LMFDB - Embedded newform 147.4.g.c.80.2

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			80.2
Root			$-2.17132 + 2.07011i$ of defining polynomial
Character	$\chi$	$=$	147.80
Dual form			147.4.g.c.68.2

$q$-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 $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−3.57071	+	2.06155i	−1.26244	+	0.728869i	−0.973546	−	0.228493i	$-0.926620\pi$
$2$	−3.57071	+	2.06155i	−1.26244	+	0.728869i	−0.288892	+	0.957362i	$0.593287\pi$
$3$	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	0.546826	−	0.837246i	$-0.315836\pi$
$5$	−5.04975	−	8.74643i	−0.451664	−	0.782304i	−0.998490	+	0.0549420i	$0.982503\pi$
$6$	−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	0.0544991	−	0.998514i	$-0.482644\pi$
$11$	−28.5657	−	16.4924i	−0.782990	−	0.452059i	−0.837489	+	0.546455i	$0.815977\pi$
$12$	−13.1779	−	44.8703i	−0.317012	−	1.07941i
$13$			56.3383i			1.20196i	0.799266	+	0.600978i	$0.205222\pi$
$13$			56.3383i			1.20196i	−0.799266	+	0.600978i	$0.794778\pi$
$14$		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	−0.997068	−	0.0765232i	$-0.975618\pi$
$17$	−30.2985	+	52.4786i	−0.432263	+	0.748701i	0.564805	+	0.825224i	$0.308951\pi$
$18$	60.1971	+	93.6446i	0.788256	+	1.22624i
$19$	−31.8198	+	18.3712i	−0.384209	+	0.221823i	−0.679648	−	0.733539i	$-0.737867\pi$
$19$	−31.8198	+	18.3712i	−0.384209	+	0.221823i	0.295439	+	0.955362i	$0.404534\pi$
$20$	−90.8955			−1.01624
$21$		0			0
$22$	136.000			1.31797
$23$	−78.5557	+	45.3542i	−0.712174	+	0.411174i	−0.811865	−	0.583845i	$-0.801548\pi$
$23$	−78.5557	+	45.3542i	−0.712174	+	0.411174i	0.0996916	+	0.995018i	$0.468214\pi$
$24$	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	$0.0591670\pi$
$29$			57.7235i			0.369620i	−0.982774	+	0.184810i	$0.940833\pi$
$30$	207.606	−	60.9719i	1.26345	−	0.371063i
$31$	−220.617	−	127.373i	−1.27819	−	0.737966i	−0.301679	−	0.953410i	$-0.597547\pi$
$31$	−220.617	−	127.373i	−1.27819	−	0.737966i	−0.976516	+	0.215444i	$0.930880\pi$
$32$	−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	−0.999919	−	0.0127135i	$-0.995953\pi$
$37$	−115.000	−	199.186i	−0.510970	−	0.885026i	0.488949	−	0.872312i	$-0.337380\pi$
$38$	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	0.999264	+	0.0383528i	$0.0122111\pi$
$47$	171.692	+	297.379i	0.532847	+	0.922917i	−0.466418	+	0.884565i	$0.654456\pi$
$48$	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	0.250472	−	0.968124i	$-0.419414\pi$
$53$	−178.536	−	103.078i	−0.462713	−	0.267147i	−0.713184	+	0.700977i	$0.752748\pi$
$54$	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	−0.929319	−	0.369278i	$-0.879605\pi$
$59$	−65.6468	+	113.704i	−0.144856	+	0.250897i	0.784463	+	0.620175i	$0.212938\pi$
$60$	−325.909	+	341.844i	−0.701245	+	0.735531i
$61$	−61.5183	+	35.5176i	−0.129125	+	0.0745502i	−0.563171	−	0.826340i	$-0.690419\pi$
$61$	−61.5183	+	35.5176i	−0.129125	+	0.0745502i	0.434046	+	0.900891i	$0.357085\pi$
$62$	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	−0.835375	−	0.549680i	$-0.814750\pi$
$67$	32.0000	−	55.4256i	0.0583496	−	0.101064i	0.893725	+	0.448616i	$0.148083\pi$
$68$	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	$-0.873876\pi$
$71$		−	461.788i		−	0.771889i	0.922522	−	0.385945i	$-0.126124\pi$
$72$	111.197	−	5.30997i	0.182010	−	0.00869147i
$73$	76.3675	+	44.0908i	0.122440	+	0.0706910i	0.559969	−	0.828513i	$-0.310813\pi$
$73$	76.3675	+	44.0908i	0.122440	+	0.0706910i	−0.437529	+	0.899204i	$0.644146\pi$
