LMFDB - Embedded newform 36.4.h.b.11.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,4,Mod(11,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, 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("36.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	36.h (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:	$2.12406876021$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.4
Character	$\chi$	$=$	36.11
Dual form			36.4.h.b.23.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.65391 - 2.29447i) q^{2} +(0.828122 + 5.12974i) q^{3} +(-2.52915 + 7.58969i) q^{4} +(-14.4924 + 8.36717i) q^{5} +(10.4004 - 10.3842i) q^{6} +(16.7175 + 9.65186i) q^{7} +(21.5973 - 6.74964i) q^{8} +(-25.6284 + 8.49610i) q^{9} +O(q^{10})$	\(q+(-1.65391 - 2.29447i) q^{2} +(0.828122 + 5.12974i) q^{3} +(-2.52915 + 7.58969i) q^{4} +(-14.4924 + 8.36717i) q^{5} +(10.4004 - 10.3842i) q^{6} +(16.7175 + 9.65186i) q^{7} +(21.5973 - 6.74964i) q^{8} +(-25.6284 + 8.49610i) q^{9} +(43.1673 + 19.4137i) q^{10} +(-2.44092 + 4.22780i) q^{11} +(-41.0276 - 6.68868i) q^{12} +(6.03848 + 10.4590i) q^{13} +(-5.50343 - 54.3211i) q^{14} +(-54.9229 - 67.4130i) q^{15} +(-51.2068 - 38.3909i) q^{16} -71.2528i q^{17} +(61.8812 + 44.7518i) q^{18} +68.3003i q^{19} +(-26.8509 - 131.154i) q^{20} +(-35.6674 + 93.7494i) q^{21} +(13.7376 - 1.39180i) q^{22} +(68.0491 + 117.865i) q^{23} +(52.5091 + 105.199i) q^{24} +(77.5192 - 134.267i) q^{25} +(14.0106 - 31.1533i) q^{26} +(-64.8062 - 124.431i) q^{27} +(-115.536 + 102.470i) q^{28} +(190.237 + 109.833i) q^{29} +(-63.8393 + 237.514i) q^{30} +(285.221 - 164.672i) q^{31} +(-3.39507 + 180.987i) q^{32} +(-23.7089 - 9.02015i) q^{33} +(-163.487 + 117.846i) q^{34} -323.035 q^{35} +(0.335328 - 216.000i) q^{36} -133.618 q^{37} +(156.713 - 112.963i) q^{38} +(-48.6511 + 39.6371i) q^{39} +(-256.520 + 278.526i) q^{40} +(-29.5326 + 17.0507i) q^{41} +(274.096 - 73.2157i) q^{42} +(0.558209 + 0.322282i) q^{43} +(-25.9142 - 29.2186i) q^{44} +(300.328 - 337.566i) q^{45} +(157.889 - 351.074i) q^{46} +(-93.4753 + 161.904i) q^{47} +(154.530 - 294.470i) q^{48} +(14.8169 + 25.6636i) q^{49} +(-436.282 + 44.2010i) q^{50} +(365.508 - 59.0060i) q^{51} +(-94.6525 + 19.3780i) q^{52} +266.453i q^{53} +(-178.320 + 354.494i) q^{54} -81.6944i q^{55} +(426.199 + 95.6168i) q^{56} +(-350.363 + 56.5610i) q^{57} +(-62.6263 - 618.147i) q^{58} +(104.347 + 180.734i) q^{59} +(650.552 - 246.350i) q^{60} +(0.801886 - 1.38891i) q^{61} +(-849.565 - 382.076i) q^{62} +(-510.447 - 105.328i) q^{63} +(420.885 - 291.548i) q^{64} +(-175.024 - 101.050i) q^{65} +(18.5160 + 69.3177i) q^{66} +(-371.407 + 214.432i) q^{67} +(540.787 + 180.209i) q^{68} +(-548.261 + 446.680i) q^{69} +(534.272 + 741.193i) q^{70} +386.365 q^{71} +(-496.159 + 356.475i) q^{72} -776.832 q^{73} +(220.992 + 306.582i) q^{74} +(752.951 + 286.464i) q^{75} +(-518.378 - 172.742i) q^{76} +(-81.6122 + 47.1188i) q^{77} +(171.411 + 46.0720i) q^{78} +(-68.5000 - 39.5485i) q^{79} +(1063.33 + 127.919i) q^{80} +(584.633 - 435.483i) q^{81} +(87.9665 + 39.5613i) q^{82} +(462.668 - 801.365i) q^{83} +(-621.321 - 507.811i) q^{84} +(596.185 + 1032.62i) q^{85} +(-0.183763 - 1.81382i) q^{86} +(-405.877 + 1066.82i) q^{87} +(-24.1811 + 107.784i) q^{88} -1044.26i q^{89} +(-1271.25 - 130.788i) q^{90} +233.130i q^{91} +(-1066.66 + 218.375i) q^{92} +(1080.92 + 1326.74i) q^{93} +(526.083 - 53.2991i) q^{94} +(-571.481 - 989.834i) q^{95} +(-931.230 + 132.464i) q^{96} +(733.184 - 1269.91i) q^{97} +(34.3784 - 76.4422i) q^{98} +(26.6372 - 129.090i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9}+O(q^{10}) $ 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9	$ 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9} + 96 q^{10} + 216 q^{12} - 216 q^{13} - 36 q^{14} - 72 q^{16} + 276 q^{18} - 540 q^{20} + 384 q^{21} - 192 q^{22} - 168 q^{24} + 252 q^{25} - 672 q^{28} + 576 q^{29} + 660 q^{30} + 360 q^{32} - 1236 q^{33} - 660 q^{34} + 276 q^{36} + 1248 q^{37} - 144 q^{38} + 636 q^{40} + 1116 q^{41} - 288 q^{42} - 1296 q^{45} + 960 q^{46} - 288 q^{48} + 348 q^{49} - 648 q^{50} + 132 q^{52} - 2616 q^{54} - 1692 q^{56} - 1668 q^{57} + 516 q^{58} - 192 q^{60} - 264 q^{61} + 960 q^{64} - 2592 q^{65} + 1068 q^{66} + 5688 q^{68} + 1608 q^{69} + 564 q^{70} + 4224 q^{72} - 4776 q^{73} + 5652 q^{74} - 600 q^{76} + 648 q^{77} + 3660 q^{78} + 3948 q^{81} - 4104 q^{82} - 4872 q^{84} + 720 q^{85} - 9540 q^{86} + 1956 q^{88} - 7656 q^{90} - 7416 q^{92} + 5400 q^{93} - 1188 q^{94} - 5640 q^{96} + 588 q^{97}+O(q^{100}) $ 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9 + 96 * q^10 + 216 * q^12 - 216 * q^13 - 36 * q^14 - 72 * q^16 + 276 * q^18 - 540 * q^20 + 384 * q^21 - 192 * q^22 - 168 * q^24 + 252 * q^25 - 672 * q^28 + 576 * q^29 + 660 * q^30 + 360 * q^32 - 1236 * q^33 - 660 * q^34 + 276 * q^36 + 1248 * q^37 - 144 * q^38 + 636 * q^40 + 1116 * q^41 - 288 * q^42 - 1296 * q^45 + 960 * q^46 - 288 * q^48 + 348 * q^49 - 648 * q^50 + 132 * q^52 - 2616 * q^54 - 1692 * q^56 - 1668 * q^57 + 516 * q^58 - 192 * q^60 - 264 * q^61 + 960 * q^64 - 2592 * q^65 + 1068 * q^66 + 5688 * q^68 + 1608 * q^69 + 564 * q^70 + 4224 * q^72 - 4776 * q^73 + 5652 * q^74 - 600 * q^76 + 648 * q^77 + 3660 * q^78 + 3948 * q^81 - 4104 * q^82 - 4872 * q^84 + 720 * q^85 - 9540 * q^86 + 1956 * q^88 - 7656 * q^90 - 7416 * q^92 + 5400 * q^93 - 1188 * q^94 - 5640 * q^96 + 588 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.65391	−	2.29447i	−0.584746	−	0.811216i
$2$	−1.65391	−	2.29447i	−0.584746	−	0.811216i
$3$	0.828122	+	5.12974i	0.159372	+	0.987219i
$3$	0.828122	+	5.12974i	0.159372	+	0.987219i
$4$	−2.52915	+	7.58969i	−0.316144	+	0.948711i
$5$	−14.4924	+	8.36717i	−1.29624	+	0.748383i	−0.979752	−	0.200215i	$-0.935836\pi$
$5$	−14.4924	+	8.36717i	−1.29624	+	0.748383i	−0.316485	+	0.948598i	$0.602503\pi$
$6$	10.4004	−	10.3842i	0.707655	−	0.706558i
$7$	16.7175	+	9.65186i	0.902661	+	0.521152i	0.878063	−	0.478546i	$-0.158836\pi$
$7$	16.7175	+	9.65186i	0.902661	+	0.521152i	0.0245984	+	0.999697i	$0.492169\pi$
$8$	21.5973	−	6.74964i	0.954474	−	0.298295i
$9$	−25.6284	+	8.49610i	−0.949201	+	0.314670i
$10$	43.1673	+	19.4137i	1.36507	+	0.613915i
$11$	−2.44092	+	4.22780i	−0.0669059	+	0.115884i	−0.897538	−	0.440937i	$-0.854646\pi$
$11$	−2.44092	+	4.22780i	−0.0669059	+	0.115884i	0.830632	+	0.556822i	$0.187979\pi$
$12$	−41.0276	−	6.68868i	−0.986970	−	0.160905i
$13$	6.03848	+	10.4590i	0.128829	+	0.223138i	0.923223	−	0.384264i	$-0.125545\pi$
$13$	6.03848	+	10.4590i	0.128829	+	0.223138i	−0.794394	+	0.607402i	$0.792212\pi$
$14$	−5.50343	−	54.3211i	−0.105061	−	1.03699i
$15$	−54.9229	−	67.4130i	−0.945402	−	1.16040i
$16$	−51.2068	−	38.3909i	−0.800106	−	0.599858i
$17$		−	71.2528i		−	1.01655i	−0.861195	−	0.508275i	$-0.830283\pi$
$17$		−	71.2528i		−	1.01655i	0.861195	−	0.508275i	$-0.169717\pi$
$18$	61.8812	+	44.7518i	0.810307	+	0.586005i
$19$			68.3003i			0.824693i	0.911027	+	0.412347i	$0.135291\pi$
$19$			68.3003i			0.824693i	−0.911027	+	0.412347i	$0.864709\pi$
$20$	−26.8509	−	131.154i	−0.300202	−	1.46635i
$21$	−35.6674	+	93.7494i	−0.370631	+	0.974181i
$22$	13.7376	−	1.39180i	0.133130	−	0.0134878i
$23$	68.0491	+	117.865i	0.616923	+	1.06854i	0.990044	+	0.140759i	$0.0449543\pi$
$23$	68.0491	+	117.865i	0.616923	+	1.06854i	−0.373121	+	0.927783i	$0.621712\pi$
$24$	52.5091	+	105.199i	0.446599	+	0.894734i
$25$	77.5192	−	134.267i	0.620154	−	1.07414i
$26$	14.0106	−	31.1533i	0.105681	−	0.234987i
$27$	−64.8062	−	124.431i	−0.461925	−	0.886919i
$28$	−115.536	+	102.470i	−0.779793	+	0.691606i
$29$	190.237	+	109.833i	1.21814	+	0.703295i	0.964520	−	0.264009i	$-0.0850448\pi$
$29$	190.237	+	109.833i	1.21814	+	0.703295i	0.253622	+	0.967303i	$0.418378\pi$
$30$	−63.8393	+	237.514i	−0.388514	+	1.44546i
$31$	285.221	−	164.672i	1.65249	−	0.954065i	0.676444	−	0.736494i	$-0.263520\pi$
$31$	285.221	−	164.672i	1.65249	−	0.954065i	0.976044	−	0.217571i	$-0.0698134\pi$
$32$	−3.39507	+	180.987i	−0.0187553	+	0.999824i
$33$	−23.7089	−	9.02015i	−0.125066	−	0.0475820i
$34$	−163.487	+	117.846i	−0.824642	+	0.594424i
$35$	−323.035			−1.56008
$36$	0.335328	−	216.000i	0.00155245	−	0.999999i
$37$	−133.618			−0.593693			−0.296847	−	0.954925i	$-0.595935\pi$
$37$	−133.618			−0.593693			−0.296847	+	0.954925i	$0.595935\pi$
$38$	156.713	−	112.963i	0.669005	−	0.482236i
$39$	−48.6511	+	39.6371i	−0.199754	+	0.162744i
$40$	−256.520	+	278.526i	−1.01399	+	1.10097i
$41$	−29.5326	+	17.0507i	−0.112493	+	0.0649480i	−0.555191	−	0.831723i	$-0.687355\pi$
$41$	−29.5326	+	17.0507i	−0.112493	+	0.0649480i	0.442698	+	0.896671i	$0.354021\pi$
$42$	274.096	−	73.2157i	1.00700	−	0.268986i
$43$	0.558209	+	0.322282i	0.00197967	+	0.00114297i	0.500990	−	0.865453i	$-0.332970\pi$
$43$	0.558209	+	0.322282i	0.00197967	+	0.00114297i	−0.499010	+	0.866596i	$0.666303\pi$
$44$	−25.9142	−	29.2186i	−0.0887890	−	0.100111i
$45$	300.328	−	337.566i	0.994896	−	1.11825i
$46$	157.889	−	351.074i	0.506075	−	1.12528i
$47$	−93.4753	+	161.904i	−0.290102	+	0.502471i	−0.973834	−	0.227263i	$-0.927022\pi$
$47$	−93.4753	+	161.904i	−0.290102	+	0.502471i	0.683732	+	0.729733i	$0.260356\pi$
$48$	154.530	−	294.470i	0.464676	−	0.885481i
$49$	14.8169	+	25.6636i	0.0431979	+	0.0748210i
$50$	−436.282	+	44.2010i	−1.23399	+	0.125019i
$51$	365.508	−	59.0060i	1.00356	−	0.162010i
$52$	−94.6525	+	19.3780i	−0.252422	+	0.0516777i
$53$			266.453i			0.690569i	0.938498	+	0.345284i	$0.112218\pi$
$53$			266.453i			0.690569i	−0.938498	+	0.345284i	$0.887782\pi$
$54$	−178.320	+	354.494i	−0.449374	+	0.893343i
$55$		−	81.6944i		−	0.200285i
