LMFDB - Embedded newform 336.4.k.b.209.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,4,Mod(209,336)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(336, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 1, 1])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("336.209"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.k (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,0,0,-28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-6}, \sqrt{-17})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 46x^{2} + 121 $ x^4 + 46*x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			209.4
Root			$-6.57260i$ of defining polynomial
Character	$\chi$	$=$	336.209
Dual form			336.4.k.b.209.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(5.04975 + 1.22474i) q^{3} +10.0995 q^{5} +(-7.00000 + 17.1464i) q^{7} +(24.0000 + 12.3693i) q^{9} -32.9848i q^{11} +56.3383i q^{13} +(51.0000 + 12.3693i) q^{15} +60.5970 q^{17} +36.7423i q^{19} +(-56.3483 + 78.0120i) q^{21} +90.7083i q^{23} -23.0000 q^{25} +(106.045 + 91.8559i) q^{27} +57.7235i q^{29} -254.747i q^{31} +(40.3980 - 166.565i) q^{33} +(-70.6965 + 173.170i) q^{35} +230.000 q^{37} +(-69.0000 + 284.494i) q^{39} -141.393 q^{41} -44.0000 q^{43} +(242.388 + 124.924i) q^{45} +343.383 q^{47} +(-245.000 - 240.050i) q^{49} +(306.000 + 74.2159i) q^{51} +206.155i q^{53} -333.131i q^{55} +(-45.0000 + 185.540i) q^{57} -131.294 q^{59} -71.0352i q^{61} +(-380.090 + 324.929i) q^{63} +568.989i q^{65} +64.0000 q^{67} +(-111.095 + 458.055i) q^{69} +461.788i q^{71} -88.1816i q^{73} +(-116.144 - 28.1691i) q^{75} +(565.572 + 230.894i) q^{77} +442.000 q^{79} +(423.000 + 593.727i) q^{81} +494.876 q^{83} +612.000 q^{85} +(-70.6965 + 291.489i) q^{87} -484.776 q^{89} +(-966.000 - 394.368i) q^{91} +(312.000 - 1286.41i) q^{93} +371.080i q^{95} -1092.47i q^{97} +(408.000 - 791.636i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 28 q^{7} + 96 q^{9} + 204 q^{15} - 84 q^{21} - 92 q^{25} + 920 q^{37} - 276 q^{39} - 176 q^{43} - 980 q^{49} + 1224 q^{51} - 180 q^{57} - 672 q^{63} + 256 q^{67} + 1768 q^{79} + 1692 q^{81} + 2448 q^{85}+ \cdots + 1632 q^{99}+O(q^{100}) $ 4 * q - 28 * q^7 + 96 * q^9 + 204 * q^15 - 84 * q^21 - 92 * q^25 + 920 * q^37 - 276 * q^39 - 176 * q^43 - 980 * q^49 + 1224 * q^51 - 180 * q^57 - 672 * q^63 + 256 * q^67 + 1768 * q^79 + 1692 * q^81 + 2448 * q^85 - 3864 * q^91 + 1248 * q^93 + 1632 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	5.04975	+	1.22474i	0.971825	+	0.235702i
$3$	5.04975	+	1.22474i	0.971825	+	0.235702i
$4$		0			0
$5$	10.0995			0.903327			0.451664	−	0.892188i	$-0.350831\pi$
$5$	10.0995			0.903327			0.451664	+	0.892188i	$0.350831\pi$
$6$		0			0
$7$	−7.00000	+	17.1464i	−0.377964	+	0.925820i
$7$	−7.00000	+	17.1464i	−0.377964	+	0.925820i
$8$		0			0
$9$	24.0000	+	12.3693i	0.888889	+	0.458123i
$10$		0			0
$11$		−	32.9848i		−	0.904119i	−0.891988	−	0.452059i	$-0.850690\pi$
$11$		−	32.9848i		−	0.904119i	0.891988	−	0.452059i	$-0.149310\pi$
$12$		0			0
$13$			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
$16$		0			0
$17$	60.5970			0.864526			0.432263	−	0.901748i	$-0.357715\pi$
$17$	60.5970			0.864526			0.432263	+	0.901748i	$0.357715\pi$
$18$		0			0
$19$			36.7423i			0.443646i	0.975087	+	0.221823i	$0.0712007\pi$
$19$			36.7423i			0.443646i	−0.975087	+	0.221823i	$0.928799\pi$
$20$		0			0
$21$	−56.3483	+	78.0120i	−0.585533	+	0.810648i
$22$		0			0
$23$			90.7083i			0.822348i	0.911557	+	0.411174i	$0.134881\pi$
$23$			90.7083i			0.822348i	−0.911557	+	0.411174i	$0.865119\pi$
$24$		0			0
$25$	−23.0000			−0.184000
$26$		0			0
$27$	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	$0.940833\pi$
$30$		0			0
$31$		−	254.747i		−	1.47593i	−0.674838	−	0.737966i	$-0.735786\pi$
$31$		−	254.747i		−	1.47593i	0.674838	−	0.737966i	$-0.264214\pi$
$32$		0			0
$33$	40.3980	−	166.565i	0.213103	−	0.878645i
$34$		0			0
$35$	−70.6965	+	173.170i	−0.341426	+	0.836318i
$36$		0			0
$37$	230.000			1.02194			0.510970	−	0.859599i	$-0.329286\pi$
$37$	230.000			1.02194			0.510970	+	0.859599i	$0.329286\pi$
$38$		0			0
$39$	−69.0000	+	284.494i	−0.283304	+	1.16809i
$40$		0			0
$41$	−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	$-0.524861\pi$
$43$	−44.0000			−0.156045			−0.0780225	+	0.996952i	$0.524861\pi$
$44$		0			0
$45$	242.388	+	124.924i	0.802957	+	0.413835i
$46$		0			0
$47$	343.383			1.06569			0.532847	−	0.846212i	$-0.321122\pi$
$47$	343.383			1.06569			0.532847	+	0.846212i	$0.321122\pi$
$48$		0			0
$49$	−245.000	−	240.050i	−0.714286	−	0.699854i
$50$		0			0
$51$	306.000	+	74.2159i	0.840168	+	0.203771i
$52$		0			0
$53$			206.155i			0.534294i	0.963656	+	0.267147i	$0.0860810\pi$
$53$			206.155i			0.534294i	−0.963656	+	0.267147i	$0.913919\pi$
$54$		0			0
$55$		−	333.131i		−	0.816715i
$56$		0			0
$57$	−45.0000	+	185.540i	−0.104568	+	0.431146i
$58$		0			0
$59$	−131.294			−0.289711			−0.144856	−	0.989453i	$-0.546272\pi$
$59$	−131.294			−0.289711			−0.144856	+	0.989453i	$0.546272\pi$
$60$		0			0
$61$		−	71.0352i		−	0.149100i	−0.997217	−	0.0745502i	$-0.976248\pi$
$61$		−	71.0352i		−	0.149100i	0.997217	−	0.0745502i	$-0.0237521\pi$
$62$		0			0
$63$	−380.090	+	324.929i	−0.760108	+	0.649797i
$64$		0			0
$65$			568.989i			1.08576i
$66$		0			0
$67$	64.0000			0.116699			0.0583496	−	0.998296i	$-0.481416\pi$
