LMFDB - Embedded newform 169.4.e.h.23.17

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			23.17
Character	$\chi$	$=$	169.23
Dual form			169.4.e.h.147.17

$q$-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	0.482204	−	0.876059i	$-0.339836\pi$
$2$	4.19172	−	2.42009i	1.48200	−	0.855630i	0.999791	+	0.0204286i	$0.00650307\pi$
$3$	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	$-0.761308\pi$
$5$		−	15.2399i		−	1.36309i	0.731774	−	0.681547i	$-0.238692\pi$
$6$	25.9745	+	14.9964i	1.76734	+	1.02037i
$7$	−3.73794	−	2.15810i	−0.201830	−	0.116527i	0.395679	−	0.918389i	$-0.370509\pi$
$7$	−3.73794	−	2.15810i	−0.201830	−	0.116527i	−0.597509	+	0.801862i	$0.703843\pi$
$8$		−	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	−0.179193	−	0.983814i	$-0.557349\pi$
$11$	21.2775	−	12.2846i	0.583219	−	0.336722i	0.762412	+	0.647092i	$0.224015\pi$
$12$	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	0.745525	−	0.666478i	$-0.232199\pi$
$19$	44.8135	+	25.8731i	0.541101	+	0.312405i	−0.204424	+	0.978882i	$0.565532\pi$
$20$	−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	$0.101987\pi$
$31$			108.720i			0.629895i	−0.949109	+	0.314948i	$0.898013\pi$
$32$	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	−0.705895	−	0.708316i	$-0.749455\pi$
$37$	−100.248	+	57.8782i	−0.445423	+	0.257165i	0.260472	+	0.965481i	$0.416122\pi$
$38$	250.461			1.06921
$39$		0			0
$40$	−547.865			−2.16563
$41$	−166.177	+	95.9425i	−0.632988	+	0.365456i	−0.781908	−	0.623393i	$-0.785754\pi$
$41$	−166.177	+	95.9425i	−0.632988	+	0.365456i	0.148920	+	0.988849i	$0.452420\pi$
$42$	−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	$0.0181541\pi$
$47$			36.7339i			0.114004i	−0.998374	+	0.0570020i	$0.981846\pi$
$48$	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	$-0.985663\pi$
$59$	−696.763	−	402.276i	−1.53747	−	0.887660i	−0.538486	−	0.842634i	$-0.681003\pi$
$60$		−	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	−0.567479	−	0.823388i	$-0.692081\pi$
$67$	−75.7604	+	43.7403i	−0.138143	+	0.0797571i	0.429335	+	0.903145i	$0.358748\pi$
$68$	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	0.996311	−	0.0858146i	$-0.0273493\pi$
$71$	849.614	+	490.525i	1.42015	+	0.819923i	0.423838	+	0.905738i	$0.360683\pi$
$72$	354.858	+	204.877i	0.580839	+	0.335348i
$73$		−	263.862i		−	0.423051i	−0.977372	−	0.211526i	$-0.932157\pi$
$73$		−	263.862i		−	0.423051i	0.977372	−	0.211526i	$-0.0678432\pi$
$74$	−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	$-0.757891\pi$
$83$		−	1042.54i		−	1.37872i	0.724417	−	0.689362i	$-0.242109\pi$
$84$	−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	−0.311557	−	0.950227i	$-0.600850\pi$
$89$	298.558	−	172.373i	0.355586	−	0.205298i	0.667143	+	0.744930i	$0.267517\pi$
$90$	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	0.702499	−	0.711685i	$-0.252068\pi$
$97$	417.876	+	241.261i	0.437411	+	0.252539i	−0.265088	+	0.964224i	$0.585401\pi$
$98$	−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	$-0.829497\pi$
$109$		−	1161.67i		−	1.02080i	0.859936	−	0.510401i	$-0.170503\pi$
$110$	−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	0.695526	−	0.718501i	$-0.255171\pi$
