LMFDB - Embedded newform 343.3.l.a.10.51

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [343,3,Mod(3,343)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(343, base_ring=CyclotomicField(294))

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

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

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

chi := DirichletCharacter("343.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 343 = 7^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	343.l (of order $294$, degree $84$, 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:	$9.34607306756$
Analytic rank:	$0$
Dimension:	$5376$
Relative dimension:	$64$ over $\Q(\zeta_{294})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{294}]$

Embedding invariants

Embedding label			10.51
Character	$\chi$	$=$	343.10
Dual form			343.3.l.a.103.51

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.04496 + 1.03921i) q^{2} +(2.07598 - 1.96793i) q^{3} +(0.743846 + 1.01923i) q^{4} +(-0.325399 + 0.00347725i) q^{5} +(6.29037 - 1.86695i) q^{6} +(4.62984 - 5.25020i) q^{7} +(-1.00246 - 6.20054i) q^{8} +(-0.0436606 + 0.816401i) q^{9} +(-0.669041 - 0.331046i) q^{10} +(3.54855 - 3.15417i) q^{11} +(3.54998 + 0.652066i) q^{12} +(-5.61375 - 3.40309i) q^{13} +(14.9239 - 5.92507i) q^{14} +(-0.668680 + 0.647580i) q^{15} +(5.93280 - 18.5284i) q^{16} +(6.57664 - 0.776615i) q^{17} +(-0.937693 + 1.62413i) q^{18} +(3.20631 - 1.85116i) q^{19} +(-0.245591 - 0.329070i) q^{20} +(-0.720540 - 20.0105i) q^{21} +(10.5345 - 2.76246i) q^{22} +(6.46408 + 18.7948i) q^{23} +(-14.2833 - 10.8995i) q^{24} +(-24.8884 + 0.531981i) q^{25} +(-7.94336 - 12.7930i) q^{26} +(18.2043 + 21.3838i) q^{27} +(8.79504 + 0.813525i) q^{28} +(17.5949 - 3.42660i) q^{29} +(-2.04039 + 0.629377i) q^{30} +(3.81606 - 1.49769i) q^{31} +(13.7168 - 13.8642i) q^{32} +(1.15955 - 13.5313i) q^{33} +(14.2560 + 5.24634i) q^{34} +(-1.48829 + 1.72451i) q^{35} +(-0.864576 + 0.562776i) q^{36} +(29.9777 + 12.8889i) q^{37} +(8.48051 - 0.453532i) q^{38} +(-18.3511 + 3.98269i) q^{39} +(0.347759 + 2.01417i) q^{40} +(7.43719 - 5.18786i) q^{41} +(19.3216 - 41.6694i) q^{42} +(-6.70834 + 41.4935i) q^{43} +(5.85440 + 1.27057i) q^{44} +(0.0113683 - 0.265808i) q^{45} +(-6.31291 + 45.1521i) q^{46} +(-10.1707 - 2.55124i) q^{47} +(-24.1461 - 50.1399i) q^{48} +(-6.12917 - 48.6152i) q^{49} +(-51.4486 - 24.7763i) q^{50} +(12.1247 - 14.5546i) q^{51} +(-0.707241 - 8.25307i) q^{52} +(-23.8065 + 86.9853i) q^{53} +(15.0048 + 62.6469i) q^{54} +(-1.14373 + 1.03870i) q^{55} +(-37.1953 - 23.4444i) q^{56} +(3.01329 - 10.1528i) q^{57} +(39.5417 + 11.2774i) q^{58} +(-41.9312 + 19.6438i) q^{59} +(-1.15743 - 0.199837i) q^{60} +(-0.517239 - 12.0938i) q^{61} +(9.36009 + 0.902957i) q^{62} +(4.08412 + 4.00903i) q^{63} +(-31.3977 + 10.4248i) q^{64} +(1.83854 + 1.08784i) q^{65} +(16.4330 - 26.4659i) q^{66} +(-63.7764 + 9.61275i) q^{67} +(5.68356 + 6.12542i) q^{68} +(50.4061 + 26.2968i) q^{69} +(-4.83561 + 1.97991i) q^{70} +(-56.3744 - 10.9789i) q^{71} +(5.10590 - 0.547686i) q^{72} +(8.43630 - 2.11618i) q^{73} +(47.9089 + 57.5103i) q^{74} +(-50.6210 + 50.0829i) q^{75} +(4.27176 + 1.89098i) q^{76} +(-0.130792 - 33.2339i) q^{77} +(-41.6660 - 10.9261i) q^{78} +(10.0526 + 134.143i) q^{79} +(-1.86610 + 6.04975i) q^{80} +(72.5573 + 7.78289i) q^{81} +(20.6000 - 2.88018i) q^{82} +(70.2344 - 6.77543i) q^{83} +(19.8593 - 15.6191i) q^{84} +(-2.13733 + 0.275578i) q^{85} +(-56.8385 + 77.8810i) q^{86} +(29.7833 - 41.7390i) q^{87} +(-23.1148 - 18.8410i) q^{88} +(108.907 - 45.4519i) q^{89} +(0.299477 - 0.531752i) q^{90} +(-43.8576 + 13.7175i) q^{91} +(-14.3479 + 20.5688i) q^{92} +(4.97472 - 10.6189i) q^{93} +(-18.1474 - 15.7866i) q^{94} +(-1.03689 + 0.613516i) q^{95} +(1.19218 - 55.7754i) q^{96} +(97.8283 + 78.0154i) q^{97} +(37.9873 - 105.785i) q^{98} +(2.42013 + 3.03475i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5376 q - 84 q^{2} - 84 q^{3} - 84 q^{4} - 84 q^{5} - 112 q^{6} - 84 q^{7} - 84 q^{8} - 28 q^{9} - 84 q^{10} - 119 q^{11} - 119 q^{12} - 84 q^{13} + 21 q^{14} - 168 q^{15} - 84 q^{16} - 35 q^{17} - 42 q^{18}+ \cdots + 42 q^{99}+O(q^{100}) $ 5376 * q - 84 * q^2 - 84 * q^3 - 84 * q^4 - 84 * q^5 - 112 * q^6 - 84 * q^7 - 84 * q^8 - 28 * q^9 - 84 * q^10 - 119 * q^11 - 119 * q^12 - 84 * q^13 + 21 * q^14 - 168 * q^15 - 84 * q^16 - 35 * q^17 - 42 * q^18 - 126 * q^19 - 420 * q^20 - 84 * q^21 + 28 * q^22 - 147 * q^23 - 210 * q^24 - 84 * q^25 - 196 * q^26 + 21 * q^27 + 126 * q^28 - 336 * q^29 - 91 * q^30 - 77 * q^31 - 84 * q^33 - 616 * q^34 + 56 * q^35 + 420 * q^36 - 539 * q^37 - 532 * q^38 - 441 * q^39 - 364 * q^40 - 280 * q^41 - 700 * q^42 - 84 * q^43 - 112 * q^44 - 315 * q^45 - 252 * q^46 - 7 * q^47 - 98 * q^48 - 28 * q^49 + 56 * q^50 + 84 * q^51 + 84 * q^52 + 371 * q^53 + 798 * q^54 + 1267 * q^55 - 42 * q^56 - 735 * q^57 - 868 * q^58 + 1400 * q^59 + 406 * q^60 + 637 * q^61 + 336 * q^62 + 735 * q^63 - 420 * q^64 - 84 * q^65 + 1372 * q^66 - 91 * q^67 - 77 * q^68 + 84 * q^69 - 1078 * q^70 + 679 * q^71 + 273 * q^72 + 294 * q^73 - 1428 * q^74 - 1344 * q^75 - 231 * q^76 - 714 * q^77 + 5040 * q^78 - 91 * q^79 - 1148 * q^80 - 784 * q^81 - 224 * q^82 - 1414 * q^83 - 1246 * q^84 + 364 * q^85 - 1582 * q^86 - 952 * q^87 - 1974 * q^88 - 910 * q^89 - 287 * q^90 + 1456 * q^91 - 6384 * q^92 - 154 * q^93 - 770 * q^94 - 1358 * q^95 - 4284 * q^96 + 3430 * q^97 + 7 * q^98 + 42 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/343\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{223}{294}\right)$

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 $

$2$	2.04496	+	1.03921i	1.02248	+	0.519603i	0.882382	−	0.470535i	$-0.155939\pi$
$2$	2.04496	+	1.03921i	1.02248	+	0.519603i	0.140097	+	0.990138i	$0.455259\pi$
$3$	2.07598	−	1.96793i	0.691994	−	0.655975i	−0.258753	−	0.965944i	$-0.583312\pi$
$3$	2.07598	−	1.96793i	0.691994	−	0.655975i	0.950747	+	0.309968i	$0.100318\pi$
$4$	0.743846	+	1.01923i	0.185962	+	0.254807i
$5$	−0.325399	+	0.00347725i	−0.0650798	+	0.000695449i	−0.0432197	−	0.999066i	$-0.513762\pi$
$5$	−0.325399	+	0.00347725i	−0.0650798	+	0.000695449i	−0.0218601	+	0.999761i	$0.506959\pi$
$6$	6.29037	−	1.86695i	1.04840	−	0.311158i
$7$	4.62984	−	5.25020i	0.661406	−	0.750028i
$7$	4.62984	−	5.25020i	0.661406	−	0.750028i
$8$	−1.00246	−	6.20054i	−0.125307	−	0.775068i
$9$	−0.0436606	+	0.816401i	−0.00485118	+	0.0907112i
$10$	−0.669041	−	0.331046i	−0.0669041	−	0.0331046i
$11$	3.54855	−	3.15417i	0.322596	−	0.286743i	−0.487400	−	0.873179i	$-0.662055\pi$
$11$	3.54855	−	3.15417i	0.322596	−	0.286743i	0.809995	+	0.586436i	$0.199470\pi$
$12$	3.54998	+	0.652066i	0.295831	+	0.0543388i
$13$	−5.61375	−	3.40309i	−0.431827	−	0.261776i	0.285683	−	0.958324i	$-0.407779\pi$
$13$	−5.61375	−	3.40309i	−0.431827	−	0.261776i	−0.717510	+	0.696548i	$0.754718\pi$
$14$	14.9239	−	5.92507i	1.06599	−	0.423219i
$15$	−0.668680	+	0.647580i	−0.0445786	+	0.0431720i
$16$	5.93280	−	18.5284i	0.370800	−	1.15802i
$17$	6.57664	−	0.776615i	0.386861	−	0.0456832i	0.0784044	−	0.996922i	$-0.475017\pi$
$17$	6.57664	−	0.776615i	0.386861	−	0.0456832i	0.308457	+	0.951238i	$0.400188\pi$
$18$	−0.937693	+	1.62413i	−0.0520941	+	0.0902295i
$19$	3.20631	−	1.85116i	0.168753	−	0.0974297i	−0.413245	−	0.910620i	$-0.635605\pi$
$19$	3.20631	−	1.85116i	0.168753	−	0.0974297i	0.581998	+	0.813190i	$0.302271\pi$
$20$	−0.245591	−	0.329070i	−0.0122796	−	0.0164535i
$21$	−0.720540	−	20.0105i	−0.0343114	−	0.952881i
$22$	10.5345	−	2.76246i	0.478839	−	0.125567i
$23$	6.46408	+	18.7948i	0.281047	+	0.817166i	0.993333	+	0.115277i	$0.0367754\pi$
$23$	6.46408	+	18.7948i	0.281047	+	0.817166i	−0.712286	+	0.701889i	$0.752340\pi$
$24$	−14.2833	−	10.8995i	−0.595137	−	0.454144i
$25$	−24.8884	+	0.531981i	−0.995537	+	0.0212792i
$26$	−7.94336	−	12.7930i	−0.305514	−	0.492039i
$27$	18.2043	+	21.3838i	0.674232	+	0.791991i
$28$	8.79504	+	0.813525i	0.314109	+	0.0290545i
$29$	17.5949	−	3.42660i	0.606719	−	0.118159i	0.121560	−	0.992584i	$-0.461210\pi$
$29$	17.5949	−	3.42660i	0.606719	−	0.118159i	0.485160	+	0.874426i	$0.338761\pi$
$30$	−2.04039	+	0.629377i	−0.0680130	+	0.0209792i
$31$	3.81606	−	1.49769i	0.123099	−	0.0483127i	−0.302992	−	0.952993i	$-0.597986\pi$
$31$	3.81606	−	1.49769i	0.123099	−	0.0483127i	0.426091	+	0.904680i	$0.359890\pi$
$32$	13.7168	−	13.8642i	0.428650	−	0.433255i
$33$	1.15955	−	13.5313i	0.0351380	−	0.410039i
$34$	14.2560	+	5.24634i	0.419294	+	0.154304i
$35$	−1.48829	+	1.72451i	−0.0425226	+	0.0492717i
$36$	−0.864576	+	0.562776i	−0.0240160	+	0.0156327i
$37$	29.9777	+	12.8889i	0.810209	+	0.348350i	0.759618	−	0.650370i	$-0.225386\pi$
$37$	29.9777	+	12.8889i	0.810209	+	0.348350i	0.0505910	+	0.998719i	$0.483890\pi$
$38$	8.48051	−	0.453532i	0.223171	−	0.0119351i
$39$	−18.3511	+	3.98269i	−0.470540	+	0.102120i
$40$	0.347759	+	2.01417i	0.00869398	+	0.0503541i
$41$	7.43719	−	5.18786i	0.181395	−	0.126533i	−0.477910	−	0.878409i	$-0.658606\pi$
$41$	7.43719	−	5.18786i	0.181395	−	0.126533i	0.659305	+	0.751875i	$0.270851\pi$
$42$	19.3216	−	41.6694i	0.460037	−	0.992128i
$43$	−6.70834	+	41.4935i	−0.156008	+	0.964964i	0.783239	+	0.621721i	$0.213566\pi$
$43$	−6.70834	+	41.4935i	−0.156008	+	0.964964i	−0.939247	+	0.343243i	$0.888475\pi$
$44$	5.85440	+	1.27057i	0.133054	+	0.0288766i
$45$	0.0113683	−	0.265808i	0.000252629	−	0.00590684i
$46$	−6.31291	+	45.1521i	−0.137237	+	0.981567i
$47$	−10.1707	−	2.55124i	−0.216398	−	0.0542816i	0.133587	−	0.991037i	$-0.457351\pi$
$47$	−10.1707	−	2.55124i	−0.216398	−	0.0542816i	−0.349984	+	0.936756i	$0.613813\pi$
$48$	−24.1461	−	50.1399i	−0.503044	−	1.04458i
$49$	−6.12917	−	48.6152i	−0.125085	−	0.992146i
$50$	−51.4486	−	24.7763i	−1.02897	−	0.495527i
$51$	12.1247	−	14.5546i	0.237738	−	0.285384i
$52$	−0.707241	−	8.25307i	−0.0136008	−	0.158713i
$53$	−23.8065	+	86.9853i	−0.449179	+	1.64123i	0.282269	+	0.959335i	$0.408913\pi$
$53$	−23.8065	+	86.9853i	−0.449179	+	1.64123i	−0.731448	+	0.681897i	$0.761155\pi$
