LMFDB - Embedded newform 1050.3.q.d.199.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(199,1050)]

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, 3, 1]))

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

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

chi := DirichletCharacter("1050.199");

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.q (of order $6$, degree $2$, not 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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.9
Character	$\chi$	$=$	1050.199
Dual form			1050.3.q.d.649.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-6.34914 - 2.94762i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-6.34914 - 2.94762i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-8.87118 + 15.3653i) q^{11} +(-1.73205 - 3.00000i) q^{12} +8.10715 q^{13} +(-9.86035 + 0.879440i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-3.93681 + 6.81875i) q^{17} +(-3.67423 - 2.12132i) q^{18} +(-17.5951 + 10.1585i) q^{19} +(-9.91994 + 6.97100i) q^{21} +25.0915i q^{22} +(-28.2223 + 16.2941i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(9.92919 - 5.73262i) q^{26} -5.19615 q^{27} +(-11.4546 + 8.04941i) q^{28} +25.0915 q^{29} +(-46.0686 - 26.5977i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(15.3653 + 26.6135i) q^{33} +11.1350i q^{34} -6.00000 q^{36} +(37.7270 - 21.7817i) q^{37} +(-14.3664 + 24.8833i) q^{38} +(7.02100 - 12.1607i) q^{39} +70.3424i q^{41} +(-7.22016 + 15.5521i) q^{42} -2.43179i q^{43} +(17.7424 + 30.7307i) q^{44} +(-23.0434 + 39.9123i) q^{46} +(7.69399 + 13.3264i) q^{47} -6.92820 q^{48} +(31.6231 + 37.4297i) q^{49} +(6.81875 + 11.8104i) q^{51} +(8.10715 - 14.0420i) q^{52} +(-44.0765 - 25.4476i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(-8.33712 + 17.9581i) q^{56} +35.1902i q^{57} +(30.7307 - 17.7424i) q^{58} +(-22.9688 - 13.2610i) q^{59} +(-28.7553 + 16.6019i) q^{61} -75.2297 q^{62} +(1.86557 + 20.9170i) q^{63} -8.00000 q^{64} +(37.6372 + 21.7299i) q^{66} +(86.4589 + 49.9171i) q^{67} +(7.87362 + 13.6375i) q^{68} +56.4445i q^{69} -97.0831 q^{71} +(-7.34847 + 4.24264i) q^{72} +(-27.0175 + 46.7957i) q^{73} +(30.8040 - 53.3541i) q^{74} +40.6342i q^{76} +(101.615 - 71.4078i) q^{77} -19.8584i q^{78} +(-37.3591 - 64.7079i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(49.7396 + 86.1515i) q^{82} +85.2206 q^{83} +(2.15418 + 24.1528i) q^{84} +(-1.71954 - 2.97833i) q^{86} +(21.7299 - 37.6372i) q^{87} +(43.4597 + 25.0915i) q^{88} +(115.343 - 66.5932i) q^{89} +(-51.4734 - 23.8968i) q^{91} +65.1765i q^{92} +(-79.7931 + 46.0686i) q^{93} +(18.8464 + 10.8809i) q^{94} +(-8.48528 + 4.89898i) q^{96} -49.9973 q^{97} +(65.1970 + 23.4809i) q^{98} +53.2271 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4} - 36 q^{9}+O(q^{10}) $ 24 * q + 24 * q^4 - 36 * q^9	$ 24 q + 24 q^{4} - 36 q^{9} - 8 q^{11} - 16 q^{14} - 48 q^{16} - 24 q^{19} + 36 q^{21} - 48 q^{26} + 48 q^{29} - 396 q^{31} - 144 q^{36} + 72 q^{39} + 16 q^{44} + 64 q^{46} - 56 q^{49} - 48 q^{51} + 80 q^{56} + 96 q^{59} + 372 q^{61} - 192 q^{64} + 72 q^{66} - 272 q^{71} + 128 q^{74} + 140 q^{79} - 108 q^{81} + 24 q^{84} - 416 q^{86} - 336 q^{89} + 584 q^{91} + 408 q^{94} + 48 q^{99}+O(q^{100}) $ 24 * q + 24 * q^4 - 36 * q^9 - 8 * q^11 - 16 * q^14 - 48 * q^16 - 24 * q^19 + 36 * q^21 - 48 * q^26 + 48 * q^29 - 396 * q^31 - 144 * q^36 + 72 * q^39 + 16 * q^44 + 64 * q^46 - 56 * q^49 - 48 * q^51 + 80 * q^56 + 96 * q^59 + 372 * q^61 - 192 * q^64 + 72 * q^66 - 272 * q^71 + 128 * q^74 + 140 * q^79 - 108 * q^81 + 24 * q^84 - 416 * q^86 - 336 * q^89 + 584 * q^91 + 408 * q^94 + 48 * 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 $

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		−	2.44949i		−	0.408248i
$7$	−6.34914	−	2.94762i	−0.907020	−	0.421088i
$7$	−6.34914	−	2.94762i	−0.907020	−	0.421088i
$8$		−	2.82843i		−	0.353553i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$		0			0
$11$	−8.87118	+	15.3653i	−0.806471	+	1.39685i	0.108822	+	0.994061i	$0.465292\pi$
$11$	−8.87118	+	15.3653i	−0.806471	+	1.39685i	−0.915293	+	0.402788i	$0.868041\pi$
$12$	−1.73205	−	3.00000i	−0.144338	−	0.250000i
$13$	8.10715			0.623627			0.311813	−	0.950143i	$-0.399064\pi$
$13$	8.10715			0.623627			0.311813	+	0.950143i	$0.399064\pi$
$14$	−9.86035	+	0.879440i	−0.704311	+	0.0628172i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−3.93681	+	6.81875i	−0.231577	+	0.401103i	−0.958272	−	0.285857i	$-0.907722\pi$
$17$	−3.93681	+	6.81875i	−0.231577	+	0.401103i	0.726695	+	0.686960i	$0.241055\pi$
$18$	−3.67423	−	2.12132i	−0.204124	−	0.117851i
$19$	−17.5951	+	10.1585i	−0.926059	+	0.534660i	−0.885563	−	0.464519i	$-0.846227\pi$
$19$	−17.5951	+	10.1585i	−0.926059	+	0.534660i	−0.0404958	+	0.999180i	$0.512894\pi$
$20$		0			0
$21$	−9.91994	+	6.97100i	−0.472378	+	0.331952i
$22$			25.0915i			1.14052i
$23$	−28.2223	+	16.2941i	−1.22706	+	0.708441i	−0.966413	−	0.256995i	$-0.917268\pi$
$23$	−28.2223	+	16.2941i	−1.22706	+	0.708441i	−0.260642	+	0.965435i	$0.583934\pi$
$24$	−4.24264	−	2.44949i	−0.176777	−	0.102062i
$25$		0			0
$26$	9.92919	−	5.73262i	0.381892	−	0.220485i
$27$	−5.19615			−0.192450
$28$	−11.4546	+	8.04941i	−0.409091	+	0.287479i
$29$	25.0915			0.865224			0.432612	−	0.901580i	$-0.357592\pi$
$29$	25.0915			0.865224			0.432612	+	0.901580i	$0.357592\pi$
$30$		0			0
$31$	−46.0686	−	26.5977i	−1.48608	−	0.857991i	−0.486209	−	0.873843i	$-0.661621\pi$
$31$	−46.0686	−	26.5977i	−1.48608	−	0.857991i	−0.999874	+	0.0158519i	$0.994954\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$	15.3653	+	26.6135i	0.465616	+	0.806471i
$34$			11.1350i			0.327499i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	37.7270	−	21.7817i	1.01965	−	0.588695i	0.105647	−	0.994404i	$-0.466309\pi$
$37$	37.7270	−	21.7817i	1.01965	−	0.588695i	0.914002	+	0.405709i	$0.132975\pi$
$38$	−14.3664	+	24.8833i	−0.378062	+	0.654822i
$39$	7.02100	−	12.1607i	0.180026	−	0.311813i
$40$		0			0
$41$			70.3424i			1.71567i	0.513927	+	0.857834i	$0.328190\pi$
$41$			70.3424i			1.71567i	−0.513927	+	0.857834i	$0.671810\pi$
$42$	−7.22016	+	15.5521i	−0.171908	+	0.370289i
$43$		−	2.43179i		−	0.0565533i	−0.999600	−	0.0282767i	$-0.990998\pi$
$43$		−	2.43179i		−	0.0565533i	0.999600	−	0.0282767i	$-0.00900194\pi$
$44$	17.7424	+	30.7307i	0.403236	+	0.698424i
$45$		0			0
$46$	−23.0434	+	39.9123i	−0.500943	+	0.867659i
$47$	7.69399	+	13.3264i	0.163702	+	0.283540i	0.936194	−	0.351485i	$-0.114323\pi$
$47$	7.69399	+	13.3264i	0.163702	+	0.283540i	−0.772492	+	0.635025i	$0.780990\pi$
$48$	−6.92820			−0.144338
$49$	31.6231	+	37.4297i	0.645370	+	0.763870i
$50$		0			0
$51$	6.81875	+	11.8104i	0.133701	+	0.231577i
$52$	8.10715	−	14.0420i	0.155907	−	0.270038i
$53$	−44.0765	−	25.4476i	−0.831632	−	0.480143i	0.0227791	−	0.999741i	$-0.492749\pi$
$53$	−44.0765	−	25.4476i	−0.831632	−	0.480143i	−0.854411	+	0.519598i	$0.826082\pi$
$54$	−6.36396	+	3.67423i	−0.117851	+	0.0680414i
$55$		0			0
$56$	−8.33712	+	17.9581i	−0.148877	+	0.320680i
$57$			35.1902i			0.617372i
$58$	30.7307	−	17.7424i	0.529839	−	0.305903i
$59$	−22.9688	−	13.2610i	−0.389302	−	0.224763i	0.292556	−	0.956248i	$-0.405494\pi$
$59$	−22.9688	−	13.2610i	−0.389302	−	0.224763i	−0.681858	+	0.731485i	$0.738828\pi$
$60$		0			0
$61$	−28.7553	+	16.6019i	−0.471399	+	0.272162i	−0.716825	−	0.697253i	$-0.754405\pi$
$61$	−28.7553	+	16.6019i	−0.471399	+	0.272162i	0.245426	+	0.969415i	$0.421072\pi$
$62$	−75.2297			−1.21338
$63$	1.86557	+	20.9170i	0.0296123	+	0.332015i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	37.6372	+	21.7299i	0.570261	+	0.329240i
$67$	86.4589	+	49.9171i	1.29043	+	0.745031i	0.978731	−	0.205149i	$-0.0657680\pi$
$67$	86.4589	+	49.9171i	1.29043	+	0.745031i	0.311701	+	0.950180i	$0.399101\pi$
$68$	7.87362	+	13.6375i	0.115789	+	0.200552i
$69$			56.4445i			0.818037i
$70$		0			0