$67$	64.0000			0.116699			0.0583496	+	0.998296i	$0.481416\pi$
$68$		0			0
$69$	−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	$0.873876\pi$
$72$		0			0
$73$		−	88.1816i		−	0.141382i	−0.997498	−	0.0706910i	$-0.977480\pi$
$73$		−	88.1816i		−	0.141382i	0.997498	−	0.0706910i	$-0.0225204\pi$
$74$		0			0
$75$	−116.144	−	28.1691i	−0.178816	−	0.0433692i
$76$		0			0
$77$	565.572	+	230.894i	0.837051	+	0.341725i
$78$		0			0
$79$	442.000			0.629480			0.314740	−	0.949178i	$-0.398083\pi$
$79$	442.000			0.629480			0.314740	+	0.949178i	$0.398083\pi$
$80$		0			0
$81$	423.000	+	593.727i	0.580247	+	0.814441i
$82$		0			0
$83$	494.876			0.654454			0.327227	−	0.944946i	$-0.393886\pi$
$83$	494.876			0.654454			0.327227	+	0.944946i	$0.393886\pi$
$84$		0			0
$85$	612.000			0.780950
$86$		0			0
$87$	−70.6965	+	291.489i	−0.0871203	+	0.359206i
$88$		0			0
$89$	−484.776			−0.577373			−0.288686	−	0.957424i	$-0.593218\pi$
$89$	−484.776			−0.577373			−0.288686	+	0.957424i	$0.593218\pi$
$90$		0			0
$91$	−966.000	−	394.368i	−1.11279	−	0.454297i
$92$		0			0
$93$	312.000	−	1286.41i	0.347881	−	1.43435i
$94$		0			0
$95$			371.080i			0.400757i
$96$		0			0
$97$		−	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
$100$		0			0
$101$	1262.44			1.24374			0.621868	−	0.783122i	$-0.286374\pi$
$101$	1262.44			1.24374			0.621868	+	0.783122i	$0.286374\pi$
$102$		0			0
$103$		−	48.9898i		−	0.0468651i	−0.999725	−	0.0234326i	$-0.992541\pi$
$103$		−	48.9898i		−	0.0468651i	0.999725	−	0.0234326i	$-0.00745950\pi$
$104$		0			0
$105$	−569.090	+	787.883i	−0.528928	+	0.732281i
$106$		0			0
$107$		−	1467.83i		−	1.32617i	−0.748545	−	0.663084i	$-0.769247\pi$
$107$		−	1467.83i		−	1.32617i	0.748545	−	0.663084i	$-0.230753\pi$
$108$		0			0
$109$	−1870.00			−1.64324			−0.821622	−	0.570033i	$-0.806930\pi$
$109$	−1870.00			−1.64324			−0.821622	+	0.570033i	$0.806930\pi$
$110$		0			0
$111$	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	$-0.245390\pi$
$114$		0			0
$115$			916.109i			0.742849i
$116$		0			0
$117$	−696.866	+	1352.12i	−0.550643	+	1.06840i
$118$		0			0
$119$	−424.179	+	1039.02i	−0.326760	+	0.800395i
$120$		0			0
$121$	243.000			0.182569
$122$		0			0
$123$	−714.000	−	173.170i	−0.523408	−	0.126945i
$124$		0			0
$125$	−1494.73			−1.06954
$126$		0			0
$127$	1048.00			0.732244			0.366122	−	0.930567i	$-0.380685\pi$
$127$	1048.00			0.732244			0.366122	+	0.930567i	$0.380685\pi$
$128$		0			0
$129$	−222.189	−	53.8888i	−0.151649	−	0.0367802i
$130$		0			0
$131$	−2555.17			−1.70417			−0.852086	−	0.523401i	$-0.824663\pi$
$131$	−2555.17			−1.70417			−0.852086	+	0.523401i	$0.824663\pi$
$132$		0			0
$133$	−630.000	−	257.196i	−0.410736	−	0.167682i
$134$		0			0
$135$	1071.00	+	927.699i	0.682793	+	0.591434i
$136$		0			0
$137$		−	1006.04i		−	0.627384i	−0.949525	−	0.313692i	$-0.898434\pi$
$137$		−	1006.04i		−	0.627384i	0.949525	−	0.313692i	$-0.101566\pi$
$138$		0			0
$139$		−	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
$142$		0			0
$143$	1858.31			1.08671
$144$		0			0
$145$			582.979i			0.333888i
$146$		0			0
$147$	−943.189	−	1512.26i	−0.529204	−	0.848495i
$148$		0			0
$149$			255.633i			0.140552i	0.997528	+	0.0702760i	$0.0223880\pi$
$149$			255.633i			0.140552i	−0.997528	+	0.0702760i	$0.977612\pi$
$150$		0			0
$151$	−1448.00			−0.780375			−0.390187	−	0.920735i	$-0.627590\pi$
$151$	−1448.00			−0.780375			−0.390187	+	0.920735i	$0.627590\pi$
$152$		0			0
$153$	1454.33	+	749.544i	0.768467	+	0.396059i
$154$		0			0
$155$		−	2572.82i		−	1.33325i
$156$		0			0
$157$		−	3397.44i		−	1.72704i	−0.504314	−	0.863520i	$-0.668255\pi$
$157$		−	3397.44i		−	1.72704i	0.504314	−	0.863520i	$-0.331745\pi$
$158$		0			0
$159$	−252.488	+	1041.03i	−0.125934	+	0.519241i
$160$		0			0
$161$	−1555.32	−	634.958i	−0.761346	−	0.310818i
$162$		0			0
$163$	−3128.00			−1.50309			−0.751546	−	0.659681i	$-0.770691\pi$
$163$	−3128.00			−1.50309			−0.751546	+	0.659681i	$0.770691\pi$
$164$		0			0
$165$	408.000	−	1682.23i	0.192502	−	0.793704i
$166$		0			0
$167$	−706.965			−0.327585			−0.163792	−	0.986495i	$-0.552373\pi$
$167$	−706.965			−0.327585			−0.163792	+	0.986495i	$0.552373\pi$
$168$		0			0
$169$	−977.000			−0.444697
$170$		0			0
$171$	−454.478	+	881.816i	−0.203244	+	0.394352i
$172$		0			0
$173$	−2252.19			−0.989773			−0.494887	−	0.868957i	$-0.664790\pi$
$173$	−2252.19			−0.989773			−0.494887	+	0.868957i	$0.664790\pi$
$174$		0			0
$175$	161.000	−	394.368i	0.0695455	−	0.170351i
$176$		0			0
$177$	−663.000	−	160.801i	−0.281549	−	0.0682856i
$178$		0			0
$179$		−	3496.39i		−	1.45996i	−0.683469	−	0.729980i	$-0.739529\pi$
$179$		−	3496.39i		−	1.45996i	0.683469	−	0.729980i	$-0.260471\pi$
$180$		0			0
$181$		−	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
$184$		0			0
$185$	2322.89			0.923146
$186$		0			0
$187$		−	1998.78i		−	0.781634i
$188$		0			0
$189$	−2317.31	+	1175.30i	−0.891851	+	0.452330i
$190$		0			0
$191$			263.879i			0.0999665i	0.998750	+	0.0499832i	$0.0159168\pi$
$191$			263.879i			0.0999665i	−0.998750	+	0.0499832i	$0.984083\pi$
$192$		0			0
$193$	−652.000			−0.243171			−0.121585	−	0.992581i	$-0.538798\pi$
$193$	−652.000			−0.243171			−0.121585	+	0.992581i	$0.538798\pi$
$194$		0			0
$195$	−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	$-0.119046\pi$
$198$		0			0
$199$		−	4849.99i		−	1.72767i	−0.503773	−	0.863836i	$-0.668055\pi$