$54$	15.0048	+	62.6469i	0.277866	+	1.16013i
$55$	−1.14373	+	1.03870i	−0.0207951	+	0.0188855i
$56$	−37.1953	−	23.4444i	−0.664202	−	0.418650i
$57$	3.01329	−	10.1528i	0.0528647	−	0.178119i
$58$	39.5417	+	11.2774i	0.681753	+	0.194439i
$59$	−41.9312	+	19.6438i	−0.710698	+	0.332946i	−0.745553	−	0.666446i	$-0.767815\pi$
$59$	−41.9312	+	19.6438i	−0.710698	+	0.332946i	0.0348549	+	0.999392i	$0.488903\pi$
$60$	−1.15743	−	0.199837i	−0.0192905	−	0.00333062i
$61$	−0.517239	−	12.0938i	−0.00847933	−	0.198260i	−0.998396	−	0.0566109i	$-0.981971\pi$
$61$	−0.517239	−	12.0938i	−0.00847933	−	0.198260i	0.989917	−	0.141649i	$-0.0452403\pi$
$62$	9.36009	+	0.902957i	0.150969	+	0.0145638i
$63$	4.08412	+	4.00903i	0.0648274	+	0.0636354i
$64$	−31.3977	+	10.4248i	−0.490589	+	0.162887i
$65$	1.83854	+	1.08784i	0.0282853	+	0.0167360i
$66$	16.4330	−	26.4659i	0.248985	−	0.400998i
$67$	−63.7764	+	9.61275i	−0.951887	+	0.143474i	−0.606586	−	0.795018i	$-0.707461\pi$
$67$	−63.7764	+	9.61275i	−0.951887	+	0.143474i	−0.345301	+	0.938492i	$0.612223\pi$
$68$	5.68356	+	6.12542i	0.0835817	+	0.0900796i
$69$	50.4061	+	26.2968i	0.730523	+	0.381114i
$70$	−4.83561	+	1.97991i	−0.0690801	+	0.0282844i
$71$	−56.3744	−	10.9789i	−0.794005	−	0.154633i	−0.222178	−	0.975006i	$-0.571316\pi$
$71$	−56.3744	−	10.9789i	−0.794005	−	0.154633i	−0.571828	+	0.820374i	$0.693765\pi$
$72$	5.10590	−	0.547686i	0.0709152	−	0.00760675i
$73$	8.43630	−	2.11618i	0.115566	−	0.0289887i	−0.185089	−	0.982722i	$-0.559257\pi$
$73$	8.43630	−	2.11618i	0.115566	−	0.0289887i	0.300655	+	0.953733i	$0.402795\pi$
$74$	47.9089	+	57.5103i	0.647417	+	0.777167i
$75$	−50.6210	+	50.0829i	−0.674947	+	0.667773i
$76$	4.27176	+	1.89098i	0.0562074	+	0.0248813i
$77$	−0.130792	−	33.2339i	−0.00169860	−	0.431609i
$78$	−41.6660	−	10.9261i	−0.534179	−	0.140078i
$79$	10.0526	+	134.143i	0.127248	+	1.69801i	0.586698	+	0.809806i	$0.300428\pi$
$79$	10.0526	+	134.143i	0.127248	+	1.69801i	−0.459450	+	0.888204i	$0.651953\pi$
$80$	−1.86610	+	6.04975i	−0.0233263	+	0.0756219i
$81$	72.5573	+	7.78289i	0.895769	+	0.0960850i
$82$	20.6000	−	2.88018i	0.251219	−	0.0351241i
$83$	70.2344	−	6.77543i	0.846198	−	0.0816317i	0.336182	−	0.941797i	$-0.390864\pi$
$83$	70.2344	−	6.77543i	0.846198	−	0.0816317i	0.510015	+	0.860165i	$0.329640\pi$
$84$	19.8593	−	15.6191i	0.236420	−	0.185942i
$85$	−2.13733	+	0.275578i	−0.0251451	+	0.00324210i
$86$	−56.8385	+	77.8810i	−0.660913	+	0.905593i
$87$	29.7833	−	41.7390i	0.342337	−	0.479758i
$88$	−23.1148	−	18.8410i	−0.262669	−	0.214103i
$89$	108.907	−	45.4519i	1.22367	−	0.510696i	0.323499	−	0.946228i	$-0.395141\pi$
$89$	108.907	−	45.4519i	1.22367	−	0.510696i	0.900173	+	0.435533i	$0.143440\pi$
$90$	0.299477	−	0.531752i	0.00332752	−	0.00590835i
$91$	−43.8576	+	13.7175i	−0.481952	+	0.150742i
$92$	−14.3479	+	20.5688i	−0.155956	+	0.223574i
$93$	4.97472	−	10.6189i	0.0534916	−	0.114182i
$94$	−18.1474	−	15.7866i	−0.193057	−	0.167943i
$95$	−1.03689	+	0.613516i	−0.0109147	+	0.00645807i
$96$	1.19218	−	55.7754i	0.0124185	−	0.580994i
$97$	97.8283	+	78.0154i	1.00854	+	0.804283i	0.980737	−	0.195331i	$-0.0625780\pi$
$97$	97.8283	+	78.0154i	1.00854	+	0.804283i	0.0278013	+	0.999613i	$0.491149\pi$
$98$	37.9873	−	105.785i	0.387626	−	1.07944i
$99$	2.42013	+	3.03475i	0.0244458	+	0.0306541i
$100$	−19.0554	−	24.9713i	−0.190554	−	0.249713i
$101$	−54.5588	−	36.3497i	−0.540186	−	0.359898i	0.254353	−	0.967112i	$-0.418138\pi$
$101$	−54.5588	−	36.3497i	−0.540186	−	0.359898i	−0.794539	+	0.607213i	$0.792287\pi$
$102$	39.9196	−	17.1635i	0.391369	−	0.168269i
$103$	−15.1424	+	7.49254i	−0.147013	+	0.0727431i	−0.515499	−	0.856890i	$-0.672393\pi$
$103$	−15.1424	+	7.49254i	−0.147013	+	0.0727431i	0.368486	+	0.929633i	$0.379876\pi$
$104$	−15.4735	+	38.2197i	−0.148783	+	0.367497i
$105$	0.304045	+	6.50889i	0.00289566	+	0.0619895i
$106$	−139.079	+	153.141i	−1.31207	+	1.44473i
$107$	5.95388	−	10.8410i	0.0556438	−	0.101318i	−0.847225	−	0.531233i	$-0.821729\pi$
$107$	5.95388	−	10.8410i	0.0556438	−	0.101318i	0.902869	+	0.429915i	$0.141457\pi$
$108$	−8.25377	+	34.4605i	−0.0764238	+	0.319079i
$109$	−43.3000	−	78.8423i	−0.397248	−	0.723324i	0.599796	−	0.800153i	$-0.295248\pi$
$109$	−43.3000	−	78.8423i	−0.397248	−	0.723324i	−0.997044	+	0.0768291i	$0.975520\pi$
$110$	−3.41830	+	0.935534i	−0.0310755	+	0.00850485i
$111$	87.5977	−	32.2367i	0.789168	−	0.290421i
$112$	−69.8098	−	116.932i	−0.623302	−	1.04403i
$113$	−111.587	−	14.3876i	−0.987498	−	0.127324i	−0.382845	−	0.923813i	$-0.625056\pi$
$113$	−111.587	−	14.3876i	−0.987498	−	0.127324i	−0.604653	+	0.796489i	$0.706688\pi$
$114$	16.7129	−	17.6305i	0.146604	−	0.154654i
$115$	−2.16876	−	6.09334i	−0.0188588	−	0.0529855i
$116$	16.5804	+	15.3843i	0.142934	+	0.132624i
$117$	3.02338	−	4.43449i	0.0258409	−	0.0379016i
$118$	−106.161	−	3.40439i	−0.899674	−	0.0288508i
$119$	26.3714	−	38.1243i	0.221608	−	0.320372i
$120$	4.68567	+	3.49701i	0.0390472	+	0.0291417i
$121$	−11.5465	+	97.7796i	−0.0954256	+	0.808096i
$122$	11.5103	−	25.2689i	0.0943464	−	0.207122i
$123$	5.23014	−	25.4057i	0.0425215	−	0.206551i
$124$	4.36505	+	2.77539i	0.0352021	+	0.0223821i
$125$	16.2281	−	0.520403i	0.129825	−	0.00416322i
$126$	4.18565	+	12.4425i	0.0332194	+	0.0987504i
$127$	−121.650	−	103.562i	−0.957872	−	0.815449i	0.0250092	−	0.999687i	$-0.492039\pi$
$127$	−121.650	−	103.562i	−0.957872	−	0.815449i	−0.982882	+	0.184239i	$0.941018\pi$
$128$	−152.181	−	22.9376i	−1.18891	−	0.179200i
$129$	67.7297	+	99.3412i	0.525036	+	0.770087i
$130$	2.62925	+	4.13521i	0.0202250	+	0.0318093i
$131$	45.6446	+	120.057i	0.348432	+	0.916467i	0.988913	+	0.148493i	$0.0474423\pi$
$131$	45.6446	+	120.057i	0.348432	+	0.916467i	−0.640482	+	0.767974i	$0.721265\pi$
$132$	14.6540	−	8.88334i	0.111015	−	0.0672981i
$133$	5.12572	−	25.4044i	0.0385393	−	0.191010i
$134$	−140.410	−	46.6192i	−1.04783	−	0.347905i
$135$	−5.99801	−	6.89496i	−0.0444297	−	0.0510738i
$136$	−11.4082	−	40.0002i	−0.0838840	−	0.294119i
$137$	0.421542	−	39.4477i	0.00307695	−	0.287939i	−0.987986	−	0.154544i	$-0.950609\pi$
$137$	0.421542	−	39.4477i	0.00307695	−	0.287939i	0.991063	−	0.133395i	$-0.0425880\pi$
$138$	75.7505	+	106.158i	0.548917	+	0.769263i
$139$	0.880280	−	13.7111i	0.00633295	−	0.0986408i	−0.993559	−	0.113312i	$-0.963854\pi$
$139$	0.880280	−	13.7111i	0.00633295	−	0.0986408i	0.999892	+	0.0146715i	$0.00467026\pi$
$140$	−2.86473	−	0.234138i	−0.0204623	−	0.00167241i
$141$	−26.1348	+	14.7189i	−0.185353	+	0.104389i
$142$	−103.874	−	81.0360i	−0.731506	−	0.570676i
$143$	−30.6546	+	5.63068i	−0.214368	+	0.0393754i
$144$	14.8676	+	5.65250i	0.103247	+	0.0392535i
$145$	−5.71344	+	1.17619i	−0.0394030	+	0.00811168i
$146$	19.4510	+	4.43957i	0.133226	+	0.0304080i
$147$	−108.395	−	88.8624i	−0.737381	−	0.604506i
$148$	9.16204	+	40.1415i	0.0619057	+	0.271227i
$149$	7.17458	−	3.26810i	0.0481515	−	0.0219336i	−0.390310	−	0.920683i	$-0.627632\pi$
$149$	7.17458	−	3.26810i	0.0481515	−	0.0219336i	0.438462	+	0.898750i	$0.355523\pi$
$150$	−155.564	+	49.8118i	−1.03710	+	0.332079i
$151$	−54.3281	−	29.0856i	−0.359789	−	0.192620i	0.282161	−	0.959367i	$-0.408949\pi$
$151$	−54.3281	−	29.0856i	−0.359789	−	0.192620i	−0.641949	+	0.766747i	$0.721874\pi$
$152$	−14.6924	−	18.0252i	−0.0966606	−	0.118587i
$153$	0.346889	+	5.40308i	0.00226725	+	0.0353142i
$154$	34.2694	−	68.0978i	0.222529	−	0.442194i
$155$	−1.23654	+	0.500618i	−0.00797765	+	0.00322979i
$156$	−17.7096	−	15.7414i	−0.113523	−	0.100907i
$157$	−123.362	−	158.129i	−0.785748	−	1.00719i	−0.999541	−	0.0303110i	$-0.990350\pi$
$157$	−123.362	−	158.129i	−0.785748	−	1.00719i	0.213792	−	0.976879i	$-0.431418\pi$
$158$	−118.845	+	284.763i	−0.752183	+	1.80230i
$159$	121.759	+	227.429i	0.765779	+	1.43037i
$160$	−4.41523	+	4.55909i	−0.0275952	+	0.0284943i
$161$	128.604	+	53.0792i	0.798784	+	0.329685i
$162$	140.288	+	91.3176i	0.865978	+	0.563689i
$163$	12.1204	+	18.1921i	0.0743586	+	0.111608i	0.867517	−	0.497407i	$-0.165715\pi$
$163$	12.1204	+	18.1921i	0.0743586	+	0.111608i	−0.793159	+	0.609015i	$0.791565\pi$
$164$	10.8197	+	3.72122i	0.0659740	+	0.0226904i
$165$	−0.330267	+	4.40710i	−0.00200162	+	0.0267097i
$166$	150.667	+	59.1326i	0.907635	+	0.356220i
$167$	245.509	−	108.679i	1.47011	−	0.650775i	0.494282	−	0.869302i	$-0.335431\pi$
$167$	245.509	−	108.679i	1.47011	−	0.650775i	0.975831	+	0.218526i	$0.0701249\pi$
$168$	−123.354	+	24.5274i	−0.734248	+	0.145996i
$169$	−58.2358	−	111.627i	−0.344591	−	0.660516i
$170$	−4.65713	−	1.65758i	−0.0273949	−	0.00975049i
$171$	1.37130	+	2.69846i	0.00801931	+	0.0157804i
$172$	−47.2813	+	24.0274i	−0.274891	+	0.139694i
$173$	57.8679	−	162.585i	0.334497	−	0.939799i	−0.649303	−	0.760530i	$-0.724939\pi$
$173$	57.8679	−	162.585i	0.334497	−	0.939799i	0.983800	−	0.179270i	$-0.0573735\pi$
$174$	104.281	−	54.4033i	0.599316	−	0.312663i
$175$	−112.436	+	133.132i	−0.642494	+	0.760755i
$176$	−37.3888	−	84.4620i	−0.212437	−	0.479898i
$177$	−48.3908	+	123.298i	−0.273394	+	0.696597i
$178$	269.944	+	20.2295i	1.51654	+	0.113649i
$179$	48.3095	−	140.463i	0.269885	−	0.784711i	−0.725454	−	0.688271i	$-0.758370\pi$
$179$	48.3095	−	140.463i	0.269885	−	0.784711i	0.995339	−	0.0964403i	$-0.0307457\pi$
$180$	0.279375	−	0.186133i	0.00155209	−	0.00103407i
$181$	72.9721	−	112.105i	0.403161	−	0.619363i	−0.577194	−	0.816607i	$-0.695852\pi$
$181$	72.9721	−	112.105i	0.403161	−	0.619363i	0.980354	+	0.197244i	$0.0631991\pi$
$182$	−103.942	−	17.5254i	−0.571112	−	0.0962932i
$183$	−24.8736	−	24.0887i	−0.135921	−	0.131632i
$184$	110.058	−	58.9218i	0.598142	−	0.320227i
$185$	−9.79954	−	4.08981i	−0.0529705	−	0.0221071i
$186$	21.2083	−	16.5454i	0.114023	−	0.0889540i
$187$	20.8880	−	23.4997i	0.111700	−	0.125667i
$188$	−4.96514	−	12.2640i	−0.0264103	−	0.0652340i
$189$	196.552	+	3.42740i	1.03996	+	0.0181344i
$190$	−2.75797	+	0.177068i	−0.0145156	+	0.000931935i
$191$	49.4613	−	40.3162i	0.258960	−	0.211080i	−0.493451	−	0.869773i	$-0.664265\pi$