$74$	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	0.979382	−	0.202016i	$-0.0647494\pi$
$79$	221.000	+	382.783i	0.314740	+	0.545145i	−0.664642	+	0.747162i	$0.731416\pi$
$80$	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	0.973496	−	0.228702i	$-0.0734482\pi$
$89$	242.388	+	419.829i	0.288686	+	0.500020i	−0.684810	+	0.728722i	$0.740115\pi$
$90$	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	$-0.806256\pi$
$97$		−	1092.47i		−	1.14354i	0.820413	−	0.571772i	$-0.193744\pi$
$98$		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	0.367270	+	0.930114i	$0.380293\pi$
$101$	−631.219	+	1093.30i	−0.621868	+	1.07711i	−0.989138	+	0.146992i	$0.953041\pi$
$102$	−939.639	−	895.839i	−0.912138	−	0.869620i
$103$	42.4264	−	24.4949i	0.0405864	−	0.0234326i	−0.479570	−	0.877504i	$-0.659207\pi$
$103$	42.4264	−	24.4949i	0.0405864	−	0.0234326i	0.520156	+	0.854071i	$0.325874\pi$
$104$	−232.289			−0.219017
$105$		0			0
$106$	850.000			0.778861
$107$	1271.17	−	733.913i	1.14850	−	0.663084i	0.199976	−	0.979801i	$-0.435914\pi$
$107$	1271.17	−	733.913i	1.14850	−	0.663084i	0.948520	+	0.316717i	$0.102580\pi$
$108$	−1193.15	+	413.186i	−1.06306	+	0.368137i
$109$	935.000	−	1619.47i	0.821622	−	1.42309i	−0.0828525	−	0.996562i	$-0.526403\pi$
$109$	935.000	−	1619.47i	0.821622	−	1.42309i	0.904474	−	0.426529i	$-0.140264\pi$
$110$	−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	$-0.754610\pi$
$113$		−	1673.98i		−	1.39358i	0.717274	−	0.696791i	$-0.245390\pi$
$114$	−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	−0.879322	−	0.476228i	$-0.842004\pi$
$131$	−1277.59	−	2212.85i	−0.852086	−	1.47586i	0.0272354	−	0.999629i	$-0.491330\pi$
$132$	−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	0.746428	−	0.665467i	$-0.231767\pi$
$137$	871.254	+	503.019i	0.543330	+	0.313692i	−0.203097	+	0.979159i	$0.565101\pi$
$138$	−547.617	−	1864.61i	−0.337799	−	1.15019i
$139$			1393.76i			0.850483i	0.905080	+	0.425242i	$0.139811\pi$
$139$			1393.76i			0.850483i	−0.905080	+	0.425242i	$0.860189\pi$
$140$		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	−0.437903	−	0.899022i	$-0.644279\pi$
$149$	221.384	−	127.816i	0.121722	−	0.0702760i	0.559625	+	0.828746i	$0.310945\pi$
$150$	356.646	+	340.022i	0.194133	+	0.185084i
$151$	−724.000	+	1254.00i	−0.390187	+	0.675824i	−0.992474	−	0.122456i	$-0.960923\pi$
$151$	−724.000	+	1254.00i	−0.390187	+	0.675824i	0.602287	+	0.798280i	$0.294256\pi$
$152$	−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	0.999988	−	0.00498842i	$-0.00158787\pi$
$157$	2942.27	+	1698.72i	1.49566	+	0.863520i	0.495674	+	0.868509i	$0.334921\pi$
$158$	−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	−0.947073	−	0.321017i	$-0.895975\pi$
$163$	−1564.00	−	2708.93i	−0.751546	−	1.30172i	0.195528	−	0.980698i	$-0.437358\pi$
$164$	−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	0.999983	−	0.00589428i	$-0.00187622\pi$
$173$	1126.09	+	1950.45i	0.494887	+	0.857169i	−0.505096	+	0.863063i	$0.668543\pi$
$174$	−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	−0.290447	−	0.956891i	$-0.593804\pi$
$179$	−3027.97	−	1748.20i	−1.26436	−	0.729980i	−0.973915	+	0.226912i	$0.927137\pi$
$180$	117.060	+	2451.39i	0.0484732	+	1.01509i
$181$		−	183.712i		−	0.0754430i	−0.999288	−	0.0377215i	$-0.987990\pi$
$181$		−	183.712i		−	0.0754430i	0.999288	−	0.0377215i	$-0.0120100\pi$
$182$		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	−0.542662	−	0.839951i	$-0.682583\pi$
