LMFDB - Embedded newform 169.4.e.g.23.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,4,Mod(23,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("169.23");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	169.e (of order $6$, degree $2$, not 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:	$9.97132279097$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.1731891456.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 $ x^8 - 9x^6 + 65x^4 - 144*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.4
Root			$-2.21837 - 1.28078i$ of defining polynomial
Character	$\chi$	$=$	169.23
Dual form			169.4.e.g.147.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.95042 - 2.28078i) q^{2} +(-4.34233 - 7.52113i) q^{3} +(6.40388 - 11.0918i) q^{4} -2.80776i q^{5} +(-34.3081 - 19.8078i) q^{6} +(-8.28055 - 4.78078i) q^{7} -21.9309i q^{8} +(-24.2116 + 41.9358i) q^{9} +O(q^{10})$	\(q+(3.95042 - 2.28078i) q^{2} +(-4.34233 - 7.52113i) q^{3} +(6.40388 - 11.0918i) q^{4} -2.80776i q^{5} +(-34.3081 - 19.8078i) q^{6} +(-8.28055 - 4.78078i) q^{7} -21.9309i q^{8} +(-24.2116 + 41.9358i) q^{9} +(-6.40388 - 11.0918i) q^{10} +(34.1416 - 19.7116i) q^{11} -111.231 q^{12} -43.6155 q^{14} +(-21.1176 + 12.1922i) q^{15} +(1.21165 + 2.09863i) q^{16} +(1.00758 - 1.74518i) q^{17} +220.885i q^{18} +(-52.1280 - 30.0961i) q^{19} +(-31.1433 - 17.9806i) q^{20} +83.0388i q^{21} +(89.9157 - 155.739i) q^{22} +(2.23438 + 3.87006i) q^{23} +(-164.945 + 95.2311i) q^{24} +117.116 q^{25} +186.054 q^{27} +(-106.055 + 61.2311i) q^{28} +(-70.3466 - 121.844i) q^{29} +(-55.6155 + 96.3289i) q^{30} -136.155i q^{31} +(161.515 + 93.2505i) q^{32} +(-296.508 - 171.189i) q^{33} -9.19224i q^{34} +(-13.4233 + 23.2498i) q^{35} +(310.097 + 537.104i) q^{36} +(-160.828 + 92.8542i) q^{37} -274.570 q^{38} -61.5767 q^{40} +(-268.668 + 155.116i) q^{41} +(189.393 + 328.038i) q^{42} +(213.735 - 370.200i) q^{43} -504.924i q^{44} +(117.746 + 67.9806i) q^{45} +(17.6535 + 10.1922i) q^{46} -258.617i q^{47} +(10.5227 - 18.2259i) q^{48} +(-125.788 - 217.872i) q^{49} +(462.659 - 267.116i) q^{50} -17.5009 q^{51} +612.656 q^{53} +(734.991 - 424.348i) q^{54} +(-55.3457 - 95.8615i) q^{55} +(-104.847 + 181.600i) q^{56} +522.749i q^{57} +(-555.797 - 320.890i) q^{58} +(448.502 + 258.943i) q^{59} +312.311i q^{60} +(80.6553 - 139.699i) q^{61} +(-310.540 - 537.871i) q^{62} +(400.971 - 231.501i) q^{63} +831.348 q^{64} -1561.77 q^{66} +(43.2135 - 24.9493i) q^{67} +(-12.9048 - 22.3518i) q^{68} +(19.4048 - 33.6101i) q^{69} +122.462i q^{70} +(242.455 + 139.982i) q^{71} +(919.689 + 530.982i) q^{72} +467.732i q^{73} +(-423.559 + 733.626i) q^{74} +(-508.558 - 880.849i) q^{75} +(-667.643 + 385.464i) q^{76} -376.948 q^{77} +37.5379 q^{79} +(5.89247 - 3.40202i) q^{80} +(-154.193 - 267.070i) q^{81} +(-707.568 + 1225.54i) q^{82} +76.1553i q^{83} +(921.054 + 531.771i) q^{84} +(-4.90004 - 2.82904i) q^{85} -1949.93i q^{86} +(-610.936 + 1058.17i) q^{87} +(-432.294 - 748.754i) q^{88} +(175.635 - 101.403i) q^{89} +620.194 q^{90} +57.2348 q^{92} +(-1024.04 + 591.231i) q^{93} +(-589.848 - 1021.65i) q^{94} +(-84.5028 + 146.363i) q^{95} -1619.70i q^{96} +(-1017.03 - 587.184i) q^{97} +(-993.834 - 573.790i) q^{98} +1909.01i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 10 q^{3} + 10 q^{4} - 70 q^{9}+O(q^{10}) $ 8 * q - 10 * q^3 + 10 * q^4 - 70 * q^9	$ 8 q - 10 q^{3} + 10 q^{4} - 70 q^{9} - 10 q^{10} - 560 q^{12} - 184 q^{14} - 114 q^{16} + 140 q^{17} + 340 q^{22} + 290 q^{23} - 300 q^{25} + 1340 q^{27} - 68 q^{29} - 280 q^{30} + 140 q^{35} + 1450 q^{36} - 1240 q^{38} - 740 q^{40} + 740 q^{42} + 910 q^{43} + 480 q^{48} - 1130 q^{49} + 932 q^{51} + 2180 q^{53} - 1020 q^{55} - 344 q^{56} - 1004 q^{61} - 1000 q^{62} + 5084 q^{64} - 6392 q^{66} + 1010 q^{68} - 958 q^{69} - 1698 q^{74} - 3450 q^{75} - 1020 q^{77} + 960 q^{79} - 244 q^{81} - 3030 q^{82} - 3230 q^{87} - 2040 q^{88} + 2900 q^{90} - 4160 q^{92} - 2080 q^{94} + 2540 q^{95}+O(q^{100}) $ 8 * q - 10 * q^3 + 10 * q^4 - 70 * q^9 - 10 * q^10 - 560 * q^12 - 184 * q^14 - 114 * q^16 + 140 * q^17 + 340 * q^22 + 290 * q^23 - 300 * q^25 + 1340 * q^27 - 68 * q^29 - 280 * q^30 + 140 * q^35 + 1450 * q^36 - 1240 * q^38 - 740 * q^40 + 740 * q^42 + 910 * q^43 + 480 * q^48 - 1130 * q^49 + 932 * q^51 + 2180 * q^53 - 1020 * q^55 - 344 * q^56 - 1004 * q^61 - 1000 * q^62 + 5084 * q^64 - 6392 * q^66 + 1010 * q^68 - 958 * q^69 - 1698 * q^74 - 3450 * q^75 - 1020 * q^77 + 960 * q^79 - 244 * q^81 - 3030 * q^82 - 3230 * q^87 - 2040 * q^88 + 2900 * q^90 - 4160 * q^92 - 2080 * q^94 + 2540 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	3.95042	−	2.28078i	1.39668	−	0.806376i	0.402641	−	0.915358i	$-0.368092\pi$
$2$	3.95042	−	2.28078i	1.39668	−	0.806376i	0.994044	+	0.108982i	$0.0347590\pi$
$3$	−4.34233	−	7.52113i	−0.835682	−	1.44744i	−0.893474	−	0.449114i	$-0.851740\pi$
$3$	−4.34233	−	7.52113i	−0.835682	−	1.44744i	0.0577926	−	0.998329i	$-0.481594\pi$
$4$	6.40388	−	11.0918i	0.800485	−	1.38648i
$5$		−	2.80776i		−	0.251134i	−0.992085	−	0.125567i	$-0.959925\pi$
$5$		−	2.80776i		−	0.251134i	0.992085	−	0.125567i	$-0.0400750\pi$
$6$	−34.3081	−	19.8078i	−2.33437	−	1.34775i
$7$	−8.28055	−	4.78078i	−0.447108	−	0.258138i	0.259500	−	0.965743i	$-0.416442\pi$
$7$	−8.28055	−	4.78078i	−0.447108	−	0.258138i	−0.706608	+	0.707605i	$0.749775\pi$
$8$		−	21.9309i		−	0.969217i
$9$	−24.2116	+	41.9358i	−0.896728	+	1.55318i
$10$	−6.40388	−	11.0918i	−0.202509	−	0.350755i
$11$	34.1416	−	19.7116i	0.935825	−	0.540299i	0.0471757	−	0.998887i	$-0.484978\pi$
$11$	34.1416	−	19.7116i	0.935825	−	0.540299i	0.888649	+	0.458588i	$0.151645\pi$
$12$	−111.231			−2.67580
$13$		0			0
$13$		0			0
$14$	−43.6155			−0.832624
$15$	−21.1176	+	12.1922i	−0.363502	+	0.209868i
$16$	1.21165	+	2.09863i	0.0189320	+	0.0327911i
$17$	1.00758	−	1.74518i	0.0143749	−	0.0248981i	−0.858748	−	0.512397i	$-0.828758\pi$
$17$	1.00758	−	1.74518i	0.0143749	−	0.0248981i	0.873123	+	0.487499i	$0.162091\pi$
$18$			220.885i			2.89240i
$19$	−52.1280	−	30.0961i	−0.629420	−	0.363396i	0.151107	−	0.988517i	$-0.451716\pi$
$19$	−52.1280	−	30.0961i	−0.629420	−	0.363396i	−0.780528	+	0.625121i	$0.785049\pi$
$20$	−31.1433	−	17.9806i	−0.348193	−	0.201029i
$21$			83.0388i			0.862884i
$22$	89.9157	−	155.739i	0.871368	−	1.50925i
$23$	2.23438	+	3.87006i	0.0202565	+	0.0350853i	0.875976	−	0.482355i	$-0.160218\pi$
$23$	2.23438	+	3.87006i	0.0202565	+	0.0350853i	−0.855719	+	0.517440i	$0.826885\pi$
$24$	−164.945	+	95.2311i	−1.40289	+	0.809957i
$25$	117.116			0.936932
$26$		0			0
$27$	186.054			1.32615
$28$	−106.055	+	61.2311i	−0.715806	+	0.413271i
$29$	−70.3466	−	121.844i	−0.450449	−	0.780201i	0.547964	−	0.836502i	$-0.315403\pi$
$29$	−70.3466	−	121.844i	−0.450449	−	0.780201i	−0.998414	+	0.0563003i	$0.982070\pi$
$30$	−55.6155	+	96.3289i	−0.338465	+	0.586239i
$31$		−	136.155i		−	0.788845i	−0.918929	−	0.394423i	$-0.870945\pi$
$31$		−	136.155i		−	0.788845i	0.918929	−	0.394423i	$-0.129055\pi$
$32$	161.515	+	93.2505i	0.892250	+	0.515141i
$33$	−296.508	−	171.189i	−1.56410	−	0.903035i
$34$		−	9.19224i		−	0.0463663i
$35$	−13.4233	+	23.2498i	−0.0648272	+	0.112284i
$36$	310.097	+	537.104i	1.43563	+	2.48659i
$37$	−160.828	+	92.8542i	−0.714594	+	0.412571i	−0.812760	−	0.582599i	$-0.802036\pi$
$37$	−160.828	+	92.8542i	−0.714594	+	0.412571i	0.0981657	+	0.995170i	$0.468702\pi$
$38$	−274.570			−1.17214
$39$		0			0
$40$	−61.5767			−0.243403
$41$	−268.668	+	155.116i	−1.02339	+	0.590853i	−0.915083	−	0.403265i	$-0.867875\pi$
$41$	−268.668	+	155.116i	−1.02339	+	0.590853i	−0.108304	+	0.994118i	$0.534542\pi$
$42$	189.393	+	328.038i	0.695809	+	1.20518i
$43$	213.735	−	370.200i	0.758008	−	1.31291i	−0.185857	−	0.982577i	$-0.559506\pi$
$43$	213.735	−	370.200i	0.758008	−	1.31291i	0.943865	−	0.330331i	$-0.107160\pi$
$44$		−	504.924i		−	1.73000i
$45$	117.746	+	67.9806i	0.390056	+	0.225199i
$46$	17.6535	+	10.1922i	0.0565840	+	0.0326688i
$47$		−	258.617i		−	0.802622i	−0.915942	−	0.401311i	$-0.868555\pi$
$47$		−	258.617i		−	0.802622i	0.915942	−	0.401311i	$-0.131445\pi$
$48$	10.5227	−	18.2259i	0.0316422	−	0.0548059i
$49$	−125.788	−	217.872i	−0.366730	−	0.635195i
$50$	462.659	−	267.116i	1.30860	−	0.755519i
$51$	−17.5009			−0.0480514
$52$		0			0
$53$	612.656			1.58783			0.793913	−	0.608031i	$-0.208040\pi$
$53$	612.656			1.58783			0.793913	+	0.608031i	$0.208040\pi$
$54$	734.991	−	424.348i	1.85222	−	1.06938i
$55$	−55.3457	−	95.8615i	−0.135687	−	0.235017i
$56$	−104.847	+	181.600i	−0.250191	+	0.433344i
$57$			522.749i			1.21473i
