LMFDB - Embedded newform 169.4.e.g.147.1

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			147.1
Root			$2.21837 - 1.28078i$ of defining polynomial
Character	$\chi$	$=$	169.147
Dual form			169.4.e.g.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+(-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} - 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}+ \cdots + 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

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−3.95042	−	2.28078i	−1.39668	−	0.806376i	−0.402641	−	0.915358i	$-0.631908\pi$
$2$	−3.95042	−	2.28078i	−1.39668	−	0.806376i	−0.994044	+	0.108982i	$0.965241\pi$
$3$	−4.34233	+	7.52113i	−0.835682	+	1.44744i	0.0577926	+	0.998329i	$0.481594\pi$
$3$	−4.34233	+	7.52113i	−0.835682	+	1.44744i	−0.893474	+	0.449114i	$0.851740\pi$
$4$	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	$-0.583558\pi$
$7$	8.28055	−	4.78078i	0.447108	−	0.258138i	0.706608	+	0.707605i	$0.250225\pi$
$8$		−	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	$-0.515022\pi$
$11$	−34.1416	−	19.7116i	−0.935825	−	0.540299i	−0.888649	+	0.458588i	$0.848355\pi$
$12$	−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	0.873123	−	0.487499i	$-0.162091\pi$
$17$	1.00758	+	1.74518i	0.0143749	+	0.0248981i	−0.858748	+	0.512397i	$0.828758\pi$
$18$			220.885i			2.89240i
$19$	52.1280	−	30.0961i	0.629420	−	0.363396i	−0.151107	−	0.988517i	$-0.548284\pi$
$19$	52.1280	−	30.0961i	0.629420	−	0.363396i	0.780528	+	0.625121i	$0.214951\pi$
$20$	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	−0.855719	−	0.517440i	$-0.826885\pi$
$23$	2.23438	−	3.87006i	0.0202565	−	0.0350853i	0.875976	+	0.482355i	$0.160218\pi$
$24$	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	−0.998414	−	0.0563003i	$-0.982070\pi$
$29$	−70.3466	+	121.844i	−0.450449	+	0.780201i	0.547964	+	0.836502i	$0.315403\pi$
$30$	−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	$-0.197964\pi$
$37$	160.828	+	92.8542i	0.714594	+	0.412571i	−0.0981657	+	0.995170i	$0.531298\pi$
$38$	−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	$-0.132125\pi$
$41$	268.668	+	155.116i	1.02339	+	0.590853i	0.108304	+	0.994118i	$0.465458\pi$
$42$	189.393	−	328.038i	0.695809	−	1.20518i
$43$	213.735	+	370.200i	0.758008	+	1.31291i	0.943865	+	0.330331i	$0.107160\pi$
$43$	213.735	+	370.200i	0.758008	+	1.31291i	−0.185857	+	0.982577i	$0.559506\pi$
$44$		−	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	$-0.860259\pi$
$59$	−448.502	+	258.943i	−0.989661	+	0.571381i	−0.0844878	+	0.996425i	$0.526925\pi$
$60$			312.311i			0.671985i
$61$	80.6553	+	139.699i	0.169293	+	0.293223i	0.938171	−	0.346171i	$-0.112518\pi$
$61$	80.6553	+	139.699i	0.169293	+	0.293223i	−0.768879	+	0.639395i	$0.779185\pi$
$62$	−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	$-0.347819\pi$
$67$	−43.2135	−	24.9493i	−0.0787966	−	0.0454933i	−0.538881	+	0.842382i	$0.681153\pi$
$68$	−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	$-0.741842\pi$
$71$	−242.455	+	139.982i	−0.405269	+	0.233982i	0.283486	+	0.958976i	$0.408509\pi$
$72$	−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	$-0.371870\pi$