$199$		−	4849.99i		−	1.72767i	0.503773	−	0.863836i	$-0.331945\pi$
$200$		0			0
$201$	323.184	+	78.3837i	0.113411	+	0.0275063i
$202$		0			0
$203$	−989.751	−	404.064i	−0.342202	−	0.139703i
$204$		0			0
$205$	−1428.00			−0.486516
$206$		0			0
$207$	−1122.00	+	2177.00i	−0.376736	+	0.730976i
$208$		0			0
$209$	1211.94			0.401109
$210$		0			0
$211$	2224.00			0.725623			0.362812	−	0.931863i	$-0.381817\pi$
$211$	2224.00			0.725623			0.362812	+	0.931863i	$0.381817\pi$
$212$		0			0
$213$	−565.572	+	2331.91i	−0.181936	+	0.750141i
$214$		0			0
$215$	−444.378			−0.140960
$216$		0			0
$217$	4368.00	+	1783.23i	1.36645	+	0.557850i
$218$		0			0
$219$	108.000	−	445.295i	0.0333240	−	0.137399i
$220$		0			0
$221$			3413.93i			1.03912i
$222$		0			0
$223$			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
$226$		0			0
$227$	5948.61			1.73931			0.869654	−	0.493661i	$-0.164342\pi$
$227$	5948.61			1.73931			0.869654	+	0.493661i	$0.164342\pi$
$228$		0			0
$229$		−	3706.08i		−	1.06945i	−0.845025	−	0.534726i	$-0.820415\pi$
$229$		−	3706.08i		−	1.06945i	0.845025	−	0.534726i	$-0.179585\pi$
$230$		0			0
$231$	2573.21	+	1858.64i	0.732922	+	0.529392i
$232$		0			0
$233$		−	956.561i		−	0.268954i	−0.990917	−	0.134477i	$-0.957065\pi$
$233$		−	956.561i		−	0.268954i	0.990917	−	0.134477i	$-0.0429355\pi$
$234$		0			0
$235$	3468.00			0.962670
$236$		0			0
$237$	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	$0.775463\pi$
$240$		0			0
$241$			3786.91i			1.01218i	0.862479	+	0.506092i	$0.168910\pi$
$241$			3786.91i			1.01218i	−0.862479	+	0.506092i	$0.831090\pi$
$242$		0			0
$243$	1408.88	+	3516.24i	0.371933	+	0.928260i
$244$		0			0
$245$	−2474.38	−	2424.39i	−0.645234	−	0.632197i
$246$		0			0
$247$	−2070.00			−0.533243
$248$		0			0
$249$	2499.00	+	606.097i	0.636015	+	0.154256i
$250$		0			0
$251$	−4029.70			−1.01336			−0.506678	−	0.862135i	$-0.669127\pi$
$251$	−4029.70			−1.01336			−0.506678	+	0.862135i	$0.669127\pi$
$252$		0			0
$253$	2992.00			0.743500
$254$		0			0
$255$	3090.45	+	749.544i	0.758947	+	0.184072i
$256$		0			0
$257$	−201.990			−0.0490264			−0.0245132	−	0.999700i	$-0.507804\pi$
$257$	−201.990			−0.0490264			−0.0245132	+	0.999700i	$0.507804\pi$
$258$		0			0
$259$	−1610.00	+	3943.68i	−0.386257	+	0.946132i
$260$		0			0
$261$	−714.000	+	1385.36i	−0.169331	+	0.328551i
$262$		0			0
$263$			8279.20i			1.94113i	0.240840	+	0.970565i	$0.422577\pi$
$263$			8279.20i			1.94113i	−0.240840	+	0.970565i	$0.577423\pi$
$264$		0			0
$265$			2082.07i			0.482643i
$266$		0			0
$267$	−2448.00	−	593.727i	−0.561105	−	0.136088i
$268$		0			0
$269$	5787.02			1.31168			0.655838	−	0.754902i	$-0.272316\pi$
$269$	5787.02			1.31168			0.655838	+	0.754902i	$0.272316\pi$
$270$		0			0
$271$			1219.85i			0.273433i	0.990610	+	0.136717i	$0.0436549\pi$
$271$			1219.85i			0.273433i	−0.990610	+	0.136717i	$0.956345\pi$
$272$		0			0
$273$	−4395.06	−	3174.56i	−0.974363	−	0.703785i
$274$		0			0
$275$			758.651i			0.166358i
$276$		0			0
$277$	−3214.00			−0.697150			−0.348575	−	0.937281i	$-0.613334\pi$
$277$	−3214.00			−0.697150			−0.348575	+	0.937281i	$0.613334\pi$
$278$		0			0
$279$	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	$0.563200\pi$
$282$		0			0
$283$		−	2981.03i		−	0.626162i	−0.949726	−	0.313081i	$-0.898639\pi$
$283$		−	2981.03i		−	0.626162i	0.949726	−	0.313081i	$-0.101361\pi$
$284$		0			0
$285$	−454.478	+	1873.86i	−0.0944594	+	0.389466i
$286$		0			0
$287$	989.751	−	2424.39i	0.203565	−	0.498631i
$288$		0			0
$289$	−1241.00			−0.252595
$290$		0			0
$291$	1338.00	−	5516.72i	0.269536	−	1.11133i
$292$		0			0
$293$	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
$296$		0			0
$297$	3029.85	−	3497.87i	0.591952	−	0.683391i
$298$		0			0
$299$	−5110.35			−0.988425
$300$		0			0
$301$	308.000	−	754.443i	0.0589795	−	0.144470i
$302$		0			0
$303$	6375.00	+	1546.16i	1.20869	+	0.293151i
$304$		0			0
$305$		−	717.420i		−	0.134686i
$306$		0			0
$307$		−	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
$310$		0			0
$311$	8564.38			1.56155			0.780774	−	0.624814i	$-0.214825\pi$
$311$	8564.38			1.56155			0.780774	+	0.624814i	$0.214825\pi$
$312$		0			0
$313$		−	533.989i		−	0.0964308i	−0.998837	−	0.0482154i	$-0.984647\pi$
$313$		−	533.989i		−	0.0964308i	0.998837	−	0.0482154i	$-0.0153534\pi$
$314$		0			0
$315$	−3838.72	+	3281.62i	−0.686626	+	0.586979i
$316$		0			0
$317$			5104.40i			0.904391i	0.891919	+	0.452195i	$0.149359\pi$
$317$			5104.40i			0.904391i	−0.891919	+	0.452195i	$0.850641\pi$
$318$		0			0
$319$	1904.00			0.334180
$320$		0			0
$321$	1797.71	−	7412.16i	0.312581	−	1.28880i
$322$		0			0
$323$			2226.48i			0.383543i
$324$		0			0
$325$		−	1295.78i		−	0.221160i
$326$		0			0
$327$	−9443.04	−	2290.27i	−1.59695	−	0.387316i
$328$		0			0
$329$	−2403.68	+	5887.79i	−0.402794	+	0.986640i
$330$		0			0
$331$	−3632.00			−0.603120			−0.301560	−	0.953447i	$-0.597507\pi$
$331$	−3632.00			−0.603120			−0.301560	+	0.953447i	$0.597507\pi$
$332$		0			0
$333$	5520.00	+	2844.94i	0.908391	+	0.468174i
$334$		0			0
$335$	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	$0.668735\pi$
$338$		0			0
$339$	2050.20	−	8453.19i	0.328471	−	1.35432i
$340$		0			0
$341$	−8402.79			−1.33442
$342$		0			0
$343$	5831.00	−	2520.52i	0.917914	−	0.396780i
$344$		0			0
$345$	−1122.00	+	4626.12i	−0.175091	+	0.721919i
$346$		0			0
$347$		−	1072.01i		−	0.165845i	−0.996556	−	0.0829227i	$-0.973575\pi$
