LMFDB - Embedded newform 147.4.g.c.68.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [147,4,Mod(68,147)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(147, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("147.68"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	147.g (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.67328077084$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.443364212736.6
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 16x^{6} + 175x^{4} - 1296x^{2} + 6561 $ x^8 - 16x^6 + 175x^4 - 1296*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			68.2
Root			$-2.17132 - 2.07011i$ of defining polynomial
Character	$\chi$	$=$	147.68
Dual form			147.4.g.c.80.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.57071 - 2.06155i) q^{2} +(3.58554 + 3.76084i) q^{3} +(4.50000 + 7.79423i) q^{4} +(-5.04975 + 8.74643i) q^{5} +(-5.04975 - 20.8207i) q^{6} -4.12311i q^{8} +(-1.28786 + 26.9693i) q^{9} +(36.0624 - 20.8207i) q^{10} +(-28.5657 + 16.4924i) q^{11} +(-13.1779 + 44.8703i) q^{12} -56.3383i q^{13} +(-51.0000 + 12.3693i) q^{15} +(27.5000 - 47.6314i) q^{16} +(-30.2985 - 52.4786i) q^{17} +(60.1971 - 93.6446i) q^{18} +(-31.8198 - 18.3712i) q^{19} -90.8955 q^{20} +136.000 q^{22} +(-78.5557 - 45.3542i) q^{23} +(15.5063 - 14.7835i) q^{24} +(11.5000 + 19.9186i) q^{25} +(-116.144 + 201.168i) q^{26} +(-106.045 + 91.8559i) q^{27} -57.7235i q^{29} +(207.606 + 60.9719i) q^{30} +(-220.617 + 127.373i) q^{31} +(-224.955 + 129.878i) q^{32} +(-164.449 - 48.2969i) q^{33} +249.848i q^{34} +(-216.000 + 111.324i) q^{36} +(-115.000 + 199.186i) q^{37} +(75.7463 + 131.196i) q^{38} +(211.879 - 202.003i) q^{39} +(36.0624 + 20.8207i) q^{40} -141.393 q^{41} +44.0000 q^{43} +(-257.091 - 148.432i) q^{44} +(-229.381 - 147.452i) q^{45} +(187.000 + 323.894i) q^{46} +(171.692 - 297.379i) q^{47} +(277.736 - 67.3610i) q^{48} -94.8314i q^{50} +(88.7271 - 302.112i) q^{51} +(439.113 - 253.522i) q^{52} +(-178.536 + 103.078i) q^{53} +(568.021 - 109.374i) q^{54} -333.131i q^{55} +(-45.0000 - 185.540i) q^{57} +(-119.000 + 206.114i) q^{58} +(-65.6468 - 113.704i) q^{59} +(-325.909 - 341.844i) q^{60} +(-61.5183 - 35.5176i) q^{61} +1050.35 q^{62} +631.000 q^{64} +(492.759 + 284.494i) q^{65} +(487.633 + 511.474i) q^{66} +(32.0000 + 55.4256i) q^{67} +(272.687 - 472.307i) q^{68} +(-111.095 - 458.055i) q^{69} +461.788i q^{71} +(111.197 + 5.30997i) q^{72} +(76.3675 - 44.0908i) q^{73} +(821.264 - 474.157i) q^{74} +(-33.6770 + 114.668i) q^{75} -330.681i q^{76} +(-1173.00 + 284.494i) q^{78} +(221.000 - 382.783i) q^{79} +(277.736 + 481.054i) q^{80} +(-725.683 - 69.4651i) q^{81} +(504.874 + 291.489i) q^{82} -494.876 q^{83} +612.000 q^{85} +(-157.111 - 90.7083i) q^{86} +(217.089 - 206.970i) q^{87} +(68.0000 + 117.779i) q^{88} +(242.388 - 419.829i) q^{89} +(515.075 + 999.392i) q^{90} -816.375i q^{92} +(-1270.06 - 373.005i) q^{93} +(-1226.12 + 707.903i) q^{94} +(321.364 - 185.540i) q^{95} +(-1295.03 - 380.338i) q^{96} +1092.47i q^{97} +(-408.000 - 791.636i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 36 q^{4} - 96 q^{9} - 408 q^{15} + 220 q^{16} - 204 q^{18} + 1088 q^{22} + 92 q^{25} + 204 q^{30} - 1728 q^{36} - 920 q^{37} - 276 q^{39} + 352 q^{43} + 1496 q^{46} + 1224 q^{51} - 360 q^{57} - 952 q^{58}+ \cdots - 3264 q^{99}+O(q^{100}) $ 8 * q + 36 * q^4 - 96 * q^9 - 408 * q^15 + 220 * q^16 - 204 * q^18 + 1088 * q^22 + 92 * q^25 + 204 * q^30 - 1728 * q^36 - 920 * q^37 - 276 * q^39 + 352 * q^43 + 1496 * q^46 + 1224 * q^51 - 360 * q^57 - 952 * q^58 - 1836 * q^60 + 5048 * q^64 + 256 * q^67 + 204 * q^72 - 9384 * q^78 + 1768 * q^79 - 1692 * q^81 + 4896 * q^85 + 544 * q^88 - 1248 * q^93 - 3264 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−3.57071	−	2.06155i	−1.26244	−	0.728869i	−0.288892	−	0.957362i	$-0.593287\pi$
$2$	−3.57071	−	2.06155i	−1.26244	−	0.728869i	−0.973546	+	0.228493i	$0.926620\pi$
$3$	3.58554	+	3.76084i	0.690037	+	0.723774i
$3$	3.58554	+	3.76084i	0.690037	+	0.723774i
$4$	4.50000	+	7.79423i	0.562500	+	0.974279i
$5$	−5.04975	+	8.74643i	−0.451664	+	0.782304i	−0.998490	−	0.0549420i	$-0.982503\pi$
$5$	−5.04975	+	8.74643i	−0.451664	+	0.782304i	0.546826	+	0.837246i	$0.315836\pi$
$6$	−5.04975	−	20.8207i	−0.343592	−	1.41667i
$7$		0			0
$7$		0			0
$8$		−	4.12311i		−	0.182217i
$9$	−1.28786	+	26.9693i	−0.0476984	+	0.998862i
$10$	36.0624	−	20.8207i	1.14039	−	0.658407i
$11$	−28.5657	+	16.4924i	−0.782990	+	0.452059i	−0.837489	−	0.546455i	$-0.815977\pi$
$11$	−28.5657	+	16.4924i	−0.782990	+	0.452059i	0.0544991	+	0.998514i	$0.482644\pi$
$12$	−13.1779	+	44.8703i	−0.317012	+	1.07941i
$13$		−	56.3383i		−	1.20196i	−0.799266	−	0.600978i	$-0.794778\pi$
$13$		−	56.3383i		−	1.20196i	0.799266	−	0.600978i	$-0.205222\pi$
$14$		0			0
$15$	−51.0000	+	12.3693i	−0.877876	+	0.212916i
$16$	27.5000	−	47.6314i	0.429688	−	0.744241i
$17$	−30.2985	−	52.4786i	−0.432263	−	0.748701i	0.564805	−	0.825224i	$-0.308951\pi$
$17$	−30.2985	−	52.4786i	−0.432263	−	0.748701i	−0.997068	+	0.0765232i	$0.975618\pi$
$18$	60.1971	−	93.6446i	0.788256	−	1.22624i
$19$	−31.8198	−	18.3712i	−0.384209	−	0.221823i	0.295439	−	0.955362i	$-0.404534\pi$
$19$	−31.8198	−	18.3712i	−0.384209	−	0.221823i	−0.679648	+	0.733539i	$0.737867\pi$
$20$	−90.8955			−1.01624
$21$		0			0
$22$	136.000			1.31797
$23$	−78.5557	−	45.3542i	−0.712174	−	0.411174i	0.0996916	−	0.995018i	$-0.468214\pi$
$23$	−78.5557	−	45.3542i	−0.712174	−	0.411174i	−0.811865	+	0.583845i	$0.801548\pi$
$24$	15.5063	−	14.7835i	0.131884	−	0.125737i
$25$	11.5000	+	19.9186i	0.0920000	+	0.159349i
$26$	−116.144	+	201.168i	−0.876068	+	1.51739i
$27$	−106.045	+	91.8559i	−0.755864	+	0.654729i
$28$		0			0
$29$		−	57.7235i		−	0.369620i	−0.982774	−	0.184810i	$-0.940833\pi$
$29$		−	57.7235i		−	0.369620i	0.982774	−	0.184810i	$-0.0591670\pi$
$30$	207.606	+	60.9719i	1.26345	+	0.371063i
$31$	−220.617	+	127.373i	−1.27819	+	0.737966i	−0.976516	−	0.215444i	$-0.930880\pi$
$31$	−220.617	+	127.373i	−1.27819	+	0.737966i	−0.301679	+	0.953410i	$0.597547\pi$
$32$	−224.955	+	129.878i	−1.24271	+	0.717480i
$33$	−164.449	−	48.2969i	−0.867481	−	0.254770i
$34$			249.848i			1.26025i
$35$		0			0
$36$	−216.000	+	111.324i	−1.00000	+	0.515388i
$37$	−115.000	+	199.186i	−0.510970	+	0.885026i	0.488949	+	0.872312i	$0.337380\pi$
$37$	−115.000	+	199.186i	−0.510970	+	0.885026i	−0.999919	+	0.0127135i	$0.995953\pi$
$38$	75.7463	+	131.196i	0.323360	+	0.560076i
$39$	211.879	−	202.003i	0.869945	−	0.829394i
$40$	36.0624	+	20.8207i	0.142549	+	0.0823009i
$41$	−141.393			−0.538583			−0.269291	−	0.963059i	$-0.586789\pi$
$41$	−141.393			−0.538583			−0.269291	+	0.963059i	$0.586789\pi$
$42$		0			0
$43$	44.0000			0.156045			0.0780225	−	0.996952i	$-0.475139\pi$
$43$	44.0000			0.156045			0.0780225	+	0.996952i	$0.475139\pi$
$44$	−257.091	−	148.432i	−0.880863	−	0.508567i
$45$	−229.381	−	147.452i	−0.759870	−	0.488464i
$46$	187.000	+	323.894i	0.599384	+	1.03816i
$47$	171.692	−	297.379i	0.532847	−	0.922917i	−0.466418	−	0.884565i	$-0.654456\pi$
$47$	171.692	−	297.379i	0.532847	−	0.922917i	0.999264	−	0.0383528i	$-0.0122111\pi$
$48$	277.736	−	67.3610i	0.835162	−	0.202557i
$49$		0			0
$50$		−	94.8314i		−	0.268224i
$51$	88.7271	−	302.112i	0.243613	−	0.829492i
$52$	439.113	−	253.522i	1.17104	−	0.676100i
$53$	−178.536	+	103.078i	−0.462713	+	0.267147i	−0.713184	−	0.700977i	$-0.752748\pi$
$53$	−178.536	+	103.078i	−0.462713	+	0.267147i	0.250472	+	0.968124i	$0.419414\pi$
$54$	568.021	−	109.374i	1.43144	−	0.275628i
$55$		−	333.131i		−	0.816715i
$56$		0			0
$57$	−45.0000	−	185.540i	−0.104568	−	0.431146i
$58$	−119.000	+	206.114i	−0.269405	+	0.466622i
$59$	−65.6468	−	113.704i	−0.144856	−	0.250897i	0.784463	−	0.620175i	$-0.212938\pi$
$59$	−65.6468	−	113.704i	−0.144856	−	0.250897i	−0.929319	+	0.369278i	$0.879605\pi$
$60$	−325.909	−	341.844i	−0.701245	−	0.735531i
$61$	−61.5183	−	35.5176i	−0.129125	−	0.0745502i	0.434046	−	0.900891i	$-0.357085\pi$
$61$	−61.5183	−	35.5176i	−0.129125	−	0.0745502i	−0.563171	+	0.826340i	$0.690419\pi$
$62$	1050.35			2.15152
$63$		0			0
$64$	631.000			1.23242
$65$	492.759	+	284.494i	0.940295	+	0.542880i
$66$	487.633	+	511.474i	0.909446	+	0.953911i
$67$	32.0000	+	55.4256i	0.0583496	+	0.101064i	0.893725	−	0.448616i	$-0.148083\pi$
