LMFDB - Embedded newform 169.4.e.h.23.2

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:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.2
Character	$\chi$	$=$	169.23
Dual form			169.4.e.h.147.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.19172 + 2.42009i) q^{2} +(3.09831 + 5.36643i) q^{3} +(7.71365 - 13.3604i) q^{4} +15.2399i q^{5} +(-25.9745 - 14.9964i) q^{6} +(3.73794 + 2.15810i) q^{7} +35.9495i q^{8} +(-5.69903 + 9.87102i) q^{9} +O(q^{10})$	\(q+(-4.19172 + 2.42009i) q^{2} +(3.09831 + 5.36643i) q^{3} +(7.71365 - 13.3604i) q^{4} +15.2399i q^{5} +(-25.9745 - 14.9964i) q^{6} +(3.73794 + 2.15810i) q^{7} +35.9495i q^{8} +(-5.69903 + 9.87102i) q^{9} +(-36.8818 - 63.8811i) q^{10} +(-21.2775 + 12.2846i) q^{11} +95.5971 q^{12} -20.8912 q^{14} +(-81.7836 + 47.2178i) q^{15} +(-25.2917 - 43.8065i) q^{16} +(-63.5802 + 110.124i) q^{17} -55.1687i q^{18} +(-44.8135 - 25.8731i) q^{19} +(203.611 + 117.555i) q^{20} +26.7459i q^{21} +(59.4595 - 102.987i) q^{22} +(43.6842 + 75.6632i) q^{23} +(-192.920 + 111.383i) q^{24} -107.253 q^{25} +96.6792 q^{27} +(57.6664 - 33.2937i) q^{28} +(-112.863 - 195.484i) q^{29} +(228.542 - 395.847i) q^{30} -108.720i q^{31} +(-37.0342 - 21.3817i) q^{32} +(-131.849 - 76.1228i) q^{33} -615.479i q^{34} +(-32.8892 + 56.9657i) q^{35} +(87.9208 + 152.283i) q^{36} +(100.248 - 57.8782i) q^{37} +250.461 q^{38} -547.865 q^{40} +(166.177 - 95.9425i) q^{41} +(-64.7274 - 112.111i) q^{42} +(-61.6504 + 106.782i) q^{43} +379.036i q^{44} +(-150.433 - 86.8524i) q^{45} +(-366.223 - 211.439i) q^{46} -36.7339i q^{47} +(156.723 - 271.452i) q^{48} +(-162.185 - 280.913i) q^{49} +(449.574 - 259.562i) q^{50} -787.965 q^{51} +119.162 q^{53} +(-405.252 + 233.972i) q^{54} +(-187.215 - 324.266i) q^{55} +(-77.5827 + 134.377i) q^{56} -320.651i q^{57} +(946.178 + 546.276i) q^{58} +(696.763 + 402.276i) q^{59} +1456.89i q^{60} +(-339.443 + 587.933i) q^{61} +(263.113 + 455.725i) q^{62} +(-42.6053 + 24.5982i) q^{63} +611.650 q^{64} +736.896 q^{66} +(75.7604 - 43.7403i) q^{67} +(980.872 + 1698.92i) q^{68} +(-270.694 + 468.856i) q^{69} -318.379i q^{70} +(-849.614 - 490.525i) q^{71} +(-354.858 - 204.877i) q^{72} +263.862i q^{73} +(-280.140 + 485.218i) q^{74} +(-332.303 - 575.566i) q^{75} +(-691.352 + 399.152i) q^{76} -106.045 q^{77} +321.051 q^{79} +(667.604 - 385.441i) q^{80} +(453.416 + 785.339i) q^{81} +(-464.378 + 804.327i) q^{82} +1042.54i q^{83} +(357.337 + 206.308i) q^{84} +(-1678.28 - 968.953i) q^{85} -596.798i q^{86} +(699.368 - 1211.34i) q^{87} +(-441.624 - 764.915i) q^{88} +(-298.558 + 172.373i) q^{89} +840.762 q^{90} +1347.86 q^{92} +(583.440 - 336.849i) q^{93} +(88.8993 + 153.978i) q^{94} +(394.302 - 682.951i) q^{95} -264.989i q^{96} +(-417.876 - 241.261i) q^{97} +(1359.67 + 785.005i) q^{98} -280.041i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9}+O(q^{10}) $ 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9	$ 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9} - 294 q^{10} - 156 q^{12} - 588 q^{14} - 538 q^{16} - 110 q^{17} - 680 q^{22} - 408 q^{23} - 1228 q^{25} - 2672 q^{27} - 560 q^{29} + 1042 q^{30} - 40 q^{35} - 1818 q^{36} + 2956 q^{38} + 52 q^{40} + 8 q^{42} - 1066 q^{43} + 264 q^{48} + 806 q^{49} - 1880 q^{51} - 1112 q^{53} + 500 q^{55} + 500 q^{56} + 272 q^{61} + 4070 q^{62} - 1136 q^{64} + 13116 q^{66} + 3072 q^{68} - 4100 q^{69} + 3980 q^{74} + 4786 q^{75} + 2872 q^{77} + 1648 q^{79} + 1670 q^{81} + 5514 q^{82} + 1572 q^{87} - 1272 q^{88} + 5120 q^{90} + 16040 q^{92} + 5062 q^{94} - 3228 q^{95}+O(q^{100}) $ 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9 - 294 * q^10 - 156 * q^12 - 588 * q^14 - 538 * q^16 - 110 * q^17 - 680 * q^22 - 408 * q^23 - 1228 * q^25 - 2672 * q^27 - 560 * q^29 + 1042 * q^30 - 40 * q^35 - 1818 * q^36 + 2956 * q^38 + 52 * q^40 + 8 * q^42 - 1066 * q^43 + 264 * q^48 + 806 * q^49 - 1880 * q^51 - 1112 * q^53 + 500 * q^55 + 500 * q^56 + 272 * q^61 + 4070 * q^62 - 1136 * q^64 + 13116 * q^66 + 3072 * q^68 - 4100 * q^69 + 3980 * q^74 + 4786 * q^75 + 2872 * q^77 + 1648 * q^79 + 1670 * q^81 + 5514 * q^82 + 1572 * q^87 - 1272 * q^88 + 5120 * q^90 + 16040 * q^92 + 5062 * q^94 - 3228 * 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 $

$2$	−4.19172	+	2.42009i	−1.48200	+	0.855630i	−0.999791	−	0.0204286i	$-0.993497\pi$
$2$	−4.19172	+	2.42009i	−1.48200	+	0.855630i	−0.482204	+	0.876059i	$0.660164\pi$
$3$	3.09831	+	5.36643i	0.596270	+	1.03277i	0.993366	+	0.114993i	$0.0366845\pi$
$3$	3.09831	+	5.36643i	0.596270	+	1.03277i	−0.397097	+	0.917777i	$0.629982\pi$
$4$	7.71365	−	13.3604i	0.964207	−	1.67006i
$5$			15.2399i			1.36309i	0.731774	+	0.681547i	$0.238692\pi$
$5$			15.2399i			1.36309i	−0.731774	+	0.681547i	$0.761308\pi$
$6$	−25.9745	−	14.9964i	−1.76734	−	1.02037i
$7$	3.73794	+	2.15810i	0.201830	+	0.116527i	0.597509	−	0.801862i	$-0.296157\pi$
$7$	3.73794	+	2.15810i	0.201830	+	0.116527i	−0.395679	+	0.918389i	$0.629491\pi$
$8$			35.9495i			1.58876i
$9$	−5.69903	+	9.87102i	−0.211075	+	0.365593i
$10$	−36.8818	−	63.8811i	−1.16630	−	2.02010i
$11$	−21.2775	+	12.2846i	−0.583219	+	0.336722i	−0.762412	−	0.647092i	$-0.775985\pi$
$11$	−21.2775	+	12.2846i	−0.583219	+	0.336722i	0.179193	+	0.983814i	$0.442651\pi$
$12$	95.5971			2.29971
$13$		0			0
$13$		0			0
$14$	−20.8912			−0.398815
$15$	−81.7836	+	47.2178i	−1.40776	+	0.812772i
$16$	−25.2917	−	43.8065i	−0.395183	−	0.684476i
$17$	−63.5802	+	110.124i	−0.907086	+	1.57112i	−0.0889948	+	0.996032i	$0.528365\pi$
$17$	−63.5802	+	110.124i	−0.907086	+	1.57112i	−0.818092	+	0.575088i	$0.804968\pi$
$18$		−	55.1687i		−	0.722410i
$19$	−44.8135	−	25.8731i	−0.541101	−	0.312405i	0.204424	−	0.978882i	$-0.434468\pi$
$19$	−44.8135	−	25.8731i	−0.541101	−	0.312405i	−0.745525	+	0.666478i	$0.767801\pi$
$20$	203.611	+	117.555i	2.27644	+	1.31430i
$21$			26.7459i			0.277925i
$22$	59.4595	−	102.987i	0.576219	−	0.998040i
$23$	43.6842	+	75.6632i	0.396034	+	0.685951i	0.993233	−	0.116142i	$-0.0370529\pi$
$23$	43.6842	+	75.6632i	0.396034	+	0.685951i	−0.597199	+	0.802093i	$0.703720\pi$
$24$	−192.920	+	111.383i	−1.64082	+	0.947328i
$25$	−107.253			−0.858024
$26$		0			0
$27$	96.6792			0.689108
$28$	57.6664	−	33.2937i	0.389212	−	0.224711i
$29$	−112.863	−	195.484i	−0.722693	−	1.25174i	−0.959917	−	0.280286i	$-0.909571\pi$
$29$	−112.863	−	195.484i	−0.722693	−	1.25174i	0.237223	−	0.971455i	$-0.423763\pi$
$30$	228.542	−	395.847i	1.39086	−	2.40905i
$31$		−	108.720i		−	0.629895i	−0.949109	−	0.314948i	$-0.898013\pi$
$31$		−	108.720i		−	0.629895i	0.949109	−	0.314948i	$-0.101987\pi$
$32$	−37.0342	−	21.3817i	−0.204587	−	0.118118i
$33$	−131.849	−	76.1228i	−0.695512	−	0.401554i
$34$		−	615.479i		−	3.10452i
$35$	−32.8892	+	56.9657i	−0.158837	+	0.275113i
$36$	87.9208	+	152.283i	0.407041	+	0.705015i
$37$	100.248	−	57.8782i	0.445423	−	0.257165i	−0.260472	−	0.965481i	$-0.583878\pi$
$37$	100.248	−	57.8782i	0.445423	−	0.257165i	0.705895	+	0.708316i	$0.250545\pi$
$38$	250.461			1.06921
$39$		0			0
$40$	−547.865			−2.16563
$41$	166.177	−	95.9425i	0.632988	−	0.365456i	−0.148920	−	0.988849i	$-0.547580\pi$
$41$	166.177	−	95.9425i	0.632988	−	0.365456i	0.781908	+	0.623393i	$0.214246\pi$
$42$	−64.7274	−	112.111i	−0.237801	−	0.411884i
$43$	−61.6504	+	106.782i	−0.218642	+	0.378699i	−0.954393	−	0.298553i	$-0.903496\pi$
$43$	−61.6504	+	106.782i	−0.218642	+	0.378699i	0.735751	+	0.677252i	$0.236829\pi$
$44$			379.036i			1.29868i
$45$	−150.433	−	86.8524i	−0.498338	−	0.287715i
$46$	−366.223	−	211.439i	−1.17384	−	0.677717i
$47$		−	36.7339i		−	0.114004i	−0.998374	−	0.0570020i	$-0.981846\pi$
$47$		−	36.7339i		−	0.114004i	0.998374	−	0.0570020i	$-0.0181541\pi$
$48$	156.723	−	271.452i	0.471271	−	0.816265i
$49$	−162.185	−	280.913i	−0.472843	−	0.818988i
$50$	449.574	−	259.562i	1.27159	−	0.734152i
$51$	−787.965			−2.16347
$52$		0			0
$53$	119.162			0.308833			0.154416	−	0.988006i	$-0.450650\pi$
$53$	119.162			0.308833			0.154416	+	0.988006i	$0.450650\pi$
$54$	−405.252	+	233.972i	−1.02126	+	0.589622i
$55$	−187.215	−	324.266i	−0.458983	−	0.794982i
$56$	−77.5827	+	134.377i	−0.185132	+	0.320659i
$57$		−	320.651i		−	0.745110i
$58$	946.178	+	546.276i	2.14206	+	1.23672i
$59$	696.763	+	402.276i	1.53747	+	0.887660i	0.998986	+	0.0450253i	$0.0143368\pi$
$59$	696.763	+	402.276i	1.53747	+	0.887660i	0.538486	+	0.842634i	$0.318997\pi$
$60$			1456.89i			3.13472i
$61$	−339.443	+	587.933i	−0.712479	+	1.23405i	0.251444	+	0.967872i	$0.419094\pi$
