LMFDB - Embedded newform 48.3.i.b.5.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,3,Mod(5,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("48.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	48.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.30790526893$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + 24576 x^{4} - 131072 x^{2} + 1048576 $ x^20 - 2x^18 + 6x^16 - 24x^14 - 24x^12 + 1216x^10 - 384x^8 - 6144x^6 + 24576x^4 - 131072*x^2 + 1048576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{13} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.3
Root			$-1.28499 + 1.53258i$ of defining polynomial
Character	$\chi$	$=$	48.5
Dual form			48.3.i.b.29.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28499 - 1.53258i) q^{2} +(-2.06336 + 2.17774i) q^{3} +(-0.697601 + 3.93870i) q^{4} +(-3.17955 + 3.17955i) q^{5} +(5.98896 + 0.363879i) q^{6} +6.03979i q^{7} +(6.93278 - 3.99206i) q^{8} +(-0.485128 - 8.98692i) q^{9} +O(q^{10})$	\(q+(-1.28499 - 1.53258i) q^{2} +(-2.06336 + 2.17774i) q^{3} +(-0.697601 + 3.93870i) q^{4} +(-3.17955 + 3.17955i) q^{5} +(5.98896 + 0.363879i) q^{6} +6.03979i q^{7} +(6.93278 - 3.99206i) q^{8} +(-0.485128 - 8.98692i) q^{9} +(8.95859 + 0.787223i) q^{10} +(-13.0097 + 13.0097i) q^{11} +(-7.13808 - 9.64613i) q^{12} +(6.39520 - 6.39520i) q^{13} +(9.25646 - 7.76107i) q^{14} +(-0.363700 - 13.4848i) q^{15} +(-15.0267 - 5.49528i) q^{16} -4.39848i q^{17} +(-13.1498 + 12.2916i) q^{18} +(-3.21075 + 3.21075i) q^{19} +(-10.3052 - 14.7413i) q^{20} +(-13.1531 - 12.4622i) q^{21} +(36.6557 + 3.22107i) q^{22} +34.0396 q^{23} +(-5.61111 + 23.3349i) q^{24} +4.78097i q^{25} +(-18.0189 - 1.58339i) q^{26} +(20.5722 + 17.4867i) q^{27} +(-23.7889 - 4.21336i) q^{28} +(27.9597 + 27.9597i) q^{29} +(-20.1991 + 17.8852i) q^{30} -7.90993 q^{31} +(10.8872 + 30.0910i) q^{32} +(-1.48814 - 55.1754i) q^{33} +(-6.74102 + 5.65200i) q^{34} +(-19.2038 - 19.2038i) q^{35} +(35.7352 + 4.35851i) q^{36} +(20.0443 + 20.0443i) q^{37} +(9.04650 + 0.794947i) q^{38} +(0.731530 + 27.1227i) q^{39} +(-9.35016 + 34.7360i) q^{40} -45.1067 q^{41} +(-2.19775 + 36.1720i) q^{42} +(-36.0095 - 36.0095i) q^{43} +(-42.1657 - 60.3168i) q^{44} +(30.1168 + 27.0318i) q^{45} +(-43.7406 - 52.1684i) q^{46} +5.08935i q^{47} +(42.9727 - 21.3856i) q^{48} +12.5209 q^{49} +(7.32721 - 6.14349i) q^{50} +(9.57876 + 9.07563i) q^{51} +(20.7275 + 29.6501i) q^{52} +(20.7687 - 20.7687i) q^{53} +(0.364741 - 53.9988i) q^{54} -82.7299i q^{55} +(24.1112 + 41.8725i) q^{56} +(-0.367268 - 13.6171i) q^{57} +(6.92253 - 78.7784i) q^{58} +(-39.0656 + 39.0656i) q^{59} +(53.3662 + 7.97449i) q^{60} +(-49.8322 + 49.8322i) q^{61} +(10.1642 + 12.1226i) q^{62} +(54.2791 - 2.93007i) q^{63} +(32.1269 - 55.3522i) q^{64} +40.6677i q^{65} +(-82.6484 + 73.1805i) q^{66} +(44.9162 - 44.9162i) q^{67} +(17.3243 + 3.06838i) q^{68} +(-70.2358 + 74.1295i) q^{69} +(-4.75466 + 54.1080i) q^{70} +46.6947 q^{71} +(-39.2396 - 60.3677i) q^{72} +97.3523i q^{73} +(4.96275 - 56.4761i) q^{74} +(-10.4117 - 9.86483i) q^{75} +(-10.4063 - 14.8860i) q^{76} +(-78.5758 - 78.5758i) q^{77} +(40.6277 - 35.9735i) q^{78} -40.1637 q^{79} +(65.2506 - 30.3056i) q^{80} +(-80.5293 + 8.71960i) q^{81} +(57.9616 + 69.1296i) q^{82} +(-35.5451 - 35.5451i) q^{83} +(58.2606 - 43.1125i) q^{84} +(13.9852 + 13.9852i) q^{85} +(-8.91558 + 101.459i) q^{86} +(-118.580 + 3.19823i) q^{87} +(-38.2579 + 142.129i) q^{88} +69.6795 q^{89} +(2.72864 - 80.8920i) q^{90} +(38.6257 + 38.6257i) q^{91} +(-23.7461 + 134.072i) q^{92} +(16.3210 - 17.2258i) q^{93} +(7.79984 - 6.53977i) q^{94} -20.4174i q^{95} +(-87.9947 - 38.3789i) q^{96} +61.0939 q^{97} +(-16.0893 - 19.1893i) q^{98} +(123.228 + 110.606i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{3} + 4 q^{4} - 12 q^{6}+O(q^{10}) $ 20 * q - 6 * q^3 + 4 * q^4 - 12 * q^6	$ 20 q - 6 q^{3} + 4 q^{4} - 12 q^{6} + 32 q^{10} - 88 q^{12} + 92 q^{13} - 116 q^{15} - 16 q^{16} + 4 q^{18} - 52 q^{19} + 48 q^{21} + 24 q^{22} - 8 q^{24} + 18 q^{27} + 56 q^{28} + 28 q^{30} - 80 q^{31} + 60 q^{33} + 104 q^{34} + 92 q^{36} - 116 q^{37} + 88 q^{40} + 304 q^{42} + 172 q^{43} + 60 q^{45} - 424 q^{46} + 176 q^{48} - 364 q^{49} + 128 q^{51} - 208 q^{52} + 40 q^{54} - 512 q^{58} - 240 q^{60} - 244 q^{61} + 296 q^{63} + 88 q^{64} - 492 q^{66} + 356 q^{67} - 20 q^{69} + 200 q^{70} - 472 q^{72} - 146 q^{75} + 328 q^{76} + 84 q^{78} + 384 q^{79} - 188 q^{81} + 560 q^{82} + 816 q^{84} + 48 q^{85} + 416 q^{88} + 616 q^{90} + 136 q^{91} - 132 q^{93} + 32 q^{94} - 24 q^{96} + 472 q^{97} - 452 q^{99}+O(q^{100}) $ 20 * q - 6 * q^3 + 4 * q^4 - 12 * q^6 + 32 * q^10 - 88 * q^12 + 92 * q^13 - 116 * q^15 - 16 * q^16 + 4 * q^18 - 52 * q^19 + 48 * q^21 + 24 * q^22 - 8 * q^24 + 18 * q^27 + 56 * q^28 + 28 * q^30 - 80 * q^31 + 60 * q^33 + 104 * q^34 + 92 * q^36 - 116 * q^37 + 88 * q^40 + 304 * q^42 + 172 * q^43 + 60 * q^45 - 424 * q^46 + 176 * q^48 - 364 * q^49 + 128 * q^51 - 208 * q^52 + 40 * q^54 - 512 * q^58 - 240 * q^60 - 244 * q^61 + 296 * q^63 + 88 * q^64 - 492 * q^66 + 356 * q^67 - 20 * q^69 + 200 * q^70 - 472 * q^72 - 146 * q^75 + 328 * q^76 + 84 * q^78 + 384 * q^79 - 188 * q^81 + 560 * q^82 + 816 * q^84 + 48 * q^85 + 416 * q^88 + 616 * q^90 + 136 * q^91 - 132 * q^93 + 32 * q^94 - 24 * q^96 + 472 * q^97 - 452 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.28499	−	1.53258i	−0.642495	−	0.766290i
$2$	−1.28499	−	1.53258i	−0.642495	−	0.766290i
$3$	−2.06336	+	2.17774i	−0.687785	+	0.725914i
$3$	−2.06336	+	2.17774i	−0.687785	+	0.725914i
$4$	−0.697601	+	3.93870i	−0.174400	+	0.984675i
$5$	−3.17955	+	3.17955i	−0.635909	+	0.635909i	−0.949544	−	0.313634i	$-0.898453\pi$
$5$	−3.17955	+	3.17955i	−0.635909	+	0.635909i	0.313634	+	0.949544i	$0.398453\pi$
$6$	5.98896	+	0.363879i	0.998159	+	0.0606465i
$7$			6.03979i			0.862827i	0.902154	+	0.431414i	$0.141985\pi$
$7$			6.03979i			0.862827i	−0.902154	+	0.431414i	$0.858015\pi$
$8$	6.93278	−	3.99206i	0.866598	−	0.499008i
$9$	−0.485128	−	8.98692i	−0.0539031	−	0.998546i
$10$	8.95859	+	0.787223i	0.895859	+	0.0787223i
$11$	−13.0097	+	13.0097i	−1.18270	+	1.18270i	−0.203657	+	0.979042i	$0.565283\pi$
$11$	−13.0097	+	13.0097i	−1.18270	+	1.18270i	−0.979042	+	0.203657i	$0.934717\pi$
$12$	−7.13808	−	9.64613i	−0.594840	−	0.803844i
$13$	6.39520	−	6.39520i	0.491939	−	0.491939i	−0.416978	−	0.908917i	$-0.636911\pi$
$13$	6.39520	−	6.39520i	0.491939	−	0.491939i	0.908917	+	0.416978i	$0.136911\pi$
$14$	9.25646	−	7.76107i	0.661176	−	0.554362i
$15$	−0.363700	−	13.4848i	−0.0242466	−	0.898985i
$16$	−15.0267	−	5.49528i	−0.939169	−	0.343455i
$17$		−	4.39848i		−	0.258734i	−0.991597	−	0.129367i	$-0.958705\pi$
$17$		−	4.39848i		−	0.258734i	0.991597	−	0.129367i	$-0.0412945\pi$
$18$	−13.1498	+	12.2916i	−0.730543	+	0.682866i
$19$	−3.21075	+	3.21075i	−0.168987	+	0.168987i	−0.786534	−	0.617547i	$-0.788126\pi$
$19$	−3.21075	+	3.21075i	−0.168987	+	0.168987i	0.617547	+	0.786534i	$0.288126\pi$
$20$	−10.3052	−	14.7413i	−0.515261	−	0.737067i
$21$	−13.1531	−	12.4622i	−0.626339	−	0.593440i
$22$	36.6557	+	3.22107i	1.66617	+	0.146412i
$23$	34.0396			1.47998			0.739992	−	0.672616i	$-0.234829\pi$
$23$	34.0396			1.47998			0.739992	+	0.672616i	$0.234829\pi$
$24$	−5.61111	+	23.3349i	−0.233796	+	0.972286i
$25$			4.78097i			0.191239i
$26$	−18.0189	−	1.58339i	−0.693036	−	0.0608994i
$27$	20.5722	+	17.4867i	0.761933	+	0.647656i
$28$	−23.7889	−	4.21336i	−0.849604	−	0.150477i
