LMFDB - Embedded newform 1050.3.p.i.451.6

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			451.6
Root			$-2.63284 + 4.56021i$ of defining polynomial
Character	$\chi$	$=$	1050.451
Dual form			1050.3.p.i.901.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(-1.94434 + 6.72455i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(-1.94434 + 6.72455i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(0.263223 - 0.455915i) q^{11} +(-3.00000 + 1.73205i) q^{12} +4.22307i q^{13} +(-9.61071 + 2.37366i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(28.8825 + 16.6753i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(2.75133 - 1.58848i) q^{19} +(-8.74014 + 8.40298i) q^{21} +0.744507 q^{22} +(5.52954 + 9.57744i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-5.17218 + 2.98616i) q^{26} +5.19615i q^{27} +(-9.70292 - 10.0922i) q^{28} -56.1302 q^{29} +(-1.63817 - 0.945800i) q^{31} +(2.82843 - 4.89898i) q^{32} +(0.789668 - 0.455915i) q^{33} +47.1649i q^{34} -6.00000 q^{36} +(-4.87682 - 8.44690i) q^{37} +(3.89097 + 2.24645i) q^{38} +(-3.65729 + 6.33460i) q^{39} +4.07377i q^{41} +(-16.4717 - 4.76263i) q^{42} -46.3519 q^{43} +(0.526446 + 0.911831i) q^{44} +(-7.81995 + 13.5445i) q^{46} +(-54.7969 + 31.6370i) q^{47} -6.92820i q^{48} +(-41.4391 - 26.1496i) q^{49} +(28.8825 + 50.0259i) q^{51} +(-7.31457 - 4.22307i) q^{52} +(-23.2606 + 40.2885i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(5.49942 - 19.0199i) q^{56} +5.50267 q^{57} +(-39.6900 - 68.7452i) q^{58} +(-43.7614 - 25.2657i) q^{59} +(89.4583 - 51.6488i) q^{61} -2.67513i q^{62} +(-20.3874 + 5.03529i) q^{63} +8.00000 q^{64} +(1.11676 + 0.644762i) q^{66} +(4.36948 - 7.56816i) q^{67} +(-57.7649 + 33.3506i) q^{68} +19.1549i q^{69} +29.0608 q^{71} +(-4.24264 - 7.34847i) q^{72} +(-14.4912 - 8.36647i) q^{73} +(6.89686 - 11.9457i) q^{74} +6.35393i q^{76} +(2.55403 + 2.65651i) q^{77} -10.3444 q^{78} +(66.1473 + 114.571i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-4.98933 + 2.88059i) q^{82} -12.4838i q^{83} +(-5.81425 - 23.5413i) q^{84} +(-32.7757 - 56.7692i) q^{86} +(-84.1953 - 48.6102i) q^{87} +(-0.744507 + 1.28952i) q^{88} +(-59.1101 + 34.1272i) q^{89} +(-28.3982 - 8.21107i) q^{91} -22.1182 q^{92} +(-1.63817 - 2.83740i) q^{93} +(-77.4945 - 44.7415i) q^{94} +(8.48528 - 4.89898i) q^{96} +149.281i q^{97} +(2.72468 - 69.2429i) q^{98} +1.57934 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 $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.707107	+	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
$7$	−1.94434	+	6.72455i	−0.277762	+	0.960650i
$7$	−1.94434	+	6.72455i	−0.277762	+	0.960650i
$8$	−2.82843			−0.353553
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	0.263223	−	0.455915i	0.0239293	−	0.0414468i	−0.853813	−	0.520580i	$-0.825716\pi$
$11$	0.263223	−	0.455915i	0.0239293	−	0.0414468i	0.877742	+	0.479133i	$0.159049\pi$
$12$	−3.00000	+	1.73205i	−0.250000	+	0.144338i
$13$			4.22307i			0.324851i	0.986721	+	0.162426i	$0.0519318\pi$
$13$			4.22307i			0.324851i	−0.986721	+	0.162426i	$0.948068\pi$
$14$	−9.61071	+	2.37366i	−0.686479	+	0.169547i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	28.8825	+	16.6753i	1.69897	+	0.980900i	0.946741	+	0.321997i	$0.104354\pi$
$17$	28.8825	+	16.6753i	1.69897	+	0.980900i	0.752228	+	0.658903i	$0.228979\pi$
$18$	−2.12132	+	3.67423i	−0.117851	+	0.204124i
$19$	2.75133	−	1.58848i	0.144807	−	0.0836044i	−0.425846	−	0.904796i	$-0.640023\pi$
$19$	2.75133	−	1.58848i	0.144807	−	0.0836044i	0.570653	+	0.821191i	$0.306690\pi$
$20$		0			0
$21$	−8.74014	+	8.40298i	−0.416197	+	0.400142i
$22$	0.744507			0.0338412
$23$	5.52954	+	9.57744i	0.240415	+	0.416410i	0.960832	−	0.277130i	$-0.0893832\pi$
$23$	5.52954	+	9.57744i	0.240415	+	0.416410i	−0.720418	+	0.693540i	$0.756050\pi$
$24$	−4.24264	−	2.44949i	−0.176777	−	0.102062i
$25$		0			0
$26$	−5.17218	+	2.98616i	−0.198930	+	0.114852i
$27$			5.19615i			0.192450i
$28$	−9.70292	−	10.0922i	−0.346533	−	0.360437i
$29$	−56.1302			−1.93552			−0.967762	−	0.251866i	$-0.918956\pi$
$29$	−56.1302			−1.93552			−0.967762	+	0.251866i	$0.918956\pi$
$30$		0			0
$31$	−1.63817	−	0.945800i	−0.0528443	−	0.0305097i	0.473345	−	0.880877i	$-0.343046\pi$
$31$	−1.63817	−	0.945800i	−0.0528443	−	0.0305097i	−0.526189	+	0.850367i	$0.676380\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$	0.789668	−	0.455915i	0.0239293	−	0.0138156i
$34$			47.1649i			1.38720i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	−4.87682	−	8.44690i	−0.131806	−	0.228294i	0.792567	−	0.609785i	$-0.208744\pi$
$37$	−4.87682	−	8.44690i	−0.131806	−	0.228294i	−0.924373	+	0.381491i	$0.875411\pi$
$38$	3.89097	+	2.24645i	0.102394	+	0.0591172i
$39$	−3.65729	+	6.33460i	−0.0937765	+	0.162426i
$40$		0			0
$41$			4.07377i			0.0993603i	0.998765	+	0.0496802i	$0.0158202\pi$
$41$			4.07377i			0.0993603i	−0.998765	+	0.0496802i	$0.984180\pi$
$42$	−16.4717	−	4.76263i	−0.392184	−	0.113396i
$43$	−46.3519			−1.07795			−0.538975	−	0.842322i	$-0.681188\pi$
$43$	−46.3519			−1.07795			−0.538975	+	0.842322i	$0.681188\pi$
$44$	0.526446	+	0.911831i	0.0119647	+	0.0207234i
$45$		0			0
$46$	−7.81995	+	13.5445i	−0.169999	+	0.294447i
$47$	−54.7969	+	31.6370i	−1.16589	+	0.673127i	−0.952709	−	0.303885i	$-0.901716\pi$
$47$	−54.7969	+	31.6370i	−1.16589	+	0.673127i	−0.213182	+	0.977012i	$0.568383\pi$
$48$		−	6.92820i		−	0.144338i
$49$	−41.4391	−	26.1496i	−0.845696	−	0.533665i
$50$		0			0
$51$	28.8825	+	50.0259i	0.566323	+	0.980900i
$52$	−7.31457	−	4.22307i	−0.140665	−	0.0812129i
$53$	−23.2606	+	40.2885i	−0.438878	+	0.760160i	−0.997603	−	0.0691934i	$-0.977957\pi$
$53$	−23.2606	+	40.2885i	−0.438878	+	0.760160i	0.558725	+	0.829353i	$0.311291\pi$
$54$	−6.36396	+	3.67423i	−0.117851	+	0.0680414i
$55$		0			0
$56$	5.49942	−	19.0199i	0.0982038	−	0.339641i
$57$	5.50267			0.0965380
$58$	−39.6900	−	68.7452i	−0.684311	−	1.18526i
$59$	−43.7614	−	25.2657i	−0.741719	−	0.428231i	0.0809752	−	0.996716i	$-0.474197\pi$
$59$	−43.7614	−	25.2657i	−0.741719	−	0.428231i	−0.822694	+	0.568485i	$0.807530\pi$
$60$		0			0
$61$	89.4583	−	51.6488i	1.46653	−	0.846702i	0.467231	−	0.884135i	$-0.345252\pi$
$61$	89.4583	−	51.6488i	1.46653	−	0.846702i	0.999299	+	0.0374335i	$0.0119182\pi$
$62$		−	2.67513i		−	0.0431472i
$63$	−20.3874	+	5.03529i	−0.323609	+	0.0799252i
$64$	8.00000			0.125000
$65$		0			0
$66$	1.11676	+	0.644762i	0.0169206	+	0.00976912i
$67$	4.36948	−	7.56816i	0.0652161	−	0.112958i	−0.831574	−	0.555414i	$-0.812560\pi$
$67$	4.36948	−	7.56816i	0.0652161	−	0.112958i	0.896790	+	0.442457i	$0.145893\pi$
$68$	−57.7649	+	33.3506i	−0.849484	+	0.490450i
$69$			19.1549i			0.277607i
$70$		0			0
$71$	29.0608			0.409307			0.204653	−	0.978835i	$-0.434393\pi$
$71$	29.0608			0.409307			0.204653	+	0.978835i	$0.434393\pi$
$72$	−4.24264	−	7.34847i	−0.0589256	−	0.102062i
$73$	−14.4912	−	8.36647i	−0.198509	−	0.114609i	0.397451	−	0.917623i	$-0.369895\pi$
$73$	−14.4912	−	8.36647i	−0.198509	−	0.114609i	−0.595960	+	0.803014i	$0.703228\pi$
$74$	6.89686	−	11.9457i	0.0932008	−	0.161429i
$75$		0			0
$76$			6.35393i			0.0836044i
$77$	2.55403	+	2.65651i	0.0331692	+	0.0345001i
$78$	−10.3444			−0.132620
$79$	66.1473	+	114.571i	0.837308	+	1.45026i	0.892137	+	0.451764i	$0.149205\pi$
$79$	66.1473	+	114.571i	0.837308	+	1.45026i	−0.0548297	+	0.998496i	$0.517462\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−4.98933	+	2.88059i	−0.0608455	+	0.0351292i
$83$		−	12.4838i		−	0.150407i	−0.997168	−	0.0752033i	$-0.976039\pi$
$83$		−	12.4838i		−	0.150407i	0.997168	−	0.0752033i	$-0.0239606\pi$
$84$	−5.81425	−	23.5413i	−0.0692173	−	0.280254i
$85$		0			0
$86$	−32.7757	−	56.7692i	−0.381113	−	0.660107i