$191$	−228.526	+	131.939i	−0.0865735	+	0.0499832i	0.456088	+	0.889935i	$0.349250\pi$
$192$	2262.47	−	2373.09i	0.850416	−	0.891995i
$193$	326.000	−	564.649i	0.121585	−	0.210592i	−0.798808	−	0.601587i	$-0.794535\pi$
$193$	326.000	−	564.649i	0.121585	−	0.210592i	0.920393	+	0.390994i	$0.127869\pi$
$194$	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	$-0.880954\pi$
$197$		−	2020.32i		−	0.730670i	0.930876	−	0.365335i	$-0.119046\pi$
$198$	−175.149	−	3667.82i	−0.0628650	−	1.31647i
$199$	−4200.21	−	2424.99i	−1.49621	−	0.863836i	−0.496217	−	0.868199i	$-0.665278\pi$
$199$	−4200.21	−	2424.99i	−1.49621	−	0.863836i	−0.999990	+	0.00436270i	$0.998611\pi$
$200$	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	$-0.907141\pi$
$223$		−	1915.50i		−	0.575208i	0.957749	−	0.287604i	$-0.0928587\pi$
$224$		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	0.00730379	−	0.999973i	$-0.497675\pi$
$227$	2974.30	−	5151.65i	0.869654	−	1.50629i	0.862350	−	0.506312i	$-0.168992\pi$
$228$	1243.64	+	1185.67i	0.361237	+	0.344399i
$229$	−3209.56	+	1853.04i	−0.926173	+	0.534726i	−0.885599	−	0.464451i	$-0.846252\pi$
$229$	−3209.56	+	1853.04i	−0.926173	+	0.534726i	−0.0405736	+	0.999177i	$0.512919\pi$
$230$	−3777.21			−1.08288
$231$		0			0
$232$	−238.000			−0.0673511
$233$	−828.406	+	478.280i	−0.232921	+	0.134477i	−0.611919	−	0.790920i	$-0.709602\pi$
$233$	−828.406	+	478.280i	−0.232921	+	0.134477i	0.378998	+	0.925398i	$0.376269\pi$
$234$	−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	$-0.775463\pi$
$239$		−	4791.05i		−	1.29668i	0.761350	−	0.648341i	$-0.224537\pi$
$240$	−813.332	−	2769.36i	−0.218752	−	0.744839i
$241$	−3279.56	−	1893.46i	−0.876577	−	0.506092i	−0.00704889	−	0.999975i	$-0.502244\pi$
$241$	−3279.56	−	1893.46i	−0.876577	−	0.506092i	−0.869528	+	0.493883i	$0.835577\pi$
$242$	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	0.878022	−	0.478621i	$-0.158863\pi$
$257$	100.995	+	174.929i	0.0245132	+	0.0424581i	−0.853509	+	0.521079i	$0.825530\pi$
$258$	−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	0.960954	+	0.276709i	$0.0892438\pi$
$263$	7169.99	+	4139.60i	1.68107	+	0.970565i	0.720114	+	0.693856i	$0.244090\pi$
$264$	−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	0.325846	+	0.945423i	$0.394351\pi$
$269$	−2893.51	+	5011.70i	−0.655838	+	1.13594i	−0.981683	+	0.190521i	$0.938982\pi$
$270$	−1911.73	−	5520.47i	−0.430905	−	1.24432i
$271$	−1056.42	+	609.923i	−0.236800	+	0.136717i	−0.613705	−	0.789535i	$-0.710322\pi$
$271$	−1056.42	+	609.923i	−0.236800	+	0.136717i	0.376905	+	0.926252i	$0.376988\pi$
$272$	−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	−0.637422	−	0.770515i	$-0.719999\pi$
$277$	1607.00	−	2783.41i	0.348575	−	0.603750i	0.985997	+	0.166766i	$0.0533323\pi$
$278$	−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	$0.436800\pi$
$281$			9235.76i			1.96071i	−0.197245	+	0.980354i	$0.563200\pi$
$282$	−7058.62	+	2073.04i	−1.49055	+	0.437759i
$283$	−2581.65	−	1490.51i	−0.542272	−	0.313081i	0.203727	−	0.979028i	$-0.434694\pi$
$283$	−2581.65	−	1490.51i	−0.542272	−	0.313081i	−0.745999	+	0.665947i	$0.768028\pi$
$284$	−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	$0.0557276\pi$
$307$			1873.86i			0.348361i	−0.984714	+	0.174180i	$0.944272\pi$
$308$		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	−0.150717	−	0.988577i	$-0.548158\pi$
