LMFDB - Embedded newform 36.4.h.b.11.1

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			11.1
Character	$\chi$	$=$	36.11
Dual form			36.4.h.b.23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.81402 - 0.285097i) q^{2} +(-0.828122 - 5.12974i) q^{3} +(7.83744 + 1.60454i) q^{4} +(-14.4924 + 8.36717i) q^{5} +(0.867881 + 14.6713i) q^{6} +(-16.7175 - 9.65186i) q^{7} +(-21.5973 - 6.74964i) q^{8} +(-25.6284 + 8.49610i) q^{9} +O(q^{10})$	\(q+(-2.81402 - 0.285097i) q^{2} +(-0.828122 - 5.12974i) q^{3} +(7.83744 + 1.60454i) q^{4} +(-14.4924 + 8.36717i) q^{5} +(0.867881 + 14.6713i) 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} +(1.74050 - 41.5328i) q^{12} +(6.03848 + 10.4590i) q^{13} +(44.2917 + 31.9267i) q^{14} +(54.9229 + 67.4130i) q^{15} +(58.8509 + 25.1509i) q^{16} -71.2528i q^{17} +(74.5412 - 16.6016i) q^{18} -68.3003i q^{19} +(-127.009 + 42.3237i) q^{20} +(-35.6674 + 93.7494i) q^{21} +(-8.07414 + 11.2012i) q^{22} +(-68.0491 - 117.865i) q^{23} +(-16.7387 + 116.378i) 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} +(-135.335 - 205.360i) q^{30} +(-285.221 + 164.672i) q^{31} +(-158.437 - 87.5535i) q^{32} +(-23.7089 - 9.02015i) q^{33} +(-20.3140 + 200.507i) q^{34} +323.035 q^{35} +(-214.494 + 25.4659i) q^{36} -133.618 q^{37} +(-19.4722 + 192.199i) q^{38} +(48.6511 - 39.6371i) q^{39} +(369.471 - 82.8899i) q^{40} +(-29.5326 + 17.0507i) q^{41} +(127.096 - 253.644i) 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} +(80.2820 - 322.718i) q^{48} +(14.8169 + 25.6636i) q^{49} +(-256.420 + 355.730i) q^{50} +(-365.508 + 59.0060i) q^{51} +(30.5444 + 91.6604i) q^{52} +266.453i q^{53} +(-146.891 - 368.629i) q^{54} +81.6944i q^{55} +(295.906 + 321.291i) q^{56} +(-350.363 + 56.5610i) q^{57} +(-504.018 - 363.309i) q^{58} +(-104.347 - 180.734i) q^{59} +(322.288 + 616.471i) 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} +(64.1457 + 32.1422i) q^{66} +(371.407 - 214.432i) q^{67} +(114.328 - 558.440i) q^{68} +(-548.261 + 446.680i) q^{69} +(-909.028 - 92.0964i) q^{70} -386.365 q^{71} +(610.850 - 10.5101i) q^{72} -776.832 q^{73} +(376.004 + 38.0941i) q^{74} +(-752.951 - 286.464i) q^{75} +(109.591 - 535.300i) q^{76} +(-81.6122 + 47.1188i) q^{77} +(-148.206 + 97.6695i) 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} +(-429.965 + 677.526i) q^{84} +(596.185 + 1032.62i) q^{85} +(1.47893 + 1.06605i) q^{86} +(405.877 - 1066.82i) q^{87} +(-81.2533 + 74.8336i) q^{88} -1044.26i q^{89} +(-941.370 + 864.296i) q^{90} -233.130i q^{91} +(-344.213 - 1032.94i) q^{92} +(1080.92 + 1326.74i) q^{93} +(-309.200 + 428.952i) q^{94} +(571.481 + 989.834i) q^{95} +(-317.921 + 885.247i) 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 $

$2$	−2.81402	−	0.285097i	−0.994907	−	0.100797i
$2$	−2.81402	−	0.285097i	−0.994907	−	0.100797i
$3$	−0.828122	−	5.12974i	−0.159372	−	0.987219i
$3$	−0.828122	−	5.12974i	−0.159372	−	0.987219i
$4$	7.83744	+	1.60454i	0.979680	+	0.200567i
$5$	−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	$0.602503\pi$
$6$	0.867881	+	14.6713i	0.0590518	+	0.998255i
$7$	−16.7175	−	9.65186i	−0.902661	−	0.521152i	−0.0245984	−	0.999697i	$-0.507831\pi$
$7$	−16.7175	−	9.65186i	−0.902661	−	0.521152i	−0.878063	+	0.478546i	$0.841164\pi$
$8$	−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	−0.830632	−	0.556822i	$-0.812021\pi$
$11$	2.44092	−	4.22780i	0.0669059	−	0.115884i	0.897538	+	0.440937i	$0.145354\pi$
$12$	1.74050	−	41.5328i	0.0418700	−	0.999123i
$13$	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	$0.792212\pi$
$14$	44.2917	+	31.9267i	0.845533	+	0.609483i
$15$	54.9229	+	67.4130i	0.945402	+	1.16040i
$16$	58.8509	+	25.1509i	0.919546	+	0.392984i
$17$		−	71.2528i		−	1.01655i	−0.861195	−	0.508275i	$-0.830283\pi$
$17$		−	71.2528i		−	1.01655i	0.861195	−	0.508275i	$-0.169717\pi$
$18$	74.5412	−	16.6016i	0.976085	−	0.217391i
$19$		−	68.3003i		−	0.824693i	−0.911027	−	0.412347i	$-0.864709\pi$
$19$		−	68.3003i		−	0.824693i	0.911027	−	0.412347i	$-0.135291\pi$
$20$	−127.009	+	42.3237i	−1.42000	+	0.473193i
$21$	−35.6674	+	93.7494i	−0.370631	+	0.974181i
$22$	−8.07414	+	11.2012i	−0.0782460	+	0.108550i
$23$	−68.0491	−	117.865i	−0.616923	−	1.06854i	−0.990044	−	0.140759i	$-0.955046\pi$
$23$	−68.0491	−	117.865i	−0.616923	−	1.06854i	0.373121	−	0.927783i	$-0.378288\pi$
$24$	−16.7387	+	116.378i	−0.142365	+	0.989814i
$25$	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	$0.418378\pi$
$30$	−135.335	−	205.360i	−0.823622	−	1.24978i
$31$	−285.221	+	164.672i	−1.65249	+	0.954065i	−0.676444	+	0.736494i	$0.736480\pi$
$31$	−285.221	+	164.672i	−1.65249	+	0.954065i	−0.976044	+	0.217571i	$0.930187\pi$
$32$	−158.437	−	87.5535i	−0.875251	−	0.483669i
$33$	−23.7089	−	9.02015i	−0.125066	−	0.0475820i
$34$	−20.3140	+	200.507i	−0.102465	+	1.01137i
$35$	323.035			1.56008
$36$	−214.494	+	25.4659i	−0.993026	+	0.117898i
$37$	−133.618			−0.593693			−0.296847	−	0.954925i	$-0.595935\pi$
$37$	−133.618			−0.593693			−0.296847	+	0.954925i	$0.595935\pi$
$38$	−19.4722	+	192.199i	−0.0831266	+	0.820493i
$39$	48.6511	−	39.6371i	0.199754	−	0.162744i
$40$	369.471	−	82.8899i	1.46046	−	0.327651i
$41$	−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	$0.354021\pi$
$42$	127.096	−	253.644i	0.466938	−	0.931861i
$43$	−0.558209	−	0.322282i	−0.00197967	−	0.00114297i	0.499010	−	0.866596i	$-0.333697\pi$
$43$	−0.558209	−	0.322282i	−0.00197967	−	0.00114297i	−0.500990	+	0.865453i	$0.667030\pi$
$44$	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	−0.683732	−	0.729733i	$-0.739644\pi$
$47$	93.4753	−	161.904i	0.290102	−	0.502471i	0.973834	+	0.227263i	$0.0729775\pi$
$48$	80.2820	−	322.718i	0.241411	−	0.970423i
$49$	14.8169	+	25.6636i	0.0431979	+	0.0748210i
$50$	−256.420	+	355.730i	−0.725265	+	1.00616i
$51$	−365.508	+	59.0060i	−1.00356	+	0.162010i
$52$	30.5444	+	91.6604i	0.0814568	+	0.244443i
$53$			266.453i			0.690569i	0.938498	+	0.345284i	$0.112218\pi$
$53$			266.453i			0.690569i	−0.938498	+	0.345284i	$0.887782\pi$
$54$	−146.891	−	368.629i	−0.370173	−	0.928963i
$55$			81.6944i			0.200285i
$56$	295.906	+	321.291i	0.706110	+	0.766684i
$57$	−350.363	+	56.5610i	−0.814153	+	0.131433i
$58$	−504.018	−	363.309i	−1.14105	−	0.822498i
$59$	−104.347	−	180.734i	−0.230251	−	0.398806i	0.727631	−	0.685969i	$-0.240621\pi$
$59$	−104.347	−	180.734i	−0.230251	−	0.398806i	−0.957882	+	0.287163i	$0.907288\pi$
$60$	322.288	+	616.471i	0.693453	+	1.32644i
$61$	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
$66$	64.1457	+	32.1422i	0.119633	+	0.0599460i
$67$	371.407	−	214.432i	0.677233	−	0.391001i	−0.121579	−	0.992582i	$-0.538796\pi$
$67$	371.407	−	214.432i	0.677233	−	0.391001i	0.798812	+	0.601581i	$0.205462\pi$
$68$	114.328	−	558.440i	0.203887	−	0.995893i
$69$	−548.261	+	446.680i	−0.956564	+	0.779333i
$70$	−909.028	−	92.0964i	−1.55214	−	0.157252i
$71$	−386.365			−0.645817			−0.322909	−	0.946430i	$-0.604661\pi$
$71$	−386.365			−0.645817			−0.322909	+	0.946430i	$0.604661\pi$
$72$	610.850	−	10.5101i	0.999852	−	0.0172031i
