739i	0.254894	−	0.966969i	$-0.417959\pi$
$173$	−78.7285	−	45.4539i	−0.455078	−	0.262739i	−0.709972	+	0.704230i	$0.751293\pi$
$174$			46.7579i			0.268723i
$175$		0			0
$176$	−43.2879			−0.245954
$177$	−24.4105	+	42.2802i	−0.137912	+	0.238871i
$178$	−48.5184	+	28.0121i	−0.272575	+	0.157371i
$179$	121.577	+	210.577i	0.679200	+	1.17641i	0.975222	+	0.221228i	$0.0710066\pi$
$179$	121.577	+	210.577i	0.679200	+	1.17641i	−0.296022	+	0.955181i	$0.595660\pi$
$180$		0			0
$181$			245.993i			1.35907i	0.733641	+	0.679537i	$0.237819\pi$
$181$			245.993i			1.35907i	−0.733641	+	0.679537i	$0.762181\pi$
$182$	187.113	−	37.2125i	1.02810	−	0.204464i
$183$	−121.398			−0.663375
$184$	29.8040	−	51.6220i	0.161978	−	0.280554i
$185$		0			0
$186$	−49.0105	−	84.8886i	−0.263497	−	0.456390i
$187$	96.2864	+	55.5910i	0.514901	+	0.297278i
$188$			133.076i			0.707851i
$189$	−23.9815	−	27.3475i	−0.126886	−	0.144696i
$190$		0			0
$191$	20.6108	−	35.6989i	0.107910	−	0.186905i	−0.807014	−	0.590533i	$-0.798918\pi$
$191$	20.6108	−	35.6989i	0.107910	−	0.186905i	0.914923	+	0.403628i	$0.132251\pi$
$192$	12.0000	−	6.92820i	0.0625000	−	0.0360844i
$193$	−94.8727	−	164.324i	−0.491568	−	0.851422i	0.508384	−	0.861130i	$-0.330243\pi$
$193$	−94.8727	−	164.324i	−0.491568	−	0.851422i	−0.999953	+	0.00970872i	$0.996910\pi$
$194$	−84.1331	−	48.5743i	−0.433676	−	0.250383i
$195$		0			0
$196$	−90.5428	+	37.4967i	−0.461953	+	0.191310i
$197$	362.318			1.83918			0.919589	−	0.392882i	$-0.128522\pi$
$197$	362.318			1.83918			0.919589	+	0.392882i	$0.128522\pi$
$198$	−22.9569	+	39.7625i	−0.115944	+	0.200821i
$199$	−33.4433	+	19.3085i	−0.168057	+	0.0970278i	−0.581669	−	0.813425i	$-0.697600\pi$
$199$	−33.4433	+	19.3085i	−0.168057	+	0.0970278i	0.413612	+	0.910453i	$0.364267\pi$
$200$		0			0
$201$	28.9586	+	16.7193i	0.144073	+	0.0831804i
$202$		−	11.3689i		−	0.0562816i
$203$	100.465	−	88.0995i	0.494902	−	0.433987i
$204$	−35.5892			−0.174457
$205$		0			0
$206$	250.540	−	144.649i	1.21621	−	0.702180i
$207$	−31.6119	−	54.7534i	−0.152714	−	0.264509i
$208$	66.7584	+	38.5430i	0.320954	+	0.185303i
$209$		−	225.875i		−	1.08074i
$210$		0			0
$211$	−136.551			−0.647163			−0.323581	−	0.946200i	$-0.604887\pi$
$211$	−136.551			−0.647163			−0.323581	+	0.946200i	$0.604887\pi$
$212$	4.95062	−	8.57473i	0.0233520	−	0.0404468i
$213$	74.2452	−	42.8655i	0.348569	−	0.201246i
$214$	116.357	+	201.537i	0.543725	+	0.941760i
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	−90.0502	+	265.249i	−0.414978	+	1.22235i
$218$	−111.737			−0.512556
$219$	115.159	−	199.461i	0.525841	−	0.910783i
$220$		0			0
$221$	−98.9949	−	171.464i	−0.447941	−	0.775856i
$222$	−106.841	−	61.6848i	−0.481266	−	0.277859i
$223$			154.949i			0.694839i	0.937710	+	0.347419i	$0.112942\pi$
$223$			154.949i			0.694839i	−0.937710	+	0.347419i	$0.887058\pi$
$224$	−37.4961	−	12.7296i	−0.167393	−	0.0568288i
$225$		0			0
$226$	59.7993	−	103.575i	0.264599	−	0.458299i
$227$	−19.3590	+	11.1769i	−0.0852818	+	0.0492375i	−0.542034	−	0.840356i	$-0.682346\pi$
$227$	−19.3590	+	11.1769i	−0.0852818	+	0.0492375i	0.456753	+	0.889594i	$0.349012\pi$
$228$	36.1511	+	62.6156i	0.158558	+	0.274630i
$229$	25.9105	+	14.9594i	0.113146	+	0.0653250i	0.555505	−	0.831513i	$-0.312525\pi$
$229$	25.9105	+	14.9594i	0.113146	+	0.0653250i	−0.442359	+	0.896838i	$0.645858\pi$
$230$		0			0
$231$	128.689	−	25.5933i	0.557096	−	0.110793i
$232$	53.9913			0.232721
$233$	−126.541	+	219.176i	−0.543095	+	0.940669i	0.455629	+	0.890170i	$0.349414\pi$
$233$	−126.541	+	219.176i	−0.543095	+	0.940669i	−0.998724	+	0.0504987i	$0.983919\pi$
$234$	70.8079	−	40.8810i	0.302598	−	0.174705i
$235$		0			0
$236$	48.8209	+	28.1868i	0.206868	+	0.119436i
$237$		−	156.024i		−	0.658331i
$238$	67.0559	+	76.4679i	0.281747	+	0.321294i
$239$	121.009			0.506315			0.253158	−	0.967425i	$-0.418531\pi$
$239$	121.009			0.506315			0.253158	+	0.967425i	$0.418531\pi$
$240$		0			0
$241$	249.755	−	144.196i	1.03633	−	0.598323i	0.117536	−	0.993069i	$-0.462501\pi$
$241$	249.755	−	144.196i	1.03633	−	0.598323i	0.918791	+	0.394745i	$0.129167\pi$
$242$	2.74697	+	4.75789i	0.0113511	+	0.0196607i
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$			140.178i			0.574499i
$245$		0			0
$246$	55.7765			0.226734
$247$	−201.116	+	348.343i	−0.814234	+	1.41030i
$248$	−98.0209	+	56.5924i	−0.395246	+	0.228195i
$249$	−87.5076	−	151.568i	−0.351436	−	0.608706i
$250$		0			0
$251$		−	422.260i		−	1.68231i	−0.540795	−	0.841155i	$-0.681876\pi$
$251$		−	422.260i		−	1.68231i	0.540795	−	0.841155i	$-0.318124\pi$
$252$	−31.5782	+	27.6914i	−0.125310	+	0.109887i
$253$	228.069			0.901457
$254$	−71.9672	+	124.651i	−0.283335	+	0.490751i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−64.5077	−	37.2435i	−0.251003	−	0.144916i	0.369221	−	0.929342i	$-0.379625\pi$
$257$	−64.5077	−	37.2435i	−0.251003	−	0.144916i	−0.620223	+	0.784425i	$0.712958\pi$
$258$			118.630i			0.459808i
$259$	68.7687	+	345.786i	0.265516	+	1.33508i
$260$		0			0
$261$	28.6332	−	49.5942i	0.109706	−	0.190016i
$262$	−86.5872	+	49.9911i	−0.330486	+	0.190806i
$263$	156.637	+	271.304i	0.595579	+	1.03157i	0.993465	+	0.114139i	$0.0364108\pi$
$263$	156.637	+	271.304i	0.595579	+	1.03157i	−0.397885	+	0.917435i	$0.630256\pi$
$264$	45.9138	+	26.5083i	0.173916	+	0.100410i
$265$		0			0
$266$	66.4229	−	195.653i	0.249710	−	0.735539i
$267$	68.6153			0.256986
$268$	19.3057	−	33.4385i	0.0720363	−	0.124771i
$269$	−138.011	+	79.6809i	−0.513053	+	0.296211i	−0.734088	−	0.679055i	$-0.762390\pi$
$269$	−138.011	+	79.6809i	−0.513053	+	0.296211i	0.221035	+	0.975266i	$0.429057\pi$
$270$		0			0
$271$	−163.041	−	94.1320i	−0.601629	−	0.347350i	0.168053	−	0.985778i	$-0.446252\pi$
$271$	−163.041	−	94.1320i	−0.601629	−	0.347350i	−0.769682	+	0.638427i	$0.779585\pi$
$272$			41.0949i			0.151084i
$273$	−221.252	−	75.1133i	−0.810446	−	0.275140i
$274$	166.633			0.608151
$275$		0			0
$276$	−63.2238	+	36.5023i	−0.229072	+	0.132255i
$277$	3.52372	+	6.10326i	0.0127210	+	0.0220334i	0.872316	−	0.488943i	$-0.162617\pi$
$277$	3.52372	+	6.10326i	0.0127210	+	0.0220334i	−0.859595	+	0.510976i	$0.829284\pi$
$278$	−194.130	−	112.081i	−0.698311	−	0.403170i
$279$			120.051i			0.430289i
$280$		0			0
$281$	198.386			0.705998			0.352999	−	0.935624i	$-0.385162\pi$