$29$	27.9597	+	27.9597i	0.964128	+	0.964128i	0.999378	−	0.0352510i	$-0.0112231\pi$
$29$	27.9597	+	27.9597i	0.964128	+	0.964128i	−0.0352510	+	0.999378i	$0.511223\pi$
$30$	−20.1991	+	17.8852i	−0.673304	+	0.596173i
$31$	−7.90993			−0.255159			−0.127580	−	0.991828i	$-0.540721\pi$
$31$	−7.90993			−0.255159			−0.127580	+	0.991828i	$0.540721\pi$
$32$	10.8872	+	30.0910i	0.340225	+	0.940344i
$33$	−1.48814	−	55.1754i	−0.0450952	−	1.67198i
$34$	−6.74102	+	5.65200i	−0.198265	+	0.166235i
$35$	−19.2038	−	19.2038i	−0.548680	−	0.548680i
$36$	35.7352	+	4.35851i	0.992644	+	0.121070i
$37$	20.0443	+	20.0443i	0.541736	+	0.541736i	0.924038	−	0.382301i	$-0.124868\pi$
$37$	20.0443	+	20.0443i	0.541736	+	0.541736i	−0.382301	+	0.924038i	$0.624868\pi$
$38$	9.04650	+	0.794947i	0.238066	+	0.0209197i
$39$	0.731530	+	27.1227i	0.0187572	+	0.695453i
$40$	−9.35016	+	34.7360i	−0.233754	+	0.868401i
$41$	−45.1067			−1.10016			−0.550081	−	0.835111i	$-0.685403\pi$
$41$	−45.1067			−1.10016			−0.550081	+	0.835111i	$0.685403\pi$
$42$	−2.19775	+	36.1720i	−0.0523274	+	0.861239i
$43$	−36.0095	−	36.0095i	−0.837431	−	0.837431i	0.151089	−	0.988520i	$-0.451722\pi$
$43$	−36.0095	−	36.0095i	−0.837431	−	0.837431i	−0.988520	+	0.151089i	$0.951722\pi$
$44$	−42.1657	−	60.3168i	−0.958311	−	1.37084i
$45$	30.1168	+	27.0318i	0.669262	+	0.600707i
$46$	−43.7406	−	52.1684i	−0.950882	−	1.13410i
$47$			5.08935i			0.108284i	0.998533	+	0.0541421i	$0.0172424\pi$
$47$			5.08935i			0.108284i	−0.998533	+	0.0541421i	$0.982758\pi$
$48$	42.9727	−	21.3856i	0.895266	−	0.445533i
$49$	12.5209			0.255529
$50$	7.32721	−	6.14349i	0.146544	−	0.122870i
$51$	9.57876	+	9.07563i	0.187819	+	0.177953i
$52$	20.7275	+	29.6501i	0.398605	+	0.570194i
$53$	20.7687	−	20.7687i	0.391863	−	0.391863i	−0.483488	−	0.875351i	$-0.660630\pi$
$53$	20.7687	−	20.7687i	0.391863	−	0.391863i	0.875351	+	0.483488i	$0.160630\pi$
$54$	0.364741	−	53.9988i	0.00675447	−	0.999977i
$55$		−	82.7299i		−	1.50418i
$56$	24.1112	+	41.8725i	0.430557	+	0.747724i
$57$	−0.367268	−	13.6171i	−0.00644331	−	0.238896i
$58$	6.92253	−	78.7784i	0.119354	−	1.35825i
$59$	−39.0656	+	39.0656i	−0.662129	+	0.662129i	−0.955881	−	0.293753i	$-0.905096\pi$
$59$	−39.0656	+	39.0656i	−0.662129	+	0.662129i	0.293753	+	0.955881i	$0.405096\pi$
$60$	53.3662	+	7.97449i	0.889436	+	0.132908i
$61$	−49.8322	+	49.8322i	−0.816921	+	0.816921i	−0.985661	−	0.168739i	$-0.946030\pi$
$61$	−49.8322	+	49.8322i	−0.816921	+	0.816921i	0.168739	+	0.985661i	$0.446030\pi$
$62$	10.1642	+	12.1226i	0.163938	+	0.195526i
$63$	54.2791	−	2.93007i	0.861573	−	0.0465090i
$64$	32.1269	−	55.3522i	0.501983	−	0.864878i
$65$			40.6677i			0.625657i
$66$	−82.6484	+	73.1805i	−1.25225	+	1.10880i
$67$	44.9162	−	44.9162i	0.670390	−	0.670390i	−0.287416	−	0.957806i	$-0.592796\pi$
$67$	44.9162	−	44.9162i	0.670390	−	0.670390i	0.957806	+	0.287416i	$0.0927961\pi$
$68$	17.3243	+	3.06838i	0.254769	+	0.0451233i
$69$	−70.2358	+	74.1295i	−1.01791	+	1.07434i
$70$	−4.75466	+	54.1080i	−0.0679237	+	0.772972i
$71$	46.6947			0.657672			0.328836	−	0.944387i	$-0.393344\pi$
$71$	46.6947			0.657672			0.328836	+	0.944387i	$0.393344\pi$
$72$	−39.2396	−	60.3677i	−0.544994	−	0.838440i
$73$			97.3523i			1.33359i	0.745240	+	0.666797i	$0.232335\pi$
$73$			97.3523i			1.33359i	−0.745240	+	0.666797i	$0.767665\pi$
$74$	4.96275	−	56.4761i	0.0670642	−	0.763190i
$75$	−10.4117	−	9.86483i	−0.138823	−	0.131531i
$76$	−10.4063	−	14.8860i	−0.136926	−	0.195868i
$77$	−78.5758	−	78.5758i	−1.02047	−	1.02047i
$78$	40.6277	−	35.9735i	0.520867	−	0.461199i
$79$	−40.1637			−0.508402			−0.254201	−	0.967151i	$-0.581812\pi$
$79$	−40.1637			−0.508402			−0.254201	+	0.967151i	$0.581812\pi$
$80$	65.2506	−	30.3056i	0.815633	−	0.378820i
$81$	−80.5293	+	8.71960i	−0.994189	+	0.107649i
$82$	57.9616	+	69.1296i	0.706849	+	0.843043i
$83$	−35.5451	−	35.5451i	−0.428254	−	0.428254i	0.459779	−	0.888033i	$-0.347929\pi$
$83$	−35.5451	−	35.5451i	−0.428254	−	0.428254i	−0.888033	+	0.459779i	$0.847929\pi$
$84$	58.2606	−	43.1125i	0.693579	−	0.513244i
$85$	13.9852	+	13.9852i	0.164531	+	0.164531i
$86$	−8.91558	+	101.459i	−0.103670	+	1.17976i
$87$	−118.580	+	3.19823i	−1.36299	+	0.0367613i
$88$	−38.2579	+	142.129i	−0.434749	+	1.61510i
$89$	69.6795			0.782916			0.391458	−	0.920196i	$-0.371971\pi$
$89$	69.6795			0.782916			0.391458	+	0.920196i	$0.371971\pi$
$90$	2.72864	−	80.8920i	0.0303182	−	0.898800i
$91$	38.6257	+	38.6257i	0.424458	+	0.424458i
$92$	−23.7461	+	134.072i	−0.258109	+	1.45730i
$93$	16.3210	−	17.2258i	0.175495	−	0.185224i
$94$	7.79984	−	6.53977i	0.0829770	−	0.0695720i
$95$		−	20.4174i		−	0.214920i
$96$	−87.9947	−	38.3789i	−0.916611	−	0.399780i
$97$	61.0939			0.629834			0.314917	−	0.949119i	$-0.398023\pi$
$97$	61.0939			0.629834			0.314917	+	0.949119i	$0.398023\pi$
$98$	−16.0893	−	19.1893i	−0.164176	−	0.195809i
$99$	123.228	+	110.606i	1.24473	+	1.11723i
$100$	−18.8308	−	3.33521i	−0.188308	−	0.0333521i
$101$	104.036	−	104.036i	1.03006	−	1.03006i	0.0305280	−	0.999534i	$-0.490281\pi$
$101$	104.036	−	104.036i	1.03006	−	1.03006i	0.999534	−	0.0305280i	$-0.00971886\pi$
$102$	1.60051	−	26.3423i	0.0156913	−	0.258258i
$103$			57.2961i			0.556272i	0.960542	+	0.278136i	$0.0897167\pi$
$103$			57.2961i			0.556272i	−0.960542	+	0.278136i	$0.910283\pi$
$104$	18.8065	−	69.8666i	0.180832	−	0.671794i
$105$	81.4452	−	2.19667i	0.775668	−	0.0209207i
$106$	−58.5173	−	5.14212i	−0.552050	−	0.0485105i
$107$	92.4468	−	92.4468i	0.863989	−	0.863989i	−0.127810	−	0.991799i	$-0.540795\pi$
$107$	92.4468	−	92.4468i	0.863989	−	0.863989i	0.991799	+	0.127810i	$0.0407947\pi$
$108$	−83.2261	+	68.8289i	−0.770612	+	0.637305i
$109$	75.3749	−	75.3749i	0.691513	−	0.691513i	−0.271052	−	0.962565i	$-0.587371\pi$
$109$	75.3749	−	75.3749i	0.691513	−	0.691513i	0.962565	+	0.271052i	$0.0873714\pi$
$110$	−126.790	+	106.307i	−1.15264	+	0.966428i
$111$	−85.0096	+	2.29281i	−0.765853	+	0.0206559i
$112$	33.1903	−	90.7581i	0.296342	−	0.810341i
$113$			112.254i			0.993401i	0.867922	+	0.496701i	$0.165455\pi$
$113$			112.254i			0.993401i	−0.867922	+	0.496701i	$0.834545\pi$
$114$	−20.3973	+	18.0607i	−0.178924	+	0.158427i
$115$	−108.231	+	108.231i	−0.941135	+	0.941135i
$116$	−129.630	+	90.6201i	−1.11750	+	0.781208i
$117$	−60.5756	−	54.3707i	−0.517740	−	0.464706i
$118$	110.070	+	9.67223i	0.932797	+	0.0819681i
$119$	26.5659			0.223243
$120$	−56.3535	−	92.0350i	−0.469612	−	0.766959i
$121$		−	217.504i		−	1.79756i
$122$	140.406	+	12.3379i	1.15087	+	0.101131i
$123$	93.0711	−	98.2307i	0.756676	−	0.798624i
$124$	5.51798	−	31.1548i	0.0444998	−	0.251249i
$125$	−94.6900	−	94.6900i	−0.757520	−	0.757520i
$126$	−74.2386	−	79.4219i	−0.589196	−	0.630333i
$127$	93.6335			0.737272			0.368636	−	0.929574i	$-0.379825\pi$
$127$	93.6335			0.737272			0.368636	+	0.929574i	$0.379825\pi$
$128$	−126.114	+	21.8899i	−0.985268	+	0.171015i
$129$	152.720	−	4.11903i	1.18388	−	0.0319305i
$130$	62.3265	−	52.2576i	0.479434	−	0.401981i
$131$	−81.5208	−	81.5208i	−0.622296	−	0.622296i	0.323822	−	0.946118i	$-0.395032\pi$
$131$	−81.5208	−	81.5208i	−0.622296	−	0.622296i	−0.946118	+	0.323822i	$0.895032\pi$
$132$	218.357	+	32.6291i	1.65422	+	0.247190i
$133$	−19.3922	−	19.3922i	−0.145806	−	0.145806i
$134$	−126.554	−	11.1208i	−0.944436	−	0.0829909i
$135$	−121.010	+	9.81037i	−0.896371	+	0.0726694i
$136$	−17.5590	−	30.4937i	−0.129110	−	0.224218i
$137$	−24.5510			−0.179205			−0.0896023	−	0.995978i	$-0.528560\pi$
