LMFDB - Embedded newform 1050.3.p.f.901.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1050.451");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 56 x^{10} + 300 x^{9} + 1007 x^{8} + 12456 x^{7} + 209990 x^{6} - 250384 x^{5} + \cdots + 6882692292 $ x^12 - 4x^11 + 56x^10 + 300x^9 + 1007x^8 + 12456x^7 + 209990x^6 - 250384x^5 + 4799806x^4 + 51487320x^3 - 123648876x^2 + 379489320*x + 6882692292
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.3
Root			$4.40732 - 3.68164i$ of defining polynomial
Character	$\chi$	$=$	1050.901
Dual form			1050.3.p.f.451.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(6.59916 - 2.33475i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(6.59916 - 2.33475i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(4.09284 + 7.08900i) q^{11} +(-3.00000 - 1.73205i) q^{12} +22.1215i q^{13} +(-1.80684 + 9.73321i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-22.2401 + 12.8403i) q^{17} +(2.12132 + 3.67423i) q^{18} +(-4.69318 - 2.70961i) q^{19} +(7.87679 - 9.21717i) q^{21} -11.5763 q^{22} +(0.965431 - 1.67218i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-27.0932 - 15.6423i) q^{26} -5.19615i q^{27} +(-10.6431 - 9.09533i) q^{28} +11.5763 q^{29} +(-52.5810 + 30.3576i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(12.2785 + 7.08900i) q^{33} -36.3179i q^{34} -6.00000 q^{36} +(30.9809 - 53.6605i) q^{37} +(6.63716 - 3.83197i) q^{38} +(19.1578 + 33.1823i) q^{39} +78.1950i q^{41} +(5.71895 + 16.1646i) q^{42} +52.6407 q^{43} +(8.18568 - 14.1780i) q^{44} +(1.36533 + 2.36481i) q^{46} +(23.5689 + 13.6075i) q^{47} +6.92820i q^{48} +(38.0979 - 30.8148i) q^{49} +(-22.2401 + 38.5210i) q^{51} +(38.3156 - 22.1215i) q^{52} +(-5.68256 - 9.84247i) q^{53} +(6.36396 + 3.67423i) q^{54} +(18.6652 - 6.60367i) q^{56} -9.38637 q^{57} +(-8.18568 + 14.1780i) q^{58} +(-59.0395 + 34.0865i) q^{59} +(77.6783 + 44.8476i) q^{61} -85.8644i q^{62} +(3.83288 - 20.6473i) q^{63} +8.00000 q^{64} +(-17.3644 + 10.0254i) q^{66} +(24.8169 + 42.9841i) q^{67} +(44.4802 + 25.6807i) q^{68} -3.34435i q^{69} -108.461 q^{71} +(4.24264 - 7.34847i) q^{72} +(-11.2023 + 6.46763i) q^{73} +(43.8136 + 75.8874i) q^{74} +10.8384i q^{76} +(43.5604 + 37.2257i) q^{77} -54.1864 q^{78} +(-29.6096 + 51.2854i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-95.7689 - 55.2922i) q^{82} +52.9289i q^{83} +(-23.8414 - 4.42583i) q^{84} +(-37.2226 + 64.4714i) q^{86} +(17.3644 - 10.0254i) q^{87} +(11.5763 + 20.0507i) q^{88} +(34.4210 + 19.8730i) q^{89} +(51.6482 + 145.983i) q^{91} -3.86172 q^{92} +(-52.5810 + 91.0729i) q^{93} +(-33.3315 + 19.2439i) q^{94} +(-8.48528 - 4.89898i) q^{96} -70.3576i q^{97} +(10.8010 + 68.4495i) q^{98} +24.5570 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 18 q^{3} - 12 q^{4} + 8 q^{7} + 18 q^{9}+O(q^{10}) $ 12 * q + 18 * q^3 - 12 * q^4 + 8 * q^7 + 18 * q^9	$ 12 q + 18 q^{3} - 12 q^{4} + 8 q^{7} + 18 q^{9} - 4 q^{11} - 36 q^{12} + 8 q^{14} - 24 q^{16} - 24 q^{17} + 12 q^{19} + 18 q^{21} + 24 q^{22} - 60 q^{23} - 24 q^{26} + 4 q^{28} - 24 q^{29} - 198 q^{31} - 12 q^{33} - 72 q^{36} + 70 q^{37} - 60 q^{38} - 36 q^{39} + 36 q^{42} - 84 q^{43} - 8 q^{44} + 32 q^{46} - 60 q^{47} + 28 q^{49} - 24 q^{51} - 72 q^{52} + 44 q^{53} + 40 q^{56} + 24 q^{57} + 8 q^{58} - 48 q^{59} + 186 q^{61} + 30 q^{63} + 96 q^{64} + 36 q^{66} + 152 q^{67} + 48 q^{68} - 136 q^{71} + 18 q^{73} - 64 q^{74} + 132 q^{77} - 48 q^{78} - 70 q^{79} - 54 q^{81} - 84 q^{82} - 12 q^{84} - 208 q^{86} - 36 q^{87} - 24 q^{88} + 168 q^{89} + 292 q^{91} + 240 q^{92} - 198 q^{93} - 204 q^{94} + 48 q^{98} - 24 q^{99}+O(q^{100}) $ 12 * q + 18 * q^3 - 12 * q^4 + 8 * q^7 + 18 * q^9 - 4 * q^11 - 36 * q^12 + 8 * q^14 - 24 * q^16 - 24 * q^17 + 12 * q^19 + 18 * q^21 + 24 * q^22 - 60 * q^23 - 24 * q^26 + 4 * q^28 - 24 * q^29 - 198 * q^31 - 12 * q^33 - 72 * q^36 + 70 * q^37 - 60 * q^38 - 36 * q^39 + 36 * q^42 - 84 * q^43 - 8 * q^44 + 32 * q^46 - 60 * q^47 + 28 * q^49 - 24 * q^51 - 72 * q^52 + 44 * q^53 + 40 * q^56 + 24 * q^57 + 8 * q^58 - 48 * q^59 + 186 * q^61 + 30 * q^63 + 96 * q^64 + 36 * q^66 + 152 * q^67 + 48 * q^68 - 136 * q^71 + 18 * q^73 - 64 * q^74 + 132 * q^77 - 48 * q^78 - 70 * q^79 - 54 * q^81 - 84 * q^82 - 12 * q^84 - 208 * q^86 - 36 * q^87 - 24 * q^88 + 168 * q^89 + 292 * q^91 + 240 * q^92 - 198 * q^93 - 204 * q^94 + 48 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$			2.44949i			0.408248i
$7$	6.59916	−	2.33475i	0.942737	−	0.333536i
$7$	6.59916	−	2.33475i	0.942737	−	0.333536i
$8$	2.82843			0.353553
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	4.09284	+	7.08900i	0.372076	+	0.644455i	0.989885	−	0.141874i	$-0.0453127\pi$
$11$	4.09284	+	7.08900i	0.372076	+	0.644455i	−0.617809	+	0.786329i	$0.711979\pi$
$12$	−3.00000	−	1.73205i	−0.250000	−	0.144338i
$13$			22.1215i			1.70165i	0.525446	+	0.850827i	$0.323899\pi$
$13$			22.1215i			1.70165i	−0.525446	+	0.850827i	$0.676101\pi$
$14$	−1.80684	+	9.73321i	−0.129060	+	0.695229i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−22.2401	+	12.8403i	−1.30824	+	0.755314i	−0.981803	−	0.189905i	$-0.939182\pi$
$17$	−22.2401	+	12.8403i	−1.30824	+	0.755314i	−0.326439	+	0.945218i	$0.605849\pi$
$18$	2.12132	+	3.67423i	0.117851	+	0.204124i
$19$	−4.69318	−	2.70961i	−0.247010	−	0.142611i	0.371385	−	0.928479i	$-0.378883\pi$
$19$	−4.69318	−	2.70961i	−0.247010	−	0.142611i	−0.618394	+	0.785868i	$0.712216\pi$
$20$		0			0
$21$	7.87679	−	9.21717i	0.375085	−	0.438913i
$22$	−11.5763			−0.526195
$23$	0.965431	−	1.67218i	0.0419753	−	0.0727033i	−0.844274	−	0.535911i	$-0.819968\pi$
$23$	0.965431	−	1.67218i	0.0419753	−	0.0727033i	0.886250	+	0.463208i	$0.153302\pi$
$24$	4.24264	−	2.44949i	0.176777	−	0.102062i
$25$		0			0
$26$	−27.0932	−	15.6423i	−1.04205	−	0.601626i
$27$		−	5.19615i		−	0.192450i
$28$	−10.6431	−	9.09533i	−0.380110	−	0.324833i
$29$	11.5763			0.399183			0.199591	−	0.979879i	$-0.436039\pi$
$29$	11.5763			0.399183			0.199591	+	0.979879i	$0.436039\pi$
$30$		0			0
$31$	−52.5810	+	30.3576i	−1.69616	+	0.979278i	−0.746821	+	0.665025i	$0.768421\pi$
$31$	−52.5810	+	30.3576i	−1.69616	+	0.979278i	−0.949339	+	0.314253i	$0.898246\pi$
$32$	−2.82843	−	4.89898i	−0.0883883	−	0.153093i
$33$	12.2785	+	7.08900i	0.372076	+	0.214818i
$34$		−	36.3179i		−	1.06817i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	30.9809	−	53.6605i	0.837322	−	1.45028i	−0.0548034	−	0.998497i	$-0.517453\pi$
$37$	30.9809	−	53.6605i	0.837322	−	1.45028i	0.892126	−	0.451787i	$-0.149213\pi$
$38$	6.63716	−	3.83197i	0.174662	−	0.100841i
$39$	19.1578	+	33.1823i	0.491225	+	0.850827i
$40$		0			0
$41$			78.1950i			1.90719i	0.301085	+	0.953597i	$0.402651\pi$
$41$			78.1950i			1.90719i	−0.301085	+	0.953597i	$0.597349\pi$
$42$	5.71895	+	16.1646i	0.136165	+	0.384871i
$43$	52.6407			1.22420			0.612101	−	0.790779i	$-0.290325\pi$
$43$	52.6407			1.22420			0.612101	+	0.790779i	$0.290325\pi$
$44$	8.18568	−	14.1780i	0.186038	−	0.322227i
$45$		0			0
$46$	1.36533	+	2.36481i	0.0296810	+	0.0514090i
$47$	23.5689	+	13.6075i	0.501466	+	0.289522i	0.729319	−	0.684174i	$-0.239837\pi$
$47$	23.5689	+	13.6075i	0.501466	+	0.289522i	−0.227853	+	0.973696i	$0.573170\pi$
$48$			6.92820i			0.144338i
$49$	38.0979	−	30.8148i	0.777508	−	0.628873i
$50$		0			0
$51$	−22.2401	+	38.5210i	−0.436080	+	0.755314i
$52$	38.3156	−	22.1215i	0.736838	−	0.425414i
$53$	−5.68256	−	9.84247i	−0.107218	−	0.185707i	0.807424	−	0.589971i	$-0.200861\pi$
$53$	−5.68256	−	9.84247i	−0.107218	−	0.185707i	−0.914642	+	0.404264i	$0.867528\pi$
$54$	6.36396	+	3.67423i	0.117851	+	0.0680414i
$55$		0			0
$56$	18.6652	−	6.60367i	0.333308	−	0.117923i
$57$	−9.38637			−0.164673
$58$	−8.18568	+	14.1780i	−0.141132	+	0.244448i
$59$	−59.0395	+	34.0865i	−1.00067	+	0.577737i	−0.908446	−	0.418002i	$-0.862731\pi$
$59$	−59.0395	+	34.0865i	−1.00067	+	0.577737i	−0.0922232	+	0.995738i	$0.529397\pi$
$60$		0			0
$61$	77.6783	+	44.8476i	1.27342	+	0.735207i	0.975629	−	0.219426i	$-0.0704184\pi$
$61$	77.6783	+	44.8476i	1.27342	+	0.735207i	0.297786	+	0.954633i	$0.403752\pi$
