LMFDB - Embedded newform 28.4.f.a.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [28,4,Mod(3,28)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(28, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("28.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$28 = 2^{2} \cdot 7$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	28.f (of order $6$ , degree $2$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.65205348016$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{20} - 2 x^{18} - 24 x^{17} + 28 x^{16} + 56 x^{15} - 192 x^{14} + 352 x^{13} - 448 x^{12} + \cdots + 1073741824$ x^20 - 2x^18 - 24x^17 + 28x^16 + 56x^15 - 192x^14 + 352x^13 - 448x^12 + 5376x^11 - 41472x^10 + 43008x^9 - 28672x^8 + 180224x^7 - 786432x^6 + 1835008x^5 + 7340032x^4 - 50331648x^3 - 33554432*x^2 + 1073741824
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$2^{24}$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.4
Root			$2.82698 - 0.0903966i$ of defining polynomial
Character	$\chi$	$=$	28.19
Dual form			28.4.f.a.3.4

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49178 - 2.40304i) q^{2} +(4.65345 + 8.06002i) q^{3} +(-3.54920 + 7.16960i) q^{4} +(5.11538 + 2.95337i) q^{5} +(12.4266 - 23.2062i) q^{6} +(1.92900 - 18.4195i) q^{7} +(22.5235 - 2.16656i) q^{8} +(-29.8092 + 51.6311i) q^{9} +(-0.533949 - 16.6982i) q^{10} +(0.267527 - 0.154457i) q^{11} +(-74.3031 + 4.75675i) q^{12} -43.7232i q^{13} +(-47.1405 + 22.8424i) q^{14} +54.9734i q^{15} +(-38.8063 - 50.8927i) q^{16} +(-27.0788 + 15.6339i) q^{17} +(168.540 - 5.38931i) q^{18} +(39.7315 - 68.8169i) q^{19} +(-39.3300 + 26.1931i) q^{20} +(157.438 - 70.1666i) q^{21} +(-0.770257 - 0.412464i) q^{22} +(16.5061 + 9.52978i) q^{23} +(122.274 + 171.457i) q^{24} +(-45.0553 - 78.0380i) q^{25} +(-105.069 + 65.2253i) q^{26} -303.577 q^{27} +(125.214 + 79.2048i) q^{28} -40.1025 q^{29} +(132.103 - 82.0080i) q^{30} +(42.8504 + 74.2190i) q^{31} +(-64.4069 + 169.174i) q^{32} +(2.48985 + 1.43752i) q^{33} +(77.9645 + 41.7490i) q^{34} +(64.2672 - 88.5258i) q^{35} +(-264.375 - 396.970i) q^{36} +(72.4561 - 125.498i) q^{37} +(-224.640 + 7.18318i) q^{38} +(352.410 - 203.464i) q^{39} +(121.615 + 55.4372i) q^{40} +254.872i q^{41} +(-403.476 - 273.657i) q^{42} +366.848i q^{43} +(0.157886 + 2.46626i) q^{44} +(-304.971 + 176.075i) q^{45} +(-1.72292 - 53.8810i) q^{46} +(-5.12388 + 8.87482i) q^{47} +(229.613 - 549.606i) q^{48} +(-335.558 - 71.0625i) q^{49} +(-120.316 + 224.685i) q^{50} +(-252.020 - 145.504i) q^{51} +(313.478 + 155.183i) q^{52} +(315.245 + 546.021i) q^{53} +(452.869 + 729.508i) q^{54} +1.82467 q^{55} +(3.54064 - 419.051i) q^{56} +739.554 q^{57} +(59.8240 + 96.3679i) q^{58} +(-257.625 - 446.219i) q^{59} +(-394.137 - 195.112i) q^{60} +(-669.083 - 386.295i) q^{61} +(114.428 - 213.689i) q^{62} +(893.519 + 648.669i) q^{63} +(502.612 - 97.5970i) q^{64} +(129.131 - 223.661i) q^{65} +(-0.259893 - 8.12767i) q^{66} +(-450.318 + 259.991i) q^{67} +(-15.9810 - 249.632i) q^{68} +177.386i q^{69} +(-308.603 - 22.3758i) q^{70} +261.211i q^{71} +(-559.545 + 1227.49i) q^{72} +(588.256 - 339.630i) q^{73} +(-409.664 + 13.0996i) q^{74} +(419.325 - 726.292i) q^{75} +(352.375 + 529.104i) q^{76} +(-2.32896 - 5.22567i) q^{77} +(-1014.65 - 543.332i) q^{78} +(-299.565 - 172.954i) q^{79} +(-48.2041 - 374.945i) q^{80} +(-607.833 - 1052.80i) q^{81} +(612.467 - 380.212i) q^{82} -805.619 q^{83} +(-55.7136 + 1377.80i) q^{84} -184.691 q^{85} +(881.550 - 547.255i) q^{86} +(-186.615 - 323.227i) q^{87} +(5.69100 - 4.05852i) q^{88} +(-40.7034 - 23.5001i) q^{89} +(878.065 + 470.193i) q^{90} +(-805.361 - 84.3421i) q^{91} +(-126.908 + 84.5187i) q^{92} +(-398.804 + 690.749i) q^{93} +(28.9702 - 0.926362i) q^{94} +(406.483 - 234.683i) q^{95} +(-1663.26 + 268.121i) q^{96} +763.587i q^{97} +(329.811 + 912.369i) q^{98} +18.4170i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$20 q + 4 q^{4} - 6 q^{5} + 72 q^{8} - 56 q^{9} - 12 q^{10} - 168 q^{12} - 56 q^{14} - 104 q^{16} - 6 q^{17} + 68 q^{18} + 238 q^{21} - 184 q^{22} + 348 q^{24} - 36 q^{25} + 396 q^{26} + 448 q^{28} - 352 q^{29}+ \cdots - 4900 q^{98}+O(q^{100})$ 20 * q + 4 * q^4 - 6 * q^5 + 72 * q^8 - 56 * q^9 - 12 * q^10 - 168 * q^12 - 56 * q^14 - 104 * q^16 - 6 * q^17 + 68 * q^18 + 238 * q^21 - 184 * q^22 + 348 * q^24 - 36 * q^25 + 396 * q^26 + 448 * q^28 - 352 * q^29 + 644 * q^30 - 40 * q^32 + 30 * q^33 + 208 * q^36 + 258 * q^37 - 1620 * q^38 - 1548 * q^40 - 980 * q^42 - 1248 * q^44 - 504 * q^45 + 232 * q^46 - 644 * q^49 - 864 * q^50 + 2592 * q^52 + 570 * q^53 + 4572 * q^54 + 1904 * q^56 + 1452 * q^57 + 2244 * q^58 - 736 * q^60 + 294 * q^61 + 2560 * q^64 - 124 * q^65 - 4272 * q^66 - 6084 * q^68 - 4144 * q^70 - 4672 * q^72 + 966 * q^73 + 832 * q^74 - 378 * q^77 - 4056 * q^78 + 7032 * q^80 - 1262 * q^81 + 7692 * q^82 + 6188 * q^84 - 2980 * q^85 + 5696 * q^86 - 1396 * q^88 - 3186 * q^89 + 3312 * q^92 - 306 * q^93 - 6780 * q^94 - 11784 * q^96 - 4900 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/28\mathbb{Z}\right)^\times$ .

$n$	$15$	$17$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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

)

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

$2$	−1.49178	−	2.40304i	−0.527423	−	0.849603i
$2$	−1.49178	−	2.40304i	−0.527423	−	0.849603i
$3$	4.65345	+	8.06002i	0.895557	+	1.55115i	0.833113	+	0.553102i	$0.186556\pi$
$3$	4.65345	+	8.06002i	0.895557	+	1.55115i	0.0624441	+	0.998048i	$0.480110\pi$
$4$	−3.54920	+	7.16960i	−0.443650	+	0.896200i
$5$	5.11538	+	2.95337i	0.457533	+	0.264157i	0.711007	−	0.703185i	$-0.248240\pi$
$5$	5.11538	+	2.95337i	0.457533	+	0.264157i	−0.253473	+	0.967342i	$0.581573\pi$
$6$	12.4266	−	23.2062i	0.845525	−	1.57898i
$7$	1.92900	−	18.4195i	0.104156	−	0.994561i
$7$	1.92900	−	18.4195i	0.104156	−	0.994561i
$8$	22.5235	−	2.16656i	0.995405	−	0.0957495i
$9$	−29.8092	+	51.6311i	−1.10405	+	1.91226i
$10$	−0.533949	−	16.6982i	−0.0168849	−	0.528044i
$11$	0.267527	−	0.154457i	0.00733296	−	0.00423368i	−0.496329	−	0.868134i	$-0.665319\pi$
$11$	0.267527	−	0.154457i	0.00733296	−	0.00423368i	0.503662	+	0.863901i	$0.331986\pi$
$12$	−74.3031	+	4.75675i	−1.78746	+	0.114430i
$13$		−	43.7232i		−	0.932818i	−0.884569	−	0.466409i	$-0.845547\pi$
$13$		−	43.7232i		−	0.932818i	0.884569	−	0.466409i	$-0.154453\pi$
$14$	−47.1405	+	22.8424i	−0.899916	+	0.436063i
$15$			54.9734i			0.946271i
$16$	−38.8063	−	50.8927i	−0.606349	−	0.795199i
$17$	−27.0788	+	15.6339i	−0.386328	+	0.223046i	−0.680568	−	0.732685i	$-0.738267\pi$
$17$	−27.0788	+	15.6339i	−0.386328	+	0.223046i	0.294240	+	0.955732i	$0.404933\pi$
$18$	168.540	−	5.38931i	2.20696	−	0.0705707i
$19$	39.7315	−	68.8169i	0.479738	−	0.830930i	−0.519992	−	0.854171i	$-0.674065\pi$
$19$	39.7315	−	68.8169i	0.479738	−	0.830930i	0.999730	+	0.0232407i	$0.00739841\pi$
$20$	−39.3300	+	26.1931i	−0.439722	+	0.292848i
$21$	157.438	−	70.1666i	1.63599	−	0.729124i
$22$	−0.770257	−	0.412464i	−0.00746452	−	0.00399716i
$23$	16.5061	+	9.52978i	0.149641	+	0.0863955i	0.572951	−	0.819590i	$-0.305798\pi$
$23$	16.5061	+	9.52978i	0.149641	+	0.0863955i	−0.423310	+	0.905985i	$0.639132\pi$
$24$	122.274	+	171.457i	1.03996	+	1.45827i
$25$	−45.0553	−	78.0380i	−0.360442	−	0.624304i
$26$	−105.069	+	65.2253i	−0.792525	+	0.491990i
$27$	−303.577			−2.16383
$28$	125.214	+	79.2048i	0.845117	+	0.534582i
$29$	−40.1025			−0.256788			−0.128394	−	0.991723i	$-0.540982\pi$
$29$	−40.1025			−0.256788			−0.128394	+	0.991723i	$0.540982\pi$
$30$	132.103	−	82.0080i	0.803955	−	0.499085i
$31$	42.8504	+	74.2190i	0.248263	+	0.430004i	0.963044	−	0.269344i	$-0.0868069\pi$
$31$	42.8504	+	74.2190i	0.248263	+	0.430004i	−0.714781	+	0.699348i	$0.753474\pi$
$32$	−64.4069	+	169.174i	−0.355801	+	0.934562i
$33$	2.48985	+	1.43752i	0.0131342	+	0.00758302i
$34$	77.9645	+	41.7490i	0.393259	+	0.210585i
$35$	64.2672	−	88.5258i	0.310375	−	0.427531i
$36$	−264.375	−	396.970i	−1.22396	−	1.83782i
$37$	72.4561	−	125.498i	0.321938	−	0.557613i	−0.658950	−	0.752187i	$-0.728999\pi$
$37$	72.4561	−	125.498i	0.321938	−	0.557613i	0.980888	+	0.194574i	$0.0623323\pi$
$38$	−224.640	+	7.18318i	−0.958986	+	0.0306649i
$39$	352.410	−	203.464i	1.44694	−	0.835392i
$40$	121.615	+	55.4372i	0.480724	+	0.219135i
$41$			254.872i			0.970837i	0.874282	+	0.485418i	$0.161333\pi$
$41$			254.872i			0.970837i	−0.874282	+	0.485418i	$0.838667\pi$
$42$	−403.476	−	273.657i	−1.48233	−	1.00539i
$43$			366.848i			1.30102i	0.759499	+	0.650509i	$0.225444\pi$
$43$			366.848i			1.30102i	−0.759499	+	0.650509i	$0.774556\pi$
$44$	0.157886	+	2.46626i	0.000540958	+	0.00845007i
$45$	−304.971	+	176.075i	−1.01028	+	0.583283i
$46$	−1.72292	−	53.8810i	−0.00552241	−	0.172703i
$47$	−5.12388	+	8.87482i	−0.0159020	+	0.0275431i	−0.873867	−	0.486165i	$-0.838395\pi$
$47$	−5.12388	+	8.87482i	−0.0159020	+	0.0275431i	0.857965	+	0.513708i	$0.171729\pi$
