LMFDB - Embedded newform 1050.3.p.i.451.5

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			451.5
Root			$2.96377 - 5.13339i$ of defining polynomial
Character	$\chi$	$=$	1050.451
Dual form			1050.3.p.i.901.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(-5.73733 - 4.01037i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(-5.73733 - 4.01037i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(8.69259 - 15.0560i) q^{11} +(-3.00000 + 1.73205i) q^{12} +7.22559i q^{13} +(0.854777 - 9.86252i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(2.29669 + 1.32600i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(2.20128 - 1.27091i) q^{19} +(-5.13291 - 10.9842i) q^{21} +24.5864 q^{22} +(20.0507 + 34.7289i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-8.84951 + 5.10926i) q^{26} +5.19615i q^{27} +(12.6835 - 5.92697i) q^{28} +47.0080 q^{29} +(34.9025 + 20.1510i) q^{31} +(2.82843 - 4.89898i) q^{32} +(26.0778 - 15.0560i) q^{33} +3.75049i q^{34} -6.00000 q^{36} +(16.2514 + 28.1482i) q^{37} +(3.11308 + 1.79734i) q^{38} +(-6.25755 + 10.8384i) q^{39} -70.6679i q^{41} +(9.82336 - 14.0535i) q^{42} -37.3732 q^{43} +(17.3852 + 30.1120i) q^{44} +(-28.3560 + 49.1141i) q^{46} +(28.9672 - 16.7242i) q^{47} -6.92820i q^{48} +(16.8339 + 46.0176i) q^{49} +(2.29669 + 3.97799i) q^{51} +(-12.5151 - 7.22559i) q^{52} +(-35.4442 + 61.3911i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(16.2276 + 11.3430i) q^{56} +4.40256 q^{57} +(33.2397 + 57.5728i) q^{58} +(87.0863 + 50.2793i) q^{59} +(-11.1621 + 6.44446i) q^{61} +56.9955i q^{62} +(1.81326 - 20.9216i) q^{63} +8.00000 q^{64} +(36.8795 + 21.2924i) q^{66} +(47.0361 - 81.4689i) q^{67} +(-4.59339 + 2.65199i) q^{68} +69.4578i q^{69} -11.5793 q^{71} +(-4.24264 - 7.34847i) q^{72} +(19.6320 + 11.3345i) q^{73} +(-22.9829 + 39.8076i) q^{74} +5.08364i q^{76} +(-110.252 + 51.5208i) q^{77} -17.6990 q^{78} +(12.0542 + 20.8785i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(86.5502 - 49.9698i) q^{82} -111.664i q^{83} +(24.1581 + 2.09377i) q^{84} +(-26.4268 - 45.7726i) q^{86} +(70.5120 + 40.7101i) q^{87} +(-24.5864 + 42.5848i) q^{88} +(-110.770 + 63.9533i) q^{89} +(28.9773 - 41.4556i) q^{91} -80.2029 q^{92} +(34.9025 + 60.4529i) q^{93} +(40.9658 + 23.6516i) q^{94} +(8.48528 - 4.89898i) q^{96} +7.48256i q^{97} +(-44.4565 + 53.1566i) q^{98} +52.1556 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
$7$	−5.73733	−	4.01037i	−0.819618	−	0.572910i
$7$	−5.73733	−	4.01037i	−0.819618	−	0.572910i
$8$	−2.82843			−0.353553
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	8.69259	−	15.0560i	0.790236	−	1.36873i	−0.135585	−	0.990766i	$-0.543291\pi$
$11$	8.69259	−	15.0560i	0.790236	−	1.36873i	0.925821	−	0.377963i	$-0.123375\pi$
$12$	−3.00000	+	1.73205i	−0.250000	+	0.144338i
$13$			7.22559i			0.555815i	0.960608	+	0.277907i	$0.0896408\pi$
$13$			7.22559i			0.555815i	−0.960608	+	0.277907i	$0.910359\pi$
$14$	0.854777	−	9.86252i	0.0610555	−	0.704466i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	2.29669	+	1.32600i	0.135100	+	0.0779998i	0.566027	−	0.824387i	$-0.308480\pi$
$17$	2.29669	+	1.32600i	0.135100	+	0.0779998i	−0.430927	+	0.902387i	$0.641813\pi$
$18$	−2.12132	+	3.67423i	−0.117851	+	0.204124i
$19$	2.20128	−	1.27091i	0.115857	−	0.0668900i	−0.440952	−	0.897531i	$-0.645359\pi$
$19$	2.20128	−	1.27091i	0.115857	−	0.0668900i	0.556809	+	0.830641i	$0.312026\pi$
$20$		0			0
$21$	−5.13291	−	10.9842i	−0.244424	−	0.523058i
$22$	24.5864			1.11756
$23$	20.0507	+	34.7289i	0.871771	+	1.50995i	0.860163	+	0.510019i	$0.170361\pi$
$23$	20.0507	+	34.7289i	0.871771	+	1.50995i	0.0116074	+	0.999933i	$0.496305\pi$
$24$	−4.24264	−	2.44949i	−0.176777	−	0.102062i
$25$		0			0
$26$	−8.84951	+	5.10926i	−0.340366	+	0.196510i
$27$			5.19615i			0.192450i
$28$	12.6835	−	5.92697i	0.452982	−	0.211678i
$29$	47.0080			1.62096			0.810482	−	0.585763i	$-0.199205\pi$
$29$	47.0080			1.62096			0.810482	+	0.585763i	$0.199205\pi$
$30$		0			0
$31$	34.9025	+	20.1510i	1.12589	+	0.650031i	0.942897	−	0.333084i	$-0.108089\pi$
$31$	34.9025	+	20.1510i	1.12589	+	0.650031i	0.182990	+	0.983115i	$0.441422\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$	26.0778	−	15.0560i	0.790236	−	0.456243i
$34$			3.75049i			0.110308i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	16.2514	+	28.1482i	0.439226	+	0.760762i	0.997630	−	0.0688071i	$-0.0219193\pi$
$37$	16.2514	+	28.1482i	0.439226	+	0.760762i	−0.558404	+	0.829569i	$0.688586\pi$
$38$	3.11308	+	1.79734i	0.0819232	+	0.0472984i
$39$	−6.25755	+	10.8384i	−0.160450	+	0.277907i
$40$		0			0
$41$		−	70.6679i		−	1.72361i	−0.507241	−	0.861804i	$-0.669335\pi$
$41$		−	70.6679i		−	1.72361i	0.507241	−	0.861804i	$-0.330665\pi$
$42$	9.82336	−	14.0535i	0.233890	−	0.334608i
$43$	−37.3732			−0.869144			−0.434572	−	0.900637i	$-0.643100\pi$
$43$	−37.3732			−0.869144			−0.434572	+	0.900637i	$0.643100\pi$
$44$	17.3852	+	30.1120i	0.395118	+	0.684364i
$45$		0			0
$46$	−28.3560	+	49.1141i	−0.616435	+	1.06770i
$47$	28.9672	−	16.7242i	0.616324	−	0.355835i	−0.159113	−	0.987260i	$-0.550863\pi$
$47$	28.9672	−	16.7242i	0.616324	−	0.355835i	0.775436	+	0.631426i	$0.217530\pi$
$48$		−	6.92820i		−	0.144338i
$49$	16.8339	+	46.0176i	0.343548	+	0.939135i
$50$		0			0
$51$	2.29669	+	3.97799i	0.0450332	+	0.0779998i
$52$	−12.5151	−	7.22559i	−0.240675	−	0.138954i
$53$	−35.4442	+	61.3911i	−0.668758	+	1.15832i	0.309493	+	0.950902i	$0.399841\pi$
$53$	−35.4442	+	61.3911i	−0.668758	+	1.15832i	−0.978252	+	0.207422i	$0.933493\pi$
$54$	−6.36396	+	3.67423i	−0.117851	+	0.0680414i
$55$		0			0
$56$	16.2276	+	11.3430i	0.289779	+	0.202554i
$57$	4.40256			0.0772379
$58$	33.2397	+	57.5728i	0.573098	+	0.992634i
$59$	87.0863	+	50.2793i	1.47604	+	0.852192i	0.999635	−	0.0270340i	$-0.00860625\pi$
$59$	87.0863	+	50.2793i	1.47604	+	0.852192i	0.476405	+	0.879226i	$0.341940\pi$
$60$		0			0
$61$	−11.1621	+	6.44446i	−0.182986	+	0.105647i	−0.588695	−	0.808355i	$-0.700358\pi$
$61$	−11.1621	+	6.44446i	−0.182986	+	0.105647i	0.405709	+	0.914002i	$0.367025\pi$
$62$			56.9955i			0.919283i
$63$	1.81326	−	20.9216i	0.0287819	−	0.332088i
$64$	8.00000			0.125000
$65$		0			0
$66$	36.8795	+	21.2924i	0.558781	+	0.322612i
$67$	47.0361	−	81.4689i	0.702031	−	1.21595i	−0.265721	−	0.964050i	$-0.585610\pi$
$67$	47.0361	−	81.4689i	0.702031	−	1.21595i	0.967752	−	0.251904i	$-0.0810567\pi$
$68$	−4.59339	+	2.65199i	−0.0675498	+	0.0389999i
$69$			69.4578i			1.00663i
$70$		0			0
$71$	−11.5793			−0.163088			−0.0815440	−	0.996670i	$-0.525985\pi$
$71$	−11.5793			−0.163088			−0.0815440	+	0.996670i	$0.525985\pi$
$72$	−4.24264	−	7.34847i	−0.0589256	−	0.102062i
$73$	19.6320	+	11.3345i	0.268931	+	0.155267i	0.628402	−	0.777889i	$-0.283709\pi$
$73$	19.6320	+	11.3345i	0.268931	+	0.155267i	−0.359471	+	0.933156i	$0.617043\pi$
$74$	−22.9829	+	39.8076i	−0.310580	+	0.537940i
$75$		0			0
$76$			5.08364i			0.0668900i
$77$	−110.252	+	51.5208i	−1.43185	+	0.669101i
$78$	−17.6990			−0.226910
$79$	12.0542	+	20.8785i	0.152585	+	0.264285i	0.932177	−	0.362003i	$-0.117907\pi$
$79$	12.0542	+	20.8785i	0.152585	+	0.264285i	−0.779592	+	0.626287i	$0.784574\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	86.5502	−	49.9698i	1.05549	−	0.609388i
$83$		−	111.664i		−	1.34535i	−0.739937	−	0.672676i	$-0.765145\pi$
$83$		−	111.664i		−	1.34535i	0.739937	−	0.672676i	$-0.234855\pi$
$84$	24.1581	+	2.09377i	0.287597	+	0.0249258i
$85$		0			0
$86$	−26.4268	−	45.7726i	−0.307289	−	0.532240i
$87$	70.5120	+	40.7101i	0.810482	+	0.467932i
$88$	−24.5864	+	42.5848i	−0.279390	+	0.483919i
$89$	−110.770	+	63.9533i	−1.24461	+	0.718577i	−0.970030	−	0.242987i	$-0.921873\pi$