$71$	−97.0831			−1.36737			−0.683684	−	0.729778i	$-0.739623\pi$
$71$	−97.0831			−1.36737			−0.683684	+	0.729778i	$0.739623\pi$
$72$	−7.34847	+	4.24264i	−0.102062	+	0.0589256i
$73$	−27.0175	+	46.7957i	−0.370103	+	0.641037i	−0.989581	−	0.143977i	$-0.954011\pi$
$73$	−27.0175	+	46.7957i	−0.370103	+	0.641037i	0.619478	+	0.785014i	$0.287344\pi$
$74$	30.8040	−	53.3541i	0.416270	−	0.721001i
$75$		0			0
$76$			40.6342i			0.534660i
$77$	101.615	−	71.4078i	1.31968	−	0.927374i
$78$		−	19.8584i		−	0.254595i
$79$	−37.3591	−	64.7079i	−0.472900	−	0.819087i	0.526619	−	0.850102i	$-0.323460\pi$
$79$	−37.3591	−	64.7079i	−0.472900	−	0.819087i	−0.999519	+	0.0310142i	$0.990126\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	49.7396	+	86.1515i	0.606580	+	1.05063i
$83$	85.2206			1.02675			0.513377	−	0.858163i	$-0.328394\pi$
$83$	85.2206			1.02675			0.513377	+	0.858163i	$0.328394\pi$
$84$	2.15418	+	24.1528i	0.0256450	+	0.287534i
$85$		0			0
$86$	−1.71954	−	2.97833i	−0.0199946	−	0.0346317i
$87$	21.7299	−	37.6372i	0.249769	−	0.432612i
$88$	43.4597	+	25.0915i	0.493861	+	0.285131i
$89$	115.343	−	66.5932i	1.29599	−	0.748238i	0.316279	−	0.948666i	$-0.397567\pi$
$89$	115.343	−	66.5932i	1.29599	−	0.748238i	0.979708	+	0.200428i	$0.0642332\pi$
$90$		0			0
$91$	−51.4734	−	23.8968i	−0.565642	−	0.262602i
$92$			65.1765i			0.708441i
$93$	−79.7931	+	46.0686i	−0.857991	+	0.495361i
$94$	18.8464	+	10.8809i	0.200493	+	0.115755i
$95$		0			0
$96$	−8.48528	+	4.89898i	−0.0883883	+	0.0510310i
$97$	−49.9973			−0.515436			−0.257718	−	0.966220i	$-0.582971\pi$
$97$	−49.9973			−0.515436			−0.257718	+	0.966220i	$0.582971\pi$
$98$	65.1970	+	23.4809i	0.665276	+	0.239601i
$99$	53.2271			0.537647
$100$		0			0
$101$	−142.296	−	82.1544i	−1.40887	−	0.813410i	−0.413588	−	0.910464i	$-0.635725\pi$
$101$	−142.296	−	82.1544i	−1.40887	−	0.813410i	−0.995279	+	0.0970542i	$0.969058\pi$
$102$	16.7025	+	9.64318i	0.163750	+	0.0945409i
$103$	−48.7198	−	84.3852i	−0.473008	−	0.819274i	0.526515	−	0.850166i	$-0.323498\pi$
$103$	−48.7198	−	84.3852i	−0.473008	−	0.819274i	−0.999523	+	0.0308923i	$0.990165\pi$
$104$		−	22.9305i		−	0.220485i
$105$		0			0
$106$	−71.9766			−0.679025
$107$	−84.4097	+	48.7339i	−0.788875	+	0.455457i	−0.839567	−	0.543257i	$-0.817191\pi$
$107$	−84.4097	+	48.7339i	−0.788875	+	0.455457i	0.0506910	+	0.998714i	$0.483858\pi$
$108$	−5.19615	+	9.00000i	−0.0481125	+	0.0833333i
$109$	−32.1284	+	55.6480i	−0.294756	+	0.510532i	−0.974928	−	0.222520i	$-0.928572\pi$
$109$	−32.1284	+	55.6480i	−0.294756	+	0.510532i	0.680172	+	0.733052i	$0.261905\pi$
$110$		0			0
$111$		−	75.4540i		−	0.679766i
$112$	2.48743	+	27.8893i	0.0222092	+	0.249012i
$113$			43.4647i			0.384643i	0.981332	+	0.192321i	$0.0616016\pi$
$113$			43.4647i			0.384643i	−0.981332	+	0.192321i	$0.938398\pi$
$114$	24.8833	+	43.0991i	0.218274	+	0.378062i
$115$		0			0
$116$	25.0915	−	43.4597i	0.216306	−	0.374653i
$117$	−12.1607	−	21.0630i	−0.103938	−	0.180026i
$118$	−37.5079			−0.317864
$119$	45.0944	−	31.6890i	0.378945	−	0.266294i
$120$		0			0
$121$	−96.8957	−	167.828i	−0.800791	−	1.38701i
$122$	−23.4786	+	40.6662i	−0.192448	+	0.333329i
$123$	105.514	+	60.9183i	0.857834	+	0.495271i
$124$	−92.1372	+	53.1954i	−0.743042	+	0.428995i
$125$		0			0
$126$	17.0754	+	24.2988i	0.135519	+	0.192848i
$127$			186.018i			1.46471i	0.680924	+	0.732354i	$0.261578\pi$
$127$			186.018i			1.46471i	−0.680924	+	0.732354i	$0.738422\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$	−3.64769	−	2.10599i	−0.0282767	−	0.0163255i
$130$		0			0
$131$	−78.0331	+	45.0524i	−0.595672	+	0.343912i	−0.767337	−	0.641244i	$-0.778419\pi$
$131$	−78.0331	+	45.0524i	−0.595672	+	0.343912i	0.171665	+	0.985155i	$0.445085\pi$
$132$	61.4613			0.465616
$133$	141.657	−	12.6343i	1.06509	−	0.0949951i
$134$	141.187			1.05363
$135$		0			0
$136$	19.2864	+	11.1350i	0.141811	+	0.0818749i
$137$	−9.38380	−	5.41774i	−0.0684949	−	0.0395456i	0.465361	−	0.885121i	$-0.345924\pi$
$137$	−9.38380	−	5.41774i	−0.0684949	−	0.0395456i	−0.533856	+	0.845575i	$0.679258\pi$
$138$	39.9123	+	69.1302i	0.289220	+	0.500943i
$139$		−	222.126i		−	1.59803i	−0.601314	−	0.799013i	$-0.705356\pi$
$139$		−	222.126i		−	1.59803i	0.601314	−	0.799013i	$-0.294644\pi$
$140$		0			0
$141$	26.6528			0.189027
$142$	−118.902	+	68.6481i	−0.837338	+	0.483438i
$143$	−71.9200	+	124.569i	−0.502937	+	0.871112i
$144$	−6.00000	+	10.3923i	−0.0416667	+	0.0721688i
$145$		0			0
$146$			76.4171i			0.523405i
$147$	83.5309	−	15.0196i	0.568237	−	0.102174i
$148$		−	87.1268i		−	0.588695i
$149$	−4.33681	−	7.51157i	−0.0291061	−	0.0504132i	0.851105	−	0.524995i	$-0.175933\pi$
$149$	−4.33681	−	7.51157i	−0.0291061	−	0.0504132i	−0.880212	+	0.474582i	$0.842599\pi$
$150$		0			0
$151$	−106.283	+	184.088i	−0.703861	+	1.21912i	0.263240	+	0.964730i	$0.415209\pi$
$151$	−106.283	+	184.088i	−0.703861	+	1.21912i	−0.967101	+	0.254392i	$0.918125\pi$
$152$	28.7327	+	49.7665i	0.189031	+	0.327411i
$153$	23.6209			0.154385
$154$	73.9601	−	159.309i	0.480260	−	1.03448i
$155$		0			0
$156$	−14.0420	−	24.3214i	−0.0900128	−	0.155907i
$157$	65.7193	−	113.829i	0.418594	−	0.725027i	−0.577204	−	0.816600i	$-0.695856\pi$
$157$	65.7193	−	113.829i	0.418594	−	0.725027i	0.995798	+	0.0915732i	$0.0291896\pi$
$158$	−91.5108	−	52.8338i	−0.579182	−	0.334391i
$159$	−76.3427	+	44.0765i	−0.480143	+	0.277211i
$160$		0			0
$161$	227.216	−	20.2653i	1.41128	−	0.125871i
$162$			12.7279i			0.0785674i
$163$	−38.8465	+	22.4281i	−0.238322	+	0.137595i	−0.614405	−	0.788990i	$-0.710604\pi$
$163$	−38.8465	+	22.4281i	−0.238322	+	0.137595i	0.376083	+	0.926586i	$0.377271\pi$
$164$	121.837	+	70.3424i	0.742906	+	0.428917i
$165$		0			0
$166$	104.374	−	60.2601i	0.628756	−	0.363013i
$167$	139.845			0.837398			0.418699	−	0.908125i	$-0.362486\pi$
$167$	139.845			0.837398			0.418699	+	0.908125i	$0.362486\pi$
$168$	19.7170	+	28.0578i	0.117363	+	0.167011i
$169$	−103.274			−0.611090
$170$		0			0
$171$	52.7853	+	30.4756i	0.308686	+	0.178220i
$172$	−4.21199	−	2.43179i	−0.0244883	−	0.0141383i
$173$	72.4165	+	125.429i	0.418593	+	0.725024i	0.995798	−	0.0915753i	$-0.0291902\pi$
$173$	72.4165	+	125.429i	0.418593	+	0.725024i	−0.577206	+	0.816599i	$0.695857\pi$
$174$		−	61.4613i		−	0.353226i
$175$		0			0
$176$	70.9695			0.403236
$177$	−39.7831	+	22.9688i	−0.224763	+	0.129767i
$178$	94.1770	−	163.119i	0.529084	−	0.916401i
$179$	−16.2046	+	28.0672i	−0.0905284	+	0.156800i	−0.907734	−	0.419547i	$-0.862189\pi$
$179$	−16.2046	+	28.0672i	−0.0905284	+	0.156800i	0.817205	+	0.576347i	$0.195522\pi$
$180$		0			0
$181$		−	119.139i		−	0.658227i	−0.944290	−	0.329113i	$-0.893250\pi$
$181$		−	119.139i		−	0.658227i	0.944290	−	0.329113i	$-0.106750\pi$
$182$	−79.9393	+	7.12975i	−0.439227	+	0.0391745i
$183$			57.5107i			0.314266i
$184$	46.0868	+	79.8246i	0.250472	+	0.433830i
$185$		0			0
$186$	−65.1508	+	112.845i	−0.350273	+	0.606691i
$187$	−69.8483	−	120.981i	−0.373520	−	0.646956i
$188$	30.7760			0.163702
$189$	32.9911	+	15.3163i	0.174556	+	0.0810384i
$190$		0			0
$191$	122.229	+	211.706i	0.639940	+	1.10841i	0.985445	+	0.169992i	$0.0543743\pi$
$191$	122.229	+	211.706i	0.639940	+	1.10841i	−0.345505	+	0.938417i	$0.612292\pi$
$192$	−6.92820	+	12.0000i	−0.0360844	+	0.0625000i
$193$	221.323	+	127.781i	1.14675	+	0.662077i	0.948093	−	0.317992i	$-0.103009\pi$
$193$	221.323	+	127.781i	1.14675	+	0.662077i	0.198657	+	0.980069i	$0.436342\pi$
$194$	−61.2339	+	35.3534i	−0.315639	+	0.182234i
$195$		0			0
$196$	96.4532	−	17.3432i	0.492108	−	0.0884856i
$197$		−	351.495i		−	1.78424i	−0.451802	−	0.892118i	$-0.649218\pi$
$197$		−	351.495i		−	1.78424i	0.451802	−	0.892118i	$-0.350782\pi$
$198$	65.1896	−	37.6372i	0.329240	−	0.190087i
$199$	−266.168	−	153.672i	−1.33753	−	0.772222i	−0.351087	−	0.936343i	$-0.614188\pi$
$199$	−266.168	−	153.672i	−1.33753	−	0.772222i	−0.986440	+	0.164121i	$0.947521\pi$
$200$		0			0