$89$	−175.635	−	101.403i	−0.209183	−	0.120772i	−0.600932	+	0.799300i	$0.705204\pi$
$90$	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	$-0.455970\pi$
$97$	1017.03	−	587.184i	1.06458	−	0.614634i	0.926695	+	0.375814i	$0.122637\pi$
$98$	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	−0.521528	−	0.853234i	$-0.674638\pi$
$101$	485.348	−	840.648i	0.478158	−	0.828194i	0.999686	+	0.0250397i	$0.00797123\pi$
$102$	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	−0.00947163	−	0.999955i	$-0.503015\pi$
$107$	953.247	−	1651.07i	0.861251	−	1.49173i	0.870722	−	0.491775i	$-0.163652\pi$
$108$	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	0.927267	−	0.374400i	$-0.122151\pi$
$113$	167.441	+	290.017i	0.139394	+	0.241438i	−0.787873	+	0.615837i	$0.788818\pi$
$114$	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	−0.736951	−	0.675946i	$-0.763735\pi$
$127$	310.447	−	537.709i	0.216911	−	0.375701i	0.953862	+	0.300245i	$0.0970686\pi$
$128$	−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	$-0.604537\pi$
$137$	538.681	−	311.008i	0.335932	−	0.193950i	0.658471	+	0.752606i	$0.271203\pi$
$138$		−	177.032i		−	0.109203i
$139$	−165.290	−	286.291i	−0.100861	−	0.174697i	0.811178	−	0.584799i	$-0.198827\pi$
$139$	−165.290	−	286.291i	−0.100861	−	0.174697i	−0.912040	+	0.410102i	$0.865493\pi$
$140$	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	$-0.500832\pi$
$149$	1567.97	−	905.269i	0.862102	−	0.497735i	0.864716	+	0.502262i	$0.167499\pi$
$150$	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	−0.500798	+	0.865564i	$0.666960\pi$
$163$	−3123.23	+	1803.20i	−1.50080	+	0.866486i	−1.00000		0.000922205i	$0.999706\pi$
$164$			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	$-0.0427381\pi$
$167$	2957.85	+	1707.72i	1.37057	+	0.791300i	0.379571	+	0.925162i	$0.376071\pi$
$168$	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	0.999855	+	0.0170243i	$0.00541926\pi$
$173$	1171.11	+	2028.43i	0.514671	+	0.891436i	−0.485184	+	0.874412i	$0.661247\pi$
$174$			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	−0.927207	−	0.374550i	$-0.877797\pi$
$179$	−333.446	+	577.545i	−0.139234	+	0.241160i	0.787973	+	0.615710i	$0.211131\pi$
$180$	−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	0.716118	−	0.697980i	$-0.245917\pi$
$191$	−650.440	−	1126.59i	−0.246409	−	0.426793i	−0.962527	+	0.271186i	$0.912584\pi$
$192$	−3609.98	+	6252.68i	−1.35692	+	2.35025i
$193$	449.756	+	259.667i	0.167742	+	0.0968457i	0.581521	−	0.813532i	$-0.302458\pi$
$193$	449.756	+	259.667i	0.167742	+	0.0968457i	−0.413779	+	0.910377i	$0.635791\pi$
$194$	−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	$-0.142449\pi$
$197$	2702.91	+	1560.52i	0.977534	+	0.564379i	0.0760091	+	0.997107i	$0.475782\pi$
$198$	4354.01	−	7541.38i	1.56276	−	2.70678i
$199$	618.529	+	1071.32i	0.220333	+	0.381629i	0.954909	−	0.296898i	$-0.0959521\pi$
$199$	618.529	+	1071.32i	0.220333	+	0.381629i	−0.734576	+	0.678527i	$0.762619\pi$
$200$		−	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	−0.582214	−	0.813036i	$-0.697813\pi$
$211$	1265.83	−	2192.49i	0.413003	−	0.715342i	0.995217	+	0.0976940i	$0.0311466\pi$
$212$	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	$-0.390783\pi$