$137$	−24.5510			−0.179205			−0.0896023	+	0.995978i	$0.528560\pi$
$138$	203.862	+	12.3863i	1.47726	+	0.0897558i
$139$	3.06917	+	3.06917i	0.0220804	+	0.0220804i	0.718061	−	0.695980i	$-0.245030\pi$
$139$	3.06917	+	3.06917i	0.0220804	+	0.0220804i	−0.695980	+	0.718061i	$0.745030\pi$
$140$	89.0346	−	62.2414i	0.635961	−	0.444581i
$141$	−11.0833	−	10.5011i	−0.0786050	−	0.0744762i
$142$	−60.0022	−	71.5633i	−0.422551	−	0.503967i
$143$			166.399i			1.16363i
$144$	−42.0958	+	137.710i	−0.292332	+	0.956317i
$145$	−177.798			−1.22620
$146$	149.200	−	125.097i	1.02192	−	0.856827i
$147$	−25.8351	+	27.2674i	−0.175749	+	0.185492i
$148$	−92.9312	+	64.9654i	−0.627913	+	0.438955i
$149$	5.86344	−	5.86344i	0.0393519	−	0.0393519i	−0.687157	−	0.726509i	$-0.741142\pi$
$149$	5.86344	−	5.86344i	0.0393519	−	0.0393519i	0.726509	+	0.687157i	$0.241142\pi$
$150$	−1.73969	+	28.6330i	−0.0115980	+	0.190887i
$151$			179.561i			1.18914i	0.804043	+	0.594571i	$0.202678\pi$
$151$			179.561i			1.18914i	−0.804043	+	0.594571i	$0.797322\pi$
$152$	−9.44191	+	35.0769i	−0.0621178	+	0.230769i
$153$	−39.5288	+	2.13382i	−0.258358	+	0.0139466i
$154$	−19.4546	+	221.393i	−0.126328	+	1.43762i
$155$	25.1500	−	25.1500i	0.162258	−	0.162258i
$156$	−107.338	−	16.0395i	−0.688067	−	0.102818i
$157$	−14.8689	+	14.8689i	−0.0947067	+	0.0947067i	−0.752873	−	0.658166i	$-0.771332\pi$
$157$	−14.8689	+	14.8689i	−0.0947067	+	0.0947067i	0.658166	+	0.752873i	$0.271332\pi$
$158$	51.6100	+	61.5541i	0.326646	+	0.389583i
$159$	2.37568	+	88.0822i	0.0149414	+	0.553976i
$160$	−130.292	−	61.0594i	−0.814326	−	0.381621i
$161$			205.592i			1.27697i
$162$	116.843	+	112.213i	0.721252	+	0.692673i
$163$	66.1190	−	66.1190i	0.405638	−	0.405638i	−0.474577	−	0.880214i	$-0.657399\pi$
$163$	66.1190	−	66.1190i	0.405638	−	0.405638i	0.880214	+	0.474577i	$0.157399\pi$
$164$	31.4665	−	177.662i	0.191869	−	1.08330i
$165$	180.164	+	170.701i	1.09191	+	1.03455i
$166$	−8.80060	+	100.151i	−0.0530156	+	0.603318i
$167$	−158.709			−0.950353			−0.475176	−	0.879891i	$-0.657616\pi$
$167$	−158.709			−0.950353			−0.475176	+	0.879891i	$0.657616\pi$
$168$	−140.938	−	33.8899i	−0.838914	−	0.201726i
$169$			87.2028i			0.515993i
$170$	3.46258	−	39.4042i	0.0203681	−	0.231789i
$171$	30.4123	+	27.2971i	0.177850	+	0.159632i
$172$	166.951	−	116.710i	0.970645	−	0.678549i
$173$	76.9955	+	76.9955i	0.445061	+	0.445061i	0.893709	−	0.448648i	$-0.148094\pi$
$173$	76.9955	+	76.9955i	0.445061	+	0.445061i	−0.448648	+	0.893709i	$0.648094\pi$
$174$	157.275	+	177.623i	0.903882	+	1.02082i
$175$	−28.8760			−0.165006
$176$	266.985	−	124.001i	1.51696	−	0.704551i
$177$	−4.46861	−	165.681i	−0.0252464	−	0.936051i
$178$	−89.5375	−	106.789i	−0.503020	−	0.599941i
$179$	101.360	+	101.360i	0.566257	+	0.566257i	0.931078	−	0.364821i	$-0.118870\pi$
$179$	101.360	+	101.360i	0.566257	+	0.566257i	−0.364821	+	0.931078i	$0.618870\pi$
$180$	−127.480	+	99.7636i	−0.708221	+	0.554242i
$181$	−212.373	−	212.373i	−1.17333	−	1.17333i	−0.981411	−	0.191920i	$-0.938529\pi$
$181$	−212.373	−	212.373i	−1.17333	−	1.17333i	−0.191920	−	0.981411i	$-0.561471\pi$
$182$	9.56332	−	108.831i	0.0525457	−	0.597970i
$183$	−5.70017	−	211.343i	−0.0311485	−	1.15488i
$184$	235.989	−	135.888i	1.28255	−	0.738523i
$185$	−127.463			−0.688991
$186$	−47.3722	−	2.87826i	−0.254689	−	0.0154745i
$187$	57.2229	+	57.2229i	0.306005	+	0.306005i
$188$	−20.0454	−	3.55034i	−0.106625	−	0.0188848i
$189$	−105.616	+	124.252i	−0.558815	+	0.657416i
$190$	−31.2913	+	26.2362i	−0.164691	+	0.138085i
$191$			36.3314i			0.190217i	0.995467	+	0.0951083i	$0.0303197\pi$
$191$			36.3314i			0.190217i	−0.995467	+	0.0951083i	$0.969680\pi$
$192$	54.2535	+	184.175i	0.282571	+	0.959247i
$193$	47.1090			0.244088			0.122044	−	0.992525i	$-0.461055\pi$
$193$	47.1090			0.244088			0.122044	+	0.992525i	$0.461055\pi$
$194$	−78.5050	−	93.6313i	−0.404665	−	0.482635i
$195$	−88.5638	−	83.9119i	−0.454173	−	0.430317i
$196$	−8.73462	+	49.3162i	−0.0445644	+	0.251613i
$197$	−32.2783	+	32.2783i	−0.163849	+	0.163849i	−0.784269	−	0.620420i	$-0.786962\pi$
$197$	−32.2783	+	32.2783i	−0.163849	+	0.163849i	0.620420	+	0.784269i	$0.286962\pi$
$198$	11.1647	−	330.984i	0.0563876	−	1.67164i
$199$		−	118.181i		−	0.593874i	−0.954897	−	0.296937i	$-0.904035\pi$
$199$		−	118.181i		−	0.593874i	0.954897	−	0.296937i	$-0.0959651\pi$
$200$	19.0859	+	33.1454i	0.0954295	+	0.165727i
$201$	5.13784	+	190.494i	0.0255614	+	0.947731i
$202$	−293.129	−	25.7583i	−1.45114	−	0.127516i
$203$	−168.871	+	168.871i	−0.831875	+	0.831875i
$204$	−42.4283	+	31.3967i	−0.207982	+	0.153905i
$205$	143.419	−	143.419i	0.699604	−	0.699604i
$206$	87.8108	−	73.6249i	0.426266	−	0.357402i
$207$	−16.5136	−	305.911i	−0.0797756	−	1.47783i
$208$	−131.242	+	60.9554i	−0.630972	+	0.293055i
$209$		−	83.5416i		−	0.399721i
$210$	−108.023	−	121.999i	−0.514394	−	0.580945i
$211$	63.8884	−	63.8884i	0.302789	−	0.302789i	−0.539315	−	0.842104i	$-0.681317\pi$
$211$	63.8884	−	63.8884i	0.302789	−	0.302789i	0.842104	+	0.539315i	$0.181317\pi$
$212$	67.3134	+	96.2900i	0.317516	+	0.454198i
$213$	−96.3478	+	101.689i	−0.452337	+	0.477413i
$214$	−260.475	−	22.8889i	−1.21717	−	0.106957i
$215$	228.988			1.06506
$216$	212.430	+	39.1062i	0.983474	+	0.181047i
$217$		−	47.7743i		−	0.220158i
$218$	−212.374	−	18.6621i	−0.974193	−	0.0856057i
$219$	−212.008	−	200.872i	−0.968075	−	0.917226i
$220$	325.848	+	57.7124i	1.48113	+	0.262329i
$221$	−28.1292	−	28.1292i	−0.127281	−	0.127281i
$222$	112.750	+	127.338i	0.507885	+	0.573594i
$223$	−42.8886			−0.192326			−0.0961628	−	0.995366i	$-0.530657\pi$
$223$	−42.8886			−0.192326			−0.0961628	+	0.995366i	$0.530657\pi$
$224$	−181.743	+	65.7565i	−0.811354	+	0.293556i
$225$	42.9661	−	2.31938i	0.190961	−	0.0103084i
$226$	172.039	−	144.246i	0.761233	−	0.638255i
$227$	23.0035	+	23.0035i	0.101337	+	0.101337i	0.755958	−	0.654621i	$-0.227172\pi$
$227$	23.0035	+	23.0035i	0.101337	+	0.101337i	−0.654621	+	0.755958i	$0.727172\pi$
$228$	53.8898	+	8.05273i	0.236359	+	0.0353190i
$229$	241.282	+	241.282i	1.05363	+	1.05363i	0.998478	+	0.0551571i	$0.0175660\pi$
$229$	241.282	+	241.282i	1.05363	+	1.05363i	0.0551571	+	0.998478i	$0.482434\pi$
$230$	304.947	+	26.7968i	1.32586	+	0.116508i
$231$	333.248	−	8.98807i	1.44263	−	0.0389094i
$232$	305.455	+	82.2217i	1.31662	+	0.354404i
$233$	240.310			1.03137			0.515687	−	0.856777i	$-0.327537\pi$
$233$	240.310			1.03137			0.515687	+	0.856777i	$0.327537\pi$
$234$	−5.48827	+	162.703i	−0.0234542	+	0.695311i
$235$	−16.1818	−	16.1818i	−0.0688589	−	0.0688589i
$236$	−126.615	−	181.120i	−0.536506	−	0.767457i
$237$	82.8721	−	87.4663i	0.349671	−	0.369056i
$238$	−34.1369	−	40.7143i	−0.143432	−	0.171069i
$239$		−	218.171i		−	0.912851i	−0.889762	−	0.456425i	$-0.849130\pi$
$239$		−	218.171i		−	0.912851i	0.889762	−	0.456425i	$-0.150870\pi$
$240$	−68.6374	+	204.630i	−0.285989	+	0.852626i
$241$	−88.9611			−0.369133			−0.184567	−	0.982820i	$-0.559088\pi$
$241$	−88.9611			−0.369133			−0.184567	+	0.982820i	$0.559088\pi$
$242$	−333.343	+	279.491i	−1.37745	+	1.15492i
$243$	147.172	−	193.364i	0.605644	−	0.795736i
$244$	−161.511	−	231.037i	−0.661931	−	0.946873i
$245$	−39.8109	+	39.8109i	−0.162493	+	0.162493i
$246$	−270.142	−	16.4134i	−1.09814	−	0.0667210i
$247$			41.0667i			0.166262i
$248$	−54.8378	+	31.5769i	−0.221120	+	0.127326i
$249$	150.750	−	4.06591i	0.605423	−	0.0163289i
$250$	−23.4443	+	266.796i	−0.0937770	+	1.06718i