$201$	149.751	−	86.4589i	0.745031	−	0.430144i
$202$	−232.368			−1.15034
$203$	−159.309	−	73.9601i	−0.784775	−	0.364335i
$204$	27.2750			0.133701
$205$		0			0
$206$	−119.339	−	68.9002i	−0.579314	−	0.334467i
$207$	84.6668	+	48.8824i	0.409018	+	0.236147i
$208$	−16.2143	−	28.0840i	−0.0779533	−	0.135019i
$209$		−	360.473i		−	1.72475i
$210$		0			0
$211$	−335.164			−1.58845			−0.794227	−	0.607621i	$-0.792124\pi$
$211$	−335.164			−1.58845			−0.794227	+	0.607621i	$0.792124\pi$
$212$	−88.1530	+	50.8952i	−0.415816	+	0.240071i
$213$	−84.0765	+	145.625i	−0.394725	+	0.683684i
$214$	−68.9202	+	119.373i	−0.322057	+	0.557819i
$215$		0			0
$216$			14.6969i			0.0680414i
$217$	214.096	+	304.665i	0.986617	+	1.40399i
$218$			90.8728i			0.416847i
$219$	46.7957	+	81.0526i	0.213679	+	0.370103i
$220$		0			0
$221$	−31.9163	+	55.2806i	−0.144418	+	0.250139i
$222$	−53.3541	−	92.4119i	−0.240334	−	0.416270i
$223$	−50.9497			−0.228474			−0.114237	−	0.993454i	$-0.536442\pi$
$223$	−50.9497			−0.228474			−0.114237	+	0.993454i	$0.536442\pi$
$224$	22.7672	+	32.3984i	0.101639	+	0.144636i
$225$		0			0
$226$	30.7342	+	53.2331i	0.135992	+	0.235545i
$227$	66.2128	−	114.684i	0.291686	−	0.505215i	−0.682522	−	0.730865i	$-0.739117\pi$
$227$	66.2128	−	114.684i	0.291686	−	0.505215i	0.974209	+	0.225649i	$0.0724504\pi$
$228$	60.9513	+	35.1902i	0.267330	+	0.154343i
$229$	−159.636	+	92.1659i	−0.697101	+	0.402471i	−0.806267	−	0.591552i	$-0.798515\pi$
$229$	−159.636	+	92.1659i	−0.697101	+	0.402471i	0.109166	+	0.994024i	$0.465182\pi$
$230$		0			0
$231$	−19.1101	−	214.264i	−0.0827278	−	0.927551i
$232$		−	70.9695i		−	0.305903i
$233$	−121.821	+	70.3332i	−0.522836	+	0.301859i	−0.738094	−	0.674698i	$-0.764274\pi$
$233$	−121.821	+	70.3332i	−0.522836	+	0.301859i	0.215258	+	0.976557i	$0.430941\pi$
$234$	−29.7876	−	17.1979i	−0.127297	−	0.0734951i
$235$		0			0
$236$	−45.9376	+	26.5221i	−0.194651	+	0.112382i
$237$	−129.416			−0.546058
$238$	32.8217	−	70.6975i	0.137906	−	0.297048i
$239$	247.975			1.03755			0.518777	−	0.854910i	$-0.326388\pi$
$239$	247.975			1.03755			0.518777	+	0.854910i	$0.326388\pi$
$240$		0			0
$241$	−189.530	−	109.425i	−0.786431	−	0.454046i	0.0522735	−	0.998633i	$-0.483353\pi$
$241$	−189.530	−	109.425i	−0.786431	−	0.454046i	−0.838705	+	0.544587i	$0.816687\pi$
$242$	−237.345	−	137.031i	−0.980765	−	0.566245i
$243$	7.79423	+	13.5000i	0.0320750	+	0.0555556i
$244$			66.4076i			0.272162i
$245$		0			0
$246$	172.303			0.700419
$247$	−142.646	+	82.3568i	−0.577515	+	0.333428i
$248$	−75.2297	+	130.302i	−0.303345	+	0.525410i
$249$	73.8032	−	127.831i	0.296399	−	0.513377i
$250$		0			0
$251$		−	37.7083i		−	0.150232i	−0.997175	−	0.0751161i	$-0.976067\pi$
$251$		−	37.7083i		−	0.150232i	0.997175	−	0.0751161i	$-0.0239327\pi$
$252$	38.0948	+	17.6857i	0.151170	+	0.0701814i
$253$		−	578.193i		−	2.28535i
$254$	131.534	+	227.824i	0.517852	+	0.896946i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−9.53153	−	16.5091i	−0.0370877	−	0.0642377i	0.846886	−	0.531775i	$-0.178475\pi$
$257$	−9.53153	−	16.5091i	−0.0370877	−	0.0642377i	−0.883973	+	0.467537i	$0.845141\pi$
$258$	−5.95665			−0.0230878
$259$	−303.738	+	27.0903i	−1.17273	+	0.104596i
$260$		0			0
$261$	−37.6372	−	65.1896i	−0.144204	−	0.249769i
$262$	−63.7137	+	110.355i	−0.243182	+	0.421204i
$263$	207.590	+	119.852i	0.789316	+	0.455712i	0.839722	−	0.543017i	$-0.182718\pi$
$263$	207.590	+	119.852i	0.789316	+	0.455712i	−0.0504060	+	0.998729i	$0.516052\pi$
$264$	75.2745	−	43.4597i	0.285131	−	0.164620i
$265$		0			0
$266$	164.560	−	115.641i	0.618647	−	0.434739i
$267$		−	230.686i		−	0.863991i
$268$	172.918	−	99.8341i	0.645216	−	0.372515i
$269$	−230.871	−	133.293i	−0.858256	−	0.495514i	0.00517171	−	0.999987i	$-0.498354\pi$
$269$	−230.871	−	133.293i	−0.858256	−	0.495514i	−0.863428	+	0.504472i	$0.831687\pi$
$270$		0			0
$271$	316.324	−	182.630i	1.16725	−	0.673911i	0.214218	−	0.976786i	$-0.431280\pi$
$271$	316.324	−	182.630i	1.16725	−	0.673911i	0.953030	+	0.302875i	$0.0979464\pi$
$272$	31.4945			0.115789
$273$	−80.4224	+	56.5149i	−0.294588	+	0.207014i
$274$	−15.3237			−0.0559259
$275$		0			0
$276$	97.7648	+	56.4445i	0.354220	+	0.204509i
$277$	−368.004	−	212.467i	−1.32853	−	0.767030i	−0.343461	−	0.939167i	$-0.611599\pi$
$277$	−368.004	−	212.467i	−1.32853	−	0.767030i	−0.985073	+	0.172137i	$0.944933\pi$
$278$	−157.066	−	272.047i	−0.564987	−	0.978587i
$279$			159.586i			0.571994i
$280$		0			0
$281$	144.818			0.515368			0.257684	−	0.966229i	$-0.417041\pi$
$281$	144.818			0.515368			0.257684	+	0.966229i	$0.417041\pi$
$282$	32.6428	−	18.8464i	0.115755	−	0.0668310i
$283$	162.433	−	281.343i	0.573969	−	0.994143i	−0.422184	−	0.906510i	$-0.638736\pi$
$283$	162.433	−	281.343i	0.573969	−	0.994143i	0.996153	−	0.0876331i	$-0.0279303\pi$
$284$	−97.0831	+	168.153i	−0.341842	+	0.592088i
$285$		0			0
$286$			203.420i			0.711260i
$287$	207.342	−	446.614i	0.722447	−	1.55614i
$288$			16.9706i			0.0589256i
$289$	113.503	+	196.593i	0.392744	+	0.680253i
$290$		0			0
$291$	−43.2989	+	74.9959i	−0.148793	+	0.257718i
$292$	54.0350	+	93.5914i	0.185052	+	0.320519i
$293$	171.836			0.586470			0.293235	−	0.956040i	$-0.405268\pi$
$293$	171.836			0.586470			0.293235	+	0.956040i	$0.405268\pi$
$294$	91.6835	−	77.4605i	0.311849	−	0.263471i
$295$		0			0
$296$	−61.6080	−	106.708i	−0.208135	−	0.360500i
$297$	46.0960	−	79.8406i	0.155205	−	0.268824i
$298$	−10.6230	−	6.13317i	−0.0356475	−	0.0205811i
$299$	−228.802	+	132.099i	−0.765224	+	0.441802i
$300$		0			0
$301$	−7.16799	+	15.4398i	−0.0238139	+	0.0512950i
$302$			300.614i			0.995410i
$303$	−246.463	+	142.296i	−0.813410	+	0.469622i
$304$	70.3805	+	40.6342i	0.231515	+	0.133665i
$305$		0			0
$306$	28.9295	−	16.7025i	0.0945409	−	0.0545832i
$307$	114.101			0.371663			0.185832	−	0.982582i	$-0.440502\pi$
$307$	114.101			0.371663			0.185832	+	0.982582i	$0.440502\pi$
$308$	−22.0665	−	247.411i	−0.0716444	−	0.803282i
$309$	−168.770			−0.546182
$310$		0			0
$311$	134.405	+	77.5988i	0.432171	+	0.249514i	0.700271	−	0.713877i	$-0.253063\pi$
$311$	134.405	+	77.5988i	0.432171	+	0.249514i	−0.268100	+	0.963391i	$0.586396\pi$
$312$	−34.3957	−	19.8584i	−0.110243	−	0.0636486i
$313$	−212.548	−	368.143i	−0.679066	−	1.17618i	−0.975263	−	0.221050i	$-0.929052\pi$
$313$	−212.548	−	368.143i	−0.679066	−	1.17618i	0.296197	−	0.955127i	$-0.404282\pi$
$314$		−	185.882i		−	0.591982i
$315$		0			0
$316$	−149.437			−0.472900
$317$	−12.4651	+	7.19672i	−0.0393220	+	0.0227026i	−0.519532	−	0.854451i	$-0.673894\pi$
$317$	−12.4651	+	7.19672i	−0.0393220	+	0.0227026i	0.480210	+	0.877153i	$0.340560\pi$
$318$	−62.3336	+	107.965i	−0.196018	+	0.339512i
$319$	−222.591	+	385.539i	−0.697778	+	1.20859i
$320$		0			0
$321$			168.819i			0.525917i
$322$	263.952	−	185.486i	0.819726	−	0.576043i
$323$		−	159.969i		−	0.495260i
$324$	9.00000	+	15.5885i	0.0277778	+	0.0481125i
$325$		0			0
$326$	−31.7181	+	54.9373i	−0.0972947	+	0.168519i
$327$	55.6480	+	96.3851i	0.170177	+	0.294756i
$328$	198.958			0.606580
$329$	−9.56914	−	107.290i	−0.0290855	−	0.326109i
$330$		0			0
$331$	42.5972	+	73.7805i	0.128692	+	0.222902i	0.923170	−	0.384391i	$-0.125589\pi$
$331$	42.5972	+	73.7805i	0.128692	+	0.222902i	−0.794478	+	0.607293i	$0.792255\pi$
$332$	85.2206	−	147.606i	0.256689	−	0.444598i
$333$	−113.181	−	65.3451i	−0.339883	−	0.196232i
$334$	171.275	−	98.8857i	0.512800	−	0.296065i
$335$		0			0
$336$	43.9881	+	20.4217i	0.130917	+	0.0607788i
$337$			122.057i			0.362186i	0.983466	+	0.181093i	$0.0579635\pi$
$337$			122.057i			0.362186i	−0.983466	+	0.181093i	$0.942036\pi$
$338$	−126.485	+	73.0259i	−0.374215	+	0.216053i
$339$	65.1970	+	37.6415i	0.192321	+	0.111037i
$340$		0			0
$341$	817.366	−	471.906i	2.39697	−	1.38389i
$342$	86.1981			0.252041
$343$	−90.4512	−	330.859i	−0.263706	−	0.964603i
$344$	−6.87815			−0.0199946
$345$		0			0
$346$	177.383	+	102.412i	0.512669	+	0.295990i