$281$	198.386			0.705998			0.352999	+	0.935624i	$0.385162\pi$
$282$	81.4920	−	141.148i	0.288979	−	0.500526i
$283$	163.790	−	94.5641i	0.578763	−	0.334149i	−0.181879	−	0.983321i	$-0.558218\pi$
$283$	163.790	−	94.5641i	0.578763	−	0.334149i	0.760641	+	0.649172i	$0.224885\pi$
$284$	−49.4968	−	85.7309i	−0.174284	−	0.301869i
$285$		0			0
$286$			294.942i			1.03127i
$287$	−105.092	−	119.843i	−0.366174	−	0.417571i
$288$	−16.9706			−0.0589256
$289$	−91.7253	+	158.873i	−0.317389	+	0.549733i
$290$		0			0
$291$	59.4911	+	103.042i	0.204437	+	0.354095i
$292$	−230.318	−	132.974i	−0.788761	−	0.455391i
$293$			486.090i			1.65901i	0.558499	+	0.829505i	$0.311378\pi$
$293$			486.090i			1.65901i	−0.558499	+	0.829505i	$0.688622\pi$
$294$	118.997	+	15.6746i	0.404752	+	0.0533150i
$295$		0			0
$296$	−71.2274	+	123.370i	−0.240633	+	0.416789i
$297$	48.6989	−	28.1163i	0.163969	−	0.0946678i
$298$	209.230	+	362.397i	0.702115	+	1.21610i
$299$	−351.726	−	203.069i	−1.17634	−	0.679161i
$300$		0			0
$301$	254.892	−	223.519i	0.846818	−	0.742588i
$302$	−177.195			−0.586738
$303$	−6.96199	+	12.0585i	−0.0229769	+	0.0397971i
$304$	72.3023	−	41.7437i	0.237836	−	0.137315i
$305$		0			0
$306$	37.7481	+	21.7939i	0.123360	+	0.0712217i
$307$			427.589i			1.39280i	0.717655	+	0.696399i	$0.245216\pi$
$307$			427.589i			1.39280i	−0.717655	+	0.696399i	$0.754784\pi$
$308$	−29.5526	−	148.598i	−0.0959499	−	0.482460i
$309$	−354.317			−1.14666
$310$		0			0
$311$	−311.852	+	180.048i	−1.00274	+	0.578931i	−0.909057	−	0.416671i	$-0.863197\pi$
$311$	−311.852	+	180.048i	−1.00274	+	0.578931i	−0.0936811	+	0.995602i	$0.529863\pi$
$312$	−47.2053	−	81.7620i	−0.151299	−	0.262058i
$313$	−505.696	−	291.964i	−1.61564	−	0.932792i	−0.988029	−	0.154267i	$-0.950698\pi$
$313$	−505.696	−	291.964i	−1.61564	−	0.932792i	−0.627614	−	0.778525i	$-0.715968\pi$
$314$		−	7.54295i		−	0.0240221i
$315$		0			0
$316$	−180.162			−0.570132
$317$	180.700	−	312.982i	0.570032	−	0.987324i	−0.426530	−	0.904473i	$-0.640264\pi$
$317$	180.700	−	312.982i	0.570032	−	0.987324i	0.996562	−	0.0828508i	$-0.0264025\pi$
$318$	−10.5019	+	6.06325i	−0.0330247	+	0.0190668i
$319$	103.289	+	178.902i	0.323791	+	0.560823i
$320$		0			0
$321$		−	285.016i		−	0.887899i
$322$	197.554	+	67.0680i	0.613521	+	0.208286i
$323$	−214.432			−0.663875
$324$	−9.00000	+	15.5885i	−0.0277778	+	0.0481125i
$325$		0			0
$326$	169.172	+	293.015i	0.518934	+	0.898819i
$327$	118.515	+	68.4247i	0.362432	+	0.209250i
$328$		−	64.4051i		−	0.196357i
$329$	−456.819	+	90.8507i	−1.38851	+	0.276142i
$330$		0			0
$331$	−147.993	+	256.331i	−0.447108	+	0.774415i	−0.998196	−	0.0600326i	$-0.980880\pi$
$331$	−147.993	+	256.331i	−0.447108	+	0.774415i	0.551088	+	0.834447i	$0.314213\pi$
$332$	−175.015	+	101.045i	−0.527154	+	0.304353i
$333$	75.5481	+	130.853i	0.226871	+	0.392952i
$334$	−380.210	−	219.514i	−1.13835	−	0.657229i
$335$		0			0
$336$	31.9753	+	36.4634i	0.0951646	+	0.108522i
$337$	22.0162			0.0653300			0.0326650	−	0.999466i	$-0.489601\pi$
$337$	22.0162			0.0653300			0.0326650	+	0.999466i	$0.489601\pi$
$338$	143.111	−	247.876i	0.423406	−	0.733361i
$339$	−126.854	+	73.2389i	−0.374199	+	0.216044i
$340$		0			0
$341$	−375.043	−	216.531i	−1.09983	−	0.634988i
$342$		−	88.5519i		−	0.258924i
$343$	−190.531	−	285.214i	−0.555484	−	0.831527i
$344$	136.983			0.398205
$345$		0			0
$346$	111.339	−	64.2815i	0.321789	−	0.185785i
$347$	−141.953	−	245.870i	−0.409086	−	0.708559i	0.585701	−	0.810527i	$-0.300819\pi$
$347$	−141.953	−	245.870i	−0.409086	−	0.708559i	−0.994788	+	0.101969i	$0.967486\pi$
$348$	−57.2665	−	33.0628i	−0.164559	−	0.0950080i
$349$			317.175i			0.908811i	0.890795	+	0.454406i	$0.150148\pi$
$349$			317.175i			0.908811i	−0.890795	+	0.454406i	$0.849852\pi$
$350$		0			0
$351$	−100.138			−0.285292
$352$	30.6092	−	53.0166i	0.0869579	−	0.150615i
$353$	101.275	−	58.4712i	0.286898	−	0.165641i	−0.349644	−	0.936883i	$-0.613697\pi$
$353$	101.275	−	58.4712i	0.286898	−	0.165641i	0.636542	+	0.771242i	$0.280364\pi$
$354$	−34.5216	−	59.7932i	−0.0975187	−	0.168907i
$355$		0			0
$356$		−	79.2302i		−	0.222557i
$357$	−24.2967	−	122.170i	−0.0680579	−	0.342212i
$358$	−343.871			−0.960534
$359$	−116.793	+	202.291i	−0.325329	+	0.563486i	−0.981579	−	0.191058i	$-0.938808\pi$
$359$	−116.793	+	202.291i	−0.325329	+	0.563486i	0.656250	+	0.754543i	$0.272142\pi$
$360$		0			0
$361$	37.3175	+	64.6359i	0.103373	+	0.179047i
$362$	−301.278	−	173.943i	−0.832260	−	0.480505i
$363$		−	6.72867i		−	0.0185363i
$364$	−86.7334	+	255.479i	−0.238279	+	0.701866i
$365$		0			0
$366$	85.8410	−	148.681i	0.234538	−	0.406232i
$367$	−443.469	+	256.037i	−1.20836	+	0.697648i	−0.962401	−	0.271632i	$-0.912437\pi$
$367$	−443.469	+	256.037i	−1.20836	+	0.697648i	−0.245960	+	0.969280i	$0.579103\pi$
$368$	42.1492	+	73.0045i	0.114536	+	0.198382i
$369$	−59.1599	−	34.1560i	−0.160325	−	0.0925636i
$370$		0			0
$371$	32.8149	+	11.1404i	0.0884498	+	0.0300280i
$372$	138.623			0.372641
$373$	−278.204	+	481.863i	−0.745854	+	1.29186i	0.203941	+	0.978983i	$0.434625\pi$
$373$	−278.204	+	481.863i	−0.745854	+	1.29186i	−0.949795	+	0.312874i	$0.898708\pi$
$374$	−136.170	+	78.6175i	−0.364090	+	0.210207i
$375$		0			0
$376$	−162.984	−	94.0989i	−0.433468	−	0.250263i
$377$		−	367.870i		−	0.975782i
$378$	50.4512	−	10.0336i	0.133469	−	0.0265438i
$379$	−536.301			−1.41504			−0.707521	−	0.706692i	$-0.750187\pi$
$379$	−536.301			−1.41504			−0.707521	+	0.706692i	$0.750187\pi$
$380$		0			0
$381$	152.665	−	88.1414i	0.400697	−	0.231342i
$382$	29.1480	+	50.4859i	0.0763038	+	0.132162i
$383$	−25.4184	−	14.6753i	−0.0663666	−	0.0383168i	0.466450	−	0.884548i	$-0.345533\pi$
$383$	−25.4184	−	14.6753i	−0.0663666	−	0.0383168i	−0.532816	+	0.846231i	$0.678866\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	268.341			0.695183
$387$	72.6460	−	125.827i	0.187716	−	0.325133i
$388$	118.982	−	68.6944i	0.306655	−	0.177047i
$389$	349.242	+	604.905i	0.897795	+	1.55503i	0.830307	+	0.557306i	$0.188165\pi$
$389$	349.242	+	604.905i	0.897795	+	1.55503i	0.0674875	+	0.997720i	$0.478502\pi$
$390$		0			0
$391$		−	216.514i		−	0.553745i
$392$	18.0995	−	137.406i	0.0461721	−	0.350526i
$393$	122.453			0.311585
$394$	−256.198	+	443.747i	−0.650248	+	1.12626i
$395$		0			0