$61$	−339.443	+	587.933i	−0.712479	+	1.23405i	−0.963924	+	0.266179i	$0.914239\pi$
$62$	263.113	+	455.725i	0.538957	+	0.933502i
$63$	−42.6053	+	24.5982i	−0.0852027	+	0.0491918i
$64$	611.650			1.19463
$65$		0			0
$66$	736.896			1.37433
$67$	75.7604	−	43.7403i	0.138143	−	0.0797571i	−0.429335	−	0.903145i	$-0.641252\pi$
$67$	75.7604	−	43.7403i	0.138143	−	0.0797571i	0.567479	+	0.823388i	$0.307919\pi$
$68$	980.872	+	1698.92i	1.74924	+	3.02977i
$69$	−270.694	+	468.856i	−0.472286	+	0.818024i
$70$		−	318.379i		−	0.543622i
$71$	−849.614	−	490.525i	−1.42015	−	0.819923i	−0.423838	−	0.905738i	$-0.639317\pi$
$71$	−849.614	−	490.525i	−1.42015	−	0.819923i	−0.996311	+	0.0858146i	$0.972651\pi$
$72$	−354.858	−	204.877i	−0.580839	−	0.335348i
$73$			263.862i			0.423051i	0.977372	+	0.211526i	$0.0678432\pi$
$73$			263.862i			0.423051i	−0.977372	+	0.211526i	$0.932157\pi$
$74$	−280.140	+	485.218i	−0.440077	+	0.762235i
$75$	−332.303	−	575.566i	−0.511614	−	0.886141i
$76$	−691.352	+	399.152i	−1.04347	+	0.602446i
$77$	−106.045			−0.156948
$78$		0			0
$79$	321.051			0.457228			0.228614	−	0.973517i	$-0.426581\pi$
$79$	321.051			0.457228			0.228614	+	0.973517i	$0.426581\pi$
$80$	667.604	−	385.441i	0.933005	−	0.538671i
$81$	453.416	+	785.339i	0.621970	+	1.07728i
$82$	−464.378	+	804.327i	−0.625390	+	1.08321i
$83$			1042.54i			1.37872i	0.724417	+	0.689362i	$0.242109\pi$
$83$			1042.54i			1.37872i	−0.724417	+	0.689362i	$0.757891\pi$
$84$	357.337	+	206.308i	0.464150	+	0.267977i
$85$	−1678.28	−	968.953i	−2.14158	−	1.23644i
$86$		−	596.798i		−	0.748307i
$87$	699.368	−	1211.34i	0.861840	−	1.49275i
$88$	−441.624	−	764.915i	−0.534969	−	0.926594i
$89$	−298.558	+	172.373i	−0.355586	+	0.205298i	−0.667143	−	0.744930i	$-0.732483\pi$
$89$	−298.558	+	172.373i	−0.355586	+	0.205298i	0.311557	+	0.950227i	$0.399150\pi$
$90$	840.762			0.984712
$91$		0			0
$92$	1347.86			1.52743
$93$	583.440	−	336.849i	0.650537	−	0.375587i
$94$	88.8993	+	153.978i	0.0975453	+	0.168953i
$95$	394.302	−	682.951i	0.425837	−	0.737572i
$96$		−	264.989i		−	0.281722i
$97$	−417.876	−	241.261i	−0.437411	−	0.252539i	0.265088	−	0.964224i	$-0.414599\pi$
$97$	−417.876	−	241.261i	−0.437411	−	0.252539i	−0.702499	+	0.711685i	$0.747932\pi$
$98$	1359.67	+	785.005i	1.40150	+	0.809158i
$99$		−	280.041i		−	0.284295i
$100$	−827.313	+	1432.95i	−0.827313	+	1.43295i
$101$	419.890	+	727.270i	0.413669	+	0.716496i	0.995288	−	0.0969656i	$-0.0309137\pi$
$101$	419.890	+	727.270i	0.413669	+	0.716496i	−0.581619	+	0.813462i	$0.697580\pi$
$102$	3302.92	−	1906.94i	3.20626	−	1.85113i
$103$	−159.823			−0.152892			−0.0764459	−	0.997074i	$-0.524357\pi$
$103$	−159.823			−0.152892			−0.0764459	+	0.997074i	$0.524357\pi$
$104$		0			0
$105$	−407.603			−0.378838
$106$	−499.493	+	288.382i	−0.457689	+	0.264247i
$107$	−537.812	−	931.518i	−0.485909	−	0.841619i	0.513960	−	0.857814i	$-0.328178\pi$
$107$	−537.812	−	931.518i	−0.485909	−	0.841619i	−0.999869	+	0.0161950i	$0.994845\pi$
$108$	745.750	−	1291.68i	0.664443	−	1.15085i
$109$			1161.67i			1.02080i	0.859936	+	0.510401i	$0.170503\pi$
$109$			1161.67i			1.02080i	−0.859936	+	0.510401i	$0.829497\pi$
$110$	1569.50	+	906.154i	1.36042	+	0.785440i
$111$	621.198	+	358.649i	0.531185	+	0.306680i
$112$		−	218.328i		−	0.184197i
$113$	731.742	−	1267.41i	0.609172	−	1.05512i	−0.382205	−	0.924078i	$-0.624835\pi$
$113$	731.742	−	1267.41i	0.609172	−	1.05512i	0.991377	−	0.131040i	$-0.0418316\pi$
$114$	776.004	+	1344.08i	0.637539	+	1.10425i
$115$	−1153.10	+	665.740i	−0.935015	+	0.539831i
$116$	−3482.34			−2.78730
$117$		0			0
$118$	−3894.18			−3.03803
$119$	−475.319	+	274.425i	−0.366154	+	0.211399i
$120$	−1697.45	−	2940.08i	−1.29130	−	2.23659i
$121$	−363.678	+	629.910i	−0.273237	+	0.473260i
$122$		−	3285.93i		−	2.43848i
$123$	1029.74	+	594.519i	0.754864	+	0.435821i
$124$	−1452.55	−	838.631i	−1.05196	−	0.607349i
$125$			270.461i			0.193526i
$126$	119.060	−	206.217i	0.0841800	−	0.145804i
$127$	144.962	+	251.081i	0.101285	+	0.175432i	0.912215	−	0.409713i	$-0.134371\pi$
$127$	144.962	+	251.081i	0.101285	+	0.175432i	−0.810929	+	0.585145i	$0.801038\pi$
$128$	−2267.59	+	1309.19i	−1.56585	+	0.904042i
$129$	−764.048			−0.521478
$130$		0			0
$131$	−1201.97			−0.801653			−0.400826	−	0.916154i	$-0.631277\pi$
$131$	−1201.97			−0.801653			−0.400826	+	0.916154i	$0.631277\pi$
$132$	−2034.07	+	1174.37i	−1.34123	+	0.774362i
$133$	−111.674	−	193.424i	−0.0728069	−	0.126105i
$134$	−211.711	+	366.694i	−0.136485	+	0.236399i
$135$			1473.38i			0.939319i
$136$	−3958.91	−	2285.68i	−2.49613	−	1.44114i
$137$	−675.171	−	389.810i	−0.421049	−	0.243093i	0.274477	−	0.961594i	$-0.411495\pi$
$137$	−675.171	−	389.810i	−0.421049	−	0.243093i	−0.695526	+	0.718501i	$0.744829\pi$
$138$		−	2620.41i		−	1.61641i
$139$	−1015.74	+	1759.32i	−0.619814	+	1.07355i	0.369706	+	0.929149i	$0.379459\pi$
$139$	−1015.74	+	1759.32i	−0.619814	+	1.07355i	−0.989519	+	0.144400i	$0.953875\pi$
$140$	507.391	+	878.827i	0.306303	+	0.530532i
$141$	197.130	−	113.813i	0.117740	−	0.0679772i
$142$	4748.45			2.80621
$143$		0			0
$144$	576.553			0.333653
$145$	2979.15	−	1720.01i	1.70624	−	0.985098i
$146$	−638.570	−	1106.04i	−0.361976	−	0.626960i
$147$	1005.00	−	1740.71i	0.563884	−	0.976676i
$148$		−	1785.81i		−	0.991841i
$149$	2254.79	+	1301.80i	1.23973	+	0.715757i	0.969038	−	0.246910i	$-0.0794153\pi$
$149$	2254.79	+	1301.80i	1.23973	+	0.715757i	0.270688	+	0.962667i	$0.412749\pi$
$150$	2785.84	+	1608.41i	1.51642	+	0.875505i
$151$			206.776i			0.111438i	0.998446	+	0.0557192i	$0.0177452\pi$
$151$			206.776i			0.111438i	−0.998446	+	0.0557192i	$0.982255\pi$
$152$	930.124	−	1611.02i	0.496336	−	0.859679i
$153$	−724.692	−	1255.20i	−0.382927	−	0.663249i
$154$	444.513	−	256.639i	0.232596	−	0.134290i
$155$	1656.88			0.858606
$156$		0			0
$157$	699.208			0.355433			0.177716	−	0.984082i	$-0.443129\pi$
$157$	699.208			0.355433			0.177716	+	0.984082i	$0.443129\pi$
$158$	−1345.75	+	776.971i	−0.677610	+	0.391218i
$159$	369.200	+	639.474i	0.184148	+	0.318953i
$160$	325.854	−	564.396i	0.161006	−	0.278871i
$161$			377.100i			0.184594i
$162$	−3801.18	−	2194.61i	−1.84351	−	1.06435i
$163$	2549.70	+	1472.07i	1.22520	+	0.707371i	0.966023	−	0.258458i	$-0.0832142\pi$
$163$	2549.70	+	1472.07i	1.22520	+	0.707371i	0.259180	+	0.965829i	$0.416548\pi$
$164$		−	2960.27i		−	1.40950i
$165$	1160.10	−	2009.35i	0.547356	−	0.948048i
$166$	−2523.05	−	4370.05i	−1.17968	−	2.04326i
$167$	−2373.62	+	1370.41i	−1.09986	+	0.635002i	−0.936183	−	0.351513i	$-0.885667\pi$
$167$	−2373.62	+	1370.41i	−1.09986	+	0.635002i	−0.163673	+	0.986515i	$0.552334\pi$
$168$	−961.500			−0.441556
$169$		0			0
$170$	9379.81			4.23176
$171$	510.787	−	294.903i	0.228426	−	0.131882i
$172$	951.100	+	1647.35i	0.421632	+	0.730288i
$173$	169.406	−	293.420i	0.0744491	−	0.128950i	−0.826397	−	0.563087i	$-0.809614\pi$
$173$	169.406	−	293.420i	0.0744491	−	0.128950i	0.900847	+	0.434138i	$0.142947\pi$
$174$			6770.13i			2.94967i
$175$	−400.906	−	231.463i	−0.173175	−	0.0999826i
$176$	1076.29	+	621.395i	0.460956	+	0.266133i
$177$			4985.51i			2.11714i
$178$	834.315	−	1445.08i	0.351318	−	0.608500i
$179$	−547.199	−	947.777i	−0.228489	−	0.395755i	0.728871	−	0.684651i	$-0.240045\pi$
$179$	−547.199	−	947.777i	−0.228489	−	0.395755i	−0.957361	+	0.288896i	$0.906712\pi$
$180$	−2320.77	+	1339.90i	−0.961001	+	0.554834i
$181$	1420.26			0.583243			0.291622	−	0.956534i	$-0.405805\pi$
$181$	1420.26			0.583243			0.291622	+	0.956534i	$0.405805\pi$
$182$		0			0
$183$	−4206.80			−1.69932
$184$	−2720.05	+	1570.42i	−1.08981	+	0.629202i
$185$	882.054	+	1527.76i	0.350540	+	0.607153i
$186$	−1630.41	+	2823.95i	−0.642728	+	1.11324i
$187$		−	3124.22i		−	1.22174i
$188$	−490.781	−	283.353i	−0.190393	−	0.109923i
$189$	361.381	+	208.644i	0.139083	+	0.0802994i
$190$			3816.98i			1.45744i
$191$	448.390	−	776.633i	0.169866	−	0.294216i	−0.768507	−	0.639842i	$-0.779000\pi$
$191$	448.390	−	776.633i	0.169866	−	0.294216i	0.938372	+	0.345626i	$0.112333\pi$
$192$	1895.08	+	3282.37i	0.712321	+	1.23378i
$193$	2242.98	−	1294.98i	0.836545	−	0.482980i	−0.0195433	−	0.999809i	$-0.506221\pi$
$193$	2242.98	−	1294.98i	0.836545	−	0.482980i	0.856088	+	0.516829i	$0.172888\pi$
$194$	2335.49			0.864321
$195$		0			0
$196$	−5004.16			−1.82367
$197$	−1283.33	+	740.934i	−0.464131	+	0.267966i	−0.713780	−	0.700370i	$-0.753018\pi$
$197$	−1283.33	+	740.934i	−0.464131	+	0.267966i	0.249649	+	0.968336i	$0.419685\pi$