$137$	675.171	+	389.810i	0.421049	+	0.243093i	−0.274477	+	0.961594i	$0.588505\pi$
$138$			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	−0.270688	−	0.962667i	$-0.587251\pi$
$149$	−2254.79	−	1301.80i	−1.23973	−	0.715757i	−0.969038	+	0.246910i	$0.920585\pi$
$150$	−2785.84	−	1608.41i	−1.51642	−	0.875505i
$151$		−	206.776i		−	0.111438i	−0.998446	−	0.0557192i	$-0.982255\pi$
$151$		−	206.776i		−	0.111438i	0.998446	−	0.0557192i	$-0.0177452\pi$
$152$	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	−0.259180	−	0.965829i	$-0.583452\pi$
$163$	−2549.70	−	1472.07i	−1.22520	−	0.707371i	−0.966023	+	0.258458i	$0.916786\pi$
$164$			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	0.163673	−	0.986515i	$-0.447666\pi$
$167$	2373.62	−	1370.41i	1.09986	−	0.635002i	0.936183	+	0.351513i	$0.114333\pi$
$168$	−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	−0.856088	−	0.516829i	$-0.827112\pi$
$193$	−2242.98	+	1294.98i	−0.836545	+	0.482980i	0.0195433	+	0.999809i	$0.493779\pi$
$194$	2335.49			0.864321
$195$		0			0
$196$	−5004.16			−1.82367
$197$	1283.33	−	740.934i	0.464131	−	0.267966i	−0.249649	−	0.968336i	$-0.580315\pi$
$197$	1283.33	−	740.934i	0.464131	−	0.267966i	0.713780	+	0.700370i	$0.246982\pi$
$198$	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	−0.122271	−	0.992497i	$-0.539018\pi$
$223$	2251.55	−	1299.93i	0.676121	−	0.390359i	0.798392	+	0.602138i	$0.205684\pi$
$224$	−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	0.368953	−	0.929448i	$-0.379716\pi$
$227$	−860.144	−	496.604i	−0.251497	−	0.145202i	−0.620449	+	0.784246i	$0.713050\pi$
$228$	4284.04	+	2473.39i	1.24438	+	0.718440i
$229$			437.772i			0.126327i	0.998003	+	0.0631633i	$0.0201189\pi$
$229$			437.772i			0.126327i	−0.998003	+	0.0631633i	$0.979881\pi$
$230$	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	$-0.711788\pi$
$239$		−	5813.48i		−	1.57340i	0.617335	−	0.786700i	$-0.288212\pi$
$240$	−4136.89	−	2388.43i	−1.11265	−	0.642386i
$241$	−994.413	−	574.125i	−0.265792	−	0.153455i	0.361182	−	0.932495i	$-0.382373\pi$
$241$	−994.413	−	574.125i	−0.265792	−	0.153455i	−0.626974	+	0.779040i	$0.715707\pi$
$242$			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	−0.686694	−	0.726947i	$-0.740939\pi$
$271$	−1786.66	+	1031.53i	−0.400486	+	0.231221i	0.286208	+	0.958168i	$0.407605\pi$
$272$	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	$-0.968355\pi$
$281$		−	935.025i		−	0.198502i	0.995062	−	0.0992508i	$-0.0316446\pi$
$282$	−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	0.644489	−	0.764614i	$-0.277070\pi$
$293$	1527.46	+	881.882i	0.304558	+	0.175837i	−0.339931	+	0.940450i	$0.610404\pi$
$294$		−	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	$-0.854879\pi$
$307$		−	4736.59i		−	0.880558i	0.897861	−	0.440279i	$-0.145121\pi$
$308$	−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	$0.175269\pi$
$317$			5906.13i			1.04644i	−0.852198	+	0.523219i	$0.824731\pi$
$318$	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	0.284736	−	0.958606i	$-0.408094\pi$
$331$	−2427.32	−	1401.41i	−0.403074	−	0.232715i	−0.687809	+	0.725891i	$0.741427\pi$
$332$	−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	−0.941458	−	0.337131i	$-0.890544\pi$