$89$	−110.770	+	63.9533i	−1.24461	+	0.718577i	−0.274582	+	0.961564i	$0.588540\pi$
$90$		0			0
$91$	28.9773	−	41.4556i	0.318432	−	0.455556i
$92$	−80.2029			−0.871771
$93$	34.9025	+	60.4529i	0.375296	+	0.650031i
$94$	40.9658	+	23.6516i	0.435807	+	0.251613i
$95$		0			0
$96$	8.48528	−	4.89898i	0.0883883	−	0.0510310i
$97$			7.48256i			0.0771398i	0.999256	+	0.0385699i	$0.0122802\pi$
$97$			7.48256i			0.0771398i	−0.999256	+	0.0385699i	$0.987720\pi$
$98$	−44.4565	+	53.1566i	−0.453638	+	0.542414i
$99$	52.1556			0.526824
$100$		0			0
$101$	−81.9228	−	47.2982i	−0.811117	−	0.468299i	0.0362267	−	0.999344i	$-0.488466\pi$
$101$	−81.9228	−	47.2982i	−0.811117	−	0.468299i	−0.847344	+	0.531045i	$0.821799\pi$
$102$	−3.24802	+	5.62573i	−0.0318433	+	0.0551542i
$103$	51.8072	−	29.9109i	0.502982	−	0.290397i	−0.226962	−	0.973904i	$-0.572879\pi$
$103$	51.8072	−	29.9109i	0.502982	−	0.290397i	0.729944	+	0.683507i	$0.239546\pi$
$104$		−	20.4371i		−	0.196510i
$105$		0			0
$106$	−100.251			−0.945767
$107$	3.23081	+	5.59592i	0.0301945	+	0.0522983i	0.880728	−	0.473623i	$-0.157054\pi$
$107$	3.23081	+	5.59592i	0.0301945	+	0.0522983i	−0.850533	+	0.525921i	$0.823721\pi$
$108$	−9.00000	−	5.19615i	−0.0833333	−	0.0481125i
$109$	81.9201	−	141.890i	0.751560	−	1.30174i	−0.195506	−	0.980703i	$-0.562635\pi$
$109$	81.9201	−	141.890i	0.751560	−	1.30174i	0.947066	−	0.321038i	$-0.104032\pi$
$110$		0			0
$111$			56.2964i			0.507175i
$112$	−2.41768	+	27.8954i	−0.0215864	+	0.249066i
$113$	105.434			0.933040			0.466520	−	0.884511i	$-0.345508\pi$
$113$	105.434			0.933040			0.466520	+	0.884511i	$0.345508\pi$
$114$	3.11308	+	5.39202i	0.0273077	+	0.0472984i
$115$		0			0
$116$	−47.0080	+	81.4202i	−0.405241	+	0.701898i
$117$	−18.7726	+	10.8384i	−0.160450	+	0.0926358i
$118$			142.211i			1.20518i
$119$	−7.85915	−	16.8183i	−0.0660433	−	0.141330i
$120$		0			0
$121$	−90.6223	−	156.962i	−0.748945	−	1.29721i
$122$	−15.7856	−	9.11384i	−0.129391	−	0.0747036i
$123$	61.2002	−	106.002i	0.497563	−	0.861804i
$124$	−69.8050	+	40.3019i	−0.562944	+	0.325016i
$125$		0			0
$126$	26.9058	−	12.5730i	0.213538	−	0.0997858i
$127$	−53.7033			−0.422860			−0.211430	−	0.977393i	$-0.567812\pi$
$127$	−53.7033			−0.422860			−0.211430	+	0.977393i	$0.567812\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$	−56.0598	−	32.3661i	−0.434572	−	0.250900i
$130$		0			0
$131$	−50.6489	+	29.2421i	−0.386632	+	0.223222i	−0.680700	−	0.732562i	$-0.738324\pi$
$131$	−50.6489	+	29.2421i	−0.386632	+	0.223222i	0.294068	+	0.955785i	$0.404991\pi$
$132$			60.2240i			0.456243i
$133$	−17.7263	−	1.53632i	−0.133280	−	0.0115513i
$134$	133.038			0.992822
$135$		0			0
$136$	−6.49603	−	3.75049i	−0.0477650	−	0.0275771i
$137$	−6.05848	+	10.4936i	−0.0442225	+	0.0765956i	−0.887289	−	0.461213i	$-0.847414\pi$
$137$	−6.05848	+	10.4936i	−0.0442225	+	0.0765956i	0.843067	+	0.537809i	$0.180748\pi$
$138$	−85.0680	+	49.1141i	−0.616435	+	0.355899i
$139$			45.2562i			0.325584i	0.986660	+	0.162792i	$0.0520500\pi$
$139$			45.2562i			0.325584i	−0.986660	+	0.162792i	$0.947950\pi$
$140$		0			0
$141$	57.9344			0.410882
$142$	−8.18777	−	14.1816i	−0.0576603	−	0.0998706i
$143$	108.789	+	62.8091i	0.760759	+	0.439225i
$144$	6.00000	−	10.3923i	0.0416667	−	0.0721688i
$145$		0			0
$146$			32.0589i			0.219581i
$147$	−14.6016	+	83.6050i	−0.0993309	+	0.568741i
$148$	−65.0055			−0.439226
$149$	25.4474	+	44.0762i	0.170788	+	0.295814i	0.938696	−	0.344747i	$-0.112035\pi$
$149$	25.4474	+	44.0762i	0.170788	+	0.295814i	−0.767908	+	0.640561i	$0.778702\pi$
$150$		0			0
$151$	78.8476	−	136.568i	0.522169	−	0.904424i	−0.477498	−	0.878633i	$-0.658456\pi$
$151$	78.8476	−	136.568i	0.522169	−	0.904424i	0.999667	−	0.0257911i	$-0.00821047\pi$
$152$	−6.22616	+	3.59468i	−0.0409616	+	0.0236492i
$153$			7.95598i			0.0519999i
$154$	−141.060	−	98.6004i	−0.915974	−	0.640263i
$155$		0			0
$156$	−12.5151	−	21.6768i	−0.0802249	−	0.138954i
$157$	−145.359	−	83.9231i	−0.925854	−	0.534542i	−0.0403562	−	0.999185i	$-0.512849\pi$
$157$	−145.359	−	83.9231i	−0.925854	−	0.534542i	−0.885498	+	0.464643i	$0.846183\pi$
$158$	−17.0472	+	29.5266i	−0.107894	+	0.186877i
$159$	−106.333	+	61.3911i	−0.668758	+	0.386108i
$160$		0			0
$161$	24.2381	−	279.662i	0.150547	−	1.73703i
$162$	−12.7279			−0.0785674
$163$	138.285	+	239.517i	0.848374	+	1.46943i	0.882658	+	0.470015i	$0.155752\pi$
$163$	138.285	+	239.517i	0.848374	+	1.46943i	−0.0342839	+	0.999412i	$0.510915\pi$
$164$	122.400	+	70.6679i	0.746344	+	0.430902i
$165$		0			0
$166$	136.760	−	78.9586i	0.823857	−	0.475654i
$167$			48.4258i			0.289975i	0.989433	+	0.144987i	$0.0463142\pi$
$167$			48.4258i			0.289975i	−0.989433	+	0.144987i	$0.953686\pi$
$168$	14.5181	+	31.0681i	0.0864170	+	0.184929i
$169$	116.791			0.691070
$170$		0			0
$171$	6.60384	+	3.81273i	0.0386190	+	0.0222967i
$172$	37.3732	−	64.7323i	0.217286	−	0.376351i
$173$	97.8337	−	56.4843i	0.565513	−	0.326499i	−0.189842	−	0.981815i	$-0.560798\pi$
$173$	97.8337	−	56.4843i	0.565513	−	0.326499i	0.755355	+	0.655316i	$0.227464\pi$
$174$			115.146i			0.661756i
$175$		0			0
$176$	−69.5407			−0.395118
$177$	87.0863	+	150.838i	0.492013	+	0.852192i
$178$	−156.653	−	90.4437i	−0.880073	−	0.508111i
$179$	−165.708	+	287.015i	−0.925744	+	1.60344i	−0.135384	+	0.990793i	$0.543227\pi$
$179$	−165.708	+	287.015i	−0.925744	+	1.60344i	−0.790360	+	0.612642i	$0.790107\pi$
$180$		0			0
$181$			213.328i			1.17861i	0.807912	+	0.589303i	$0.200598\pi$
$181$			213.328i			1.17861i	−0.807912	+	0.589303i	$0.799402\pi$
$182$	71.2626	+	6.17627i	0.391553	+	0.0339356i
$183$	−22.3243			−0.121991
$184$	−56.7120	−	98.2281i	−0.308218	−	0.533848i
$185$		0			0
$186$	−49.3596	+	85.4933i	−0.265374	+	0.459642i
$187$	39.9285	−	23.0527i	0.213521	−	0.123277i
$188$			66.8969i			0.355835i
$189$	20.8385	−	29.8120i	0.110257	−	0.157736i
$190$		0			0
$191$	33.4517	+	57.9400i	0.175140	+	0.303351i	0.940210	−	0.340596i	$-0.110629\pi$
$191$	33.4517	+	57.9400i	0.175140	+	0.303351i	−0.765070	+	0.643947i	$0.777296\pi$
$192$	12.0000	+	6.92820i	0.0625000	+	0.0360844i
$193$	−56.3020	+	97.5179i	−0.291720	+	0.505274i	−0.974217	−	0.225615i	$-0.927561\pi$
$193$	−56.3020	+	97.5179i	−0.291720	+	0.505274i	0.682497	+	0.730889i	$0.260894\pi$
$194$	−9.16422	+	5.29097i	−0.0472383	+	0.0272730i
$195$		0			0
$196$	−96.5387	−	16.8605i	−0.492544	−	0.0860231i
$197$	61.0211			0.309752			0.154876	−	0.987934i	$-0.450502\pi$
$197$	61.0211			0.309752			0.154876	+	0.987934i	$0.450502\pi$
$198$	36.8795	+	63.8772i	0.186260	+	0.322612i
$199$	−165.554	−	95.5826i	−0.831929	−	0.480314i	0.0225837	−	0.999745i	$-0.492811\pi$
$199$	−165.554	−	95.5826i	−0.831929	−	0.480314i	−0.854513	+	0.519431i	$0.826144\pi$
$200$		0			0
$201$	141.108	−	81.4689i	0.702031	−	0.405318i
$202$		−	133.779i		−	0.662274i
$203$	−269.700	−	188.519i	−1.32857	−	0.928667i
$204$	−9.18678			−0.0450332
$205$		0			0
$206$	73.2664	+	42.3004i	0.355662	+	0.205342i
$207$	−60.1522	+	104.187i	−0.290590	+	0.503317i
$208$	25.0302	−	14.4512i	0.120337	−	0.0694768i
$209$		−	44.1900i		−	0.211435i
$210$		0			0
$211$	280.115			1.32756			0.663781	−	0.747927i	$-0.268951\pi$
$211$	280.115			1.32756			0.663781	+	0.747927i	$0.268951\pi$
$212$	−70.8884	−	122.782i	−0.334379	−	0.579162i
$213$	−17.3689	−	10.0279i	−0.0815440	−	0.0470795i
$214$	−4.56905	+	7.91383i	−0.0213507	+	0.0369805i
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	−119.434	−	255.585i	−0.550388	−	1.17781i
$218$	231.705			1.06287
$219$	19.6320	+	34.0036i	0.0896437	+	0.155267i
$220$		0			0
$221$	−9.58111	+	16.5950i	−0.0433535	+	0.0750904i
$222$	−68.9487	+	39.8076i	−0.310580	+	0.179313i