$223$	−1035.36	−	597.766i	−0.310910	−	0.179504i	−0.647333	+	0.762207i	$0.724116\pi$
$224$	−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	$-0.626109\pi$
$227$	752.742	−	434.596i	0.220094	−	0.127071i	0.605994	+	0.795469i	$0.292776\pi$
$228$	−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	$-0.379187\pi$
$241$	5088.73	−	2937.98i	1.36014	−	0.785278i	0.989642	+	0.143555i	$0.0458534\pi$
$242$		−	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	0.956858	+	0.290554i	$0.0938397\pi$
$251$	2903.13	+	5028.38i	0.730057	+	1.26450i	−0.226802	+	0.973941i	$0.572827\pi$
$252$		−	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	−0.929421	−	0.369022i	$-0.879693\pi$
$257$	−597.930	+	1035.65i	−0.145128	+	0.251369i	0.784293	+	0.620391i	$0.213026\pi$
$258$	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	−0.879426	−	0.476036i	$-0.842073\pi$
$263$	−117.092	+	202.810i	−0.0274533	+	0.0475505i	0.851972	+	0.523587i	$0.175406\pi$
$264$	−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	0.976677	−	0.214712i	$-0.0688813\pi$
$269$	1334.13	+	2310.79i	0.302393	+	0.523760i	−0.674285	+	0.738471i	$0.735548\pi$
$270$	−1191.47	+	2063.68i	−0.268557	+	0.465155i
$271$	−4937.45	−	2850.64i	−1.10675	−	0.638982i	−0.168763	−	0.985657i	$-0.553977\pi$
$271$	−4937.45	−	2850.64i	−1.10675	−	0.638982i	−0.937985	+	0.346675i	$0.887311\pi$
$272$	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	−0.934386	−	0.356261i	$-0.884051\pi$
$277$	−3576.24	−	6194.24i	−0.775725	−	1.34359i	0.158662	−	0.987333i	$-0.449282\pi$
$278$			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	−0.632380	−	0.774658i	$-0.717922\pi$
$283$	1688.58	−	2924.70i	0.354683	−	0.614330i	0.987064	+	0.160328i	$0.0512553\pi$
$284$	−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	$-0.822065\pi$
$293$	−4074.45	+	2352.38i	−0.812395	+	0.469037i	0.0353917	+	0.999374i	$0.488732\pi$
$294$			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	$-0.561373\pi$
$331$	3387.69	−	1955.89i	0.562551	−	0.324789i	0.754169	+	0.656681i	$0.228040\pi$
$332$	−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	0.975152	−	0.221535i	$-0.0711068\pi$
$347$	1911.51	+	3310.83i	0.295721	+	0.512204i	−0.679431	+	0.733739i	$0.737773\pi$
$348$	7824.72	−	13552.8i	1.20531	−	2.08767i
$349$	−2953.72	−	1705.33i	−0.453035	−	0.261560i	0.256076	−	0.966657i	$-0.417570\pi$
$349$	−2953.72	−	1705.33i	−0.453035	−	0.261560i	−0.709111	+	0.705097i	$0.750904\pi$
$350$	−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	$-0.471741\pi$
$353$	−4839.03	−	2793.82i	−0.729620	−	0.421246i	−0.818283	+	0.574815i	$0.805074\pi$
$354$	−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	−0.371078	−	0.928602i	$-0.621012\pi$
$367$	4349.57	−	7533.68i	0.618653	−	1.07154i	0.989732	−	0.142938i	$-0.0456548\pi$
$368$	−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	−0.942337	−	0.334665i	$-0.891377\pi$
$373$	−5482.09	−	9495.26i	−0.760997	−	1.31809i	0.181340	−	0.983420i	$-0.441956\pi$
$374$	−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	0.983260	+	0.182206i	$0.0583237\pi$
$379$	12046.5	+	6955.06i	1.63269	+	0.942631i	0.649425	+	0.760426i	$0.275010\pi$