$349$	−7303.69	+	4216.79i	−1.12022	+	0.646761i	−0.178765	+	0.983892i	$0.557210\pi$
$350$	2240.64			0.342193
$351$		0			0
$352$	1050.66			0.159092
$353$	−4099.52	+	2366.86i	−0.618118	+	0.356871i	−0.776136	−	0.630566i	$-0.782823\pi$
$353$	−4099.52	+	2366.86i	−0.618118	+	0.356871i	0.158018	+	0.987436i	$0.449490\pi$
$354$	−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	$0.187592\pi$
$359$			7561.34i			1.11162i	−0.831309	+	0.555811i	$0.812408\pi$
$360$	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	−0.919359	−	0.393420i	$-0.871292\pi$
$379$	−7661.13	+	4423.15i	−1.03833	+	0.599478i	−0.118968	+	0.992898i	$0.537958\pi$
$380$	−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	0.559298	−	0.828967i	$-0.311071\pi$
$383$	907.256	+	523.805i	0.121041	+	0.0698830i	−0.438257	+	0.898850i	$0.644404\pi$
$384$	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	−0.199159	−	0.979967i	$-0.563821\pi$
$397$	−9076.25	−	5240.17i	−1.14741	−	0.662460i	−0.948256	+	0.317507i	$0.897154\pi$
$398$			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	−0.00671803	−	0.999977i	$-0.502138\pi$
$401$	6873.12	−	3968.20i	0.855929	−	0.494171i	0.862647	+	0.505807i	$0.168805\pi$
$402$	−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	0.162360	−	0.986732i	$-0.448089\pi$
$409$	−5053.85	−	2917.84i	−0.610994	−	0.352758i	−0.773355	+	0.633974i	$0.781423\pi$
$410$	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	$0.405750\pi$
$421$			16524.6i			1.91297i	−0.291786	+	0.956484i	$0.594250\pi$
$422$	−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	−0.131231	−	0.991352i	$-0.541893\pi$
$431$	5920.65	−	3418.29i	0.661689	−	0.382026i	0.792920	+	0.609326i	$0.208560\pi$
$432$	−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	0.694702	−	0.719298i	$-0.255536\pi$
$449$	3987.59	+	2302.24i	0.419123	+	0.241981i	−0.275579	+	0.961278i	$0.588870\pi$
$450$		−	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	−0.998592	−	0.0530498i	$-0.983106\pi$
$457$	−14184.8	+	8189.62i	−1.45195	+	0.838281i	−0.453353	+	0.891331i	$0.649772\pi$
$458$	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	0.858182	−	0.513346i	$-0.171594\pi$
$461$	8341.13	+	4815.76i	0.842701	+	0.486534i	−0.0154801	+	0.999880i	$0.504928\pi$
$462$	−2754.47	−	1590.30i	−0.277380	−	0.160146i
$463$		−	17855.0i		−	1.79220i	−0.443848	−	0.896102i	$-0.646387\pi$
$463$		−	17855.0i		−	1.79220i	0.443848	−	0.896102i	$-0.353613\pi$
$464$	−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	−0.624965	−	0.780653i	$-0.714887\pi$
$479$	−2740.19	+	1582.05i	−0.261383	+	0.150909i	0.363582	+	0.931562i	$0.381554\pi$
$480$	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	0.166981	−	0.985960i	$-0.446598\pi$
$487$	−6484.79	−	3743.99i	−0.603396	−	0.348371i	−0.770376	+	0.637590i	$0.779932\pi$
$488$	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	$-0.846431\pi$
$499$		−	10343.2i		−	0.927904i	0.885860	−	0.463952i	$-0.153569\pi$
$500$	−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	−0.356904	−	0.934141i	$-0.616168\pi$
$509$	3142.29	−	1814.20i	0.273634	−	0.157983i	0.630538	+	0.776158i	$0.282834\pi$
$510$	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	$-0.792770\pi$
$541$		−	15251.2i		−	1.21202i	0.795459	−	0.606008i	$-0.207230\pi$
