LMFDB - Embedded newform 432.4.i.c.289.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,4,Mod(145,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("432.145");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	432.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$25.4888251225$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.2
Root			$1.68614 + 0.396143i$ of defining polynomial
Character	$\chi$	$=$	432.289
Dual form			432.4.i.c.145.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.18614 + 8.98266i) q^{5} +(-2.55842 + 4.43132i) q^{7} +O(q^{10})$	$q+(5.18614 + 8.98266i) q^{5} +(-2.55842 + 4.43132i) q^{7} +(-27.9891 + 48.4786i) q^{11} +(-18.7921 - 32.5489i) q^{13} -23.6495 q^{17} -39.0516 q^{19} +(-35.5367 - 61.5513i) q^{23} +(8.70789 - 15.0825i) q^{25} +(-14.1861 + 24.5711i) q^{29} +(6.44158 + 11.1571i) q^{31} -53.0733 q^{35} -180.103 q^{37} +(-107.742 - 186.614i) q^{41} +(30.6168 - 53.0299i) q^{43} +(30.9388 - 53.5876i) q^{47} +(158.409 + 274.372i) q^{49} -492.310 q^{53} -580.622 q^{55} +(-394.815 - 683.840i) q^{59} +(-260.545 + 451.277i) q^{61} +(194.917 - 337.606i) q^{65} +(152.215 + 263.644i) q^{67} +270.391 q^{71} -925.464 q^{73} +(-143.216 - 248.057i) q^{77} +(-644.517 + 1116.34i) q^{79} +(-356.917 + 618.198i) q^{83} +(-122.649 - 212.435i) q^{85} +404.804 q^{89} +192.313 q^{91} +(-202.527 - 350.787i) q^{95} +(-37.5137 + 64.9756i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 15 q^{5} + 7 q^{7}+O(q^{10}) $ 4 * q + 15 * q^5 + 7 * q^7	$ 4 q + 15 q^{5} + 7 q^{7} - 66 q^{11} + 11 q^{13} - 198 q^{17} + 154 q^{19} - 33 q^{23} + 121 q^{25} - 51 q^{29} + 43 q^{31} + 6 q^{35} - 100 q^{37} + 132 q^{41} + 88 q^{43} - 399 q^{47} + 513 q^{49} - 108 q^{53} - 1254 q^{55} - 798 q^{59} - 439 q^{61} + 165 q^{65} + 988 q^{67} + 2736 q^{71} - 910 q^{73} - 165 q^{77} - 803 q^{79} - 813 q^{83} - 594 q^{85} + 792 q^{89} + 1562 q^{91} + 132 q^{95} - 736 q^{97}+O(q^{100}) $ 4 * q + 15 * q^5 + 7 * q^7 - 66 * q^11 + 11 * q^13 - 198 * q^17 + 154 * q^19 - 33 * q^23 + 121 * q^25 - 51 * q^29 + 43 * q^31 + 6 * q^35 - 100 * q^37 + 132 * q^41 + 88 * q^43 - 399 * q^47 + 513 * q^49 - 108 * q^53 - 1254 * q^55 - 798 * q^59 - 439 * q^61 + 165 * q^65 + 988 * q^67 + 2736 * q^71 - 910 * q^73 - 165 * q^77 - 803 * q^79 - 813 * q^83 - 594 * q^85 + 792 * q^89 + 1562 * q^91 + 132 * q^95 - 736 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	5.18614	+	8.98266i	0.463863	+	0.803433i	0.999149	−	0.0412369i	$-0.0131298\pi$
$5$	5.18614	+	8.98266i	0.463863	+	0.803433i	−0.535287	+	0.844670i	$0.679796\pi$
$6$		0			0
$7$	−2.55842	+	4.43132i	−0.138142	+	0.239269i	−0.926793	−	0.375572i	$-0.877446\pi$
$7$	−2.55842	+	4.43132i	−0.138142	+	0.239269i	0.788651	+	0.614841i	$0.210780\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−27.9891	+	48.4786i	−0.767185	+	1.32880i	0.171898	+	0.985115i	$0.445010\pi$
$11$	−27.9891	+	48.4786i	−0.767185	+	1.32880i	−0.939083	+	0.343689i	$0.888323\pi$
$12$		0			0
$13$	−18.7921	−	32.5489i	−0.400923	−	0.694418i	0.592915	−	0.805265i	$-0.297977\pi$
$13$	−18.7921	−	32.5489i	−0.400923	−	0.694418i	−0.993838	+	0.110847i	$0.964644\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−23.6495			−0.337402			−0.168701	−	0.985667i	$-0.553957\pi$
$17$	−23.6495			−0.337402			−0.168701	+	0.985667i	$0.553957\pi$
$18$		0			0
$19$	−39.0516			−0.471529			−0.235764	−	0.971810i	$-0.575759\pi$
$19$	−39.0516			−0.471529			−0.235764	+	0.971810i	$0.575759\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−35.5367	−	61.5513i	−0.322170	−	0.558015i	0.658766	−	0.752348i	$-0.271079\pi$
$23$	−35.5367	−	61.5513i	−0.322170	−	0.558015i	−0.980936	+	0.194334i	$0.937746\pi$
$24$		0			0
$25$	8.70789	−	15.0825i	0.0696631	−	0.120660i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−14.1861	+	24.5711i	−0.0908379	+	0.157336i	−0.907864	−	0.419265i	$-0.862288\pi$
$29$	−14.1861	+	24.5711i	−0.0908379	+	0.157336i	0.817026	+	0.576601i	$0.195621\pi$
$30$		0			0
$31$	6.44158	+	11.1571i	0.0373207	+	0.0646413i	0.884082	−	0.467331i	$-0.154784\pi$
$31$	6.44158	+	11.1571i	0.0373207	+	0.0646413i	−0.846762	+	0.531972i	$0.821451\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−53.0733			−0.256315
$36$		0			0
$37$	−180.103			−0.800237			−0.400119	−	0.916463i	$-0.631031\pi$
$37$	−180.103			−0.800237			−0.400119	+	0.916463i	$0.631031\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−107.742	−	186.614i	−0.410401	−	0.710835i	0.584533	−	0.811370i	$-0.301278\pi$
$41$	−107.742	−	186.614i	−0.410401	−	0.710835i	−0.994934	+	0.100535i	$0.967945\pi$
$42$		0			0
$43$	30.6168	−	53.0299i	0.108582	−	0.188069i	−0.806614	−	0.591078i	$-0.798702\pi$
$43$	30.6168	−	53.0299i	0.108582	−	0.188069i	0.915196	+	0.403009i	$0.132036\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	30.9388	−	53.5876i	0.0960189	−	0.166310i	−0.814014	−	0.580845i	$-0.802722\pi$
$47$	30.9388	−	53.5876i	0.0960189	−	0.166310i	0.910033	+	0.414535i	$0.136056\pi$
$48$		0			0
$49$	158.409	+	274.372i	0.461834	+	0.799919i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−492.310			−1.27592			−0.637962	−	0.770068i	$-0.720222\pi$
$53$	−492.310			−1.27592			−0.637962	+	0.770068i	$0.720222\pi$
$54$		0			0
$55$	−580.622			−1.42347
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−394.815	−	683.840i	−0.871196	−	1.50896i	−0.860761	−	0.509010i	$-0.830012\pi$
$59$	−394.815	−	683.840i	−0.871196	−	1.50896i	−0.0104351	−	0.999946i	$-0.503322\pi$
$60$		0			0
$61$	−260.545	+	451.277i	−0.546874	+	0.947214i	0.451612	+	0.892214i	$0.350849\pi$
$61$	−260.545	+	451.277i	−0.546874	+	0.947214i	−0.998486	+	0.0549998i	$0.982484\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	194.917	−	337.606i	0.371946	−	0.644229i
