LMFDB - Embedded newform 28.4.f.a.3.4

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			3.4
Root			$2.82698 + 0.0903966i$ of defining polynomial
Character	$\chi$	$=$	28.3
Dual form			28.4.f.a.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49178 + 2.40304i) q^{2} +(4.65345 - 8.06002i) q^{3} +(-3.54920 - 7.16960i) q^{4} +(5.11538 - 2.95337i) q^{5} +(12.4266 + 23.2062i) q^{6} +(1.92900 + 18.4195i) q^{7} +(22.5235 + 2.16656i) q^{8} +(-29.8092 - 51.6311i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 20 * q + 4 * q^4 - 6 * q^5 + 72 * q^8 - 56 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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	0.0624441	−	0.998048i	$-0.480110\pi$
$3$	4.65345	−	8.06002i	0.895557	−	1.55115i	0.833113	−	0.553102i	$-0.186556\pi$
$4$	−3.54920	−	7.16960i	−0.443650	−	0.896200i
$5$	5.11538	−	2.95337i	0.457533	−	0.264157i	−0.253473	−	0.967342i	$-0.581573\pi$
$5$	5.11538	−	2.95337i	0.457533	−	0.264157i	0.711007	+	0.703185i	$0.248240\pi$
$6$	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	0.503662	−	0.863901i	$-0.331986\pi$
$11$	0.267527	+	0.154457i	0.00733296	+	0.00423368i	−0.496329	+	0.868134i	$0.665319\pi$
$12$	−74.3031	−	4.75675i	−1.78746	−	0.114430i
$13$			43.7232i			0.932818i	0.884569	+	0.466409i	$0.154453\pi$
$13$			43.7232i			0.932818i	−0.884569	+	0.466409i	$0.845547\pi$
$14$	−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	0.294240	−	0.955732i	$-0.404933\pi$
$17$	−27.0788	−	15.6339i	−0.386328	−	0.223046i	−0.680568	+	0.732685i	$0.738267\pi$
$18$	168.540	+	5.38931i	2.20696	+	0.0705707i
$19$	39.7315	+	68.8169i	0.479738	+	0.830930i	0.999730	−	0.0232407i	$-0.00739841\pi$
$19$	39.7315	+	68.8169i	0.479738	+	0.830930i	−0.519992	+	0.854171i	$0.674065\pi$
$20$	−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	−0.423310	−	0.905985i	$-0.639132\pi$
$23$	16.5061	−	9.52978i	0.149641	−	0.0863955i	0.572951	+	0.819590i	$0.305798\pi$
$24$	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	−0.714781	−	0.699348i	$-0.753474\pi$
$31$	42.8504	−	74.2190i	0.248263	−	0.430004i	0.963044	+	0.269344i	$0.0868069\pi$
$32$	−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	0.980888	−	0.194574i	$-0.0623323\pi$
$37$	72.4561	+	125.498i	0.321938	+	0.557613i	−0.658950	+	0.752187i	$0.728999\pi$
$38$	−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	$-0.838667\pi$
$41$		−	254.872i		−	0.970837i	0.874282	−	0.485418i	$-0.161333\pi$
$42$	−403.476	+	273.657i	−1.48233	+	1.00539i
$43$		−	366.848i		−	1.30102i	−0.759499	−	0.650509i	$-0.774556\pi$
$43$		−	366.848i		−	1.30102i	0.759499	−	0.650509i	$-0.225444\pi$
$44$	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	0.857965	−	0.513708i	$-0.171729\pi$
$47$	−5.12388	−	8.87482i	−0.0159020	−	0.0275431i	−0.873867	+	0.486165i	$0.838395\pi$
$48$	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	−0.0908416	−	0.995865i	$-0.528956\pi$
$53$	315.245	−	546.021i	0.817024	−	1.41513i	0.907865	−	0.419262i	$-0.137711\pi$
$54$	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	0.428244	+	0.903663i	$0.359132\pi$
$59$	−257.625	+	446.219i	−0.568473	+	0.984624i	−0.996717	+	0.0809610i	$0.974201\pi$
$60$	−394.137	+	195.112i	−0.848048	+	0.419814i
$61$	−669.083	+	386.295i	−1.40438	+	0.810820i	−0.994839	−	0.101470i	$-0.967645\pi$
$61$	−669.083	+	386.295i	−1.40438	+	0.810820i	−0.409543	+	0.912291i	$0.634312\pi$
$62$	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	0.0296822	−	0.999559i	$-0.490550\pi$