$191$	49.4613	−	40.3162i	0.258960	−	0.211080i	0.752411	+	0.658694i	$0.228891\pi$
$192$	−44.6659	+	83.4300i	−0.232635	+	0.434531i
$193$	38.5335	+	120.342i	0.199656	+	0.623533i	0.999721	+	0.0236199i	$0.00751915\pi$
$193$	38.5335	+	120.342i	0.199656	+	0.623533i	−0.800065	+	0.599913i	$0.795202\pi$
$194$	118.980	+	261.202i	0.613301	+	1.34640i
$195$	5.95757	−	1.35978i	0.0305516	−	0.00697321i
$196$	44.9908	−	42.4092i	0.229545	−	0.216374i
$197$	10.2714	−	45.0018i	0.0521390	−	0.228436i	−0.942145	−	0.335206i	$-0.891194\pi$
$197$	10.2714	−	45.0018i	0.0521390	−	0.228436i	0.994284	+	0.106771i	$0.0340511\pi$
$198$	1.79534	+	8.72096i	0.00906735	+	0.0440452i
$199$	−36.2233	+	95.2767i	−0.182027	+	0.478777i	−0.994563	−	0.104132i	$-0.966793\pi$
$199$	−36.2233	+	95.2767i	−0.182027	+	0.478777i	0.812537	+	0.582910i	$0.198086\pi$
$200$	28.2481	+	153.788i	0.141241	+	0.768942i
$201$	−113.481	+	145.463i	−0.564585	+	0.723697i
$202$	−73.7955	−	131.031i	−0.365324	−	0.648670i
$203$	63.4711	−	108.241i	0.312665	−	0.533208i
$204$	23.8533	+	1.53143i	0.116928	+	0.00750703i
$205$	−2.40201	+	1.71399i	−0.0117171	+	0.00836091i
$206$	−38.7518	−	0.414105i	−0.188115	−	0.00201022i
$207$	−15.6263	+	4.45669i	−0.0754895	+	0.0215299i
$208$	−96.3590	+	83.8238i	−0.463264	+	0.402999i
$209$	5.53887	−	16.6822i	0.0265018	−	0.0798191i
$210$	−6.14233	+	13.6264i	−0.0292492	+	0.0648875i
$211$	43.9375	+	72.4796i	0.208235	+	0.343505i	0.941835	−	0.336077i	$-0.109100\pi$
$211$	43.9375	+	72.4796i	0.208235	+	0.343505i	−0.733600	+	0.679582i	$0.762161\pi$
$212$	−106.366	+	40.4395i	−0.501728	+	0.190752i
$213$	−138.638	+	88.1486i	−0.650882	+	0.413843i
$214$	23.4415	−	15.9822i	0.109540	−	0.0746830i
$215$	2.03861	−	13.5253i	0.00948189	−	0.0629082i
$216$	114.342	−	134.313i	0.529361	−	0.621818i
$217$	9.80456	−	26.9692i	0.0451823	−	0.124282i
$218$	−6.61329	−	206.227i	−0.0303362	−	0.945994i
$219$	13.3491	−	20.9952i	0.0609549	−	0.0958683i
$220$	−1.90943	−	0.393085i	−0.00867925	−	0.00178675i
$221$	−39.5625	−	18.0211i	−0.179016	−	0.0815437i
$222$	212.634	+	25.1093i	0.957811	+	0.113105i
$223$	79.6304	−	106.697i	0.357087	−	0.478464i	−0.586330	−	0.810072i	$-0.699428\pi$
$223$	79.6304	−	106.697i	0.357087	−	0.478464i	0.943417	+	0.331608i	$0.107591\pi$
$224$	−9.28302	−	136.205i	−0.0414421	−	0.608058i
$225$	0.652333	−	20.3422i	0.00289926	−	0.0904096i
$226$	−213.239	−	145.384i	−0.943537	−	0.643293i
$227$	4.62818	−	4.98799i	0.0203885	−	0.0219735i	−0.722775	−	0.691083i	$-0.757134\pi$
$227$	4.62818	−	4.98799i	0.0203885	−	0.0219735i	0.743164	+	0.669110i	$0.233324\pi$
$228$	12.5894	−	4.48087i	0.0552167	−	0.0196529i
$229$	136.746	+	129.628i	0.597142	+	0.566061i	0.925622	−	0.378450i	$-0.123543\pi$
$229$	136.746	+	129.628i	0.597142	+	0.566061i	−0.328479	+	0.944511i	$0.606536\pi$
$230$	1.89721	−	14.7144i	0.00824875	−	0.0639757i
$231$	−65.6734	−	68.7356i	−0.284300	−	0.297557i
$232$	−38.8848	−	105.663i	−0.167607	−	0.455443i
$233$	65.6247	+	239.783i	0.281651	+	1.02911i	0.956637	+	0.291281i	$0.0940815\pi$
$233$	65.6247	+	239.783i	0.281651	+	1.02911i	−0.674986	+	0.737830i	$0.735850\pi$
$234$	10.7910	−	5.92642i	0.0461155	−	0.0253266i
$235$	3.31841	+	0.794804i	0.0141209	+	0.00338214i
$236$	−51.2119	−	28.1255i	−0.217000	−	0.119176i
$237$	284.852	+	258.695i	1.20191	+	1.09154i
$238$	93.5473	−	50.5571i	0.393056	−	0.212425i
$239$	268.028	+	108.512i	1.12145	+	0.454027i	0.859542	−	0.511065i	$-0.170749\pi$
$239$	268.028	+	108.512i	1.12145	+	0.454027i	0.261913	+	0.965092i	$0.415647\pi$
$240$	8.03147	+	16.2315i	0.0334645	+	0.0676313i
$241$	185.703	+	431.918i	0.770554	+	1.79219i	0.587751	+	0.809042i	$0.300014\pi$
$241$	185.703	+	431.918i	0.770554	+	1.79219i	0.182803	+	0.983150i	$0.441483\pi$
$242$	−125.225	+	187.956i	−0.517460	+	0.776677i
$243$	−34.9851	+	26.6968i	−0.143971	+	0.109863i
$244$	11.9416	−	9.52314i	0.0489411	−	0.0390293i
$245$	2.16347	+	15.7980i	0.00883050	+	0.0644817i
$246$	37.0972	−	46.5184i	0.150802	−	0.189099i
$247$	−24.2991	−	0.519384i	−0.0983769	−	0.00210277i
$248$	−13.1119	−	22.1603i	−0.0528707	−	0.0893560i
$249$	132.472	−	152.282i	0.532015	−	0.611573i
$250$	33.7265	+	15.8001i	0.134906	+	0.0632005i
$251$	−241.757	−	168.639i	−0.963174	−	0.671869i	−0.0184827	−	0.999829i	$-0.505884\pi$
$251$	−241.757	−	168.639i	−0.963174	−	0.671869i	−0.944691	+	0.327961i	$0.893639\pi$
$252$	−1.04816	+	7.14476i	−0.00415936	+	0.0283522i
$253$	82.2202	+	46.3055i	0.324981	+	0.183026i
$254$	−141.146	−	338.199i	−0.555694	−	1.33149i
$255$	−3.89474	+	4.77821i	−0.0152735	+	0.0187381i
$256$	−179.647	−	128.189i	−0.701744	−	0.500738i
$257$	−245.587	−	179.233i	−0.955593	−	0.697404i	−0.00247288	−	0.999997i	$-0.500787\pi$
$257$	−245.587	−	179.233i	−0.955593	−	0.697404i	−0.953120	+	0.302593i	$0.902148\pi$
$258$	35.2682	+	273.534i	0.136699	+	1.06021i
$259$	206.461	−	97.7153i	0.797149	−	0.377279i
$260$	0.258834	+	2.68308i	0.000995514	+	0.0103195i
$261$	2.02928	+	14.5141i	0.00777501	+	0.0556095i
$262$	−31.4230	+	292.946i	−0.119935	+	1.11811i
$263$	42.2591	+	13.0352i	0.160681	+	0.0495635i	0.374052	−	0.927408i	$-0.377968\pi$
$263$	42.2591	+	13.0352i	0.160681	+	0.0495635i	−0.213371	+	0.976971i	$0.568444\pi$
$264$	−85.0637	+	6.37464i	−0.322211	+	0.0241464i
$265$	7.44414	−	28.3877i	0.0280911	−	0.107124i
$266$	36.8823	−	46.6241i	0.138655	−	0.175279i
$267$	136.643	−	308.678i	0.511770	−	1.15610i
$268$	−57.2374	−	57.8523i	−0.213573	−	0.215867i
$269$	51.8511	−	43.1945i	0.192755	−	0.160574i	−0.538622	−	0.842548i	$-0.681055\pi$
$269$	51.8511	−	43.1945i	0.192755	−	0.160574i	0.731377	+	0.681973i	$0.238878\pi$
$270$	−5.10038	−	20.3331i	−0.0188903	−	0.0753076i
$271$	−45.4149	−	423.388i	−0.167583	−	1.56232i	−0.698947	−	0.715173i	$-0.746348\pi$
$271$	−45.4149	−	423.388i	−0.167583	−	1.56232i	0.531365	−	0.847143i	$-0.321679\pi$
$272$	24.6285	−	126.462i	0.0905459	−	0.464934i
$273$	−64.0525	+	114.786i	−0.234625	+	0.420461i
$274$	41.8563	−	80.2307i	0.152760	−	0.292813i
$275$	−86.6399	+	80.3901i	−0.315054	+	0.292328i
$276$	10.6919	+	70.9362i	0.0387388	+	0.257015i
$277$	299.880	+	186.200i	1.08260	+	0.672202i	0.947863	−	0.318679i	$-0.103239\pi$
$277$	299.880	+	186.200i	1.08260	+	0.672202i	0.134738	+	0.990881i	$0.456981\pi$
$278$	16.0488	−	27.1237i	0.0577294	−	0.0975674i
$279$	1.05611	+	3.18083i	0.00378533	+	0.0114008i
$280$	12.1848	+	7.49946i	0.0435173	+	0.0267838i
$281$	45.6722	−	473.440i	0.162534	−	1.68484i	−0.448929	−	0.893567i	$-0.648194\pi$
$281$	45.6722	−	473.440i	0.162534	−	1.68484i	0.611464	−	0.791273i	$-0.290581\pi$
$282$	−68.7405	+	2.93995i	−0.243761	+	0.0104254i
$283$	−20.9336	+	121.244i	−0.0739704	+	0.428425i	0.924870	+	0.380283i	$0.124173\pi$
$283$	−20.9336	+	121.244i	−0.0739704	+	0.428425i	−0.998841	+	0.0481416i	$0.984670\pi$
$284$	−30.7439	−	65.6250i	−0.108253	−	0.231074i
$285$	−0.945217	+	3.31418i	−0.00331655	+	0.0116287i
$286$	−68.5387	−	20.3419i	−0.239646	−	0.0711257i
$287$	7.19569	−	63.0657i	0.0250721	−	0.219741i
$288$	10.7198	+	11.8037i	0.0372217	+	0.0409852i
$289$	−238.402	+	57.1005i	−0.824920	+	0.197580i
$290$	−12.9060	−	3.53218i	−0.0445036	−	0.0121799i
$291$	356.618	−	30.5602i	1.22549	−	0.105018i
$292$	8.43218	+	7.02441i	0.0288773	+	0.0240562i
$293$	171.372	−	355.858i	0.584887	−	1.21453i	−0.373119	−	0.927784i	$-0.621712\pi$
$293$	171.372	−	355.858i	0.584887	−	1.21453i	0.958006	−	0.286748i	$-0.0925741\pi$
$294$	−129.317	−	294.365i	−0.439853	−	1.00124i
$295$	13.5761	−	6.53789i	0.0460206	−	0.0221623i
$296$	49.8670	−	198.799i	0.168470	−	0.671617i
$297$	132.047	+	18.4621i	0.444602	+	0.0621618i
$298$	18.0679	+	0.772744i	0.0606307	+	0.00259310i
$299$	27.6726	−	127.507i	0.0925506	−	0.426445i
$300$	−88.7002	−	14.3404i	−0.295667	−	0.0478012i
$301$	186.790	+	227.328i	0.620566	+	0.755243i
$302$	−80.8726	−	115.937i	−0.267790	−	0.383897i
$303$	−184.797	+	31.9064i	−0.609890	+	0.105301i
$304$	−15.2767	−	70.3903i	−0.0502522	−	0.231547i
$305$	0.210362	+	3.93353i	0.000689713	+	0.0128968i
$306$	−4.90554	+	11.4096i	−0.0160312	+	0.0372861i
$307$	−130.939	−	201.158i	−0.426512	−	0.655237i	0.558144	−	0.829744i	$-0.311514\pi$
$307$	−130.939	−	201.158i	−0.426512	−	0.655237i	−0.984656	+	0.174507i	$0.944167\pi$
$308$	33.7757	−	24.8542i	0.109661	−	0.0806955i
$309$	−16.6905	+	45.3534i	−0.0540145	+	0.146775i
$310$	−3.04891	−	0.261274i	−0.00983518	−	0.000842819i
$311$	−192.507	−	190.461i	−0.618995	−	0.612416i	0.323665	−	0.946172i	$-0.395085\pi$
$311$	−192.507	−	190.461i	−0.618995	−	0.612416i	−0.942659	+	0.333756i	$0.891684\pi$
$312$	43.0910	+	109.794i	0.138112	+	0.351904i
$313$	46.1122	+	149.492i	0.147323	+	0.477611i	0.998914	−	0.0465970i	$-0.0148377\pi$
$313$	46.1122	+	149.492i	0.147323	+	0.477611i	−0.851590	+	0.524208i	$0.824361\pi$
$314$	−87.9424	−	451.566i	−0.280071	−	1.43811i
$315$	−1.34291	−	1.29033i	−0.00426321	−	0.00409630i
$316$	−129.245	+	110.027i	−0.409002	+	0.348188i
$317$	32.7372	−	20.3270i	0.103272	−	0.0641231i	−0.474889	−	0.880046i	$-0.657512\pi$
$317$	32.7372	−	20.3270i	0.103272	−	0.0641231i	0.578161	+	0.815922i	$0.303770\pi$
$318$	12.6456	+	591.616i	0.0397659	+	1.86043i
$319$	51.6282	−	67.6567i	0.161844	−	0.212090i
$320$	10.1805	−	3.50139i	0.0318142	−	0.0109418i
$321$	−8.97422	−	34.2226i	−0.0279571	−	0.106612i
$322$	207.830	+	242.191i	0.645434	+	0.752146i
$323$	19.6491	−	14.6645i	0.0608331	−	0.0454009i
$324$	46.0389	+	79.7417i	0.142095	+	0.246116i
$325$	141.528	+	81.7110i	0.435470	+	0.251419i
$326$	5.88045	+	49.7977i	0.0180382	+	0.152754i
$327$	−245.046	−	78.4639i	−0.749376	−	0.239951i
$328$	−39.6230	−	40.9140i	−0.120802	−	0.124738i
$329$	−60.4832	+	41.5864i	−0.183839	+	0.126402i
$330$	−5.25527	+	8.66912i	−0.0159251	+	0.0262700i
$331$	−58.0975	+	316.295i	−0.175521	+	0.955573i	0.771938	+	0.635697i	$0.219287\pi$
$331$	−58.0975	+	316.295i	−0.175521	+	0.955573i	−0.947460	+	0.319876i	$0.896359\pi$
$332$	59.1493	+	66.5450i	0.178161	+	0.200437i
$333$	−11.8314	+	23.9111i	−0.0355297	+	0.0718051i
$334$	614.995	+	32.8896i	1.84130	+	0.0984717i
$335$	20.7194	−	3.34975i	0.0618489	−	0.00999924i