$73$	−776.832			−1.24550			−0.622749	−	0.782422i	$-0.713984\pi$
$73$	−776.832			−1.24550			−0.622749	+	0.782422i	$0.713984\pi$
$74$	376.004	+	38.0941i	0.590670	+	0.0598425i
$75$	−752.951	−	286.464i	−1.15924	−	0.441040i
$76$	109.591	−	535.300i	0.165407	−	0.807935i
$77$	−81.6122	+	47.1188i	−0.120787	+	0.0697362i
$78$	−148.206	+	97.6695i	−0.215141	+	0.141781i
$79$	68.5000	+	39.5485i	0.0975551	+	0.0563235i	0.547984	−	0.836489i	$-0.315396\pi$
$79$	68.5000	+	39.5485i	0.0975551	+	0.0563235i	−0.450429	+	0.892812i	$0.648729\pi$
$80$	−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	$0.376245\pi$
$83$	−462.668	+	801.365i	−0.611861	+	1.05977i	−0.990927	+	0.134404i	$0.957088\pi$
$84$	−429.965	+	677.526i	−0.558489	+	0.880049i
$85$	596.185	+	1032.62i	0.760768	+	1.31769i
$86$	1.47893	+	1.06605i	0.00185438	+	0.00133669i
$87$	405.877	−	1066.82i	0.500168	−	1.31466i
$88$	−81.2533	+	74.8336i	−0.0984277	+	0.0906510i
$89$		−	1044.26i		−	1.24372i	−0.783128	−	0.621861i	$-0.786377\pi$
$89$		−	1044.26i		−	1.24372i	0.783128	−	0.621861i	$-0.213623\pi$
$90$	−941.370	+	864.296i	−1.10255	+	1.01228i
$91$		−	233.130i		−	0.268557i
$92$	−344.213	−	1032.94i	−0.390072	−	1.17056i
$93$	1080.92	+	1326.74i	1.20523	+	1.47932i
$94$	−309.200	+	428.952i	−0.339272	+	0.470670i
$95$	571.481	+	989.834i	0.617186	+	1.06900i
$96$	−317.921	+	885.247i	−0.337997	+	0.941147i
$97$	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	$0.723880\pi$
$102$	1045.37	−	61.8390i	1.01478	−	0.0600291i
$103$	466.128	−	269.119i	0.445912	−	0.257447i	−0.260190	−	0.965557i	$-0.583785\pi$
$103$	466.128	−	269.119i	0.445912	−	0.257447i	0.706102	+	0.708110i	$0.250452\pi$
$104$	−59.8206	−	266.643i	−0.0564028	−	0.251408i
$105$	−267.513	−	1657.09i	−0.248634	−	1.54014i
$106$	75.9650	−	749.805i	0.0696073	−	0.687052i
$107$	−430.456			−0.388914			−0.194457	−	0.980911i	$-0.562294\pi$
$107$	−430.456			−0.388914			−0.194457	+	0.980911i	$0.562294\pi$
$108$	308.260	+	1079.21i	0.274651	+	0.961544i
$109$	899.324			0.790272			0.395136	−	0.918623i	$-0.370697\pi$
$109$	899.324			0.790272			0.395136	+	0.918623i	$0.370697\pi$
$110$	23.2908	−	229.890i	0.0201881	−	0.199265i
$111$	110.652	+	685.425i	0.0946182	+	0.586105i
$112$	−741.088	−	988.482i	−0.625234	−	0.833953i
$113$	−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	$0.384168\pi$
$114$	1002.05	−	59.2766i	0.823254	−	0.0486997i
$115$	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
$120$	−731.171	−	1826.65i	−0.556221	−	1.38958i
$121$	653.584	+	1132.04i	0.491047	+	0.850519i
$122$	−2.65250	+	3.67980i	−0.00196841	+	0.00273077i
$123$	111.922	+	137.375i	0.0820461	+	0.100704i
$124$	−2499.62	+	832.961i	−1.81026	+	0.603243i
$125$			502.674i			0.359684i
$126$	−1406.38	−	441.923i	−0.994367	−	0.312457i
$127$		−	1677.92i		−	1.17237i	−0.810177	−	0.586186i	$-0.800629\pi$
$127$		−	1677.92i		−	1.17237i	0.810177	−	0.586186i	$-0.199371\pi$
$128$	−1101.26	−	940.414i	−0.760457	−	0.649388i
$129$	−1.19096	+	3.13035i	−0.000812852	+	0.00213653i
$130$	463.712	+	334.256i	0.312848	+	0.225509i
$131$	−712.418	−	1233.94i	−0.475147	−	0.822979i	0.524448	−	0.851443i	$-0.324272\pi$
$131$	−712.418	−	1233.94i	−0.475147	−	0.822979i	−0.999595	+	0.0284637i	$0.990938\pi$
$132$	−171.344	−	108.737i	−0.112981	−	0.0716993i
$133$	−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	$0.664004\pi$
$138$	1670.17	−	1100.66i	1.03025	−	0.678946i
$139$	−1434.57	+	828.252i	−0.875388	+	0.505406i	−0.869135	−	0.494575i	$-0.835324\pi$
$139$	−1434.57	+	828.252i	−0.875388	+	0.505406i	−0.00625321	+	0.999980i	$0.501990\pi$
$140$	2531.77	+	518.322i	1.52838	+	0.312902i
$141$	−907.934	−	345.428i	−0.542283	−	0.206314i
$142$	1087.24	+	110.151i	0.642528	+	0.0650965i
$143$	58.9578			0.0344776
$144$	−1721.94	−	144.576i	−0.996494	−	0.0836666i
$145$	−3675.98			−2.10533
$146$	2186.02	+	221.473i	1.23915	+	0.125542i
$147$	119.377	−	97.2593i	0.0669801	−	0.0545702i
$148$	−1047.22	−	214.395i	−0.581629	−	0.119075i
$149$	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	$0.258034\pi$
$150$	2037.15	+	1020.78i	1.10888	+	0.555642i
$151$	−1272.06	−	734.422i	−0.685553	−	0.395804i	0.116391	−	0.993203i	$-0.462867\pi$
$151$	−1272.06	−	734.422i	−0.685553	−	0.395804i	−0.801944	+	0.597399i	$0.796201\pi$
$152$	−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
$156$	444.899	−	232.591i	0.228336	−	0.119373i
$157$	−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	$-0.406196\pi$
$158$	−181.485	−	130.820i	−0.0913811	−	0.0658699i
$159$	1366.83	−	220.656i	0.681742	−	0.110057i
$160$	3028.71	−	56.8143i	1.49650	−	0.0280723i
$161$			2627.20i			1.28604i
$162$	−1769.32	+	1058.78i	−0.858094	+	0.513493i
$163$			2186.50i			1.05067i	0.850895	+	0.525336i	$0.176060\pi$
$163$			2186.50i			1.05067i	−0.850895	+	0.525336i	$0.823940\pi$
$164$	−258.819	+	86.2473i	−0.123234	+	0.0410658i
$165$	419.071	−	67.6530i	0.197725	−	0.0319199i
$166$	1530.43	−	2123.15i	0.715567	−	0.992703i
$167$	1790.65	+	3101.49i	0.829726	+	1.43713i	0.898253	+	0.439479i	$0.144837\pi$
$167$	1790.65	+	3101.49i	0.829726	+	1.43713i	−0.0685268	+	0.997649i	$0.521830\pi$
$168$	1403.09	−	1783.99i	0.644351	−	0.819273i
$169$	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	$0.674300\pi$
$174$	−1446.29	+	2886.34i	−0.630134	+	1.25755i
$175$	−2591.86	+	1496.41i	−1.11958	+	0.646388i
$176$	249.983	−	187.418i	0.107064	−	0.0802681i
$177$	−840.706	+	684.941i	−0.357013	+	0.290866i
$178$	−297.715	+	2938.57i	−0.125363	+	1.23739i
$179$	−268.397			−0.112072			−0.0560361	−	0.998429i	$-0.517846\pi$
$179$	−268.397			−0.112072			−0.0560361	+	0.998429i	$0.517846\pi$
$180$	2895.44	−	2163.77i	1.19896	−	0.895987i
$181$	898.582			0.369011			0.184506	−	0.982831i	$-0.440932\pi$
$181$	898.582			0.369011			0.184506	+	0.982831i	$0.440932\pi$
$182$	−66.4648	+	656.034i	−0.0270698	+	0.267189i
$183$	−7.78879	−	2.96328i	−0.00314625	−	0.00119701i
$184$	674.133	+	3004.86i	0.270096	+	1.20392i
$185$	1936.44	−	1118.00i	0.769567	−	0.444310i
$186$	−2663.49	−	4041.64i	−1.04998	−	1.59327i
$187$	−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	−0.813157	−	0.582044i	$-0.802253\pi$
$191$	257.331	−	445.711i	0.0974860	−	0.168851i	0.910643	+	0.413193i	$0.135587\pi$
$192$	1147.02	−	2400.47i	0.431140	−	0.902285i
$193$	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	$0.681679\pi$
$194$	−2425.24	+	3364.53i	−0.897538	+	1.24515i
$195$	−373.419	+	981.508i	−0.137134	+	0.360448i
$196$	74.9482	+	224.911i	0.0273135	+	0.0819647i
$197$			646.506i			0.233815i	0.993143	+	0.116908i	$0.0372982\pi$
$197$			646.506i			0.233815i	−0.993143	+	0.116908i	$0.962702\pi$
$198$	111.761	−	355.668i	0.0401136	−	0.127658i
$199$		−	1742.98i		−	0.620886i	−0.950592	−	0.310443i	$-0.899523\pi$
$199$		−	1742.98i		−	0.620886i	0.950592	−	0.310443i	$-0.100477\pi$
$200$	−2580.46	+	2376.58i	−0.912330	+	0.840248i
$201$	−1407.55	−	1727.65i	−0.493935	−	0.606262i
$202$	832.719	+	600.246i	0.290049	+	0.209075i
$203$	−2120.19	−	3672.28i	−0.733046	−	1.26967i