$67$	−450.318	−	259.991i	−0.821121	−	0.474074i	−0.850803	+	0.525485i	$0.823884\pi$
$68$	−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	$-0.929945\pi$
$71$		−	261.211i		−	0.436621i	0.975879	−	0.218310i	$-0.0700545\pi$
$72$	−559.545	−	1227.49i	−0.915875	−	2.00919i
$73$	588.256	+	339.630i	0.943154	+	0.544530i	0.890947	−	0.454106i	$-0.150041\pi$
$73$	588.256	+	339.630i	0.943154	+	0.544530i	0.0522061	+	0.998636i	$0.483375\pi$
$74$	−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	−0.697909	−	0.716186i	$-0.745886\pi$
$79$	−299.565	+	172.954i	−0.426629	+	0.246314i	0.271280	+	0.962500i	$0.412553\pi$
$80$	−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	−0.524043	−	0.851692i	$-0.675577\pi$
$89$	−40.7034	+	23.5001i	−0.0484782	+	0.0279889i	0.475565	+	0.879681i	$0.342244\pi$
$90$	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	$-0.869135\pi$
$97$		−	763.587i		−	0.799283i	0.916671	−	0.399642i	$-0.130865\pi$
$98$	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	0.792219	−	0.610236i	$-0.208926\pi$
$101$	669.771	+	386.693i	0.659849	+	0.380964i	−0.132371	+	0.991200i	$0.542259\pi$
$102$	26.3061	−	822.672i	0.0255362	−	0.798595i
$103$	−142.848	−	247.420i	−0.136653	−	0.236690i	0.789575	−	0.613654i	$-0.210301\pi$
$103$	−142.848	−	247.420i	−0.136653	−	0.236690i	−0.926228	+	0.376965i	$0.876968\pi$
$104$	−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	0.685830	−	0.727762i	$-0.259439\pi$
$107$	1836.21	−	1060.14i	1.65900	−	0.957827i	0.973175	−	0.230065i	$-0.0738938\pi$
$108$	1077.46	+	2176.53i	0.959985	+	1.93923i
$109$	−420.749	+	728.759i	−0.369729	+	0.640389i	−0.989523	−	0.144375i	$-0.953883\pi$
$109$	−420.749	+	728.759i	−0.369729	+	0.640389i	0.619794	+	0.784764i	$0.287216\pi$
$110$	−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	$0.0480292\pi$
$127$			430.270i			0.300633i	−0.988638	+	0.150316i	$0.951971\pi$
$128$	−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	0.998500	+	0.0547434i	$0.0174341\pi$
$131$	819.641	+	1419.66i	0.546659	+	0.946842i	−0.451841	+	0.892098i	$0.649233\pi$
$132$	−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	−0.438412	−	0.898774i	$-0.644459\pi$
$137$	896.630	−	1553.01i	0.559155	−	0.968485i	0.997567	−	0.0697109i	$-0.0222077\pi$
$138$	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	0.992168	−	0.124908i	$-0.0398637\pi$
$149$	705.522	+	1222.00i	0.387910	+	0.671881i	−0.604258	+	0.796789i	$0.706530\pi$
$150$	−2370.85	−	75.8111i	−1.29053	−	0.0412664i
$151$	2099.21	+	1211.98i	1.13133	+	0.653176i	0.944270	−	0.329172i	$-0.106770\pi$
$151$	2099.21	+	1211.98i	1.13133	+	0.653176i	0.187063	+	0.982348i	$0.440103\pi$
$152$	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	0.987865	−	0.155315i	$-0.0496393\pi$
$157$	2650.40	+	1530.21i	1.34729	+	0.777859i	0.359426	+	0.933174i	$0.382973\pi$
$158$	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	−0.298961	−	0.954265i	$-0.596640\pi$
$163$	786.587	−	454.136i	0.377977	−	0.218225i	0.676938	+	0.736040i	$0.263307\pi$
$164$	−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	−0.711829	−	0.702352i	$-0.752133\pi$
$173$	−1045.55	+	603.648i	−0.459489	+	0.265286i	0.252340	+	0.967639i	$0.418800\pi$
$174$	−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	0.749960	−	0.661484i	$-0.230073\pi$
$179$	1322.15	+	763.342i	0.552078	+	0.318742i	−0.197882	+	0.980226i	$0.563406\pi$
$180$	−179.984	+	2811.45i	−0.0745289	+	1.16418i
$181$		−	987.406i		−	0.405488i	−0.979232	−	0.202744i	$-0.935014\pi$
$181$		−	987.406i		−	0.405488i	0.979232	−	0.202744i	$-0.0649859\pi$