$67$	32.0000	+	55.4256i	0.0583496	+	0.101064i	−0.835375	+	0.549680i	$0.814750\pi$
$68$	272.687	−	472.307i	0.486296	−	0.842289i
$69$	−111.095	−	458.055i	−0.193829	−	0.799178i
$70$		0			0
$71$			461.788i			0.771889i	0.922522	+	0.385945i	$0.126124\pi$
$71$			461.788i			0.771889i	−0.922522	+	0.385945i	$0.873876\pi$
$72$	111.197	+	5.30997i	0.182010	+	0.00869147i
$73$	76.3675	−	44.0908i	0.122440	−	0.0706910i	−0.437529	−	0.899204i	$-0.644146\pi$
$73$	76.3675	−	44.0908i	0.122440	−	0.0706910i	0.559969	+	0.828513i	$0.310813\pi$
$74$	821.264	−	474.157i	1.29014	−	0.744860i
$75$	−33.6770	+	114.668i	−0.0518491	+	0.176544i
$76$		−	330.681i		−	0.499102i
$77$		0			0
$78$	−1173.00	+	284.494i	−1.70277	+	0.412982i
$79$	221.000	−	382.783i	0.314740	−	0.545145i	−0.664642	−	0.747162i	$-0.731416\pi$
$79$	221.000	−	382.783i	0.314740	−	0.545145i	0.979382	+	0.202016i	$0.0647494\pi$
$80$	277.736	+	481.054i	0.388148	+	0.672293i
$81$	−725.683	−	69.4651i	−0.995450	−	0.0952883i
$82$	504.874	+	291.489i	0.679927	+	0.392556i
$83$	−494.876			−0.654454			−0.327227	−	0.944946i	$-0.606114\pi$
$83$	−494.876			−0.654454			−0.327227	+	0.944946i	$0.606114\pi$
$84$		0			0
$85$	612.000			0.780950
$86$	−157.111	−	90.7083i	−0.196997	−	0.113736i
$87$	217.089	−	206.970i	0.267521	−	0.255051i
$88$	68.0000	+	117.779i	0.0823730	+	0.142674i
$89$	242.388	−	419.829i	0.288686	−	0.500020i	−0.684810	−	0.728722i	$-0.740115\pi$
$89$	242.388	−	419.829i	0.288686	−	0.500020i	0.973496	+	0.228702i	$0.0734482\pi$
$90$	515.075	+	999.392i	0.603263	+	1.17050i
$91$		0			0
$92$		−	816.375i		−	0.925141i
$93$	−1270.06	−	373.005i	−1.41612	−	0.415901i
$94$	−1226.12	+	707.903i	−1.34537	+	0.776751i
$95$	321.364	−	185.540i	0.347066	−	0.200379i
$96$	−1295.03	−	380.338i	−1.37681	−	0.404355i
$97$			1092.47i			1.14354i	0.820413	+	0.571772i	$0.193744\pi$
$97$			1092.47i			1.14354i	−0.820413	+	0.571772i	$0.806256\pi$
$98$		0			0
$99$	−408.000	−	791.636i	−0.414197	−	0.803661i
$100$	−103.500	+	179.267i	−0.103500	+	0.179267i
$101$	−631.219	−	1093.30i	−0.621868	−	1.07711i	−0.989138	−	0.146992i	$-0.953041\pi$
$101$	−631.219	−	1093.30i	−0.621868	−	1.07711i	0.367270	−	0.930114i	$-0.380293\pi$
$102$	−939.639	+	895.839i	−0.912138	+	0.869620i
$103$	42.4264	+	24.4949i	0.0405864	+	0.0234326i	0.520156	−	0.854071i	$-0.325874\pi$
$103$	42.4264	+	24.4949i	0.0405864	+	0.0234326i	−0.479570	+	0.877504i	$0.659207\pi$
$104$	−232.289			−0.219017
$105$		0			0
$106$	850.000			0.778861
$107$	1271.17	+	733.913i	1.14850	+	0.663084i	0.948520	−	0.316717i	$-0.102580\pi$
$107$	1271.17	+	733.913i	1.14850	+	0.663084i	0.199976	+	0.979801i	$0.435914\pi$
$108$	−1193.15	−	413.186i	−1.06306	−	0.368137i
$109$	935.000	+	1619.47i	0.821622	+	1.42309i	0.904474	+	0.426529i	$0.140264\pi$
$109$	935.000	+	1619.47i	0.821622	+	1.42309i	−0.0828525	+	0.996562i	$0.526403\pi$
$110$	−686.766	+	1189.51i	−0.595278	+	1.03105i
$111$	−1161.44	+	281.691i	−0.993147	+	0.240873i
$112$		0			0
$113$			1673.98i			1.39358i	0.717274	+	0.696791i	$0.245390\pi$
$113$			1673.98i			1.39358i	−0.717274	+	0.696791i	$0.754610\pi$
$114$	−221.818	+	755.279i	−0.182238	+	0.620512i
$115$	793.374	−	458.055i	0.643326	−	0.371424i
$116$	449.910	−	259.756i	0.360113	−	0.207911i
$117$	1519.40	+	72.5556i	1.20059	+	0.0573314i
$118$			541.337i			0.422323i
$119$		0			0
$120$	51.0000	+	210.278i	0.0387970	+	0.159964i
$121$	−121.500	+	210.444i	−0.0912847	+	0.158110i
$122$	146.443	+	253.646i	0.108675	+	0.188230i
$123$	−506.970	−	531.757i	−0.371642	−	0.389812i
$124$	−1985.56	−	1146.36i	−1.43797	−	0.830212i
$125$	−1494.73			−1.06954
$126$		0			0
$127$	−1048.00			−0.732244			−0.366122	−	0.930567i	$-0.619315\pi$
$127$	−1048.00			−0.732244			−0.366122	+	0.930567i	$0.619315\pi$
$128$	−453.481	−	261.817i	−0.313144	−	0.180794i
$129$	157.764	+	165.477i	0.107677	+	0.112941i
$130$	−1173.00	−	2031.70i	−0.791376	−	1.37070i
$131$	−1277.59	+	2212.85i	−0.852086	+	1.47586i	0.0272354	+	0.999629i	$0.491330\pi$
$131$	−1277.59	+	2212.85i	−0.852086	+	1.47586i	−0.879322	+	0.476228i	$0.842004\pi$
$132$	−363.582	−	1499.09i	−0.239741	−	0.988476i
$133$		0			0
$134$		−	263.879i		−	0.170117i
$135$	−267.911	−	1391.36i	−0.170801	−	0.887033i
$136$	−216.375	+	124.924i	−0.136426	+	0.0787658i
$137$	871.254	−	503.019i	0.543330	−	0.313692i	−0.203097	−	0.979159i	$-0.565101\pi$
$137$	871.254	−	503.019i	0.543330	−	0.313692i	0.746428	+	0.665467i	$0.231767\pi$
$138$	−547.617	+	1864.61i	−0.337799	+	1.15019i
$139$		−	1393.76i		−	0.850483i	−0.905080	−	0.425242i	$-0.860189\pi$
$139$		−	1393.76i		−	0.850483i	0.905080	−	0.425242i	$-0.139811\pi$
$140$		0			0
$141$	1734.00	−	420.557i	1.03567	−	0.251186i
$142$	952.000	−	1648.91i	0.562606	−	0.974462i
$143$	929.154	+	1609.34i	0.543355	+	0.941119i
$144$	1249.17	+	802.997i	0.722898	+	0.464698i
$145$	504.874	+	291.489i	0.289155	+	0.166944i
$146$	−363.582			−0.206098
$147$		0			0
$148$	−2070.00			−1.14968
$149$	221.384	+	127.816i	0.121722	+	0.0702760i	0.559625	−	0.828746i	$-0.310945\pi$
$149$	221.384	+	127.816i	0.121722	+	0.0702760i	−0.437903	+	0.899022i	$0.644279\pi$
$150$	356.646	−	340.022i	0.194133	−	0.185084i
$151$	−724.000	−	1254.00i	−0.390187	−	0.675824i	0.602287	−	0.798280i	$-0.294256\pi$
$151$	−724.000	−	1254.00i	−0.390187	−	0.675824i	−0.992474	+	0.122456i	$0.960923\pi$
$152$	−75.7463	+	131.196i	−0.0404200	+	0.0700094i
$153$	1454.33	−	749.544i	0.768467	−	0.396059i
$154$		0			0
$155$		−	2572.82i		−	1.33325i
$156$	2527.91	+	742.423i	1.29740	+	0.381034i
$157$	2942.27	−	1698.72i	1.49566	−	0.863520i	0.495674	−	0.868509i	$-0.334921\pi$
$157$	2942.27	−	1698.72i	1.49566	−	0.863520i	0.999988	+	0.00498842i	$0.00158787\pi$
$158$	−1578.26	+	911.206i	−0.794679	+	0.458808i
$159$	−1027.80	−	301.856i	−0.512643	−	0.150558i
$160$		−	2623.40i		−	1.29624i
$161$		0			0
$162$	2448.00	+	1744.07i	1.18724	+	0.845848i
$163$	−1564.00	+	2708.93i	−0.751546	+	1.30172i	0.195528	+	0.980698i	$0.437358\pi$
$163$	−1564.00	+	2708.93i	−0.751546	+	1.30172i	−0.947073	+	0.321017i	$0.895975\pi$
$164$	−636.269	−	1102.05i	−0.302953	−	0.524730i
$165$	1252.85	−	1194.45i	0.591117	−	0.563563i
$166$	1767.06	+	1020.21i	0.826207	+	0.477011i
$167$	706.965			0.327585			0.163792	−	0.986495i	$-0.447627\pi$
$167$	706.965			0.327585			0.163792	+	0.986495i	$0.447627\pi$
$168$		0			0
$169$	−977.000			−0.444697
$170$	−2185.28	−	1261.67i	−0.985901	−	0.569210i
$171$	536.436	−	834.497i	0.239897	−	0.373191i
$172$	198.000	+	342.946i	0.0877753	+	0.152031i
$173$	1126.09	−	1950.45i	0.494887	−	0.857169i	−0.505096	−	0.863063i	$-0.668543\pi$
$173$	1126.09	−	1950.45i	0.494887	−	0.857169i	0.999983	+	0.00589428i	$0.00187622\pi$
$174$	−1201.84	+	291.489i	−0.523628	+	0.126999i
$175$		0			0
$176$			1814.17i			0.776977i
$177$	192.242	−	654.575i	0.0816373	−	0.277971i
$178$	−1731.00	+	999.392i	−0.728897	+	0.420829i
$179$	−3027.97	+	1748.20i	−1.26436	+	0.729980i	−0.973915	−	0.226912i	$-0.927137\pi$
$179$	−3027.97	+	1748.20i	−1.26436	+	0.729980i	−0.290447	+	0.956891i	$0.593804\pi$
$180$	117.060	−	2451.39i	0.0484732	−	1.01509i
$181$			183.712i			0.0754430i	0.999288	+	0.0377215i	$0.0120100\pi$
$181$			183.712i			0.0754430i	−0.999288	+	0.0377215i	$0.987990\pi$
$182$		0			0
$183$	−87.0000	−	358.710i	−0.0351433	−	0.144900i
$184$	−187.000	+	323.894i	−0.0749230	+	0.129770i
$185$	−1161.44	−	2011.68i	−0.461573	−	0.799468i
$186$	3766.06	+	3950.19i	1.48463	+	1.55722i
$187$	1731.00	+	999.392i	0.676915	+	0.390817i
$188$	3090.45			1.19890
$189$		0			0
$190$	−1530.00			−0.584199
$191$	−228.526	−	131.939i	−0.0865735	−	0.0499832i	0.456088	−	0.889935i	$-0.349250\pi$
$191$	−228.526	−	131.939i	−0.0865735	−	0.0499832i	−0.542662	+	0.839951i	$0.682583\pi$
$192$	2262.47	+	2373.09i	0.850416	+	0.891995i
$193$	326.000	+	564.649i	0.121585	+	0.210592i	0.920393	−	0.390994i	$-0.127869\pi$
$193$	326.000	+	564.649i	0.121585	+	0.210592i	−0.798808	+	0.601587i	$0.794535\pi$
$194$	2252.19	−	3900.91i	0.833494	−	1.44365i
$195$	696.866	+	2873.25i	0.255916	+	1.05517i
$196$		0			0
$197$			2020.32i			0.730670i	0.930876	+	0.365335i	$0.119046\pi$
$197$			2020.32i			0.730670i	−0.930876	+	0.365335i	$0.880954\pi$
$198$	−175.149	+	3667.82i	−0.0628650	+	1.31647i
$199$	−4200.21	+	2424.99i	−1.49621	+	0.863836i	−0.999990	−	0.00436270i	$-0.998611\pi$
$199$	−4200.21	+	2424.99i	−1.49621	+	0.863836i	−0.496217	+	0.868199i	$0.665278\pi$