$58$	−555.797	−	320.890i	−1.25827	−	0.726463i
$59$	448.502	+	258.943i	0.989661	+	0.571381i	0.905173	−	0.425044i	$-0.139741\pi$
$59$	448.502	+	258.943i	0.989661	+	0.571381i	0.0844878	+	0.996425i	$0.473075\pi$
$60$			312.311i			0.671985i
$61$	80.6553	−	139.699i	0.169293	−	0.293223i	−0.768879	−	0.639395i	$-0.779185\pi$
$61$	80.6553	−	139.699i	0.169293	−	0.293223i	0.938171	+	0.346171i	$0.112518\pi$
$62$	−310.540	−	537.871i	−0.636106	−	1.10177i
$63$	400.971	−	231.501i	0.801867	−	0.462958i
$64$	831.348			1.62373
$65$		0			0
$66$	−1561.77			−2.91274
$67$	43.2135	−	24.9493i	0.0787966	−	0.0454933i	−0.460084	−	0.887875i	$-0.652181\pi$
$67$	43.2135	−	24.9493i	0.0787966	−	0.0454933i	0.538881	+	0.842382i	$0.318847\pi$
$68$	−12.9048	−	22.3518i	−0.0230138	−	0.0398611i
$69$	19.4048	−	33.6101i	0.0338560	−	0.0586403i
$70$			122.462i			0.209100i
$71$	242.455	+	139.982i	0.405269	+	0.233982i	0.688755	−	0.724994i	$-0.258158\pi$
$71$	242.455	+	139.982i	0.405269	+	0.233982i	−0.283486	+	0.958976i	$0.591491\pi$
$72$	919.689	+	530.982i	1.50537	+	0.869123i
$73$			467.732i			0.749916i	0.927042	+	0.374958i	$0.122343\pi$
$73$			467.732i			0.749916i	−0.927042	+	0.374958i	$0.877657\pi$
$74$	−423.559	+	733.626i	−0.665375	+	1.15246i
$75$	−508.558	−	880.849i	−0.782977	−	1.35616i
$76$	−667.643	+	385.464i	−1.00768	+	0.581786i
$77$	−376.948			−0.557886
$78$		0			0
$79$	37.5379			0.0534600			0.0267300	−	0.999643i	$-0.491491\pi$
$79$	37.5379			0.0534600			0.0267300	+	0.999643i	$0.491491\pi$
$80$	5.89247	−	3.40202i	0.00823497	−	0.00475446i
$81$	−154.193	−	267.070i	−0.211513	−	0.366352i
$82$	−707.568	+	1225.54i	−0.952900	+	1.65047i
$83$			76.1553i			0.100712i	0.998731	+	0.0503562i	$0.0160357\pi$
$83$			76.1553i			0.100712i	−0.998731	+	0.0503562i	$0.983964\pi$
$84$	921.054	+	531.771i	1.19637	+	0.690726i
$85$	−4.90004	−	2.82904i	−0.00625275	−	0.00361003i
$86$		−	1949.93i		−	2.44496i
$87$	−610.936	+	1058.17i	−0.752865	+	1.30400i
$88$	−432.294	−	748.754i	−0.523666	−	0.907017i
$89$	175.635	−	101.403i	0.209183	−	0.120772i	−0.391749	−	0.920072i	$-0.628130\pi$
$89$	175.635	−	101.403i	0.209183	−	0.120772i	0.600932	+	0.799300i	$0.294796\pi$
$90$	620.194			0.726380
$91$		0			0
$92$	57.2348			0.0648602
$93$	−1024.04	+	591.231i	−1.14181	+	0.659224i
$94$	−589.848	−	1021.65i	−0.647215	−	1.12101i
$95$	−84.5028	+	146.363i	−0.0912611	+	0.158069i
$96$		−	1619.70i		−	1.72198i
$97$	−1017.03	−	587.184i	−1.06458	−	0.614634i	−0.137883	−	0.990449i	$-0.544030\pi$
$97$	−1017.03	−	587.184i	−1.06458	−	0.614634i	−0.926695	+	0.375814i	$0.877363\pi$
$98$	−993.834	−	573.790i	−1.02441	−	0.591445i
$99$			1909.01i			1.93800i
$100$	750.000	−	1299.04i	0.750000	−	1.29904i
$101$	485.348	+	840.648i	0.478158	+	0.828194i	0.999686	−	0.0250397i	$-0.00797123\pi$
$101$	485.348	+	840.648i	0.478158	+	0.828194i	−0.521528	+	0.853234i	$0.674638\pi$
$102$	−69.1360	+	39.9157i	−0.0671126	+	0.0387475i
$103$	1899.70			1.81731			0.908654	−	0.417550i	$-0.137111\pi$
$103$	1899.70			1.81731			0.908654	+	0.417550i	$0.137111\pi$
$104$		0			0
$105$	233.153			0.216699
$106$	2420.25	−	1397.33i	2.21769	−	1.28039i
$107$	953.247	+	1651.07i	0.861251	+	1.49173i	0.870722	+	0.491775i	$0.163652\pi$
$107$	953.247	+	1651.07i	0.861251	+	1.49173i	−0.00947163	+	0.999955i	$0.503015\pi$
$108$	1191.47	−	2063.68i	1.06157	−	1.83868i
$109$			896.004i			0.787354i	0.919249	+	0.393677i	$0.128797\pi$
$109$			896.004i			0.787354i	−0.919249	+	0.393677i	$0.871203\pi$
$110$	−437.277	−	252.462i	−0.379025	−	0.218830i
$111$	1396.74	+	806.407i	1.19435	+	0.689556i
$112$		−	23.1704i		−	0.0195482i
$113$	167.441	−	290.017i	0.139394	−	0.241438i	−0.787873	−	0.615837i	$-0.788818\pi$
$113$	167.441	−	290.017i	0.139394	−	0.241438i	0.927267	+	0.374400i	$0.122151\pi$
$114$	1192.27	+	2065.08i	0.979532	+	1.69660i
$115$	10.8662	−	6.27361i	0.00881112	−	0.00508710i
$116$	−1801.96			−1.44231
$117$		0			0
$118$	2362.36			1.84299
$119$	−16.6866	+	9.63401i	−0.0128543	+	0.00742141i
$120$	267.386	+	463.127i	0.203408	+	0.352312i
$121$	111.598	−	193.293i	0.0838452	−	0.145224i
$122$		−	735.827i		−	0.546054i
$123$	2333.29	+	1347.13i	1.71045	+	0.987530i
$124$	−1510.21	−	871.922i	−1.09372	−	0.631459i
$125$		−	679.806i		−	0.486430i
$126$	1056.00	−	1829.05i	0.746637	−	1.29321i
$127$	310.447	+	537.709i	0.216911	+	0.375701i	0.953862	−	0.300245i	$-0.0970686\pi$
$127$	310.447	+	537.709i	0.216911	+	0.375701i	−0.736951	+	0.675946i	$0.763735\pi$
$128$	1992.06	−	1150.11i	1.37558	−	0.794193i
$129$	−3712.44			−2.53381
$130$		0			0
$131$	−1331.70			−0.888180			−0.444090	−	0.895982i	$-0.646473\pi$
$131$	−1331.70			−0.888180			−0.444090	+	0.895982i	$0.646473\pi$
$132$	−3797.60	+	2192.55i	−2.50408	+	1.44573i
$133$	287.766	+	498.425i	0.187612	+	0.324954i
$134$	113.808	−	197.121i	0.0733694	−	0.127079i
$135$		−	522.396i		−	0.333042i
$136$	−38.2732	−	22.0971i	−0.0241316	−	0.0139324i
$137$	−538.681	−	311.008i	−0.335932	−	0.193950i	0.322540	−	0.946556i	$-0.395463\pi$
$137$	−538.681	−	311.008i	−0.335932	−	0.193950i	−0.658471	+	0.752606i	$0.728797\pi$
$138$		−	177.032i		−	0.109203i
$139$	−165.290	+	286.291i	−0.100861	+	0.174697i	−0.912040	−	0.410102i	$-0.865493\pi$
$139$	−165.290	+	286.291i	−0.100861	+	0.174697i	0.811178	+	0.584799i	$0.198827\pi$
$140$	171.922	+	297.778i	0.103786	+	0.179763i
$141$	−1945.10	+	1123.00i	−1.16175	+	0.670736i
$142$	1277.07			0.754711
$143$		0			0
$144$	−117.344			−0.0679073
$145$	−342.109	+	197.517i	−0.195935	+	0.113123i
$146$	1066.79	+	1847.74i	0.604715	+	1.04740i
$147$	−1092.43	+	1892.14i	−0.612939	+	1.06164i
$148$			2378.51i			1.32103i
$149$	−1567.97	−	905.269i	−0.862102	−	0.497735i	0.00261337	−	0.999997i	$-0.499168\pi$
$149$	−1567.97	−	905.269i	−0.862102	−	0.497735i	−0.864716	+	0.502262i	$0.832501\pi$
$150$	−4018.04	−	2319.82i	−2.18714	−	1.26275i
$151$		−	423.239i		−	0.228097i	−0.993475	−	0.114049i	$-0.963618\pi$
$151$		−	423.239i		−	0.228097i	0.993475	−	0.114049i	$-0.0363819\pi$
$152$	−660.034	+	1143.21i	−0.352209	+	0.610045i
$153$	48.7902	+	84.5071i	0.0257808	+	0.0446536i
$154$	−1489.10	+	859.734i	−0.779190	+	0.449866i
$155$	−382.292			−0.198106
$156$		0			0
$157$	1322.17			0.672105			0.336052	−	0.941843i	$-0.390908\pi$
$157$	1322.17			0.672105			0.336052	+	0.941843i	$0.390908\pi$
$158$	148.290	−	85.6155i	0.0746668	−	0.0431089i
$159$	−2660.35	−	4607.87i	−1.32692	−	2.29829i
$160$	261.825	−	453.495i	0.129369	−	0.224074i
$161$		−	42.7283i		−	0.0209159i
$162$	−1218.26	−	703.360i	−0.590835	−	0.341119i
$163$	3123.23	+	1803.20i	1.50080	+	0.866486i	1.00000		0.000922205i	$0.000293547\pi$
$163$	3123.23	+	1803.20i	1.50080	+	0.866486i	0.500798	+	0.865564i	$0.333040\pi$
$164$			3973.37i			1.89188i
$165$	−480.658	+	832.524i	−0.226783	+	0.392800i
$166$	173.693	+	300.845i	0.0812121	+	0.140663i
$167$	−2957.85	+	1707.72i	−1.37057	+	0.791300i	−0.991000	−	0.133863i	$-0.957262\pi$
$167$	−2957.85	+	1707.72i	−1.37057	+	0.791300i	−0.379571	+	0.925162i	$0.623929\pi$
$168$	1821.11			0.836321
$169$		0			0
$170$	−25.8096			−0.0116442
$171$	2524.21	−	1457.35i	1.12884	−	0.651734i
$172$	−2737.47	−	4741.44i	−1.21355	−	2.10193i
$173$	1171.11	−	2028.43i	0.514671	−	0.891436i	−0.485184	−	0.874412i	$-0.661247\pi$
$173$	1171.11	−	2028.43i	0.514671	−	0.891436i	0.999855	−	0.0170243i	$-0.00541926\pi$
$174$			5573.63i			2.42837i
$175$	−969.788	−	559.908i	−0.418909	−	0.241857i
$176$	82.7350	+	47.7671i	0.0354340	+	0.0204578i
$177$		−	4497.66i		−	1.90997i
$178$	462.555	−	801.169i	0.194775	−	0.337360i
$179$	−333.446	−	577.545i	−0.139234	−	0.241160i	0.787973	−	0.615710i	$-0.211131\pi$
$179$	−333.446	−	577.545i	−0.139234	−	0.241160i	−0.927207	+	0.374550i	$0.877797\pi$
$180$	1508.06	−	870.679i	0.624468	−	0.360537i
$181$	701.037			0.287888			0.143944	−	0.989586i	$-0.454022\pi$
$181$	701.037			0.287888			0.143944	+	0.989586i	$0.454022\pi$
$182$		0			0
$183$	−1400.93			−0.565899
$184$	84.8737	−	49.0019i	0.0340053	−	0.0196330i
$185$	260.713	+	451.567i	0.103611	+	0.179459i
$186$	−2696.93	+	4671.22i	−1.06316	+	1.84146i
$187$		−	79.4440i		−	0.0310670i
$188$	−2868.55	−	1656.16i	−1.11282	−	0.642487i
$189$	−1540.63	−	889.482i	−0.592933	−	0.342330i
$190$			770.928i			0.294363i
$191$	−650.440	+	1126.59i	−0.246409	+	0.426793i	−0.962527	−	0.271186i	$-0.912584\pi$
$191$	−650.440	+	1126.59i	−0.246409	+	0.426793i	0.716118	+	0.697980i	$0.245917\pi$
$192$	−3609.98	−	6252.68i	−1.35692	−	2.35025i
$193$	−449.756	+	259.667i	−0.167742	+	0.0968457i	−0.581521	−	0.813532i	$-0.697542\pi$
$193$	−449.756	+	259.667i	−0.167742	+	0.0968457i	0.413779	+	0.910377i	$0.364209\pi$
$194$	−5356.94			−1.98251