$380$	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	$-0.656159\pi$
$383$	428.469	−	247.377i	0.0571638	−	0.0330035i	0.528310	+	0.849052i	$0.322826\pi$
$384$	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	$-0.704619\pi$
$397$	−1629.68	+	940.896i	−0.206023	+	0.118948i	0.393439	+	0.919351i	$0.371285\pi$
$398$		−	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	$-0.341694\pi$
$401$	−365.259	−	210.883i	−0.0454867	−	0.0262618i	−0.522571	+	0.852596i	$0.675027\pi$
$402$	−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	$-0.715933\pi$
$409$	−2208.55	+	1275.11i	−0.267007	+	0.154157i	0.360520	+	0.932752i	$0.382599\pi$
$410$	−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	0.238194	+	0.971218i	$0.423445\pi$
$419$	−6192.41	+	10725.6i	−0.722002	+	1.25054i	−0.960196	+	0.279327i	$0.909889\pi$
$420$	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	$-0.404402\pi$
$431$	−3431.53	−	1981.19i	−0.383506	−	0.221417i	−0.679342	+	0.733821i	$0.737735\pi$
$432$	225.432	−	390.459i	0.0251067	−	0.0434860i
$433$	−4197.07	−	7269.54i	−0.465816	−	0.806817i	0.533422	−	0.845849i	$-0.320906\pi$
$433$	−4197.07	−	7269.54i	−0.465816	−	0.806817i	−0.999238	+	0.0390321i	$0.987573\pi$
$434$			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	−0.444972	−	0.895545i	$-0.646786\pi$
$439$	5087.26	−	8811.39i	0.553079	−	0.957960i	0.998050	−	0.0624156i	$-0.0198804\pi$
$440$	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	$-0.477285\pi$
$449$	9236.05	−	5332.43i	0.970771	−	0.560475i	0.899471	+	0.436980i	$0.143952\pi$
$450$			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	$-0.607612\pi$
$457$	−12842.2	−	7414.43i	−1.31451	−	0.758933i	−0.982840	+	0.184462i	$0.940946\pi$
$458$	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	$-0.503450\pi$
$461$	8410.58	−	4855.85i	0.849717	−	0.490585i	0.860555	+	0.509357i	$0.170117\pi$
$462$	−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	$-0.182520\pi$
$479$	8284.79	+	4783.23i	0.790275	+	0.456266i	−0.0497842	+	0.998760i	$0.515853\pi$
$480$	−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	$-0.740135\pi$
$487$	−4258.35	+	2458.56i	−0.396230	+	0.228764i	0.288626	+	0.957442i	$0.406802\pi$
$488$	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	−0.790220	−	0.612823i	$-0.790034\pi$
$491$	1475.41	−	2555.49i	0.135610	−	0.234883i	0.925830	+	0.377940i	$0.123367\pi$
$492$	−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	0.835283	−	0.549821i	$-0.185304\pi$
$503$	−660.143	−	1143.40i	−0.0585175	−	0.101355i	−0.893800	+	0.448466i	$0.851971\pi$
$504$	−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	0.995221	+	0.0976524i	$0.0311333\pi$
$509$	18114.2	+	10458.2i	1.57740	+	0.910713i	0.582180	+	0.813060i	$0.302200\pi$
$510$	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	−0.975704	−	0.219092i	$-0.929691\pi$
$523$	−3565.61	+	6175.82i	−0.298113	+	0.516347i	0.677591	+	0.735439i	$0.263024\pi$
$524$	−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	0.999990	+	0.00450060i	$0.00143259\pi$
$557$	19769.5	+	11414.0i	1.50388	+	0.868267i	0.503893	+	0.863766i	$0.331901\pi$
$558$	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	0.913157	+	0.407609i	$0.133637\pi$
