LMFDB - Embedded newform 336.4.k.b.209.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,4,Mod(209,336)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			209.1
Root			$-1.67362i$ of defining polynomial
Character	$\chi$	$=$	336.209
Dual form			336.4.k.b.209.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.04975 - 1.22474i) q^{3} -10.0995 q^{5} +(-7.00000 - 17.1464i) q^{7} +(24.0000 + 12.3693i) q^{9} +O(q^{10})$	\(q+(-5.04975 - 1.22474i) q^{3} -10.0995 q^{5} +(-7.00000 - 17.1464i) q^{7} +(24.0000 + 12.3693i) q^{9} -32.9848i q^{11} -56.3383i q^{13} +(51.0000 + 12.3693i) q^{15} -60.5970 q^{17} -36.7423i q^{19} +(14.3483 + 95.1584i) q^{21} +90.7083i q^{23} -23.0000 q^{25} +(-106.045 - 91.8559i) q^{27} +57.7235i q^{29} +254.747i q^{31} +(-40.3980 + 166.565i) q^{33} +(70.6965 + 173.170i) q^{35} +230.000 q^{37} +(-69.0000 + 284.494i) q^{39} +141.393 q^{41} -44.0000 q^{43} +(-242.388 - 124.924i) q^{45} -343.383 q^{47} +(-245.000 + 240.050i) q^{49} +(306.000 + 74.2159i) q^{51} +206.155i q^{53} +333.131i q^{55} +(-45.0000 + 185.540i) q^{57} +131.294 q^{59} +71.0352i q^{61} +(44.0896 - 498.099i) q^{63} +568.989i q^{65} +64.0000 q^{67} +(111.095 - 458.055i) q^{69} +461.788i q^{71} +88.1816i q^{73} +(116.144 + 28.1691i) q^{75} +(-565.572 + 230.894i) q^{77} +442.000 q^{79} +(423.000 + 593.727i) q^{81} -494.876 q^{83} +612.000 q^{85} +(70.6965 - 291.489i) q^{87} +484.776 q^{89} +(-966.000 + 394.368i) q^{91} +(312.000 - 1286.41i) q^{93} +371.080i q^{95} +1092.47i q^{97} +(408.000 - 791.636i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 28 q^{7} + 96 q^{9}+O(q^{10}) $ 4 * q - 28 * q^7 + 96 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	$-0.649169\pi$
$5$	−10.0995			−0.903327			−0.451664	+	0.892188i	$0.649169\pi$
$6$		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	$-0.794778\pi$
$13$		−	56.3383i		−	1.20196i	0.799266	−	0.600978i	$-0.205222\pi$
$14$		0			0
$15$	51.0000	+	12.3693i	0.877876	+	0.212916i
$16$		0			0
$17$	−60.5970			−0.864526			−0.432263	−	0.901748i	$-0.642285\pi$
$17$	−60.5970			−0.864526			−0.432263	+	0.901748i	$0.642285\pi$
$18$		0			0
$19$		−	36.7423i		−	0.443646i	−0.975087	−	0.221823i	$-0.928799\pi$
$19$		−	36.7423i		−	0.443646i	0.975087	−	0.221823i	$-0.0712007\pi$
$20$		0			0
$21$	14.3483	+	95.1584i	0.149098	+	0.988822i
$22$		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	$0.264214\pi$
$31$			254.747i			1.47593i	−0.674838	+	0.737966i	$0.735786\pi$
$32$		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	$-0.413211\pi$
$41$	141.393			0.538583			0.269291	+	0.963059i	$0.413211\pi$
$42$		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	$-0.678878\pi$
$47$	−343.383			−1.06569			−0.532847	+	0.846212i	$0.678878\pi$
$48$		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	$-0.453728\pi$
$59$	131.294			0.289711			0.144856	+	0.989453i	$0.453728\pi$
$60$		0			0
$61$			71.0352i			0.149100i	0.997217	+	0.0745502i	$0.0237521\pi$
$61$			71.0352i			0.149100i	−0.997217	+	0.0745502i	$0.976248\pi$
$62$		0			0
$63$	44.0896	−	498.099i	0.0881709	−	0.996105i
$64$		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	$0.0225204\pi$
$73$			88.1816i			0.141382i	−0.997498	+	0.0706910i	$0.977480\pi$