$195$		0			0
$196$	−3222.14			−1.17425
$197$	−2702.91	+	1560.52i	−0.977534	+	0.564379i	−0.901525	−	0.432728i	$-0.857551\pi$
$197$	−2702.91	+	1560.52i	−0.977534	+	0.564379i	−0.0760091	+	0.997107i	$0.524218\pi$
$198$	4354.01	+	7541.38i	1.56276	+	2.70678i
$199$	618.529	−	1071.32i	0.220333	−	0.381629i	−0.734576	−	0.678527i	$-0.762619\pi$
$199$	618.529	−	1071.32i	0.220333	−	0.381629i	0.954909	+	0.296898i	$0.0959521\pi$
$200$		−	2568.47i		−	0.908090i
$201$	−375.295	−	216.677i	−0.131698	−	0.0760358i
$202$	3834.66	+	2213.94i	1.33567	+	0.771151i
$203$			1345.25i			0.465112i
$204$	−112.074	+	194.118i	−0.0384644	+	0.0666223i
$205$	435.528	+	754.356i	0.148383	+	0.257007i
$206$	7504.60	−	4332.78i	2.53821	−	1.46543i
$207$	−216.392			−0.0726584
$208$		0			0
$209$	−2372.98			−0.785369
$210$	921.054	−	531.771i	0.302661	−	0.174741i
$211$	1265.83	+	2192.49i	0.413003	+	0.715342i	0.995217	−	0.0976940i	$-0.0311466\pi$
$211$	1265.83	+	2192.49i	0.413003	+	0.715342i	−0.582214	+	0.813036i	$0.697813\pi$
$212$	3923.38	−	6795.49i	1.27103	−	2.20149i
$213$		−	2431.38i		−	0.782139i
$214$	7531.45	+	4348.28i	2.40579	+	1.38898i
$215$	−1039.44	−	600.118i	−0.329716	−	0.190362i
$216$		−	4080.33i		−	1.28533i
$217$	−650.928	+	1127.44i	−0.203631	+	0.352699i
$218$	2043.58	+	3539.59i	0.634904	+	1.09969i
$219$	3517.88	−	2031.05i	1.08546	−	0.626691i
$220$	−1417.71			−0.434463
$221$		0			0
$222$	7356.93			2.22417
$223$	1035.36	−	597.766i	0.310910	−	0.179504i	−0.336424	−	0.941711i	$-0.609217\pi$
$223$	1035.36	−	597.766i	0.310910	−	0.179504i	0.647333	+	0.762207i	$0.275884\pi$
$224$	−891.619	−	1544.33i	−0.265955	−	0.460647i
$225$	−2835.58	+	4911.37i	−0.840173	+	1.45522i
$226$		−	1527.58i		−	0.449617i
$227$	−752.742	−	434.596i	−0.220094	−	0.127071i	0.385900	−	0.922541i	$-0.373891\pi$
$227$	−752.742	−	434.596i	−0.220094	−	0.127071i	−0.605994	+	0.795469i	$0.707224\pi$
$228$	5798.25	+	3347.62i	1.68420	+	0.972376i
$229$			4684.64i			1.35183i	0.736978	+	0.675916i	$0.236252\pi$
$229$			4684.64i			1.35183i	−0.736978	+	0.675916i	$0.763748\pi$
$230$	28.6174	−	49.5668i	0.00820424	−	0.0142102i
$231$	1636.83	+	2835.08i	0.466215	+	0.807508i
$232$	−2672.14	+	1542.76i	−0.756184	+	0.436583i
$233$	4868.99			1.36900			0.684502	−	0.729011i	$-0.260020\pi$
$233$	4868.99			1.36900			0.684502	+	0.729011i	$0.260020\pi$
$234$		0			0
$235$	−726.137			−0.201566
$236$	5744.31	−	3316.48i	1.58442	−	0.914764i
$237$	−163.002	−	282.328i	−0.0446756	−	0.0773803i
$238$	−43.9460	+	76.1167i	−0.0119689	+	0.0207307i
$239$		−	4807.53i		−	1.30114i	−0.759444	−	0.650572i	$-0.774529\pi$
$239$		−	4807.53i		−	1.30114i	0.759444	−	0.650572i	$-0.225471\pi$
$240$	−51.1740	−	29.5454i	−0.0137636	−	0.00794643i
$241$	−5088.73	−	2937.98i	−1.36014	−	0.785278i	−0.370499	−	0.928833i	$-0.620813\pi$
$241$	−5088.73	−	2937.98i	−1.36014	−	0.785278i	−0.989642	+	0.143555i	$0.954147\pi$
$242$		−	1018.12i		−	0.270443i
$243$	1172.61	−	2031.03i	0.309561	−	0.536175i
$244$	−1033.01	−	1789.23i	−0.271033	−	0.469442i
$245$	−611.733	+	353.184i	−0.159519	+	0.0920984i
$246$	12290.0			3.18528
$247$		0			0
$248$	−2986.00			−0.764562
$249$	572.774	−	330.691i	0.145775	−	0.0841635i
$250$	−1550.49	−	2685.52i	−0.392245	−	0.679389i
$251$	2903.13	−	5028.38i	0.730057	−	1.26450i	−0.226802	−	0.973941i	$-0.572827\pi$
$251$	2903.13	−	5028.38i	0.730057	−	1.26450i	0.956858	−	0.290554i	$-0.0938397\pi$
$252$		−	5930.02i		−	1.48237i
$253$	152.570	+	88.0866i	0.0379131	+	0.0218891i
$254$	2452.79	+	1416.12i	0.605912	+	0.349823i
$255$			49.1385i			0.0120673i
$256$	1920.92	−	3327.12i	0.468974	−	0.812286i
$257$	−597.930	−	1035.65i	−0.145128	−	0.251369i	0.784293	−	0.620391i	$-0.213026\pi$
$257$	−597.930	−	1035.65i	−0.145128	−	0.251369i	−0.929421	+	0.369022i	$0.879693\pi$
$258$	−14665.7	+	8467.24i	−3.53894	+	2.04321i
$259$	1775.66			0.426001
$260$		0			0
$261$	6812.83			1.61572
$262$	−5260.79	+	3037.32i	−1.24051	+	0.716207i
$263$	−117.092	−	202.810i	−0.0274533	−	0.0475505i	0.851972	−	0.523587i	$-0.175406\pi$
$263$	−117.092	−	202.810i	−0.0274533	−	0.0475505i	−0.879426	+	0.476036i	$0.842073\pi$
$264$	−3754.32	+	6502.68i	−0.875237	+	1.51595i
$265$		−	1720.19i		−	0.398757i
$266$	2273.59	+	1312.66i	0.524071	+	0.302572i
$267$	−1525.33	−	880.650i	−0.349621	−	0.201854i
$268$		−	639.091i		−	0.145667i
$269$	1334.13	−	2310.79i	0.302393	−	0.523760i	−0.674285	−	0.738471i	$-0.735548\pi$
$269$	1334.13	−	2310.79i	0.302393	−	0.523760i	0.976677	+	0.214712i	$0.0688813\pi$
$270$	−1191.47	−	2063.68i	−0.268557	−	0.465155i
$271$	4937.45	−	2850.64i	1.10675	−	0.638982i	0.168763	−	0.985657i	$-0.446023\pi$
$271$	4937.45	−	2850.64i	1.10675	−	0.638982i	0.937985	+	0.346675i	$0.112689\pi$
$272$	4.88331			0.00108858
$273$		0			0
$274$	−2837.35			−0.625587
$275$	3998.54	−	2308.56i	0.876804	−	0.506223i
$276$	−248.532	−	430.471i	−0.0542025	−	0.0938815i
$277$	−3576.24	+	6194.24i	−0.775725	+	1.34359i	0.158662	+	0.987333i	$0.449282\pi$
$277$	−3576.24	+	6194.24i	−0.775725	+	1.34359i	−0.934386	+	0.356261i	$0.884051\pi$
$278$			1507.96i			0.325329i
$279$	5709.78	+	3296.54i	1.22522	+	0.707380i
$280$	509.889	+	294.384i	0.108827	+	0.0628316i
$281$		−	6132.87i		−	1.30198i	−0.759086	−	0.650990i	$-0.774354\pi$
$281$		−	6132.87i		−	1.30198i	0.759086	−	0.650990i	$-0.225646\pi$
$282$	−5122.63	+	8872.66i	−1.08173	+	1.87361i
$283$	1688.58	+	2924.70i	0.354683	+	0.614330i	0.987064	−	0.160328i	$-0.0512553\pi$
$283$	1688.58	+	2924.70i	0.354683	+	0.614330i	−0.632380	+	0.774658i	$0.717922\pi$
$284$	3105.31	−	1792.85i	0.648824	−	0.374599i
$285$	1467.76			0.305061
$286$		0			0
$287$	2966.29			0.610086
$288$	−7821.07	+	4515.49i	−1.60021	+	0.923882i
$289$	2454.47	+	4251.27i	0.499587	+	0.865310i
$290$	−900.982	+	1560.55i	−0.182440	+	0.315995i
$291$			10199.0i			2.05455i
$292$	5188.01	+	2995.30i	1.03974	+	0.600297i
$293$	4074.45	+	2352.38i	0.812395	+	0.469037i	0.847787	−	0.530337i	$-0.177935\pi$
$293$	4074.45	+	2352.38i	0.812395	+	0.469037i	−0.0353917	+	0.999374i	$0.511268\pi$
$294$			9966.34i			1.97704i
$295$	727.050	−	1259.29i	0.143493	−	0.248537i
$296$	2036.37	+	3527.10i	0.399871	+	0.692596i
$297$	6352.18	−	3667.43i	1.24105	−	0.716518i
$298$	−8258.86			−1.60545
$299$		0			0
$300$	−13027.0			−2.50704
$301$	−3539.69	+	2043.64i	−0.677822	+	0.391341i
$302$	−965.312	−	1671.97i	−0.183932	−	0.318580i
$303$	4215.09	−	7300.74i	0.799176	−	1.38421i
$304$		−	145.863i		−	0.0275192i
$305$	−392.242	−	226.461i	−0.0736384	−	0.0425151i
$306$	385.484	+	222.559i	0.0720152	+	0.0415780i
$307$			5130.49i			0.953787i	0.878961	+	0.476894i	$0.158237\pi$
$307$			5130.49i			0.953787i	−0.878961	+	0.476894i	$0.841763\pi$
$308$	−2413.93	+	4181.05i	−0.446579	+	0.773498i
$309$	−8249.11	−	14287.9i	−1.51869	−	2.63045i
$310$	−1510.21	+	871.922i	−0.276692	+	0.159748i
$311$	−7948.94			−1.44933			−0.724667	−	0.689099i	$-0.758006\pi$
$311$	−7948.94			−1.44933			−0.724667	+	0.689099i	$0.758006\pi$
$312$		0			0
$313$	−8521.87			−1.53893			−0.769465	−	0.638689i	$-0.779477\pi$
$313$	−8521.87			−1.53893			−0.769465	+	0.638689i	$0.779477\pi$
$314$	5223.12	−	3015.57i	0.938718	−	0.541969i
$315$	−650.000	−	1125.83i	−0.116265	−	0.201376i
$316$	240.388	−	416.365i	0.0427940	−	0.0741213i
$317$			6662.46i			1.18044i	0.807241	+	0.590222i	$0.200960\pi$
$317$			6662.46i			1.18044i	−0.807241	+	0.590222i	$0.799040\pi$
$318$	−21019.0	−	12135.3i	−3.70657	−	2.13999i
$319$	−4803.49	−	2773.29i	−0.843083	−	0.486754i
$320$		−	2334.23i		−	0.407773i
$321$	8278.62	−	14339.0i	1.43946	−	2.49322i
$322$	−97.4536	−	168.795i	−0.0168661	−	0.0292129i
$323$	−105.046	+	60.6483i	−0.0180957	+	0.0104476i
$324$	−3949.74			−0.677253
$325$		0			0
$326$	16450.8			2.79486
$327$	6738.96	−	3890.74i	1.13965	−	0.657977i
$328$	3401.82	+	5892.12i	0.572665	+	0.991884i
$329$	−1236.39	+	2141.49i	−0.207187	+	0.358858i
$330$			4385.09i			0.731489i
$331$	−3387.69	−	1955.89i	−0.562551	−	0.324789i	0.191618	−	0.981470i	$-0.438627\pi$
$331$	−3387.69	−	1955.89i	−0.562551	−	0.324789i	−0.754169	+	0.656681i	$0.771960\pi$
$332$	844.703	+	487.689i	0.139636	+	0.0806188i
$333$		−	8992.61i		−	1.47986i
$334$	−7789.84	+	13492.4i	−1.27617	+	2.21039i
$335$	−70.0519	−	121.333i	−0.0114249	−	0.0197885i
$336$	−174.268	+	100.614i	−0.0282949	+	0.0163361i
$337$	627.211			0.101384			0.0506919	−	0.998714i	$-0.483857\pi$
$337$	627.211			0.101384			0.0506919	+	0.998714i	$0.483857\pi$
$338$		0			0
$339$	−2908.34			−0.465957
$340$	−62.7586	+	36.2337i	−0.0100105	+	0.00577955i
$341$	−2683.84	−	4648.56i	−0.426212	−	0.738221i
$342$	6647.79	−	11514.3i	1.05109	−	1.82053i