$198$	677.724	+	1173.85i	0.243251	+	0.421323i
$199$	−1799.73	+	3117.22i	−0.641101	+	1.11042i	0.344086	+	0.938938i	$0.388189\pi$
$199$	−1799.73	+	3117.22i	−0.641101	+	1.11042i	−0.985187	+	0.171482i	$0.945144\pi$
$200$		−	3855.69i		−	1.36319i
$201$	469.458	+	271.042i	0.164741	+	0.0951135i
$202$	−3520.12	−	2032.34i	−1.22611	−	0.707896i
$203$		−	974.278i		−	0.336852i
$204$	−6078.09	+	10527.6i	−2.08604	+	3.61312i
$205$	1462.15	+	2532.52i	0.498151	+	0.862822i
$206$	669.933	−	386.786i	0.226585	−	0.130819i
$207$	−995.830			−0.334372
$208$		0			0
$209$	1271.36			0.420774
$210$	1708.56	−	986.435i	0.561436	−	0.324145i
$211$	−1525.61	−	2642.43i	−0.497759	−	0.862144i	0.502238	−	0.864730i	$-0.332510\pi$
$211$	−1525.61	−	2642.43i	−0.497759	−	0.862144i	−0.999997	+	0.00258567i	$0.999177\pi$
$212$	919.173	−	1592.05i	0.297779	−	0.515768i
$213$		−	6079.19i		−	1.95558i
$214$	4508.71	+	2603.11i	1.44023	+	0.831517i
$215$	−1627.34	−	939.544i	−0.516202	−	0.298030i
$216$			3475.57i			1.09483i
$217$	234.630	−	406.390i	0.0733995	−	0.127132i
$218$	−2811.34	−	4869.38i	−0.873430	−	1.51282i
$219$	−1416.00	+	817.527i	−0.436915	+	0.252253i
$220$	−5776.45			−1.77022
$221$		0			0
$222$	−3471.85			−1.04962
$223$	−2251.55	+	1299.93i	−0.676121	+	0.390359i	−0.798392	−	0.602138i	$-0.794316\pi$
$223$	−2251.55	+	1299.93i	−0.676121	+	0.390359i	0.122271	+	0.992497i	$0.460982\pi$
$224$	−92.2879	−	159.847i	−0.0275279	−	0.0476797i
$225$	611.239	−	1058.70i	0.181108	−	0.313688i
$226$			7083.52i			2.08491i
$227$	860.144	+	496.604i	0.251497	+	0.145202i	0.620449	−	0.784246i	$-0.286950\pi$
$227$	860.144	+	496.604i	0.251497	+	0.145202i	−0.368953	+	0.929448i	$0.620284\pi$
$228$	−4284.04	−	2473.39i	−1.24438	−	0.718440i
$229$		−	437.772i		−	0.126327i	−0.998003	−	0.0631633i	$-0.979881\pi$
$229$		−	437.772i		−	0.126327i	0.998003	−	0.0631633i	$-0.0201189\pi$
$230$	3222.30	−	5581.19i	0.923792	−	1.60006i
$231$	−328.562	−	569.085i	−0.0935834	−	0.162091i
$232$	7027.55	−	4057.36i	1.98871	−	1.14818i
$233$	−2933.08			−0.824689			−0.412344	−	0.911028i	$-0.635290\pi$
$233$	−2933.08			−0.824689			−0.412344	+	0.911028i	$0.635290\pi$
$234$		0			0
$235$	559.819			0.155398
$236$	10749.2	−	6206.04i	2.96488	−	1.71178i
$237$	994.714	+	1722.90i	0.272631	+	0.472211i
$238$	1328.27	−	2300.63i	0.361759	−	0.626586i
$239$			5813.48i			1.57340i	0.617335	+	0.786700i	$0.288212\pi$
$239$			5813.48i			1.57340i	−0.617335	+	0.786700i	$0.711788\pi$
$240$	4136.89	+	2388.43i	1.11265	+	0.642386i
$241$	994.413	+	574.125i	0.265792	+	0.153455i	0.626974	−	0.779040i	$-0.284293\pi$
$241$	994.413	+	574.125i	0.265792	+	0.153455i	−0.361182	+	0.932495i	$0.617627\pi$
$242$		−	3520.54i		−	0.935160i
$243$	−1504.48	+	2605.83i	−0.397169	+	0.687918i
$244$	5236.69	+	9070.22i	1.37395	+	2.37976i
$245$	4281.07	−	2471.68i	1.11636	−	0.644529i
$246$	−5755.15			−1.49161
$247$		0			0
$248$	3908.44			1.00075
$249$	−5594.74	+	3230.12i	−1.42390	+	0.822091i
$250$	−654.539	−	1133.70i	−0.165587	−	0.286805i
$251$	−1627.90	+	2819.60i	−0.409371	+	0.709051i	−0.994819	−	0.101659i	$-0.967585\pi$
$251$	−1627.90	+	2819.60i	−0.409371	+	0.709051i	0.585449	+	0.810709i	$0.300918\pi$
$252$			758.968i			0.189724i
$253$	−1858.98	−	1073.28i	−0.461949	−	0.266706i
$254$	−1215.28	−	701.639i	−0.300209	−	0.173326i
$255$		−	12008.5i		−	2.94902i
$256$	3890.12	−	6737.89i	0.949737	−	1.64499i
$257$	3160.45	+	5474.06i	0.767095	+	1.32865i	0.939132	+	0.343557i	$0.111632\pi$
$257$	3160.45	+	5474.06i	0.767095	+	1.32865i	−0.172037	+	0.985090i	$0.555035\pi$
$258$	3202.67	−	1849.06i	0.772829	−	0.446193i
$259$	499.628			0.119866
$260$		0			0
$261$	2572.84			0.610171
$262$	5038.31	−	2908.87i	1.18805	−	0.685919i
$263$	3084.49	+	5342.50i	0.723187	+	1.25260i	0.959716	+	0.280972i	$0.0906567\pi$
$263$	3084.49	+	5342.50i	0.723187	+	1.25260i	−0.236529	+	0.971624i	$0.576010\pi$
$264$	2736.58	−	4739.89i	0.637972	−	1.10500i
$265$			1816.01i			0.420968i
$266$	936.207	+	540.520i	0.215799	+	0.124592i
$267$	−1850.05	−	1068.13i	−0.424050	−	0.244825i
$268$		−	1349.59i		−	0.307609i
$269$	−421.799	+	730.578i	−0.0956043	+	0.165591i	−0.909861	−	0.414914i	$-0.863812\pi$
$269$	−421.799	+	730.578i	−0.0956043	+	0.165591i	0.814256	+	0.580505i	$0.197145\pi$
$270$	−3565.70	−	6175.98i	−0.803710	−	1.39207i
$271$	1786.66	−	1031.53i	0.400486	−	0.231221i	−0.286208	−	0.958168i	$-0.592395\pi$
$271$	1786.66	−	1031.53i	0.400486	−	0.231221i	0.686694	+	0.726947i	$0.259061\pi$
$272$	6432.20			1.43386
$273$		0			0
$274$	3773.50			0.831990
$275$	2282.08	−	1317.56i	0.500416	−	0.288915i
$276$	4176.08	+	7233.19i	0.910763	+	1.57749i
$277$	3291.24	−	5700.60i	0.713905	−	1.23652i	−0.249475	−	0.968381i	$-0.580258\pi$
$277$	3291.24	−	5700.60i	0.713905	−	1.23652i	0.963380	−	0.268139i	$-0.0864086\pi$
$278$		−	9832.74i		−	2.12133i
$279$	1073.18	+	619.601i	0.230285	+	0.132955i
$280$	−2047.89	−	1182.35i	−0.437088	−	0.252353i
$281$			935.025i			0.198502i	0.995062	+	0.0992508i	$0.0316446\pi$
$281$			935.025i			0.198502i	−0.995062	+	0.0992508i	$0.968355\pi$
$282$	−550.875	+	954.143i	−0.116327	+	0.201484i
$283$	−2669.38	−	4623.51i	−0.560701	−	0.971163i	−0.997435	−	0.0715723i	$-0.977198\pi$
$283$	−2669.38	−	4623.51i	−0.560701	−	0.971163i	0.436734	−	0.899591i	$-0.356135\pi$
$284$	−13107.3	+	7567.47i	−2.73863	+	1.58115i
$285$	4886.68			1.01566
$286$		0			0
$287$	828.215			0.170341
$288$	422.119	−	243.710i	0.0863666	−	0.0498638i
$289$	−5628.39	−	9748.66i	−1.14561	−	1.98426i
$290$	−8325.16	+	14419.6i	−1.68576	+	2.91982i
$291$		−	2990.00i		−	0.602326i
$292$	3525.32	+	2035.34i	0.706519	+	0.407909i
$293$	−1527.46	−	881.882i	−0.304558	−	0.175837i	0.339931	−	0.940450i	$-0.389596\pi$
$293$	−1527.46	−	881.882i	−0.304558	−	0.175837i	−0.644489	+	0.764614i	$0.722930\pi$
$294$			9728.75i			1.92991i
$295$	−6130.63	+	10618.6i	−1.20996	+	2.09572i
$296$	2080.69	+	3603.86i	0.408573	+	0.707669i
$297$	−2057.09	+	1187.66i	−0.401901	+	0.232038i
$298$	−12601.9			−2.44969
$299$		0			0
$300$	−10253.1			−1.97321
$301$	−460.892	+	266.096i	−0.0882570	+	0.0509552i
$302$	−500.416	−	866.747i	−0.0953501	−	0.165151i
$303$	−2601.90	+	4506.62i	−0.493317	+	0.854450i
$304$			2617.50i			0.493828i
$305$	−8960.01	−	5173.06i	−1.68213	−	0.971176i
$306$	6075.40	+	3507.64i	1.13499	+	0.655288i
$307$			4736.59i			0.880558i	0.897861	+	0.440279i	$0.145121\pi$
$307$			4736.59i			0.880558i	−0.897861	+	0.440279i	$0.854879\pi$
$308$	−817.998	+	1416.81i	−0.151330	+	0.262112i
$309$	−495.182	−	857.680i	−0.0911647	−	0.157902i
$310$	−6945.18	+	4009.80i	−1.27245	+	0.734649i
$311$	4746.90			0.865505			0.432753	−	0.901513i	$-0.357542\pi$
$311$	4746.90			0.865505			0.432753	+	0.901513i	$0.357542\pi$
$312$		0			0
$313$	10115.9			1.82679			0.913393	−	0.407078i	$-0.133452\pi$
$313$	10115.9			1.82679			0.913393	+	0.407078i	$0.133452\pi$
$314$	−2930.88	+	1692.15i	−0.526749	+	0.304119i
$315$	−374.873	−	649.299i	−0.0670530	−	0.116139i
$316$	2476.47	−	4289.38i	0.440862	−	0.763596i
$317$		−	5906.13i		−	1.04644i	−0.852198	−	0.523219i	$-0.824731\pi$
$317$		−	5906.13i		−	1.04644i	0.852198	−	0.523219i	$-0.175269\pi$
$318$	−3095.16	−	1786.99i	−0.545812	−	0.315125i
$319$	4802.88	+	2772.94i	0.842977	+	0.486693i
$320$			9321.45i			1.62839i
$321$	3332.62	−	5772.26i	0.579466	−	1.00366i
$322$	−912.615	−	1580.69i	−0.157944	−	0.273567i
$323$	5698.51	−	3290.03i	0.981651	−	0.566757i
$324$	13990.0			2.39883
$325$		0			0
$326$	−14250.2			−2.42099
$327$	−6234.00	+	3599.20i	−1.05425	+	0.608674i
$328$	3449.08	+	5973.98i	0.580621	+	1.00567i
$329$	79.2755	−	137.309i	0.0132845	−	0.0230094i
$330$			11230.2i			1.87334i
$331$	2427.32	+	1401.41i	0.403074	+	0.232715i	0.687809	−	0.725891i	$-0.258573\pi$
$331$	2427.32	+	1401.41i	0.403074	+	0.232715i	−0.284736	+	0.958606i	$0.591906\pi$
$332$	13928.8	+	8041.82i	2.30254	+	1.32937i
$333$			1319.40i			0.217125i
$334$	6633.02	−	11488.7i	1.08665	−	1.88214i
$335$	666.596	+	1154.58i	0.108716	+	0.188302i
$336$	1171.64	−	676.448i	0.190233	−	0.109831i
$337$	244.919			0.0395892			0.0197946	−	0.999804i	$-0.493699\pi$
$337$	244.919			0.0395892			0.0197946	+	0.999804i	$0.493699\pi$
$338$		0			0
$339$	9068.65			1.45292
$340$	−25891.3	+	14948.3i	−4.12986	+	2.38438i
$341$	1335.58	+	2313.30i	0.212099	+	0.367367i
$342$	−1427.38	+	2472.30i	−0.225684	+	0.390897i
$343$		−	2880.51i		−	0.453448i
$344$	−3838.75	−	2216.30i	−0.601661	−	0.347369i
$345$	−7145.30	−	4125.34i	−1.11504	−	0.643770i
$346$			1639.91i			0.254804i