$62$		−	85.8644i		−	1.38491i
$63$	3.83288	−	20.6473i	0.0608394	−	0.327734i
$64$	8.00000			0.125000
$65$		0			0
$66$	−17.3644	+	10.0254i	−0.263098	+	0.151899i
$67$	24.8169	+	42.9841i	0.370401	+	0.641554i	0.989627	−	0.143659i	$-0.0458869\pi$
$67$	24.8169	+	42.9841i	0.370401	+	0.641554i	−0.619226	+	0.785213i	$0.712554\pi$
$68$	44.4802	+	25.6807i	0.654121	+	0.377657i
$69$		−	3.34435i		−	0.0484689i
$70$		0			0
$71$	−108.461			−1.52762			−0.763808	−	0.645444i	$-0.776672\pi$
$71$	−108.461			−1.52762			−0.763808	+	0.645444i	$0.776672\pi$
$72$	4.24264	−	7.34847i	0.0589256	−	0.102062i
$73$	−11.2023	+	6.46763i	−0.153456	+	0.0885977i	−0.574762	−	0.818321i	$-0.694905\pi$
$73$	−11.2023	+	6.46763i	−0.153456	+	0.0885977i	0.421306	+	0.906919i	$0.361572\pi$
$74$	43.8136	+	75.8874i	0.592076	+	1.02551i
$75$		0			0
$76$			10.8384i			0.142611i
$77$	43.5604	+	37.2257i	0.565719	+	0.483451i
$78$	−54.1864			−0.694697
$79$	−29.6096	+	51.2854i	−0.374805	+	0.649182i	−0.990298	−	0.138961i	$-0.955624\pi$
$79$	−29.6096	+	51.2854i	−0.374805	+	0.649182i	0.615492	+	0.788143i	$0.288957\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	−95.7689	−	55.2922i	−1.16791	−	0.674295i
$83$			52.9289i			0.637697i	0.947806	+	0.318849i	$0.103296\pi$
$83$			52.9289i			0.637697i	−0.947806	+	0.318849i	$0.896704\pi$
$84$	−23.8414	−	4.42583i	−0.283826	−	0.0526885i
$85$		0			0
$86$	−37.2226	+	64.4714i	−0.432821	+	0.749668i
$87$	17.3644	−	10.0254i	0.199591	−	0.115234i
$88$	11.5763	+	20.0507i	0.131549	+	0.227849i
$89$	34.4210	+	19.8730i	0.386753	+	0.223292i	0.680752	−	0.732514i	$-0.261653\pi$
$89$	34.4210	+	19.8730i	0.386753	+	0.223292i	−0.293999	+	0.955806i	$0.594986\pi$
$90$		0			0
$91$	51.6482	+	145.983i	0.567563	+	1.60421i
$92$	−3.86172			−0.0419753
$93$	−52.5810	+	91.0729i	−0.565387	+	0.979278i
$94$	−33.3315	+	19.2439i	−0.354590	+	0.204723i
$95$		0			0
$96$	−8.48528	−	4.89898i	−0.0883883	−	0.0510310i
$97$		−	70.3576i		−	0.725336i	−0.931918	−	0.362668i	$-0.881866\pi$
$97$		−	70.3576i		−	0.725336i	0.931918	−	0.362668i	$-0.118134\pi$
$98$	10.8010	+	68.4495i	0.110214	+	0.698465i
$99$	24.5570			0.248051
$100$		0			0
$101$	−25.7576	+	14.8712i	−0.255026	+	0.147239i	−0.622063	−	0.782967i	$-0.713705\pi$
$101$	−25.7576	+	14.8712i	−0.255026	+	0.147239i	0.367037	+	0.930206i	$0.380372\pi$
$102$	−31.4523	−	54.4769i	−0.308355	−	0.534087i
$103$	−94.2236	−	54.4000i	−0.914792	−	0.528155i	−0.0328221	−	0.999461i	$-0.510449\pi$
$103$	−94.2236	−	54.4000i	−0.914792	−	0.528155i	−0.881970	+	0.471306i	$0.843783\pi$
$104$			62.5691i			0.601626i
$105$		0			0
$106$	16.0727			0.151629
$107$	31.6569	−	54.8314i	0.295859	−	0.512443i	−0.679325	−	0.733837i	$-0.737727\pi$
$107$	31.6569	−	54.8314i	0.295859	−	0.512443i	0.975184	+	0.221394i	$0.0710607\pi$
$108$	−9.00000	+	5.19615i	−0.0833333	+	0.0481125i
$109$	−34.9990	−	60.6200i	−0.321091	−	0.556147i	0.659622	−	0.751597i	$-0.270716\pi$
$109$	−34.9990	−	60.6200i	−0.321091	−	0.556147i	−0.980714	+	0.195451i	$0.937383\pi$
$110$		0			0
$111$		−	107.321i		−	0.966856i
$112$	−5.11051	+	27.5297i	−0.0456296	+	0.245801i
$113$	86.5407			0.765847			0.382923	−	0.923780i	$-0.374917\pi$
$113$	86.5407			0.765847			0.382923	+	0.923780i	$0.374917\pi$
$114$	6.63716	−	11.4959i	0.0582207	−	0.100841i
$115$		0			0
$116$	−11.5763	−	20.0507i	−0.0997957	−	0.172851i
$117$	57.4734	+	33.1823i	0.491225	+	0.283609i
$118$		−	96.4111i		−	0.817043i
$119$	−116.787	+	136.661i	−0.981404	+	1.14841i
$120$		0			0
$121$	26.9973	−	46.7608i	0.223119	−	0.386453i
$122$	−109.854	+	63.4241i	−0.900441	+	0.519870i
$123$	67.7188	+	117.292i	0.550560	+	0.953597i
$124$	105.162	+	60.7153i	0.848080	+	0.489639i
$125$		0			0
$126$	22.5774	+	19.2941i	0.179185	+	0.153128i
$127$	174.800			1.37638			0.688188	−	0.725532i	$-0.258406\pi$
$127$	174.800			1.37638			0.688188	+	0.725532i	$0.258406\pi$
$128$	−5.65685	+	9.79796i	−0.0441942	+	0.0765466i
$129$	78.9611	−	45.5882i	0.612101	−	0.353397i
$130$		0			0
$131$	188.722	+	108.959i	1.44063	+	0.831747i	0.997891	−	0.0649046i	$-0.0206743\pi$
$131$	188.722	+	108.959i	1.44063	+	0.831747i	0.442737	+	0.896652i	$0.354008\pi$
$132$		−	28.3560i		−	0.214818i
$133$	−37.2973	−	6.92375i	−0.280431	−	0.0520582i
$134$	−70.1927			−0.523826
$135$		0			0
$136$	−62.9045	+	36.3179i	−0.462533	+	0.267044i
$137$	−21.1849	−	36.6933i	−0.154634	−	0.267834i	0.778291	−	0.627903i	$-0.216087\pi$
$137$	−21.1849	−	36.6933i	−0.154634	−	0.267834i	−0.932926	+	0.360069i	$0.882753\pi$
$138$	4.09598	+	2.36481i	0.0296810	+	0.0171363i
$139$		−	113.408i		−	0.815887i	−0.913007	−	0.407943i	$-0.866246\pi$
$139$		−	113.408i		−	0.815887i	0.913007	−	0.407943i	$-0.133754\pi$
$140$		0			0
$141$	47.1378			0.334311
$142$	76.6933	−	132.837i	0.540094	−	0.935470i
$143$	−156.819	+	90.5398i	−1.09664	+	0.633145i
$144$	6.00000	+	10.3923i	0.0416667	+	0.0721688i
$145$		0			0
$146$		−	18.2932i		−	0.125296i
$147$	30.4604	−	79.2159i	0.207214	−	0.538884i
$148$	−123.924			−0.837322
$149$	−113.169	+	196.014i	−0.759520	+	1.31553i	0.183575	+	0.983006i	$0.441233\pi$
$149$	−113.169	+	196.014i	−0.759520	+	1.31553i	−0.943095	+	0.332522i	$0.892100\pi$
$150$		0			0
$151$	100.994	+	174.927i	0.668837	+	1.15846i	0.978230	+	0.207525i	$0.0665408\pi$
$151$	100.994	+	174.927i	0.668837	+	1.15846i	−0.309393	+	0.950934i	$0.600126\pi$
$152$	−13.2743	−	7.66394i	−0.0873311	−	0.0504206i
$153$			77.0420i			0.503542i
$154$	−76.3939	+	27.0278i	−0.496064	+	0.175505i
$155$		0			0
$156$	38.3156	−	66.3645i	0.245613	−	0.425414i
$157$	40.7193	−	23.5093i	0.259359	−	0.149741i	−0.364683	−	0.931132i	$-0.618823\pi$
$157$	40.7193	−	23.5093i	0.259359	−	0.149741i	0.624042	+	0.781391i	$0.285489\pi$
$158$	−41.8743	−	72.5285i	−0.265027	−	0.459041i
$159$	−17.0477	−	9.84247i	−0.107218	−	0.0619024i
$160$		0			0
$161$	2.46692	−	13.2890i	0.0153225	−	0.0825404i
$162$	12.7279			0.0785674
$163$	−10.2177	+	17.6975i	−0.0626852	+	0.108574i	−0.895665	−	0.444730i	$-0.853300\pi$
$163$	−10.2177	+	17.6975i	−0.0626852	+	0.108574i	0.832980	+	0.553304i	$0.186633\pi$
$164$	135.438	−	78.1950i	0.825839	−	0.476799i
$165$		0			0
$166$	−64.8244	−	37.4264i	−0.390508	−	0.225460i
$167$			79.0026i			0.473069i	0.971623	+	0.236535i	$0.0760117\pi$
$167$			79.0026i			0.473069i	−0.971623	+	0.236535i	$0.923988\pi$
$168$	22.2789	−	26.0701i	0.132613	−	0.155179i
$169$	−320.361			−1.89563
$170$		0			0
$171$	−14.0796	+	8.12883i	−0.0823366	+	0.0475370i
$172$	−52.6407	−	91.1764i	−0.306051	−	0.530095i
$173$	154.993	+	89.4851i	0.895912	+	0.517255i	0.875872	−	0.482544i	$-0.160287\pi$
$173$	154.993	+	89.4851i	0.895912	+	0.517255i	0.0200403	+	0.999799i	$0.493621\pi$
$174$			28.3560i			0.162966i
$175$		0			0
$176$	−32.7427			−0.186038
$177$	−59.0395	+	102.259i	−0.333556	+	0.577737i
$178$	−48.6787	+	28.1047i	−0.273476	+	0.157891i
$179$	−112.978	−	195.684i	−0.631163	−	1.09321i	−0.987314	−	0.158779i	$-0.949244\pi$
$179$	−112.978	−	195.684i	−0.631163	−	1.09321i	0.356151	−	0.934428i	$-0.384089\pi$
$180$		0			0
$181$			152.776i			0.844066i	0.906580	+	0.422033i	$0.138683\pi$
$181$			152.776i			0.844066i	−0.906580	+	0.422033i	$0.861317\pi$
$182$	−215.313	−	39.9700i	−1.18304	−	0.219615i
$183$	155.357			0.848944
$184$	2.73065	−	4.72963i	0.0148405	−	0.0257045i
$185$		0			0
$186$	−74.3607	−	128.797i	−0.399789	−	0.692454i
$187$	−182.050	−	105.107i	−0.973531	−	0.562068i
$188$		−	54.4301i		−	0.289522i
$189$	−12.1317	−	34.2903i	−0.0641890	−	0.181430i
$190$		0			0
$191$	−101.415	+	175.656i	−0.530967	+	0.919662i	0.468380	+	0.883527i	$0.344838\pi$
$191$	−101.415	+	175.656i	−0.530967	+	0.919662i	−0.999347	+	0.0361351i	$0.988495\pi$
$192$	12.0000	−	6.92820i	0.0625000	−	0.0360844i
$193$	−68.7171	−	119.021i	−0.356047	−	0.616692i	0.631250	−	0.775580i	$-0.282542\pi$
$193$	−68.7171	−	119.021i	−0.356047	−	0.616692i	−0.987297	+	0.158888i	$0.949209\pi$
$194$	86.1701	+	49.7503i	0.444176	+	0.256445i
$195$		0			0
$196$	−91.4707	−	35.1727i	−0.466687	−	0.179452i
$197$	108.408			0.550293			0.275147	−	0.961402i	$-0.411274\pi$
$197$	108.408			0.550293			0.275147	+	0.961402i	$0.411274\pi$