$251$	−169.225	+	169.225i	−0.674205	+	0.674205i	−0.958683	−	0.284478i	$-0.908180\pi$
$251$	−169.225	+	169.225i	−0.674205	+	0.674205i	0.284478	+	0.958683i	$0.408180\pi$
$252$	−26.3245	+	215.833i	−0.104462	+	0.856480i
$253$	−442.845	+	442.845i	−1.75038	+	1.75038i
$254$	−120.318	−	143.501i	−0.473693	−	0.564964i
$255$	−59.3125	+	1.59973i	−0.232598	+	0.00627343i
$256$	195.604	+	165.152i	0.764077	+	0.645125i
$257$		−	393.109i		−	1.52961i	−0.644262	−	0.764804i	$-0.722836\pi$
$257$		−	393.109i		−	1.52961i	0.644262	−	0.764804i	$-0.277164\pi$
$258$	−202.556	−	228.763i	−0.785102	−	0.886676i
$259$	−121.063	+	121.063i	−0.467425	+	0.467425i
$260$	−160.178	−	28.3698i	−0.616068	−	0.109115i
$261$	237.707	−	264.835i	0.910756	−	1.01470i
$262$	−20.1837	+	229.690i	−0.0770370	+	0.876681i
$263$	179.865			0.683897			0.341948	−	0.939719i	$-0.388913\pi$
$263$	179.865			0.683897			0.341948	+	0.939719i	$0.388913\pi$
$264$	−230.580	−	376.578i	−0.873411	−	1.42643i
$265$			132.070i			0.498378i
$266$	−4.80131	+	54.6390i	−0.0180501	+	0.205410i
$267$	−143.774	+	151.744i	−0.538478	+	0.568330i
$268$	145.578	+	208.245i	0.543200	+	0.777033i
$269$	290.530	+	290.530i	1.08004	+	1.08004i	0.996505	+	0.0835324i	$0.0266202\pi$
$269$	290.530	+	290.530i	1.08004	+	1.08004i	0.0835324	+	0.996505i	$0.473380\pi$
$270$	170.532	+	172.851i	0.631600	+	0.640190i
$271$	496.550			1.83229			0.916144	−	0.400849i	$-0.131285\pi$
$271$	496.550			1.83229			0.916144	+	0.400849i	$0.131285\pi$
$272$	−24.1709	+	66.0947i	−0.0888635	+	0.242995i
$273$	−163.815	+	4.41829i	−0.600056	+	0.0161842i
$274$	31.5478	+	37.6264i	0.115138	+	0.137323i
$275$	−62.1989	−	62.1989i	−0.226178	−	0.226178i
$276$	−242.977	−	328.351i	−0.880353	−	1.18968i
$277$	−93.0101	−	93.0101i	−0.335776	−	0.335776i	0.518999	−	0.854775i	$-0.326305\pi$
$277$	−93.0101	−	93.0101i	−0.335776	−	0.335776i	−0.854775	+	0.518999i	$0.826305\pi$
$278$	0.759895	−	8.64760i	0.00273343	−	0.0311065i
$279$	3.83733	+	71.0859i	0.0137539	+	0.254788i
$280$	−209.798	−	56.4730i	−0.749280	−	0.201689i
$281$	−300.875			−1.07073			−0.535365	−	0.844621i	$-0.679826\pi$
$281$	−300.875			−1.07073			−0.535365	+	0.844621i	$0.679826\pi$
$282$	−1.85191	+	30.4799i	−0.00656705	+	0.108085i
$283$	101.469	+	101.469i	0.358549	+	0.358549i	0.863278	−	0.504729i	$-0.168408\pi$
$283$	101.469	+	101.469i	0.358549	+	0.358549i	−0.504729	+	0.863278i	$0.668408\pi$
$284$	−32.5743	+	183.916i	−0.114698	+	0.647593i
$285$	44.4639	+	42.1284i	0.156014	+	0.147819i
$286$	255.020	−	213.821i	0.891679	−	0.747627i
$287$		−	272.435i		−	0.949250i
$288$	265.144	−	112.440i	0.920638	−	0.390418i
$289$	269.653			0.933057
$290$	228.469	+	272.490i	0.787824	+	0.939621i
$291$	−126.058	+	133.047i	−0.433190	+	0.457205i
$292$	−383.442	−	67.9131i	−1.31316	−	0.232579i
$293$	−321.104	+	321.104i	−1.09592	+	1.09592i	−0.101037	+	0.994883i	$0.532216\pi$
$293$	−321.104	+	321.104i	−1.09592	+	1.09592i	−0.994883	+	0.101037i	$0.967784\pi$
$294$	74.9873	+	4.55610i	0.255059	+	0.0154970i
$295$		−	248.422i		−	0.842107i
$296$	218.980	+	58.9445i	0.739798	+	0.199137i
$297$	−495.135	+	40.1409i	−1.66712	+	0.135155i
$298$	−16.5206	−	1.45173i	−0.0554384	−	0.00487156i
$299$	217.690	−	217.690i	0.728061	−	0.728061i
$300$	46.1178	−	34.1269i	0.153726	−	0.113756i
$301$	217.490	−	217.490i	0.722558	−	0.722558i
$302$	275.191	−	230.733i	0.911228	−	0.764018i
$303$	11.9004	+	441.228i	0.0392753	+	1.45620i
$304$	65.8909	−	30.6030i	0.216746	−	0.100668i
$305$		−	316.888i		−	1.03898i
$306$	54.0643	+	57.8390i	0.176681	+	0.189016i
$307$	94.2282	−	94.2282i	0.306932	−	0.306932i	−0.536786	−	0.843718i	$-0.680362\pi$
$307$	94.2282	−	94.2282i	0.306932	−	0.306932i	0.843718	+	0.536786i	$0.180362\pi$
$308$	364.301	−	254.672i	1.18280	−	0.826857i
$309$	−124.776	−	118.222i	−0.403806	−	0.382596i
$310$	−70.8619	−	6.22688i	−0.228587	−	0.0200867i
$311$	−245.712			−0.790070			−0.395035	−	0.918666i	$-0.629268\pi$
$311$	−245.712			−0.790070			−0.395035	+	0.918666i	$0.629268\pi$
$312$	113.347	+	185.115i	0.363291	+	0.593318i
$313$		−	353.841i		−	1.13048i	−0.824925	−	0.565242i	$-0.808783\pi$
$313$		−	353.841i		−	1.13048i	0.824925	−	0.565242i	$-0.191217\pi$
$314$	41.8943	+	3.68140i	0.133421	+	0.0117242i
$315$	−163.267	+	181.899i	−0.518307	+	0.577458i
$316$	28.0183	−	158.193i	0.0886654	−	0.500610i
$317$	234.024	+	234.024i	0.738245	+	0.738245i	0.972238	−	0.233994i	$-0.0751795\pi$
$317$	234.024	+	234.024i	0.738245	+	0.738245i	−0.233994	+	0.972238i	$0.575179\pi$
$318$	131.940	−	116.826i	0.414906	−	0.367376i
$319$	−727.494			−2.28055
$320$	73.8458	+	278.144i	0.230768	+	0.869199i
$321$	10.5747	+	392.076i	0.0329431	+	1.22142i
$322$	315.086	−	264.184i	0.978529	−	0.820447i
$323$	14.1224	+	14.1224i	0.0437226	+	0.0437226i
$324$	21.8334	−	323.264i	0.0673871	−	0.997727i
$325$	30.5752	+	30.5752i	0.0940777	+	0.0940777i
$326$	−186.295	−	16.3704i	−0.571456	−	0.0502158i
$327$	8.62193	+	319.673i	0.0263668	+	0.977592i
$328$	−312.715	+	180.069i	−0.953398	+	0.548989i
$329$	−30.7386			−0.0934305
$330$	30.1037	−	495.465i	0.0912232	−	1.50141i
$331$	−32.5392	−	32.5392i	−0.0983058	−	0.0983058i	0.656243	−	0.754549i	$-0.272144\pi$
$331$	−32.5392	−	32.5392i	−0.0983058	−	0.0983058i	−0.754549	+	0.656243i	$0.772144\pi$
$332$	164.798	−	115.205i	0.496379	−	0.347004i
$333$	170.412	−	189.860i	0.511748	−	0.570150i
$334$	203.939	+	243.234i	0.610597	+	0.728246i
$335$			285.626i			0.852615i
$336$	129.164	+	259.546i	0.384418	+	0.772459i
$337$	−185.573			−0.550660			−0.275330	−	0.961350i	$-0.588787\pi$
$337$	−185.573			−0.550660			−0.275330	+	0.961350i	$0.588787\pi$
$338$	133.645	−	112.055i	0.395400	−	0.331523i
$339$	−244.461	−	231.621i	−0.721124	−	0.683247i
$340$	−64.8395	+	45.3273i	−0.190704	+	0.133316i
$341$	102.906	−	102.906i	0.301776	−	0.301776i
$342$	2.75542	−	81.6858i	0.00805678	−	0.238847i
$343$			371.574i			1.08330i
$344$	−393.398	−	105.894i	−1.14360	−	0.307831i
$345$	−12.3802	−	459.016i	−0.0358846	−	1.33048i
$346$	19.0633	−	216.940i	0.0550962	−	0.626995i
$347$	51.9585	−	51.9585i	0.149736	−	0.149736i	−0.628264	−	0.778000i	$-0.716234\pi$
$347$	51.9585	−	51.9585i	0.149736	−	0.149736i	0.778000	+	0.628264i	$0.216234\pi$
$348$	70.1245	−	469.281i	0.201507	−	1.34851i
$349$	378.719	−	378.719i	1.08515	−	1.08515i	0.0891344	−	0.996020i	$-0.471590\pi$
$349$	378.719	−	378.719i	1.08515	−	1.08515i	0.996020	−	0.0891344i	$-0.0284101\pi$
$350$	37.1054	+	44.2548i	0.106015	+	0.126442i
$351$	243.394	−	19.7322i	0.693431	−	0.0562170i
$352$	−533.114	−	249.835i	−1.51453	−	0.709760i
$353$		−	326.435i		−	0.924744i	−0.886686	−	0.462372i	$-0.846998\pi$
$353$		−	326.435i		−	0.924744i	0.886686	−	0.462372i	$-0.153002\pi$
$354$	−248.177	+	219.747i	−0.701066	+	0.620754i
$355$	−148.468	+	148.468i	−0.418220	+	0.418220i
$356$	−48.6085	+	274.447i	−0.136541	+	0.770918i
$357$	−54.8149	+	57.8537i	−0.153543	+	0.162055i
$358$	25.0957	−	285.589i	0.0700997	−	0.797734i
$359$	−254.927			−0.710103			−0.355051	−	0.934847i	$-0.615537\pi$
$359$	−254.927			−0.710103			−0.355051	+	0.934847i	$0.615537\pi$
$360$	316.706	+	67.1777i	0.879739	+	0.186605i
$361$			340.382i			0.942887i
$362$	−52.5813	+	598.375i	−0.145252	+	1.65297i
$363$	473.668	+	448.789i	1.30487	+	1.23633i
$364$	−179.080	+	125.190i	−0.491979	+	0.343928i
$365$	−309.536	−	309.536i	−0.848045	−	0.848045i
$366$	−316.576	+	280.310i	−0.864961	+	0.765874i
$367$	−124.247			−0.338548			−0.169274	−	0.985569i	$-0.554142\pi$