$182$	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	−0.978216	−	0.207589i	$-0.933438\pi$
$191$	−3398.70	+	1962.24i	−1.28755	+	0.743366i	−0.309331	+	0.950954i	$0.600105\pi$
$192$	3125.51	−	3596.90i	1.17482	−	1.35200i
$193$	1857.81	−	3217.81i	0.692890	−	1.20012i	−0.277997	−	0.960582i	$-0.589670\pi$
$193$	1857.81	−	3217.81i	0.692890	−	1.20012i	0.970887	−	0.239539i	$-0.0769963\pi$
$194$	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	−0.865204	−	0.501420i	$-0.832811\pi$
$199$	4.60370	−	7.97385i	0.00163994	−	0.00284046i	0.866844	+	0.498579i	$0.166145\pi$
$200$	−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	$-0.964509\pi$
$211$		−	682.060i		−	0.222535i	0.993790	−	0.111268i	$-0.0354911\pi$
$212$	−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	−0.999751	−	0.0223066i	$-0.992899\pi$
$227$	−1643.55	+	2846.72i	−0.480558	+	0.832350i	0.519194	+	0.854657i	$0.326232\pi$
$228$	−2624.83	−	5302.30i	−0.762427	−	1.54015i
$229$	2441.03	−	1409.33i	0.704402	−	0.406687i	−0.104583	−	0.994516i	$-0.533351\pi$
$229$	2441.03	−	1409.33i	0.704402	−	0.406687i	0.808985	+	0.587829i	$0.200017\pi$
$230$	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	−0.908683	−	0.417487i	$-0.862911\pi$
$233$	−2901.81	−	5026.08i	−0.815896	−	1.41317i	0.0927866	−	0.995686i	$-0.470423\pi$
$234$	−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	$-0.701432\pi$
$239$		−	5958.79i		−	1.61273i	0.591419	−	0.806364i	$-0.298568\pi$
$240$	2797.75	+	2133.31i	0.752474	+	0.573770i
$241$	1833.99	+	1058.85i	0.490197	+	0.283016i	0.724656	−	0.689110i	$-0.241999\pi$
$241$	1833.99	+	1058.85i	0.490197	+	0.283016i	−0.234459	+	0.972126i	$0.575332\pi$
$242$	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	0.446606	−	0.894731i	$-0.352632\pi$
$257$	5952.48	−	3436.67i	1.44477	−	0.834138i	0.998163	+	0.0605927i	$0.0192991\pi$
$258$	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	0.254999	−	0.966941i	$-0.417925\pi$
$263$	−1940.20	−	1120.18i	−0.454897	−	0.262635i	−0.709896	+	0.704306i	$0.751258\pi$
$264$	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	0.527459	−	0.849581i	$-0.323145\pi$
$269$	244.551	+	141.192i	0.0554295	+	0.0320023i	−0.472029	+	0.881583i	$0.656478\pi$
$270$	162.095	−	5069.20i	0.0365362	−	1.14260i
$271$	2104.49	+	3645.09i	0.471730	+	0.817061i	0.999477	−	0.0323409i	$-0.0102962\pi$
$271$	2104.49	+	3645.09i	0.471730	+	0.817061i	−0.527746	+	0.849402i	$0.676963\pi$
$272$	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	−0.972801	−	0.231644i	$-0.925589\pi$
$277$	−1317.55	+	2282.06i	−0.285790	+	0.495003i	0.687010	+	0.726648i	$0.258923\pi$
$278$	−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	−0.717512	−	0.696546i	$-0.754719\pi$
$283$	1163.88	−	2015.89i	0.244471	−	0.423436i	0.961983	+	0.273110i	$0.0880523\pi$
$284$	−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	$0.190646\pi$
$293$			5654.92i			1.12752i	−0.825938	+	0.563761i	$0.809354\pi$
$294$	−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	0.476001	+	0.879445i	$0.342086\pi$
$311$	−2871.82	+	4974.14i	−0.523621	+	0.906938i	−0.999622	+	0.0274932i	$0.991248\pi$
$312$	7496.67	+	5346.23i	1.36031	+	0.970098i
$313$	−5410.52	+	3123.77i	−0.977063	+	0.564108i	−0.901382	−	0.433024i	$-0.857446\pi$
$313$	−5410.52	+	3123.77i	−0.977063	+	0.564108i	−0.0756809	+	0.997132i	$0.524113\pi$
$314$	−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	0.994867	−	0.101194i	$-0.0322664\pi$
$317$	2312.90	+	4006.06i	0.409796	+	0.709788i	−0.585070	+	0.810983i	$0.698933\pi$