$204$	−2959.33	−	124.016i	−1.01566	−	0.0425630i
$205$	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
$210$	280.356	+	4739.34i	0.0921258	+	1.55736i
$211$	3648.27	−	2106.33i	1.19032	−	0.687231i	0.231940	−	0.972730i	$-0.425493\pi$
$211$	3648.27	−	2106.33i	1.19032	−	0.687231i	0.958379	+	0.285499i	$0.0921593\pi$
$212$	−427.534	+	2088.31i	−0.138506	+	0.676537i
$213$	319.957	+	1981.95i	0.102925	+	0.637563i
$214$	1211.31	+	122.722i	0.386933	+	0.0392013i
$215$	10.7864			0.00342150
$216$	−559.772	−	3124.80i	−0.176332	−	0.984331i
$217$	6357.58			1.98885
$218$	−2530.72	−	256.395i	−0.786247	−	0.0796570i
$219$	643.312	+	3984.95i	0.198498	+	1.22958i
$220$	−131.082	+	640.275i	−0.0401706	+	0.196215i
$221$	745.230	−	430.259i	0.226831	−	0.130961i
$222$	−115.965	−	1960.35i	−0.0350587	−	0.592657i
$223$	−5558.55	−	3209.23i	−1.66918	−	0.963703i	−0.968080	−	0.250643i	$-0.919358\pi$
$223$	−5558.55	−	3209.23i	−1.66918	−	0.963703i	−0.701103	−	0.713060i	$-0.747309\pi$
$224$	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	−0.982292	−	0.187358i	$-0.940008\pi$
$227$	−1124.83	+	1948.27i	−0.328889	+	0.569653i	0.653403	+	0.757011i	$0.273341\pi$
$228$	−2836.70	−	118.877i	−0.823970	−	0.0345299i
$229$	−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	$-0.333616\pi$
$230$	−5225.68	−	3766.81i	−1.49814	−	1.07990i
$231$	309.292	+	379.629i	0.0880950	+	0.108129i
$232$	−3367.27	−	3656.13i	−0.952896	−	1.03464i
$233$		−	3852.67i		−	1.08325i	−0.840621	−	0.541624i	$-0.817810\pi$
$233$		−	3852.67i		−	1.08325i	0.840621	−	0.541624i	$-0.182190\pi$
$234$	623.751	+	679.374i	0.174256	+	0.189795i
$235$			3128.50i			0.868428i
$236$	−527.817	−	1583.92i	−0.145585	−	0.436883i
$237$	146.147	−	384.138i	0.0400560	−	0.105285i
$238$	2274.86	−	3155.91i	0.619570	−	0.859527i
$239$	19.9334	+	34.5257i	0.00539491	+	0.00934426i	0.868710	−	0.495321i	$-0.164949\pi$
$239$	19.9334	+	34.5257i	0.00539491	+	0.00934426i	−0.863315	+	0.504665i	$0.831616\pi$
$240$	1536.76	+	5348.68i	0.413323	+	1.43857i
$241$	−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
$246$	−275.786	−	418.484i	−0.0714776	−	0.108462i
$247$	714.350	−	412.430i	0.184020	−	0.106244i
$248$	7271.47	−	1631.34i	1.86185	−	0.417701i
$249$	4493.94	+	1709.74i	1.14374	+	0.435142i
$250$	143.311	−	1414.53i	0.0362551	−	0.357852i
$251$	2977.61			0.748786			0.374393	−	0.927270i	$-0.377851\pi$
$251$	2977.61			0.748786			0.374393	+	0.927270i	$0.377851\pi$
$252$	3831.59	+	1644.54i	0.957808	+	0.411095i
$253$	−664.410			−0.165103
$254$	−478.369	+	4721.70i	−0.118172	+	1.16640i
$255$	4803.37	−	3913.41i	1.17960	−	0.961048i
$256$	2830.86	+	2960.31i	0.691128	+	0.722732i
$257$	−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	$0.620056\pi$
$258$	4.24383	−	8.46934i	0.00102407	−	0.00204371i
$259$	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	$0.408854\pi$
$263$	−2940.99	+	5093.94i	−0.689540	+	1.19432i	−0.971987	+	0.235036i	$0.924479\pi$
$264$	451.164	+	354.837i	0.105179	+	0.0827224i
$265$	−2229.46	−	3861.54i	−0.516810	−	0.895141i
$266$	2180.60	−	3025.14i	0.502636	−	0.697306i
$267$	−5356.78	+	864.774i	−1.22783	+	0.198215i
$268$	3254.95	−	1084.66i	0.741894	−	0.247225i
$269$		−	2967.07i		−	0.672510i	−0.941771	−	0.336255i	$-0.890840\pi$
$269$		−	2967.07i		−	0.672510i	0.941771	−	0.336255i	$-0.109160\pi$
$270$	5213.18	+	4113.24i	1.17505	+	0.927125i
$271$			1985.78i			0.445121i	0.974919	+	0.222561i	$0.0714415\pi$
$271$			1985.78i			0.445121i	−0.974919	+	0.222561i	$0.928559\pi$
$272$	1792.08	−	4193.29i	0.399487	−	0.934764i
$273$	−1195.90	+	193.060i	−0.265125	+	0.0428006i
$274$	−61.5447	−	44.3631i	−0.0135695	−	0.00978128i
$275$	−378.436	−	655.471i	−0.0829839	−	0.143732i
$276$	−5013.68	+	2621.12i	−1.09344	+	0.571642i
$277$	−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	$0.356374\pi$
$282$	2456.47	+	1230.89i	0.518725	+	0.259924i
$283$	1771.47	−	1022.76i	0.372094	−	0.214829i	−0.302279	−	0.953220i	$-0.597747\pi$
$283$	1771.47	−	1022.76i	0.372094	−	0.214829i	0.674373	+	0.738391i	$0.264414\pi$
$284$	−3028.11	−	619.937i	−0.632694	−	0.129530i
$285$	4604.33	−	3751.25i	0.956972	−	0.779666i
$286$	−165.909	−	16.8087i	−0.0343020	−	0.00347524i
$287$	658.283			0.135391
$288$	4804.36	+	897.760i	0.982985	+	0.183684i
$289$	−163.963			−0.0333732
$290$	10344.3	+	1048.01i	2.09461	+	0.212211i
$291$	−7121.48	−	2709.40i	−1.43460	−	0.545800i
$292$	−6088.38	−	1246.46i	−1.22019	−	0.249806i
$293$	−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	$0.408849\pi$
$294$	−363.659	+	239.656i	−0.0721395	+	0.0475408i
$295$	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
$300$	−5441.57	−	3453.28i	−1.04723	−	0.664584i
$301$	6.22124	+	10.7755i	0.00119132	+	0.00206342i
$302$	3370.21	+	2429.34i	0.642165	+	0.462890i
$303$	−670.574	+	1762.56i	−0.127140	+	0.334180i
$304$	1717.82	−	4019.54i	0.324091	−	0.758343i
$305$			26.8381i			0.00503851i
$306$	−1182.91	−	5311.27i	−0.220989	−	0.992238i
$307$		−	5521.27i		−	1.02643i	−0.858259	−	0.513217i	$-0.828454\pi$
$307$		−	5521.27i		−	1.02643i	0.858259	−	0.513217i	$-0.171546\pi$
$308$	−715.235	+	238.341i	−0.132319	+	0.0440933i
$309$	−1766.52	−	2168.25i	−0.325223	−	0.399183i
$310$	−9115.32	+	12645.6i	−1.67005	+	2.31685i
$311$	−767.330	−	1329.05i	−0.139908	−	0.242327i	0.787554	−	0.616246i	$-0.211347\pi$
$311$	−767.330	−	1329.05i	−0.139908	−	0.242327i	−0.927461	+	0.373919i	$0.878014\pi$
$312$	−1318.27	+	527.677i	−0.239206	+	0.0957494i
$313$	−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	$0.880094\pi$
$318$	−3909.21	+	231.250i	−0.689364	+	0.0407794i
$319$	928.706	−	536.189i	0.163002	−	0.0941091i
$320$	−8539.05	−	703.599i	−1.49171	−	0.122914i
$321$	356.470	+	2208.13i	0.0619820	+	0.383943i
$322$	749.008	−	7393.01i	0.129629	−	1.27949i
$323$	−4866.59			−0.838342
$324$	5280.77	−	2475.01i	0.905482	−	0.424384i
$325$	1872.39			0.319574
$326$	623.363	−	6152.85i	0.105905	−	1.04532i
$327$	−744.750	−	4613.30i	−0.125947	−	0.780171i
$328$	752.910	−	168.914i	0.126745	−	0.0284350i
$329$	−3125.35	+	1804.42i	−0.523727	+	0.302374i
$330$	−1198.56	+	70.9011i	−0.199935	+	0.0118272i
$331$	8563.21	+	4943.97i	1.42198	+	0.820982i	0.996468	−	0.0839692i	$-0.0267597\pi$
$331$	8563.21	+	4943.97i	1.42198	+	0.820982i	0.425515	+	0.904951i	$0.360093\pi$
$332$	−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
$336$	−4456.94	+	4620.17i	−0.723649	+	0.750152i
$337$	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	$0.700686\pi$
$338$	−3392.42	+	4706.29i	−0.545927	+	0.757362i
$339$	1253.89	+	1539.04i	0.200890	+	0.246575i
$340$	3015.68	+	9049.71i	0.481024	+	1.44350i
$341$			1607.81i			0.255330i
$342$	−1133.90	−	5091.19i	−0.179281	−	0.804970i
$343$			6049.14i			0.952252i
$344$	9.88050	+	10.7281i	0.00154861	+	0.00168146i
$345$	4208.15	−	11060.9i	0.656694	−	1.72608i
$346$	250.384	+	180.483i	0.0389038	+	0.0280429i
$347$	3897.53	+	6750.72i	0.602969	+	1.04437i	0.992369	+	0.123305i	$0.0393493\pi$
$347$	3897.53	+	6750.72i	0.602969	+	1.04437i	−0.389399	+	0.921069i	$0.627317\pi$