$198$	−17.3644	+	30.0761i	−0.0876992	+	0.151899i
$199$	228.371	−	131.850i	1.14759	−	0.662562i	0.199293	−	0.979940i	$-0.436136\pi$
$199$	228.371	−	131.850i	1.14759	−	0.662562i	0.948299	+	0.317378i	$0.102802\pi$
$200$		0			0
$201$	74.4506	+	42.9841i	0.370401	+	0.213851i
$202$		−	42.0620i		−	0.208228i
$203$	76.3939	−	27.0278i	0.376324	−	0.133142i
$204$	88.9604			0.436080
$205$		0			0
$206$	133.252	−	76.9332i	0.646856	−	0.373462i
$207$	−2.89629	−	5.01653i	−0.0139918	−	0.0242344i
$208$	−76.6311	−	44.2430i	−0.368419	−	0.212707i
$209$		−	44.3600i		−	0.212249i
$210$		0			0
$211$	−73.7590			−0.349569			−0.174784	−	0.984607i	$-0.555923\pi$
$211$	−73.7590			−0.349569			−0.174784	+	0.984607i	$0.555923\pi$
$212$	−11.3651	+	19.6849i	−0.0536090	+	0.0928535i
$213$	−162.691	+	93.9297i	−0.763808	+	0.440985i
$214$	44.7697	+	77.5434i	0.209204	+	0.362352i
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	−276.113	+	323.098i	−1.27241	+	1.48893i
$218$	98.9920			0.454092
$219$	−11.2023	+	19.4029i	−0.0511519	+	0.0885977i
$220$		0			0
$221$	−284.047	−	491.985i	−1.28528	−	2.22617i
$222$	131.441	+	75.8874i	0.592076	+	0.341835i
$223$		−	301.777i		−	1.35326i	−0.736323	−	0.676630i	$-0.763440\pi$
$223$		−	301.777i		−	1.35326i	0.736323	−	0.676630i	$-0.236560\pi$
$224$	−30.1031	−	25.7255i	−0.134389	−	0.114846i
$225$		0			0
$226$	−61.1935	+	105.990i	−0.270768	+	0.468983i
$227$	−183.031	+	105.673i	−0.806304	+	0.465520i	−0.845671	−	0.533705i	$-0.820799\pi$
$227$	−183.031	+	105.673i	−0.806304	+	0.465520i	0.0393668	+	0.999225i	$0.487466\pi$
$228$	9.38637	+	16.2577i	0.0411683	+	0.0713055i
$229$	−20.8073	−	12.0131i	−0.0908618	−	0.0524591i	0.453881	−	0.891062i	$-0.350039\pi$
$229$	−20.8073	−	12.0131i	−0.0908618	−	0.0524591i	−0.544742	+	0.838603i	$0.683373\pi$
$230$		0			0
$231$	97.5790	+	18.1142i	0.422420	+	0.0784165i
$232$	32.7427			0.141132
$233$	−206.808	+	358.202i	−0.887587	+	1.53735i	−0.0448680	+	0.998993i	$0.514287\pi$
$233$	−206.808	+	358.202i	−0.887587	+	1.53735i	−0.842719	+	0.538353i	$0.819047\pi$
$234$	−81.2796	+	46.9268i	−0.347349	+	0.200542i
$235$		0			0
$236$	118.079	+	68.1729i	0.500335	+	0.288868i
$237$			102.571i			0.432788i
$238$	−84.7933	−	239.668i	−0.356275	−	1.00701i
$239$	−191.139			−0.799743			−0.399872	−	0.916571i	$-0.630945\pi$
$239$	−191.139			−0.799743			−0.399872	+	0.916571i	$0.630945\pi$
$240$		0			0
$241$	90.5397	−	52.2731i	0.375683	−	0.216901i	−0.300255	−	0.953859i	$-0.597072\pi$
$241$	90.5397	−	52.2731i	0.375683	−	0.216901i	0.675938	+	0.736958i	$0.263739\pi$
$242$	38.1800	+	66.1297i	0.157769	+	0.273263i
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$		−	179.390i		−	0.735207i
$245$		0			0
$246$	−191.538			−0.778609
$247$	59.9407	−	103.820i	0.242675	−	0.420325i
$248$	−148.721	+	85.8644i	−0.599683	+	0.346227i
$249$	45.8377	+	79.3933i	0.184087	+	0.318849i
$250$		0			0
$251$		−	215.816i		−	0.859824i	−0.902871	−	0.429912i	$-0.858545\pi$
$251$		−	215.816i		−	0.859824i	0.902871	−	0.429912i	$-0.141455\pi$
$252$	−39.5950	+	14.0085i	−0.157123	+	0.0555893i
$253$	15.8054			0.0624720
$254$	−123.602	+	214.085i	−0.486623	+	0.842855i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	435.301	+	251.321i	1.69378	+	0.977903i	0.951418	+	0.307902i	$0.0996270\pi$
$257$	435.301	+	251.321i	1.69378	+	0.977903i	0.742360	+	0.670001i	$0.233706\pi$
$258$			128.943i			0.499779i
$259$	79.1642	−	426.447i	0.305653	−	1.64651i
$260$		0			0
$261$	17.3644	−	30.0761i	0.0665304	−	0.115234i
$262$	−266.894	+	154.091i	−1.01868	+	0.588134i
$263$	−17.2083	−	29.8056i	−0.0654307	−	0.113329i	0.831454	−	0.555593i	$-0.187509\pi$
$263$	−17.2083	−	29.8056i	−0.0654307	−	0.113329i	−0.896885	+	0.442264i	$0.854175\pi$
$264$	34.7289	+	20.0507i	0.131549	+	0.0759497i
$265$		0			0
$266$	34.8530	−	40.7839i	0.131026	−	0.153323i
$267$	68.8421			0.257836
$268$	49.6337	−	85.9682i	0.185201	−	0.320777i
$269$	104.576	−	60.3768i	0.388757	−	0.224449i	−0.292864	−	0.956154i	$-0.594608\pi$
$269$	104.576	−	60.3768i	0.388757	−	0.224449i	0.681621	+	0.731705i	$0.261275\pi$
$270$		0			0
$271$	266.259	+	153.725i	0.982504	+	0.567249i	0.903025	−	0.429587i	$-0.141341\pi$
$271$	266.259	+	153.725i	0.982504	+	0.567249i	0.0794792	+	0.996837i	$0.474674\pi$
$272$		−	102.723i		−	0.377657i
$273$	203.898	+	174.246i	0.746878	+	0.638265i
$274$	59.9199			0.218686
$275$		0			0
$276$	−5.79259	+	3.34435i	−0.0209876	+	0.0121172i
$277$	15.3888	+	26.6542i	0.0555552	+	0.0962244i	0.892466	−	0.451116i	$-0.148974\pi$
$277$	15.3888	+	26.6542i	0.0555552	+	0.0962244i	−0.836910	+	0.547340i	$0.815640\pi$
$278$	138.896	+	80.1918i	0.499627	+	0.288460i
$279$			182.146i			0.652852i
$280$		0			0
$281$	355.411			1.26481			0.632404	−	0.774638i	$-0.282068\pi$
$281$	355.411			1.26481			0.632404	+	0.774638i	$0.282068\pi$
$282$	−33.3315	+	57.7318i	−0.118197	+	0.204723i
$283$	31.1096	−	17.9611i	0.109928	−	0.0634669i	−0.444028	−	0.896013i	$-0.646451\pi$
$283$	31.1096	−	17.9611i	0.109928	−	0.0634669i	0.553956	+	0.832546i	$0.313118\pi$
$284$	108.461	+	187.859i	0.381904	+	0.661477i
$285$		0			0
$286$		−	256.085i		−	0.895402i
$287$	182.566	+	516.021i	0.636118	+	1.79798i
$288$	−16.9706			−0.0589256
$289$	185.248	−	320.859i	0.640997	−	1.11024i
$290$		0			0
$291$	−60.9315	−	105.536i	−0.209387	−	0.362668i
$292$	22.4045	+	12.9353i	0.0767278	+	0.0442988i
$293$		−	300.389i		−	1.02522i	−0.858622	−	0.512610i	$-0.828679\pi$
$293$		−	300.389i		−	1.02522i	0.858622	−	0.512610i	$-0.171321\pi$
$294$	75.4805	+	93.3204i	0.256736	+	0.317416i
$295$		0			0
$296$	87.6273	−	151.775i	0.296038	−	0.512753i
$297$	36.8355	−	21.2670i	0.124025	−	0.0716061i
$298$	−160.044	−	277.205i	−0.537062	−	0.930219i
$299$	36.9910	+	21.3568i	0.123716	+	0.0714274i
$300$		0			0
$301$	347.385	−	122.903i	1.15410	−	0.408315i
$302$	−285.655			−0.945878
$303$	−25.7576	+	44.6135i	−0.0850087	+	0.147239i
$304$	18.7727	−	10.8384i	0.0617524	−	0.0356528i
$305$		0			0
$306$	−94.3568	−	54.4769i	−0.308355	−	0.178029i
$307$		−	380.037i		−	1.23791i	−0.785428	−	0.618953i	$-0.787557\pi$
$307$		−	380.037i		−	1.23791i	0.785428	−	0.618953i	$-0.212443\pi$
$308$	20.9165	−	112.674i	0.0679107	−	0.365826i
$309$	−188.447			−0.609861
$310$		0			0
$311$	−373.982	+	215.918i	−1.20251	+	0.694271i	−0.961113	−	0.276155i	$-0.910940\pi$
$311$	−373.982	+	215.918i	−1.20251	+	0.694271i	−0.241400	+	0.970426i	$0.577607\pi$
$312$	54.1864	+	93.8536i	0.173674	+	0.300813i
$313$	54.7703	+	31.6216i	0.174985	+	0.101028i	0.584934	−	0.811081i	$-0.301120\pi$
$313$	54.7703	+	31.6216i	0.174985	+	0.101028i	−0.409949	+	0.912108i	$0.634454\pi$
$314$			66.4944i			0.211766i
$315$		0			0
$316$	118.439			0.374805
$317$	26.2573	−	45.4790i	0.0828307	−	0.143467i	−0.821634	−	0.570015i	$-0.806937\pi$
$317$	26.2573	−	45.4790i	0.0828307	−	0.143467i	0.904465	+	0.426548i	$0.140271\pi$
$318$	24.1090	−	13.9194i	0.0758146	−	0.0437716i
$319$	47.3799	+	82.0644i	0.148526	+	0.257255i
$320$		0			0
$321$		−	109.663i		−	0.341629i
$322$	14.5313	+	12.4181i	0.0451281	+	0.0385655i
$323$	139.169			0.430864
$324$	−9.00000	+	15.5885i	−0.0277778	+	0.0481125i
$325$		0			0
$326$	−14.4500	−	25.0281i	−0.0443251	−	0.0767733i
$327$	−104.997	−	60.6200i	−0.321091	−	0.185382i
$328$			221.169i			0.674295i
$329$	187.305	+	34.7707i	0.569317	+	0.105686i
$330$		0			0
$331$	91.8214	−	159.039i	0.277406	−	0.480481i	−0.693333	−	0.720617i	$-0.743859\pi$
$331$	91.8214	−	159.039i	0.277406	−	0.480481i	0.970739	+	0.240136i	$0.0771919\pi$
$332$	91.6755	−	52.9289i	0.276131	−	0.159424i
$333$	−92.9428	−	160.982i	−0.279107	−	0.483428i
$334$	−96.7580	−	55.8633i	−0.289695	−	0.167255i
$335$		0			0
$336$	16.1756	+	45.7203i	0.0481417	+	0.136072i
$337$	−86.1749			−0.255712			−0.127856	−	0.991793i	$-0.540810\pi$
$337$	−86.1749			−0.255712			−0.127856	+	0.991793i	$0.540810\pi$
$338$	226.529	−	392.361i	0.670206	−	1.16083i
$339$	129.811	−	74.9464i	0.382923	−	0.221081i
$340$		0			0
$341$	−430.411	−	248.498i	−1.26220	−	0.728733i
$342$		−	22.9918i		−	0.0672275i
$343$	179.469	−	292.301i	0.523234	−	0.852189i
$344$	148.890			0.432821
$345$		0			0