$343$			5685.08i			0.894943i
$344$	−8118.82	−	4687.40i	−1.27249	−	0.734674i
$345$	−94.3693	−	54.4841i	−0.0147266	−	0.00850240i
$346$		−	10684.2i		−	1.66007i
$347$	1911.51	−	3310.83i	0.295721	−	0.512204i	−0.679431	−	0.733739i	$-0.737773\pi$
$347$	1911.51	−	3310.83i	0.295721	−	0.512204i	0.975152	+	0.221535i	$0.0711068\pi$
$348$	7824.72	+	13552.8i	1.20531	+	2.08767i
$349$	2953.72	−	1705.33i	0.453035	−	0.261560i	−0.256076	−	0.966657i	$-0.582430\pi$
$349$	2953.72	−	1705.33i	0.453035	−	0.261560i	0.709111	+	0.705097i	$0.249096\pi$
$350$	−5108.10			−0.780112
$351$		0			0
$352$	7352.48			1.11332
$353$	4839.03	−	2793.82i	0.729620	−	0.421246i	−0.0886632	−	0.996062i	$-0.528259\pi$
$353$	4839.03	−	2793.82i	0.729620	−	0.421246i	0.818283	+	0.574815i	$0.194926\pi$
$354$	−10258.2	−	17767.6i	−1.54015	−	2.66763i
$355$	393.035	−	680.757i	0.0587609	−	0.101777i
$356$		−	2597.49i		−	0.386704i
$357$	144.917	+	83.6680i	0.0214841	+	0.0124039i
$358$	−2634.50	−	1521.03i	−0.388932	−	0.224550i
$359$			2230.14i			0.327861i	0.986472	+	0.163931i	$0.0524173\pi$
$359$			2230.14i			0.327861i	−0.986472	+	0.163931i	$0.947583\pi$
$360$	1490.87	−	2582.27i	0.218266	−	0.378049i
$361$	−1617.95	−	2802.37i	−0.235887	−	0.408568i
$362$	2769.39	−	1598.91i	0.402088	−	0.232146i
$363$	−1938.38			−0.280272
$364$		0			0
$365$	1313.28			0.188330
$366$	−5534.25	+	3195.20i	−0.790382	+	0.456327i
$367$	4349.57	+	7533.68i	0.618653	+	1.07154i	0.989732	+	0.142938i	$0.0456548\pi$
$367$	4349.57	+	7533.68i	0.618653	+	1.07154i	−0.371078	+	0.928602i	$0.621012\pi$
$368$	−5.41455	+	9.37828i	−0.000766992	+	0.00132847i
$369$		−	15022.4i		−	2.11934i
$370$	2059.85	+	1189.25i	0.289423	+	0.167098i
$371$	−5073.13	−	2928.97i	−0.709929	−	0.409878i
$372$			15144.7i			2.11080i
$373$	−5482.09	+	9495.26i	−0.760997	+	1.31809i	0.181340	+	0.983420i	$0.441956\pi$
$373$	−5482.09	+	9495.26i	−0.760997	+	1.31809i	−0.942337	+	0.334665i	$0.891377\pi$
$374$	−181.194	−	313.837i	−0.0250517	−	0.0433908i
$375$	−5112.91	+	2951.94i	−0.704079	+	0.406500i
$376$	−5671.70			−0.777914
$377$		0			0
$378$	−8114.84			−1.10419
$379$	−12046.5	+	6955.06i	−1.63269	+	0.942631i	−0.649425	+	0.760426i	$0.724990\pi$
$379$	−12046.5	+	6955.06i	−1.63269	+	0.942631i	−0.983260	+	0.182206i	$0.941676\pi$
$380$	1082.29	+	1874.58i	0.146106	+	0.253064i
$381$	2696.12	−	4669.82i	0.362537	−	0.627932i
$382$			5934.03i			0.794794i
$383$	−428.469	−	247.377i	−0.0571638	−	0.0330035i	0.471146	−	0.882055i	$-0.343841\pi$
$383$	−428.469	−	247.377i	−0.0571638	−	0.0330035i	−0.528310	+	0.849052i	$0.677174\pi$
$384$	−17300.3	−	9988.35i	−2.29910	−	1.32738i
$385$			1058.38i			0.140104i
$386$	−1184.48	+	2051.59i	−0.156188	+	0.270526i
$387$	10349.8	+	17926.3i	1.35945	+	2.35464i
$388$	−13025.9	+	7520.52i	−1.70436	+	0.984011i
$389$	4140.47			0.539666			0.269833	−	0.962907i	$-0.413032\pi$
$389$	4140.47			0.539666			0.269833	+	0.962907i	$0.413032\pi$
$390$		0			0
$391$	9.00524			0.00116474
$392$	−4778.12	+	2758.65i	−0.615641	+	0.355441i
$393$	5782.70	+	10015.9i	0.742236	+	1.28559i
$394$	−7118.41	+	12329.5i	−0.910204	+	1.57652i
$395$		−	105.398i		−	0.0134256i
$396$	21174.4	+	12225.0i	2.68700	+	1.55134i
$397$	1629.68	+	940.896i	0.206023	+	0.118948i	0.599462	−	0.800403i	$-0.295381\pi$
$397$	1629.68	+	940.896i	0.206023	+	0.118948i	−0.393439	+	0.919351i	$0.628715\pi$
$398$		−	5642.90i		−	0.710686i
$399$	2499.15	−	4328.65i	0.313568	−	0.543116i
$400$	141.904	+	245.784i	0.0177380	+	0.0307231i
$401$	365.259	−	210.883i	0.0454867	−	0.0262618i	−0.477084	−	0.878858i	$-0.658306\pi$
$401$	365.259	−	210.883i	0.0454867	−	0.0262618i	0.522571	+	0.852596i	$0.324973\pi$
$402$	−1976.76			−0.245254
$403$		0			0
$404$	12432.5			1.53103
$405$	−749.871	+	432.938i	−0.0920034	+	0.0531182i
$406$	3068.20	+	5314.28i	0.375055	+	0.649615i
$407$	−3660.62	+	6340.37i	−0.445823	+	0.772188i
$408$			383.811i			0.0465722i
$409$	2208.55	+	1275.11i	0.267007	+	0.154157i	0.627527	−	0.778595i	$-0.284067\pi$
$409$	2208.55	+	1275.11i	0.267007	+	0.154157i	−0.360520	+	0.932752i	$0.617401\pi$
$410$	3441.04	+	1986.68i	0.414489	+	0.239306i
$411$			5401.99i			0.648322i
$412$	12165.4	−	21071.2i	1.45473	−	2.51966i
$413$	−2475.89	−	4288.37i	−0.294990	−	0.510937i
$414$	−854.839	+	493.542i	−0.101481	+	0.0585900i
$415$	213.826			0.0252923
$416$		0			0
$417$	2870.98			0.337152
$418$	−9374.25	+	5412.23i	−1.09691	+	0.633303i
$419$	−6192.41	−	10725.6i	−0.722002	−	1.25054i	−0.960196	−	0.279327i	$-0.909889\pi$
$419$	−6192.41	−	10725.6i	−0.722002	−	1.25054i	0.238194	−	0.971218i	$-0.423445\pi$
$420$	1493.09	−	2586.10i	0.173465	−	0.300450i
$421$		−	10463.0i		−	1.21124i	−0.795752	−	0.605622i	$-0.792924\pi$
$421$		−	10463.0i		−	1.21124i	0.795752	−	0.605622i	$-0.207076\pi$
$422$	10001.2	+	5774.17i	1.15367	+	0.666071i
$423$	10845.3	+	6261.55i	1.24661	+	0.719733i
$424$		−	13436.1i		−	1.53895i
$425$	118.004	−	204.389i	0.0134683	−	0.0233278i
$426$	−5545.44	−	9604.99i	−0.630698	−	1.09240i
$427$	−1335.74	+	771.190i	−0.151384	+	0.0874016i
$428$	24417.9			2.75767
$429$		0			0
$430$	−5474.94			−0.614012
$431$	3431.53	−	1981.19i	0.383506	−	0.221417i	−0.295837	−	0.955238i	$-0.595598\pi$
$431$	3431.53	−	1981.19i	0.383506	−	0.221417i	0.679342	+	0.733821i	$0.262265\pi$
$432$	225.432	+	390.459i	0.0251067	+	0.0434860i
$433$	−4197.07	+	7269.54i	−0.465816	+	0.806817i	−0.999238	−	0.0390321i	$-0.987573\pi$
$433$	−4197.07	+	7269.54i	−0.465816	+	0.806817i	0.533422	+	0.845849i	$0.320906\pi$
$434$			5938.48i			0.656812i
$435$	2971.10	+	1715.36i	0.327479	+	0.189070i
$436$	9938.34	+	5737.90i	1.09165	+	0.630265i
$437$		−	268.984i		−	0.0294446i
$438$	9264.72	−	16047.0i	1.01070	−	1.75058i
$439$	5087.26	+	8811.39i	0.553079	+	0.957960i	0.998050	+	0.0624156i	$0.0198804\pi$
$439$	5087.26	+	8811.39i	0.553079	+	0.957960i	−0.444972	+	0.895545i	$0.646786\pi$
$440$	−2102.33	+	1213.78i	−0.227783	+	0.131510i
$441$	12182.2			1.31543
$442$		0			0
$443$	−5880.74			−0.630705			−0.315353	−	0.948975i	$-0.602123\pi$
$443$	−5880.74			−0.630705			−0.315353	+	0.948975i	$0.602123\pi$
$444$	17889.1	−	10328.3i	1.91211	−	1.10396i
$445$	−284.716	−	493.142i	−0.0303299	−	0.0525330i
$446$	2726.74	−	4722.85i	0.289495	−	0.501420i
$447$			15723.9i			1.66379i
$448$	−6884.01	−	3974.49i	−0.725980	−	0.419145i
$449$	−9236.05	−	5332.43i	−0.970771	−	0.560475i	−0.0712996	−	0.997455i	$-0.522715\pi$
$449$	−9236.05	−	5332.43i	−0.970771	−	0.560475i	−0.899471	+	0.436980i	$0.856048\pi$
$450$			25869.3i			2.70998i
$451$	−6115.16	+	10591.8i	−0.638474	+	1.10587i
$452$	−2144.55	−	3714.47i	−0.223166	−	0.386535i
$453$	−3183.23	+	1837.84i	−0.330158	+	0.190617i
$454$	−3964.87			−0.409869
$455$		0			0
$456$	11464.3			1.17734
$457$	12842.2	−	7414.43i	1.31451	−	0.758933i	0.331671	−	0.943395i	$-0.392388\pi$
$457$	12842.2	−	7414.43i	1.31451	−	0.758933i	0.982840	+	0.184462i	$0.0590544\pi$
$458$	10684.6	+	18506.3i	1.09009	+	1.88808i
$459$	187.464	−	324.697i	0.0190633	−	0.0330186i
$460$		−	160.702i		−	0.0162886i
$461$	−8410.58	−	4855.85i	−0.849717	−	0.490585i	0.0108381	−	0.999941i	$-0.496550\pi$
$461$	−8410.58	−	4855.85i	−0.849717	−	0.490585i	−0.860555	+	0.509357i	$0.829883\pi$
$462$	12932.3	+	7466.49i	1.30231	+	0.751889i
$463$			11353.5i			1.13962i	0.821777	+	0.569809i	$0.192983\pi$
$463$			11353.5i			1.13962i	−0.821777	+	0.569809i	$0.807017\pi$
$464$	170.470	−	295.263i	0.0170558	−	0.0295415i
$465$	1660.04	+	2875.27i	0.165554	+	0.286747i
$466$	19234.6	−	11105.1i	1.91207	−	1.10393i
$467$	−6451.31			−0.639252			−0.319626	−	0.947544i	$-0.603557\pi$
$467$	−6451.31			−0.639252			−0.319626	+	0.947544i	$0.603557\pi$
$468$		0			0
$469$	−477.109			−0.0469741
$470$	−2868.55	+	1656.16i	−0.281524	+	0.162538i
$471$	−5741.29	−	9944.20i	−0.561666	−	0.972833i
$472$	5678.84	−	9836.04i	0.553792	−	0.959196i
$473$		−	16852.3i		−	1.63820i
$474$	−1287.85	−	743.542i	−0.124795	−	0.0720506i
$475$	−6105.05	−	3524.75i	−0.589724	−	0.340477i
$476$			246.780i			0.0237629i
$477$	−14833.4	+	25692.2i	−1.42385	+	2.46618i
$478$	−10964.9	−	18991.8i	−1.04921	−	1.81729i
$479$	−8284.79	+	4783.23i	−0.790275	+	0.456266i	−0.840059	−	0.542494i	$-0.817480\pi$
$479$	−8284.79	+	4783.23i	−0.790275	+	0.456266i	0.0497842	+	0.998760i	$0.484147\pi$
$480$	−4547.73			−0.432447
$481$		0			0
$482$	−26803.5			−2.53292
$483$	−321.365	+	185.540i	−0.0302746	+	0.0174790i
$484$	−1429.32	−	2475.66i	−0.134234	−	0.232500i
$485$	−1648.67	+	2855.59i	−0.154356	+	0.267352i
$486$		−	10697.9i		−	0.998489i
$487$	4258.35	+	2458.56i	0.396230	+	0.228764i	0.684856	−	0.728678i	$-0.259865\pi$