$223$		−	272.759i		−	1.22313i	−0.791192	−	0.611567i	$-0.790539\pi$
$223$		−	272.759i		−	1.22313i	0.791192	−	0.611567i	$-0.209461\pi$
$224$	−35.8743	+	16.7640i	−0.160153	+	0.0748393i
$225$		0			0
$226$	74.5528	+	129.129i	0.329879	+	0.571368i
$227$	−13.9191	−	8.03620i	−0.0613176	−	0.0354018i	0.469028	−	0.883183i	$-0.344604\pi$
$227$	−13.9191	−	8.03620i	−0.0613176	−	0.0354018i	−0.530345	+	0.847782i	$0.677938\pi$
$228$	−4.40256	+	7.62546i	−0.0193095	+	0.0334450i
$229$	128.261	−	74.0517i	0.560093	−	0.323370i	−0.193090	−	0.981181i	$-0.561851\pi$
$229$	128.261	−	74.0517i	0.560093	−	0.323370i	0.753183	+	0.657811i	$0.228518\pi$
$230$		0			0
$231$	−209.997	−	18.2003i	−0.909078	−	0.0787891i
$232$	−132.959			−0.573098
$233$	−149.559	−	259.044i	−0.641885	−	1.11178i	−0.985012	−	0.172488i	$-0.944819\pi$
$233$	−149.559	−	259.044i	−0.641885	−	1.11178i	0.343127	−	0.939289i	$-0.388514\pi$
$234$	−26.5485	−	15.3278i	−0.113455	−	0.0655034i
$235$		0			0
$236$	−174.173	+	100.559i	−0.738020	+	0.426096i
$237$			41.7570i			0.176190i
$238$	15.0408	−	21.5178i	0.0631968	−	0.0904108i
$239$	−114.253			−0.478046			−0.239023	−	0.971014i	$-0.576827\pi$
$239$	−114.253			−0.478046			−0.239023	+	0.971014i	$0.576827\pi$
$240$		0			0
$241$	−118.162	−	68.2209i	−0.490299	−	0.283074i	0.234399	−	0.972140i	$-0.424688\pi$
$241$	−118.162	−	68.2209i	−0.490299	−	0.283074i	−0.724699	+	0.689066i	$0.758021\pi$
$242$	128.159	−	221.978i	0.529584	−	0.917266i
$243$	−13.5000	+	7.79423i	−0.0555556	+	0.0320750i
$244$		−	25.7778i		−	0.105647i
$245$		0			0
$246$	173.100			0.703660
$247$	9.18308	+	15.9056i	0.0371785	+	0.0643950i
$248$	−98.7192	−	56.9955i	−0.398061	−	0.229821i
$249$	96.7041	−	167.496i	0.388370	−	0.672676i
$250$		0			0
$251$			457.024i			1.82081i	0.413717	+	0.910406i	$0.364230\pi$
$251$			457.024i			1.82081i	−0.413717	+	0.910406i	$0.635770\pi$
$252$	34.4240	+	24.0622i	0.136603	+	0.0954850i
$253$	697.171			2.75562
$254$	−37.9739	−	65.7728i	−0.149504	−	0.258948i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−43.2997	+	24.9991i	−0.168481	+	0.0972726i	−0.581869	−	0.813282i	$-0.697679\pi$
$257$	−43.2997	+	24.9991i	−0.168481	+	0.0972726i	0.413388	+	0.910555i	$0.364345\pi$
$258$		−	91.5453i		−	0.354827i
$259$	19.6453	−	226.669i	0.0758505	−	0.875172i
$260$		0			0
$261$	70.5120	+	122.130i	0.270161	+	0.467932i
$262$	−71.6283	−	41.3546i	−0.273390	−	0.157842i
$263$	91.1388	−	157.857i	0.346535	−	0.600217i	−0.639096	−	0.769127i	$-0.720691\pi$
$263$	91.1388	−	157.857i	0.346535	−	0.600217i	0.985631	+	0.168910i	$0.0540247\pi$
$264$	−73.7591	+	42.5848i	−0.279390	+	0.161306i
$265$		0			0
$266$	−10.6528	−	22.7965i	−0.0400480	−	0.0857012i
$267$	−221.541			−0.829741
$268$	94.0722	+	162.938i	0.351016	+	0.607977i
$269$	−32.5814	−	18.8109i	−0.121120	−	0.0699289i	0.438216	−	0.898870i	$-0.355611\pi$
$269$	−32.5814	−	18.8109i	−0.121120	−	0.0699289i	−0.559336	+	0.828941i	$0.688944\pi$
$270$		0			0
$271$	175.576	−	101.369i	0.647880	−	0.374054i	−0.139763	−	0.990185i	$-0.544634\pi$
$271$	175.576	−	101.369i	0.647880	−	0.374054i	0.787644	+	0.616131i	$0.211301\pi$
$272$		−	10.6080i		−	0.0389999i
$273$	79.3675	−	37.0883i	0.290724	−	0.135855i
$274$	−17.1360			−0.0625401
$275$		0			0
$276$	−120.304	−	69.4578i	−0.435885	−	0.251659i
$277$	128.121	−	221.912i	0.462530	−	0.801126i	−0.536556	−	0.843865i	$-0.680275\pi$
$277$	128.121	−	221.912i	0.462530	−	0.801126i	0.999086	+	0.0427390i	$0.0136084\pi$
$278$	−55.4273	+	32.0010i	−0.199379	+	0.115111i
$279$			120.906i			0.433354i
$280$		0			0
$281$	−141.462			−0.503423			−0.251711	−	0.967802i	$-0.580993\pi$
$281$	−141.462			−0.503423			−0.251711	+	0.967802i	$0.580993\pi$
$282$	40.9658	+	70.9549i	0.145269	+	0.251613i
$283$	−470.571	−	271.684i	−1.66279	−	0.960014i	−0.971372	−	0.237562i	$-0.923652\pi$
$283$	−470.571	−	271.684i	−1.66279	−	0.960014i	−0.691421	−	0.722452i	$-0.743015\pi$
$284$	11.5793	−	20.0559i	0.0407720	−	0.0706192i
$285$		0			0
$286$			177.651i			0.621157i
$287$	−283.405	+	405.445i	−0.987472	+	1.41270i
$288$	16.9706			0.0589256
$289$	−140.983	−	244.191i	−0.487832	−	0.844950i
$290$		0			0
$291$	−6.48008	+	11.2238i	−0.0222683	+	0.0385699i
$292$	−39.2639	+	22.6690i	−0.134466	+	0.0776337i
$293$			375.289i			1.28085i	0.768021	+	0.640424i	$0.221241\pi$
$293$			375.289i			1.28085i	−0.768021	+	0.640424i	$0.778759\pi$
$294$	−112.720	+	41.2344i	−0.383400	+	0.140253i
$295$		0			0
$296$	−45.9658	−	79.6151i	−0.155290	−	0.268970i
$297$	78.2333	+	45.1680i	0.263412	+	0.152081i
$298$	−35.9881	+	62.3332i	−0.120765	+	0.209172i
$299$	−250.937	+	144.878i	−0.839253	+	0.484543i
$300$		0			0
$301$	214.422	+	149.880i	0.712367	+	0.497942i
$302$	223.015			0.738459
$303$	−81.9228	−	141.894i	−0.270372	−	0.468299i
$304$	−8.80512	−	5.08364i	−0.0289642	−	0.0167225i
$305$		0			0
$306$	−9.74405	+	5.62573i	−0.0318433	+	0.0183847i
$307$		−	41.3436i		−	0.134670i	−0.997730	−	0.0673349i	$-0.978550\pi$
$307$		−	41.3436i		−	0.134670i	0.997730	−	0.0673349i	$-0.0214496\pi$
$308$	21.0159	−	242.484i	0.0682333	−	0.787284i
$309$	103.614			0.335321
$310$		0			0
$311$	−126.924	−	73.2794i	−0.408115	−	0.235625i	0.281865	−	0.959454i	$-0.409047\pi$
$311$	−126.924	−	73.2794i	−0.408115	−	0.235625i	−0.689979	+	0.723829i	$0.742380\pi$
$312$	17.6990	−	30.6556i	0.0567276	−	0.0982551i
$313$	−194.744	+	112.435i	−0.622184	+	0.359218i	−0.777719	−	0.628612i	$-0.783623\pi$
$313$	−194.744	+	112.435i	−0.622184	+	0.359218i	0.155535	+	0.987830i	$0.450290\pi$
$314$		−	237.370i		−	0.755957i
$315$		0			0
$316$	−48.2168			−0.152585
$317$	−113.113	−	195.918i	−0.356825	−	0.618038i	0.630604	−	0.776105i	$-0.282807\pi$
$317$	−113.113	−	195.918i	−0.356825	−	0.618038i	−0.987428	+	0.158067i	$0.949474\pi$
$318$	−150.377	−	86.8202i	−0.472884	−	0.273019i
$319$	408.621	−	707.753i	1.28094	−	2.21866i
$320$		0			0
$321$			11.1918i			0.0348656i
$322$	359.653	−	168.065i	1.11694	−	0.521942i
$323$	6.74089			0.0208696
$324$	−9.00000	−	15.5885i	−0.0277778	−	0.0481125i
$325$		0			0
$326$	−195.565	+	338.728i	−0.599891	+	1.03904i
$327$	245.760	−	141.890i	0.751560	−	0.433914i
$328$			199.879i			0.609388i
$329$	−233.265	−	20.2169i	−0.709011	−	0.0614495i
$330$		0			0
$331$	−69.9082	−	121.085i	−0.211203	−	0.365814i	0.740888	−	0.671628i	$-0.234405\pi$
$331$	−69.9082	−	121.085i	−0.211203	−	0.365814i	−0.952091	+	0.305814i	$0.901071\pi$
$332$	193.408	+	111.664i	0.582555	+	0.336338i
$333$	−48.7541	+	84.4446i	−0.146409	+	0.253587i
$334$	−59.3093	+	34.2422i	−0.177573	+	0.102522i
$335$		0			0
$336$	−27.7847	+	39.7494i	−0.0826924	+	0.118302i
$337$	−30.1128			−0.0893556			−0.0446778	−	0.999001i	$-0.514226\pi$
$337$	−30.1128			−0.0893556			−0.0446778	+	0.999001i	$0.514226\pi$
$338$	82.5836	+	143.039i	0.244330	+	0.423192i
$339$	158.150	+	91.3081i	0.466520	+	0.269345i
$340$		0			0
$341$	606.786	−	350.328i	1.77943	−	1.02736i
$342$			10.7840i			0.0315323i
$343$	87.9664	−	331.528i	0.256462	−	0.966554i
$344$	105.707			0.307289
$345$		0			0
$346$	138.358	+	79.8809i	0.399878	+	0.230870i
$347$	−207.954	+	360.186i	−0.599290	+	1.03800i	0.393636	+	0.919266i	$0.371217\pi$
$347$	−207.954	+	360.186i	−0.599290	+	1.03800i	−0.992926	+	0.118734i	$0.962116\pi$
$348$	−141.024	+	81.4202i	−0.405241	+	0.233966i
$349$		−	594.950i		−	1.70473i	−0.522950	−	0.852363i	$-0.675169\pi$
$349$		−	594.950i		−	1.70473i	0.522950	−	0.852363i	$-0.324831\pi$
$350$		0			0
$351$	−37.5453			−0.106967
$352$	−49.1727	−	85.1697i	−0.139695	−	0.241959i
$353$	−315.509	−	182.159i	−0.893793	−	0.516031i	−0.0186116	−	0.999827i	$-0.505925\pi$
$353$	−315.509	−	182.159i	−0.893793	−	0.516031i	−0.875181	+	0.483795i	$0.839258\pi$
$354$	−123.159	+	213.317i	−0.347906	+	0.602591i