$347$	−213.607	−	123.326i	−0.615581	−	0.355406i	0.159565	−	0.987187i	$-0.448991\pi$
$347$	−213.607	−	123.326i	−0.615581	−	0.355406i	−0.775147	+	0.631781i	$0.782324\pi$
$348$	−43.4597	−	75.2745i	−0.124884	−	0.216306i
$349$			265.448i			0.760596i	0.924864	+	0.380298i	$0.124179\pi$
$349$			265.448i			0.760596i	−0.924864	+	0.380298i	$0.875821\pi$
$350$		0			0
$351$	−42.1260			−0.120017
$352$	86.9195	−	50.1830i	0.246930	−	0.142565i
$353$	−140.800	+	243.873i	−0.398867	+	0.690858i	−0.993586	−	0.113076i	$-0.963930\pi$
$353$	−140.800	+	243.873i	−0.398867	+	0.690858i	0.594720	+	0.803933i	$0.297263\pi$
$354$	−32.4828	+	56.2619i	−0.0917593	+	0.158932i
$355$		0			0
$356$		−	266.373i		−	0.748238i
$357$	−8.48060	−	95.0851i	−0.0237552	−	0.266345i
$358$			45.8335i			0.128026i
$359$	3.21594	+	5.57016i	0.00895804	+	0.0155158i	0.870470	−	0.492222i	$-0.163815\pi$
$359$	3.21594	+	5.57016i	0.00895804	+	0.0155158i	−0.861512	+	0.507738i	$0.830482\pi$
$360$		0			0
$361$	25.8921	−	44.8463i	0.0717231	−	0.124228i
$362$	−84.2440	−	145.915i	−0.232718	−	0.403080i
$363$	−335.657			−0.924674
$364$	−92.8638	+	65.2578i	−0.255120	+	0.179280i
$365$		0			0
$366$	40.6662	+	70.4359i	0.111110	+	0.192448i
$367$	125.255	−	216.948i	0.341295	−	0.591140i	−0.643379	−	0.765548i	$-0.722468\pi$
$367$	125.255	−	216.948i	0.341295	−	0.591140i	0.984673	+	0.174408i	$0.0558012\pi$
$368$	112.889	+	65.1765i	0.306764	+	0.177110i
$369$	182.755	−	105.514i	0.495271	−	0.285945i
$370$		0			0
$371$	204.838	+	291.491i	0.552124	+	0.785689i
$372$			184.274i			0.495361i
$373$	−366.119	+	211.379i	−0.981552	+	0.566700i	−0.902738	−	0.430190i	$-0.858447\pi$
$373$	−366.119	+	211.379i	−0.981552	+	0.566700i	−0.0788140	+	0.996889i	$0.525113\pi$
$374$	−171.093	−	98.7804i	−0.457467	−	0.264119i
$375$		0			0
$376$	37.6927	−	21.7619i	0.100247	−	0.0578774i
$377$	203.420			0.539577
$378$	51.2359	−	4.56971i	0.135545	−	0.0120892i
$379$	510.205			1.34619			0.673093	−	0.739558i	$-0.264965\pi$
$379$	510.205			1.34619			0.673093	+	0.739558i	$0.264965\pi$
$380$		0			0
$381$	279.027	+	161.096i	0.732354	+	0.422825i
$382$	299.398	+	172.857i	0.783764	+	0.452506i
$383$	−134.443	−	232.862i	−0.351026	−	0.607995i	0.635404	−	0.772180i	$-0.280834\pi$
$383$	−134.443	−	232.862i	−0.351026	−	0.607995i	−0.986429	+	0.164185i	$0.947500\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	361.419			0.936318
$387$	−6.31798	+	3.64769i	−0.0163255	+	0.00942555i
$388$	−49.9973	+	86.5978i	−0.128859	+	0.223190i
$389$	−83.8883	+	145.299i	−0.215651	+	0.373519i	−0.953474	−	0.301476i	$-0.902521\pi$
$389$	−83.8883	+	145.299i	−0.215651	+	0.373519i	0.737823	+	0.674995i	$0.235854\pi$
$390$		0			0
$391$		−	256.588i		−	0.656234i
$392$	105.867	−	89.4437i	0.270069	−	0.228173i
$393$			156.066i			0.397115i
$394$	−248.544	−	430.491i	−0.630823	−	1.09262i
$395$		0			0
$396$	53.2271	−	92.1920i	0.134412	−	0.232808i
$397$	−181.784	−	314.858i	−0.457893	−	0.793094i	0.540956	−	0.841051i	$-0.318062\pi$
$397$	−181.784	−	314.858i	−0.457893	−	0.793094i	−0.998849	+	0.0479565i	$0.984729\pi$
$398$	−434.650			−1.09209
$399$	103.727	−	223.428i	0.259968	−	0.559969i
$400$		0			0
$401$	−139.416	−	241.475i	−0.347670	−	0.602182i	0.638165	−	0.769900i	$-0.279694\pi$
$401$	−139.416	−	241.475i	−0.347670	−	0.602182i	−0.985835	+	0.167717i	$0.946360\pi$
$402$	122.271	−	211.780i	0.304158	−	0.526816i
$403$	−373.485	−	215.632i	−0.926761	−	0.535066i
$404$	−284.591	+	164.309i	−0.704434	+	0.406705i
$405$		0			0
$406$	−247.411	+	22.0665i	−0.609387	+	0.0543509i
$407$			772.918i			1.89906i
$408$	33.4049	−	19.2864i	0.0818749	−	0.0472705i
$409$	−337.862	−	195.065i	−0.826068	−	0.476931i	0.0264364	−	0.999650i	$-0.491584\pi$
$409$	−337.862	−	195.065i	−0.826068	−	0.476931i	−0.852505	+	0.522720i	$0.824917\pi$
$410$		0			0
$411$	−16.2532	+	9.38380i	−0.0395456	+	0.0228316i
$412$	−194.879			−0.473008
$413$	106.744	+	151.899i	0.258459	+	0.367795i
$414$	138.260			0.333962
$415$		0			0
$416$	−39.7167	−	22.9305i	−0.0954729	−	0.0551213i
$417$	−333.188	−	192.366i	−0.799013	−	0.461310i
$418$	−254.893	−	441.488i	−0.609792	−	1.05619i
$419$			576.896i			1.37684i	0.725313	+	0.688419i	$0.241695\pi$
$419$			576.896i			1.37684i	−0.725313	+	0.688419i	$0.758305\pi$
$420$		0			0
$421$	649.851			1.54359			0.771795	−	0.635871i	$-0.219359\pi$
$421$	649.851			1.54359			0.771795	+	0.635871i	$0.219359\pi$
$422$	−410.490	+	236.997i	−0.972725	+	0.561603i
$423$	23.0820	−	39.9792i	0.0545673	−	0.0945134i
$424$	−71.9766	+	124.667i	−0.169756	+	0.294026i
$425$		0			0
$426$			237.804i			0.558226i
$427$	231.508	−	20.6481i	0.542172	−	0.0483561i
$428$			194.936i			0.455457i
$429$	124.569	+	215.760i	0.290371	+	0.502937i
$430$		0			0
$431$	−346.089	+	599.444i	−0.802991	+	1.39082i	0.114648	+	0.993406i	$0.463426\pi$
$431$	−346.089	+	599.444i	−0.802991	+	1.39082i	−0.917639	+	0.397415i	$0.869907\pi$
$432$	10.3923	+	18.0000i	0.0240563	+	0.0416667i
$433$	−116.563			−0.269200			−0.134600	−	0.990900i	$-0.542975\pi$
$433$	−116.563			−0.269200			−0.134600	+	0.990900i	$0.542975\pi$
$434$	477.644	+	221.748i	1.10056	+	0.510941i
$435$		0			0
$436$	64.2567	+	111.296i	0.147378	+	0.255266i
$437$	331.049	−	573.394i	0.757550	−	1.31212i
$438$	114.626	+	66.1791i	0.261702	+	0.151094i
$439$	−152.664	+	88.1408i	−0.347755	+	0.200776i	−0.663696	−	0.748002i	$-0.731013\pi$
$439$	−152.664	+	88.1408i	−0.347755	+	0.200776i	0.315941	+	0.948779i	$0.397680\pi$
$440$		0			0
$441$	49.8104	−	138.304i	0.112949	−	0.313614i
$442$			90.2729i			0.204237i
$443$	284.069	−	164.007i	0.641239	−	0.370219i	−0.143853	−	0.989599i	$-0.545949\pi$
$443$	284.069	−	164.007i	0.641239	−	0.370219i	0.785092	+	0.619380i	$0.212616\pi$
$444$	−130.690	−	75.4540i	−0.294347	−	0.169942i
$445$		0			0
$446$	−62.4003	+	36.0268i	−0.139911	+	0.0807777i
$447$	−15.0231			−0.0336088
$448$	50.7931	+	23.5809i	0.113377	+	0.0526360i
$449$	808.713			1.80114			0.900571	−	0.434709i	$-0.143149\pi$
$449$	808.713			1.80114			0.900571	+	0.434709i	$0.143149\pi$
$450$		0			0
$451$	−1080.83	−	624.020i	−2.39653	−	1.38364i
$452$	75.2830	+	43.4647i	0.166555	+	0.0961607i
$453$	184.088	+	318.849i	0.406374	+	0.703861i
$454$		−	187.278i		−	0.412507i
$455$		0			0
$456$	99.5330			0.218274
$457$	−291.757	+	168.446i	−0.638418	+	0.368591i	−0.784005	−	0.620755i	$-0.786826\pi$
$457$	−291.757	+	168.446i	−0.638418	+	0.368591i	0.145587	+	0.989345i	$0.453493\pi$
$458$	−130.342	+	225.760i	−0.284590	+	0.492925i
$459$	20.4563	−	35.4313i	0.0445670	−	0.0771924i
$460$		0			0
$461$			614.879i			1.33379i	0.745150	+	0.666897i	$0.232378\pi$
$461$			614.879i			1.33379i	−0.745150	+	0.666897i	$0.767622\pi$
$462$	−174.913	−	248.906i	−0.378599	−	0.538758i
$463$		−	818.194i		−	1.76716i	−0.468283	−	0.883578i	$-0.655127\pi$
$463$		−	818.194i		−	1.76716i	0.468283	−	0.883578i	$-0.344873\pi$
$464$	−50.1830	−	86.9195i	−0.108153	−	0.187326i
$465$		0			0
$466$	−99.4662	+	172.281i	−0.213447	+	0.369701i
$467$	265.894	+	460.542i	0.569367	+	0.986172i	0.996629	+	0.0820440i	$0.0261448\pi$
$467$	265.894	+	460.542i	0.569367	+	0.986172i	−0.427262	+	0.904128i	$0.640522\pi$
$468$	−48.6429			−0.103938
$469$	−401.803	−	571.778i	−0.856723	−	1.21914i
$470$		0			0
$471$	−113.829	−	197.158i	−0.241676	−	0.418594i
$472$	−37.5079	+	64.9656i	−0.0794659	+	0.137639i
$473$	37.3653	+	21.5729i	0.0789964	+	0.0456086i
$474$	−158.501	+	91.5108i	−0.334391	+	0.193061i
$475$		0			0
$476$	−9.79255	−	109.795i	−0.0205726	−	0.230661i
$477$			152.685i			0.320095i
$478$	303.706	−	175.345i	0.635369	−	0.366830i
$479$	−552.718	−	319.112i	−1.15390	−	0.666204i	−0.204065	−	0.978957i	$-0.565415\pi$
$479$	−552.718	−	319.112i	−1.15390	−	0.666204i	−0.949834	+	0.312753i	$0.898749\pi$
$480$		0			0
$481$	305.858	−	176.587i	0.635880	−	0.367126i
$482$	−309.501			−0.642118
$483$	166.377	−	358.374i	0.344466	−	0.741976i
$484$	−387.583			−0.800791
$485$		0			0