$318$	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	−0.889917	−	0.456122i	$-0.849238\pi$
$331$	−5659.87	+	3267.73i	−0.939863	+	0.542630i	−0.0499455	+	0.998752i	$0.515905\pi$
$332$	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	0.967586	−	0.252543i	$-0.0812668\pi$
$347$	7967.85	+	4600.24i	1.23267	+	0.711683i	0.265085	+	0.964225i	$0.414600\pi$
$348$	2979.74	+	190.758i	0.458997	+	0.0293841i
$349$			6940.92i			1.06458i	0.846562	+	0.532290i	$0.178669\pi$
$349$			6940.92i			1.06458i	−0.846562	+	0.532290i	$0.821331\pi$
$350$	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	0.599350	−	0.800487i	$-0.295426\pi$
$353$	1364.81	+	787.975i	0.205784	+	0.118809i	−0.393567	+	0.919296i	$0.628759\pi$
$354$	−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	0.0659267	−	0.997824i	$-0.479000\pi$
$359$	6550.62	−	3782.00i	0.963031	−	0.556006i	0.897105	+	0.441818i	$0.145666\pi$
$360$	−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	−0.0487544	−	0.998811i	$-0.515525\pi$
$367$	5910.14	−	10236.7i	0.840618	−	1.45599i	0.889373	−	0.457183i	$-0.151142\pi$
$368$	−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	0.721044	−	0.692890i	$-0.243663\pi$
$373$	−1725.59	−	2988.81i	−0.239538	−	0.414892i	−0.960582	+	0.277997i	$0.910329\pi$
$374$	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	$0.00783973\pi$
$379$			363.409i			0.0492535i	−0.999697	+	0.0246267i	$0.992160\pi$
$380$	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	0.811234	−	0.584721i	$-0.198796\pi$
$383$	−755.287	−	1308.20i	−0.100766	−	0.174532i	−0.912000	+	0.410189i	$0.865463\pi$
$384$	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	−0.796990	−	0.603992i	$-0.793576\pi$
$389$	955.790	−	1655.48i	0.124577	−	0.215774i	0.921568	+	0.388218i	$0.126909\pi$
$390$	−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	−0.956397	−	0.292068i	$-0.905657\pi$
$397$	−9347.11	+	5396.56i	−1.18166	+	0.682230i	−0.225260	+	0.974299i	$0.572323\pi$
$398$	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	0.997501	+	0.0706511i	$0.0225077\pi$
$401$	4496.30	+	7787.82i	0.559936	+	0.969838i	−0.437565	+	0.899187i	$0.644159\pi$
$402$	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	0.0747922	−	0.997199i	$-0.476171\pi$
$409$	−6215.31	−	3588.41i	−0.751411	−	0.433828i	−0.826204	+	0.563372i	$0.809504\pi$
$410$	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	−0.271145	−	0.962539i	$-0.587402\pi$
$431$	−11097.9	−	6407.40i	−1.24030	−	0.716087i	−0.969155	+	0.246451i	$0.920735\pi$
$432$	11780.7	−	15449.9i	1.31204	−	1.72068i
$433$			12764.8i			1.41672i	0.705854	+	0.708358i	$0.250564\pi$
$433$			12764.8i			1.41672i	−0.705854	+	0.708358i	$0.749436\pi$
$434$	−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	0.898808	+	0.438344i	$0.144435\pi$
$439$	7625.39	+	13207.6i	0.829020	+	1.43591i	−0.0697871	+	0.997562i	$0.522232\pi$
$440$	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	−0.0948055	−	0.995496i	$-0.530223\pi$
$443$	6712.55	−	3875.49i	0.719916	−	0.415644i	0.814722	+	0.579852i	$0.196890\pi$
$444$	−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	0.972999	−	0.230811i	$-0.0741380\pi$
$457$	2800.06	+	4849.84i	0.286611	+	0.496425i	−0.686388	+	0.727236i	$0.740805\pi$
$458$	−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	$-0.769205\pi$
$461$		−	13128.5i		−	1.32637i	0.748458	−	0.663183i	$-0.230795\pi$
$462$	−150.209	+	10.8912i	−0.0151263	+	0.00109676i
$463$		−	3349.52i		−	0.336210i	−0.985769	−	0.168105i	$-0.946235\pi$