$336$	−375.037	−	105.368i	−1.11618	−	0.313595i
$337$	8.97957	+	30.2551i	0.0266456	+	0.0897779i	0.970939	−	0.239327i	$-0.0769267\pi$
$337$	8.97957	+	30.2551i	0.0266456	+	0.0897779i	−0.944294	+	0.329104i	$0.893253\pi$
$338$	−3.08606	−	288.792i	−0.00913034	−	0.854413i
$339$	−259.967	+	189.727i	−0.766864	+	0.559667i
$340$	−1.87072	−	1.97344i	−0.00550213	−	0.00580424i
$341$	8.81751	−	17.3511i	0.0258578	−	0.0508831i
$342$			6.94329i			0.0203020i
$343$	−283.616	−	192.901i	−0.826870	−	0.562394i
$344$	264.007			0.767462
$345$	−16.4935	−	8.38169i	−0.0478074	−	0.0242948i
$346$	287.297	−	272.343i	0.830338	−	0.787119i
$347$	−155.917	−	213.640i	−0.449329	−	0.615678i	0.522135	−	0.852863i	$-0.325136\pi$
$347$	−155.917	−	213.640i	−0.449329	−	0.615678i	−0.971464	+	0.237185i	$0.923775\pi$
$348$	64.6957	−	0.691345i	0.185907	−	0.00198662i
$349$	−27.8963	+	8.27947i	−0.0799321	+	0.0237234i	−0.324246	−	0.945973i	$-0.605111\pi$
$349$	−27.8963	+	8.27947i	−0.0799321	+	0.0237234i	0.244314	+	0.969696i	$0.421437\pi$
$350$	−368.279	+	155.405i	−1.05223	+	0.444014i
$351$	−29.4233	−	181.994i	−0.0838272	−	0.518501i
$352$	4.94485	−	92.4629i	0.0140479	−	0.262679i
$353$	−362.734	−	179.483i	−1.02757	−	0.508451i	−0.150401	−	0.988625i	$-0.548056\pi$
$353$	−362.734	−	179.483i	−1.02757	−	0.508451i	−0.877173	+	0.480174i	$0.840573\pi$
$354$	−227.089	+	201.850i	−0.641494	+	0.570199i
$355$	18.3824	+	3.37650i	0.0517813	+	0.00951127i
$356$	127.336	+	77.1917i	0.357685	+	0.216831i
$357$	−20.2792	−	131.042i	−0.0568044	−	0.367065i
$358$	244.761	−	237.038i	0.683690	−	0.662117i
$359$	−73.9719	+	231.017i	−0.206050	+	0.643502i	0.793347	+	0.608770i	$0.208337\pi$
$359$	−73.9719	+	231.017i	−0.206050	+	0.643502i	−0.999397	+	0.0347321i	$0.988942\pi$
$360$	−1.65955	+	0.195971i	−0.00460986	+	0.000544364i
$361$	−173.646	+	300.764i	−0.481015	+	0.833142i
$362$	265.725	−	153.416i	0.734046	−	0.423802i
$363$	168.453	+	225.711i	0.464057	+	0.621794i
$364$	−46.6046	−	34.4972i	−0.128035	−	0.0947726i
$365$	−2.73781	+	0.717938i	−0.00750084	+	0.00196695i
$366$	−25.8322	−	75.1091i	−0.0705798	−	0.205216i
$367$	236.945	+	180.811i	0.645627	+	0.492672i	0.877187	−	0.480148i	$-0.159417\pi$
$367$	236.945	+	180.811i	0.645627	+	0.492672i	−0.231561	+	0.972820i	$0.574383\pi$
$368$	386.588	−	8.26317i	1.05051	−	0.0224543i
$369$	3.91066	+	6.29823i	0.0105980	+	0.0170684i
$370$	−15.7895	−	18.5472i	−0.0426743	−	0.0501276i
$371$	346.470	+	527.717i	0.933882	+	1.42242i
$372$	14.5235	−	2.82846i	0.0390417	−	0.00760338i
$373$	−401.034	+	123.703i	−1.07516	+	0.331642i	−0.781267	−	0.624197i	$-0.785426\pi$
$373$	−401.034	+	123.703i	−1.07516	+	0.331642i	−0.293891	+	0.955839i	$0.594950\pi$
$374$	67.1360	−	26.3489i	0.179508	−	0.0704517i
$375$	32.6651	−	33.0160i	0.0871069	−	0.0880427i
$376$	−5.62338	+	65.6213i	−0.0149558	+	0.174525i
$377$	−110.434	−	40.6408i	−0.292929	−	0.107800i
$378$	398.378	+	211.267i	1.05391	+	0.558907i
$379$	−407.452	+	265.222i	−1.07507	+	0.699794i	−0.956081	−	0.293101i	$-0.905313\pi$
$379$	−407.452	+	265.222i	−1.07507	+	0.699794i	−0.118990	+	0.992895i	$0.537966\pi$
$380$	−1.39660	−	0.600470i	−0.00367527	−	0.00158018i
$381$	−456.345	+	24.4050i	−1.19776	+	0.0640552i
$382$	143.043	−	31.0444i	0.374458	−	0.0812680i
$383$	35.4181	+	205.136i	0.0924755	+	0.535604i	0.994570	+	0.104066i	$0.0331853\pi$
$383$	35.4181	+	205.136i	0.0924755	+	0.535604i	−0.902095	+	0.431538i	$0.857971\pi$
$384$	−361.065	+	251.863i	−0.940272	+	0.655893i
$385$	0.158122	+	10.8138i	0.000410707	+	0.0280879i
$386$	−46.2606	+	286.138i	−0.119846	+	0.741290i
$387$	−33.5824	−	7.28832i	−0.0867762	−	0.0188329i
$388$	−6.74639	+	157.741i	−0.0173876	+	0.406549i
$389$	−62.0935	+	444.113i	−0.159623	+	1.14168i	0.729490	+	0.683992i	$0.239758\pi$
$389$	−62.0935	+	444.113i	−0.159623	+	1.14168i	−0.889113	+	0.457688i	$0.848678\pi$
$390$	13.5961	+	3.41046i	0.0348617	+	0.00874477i
$391$	57.1083	+	118.587i	0.146057	+	0.303290i
$392$	−295.296	+	86.7387i	−0.753306	+	0.221272i
$393$	331.021	+	159.411i	0.842292	+	0.405627i
$394$	67.7707	−	81.3527i	0.172007	−	0.206479i
$395$	−3.73756	−	43.6150i	−0.00946217	−	0.110418i
$396$	−1.29290	+	4.72406i	−0.00326490	+	0.0119294i
$397$	−64.7672	−	270.411i	−0.163142	−	0.681137i	−0.992482	−	0.122393i	$-0.960943\pi$
$397$	−64.7672	−	270.411i	−0.163142	−	0.681137i	0.829340	−	0.558744i	$-0.188717\pi$
$398$	−173.087	+	157.193i	−0.434893	+	0.394958i
$399$	−39.3530	−	62.8260i	−0.0986290	−	0.157459i
$400$	−137.801	+	464.298i	−0.344503	+	1.16075i
$401$	−301.044	−	85.8591i	−0.750734	−	0.214112i	−0.122856	−	0.992424i	$-0.539205\pi$
$401$	−301.044	−	85.8591i	−0.750734	−	0.214112i	−0.627878	+	0.778312i	$0.716076\pi$
$402$	−383.231	+	179.535i	−0.953311	+	0.446605i
$403$	−26.5192	−	4.57871i	−0.0658044	−	0.0113616i
$404$	−3.53469	−	82.6465i	−0.00874924	−	0.204570i
$405$	−23.6371	−	2.28025i	−0.0583633	−	0.00563024i
$406$	242.280	−	155.389i	0.596750	−	0.382731i
$407$	147.031	−	48.8178i	0.361256	−	0.119945i
$408$	−102.401	−	60.5891i	−0.250982	−	0.148503i
$409$	−59.1468	+	95.2575i	−0.144613	+	0.232904i	−0.913842	−	0.406070i	$-0.866899\pi$
$409$	−59.1468	+	95.2575i	−0.144613	+	0.232904i	0.769229	+	0.638973i	$0.220641\pi$
$410$	−6.69320	+	1.00884i	−0.0163249	+	0.00246058i
$411$	−76.7550	−	82.7222i	−0.186752	−	0.201271i
$412$	−18.9002	−	9.86022i	−0.0458743	−	0.0239326i
$413$	−91.0007	+	311.095i	−0.220341	+	0.753256i
$414$	−36.5866	−	7.12523i	−0.0883734	−	0.0172107i
$415$	−22.8307	+	2.44894i	−0.0550136	+	0.00590106i
$416$	−124.184	+	31.1505i	−0.298519	+	0.0748809i
$417$	−25.1549	−	30.1963i	−0.0603236	−	0.0724131i
$418$	28.6630	−	28.3583i	0.0685718	−	0.0678429i
$419$	−182.394	−	80.7406i	−0.435309	−	0.192698i	0.175495	−	0.984480i	$-0.443847\pi$
$419$	−182.394	−	80.7406i	−0.435309	−	0.192698i	−0.610804	+	0.791782i	$0.709154\pi$
$420$	−6.40789	+	5.15151i	−0.0152569	+	0.0122655i
$421$	40.4845	+	10.6163i	0.0961627	+	0.0252168i	0.301422	−	0.953491i	$-0.402539\pi$
$421$	40.4845	+	10.6163i	0.0961627	+	0.0252168i	−0.205260	+	0.978708i	$0.565804\pi$
$422$	14.5291	+	193.878i	0.0344292	+	0.459426i
$423$	2.52689	−	8.19197i	0.00597373	−	0.0193664i
$424$	563.221	+	60.4142i	1.32835	+	0.142486i
$425$	−163.269	+	22.8274i	−0.384162	+	0.0537114i
$426$	−375.113	+	36.1867i	−0.880547	+	0.0849453i
$427$	−65.8898	−	53.2769i	−0.154309	−	0.124770i
$428$	15.4783	−	1.99570i	0.0361642	−	0.00466286i
$429$	−52.5576	+	72.0152i	−0.122512	+	0.167868i
$430$	18.2244	−	25.5400i	0.0423823	−	0.0593955i
$431$	−127.185	−	103.669i	−0.295092	−	0.240532i	0.472710	−	0.881218i	$-0.343276\pi$
$431$	−127.185	−	103.669i	−0.295092	−	0.240532i	−0.767803	+	0.640686i	$0.778650\pi$
$432$	504.209	−	210.430i	1.16715	−	0.487107i
$433$	−301.128	+	534.683i	−0.695446	+	1.23483i	0.267088	+	0.963672i	$0.413939\pi$
$433$	−301.128	+	534.683i	−0.695446	+	1.23483i	−0.962534	+	0.271162i	$0.912592\pi$
$434$	48.0764	−	44.9618i	0.110775	−	0.103599i
$435$	−9.54633	+	13.6854i	−0.0219456	+	0.0314606i
$436$	48.1498	−	102.779i	0.110435	−	0.235732i
$437$	55.5181	+	48.2959i	0.127044	+	0.110517i
$438$	49.1167	−	29.0617i	0.112139	−	0.0663509i
$439$	4.49563	−	210.326i	0.0102406	−	0.479101i	−0.965528	−	0.260298i	$-0.916179\pi$
$439$	4.49563	−	210.326i	0.0102406	−	0.479101i	0.975769	−	0.218803i	$-0.0702154\pi$
$440$	7.58706	+	6.05048i	0.0172433	+	0.0137511i
$441$	39.9571	−	2.88129i	0.0906056	−	0.00653354i
$442$	−62.1758	−	77.9660i	−0.140669	−	0.176394i
$443$	−483.875	−	634.099i	−1.09227	−	1.43137i	−0.892227	−	0.451586i	$-0.850858\pi$
$443$	−483.875	−	634.099i	−1.09227	−	1.43137i	−0.200041	−	0.979787i	$-0.564108\pi$
$444$	98.0158	+	65.3029i	0.220756	+	0.147079i
$445$	−35.2801	+	15.1687i	−0.0792812	+	0.0340870i
$446$	273.721	−	135.439i	0.613725	−	0.303676i
$447$	8.46292	−	20.9036i	0.0189327	−	0.0467641i
$448$	−90.6343	+	213.109i	−0.202309	+	0.475690i
$449$	−227.924	+	250.970i	−0.507626	+	0.558953i	−0.939309	−	0.343073i	$-0.888532\pi$
$449$	−227.924	+	250.970i	−0.507626	+	0.558953i	0.431683	+	0.902026i	$0.357920\pi$
$450$	22.4737	−	40.9209i	0.0499415	−	0.0909354i
$451$	10.0279	−	41.8675i	0.0222347	−	0.0928327i
$452$	−68.3395	−	124.435i	−0.151194	−	0.275299i
$453$	−170.022	+	46.5324i	−0.375325	+	0.102721i
$454$	14.6480	−	5.39059i	0.0322643	−	0.0118736i
$455$	14.2235	−	4.61618i	0.0312605	−	0.0101455i
$456$	−65.9733	−	8.50632i	−0.144678	−	0.0186542i
$457$	115.032	−	121.349i	0.251712	−	0.265533i	−0.587639	−	0.809123i	$-0.699942\pi$
$457$	115.032	−	121.349i	0.251712	−	0.265533i	0.839351	+	0.543590i	$0.182936\pi$
$458$	144.929	+	407.190i	0.316438	+	0.889062i
$459$	136.330	+	126.496i	0.297015	+	0.275590i
$460$	4.59728	−	6.74297i	0.00999409	−	0.0146586i
$461$	258.989	+	8.30528i	0.561799	+	0.0180158i	0.311659	−	0.950194i	$-0.399115\pi$
$461$	258.989	+	8.30528i	0.561799	+	0.0180158i	0.250140	+	0.968210i	$0.419523\pi$
$462$	−62.8688	−	208.810i	−0.136080	−	0.451969i
$463$	−147.540	−	110.112i	−0.318661	−	0.237823i	0.426840	−	0.904327i	$-0.359627\pi$
$463$	−147.540	−	110.112i	−0.318661	−	0.237823i	−0.745501	+	0.666504i	$0.767790\pi$
$464$	40.8975	−	346.334i	0.0881411	−	0.746409i
$465$	−1.58185	+	3.47268i	−0.00340182	+	0.00746813i
$466$	−114.984	+	558.543i	−0.246747	+	1.19859i
$467$	−688.165	−	437.549i	−1.47359	−	0.936935i	−0.998370	−	0.0570665i	$-0.981825\pi$
$467$	−688.165	−	437.549i	−1.47359	−	0.936935i	−0.475217	−	0.879869i	$-0.657630\pi$
$468$	6.76869	−	0.217059i	0.0144630	−	0.000463801i
$469$	−244.806	+	379.344i	−0.521974	+	0.808837i
$470$	5.96003	+	5.07385i	0.0126809	+	0.0107954i
$471$	−567.284	−	85.5043i	−1.20443	−	0.181538i
$472$	163.837	+	240.304i	0.347111	+	0.509119i
$473$	107.073	+	168.401i	0.226369	+	0.356027i
$474$	313.672	+	825.040i	0.661756	+	1.74059i
$475$	−78.8152	+	47.7782i	−0.165927	+	0.100586i
$476$	58.4736	−	1.48010i	0.122844	−	0.00310945i
$477$	−69.9755	−	23.2335i	−0.146699	−	0.0487075i
$478$	435.338	+	500.439i	0.910750	+	1.04694i
$479$	−188.708	−	661.659i	−0.393962	−	1.38133i	−0.866127	−	0.499824i	$-0.833398\pi$