$347$	−5178.41	+	8969.27i	−0.801129	+	1.38760i	0.117745	+	0.993044i	$0.462434\pi$
$347$	−5178.41	+	8969.27i	−0.801129	+	1.38760i	−0.918874	+	0.394552i	$0.870900\pi$
$348$	−10789.4	−	18687.7i	−1.66198	−	2.87864i
$349$	7303.69	−	4216.79i	1.12022	−	0.646761i	0.178765	−	0.983892i	$-0.442790\pi$
$349$	7303.69	−	4216.79i	1.12022	−	0.646761i	0.941458	+	0.337131i	$0.109456\pi$
$350$	2240.64			0.342193
$351$		0			0
$352$	1050.66			0.159092
$353$	4099.52	−	2366.86i	0.618118	−	0.356871i	−0.158018	−	0.987436i	$-0.550510\pi$
$353$	4099.52	−	2366.86i	0.618118	−	0.356871i	0.776136	+	0.630566i	$0.217177\pi$
$354$	−12065.4	−	20897.8i	−1.81149	−	3.13759i
$355$	7475.52	−	12948.0i	1.11763	−	1.93580i
$356$			5318.50i			0.791797i
$357$	−2945.37	−	1700.51i	−0.436654	−	0.252102i
$358$	4587.41	+	2648.54i	0.677240	+	0.391005i
$359$		−	7561.34i		−	1.11162i	−0.831309	−	0.555811i	$-0.812408\pi$
$359$		−	7561.34i		−	1.11162i	0.831309	−	0.555811i	$-0.187592\pi$
$360$	3122.30	−	5407.98i	0.457110	−	0.791738i
$361$	−2090.67	−	3621.14i	−0.304806	−	0.527940i
$362$	−5953.32	+	3437.15i	−0.864364	+	0.499041i
$363$	−4507.15			−0.651692
$364$		0			0
$365$	−4021.22			−0.576659
$366$	17633.7	−	10180.8i	2.51838	−	1.45399i
$367$	5969.99	+	10340.3i	0.849130	+	1.47074i	0.881986	+	0.471276i	$0.156206\pi$
$367$	5969.99	+	10340.3i	0.849130	+	1.47074i	−0.0328557	+	0.999460i	$0.510460\pi$
$368$	2209.69	−	3827.30i	0.313011	−	0.542152i
$369$			2187.12i			0.308555i
$370$	−7394.64	−	4269.30i	−1.03900	−	0.599866i
$371$	445.420	+	257.164i	0.0623317	+	0.0359872i
$372$		−	10393.4i		−	1.44858i
$373$	2898.56	−	5020.46i	0.402364	−	0.696915i	−0.591647	−	0.806197i	$-0.701522\pi$
$373$	2898.56	−	5020.46i	0.402364	−	0.696915i	0.994011	+	0.109282i	$0.0348552\pi$
$374$	7560.90	+	13095.9i	1.04536	+	1.81062i
$375$	−1451.41	+	837.971i	−0.199868	+	0.115394i
$376$	1320.56			0.181125
$377$		0			0
$378$	−2019.74			−0.274826
$379$	7661.13	−	4423.15i	1.03833	−	0.599478i	0.118968	−	0.992898i	$-0.462042\pi$
$379$	7661.13	−	4423.15i	1.03833	−	0.599478i	0.919359	+	0.393420i	$0.128708\pi$
$380$	−6083.02	−	10536.1i	−0.821190	−	1.42234i
$381$	−898.271	+	1555.85i	−0.120787	+	0.209209i
$382$			4340.57i			0.581369i
$383$	−907.256	−	523.805i	−0.121041	−	0.0698830i	0.438257	−	0.898850i	$-0.355596\pi$
$383$	−907.256	−	523.805i	−0.121041	−	0.0698830i	−0.559298	+	0.828967i	$0.688929\pi$
$384$	−14051.4	−	8112.56i	−1.86733	−	1.07811i
$385$		−	1616.12i		−	0.213935i
$386$	−6267.96	+	10856.4i	−0.826504	+	1.43155i
$387$	−702.696	−	1217.11i	−0.0922999	−	0.159868i
$388$	−6446.70	+	3722.00i	−0.843509	+	0.487000i
$389$	11858.4			1.54562			0.772808	−	0.634640i	$-0.218852\pi$
$389$	11858.4			1.54562			0.772808	+	0.634640i	$0.218852\pi$
$390$		0			0
$391$	−11109.8			−1.43695
$392$	10098.7	−	5830.47i	1.30117	−	0.751233i
$393$	−3724.07	−	6450.28i	−0.478001	−	0.827923i
$394$	3586.25	−	6211.57i	0.458560	−	0.794249i
$395$			4892.76i			0.623245i
$396$	−3741.47	−	2160.14i	−0.474788	−	0.274119i
$397$	9076.25	+	5240.17i	1.14741	+	0.662460i	0.948256	−	0.317507i	$-0.102846\pi$
$397$	9076.25	+	5240.17i	1.14741	+	0.662460i	0.199159	+	0.979967i	$0.436179\pi$
$398$		−	17422.0i		−	2.19418i
$399$	691.998	−	1198.58i	0.0868252	−	0.150386i
$400$	2712.61	+	4698.38i	0.339076	+	0.587297i
$401$	−6873.12	+	3968.20i	−0.855929	+	0.494171i	−0.862647	−	0.505807i	$-0.831195\pi$
$401$	−6873.12	+	3968.20i	−0.855929	+	0.494171i	0.00671803	+	0.999977i	$0.497862\pi$
$402$	−2623.78			−0.325528
$403$		0			0
$404$	12955.5			1.59545
$405$	−11968.5	+	6909.99i	−1.46844	+	0.847803i
$406$	2357.84	+	4083.90i	0.288221	+	0.499213i
$407$	−1422.02	+	2463.01i	−0.173186	+	0.299967i
$408$		−	28326.9i		−	3.43723i
$409$	5053.85	+	2917.84i	0.610994	+	0.352758i	0.773355	−	0.633974i	$-0.218577\pi$
$409$	5053.85	+	2917.84i	0.610994	+	0.352758i	−0.162360	+	0.986732i	$0.551911\pi$
$410$	−12257.8	−	7077.06i	−1.47651	−	0.852466i
$411$		−	4831.01i		−	0.579796i
$412$	−1232.82	+	2135.31i	−0.147419	+	0.255338i
$413$	1736.31	+	3007.37i	0.206872	+	0.358313i
$414$	4174.24	−	2410.00i	0.495538	−	0.286099i
$415$	−15888.2			−1.87933
$416$		0			0
$417$	−12588.3			−1.47830
$418$	−5329.18	+	3076.80i	−0.623585	+	0.360027i
$419$	4272.14	+	7399.57i	0.498109	+	0.862751i	0.999998	−	0.00218165i	$-0.000694441\pi$
$419$	4272.14	+	7399.57i	0.498109	+	0.862751i	−0.501888	+	0.864933i	$0.667361\pi$
$420$	−3144.11	+	5445.76i	−0.365278	+	0.632680i
$421$		−	16524.6i		−	1.91297i	−0.291786	−	0.956484i	$-0.594250\pi$
$421$		−	16524.6i		−	1.91297i	0.291786	−	0.956484i	$-0.405750\pi$
$422$	12789.8	+	7384.21i	1.47535	+	0.851796i
$423$	362.601	+	209.348i	0.0416791	+	0.0240634i
$424$			4283.81i			0.490661i
$425$	6819.17	−	11811.2i	0.778302	−	1.34806i
$426$	14712.2	+	25482.2i	1.67326	+	2.89816i
$427$	−2537.64	+	1465.11i	−0.287599	+	0.166046i
$428$	−16594.0			−1.87407
$429$		0			0
$430$	9095.11			1.02001
$431$	−5920.65	+	3418.29i	−0.661689	+	0.382026i	−0.792920	−	0.609326i	$-0.791440\pi$
$431$	−5920.65	+	3418.29i	−0.661689	+	0.382026i	0.131231	+	0.991352i	$0.458107\pi$
$432$	−2445.18	−	4235.18i	−0.272324	−	0.471678i
$433$	−3145.32	+	5447.86i	−0.349087	+	0.604636i	−0.986088	−	0.166227i	$-0.946842\pi$
$433$	−3145.32	+	5447.86i	−0.349087	+	0.604636i	0.637001	+	0.770863i	$0.280175\pi$
$434$			2271.30i			0.251211i
$435$	18460.6	+	10658.3i	2.03476	+	1.17477i
$436$	15520.4	+	8960.70i	1.70480	+	0.984265i
$437$		−	4520.98i		−	0.494892i
$438$	3956.97	−	6853.68i	0.431670	−	0.747675i
$439$	4434.30	+	7680.43i	0.482090	+	0.835004i	0.999789	−	0.0205589i	$-0.00654457\pi$
$439$	4434.30	+	7680.43i	0.482090	+	0.835004i	−0.517699	+	0.855563i	$0.673211\pi$
$440$	11657.2	−	6730.28i	1.26303	−	0.729213i
$441$	3697.20			0.399222
$442$		0			0
$443$	−4310.67			−0.462316			−0.231158	−	0.972916i	$-0.574251\pi$
$443$	−4310.67			−0.462316			−0.231158	+	0.972916i	$0.574251\pi$
$444$	9583.41	−	5532.98i	1.02434	−	0.591405i
$445$	−2626.94	−	4549.99i	−0.279840	−	0.484697i
$446$	6291.91	−	10897.9i	0.668006	−	1.15702i
$447$			16133.5i			1.70714i
$448$	2286.31	+	1320.00i	0.241112	+	0.139206i
$449$	−3987.59	−	2302.24i	−0.419123	−	0.241981i	0.275579	−	0.961278i	$-0.411130\pi$
$449$	−3987.59	−	2302.24i	−0.419123	−	0.241981i	−0.694702	+	0.719298i	$0.744464\pi$
$450$			5917.01i			0.619845i
$451$	−2357.22	+	4082.83i	−0.246114	+	0.426282i
$452$	−11288.8	−	19552.8i	−1.17474	−	2.03470i
$453$	−1109.65	+	640.656i	−0.115090	+	0.0664474i
$454$	−4807.30			−0.496956
$455$		0			0
$456$	11527.2			1.18380
$457$	14184.8	−	8189.62i	1.45195	−	0.838281i	0.453353	−	0.891331i	$-0.350228\pi$
$457$	14184.8	−	8189.62i	1.45195	−	0.838281i	0.998592	+	0.0530498i	$0.0168942\pi$
$458$	1059.45	+	1835.02i	0.108089	+	0.187215i
$459$	−6146.89	+	10646.7i	−0.625081	+	1.08267i
$460$			20541.2i			2.08204i
$461$	−8341.13	−	4815.76i	−0.842701	−	0.486534i	0.0154801	−	0.999880i	$-0.495072\pi$
$461$	−8341.13	−	4815.76i	−0.842701	−	0.486534i	−0.858182	+	0.513346i	$0.828406\pi$
$462$	2754.47	+	1590.30i	0.277380	+	0.160146i
$463$			17855.0i			1.79220i	0.443848	+	0.896102i	$0.353613\pi$
$463$			17855.0i			1.79220i	−0.443848	+	0.896102i	$0.646387\pi$
$464$	−5708.98	+	9888.25i	−0.571191	+	0.989332i
$465$	5133.53	+	8891.54i	0.511961	+	0.886742i
$466$	12294.6	−	7098.31i	1.22219	−	0.705629i
$467$	−8220.28			−0.814538			−0.407269	−	0.913308i	$-0.633519\pi$
$467$	−8220.28			−0.814538			−0.407269	+	0.913308i	$0.633519\pi$
$468$		0			0
$469$	377.584			0.0371753
$470$	−2346.60	+	1354.81i	−0.230299	+	0.132963i
$471$	2166.36	+	3752.25i	0.211934	+	0.367080i
$472$	−14461.6	+	25048.3i	−1.41028	+	2.44267i
$473$		−	3029.40i		−	0.294486i
$474$	−8339.12	−	4814.59i	−0.808077	−	0.466543i
$475$	4806.38	+	2774.97i	0.464278	+	0.268051i
$476$			8467.29i			0.815331i
$477$	−679.108	+	1176.25i	−0.0651870	+	0.112907i
$478$	−14069.1	−	24368.5i	−1.34625	−	2.33177i
$479$	2740.19	−	1582.05i	0.261383	−	0.150909i	−0.363582	−	0.931562i	$-0.618446\pi$
$479$	2740.19	−	1582.05i	0.261383	−	0.150909i	0.624965	+	0.780653i	$0.285113\pi$
$480$	4038.39			0.384013
$481$		0			0
$482$	−5557.73			−0.525203
$483$	−2023.68	+	1168.37i	−0.190643	+	0.110068i
$484$	5610.58	+	9717.81i	0.526914	+	0.912642i
$485$	3676.78	−	6368.36i	0.344235	−	0.596232i
$486$		−	14563.9i		−	1.35932i
$487$	6484.79	+	3743.99i	0.603396	+	0.348371i	0.770376	−	0.637590i	$-0.220068\pi$
$487$	6484.79	+	3743.99i	0.603396	+	0.348371i	−0.166981	+	0.985960i	$0.553402\pi$
$488$	−21135.9	−	12202.8i	−1.96061	−	1.13196i