$87$	−84.1953	−	48.6102i	−0.967762	−	0.558738i
$88$	−0.744507	+	1.28952i	−0.00846030	+	0.0146537i
$89$	−59.1101	+	34.1272i	−0.664158	+	0.383452i	−0.793860	−	0.608101i	$-0.791931\pi$
$89$	−59.1101	+	34.1272i	−0.664158	+	0.383452i	0.129701	+	0.991553i	$0.458598\pi$
$90$		0			0
$91$	−28.3982	−	8.21107i	−0.312068	−	0.0902315i
$92$	−22.1182			−0.240415
$93$	−1.63817	−	2.83740i	−0.0176148	−	0.0305097i
$94$	−77.4945	−	44.7415i	−0.824409	−	0.475973i
$95$		0			0
$96$	8.48528	−	4.89898i	0.0883883	−	0.0510310i
$97$			149.281i			1.53898i	0.638659	+	0.769490i	$0.279490\pi$
$97$			149.281i			1.53898i	−0.638659	+	0.769490i	$0.720510\pi$
$98$	2.72468	−	69.2429i	0.0278029	−	0.706560i
$99$	1.57934			0.0159529
$100$		0			0
$101$	83.7839	+	48.3726i	0.829543	+	0.478937i	0.853696	−	0.520771i	$-0.174356\pi$
$101$	83.7839	+	48.3726i	0.829543	+	0.478937i	−0.0241531	+	0.999708i	$0.507689\pi$
$102$	−40.8460	+	70.7473i	−0.400451	+	0.693601i
$103$	−90.7268	+	52.3811i	−0.880843	+	0.508555i	−0.870936	−	0.491396i	$-0.836487\pi$
$103$	−90.7268	+	52.3811i	−0.880843	+	0.508555i	−0.00990642	+	0.999951i	$0.503153\pi$
$104$		−	11.9446i		−	0.114852i
$105$		0			0
$106$	−65.7908			−0.620668
$107$	−62.3022	−	107.911i	−0.582263	−	1.00851i	−0.995211	−	0.0977548i	$-0.968834\pi$
$107$	−62.3022	−	107.911i	−0.582263	−	1.00851i	0.412947	−	0.910755i	$-0.364499\pi$
$108$	−9.00000	−	5.19615i	−0.0833333	−	0.0481125i
$109$	−42.3042	+	73.2731i	−0.388112	+	0.672230i	−0.992196	−	0.124691i	$-0.960206\pi$
$109$	−42.3042	+	73.2731i	−0.388112	+	0.672230i	0.604083	+	0.796921i	$0.293539\pi$
$110$		0			0
$111$		−	16.8938i		−	0.152196i
$112$	27.1832	−	6.71372i	0.242707	−	0.0599439i
$113$	116.241			1.02868			0.514340	−	0.857586i	$-0.328037\pi$
$113$	116.241			1.02868			0.514340	+	0.857586i	$0.328037\pi$
$114$	3.89097	+	6.73936i	0.0341313	+	0.0591172i
$115$		0			0
$116$	56.1302	−	97.2204i	0.483881	−	0.838107i
$117$	−10.9719	+	6.33460i	−0.0937765	+	0.0541419i
$118$		−	71.4621i		−	0.605611i
$119$	−168.291	+	161.799i	−1.41421	+	1.35966i
$120$		0			0
$121$	60.3614	+	104.549i	0.498855	+	0.864042i
$122$	126.513	+	73.0424i	1.03699	+	0.598708i
$123$	−3.52799	+	6.11066i	−0.0286829	+	0.0496802i
$124$	3.27635	−	1.89160i	0.0264222	−	0.0152548i
$125$		0			0
$126$	−20.5830	−	21.4089i	−0.163357	−	0.169912i
$127$	81.3744			0.640743			0.320372	−	0.947292i	$-0.396192\pi$
$127$	81.3744			0.640743			0.320372	+	0.947292i	$0.396192\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$	−69.5278	−	40.1419i	−0.538975	−	0.311178i
$130$		0			0
$131$	208.389	−	120.313i	1.59075	−	0.918421i	0.597574	−	0.801814i	$-0.296131\pi$
$131$	208.389	−	120.313i	1.59075	−	0.918421i	0.993178	−	0.116608i	$-0.0372020\pi$
$132$			1.82366i			0.0138156i
$133$	5.33231	+	21.5900i	0.0400926	+	0.162331i
$134$	12.3588			0.0922295
$135$		0			0
$136$	−81.6919	−	47.1649i	−0.600676	−	0.346800i
$137$	116.831	−	202.357i	0.852778	−	1.47706i	−0.0259125	−	0.999664i	$-0.508249\pi$
$137$	116.831	−	202.357i	0.852778	−	1.47706i	0.878691	−	0.477391i	$-0.158418\pi$
$138$	−23.4598	+	13.5445i	−0.169999	+	0.0981489i
$139$		−	211.491i		−	1.52152i	−0.649033	−	0.760760i	$-0.724826\pi$
$139$		−	211.491i		−	1.52152i	0.649033	−	0.760760i	$-0.275174\pi$
$140$		0			0
$141$	−109.594			−0.777261
$142$	20.5491	+	35.5920i	0.144712	+	0.250648i
$143$	1.92536	+	1.11161i	0.0134641	+	0.00777348i
$144$	6.00000	−	10.3923i	0.0416667	−	0.0721688i
$145$		0			0
$146$		−	23.6640i		−	0.162082i
$147$	−39.5125	−	75.1117i	−0.268792	−	0.510964i
$148$	19.5073			0.131806
$149$	−72.0402	−	124.777i	−0.483491	−	0.837431i	0.516329	−	0.856390i	$-0.327298\pi$
$149$	−72.0402	−	124.777i	−0.483491	−	0.837431i	−0.999820	+	0.0189590i	$0.993965\pi$
$150$		0			0
$151$	−46.7563	+	80.9842i	−0.309644	+	0.536319i	−0.978285	−	0.207267i	$-0.933543\pi$
$151$	−46.7563	+	80.9842i	−0.309644	+	0.536319i	0.668640	+	0.743586i	$0.266877\pi$
$152$	−7.78195	+	4.49291i	−0.0511970	+	0.0295586i
$153$			100.052i			0.653933i
$154$	−1.44757	+	5.00647i	−0.00939982	+	0.0325095i
$155$		0			0
$156$	−7.31457	−	12.6692i	−0.0468883	−	0.0812129i
$157$	148.286	+	85.6127i	0.944494	+	0.545304i	0.891366	−	0.453284i	$-0.149748\pi$
$157$	148.286	+	85.6127i	0.944494	+	0.545304i	0.0531280	+	0.998588i	$0.483081\pi$
$158$	−93.5464	+	162.027i	−0.592066	+	1.02549i
$159$	−69.7817	+	40.2885i	−0.438878	+	0.253387i
$160$		0			0
$161$	−75.1553	+	18.5619i	−0.466803	+	0.115291i
$162$	−12.7279			−0.0785674
$163$	46.5064	+	80.5515i	0.285316	+	0.494181i	0.972686	−	0.232126i	$-0.0745682\pi$
$163$	46.5064	+	80.5515i	0.285316	+	0.494181i	−0.687370	+	0.726307i	$0.741235\pi$
$164$	−7.05598	−	4.07377i	−0.0430243	−	0.0248401i
$165$		0			0
$166$	15.2894	−	8.82735i	0.0921049	−	0.0531768i
$167$		−	104.991i		−	0.628688i	−0.949309	−	0.314344i	$-0.898216\pi$
$167$		−	104.991i		−	0.628688i	0.949309	−	0.314344i	$-0.101784\pi$
$168$	24.7208	−	23.7672i	0.147148	−	0.141471i
$169$	151.166			0.894472
$170$		0			0
$171$	8.25400	+	4.76545i	0.0482690	+	0.0278681i
$172$	46.3519	−	80.2838i	0.269488	−	0.466766i
$173$	−176.805	+	102.079i	−1.02200	+	0.590049i	−0.914681	−	0.404176i	$-0.867558\pi$
$173$	−176.805	+	102.079i	−1.02200	+	0.590049i	−0.107314	+	0.994225i	$0.534225\pi$
$174$		−	137.490i		−	0.790174i
$175$		0			0
$176$	−2.10578			−0.0119647
$177$	−43.7614	−	75.7970i	−0.247240	−	0.428231i
$178$	−83.5943	−	48.2632i	−0.469631	−	0.271141i
$179$	97.9495	−	169.653i	0.547204	−	0.947785i	−0.451261	−	0.892392i	$-0.649026\pi$
$179$	97.9495	−	169.653i	0.547204	−	0.947785i	0.998465	−	0.0553926i	$-0.0176410\pi$
$180$		0			0
$181$			119.031i			0.657632i	0.944394	+	0.328816i	$0.106650\pi$
$181$			119.031i			0.657632i	−0.944394	+	0.328816i	$0.893350\pi$
$182$	−10.0241	−	40.5867i	−0.0550776	−	0.223004i
$183$	178.917			0.977687
$184$	−15.6399	−	27.0891i	−0.0849994	−	0.147223i
$185$		0			0
$186$	2.31673	−	4.01269i	0.0124555	−	0.0215736i
$187$	15.2050	−	8.77864i	0.0813104	−	0.0469446i
$188$		−	126.548i		−	0.673127i
$189$	−34.9418	−	10.1031i	−0.184877	−	0.0534554i
$190$		0			0
$191$	32.8657	+	56.9250i	0.172072	+	0.298037i	0.939144	−	0.343524i	$-0.111621\pi$
$191$	32.8657	+	56.9250i	0.172072	+	0.298037i	−0.767072	+	0.641561i	$0.778287\pi$
$192$	12.0000	+	6.92820i	0.0625000	+	0.0360844i
$193$	−48.4350	+	83.8919i	−0.250959	+	0.434673i	−0.963790	−	0.266662i	$-0.914079\pi$
$193$	−48.4350	+	83.8919i	−0.250959	+	0.434673i	0.712831	+	0.701335i	$0.247412\pi$
$194$	−182.831	+	105.558i	−0.942429	+	0.544112i
$195$		0			0
$196$	86.7315	−	45.6251i	0.442508	−	0.232781i
$197$	−186.672			−0.947574			−0.473787	−	0.880640i	$-0.657113\pi$
$197$	−186.672			−0.947574			−0.473787	+	0.880640i	$0.657113\pi$
$198$	1.11676	+	1.93428i	0.00564020	+	0.00976912i
$199$	99.8454	+	57.6458i	0.501736	+	0.289677i	0.729430	−	0.684055i	$-0.239785\pi$
$199$	99.8454	+	57.6458i	0.501736	+	0.289677i	−0.227694	+	0.973733i	$0.573119\pi$
$200$		0			0
$201$	13.1084	−	7.56816i	0.0652161	−	0.0376525i
$202$			136.818i			0.677319i
$203$	109.136	−	377.450i	0.537616	−	1.85936i
$204$	−115.530			−0.566323
$205$		0			0
$206$	−128.307	−	74.0781i	−0.622850	−	0.359602i
$207$	−16.5886	+	28.7323i	−0.0801382	+	0.138803i
$208$	14.6291	−	8.44614i	0.0703324	−	0.0406064i
$209$		−	1.67250i		−	0.00800239i
$210$		0			0
$211$	139.433			0.660819			0.330409	−	0.943838i	$-0.392813\pi$
$211$	139.433			0.660819			0.330409	+	0.943838i	$0.392813\pi$
$212$	−46.5211	−	80.5769i	−0.219439	−	0.380080i
$213$	43.5912	+	25.1674i	0.204653	+	0.118157i
$214$	88.1086	−	152.609i	0.411722	−	0.713124i
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	9.54524	−	9.17703i	0.0439873	−	0.0422905i
$218$	−119.654			−0.548874
$219$	−14.4912	−	25.0994i	−0.0661697	−	0.114609i