$367$	−124.247			−0.338548			−0.169274	+	0.985569i	$0.554142\pi$
$368$	−511.503	−	187.057i	−1.38995	−	0.508308i
$369$	21.8825	+	405.370i	0.0593021	+	1.09856i
$370$	163.789	+	195.348i	0.442673	+	0.527966i
$371$	125.439	+	125.439i	0.338110	+	0.338110i
$372$	56.4617	+	76.3002i	0.151779	+	0.205108i
$373$	−201.674	−	201.674i	−0.540680	−	0.540680i	0.383048	−	0.923728i	$-0.374874\pi$
$373$	−201.674	−	201.674i	−0.540680	−	0.540680i	−0.923728	+	0.383048i	$0.874874\pi$
$374$	14.1678	−	161.229i	0.0378818	−	0.431095i
$375$	401.589	−	10.8313i	1.07091	−	0.0288835i
$376$	20.3170	+	35.2834i	0.0540346	+	0.0938388i
$377$	357.616			0.948583
$378$	326.141	+	2.20296i	0.862807	+	0.00582794i
$379$	−227.541	−	227.541i	−0.600372	−	0.600372i	0.340040	−	0.940411i	$-0.389560\pi$
$379$	−227.541	−	227.541i	−0.600372	−	0.600372i	−0.940411	+	0.340040i	$0.889560\pi$
$380$	80.4181	+	14.2432i	0.211627	+	0.0374822i
$381$	−193.199	+	203.910i	−0.507084	+	0.535196i
$382$	55.6807	−	46.6854i	0.145761	−	0.122213i
$383$		−	128.933i		−	0.336641i	−0.985732	−	0.168320i	$-0.946166\pi$
$383$		−	128.933i		−	0.336641i	0.985732	−	0.168320i	$-0.0538343\pi$
$384$	212.548	−	319.811i	0.553511	−	0.832842i
$385$	499.671			1.29785
$386$	−60.5346	−	72.1982i	−0.156825	−	0.187042i
$387$	−306.145	+	341.084i	−0.791073	+	0.881353i
$388$	−42.6192	+	240.630i	−0.109843	+	0.620182i
$389$	107.474	−	107.474i	0.276283	−	0.276283i	−0.555340	−	0.831623i	$-0.687412\pi$
$389$	107.474	−	107.474i	0.276283	−	0.276283i	0.831623	+	0.555340i	$0.187412\pi$
$390$	−14.7981	+	243.557i	−0.0379439	+	0.624505i
$391$		−	149.723i		−	0.382922i
$392$	86.8049	−	49.9843i	0.221441	−	0.127511i
$393$	345.738	−	9.32494i	0.879739	−	0.0237276i
$394$	90.9463	+	7.99176i	0.230828	+	0.0202837i
$395$	127.702	−	127.702i	0.323297	−	0.323297i
$396$	−521.607	+	408.201i	−1.31719	+	1.03081i
$397$	−259.306	+	259.306i	−0.653163	+	0.653163i	−0.953753	−	0.300591i	$-0.902816\pi$
$397$	−259.306	+	259.306i	−0.653163	+	0.653163i	0.300591	+	0.953753i	$0.402816\pi$
$398$	−181.122	+	151.861i	−0.455080	+	0.381561i
$399$	82.2444	−	2.21822i	0.206126	−	0.00555946i
$400$	26.2728	−	71.8422i	0.0656819	−	0.179605i
$401$			335.810i			0.837431i	0.908117	+	0.418716i	$0.137520\pi$
$401$			335.810i			0.837431i	−0.908117	+	0.418716i	$0.862480\pi$
$402$	285.345	−	252.657i	0.709813	−	0.628500i
$403$	−50.5856	+	50.5856i	−0.125523	+	0.125523i
$404$	337.192	+	482.343i	0.834633	+	1.19392i
$405$	228.322	−	283.771i	0.563759	−	0.700669i
$406$	475.805	+	41.8106i	1.17193	+	0.102982i
$407$	−521.539			−1.28142
$408$	102.638	+	24.6804i	0.251563	+	0.0604911i
$409$			66.3618i			0.162254i	0.996704	+	0.0811269i	$0.0258519\pi$
$409$			66.3618i			0.162254i	−0.996704	+	0.0811269i	$0.974148\pi$
$410$	−404.092	−	35.5090i	−0.985591	−	0.0866073i
$411$	50.6575	−	53.4658i	0.123254	−	0.130087i
$412$	−225.672	−	39.9698i	−0.547747	−	0.0970140i
$413$	−235.948	−	235.948i	−0.571303	−	0.571303i
$414$	−447.613	+	418.401i	−1.08119	+	1.01063i
$415$	226.035			0.544662
$416$	262.064	+	122.812i	0.629961	+	0.295222i
$417$	−13.0167	+	0.351074i	−0.0312150	+	0.000841904i
$418$	−128.034	+	107.350i	−0.306302	+	0.256819i
$419$	371.566	+	371.566i	0.886792	+	0.886792i	0.994214	−	0.107422i	$-0.0342596\pi$
$419$	371.566	+	371.566i	0.886792	+	0.886792i	−0.107422	+	0.994214i	$0.534260\pi$
$420$	−48.1642	+	322.320i	−0.114677	+	0.767430i
$421$	487.629	+	487.629i	1.15826	+	1.15826i	0.984849	+	0.173416i	$0.0554806\pi$
$421$	487.629	+	487.629i	1.15826	+	1.15826i	0.173416	+	0.984849i	$0.444519\pi$
$422$	−180.010	−	15.8181i	−0.426564	−	0.0374837i
$423$	45.7376	−	2.46899i	0.108127	−	0.00583685i
$424$	61.0750	−	226.895i	0.144045	−	0.535129i
$425$	21.0290			0.0494800
$426$	279.652	+	16.9912i	0.656461	+	0.0398855i
$427$	−300.976	−	300.976i	−0.704862	−	0.704862i
$428$	299.629	+	428.611i	0.700068	+	1.00143i
$429$	−362.375	−	343.341i	−0.844696	−	0.800328i
$430$	−294.247	−	350.942i	−0.684296	−	0.816145i
$431$		−	505.901i		−	1.17378i	−0.809665	−	0.586892i	$-0.800351\pi$
$431$		−	505.901i		−	1.17378i	0.809665	−	0.586892i	$-0.199649\pi$
$432$	−213.038	−	375.818i	−0.493143	−	0.869948i
$433$	−758.226			−1.75110			−0.875550	−	0.483128i	$-0.839500\pi$
$433$	−758.226			−1.75110			−0.875550	+	0.483128i	$0.839500\pi$
$434$	−73.2180	+	61.3895i	−0.168705	+	0.141451i
$435$	366.861	−	387.199i	0.843359	−	0.890113i
$436$	244.298	+	349.461i	0.560316	+	0.801516i
$437$	−109.293	+	109.293i	−0.250097	+	0.250097i
$438$	−35.4245	+	583.039i	−0.0808778	+	1.33114i
$439$		−	145.760i		−	0.332026i	−0.986124	−	0.166013i	$-0.946911\pi$
$439$		−	145.760i		−	0.332026i	0.986124	−	0.166013i	$-0.0530895\pi$
$440$	−330.263	−	573.548i	−0.750597	−	1.30352i
$441$	−6.07425	−	112.525i	−0.0137738	−	0.255158i
$442$	−6.96449	+	79.2559i	−0.0157568	+	0.179312i
$443$	607.046	−	607.046i	1.37031	−	1.37031i	0.510323	−	0.859983i	$-0.329526\pi$
$443$	607.046	−	607.046i	1.37031	−	1.37031i	0.859983	−	0.510323i	$-0.170474\pi$
$444$	50.2721	−	336.427i	0.113226	−	0.757718i
$445$	−221.549	+	221.549i	−0.497864	+	0.497864i
$446$	55.1114	+	65.7302i	0.123568	+	0.147377i
$447$	0.670702	+	24.8674i	0.00150045	+	0.0556318i
$448$	334.315	+	194.040i	0.746240	+	0.433124i
$449$			190.654i			0.424620i	0.977202	+	0.212310i	$0.0680986\pi$
$449$			190.654i			0.424620i	−0.977202	+	0.212310i	$0.931901\pi$
$450$	−58.7657	−	62.8687i	−0.130590	−	0.139708i
$451$	586.824	−	586.824i	1.30116	−	1.30116i
$452$	−442.136	−	78.3087i	−0.978177	−	0.173249i
$453$	−391.037	−	370.497i	−0.863216	−	0.817875i
$454$	5.69542	−	64.8139i	0.0125450	−	0.142762i
$455$	−245.624			−0.539834
$456$	−56.9064	−	92.9381i	−0.124795	−	0.203812i
$457$			128.091i			0.280287i	0.990131	+	0.140143i	$0.0447563\pi$
$457$			128.091i			0.280287i	−0.990131	+	0.140143i	$0.955244\pi$
$458$	59.7390	−	679.830i	0.130435	−	1.48434i
$459$	76.9150	−	90.4863i	0.167571	−	0.197138i
$460$	−350.786	−	501.789i	−0.762578	−	1.09085i
$461$	−74.2060	−	74.2060i	−0.160968	−	0.160968i	0.622028	−	0.782995i	$-0.286309\pi$
$461$	−74.2060	−	74.2060i	−0.160968	−	0.160968i	−0.782995	+	0.622028i	$0.786309\pi$
$462$	−441.995	−	499.179i	−0.956699	−	1.08047i
$463$	620.192			1.33951			0.669753	−	0.742584i	$-0.266400\pi$
$463$	620.192			1.33951			0.669753	+	0.742584i	$0.266400\pi$
$464$	−266.496	−	573.789i	−0.574344	−	1.23661i
$465$	2.87684	+	106.664i	0.00618675	+	0.229384i
$466$	−308.796	−	368.294i	−0.662653	−	0.790331i
$467$	331.708	+	331.708i	0.710296	+	0.710296i	0.966597	−	0.256301i	$-0.0825038\pi$
$467$	331.708	+	331.708i	0.710296	+	0.710296i	−0.256301	+	0.966597i	$0.582504\pi$
$468$	256.407	−	200.660i	0.547879	−	0.428761i
$469$	271.284	+	271.284i	0.578431	+	0.578431i
$470$	−4.00646	+	45.5935i	−0.00852437	+	0.0970074i
$471$	−1.70082	−	63.0607i	−0.00361108	−	0.133887i
$472$	−114.881	+	426.785i	−0.243392	+	0.904206i
$473$	936.946			1.98086
$474$	−240.539	−	14.6147i	−0.507466	−	0.0308328i
$475$	−15.3505	−	15.3505i	−0.0323168	−	0.0323168i
$476$	−18.5324	+	104.635i	−0.0389336	+	0.219822i
$477$	−196.722	−	176.571i	−0.412415	−	0.370170i
$478$	−334.365	+	280.348i	−0.699508	+	0.586502i
$479$			867.941i			1.81198i	0.423294	+	0.905992i	$0.360874\pi$
$479$			867.941i			1.81198i	−0.423294	+	0.905992i	$0.639126\pi$
$480$	401.811	−	157.756i	0.837105	−	0.328658i
$481$	256.374			0.533002
$482$	114.314	+	136.340i	0.237166	+	0.282863i
$483$	−447.727	−	424.210i	−0.926970	−	0.878281i
$484$	856.684	+	151.731i	1.77001	+	0.313494i