$66$		0			0
$67$	152.215	+	263.644i	0.277552	+	0.480734i	0.970776	−	0.239988i	$-0.0771436\pi$
$67$	152.215	+	263.644i	0.277552	+	0.480734i	−0.693224	+	0.720722i	$0.743810\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	270.391			0.451966			0.225983	−	0.974131i	$-0.427441\pi$
$71$	270.391			0.451966			0.225983	+	0.974131i	$0.427441\pi$
$72$		0			0
$73$	−925.464			−1.48380			−0.741900	−	0.670510i	$-0.766075\pi$
$73$	−925.464			−1.48380			−0.741900	+	0.670510i	$0.766075\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−143.216	−	248.057i	−0.211961	−	0.367127i
$78$		0			0
$79$	−644.517	+	1116.34i	−0.917897	+	1.58984i	−0.115294	+	0.993331i	$0.536781\pi$
$79$	−644.517	+	1116.34i	−0.917897	+	1.58984i	−0.802603	+	0.596513i	$0.796552\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−356.917	+	618.198i	−0.472009	+	0.817543i	−0.999487	−	0.0320252i	$-0.989804\pi$
$83$	−356.917	+	618.198i	−0.472009	+	0.817543i	0.527478	+	0.849569i	$0.323138\pi$
$84$		0			0
$85$	−122.649	−	212.435i	−0.156508	−	0.271080i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	404.804			0.482125			0.241063	−	0.970510i	$-0.422504\pi$
$89$	404.804			0.482125			0.241063	+	0.970510i	$0.422504\pi$
$90$		0			0
$91$	192.313			0.221537
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−202.527	−	350.787i	−0.218725	−	0.378842i
$96$		0			0
$97$	−37.5137	+	64.9756i	−0.0392674	+	0.0680131i	−0.884991	−	0.465608i	$-0.845836\pi$
$97$	−37.5137	+	64.9756i	−0.0392674	+	0.0680131i	0.845724	+	0.533621i	$0.179169\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−543.939	+	942.130i	−0.535881	+	0.928172i	0.463240	+	0.886233i	$0.346687\pi$
$101$	−543.939	+	942.130i	−0.535881	+	0.928172i	−0.999120	+	0.0419392i	$0.986646\pi$
$102$		0			0
$103$	−545.909	−	945.542i	−0.522233	−	0.904534i	−0.999665	−	0.0258657i	$-0.991766\pi$
$103$	−545.909	−	945.542i	−0.522233	−	0.904534i	0.477432	−	0.878669i	$-0.341568\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1029.15			−0.929833			−0.464917	−	0.885354i	$-0.653916\pi$
$107$	−1029.15			−0.929833			−0.464917	+	0.885354i	$0.653916\pi$
$108$		0			0
$109$	1776.52			1.56110			0.780548	−	0.625096i	$-0.214940\pi$
$109$	1776.52			1.56110			0.780548	+	0.625096i	$0.214940\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−807.969	−	1399.44i	−0.672631	−	1.16503i	−0.977155	−	0.212526i	$-0.931831\pi$
$113$	−807.969	−	1399.44i	−0.672631	−	1.16503i	0.304524	−	0.952505i	$-0.401502\pi$
$114$		0			0
$115$	368.596	−	638.428i	0.298885	−	0.517684i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	60.5053	−	104.798i	0.0466094	−	0.0807298i
$120$		0			0
$121$	−901.282	−	1561.07i	−0.677147	−	1.17285i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1477.18			1.05698
$126$		0			0
$127$	1206.10			0.842711			0.421356	−	0.906895i	$-0.361554\pi$
$127$	1206.10			0.842711			0.421356	+	0.906895i	$0.361554\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	513.928	+	890.149i	0.342764	+	0.593684i	0.984945	−	0.172869i	$-0.0553036\pi$
$131$	513.928	+	890.149i	0.342764	+	0.593684i	−0.642181	+	0.766553i	$0.721970\pi$
$132$		0			0
$133$	99.9105	−	173.050i	0.0651379	−	0.112822i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−630.454	+	1091.98i	−0.393163	+	0.680978i	−0.992865	−	0.119245i	$-0.961952\pi$
$137$	−630.454	+	1091.98i	−0.393163	+	0.680978i	0.599702	+	0.800223i	$0.295286\pi$
$138$		0			0
$139$	230.916	+	399.958i	0.140907	+	0.244057i	0.927838	−	0.372983i	$-0.121665\pi$
$139$	230.916	+	399.958i	0.140907	+	0.244057i	−0.786932	+	0.617040i	$0.788332\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2103.90			1.23033
$144$		0			0
$145$	−294.285			−0.168545
$146$		0			0
$147$		0			0
$148$		0			0
$149$	729.661	+	1263.81i	0.401182	+	0.694868i	0.993869	−	0.110565i	$-0.0352660\pi$
$149$	729.661	+	1263.81i	0.401182	+	0.694868i	−0.592687	+	0.805433i	$0.701933\pi$
$150$		0			0
$151$	770.659	−	1334.82i	0.415333	−	0.719378i	−0.580130	−	0.814524i	$-0.696998\pi$
$151$	770.659	−	1334.82i	0.415333	−	0.719378i	0.995463	+	0.0951456i	$0.0303317\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−66.8139	+	115.725i	−0.0346233	+	0.0599694i
$156$		0			0
$157$	1607.79	+	2784.77i	0.817295	+	1.41560i	0.907668	+	0.419688i	$0.137861\pi$
$157$	1607.79	+	2784.77i	0.817295	+	1.41560i	−0.0903734	+	0.995908i	$0.528806\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	363.671			0.178021
$162$		0			0
$163$	−947.587			−0.455342			−0.227671	−	0.973738i	$-0.573111\pi$
$163$	−947.587			−0.455342			−0.227671	+	0.973738i	$0.573111\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−342.980	−	594.058i	−0.158926	−	0.275267i	0.775556	−	0.631279i	$-0.217470\pi$
$167$	−342.980	−	594.058i	−0.158926	−	0.275267i	−0.934481	+	0.356012i	$0.884136\pi$
$168$		0			0
$169$	392.213	−	679.333i	0.178522	−	0.309209i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1106.41	+	1916.36i	−0.486237	+	0.842188i	−0.999875	−	0.0158193i	$-0.994964\pi$
$173$	−1106.41	+	1916.36i	−0.486237	+	0.842188i	0.513637	+	0.858007i	$0.328298\pi$
$174$		0			0
$175$	44.5569	+	77.1748i	0.0192468	+	0.0333364i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3023.22			1.26238			0.631190	−	0.775629i	$-0.282567\pi$
$179$	3023.22			1.26238			0.631190	+	0.775629i	$0.282567\pi$
$180$		0			0
$181$	391.445			0.160751			0.0803753	−	0.996765i	$-0.474388\pi$
$181$	391.445			0.160751			0.0803753	+	0.996765i	$0.474388\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−934.040	−	1617.81i	−0.371200	−	0.642937i
$186$		0			0
$187$	661.928	−	1146.49i	0.258850	−	0.448341i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1742.79	+	3018.61i	−0.660231	+	1.14355i	0.320324	+	0.947308i	$0.396208\pi$