$347$		−	1072.01i		−	0.165845i	0.996556	−	0.0829227i	$-0.0264255\pi$
$348$		0			0
$349$		−	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
$352$		0			0
$353$	5292.14			0.797938			0.398969	−	0.916964i	$-0.369368\pi$
$353$	5292.14			0.797938			0.398969	+	0.916964i	$0.369368\pi$
$354$		0			0
$355$			4663.83i			0.697268i
$356$		0			0
$357$	−3414.54	+	4727.30i	−0.506209	+	0.700826i
$358$		0			0
$359$			3207.78i			0.471588i	0.971803	+	0.235794i	$0.0757690\pi$
$359$			3207.78i			0.471588i	−0.971803	+	0.235794i	$0.924231\pi$
$360$		0			0
$361$	5509.00			0.803178
$362$		0			0
$363$	1227.09	+	297.613i	0.177426	+	0.0430320i
$364$		0			0
$365$		−	890.591i		−	0.127714i
$366$		0			0
$367$			9381.55i			1.33437i	0.744893	+	0.667184i	$0.232500\pi$
$367$			9381.55i			1.33437i	−0.744893	+	0.667184i	$0.767500\pi$
$368$		0			0
$369$	−3393.43	−	1748.94i	−0.478740	−	0.246737i
$370$		0			0
$371$	−3534.83	−	1443.09i	−0.494661	−	0.201944i
$372$		0			0
$373$	4598.00			0.638272			0.319136	−	0.947709i	$-0.396607\pi$
$373$	4598.00			0.638272			0.319136	+	0.947709i	$0.396607\pi$
$374$		0			0
$375$	−7548.00	−	1830.66i	−1.03941	−	0.252093i
$376$		0			0
$377$	−3252.04			−0.444267
$378$		0			0
$379$	−5252.00			−0.711813			−0.355906	−	0.934522i	$-0.615828\pi$
$379$	−5252.00			−0.711813			−0.355906	+	0.934522i	$0.615828\pi$
$380$		0			0
$381$	5292.14	+	1283.53i	0.711613	+	0.172592i
$382$		0			0
$383$	−1918.91			−0.256009			−0.128005	−	0.991774i	$-0.540857\pi$
$383$	−1918.91			−0.256009			−0.128005	+	0.991774i	$0.540857\pi$
$384$		0			0
$385$	5712.00	+	2331.91i	0.756131	+	0.308689i
$386$		0			0
$387$	−1056.00	−	544.250i	−0.138707	−	0.0714878i
$388$		0			0
$389$		−	7067.00i		−	0.921109i	−0.887632	−	0.460554i	$-0.847651\pi$
$389$		−	7067.00i		−	0.921109i	0.887632	−	0.460554i	$-0.152349\pi$
$390$		0			0
$391$			5496.65i			0.710941i
$392$		0			0
$393$	−12903.0	−	3129.44i	−1.65616	−	0.401677i
$394$		0			0
$395$	4463.98			0.568626
$396$		0			0
$397$			13337.5i			1.68612i	0.537822	+	0.843059i	$0.319247\pi$
$397$			13337.5i			1.68612i	−0.537822	+	0.843059i	$0.680753\pi$
$398$		0			0
$399$	−2866.34	−	2070.37i	−0.359641	−	0.259769i
$400$		0			0
$401$		−	13251.7i		−	1.65027i	−0.564939	−	0.825133i	$-0.691100\pi$
$401$		−	13251.7i		−	1.65027i	0.564939	−	0.825133i	$-0.308900\pi$
$402$		0			0
$403$	14352.0			1.77401
$404$		0			0
$405$	4272.09	+	5996.35i	0.524153	+	0.735706i
$406$		0			0
$407$		−	7586.51i		−	0.923955i
$408$		0			0
$409$		−	7461.15i		−	0.902029i	−0.892517	−	0.451015i	$-0.851062\pi$
$409$		−	7461.15i		−	0.902029i	0.892517	−	0.451015i	$-0.148938\pi$
$410$		0			0
$411$	1232.14	−	5080.24i	0.147876	−	0.609708i
$412$		0			0
$413$	919.055	−	2251.22i	0.109501	−	0.268221i
$414$		0			0
$415$	4998.00			0.591186
$416$		0			0
$417$	1707.00	−	7038.14i	0.200461	−	0.826521i
$418$		0			0
$419$	9261.25			1.07981			0.539906	−	0.841725i	$-0.318460\pi$
$419$	9261.25			1.07981			0.539906	+	0.841725i	$0.318460\pi$
$420$		0			0
$421$	−2854.00			−0.330393			−0.165196	−	0.986261i	$-0.552826\pi$
$421$	−2854.00			−0.330393			−0.165196	+	0.986261i	$0.552826\pi$
$422$		0			0
$423$	8241.20	+	4247.42i	0.947283	+	0.488218i
$424$		0			0
$425$	−1393.73			−0.159073
$426$		0			0
$427$	1218.00	+	497.246i	0.138040	+	0.0563547i
$428$		0			0
$429$	9384.00	+	2275.95i	1.05609	+	0.256140i
$430$		0			0
$431$		−	11289.1i		−	1.26166i	−0.775921	−	0.630830i	$-0.782715\pi$
$431$		−	11289.1i		−	1.26166i	0.775921	−	0.630830i	$-0.217285\pi$
$432$		0			0
$433$			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
$436$		0			0
$437$	−3332.84			−0.364831
$438$		0			0
$439$			3003.07i			0.326490i	0.986586	+	0.163245i	$0.0521960\pi$
$439$			3003.07i			0.326490i	−0.986586	+	0.163245i	$0.947804\pi$
$440$		0			0
$441$	−2910.75	−	8791.68i	−0.314301	−	0.949323i
$442$		0			0
$443$			6844.36i			0.734052i	0.930211	+	0.367026i	$0.119624\pi$
$443$			6844.36i			0.734052i	−0.930211	+	0.367026i	$0.880376\pi$
$444$		0			0
$445$	−4896.00			−0.521557
$446$		0			0
$447$	−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	$0.955436\pi$
$450$		0			0
$451$			4663.83i			0.486943i
$452$		0			0
$453$	−7312.04	−	1773.43i	−0.758388	−	0.183936i
$454$		0			0
$455$	−9756.12	−	3982.92i	−1.00522	−	0.410378i
$456$		0			0
$457$	1196.00			0.122421			0.0612106	−	0.998125i	$-0.480504\pi$
$457$	1196.00			0.122421			0.0612106	+	0.998125i	$0.480504\pi$
$458$		0			0
$459$	6426.00	+	5566.19i	0.653464	+	0.566030i
$460$		0			0
$461$	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	$-0.514798\pi$
$463$	−926.000			−0.0929479			−0.0464739	+	0.998920i	$0.514798\pi$
$464$		0			0
$465$	3151.05	−	12992.1i	0.314250	−	1.29569i
$466$		0			0
$467$	−7786.72			−0.771577			−0.385788	−	0.922587i	$-0.626071\pi$
$467$	−7786.72			−0.771577			−0.385788	+	0.922587i	$0.626071\pi$
$468$		0			0
$469$	−448.000	+	1097.37i	−0.0441081	+	0.108042i
$470$		0			0
$471$	4161.00	−	17156.2i	0.407067	−	1.67838i
$472$		0			0
$473$			1451.33i			0.141083i
$474$		0			0
$475$		−	845.074i		−	0.0816308i
$476$		0			0
$477$	−2550.00	+	4947.73i	−0.244772	+	0.474928i
$478$		0			0
$479$	−12503.2			−1.19266			−0.596331	−	0.802739i	$-0.703375\pi$
$479$	−12503.2			−1.19266			−0.596331	+	0.802739i	$0.703375\pi$
$480$		0			0
$481$			12957.8i			1.22833i
$482$		0			0
$483$	−7076.34	−	5111.26i	−0.666635	−	0.481512i