$348$	4892.79	−	7709.90i	0.753681	−	1.18763i
$349$	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	$0.555095\pi$
$354$	2561.04	−	1687.76i	0.384513	−	0.253399i
$355$	5599.34	−	3232.78i	0.837133	−	0.483319i
$356$	1675.55	−	8184.32i	0.249450	−	1.21845i
$357$	6679.91	+	2541.40i	0.990303	+	0.376765i
$358$	755.275	+	76.5192i	0.111501	+	0.0112965i
$359$	5415.10			0.796095			0.398047	−	0.917365i	$-0.369688\pi$
$359$	5415.10			0.796095			0.398047	+	0.917365i	$0.369688\pi$
$360$	−8764.72	+	5263.40i	−1.28317	+	0.770571i
$361$	2194.06			0.319881
$362$	−2528.63	−	256.183i	−0.367132	−	0.0371953i
$363$	5265.82	−	4290.18i	0.761389	−	0.620320i
$364$	374.067	−	1827.15i	0.0538638	−	0.263100i
$365$	11258.1	−	6499.89i	1.61446	−	0.932109i
$366$	21.0730	+	10.5593i	0.00300957	+	0.00150804i
$367$	−9228.51	−	5328.08i	−1.31260	−	0.757830i	−0.330074	−	0.943955i	$-0.607074\pi$
$367$	−9228.51	−	5328.08i	−1.31260	−	0.757830i	−0.982526	+	0.186125i	$0.940407\pi$
$368$	−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
$372$	6342.87	+	12132.6i	0.884039	+	1.69099i
$373$	−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	$0.893564\pi$
$374$	798.118	+	575.305i	0.110347	+	0.0795409i
$375$	2578.58	−	416.275i	0.355087	−	0.0573236i
$376$	−3111.61	+	2865.76i	−0.426779	+	0.393059i
$377$			2652.91i			0.362418i
$378$	−1102.30	+	7580.33i	−0.149989	+	1.03145i
$379$			6395.35i			0.866774i	0.901208	+	0.433387i	$0.142682\pi$
$379$			6395.35i			0.866774i	−0.901208	+	0.433387i	$0.857318\pi$
$380$	2890.72	+	8674.73i	0.390239	+	1.17106i
$381$	−8607.28	+	1389.52i	−1.15739	+	0.186843i
$382$	−851.206	+	1180.88i	−0.114009	+	0.158164i
$383$	−682.579	−	1182.26i	−0.0910656	−	0.157730i	0.816894	−	0.576788i	$-0.195694\pi$
$383$	−682.579	−	1182.26i	−0.0910656	−	0.157730i	−0.907960	+	0.419057i	$0.862361\pi$
$384$	−3912.10	+	6427.95i	−0.519892	+	0.854232i
$385$	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	$0.799366\pi$
$390$	1330.64	−	2655.53i	0.172768	−	0.344789i
$391$	−8398.18	+	4848.69i	−1.08623	+	0.627133i
$392$	−146.784	−	654.272i	−0.0189126	−	0.0843004i
$393$	−5739.84	+	4676.38i	−0.736735	+	0.600234i
$394$	184.317	−	1819.28i	0.0235679	−	0.232625i
$395$	−1323.64			−0.168606
$396$	−415.897	+	968.996i	−0.0527768	+	0.122964i
$397$	3291.69			0.416134			0.208067	−	0.978115i	$-0.433283\pi$
$397$	3291.69			0.416134			0.208067	+	0.978115i	$0.433283\pi$
$398$	−496.917	+	4904.77i	−0.0625834	+	0.617723i
$399$	6403.12	+	2436.09i	0.803400	+	0.305657i
$400$	7939.02	−	5952.07i	0.992378	−	0.744008i
$401$	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	$0.251663\pi$
$402$	3468.33	+	5262.92i	0.430310	+	0.652962i
$403$	−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
$408$	8292.25	+	1192.68i	1.00620	+	0.144721i
$409$	−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	$-0.491825\pi$
$410$	−943.828	+	1309.37i	−0.113689	+	0.157720i
$411$	49.5609	−	130.268i	0.00594808	−	0.0156341i
$412$	4085.06	−	1361.28i	0.488487	−	0.162781i
$413$			4028.56i			0.479982i
$414$	−7029.20	−	7656.03i	−0.834460	−	0.908873i
$415$		−	15484.9i		−	1.83162i
$416$	−41.0022	−	2185.78i	−0.00483244	−	0.257612i
$417$	5436.72	+	6673.10i	0.638458	+	0.783652i
$418$	765.047	+	551.466i	0.0895207	+	0.0645289i
$419$	−3184.20	−	5515.19i	−0.371261	−	0.643042i	0.618499	−	0.785786i	$-0.287741\pi$
$419$	−3184.20	−	5515.19i	−0.371261	−	0.643042i	−0.989760	+	0.142743i	$0.954408\pi$
$420$	562.244	−	13416.5i	0.0653207	−	1.55872i
$421$	−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
$426$	−335.319	−	5668.47i	−0.0381367	−	0.644690i
$427$	−26.8111	+	15.4794i	−0.00303859	+	0.00175433i
$428$	−3373.67	−	690.683i	−0.381011	−	0.0780034i
$429$	−48.8243	−	302.438i	−0.00549477	−	0.0340369i
$430$	−30.3530	−	3.07516i	−0.00340408	−	0.000344877i
$431$	−10968.4			−1.22583			−0.612913	−	0.790150i	$-0.710002\pi$
$431$	−10968.4			−1.22583			−0.612913	+	0.790150i	$0.710002\pi$
$432$	684.341	+	8952.83i	0.0762162	+	0.997091i
$433$	−1491.10			−0.165491			−0.0827457	−	0.996571i	$-0.526369\pi$
$433$	−1491.10			−0.165491			−0.0827457	+	0.996571i	$0.526369\pi$
$434$	−17890.4	−	1812.53i	−1.97872	−	0.200470i
$435$	3044.16	+	18856.8i	0.335532	+	2.07843i
$436$	7048.40	+	1443.00i	0.774213	+	0.158503i
$437$	−8050.19	+	4647.78i	−0.881219	+	0.508772i
$438$	−674.198	−	11397.1i	−0.0735489	−	1.24332i
$439$	−1927.62	−	1112.91i	−0.209567	−	0.120994i	0.391543	−	0.920160i	$-0.371941\pi$
$439$	−1927.62	−	1112.91i	−0.209567	−	0.120994i	−0.601110	+	0.799166i	$0.705275\pi$
$440$	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	$-0.509073\pi$
$443$	7938.74	−	13750.3i	0.851425	−	1.47471i	0.879923	−	0.475117i	$-0.157594\pi$
$444$	−232.563	+	5549.52i	−0.0248580	+	0.593173i
$445$	8737.50	+	15133.8i	0.930780	+	1.61216i
$446$	14726.9	+	10615.6i	1.56354	+	1.12704i
$447$	−2797.94	−	3434.22i	−0.296058	−	0.363385i
$448$	−4222.17	−	8936.27i	−0.445265	−	0.942409i
$449$		−	11558.7i		−	1.21490i	−0.794358	−	0.607450i	$-0.792193\pi$
$449$		−	11558.7i		−	1.21490i	0.794358	−	0.607450i	$-0.207807\pi$
$450$	3549.32	−	11295.4i	0.371814	−	1.18327i
$451$			166.477i			0.0173816i
$452$	−2899.60	+	966.246i	−0.301738	+	0.100550i
$453$	−2713.97	+	7133.51i	−0.281487	+	0.739871i
$454$	3720.75	−	5161.78i	0.384633	−	0.533600i
$455$	1950.64	+	3378.61i	0.200984	+	0.348114i
$456$	7948.65	+	1143.26i	0.816293	+	0.117408i
$457$	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	$0.463892\pi$
$462$	−762.124	−	1156.46i	−0.0767472	−	0.116458i
$463$	2303.58	−	1329.97i	0.231223	−	0.133497i	−0.379913	−	0.925022i	$-0.624046\pi$
$463$	2303.58	−	1329.97i	0.231223	−	0.133497i	0.611136	+	0.791525i	$0.290713\pi$
$464$	8433.21	+	11248.4i	0.843754	+	1.12542i
$465$	−26766.2	−	10183.3i	−2.66936	−	1.01557i
$466$	−1098.39	+	10841.5i	−0.109188	+	1.07773i
$467$	32.9750			0.00326746			0.00163373	−	0.999999i	$-0.499480\pi$
$467$	32.9750			0.00326746			0.00163373	+	0.999999i	$0.499480\pi$
$468$	−1561.56	−	2089.60i	−0.154238	−	0.206393i
$469$	−8278.68			−0.815083
$470$	891.925	−	8803.66i	0.0875350	−	0.864006i
$471$	−10832.6	+	8825.57i	−1.05975	+	0.863399i
$472$	1033.72	+	4607.66i	0.100807	+	0.449332i
$473$	−2.72509	+	1.57333i	−0.000264904	+	0.000152942i
$474$	−520.778	+	1039.31i	−0.0504644	+	0.100711i
$475$	−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	−0.604056	−	0.796942i	$-0.706450\pi$
$479$	4069.08	−	7047.85i	0.388144	−	0.672284i	0.992200	+	0.124657i	$0.0397831\pi$
$480$	−2799.58	−	15489.4i	−0.266214	−	1.47290i
$481$	−806.850	−	1397.50i	−0.0764848	−	0.132476i
$482$	5719.83	−	7935.10i	0.540521	−	0.749863i
$483$	13476.9	−	2175.65i	1.26960	−	0.204959i
$484$	3306.02	+	9921.00i	0.310483	+	0.931724i
$485$			24538.7i			2.29741i
$486$	6896.50	+	8199.37i	0.643686	+	0.765290i
$487$			1992.29i			0.185378i	0.995695	+	0.0926891i	$0.0295463\pi$
$487$			1992.29i			0.185378i	−0.995695	+	0.0926891i	$0.970454\pi$
$488$	−26.6932	+	24.5842i	−0.00247611	+	0.00228048i
$489$	11216.2	−	1810.69i	1.03724	−	0.167448i