$563$	10814.9	+	18731.9i	0.809578	+	1.40223i	−0.103579	+	0.994621i	$0.533029\pi$
$564$			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	−0.992464	−	0.122534i	$-0.960898\pi$
$569$	−5294.93	+	9171.09i	−0.390114	+	0.675698i	0.602350	+	0.798232i	$0.294231\pi$
$570$	−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	$-0.344049\pi$
$587$	−829.068	−	478.663i	−0.0582952	−	0.0336568i	−0.528864	+	0.848706i	$0.677382\pi$
$588$	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	−0.953962	−	0.299926i	$-0.903038\pi$
$601$	−3200.71	+	5543.79i	−0.217237	+	0.376266i	0.736725	+	0.676192i	$0.236371\pi$
$602$	−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	0.815818	−	0.578308i	$-0.196287\pi$
$607$	−1389.62	−	2406.89i	−0.0929207	−	0.160943i	−0.908739	+	0.417365i	$0.862954\pi$
$608$	−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	$-0.0656750\pi$
$613$	19590.2	+	11310.4i	1.29077	+	0.745226i	0.311979	+	0.950089i	$0.399008\pi$
$614$	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	$-0.921101\pi$
$617$	−19030.1	+	10987.0i	−1.24169	+	0.716889i	−0.272250	+	0.962226i	$0.587768\pi$
$618$	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	$-0.869778\pi$
$631$	−16353.4	+	9441.62i	−1.03172	+	0.595666i	−0.114245	+	0.993453i	$0.536445\pi$
$632$		−	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	0.804653	−	0.593745i	$-0.202351\pi$
$641$	−1815.54	−	3144.61i	−0.111871	−	0.193767i	−0.916525	+	0.399978i	$0.869018\pi$
$642$		−	75526.7i		−	4.64299i
$643$	9328.78	−	5385.98i	0.572148	−	0.330330i	−0.185859	−	0.982576i	$-0.559507\pi$
$643$	9328.78	−	5385.98i	0.572148	−	0.330330i	0.758007	+	0.652247i	$0.226173\pi$
$644$	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	−0.538740	−	0.842472i	$-0.681099\pi$
$647$	7574.14	−	13118.8i	0.460232	−	0.797146i	0.998972	+	0.0453265i	$0.0144328\pi$
$648$	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	−0.954961	−	0.296733i	$-0.904103\pi$
$653$	−3679.45	+	6372.99i	−0.220502	+	0.381921i	0.734458	+	0.678654i	$0.237436\pi$
$654$	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	−0.892052	−	0.451932i	$-0.850735\pi$
$659$	−14166.6	−	24537.3i	−0.837411	−	1.45044i	0.0546414	−	0.998506i	$-0.482598\pi$
$660$	6156.16	−	10662.8i	0.363073	−	0.628860i
$661$	−961.014	−	554.842i	−0.0565493	−	0.0326488i	0.471459	−	0.881888i	$-0.343728\pi$
$661$	−961.014	−	554.842i	−0.0565493	−	0.0326488i	−0.528008	+	0.849239i	$0.677061\pi$
$662$	−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	−0.391893	−	0.920011i	$-0.628180\pi$
$673$	10489.5	−	18168.4i	0.600806	−	1.04063i	0.992699	−	0.120616i	$-0.0384868\pi$
$674$	−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	$-0.618096\pi$
$683$	4699.24	−	2713.11i	0.263267	−	0.151997i	0.625824	+	0.779964i	$0.284763\pi$
$684$		−	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	−0.989104	−	0.147219i	$-0.952968\pi$
$691$	−29265.3	−	16896.3i	−1.61115	−	0.930199i	−0.622048	−	0.782979i	$-0.713699\pi$
$692$	−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	$-0.683596\pi$
$709$	−1738.22	+	1003.56i	−0.0920739	+	0.0531589i	0.453256	+	0.891380i	$0.350262\pi$
$710$		−	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	0.651198	−	0.758908i	$-0.274267\pi$