$191$	−1742.79	+	3018.61i	−0.660231	+	1.14355i	−0.980555	+	0.196246i	$0.937125\pi$
$192$		0			0
$193$	−1107.53	−	1918.31i	−0.413068	−	0.715455i	0.582156	−	0.813077i	$-0.302209\pi$
$193$	−1107.53	−	1918.31i	−0.413068	−	0.715455i	−0.995223	+	0.0976228i	$0.968876\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	3975.11			1.43764			0.718820	−	0.695196i	$-0.244682\pi$
$197$	3975.11			1.43764			0.718820	+	0.695196i	$0.244682\pi$
$198$		0			0
$199$	1555.34			0.554046			0.277023	−	0.960863i	$-0.410652\pi$
$199$	1555.34			0.554046			0.277023	+	0.960863i	$0.410652\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−72.5883	−	125.727i	−0.0250970	−	0.0434693i
$204$		0			0
$205$	1117.53	−	1935.62i	0.380739	−	0.659460i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1093.02	−	1893.17i	0.361750	−	0.626570i
$210$		0			0
$211$	873.865	+	1513.58i	0.285115	+	0.493834i	0.972637	−	0.232329i	$-0.0746347\pi$
$211$	873.865	+	1513.58i	0.285115	+	0.493834i	−0.687522	+	0.726164i	$0.741301\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	635.133			0.201468
$216$		0			0
$217$	−65.9211			−0.0206222
$218$		0			0
$219$		0			0
$220$		0			0
$221$	444.423	+	769.764i	0.135272	+	0.234298i
$222$		0			0
$223$	−1270.97	+	2201.39i	−0.381662	+	0.661057i	−0.991300	−	0.131622i	$-0.957981\pi$
$223$	−1270.97	+	2201.39i	−0.381662	+	0.661057i	0.609638	+	0.792680i	$0.291315\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1496.63	−	2592.24i	0.437598	−	0.757943i	−0.559905	−	0.828557i	$-0.689163\pi$
$227$	1496.63	−	2592.24i	0.437598	−	0.757943i	0.997504	+	0.0706140i	$0.0224959\pi$
$228$		0			0
$229$	2152.65	+	3728.50i	0.621185	+	1.07592i	0.989265	+	0.146130i	$0.0466816\pi$
$229$	2152.65	+	3728.50i	0.621185	+	1.07592i	−0.368081	+	0.929794i	$0.619985\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	5581.34			1.56930			0.784648	−	0.619942i	$-0.212844\pi$
$233$	5581.34			1.56930			0.784648	+	0.619942i	$0.212844\pi$
$234$		0			0
$235$	641.812			0.178158
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−704.814	−	1220.77i	−0.190756	−	0.330399i	0.754745	−	0.656018i	$-0.227761\pi$
$239$	−704.814	−	1220.77i	−0.190756	−	0.330399i	−0.945501	+	0.325619i	$0.894427\pi$
$240$		0			0
$241$	−313.286	+	542.627i	−0.0837366	+	0.145036i	−0.904852	−	0.425726i	$-0.860019\pi$
$241$	−313.286	+	542.627i	−0.0837366	+	0.145036i	0.821116	+	0.570762i	$0.193352\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1643.06	+	2845.87i	−0.428455	+	0.742105i
$246$		0			0
$247$	733.862	+	1271.09i	0.189047	+	0.327438i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	1705.53			0.428892			0.214446	−	0.976736i	$-0.431205\pi$
$251$	1705.53			0.428892			0.214446	+	0.976736i	$0.431205\pi$
$252$		0			0
$253$	3978.56			0.988656
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1798.69	−	3115.42i	−0.436573	−	0.756166i	0.560850	−	0.827918i	$-0.310475\pi$
$257$	−1798.69	−	3115.42i	−0.436573	−	0.756166i	−0.997423	+	0.0717513i	$0.977141\pi$
$258$		0			0
$259$	460.780	−	798.094i	0.110546	−	0.191472i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2068.75	+	3583.18i	−0.485037	+	0.840108i	−0.999852	−	0.0171926i	$-0.994527\pi$
$263$	−2068.75	+	3583.18i	−0.485037	+	0.840108i	0.514815	+	0.857301i	$0.327860\pi$
$264$		0			0
$265$	−2553.19	−	4422.25i	−0.591853	−	1.02512i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−6090.99			−1.38057			−0.690287	−	0.723536i	$-0.742516\pi$
$269$	−6090.99			−1.38057			−0.690287	+	0.723536i	$0.742516\pi$
$270$		0			0
$271$	3196.62			0.716534			0.358267	−	0.933619i	$-0.383368\pi$
$271$	3196.62			0.716534			0.358267	+	0.933619i	$0.383368\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	487.452	+	844.292i	0.106889	+	0.185137i
$276$		0			0
$277$	1559.68	−	2701.45i	0.338311	−	0.585972i	−0.645804	−	0.763503i	$-0.723478\pi$
$277$	1559.68	−	2701.45i	0.338311	−	0.585972i	0.984115	+	0.177531i	$0.0568111\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	2474.17	−	4285.38i	0.525254	−	0.909767i	−0.474313	−	0.880356i	$-0.657304\pi$
$281$	2474.17	−	4285.38i	0.525254	−	0.909767i	0.999567	−	0.0294105i	$-0.00936301\pi$
$282$		0			0
$283$	−2272.47	−	3936.03i	−0.477329	−	0.826758i	0.522333	−	0.852741i	$-0.325062\pi$
$283$	−2272.47	−	3936.03i	−0.477329	−	0.826758i	−0.999662	+	0.0259834i	$0.991728\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1102.60			0.226774
$288$		0			0
$289$	−4353.70			−0.886160
$290$		0			0
$291$		0			0
$292$		0			0
$293$	3430.05	+	5941.03i	0.683911	+	1.18457i	0.973778	+	0.227501i	$0.0730555\pi$
$293$	3430.05	+	5941.03i	0.683911	+	1.18457i	−0.289867	+	0.957067i	$0.593611\pi$
$294$		0			0
$295$	4095.13	−	7092.98i	0.808230	−	1.39990i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1335.62	+	2313.36i	−0.258330	+	0.447441i
$300$		0			0
$301$	156.662	+	271.346i	0.0299994	+	0.0519605i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−5404.89			−1.01470
$306$		0			0
$307$	−6332.25			−1.17720			−0.588600	−	0.808424i	$-0.700321\pi$
$307$	−6332.25			−1.17720			−0.588600	+	0.808424i	$0.700321\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3538.84	−	6129.44i	−0.645238	−	1.11758i	−0.984247	−	0.176801i	$-0.943425\pi$
$311$	−3538.84	−	6129.44i	−0.645238	−	1.11758i	0.339009	−	0.940783i	$-0.389908\pi$
$312$		0			0
$313$	−690.649	+	1196.24i	−0.124721	+	0.216024i	−0.921624	−	0.388084i	$-0.873137\pi$
$313$	−690.649	+	1196.24i	−0.124721	+	0.216024i	0.796903	+	0.604108i	$0.206470\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4087.47	+	7079.70i	−0.724211	+	1.25437i	0.235086	+	0.971974i	$0.424463\pi$
$317$	−4087.47	+	7079.70i	−0.724211	+	1.25437i	−0.959298	+	0.282396i	$0.908871\pi$