$489$			18243.7i			1.68714i
$490$	−11963.4	+	20721.1i	−1.10296	+	1.91038i
$491$	−8006.83	−	13868.2i	−0.735933	−	1.27467i	−0.954313	−	0.298809i	$-0.903410\pi$
$491$	−8006.83	−	13868.2i	−0.735933	−	1.27467i	0.218380	−	0.975864i	$-0.429923\pi$
$492$	15886.1	−	9171.82i	1.45569	−	0.840443i
$493$	28703.4			2.62218
$494$		0			0
$495$	4267.78			0.387520
$496$	−4762.66	+	2749.72i	−0.431148	+	0.248924i
$497$	−2117.20	−	3667.11i	−0.191086	−	0.330970i
$498$	15634.4	−	27079.5i	1.40681	−	2.43667i
$499$			10343.2i			0.927904i	0.885860	+	0.463952i	$0.153569\pi$
$499$			10343.2i			0.927904i	−0.885860	+	0.463952i	$0.846431\pi$
$500$	3613.48	+	2086.24i	0.323199	+	0.186599i
$501$	−14708.4	−	8491.89i	−1.31162	−	0.757265i
$502$		−	15758.6i		−	1.40108i
$503$	9307.63	−	16121.3i	0.825063	−	1.42905i	−0.0768077	−	0.997046i	$-0.524473\pi$
$503$	9307.63	−	16121.3i	0.825063	−	1.42905i	0.901871	−	0.432006i	$-0.142194\pi$
$504$	−884.292	−	1531.64i	−0.0781538	−	0.135366i
$505$	−11083.5	+	6399.06i	−0.976651	+	0.563870i
$506$	10389.8			0.912809
$507$		0			0
$508$	4472.73			0.390641
$509$	−3142.29	+	1814.20i	−0.273634	+	0.157983i	−0.630538	−	0.776158i	$-0.717166\pi$
$509$	−3142.29	+	1814.20i	−0.273634	+	0.157983i	0.356904	+	0.934141i	$0.383832\pi$
$510$	29061.5	+	50336.1i	2.52327	+	4.37043i
$511$	−569.442	+	986.302i	−0.0492967	+	0.0853844i
$512$			16710.7i			1.44241i
$513$	−4332.53	−	2501.39i	−0.372877	−	0.215281i
$514$	−26495.4	−	15297.1i	−2.27366	−	1.31270i
$515$		−	2435.68i		−	0.208406i
$516$	−5893.61	+	10208.0i	−0.502813	+	0.870898i
$517$	451.260	+	781.606i	0.0383876	+	0.0664893i
$518$	−2094.30	+	1209.14i	−0.177641	+	0.102561i
$519$	2099.49			0.177567
$520$		0			0
$521$	−3105.46			−0.261137			−0.130569	−	0.991439i	$-0.541680\pi$
$521$	−3105.46			−0.261137			−0.130569	+	0.991439i	$0.541680\pi$
$522$	−10784.6	+	6226.49i	−0.904270	+	0.522081i
$523$	−955.613	−	1655.17i	−0.0798969	−	0.138385i	0.823308	−	0.567594i	$-0.192126\pi$
$523$	−955.613	−	1655.17i	−0.0798969	−	0.138385i	−0.903205	+	0.429209i	$0.858792\pi$
$524$	−9271.57	+	16058.8i	−0.772959	+	1.33880i
$525$		−	2868.58i		−	0.238467i
$526$	−25858.6	−	14929.5i	−2.14352	−	1.23756i
$527$	11972.7	+	6912.46i	0.989641	+	0.571369i
$528$			7701.10i			0.634748i
$529$	2266.89	−	3926.36i	0.186314	−	0.322706i
$530$	−4394.90	−	7612.19i	−0.360193	−	0.623873i
$531$	−7941.75	+	4585.17i	−0.649045	+	0.374726i
$532$	−3445.64			−0.280804
$533$		0			0
$534$	10339.9			0.837920
$535$	14196.2	−	8196.18i	1.14721	−	0.662340i
$536$	1572.44	+	2723.55i	0.126715	+	0.219476i
$537$	3390.78	−	5873.01i	0.272483	−	0.471954i
$538$		−	4083.16i		−	0.327208i
$539$	6901.79	+	3984.75i	0.551542	+	0.318433i
$540$	19685.0	+	11365.1i	1.56871	+	0.905698i
$541$			15251.2i			1.21202i	0.795459	+	0.606008i	$0.207230\pi$
$541$			15251.2i			1.21202i	−0.795459	+	0.606008i	$0.792770\pi$
$542$	−4992.78	+	8647.74i	−0.395679	+	0.685336i
$543$	4400.40	+	7621.72i	0.347770	+	0.602356i
$544$	4709.29	−	2718.91i	0.371156	−	0.214287i
$545$	−17703.6			−1.39145
$546$		0			0
$547$	1838.85			0.143736			0.0718681	−	0.997414i	$-0.477104\pi$
$547$	1838.85			0.143736			0.0718681	+	0.997414i	$0.477104\pi$
$548$	−10416.1	+	6013.72i	−0.811957	+	0.468783i
$549$	−3869.00	−	6701.30i	−0.300774	−	0.520955i
$550$	−6377.21	+	11045.7i	−0.494410	+	0.856343i
$551$			11680.4i			0.903091i
$552$	−16855.1	−	9731.31i	−1.29964	−	0.750348i
$553$	1200.07	+	692.860i	0.0922823	+	0.0532792i
$554$			31860.4i			2.44336i
$555$	−5465.75	+	9466.96i	−0.418033	+	0.724054i
$556$	15670.2	+	27141.5i	1.19526	+	2.07025i
$557$	−5457.08	+	3150.64i	−0.415123	+	0.239672i	−0.692989	−	0.720948i	$-0.743706\pi$
$557$	−5457.08	+	3150.64i	−0.415123	+	0.239672i	0.277865	+	0.960620i	$0.410373\pi$
$558$	−5997.96			−0.455042
$559$		0			0
$560$	3327.29			0.251078
$561$	16765.9	−	9679.81i	1.26178	−	0.728488i
$562$	−2262.84	−	3919.36i	−0.169844	−	0.294178i
$563$	5879.92	−	10184.3i	0.440158	−	0.762376i	−0.557543	−	0.830148i	$-0.688256\pi$
$563$	5879.92	−	10184.3i	0.440158	−	0.762376i	0.997701	+	0.0677720i	$0.0215890\pi$
$564$		−	3511.66i		−	0.262176i
$565$	19315.2	+	11151.6i	1.43822	+	0.830359i
$566$	22378.6	+	12920.3i	1.66191	+	0.959506i
$567$			3914.07i			0.289904i
$568$	17634.1	−	30543.2i	1.30266	−	2.25627i
$569$	−8609.71	−	14912.5i	−0.634337	−	1.09870i	−0.986655	−	0.162824i	$-0.947940\pi$
$569$	−8609.71	−	14912.5i	−0.634337	−	1.09870i	0.352318	−	0.935880i	$-0.385394\pi$
$570$	−20483.6	+	11826.2i	−1.50520	+	0.869026i
$571$	−825.501			−0.0605011			−0.0302506	−	0.999542i	$-0.509631\pi$
$571$	−825.501			−0.0605011			−0.0302506	+	0.999542i	$0.509631\pi$
$572$		0			0
$573$	5557.00			0.405143
$574$	−3471.64	+	2004.35i	−0.252445	+	0.145749i
$575$	−4685.26	−	8115.11i	−0.339807	−	0.588563i
$576$	−3485.81	+	6037.60i	−0.252156	+	0.436748i
$577$			1073.19i			0.0774308i	0.999250	+	0.0387154i	$0.0123266\pi$
$577$			1073.19i			0.0774308i	−0.999250	+	0.0387154i	$0.987673\pi$
$578$	47185.2	+	27242.4i	3.39558	+	1.96044i
$579$	13898.9	+	8024.53i	0.997613	+	0.575972i
$580$		−	53070.3i		−	3.79935i
$581$	−2249.92	+	3896.97i	−0.160658	+	0.278268i
$582$	7236.06	+	12533.2i	0.515369	+	0.892645i
$583$	−2535.47	+	1463.85i	−0.180117	+	0.103991i
$584$	−9485.71			−0.672126
$585$		0			0
$586$	8536.93			0.601804
$587$	−12937.9	+	7469.69i	−0.909717	+	0.525225i	−0.880340	−	0.474343i	$-0.842686\pi$
$587$	−12937.9	+	7469.69i	−0.909717	+	0.525225i	−0.0293768	+	0.999568i	$0.509352\pi$
$588$	−15504.4	−	26854.5i	−1.08740	−	1.88344i
$589$	−2812.93	+	4872.14i	−0.196782	+	0.340837i
$590$		−	59346.7i		−	4.14113i
$591$	−7952.33	−	4591.28i	−0.553495	−	0.319560i
$592$	−5070.88	−	2927.67i	−0.352047	−	0.203254i
$593$		−	6296.13i		−	0.436006i	−0.975948	−	0.218003i	$-0.930046\pi$
$593$		−	6296.13i		−	0.436006i	0.975948	−	0.218003i	$-0.0699542\pi$
$594$	5748.50	−	9956.69i	0.397077	−	0.687757i
$595$	−4182.20	−	7243.78i	−0.288157	−	0.499103i
$596$	34785.3	−	20083.3i	2.39071	−	1.38027i
$597$	−22304.4			−1.52908
$598$		0			0
$599$	−3518.96			−0.240035			−0.120017	−	0.992772i	$-0.538295\pi$
$599$	−3518.96			−0.240035			−0.120017	+	0.992772i	$0.538295\pi$
$600$	20691.3	−	11946.1i	1.40786	−	0.812831i
$601$	−2690.33	−	4659.78i	−0.182597	−	0.316267i	0.760167	−	0.649727i	$-0.225117\pi$
$601$	−2690.33	−	4659.78i	−0.182597	−	0.316267i	−0.942764	+	0.333460i	$0.891784\pi$
$602$	1287.95	−	2230.80i	0.0871976	−	0.151031i
$603$			997.110i			0.0673391i
$604$	2762.62	+	1595.00i	0.186108	+	0.107450i
$605$	−9599.73	−	5542.41i	−0.645098	−	0.372448i
$606$		−	25187.3i		−	1.68839i
$607$	−10354.3	+	17934.2i	−0.692369	+	1.19922i	0.278690	+	0.960381i	$0.410100\pi$
$607$	−10354.3	+	17934.2i	−0.692369	+	1.19922i	−0.971059	+	0.238838i	$0.923234\pi$
$608$	1106.42	+	1916.38i	0.0738016	+	0.127828i
$609$	5228.39	−	3018.61i	0.347890	−	0.200855i
$610$	50077.1			3.32387
$611$		0			0
$612$	−22360.1			−1.47688
$613$	7416.35	−	4281.83i	0.488652	−	0.282123i	−0.235363	−	0.971907i	$-0.575628\pi$
$613$	7416.35	−	4281.83i	0.488652	−	0.282123i	0.724015	+	0.689784i	$0.242295\pi$
$614$	−11463.0	−	19854.4i	−0.753433	−	1.30498i
$615$	−9060.38	+	15693.0i	−0.594064	+	1.02895i
$616$		−	3812.28i		−	0.249352i
$617$	−26370.1	−	15224.8i	−1.72062	−	0.993400i	−0.917661	−	0.397365i	$-0.869925\pi$
$617$	−26370.1	−	15224.8i	−1.72062	−	0.993400i	−0.802958	−	0.596035i	$-0.796742\pi$
$618$	4151.32	+	2396.77i	0.270211	+	0.156007i
$619$		−	26233.1i		−	1.70339i	−0.524041	−	0.851693i	$-0.675576\pi$
$619$		−	26233.1i		−	1.70339i	0.524041	−	0.851693i	$-0.324424\pi$
$620$	12780.6	−	22136.7i	0.827874	−	1.43392i
$621$	4223.35	+	7315.06i	0.272910	+	0.472694i
$622$	−19897.7	+	11487.9i	−1.28267	+	0.740553i
$623$	−1487.99			−0.0956905
$624$		0			0
$625$	−17528.4			−1.12182
$626$	−42403.0	+	24481.4i	−2.70729	+	1.56305i
$627$	3939.06	+	6822.66i	0.250895	+	0.434563i
$628$	5393.45	−	9341.73i	0.342710	−	0.593592i
$629$			14719.6i			0.933084i
$630$	3142.72	+	1814.45i	0.198744	+	0.114745i
$631$	−17874.3	−	10319.7i	−1.12768	−	0.651066i	−0.184329	−	0.982865i	$-0.559011\pi$
$631$	−17874.3	−	10319.7i	−1.12768	−	0.651066i	−0.943350	+	0.331799i	$0.892344\pi$
$632$			11541.6i			0.726425i
$633$	9453.61	−	16374.1i	0.593597	−	1.02814i
$634$	14293.3	+	24756.8i	0.895365	+	1.55082i
$635$	−3826.43	+	2209.19i	−0.239130	+	0.138062i
$636$	11391.5			0.710226
$637$		0			0
$638$	−26843.1			−1.66572
$639$	9683.95	−	5591.03i	0.599517	−	0.346131i
$640$	−19951.9	−	34557.7i	−1.23229	−	2.13439i