$487$	4258.35	+	2458.56i	0.396230	+	0.228764i	−0.288626	+	0.957442i	$0.593198\pi$
$488$	−3063.72	−	1768.84i	−0.284197	−	0.164081i
$489$		−	31320.3i		−	2.89643i
$490$	−1611.07	+	2790.45i	−0.148532	+	0.257265i
$491$	1475.41	+	2555.49i	0.135610	+	0.234883i	0.925830	−	0.377940i	$-0.123367\pi$
$491$	1475.41	+	2555.49i	0.135610	+	0.234883i	−0.790220	+	0.612823i	$0.790034\pi$
$492$	29884.2	−	17253.7i	2.73838	−	1.58101i
$493$	−283.519			−0.0259007
$494$		0			0
$495$	5360.04			0.486699
$496$	285.740	−	164.972i	0.0258671	−	0.0149344i
$497$	−1338.44	−	2318.25i	−0.120799	−	0.209231i
$498$	1508.47	−	2612.74i	0.135735	−	0.235100i
$499$		−	13430.1i		−	1.20484i	−0.798180	−	0.602418i	$-0.794204\pi$
$499$		−	13430.1i		−	1.20484i	0.798180	−	0.602418i	$-0.205796\pi$
$500$	−7540.30	−	4353.40i	−0.674425	−	0.389380i
$501$	25687.9	+	14830.9i	2.29072	+	1.32255i
$502$		−	26485.6i		−	2.35480i
$503$	−660.143	+	1143.40i	−0.0585175	+	0.101355i	−0.893800	−	0.448466i	$-0.851971\pi$
$503$	−660.143	+	1143.40i	−0.0585175	+	0.101355i	0.835283	+	0.549821i	$0.185304\pi$
$504$	−5077.02	−	8793.65i	−0.448707	−	0.777183i
$505$	2360.34	−	1362.74i	0.207988	−	0.120082i
$506$	803.623			0.0706036
$507$		0			0
$508$	7952.25			0.694536
$509$	−18114.2	+	10458.2i	−1.57740	+	0.910713i	−0.582180	+	0.813060i	$0.697800\pi$
$509$	−18114.2	+	10458.2i	−1.57740	+	0.910713i	−0.995221	+	0.0976524i	$0.968867\pi$
$510$	112.074	+	194.118i	0.00973082	+	0.0168543i
$511$	2236.12	−	3873.08i	0.193582	−	0.335293i
$512$			877.105i			0.0757089i
$513$	−9698.62	−	5599.50i	−0.834707	−	0.481918i
$514$	−4724.15	−	2727.49i	−0.405396	−	0.234055i
$515$		−	5333.90i		−	0.456388i
$516$	−23774.0	+	41177.8i	−2.02828	+	3.51308i
$517$	−5097.77	−	8829.60i	−0.433655	−	0.751113i
$518$	7014.60	−	4049.88i	0.594988	−	0.343517i
$519$	−20341.4			−1.72040
$520$		0			0
$521$	−10104.2			−0.849661			−0.424831	−	0.905273i	$-0.639666\pi$
$521$	−10104.2			−0.849661			−0.424831	+	0.905273i	$0.639666\pi$
$522$	26913.5	−	15538.5i	2.25665	−	1.30288i
$523$	−3565.61	−	6175.82i	−0.298113	−	0.516347i	0.677591	−	0.735439i	$-0.263024\pi$
$523$	−3565.61	−	6175.82i	−0.298113	−	0.516347i	−0.975704	+	0.219092i	$0.929691\pi$
$524$	−8528.08	+	14771.1i	−0.710975	+	1.23144i
$525$			9725.21i			0.808463i
$526$	−925.127	−	534.122i	−0.0766871	−	0.0442753i
$527$	−237.615	−	137.187i	−0.0196407	−	0.0113396i
$528$		−	829.682i		−	0.0683849i
$529$	6073.52	−	10519.6i	0.499179	−	0.864604i
$530$	−3923.38	−	6795.49i	−0.321548	−	0.556938i
$531$	−21717.9	+	12538.9i	−1.77491	+	1.02475i
$532$	7371.27			0.600724
$533$		0			0
$534$	−8034.26			−0.651080
$535$	4635.82	−	2676.49i	0.374624	−	0.216289i
$536$	−547.161	−	947.710i	−0.0440928	−	0.0763710i
$537$	−2895.86	+	5015.78i	−0.232711	+	0.403067i
$538$		−	12171.5i		−	0.975369i
$539$	−8589.22	−	4958.99i	−0.686390	−	0.396287i
$540$	−5794.33	−	3345.36i	−0.461756	−	0.266595i
$541$			16831.7i			1.33762i	0.743435	+	0.668809i	$0.233195\pi$
$541$			16831.7i			1.33762i	−0.743435	+	0.668809i	$0.766805\pi$
$542$	13003.3	−	22522.5i	1.03052	−	1.78491i
$543$	−3044.13	−	5272.59i	−0.240582	−	0.416701i
$544$	325.477	−	187.914i	0.0256520	−	0.0148102i
$545$	2515.77			0.197731
$546$		0			0
$547$	−9560.55			−0.747312			−0.373656	−	0.927567i	$-0.621896\pi$
$547$	−9560.55			−0.747312			−0.373656	+	0.927567i	$0.621896\pi$
$548$	−6899.30	+	3983.31i	−0.537816	+	0.310508i
$549$	3905.59	+	6764.69i	0.303619	+	0.525883i
$550$	10530.6	−	18239.6i	0.816412	−	1.41407i
$551$			8468.64i			0.654766i
$552$	−737.099	−	425.564i	−0.0568352	−	0.0328138i
$553$	−310.834	−	179.460i	−0.0239024	−	0.0138000i
$554$			32626.5i			2.50210i
$555$	2264.20	−	3921.71i	0.173171	−	0.299941i
$556$	2117.00	+	3666.75i	0.161476	+	0.279685i
$557$	−19769.5	+	11414.0i	−1.50388	+	0.868267i	−0.503893	+	0.863766i	$0.668099\pi$
$557$	−19769.5	+	11414.0i	−1.50388	+	0.868267i	−0.999990	+	0.00450060i	$0.998567\pi$
$558$	30074.7			2.28166
$559$		0			0
$560$	−65.0571			−0.00490922
$561$	−597.509	+	344.972i	−0.0449677	+	0.0259621i
$562$	−13987.7	−	24227.4i	−1.04989	−	1.81846i
$563$	10814.9	−	18731.9i	0.809578	−	1.40223i	−0.103579	−	0.994621i	$-0.533029\pi$
$563$	10814.9	−	18731.9i	0.809578	−	1.40223i	0.913157	−	0.407609i	$-0.133637\pi$
$564$			28766.3i			2.14766i
$565$	−814.299	−	470.136i	−0.0606333	−	0.0350066i
$566$	13341.2	+	7702.53i	0.990761	+	0.572016i
$567$			2948.65i			0.218398i
$568$	3069.92	−	5317.25i	0.226780	−	0.392794i
$569$	−5294.93	−	9171.09i	−0.390114	−	0.675698i	0.602350	−	0.798232i	$-0.294231\pi$
$569$	−5294.93	−	9171.09i	−0.390114	−	0.675698i	−0.992464	+	0.122534i	$0.960898\pi$
$570$	5798.25	−	3347.62i	0.426074	−	0.245994i
$571$	1757.27			0.128791			0.0643954	−	0.997924i	$-0.479488\pi$
$571$	1757.27			0.128791			0.0643954	+	0.997924i	$0.479488\pi$
$572$		0			0
$573$	11297.7			0.823679
$574$	11718.1	−	6765.45i	0.852097	−	0.491959i
$575$	261.683	+	453.247i	0.0189790	+	0.0328726i
$576$	−20128.3	+	34863.2i	−1.45604	+	2.52193i
$577$			13580.6i			0.979840i	0.871767	+	0.489920i	$0.162974\pi$
$577$			13580.6i			0.979840i	−0.871767	+	0.489920i	$0.837026\pi$
$578$	19392.4	+	11196.2i	1.39553	+	0.805710i
$579$	3905.98	+	2255.12i	0.280357	+	0.161864i
$580$			5059.49i			0.362214i
$581$	364.081	−	630.607i	0.0259977	−	0.0450293i
$582$	23261.6	+	40290.3i	1.65674	+	2.86956i
$583$	20917.0	−	12076.5i	1.48593	−	0.857900i
$584$	10257.8			0.726831
$585$		0			0
$586$	21461.0			1.51288
$587$	829.068	−	478.663i	0.0582952	−	0.0336568i	−0.470569	−	0.882363i	$-0.655951\pi$
$587$	829.068	−	478.663i	0.0582952	−	0.0336568i	0.528864	+	0.848706i	$0.322618\pi$
$588$	13991.6	+	24234.1i	0.981297	+	1.69966i
$589$	−4097.75	+	7097.50i	−0.286663	+	0.496515i
$590$		−	6632.95i		−	0.462838i
$591$	23473.8	+	13552.6i	1.63381	+	0.943283i
$592$	−389.734	−	225.013i	−0.0270573	−	0.0156216i
$593$			6729.49i			0.466015i	0.972475	+	0.233007i	$0.0748567\pi$
$593$			6729.49i			0.466015i	−0.972475	+	0.233007i	$0.925143\pi$
$594$	16729.2	−	28975.8i	1.15557	−	2.00150i
$595$	27.0500	+	46.8520i	0.00186377	+	0.00322814i
$596$	−20082.2	+	11594.5i	−1.38020	+	0.796859i
$597$	−10743.4			−0.736514
$598$		0			0
$599$	2281.52			0.155626			0.0778132	−	0.996968i	$-0.475206\pi$
$599$	2281.52			0.155626			0.0778132	+	0.996968i	$0.475206\pi$
$600$	−19317.8	+	11153.1i	−1.31441	+	0.758874i
$601$	−3200.71	−	5543.79i	−0.217237	−	0.376266i	0.736725	−	0.676192i	$-0.236371\pi$
$601$	−3200.71	−	5543.79i	−0.217237	−	0.376266i	−0.953962	+	0.299926i	$0.903038\pi$
$602$	−9322.18	+	16146.5i	−0.631136	+	1.09316i
$603$			2416.26i			0.163180i
$604$	−4694.50	−	2710.37i	−0.316252	−	0.182588i
$605$	−542.722	−	313.341i	−0.0364707	−	0.0210564i
$606$		−	38454.7i		−	2.57775i
$607$	−1389.62	+	2406.89i	−0.0929207	+	0.160943i	−0.908739	−	0.417365i	$-0.862954\pi$
$607$	−1389.62	+	2406.89i	−0.0929207	+	0.160943i	0.815818	+	0.578308i	$0.196287\pi$
$608$	−5612.95	−	9721.92i	−0.374400	−	0.648480i
$609$	10117.8	−	5841.50i	0.673223	−	0.388685i
$610$	−2066.03			−0.137133
$611$		0			0
$612$	1249.79			0.0825485
$613$	−19590.2	+	11310.4i	−1.29077	+	0.745226i	−0.978791	−	0.204863i	$-0.934325\pi$
$613$	−19590.2	+	11310.4i	−1.29077	+	0.745226i	−0.311979	+	0.950089i	$0.600992\pi$
$614$	11701.5	+	20267.6i	0.769111	+	1.33214i
$615$	3782.41	−	6551.33i	0.248002	−	0.429553i
$616$			8266.80i			0.540712i
$617$	19030.1	+	10987.0i	1.24169	+	0.716889i	0.969438	−	0.245337i	$-0.0788988\pi$
$617$	19030.1	+	10987.0i	1.24169	+	0.716889i	0.272250	+	0.962226i	$0.412232\pi$
$618$	−65174.9	−	37628.7i	−4.24226	−	2.44927i
$619$			7145.19i			0.463957i	0.972721	+	0.231979i	$0.0745199\pi$
$619$			7145.19i			0.463957i	−0.972721	+	0.231979i	$0.925480\pi$
$620$	−2448.15	+	4240.32i	−0.158581	+	0.274670i
$621$	415.715	+	720.040i	0.0268632	+	0.0465285i
$622$	−31401.7	+	18129.8i	−2.02426	+	1.16871i
$623$	−1939.14			−0.124703
$624$		0			0
$625$	12730.8			0.814773
$626$	−33665.0	+	19436.5i	−2.14940	+	1.24096i
$627$	10304.2	+	17847.5i	0.656319	+	1.13678i
$628$	8467.00	−	14665.3i	0.538010	−	0.931861i
$629$			374.231i			0.0237227i
$630$	−5135.55	−	2965.01i	−0.324770	−	0.187506i
$631$	16353.4	+	9441.62i	1.03172	+	0.595666i	0.917478	−	0.397787i	$-0.130222\pi$
$631$	16353.4	+	9441.62i	1.03172	+	0.595666i	0.114245	+	0.993453i	$0.463555\pi$
$632$		−	823.239i		−	0.0518144i
$633$	10993.3	−	19041.0i	0.690278	−	1.19560i
$634$	15195.6	+	26319.5i	0.951882	+	1.64871i
$635$	1509.76	−	871.661i	0.0943512	−	0.0544737i
$636$	−68146.4			−4.24871
$637$		0			0
$638$	−25301.1			−1.57003
$639$	−11740.5	+	6778.37i	−0.726833	+	0.419637i
$640$	−3229.25	−	5593.22i	−0.199449	−	0.345456i