$542$	−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	−0.277865	−	0.960620i	$-0.589627\pi$
$557$	5457.08	−	3150.64i	0.415123	−	0.239672i	0.692989	+	0.720948i	$0.256294\pi$
$558$	−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	$-0.987673\pi$
$577$		−	1073.19i		−	0.0774308i	0.999250	−	0.0387154i	$-0.0123266\pi$
$578$	−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	0.0293768	−	0.999568i	$-0.490648\pi$
$587$	12937.9	−	7469.69i	0.909717	−	0.525225i	0.880340	+	0.474343i	$0.157314\pi$
$588$	−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	$0.0699542\pi$
$593$			6296.13i			0.436006i	−0.975948	+	0.218003i	$0.930046\pi$
$594$	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	−0.724015	−	0.689784i	$-0.757705\pi$
$613$	−7416.35	+	4281.83i	−0.488652	+	0.282123i	0.235363	+	0.971907i	$0.424372\pi$
$614$	−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	$0.130075\pi$
$617$	26370.1	+	15224.8i	1.72062	+	0.993400i	0.802958	+	0.596035i	$0.203258\pi$
$618$	−4151.32	−	2396.77i	−0.270211	−	0.156007i
$619$			26233.1i			1.70339i	0.524041	+	0.851693i	$0.324424\pi$
$619$			26233.1i			1.70339i	−0.524041	+	0.851693i	$0.675576\pi$
$620$	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	0.943350	−	0.331799i	$-0.107656\pi$
$631$	17874.3	+	10319.7i	1.12768	+	0.651066i	0.184329	+	0.982865i	$0.440989\pi$
$632$		−	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	0.826761	−	0.562553i	$-0.190181\pi$
$643$	12276.8	+	7088.03i	0.752956	+	0.434719i	−0.0738050	+	0.997273i	$0.523514\pi$
$644$	−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	−0.945476	−	0.325691i	$-0.894403\pi$
$661$	−19308.2	+	11147.6i	−1.13616	+	0.655961i	−0.190681	+	0.981652i	$0.561070\pi$
$662$	−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	0.933724	−	0.357993i	$-0.116539\pi$
$683$	19466.1	+	11238.7i	1.09055	+	0.629632i	0.156831	+	0.987625i	$0.449872\pi$
$684$			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	−0.307255	−	0.951627i	$-0.599410\pi$
$691$	6598.19	−	3809.47i	0.363252	−	0.209723i	0.670506	+	0.741904i	$0.266077\pi$
$692$	−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	0.0651986	−	0.997872i	$-0.479232\pi$
$709$	−14468.3	−	8353.25i	−0.766385	−	0.442472i	−0.831583	+	0.555400i	$0.812565\pi$
$710$		−	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	$0.0276804\pi$
$733$			3447.16i			0.173702i	−0.996221	+	0.0868511i	$0.972320\pi$
$734$	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	$-0.293464\pi$
$739$	32071.4	−	18516.5i	1.59644	−	0.921703i	0.992166	−	0.124925i	$-0.0398689\pi$
$740$	27215.4			1.35197
$741$		0			0
$742$	−2489.43			−0.123167
$743$	−13248.5	+	7649.01i	−0.654158	+	0.377678i	−0.790047	−	0.613046i	$-0.789944\pi$
$743$	−13248.5	+	7649.01i	−0.654158	+	0.377678i	0.135890	+	0.990724i	$0.456611\pi$
$744$	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	0.821083	−	0.570809i	$-0.193370\pi$
$761$	15478.0	+	8936.23i	0.737289	+	0.425674i	−0.0837936	+	0.996483i	$0.526704\pi$
$762$			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	−0.253499	−	0.967336i	$-0.581582\pi$
$769$	9755.95	−	5632.60i	0.457488	−	0.264131i	0.710988	+	0.703205i	$0.248248\pi$