$74$		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	$-0.606114\pi$
$83$	−494.876			−0.654454			−0.327227	+	0.944946i	$0.606114\pi$
$84$		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	$-0.406782\pi$
$89$	484.776			0.577373			0.288686	+	0.957424i	$0.406782\pi$
$90$		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	$0.193744\pi$
$97$			1092.47i			1.14354i	−0.820413	+	0.571772i	$0.806256\pi$
$98$		0			0
$99$	408.000	−	791.636i	0.414197	−	0.803661i
$100$		0			0
$101$	−1262.44			−1.24374			−0.621868	−	0.783122i	$-0.713626\pi$
$101$	−1262.44			−1.24374			−0.621868	+	0.783122i	$0.713626\pi$
$102$		0			0
$103$			48.9898i			0.0468651i	0.999725	+	0.0234326i	$0.00745950\pi$
$103$			48.9898i			0.0468651i	−0.999725	+	0.0234326i	$0.992541\pi$
$104$		0			0
$105$	−144.910	−	961.053i	−0.134684	−	0.893230i
$106$		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	$-0.175337\pi$
$131$	2555.17			1.70417			0.852086	+	0.523401i	$0.175337\pi$
$132$		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	$0.139811\pi$
$139$			1393.76i			0.850483i	−0.905080	+	0.425242i	$0.860189\pi$
$140$		0			0
$141$	1734.00	+	420.557i	1.03567	+	0.251186i
$142$		0			0
$143$	−1858.31			−1.08671
$144$		0			0
$145$		−	582.979i		−	0.333888i
$146$		0			0
$147$	1531.19	−	912.131i	0.859118	−	0.511777i
$148$		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	$0.331745\pi$
$157$			3397.44i			1.72704i	−0.504314	+	0.863520i	$0.668255\pi$
$158$		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	$-0.447627\pi$
$167$	706.965			0.327585			0.163792	+	0.986495i	$0.447627\pi$
$168$		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	$-0.335210\pi$
$173$	2252.19			0.989773			0.494887	+	0.868957i	$0.335210\pi$
$174$		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	$0.0120100\pi$
$181$			183.712i			0.0754430i	−0.999288	+	0.0377215i	$0.987990\pi$
$182$		0			0
$183$	87.0000	−	358.710i	0.0351433	−	0.144900i
$184$		0			0
$185$	−2322.89			−0.923146
$186$		0			0
$187$			1998.78i			0.781634i
$188$		0			0
$189$	−832.686	+	2461.28i	−0.320471	+	0.947258i
$190$		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	$0.331945\pi$
$199$			4849.99i			1.72767i	−0.503773	+	0.863836i	$0.668055\pi$
$200$		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	$-0.907141\pi$
$223$		−	1915.50i		−	0.575208i	0.957749	−	0.287604i	$-0.0928587\pi$
$224$		0			0
$225$	−552.000	−	284.494i	−0.163556	−	0.0842946i
$226$		0			0
$227$	−5948.61			−1.73931			−0.869654	−	0.493661i	$-0.835658\pi$
$227$	−5948.61			−1.73931			−0.869654	+	0.493661i	$0.835658\pi$
$228$		0			0
$229$			3706.08i			1.06945i	0.845025	+	0.534726i	$0.179585\pi$
$229$			3706.08i			1.06945i	−0.845025	+	0.534726i	$0.820415\pi$
$230$		0			0
$231$	3138.79	−	473.275i	0.894013	−	0.134802i
$232$		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	$-0.831090\pi$
$241$		−	3786.91i		−	1.01218i	0.862479	−	0.506092i	$-0.168910\pi$
$242$		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	$-0.330873\pi$
$251$	4029.70			1.01336			0.506678	+	0.862135i	$0.330873\pi$
$252$		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	$-0.492196\pi$