$318$		0			0
$319$	−794.115	−	1375.45i	−0.139379	−	0.241412i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	923.549			0.159095
$324$		0			0
$325$	−654.559			−0.111718
$326$		0			0
$327$		0			0
$328$		0			0
$329$	158.309	+	274.199i	0.0265284	+	0.0459486i
$330$		0			0
$331$	−4830.64	+	8366.92i	−0.802163	+	1.38939i	0.116026	+	0.993246i	$0.462984\pi$
$331$	−4830.64	+	8366.92i	−0.802163	+	1.38939i	−0.918189	+	0.396142i	$0.870349\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−1578.81	+	2734.59i	−0.257492	+	0.445989i
$336$		0			0
$337$	2478.01	+	4292.04i	0.400552	+	0.693776i	0.993793	−	0.111249i	$-0.0354852\pi$
$337$	2478.01	+	4292.04i	0.400552	+	0.693776i	−0.593241	+	0.805025i	$0.702152\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−721.177			−0.114528
$342$		0			0
$343$	−3376.19			−0.531478
$344$		0			0
$345$		0			0
$346$		0			0
$347$	507.802	+	879.540i	0.0785598	+	0.136070i	0.902629	−	0.430420i	$-0.141635\pi$
$347$	507.802	+	879.540i	0.0785598	+	0.136070i	−0.824069	+	0.566490i	$0.808301\pi$
$348$		0			0
$349$	−6079.29	+	10529.6i	−0.932426	+	1.61501i	−0.153267	+	0.988185i	$0.548979\pi$
$349$	−6079.29	+	10529.6i	−0.932426	+	1.61501i	−0.779160	+	0.626825i	$0.784354\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	2118.04	−	3668.56i	0.319354	−	0.553138i	−0.660999	−	0.750387i	$-0.729867\pi$
$353$	2118.04	−	3668.56i	0.319354	−	0.553138i	0.980353	+	0.197249i	$0.0632007\pi$
$354$		0			0
$355$	1402.29	+	2428.83i	0.209650	+	0.363124i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−517.939			−0.0761443			−0.0380721	−	0.999275i	$-0.512122\pi$
$359$	−517.939			−0.0761443			−0.0380721	+	0.999275i	$0.512122\pi$
$360$		0			0
$361$	−5333.97			−0.777660
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−4799.59	−	8313.13i	−0.688279	−	1.19213i
$366$		0			0
$367$	−2308.15	+	3997.83i	−0.328295	+	0.568624i	−0.982174	−	0.187976i	$-0.939807\pi$
$367$	−2308.15	+	3997.83i	−0.328295	+	0.568624i	0.653879	+	0.756600i	$0.273141\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1259.54	−	2181.58i	0.176258	−	0.305288i
$372$		0			0
$373$	−2382.71	−	4126.98i	−0.330756	−	0.572887i	0.651904	−	0.758301i	$-0.273970\pi$
$373$	−2382.71	−	4126.98i	−0.330756	−	0.572887i	−0.982660	+	0.185415i	$0.940637\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1066.35			0.145676
$378$		0			0
$379$	2000.33			0.271108			0.135554	−	0.990770i	$-0.456719\pi$
$379$	2000.33			0.271108			0.135554	+	0.990770i	$0.456719\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−495.147	−	857.619i	−0.0660596	−	0.114419i	0.831104	−	0.556117i	$-0.187709\pi$
$383$	−495.147	−	857.619i	−0.0660596	−	0.114419i	−0.897164	+	0.441699i	$0.854376\pi$
$384$		0			0
$385$	1485.48	−	2572.92i	0.196641	−	0.340593i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	202.205	−	350.230i	0.0263553	−	0.0456487i	−0.852547	−	0.522651i	$-0.824943\pi$
$389$	202.205	−	350.230i	0.0263553	−	0.0456487i	0.878902	+	0.477002i	$0.158277\pi$
$390$		0			0
$391$	840.423	+	1455.66i	0.108701	+	0.188275i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−13370.2			−1.70311
$396$		0			0
$397$	2919.61			0.369096			0.184548	−	0.982824i	$-0.440918\pi$
$397$	2919.61			0.369096			0.184548	+	0.982824i	$0.440918\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5093.10	−	8821.52i	−0.634258	−	1.09857i	−0.986672	−	0.162723i	$-0.947972\pi$
$401$	−5093.10	−	8821.52i	−0.634258	−	1.09857i	0.352414	−	0.935844i	$-0.385361\pi$
$402$		0			0
$403$	242.102	−	419.332i	0.0299254	−	0.0518323i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	5040.93	−	8731.15i	0.613930	−	1.06336i
$408$		0			0
$409$	−3457.12	−	5987.91i	−0.417955	−	0.723920i	0.577778	−	0.816194i	$-0.303920\pi$
$409$	−3457.12	−	5987.91i	−0.417955	−	0.723920i	−0.995734	+	0.0922740i	$0.970586\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	4040.41			0.481394
$414$		0			0
$415$	−7404.09			−0.875789
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−2560.16	−	4434.32i	−0.298501	−	0.517019i	0.677292	−	0.735714i	$-0.263153\pi$
$419$	−2560.16	−	4434.32i	−0.298501	−	0.517019i	−0.975793	+	0.218695i	$0.929820\pi$
$420$		0			0
$421$	−933.246	+	1616.43i	−0.108037	+	0.187126i	−0.914975	−	0.403511i	$-0.867790\pi$
$421$	−933.246	+	1616.43i	−0.108037	+	0.187126i	0.806938	+	0.590636i	$0.201123\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−205.937	+	356.693i	−0.0235045	+	0.0407110i
$426$		0			0
$427$	−1333.17	−	2309.11i	−0.151092	−	0.261700i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−4090.64			−0.457168			−0.228584	−	0.973524i	$-0.573410\pi$
$431$	−4090.64			−0.457168			−0.228584	+	0.973524i	$0.573410\pi$
$432$		0			0
$433$	633.052			0.0702599			0.0351299	−	0.999383i	$-0.488815\pi$
$433$	633.052			0.0702599			0.0351299	+	0.999383i	$0.488815\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1387.76	+	2403.68i	0.151912	+	0.263120i
$438$		0			0
$439$	−5653.26	+	9791.74i	−0.614614	+	1.06454i	0.375838	+	0.926685i	$0.377355\pi$
$439$	−5653.26	+	9791.74i	−0.614614	+	1.06454i	−0.990452	+	0.137857i	$0.955979\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	4140.65	−	7171.82i	0.444082	−	0.769172i	−0.553906	−	0.832579i	$-0.686863\pi$
$443$	4140.65	−	7171.82i	0.444082	−	0.769172i	0.997988	+	0.0634071i	$0.0201967\pi$
$444$		0			0
$445$	2099.37	+	3636.22i	0.223640	+	0.387356i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−6888.40			−0.724017			−0.362008	−	0.932175i	$-0.617909\pi$
$449$	−6888.40			−0.724017			−0.362008	+	0.932175i	$0.617909\pi$
$450$		0			0
$451$	12062.4			1.25941
$452$		0			0
$453$		0			0
$454$		0			0
$455$	997.360	+	1727.48i	0.102763	+	0.177990i