$56$	426.199	+	95.6168i	1.01702	+	0.228167i
$57$	−350.363	+	56.5610i	−0.814153	+	0.131433i
$58$	−62.6263	−	618.147i	−0.141780	−	1.39943i
$59$	104.347	+	180.734i	0.230251	+	0.398806i	0.957882	−	0.287163i	$-0.0927120\pi$
$59$	104.347	+	180.734i	0.230251	+	0.398806i	−0.727631	+	0.685969i	$0.759379\pi$
$60$	650.552	−	246.350i	1.39977	−	0.530061i
$61$	0.801886	−	1.38891i	0.00168313	−	0.00291527i	−0.865183	−	0.501457i	$-0.832798\pi$
$61$	0.801886	−	1.38891i	0.00168313	−	0.00291527i	0.866866	+	0.498542i	$0.166131\pi$
$62$	−849.565	−	382.076i	−1.74024	−	0.782640i
$63$	−510.447	−	105.328i	−1.02080	−	0.210637i
$64$	420.885	−	291.548i	0.822041	−	0.569429i
$65$	−175.024	−	101.050i	−0.333985	−	0.192826i
$66$	18.5160	+	69.3177i	0.0345327	+	0.129279i
$67$	−371.407	+	214.432i	−0.677233	+	0.391001i	−0.798812	−	0.601581i	$-0.794538\pi$
$67$	−371.407	+	214.432i	−0.677233	+	0.391001i	0.121579	+	0.992582i	$0.461204\pi$
$68$	540.787	+	180.209i	0.964412	+	0.321376i
$69$	−548.261	+	446.680i	−0.956564	+	0.779333i
$70$	534.272	+	741.193i	0.912253	+	1.26557i
$71$	386.365			0.645817			0.322909	−	0.946430i	$-0.395339\pi$
$71$	386.365			0.645817			0.322909	+	0.946430i	$0.395339\pi$
$72$	−496.159	+	356.475i	−0.812123	+	0.583486i
$73$	−776.832			−1.24550			−0.622749	−	0.782422i	$-0.713984\pi$
$73$	−776.832			−1.24550			−0.622749	+	0.782422i	$0.713984\pi$
$74$	220.992	+	306.582i	0.347160	+	0.481614i
$75$	752.951	+	286.464i	1.15924	+	0.441040i
$76$	−518.378	−	172.742i	−0.782396	−	0.260721i
$77$	−81.6122	+	47.1188i	−0.120787	+	0.0697362i
$78$	171.411	+	46.0720i	0.248826	+	0.0668798i
$79$	−68.5000	−	39.5485i	−0.0975551	−	0.0563235i	0.450429	−	0.892812i	$-0.351271\pi$
$79$	−68.5000	−	39.5485i	−0.0975551	−	0.0563235i	−0.547984	+	0.836489i	$0.684604\pi$
$80$	1063.33	+	127.919i	1.48605	+	0.178772i
$81$	584.633	−	435.483i	0.801965	−	0.597371i
$82$	87.9665	+	39.5613i	0.118467	+	0.0532782i
$83$	462.668	−	801.365i	0.611861	−	1.05977i	−0.379066	−	0.925370i	$-0.623755\pi$
$83$	462.668	−	801.365i	0.611861	−	1.05977i	0.990927	−	0.134404i	$-0.0429121\pi$
$84$	−621.321	−	507.811i	−0.807044	−	0.659603i
$85$	596.185	+	1032.62i	0.760768	+	1.31769i
$86$	−0.183763	−	1.81382i	−0.000230415	−	0.00227429i
$87$	−405.877	+	1066.82i	−0.500168	+	1.31466i
$88$	−24.1811	+	107.784i	−0.0292922	+	0.130566i
$89$		−	1044.26i		−	1.24372i	−0.783128	−	0.621861i	$-0.786377\pi$
$89$		−	1044.26i		−	1.24372i	0.783128	−	0.621861i	$-0.213623\pi$
$90$	−1271.25	−	130.788i	−1.48891	−	0.153181i
$91$			233.130i			0.268557i
$92$	−1066.66	+	218.375i	−1.20877	+	0.247469i
$93$	1080.92	+	1326.74i	1.20523	+	1.47932i
$94$	526.083	−	53.2991i	0.577248	−	0.0584828i
$95$	−571.481	−	989.834i	−0.617186	−	1.06900i
$96$	−931.230	+	132.464i	−0.990034	+	0.140829i
$97$	733.184	−	1269.91i	0.767460	−	1.32928i	−0.171477	−	0.985188i	$-0.554854\pi$
$97$	733.184	−	1269.91i	0.767460	−	1.32928i	0.938936	−	0.344091i	$-0.111813\pi$
$98$	34.3784	−	76.4422i	0.0354362	−	0.0787941i
$99$	26.6372	−	129.090i	0.0270418	−	0.131051i
$100$	822.989	+	927.929i	0.822989	+	0.927929i
$101$	−314.302	−	181.462i	−0.309646	−	0.178774i	0.337122	−	0.941461i	$-0.390546\pi$
$101$	−314.302	−	181.462i	−0.309646	−	0.178774i	−0.646768	+	0.762687i	$0.723880\pi$
$102$	−739.906	−	741.055i	−0.718251	−	0.719367i
$103$	−466.128	+	269.119i	−0.445912	+	0.257447i	−0.706102	−	0.708110i	$-0.749548\pi$
$103$	−466.128	+	269.119i	−0.445912	+	0.257447i	0.260190	+	0.965557i	$0.416215\pi$
$104$	201.009	+	185.127i	0.189525	+	0.174550i
$105$	−267.513	−	1657.09i	−0.248634	−	1.54014i
$106$	611.368	−	440.690i	0.560201	−	0.403808i
$107$	430.456			0.388914			0.194457	−	0.980911i	$-0.437706\pi$
$107$	430.456			0.388914			0.194457	+	0.980911i	$0.437706\pi$
$108$	1108.30	−	177.154i	0.987465	−	0.157839i
$109$	899.324			0.790272			0.395136	−	0.918623i	$-0.370697\pi$
$109$	899.324			0.790272			0.395136	+	0.918623i	$0.370697\pi$
$110$	−187.445	+	135.115i	−0.162474	+	0.117116i
$111$	−110.652	−	685.425i	−0.0946182	−	0.586105i
$112$	−485.507	−	1136.04i	−0.409608	−	0.958445i
$113$	−330.860	+	191.022i	−0.275440	+	0.159025i	−0.631357	−	0.775492i	$-0.717502\pi$
$113$	−330.860	+	191.022i	−0.275440	+	0.159025i	0.355917	+	0.934517i	$0.384168\pi$
$114$	709.247	+	710.349i	0.582693	+	0.583599i
$115$	−1972.39	−	1138.76i	−1.59936	−	0.923389i
$116$	−1314.74	+	1166.05i	−1.05233	+	0.933323i
$117$	−243.617	−	216.743i	−0.192499	−	0.171264i
$118$	242.107	−	538.338i	0.188880	−	0.419983i
$119$	687.722	−	1191.17i	0.529776	−	0.917600i
$120$	−1641.20	−	1085.23i	−1.24850	−	0.825561i
$121$	653.584	+	1132.04i	0.491047	+	0.850519i
$122$	−4.51305	+	0.457231i	−0.00334912	+	0.000339309i
$123$	−111.922	−	137.375i	−0.0820461	−	0.100704i
$124$	528.446	+	2581.22i	0.382708	+	1.86936i
$125$			502.674i			0.359684i
$126$	602.562	+	1345.41i	0.426036	+	0.951257i
$127$			1677.92i			1.17237i	0.810177	+	0.586186i	$0.199371\pi$
$127$			1677.92i			1.17237i	−0.810177	+	0.586186i	$0.800629\pi$
$128$	−1365.05	−	483.512i	−0.942615	−	0.333881i
$129$	−1.19096	+	3.13035i	−0.000812852	+	0.00213653i
$130$	57.6181	+	568.714i	0.0388727	+	0.383689i
$131$	712.418	+	1233.94i	0.475147	+	0.822979i	0.999595	−	0.0284637i	$-0.00906150\pi$
$131$	712.418	+	1233.94i	0.475147	+	0.822979i	−0.524448	+	0.851443i	$0.675728\pi$
$132$	128.423	−	157.130i	0.0846805	−	0.103609i
$133$	−659.225	+	1141.81i	−0.429790	+	0.744418i
$134$	1106.28	+	497.529i	0.713196	+	0.320746i
$135$	1980.33	+	1261.06i	1.26252	+	0.803961i
$136$	−480.931	−	1538.87i	−0.303231	−	0.970270i
$137$	23.2295	+	13.4116i	0.0144864	+	0.00836370i	0.507226	−	0.861813i	$-0.330671\pi$
$137$	23.2295	+	13.4116i	0.0144864	+	0.00836370i	−0.492739	+	0.870177i	$0.664004\pi$
$138$	1931.67	+	519.197i	1.19156	+	0.320268i
$139$	1434.57	−	828.252i	0.875388	−	0.505406i	0.00625321	−	0.999980i	$-0.498010\pi$
$139$	1434.57	−	828.252i	0.875388	−	0.505406i	0.869135	+	0.494575i	$0.164676\pi$
$140$	817.004	−	2451.74i	0.493210	−	1.48007i
$141$	−907.934	−	345.428i	−0.542283	−	0.206314i
$142$	−639.013	−	886.500i	−0.377639	−	0.523898i
$143$	−58.9578			−0.0344776
$144$	1638.52	+	548.840i	0.948219	+	0.317616i
$145$	−3675.98			−2.10533
$146$	1284.81	+	1782.42i	0.728300	+	1.01037i
$147$	−119.377	+	97.2593i	−0.0669801	+	0.0545702i
$148$	337.940	−	1014.12i	0.187692	−	0.563244i
$149$	738.285	−	426.249i	0.405924	−	0.234360i	−0.283113	−	0.959087i	$-0.591367\pi$
$149$	738.285	−	426.249i	0.405924	−	0.234360i	0.689037	+	0.724726i	$0.258034\pi$
$150$	−588.034	−	2201.41i	−0.320085	−	1.19829i
$151$	1272.06	+	734.422i	0.685553	+	0.395804i	0.801944	−	0.597399i	$-0.203799\pi$
$151$	1272.06	+	734.422i	0.685553	+	0.395804i	−0.116391	+	0.993203i	$0.537133\pi$
$152$	461.002	+	1475.10i	0.246002	+	0.787148i
$153$	605.371	+	1826.10i	0.319878	+	0.964910i
$154$	243.092	+	109.326i	0.127201	+	0.0572061i
$155$	−2755.68	+	4772.98i	−1.42801	+	2.47339i
$156$	−177.788	−	469.495i	−0.0912462	−	0.240960i
$157$	−1344.52	−	2328.78i	−0.683469	−	1.18380i	−0.973915	−	0.226912i	$-0.927137\pi$
$157$	−1344.52	−	2328.78i	−0.683469	−	1.18380i	0.290446	−	0.956891i	$-0.406196\pi$
$158$	22.5503	+	222.581i	0.0113545	+	0.112073i
$159$	−1366.83	+	220.656i	−0.681742	+	0.110057i
$160$	−1465.15	−	2651.35i	−0.723940	−	1.31005i
$161$			2627.20i			1.28604i
$162$	−1966.13	−	621.168i	−0.953543	−	0.301257i
$163$		−	2186.50i		−	1.05067i	−0.850895	−	0.525336i	$-0.823940\pi$
$163$		−	2186.50i		−	1.05067i	0.850895	−	0.525336i	$-0.176060\pi$
$164$	−54.7169	−	267.267i	−0.0260529	−	0.127256i
$165$	419.071	−	67.6530i	0.197725	−	0.0319199i
$166$	−2603.92	+	263.811i	−1.21749	+	0.123348i
$167$	−1790.65	−	3101.49i	−0.829726	−	1.43713i	−0.898253	−	0.439479i	$-0.855163\pi$
$167$	−1790.65	−	3101.49i	−0.829726	−	1.43713i	0.0685268	−	0.997649i	$-0.478170\pi$
$168$	−137.544	+	2265.47i	−0.0631651	+	1.04039i
$169$	1025.57	−	1776.35i	0.466806	−	0.808532i
$170$	1383.28	−	3075.79i	0.624075	−	1.38766i
$171$	−580.287	−	1750.43i	−0.259507	−	0.782800i
$172$	−3.85781	+	3.42153i	−0.00171021	+	0.00151680i
$173$	−94.5051	−	54.5625i	−0.0415323	−	0.0239787i	0.479090	−	0.877766i	$-0.340967\pi$
$173$	−94.5051	−	54.5625i	−0.0415323	−	0.0239787i	−0.520622	+	0.853787i	$0.674300\pi$
$174$	3119.07	−	833.158i	1.35894	−	0.362997i
$175$	2591.86	−	1496.41i	1.11958	−	0.646388i
$176$	287.301	−	122.783i	0.123046	−	0.0525858i
$177$	−840.706	+	684.941i	−0.357013	+	0.290866i
$178$	−2396.02	+	1727.11i	−1.00893	+	0.727262i
$179$	268.397			0.112072			0.0560361	−	0.998429i	$-0.482154\pi$
$179$	268.397			0.112072			0.0560361	+	0.998429i	$0.482154\pi$
$180$	1802.45	+	3133.15i	0.746370	+	1.29740i
$181$	898.582			0.369011			0.184506	−	0.982831i	$-0.440932\pi$
$181$	898.582			0.369011			0.184506	+	0.982831i	$0.440932\pi$
$182$	534.910	−	385.577i	0.217858	−	0.157038i
$183$	7.78879	+	2.96328i	0.00314625	+	0.00119701i
$184$	2265.22	+	2086.25i	0.907577	+	0.835870i
$185$	1936.44	−	1118.00i	0.769567	−	0.444310i
$186$	1256.41	−	4674.45i	0.495291	−	1.84273i
$187$	301.242	+	173.922i	0.117802	+	0.0680132i
$188$	−992.388	−	1118.93i	−0.384986	−	0.434076i
$189$	117.595	−	2705.68i	0.0452579	−	1.04132i
$190$	−1325.96	+	2948.34i	−0.506291	+	1.12576i
$191$	−257.331	+	445.711i	−0.0974860	+	0.168851i	−0.910643	−	0.413193i	$-0.864413\pi$
$191$	−257.331	+	445.711i	−0.0974860	+	0.168851i	0.813157	+	0.582044i	$0.197747\pi$
$192$	1844.11	+	1917.59i	0.693161	+	0.720783i
$193$	1229.66	+	2129.83i	0.458616	+	0.794346i	0.998888	−	0.0471443i	$-0.0150121\pi$
$193$	1229.66	+	2129.83i	0.458616	+	0.794346i	−0.540272	+	0.841490i	$0.681679\pi$