$490$	1137.83	+	820.178i	0.104902	+	0.0756161i
$491$	−4407.34	−	7633.75i	−0.405093	−	0.701642i	0.589239	−	0.807959i	$-0.299428\pi$
$491$	−4407.34	−	7633.75i	−0.405093	−	0.701642i	−0.994332	+	0.106317i	$0.966094\pi$
$492$	656.760	+	1256.25i	0.0601809	+	0.115114i
$493$	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
$498$	−12158.6	−	6092.45i	−1.09406	−	0.548212i
$499$	−18252.9	+	10538.3i	−1.63750	+	0.945409i	−0.655806	+	0.754930i	$0.727671\pi$
$499$	−18252.9	+	10538.3i	−1.63750	+	0.945409i	−0.981691	+	0.190479i	$0.938996\pi$
$500$	−806.559	+	3939.67i	−0.0721408	+	0.352375i
$501$	14426.9	−	11754.0i	1.28652	−	1.04816i
$502$	−8379.07	−	848.909i	−0.744973	−	0.0754754i
$503$	19011.6			1.68526			0.842629	−	0.538494i	$-0.181006\pi$
$503$	19011.6			1.68526			0.842629	+	0.538494i	$0.181006\pi$
$504$	−10313.3	−	5720.14i	−0.911493	−	0.505546i
$505$	6073.31			0.535166
$506$	1869.66	+	189.421i	0.164262	+	0.0166419i
$507$	−9961.49	−	3789.89i	−0.872594	−	0.331982i
$508$	2692.28	−	13150.6i	0.235139	−	1.14855i
$509$	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	$0.144954\pi$
$510$	−14632.5	+	9642.99i	−1.27047	+	0.837253i
$511$	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
$516$	−14.3568	+	22.6230i	−0.00122485	+	0.00193008i
$517$	−456.332	−	790.390i	−0.0388190	−	0.0672365i
$518$	−5918.17	−	4265.98i	−0.501987	−	0.361846i
$519$	−201.630	+	529.971i	−0.0170531	+	0.0448230i
$520$	3097.99	+	3363.75i	0.261261	+	0.283674i
$521$		−	14455.7i		−	1.21558i	−0.794100	−	0.607788i	$-0.792057\pi$
$521$		−	14455.7i		−	1.21558i	0.794100	−	0.607788i	$-0.207943\pi$
$522$	16003.9	+	5028.86i	1.34190	+	0.421662i
$523$			15232.9i			1.27359i	0.771032	+	0.636796i	$0.219741\pi$
$523$			15232.9i			1.27359i	−0.771032	+	0.636796i	$0.780259\pi$
$524$	−3603.62	−	10814.1i	−0.300429	−	0.901555i
$525$	9822.56	+	12056.3i	0.816556	+	1.00225i
$526$	9728.27	−	13496.0i	0.806412	−	1.11873i
$527$	11733.4	+	20322.8i	0.969854	+	1.67984i
$528$	−1168.42	−	1127.14i	−0.0963051	−	0.0929028i
$529$	−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
$534$	15320.6	−	906.293i	1.24155	−	0.0734441i
$535$	6238.33	−	3601.70i	0.504124	−	0.291056i
$536$	−9468.72	+	2124.29i	−0.763035	+	0.171185i
$537$	222.265	+	1376.81i	0.0178612	+	0.110640i
$538$	−845.902	+	8349.39i	−0.0677870	+	0.669085i
$539$	144.667			0.0115608
$540$	−13497.3	−	13061.0i	−1.07562	−	1.04084i
$541$	−23075.7			−1.83383			−0.916915	−	0.399083i	$-0.869328\pi$
$541$	−23075.7			−1.83383			−0.916915	+	0.399083i	$0.869328\pi$
$542$	566.141	−	5588.04i	0.0448669	−	0.442854i
$543$	−744.136	−	4609.49i	−0.0588102	−	0.364295i
$544$	−6238.43	+	11289.1i	−0.491674	+	0.889736i
$545$	−13033.3	+	7524.80i	−1.02438	+	0.591426i
$546$	3420.32	−	202.329i	0.268089	−	0.0158588i
$547$	−317.151	−	183.107i	−0.0247905	−	0.0143128i	0.487554	−	0.873093i	$-0.337889\pi$
$547$	−317.151	−	183.107i	−0.0247905	−	0.0143128i	−0.512344	+	0.858780i	$0.671223\pi$
$548$	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
$552$	14855.9	−	5946.52i	1.14549	−	0.458516i
$553$	−763.434	−	1322.31i	−0.0587061	−	0.101682i
$554$	7182.88	−	9964.78i	0.550851	−	0.764193i
$555$	−7338.68	−	9007.59i	−0.561279	−	0.688921i
$556$	−12572.3	+	4189.54i	−0.958968	+	0.319562i
$557$		−	3402.66i		−	0.258842i	−0.991590	−	0.129421i	$-0.958688\pi$
$557$		−	3402.66i		−	0.258842i	0.991590	−	0.129421i	$-0.0413119\pi$
$558$	−18526.9	+	17010.0i	−1.40556	+	1.29048i
$559$		−	7.78437i		−	0.000588987i
$560$	19010.9	+	8124.64i	1.43457	+	0.613087i
$561$	−642.711	+	1689.32i	−0.0483695	+	0.127136i
$562$	−17889.2	−	12895.0i	−1.34272	−	0.967868i
$563$	−2461.45	−	4263.36i	−0.184259	−	0.319146i	0.759068	−	0.651012i	$-0.225655\pi$
$563$	−2461.45	−	4263.36i	−0.184259	−	0.319146i	−0.943327	+	0.331866i	$0.892322\pi$
$564$	−6561.63	−	4164.08i	−0.489884	−	0.310886i
$565$	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	$0.520439\pi$
$570$	−14026.2	+	9243.42i	−1.03069	+	0.679236i
$571$	522.706	−	301.784i	0.0383092	−	0.0221178i	−0.480723	−	0.876872i	$-0.659626\pi$
$571$	522.706	−	301.784i	0.0383092	−	0.0221178i	0.519032	+	0.854755i	$0.326292\pi$
$572$	462.078	+	94.6001i	0.0337770	+	0.00691508i
$573$	−2499.48	−	950.939i	−0.182229	−	0.0693299i
$574$	−1852.42	−	187.674i	−0.134701	−	0.0136470i
$575$	−21100.5			−1.53035
$576$	−13263.6	−	3896.03i	−0.959464	−	0.281831i
$577$	−6971.52			−0.502995			−0.251497	−	0.967858i	$-0.580923\pi$
$577$	−6971.52			−0.502995			−0.251497	+	0.967858i	$0.580923\pi$
$578$	461.395	+	46.7453i	0.0332033	+	0.00336392i
$579$	9907.18	−	8071.60i	0.711103	−	0.579351i
$580$	−28810.3	−	5898.25i	−2.06255	−	0.422261i
$581$	15469.3	−	8931.22i	1.10461	−	0.637745i
$582$	19267.6	+	9654.63i	1.37228	+	0.687624i
$583$	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	$0.425610\pi$
$587$	−10334.9	+	17900.6i	−0.726691	+	1.25867i	−0.958274	+	0.285851i	$0.907724\pi$
$588$	1091.67	−	570.719i	0.0765641	−	0.0400273i
$589$	11247.2	+	19480.7i	0.786811	+	1.36280i
$590$	−8013.08	−	5776.04i	−0.559141	−	0.403044i
$591$	3316.40	−	535.386i	0.230827	−	0.0372637i
$592$	−7863.54	−	3360.62i	−0.545928	−	0.233312i
$593$			2417.22i			0.167392i	0.996491	+	0.0836958i	$0.0266724\pi$
$593$			2417.22i			0.167392i	−0.996491	+	0.0836958i	$0.973328\pi$
$594$	−1917.04	−	278.767i	−0.132419	−	0.0192558i
$595$		−	23017.2i		−	1.58590i
$596$	6470.19	−	2156.09i	0.444680	−	0.148183i
$597$	−8941.01	+	1443.40i	−0.612950	+	0.0989519i
$598$	−2718.46	+	3771.31i	−0.185896	+	0.257893i
$599$	−14467.5	−	25058.4i	−0.986852	−	1.70928i	−0.633400	−	0.773825i	$-0.718341\pi$
$599$	−14467.5	−	25058.4i	−0.986852	−	1.70928i	−0.353452	−	0.935453i	$-0.614992\pi$
$600$	14328.2	+	11269.0i	0.974908	+	0.766757i
$601$	−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
$606$	2389.51	−	4768.71i	0.160177	−	0.319662i
$607$	16616.3	−	9593.41i	1.11109	−	0.641490i	0.171981	−	0.985100i	$-0.444983\pi$
$607$	16616.3	−	9593.41i	1.11109	−	0.641490i	0.939112	+	0.343610i	$0.111650\pi$
$608$	−5979.94	+	10821.3i	−0.398879	+	0.721813i
$609$	−17082.1	+	13917.1i	−1.13662	+	0.926027i
$610$	7.65146	−	75.5230i	0.000507866	−	0.00501284i
$611$	2257.80			0.149494
$612$	1814.52	+	15283.3i	0.119849	+	1.00946i
$613$	6429.22			0.423612			0.211806	−	0.977312i	$-0.432066\pi$
$613$	6429.22			0.423612			0.211806	+	0.977312i	$0.432066\pi$
$614$	−1574.10	+	15537.0i	−0.103462	+	1.02121i
$615$	−2771.45	−	1054.41i	−0.181717	−	0.0691349i
$616$	2080.64	−	466.786i	0.136090	−	0.0305314i
$617$	−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	$0.406213\pi$
$618$	4352.87	+	6605.13i	0.283330	+	0.429931i
$619$	19227.5	+	11101.0i	1.24850	+	0.720819i	0.970809	−	0.239853i	$-0.0770992\pi$
$619$	19227.5	+	11101.0i	1.24850	+	0.720819i	0.277686	+	0.960672i	$0.410433\pi$
$620$	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
$624$	3860.07	−	1109.06i	0.247639	−	0.0711505i
$625$	5483.94	+	9498.47i	0.350972	+	0.607902i
$626$	14499.1	−	20114.6i	0.925720	−	1.28425i
$627$	−616.079	+	1619.32i	−0.0392406	+	0.103141i