$456$		0			0
$457$	−2141.80	+	3709.71i	−0.219233	+	0.379722i	−0.954574	−	0.297975i	$-0.903689\pi$
$457$	−2141.80	+	3709.71i	−0.219233	+	0.379722i	0.735341	+	0.677697i	$0.237022\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	6889.16	−	11932.4i	0.696009	−	1.20552i	−0.273831	−	0.961778i	$-0.588291\pi$
$461$	6889.16	−	11932.4i	0.696009	−	1.20552i	0.969840	−	0.243744i	$-0.0783758\pi$
$462$		0			0
$463$	2867.27	+	4966.25i	0.287804	+	0.498491i	0.973285	−	0.229599i	$-0.0737415\pi$
$463$	2867.27	+	4966.25i	0.287804	+	0.498491i	−0.685481	+	0.728090i	$0.740408\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−8950.97			−0.886941			−0.443470	−	0.896289i	$-0.646253\pi$
$467$	−8950.97			−0.886941			−0.443470	+	0.896289i	$0.646253\pi$
$468$		0			0
$469$	−1557.72			−0.153366
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1713.88	+	2968.52i	0.166605	+	0.288568i
$474$		0			0
$475$	−340.057	+	588.996i	−0.0328482	+	0.0568947i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−4840.51	+	8384.00i	−0.461729	+	0.799739i	−0.999047	−	0.0436411i	$-0.986104\pi$
$479$	−4840.51	+	8384.00i	−0.461729	+	0.799739i	0.537318	+	0.843380i	$0.319438\pi$
$480$		0			0
$481$	3384.52	+	5862.16i	0.320833	+	0.555699i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−778.204			−0.0728586
$486$		0			0
$487$	−8704.66			−0.809950			−0.404975	−	0.914328i	$-0.632720\pi$
$487$	−8704.66			−0.809950			−0.404975	+	0.914328i	$0.632720\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	7797.85	+	13506.3i	0.716725	+	1.24140i	0.962290	+	0.272024i	$0.0876930\pi$
$491$	7797.85	+	13506.3i	0.716725	+	1.24140i	−0.245565	+	0.969380i	$0.578974\pi$
$492$		0			0
$493$	335.495	−	581.094i	0.0306489	−	0.0530855i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−691.776	+	1198.19i	−0.0624354	+	0.108141i
$498$		0			0
$499$	−4848.14	−	8397.22i	−0.434935	−	0.753329i	0.562355	−	0.826896i	$-0.309895\pi$
$499$	−4848.14	−	8397.22i	−0.434935	−	0.753329i	−0.997290	+	0.0735663i	$0.976562\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	20949.7			1.85706			0.928532	−	0.371253i	$-0.121072\pi$
$503$	20949.7			1.85706			0.928532	+	0.371253i	$0.121072\pi$
$504$		0			0
$505$	−11283.8			−0.994300
$506$		0			0
$507$		0			0
$508$		0			0
$509$	5637.37	+	9764.22i	0.490908	+	0.850278i	0.999945	−	0.0104668i	$-0.00333174\pi$
$509$	5637.37	+	9764.22i	0.490908	+	0.850278i	−0.509037	+	0.860745i	$0.669998\pi$
$510$		0			0
$511$	2367.73	−	4101.03i	0.204975	−	0.355027i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	5662.32	−	9807.43i	0.484489	−	0.839159i
$516$		0			0
$517$	1731.90	+	2999.74i	0.147329	+	0.255181i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−8675.49			−0.729520			−0.364760	−	0.931102i	$-0.618849\pi$
$521$	−8675.49			−0.729520			−0.364760	+	0.931102i	$0.618849\pi$
$522$		0			0
$523$	4226.14			0.353339			0.176670	−	0.984270i	$-0.443468\pi$
$523$	4226.14			0.353339			0.176670	+	0.984270i	$0.443468\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−152.340	−	263.860i	−0.0125921	−	0.0218101i
$528$		0			0
$529$	3557.79	−	6162.27i	0.292413	−	0.506474i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−4049.39	+	7013.75i	−0.329078	+	0.569980i
$534$		0			0
$535$	−5337.34	−	9244.55i	−0.431315	−	0.747059i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−17734.9			−1.41725
$540$		0			0
$541$	13357.8			1.06154			0.530771	−	0.847515i	$-0.321902\pi$
$541$	13357.8			1.06154			0.530771	+	0.847515i	$0.321902\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	9213.26	+	15957.8i	0.724134	+	1.25424i
$546$		0			0
$547$	10835.6	−	18767.7i	0.846974	−	1.46700i	−0.0369219	−	0.999318i	$-0.511755\pi$
$547$	10835.6	−	18767.7i	0.846974	−	1.46700i	0.883896	−	0.467684i	$-0.154911\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	553.991	−	959.541i	0.0428327	−	0.0741884i
$552$		0			0
$553$	−3297.90	−	5712.12i	−0.253600	−	0.439248i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−7477.63			−0.568828			−0.284414	−	0.958702i	$-0.591799\pi$
$557$	−7477.63			−0.568828			−0.284414	+	0.958702i	$0.591799\pi$
$558$		0			0
$559$	−2301.42			−0.174132
$560$		0			0
$561$		0			0
$562$		0			0
$563$	11652.3	+	20182.4i	0.872269	+	1.51082i	0.859643	+	0.510895i	$0.170686\pi$
$563$	11652.3	+	20182.4i	0.872269	+	1.51082i	0.0126262	+	0.999920i	$0.495981\pi$
$564$		0			0
$565$	8380.48	−	14515.4i	0.624017	−	1.08083i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−7324.54	+	12686.5i	−0.539650	+	0.934701i	0.459273	+	0.888295i	$0.348110\pi$
$569$	−7324.54	+	12686.5i	−0.539650	+	0.934701i	−0.998923	+	0.0464057i	$0.985223\pi$
$570$		0			0
$571$	11582.0	+	20060.6i	0.848846	+	1.47025i	0.882239	+	0.470803i	$0.156036\pi$
$571$	11582.0	+	20060.6i	0.848846	+	1.47025i	−0.0333922	+	0.999442i	$0.510631\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1237.80			−0.0897735
$576$		0			0
$577$	7865.97			0.567529			0.283765	−	0.958894i	$-0.408417\pi$
$577$	7865.97			0.567529			0.283765	+	0.958894i	$0.408417\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1826.29	−	3163.23i	−0.130408	−	0.225874i
$582$		0			0
$583$	13779.3	−	23866.5i	0.978869	−	1.69545i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	478.091	−	828.078i	0.0336166	−	0.0582256i	−0.848728	−	0.528830i	$-0.822631\pi$
$587$	478.091	−	828.078i	0.0336166	−	0.0582256i	0.882344	+	0.470605i	$0.155964\pi$
$588$		0			0
$589$	−251.554	−	435.704i	−0.0175978	−	0.0304803i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	16966.0			1.17489			0.587444	−	0.809265i	$-0.300134\pi$
$593$	16966.0			1.17489			0.587444	+	0.809265i	$0.300134\pi$
$594$		0			0
$595$	1255.16			0.0864813
$596$		0			0
$597$		0			0