$194$	−4126.39	+	418.057i	−1.52710	+	0.154715i
$195$	373.419	−	981.508i	0.137134	−	0.360448i
$196$	−232.253	+	47.5485i	−0.0846403	+	0.0173282i
$197$			646.506i			0.233815i	0.993143	+	0.116908i	$0.0372982\pi$
$197$			646.506i			0.233815i	−0.993143	+	0.116908i	$0.962702\pi$
$198$	−340.248	+	152.386i	−0.122123	+	0.0546948i
$199$			1742.98i			0.620886i	0.950592	+	0.310443i	$0.100477\pi$
$199$			1742.98i			0.620886i	−0.950592	+	0.310443i	$0.899523\pi$
$200$	767.949	−	3423.03i	0.271511	−	1.21022i
$201$	−1407.55	−	1727.65i	−0.493935	−	0.606262i
$202$	103.469	+	1021.28i	0.0360398	+	0.355727i
$203$	2120.19	+	3672.28i	0.733046	+	1.26967i
$204$	−476.587	+	2923.33i	−0.163568	+	1.00330i
$205$	285.332	−	494.209i	0.0972119	−	0.168376i
$206$	1388.42	+	624.415i	0.469591	+	0.211190i
$207$	−2745.38	−	2442.53i	−0.921822	−	0.820133i
$208$	92.3175	−	767.393i	0.0307744	−	0.255813i
$209$	−288.760	−	166.716i	−0.0955691	−	0.0551769i
$210$	−3359.69	+	3354.47i	−1.10400	+	1.10229i
$211$	−3648.27	+	2106.33i	−1.19032	+	0.687231i	−0.958379	−	0.285499i	$-0.907841\pi$
$211$	−3648.27	+	2106.33i	−1.19032	+	0.687231i	−0.231940	+	0.972730i	$0.574507\pi$
$212$	−2022.30	−	673.900i	−0.655151	−	0.218319i
$213$	319.957	+	1981.95i	0.102925	+	0.637563i
$214$	−711.937	−	987.667i	−0.227416	−	0.315493i
$215$	−10.7864			−0.00342150
$216$	−2239.50	−	2249.96i	−0.705458	−	0.708751i
$217$	6357.58			1.98885
$218$	−1487.40	−	2063.47i	−0.462109	−	0.641081i
$219$	−643.312	−	3984.95i	−0.198498	−	1.22958i
$220$	620.035	+	206.617i	0.190013	+	0.0633188i
$221$	745.230	−	430.259i	0.226831	−	0.130961i
$222$	−1389.68	+	1387.52i	−0.420130	+	0.419479i
$223$	5558.55	+	3209.23i	1.66918	+	0.963703i	0.968080	+	0.250643i	$0.0806420\pi$
$223$	5558.55	+	3209.23i	1.66918	+	0.963703i	0.701103	+	0.713060i	$0.252691\pi$
$224$	−1803.62	+	2992.89i	−0.537990	+	0.892728i
$225$	−845.948	+	4099.67i	−0.250651	+	1.21472i
$226$	985.507	+	443.213i	0.290066	+	0.130452i
$227$	1124.83	−	1948.27i	0.328889	−	0.569653i	−0.653403	−	0.757011i	$-0.726659\pi$
$227$	1124.83	−	1948.27i	0.328889	−	0.569653i	0.982292	+	0.187358i	$0.0599924\pi$
$228$	456.839	−	2802.20i	0.132697	−	0.813948i
$229$	−1735.36	−	3005.74i	−0.500769	−	0.867357i	−1.00000		0.000888202i	$-0.999717\pi$
$229$	−1735.36	−	3005.74i	−0.500769	−	0.867357i	0.499231	−	0.866469i	$-0.333616\pi$
$230$	649.313	+	6408.98i	0.186150	+	1.83737i
$231$	−309.292	−	379.629i	−0.0880950	−	0.108129i
$232$	4849.94	+	1088.07i	1.37247	+	0.307911i
$233$		−	3852.67i		−	1.08325i	−0.840621	−	0.541624i	$-0.817810\pi$
$233$		−	3852.67i		−	1.08325i	0.840621	−	0.541624i	$-0.182190\pi$
$234$	−94.3883	+	917.445i	−0.0263690	+	0.256305i
$235$		−	3128.50i		−	0.868428i
$236$	−1635.62	+	334.857i	−0.451144	+	0.0923615i
$237$	146.147	−	384.138i	0.0400560	−	0.105285i
$238$	−3870.53	+	392.135i	−1.05416	+	0.106800i
$239$	−19.9334	−	34.5257i	−0.00539491	−	0.00934426i	0.863315	−	0.504665i	$-0.168384\pi$
$239$	−19.9334	−	34.5257i	−0.00539491	−	0.00934426i	−0.868710	+	0.495321i	$0.835051\pi$
$240$	224.377	+	5560.55i	0.0603479	+	1.49555i
$241$	−1729.18	+	2995.03i	−0.462184	+	0.800527i	−0.999070	−	0.0431286i	$-0.986267\pi$
$241$	−1729.18	+	2995.03i	−0.462184	+	0.800527i	0.536885	+	0.843655i	$0.319601\pi$
$242$	1516.46	−	3371.92i	0.402817	−	0.895683i
$243$	2718.06	+	2638.38i	0.717547	+	0.696511i
$244$	8.51329	+	9.59882i	0.00223364	+	0.00251845i
$245$	−429.464	−	247.951i	−0.111989	−	0.0646572i
$246$	−130.092	+	484.007i	−0.0337169	+	0.125444i
$247$	−714.350	+	412.430i	−0.184020	+	0.106244i
$248$	5048.51	−	5481.61i	1.29267	−	1.40356i
$249$	4493.94	+	1709.74i	1.14374	+	0.435142i
$250$	1153.37	−	831.378i	0.291781	−	0.210324i
$251$	−2977.61			−0.748786			−0.374393	−	0.927270i	$-0.622149\pi$
$251$	−2977.61			−0.748786			−0.374393	+	0.927270i	$0.622149\pi$
$252$	2090.41	−	3607.74i	0.522552	−	0.901851i
$253$	−664.410			−0.165103
$254$	3849.93	−	2775.13i	0.951047	−	0.685540i
$255$	−4803.37	+	3913.41i	−1.17960	+	0.961048i
$256$	1148.28	+	3931.75i	0.280341	+	0.959901i
$257$	−5593.28	+	3229.28i	−1.35758	+	0.783802i	−0.989298	−	0.145910i	$-0.953389\pi$
$257$	−5593.28	+	3229.28i	−1.35758	+	0.783802i	−0.368287	+	0.929712i	$0.620056\pi$
$258$	9.15223	−	2.44472i	0.00220850	−	0.000589929i
$259$	−2233.76	−	1289.66i	−0.535904	−	0.309404i
$260$	1209.60	−	1072.81i	0.288524	−	0.255895i
$261$	−5808.63	−	1198.58i	−1.37757	−	0.284255i
$262$	1652.97	−	3675.46i	0.389773	−	0.866681i
$263$	2940.99	−	5093.94i	0.689540	−	1.19432i	−0.282447	−	0.959283i	$-0.591146\pi$
$263$	2940.99	−	5093.94i	0.689540	−	1.19432i	0.971987	−	0.235036i	$-0.0755207\pi$
$264$	−572.930	−	34.7843i	−0.133566	−	0.00810920i
$265$	−2229.46	−	3861.54i	−0.516810	−	0.895141i
$266$	3710.15	−	375.886i	0.855203	−	0.0866431i
$267$	5356.78	−	864.774i	1.22783	−	0.198215i
$268$	−688.129	−	3361.20i	−0.156844	−	0.766111i
$269$		−	2967.07i		−	0.672510i	−0.941771	−	0.336255i	$-0.890840\pi$
$269$		−	2967.07i		−	0.672510i	0.941771	−	0.336255i	$-0.109160\pi$
$270$	−381.841	−	6629.49i	−0.0860671	−	1.49429i
$271$		−	1985.78i		−	0.445121i	−0.974919	−	0.222561i	$-0.928559\pi$
$271$		−	1985.78i		−	0.445121i	0.974919	−	0.222561i	$-0.0714415\pi$
$272$	−2735.46	+	3648.63i	−0.609785	+	0.813348i
$273$	−1195.90	+	193.060i	−0.265125	+	0.0428006i
$274$	−7.64719	−	75.4808i	−0.00168607	−	0.0166422i
$275$	378.436	+	655.471i	0.0829839	+	0.143732i
$276$	−2003.53	−	5290.85i	−0.436951	−	1.15388i
$277$	−2171.48	+	3761.12i	−0.471017	+	0.815825i	−0.999450	−	0.0331494i	$-0.989446\pi$
$277$	−2171.48	+	3761.12i	−0.471017	+	0.815825i	0.528433	+	0.848975i	$0.322780\pi$
$278$	−4273.05	−	1921.73i	−0.921873	−	0.414595i
$279$	−5910.69	+	6643.56i	−1.26833	+	1.42559i
$280$	−6976.68	+	2180.37i	−1.48906	+	0.465365i
$281$	6752.10	+	3898.33i	1.43344	+	0.827597i	0.997381	−	0.0723220i	$-0.0230409\pi$
$281$	6752.10	+	3898.33i	1.43344	+	0.827597i	0.436058	+	0.899919i	$0.356374\pi$
$282$	709.072	+	2654.53i	0.149733	+	0.560550i
$283$	−1771.47	+	1022.76i	−0.372094	+	0.214829i	−0.674373	−	0.738391i	$-0.735586\pi$
$283$	−1771.47	+	1022.76i	−0.372094	+	0.214829i	0.302279	+	0.953220i	$0.402253\pi$
$284$	−977.173	+	2932.39i	−0.204171	+	0.612694i
$285$	4604.33	−	3751.25i	0.956972	−	0.779666i
$286$	97.5110	+	135.277i	0.0201607	+	0.0279688i
$287$	−658.283			−0.135391
$288$	−1450.68	−	4667.27i	−0.296812	−	0.954936i
$289$	−163.963			−0.0333732
$290$	6079.75	+	8434.41i	1.23109	+	1.70788i
$291$	7121.48	+	2709.40i	1.43460	+	0.545800i
$292$	1964.72	−	5895.92i	0.393756	−	1.18162i
$293$	−2041.60	+	1178.72i	−0.407070	+	0.235022i	−0.689530	−	0.724257i	$-0.742183\pi$
$293$	−2041.60	+	1178.72i	−0.407070	+	0.235022i	0.282460	+	0.959279i	$0.408849\pi$
$294$	420.598	+	113.049i	0.0834346	+	0.0224257i
$295$	−3024.46	−	1746.18i	−0.596919	−	0.344631i
$296$	−2885.78	+	901.873i	−0.566665	+	0.177096i
$297$	684.257	+	29.7392i	0.133686	+	0.00581025i
$298$	−2199.07	−	988.991i	−0.427479	−	0.192251i
$299$	−821.827	+	1423.45i	−0.158955	+	0.275318i
$300$	−4078.50	+	4990.16i	−0.784907	+	0.960356i
$301$	6.22124	+	10.7755i	0.00119132	+	0.00206342i
$302$	−418.763	−	4133.36i	−0.0797917	−	0.787576i
$303$	670.574	−	1762.56i	0.127140	−	0.334180i
$304$	2622.11	−	3497.44i	0.494699	−	0.659842i
$305$			26.8381i			0.00503851i
$306$	3188.69	−	4409.21i	0.595703	−	0.823718i
$307$			5521.27i			1.02643i	0.858259	+	0.513217i	$0.171546\pi$
$307$			5521.27i			1.02643i	−0.858259	+	0.513217i	$0.828454\pi$
$308$	−151.208	−	738.582i	−0.0279736	−	0.136638i
$309$	−1766.52	−	2168.25i	−0.325223	−	0.399183i
$310$	15509.1	−	1571.27i	2.84148	−	0.287879i
$311$	767.330	+	1329.05i	0.139908	+	0.242327i	0.927461	−	0.373919i	$-0.121986\pi$
$311$	767.330	+	1329.05i	0.139908	+	0.242327i	−0.787554	+	0.616246i	$0.788653\pi$
$312$	−783.195	+	1184.43i	−0.142114	+	0.214921i
$313$	−4383.28	+	7592.06i	−0.791557	+	1.37102i	0.133446	+	0.991056i	$0.457396\pi$
$313$	−4383.28	+	7592.06i	−0.791557	+	1.37102i	−0.925003	+	0.379961i	$0.875937\pi$
$314$	−3119.59	+	6936.57i	−0.560664	+	1.24667i
$315$	8278.89	−	2744.54i	1.48083	−	0.490912i
$316$	473.408	−	419.870i	0.0842762	−	0.0747454i
$317$	−6074.45	−	3507.08i	−1.07626	−	0.621380i	−0.146376	−	0.989229i	$-0.546761\pi$
$317$	−6074.45	−	3507.08i	−1.07626	−	0.621380i	−0.929886	+	0.367849i	$0.880094\pi$
$318$	2766.91	+	2771.21i	0.487927	+	0.488685i
$319$	−928.706	+	536.189i	−0.163002	+	0.0941091i
$320$	−3660.19	+	7746.83i	−0.639409	+	1.35332i
$321$	356.470	+	2208.13i	0.0619820	+	0.383943i
$322$	6028.03	−	4345.16i	1.04326	−	0.752008i
$323$	4866.59			0.838342
$324$	1826.56	+	5538.58i	0.313196	+	0.949688i
$325$	1872.39			0.319574
$326$	−5016.84	+	3616.27i	−0.852323	+	0.614377i
$327$	744.750	+	4613.30i	0.125947	+	0.780171i
$328$	−522.738	+	567.582i	−0.0879982	+	0.0955473i
$329$	−3125.35	+	1804.42i	−0.523727	+	0.302374i
$330$	−848.334	−	849.652i	−0.141513	−	0.141733i
$331$	−8563.21	−	4943.97i	−1.42198	−	0.820982i	−0.425515	−	0.904951i	$-0.639907\pi$
$331$	−8563.21	−	4943.97i	−1.42198	−	0.820982i	−0.996468	+	0.0839692i	$0.973240\pi$
$332$	4911.96	+	5538.28i	0.811984	+	0.915520i
$333$	3424.42	−	1135.23i	0.563534	−	0.186818i
$334$	−4154.69	+	9238.16i	−0.680642	+	1.51344i
$335$	3588.38	−	6215.26i	0.585236	−	1.01366i
$336$	5425.54	−	3431.30i	0.880915	−	0.557122i
$337$	2504.10	+	4337.22i	0.404768	+	0.701079i	0.994294	−	0.106670i	$-0.0340190\pi$
$337$	2504.10	+	4337.22i	0.404768	+	0.701079i	−0.589527	+	0.807749i	$0.700686\pi$
$338$	−5771.97	+	584.776i	−0.928858	+	0.0941054i
$339$	−1253.89	−	1539.04i	−0.200890	−	0.246575i
$340$	−9345.12	+	1913.20i	−1.49062	+	0.305170i
$341$			1607.81i			0.255330i