$486$	19.0919	+	11.0227i	0.0392837	+	0.0226805i
$487$	−336.754	−	194.425i	−0.691486	−	0.399230i	0.112683	−	0.993631i	$-0.464056\pi$
$487$	−336.754	−	194.425i	−0.691486	−	0.399230i	−0.804168	+	0.594402i	$0.797389\pi$
$488$	46.9573	+	81.3324i	0.0962239	+	0.166665i
$489$			77.6931i			0.158882i
$490$		0			0
$491$	695.908			1.41733			0.708664	−	0.705546i	$-0.249298\pi$
$491$	695.908			1.41733			0.708664	+	0.705546i	$0.249298\pi$
$492$	211.027	−	121.837i	0.428917	−	0.247635i
$493$	−98.7804	+	171.093i	−0.200366	+	0.347044i
$494$	−116.470	+	201.732i	−0.235769	+	0.408365i
$495$		0			0
$496$			212.782i			0.428995i
$497$	616.394	+	286.164i	1.24023	+	0.575782i
$498$		−	208.747i		−	0.419171i
$499$	−265.395	−	459.678i	−0.531854	−	0.921199i	−0.999309	−	0.0371815i	$-0.988162\pi$
$499$	−265.395	−	459.678i	−0.531854	−	0.921199i	0.467454	−	0.884017i	$-0.345171\pi$
$500$		0			0
$501$	121.110	−	209.768i	0.241736	−	0.418699i
$502$	−26.6638	−	46.1830i	−0.0531151	−	0.0919980i
$503$	694.388			1.38049			0.690247	−	0.723574i	$-0.257502\pi$
$503$	694.388			1.38049			0.690247	+	0.723574i	$0.257502\pi$
$504$	59.1621	−	5.27664i	0.117385	−	0.0104695i
$505$		0			0
$506$	−408.844	−	708.139i	−0.807992	−	1.39948i
$507$	−89.4381	+	154.911i	−0.176406	+	0.305545i
$508$	322.192	+	186.018i	0.634237	+	0.366177i
$509$	246.728	−	142.448i	0.484730	−	0.279859i	−0.237656	−	0.971349i	$-0.576379\pi$
$509$	246.728	−	142.448i	0.484730	−	0.279859i	0.722386	+	0.691491i	$0.243046\pi$
$510$		0			0
$511$	309.474	−	217.475i	0.605624	−	0.425588i
$512$			22.6274i			0.0441942i
$513$	91.4269	−	52.7853i	0.178220	−	0.102895i
$514$	−23.3474	−	13.4796i	−0.0454229	−	0.0262250i
$515$		0			0
$516$	−7.29538	+	4.21199i	−0.0141383	+	0.00816277i
$517$	−273.019			−0.528084
$518$	−352.846	+	247.954i	−0.681170	+	0.478676i
$519$	250.858			0.483349
$520$		0			0
$521$	450.682	+	260.201i	0.865033	+	0.499427i	0.865694	−	0.500573i	$-0.166877\pi$
$521$	450.682	+	260.201i	0.865033	+	0.499427i	−0.000661748		1.00000i	$0.500211\pi$
$522$	−92.1920	−	53.2271i	−0.176613	−	0.101968i
$523$	85.7878	+	148.589i	0.164030	+	0.284109i	0.936310	−	0.351173i	$-0.114217\pi$
$523$	85.7878	+	148.589i	0.164030	+	0.284109i	−0.772280	+	0.635282i	$0.780884\pi$
$524$			180.210i			0.343912i
$525$		0			0
$526$	338.993			0.644473
$527$	362.727	−	209.420i	0.688286	−	0.397382i
$528$	61.4613	−	106.454i	0.116404	−	0.201618i
$529$	266.498	−	461.587i	0.503776	−	0.872566i
$530$		0			0
$531$			79.5663i			0.149842i
$532$	119.774	−	257.992i	0.225139	−	0.484947i
$533$			570.276i			1.06994i
$534$	−163.119	−	282.531i	−0.305467	−	0.529084i
$535$		0			0
$536$	141.187	−	244.543i	0.263408	−	0.456236i
$537$	28.0672	+	48.6137i	0.0522666	+	0.0905284i
$538$	−377.011			−0.700763
$539$	−855.654	+	153.855i	−1.58748	+	0.285444i
$540$		0			0
$541$	188.929	+	327.235i	0.349222	+	0.604871i	0.986111	−	0.166085i	$-0.0531125\pi$
$541$	188.929	+	327.235i	0.349222	+	0.604871i	−0.636889	+	0.770955i	$0.719779\pi$
$542$	258.278	−	447.350i	0.476527	−	0.825369i
$543$	−178.709	−	103.177i	−0.329113	−	0.190014i
$544$	38.5727	−	22.2700i	0.0709057	−	0.0409374i
$545$		0			0
$546$	−58.5349	+	126.084i	−0.107207	+	0.230922i
$547$			982.972i			1.79702i	0.438950	+	0.898511i	$0.355350\pi$
$547$			982.972i			1.79702i	−0.438950	+	0.898511i	$0.644650\pi$
$548$	−18.7676	+	10.8355i	−0.0342475	+	0.0197728i
$549$	86.2660	+	49.8057i	0.157133	+	0.0907208i
$550$		0			0
$551$	−441.488	+	254.893i	−0.801248	+	0.462601i
$552$	159.649			0.289220
$553$	46.4642	+	520.960i	0.0840220	+	0.942061i
$554$	−600.948			−1.08474
$555$		0			0
$556$	−384.733	−	222.126i	−0.691965	−	0.399506i
$557$	−312.143	−	180.216i	−0.560401	−	0.323548i	0.192905	−	0.981217i	$-0.438209\pi$
$557$	−312.143	−	180.216i	−0.560401	−	0.323548i	−0.753306	+	0.657670i	$0.771542\pi$
$558$	112.845	+	195.452i	0.202230	+	0.350273i
$559$		−	19.7149i		−	0.0352682i
$560$		0			0
$561$	−241.962			−0.431304
$562$	177.366	−	102.402i	0.315597	−	0.182210i
$563$	337.825	−	585.130i	0.600044	−	1.03931i	−0.392770	−	0.919637i	$-0.628483\pi$
$563$	337.825	−	585.130i	0.600044	−	1.03931i	0.992814	−	0.119670i	$-0.0381836\pi$
$564$	26.6528	−	46.1640i	0.0472567	−	0.0818510i
$565$		0			0
$566$		−	459.430i		−	0.811715i
$567$	51.5455	−	36.2224i	0.0909092	−	0.0638842i
$568$			274.593i			0.483438i
$569$	500.576	+	867.022i	0.879746	+	1.52376i	0.851620	+	0.524160i	$0.175621\pi$
$569$	500.576	+	867.022i	0.879746	+	1.52376i	0.0281265	+	0.999604i	$0.491046\pi$
$570$		0			0
$571$	−363.407	+	629.439i	−0.636439	+	1.10235i	0.349769	+	0.936836i	$0.386260\pi$
$571$	−363.407	+	629.439i	−0.636439	+	1.10235i	−0.986208	+	0.165509i	$0.947073\pi$
$572$	143.840	+	249.138i	0.251468	+	0.435556i
$573$	423.412			0.738940
$574$	−61.8619	−	693.601i	−0.107773	−	1.20836i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	−33.5564	+	58.1213i	−0.0581566	+	0.100730i	−0.893638	−	0.448789i	$-0.851856\pi$
$577$	−33.5564	+	58.1213i	−0.0581566	+	0.100730i	0.835481	+	0.549519i	$0.185189\pi$
$578$	278.025	+	160.518i	0.481011	+	0.277712i
$579$	383.342	−	221.323i	0.662077	−	0.382250i
$580$		0			0
$581$	−541.078	−	251.198i	−0.931287	−	0.432354i
$582$			122.468i			0.210426i
$583$	782.021	−	451.500i	1.34137	−	0.774443i
$584$	132.358	+	76.4171i	0.226641	+	0.130851i
$585$		0			0
$586$	210.455	−	121.506i	0.359138	−	0.207349i
$587$	−964.783			−1.64358			−0.821791	−	0.569788i	$-0.807025\pi$
$587$	−964.783			−1.64358			−0.821791	+	0.569788i	$0.807025\pi$
$588$	57.5161	−	159.699i	0.0978165	−	0.271598i
$589$	1080.78			1.83493
$590$		0			0
$591$	−527.242	−	304.403i	−0.892118	−	0.515065i
$592$	−150.908	−	87.1268i	−0.254912	−	0.147174i
$593$	−0.846966	−	1.46699i	−0.00142827	−	0.00247384i	0.865310	−	0.501236i	$-0.167121\pi$
$593$	−0.846966	−	1.46699i	−0.00142827	−	0.00247384i	−0.866739	+	0.498763i	$0.833788\pi$
$594$		−	130.379i		−	0.219494i
$595$		0			0
$596$	−17.3472			−0.0291061
$597$	−461.016	+	266.168i	−0.772222	+	0.445842i
$598$	−186.816	+	323.575i	−0.312402	+	0.541095i
$599$	46.3714	−	80.3177i	0.0774147	−	0.134086i	−0.824719	−	0.565543i	$-0.808667\pi$
$599$	46.3714	−	80.3177i	0.0774147	−	0.134086i	0.902134	+	0.431456i	$0.142000\pi$
$600$		0			0
$601$			393.426i			0.654618i	0.944917	+	0.327309i	$0.106142\pi$
$601$			393.426i			0.654618i	−0.944917	+	0.327309i	$0.893858\pi$
$602$	2.13862	+	23.9783i	0.00355252	+	0.0398311i
$603$		−	299.502i		−	0.496687i
$604$	212.566	+	368.175i	0.351930	+	0.609561i
$605$		0			0
$606$	−201.236	+	348.552i	−0.332073	+	0.575168i
$607$	−148.539	−	257.278i	−0.244711	−	0.423851i	0.717340	−	0.696724i	$-0.245360\pi$
$607$	−148.539	−	257.278i	−0.244711	−	0.423851i	−0.962050	+	0.272872i	$0.912026\pi$
$608$	114.931			0.189031
$609$	−248.906	+	174.913i	−0.408713	+	0.287213i
$610$		0			0
$611$	62.3763	+	108.039i	0.102089	+	0.176823i
$612$	23.6209	−	40.9125i	0.0385962	−	0.0668505i
$613$	876.111	+	505.823i	1.42922	+	0.825160i	0.997059	−	0.0766368i	$-0.0244182\pi$
$613$	876.111	+	505.823i	1.42922	+	0.825160i	0.432160	+	0.901797i	$0.357752\pi$
$614$	139.744	−	80.6813i	0.227596	−	0.131403i
$615$		0			0
$616$	−201.972	−	287.412i	−0.327876	−	0.466578i
$617$		−	467.794i		−	0.758174i	−0.925361	−	0.379087i	$-0.876238\pi$
$617$		−	467.794i		−	0.758174i	0.925361	−	0.379087i	$-0.123762\pi$
$618$	−206.701	+	119.339i	−0.334467	+	0.193105i
$619$	919.996	+	531.160i	1.48626	+	0.858094i	0.999878	−	0.0156508i	$-0.00498201\pi$
$619$	919.996	+	531.160i	1.48626	+	0.858094i	0.486385	+	0.873745i	$0.338315\pi$
$620$		0			0
$621$	146.647	−	84.6668i	0.236147	−	0.136339i
$622$	219.483			0.352866
$623$	−928.619	+	82.8231i	−1.49056	+	0.132942i
$624$	−56.1680			−0.0900128
$625$		0			0
$626$	−520.633	−	300.588i	−0.831682	−	0.480172i
$627$	−540.710	−	312.179i	−0.862376	−	0.497893i
$628$	−131.439	−	227.658i	−0.209297	−	0.362513i
$629$			343.002i			0.545313i
$630$		0			0