$346$	−219.193	+	126.551i	−0.633505	+	0.365755i
$347$	33.1462	+	57.4109i	0.0955221	+	0.165449i	0.909826	−	0.414989i	$-0.136215\pi$
$347$	33.1462	+	57.4109i	0.0955221	+	0.165449i	−0.814304	+	0.580438i	$0.802881\pi$
$348$	−34.7289	−	20.0507i	−0.0997957	−	0.0576170i
$349$		−	331.791i		−	0.950689i	−0.879800	−	0.475345i	$-0.842323\pi$
$349$		−	331.791i		−	0.950689i	0.879800	−	0.475345i	$-0.157677\pi$
$350$		0			0
$351$	114.947			0.327484
$352$	23.1526	−	40.1015i	0.0657744	−	0.113925i
$353$	577.040	−	333.154i	1.63467	−	0.943780i	0.652049	−	0.758177i	$-0.273910\pi$
$353$	577.040	−	333.154i	1.63467	−	0.943780i	0.982625	−	0.185603i	$-0.0594238\pi$
$354$	−83.4945	−	144.617i	−0.235860	−	0.408522i
$355$		0			0
$356$		−	79.4920i		−	0.223292i
$357$	−56.8291	+	306.131i	−0.159185	+	0.857511i
$358$	319.551			0.892600
$359$	139.714	−	241.992i	0.389175	−	0.674072i	−0.603163	−	0.797618i	$-0.706093\pi$
$359$	139.714	−	241.992i	0.389175	−	0.674072i	0.992339	+	0.123546i	$0.0394267\pi$
$360$		0			0
$361$	−165.816	−	287.202i	−0.459324	−	0.795573i
$362$	−187.112	−	108.029i	−0.516883	−	0.298422i
$363$		−	93.5215i		−	0.257635i
$364$	201.202	−	235.441i	0.552754	−	0.646815i
$365$		0			0
$366$	−109.854	+	190.272i	−0.300147	+	0.519870i
$367$	−168.793	+	97.4526i	−0.459926	+	0.265538i	−0.712013	−	0.702166i	$-0.752216\pi$
$367$	−168.793	+	97.4526i	−0.459926	+	0.265538i	0.252087	+	0.967705i	$0.418883\pi$
$368$	3.86172	+	6.68870i	0.0104938	+	0.0181758i
$369$	203.157	+	117.292i	0.550560	+	0.317866i
$370$		0			0
$371$	−60.4798	−	51.6847i	−0.163018	−	0.139312i
$372$	210.324			0.565387
$373$	229.107	−	396.825i	0.614228	−	1.06387i	−0.376292	−	0.926501i	$-0.622801\pi$
$373$	229.107	−	396.825i	0.614228	−	1.06387i	0.990520	−	0.137372i	$-0.0438656\pi$
$374$	257.458	−	148.643i	0.688390	−	0.397442i
$375$		0			0
$376$	66.6629	+	38.4879i	0.177295	+	0.102361i
$377$			256.085i			0.679271i
$378$	50.5752	+	9.38861i	0.133797	+	0.0248376i
$379$	−227.464			−0.600170			−0.300085	−	0.953913i	$-0.597015\pi$
$379$	−227.464			−0.600170			−0.300085	+	0.953913i	$0.597015\pi$
$380$		0			0
$381$	262.200	−	151.381i	0.688188	−	0.397326i
$382$	−143.422	−	248.414i	−0.375451	−	0.650300i
$383$	69.3798	+	40.0564i	0.181148	+	0.104586i	0.587832	−	0.808983i	$-0.299982\pi$
$383$	69.3798	+	40.0564i	0.181148	+	0.104586i	−0.406684	+	0.913569i	$0.633315\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	194.361			0.503527
$387$	78.9611	−	136.765i	0.204034	−	0.353397i
$388$	−121.863	+	70.3576i	−0.314080	+	0.181334i
$389$	379.480	+	657.278i	0.975526	+	1.68966i	0.678187	+	0.734889i	$0.262766\pi$
$389$	379.480	+	657.278i	0.975526	+	1.68966i	0.297339	+	0.954772i	$0.403901\pi$
$390$		0			0
$391$			49.5858i			0.126818i
$392$	107.757	−	87.1574i	0.274890	−	0.222340i
$393$	377.445			0.960419
$394$	−76.6559	+	132.772i	−0.194558	+	0.336984i
$395$		0			0
$396$	−24.5570	−	42.5340i	−0.0620127	−	0.107409i
$397$	−37.0273	−	21.3777i	−0.0932677	−	0.0538481i	0.452641	−	0.891693i	$-0.350482\pi$
$397$	−37.0273	−	21.3777i	−0.0932677	−	0.0538481i	−0.545908	+	0.837845i	$0.683815\pi$
$398$			372.928i			0.937005i
$399$	−61.9422	+	21.9148i	−0.155243	+	0.0549244i
$400$		0			0
$401$	219.814	−	380.729i	0.548164	−	0.949448i	−0.450236	−	0.892909i	$-0.648660\pi$
$401$	219.814	−	380.729i	0.548164	−	0.949448i	0.998400	−	0.0565387i	$-0.0180064\pi$
$402$	−105.289	+	60.7887i	−0.261913	+	0.151216i
$403$	−671.557	−	1163.17i	−1.66639	−	2.88628i
$404$	51.5153	+	29.7424i	0.127513	+	0.0736197i
$405$		0			0
$406$	−20.9165	+	112.674i	−0.0515185	+	0.277523i
$407$	507.200			1.24619
$408$	−62.9045	+	108.954i	−0.154178	+	0.267044i
$409$	−351.729	+	203.071i	−0.859974	+	0.496506i	−0.864004	−	0.503486i	$-0.832051\pi$
$409$	−351.729	+	203.071i	−0.859974	+	0.496506i	0.00402949	+	0.999992i	$0.498717\pi$
$410$		0			0
$411$	−63.5547	−	36.6933i	−0.154634	−	0.0892782i
$412$			217.600i			0.528155i
$413$	−310.028	+	362.785i	−0.750673	+	0.878413i
$414$	8.19195			0.0197873
$415$		0			0
$416$	108.373	−	62.5691i	0.260512	−	0.150406i
$417$	−98.2145	−	170.112i	−0.235526	−	0.407943i
$418$	54.3297	+	31.3673i	0.129975	+	0.0750413i
$419$		−	574.820i		−	1.37188i	−0.727656	−	0.685942i	$-0.759390\pi$
$419$		−	574.820i		−	1.37188i	0.727656	−	0.685942i	$-0.240610\pi$
$420$		0			0
$421$	−386.856			−0.918898			−0.459449	−	0.888204i	$-0.651953\pi$
$421$	−386.856			−0.918898			−0.459449	+	0.888204i	$0.651953\pi$
$422$	52.1555	−	90.3359i	0.123591	−	0.214066i
$423$	70.7067	−	40.8225i	0.167155	−	0.0965072i
$424$	−16.0727	−	27.8387i	−0.0379073	−	0.0656574i
$425$		0			0
$426$		−	265.673i		−	0.623646i
$427$	617.320	+	114.597i	1.44571	+	0.268377i
$428$	−126.628			−0.295859
$429$	−156.819	+	271.619i	−0.365547	+	0.633145i
$430$		0			0
$431$	−336.320	−	582.524i	−0.780326	−	1.35156i	−0.931752	−	0.363095i	$-0.881720\pi$
$431$	−336.320	−	582.524i	−0.780326	−	1.35156i	0.151426	−	0.988469i	$-0.451613\pi$
$432$	18.0000	+	10.3923i	0.0416667	+	0.0240563i
$433$			61.8825i			0.142916i	0.997444	+	0.0714579i	$0.0227652\pi$
$433$			61.8825i			0.142916i	−0.997444	+	0.0714579i	$0.977235\pi$
$434$	−200.472	−	566.633i	−0.461917	−	1.30561i
$435$		0			0
$436$	−69.9979	+	121.240i	−0.160546	+	0.278073i
$437$	−9.06189	+	5.23189i	−0.0207366	+	0.0119723i
$438$	−15.8424	−	27.4398i	−0.0361699	−	0.0626480i
$439$	−355.198	−	205.074i	−0.809108	−	0.467139i	0.0375381	−	0.999295i	$-0.488048\pi$
$439$	−355.198	−	205.074i	−0.809108	−	0.467139i	−0.846646	+	0.532157i	$0.821382\pi$
$440$		0			0
$441$	−22.9124	−	145.203i	−0.0519555	−	0.329259i
$442$	803.408			1.81766
$443$	−179.903	+	311.601i	−0.406101	+	0.703388i	−0.994449	−	0.105220i	$-0.966445\pi$
$443$	−179.903	+	311.601i	−0.406101	+	0.703388i	0.588348	+	0.808608i	$0.299779\pi$
$444$	−185.886	+	107.321i	−0.418661	+	0.241714i
$445$		0			0
$446$	369.600	+	213.388i	0.828699	+	0.478450i
$447$			392.027i			0.877019i
$448$	52.7933	−	18.6780i	0.117842	−	0.0416920i
$449$	−808.078			−1.79973			−0.899864	−	0.436170i	$-0.856335\pi$
$449$	−808.078			−1.79973			−0.899864	+	0.436170i	$0.856335\pi$
$450$		0			0
$451$	−554.325	+	320.039i	−1.22910	+	0.709622i
$452$	−86.5407	−	149.893i	−0.191462	−	0.331621i
$453$	302.983	+	174.927i	0.668837	+	0.386153i
$454$		−	298.888i		−	0.658344i
$455$		0			0
$456$	−26.5487			−0.0582207
$457$	−72.3734	+	125.354i	−0.158366	+	0.274298i	−0.934280	−	0.356541i	$-0.883956\pi$
$457$	−72.3734	+	125.354i	−0.158366	+	0.274298i	0.775913	+	0.630839i	$0.217289\pi$
$458$	29.4260	−	16.9891i	0.0642490	−	0.0370942i
$459$	66.7203	+	115.563i	0.145360	+	0.251771i
$460$		0			0
$461$		−	235.655i		−	0.511182i	−0.966785	−	0.255591i	$-0.917730\pi$
$461$		−	235.655i		−	0.511182i	0.966785	−	0.255591i	$-0.0822701\pi$
$462$	−91.1841	+	106.701i	−0.197368	+	0.230954i
$463$	373.547			0.806797			0.403398	−	0.915024i	$-0.367829\pi$
$463$	373.547			0.806797			0.403398	+	0.915024i	$0.367829\pi$
$464$	−23.1526	+	40.1015i	−0.0498978	+	0.0864256i
$465$		0			0
$466$	−292.470	−	506.574i	−0.627619	−	1.08707i
$467$	−186.106	−	107.449i	−0.398515	−	0.230083i	0.287328	−	0.957832i	$-0.407233\pi$
$467$	−186.106	−	107.449i	−0.398515	−	0.230083i	−0.685843	+	0.727750i	$0.740566\pi$
$468$		−	132.729i		−	0.283609i
$469$	264.128	+	225.718i	0.563172	+	0.481274i
$470$		0			0
$471$	40.7193	−	70.5279i	0.0864529	−	0.149741i
$472$	−166.989	+	96.4111i	−0.353790	+	0.204261i
$473$	215.450	+	373.170i	0.455497	+	0.788943i
$474$	−125.623	−	72.5285i	−0.265027	−	0.153014i
$475$		0			0
$476$	353.490	+	65.6206i	0.742626	+	0.137858i
$477$	−34.0953			−0.0714787
$478$	135.155	−	234.096i	0.282752	−	0.489741i
$479$	799.882	−	461.812i	1.66990	−	0.964117i	0.702212	−	0.711968i	$-0.252196\pi$
$479$	799.882	−	461.812i	1.66990	−	0.964117i	0.967688	−	0.252149i	$-0.0811373\pi$
$480$		0			0
$481$	1187.05	+	685.345i	2.46788	+	1.42483i
$482$			147.851i			0.306744i
$483$	−7.80823	−	22.0699i	−0.0161661	−	0.0456934i
$484$	−107.989			−0.223119
$485$		0			0
$486$	19.0919	−	11.0227i	0.0392837	−	0.0226805i
$487$	−278.646	−	482.630i	−0.572169	−	0.991026i	−0.996343	−	0.0854452i	$-0.972769\pi$