$220$		0			0
$221$	−70.4209	+	121.973i	−0.318647	+	0.551912i
$222$	20.6906	−	11.9457i	0.0932008	−	0.0538095i
$223$			258.055i			1.15720i	0.815612	+	0.578599i	$0.196400\pi$
$223$			258.055i			1.15720i	−0.815612	+	0.578599i	$0.803600\pi$
$224$	27.4440	+	28.5452i	0.122518	+	0.127434i
$225$		0			0
$226$	82.1947	+	142.365i	0.363693	+	0.629935i
$227$	−286.682	−	165.516i	−1.26292	−	0.729146i	−0.289280	−	0.957245i	$-0.593416\pi$
$227$	−286.682	−	165.516i	−1.26292	−	0.729146i	−0.973638	+	0.228099i	$0.926749\pi$
$228$	−5.50267	+	9.53090i	−0.0241345	+	0.0418022i
$229$	211.516	−	122.119i	0.923653	−	0.533271i	0.0388541	−	0.999245i	$-0.487629\pi$
$229$	211.516	−	122.119i	0.923653	−	0.533271i	0.884799	+	0.465974i	$0.154296\pi$
$230$		0			0
$231$	1.53044	+	6.19662i	0.00662529	+	0.0268252i
$232$	158.760			0.684311
$233$	105.745	+	183.155i	0.453840	+	0.786074i	0.998621	−	0.0525044i	$-0.0167204\pi$
$233$	105.745	+	183.155i	0.453840	+	0.786074i	−0.544781	+	0.838579i	$0.683387\pi$
$234$	−15.5165	−	8.95848i	−0.0663100	−	0.0382841i
$235$		0			0
$236$	87.5228	−	50.5313i	0.370859	−	0.214116i
$237$			229.141i			0.966840i
$238$	−317.162	−	91.7044i	−1.33262	−	0.385313i
$239$	344.134			1.43989			0.719946	−	0.694030i	$-0.244167\pi$
$239$	344.134			1.43989			0.719946	+	0.694030i	$0.244167\pi$
$240$		0			0
$241$	−148.392	−	85.6742i	−0.615735	−	0.355495i	0.159472	−	0.987203i	$-0.449021\pi$
$241$	−148.392	−	85.6742i	−0.615735	−	0.355495i	−0.775207	+	0.631708i	$0.782354\pi$
$242$	−85.3639	+	147.855i	−0.352744	+	0.610970i
$243$	−13.5000	+	7.79423i	−0.0555556	+	0.0320750i
$244$			206.595i			0.846702i
$245$		0			0
$246$	−9.97867			−0.0405637
$247$	6.70827	+	11.6191i	0.0271590	+	0.0470408i
$248$	4.63346	+	2.67513i	0.0186833	+	0.0107868i
$249$	10.8112	−	18.7256i	0.0434187	−	0.0752033i
$250$		0			0
$251$			327.538i			1.30493i	0.757818	+	0.652467i	$0.226266\pi$
$251$			327.538i			1.30493i	−0.757818	+	0.652467i	$0.773734\pi$
$252$	11.6660	−	40.3473i	0.0462937	−	0.160108i
$253$	5.82200			0.0230119
$254$	57.5404	+	99.6629i	0.226537	+	0.392374i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	190.836	−	110.179i	0.742552	−	0.428713i	−0.0804442	−	0.996759i	$-0.525634\pi$
$257$	190.836	−	110.179i	0.742552	−	0.428713i	0.822997	+	0.568046i	$0.192301\pi$
$258$		−	113.538i		−	0.440072i
$259$	66.2837	−	16.3708i	0.255922	−	0.0632077i
$260$		0			0
$261$	−84.1953	−	145.831i	−0.322587	−	0.558738i
$262$	294.706	+	170.149i	1.12483	+	0.649422i
$263$	66.5976	−	115.350i	0.253223	−	0.438594i	−0.711189	−	0.703001i	$-0.751843\pi$
$263$	66.5976	−	115.350i	0.253223	−	0.438594i	0.964411	+	0.264407i	$0.0851761\pi$
$264$	−2.23352	+	1.28952i	−0.00846030	+	0.00488456i
$265$		0			0
$266$	−22.6718	+	21.7972i	−0.0852322	+	0.0819443i
$267$	−118.220			−0.442772
$268$	8.73896	+	15.1363i	0.0326080	+	0.0564788i
$269$	−22.9633	−	13.2578i	−0.0853653	−	0.0492857i	0.456710	−	0.889616i	$-0.349028\pi$
$269$	−22.9633	−	13.2578i	−0.0853653	−	0.0492857i	−0.542075	+	0.840330i	$0.682361\pi$
$270$		0			0
$271$	−92.6776	+	53.5074i	−0.341984	+	0.197444i	−0.661149	−	0.750255i	$-0.729931\pi$
$271$	−92.6776	+	53.5074i	−0.341984	+	0.197444i	0.319165	+	0.947699i	$0.396598\pi$
$272$		−	133.402i		−	0.490450i
$273$	−35.4864	−	36.9102i	−0.129987	−	0.135202i
$274$	330.447			1.20601
$275$		0			0
$276$	−33.1772	−	19.1549i	−0.120207	−	0.0694017i
$277$	220.191	−	381.381i	0.794912	−	1.37683i	−0.127983	−	0.991776i	$-0.540850\pi$
$277$	220.191	−	381.381i	0.794912	−	1.37683i	0.922895	−	0.385052i	$-0.125816\pi$
$278$	259.023	−	149.547i	0.931737	−	0.537939i
$279$		−	5.67480i		−	0.0203398i
$280$		0			0
$281$	322.069			1.14615			0.573076	−	0.819502i	$-0.305750\pi$
$281$	322.069			1.14615			0.573076	+	0.819502i	$0.305750\pi$
$282$	−77.4945	−	134.224i	−0.274803	−	0.475973i
$283$	59.3514	+	34.2665i	0.209722	+	0.121083i	0.601182	−	0.799112i	$-0.294697\pi$
$283$	59.3514	+	34.2665i	0.209722	+	0.121083i	−0.391460	+	0.920195i	$0.628030\pi$
$284$	−29.0608	+	50.3347i	−0.102327	+	0.177235i
$285$		0			0
$286$			3.14410i			0.0109934i
$287$	−27.3943	−	7.92079i	−0.0954505	−	0.0275986i
$288$	16.9706			0.0589256
$289$	411.631	+	712.966i	1.42433	+	2.46701i
$290$		0			0
$291$	−129.281	+	223.922i	−0.444265	+	0.769490i
$292$	28.9823	−	16.7329i	0.0992545	−	0.0573046i
$293$			147.510i			0.503448i	0.967799	+	0.251724i	$0.0809975\pi$
$293$			147.510i			0.503448i	−0.967799	+	0.251724i	$0.919003\pi$
$294$	64.0531	−	101.505i	0.217868	−	0.345254i
$295$		0			0
$296$	13.7937	+	23.8914i	0.0466004	+	0.0807143i
$297$	2.36901	+	1.36775i	0.00797645	+	0.00460521i
$298$	101.880	−	176.462i	0.341880	−	0.592153i
$299$	−40.4462	+	23.3516i	−0.135272	+	0.0780991i
$300$		0			0
$301$	90.1237	−	311.695i	0.299414	−	1.03553i
$302$	−132.247			−0.437903
$303$	83.7839	+	145.118i	0.276514	+	0.478937i
$304$	−11.0053	−	6.35393i	−0.0362018	−	0.0209011i
$305$		0			0
$306$	−122.538	+	70.7473i	−0.400451	+	0.231200i
$307$			376.010i			1.22479i	0.790553	+	0.612394i	$0.209793\pi$
$307$			376.010i			1.22479i	−0.790553	+	0.612394i	$0.790207\pi$
$308$	−7.15524	+	1.76720i	−0.0232313	+	0.00573767i
$309$	−181.454			−0.587228
$310$		0			0
$311$	−337.599	−	194.913i	−1.08553	−	0.626730i	−0.153146	−	0.988204i	$-0.548941\pi$
$311$	−337.599	−	194.913i	−1.08553	−	0.626730i	−0.932383	+	0.361473i	$0.882274\pi$
$312$	10.3444	−	17.9170i	0.0331550	−	0.0574262i
$313$	123.890	−	71.5282i	0.395816	−	0.228524i	−0.288861	−	0.957371i	$-0.593277\pi$
$313$	123.890	−	71.5282i	0.395816	−	0.228524i	0.684677	+	0.728847i	$0.259943\pi$
$314$			242.149i			0.771176i
$315$		0			0
$316$	−264.589			−0.837308
$317$	192.222	+	332.938i	0.606378	+	1.05028i	0.991832	+	0.127551i	$0.0407117\pi$
$317$	192.222	+	332.938i	0.606378	+	1.05028i	−0.385454	+	0.922727i	$0.625955\pi$
$318$	−98.6862	−	56.9765i	−0.310334	−	0.179171i
$319$	−14.7747	+	25.5906i	−0.0463158	+	0.0802214i
$320$		0			0
$321$		−	215.821i		−	0.672340i
$322$	−75.8764	−	78.9208i	−0.235641	−	0.245096i
$323$	105.954			0.328030
$324$	−9.00000	−	15.5885i	−0.0277778	−	0.0481125i
$325$		0			0
$326$	−65.7700	+	113.917i	−0.201749	+	0.349439i
$327$	−126.913	+	73.2731i	−0.388112	+	0.224077i
$328$		−	11.5224i		−	0.0351292i
$329$	−106.201	−	429.997i	−0.322799	−	1.30698i
$330$		0			0
$331$	−96.9539	−	167.929i	−0.292912	−	0.507338i	0.681585	−	0.731739i	$-0.261291\pi$
$331$	−96.9539	−	167.929i	−0.292912	−	0.507338i	−0.974497	+	0.224400i	$0.927958\pi$
$332$	21.6225	+	12.4838i	0.0651280	+	0.0376017i
$333$	14.6305	−	25.3407i	0.0439353	−	0.0760982i
$334$	128.587	−	74.2397i	0.384991	−	0.222275i
$335$		0			0
$336$	46.5890	+	13.4708i	0.138658	+	0.0400916i
$337$	−125.477			−0.372337			−0.186168	−	0.982518i	$-0.559607\pi$
$337$	−125.477			−0.372337			−0.186168	+	0.982518i	$0.559607\pi$
$338$	106.890	+	185.139i	0.316243	+	0.547750i
$339$	174.361	+	100.668i	0.514340	+	0.296954i
$340$		0			0
$341$	−0.862410	+	0.497912i	−0.00252906	+	0.00146015i
$342$			13.4787i			0.0394115i
$343$	256.416	−	227.816i	0.747568	−	0.664186i
$344$	131.103			0.381113
$345$		0			0
$346$	−250.040	−	144.361i	−0.722660	−	0.417228i
$347$	−251.798	+	436.128i	−0.725644	+	1.25685i	0.233065	+	0.972461i	$0.425125\pi$
$347$	−251.798	+	436.128i	−0.725644	+	1.25685i	−0.958708	+	0.284391i	$0.908209\pi$
$348$	168.391	−	97.2204i	0.483881	−	0.279369i
$349$			47.7682i			0.136872i	0.997656	+	0.0684358i	$0.0218008\pi$
$349$			47.7682i			0.136872i	−0.997656	+	0.0684358i	$0.978199\pi$
$350$		0			0
$351$	−21.9437			−0.0625177
$352$	−1.48901	−	2.57905i	−0.00423015	−	0.00732684i
$353$	−28.5012	−	16.4552i	−0.0807399	−	0.0466152i	0.459087	−	0.888392i	$-0.348177\pi$
$353$	−28.5012	−	16.4552i	−0.0807399	−	0.0466152i	−0.539826	+	0.841776i	$0.681510\pi$