$355$		0			0
$356$		−	255.813i		−	0.718577i
$357$	2.77633	−	32.0336i	0.00777684	−	0.0897301i
$358$	−468.693			−1.30920
$359$	306.381	+	530.668i	0.853430	+	1.47818i	0.878094	+	0.478488i	$0.158815\pi$
$359$	306.381	+	530.668i	0.853430	+	1.47818i	−0.0246647	+	0.999696i	$0.507852\pi$
$360$		0			0
$361$	−177.270	+	307.040i	−0.491051	+	0.850526i
$362$	−261.272	+	150.846i	−0.721746	+	0.416700i
$363$		−	313.925i		−	0.864807i
$364$	42.8259	+	91.6457i	0.117654	+	0.251774i
$365$		0			0
$366$	−15.7856	−	27.3415i	−0.0431302	−	0.0747036i
$367$	426.967	+	246.509i	1.16340	+	0.671687i	0.952116	−	0.305738i	$-0.0989032\pi$
$367$	426.967	+	246.509i	1.16340	+	0.671687i	0.211281	+	0.977425i	$0.432236\pi$
$368$	80.2029	−	138.916i	0.217943	−	0.377488i
$369$	183.601	−	106.002i	0.497563	−	0.287268i
$370$		0			0
$371$	449.556	−	210.077i	1.21174	−	0.566245i
$372$	−139.610			−0.375296
$373$	82.7013	+	143.243i	0.221719	+	0.384029i	0.955330	−	0.295541i	$-0.0954998\pi$
$373$	82.7013	+	143.243i	0.221719	+	0.384029i	−0.733611	+	0.679570i	$0.762166\pi$
$374$	56.4674	+	32.6015i	0.150982	+	0.0871697i
$375$		0			0
$376$	−81.9317	+	47.3033i	−0.217903	+	0.125807i
$377$			339.660i			0.900956i
$378$	51.2472	+	4.44155i	0.135575	+	0.0117501i
$379$	−179.349			−0.473215			−0.236608	−	0.971605i	$-0.576036\pi$
$379$	−179.349			−0.473215			−0.236608	+	0.971605i	$0.576036\pi$
$380$		0			0
$381$	−80.5549	−	46.5084i	−0.211430	−	0.122069i
$382$	−47.3078	+	81.9395i	−0.123842	+	0.214501i
$383$	−233.108	+	134.585i	−0.608636	+	0.351396i	−0.772432	−	0.635098i	$-0.780960\pi$
$383$	−233.108	+	134.585i	−0.608636	+	0.351396i	0.163795	+	0.986494i	$0.447626\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	−159.246			−0.412554
$387$	−56.0598	−	97.0984i	−0.144857	−	0.250900i
$388$	−12.9602	−	7.48256i	−0.0334025	−	0.0192849i
$389$	236.874	−	410.277i	0.608930	−	1.05470i	−0.382487	−	0.923961i	$-0.624932\pi$
$389$	236.874	−	410.277i	0.608930	−	1.05470i	0.991417	−	0.130737i	$-0.0417344\pi$
$390$		0			0
$391$			106.349i			0.271992i
$392$	−47.6133	−	130.157i	−0.121463	−	0.332034i
$393$	−101.298			−0.257755
$394$	43.1484	+	74.7353i	0.109514	+	0.189683i
$395$		0			0
$396$	−52.1556	+	90.3361i	−0.131706	+	0.228121i
$397$	445.080	−	256.967i	1.12111	−	0.647271i	0.179424	−	0.983772i	$-0.442577\pi$
$397$	445.080	−	256.967i	1.12111	−	0.647271i	0.941683	+	0.336500i	$0.109243\pi$
$398$		−	270.348i		−	0.679267i
$399$	−25.2589	−	17.6559i	−0.0633056	−	0.0442504i
$400$		0			0
$401$	203.367	+	352.242i	0.507150	+	0.878410i	0.999966	+	0.00827591i	$0.00263433\pi$
$401$	203.367	+	352.242i	0.507150	+	0.878410i	−0.492816	+	0.870134i	$0.664032\pi$
$402$	199.557	+	115.214i	0.496411	+	0.286603i
$403$	−145.603	+	252.191i	−0.361297	+	0.625785i
$404$	163.846	−	94.5963i	0.405558	−	0.234149i
$405$		0			0
$406$	40.1814	−	463.617i	0.0989689	−	1.14191i
$407$	565.066			1.38837
$408$	−6.49603	−	11.2515i	−0.0159217	−	0.0275771i
$409$	−422.173	−	243.742i	−1.03221	−	0.595946i	−0.114592	−	0.993413i	$-0.536556\pi$
$409$	−422.173	−	243.742i	−1.03221	−	0.595946i	−0.917617	+	0.397467i	$0.869889\pi$
$410$		0			0
$411$	−18.1755	+	10.4936i	−0.0442225	+	0.0255319i
$412$			119.643i			0.290397i
$413$	−298.004	−	637.717i	−0.721560	−	1.54411i
$414$	−170.136			−0.410957
$415$		0			0
$416$	35.3980	+	20.4371i	0.0850914	+	0.0491275i
$417$	−39.1930	+	67.8843i	−0.0939881	+	0.162792i
$418$	54.1215	−	31.2471i	0.129477	−	0.0747537i
$419$		−	552.257i		−	1.31804i	−0.752127	−	0.659018i	$-0.770972\pi$
$419$		−	552.257i		−	1.31804i	0.752127	−	0.659018i	$-0.229028\pi$
$420$		0			0
$421$	−74.6870			−0.177404			−0.0887019	−	0.996058i	$-0.528272\pi$
$421$	−74.6870			−0.177404			−0.0887019	+	0.996058i	$0.528272\pi$
$422$	198.072	+	343.070i	0.469364	+	0.812962i
$423$	86.9016	+	50.1727i	0.205441	+	0.118612i
$424$	100.251	−	173.640i	0.236442	−	0.409529i
$425$		0			0
$426$		−	28.3633i		−	0.0665804i
$427$	89.8855	+	7.79031i	0.210505	+	0.0182443i
$428$	−12.9232			−0.0301945
$429$	108.789	+	188.427i	0.253586	+	0.439225i
$430$		0			0
$431$	−242.339	+	419.743i	−0.562271	+	0.973881i	0.435027	+	0.900417i	$0.356739\pi$
$431$	−242.339	+	419.743i	−0.562271	+	0.973881i	−0.997298	+	0.0734641i	$0.976595\pi$
$432$	18.0000	−	10.3923i	0.0416667	−	0.0240563i
$433$		−	458.196i		−	1.05819i	−0.848563	−	0.529094i	$-0.822532\pi$
$433$		−	458.196i		−	1.05819i	0.848563	−	0.529094i	$-0.177468\pi$
$434$	228.573	−	327.002i	0.526667	−	0.753461i
$435$		0			0
$436$	163.840	+	283.779i	0.375780	+	0.650870i
$437$	88.2746	+	50.9653i	0.202001	+	0.116626i
$438$	−27.7638	+	48.0883i	−0.0633877	+	0.109791i
$439$	121.167	−	69.9559i	0.276007	−	0.159353i	−0.355607	−	0.934635i	$-0.615726\pi$
$439$	121.167	−	69.9559i	0.276007	−	0.159353i	0.631614	+	0.775283i	$0.282393\pi$
$440$		0			0
$441$	−94.3065	+	112.762i	−0.213847	+	0.255696i
$442$	−27.0995			−0.0613110
$443$	−8.04616	−	13.9364i	−0.0181629	−	0.0314591i	0.856801	−	0.515647i	$-0.172448\pi$
$443$	−8.04616	−	13.9364i	−0.0181629	−	0.0314591i	−0.874964	+	0.484188i	$0.839115\pi$
$444$	−97.5082	−	56.2964i	−0.219613	−	0.126794i
$445$		0			0
$446$	334.060	−	192.870i	0.749014	−	0.432444i
$447$			88.1524i			0.197209i
$448$	−45.8986	−	32.0830i	−0.102452	−	0.0716138i
$449$	−329.314			−0.733439			−0.366720	−	0.930332i	$-0.619519\pi$
$449$	−329.314			−0.733439			−0.366720	+	0.930332i	$0.619519\pi$
$450$		0			0
$451$	−1063.98	−	614.288i	−2.35915	−	1.36206i
$452$	−105.434	+	182.616i	−0.233260	+	0.404018i
$453$	236.543	−	136.568i	0.522169	−	0.301475i
$454$		−	22.7298i		−	0.0500657i
$455$		0			0
$456$	−12.4523			−0.0273077
$457$	−445.459	−	771.557i	−0.974745	−	1.68831i	−0.680773	−	0.732494i	$-0.738356\pi$
$457$	−445.459	−	771.557i	−0.974745	−	1.68831i	−0.293972	−	0.955814i	$-0.594977\pi$
$458$	181.389	+	104.725i	0.396046	+	0.228657i
$459$	−6.89008	+	11.9340i	−0.0150111	+	0.0259999i
$460$		0			0
$461$		−	534.019i		−	1.15839i	−0.815188	−	0.579196i	$-0.803367\pi$
$461$		−	534.019i		−	1.15839i	0.815188	−	0.579196i	$-0.196633\pi$
$462$	−126.200	−	270.062i	−0.273159	−	0.584550i
$463$	−158.679			−0.342719			−0.171359	−	0.985209i	$-0.554816\pi$
$463$	−158.679			−0.342719			−0.171359	+	0.985209i	$0.554816\pi$
$464$	−94.0160	−	162.840i	−0.202621	−	0.350949i
$465$		0			0
$466$	211.509	−	366.344i	0.453881	−	0.786145i
$467$	97.1671	−	56.0995i	0.208067	−	0.120127i	−0.392346	−	0.919818i	$-0.628336\pi$
$467$	97.1671	−	56.0995i	0.208067	−	0.120127i	0.600413	+	0.799690i	$0.295003\pi$
$468$		−	43.3535i		−	0.0926358i
$469$	−596.582	+	278.782i	−1.27203	+	0.594417i
$470$		0			0
$471$	−145.359	−	251.769i	−0.308618	−	0.534542i
$472$	−246.317	−	142.211i	−0.521859	−	0.301295i
$473$	−324.870	+	562.691i	−0.686829	+	1.18962i
$474$	−51.1416	+	29.5266i	−0.107894	+	0.0622925i
$475$		0			0
$476$	36.9893	+	3.20583i	0.0777085	+	0.00673494i
$477$	−212.665			−0.445839
$478$	−80.7891	−	139.931i	−0.169015	−	0.292742i
$479$	−598.669	−	345.642i	−1.24983	−	0.721590i	−0.278755	−	0.960362i	$-0.589922\pi$
$479$	−598.669	−	345.642i	−1.24983	−	0.721590i	−0.971076	+	0.238772i	$0.923255\pi$
$480$		0			0
$481$	−203.387	+	117.426i	−0.422843	+	0.244128i
$482$		−	192.958i		−	0.400328i
$483$	278.551	−	398.502i	0.576711	−	0.825056i
$484$	362.489			0.748945
$485$		0			0
$486$	−19.0919	−	11.0227i	−0.0392837	−	0.0226805i
$487$	360.410	−	624.248i	0.740062	−	1.28182i	−0.212405	−	0.977182i	$-0.568130\pi$
$487$	360.410	−	624.248i	0.740062	−	1.28182i	0.952467	−	0.304643i	$-0.0985370\pi$
$488$	31.5713	−	18.2277i	0.0646953	−	0.0373518i
$489$			479.033i			0.979618i
$490$		0			0
$491$	589.995			1.20162			0.600809	−	0.799392i	$-0.294845\pi$