$463$		−	3349.52i		−	0.336210i	0.985769	−	0.168105i	$-0.0537648\pi$
$464$	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	0.808657	−	0.588281i	$-0.200195\pi$
$467$	−1061.05	−	1837.78i	−0.105138	−	0.182104i	−0.913794	+	0.406177i	$0.866862\pi$
$468$	−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	−0.612476	−	0.790489i	$-0.709826\pi$
$479$	3966.36	−	6869.94i	0.378346	−	0.655314i	0.990822	+	0.135175i	$0.0431597\pi$
$480$	−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	−0.0444880	−	0.999010i	$-0.514166\pi$
$487$	−10015.3	−	5782.32i	−0.931900	−	0.538033i	−0.887412	+	0.460977i	$0.847499\pi$
$488$	−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	$0.285454\pi$
$491$			17001.3i			1.56264i	−0.624129	+	0.781322i	$0.714546\pi$
$492$	−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	−0.913640	−	0.406525i	$-0.866740\pi$
$499$	−11351.9	+	6554.02i	−1.01840	+	0.587972i	−0.104759	+	0.994498i	$0.533407\pi$
$500$	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	0.500100	−	0.865968i	$-0.333297\pi$
$509$	17226.5	−	9945.72i	1.50010	−	0.866083i	1.00000		0.000115072i	$-3.66284e-5\pi$
$510$	−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	−0.992791	−	0.119861i	$-0.961755\pi$
$521$	−18943.9	−	10937.3i	−1.59299	−	0.919712i	−0.600198	−	0.799851i	$-0.704912\pi$
$522$	−6758.89	−	216.125i	−0.566721	−	0.0181217i
$523$	2620.60	+	4539.02i	0.219103	+	0.379498i	0.954534	−	0.298102i	$-0.0963535\pi$
$523$	2620.60	+	4539.02i	0.219103	+	0.379498i	−0.735431	+	0.677600i	$0.763020\pi$
$524$	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	0.975042	−	0.222020i	$-0.0712652\pi$
$541$	3715.18	+	6434.87i	0.295246	+	0.511381i	−0.679796	+	0.733401i	$0.737932\pi$
$542$	−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	$-0.783119\pi$
$547$		−	16115.5i		−	1.25969i	0.776722	−	0.629843i	$-0.216881\pi$
$548$	−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	−0.908455	−	0.417982i	$-0.862737\pi$
$557$	−1212.61	+	2100.30i	−0.0922442	+	0.159772i	0.816211	+	0.577754i	$0.196071\pi$
$558$	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	−0.997547	−	0.0700065i	$-0.977698\pi$
$563$	−5853.04	+	10137.8i	−0.438146	+	0.758891i	0.559401	+	0.828897i	$0.311031\pi$
$564$	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	0.951082	−	0.308939i	$-0.0999739\pi$
$569$	2823.03	+	4889.62i	0.207992	+	0.360253i	−0.743090	+	0.669192i	$0.766641\pi$
$570$	−394.884	+	12349.2i	−0.0290173	+	0.907461i
$571$	−3710.60	−	2142.31i	−0.271950	−	0.157011i	0.357823	−	0.933789i	$-0.383519\pi$
$571$	−3710.60	−	2142.31i	−0.271950	−	0.157011i	−0.629774	+	0.776779i	$0.716852\pi$
$572$	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	0.630100	−	0.776514i	$-0.283014\pi$
$577$	3779.21	+	2181.93i	0.272670	+	0.157426i	−0.357430	+	0.933940i	$0.616347\pi$
$578$	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	−0.552498	+	0.833514i	$0.686325\pi$
$593$	−22391.3	+	12927.6i	−1.55059	+	0.895235i	−0.998093	+	0.0617205i	$0.980341\pi$
$594$	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	0.0567142	−	0.998390i	$-0.481938\pi$
$599$	−11428.5	−	6598.26i	−0.779560	−	0.450079i	−0.836274	+	0.548311i	$0.815271\pi$
$600$	7871.09	+	17267.1i	0.535560	+	1.17488i
$601$		−	1378.53i		−	0.0935630i	−0.998905	−	0.0467815i	$-0.985104\pi$
$601$		−	1378.53i		−	0.0935630i	0.998905	−	0.0467815i	$-0.0148964\pi$
$602$	−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	0.999846	+	0.0175378i	$0.00558275\pi$
$607$	7703.43	+	13342.7i	0.515111	+	0.892199i	−0.484735	+	0.874661i	$0.661084\pi$