$484$		0			0
$485$		−	11033.4i		−	1.03299i
$486$		0			0
$487$	−13712.0			−1.27587			−0.637936	−	0.770089i	$-0.720212\pi$
$487$	−13712.0			−1.27587			−0.637936	+	0.770089i	$0.720212\pi$
$488$		0			0
$489$	−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	$-0.0854635\pi$
$492$		0			0
$493$			3497.87i			0.319546i
$494$		0			0
$495$	4120.60	−	7995.13i	0.374156	−	0.725969i
$496$		0			0
$497$	−7918.01	−	3232.51i	−0.714631	−	0.291747i
$498$		0			0
$499$	−15476.0			−1.38838			−0.694189	−	0.719792i	$-0.744237\pi$
$499$	−15476.0			−1.38838			−0.694189	+	0.719792i	$0.744237\pi$
$500$		0			0
$501$	−3570.00	−	865.852i	−0.318355	−	0.0772124i
$502$		0			0
$503$	1696.72			0.150403			0.0752017	−	0.997168i	$-0.476040\pi$
$503$	1696.72			0.150403			0.0752017	+	0.997168i	$0.476040\pi$
$504$		0			0
$505$	12750.0			1.12350
$506$		0			0
$507$	−4933.61	−	1196.58i	−0.432168	−	0.104816i
$508$		0			0
$509$	−4231.69			−0.368500			−0.184250	−	0.982879i	$-0.558986\pi$
$509$	−4231.69			−0.368500			−0.184250	+	0.982879i	$0.558986\pi$
$510$		0			0
$511$	1512.00	+	617.271i	0.130894	+	0.0534373i
$512$		0			0
$513$	−3375.00	+	3896.33i	−0.290468	+	0.335336i
$514$		0			0
$515$		−	494.773i		−	0.0423345i
$516$		0			0
$517$		−	11326.4i		−	0.963513i
$518$		0			0
$519$	−11373.0	−	2758.36i	−0.961887	−	0.233292i
$520$		0			0
$521$	19572.8			1.64588			0.822938	−	0.568131i	$-0.192333\pi$
$521$	19572.8			1.64588			0.822938	+	0.568131i	$0.192333\pi$
$522$		0			0
$523$			8369.91i			0.699791i	0.936789	+	0.349895i	$0.113783\pi$
$523$			8369.91i			0.699791i	−0.936789	+	0.349895i	$0.886217\pi$
$524$		0			0
$525$	1296.01	−	1794.28i	0.107738	−	0.149159i
$526$		0			0
$527$		−	15436.9i		−	1.27598i
$528$		0			0
$529$	3939.00			0.323745
$530$		0			0
$531$	−3151.05	−	1624.01i	−0.257521	−	0.132723i
$532$		0			0
$533$		−	7965.84i		−	0.647352i
$534$		0			0
$535$		−	14824.3i		−	1.19796i
$536$		0			0
$537$	4282.19	−	17655.9i	0.344116	−	1.41883i
$538$		0			0
$539$	−7918.01	+	8081.29i	−0.632751	+	0.645799i
$540$		0			0
$541$	−16150.0			−1.28344			−0.641722	−	0.766938i	$-0.721780\pi$
$541$	−16150.0			−1.28344			−0.641722	+	0.766938i	$0.721780\pi$
$542$		0			0
$543$	225.000	−	927.699i	0.0177821	−	0.0733174i
$544$		0			0
$545$	−18886.1			−1.48439
$546$		0			0
$547$	18352.0			1.43451			0.717253	−	0.696813i	$-0.245399\pi$
$547$	18352.0			1.43451			0.717253	+	0.696813i	$0.245399\pi$
$548$		0			0
$549$	878.657	−	1704.84i	0.0683063	−	0.132534i
$550$		0			0
$551$	−2120.90			−0.163980
$552$		0			0
$553$	−3094.00	+	7578.72i	−0.237921	+	0.582785i
$554$		0			0
$555$	11730.0	+	2844.94i	0.897137	+	0.217588i
$556$		0			0
$557$			3323.22i			0.252800i	0.991979	+	0.126400i	$0.0403423\pi$
$557$			3323.22i			0.252800i	−0.991979	+	0.126400i	$0.959658\pi$
$558$		0			0
$559$		−	2478.88i		−	0.187559i
$560$		0			0
$561$	2448.00	−	10093.4i	0.184233	−	0.759612i
$562$		0			0
$563$	14290.8			1.06978			0.534889	−	0.844922i	$-0.320353\pi$
$563$	14290.8			1.06978			0.534889	+	0.844922i	$0.320353\pi$
$564$		0			0
$565$		−	16906.4i		−	1.25886i
$566$		0			0
$567$	−13141.3	+	3096.85i	−0.973338	+	0.229375i
$568$		0			0
$569$			14801.9i			1.09056i	0.838253	+	0.545281i	$0.183577\pi$
$569$			14801.9i			1.09056i	−0.838253	+	0.545281i	$0.816423\pi$
$570$		0			0
$571$	−4136.00			−0.303128			−0.151564	−	0.988447i	$-0.548431\pi$
$571$	−4136.00			−0.303128			−0.151564	+	0.988447i	$0.548431\pi$
$572$		0			0
$573$	−323.184	+	1332.52i	−0.0235623	+	0.0971500i
$574$		0			0
$575$		−	2086.29i		−	0.151312i
$576$		0			0
$577$			19458.7i			1.40395i	0.712202	+	0.701974i	$0.247698\pi$
$577$			19458.7i			1.40395i	−0.712202	+	0.701974i	$0.752302\pi$
$578$		0			0
$579$	−3292.44	−	798.534i	−0.236320	−	0.0573159i
$580$		0			0
$581$	−3464.13	+	8485.35i	−0.247360	+	0.605907i
$582$		0			0
$583$	6800.00			0.483066
$584$		0			0
$585$	−7038.00	+	13655.7i	−0.497411	+	0.965119i
$586$		0			0
$587$	18310.4			1.28748			0.643740	−	0.765244i	$-0.277382\pi$
$587$	18310.4			1.28748			0.643740	+	0.765244i	$0.277382\pi$
$588$		0			0
$589$	9360.00			0.654791
$590$		0			0
$591$	2474.38	−	10202.1i	0.172221	−	0.710083i
$592$		0			0
$593$	7998.81			0.553915			0.276958	−	0.960882i	$-0.410674\pi$
$593$	7998.81			0.553915			0.276958	+	0.960882i	$0.410674\pi$
$594$		0			0
$595$	−4284.00	+	10493.6i	−0.295171	+	0.723019i
$596$		0			0
$597$	5940.00	−	24491.2i	0.407216	−	1.67900i
$598$		0			0
$599$			12435.3i			0.848234i	0.905607	+	0.424117i	$0.139415\pi$
$599$			12435.3i			0.848234i	−0.905607	+	0.424117i	$0.860585\pi$
$600$		0			0
$601$			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
$604$		0			0
$605$	2454.18			0.164920
$606$		0			0
$607$		−	1592.17i		−	0.106465i	−0.998582	−	0.0532324i	$-0.983048\pi$
$607$		−	1592.17i		−	0.106465i	0.998582	−	0.0532324i	$-0.0169524\pi$
$608$		0			0
$609$	−4503.12	−	3252.62i	−0.299632	−	0.216425i
$610$		0			0
$611$			19345.6i			1.28092i
$612$		0			0
$613$	−1786.00			−0.117677			−0.0588384	−	0.998268i	$-0.518740\pi$
$613$	−1786.00			−0.117677			−0.0588384	+	0.998268i	$0.518740\pi$
$614$		0			0
$615$	−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	$-0.0867912\pi$
$618$		0			0
$619$			8301.32i			0.539028i	0.962996	+	0.269514i	$0.0868630\pi$
$619$			8301.32i			0.539028i	−0.962996	+	0.269514i	$0.913137\pi$
$620$		0			0
$621$	−8332.09	+	9619.15i	−0.538414	+	0.621583i
$622$		0			0