$48$	229.613	−	549.606i	0.690454	−	1.65268i
$49$	−335.558	−	71.0625i	−0.978303	−	0.207179i
$50$	−120.316	+	224.685i	−0.340305	+	0.635505i
$51$	−252.020	−	145.504i	−0.691957	−	0.399502i
$52$	313.478	+	155.183i	0.835992	+	0.413845i
$53$	315.245	+	546.021i	0.817024	+	1.41513i	0.907865	+	0.419262i	$0.137711\pi$
$53$	315.245	+	546.021i	0.817024	+	1.41513i	−0.0908416	+	0.995865i	$0.528956\pi$
$54$	452.869	+	729.508i	1.14125	+	1.83840i
$55$	1.82467			0.00447343
$56$	3.54064	−	419.051i	0.00844889	−	0.999964i
$57$	739.554			1.71853
$58$	59.8240	+	96.3679i	0.135436	+	0.218168i
$59$	−257.625	−	446.219i	−0.568473	−	0.984624i	−0.996717	−	0.0809610i	$-0.974201\pi$
$59$	−257.625	−	446.219i	−0.568473	−	0.984624i	0.428244	−	0.903663i	$-0.359132\pi$
$60$	−394.137	−	195.112i	−0.848048	−	0.419814i
$61$	−669.083	−	386.295i	−1.40438	−	0.810820i	−0.409543	−	0.912291i	$-0.634312\pi$
$61$	−669.083	−	386.295i	−1.40438	−	0.810820i	−0.994839	+	0.101470i	$0.967645\pi$
$62$	114.428	−	213.689i	0.234393	−	0.437719i
$63$	893.519	+	648.669i	1.78687	+	1.29722i
$64$	502.612	−	97.5970i	0.981664	−	0.190619i
$65$	129.131	−	223.661i	0.246411	−	0.426796i
$66$	−0.259893	−	8.12767i	−0.000484707	−	0.0151583i
$67$	−450.318	+	259.991i	−0.821121	+	0.474074i	−0.850803	−	0.525485i	$-0.823884\pi$
$67$	−450.318	+	259.991i	−0.821121	+	0.474074i	0.0296822	+	0.999559i	$0.490550\pi$
$68$	−15.9810	−	249.632i	−0.0284997	−	0.445181i
$69$			177.386i			0.309489i
$70$	−308.603	−	22.3758i	−0.526931	−	0.0382060i
$71$			261.211i			0.436621i	0.975879	+	0.218310i	$0.0700545\pi$
$71$			261.211i			0.436621i	−0.975879	+	0.218310i	$0.929945\pi$
$72$	−559.545	+	1227.49i	−0.915875	+	2.00919i
$73$	588.256	−	339.630i	0.943154	−	0.544530i	0.0522061	−	0.998636i	$-0.483375\pi$
$73$	588.256	−	339.630i	0.943154	−	0.544530i	0.890947	+	0.454106i	$0.150041\pi$
$74$	−409.664	+	13.0996i	−0.643547	+	0.0205783i
$75$	419.325	−	726.292i	0.645593	−	1.11820i
$76$	352.375	+	529.104i	0.531844	+	0.798584i
$77$	−2.32896	−	5.22567i	−0.00344688	−	0.00773404i
$78$	−1014.65	−	543.332i	−1.47290	−	0.788721i
$79$	−299.565	−	172.954i	−0.426629	−	0.246314i	0.271280	−	0.962500i	$-0.412553\pi$
$79$	−299.565	−	172.954i	−0.426629	−	0.246314i	−0.697909	+	0.716186i	$0.745886\pi$
$80$	−48.2041	−	374.945i	−0.0673673	−	0.524001i
$81$	−607.833	−	1052.80i	−0.833789	−	1.44417i
$82$	612.467	−	380.212i	0.824826	−	0.512041i
$83$	−805.619			−1.06540			−0.532700	−	0.846304i	$-0.678823\pi$
$83$	−805.619			−1.06540			−0.532700	+	0.846304i	$0.678823\pi$
$84$	−55.7136	+	1377.80i	−0.0723672	+	1.78965i
$85$	−184.691			−0.235677
$86$	881.550	−	547.255i	1.10535	−	0.686186i
$87$	−186.615	−	323.227i	−0.229968	−	0.398317i
$88$	5.69100	−	4.05852i	0.00689389	−	0.00491636i
$89$	−40.7034	−	23.5001i	−0.0484782	−	0.0279889i	0.475565	−	0.879681i	$-0.342244\pi$
$89$	−40.7034	−	23.5001i	−0.0484782	−	0.0279889i	−0.524043	+	0.851692i	$0.675577\pi$
$90$	878.065	+	470.193i	1.02840	+	0.550697i
$91$	−805.361	−	84.3421i	−0.927745	−	0.0971588i
$92$	−126.908	+	84.5187i	−0.143816	+	0.0957792i
$93$	−398.804	+	690.749i	−0.444668	+	0.770187i
$94$	28.9702	−	0.926362i	0.0317878	−	0.00101646i
$95$	406.483	−	234.683i	0.438992	−	0.253452i
$96$	−1663.26	+	268.121i	−1.76829	+	0.285052i
$97$			763.587i			0.799283i	0.916671	+	0.399642i	$0.130865\pi$
$97$			763.587i			0.799283i	−0.916671	+	0.399642i	$0.869135\pi$
$98$	329.811	+	912.369i	0.339959	+	0.940440i
$99$			18.4170i			0.0186967i
$100$	719.412	−	46.0554i	0.719412	−	0.0460554i
$101$	669.771	−	386.693i	0.659849	−	0.380964i	−0.132371	−	0.991200i	$-0.542259\pi$
$101$	669.771	−	386.693i	0.659849	−	0.380964i	0.792219	+	0.610236i	$0.208926\pi$
$102$	26.3061	+	822.672i	0.0255362	+	0.798595i
$103$	−142.848	+	247.420i	−0.136653	+	0.236690i	−0.926228	−	0.376965i	$-0.876968\pi$
$103$	−142.848	+	247.420i	−0.136653	+	0.236690i	0.789575	+	0.613654i	$0.210301\pi$
$104$	−94.7292	−	984.798i	−0.0893169	−	0.928532i
$105$	1012.58	+	106.044i	0.941124	+	0.0985600i
$106$	841.834	−	1572.09i	0.771379	−	1.44052i
$107$	1836.21	+	1060.14i	1.65900	+	0.957827i	0.973175	+	0.230065i	$0.0738938\pi$
$107$	1836.21	+	1060.14i	1.65900	+	0.957827i	0.685830	+	0.727762i	$0.259439\pi$
$108$	1077.46	−	2176.53i	0.959985	−	1.93923i
$109$	−420.749	−	728.759i	−0.369729	−	0.640389i	0.619794	−	0.784764i	$-0.287216\pi$
$109$	−420.749	−	728.759i	−0.369729	−	0.640389i	−0.989523	+	0.144375i	$0.953883\pi$
$110$	−2.72200	−	4.38476i	−0.00235939	−	0.00380064i
$111$	1348.68			1.15326
$112$	−1012.28	+	616.622i	−0.854029	+	0.520226i
$113$	−777.276			−0.647079			−0.323540	−	0.946215i	$-0.604873\pi$
$113$	−777.276			−0.647079			−0.323540	+	0.946215i	$0.604873\pi$
$114$	−1103.25	−	1777.18i	−0.906393	−	1.46007i
$115$	56.2899	+	97.4969i	0.0456440	+	0.0790577i
$116$	142.332	−	287.519i	0.113924	−	0.230133i
$117$	2257.48	+	1303.36i	1.78379	+	1.02987i
$118$	−687.964	+	1284.74i	−0.536714	+	1.00229i
$119$	235.735	+	528.936i	0.181595	+	0.407458i
$120$	119.103	+	1238.19i	0.0906050	+	0.941924i
$121$	−665.452	+	1152.60i	−0.499964	+	0.865963i
$122$	69.8396	+	2184.10i	0.0518277	+	1.62081i
$123$	−2054.27	+	1186.03i	−1.50591	+	0.869440i
$124$	−684.205	+	43.8016i	−0.495512	+	0.0317218i
$125$		−	1270.60i		−	0.909167i
$126$	225.846	−	3114.83i	0.159682	−	2.20231i
$127$		−	430.270i		−	0.300633i	−0.988638	−	0.150316i	$-0.951971\pi$
$127$		−	430.270i		−	0.300633i	0.988638	−	0.150316i	$-0.0480292\pi$
$128$	−984.315	−	1062.20i	−0.679703	−	0.733488i
$129$	−2956.80	+	1707.11i	−2.01807	+	1.16514i
$130$	−730.100	+	23.3459i	−0.492569	+	0.0157506i
$131$	819.641	−	1419.66i	0.546659	−	0.946842i	−0.451841	−	0.892098i	$-0.649233\pi$
$131$	819.641	−	1419.66i	0.546659	−	0.946842i	0.998500	−	0.0547434i	$-0.0174341\pi$
$132$	−19.1434	+	12.7492i	−0.0126229	+	0.00840663i
$133$	−1190.93	−	864.582i	−0.776443	−	0.563675i
$134$	1296.54	+	694.283i	0.835852	+	0.447589i
$135$	−1552.91	−	896.574i	−0.990025	−	0.571591i
$136$	−576.036	+	410.798i	−0.363196	+	0.259012i
$137$	896.630	+	1553.01i	0.559155	+	0.968485i	0.997567	+	0.0697109i	$0.0222077\pi$
$137$	896.630	+	1553.01i	0.559155	+	0.968485i	−0.438412	+	0.898774i	$0.644459\pi$
$138$	426.265	−	264.620i	0.262942	−	0.163231i
$139$	678.322			0.413918			0.206959	−	0.978350i	$-0.433643\pi$
$139$	678.322			0.413918			0.206959	+	0.978350i	$0.433643\pi$
$140$	406.597	+	774.966i	0.245455	+	0.467833i
$141$	−95.3749			−0.0569646
$142$	627.701	−	389.669i	0.370954	−	0.230284i
$143$	−6.75336	−	11.6972i	−0.00394926	−	0.00684032i
$144$	3784.44	−	486.540i	2.19007	−	0.281562i
$145$	−205.139	−	118.437i	−0.117489	−	0.0678323i
$146$	−1693.69	−	906.952i	−0.960075	−	0.514109i
$147$	−988.738	−	3035.29i	−0.554760	−	1.70304i
$148$	642.607	+	964.898i	0.356905	+	0.535906i
$149$	705.522	−	1222.00i	0.387910	−	0.671881i	−0.604258	−	0.796789i	$-0.706530\pi$
$149$	705.522	−	1222.00i	0.387910	−	0.671881i	0.992168	+	0.124908i	$0.0398637\pi$
$150$	−2370.85	+	75.8111i	−1.29053	+	0.0412664i
$151$	2099.21	−	1211.98i	1.13133	−	0.653176i	0.187063	−	0.982348i	$-0.440103\pi$
$151$	2099.21	−	1211.98i	1.13133	−	0.653176i	0.944270	+	0.329172i	$0.106770\pi$
$152$	745.793	−	1636.07i	0.397973	−	0.873047i
$153$		−	1864.14i		−	0.985014i
$154$	−9.08321	+	13.3921i	−0.00475290	+	0.00700759i
$155$			506.211i			0.262322i
$156$	207.981	+	3248.77i	0.106742	+	1.66737i
$157$	2650.40	−	1530.21i	1.34729	−	0.777859i	0.359426	−	0.933174i	$-0.382973\pi$
$157$	2650.40	−	1530.21i	1.34729	−	0.777859i	0.987865	+	0.155315i	$0.0496393\pi$
$158$	31.2689	+	977.875i	0.0157444	+	0.492377i
$159$	−2933.96	+	5081.76i	−1.46338	+	2.53465i
$160$	−829.098	+	675.171i	−0.409662	+	0.333606i
$161$	207.374	−	285.651i	0.101512	−	0.139829i
$162$	−1623.16	+	3031.18i	−0.787208	+	1.47008i
$163$	786.587	+	454.136i	0.377977	+	0.218225i	0.676938	−	0.736040i	$-0.263307\pi$
$163$	786.587	+	454.136i	0.377977	+	0.218225i	−0.298961	+	0.954265i	$0.596640\pi$
$164$	−1827.33	−	904.592i	−0.870064	−	0.430712i
$165$	8.49102	+	14.7069i	0.00400621	+	0.00693897i
$166$	1201.80	+	1935.94i	0.561916	+	0.905167i
$167$	−1203.87			−0.557832			−0.278916	−	0.960315i	$-0.589975\pi$
$167$	−1203.87			−0.557832			−0.278916	+	0.960315i	$0.589975\pi$
$168$	3394.03	−	1921.49i	1.55866	−	0.882420i
$169$	285.280			0.129850
$170$	275.518	+	443.820i	0.124301	+	0.200232i
$171$	2368.73	+	4102.76i	1.05931	+	1.83477i
$172$	−2630.15	−	1302.02i	−1.16597	−	0.577197i
$173$	−1045.55	−	603.648i	−0.459489	−	0.265286i	0.252340	−	0.967639i	$-0.418800\pi$
$173$	−1045.55	−	603.648i	−0.459489	−	0.265286i	−0.711829	+	0.702352i	$0.752133\pi$
$174$	−498.339	+	930.626i	−0.217121	+	0.405463i
$175$	−1524.33	+	679.361i	−0.658451	+	0.293457i
$176$	−18.2425	−	7.62129i	−0.00781295	−	0.00326407i
$177$	2397.69	−	4152.92i	1.01820	−	1.76357i
$178$	4.24867	+	132.869i	0.00178905	+	0.0559492i
$179$	1322.15	−	763.342i	0.552078	−	0.318742i	−0.197882	−	0.980226i	$-0.563406\pi$