$485$	−194.251	+	194.251i	−0.400517	+	0.400517i
$486$	−485.459	+	22.9184i	−0.998887	+	0.0471572i
$487$		−	815.778i		−	1.67511i	−0.546354	−	0.837554i	$-0.683985\pi$
$487$		−	815.778i		−	1.67511i	0.546354	−	0.837554i	$-0.316015\pi$
$488$	−146.543	+	544.409i	−0.300292	+	1.11559i
$489$	7.56317	+	280.417i	0.0154666	+	0.573450i
$490$	112.170	+	9.85676i	0.228918	+	0.0201158i
$491$	−337.746	+	337.746i	−0.687874	+	0.687874i	−0.961762	−	0.273888i	$-0.911690\pi$
$491$	−337.746	+	337.746i	−0.687874	+	0.687874i	0.273888	+	0.961762i	$0.411690\pi$
$492$	321.975	+	435.105i	0.654420	+	0.884360i
$493$	122.980	−	122.980i	0.249453	−	0.249453i
$494$	62.9380	−	52.7703i	0.127405	−	0.106823i
$495$	−743.486	+	40.1345i	−1.50199	+	0.0810799i
$496$	118.860	+	43.4673i	0.239637	+	0.0876357i
$497$			282.026i			0.567457i
$498$	−199.944	−	225.812i	−0.401494	−	0.453438i
$499$	−515.289	+	515.289i	−1.03264	+	1.03264i	−0.0331940	+	0.999449i	$0.510568\pi$
$499$	−515.289	+	515.289i	−1.03264	+	1.03264i	−0.999449	+	0.0331940i	$0.989432\pi$
$500$	439.011	−	306.900i	0.878022	−	0.613799i
$501$	327.473	−	345.627i	0.653639	−	0.689875i
$502$	476.805	+	41.8985i	0.949810	+	0.0834631i
$503$	−196.781			−0.391215			−0.195607	−	0.980682i	$-0.562668\pi$
$503$	−196.781			−0.391215			−0.195607	+	0.980682i	$0.562668\pi$
$504$	364.608	−	236.999i	0.723429	−	0.470236i
$505$			661.576i			1.31005i
$506$	1247.75	+	109.644i	2.46590	+	0.216687i
$507$	−189.905	−	179.930i	−0.374567	−	0.354892i
$508$	−65.3188	+	368.794i	−0.128580	+	0.725973i
$509$	29.3054	+	29.3054i	0.0575744	+	0.0575744i	0.735308	−	0.677733i	$-0.237038\pi$
$509$	29.3054	+	29.3054i	0.0575744	+	0.0575744i	−0.677733	+	0.735308i	$0.737038\pi$
$510$	78.6677	+	88.8455i	0.154250	+	0.174207i
$511$	−587.988			−1.15066
$512$	1.75962	−	511.997i	0.00343675	−	0.999994i
$513$	−122.197	+	9.90664i	−0.238202	+	0.0193112i
$514$	−602.472	+	505.142i	−1.17212	+	0.982766i
$515$	−182.175	−	182.175i	−0.353739	−	0.353739i
$516$	−90.3139	+	604.391i	−0.175027	+	1.17130i
$517$	−66.2109	−	66.2109i	−0.128068	−	0.128068i
$518$	341.104	+	29.9740i	0.658501	+	0.0578648i
$519$	−326.546	+	8.80731i	−0.629182	+	0.0169698i
$520$	162.348	+	281.940i	0.312207	+	0.542193i
$521$	−770.641			−1.47916			−0.739578	−	0.673071i	$-0.764975\pi$
$521$	−770.641			−1.47916			−0.739578	+	0.673071i	$0.764975\pi$
$522$	−711.333	−	23.9946i	−1.36271	−	0.0459667i
$523$	258.725	+	258.725i	0.494694	+	0.494694i	0.909782	−	0.415087i	$-0.136249\pi$
$523$	258.725	+	258.725i	0.494694	+	0.494694i	−0.415087	+	0.909782i	$0.636249\pi$
$524$	377.955	−	264.217i	0.721288	−	0.504231i
$525$	59.5815	−	62.8846i	0.113489	−	0.119780i
$526$	−231.125	−	275.657i	−0.439400	−	0.524063i
$527$			34.7917i			0.0660183i
$528$	−280.842	+	837.282i	−0.531899	+	1.58576i
$529$	629.695			1.19035
$530$	202.408	−	169.709i	0.381902	−	0.320205i
$531$	370.031	+	332.127i	0.696857	+	0.625475i
$532$	89.9082	−	62.8521i	0.169000	−	0.118143i
$533$	−288.466	+	288.466i	−0.541212	+	0.541212i
$534$	417.308	+	25.3549i	0.781475	+	0.0474811i
$535$			587.878i			1.09884i
$536$	132.086	−	490.702i	0.246429	−	0.915489i
$537$	−429.878	+	11.5943i	−0.800517	+	0.0215909i
$538$	71.9322	−	818.589i	0.133703	−	1.52154i
$539$	−162.894	+	162.894i	−0.302214	+	0.302214i
$540$	45.7766	−	483.466i	0.0847715	−	0.895307i
$541$	−122.667	+	122.667i	−0.226742	+	0.226742i	−0.811330	−	0.584588i	$-0.801256\pi$
$541$	−122.667	+	122.667i	−0.226742	+	0.226742i	0.584588	+	0.811330i	$0.301256\pi$
$542$	−638.062	−	761.003i	−1.17724	−	1.40406i
$543$	900.694	−	24.2927i	1.65874	−	0.0447380i
$544$	132.355	−	47.8872i	0.243299	−	0.0880279i
$545$			479.316i			0.879479i
$546$	217.272	+	245.383i	0.397935	+	0.449419i
$547$	334.075	−	334.075i	0.610740	−	0.610740i	−0.332399	−	0.943139i	$-0.607858\pi$
$547$	334.075	−	334.075i	0.610740	−	0.610740i	0.943139	+	0.332399i	$0.107858\pi$
$548$	17.1268	−	96.6991i	0.0312533	−	0.176458i
$549$	472.013	+	423.663i	0.859768	+	0.771699i
$550$	−15.3998	+	175.250i	−0.0279996	+	0.318636i
$551$	−179.543			−0.325849
$552$	−191.000	+	794.309i	−0.346015	+	1.43897i
$553$		−	242.581i		−	0.438663i
$554$	−23.0283	+	262.062i	−0.0415674	+	0.473037i
$555$	263.002	−	277.582i	0.473878	−	0.500148i
$556$	−14.2296	+	9.94748i	−0.0255928	+	0.0178912i
$557$	159.480	+	159.480i	0.286320	+	0.286320i	0.835623	−	0.549303i	$-0.185107\pi$
$557$	159.480	+	159.480i	0.286320	+	0.286320i	−0.549303	+	0.835623i	$0.685107\pi$
$558$	104.014	−	97.2257i	0.186405	−	0.174240i
$559$	−460.576			−0.823929
$560$	183.040	+	394.100i	0.326856	+	0.703750i
$561$	−242.688	+	6.54557i	−0.432599	+	0.0116677i
$562$	386.621	+	461.115i	0.687938	+	0.820489i
$563$	−341.226	−	341.226i	−0.606086	−	0.606086i	0.335835	−	0.941921i	$-0.390982\pi$
$563$	−341.226	−	341.226i	−0.606086	−	0.606086i	−0.941921	+	0.335835i	$0.890982\pi$
$564$	49.0926	−	36.3282i	0.0870436	−	0.0644117i
$565$	−356.918	−	356.918i	−0.631713	−	0.631713i
$566$	25.1227	−	285.897i	0.0443865	−	0.505118i
$567$	−52.6646	−	486.380i	−0.0928828	−	0.857813i
$568$	323.724	−	186.408i	0.569937	−	0.328183i
$569$	−882.975			−1.55180			−0.775901	−	0.630855i	$-0.782704\pi$
$569$	−882.975			−1.55180			−0.775901	+	0.630855i	$0.782704\pi$
$570$	7.42947	−	122.279i	0.0130342	−	0.214525i
$571$	370.112	+	370.112i	0.648181	+	0.648181i	0.952553	−	0.304372i	$-0.0984466\pi$
$571$	370.112	+	370.112i	0.648181	+	0.648181i	−0.304372	+	0.952553i	$0.598447\pi$
$572$	−655.397	−	116.080i	−1.14580	−	0.202938i
$573$	−79.1204	−	74.9645i	−0.138081	−	0.130828i
$574$	−417.528	+	350.076i	−0.727401	+	0.609889i
$575$			162.742i			0.283030i
$576$	−513.031	−	261.869i	−0.890679	−	0.454634i
$577$	−698.607			−1.21076			−0.605378	−	0.795938i	$-0.706978\pi$
$577$	−698.607			−1.21076			−0.605378	+	0.795938i	$0.706978\pi$
$578$	−346.502	−	413.265i	−0.599484	−	0.714992i
$579$	−97.2025	+	102.591i	−0.167880	+	0.177187i
$580$	124.032	−	700.294i	0.213849	−	1.20740i
$581$	214.685	−	214.685i	0.369509	−	0.369509i
$582$	365.889	+	22.2308i	0.628675	+	0.0381972i
$583$			540.389i			0.926911i
$584$	388.636	+	674.922i	0.665473	+	1.15569i
$585$	365.477	−	19.7290i	0.624747	−	0.0337248i
$586$	904.734	+	79.5021i	1.54392	+	0.135669i
$587$	196.072	−	196.072i	0.334024	−	0.334024i	−0.520088	−	0.854112i	$-0.674101\pi$
$587$	196.072	−	196.072i	0.334024	−	0.334024i	0.854112	+	0.520088i	$0.174101\pi$
$588$	−89.3754	−	120.779i	−0.151999	−	0.205406i
$589$	25.3968	−	25.3968i	0.0431185	−	0.0431185i
$590$	−380.726	+	319.219i	−0.645298	+	0.541050i
$591$	−3.69222	−	136.895i	−0.00624742	−	0.231633i
$592$	−191.050	−	411.348i	−0.322720	−	0.694844i
$593$		−	774.011i		−	1.30525i	−0.757683	−	0.652623i	$-0.773669\pi$
$593$		−	774.011i		−	1.30525i	0.757683	−	0.652623i	$-0.226331\pi$
$594$	697.762	+	707.253i	1.17468	+	1.19066i
$595$	−84.4675	+	84.4675i	−0.141962	+	0.141962i
$596$	19.0040	+	27.1847i	0.0318859	+	0.0456118i
$597$	257.368	+	243.849i	0.431102	+	0.408458i
$598$	−613.357	−	53.8978i	−1.02568	−	0.0901301i
$599$	783.533			1.30807			0.654034	−	0.756465i	$-0.273075\pi$
$599$	783.533			1.30807			0.654034	+	0.756465i	$0.273075\pi$
$600$	−111.563	−	26.8265i	−0.185939	−	0.0447109i
$601$		−	797.210i		−	1.32647i	−0.748410	−	0.663236i	$-0.769182\pi$
$601$		−	797.210i		−	1.32647i	0.748410	−	0.663236i	$-0.230818\pi$
$602$	−612.793	−	53.8482i	−1.01793	−	0.0894489i
$603$	−425.448	−	381.868i	−0.705552	−	0.633280i