$200$	82.1264	−	47.4157i	0.0290361	−	0.0167640i
$201$	−93.7098	+	319.078i	−0.0328845	+	0.111970i
$202$			5205.17i			1.81304i
$203$		0			0
$204$	2754.00	−	667.943i	0.945189	−	0.229242i
$205$	714.000	−	1236.68i	0.243258	−	0.421335i
$206$	−100.995	−	174.929i	−0.0341585	−	0.0591643i
$207$	1324.34	−	2060.18i	0.444675	−	0.691751i
$208$	−2683.47	−	1549.30i	−0.894544	−	0.516465i
$209$	1211.94			0.401109
$210$		0			0
$211$	−2224.00			−0.725623			−0.362812	−	0.931863i	$-0.618183\pi$
$211$	−2224.00			−0.725623			−0.362812	+	0.931863i	$0.618183\pi$
$212$	−1606.82	−	927.699i	−0.520552	−	0.300541i
$213$	−1736.71	+	1655.76i	−0.558674	+	0.532632i
$214$	−3026.00	−	5241.19i	−0.966603	−	1.67421i
$215$	−222.189	+	384.843i	−0.0704799	+	0.122075i
$216$	378.731	+	437.234i	0.119303	+	0.137731i
$217$		0			0
$218$		−	7710.21i		−	2.39542i
$219$	439.637	+	129.117i	0.135653	+	0.0398398i
$220$	2596.50	−	1499.09i	0.795708	−	0.459402i
$221$	−2956.55	+	1706.97i	−0.899906	+	0.519561i
$222$	4727.90	+	1388.54i	1.42935	+	0.419786i
$223$			1915.50i			0.575208i	0.957749	+	0.287604i	$0.0928587\pi$
$223$			1915.50i			0.575208i	−0.957749	+	0.287604i	$0.907141\pi$
$224$		0			0
$225$	−552.000	+	284.494i	−0.163556	+	0.0842946i
$226$	3451.00	−	5977.31i	1.01574	−	1.75931i
$227$	2974.30	+	5151.65i	0.869654	+	1.50629i	0.862350	+	0.506312i	$0.168992\pi$
$227$	2974.30	+	5151.65i	0.869654	+	1.50629i	0.00730379	+	0.999973i	$0.497675\pi$
$228$	1243.64	−	1185.67i	0.361237	−	0.344399i
$229$	−3209.56	−	1853.04i	−0.926173	−	0.534726i	−0.0405736	−	0.999177i	$-0.512919\pi$
$229$	−3209.56	−	1853.04i	−0.926173	−	0.534726i	−0.885599	+	0.464451i	$0.846252\pi$
$230$	−3777.21			−1.08288
$231$		0			0
$232$	−238.000			−0.0673511
$233$	−828.406	−	478.280i	−0.232921	−	0.134477i	0.378998	−	0.925398i	$-0.376269\pi$
$233$	−828.406	−	478.280i	−0.232921	−	0.134477i	−0.611919	+	0.790920i	$0.709602\pi$
$234$	−5275.77	−	3391.40i	−1.47388	−	0.947448i
$235$	1734.00	+	3003.38i	0.481335	+	0.833696i
$236$	590.821	−	1023.33i	0.162963	−	0.282260i
$237$	2231.99	−	541.337i	0.611744	−	0.148370i
$238$		0			0
$239$			4791.05i			1.29668i	0.761350	+	0.648341i	$0.224537\pi$
$239$			4791.05i			1.29668i	−0.761350	+	0.648341i	$0.775463\pi$
$240$	−813.332	+	2769.36i	−0.218752	+	0.744839i
$241$	−3279.56	+	1893.46i	−0.876577	+	0.506092i	−0.869528	−	0.493883i	$-0.835577\pi$
$241$	−3279.56	+	1893.46i	−0.876577	+	0.506092i	−0.00704889	+	0.999975i	$0.502244\pi$
$242$	867.684	−	500.957i	0.230483	−	0.133069i
$243$	−2340.71	−	2978.25i	−0.617930	−	0.786233i
$244$		−	639.317i		−	0.167738i
$245$		0			0
$246$	714.000	+	2943.90i	0.185053	+	0.762992i
$247$	−1035.00	+	1792.67i	−0.266621	+	0.461802i
$248$	525.174	+	909.628i	0.134470	+	0.232909i
$249$	−1774.39	−	1861.15i	−0.451597	−	0.473677i
$250$	5337.24	+	3081.46i	1.35023	+	0.779554i
$251$	4029.70			1.01336			0.506678	−	0.862135i	$-0.330873\pi$
$251$	4029.70			1.01336			0.506678	+	0.862135i	$0.330873\pi$
$252$		0			0
$253$	2992.00			0.743500
$254$	3742.11	+	2160.51i	0.924412	+	0.533710i
$255$	2194.35	+	2301.63i	0.538884	+	0.565231i
$256$	−1444.50	−	2501.95i	−0.352661	−	0.610827i
$257$	100.995	−	174.929i	0.0245132	−	0.0424581i	−0.853509	−	0.521079i	$-0.825530\pi$
$257$	100.995	−	174.929i	0.0245132	−	0.0424581i	0.878022	+	0.478621i	$0.158863\pi$
$258$	−222.189	−	916.109i	−0.0536159	−	0.221064i
$259$		0			0
$260$			5120.90i			1.22148i
$261$	1556.76	+	74.3396i	0.369199	+	0.0176303i
$262$	9123.80	−	5267.63i	2.15141	−	1.24212i
$263$	7169.99	−	4139.60i	1.68107	−	0.970565i	0.720114	−	0.693856i	$-0.244090\pi$
$263$	7169.99	−	4139.60i	1.68107	−	0.970565i	0.960954	−	0.276709i	$-0.0892438\pi$
$264$	−199.133	+	678.040i	−0.0464235	+	0.158070i
$265$		−	2082.07i		−	0.482643i
$266$		0			0
$267$	2448.00	−	593.727i	0.561105	−	0.136088i
$268$	−288.000	+	498.831i	−0.0656433	+	0.113698i
$269$	−2893.51	−	5011.70i	−0.655838	−	1.13594i	−0.981683	−	0.190521i	$-0.938982\pi$
$269$	−2893.51	−	5011.70i	−0.655838	−	1.13594i	0.325846	−	0.945423i	$-0.394351\pi$
$270$	−1911.73	+	5520.47i	−0.430905	+	1.24432i
$271$	−1056.42	−	609.923i	−0.236800	−	0.136717i	0.376905	−	0.926252i	$-0.376988\pi$
$271$	−1056.42	−	609.923i	−0.236800	−	0.136717i	−0.613705	+	0.789535i	$0.710322\pi$
$272$	−3332.84			−0.742952
$273$		0			0
$274$	−4148.00			−0.914561
$275$	−657.011	−	379.326i	−0.144070	−	0.0831789i
$276$	3070.26	−	2927.14i	0.669593	−	0.638381i
$277$	1607.00	+	2783.41i	0.348575	+	0.603750i	0.985997	−	0.166766i	$-0.0533323\pi$
$277$	1607.00	+	2783.41i	0.348575	+	0.603750i	−0.637422	+	0.770515i	$0.719999\pi$
$278$	−2873.31	+	4976.72i	−0.619891	+	1.07368i
$279$	−3151.05	−	6113.93i	−0.676158	−	1.31194i
$280$		0			0
$281$		−	9235.76i		−	1.96071i	−0.197245	−	0.980354i	$-0.563200\pi$
$281$		−	9235.76i		−	1.96071i	0.197245	−	0.980354i	$-0.436800\pi$
$282$	−7058.62	−	2073.04i	−1.49055	−	0.437759i
$283$	−2581.65	+	1490.51i	−0.542272	+	0.313081i	−0.745999	−	0.665947i	$-0.768028\pi$
$283$	−2581.65	+	1490.51i	−0.542272	+	0.313081i	0.203727	+	0.979028i	$0.434694\pi$
$284$	−3599.28	+	2078.05i	−0.752035	+	0.434188i
$285$	1850.05	+	543.341i	0.384517	+	0.112929i
$286$		−	7662.00i		−	1.58414i
$287$		0			0
$288$	−3213.00	−	6234.14i	−0.657388	−	1.27552i
$289$	620.500	−	1074.74i	0.126298	−	0.218754i
$290$	−1201.84	−	2081.65i	−0.243360	−	0.421513i
$291$	−4108.62	+	3917.10i	−0.827668	+	0.789087i
$292$	687.308	+	396.817i	0.137745	+	0.0795273i
$293$	5160.85			1.02901			0.514505	−	0.857487i	$-0.327976\pi$
$293$	5160.85			1.02901			0.514505	+	0.857487i	$0.327976\pi$
$294$		0			0
$295$	1326.00			0.261704
$296$	821.264	+	474.157i	0.161267	+	0.0931075i
$297$	1514.32	−	4372.86i	0.295858	−	0.854341i
$298$	−527.000	−	912.791i	−0.102444	−	0.177438i
$299$	−2555.17	+	4425.69i	−0.494213	+	0.856001i
$300$	−1045.30	+	253.522i	−0.201168	+	0.0487904i
$301$		0			0
$302$			5970.26i			1.13758i
$303$	1848.48	−	6293.99i	0.350470	−	1.19334i
$304$	−1750.09	+	1010.41i	−0.330179	+	0.190629i
$305$	621.304	−	358.710i	0.116642	−	0.0673432i
$306$	−6738.22	−	321.769i	−1.25882	−	0.0601120i
$307$		−	1873.86i		−	0.348361i	−0.984714	−	0.174180i	$-0.944272\pi$
$307$		−	1873.86i		−	0.348361i	0.984714	−	0.174180i	$-0.0557276\pi$
$308$		0			0
$309$	60.0000	+	247.386i	0.0110462	+	0.0455447i
$310$	−5304.00	+	9186.80i	−0.971764	+	1.68315i
$311$	4282.19	+	7416.97i	0.780774	+	1.35234i	0.931491	+	0.363763i	$0.118508\pi$
$311$	4282.19	+	7416.97i	0.780774	+	1.35234i	−0.150717	+	0.988577i	$0.548158\pi$
$312$	−832.879	−	873.601i	−0.151130	−	0.158519i
$313$	−462.448	−	266.994i	−0.0835115	−	0.0482154i	0.457663	−	0.889126i	$-0.348687\pi$
$313$	−462.448	−	266.994i	−0.0835115	−	0.0482154i	−0.541174	+	0.840910i	$0.682020\pi$
$314$	−14008.0			−2.51757
$315$		0			0
$316$	3978.00			0.708165
$317$	4420.54	+	2552.20i	0.783226	+	0.452195i	0.837572	−	0.546327i	$-0.183974\pi$
$317$	4420.54	+	2552.20i	0.783226	+	0.452195i	−0.0543467	+	0.998522i	$0.517308\pi$
$318$	3047.71	+	3196.72i	0.537443	+	0.563720i
$319$	952.000	+	1648.91i	0.167090	+	0.289409i
$320$	−3186.39	+	5519.00i	−0.556640	+	0.964129i
$321$	1797.71	+	7412.16i	0.312581	+	1.28880i
$322$		0			0
$323$			2226.48i			0.383543i
$324$	−2724.15	−	5968.73i	−0.467103	−	1.02344i
$325$	1122.18	−	647.890i	0.191530	−	0.110580i
$326$	11169.2	−	6448.54i	1.89756	−	1.09556i
$327$	−2738.08	+	9323.05i	−0.463047	+	1.57665i
$328$			582.979i			0.0981390i
$329$		0			0
$330$	−6936.00	+	1682.23i	−1.15701	+	0.280617i
$331$	−1816.00	+	3145.40i	−0.301560	+	0.522317i	−0.976490	−	0.215565i	$-0.930841\pi$
$331$	−1816.00	+	3145.40i	−0.301560	+	0.522317i	0.674929	+	0.737882i	$0.264174\pi$
$332$	−2226.94	−	3857.17i	−0.368130	−	0.637620i
$333$	−5223.79	−	3357.99i	−0.859646	−	0.552603i
$334$	−2524.37	−	1457.45i	−0.413555	−	0.238766i
$335$	−646.368			−0.105418
$336$		0			0
$337$	−6256.00			−1.01123			−0.505617	−	0.862758i	$-0.668735\pi$
$337$	−6256.00			−1.01123			−0.505617	+	0.862758i	$0.668735\pi$
$338$	3488.59	+	2014.14i	0.561403	+	0.324126i
$339$	−6295.58	+	6002.12i	−1.00864	+	0.961624i
$340$	2754.00	+	4770.07i	0.439284	+	0.760863i
$341$	4201.39	−	7277.03i	0.667209	−	1.15564i
$342$	−3635.82	+	1873.86i	−0.574862	+	0.296277i
$343$		0			0
$344$		−	181.417i		−	0.0284341i
$345$	4567.34	+	1341.38i	0.712746	+	0.209326i
$346$	−8041.93	+	4643.01i	−1.24953	+	0.721415i