$631$	−970.749			−1.53843			−0.769215	−	0.638990i	$-0.779352\pi$
$631$	−970.749			−1.53843			−0.769215	+	0.638990i	$0.779352\pi$
$632$	−183.022	+	105.668i	−0.289591	+	0.167196i
$633$	−290.260	+	502.746i	−0.458547	+	0.794227i
$634$	−10.1777	+	17.6283i	−0.0160531	+	0.0278049i
$635$		0			0
$636$			176.306i			0.277211i
$637$	256.373	+	303.448i	0.402470	+	0.476370i
$638$			629.583i			0.986807i
$639$	145.625	+	252.229i	0.227895	+	0.394725i
$640$		0			0
$641$	−523.506	+	906.739i	−0.816702	+	1.41457i	0.0913975	+	0.995814i	$0.470867\pi$
$641$	−523.506	+	906.739i	−0.816702	+	1.41457i	−0.908099	+	0.418755i	$0.862467\pi$
$642$	119.373	+	206.761i	0.185940	+	0.322057i
$643$	−704.161			−1.09512			−0.547559	−	0.836767i	$-0.684443\pi$
$643$	−704.161			−1.09512			−0.547559	+	0.836767i	$0.684443\pi$
$644$	192.115	−	413.815i	0.298316	−	0.642570i
$645$		0			0
$646$	−113.115	−	195.921i	−0.175101	−	0.303284i
$647$	−188.237	+	326.037i	−0.290939	+	0.503921i	−0.974032	−	0.226411i	$-0.927301\pi$
$647$	−188.237	+	326.037i	−0.290939	+	0.503921i	0.683093	+	0.730331i	$0.260634\pi$
$648$	22.0454	+	12.7279i	0.0340207	+	0.0196419i
$649$	407.521	−	235.282i	0.627921	−	0.362530i
$650$		0			0
$651$	642.410	−	57.2962i	0.986805	−	0.0880127i
$652$			89.7122i			0.137595i
$653$	−23.5767	+	13.6120i	−0.0361052	+	0.0208454i	−0.517944	−	0.855415i	$-0.673302\pi$
$653$	−23.5767	+	13.6120i	−0.0361052	+	0.0208454i	0.481839	+	0.876260i	$0.339969\pi$
$654$	136.309	+	78.6981i	0.208424	+	0.120334i
$655$		0			0
$656$	243.673	−	140.685i	0.371453	−	0.214459i
$657$	162.105			0.246735
$658$	−87.5852	−	124.636i	−0.133108	−	0.189417i
$659$	−501.943			−0.761674			−0.380837	−	0.924642i	$-0.624364\pi$
$659$	−501.943			−0.761674			−0.380837	+	0.924642i	$0.624364\pi$
$660$		0			0
$661$	−748.339	−	432.054i	−1.13213	−	0.653637i	−0.187662	−	0.982234i	$-0.560091\pi$
$661$	−748.339	−	432.054i	−1.13213	−	0.653637i	−0.944470	+	0.328597i	$0.893424\pi$
$662$	104.341	+	60.2415i	0.157615	+	0.0909992i
$663$	55.2806	+	95.7489i	0.0833796	+	0.144418i
$664$		−	241.040i		−	0.363013i
$665$		0			0
$666$	−184.824			−0.277513
$667$	−708.139	+	408.844i	−1.06168	+	0.612960i
$668$	139.845	−	242.219i	0.209350	−	0.362604i
$669$	−44.1237	+	76.4245i	−0.0659547	+	0.114237i
$670$		0			0
$671$		−	589.114i		−	0.877964i
$672$	68.3145	−	6.09294i	0.101659	−	0.00906688i
$673$			726.018i			1.07878i	0.842057	+	0.539389i	$0.181345\pi$
$673$			726.018i			1.07878i	−0.842057	+	0.539389i	$0.818655\pi$
$674$	86.3071	+	149.488i	0.128052	+	0.221793i
$675$		0			0
$676$	−103.274	+	178.876i	−0.152772	+	0.264610i
$677$	220.550	+	382.003i	0.325775	+	0.564259i	0.981669	−	0.190594i	$-0.0610415\pi$
$677$	220.550	+	382.003i	0.325775	+	0.564259i	−0.655894	+	0.754853i	$0.727708\pi$
$678$	106.466			0.157030
$679$	317.440	+	147.373i	0.467510	+	0.217044i
$680$		0			0
$681$	−114.684	−	198.638i	−0.168405	−	0.291686i
$682$	667.376	−	1155.93i	0.978557	−	1.69491i
$683$	1030.09	+	594.725i	1.50819	+	0.870754i	0.999955	+	0.00953518i	$0.00303519\pi$
$683$	1030.09	+	594.725i	1.50819	+	0.870754i	0.508235	+	0.861218i	$0.330298\pi$
$684$	105.571	−	60.9513i	0.154343	−	0.0891100i
$685$		0			0
$686$	−344.732	−	341.259i	−0.502525	−	0.497462i
$687$			319.272i			0.464734i
$688$	−8.42398	+	4.86359i	−0.0122442	+	0.00706917i
$689$	−357.335	−	206.307i	−0.518628	−	0.299430i
$690$		0			0
$691$	37.0369	−	21.3832i	0.0535989	−	0.0309453i	−0.472961	−	0.881083i	$-0.656815\pi$
$691$	37.0369	−	21.3832i	0.0535989	−	0.0309453i	0.526560	+	0.850138i	$0.323482\pi$
$692$	289.666			0.418593
$693$	−337.946	−	156.893i	−0.487657	−	0.226397i
$694$	−348.818			−0.502620
$695$		0			0
$696$	−106.454	−	61.4613i	−0.152951	−	0.0883065i
$697$	−479.648	−	276.925i	−0.688160	−	0.397309i
$698$	187.700	+	325.106i	0.268911	+	0.465768i
$699$			243.642i			0.348557i
$700$		0			0
$701$	368.695			0.525956			0.262978	−	0.964802i	$-0.415295\pi$
$701$	368.695			0.525956			0.262978	+	0.964802i	$0.415295\pi$
$702$	−51.5936	+	29.7876i	−0.0734951	+	0.0424324i
$703$	−442.541	+	766.503i	−0.629503	+	1.09033i
$704$	70.9695	−	122.923i	0.100809	−	0.174606i
$705$		0			0
$706$			398.243i			0.564083i
$707$	661.295	+	941.043i	0.935353	+	1.33104i
$708$			91.8752i			0.129767i
$709$	−93.3436	−	161.676i	−0.131655	−	0.228034i	0.792660	−	0.609665i	$-0.208696\pi$
$709$	−93.3436	−	161.676i	−0.131655	−	0.228034i	−0.924315	+	0.381631i	$0.875363\pi$
$710$		0			0
$711$	−112.077	+	194.124i	−0.157633	+	0.273029i
$712$	−188.354	−	326.239i	−0.264542	−	0.458201i
$713$	1733.55			2.43134
$714$	−77.6219	−	110.458i	−0.108714	−	0.154704i
$715$		0			0
$716$	32.4092	+	56.1343i	0.0452642	+	0.0783999i
$717$	214.753	−	371.963i	0.299516	−	0.518777i
$718$	7.87740	+	4.54802i	0.0109713	+	0.00633429i
$719$	447.220	−	258.203i	0.622003	−	0.359113i	−0.155646	−	0.987813i	$-0.549746\pi$
$719$	447.220	−	258.203i	0.622003	−	0.359113i	0.777648	+	0.628700i	$0.216412\pi$
$720$		0			0
$721$	60.5936	+	679.381i	0.0840411	+	0.942275i
$722$		−	73.2338i		−	0.101432i
$723$	−328.275	+	189.530i	−0.454046	+	0.262144i
$724$	−206.355	−	119.139i	−0.285020	−	0.164557i
$725$		0			0
$726$	−411.094	+	237.345i	−0.566245	+	0.326922i
$727$	986.117			1.35642			0.678210	−	0.734868i	$-0.262756\pi$
$727$	986.117			1.35642			0.678210	+	0.734868i	$0.262756\pi$
$728$	−67.5902	+	145.589i	−0.0928437	+	0.199985i
$729$	27.0000			0.0370370
$730$		0			0
$731$	16.5818	+	9.57351i	0.0226837	+	0.0130965i
$732$	99.6114	+	57.5107i	0.136081	+	0.0785665i
$733$	583.073	+	1009.91i	0.795461	+	1.37778i	0.922546	+	0.385887i	$0.126104\pi$
$733$	583.073	+	1009.91i	0.795461	+	1.37778i	−0.127085	+	0.991892i	$0.540562\pi$
$734$		−	354.275i		−	0.482664i
$735$		0			0
$736$	184.347			0.250472
$737$	−1533.99	+	885.647i	−2.08139	+	1.20169i
$738$	149.219	−	258.454i	0.202193	−	0.350209i
$739$	−519.556	+	899.897i	−0.703053	+	1.21772i	0.264337	+	0.964430i	$0.414847\pi$
$739$	−519.556	+	899.897i	−0.703053	+	1.21772i	−0.967390	+	0.253292i	$0.918487\pi$
$740$		0			0
$741$			285.292i			0.385010i
$742$	456.989	+	212.159i	0.615889	+	0.285929i
$743$		−	320.811i		−	0.431778i	−0.976418	−	0.215889i	$-0.930735\pi$
$743$		−	320.811i		−	0.431778i	0.976418	−	0.215889i	$-0.0692650\pi$
$744$	130.302	+	225.689i	0.175137	+	0.303345i
$745$		0			0
$746$	−298.935	+	517.771i	−0.400717	+	0.694062i
$747$	−127.831	−	221.410i	−0.171126	−	0.296399i
$748$	−279.393			−0.373520
$749$	679.578	−	60.6112i	0.907313	−	0.0809228i
$750$		0			0
$751$	560.762	+	971.268i	0.746687	+	1.29330i	0.949402	+	0.314062i	$0.101690\pi$
$751$	560.762	+	971.268i	0.746687	+	1.29330i	−0.202715	+	0.979238i	$0.564977\pi$
$752$	30.7760	−	53.3055i	0.0409255	−	0.0708850i
$753$	−56.5624	−	32.6563i	−0.0751161	−	0.0433683i
$754$	249.138	−	143.840i	0.330422	−	0.190769i
$755$		0			0
$756$	59.5196	−	41.8260i	0.0787297	−	0.0553254i
$757$			769.996i			1.01717i	0.861012	+	0.508584i	$0.169831\pi$
$757$			769.996i			1.01717i	−0.861012	+	0.508584i	$0.830169\pi$
$758$	624.871	−	360.769i	0.824367	−	0.475949i
$759$	−867.289	−	500.730i	−1.14267	−	0.659723i
$760$		0			0
$761$	−874.305	+	504.780i	−1.14889	+	0.663311i	−0.948616	−	0.316429i	$-0.897516\pi$
$761$	−874.305	+	504.780i	−1.14889	+	0.663311i	−0.200273	+	0.979740i	$0.564183\pi$
$762$	455.649			0.597964
$763$	368.016	−	258.615i	0.482328	−	0.338944i
$764$	488.914			0.639940
$765$		0			0
$766$	−329.317	−	190.131i	−0.429917	−	0.248213i
$767$	−186.211	−	107.509i	−0.242779	−	0.140169i
$768$	13.8564	+	24.0000i	0.0180422	+	0.0312500i
$769$			817.903i			1.06359i	0.846872	+	0.531797i	$0.178483\pi$
$769$			817.903i			1.06359i	−0.846872	+	0.531797i	$0.821517\pi$
$770$		0			0
$771$	−33.0182			−0.0428252
$772$	442.646	−	255.562i	0.573375	−	0.331038i
$773$	642.220	−	1112.36i	0.830815	−	1.43901i	−0.0665776	−	0.997781i	$-0.521208\pi$
$773$	642.220	−	1112.36i	0.830815	−	1.43901i	0.897393	−	0.441233i	$-0.145459\pi$