$598$		0			0
$599$	3095.70	+	5361.92i	0.211164	+	0.365746i	0.952079	−	0.305852i	$-0.0989414\pi$
$599$	3095.70	+	5361.92i	0.211164	+	0.365746i	−0.740915	+	0.671598i	$0.765608\pi$
$600$		0			0
$601$	1359.27	−	2354.33i	0.0922559	−	0.159792i	−0.816204	−	0.577764i	$-0.803926\pi$
$601$	1359.27	−	2354.33i	0.0922559	−	0.159792i	0.908460	+	0.417972i	$0.137259\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	9348.35	−	16191.8i	0.628206	−	1.08808i
$606$		0			0
$607$	8412.49	+	14570.9i	0.562524	+	0.974321i	0.997275	+	0.0737701i	$0.0235031\pi$
$607$	8412.49	+	14570.9i	0.562524	+	0.974321i	−0.434751	+	0.900551i	$0.643164\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2325.62			−0.153985
$612$		0			0
$613$	−20175.1			−1.32930			−0.664652	−	0.747153i	$-0.731420\pi$
$613$	−20175.1			−1.32930			−0.664652	+	0.747153i	$0.731420\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	5655.31	+	9795.29i	0.369002	+	0.639130i	0.989410	−	0.145149i	$-0.0463662\pi$
$617$	5655.31	+	9795.29i	0.369002	+	0.639130i	−0.620408	+	0.784280i	$0.713033\pi$
$618$		0			0
$619$	−8529.94	+	14774.3i	−0.553873	+	0.959336i	0.444117	+	0.895969i	$0.353517\pi$
$619$	−8529.94	+	14774.3i	−0.553873	+	0.959336i	−0.997990	+	0.0633676i	$0.979816\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1035.66	+	1793.82i	−0.0666017	+	0.115357i
$624$		0			0
$625$	6572.36	+	11383.7i	0.420631	+	0.728554i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	4259.34			0.270002
$630$		0			0
$631$	13186.3			0.831916			0.415958	−	0.909384i	$-0.363446\pi$
$631$	13186.3			0.831916			0.415958	+	0.909384i	$0.363446\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	6255.02	+	10834.0i	0.390902	+	0.677063i
$636$		0			0
$637$	5953.68	−	10312.1i	0.370319	−	0.641412i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	8180.99	−	14169.9i	0.504102	−	0.873131i	−0.495886	−	0.868387i	$-0.665157\pi$
$641$	8180.99	−	14169.9i	0.504102	−	0.873131i	0.999989	−	0.00474343i	$-0.00150989\pi$
$642$		0			0
$643$	−14022.5	−	24287.6i	−0.860019	−	1.48960i	−0.871910	−	0.489667i	$-0.837118\pi$
$643$	−14022.5	−	24287.6i	−0.860019	−	1.48960i	0.0118907	−	0.999929i	$-0.496215\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	21247.7			1.29109			0.645543	−	0.763724i	$-0.276631\pi$
$647$	21247.7			1.29109			0.645543	+	0.763724i	$0.276631\pi$
$648$		0			0
$649$	44202.1			2.67347
$650$		0			0
$651$		0			0
$652$		0			0
$653$	629.928	+	1091.07i	0.0377504	+	0.0653856i	0.884283	−	0.466951i	$-0.154647\pi$
$653$	629.928	+	1091.07i	0.0377504	+	0.0653856i	−0.846533	+	0.532336i	$0.821314\pi$
$654$		0			0
$655$	−5330.60	+	9232.87i	−0.317991	+	0.550776i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	6023.35	−	10432.7i	0.356049	−	0.616695i	−0.631248	−	0.775581i	$-0.717457\pi$
$659$	6023.35	−	10432.7i	0.356049	−	0.616695i	0.987297	+	0.158886i	$0.0507902\pi$
$660$		0			0
$661$	−6554.04	−	11351.9i	−0.385662	−	0.667986i	0.606199	−	0.795313i	$-0.292693\pi$
$661$	−6554.04	−	11351.9i	−0.385662	−	0.667986i	−0.991861	+	0.127327i	$0.959360\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2072.60			0.120860
$666$		0			0
$667$	2016.51			0.117061
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−14584.8	−	25261.7i	−0.839108	−	1.45338i
$672$		0			0
$673$	−1371.82	+	2376.07i	−0.0785734	+	0.136093i	−0.902635	−	0.430408i	$-0.858370\pi$
$673$	−1371.82	+	2376.07i	−0.0785734	+	0.136093i	0.824061	+	0.566501i	$0.191703\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	12502.0	−	21654.1i	0.709735	−	1.22930i	−0.255220	−	0.966883i	$-0.582148\pi$
$677$	12502.0	−	21654.1i	0.709735	−	1.22930i	0.964955	−	0.262415i	$-0.0845189\pi$
$678$		0			0
$679$	−191.952	−	332.470i	−0.0108489	−	0.0187909i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−4846.23			−0.271502			−0.135751	−	0.990743i	$-0.543345\pi$
$683$	−4846.23			−0.271502			−0.135751	+	0.990743i	$0.543345\pi$
$684$		0			0
$685$	−13078.5			−0.729494
$686$		0			0
$687$		0			0
$688$		0			0
$689$	9251.54	+	16024.1i	0.511546	+	0.886024i
$690$		0			0
$691$	1742.29	−	3017.73i	0.0959187	−	0.166136i	−0.814073	−	0.580763i	$-0.802754\pi$
$691$	1742.29	−	3017.73i	0.0959187	−	0.166136i	0.909992	+	0.414627i	$0.136088\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−2395.12	+	4148.48i	−0.130723	+	0.226418i
$696$		0			0
$697$	2548.04	+	4413.33i	0.138470	+	0.239837i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−15701.4			−0.845981			−0.422991	−	0.906134i	$-0.639020\pi$
$701$	−15701.4			−0.845981			−0.422991	+	0.906134i	$0.639020\pi$
$702$		0			0
$703$	7033.32			0.377335
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2783.25	−	4820.73i	−0.148055	−	0.256439i
$708$		0			0
$709$	−7821.72	+	13547.6i	−0.414317	+	0.717618i	−0.995356	−	0.0962572i	$-0.969313\pi$
$709$	−7821.72	+	13547.6i	−0.414317	+	0.717618i	0.581039	+	0.813875i	$0.302646\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	457.824	−	792.975i	0.0240472	−	0.0416510i
$714$		0			0
$715$	10911.1	+	18898.6i	0.570703	+	0.988486i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−6964.13			−0.361222			−0.180611	−	0.983555i	$-0.557807\pi$
$719$	−6964.13			−0.361222			−0.180611	+	0.983555i	$0.557807\pi$
$720$		0			0
$721$	5586.66			0.288569
$722$		0			0
$723$		0			0
$724$		0			0
$725$	247.063	+	427.925i	0.0126561	+	0.0219210i
$726$		0			0
$727$	−7103.61	+	12303.8i	−0.362391	+	0.627680i	−0.988354	−	0.152173i	$-0.951373\pi$
$727$	−7103.61	+	12303.8i	−0.362391	+	0.627680i	0.625963	+	0.779853i	$0.284706\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−724.072	+	1254.13i	−0.0366358	+	0.0634551i
$732$		0			0
$733$	−13265.3	−	22976.1i	−0.668437	−	1.15777i	−0.978341	−	0.206998i	$-0.933630\pi$