$354$	61.8880	−	107.193i	0.174825	−	0.302805i
$355$		0			0
$356$		−	136.509i		−	0.383452i
$357$	−392.559	+	96.9543i	−1.09960	+	0.271581i
$358$	277.043			0.773863
$359$	−133.898	−	231.919i	−0.372976	−	0.646013i	0.617046	−	0.786927i	$-0.288329\pi$
$359$	−133.898	−	231.919i	−0.372976	−	0.646013i	−0.990022	+	0.140914i	$0.954996\pi$
$360$		0			0
$361$	−175.453	+	303.894i	−0.486021	+	0.841812i
$362$	−145.783	+	84.1679i	−0.402716	+	0.232508i
$363$			209.098i			0.576028i
$364$	42.6202	−	40.9761i	0.117089	−	0.112572i
$365$		0			0
$366$	126.513	+	219.127i	0.345665	+	0.598708i
$367$	137.458	+	79.3613i	0.374545	+	0.216243i	0.675442	−	0.737413i	$-0.263953\pi$
$367$	137.458	+	79.3613i	0.374545	+	0.216243i	−0.300897	+	0.953657i	$0.597286\pi$
$368$	22.1182	−	38.3098i	0.0601037	−	0.104103i
$369$	−10.5840	+	6.11066i	−0.0286829	+	0.0165601i
$370$		0			0
$371$	−225.695	−	234.751i	−0.608343	−	0.632752i
$372$	6.55270			0.0176148
$373$	207.172	+	358.832i	0.555421	+	0.962017i	0.997871	+	0.0652235i	$0.0207760\pi$
$373$	207.172	+	358.832i	0.555421	+	0.962017i	−0.442450	+	0.896793i	$0.645891\pi$
$374$	21.5032	+	12.4149i	0.0574951	+	0.0331948i
$375$		0			0
$376$	154.989	−	89.4829i	0.412205	−	0.237986i
$377$		−	237.042i		−	0.628758i
$378$	−12.3339	−	49.9387i	−0.0326293	−	0.132113i
$379$	−72.8000			−0.192084			−0.0960422	−	0.995377i	$-0.530618\pi$
$379$	−72.8000			−0.192084			−0.0960422	+	0.995377i	$0.530618\pi$
$380$		0			0
$381$	122.062	+	70.4723i	0.320372	+	0.184967i
$382$	−46.4791	+	80.5042i	−0.121673	+	0.210744i
$383$	246.830	−	142.507i	0.644464	−	0.372082i	−0.141868	−	0.989886i	$-0.545311\pi$
$383$	246.830	−	142.507i	0.644464	−	0.372082i	0.786332	+	0.617804i	$0.211977\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	−136.995			−0.354909
$387$	−69.5278	−	120.426i	−0.179658	−	0.311178i
$388$	−258.562	−	149.281i	−0.666398	−	0.384745i
$389$	48.5692	−	84.1242i	0.124856	−	0.216258i	−0.796820	−	0.604216i	$-0.793486\pi$
$389$	48.5692	−	84.1242i	0.124856	−	0.216258i	0.921677	+	0.387959i	$0.126820\pi$
$390$		0			0
$391$			368.827i			0.943291i
$392$	117.207	+	73.9622i	0.298999	+	0.188679i
$393$	416.777			1.06050
$394$	−131.997	−	228.626i	−0.335018	−	0.580268i
$395$		0			0
$396$	−1.57934	+	2.73549i	−0.00398822	+	0.00690781i
$397$	685.636	−	395.852i	1.72704	−	0.997108i	0.825522	−	0.564371i	$-0.190881\pi$
$397$	685.636	−	395.852i	1.72704	−	0.997108i	0.901520	−	0.432737i	$-0.142452\pi$
$398$			163.047i			0.409665i
$399$	−10.6990	+	37.0030i	−0.0268146	+	0.0927392i
$400$		0			0
$401$	−251.613	−	435.807i	−0.627464	−	1.08680i	−0.988059	−	0.154077i	$-0.950759\pi$
$401$	−251.613	−	435.807i	−0.627464	−	1.08680i	0.360594	−	0.932723i	$-0.382574\pi$
$402$	18.5381	+	10.7030i	0.0461147	+	0.0266244i
$403$	3.99418	−	6.91812i	0.00991112	−	0.0171666i
$404$	−167.568	+	96.7453i	−0.414772	+	0.239468i
$405$		0			0
$406$	539.451	−	133.234i	1.32870	−	0.328162i
$407$	−5.13476			−0.0126161
$408$	−81.6919	−	141.495i	−0.200225	−	0.346800i
$409$	649.395	+	374.928i	1.58776	+	0.916696i	0.993675	+	0.112296i	$0.0358204\pi$
$409$	649.395	+	374.928i	1.58776	+	0.916696i	0.594088	+	0.804400i	$0.297513\pi$
$410$		0			0
$411$	350.492	−	202.357i	0.852778	−	0.492352i
$412$		−	209.525i		−	0.508555i
$413$	254.987	−	245.151i	0.617402	−	0.593585i
$414$	−46.9197			−0.113333
$415$		0			0
$416$	20.6887	+	11.9446i	0.0497325	+	0.0287131i
$417$	183.157	−	317.237i	0.439225	−	0.760760i
$418$	2.04839	−	1.18264i	0.00490044	−	0.00282927i
$419$		−	465.759i		−	1.11160i	−0.831317	−	0.555799i	$-0.812413\pi$
$419$		−	465.759i		−	1.11160i	0.831317	−	0.555799i	$-0.187587\pi$
$420$		0			0
$421$	345.980			0.821805			0.410902	−	0.911679i	$-0.365214\pi$
$421$	345.980			0.821805			0.410902	+	0.911679i	$0.365214\pi$
$422$	98.5939	+	170.770i	0.233635	+	0.404667i
$423$	−164.391	−	94.9110i	−0.388630	−	0.224376i
$424$	65.7908	−	113.953i	0.155167	−	0.268757i
$425$		0			0
$426$			71.1841i			0.167099i
$427$	173.378	+	701.990i	0.406037	+	1.64400i
$428$	249.209			0.582263
$429$	1.92536	+	3.33482i	0.00448802	+	0.00777348i
$430$		0			0
$431$	−247.300	+	428.336i	−0.573782	+	0.993819i	0.422391	+	0.906414i	$0.361191\pi$
$431$	−247.300	+	428.336i	−0.573782	+	0.993819i	−0.996173	+	0.0874056i	$0.972142\pi$
$432$	18.0000	−	10.3923i	0.0416667	−	0.0240563i
$433$		−	730.022i		−	1.68596i	−0.537943	−	0.842981i	$-0.680799\pi$
$433$		−	730.022i		−	1.68596i	0.537943	−	0.842981i	$-0.319201\pi$
$434$	17.9890	+	5.20135i	0.0414494	+	0.0119847i
$435$		0			0
$436$	−84.6085	−	146.546i	−0.194056	−	0.336115i
$437$	30.4272	+	17.5672i	0.0696275	+	0.0401994i
$438$	20.4936	−	35.4959i	0.0467890	−	0.0810410i
$439$	−321.631	+	185.694i	−0.732645	+	0.422993i	−0.819389	−	0.573238i	$-0.805687\pi$
$439$	−321.631	+	185.694i	−0.732645	+	0.422993i	0.0867437	+	0.996231i	$0.472354\pi$
$440$		0			0
$441$	5.77993	−	146.886i	0.0131064	−	0.333076i
$442$	−199.180			−0.450635
$443$	204.354	+	353.951i	0.461295	+	0.798987i	0.999026	−	0.0441299i	$-0.0140515\pi$
$443$	204.354	+	353.951i	0.461295	+	0.798987i	−0.537731	+	0.843117i	$0.680718\pi$
$444$	29.2609	+	16.8938i	0.0659029	+	0.0380491i
$445$		0			0
$446$	−316.052	+	182.473i	−0.708636	+	0.409131i
$447$		−	249.555i		−	0.558288i
$448$	−15.5547	+	53.7964i	−0.0347203	+	0.120081i
$449$	725.469			1.61574			0.807872	−	0.589358i	$-0.200619\pi$
$449$	725.469			1.61574			0.807872	+	0.589358i	$0.200619\pi$
$450$		0			0
$451$	1.85730	+	1.07231i	0.00411817	+	0.00237763i
$452$	−116.241	+	201.335i	−0.257170	+	0.445432i
$453$	−140.269	+	80.9842i	−0.309644	+	0.178773i
$454$		−	468.150i		−	1.03117i
$455$		0			0
$456$	−15.5639			−0.0341313
$457$	200.765	+	347.736i	0.439311	+	0.760909i	0.997636	−	0.0687128i	$-0.0218892\pi$
$457$	200.765	+	347.736i	0.439311	+	0.760909i	−0.558325	+	0.829622i	$0.688556\pi$
$458$	299.129	+	172.702i	0.653121	+	0.377080i
$459$	−86.6474	+	150.078i	−0.188774	+	0.326967i
$460$		0			0
$461$			653.050i			1.41659i	0.705915	+	0.708297i	$0.250536\pi$
$461$			653.050i			1.41659i	−0.705915	+	0.708297i	$0.749464\pi$
$462$	−6.50709	+	6.25607i	−0.0140846	+	0.0135413i
$463$	869.580			1.87814			0.939072	−	0.343722i	$-0.111688\pi$
$463$	869.580			1.87814			0.939072	+	0.343722i	$0.111688\pi$
$464$	112.260	+	194.441i	0.241941	+	0.419053i
$465$		0			0
$466$	−149.546	+	259.021i	−0.320913	+	0.555838i
$467$	−640.168	+	369.601i	−1.37081	+	0.791437i	−0.991030	−	0.133641i	$-0.957333\pi$
$467$	−640.168	+	369.601i	−1.37081	+	0.791437i	−0.379779	+	0.925077i	$0.624000\pi$
$468$		−	25.3384i		−	0.0541419i
$469$	42.3967	+	44.0978i	0.0903981	+	0.0940252i
$470$		0			0
$471$	148.286	+	256.838i	0.314831	+	0.545304i
$472$	123.776	+	71.4621i	0.262237	+	0.151403i
$473$	−12.2009	+	21.1325i	−0.0257947	+	0.0446777i
$474$	−280.639	+	162.027i	−0.592066	+	0.341829i
$475$		0			0
$476$	−111.953	−	453.288i	−0.235196	−	0.952285i
$477$	−139.563			−0.292586
$478$	243.339	+	421.476i	0.509078	+	0.881750i
$479$	−525.006	−	303.112i	−1.09605	−	0.632802i	−0.160866	−	0.986976i	$-0.551429\pi$
$479$	−525.006	−	303.112i	−1.09605	−	0.632802i	−0.935180	+	0.354174i	$0.884762\pi$
$480$		0			0
$481$	35.6718	−	20.5951i	0.0741618	−	0.0428173i
$482$		−	242.323i		−	0.502745i
$483$	−128.808	−	37.2435i	−0.266683	−	0.0771088i
$484$	−241.446			−0.498855
$485$		0			0
$486$	−19.0919	−	11.0227i	−0.0392837	−	0.0226805i
$487$	324.788	−	562.549i	0.666916	−	1.15513i	−0.311846	−	0.950133i	$-0.600947\pi$
$487$	324.788	−	562.549i	0.666916	−	1.15513i	0.978762	−	0.205000i	$-0.0657193\pi$
$488$	−253.026	+	146.085i	−0.518497	+	0.299354i
$489$			161.103i			0.329454i
$490$		0			0
$491$	266.629			0.543033			0.271516	−	0.962434i	$-0.412475\pi$
$491$	266.629			0.543033			0.271516	+	0.962434i	$0.412475\pi$