$342$	−3056.56	+	4226.51i	−0.483274	+	0.668255i
$343$		−	6049.14i		−	0.952252i
$344$	14.2311	+	3.19271i	0.00223049	+	0.000500405i
$345$	4208.15	−	11060.9i	0.656694	−	1.72608i
$346$	31.1112	+	307.080i	0.00483396	+	0.0477131i
$347$	−3897.53	−	6750.72i	−0.602969	−	1.04437i	−0.992369	−	0.123305i	$-0.960651\pi$
$347$	−3897.53	−	6750.72i	−0.602969	−	1.04437i	0.389399	−	0.921069i	$-0.372683\pi$
$348$	−7070.32	−	5778.63i	−1.08911	−	0.890135i
$349$	4540.81	−	7864.91i	0.696458	−	1.20630i	−0.273228	−	0.961949i	$-0.588091\pi$
$349$	4540.81	−	7864.91i	0.696458	−	1.20630i	0.969687	−	0.244352i	$-0.0785753\pi$
$350$	−7720.17	−	3472.00i	−1.17903	−	0.530246i
$351$	910.091	−	1429.18i	0.138396	−	0.217334i
$352$	−756.891	−	456.130i	−0.114609	−	0.0690676i
$353$	3944.55	+	2277.39i	0.594752	+	0.343380i	0.766974	−	0.641678i	$-0.221761\pi$
$353$	3944.55	+	2277.39i	0.594752	+	0.343380i	−0.172222	+	0.985058i	$0.555095\pi$
$354$	2962.03	+	796.138i	0.444718	+	0.119532i
$355$	−5599.34	+	3232.78i	−0.837133	+	0.483319i
$356$	7925.61	+	2641.09i	1.17993	+	0.393195i
$357$	6679.91	+	2541.40i	0.990303	+	0.376765i
$358$	−443.905	−	615.828i	−0.0655338	−	0.0909148i
$359$	−5415.10			−0.796095			−0.398047	−	0.917365i	$-0.630312\pi$
$359$	−5415.10			−0.796095			−0.398047	+	0.917365i	$0.630312\pi$
$360$	4207.83	−	9317.62i	0.616033	−	1.36412i
$361$	2194.06			0.319881
$362$	−1486.18	−	2061.77i	−0.215778	−	0.299348i
$363$	−5265.82	+	4290.18i	−0.761389	+	0.620320i
$364$	−1769.39	−	589.621i	−0.254783	−	0.0849026i
$365$	11258.1	−	6499.89i	1.61446	−	0.932109i
$366$	−6.08283	−	22.7721i	−0.000868729	−	0.00325223i
$367$	9228.51	+	5328.08i	1.31260	+	0.757830i	0.982526	−	0.186125i	$-0.0595928\pi$
$367$	9228.51	+	5328.08i	1.31260	+	0.757830i	0.330074	+	0.943955i	$0.392926\pi$
$368$	1040.35	−	8647.94i	0.147369	−	1.22501i
$369$	612.010	−	687.894i	0.0863414	−	0.0970470i
$370$	−5767.93	−	2594.02i	−0.810433	−	0.364477i
$371$	−2571.77	+	4454.43i	−0.359891	+	0.623350i
$372$	−12803.4	+	4848.35i	−1.78447	+	0.675740i
$373$	−1354.99	−	2346.91i	−0.188093	−	0.325786i	0.756522	−	0.653969i	$-0.226897\pi$
$373$	−1354.99	−	2346.91i	−0.188093	−	0.325786i	−0.944614	+	0.328183i	$0.893564\pi$
$374$	−99.1695	−	978.843i	−0.0137111	−	0.135334i
$375$	−2578.58	+	416.275i	−0.355087	+	0.0573236i
$376$	−926.019	+	4127.61i	−0.127010	+	0.566131i
$377$			2652.91i			0.362418i
$378$	−6402.59	+	4205.15i	−0.871200	+	0.572194i
$379$		−	6395.35i		−	0.866774i	−0.901208	−	0.433387i	$-0.857318\pi$
$379$		−	6395.35i		−	0.866774i	0.901208	−	0.433387i	$-0.142682\pi$
$380$	8957.89	−	1833.93i	1.20929	−	0.247575i
$381$	−8607.28	+	1389.52i	−1.15739	+	0.186843i
$382$	1448.27	−	146.729i	0.193979	−	0.0196526i
$383$	682.579	+	1182.26i	0.0910656	+	0.157730i	0.907960	−	0.419057i	$-0.137639\pi$
$383$	682.579	+	1182.26i	0.0910656	+	0.157730i	−0.816894	+	0.576788i	$0.804306\pi$
$384$	1349.86	−	7402.77i	0.179387	−	0.983779i
$385$	788.503	−	1365.73i	0.104379	−	0.180789i
$386$	2853.08	−	6343.97i	0.376212	−	0.836528i
$387$	−17.0441	−	3.51698i	−0.00223877	−	0.000461959i
$388$	7783.91	+	8776.44i	1.01847	+	1.14834i
$389$	−5380.83	−	3106.62i	−0.701333	−	0.404915i	0.106510	−	0.994312i	$-0.466032\pi$
$389$	−5380.83	−	3106.62i	−0.701333	−	0.404915i	−0.807844	+	0.589397i	$0.799366\pi$
$390$	−2869.64	+	766.531i	−0.372589	+	0.0995251i
$391$	8398.18	−	4848.69i	1.08623	−	0.627133i
$392$	493.224	+	454.255i	0.0635500	+	0.0585290i
$393$	−5739.84	+	4676.38i	−0.736735	+	0.600234i
$394$	1483.39	−	1069.26i	0.189675	−	0.136723i
$395$	1323.64			0.168606
$396$	912.385	+	528.656i	0.115780	+	0.0670857i
$397$	3291.69			0.416134			0.208067	−	0.978115i	$-0.433283\pi$
$397$	3291.69			0.416134			0.208067	+	0.978115i	$0.433283\pi$
$398$	3999.20	−	2882.73i	0.503672	−	0.363061i
$399$	−6403.12	−	2436.09i	−0.803400	−	0.305657i
$400$	−9124.15	+	3899.36i	−1.14052	+	0.487420i
$401$	3529.51	−	2037.76i	0.439539	−	0.253768i	−0.263863	−	0.964560i	$-0.584997\pi$
$401$	3529.51	−	2037.76i	0.439539	−	0.253768i	0.703402	+	0.710792i	$0.251663\pi$
$402$	−1636.06	+	6086.95i	−0.202983	+	0.755198i
$403$	3444.60	+	1988.74i	0.425776	+	0.245822i
$404$	2172.16	−	1926.51i	0.267498	−	0.237246i
$405$	−4828.95	+	11202.9i	−0.592475	+	1.37451i
$406$	4919.31	−	10938.3i	0.601333	−	1.33710i
$407$	326.151	−	564.910i	0.0397216	−	0.0687998i
$408$	7495.71	−	3741.42i	0.909542	−	0.453990i
$409$	−7054.78	−	12219.2i	−0.852900	−	1.47727i	−0.878579	−	0.477597i	$-0.841508\pi$
$409$	−7054.78	−	12219.2i	−0.852900	−	1.47727i	0.0256787	−	0.999670i	$-0.491825\pi$
$410$	−1605.86	+	162.694i	−0.193434	+	0.0195973i
$411$	−49.5609	+	130.268i	−0.00594808	+	0.0156341i
$412$	−863.624	−	4218.41i	−0.103271	−	0.504432i
$413$			4028.56i			0.479982i
$414$	−1063.68	+	10338.9i	−0.126274	+	1.22737i
$415$			15484.9i			1.83162i
$416$	−1913.44	+	1057.38i	−0.225515	+	0.124621i
$417$	5436.72	+	6673.10i	0.638458	+	0.783652i
$418$	95.0603	+	938.283i	0.0111233	+	0.109792i
$419$	3184.20	+	5515.19i	0.371261	+	0.643042i	0.989760	−	0.142743i	$-0.0455923\pi$
$419$	3184.20	+	5515.19i	0.371261	+	0.643042i	−0.618499	+	0.785786i	$0.712259\pi$
$420$	13253.4	+	2160.68i	1.53976	+	0.251025i
$421$	−5406.24	+	9363.89i	−0.625853	+	1.08401i	0.362522	+	0.931975i	$0.381916\pi$
$421$	−5406.24	+	9363.89i	−0.625853	+	1.08401i	−0.988375	+	0.152034i	$0.951418\pi$
$422$	10866.8	+	4887.15i	1.25353	+	0.563750i
$423$	1020.07	−	4943.52i	0.117252	−	0.568232i
$424$	1798.46	+	5754.66i	0.205993	+	0.659130i
$425$	−9566.92	−	5523.46i	−1.09191	−	0.630417i
$426$	4018.33	−	4012.10i	0.457016	−	0.456307i
$427$	26.8111	−	15.4794i	0.00303859	−	0.00175433i
$428$	−1088.69	+	3267.03i	−0.122953	+	0.368967i
$429$	−48.8243	−	302.438i	−0.00549477	−	0.0340369i
$430$	17.8397	+	24.7489i	0.00200071	+	0.00277558i
$431$	10968.4			1.22583			0.612913	−	0.790150i	$-0.289998\pi$
$431$	10968.4			1.22583			0.612913	+	0.790150i	$0.289998\pi$
$432$	−1458.51	+	8859.70i	−0.162437	+	0.986719i
$433$	−1491.10			−0.165491			−0.0827457	−	0.996571i	$-0.526369\pi$
$433$	−1491.10			−0.165491			−0.0827457	+	0.996571i	$0.526369\pi$
$434$	−10514.9	−	14587.2i	−1.16297	−	1.61339i
$435$	−3044.16	−	18856.8i	−0.335532	−	2.07843i
$436$	−2274.52	+	6825.59i	−0.249839	+	0.749740i
$437$	−8050.19	+	4647.78i	−0.881219	+	0.508772i
$438$	−8079.34	+	8066.81i	−0.881383	+	0.880016i
$439$	1927.62	+	1112.91i	0.209567	+	0.120994i	0.601110	−	0.799166i	$-0.294725\pi$
$439$	1927.62	+	1112.91i	0.209567	+	0.120994i	−0.391543	+	0.920160i	$0.628059\pi$
$440$	−551.408	−	1764.38i	−0.0597439	−	0.191167i
$441$	−597.774	−	531.832i	−0.0645474	−	0.0574270i
$442$	−2219.76	−	998.295i	−0.238876	−	0.107430i
$443$	−7938.74	+	13750.3i	−0.851425	+	1.47471i	0.0284982	+	0.999594i	$0.490927\pi$
$443$	−7938.74	+	13750.3i	−0.851425	+	1.47471i	−0.879923	+	0.475117i	$0.842406\pi$
$444$	5482.02	+	893.727i	0.585957	+	0.0955280i
$445$	8737.50	+	15133.8i	0.930780	+	1.61216i
$446$	−1829.88	−	18061.7i	−0.194277	−	1.91759i
$447$	2797.94	+	3434.22i	0.296058	+	0.363385i
$448$	9850.13	−	811.629i	1.03878	−	0.0855934i
$449$		−	11558.7i		−	1.21490i	−0.794358	−	0.607450i	$-0.792193\pi$
$449$		−	11558.7i		−	1.21490i	0.794358	−	0.607450i	$-0.207807\pi$
$450$	10805.7	−	4839.49i	1.13197	−	0.506969i
$451$		−	166.477i		−	0.0173816i
$452$	−613.004	−	2994.25i	−0.0637905	−	0.311588i
$453$	−2713.97	+	7133.51i	−0.281487	+	0.739871i
$454$	−6330.61	+	641.373i	−0.654428	+	0.0663021i
$455$	−1950.64	−	3378.61i	−0.200984	−	0.348114i
$456$	−7185.12	+	3586.39i	−0.737881	+	0.368307i
$457$	5444.85	−	9430.75i	0.557329	−	0.965322i	−0.440390	−	0.897807i	$-0.645160\pi$
$457$	5444.85	−	9430.75i	0.557329	−	0.965322i	0.997718	−	0.0675148i	$-0.0215070\pi$
$458$	−4026.43	+	8952.96i	−0.410792	+	0.913416i
$459$	−8866.08	+	4617.63i	−0.901597	+	0.469569i
$460$	13631.3	−	12089.7i	1.38166	−	1.22540i
$461$	10197.5	+	5887.54i	1.03025	+	0.594816i	0.917057	−	0.398757i	$-0.130558\pi$
$461$	10197.5	+	5887.54i	1.03025	+	0.594816i	0.113195	+	0.993573i	$0.463892\pi$
$462$	−359.504	+	1337.53i	−0.0362027	+	0.134692i
$463$	−2303.58	+	1329.97i	−0.231223	+	0.133497i	−0.611136	−	0.791525i	$-0.709287\pi$
$463$	−2303.58	+	1329.97i	−0.231223	+	0.133497i	0.379913	+	0.925022i	$0.375954\pi$
$464$	−5524.83	−	12927.6i	−0.552766	−	1.29342i
$465$	−26766.2	−	10183.3i	−2.66936	−	1.01557i
$466$	−8839.82	+	6371.98i	−0.878749	+	0.633426i
$467$	−32.9750			−0.00326746			−0.00163373	−	0.999999i	$-0.500520\pi$
$467$	−32.9750			−0.00326746			−0.00163373	+	0.999999i	$0.500520\pi$
$468$	2261.16	−	1300.80i	0.223338	−	0.128482i
$469$	−8278.68			−0.815083
$470$	−7178.23	+	5174.26i	−0.704483	+	0.507810i
$471$	10832.6	−	8825.57i	1.05975	−	0.863399i
$472$	3473.49	+	3199.06i	0.338730	+	0.311967i
$473$	−2.72509	+	1.57333i	−0.000264904	+	0.000152942i
$474$	−1123.11	+	300.001i	−0.108831	+	0.0290707i
$475$	9170.50	+	5294.59i	0.885834	+	0.511437i
$476$	7301.26	+	8232.25i	0.703052	+	0.792698i
$477$	−2263.81	−	6828.77i	−0.217302	−	0.655489i
$478$	−46.2499	+	102.839i	−0.00442556	+	0.00984046i
$479$	−4069.08	+	7047.85i	−0.388144	+	0.672284i	−0.992200	−	0.124657i	$-0.960217\pi$
$479$	−4069.08	+	7047.85i	−0.388144	+	0.672284i	0.604056	+	0.796942i	$0.293550\pi$
$480$	12387.4	−	9711.48i	1.17793	−	0.923472i
$481$	−806.850	−	1397.50i	−0.0764848	−	0.132476i
$482$	9731.91	−	985.969i	0.919661	−	0.0931736i
$483$	−13476.9	+	2175.65i	−1.26960	+	0.204959i
$484$	−10244.8	+	2097.40i	−0.962138	+	0.196976i
$485$			24538.7i			2.29741i
$486$	1558.23	−	10600.1i	0.145438	−	0.989367i
$487$		−	1992.29i		−	0.185378i	−0.995695	−	0.0926891i	$-0.970454\pi$