$257$	201.990			0.0490264			0.0245132	+	0.999700i	$0.492196\pi$
$258$		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	$-0.727684\pi$
$269$	−5787.02			−1.31168			−0.655838	+	0.754902i	$0.727684\pi$
$270$		0			0
$271$		−	1219.85i		−	0.273433i	−0.990610	−	0.136717i	$-0.956345\pi$
$271$		−	1219.85i		−	0.273433i	0.990610	−	0.136717i	$-0.0436549\pi$
$272$		0			0
$273$	5361.06	−	808.356i	1.18852	−	0.179209i
$274$		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	$0.101361\pi$
$283$			2981.03i			0.626162i	−0.949726	+	0.313081i	$0.898639\pi$
$284$		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	$-0.672024\pi$
$293$	−5160.85			−1.02901			−0.514505	+	0.857487i	$0.672024\pi$
$294$		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	$0.0557276\pi$
$307$			1873.86i			0.348361i	−0.984714	+	0.174180i	$0.944272\pi$
$308$		0			0
$309$	60.0000	−	247.386i	0.0110462	−	0.0455447i
$310$		0			0
$311$	−8564.38			−1.56155			−0.780774	−	0.624814i	$-0.785175\pi$
$311$	−8564.38			−1.56155			−0.780774	+	0.624814i	$0.785175\pi$
$312$		0			0
$313$			533.989i			0.0964308i	0.998837	+	0.0482154i	$0.0153534\pi$
$313$			533.989i			0.0964308i	−0.998837	+	0.0482154i	$0.984647\pi$
$314$		0			0
$315$	−445.283	+	5030.56i	−0.0796472	+	0.899809i
$316$		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	$0.160165\pi$
$349$			6287.84i			0.964414i	−0.876057	+	0.482207i	$0.839835\pi$
$350$		0			0
$351$	−5175.00	+	5974.38i	−0.786955	+	0.908515i
$352$		0			0
$353$	−5292.14			−0.797938			−0.398969	−	0.916964i	$-0.630632\pi$
$353$	−5292.14			−0.797938			−0.398969	+	0.916964i	$0.630632\pi$
$354$		0			0
$355$		−	4663.83i		−	0.697268i
$356$		0			0
$357$	−869.462	−	5766.32i	−0.128899	−	0.854863i
$358$		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	$-0.767500\pi$
$367$		−	9381.55i		−	1.33437i	0.744893	−	0.667184i	$-0.232500\pi$
$368$		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	$-0.459143\pi$
$383$	1918.91			0.256009			0.128005	+	0.991774i	$0.459143\pi$
$384$		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	$-0.680753\pi$
$397$		−	13337.5i		−	1.68612i	0.537822	−	0.843059i	$-0.319247\pi$
$398$		0			0
$399$	3496.34	−	527.189i	0.438687	−	0.0661465i
$400$		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	$0.148938\pi$
$409$			7461.15i			0.902029i	−0.892517	+	0.451015i	$0.851062\pi$
$410$		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	$-0.681540\pi$
$419$	−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	$0.552826\pi$
$422$		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	$-0.742570\pi$
$433$		−	13036.2i		−	1.44683i	0.690411	−	0.723417i	$-0.257430\pi$
$434$		0			0
$435$	−714.000	+	2943.90i	−0.0786981	+	0.324481i
$436$		0			0
$437$	3332.84			0.364831
$438$		0			0
$439$		−	3003.07i		−	0.326490i	−0.986586	−	0.163245i	$-0.947804\pi$
$439$		−	3003.07i		−	0.326490i	0.986586	−	0.163245i	$-0.0521960\pi$
$440$		0			0
$441$	−8849.25	+	2730.72i	−0.955540	+	0.294862i
$442$		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	$-0.588673\pi$
$461$	−5443.63			−0.549968			−0.274984	+	0.961449i	$0.588673\pi$
$462$		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	$-0.373929\pi$
$467$	7786.72			0.771577			0.385788	+	0.922587i	$0.373929\pi$