$492$	−7.05598	−	12.2213i	−0.0143414	−	0.0248401i
$493$	−1621.18	−	935.988i	−3.28839	−	1.89856i
$494$	−9.48693	+	16.4318i	−0.0192043	+	0.0332628i
$495$		0			0
$496$			7.56640i			0.0152548i
$497$	−56.5039	+	195.421i	−0.113690	+	0.393200i
$498$	30.5788			0.0614033
$499$	340.553	+	589.855i	0.682471	+	1.18207i	0.974225	+	0.225581i	$0.0724279\pi$
$499$	340.553	+	589.855i	0.682471	+	1.18207i	−0.291754	+	0.956493i	$0.594239\pi$
$500$		0			0
$501$	90.9247	−	157.486i	0.181487	−	0.314344i
$502$	−401.151	+	231.604i	−0.799105	+	0.461364i
$503$		−	453.326i		−	0.901245i	−0.892715	−	0.450622i	$-0.851202\pi$
$503$		−	453.326i		−	0.901245i	0.892715	−	0.450622i	$-0.148798\pi$
$504$	57.6643	−	14.2419i	0.114413	−	0.0282578i
$505$		0			0
$506$	4.11678	+	7.13047i	0.00813592	+	0.0140918i
$507$	226.749	+	130.913i	0.447236	+	0.258212i
$508$	−81.3744	+	140.945i	−0.160186	+	0.277450i
$509$	−43.5300	+	25.1321i	−0.0855206	+	0.0493754i	−0.542150	−	0.840281i	$-0.682390\pi$
$509$	−43.5300	+	25.1321i	−0.0855206	+	0.0493754i	0.456630	+	0.889657i	$0.349056\pi$
$510$		0			0
$511$	84.4364	−	81.1792i	0.165238	−	0.158863i
$512$	−22.6274			−0.0441942
$513$	8.25400	+	14.2963i	0.0160897	+	0.0278681i
$514$	269.883	+	155.817i	0.525064	+	0.303146i
$515$		0			0
$516$	139.056	−	80.2838i	0.269488	−	0.155589i
$517$			33.3103i			0.0644300i
$518$	66.9197	+	69.6048i	0.129189	+	0.134372i
$519$	−353.610			−0.681330
$520$		0			0
$521$	−89.2971	−	51.5557i	−0.171396	−	0.0989553i	0.411848	−	0.911252i	$-0.364883\pi$
$521$	−89.2971	−	51.5557i	−0.171396	−	0.0989553i	−0.583244	+	0.812297i	$0.698217\pi$
$522$	119.070	−	206.236i	0.228104	−	0.395087i
$523$	317.716	−	183.434i	0.607488	−	0.350733i	−0.164494	−	0.986378i	$-0.552599\pi$
$523$	317.716	−	183.434i	0.607488	−	0.350733i	0.771982	+	0.635645i	$0.219266\pi$
$524$			481.253i			0.918421i
$525$		0			0
$526$	188.366			0.358111
$527$	−31.5430	−	54.6341i	−0.0598539	−	0.103670i
$528$	−3.15867	−	1.82366i	−0.00598234	−	0.00345390i
$529$	203.348	−	352.210i	0.384402	−	0.665803i
$530$		0			0
$531$		−	151.594i		−	0.285488i
$532$	−42.7273	−	12.3542i	−0.0803145	−	0.0232222i
$533$	−17.2038			−0.0322773
$534$	−83.5943	−	144.790i	−0.156544	−	0.271141i
$535$		0			0
$536$	−12.3588	+	21.4060i	−0.0230574	+	0.0399365i
$537$	293.848	−	169.653i	0.547204	−	0.315928i
$538$		−	37.4988i		−	0.0697005i
$539$	−22.8297	+	12.0096i	−0.0423557	+	0.0222812i
$540$		0			0
$541$	266.559	+	461.693i	0.492714	+	0.853407i	0.999965	−	0.00839227i	$-0.00267137\pi$
$541$	266.559	+	461.693i	0.492714	+	0.853407i	−0.507250	+	0.861799i	$0.669338\pi$
$542$	−131.066	−	75.6709i	−0.241819	−	0.139614i
$543$	−103.084	+	178.547i	−0.189842	+	0.328816i
$544$	163.384	−	94.3297i	0.300338	−	0.173400i
$545$		0			0
$546$	20.1129	−	69.5612i	0.0368369	−	0.127401i
$547$	−69.6218			−0.127279			−0.0636396	−	0.997973i	$-0.520271\pi$
$547$	−69.6218			−0.127279			−0.0636396	+	0.997973i	$0.520271\pi$
$548$	233.661	+	404.713i	0.426389	+	0.738528i
$549$	268.375	+	154.946i	0.488843	+	0.282234i
$550$		0			0
$551$	−154.433	+	89.1619i	−0.280277	+	0.161818i
$552$		−	54.1782i		−	0.0981489i
$553$	−899.048	+	222.047i	−1.62576	+	0.401532i
$554$	622.793			1.12418
$555$		0			0
$556$	366.314	+	211.491i	0.658838	+	0.380380i
$557$	8.43122	−	14.6033i	0.0151368	−	0.0262178i	−0.858358	−	0.513052i	$-0.828515\pi$
$557$	8.43122	−	14.6033i	0.0151368	−	0.0262178i	0.873495	+	0.486834i	$0.161848\pi$
$558$	6.95018	−	4.01269i	0.0124555	−	0.00719120i
$559$		−	195.747i		−	0.350174i
$560$		0			0
$561$	30.4101			0.0542069
$562$	227.737	+	394.452i	0.405226	+	0.701872i
$563$	−793.093	−	457.892i	−1.40869	−	0.813308i	−0.413428	−	0.910537i	$-0.635669\pi$
$563$	−793.093	−	457.892i	−1.40869	−	0.813308i	−0.995262	+	0.0972290i	$0.969002\pi$
$564$	109.594	−	189.822i	0.194315	−	0.336564i
$565$		0			0
$566$			96.9204i			0.171237i
$567$	−43.6632	−	45.4151i	−0.0770073	−	0.0800971i
$568$	−82.1963			−0.144712
$569$	−203.828	−	353.040i	−0.358221	−	0.620456i	0.629443	−	0.777047i	$-0.283283\pi$
$569$	−203.828	−	353.040i	−0.358221	−	0.620456i	−0.987664	+	0.156590i	$0.949950\pi$
$570$		0			0
$571$	447.910	−	775.803i	0.784431	−	1.35867i	−0.144908	−	0.989445i	$-0.546289\pi$
$571$	447.910	−	775.803i	0.784431	−	1.35867i	0.929339	−	0.369229i	$-0.120378\pi$
$572$	−3.85072	+	2.22322i	−0.00673203	+	0.00388674i
$573$			113.850i			0.198691i
$574$	−9.66974	−	39.1519i	−0.0168462	−	0.0682088i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	−590.115	−	340.703i	−1.02273	−	0.590473i	−0.107836	−	0.994169i	$-0.534392\pi$
$577$	−590.115	−	340.703i	−1.02273	−	0.590473i	−0.914893	+	0.403695i	$0.867726\pi$
$578$	−582.134	+	1008.29i	−1.00715	+	1.74444i
$579$	−145.305	+	83.8919i	−0.250959	+	0.144891i
$580$		0			0
$581$	83.9476	+	24.2726i	0.144488	+	0.0417773i
$582$	−365.662			−0.628286
$583$	12.2454	+	21.2097i	0.0210041	+	0.0363802i
$584$	40.9872	+	23.6640i	0.0701835	+	0.0405205i
$585$		0			0
$586$	−180.662	+	104.305i	−0.308297	+	0.177996i
$587$		−	833.001i		−	1.41908i	−0.704665	−	0.709541i	$-0.748903\pi$
$587$		−	833.001i		−	1.41908i	0.704665	−	0.709541i	$-0.251097\pi$
$588$	169.610	+	6.67408i	0.288452	+	0.0113505i
$589$	−6.00955			−0.0102030
$590$		0			0
$591$	−280.008	−	161.663i	−0.473787	−	0.273541i
$592$	−19.5073	+	33.7876i	−0.0329515	+	0.0570736i
$593$	−270.842	+	156.371i	−0.456731	+	0.263694i	−0.710669	−	0.703527i	$-0.751608\pi$
$593$	−270.842	+	156.371i	−0.456731	+	0.263694i	0.253938	+	0.967221i	$0.418274\pi$
$594$			3.86857i			0.00651274i
$595$		0			0
$596$	288.161			0.483491
$597$	99.8454	+	172.937i	0.167245	+	0.289677i
$598$	−57.1996	−	33.0242i	−0.0956514	−	0.0552244i
$599$	−107.121	+	185.540i	−0.178834	+	0.309749i	−0.941481	−	0.337065i	$-0.890566\pi$
$599$	−107.121	+	185.540i	−0.178834	+	0.309749i	0.762648	+	0.646814i	$0.223899\pi$
$600$		0			0
$601$		−	176.849i		−	0.294257i	−0.989117	−	0.147129i	$-0.952997\pi$
$601$		−	176.849i		−	0.294257i	0.989117	−	0.147129i	$-0.0470031\pi$
$602$	445.474	−	110.023i	0.739991	−	0.182763i
$603$	26.2169			0.0434774
$604$	−93.5125	−	161.968i	−0.154822	−	0.268160i
$605$		0			0
$606$	−118.488	+	205.228i	−0.195525	+	0.338660i
$607$	−32.1304	+	18.5505i	−0.0529331	+	0.0305609i	−0.526233	−	0.850340i	$-0.676396\pi$
$607$	−32.1304	+	18.5505i	−0.0529331	+	0.0305609i	0.473300	+	0.880901i	$0.343063\pi$
$608$		−	17.9716i		−	0.0295586i
$609$	490.586	−	471.661i	0.805559	−	0.774484i
$610$		0			0
$611$	−133.605	−	231.411i	−0.218666	−	0.378741i
$612$	−173.295	−	100.052i	−0.283161	−	0.163483i
$613$	−449.860	+	779.180i	−0.733866	+	1.27109i	0.221353	+	0.975194i	$0.428953\pi$
$613$	−449.860	+	779.180i	−0.733866	+	1.27109i	−0.955219	+	0.295899i	$0.904381\pi$
$614$	−460.516	+	265.879i	−0.750027	+	0.433028i
$615$		0			0
$616$	−7.22389	−	7.51374i	−0.0117271	−	0.0121976i
$617$	626.244			1.01498			0.507491	−	0.861657i	$-0.330573\pi$
$617$	626.244			1.01498			0.507491	+	0.861657i	$0.330573\pi$
$618$	−128.307	−	222.234i	−0.207617	−	0.359602i
$619$	−776.375	−	448.240i	−1.25424	−	0.724136i	−0.282291	−	0.959329i	$-0.591094\pi$
$619$	−776.375	−	448.240i	−1.25424	−	0.724136i	−0.971949	+	0.235193i	$0.924428\pi$
$620$		0			0
$621$	−49.7658	+	28.7323i	−0.0801382	+	0.0462678i
$622$		−	551.298i		−	0.886331i
$623$	−114.560	−	463.843i	−0.183885	−	0.744532i
$624$	29.2583			0.0468883
$625$		0			0
$626$	175.207	+	101.156i	0.279884	+	0.161591i
$627$	1.44843	−	2.50875i	0.00231009	−	0.00400120i
$628$	−296.571	+	171.225i	−0.472247	+	0.272652i
$629$		−	325.290i		−	0.517153i
$630$		0			0
$631$	−500.730			−0.793550			−0.396775	−	0.917916i	$-0.629871\pi$
$631$	−500.730			−0.793550			−0.396775	+	0.917916i	$0.629871\pi$