$179$	1322.15	−	763.342i	0.552078	−	0.318742i	0.749960	+	0.661484i	$0.230073\pi$
$180$	−179.984	−	2811.45i	−0.0745289	−	1.16418i
$181$			987.406i			0.405488i	0.979232	+	0.202744i	$0.0649859\pi$
$181$			987.406i			0.405488i	−0.979232	+	0.202744i	$0.935014\pi$
$182$	998.741	+	2061.13i	0.406767	+	0.839458i
$183$		−	7190.43i		−	2.90454i
$184$	392.420	+	178.882i	0.157226	+	0.0716705i
$185$	741.281	−	427.979i	0.294595	−	0.170084i
$186$	2254.83	−	72.1011i	0.888881	−	0.0284232i
$187$	−4.82954	+	8.36501i	−0.00188862	+	0.00327118i
$188$	−45.4432	−	68.2347i	−0.0176292	−	0.0264709i
$189$	−585.600	+	5591.75i	−0.225376	+	2.15206i
$190$	−1170.33	−	626.700i	−0.446868	−	0.239293i
$191$	−3398.70	−	1962.24i	−1.28755	−	0.743366i	−0.309331	−	0.950954i	$-0.600105\pi$
$191$	−3398.70	−	1962.24i	−1.28755	−	0.743366i	−0.978216	+	0.207589i	$0.933438\pi$
$192$	3125.51	+	3596.90i	1.17482	+	1.35200i
$193$	1857.81	+	3217.81i	0.692890	+	1.20012i	0.970887	+	0.239539i	$0.0769963\pi$
$193$	1857.81	+	3217.81i	0.692890	+	1.20012i	−0.277997	+	0.960582i	$0.589670\pi$
$194$	1834.93	−	1139.10i	0.679073	−	0.421560i
$195$	2403.61			0.882699
$196$	1700.45	−	2153.60i	0.619699	−	0.784840i
$197$	−4711.80			−1.70407			−0.852035	−	0.523485i	$-0.824632\pi$
$197$	−4711.80			−1.70407			−0.852035	+	0.523485i	$0.824632\pi$
$198$	44.2567	−	27.4740i	0.0158848	−	0.00986108i
$199$	4.60370	+	7.97385i	0.00163994	+	0.00284046i	0.866844	−	0.498579i	$-0.166145\pi$
$199$	4.60370	+	7.97385i	0.00163994	+	0.00284046i	−0.865204	+	0.501420i	$0.832811\pi$
$200$	−1183.87	−	1660.07i	−0.418563	−	0.586923i
$201$	−4191.07	−	2419.71i	−1.47072	−	0.849121i
$202$	−1928.39	−	1032.63i	−0.671687	−	0.359680i
$203$	−77.3577	+	738.669i	−0.0267460	+	0.255391i
$204$	1937.67	−	1290.46i	0.665020	−	0.442893i
$205$	−752.730	+	1303.77i	−0.256453	+	0.444190i
$206$	807.658	−	25.8260i	0.273166	−	0.00873486i
$207$	−984.067	+	568.151i	−0.330422	+	0.190769i
$208$	−2225.19	+	1696.74i	−0.741776	+	0.565613i
$209$		−	24.5472i		−	0.00812424i
$210$	−1255.72	−	2591.47i	−0.412634	−	0.851565i
$211$			682.060i			0.222535i	0.993790	+	0.111268i	$0.0354911\pi$
$211$			682.060i			0.222535i	−0.993790	+	0.111268i	$0.964509\pi$
$212$	−5033.62	+	322.243i	−1.63071	+	0.104395i
$213$	−2105.37	+	1215.53i	−0.677265	+	0.391019i
$214$	−191.666	−	5993.99i	−0.0612244	−	1.91468i
$215$	−1083.44	+	1876.57i	−0.343673	+	0.595259i
$216$	−6837.61	+	657.719i	−2.15389	+	0.207186i
$217$	1449.74	−	646.115i	0.453524	−	0.202125i
$218$	−1123.57	+	2098.22i	−0.349073	+	0.651879i
$219$	5474.85	+	3160.90i	1.68930	+	0.975316i
$220$	−6.47613	+	13.0822i	−0.00198464	+	0.00400909i
$221$	683.566	+	1183.97i	0.208062	+	0.360374i
$222$	−2011.94	−	3240.94i	−0.608254	−	0.979810i
$223$	3872.62			1.16292			0.581458	−	0.813577i	$-0.302483\pi$
$223$	3872.62			1.16292			0.581458	+	0.813577i	$0.302483\pi$
$224$	2991.86	+	1512.68i	0.892420	+	0.451206i
$225$	5372.25			1.59178
$226$	1159.52	+	1867.82i	0.341284	+	0.549760i
$227$	−1643.55	−	2846.72i	−0.480558	−	0.832350i	0.519194	−	0.854657i	$-0.326232\pi$
$227$	−1643.55	−	2846.72i	−0.480558	−	0.832350i	−0.999751	+	0.0223066i	$0.992899\pi$
$228$	−2624.83	+	5302.30i	−0.762427	+	1.54015i
$229$	2441.03	+	1409.33i	0.704402	+	0.406687i	0.808985	−	0.587829i	$-0.200017\pi$
$229$	2441.03	+	1409.33i	0.704402	+	0.406687i	−0.104583	+	0.994516i	$0.533351\pi$
$230$	150.317	−	280.710i	0.0430940	−	0.0804761i
$231$	31.2813	−	43.0889i	0.00890978	−	0.0122729i
$232$	−903.247	+	86.8846i	−0.255608	+	0.0245873i
$233$	−2901.81	+	5026.08i	−0.815896	+	1.41317i	0.0927866	+	0.995686i	$0.470423\pi$
$233$	−2901.81	+	5026.08i	−0.815896	+	1.41317i	−0.908683	+	0.417487i	$0.862911\pi$
$234$	−235.638	−	7369.13i	−0.0658296	−	2.05870i
$235$	−52.4211	+	30.2654i	−0.0145514	+	0.00840125i
$236$	4113.58	−	263.344i	1.13462	−	0.0726365i
$237$		−	3219.33i		−	0.882355i
$238$	919.391	−	1355.54i	0.250400	−	0.369186i
$239$			5958.79i			1.61273i	0.591419	+	0.806364i	$0.298568\pi$
$239$			5958.79i			1.61273i	−0.591419	+	0.806364i	$0.701432\pi$
$240$	2797.75	−	2133.31i	0.752474	−	0.573770i
$241$	1833.99	−	1058.85i	0.490197	−	0.283016i	−0.234459	−	0.972126i	$-0.575332\pi$
$241$	1833.99	−	1058.85i	0.490197	−	0.283016i	0.724656	+	0.689110i	$0.241999\pi$
$242$	3762.44	−	120.309i	0.999417	−	0.0319577i
$243$	1558.75	−	2699.83i	0.411497	−	0.712733i
$244$	5144.29	−	3426.02i	1.34971	−	0.898886i
$245$	−1506.63	−	1354.54i	−0.392878	−	0.353217i
$246$	5914.60	+	3167.20i	1.53293	+	0.820867i
$247$	−3008.90	−	1737.19i	−0.775107	−	0.447508i
$248$	1125.94	+	1578.83i	0.288295	+	0.404257i
$249$	−3748.91	−	6493.30i	−0.954127	−	1.65260i
$250$	−3053.30	+	1895.45i	−0.772431	+	0.479516i
$251$	−1950.88			−0.490591			−0.245296	−	0.969448i	$-0.578885\pi$
$251$	−1950.88			−0.490591			−0.245296	+	0.969448i	$0.578885\pi$
$252$	−7821.97	+	4103.92i	−1.95531	+	1.02588i
$253$	5.88776			0.00146309
$254$	−1033.96	+	641.868i	−0.255418	+	0.158560i
$255$	−859.451	−	1488.61i	−0.211062	−	0.365571i
$256$	−1084.14	+	3949.92i	−0.264683	+	0.964336i
$257$	5952.48	+	3436.67i	1.44477	+	0.834138i	0.998163	−	0.0605927i	$-0.0192991\pi$
$257$	5952.48	+	3436.67i	1.44477	+	0.834138i	0.446606	+	0.894731i	$0.352632\pi$
$258$	8513.13	+	4558.68i	2.05428	+	1.10004i
$259$	−2171.84	−	1576.69i	−0.521049	−	0.378266i
$260$	1145.25	+	1719.63i	0.273174	+	0.410181i
$261$	1195.42	−	2070.54i	0.283506	−	0.491046i
$262$	−4634.22	+	148.186i	−1.09276	+	0.0349425i
$263$	−1940.20	+	1120.18i	−0.454897	+	0.262635i	−0.709896	−	0.704306i	$-0.751258\pi$
$263$	−1940.20	+	1120.18i	−0.454897	+	0.262635i	0.254999	+	0.966941i	$0.417925\pi$
$264$	59.1945	+	26.9834i	0.0137999	+	0.00629058i
$265$			3724.14i			0.863290i
$266$	−301.020	+	4151.62i	−0.0693862	+	0.956964i
$267$		−	437.427i		−	0.100263i
$268$	−265.763	−	4151.36i	−0.0605747	−	0.946211i
$269$	244.551	−	141.192i	0.0554295	−	0.0320023i	−0.472029	−	0.881583i	$-0.656478\pi$
$269$	244.551	−	141.192i	0.0554295	−	0.0320023i	0.527459	+	0.849581i	$0.323145\pi$
$270$	162.095	+	5069.20i	0.0365362	+	1.14260i
$271$	2104.49	−	3645.09i	0.471730	−	0.817061i	−0.527746	−	0.849402i	$-0.676963\pi$
$271$	2104.49	−	3645.09i	0.471730	−	0.817061i	0.999477	+	0.0323409i	$0.0102962\pi$
$272$	1846.48	+	771.418i	0.411615	+	0.171963i
$273$	−3067.91	−	6883.70i	−0.680141	−	1.52608i
$274$	2394.37	−	4471.38i	0.527917	−	0.985861i
$275$	−24.1070	−	13.9182i	−0.00528621	−	0.00305200i
$276$	−1271.78	−	629.577i	−0.277364	−	0.137305i
$277$	−1317.55	−	2282.06i	−0.285790	−	0.495003i	0.687010	−	0.726648i	$-0.258923\pi$
$277$	−1317.55	−	2282.06i	−0.285790	−	0.495003i	−0.972801	+	0.231644i	$0.925589\pi$
$278$	−1011.91	−	1630.04i	−0.218310	−	0.351666i
$279$	−5109.35			−1.09638
$280$	1255.72	−	2133.15i	0.268013	−	0.455285i
$281$	−2512.44			−0.533380			−0.266690	−	0.963782i	$-0.585930\pi$
$281$	−2512.44			−0.533380			−0.266690	+	0.963782i	$0.585930\pi$
$282$	142.278	+	229.190i	0.0300444	+	0.0483973i
$283$	1163.88	+	2015.89i	0.244471	+	0.423436i	0.961983	−	0.273110i	$-0.0880523\pi$
$283$	1163.88	+	2015.89i	0.244471	+	0.423436i	−0.717512	+	0.696546i	$0.754719\pi$
$284$	−1872.78	−	927.092i	−0.391299	−	0.193707i
$285$	3783.10	+	2184.17i	0.786286	+	0.453962i
$286$	−18.0342	+	33.6781i	−0.00372862	+	0.00696304i
$287$	4694.62	+	491.648i	0.965556	+	0.101119i
$288$	−6814.71	−	8368.34i	−1.39431	−	1.71219i
$289$	−1967.66	+	3408.09i	−0.400501	+	0.693687i
$290$	21.4127	+	669.640i	0.00433585	+	0.135595i
$291$	−6154.52	+	3553.31i	−1.23981	+	0.715804i
$292$	347.169	+	5422.98i	0.0695772	+	1.08684i
$293$		−	5654.92i		−	1.12752i	−0.825938	−	0.563761i	$-0.809354\pi$
$293$		−	5654.92i		−	1.12752i	0.825938	−	0.563761i	$-0.190646\pi$
$294$	−5818.94	+	6903.95i	−1.15431	+	1.36955i
$295$		−	3043.44i		−	0.600665i
$296$	1360.06	−	2983.62i	0.267068	−	0.585877i
$297$	−81.2152	+	46.8896i	−0.0158673	+	0.00916098i
$298$	−3989.00	+	127.554i	−0.775424	+	0.0247953i
$299$	416.673	−	721.698i	0.0805913	−	0.139588i
$300$	3718.95	+	5584.15i	0.715713	+	1.07467i
$301$	6757.16	+	707.649i	1.29394	+	0.135509i
$302$	−6043.99	−	3236.48i	−1.15163	−	0.616684i
$303$	6233.50	+	3598.91i	1.18186	+	0.682350i
$304$	−5044.11	+	648.487i	−0.951643	+	0.122346i
$305$	−2281.74	−	3952.09i	−0.428368	−	0.741955i
$306$	−4479.61	+	2780.89i	−0.836871	+	0.519519i
$307$	3797.48			0.705972			0.352986	−	0.935629i	$-0.385166\pi$
$307$	3797.48			0.705972			0.352986	+	0.935629i	$0.385166\pi$
$308$	45.7320	+	1.84924i	0.00846046	+	0.000342111i
$309$	−2658.95			−0.489522
$310$	1216.45	−	755.154i	0.222869	−	0.138354i
$311$	−2871.82	−	4974.14i	−0.523621	−	0.906938i	−0.999622	−	0.0274932i	$-0.991248\pi$
$311$	−2871.82	−	4974.14i	−0.523621	−	0.906938i	0.476001	−	0.879445i	$-0.342086\pi$
$312$	7496.67	−	5346.23i	1.36031	−	0.970098i
$313$	−5410.52	−	3123.77i	−0.977063	−	0.564108i	−0.0756809	−	0.997132i	$-0.524113\pi$
$313$	−5410.52	−	3123.77i	−0.977063	−	0.564108i	−0.901382	+	0.433024i	$0.857446\pi$