$608$	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	−0.723852	−	0.689955i	$-0.757630\pi$
$613$	3575.63	−	6193.18i	0.235593	−	0.408059i	0.959445	+	0.281897i	$0.0909635\pi$
$614$	−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	−0.533679	−	0.845687i	$-0.679191\pi$
$619$	7169.67	−	12418.2i	0.465547	−	0.806351i	0.999226	+	0.0393363i	$0.0125244\pi$
$620$	−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	$0.0889722\pi$
$631$			8745.97i			0.551778i	−0.961190	+	0.275889i	$0.911028\pi$
$632$	−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	−0.999718	−	0.0237532i	$-0.992438\pi$
$641$	−7778.28	+	13472.4i	−0.479288	+	0.830151i	0.520430	+	0.853904i	$0.325772\pi$
$642$	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	−0.250318	−	0.968164i	$-0.580535\pi$
$647$	11738.9	−	20332.3i	0.713296	−	1.23546i	0.963613	−	0.267301i	$-0.0861317\pi$
$648$	−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	0.999453	+	0.0330667i	$0.0105274\pi$
$653$	8816.62	+	15270.8i	0.528363	+	0.915152i	−0.471090	+	0.882085i	$0.656139\pi$
$654$	−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	$-0.996247\pi$
$659$		−	398.945i		−	0.0235822i	0.999930	−	0.0117911i	$-0.00375331\pi$
$660$	−135.579	−	8.67951i	−0.00799606	−	0.000511893i
$661$	5167.67	+	2983.55i	0.304083	+	0.175563i	0.644276	−	0.764793i	$-0.277159\pi$
$661$	5167.67	+	2983.55i	0.304083	+	0.175563i	−0.340193	+	0.940356i	$0.610492\pi$
$662$	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	−0.716072	−	0.698027i	$-0.754062\pi$
$677$	−8272.00	+	4775.84i	−0.469599	+	0.271123i	0.246473	+	0.969150i	$0.420728\pi$
$678$	−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	0.918060	−	0.396441i	$-0.129755\pi$
$683$	18452.4	+	10653.5i	1.03376	+	0.596843i	0.115702	+	0.993284i	$0.463088\pi$
$684$	−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	0.955656	−	0.294485i	$-0.0951482\pi$
$691$	4046.92	+	7009.48i	0.222796	+	0.385895i	−0.732860	+	0.680380i	$0.761815\pi$
$692$	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	−0.984680	−	0.174372i	$-0.944210\pi$
$709$	−12145.5	−	21036.7i	−0.643351	−	1.11432i	0.341329	−	0.939944i	$-0.389123\pi$
$710$	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	−0.931220	−	0.364457i	$-0.881254\pi$
$719$	−15061.8	−	26087.8i	−0.781239	−	1.35315i	0.149981	−	0.988689i	$-0.452079\pi$
$720$	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	0.322496	−	0.946571i	$-0.395478\pi$
$733$	25868.2	−	14935.0i	1.30350	−	0.752575i	0.981002	+	0.193995i	$0.0621447\pi$
$734$	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	0.593576	−	0.804778i	$-0.297716\pi$
$739$	3885.39	+	2243.23i	0.193405	+	0.111662i	−0.400171	+	0.916441i	$0.631049\pi$
$740$	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	$0.178795\pi$
$743$			21574.3i			1.06525i	−0.846350	+	0.532627i	$0.821205\pi$
$744$	−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	−0.643652	+	0.765318i	$0.722582\pi$
$751$	−33510.8	+	19347.5i	−1.62826	+	0.940078i	−0.984611	+	0.174760i	$0.944085\pi$
$752$	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	−0.418626	−	0.908159i	$-0.637488\pi$
$761$	3328.46	−	1921.69i	0.158550	−	0.0915390i	0.577176	+	0.816620i	$0.304155\pi$
$762$	−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	$0.0832046\pi$
$769$			11022.0i			0.516857i	−0.966030	+	0.258428i	$0.916795\pi$
$770$	−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	−0.422796	−	0.906225i	$-0.638951\pi$
$773$	−30496.8	−	17607.3i	−1.41901	−	0.819264i	−0.996212	+	0.0869605i	$0.972285\pi$