$396$	−32.4659	−	56.2326i	−0.0819847	−	0.142002i
$397$	177.270	+	102.347i	0.446525	+	0.257801i	0.706361	−	0.707851i	$-0.250335\pi$
$397$	177.270	+	102.347i	0.446525	+	0.257801i	−0.259837	+	0.965653i	$0.583669\pi$
$398$		−	54.6127i		−	0.137218i
$399$	−190.265	+	166.846i	−0.476854	+	0.418161i
$400$		0			0
$401$	−214.984	+	372.363i	−0.536119	+	0.928585i	0.462989	+	0.886364i	$0.346777\pi$
$401$	−214.984	+	372.363i	−0.536119	+	0.928585i	−0.999108	+	0.0422215i	$0.986556\pi$
$402$	−40.9537	+	23.6446i	−0.101875	+	0.0588174i
$403$	385.592	+	667.865i	0.956805	+	1.65723i
$404$	13.9240	+	8.03902i	0.0344653	+	0.0198986i
$405$		0			0
$406$	36.8598	+	185.340i	0.0907876	+	0.456502i
$407$	−545.053			−1.33920
$408$	25.1654	−	43.5877i	0.0616798	−	0.106833i
$409$	15.3567	−	8.86618i	0.0375469	−	0.0216777i	−0.481109	−	0.876661i	$-0.659766\pi$
$409$	15.3567	−	8.86618i	0.0375469	−	0.0216777i	0.518656	+	0.854983i	$0.326433\pi$
$410$		0			0
$411$	−176.741	−	102.042i	−0.430027	−	0.248276i
$412$			409.129i			0.993033i
$413$	−63.4289	+	186.834i	−0.153581	+	0.452383i
$414$	89.4119			0.215971
$415$		0			0
$416$	−94.4106	+	54.5080i	−0.226948	+	0.131029i
$417$	137.271	+	237.760i	0.329187	+	0.570168i
$418$	276.639	+	159.718i	0.661816	+	0.382100i
$419$			440.768i			1.05195i	0.850499	+	0.525977i	$0.176300\pi$
$419$			440.768i			1.05195i	−0.850499	+	0.525977i	$0.823700\pi$
$420$		0			0
$421$	−143.012			−0.339696			−0.169848	−	0.985470i	$-0.554328\pi$
$421$	−143.012			−0.339696			−0.169848	+	0.985470i	$0.554328\pi$
$422$	96.5564	−	167.241i	0.228807	−	0.396305i
$423$	−172.871	+	99.8070i	−0.408678	+	0.235950i
$424$	7.00124	+	12.1265i	0.0165123	+	0.0286002i
$425$		0			0
$426$			121.242i			0.284605i
$427$	−481.199	+	95.6991i	−1.12693	+	0.224120i
$428$	−329.108			−0.768943
$429$	180.614	−	312.833i	0.421012	−	0.729215i
$430$		0			0
$431$	391.608	+	678.285i	0.908604	+	1.57375i	0.816005	+	0.578045i	$0.196184\pi$
$431$	391.608	+	678.285i	0.908604	+	1.57375i	0.0925988	+	0.995704i	$0.470483\pi$
$432$	18.0000	+	10.3923i	0.0416667	+	0.0240563i
$433$		−	286.669i		−	0.662053i	−0.943622	−	0.331026i	$-0.892605\pi$
$433$		−	286.669i		−	0.662053i	0.943622	−	0.331026i	$-0.107395\pi$
$434$	−261.188	−	297.848i	−0.601815	−	0.686286i
$435$		0			0
$436$	79.0101	−	136.849i	0.181216	−	0.313875i
$437$	−380.935	+	219.933i	−0.871705	+	0.503279i
$438$	162.860	+	282.081i	0.371826	+	0.644021i
$439$	−295.016	−	170.328i	−0.672018	−	0.387990i	0.124823	−	0.992179i	$-0.460164\pi$
$439$	−295.016	−	170.328i	−0.672018	−	0.387990i	−0.796841	+	0.604189i	$0.793497\pi$
$440$		0			0
$441$	−116.617	−	89.4960i	−0.264437	−	0.202939i
$442$	280.000			0.633484
$443$	197.629	−	342.304i	0.446116	−	0.772696i	−0.552013	−	0.833835i	$-0.686140\pi$
$443$	197.629	−	342.304i	0.446116	−	0.772696i	0.998129	+	0.0611396i	$0.0194735\pi$
$444$	151.096	−	87.2354i	0.340307	−	0.196476i
$445$		0			0
$446$	−189.773	−	109.566i	−0.425500	−	0.245663i
$447$		−	512.507i		−	1.14655i
$448$	42.1043	−	36.9219i	0.0939828	−	0.0824150i
$449$	665.078			1.48124			0.740621	−	0.671923i	$-0.234531\pi$
$449$	665.078			1.48124			0.740621	+	0.671923i	$0.234531\pi$
$450$		0			0
$451$	213.409	−	123.212i	0.473190	−	0.273197i
$452$	84.5690	+	146.478i	0.187100	+	0.324066i
$453$	187.944	+	108.509i	0.414886	+	0.239535i
$454$		−	31.6131i		−	0.0696323i
$455$		0			0
$456$	−102.251			−0.224234
$457$	255.468	−	442.484i	0.559012	−	0.968236i	−0.438568	−	0.898698i	$-0.644514\pi$
$457$	255.468	−	442.484i	0.559012	−	0.968236i	0.997579	−	0.0695382i	$-0.0221526\pi$
$458$	−36.6429	+	21.1558i	−0.0800064	+	0.0461917i
$459$	−26.6919	−	46.2317i	−0.0581523	−	0.100723i
$460$		0			0
$461$		−	174.303i		−	0.378097i	−0.981968	−	0.189049i	$-0.939460\pi$
$461$		−	174.303i		−	0.378097i	0.981968	−	0.189049i	$-0.0605404\pi$
$462$	−59.6518	+	175.709i	−0.129116	+	0.380322i
$463$	−755.187			−1.63107			−0.815537	−	0.578705i	$-0.803558\pi$
$463$	−755.187			−1.63107			−0.815537	+	0.578705i	$0.803558\pi$
$464$	−38.1776	+	66.1256i	−0.0822794	+	0.142512i
$465$		0			0
$466$	−178.956	−	309.961i	−0.384026	−	0.665153i
$467$	490.666	+	283.286i	1.05068	+	0.606609i	0.922839	−	0.385186i	$-0.125863\pi$
$467$	490.666	+	283.286i	1.05068	+	0.606609i	0.127839	+	0.991795i	$0.459196\pi$
$468$			115.629i			0.247070i
$469$	127.967	+	43.4438i	0.272850	+	0.0926307i
$470$		0			0
$471$	−4.61909	+	8.00051i	−0.00980699	+	0.0169862i
$472$	−69.0432	+	39.8621i	−0.146278	+	0.0844537i
$473$	262.058	+	453.897i	0.554033	+	0.959614i
$474$	191.090	+	110.326i	0.403144	+	0.232755i
$475$		0			0
$476$	−141.069	+	28.0554i	−0.296364	+	0.0589399i
$477$	14.8519			0.0311360
$478$	−85.5665	+	148.206i	−0.179009	+	0.310053i
$479$	445.286	−	257.086i	0.929615	−	0.536714i	0.0429255	−	0.999078i	$-0.486332\pi$
$479$	445.286	−	257.086i	0.929615	−	0.536714i	0.886690	+	0.462365i	$0.152999\pi$
$480$		0			0
$481$	840.578	+	485.308i	1.74756	+	1.00896i
$482$			407.848i			0.846157i
$483$	−168.467	−	192.113i	−0.348792	−	0.397749i
$484$	−7.76960			−0.0160529
$485$		0			0
$486$	19.0919	−	11.0227i	0.0392837	−	0.0226805i
$487$	163.663	+	283.473i	0.336064	+	0.582081i	0.983689	−	0.179879i	$-0.0575707\pi$
$487$	163.663	+	283.473i	0.336064	+	0.582081i	−0.647624	+	0.761960i	$0.724237\pi$
$488$	−171.682	−	99.1207i	−0.351808	−	0.203116i
$489$		−	414.386i		−	0.847415i
$490$		0			0
$491$	−41.8889			−0.0853134			−0.0426567	−	0.999090i	$-0.513582\pi$
$491$	−41.8889			−0.0853134			−0.0426567	+	0.999090i	$0.513582\pi$
$492$	−39.4399	+	68.3119i	−0.0801624	+	0.138845i
$493$	169.839	−	98.0566i	0.344501	−	0.198898i
$494$	−284.421	−	492.631i	−0.575751	−	0.997229i
$495$		0			0
$496$		−	160.068i		−	0.322717i
$497$	260.503	−	228.439i	0.524152	−	0.459637i
$498$	247.509			0.497006
$499$	−207.685	+	359.721i	−0.416203	+	0.720885i	−0.995554	−	0.0941936i	$-0.969973\pi$
$499$	−207.685	+	359.721i	−0.416203	+	0.720885i	0.579351	+	0.815078i	$0.303306\pi$
$500$		0			0
$501$	268.849	+	465.660i	0.536625	+	0.929462i
$502$	517.160	+	298.583i	1.03020	+	0.594786i
$503$			51.7604i			0.102903i	0.998675	+	0.0514517i	$0.0163848\pi$
$503$			51.7604i			0.102903i	−0.998675	+	0.0514517i	$0.983615\pi$
$504$	−11.5858	−	58.2561i	−0.0229876	−	0.115587i
$505$		0			0
$506$	−161.269	+	279.326i	−0.318713	+	0.552028i