$487$		−	1992.29i		−	0.185378i	0.995695	−	0.0926891i	$-0.0295463\pi$
$488$	7.94394	−	35.4091i	0.000736896	−	0.00328462i
$489$	11216.2	−	1810.69i	1.03724	−	0.167448i
$490$	141.380	+	1395.48i	0.0130345	+	0.128656i
$491$	4407.34	+	7633.75i	0.405093	+	0.701642i	0.994332	−	0.106317i	$-0.0339058\pi$
$491$	4407.34	+	7633.75i	0.405093	+	0.701642i	−0.589239	+	0.807959i	$0.700572\pi$
$492$	1325.70	−	502.013i	0.121478	−	0.0460010i
$493$	7825.94	−	13554.9i	0.714934	−	1.23830i
$494$	2127.78	+	956.929i	0.193792	+	0.0871544i
$495$	694.084	+	2093.70i	0.0630237	+	0.190111i
$496$	−20927.2	−	2517.54i	−1.89447	−	0.227905i
$497$	6459.06	+	3729.14i	0.582954	+	0.336569i
$498$	−3509.64	−	13139.0i	−0.315805	−	1.18227i
$499$	18252.9	−	10538.3i	1.63750	−	0.945409i	0.655806	−	0.754930i	$-0.272329\pi$
$499$	18252.9	−	10538.3i	1.63750	−	0.945409i	0.981691	−	0.190479i	$-0.0610042\pi$
$500$	−3815.14	−	1271.34i	−0.341236	−	0.113712i
$501$	14426.9	−	11754.0i	1.28652	−	1.04816i
$502$	4924.71	+	6832.04i	0.437850	+	0.607428i
$503$	−19011.6			−1.68526			−0.842629	−	0.538494i	$-0.818994\pi$
$503$	−19011.6			−1.68526			−0.842629	+	0.538494i	$0.818994\pi$
$504$	−11735.2	+	1170.52i	−1.03716	+	0.103451i
$505$	6073.31			0.535166
$506$	1098.88	+	1524.47i	0.0965434	+	0.133934i
$507$	9961.49	+	3789.89i	0.872594	+	0.331982i
$508$	−12734.9	−	4243.70i	−1.11224	−	0.370638i
$509$	11096.0	−	6406.27i	0.966250	−	0.557865i	0.0681588	−	0.997674i	$-0.478288\pi$
$509$	11096.0	−	6406.27i	0.966250	−	0.557865i	0.898091	+	0.439810i	$0.144954\pi$
$510$	16923.5	+	4548.73i	1.46939	+	0.394943i
$511$	−12986.7	−	7497.88i	−1.12426	−	0.649093i
$512$	7122.13	−	9137.45i	0.614759	−	0.788715i
$513$	8498.70	−	4426.29i	0.731436	−	0.380946i
$514$	16660.3	+	7492.64i	1.42968	+	0.642970i
$515$	4503.53	−	7800.35i	0.385339	−	0.667426i
$516$	−20.7463	−	16.9561i	−0.00176997	−	0.00144661i
$517$	−456.332	−	790.390i	−0.0388190	−	0.0672365i
$518$	735.357	+	7258.27i	0.0623740	+	0.615657i
$519$	201.630	−	529.971i	0.0170531	−	0.0448230i
$520$	−4462.09	−	1001.06i	−0.376299	−	0.0844218i
$521$		−	14455.7i		−	1.21558i	−0.794100	−	0.607788i	$-0.792057\pi$
$521$		−	14455.7i		−	1.21558i	0.794100	−	0.607788i	$-0.207943\pi$
$522$	6856.85	+	15310.1i	0.574935	+	1.28372i
$523$		−	15232.9i		−	1.27359i	−0.771032	−	0.636796i	$-0.780259\pi$
$523$		−	15232.9i		−	1.27359i	0.771032	−	0.636796i	$-0.219741\pi$
$524$	−11167.1	+	2286.20i	−0.930984	+	0.190598i
$525$	9822.56	+	12056.3i	0.816556	+	1.00225i
$526$	−16552.0	+	1676.93i	−1.37206	+	0.139007i
$527$	−11733.4	−	20322.8i	−0.969854	−	1.67984i
$528$	867.764	+	1372.10i	0.0715238	+	0.113093i
$529$	−3177.87	+	5504.23i	−0.261187	+	0.452390i
$530$	−5172.84	+	11502.1i	−0.423950	+	0.942675i
$531$	−4209.78	−	3745.39i	−0.344047	−	0.306094i
$532$	−6998.72	−	7891.13i	−0.570363	−	0.643090i
$533$	−356.664	−	205.920i	−0.0289847	−	0.0167343i
$534$	−10843.8	−	10860.7i	−0.878761	−	0.880127i
$535$	−6238.33	+	3601.70i	−0.504124	+	0.291056i
$536$	−6574.05	+	7138.01i	−0.529768	+	0.575215i
$537$	222.265	+	1376.81i	0.0178612	+	0.110640i
$538$	−6807.83	+	4907.27i	−0.545551	+	0.393248i
$539$	−144.667			−0.0115608
$540$	−14579.6	+	11840.7i	−1.16186	+	0.943599i
$541$	−23075.7			−1.83383			−0.916915	−	0.399083i	$-0.869328\pi$
$541$	−23075.7			−1.83383			−0.916915	+	0.399083i	$0.869328\pi$
$542$	−4556.31	+	3284.31i	−0.361089	+	0.260283i
$543$	744.136	+	4609.49i	0.0588102	+	0.364295i
$544$	12895.9	+	241.908i	1.01637	+	0.0190657i
$545$	−13033.3	+	7524.80i	−1.02438	+	0.591426i
$546$	2420.88	+	2424.64i	0.189751	+	0.190046i
$547$	317.151	+	183.107i	0.0247905	+	0.0143128i	0.512344	−	0.858780i	$-0.328777\pi$
$547$	317.151	+	183.107i	0.0247905	+	0.0143128i	−0.487554	+	0.873093i	$0.662111\pi$
$548$	−160.540	+	142.385i	−0.0125145	+	0.0110992i
$549$	−8.75078	+	42.4084i	−0.000680281	+	0.00329681i
$550$	878.056	−	1952.40i	0.0680735	−	0.151365i
$551$	−7501.66	+	12993.2i	−0.580002	+	1.00459i
$552$	−8826.02	+	13347.6i	−0.680544	+	1.02919i
$553$	−763.434	−	1322.31i	−0.0587061	−	0.101682i
$554$	12221.2	−	1238.17i	0.937236	−	0.0949542i
$555$	7338.68	+	9007.59i	0.561279	+	0.688921i
$556$	2657.92	+	12982.7i	0.202736	+	0.990272i
$557$		−	3402.66i		−	0.258842i	−0.991590	−	0.129421i	$-0.958688\pi$
$557$		−	3402.66i		−	0.258842i	0.991590	−	0.129421i	$-0.0413119\pi$
$558$	25019.2	+	2574.01i	1.89811	+	0.195281i
$559$			7.78437i			0.000588987i
$560$	16541.6	+	12401.6i	1.24823	+	0.935829i
$561$	−642.711	+	1689.32i	−0.0483695	+	0.127136i
$562$	−2222.80	−	21940.0i	−0.166839	−	1.64676i
$563$	2461.45	+	4263.36i	0.184259	+	0.319146i	0.943327	−	0.331866i	$-0.107678\pi$
$563$	2461.45	+	4263.36i	0.184259	+	0.319146i	−0.759068	+	0.651012i	$0.774345\pi$
$564$	4917.99	−	6017.30i	0.367171	−	0.449245i
$565$	3196.63	−	5536.73i	0.238023	−	0.412269i
$566$	5276.53	+	2373.02i	0.391854	+	0.176229i
$567$	13976.8	−	1637.41i	1.03522	−	0.121278i
$568$	8344.42	−	2607.82i	0.616416	−	0.192644i
$569$	10423.8	+	6018.16i	0.767990	+	0.443399i	0.832157	−	0.554540i	$-0.187106\pi$
$569$	10423.8	+	6018.16i	0.767990	+	0.443399i	−0.0641669	+	0.997939i	$0.520439\pi$
$570$	−16222.3	−	4360.25i	−1.19206	−	0.320405i
$571$	−522.706	+	301.784i	−0.0383092	+	0.0221178i	−0.519032	−	0.854755i	$-0.673708\pi$
$571$	−522.706	+	301.784i	−0.0383092	+	0.0221178i	0.480723	+	0.876872i	$0.340374\pi$
$572$	149.113	−	447.472i	0.0108999	−	0.0327093i
$573$	−2499.48	−	950.939i	−0.182229	−	0.0693299i
$574$	1088.74	+	1510.41i	0.0791694	+	0.109831i
$575$	21100.5			1.53035
$576$	−8309.60	+	11047.8i	−0.601099	+	0.799174i
$577$	−6971.52			−0.502995			−0.251497	−	0.967858i	$-0.580923\pi$
$577$	−6971.52			−0.502995			−0.251497	+	0.967858i	$0.580923\pi$
$578$	271.180	+	376.207i	0.0195149	+	0.0270729i
$579$	−9907.18	+	8071.60i	−0.711103	+	0.579351i
$580$	9297.10	−	27899.5i	0.665588	−	1.99735i
$581$	15469.3	−	8931.22i	1.10461	−	0.637745i
$582$	−5561.68	−	20821.1i	−0.396115	−	1.48293i
$583$	−1126.51	−	650.391i	−0.0800262	−	0.0462032i
$584$	−16777.5	+	5243.34i	−1.18880	+	0.371525i
$585$	5344.12	+	1102.73i	0.377696	+	0.0779358i
$586$	6081.15	+	2734.88i	0.428686	+	0.192793i
$587$	10334.9	−	17900.6i	0.726691	−	1.25867i	−0.231583	−	0.972815i	$-0.574390\pi$
$587$	10334.9	−	17900.6i	0.726691	−	1.25867i	0.958274	−	0.285851i	$-0.0922762\pi$
$588$	−436.245	−	1152.02i	−0.0305960	−	0.0807968i
$589$	11247.2	+	19480.7i	0.786811	+	1.36280i
$590$	995.659	+	9827.55i	0.0694756	+	0.685752i
$591$	−3316.40	+	535.386i	−0.230827	+	0.0372637i
$592$	6842.15	+	5129.71i	0.475018	+	0.356132i
$593$			2417.22i			0.167392i	0.996491	+	0.0836958i	$0.0266724\pi$
$593$			2417.22i			0.167392i	−0.996491	+	0.0836958i	$0.973328\pi$
$594$	−1063.47	−	1619.19i	−0.0734588	−	0.111845i
$595$			23017.2i			1.58590i
$596$	1367.87	+	6681.40i	0.0940100	+	0.459196i
$597$	−8941.01	+	1443.40i	−0.612950	+	0.0989519i
$598$	4625.28	−	468.601i	0.316290	−	0.0320443i
$599$	14467.5	+	25058.4i	0.986852	+	1.70928i	0.633400	+	0.773825i	$0.281659\pi$
$599$	14467.5	+	25058.4i	0.986852	+	1.70928i	0.353452	+	0.935453i	$0.385008\pi$
$600$	18195.2	+	1104.69i	1.23803	+	0.0751645i
$601$	−318.246	+	551.219i	−0.0215999	+	0.0374121i	−0.876623	−	0.481177i	$-0.840209\pi$
$601$	−318.246	+	551.219i	−0.0215999	+	0.0374121i	0.855023	+	0.518589i	$0.173543\pi$
$602$	14.4346	−	32.0962i	0.000977263	−	0.00217299i
$603$	7696.75	−	8651.07i	0.519794	−	0.584243i
$604$	−8791.25	+	7797.05i	−0.592237	+	0.525261i
$605$	−18944.0	−	10937.3i	−1.27303	−	0.734983i
$606$	−5153.21	+	1376.51i	−0.345437	+	0.0922722i
$607$	−16616.3	+	9593.41i	−1.11109	+	0.641490i	−0.939112	−	0.343610i	$-0.888350\pi$
$607$	−16616.3	+	9593.41i	−1.11109	+	0.641490i	−0.171981	+	0.985100i	$0.555017\pi$
$608$	−12361.5	−	231.885i	−0.824548	−	0.0154674i
$609$	−17082.1	+	13917.1i	−1.13662	+	0.926027i
$610$	61.5791	−	44.3878i	0.00408732	−	0.00294625i
$611$	−2257.80			−0.149494
$612$	−15390.6	−	23.8931i	−1.01655	−	0.00157814i
$613$	6429.22			0.423612			0.211806	−	0.977312i	$-0.432066\pi$
$613$	6429.22			0.423612			0.211806	+	0.977312i	$0.432066\pi$
$614$	12668.4	−	9131.69i	0.832660	−	0.600204i
$615$	2771.45	+	1054.41i	0.181717	+	0.0691349i
$616$	−1444.57	+	1568.49i	−0.0944858	+	0.102591i
$617$	−6024.79	+	3478.41i	−0.393110	+	0.226962i	−0.683507	−	0.729944i	$-0.739546\pi$
$617$	−6024.79	+	3478.41i	−0.393110	+	0.226962i	0.290397	+	0.956906i	$0.406213\pi$
$618$	−2053.31	+	7639.32i	−0.133651	+	0.497247i
$619$	−19227.5	−	11101.0i	−1.24850	−	0.720819i	−0.277686	−	0.960672i	$-0.589567\pi$
$619$	−19227.5	−	11101.0i	−1.24850	−	0.720819i	−0.970809	+	0.239853i	$0.922901\pi$
$620$	−29255.9	−	32986.4i	−1.89508	−	2.13672i
$621$	10256.0	−	16105.8i	0.662738	−	1.04075i
$622$	1780.37	−	3958.75i	0.114769	−	0.255195i
$623$	10079.0	−	17457.4i	0.648168	−	1.12266i
$624$	4012.97	−	161.930i	0.257448	−	0.0103885i
$625$	5483.94	+	9498.47i	0.350972	+	0.607902i
$626$	24669.3	−	2499.32i	1.57505	−	0.159573i
$627$	616.079	−	1619.32i	0.0392406	−	0.103141i
$628$	21075.2	−	4314.68i	1.33916	−	0.274163i
$629$			9520.65i			0.603519i
$630$	−19989.8	−	14456.4i	−1.26415	−	0.914217i
$631$		−	529.250i		−	0.0333901i	−0.999861	−	0.0166950i	$-0.994686\pi$
$631$		−	529.250i		−	0.0333901i	0.999861	−	0.0166950i	$-0.00531444\pi$
$632$	−1746.35	−	391.790i	−0.109915	−	0.0246591i
$633$	−13826.1	−	16970.4i	−0.868151	−	1.06558i
$634$	1999.72	+	19738.0i	0.125266	+	1.23643i
$635$	−14039.4	−	24317.0i	−0.877383	−	1.51967i
$636$	1782.22	−	10931.9i	0.111116	−	0.681571i
$637$	−178.943	+	309.938i	−0.0111303	+	0.0192782i
$638$	2766.27	+	1244.08i	0.171658	+	0.0771997i
$639$	−9901.92	+	3282.59i	−0.613011	+	0.203220i