$347$	−928.386	+	536.004i	−0.143626	+	0.0829227i	−0.570091	−	0.821581i	$-0.693092\pi$
$347$	−928.386	+	536.004i	−0.143626	+	0.0829227i	0.426465	+	0.904504i	$0.359759\pi$
$348$	2590.07	+	760.677i	0.398972	+	0.117174i
$349$			6287.84i			0.964414i	0.876057	+	0.482207i	$0.160165\pi$
$349$			6287.84i			0.964414i	−0.876057	+	0.482207i	$0.839835\pi$
$350$		0			0
$351$	5175.00	+	5974.38i	0.786955	+	0.908515i
$352$	4284.00	−	7420.11i	0.648687	−	1.12356i
$353$	−2646.07	−	4583.13i	−0.398969	−	0.691035i	0.594630	−	0.804000i	$-0.297299\pi$
$353$	−2646.07	−	4583.13i	−0.398969	−	0.691035i	−0.993599	+	0.112965i	$0.963965\pi$
$354$	−2035.88	+	1940.98i	−0.305667	+	0.291419i
$355$	−4038.99	−	2331.91i	−0.603852	−	0.348634i
$356$	4362.99			0.649544
$357$		0			0
$358$	14416.0			2.12824
$359$	−2778.02	−	1603.89i	−0.408407	−	0.235794i	0.281698	−	0.959503i	$-0.409102\pi$
$359$	−2778.02	−	1603.89i	−0.408407	−	0.235794i	−0.690105	+	0.723709i	$0.742436\pi$
$360$	−607.961	+	945.764i	−0.0890066	+	0.138461i
$361$	−2754.50	−	4770.93i	−0.401589	−	0.695573i
$362$	378.731	−	655.982i	0.0549881	−	0.0952421i
$363$	−1227.09	+	297.613i	−0.177426	+	0.0430320i
$364$		0			0
$365$			890.591i			0.127714i
$366$	−428.848	+	1460.21i	−0.0612465	+	0.208542i
$367$	8124.66	−	4690.77i	1.15560	−	0.667184i	0.205351	−	0.978688i	$-0.434166\pi$
$367$	8124.66	−	4690.77i	1.15560	−	0.667184i	0.950245	+	0.311505i	$0.100833\pi$
$368$	−4320.56	+	2494.48i	−0.612024	+	0.353352i
$369$	182.094	−	3813.27i	0.0256895	−	0.537970i
$370$			9577.50i			1.34570i
$371$		0			0
$372$	−2808.00	−	11577.7i	−0.391366	−	1.61364i
$373$	−2299.00	+	3981.98i	−0.319136	+	0.552760i	−0.980308	−	0.197475i	$-0.936726\pi$
$373$	−2299.00	+	3981.98i	−0.319136	+	0.552760i	0.661172	+	0.750234i	$0.270059\pi$
$374$	−4120.60	−	7137.09i	−0.569709	−	0.986764i
$375$	−5359.40	−	5621.43i	−0.738022	−	0.774105i
$376$	−1226.12	−	707.903i	−0.168171	−	0.0970938i
$377$	−3252.04			−0.444267
$378$		0			0
$379$	5252.00			0.711813			0.355906	−	0.934522i	$-0.384172\pi$
$379$	5252.00			0.711813			0.355906	+	0.934522i	$0.384172\pi$
$380$	2892.28	+	1669.86i	0.390449	+	0.225426i
$381$	−3757.64	−	3941.36i	−0.505275	−	0.529979i
$382$	544.000	+	942.236i	0.0728625	+	0.126201i
$383$	−959.453	+	1661.82i	−0.128005	+	0.221710i	−0.922903	−	0.385032i	$-0.874191\pi$
$383$	−959.453	+	1661.82i	−0.128005	+	0.221710i	0.794899	+	0.606742i	$0.207524\pi$
$384$	−641.319	−	2644.22i	−0.0852270	−	0.351400i
$385$		0			0
$386$		−	2688.26i		−	0.354479i
$387$	−56.6657	+	1186.65i	−0.00744310	+	0.155867i
$388$	−8514.98	+	4916.13i	−1.11413	+	0.643244i
$389$	6120.20	−	3533.50i	0.797704	−	0.460554i	−0.0449640	−	0.998989i	$-0.514317\pi$
$389$	6120.20	−	3533.50i	0.797704	−	0.460554i	0.842668	+	0.538434i	$0.180984\pi$
$390$	3435.05	−	11696.2i	0.446001	−	1.51861i
$391$			5496.65i			0.710941i
$392$		0			0
$393$	−12903.0	+	3129.44i	−1.65616	+	0.401677i
$394$	4165.00	−	7213.99i	0.532563	−	0.922426i
$395$	2231.99	+	3865.92i	0.284313	+	0.492445i
$396$	4334.19	−	6742.41i	0.550004	−	0.855603i
$397$	11550.6	+	6668.74i	1.46022	+	0.843059i	0.999021	−	0.0442380i	$-0.0140860\pi$
$397$	11550.6	+	6668.74i	1.46022	+	0.843059i	0.461199	+	0.887297i	$0.347419\pi$
$398$	19997.0			2.51849
$399$		0			0
$400$	1265.00			0.158125
$401$	−11476.3	−	6625.83i	−1.42917	−	0.825133i	−0.432116	−	0.901818i	$-0.642233\pi$
$401$	−11476.3	−	6625.83i	−1.42917	−	0.825133i	−0.997055	+	0.0766852i	$0.975566\pi$
$402$	992.406	−	946.147i	0.123126	−	0.117387i
$403$	7176.00	+	12429.2i	0.887003	+	1.53633i
$404$	5680.97	−	9839.73i	0.699601	−	1.21174i
$405$	4272.09	−	5996.35i	0.524153	−	0.735706i
$406$		0			0
$407$		−	7586.51i		−	0.923955i
$408$	−1245.64	−	365.831i	−0.151148	−	0.0443906i
$409$	6461.54	−	3730.57i	0.781180	−	0.451015i	−0.0556682	−	0.998449i	$-0.517729\pi$
$409$	6461.54	−	3730.57i	0.781180	−	0.451015i	0.836848	+	0.547435i	$0.184396\pi$
$410$	−5098.98	+	2943.90i	−0.614197	+	0.354607i
$411$	5015.69	+	1473.06i	0.601960	+	0.176790i
$412$			440.908i			0.0527233i
$413$		0			0
$414$	−8976.00	+	4626.12i	−1.06557	+	0.549183i
$415$	2499.00	−	4328.39i	0.295593	−	0.511982i
$416$	7317.09	+	12673.6i	0.862380	+	1.49369i
$417$	5241.71	−	4997.38i	0.615558	−	0.586865i
$418$	−4327.49	−	2498.48i	−0.506375	−	0.292356i
$419$	−9261.25			−1.07981			−0.539906	−	0.841725i	$-0.681540\pi$
$419$	−9261.25			−1.07981			−0.539906	+	0.841725i	$0.681540\pi$
$420$		0			0
$421$	−2854.00			−0.330393			−0.165196	−	0.986261i	$-0.552826\pi$
$421$	−2854.00			−0.330393			−0.165196	+	0.986261i	$0.552826\pi$
$422$	7941.27	+	4584.89i	0.916054	+	0.528884i
$423$	7798.97	+	5013.38i	0.896451	+	0.576262i
$424$	425.000	+	736.122i	0.0486788	+	0.0843142i
$425$	696.866	−	1207.01i	0.0795364	−	0.137761i
$426$	9614.73	−	2331.91i	1.09351	−	0.265215i
$427$		0			0
$428$			13210.4i			1.49194i
$429$	−2720.97	+	9264.76i	−0.306223	+	1.04267i
$430$	1586.75	−	916.109i	0.177953	−	0.102741i
$431$	−9776.62	+	5644.53i	−1.09263	+	0.630830i	−0.934275	−	0.356553i	$-0.883952\pi$
$431$	−9776.62	+	5644.53i	−1.09263	+	0.630830i	−0.158354	+	0.987382i	$0.550619\pi$
$432$	1458.99	+	7577.10i	0.162490	+	0.843873i
$433$		−	13036.2i		−	1.44683i	−0.690411	−	0.723417i	$-0.742570\pi$
$433$		−	13036.2i		−	1.44683i	0.690411	−	0.723417i	$-0.257430\pi$
$434$		0			0
$435$	714.000	+	2943.90i	0.0786981	+	0.324481i
$436$	−8415.00	+	14575.2i	−0.924324	+	1.60098i
$437$	1666.42	+	2886.32i	0.182416	+	0.315953i
$438$	−1303.64	−	1367.37i	−0.142215	−	0.149168i
$439$	−2600.74	−	1501.54i	−0.282748	−	0.163245i	0.351919	−	0.936031i	$-0.385529\pi$
$439$	−2600.74	−	1501.54i	−0.282748	−	0.163245i	−0.634667	+	0.772786i	$0.718863\pi$
$440$	−1373.53			−0.148820
$441$		0			0
$442$	14076.0			1.51477
$443$	−5927.39	−	3422.18i	−0.635708	−	0.367026i	0.147251	−	0.989099i	$-0.452957\pi$
$443$	−5927.39	−	3422.18i	−0.635708	−	0.367026i	−0.782959	+	0.622073i	$0.786291\pi$
$444$	−7422.06	−	7784.94i	−0.793323	−	0.832110i
$445$	2448.00	+	4240.06i	0.260778	+	0.451681i
$446$	3948.91	−	6839.71i	0.419251	−	0.726165i
$447$	313.085	+	1290.88i	0.0331284	+	0.136592i
$448$		0			0
$449$		−	2655.28i		−	0.279088i	−0.990216	−	0.139544i	$-0.955436\pi$
$449$		−	2655.28i		−	0.279088i	0.990216	−	0.139544i	$-0.0445636\pi$
$450$	2557.53	+	122.129i	0.267918	+	0.0127939i
$451$	4038.99	−	2331.91i	0.421705	−	0.243471i
$452$	−13047.4	+	7532.91i	−1.35774	+	0.783890i
$453$	2120.18	−	7219.13i	0.219901	−	0.748751i
$454$		−	24526.7i		−	2.53546i
$455$		0			0
$456$	−765.000	+	185.540i	−0.0785623	+	0.0190542i
$457$	−598.000	+	1035.77i	−0.0612106	+	0.106020i	−0.895007	−	0.446052i	$-0.852829\pi$
$457$	−598.000	+	1035.77i	−0.0612106	+	0.106020i	0.833796	+	0.552072i	$0.186163\pi$
$458$	7640.28	+	13233.3i	0.779490	+	1.35012i
$459$	8033.46	+	2781.98i	0.816928	+	0.282902i
$460$	7140.36	+	4122.49i	0.723742	+	0.417852i
$461$	5443.63			0.549968			0.274984	−	0.961449i	$-0.411327\pi$
$461$	5443.63			0.549968			0.274984	+	0.961449i	$0.411327\pi$
$462$		0			0
$463$	926.000			0.0929479			0.0464739	−	0.998920i	$-0.485202\pi$
$463$	926.000			0.0929479			0.0464739	+	0.998920i	$0.485202\pi$
$464$	−2749.45	−	1587.40i	−0.275086	−	0.158821i
$465$	9675.96	−	9224.93i	0.964972	−	0.919991i
$466$	1972.00	+	3415.60i	0.196032	+	0.339538i
$467$	−3893.36	+	6743.50i	−0.385788	+	0.668205i	−0.991878	−	0.127191i	$-0.959404\pi$
$467$	−3893.36	+	6743.50i	−0.385788	+	0.668205i	0.606090	+	0.795396i	$0.292737\pi$
$468$	6271.79	+	12169.1i	0.619474	+	1.20196i
$469$		0			0
$470$		−	14298.9i		−	1.40332i
$471$	16938.2	+	4974.59i	1.65706	+	0.486660i
$472$	−468.812	+	270.669i	−0.0457178	+	0.0263952i
$473$	−1256.89	+	725.667i	−0.122182	+	0.0705416i
$474$	−9085.80	−	2668.41i	−0.880431	−	0.258574i
$475$		−	845.074i		−	0.0816308i
$476$		0			0
$477$	−2550.00	−	4947.73i	−0.244772	−	0.474928i
$478$	9877.00	−	17107.5i	0.945112	−	1.63698i
$479$	−6251.59	−	10828.1i	−0.596331	−	1.03288i	−0.993358	−	0.115069i	$-0.963291\pi$
$479$	−6251.59	−	10828.1i	−0.596331	−	1.03288i	0.397026	−	0.917807i	$-0.370042\pi$
$480$	9866.20	−	9406.31i	0.938185	−	0.894453i
$481$	11221.8	+	6478.90i	1.06376	+	0.614163i
$482$	15613.8			1.47550
$483$		0			0
$484$	−2187.00			−0.205391
$485$	−9555.23	−	5516.72i	−0.894599	−	0.516497i
$486$	2218.21	+	15460.0i	0.207037	+	1.44296i