$507$	−303.585	+	175.275i	−0.598786	+	0.345709i
$508$	−101.777	−	176.283i	−0.200348	−	0.347014i
$509$	136.916	+	79.0486i	0.268991	+	0.155302i	0.628429	−	0.777867i	$-0.283698\pi$
$509$	136.916	+	79.0486i	0.268991	+	0.155302i	−0.359438	+	0.933169i	$0.617032\pi$
$510$		0			0
$511$	299.233	−	881.411i	0.585583	−	1.72488i
$512$	22.6274			0.0441942
$513$	−54.2267	+	93.9234i	−0.105705	+	0.183087i
$514$	91.2276	−	52.6703i	0.177486	−	0.102471i
$515$		0			0
$516$	−145.292	−	83.8844i	−0.281574	−	0.162567i
$517$		−	720.073i		−	1.39279i
$518$	−472.126	−	160.283i	−0.911441	−	0.309428i
$519$	−157.457			−0.303385
$520$		0			0
$521$	306.214	−	176.793i	0.587744	−	0.339334i	−0.176461	−	0.984308i	$-0.556465\pi$
$521$	306.214	−	176.793i	0.587744	−	0.339334i	0.764205	+	0.644974i	$0.223132\pi$
$522$	40.4935	+	70.1368i	0.0775737	+	0.134362i
$523$	103.534	+	59.7756i	0.197962	+	0.114294i	0.595705	−	0.803204i	$-0.296873\pi$
$523$	103.534	+	59.7756i	0.197962	+	0.114294i	−0.397742	+	0.917497i	$0.630206\pi$
$524$		−	141.396i		−	0.269840i
$525$		0			0
$526$	−443.037			−0.842277
$527$	−205.561	+	356.042i	−0.390059	+	0.675602i
$528$	−64.9319	+	37.4884i	−0.122977	+	0.0710008i
$529$	42.4308	+	73.4924i	0.0802095	+	0.138927i
$530$		0			0
$531$			84.5604i			0.159247i
$532$	192.657	+	219.699i	0.362138	+	0.412968i
$533$	−438.824			−0.823309
$534$	−48.5184	+	84.0363i	−0.0908584	+	0.157371i
$535$		0			0
$536$	27.3024	+	47.2892i	0.0509374	+	0.0882261i
$537$	364.731	+	210.577i	0.679200	+	0.392136i
$538$		−	225.372i		−	0.418906i
$539$	489.926	−	202.894i	0.908954	−	0.376427i
$540$		0			0
$541$	−272.691	+	472.315i	−0.504051	+	0.873041i	0.495938	+	0.868358i	$0.334824\pi$
$541$	−272.691	+	472.315i	−0.504051	+	0.873041i	−0.999989	+	0.00468349i	$0.998509\pi$
$542$	230.575	−	133.123i	0.425416	−	0.245614i
$543$	213.036	+	368.989i	0.392331	+	0.679537i
$544$	−50.3307	−	29.0585i	−0.0925197	−	0.0534163i
$545$		0			0
$546$	248.443	−	217.864i	0.455024	−	0.399018i
$547$	117.783			0.215325			0.107663	−	0.994188i	$-0.465663\pi$
$547$	117.783			0.215325			0.107663	+	0.994188i	$0.465663\pi$
$548$	−117.828	+	204.083i	−0.215014	+	0.372415i
$549$	−182.096	+	105.133i	−0.331687	+	0.191500i
$550$		0			0
$551$	−345.041	−	199.210i	−0.626209	−	0.361542i
$552$		−	103.244i		−	0.187036i
$553$	−122.996	−	618.454i	−0.222416	−	1.11836i
$554$	−9.96659			−0.0179902
$555$		0			0
$556$	274.542	−	158.507i	0.493780	−	0.285084i
$557$	−307.744	−	533.028i	−0.552503	−	0.956963i	−0.998093	−	0.0617258i	$-0.980340\pi$
$557$	−307.744	−	533.028i	−0.552503	−	0.956963i	0.445590	−	0.895237i	$-0.352994\pi$
$558$	−147.031	−	84.8886i	−0.263497	−	0.152130i
$559$		−	933.330i		−	1.66964i
$560$		0			0
$561$	192.573			0.343267
$562$	−140.280	+	242.972i	−0.249608	+	0.432334i
$563$	415.047	−	239.628i	0.737207	−	0.425626i	−0.0838462	−	0.996479i	$-0.526720\pi$
$563$	415.047	−	239.628i	0.737207	−	0.425626i	0.821053	+	0.570852i	$0.193387\pi$
$564$	115.247	+	199.614i	0.204339	+	0.353925i
$565$		0			0
$566$			267.468i			0.472558i
$567$	−59.6559	−	20.2527i	−0.105213	−	0.0357191i
$568$	139.998			0.246475
$569$	228.674	−	396.074i	0.401887	−	0.696088i	−0.592067	−	0.805889i	$-0.701688\pi$
$569$	228.674	−	396.074i	0.401887	−	0.696088i	0.993954	+	0.109800i	$0.0350212\pi$
$570$		0			0
$571$	−186.601	−	323.203i	−0.326797	−	0.566029i	0.655077	−	0.755562i	$-0.272636\pi$
$571$	−186.601	−	323.203i	−0.326797	−	0.566029i	−0.981874	+	0.189532i	$0.939303\pi$
$572$	−361.229	−	208.555i	−0.631519	−	0.364607i
$573$		−	71.3978i		−	0.124604i
$574$	221.088	−	43.9692i	0.385171	−	0.0766014i
$575$		0			0
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	772.108	−	445.777i	1.33814	−	0.772577i	0.351611	−	0.936146i	$-0.385634\pi$
$577$	772.108	−	445.777i	1.33814	−	0.772577i	0.986532	+	0.163569i	$0.0523007\pi$
$578$	−129.719	−	224.680i	−0.224428	−	0.388720i
$579$	−284.618	−	164.324i	−0.491568	−	0.283807i
$580$		0			0
$581$	−466.347	−	531.804i	−0.802663	−	0.915326i
$582$	−168.266			−0.289117
$583$	−26.7878	+	46.3978i	−0.0459481	+	0.0795845i
$584$	325.719	−	188.054i	0.557738	−	0.322010i
$585$		0			0
$586$	−595.336	−	343.718i	−1.01593	−	0.586549i
$587$			786.758i			1.34030i	0.742224	+	0.670151i	$0.233771\pi$
$587$			786.758i			1.34030i	−0.742224	+	0.670151i	$0.766229\pi$
$588$	−103.341	+	134.657i	−0.175750	+	0.229009i
$589$	835.227			1.41804
$590$		0			0
$591$	543.477	−	313.777i	0.919589	−	0.530925i
$592$	−100.731	−	174.471i	−0.170153	−	0.294714i
$593$	541.571	+	312.676i	0.913273	+	0.527278i	0.881483	−	0.472216i	$-0.156546\pi$
$593$	541.571	+	312.676i	0.913273	+	0.527278i	0.0317903	+	0.999495i	$0.489879\pi$
$594$			79.5250i			0.133880i
$595$		0			0
$596$	−591.792			−0.992940
$597$	−33.4433	+	57.9256i	−0.0560190	+	0.0970278i
$598$	497.416	−	287.183i	0.831799	−	0.480240i
$599$	−75.2476	−	130.333i	−0.125622	−	0.217584i	0.796354	−	0.604831i	$-0.206759\pi$
$599$	−75.2476	−	130.333i	−0.125622	−	0.217584i	−0.921976	+	0.387247i	$0.873426\pi$
$600$		0			0
$601$			521.601i			0.867888i	0.900940	+	0.433944i	$0.142878\pi$
$601$			521.601i			0.867888i	−0.900940	+	0.433944i	$0.857122\pi$
$602$	93.5177	+	470.230i	0.155345	+	0.781113i
$603$	57.9172			0.0960485
$604$	125.296	−	217.019i	0.207443	−	0.359302i
$605$		0			0
$606$	−9.84575	−	17.0533i	−0.0162471	−	0.0281408i
$607$	603.404	+	348.375i	0.994075	+	0.573930i	0.906490	−	0.422228i	$-0.138752\pi$
$607$	603.404	+	348.375i	0.994075	+	0.573930i	0.0875852	+	0.996157i	$0.472085\pi$
$608$			118.069i			0.194193i
$609$	74.4014	−	219.155i	0.122170	−	0.359860i
$610$		0			0
$611$	−641.143	+	1110.49i	−1.04933	+	1.81750i
$612$	−53.3838	+	30.8212i	−0.0872285	+	0.0503614i
$613$	27.1244	+	46.9809i	0.0442487	+	0.0766410i	0.887302	−	0.461190i	$-0.152577\pi$
$613$	27.1244	+	46.9809i	0.0442487	+	0.0766410i	−0.843053	+	0.537831i	$0.819244\pi$
$614$	−523.687	−	302.351i	−0.852911	−	0.492428i
$615$		0			0
$616$	202.891	+	68.8800i	0.329368	+	0.111818i
$617$	969.852			1.57188			0.785941	−	0.618301i	$-0.212179\pi$
$617$	969.852			1.57188			0.785941	+	0.618301i	$0.212179\pi$
$618$	250.540	−	433.947i	0.405404	−	0.702180i
$619$	−111.240	+	64.2247i	−0.179710	+	0.103756i	−0.587156	−	0.809474i	$-0.699753\pi$