$468$		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	$-0.296625\pi$
$479$	12503.2			1.19266			0.596331	+	0.802739i	$0.296625\pi$
$480$		0			0
$481$		−	12957.8i		−	1.22833i
$482$		0			0
$483$	−8631.66	+	1301.51i	−0.813156	+	0.122610i
$484$		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	$-0.523960\pi$
$503$	−1696.72			−0.150403			−0.0752017	+	0.997168i	$0.523960\pi$
$504$		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	$-0.441014\pi$
$509$	4231.69			0.368500			0.184250	+	0.982879i	$0.441014\pi$
$510$		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	$-0.807667\pi$
$521$	−19572.8			−1.64588			−0.822938	+	0.568131i	$0.807667\pi$
$522$		0			0
$523$		−	8369.91i		−	0.699791i	−0.936789	−	0.349895i	$-0.886217\pi$
$523$		−	8369.91i		−	0.699791i	0.936789	−	0.349895i	$-0.113783\pi$
$524$		0			0
$525$	−330.010	−	2188.64i	−0.0274339	−	0.181943i
$526$		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	$-0.679647\pi$
$563$	−14290.8			−1.06978			−0.534889	+	0.844922i	$0.679647\pi$
$564$		0			0
$565$			16906.4i			1.25886i
$566$		0			0
$567$	7219.30	−	11409.0i	0.534713	−	0.845034i
$568$		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	$-0.752302\pi$
$577$		−	19458.7i		−	1.40395i	0.712202	−	0.701974i	$-0.247698\pi$
$578$		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	$-0.722618\pi$
$587$	−18310.4			−1.28748			−0.643740	+	0.765244i	$0.722618\pi$
$588$		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	$-0.589326\pi$
$593$	−7998.81			−0.553915			−0.276958	+	0.960882i	$0.589326\pi$
$594$		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	$-0.783154\pi$
$601$		−	18557.3i		−	1.25952i	0.776791	−	0.629758i	$-0.216846\pi$
$602$		0			0
$603$	1536.00	+	791.636i	0.103733	+	0.0534626i
$604$		0			0
$605$	−2454.18			−0.164920
$606$		0			0
$607$			1592.17i			0.106465i	0.998582	+	0.0532324i	$0.0169524\pi$
$607$			1592.17i			0.106465i	−0.998582	+	0.0532324i	$0.983048\pi$
$608$		0			0
$609$	−5492.88	+	828.232i	−0.365489	+	0.0551094i
$610$		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	$-0.913137\pi$
$619$		−	8301.32i		−	0.539028i	0.962996	−	0.269514i	$-0.0868630\pi$
$620$		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	$0.0953625\pi$
$643$			9624.05i			0.590257i	−0.955458	+	0.295129i	$0.904638\pi$
$644$		0			0
$645$	−2244.00	−	544.250i	−0.136988	−	0.0332245i
$646$		0			0
$647$	7695.82			0.467626			0.233813	−	0.972282i	$-0.424880\pi$
$647$	7695.82			0.467626			0.233813	+	0.972282i	$0.424880\pi$
$648$		0			0
$649$		−	4330.70i		−	0.261933i
$650$		0			0
$651$	−24241.3	+	3655.18i	−1.45944	+	0.220058i
$652$		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	$0.102975\pi$
$661$			10804.7i			0.635785i	−0.948127	+	0.317893i	$0.897025\pi$
$662$		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	$-0.302403\pi$
$677$	20491.9			1.16332			0.581660	+	0.813432i	$0.302403\pi$
$678$		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	$0.104931\pi$
$691$			11760.0i			0.647426i	−0.946155	+	0.323713i	$0.895069\pi$
$692$		0			0
$693$	−16429.7	−	1454.29i	−0.900597	−	0.0797170i
$694$		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	$-0.592855\pi$