$641$	−1815.54	+	3144.61i	−0.111871	+	0.193767i	−0.916525	−	0.399978i	$-0.869018\pi$
$641$	−1815.54	+	3144.61i	−0.111871	+	0.193767i	0.804653	+	0.593745i	$0.202351\pi$
$642$		−	75526.7i		−	4.64299i
$643$	−9328.78	−	5385.98i	−0.572148	−	0.330330i	0.185859	−	0.982576i	$-0.440493\pi$
$643$	−9328.78	−	5385.98i	−0.572148	−	0.330330i	−0.758007	+	0.652247i	$0.773827\pi$
$644$	−473.935	−	273.627i	−0.0289995	−	0.0167429i
$645$			10423.6i			0.636327i
$646$	−276.651	+	479.173i	−0.0168493	+	0.0291839i
$647$	7574.14	+	13118.8i	0.460232	+	0.797146i	0.998972	−	0.0453265i	$-0.0144328\pi$
$647$	7574.14	+	13118.8i	0.460232	+	0.797146i	−0.538740	+	0.842472i	$0.681099\pi$
$648$	−5857.09	+	3381.59i	−0.355074	+	0.205002i
$649$	20416.7			1.23487
$650$		0			0
$651$	11306.2			0.680682
$652$	40001.6	−	23094.9i	2.40273	−	1.38722i
$653$	−3679.45	−	6372.99i	−0.220502	−	0.381921i	0.734458	−	0.678654i	$-0.237436\pi$
$653$	−3679.45	−	6372.99i	−0.220502	−	0.381921i	−0.954961	+	0.296733i	$0.904103\pi$
$654$	17747.8	−	30740.1i	1.06115	−	1.83797i
$655$			3739.11i			0.223052i
$656$	−651.061	−	375.890i	−0.0387495	−	0.0223720i
$657$	−19614.7	−	11324.6i	−1.16475	−	0.672471i
$658$			11279.7i			0.668282i
$659$	−14166.6	+	24537.3i	−0.837411	+	1.45044i	0.0546414	+	0.998506i	$0.482598\pi$
$659$	−14166.6	+	24537.3i	−0.837411	+	1.45044i	−0.892052	+	0.451932i	$0.850735\pi$
$660$	6156.16	+	10662.8i	0.363073	+	0.628860i
$661$	961.014	−	554.842i	0.0565493	−	0.0326488i	−0.471459	−	0.881888i	$-0.656272\pi$
$661$	961.014	−	554.842i	0.0565493	−	0.0326488i	0.528008	+	0.849239i	$0.322939\pi$
$662$	−17843.8			−1.04761
$663$		0			0
$664$	1670.15			0.0976121
$665$	1399.46	−	807.978i	0.0816071	−	0.0471159i
$666$	−20510.1	−	35524.6i	−1.19332	−	2.06689i
$667$	314.362	−	544.491i	0.0182491	−	0.0316083i
$668$			43744.1i			2.53369i
$669$	−8991.75	−	5191.39i	−0.519643	−	0.300016i
$670$	−553.469	−	319.545i	−0.0319140	−	0.0184255i
$671$		−	6359.39i		−	0.365874i
$672$	−7743.41	+	13412.0i	−0.444507	+	0.769908i
$673$	10489.5	+	18168.4i	0.600806	+	1.04063i	0.992699	+	0.120616i	$0.0384868\pi$
$673$	10489.5	+	18168.4i	0.600806	+	1.04063i	−0.391893	+	0.920011i	$0.628180\pi$
$674$	2477.75	−	1430.53i	0.141601	−	0.0817535i
$675$	21790.0			1.24251
$676$		0			0
$677$	30941.9			1.75656			0.878282	−	0.478142i	$-0.158690\pi$
$677$	30941.9			1.75656			0.878282	+	0.478142i	$0.158690\pi$
$678$	−11489.2	+	6633.27i	−0.650795	+	0.375736i
$679$	5614.39	+	9724.41i	0.317320	+	0.549615i
$680$	−62.0433	+	107.462i	−0.00349890	+	0.00606027i
$681$			7548.64i			0.424764i
$682$	−21204.6	−	12242.5i	−1.19057	−	0.687375i
$683$	−4699.24	−	2713.11i	−0.263267	−	0.151997i	0.362557	−	0.931962i	$-0.381904\pi$
$683$	−4699.24	−	2713.11i	−0.263267	−	0.151997i	−0.625824	+	0.779964i	$0.715237\pi$
$684$		−	37330.9i		−	2.08682i
$685$	−873.236	+	1512.49i	−0.0487075	+	0.0843638i
$686$	12966.4	+	22458.4i	0.721660	+	1.24995i
$687$	35233.8	−	20342.2i	1.95670	−	1.12970i
$688$	1035.89			0.0574023
$689$		0			0
$690$	−497.065			−0.0274245
$691$	29265.3	−	16896.3i	1.61115	−	0.930199i	0.622048	−	0.782979i	$-0.286301\pi$
$691$	29265.3	−	16896.3i	1.61115	−	0.930199i	0.989104	−	0.147219i	$-0.0470324\pi$
$692$	−14999.3	−	25979.6i	−0.823973	−	1.42716i
$693$	9126.53	−	15807.6i	0.500272	−	0.866496i
$694$		−	17438.9i		−	0.953849i
$695$	803.838	+	464.096i	0.0438724	+	0.0253297i
$696$	23206.6	+	13398.4i	1.26386	+	0.729689i
$697$			625.164i			0.0339738i
$698$	7778.97	−	13473.6i	0.421831	−	0.730633i
$699$	−21142.8	−	36620.3i	−1.14405	−	1.98156i
$700$	−12420.8	+	7171.16i	−0.670661	+	0.387206i
$701$	−6905.96			−0.372089			−0.186045	−	0.982541i	$-0.559567\pi$
$701$	−6905.96			−0.372089			−0.186045	+	0.982541i	$0.559567\pi$
$702$		0			0
$703$	11178.2			0.599707
$704$	28383.5	−	16387.2i	1.51952	−	0.877297i
$705$	3153.12	+	5461.37i	0.168445	+	0.291755i
$706$	12744.1	−	22073.5i	0.679366	−	1.17670i
$707$		−	9281.37i		−	0.493723i
$708$	−49887.3	−	28802.5i	−2.64814	−	1.52890i
$709$	1738.22	+	1003.56i	0.0920739	+	0.0531589i	0.545330	−	0.838221i	$-0.316404\pi$
$709$	1738.22	+	1003.56i	0.0920739	+	0.0531589i	−0.453256	+	0.891380i	$0.649738\pi$
$710$		−	3585.70i		−	0.189534i
$711$	−908.854	+	1574.18i	−0.0479391	+	0.0830329i
$712$	−2223.85	−	3851.83i	−0.117054	−	0.202744i
$713$	526.929	−	304.222i	0.0276769	−	0.0159793i
$714$	763.312			0.0400088
$715$		0			0
$716$	−8541.38			−0.445819
$717$	−36158.1	+	20875.9i	−1.88333	+	1.08734i
$718$	5086.44	+	8809.98i	0.264379	+	0.457918i
$719$	−6393.72	+	11074.3i	−0.331635	+	0.574409i	−0.982833	−	0.184499i	$-0.940934\pi$
$719$	−6393.72	+	11074.3i	−0.331635	+	0.574409i	0.651198	+	0.758908i	$0.274267\pi$
$720$			329.474i			0.0170538i
$721$	−15730.5	−	9082.03i	−0.812532	−	0.469116i
$722$	−12783.1	−	7380.35i	−0.658919	−	0.380427i
$723$			51030.7i			2.62497i
$724$	4489.36	−	7775.80i	0.230450	−	0.399151i
$725$	−8238.74	−	14269.9i	−0.422040	−	0.730995i
$726$	−7657.42	+	4421.01i	−0.391451	+	0.226004i
$727$	6090.70			0.310717			0.155359	−	0.987858i	$-0.450347\pi$
$727$	6090.70			0.310717			0.155359	+	0.987858i	$0.450347\pi$
$728$		0			0
$729$	−28693.9			−1.45780
$730$	5188.01	−	2995.30i	0.263037	−	0.151864i
$731$	−430.710	−	746.011i	−0.0217926	−	0.0377459i
$732$	−8971.37	+	15538.9i	−0.452994	+	0.784608i
$733$			38846.5i			1.95747i	0.205117	+	0.978737i	$0.434243\pi$
$733$			38846.5i			1.95747i	−0.205117	+	0.978737i	$0.565757\pi$
$734$	34365.3	+	19840.8i	1.72813	+	0.997735i
$735$	5312.69	+	3067.28i	0.266614	+	0.153930i
$736$			833.427i			0.0417399i
$737$	983.585	−	1703.62i	0.0491599	−	0.0851474i
$738$	−34262.8	−	59344.8i	−1.70898	−	2.96005i
$739$	12520.6	−	7228.77i	0.623245	−	0.359830i	−0.154887	−	0.987932i	$-0.549501\pi$
$739$	12520.6	−	7228.77i	0.623245	−	0.359830i	0.778131	+	0.628102i	$0.216168\pi$
$740$	6678.29			0.331755
$741$		0			0
$742$	−26721.3			−1.32206
$743$	1106.61	−	638.901i	0.0546400	−	0.0315464i	−0.472431	−	0.881368i	$-0.656623\pi$
$743$	1106.61	−	638.901i	0.0546400	−	0.0315464i	0.527071	+	0.849821i	$0.323290\pi$
$744$	12966.2	+	22458.1i	0.638931	+	1.10666i
$745$	−2541.78	+	4402.49i	−0.124998	+	0.216503i
$746$			50013.7i			2.45460i
$747$	−3193.63	−	1843.84i	−0.156424	−	0.0903116i
$748$	−881.181	−	508.750i	−0.0430738	−	0.0248687i
$749$		−	18229.0i		−	0.889285i
$750$	−13465.4	+	23322.8i	−0.655584	+	1.13551i
$751$	−6503.93	−	11265.1i	−0.316021	−	0.547364i	0.663633	−	0.748058i	$-0.269014\pi$
$751$	−6503.93	−	11265.1i	−0.316021	−	0.547364i	−0.979654	+	0.200694i	$0.935680\pi$
$752$	542.743	−	313.353i	0.0263189	−	0.0151952i
$753$	−50425.5			−2.44038
$754$		0			0
$755$	−1188.35			−0.0572829
$756$	−19732.0	+	11392.3i	−0.949268	+	0.548060i
$757$	5361.61	+	9286.57i	0.257425	+	0.445874i	0.965551	−	0.260212i	$-0.0837926\pi$
$757$	5361.61	+	9286.57i	0.257425	+	0.445874i	−0.708126	+	0.706086i	$0.750459\pi$
$758$	−31725.9	+	54950.8i	−1.52023	+	2.63312i
$759$		−	1530.00i		−	0.0731694i
$760$	3209.87	+	1853.22i	0.153203	+	0.0884518i
$761$	−11796.8	−	6810.90i	−0.561938	−	0.324435i	0.191985	−	0.981398i	$-0.438508\pi$
$761$	−11796.8	−	6810.90i	−0.561938	−	0.324435i	−0.753923	+	0.656963i	$0.771841\pi$
$762$		−	24597.0i		−	1.16936i
$763$	4283.59	−	7419.40i	0.203246	−	0.352032i
$764$	8330.68	+	14429.2i	0.394494	+	0.683284i
$765$	237.276	−	136.991i	0.0112140	−	0.00647443i
$766$	−2256.84			−0.106453
$767$		0			0
$768$	−33365.0			−1.56765
$769$	7357.01	−	4247.57i	0.344994	−	0.199183i	−0.317484	−	0.948264i	$-0.602838\pi$
$769$	7357.01	−	4247.57i	0.344994	−	0.199183i	0.662478	+	0.749081i	$0.269505\pi$
$770$	2413.93	+	4181.05i	0.112977	+	0.195681i
$771$	−5192.82	+	8994.22i	−0.242561	+	0.420128i
$772$			6651.50i			0.310094i
$773$	29672.2	+	17131.3i	1.38064	+	0.797113i	0.992235	−	0.124375i	$-0.0396927\pi$
$773$	29672.2	+	17131.3i	1.38064	+	0.797113i	0.388405	+	0.921489i	$0.373026\pi$
$774$	81771.9	+	47211.0i	3.79745	+	2.19246i
$775$		−	15946.0i		−	0.739094i
$776$	−12877.5	+	22304.4i	−0.595714	+	1.03181i
$777$	−7710.50	−	13355.0i	−0.356001	−	0.616612i
$778$	16356.6	−	9443.48i	0.753743	−	0.435174i
$779$	18673.5			0.858854
$780$		0			0
$781$	11037.1			0.505681
$782$	35.5745	−	20.5389i	0.00162678	−	0.000939221i
$783$	−13088.3	−	22669.5i	−0.597364	−	1.03467i
$784$	304.822	−	527.967i	0.0138858	−	0.0240510i
$785$		−	3712.33i		−	0.168788i
$786$	45688.2	+	26378.1i	2.07334	+	1.19704i
$787$	10948.8	+	6321.29i	0.495912	+	0.286315i	0.727024	−	0.686612i	$-0.240903\pi$
$787$	10948.8	+	6321.29i	0.495912	+	0.286315i	−0.231112	+	0.972927i	$0.574236\pi$
$788$			39973.6i			1.80711i
$789$	−1016.91	+	1761.33i	−0.0458844	+	0.0794741i