$619$	−111.240	+	64.2247i	−0.179710	+	0.103756i	0.407446	+	0.913229i	$0.366419\pi$
$620$		0			0
$621$	−94.8357	−	54.7534i	−0.152714	−	0.0881697i
$622$		−	509.252i		−	0.818733i
$623$	271.979	−	54.0903i	0.436564	−	0.0868223i
$624$	133.517			0.213969
$625$		0			0
$626$	715.163	−	412.899i	1.14243	−	0.659584i
$627$	−195.613	−	338.812i	−0.311983	−	0.540371i
$628$	9.23819	+	5.33367i	0.0147105	+	0.00849311i
$629$			517.440i			0.822639i
$630$		0			0
$631$	115.457			0.182975			0.0914877	−	0.995806i	$-0.470838\pi$
$631$	115.457			0.182975			0.0914877	+	0.995806i	$0.470838\pi$
$632$	127.393	−	220.652i	0.201572	−	0.349133i
$633$	−204.827	+	118.257i	−0.323581	+	0.186820i
$634$	255.549	+	442.623i	0.403073	+	0.698144i
$635$		0			0
$636$		−	17.1495i		−	0.0269646i
$637$	−936.215	−	123.321i	−1.46973	−	0.193596i
$638$	−292.146			−0.457910
$639$	74.2452	−	128.596i	0.116190	−	0.201246i
$640$		0			0
$641$	476.249	+	824.887i	0.742978	+	1.28688i	0.951134	+	0.308780i	$0.0999206\pi$
$641$	476.249	+	824.887i	0.742978	+	1.28688i	−0.208156	+	0.978096i	$0.566746\pi$
$642$	349.072	+	201.537i	0.543725	+	0.313920i
$643$			253.254i			0.393863i	0.980417	+	0.196931i	$0.0630976\pi$
$643$			253.254i			0.393863i	−0.980417	+	0.196931i	$0.936902\pi$
$644$	−221.833	+	194.529i	−0.344461	+	0.302063i
$645$		0			0
$646$	151.626	−	262.624i	0.234715	−	0.406539i
$647$	−870.161	+	502.388i	−1.34492	+	0.776488i	−0.987524	−	0.157466i	$-0.949668\pi$
$647$	−870.161	+	502.388i	−1.34492	+	0.776488i	−0.357393	+	0.933954i	$0.616334\pi$
$648$	−12.7279	−	22.0454i	−0.0196419	−	0.0340207i
$649$	−264.170	−	152.518i	−0.407041	−	0.235005i
$650$		0			0
$651$	94.6373	+	475.860i	0.145372	+	0.730967i
$652$	−478.492			−0.733883
$653$	532.797	−	922.831i	0.815922	−	1.41322i	−0.0927422	−	0.995690i	$-0.529563\pi$
$653$	532.797	−	922.831i	0.815922	−	1.41322i	0.908664	−	0.417528i	$-0.137103\pi$
$654$	−167.606	+	96.7672i	−0.256278	+	0.147962i
$655$		0			0
$656$	78.8798	+	45.5413i	0.120244	+	0.0694227i
$657$		−	398.923i		−	0.607189i
$658$	211.751	−	623.728i	0.321810	−	0.947915i
$659$	432.265			0.655941			0.327970	−	0.944688i	$-0.393635\pi$
$659$	432.265			0.655941			0.327970	+	0.944688i	$0.393635\pi$
$660$		0			0
$661$	327.626	−	189.155i	0.495652	−	0.286165i	−0.231264	−	0.972891i	$-0.574286\pi$
$661$	327.626	−	189.155i	0.495652	−	0.286165i	0.726916	+	0.686726i	$0.240953\pi$
$662$	−209.294	−	362.507i	−0.316153	−	0.547594i
$663$	−296.985	−	171.464i	−0.447941	−	0.258619i
$664$		−	285.799i		−	0.430420i
$665$		0			0
$666$	−213.682			−0.320844
$667$	201.144	−	348.392i	0.301566	−	0.522328i
$668$	537.698	−	310.440i	0.804937	−	0.464731i
$669$	134.190	+	232.424i	0.200583	+	0.347419i
$670$		0			0
$671$		−	758.501i		−	1.13040i
$672$	−67.2683	+	13.3781i	−0.100102	+	0.0199079i
$673$	689.666			1.02476			0.512382	−	0.858758i	$-0.328763\pi$
$673$	689.666			1.02476			0.512382	+	0.858758i	$0.328763\pi$
$674$	−15.5678	+	26.9642i	−0.0230976	+	0.0400063i
$675$		0			0
$676$	202.390	+	350.549i	0.299393	+	0.518564i
$677$	−328.663	−	189.754i	−0.485470	−	0.280286i	0.237223	−	0.971455i	$-0.423763\pi$
$677$	−328.663	−	189.754i	−0.485470	−	0.280286i	−0.722693	+	0.691169i	$0.757096\pi$
$678$		−	207.151i		−	0.305532i
$679$	317.041	+	361.541i	0.466924	+	0.532461i
$680$		0			0
$681$	−19.3590	+	33.5307i	−0.0284273	+	0.0492375i
$682$	530.390	−	306.221i	0.777698	−	0.449004i
$683$	373.753	+	647.360i	0.547223	+	0.947818i	0.998463	+	0.0554159i	$0.0176485\pi$
$683$	373.753	+	647.360i	0.547223	+	0.947818i	−0.451240	+	0.892403i	$0.649018\pi$
$684$	108.453	+	62.6156i	0.158558	+	0.0915433i
$685$		0			0
$686$	484.040	−	31.6754i	0.705598	−	0.0461740i
$687$	51.8209			0.0754308
$688$	−96.8613	+	167.769i	−0.140787	+	0.243850i
$689$	82.6238	−	47.7029i	0.119918	−	0.0692350i
$690$		0			0
$691$	771.026	+	445.152i	1.11581	+	0.644214i	0.940328	−	0.340268i	$-0.110518\pi$
$691$	771.026	+	445.152i	1.11581	+	0.644214i	0.175483	+	0.984482i	$0.443851\pi$
$692$			181.816i			0.262739i
$693$	170.869	−	149.838i	0.246565	−	0.216217i
$694$	401.504			0.578536
$695$		0			0
$696$	80.9870	−	46.7579i	0.116361	−	0.0671808i
$697$	−116.970	−	202.597i	−0.167819	−	0.290670i
$698$	−388.459	−	224.277i	−0.556531	−	0.321313i
$699$			438.352i			0.627112i
$700$		0			0
$701$	−650.703			−0.928250			−0.464125	−	0.885770i	$-0.653631\pi$
$701$	−650.703			−0.928250			−0.464125	+	0.885770i	$0.653631\pi$
$702$	70.8079	−	122.643i	0.100866	−	0.174705i
$703$	910.384	−	525.610i	1.29500	−	0.747667i
$704$	43.2879	+	74.9769i	0.0614885	+	0.106501i
$705$		0			0
$706$			165.382i			0.234251i
$707$	−18.0902	+	53.2861i	−0.0255873	+	0.0753693i
$708$	97.6419			0.137912
$709$	196.427	−	340.222i	0.277048	−	0.479862i	−0.693602	−	0.720359i	$-0.743977\pi$
$709$	196.427	−	340.222i	0.277048	−	0.479862i	0.970650	+	0.240497i	$0.0773105\pi$
$710$		0			0
$711$	−135.121	−	234.037i	−0.190044	−	0.329166i
$712$	97.0368	+	56.0242i	0.136288	+	0.0786857i
$713$			843.339i			1.18280i
$714$	166.807	+	56.6298i	0.233623	+	0.0793134i
$715$		0			0
$716$	243.154	−	421.155i	0.339600	−	0.588205i
$717$	181.514	−	104.797i	0.253158	−	0.146161i
$718$	−165.170	−	286.083i	−0.230042	−	0.398444i
$719$	899.919	+	519.569i	1.25163	+	0.722627i	0.971432	−	0.237317i	$-0.0762679\pi$
$719$	899.919	+	519.569i	1.25163	+	0.722627i	0.280194	+	0.959943i	$0.409601\pi$
$720$		0			0
$721$	−1404.45	+	279.312i	−1.94792	+	0.387395i
$722$	−105.550			−0.146191
$723$	249.755	−	432.588i	0.345442	−	0.598323i
$724$	426.072	−	245.993i	0.588497	−	0.339769i
$725$		0			0
$726$	8.24091	+	4.75789i	0.0113511	+	0.00655357i
$727$		−	610.568i		−	0.839846i	−0.907560	−	0.419923i	$-0.862057\pi$
$727$		−	610.568i		−	0.839846i	0.907560	−	0.419923i	$-0.137943\pi$
$728$	−251.567	−	286.877i	−0.345559	−	0.394062i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	430.902	−	248.781i	0.589469	−	0.340330i
$732$	121.398	+	210.267i	0.165844	+	0.287250i
$733$	−934.574	−	539.576i	−1.27500	−	0.736121i	−0.299074	−	0.954230i	$-0.596678\pi$
$733$	−934.574	−	539.576i	−1.27500	−	0.736121i	−0.975924	+	0.218109i	$0.930011\pi$
$734$		−	724.181i		−	0.986623i
$735$		0			0
$736$	−119.216			−0.161978
$737$	−104.463	+	180.935i	−0.141741	+	0.245503i
$738$	83.6647	−	48.3038i	0.113367	−	0.0654523i