$479$	−188.708	−	661.659i	−0.393962	−	1.38133i	0.472165	−	0.881510i	$-0.343473\pi$
$480$	−0.193989	+	18.1534i	−0.000404144	+	0.0378196i
$481$	−124.425	−	174.372i	−0.258680	−	0.362520i
$482$	−69.0968	+	1076.24i	−0.143354	+	2.23286i
$483$	371.436	−	142.892i	0.769018	−	0.295843i
$484$	−108.249	+	60.9645i	−0.223654	+	0.125960i
$485$	−32.1045	−	25.0460i	−0.0661949	−	0.0516412i
$486$	−99.2864	+	18.2371i	−0.204293	+	0.0375249i
$487$	388.483	+	147.698i	0.797707	+	0.303281i	0.720250	−	0.693715i	$-0.244027\pi$
$487$	388.483	+	147.698i	0.797707	+	0.303281i	0.0774576	+	0.996996i	$0.475320\pi$
$488$	−74.4698	+	15.3307i	−0.152602	+	0.0314154i
$489$	60.9625	+	13.9143i	0.124668	+	0.0284546i
$490$	−11.9932	+	34.5546i	−0.0244759	+	0.0705195i
$491$	−200.756	−	879.571i	−0.408872	−	1.79139i	−0.589427	−	0.807821i	$-0.700647\pi$
$491$	−200.756	−	879.571i	−0.408872	−	1.79139i	0.180555	−	0.983565i	$-0.442211\pi$
$492$	29.7847	−	13.5673i	0.0605379	−	0.0275757i
$493$	113.054	−	36.1999i	0.229318	−	0.0734279i
$494$	−49.1508	−	26.3139i	−0.0994956	−	0.0532670i
$495$	−0.798062	−	0.979091i	−0.00161225	−	0.00197796i
$496$	−5.10991	−	79.5910i	−0.0103022	−	0.160466i
$497$	−318.646	+	245.146i	−0.641138	+	0.493252i
$498$	429.151	−	173.744i	0.861750	−	0.348884i
$499$	303.829	+	270.062i	0.608877	+	0.541207i	0.911182	−	0.412004i	$-0.135171\pi$
$499$	303.829	+	270.062i	0.608877	+	0.541207i	−0.302305	+	0.953211i	$0.597756\pi$
$500$	12.6016	+	16.1530i	0.0252032	+	0.0323061i
$501$	295.799	−	708.760i	0.590417	−	1.41469i
$502$	−319.131	−	596.095i	−0.635720	−	1.18744i
$503$	−410.986	+	424.377i	−0.817070	+	0.843692i	−0.989974	−	0.141247i	$-0.954889\pi$
$503$	−410.986	+	424.377i	−0.817070	+	0.843692i	0.172904	+	0.984939i	$0.444685\pi$
$504$	20.7640	−	29.3427i	0.0411984	−	0.0582196i
$505$	17.8798	+	11.6384i	0.0354055	+	0.0230464i
$506$	120.016	+	180.137i	0.237185	+	0.356001i
$507$	−340.570	−	117.132i	−0.671737	−	0.231030i
$508$	15.0646	−	201.023i	0.0296547	−	0.395715i
$509$	−460.712	−	180.816i	−0.905132	−	0.355238i	−0.133308	−	0.991075i	$-0.542560\pi$
$509$	−460.712	−	180.816i	−0.905132	−	0.355238i	−0.771824	+	0.635836i	$0.780655\pi$
$510$	−12.9301	+	5.72378i	−0.0253532	+	0.0112231i
$511$	27.9484	−	54.0898i	0.0546935	−	0.105851i
$512$	50.5839	+	96.9599i	0.0987967	+	0.189375i
$513$	97.9534	+	34.8639i	0.190942	+	0.0679608i
$514$	−315.956	−	621.739i	−0.614700	−	1.20961i
$515$	4.90126	−	2.49072i	0.00951700	−	0.00483635i
$516$	−50.8709	+	142.927i	−0.0985871	+	0.276990i
$517$	−44.1383	+	23.0269i	−0.0853738	+	0.0445395i
$518$	523.751	+	14.7326i	1.01110	+	0.0284413i
$519$	−199.823	−	451.404i	−0.385016	−	0.869757i
$520$	4.90215	−	12.4905i	0.00942721	−	0.0240201i
$521$	−67.1360	−	5.03115i	−0.128860	−	0.00965671i	0.0101440	−	0.999949i	$-0.496771\pi$
$521$	−67.1360	−	5.03115i	−0.128860	−	0.00965671i	−0.139004	+	0.990292i	$0.544390\pi$
$522$	−10.9333	+	31.7895i	−0.0209451	+	0.0608994i
$523$	−443.341	+	295.375i	−0.847689	+	0.564771i	−0.901006	−	0.433807i	$-0.857170\pi$
$523$	−443.341	+	295.375i	−0.847689	+	0.564771i	0.0533174	+	0.998578i	$0.483020\pi$
$524$	−88.4131	+	135.826i	−0.168727	+	0.259211i
$525$	28.5783	+	497.646i	0.0544349	+	0.947898i
$526$	72.8717	+	70.5723i	0.138539	+	0.134168i
$527$	23.9337	−	12.8134i	0.0454150	−	0.0243138i
$528$	−243.834	−	101.763i	−0.461806	−	0.192733i
$529$	105.629	−	82.4054i	0.199677	−	0.155776i
$530$	44.7237	−	50.3157i	0.0843843	−	0.0949353i
$531$	−14.2065	−	35.0903i	−0.0267542	−	0.0660835i
$532$	29.7056	−	13.6726i	0.0558376	−	0.0257005i
$533$	−59.4052	+	3.81394i	−0.111454	+	0.00715561i
$534$	600.208	−	489.233i	1.12399	−	0.916167i
$535$	−1.89969	+	3.54837i	−0.00355082	+	0.00663247i
$536$	123.537	+	385.812i	0.230480	+	0.719799i
$537$	−176.132	−	386.669i	−0.327992	−	0.720054i
$538$	150.921	−	34.4468i	0.280523	−	0.0640275i
$539$	−175.090	−	153.181i	−0.324843	−	0.284195i
$540$	2.56594	−	11.2421i	0.00475175	−	0.0208188i
$541$	68.3842	+	332.180i	0.126403	+	0.614012i	0.993304	+	0.115531i	$0.0368569\pi$
$541$	68.3842	+	332.180i	0.126403	+	0.614012i	−0.866901	+	0.498481i	$0.833891\pi$
$542$	347.116	−	913.005i	0.640435	−	1.68451i
$543$	−69.1251	−	376.331i	−0.127302	−	0.693059i
$544$	79.4434	−	101.832i	0.146036	−	0.187192i
$545$	14.3640	+	25.5046i	0.0263559	+	0.0467975i
$546$	−250.271	+	168.168i	−0.458372	+	0.308001i
$547$	−472.395	−	30.3287i	−0.863610	−	0.0554456i	−0.374043	−	0.927411i	$-0.622029\pi$
$547$	−472.395	−	30.3287i	−0.863610	−	0.0554456i	−0.489567	+	0.871966i	$0.662845\pi$
$548$	40.5198	−	28.9134i	0.0739412	−	0.0527616i
$549$	9.89600	+	0.105750i	0.0180255	+	0.000192622i
$550$	−260.717	+	74.3575i	−0.474030	+	0.135195i
$551$	50.0714	−	43.5577i	0.0908737	−	0.0790521i
$552$	112.525	−	338.907i	0.203849	−	0.613961i
$553$	750.818	+	568.281i	1.35772	+	1.02763i
$554$	419.742	+	692.409i	0.757657	+	1.24984i
$555$	−28.3921	+	10.7944i	−0.0511569	+	0.0194494i
$556$	14.6295	−	9.30172i	0.0263121	−	0.0167297i
$557$	−308.288	+	210.187i	−0.553479	+	0.377356i	−0.807522	−	0.589837i	$-0.799192\pi$
$557$	−308.288	+	210.187i	−0.553479	+	0.377356i	0.254043	+	0.967193i	$0.418239\pi$
$558$	−1.14584	+	7.60216i	−0.00205348	+	0.0136239i
$559$	178.865	−	210.105i	0.319973	−	0.375858i
$560$	23.1226	+	37.8068i	0.0412904	+	0.0675121i
$561$	−2.88263	−	89.8909i	−0.00513837	−	0.160233i
$562$	585.400	−	920.702i	1.04164	−	1.63826i
$563$	−218.578	−	44.9974i	−0.388238	−	0.0799244i	0.00351753	−	0.999994i	$-0.498880\pi$
$563$	−218.578	−	44.9974i	−0.388238	−	0.0799244i	−0.391755	+	0.920069i	$0.628132\pi$
$564$	−34.4422	−	15.6888i	−0.0610677	−	0.0278170i
$565$	36.3604	+	4.29369i	0.0643547	+	0.00759945i
$566$	−168.806	+	226.185i	−0.298244	+	0.399620i
$567$	376.790	−	344.906i	0.664533	−	0.608301i
$568$	−11.5624	+	360.558i	−0.0203563	+	0.634785i
$569$	−265.536	−	181.039i	−0.466671	−	0.318171i	0.307055	−	0.951692i	$-0.400657\pi$
$569$	−265.536	−	181.039i	−0.466671	−	0.318171i	−0.773725	+	0.633521i	$0.781609\pi$
$570$	−5.37704	+	5.79508i	−0.00943341	+	0.0101668i
$571$	378.188	−	134.606i	0.662326	−	0.235737i	0.0172449	−	0.999851i	$-0.494510\pi$
$571$	378.188	−	134.606i	0.662326	−	0.235737i	0.645081	+	0.764114i	$0.276823\pi$
$572$	−28.5413	−	27.0557i	−0.0498973	−	0.0473001i
$573$	23.3415	−	181.032i	0.0407356	−	0.315937i
$574$	80.2531	−	121.489i	0.139814	−	0.211653i
$575$	−170.879	−	464.334i	−0.297181	−	0.807538i
$576$	−7.13994	−	26.0883i	−0.0123957	−	0.0452921i
$577$	822.190	−	451.545i	1.42494	−	0.782574i	0.432076	−	0.901837i	$-0.357781\pi$
$577$	822.190	−	451.545i	1.42494	−	0.782574i	0.992863	+	0.119263i	$0.0380532\pi$
$578$	−546.861	−	130.981i	−0.946126	−	0.226610i
$579$	316.819	+	173.996i	0.547183	+	0.300512i
$580$	−5.44873	−	4.94839i	−0.00939436	−	0.00853171i
$581$	289.602	−	400.114i	0.498454	−	0.688664i
$582$	761.027	+	308.106i	1.30761	+	0.529391i
$583$	189.888	+	383.762i	0.325708	+	0.658253i
$584$	−21.5785	−	50.1883i	−0.0369494	−	0.0859388i
$585$	−0.968386	+	1.45349i	−0.00165536	+	0.00248460i
$586$	720.258	−	549.623i	1.22911	−	0.937922i
$587$	352.960	−	281.476i	0.601294	−	0.479516i	−0.274901	−	0.961473i	$-0.588645\pi$
$587$	352.960	−	281.476i	0.601294	−	0.479516i	0.876195	+	0.481956i	$0.160074\pi$
$588$	9.94187	−	176.579i	0.0169079	−	0.300305i
$589$	9.46300	−	11.8662i	0.0160662	−	0.0201464i
$590$	34.5567	+	0.738637i	0.0585707	+	0.00125193i
$591$	−67.2371	−	113.636i	−0.113768	−	0.192278i
$592$	416.663	−	478.971i	0.703823	−	0.809073i
$593$	−196.007	−	91.8251i	−0.330535	−	0.154848i	0.251839	−	0.967769i	$-0.418965\pi$
$593$	−196.007	−	91.8251i	−0.330535	−	0.154848i	−0.582374	+	0.812921i	$0.697876\pi$
$594$	250.844	+	174.978i	0.422297	+	0.294576i
$595$	−8.44866	+	12.4973i	−0.0141994	+	0.0210039i
$596$	8.66773	+	4.88157i	0.0145432	+	0.00819056i
$597$	112.299	+	269.077i	0.188105	+	0.450716i
$598$	189.096	−	231.989i	0.316213	−	0.387942i
$599$	−168.348	−	120.127i	−0.281048	−	0.200545i	0.431603	−	0.902063i	$-0.357948\pi$
$599$	−168.348	−	120.127i	−0.281048	−	0.200545i	−0.712651	+	0.701518i	$0.752506\pi$
$600$	361.287	+	263.672i	0.602145	+	0.439453i
$601$	48.9839	+	379.909i	0.0815040	+	0.632129i	0.980832	+	0.194854i	$0.0624234\pi$
$601$	48.9839	+	379.909i	0.0815040	+	0.632129i	−0.899328	+	0.437274i	$0.855944\pi$
$602$	145.737	+	658.990i	0.242088	+	1.09467i
$603$	−5.06334	−	52.4868i	−0.00839692	−	0.0870428i
$604$	−10.7668	−	77.0080i	−0.0178259	−	0.127497i
$605$	3.41722	−	31.8575i	0.00564829	−	0.0526571i
$606$	−411.058	−	126.795i	−0.678314	−	0.209232i
$607$	240.913	−	18.0539i	0.396891	−	0.0297429i	0.125210	−	0.992130i	$-0.460040\pi$
$607$	240.913	−	18.0539i	0.396891	−	0.0297429i	0.271681	+	0.962387i	$0.412420\pi$
$608$	18.3155	−	69.8449i	0.0301242	−	0.114876i
$609$	−81.2458	−	349.613i	−0.133408	−	0.574077i
$610$	−3.65756	+	8.26250i	−0.00599601	+	0.0135451i
$611$	48.4136	+	48.9338i	0.0792367	+	0.0800880i
$612$	−5.24894	+	4.37262i	−0.00857670	+	0.00714480i
$613$	−7.00300	−	27.9180i	−0.0114241	−	0.0455432i	0.963971	−	0.266009i	$-0.0857050\pi$
$613$	−7.00300	−	27.9180i	−0.0114241	−	0.0455432i	−0.975395	+	0.220465i	$0.929242\pi$
$614$	−58.7205	−	547.432i	−0.0956360	−	0.891582i
$615$	−1.61354	+	8.28519i	−0.00262364	+	0.0134719i
$616$	−205.937	+	34.1265i	−0.334314	+	0.0554002i
$617$	−90.0536	+	172.616i	−0.145954	+	0.279766i	−0.948472	−	0.316862i	$-0.897371\pi$
$617$	−90.0536	+	172.616i	−0.145954	+	0.279766i	0.802518	+	0.596628i	$0.203493\pi$
$618$	−81.2629	+	75.4009i	−0.131493	+	0.122008i
$619$	−28.6660	−	190.187i	−0.0463102	−	0.307248i	−0.999980	−	0.00639145i	$-0.997966\pi$
$619$	−28.6660	−	190.187i	−0.0463102	−	0.307248i	0.953669	−	0.300857i	$-0.0972726\pi$
$620$	−1.43004	−	0.887930i	−0.00230651	−	0.00143214i
$621$	−284.230	+	480.372i	−0.457697	+	0.773546i
$622$	−195.741	−	589.540i	−0.314696	−	0.947813i
$623$	265.590	−	782.218i	0.426308	−	1.25557i
$624$	−35.0803	+	363.644i	−0.0562184	+	0.582763i
$625$	616.505	−	26.3672i	0.986409	−	0.0421875i