$628$	−6801.00	−	20409.0i	−0.432149	−	1.29683i
$629$			9520.65i			0.603519i
$630$	24079.4	−	5362.91i	1.52277	−	0.339148i
$631$			529.250i			0.0333901i	0.999861	+	0.0166950i	$0.00531444\pi$
$631$			529.250i			0.0333901i	−0.999861	+	0.0166950i	$0.994686\pi$
$632$	−1212.48	−	1316.49i	−0.0763128	−	0.0828595i
$633$	−13826.1	−	16970.4i	−0.868151	−	1.06558i
$634$	16093.8	+	11600.8i	1.00815	+	0.726699i
$635$	14039.4	+	24317.0i	0.877383	+	1.51967i
$636$	11066.5	+	463.763i	0.689963	+	0.0289141i
$637$	−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	$0.916509\pi$
$642$	−373.585	−	6315.35i	−0.0229661	−	0.388235i
$643$	2182.17	−	1259.88i	0.133836	−	0.0772702i	−0.431587	−	0.902071i	$-0.642046\pi$
$643$	2182.17	−	1259.88i	0.133836	−	0.0772702i	0.565423	+	0.824801i	$0.308713\pi$
$644$	−4215.45	+	20590.5i	−0.257938	+	1.25991i
$645$	−8.93242	−	55.3312i	−0.000545293	−	0.00337777i
$646$	13694.7	+	1387.45i	0.834072	+	0.0845023i
$647$	5938.61			0.360851			0.180426	−	0.983589i	$-0.442252\pi$
$647$	5938.61			0.360851			0.180426	+	0.983589i	$0.442252\pi$
$648$	−15565.8	+	5459.20i	−0.943647	+	0.330953i
$649$	−1018.81			−0.0616205
$650$	−5268.96	−	533.814i	−0.317947	−	0.0322122i
$651$	−5264.85	−	32612.7i	−0.316967	−	1.96343i
$652$	−3508.32	+	17136.5i	−0.210731	+	1.02932i
$653$	−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	$0.618439\pi$
$654$	780.507	+	13194.2i	0.0466670	+	0.788893i
$655$	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	$0.482946\pi$
$659$	−14176.7	+	24554.8i	−0.838008	+	1.45147i	−0.891558	+	0.452907i	$0.850387\pi$
$660$	3393.00	+	142.189i	0.200109	+	0.00838594i
$661$	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	$0.734976\pi$
$662$	−22687.5	−	16353.8i	−1.33199	−	0.960133i
$663$	−2824.26	−	3466.53i	−0.165437	−	0.203060i
$664$	15401.3	−	14184.5i	0.900130	−	0.829012i
$665$		−	22063.4i		−	1.28659i
$666$	−9960.04	+	2218.27i	−0.579495	+	0.129064i
$667$		−	29896.3i		−	1.73551i
$668$	9057.62	+	27180.9i	0.524625	+	1.57434i
$669$	−11859.3	+	31171.5i	−0.685364	+	1.80144i
$670$	11869.7	−	16466.8i	0.684430	−	0.949507i
$671$	−3.91468	−	6.78042i	−0.000225223	−	0.000390097i
$672$	13859.1	−	11730.6i	0.795577	−	0.673389i
$673$	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	$0.793905\pi$
$678$	−3089.69	−	4688.36i	−0.175013	−	0.265568i
$679$	−24514.0	+	14153.2i	−1.38551	+	0.799925i
$680$	−5906.14	−	26325.9i	−0.333074	−	1.48463i
$681$	10925.6	+	4156.70i	0.614787	+	0.233899i
$682$	458.381	−	4524.41i	0.0257365	−	0.254030i
$683$	−807.274			−0.0452262			−0.0226131	−	0.999744i	$-0.507199\pi$
$683$	−807.274			−0.0452262			−0.0226131	+	0.999744i	$0.507199\pi$
$684$	1739.33	+	14650.0i	0.0972293	+	0.818942i
$685$	−448.867			−0.0250370
$686$	1724.59	−	17022.4i	0.0959842	−	0.947403i
$687$	−13981.6	+	11391.1i	−0.776463	+	0.632601i
$688$	−24.7454	−	33.0061i	−0.00137123	−	0.00182899i
$689$	−2786.82	+	1608.97i	−0.154092	+	0.0889651i
$690$	−14995.3	+	29925.8i	−0.827332	+	1.65109i
$691$	−19006.4	−	10973.4i	−1.04636	−	0.604119i	−0.124735	−	0.992190i	$-0.539808\pi$
$691$	−19006.4	−	10973.4i	−1.04636	−	0.604119i	−0.921629	+	0.388072i	$0.873141\pi$
$692$	−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
$696$	−15966.5	+	20300.9i	−0.869552	+	1.10561i
$697$	1214.91	+	2104.28i	0.0660228	+	0.114355i
$698$	−15020.2	+	20837.5i	−0.814503	+	1.12996i
$699$	−19763.2	+	3190.48i	−1.06940	+	0.172640i
$700$	−22714.6	+	7569.28i	−1.22647	+	0.408703i
$701$			3170.45i			0.170822i	0.996346	+	0.0854110i	$0.0272203\pi$
$701$			3170.45i			0.170822i	−0.996346	+	0.0854110i	$0.972780\pi$
$702$	2968.47	−	3762.29i	0.159598	−	0.202277i
$703$			9126.15i			0.489615i
$704$	2259.95	−	1067.77i	0.120987	−	0.0571636i
$705$	16048.4	−	2590.78i	0.857329	−	0.138403i
$706$	−10450.8	−	7533.20i	−0.557111	−	0.401580i
$707$	3502.90	+	6067.20i	0.186337	+	0.322745i
$708$	−7687.99	+	4019.24i	−0.408097	+	0.213351i
$709$	−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
$714$	−18072.9	−	9055.98i	−0.947283	−	0.474666i
$715$	−854.438	+	493.310i	−0.0446912	+	0.0258025i
$716$	−2103.54	−	430.653i	−0.109795	−	0.0224780i
$717$	160.600	−	130.845i	0.00836503	−	0.00681517i
$718$	−15238.2	−	1543.83i	−0.792040	−	0.0802440i
$719$	−15469.9			−0.802408			−0.401204	−	0.915989i	$-0.631408\pi$
$719$	−15469.9			−0.802408			−0.401204	+	0.915989i	$0.631408\pi$
$720$	26164.7	−	12312.5i	1.35431	−	0.637307i
$721$	−10390.0			−0.536677
$722$	−6174.14	−	625.521i	−0.318252	−	0.0322430i
$723$	16795.7	+	6390.00i	0.863954	+	0.328695i
$724$	7042.58	+	1441.81i	0.361513	+	0.0740116i
$725$	29494.0	−	17028.4i	1.51087	−	0.872301i
$726$	−16041.3	+	10571.4i	−0.820037	+	0.540415i
$727$	6900.11	+	3983.78i	0.352009	+	0.203233i	0.665570	−	0.746336i	$-0.268189\pi$
$727$	6900.11	+	3983.78i	0.352009	+	0.203233i	−0.313561	+	0.949568i	$0.601522\pi$
$728$	−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
$732$	−56.2895	−	35.7219i	−0.00284224	−	0.00180372i
$733$	−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	$-0.380160\pi$
$734$	24450.2	+	17624.4i	1.22953	+	0.886277i
$735$	−916.275	+	2408.37i	−0.0459827	+	0.120863i
$736$	462.063	+	24632.1i	0.0231411	+	1.23363i
$737$		−	2093.65i		−	0.104641i
$738$	−1918.33	+	1761.27i	−0.0956838	+	0.0878497i
$739$			1182.09i			0.0588414i	0.999567	+	0.0294207i	$0.00936624\pi$
$739$			1182.09i			0.0588414i	−0.999567	+	0.0294207i	$0.990634\pi$
$740$	16970.6	−	5655.20i	0.843044	−	0.280931i
$741$	−2707.23	−	3322.89i	−0.134214	−	0.164736i
$742$	−8506.96	+	11801.7i	−0.420890	+	0.583899i
$743$	−13616.4	−	23584.4i	−0.672327	−	1.16450i	−0.977243	−	0.212125i	$-0.931962\pi$
$743$	−13616.4	−	23584.4i	−0.672327	−	1.16450i	0.304916	−	0.952379i	$-0.401372\pi$
$744$	−14390.0	−	35949.8i	−0.709090	−	1.77148i
$745$	−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
$750$	−7374.87	+	436.261i	−0.359056	+	0.0212400i
$751$	12287.2	−	7093.99i	0.597024	−	0.344692i	−0.170846	−	0.985298i	$-0.554650\pi$
$751$	12287.2	−	7093.99i	0.597024	−	0.344692i	0.767870	+	0.640606i	$0.221317\pi$
$752$	9573.15	−	7177.21i	0.464224	−	0.348040i
$753$	−2465.83	−	15274.4i	−0.119336	−	0.739216i
$754$	756.336	−	7465.34i	0.0365307	−	0.360572i
$755$	24580.1			1.18485
$756$	5263.01	−	21016.9i	0.253193	−	1.01108i
$757$	30482.1			1.46353			0.731764	−	0.681559i	$-0.238698\pi$
$757$	30482.1			1.46353			0.731764	+	0.681559i	$0.238698\pi$
$758$	1823.30	−	17996.7i	0.0873682	−	0.862359i
$759$	550.213	+	3408.25i	0.0263129	+	0.162993i
$760$	−5661.41	−	25235.0i	−0.270212	−	1.20443i
$761$	−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	$0.518570\pi$
$762$	24617.2	−	1456.23i	1.17033	−	0.0692307i
$763$	−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
$768$	12841.3	−	16973.1i	0.603348	−	0.797478i
$769$	−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	$0.848793\pi$
$770$	−2608.23	+	3618.39i	−0.122070	+	0.169348i
$771$	21197.3	+	26017.8i	0.990145	+	1.21532i
$772$	6219.99	+	18665.5i	0.289977	+	0.870188i
$773$		−	35103.0i		−	1.63333i	−0.577110	−	0.816666i	$-0.695820\pi$