$491$	589.995			1.20162			0.600809	+	0.799392i	$0.294845\pi$
$492$	122.400	+	212.004i	0.248781	+	0.430902i
$493$	107.963	+	62.3325i	0.218992	+	0.126435i
$494$	−12.9868	+	22.4939i	−0.0262891	+	0.0455341i
$495$		0			0
$496$		−	161.208i		−	0.325016i
$497$	66.4340	+	46.4371i	0.133670	+	0.0934348i
$498$	273.521			0.549238
$499$	437.845	+	758.370i	0.877445	+	1.51978i	0.854135	+	0.520052i	$0.174087\pi$
$499$	437.845	+	758.370i	0.877445	+	1.51978i	0.0233104	+	0.999728i	$0.492579\pi$
$500$		0			0
$501$	−41.9380	+	72.6387i	−0.0837085	+	0.144987i
$502$	−559.737	+	323.165i	−1.11501	+	0.643754i
$503$			817.809i			1.62586i	0.582360	+	0.812931i	$0.302129\pi$
$503$			817.809i			1.62586i	−0.582360	+	0.812931i	$0.697871\pi$
$504$	−5.12866	+	59.1751i	−0.0101759	+	0.117411i
$505$		0			0
$506$	492.974	+	853.857i	0.974258	+	1.68746i
$507$	175.186	+	101.144i	0.345535	+	0.199495i
$508$	53.7033	−	93.0168i	0.105715	−	0.183104i
$509$	−657.585	+	379.657i	−1.29191	+	0.745887i	−0.978993	−	0.203892i	$-0.934641\pi$
$509$	−657.585	+	379.657i	−1.29191	+	0.745887i	−0.312921	+	0.949779i	$0.601308\pi$
$510$		0			0
$511$	−67.1794	−	143.761i	−0.131467	−	0.281333i
$512$	−22.6274			−0.0441942
$513$	6.60384	+	11.4382i	0.0128730	+	0.0222967i
$514$	−61.2350	−	35.3540i	−0.119134	−	0.0687821i
$515$		0			0
$516$	112.120	−	64.7323i	0.217286	−	0.125450i
$517$		−	581.508i		−	1.12477i
$518$	291.504	−	136.219i	0.562748	−	0.262971i
$519$	195.667			0.377009
$520$		0			0
$521$	−153.671	−	88.7220i	−0.294954	−	0.170292i	0.345220	−	0.938522i	$-0.387804\pi$
$521$	−153.671	−	88.7220i	−0.294954	−	0.170292i	−0.640174	+	0.768230i	$0.721138\pi$
$522$	−99.7190	+	172.718i	−0.191033	+	0.330878i
$523$	−91.1221	+	52.6094i	−0.174230	+	0.100592i	−0.584579	−	0.811337i	$-0.698740\pi$
$523$	−91.1221	+	52.6094i	−0.174230	+	0.100592i	0.410349	+	0.911929i	$0.365407\pi$
$524$		−	116.969i		−	0.223222i
$525$		0			0
$526$	257.780			0.490075
$527$	53.4403	+	92.5612i	0.101405	+	0.175638i
$528$	−104.311	−	60.2240i	−0.197559	−	0.114061i
$529$	−539.563	+	934.551i	−1.01997	+	1.76664i
$530$		0			0
$531$			301.676i			0.568128i
$532$	20.3873	−	29.1665i	0.0383220	−	0.0548243i
$533$	510.618			0.958007
$534$	−156.653	−	271.331i	−0.293358	−	0.508111i
$535$		0			0
$536$	−133.038	+	230.429i	−0.248206	+	0.429905i
$537$	−497.125	+	287.015i	−0.925744	+	0.534479i
$538$		−	53.2051i		−	0.0988943i
$539$	839.172	+	146.562i	1.55690	+	0.271914i
$540$		0			0
$541$	138.181	+	239.337i	0.255419	+	0.442398i	0.965009	−	0.262216i	$-0.0844534\pi$
$541$	138.181	+	239.337i	0.255419	+	0.442398i	−0.709591	+	0.704614i	$0.751120\pi$
$542$	248.301	+	143.357i	0.458121	+	0.264496i
$543$	−184.747	+	319.992i	−0.340234	+	0.589303i
$544$	12.9921	−	7.50097i	0.0238825	−	0.0137886i
$545$		0			0
$546$	101.545	+	70.9796i	0.185980	+	0.129999i
$547$	−918.409			−1.67899			−0.839496	−	0.543366i	$-0.817150\pi$
$547$	−918.409			−1.67899			−0.839496	+	0.543366i	$0.817150\pi$
$548$	−12.1170	−	20.9872i	−0.0221113	−	0.0382978i
$549$	−33.4864	−	19.3334i	−0.0609953	−	0.0352156i
$550$		0			0
$551$	103.478	−	59.7429i	0.187800	−	0.108426i
$552$		−	196.456i		−	0.355899i
$553$	14.5716	−	168.128i	0.0263500	−	0.304030i
$554$	362.380			0.654116
$555$		0			0
$556$	−78.3861	−	45.2562i	−0.140982	−	0.0813961i
$557$	367.505	−	636.538i	0.659794	−	1.14280i	−0.320875	−	0.947122i	$-0.603977\pi$
$557$	367.505	−	636.538i	0.659794	−	1.14280i	0.980669	−	0.195675i	$-0.0626898\pi$
$558$	−148.079	+	85.4933i	−0.265374	+	0.153214i
$559$		−	270.044i		−	0.483083i
$560$		0			0
$561$	79.8569			0.142347
$562$	−100.029	−	173.255i	−0.177987	−	0.308282i
$563$	−715.827	−	413.283i	−1.27145	−	0.734073i	−0.296191	−	0.955129i	$-0.595716\pi$
$563$	−715.827	−	413.283i	−1.27145	−	0.734073i	−0.975261	+	0.221056i	$0.929050\pi$
$564$	−57.9344	+	100.345i	−0.102721	+	0.177917i
$565$		0			0
$566$		−	768.438i		−	1.35767i
$567$	57.0757	−	26.6714i	0.100663	−	0.0470395i
$568$	32.7511			0.0576603
$569$	216.546	+	375.069i	0.380573	+	0.659172i	0.991144	−	0.132790i	$-0.0423935\pi$
$569$	216.546	+	375.069i	0.380573	+	0.659172i	−0.610571	+	0.791961i	$0.709060\pi$
$570$		0			0
$571$	−240.036	+	415.754i	−0.420378	+	0.728116i	−0.995976	−	0.0896166i	$-0.971436\pi$
$571$	−240.036	+	415.754i	−0.420378	+	0.728116i	0.575598	+	0.817733i	$0.304769\pi$
$572$	−217.577	+	125.618i	−0.380380	+	0.219612i
$573$			115.880i			0.202234i
$574$	−696.964	−	60.4054i	−1.21422	−	0.105236i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	75.4646	+	43.5695i	0.130788	+	0.0755104i	0.563966	−	0.825798i	$-0.309275\pi$
$577$	75.4646	+	43.5695i	0.130788	+	0.0755104i	−0.433179	+	0.901308i	$0.642608\pi$
$578$	199.381	−	345.338i	0.344949	−	0.597470i
$579$	−168.906	+	97.5179i	−0.291720	+	0.168425i
$580$		0			0
$581$	−447.815	+	640.655i	−0.770766	+	1.10268i
$582$	−18.3284			−0.0314922
$583$	616.204	+	1067.30i	1.05695	+	1.83070i
$584$	−55.5276	−	32.0589i	−0.0950815	−	0.0548953i
$585$		0			0
$586$	−459.633	+	265.369i	−0.784356	+	0.452848i
$587$		−	104.332i		−	0.177737i	−0.996043	−	0.0888687i	$-0.971675\pi$
$587$		−	104.332i		−	0.177737i	0.996043	−	0.0888687i	$-0.0283252\pi$
$588$	−130.206	−	108.896i	−0.221439	−	0.185197i
$589$	102.440			0.173922
$590$		0			0
$591$	91.5316	+	52.8458i	0.154876	+	0.0894176i
$592$	65.0055	−	112.593i	0.109807	−	0.190191i
$593$	−252.421	+	145.735i	−0.425668	+	0.245760i	−0.697499	−	0.716585i	$-0.745704\pi$
$593$	−252.421	+	145.735i	−0.425668	+	0.245760i	0.271831	+	0.962345i	$0.412371\pi$
$594$			127.754i			0.215075i
$595$		0			0
$596$	−101.790			−0.170788
$597$	−165.554	−	286.748i	−0.277310	−	0.480314i
$598$	−354.878	−	204.889i	−0.593442	−	0.342624i
$599$	−298.839	+	517.604i	−0.498896	+	0.864114i	−0.999999	−	0.00127378i	$-0.999595\pi$
$599$	−298.839	+	517.604i	−0.498896	+	0.864114i	0.501103	+	0.865388i	$0.332928\pi$
$600$		0			0
$601$			447.444i			0.744499i	0.928133	+	0.372250i	$0.121413\pi$
$601$			447.444i			0.744499i	−0.928133	+	0.372250i	$0.878587\pi$
$602$	−31.9458	+	368.594i	−0.0530661	+	0.612283i
$603$	282.217			0.468021
$604$	157.695	+	273.136i	0.261085	+	0.452212i
$605$		0			0
$606$	115.856	−	200.669i	0.191182	−	0.331137i
$607$	−533.739	+	308.155i	−0.879307	+	0.507668i	−0.870430	−	0.492293i	$-0.836159\pi$
$607$	−533.739	+	308.155i	−0.879307	+	0.507668i	−0.00887709	+	0.999961i	$0.502826\pi$
$608$		−	14.3787i		−	0.0236492i
$609$	−241.288	−	516.346i	−0.396203	−	0.847859i
$610$		0			0
$611$	120.842	+	209.305i	0.197778	+	0.342562i
$612$	−13.7802	−	7.95598i	−0.0225166	−	0.0130000i
$613$	−63.5384	+	110.052i	−0.103651	+	0.179530i	−0.913186	−	0.407542i	$-0.866386\pi$
$613$	−63.5384	+	110.052i	−0.103651	+	0.179530i	0.809535	+	0.587072i	$0.199719\pi$
$614$	50.6354	−	29.2344i	0.0824681	−	0.0476130i
$615$		0			0
$616$	311.841	−	145.723i	0.506235	−	0.236563i
$617$	−68.5630			−0.111123			−0.0555616	−	0.998455i	$-0.517695\pi$
$617$	−68.5630			−0.111123			−0.0555616	+	0.998455i	$0.517695\pi$
$618$	73.2664	+	126.901i	0.118554	+	0.205342i
$619$	833.529	+	481.238i	1.34657	+	0.777445i	0.987763	−	0.155965i	$-0.0498487\pi$
$619$	833.529	+	481.238i	1.34657	+	0.777445i	0.358812	+	0.933410i	$0.383182\pi$
$620$		0			0
$621$	−180.457	+	104.187i	−0.290590	+	0.167772i
$622$		−	207.265i		−	0.333224i
$623$	892.003	+	77.3092i	1.43179	+	0.124092i
$624$	50.0604			0.0802249
$625$		0			0
$626$	−275.409	−	159.008i	−0.439951	−	0.254006i
$627$	38.2697	−	66.2850i	0.0610362	−	0.105718i
$628$	290.718	−	167.846i	0.462927	−	0.267271i
$629$			86.1971i			0.137038i
$630$		0			0
$631$	412.586			0.653860			0.326930	−	0.945048i	$-0.393986\pi$
$631$	412.586			0.653860			0.326930	+	0.945048i	$0.393986\pi$