$733$	−13265.3	−	22976.1i	−0.668437	−	1.15777i	0.309905	−	0.950768i	$-0.399703\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−17041.4			−0.851735
$738$		0			0
$739$	5683.47			0.282909			0.141455	−	0.989945i	$-0.454822\pi$
$739$	5683.47			0.282909			0.141455	+	0.989945i	$0.454822\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	7784.28	+	13482.8i	0.384358	+	0.665727i	0.991680	−	0.128729i	$-0.0410896\pi$
$743$	7784.28	+	13482.8i	0.384358	+	0.665727i	−0.607322	+	0.794456i	$0.707756\pi$
$744$		0			0
$745$	−7568.25	+	13108.6i	−0.372187	+	0.644647i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	2633.01	−	4560.51i	0.128449	−	0.222480i
$750$		0			0
$751$	−4130.82	−	7154.79i	−0.200713	−	0.347646i	0.748045	−	0.663648i	$-0.230993\pi$
$751$	−4130.82	−	7154.79i	−0.200713	−	0.347646i	−0.948758	+	0.316002i	$0.897659\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	15987.0			0.770630
$756$		0			0
$757$	−13381.5			−0.642481			−0.321240	−	0.946998i	$-0.604100\pi$
$757$	−13381.5			−0.642481			−0.321240	+	0.946998i	$0.604100\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	2724.92	+	4719.70i	0.129801	+	0.224821i	0.923599	−	0.383359i	$-0.125233\pi$
$761$	2724.92	+	4719.70i	0.129801	+	0.224821i	−0.793799	+	0.608181i	$0.791900\pi$
$762$		0			0
$763$	−4545.08	+	7872.31i	−0.215652	+	0.373521i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−14838.8	+	25701.6i	−0.698564	+	1.20995i
$768$		0			0
$769$	9681.98	+	16769.7i	0.454020	+	0.786385i	0.998631	−	0.0523033i	$-0.0166563\pi$
$769$	9681.98	+	16769.7i	0.454020	+	0.786385i	−0.544612	+	0.838688i	$0.683323\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1865.54			0.0868033			0.0434017	−	0.999058i	$-0.486180\pi$
$773$	1865.54			0.0868033			0.0434017	+	0.999058i	$0.486180\pi$
$774$		0			0
$775$	224.370			0.0103995
$776$		0			0
$777$		0			0
$778$		0			0
$779$	4207.49	+	7287.58i	0.193516	+	0.335179i
$780$		0			0
$781$	−7568.02	+	13108.2i	−0.346741	+	0.600574i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−16676.4	+	28884.4i	−0.758225	+	1.31328i
$786$		0			0
$787$	−9603.65	−	16634.0i	−0.434985	−	0.753416i	0.562310	−	0.826927i	$-0.309913\pi$
$787$	−9603.65	−	16634.0i	−0.434985	−	0.753416i	−0.997294	+	0.0735110i	$0.976580\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	8268.50			0.371674
$792$		0			0
$793$	19584.7			0.877017
$794$		0			0
$795$		0			0
$796$		0			0
$797$	93.0372	+	161.145i	0.00413494	+	0.00716193i	0.868085	−	0.496415i	$-0.165350\pi$
$797$	93.0372	+	161.145i	0.00413494	+	0.00716193i	−0.863951	+	0.503577i	$0.832017\pi$
$798$		0			0
$799$	−731.686	+	1267.32i	−0.0323970	+	0.0561132i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	25902.9	−	44865.2i	1.13835	−	1.97168i
$804$		0			0
$805$	1886.05	+	3266.73i	0.0825771	+	0.143028i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−5903.09			−0.256541			−0.128270	−	0.991739i	$-0.540943\pi$
$809$	−5903.09			−0.256541			−0.128270	+	0.991739i	$0.540943\pi$
$810$		0			0
$811$	−23111.0			−1.00066			−0.500331	−	0.865834i	$-0.666788\pi$
$811$	−23111.0			−1.00066			−0.500331	+	0.865834i	$0.666788\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−4914.32	−	8511.85i	−0.211216	−	0.365837i
$816$		0			0
$817$	−1195.64	+	2070.90i	−0.0511995	+	0.0886802i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−4822.14	+	8352.20i	−0.204987	+	0.355047i	−0.950128	−	0.311859i	$-0.899048\pi$
$821$	−4822.14	+	8352.20i	−0.204987	+	0.355047i	0.745142	+	0.666906i	$0.232382\pi$
$822$		0			0
$823$	−16786.7	−	29075.5i	−0.710994	−	1.23148i	−0.964484	−	0.264140i	$-0.914912\pi$
$823$	−16786.7	−	29075.5i	−0.710994	−	1.23148i	0.253490	−	0.967338i	$-0.418422\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−25916.1			−1.08971			−0.544855	−	0.838530i	$-0.683415\pi$
$827$	−25916.1			−1.08971			−0.544855	+	0.838530i	$0.683415\pi$
$828$		0			0
$829$	−28650.6			−1.20033			−0.600166	−	0.799876i	$-0.704899\pi$
$829$	−28650.6			−1.20033			−0.600166	+	0.799876i	$0.704899\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−3746.29	−	6488.76i	−0.155824	−	0.269895i
$834$		0			0
$835$	3557.48	−	6161.74i	0.147439	−	0.255372i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−356.480	+	617.441i	−0.0146687	+	0.0254070i	−0.873267	−	0.487243i	$-0.838003\pi$
$839$	−356.480	+	617.441i	−0.0146687	+	0.0254070i	0.858598	+	0.512650i	$0.171336\pi$
$840$		0			0
$841$	11792.0	+	20424.4i	0.483497	+	0.837441i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	8136.29			0.331239
$846$		0			0
$847$	9223.44			0.374169
$848$		0			0
$849$		0			0
$850$		0			0
$851$	6400.27	+	11085.6i	0.257812	+	0.446544i
$852$		0			0
$853$	15183.6	−	26298.8i	0.609469	−	1.05563i	−0.381859	−	0.924221i	$-0.624716\pi$
$853$	15183.6	−	26298.8i	0.609469	−	1.05563i	0.991328	−	0.131411i	$-0.0419508\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	4540.35	−	7864.12i	0.180975	−	0.313458i	−0.761238	−	0.648473i	$-0.775408\pi$
$857$	4540.35	−	7864.12i	0.180975	−	0.313458i	0.942213	+	0.335015i	$0.108741\pi$
$858$		0			0
$859$	13080.1	+	22655.4i	0.519543	+	0.899874i	0.999742	+	0.0227150i	$0.00723102\pi$
$859$	13080.1	+	22655.4i	0.519543	+	0.899874i	−0.480199	+	0.877159i	$0.659436\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−40102.0			−1.58180			−0.790898	−	0.611949i	$-0.790386\pi$
$863$	−40102.0			−1.58180			−0.790898	+	0.611949i	$0.790386\pi$
$864$		0			0
$865$	−22952.1			−0.902189
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−36079.0	−	62490.6i	−1.40839	−	2.43941i
$870$		0			0
$871$	5720.87	−	9908.84i	0.222554	−	0.385474i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−3779.24	+	6545.84i	−0.146013	+	0.252903i