$641$	−2215.89	+	3838.03i	−0.136540	+	0.236494i	−0.926185	−	0.377070i	$-0.876932\pi$
$641$	−2215.89	+	3838.03i	−0.136540	+	0.236494i	0.789645	+	0.613565i	$0.210265\pi$
$642$			32260.9i			1.98323i
$643$	−12276.8	−	7088.03i	−0.752956	−	0.434719i	0.0738050	−	0.997273i	$-0.476486\pi$
$643$	−12276.8	−	7088.03i	−0.752956	−	0.434719i	−0.826761	+	0.562553i	$0.809819\pi$
$644$	5038.22	+	2908.82i	0.308282	+	0.177987i
$645$		−	11644.0i		−	0.710824i
$646$	−15924.3	+	27581.8i	−0.969868	+	1.67986i
$647$	2825.40	+	4893.73i	0.171681	+	0.297361i	0.939008	−	0.343896i	$-0.111747\pi$
$647$	2825.40	+	4893.73i	0.171681	+	0.297361i	−0.767327	+	0.641257i	$0.778413\pi$
$648$	−28232.5	+	16300.1i	−1.71154	+	0.988159i
$649$	−19767.2			−1.19558
$650$		0			0
$651$	2907.82			0.175064
$652$	39335.0	−	22710.1i	2.36270	−	1.36410i
$653$	9218.14	+	15966.3i	0.552425	+	0.956829i	0.998099	+	0.0616333i	$0.0196309\pi$
$653$	9218.14	+	15966.3i	0.552425	+	0.956829i	−0.445673	+	0.895196i	$0.647036\pi$
$654$	17420.8	−	30173.7i	1.04160	−	1.80410i
$655$		−	18317.8i		−	1.09273i
$656$	−8405.80	−	4853.09i	−0.500292	−	0.288844i
$657$	−2604.59	−	1503.76i	−0.154665	−	0.0892957i
$658$			767.415i			0.0454665i
$659$	7665.97	−	13277.8i	0.453147	−	0.784873i	−0.545433	−	0.838155i	$-0.683635\pi$
$659$	7665.97	−	13277.8i	0.453147	−	0.784873i	0.998580	+	0.0532813i	$0.0169680\pi$
$660$	−17897.2	−	30998.9i	−1.05553	−	1.82823i
$661$	19308.2	−	11147.6i	1.13616	−	0.655961i	0.190681	−	0.981652i	$-0.438930\pi$
$661$	19308.2	−	11147.6i	1.13616	−	0.655961i	0.945476	+	0.325691i	$0.105597\pi$
$662$	−13566.2			−0.796471
$663$		0			0
$664$	−37478.9			−2.19046
$665$	2947.76	−	1701.89i	0.171893	−	0.0992427i
$666$	−3193.06	−	5530.54i	−0.185779	−	0.321778i
$667$	9860.64	−	17079.1i	0.572422	−	0.991464i
$668$			42283.4i			2.44909i
$669$	−13952.0	−	8055.19i	−0.806301	−	0.465518i
$670$	−5588.36	−	3226.44i	−0.322235	−	0.186042i
$671$		−	16679.7i		−	0.959629i
$672$	571.873	−	990.513i	0.0328281	−	0.0568599i
$673$	−8085.84	−	14005.1i	−0.463129	−	0.802164i	0.535985	−	0.844227i	$-0.319940\pi$
$673$	−8085.84	−	14005.1i	−0.463129	−	0.802164i	−0.999115	+	0.0420635i	$0.986607\pi$
$674$	−1026.63	+	592.725i	−0.0586711	+	0.0338738i
$675$	−10369.1			−0.591272
$676$		0			0
$677$	33614.4			1.90828			0.954141	−	0.299358i	$-0.0967725\pi$
$677$	33614.4			1.90828			0.954141	+	0.299358i	$0.0967725\pi$
$678$	−38013.2	+	21946.9i	−2.15323	+	1.24317i
$679$	−1041.33	−	1803.64i	−0.0588551	−	0.101940i
$680$	34833.4	−	60333.2i	1.96441	−	3.40246i
$681$			6154.53i			0.346318i
$682$	−11196.8	−	6464.46i	−0.628661	−	0.362957i
$683$	−19466.1	−	11238.7i	−1.09055	−	0.629632i	−0.156831	−	0.987625i	$-0.550128\pi$
$683$	−19466.1	−	11238.7i	−1.09055	−	0.629632i	−0.933724	+	0.357993i	$0.883461\pi$
$684$		−	9099.12i		−	0.508646i
$685$	5940.65	−	10289.5i	0.331358	−	0.573929i
$686$	6971.08	+	12074.3i	0.387984	+	0.672008i
$687$	2349.27	−	1356.35i	0.130466	−	0.0753247i
$688$	6236.97			0.345614
$689$		0			0
$690$	39934.7			2.20332
$691$	−6598.19	+	3809.47i	−0.363252	+	0.209723i	−0.670506	−	0.741904i	$-0.733923\pi$
$691$	−6598.19	+	3809.47i	−0.363252	+	0.209723i	0.307255	+	0.951627i	$0.400590\pi$
$692$	−2613.48	−	4526.67i	−0.143569	−	0.248668i
$693$	604.357	−	1046.78i	0.0331279	−	0.0573792i
$694$		−	50128.9i		−	2.74188i
$695$	−26811.7	−	15479.8i	−1.46335	−	0.844864i
$696$	43547.1	+	25141.9i	2.37162	+	1.36926i
$697$			24400.2i			1.32600i
$698$	−20410.0	+	35351.2i	−1.10678	+	1.91699i
$699$	−9087.59	−	15740.2i	−0.491737	−	0.851714i
$700$	−6184.90	+	3570.85i	−0.333953	+	0.192808i
$701$	18164.3			0.978684			0.489342	−	0.872092i	$-0.337237\pi$
$701$	18164.3			0.978684			0.489342	+	0.872092i	$0.337237\pi$
$702$		0			0
$703$	−5989.95			−0.321359
$704$	−13014.4	+	7513.85i	−0.696730	+	0.402257i
$705$	1734.49	+	3004.23i	0.0926593	+	0.160491i
$706$	−11456.0	+	19842.4i	−0.610698	+	1.05776i
$707$			3624.66i			0.192814i
$708$	66608.6	+	38456.5i	3.53574	+	2.04136i
$709$	14468.3	+	8353.25i	0.766385	+	0.442472i	0.831583	−	0.555400i	$-0.187435\pi$
$709$	14468.3	+	8353.25i	0.766385	+	0.442472i	−0.0651986	+	0.997872i	$0.520768\pi$
$710$			72365.7i			3.82512i
$711$	−1829.68	+	3169.10i	−0.0965096	+	0.167159i
$712$	−6196.71	−	10733.0i	−0.326168	−	0.564940i
$713$	8226.13	−	4749.36i	0.432077	−	0.249460i
$714$	16461.5			0.862825
$715$		0			0
$716$	−16883.6			−0.881244
$717$	−31197.6	+	18012.0i	−1.62496	+	0.938171i
$718$	18299.1	+	31695.0i	0.951137	+	1.64742i
$719$	2274.70	−	3939.89i	0.117986	−	0.204358i	−0.800983	−	0.598686i	$-0.795690\pi$
$719$	2274.70	−	3939.89i	0.117986	−	0.204358i	0.918969	+	0.394329i	$0.129023\pi$
$720$			8786.58i			0.454800i
$721$	−597.410	−	344.915i	−0.0308581	−	0.0178159i
$722$	17527.0	+	10119.2i	0.903443	+	0.521603i
$723$			7115.26i			0.366002i
$724$	10955.4	−	18975.3i	0.562367	−	0.974048i
$725$	12104.9	+	20966.3i	0.620088	+	1.07402i
$726$	18892.7	−	10907.7i	0.965804	−	0.557607i
$727$	6246.70			0.318676			0.159338	−	0.987224i	$-0.449064\pi$
$727$	6246.70			0.318676			0.159338	+	0.987224i	$0.449064\pi$
$728$		0			0
$729$	5839.14			0.296659
$730$	16855.8	−	9731.71i	0.854605	−	0.493407i
$731$	−7839.50	−	13578.4i	−0.396654	−	0.687026i
$732$	−32449.8	+	56204.7i	−1.63850	+	2.83796i
$733$		−	3447.16i		−	0.173702i	−0.996221	−	0.0868511i	$-0.972320\pi$
$733$		−	3447.16i		−	0.173702i	0.996221	−	0.0868511i	$-0.0276804\pi$
$734$	−50049.0	−	28895.8i	−2.51681	−	1.45308i
$735$	26528.2	+	15316.0i	1.33130	+	0.768627i
$736$		−	3736.17i		−	0.187116i
$737$	−1074.66	+	1861.37i	−0.0537119	+	0.0930318i
$738$	−5293.02	−	9167.77i	−0.264009	−	0.457277i
$739$	−32071.4	+	18516.5i	−1.59644	+	0.921703i	−0.604271	+	0.796779i	$0.706536\pi$
$739$	−32071.4	+	18516.5i	−1.59644	+	0.921703i	−0.992166	+	0.124925i	$0.960131\pi$
$740$	27215.4			1.35197
$741$		0			0
$742$	−2489.43			−0.123167
$743$	13248.5	−	7649.01i	0.654158	−	0.377678i	−0.135890	−	0.990724i	$-0.543389\pi$
$743$	13248.5	−	7649.01i	0.654158	−	0.377678i	0.790047	+	0.613046i	$0.210056\pi$
$744$	12109.6	+	20974.4i	0.596717	+	1.03354i
$745$	−19839.3	+	34362.6i	−0.975643	+	1.68986i
$746$			28059.1i			1.37710i
$747$	−10291.0	−	5941.49i	−0.504052	−	0.291015i
$748$	−41741.0	−	24099.2i	−2.04038	−	1.17801i
$749$		−	4642.62i		−	0.226485i
$750$	4055.93	−	7025.08i	0.197469	−	0.342026i
$751$	−4922.27	−	8525.62i	−0.239169	−	0.414253i	0.721307	−	0.692616i	$-0.243542\pi$
$751$	−4922.27	−	8525.62i	−0.239169	−	0.414253i	−0.960476	+	0.278362i	$0.910208\pi$
$752$	−1609.18	+	929.062i	−0.0780331	+	0.0450524i
$753$	−20174.9			−0.976382
$754$		0			0
$755$	−3151.24			−0.151901
$756$	5575.14	−	3218.81i	0.268209	−	0.154850i
$757$	−2960.65	−	5128.00i	−0.142149	−	0.246209i	0.786157	−	0.618027i	$-0.212068\pi$
$757$	−2960.65	−	5128.00i	−0.142149	−	0.246209i	−0.928306	+	0.371818i	$0.878735\pi$
$758$	−21408.8	+	37081.2i	−1.02586	+	1.77685i
$759$		−	13301.4i		−	0.636116i
$760$	24551.7	+	14175.0i	1.17182	+	0.676552i
$761$	−15478.0	−	8936.23i	−0.737289	−	0.425674i	0.0837936	−	0.996483i	$-0.473296\pi$
$761$	−15478.0	−	8936.23i	−0.737289	−	0.425674i	−0.821083	+	0.570809i	$0.806630\pi$
$762$		−	8695.58i		−	0.413396i
$763$	−2507.00	+	4342.24i	−0.118951	+	0.206029i
$764$	−6917.44	−	11981.4i	−0.327571	−	0.567370i
$765$	19129.1	−	11044.2i	0.904071	−	0.521966i
$766$	5070.61			0.239176
$767$		0			0
$768$	48211.2			2.26520
$769$	−9755.95	+	5632.60i	−0.457488	+	0.264131i	−0.710988	−	0.703205i	$-0.751752\pi$
$769$	−9755.95	+	5632.60i	−0.457488	+	0.264131i	0.253499	+	0.967336i	$0.418418\pi$
$770$	3911.15	+	6774.30i	0.183049	+	0.317051i
$771$	−19584.1	+	33920.6i	−0.914791	+	1.58446i
$772$		−	39956.3i		−	1.86277i
$773$	23905.5	+	13801.8i	1.11232	+	0.642196i	0.939428	−	0.342745i	$-0.111357\pi$
$773$	23905.5	+	13801.8i	1.11232	+	0.642196i	0.172888	+	0.984941i	$0.444690\pi$
$774$	5891.00	+	3401.17i	0.273576	+	0.157949i
$775$			11660.6i			0.540465i
$776$	8673.20	−	15022.4i	0.401224	−	0.694940i
$777$	1548.00	+	2681.22i	0.0714726	+	0.123794i
$778$	−49707.0	+	28698.4i	−2.29059	+	1.32248i
$779$	−9929.31			−0.456681
$780$		0			0
$781$	24103.5			1.10434
$782$	46569.1	−	26886.7i	2.12955	−	1.22950i
$783$	−10911.5	−	18899.3i	−0.498014	−	0.862585i
$784$	−8203.87	+	14209.5i	−0.373719	+	0.647300i
$785$			10655.8i			0.484488i
$786$	31220.5	+	18025.2i	1.41679	+	0.817985i
$787$	−20925.8	−	12081.5i	−0.947809	−	0.547218i	−0.0554093	−	0.998464i	$-0.517646\pi$
$787$	−20925.8	−	12081.5i	−0.947809	−	0.547218i	−0.892400	+	0.451246i	$0.850980\pi$