$487$	−6856.00	−	11874.9i	−0.637936	−	1.10494i	−0.985885	−	0.167425i	$-0.946455\pi$
$487$	−6856.00	−	11874.9i	−0.637936	−	1.10494i	0.347949	−	0.937514i	$-0.386878\pi$
$488$	−146.443	+	253.646i	−0.0135843	+	0.0235288i
$489$	−15795.6	+	3831.00i	−1.46074	+	0.354282i
$490$		0			0
$491$		−	5772.35i		−	0.530555i	−0.964172	−	0.265277i	$-0.914536\pi$
$491$		−	5772.35i		−	0.530555i	0.964172	−	0.265277i	$-0.0854635\pi$
$492$	1863.27	−	6344.35i	0.170737	−	0.581352i
$493$	−3029.25	+	1748.94i	−0.276735	+	0.159773i
$494$	7391.38	−	4267.41i	0.673186	−	0.388664i
$495$	8984.29	+	429.025i	0.815785	+	0.0389560i
$496$			14011.1i			1.26838i
$497$		0			0
$498$	2499.00	+	10303.6i	0.224865	+	0.927143i
$499$	−7738.00	+	13402.6i	−0.694189	+	1.20237i	0.276264	+	0.961082i	$0.410904\pi$
$499$	−7738.00	+	13402.6i	−0.694189	+	1.20237i	−0.970453	+	0.241289i	$0.922430\pi$
$500$	−6726.27	−	11650.2i	−0.601616	−	1.04203i
$501$	2534.85	+	2658.78i	0.226045	+	0.237097i
$502$	−14388.9	−	8307.44i	−1.27930	−	0.738604i
$503$	−1696.72			−0.150403			−0.0752017	−	0.997168i	$-0.523960\pi$
$503$	−1696.72			−0.150403			−0.0752017	+	0.997168i	$0.523960\pi$
$504$		0			0
$505$	12750.0			1.12350
$506$	−10683.6	−	6168.17i	−0.938622	−	0.541914i
$507$	−3503.07	−	3674.34i	−0.306858	−	0.321860i
$508$	−4716.00	−	8168.35i	−0.411887	−	0.713409i
$509$	2115.85	−	3664.75i	0.184250	−	0.319130i	−0.759074	−	0.651005i	$-0.774348\pi$
$509$	2115.85	−	3664.75i	0.184250	−	0.319130i	0.943324	+	0.331875i	$0.107681\pi$
$510$	−3090.45	−	12742.2i	−0.268328	−	1.10635i
$511$		0			0
$512$			16100.7i			1.38976i
$513$	5061.82	−	974.668i	0.435643	−	0.0838843i
$514$	−721.249	+	416.413i	−0.0618929	+	0.0357339i
$515$	−428.486	+	247.386i	−0.0366628	+	0.0211673i
$516$	−579.830	+	1974.29i	−0.0494682	+	0.168437i
$517$			11326.4i			0.963513i
$518$		0			0
$519$	11373.0	−	2758.36i	0.961887	−	0.233292i
$520$	1173.00	−	2031.70i	0.0989220	−	0.171338i
$521$	−9786.42	−	16950.6i	−0.822938	−	1.42537i	−0.903485	−	0.428620i	$-0.859000\pi$
$521$	−9786.42	−	16950.6i	−0.822938	−	1.42537i	0.0805465	−	0.996751i	$-0.474333\pi$
$522$	−5405.49	−	3474.79i	−0.453241	−	0.291355i
$523$	−7248.55	−	4184.95i	−0.606036	−	0.349895i	0.165376	−	0.986231i	$-0.447116\pi$
$523$	−7248.55	−	4184.95i	−0.606036	−	0.349895i	−0.771413	+	0.636335i	$0.780449\pi$
$524$	−22996.6			−1.91719
$525$		0			0
$526$	−34136.0			−2.82966
$527$	13368.8	+	7718.45i	1.10503	+	0.637991i
$528$	−6822.79	+	6504.76i	−0.562356	+	0.536143i
$529$	−1969.50	−	3411.27i	−0.161872	−	0.280371i
$530$	−4292.29	+	7434.46i	−0.351783	+	0.609307i
$531$	3151.05	−	1624.01i	0.257521	−	0.132723i
$532$		0			0
$533$			7965.84i			0.647352i
$534$	−9965.11	−	2926.65i	−0.807551	−	0.237170i
$535$	−12838.2	+	7412.16i	−1.03747	+	0.598982i
$536$	228.526	−	131.939i	0.0184157	−	0.0106323i
$537$	−17431.6	−	5119.48i	−1.40080	−	0.411400i
$538$			23860.5i			1.91208i
$539$		0			0
$540$	9639.00	−	8349.29i	0.768142	−	0.665363i
$541$	8075.00	−	13986.3i	0.641722	−	1.11149i	−0.343327	−	0.939216i	$-0.611554\pi$
$541$	8075.00	−	13986.3i	0.641722	−	1.11149i	0.985048	−	0.172278i	$-0.0551128\pi$
$542$	2514.78	+	4355.72i	0.199297	+	0.345192i
$543$	−690.911	+	658.705i	−0.0546037	+	0.0520585i
$544$	13631.6	+	7870.21i	1.07436	+	0.620280i
$545$	−18886.1			−1.48439
$546$		0			0
$547$	−18352.0			−1.43451			−0.717253	−	0.696813i	$-0.754601\pi$
$547$	−18352.0			−1.43451			−0.717253	+	0.696813i	$0.754601\pi$
$548$	7841.29	+	4527.17i	0.611247	+	0.352903i
$549$	1037.11	−	1613.36i	0.0806244	−	0.125422i
$550$	1564.00	+	2708.93i	0.121253	+	0.210016i
$551$	−1060.45	+	1836.75i	−0.0819902	+	0.142011i
$552$	−1888.61	+	458.055i	−0.145624	+	0.0353190i
$553$		0			0
$554$		−	13251.7i		−	1.01626i
$555$	3401.21	−	11580.9i	0.260132	−	0.885737i
$556$	10863.3	−	6271.92i	0.828607	−	0.478397i
$557$	−2878.00	+	1661.61i	−0.218931	+	0.126400i	−0.605455	−	0.795879i	$-0.707009\pi$
$557$	−2878.00	+	1661.61i	−0.218931	+	0.126400i	0.386524	+	0.922279i	$0.373676\pi$
$558$	−1352.70	+	28327.1i	−0.102624	+	2.14907i
$559$		−	2478.88i		−	0.187559i
$560$		0			0
$561$	2448.00	+	10093.4i	0.184233	+	0.759612i
$562$	−19040.0	+	32978.2i	−1.42910	+	2.47527i
$563$	7145.40	+	12376.2i	0.534889	+	0.926456i	0.999169	+	0.0407667i	$0.0129800\pi$
$563$	7145.40	+	12376.2i	0.534889	+	0.926456i	−0.464279	+	0.885689i	$0.653687\pi$
$564$	11080.9	+	11622.7i	0.827289	+	0.867737i
$565$	−14641.4	−	8453.19i	−1.09021	−	0.629431i
$566$	12291.1			0.912780
$567$		0			0
$568$	1904.00			0.140652
$569$	12818.9	+	7400.97i	0.944455	+	0.545281i	0.891354	−	0.453308i	$-0.149756\pi$
$569$	12818.9	+	7400.97i	0.944455	+	0.545281i	0.0531008	+	0.998589i	$0.483090\pi$
$570$	−5485.87	−	5754.09i	−0.403119	−	0.422828i
$571$	−2068.00	−	3581.88i	−0.151564	−	0.262517i	0.780239	−	0.625482i	$-0.215098\pi$
$571$	−2068.00	−	3581.88i	−0.151564	−	0.262517i	−0.931803	+	0.362965i	$0.881764\pi$
$572$	−8362.39	+	14484.1i	−0.611275	+	1.05876i
$573$	−323.184	−	1332.52i	−0.0235623	−	0.0971500i
$574$		0			0
$575$		−	2086.29i		−	0.151312i
$576$	−812.638	+	17017.6i	−0.0587846	+	1.23102i
$577$	−16851.8	+	9729.37i	−1.21585	+	0.701974i	−0.964029	−	0.265798i	$-0.914364\pi$
$577$	−16851.8	+	9729.37i	−1.21585	+	0.701974i	−0.251826	+	0.967772i	$0.581031\pi$
$578$	−4431.26	+	2558.39i	−0.318886	+	0.184109i
$579$	−954.669	+	3250.60i	−0.0685228	+	0.233317i
$580$			5246.81i			0.375624i
$581$		0			0
$582$	22746.0	−	5516.72i	1.62002	−	0.392913i
$583$	3400.00	−	5888.97i	0.241533	−	0.418347i
$584$	−181.791	−	314.871i	−0.0128811	−	0.0223107i
$585$	−8307.21	+	12922.9i	−0.587112	+	0.913330i
$586$	−18427.9	−	10639.4i	−1.29906	−	0.750013i
$587$	−18310.4			−1.28748			−0.643740	−	0.765244i	$-0.722618\pi$
$587$	−18310.4			−1.28748			−0.643740	+	0.765244i	$0.722618\pi$
$588$		0			0
$589$	9360.00			0.654791
$590$	−4734.77	−	2733.62i	−0.330385	−	0.190748i
$591$	−7598.11	+	7243.94i	−0.528840	+	0.504189i
$592$	6325.00	+	10955.2i	0.439115	+	0.760569i
$593$	−3999.40	+	6927.17i	−0.276958	+	0.479705i	−0.970627	−	0.240589i	$-0.922659\pi$
$593$	−3999.40	+	6927.17i	−0.276958	+	0.479705i	0.693670	+	0.720293i	$0.255993\pi$
$594$	−14422.1	+	12492.4i	−0.996205	+	0.862911i
$595$		0			0
$596$			2300.69i			0.158121i
$597$	−24180.0	−	7101.43i	−1.65766	−	0.486838i
$598$	18247.6	−	10535.3i	1.24783	−	0.720432i
$599$	10769.3	−	6217.64i	0.734592	−	0.424117i	−0.0855077	−	0.996338i	$-0.527251\pi$
$599$	10769.3	−	6217.64i	0.734592	−	0.424117i	0.820100	+	0.572221i	$0.193918\pi$
$600$	472.790	+	138.854i	0.0321693	+	0.00944780i
$601$		−	18557.3i		−	1.25952i	−0.776791	−	0.629758i	$-0.783154\pi$
$601$		−	18557.3i		−	1.25952i	0.776791	−	0.629758i	$-0.216846\pi$
$602$		0			0
$603$	−1536.00	+	791.636i	−0.103733	+	0.0534626i
$604$	6516.00	−	11286.0i	0.438961	−	0.760302i
$605$	−1227.09	−	2125.38i	−0.0824600	−	0.142825i
$606$	−19575.8	+	18663.3i	−1.31223	+	1.25106i
$607$	1378.86	+	796.084i	0.0922012	+	0.0532324i	0.545392	−	0.838181i	$-0.316381\pi$
$607$	1378.86	+	796.084i	0.0922012	+	0.0532324i	−0.453190	+	0.891414i	$0.649714\pi$
$608$	9544.03			0.636614
$609$		0			0
$610$	−2958.00			−0.196338
$611$	−16753.8	−	9672.81i	−1.10931	−	0.640458i
$612$	12386.6	+	7962.42i	0.818135	+	0.525918i
$613$	893.000	+	1546.72i	0.0588384	+	0.101911i	0.893944	−	0.448178i	$-0.147927\pi$
$613$	893.000	+	1546.72i	0.0588384	+	0.101911i	−0.835106	+	0.550089i	$0.814594\pi$
$614$	−3863.06	+	6691.02i	−0.253910	+	0.439784i
$615$	7211.05	−	1748.94i	0.472809	−	0.114673i
$616$		0			0
$617$			8254.46i			0.538593i	0.963057	+	0.269297i	$0.0867912\pi$
$617$			8254.46i			0.538593i	−0.963057	+	0.269297i	$0.913209\pi$
$618$	295.757	−	1007.04i	0.0192510	−	0.0655486i
$619$	7189.15	−	4150.66i	0.466812	−	0.269514i	−0.248092	−	0.968736i	$-0.579804\pi$
$619$	7189.15	−	4150.66i	0.466812	−	0.269514i	0.714904	+	0.699222i	$0.246470\pi$
$620$	20053.1	−	11577.7i	1.29896	−	0.749953i
$621$	12496.5	−	2406.23i	0.807514	−	0.155489i
$622$		−	35311.8i		−	2.27633i
$623$		0			0
$624$	−3795.00	−	15647.2i	−0.243464	−	1.00383i
$625$	6110.50	−	10583.7i	0.391072	−	0.677357i
$626$	1100.85	+	1906.72i	0.0702854	+	0.121738i
$627$	4345.46	+	4557.92i	0.276780	+	0.290312i
$628$	26480.4	+	15288.5i	1.68262	+	0.971460i
$629$	13937.3			0.883493
$630$		0			0
$631$	−13102.0			−0.826596			−0.413298	−	0.910596i	$-0.635623\pi$
$631$	−13102.0			−0.826596			−0.413298	+	0.910596i	$0.635623\pi$