$314$	−7630.95	−	4086.28i	−1.37146	−	0.734402i
$315$	2654.93	+	5957.07i	0.474884	+	1.06553i
$316$	2303.23	−	1533.91i	0.410021	−	0.273067i
$317$	2312.90	−	4006.06i	0.409796	−	0.709788i	−0.585070	−	0.810983i	$-0.698933\pi$
$317$	2312.90	−	4006.06i	0.409796	−	0.709788i	0.994867	+	0.101194i	$0.0322664\pi$
$318$	16588.5	−	530.440i	2.92527	−	0.0935396i
$319$	−10.7285	+	6.19411i	−0.00188301	+	0.00108716i
$320$	2859.29	+	985.151i	0.499498	+	0.172099i
$321$			19733.2i			3.43116i
$322$	−995.787	−	72.2011i	−0.172339	−	0.0124957i
$323$			2484.64i			0.428015i
$324$	9705.45	−	621.326i	1.66417	−	0.106537i
$325$	−3412.07	+	1969.96i	−0.582362	+	0.336227i
$326$	−82.1047	−	2567.67i	−0.0139490	−	0.436227i
$327$	3915.87	−	6782.49i	0.662227	−	1.14701i
$328$	552.196	+	5740.60i	0.0929572	+	0.966376i
$329$	153.586	+	111.499i	0.0257370	+	0.0186843i
$330$	22.6745	−	42.3437i	0.00378240	−	0.00706346i
$331$	−5659.87	−	3267.73i	−0.939863	−	0.542630i	−0.0499455	−	0.998752i	$-0.515905\pi$
$331$	−5659.87	−	3267.73i	−0.939863	−	0.542630i	−0.889917	+	0.456122i	$0.849238\pi$
$332$	2859.31	−	5775.97i	0.472665	−	0.954811i
$333$	4319.72	+	7481.98i	0.710869	+	1.23126i
$334$	1795.90	+	2892.94i	0.294214	+	0.473936i
$335$	−3071.40			−0.500920
$336$	−9680.57	−	5289.55i	−1.57178	−	0.858836i
$337$	4777.67			0.772274			0.386137	−	0.922441i	$-0.373809\pi$
$337$	4777.67			0.772274			0.386137	+	0.922441i	$0.373809\pi$
$338$	−425.575	−	685.540i	−0.0684858	−	0.110321i
$339$	−3617.02	−	6264.86i	−0.579497	−	1.00372i
$340$	655.506	−	1324.16i	0.104558	−	0.211214i
$341$	22.9273	+	13.2371i	0.00364100	+	0.00210213i
$342$	6325.48	−	11812.6i	1.00013	−	1.86769i
$343$	−1956.23	+	6043.74i	−0.307949	+	0.951403i
$344$	794.799	+	8262.68i	0.124572	+	1.29504i
$345$	−523.884	+	907.394i	−0.0817536	+	0.141601i
$346$	109.135	+	3413.00i	0.0169571	+	0.530301i
$347$	7967.85	−	4600.24i	1.23267	−	0.711683i	0.265085	−	0.964225i	$-0.414600\pi$
$347$	7967.85	−	4600.24i	1.23267	−	0.711683i	0.967586	+	0.252543i	$0.0812668\pi$
$348$	2979.74	−	190.758i	0.458997	−	0.0293841i
$349$		−	6940.92i		−	1.06458i	−0.846562	−	0.532290i	$-0.821331\pi$
$349$		−	6940.92i		−	1.06458i	0.846562	−	0.532290i	$-0.178669\pi$
$350$	3906.50	+	2649.58i	0.596603	+	0.404646i
$351$			13273.4i			2.01846i
$352$	8.89945	+	55.2067i	0.00134756	+	0.00835945i
$353$	1364.81	−	787.975i	0.205784	−	0.118809i	−0.393567	−	0.919296i	$-0.628759\pi$
$353$	1364.81	−	787.975i	0.205784	−	0.118809i	0.599350	+	0.800487i	$0.295426\pi$
$354$	−13556.5	+	433.486i	−2.03536	+	0.0650834i
$355$	−771.452	+	1336.19i	−0.115336	+	0.199769i
$356$	312.951	−	208.421i	0.0465910	−	0.0310288i
$357$	−3166.25	+	4361.41i	−0.469400	+	0.646583i
$358$	−3806.69	−	2038.44i	−0.561983	−	0.300935i
$359$	6550.62	+	3782.00i	0.963031	+	0.556006i	0.897105	−	0.441818i	$-0.145666\pi$
$359$	6550.62	+	3782.00i	0.963031	+	0.556006i	0.0659267	+	0.997824i	$0.479000\pi$
$360$	−6487.53	+	4626.56i	−0.949785	+	0.677337i
$361$	272.323	+	471.678i	0.0397031	+	0.0687677i
$362$	2372.78	−	1472.99i	0.344504	−	0.213864i
$363$	−12386.6			−1.79099
$364$	3463.09	−	5474.77i	0.498668	−	0.788340i
$365$	4012.21			0.575366
$366$	−17278.9	+	10726.5i	−2.46771	+	1.53192i
$367$	5910.14	+	10236.7i	0.840618	+	1.45599i	0.889373	+	0.457183i	$0.151142\pi$
$367$	5910.14	+	10236.7i	0.840618	+	1.45599i	−0.0487544	+	0.998811i	$0.515525\pi$
$368$	−155.543	−	1209.85i	−0.0220332	−	0.171380i
$369$	−13159.3	−	7597.54i	−1.85650	−	1.07185i
$370$	−2134.28	−	1142.88i	−0.299880	−	0.160582i
$371$	10665.6	−	4753.39i	1.49253	−	0.665186i
$372$	−3536.96	−	5310.88i	−0.492964	−	0.740205i
$373$	−1725.59	+	2988.81i	−0.239538	+	0.414892i	−0.960582	−	0.277997i	$-0.910329\pi$
$373$	−1725.59	+	2988.81i	−0.239538	+	0.414892i	0.721044	+	0.692890i	$0.243663\pi$
$374$	27.3061	−	0.873149i	0.00377530	−	0.000120720i
$375$	10241.1	−	5912.68i	1.41026	−	0.814212i
$376$	−96.1796	+	210.993i	−0.0131917	+	0.0289391i
$377$			1753.41i			0.239536i
$378$	14310.8	−	6934.42i	1.94727	−	0.943566i
$379$		−	363.409i		−	0.0492535i	−0.999697	−	0.0246267i	$-0.992160\pi$
$379$		−	363.409i		−	0.0492535i	0.999697	−	0.0246267i	$-0.00783973\pi$
$380$	239.893	+	3747.26i	0.0323848	+	0.505869i
$381$	3467.99	−	2002.24i	0.466326	−	0.269234i
$382$	354.760	+	11094.4i	0.0475160	+	1.48597i
$383$	−755.287	+	1308.20i	−0.100766	+	0.174532i	−0.912000	−	0.410189i	$-0.865463\pi$
$383$	−755.287	+	1308.20i	−0.100766	+	0.174532i	0.811234	+	0.584721i	$0.198796\pi$
$384$	3980.92	−	12876.5i	0.529038	−	1.71120i
$385$	3.51979	−	33.6096i	0.000465935	−	0.00444910i
$386$	4961.11	−	9264.64i	0.654180	−	1.22165i
$387$	−18940.8	−	10935.5i	−2.48789	−	1.43638i
$388$	−5474.61	−	2710.12i	−0.716318	−	0.354602i
$389$	955.790	+	1655.48i	0.124577	+	0.215774i	0.921568	−	0.388218i	$-0.126909\pi$
$389$	955.790	+	1655.48i	0.124577	+	0.215774i	−0.796990	+	0.603992i	$0.793576\pi$
$390$	−3585.65	−	5775.98i	−0.465556	−	0.749944i
$391$	−595.952			−0.0770808
$392$	−7711.89	−	873.565i	−0.993645	−	0.112555i
$393$	15256.6			1.95826
$394$	7028.95	+	11322.6i	0.898765	+	1.44778i
$395$	−1021.59	−	1769.45i	−0.130131	−	0.225394i
$396$	−132.042	−	65.3656i	−0.0167560	−	0.00829481i
$397$	−9347.11	−	5396.56i	−1.18166	−	0.682230i	−0.225260	−	0.974299i	$-0.572323\pi$
$397$	−9347.11	−	5396.56i	−1.18166	−	0.682230i	−0.956397	+	0.292068i	$0.905657\pi$
$398$	12.2938	−	22.9581i	0.00154832	−	0.00289142i
$399$	1426.60	−	13622.2i	0.178996	−	1.70918i
$400$	−2223.14	+	5321.35i	−0.277892	+	0.665169i
$401$	4496.30	−	7787.82i	0.559936	−	0.969838i	−0.437565	−	0.899187i	$-0.644159\pi$
$401$	4496.30	−	7787.82i	0.559936	−	0.969838i	0.997501	−	0.0706511i	$-0.0225077\pi$
$402$	437.468	+	13681.0i	0.0542759	+	1.69737i
$403$	3245.09	−	1873.56i	0.401116	−	0.231584i
$404$	395.277	+	6174.44i	0.0486776	+	0.760371i
$405$		−	7180.61i		−	0.881005i
$406$	1890.45	−	916.036i	0.231088	−	0.111976i
$407$		−	44.7654i		−	0.00545194i
$408$	−5991.60	−	2731.23i	−0.727030	−	0.331412i
$409$	−6215.31	+	3588.41i	−0.751411	+	0.433828i	−0.826204	−	0.563372i	$-0.809504\pi$
$409$	−6215.31	+	3588.41i	−0.751411	+	0.433828i	0.0747922	+	0.997199i	$0.476171\pi$
$410$	4255.91	−	136.089i	0.512645	−	0.0163925i
$411$	−8344.85	+	14453.7i	−1.00151	+	1.73467i
$412$	−1266.91	−	1902.31i	−0.151495	−	0.227476i
$413$	−8716.11	+	3884.57i	−1.03848	+	0.462826i
$414$	2833.30	+	1517.20i	0.336350	+	0.180111i
$415$	−4121.05	−	2379.29i	−0.487456	−	0.281433i
$416$	7396.82	+	2816.08i	0.871776	+	0.331898i
$417$	3156.54	+	5467.29i	0.370687	+	0.642049i
$418$	−58.9879	+	36.6189i	−0.00690238	+	0.00428491i
$419$	−1863.89			−0.217320			−0.108660	−	0.994079i	$-0.534656\pi$
$419$	−1863.89			−0.217320			−0.108660	+	0.994079i	$0.534656\pi$
$420$	−4354.16	+	6883.45i	−0.505860	+	0.799709i
$421$	−4925.47			−0.570196			−0.285098	−	0.958498i	$-0.592026\pi$
$421$	−4925.47			−0.570196			−0.285098	+	0.958498i	$0.592026\pi$
$422$	1639.02	−	1017.48i	0.189067	−	0.117370i
$423$	−305.478	−	529.103i	−0.0351131	−	0.0608177i
$424$	8283.40	+	11615.3i	0.948768	+	1.33040i
$425$	2440.08	+	1408.78i	0.278497	+	0.160791i
$426$	6061.72	+	3245.98i	0.689416	+	0.369174i
$427$	−8406.04	+	11579.0i	−0.952685	+	1.31229i
$428$	−14117.9	+	9402.27i	−1.59442	+	1.06186i
$429$	62.8528	−	108.864i	0.00707358	−	0.0122518i
$430$	6125.71	−	195.878i	0.686995	−	0.0219676i
$431$	−11097.9	+	6407.40i	−1.24030	+	0.716087i	−0.969155	−	0.246451i	$-0.920735\pi$
$431$	−11097.9	+	6407.40i	−1.24030	+	0.716087i	−0.271145	+	0.962539i	$0.587402\pi$
$432$	11780.7	+	15449.9i	1.31204	+	1.72068i
$433$		−	12764.8i		−	1.41672i	−0.705854	−	0.708358i	$-0.749436\pi$
$433$		−	12764.8i		−	1.41672i	0.705854	−	0.708358i	$-0.250564\pi$
$434$	−3715.33	−	2519.92i	−0.410925	−	0.278710i
$435$		−	2204.57i		−	0.242991i
$436$	6718.23	−	430.089i	0.737947	−	0.0472420i
$437$	1311.62	−	757.264i	0.143577	−	0.0828944i
$438$	−571.470	−	17871.6i	−0.0623422	−	1.94963i
$439$	7625.39	−	13207.6i	0.829020	−	1.43591i	−0.0697871	−	0.997562i	$-0.522232\pi$
$439$	7625.39	−	13207.6i	0.829020	−	1.43591i	0.898808	−	0.438344i	$-0.144435\pi$
$440$	41.0979	−	3.95327i	0.00445288	−	0.000428329i
$441$	13671.8	−	15206.9i	1.47627	−	1.64204i
$442$	1825.40	−	3408.86i	0.196438	−	0.366839i
$443$	6712.55	+	3875.49i	0.719916	+	0.415644i	0.814722	−	0.579852i	$-0.196890\pi$
$443$	6712.55	+	3875.49i	0.719916	+	0.415644i	−0.0948055	+	0.995496i	$0.530223\pi$
$444$	−4786.76	+	9669.53i	−0.511643	+	1.03355i
$445$	−138.809	−	240.424i	−0.0147869	−	0.0256117i
$446$	−5777.09	−	9306.07i	−0.613348	−	0.988016i
$447$	13132.5			1.38958
$448$	−828.153	−	9446.14i	−0.0873360	−	0.996179i
$449$	862.920			0.0906987			0.0453493	−	0.998971i	$-0.485560\pi$
$449$	862.920			0.0906987			0.0453493	+	0.998971i	$0.485560\pi$
$450$	−8014.20	−	12909.7i	−0.839540	−	1.35238i
$451$	39.3667	+	68.1852i	0.00411022	+	0.00711910i
$452$	2758.71	−	5572.76i	0.287077	−	0.579912i
$453$	19537.2	+	11279.8i	2.02635	+	1.16991i