$788$			22861.2i			1.03350i
$789$	−19113.4	+	33105.4i	−0.862429	+	1.49377i
$790$	−11840.9	−	20509.1i	−0.533267	−	0.923646i
$791$	5470.42	−	3158.35i	0.245899	−	0.141970i
$792$	10067.3			0.451675
$793$		0			0
$794$	−50726.7			−2.26728
$795$	−9745.48	+	5626.56i	−0.434763	+	0.251011i
$796$	27764.9	+	48090.3i	1.23631	+	2.14135i
$797$	15192.8	−	26314.7i	0.675228	−	1.16953i	−0.301174	−	0.953569i	$-0.597378\pi$
$797$	15192.8	−	26314.7i	0.675228	−	1.16953i	0.976402	−	0.215961i	$-0.0692883\pi$
$798$			6698.79i			0.297161i
$799$	4045.29	+	2335.55i	0.179114	+	0.103412i
$800$	3972.03	+	2293.25i	0.175541	+	0.101348i
$801$		−	3929.43i		−	0.173333i
$802$	19206.8	−	33267.1i	0.845655	−	1.46472i
$803$	−3241.44	−	5614.33i	−0.142451	−	0.246732i
$804$	7242.48	−	4181.45i	0.317690	−	0.183418i
$805$	−5746.94			−0.251619
$806$		0			0
$807$	−5227.46			−0.228024
$808$	−26145.0	+	15094.8i	−1.13834	+	0.657220i
$809$	20988.4	+	36353.0i	0.912131	+	1.57986i	0.811048	+	0.584979i	$0.198897\pi$
$809$	20988.4	+	36353.0i	0.912131	+	1.57986i	0.101083	+	0.994878i	$0.467769\pi$
$810$	33445.6	−	57929.4i	1.45081	−	2.51288i
$811$		−	9674.05i		−	0.418868i	−0.977823	−	0.209434i	$-0.932838\pi$
$811$		−	9674.05i		−	0.418868i	0.977823	−	0.209434i	$-0.0671621\pi$
$812$	−13016.8	−	7515.24i	−0.562561	−	0.324795i
$813$	11071.2	+	6391.98i	0.477596	+	0.275740i
$814$		−	13765.6i		−	0.592733i
$815$	−22434.1	+	38857.1i	−0.964213	+	1.67007i
$816$	19929.0	+	34518.0i	0.854967	+	1.48085i
$817$	5525.54	−	3190.17i	0.236615	−	0.136610i
$818$	−28245.7			−1.20732
$819$		0			0
$820$	45114.0			1.92128
$821$	22019.6	−	12713.0i	0.936040	−	0.540423i	0.0473231	−	0.998880i	$-0.484931\pi$
$821$	22019.6	−	12713.0i	0.936040	−	0.540423i	0.888717	+	0.458457i	$0.151598\pi$
$822$	11691.5	+	20250.2i	0.496091	+	0.859254i
$823$	7194.13	−	12460.6i	0.304704	−	0.527763i	−0.672491	−	0.740105i	$-0.734776\pi$
$823$	7194.13	−	12460.6i	0.304704	−	0.527763i	0.977195	+	0.212342i	$0.0681091\pi$
$824$		−	5745.56i		−	0.242908i
$825$	14141.2	+	8164.40i	0.596766	+	0.344543i
$826$	−14556.2	−	8404.03i	−0.613166	−	0.354012i
$827$		−	3850.25i		−	0.161894i	−0.996718	−	0.0809469i	$-0.974206\pi$
$827$		−	3850.25i		−	0.161894i	0.996718	−	0.0809469i	$-0.0257944\pi$
$828$	−7681.49	+	13304.7i	−0.322404	+	0.558420i
$829$	−959.292	−	1661.54i	−0.0401901	−	0.0696113i	0.845231	−	0.534402i	$-0.179463\pi$
$829$	−959.292	−	1661.54i	−0.0401901	−	0.0696113i	−0.885421	+	0.464790i	$0.846130\pi$
$830$	66598.9	−	38450.9i	2.78516	−	1.60801i
$831$	40789.2			1.70272
$832$		0			0
$833$	41247.1			1.71564
$834$	52766.7	−	30464.9i	2.19084	−	1.26488i
$835$	−20884.8	−	36173.6i	−0.865567	−	1.49921i
$836$	9806.83	−	16985.9i	0.405713	−	0.702716i
$837$		−	10511.0i		−	0.434066i
$838$	−35815.2	−	20677.9i	−1.47639	−	0.852395i
$839$	27203.7	+	15706.1i	1.11940	+	0.646285i	0.941247	−	0.337718i	$-0.109655\pi$
$839$	27203.7	+	15706.1i	1.11940	+	0.646285i	0.178152	+	0.984003i	$0.442988\pi$
$840$		−	14653.1i		−	0.601882i
$841$	−13281.5	+	23004.3i	−0.544571	+	0.943224i
$842$	39991.0	+	69266.4i	1.63679	+	2.83501i
$843$	−5017.75	+	2897.00i	−0.205006	+	0.118360i
$844$	−47072.0			−1.91977
$845$		0			0
$846$	−2026.56			−0.0823577
$847$	−2718.82	+	1569.71i	−0.110295	+	0.0636787i
$848$	−3013.80	−	5220.06i	−0.122045	−	0.211389i
$849$	16541.2	−	28650.1i	0.668658	−	1.15815i
$850$			66012.0i			2.66376i
$851$	8758.49	+	5056.72i	0.352805	+	0.203692i
$852$	−81220.6	−	46892.7i	−3.26593	−	1.88559i
$853$		−	18315.5i		−	0.735184i	−0.929987	−	0.367592i	$-0.880182\pi$
$853$		−	18315.5i		−	0.735184i	0.929987	−	0.367592i	$-0.119818\pi$
$854$	7091.37	−	12282.6i	0.284147	−	0.492157i
$855$	4494.28	+	7784.32i	0.179767	+	0.311366i
$856$	33487.6	−	19334.1i	1.33713	−	0.771992i
$857$	−9579.31			−0.381824			−0.190912	−	0.981607i	$-0.561144\pi$
$857$	−9579.31			−0.381824			−0.190912	+	0.981607i	$0.561144\pi$
$858$		0			0
$859$	−7136.55			−0.283465			−0.141732	−	0.989905i	$-0.545267\pi$
$859$	−7136.55			−0.283465			−0.141732	+	0.989905i	$0.545267\pi$
$860$	−25105.4	+	14494.6i	−0.995451	+	0.574724i
$861$	2566.06	+	4444.55i	0.101569	+	0.175923i
$862$	16545.1	−	28657.0i	0.653746	−	1.13232i
$863$			17239.2i			0.679986i	0.940428	+	0.339993i	$0.110425\pi$
$863$			17239.2i			0.679986i	−0.940428	+	0.339993i	$0.889575\pi$
$864$	−3580.44	−	2067.17i	−0.140983	−	0.0813964i
$865$	4471.67	+	2581.72i	0.175770	+	0.101481i
$866$		−	30447.8i		−	1.19476i
$867$	34877.0	−	60408.7i	1.36619	−	2.36631i
$868$	−3619.70	−	6269.51i	−0.141545	−	0.245163i
$869$	−6831.16	+	3943.97i	−0.266664	+	0.153959i
$870$	−103176.			−4.02067
$871$		0			0
$872$	−41761.3			−1.62181
$873$	4762.98	−	2749.91i	0.184653	−	0.106610i
$874$	10941.2	+	18950.7i	0.423444	+	0.733427i
$875$	−583.682	+	1010.97i	−0.0225509	+	0.0390594i
$876$			25224.5i			0.972895i
$877$	28621.1	+	16524.4i	1.10201	+	0.636247i	0.936749	−	0.350003i	$-0.113819\pi$
$877$	28621.1	+	16524.4i	1.10201	+	0.636247i	0.165263	+	0.986250i	$0.447153\pi$
$878$	−37174.6	−	21462.8i	−1.42891	−	0.824981i
$879$		−	10929.4i		−	0.419384i
$880$	−9469.97	+	16402.5i	−0.362764	+	0.628326i
$881$	9763.90	+	16911.6i	0.373387	+	0.646726i	0.990084	−	0.140475i	$-0.0448629\pi$
$881$	9763.90	+	16911.6i	0.373387	+	0.646726i	−0.616697	+	0.787201i	$0.711530\pi$
$882$	−15497.6	+	8947.54i	−0.591645	+	0.341587i
$883$	26361.3			1.00467			0.502337	−	0.864672i	$-0.332474\pi$
$883$	26361.3			1.00467			0.502337	+	0.864672i	$0.332474\pi$
$884$		0			0
$885$	−75978.4			−2.88586
$886$	18069.1	−	10432.2i	0.685151	−	0.395572i
$887$	−10702.9	−	18538.0i	−0.405151	−	0.701742i	0.589188	−	0.807996i	$-0.299448\pi$
$887$	−10702.9	−	18538.0i	−0.405151	−	0.701742i	−0.994339	+	0.106254i	$0.966114\pi$
$888$	−12893.2	+	22331.7i	−0.487240	+	0.843924i
$889$			1251.37i			0.0472098i
$890$	22022.7	+	12714.8i	0.829442	+	0.478879i
$891$	−19295.1	−	11140.0i	−0.725489	−	0.418861i
$892$			40109.0i			1.50555i
$893$	−950.419	+	1646.17i	−0.0356154	+	0.0616877i
$894$	−39044.6	−	67627.2i	−1.46068	−	2.52997i
$895$	14444.0	−	8339.23i	0.539451	−	0.311452i
$896$	−11301.5			−0.421379
$897$		0			0
$898$	22286.5			0.828184
$899$	−21253.1	+	12270.5i	−0.788466	+	0.455221i
$900$	−9429.77	−	16332.8i	−0.349251	−	0.604920i
$901$	−7576.34	+	13122.6i	−0.280138	+	0.485213i
$902$		−	22818.8i		−	0.842330i
$903$	−2855.97	−	1648.89i	−0.105250	−	0.0607661i
$904$	45562.9	+	26305.7i	1.67633	+	0.967827i
$905$			21644.5i			0.795015i
$906$	3100.89	−	5370.90i	0.113709	−	0.196949i
$907$	14443.7	+	25017.3i	0.528772	+	0.915860i	0.999437	+	0.0335483i	$0.0106808\pi$
$907$	14443.7	+	25017.3i	0.528772	+	0.915860i	−0.470665	+	0.882312i	$0.655986\pi$
$908$	13269.7	−	7661.27i	0.484990	−	0.280009i
$909$	−9571.86			−0.349261
$910$		0			0
$911$	−31360.9			−1.14054			−0.570271	−	0.821456i	$-0.693162\pi$
$911$	−31360.9			−1.14054			−0.570271	+	0.821456i	$0.693162\pi$
$912$	−14046.6	+	8109.81i	−0.510010	+	0.294455i
$913$	−12807.2	−	22182.7i	−0.464246	−	0.804098i
$914$	−39639.2	+	68657.1i	−1.43452	+	2.48466i
$915$		−	64111.0i		−	2.31633i
$916$	−5848.82	−	3376.82i	−0.210972	−	0.121805i
$917$	−4492.89	−	2593.97i	−0.161798	−	0.0934139i
$918$		−	59504.0i		−	2.13935i
$919$	552.304	−	956.619i	0.0198246	−	0.0343373i	−0.855943	−	0.517070i	$-0.827023\pi$
$919$	552.304	−	956.619i	0.0198246	−	0.0343373i	0.875768	+	0.482733i	$0.160356\pi$
$920$	−23933.0	−	41453.2i	−0.857661	−	1.48551i
$921$	−25418.6	+	14675.4i	−0.909414	+	0.525050i
$922$	46618.2			1.66517
$923$		0			0
$924$	−10137.6			−0.360935
$925$	−10751.9	+	6207.61i	−0.382184	+	0.220654i
$926$	−43210.6	−	74842.9i	−1.53346	−	2.65604i
$927$	910.838	−	1577.62i	0.0322717	−	0.0558962i
$928$			9652.81i			0.341454i
$929$	33286.4	+	19217.9i	1.17556	+	0.678708i	0.954982	−	0.296663i	$-0.0958737\pi$
$929$	33286.4	+	19217.9i	1.17556	+	0.678708i	0.220574	+	0.975370i	$0.429207\pi$
$930$	−43036.6	−	24847.2i	−1.51745	−	0.876099i
$931$			16784.9i			0.590874i
$932$	−22624.8	+	39187.3i	−0.795171	+	1.37728i
$933$	14707.4	+	25473.9i	0.516075	+	0.893867i
$934$	34457.1	−	19893.8i	1.20714	−	0.696944i
$935$	47612.7			1.66535
$936$		0			0
$937$	21008.7			0.732469			0.366235	−	0.930522i	$-0.380647\pi$
$937$	21008.7			0.732469			0.366235	+	0.930522i	$0.380647\pi$
$938$	−1582.73	+	913.787i	−0.0550936	+	0.0318083i
$939$	31342.2	+	54286.2i	1.08926	+	1.88665i
$940$	4318.25	−	7479.43i	0.149836	−	0.259524i
$941$		−	12695.6i		−	0.439814i	−0.975521	−	0.219907i	$-0.929425\pi$