$770$	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	−0.172888	−	0.984941i	$-0.555310\pi$
$773$	−23905.5	−	13801.8i	−1.11232	−	0.642196i	−0.939428	+	0.342745i	$0.888643\pi$
$774$	−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	0.892400	−	0.451246i	$-0.149020\pi$
$787$	20925.8	+	12081.5i	0.947809	+	0.547218i	0.0554093	+	0.998464i	$0.482354\pi$
$788$		−	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	$0.0671621\pi$
$811$			9674.05i			0.418868i	−0.977823	+	0.209434i	$0.932838\pi$
$812$	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	−0.888717	−	0.458457i	$-0.848402\pi$
$821$	−22019.6	+	12713.0i	−0.936040	+	0.540423i	−0.0473231	+	0.998880i	$0.515069\pi$
$822$	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	$0.0257944\pi$
$827$			3850.25i			0.161894i	−0.996718	+	0.0809469i	$0.974206\pi$
$828$	−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	−0.178152	−	0.984003i	$-0.557012\pi$
$839$	−27203.7	−	15706.1i	−1.11940	−	0.646285i	−0.941247	+	0.337718i	$0.890345\pi$
$840$			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	$0.119818\pi$
$853$			18315.5i			0.735184i	−0.929987	+	0.367592i	$0.880182\pi$
$854$	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	$-0.889575\pi$
$863$		−	17239.2i		−	0.679986i	0.940428	−	0.339993i	$-0.110425\pi$
$864$	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	−0.165263	−	0.986250i	$-0.552847\pi$
$877$	−28621.1	−	16524.4i	−1.10201	−	0.636247i	−0.936749	+	0.350003i	$0.886181\pi$
$878$	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	−0.220574	−	0.975370i	$-0.570793\pi$
$929$	−33286.4	−	19217.9i	−1.17556	−	0.678708i	−0.954982	+	0.296663i	$0.904126\pi$
$930$	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	$0.0705754\pi$
$941$			12695.6i			0.439814i	−0.975521	+	0.219907i	$0.929425\pi$
$942$	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	−0.998350	−	0.0574201i	$-0.981713\pi$
$947$	−42192.3	+	24359.7i	−1.44780	+	0.835886i	−0.449448	+	0.893307i	$0.648379\pi$
$948$	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	$-0.943682\pi$
$967$		−	10585.2i		−	0.352014i	0.984389	−	0.176007i	$-0.0563181\pi$
$968$	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	−0.358679	−	0.933461i	$-0.616773\pi$
$977$	8256.96	−	4767.16i	0.270382	−	0.156105i	0.629061	+	0.777356i	$0.283439\pi$
$978$	−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	$-0.953498\pi$
$983$		−	8972.94i		−	0.291142i	0.989348	−	0.145571i	$-0.0465019\pi$
$984$	−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.23.17		36
13.2	odd	12		169.4.a.k.1.9	✓	9
13.3	even	3		169.4.b.g.168.17		18
13.4	even	6	inner	169.4.e.h.147.17		36
13.5	odd	4		169.4.c.l.146.1		18
13.6	odd	12		169.4.c.l.22.1		18
13.7	odd	12		169.4.c.k.22.9		18
13.8	odd	4		169.4.c.k.146.9		18
13.9	even	3	inner	169.4.e.h.147.2		36
13.10	even	6		169.4.b.g.168.2		18
13.11	odd	12		169.4.a.l.1.1	yes	9
13.12	even	2	inner	169.4.e.h.23.2		36
39.2	even	12		1521.4.a.bh.1.1		9
39.11	even	12		1521.4.a.bg.1.9		9

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

Varieties

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Representations

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Database

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