$632$	−1578.26	−	911.206i	−0.0993349	−	0.0573510i
$633$	−7974.23	−	8364.11i	−0.500707	−	0.525187i
$634$	−10523.0	−	18226.4i	−0.659183	−	1.14174i
$635$	5292.14	−	9166.26i	0.330728	−	0.572837i
$636$	−2272.39	−	9369.30i	−0.141676	−	0.584146i
$637$		0			0
$638$		−	7850.39i		−	0.487147i
$639$	−12454.1	−	594.717i	−0.771011	−	0.0368179i
$640$	4579.93	−	2644.22i	0.282871	−	0.163316i
$641$	8519.72	−	4918.87i	0.524975	−	0.303094i	−0.213993	−	0.976835i	$-0.568647\pi$
$641$	8519.72	−	4918.87i	0.524975	−	0.303094i	0.738968	+	0.673741i	$0.235314\pi$
$642$	8861.44	−	30172.8i	0.544755	−	1.85487i
$643$		−	9624.05i		−	0.590257i	−0.955458	−	0.295129i	$-0.904638\pi$
$643$		−	9624.05i		−	0.590257i	0.955458	−	0.295129i	$-0.0953625\pi$
$644$		0			0
$645$	−2244.00	+	544.250i	−0.136988	+	0.0332245i
$646$	4590.00	−	7950.11i	0.279553	−	0.484200i
$647$	−3847.91	−	6664.78i	−0.233813	−	0.404976i	0.725114	−	0.688629i	$-0.241787\pi$
$647$	−3847.91	−	6664.78i	−0.233813	−	0.404976i	−0.958927	+	0.283653i	$0.908454\pi$
$648$	−286.412	+	2992.07i	−0.0173632	+	0.181388i
$649$	3750.49	+	2165.35i	0.226841	+	0.130967i
$650$	−5342.64			−0.322393
$651$		0			0
$652$	−28152.0			−1.69098
$653$	24516.5	+	14154.6i	1.46923	+	0.848259i	0.999405	−	0.0345016i	$-0.0109844\pi$
$653$	24516.5	+	14154.6i	1.46923	+	0.848259i	0.469823	+	0.882761i	$0.344318\pi$
$654$	28996.9	−	27645.2i	1.73374	−	1.65293i
$655$	−12903.0	−	22348.7i	−0.769713	−	1.33318i
$656$	−3888.31	+	6734.75i	−0.231422	+	0.400835i
$657$	1090.75	+	2116.36i	0.0647703	+	0.125673i
$658$		0			0
$659$			22973.9i			1.35802i	0.734127	+	0.679012i	$0.237592\pi$
$659$			22973.9i			1.35802i	−0.734127	+	0.679012i	$0.762408\pi$
$660$	14947.7	+	4389.98i	0.881571	+	0.258908i
$661$	9357.14	−	5402.35i	0.550606	−	0.317893i	−0.198760	−	0.980048i	$-0.563692\pi$
$661$	9357.14	−	5402.35i	0.550606	−	0.317893i	0.749366	+	0.662155i	$0.230358\pi$
$662$	12968.8	−	7487.56i	0.761402	−	0.439596i
$663$	−17020.5	−	4998.73i	−0.997013	−	0.292813i
$664$			2040.42i			0.119253i
$665$		0			0
$666$	11730.0	+	22759.5i	0.682475	+	1.32420i
$667$	−2618.00	+	4534.51i	−0.151978	+	0.263234i
$668$	3181.34	+	5510.25i	0.184266	+	0.319159i
$669$	−7203.90	+	6868.10i	−0.416321	+	0.396915i
$670$	2308.00	+	1332.52i	0.133083	+	0.0768356i
$671$	2343.09			0.134804
$672$		0			0
$673$	26882.0			1.53971			0.769855	−	0.638219i	$-0.220328\pi$
$673$	26882.0			1.53971			0.769855	+	0.638219i	$0.220328\pi$
$674$	22338.4	+	12897.1i	1.27662	+	0.737057i
$675$	−3049.15	−	1055.92i	−0.173870	−	0.0602109i
$676$	−4396.50	−	7614.96i	−0.250142	−	0.433259i
$677$	10245.9	−	17746.5i	0.581660	−	1.00746i	−0.413623	−	0.910448i	$-0.635737\pi$
$677$	10245.9	−	17746.5i	0.581660	−	1.00746i	0.995283	−	0.0970162i	$-0.0309299\pi$
$678$	34853.4	−	8453.19i	1.97424	−	0.478824i
$679$		0			0
$680$		−	2523.34i		−	0.142302i
$681$	−8710.05	+	29657.3i	−0.490117	+	1.66883i
$682$	−30004.0	+	17322.8i	−1.68462	+	0.972616i
$683$	−628.446	+	362.833i	−0.0352076	+	0.0203271i	−0.517501	−	0.855683i	$-0.673137\pi$
$683$	−628.446	+	362.833i	−0.0352076	+	0.0203271i	0.482293	+	0.876010i	$0.339804\pi$
$684$	8918.23	+	425.870i	0.498534	+	0.0238064i
$685$			10160.5i			0.566733i
$686$		0			0
$687$	−4539.00	−	18714.8i	−0.252072	−	1.03932i
$688$	1210.00	−	2095.78i	0.0670506	−	0.116135i
$689$	5807.22	+	10058.4i	0.321099	+	0.556160i
$690$	−13543.3	−	14205.5i	−0.747226	−	0.783760i
$691$	10184.5	+	5880.00i	0.560688	+	0.323713i	0.753421	−	0.657538i	$-0.228402\pi$
$691$	10184.5	+	5880.00i	0.560688	+	0.323713i	−0.192734	+	0.981251i	$0.561735\pi$
$692$	20269.7			1.11350
$693$		0			0
$694$	4420.00			0.241759
$695$	12190.4	+	7038.14i	0.665337	+	0.384132i
$696$	−853.358	−	895.080i	−0.0464748	−	0.0487470i
$697$	4284.00	+	7420.11i	0.232809	+	0.403238i
$698$	12962.7	−	22452.1i	0.702931	−	1.21751i
$699$	−1171.54	−	4830.39i	−0.0633931	−	0.261377i
$700$		0			0
$701$		−	21877.2i		−	1.17873i	−0.807867	−	0.589365i	$-0.799378\pi$
$701$		−	21877.2i		−	1.17873i	0.807867	−	0.589365i	$-0.200622\pi$
$702$	−6161.95	−	32001.3i	−0.331293	−	1.72053i
$703$	7318.56	−	4225.37i	0.392638	−	0.226690i
$704$	−18025.0	+	10406.7i	−0.964974	+	0.557128i
$705$	−5077.90	+	17290.0i	−0.271269	+	0.923659i
$706$			21820.1i			1.16318i
$707$		0			0
$708$	5967.00	−	1447.21i	0.316742	−	0.0768213i
$709$	12191.0	−	21115.4i	0.645758	−	1.11849i	−0.338368	−	0.941014i	$-0.609875\pi$
$709$	12191.0	−	21115.4i	0.645758	−	1.11849i	0.984126	−	0.177472i	$-0.0567920\pi$
$710$	9614.73	+	16653.2i	0.508217	+	0.880258i
$711$	10038.8	+	6453.18i	0.529512	+	0.340384i
$712$	−1731.00	−	999.392i	−0.0911122	−	0.0526036i
$713$	23107.7			1.21373
$714$		0			0
$715$	−18768.0			−0.981655
$716$	−27251.7	−	15733.8i	−1.42241	−	0.821227i
$717$	−18018.4	+	17178.5i	−0.938506	+	0.894759i
$718$	6613.00	+	11454.1i	0.343726	+	0.595350i
$719$	5544.63	−	9603.58i	0.287594	−	0.498127i	−0.685641	−	0.727940i	$-0.740478\pi$
$719$	5544.63	−	9603.58i	0.287594	−	0.498127i	0.973235	+	0.229813i	$0.0738115\pi$
$720$	−13331.3	+	6870.82i	−0.690042	+	0.355639i
$721$		0			0
$722$			22714.2i			1.17082i
$723$	−18880.0	−	5544.86i	−0.971167	−	0.285222i
$724$	−1431.89	+	826.703i	−0.0735025	+	0.0424367i
$725$	1149.77	−	663.820i	0.0588985	−	0.0340050i
$726$	4995.13	+	1467.02i	0.255354	+	0.0749948i
$727$			5927.77i			0.302405i	0.988503	+	0.151203i	$0.0483146\pi$
$727$			5927.77i			0.302405i	−0.988503	+	0.151203i	$0.951685\pi$
$728$		0			0
$729$	2808.00	−	19481.7i	0.142661	−	0.989772i
$730$	1836.00	−	3180.05i	0.0930869	−	0.161231i
$731$	−1333.13	−	2309.06i	−0.0674525	−	0.116831i
$732$	2404.37	−	2292.29i	0.121404	−	0.115745i
$733$	−19514.0	−	11266.4i	−0.983311	−	0.567715i	−0.0800429	−	0.996791i	$-0.525506\pi$
$733$	−19514.0	−	11266.4i	−0.983311	−	0.567715i	−0.903268	+	0.429077i	$0.858839\pi$
$734$	−38681.1			−1.94516
$735$		0			0
$736$	23562.0			1.18004
$737$	−1828.21	−	1055.52i	−0.0913742	−	0.0527549i
$738$	−8511.46	+	13240.7i	−0.424541	+	0.660429i
$739$	4610.00	+	7984.75i	0.229474	+	0.397461i	0.957652	−	0.287927i	$-0.0929659\pi$
$739$	4610.00	+	7984.75i	0.229474	+	0.397461i	−0.728178	+	0.685388i	$0.759633\pi$
$740$	10453.0	−	18105.1i	0.519270	−	0.899401i
$741$	−10453.0	+	2535.22i	−0.518219	+	0.125687i
$742$		0			0
$743$		−	14950.4i		−	0.738191i	−0.929391	−	0.369096i	$-0.879667\pi$
$743$		−	14950.4i		−	0.738191i	0.929391	−	0.369096i	$-0.120333\pi$
$744$	−1537.94	+	5236.60i	−0.0757843	+	0.258042i
$745$	−2235.87	+	1290.88i	−0.109954	+	0.0634822i
$746$	16418.1	−	9479.02i	0.805779	−	0.465217i
$747$	637.329	−	13346.4i	0.0312164	−	0.653709i
$748$			17989.1i			0.879338i
$749$		0			0
$750$	7548.00	+	31121.2i	0.367485	+	1.51518i
$751$	−13324.0	+	23077.8i	−0.647403	+	1.12133i	0.336338	+	0.941741i	$0.390812\pi$
$751$	−13324.0	+	23077.8i	−0.647403	+	1.12133i	−0.983741	+	0.179594i	$0.942522\pi$
$752$	−9443.04	−	16355.8i	−0.457915	−	0.793132i
$753$	14448.6	+	15155.1i	0.699254	+	0.733442i
$754$	11612.1	+	6704.25i	0.560859	+	0.323812i
$755$	14624.1			0.704934
$756$		0			0
$757$	−3274.00			−0.157194			−0.0785968	−	0.996906i	$-0.525044\pi$
$757$	−3274.00			−0.157194			−0.0785968	+	0.996906i	$0.525044\pi$
$758$	−18753.4	−	10827.3i	−0.898620	−	0.518818i
$759$	10727.9	+	11252.4i	0.513042	+	0.538126i
$760$	−765.000	−	1325.02i	−0.0365125	−	0.0632414i
$761$	−18350.8	+	31784.5i	−0.874134	+	1.51404i	−0.0164517	+	0.999865i	$0.505237\pi$
$761$	−18350.8	+	31784.5i	−0.874134	+	1.51404i	−0.857682	+	0.514180i	$0.828096\pi$
$762$	5292.14	+	21820.1i	0.251593	+	1.03735i
$763$		0			0
$764$		−	2374.91i		−	0.112462i
$765$	−788.169	+	16505.2i	−0.0372501	+	0.780061i
$766$	6851.86	−	3955.93i	0.323196	−	0.186597i
$767$	−6405.86	+	3698.43i	−0.301567	+	0.174110i
$768$	4230.12	−	14403.4i	0.198752	−	0.676740i
$769$			20570.8i			0.964633i	0.875997	+	0.482316i	$0.160204\pi$
$769$			20570.8i			0.964633i	−0.875997	+	0.482316i	$0.839796\pi$
$770$		0			0
$771$	1020.00	−	247.386i	0.0476451	−	0.0115556i
$772$	−2934.00	+	5081.84i	−0.136784	+	0.236916i
$773$	13225.3	+	22906.9i	0.615370	+	1.06585i	0.990319	+	0.138807i	$0.0443267\pi$
$773$	13225.3	+	22906.9i	0.615370	+	1.06585i	−0.374949	+	0.927045i	$0.622340\pi$
$774$	2648.67	−	4120.36i	0.123003	−	0.191348i
$775$	−5074.20	−	2929.59i	−0.235188	−	0.135786i
$776$	4504.38			0.208373
$777$		0			0