$774$	−5.15861	+	8.93498i	−0.00666487	+	0.0115439i
$775$		0			0
$776$			141.414i			0.182234i
$777$	−222.410	+	479.068i	−0.286241	+	0.616561i
$778$			237.272i			0.304977i
$779$	−714.576	−	1237.68i	−0.917300	−	1.58881i
$780$		0			0
$781$	861.242	−	1491.71i	1.10274	−	1.91001i
$782$	−181.435	−	314.254i	−0.232014	−	0.401860i
$783$	−130.379			−0.166512
$784$	66.4139	−	184.405i	0.0847116	−	0.235210i
$785$		0			0
$786$	110.355	+	191.141i	0.140401	+	0.243182i
$787$	401.113	−	694.748i	0.509673	−	0.882780i	−0.490264	−	0.871574i	$-0.663100\pi$
$787$	401.113	−	694.748i	0.509673	−	0.882780i	0.999937	−	0.0112060i	$-0.00356705\pi$
$788$	−608.807	−	351.495i	−0.772597	−	0.446059i
$789$	359.556	−	207.590i	0.455712	−	0.263105i
$790$		0			0
$791$	128.117	−	275.963i	0.161969	−	0.348879i
$792$		−	150.549i		−	0.190087i
$793$	−233.124	+	134.594i	−0.293977	+	0.169728i
$794$	−445.277	−	257.081i	−0.560802	−	0.323779i
$795$		0			0
$796$	−532.336	+	307.344i	−0.668764	+	0.386111i
$797$	1242.74			1.55927			0.779636	−	0.626233i	$-0.215404\pi$
$797$	1242.74			1.55927			0.779636	+	0.626233i	$0.215404\pi$
$798$	−30.9477	−	346.988i	−0.0387816	−	0.434822i
$799$	−121.159			−0.151638
$800$		0			0
$801$	−346.029	−	199.780i	−0.431996	−	0.249413i
$802$	−341.497	−	197.164i	−0.425807	−	0.245840i
$803$	−479.355	−	830.267i	−0.596955	−	1.03396i
$804$		−	345.836i		−	0.430144i
$805$		0			0
$806$	−609.898			−0.756697
$807$	−399.880	+	230.871i	−0.495514	+	0.286085i
$808$	−232.368	+	402.473i	−0.287584	+	0.498110i
$809$	55.3589	−	95.8845i	0.0684288	−	0.118522i	−0.829781	−	0.558089i	$-0.811535\pi$
$809$	55.3589	−	95.8845i	0.0684288	−	0.118522i	0.898210	+	0.439567i	$0.144868\pi$
$810$		0			0
$811$		−	437.207i		−	0.539096i	−0.962987	−	0.269548i	$-0.913126\pi$
$811$		−	437.207i		−	0.539096i	0.962987	−	0.269548i	$-0.0868743\pi$
$812$	−287.412	+	201.972i	−0.353956	+	0.248734i
$813$		−	632.649i		−	0.778165i
$814$	546.535	+	946.627i	0.671419	+	1.16293i
$815$		0			0
$816$	27.2750	−	47.2417i	0.0334253	−	0.0578943i
$817$	24.7035	+	42.7877i	0.0302368	+	0.0523717i
$818$	−551.726			−0.674482
$819$	15.1245	+	169.577i	0.0184670	+	0.207054i
$820$		0			0
$821$	340.004	+	588.903i	0.414133	+	0.717300i	0.995337	−	0.0964580i	$-0.0307513\pi$
$821$	340.004	+	588.903i	0.414133	+	0.717300i	−0.581204	+	0.813758i	$0.697418\pi$
$822$	−13.2707	+	22.9855i	−0.0161444	+	0.0279629i
$823$	−435.049	−	251.176i	−0.528613	−	0.305195i	0.211838	−	0.977305i	$-0.432055\pi$
$823$	−435.049	−	251.176i	−0.528613	−	0.305195i	−0.740452	+	0.672110i	$0.765388\pi$
$824$	−238.677	+	137.800i	−0.289657	+	0.167234i
$825$		0			0
$826$	238.143	+	110.559i	0.288309	+	0.133849i
$827$			404.323i			0.488904i	0.969661	+	0.244452i	$0.0786080\pi$
$827$			404.323i			0.488904i	−0.969661	+	0.244452i	$0.921392\pi$
$828$	169.334	−	97.7648i	0.204509	−	0.118073i
$829$	587.862	+	339.402i	0.709122	+	0.409412i	0.810736	−	0.585412i	$-0.199067\pi$
$829$	587.862	+	339.402i	0.709122	+	0.409412i	−0.101614	+	0.994824i	$0.532401\pi$
$830$		0			0
$831$	−637.402	+	368.004i	−0.767030	+	0.442845i
$832$	−64.8572			−0.0779533
$833$	−379.718	+	68.2768i	−0.455844	+	0.0819650i
$834$	−544.094			−0.652391
$835$		0			0
$836$	−624.358	−	360.473i	−0.746840	−	0.431188i
$837$	239.379	+	138.206i	0.285997	+	0.165120i
$838$	407.927	+	706.550i	0.486786	+	0.843138i
$839$			230.404i			0.274617i	0.990528	+	0.137309i	$0.0438452\pi$
$839$			230.404i			0.274617i	−0.990528	+	0.137309i	$0.956155\pi$
$840$		0			0
$841$	−211.417			−0.251388
$842$	795.902	−	459.514i	0.945252	−	0.545742i
$843$	125.416	−	217.228i	0.148774	−	0.257684i
$844$	−335.164	+	580.521i	−0.397113	+	0.687821i
$845$		0			0
$846$		−	65.2857i		−	0.0771698i
$847$	120.511	+	1351.18i	0.142280	+	1.59525i
$848$			203.581i			0.240071i
$849$	−281.343	−	487.300i	−0.331381	−	0.573969i
$850$		0			0
$851$	−709.828	+	1229.46i	−0.834111	+	1.44472i
$852$	168.153	+	291.249i	0.197363	+	0.341842i
$853$	234.440			0.274842			0.137421	−	0.990513i	$-0.456119\pi$
$853$	234.440			0.274842			0.137421	+	0.990513i	$0.456119\pi$
$854$	268.937	−	188.989i	0.314915	−	0.221299i
$855$		0			0
$856$	137.840	+	238.747i	0.161029	+	0.278910i
$857$	309.636	−	536.305i	0.361302	−	0.625794i	−0.626873	−	0.779121i	$-0.715666\pi$
$857$	309.636	−	536.305i	0.361302	−	0.625794i	0.988175	+	0.153327i	$0.0489989\pi$
$858$	305.131	+	176.167i	0.355630	+	0.205323i
$859$	546.499	−	315.521i	0.636204	−	0.367313i	−0.146947	−	0.989144i	$-0.546945\pi$
$859$	546.499	−	315.521i	0.636204	−	0.367313i	0.783151	+	0.621832i	$0.213611\pi$
$860$		0			0
$861$	−490.357	−	697.792i	−0.569520	−	0.810444i
$862$			978.888i			1.13560i
$863$	−1103.50	+	637.108i	−1.27868	+	0.738247i	−0.976606	−	0.215036i	$-0.931013\pi$
$863$	−1103.50	+	637.108i	−1.27868	+	0.738247i	−0.302076	+	0.953284i	$0.597680\pi$
$864$	25.4558	+	14.6969i	0.0294628	+	0.0170103i
$865$		0			0
$866$	−142.760	+	82.4228i	−0.164850	+	0.0951764i
$867$	393.186			0.453502
$868$	741.791	−	66.1600i	0.854598	−	0.0762212i
$869$	1325.68			1.52552
$870$		0			0
$871$	700.935	+	404.685i	0.804747	+	0.464621i
$872$	157.396	+	90.8728i	0.180500	+	0.104212i
$873$	74.9959	+	129.897i	0.0859060	+	0.148793i
$874$		−	936.349i		−	1.07134i
$875$		0			0
$876$	187.183			0.213679
$877$	1.86172	−	1.07486i	0.00212283	−	0.00122562i	−0.498938	−	0.866638i	$-0.666277\pi$
$877$	1.86172	−	1.07486i	0.00212283	−	0.00122562i	0.501061	+	0.865412i	$0.332943\pi$
$878$	−124.650	+	215.900i	−0.141970	+	0.245900i
$879$	148.814	−	257.754i	0.169299	−	0.293235i
$880$		0			0
$881$		−	839.378i		−	0.952756i	−0.879241	−	0.476378i	$-0.841949\pi$
$881$		−	839.378i		−	0.952756i	0.879241	−	0.476378i	$-0.158051\pi$
$882$	−36.7904	−	204.608i	−0.0417125	−	0.231982i
$883$			1326.53i			1.50230i	0.660131	+	0.751150i	$0.270501\pi$
$883$			1326.53i			1.50230i	−0.660131	+	0.751150i	$0.729499\pi$
$884$	63.8326	+	110.561i	0.0722088	+	0.125069i
$885$		0			0
$886$	231.941	−	401.734i	0.261785	−	0.453424i
$887$	508.507	+	880.761i	0.573289	+	0.992966i	0.996225	+	0.0868064i	$0.0276662\pi$
$887$	508.507	+	880.761i	0.573289	+	0.992966i	−0.422936	+	0.906160i	$0.639001\pi$
$888$	−213.416			−0.240334
$889$	548.309	−	1181.05i	0.616771	−	1.32852i
$890$		0			0
$891$	−79.8406	−	138.288i	−0.0896079	−	0.155205i
$892$	−50.9497	+	88.2474i	−0.0571185	+	0.0989321i
$893$	−270.753	−	156.320i	−0.303195	−	0.175050i
$894$	−18.3995	+	10.6230i	−0.0205811	+	0.0118825i
$895$		0			0
$896$	78.8828	−	7.03552i	0.0880389	−	0.00785214i
$897$			457.604i			0.510150i
$898$	990.467	−	571.846i	1.10297	−	0.636800i
$899$	−1155.93	−	667.376i	−1.28579	−	0.742354i
$900$		0			0
$901$	347.042	−	200.365i	0.385174	−	0.222380i
$902$	−1765.00			−1.95676
$903$	16.9520	+	24.1232i	0.0187730	+	0.0267146i
$904$	122.937			0.135992
$905$		0			0
$906$	450.921	+	260.339i	0.497705	+	0.287350i
$907$	−535.675	−	309.272i	−0.590601	−	0.340984i	0.174734	−	0.984616i	$-0.444093\pi$
$907$	−535.675	−	309.272i	−0.590601	−	0.340984i	−0.765335	+	0.643632i	$0.777427\pi$
$908$	−132.426	−	229.368i	−0.145843	−	0.252608i
$909$			492.926i			0.542273i
$910$		0			0
$911$	821.498			0.901754			0.450877	−	0.892586i	$-0.351111\pi$
$911$	821.498			0.901754			0.450877	+	0.892586i	$0.351111\pi$
$912$	121.903	−	70.3805i	0.133665	−	0.0771716i
$913$	−756.008	+	1309.44i	−0.828048	+	1.43422i
$914$	−238.218	+	412.607i	−0.260633	+	0.451429i
$915$		0			0
$916$			368.664i			0.402471i
$917$	628.240	−	56.0324i	0.685104	−	0.0611041i
$918$		−	57.8591i		−	0.0630273i
$919$	408.435	+	707.430i	0.444434	+	0.769782i	0.998013	−	0.0630149i	$-0.0200716\pi$
$919$	408.435	+	707.430i	0.444434	+	0.769782i	−0.553579	+	0.832797i	$0.686738\pi$
$920$		0			0
$921$	98.8141	−	171.151i	0.107290	−	0.185832i
$922$	434.785	+	753.069i	0.471567	+	0.816778i
$923$	−787.067			−0.852727
$924$	−390.227	−	181.164i	−0.422323	−	0.196065i
$925$		0			0
$926$	−578.550	−	1002.08i	−0.624784	−	1.08216i