$487$	−278.646	−	482.630i	−0.572169	−	0.991026i	0.424174	−	0.905581i	$-0.360565\pi$
$488$	219.708	+	126.848i	0.450220	+	0.259935i
$489$			35.3951i			0.0723826i
$490$		0			0
$491$	−5.04505			−0.0102750			−0.00513752	−	0.999987i	$-0.501635\pi$
$491$	−5.04505			−0.0102750			−0.00513752	+	0.999987i	$0.501635\pi$
$492$	135.438	−	234.585i	0.275280	−	0.476799i
$493$	−257.458	+	148.643i	−0.522227	+	0.301508i
$494$	84.7689	+	146.824i	0.171597	+	0.297215i
$495$		0			0
$496$		−	242.861i		−	0.489639i
$497$	−715.750	+	253.229i	−1.44014	+	0.509515i
$498$	−129.649			−0.260339
$499$	−79.8251	+	138.261i	−0.159970	+	0.277076i	−0.934858	−	0.355023i	$-0.884473\pi$
$499$	−79.8251	+	138.261i	−0.159970	+	0.277076i	0.774888	+	0.632099i	$0.217806\pi$
$500$		0			0
$501$	68.4182	+	118.504i	0.136563	+	0.236535i
$502$	264.319	+	152.605i	0.526532	+	0.303994i
$503$		−	515.554i		−	1.02496i	−0.858700	−	0.512479i	$-0.828727\pi$
$503$		−	515.554i		−	1.02496i	0.858700	−	0.512479i	$-0.171273\pi$
$504$	10.8410	−	58.3992i	0.0215100	−	0.115872i
$505$		0			0
$506$	−11.1761	+	19.3576i	−0.0220872	+	0.0382561i
$507$	−480.542	+	277.441i	−0.947814	+	0.547221i
$508$	−174.800	−	302.762i	−0.344094	−	0.595988i
$509$	−125.864	−	72.6674i	−0.247276	−	0.142765i	0.371240	−	0.928537i	$-0.378933\pi$
$509$	−125.864	−	72.6674i	−0.247276	−	0.142765i	−0.618516	+	0.785772i	$0.712266\pi$
$510$		0			0
$511$	−58.8253	+	68.8354i	−0.115118	+	0.134707i
$512$	22.6274			0.0441942
$513$	−14.0796	+	24.3865i	−0.0274455	+	0.0475370i
$514$	−615.609	+	355.422i	−1.19768	+	0.691482i
$515$		0			0
$516$	−157.922	−	91.1764i	−0.306051	−	0.176698i
$517$			222.773i			0.430896i
$518$	466.312	+	398.500i	0.900215	+	0.769304i
$519$	309.986			0.597275
$520$		0			0
$521$	−81.2178	+	46.8911i	−0.155888	+	0.0900021i	−0.575915	−	0.817510i	$-0.695354\pi$
$521$	−81.2178	+	46.8911i	−0.155888	+	0.0900021i	0.420027	+	0.907512i	$0.362021\pi$
$522$	24.5570	+	42.5340i	0.0470441	+	0.0814828i
$523$	421.341	+	243.261i	0.805623	+	0.465127i	0.845434	−	0.534081i	$-0.179342\pi$
$523$	421.341	+	243.261i	0.805623	+	0.465127i	−0.0398106	+	0.999207i	$0.512675\pi$
$524$		−	435.835i		−	0.831747i
$525$		0			0
$526$	48.6723			0.0925330
$527$	779.604	−	1350.31i	1.47932	−	2.56227i
$528$	−49.1141	+	28.3560i	−0.0930191	+	0.0537046i
$529$	262.636	+	454.899i	0.496476	+	0.859922i
$530$		0			0
$531$			204.519i			0.385158i
$532$	25.3051	+	71.5246i	0.0475659	+	0.134445i
$533$	−1729.79			−3.24539
$534$	−48.6787	+	84.3140i	−0.0911586	+	0.157891i
$535$		0			0
$536$	70.1927	+	121.577i	0.130957	+	0.226823i
$537$	−338.935	−	195.684i	−0.631163	−	0.364402i
$538$			170.771i			0.317419i
$539$	374.375	+	143.956i	0.694573	+	0.267080i
$540$		0			0
$541$	27.8248	−	48.1940i	0.0514322	−	0.0890832i	−0.839163	−	0.543880i	$-0.816955\pi$
$541$	27.8248	−	48.1940i	0.0514322	−	0.0890832i	0.890595	+	0.454797i	$0.150288\pi$
$542$	−376.547	+	217.399i	−0.694736	+	0.401106i
$543$	132.308	+	229.164i	0.243661	+	0.422033i
$544$	125.809	+	72.6359i	0.231267	+	0.133522i
$545$		0			0
$546$	−357.585	+	126.512i	−0.654917	+	0.231706i
$547$	−475.854			−0.869934			−0.434967	−	0.900446i	$-0.643240\pi$
$547$	−475.854			−0.869934			−0.434967	+	0.900446i	$0.643240\pi$
$548$	−42.3698	+	73.3867i	−0.0773172	+	0.133917i
$549$	233.035	−	134.543i	0.424472	−	0.245069i
$550$		0			0
$551$	−54.3297	−	31.3673i	−0.0986020	−	0.0569279i
$552$		−	9.45925i		−	0.0171363i
$553$	−75.6602	+	407.572i	−0.136818	+	0.737019i
$554$	−43.5261			−0.0785669
$555$		0			0
$556$	−196.429	+	113.408i	−0.353289	+	0.203972i
$557$	−450.803	−	780.813i	−0.809341	−	1.40182i	−0.913321	−	0.407240i	$-0.866491\pi$
$557$	−450.803	−	780.813i	−0.809341	−	1.40182i	0.103980	−	0.994579i	$-0.466842\pi$
$558$	−223.082	−	128.797i	−0.399789	−	0.230818i
$559$			1164.49i			2.08317i
$560$		0			0
$561$	−364.101			−0.649021
$562$	−251.314	+	435.288i	−0.447177	+	0.774534i
$563$	−524.309	+	302.710i	−0.931277	+	0.537673i	−0.887215	−	0.461356i	$-0.847363\pi$
$563$	−524.309	+	302.710i	−0.931277	+	0.537673i	−0.0440619	+	0.999029i	$0.514030\pi$
$564$	−47.1378	−	81.6451i	−0.0835777	−	0.144761i
$565$		0			0
$566$			50.8017i			0.0897557i
$567$	−47.8938	−	40.9290i	−0.0844688	−	0.0721852i
$568$	−306.773			−0.540094
$569$	−201.858	+	349.628i	−0.354759	+	0.614460i	−0.987077	−	0.160249i	$-0.948770\pi$
$569$	−201.858	+	349.628i	−0.354759	+	0.614460i	0.632318	+	0.774709i	$0.282104\pi$
$570$		0			0
$571$	33.1380	+	57.3967i	0.0580351	+	0.100520i	0.893583	−	0.448897i	$-0.148183\pi$
$571$	33.1380	+	57.3967i	0.0580351	+	0.100520i	−0.835548	+	0.549417i	$0.814850\pi$
$572$	313.639	+	181.080i	0.548320	+	0.316573i
$573$			351.311i			0.613108i
$574$	−761.088	−	141.286i	−1.32594	−	0.246142i
$575$		0			0
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	−699.121	+	403.638i	−1.21165	+	0.699546i	−0.963118	−	0.269079i	$-0.913281\pi$
$577$	−699.121	+	403.638i	−1.21165	+	0.699546i	−0.248530	+	0.968624i	$0.579948\pi$
$578$	261.980	+	453.764i	0.453253	+	0.785058i
$579$	−206.151	−	119.021i	−0.356047	−	0.205564i
$580$		0			0
$581$	123.576	+	349.286i	0.212695	+	0.601181i
$582$	172.340			0.296117
$583$	46.5156	−	80.5673i	0.0797866	−	0.138194i
$584$	−31.6848	+	18.2932i	−0.0542548	+	0.0313240i
$585$		0			0
$586$	367.900	+	212.407i	0.627816	+	0.362470i
$587$		−	183.513i		−	0.312628i	−0.987707	−	0.156314i	$-0.950039\pi$
$587$		−	183.513i		−	0.312628i	0.987707	−	0.156314i	$-0.0499611\pi$
$588$	−167.666	+	26.4569i	−0.285147	+	0.0449948i
$589$	329.029			0.558624
$590$		0			0
$591$	162.612	−	93.8839i	0.275147	−	0.158856i
$592$	123.924	+	214.642i	0.209331	+	0.362571i
$593$	−552.893	−	319.213i	−0.932366	−	0.538302i	−0.0448070	−	0.998996i	$-0.514267\pi$
$593$	−552.893	−	319.213i	−0.932366	−	0.538302i	−0.887559	+	0.460694i	$0.847601\pi$
$594$			60.1522i			0.101266i
$595$		0			0
$596$	452.674			0.759520
$597$	228.371	−	395.550i	0.382531	−	0.662562i
$598$	−52.3132	+	30.2031i	−0.0874803	+	0.0505068i
$599$	−531.929	−	921.328i	−0.888029	−	1.53811i	−0.842203	−	0.539161i	$-0.818741\pi$
$599$	−531.929	−	921.328i	−0.888029	−	1.53811i	−0.0458259	−	0.998949i	$-0.514592\pi$
$600$		0			0
$601$		−	212.446i		−	0.353487i	−0.984257	−	0.176743i	$-0.943444\pi$
$601$		−	212.446i		−	0.353487i	0.984257	−	0.176743i	$-0.0565563\pi$
$602$	−95.1132	+	512.363i	−0.157995	+	0.851101i
$603$	148.901			0.246934
$604$	201.989	−	349.855i	0.334418	−	0.579230i
$605$		0			0
$606$	−36.4268	−	63.0931i	−0.0601102	−	0.104114i
$607$	−230.216	−	132.915i	−0.379269	−	0.218971i	0.298231	−	0.954494i	$-0.403603\pi$
$607$	−230.216	−	132.915i	−0.379269	−	0.218971i	−0.677500	+	0.735523i	$0.736937\pi$
$608$			30.6557i			0.0504206i
$609$	91.1841	−	106.701i	0.149728	−	0.175206i
$610$		0			0
$611$	−301.019	+	521.380i	−0.492666	+	0.853322i
$612$	133.441	−	77.0420i	0.218040	−	0.125886i
$613$	358.967	+	621.749i	0.585590	+	1.01427i	0.994802	+	0.101833i	$0.0324706\pi$
$613$	358.967	+	621.749i	0.585590	+	1.01427i	−0.409211	+	0.912440i	$0.634196\pi$
$614$	465.449	+	268.727i	0.758060	+	0.437666i
$615$		0			0
$616$	123.207	+	105.290i	0.200012	+	0.170926i
$617$	810.489			1.31360			0.656798	−	0.754066i	$-0.271910\pi$
$617$	810.489			1.31360			0.656798	+	0.754066i	$0.271910\pi$
$618$	133.252	−	230.800i	0.215619	−	0.373462i
$619$	714.595	−	412.572i	1.15443	−	0.666513i	0.204471	−	0.978873i	$-0.434453\pi$
$619$	714.595	−	412.572i	1.15443	−	0.666513i	0.949964	+	0.312360i	$0.101119\pi$
$620$		0			0
$621$	−8.68888	−	5.01653i	−0.0139918	−	0.00807814i
$622$		−	610.709i		−	0.981848i
$623$	273.549	+	50.7806i	0.439083	+	0.0815098i
$624$	−153.262			−0.245613
$625$		0			0
$626$	−77.4569	+	44.7198i	−0.123733	+	0.0714373i
$627$	−38.4169	−	66.5400i	−0.0612710	−	0.106124i
$628$	−81.4386	−	47.0186i	−0.129679	−	0.0748704i
$629$			1591.22i			2.52976i
$630$		0			0
$631$	1025.04			1.62447			0.812236	−	0.583329i	$-0.198250\pi$
$631$	1025.04			1.62447			0.812236	+	0.583329i	$0.198250\pi$
$632$	−83.7487	+	145.057i	−0.132514	+	0.229521i
$633$	−110.638	+	63.8772i	−0.174784	+	0.100912i