$640$	23828.5	−	4414.40i	1.47172	−	0.272648i
$641$	−19866.3	−	11469.8i	−1.22414	−	0.706755i	−0.258339	−	0.966054i	$-0.583175\pi$
$641$	−19866.3	−	11469.8i	−1.22414	−	0.706755i	−0.965797	+	0.259299i	$0.916509\pi$
$642$	4476.90	−	4469.96i	0.275217	−	0.274790i
$643$	−2182.17	+	1259.88i	−0.133836	+	0.0772702i	−0.565423	−	0.824801i	$-0.691287\pi$
$643$	−2182.17	+	1259.88i	−0.133836	+	0.0772702i	0.431587	+	0.902071i	$0.357954\pi$
$644$	−19939.7	−	6644.59i	−1.22008	−	0.406574i
$645$	−8.93242	−	55.3312i	−0.000545293	−	0.00337777i
$646$	−8048.91	−	11166.2i	−0.490217	−	0.680076i
$647$	−5938.61			−0.360851			−0.180426	−	0.983589i	$-0.557748\pi$
$647$	−5938.61			−0.360851			−0.180426	+	0.983589i	$0.557748\pi$
$648$	9687.12	−	13351.3i	0.587262	−	0.809397i
$649$	−1018.81			−0.0616205
$650$	−3096.77	−	4296.14i	−0.186870	−	0.259244i
$651$	5264.85	+	32612.7i	0.316967	+	1.96343i
$652$	16594.8	+	5529.97i	0.996785	+	0.332163i
$653$	−22562.1	+	13026.3i	−1.35210	+	0.780638i	−0.988544	−	0.150933i	$-0.951772\pi$
$653$	−22562.1	+	13026.3i	−1.35210	+	0.780638i	−0.363561	+	0.931571i	$0.618439\pi$
$654$	9353.30	−	9338.79i	0.559240	−	0.558373i
$655$	−20649.3	−	11921.9i	−1.23181	−	0.711184i
$656$	2166.86	+	260.674i	0.128966	+	0.0155146i
$657$	19909.0	−	6600.05i	1.18223	−	0.391921i
$658$	9309.24	+	4186.66i	0.551538	+	0.248044i
$659$	14176.7	−	24554.8i	0.838008	−	1.45147i	−0.0535504	−	0.998565i	$-0.517054\pi$
$659$	14176.7	−	24554.8i	0.838008	−	1.45147i	0.891558	−	0.452907i	$-0.149613\pi$
$660$	−546.428	+	3351.72i	−0.0322268	+	0.197675i
$661$	5168.04	+	8951.31i	0.304105	+	0.526725i	0.977062	−	0.212957i	$-0.0683093\pi$
$661$	5168.04	+	8951.31i	0.304105	+	0.526725i	−0.672957	+	0.739682i	$0.734976\pi$
$662$	2819.02	+	27824.9i	0.165505	+	1.63360i
$663$	2824.26	+	3466.53i	0.165437	+	0.203060i
$664$	4583.45	−	20430.2i	0.267880	−	1.19404i
$665$		−	22063.4i		−	1.28659i
$666$	−8268.44	−	5979.64i	−0.481074	−	0.347907i
$667$			29896.3i			1.73551i
$668$	28068.1	−	5746.32i	1.62573	−	0.332832i
$669$	−11859.3	+	31171.5i	−0.685364	+	1.80144i
$670$	−20195.6	+	2046.07i	−1.16451	+	0.117980i
$671$	3.91468	+	6.78042i	0.000225223	+	0.000390097i
$672$	−16846.4	−	6773.64i	−0.967058	−	0.388837i
$673$	7541.97	−	13063.1i	0.431979	−	0.748209i	−0.565065	−	0.825046i	$-0.691149\pi$
$673$	7541.97	−	13063.1i	0.431979	−	0.748209i	0.997044	+	0.0768374i	$0.0244822\pi$
$674$	5810.05	−	12918.9i	0.332040	−	0.738307i
$675$	−21730.8	−	944.464i	−1.23914	−	0.0538555i
$676$	10888.1	+	12276.4i	0.619486	+	0.698477i
$677$	−11873.7	−	6855.26i	−0.674065	−	0.389172i	0.123550	−	0.992338i	$-0.460572\pi$
$677$	−11873.7	−	6855.26i	−0.674065	−	0.389172i	−0.797615	+	0.603167i	$0.793905\pi$
$678$	−1457.45	+	5422.43i	−0.0825559	+	0.307149i
$679$	24514.0	−	14153.2i	1.38551	−	0.799925i
$680$	19845.8	+	18277.8i	1.11919	+	1.03077i
$681$	10925.6	+	4156.70i	0.614787	+	0.233899i
$682$	3689.06	−	2659.17i	0.207128	−	0.149303i
$683$	807.274			0.0452262			0.0226131	−	0.999744i	$-0.492801\pi$
$683$	807.274			0.0452262			0.0226131	+	0.999744i	$0.492801\pi$
$684$	14752.9	+	22.9030i	0.824692	+	0.00128029i
$685$	−448.867			−0.0250370
$686$	−13879.5	+	10004.7i	−0.772483	+	0.556826i
$687$	13981.6	−	11391.1i	0.776463	−	0.632601i
$688$	−16.2114	−	37.9332i	−0.000898333	−	0.00210202i
$689$	−2786.82	+	1608.97i	−0.154092	+	0.0889651i
$690$	−32338.7	+	8638.22i	−1.78422	+	0.476596i
$691$	19006.4	+	10973.4i	1.04636	+	0.604119i	0.921629	−	0.388072i	$-0.126859\pi$
$691$	19006.4	+	10973.4i	1.04636	+	0.604119i	0.124735	+	0.992190i	$0.460192\pi$
$692$	653.130	−	579.268i	0.0358790	−	0.0318215i
$693$	1691.27	−	1900.97i	0.0927070	−	0.104202i
$694$	−9043.13	+	20107.9i	−0.494629	+	1.09983i
$695$	−13860.3	+	24006.7i	−0.756474	+	1.31025i
$696$	−1565.18	+	25780.0i	−0.0852414	+	1.40400i
$697$	1214.91	+	2104.28i	0.0660228	+	0.114355i
$698$	−25555.9	+	2589.14i	−1.38582	+	0.140402i
$699$	19763.2	−	3190.48i	1.06940	−	0.172640i
$700$	4802.09	+	23456.0i	0.259289	+	1.26651i
$701$			3170.45i			0.170822i	0.996346	+	0.0854110i	$0.0272203\pi$
$701$			3170.45i			0.170822i	−0.996346	+	0.0854110i	$0.972780\pi$
$702$	−4784.42	+	275.570i	−0.257231	+	0.0148158i
$703$		−	9126.15i		−	0.489615i
$704$	205.258	+	2491.06i	0.0109886	+	0.133360i
$705$	16048.4	−	2590.78i	0.857329	−	0.138403i
$706$	−1298.55	−	12817.2i	−0.0692234	−	0.683263i
$707$	−3502.90	−	6067.20i	−0.186337	−	0.322745i
$708$	−3072.22	−	8113.02i	−0.163081	−	0.430658i
$709$	−1413.03	+	2447.45i	−0.0748485	+	0.129641i	−0.901020	−	0.433777i	$-0.857181\pi$
$709$	−1413.03	+	2447.45i	−0.0748485	+	0.129641i	0.826172	+	0.563418i	$0.190514\pi$
$710$	16678.3	+	7500.76i	0.881586	+	0.396477i
$711$	2091.56	+	431.583i	0.110323	+	0.0227646i
$712$	−7048.37	−	22553.2i	−0.370996	−	1.18710i
$713$	38818.0	+	22411.6i	2.03892	+	1.17717i
$714$	−5216.82	−	19530.1i	−0.273438	−	1.02366i
$715$	854.438	−	493.310i	0.0446912	−	0.0258025i
$716$	−678.816	+	2037.05i	−0.0354309	+	0.106324i
$717$	160.600	−	130.845i	0.00836503	−	0.00681517i
$718$	8956.10	+	12424.8i	0.465514	+	0.645805i
$719$	15469.9			0.802408			0.401204	−	0.915989i	$-0.368592\pi$
$719$	15469.9			0.802408			0.401204	+	0.915989i	$0.368592\pi$
$720$	−28338.3	+	5755.81i	−1.46682	+	0.297925i
$721$	−10390.0			−0.536677
$722$	−3628.79	−	5034.20i	−0.187049	−	0.259493i
$723$	−16795.7	−	6390.00i	−0.863954	−	0.328695i
$724$	−2272.65	+	6819.96i	−0.116661	+	0.350085i
$725$	29494.0	−	17028.4i	1.51087	−	0.872301i
$726$	18552.9	+	4986.67i	0.948433	+	0.254921i
$727$	−6900.11	−	3983.78i	−0.352009	−	0.203233i	0.313561	−	0.949568i	$-0.398478\pi$
$727$	−6900.11	−	3983.78i	−0.352009	−	0.203233i	−0.665570	+	0.746336i	$0.731811\pi$
$728$	1573.55	+	5034.98i	0.0801092	+	0.256331i
$729$	−11283.3	+	16127.9i	−0.573251	+	0.819380i
$730$	−33533.8	−	15081.2i	−1.70019	−	0.764629i
$731$	22.9635	−	39.7739i	0.00116188	−	0.00201244i
$732$	−42.1894	+	51.6199i	−0.00213028	+	0.00260646i
$733$	−12334.6	−	21364.2i	−0.621542	−	1.07654i	−0.989199	−	0.146581i	$-0.953173\pi$
$733$	−12334.6	−	21364.2i	−0.621542	−	1.07654i	0.367656	−	0.929962i	$-0.380160\pi$
$734$	−3038.04	−	29986.7i	−0.152774	−	1.50794i
$735$	916.275	−	2408.37i	0.0459827	−	0.120863i
$736$	−21563.0	+	11915.9i	−1.07992	+	0.596773i
$737$		−	2093.65i		−	0.104641i
$738$	−2590.56	−	266.521i	−0.129214	−	0.0132937i
$739$		−	1182.09i		−	0.0588414i	−0.999567	−	0.0294207i	$-0.990634\pi$
$739$		−	1182.09i		−	0.0588414i	0.999567	−	0.0294207i	$-0.00936624\pi$
$740$	3587.76	+	17524.6i	0.178228	+	0.870563i
$741$	−2707.23	−	3322.89i	−0.134214	−	0.164736i
$742$	14474.0	−	1466.41i	0.716116	−	0.0725519i
$743$	13616.4	+	23584.4i	0.672327	+	1.16450i	0.977243	+	0.212125i	$0.0680383\pi$
$743$	13616.4	+	23584.4i	0.672327	+	1.16450i	−0.304916	+	0.952379i	$0.598628\pi$
$744$	32300.0	+	21358.1i	1.59163	+	1.05245i
$745$	−7133.00	+	12354.7i	−0.350782	+	0.607573i
$746$	−3143.87	+	6990.55i	−0.154296	+	0.343086i
$747$	−5048.98	+	24468.6i	−0.247299	+	1.19847i
$748$	−2081.90	+	1846.46i	−0.101767	+	0.0902584i
$749$	7196.16	+	4154.70i	0.351057	+	0.202683i
$750$	5219.88	+	5227.99i	0.254137	+	0.254532i
$751$	−12287.2	+	7093.99i	−0.597024	+	0.344692i	−0.767870	−	0.640606i	$-0.778683\pi$
$751$	−12287.2	+	7093.99i	−0.597024	+	0.344692i	0.170846	+	0.985298i	$0.445350\pi$
$752$	11002.2	−	4701.99i	0.533523	−	0.228010i
$753$	−2465.83	−	15274.4i	−0.119336	−	0.739216i
$754$	6087.01	−	4387.68i	0.294000	−	0.211923i
$755$	−24580.1			−1.18485
$756$	20237.9	+	7735.58i	0.973604	+	0.372143i
$757$	30482.1			1.46353			0.731764	−	0.681559i	$-0.238698\pi$
$757$	30482.1			1.46353			0.731764	+	0.681559i	$0.238698\pi$
$758$	−14673.9	+	10577.4i	−0.703141	+	0.506843i
$759$	−550.213	−	3408.25i	−0.0263129	−	0.162993i
$760$	−19023.4	−	17520.4i	−0.907965	−	0.836227i
$761$	−19985.7	+	11538.8i	−0.952013	+	0.549645i	−0.893706	−	0.448654i	$-0.851904\pi$
$761$	−19985.7	+	11538.8i	−0.952013	+	0.549645i	−0.0583074	+	0.998299i	$0.518570\pi$
$762$	17423.9	+	17451.0i	0.828348	+	0.829635i
$763$	15034.5	+	8680.15i	0.713348	+	0.411851i
$764$	−2731.98	−	3080.33i	−0.129371	−	0.145867i
$765$	−24052.5	−	21399.2i	−1.13676	−	1.01136i
$766$	1583.73	−	3521.51i	0.0747031	−	0.166106i
$767$	−1260.19	+	2182.72i	−0.0593258	+	0.102755i
$768$	−19217.9	+	9146.32i	−0.902953	+	0.429739i
$769$	−1035.31	−	1793.21i	−0.0485491	−	0.0840895i	0.840730	−	0.541455i	$-0.182126\pi$
$769$	−1035.31	−	1793.21i	−0.0485491	−	0.0840895i	−0.889279	+	0.457366i	$0.848793\pi$
$770$	−4437.73	+	449.600i	−0.207694	+	0.0210421i
$771$	−21197.3	−	26017.8i	−0.990145	−	1.21532i
$772$	−19274.8	+	3946.07i	−0.898594	+	0.183967i
$773$		−	35103.0i		−	1.63333i	−0.577110	−	0.816666i	$-0.695820\pi$
$773$		−	35103.0i		−	1.63333i	0.577110	−	0.816666i	$-0.304180\pi$
$774$	20.1199	+	44.9240i	0.000934362	+	0.00208625i
$775$		−	51061.1i		−	2.36667i
$776$	7263.34	−	32375.4i	0.336003	−	1.49769i
$777$	4765.80	−	12526.6i	0.220041	−	0.578365i
$778$	1771.38	+	17484.2i	0.0816285	+	0.805706i
$779$	−1164.57	−	2017.09i	−0.0535622	−	0.0927724i
$780$	6504.91	+	5316.52i	0.298607	+	0.244054i
$781$	−943.085	+	1633.47i	−0.0432090	+	0.0748402i
$782$	−25015.0	−	11250.0i	−1.14391	−	0.514450i
$783$	1338.17	−	30789.3i	0.0610756	−	1.40526i
$784$	226.523	−	1882.98i	0.0103190	−	0.0857774i
$785$	38970.7	+	22499.7i	1.77188	+	1.02299i
$786$	20223.0	+	5435.56i	0.917723	+	0.246667i
$787$	−20621.0	+	11905.5i	−0.934000	+	0.539245i	−0.888074	−	0.459700i	$-0.847957\pi$
$787$	−20621.0	+	11905.5i	−0.934000	+	0.539245i	−0.0459253	+	0.998945i	$0.514624\pi$
$788$	−4906.78	−	1635.11i	−0.221823	−	0.0739192i
$789$	28566.1	+	10868.1i	1.28895	+	0.490386i