$311$	4282.19	−	7416.97i	0.780774	−	1.35234i	0.931491	−	0.363763i	$-0.118508\pi$
$312$	−832.879	+	873.601i	−0.151130	+	0.158519i
$313$	−462.448	+	266.994i	−0.0835115	+	0.0482154i	−0.541174	−	0.840910i	$-0.682020\pi$
$313$	−462.448	+	266.994i	−0.0835115	+	0.0482154i	0.457663	+	0.889126i	$0.348687\pi$
$314$	−14008.0			−2.51757
$315$		0			0
$316$	3978.00			0.708165
$317$	4420.54	−	2552.20i	0.783226	−	0.452195i	−0.0543467	−	0.998522i	$-0.517308\pi$
$317$	4420.54	−	2552.20i	0.783226	−	0.452195i	0.837572	+	0.546327i	$0.183974\pi$
$318$	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	0.674929	−	0.737882i	$-0.264174\pi$
$331$	−1816.00	−	3145.40i	−0.301560	−	0.522317i	−0.976490	+	0.215565i	$0.930841\pi$
$332$	−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	0.426465	−	0.904504i	$-0.359759\pi$
$347$	−928.386	−	536.004i	−0.143626	−	0.0829227i	−0.570091	+	0.821581i	$0.693092\pi$
$348$	2590.07	−	760.677i	0.398972	−	0.117174i
$349$		−	6287.84i		−	0.964414i	−0.876057	−	0.482207i	$-0.839835\pi$
$349$		−	6287.84i		−	0.964414i	0.876057	−	0.482207i	$-0.160165\pi$
$350$		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	−0.993599	−	0.112965i	$-0.963965\pi$
$353$	−2646.07	+	4583.13i	−0.398969	+	0.691035i	0.594630	+	0.804000i	$0.297299\pi$
$354$	−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	−0.690105	−	0.723709i	$-0.742436\pi$
$359$	−2778.02	+	1603.89i	−0.408407	+	0.235794i	0.281698	+	0.959503i	$0.409102\pi$
$360$	−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	0.950245	−	0.311505i	$-0.100833\pi$
$367$	8124.66	+	4690.77i	1.15560	+	0.667184i	0.205351	+	0.978688i	$0.434166\pi$
$368$	−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	0.661172	−	0.750234i	$-0.270059\pi$
$373$	−2299.00	−	3981.98i	−0.319136	−	0.552760i	−0.980308	+	0.197475i	$0.936726\pi$
$374$	−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	0.794899	−	0.606742i	$-0.207524\pi$
$383$	−959.453	−	1661.82i	−0.128005	−	0.221710i	−0.922903	+	0.385032i	$0.874191\pi$
$384$	−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	0.842668	−	0.538434i	$-0.180984\pi$
$389$	6120.20	+	3533.50i	0.797704	+	0.460554i	−0.0449640	+	0.998989i	$0.514317\pi$
$390$	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	0.461199	−	0.887297i	$-0.347419\pi$
$397$	11550.6	−	6668.74i	1.46022	−	0.843059i	0.999021	+	0.0442380i	$0.0140860\pi$
$398$	19997.0			2.51849
$399$		0			0
$400$	1265.00			0.158125
$401$	−11476.3	+	6625.83i	−1.42917	+	0.825133i	−0.997055	−	0.0766852i	$-0.975566\pi$
$401$	−11476.3	+	6625.83i	−1.42917	+	0.825133i	−0.432116	+	0.901818i	$0.642233\pi$
$402$	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	0.836848	−	0.547435i	$-0.184396\pi$
$409$	6461.54	+	3730.57i	0.781180	+	0.451015i	−0.0556682	+	0.998449i	$0.517729\pi$
$410$	−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	−0.158354	−	0.987382i	$-0.550619\pi$
$431$	−9776.62	−	5644.53i	−1.09263	−	0.630830i	−0.934275	+	0.356553i	$0.883952\pi$
$432$	1458.99	−	7577.10i	0.162490	−	0.843873i
$433$			13036.2i			1.44683i	0.690411	+	0.723417i	$0.257430\pi$
$433$			13036.2i			1.44683i	−0.690411	+	0.723417i	$0.742570\pi$
$434$		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	−0.634667	−	0.772786i	$-0.718863\pi$
$439$	−2600.74	+	1501.54i	−0.282748	+	0.163245i	0.351919	+	0.936031i	$0.385529\pi$
$440$	−1373.53			−0.148820
$441$		0			0
$442$	14076.0			1.51477
$443$	−5927.39	+	3422.18i	−0.635708	+	0.367026i	−0.782959	−	0.622073i	$-0.786291\pi$