$604$	−707.235	−	125.262i	−1.17092	−	0.207387i
$605$	691.565	+	691.565i	1.14308	+	1.14308i
$606$	660.925	−	585.212i	1.09064	−	0.965696i
$607$	433.576			0.714293			0.357146	−	0.934048i	$-0.383750\pi$
$607$	433.576			0.714293			0.357146	+	0.934048i	$0.383750\pi$
$608$	−131.571	−	61.6585i	−0.216399	−	0.101412i
$609$	−19.3167	−	716.197i	−0.0317186	−	1.17602i
$610$	−485.656	+	407.197i	−0.796157	+	0.667537i
$611$	32.5475	+	32.5475i	0.0532692	+	0.0532692i
$612$	19.1708	−	157.180i	0.0313249	−	0.256831i
$613$	−493.642	−	493.642i	−0.805289	−	0.805289i	0.178628	−	0.983917i	$-0.442834\pi$
$613$	−493.642	−	493.642i	−0.805289	−	0.805289i	−0.983917	+	0.178628i	$0.942834\pi$
$614$	−265.494	−	23.3299i	−0.432401	−	0.0379966i
$615$	16.4053	+	608.253i	0.0266752	+	0.989029i
$616$	−858.428	−	231.070i	−1.39355	−	0.375113i
$617$	685.069			1.11032			0.555161	−	0.831743i	$-0.312657\pi$
$617$	685.069			1.11032			0.555161	+	0.831743i	$0.312657\pi$
$618$	−20.8488	+	343.144i	−0.0337360	+	0.555248i
$619$	−379.995	−	379.995i	−0.613885	−	0.613885i	0.330071	−	0.943956i	$-0.392927\pi$
$619$	−379.995	−	379.995i	−0.613885	−	0.613885i	−0.943956	+	0.330071i	$0.892927\pi$
$620$	81.5136	+	116.603i	0.131474	+	0.188069i
$621$	700.269	+	595.241i	1.12765	+	0.958520i
$622$	315.737	+	376.573i	0.507616	+	0.605422i
$623$			420.850i			0.675521i
$624$	138.054	−	411.585i	0.221241	−	0.659591i
$625$	482.618			0.772189
$626$	−542.290	+	454.683i	−0.866278	+	0.726330i
$627$	181.932	+	172.376i	0.290163	+	0.274922i
$628$	−48.1917	−	68.9369i	−0.0767384	−	0.109772i
$629$	88.1642	−	88.1642i	0.140166	−	0.140166i
$630$	488.571	+	16.4804i	0.775509	+	0.0261594i
$631$		−	489.285i		−	0.775412i	−0.921783	−	0.387706i	$-0.873268\pi$
$631$		−	489.285i		−	0.775412i	0.921783	−	0.387706i	$-0.126732\pi$
$632$	−278.446	+	160.336i	−0.440580	+	0.253696i
$633$	7.30802	+	270.957i	0.0115451	+	0.428052i
$634$	57.9418	−	659.378i	0.0913908	−	1.04003i
$635$	−297.712	+	297.712i	−0.468838	+	0.468838i
$636$	−348.586	−	52.0891i	−0.548092	−	0.0819011i
$637$	80.0739	−	80.0739i	0.125705	−	0.125705i
$638$	934.823	+	1114.94i	1.46524	+	1.74756i
$639$	−22.6529	−	419.641i	−0.0354505	−	0.656716i
$640$	331.386	−	470.587i	0.517791	−	0.735291i
$641$		−	492.158i		−	0.767797i	−0.923375	−	0.383898i	$-0.874581\pi$
$641$		−	492.158i		−	0.767797i	0.923375	−	0.383898i	$-0.125419\pi$
$642$	587.299	−	520.020i	0.914796	−	0.810001i
$643$	−169.985	+	169.985i	−0.264362	+	0.264362i	−0.826823	−	0.562462i	$-0.809854\pi$
$643$	−169.985	+	169.985i	−0.264362	+	0.264362i	0.562462	+	0.826823i	$0.309854\pi$
$644$	−809.766	−	143.421i	−1.25740	−	0.222704i
$645$	−472.483	+	498.677i	−0.732532	+	0.773142i
$646$	3.49656	−	39.7908i	0.00541263	−	0.0615957i
$647$	1003.50			1.55101			0.775503	−	0.631343i	$-0.217496\pi$
$647$	1003.50			1.55101			0.775503	+	0.631343i	$0.217496\pi$
$648$	−523.483	+	381.929i	−0.807844	+	0.589397i
$649$		−	1016.46i		−	1.56620i
$650$	7.57011	−	86.1479i	0.0116463	−	0.132535i
$651$	104.040	+	98.5754i	0.159816	+	0.151422i
$652$	214.298	+	306.547i	0.328678	+	0.470165i
$653$	−407.090	−	407.090i	−0.623415	−	0.623415i	0.322988	−	0.946403i	$-0.395313\pi$
$653$	−407.090	−	407.090i	−0.623415	−	0.623415i	−0.946403	+	0.322988i	$0.895313\pi$
$654$	478.845	−	423.990i	0.732178	−	0.648303i
$655$	518.398			0.791448
$656$	677.805	+	247.874i	1.03324	+	0.377856i
$657$	874.897	−	47.2283i	1.33165	−	0.0718848i
$658$	39.4988	+	47.1094i	0.0600286	+	0.0715948i
$659$	−635.355	−	635.355i	−0.964119	−	0.964119i	0.0352587	−	0.999378i	$-0.488774\pi$
$659$	−635.355	−	635.355i	−0.964119	−	0.964119i	−0.999378	+	0.0352587i	$0.988774\pi$
$660$	−798.023	+	590.532i	−1.20913	+	0.894745i
$661$	−196.325	−	196.325i	−0.297013	−	0.297013i	0.542830	−	0.839843i	$-0.317353\pi$
$661$	−196.325	−	196.325i	−0.297013	−	0.297013i	−0.839843	+	0.542830i	$0.817353\pi$
$662$	−8.05637	+	91.6815i	−0.0121697	+	0.138492i
$663$	119.299	−	3.21762i	0.179937	−	0.00485312i
$664$	−388.325	−	104.528i	−0.584826	−	0.157422i
$665$	123.317			0.185439
$666$	−509.953	−	17.2017i	−0.765696	−	0.0258284i
$667$	951.737	+	951.737i	1.42689	+	1.42689i
$668$	110.715	−	625.107i	0.165742	−	0.935788i
$669$	88.4944	−	93.4003i	0.132279	−	0.139612i
$670$	437.745	−	367.027i	0.653350	−	0.547801i
$671$		−	1296.60i		−	1.93234i
$672$	231.800	−	531.469i	0.344941	−	0.790877i
$673$	−489.653			−0.727568			−0.363784	−	0.931483i	$-0.618515\pi$
$673$	−489.653			−0.727568			−0.363784	+	0.931483i	$0.618515\pi$
$674$	238.459	+	284.405i	0.353797	+	0.421966i
$675$	−83.6034	+	98.3549i	−0.123857	+	0.145711i
$676$	−343.466	−	60.8327i	−0.508085	−	0.0899893i
$677$	832.940	−	832.940i	1.23034	−	1.23034i	0.266507	−	0.963833i	$-0.414131\pi$
$677$	832.940	−	832.940i	1.23034	−	1.23034i	0.963833	−	0.266507i	$-0.0858695\pi$
$678$	−40.8470	+	672.286i	−0.0602463	+	0.991573i
$679$			368.994i			0.543438i
$680$	152.786	+	41.1265i	0.224685	+	0.0604801i
$681$	−97.5600	+	2.63131i	−0.143260	+	0.00386388i
$682$	−289.944	−	25.4784i	−0.425138	−	0.0373584i
$683$	−773.804	+	773.804i	−1.13295	+	1.13295i	−0.143264	+	0.989684i	$0.545760\pi$
$683$	−773.804	+	773.804i	−1.13295	+	1.13295i	−0.989684	+	0.143264i	$0.954240\pi$
$684$	−128.731	+	100.743i	−0.188203	+	0.147284i
$685$	78.0611	−	78.0611i	0.113958	−	0.113958i
$686$	569.466	−	477.468i	0.830125	−	0.696018i
$687$	−1023.30	+	27.5996i	−1.48952	+	0.0401741i
$688$	343.222	+	738.987i	0.498869	+	1.07411i
$689$		−	265.640i		−	0.385545i
$690$	−687.571	+	608.805i	−0.996479	+	0.882326i
$691$	−840.306	+	840.306i	−1.21607	+	1.21607i	−0.247077	+	0.968996i	$0.579470\pi$
$691$	−840.306	+	840.306i	−1.21607	+	1.21607i	−0.968996	+	0.247077i	$0.920530\pi$
$692$	−356.974	+	249.550i	−0.515859	+	0.360622i
$693$	−668.035	+	744.274i	−0.963975	+	1.07399i
$694$	−146.397	−	12.8644i	−0.210946	−	0.0185366i
$695$	−19.5171			−0.0280822
$696$	−809.320	+	495.551i	−1.16282	+	0.711998i
$697$			198.401i			0.284650i
$698$	−1067.07	−	93.7668i	−1.52875	−	0.134336i
$699$	−495.845	+	523.334i	−0.709364	+	0.748689i
$700$	20.1440	−	113.734i	0.0287771	−	0.162477i
$701$	−529.432	−	529.432i	−0.755253	−	0.755253i	0.220201	−	0.975454i	$-0.429329\pi$
$701$	−529.432	−	529.432i	−0.755253	−	0.755253i	−0.975454	+	0.220201i	$0.929329\pi$
$702$	−343.000	−	347.666i	−0.488605	−	0.495250i
$703$	−128.714			−0.183092
$704$	302.153	+	1138.08i	0.429195	+	1.61659i
$705$	68.6288	−	1.85100i	0.0973458	−	0.00262553i
$706$	−500.287	+	419.465i	−0.708622	+	0.594144i
$707$	628.357	+	628.357i	0.888765	+	0.888765i
$708$	655.685	+	97.9787i	0.926109	+	0.138388i
$709$	−56.2182	−	56.2182i	−0.0792923	−	0.0792923i	0.666348	−	0.745641i	$-0.267856\pi$
$709$	−56.2182	−	56.2182i	−0.0792923	−	0.0792923i	−0.745641	+	0.666348i	$0.767856\pi$
$710$	418.319	+	36.7591i	0.589181	+	0.0517734i
$711$	19.4845	+	360.948i	0.0274044	+	0.507663i
$712$	483.073	−	278.165i	0.678473	−	0.390681i
$713$	−269.251			−0.377631
$714$	159.102	+	9.66677i	0.222832	+	0.0135389i
$715$	−529.074	−	529.074i	−0.739964	−	0.739964i
$716$	−469.936	+	328.518i	−0.656335	+	0.458824i
$717$	475.121	+	450.165i	0.662651	+	0.627845i
$718$	327.578	+	390.696i	0.456237	+	0.544144i
$719$		−	966.944i		−	1.34485i	−0.740167	−	0.672423i	$-0.765254\pi$
$719$		−	966.944i		−	1.34485i	0.740167	−	0.672423i	$-0.234746\pi$
$720$	−304.009	−	571.700i	−0.422234	−	0.794027i
$721$	−346.056			−0.479967
$722$	521.663	−	437.388i	0.722525	−	0.605800i
$723$	183.558	−	193.734i	0.253884	−	0.267959i