$454$	−4388.97	+	8196.20i	−0.453710	+	0.847283i
$455$	−3870.63	−	2809.97i	−0.398809	−	0.289524i
$456$	16657.3	−	1602.29i	1.71064	−	0.164549i
$457$	2800.06	−	4849.84i	0.286611	−	0.496425i	−0.686388	−	0.727236i	$-0.740805\pi$
$457$	2800.06	−	4849.84i	0.286611	−	0.496425i	0.972999	+	0.230811i	$0.0741380\pi$
$458$	−254.798	−	7968.31i	−0.0259954	−	0.812958i
$459$	8220.50	−	4746.11i	0.835948	−	0.482635i
$460$	−898.798	+	57.5394i	−0.0911014	+	0.00583215i
$461$			13128.5i			1.32637i	0.748458	+	0.663183i	$0.230795\pi$
$461$			13128.5i			1.32637i	−0.748458	+	0.663183i	$0.769205\pi$
$462$	−150.209	−	10.8912i	−0.0151263	−	0.00109676i
$463$			3349.52i			0.336210i	0.985769	+	0.168105i	$0.0537648\pi$
$463$			3349.52i			0.336210i	−0.985769	+	0.168105i	$0.946235\pi$
$464$	1556.23	+	2040.93i	0.155703	+	0.204197i
$465$	−4080.07	+	2355.63i	−0.406901	+	0.234924i
$466$	16406.7	−	524.627i	1.63096	−	0.0521521i
$467$	−1061.05	+	1837.78i	−0.105138	+	0.182104i	−0.913794	−	0.406177i	$-0.866862\pi$
$467$	−1061.05	+	1837.78i	−0.105138	+	0.182104i	0.808657	+	0.588281i	$0.200195\pi$
$468$	−17356.8	+	11559.3i	−1.71435	+	1.14173i
$469$	3920.25	+	8796.16i	0.385971	+	0.866032i
$470$	150.930	+	80.8210i	0.0148125	+	0.00793190i
$471$	24667.0	+	14241.5i	2.41315	+	1.39323i
$472$	−6769.36	−	9492.24i	−0.660138	−	0.925669i
$473$	56.6622	+	98.1418i	0.00550810	+	0.00954031i
$474$	−7736.18	+	4802.52i	−0.749651	+	0.465374i
$475$	−7160.44			−0.691671
$476$	−4628.93	−	187.178i	−0.445728	−	0.0180237i
$477$	−37588.9			−3.60813
$478$	14319.2	−	8889.19i	1.37018	−	0.850590i
$479$	3966.36	+	6869.94i	0.378346	+	0.655314i	0.990822	−	0.135175i	$-0.0431597\pi$
$479$	3966.36	+	6869.94i	0.378346	+	0.655314i	−0.612476	+	0.790489i	$0.709826\pi$
$480$	−9300.05	−	3540.67i	−0.884349	−	0.336685i
$481$	−5487.16	−	3168.01i	−0.520152	−	0.300310i
$482$	−5280.37	−	2827.57i	−0.498992	−	0.267204i
$483$	3267.36	+	342.177i	0.307805	+	0.0322351i
$484$	−5901.83	−	8861.83i	−0.554267	−	0.832253i
$485$	−2255.15	+	3906.04i	−0.211136	+	0.365699i
$486$	−8813.10	+	281.811i	−0.822573	+	0.0263029i
$487$	−10015.3	+	5782.32i	−0.931900	+	0.538033i	−0.887412	−	0.460977i	$-0.847499\pi$
$487$	−10015.3	+	5782.32i	−0.931900	+	0.538033i	−0.0444880	+	0.999010i	$0.514166\pi$
$488$	−15907.0	−	7251.09i	−1.47557	−	0.672626i
$489$			8453.20i			0.781732i
$490$	−1007.45	+	5641.17i	−0.0928813	+	0.520085i
$491$		−	17001.3i		−	1.56264i	−0.624129	−	0.781322i	$-0.714546\pi$
$491$		−	17001.3i		−	1.56264i	0.624129	−	0.781322i	$-0.285454\pi$
$492$	−1212.36	−	18937.8i	−0.111093	−	1.73533i
$493$	1085.93	−	626.960i	0.0992042	−	0.0572756i
$494$	314.072	+	9821.99i	0.0286048	+	0.894559i
$495$	−54.3921	+	94.2099i	−0.00493887	+	0.00855438i
$496$	2114.34	−	5060.94i	0.191405	−	0.458151i
$497$	4811.39	+	503.876i	0.434246	+	0.0454767i
$498$	−10011.1	+	18695.3i	−0.900822	+	1.68225i
$499$	−11351.9	−	6554.02i	−1.01840	−	0.587972i	−0.104759	−	0.994498i	$-0.533407\pi$
$499$	−11351.9	−	6554.02i	−1.01840	−	0.587972i	−0.913640	+	0.406525i	$0.866740\pi$
$500$	9109.69	+	4509.62i	0.814796	+	0.403353i
$501$	−5602.14	−	9703.19i	−0.499571	−	0.865282i
$502$	2910.28	+	4688.04i	0.258749	+	0.416808i
$503$	−16393.8			−1.45321			−0.726605	−	0.687055i	$-0.758903\pi$
$503$	−16393.8			−1.45321			−0.726605	+	0.687055i	$0.758903\pi$
$504$	21530.5	+	12674.4i	1.90287	+	1.12016i
$505$	4568.18			0.402537
$506$	−8.78323	−	14.1485i	−0.000771664	−	0.00124304i
$507$	1327.54	+	2299.36i	0.116288	+	0.201417i
$508$	3084.87	+	1527.12i	0.269427	+	0.133376i
$509$	17226.5	+	9945.72i	1.50010	+	0.866083i	1.00000		0.000115072i	$3.66284e-5\pi$
$509$	17226.5	+	9945.72i	1.50010	+	0.866083i	0.500100	+	0.865968i	$0.333297\pi$
$510$	−2295.09	+	4285.97i	−0.199271	+	0.372130i
$511$	−5121.08	−	11490.6i	−0.443333	−	0.994740i
$512$	11109.1	−	3287.16i	0.958902	−	0.283737i
$513$	−12061.6	+	20891.2i	−1.03807	+	1.79799i
$514$	−621.326	−	19430.8i	−0.0533181	−	1.66742i
$515$	−1461.44	+	843.766i	−0.125047	+	0.0721956i
$516$	−1745.00	−	27257.9i	−0.148875	−	2.32551i
$517$			3.16567i			0.000269296i
$518$	−548.954	+	7571.09i	−0.0465631	+	0.642191i
$519$		−	11236.2i		−	0.950316i
$520$	2423.89	−	5317.38i	0.204413	−	0.448428i
$521$	−18943.9	+	10937.3i	−1.59299	+	0.919712i	−0.600198	+	0.799851i	$0.704912\pi$
$521$	−18943.9	+	10937.3i	−1.59299	+	0.919712i	−0.992791	+	0.119861i	$0.961755\pi$
$522$	−6758.89	+	216.125i	−0.566721	+	0.0181217i
$523$	2620.60	−	4539.02i	0.219103	−	0.379498i	−0.735431	−	0.677600i	$-0.763020\pi$
$523$	2620.60	−	4539.02i	0.219103	−	0.379498i	0.954534	+	0.298102i	$0.0963535\pi$
$524$	7269.32	+	10915.2i	0.606034	+	0.909983i
$525$	−12569.1	−	9124.79i	−1.04488	−	0.758549i
$526$	5586.18	+	2991.33i	0.463059	+	0.247962i
$527$	−2320.67	−	1339.84i	−0.191822	−	0.110748i
$528$	−23.4628	−	182.500i	−0.00193388	−	0.0150422i
$529$	−5901.87	−	10222.3i	−0.485072	−	0.840169i
$530$	8949.25	−	5555.58i	0.733454	−	0.455319i
$531$	30718.4			2.51048
$532$	10425.6	−	5469.93i	0.849635	−	0.445774i
$533$	11143.8			0.905614
$534$	−1051.16	+	652.544i	−0.0851834	+	0.0528808i
$535$	6261.95	+	10846.0i	0.506033	+	0.876476i
$536$	−9579.43	+	6831.54i	−0.771955	+	0.550518i
$537$	12305.1	+	7104.35i	0.988834	+	0.570904i
$538$	−704.105	−	377.040i	−0.0564240	−	0.0302144i
$539$	−100.747	+	32.8181i	−0.00805099	+	0.00262259i
$540$	11939.7	−	7951.64i	0.951485	−	0.633674i
$541$	3715.18	−	6434.87i	0.295246	−	0.511381i	−0.679796	−	0.733401i	$-0.737932\pi$
$541$	3715.18	−	6434.87i	0.295246	−	0.511381i	0.975042	+	0.222020i	$0.0712652\pi$
$542$	−11898.7	+	380.478i	−0.942979	+	0.0301530i
$543$	−7958.51	+	4594.85i	−0.628973	+	0.363138i
$544$	−900.791	−	5587.95i	−0.0709947	−	0.440407i
$545$		−	4970.50i		−	0.390666i
$546$	−11965.2	+	17641.3i	−0.937843	+	1.38274i
$547$			16115.5i			1.25969i	0.776722	+	0.629843i	$0.216881\pi$
$547$			16115.5i			1.25969i	−0.776722	+	0.629843i	$0.783119\pi$
$548$	−14316.8	+	916.534i	−1.11603	+	0.0714459i
$549$	39889.7	−	23030.3i	3.10101	−	1.79037i
$550$	2.51632	+	78.6930i	0.000195084	+	0.00610087i
$551$	−1593.33	+	2759.73i	−0.123191	+	0.213373i
$552$	384.317	+	3995.33i	0.0296334	+	0.308067i
$553$	−3763.59	+	5184.22i	−0.289411	+	0.398653i
$554$	−3518.40	+	6570.46i	−0.269824	+	0.503884i
$555$	6899.03	+	3983.16i	0.527653	+	0.304641i
$556$	−2407.50	+	4863.30i	−0.183635	+	0.370953i
$557$	−1212.61	−	2100.30i	−0.0922442	−	0.159772i	0.816211	−	0.577754i	$-0.196071\pi$
$557$	−1212.61	−	2100.30i	−0.0922442	−	0.159772i	−0.908455	+	0.417982i	$0.862737\pi$
$558$	7622.01	+	12278.0i	0.578253	+	0.931484i
$559$	16039.8			1.21361
$560$	−6999.29	+	164.629i	−0.528168	+	0.0124229i
$561$	−89.8962			−0.00676546
$562$	3748.00	+	6037.50i	0.281317	+	0.453161i
$563$	−5853.04	−	10137.8i	−0.438146	−	0.758891i	0.559401	−	0.828897i	$-0.311031\pi$
$563$	−5853.04	−	10137.8i	−0.438146	−	0.758891i	−0.997547	+	0.0700065i	$0.977698\pi$
$564$	338.505	−	683.800i	0.0252724	−	0.0510517i
$565$	−3976.06	−	2295.58i	−0.296060	−	0.170931i
$566$	3108.03	−	5804.11i	0.230813	−	0.431033i
$567$	−20564.5	+	9165.14i	−1.52316	+	0.678836i
$568$	565.931	+	5883.38i	0.0418062	+	0.434615i
$569$	2823.03	−	4889.62i	0.207992	−	0.360253i	−0.743090	−	0.669192i	$-0.766641\pi$
$569$	2823.03	−	4889.62i	0.207992	−	0.360253i	0.951082	+	0.308939i	$0.0999739\pi$
$570$	−394.884	−	12349.2i	−0.0290173	−	0.907461i
$571$	−3710.60	+	2142.31i	−0.271950	+	0.157011i	−0.629774	−	0.776779i	$-0.716852\pi$
$571$	−3710.60	+	2142.31i	−0.271950	+	0.157011i	0.357823	+	0.933789i	$0.383519\pi$
$572$	107.833	−	6.90327i	0.00788238	−	0.000504616i
$573$		−	36524.8i		−	2.66291i
$574$	−5821.88	−	12014.8i	−0.423346	−	0.873672i
$575$		−	1717.47i		−	0.124562i
$576$	−9943.44	+	28859.7i	−0.719288	+	2.08765i
$577$	3779.21	−	2181.93i	0.272670	−	0.157426i	−0.357430	−	0.933940i	$-0.616347\pi$
$577$	3779.21	−	2181.93i	0.272670	−	0.157426i	0.630100	+	0.776514i	$0.283014\pi$
$578$	11125.1	−	355.740i	0.800592	−	0.0256000i
$579$	−17290.4	+	29947.9i	−1.24105	+	2.14955i
$580$	1577.23	−	1050.41i	0.112915	−	0.0751998i
$581$	−1554.04	+	14839.1i	−0.110968	+	1.05961i
$582$	17719.9	+	9488.81i	1.26205	+	0.675814i
$583$	168.673	+	97.3837i	0.0119824	+	0.00691804i
$584$	12513.7	−	8924.14i	0.886682	−	0.632335i
$585$	7698.57	+	13334.3i	0.544097	+	0.942404i
$586$	−13589.0	+	8435.88i	−0.957947	+	0.594681i
$587$	23904.0			1.68079			0.840395	−	0.541974i	$-0.182323\pi$
$587$	23904.0			1.68079			0.840395	+	0.541974i	$0.182323\pi$
$588$	25271.0	+	3684.00i	1.77238	+	0.258377i
$589$	6810.03			0.476405
$590$	−7313.51	+	4540.14i	−0.510326	+	0.316804i
$591$	−21926.1	−	37977.2i	−1.52609	−	2.64327i
$592$	−9198.68	+	1182.61i	−0.638620	+	0.0821031i
$593$	−22391.3	−	12927.6i	−1.55059	−	0.895235i	−0.998093	−	0.0617205i	$-0.980341\pi$
$593$	−22391.3	−	12927.6i	−1.55059	−	0.895235i	−0.552498	−	0.833514i	$-0.686325\pi$
$594$	233.833	+	125.215i	0.0161520	+	0.00864918i