$941$		−	12695.6i		−	0.439814i	0.975521	−	0.219907i	$-0.0705754\pi$
$942$	−18161.6	−	10485.6i	−0.628169	−	0.362674i
$943$	14518.6	+	8382.34i	0.501370	+	0.289466i
$944$		−	40697.0i		−	1.40315i
$945$	−3179.70	+	5507.40i	−0.109456	+	0.189583i
$946$	7331.41	+	12698.4i	0.251971	+	0.436427i
$947$	42192.3	−	24359.7i	1.44780	−	0.835886i	0.449448	−	0.893307i	$-0.351621\pi$
$947$	42192.3	−	24359.7i	1.44780	−	0.835886i	0.998350	+	0.0574201i	$0.0182875\pi$
$948$	30691.5			1.05149
$949$		0			0
$950$	−26862.7			−0.917410
$951$	31694.8	−	18299.0i	1.08073	−	0.623960i
$952$	−9865.45	−	17087.5i	−0.335862	−	0.581731i
$953$	−5673.66	+	9827.06i	−0.192852	+	0.334029i	−0.946194	−	0.323599i	$-0.895107\pi$
$953$	−5673.66	+	9827.06i	−0.192852	+	0.334029i	0.753342	+	0.657628i	$0.228440\pi$
$954$		−	6574.00i		−	0.223104i
$955$	11835.8	+	6833.39i	0.401044	+	0.231543i
$956$	77670.7	+	44843.2i	2.62767	+	1.51708i
$957$			34365.7i			1.16080i
$958$	−7657.39	+	13263.0i	−0.258245	+	0.447294i
$959$	−1682.50	−	2914.18i	−0.0566535	−	0.0981268i
$960$	−50022.9	+	28880.7i	−1.68175	+	0.970960i
$961$	17970.9			0.603232
$962$		0			0
$963$	12260.0			0.410254
$964$	15341.1	−	8857.20i	0.512556	−	0.295925i
$965$	19735.4	+	34182.7i	0.658346	+	1.14029i
$966$	5655.12	−	9794.96i	0.188355	−	0.326240i
$967$			10585.2i			0.352014i	0.984389	+	0.176007i	$0.0563181\pi$
$967$			10585.2i			0.352014i	−0.984389	+	0.176007i	$0.943682\pi$
$968$	−22644.9	−	13074.1i	−0.751896	−	0.434107i
$969$	35311.5	+	20387.1i	1.17066	+	0.675880i
$970$			35592.5i			1.17815i
$971$	26865.4	−	46532.2i	0.887900	−	1.53789i	0.0455470	−	0.998962i	$-0.485497\pi$
$971$	26865.4	−	46532.2i	0.887900	−	1.53789i	0.842353	−	0.538926i	$-0.181170\pi$
$972$	23210.0	+	40200.9i	0.765907	+	1.32659i
$973$	−7593.57	+	4384.15i	−0.250194	+	0.144450i
$974$	−36243.2			−1.19231
$975$		0			0
$976$	34340.4			1.12624
$977$	−8256.96	+	4767.16i	−0.270382	+	0.156105i	−0.629061	−	0.777356i	$-0.716561\pi$
$977$	−8256.96	+	4767.16i	−0.270382	+	0.156105i	0.358679	+	0.933461i	$0.383227\pi$
$978$	−44151.4	−	76472.5i	−1.44357	−	2.50033i
$979$	4235.05	−	7335.33i	0.138256	−	0.239467i
$980$		−	76262.7i		−	2.48584i
$981$	−11466.8	−	6620.38i	−0.373199	−	0.215466i
$982$	67124.7	+	38754.5i	2.18130	+	1.25937i
$983$			8972.94i			0.291142i	0.989348	+	0.145571i	$0.0465019\pi$
$983$			8972.94i			0.291142i	−0.989348	+	0.145571i	$0.953498\pi$
$984$	−21372.6	+	37018.5i	−0.692413	+	1.19930i
$985$	−11291.7	−	19557.8i	−0.365263	−	0.632654i
$986$	−120316.	+	69464.7i	−3.88606	+	2.24362i
$987$	982.480			0.0316846
$988$		0			0
$989$	−10772.6			−0.346359
$990$	−17889.3	+	10328.4i	−0.574303	+	0.331574i
$991$	17450.3	+	30224.8i	0.559362	+	0.968843i	0.997550	+	0.0699598i	$0.0222871\pi$
$991$	17450.3	+	30224.8i	0.559362	+	0.968843i	−0.438188	+	0.898883i	$0.644380\pi$
$992$	−2324.63	+	4026.37i	−0.0744022	+	0.128868i
$993$			17368.0i			0.555043i
$994$	17749.4	+	10247.6i	0.566376	+	0.326998i
$995$	−47505.9	−	27427.6i	−1.51361	−	0.873881i
$996$			99664.2i			3.17066i
$997$	24077.5	−	41703.4i	0.764836	−	1.32473i	−0.175498	−	0.984480i	$-0.556153\pi$
$997$	24077.5	−	41703.4i	0.764836	−	1.32473i	0.940333	−	0.340254i	$-0.110513\pi$
$998$	−25031.4	−	43355.6i	−0.793942	−	1.37515i
$999$	9691.89	−	5595.61i	0.306945	−	0.177215i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.e.h.23.2		36
13.2	odd	12		169.4.a.l.1.1	yes	9
13.3	even	3		169.4.b.g.168.2		18
13.4	even	6	inner	169.4.e.h.147.2		36
13.5	odd	4		169.4.c.k.146.9		18
13.6	odd	12		169.4.c.k.22.9		18
13.7	odd	12		169.4.c.l.22.1		18
13.8	odd	4		169.4.c.l.146.1		18
13.9	even	3	inner	169.4.e.h.147.17		36
13.10	even	6		169.4.b.g.168.17		18
13.11	odd	12		169.4.a.k.1.9	✓	9
13.12	even	2	inner	169.4.e.h.23.17		36
39.2	even	12		1521.4.a.bg.1.9		9
39.11	even	12		1521.4.a.bh.1.1		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.4.a.k.1.9	✓	9	13.11	odd	12
169.4.a.l.1.1	yes	9	13.2	odd	12
169.4.b.g.168.2		18	13.3	even	3
169.4.b.g.168.17		18	13.10	even	6
169.4.c.k.22.9		18	13.6	odd	12
169.4.c.k.146.9		18	13.5	odd	4
169.4.c.l.22.1		18	13.7	odd	12
169.4.c.l.146.1		18	13.8	odd	4
169.4.e.h.23.2		36	1.1	even	1	trivial
169.4.e.h.23.17		36	13.12	even	2	inner
169.4.e.h.147.2		36	13.4	even	6	inner
169.4.e.h.147.17		36	13.9	even	3	inner
1521.4.a.bg.1.9		9	39.2	even	12
1521.4.a.bh.1.1		9	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)

\(f(q)\)	\(=\)	\(q+(-4.19172 + 2.42009i) q^{2} +(3.09831 + 5.36643i) q^{3} +(7.71365 - 13.3604i) q^{4} +15.2399i q^{5} +(-25.9745 - 14.9964i) q^{6} +(3.73794 + 2.15810i) q^{7} +35.9495i q^{8} +(-5.69903 + 9.87102i) q^{9} +O(q^{10})\)	\(q+(-4.19172 + 2.42009i) q^{2} +(3.09831 + 5.36643i) q^{3} +(7.71365 - 13.3604i) q^{4} +15.2399i q^{5} +(-25.9745 - 14.9964i) q^{6} +(3.73794 + 2.15810i) q^{7} +35.9495i q^{8} +(-5.69903 + 9.87102i) q^{9} +(-36.8818 - 63.8811i) q^{10} +(-21.2775 + 12.2846i) q^{11} +95.5971 q^{12} -20.8912 q^{14} +(-81.7836 + 47.2178i) q^{15} +(-25.2917 - 43.8065i) q^{16} +(-63.5802 + 110.124i) q^{17} -55.1687i q^{18} +(-44.8135 - 25.8731i) q^{19} +(203.611 + 117.555i) q^{20} +26.7459i q^{21} +(59.4595 - 102.987i) q^{22} +(43.6842 + 75.6632i) q^{23} +(-192.920 + 111.383i) q^{24} -107.253 q^{25} +96.6792 q^{27} +(57.6664 - 33.2937i) q^{28} +(-112.863 - 195.484i) q^{29} +(228.542 - 395.847i) q^{30} -108.720i q^{31} +(-37.0342 - 21.3817i) q^{32} +(-131.849 - 76.1228i) q^{33} -615.479i q^{34} +(-32.8892 + 56.9657i) q^{35} +(87.9208 + 152.283i) q^{36} +(100.248 - 57.8782i) q^{37} +250.461 q^{38} -547.865 q^{40} +(166.177 - 95.9425i) q^{41} +(-64.7274 - 112.111i) q^{42} +(-61.6504 + 106.782i) q^{43} +379.036i q^{44} +(-150.433 - 86.8524i) q^{45} +(-366.223 - 211.439i) q^{46} -36.7339i q^{47} +(156.723 - 271.452i) q^{48} +(-162.185 - 280.913i) q^{49} +(449.574 - 259.562i) q^{50} -787.965 q^{51} +119.162 q^{53} +(-405.252 + 233.972i) q^{54} +(-187.215 - 324.266i) q^{55} +(-77.5827 + 134.377i) q^{56} -320.651i q^{57} +(946.178 + 546.276i) q^{58} +(696.763 + 402.276i) q^{59} +1456.89i q^{60} +(-339.443 + 587.933i) q^{61} +(263.113 + 455.725i) q^{62} +(-42.6053 + 24.5982i) q^{63} +611.650 q^{64} +736.896 q^{66} +(75.7604 - 43.7403i) q^{67} +(980.872 + 1698.92i) q^{68} +(-270.694 + 468.856i) q^{69} -318.379i q^{70} +(-849.614 - 490.525i) q^{71} +(-354.858 - 204.877i) q^{72} +263.862i q^{73} +(-280.140 + 485.218i) q^{74} +(-332.303 - 575.566i) q^{75} +(-691.352 + 399.152i) q^{76} -106.045 q^{77} +321.051 q^{79} +(667.604 - 385.441i) q^{80} +(453.416 + 785.339i) q^{81} +(-464.378 + 804.327i) q^{82} +1042.54i q^{83} +(357.337 + 206.308i) q^{84} +(-1678.28 - 968.953i) q^{85} -596.798i q^{86} +(699.368 - 1211.34i) q^{87} +(-441.624 - 764.915i) q^{88} +(-298.558 + 172.373i) q^{89} +840.762 q^{90} +1347.86 q^{92} +(583.440 - 336.849i) q^{93} +(88.8993 + 153.978i) q^{94} +(394.302 - 682.951i) q^{95} -264.989i q^{96} +(-417.876 - 241.261i) q^{97} +(1359.67 + 785.005i) q^{98} -280.041i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9}+O(q^{10}) \) 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9	\( 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9} - 294 q^{10} - 156 q^{12} - 588 q^{14} - 538 q^{16} - 110 q^{17} - 680 q^{22} - 408 q^{23} - 1228 q^{25} - 2672 q^{27} - 560 q^{29} + 1042 q^{30} - 40 q^{35} - 1818 q^{36} + 2956 q^{38} + 52 q^{40} + 8 q^{42} - 1066 q^{43} + 264 q^{48} + 806 q^{49} - 1880 q^{51} - 1112 q^{53} + 500 q^{55} + 500 q^{56} + 272 q^{61} + 4070 q^{62} - 1136 q^{64} + 13116 q^{66} + 3072 q^{68} - 4100 q^{69} + 3980 q^{74} + 4786 q^{75} + 2872 q^{77} + 1648 q^{79} + 1670 q^{81} + 5514 q^{82} + 1572 q^{87} - 1272 q^{88} + 5120 q^{90} + 16040 q^{92} + 5062 q^{94} - 3228 q^{95}+O(q^{100}) \) 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9 - 294 * q^10 - 156 * q^12 - 588 * q^14 - 538 * q^16 - 110 * q^17 - 680 * q^22 - 408 * q^23 - 1228 * q^25 - 2672 * q^27 - 560 * q^29 + 1042 * q^30 - 40 * q^35 - 1818 * q^36 + 2956 * q^38 + 52 * q^40 + 8 * q^42 - 1066 * q^43 + 264 * q^48 + 806 * q^49 - 1880 * q^51 - 1112 * q^53 + 500 * q^55 + 500 * q^56 + 272 * q^61 + 4070 * q^62 - 1136 * q^64 + 13116 * q^66 + 3072 * q^68 - 4100 * q^69 + 3980 * q^74 + 4786 * q^75 + 2872 * q^77 + 1648 * q^79 + 1670 * q^81 + 5514 * q^82 + 1572 * q^87 - 1272 * q^88 + 5120 * q^90 + 16040 * q^92 + 5062 * q^94 - 3228 * q^95

Introduction

L-functions

Modular forms

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