$739$	−378.082	−	654.857i	−0.511613	−	0.886139i	−0.999909	−	0.0134615i	$-0.995715\pi$
$739$	−378.082	−	654.857i	−0.511613	−	0.886139i	0.488297	−	0.872678i	$-0.337618\pi$
$740$		0			0
$741$			696.686i			0.940197i
$742$	−36.8478	+	32.3124i	−0.0496601	+	0.0435477i
$743$	−963.993			−1.29743			−0.648717	−	0.761030i	$-0.724694\pi$
$743$	−963.993			−1.29743			−0.648717	+	0.761030i	$0.724694\pi$
$744$	−98.0209	+	169.777i	−0.131749	+	0.228195i
$745$		0			0
$746$	−393.439	−	681.457i	−0.527398	−	0.913481i
$747$	−262.523	−	151.568i	−0.351436	−	0.202902i
$748$		−	222.364i		−	0.297278i
$749$	−224.681	−	1129.75i	−0.299975	−	1.50835i
$750$		0			0
$751$	−416.806	+	721.929i	−0.555001	+	0.961290i	0.442902	+	0.896570i	$0.353949\pi$
$751$	−416.806	+	721.929i	−0.555001	+	0.961290i	−0.997903	+	0.0647203i	$0.979384\pi$
$752$	230.494	−	133.076i	0.306508	−	0.176963i
$753$	−365.688	−	633.389i	−0.485641	−	0.841155i
$754$	450.547	+	260.123i	0.597542	+	0.344991i
$755$		0			0
$756$	−23.3859	+	68.8847i	−0.0309337	+	0.0911173i
$757$	744.966			0.984103			0.492051	−	0.870566i	$-0.336247\pi$
$757$	744.966			0.984103			0.492051	+	0.870566i	$0.336247\pi$
$758$	379.222	−	656.832i	0.500293	−	0.866533i
$759$	342.103	−	197.513i	0.450729	−	0.260228i
$760$		0			0
$761$	−64.1518	−	37.0381i	−0.0842993	−	0.0486702i	0.457258	−	0.889334i	$-0.348832\pi$
$761$	−64.1518	−	37.0381i	−0.0842993	−	0.0486702i	−0.541557	+	0.840664i	$0.682165\pi$
$762$			249.302i			0.327167i
$763$	523.713	+	177.797i	0.686387	+	0.233023i
$764$	−82.4431			−0.107910
$765$		0			0
$766$	35.9471	−	20.7540i	0.0469283	−	0.0270941i
$767$	271.601	+	470.426i	0.354108	+	0.613332i
$768$	−24.0000	−	13.8564i	−0.0312500	−	0.0180422i
$769$		−	961.553i		−	1.25039i	−0.780467	−	0.625197i	$-0.785019\pi$
$769$		−	961.553i		−	1.25039i	0.780467	−	0.625197i	$-0.214981\pi$
$770$		0			0
$771$	−129.015			−0.167335
$772$	−189.745	+	328.649i	−0.245784	+	0.425711i
$773$	1191.17	−	687.723i	1.54097	−	0.889680i	0.542194	−	0.840253i	$-0.317594\pi$
$773$	1191.17	−	687.723i	1.54097	−	0.889680i	0.998778	−	0.0494271i	$-0.0157395\pi$
$774$	102.737	+	177.946i	0.132735	+	0.229904i
$775$		0			0
$776$			194.297i			0.250383i
$777$	402.612	+	459.123i	0.518163	+	0.590892i
$778$	−987.806			−1.26967
$779$	−237.633	+	411.592i	−0.305049	+	0.528360i
$780$		0			0
$781$	267.826	+	463.889i	0.342928	+	0.593968i
$782$	265.175	+	153.099i	0.339098	+	0.195779i
$783$		−	99.1884i		−	0.126677i
$784$	155.489	+	119.328i	0.198328	+	0.152204i
$785$		0			0
$786$	−86.5872	+	149.973i	−0.110162	+	0.190806i
$787$	−329.679	+	190.340i	−0.418906	+	0.241856i	−0.694609	−	0.719387i	$-0.744423\pi$
$787$	−329.679	+	190.340i	−0.418906	+	0.241856i	0.275703	+	0.961243i	$0.411089\pi$
$788$	−362.318	−	627.553i	−0.459795	−	0.796387i
$789$	469.912	+	271.304i	0.595579	+	0.343858i
$790$		0			0
$791$	−445.090	+	390.306i	−0.562693	+	0.493434i
$792$	91.8275			0.115944
$793$	−675.358	+	1169.76i	−0.851650	+	1.47510i
$794$	−250.698	+	144.741i	−0.315741	+	0.182293i
$795$		0			0
$796$	66.8867	+	38.6170i	0.0840285	+	0.0485139i
$797$		−	511.440i		−	0.641706i	−0.947129	−	0.320853i	$-0.896030\pi$
$797$		−	511.440i		−	0.641706i	0.947129	−	0.320853i	$-0.103970\pi$
$798$	−69.8064	−	351.004i	−0.0874768	−	0.439855i
$799$	−683.593			−0.855560
$800$		0			0
$801$	102.923	−	59.4226i	0.128493	−	0.0741856i
$802$	−304.033	−	526.600i	−0.379093	−	0.656609i
$803$	1246.25	+	719.522i	1.55199	+	0.896043i
$804$		−	66.8770i		−	0.0831804i
$805$		0			0
$806$	−1090.62			−1.35313
$807$	−138.011	+	239.043i	−0.171018	+	0.296211i
$808$	−19.6915	+	11.3689i	−0.0243707	+	0.0140704i
$809$	−579.187	−	1003.18i	−0.715930	−	1.24003i	−0.962600	−	0.270927i	$-0.912670\pi$
$809$	−579.187	−	1003.18i	−0.715930	−	1.24003i	0.246670	−	0.969099i	$-0.420664\pi$
$810$		0			0
$811$		−	92.0692i		−	0.113526i	−0.998388	−	0.0567628i	$-0.981922\pi$
$811$		−	92.0692i		−	0.113526i	0.998388	−	0.0567628i	$-0.0180779\pi$
$812$	−253.058	−	85.9113i	−0.311648	−	0.105802i
$813$	−326.083			−0.401086
$814$	385.411	−	667.551i	0.473478	−	0.820088i
$815$		0			0
$816$	35.5892	+	61.6423i	0.0436142	+	0.0755421i
$817$	−875.412	−	505.419i	−1.07150	−	0.618628i
$818$			25.0774i			0.0306569i
$819$	−396.928	+	78.9396i	−0.484649	+	0.0963853i
$820$		0			0
$821$	493.467	−	854.711i	0.601057	−	1.04106i	−0.391605	−	0.920134i	$-0.628080\pi$
$821$	493.467	−	854.711i	0.601057	−	1.04106i	0.992661	−	0.120927i	$-0.0385867\pi$
$822$	249.950	−	144.309i	0.304075	−	0.175558i
$823$	277.748	+	481.074i	0.337483	+	0.584537i	0.983959	−	0.178397i	$-0.0570912\pi$
$823$	277.748	+	481.074i	0.337483	+	0.584537i	−0.646476	+	0.762935i	$0.723758\pi$
$824$	−501.079	−	289.298i	−0.608106	−	0.351090i
$825$		0			0
$826$	−183.973	−	209.796i	−0.222728	−	0.253990i
$827$	1323.46			1.60032			0.800160	−	0.599787i	$-0.204748\pi$
$827$	1323.46			1.60032			0.800160	+	0.599787i	$0.204748\pi$
$828$	−63.2238	+	109.507i	−0.0763572	+	0.132255i
$829$	911.903	−	526.488i	1.10000	−	0.635088i	0.163782	−	0.986497i	$-0.447631\pi$
$829$	911.903	−	526.488i	1.10000	−	0.635088i	0.936222	+	0.351409i	$0.114297\pi$
$830$		0			0
$831$	10.5712	+	6.10326i	0.0127210	+	0.00734448i
$832$		−	154.172i		−	0.185303i
$833$	−192.615	−	465.106i	−0.231231	−	0.558350i
$834$	−388.261			−0.465540
$835$		0			0
$836$	−391.227	+	225.875i	−0.467975	+	0.270185i
$837$	103.967	+	180.076i	0.124214	+	0.215145i
$838$	−539.829	−	311.670i	−0.644187	−	0.371922i
$839$			1254.98i			1.49580i	0.663810	+	0.747901i	$0.268938\pi$
$839$			1254.98i			1.49580i	−0.663810	+	0.747901i	$0.731062\pi$
$840$		0			0
$841$	−476.617			−0.566727
$842$	101.125	−	175.153i	0.120101	−	0.208020i
$843$	297.578	−	171.807i	0.352999	−	0.203804i
$844$	136.551	+	236.514i	0.161791	+	0.280230i
$845$		0			0
$846$		−	282.297i		−	0.333684i
$847$	−5.30429	−	26.6713i	−0.00626244	−	0.0314891i
$848$	−19.8025			−0.0233520
$849$	163.790	−	283.692i	0.192921	−	0.334149i
$850$		0			0
$851$	530.715	+	919.226i	0.623637	+	1.08017i
$852$	−148.490	−	85.7309i	−0.174284	−	0.100623i
$853$			454.825i			0.533207i	0.963806	+	0.266603i	$0.0859014\pi$
$853$			454.825i			0.533207i	−0.963806	+	0.266603i	$0.914099\pi$
$854$	223.052	−	657.015i	0.261185	−	0.769338i
$855$		0			0
$856$	232.714	−	403.073i	0.271863	−	0.470880i