$927$	−146.159	+	253.156i	−0.157669	+	0.273091i
$928$	−122.923	−	70.9695i	−0.132460	−	0.0764757i
$929$	−109.848	+	63.4209i	−0.118243	+	0.0682679i	−0.557955	−	0.829871i	$-0.688414\pi$
$929$	−109.848	+	63.4209i	−0.118243	+	0.0682679i	0.439712	+	0.898139i	$0.355081\pi$
$930$		0			0
$931$	−936.643	−	337.334i	−1.00606	−	0.362335i
$932$			281.333i			0.301859i
$933$	232.796	−	134.405i	0.249514	−	0.144057i
$934$	651.305	+	376.031i	0.697329	+	0.402603i
$935$		0			0
$936$	−59.5751	+	34.3957i	−0.0636486	+	0.0367476i
$937$	−1128.69			−1.20458			−0.602289	−	0.798278i	$-0.705745\pi$
$937$	−1128.69			−1.20458			−0.602289	+	0.798278i	$0.705745\pi$
$938$	−896.414	−	416.165i	−0.955666	−	0.443672i
$939$	−736.287			−0.784118
$940$		0			0
$941$	232.437	+	134.197i	0.247010	+	0.142611i	0.618395	−	0.785868i	$-0.287783\pi$
$941$	232.437	+	134.197i	0.247010	+	0.142611i	−0.371384	+	0.928479i	$0.621117\pi$
$942$	−278.823	−	160.979i	−0.295991	−	0.170890i
$943$	−1146.17	−	1985.22i	−1.21545	−	2.10522i
$944$			106.088i			0.112382i
$945$		0			0
$946$	61.0173			0.0645003
$947$	−769.482	+	444.261i	−0.812547	+	0.469124i	−0.847840	−	0.530253i	$-0.822097\pi$
$947$	−769.482	+	444.261i	−0.812547	+	0.469124i	0.0352923	+	0.999377i	$0.488764\pi$
$948$	−129.416	+	224.155i	−0.136515	+	0.236450i
$949$	−219.035	+	379.380i	−0.230806	+	0.399768i
$950$		0			0
$951$			24.9302i			0.0262147i
$952$	−89.6301	−	127.546i	−0.0941492	−	0.133977i
$953$			300.519i			0.315340i	0.987492	+	0.157670i	$0.0503983\pi$
$953$			300.519i			0.315340i	−0.987492	+	0.157670i	$0.949602\pi$
$954$	107.965	+	187.001i	0.113171	+	0.196018i
$955$		0			0
$956$	247.975	−	429.506i	0.259388	−	0.449274i
$957$	385.539	+	667.773i	0.402862	+	0.697778i
$958$	−902.585			−0.942155
$959$	43.6096	+	62.0578i	0.0454741	+	0.0647110i
$960$		0			0
$961$	934.376	+	1618.39i	0.972296	+	1.68407i
$962$	249.732	−	432.549i	0.259597	−	0.449635i
$963$	253.229	+	146.202i	0.262958	+	0.151819i
$964$	−379.060	+	218.850i	−0.393216	+	0.227023i
$965$		0			0
$966$	−49.6396	−	556.563i	−0.0513867	−	0.576152i
$967$		−	391.420i		−	0.404778i	−0.979305	−	0.202389i	$-0.935130\pi$
$967$		−	391.420i		−	0.404778i	0.979305	−	0.202389i	$-0.0648705\pi$
$968$	−474.690	+	274.062i	−0.490382	+	0.283122i
$969$	−239.954	−	138.537i	−0.247630	−	0.142969i
$970$		0			0
$971$	−1370.55	+	791.285i	−1.41148	+	0.814918i	−0.995528	−	0.0944692i	$-0.969885\pi$
$971$	−1370.55	+	791.285i	−1.41148	+	0.814918i	−0.415951	+	0.909387i	$0.636551\pi$
$972$	31.1769			0.0320750
$973$	−654.741	+	1410.31i	−0.672910	+	1.44944i
$974$	−549.916			−0.564596
$975$		0			0
$976$	115.021	+	66.4076i	0.117850	+	0.0680406i
$977$	−737.340	−	425.703i	−0.754698	−	0.435725i	0.0726910	−	0.997355i	$-0.476841\pi$
$977$	−737.340	−	425.703i	−0.754698	−	0.435725i	−0.827389	+	0.561630i	$0.810175\pi$
$978$	54.9373	+	95.1542i	0.0561731	+	0.0972947i
$979$			2363.04i			2.41373i
$980$		0			0
$981$	192.770			0.196504
$982$	852.310	−	492.082i	0.867933	−	0.501101i
$983$	−113.507	+	196.599i	−0.115470	+	0.199999i	−0.917967	−	0.396656i	$-0.870171\pi$
$983$	−113.507	+	196.599i	−0.115470	+	0.199999i	0.802498	+	0.596655i	$0.203504\pi$
$984$	172.303	−	298.437i	0.175105	−	0.303290i
$985$		0			0
$986$			279.393i			0.283360i
$987$	−169.222	−	78.5621i	−0.171451	−	0.0795969i
$988$			329.427i			0.333428i
$989$	39.6240	+	68.6307i	0.0400647	+	0.0693940i
$990$		0			0
$991$	−276.368	+	478.683i	−0.278878	+	0.483031i	−0.971106	−	0.238648i	$-0.923296\pi$
$991$	−276.368	+	478.683i	−0.278878	+	0.483031i	0.692228	+	0.721679i	$0.256629\pi$
$992$	150.459	+	260.603i	0.151673	+	0.262705i
$993$	147.561			0.148601
$994$	957.274	−	85.3788i	0.963052	−	0.0858942i
$995$		0			0
$996$	−147.606	−	255.662i	−0.148199	−	0.256689i
$997$	−134.953	+	233.746i	−0.135359	+	0.234449i	−0.925735	−	0.378174i	$-0.876552\pi$
$997$	−134.953	+	233.746i	−0.135359	+	0.234449i	0.790375	+	0.612623i	$0.209886\pi$
$998$	−650.083	−	375.326i	−0.651386	−	0.376078i
$999$	−196.035	+	113.181i	−0.196232	+	0.113294i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.q.d.199.9		24
5.2	odd	4		1050.3.p.e.451.6	✓	12
5.3	odd	4		1050.3.p.f.451.1	yes	12
5.4	even	2	inner	1050.3.q.d.199.6		24
7.5	odd	6	inner	1050.3.q.d.649.6		24
35.12	even	12		1050.3.p.e.901.6	yes	12
35.19	odd	6	inner	1050.3.q.d.649.9		24
35.33	even	12		1050.3.p.f.901.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.p.e.451.6	✓	12	5.2	odd	4
1050.3.p.e.901.6	yes	12	35.12	even	12
1050.3.p.f.451.1	yes	12	5.3	odd	4
1050.3.p.f.901.1	yes	12	35.33	even	12
1050.3.q.d.199.6		24	5.4	even	2	inner
1050.3.q.d.199.9		24	1.1	even	1	trivial
1050.3.q.d.649.6		24	7.5	odd	6	inner
1050.3.q.d.649.9		24	35.19	odd	6	inner

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.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-6.34914 - 2.94762i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-6.34914 - 2.94762i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-8.87118 + 15.3653i) q^{11} +(-1.73205 - 3.00000i) q^{12} +8.10715 q^{13} +(-9.86035 + 0.879440i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-3.93681 + 6.81875i) q^{17} +(-3.67423 - 2.12132i) q^{18} +(-17.5951 + 10.1585i) q^{19} +(-9.91994 + 6.97100i) q^{21} +25.0915i q^{22} +(-28.2223 + 16.2941i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(9.92919 - 5.73262i) q^{26} -5.19615 q^{27} +(-11.4546 + 8.04941i) q^{28} +25.0915 q^{29} +(-46.0686 - 26.5977i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(15.3653 + 26.6135i) q^{33} +11.1350i q^{34} -6.00000 q^{36} +(37.7270 - 21.7817i) q^{37} +(-14.3664 + 24.8833i) q^{38} +(7.02100 - 12.1607i) q^{39} +70.3424i q^{41} +(-7.22016 + 15.5521i) q^{42} -2.43179i q^{43} +(17.7424 + 30.7307i) q^{44} +(-23.0434 + 39.9123i) q^{46} +(7.69399 + 13.3264i) q^{47} -6.92820 q^{48} +(31.6231 + 37.4297i) q^{49} +(6.81875 + 11.8104i) q^{51} +(8.10715 - 14.0420i) q^{52} +(-44.0765 - 25.4476i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(-8.33712 + 17.9581i) q^{56} +35.1902i q^{57} +(30.7307 - 17.7424i) q^{58} +(-22.9688 - 13.2610i) q^{59} +(-28.7553 + 16.6019i) q^{61} -75.2297 q^{62} +(1.86557 + 20.9170i) q^{63} -8.00000 q^{64} +(37.6372 + 21.7299i) q^{66} +(86.4589 + 49.9171i) q^{67} +(7.87362 + 13.6375i) q^{68} +56.4445i q^{69} -97.0831 q^{71} +(-7.34847 + 4.24264i) q^{72} +(-27.0175 + 46.7957i) q^{73} +(30.8040 - 53.3541i) q^{74} +40.6342i q^{76} +(101.615 - 71.4078i) q^{77} -19.8584i q^{78} +(-37.3591 - 64.7079i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(49.7396 + 86.1515i) q^{82} +85.2206 q^{83} +(2.15418 + 24.1528i) q^{84} +(-1.71954 - 2.97833i) q^{86} +(21.7299 - 37.6372i) q^{87} +(43.4597 + 25.0915i) q^{88} +(115.343 - 66.5932i) q^{89} +(-51.4734 - 23.8968i) q^{91} +65.1765i q^{92} +(-79.7931 + 46.0686i) q^{93} +(18.8464 + 10.8809i) q^{94} +(-8.48528 + 4.89898i) q^{96} -49.9973 q^{97} +(65.1970 + 23.4809i) q^{98} +53.2271 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} - 36 q^{9}+O(q^{10}) \) 24 * q + 24 * q^4 - 36 * q^9	\( 24 q + 24 q^{4} - 36 q^{9} - 8 q^{11} - 16 q^{14} - 48 q^{16} - 24 q^{19} + 36 q^{21} - 48 q^{26} + 48 q^{29} - 396 q^{31} - 144 q^{36} + 72 q^{39} + 16 q^{44} + 64 q^{46} - 56 q^{49} - 48 q^{51} + 80 q^{56} + 96 q^{59} + 372 q^{61} - 192 q^{64} + 72 q^{66} - 272 q^{71} + 128 q^{74} + 140 q^{79} - 108 q^{81} + 24 q^{84} - 416 q^{86} - 336 q^{89} + 584 q^{91} + 408 q^{94} + 48 q^{99}+O(q^{100}) \) 24 * q + 24 * q^4 - 36 * q^9 - 8 * q^11 - 16 * q^14 - 48 * q^16 - 24 * q^19 + 36 * q^21 - 48 * q^26 + 48 * q^29 - 396 * q^31 - 144 * q^36 + 72 * q^39 + 16 * q^44 + 64 * q^46 - 56 * q^49 - 48 * q^51 + 80 * q^56 + 96 * q^59 + 372 * q^61 - 192 * q^64 + 72 * q^66 - 272 * q^71 + 128 * q^74 + 140 * q^79 - 108 * q^81 + 24 * q^84 - 416 * q^86 - 336 * q^89 + 584 * q^91 + 408 * q^94 + 48 * q^99

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