$443$	−5927.39	+	3422.18i	−0.635708	+	0.367026i	0.147251	+	0.989099i	$0.452957\pi$
$444$	−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	$0.0445636\pi$
$449$			2655.28i			0.279088i	−0.990216	+	0.139544i	$0.955436\pi$
$450$	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	0.833796	−	0.552072i	$-0.186163\pi$
$457$	−598.000	−	1035.77i	−0.0612106	−	0.106020i	−0.895007	+	0.446052i	$0.852829\pi$
$458$	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	0.606090	−	0.795396i	$-0.292737\pi$
$467$	−3893.36	−	6743.50i	−0.385788	−	0.668205i	−0.991878	+	0.127191i	$0.959404\pi$
$468$	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	0.397026	+	0.917807i	$0.370042\pi$
$479$	−6251.59	+	10828.1i	−0.596331	+	1.03288i	−0.993358	+	0.115069i	$0.963291\pi$
$480$	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	0.347949	+	0.937514i	$0.386878\pi$
$487$	−6856.00	+	11874.9i	−0.637936	+	1.10494i	−0.985885	+	0.167425i	$0.946455\pi$
$488$	−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	$0.0854635\pi$
$491$			5772.35i			0.530555i	−0.964172	+	0.265277i	$0.914536\pi$
$492$	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	−0.970453	−	0.241289i	$-0.922430\pi$
$499$	−7738.00	−	13402.6i	−0.694189	−	1.20237i	0.276264	−	0.961082i	$-0.410904\pi$
$500$	−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	0.943324	−	0.331875i	$-0.107681\pi$
$509$	2115.85	+	3664.75i	0.184250	+	0.319130i	−0.759074	+	0.651005i	$0.774348\pi$
$510$	−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	0.0805465	+	0.996751i	$0.474333\pi$
$521$	−9786.42	+	16950.6i	−0.822938	+	1.42537i	−0.903485	+	0.428620i	$0.859000\pi$
$522$	−5405.49	+	3474.79i	−0.453241	+	0.291355i
$523$	−7248.55	+	4184.95i	−0.606036	+	0.349895i	−0.771413	−	0.636335i	$-0.780449\pi$
$523$	−7248.55	+	4184.95i	−0.606036	+	0.349895i	0.165376	+	0.986231i	$0.447116\pi$
$524$	−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	0.985048	+	0.172278i	$0.0551128\pi$
$541$	8075.00	+	13986.3i	0.641722	+	1.11149i	−0.343327	+	0.939216i	$0.611554\pi$
$542$	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	0.386524	−	0.922279i	$-0.373676\pi$
$557$	−2878.00	−	1661.61i	−0.218931	−	0.126400i	−0.605455	+	0.795879i	$0.707009\pi$
$558$	−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	−0.464279	−	0.885689i	$-0.653687\pi$
$563$	7145.40	−	12376.2i	0.534889	−	0.926456i	0.999169	−	0.0407667i	$-0.0129800\pi$
$564$	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	0.0531008	−	0.998589i	$-0.483090\pi$
$569$	12818.9	−	7400.97i	0.944455	−	0.545281i	0.891354	+	0.453308i	$0.149756\pi$
$570$	−5485.87	+	5754.09i	−0.403119	+	0.422828i
$571$	−2068.00	+	3581.88i	−0.151564	+	0.262517i	−0.931803	−	0.362965i	$-0.881764\pi$
$571$	−2068.00	+	3581.88i	−0.151564	+	0.262517i	0.780239	+	0.625482i	$0.215098\pi$
$572$	−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	−0.251826	−	0.967772i	$-0.581031\pi$
$577$	−16851.8	−	9729.37i	−1.21585	−	0.701974i	−0.964029	+	0.265798i	$0.914364\pi$
$578$	−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	0.693670	−	0.720293i	$-0.255993\pi$
$593$	−3999.40	−	6927.17i	−0.276958	−	0.479705i	−0.970627	+	0.240589i	$0.922659\pi$
$594$	−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	0.820100	−	0.572221i	$-0.193918\pi$
$599$	10769.3	+	6217.64i	0.734592	+	0.424117i	−0.0855077	+	0.996338i	$0.527251\pi$
$600$	472.790	−	138.854i	0.0321693	−	0.00944780i
$601$			18557.3i			1.25952i	0.776791	+	0.629758i	$0.216846\pi$