$719$	−11089.3			−0.575187			−0.287594	+	0.957753i	$0.592855\pi$
$720$		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	$-0.951685\pi$
$727$		−	5927.77i		−	0.302405i	0.988503	−	0.151203i	$-0.0483146\pi$
$728$		0			0
$729$	2808.00	+	19481.7i	0.142661	+	0.989772i
$730$		0			0
$731$	2666.27			0.134905
$732$		0			0
$733$			22532.9i			1.13543i	0.823225	+	0.567715i	$0.192172\pi$
$733$			22532.9i			1.13543i	−0.823225	+	0.567715i	$0.807828\pi$
$734$		0			0
$735$	−15464.3	+	9212.07i	−0.776065	+	0.462302i
$736$		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	$-0.838570\pi$
$761$	−36701.6			−1.74827			−0.874134	+	0.485685i	$0.838570\pi$
$762$		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	$0.160204\pi$
$769$			20570.8i			0.964633i	−0.875997	+	0.482316i	$0.839796\pi$
$770$		0			0
$771$	−1020.00	−	247.386i	−0.0476451	−	0.0115556i
$772$		0			0
$773$	26450.6			1.23074			0.615370	−	0.788238i	$-0.289007\pi$
$773$	26450.6			1.23074			0.615370	+	0.788238i	$0.289007\pi$
$774$		0			0
$775$		−	5859.18i		−	0.271572i
$776$		0			0
$777$	3300.10	+	21886.4i	0.152369	+	1.01052i
$778$		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	$0.183522\pi$
$787$			24071.1i			1.09027i	−0.838348	+	0.545136i	$0.816478\pi$
$788$		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	$-0.684719\pi$
$797$	−24673.1			−1.09657			−0.548285	+	0.836292i	$0.684719\pi$
$798$		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	$-0.771073\pi$
$811$		−	30430.0i		−	1.31756i	0.752335	−	0.658781i	$-0.228927\pi$
$812$		0			0
$813$	−1494.00	+	6159.92i	−0.0644488	+	0.265729i
$814$		0			0
$815$	31591.3			1.35778
$816$		0			0
$817$			1616.66i			0.0692287i
$818$		0			0
$819$	−28062.1	−	2483.93i	−1.19727	−	0.105978i
$820$		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	$0.253164\pi$
$829$			34089.5i			1.42820i	−0.700043	+	0.714101i	$0.746836\pi$
$830$		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	$-0.493518\pi$
$839$	989.751			0.0407271			0.0203635	+	0.999793i	$0.493518\pi$
$840$		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	$-0.857329\pi$
$853$		−	21592.3i		−	0.866711i	0.901223	−	0.433356i	$-0.142671\pi$
$854$		0			0
$855$	−4590.00	+	8905.91i	−0.183596	+	0.356229i
$856$		0			0
$857$	46881.9			1.86868			0.934338	−	0.356388i	$-0.115992\pi$
$857$	46881.9			1.86868			0.934338	+	0.356388i	$0.115992\pi$
$858$		0			0
$859$			35593.5i			1.41378i	0.707324	+	0.706889i	$0.249902\pi$
$859$			35593.5i			1.41378i	−0.707324	+	0.706889i	$0.750098\pi$
$860$		0			0
$861$	2028.75	+	13454.7i	0.0803014	+	0.532563i
$862$		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	$-0.254289\pi$
$881$	36479.4			1.39503			0.697516	+	0.716570i	$0.254289\pi$
$882$		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	$-0.519117\pi$
$887$	−3171.24			−0.120045			−0.0600225	+	0.998197i	$0.519117\pi$
$888$		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
$903$	−631.324	−	4186.97i	−0.0232659	−	0.154301i
$904$		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	$-0.759541\pi$
$929$	−41226.2			−1.45596			−0.727980	+	0.685598i	$0.759541\pi$
$930$		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	$0.0703811\pi$
$937$			12580.6i			0.438623i	−0.975655	+	0.219311i	$0.929619\pi$