$632$	−187.093	−	324.054i	−0.296033	−	0.512744i
$633$	209.149	+	120.752i	0.330409	+	0.190762i
$634$	−271.843	+	470.846i	−0.428774	+	0.742659i
$635$		0			0
$636$		−	161.154i		−	0.253387i
$637$	110.431	−	175.000i	0.173362	−	0.274726i
$638$	−41.7893			−0.0655005
$639$	43.5912	+	75.5021i	0.0682178	+	0.118157i
$640$		0			0
$641$	−310.289	+	537.436i	−0.484070	+	0.838434i	−0.999833	−	0.0182978i	$-0.994175\pi$
$641$	−310.289	+	537.436i	−0.484070	+	0.838434i	0.515763	+	0.856732i	$0.327509\pi$
$642$	264.326	−	152.609i	0.411722	−	0.237708i
$643$			1127.93i			1.75417i	0.480334	+	0.877086i	$0.340516\pi$
$643$			1127.93i			1.75417i	−0.480334	+	0.877086i	$0.659484\pi$
$644$	43.0051	−	148.735i	0.0667782	−	0.230954i
$645$		0			0
$646$	74.9206	+	129.766i	0.115976	+	0.200877i
$647$	117.130	+	67.6248i	0.181035	+	0.104521i	0.587779	−	0.809022i	$-0.300003\pi$
$647$	117.130	+	67.6248i	0.181035	+	0.104521i	−0.406744	+	0.913542i	$0.633336\pi$
$648$	12.7279	−	22.0454i	0.0196419	−	0.0340207i
$649$	−23.0380	+	13.3010i	−0.0354977	+	0.0204946i
$650$		0			0
$651$	22.2654	−	5.49912i	0.0342018	−	0.00844719i
$652$	−186.026			−0.285316
$653$	−195.145	−	338.001i	−0.298843	−	0.517612i	0.677028	−	0.735957i	$-0.263267\pi$
$653$	−195.145	−	338.001i	−0.298843	−	0.517612i	−0.975872	+	0.218345i	$0.929934\pi$
$654$	−179.482	−	103.624i	−0.274437	−	0.158446i
$655$		0			0
$656$	14.1120	−	8.14755i	0.0215121	−	0.0124200i
$657$		−	50.1988i		−	0.0764061i
$658$	451.542	−	434.123i	0.686233	−	0.659761i
$659$	−864.853			−1.31237			−0.656186	−	0.754599i	$-0.727831\pi$
$659$	−864.853			−1.31237			−0.656186	+	0.754599i	$0.727831\pi$
$660$		0			0
$661$	−873.134	−	504.104i	−1.32093	−	0.762638i	−0.337052	−	0.941486i	$-0.609430\pi$
$661$	−873.134	−	504.104i	−1.32093	−	0.762638i	−0.983877	+	0.178848i	$0.942763\pi$
$662$	137.113	−	237.487i	0.207120	−	0.358742i
$663$	−211.263	+	121.973i	−0.318647	+	0.183971i
$664$			35.3094i			0.0531768i
$665$		0			0
$666$	41.3812			0.0621339
$667$	−310.374	−	537.584i	−0.465328	−	0.805973i
$668$	181.849	+	104.991i	0.272230	+	0.157172i
$669$	−223.482	+	387.083i	−0.334054	+	0.578599i
$670$		0			0
$671$		−	54.3806i		−	0.0810441i
$672$	16.4452	+	66.5850i	0.0244720	+	0.0990848i
$673$	109.959			0.163386			0.0816928	−	0.996658i	$-0.473967\pi$
$673$	109.959			0.163386			0.0816928	+	0.996658i	$0.473967\pi$
$674$	−88.7259	−	153.678i	−0.131641	−	0.228009i
$675$		0			0
$676$	−151.166	+	261.827i	−0.223618	+	0.387318i
$677$	−146.213	+	84.4163i	−0.215972	+	0.124692i	−0.604084	−	0.796921i	$-0.706461\pi$
$677$	−146.213	+	84.4163i	−0.215972	+	0.124692i	0.388112	+	0.921612i	$0.373128\pi$
$678$			284.731i			0.419957i
$679$	−1003.85	−	290.253i	−1.47842	−	0.427471i
$680$		0			0
$681$	−286.682	−	496.548i	−0.420973	−	0.729146i
$682$	−1.21963	−	0.704155i	−0.00178832	−	0.00103248i
$683$	−218.065	+	377.700i	−0.319276	+	0.553002i	−0.980337	−	0.197330i	$-0.936773\pi$
$683$	−218.065	+	377.700i	−0.319276	+	0.553002i	0.661061	+	0.750332i	$0.270106\pi$
$684$	−16.5080	+	9.53090i	−0.0241345	+	0.0139341i
$685$		0			0
$686$	460.329	+	152.954i	0.671034	+	0.222965i
$687$	423.033			0.615768
$688$	92.7038	+	160.568i	0.134744	+	0.233383i
$689$	−170.141	−	98.2309i	−0.246939	−	0.142570i
$690$		0			0
$691$	−59.2770	+	34.2236i	−0.0857843	+	0.0495276i	−0.542279	−	0.840199i	$-0.682438\pi$
$691$	−59.2770	+	34.2236i	−0.0857843	+	0.0495276i	0.456494	+	0.889726i	$0.349105\pi$
$692$		−	408.314i		−	0.590049i
$693$	−3.07076	+	10.6203i	−0.00443112	+	0.0153251i
$694$	−712.193			−1.02622
$695$		0			0
$696$	238.140	+	137.490i	0.342156	+	0.197544i
$697$	−67.9314	+	117.661i	−0.0974625	+	0.168810i
$698$	−58.5039	+	33.7772i	−0.0838164	+	0.0483914i
$699$			366.311i			0.524050i
$700$		0			0
$701$	1283.41			1.83083			0.915414	−	0.402514i	$-0.131864\pi$
$701$	1283.41			1.83083			0.915414	+	0.402514i	$0.131864\pi$
$702$	−15.5165	−	26.8754i	−0.0221033	−	0.0382841i
$703$	−26.8355	−	15.4935i	−0.0381728	−	0.0220391i
$704$	2.10578	−	3.64732i	0.00299117	−	0.00518086i
$705$		0			0
$706$		−	46.5422i		−	0.0659238i
$707$	−488.188	+	469.356i	−0.690507	+	0.663870i
$708$	175.046			0.247240
$709$	−86.2000	−	149.303i	−0.121580	−	0.210582i	0.798811	−	0.601582i	$-0.205463\pi$
$709$	−86.2000	−	149.303i	−0.121580	−	0.210582i	−0.920391	+	0.391000i	$0.872129\pi$
$710$		0			0
$711$	−198.442	+	343.712i	−0.279103	+	0.483420i
$712$	167.189	−	96.5264i	0.234815	−	0.135571i
$713$		−	20.9194i		−	0.0293399i
$714$	−396.325	−	412.227i	−0.555077	−	0.577349i
$715$		0			0
$716$	195.899	+	339.307i	0.273602	+	0.473892i
$717$	516.201	+	298.029i	0.719946	+	0.415661i
$718$	189.361	−	327.983i	0.263734	−	0.456801i
$719$	−435.015	+	251.156i	−0.605028	+	0.349313i	−0.771017	−	0.636815i	$-0.780252\pi$
$719$	−435.015	+	251.156i	−0.605028	+	0.349313i	0.165989	+	0.986128i	$0.446918\pi$
$720$		0			0
$721$	−175.836	−	711.943i	−0.243878	−	0.987439i
$722$	−496.257			−0.687337
$723$	−148.392	−	257.023i	−0.205245	−	0.355495i
$724$	−206.168	−	119.031i	−0.284763	−	0.164408i
$725$		0			0
$726$	−256.092	+	147.855i	−0.352744	+	0.203657i
$727$			748.693i			1.02984i	0.857238	+	0.514920i	$0.172178\pi$
$727$			748.693i			1.02984i	−0.857238	+	0.514920i	$0.827822\pi$
$728$	80.3223	+	23.2244i	0.110333	+	0.0319017i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−1338.76	−	772.931i	−1.83140	−	1.05736i
$732$	−178.917	+	309.893i	−0.244422	+	0.423351i
$733$	812.761	−	469.248i	1.10881	−	0.640175i	0.170293	−	0.985394i	$-0.445529\pi$
$733$	812.761	−	469.248i	1.10881	−	0.640175i	0.938522	+	0.345219i	$0.112195\pi$
$734$			224.468i			0.305814i
$735$		0			0
$736$	62.5596			0.0849994
$737$	−2.30029	−	3.98422i	−0.00312116	−	0.00540600i
$738$	−14.9680	−	8.64178i	−0.0202818	−	0.0117097i
$739$	−106.820	+	185.018i	−0.144547	+	0.250363i	−0.929204	−	0.369567i	$-0.879506\pi$
$739$	−106.820	+	185.018i	−0.144547	+	0.250363i	0.784657	+	0.619931i	$0.212839\pi$
$740$		0			0
$741$			23.2381i			0.0313605i
$742$	127.919	−	442.413i	0.172398	−	0.596244i
$743$	−544.013			−0.732184			−0.366092	−	0.930579i	$-0.619304\pi$
$743$	−544.013			−0.732184			−0.366092	+	0.930579i	$0.619304\pi$
$744$	4.63346	+	8.02538i	0.00622776	+	0.0107868i
$745$		0			0
$746$	−292.985	+	507.465i	−0.392742	+	0.680249i
$747$	32.4337	−	18.7256i	0.0434187	−	0.0250678i
$748$			35.1146i			0.0469446i
$749$	846.786	−	209.140i	1.13056	−	0.279225i
$750$		0			0
$751$	−294.705	−	510.443i	−0.392416	−	0.679685i	0.600351	−	0.799736i	$-0.295027\pi$
$751$	−294.705	−	510.443i	−0.392416	−	0.679685i	−0.992768	+	0.120051i	$0.961694\pi$
$752$	219.187	+	126.548i	0.291473	+	0.168282i
$753$	−283.656	+	491.307i	−0.376702	+	0.652467i
$754$	290.316	−	167.614i	0.385034	−	0.222299i
$755$		0			0
$756$	52.4408	−	50.4179i	0.0693662	−	0.0666903i
$757$	448.997			0.593127			0.296564	−	0.955013i	$-0.404159\pi$
$757$	448.997			0.593127			0.296564	+	0.955013i	$0.404159\pi$
$758$	−51.4774	−	89.1614i	−0.0679121	−	0.117627i
$759$	8.73300	+	5.04200i	0.0115059	+	0.00664295i
$760$		0			0
$761$	371.914	−	214.725i	0.488718	−	0.282161i	−0.235325	−	0.971917i	$-0.575615\pi$
$761$	371.914	−	214.725i	0.488718	−	0.282161i	0.724042	+	0.689756i	$0.242282\pi$
$762$			199.326i			0.261582i
$763$	−410.475	−	426.944i	−0.537975	−	0.559560i
$764$	−131.463			−0.172072
$765$		0			0
$766$	349.070	+	201.536i	0.455705	+	0.263101i
$767$	106.699	−	184.807i	0.139112	−	0.240948i
$768$	−24.0000	+	13.8564i	−0.0312500	+	0.0180422i
$769$			32.5790i			0.0423655i	0.999776	+	0.0211827i	$0.00674318\pi$
$769$			32.5790i			0.0423655i	−0.999776	+	0.0211827i	$0.993257\pi$
$770$		0			0
$771$	381.672			0.495035
$772$	−96.8700	−	167.784i	−0.125479	−	0.217337i
$773$	−1076.93	−	621.768i	−1.39319	−	0.804357i	−0.399520	−	0.916724i	$-0.630823\pi$