$601$			18557.3i			1.25952i	−0.776791	+	0.629758i	$0.783154\pi$
$602$		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	−0.453190	−	0.891414i	$-0.649714\pi$
$607$	1378.86	−	796.084i	0.0922012	−	0.0532324i	0.545392	+	0.838181i	$0.316381\pi$
$608$	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	−0.835106	−	0.550089i	$-0.814594\pi$
$613$	893.000	−	1546.72i	0.0588384	−	0.101911i	0.893944	+	0.448178i	$0.147927\pi$
$614$	−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	$-0.913209\pi$
$617$		−	8254.46i		−	0.538593i	0.963057	−	0.269297i	$-0.0867912\pi$
$618$	295.757	+	1007.04i	0.0192510	+	0.0655486i
$619$	7189.15	+	4150.66i	0.466812	+	0.269514i	0.714904	−	0.699222i	$-0.246470\pi$
$619$	7189.15	+	4150.66i	0.466812	+	0.269514i	−0.248092	+	0.968736i	$0.579804\pi$
$620$	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	0.738968	−	0.673741i	$-0.235314\pi$
$641$	8519.72	+	4918.87i	0.524975	+	0.303094i	−0.213993	+	0.976835i	$0.568647\pi$
$642$	8861.44	+	30172.8i	0.544755	+	1.85487i
$643$			9624.05i			0.590257i	0.955458	+	0.295129i	$0.0953625\pi$
$643$			9624.05i			0.590257i	−0.955458	+	0.295129i	$0.904638\pi$
$644$		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	−0.958927	−	0.283653i	$-0.908454\pi$
$647$	−3847.91	+	6664.78i	−0.233813	+	0.404976i	0.725114	+	0.688629i	$0.241787\pi$
$648$	−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	0.469823	−	0.882761i	$-0.344318\pi$
$653$	24516.5	−	14154.6i	1.46923	−	0.848259i	0.999405	+	0.0345016i	$0.0109844\pi$
$654$	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	$-0.762408\pi$
$659$		−	22973.9i		−	1.35802i	0.734127	−	0.679012i	$-0.237592\pi$
$660$	14947.7	−	4389.98i	0.881571	−	0.258908i
$661$	9357.14	+	5402.35i	0.550606	+	0.317893i	0.749366	−	0.662155i	$-0.230358\pi$
$661$	9357.14	+	5402.35i	0.550606	+	0.317893i	−0.198760	+	0.980048i	$0.563692\pi$
$662$	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	0.995283	+	0.0970162i	$0.0309299\pi$
$677$	10245.9	+	17746.5i	0.581660	+	1.00746i	−0.413623	+	0.910448i	$0.635737\pi$
$678$	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	0.482293	−	0.876010i	$-0.339804\pi$
$683$	−628.446	−	362.833i	−0.0352076	−	0.0203271i	−0.517501	+	0.855683i	$0.673137\pi$
$684$	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	−0.192734	−	0.981251i	$-0.561735\pi$
$691$	10184.5	−	5880.00i	0.560688	−	0.323713i	0.753421	+	0.657538i	$0.228402\pi$
$692$	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	$0.200622\pi$
$701$			21877.2i			1.17873i	−0.807867	+	0.589365i	$0.799378\pi$
$702$	−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	0.984126	+	0.177472i	$0.0567920\pi$
$709$	12191.0	+	21115.4i	0.645758	+	1.11849i	−0.338368	+	0.941014i	$0.609875\pi$
$710$	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	0.973235	−	0.229813i	$-0.0738115\pi$
$719$	5544.63	+	9603.58i	0.287594	+	0.498127i	−0.685641	+	0.727940i	$0.740478\pi$
$720$	−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	$-0.951685\pi$
$727$		−	5927.77i		−	0.302405i	0.988503	−	0.151203i	$-0.0483146\pi$
$728$		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	−0.903268	−	0.429077i	$-0.858839\pi$
$733$	−19514.0	+	11266.4i	−0.983311	+	0.567715i	−0.0800429	+	0.996791i	$0.525506\pi$
$734$	−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	−0.728178	−	0.685388i	$-0.759633\pi$
$739$	4610.00	−	7984.75i	0.229474	−	0.397461i	0.957652	+	0.287927i	$0.0929659\pi$