$857$	146.132	−	84.3691i	0.170515	−	0.0984470i	−0.412314	−	0.911042i	$-0.635279\pi$
$857$	146.132	−	84.3691i	0.170515	−	0.0984470i	0.582829	+	0.812595i	$0.301946\pi$
$858$	255.427	+	442.413i	0.297701	+	0.515633i
$859$	−707.715	−	408.599i	−0.823882	−	0.475669i	0.0278711	−	0.999612i	$-0.491127\pi$
$859$	−707.715	−	408.599i	−0.823882	−	0.475669i	−0.851753	+	0.523943i	$0.824461\pi$
$860$		0			0
$861$	−261.425	−	88.7518i	−0.303629	−	0.103080i
$862$	−1107.64			−1.28496
$863$	−616.950	+	1068.59i	−0.714890	+	1.23823i	0.248112	+	0.968731i	$0.420190\pi$
$863$	−616.950	+	1068.59i	−0.714890	+	1.23823i	−0.963002	+	0.269495i	$0.913143\pi$
$864$	−25.4558	+	14.6969i	−0.0294628	+	0.0170103i
$865$		0			0
$866$	351.096	+	202.705i	0.405423	+	0.234071i
$867$			317.746i			0.366489i
$868$	549.475	−	109.278i	0.633036	−	0.125896i
$869$	974.852			1.12181
$870$		0			0
$871$	322.205	−	186.025i	0.369925	−	0.213576i
$872$	111.737	+	193.534i	0.128139	+	0.221943i
$873$	178.473	+	103.042i	0.204437	+	0.118032i
$874$		−	622.065i		−	0.711744i
$875$		0			0
$876$	−460.637			−0.525841
$877$	37.4779	−	64.9136i	0.0427342	−	0.0740177i	−0.843867	−	0.536552i	$-0.819726\pi$
$877$	37.4779	−	64.9136i	0.0427342	−	0.0740177i	0.886601	+	0.462534i	$0.153060\pi$
$878$	417.216	−	240.880i	0.475189	−	0.274350i
$879$	420.966	+	729.135i	0.478915	+	0.829505i
$880$		0			0
$881$			461.343i			0.523658i	0.965114	+	0.261829i	$0.0843257\pi$
$881$			461.343i			0.523658i	−0.965114	+	0.261829i	$0.915674\pi$
$882$	192.070	−	79.5426i	0.217767	−	0.0901843i
$883$	−237.840			−0.269354			−0.134677	−	0.990890i	$-0.543000\pi$
$883$	−237.840			−0.269354			−0.134677	+	0.990890i	$0.543000\pi$
$884$	−197.990	+	342.928i	−0.223970	+	0.387928i
$885$		0			0
$886$	279.490	+	484.091i	0.315452	+	0.546379i
$887$	−7.89260	−	4.55679i	−0.00889808	−	0.00513731i	0.495544	−	0.868583i	$-0.334969\pi$
$887$	−7.89260	−	4.55679i	−0.00889808	−	0.00513731i	−0.504442	+	0.863445i	$0.668302\pi$
$888$			246.739i			0.277859i
$889$	535.656	−	469.725i	0.602538	−	0.528375i
$890$		0			0
$891$	48.6989	−	84.3490i	0.0546565	−	0.0946678i
$892$	268.380	−	154.949i	0.300874	−	0.173710i
$893$	694.386	+	1202.71i	0.777588	+	1.34682i
$894$	627.691	+	362.397i	0.702115	+	0.405366i
$895$		0			0
$896$	15.4477	+	77.6748i	0.0172407	+	0.0866906i
$897$	−703.452			−0.784228
$898$	−470.281	+	814.551i	−0.523698	+	0.907072i
$899$	−661.535	+	381.938i	−0.735857	+	0.424847i
$900$		0			0
$901$	44.0472	+	25.4306i	0.0488870	+	0.0282249i
$902$			348.495i			0.386358i
$903$	188.765	−	556.022i	0.209042	−	0.615750i
$904$	−239.197			−0.264599
$905$		0			0
$906$	−265.792	+	153.455i	−0.293369	+	0.169377i
$907$	420.352	+	728.070i	0.463453	+	0.802723i	0.999130	−	0.0416991i	$-0.0132771\pi$
$907$	420.352	+	728.070i	0.463453	+	0.802723i	−0.535678	+	0.844423i	$0.679944\pi$
$908$	38.7179	+	22.3538i	0.0426409	+	0.0246187i
$909$			24.1171i			0.0265314i
$910$		0			0
$911$	−35.4735			−0.0389390			−0.0194695	−	0.999810i	$-0.506198\pi$
$911$	−35.4735			−0.0389390			−0.0194695	+	0.999810i	$0.506198\pi$
$912$	72.3023	−	125.231i	0.0792788	−	0.137315i
$913$	947.006	−	546.754i	1.03725	−	0.598854i
$914$	361.287	+	625.767i	0.395281	+	0.684646i
$915$		0			0
$916$		−	59.8377i		−	0.0653250i
$917$	485.381	−	96.5310i	0.529314	−	0.105268i
$918$	75.4961			0.0822398
$919$	−215.680	+	373.569i	−0.234690	+	0.406495i	−0.959182	−	0.282788i	$-0.908741\pi$
$919$	−215.680	+	373.569i	−0.234690	+	0.406495i	0.724493	+	0.689282i	$0.242074\pi$
$920$		0			0
$921$	370.303	+	641.384i	0.402066	+	0.696399i
$922$	213.477	+	123.251i	0.231536	+	0.133678i
$923$		−	953.876i		−	1.03345i
$924$	−173.018	−	197.303i	−0.187249	−	0.213531i
$925$		0			0
$926$	533.998	−	924.911i	0.576671	−	0.998824i
$927$	−531.475	+	306.847i	−0.573328	+	0.331011i
$928$	−53.9913	−	93.5157i	−0.0581803	−	0.100771i
$929$	531.053	+	306.603i	0.571639	+	0.330036i	0.757804	−	0.652483i	$-0.226272\pi$
$929$	531.053	+	306.603i	0.571639	+	0.330036i	−0.186165	+	0.982519i	$0.559606\pi$
$930$		0			0
$931$	−622.649	+	811.337i	−0.668796	+	0.871468i
$932$	506.165			0.543095
$933$	−311.852	+	540.143i	−0.334246	+	0.578931i
$934$	−693.907	+	400.627i	−0.742941	+	0.428937i
$935$		0			0
$936$	−141.616	−	81.7620i	−0.151299	−	0.0873525i
$937$		−	1360.68i		−	1.45216i	−0.687609	−	0.726081i	$-0.741340\pi$
$937$		−	1360.68i		−	1.45216i	0.687609	−	0.726081i	$-0.258660\pi$
$938$	−143.694	+	126.007i	−0.153192	+	0.134336i
$939$	−1011.39			−1.07710
$940$		0			0
$941$	−146.671	+	84.6806i	−0.155867	+	0.0899900i	−0.575905	−	0.817517i	$-0.695350\pi$
$941$	−146.671	+	84.6806i	−0.155867	+	0.0899900i	0.420038	+	0.907507i	$0.362017\pi$
$942$	−6.53239	−	11.3144i	−0.00693459	−	0.0120111i
$943$	−415.590	−	239.941i	−0.440710	−	0.254444i
$944$		−	112.747i		−	0.119436i
$945$		0			0
$946$	−741.211			−0.783521
$947$	−639.583	+	1107.79i	−0.675378	+	1.16979i	0.300981	+	0.953630i	$0.402686\pi$
$947$	−639.583	+	1107.79i	−0.675378	+	1.16979i	−0.976358	+	0.216158i	$0.930647\pi$
$948$	−270.242	+	156.024i	−0.285066	+	0.164583i
$949$	−1281.31	−	2219.29i	−1.35016	−	2.33855i
$950$		0			0
$951$		−	625.964i		−	0.658216i
$952$	65.3904	−	192.612i	0.0686874	−	0.202324i
$953$	1.43779			0.00150870			0.000754349	−	1.00000i	$-0.499760\pi$
$953$	1.43779			0.00150870			0.000754349		1.00000i	$0.499760\pi$
$954$	−10.5019	+	18.1897i	−0.0110082	+	0.0190668i
$955$		0			0
$956$	−121.009	−	209.594i	−0.126579	−	0.219241i
$957$	309.868	+	178.902i	0.323791	+	0.186941i
$958$			727.149i			0.759028i
$959$	−781.012	−	265.148i	−0.814402	−	0.276484i
$960$		0			0
$961$	320.176	−	554.560i	0.333169	−	0.577066i
$962$	−1188.76	+	686.329i	−1.23571	+	0.713440i
$963$	−246.831	−	427.524i	−0.256314	−	0.443950i
$964$	−499.509	−	288.392i	−0.518163	−	0.299162i
$965$		0			0
$966$	354.413	−	70.4844i	0.366887	−	0.0729653i
$967$	−486.815			−0.503428			−0.251714	−	0.967802i	$-0.580994\pi$
$967$	−486.815			−0.503428			−0.251714	+	0.967802i	$0.580994\pi$
$968$	5.49394	−	9.51578i	0.00567556	−	0.00983035i
$969$	−321.648	+	185.703i	−0.331938	+	0.191644i
$970$		0			0
$971$	378.215	+	218.362i	0.389511	+	0.224884i	0.681948	−	0.731401i	$-0.261133\pi$
$971$	378.215	+	218.362i	0.389511	+	0.224884i	−0.292437	+	0.956285i	$0.594466\pi$
$972$			31.1769i			0.0320750i