$719$	−6393.72	−	11074.3i	−0.331635	−	0.574409i	−0.982833	+	0.184499i	$0.940934\pi$
$720$			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	$-0.450499\pi$
$739$	−12520.6	−	7228.77i	−0.623245	−	0.359830i	−0.778131	+	0.628102i	$0.783832\pi$
$740$	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	$-0.343377\pi$
$743$	−1106.61	−	638.901i	−0.0546400	−	0.0315464i	−0.527071	+	0.849821i	$0.676710\pi$
$744$	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	−0.979654	−	0.200694i	$-0.935680\pi$
$751$	−6503.93	+	11265.1i	−0.316021	+	0.547364i	0.663633	+	0.748058i	$0.269014\pi$
$752$	−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	−0.708126	−	0.706086i	$-0.750459\pi$
$757$	5361.61	−	9286.57i	0.257425	−	0.445874i	0.965551	+	0.260212i	$0.0837926\pi$
$758$	−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	$-0.561492\pi$
$761$	11796.8	−	6810.90i	0.561938	−	0.324435i	0.753923	+	0.656963i	$0.228159\pi$
$762$		−	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	$-0.397162\pi$
$769$	−7357.01	−	4247.57i	−0.344994	−	0.199183i	−0.662478	+	0.749081i	$0.730495\pi$
$770$	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	$-0.960307\pi$
$773$	−29672.2	+	17131.3i	−1.38064	+	0.797113i	−0.388405	+	0.921489i	$0.626974\pi$
$774$	−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	$-0.759097\pi$
$787$	−10948.8	+	6321.29i	−0.495912	+	0.286315i	0.231112	+	0.972927i	$0.425764\pi$
$788$			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	0.996335	−	0.0855350i	$-0.0272600\pi$
$797$	9542.18	+	16527.5i	0.424092	+	0.734549i	−0.572243	+	0.820084i	$0.693927\pi$
$798$		−	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	−0.964153	−	0.265347i	$-0.914513\pi$
$809$	−5805.02	+	10054.6i	−0.252279	+	0.436960i	0.711874	+	0.702307i	$0.247847\pi$
$810$	−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	$-0.523631\pi$
$821$	−22933.6	−	13240.7i	−0.974895	−	0.562856i	−0.900725	+	0.434390i	$0.856964\pi$
$822$	12320.7	−	21340.1i	0.522792	−	0.905502i
$823$	6907.25	+	11963.7i	0.292553	+	0.506718i	0.974413	−	0.224766i	$-0.0721617\pi$
$823$	6907.25	+	11963.7i	0.292553	+	0.506718i	−0.681859	+	0.731483i	$0.738828\pi$
$824$		−	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	−0.490120	−	0.871655i	$-0.663047\pi$
$829$	12168.7	−	21076.8i	0.509815	−	0.883025i	0.999935	−	0.0113707i	$-0.00361948\pi$
$830$	−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	$-0.836200\pi$
$839$	−21373.6	+	12340.0i	−0.879497	+	0.507778i	−0.00900472	+	0.999959i	$0.502866\pi$
$840$		−	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	$-0.866031\pi$
$877$	−26368.3	+	15223.8i	−1.01527	+	0.586168i	−0.102542	+	0.994729i	$0.532698\pi$
$878$	−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	−0.366840	−	0.930284i	$-0.619560\pi$
$881$	16271.0	−	28182.2i	0.622230	−	1.07773i	0.989070	−	0.147450i	$-0.0471065\pi$
$882$	−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	0.184397	+	0.982852i	$0.440967\pi$
$887$	−20050.0	+	34727.5i	−0.758976	+	1.31458i	−0.943373	+	0.331733i	$0.892367\pi$
$888$	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	0.302679	+	0.953092i	$0.402119\pi$