$595$	−356.269	+	3401.92i	−0.0245472	+	0.234395i
$596$	6257.21	+	9395.44i	0.430043	+	0.645725i
$597$	−42.8462	+	74.2118i	−0.00293732	+	0.00508758i
$598$	−2355.85	+	75.3316i	−0.161100	+	0.00515140i
$599$	−11428.5	+	6598.26i	−0.779560	+	0.450079i	−0.836274	−	0.548311i	$-0.815271\pi$
$599$	−11428.5	+	6598.26i	−0.779560	+	0.450079i	0.0567142	+	0.998390i	$0.481938\pi$
$600$	7871.09	−	17267.1i	0.535560	−	1.17488i
$601$			1378.53i			0.0935630i	0.998905	+	0.0467815i	$0.0148964\pi$
$601$			1378.53i			0.0935630i	−0.998905	+	0.0467815i	$0.985104\pi$
$602$	−8379.67	−	17293.4i	−0.567325	−	1.17081i
$603$		−	31000.6i		−	2.09360i
$604$	1238.88	+	19352.1i	0.0834594	+	1.30368i
$605$	−6808.08	+	3930.65i	−0.457501	+	0.264138i
$606$	−650.659	−	20348.1i	−0.0436159	−	1.36400i
$607$	7703.43	−	13342.7i	0.515111	−	0.892199i	−0.484735	−	0.874661i	$-0.661084\pi$
$607$	7703.43	−	13342.7i	0.515111	−	0.892199i	0.999846	−	0.0175378i	$-0.00558275\pi$
$608$	9083.03	+	11153.8i	0.605864	+	0.743991i
$609$	−6313.66	+	2813.86i	−0.420103	+	0.187230i
$610$	−6093.19	+	11378.8i	−0.404436	+	0.755266i
$611$	388.035	+	224.032i	0.0256927	+	0.0148337i
$612$	13365.2	+	6616.23i	0.882769	+	0.437002i
$613$	3575.63	+	6193.18i	0.235593	+	0.408059i	0.959445	−	0.281897i	$-0.0909635\pi$
$613$	3575.63	+	6193.18i	0.235593	+	0.408059i	−0.723852	+	0.689955i	$0.757630\pi$
$614$	−5664.99	−	9125.49i	−0.372346	−	0.599796i
$615$	−14011.2			−0.918675
$616$	−63.7781	−	112.654i	−0.00417158	−	0.00736847i
$617$	3499.63			0.228347			0.114173	−	0.993461i	$-0.463578\pi$
$617$	3499.63			0.228347			0.114173	+	0.993461i	$0.463578\pi$
$618$	3966.56	+	6389.56i	0.258185	+	0.415899i
$619$	7169.67	+	12418.2i	0.465547	+	0.806351i	0.999226	−	0.0393363i	$-0.0125244\pi$
$619$	7169.67	+	12418.2i	0.465547	+	0.806351i	−0.533679	+	0.845687i	$0.679191\pi$
$620$	−3629.33	−	1796.65i	−0.235093	−	0.116379i
$621$	−5010.86	−	2893.02i	−0.323799	−	0.186945i
$622$	−7668.94	+	14321.4i	−0.494368	+	0.923209i
$623$	−511.378	+	704.406i	−0.0328859	+	0.0452993i
$624$	−24030.6	−	10039.4i	−1.54165	−	0.644068i
$625$	−1879.36	+	3255.15i	−0.120279	+	0.208330i
$626$	564.756	+	17661.7i	0.0360578	+	1.12764i
$627$	197.851	−	114.229i	0.0126019	−	0.00727572i
$628$	1564.18	+	24433.3i	0.0993907	+	1.55254i
$629$			4531.10i			0.287229i
$630$	10354.5	−	15266.5i	0.654816	−	0.965450i
$631$		−	8745.97i		−	0.551778i	−0.961190	−	0.275889i	$-0.911028\pi$
$631$		−	8745.97i		−	0.551778i	0.961190	−	0.275889i	$-0.0889722\pi$
$632$	−7121.95	−	3246.49i	−0.448253	−	0.204333i
$633$	−5497.41	+	3173.93i	−0.345186	+	0.199293i
$634$	−13077.1	+	418.157i	−0.819174	+	0.0261942i
$635$	1270.75	−	2201.00i	0.0794142	−	0.137549i
$636$	−26021.0	−	39071.5i	−1.62233	−	2.43598i
$637$	−3107.08	+	14671.7i	−0.193261	+	0.912579i
$638$	30.8892	+	16.5408i	0.00191680	+	0.00102642i
$639$	−13486.6	−	7786.51i	−0.834934	−	0.482049i
$640$	−1898.07	−	8340.62i	−0.117231	−	0.515143i
$641$	−7778.28	−	13472.4i	−0.479288	−	0.830151i	0.520430	−	0.853904i	$-0.325772\pi$
$641$	−7778.28	−	13472.4i	−0.479288	−	0.830151i	−0.999718	+	0.0237532i	$0.992438\pi$
$642$	47419.7	−	29437.6i	2.91512	−	1.80967i
$643$	15506.4			0.951029			0.475514	−	0.879708i	$-0.342262\pi$
$643$	15506.4			0.951029			0.475514	+	0.879708i	$0.342262\pi$
$644$	1311.99	+	2500.62i	0.0802789	+	0.153010i
$645$	−20166.9			−1.23112
$646$	5970.68	−	3706.52i	0.363643	−	0.225745i
$647$	11738.9	+	20332.3i	0.713296	+	1.23546i	0.963613	+	0.267301i	$0.0861317\pi$
$647$	11738.9	+	20332.3i	0.713296	+	1.23546i	−0.250318	+	0.968164i	$0.580535\pi$
$648$	−15971.4	−	22395.7i	−0.968237	−	1.35770i
$649$	−137.843	−	79.5839i	−0.00833717	−	0.00481347i
$650$	9823.95	+	5260.60i	0.592811	+	0.317443i
$651$	11954.0	+	8678.24i	0.719683	+	0.522469i
$652$	−6047.73	+	4027.69i	−0.363263	+	0.241927i
$653$	8816.62	−	15270.8i	0.528363	−	0.915152i	−0.471090	−	0.882085i	$-0.656139\pi$
$653$	8816.62	−	15270.8i	0.528363	−	0.915152i	0.999453	−	0.0330667i	$-0.0105274\pi$
$654$	−22140.2	+	707.963i	−1.32378	+	0.0423296i
$655$	8385.55	−	4841.40i	0.500230	−	0.288808i
$656$	12971.1	−	9890.64i	0.772008	−	0.588666i
$657$			40496.5i			2.40474i
$658$	38.8204	−	535.405i	0.00229996	−	0.0317207i
$659$			398.945i			0.0235822i	0.999930	+	0.0117911i	$0.00375331\pi$
$659$			398.945i			0.0235822i	−0.999930	+	0.0117911i	$0.996247\pi$
$660$	−135.579	+	8.67951i	−0.00799606	+	0.000511893i
$661$	5167.67	−	2983.55i	0.304083	−	0.175563i	−0.340193	−	0.940356i	$-0.610492\pi$
$661$	5167.67	−	2983.55i	0.304083	−	0.175563i	0.644276	+	0.764793i	$0.277159\pi$
$662$	590.783	+	18475.6i	0.0346849	+	1.08471i
$663$	−6361.89	+	11019.1i	−0.372662	+	0.645470i
$664$	−18145.3	+	1745.43i	−1.06050	+	0.102012i
$665$	−3538.64	−	7939.93i	−0.206350	−	0.463003i
$666$	11535.4	−	21541.9i	0.671155	−	1.25335i
$667$	−661.934	−	382.168i	−0.0384261	−	0.0221853i
$668$	4272.77	−	8631.24i	0.247483	−	0.499929i
$669$	18021.1	+	31213.4i	1.04146	+	1.80386i
$670$	4581.84	+	7380.69i	0.264197	+	0.425583i
$671$	−238.664			−0.0137310
$672$	1730.24	+	31153.6i	0.0993236	+	1.78836i
$673$	19669.6			1.12661			0.563304	−	0.826250i	$-0.309530\pi$
$673$	19669.6			1.12661			0.563304	+	0.826250i	$0.309530\pi$
$674$	−7127.22	−	11480.9i	−0.407315	−	0.656126i
$675$	13677.8	+	23690.6i	0.779936	+	1.35089i
$676$	−1012.52	+	2045.35i	−0.0576080	+	0.116372i
$677$	−8272.00	−	4775.84i	−0.469599	−	0.271123i	0.246473	−	0.969150i	$-0.420728\pi$
$677$	−8272.00	−	4775.84i	−0.469599	−	0.271123i	−0.716072	+	0.698027i	$0.754062\pi$
$678$	−9658.92	+	18037.6i	−0.547122	+	1.02173i
$679$	14064.9	+	1472.96i	0.794936	+	0.0832503i
$680$	−4159.88	+	400.145i	−0.234594	+	0.0225660i
$681$	15296.4	−	26494.2i	0.860734	−	1.49083i
$682$	−2.39317	−	74.8420i	−0.000134369	−	0.00420212i
$683$	18452.4	−	10653.5i	1.03376	−	0.596843i	0.115702	−	0.993284i	$-0.463088\pi$
$683$	18452.4	−	10653.5i	1.03376	−	0.596843i	0.918060	+	0.396441i	$0.129755\pi$
$684$	−37822.2	+	2421.31i	−2.11428	+	0.135353i
$685$			10592.3i			0.590819i
$686$	17441.6	−	4315.01i	0.970734	−	0.240157i
$687$			26233.0i			1.45685i
$688$	18669.9	−	14236.0i	1.03457	−	0.788870i
$689$	23873.8	−	13783.5i	1.32006	−	0.762135i
$690$	2962.02	−	94.7148i	0.163424	−	0.00522569i
$691$	4046.92	−	7009.48i	0.222796	−	0.385895i	−0.732860	−	0.680380i	$-0.761815\pi$
$691$	4046.92	−	7009.48i	0.222796	−	0.385895i	0.955656	+	0.294485i	$0.0951482\pi$
$692$	8038.78	−	5353.70i	0.441602	−	0.294100i
$693$	339.232	+	35.5263i	0.0185950	+	0.00194738i
$694$	−22940.8	−	12284.5i	−1.25479	−	0.671923i
$695$	3469.88	+	2003.33i	0.189381	+	0.109339i
$696$	−4903.51	−	6875.87i	−0.267050	−	0.374467i
$697$	−3984.65	−	6901.62i	−0.216542	−	0.375061i
$698$	−16679.3	+	10354.3i	−0.904471	+	0.561484i
$699$	−54013.7			−2.92273
$700$	539.425	−	13340.1i	0.0291262	−	0.720296i
$701$	−15840.9			−0.853498			−0.426749	−	0.904370i	$-0.640341\pi$
$701$	−15840.9			−0.853498			−0.426749	+	0.904370i	$0.640341\pi$
$702$	31896.4	−	19800.9i	1.71489	−	1.06458i
$703$	−5757.57	−	9972.41i	−0.308892	−	0.535016i
$704$	119.388	−	103.742i	0.00639148	−	0.00555386i
$705$	−487.879	−	281.677i	−0.0260632	−	0.0150476i
$706$	−3929.53	−	2104.22i	−0.209476	−	0.112172i
$707$	−5830.71	−	13082.8i	−0.310164	−	0.695940i
$708$	21264.9	+	31930.0i	1.12879	+	1.69492i
$709$	−12145.5	+	21036.7i	−0.643351	+	1.11432i	0.341329	+	0.939944i	$0.389123\pi$
$709$	−12145.5	+	21036.7i	−0.643351	+	1.11432i	−0.984680	+	0.174372i	$0.944210\pi$
$710$	4361.76	−	139.473i	0.230555	−	0.00737231i
$711$	17859.6	−	10311.3i	0.942036	−	0.543885i
$712$	−967.697	−	441.118i	−0.0509353	−	0.0232185i
$713$			1633.42i			0.0857952i
$714$	15204.0	+	1102.39i	0.796911	+	0.0577813i
$715$		−	79.7805i		−	0.00417290i
$716$	780.287	+	12188.5i	0.0407272	+	0.636182i
$717$	−48027.9	+	27728.9i	−2.50159	+	1.44429i
$718$	−683.760	−	21383.3i	−0.0355400	−	1.11144i
$719$	−15061.8	+	26087.8i	−0.781239	+	1.35315i	0.149981	+	0.988689i	$0.452079\pi$
$719$	−15061.8	+	26087.8i	−0.781239	+	1.35315i	−0.931220	+	0.364457i	$0.881254\pi$
$720$	20795.8	+	8687.99i	1.07641	+	0.449698i
$721$	4281.81	+	3108.47i	0.221169	+	0.160562i
$722$	727.215	−	1358.04i	0.0374850	−	0.0700015i
$723$	17068.8	+	9854.65i	0.878000	+	0.506913i
$724$	−7079.31	−	3504.51i	−0.363398	−	0.179895i
$725$	1806.83	+	3129.52i	0.0925571	+	0.160314i
$726$	18478.0	+	29765.5i	0.944607	+	1.52163i
$727$	−14109.8			−0.719810			−0.359905	−	0.932989i	$-0.617191\pi$
$727$	−14109.8			−0.719810			−0.359905	+	0.932989i	$0.617191\pi$
$728$	−18322.2	−	154.808i	−0.932785	−	0.00788128i
$729$	−3808.72			−0.193503
$730$	−5985.32	−	9641.49i	−0.303461	−	0.488832i
$731$	−5735.28	−	9933.79i	−0.290187	−	0.502619i
$732$	51552.5	+	25520.3i	2.60305	+	1.28860i
$733$	25868.2	+	14935.0i	1.30350	+	0.752575i	0.981002	−	0.193995i	$-0.0621447\pi$
$733$	25868.2	+	14935.0i	1.30350	+	0.752575i	0.322496	+	0.946571i	$0.395478\pi$
$734$	15782.5	−	29473.1i	0.793655	−	1.48212i