$626$	−61.0557	+	353.625i	−0.0975331	+	0.564897i
$627$	−21.3307	−	45.5320i	−0.0340203	−	0.0726189i
$628$	69.4067	−	243.358i	0.110520	−	0.387513i
$629$	207.162	+	61.4847i	0.329352	+	0.0977499i
$630$	−1.40527	−	4.03424i	−0.00223059	−	0.00640355i
$631$	507.038	+	558.305i	0.803547	+	0.884794i	0.995319	−	0.0966453i	$-0.0308112\pi$
$631$	507.038	+	558.305i	0.803547	+	0.884794i	−0.191772	+	0.981439i	$0.561423\pi$
$632$	821.680	−	196.804i	1.30013	−	0.311398i
$633$	233.848	+	64.0004i	0.369428	+	0.101107i
$634$	88.0702	−	7.54712i	0.138912	−	0.0119040i
$635$	39.9448	+	33.2760i	0.0629053	+	0.0524031i
$636$	−141.233	+	293.273i	−0.222064	+	0.461120i
$637$	−131.034	+	293.771i	−0.205705	+	0.461179i
$638$	175.887	−	84.7026i	0.275684	−	0.132763i
$639$	11.4245	−	45.5447i	0.0178788	−	0.0712750i
$640$	49.5993	+	6.93470i	0.0774990	+	0.0108355i
$641$	963.482	+	41.2070i	1.50309	+	0.0642854i	0.779700	−	0.626153i	$-0.215371\pi$
$641$	963.482	+	41.2070i	1.50309	+	0.0642854i	0.723391	+	0.690438i	$0.242582\pi$
$642$	17.2125	−	79.3098i	0.0268107	−	0.123536i
$643$	−514.593	−	83.1953i	−0.800299	−	0.129386i	−0.254249	−	0.967139i	$-0.581828\pi$
$643$	−514.593	−	83.1953i	−0.800299	−	0.129386i	−0.546050	+	0.837752i	$0.683869\pi$
$644$	41.5618	+	170.560i	0.0645370	+	0.264844i
$645$	−22.3846	−	32.0900i	−0.0347048	−	0.0497520i
$646$	55.4210	−	9.56880i	0.0857910	−	0.0148124i
$647$	−27.4038	−	126.269i	−0.0423552	−	0.195160i	0.951188	−	0.308611i	$-0.0998641\pi$
$647$	−27.4038	−	126.269i	−0.0423552	−	0.195160i	−0.993544	+	0.113451i	$0.963810\pi$
$648$	−24.4773	−	457.696i	−0.0377736	−	0.706322i
$649$	−86.8350	+	201.965i	−0.133798	+	0.311195i
$650$	204.503	+	314.172i	0.314620	+	0.483342i
$651$	−32.7192	−	75.2821i	−0.0502599	−	0.115641i
$652$	−9.52615	+	25.8856i	−0.0146107	+	0.0397019i
$653$	363.862	+	31.1809i	0.557216	+	0.0477503i	0.360583	−	0.932727i	$-0.382578\pi$
$653$	363.862	+	31.1809i	0.557216	+	0.0477503i	0.196633	+	0.980477i	$0.436999\pi$
$654$	−419.568	−	415.108i	−0.641541	−	0.634722i
$655$	−15.2702	−	38.9078i	−0.0233132	−	0.0594012i
$656$	−51.9993	−	168.578i	−0.0792672	−	0.256978i
$657$	1.35932	+	6.97980i	0.00206897	+	0.0106237i
$658$	−166.902	+	22.1878i	−0.253651	+	0.0337200i
$659$	709.583	−	604.076i	1.07676	−	0.916656i	0.0799730	−	0.996797i	$-0.474517\pi$
$659$	709.583	−	604.076i	1.07676	−	0.916656i	0.996784	+	0.0801409i	$0.0255370\pi$
$660$	−4.73751	+	2.94159i	−0.00717805	+	0.00445695i
$661$	13.3812	+	626.033i	0.0202439	+	0.947099i	0.890630	+	0.454729i	$0.150264\pi$
$661$	13.3812	+	626.033i	0.0202439	+	0.947099i	−0.870386	+	0.492370i	$0.836131\pi$
$662$	−447.502	+	586.434i	−0.675986	+	0.885851i
$663$	−117.595	+	40.4444i	−0.177368	+	0.0610022i
$664$	−112.418	−	428.699i	−0.169305	−	0.645632i
$665$	−1.57957	+	8.28438i	−0.00237529	+	0.0124577i
$666$	−49.0432	+	36.6019i	−0.0736385	+	0.0549578i
$667$	178.137	+	308.542i	0.267072	+	0.462582i
$668$	293.390	+	169.389i	0.439207	+	0.253576i
$669$	−44.6615	−	378.209i	−0.0667586	−	0.565334i
$670$	45.8513	+	14.6816i	0.0684348	+	0.0219129i
$671$	−39.9815	−	41.2841i	−0.0595849	−	0.0615263i
$672$	−287.313	−	264.491i	−0.427548	−	0.393587i
$673$	−554.964	+	915.471i	−0.824612	+	1.36028i	0.106034	+	0.994363i	$0.466185\pi$
$673$	−554.964	+	915.471i	−0.824612	+	1.36028i	−0.930646	+	0.365921i	$0.880754\pi$
$674$	−13.0785	+	71.2021i	−0.0194043	+	0.105641i
$675$	−464.451	−	522.524i	−0.688076	−	0.774109i
$676$	70.4551	−	142.389i	0.104224	−	0.210635i
$677$	379.145	+	20.2764i	0.560037	+	0.0299504i	0.331279	−	0.943533i	$-0.392520\pi$
$677$	379.145	+	20.2764i	0.560037	+	0.0299504i	0.228758	+	0.973483i	$0.426534\pi$
$678$	−728.786	+	117.825i	−1.07491	+	0.173782i
$679$	862.526	−	152.419i	1.27029	−	0.224475i
$680$	3.85132	+	12.9764i	0.00566370	+	0.0190829i
$681$	−0.207982	−	19.4629i	−0.000305407	−	0.0285799i
$682$	36.0629	−	26.3191i	0.0528781	−	0.0385911i
$683$	−131.895	−	139.137i	−0.193111	−	0.203714i	0.622003	−	0.783014i	$-0.286319\pi$
$683$	−131.895	−	139.137i	−0.193111	−	0.203714i	−0.815114	+	0.579301i	$0.803326\pi$
$684$	−1.73031	+	3.40491i	−0.00252969	+	0.00497793i
$685$			12.8377i			0.0187412i
$686$	−379.519	−	689.210i	−0.553235	−	1.00468i
$687$	538.979			0.784541
$688$	729.008	+	370.467i	1.05960	+	0.538470i
$689$	429.662	−	407.298i	0.623603	−	0.591144i
$690$	−25.0183	−	34.2804i	−0.0362584	−	0.0496817i
$691$	−873.172	+	9.33080i	−1.26364	+	0.0135033i	−0.640100	−	0.768292i	$-0.721107\pi$
$691$	−873.172	+	9.33080i	−1.26364	+	0.0135033i	−0.623536	+	0.781795i	$0.714304\pi$
$692$	208.756	−	61.9578i	0.301671	−	0.0895344i
$693$	27.1379	+	1.34423i	0.0391600	+	0.00193973i
$694$	−96.8280	−	598.915i	−0.139522	−	0.862990i
$695$	−0.238766	+	4.46463i	−0.000343548	+	0.00642393i
$696$	−288.661	−	142.831i	−0.414742	−	0.205217i
$697$	44.8827	−	39.8945i	0.0643941	−	0.0572374i
$698$	−65.6508	−	12.0588i	−0.0940556	−	0.0172763i
$699$	608.111	+	368.640i	0.869973	+	0.527383i
$700$	−219.327	−	15.5686i	−0.313325	−	0.0222408i
$701$	145.605	−	141.010i	0.207710	−	0.201156i	−0.584519	−	0.811380i	$-0.698717\pi$
$701$	145.605	−	141.010i	0.207710	−	0.201156i	0.792229	+	0.610224i	$0.208921\pi$
$702$	128.960	−	402.746i	0.183703	−	0.573713i
$703$	119.977	−	14.1678i	0.170665	−	0.0201533i
$704$	−78.5350	+	136.027i	−0.111555	+	0.193220i
$705$	8.45307	−	4.88038i	0.0119902	−	0.00692253i
$706$	−555.255	−	743.991i	−0.786480	−	1.05381i
$707$	−443.442	+	118.151i	−0.627216	+	0.167116i
$708$	−161.664	+	42.3933i	−0.228339	+	0.0598775i
$709$	30.4467	+	88.5260i	0.0429431	+	0.124860i	0.965043	−	0.262092i	$-0.0844123\pi$
$709$	30.4467	+	88.5260i	0.0429431	+	0.124860i	−0.922100	+	0.386952i	$0.873528\pi$
$710$	34.0822	+	26.0079i	0.0480031	+	0.0366308i
$711$	−109.953	+	2.35021i	−0.154646	+	0.00330550i
$712$	−391.001	−	629.718i	−0.549158	−	0.884435i
$713$	52.8162	+	62.0409i	0.0740760	+	0.0870139i
$714$	94.7099	−	289.050i	0.132647	−	0.404832i
$715$	9.95540	−	1.93881i	0.0139236	−	0.00271163i
$716$	179.099	−	55.2447i	0.250138	−	0.0771575i
$717$	769.965	−	302.189i	1.07387	−	0.421463i
$718$	−391.344	+	395.548i	−0.545047	+	0.550903i
$719$	−86.5179	+	1009.61i	−0.120331	+	1.40419i	0.646782	+	0.762675i	$0.276114\pi$
$719$	−86.5179	+	1009.61i	−0.120331	+	1.40419i	−0.767113	+	0.641512i	$0.778307\pi$
$720$	−4.85755	−	1.78762i	−0.00674659	−	0.00248281i
$721$	−30.7693	+	114.190i	−0.0426759	+	0.158377i
$722$	−667.656	+	434.596i	−0.924731	+	0.601933i
$723$	1235.50	+	531.204i	1.70885	+	0.734722i
$724$	168.540	−	9.01343i	0.232791	−	0.0124495i
$725$	−436.085	+	94.6428i	−0.601497	+	0.130542i
$726$	109.918	+	636.627i	0.151402	+	0.876897i
$727$	−53.8429	+	37.5585i	−0.0740618	+	0.0516623i	−0.608564	−	0.793505i	$-0.708254\pi$
$727$	−53.8429	+	37.5585i	−0.0740618	+	0.0516623i	0.534502	+	0.845167i	$0.320499\pi$
$728$	129.022	+	258.190i	0.177227	+	0.354656i
$729$	−124.910	+	772.613i	−0.171344	+	1.05983i
$730$	−6.34478	−	1.37700i	−0.00869148	−	0.00188630i
$731$	−11.8939	+	278.097i	−0.0162707	+	0.380434i
$732$	6.04979	−	43.2701i	0.00826474	−	0.0591122i
$733$	−1410.18	−	353.732i	−1.92384	−	0.482581i	−0.993161	−	0.116756i	$-0.962751\pi$
$733$	−1410.18	−	353.732i	−1.92384	−	0.482581i	−0.930684	−	0.365825i	$-0.880787\pi$
$734$	296.643	+	615.985i	0.404145	+	0.839216i
$735$	35.5807	+	28.5388i	0.0484091	+	0.0388284i
$736$	349.241	+	168.186i	0.474512	+	0.228513i
$737$	−195.994	+	235.273i	−0.265934	+	0.319231i
$738$	1.45197	+	16.9436i	0.00196744	+	0.0229588i
$739$	366.862	−	1340.46i	0.496431	−	1.81388i	−0.0800732	−	0.996789i	$-0.525515\pi$
$739$	366.862	−	1340.46i	0.496431	−	1.81388i	0.576504	−	0.817094i	$-0.304417\pi$
$740$	−3.12090	−	13.0302i	−0.00421744	−	0.0176083i
$741$	−51.4666	+	46.7406i	−0.0694556	+	0.0630777i
$742$	160.109	+	1439.21i	0.215781	+	1.93964i
$743$	−134.911	+	454.560i	−0.181576	+	0.611790i	0.817767	+	0.575549i	$0.195212\pi$
$743$	−134.911	+	454.560i	−0.181576	+	0.611790i	−0.999343	+	0.0362408i	$0.988462\pi$
$744$	−70.8299	−	20.2010i	−0.0952015	−	0.0271519i
$745$	−2.32324	+	1.08839i	−0.00311844	+	0.00146092i
$746$	−948.649	−	163.791i	−1.27165	−	0.219558i
$747$	2.46499	+	57.6352i	0.00329985	+	0.0771556i
$748$	39.4890	+	3.80946i	0.0527928	+	0.00509286i
$749$	−29.3521	−	81.4514i	−0.0391884	−	0.108747i
$750$	101.109	−	33.5705i	0.134812	−	0.0447607i
$751$	516.279	+	305.476i	0.687456	+	0.406759i	0.810576	−	0.585633i	$-0.199154\pi$
$751$	516.279	+	305.476i	0.687456	+	0.406759i	−0.123120	+	0.992392i	$0.539290\pi$
$752$	−107.611	+	173.311i	−0.143100	+	0.230466i
$753$	−833.752	+	125.668i	−1.10724	+	0.166890i
$754$	−183.599	−	197.873i	−0.243500	−	0.262430i
$755$	17.7794	+	9.27552i	0.0235489	+	0.0122855i
$756$	142.711	+	202.881i	0.188771	+	0.268361i
$757$	440.857	+	85.8568i	0.582373	+	0.113417i	0.473740	−	0.880665i	$-0.342904\pi$
$757$	440.857	+	85.8568i	0.582373	+	0.113417i	0.108633	+	0.994082i	$0.465353\pi$
$758$	−1108.84	+	118.940i	−1.46285	+	0.156914i
$759$	261.813	−	65.6738i	0.344945	−	0.0865267i
$760$	4.84357	+	5.81428i	0.00637312	+	0.00765037i
$761$	−1029.48	+	1018.54i	−1.35280	+	1.33842i	−0.460025	+	0.887906i	$0.652160\pi$
$761$	−1029.48	+	1018.54i	−1.35280	+	1.33842i	−0.892771	+	0.450511i	$0.851242\pi$
$762$	−958.568	−	424.329i	−1.25796	−	0.556863i
$763$	−614.410	−	137.693i	−0.805255	−	0.180463i
$764$	77.8830	+	20.4233i	0.101941	+	0.0267321i
$765$	−0.131665	−	1.75695i	−0.000172111	−	0.00229667i
$766$	−140.750	+	456.301i	−0.183747	+	0.595694i
$767$	302.241	+	32.4200i	0.394056	+	0.0422686i
$768$	−625.209	+	87.4133i	−0.814074	+	0.113819i
$769$	−1501.51	+	144.849i	−1.95255	+	0.188360i	−0.994997	−	0.0999093i	$-0.968145\pi$
$769$	−1501.51	+	144.849i	−1.95255	+	0.188360i	−0.957549	+	0.288269i	$0.906920\pi$
$770$	−10.9144	+	22.2781i	−0.0141746	+	0.0289326i
$771$	−862.552	+	111.214i	−1.11874	+	0.144246i
$772$	−93.9928	+	128.790i	−0.121752	+	0.166827i
$773$	218.709	−	306.504i	0.282936	−	0.396512i	−0.648032	−	0.761613i	$-0.724408\pi$
$773$	218.709	−	306.504i	0.282936	−	0.396512i	0.930968	+	0.365101i	$0.118966\pi$