$790$	−2189.18	−	3037.04i	−0.0985918	−	0.136776i
$791$	−7374.87			−0.331505
$792$	−296.021	−	2967.79i	−0.0132811	−	0.133151i
$793$	19.3687			0.000867343
$794$	−5444.17	−	7552.68i	−0.243333	−	0.337575i
$795$	17962.4	−	14634.4i	0.801335	−	0.652865i
$796$	−13228.6	−	4408.24i	−0.589041	−	0.196289i
$797$	−2079.48	+	1200.59i	−0.0924202	+	0.0533588i	−0.545498	−	0.838112i	$-0.683659\pi$
$797$	−2079.48	+	1200.59i	−0.0924202	+	0.0533588i	0.453078	+	0.891471i	$0.350326\pi$
$798$	5000.66	+	18720.8i	0.221831	+	0.830463i
$799$	11536.1	+	6660.38i	0.510787	+	0.294903i
$800$	24037.5	+	14485.9i	1.06232	+	0.640190i
$801$	8872.13	+	26762.7i	0.391363	+	1.18054i
$802$	−10513.1	−	4728.06i	−0.462880	−	0.208171i
$803$	1896.19	−	3284.29i	0.0833312	−	0.144334i
$804$	16672.2	−	6313.40i	0.731323	−	0.276936i
$805$	−21982.3	−	38074.4i	−0.962451	−	1.66701i
$806$	−1133.97	−	11192.7i	−0.0495562	−	0.489140i
$807$	15220.3	−	2457.09i	0.663914	−	0.107179i
$808$	−8012.88	−	1797.67i	−0.348876	−	0.0782695i
$809$			29338.0i			1.27499i	0.770453	+	0.637497i	$0.220030\pi$
$809$			29338.0i			1.27499i	−0.770453	+	0.637497i	$0.779970\pi$
$810$	33691.3	−	7448.77i	1.46147	−	0.323115i
$811$		−	30884.9i		−	1.33726i	−0.743597	−	0.668629i	$-0.766882\pi$
$811$		−	30884.9i		−	1.33726i	0.743597	−	0.668629i	$-0.233118\pi$
$812$	−33233.8	+	6803.86i	−1.43630	+	0.294050i
$813$	10186.6	−	1644.47i	0.439432	−	0.0709399i
$814$	−1835.59	+	185.969i	−0.0790386	+	0.00800764i
$815$	18294.8	+	31687.5i	0.786305	+	1.36192i
$816$	−20981.8	−	11010.7i	−0.900135	−	0.472366i
$817$	−22.0120	+	38.1258i	−0.000942596	+	0.00163262i
$818$	−16368.6	+	36396.5i	−0.699653	+	1.55571i
$819$	−1980.70	−	5974.77i	−0.0845070	−	0.254915i
$820$	3029.25	+	3415.51i	0.129007	+	0.145457i
$821$	−17356.7	−	10020.9i	−0.737824	−	0.425983i	0.0834539	−	0.996512i	$-0.473405\pi$
$821$	−17356.7	−	10020.9i	−0.737824	−	0.425983i	−0.821277	+	0.570529i	$0.806738\pi$
$822$	380.864	−	101.735i	0.0161608	−	0.00431683i
$823$	5398.43	−	3116.78i	0.228648	−	0.132010i	−0.381300	−	0.924451i	$-0.624524\pi$
$823$	5398.43	−	3116.78i	0.228648	−	0.132010i	0.609948	+	0.792441i	$0.291190\pi$
$824$	−8250.64	+	8958.43i	−0.348816	+	0.378740i
$825$	−3049.00	+	2484.09i	−0.128670	+	0.104830i
$826$	9243.40	−	6662.89i	0.389369	−	0.280668i
$827$	−43288.8			−1.82019			−0.910096	−	0.414397i	$-0.863993\pi$
$827$	−43288.8			−1.82019			−0.910096	+	0.414397i	$0.863993\pi$
$828$	25481.5	−	14659.1i	1.06950	−	0.615263i
$829$	−15655.6			−0.655902			−0.327951	−	0.944695i	$-0.606358\pi$
$829$	−15655.6			−0.655902			−0.327951	+	0.944695i	$0.606358\pi$
$830$	35529.6	−	25610.7i	1.48584	−	1.07104i
$831$	−21091.8	−	8024.47i	−0.880465	−	0.334977i
$832$	5590.79	+	2641.51i	0.232964	+	0.110070i
$833$	1828.60	−	1055.74i	0.0760592	−	0.0439128i
$834$	6319.34	−	23511.1i	0.262375	−	0.976165i
$835$	51901.4	+	29965.3i	2.15104	+	1.24191i
$836$	1995.64	−	1769.95i	0.0825605	−	0.0732237i
$837$	−38974.5	−	24818.6i	−1.60950	−	1.02492i
$838$	7388.04	−	16427.7i	0.304553	−	0.677189i
$839$	−22793.5	+	39479.4i	−0.937924	+	1.62453i	−0.168588	+	0.985687i	$0.553921\pi$
$839$	−22793.5	+	39479.4i	−0.937924	+	1.62453i	−0.769336	+	0.638845i	$0.779413\pi$
$840$	−16962.3	−	33982.9i	−0.696731	−	1.39586i
$841$	11932.2	+	20667.2i	0.489247	+	0.847400i
$842$	30426.6	−	3082.61i	1.24533	−	0.126168i
$843$	−14405.8	+	37864.8i	−0.588568	+	1.54701i
$844$	−6759.38	−	33016.5i	−0.275672	−	1.34653i
$845$			34324.6i			1.39740i
$846$	−13029.9	+	5835.63i	−0.529522	+	0.237155i
$847$			25233.2i			1.02364i
$848$	10229.4	−	13644.2i	0.414243	−	0.552529i
$849$	−6713.46	−	8240.19i	−0.271385	−	0.333101i
$850$	3149.44	+	31086.3i	0.127088	+	1.25441i
$851$	−9092.58	−	15748.8i	−0.366263	−	0.634386i
$852$	−15851.6	−	2584.27i	−0.637402	−	0.103915i
$853$	−1318.98	+	2284.55i	−0.0529439	+	0.0917016i	−0.891283	−	0.453448i	$-0.850194\pi$
$853$	−1318.98	+	2284.55i	−0.0529439	+	0.0917016i	0.838339	+	0.545150i	$0.183527\pi$
$854$	−79.8601	−	35.9156i	−0.00319995	−	0.00143912i
$855$	23055.9	+	20512.5i	0.922216	+	0.820484i
$856$	9296.68	−	2905.42i	0.371208	−	0.116011i
$857$	−21068.1	−	12163.7i	−0.839759	−	0.484835i	0.0174233	−	0.999848i	$-0.494454\pi$
$857$	−21068.1	−	12163.7i	−0.839759	−	0.484835i	−0.857182	+	0.515013i	$0.827787\pi$
$858$	−613.183	+	612.232i	−0.0243983	+	0.0243604i
$859$	38889.0	−	22452.6i	1.54468	−	0.891819i	0.546143	−	0.837692i	$-0.316096\pi$
$859$	38889.0	−	22452.6i	1.54468	−	0.891819i	0.998534	−	0.0541273i	$-0.0172377\pi$
$860$	27.2803	−	81.8651i	0.00108169	−	0.00324602i
$861$	−545.139	−	3376.82i	−0.0215776	−	0.133660i
$862$	−18140.8	−	25166.7i	−0.716797	−	0.994410i
$863$	−3830.25			−0.151081			−0.0755406	−	0.997143i	$-0.524068\pi$
$863$	−3830.25			−0.151081			−0.0755406	+	0.997143i	$0.524068\pi$
$864$	22740.5	−	11306.7i	0.895427	−	0.445209i
$865$	1826.14			0.0717809
$866$	2466.15	+	3421.28i	0.0967705	+	0.134249i
$867$	−135.781	−	841.086i	−0.00531877	−	0.0329467i
$868$	−16079.3	+	48252.0i	−0.628762	+	1.88684i
$869$	334.406	−	193.070i	0.0130540	−	0.00753675i
$870$	−38231.5	+	38172.2i	−1.48985	+	1.48754i
$871$	−4485.47	−	2589.69i	−0.174494	−	0.100744i
$872$	19423.0	−	6070.11i	0.754294	−	0.235734i
$873$	−8001.06	+	38775.1i	−0.310189	+	1.50325i
$874$	23978.5	+	10783.9i	0.928014	+	0.417357i
$875$	−4851.74	+	8403.45i	−0.187450	+	0.324673i
$876$	31871.5	+	5195.98i	1.22927	+	0.200406i
$877$	−12549.7	−	21736.6i	−0.483206	−	0.836938i	0.516608	−	0.856222i	$-0.327195\pi$
$877$	−12549.7	−	21736.6i	−0.483206	−	0.836938i	−0.999814	+	0.0192844i	$0.993861\pi$
$878$	−634.574	−	6263.50i	−0.0243916	−	0.240755i
$879$	−7737.20	−	9496.74i	−0.296893	−	0.364411i
$880$	−3136.32	+	4183.31i	−0.120143	+	0.160249i
$881$		−	3336.88i		−	0.127608i	−0.997962	−	0.0638038i	$-0.979677\pi$
$881$		−	3336.88i		−	0.127608i	0.997962	−	0.0638038i	$-0.0203232\pi$
$882$	−231.605	+	2251.18i	−0.00884187	+	0.0859422i
$883$			26792.8i			1.02112i	0.859841	+	0.510561i	$0.170562\pi$
$883$			26792.8i			1.02112i	−0.859841	+	0.510561i	$0.829438\pi$
$884$	1380.73	+	6744.25i	0.0525329	+	0.256599i
$885$	6452.80	−	16960.8i	0.245094	−	0.644214i
$886$	44679.6	−	4526.62i	1.69418	−	0.171642i
$887$	−13004.9	−	22525.1i	−0.492290	−	0.852672i	0.507670	−	0.861551i	$-0.330507\pi$
$887$	−13004.9	−	22525.1i	−0.492290	−	0.852672i	−0.999961	+	0.00887981i	$0.997173\pi$
$888$	−7016.15	−	14056.5i	−0.265143	−	0.531198i
$889$	−16195.0	+	28050.6i	−0.610983	+	1.05825i
$890$	20272.9	−	45077.9i	0.763539	−	1.69777i
$891$	414.094	+	3534.69i	0.0155698	+	0.132903i
$892$	−38415.4	+	34071.0i	−1.44198	+	1.27890i
$893$	−11058.1	−	6384.40i	−0.414384	−	0.239245i
$894$	3252.16	−	12099.7i	0.121665	−	0.452655i
$895$	−3889.71	+	2245.72i	−0.145272	+	0.0838729i
$896$	−18153.5	−	21258.4i	−0.676859	−	0.792627i
$897$	−7982.48	−	3036.97i	−0.297132	−	0.113045i
$898$	−26521.1	+	19117.1i	−0.985547	+	0.710408i
$899$	72346.0			2.68395
$900$	−28975.7	−	16789.2i	−1.07317	−	0.621821i
$901$	18985.5			0.701998
$902$	−381.976	+	275.339i	−0.0141002	+	0.0101638i
$903$	−50.1236	+	40.8368i	−0.00184719	+	0.00150494i
$904$	−5856.34	+	6358.74i	−0.215464	+	0.233948i
$905$	−13022.6	+	7518.59i	−0.478326	+	0.276162i
$906$	20856.3	−	5571.07i	0.764794	−	0.204290i
$907$	−23690.0	−	13677.4i	−0.867269	−	0.500718i	−0.000829418	−	1.00000i	$-0.500264\pi$
$907$	−23690.0	−	13677.4i	−0.867269	−	0.500718i	−0.866440	+	0.499282i	$0.833597\pi$
$908$	11941.9	+	13464.6i	0.436460	+	0.492113i
$909$	9596.79	+	1980.25i	0.350171	+	0.0722562i
$910$	−4525.92	+	10063.6i	−0.164871	+	0.366599i
$911$	−2661.94	+	4610.61i	−0.0968100	+	0.167680i	−0.910363	−	0.413812i	$-0.864197\pi$
$911$	−2661.94	+	4610.61i	−0.0968100	+	0.167680i	0.813553	+	0.581491i	$0.197531\pi$
$912$	20112.4	+	10554.4i	0.730250	+	0.383215i
$913$	2258.67	+	3912.14i	0.0818742	+	0.141810i
$914$	−30643.8	+	3104.62i	−1.10898	+	0.112354i
$915$	−137.672	+	22.2252i	−0.00497411	+	0.000802998i
$916$	27201.6	−	5568.92i	0.981187	−	0.200876i
$917$			27504.7i			0.990495i
$918$	25258.7	+	12705.8i	0.908128	+	0.456811i
$919$			3951.52i			0.141837i	0.997482	+	0.0709187i	$0.0225931\pi$
$919$			3951.52i			0.141837i	−0.997482	+	0.0709187i	$0.977407\pi$
$920$	−50284.4	−	11281.2i	−1.80199	−	0.404271i
$921$	−28322.7	+	4572.28i	−1.01332	+	0.163585i
$922$	−3357.04	−	33135.3i	−0.119911	−	1.18357i
$923$	2333.06	+	4040.97i	0.0831999	+	0.144106i
$924$	3663.51	−	1387.29i	0.130434	−	0.0493924i
$925$	−10358.0	+	17940.5i	−0.368181	+	0.637708i
$926$	6861.49	+	3085.82i	0.243502	+	0.109510i
$927$	9659.66	−	10857.4i	0.342249	−	0.384685i
$928$	−20524.3	+	34057.6i	−0.726017	+	1.20474i
$929$	2705.24	+	1561.87i	0.0955394	+	0.0551597i	0.547008	−	0.837127i	$-0.315767\pi$
$929$	2705.24	+	1561.87i	0.0955394	+	0.0551597i	−0.451469	+	0.892287i	$0.649100\pi$
$930$	20903.7	+	78256.4i	0.737052	+	2.75928i
$931$	−1752.83	+	1012.00i	−0.0617044	+	0.0356250i
$932$	29240.6	+	9743.98i	1.02769	+	0.342462i
$933$	−6182.26	+	5036.82i	−0.216932	+	0.176740i
$934$	54.5378	+	75.6601i	0.00191063	+	0.00265061i
$935$	−5820.96			−0.203600
$936$	−6724.40	−	3036.73i	−0.234823	−	0.106046i
$937$	24002.2			0.836838			0.418419	−	0.908254i	$-0.362584\pi$
$937$	24002.2			0.836838			0.418419	+	0.908254i	$0.362584\pi$
$938$	13692.2	+	18995.1i	0.476616	+	0.661208i
$939$	−42575.1	−	16197.9i	−1.47965	−	0.562938i
$940$	23744.3	+	7912.44i	0.823888	+	0.274548i
$941$	42104.3	−	24308.9i	1.45862	−	0.842135i	0.459676	−	0.888086i	$-0.347965\pi$
$941$	42104.3	−	24308.9i	1.45862	−	0.842135i	0.998944	+	0.0459518i	$0.0146320\pi$
$942$	−38166.2	−	10258.4i	−1.32009	−	0.354814i