$632$	−34.0944	−	59.0533i	−0.0539469	−	0.0934387i
$633$	420.173	+	242.587i	0.663781	+	0.383234i
$634$	159.966	−	277.070i	0.252313	−	0.437019i
$635$		0			0
$636$		−	245.565i		−	0.386108i
$637$	−332.504	+	121.635i	−0.521985	+	0.190949i
$638$	1155.76			1.81153
$639$	−17.3689	−	30.0838i	−0.0271813	−	0.0470795i
$640$		0			0
$641$	71.3374	−	123.560i	0.111291	−	0.192761i	−0.805000	−	0.593275i	$-0.797835\pi$
$641$	71.3374	−	123.560i	0.111291	−	0.192761i	0.916291	+	0.400513i	$0.131168\pi$
$642$	−13.7072	+	7.91383i	−0.0213507	+	0.0123268i
$643$			239.942i			0.373160i	0.982440	+	0.186580i	$0.0597403\pi$
$643$			239.942i			0.373160i	−0.982440	+	0.186580i	$0.940260\pi$
$644$	460.150	+	321.643i	0.714519	+	0.499446i
$645$		0			0
$646$	4.76653	+	8.25588i	0.00737853	+	0.0127800i
$647$	128.817	+	74.3724i	0.199098	+	0.114950i	0.596235	−	0.802810i	$-0.296663\pi$
$647$	128.817	+	74.3724i	0.199098	+	0.114950i	−0.397136	+	0.917760i	$0.629996\pi$
$648$	12.7279	−	22.0454i	0.0196419	−	0.0340207i
$649$	1514.01	−	874.115i	2.33284	−	1.34686i
$650$		0			0
$651$	42.1915	−	486.810i	0.0648102	−	0.747788i
$652$	−553.140			−0.848374
$653$	144.011	+	249.434i	0.220537	+	0.381982i	0.954971	−	0.296698i	$-0.0958856\pi$
$653$	144.011	+	249.434i	0.220537	+	0.381982i	−0.734434	+	0.678680i	$0.762552\pi$
$654$	347.557	+	200.662i	0.531433	+	0.306823i
$655$		0			0
$656$	−244.801	+	141.336i	−0.373172	+	0.215451i
$657$			68.0071i			0.103512i
$658$	−140.183	−	299.985i	−0.213043	−	0.455905i
$659$	−175.647			−0.266536			−0.133268	−	0.991080i	$-0.542547\pi$
$659$	−175.647			−0.266536			−0.133268	+	0.991080i	$0.542547\pi$
$660$		0			0
$661$	−615.015	−	355.079i	−0.930432	−	0.537185i	−0.0434835	−	0.999054i	$-0.513846\pi$
$661$	−615.015	−	355.079i	−0.930432	−	0.537185i	−0.886948	+	0.461869i	$0.847179\pi$
$662$	98.8651	−	171.239i	0.149343	−	0.258670i
$663$	−28.7433	+	16.5950i	−0.0433535	+	0.0250301i
$664$			315.834i			0.475654i
$665$		0			0
$666$	−137.897			−0.207053
$667$	942.544	+	1632.53i	1.41311	+	2.44758i
$668$	−83.8760	−	48.4258i	−0.125563	−	0.0724937i
$669$	236.216	−	409.139i	0.353089	−	0.611567i
$670$		0			0
$671$			224.076i			0.333944i
$672$	−68.3296	−	5.92207i	−0.101681	−	0.00881261i
$673$	1173.04			1.74301			0.871504	−	0.490389i	$-0.163145\pi$
$673$	1173.04			1.74301			0.871504	+	0.490389i	$0.163145\pi$
$674$	−21.2930	−	36.8806i	−0.0315920	−	0.0547189i
$675$		0			0
$676$	−116.791	+	202.288i	−0.172768	+	0.299242i
$677$	−586.699	+	338.731i	−0.866616	+	0.500341i	−0.866222	−	0.499659i	$-0.833459\pi$
$677$	−586.699	+	338.731i	−0.866616	+	0.500341i	−0.000393478		1.00000i	$0.500125\pi$
$678$			258.258i			0.380912i
$679$	30.0078	−	42.9299i	0.0441941	−	0.0632252i
$680$		0			0
$681$	−13.9191	−	24.1086i	−0.0204392	−	0.0354018i
$682$	858.126	+	495.439i	1.25825	+	0.726450i
$683$	−415.514	+	719.691i	−0.608366	+	1.05372i	0.383144	+	0.923689i	$0.374841\pi$
$683$	−415.514	+	719.691i	−0.608366	+	1.05372i	−0.991510	+	0.130032i	$0.958492\pi$
$684$	−13.2077	+	7.62546i	−0.0193095	+	0.0111483i
$685$		0			0
$686$	468.239	−	126.689i	0.682564	−	0.184679i
$687$	256.523			0.373395
$688$	74.7464	+	129.465i	0.108643	+	0.188175i
$689$	−443.587	−	256.105i	−0.643813	−	0.371706i
$690$		0			0
$691$	541.436	−	312.598i	0.783554	−	0.452385i	−0.0541345	−	0.998534i	$-0.517240\pi$
$691$	541.436	−	312.598i	0.783554	−	0.452385i	0.837688	+	0.546149i	$0.183907\pi$
$692$			225.937i			0.326499i
$693$	−299.233	−	209.163i	−0.431794	−	0.301823i
$694$	−588.181			−0.847524
$695$		0			0
$696$	−199.438	−	115.146i	−0.286549	−	0.165439i
$697$	93.7055	−	162.303i	0.134441	−	0.232859i
$698$	728.661	−	420.693i	1.04393	−	0.602712i
$699$		−	518.088i		−	0.741185i
$700$		0			0
$701$	1030.02			1.46936			0.734678	−	0.678416i	$-0.237333\pi$
$701$	1030.02			1.46936			0.734678	+	0.678416i	$0.237333\pi$
$702$	−26.5485	−	45.9834i	−0.0378184	−	0.0655034i
$703$	71.5477	+	41.3081i	0.101775	+	0.0587597i
$704$	69.5407	−	120.448i	0.0987795	−	0.171091i
$705$		0			0
$706$		−	515.224i		−	0.729779i
$707$	280.335	+	599.906i	0.396513	+	0.848523i
$708$	−348.345			−0.492013
$709$	329.126	+	570.062i	0.464211	+	0.804037i	0.999166	−	0.0408438i	$-0.0130046\pi$
$709$	329.126	+	570.062i	0.464211	+	0.804037i	−0.534955	+	0.844881i	$0.679671\pi$
$710$		0			0
$711$	−36.1626	+	62.6354i	−0.0508616	+	0.0880949i
$712$	313.306	−	180.887i	0.440037	−	0.254055i
$713$			1616.17i			2.26671i
$714$	41.1962	−	19.2509i	0.0576978	−	0.0269621i
$715$		0			0
$716$	−331.416	−	574.030i	−0.462872	−	0.801718i
$717$	−171.380	−	98.9461i	−0.239023	−	0.138000i
$718$	−433.288	+	750.478i	−0.603466	+	1.04523i
$719$	−1166.99	+	673.760i	−1.62307	+	0.937079i	−0.636975	+	0.770884i	$0.719815\pi$
$719$	−1166.99	+	673.760i	−1.62307	+	0.937079i	−0.986093	+	0.166195i	$0.946852\pi$
$720$		0			0
$721$	−417.188	−	36.1574i	−0.578625	−	0.0501490i
$722$	−501.394			−0.694452
$723$	−118.162	−	204.663i	−0.163433	−	0.283074i
$724$	−369.495	−	213.328i	−0.510352	−	0.294652i
$725$		0			0
$726$	384.478	−	221.978i	0.529584	−	0.305755i
$727$			1126.18i			1.54907i	0.632530	+	0.774536i	$0.282017\pi$
$727$			1126.18i			1.54907i	−0.632530	+	0.774536i	$0.717983\pi$
$728$	−81.9602	+	117.254i	−0.112583	+	0.161063i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−85.8348	−	49.5568i	−0.117421	−	0.0677931i
$732$	22.3243	−	38.6668i	0.0304976	−	0.0528235i
$733$	−525.395	+	303.337i	−0.716773	+	0.413829i	−0.813564	−	0.581476i	$-0.802476\pi$
$733$	−525.395	+	303.337i	−0.716773	+	0.413829i	0.0967907	+	0.995305i	$0.469142\pi$
$734$			697.233i			0.949909i
$735$		0			0
$736$	226.848			0.308218
$737$	−817.731	−	1416.35i	−1.10954	−	1.92178i
$738$	259.651	+	149.909i	0.351830	+	0.203129i
$739$	−461.084	+	798.622i	−0.623930	+	1.08068i	0.364817	+	0.931079i	$0.381132\pi$
$739$	−461.084	+	798.622i	−0.623930	+	1.08068i	−0.988747	+	0.149599i	$0.952202\pi$
$740$		0			0
$741$			31.8111i			0.0429300i
$742$	575.175	+	402.045i	0.775168	+	0.541840i
$743$	−13.3994			−0.0180342			−0.00901712	−	0.999959i	$-0.502870\pi$
$743$	−13.3994			−0.0180342			−0.00901712	+	0.999959i	$0.502870\pi$
$744$	−98.7192	−	170.987i	−0.132687	−	0.229821i
$745$		0			0
$746$	−116.957	+	202.576i	−0.156779	+	0.271550i
$747$	290.112	−	167.496i	0.388370	−	0.224225i
$748$			92.2108i			0.123277i
$749$	3.90552	−	45.0624i	0.00521431	−	0.0601634i
$750$		0			0
$751$	−538.071	−	931.967i	−0.716473	−	1.24097i	−0.962389	−	0.271676i	$-0.912422\pi$
$751$	−538.071	−	931.967i	−0.716473	−	1.24097i	0.245916	−	0.969291i	$-0.420911\pi$
$752$	−115.869	−	66.8969i	−0.154081	−	0.0889587i
$753$	−395.794	+	685.536i	−0.525623	+	0.910406i
$754$	−415.997	+	240.176i	−0.551721	+	0.318536i
$755$		0			0
$756$	30.7975	+	65.9054i	0.0407374	+	0.0871764i
$757$	254.117			0.335690			0.167845	−	0.985813i	$-0.446319\pi$
$757$	254.117			0.335690			0.167845	+	0.985813i	$0.446319\pi$
$758$	−126.819	−	219.656i	−0.167307	−	0.289784i
$759$	1045.76	+	603.768i	1.37781	+	0.795478i
$760$		0			0
$761$	−685.095	+	395.540i	−0.900256	+	0.519763i	−0.877283	−	0.479973i	$-0.840646\pi$
$761$	−685.095	+	395.540i	−0.900256	+	0.519763i	−0.0229729	+	0.999736i	$0.507313\pi$
$762$		−	131.546i		−	0.172632i
$763$	−1039.03	+	485.538i	−1.36177	+	0.636354i
$764$	−133.807			−0.175140
$765$		0			0
$766$	−329.664	−	190.332i	−0.430371	−	0.248475i
$767$	−363.298	+	629.250i	−0.473661	+	0.820405i
$768$	−24.0000	+	13.8564i	−0.0312500	+	0.0180422i
$769$			464.403i			0.603905i	0.953323	+	0.301952i	$0.0976384\pi$
$769$			464.403i			0.603905i	−0.953323	+	0.301952i	$0.902362\pi$
$770$		0			0
$771$	−86.5993			−0.112321
$772$	−112.604	−	195.036i	−0.145860	−	0.252637i