$773$		−	35103.0i		−	1.63333i	0.577110	−	0.816666i	$-0.304180\pi$
$774$	−46.9599	−	14.7561i	−0.00218080	−	0.000685267i
$775$			51061.1i			2.36667i
$776$	−24406.2	+	22477.9i	−1.12904	+	1.03983i
$777$	4765.80	−	12526.6i	0.220041	−	0.578365i
$778$	14256.1	+	10276.2i	0.656947	+	0.473545i
$779$	1164.57	+	2017.09i	0.0535622	+	0.0927724i
$780$	−4501.52	+	7093.35i	−0.206641	+	0.325619i
$781$	−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
$786$	17485.3	−	11523.0i	0.793484	−	0.522916i
$787$	20621.0	−	11905.5i	0.934000	−	0.539245i	0.0459253	−	0.998945i	$-0.485376\pi$
$787$	20621.0	−	11905.5i	0.934000	−	0.539245i	0.888074	+	0.459700i	$0.152043\pi$
$788$	−1037.34	+	5066.95i	−0.0468957	+	0.229064i
$789$	28566.1	+	10868.1i	1.28895	+	0.490386i
$790$	3724.74	+	377.365i	0.167747	+	0.0169950i
$791$	7374.87			0.331505
$792$	1446.60	−	2608.20i	0.0649024	−	0.117018i
$793$	19.3687			0.000867343
$794$	−9262.90	−	938.452i	−0.414015	−	0.0419451i
$795$	−17962.4	+	14634.4i	−0.801335	+	0.652865i
$796$	2796.67	−	13660.5i	0.124529	−	0.608269i
$797$	−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	$0.350326\pi$
$798$	−17324.0	−	8680.73i	−0.768499	−	0.385081i
$799$	−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
$804$	−8259.52	−	15798.8i	−0.362302	−	0.693010i
$805$	−21982.3	−	38074.4i	−0.962451	−	1.66701i
$806$	9126.20	+	6578.41i	0.398830	+	0.287487i
$807$	−15220.3	+	2457.09i	−0.663914	+	0.107179i
$808$	5563.27	+	6040.52i	0.242222	+	0.263001i
$809$			29338.0i			1.27499i	0.770453	+	0.637497i	$0.220030\pi$
$809$			29338.0i			1.27499i	−0.770453	+	0.637497i	$0.779970\pi$
$810$	16782.7	−	30148.5i	0.728004	−	1.30779i
$811$			30884.9i			1.33726i	0.743597	+	0.668629i	$0.233118\pi$
$811$			30884.9i			1.33726i	−0.743597	+	0.668629i	$0.766882\pi$
$812$	−10724.6	−	32183.2i	−0.463496	−	1.39090i
$813$	10186.6	−	1644.47i	0.439432	−	0.0709399i
$814$	1078.85	−	1496.68i	0.0464541	−	0.0644456i
$815$	−18294.8	−	31687.5i	−0.786305	−	1.36192i
$816$	−22994.6	−	5720.32i	−0.986483	−	0.245406i
$817$	−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	$0.806738\pi$
$822$	−176.604	+	352.446i	−0.00749366	+	0.0149550i
$823$	−5398.43	+	3116.78i	−0.228648	+	0.132010i	−0.609948	−	0.792441i	$-0.708810\pi$
$823$	−5398.43	+	3116.78i	−0.228648	+	0.132010i	0.381300	+	0.924451i	$0.375476\pi$
$824$	−11883.5	+	2666.05i	−0.502407	+	0.112714i
$825$	−3049.00	+	2484.09i	−0.128670	+	0.104830i
$826$	1148.53	−	11336.5i	0.0483808	−	0.477538i
$827$	43288.8			1.82019			0.910096	−	0.414397i	$-0.136007\pi$
$827$	43288.8			1.82019			0.910096	+	0.414397i	$0.136007\pi$
$828$	17597.6	+	23548.3i	0.738599	+	0.988356i
$829$	−15655.6			−0.655902			−0.327951	−	0.944695i	$-0.606358\pi$
$829$	−15655.6			−0.655902			−0.327951	+	0.944695i	$0.606358\pi$
$830$	−4414.70	+	43574.9i	−0.184622	+	1.82230i
$831$	21091.8	+	8024.47i	0.880465	+	0.334977i
$832$	−507.778	+	6162.52i	−0.0211587	+	0.256787i
$833$	1828.60	−	1055.74i	0.0760592	−	0.0439128i
$834$	−13396.6	−	20328.2i	−0.556217	−	0.844016i
$835$	−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	$-0.446079\pi$
$839$	22793.5	−	39479.4i	0.937924	−	1.62453i	0.769336	−	0.638845i	$-0.220587\pi$
$840$	−5407.18	+	37594.2i	−0.222102	+	1.54419i
$841$	11932.2	+	20667.2i	0.489247	+	0.847400i
$842$	17882.9	−	24808.9i	0.731931	−	1.01540i
$843$	14405.8	−	37864.8i	0.588568	−	1.54701i
$844$	31972.8	−	10654.4i	1.30397	−	0.434527i
$845$			34324.6i			1.39740i
$846$	4279.89	−	13620.4i	0.173931	−	0.553520i
$847$		−	25233.2i		−	1.02364i
$848$	−6701.55	+	15681.0i	−0.271382	+	0.635010i
$849$	−6713.46	−	8240.19i	−0.271385	−	0.333101i
$850$	25346.8	+	18270.6i	1.02281	+	0.737268i
$851$	9092.58	+	15748.8i	0.366263	+	0.634386i
$852$	−672.469	+	16046.8i	−0.0270404	+	0.645251i
$853$	−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	$0.827787\pi$
$858$	51.1684	+	864.987i	0.00203597	+	0.0344175i
$859$	−38889.0	+	22452.6i	−1.54468	+	0.891819i	−0.546143	+	0.837692i	$0.683904\pi$
$859$	−38889.0	+	22452.6i	−1.54468	+	0.891819i	−0.998534	+	0.0541273i	$0.982762\pi$
$860$	84.5374	+	17.3071i	0.00335198	+	0.000686242i
$861$	−545.139	−	3376.82i	−0.0215776	−	0.133660i
$862$	30865.4	+	3127.07i	1.21958	+	0.123560i
$863$	3830.25			0.151081			0.0755406	−	0.997143i	$-0.475932\pi$
$863$	3830.25			0.151081			0.0755406	+	0.997143i	$0.475932\pi$
$864$	626.674	−	25388.6i	0.0246758	−	0.999696i
$865$	1826.14			0.0717809
$866$	4195.99	+	425.109i	0.164649	+	0.0166810i
$867$	135.781	+	841.086i	0.00531877	+	0.0329467i
$868$	49827.1	+	10201.0i	1.94844	+	0.398898i
$869$	334.406	−	193.070i	0.0130540	−	0.00753675i
$870$	−3190.31	−	53931.4i	−0.124324	−	2.10166i
$871$	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
$876$	−1352.08	+	32264.0i	−0.0521490	+	1.24441i
$877$	−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	$0.993861\pi$
$878$	5107.07	+	3681.31i	0.196304	+	0.141501i
$879$	7737.20	+	9496.74i	0.296893	+	0.364411i
$880$	−2054.69	+	4807.79i	−0.0787087	+	0.184171i
$881$		−	3336.88i		−	0.127608i	−0.997962	−	0.0638038i	$-0.979677\pi$
$881$		−	3336.88i		−	0.127608i	0.997962	−	0.0638038i	$-0.0203232\pi$
$882$	1530.53	+	1667.01i	0.0584302	+	0.0636408i
$883$		−	26792.8i		−	1.02112i	−0.859841	−	0.510561i	$-0.829438\pi$
$883$		−	26792.8i		−	1.02112i	0.859841	−	0.510561i	$-0.170562\pi$
$884$	6531.06	−	2176.38i	0.248488	−	0.0828048i
$885$	6452.80	−	16960.8i	0.245094	−	0.644214i
$886$	−26260.0	+	36430.4i	−0.995735	+	1.38138i
$887$	13004.9	+	22525.1i	0.492290	+	0.852672i	0.999961	−	0.00887981i	$-0.00282657\pi$
$887$	13004.9	+	22525.1i	0.492290	+	0.852672i	−0.507670	+	0.861551i	$0.669493\pi$
$888$	2236.59	−	15550.2i	0.0845214	−	0.587646i
$889$	−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
$894$	6894.37	+	10461.7i	0.257922	+	0.391376i
$895$	3889.71	−	2245.72i	0.145272	−	0.0838729i
$896$	9333.58	+	26350.6i	0.348006	+	0.982491i
$897$	−7982.48	−	3036.97i	−0.297132	−	0.113045i
$898$	−3295.36	+	32526.5i	−0.122458	+	1.20871i
$899$	−72346.0			−2.68395
$900$	−13208.1	+	30773.5i	−0.489190	+	1.13976i
$901$	18985.5			0.701998
$902$	47.4622	−	468.471i	0.00175201	−	0.0172931i
$903$	50.1236	−	40.8368i	0.00184719	−	0.00150494i
$904$	8435.00	−	1892.37i	0.310336	−	0.0696232i
$905$	−13022.6	+	7518.59i	−0.478326	+	0.276162i
$906$	9670.92	−	19300.1i	0.354630	−	0.707729i
$907$	23690.0	+	13677.4i	0.867269	+	0.500718i	0.866440	−	0.499282i	$-0.166403\pi$
$907$	23690.0	+	13677.4i	0.867269	+	0.500718i	0.000829418		1.00000i	$0.499736\pi$
$908$	−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	−0.813553	−	0.581491i	$-0.802469\pi$
$911$	2661.94	−	4610.61i	0.0968100	−	0.167680i	0.910363	+	0.413812i	$0.135803\pi$
$912$	−22041.7	−	5483.29i	−0.800301	−	0.199090i
$913$	2258.67	+	3912.14i	0.0818742	+	0.141810i
$914$	−18010.6	+	24986.0i	−0.651792	+	0.904228i
$915$	137.672	−	22.2252i	0.00497411	−	0.000802998i
$916$	−8777.99	−	26341.8i	−0.316630	−	0.950170i
$917$			27504.7i			0.990495i
$918$	−26265.8	+	10466.4i	−0.944337	+	0.376300i