$634$	37.1335	+	64.3171i	0.0585701	+	0.101446i
$635$		0			0
$636$			39.3699i			0.0619024i
$637$	681.670	+	842.782i	1.07013	+	1.32305i
$638$	−134.011			−0.210048
$639$	−162.691	+	281.789i	−0.254603	+	0.440985i
$640$		0			0
$641$	−210.593	−	364.758i	−0.328539	−	0.569046i	0.653684	−	0.756768i	$-0.273223\pi$
$641$	−210.593	−	364.758i	−0.328539	−	0.569046i	−0.982222	+	0.187722i	$0.939889\pi$
$642$	134.309	+	77.5434i	0.209204	+	0.120784i
$643$		−	138.944i		−	0.216087i	−0.994146	−	0.108044i	$-0.965541\pi$
$643$		−	138.944i		−	0.216087i	0.994146	−	0.108044i	$-0.0344586\pi$
$644$	−25.4841	+	9.01616i	−0.0395717	+	0.0140003i
$645$		0			0
$646$	−98.4075	+	170.447i	−0.152334	+	0.263849i
$647$	−226.195	+	130.594i	−0.349606	+	0.201845i	−0.664512	−	0.747278i	$-0.731360\pi$
$647$	−226.195	+	130.594i	−0.349606	+	0.201845i	0.314906	+	0.949123i	$0.398027\pi$
$648$	−12.7279	−	22.0454i	−0.0196419	−	0.0340207i
$649$	−483.278	−	279.021i	−0.744651	−	0.429924i
$650$		0			0
$651$	−134.358	+	723.768i	−0.206387	+	1.11178i
$652$	40.8707			0.0626852
$653$	3.00785	−	5.20975i	0.00460620	−	0.00797818i	−0.863713	−	0.503984i	$-0.831867\pi$
$653$	3.00785	−	5.20975i	0.00460620	−	0.00797818i	0.868319	+	0.496006i	$0.165200\pi$
$654$	148.488	−	85.7296i	0.227046	−	0.131085i
$655$		0			0
$656$	−270.875	−	156.390i	−0.412920	−	0.238399i
$657$			38.8058i			0.0590651i
$658$	−175.030	+	204.814i	−0.266003	+	0.311268i
$659$	−316.710			−0.480592			−0.240296	−	0.970700i	$-0.577245\pi$
$659$	−316.710			−0.480592			−0.240296	+	0.970700i	$0.577245\pi$
$660$		0			0
$661$	−614.117	+	354.561i	−0.929073	+	0.536400i	−0.886518	−	0.462694i	$-0.846883\pi$
$661$	−614.117	+	354.561i	−0.929073	+	0.536400i	−0.0425544	+	0.999094i	$0.513550\pi$
$662$	129.855	+	224.916i	0.196156	+	0.339752i
$663$	−852.142	−	491.985i	−1.28528	−	0.742058i
$664$			149.705i			0.225460i
$665$		0			0
$666$	262.882			0.394717
$667$	11.1761	−	19.3576i	0.0167558	−	0.0290219i
$668$	136.836	−	79.0026i	0.204845	−	0.118267i
$669$	−261.346	−	452.665i	−0.390652	−	0.676630i
$670$		0			0
$671$			734.216i			1.09421i
$672$	−67.4336	−	12.5181i	−0.100348	−	0.0186282i
$673$	152.220			0.226181			0.113090	−	0.993585i	$-0.463925\pi$
$673$	152.220			0.226181			0.113090	+	0.993585i	$0.463925\pi$
$674$	60.9349	−	105.542i	0.0904078	−	0.156591i
$675$		0			0
$676$	320.361	+	554.882i	0.473907	+	0.820831i
$677$	205.707	+	118.765i	0.303851	+	0.175428i	0.644171	−	0.764881i	$-0.277202\pi$
$677$	205.707	+	118.765i	0.303851	+	0.175428i	−0.340321	+	0.940309i	$0.610536\pi$
$678$			211.980i			0.312656i
$679$	−164.267	−	464.301i	−0.241926	−	0.683802i
$680$		0			0
$681$	−183.031	+	317.019i	−0.268768	+	0.465520i
$682$	608.693	−	351.429i	0.892511	−	0.515292i
$683$	−401.020	−	694.587i	−0.587145	−	1.01696i	−0.994604	−	0.103741i	$-0.966919\pi$
$683$	−401.020	−	694.587i	−0.587145	−	1.01696i	0.407460	−	0.913223i	$-0.366415\pi$
$684$	28.1591	+	16.2577i	0.0411683	+	0.0237685i
$685$		0			0
$686$	231.090	+	426.492i	0.336866	+	0.621708i
$687$	−41.6147			−0.0605745
$688$	−105.281	+	182.353i	−0.153025	+	0.265048i
$689$	217.730	−	125.707i	0.316009	−	0.182448i
$690$		0			0
$691$	−35.8833	−	20.7172i	−0.0519295	−	0.0299815i	0.473810	−	0.880627i	$-0.342878\pi$
$691$	−35.8833	−	20.7172i	−0.0519295	−	0.0299815i	−0.525740	+	0.850645i	$0.676212\pi$
$692$		−	357.940i		−	0.517255i
$693$	162.056	−	57.3345i	0.233847	−	0.0827338i
$694$	−93.7516			−0.135089
$695$		0			0
$696$	49.1141	−	28.3560i	0.0705662	−	0.0407414i
$697$	−1004.05	−	1739.06i	−1.44053	−	2.49507i
$698$	406.359	+	234.611i	0.582176	+	0.336119i
$699$			716.403i			1.02490i
$700$		0			0
$701$	−140.218			−0.200026			−0.100013	−	0.994986i	$-0.531888\pi$
$701$	−140.218			−0.200026			−0.100013	+	0.994986i	$0.531888\pi$
$702$	−81.2796	+	140.780i	−0.115783	+	0.200542i
$703$	−290.798	+	167.892i	−0.413653	+	0.238823i
$704$	32.7427	+	56.7120i	0.0465095	+	0.0805569i
$705$		0			0
$706$			942.302i			1.33471i
$707$	−135.258	+	158.275i	−0.191313	+	0.223868i
$708$	236.158			0.333556
$709$	−34.2245	+	59.2786i	−0.0482716	+	0.0836088i	−0.889152	−	0.457613i	$-0.848705\pi$
$709$	−34.2245	+	59.2786i	−0.0482716	+	0.0836088i	0.840880	+	0.541222i	$0.182038\pi$
$710$		0			0
$711$	88.8289	+	153.856i	0.124935	+	0.216394i
$712$	97.3574	+	56.2093i	0.136738	+	0.0789457i
$713$			117.233i			0.164422i
$714$	−334.749	−	286.069i	−0.468835	−	0.400657i
$715$		0			0
$716$	−225.956	+	391.368i	−0.315582	+	0.546603i
$717$	−286.708	+	165.531i	−0.399872	+	0.230866i
$718$	197.585	+	342.228i	0.275189	+	0.476641i
$719$	118.917	+	68.6567i	0.165392	+	0.0954891i	0.580411	−	0.814324i	$-0.302892\pi$
$719$	118.917	+	68.6567i	0.165392	+	0.0954891i	−0.415019	+	0.909813i	$0.636225\pi$
$720$		0			0
$721$	−748.807	−	139.006i	−1.03857	−	0.192796i
$722$	468.999			0.649582
$723$	90.5397	−	156.819i	0.125228	−	0.216901i
$724$	264.616	−	152.776i	0.365491	−	0.211016i
$725$		0			0
$726$	114.540	+	66.1297i	0.157769	+	0.0910878i
$727$		−	174.040i		−	0.239395i	−0.992810	−	0.119697i	$-0.961808\pi$
$727$		−	174.040i		−	0.239395i	0.992810	−	0.119697i	$-0.0381924\pi$
$728$	146.083	+	412.903i	0.200664	+	0.567175i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−1170.73	+	675.924i	−1.60155	+	0.924657i
$732$	−155.357	−	269.086i	−0.212236	−	0.367603i
$733$	406.868	+	234.905i	0.555072	+	0.320471i	0.751165	−	0.660114i	$-0.229492\pi$
$733$	406.868	+	234.905i	0.555072	+	0.320471i	−0.196093	+	0.980585i	$0.562825\pi$
$734$		−	275.638i		−	0.375528i
$735$		0			0
$736$	−10.9226			−0.0148405
$737$	−203.143	+	351.854i	−0.275635	+	0.477414i
$738$	−287.307	+	165.877i	−0.389304	+	0.224765i
$739$	505.098	+	874.856i	0.683489	+	1.18384i	0.973909	+	0.226938i	$0.0728716\pi$
$739$	505.098	+	874.856i	0.683489	+	1.18384i	−0.290420	+	0.956899i	$0.593795\pi$
$740$		0			0
$741$		−	207.641i		−	0.280217i
$742$	106.066	−	37.5257i	0.142947	−	0.0505738i
$743$	844.947			1.13721			0.568605	−	0.822611i	$-0.307483\pi$
$743$	844.947			1.13721			0.568605	+	0.822611i	$0.307483\pi$
$744$	−148.721	+	257.593i	−0.199894	+	0.346227i
$745$		0			0
$746$	324.006	+	561.195i	0.434324	+	0.752272i
$747$	137.513	+	79.3933i	0.184087	+	0.106283i
$748$			420.427i			0.562068i
$749$	80.8916	−	435.753i	0.107999	−	0.581779i
$750$		0			0
$751$	232.862	−	403.328i	0.310069	−	0.537055i	−0.668308	−	0.743884i	$-0.732981\pi$
$751$	232.862	−	403.328i	0.310069	−	0.537055i	0.978377	+	0.206830i	$0.0663146\pi$
$752$	−94.2756	+	54.4301i	−0.125367	+	0.0723804i
$753$	−186.902	−	323.724i	−0.248210	−	0.429912i
$754$	−313.639	−	181.080i	−0.415967	−	0.240159i
$755$		0			0
$756$	−47.2607	+	55.3030i	−0.0625142	+	0.0731521i
$757$	993.329			1.31219			0.656096	−	0.754677i	$-0.272207\pi$
$757$	993.329			1.31219			0.656096	+	0.754677i	$0.272207\pi$
$758$	160.842	−	278.586i	0.212192	−	0.367527i
$759$	23.7081	−	13.6879i	0.0312360	−	0.0180341i
$760$		0			0
$761$	−655.950	−	378.713i	−0.861958	−	0.497652i	0.00270939	−	0.999996i	$-0.499138\pi$
$761$	−655.950	−	378.713i	−0.861958	−	0.497652i	−0.864668	+	0.502345i	$0.832471\pi$
$762$			428.170i			0.561903i
$763$	−372.496	−	318.327i	−0.488200	−	0.417205i
$764$	405.659			0.530967
$765$		0			0
$766$	−98.1179	+	56.6484i	−0.128091	+	0.0739535i
$767$	−754.044	−	1306.04i	−0.983108	−	1.70279i
$768$	−24.0000	−	13.8564i	−0.0312500	−	0.0180422i
$769$			1383.63i			1.79926i	0.436658	+	0.899628i	$0.356162\pi$
$769$			1383.63i			1.79926i	−0.436658	+	0.899628i	$0.643838\pi$
$770$		0			0
$771$	870.602			1.12919
$772$	−137.434	+	238.043i	−0.178024	+	0.308346i
$773$	−1260.83	+	727.943i	−1.63109	+	0.941711i	−0.647334	+	0.762207i	$0.724116\pi$
$773$	−1260.83	+	727.943i	−1.63109	+	0.941711i	−0.983757	+	0.179504i	$0.942551\pi$
$774$	111.668	+	193.414i	0.144274	+	0.249889i
$775$		0			0
$776$		−	199.001i		−	0.256445i
$777$	−250.568	−	708.229i	−0.322481	−	0.911492i
$778$	−1073.33			−1.37960
$779$	211.878	−	366.983i	0.271987	−	0.471095i
$780$		0			0
$781$	−443.912	−	768.878i	−0.568390	−	0.984480i
$782$	−60.7300	−	35.0625i	−0.0776598	−	0.0448369i
$783$		−	60.1522i		−	0.0768227i
$784$	30.5498	+	193.605i	0.0389666	+	0.246945i