$774$	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	−0.908107	−	0.418738i	$-0.862473\pi$
$787$	−2018.30	+	3495.79i	−0.0914162	+	0.158337i	0.816691	+	0.577075i	$0.195806\pi$
$788$	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	$0.196119\pi$
$797$			26004.8i			1.15575i	−0.816124	+	0.577877i	$0.803881\pi$
$798$	−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	−0.868605	−	0.495505i	$-0.834983\pi$
$809$	−119.264	+	206.571i	−0.00518305	+	0.00897730i	0.863422	+	0.504482i	$0.168316\pi$
$810$	−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	−0.999928	−	0.0120288i	$-0.996171\pi$
$821$	−12006.3	−	20795.5i	−0.510381	−	0.884006i	0.489547	−	0.871977i	$-0.337162\pi$
$822$	47181.5	+	1508.69i	2.00200	+	0.0640166i
$823$	25433.1	+	14683.8i	1.07721	+	0.621925i	0.930141	−	0.367201i	$-0.119684\pi$
$823$	25433.1	+	14683.8i	1.07721	+	0.621925i	0.147065	+	0.989127i	$0.453017\pi$
$824$	−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	$-0.981534\pi$
$827$		−	2757.80i		−	0.115959i	0.998318	−	0.0579796i	$-0.0184658\pi$
$828$	−580.763	+	9071.85i	−0.0243755	+	0.380759i
$829$	24688.8	+	14254.1i	1.03435	+	0.597184i	0.918229	−	0.396050i	$-0.129619\pi$
$829$	24688.8	+	14254.1i	1.03435	+	0.597184i	0.116125	+	0.993235i	$0.462953\pi$
$830$	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	$-0.783664\pi$
$853$		−	31316.1i		−	1.25703i	0.777799	−	0.628513i	$-0.216336\pi$
$854$	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	0.110730	−	0.993851i	$-0.464681\pi$
$857$	−17426.4	−	10061.2i	−0.694605	−	0.401030i	−0.805335	+	0.592820i	$0.798014\pi$
$858$	−355.368	−	11.3634i	−0.0141399	−	0.000452143i
$859$	6020.90	+	10428.5i	0.239151	+	0.414221i	0.960471	−	0.278381i	$-0.0897977\pi$
$859$	6020.90	+	10428.5i	0.239151	+	0.414221i	−0.721320	+	0.692602i	$0.756464\pi$
$860$	−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	−0.450142	−	0.892957i	$-0.648627\pi$
$863$	2487.30	−	1436.04i	0.0981098	−	0.0566437i	0.548252	+	0.836313i	$0.315293\pi$
$864$	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	0.961590	−	0.274488i	$-0.0885084\pi$
$877$	6313.22	+	10934.8i	0.243081	+	0.421029i	−0.718509	+	0.695518i	$0.755175\pi$
$878$	−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	$-0.734892\pi$
$881$		−	38693.9i		−	1.47972i	0.672762	−	0.739859i	$-0.265108\pi$
$882$	−56938.0	+	10168.5i	−2.17370	+	0.388198i
$883$		−	33659.7i		−	1.28283i	−0.767193	−	0.641416i	$-0.778347\pi$
$883$		−	33659.7i		−	1.28283i	0.767193	−	0.641416i	$-0.221653\pi$
$884$	−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	−0.987719	−	0.156241i	$-0.950062\pi$
$887$	−16620.8	−	28788.1i	−0.629168	−	1.08975i	0.358551	−	0.933510i	$-0.383271\pi$
$888$	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	0.639794	−	0.768547i	$-0.279020\pi$
$907$	8033.78	+	4638.30i	0.294109	+	0.169804i	−0.345684	+	0.938351i	$0.612353\pi$
$908$	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	$0.188670\pi$
$911$			30720.4i			1.11725i	−0.829422	+	0.558623i	$0.811330\pi$
$912$	−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	−0.254080	−	0.967183i	$-0.581773\pi$
$919$	12717.5	−	7342.43i	0.456486	−	0.263552i	0.710565	+	0.703631i	$0.248439\pi$
$920$	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	−0.556147	−	0.831084i	$-0.687721\pi$
$929$	−3241.56	+	1871.51i	−0.114480	+	0.0660951i	0.441667	+	0.897179i	$0.354387\pi$
$930$	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	$0.0909651\pi$
$937$			16171.0i			0.563803i	−0.959443	+	0.281901i	$0.909035\pi$