$623$	3393.43	−	8312.18i	0.218226	−	0.534543i
$624$		0			0
$625$	−12221.0			−0.782144
$626$		0			0
$627$	6120.00	+	1484.32i	0.389807	+	0.0945422i
$628$		0			0
$629$	13937.3			0.883493
$630$		0			0
$631$	13102.0			0.826596			0.413298	−	0.910596i	$-0.364377\pi$
$631$	13102.0			0.826596			0.413298	+	0.910596i	$0.364377\pi$
$632$		0			0
$633$	11230.6	+	2723.83i	0.705179	+	0.171031i
$634$		0			0
$635$	10584.3			0.661456
$636$		0			0
$637$	13524.0	−	13802.9i	0.841194	−	0.858540i
$638$		0			0
$639$	−5712.00	+	11082.9i	−0.353620	+	0.686124i
$640$		0			0
$641$		−	9837.73i		−	0.606189i	−0.952961	−	0.303094i	$-0.901980\pi$
$641$		−	9837.73i		−	0.606189i	0.952961	−	0.303094i	$-0.0980197\pi$
$642$		0			0
$643$		−	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
$646$		0			0
$647$	−7695.82			−0.467626			−0.233813	−	0.972282i	$-0.575120\pi$
$647$	−7695.82			−0.467626			−0.233813	+	0.972282i	$0.575120\pi$
$648$		0			0
$649$			4330.70i			0.261933i
$650$		0			0
$651$	19873.3	+	14354.5i	1.19646	+	0.864208i
$652$		0			0
$653$			28309.2i			1.69652i	0.529582	+	0.848259i	$0.322349\pi$
$653$			28309.2i			1.69652i	−0.529582	+	0.848259i	$0.677651\pi$
$654$		0			0
$655$	−25806.0			−1.53943
$656$		0			0
$657$	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	$0.762408\pi$
$660$		0			0
$661$		−	10804.7i		−	0.635785i	−0.948127	−	0.317893i	$-0.897025\pi$
$661$		−	10804.7i		−	0.635785i	0.948127	−	0.317893i	$-0.102975\pi$
$662$		0			0
$663$	−4181.20	+	17239.5i	−0.244923	+	1.00984i
$664$		0			0
$665$	−6362.69	−	2597.56i	−0.371029	−	0.151472i
$666$		0			0
$667$	−5236.00			−0.303956
$668$		0			0
$669$	−2346.00	+	9672.81i	−0.135578	+	0.559002i
$670$		0			0
$671$	−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	$0.220328\pi$
$674$		0			0
$675$	−2439.03	−	2112.68i	−0.139079	−	0.120470i
$676$		0			0
$677$	−20491.9			−1.16332			−0.581660	−	0.813432i	$-0.697597\pi$
$677$	−20491.9			−1.16332			−0.581660	+	0.813432i	$0.697597\pi$
$678$		0			0
$679$	18732.0	+	7647.31i	1.05872	+	0.432219i
$680$		0			0
$681$	30039.0	+	7285.53i	1.69030	+	0.409959i
$682$		0			0
$683$		−	725.667i		−	0.0406543i	−0.999793	−	0.0203271i	$-0.993529\pi$
$683$		−	725.667i		−	0.0406543i	0.999793	−	0.0203271i	$-0.00647077\pi$
$684$		0			0
$685$		−	10160.5i		−	0.566733i
$686$		0			0
$687$	4539.00	−	18714.8i	0.252072	−	1.03932i
$688$		0			0
$689$	−11614.4			−0.642198
$690$		0			0
$691$		−	11760.0i		−	0.647426i	−0.946155	−	0.323713i	$-0.895069\pi$
$691$		−	11760.0i		−	0.647426i	0.946155	−	0.323713i	$-0.104931\pi$
$692$		0			0
$693$	10717.7	+	12537.2i	0.587494	+	0.687228i
$694$		0			0
$695$		−	14076.3i		−	0.768265i
$696$		0			0
$697$	−8568.00			−0.465619
$698$		0			0
$699$	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	$0.799378\pi$
$702$		0			0
$703$			8450.74i			0.453379i
$704$		0			0
$705$	17512.5	+	4247.42i	0.935547	+	0.226903i
$706$		0			0
$707$	−8837.07	+	21646.3i	−0.470088	+	1.15148i
$708$		0			0
$709$	−24382.0			−1.29152			−0.645758	−	0.763542i	$-0.723459\pi$
$709$	−24382.0			−1.29152			−0.645758	+	0.763542i	$0.723459\pi$
$710$		0			0
$711$	10608.0	+	5467.24i	0.559537	+	0.288379i
$712$		0			0
$713$	23107.7			1.21373
$714$		0			0
$715$	18768.0			0.981655
$716$		0			0
$717$	−5867.81	+	24193.6i	−0.305631	+	1.26015i
$718$		0			0
$719$	11089.3			0.575187			0.287594	−	0.957753i	$-0.407145\pi$
$719$	11089.3			0.575187			0.287594	+	0.957753i	$0.407145\pi$
$720$		0			0
$721$	840.000	+	342.929i	0.0433887	+	0.0177134i
$722$		0			0
$723$	−4638.00	+	19123.0i	−0.238574	+	0.983666i
$724$		0			0
$725$		−	1327.64i		−	0.0680101i
$726$		0			0
$727$			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
$730$		0			0
$731$	−2666.27			−0.134905
$732$		0			0
$733$		−	22532.9i		−	1.13543i	−0.823225	−	0.567715i	$-0.807828\pi$
$733$		−	22532.9i		−	1.13543i	0.823225	−	0.567715i	$-0.192172\pi$
$734$		0			0
$735$	−9525.75	−	15273.0i	−0.478044	−	0.766468i
$736$		0			0
$737$		−	2111.03i		−	0.105510i
$738$		0			0
$739$	9220.00			0.458949			0.229474	−	0.973315i	$-0.426299\pi$
$739$	9220.00			0.458949			0.229474	+	0.973315i	$0.426299\pi$
$740$		0			0
$741$	−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	$-0.120333\pi$
$744$		0			0
$745$			2581.76i			0.126964i
$746$		0			0
$747$	11877.0	+	6121.27i	0.581737	+	0.299820i
$748$		0			0
$749$	25168.0	+	10274.8i	1.22779	+	0.501245i
$750$		0			0
$751$	−26648.0			−1.29481			−0.647403	−	0.762148i	$-0.724145\pi$
$751$	−26648.0			−1.29481			−0.647403	+	0.762148i	$0.724145\pi$
$752$		0			0
$753$	−20349.0	−	4935.36i	−0.984806	−	0.238850i
$754$		0			0
$755$	−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	$0.525044\pi$
$758$		0			0
$759$	15108.9	+	3664.44i	0.722552	+	0.175245i
$760$		0			0
$761$	36701.6			1.74827			0.874134	−	0.485685i	$-0.161430\pi$
$761$	36701.6			1.74827			0.874134	+	0.485685i	$0.161430\pi$
$762$		0			0
$763$	13090.0	−	32063.8i	0.621088	−	1.52135i
$764$		0			0
$765$	14688.0	+	7570.02i	0.694177	+	0.357771i
$766$		0			0
$767$		−	7396.85i		−	0.348220i
$768$		0			0
$769$		−	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
$772$		0			0
$773$	−26450.6			−1.23074			−0.615370	−	0.788238i	$-0.710993\pi$
$773$	−26450.6			−1.23074			−0.615370	+	0.788238i	$0.710993\pi$
$774$		0			0
$775$			5859.18i			0.271572i
$776$		0			0
$777$	−12960.1	+	17942.8i	−0.598380	+	0.828434i
$778$		0			0