$778$	−29138.0			−1.34274
$779$	4499.10	+	2597.56i	0.206928	+	0.119470i
$780$	−19258.9	+	18361.2i	−0.884075	+	0.842866i
$781$	−7616.00	−	13191.3i	−0.348940	−	0.604381i
$782$	11331.6	−	19627.0i	0.518183	−	0.897519i
$783$	5302.24	+	6121.27i	0.242001	+	0.279383i
$784$		0			0
$785$			34312.5i			1.56008i
$786$	52524.4	+	15425.9i	2.38357	+	0.700030i
$787$	−20846.2	+	12035.6i	−0.944202	+	0.545136i	−0.891275	−	0.453463i	$-0.850188\pi$
$787$	−20846.2	+	12035.6i	−0.944202	+	0.545136i	−0.0529272	+	0.998598i	$0.516855\pi$
$788$	−15746.8	+	9091.45i	−0.711876	+	0.411002i
$789$	41276.6	+	12122.5i	1.86247	+	0.546988i
$790$		−	18405.5i		−	0.828908i
$791$		0			0
$792$	−3264.00	+	1682.23i	−0.146441	+	0.0754739i
$793$	−2001.00	+	3465.83i	−0.0896060	+	0.155202i
$794$	−27495.9	−	47624.3i	−1.22896	−	2.12862i
$795$	7830.32	−	7465.32i	0.349324	−	0.333041i
$796$	−37801.9	−	21825.0i	−1.68323	−	0.971815i
$797$	24673.1			1.09657			0.548285	−	0.836292i	$-0.315281\pi$
$797$	24673.1			1.09657			0.548285	+	0.836292i	$0.315281\pi$
$798$		0			0
$799$	−20808.0			−0.921319
$800$	−5173.96	−	2987.19i	−0.228659	−	0.132016i
$801$	11010.3	+	7077.71i	0.485680	+	0.312208i
$802$	27319.0	+	47317.9i	1.20283	+	2.08336i
$803$	−1454.33	+	2518.97i	−0.0639130	+	0.110701i
$804$	−2908.66	+	705.453i	−0.127588	+	0.0309445i
$805$		0			0
$806$		−	59174.8i		−	2.58603i
$807$	8473.44	−	28851.7i	0.369615	−	1.25852i
$808$	−4507.81	+	2602.58i	−0.196267	+	0.113315i
$809$	−38870.8	+	22442.1i	−1.68928	+	0.975304i	−0.734205	+	0.678928i	$0.762445\pi$
$809$	−38870.8	+	22442.1i	−1.68928	+	0.975304i	−0.955071	+	0.296376i	$0.904222\pi$
$810$	−27616.2	+	12604.1i	−1.19794	+	0.546745i
$811$			30430.0i			1.31756i	0.752335	+	0.658781i	$0.228927\pi$
$811$			30430.0i			1.31756i	−0.752335	+	0.658781i	$0.771073\pi$
$812$		0			0
$813$	−1494.00	−	6159.92i	−0.0644488	−	0.265729i
$814$	−15640.0	+	27089.3i	−0.673442	+	1.16644i
$815$	−15795.6	−	27358.8i	−0.678892	−	1.17587i
$816$	−11950.0	−	12534.3i	−0.512664	−	0.537729i
$817$	−1400.07	−	808.332i	−0.0599539	−	0.0346144i
$818$	−30763.1			−1.31492
$819$		0			0
$820$	12852.0			0.547331
$821$	−15975.4	−	9223.39i	−0.679104	−	0.392081i	0.120413	−	0.992724i	$-0.461578\pi$
$821$	−15975.4	−	9223.39i	−0.679104	−	0.392081i	−0.799517	+	0.600643i	$0.794911\pi$
$822$	−14872.8	−	15600.0i	−0.631081	−	0.661936i
$823$	−17503.0	−	30316.1i	−0.741332	−	1.28402i	−0.951889	−	0.306443i	$-0.900861\pi$
$823$	−17503.0	−	30316.1i	−0.741332	−	1.28402i	0.210557	−	0.977582i	$-0.432472\pi$
$824$	100.995	−	174.929i	0.00426982	−	0.00739554i
$825$	−929.154	−	3831.00i	−0.0392109	−	0.161671i
$826$		0			0
$827$			1500.81i			0.0631056i	0.999502	+	0.0315528i	$0.0100452\pi$
$827$			1500.81i			0.0631056i	−0.999502	+	0.0315528i	$0.989955\pi$
$828$	22017.0	+	1051.37i	0.924088	+	0.0441278i
$829$	29522.4	−	17044.8i	1.23686	−	0.714101i	0.268408	−	0.963305i	$-0.413503\pi$
$829$	29522.4	−	17044.8i	1.23686	−	0.714101i	0.968451	+	0.249205i	$0.0801692\pi$
$830$	−17846.4	+	10303.6i	−0.746336	+	0.430897i
$831$	−4705.99	+	16023.7i	−0.196449	+	0.668899i
$832$		−	35549.4i		−	1.48132i
$833$		0			0
$834$	−29019.0	+	7038.14i	−1.20485	+	0.292219i
$835$	−3570.00	+	6183.42i	−0.147958	+	0.256271i
$836$	5453.73	+	9446.14i	0.225624	+	0.390791i
$837$	11695.3	−	33772.3i	0.482974	−	1.39467i
$838$	33069.3	+	19092.5i	1.36320	+	0.787042i
$839$	989.751			0.0407271			0.0203635	−	0.999793i	$-0.493518\pi$
$839$	989.751			0.0407271			0.0203635	+	0.999793i	$0.493518\pi$
$840$		0			0
$841$	21057.0			0.863381
$842$	10190.8	+	5883.67i	0.417101	+	0.240813i
$843$	34734.2	−	33115.1i	1.41911	−	1.35296i
$844$	−10008.0	−	17334.4i	−0.408163	−	0.706959i
$845$	4933.61	−	8545.26i	0.200854	−	0.347889i
$846$	−17512.5	−	33979.3i	−0.711695	−	1.38089i
$847$		0			0
$848$			11338.5i			0.459159i
$849$	−14862.2	−	4364.87i	−0.600788	−	0.176445i
$850$	−4976.62	+	2873.25i	−0.200819	+	0.115943i
$851$	18067.8	−	10431.5i	0.727799	−	0.420195i
$852$	−20720.5	−	6085.41i	−0.833186	−	0.244698i
$853$		−	21592.3i		−	0.866711i	−0.901223	−	0.433356i	$-0.857329\pi$
$853$		−	21592.3i		−	0.866711i	0.901223	−	0.433356i	$-0.142671\pi$
$854$		0			0
$855$	4590.00	+	8905.91i	0.183596	+	0.356229i
$856$	3026.00	−	5241.19i	0.120825	−	0.209276i
$857$	23441.0	+	40600.9i	0.934338	+	1.61832i	0.775810	+	0.630966i	$0.217341\pi$
$857$	23441.0	+	40600.9i	0.934338	+	1.61832i	0.158528	+	0.987355i	$0.449325\pi$
$858$	28815.6	−	27472.4i	1.14656	−	1.09311i
$859$	30824.9	+	17796.8i	1.22437	+	0.706889i	0.965846	−	0.259116i	$-0.0834312\pi$
$859$	30824.9	+	17796.8i	1.22437	+	0.706889i	0.258522	+	0.966005i	$0.416765\pi$
$860$	−3999.40			−0.158580
$861$		0			0
$862$	46546.0			1.83917
$863$	−3227.93	−	1863.64i	−0.127323	−	0.0735100i	0.434986	−	0.900437i	$-0.356753\pi$
$863$	−3227.93	−	1863.64i	−0.127323	−	0.0735100i	−0.562309	+	0.826927i	$0.690087\pi$
$864$	11925.3	−	34436.3i	0.469567	−	1.35596i
$865$	11373.0	+	19698.6i	0.447045	+	0.774304i
$866$	−26874.8	+	46548.5i	−1.05455	+	1.82654i
$867$	6266.74	−	1519.91i	0.245478	−	0.0595372i
$868$		0			0
$869$			14579.3i			0.569124i
$870$	3519.51	−	11983.8i	0.137152	−	0.466997i
$871$	3122.58	−	1802.82i	0.121475	−	0.0701336i
$872$	6677.24	−	3855.10i	0.259312	−	0.149714i
$873$	−29463.2	−	1406.95i	−1.14224	−	0.0545452i
$874$		−	13741.6i		−	0.531828i
$875$		0			0
$876$	972.000	+	4007.66i	0.0374895	+	0.154573i
$877$	15215.0	−	26353.2i	0.585831	−	1.01469i	−0.408940	−	0.912561i	$-0.634101\pi$
$877$	15215.0	−	26353.2i	0.585831	−	1.01469i	0.994771	−	0.102128i	$-0.0325652\pi$
$878$	6191.00	+	10723.1i	0.237968	+	0.412173i
$879$	18504.4	+	19409.1i	0.710055	+	0.744771i
$880$	−15867.5	−	9161.09i	−0.607832	−	0.350932i
$881$	−36479.4			−1.39503			−0.697516	−	0.716570i	$-0.745711\pi$
$881$	−36479.4			−1.39503			−0.697516	+	0.716570i	$0.745711\pi$
$882$		0			0
$883$	21632.0			0.824433			0.412217	−	0.911086i	$-0.364755\pi$
$883$	21632.0			0.824433			0.412217	+	0.911086i	$0.364755\pi$
$884$	−26609.0	−	15362.7i	−1.01239	−	0.584506i
$885$	4754.42	+	4986.88i	0.180585	+	0.189415i
$886$	14110.0	+	24439.2i	0.535028	+	0.926696i
$887$	1585.62	−	2746.38i	0.0600225	−	0.103962i	−0.834453	−	0.551080i	$-0.814216\pi$
$887$	1585.62	−	2746.38i	0.0600225	−	0.103962i	0.894475	+	0.447117i	$0.147549\pi$
$888$	1161.44	+	4788.75i	0.0438913	+	0.180968i
$889$		0			0
$890$		−	20186.7i		−	0.760293i
$891$	21875.3	−	9983.95i	0.822503	−	0.375393i
$892$	−14929.9	+	8619.75i	−0.560413	+	0.323555i
$893$	−10926.4	+	6308.35i	−0.409449	+	0.236395i
$894$	1543.28	−	5254.81i	0.0577350	−	0.196585i
$895$		−	35311.8i		−	1.31882i
$896$		0			0
$897$	−25806.0	+	6258.87i	−0.960577	+	0.232974i
$898$	−5474.00	+	9481.25i	−0.203418	+	0.352331i
$899$	7352.44	+	12734.8i	0.272767	+	0.472446i
$900$	−4701.41	−	3022.19i	−0.174126	−	0.111933i
$901$	10818.7	+	6246.20i	0.400027	+	0.230956i
$902$	−19229.5			−0.709835
$903$		0			0
$904$	6902.00			0.253935
$905$	−1606.82	−	927.699i	−0.0590194	−	0.0340749i
$906$	−22453.2	+	21406.6i	−0.823352	+	0.784973i
$907$	−13450.0	−	23296.1i	−0.492392	−	0.852849i	0.507569	−	0.861611i	$-0.330544\pi$
$907$	−13450.0	−	23296.1i	−0.492392	−	0.852849i	−0.999962	+	0.00876232i	$0.997211\pi$
$908$	−26768.7	+	46364.8i	−0.978361	+	1.69457i
$909$	30298.5	−	15615.5i	1.10554	−	0.569784i
$910$		0			0
$911$			25917.8i			0.942587i	0.881977	+	0.471293i	$0.156213\pi$
$911$			25917.8i			0.942587i	−0.881977	+	0.471293i	$0.843787\pi$
$912$	−10075.0	−	2958.93i	−0.365808	−	0.107434i
$913$	14136.5	−	8161.70i	0.512431	−	0.295852i
$914$	4270.57	−	2465.62i	0.154549	−	0.0892291i
$915$	3576.76	+	1050.46i	0.129229	+	0.0379531i
$916$		−	33354.7i		−	1.20313i
$917$		0			0
$918$	−22950.0	−	26495.1i	−0.825123	−	0.952579i
$919$	6563.00	−	11367.4i	0.235575	−	0.408028i	−0.723865	−	0.689942i	$-0.757636\pi$
$919$	6563.00	−	11367.4i	0.235575	−	0.408028i	0.959440	+	0.281914i	$0.0909693\pi$
$920$	−1888.61	−	3271.16i	−0.0676799	−	0.117225i
$921$	7047.29	−	6718.79i	0.252135	−	0.240382i
$922$	−19437.7	−	11222.3i	−0.694301	−	0.400855i
$923$	26016.3			0.927777
$924$		0			0
$925$	−5290.00			−0.188037
$926$	−3306.48	−	1909.00i	−0.117341	−	0.0677468i
$927$	−715.249	+	1112.66i	−0.0253418	+	0.0394225i
$928$	7497.00	+	12985.2i	0.265195	+	0.459331i
$929$	−20613.1	+	35702.9i	−0.727980	+	1.26090i	0.229755	+	0.973248i	$0.426207\pi$