$785$		0			0
$786$	−266.894	+	462.273i	−0.339559	+	0.588134i
$787$	−567.144	+	327.440i	−0.720640	+	0.416062i	−0.814988	−	0.579478i	$-0.803257\pi$
$787$	−567.144	+	327.440i	−0.720640	+	0.416062i	0.0943483	+	0.995539i	$0.469923\pi$
$788$	−108.408	−	187.768i	−0.137573	−	0.238284i
$789$	−51.6248	−	29.8056i	−0.0654307	−	0.0377764i
$790$		0			0
$791$	571.096	−	202.051i	0.721992	−	0.255437i
$792$	69.4578			0.0876992
$793$	−992.097	+	1718.36i	−1.25107	+	2.16691i
$794$	52.3645	−	30.2327i	0.0659502	−	0.0380764i
$795$		0			0
$796$	−456.742	−	263.700i	−0.573796	−	0.331281i
$797$			15.9082i			0.0199601i	0.999950	+	0.00998004i	$0.00317680\pi$
$797$			15.9082i			0.0199601i	−0.999950	+	0.00998004i	$0.996823\pi$
$798$	16.9596	−	91.3595i	0.0212527	−	0.114486i
$799$	−698.900			−0.874718
$800$		0			0
$801$	103.263	−	59.6190i	0.128918	−	0.0744307i
$802$	310.864	+	538.432i	0.387611	+	0.671361i
$803$	−91.6981	−	52.9419i	−0.114194	−	0.0659302i
$804$		−	171.936i		−	0.213851i
$805$		0			0
$806$	1899.45			2.35664
$807$	104.576	−	181.130i	0.129586	−	0.224449i
$808$	−72.8536	+	42.0620i	−0.0901653	+	0.0520570i
$809$	192.023	+	332.593i	0.237358	+	0.411117i	0.959955	−	0.280153i	$-0.0903851\pi$
$809$	192.023	+	332.593i	0.237358	+	0.411117i	−0.722597	+	0.691269i	$0.757052\pi$
$810$		0			0
$811$			165.942i			0.204614i	0.994753	+	0.102307i	$0.0326223\pi$
$811$			165.942i			0.204614i	−0.994753	+	0.102307i	$0.967378\pi$
$812$	−123.207	−	105.290i	−0.151733	−	0.129668i
$813$	532.517			0.655003
$814$	−358.644	+	621.190i	−0.440595	+	0.763133i
$815$		0			0
$816$	−88.9604	−	154.084i	−0.109020	−	0.188828i
$817$	−247.052	−	142.636i	−0.302390	−	0.174585i
$818$		−	574.372i		−	0.702166i
$819$	456.748	+	84.7891i	0.557690	+	0.103528i
$820$		0			0
$821$	−138.501	+	239.890i	−0.168698	+	0.292193i	−0.937962	−	0.346738i	$-0.887289\pi$
$821$	−138.501	+	239.890i	−0.168698	+	0.292193i	0.769265	+	0.638930i	$0.220623\pi$
$822$	89.8799	−	51.8922i	0.109343	−	0.0631292i
$823$	460.773	+	798.083i	0.559871	+	0.969724i	0.997507	+	0.0705720i	$0.0224825\pi$
$823$	460.773	+	798.083i	0.559871	+	0.969724i	−0.437636	+	0.899152i	$0.644184\pi$
$824$	−266.505	−	153.866i	−0.323428	−	0.186731i
$825$		0			0
$826$	−225.096	−	636.232i	−0.272513	−	0.770257i
$827$	−260.719			−0.315259			−0.157630	−	0.987498i	$-0.550385\pi$
$827$	−260.719			−0.315259			−0.157630	+	0.987498i	$0.550385\pi$
$828$	−5.79259	+	10.0331i	−0.00699588	+	0.0121172i
$829$	21.5479	−	12.4407i	0.0259926	−	0.0150068i	−0.486947	−	0.873431i	$-0.661890\pi$
$829$	21.5479	−	12.4407i	0.0259926	−	0.0150068i	0.512940	+	0.858424i	$0.328556\pi$
$830$		0			0
$831$	46.1664	+	26.6542i	0.0555552	+	0.0320748i
$832$			176.972i			0.212707i
$833$	−451.629	+	1174.51i	−0.542171	+	1.40998i
$834$	277.792			0.333084
$835$		0			0
$836$	−76.8338	+	44.3600i	−0.0919064	+	0.0530622i
$837$	157.743	+	273.219i	0.188462	+	0.326426i
$838$	704.007	+	406.459i	0.840104	+	0.485034i
$839$		−	571.207i		−	0.680819i	−0.940277	−	0.340410i	$-0.889434\pi$
$839$		−	571.207i		−	0.680819i	0.940277	−	0.340410i	$-0.110566\pi$
$840$		0			0
$841$	−706.989			−0.840653
$842$	273.549	−	473.800i	0.324880	−	0.562708i
$843$	533.117	−	307.795i	0.632404	−	0.365119i
$844$	73.7590	+	127.754i	0.0873922	+	0.151368i
$845$		0			0
$846$			115.464i			0.136482i
$847$	68.9851	−	371.614i	0.0814464	−	0.438741i
$848$	45.4604			0.0536090
$849$	31.1096	−	53.8834i	0.0366426	−	0.0634669i
$850$		0			0
$851$	−59.8199	−	103.611i	−0.0702936	−	0.121752i
$852$	325.382	+	187.859i	0.381904	+	0.220492i
$853$			1384.88i			1.62354i	0.583979	+	0.811769i	$0.301495\pi$
$853$			1384.88i			1.62354i	−0.583979	+	0.811769i	$0.698505\pi$
$854$	−576.863	+	675.027i	−0.675484	+	0.790430i
$855$		0			0
$856$	89.5394	−	155.087i	0.104602	−	0.181176i
$857$	252.174	−	145.593i	0.294252	−	0.169887i	−0.345606	−	0.938380i	$-0.612327\pi$
$857$	252.174	−	145.593i	0.294252	−	0.169887i	0.639858	+	0.768493i	$0.278993\pi$
$858$	−221.776	−	384.128i	−0.258480	−	0.447701i
$859$	240.701	+	138.969i	0.280210	+	0.161780i	0.633519	−	0.773727i	$-0.281610\pi$
$859$	240.701	+	138.969i	0.280210	+	0.161780i	−0.353308	+	0.935507i	$0.614943\pi$
$860$		0			0
$861$	720.736	+	615.925i	0.837092	+	0.715361i
$862$	951.258			1.10355
$863$	483.934	−	838.198i	0.560758	−	0.971261i	−0.436673	−	0.899620i	$-0.643843\pi$
$863$	483.934	−	838.198i	0.560758	−	0.971261i	0.997431	−	0.0716405i	$-0.0228234\pi$
$864$	−25.4558	+	14.6969i	−0.0294628	+	0.0170103i
$865$		0			0
$866$	−75.7903	−	43.7576i	−0.0875177	−	0.0505284i
$867$		−	641.719i		−	0.740160i
$868$	835.736	+	155.143i	0.962829	+	0.178736i
$869$	−484.750			−0.557825
$870$		0			0
$871$	−950.873	+	548.987i	−1.09170	+	0.630295i
$872$	−98.9920	−	171.459i	−0.113523	−	0.196628i
$873$	−182.794	−	105.536i	−0.209387	−	0.120889i
$874$		−	14.7980i		−	0.0169314i
$875$		0			0
$876$	44.8091			0.0511519
$877$	711.644	−	1232.60i	0.811452	−	1.40548i	−0.100395	−	0.994948i	$-0.532011\pi$
$877$	711.644	−	1232.60i	0.811452	−	1.40548i	0.911847	−	0.410529i	$-0.134656\pi$
$878$	502.326	−	290.018i	0.572126	−	0.330317i
$879$	−260.145	−	450.584i	−0.295955	−	0.512610i
$880$		0			0
$881$			788.336i			0.894819i	0.894329	+	0.447410i	$0.147653\pi$
$881$			788.336i			0.894819i	−0.894329	+	0.447410i	$0.852347\pi$
$882$	194.039	+	74.6125i	0.219998	+	0.0845947i
$883$	1209.73			1.37002			0.685011	−	0.728533i	$-0.259798\pi$
$883$	1209.73			1.37002			0.685011	+	0.728533i	$0.259798\pi$
$884$	−568.095	+	983.969i	−0.642641	+	1.11309i
$885$		0			0
$886$	−254.421	−	440.670i	−0.287157	−	0.497371i
$887$	138.774	+	80.1213i	0.156453	+	0.0903285i	0.576183	−	0.817321i	$-0.304542\pi$
$887$	138.774	+	80.1213i	0.156453	+	0.0903285i	−0.419729	+	0.907649i	$0.637875\pi$
$888$		−	303.550i		−	0.341835i
$889$	1153.53	−	408.114i	1.29756	−	0.459071i
$890$		0			0
$891$	36.8355	−	63.8010i	0.0413418	−	0.0716061i
$892$	−522.693	+	301.777i	−0.585979	+	0.338315i
$893$	−73.7421	−	127.725i	−0.0825780	−	0.143029i
$894$	−480.133	−	277.205i	−0.537062	−	0.310073i
$895$		0			0
$896$	−14.4547	+	77.8657i	−0.0161325	+	0.0869036i
$897$	73.9821			0.0824773
$898$	571.397	−	989.689i	0.636300	−	1.10210i
$899$	−608.693	+	351.429i	−0.677078	+	0.390911i
$900$		0			0
$901$	252.761	+	145.932i	0.280534	+	0.161966i
$902$		−	905.208i		−	1.00356i
$903$	414.640	−	485.198i	0.459180	−	0.537318i
$904$	244.774			0.270768
$905$		0			0
$906$	−428.483	+	247.385i	−0.472939	+	0.273051i
$907$	87.1283	+	150.911i	0.0960621	+	0.166384i	0.910051	−	0.414495i	$-0.136042\pi$
$907$	87.1283	+	150.911i	0.0960621	+	0.166384i	−0.813989	+	0.580880i	$0.802709\pi$
$908$	366.062	+	211.346i	0.403152	+	0.232760i
$909$			89.2271i			0.0981596i
$910$		0			0
$911$	97.1630			0.106655			0.0533276	−	0.998577i	$-0.483017\pi$
$911$	97.1630			0.106655			0.0533276	+	0.998577i	$0.483017\pi$
$912$	18.7727	−	32.5153i	0.0205841	−	0.0356528i
$913$	−375.213	+	216.629i	−0.410967	+	0.237272i
$914$	−102.351	−	177.278i	−0.111982	−	0.193958i
$915$		0			0
$916$			48.0525i			0.0524591i
$917$	1499.80	+	278.418i	1.63555	+	0.303618i
$918$	−188.714			−0.205570
$919$	443.487	−	768.143i	0.482576	−	0.835846i	−0.517224	−	0.855850i	$-0.673035\pi$
$919$	443.487	−	768.143i	0.482576	−	0.835846i	0.999800	+	0.0200039i	$0.00636785\pi$
$920$		0			0
$921$	−329.122	−	570.056i	−0.357353	−	0.618953i
$922$	288.617	+	166.633i	0.313034	+	0.180730i
$923$		−	2399.31i		−	2.59947i
$924$	−66.2042	−	187.126i	−0.0716496	−	0.202517i
$925$		0			0
$926$	−264.137	+	457.500i	−0.285246	+	0.494060i
$927$	−282.671	+	163.200i	−0.304931	+	0.176052i
$928$	−32.7427	−	56.7120i	−0.0352831	−	0.0611121i
$929$	−758.377	−	437.849i	−0.816336	−	0.471312i	0.0328150	−	0.999461i	$-0.489553\pi$
$929$	−758.377	−	437.849i	−0.816336	−	0.471312i	−0.849151	+	0.528149i	$0.822886\pi$
$930$		0			0
$931$	−262.296	+	41.3891i	−0.281736	+	0.0444566i
$932$	827.231			0.887587
$933$	−373.982	+	647.755i	−0.400838	+	0.694271i
$934$	263.194	−	151.955i	0.281792	−	0.162693i
$935$		0			0
$936$	162.559	+	93.8536i	0.173674	+	0.100271i