$938$		0			0
$939$	654.000	−	2696.51i	0.0227289	−	0.0937139i
$940$		0			0
$941$	5383.04			0.186485			0.0932423	−	0.995643i	$-0.470277\pi$
$941$	5383.04			0.186485			0.0932423	+	0.995643i	$0.470277\pi$
$942$		0			0
$943$			12825.5i			0.442902i
$944$		0			0
$945$	8409.72	−	24857.7i	0.289490	−	0.855684i
$946$		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	$-0.606019\pi$
$971$	−19784.9			−0.653891			−0.326946	+	0.945043i	$0.606019\pi$
$972$		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	$-0.380042\pi$
$983$	22683.5			0.736003			0.368001	+	0.929825i	$0.380042\pi$
$984$		0			0
$985$			20404.2i			0.660034i
$986$		0			0
$987$	−4926.95	−	32675.8i	−0.158892	−	1.05378i
$988$		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	$-0.738336\pi$
$997$		−	46121.4i		−	1.46508i	0.680726	−	0.732538i	$-0.261664\pi$
$998$		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.209.1		4
3.2	odd	2	inner	336.4.k.b.209.3		4
4.3	odd	2		21.4.c.b.20.2	yes	4
7.6	odd	2	inner	336.4.k.b.209.4		4
12.11	even	2		21.4.c.b.20.3	yes	4
21.20	even	2	inner	336.4.k.b.209.2		4
28.3	even	6		147.4.g.c.68.4		8
28.11	odd	6		147.4.g.c.68.3		8
28.19	even	6		147.4.g.c.80.2		8
28.23	odd	6		147.4.g.c.80.1		8
28.27	even	2		21.4.c.b.20.1	✓	4
84.11	even	6		147.4.g.c.68.2		8
84.23	even	6		147.4.g.c.80.4		8
84.47	odd	6		147.4.g.c.80.3		8
84.59	odd	6		147.4.g.c.68.1		8
84.83	odd	2		21.4.c.b.20.4	yes	4

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-5.04975 - 1.22474i) q^{3} -10.0995 q^{5} +(-7.00000 - 17.1464i) q^{7} +(24.0000 + 12.3693i) q^{9} +O(q^{10})\)	\(q+(-5.04975 - 1.22474i) q^{3} -10.0995 q^{5} +(-7.00000 - 17.1464i) q^{7} +(24.0000 + 12.3693i) q^{9} -32.9848i q^{11} -56.3383i q^{13} +(51.0000 + 12.3693i) q^{15} -60.5970 q^{17} -36.7423i q^{19} +(14.3483 + 95.1584i) q^{21} +90.7083i q^{23} -23.0000 q^{25} +(-106.045 - 91.8559i) q^{27} +57.7235i q^{29} +254.747i q^{31} +(-40.3980 + 166.565i) q^{33} +(70.6965 + 173.170i) q^{35} +230.000 q^{37} +(-69.0000 + 284.494i) q^{39} +141.393 q^{41} -44.0000 q^{43} +(-242.388 - 124.924i) q^{45} -343.383 q^{47} +(-245.000 + 240.050i) q^{49} +(306.000 + 74.2159i) q^{51} +206.155i q^{53} +333.131i q^{55} +(-45.0000 + 185.540i) q^{57} +131.294 q^{59} +71.0352i q^{61} +(44.0896 - 498.099i) q^{63} +568.989i q^{65} +64.0000 q^{67} +(111.095 - 458.055i) q^{69} +461.788i q^{71} +88.1816i q^{73} +(116.144 + 28.1691i) q^{75} +(-565.572 + 230.894i) q^{77} +442.000 q^{79} +(423.000 + 593.727i) q^{81} -494.876 q^{83} +612.000 q^{85} +(70.6965 - 291.489i) q^{87} +484.776 q^{89} +(-966.000 + 394.368i) q^{91} +(312.000 - 1286.41i) q^{93} +371.080i q^{95} +1092.47i q^{97} +(408.000 - 791.636i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 28 q^{7} + 96 q^{9}+O(q^{10}) \) 4 * q - 28 * q^7 + 96 * q^9	\( 4 q - 28 q^{7} + 96 q^{9} + 204 q^{15} - 84 q^{21} - 92 q^{25} + 920 q^{37} - 276 q^{39} - 176 q^{43} - 980 q^{49} + 1224 q^{51} - 180 q^{57} - 672 q^{63} + 256 q^{67} + 1768 q^{79} + 1692 q^{81} + 2448 q^{85} - 3864 q^{91} + 1248 q^{93} + 1632 q^{99}+O(q^{100}) \) 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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