$929$	−20613.1	+	35702.9i	−0.727980	+	1.26090i	−0.957736	+	0.287650i	$0.907126\pi$
$930$	−53567.8	+	12992.1i	−1.88877	+	0.458094i
$931$		0			0
$932$		−	8609.04i		−	0.302574i
$933$	−12540.1	+	42698.5i	−0.440026	+	1.49827i
$934$	27804.1	−	16052.7i	0.974068	−	0.562378i
$935$	−17482.2	+	10093.4i	−0.611476	+	0.353036i
$936$	299.155	−	6264.65i	0.0104468	−	0.218768i
$937$			12580.6i			0.438623i	0.975655	+	0.219311i	$0.0703811\pi$
$937$			12580.6i			0.438623i	−0.975655	+	0.219311i	$0.929619\pi$
$938$		0			0
$939$	−654.000	−	2696.51i	−0.0227289	−	0.0937139i
$940$	−15606.0	+	27030.4i	−0.541502	+	0.937908i
$941$	2691.52	+	4661.85i	0.0932423	+	0.161500i	0.908874	−	0.417072i	$-0.136944\pi$
$941$	2691.52	+	4661.85i	0.0932423	+	0.161500i	−0.815631	+	0.578572i	$0.803610\pi$
$942$	−50226.2	−	52681.9i	−1.73722	−	1.82215i
$943$	11107.2	+	6412.76i	0.383564	+	0.221451i
$944$	−7221.15			−0.248971
$945$		0			0
$946$	5984.00			0.205662
$947$	44462.5	+	25670.5i	1.52570	+	0.880863i	0.999535	+	0.0304810i	$0.00970390\pi$
$947$	44462.5	+	25670.5i	1.52570	+	0.880863i	0.526165	+	0.850383i	$0.323629\pi$
$948$	14263.3	+	14960.6i	0.488660	+	0.512551i
$949$	−2484.00	−	4302.41i	−0.0849674	−	0.147168i
$950$	−1742.16	+	3017.52i	−0.0594982	+	0.103054i
$951$	6251.59	+	25776.0i	0.213167	+	0.878910i
$952$		0			0
$953$		−	32440.6i		−	1.10268i	−0.834281	−	0.551340i	$-0.814117\pi$
$953$		−	32440.6i		−	1.10268i	0.834281	−	0.551340i	$-0.185883\pi$
$954$	−1094.68	+	22923.9i	−0.0371505	+	0.777975i
$955$	2308.00	−	1332.52i	0.0782042	−	0.0451512i
$956$	−37342.5	+	21559.7i	−1.26333	+	0.729384i
$957$	−2787.87	+	9492.56i	−0.0941682	+	0.320638i
$958$			51552.0i			1.73859i
$959$		0			0
$960$	−32181.0	+	7805.04i	−1.08191	+	0.262403i
$961$	17552.5	−	30401.8i	0.589188	−	1.02050i
$962$	−26713.2	−	46268.6i	−0.895289	−	1.55069i
$963$	−21430.2	+	33337.5i	−0.717111	+	1.11556i
$964$	−29516.1	−	17041.1i	−0.986149	−	0.569354i
$965$	−6584.88			−0.219663
$966$		0			0
$967$	34232.0			1.13839			0.569197	−	0.822201i	$-0.307254\pi$
$967$	34232.0			1.13839			0.569197	+	0.822201i	$0.307254\pi$
$968$	867.684	+	500.957i	0.0288103	+	0.0166337i
$969$	−8373.43	+	7983.11i	−0.277599	+	0.264659i
$970$	22746.0	+	39397.2i	0.752918	+	1.30409i
$971$	9892.47	−	17134.3i	0.326946	−	0.566287i	−0.654958	−	0.755665i	$-0.727314\pi$
$971$	9892.47	−	17134.3i	0.326946	−	0.566287i	0.981904	+	0.189378i	$0.0606472\pi$
$972$	12679.9	−	31646.2i	0.418425	−	1.04429i
$973$		0			0
$974$			56536.0i			1.85989i
$975$	6460.22	+	1897.30i	0.212198	+	0.0623203i
$976$	−3383.51	+	1953.47i	−0.110967	+	0.0640666i
$977$	34464.5	−	19898.1i	1.12858	−	0.651583i	0.184999	−	0.982739i	$-0.440772\pi$
$977$	34464.5	−	19898.1i	1.12858	−	0.651583i	0.943576	+	0.331155i	$0.107438\pi$
$978$	64299.5	+	18884.1i	2.10232	+	0.617431i
$979$			15990.3i			0.522013i
$980$		0			0
$981$	−44880.0	+	23130.6i	−1.46066	+	0.752807i
$982$	−11900.0	+	20611.4i	−0.386705	+	0.669793i
$983$	−11341.7	−	19644.5i	−0.368001	−	0.637397i	0.621252	−	0.783611i	$-0.286625\pi$
$983$	−11341.7	−	19644.5i	−0.368001	−	0.637397i	−0.989253	+	0.146214i	$0.953291\pi$
$984$	−2192.49	+	2090.29i	−0.0710305	+	0.0677196i
$985$	−17670.6	−	10202.1i	−0.571606	−	0.330017i
$986$	14422.1			0.465814
$987$		0			0
$988$	−18630.0			−0.599898
$989$	−3456.45	−	1995.58i	−0.111131	−	0.0641616i
$990$	−31195.9	−	20053.5i	−1.00148	−	0.643780i
$991$	25211.0	+	43666.7i	0.808127	+	1.39972i	0.914160	+	0.405354i	$0.132852\pi$
$991$	25211.0	+	43666.7i	0.808127	+	1.39972i	−0.106033	+	0.994363i	$0.533815\pi$
$992$	33086.0	−	57306.6i	1.05895	−	1.83416i
$993$	−18340.7	+	4448.27i	−0.586127	+	0.142157i
$994$		0			0
$995$		−	48982.5i		−	1.56065i
$996$	6521.45	−	22205.2i	0.207470	−	0.706425i
$997$	−39942.3	+	23060.7i	−1.26879	+	0.732538i	−0.974760	−	0.223257i	$-0.928331\pi$
$997$	−39942.3	+	23060.7i	−1.26879	+	0.732538i	−0.294033	+	0.955795i	$0.594998\pi$
$998$	55260.4	−	31904.6i	1.75274	−	1.01195i
$999$	−6101.24	−	31686.0i	−0.193228	−	1.00351i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.g.c.68.2		8
3.2	odd	2	inner	147.4.g.c.68.3		8
7.2	even	3		21.4.c.b.20.3	yes	4
7.3	odd	6	inner	147.4.g.c.80.3		8
7.4	even	3	inner	147.4.g.c.80.4		8
7.5	odd	6		21.4.c.b.20.4	yes	4
7.6	odd	2	inner	147.4.g.c.68.1		8
21.2	odd	6		21.4.c.b.20.2	yes	4
21.5	even	6		21.4.c.b.20.1	✓	4
21.11	odd	6	inner	147.4.g.c.80.1		8
21.17	even	6	inner	147.4.g.c.80.2		8
21.20	even	2	inner	147.4.g.c.68.4		8
28.19	even	6		336.4.k.b.209.2		4
28.23	odd	6		336.4.k.b.209.3		4
84.23	even	6		336.4.k.b.209.1		4
84.47	odd	6		336.4.k.b.209.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.c.b.20.1	✓	4	21.5	even	6
21.4.c.b.20.2	yes	4	21.2	odd	6
21.4.c.b.20.3	yes	4	7.2	even	3
21.4.c.b.20.4	yes	4	7.5	odd	6
147.4.g.c.68.1		8	7.6	odd	2	inner
147.4.g.c.68.2		8	1.1	even	1	trivial
147.4.g.c.68.3		8	3.2	odd	2	inner
147.4.g.c.68.4		8	21.20	even	2	inner
147.4.g.c.80.1		8	21.11	odd	6	inner
147.4.g.c.80.2		8	21.17	even	6	inner
147.4.g.c.80.3		8	7.3	odd	6	inner
147.4.g.c.80.4		8	7.4	even	3	inner
336.4.k.b.209.1		4	84.23	even	6
336.4.k.b.209.2		4	28.19	even	6
336.4.k.b.209.3		4	28.23	odd	6
336.4.k.b.209.4		4	84.47	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.g (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.57071 - 2.06155i) q^{2} +(3.58554 + 3.76084i) q^{3} +(4.50000 + 7.79423i) q^{4} +(-5.04975 + 8.74643i) q^{5} +(-5.04975 - 20.8207i) q^{6} -4.12311i q^{8} +(-1.28786 + 26.9693i) q^{9} +(36.0624 - 20.8207i) q^{10} +(-28.5657 + 16.4924i) q^{11} +(-13.1779 + 44.8703i) q^{12} -56.3383i q^{13} +(-51.0000 + 12.3693i) q^{15} +(27.5000 - 47.6314i) q^{16} +(-30.2985 - 52.4786i) q^{17} +(60.1971 - 93.6446i) q^{18} +(-31.8198 - 18.3712i) q^{19} -90.8955 q^{20} +136.000 q^{22} +(-78.5557 - 45.3542i) q^{23} +(15.5063 - 14.7835i) q^{24} +(11.5000 + 19.9186i) q^{25} +(-116.144 + 201.168i) q^{26} +(-106.045 + 91.8559i) q^{27} -57.7235i q^{29} +(207.606 + 60.9719i) q^{30} +(-220.617 + 127.373i) q^{31} +(-224.955 + 129.878i) q^{32} +(-164.449 - 48.2969i) q^{33} +249.848i q^{34} +(-216.000 + 111.324i) q^{36} +(-115.000 + 199.186i) q^{37} +(75.7463 + 131.196i) q^{38} +(211.879 - 202.003i) q^{39} +(36.0624 + 20.8207i) q^{40} -141.393 q^{41} +44.0000 q^{43} +(-257.091 - 148.432i) q^{44} +(-229.381 - 147.452i) q^{45} +(187.000 + 323.894i) q^{46} +(171.692 - 297.379i) q^{47} +(277.736 - 67.3610i) q^{48} -94.8314i q^{50} +(88.7271 - 302.112i) q^{51} +(439.113 - 253.522i) q^{52} +(-178.536 + 103.078i) q^{53} +(568.021 - 109.374i) q^{54} -333.131i q^{55} +(-45.0000 - 185.540i) q^{57} +(-119.000 + 206.114i) q^{58} +(-65.6468 - 113.704i) q^{59} +(-325.909 - 341.844i) q^{60} +(-61.5183 - 35.5176i) q^{61} +1050.35 q^{62} +631.000 q^{64} +(492.759 + 284.494i) q^{65} +(487.633 + 511.474i) q^{66} +(32.0000 + 55.4256i) q^{67} +(272.687 - 472.307i) q^{68} +(-111.095 - 458.055i) q^{69} +461.788i q^{71} +(111.197 + 5.30997i) q^{72} +(76.3675 - 44.0908i) q^{73} +(821.264 - 474.157i) q^{74} +(-33.6770 + 114.668i) q^{75} -330.681i q^{76} +(-1173.00 + 284.494i) q^{78} +(221.000 - 382.783i) q^{79} +(277.736 + 481.054i) q^{80} +(-725.683 - 69.4651i) q^{81} +(504.874 + 291.489i) q^{82} -494.876 q^{83} +612.000 q^{85} +(-157.111 - 90.7083i) q^{86} +(217.089 - 206.970i) q^{87} +(68.0000 + 117.779i) q^{88} +(242.388 - 419.829i) q^{89} +(515.075 + 999.392i) q^{90} -816.375i q^{92} +(-1270.06 - 373.005i) q^{93} +(-1226.12 + 707.903i) q^{94} +(321.364 - 185.540i) q^{95} +(-1295.03 - 380.338i) q^{96} +1092.47i q^{97} +(-408.000 - 791.636i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 36 q^{4} - 96 q^{9} - 408 q^{15} + 220 q^{16} - 204 q^{18} + 1088 q^{22} + 92 q^{25} + 204 q^{30} - 1728 q^{36} - 920 q^{37} - 276 q^{39} + 352 q^{43} + 1496 q^{46} + 1224 q^{51} - 360 q^{57} - 952 q^{58}+ \cdots - 3264 q^{99}+O(q^{100}) \) 8 * q + 36 * q^4 - 96 * q^9 - 408 * q^15 + 220 * q^16 - 204 * q^18 + 1088 * q^22 + 92 * q^25 + 204 * q^30 - 1728 * q^36 - 920 * q^37 - 276 * q^39 + 352 * q^43 + 1496 * q^46 + 1224 * q^51 - 360 * q^57 - 952 * q^58 - 1836 * q^60 + 5048 * q^64 + 256 * q^67 + 204 * q^72 - 9384 * q^78 + 1768 * q^79 - 1692 * q^81 + 4896 * q^85 + 544 * q^88 - 1248 * q^93 - 3264 * q^99

Introduction

L-functions

Modular forms

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