$735$	3906.55	−	18446.8i	0.196048	−	0.925740i
$736$	−2675.29	+	2178.61i	−0.133985	+	0.109109i
$737$	−80.3149	+	139.109i	−0.00401416	+	0.00695273i
$738$	1373.58	+	42956.2i	0.0685126	+	2.14260i
$739$	3885.39	−	2243.23i	0.193405	−	0.111662i	−0.400171	−	0.916441i	$-0.631049\pi$
$739$	3885.39	−	2243.23i	0.193405	−	0.111662i	0.593576	+	0.804778i	$0.297716\pi$
$740$	437.479	+	6833.67i	0.0217325	+	0.339474i
$741$		−	32335.7i		−	1.60308i
$742$	−27333.2	−	18538.7i	−1.35234	−	0.917222i
$743$		−	21574.3i		−	1.06525i	−0.846350	−	0.532627i	$-0.821205\pi$
$743$		−	21574.3i		−	1.06525i	0.846350	−	0.532627i	$-0.178795\pi$
$744$	−7485.90	+	16422.1i	−0.368880	+	0.809225i
$745$	7218.03	−	4167.33i	0.354964	−	0.204939i
$746$	9756.43	−	311.975i	0.478832	−	0.0153113i
$747$	24014.9	−	41595.0i	1.17625	−	2.03733i
$748$	−42.8328	−	64.3150i	−0.00209374	−	0.00314384i
$749$	23069.3	−	31777.2i	1.12541	−	1.55022i
$750$	−29485.8	−	15789.3i	−1.43556	−	0.768724i
$751$	−33510.8	−	19347.5i	−1.62826	−	0.940078i	−0.984611	−	0.174760i	$-0.944085\pi$
$751$	−33510.8	−	19347.5i	−1.62826	−	0.940078i	−0.643652	−	0.765318i	$-0.722582\pi$
$752$	650.502	−	83.6307i	0.0315444	−	0.00405545i
$753$	−9078.33	−	15724.1i	−0.439353	−	0.760981i
$754$	4213.51	−	2615.70i	0.203511	−	0.126337i
$755$	14317.7			0.690164
$756$	−38012.2	−	24044.8i	−1.82869	−	1.15675i
$757$	−4171.12			−0.200267			−0.100133	−	0.994974i	$-0.531927\pi$
$757$	−4171.12			−0.200267			−0.100133	+	0.994974i	$0.531927\pi$
$758$	−873.287	+	542.125i	−0.0418459	+	0.0259774i
$759$	27.3984	+	47.4555i	0.00131028	+	0.00226947i
$760$	8646.94	−	6166.54i	0.412707	−	0.294321i
$761$	3328.46	+	1921.69i	0.158550	+	0.0915390i	0.577176	−	0.816620i	$-0.304155\pi$
$761$	3328.46	+	1921.69i	0.158550	+	0.0915390i	−0.418626	+	0.908159i	$0.637488\pi$
$762$	−9984.93	−	5346.81i	−0.474693	−	0.254192i
$763$	−14235.0	+	6344.22i	−0.675416	+	0.301017i
$764$	26131.2	−	17402.9i	1.23743	−	0.824105i
$765$	5505.50	−	9535.80i	0.260198	−	0.450677i
$766$	4270.37	−	136.551i	0.201429	−	0.00644097i
$767$	−19510.1	+	11264.2i	−0.918475	+	0.530282i
$768$	−36881.4	+	9642.57i	−1.73287	+	0.453055i
$769$		−	11022.0i		−	0.516857i	−0.966030	−	0.258428i	$-0.916795\pi$
$769$		−	11022.0i		−	0.516857i	0.966030	−	0.258428i	$-0.0832046\pi$
$770$	−86.0159	+	41.6798i	−0.00402571	+	0.00195070i
$771$			63969.5i			2.98807i
$772$	−29664.2	+	1899.05i	−1.38295	+	0.0885339i
$773$	−30496.8	+	17607.3i	−1.41901	+	0.819264i	−0.996212	−	0.0869605i	$-0.972285\pi$
$773$	−30496.8	+	17607.3i	−1.41901	+	0.819264i	−0.422796	+	0.906225i	$0.638951\pi$
$774$	1977.06	+	61828.7i	0.0918137	+	2.87130i
$775$	3861.27	−	6687.92i	0.178969	−	0.309983i
$776$	1654.36	+	17198.6i	0.0765310	+	0.795611i
$777$	2601.61	−	24842.1i	0.120119	−	1.14698i
$778$	2552.35	−	4766.40i	0.117617	−	0.219645i
$779$	17539.5	+	10126.4i	0.806698	+	0.465747i
$780$	−8530.91	+	17232.9i	−0.391610	+	0.791075i
$781$	40.3459	+	69.8811i	0.00184851	+	0.00320172i
$782$	889.028	+	1432.10i	0.0406542	+	0.0654881i
$783$	12174.2			0.555646
$784$	9405.20	+	19835.1i	0.428444	+	0.903568i
$785$	18077.0			0.821907
$786$	−22759.5	−	36662.3i	−1.03283	−	1.66374i
$787$	−2018.30	−	3495.79i	−0.0914162	−	0.158337i	0.816691	−	0.577075i	$-0.195806\pi$
$787$	−2018.30	−	3495.79i	−0.0914162	−	0.158337i	−0.908107	+	0.418738i	$0.862473\pi$
$788$	16723.1	−	33781.7i	0.756011	−	1.52719i
$789$	−18057.3	−	10425.4i	−0.814773	−	0.470410i
$790$	−2728.07	+	5094.55i	−0.122861	+	0.229438i
$791$	−1499.36	+	14317.1i	−0.0673973	+	0.643560i
$792$	39.9016	+	414.814i	0.00179020	+	0.0186108i
$793$	−16890.1	+	29254.5i	−0.756348	+	1.31003i
$794$	975.661	+	30511.9i	0.0436082	+	1.36376i
$795$	−30016.6	+	17330.1i	−1.33909	+	0.773126i
$796$	−73.5088	+	4.70590i	−0.00327318	+	0.000209543i
$797$		−	26004.8i		−	1.15575i	−0.816124	−	0.577877i	$-0.803881\pi$
$797$		−	26004.8i		−	1.15575i	0.816124	−	0.577877i	$-0.196119\pi$
$798$	−34862.9	+	16893.2i	−1.54653	+	0.749387i
$799$		−	320.426i		−	0.0141875i
$800$	16103.9	−	2595.98i	0.711696	−	0.114727i
$801$	2426.68	−	1401.04i	0.107044	−	0.0618020i
$802$	−25421.9	+	812.900i	−1.11930	+	0.0357912i
$803$	104.916	−	181.721i	0.00461074	−	0.00798603i
$804$	32223.3	−	21460.2i	1.41347	−	0.941347i
$805$	1904.43	−	848.761i	0.0833818	−	0.0371614i
$806$	−9343.19	−	5003.16i	−0.408312	−	0.218646i
$807$	2276.01	+	1314.06i	0.0992807	+	0.0573197i
$808$	14247.8	−	10160.8i	0.620340	−	0.442394i
$809$	−119.264	−	206.571i	−0.00518305	−	0.00897730i	0.863422	−	0.504482i	$-0.168316\pi$
$809$	−119.264	−	206.571i	−0.00518305	−	0.00897730i	−0.868605	+	0.495505i	$0.834983\pi$
$810$	−17255.3	+	10711.9i	−0.748505	+	0.464662i
$811$	−25463.7			−1.10253			−0.551264	−	0.834331i	$-0.685854\pi$
$811$	−25463.7			−1.10253			−0.551264	+	0.834331i	$0.685854\pi$
$812$	−5021.40	−	3176.31i	−0.217016	−	0.137274i
$813$	39172.7			1.68985
$814$	−107.573	+	66.7800i	−0.00463198	+	0.00287548i
$815$	2682.46	+	4646.16i	0.115291	+	0.199691i
$816$	2374.88	+	18472.4i	0.101884	+	0.792481i
$817$	25245.3	+	14575.4i	1.08106	+	0.624147i
$818$	17894.9	+	9582.53i	0.764893	+	0.409591i
$819$	28361.9	−	39067.5i	1.21007	−	1.66682i
$820$	−6675.89	−	10024.1i	−0.284308	−	0.426899i
$821$	−12006.3	+	20795.5i	−0.510381	+	0.884006i	0.489547	+	0.871977i	$0.337162\pi$
$821$	−12006.3	+	20795.5i	−0.510381	+	0.884006i	−0.999928	+	0.0120288i	$0.996171\pi$
$822$	47181.5	−	1508.69i	2.00200	−	0.0640166i
$823$	25433.1	−	14683.8i	1.07721	−	0.621925i	0.147065	−	0.989127i	$-0.453017\pi$
$823$	25433.1	−	14683.8i	1.07721	−	0.621925i	0.930141	+	0.367201i	$0.119684\pi$
$824$	−2681.38	+	5882.25i	−0.113362	+	0.248687i
$825$		−	259.071i		−	0.0109330i
$826$	22337.3	+	15150.2i	0.940936	+	0.638189i
$827$			2757.80i			0.115959i	0.998318	+	0.0579796i	$0.0184658\pi$
$827$			2757.80i			0.115959i	−0.998318	+	0.0579796i	$0.981534\pi$
$828$	−580.763	−	9071.85i	−0.0243755	−	0.380759i
$829$	24688.8	−	14254.1i	1.03435	−	0.597184i	0.116125	−	0.993235i	$-0.462953\pi$
$829$	24688.8	−	14254.1i	1.03435	−	0.597184i	0.918229	+	0.396050i	$0.129619\pi$
$830$	430.159	+	13452.4i	0.0179892	+	0.562578i
$831$	12262.3	−	21239.0i	0.511883	−	0.886608i
$832$	−4267.26	−	21975.8i	−0.177813	−	0.915714i
$833$	10197.5	−	3321.81i	0.424156	−	0.138168i
$834$	8429.26	−	15741.3i	0.349978	−	0.653568i
$835$	−6158.24	−	3555.46i	−0.255227	−	0.147355i
$836$	175.994	+	87.1230i	0.00728094	+	0.00360432i
$837$	−13008.4	−	22531.2i	−0.537199	−	0.930457i
$838$	2780.51	+	4479.01i	0.114620	+	0.184636i
$839$	−22706.3			−0.934337			−0.467169	−	0.884168i	$-0.654726\pi$
$839$	−22706.3			−0.934337			−0.467169	+	0.884168i	$0.654726\pi$
$840$	23036.6	+	194.641i	0.946237	+	0.00799494i
$841$	−22780.8			−0.934060
$842$	7347.70	+	11836.1i	0.300735	+	0.484440i
$843$	−11691.5	−	20250.3i	−0.477672	−	0.827353i
$844$	−4890.10	−	2420.77i	−0.199436	−	0.0987279i
$845$	1459.32	+	842.537i	0.0594107	+	0.0343008i
$846$	−815.751	+	1523.38i	−0.0331514	+	0.0619088i
$847$	19946.6	+	14480.7i	0.809179	+	0.587440i
$848$	15555.0	−	37232.7i	0.629906	−	1.50776i
$849$	−10832.1	+	18761.7i	−0.437876	+	0.758423i
$850$	−254.698	−	7965.21i	−0.0102777	−	0.321417i
$851$	2391.93	−	1380.98i	0.0963506	−	0.0556280i
$852$	−1242.52	−	19408.8i	−0.0499624	−	0.780440i
$853$			31316.1i			1.25703i	0.777799	+	0.628513i	$0.216336\pi$
$853$			31316.1i			1.25703i	−0.777799	+	0.628513i	$0.783664\pi$
$854$	40364.8	+	2926.71i	1.61739	+	0.117272i
$855$			27982.9i			1.11929i
$856$	43654.7	+	19899.7i	1.74309	+	0.794577i
$857$	−17426.4	+	10061.2i	−0.694605	+	0.401030i	−0.805335	−	0.592820i	$-0.798014\pi$
$857$	−17426.4	+	10061.2i	−0.694605	+	0.401030i	0.110730	+	0.993851i	$0.464681\pi$
$858$	−355.368	+	11.3634i	−0.0141399	+	0.000452143i
$859$	6020.90	−	10428.5i	0.239151	−	0.414221i	−0.721320	−	0.692602i	$-0.756464\pi$
$859$	6020.90	−	10428.5i	0.239151	−	0.414221i	0.960471	+	0.278381i	$0.0897977\pi$
$860$	−9608.89	−	14428.1i	−0.381000	−	0.572087i
$861$	17883.5	+	40126.6i	0.707861	+	1.58828i
$862$	31952.9	+	17110.4i	1.26255	+	0.676082i
$863$	2487.30	+	1436.04i	0.0981098	+	0.0566437i	0.548252	−	0.836313i	$-0.315293\pi$
$863$	2487.30	+	1436.04i	0.0981098	+	0.0566437i	−0.450142	+	0.892957i	$0.648627\pi$
$864$	19552.5	−	51357.3i	0.769894	−	2.02223i
$865$	−3565.59	−	6175.77i	−0.140154	−	0.242754i
$866$	−30674.4	+	19042.2i	−1.20365	+	0.747208i
$867$	−36625.6			−1.43469
$868$	−513.027	+	12687.2i	−0.0200614	+	0.496121i
$869$	−106.856			−0.00417127
$870$	−5297.67	+	3288.73i	−0.206446	+	0.128159i
$871$	11367.6	+	19689.3i	0.442225	+	0.765956i
$872$	−11055.6	−	15502.6i	−0.429347	−	0.602045i
$873$	−39424.8	−	22761.9i	−1.52844	−	0.882446i
$874$	−3776.38	−	2022.21i	−0.146153	−	0.0782633i
$875$	−23403.9	−	2450.99i	−0.904222	−	0.0946954i
$876$	−42093.8	+	28033.8i	−1.62353	+	1.08125i
$877$	6313.22	−	10934.8i	0.243081	−	0.421029i	−0.718509	−	0.695518i	$-0.755175\pi$
$877$	6313.22	−	10934.8i	0.243081	−	0.421029i	0.961590	+	0.274488i	$0.0885084\pi$