$779$		−	5195.11i		−	0.238940i
$780$		0			0
$781$	15232.0			0.697879
$782$		0			0
$783$	−5302.24	+	6121.27i	−0.242001	+	0.279383i
$784$		0			0
$785$		−	34312.5i		−	1.56008i
$786$		0			0
$787$		−	24071.1i		−	1.09027i	−0.838348	−	0.545136i	$-0.816478\pi$
$787$		−	24071.1i		−	1.09027i	0.838348	−	0.545136i	$-0.183522\pi$
$788$		0			0
$789$	−10139.9	+	41807.9i	−0.457529	+	1.88644i
$790$		0			0
$791$	28702.8	+	11717.9i	1.29021	+	0.526725i
$792$		0			0
$793$	4002.00			0.179212
$794$		0			0
$795$	−2550.00	+	10513.9i	−0.113760	+	0.469044i
$796$		0			0
$797$	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
$800$		0			0
$801$	−11634.6	−	5996.35i	−0.513220	−	0.264508i
$802$		0			0
$803$	−2908.66			−0.127826
$804$		0			0
$805$	−15708.0	−	6412.76i	−0.687744	−	0.280770i
$806$		0			0
$807$	29223.0	+	7087.62i	1.27472	+	0.309165i
$808$		0			0
$809$			44884.1i			1.95061i	0.220867	+	0.975304i	$0.429111\pi$
$809$			44884.1i			1.95061i	−0.220867	+	0.975304i	$0.570889\pi$
$810$		0			0
$811$			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
$814$		0			0
$815$	−31591.3			−1.35778
$816$		0			0
$817$		−	1616.66i		−	0.0692287i
$818$		0			0
$819$	−18305.9	−	21413.6i	−0.781027	−	0.913616i
$820$		0			0
$821$		−	18446.8i		−	0.784162i	−0.919931	−	0.392081i	$-0.871755\pi$
$821$		−	18446.8i		−	0.784162i	0.919931	−	0.392081i	$-0.128245\pi$
$822$		0			0
$823$	−35006.0			−1.48266			−0.741332	−	0.671138i	$-0.765806\pi$
$823$	−35006.0			−1.48266			−0.741332	+	0.671138i	$0.765806\pi$
$824$		0			0
$825$	−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	$0.989955\pi$
$828$		0			0
$829$		−	34089.5i		−	1.42820i	−0.700043	−	0.714101i	$-0.746836\pi$
$829$		−	34089.5i		−	1.42820i	0.700043	−	0.714101i	$-0.253164\pi$
$830$		0			0
$831$	−16229.9	−	3936.33i	−0.677508	−	0.164320i
$832$		0			0
$833$	−14846.3	−	14546.3i	−0.617518	−	0.605042i
$834$		0			0
$835$	−7140.00			−0.295916
$836$		0			0
$837$	23400.0	−	27014.6i	0.966335	−	1.11560i
$838$		0			0
$839$	−989.751			−0.0407271			−0.0203635	−	0.999793i	$-0.506482\pi$
$839$	−989.751			−0.0407271			−0.0203635	+	0.999793i	$0.506482\pi$
$840$		0			0
$841$	21057.0			0.863381
$842$		0			0
$843$	−11311.4	+	46638.3i	−0.462143	+	1.90547i
$844$		0			0
$845$	−9867.22			−0.401707
$846$		0			0
$847$	−1701.00	+	4166.58i	−0.0690048	+	0.169027i
$848$		0			0
$849$	3651.00	−	15053.5i	0.147588	−	0.608520i
$850$		0			0
$851$			20862.9i			0.840390i
$852$		0			0
$853$			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
$856$		0			0
$857$	−46881.9			−1.86868			−0.934338	−	0.356388i	$-0.884008\pi$
$857$	−46881.9			−1.86868			−0.934338	+	0.356388i	$0.884008\pi$
$858$		0			0
$859$		−	35593.5i		−	1.41378i	−0.707324	−	0.706889i	$-0.750098\pi$
$859$		−	35593.5i		−	1.41378i	0.707324	−	0.706889i	$-0.249902\pi$
$860$		0			0
$861$	7967.25	−	11030.4i	0.315358	−	0.436601i
$862$		0			0
$863$			3727.29i			0.147020i	0.997294	+	0.0735100i	$0.0234201\pi$
$863$			3727.29i			0.147020i	−0.997294	+	0.0735100i	$0.976580\pi$
$864$		0			0
$865$	−22746.0			−0.894089
$866$		0			0
$867$	−6266.74	−	1519.91i	−0.245478	−	0.0595372i
$868$		0			0
$869$		−	14579.3i		−	0.569124i
$870$		0			0
$871$			3605.65i			0.140267i
$872$		0			0
$873$	13513.1	−	26219.3i	0.523884	−	1.01648i
$874$		0			0
$875$	10463.1	−	25629.2i	0.404248	−	0.990201i
$876$		0			0
$877$	−30430.0			−1.17166			−0.585831	−	0.810433i	$-0.699232\pi$
$877$	−30430.0			−1.17166			−0.585831	+	0.810433i	$0.699232\pi$
$878$		0			0
$879$	26061.0	+	6320.72i	1.00002	+	0.242540i
$880$		0			0
$881$	−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	$-0.635245\pi$
$883$	−21632.0			−0.824433			−0.412217	+	0.911086i	$0.635245\pi$
$884$		0			0
$885$	−6695.97	−	1624.01i	−0.254331	−	0.0616842i
$886$		0			0
$887$	3171.24			0.120045			0.0600225	−	0.998197i	$-0.480883\pi$
$887$	3171.24			0.120045			0.0600225	+	0.998197i	$0.480883\pi$
$888$		0			0
$889$	−7336.00	+	17969.5i	−0.276762	+	0.677926i
$890$		0			0
$891$	19584.0	−	13952.6i	0.736351	−	0.524612i
$892$		0			0
$893$			12616.7i			0.472790i
$894$		0			0
$895$		−	35311.8i		−	1.31882i
$896$		0			0
$897$	−25806.0	−	6258.87i	−0.960577	−	0.232974i
$898$		0			0
$899$	14704.9			0.545534
$900$		0			0
$901$			12492.4i			0.461911i
$902$		0			0
$903$	2479.32	−	3432.53i	0.0913696	−	0.126498i
$904$		0			0
$905$		−	1855.40i		−	0.0681497i
$906$		0			0
$907$	−26900.0			−0.984785			−0.492392	−	0.870373i	$-0.663877\pi$
$907$	−26900.0			−0.984785			−0.492392	+	0.870373i	$0.663877\pi$
$908$		0			0
$909$	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	$0.843787\pi$
$912$		0			0
$913$		−	16323.4i		−	0.591704i
$914$		0			0
$915$	878.657	−	3622.80i	0.0317459	−	0.130892i
$916$		0			0
$917$	17886.2	−	43812.1i	0.644117	−	1.57776i
$918$		0			0
$919$	13126.0			0.471150			0.235575	−	0.971856i	$-0.424303\pi$
$919$	13126.0			0.471150			0.235575	+	0.971856i	$0.424303\pi$
$920$		0			0
$921$	2295.00	−	9462.53i	0.0821095	−	0.338546i
$922$		0			0
$923$	−26016.3			−0.927777
$924$		0			0
$925$	−5290.00			−0.188037
$926$		0			0
$927$	605.970	−	1175.76i	0.0214700	−	0.0416579i
$928$		0			0
$929$	41226.2			1.45596			0.727980	−	0.685598i	$-0.240459\pi$
$929$	41226.2			1.45596			0.727980	+	0.685598i	$0.240459\pi$
$930$		0			0
$931$	8820.00	−	9001.87i	0.310487	−	0.316890i
$932$		0			0
$933$	43248.0	+	10489.2i	1.51755	+	0.368060i
$934$		0			0