$740$	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	$0.120333\pi$
$743$			14950.4i			0.738191i	−0.929391	+	0.369096i	$0.879667\pi$
$744$	−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	−0.983741	−	0.179594i	$-0.942522\pi$
$751$	−13324.0	−	23077.8i	−0.647403	−	1.12133i	0.336338	−	0.941741i	$-0.390812\pi$
$752$	−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	−0.857682	−	0.514180i	$-0.828096\pi$
$761$	−18350.8	−	31784.5i	−0.874134	−	1.51404i	−0.0164517	−	0.999865i	$-0.505237\pi$
$762$	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	$-0.839796\pi$
$769$		−	20570.8i		−	0.964633i	0.875997	−	0.482316i	$-0.160204\pi$
$770$		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	−0.374949	−	0.927045i	$-0.622340\pi$
$773$	13225.3	−	22906.9i	0.615370	−	1.06585i	0.990319	−	0.138807i	$-0.0443267\pi$
$774$	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	−0.0529272	−	0.998598i	$-0.516855\pi$
$787$	−20846.2	−	12035.6i	−0.944202	−	0.545136i	−0.891275	+	0.453463i	$0.850188\pi$
$788$	−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	−0.955071	−	0.296376i	$-0.904222\pi$
$809$	−38870.8	−	22442.1i	−1.68928	−	0.975304i	−0.734205	−	0.678928i	$-0.762445\pi$
$810$	−27616.2	−	12604.1i	−1.19794	−	0.546745i
$811$		−	30430.0i		−	1.31756i	−0.752335	−	0.658781i	$-0.771073\pi$
$811$		−	30430.0i		−	1.31756i	0.752335	−	0.658781i	$-0.228927\pi$
$812$		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	−0.799517	−	0.600643i	$-0.794911\pi$
$821$	−15975.4	+	9223.39i	−0.679104	+	0.392081i	0.120413	+	0.992724i	$0.461578\pi$
$822$	−14872.8	+	15600.0i	−0.631081	+	0.661936i
$823$	−17503.0	+	30316.1i	−0.741332	+	1.28402i	0.210557	+	0.977582i	$0.432472\pi$
$823$	−17503.0	+	30316.1i	−0.741332	+	1.28402i	−0.951889	+	0.306443i	$0.900861\pi$
$824$	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	$-0.989955\pi$
$827$		−	1500.81i		−	0.0631056i	0.999502	−	0.0315528i	$-0.0100452\pi$
$828$	22017.0	−	1051.37i	0.924088	−	0.0441278i
$829$	29522.4	+	17044.8i	1.23686	+	0.714101i	0.968451	−	0.249205i	$-0.0801692\pi$
$829$	29522.4	+	17044.8i	1.23686	+	0.714101i	0.268408	+	0.963305i	$0.413503\pi$
$830$	−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	$0.142671\pi$
$853$			21592.3i			0.866711i	−0.901223	+	0.433356i	$0.857329\pi$
$854$		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	0.158528	−	0.987355i	$-0.449325\pi$
$857$	23441.0	−	40600.9i	0.934338	−	1.61832i	0.775810	−	0.630966i	$-0.217341\pi$
$858$	28815.6	+	27472.4i	1.14656	+	1.09311i
$859$	30824.9	−	17796.8i	1.22437	−	0.706889i	0.258522	−	0.966005i	$-0.416765\pi$
$859$	30824.9	−	17796.8i	1.22437	−	0.706889i	0.965846	+	0.259116i	$0.0834312\pi$
$860$	−3999.40			−0.158580
$861$		0			0
$862$	46546.0			1.83917
$863$	−3227.93	+	1863.64i	−0.127323	+	0.0735100i	−0.562309	−	0.826927i	$-0.690087\pi$
$863$	−3227.93	+	1863.64i	−0.127323	+	0.0735100i	0.434986	+	0.900437i	$0.356753\pi$
$864$	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	0.994771	+	0.102128i	$0.0325652\pi$
$877$	15215.0	+	26353.2i	0.585831	+	1.01469i	−0.408940	+	0.912561i	$0.634101\pi$
$878$	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	0.894475	−	0.447117i	$-0.147549\pi$
$887$	1585.62	+	2746.38i	0.0600225	+	0.103962i	−0.834453	+	0.551080i	$0.814216\pi$
$888$	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	−0.999962	−	0.00876232i	$-0.997211\pi$
$907$	−13450.0	+	23296.1i	−0.492392	+	0.852849i	0.507569	+	0.861611i	$0.330544\pi$