$938$	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	0.785368	−	0.619029i	$-0.212474\pi$
$941$	18530.6	+	10698.7i	0.641957	+	0.370634i	−0.143411	+	0.989663i	$0.545807\pi$
$942$	−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	−0.584431	−	0.811443i	$-0.698682\pi$
$947$	−5068.33	+	2926.20i	−0.173916	+	0.100410i	0.410515	+	0.911854i	$0.365349\pi$
$948$	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	$0.0336412\pi$
$967$			6344.28i			0.210981i	−0.994420	+	0.105490i	$0.966359\pi$
$968$	−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	0.844216	−	0.536003i	$-0.180066\pi$
$971$	−1273.33	−	2205.48i	−0.0420836	−	0.0728909i	−0.886300	+	0.463112i	$0.846733\pi$
$972$	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	−0.254249	−	0.967139i	$-0.581828\pi$
$977$	21695.6	−	37577.8i	0.710442	−	1.23052i	0.964691	−	0.263384i	$-0.0848385\pi$
$978$	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	0.185062	+	0.982727i	$0.440752\pi$
$983$	−23377.9	+	40491.8i	−0.758536	+	1.31382i	−0.943597	+	0.331095i	$0.892582\pi$
$984$	−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	0.0931634	−	0.995651i	$-0.470302\pi$
$991$	−22540.1	−	13013.6i	−0.722514	−	0.417144i	−0.815677	+	0.578507i	$0.803635\pi$
$992$	−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	0.816723	−	0.577030i	$-0.195788\pi$
$997$	22834.8	+	13183.7i	0.725362	+	0.418788i	−0.0913611	+	0.995818i	$0.529122\pi$
$998$	1184.92	−	37056.2i	0.0375832	−	1.17534i
$999$	−21996.0	−	38098.2i	−0.696620	−	1.20658i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.4.f.a.3.4	✓	20	1.1	even	1	trivial
28.4.f.a.3.10	yes	20	4.3	odd	2	inner
28.4.f.a.19.4	yes	20	28.19	even	6	inner
28.4.f.a.19.10	yes	20	7.5	odd	6	inner
196.4.d.b.195.5		20	7.4	even	3
196.4.d.b.195.6		20	7.3	odd	6
196.4.d.b.195.7		20	28.3	even	6
196.4.d.b.195.8		20	28.11	odd	6
196.4.f.d.19.4		20	28.23	odd	6
196.4.f.d.19.10		20	7.2	even	3
196.4.f.d.31.4		20	7.6	odd	2
196.4.f.d.31.10		20	28.27	even	2
448.4.p.h.255.1		20	8.5	even	2
448.4.p.h.255.10		20	8.3	odd	2
448.4.p.h.383.1		20	56.19	even	6
448.4.p.h.383.10		20	56.5	odd	6

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

\(f(q)\)	\(=\)	\(q+(-1.49178 + 2.40304i) q^{2} +(4.65345 - 8.06002i) q^{3} +(-3.54920 - 7.16960i) q^{4} +(5.11538 - 2.95337i) q^{5} +(12.4266 + 23.2062i) q^{6} +(1.92900 + 18.4195i) q^{7} +(22.5235 + 2.16656i) q^{8} +(-29.8092 - 51.6311i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{4} - 6 q^{5} + 72 q^{8} - 56 q^{9}+O(q^{10}) \) 20 * q + 4 * q^4 - 6 * q^5 + 72 * q^8 - 56 * q^9	\( 20 q + 4 q^{4} - 6 q^{5} + 72 q^{8} - 56 q^{9} - 12 q^{10} - 168 q^{12} - 56 q^{14} - 104 q^{16} - 6 q^{17} + 68 q^{18} + 238 q^{21} - 184 q^{22} + 348 q^{24} - 36 q^{25} + 396 q^{26} + 448 q^{28} - 352 q^{29} + 644 q^{30} - 40 q^{32} + 30 q^{33} + 208 q^{36} + 258 q^{37} - 1620 q^{38} - 1548 q^{40} - 980 q^{42} - 1248 q^{44} - 504 q^{45} + 232 q^{46} - 644 q^{49} - 864 q^{50} + 2592 q^{52} + 570 q^{53} + 4572 q^{54} + 1904 q^{56} + 1452 q^{57} + 2244 q^{58} - 736 q^{60} + 294 q^{61} + 2560 q^{64} - 124 q^{65} - 4272 q^{66} - 6084 q^{68} - 4144 q^{70} - 4672 q^{72} + 966 q^{73} + 832 q^{74} - 378 q^{77} - 4056 q^{78} + 7032 q^{80} - 1262 q^{81} + 7692 q^{82} + 6188 q^{84} - 2980 q^{85} + 5696 q^{86} - 1396 q^{88} - 3186 q^{89} + 3312 q^{92} - 306 q^{93} - 6780 q^{94} - 11784 q^{96} - 4900 q^{98}+O(q^{100}) \) 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

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