$973$	731.547	+	834.227i	0.751847	+	0.857376i
$974$	−462.910			−0.475267
$975$		0			0
$976$	242.795	−	140.178i	0.248766	−	0.143625i
$977$	127.517	+	220.866i	0.130519	+	0.226066i	0.923877	−	0.382690i	$-0.125002\pi$
$977$	127.517	+	220.866i	0.130519	+	0.226066i	−0.793358	+	0.608756i	$0.791669\pi$
$978$	507.517	+	293.015i	0.518934	+	0.299606i
$979$			428.714i			0.437910i
$980$		0			0
$981$	237.030			0.241621
$982$	29.6199	−	51.3032i	0.0301628	−	0.0522436i
$983$	−1195.88	+	690.443i	−1.21656	+	0.702383i	−0.964181	−	0.265244i	$-0.914547\pi$
$983$	−1195.88	+	690.443i	−1.21656	+	0.702383i	−0.252383	+	0.967628i	$0.581214\pi$
$984$	−55.7765	−	96.6077i	−0.0566834	−	0.0981785i
$985$		0			0
$986$			277.346i			0.281284i
$987$	−606.550	+	531.893i	−0.614539	+	0.538899i
$988$	804.464			0.814234
$989$	510.328	−	883.914i	0.516004	−	0.893745i
$990$		0			0
$991$	311.554	+	539.628i	0.314384	+	0.544528i	0.979306	−	0.202384i	$-0.0648688\pi$
$991$	311.554	+	539.628i	0.314384	+	0.544528i	−0.664923	+	0.746912i	$0.731535\pi$
$992$	196.042	+	113.185i	0.197623	+	0.114098i
$993$			512.662i			0.516276i
$994$	95.5763	+	480.581i	0.0961533	+	0.483482i
$995$		0			0
$996$	−175.015	+	303.135i	−0.175718	+	0.304353i
$997$	−485.248	+	280.158i	−0.486708	+	0.281001i	−0.723208	−	0.690630i	$-0.757333\pi$
$997$	−485.248	+	280.158i	−0.486708	+	0.281001i	0.236499	+	0.971632i	$0.424000\pi$
$998$	−293.711	−	508.723i	−0.294300	−	0.509742i
$999$	226.644	+	130.853i	0.226871	+	0.130984i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.p.i.901.3		16
5.2	odd	4		1050.3.q.e.649.7		32
5.3	odd	4		1050.3.q.e.649.16		32
5.4	even	2		210.3.o.b.61.5	yes	16
7.3	odd	6	inner	1050.3.p.i.451.3		16
15.14	odd	2		630.3.v.c.271.3		16
35.3	even	12		1050.3.q.e.199.7		32
35.9	even	6		1470.3.f.d.391.3		16
35.17	even	12		1050.3.q.e.199.16		32
35.19	odd	6		1470.3.f.d.391.5		16
35.24	odd	6		210.3.o.b.31.5	✓	16
105.59	even	6		630.3.v.c.451.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.5	✓	16	35.24	odd	6
210.3.o.b.61.5	yes	16	5.4	even	2
630.3.v.c.271.3		16	15.14	odd	2
630.3.v.c.451.3		16	105.59	even	6
1050.3.p.i.451.3		16	7.3	odd	6	inner
1050.3.p.i.901.3		16	1.1	even	1	trivial
1050.3.q.e.199.7		32	35.3	even	12
1050.3.q.e.199.16		32	35.17	even	12
1050.3.q.e.649.7		32	5.2	odd	4
1050.3.q.e.649.16		32	5.3	odd	4
1470.3.f.d.391.3		16	35.9	even	6
1470.3.f.d.391.5		16	35.19	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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(5.26304 - 4.61524i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(5.26304 - 4.61524i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(5.41099 + 9.37211i) q^{11} +(-3.00000 - 1.73205i) q^{12} -19.2715i q^{13} +(1.93096 + 9.70935i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(8.89730 - 5.13686i) q^{17} +(2.12132 + 3.67423i) q^{18} +(-18.0756 - 10.4359i) q^{19} +(3.89764 - 11.4808i) q^{21} -15.3046 q^{22} +(10.5373 - 18.2511i) q^{23} +(4.24264 - 2.44949i) q^{24} +(23.6026 + 13.6270i) q^{26} -5.19615i q^{27} +(-13.2569 - 4.50061i) q^{28} +19.0888 q^{29} +(-34.6556 + 20.0084i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(16.2330 + 9.37211i) q^{33} +14.5292i q^{34} -6.00000 q^{36} +(-25.1827 + 43.6177i) q^{37} +(25.5627 - 14.7586i) q^{38} +(-16.6896 - 28.9072i) q^{39} -22.7706i q^{41} +(11.3050 + 12.8918i) q^{42} +48.4307 q^{43} +(10.8220 - 18.7442i) q^{44} +(14.9020 + 25.8110i) q^{46} +(-57.6236 - 33.2690i) q^{47} +6.92820i q^{48} +(6.39913 - 48.5804i) q^{49} +(8.89730 - 15.4106i) q^{51} +(-33.3792 + 19.2715i) q^{52} +(2.47531 + 4.28736i) q^{53} +(6.36396 + 3.67423i) q^{54} +(14.8861 - 13.0539i) q^{56} -36.1511 q^{57} +(-13.4978 + 23.3789i) q^{58} +(-24.4105 + 14.0934i) q^{59} +(-60.6988 - 35.0445i) q^{61} -56.5924i q^{62} +(-4.09619 - 20.5966i) q^{63} +8.00000 q^{64} +(-22.9569 + 13.2542i) q^{66} +(9.65287 + 16.7193i) q^{67} +(-17.7946 - 10.2737i) q^{68} -36.5023i q^{69} +49.4968 q^{71} +(4.24264 - 7.34847i) q^{72} +(115.159 - 66.4872i) q^{73} +(-35.6137 - 61.6848i) q^{74} +41.7437i q^{76} +(71.7328 + 24.3527i) q^{77} +47.2053 q^{78} +(45.0404 - 78.0122i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(27.8882 + 16.1013i) q^{82} -101.045i q^{83} +(-23.7829 + 4.72987i) q^{84} +(-34.2456 + 59.3152i) q^{86} +(28.6332 - 16.5314i) q^{87} +(15.3046 + 26.5083i) q^{88} +(34.3077 + 19.8075i) q^{89} +(-88.9425 - 101.427i) q^{91} -42.1492 q^{92} +(-34.6556 + 60.0253i) q^{93} +(81.4920 - 47.0495i) q^{94} +(-8.48528 - 4.89898i) q^{96} +68.6944i q^{97} +(54.9737 + 42.1888i) q^{98} +32.4659 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 24 q^{3} - 16 q^{4} - 4 q^{7} + 24 q^{9}+O(q^{10}) \) 16 * q + 24 * q^3 - 16 * q^4 - 4 * q^7 + 24 * q^9	\( 16 q + 24 q^{3} - 16 q^{4} - 4 q^{7} + 24 q^{9} - 4 q^{11} - 48 q^{12} + 8 q^{14} - 32 q^{16} - 12 q^{17} - 72 q^{19} - 24 q^{21} + 48 q^{22} + 12 q^{23} - 32 q^{28} + 72 q^{29} + 120 q^{31} - 12 q^{33} - 96 q^{36} - 44 q^{37} + 72 q^{38} + 36 q^{39} + 24 q^{42} + 56 q^{43} - 8 q^{44} + 8 q^{46} + 24 q^{47} - 40 q^{49} - 12 q^{51} + 72 q^{52} - 32 q^{53} + 16 q^{56} - 144 q^{57} + 88 q^{58} + 132 q^{59} + 96 q^{61} - 60 q^{63} + 128 q^{64} + 72 q^{66} + 164 q^{67} + 24 q^{68} - 136 q^{71} + 348 q^{73} - 112 q^{74} - 96 q^{77} + 280 q^{79} - 72 q^{81} - 264 q^{82} - 24 q^{84} - 88 q^{86} + 108 q^{87} - 48 q^{88} - 300 q^{89} - 272 q^{91} - 48 q^{92} + 120 q^{93} - 384 q^{98} - 24 q^{99}+O(q^{100}) \) 16 * q + 24 * q^3 - 16 * q^4 - 4 * q^7 + 24 * q^9 - 4 * q^11 - 48 * q^12 + 8 * q^14 - 32 * q^16 - 12 * q^17 - 72 * q^19 - 24 * q^21 + 48 * q^22 + 12 * q^23 - 32 * q^28 + 72 * q^29 + 120 * q^31 - 12 * q^33 - 96 * q^36 - 44 * q^37 + 72 * q^38 + 36 * q^39 + 24 * q^42 + 56 * q^43 - 8 * q^44 + 8 * q^46 + 24 * q^47 - 40 * q^49 - 12 * q^51 + 72 * q^52 - 32 * q^53 + 16 * q^56 - 144 * q^57 + 88 * q^58 + 132 * q^59 + 96 * q^61 - 60 * q^63 + 128 * q^64 + 72 * q^66 + 164 * q^67 + 24 * q^68 - 136 * q^71 + 348 * q^73 - 112 * q^74 - 96 * q^77 + 280 * q^79 - 72 * q^81 - 264 * q^82 - 24 * q^84 - 88 * q^86 + 108 * q^87 - 48 * q^88 - 300 * q^89 - 272 * q^91 - 48 * q^92 + 120 * q^93 - 384 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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