$790$	−240.388	−	416.365i	−0.0108261	−	0.0187514i
$791$	−2773.01	+	1601.00i	−0.124648	+	0.0719658i
$792$	41866.2			1.87834
$793$		0			0
$794$	8583.89			0.383666
$795$	−12937.8	+	7469.65i	−0.577178	+	0.333234i
$796$	−7921.97	−	13721.3i	−0.352747	−	0.610976i
$797$	9542.18	−	16527.5i	0.424092	−	0.734549i	−0.572243	−	0.820084i	$-0.693927\pi$
$797$	9542.18	−	16527.5i	0.424092	−	0.734549i	0.996335	+	0.0855350i	$0.0272600\pi$
$798$		−	22800.0i		−	1.01142i
$799$	−451.333	−	260.577i	−0.0199837	−	0.0115376i
$800$	18916.0	+	10921.2i	0.835978	+	0.482652i
$801$			9820.53i			0.433198i
$802$	961.952	−	1666.15i	0.0423538	−	0.0733589i
$803$	9219.77	+	15969.1i	0.405179	+	0.701790i
$804$	−4806.69	+	2775.14i	−0.210844	+	0.121731i
$805$	−119.971			−0.00525269
$806$		0			0
$807$	−23173.0			−1.01082
$808$	18436.1	−	10644.1i	0.802700	−	0.463439i
$809$	−5805.02	−	10054.6i	−0.252279	−	0.436960i	0.711874	−	0.702307i	$-0.247847\pi$
$809$	−5805.02	−	10054.6i	−0.252279	−	0.436960i	−0.964153	+	0.265347i	$0.914513\pi$
$810$	−1974.87	+	3420.57i	−0.0856665	+	0.148379i
$811$		−	9613.36i		−	0.416240i	−0.978103	−	0.208120i	$-0.933266\pi$
$811$		−	9613.36i		−	0.416240i	0.978103	−	0.208120i	$-0.0667345\pi$
$812$	14921.3	+	8614.79i	0.644869	+	0.372315i
$813$	−42880.1	−	24756.8i	−1.84978	−	1.06797i
$814$			33396.2i			1.43800i
$815$	5062.95	−	8769.29i	0.217604	−	0.376901i
$816$	−21.2049	−	36.7280i	−0.000909707	−	0.00157566i
$817$	−22283.2	+	12865.2i	−0.954211	+	0.550914i
$818$	11632.9			0.497233
$819$		0			0
$820$	11156.3			0.475115
$821$	22933.6	−	13240.7i	0.974895	−	0.562856i	0.0741699	−	0.997246i	$-0.476369\pi$
$821$	22933.6	−	13240.7i	0.974895	−	0.562856i	0.900725	+	0.434390i	$0.143036\pi$
$822$	12320.7	+	21340.1i	0.522792	+	0.905502i
$823$	6907.25	−	11963.7i	0.292553	−	0.506718i	−0.681859	−	0.731483i	$-0.738828\pi$
$823$	6907.25	−	11963.7i	0.292553	−	0.506718i	0.974413	+	0.224766i	$0.0721617\pi$
$824$		−	41662.0i		−	1.76136i
$825$	−34726.0	−	20049.0i	−1.46546	−	0.846082i
$826$	−19561.6	−	11293.9i	−0.824015	−	0.475746i
$827$		−	44401.0i		−	1.86696i	−0.358633	−	0.933479i	$-0.616757\pi$
$827$		−	44401.0i		−	1.86696i	0.358633	−	0.933479i	$-0.383243\pi$
$828$	−1385.75	+	2400.19i	−0.0581619	+	0.100739i
$829$	12168.7	+	21076.8i	0.509815	+	0.883025i	0.999935	+	0.0113707i	$0.00361948\pi$
$829$	12168.7	+	21076.8i	0.509815	+	0.883025i	−0.490120	+	0.871655i	$0.663047\pi$
$830$	844.703	−	487.689i	0.0353254	−	0.0203951i
$831$	62116.9			2.59303
$832$		0			0
$833$	−506.966			−0.0210868
$834$	11341.6	−	6548.06i	0.470895	−	0.271871i
$835$	4794.86	+	8304.95i	0.198722	+	0.344197i
$836$	−15196.3	+	26320.7i	−0.628677	+	1.08890i
$837$		−	25332.2i		−	1.04613i
$838$	−48925.2	−	28247.0i	−2.01682	−	1.16441i
$839$	21373.6	+	12340.0i	0.879497	+	0.507778i	0.870493	−	0.492181i	$-0.163800\pi$
$839$	21373.6	+	12340.0i	0.879497	+	0.507778i	0.00900472	+	0.999959i	$0.497134\pi$
$840$		−	5113.26i		−	0.210029i
$841$	2297.22	−	3978.90i	0.0941907	−	0.163143i
$842$	−23863.7	−	41333.1i	−0.976719	−	1.69173i
$843$	−46126.2	+	26631.0i	−1.88454	+	1.08804i
$844$	32425.0			1.32241
$845$		0			0
$846$	57124.8			2.32150
$847$	−1848.18	+	1067.05i	−0.0749757	+	0.0432872i
$848$	742.323	+	1285.74i	0.0300607	+	0.0520666i
$849$	14664.7	−	25400.0i	0.592805	−	1.02677i
$850$		−	1076.56i		−	0.0434421i
$851$	−718.702	−	414.943i	−0.0289504	−	0.0167145i
$852$	−26968.5	−	15570.3i	−1.08442	−	0.626091i
$853$		−	10151.7i		−	0.407490i	−0.979024	−	0.203745i	$-0.934689\pi$
$853$		−	10151.7i		−	0.407490i	0.979024	−	0.203745i	$-0.0653113\pi$
$854$	−3517.82	+	6093.05i	−0.140957	+	0.244145i
$855$	−4091.90	−	7087.39i	−0.163673	−	0.283489i
$856$	36209.4	−	20905.5i	1.44581	−	0.834739i
$857$	−2028.92			−0.0808713			−0.0404357	−	0.999182i	$-0.512875\pi$
$857$	−2028.92			−0.0808713			−0.0404357	+	0.999182i	$0.512875\pi$
$858$		0			0
$859$	6655.76			0.264367			0.132184	−	0.991225i	$-0.457801\pi$
$859$	6655.76			0.264367			0.132184	+	0.991225i	$0.457801\pi$
$860$	−13312.8	+	7686.17i	−0.527865	+	0.304763i
$861$	−12880.6	−	22309.9i	−0.509837	−	0.883064i
$862$	9037.32	−	15653.1i	0.357091	−	0.618500i
$863$		−	45690.8i		−	1.80224i	−0.433568	−	0.901121i	$-0.642746\pi$
$863$		−	45690.8i		−	1.80224i	0.433568	−	0.901121i	$-0.357254\pi$
$864$	30050.4	+	17349.6i	1.18326	+	0.683155i
$865$	−5695.35	−	3288.21i	−0.223870	−	0.129251i
$866$			38290.3i			1.50249i
$867$	21316.2	−	36920.8i	0.834991	−	1.44625i
$868$	8336.93	+	14440.0i	0.326007	+	0.564660i
$869$	1281.60	−	739.934i	0.0500292	−	0.0288844i
$870$	15649.4			0.609846
$871$		0			0
$872$	19650.1			0.763117
$873$	49248.1	−	28433.4i	1.90927	−	1.10232i
$874$	−613.493	−	1062.60i	−0.0237434	−	0.0411248i
$875$	−3250.00	+	5629.17i	−0.125566	+	0.217486i
$876$		−	52026.3i		−	2.00663i
$877$	26368.3	+	15223.8i	1.01527	+	0.586168i	0.912731	−	0.408560i	$-0.133969\pi$
$877$	26368.3	+	15223.8i	1.01527	+	0.586168i	0.102542	+	0.994729i	$0.467302\pi$
$878$	40193.6	+	23205.8i	1.54495	+	0.891979i
$879$		−	40859.3i		−	1.56786i
$880$	134.119	−	232.300i	0.00513766	−	0.00889869i
$881$	16271.0	+	28182.2i	0.622230	+	1.07773i	0.989070	+	0.147450i	$0.0471065\pi$
$881$	16271.0	+	28182.2i	0.622230	+	1.07773i	−0.366840	+	0.930284i	$0.619560\pi$
$882$	48124.7	−	27784.8i	1.83724	−	1.06073i
$883$	−27641.9			−1.05348			−0.526741	−	0.850026i	$-0.676586\pi$
$883$	−27641.9			−1.05348			−0.526741	+	0.850026i	$0.676586\pi$
$884$		0			0
$885$	−12628.4			−0.479658
$886$	−23231.4	+	13412.7i	−0.880896	+	0.508586i
$887$	−20050.0	−	34727.5i	−0.758976	−	1.31458i	−0.943373	−	0.331733i	$-0.892367\pi$
$887$	−20050.0	−	34727.5i	−0.758976	−	1.31458i	0.184397	−	0.982852i	$-0.440967\pi$
$888$	17685.2	−	30631.7i	0.668329	−	1.15758i
$889$		−	5936.70i		−	0.223971i
$890$	−2249.49	−	1298.75i	−0.0847226	−	0.0489146i
$891$	−10528.8	−	6078.80i	−0.395879	−	0.228561i
$892$		−	15312.1i		−	0.574761i
$893$	−7783.38	+	13481.2i	−0.291670	+	0.505186i
$894$	35862.7	+	62116.0i	1.34164	+	2.32379i
$895$	−1621.61	+	936.236i	−0.0605636	+	0.0349664i
$896$	−21993.8			−0.820044
$897$		0			0
$898$	−48648.4			−1.80781
$899$	−16589.7	+	9578.06i	−0.615458	+	0.355335i
$900$	36317.5	+	62903.7i	1.34509	+	2.32977i
$901$	617.299	−	1069.19i	0.0228249	−	0.0395338i
$902$			55789.3i			2.05940i
$903$	30741.0	+	17748.3i	1.13289	+	0.654072i
$904$	−6360.32	−	3672.13i	−0.234006	−	0.135103i
$905$		−	1968.35i		−	0.0722984i
$906$	−8383.41	+	14520.5i	−0.307417	+	0.532462i
$907$	−18412.4	−	31891.3i	−0.674062	−	1.16751i	−0.976742	−	0.214418i	$-0.931215\pi$
$907$	−18412.4	−	31891.3i	−0.674062	−	1.16751i	0.302679	−	0.953092i	$-0.402119\pi$
$908$	−9640.95	+	5566.20i	−0.352363	+	0.203437i
$909$	−47004.3			−1.71511
$910$		0			0
$911$	34520.5			1.25545			0.627725	−	0.778435i	$-0.283986\pi$
$911$	34520.5			1.25545			0.627725	+	0.778435i	$0.283986\pi$
$912$	−1097.06	+	633.387i	−0.0398325	+	0.0229973i
$913$	1501.15	+	2600.06i	0.0544148	+	0.0942491i
$914$	33821.3	−	58580.2i	1.22397	−	2.11998i
$915$			3933.47i			0.142117i
$916$	51961.3	+	29999.9i	1.87429	+	1.08212i
$917$	11027.2	+	6366.58i	0.397112	+	0.229273i
$918$		−	1710.25i		−	0.0614888i
$919$	−11761.4	+	20371.3i	−0.422168	+	0.731216i	−0.996151	−	0.0876506i	$-0.972064\pi$
$919$	−11761.4	+	20371.3i	−0.422168	+	0.731216i	0.573983	+	0.818867i	$0.305397\pi$
$920$	−137.586	−	238.305i	−0.00493051	−	0.00853989i
$921$	38587.1	−	22278.3i	1.38055	−	0.797062i
$922$	−44300.4			−1.58238
$923$		0			0
$924$	41928.3			1.49279
$925$	−18835.6	+	10874.8i	−0.669526	+	0.386551i
$926$	25894.8	+	44851.2i	0.918961	+	1.59169i
$927$	−45994.8	+	79665.3i	−1.62963	+	2.82260i
$928$		−	26239.4i		−	0.928180i
$929$	−21272.3	−	12281.6i	−0.751262	−	0.433741i	0.0748880	−	0.997192i	$-0.476140\pi$
$929$	−21272.3	−	12281.6i	−0.751262	−	0.433741i	−0.826150	+	0.563451i	$0.809473\pi$
$930$	13115.7	+	7572.35i	0.462452	+	0.266997i
$931$			15143.0i			0.533073i
$932$	31180.4	−	54006.1i	1.09587	−	1.89810i
$933$	34516.9	+	59785.0i	1.21118	+	2.09783i
$934$	−25485.4	+	14714.0i	−0.892834	+	0.515478i
$935$	−223.060			−0.00780197
$936$		0			0
$937$	−12115.6			−0.422411			−0.211206	−	0.977442i	$-0.567739\pi$
$937$	−12115.6			−0.422411			−0.211206	+	0.977442i	$0.567739\pi$
$938$	−1884.78	+	1088.18i	−0.0656080	+	0.0378788i
$939$	37004.8	+	64094.2i	1.28605	+	2.22751i
$940$	−4650.09	+	8054.20i	−0.161350	+	0.279467i
$941$		−	14898.3i		−	0.516123i	−0.966128	−	0.258062i	$-0.916916\pi$
$941$		−	14898.3i		−	0.516123i	0.966128	−	0.258062i	$-0.0830837\pi$
$942$	−45361.0	−	26189.2i	−1.56894	−	0.905828i
$943$	−1200.61	−	693.174i	−0.0414606	−	0.0239373i