$773$	−675.608	−	390.063i	−0.874008	−	0.504609i	−0.00533002	−	0.999986i	$-0.501697\pi$
$773$	−675.608	−	390.063i	−0.874008	−	0.504609i	−0.868678	+	0.495377i	$0.835030\pi$
$774$	79.2805	−	137.318i	0.102430	−	0.177413i
$775$		0			0
$776$		−	21.1639i		−	0.0272730i
$777$	225.769	−	322.991i	0.290566	−	0.415690i
$778$	669.980			0.861157
$779$	−89.8126	−	155.560i	−0.115292	−	0.199692i
$780$		0			0
$781$	−100.654	+	174.337i	−0.128878	+	0.223223i
$782$	−130.250	+	75.2000i	−0.166560	+	0.0961637i
$783$			244.261i			0.311955i
$784$	125.742	−	150.349i	0.160385	−	0.191772i
$785$		0			0
$786$	−71.6283	−	124.064i	−0.0911302	−	0.157842i
$787$	−998.358	−	576.402i	−1.26856	−	0.732404i	−0.293845	−	0.955853i	$-0.594935\pi$
$787$	−998.358	−	576.402i	−1.26856	−	0.732404i	−0.974716	+	0.223449i	$0.928268\pi$
$788$	−61.0211	+	105.692i	−0.0774379	+	0.134126i
$789$	273.416	−	157.857i	0.346535	−	0.200072i
$790$		0			0
$791$	−604.907	−	422.827i	−0.764737	−	0.534548i
$792$	−147.518			−0.186260
$793$	−46.5650	−	80.6530i	−0.0587201	−	0.101706i
$794$	629.437	+	363.406i	0.792742	+	0.457690i
$795$		0			0
$796$	331.108	−	191.165i	0.415964	−	0.240157i
$797$		−	1475.63i		−	1.85148i	−0.378156	−	0.925742i	$-0.623442\pi$
$797$		−	1475.63i		−	1.85148i	0.378156	−	0.925742i	$-0.376558\pi$
$798$	3.76321	−	43.4204i	0.00471580	−	0.0544115i
$799$	88.7051			0.111020
$800$		0			0
$801$	−332.311	−	191.860i	−0.414871	−	0.239526i
$802$	−287.605	+	498.146i	−0.358609	+	0.621129i
$803$	341.305	−	197.053i	0.425038	−	0.245396i
$804$			325.876i			0.405318i
$805$		0			0
$806$	−411.827			−0.510951
$807$	−32.5814	−	56.4326i	−0.0403734	−	0.0699289i
$808$	231.713	+	133.779i	0.286773	+	0.165569i
$809$	6.88050	−	11.9174i	0.00850495	−	0.0147310i	−0.861742	−	0.507347i	$-0.830626\pi$
$809$	6.88050	−	11.9174i	0.00850495	−	0.0147310i	0.870247	+	0.492616i	$0.163959\pi$
$810$		0			0
$811$			1274.65i			1.57170i	0.618416	+	0.785851i	$0.287775\pi$
$811$			1274.65i			1.57170i	−0.618416	+	0.785851i	$0.712225\pi$
$812$	596.225	−	278.615i	0.734268	−	0.343122i
$813$	351.151			0.431920
$814$	399.562	+	692.062i	0.490863	+	0.850199i
$815$		0			0
$816$	9.18678	−	15.9120i	0.0112583	−	0.0195000i
$817$	−82.2689	+	47.4980i	−0.100696	+	0.0581371i
$818$		−	689.406i		−	0.842795i
$819$	151.171	+	13.1019i	0.184580	+	0.0159974i
$820$		0			0
$821$	−292.249	−	506.190i	−0.355967	−	0.616553i	0.631316	−	0.775526i	$-0.282515\pi$
$821$	−292.249	−	506.190i	−0.355967	−	0.616553i	−0.987283	+	0.158973i	$0.949182\pi$
$822$	−25.7040	−	14.8402i	−0.0312700	−	0.0180538i
$823$	−40.4835	+	70.1196i	−0.0491902	+	0.0851999i	−0.889572	−	0.456795i	$-0.848997\pi$
$823$	−40.4835	+	70.1196i	−0.0491902	+	0.0851999i	0.840382	+	0.541995i	$0.182331\pi$
$824$	−146.533	+	84.6007i	−0.177831	+	0.102671i
$825$		0			0
$826$	570.320	−	815.913i	0.690461	−	0.987789i
$827$	1628.46			1.96911			0.984556	−	0.175072i	$-0.0560158\pi$
$827$	1628.46			1.96911			0.984556	+	0.175072i	$0.0560158\pi$
$828$	−120.304	−	208.373i	−0.145295	−	0.251659i
$829$	−761.982	−	439.931i	−0.919158	−	0.530676i	−0.0357920	−	0.999359i	$-0.511395\pi$
$829$	−761.982	−	439.931i	−0.919158	−	0.530676i	−0.883366	+	0.468683i	$0.844729\pi$
$830$		0			0
$831$	384.362	−	221.912i	0.462530	−	0.267042i
$832$			57.8047i			0.0694768i
$833$	−22.3570	+	128.010i	−0.0268391	+	0.153674i
$834$	−110.855			−0.132919
$835$		0			0
$836$	76.5394	+	44.1900i	0.0915543	+	0.0528589i
$837$	−104.708	+	181.359i	−0.125099	+	0.216677i
$838$	676.374	−	390.505i	0.807129	−	0.465996i
$839$			647.389i			0.771619i	0.922578	+	0.385810i	$0.126078\pi$
$839$			647.389i			0.771619i	−0.922578	+	0.385810i	$0.873922\pi$
$840$		0			0
$841$	1368.75			1.62753
$842$	−52.8117	−	91.4725i	−0.0627217	−	0.108637i
$843$	−212.193	−	122.510i	−0.251711	−	0.145326i
$844$	−280.115	+	485.174i	−0.331890	+	0.574851i
$845$		0			0
$846$			141.910i			0.167742i
$847$	−109.548	+	1263.97i	−0.129336	+	1.49230i
$848$	283.554			0.334379
$849$	−470.571	−	815.052i	−0.554264	−	0.960014i
$850$		0			0
$851$	−651.704	+	1128.78i	−0.765809	+	1.32642i
$852$	34.7378	−	20.0559i	0.0407720	−	0.0235397i
$853$			569.518i			0.667665i	0.942632	+	0.333833i	$0.108342\pi$
$853$			569.518i			0.667665i	−0.942632	+	0.333833i	$0.891658\pi$
$854$	54.0175	+	115.595i	0.0632524	+	0.135358i
$855$		0			0
$856$	−9.13810	−	15.8277i	−0.0106754	−	0.0184903i
$857$	−553.041	−	319.299i	−0.645322	−	0.372577i	0.141339	−	0.989961i	$-0.454859\pi$
$857$	−553.041	−	319.299i	−0.645322	−	0.372577i	−0.786662	+	0.617384i	$0.788192\pi$
$858$	−153.850	+	266.477i	−0.179313	+	0.310579i
$859$	1097.36	−	633.562i	1.27749	−	0.737558i	0.301102	−	0.953592i	$-0.402645\pi$
$859$	1097.36	−	633.562i	1.27749	−	0.737558i	0.976386	+	0.216034i	$0.0693122\pi$
$860$		0			0
$861$	−776.233	+	362.732i	−0.901548	+	0.421292i
$862$	−685.437			−0.795171
$863$	−103.017	−	178.430i	−0.119371	−	0.206756i	0.800148	−	0.599803i	$-0.204754\pi$
$863$	−103.017	−	178.430i	−0.119371	−	0.206756i	−0.919518	+	0.393047i	$0.871421\pi$
$864$	25.4558	+	14.6969i	0.0294628	+	0.0170103i
$865$		0			0
$866$	561.173	−	323.993i	0.648006	−	0.374126i
$867$		−	488.381i		−	0.563300i
$868$	562.120	+	48.7185i	0.647604	+	0.0561273i
$869$	419.129			0.482312
$870$		0			0
$871$	588.661	+	339.864i	0.675845	+	0.390199i
$872$	−231.705	+	401.325i	−0.265717	+	0.460235i
$873$	−19.4403	+	11.2238i	−0.0222683	+	0.0128566i
$874$			144.152i			0.164933i
$875$		0			0
$876$	−78.5279			−0.0896437
$877$	412.272	+	714.076i	0.470093	+	0.814226i	0.999415	−	0.0341955i	$-0.0108869\pi$
$877$	412.272	+	714.076i	0.470093	+	0.814226i	−0.529322	+	0.848421i	$0.677554\pi$
$878$	171.356	+	98.9325i	0.195167	+	0.112679i
$879$	−325.009	+	562.933i	−0.369749	+	0.640424i
$880$		0			0
$881$		−	416.337i		−	0.472574i	−0.971683	−	0.236287i	$-0.924070\pi$
$881$		−	416.337i		−	0.472574i	0.971683	−	0.236287i	$-0.0759305\pi$
$882$	−204.790	−	35.7666i	−0.232188	−	0.0405517i
$883$	−650.529			−0.736726			−0.368363	−	0.929682i	$-0.620082\pi$
$883$	−650.529			−0.736726			−0.368363	+	0.929682i	$0.620082\pi$
$884$	−19.1622	−	33.1900i	−0.0216767	−	0.0375452i
$885$		0			0
$886$	11.3790	−	19.7090i	0.0128431	−	0.0222449i
$887$	299.987	−	173.198i	0.338204	−	0.195262i	−0.321273	−	0.946987i	$-0.604111\pi$
$887$	299.987	−	173.198i	0.338204	−	0.195262i	0.659478	+	0.751724i	$0.270777\pi$
$888$		−	159.230i		−	0.179313i
$889$	308.113	+	215.370i	0.346584	+	0.242261i
$890$		0			0
$891$	78.2333	+	135.504i	0.0878040	+	0.152081i
$892$	472.433	+	272.759i	0.529633	+	0.305784i
$893$	42.5100	−	73.6295i	0.0476036	−	0.0824518i
$894$	−107.964	+	62.3332i	−0.120765	+	0.0697239i
$895$		0			0
$896$	6.83822	−	78.9002i	0.00763194	−	0.0880582i
$897$	−501.873			−0.559502
$898$	−232.860	−	403.326i	−0.259310	−	0.449138i
$899$	1640.70	+	947.256i	1.82502	+	1.05368i
$900$		0			0
$901$	−162.809	+	93.9978i	−0.180698	+	0.104326i
$902$		−	1737.47i		−	1.92624i
$903$	191.833	+	410.516i	0.212440	+	0.454613i
$904$	−298.211			−0.329879
$905$		0			0
$906$	334.522	+	193.136i	0.369230	+	0.213175i
$907$	210.091	−	363.888i	0.231633	−	0.401199i	−0.726656	−	0.687001i	$-0.758927\pi$
$907$	210.091	−	363.888i	0.231633	−	0.401199i	0.958289	+	0.285802i	$0.0922600\pi$
$908$	27.8382	−	16.0724i	0.0306588	−	0.0177009i
$909$		−	283.789i		−	0.312199i
$910$		0			0
$911$	717.087			0.787142			0.393571	−	0.919294i	$-0.371239\pi$
$911$	717.087			0.787142			0.393571	+	0.919294i	$0.371239\pi$
$912$	−8.80512	−	15.2509i	−0.00965474	−	0.0167225i
$913$	−1681.22	−	970.652i	−1.84142	−	1.06315i
$914$	629.974	−	1091.15i	0.689249	−	1.19381i
$915$		0			0
$916$			296.207i			0.323370i
$917$	407.861	+	35.3490i	0.444777	+	0.0385485i