$773$	−1076.93	−	621.768i	−1.39319	−	0.804357i	−0.993667	+	0.112367i	$0.964157\pi$
$774$	98.3272	−	170.308i	0.127038	−	0.220036i
$775$		0			0
$776$		−	422.231i		−	0.544112i
$777$	113.603	+	32.8472i	0.146207	+	0.0422744i
$778$	137.374			0.176574
$779$	6.47112	+	11.2083i	0.00830696	+	0.0143881i
$780$		0			0
$781$	7.64946	−	13.2493i	0.00979444	−	0.0169645i
$782$	−451.719	+	260.800i	−0.577645	+	0.333504i
$783$		−	291.661i		−	0.372492i
$784$	−7.70657	+	195.848i	−0.00982981	+	0.249807i
$785$		0			0
$786$	294.706	+	510.446i	0.374944	+	0.649422i
$787$	−165.088	−	95.3138i	−0.209769	−	0.121110i	0.391435	−	0.920206i	$-0.371979\pi$
$787$	−165.088	−	95.3138i	−0.209769	−	0.121110i	−0.601204	+	0.799096i	$0.705312\pi$
$788$	186.672	−	323.325i	0.236893	−	0.410311i
$789$	199.793	−	115.350i	0.253223	−	0.146198i
$790$		0			0
$791$	−226.011	+	781.667i	−0.285729	+	0.988202i
$792$	−4.46704			−0.00564020
$793$	218.116	+	377.789i	0.275052	+	0.476405i
$794$	969.635	+	559.819i	1.22120	+	0.705062i
$795$		0			0
$796$	−199.691	+	115.292i	−0.250868	+	0.144839i
$797$		−	387.796i		−	0.486570i	−0.969955	−	0.243285i	$-0.921775\pi$
$797$		−	387.796i		−	0.486570i	0.969955	−	0.243285i	$-0.0782250\pi$
$798$	−52.8845	+	13.0614i	−0.0662713	+	0.0163677i
$799$	−2110.23			−2.64108
$800$		0			0
$801$	−177.330	−	102.382i	−0.221386	−	0.127817i
$802$	355.835	−	616.324i	0.443684	−	0.768484i
$803$	−7.62881	+	4.40449i	−0.00950038	+	0.00548505i
$804$			30.2726i			0.0376525i
$805$		0			0
$806$	11.2972			0.0140164
$807$	−22.9633	−	39.7735i	−0.0284551	−	0.0492857i
$808$	−236.977	−	136.818i	−0.293288	−	0.169330i
$809$	−182.613	+	316.295i	−0.225727	+	0.390970i	−0.956537	−	0.291610i	$-0.905809\pi$
$809$	−182.613	+	316.295i	−0.225727	+	0.390970i	0.730811	+	0.682580i	$0.239142\pi$
$810$		0			0
$811$		−	944.189i		−	1.16423i	−0.813107	−	0.582114i	$-0.802226\pi$
$811$		−	944.189i		−	1.16423i	0.813107	−	0.582114i	$-0.197774\pi$
$812$	544.627	+	566.479i	0.670723	+	0.697635i
$813$	−185.355			−0.227989
$814$	−3.63082	−	6.28877i	−0.00446047	−	0.00772576i
$815$		0			0
$816$	115.530	−	200.104i	0.141581	−	0.245225i
$817$	−127.529	+	73.6292i	−0.156095	+	0.0901214i
$818$			1060.46i			1.29640i
$819$	−21.2644	−	86.0974i	−0.0259638	−	0.105125i
$820$		0			0
$821$	342.337	+	592.946i	0.416976	+	0.722224i	0.995634	−	0.0933467i	$-0.0297565\pi$
$821$	342.337	+	592.946i	0.416976	+	0.722224i	−0.578657	+	0.815571i	$0.696423\pi$
$822$	495.670	+	286.175i	0.603005	+	0.348145i
$823$	−522.835	+	905.578i	−0.635280	+	1.10034i	0.351176	+	0.936310i	$0.385782\pi$
$823$	−522.835	+	905.578i	−0.635280	+	1.10034i	−0.986456	+	0.164028i	$0.947551\pi$
$824$	256.614	−	148.156i	0.311425	−	0.179801i
$825$		0			0
$826$	480.550	+	138.946i	0.581780	+	0.168216i
$827$	−830.505			−1.00424			−0.502119	−	0.864798i	$-0.667446\pi$
$827$	−830.505			−1.00424			−0.502119	+	0.864798i	$0.667446\pi$
$828$	−33.1772	−	57.4646i	−0.0400691	−	0.0694017i
$829$	−621.983	−	359.102i	−0.750280	−	0.433175i	0.0755148	−	0.997145i	$-0.475940\pi$
$829$	−621.983	−	359.102i	−0.750280	−	0.433175i	−0.825795	+	0.563970i	$0.809273\pi$
$830$		0			0
$831$	660.572	−	381.381i	0.794912	−	0.458943i
$832$			33.7846i			0.0406064i
$833$	−760.812	−	1446.27i	−0.913339	−	1.73622i
$834$	518.046			0.621158
$835$		0			0
$836$	2.89685	+	1.67250i	0.00346514	+	0.00200060i
$837$	4.91452	−	8.51220i	0.00587159	−	0.0101699i
$838$	570.436	−	329.342i	0.680712	−	0.393009i
$839$			55.2900i			0.0658999i	0.999457	+	0.0329499i	$0.0104902\pi$
$839$			55.2900i			0.0658999i	−0.999457	+	0.0329499i	$0.989510\pi$
$840$		0			0
$841$	2309.60			2.74625
$842$	244.645	+	423.737i	0.290552	+	0.503251i
$843$	483.103	+	278.920i	0.573076	+	0.330866i
$844$	−139.433	+	241.505i	−0.165205	+	0.286143i
$845$		0			0
$846$		−	268.449i		−	0.317315i
$847$	−820.408	+	202.625i	−0.968605	+	0.239226i
$848$	186.084			0.219439
$849$	59.3514	+	102.800i	0.0699074	+	0.121083i
$850$		0			0
$851$	53.9331	−	93.4149i	0.0633761	−	0.109771i
$852$	−87.1823	+	50.3347i	−0.102327	+	0.0590783i
$853$		−	21.9601i		−	0.0257445i	−0.999917	−	0.0128723i	$-0.995903\pi$
$853$		−	21.9601i		−	0.0257445i	0.999917	−	0.0128723i	$-0.00409748\pi$
$854$	−737.162	+	708.725i	−0.863187	+	0.829889i
$855$		0			0
$856$	176.217	+	305.217i	0.205861	+	0.356562i
$857$	1399.33	+	807.903i	1.63282	+	0.942711i	0.983217	+	0.182441i	$0.0583997\pi$
$857$	1399.33	+	807.903i	1.63282	+	0.942711i	0.649607	+	0.760271i	$0.274934\pi$
$858$	−2.72287	+	4.71615i	−0.00317351	+	0.00549668i
$859$	772.149	−	445.801i	0.898893	−	0.518976i	0.0220523	−	0.999757i	$-0.492980\pi$
$859$	772.149	−	445.801i	0.898893	−	0.518976i	0.876841	+	0.480781i	$0.159647\pi$
$860$		0			0
$861$	−34.2318	−	35.6053i	−0.0397582	−	0.0413535i
$862$	−699.470			−0.811450
$863$	−448.173	−	776.259i	−0.519320	−	0.899489i	−0.999748	−	0.0224544i	$-0.992852\pi$
$863$	−448.173	−	776.259i	−0.519320	−	0.899489i	0.480428	−	0.877034i	$-0.340481\pi$
$864$	25.4558	+	14.6969i	0.0294628	+	0.0170103i
$865$		0			0
$866$	894.090	−	516.203i	1.03244	−	0.596078i
$867$			1425.93i			1.64467i
$868$	6.34984	+	25.7099i	0.00731548	+	0.0296197i
$869$	69.6459			0.0801449
$870$		0			0
$871$	31.9609	+	18.4526i	0.0366944	+	0.0211855i
$872$	119.654	−	207.248i	0.137218	−	0.237669i
$873$	−387.844	+	223.922i	−0.444265	+	0.256497i
$874$			49.6874i			0.0568506i
$875$		0			0
$876$	57.9646			0.0661697
$877$	−168.885	−	292.517i	−0.192571	−	0.333543i	0.753530	−	0.657413i	$-0.228349\pi$
$877$	−168.885	−	292.517i	−0.192571	−	0.333543i	−0.946102	+	0.323870i	$0.895016\pi$
$878$	−454.855	−	262.611i	−0.518059	−	0.299101i
$879$	−127.748	+	221.265i	−0.145333	+	0.251724i
$880$		0			0
$881$		−	301.377i		−	0.342085i	−0.985264	−	0.171042i	$-0.945287\pi$
$881$		−	301.377i		−	0.342085i	0.985264	−	0.171042i	$-0.0547135\pi$
$882$	183.985	−	96.7854i	0.208600	−	0.109734i
$883$	−38.3679			−0.0434518			−0.0217259	−	0.999764i	$-0.506916\pi$
$883$	−38.3679			−0.0434518			−0.0217259	+	0.999764i	$0.506916\pi$
$884$	−140.842	−	243.945i	−0.159323	−	0.275956i
$885$		0			0
$886$	−289.000	+	500.563i	−0.326185	+	0.564969i
$887$	−572.834	+	330.726i	−0.645811	+	0.372859i	−0.786849	−	0.617145i	$-0.788289\pi$
$887$	−572.834	+	330.726i	−0.645811	+	0.372859i	0.141038	+	0.990004i	$0.454956\pi$
$888$			47.7829i			0.0538095i
$889$	−158.219	+	547.206i	−0.177974	+	0.615530i
$890$		0			0
$891$	2.36901	+	4.10324i	0.00265882	+	0.00460521i
$892$	−446.965	−	258.055i	−0.501082	−	0.289300i
$893$	−100.510	+	174.088i	−0.112553	+	0.194947i
$894$	305.641	−	176.462i	0.341880	−	0.197384i
$895$		0			0
$896$	−76.8857	+	18.9893i	−0.0858099	+	0.0211934i
$897$	−80.8924			−0.0901810
$898$	512.984	+	888.515i	0.571252	+	0.989437i
$899$	91.9510	+	53.0880i	0.102281	+	0.0590522i
$900$		0			0
$901$	−1343.64	+	775.753i	−1.49128	+	0.860991i
$902$			3.03295i			0.00336247i
$903$	405.122	−	389.494i	0.448640	−	0.431333i
$904$	−328.779			−0.363693
$905$		0			0
$906$	−198.370	−	114.529i	−0.218951	−	0.126412i
$907$	−484.152	+	838.576i	−0.533795	+	0.924560i	0.465426	+	0.885087i	$0.345901\pi$
$907$	−484.152	+	838.576i	−0.533795	+	0.924560i	−0.999221	+	0.0394729i	$0.987432\pi$
$908$	573.365	−	331.032i	0.631459	−	0.364573i
$909$			290.236i			0.319291i
$910$		0			0
$911$	220.674			0.242233			0.121116	−	0.992638i	$-0.461353\pi$
$911$	220.674			0.242233			0.121116	+	0.992638i	$0.461353\pi$
$912$	−11.0053	−	19.0618i	−0.0120673	−	0.0209011i
$913$	−5.69153	−	3.28601i	−0.00623388	−	0.00359913i
$914$	−283.925	+	491.772i	−0.310640	+	0.538044i
$915$		0			0
$916$			488.476i			0.533271i
$917$	403.874	+	1635.25i	0.440430	+	1.78326i
$918$	−245.076			−0.266967