$937$		−	1203.13i		−	1.28403i	−0.766693	−	0.642014i	$-0.778099\pi$
$937$		−	1203.13i		−	1.28403i	0.766693	−	0.642014i	$-0.221901\pi$
$938$	−463.213	+	163.882i	−0.493831	+	0.174715i
$939$	109.541			0.116657
$940$		0			0
$941$	542.393	−	313.150i	0.576400	−	0.332785i	−0.183301	−	0.983057i	$-0.558678\pi$
$941$	542.393	−	313.150i	0.576400	−	0.332785i	0.759701	+	0.650272i	$0.225345\pi$
$942$	57.5858	+	99.7416i	0.0611314	+	0.105883i
$943$	130.756	+	75.4919i	0.138659	+	0.0800550i
$944$		−	272.692i		−	0.288868i
$945$		0			0
$946$	−609.384			−0.644170
$947$	−90.0345	+	155.944i	−0.0950734	+	0.164672i	−0.909639	−	0.415399i	$-0.863642\pi$
$947$	−90.0345	+	155.944i	−0.0950734	+	0.164672i	0.814566	+	0.580071i	$0.196975\pi$
$948$	177.658	−	102.571i	0.187403	−	0.108197i
$949$	−143.074	−	247.811i	−0.150763	−	0.261129i
$950$		0			0
$951$		−	90.9581i		−	0.0956447i
$952$	−330.324	+	386.534i	−0.346979	+	0.406023i
$953$	1429.80			1.50031			0.750155	−	0.661262i	$-0.229979\pi$
$953$	1429.80			1.50031			0.750155	+	0.661262i	$0.229979\pi$
$954$	24.1090	−	41.7581i	0.0252715	−	0.0437716i
$955$		0			0
$956$	191.139	+	331.062i	0.199936	+	0.346299i
$957$	142.140	+	82.0644i	0.148526	+	0.0857517i
$958$			1306.20i			1.36347i
$959$	−225.472	−	192.684i	−0.235112	−	0.200922i
$960$		0			0
$961$	1362.67	−	2360.22i	1.41797	−	2.45600i
$962$	−1678.74	+	969.224i	−1.74506	+	1.00751i
$963$	−94.9708	−	164.494i	−0.0986198	−	0.170814i
$964$	−181.079	−	104.546i	−0.187842	−	0.108450i
$965$		0			0
$966$	32.5513	+	6.04270i	0.0336970	+	0.00625539i
$967$	562.524			0.581720			0.290860	−	0.956766i	$-0.406059\pi$
$967$	562.524			0.581720			0.290860	+	0.956766i	$0.406059\pi$
$968$	76.3600	−	132.259i	0.0788843	−	0.136632i
$969$	208.754	−	120.524i	0.215432	−	0.124380i
$970$		0			0
$971$	−1087.12	−	627.648i	−1.11959	−	0.646393i	−0.178290	−	0.983978i	$-0.557057\pi$
$971$	−1087.12	−	627.648i	−1.11959	−	0.646393i	−0.941295	+	0.337585i	$0.890390\pi$
$972$			31.1769i			0.0320750i
$973$	−264.780	−	748.400i	−0.272128	−	0.769167i
$974$	788.131			0.809169
$975$		0			0
$976$	−310.713	+	179.390i	−0.318354	+	0.183802i
$977$	63.8721	+	110.630i	0.0653757	+	0.113234i	0.896861	−	0.442313i	$-0.145842\pi$
$977$	63.8721	+	110.630i	0.0653757	+	0.113234i	−0.831485	+	0.555547i	$0.812509\pi$
$978$	−43.3500	−	25.0281i	−0.0443251	−	0.0255911i
$979$			325.348i			0.332327i
$980$		0			0
$981$	−209.994			−0.214061
$982$	3.56739	−	6.17890i	0.00363278	−	0.00629215i
$983$	1254.49	−	724.280i	1.27619	−	0.736806i	0.300041	−	0.953926i	$-0.403000\pi$
$983$	1254.49	−	724.280i	1.27619	−	0.736806i	0.976145	+	0.217120i	$0.0696663\pi$
$984$	191.538	+	331.753i	0.194652	+	0.337148i
$985$		0			0
$986$		−	420.427i		−	0.426397i
$987$	311.070	−	110.055i	0.315167	−	0.111505i
$988$	−239.763			−0.242675
$989$	50.8210	−	88.0245i	0.0513862	−	0.0890035i
$990$		0			0
$991$	634.178	+	1098.43i	0.639938	+	1.10840i	0.985446	+	0.169989i	$0.0543732\pi$
$991$	634.178	+	1098.43i	0.639938	+	1.10840i	−0.345508	+	0.938416i	$0.612293\pi$
$992$	297.443	+	171.729i	0.299842	+	0.173114i
$993$		−	318.079i		−	0.320321i
$994$	195.971	−	1055.67i	0.197154	−	1.06204i
$995$		0			0
$996$	91.6755	−	158.787i	0.0920437	−	0.159424i
$997$	−1339.01	+	773.076i	−1.34304	+	0.775402i	−0.987252	−	0.159166i	$-0.949120\pi$
$997$	−1339.01	+	773.076i	−1.34304	+	0.775402i	−0.355784	+	0.934568i	$0.615786\pi$
$998$	−112.890	−	195.531i	−0.113116	−	0.195923i
$999$	−278.828	−	160.982i	−0.279107	−	0.161143i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.p.f.901.3	yes	12
5.2	odd	4		1050.3.q.d.649.1		24
5.3	odd	4		1050.3.q.d.649.7		24
5.4	even	2		1050.3.p.e.901.4	yes	12
7.3	odd	6	inner	1050.3.p.f.451.3	yes	12
35.3	even	12		1050.3.q.d.199.1		24
35.17	even	12		1050.3.q.d.199.7		24
35.24	odd	6		1050.3.p.e.451.4	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.p.e.451.4	✓	12	35.24	odd	6
1050.3.p.e.901.4	yes	12	5.4	even	2
1050.3.p.f.451.3	yes	12	7.3	odd	6	inner
1050.3.p.f.901.3	yes	12	1.1	even	1	trivial
1050.3.q.d.199.1		24	35.3	even	12
1050.3.q.d.199.7		24	35.17	even	12
1050.3.q.d.649.1		24	5.2	odd	4
1050.3.q.d.649.7		24	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(6.59916 - 2.33475i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(6.59916 - 2.33475i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(4.09284 + 7.08900i) q^{11} +(-3.00000 - 1.73205i) q^{12} +22.1215i q^{13} +(-1.80684 + 9.73321i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-22.2401 + 12.8403i) q^{17} +(2.12132 + 3.67423i) q^{18} +(-4.69318 - 2.70961i) q^{19} +(7.87679 - 9.21717i) q^{21} -11.5763 q^{22} +(0.965431 - 1.67218i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-27.0932 - 15.6423i) q^{26} -5.19615i q^{27} +(-10.6431 - 9.09533i) q^{28} +11.5763 q^{29} +(-52.5810 + 30.3576i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(12.2785 + 7.08900i) q^{33} -36.3179i q^{34} -6.00000 q^{36} +(30.9809 - 53.6605i) q^{37} +(6.63716 - 3.83197i) q^{38} +(19.1578 + 33.1823i) q^{39} +78.1950i q^{41} +(5.71895 + 16.1646i) q^{42} +52.6407 q^{43} +(8.18568 - 14.1780i) q^{44} +(1.36533 + 2.36481i) q^{46} +(23.5689 + 13.6075i) q^{47} +6.92820i q^{48} +(38.0979 - 30.8148i) q^{49} +(-22.2401 + 38.5210i) q^{51} +(38.3156 - 22.1215i) q^{52} +(-5.68256 - 9.84247i) q^{53} +(6.36396 + 3.67423i) q^{54} +(18.6652 - 6.60367i) q^{56} -9.38637 q^{57} +(-8.18568 + 14.1780i) q^{58} +(-59.0395 + 34.0865i) q^{59} +(77.6783 + 44.8476i) q^{61} -85.8644i q^{62} +(3.83288 - 20.6473i) q^{63} +8.00000 q^{64} +(-17.3644 + 10.0254i) q^{66} +(24.8169 + 42.9841i) q^{67} +(44.4802 + 25.6807i) q^{68} -3.34435i q^{69} -108.461 q^{71} +(4.24264 - 7.34847i) q^{72} +(-11.2023 + 6.46763i) q^{73} +(43.8136 + 75.8874i) q^{74} +10.8384i q^{76} +(43.5604 + 37.2257i) q^{77} -54.1864 q^{78} +(-29.6096 + 51.2854i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-95.7689 - 55.2922i) q^{82} +52.9289i q^{83} +(-23.8414 - 4.42583i) q^{84} +(-37.2226 + 64.4714i) q^{86} +(17.3644 - 10.0254i) q^{87} +(11.5763 + 20.0507i) q^{88} +(34.4210 + 19.8730i) q^{89} +(51.6482 + 145.983i) q^{91} -3.86172 q^{92} +(-52.5810 + 91.0729i) q^{93} +(-33.3315 + 19.2439i) q^{94} +(-8.48528 - 4.89898i) q^{96} -70.3576i q^{97} +(10.8010 + 68.4495i) q^{98} +24.5570 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 18 q^{3} - 12 q^{4} + 8 q^{7} + 18 q^{9}+O(q^{10}) \) 12 * q + 18 * q^3 - 12 * q^4 + 8 * q^7 + 18 * q^9	\( 12 q + 18 q^{3} - 12 q^{4} + 8 q^{7} + 18 q^{9} - 4 q^{11} - 36 q^{12} + 8 q^{14} - 24 q^{16} - 24 q^{17} + 12 q^{19} + 18 q^{21} + 24 q^{22} - 60 q^{23} - 24 q^{26} + 4 q^{28} - 24 q^{29} - 198 q^{31} - 12 q^{33} - 72 q^{36} + 70 q^{37} - 60 q^{38} - 36 q^{39} + 36 q^{42} - 84 q^{43} - 8 q^{44} + 32 q^{46} - 60 q^{47} + 28 q^{49} - 24 q^{51} - 72 q^{52} + 44 q^{53} + 40 q^{56} + 24 q^{57} + 8 q^{58} - 48 q^{59} + 186 q^{61} + 30 q^{63} + 96 q^{64} + 36 q^{66} + 152 q^{67} + 48 q^{68} - 136 q^{71} + 18 q^{73} - 64 q^{74} + 132 q^{77} - 48 q^{78} - 70 q^{79} - 54 q^{81} - 84 q^{82} - 12 q^{84} - 208 q^{86} - 36 q^{87} - 24 q^{88} + 168 q^{89} + 292 q^{91} + 240 q^{92} - 198 q^{93} - 204 q^{94} + 48 q^{98} - 24 q^{99}+O(q^{100}) \) 12 * q + 18 * q^3 - 12 * q^4 + 8 * q^7 + 18 * q^9 - 4 * q^11 - 36 * q^12 + 8 * q^14 - 24 * q^16 - 24 * q^17 + 12 * q^19 + 18 * q^21 + 24 * q^22 - 60 * q^23 - 24 * q^26 + 4 * q^28 - 24 * q^29 - 198 * q^31 - 12 * q^33 - 72 * q^36 + 70 * q^37 - 60 * q^38 - 36 * q^39 + 36 * q^42 - 84 * q^43 - 8 * q^44 + 32 * q^46 - 60 * q^47 + 28 * q^49 - 24 * q^51 - 72 * q^52 + 44 * q^53 + 40 * q^56 + 24 * q^57 + 8 * q^58 - 48 * q^59 + 186 * q^61 + 30 * q^63 + 96 * q^64 + 36 * q^66 + 152 * q^67 + 48 * q^68 - 136 * q^71 + 18 * q^73 - 64 * q^74 + 132 * q^77 - 48 * q^78 - 70 * q^79 - 54 * q^81 - 84 * q^82 - 12 * q^84 - 208 * q^86 - 36 * q^87 - 24 * q^88 + 168 * q^89 + 292 * q^91 + 240 * q^92 - 198 * q^93 - 204 * q^94 + 48 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

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Database

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