$918$	−19.4881			−0.0212289
$919$	59.5137	+	103.081i	0.0647592	+	0.112166i	0.896587	−	0.442867i	$-0.146039\pi$
$919$	59.5137	+	103.081i	0.0647592	+	0.112166i	−0.831828	+	0.555034i	$0.812705\pi$
$920$		0			0
$921$	35.8046	−	62.0154i	0.0388758	−	0.0673349i
$922$	654.037	−	377.608i	0.709367	−	0.409553i
$923$		−	83.6669i		−	0.0906467i
$924$	241.521	−	345.525i	0.261386	−	0.373945i
$925$		0			0
$926$	−112.203	−	194.341i	−0.121169	−	0.209872i
$927$	155.421	+	89.7326i	0.167661	+	0.0967989i
$928$	132.959	−	230.291i	0.143274	−	0.248159i
$929$	328.049	−	189.399i	0.353121	−	0.203874i	−0.312938	−	0.949773i	$-0.601313\pi$
$929$	328.049	−	189.399i	0.353121	−	0.203874i	0.666059	+	0.745899i	$0.267980\pi$
$930$		0			0
$931$	95.5403	+	79.9034i	0.102621	+	0.0858253i
$932$	598.237			0.641885
$933$	−126.924	−	219.838i	−0.136038	−	0.235625i
$934$	137.415	+	79.3366i	0.147125	+	0.0849429i
$935$		0			0
$936$	53.0970	−	30.6556i	0.0567276	−	0.0327517i
$937$			365.585i			0.390165i	0.980787	+	0.195083i	$0.0624975\pi$
$937$			365.585i			0.390165i	−0.980787	+	0.195083i	$0.937503\pi$
$938$	−763.284	−	533.532i	−0.813735	−	0.568798i
$939$	−389.487			−0.414790
$940$		0			0
$941$	−1193.22	−	688.903i	−1.26803	−	0.732097i	−0.293414	−	0.955985i	$-0.594791\pi$
$941$	−1193.22	−	688.903i	−1.26803	−	0.732097i	−0.974615	+	0.223889i	$0.928125\pi$
$942$	205.569	−	356.056i	0.218226	−	0.377978i
$943$	2454.22	−	1416.94i	2.60256	−	1.50259i
$944$		−	402.235i		−	0.426096i
$945$		0			0
$946$	−918.871			−0.971323
$947$	237.417	+	411.218i	0.250704	+	0.434232i	0.963720	−	0.266916i	$-0.0860046\pi$
$947$	237.417	+	411.218i	0.250704	+	0.434232i	−0.713016	+	0.701148i	$0.752671\pi$
$948$	−72.3252	−	41.7570i	−0.0762924	−	0.0440474i
$949$	−81.8986	+	141.853i	−0.0862999	+	0.149476i
$950$		0			0
$951$		−	391.836i		−	0.412025i
$952$	22.2290	+	47.5693i	0.0233498	+	0.0499677i
$953$	172.839			0.181363			0.0906813	−	0.995880i	$-0.471096\pi$
$953$	172.839			0.181363			0.0906813	+	0.995880i	$0.471096\pi$
$954$	−150.377	−	260.461i	−0.157628	−	0.273019i
$955$		0			0
$956$	114.253	−	197.892i	0.119512	−	0.207000i
$957$	1225.86	−	707.753i	1.28094	−	0.739554i
$958$		−	977.622i		−	1.02048i
$959$	76.8427	−	35.9085i	0.0801280	−	0.0374437i
$960$		0			0
$961$	331.623	+	574.388i	0.345081	+	0.597698i
$962$	−287.633	−	166.065i	−0.298995	−	0.172625i
$963$	−9.69242	+	16.7878i	−0.0100648	+	0.0174328i
$964$	236.324	−	136.442i	0.245150	−	0.141537i
$965$		0			0
$966$	685.029	+	59.3709i	0.709139	+	0.0614606i
$967$	1209.88			1.25117			0.625583	−	0.780158i	$-0.284861\pi$
$967$	1209.88			1.25117			0.625583	+	0.780158i	$0.284861\pi$
$968$	256.319	+	443.957i	0.264792	+	0.458633i
$969$	10.1113	+	5.83779i	0.0104348	+	0.00602455i
$970$		0			0
$971$	−675.990	+	390.283i	−0.696180	+	0.401939i	−0.805923	−	0.592020i	$-0.798330\pi$
$971$	−675.990	+	390.283i	−0.696180	+	0.401939i	0.109743	+	0.993960i	$0.464997\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	181.494	−	259.650i	0.186531	−	0.266855i
$974$	1019.39			1.04661
$975$		0			0
$976$	44.6485	+	25.7778i	0.0457465	+	0.0264117i
$977$	794.931	−	1376.86i	0.813644	−	1.40927i	−0.0966527	−	0.995318i	$-0.530814\pi$
$977$	794.931	−	1376.86i	0.813644	−	1.40927i	0.910297	−	0.413955i	$-0.135853\pi$
$978$	−586.694	+	338.728i	−0.599891	+	0.346347i
$979$			2223.68i			2.27138i
$980$		0			0
$981$	491.520			0.501040
$982$	417.189	+	722.593i	0.424836	+	0.735838i
$983$	−607.577	−	350.785i	−0.618084	−	0.356851i	0.158039	−	0.987433i	$-0.449483\pi$
$983$	−607.577	−	350.785i	−0.618084	−	0.356851i	−0.776123	+	0.630582i	$0.782816\pi$
$984$	−173.100	+	299.819i	−0.175915	+	0.304694i
$985$		0			0
$986$			176.303i			0.178806i
$987$	−332.389	−	232.339i	−0.336767	−	0.235399i
$988$	−36.7323			−0.0371785
$989$	−749.360	−	1297.93i	−0.757695	−	1.31237i
$990$		0			0
$991$	−203.359	+	352.228i	−0.205206	+	0.355427i	−0.950198	−	0.311646i	$-0.899120\pi$
$991$	−203.359	+	352.228i	−0.205206	+	0.355427i	0.744992	+	0.667073i	$0.232453\pi$
$992$	197.438	−	113.991i	0.199031	−	0.114910i
$993$		−	242.169i		−	0.243876i
$994$	−9.89768	+	114.201i	−0.00995743	+	0.114890i
$995$		0			0
$996$	193.408	+	334.993i	0.194185	+	0.336338i
$997$	655.372	+	378.379i	0.657344	+	0.379518i	0.791264	−	0.611474i	$-0.209423\pi$
$997$	655.372	+	378.379i	0.657344	+	0.379518i	−0.133920	+	0.990992i	$0.542757\pi$
$998$	−619.207	+	1072.50i	−0.620448	+	1.07465i
$999$	−146.262	+	84.4446i	−0.146409	+	0.0845291i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.p.i.451.5		16
5.2	odd	4		1050.3.q.e.199.2		32
5.3	odd	4		1050.3.q.e.199.15		32
5.4	even	2		210.3.o.b.31.2	✓	16
7.5	odd	6	inner	1050.3.p.i.901.5		16
15.14	odd	2		630.3.v.c.451.8		16
35.4	even	6		1470.3.f.d.391.13		16
35.12	even	12		1050.3.q.e.649.15		32
35.19	odd	6		210.3.o.b.61.2	yes	16
35.24	odd	6		1470.3.f.d.391.11		16
35.33	even	12		1050.3.q.e.649.2		32
105.89	even	6		630.3.v.c.271.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.2	✓	16	5.4	even	2
210.3.o.b.61.2	yes	16	35.19	odd	6
630.3.v.c.271.8		16	105.89	even	6
630.3.v.c.451.8		16	15.14	odd	2
1050.3.p.i.451.5		16	1.1	even	1	trivial
1050.3.p.i.901.5		16	7.5	odd	6	inner
1050.3.q.e.199.2		32	5.2	odd	4
1050.3.q.e.199.15		32	5.3	odd	4
1050.3.q.e.649.2		32	35.33	even	12
1050.3.q.e.649.15		32	35.12	even	12
1470.3.f.d.391.11		16	35.24	odd	6
1470.3.f.d.391.13		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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(-5.73733 - 4.01037i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(-5.73733 - 4.01037i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(8.69259 - 15.0560i) q^{11} +(-3.00000 + 1.73205i) q^{12} +7.22559i q^{13} +(0.854777 - 9.86252i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(2.29669 + 1.32600i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(2.20128 - 1.27091i) q^{19} +(-5.13291 - 10.9842i) q^{21} +24.5864 q^{22} +(20.0507 + 34.7289i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(-8.84951 + 5.10926i) q^{26} +5.19615i q^{27} +(12.6835 - 5.92697i) q^{28} +47.0080 q^{29} +(34.9025 + 20.1510i) q^{31} +(2.82843 - 4.89898i) q^{32} +(26.0778 - 15.0560i) q^{33} +3.75049i q^{34} -6.00000 q^{36} +(16.2514 + 28.1482i) q^{37} +(3.11308 + 1.79734i) q^{38} +(-6.25755 + 10.8384i) q^{39} -70.6679i q^{41} +(9.82336 - 14.0535i) q^{42} -37.3732 q^{43} +(17.3852 + 30.1120i) q^{44} +(-28.3560 + 49.1141i) q^{46} +(28.9672 - 16.7242i) q^{47} -6.92820i q^{48} +(16.8339 + 46.0176i) q^{49} +(2.29669 + 3.97799i) q^{51} +(-12.5151 - 7.22559i) q^{52} +(-35.4442 + 61.3911i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(16.2276 + 11.3430i) q^{56} +4.40256 q^{57} +(33.2397 + 57.5728i) q^{58} +(87.0863 + 50.2793i) q^{59} +(-11.1621 + 6.44446i) q^{61} +56.9955i q^{62} +(1.81326 - 20.9216i) q^{63} +8.00000 q^{64} +(36.8795 + 21.2924i) q^{66} +(47.0361 - 81.4689i) q^{67} +(-4.59339 + 2.65199i) q^{68} +69.4578i q^{69} -11.5793 q^{71} +(-4.24264 - 7.34847i) q^{72} +(19.6320 + 11.3345i) q^{73} +(-22.9829 + 39.8076i) q^{74} +5.08364i q^{76} +(-110.252 + 51.5208i) q^{77} -17.6990 q^{78} +(12.0542 + 20.8785i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(86.5502 - 49.9698i) q^{82} -111.664i q^{83} +(24.1581 + 2.09377i) q^{84} +(-26.4268 - 45.7726i) q^{86} +(70.5120 + 40.7101i) q^{87} +(-24.5864 + 42.5848i) q^{88} +(-110.770 + 63.9533i) q^{89} +(28.9773 - 41.4556i) q^{91} -80.2029 q^{92} +(34.9025 + 60.4529i) q^{93} +(40.9658 + 23.6516i) q^{94} +(8.48528 - 4.89898i) q^{96} +7.48256i q^{97} +(-44.4565 + 53.1566i) q^{98} +52.1556 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

Related objects

Downloads

Learn more