$919$	574.019	+	994.231i	0.624613	+	1.08186i	0.988616	+	0.150464i	$0.0480766\pi$
$919$	574.019	+	994.231i	0.624613	+	1.08186i	−0.364002	+	0.931398i	$0.618590\pi$
$920$		0			0
$921$	−325.634	+	564.015i	−0.353566	+	0.612394i
$922$	−799.819	+	461.776i	−0.867483	+	0.500841i
$923$			122.726i			0.132964i
$924$	−12.2633	−	3.54581i	−0.0132720	−	0.00383746i
$925$		0			0
$926$	614.886	+	1065.01i	0.664024	+	1.15012i
$927$	−272.180	−	157.143i	−0.293614	−	0.169518i
$928$	−158.760	+	274.981i	−0.171078	+	0.296315i
$929$	−264.398	+	152.650i	−0.284605	+	0.164317i	−0.635506	−	0.772096i	$-0.719209\pi$
$929$	−264.398	+	152.650i	−0.284605	+	0.164317i	0.350901	+	0.936412i	$0.385875\pi$
$930$		0			0
$931$	−155.551	−	6.12088i	−0.167079	−	0.00657452i
$932$	−422.979			−0.453840
$933$	−337.599	−	584.739i	−0.361843	−	0.626730i
$934$	−905.334	−	522.695i	−0.969308	−	0.559630i
$935$		0			0
$936$	31.0331	−	17.9170i	0.0331550	−	0.0191421i
$937$		−	12.4049i		−	0.0132390i	−0.999978	−	0.00661948i	$-0.997893\pi$
$937$		−	12.4049i		−	0.0132390i	0.999978	−	0.00661948i	$-0.00210706\pi$
$938$	−24.0296	+	83.1070i	−0.0256179	+	0.0886002i
$939$	247.781			0.263877
$940$		0			0
$941$	−250.409	−	144.573i	−0.266109	−	0.153638i	0.361009	−	0.932562i	$-0.382432\pi$
$941$	−250.409	−	144.573i	−0.266109	−	0.153638i	−0.627118	+	0.778924i	$0.715766\pi$
$942$	−209.708	+	363.224i	−0.222619	+	0.385588i
$943$	−39.0163	+	22.5261i	−0.0413747	+	0.0238877i
$944$			202.125i			0.214116i
$945$		0			0
$946$	−34.5093			−0.0364792
$947$	−713.478	−	1235.78i	−0.753409	−	1.30494i	−0.946161	−	0.323695i	$-0.895075\pi$
$947$	−713.478	−	1235.78i	−0.753409	−	1.30494i	0.192752	−	0.981247i	$-0.438259\pi$
$948$	−396.884	−	229.141i	−0.418654	−	0.241710i
$949$	35.3322	−	61.1972i	0.0372310	−	0.0644859i
$950$		0			0
$951$			665.876i			0.700186i
$952$	475.999	−	457.637i	0.499999	−	0.480711i
$953$	668.525			0.701495			0.350747	−	0.936470i	$-0.385928\pi$
$953$	668.525			0.701495			0.350747	+	0.936470i	$0.385928\pi$
$954$	−98.6862	−	170.929i	−0.103445	−	0.179171i
$955$		0			0
$956$	−344.134	+	596.058i	−0.359973	+	0.623491i
$957$	−44.3242	+	25.5906i	−0.0463158	+	0.0267405i
$958$		−	857.331i		−	0.894918i
$959$	1133.60	+	1179.08i	1.18206	+	1.22949i
$960$		0			0
$961$	−478.711	−	829.152i	−0.498138	−	0.862801i
$962$	50.4476	+	29.1259i	0.0524403	+	0.0302764i
$963$	186.907	−	323.732i	0.194088	−	0.336170i
$964$	296.784	−	171.348i	0.307867	−	0.177747i
$965$		0			0
$966$	−45.4671	−	184.092i	−0.0470674	−	0.190571i
$967$	−1647.14			−1.70335			−0.851676	−	0.524069i	$-0.824414\pi$
$967$	−1647.14			−1.70335			−0.851676	+	0.524069i	$0.824414\pi$
$968$	−170.728	−	295.709i	−0.176372	−	0.305485i
$969$	158.931	+	91.7586i	0.164015	+	0.0946941i
$970$		0			0
$971$	1138.76	−	657.466i	1.17277	−	0.677102i	0.218443	−	0.975850i	$-0.429902\pi$
$971$	1138.76	−	657.466i	1.17277	−	0.677102i	0.954332	+	0.298748i	$0.0965690\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	1422.18	+	411.210i	1.46165	+	0.422621i
$974$	918.639			0.943161
$975$		0			0
$976$	−357.833	−	206.595i	−0.366633	−	0.211675i
$977$	778.021	−	1347.57i	0.796337	−	1.37930i	−0.125650	−	0.992075i	$-0.540102\pi$
$977$	778.021	−	1347.57i	0.796337	−	1.37930i	0.921987	−	0.387221i	$-0.126565\pi$
$978$	−197.310	+	113.917i	−0.201749	+	0.116480i
$979$			35.9323i			0.0367030i
$980$		0			0
$981$	−253.825			−0.258741
$982$	188.535	+	326.553i	0.191991	+	0.332538i
$983$	1188.87	+	686.397i	1.20944	+	0.698268i	0.962636	−	0.270799i	$-0.0872879\pi$
$983$	1188.87	+	686.397i	1.20944	+	0.698268i	0.246799	+	0.969067i	$0.420621\pi$
$984$	9.97867	−	17.2836i	0.0101409	−	0.0175646i
$985$		0			0
$986$		−	2647.37i		−	2.68496i
$987$	213.087	−	736.968i	0.215894	−	0.746675i
$988$	−26.8331			−0.0271590
$989$	−256.304	−	443.932i	−0.259155	−	0.448870i
$990$		0			0
$991$	−321.812	+	557.395i	−0.324735	+	0.562457i	−0.981459	−	0.191674i	$-0.938608\pi$
$991$	−321.812	+	557.395i	−0.324735	+	0.562457i	0.656724	+	0.754131i	$0.271942\pi$
$992$	−9.26691	+	5.35025i	−0.00934165	+	0.00539340i
$993$		−	335.858i		−	0.338226i
$994$	−279.295	+	68.9803i	−0.280981	+	0.0693967i
$995$		0			0
$996$	21.6225	+	37.4513i	0.0217093	+	0.0376017i
$997$	−610.431	−	352.433i	−0.612268	−	0.353493i	0.161584	−	0.986859i	$-0.448340\pi$
$997$	−610.431	−	352.433i	−0.612268	−	0.353493i	−0.773853	+	0.633366i	$0.781673\pi$
$998$	−481.615	+	834.181i	−0.482580	+	0.835853i
$999$	43.8914	−	25.3407i	0.0439353	−	0.0253661i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.p.i.451.6		16
5.2	odd	4		1050.3.q.e.199.4		32
5.3	odd	4		1050.3.q.e.199.12		32
5.4	even	2		210.3.o.b.31.4	✓	16
7.5	odd	6	inner	1050.3.p.i.901.6		16
15.14	odd	2		630.3.v.c.451.6		16
35.4	even	6		1470.3.f.d.391.15		16
35.12	even	12		1050.3.q.e.649.12		32
35.19	odd	6		210.3.o.b.61.4	yes	16
35.24	odd	6		1470.3.f.d.391.9		16
35.33	even	12		1050.3.q.e.649.4		32
105.89	even	6		630.3.v.c.271.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.4	✓	16	5.4	even	2
210.3.o.b.61.4	yes	16	35.19	odd	6
630.3.v.c.271.6		16	105.89	even	6
630.3.v.c.451.6		16	15.14	odd	2
1050.3.p.i.451.6		16	1.1	even	1	trivial
1050.3.p.i.901.6		16	7.5	odd	6	inner
1050.3.q.e.199.4		32	5.2	odd	4
1050.3.q.e.199.12		32	5.3	odd	4
1050.3.q.e.649.4		32	35.33	even	12
1050.3.q.e.649.12		32	35.12	even	12
1470.3.f.d.391.9		16	35.24	odd	6
1470.3.f.d.391.15		16	35.4	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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(-1.94434 + 6.72455i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(-1.94434 + 6.72455i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(0.263223 - 0.455915i) q^{11} +(-3.00000 + 1.73205i) q^{12} +4.22307i q^{13} +(-9.61071 + 2.37366i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(28.8825 + 16.6753i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(2.75133 - 1.58848i) q^{19} +(-8.74014 + 8.40298i) q^{21} +0.744507 q^{22} +(5.52954 + 9.57744i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-5.17218 + 2.98616i) q^{26} +5.19615i q^{27} +(-9.70292 - 10.0922i) q^{28} -56.1302 q^{29} +(-1.63817 - 0.945800i) q^{31} +(2.82843 - 4.89898i) q^{32} +(0.789668 - 0.455915i) q^{33} +47.1649i q^{34} -6.00000 q^{36} +(-4.87682 - 8.44690i) q^{37} +(3.89097 + 2.24645i) q^{38} +(-3.65729 + 6.33460i) q^{39} +4.07377i q^{41} +(-16.4717 - 4.76263i) q^{42} -46.3519 q^{43} +(0.526446 + 0.911831i) q^{44} +(-7.81995 + 13.5445i) q^{46} +(-54.7969 + 31.6370i) q^{47} -6.92820i q^{48} +(-41.4391 - 26.1496i) q^{49} +(28.8825 + 50.0259i) q^{51} +(-7.31457 - 4.22307i) q^{52} +(-23.2606 + 40.2885i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(5.49942 - 19.0199i) q^{56} +5.50267 q^{57} +(-39.6900 - 68.7452i) q^{58} +(-43.7614 - 25.2657i) q^{59} +(89.4583 - 51.6488i) q^{61} -2.67513i q^{62} +(-20.3874 + 5.03529i) q^{63} +8.00000 q^{64} +(1.11676 + 0.644762i) q^{66} +(4.36948 - 7.56816i) q^{67} +(-57.7649 + 33.3506i) q^{68} +19.1549i q^{69} +29.0608 q^{71} +(-4.24264 - 7.34847i) q^{72} +(-14.4912 - 8.36647i) q^{73} +(6.89686 - 11.9457i) q^{74} +6.35393i q^{76} +(2.55403 + 2.65651i) q^{77} -10.3444 q^{78} +(66.1473 + 114.571i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-4.98933 + 2.88059i) q^{82} -12.4838i q^{83} +(-5.81425 - 23.5413i) q^{84} +(-32.7757 - 56.7692i) q^{86} +(-84.1953 - 48.6102i) q^{87} +(-0.744507 + 1.28952i) q^{88} +(-59.1101 + 34.1272i) q^{89} +(-28.3982 - 8.21107i) q^{91} -22.1182 q^{92} +(-1.63817 - 2.83740i) q^{93} +(-77.4945 - 44.7415i) q^{94} +(8.48528 - 4.89898i) q^{96} +149.281i q^{97} +(2.72468 - 69.2429i) q^{98} +1.57934 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

Groups

Database

Properties

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