$944$			1254.99i			0.0432695i
$945$	−2497.46	+	4325.72i	−0.0859707	+	0.148906i
$946$	−38436.3	−	66573.7i	−1.32101	−	2.28805i
$947$	6438.31	−	3717.16i	0.220926	−	0.127552i	−0.385453	−	0.922727i	$-0.625955\pi$
$947$	6438.31	−	3717.16i	0.220926	−	0.127552i	0.606379	+	0.795176i	$0.292621\pi$
$948$	−4175.38			−0.143049
$949$		0			0
$950$	−32156.7			−1.09821
$951$	50109.2	−	28930.6i	1.70863	−	0.986476i
$952$	211.282	+	365.951i	0.00719295	+	0.0124586i
$953$	−11764.3	+	20376.3i	−0.399877	+	0.692607i	−0.993710	−	0.111981i	$-0.964280\pi$
$953$	−11764.3	+	20376.3i	−0.399877	+	0.692607i	0.593833	+	0.804588i	$0.297614\pi$
$954$			135327.i			4.59263i
$955$	3163.21	+	1826.28i	0.107182	+	0.0618818i
$956$	−53324.4	−	30786.9i	−1.80401	−	1.04155i
$957$			48170.2i			1.62709i
$958$	−21818.9	+	37791.5i	−0.735844	+	1.27452i
$959$	2973.72	+	5150.63i	0.100132	+	0.173433i
$960$	−17556.0	+	10136.0i	−0.590228	+	0.340768i
$961$	11252.7			0.377723
$962$		0			0
$963$	−92318.7			−3.08923
$964$	−65175.3	+	37629.0i	−2.17755	+	1.25721i
$965$	729.083	+	1262.81i	0.0243213	+	0.0421256i
$966$	−846.351	+	1465.92i	−0.0281893	+	0.0488254i
$967$		−	23558.0i		−	0.783427i	−0.920087	−	0.391713i	$-0.871882\pi$
$967$		−	23558.0i		−	0.783427i	0.920087	−	0.391713i	$-0.128118\pi$
$968$	−4239.09	−	2447.44i	−0.140754	−	0.0812642i
$969$	912.289	+	526.710i	0.0302445	+	0.0174617i
$970$			15041.0i			0.497875i
$971$	131.169	−	227.191i	0.00433513	−	0.00750866i	−0.863850	−	0.503750i	$-0.831953\pi$
$971$	131.169	−	227.191i	0.00433513	−	0.00750866i	0.868185	+	0.496241i	$0.165287\pi$
$972$	−15018.6	−	26012.9i	−0.495597	−	0.858400i
$973$	2737.39	−	1580.43i	0.0901918	−	0.0520722i
$974$	22429.7			0.737878
$975$		0			0
$976$	390.903			0.0128202
$977$	−28703.9	+	16572.2i	−0.939936	+	0.542673i	−0.889940	−	0.456077i	$-0.849254\pi$
$977$	−28703.9	+	16572.2i	−0.939936	+	0.542673i	−0.0499960	+	0.998749i	$0.515921\pi$
$978$	−71434.6	−	123728.i	−2.33561	−	4.04539i
$979$	3997.64	−	6924.11i	0.130506	−	0.226042i
$980$			9047.00i			0.294894i
$981$	−37574.6	−	21693.7i	−1.22290	−	0.706042i
$982$	11657.0	+	6730.17i	0.378808	+	0.218705i
$983$		−	4866.80i		−	0.157911i	−0.996878	−	0.0789557i	$-0.974841\pi$
$983$		−	4866.80i		−	0.157911i	0.996878	−	0.0789557i	$-0.0251586\pi$
$984$	29543.6	−	51171.1i	0.957131	−	1.65780i
$985$	4381.58	+	7589.12i	0.141735	+	0.245492i
$986$	−1120.02	+	646.642i	−0.0361751	+	0.0208857i
$987$	21475.3			0.692569
$988$		0			0
$989$	1910.26			0.0614184
$990$	21174.4	−	12225.0i	0.679764	−	0.392462i
$991$	−6266.97	−	10854.7i	−0.200885	−	0.347943i	0.747929	−	0.663779i	$-0.231048\pi$
$991$	−6266.97	−	10854.7i	−0.200885	−	0.347943i	−0.948814	+	0.315836i	$0.897715\pi$
$992$	12696.5	−	21991.1i	0.406367	−	0.703848i
$993$			33972.4i			1.08568i
$994$	−10574.8	−	6105.37i	−0.337437	−	0.194819i
$995$	−3008.02	−	1736.68i	−0.0958399	−	0.0553332i
$996$		−	8470.83i		−	0.269487i
$997$	1780.46	−	3083.84i	0.0565574	−	0.0979602i	−0.836361	−	0.548180i	$-0.815321\pi$
$997$	1780.46	−	3083.84i	0.0565574	−	0.0979602i	0.892918	+	0.450220i	$0.148654\pi$
$998$	−30631.0	−	53054.5i	−0.971552	−	1.68278i
$999$	−29922.7	+	17275.9i	−0.947660	+	0.547132i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.e.g.23.4		8
13.2	odd	12		169.4.a.j.1.2		2
13.3	even	3		169.4.b.e.168.4		4
13.4	even	6	inner	169.4.e.g.147.4		8
13.5	odd	4		169.4.c.f.146.1		4
13.6	odd	12		169.4.c.f.22.1		4
13.7	odd	12		13.4.c.b.9.2	yes	4
13.8	odd	4		13.4.c.b.3.2	✓	4
13.9	even	3	inner	169.4.e.g.147.1		8
13.10	even	6		169.4.b.e.168.1		4
13.11	odd	12		169.4.a.f.1.1		2
13.12	even	2	inner	169.4.e.g.23.1		8
39.2	even	12		1521.4.a.l.1.1		2
39.8	even	4		117.4.g.d.55.1		4
39.11	even	12		1521.4.a.t.1.2		2
39.20	even	12		117.4.g.d.100.1		4
52.7	even	12		208.4.i.e.113.2		4
52.47	even	4		208.4.i.e.81.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.c.b.3.2	✓	4	13.8	odd	4
13.4.c.b.9.2	yes	4	13.7	odd	12
117.4.g.d.55.1		4	39.8	even	4
117.4.g.d.100.1		4	39.20	even	12
169.4.a.f.1.1		2	13.11	odd	12
169.4.a.j.1.2		2	13.2	odd	12
169.4.b.e.168.1		4	13.10	even	6
169.4.b.e.168.4		4	13.3	even	3
169.4.c.f.22.1		4	13.6	odd	12
169.4.c.f.146.1		4	13.5	odd	4
169.4.e.g.23.1		8	13.12	even	2	inner
169.4.e.g.23.4		8	1.1	even	1	trivial
169.4.e.g.147.1		8	13.9	even	3	inner
169.4.e.g.147.4		8	13.4	even	6	inner
208.4.i.e.81.2		4	52.47	even	4
208.4.i.e.113.2		4	52.7	even	12
1521.4.a.l.1.1		2	39.2	even	12
1521.4.a.t.1.2		2	39.11	even	12

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	169.e (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.95042 - 2.28078i) q^{2} +(-4.34233 - 7.52113i) q^{3} +(6.40388 - 11.0918i) q^{4} -2.80776i q^{5} +(-34.3081 - 19.8078i) q^{6} +(-8.28055 - 4.78078i) q^{7} -21.9309i q^{8} +(-24.2116 + 41.9358i) q^{9} +O(q^{10})\)	\(q+(3.95042 - 2.28078i) q^{2} +(-4.34233 - 7.52113i) q^{3} +(6.40388 - 11.0918i) q^{4} -2.80776i q^{5} +(-34.3081 - 19.8078i) q^{6} +(-8.28055 - 4.78078i) q^{7} -21.9309i q^{8} +(-24.2116 + 41.9358i) q^{9} +(-6.40388 - 11.0918i) q^{10} +(34.1416 - 19.7116i) q^{11} -111.231 q^{12} -43.6155 q^{14} +(-21.1176 + 12.1922i) q^{15} +(1.21165 + 2.09863i) q^{16} +(1.00758 - 1.74518i) q^{17} +220.885i q^{18} +(-52.1280 - 30.0961i) q^{19} +(-31.1433 - 17.9806i) q^{20} +83.0388i q^{21} +(89.9157 - 155.739i) q^{22} +(2.23438 + 3.87006i) q^{23} +(-164.945 + 95.2311i) q^{24} +117.116 q^{25} +186.054 q^{27} +(-106.055 + 61.2311i) q^{28} +(-70.3466 - 121.844i) q^{29} +(-55.6155 + 96.3289i) q^{30} -136.155i q^{31} +(161.515 + 93.2505i) q^{32} +(-296.508 - 171.189i) q^{33} -9.19224i q^{34} +(-13.4233 + 23.2498i) q^{35} +(310.097 + 537.104i) q^{36} +(-160.828 + 92.8542i) q^{37} -274.570 q^{38} -61.5767 q^{40} +(-268.668 + 155.116i) q^{41} +(189.393 + 328.038i) q^{42} +(213.735 - 370.200i) q^{43} -504.924i q^{44} +(117.746 + 67.9806i) q^{45} +(17.6535 + 10.1922i) q^{46} -258.617i q^{47} +(10.5227 - 18.2259i) q^{48} +(-125.788 - 217.872i) q^{49} +(462.659 - 267.116i) q^{50} -17.5009 q^{51} +612.656 q^{53} +(734.991 - 424.348i) q^{54} +(-55.3457 - 95.8615i) q^{55} +(-104.847 + 181.600i) q^{56} +522.749i q^{57} +(-555.797 - 320.890i) q^{58} +(448.502 + 258.943i) q^{59} +312.311i q^{60} +(80.6553 - 139.699i) q^{61} +(-310.540 - 537.871i) q^{62} +(400.971 - 231.501i) q^{63} +831.348 q^{64} -1561.77 q^{66} +(43.2135 - 24.9493i) q^{67} +(-12.9048 - 22.3518i) q^{68} +(19.4048 - 33.6101i) q^{69} +122.462i q^{70} +(242.455 + 139.982i) q^{71} +(919.689 + 530.982i) q^{72} +467.732i q^{73} +(-423.559 + 733.626i) q^{74} +(-508.558 - 880.849i) q^{75} +(-667.643 + 385.464i) q^{76} -376.948 q^{77} +37.5379 q^{79} +(5.89247 - 3.40202i) q^{80} +(-154.193 - 267.070i) q^{81} +(-707.568 + 1225.54i) q^{82} +76.1553i q^{83} +(921.054 + 531.771i) q^{84} +(-4.90004 - 2.82904i) q^{85} -1949.93i q^{86} +(-610.936 + 1058.17i) q^{87} +(-432.294 - 748.754i) q^{88} +(175.635 - 101.403i) q^{89} +620.194 q^{90} +57.2348 q^{92} +(-1024.04 + 591.231i) q^{93} +(-589.848 - 1021.65i) q^{94} +(-84.5028 + 146.363i) q^{95} -1619.70i q^{96} +(-1017.03 - 587.184i) q^{97} +(-993.834 - 573.790i) q^{98} +1909.01i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 10 q^{3} + 10 q^{4} - 70 q^{9}+O(q^{10}) \) 8 * q - 10 * q^3 + 10 * q^4 - 70 * q^9	\( 8 q - 10 q^{3} + 10 q^{4} - 70 q^{9} - 10 q^{10} - 560 q^{12} - 184 q^{14} - 114 q^{16} + 140 q^{17} + 340 q^{22} + 290 q^{23} - 300 q^{25} + 1340 q^{27} - 68 q^{29} - 280 q^{30} + 140 q^{35} + 1450 q^{36} - 1240 q^{38} - 740 q^{40} + 740 q^{42} + 910 q^{43} + 480 q^{48} - 1130 q^{49} + 932 q^{51} + 2180 q^{53} - 1020 q^{55} - 344 q^{56} - 1004 q^{61} - 1000 q^{62} + 5084 q^{64} - 6392 q^{66} + 1010 q^{68} - 958 q^{69} - 1698 q^{74} - 3450 q^{75} - 1020 q^{77} + 960 q^{79} - 244 q^{81} - 3030 q^{82} - 3230 q^{87} - 2040 q^{88} + 2900 q^{90} - 4160 q^{92} - 2080 q^{94} + 2540 q^{95}+O(q^{100}) \) 8 * q - 10 * q^3 + 10 * q^4 - 70 * q^9 - 10 * q^10 - 560 * q^12 - 184 * q^14 - 114 * q^16 + 140 * q^17 + 340 * q^22 + 290 * q^23 - 300 * q^25 + 1340 * q^27 - 68 * q^29 - 280 * q^30 + 140 * q^35 + 1450 * q^36 - 1240 * q^38 - 740 * q^40 + 740 * q^42 + 910 * q^43 + 480 * q^48 - 1130 * q^49 + 932 * q^51 + 2180 * q^53 - 1020 * q^55 - 344 * q^56 - 1004 * q^61 - 1000 * q^62 + 5084 * q^64 - 6392 * q^66 + 1010 * q^68 - 958 * q^69 - 1698 * q^74 - 3450 * q^75 - 1020 * q^77 + 960 * q^79 - 244 * q^81 - 3030 * q^82 - 3230 * q^87 - 2040 * q^88 + 2900 * q^90 - 4160 * q^92 - 2080 * q^94 + 2540 * q^95

Introduction

L-functions

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