$878$	−43113.7	+	1378.62i	−1.65719	+	0.0529910i
$879$	45578.8	−	26314.9i	1.74896	−	1.00976i
$880$	−70.8088	−	92.8625i	−0.00271246	−	0.00355727i
$881$			38693.9i			1.47972i	0.672762	+	0.739859i	$0.265108\pi$
$881$			38693.9i			1.47972i	−0.672762	+	0.739859i	$0.734892\pi$
$882$	−56938.0	−	10168.5i	−2.17370	−	0.388198i
$883$			33659.7i			1.28283i	0.767193	+	0.641416i	$0.221653\pi$
$883$			33659.7i			1.28283i	−0.767193	+	0.641416i	$0.778347\pi$
$884$	−10914.7	+	698.740i	−0.415273	+	0.0265851i
$885$	24530.2	−	14162.5i	0.931721	−	0.537930i
$886$	−700.663	−	21911.9i	−0.0265680	−	0.830863i
$887$	−16620.8	+	28788.1i	−0.629168	+	1.08975i	0.358551	+	0.933510i	$0.383271\pi$
$887$	−16620.8	+	28788.1i	−0.629168	+	1.08975i	−0.987719	+	0.156241i	$0.950062\pi$
$888$	30377.0	−	2922.01i	1.14796	−	0.110424i
$889$	−7925.38	−	829.991i	−0.298997	−	0.0313127i
$890$	−370.677	+	692.223i	−0.0139608	+	0.0260712i
$891$	−325.224	−	187.768i	−0.0122283	−	0.00706000i
$892$	−13744.7	+	27765.2i	−0.515928	+	1.04220i
$893$	407.158	+	705.219i	0.0152576	+	0.0264269i
$894$	−19590.7	−	31557.8i	−0.732898	−	1.18059i
$895$	9017.71			0.336792
$896$	−21464.0	+	16081.6i	−0.800294	+	0.599608i
$897$	7755.87			0.288697
$898$	−1287.28	−	2073.63i	−0.0478365	−	0.0770579i
$899$	−1718.41	−	2976.37i	−0.0637509	−	0.110420i
$900$	−19067.2	+	38516.9i	−0.706193	+	1.42655i
$901$	−17072.9	−	9857.05i	−0.631278	−	0.364468i
$902$	105.125	−	196.317i	0.00388059	−	0.00724683i
$903$	25740.5	+	57755.8i	0.948604	+	2.12845i
$904$	−17506.9	+	1684.02i	−0.644106	+	0.0619575i
$905$	−2916.17	+	5050.96i	−0.107112	+	0.185524i
$906$	−2039.31	−	63775.5i	−0.0747809	−	2.33863i
$907$	8033.78	−	4638.30i	0.294109	−	0.169804i	−0.345684	−	0.938351i	$-0.612353\pi$
$907$	8033.78	−	4638.30i	0.294109	−	0.169804i	0.639794	+	0.768547i	$0.279020\pi$
$908$	26243.2	−	1680.04i	0.959152	−	0.0614032i
$909$			46108.1i			1.68241i
$910$	−978.341	+	13493.1i	−0.0356392	+	0.491531i
$911$		−	30720.4i		−	1.11725i	−0.829422	−	0.558623i	$-0.811330\pi$
$911$		−	30720.4i		−	1.11725i	0.829422	−	0.558623i	$-0.188670\pi$
$912$	−28699.4	−	37637.9i	−1.04203	−	1.36657i
$913$	−215.525	+	124.433i	−0.00781253	+	0.00451057i
$914$	−15831.4	+	506.232i	−0.572929	+	0.0183202i
$915$	21236.0	−	36781.8i	0.767256	−	1.32893i
$916$	−18768.1	+	12499.2i	−0.676981	+	0.450858i
$917$	−24568.4	−	17835.9i	−0.884754	−	0.642306i
$918$	−23668.2	−	12674.1i	−0.850946	−	0.455671i
$919$	12717.5	+	7342.43i	0.456486	+	0.263552i	0.710565	−	0.703631i	$-0.248439\pi$
$919$	12717.5	+	7342.43i	0.456486	+	0.263552i	−0.254080	+	0.967183i	$0.581773\pi$
$920$	1479.08	+	2074.01i	0.0530040	+	0.0743240i
$921$	17671.4	+	30607.7i	0.632238	+	1.09507i
$922$	31548.3	−	19584.8i	1.12688	−	0.699555i
$923$	11421.0			0.407288
$924$	197.907	+	377.206i	0.00704616	+	0.0134298i
$925$	−13058.1			−0.464160
$926$	8049.03	−	4996.74i	0.285645	−	0.177325i
$927$	−8516.39	−	14750.8i	−0.301742	−	0.522633i
$928$	2582.88	−	6784.29i	0.0913654	−	0.239984i
$929$	−3241.56	−	1871.51i	−0.114480	−	0.0660951i	0.441667	−	0.897179i	$-0.354387\pi$
$929$	−3241.56	−	1871.51i	−0.114480	−	0.0660951i	−0.556147	+	0.831084i	$0.687721\pi$
$930$	11747.2	+	6290.50i	0.414201	+	0.221800i
$931$	−18222.5	+	20268.6i	−0.641481	+	0.713510i
$932$	−25735.9	−	38643.4i	−0.904513	−	1.35816i
$933$	26727.8	−	46293.9i	0.937865	−	1.62443i
$934$	5999.11	−	191.830i	0.210168	−	0.00672041i
$935$	−49.4099	+	28.5268i	−0.00172821	+	0.000997782i
$936$	53670.0	+	24465.1i	1.87421	+	0.854345i
$937$		−	16171.0i		−	0.563803i	−0.959443	−	0.281901i	$-0.909035\pi$
$937$		−	16171.0i		−	0.563803i	0.959443	−	0.281901i	$-0.0909651\pi$
$938$	15289.4	−	22542.4i	0.532214	−	0.784687i
$939$		−	58145.2i		−	2.02076i
$940$	−30.9372	−	483.257i	−0.00107347	−	0.0167682i
$941$	18530.6	−	10698.7i	0.641957	−	0.370634i	−0.143411	−	0.989663i	$-0.545807\pi$
$941$	18530.6	−	10698.7i	0.641957	−	0.370634i	0.785368	+	0.619029i	$0.212474\pi$
$942$	−2574.77	−	80520.9i	−0.0890556	−	2.78504i
$943$	−2428.87	+	4206.93i	−0.0838759	+	0.145277i
$944$	−12711.9	+	30427.4i	−0.438279	+	1.04907i
$945$	−19510.0	+	26874.4i	−0.671600	+	0.925106i
$946$	151.311	−	282.567i	0.00520038	−	0.00971147i
$947$	−5068.33	−	2926.20i	−0.173916	−	0.100410i	0.410515	−	0.911854i	$-0.365349\pi$
$947$	−5068.33	−	2926.20i	−0.173916	−	0.100410i	−0.584431	+	0.811443i	$0.698682\pi$
$948$	23081.3	+	11426.1i	0.790766	+	0.391457i
$949$	−14849.7	−	25720.5i	−0.507948	−	0.879791i
$950$	10681.8	+	17206.8i	0.364803	+	0.587646i
$951$	43051.9			1.46798
$952$	6455.54	+	11402.7i	0.219774	+	0.388198i
$953$	−14470.9			−0.491875			−0.245938	−	0.969286i	$-0.579096\pi$
$953$	−14470.9			−0.491875			−0.245938	+	0.969286i	$0.579096\pi$
$954$	56074.2	+	90327.6i	1.90301	+	3.06548i
$955$	−11590.4	−	20075.2i	−0.392731	−	0.680229i
$956$	−42722.1	−	21149.0i	−1.44533	−	0.715488i
$957$	−99.8493	−	57.6480i	−0.00337269	−	0.00194723i
$958$	10591.8	−	19779.7i	0.357209	−	0.667071i
$959$	30335.3	−	13519.7i	1.02146	−	0.455240i
$960$	5365.24	+	27630.3i	0.180377	+	0.928920i
$961$	11223.2	−	19439.1i	0.376731	−	0.652517i
$962$	572.756	+	17911.8i	0.0191958	+	0.600313i
$963$	−109472.	+	63203.9i	−3.66324	+	2.11497i
$964$	1082.36	+	16907.0i	0.0361623	+	0.564875i
$965$			21947.1i			0.732127i
$966$	−4051.90	−	8362.04i	−0.134956	−	0.278514i
$967$		−	6344.28i		−	0.210981i	−0.994420	−	0.105490i	$-0.966359\pi$
$967$		−	6344.28i		−	0.210981i	0.994420	−	0.105490i	$-0.0336412\pi$
$968$	−12491.1	+	27402.2i	−0.414751	+	0.909856i
$969$	−20026.2	+	11562.1i	−0.663916	+	0.383312i
$970$	12750.5	−	407.716i	0.422057	−	0.0134958i
$971$	−1273.33	+	2205.48i	−0.0420836	+	0.0728909i	−0.886300	−	0.463112i	$-0.846733\pi$
$971$	−1273.33	+	2205.48i	−0.0420836	+	0.0728909i	0.844216	+	0.536003i	$0.180066\pi$
$972$	13824.4	+	20757.8i	0.456191	+	0.684988i
$973$	1308.48	−	12494.4i	0.0431121	−	0.411666i
$974$	28835.7	+	15441.2i	0.948619	+	0.507974i
$975$	−31755.8	−	18334.2i	−1.04308	−	0.602221i
$976$	6305.02	+	49042.2i	0.206782	+	1.60840i
$977$	21695.6	+	37577.8i	0.710442	+	1.23052i	0.964691	+	0.263384i	$0.0848385\pi$
$977$	21695.6	+	37577.8i	0.710442	+	1.23052i	−0.254249	+	0.967139i	$0.581828\pi$
$978$	20313.4	−	12610.3i	0.664162	−	0.412303i
$979$	−14.5190			−0.000473984
$980$	15058.8	−	5994.42i	0.490854	−	0.195393i
$981$	50168.8			1.63279
$982$	−40854.8	+	25362.1i	−1.32763	+	0.824174i
$983$	−23377.9	−	40491.8i	−0.758536	−	1.31382i	−0.943597	−	0.331095i	$-0.892582\pi$
$983$	−23377.9	−	40491.8i	−0.758536	−	1.31382i	0.185062	−	0.982727i	$-0.440752\pi$
$984$	−43699.7	+	31164.3i	−1.41575	+	1.00964i
$985$	−24102.6	−	13915.7i	−0.779669	−	0.450142i
$986$	−3126.57	−	1674.24i	−0.100984	−	0.0540758i
$987$	−183.978	+	1756.76i	−0.00593322	+	0.0566548i
$988$	23134.1	−	15406.9i	0.744934	−	0.496114i
$989$	−3495.98	+	6055.21i	−0.112402	+	0.194686i
$990$	307.531	−	9.83372i	0.00987270	−	0.000315693i
$991$	−22540.1	+	13013.6i	−0.722514	+	0.417144i	−0.815677	−	0.578507i	$-0.803635\pi$
$991$	−22540.1	+	13013.6i	−0.722514	+	0.417144i	0.0931634	+	0.995651i	$0.470302\pi$
$992$	−15315.8	+	2468.94i	−0.490198	+	0.0790210i
$993$		−	60824.9i		−	1.94383i
$994$	−5966.68	−	12313.6i	−0.190394	−	0.392922i
$995$			54.3857i			0.00173281i
$996$	59860.0	−	3832.13i	1.90436	−	0.121913i
$997$	22834.8	−	13183.7i	0.725362	−	0.418788i	−0.0913611	−	0.995818i	$-0.529122\pi$
$997$	22834.8	−	13183.7i	0.725362	−	0.418788i	0.816723	+	0.577030i	$0.195788\pi$
$998$	1184.92	+	37056.2i	0.0375832	+	1.17534i
$999$	−21996.0	+	38098.2i	−0.696620	+	1.20658i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	28.4.f.a.19.4	yes	20
4.3	odd	2	inner	28.4.f.a.19.10	yes	20
7.2	even	3		196.4.d.b.195.7		20
7.3	odd	6	inner	28.4.f.a.3.10	yes	20
7.4	even	3		196.4.f.d.31.10		20
7.5	odd	6		196.4.d.b.195.8		20
7.6	odd	2		196.4.f.d.19.4		20
8.3	odd	2		448.4.p.h.383.10		20
8.5	even	2		448.4.p.h.383.1		20
28.3	even	6	inner	28.4.f.a.3.4	✓	20
28.11	odd	6		196.4.f.d.31.4		20
28.19	even	6		196.4.d.b.195.5		20
28.23	odd	6		196.4.d.b.195.6		20
28.27	even	2		196.4.f.d.19.10		20
56.3	even	6		448.4.p.h.255.1		20
56.45	odd	6		448.4.p.h.255.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.4.f.a.3.4	✓	20	28.3	even	6	inner
28.4.f.a.3.10	yes	20	7.3	odd	6	inner
28.4.f.a.19.4	yes	20	1.1	even	1	trivial
28.4.f.a.19.10	yes	20	4.3	odd	2	inner
196.4.d.b.195.5		20	28.19	even	6
196.4.d.b.195.6		20	28.23	odd	6
196.4.d.b.195.7		20	7.2	even	3
196.4.d.b.195.8		20	7.5	odd	6
196.4.f.d.19.4		20	7.6	odd	2
196.4.f.d.19.10		20	28.27	even	2
196.4.f.d.31.4		20	28.11	odd	6
196.4.f.d.31.10		20	7.4	even	3
448.4.p.h.255.1		20	56.3	even	6
448.4.p.h.255.10		20	56.45	odd	6
448.4.p.h.383.1		20	8.5	even	2
448.4.p.h.383.10		20	8.3	odd	2

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	28.4.f.a.19.4

Level	$28$
Weight	$4$
Character	28.19
Analytic conductor	$1.652$
Analytic rank	$0$
Dimension	$20$
Inner twists	$4$