$724$	984.624	−	688.321i	1.35998	−	0.950720i
$725$	−133.674	+	133.674i	−0.184378	+	0.184378i
$726$	79.1452	−	1302.62i	0.109015	−	1.79425i
$727$			1338.18i			1.84069i	0.391110	+	0.920344i	$0.372091\pi$
$727$			1338.18i			1.84069i	−0.391110	+	0.920344i	$0.627909\pi$
$728$	421.979	+	113.587i	0.579642	+	0.156027i
$729$	117.429	+	719.480i	0.161083	+	0.986941i
$730$	−76.6380	+	872.140i	−0.104984	+	1.19471i
$731$	−158.387	+	158.387i	−0.216672	+	0.216672i
$732$	836.394	+	124.982i	1.14261	+	0.170740i
$733$	757.046	−	757.046i	1.03280	−	1.03280i	0.0333615	−	0.999443i	$-0.489379\pi$
$733$	757.046	−	757.046i	1.03280	−	1.03280i	0.999443	−	0.0333615i	$-0.0106213\pi$
$734$	159.656	+	190.418i	0.217515	+	0.259426i
$735$	−4.55386	−	168.842i	−0.00619573	−	0.229717i
$736$	370.596	+	1024.29i	0.503528	+	1.39169i
$737$			1168.69i			1.58574i
$738$	593.143	−	554.433i	0.803716	−	0.751264i
$739$	495.335	−	495.335i	0.670278	−	0.670278i	−0.287502	−	0.957780i	$-0.592825\pi$
$739$	495.335	−	495.335i	0.670278	−	0.670278i	0.957780	+	0.287502i	$0.0928249\pi$
$740$	88.9185	−	502.039i	0.120160	−	0.678432i
$741$	−89.4328	−	84.7353i	−0.120692	−	0.114353i
$742$	31.0573	−	353.432i	0.0418562	−	0.476324i
$743$	1421.01			1.91253			0.956266	−	0.292500i	$-0.0944872\pi$
$743$	1421.01			1.91253			0.956266	+	0.292500i	$0.0944872\pi$
$744$	44.3835	−	184.577i	0.0596552	−	0.248087i
$745$			37.2861i			0.0500485i
$746$	−49.9323	+	568.230i	−0.0669334	+	0.761702i
$747$	−302.197	+	336.685i	−0.404547	+	0.450716i
$748$	−265.302	+	185.465i	−0.354682	+	0.247948i
$749$	558.359	+	558.359i	0.745473	+	0.745473i
$750$	−532.638	−	601.550i	−0.710185	−	0.802066i
$751$	−143.509			−0.191090			−0.0955452	−	0.995425i	$-0.530459\pi$
$751$	−143.509			−0.191090			−0.0955452	+	0.995425i	$0.530459\pi$
$752$	27.9674	−	76.4762i	0.0371907	−	0.101697i
$753$	−19.3572	−	717.702i	−0.0257068	−	0.953123i
$754$	−459.533	−	548.075i	−0.609460	−	0.726890i
$755$	−570.921	−	570.921i	−0.756187	−	0.756187i
$756$	−415.712	−	502.668i	−0.549884	−	0.664905i
$757$	651.883	+	651.883i	0.861140	+	0.861140i	0.991471	−	0.130331i	$-0.0416040\pi$
$757$	651.883	+	651.883i	0.861140	+	0.861140i	−0.130331	+	0.991471i	$0.541604\pi$
$758$	−56.3367	+	641.112i	−0.0743229	+	0.845794i
$759$	−50.6558	−	1878.15i	−0.0667402	−	2.47450i
$760$	−81.5076	−	141.550i	−0.107247	−	0.186249i
$761$	−434.623			−0.571122			−0.285561	−	0.958361i	$-0.592180\pi$
$761$	−434.623			−0.571122			−0.285561	+	0.958361i	$0.592180\pi$
$762$	560.767	+	34.0712i	0.735914	+	0.0447129i
$763$	455.249	+	455.249i	0.596656	+	0.596656i
$764$	−143.098	−	25.3448i	−0.187301	−	0.0331738i
$765$	118.899

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	48.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28499 - 1.53258i) q^{2} +(-2.06336 + 2.17774i) q^{3} +(-0.697601 + 3.93870i) q^{4} +(-3.17955 + 3.17955i) q^{5} +(5.98896 + 0.363879i) q^{6} +6.03979i q^{7} +(6.93278 - 3.99206i) q^{8} +(-0.485128 - 8.98692i) q^{9} +O(q^{10})\)	\(q+(-1.28499 - 1.53258i) q^{2} +(-2.06336 + 2.17774i) q^{3} +(-0.697601 + 3.93870i) q^{4} +(-3.17955 + 3.17955i) q^{5} +(5.98896 + 0.363879i) q^{6} +6.03979i q^{7} +(6.93278 - 3.99206i) q^{8} +(-0.485128 - 8.98692i) q^{9} +(8.95859 + 0.787223i) q^{10} +(-13.0097 + 13.0097i) q^{11} +(-7.13808 - 9.64613i) q^{12} +(6.39520 - 6.39520i) q^{13} +(9.25646 - 7.76107i) q^{14} +(-0.363700 - 13.4848i) q^{15} +(-15.0267 - 5.49528i) q^{16} -4.39848i q^{17} +(-13.1498 + 12.2916i) q^{18} +(-3.21075 + 3.21075i) q^{19} +(-10.3052 - 14.7413i) q^{20} +(-13.1531 - 12.4622i) q^{21} +(36.6557 + 3.22107i) q^{22} +34.0396 q^{23} +(-5.61111 + 23.3349i) q^{24} +4.78097i q^{25} +(-18.0189 - 1.58339i) q^{26} +(20.5722 + 17.4867i) q^{27} +(-23.7889 - 4.21336i) q^{28} +(27.9597 + 27.9597i) q^{29} +(-20.1991 + 17.8852i) q^{30} -7.90993 q^{31} +(10.8872 + 30.0910i) q^{32} +(-1.48814 - 55.1754i) q^{33} +(-6.74102 + 5.65200i) q^{34} +(-19.2038 - 19.2038i) q^{35} +(35.7352 + 4.35851i) q^{36} +(20.0443 + 20.0443i) q^{37} +(9.04650 + 0.794947i) q^{38} +(0.731530 + 27.1227i) q^{39} +(-9.35016 + 34.7360i) q^{40} -45.1067 q^{41} +(-2.19775 + 36.1720i) q^{42} +(-36.0095 - 36.0095i) q^{43} +(-42.1657 - 60.3168i) q^{44} +(30.1168 + 27.0318i) q^{45} +(-43.7406 - 52.1684i) q^{46} +5.08935i q^{47} +(42.9727 - 21.3856i) q^{48} +12.5209 q^{49} +(7.32721 - 6.14349i) q^{50} +(9.57876 + 9.07563i) q^{51} +(20.7275 + 29.6501i) q^{52} +(20.7687 - 20.7687i) q^{53} +(0.364741 - 53.9988i) q^{54} -82.7299i q^{55} +(24.1112 + 41.8725i) q^{56} +(-0.367268 - 13.6171i) q^{57} +(6.92253 - 78.7784i) q^{58} +(-39.0656 + 39.0656i) q^{59} +(53.3662 + 7.97449i) q^{60} +(-49.8322 + 49.8322i) q^{61} +(10.1642 + 12.1226i) q^{62} +(54.2791 - 2.93007i) q^{63} +(32.1269 - 55.3522i) q^{64} +40.6677i q^{65} +(-82.6484 + 73.1805i) q^{66} +(44.9162 - 44.9162i) q^{67} +(17.3243 + 3.06838i) q^{68} +(-70.2358 + 74.1295i) q^{69} +(-4.75466 + 54.1080i) q^{70} +46.6947 q^{71} +(-39.2396 - 60.3677i) q^{72} +97.3523i q^{73} +(4.96275 - 56.4761i) q^{74} +(-10.4117 - 9.86483i) q^{75} +(-10.4063 - 14.8860i) q^{76} +(-78.5758 - 78.5758i) q^{77} +(40.6277 - 35.9735i) q^{78} -40.1637 q^{79} +(65.2506 - 30.3056i) q^{80} +(-80.5293 + 8.71960i) q^{81} +(57.9616 + 69.1296i) q^{82} +(-35.5451 - 35.5451i) q^{83} +(58.2606 - 43.1125i) q^{84} +(13.9852 + 13.9852i) q^{85} +(-8.91558 + 101.459i) q^{86} +(-118.580 + 3.19823i) q^{87} +(-38.2579 + 142.129i) q^{88} +69.6795 q^{89} +(2.72864 - 80.8920i) q^{90} +(38.6257 + 38.6257i) q^{91} +(-23.7461 + 134.072i) q^{92} +(16.3210 - 17.2258i) q^{93} +(7.79984 - 6.53977i) q^{94} -20.4174i q^{95} +(-87.9947 - 38.3789i) q^{96} +61.0939 q^{97} +(-16.0893 - 19.1893i) q^{98} +(123.228 + 110.606i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{3} + 4 q^{4} - 12 q^{6}+O(q^{10}) \) 20 * q - 6 * q^3 + 4 * q^4 - 12 * q^6	\( 20 q - 6 q^{3} + 4 q^{4} - 12 q^{6} + 32 q^{10} - 88 q^{12} + 92 q^{13} - 116 q^{15} - 16 q^{16} + 4 q^{18} - 52 q^{19} + 48 q^{21} + 24 q^{22} - 8 q^{24} + 18 q^{27} + 56 q^{28} + 28 q^{30} - 80 q^{31} + 60 q^{33} + 104 q^{34} + 92 q^{36} - 116 q^{37} + 88 q^{40} + 304 q^{42} + 172 q^{43} + 60 q^{45} - 424 q^{46} + 176 q^{48} - 364 q^{49} + 128 q^{51} - 208 q^{52} + 40 q^{54} - 512 q^{58} - 240 q^{60} - 244 q^{61} + 296 q^{63} + 88 q^{64} - 492 q^{66} + 356 q^{67} - 20 q^{69} + 200 q^{70} - 472 q^{72} - 146 q^{75} + 328 q^{76} + 84 q^{78} + 384 q^{79} - 188 q^{81} + 560 q^{82} + 816 q^{84} + 48 q^{85} + 416 q^{88} + 616 q^{90} + 136 q^{91} - 132 q^{93} + 32 q^{94} - 24 q^{96} + 472 q^{97} - 452 q^{99}+O(q^{100}) \) 20 * q - 6 * q^3 + 4 * q^4 - 12 * q^6 + 32 * q^10 - 88 * q^12 + 92 * q^13 - 116 * q^15 - 16 * q^16 + 4 * q^18 - 52 * q^19 + 48 * q^21 + 24 * q^22 - 8 * q^24 + 18 * q^27 + 56 * q^28 + 28 * q^30 - 80 * q^31 + 60 * q^33 + 104 * q^34 + 92 * q^36 - 116 * q^37 + 88 * q^40 + 304 * q^42 + 172 * q^43 + 60 * q^45 - 424 * q^46 + 176 * q^48 - 364 * q^49 + 128 * q^51 - 208 * q^52 + 40 * q^54 - 512 * q^58 - 240 * q^60 - 244 * q^61 + 296 * q^63 + 88 * q^64 - 492 * q^66 + 356 * q^67 - 20 * q^69 + 200 * q^70 - 472 * q^72 - 146 * q^75 + 328 * q^76 + 84 * q^78 + 384 * q^79 - 188 * q^81 + 560 * q^82 + 816 * q^84 + 48 * q^85 + 416 * q^88 + 616 * q^90 + 136 * q^91 - 132 * q^93 + 32 * q^94 - 24 * q^96 + 472 * q^97 - 452 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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