$774$	−61.1005	−	49.8034i	−0.0789412	−	0.0643454i
$775$	−94.1790	+	39.3053i	−0.121521	+	0.0507165i
$776$	385.670	−	684.795i	0.496997	−	0.882468i
$777$	236.314	−	609.156i	0.304136	−	0.783985i
$778$	−588.504	+	843.665i	−0.756432	+	1.08440i
$779$	14.2423	−	30.4013i	0.0182829	−	0.0390261i
$780$	5.81744	+	5.06066i	0.00745826	+	0.00648803i
$781$	−234.677	+	138.855i	−0.300482	+	0.177791i
$782$	−6.45197	+	301.852i	−0.00825060	+	0.386000i
$783$	393.575	+	313.866i	0.502650	+	0.400850i
$784$	−937.124	−	174.861i	−1.19531	−	0.223036i
$785$	40.6919	+	51.0260i	0.0518368	+	0.0650013i
$786$	511.262	+	669.988i	0.650461	+	0.852402i
$787$	905.642	+	603.383i	1.15075	+	0.766687i	0.975967	−	0.217919i	$-0.0699270\pi$
$787$	905.642	+	603.383i	1.15075	+	0.766687i	0.174786	+	0.984606i	$0.444077\pi$
$788$	53.5075	−	23.0056i	0.0679029	−	0.0291949i
$789$	113.381	−	56.1019i	0.143703	−	0.0711051i
$790$	37.6818	−	93.0748i	0.0476985	−	0.117816i
$791$	−592.169	+	519.243i	−0.748633	+	0.656439i
$792$	16.3910	−	18.0484i	0.0206958	−	0.0227883i
$793$	−38.2527	+	69.6520i	−0.0482380	+	0.0878335i
$794$	148.567	−	620.286i	0.187112	−	0.781217i
$795$	−40.4111	−	73.5819i	−0.0508315	−	0.0925559i
$796$	−124.053	+	33.9514i	−0.155846	+	0.0426525i
$797$	1157.81	−	426.084i	1.45271	−	0.534610i	0.507664	−	0.861555i	$-0.330509\pi$
$797$	1157.81	−	426.084i	1.45271	−	0.534610i	0.945043	+	0.326945i	$0.106019\pi$
$798$	−15.1859	−	169.372i	−0.0190300	−	0.212246i
$799$	−68.8703	−	8.87984i	−0.0861956	−	0.0111137i
$800$	−334.014	+	352.354i	−0.417518	+	0.440443i
$801$	32.3520	+	90.8961i	0.0403896	+	0.113478i
$802$	−526.398	−	488.426i	−0.656356	−	0.609009i
$803$	23.2619	−	34.1189i	0.0289687	−	0.0424893i
$804$	−232.673	−	7.46137i	−0.289394	−	0.00928031i
$805$	−42.0322	−	16.8247i	−0.0522140	−	0.0209003i
$806$	−49.4724	−	36.9222i	−0.0613801	−	0.0458092i
$807$	22.6384	−	191.710i	0.0280526	−	0.237559i
$808$	−170.695	+	374.733i	−0.211256	+	0.463779i
$809$	−246.673	+	1198.23i	−0.304911	+	1.48113i	0.488566	+	0.872527i	$0.337520\pi$
$809$	−246.673	+	1198.23i	−0.304911	+	1.48113i	−0.793477	+	0.608600i	$0.791732\pi$
$810$	−45.9673	−	29.2269i	−0.0567497	−	0.0360825i
$811$	−1479.78	+	47.4537i	−1.82464	+	0.0585126i	−0.925410	−	0.378968i	$-0.876279\pi$
$811$	−1479.78	+	47.4537i	−1.82464	+	0.0585126i	−0.899228	+	0.437481i	$0.855871\pi$
$812$	157.535	−	15.8232i	0.194009	−	0.0194867i
$813$	−927.476	−	789.572i	−1.14081	−	0.971183i
$814$	351.405	+	52.9657i	0.431701	+	0.0650684i
$815$	−4.00724	−	5.87754i	−0.00491686	−	0.00721171i
$816$	−197.740	−	311.000i	−0.242328	−	0.381127i
$817$	55.3022	+	145.459i	0.0676893	+	0.178041i
$818$	−219.945	+	133.332i	−0.268881	+	0.162997i
$819$	−9.28416	−	36.4043i	−0.0113360	−	0.0444497i
$820$	−3.53367	−	1.17326i	−0.00430936	−	0.00143081i
$821$	544.432	+	625.848i	0.663133	+	0.762299i	0.982688	−	0.185269i	$-0.0593156\pi$
$821$	544.432	+	625.848i	0.663133	+	0.762299i	−0.319555	+	0.947568i	$0.603533\pi$
$822$	−70.9952	−	248.928i	−0.0863688	−	0.302832i
$823$	16.8001	−	1572.15i	0.0204133	−	1.91027i	−0.285776	−	0.958296i	$-0.592251\pi$
$823$	16.8001	−	1572.15i	0.0204133	−	1.91027i	0.306190	−	0.951971i	$-0.400946\pi$
$824$	61.6374	+	86.3799i	0.0748026	+	0.104830i
$825$	−21.6611	+	337.389i	−0.0262559	+	0.408957i
$826$	−509.384	+	541.607i	−0.616688	+	0.655699i
$827$	502.598	−	283.058i	0.607736	−	0.342271i	−0.156041	−	0.987751i	$-0.549873\pi$
$827$	502.598	−	283.058i	0.607736	−	0.342271i	0.763777	+	0.645480i	$0.223343\pi$
$828$	−16.1660	−	12.6117i	−0.0195241	−	0.0152315i
$829$	1126.05	−	206.835i	1.35833	−	0.249500i	0.548491	−	0.836156i	$-0.315202\pi$
$829$	1126.05	−	206.835i	1.35833	−	0.249500i	0.809836	+	0.586657i	$0.199556\pi$
$830$	−49.2327	−	18.7178i	−0.0593165	−	0.0225515i
$831$	988.974	−	203.595i	1.19010	−	0.245000i
$832$	211.735	+	48.3272i	0.254489	+	0.0580856i
$833$	−78.0646	−	314.964i	−0.0937150	−	0.378108i
$834$	−20.0606	−	87.8912i	−0.0240535	−	0.105385i
$835$	−79.5105	+	36.2179i	−0.0952221	+	0.0433747i
$836$	21.1230	−	6.76361i	0.0252668	−	0.00809045i
$837$	101.495	+	54.3373i	0.121260	+	0.0649192i
$838$	−289.083	−	354.657i	−0.344967	−	0.423218i
$839$	16.7545	+	260.965i	0.0199696	+	0.311042i	0.995737	+	0.0922338i	$0.0294007\pi$
$839$	16.7545	+	260.965i	0.0199696	+	0.311042i	−0.975768	+	0.218809i	$0.929783\pi$
$840$	40.0539	−	8.41012i	0.0476832	−	0.0100120i
$841$	−481.699	+	195.018i	−0.572770	+	0.231889i
$842$	71.7565	+	63.7816i	0.0852215	+	0.0757501i
$843$	−836.880	−	1072.73i	−0.992741	−	1.27252i
$844$	−41.1905	+	98.6961i	−0.0488039	+	0.116938i
$845$	19.3380	+	36.1209i	0.0228853	+	0.0427466i
$846$	13.6805	−	14.1263i	0.0161708	−	0.0166977i
$847$	459.904	+	513.325i	0.542980	+	0.606051i
$848$	1470.46	+	957.163i	1.73403	+	1.12873i
$849$	195.142	+	292.896i	0.229849	+	0.344990i
$850$	−357.600	−	122.989i	−0.420706	−	0.144693i
$851$	−48.4665	+	646.741i	−0.0569524	+	0.759977i
$852$	−192.969	−	75.7347i	−0.226489	−	0.0888905i
$853$	990.313	−	438.382i	1.16098	−	0.513930i	0.267729	−	0.963494i	$-0.413727\pi$
$853$	990.313	−	438.382i	1.16098	−	0.513930i	0.893248	+	0.449565i	$0.148421\pi$
$854$	−79.3760	−	177.422i	−0.0929462	−	0.207754i
$855$	−0.455604	−	0.873307i	−0.000532870	−	0.00102141i
$856$	−73.1889	−	26.0496i	−0.0855010	−	0.0304318i
$857$	497.420	+	978.825i	0.580420	+	1.14215i	0.974774	+	0.223195i	$0.0716486\pi$
$857$	497.420	+	978.825i	0.580420	+	1.14215i	−0.394354	+	0.918959i	$0.629032\pi$
$858$	−182.317	+	92.6497i	−0.212490	+	0.107983i
$859$	−497.782	+	1398.56i	−0.579490	+	1.62813i	0.184448	+	0.982842i	$0.440950\pi$
$859$	−497.782	+	1398.56i	−0.579490	+	1.62813i	−0.763938	+	0.645289i	$0.776737\pi$
$860$	15.3017	−	7.98291i	0.0177927	−	0.00928245i
$861$	−109.170	−	145.084i	−0.126795	−	0.168506i
$862$	−152.354	−	344.170i	−0.176745	−	0.399269i
$863$	−20.9643	+	53.4161i	−0.0242923	+	0.0618959i	−0.942505	−	0.334191i	$-0.891537\pi$
$863$	−20.9643	+	53.4161i	−0.0242923	+	0.0618959i	0.918213	+	0.396087i	$0.129632\pi$
$864$	546.173	+	40.9300i	0.632144	+	0.0473727i
$865$	−18.2648	+	53.1063i	−0.0211154	+	0.0613946i
$866$	−1171.44	+	780.470i	−1.35270	+	0.901235i
$867$	−382.548	+	587.697i	−0.441232	+	0.677851i
$868$	34.7808	−	10.0678i	0.0400701	−	0.0115989i
$869$	458.781	+	444.305i	0.527942	+	0.511283i
$870$	−33.7438	+	18.0654i	−0.0387859	+	0.0207648i
$871$	390.738	+	163.073i	0.448608	+	0.187225i
$872$	−445.459	+	347.520i	−0.510847	+	0.398532i
$873$	−67.9631	+	76.4609i	−0.0778501	+	0.0875840i
$874$	63.3428	+	156.458i	0.0724746	+	0.179014i
$875$	72.4012	−	87.6100i	0.0827442	−	0.100126i
$876$	31.3286	−	2.01136i	0.0357632	−	0.00229607i
$877$	893.758	−	728.507i	1.01911	−	0.830681i	0.0334509	−	0.999440i	$-0.489350\pi$
$877$	893.758	−	728.507i	1.01911	−	0.830681i	0.985657	+	0.168759i	$0.0539761\pi$
$878$	227.765	−	425.435i	0.259413	−	0.484550i
$879$	−344.536	−	1076.00i	−0.391964	−	1.22412i
$880$	12.4600	+	27.3539i	0.0141591	+	0.0310839i
$881$	1050.70	−	239.816i	1.19263	−	0.272209i	0.420270	−	0.907399i	$-0.361935\pi$
$881$	1050.70	−	239.816i	1.19263	−	0.272209i	0.772356	+	0.635190i	$0.219078\pi$
$882$	84.7047	+	35.6315i	0.0960371	+	0.0403985i
$883$	30.3072	−	132.785i	0.0343230	−	0.150379i	−0.954863	−	0.297048i	$-0.903998\pi$
$883$	30.3072	−	132.785i	0.0343230	−	0.150379i	0.989186	+	0.146669i	$0.0468551\pi$
$884$	−11.0607	−	53.7282i	−0.0125121	−	0.0607785i
$885$	15.3176	−	40.2892i	0.0173080	−	0.0455246i
$886$	−330.544	−	1799.55i	−0.373075	−	2.03110i
$887$	1001.95	−	1284.32i	1.12959	−	1.44794i	0.252509	−	0.967594i	$-0.418744\pi$
$887$	1001.95	−	1284.32i	1.12959	−	1.44794i	0.877082	−	0.480341i	$-0.159487\pi$
$888$	−287.698	−	510.837i	−0.323984	−	0.575267i
$889$	−1106.94	+	159.210i	−1.24515	+	0.179089i
$890$	−87.9098	−	5.64400i	−0.0987750	−	0.00634157i
$891$	282.022	−	201.240i	0.316523	−	0.225859i
$892$	167.982	+	1.79507i	0.188321	+	0.00201241i
$893$	−37.3332	+	10.6476i	−0.0418064	+	0.0119234i
$894$	39.0294	−	33.9522i	0.0436571	−	0.0379778i
$895$	−15.2314	+	45.8746i	−0.0170184	+	0.0512566i
$896$	−825.001	+	692.783i	−0.920760	+	0.773196i
$897$	−193.477	−	319.160i	−0.215693	−	0.355808i
$898$	−726.905	+	276.362i	−0.809471	+	0.307753i
$899$	62.0111	−	39.4278i	0.0689778	−	0.0438574i
$900$	21.2185	−	14.4666i	0.0235762	−	0.0160739i
$901$	−89.0125	+	590.560i	−0.0987930	+	0.655449i
$902$	64.0155	−	75.1963i	0.0709707	−	0.0833662i
$903$	835.138	+	104.340i	0.924849	+	0.115548i
$904$	22.6504	+	706.324i	0.0250558	+	0.781332i
$905$	−23.3552	+	36.7325i	−0.0258069	+	0.0405884i
$906$	−396.045	−	81.5317i	−0.437136	−	0.0899908i
$907$	243.689	+	111.003i	0.268676	+	0.122385i	0.544328	−	0.838873i	$-0.316785\pi$
$907$	243.689	+	111.003i	0.268676	+	0.122385i	−0.275652	+	0.961258i	$0.588894\pi$
$908$	8.52656	+	1.00688i	0.00939049	+	0.00110889i
$909$	32.0580	−	42.9548i	0.0352673	−	0.0472550i
$910$	33.8837	+	5.34130i	0.0372348	+	0.00586956i
$911$	−10.6084	+	330.809i	−0.0116448	+	0.363127i	0.977034	+	0.213082i	$0.0683501\pi$
$911$	−10.6084	+	330.809i	−0.0116448	+	0.363127i	−0.988679	+	0.150045i	$0.952058\pi$
$912$	−170.237	−	116.066i	−0.186663	−	0.127265i
$913$	227.860	−	245.574i	0.249572	−	0.268975i
$914$	361.342	−	128.610i	0.395342	−	0.140711i
$915$	8.17760	+	7.75195i	0.00893726	+	0.00847208i
$916$	−30.4028	+	235.798i	−0.0331908	+	0.257422i
$917$	841.651	+	316.202i	0.917831	+	0.344822i
$918$	147.334	+	400.353i	0.160494	+	0.436114i
$919$	−0.449606	−	1.64279i	−0.000489234	−	0.00178759i	0.964284	−	0.264870i	$-0.0853290\pi$
$919$	−0.449606	−	1.64279i	−0.000489234	−	0.00178759i	−0.964773	+	0.263082i	$0.915261\pi$
$920$	−35.6079	+	19.5558i	−0.0387043	+	0.0212563i
$921$	−667.691	−	159.921i	−0.724963	−	0.173639i
$922$	520.991	+	286.127i	0.565066	+	0.310333i
$923$	279.109	+	253.480i	0.302394	+	0.274626i
$924$	21.2064	−	118.065i	0.0229506	−	0.127776i
$925$	−752.955	−	304.838i	−0.814005	−	0.329554i
$926$	−187.284	−	378.499i	−0.202250	−	0.408746i
$927$	−5.45579	−	12.6894i	−0.00588543	−	0.0136886i