$907$	−18412.4	+	31891.3i	−0.674062	+	1.16751i	−0.976742	+	0.214418i	$0.931215\pi$
$908$	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	0.573983	−	0.818867i	$-0.305397\pi$
$919$	−11761.4	−	20371.3i	−0.422168	−	0.731216i	−0.996151	+	0.0876506i	$0.972064\pi$
$920$	−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	$-0.523860\pi$
$929$	21272.3	−	12281.6i	0.751262	−	0.433741i	0.826150	+	0.563451i	$0.190527\pi$
$930$	−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	$-0.374045\pi$
$947$	−6438.31	−	3717.16i	−0.220926	−	0.127552i	−0.606379	+	0.795176i	$0.707379\pi$
$948$	−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	0.593833	−	0.804588i	$-0.297614\pi$
$953$	−11764.3	−	20376.3i	−0.399877	−	0.692607i	−0.993710	+	0.111981i	$0.964280\pi$
$954$			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	0.868185	−	0.496241i	$-0.165287\pi$
$971$	131.169	+	227.191i	0.00433513	+	0.00750866i	−0.863850	+	0.503750i	$0.831953\pi$
$972$	−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	$-0.150746\pi$
$977$	28703.9	+	16572.2i	0.939936	+	0.542673i	0.0499960	+	0.998749i	$0.484079\pi$
$978$	−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	−0.948814	−	0.315836i	$-0.897715\pi$
$991$	−6266.97	+	10854.7i	−0.200885	+	0.347943i	0.747929	+	0.663779i	$0.231048\pi$
$992$	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	0.892918	−	0.450220i	$-0.148654\pi$
$997$	1780.46	+	3083.84i	0.0565574	+	0.0979602i	−0.836361	+	0.548180i	$0.815321\pi$
$998$	−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.147.1		8
13.2	odd	12		169.4.c.f.146.1		4
13.3	even	3	inner	169.4.e.g.23.4		8
13.4	even	6		169.4.b.e.168.1		4
13.5	odd	4		169.4.c.f.22.1		4
13.6	odd	12		169.4.a.j.1.2		2
13.7	odd	12		169.4.a.f.1.1		2
13.8	odd	4		13.4.c.b.9.2	yes	4
13.9	even	3		169.4.b.e.168.4		4
13.10	even	6	inner	169.4.e.g.23.1		8
13.11	odd	12		13.4.c.b.3.2	✓	4
13.12	even	2	inner	169.4.e.g.147.4		8
39.8	even	4		117.4.g.d.100.1		4
39.11	even	12		117.4.g.d.55.1		4
39.20	even	12		1521.4.a.t.1.2		2
39.32	even	12		1521.4.a.l.1.1		2
52.11	even	12		208.4.i.e.81.2		4
52.47	even	4		208.4.i.e.113.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.c.b.3.2	✓	4	13.11	odd	12
13.4.c.b.9.2	yes	4	13.8	odd	4
117.4.g.d.55.1		4	39.11	even	12
117.4.g.d.100.1		4	39.8	even	4
169.4.a.f.1.1		2	13.7	odd	12
169.4.a.j.1.2		2	13.6	odd	12
169.4.b.e.168.1		4	13.4	even	6
169.4.b.e.168.4		4	13.9	even	3
169.4.c.f.22.1		4	13.5	odd	4
169.4.c.f.146.1		4	13.2	odd	12
169.4.e.g.23.1		8	13.10	even	6	inner
169.4.e.g.23.4		8	13.3	even	3	inner
169.4.e.g.147.1		8	1.1	even	1	trivial
169.4.e.g.147.4		8	13.12	even	2	inner
208.4.i.e.81.2		4	52.11	even	12
208.4.i.e.113.2		4	52.47	even	4
1521.4.a.l.1.1		2	39.32	even	12
1521.4.a.t.1.2		2	39.20	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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 10 q^{3} + 10 q^{4} - 70 q^{9} - 10 q^{10} - 560 q^{12} - 184 q^{14} - 114 q^{16} + 140 q^{17} + 340 q^{22} + 290 q^{23} - 300 q^{25} + 1340 q^{27} - 68 q^{29} - 280 q^{30} + 140 q^{35} + 1450 q^{36}+ \cdots + 2540 q^{95}+O(q^{100}) \) 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

Modular forms

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