$919$		−	3951.52i		−	0.141837i	−0.997482	−	0.0709187i	$-0.977407\pi$
$919$		−	3951.52i		−	0.141837i	0.997482	−	0.0709187i	$-0.0225931\pi$
$920$	−34912.0	−	37907.0i	−1.25110	−	1.35843i
$921$	−28322.7	+	4572.28i	−1.01332	+	0.163585i
$922$	−27017.5	−	19475.0i	−0.965049	−	0.695633i
$923$	−2333.06	−	4040.97i	−0.0831999	−	0.144106i
$924$	1814.93	+	3471.59i	0.0646178	+	0.123601i
$925$	−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	$0.649100\pi$
$930$	72417.4	+	36287.0i	2.55340	+	1.27946i
$931$	1752.83	−	1012.00i	0.0617044	−	0.0356250i
$932$	6181.76	−	30195.1i	0.217264	−	1.06124i
$933$	−6182.26	+	5036.82i	−0.216932	+	0.176740i
$934$	−92.7925	−	9.40108i	−0.00325082	−	0.000329350i
$935$	5820.96			0.203600
$936$	3798.53	+	6325.39i	0.132648	+	0.220889i
$937$	24002.2			0.836838			0.418419	−	0.908254i	$-0.362584\pi$
$937$	24002.2			0.836838			0.418419	+	0.908254i	$0.362584\pi$
$938$	23296.4	+	2360.23i	0.810931	+	0.0821579i
$939$	42575.1	+	16197.9i	1.47965	+	0.562938i
$940$	−5019.79	+	24519.4i	−0.174178	+	0.850782i
$941$	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	$0.0146320\pi$
$942$	32999.4	−	21747.0i	1.14138	−	0.752182i
$943$	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	−0.984187	−	0.177131i	$-0.943318\pi$
$947$	−9870.34	+	17095.9i	−0.338694	+	0.586635i	0.645493	+	0.763766i	$0.276652\pi$
$948$	1761.78	−	2776.16i	0.0603587	−	0.0951113i
$949$	−4690.89	−	8124.86i	−0.160456	−	0.277918i
$950$	24296.5	+	17513.6i	0.829771	+	0.598121i
$951$	−12960.0	+	34064.6i	−0.441912	+	1.16154i
$952$	22892.9	−	21084.2i	0.779373	−	0.717795i
$953$		−	47895.5i		−	1.62800i	−0.580863	−	0.814002i	$-0.697285\pi$
$953$		−	47895.5i		−	1.62800i	0.580863	−	0.814002i	$-0.302715\pi$
$954$	4423.56	+	19861.7i	0.150124	+	0.674054i
$955$			8612.54i			0.291827i
$956$	100.829	+	302.577i	0.00341113	+	0.0102364i
$957$	−3519.59	−	4319.99i	−0.118884	−	0.145920i
$958$	−13459.8	+	18672.7i	−0.453931	+	0.629737i
$959$	−258.893	−	448.416i	−0.00871751	−	0.0150992i
$960$	3462.10	+	44385.7i	0.116395	+	1.49223i
$961$	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
$966$	−38544.5	+	2280.10i	−1.28380	+	0.0759431i
$967$	39942.4	−	23060.8i	1.32830	−	0.766892i	0.343259	−	0.939241i	$-0.388469\pi$
$967$	39942.4	−	23060.8i	1.32830	−	0.766892i	0.985036	+	0.172349i	$0.0551356\pi$
$968$	−6474.77	−	28860.4i	−0.214987	−	0.958275i
$969$	4030.13	+	24964.3i	0.133608	+	0.827626i
$970$	6995.91	−	69052.5i	0.231572	−	2.28571i
$971$	−51058.5			−1.68748			−0.843741	−	0.536751i	$-0.819651\pi$
$971$	−51058.5			−1.68748			−0.843741	+	0.536751i	$0.819651\pi$
$972$	−17069.3	−	25039.4i	−0.563269	−	0.826274i
$973$	31976.7			1.05357
$974$	567.995	−	5606.34i	0.0186856	−	0.184434i
$975$	−1550.57	−	9604.89i	−0.0509313	−	0.315490i
$976$	82.1241	−	61.5703i	0.00269337	−	0.00201928i
$977$	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	$0.213831\pi$
$978$	−32078.7	+	1897.62i	−1.04884	+	0.0620441i
$979$	−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	−0.953998	−	0.299813i	$-0.903076\pi$
$983$	−6698.78	+	11602.6i	−0.217353	+	0.376466i	0.736645	+	0.676280i	$0.236409\pi$
$984$	−1489.98	−	3722.35i	−0.0482713	−	0.120594i
$985$	−5409.43	−	9369.40i	−0.174983	−	0.303080i
$986$	−25886.8	+	35912.7i	−0.836110	+	1.15993i
$987$	11844.4	+	14537.9i	0.381977	+	0.468843i
$988$	6260.44	−	2086.20i	0.201590	−	0.0671768i
$989$			87.7240i			0.00282049i
$990$	1356.26	+	6089.60i	0.0435402	+	0.195495i
$991$		−	24672.3i		−	0.790858i	−0.918496	−	0.395429i	$-0.870596\pi$
$991$		−	24672.3i		−	0.790858i	0.918496	−	0.395429i	$-0.129404\pi$
$992$	59607.2	−	1118.15i	1.90779	−	0.0357875i
$993$	18269.9	−	48021.2i	0.583864	−	1.53465i
$994$	−17112.8	−	12335.3i	−0.546060	−	0.393615i
$995$	14583.8	+	25259.8i	0.464660	+	0.804815i
$996$	32477.6	+	20610.7i	1.03323	+	0.655697i
$997$	−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.11.1	✓	24
3.2	odd	2		108.4.h.b.35.12		24
4.3	odd	2	inner	36.4.h.b.11.4	yes	24
9.2	odd	6		324.4.b.c.323.9		24
9.4	even	3		108.4.h.b.71.9		24
9.5	odd	6	inner	36.4.h.b.23.4	yes	24
9.7	even	3		324.4.b.c.323.16		24
12.11	even	2		108.4.h.b.35.9		24
36.7	odd	6		324.4.b.c.323.10		24
36.11	even	6		324.4.b.c.323.15		24
36.23	even	6	inner	36.4.h.b.23.1	yes	24
36.31	odd	6		108.4.h.b.71.12		24

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

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)

\(f(q)\)	\(=\)	\(q+(-2.81402 - 0.285097i) q^{2} +(-0.828122 - 5.12974i) q^{3} +(7.83744 + 1.60454i) q^{4} +(-14.4924 + 8.36717i) q^{5} +(0.867881 + 14.6713i) q^{6} +(-16.7175 - 9.65186i) q^{7} +(-21.5973 - 6.74964i) q^{8} +(-25.6284 + 8.49610i) q^{9} +O(q^{10})\)	\(q+(-2.81402 - 0.285097i) q^{2} +(-0.828122 - 5.12974i) q^{3} +(7.83744 + 1.60454i) q^{4} +(-14.4924 + 8.36717i) q^{5} +(0.867881 + 14.6713i) 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} +(1.74050 - 41.5328i) q^{12} +(6.03848 + 10.4590i) q^{13} +(44.2917 + 31.9267i) q^{14} +(54.9229 + 67.4130i) q^{15} +(58.8509 + 25.1509i) q^{16} -71.2528i q^{17} +(74.5412 - 16.6016i) q^{18} -68.3003i q^{19} +(-127.009 + 42.3237i) q^{20} +(-35.6674 + 93.7494i) q^{21} +(-8.07414 + 11.2012i) q^{22} +(-68.0491 - 117.865i) q^{23} +(-16.7387 + 116.378i) 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} +(-135.335 - 205.360i) q^{30} +(-285.221 + 164.672i) q^{31} +(-158.437 - 87.5535i) q^{32} +(-23.7089 - 9.02015i) q^{33} +(-20.3140 + 200.507i) q^{34} +323.035 q^{35} +(-214.494 + 25.4659i) q^{36} -133.618 q^{37} +(-19.4722 + 192.199i) q^{38} +(48.6511 - 39.6371i) q^{39} +(369.471 - 82.8899i) q^{40} +(-29.5326 + 17.0507i) q^{41} +(127.096 - 253.644i) 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} +(80.2820 - 322.718i) q^{48} +(14.8169 + 25.6636i) q^{49} +(-256.420 + 355.730i) q^{50} +(-365.508 + 59.0060i) q^{51} +(30.5444 + 91.6604i) q^{52} +266.453i q^{53} +(-146.891 - 368.629i) q^{54} +81.6944i q^{55} +(295.906 + 321.291i) q^{56} +(-350.363 + 56.5610i) q^{57} +(-504.018 - 363.309i) q^{58} +(-104.347 - 180.734i) q^{59} +(322.288 + 616.471i) 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} +(64.1457 + 32.1422i) q^{66} +(371.407 - 214.432i) q^{67} +(114.328 - 558.440i) q^{68} +(-548.261 + 446.680i) q^{69} +(-909.028 - 92.0964i) q^{70} -386.365 q^{71} +(610.850 - 10.5101i) q^{72} -776.832 q^{73} +(376.004 + 38.0941i) q^{74} +(-752.951 - 286.464i) q^{75} +(109.591 - 535.300i) q^{76} +(-81.6122 + 47.1188i) q^{77} +(-148.206 + 97.6695i) 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} +(-429.965 + 677.526i) q^{84} +(596.185 + 1032.62i) q^{85} +(1.47893 + 1.06605i) q^{86} +(405.877 - 1066.82i) q^{87} +(-81.2533 + 74.8336i) q^{88} -1044.26i q^{89} +(-941.370 + 864.296i) q^{90} -233.130i q^{91} +(-344.213 - 1032.94i) q^{92} +(1080.92 + 1326.74i) q^{93} +(-309.200 + 428.952i) q^{94} +(571.481 + 989.834i) q^{95} +(-317.921 + 885.247i) 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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