$935$		−	20186.7i		−	0.706071i
$936$		0			0
$937$		−	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
$940$		0			0
$941$	−5383.04			−0.186485			−0.0932423	−	0.995643i	$-0.529723\pi$
$941$	−5383.04			−0.186485			−0.0932423	+	0.995643i	$0.529723\pi$
$942$		0			0
$943$		−	12825.5i		−	0.442902i
$944$		0			0
$945$	−23403.7	+	11869.9i	−0.805633	+	0.408602i
$946$		0			0
$947$		−	51340.9i		−	1.76173i	−0.473370	−	0.880863i	$-0.656963\pi$
$947$		−	51340.9i		−	1.76173i	0.473370	−	0.880863i	$-0.343037\pi$
$948$		0			0
$949$	4968.00			0.169935
$950$		0			0
$951$	−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	$0.814117\pi$
$954$		0			0
$955$			2665.04i			0.0903024i
$956$		0			0
$957$	9614.73	+	2331.91i	0.324765	+	0.0787671i
$958$		0			0
$959$	17250.0	+	7042.26i	0.580845	+	0.237129i
$960$		0			0
$961$	−35105.0			−1.17838
$962$		0			0
$963$	18156.0	−	35227.8i	0.607548	−	1.17882i
$964$		0			0
$965$	−6584.88			−0.219663
$966$		0			0
$967$	−34232.0			−1.13839			−0.569197	−	0.822201i	$-0.692746\pi$
$967$	−34232.0			−1.13839			−0.569197	+	0.822201i	$0.692746\pi$
$968$		0			0
$969$	−2726.87	+	11243.2i	−0.0904020	+	0.372737i
$970$		0			0
$971$	19784.9			0.653891			0.326946	−	0.945043i	$-0.393981\pi$
$971$	19784.9			0.653891			0.326946	+	0.945043i	$0.393981\pi$
$972$		0			0
$973$	23898.0	+	9756.32i	0.787394	+	0.321452i
$974$		0			0
$975$	1587.00	−	6543.37i	0.0521279	−	0.214929i
$976$		0			0
$977$		−	39796.2i		−	1.30317i	−0.758577	−	0.651583i	$-0.774105\pi$
$977$		−	39796.2i		−	1.30317i	0.758577	−	0.651583i	$-0.225895\pi$
$978$		0			0
$979$			15990.3i			0.522013i
$980$		0			0
$981$	−44880.0	−	23130.6i	−1.46066	−	0.752807i
$982$		0			0
$983$	−22683.5			−0.736003			−0.368001	−	0.929825i	$-0.619958\pi$
$983$	−22683.5			−0.736003			−0.368001	+	0.929825i	$0.619958\pi$
$984$		0			0
$985$		−	20404.2i		−	0.660034i
$986$		0			0
$987$	−19349.0	+	26788.0i	−0.623999	+	0.863902i
$988$		0			0
$989$		−	3991.17i		−	0.128323i
$990$		0			0
$991$	50422.0			1.61625			0.808127	−	0.589008i	$-0.200481\pi$
$991$	50422.0			1.61625			0.808127	+	0.589008i	$0.200481\pi$
$992$		0			0
$993$	−18340.7	−	4448.27i	−0.586127	−	0.142157i
$994$		0			0
$995$		−	48982.5i		−	1.56065i
$996$		0			0
$997$			46121.4i			1.46508i	0.680726	+	0.732538i	$0.261664\pi$
$997$			46121.4i			1.46508i	−0.680726	+	0.732538i	$0.738336\pi$
$998$		0			0
$999$	24390.3	+	21126.8i	0.772448	+	0.669093i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.k.b.209.4		4
3.2	odd	2	inner	336.4.k.b.209.2		4
4.3	odd	2		21.4.c.b.20.1	✓	4
7.6	odd	2	inner	336.4.k.b.209.1		4
12.11	even	2		21.4.c.b.20.4	yes	4
21.20	even	2	inner	336.4.k.b.209.3		4
28.3	even	6		147.4.g.c.68.3		8
28.11	odd	6		147.4.g.c.68.4		8
28.19	even	6		147.4.g.c.80.1		8
28.23	odd	6		147.4.g.c.80.2		8
28.27	even	2		21.4.c.b.20.2	yes	4
84.11	even	6		147.4.g.c.68.1		8
84.23	even	6		147.4.g.c.80.3		8
84.47	odd	6		147.4.g.c.80.4		8
84.59	odd	6		147.4.g.c.68.2		8
84.83	odd	2		21.4.c.b.20.3	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.c.b.20.1	✓	4	4.3	odd	2
21.4.c.b.20.2	yes	4	28.27	even	2
21.4.c.b.20.3	yes	4	84.83	odd	2
21.4.c.b.20.4	yes	4	12.11	even	2
147.4.g.c.68.1		8	84.11	even	6
147.4.g.c.68.2		8	84.59	odd	6
147.4.g.c.68.3		8	28.3	even	6
147.4.g.c.68.4		8	28.11	odd	6
147.4.g.c.80.1		8	28.19	even	6
147.4.g.c.80.2		8	28.23	odd	6
147.4.g.c.80.3		8	84.23	even	6
147.4.g.c.80.4		8	84.47	odd	6
336.4.k.b.209.1		4	7.6	odd	2	inner
336.4.k.b.209.2		4	3.2	odd	2	inner
336.4.k.b.209.3		4	21.20	even	2	inner
336.4.k.b.209.4		4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.k (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(5.04975 + 1.22474i) q^{3} +10.0995 q^{5} +(-7.00000 + 17.1464i) q^{7} +(24.0000 + 12.3693i) q^{9} -32.9848i q^{11} +56.3383i q^{13} +(51.0000 + 12.3693i) q^{15} +60.5970 q^{17} +36.7423i q^{19} +(-56.3483 + 78.0120i) q^{21} +90.7083i q^{23} -23.0000 q^{25} +(106.045 + 91.8559i) q^{27} +57.7235i q^{29} -254.747i q^{31} +(40.3980 - 166.565i) q^{33} +(-70.6965 + 173.170i) q^{35} +230.000 q^{37} +(-69.0000 + 284.494i) q^{39} -141.393 q^{41} -44.0000 q^{43} +(242.388 + 124.924i) q^{45} +343.383 q^{47} +(-245.000 - 240.050i) q^{49} +(306.000 + 74.2159i) q^{51} +206.155i q^{53} -333.131i q^{55} +(-45.0000 + 185.540i) q^{57} -131.294 q^{59} -71.0352i q^{61} +(-380.090 + 324.929i) q^{63} +568.989i q^{65} +64.0000 q^{67} +(-111.095 + 458.055i) q^{69} +461.788i q^{71} -88.1816i q^{73} +(-116.144 - 28.1691i) q^{75} +(565.572 + 230.894i) q^{77} +442.000 q^{79} +(423.000 + 593.727i) q^{81} +494.876 q^{83} +612.000 q^{85} +(-70.6965 + 291.489i) q^{87} -484.776 q^{89} +(-966.000 - 394.368i) q^{91} +(312.000 - 1286.41i) q^{93} +371.080i q^{95} -1092.47i q^{97} +(408.000 - 791.636i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 28 q^{7} + 96 q^{9} + 204 q^{15} - 84 q^{21} - 92 q^{25} + 920 q^{37} - 276 q^{39} - 176 q^{43} - 980 q^{49} + 1224 q^{51} - 180 q^{57} - 672 q^{63} + 256 q^{67} + 1768 q^{79} + 1692 q^{81} + 2448 q^{85}+ \cdots + 1632 q^{99}+O(q^{100}) \) 4 * q - 28 * q^7 + 96 * q^9 + 204 * q^15 - 84 * q^21 - 92 * q^25 + 920 * q^37 - 276 * q^39 - 176 * q^43 - 980 * q^49 + 1224 * q^51 - 180 * q^57 - 672 * q^63 + 256 * q^67 + 1768 * q^79 + 1692 * q^81 + 2448 * q^85 - 3864 * q^91 + 1248 * q^93 + 1632 * q^99

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