$908$	−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	$-0.843787\pi$
$911$		−	25917.8i		−	0.942587i	0.881977	−	0.471293i	$-0.156213\pi$
$912$	−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	0.959440	−	0.281914i	$-0.0909693\pi$
$919$	6563.00	+	11367.4i	0.235575	+	0.408028i	−0.723865	+	0.689942i	$0.757636\pi$
$920$	−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	−0.957736	−	0.287650i	$-0.907126\pi$
$929$	−20613.1	−	35702.9i	−0.727980	−	1.26090i	0.229755	−	0.973248i	$-0.426207\pi$
$930$	−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	$-0.929619\pi$
$937$		−	12580.6i		−	0.438623i	0.975655	−	0.219311i	$-0.0703811\pi$
$938$		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	−0.815631	−	0.578572i	$-0.803610\pi$
$941$	2691.52	−	4661.85i	0.0932423	−	0.161500i	0.908874	+	0.417072i	$0.136944\pi$
$942$	−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	0.526165	−	0.850383i	$-0.323629\pi$
$947$	44462.5	−	25670.5i	1.52570	−	0.880863i	0.999535	−	0.0304810i	$-0.00970390\pi$
$948$	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	$0.185883\pi$
$953$			32440.6i			1.10268i	−0.834281	+	0.551340i	$0.814117\pi$
$954$	−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	0.981904	−	0.189378i	$-0.0606472\pi$
$971$	9892.47	+	17134.3i	0.326946	+	0.566287i	−0.654958	+	0.755665i	$0.727314\pi$
$972$	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	0.943576	−	0.331155i	$-0.107438\pi$
$977$	34464.5	+	19898.1i	1.12858	+	0.651583i	0.184999	+	0.982739i	$0.440772\pi$
$978$	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	−0.989253	−	0.146214i	$-0.953291\pi$
$983$	−11341.7	+	19644.5i	−0.368001	+	0.637397i	0.621252	+	0.783611i	$0.286625\pi$
$984$	−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	−0.106033	−	0.994363i	$-0.533815\pi$
$991$	25211.0	−	43666.7i	0.808127	−	1.39972i	0.914160	−	0.405354i	$-0.132852\pi$
$992$	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	−0.294033	−	0.955795i	$-0.594998\pi$
$997$	−39942.3	−	23060.7i	−1.26879	−	0.732538i	−0.974760	+	0.223257i	$0.928331\pi$
$998$	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.80.2		8
3.2	odd	2	inner	147.4.g.c.80.3		8
7.2	even	3	inner	147.4.g.c.68.4		8
7.3	odd	6		21.4.c.b.20.2	yes	4
7.4	even	3		21.4.c.b.20.1	✓	4
7.5	odd	6	inner	147.4.g.c.68.3		8
7.6	odd	2	inner	147.4.g.c.80.1		8
21.2	odd	6	inner	147.4.g.c.68.1		8
21.5	even	6	inner	147.4.g.c.68.2		8
21.11	odd	6		21.4.c.b.20.4	yes	4
21.17	even	6		21.4.c.b.20.3	yes	4
21.20	even	2	inner	147.4.g.c.80.4		8
28.3	even	6		336.4.k.b.209.1		4
28.11	odd	6		336.4.k.b.209.4		4
84.11	even	6		336.4.k.b.209.2		4
84.59	odd	6		336.4.k.b.209.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.c.b.20.1	✓	4	7.4	even	3
21.4.c.b.20.2	yes	4	7.3	odd	6
21.4.c.b.20.3	yes	4	21.17	even	6
21.4.c.b.20.4	yes	4	21.11	odd	6
147.4.g.c.68.1		8	21.2	odd	6	inner
147.4.g.c.68.2		8	21.5	even	6	inner
147.4.g.c.68.3		8	7.5	odd	6	inner
147.4.g.c.68.4		8	7.2	even	3	inner
147.4.g.c.80.1		8	7.6	odd	2	inner
147.4.g.c.80.2		8	1.1	even	1	trivial
147.4.g.c.80.3		8	3.2	odd	2	inner
147.4.g.c.80.4		8	21.20	even	2	inner
336.4.k.b.209.1		4	28.3	even	6
336.4.k.b.209.2		4	84.11	even	6
336.4.k.b.209.3		4	84.59	odd	6
336.4.k.b.209.4		4	28.11	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

Varieties

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Database

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