$928$	193.838	−	290.940i	0.208878	−	0.313513i
$929$	677.442	−	516.950i	0.729216	−	0.556459i	−0.174466	−	0.984663i	$-0.555820\pi$
$929$	677.442	−	516.950i	0.729216	−	0.556459i	0.903682	+	0.428205i	$0.140854\pi$
$930$	−6.84364	+	5.45762i	−0.00735875	+	0.00586841i
$931$	−109.647	−	144.529i	−0.117773	−	0.155241i
$932$	−195.579	+	245.248i	−0.209849	+	0.263142i
$933$	−774.455	−	16.5537i	−0.830070	−	0.0177424i
$934$	−952.565	−	1609.91i	−1.01988	−	1.72368i
$935$	−6.71521	+	7.71941i	−0.00718204	+	0.00825606i
$936$	−30.5270	−	14.3012i	−0.0326144	−	0.0152791i
$937$	1290.85	+	900.439i	1.37764	+	0.960981i	0.999377	+	0.0352823i	$0.0112330\pi$
$937$	1290.85	+	900.439i	1.37764	+	0.960981i	0.378261	+	0.925699i	$0.376522\pi$
$938$	−894.834	+	521.339i	−0.953981	+	0.555799i
$939$	389.918	+	219.598i	0.415248	+	0.233863i
$940$	1.65830	+	3.97343i	0.00176415	+	0.00422705i
$941$	848.420	−	1040.87i	0.901615	−	1.10613i	−0.0922724	−	0.995734i	$-0.529413\pi$
$941$	848.420	−	1040.87i	0.901615	−	1.10613i	0.993887	−	0.110399i	$-0.0352128\pi$
$942$	−1071.21	−	764.378i	−1.13717	−	0.811442i
$943$	145.579	+	106.246i	0.154379	+	0.112668i
$944$	115.199	+	893.460i	0.122033	+	0.946462i
$945$	−63.9697	−	0.431815i	−0.0676928	−	0.000456947i
$946$	43.9553	+	455.643i	0.0464644	+	0.481652i
$947$	−93.8648	−	671.353i	−0.0991181	−	0.708926i	−0.974320	−	0.225168i	$-0.927707\pi$
$947$	−93.8648	−	671.353i	−0.0991181	−	0.708926i	0.875202	−	0.483758i	$-0.160728\pi$
$948$	−51.7833	+	482.759i	−0.0546238	+	0.509239i
$949$	−54.5608	−	16.8298i	−0.0574930	−	0.0177342i
$950$	−210.825	+	15.7992i	−0.221921	+	0.0166307i
$951$	27.9598	−	106.623i	0.0294004	−	0.112117i
$952$	−262.827	−	125.299i	−0.276079	−	0.131617i
$953$	495.314	−	1118.92i	0.519742	−	1.17411i	−0.441213	−	0.897402i	$-0.645452\pi$
$953$	495.314	−	1118.92i	0.519742	−	1.17411i	0.960955	−	0.276704i	$-0.0892421\pi$
$954$	−118.952	−	120.230i	−0.124688	−	0.126028i
$955$	−15.9545	+	13.2908i	−0.0167063	+	0.0139171i
$956$	88.7725	+	353.898i	0.0928582	+	0.370186i
$957$	−25.9641	−	242.054i	−0.0271307	−	0.252930i
$958$	301.701	−	1549.17i	0.314928	−	1.61709i
$959$	−205.156	−	184.850i	−0.213927	−	0.192752i
$960$	14.2441	−	27.3034i	0.0148377	−	0.0284410i
$961$	−692.144	+	642.215i	−0.720233	+	0.668278i
$962$	−73.2356	−	485.887i	−0.0761285	−	0.505080i
$963$	8.59069	+	5.33408i	0.00892075	+	0.00553902i
$964$	−302.089	+	510.555i	−0.313370	+	0.529621i
$965$	−12.9572	−	39.0251i	−0.0134272	−	0.0404405i
$966$	908.064	+	93.7907i	0.940025	+	0.0970918i
$967$	25.3462	−	262.740i	0.0262112	−	0.271706i	−0.972959	−	0.230978i	$-0.925808\pi$
$967$	25.3462	−	262.740i	0.0262112	−	0.271706i	0.999170	−	0.0407286i	$-0.0129679\pi$
$968$	617.861	−	26.4252i	0.638287	−	0.0272988i
$969$	11.9325	−	69.1112i	0.0123143	−	0.0713222i
$970$	−39.6244	−	84.5812i	−0.0408499	−	0.0871971i
$971$	−323.905	+	1135.70i	−0.333579	+	1.16961i	0.596609	+	0.802532i	$0.296514\pi$
$971$	−323.905	+	1135.70i	−0.333579	+	1.16961i	−0.930188	+	0.367083i	$0.880356\pi$
$972$	−53.2337	−	15.7995i	−0.0547671	−	0.0162546i
$973$	−67.9103	−	68.1017i	−0.0697947	−	0.0699915i
$974$	640.943	+	705.750i	0.658053	+	0.724589i
$975$	454.610	−	108.885i	0.466267	−	0.111677i
$976$	−227.148	−	62.1667i	−0.232734	−	0.0636954i
$977$	−96.6676	+	8.28387i	−0.0989433	+	0.00847888i	−0.134748	−	0.990880i	$-0.543022\pi$
$977$	−96.6676	+	8.28387i	−0.0989433	+	0.00847888i	0.0358045	+	0.999359i	$0.488601\pi$
$978$	110.206	+	91.8067i	0.112685	+	0.0938719i
$979$	243.098	−	504.799i	0.248313	−	0.515627i
$980$	−14.4925	+	13.9564i	−0.0147883	+	0.0142412i
$981$	66.2574	−	31.9079i	0.0675407	−	0.0325259i
$982$	503.518	−	2007.31i	0.512747	−	2.04411i
$983$	1449.64	+	202.681i	1.47471	+	0.206186i	0.829796	−	0.558066i	$-0.188456\pi$
$983$	1449.64	+	202.681i	1.47471	+	0.206186i	0.644917	+	0.764252i	$0.276892\pi$
$984$	−162.772	−	6.96158i	−0.165419	−	0.00707477i
$985$	−3.18582	+	14.6793i	−0.00323433	+	0.0149028i
$986$	268.810	+	43.4590i	0.272626	+	0.0440761i
$987$	−43.7231	+	205.359i	−0.0442990	+	0.208064i
$988$	−17.5454	−	25.1527i	−0.0177585	−	0.0254582i
$989$	−823.225	+	142.135i	−0.832381	+	0.143716i
$990$	−0.614526	−	2.83155i	−0.000620733	−	0.00286015i
$991$	−25.8312	−	483.013i	−0.0260658	−	0.487399i	−0.981412	−	0.191911i	$-0.938531\pi$
$991$	−25.8312	−	483.013i	−0.0260658	−	0.487399i	0.955346	−	0.295488i	$-0.0954822\pi$
$992$	31.5799	−	73.4501i	0.0318346	−	0.0740425i
$993$	501.835	+	770.954i	0.505373	+	0.776388i
$994$	−906.374	+	170.174i	−0.911845	+	0.171202i
$995$	11.4557	−	31.1289i	0.0115133	−	0.0312853i
$996$	253.749	+	21.7448i	0.254768	+	0.0218322i
$997$	771.634	+	763.433i	0.773956	+	0.765730i	0.976954	−	0.213449i	$-0.0684698\pi$
$997$	771.634	+	763.433i	0.773956	+	0.765730i	−0.202998	+	0.979179i	$0.565068\pi$
$998$	340.668	+	868.007i	0.341350	+	0.869746i
$999$	270.108	+	875.670i	0.270379	+	0.876547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	343.3.l.a.10.51	✓	5376
343.103	odd	294	inner	343.3.l.a.103.51	yes	5376

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
343.3.l.a.10.51	✓	5376	1.1	even	1	trivial
343.3.l.a.103.51	yes	5376	343.103	odd	294	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:	\( N \)	\(=\)	\( 343 = 7^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	343.l (of order \(294\), degree \(84\), minimal)

\(f(q)\)	\(=\)	\(q+(2.04496 + 1.03921i) q^{2} +(2.07598 - 1.96793i) q^{3} +(0.743846 + 1.01923i) q^{4} +(-0.325399 + 0.00347725i) q^{5} +(6.29037 - 1.86695i) q^{6} +(4.62984 - 5.25020i) q^{7} +(-1.00246 - 6.20054i) q^{8} +(-0.0436606 + 0.816401i) q^{9} +(-0.669041 - 0.331046i) q^{10} +(3.54855 - 3.15417i) q^{11} +(3.54998 + 0.652066i) q^{12} +(-5.61375 - 3.40309i) q^{13} +(14.9239 - 5.92507i) q^{14} +(-0.668680 + 0.647580i) q^{15} +(5.93280 - 18.5284i) q^{16} +(6.57664 - 0.776615i) q^{17} +(-0.937693 + 1.62413i) q^{18} +(3.20631 - 1.85116i) q^{19} +(-0.245591 - 0.329070i) q^{20} +(-0.720540 - 20.0105i) q^{21} +(10.5345 - 2.76246i) q^{22} +(6.46408 + 18.7948i) q^{23} +(-14.2833 - 10.8995i) q^{24} +(-24.8884 + 0.531981i) q^{25} +(-7.94336 - 12.7930i) q^{26} +(18.2043 + 21.3838i) q^{27} +(8.79504 + 0.813525i) q^{28} +(17.5949 - 3.42660i) q^{29} +(-2.04039 + 0.629377i) q^{30} +(3.81606 - 1.49769i) q^{31} +(13.7168 - 13.8642i) q^{32} +(1.15955 - 13.5313i) q^{33} +(14.2560 + 5.24634i) q^{34} +(-1.48829 + 1.72451i) q^{35} +(-0.864576 + 0.562776i) q^{36} +(29.9777 + 12.8889i) q^{37} +(8.48051 - 0.453532i) q^{38} +(-18.3511 + 3.98269i) q^{39} +(0.347759 + 2.01417i) q^{40} +(7.43719 - 5.18786i) q^{41} +(19.3216 - 41.6694i) q^{42} +(-6.70834 + 41.4935i) q^{43} +(5.85440 + 1.27057i) q^{44} +(0.0113683 - 0.265808i) q^{45} +(-6.31291 + 45.1521i) q^{46} +(-10.1707 - 2.55124i) q^{47} +(-24.1461 - 50.1399i) q^{48} +(-6.12917 - 48.6152i) q^{49} +(-51.4486 - 24.7763i) q^{50} +(12.1247 - 14.5546i) q^{51} +(-0.707241 - 8.25307i) q^{52} +(-23.8065 + 86.9853i) q^{53} +(15.0048 + 62.6469i) q^{54} +(-1.14373 + 1.03870i) q^{55} +(-37.1953 - 23.4444i) q^{56} +(3.01329 - 10.1528i) q^{57} +(39.5417 + 11.2774i) q^{58} +(-41.9312 + 19.6438i) q^{59} +(-1.15743 - 0.199837i) q^{60} +(-0.517239 - 12.0938i) q^{61} +(9.36009 + 0.902957i) q^{62} +(4.08412 + 4.00903i) q^{63} +(-31.3977 + 10.4248i) q^{64} +(1.83854 + 1.08784i) q^{65} +(16.4330 - 26.4659i) q^{66} +(-63.7764 + 9.61275i) q^{67} +(5.68356 + 6.12542i) q^{68} +(50.4061 + 26.2968i) q^{69} +(-4.83561 + 1.97991i) q^{70} +(-56.3744 - 10.9789i) q^{71} +(5.10590 - 0.547686i) q^{72} +(8.43630 - 2.11618i) q^{73} +(47.9089 + 57.5103i) q^{74} +(-50.6210 + 50.0829i) q^{75} +(4.27176 + 1.89098i) q^{76} +(-0.130792 - 33.2339i) q^{77} +(-41.6660 - 10.9261i) q^{78} +(10.0526 + 134.143i) q^{79} +(-1.86610 + 6.04975i) q^{80} +(72.5573 + 7.78289i) q^{81} +(20.6000 - 2.88018i) q^{82} +(70.2344 - 6.77543i) q^{83} +(19.8593 - 15.6191i) q^{84} +(-2.13733 + 0.275578i) q^{85} +(-56.8385 + 77.8810i) q^{86} +(29.7833 - 41.7390i) q^{87} +(-23.1148 - 18.8410i) q^{88} +(108.907 - 45.4519i) q^{89} +(0.299477 - 0.531752i) q^{90} +(-43.8576 + 13.7175i) q^{91} +(-14.3479 + 20.5688i) q^{92} +(4.97472 - 10.6189i) q^{93} +(-18.1474 - 15.7866i) q^{94} +(-1.03689 + 0.613516i) q^{95} +(1.19218 - 55.7754i) q^{96} +(97.8283 + 78.0154i) q^{97} +(37.9873 - 105.785i) q^{98} +(2.42013 + 3.03475i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5376 q - 84 q^{2} - 84 q^{3} - 84 q^{4} - 84 q^{5} - 112 q^{6} - 84 q^{7} - 84 q^{8} - 28 q^{9} - 84 q^{10} - 119 q^{11} - 119 q^{12} - 84 q^{13} + 21 q^{14} - 168 q^{15} - 84 q^{16} - 35 q^{17} - 42 q^{18}+ \cdots + 42 q^{99}+O(q^{100}) \) 5376 * q - 84 * q^2 - 84 * q^3 - 84 * q^4 - 84 * q^5 - 112 * q^6 - 84 * q^7 - 84 * q^8 - 28 * q^9 - 84 * q^10 - 119 * q^11 - 119 * q^12 - 84 * q^13 + 21 * q^14 - 168 * q^15 - 84 * q^16 - 35 * q^17 - 42 * q^18 - 126 * q^19 - 420 * q^20 - 84 * q^21 + 28 * q^22 - 147 * q^23 - 210 * q^24 - 84 * q^25 - 196 * q^26 + 21 * q^27 + 126 * q^28 - 336 * q^29 - 91 * q^30 - 77 * q^31 - 84 * q^33 - 616 * q^34 + 56 * q^35 + 420 * q^36 - 539 * q^37 - 532 * q^38 - 441 * q^39 - 364 * q^40 - 280 * q^41 - 700 * q^42 - 84 * q^43 - 112 * q^44 - 315 * q^45 - 252 * q^46 - 7 * q^47 - 98 * q^48 - 28 * q^49 + 56 * q^50 + 84 * q^51 + 84 * q^52 + 371 * q^53 + 798 * q^54 + 1267 * q^55 - 42 * q^56 - 735 * q^57 - 868 * q^58 + 1400 * q^59 + 406 * q^60 + 637 * q^61 + 336 * q^62 + 735 * q^63 - 420 * q^64 - 84 * q^65 + 1372 * q^66 - 91 * q^67 - 77 * q^68 + 84 * q^69 - 1078 * q^70 + 679 * q^71 + 273 * q^72 + 294 * q^73 - 1428 * q^74 - 1344 * q^75 - 231 * q^76 - 714 * q^77 + 5040 * q^78 - 91 * q^79 - 1148 * q^80 - 784 * q^81 - 224 * q^82 - 1414 * q^83 - 1246 * q^84 + 364 * q^85 - 1582 * q^86 - 952 * q^87 - 1974 * q^88 - 910 * q^89 - 287 * q^90 + 1456 * q^91 - 6384 * q^92 - 154 * q^93 - 770 * q^94 - 1358 * q^95 - 4284 * q^96 + 3430 * q^97 + 7 * q^98 + 42 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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