$943$	−4019.34	−	2320.57i	−0.138799	−	0.0801358i
$944$	1595.27	−	13260.8i	0.0550019	−	0.457205i
$945$	20934.7	+	40195.7i	0.720641	+	1.38367i
$946$	8.11700	+	3.65047i	0.000278971	+	0.000125462i
$947$	9870.34	−	17095.9i	0.338694	−	0.586635i	−0.645493	−	0.763766i	$-0.723348\pi$
$947$	9870.34	−	17095.9i	0.338694	−	0.586635i	0.984187	+	0.177131i	$0.0566816\pi$
$948$	2545.86	+	2080.75i	0.0872213	+	0.0712867i
$949$	−4690.89	−	8124.86i	−0.160456	−	0.277918i
$950$	−3018.94	−	29798.2i	−0.103103	−	1.01766i
$951$	12960.0	−	34064.6i	0.441912	−	1.16154i
$952$	6812.96	−	30367.9i	0.231943	−	1.03385i
$953$		−	47895.5i		−	1.62800i	−0.580863	−	0.814002i	$-0.697285\pi$
$953$		−	47895.5i		−	1.62800i	0.580863	−	0.814002i	$-0.302715\pi$
$954$	−11924.2	+	16488.4i	−0.404677	+	0.559573i
$955$		−	8612.54i		−	0.291827i
$956$	312.454	−	63.9678i	0.0105706	−	0.00216409i
$957$	−3519.59	−	4319.99i	−0.118884	−	0.145920i
$958$	22900.9	−	2320.16i	0.772334	−	0.0782474i
$959$	258.893	+	448.416i	0.00871751	+	0.0150992i
$960$	−42770.3	−	12360.5i	−1.43792	−	0.415555i
$961$	39338.4	−	68136.1i	1.32048	−	2.28714i
$962$	−1872.07	+	4162.64i	−0.0627421	+	0.139510i
$963$	−11031.9	+	3657.20i	−0.369157	+	0.122380i
$964$	−18358.0	−	20698.8i	−0.613352	−	0.691561i
$965$	−35641.4	−	20577.6i	−1.18895	−	0.686441i
$966$	27281.5	+	27323.9i	0.908662	+	0.910074i
$967$	−39942.4	+	23060.8i	−1.32830	+	0.766892i	−0.985036	−	0.172349i	$-0.944864\pi$
$967$	−39942.4	+	23060.8i	−1.32830	+	0.766892i	−0.343259	+	0.939241i	$0.611531\pi$
$968$	21756.5	+	20037.5i	0.722397	+	0.665321i
$969$	4030.13	+	24964.3i	0.133608	+	0.827626i
$970$	56303.3	−	40584.9i	1.86370	−	1.34340i
$971$	51058.5			1.68748			0.843741	−	0.536751i	$-0.180349\pi$
$971$	51058.5			1.68748			0.843741	+	0.536751i	$0.180349\pi$
$972$	−26898.9	+	13956.4i	−0.887635	+	0.460547i
$973$	31976.7			1.05357
$974$	−4571.24	+	3295.07i	−0.150382	+	0.108399i
$975$	1550.57	+	9604.89i	0.0509313	+	0.315490i
$976$	−94.3835	+	40.3364i	−0.00309543	+	0.00132289i
$977$	19394.5	−	11197.4i	0.635093	−	0.366671i	−0.147629	−	0.989043i	$-0.547164\pi$
$977$	19394.5	−	11197.4i	0.635093	−	0.366671i	0.782722	+	0.622372i	$0.213831\pi$
$978$	−22705.1	−	22740.4i	−0.742361	−	0.743514i
$979$	4414.92	+	2548.95i	0.144128	+	0.0832124i
$980$	2968.05	−	2632.39i	0.0967457	−	0.0858047i
$981$	−23048.3	+	7640.75i	−0.750127	+	0.248675i
$982$	10226.0	−	22738.0i	0.332307	−	0.738900i
$983$	6698.78	−	11602.6i	0.217353	−	0.376466i	−0.736645	−	0.676280i	$-0.763591\pi$
$983$	6698.78	−	11602.6i	0.217353	−	0.376466i	0.953998	+	0.299813i	$0.0969244\pi$
$984$	−3344.44	−	2211.48i	−0.108350	−	0.0716459i
$985$	−5409.43	−	9369.40i	−0.174983	−	0.303080i
$986$	−44044.7	+	4462.30i	−1.42259	+	0.144126i
$987$	−11844.4	−	14537.9i	−0.381977	−	0.468843i
$988$	−1323.52	−	6464.80i	−0.0426182	−	0.208171i
$989$			87.7240i			0.00282049i
$990$	3655.97	−	5055.35i	0.117368	−	0.162292i
$991$			24672.3i			0.790858i	0.918496	+	0.395429i	$0.129404\pi$
$991$			24672.3i			0.790858i	−0.918496	+	0.395429i	$0.870596\pi$
$992$	28835.3	+	52180.5i	0.922904	+	1.67009i
$993$	18269.9	−	48021.2i	0.583864	−	1.53465i
$994$	−2126.33	−	20987.8i	−0.0678503	−	0.669709i
$995$	−14583.8	−	25259.8i	−0.464660	−	0.804815i
$996$	−24342.2	+	29783.4i	−0.774411	+	0.947514i
$997$	−29032.1	+	50285.1i	−0.922223	+	1.59734i	−0.126255	+	0.991998i	$0.540296\pi$
$997$	−29032.1	+	50285.1i	−0.922223	+	1.59734i	−0.795968	+	0.605339i	$0.793038\pi$
$998$	−54368.4	−	24451.2i	−1.72445	−	0.775539i
$999$	8659.28	+	16626.3i	0.274242	+	0.526558i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.4.h.b.11.4	yes	24
3.2	odd	2		108.4.h.b.35.9		24
4.3	odd	2	inner	36.4.h.b.11.1	✓	24
9.2	odd	6		324.4.b.c.323.15		24
9.4	even	3		108.4.h.b.71.12		24
9.5	odd	6	inner	36.4.h.b.23.1	yes	24
9.7	even	3		324.4.b.c.323.10		24
12.11	even	2		108.4.h.b.35.12		24
36.7	odd	6		324.4.b.c.323.16		24
36.11	even	6		324.4.b.c.323.9		24
36.23	even	6	inner	36.4.h.b.23.4	yes	24
36.31	odd	6		108.4.h.b.71.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.4.h.b.11.1	✓	24	4.3	odd	2	inner
36.4.h.b.11.4	yes	24	1.1	even	1	trivial
36.4.h.b.23.1	yes	24	9.5	odd	6	inner
36.4.h.b.23.4	yes	24	36.23	even	6	inner
108.4.h.b.35.9		24	3.2	odd	2
108.4.h.b.35.12		24	12.11	even	2
108.4.h.b.71.9		24	36.31	odd	6
108.4.h.b.71.12		24	9.4	even	3
324.4.b.c.323.9		24	36.11	even	6
324.4.b.c.323.10		24	9.7	even	3
324.4.b.c.323.15		24	9.2	odd	6
324.4.b.c.323.16		24	36.7	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:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	36.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.65391 - 2.29447i) q^{2} +(0.828122 + 5.12974i) q^{3} +(-2.52915 + 7.58969i) q^{4} +(-14.4924 + 8.36717i) q^{5} +(10.4004 - 10.3842i) q^{6} +(16.7175 + 9.65186i) q^{7} +(21.5973 - 6.74964i) q^{8} +(-25.6284 + 8.49610i) q^{9} +O(q^{10})\)	\(q+(-1.65391 - 2.29447i) q^{2} +(0.828122 + 5.12974i) q^{3} +(-2.52915 + 7.58969i) q^{4} +(-14.4924 + 8.36717i) q^{5} +(10.4004 - 10.3842i) q^{6} +(16.7175 + 9.65186i) q^{7} +(21.5973 - 6.74964i) q^{8} +(-25.6284 + 8.49610i) q^{9} +(43.1673 + 19.4137i) q^{10} +(-2.44092 + 4.22780i) q^{11} +(-41.0276 - 6.68868i) q^{12} +(6.03848 + 10.4590i) q^{13} +(-5.50343 - 54.3211i) q^{14} +(-54.9229 - 67.4130i) q^{15} +(-51.2068 - 38.3909i) q^{16} -71.2528i q^{17} +(61.8812 + 44.7518i) q^{18} +68.3003i q^{19} +(-26.8509 - 131.154i) q^{20} +(-35.6674 + 93.7494i) q^{21} +(13.7376 - 1.39180i) q^{22} +(68.0491 + 117.865i) q^{23} +(52.5091 + 105.199i) q^{24} +(77.5192 - 134.267i) q^{25} +(14.0106 - 31.1533i) q^{26} +(-64.8062 - 124.431i) q^{27} +(-115.536 + 102.470i) q^{28} +(190.237 + 109.833i) q^{29} +(-63.8393 + 237.514i) q^{30} +(285.221 - 164.672i) q^{31} +(-3.39507 + 180.987i) q^{32} +(-23.7089 - 9.02015i) q^{33} +(-163.487 + 117.846i) q^{34} -323.035 q^{35} +(0.335328 - 216.000i) q^{36} -133.618 q^{37} +(156.713 - 112.963i) q^{38} +(-48.6511 + 39.6371i) q^{39} +(-256.520 + 278.526i) q^{40} +(-29.5326 + 17.0507i) q^{41} +(274.096 - 73.2157i) q^{42} +(0.558209 + 0.322282i) q^{43} +(-25.9142 - 29.2186i) q^{44} +(300.328 - 337.566i) q^{45} +(157.889 - 351.074i) q^{46} +(-93.4753 + 161.904i) q^{47} +(154.530 - 294.470i) q^{48} +(14.8169 + 25.6636i) q^{49} +(-436.282 + 44.2010i) q^{50} +(365.508 - 59.0060i) q^{51} +(-94.6525 + 19.3780i) q^{52} +266.453i q^{53} +(-178.320 + 354.494i) q^{54} -81.6944i q^{55} +(426.199 + 95.6168i) q^{56} +(-350.363 + 56.5610i) q^{57} +(-62.6263 - 618.147i) q^{58} +(104.347 + 180.734i) q^{59} +(650.552 - 246.350i) q^{60} +(0.801886 - 1.38891i) q^{61} +(-849.565 - 382.076i) q^{62} +(-510.447 - 105.328i) q^{63} +(420.885 - 291.548i) q^{64} +(-175.024 - 101.050i) q^{65} +(18.5160 + 69.3177i) q^{66} +(-371.407 + 214.432i) q^{67} +(540.787 + 180.209i) q^{68} +(-548.261 + 446.680i) q^{69} +(534.272 + 741.193i) q^{70} +386.365 q^{71} +(-496.159 + 356.475i) q^{72} -776.832 q^{73} +(220.992 + 306.582i) q^{74} +(752.951 + 286.464i) q^{75} +(-518.378 - 172.742i) q^{76} +(-81.6122 + 47.1188i) q^{77} +(171.411 + 46.0720i) q^{78} +(-68.5000 - 39.5485i) q^{79} +(1063.33 + 127.919i) q^{80} +(584.633 - 435.483i) q^{81} +(87.9665 + 39.5613i) q^{82} +(462.668 - 801.365i) q^{83} +(-621.321 - 507.811i) q^{84} +(596.185 + 1032.62i) q^{85} +(-0.183763 - 1.81382i) q^{86} +(-405.877 + 1066.82i) q^{87} +(-24.1811 + 107.784i) q^{88} -1044.26i q^{89} +(-1271.25 - 130.788i) q^{90} +233.130i q^{91} +(-1066.66 + 218.375i) q^{92} +(1080.92 + 1326.74i) q^{93} +(526.083 - 53.2991i) q^{94} +(-571.481 - 989.834i) q^{95} +(-931.230 + 132.464i) q^{96} +(733.184 - 1269.91i) q^{97} +(34.3784 - 76.4422i) q^{98} +(26.6372 - 129.090i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9}+O(q^{10}) \) 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9	\( 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9} + 96 q^{10} + 216 q^{12} - 216 q^{13} - 36 q^{14} - 72 q^{16} + 276 q^{18} - 540 q^{20} + 384 q^{21} - 192 q^{22} - 168 q^{24} + 252 q^{25} - 672 q^{28} + 576 q^{29} + 660 q^{30} + 360 q^{32} - 1236 q^{33} - 660 q^{34} + 276 q^{36} + 1248 q^{37} - 144 q^{38} + 636 q^{40} + 1116 q^{41} - 288 q^{42} - 1296 q^{45} + 960 q^{46} - 288 q^{48} + 348 q^{49} - 648 q^{50} + 132 q^{52} - 2616 q^{54} - 1692 q^{56} - 1668 q^{57} + 516 q^{58} - 192 q^{60} - 264 q^{61} + 960 q^{64} - 2592 q^{65} + 1068 q^{66} + 5688 q^{68} + 1608 q^{69} + 564 q^{70} + 4224 q^{72} - 4776 q^{73} + 5652 q^{74} - 600 q^{76} + 648 q^{77} + 3660 q^{78} + 3948 q^{81} - 4104 q^{82} - 4872 q^{84} + 720 q^{85} - 9540 q^{86} + 1956 q^{88} - 7656 q^{90} - 7416 q^{92} + 5400 q^{93} - 1188 q^{94} - 5640 q^{96} + 588 q^{97}+O(q^{100}) \) 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9 + 96 * q^10 + 216 * q^12 - 216 * q^13 - 36 * q^14 - 72 * q^16 + 276 * q^18 - 540 * q^20 + 384 * q^21 - 192 * q^22 - 168 * q^24 + 252 * q^25 - 672 * q^28 + 576 * q^29 + 660 * q^30 + 360 * q^32 - 1236 * q^33 - 660 * q^34 + 276 * q^36 + 1248 * q^37 - 144 * q^38 + 636 * q^40 + 1116 * q^41 - 288 * q^42 - 1296 * q^45 + 960 * q^46 - 288 * q^48 + 348 * q^49 - 648 * q^50 + 132 * q^52 - 2616 * q^54 - 1692 * q^56 - 1668 * q^57 + 516 * q^58 - 192 * q^60 - 264 * q^61 + 960 * q^64 - 2592 * q^65 + 1068 * q^66 + 5688 * q^68 + 1608 * q^69 + 564 * q^70 + 4224 * q^72 - 4776 * q^73 + 5652 * q^74 - 600 * q^76 + 648 * q^77 + 3660 * q^78 + 3948 * q^81 - 4104 * q^82 - 4872 * q^84 + 720 * q^85 - 9540 * q^86 + 1956 * q^88 - 7656 * q^90 - 7416 * q^92 + 5400 * q^93 - 1188 * q^94 - 5640 * q^96 + 588 * q^97

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