$876$		0			0
$877$	−12626.1	−	21869.0i	−0.486149	−	0.842036i	0.513724	−	0.857956i	$-0.328266\pi$
$877$	−12626.1	−	21869.0i	−0.486149	−	0.842036i	−0.999873	+	0.0159201i	$0.994932\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	2049.26			0.0783670			0.0391835	−	0.999232i	$-0.487524\pi$
$881$	2049.26			0.0783670			0.0391835	+	0.999232i	$0.487524\pi$
$882$		0			0
$883$	−39413.4			−1.50211			−0.751057	−	0.660237i	$-0.770456\pi$
$883$	−39413.4			−1.50211			−0.751057	+	0.660237i	$0.770456\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−18484.2	−	32015.6i	−0.699707	−	1.21193i	−0.968568	−	0.248749i	$-0.919981\pi$
$887$	−18484.2	−	32015.6i	−0.699707	−	1.21193i	0.268861	−	0.963179i	$-0.413353\pi$
$888$		0			0
$889$	−3085.72	+	5344.63i	−0.116414	+	0.201634i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1208.21	+	2092.68i	−0.0452757	+	0.0784198i
$894$		0			0
$895$	15678.8	+	27156.5i	0.585570	+	1.01424i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−365.525			−0.0135605
$900$		0			0
$901$	11642.9			0.430499
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2030.09	+	3516.21i	0.0745662	+	0.129152i
$906$		0			0
$907$	1355.31	−	2347.47i	0.0496167	−	0.0859386i	−0.840150	−	0.542353i	$-0.817533\pi$
$907$	1355.31	−	2347.47i	0.0496167	−	0.0859386i	0.889767	+	0.456415i	$0.150867\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−11498.3	+	19915.6i	−0.418172	+	0.724296i	−0.995756	−	0.0920360i	$-0.970663\pi$
$911$	−11498.3	+	19915.6i	−0.418172	+	0.724296i	0.577583	+	0.816332i	$0.303996\pi$
$912$		0			0
$913$	−19979.6	−	34605.7i	−0.724237	−	1.25441i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−5259.38			−0.189400
$918$		0			0
$919$	39103.8			1.40361			0.701804	−	0.712370i	$-0.252378\pi$
$919$	39103.8			1.40361			0.701804	+	0.712370i	$0.252378\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−5081.23	−	8800.94i	−0.181203	−	0.313853i
$924$		0			0
$925$	−1568.32	+	2716.41i	−0.0557470	+	0.0965567i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−17977.3	+	31137.6i	−0.634894	+	1.09967i	0.351644	+	0.936134i	$0.385623\pi$
$929$	−17977.3	+	31137.6i	−0.634894	+	1.09967i	−0.986538	+	0.163534i	$0.947711\pi$
$930$		0			0
$931$	−6186.12	−	10714.7i	−0.217768	−	0.377185i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	13731.4			0.480283
$936$		0			0
$937$	−7263.94			−0.253258			−0.126629	−	0.991950i	$-0.540416\pi$
$937$	−7263.94			−0.253258			−0.126629	+	0.991950i	$0.540416\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	3739.45	+	6476.92i	0.129546	+	0.224380i	0.923501	−	0.383597i	$-0.125315\pi$
$941$	3739.45	+	6476.92i	0.129546	+	0.224380i	−0.793955	+	0.607977i	$0.791981\pi$
$942$		0			0
$943$	−7657.57	+	13263.3i	−0.264438	+	0.458020i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−6745.68	+	11683.9i	−0.231473	+	0.400923i	−0.958242	−	0.285959i	$-0.907688\pi$
$947$	−6745.68	+	11683.9i	−0.231473	+	0.400923i	0.726769	+	0.686882i	$0.241021\pi$
$948$		0			0
$949$	17391.4	+	30122.8i	0.594889	+	1.03038i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	13981.6			0.475246			0.237623	−	0.971357i	$-0.423632\pi$
$953$	13981.6			0.475246			0.237623	+	0.971357i	$0.423632\pi$
$954$		0			0
$955$	−36153.5			−1.22503
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−3225.93	−	5587.48i	−0.108624	−	0.188143i
$960$		0			0
$961$	14812.5	−	25656.0i	0.497214	−	0.861200i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	11487.7	−	19897.2i	0.383213	−	0.663745i
$966$		0			0
$967$	−4540.73	−	7864.78i	−0.151003	−	0.261545i	0.780593	−	0.625039i	$-0.214917\pi$
$967$	−4540.73	−	7864.78i	−0.151003	−	0.261545i	−0.931597	+	0.363494i	$0.881584\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−9709.13			−0.320887			−0.160443	−	0.987045i	$-0.551292\pi$
$971$	−9709.13			−0.320887			−0.160443	+	0.987045i	$0.551292\pi$
$972$		0			0
$973$	−2363.12			−0.0778604
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5427.45	+	9400.63i	0.177727	+	0.307833i	0.941102	−	0.338123i	$-0.109792\pi$
$977$	5427.45	+	9400.63i	0.177727	+	0.307833i	−0.763374	+	0.645956i	$0.776459\pi$
$978$		0			0
$979$	−11330.1	+	19624.3i	−0.369880	+	0.640650i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	3755.05	−	6503.94i	0.121839	−	0.211031i	−0.798654	−	0.601790i	$-0.794454\pi$
$983$	3755.05	−	6503.94i	0.121839	−	0.211031i	0.920493	+	0.390759i	$0.127788\pi$
$984$		0			0
$985$	20615.5	+	35707.1i	0.666867	+	1.15505i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4352.08			−0.139927
$990$		0			0
$991$	−46125.6			−1.47854			−0.739268	−	0.673412i	$-0.764828\pi$
$991$	−46125.6			−1.47854			−0.739268	+	0.673412i	$0.764828\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	8066.22	+	13971.1i	0.257001	+	0.445139i
$996$		0			0
$997$	−22675.0	+	39274.3i	−0.720287	+	1.24757i	0.240598	+	0.970625i	$0.422656\pi$
$997$	−22675.0	+	39274.3i	−0.720287	+	1.24757i	−0.960885	+	0.276948i	$0.910677\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.4.i.c.289.2		4
3.2	odd	2		144.4.i.c.97.2		4
4.3	odd	2		27.4.c.a.19.1		4
9.2	odd	6		1296.4.a.u.1.2		2
9.4	even	3	inner	432.4.i.c.145.2		4
9.5	odd	6		144.4.i.c.49.2		4
9.7	even	3		1296.4.a.i.1.1		2
12.11	even	2		9.4.c.a.7.2	yes	4
36.7	odd	6		81.4.a.a.1.2		2
36.11	even	6		81.4.a.d.1.1		2
36.23	even	6		9.4.c.a.4.2	✓	4
36.31	odd	6		27.4.c.a.10.1		4
60.23	odd	4		225.4.k.b.124.2		8
60.47	odd	4		225.4.k.b.124.3		8
60.59	even	2		225.4.e.b.151.1		4
180.23	odd	12		225.4.k.b.49.3		8
180.59	even	6		225.4.e.b.76.1		4
180.79	odd	6		2025.4.a.n.1.1		2
180.119	even	6		2025.4.a.g.1.2		2
180.167	odd	12		225.4.k.b.49.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.4.c.a.4.2	✓	4	36.23	even	6
9.4.c.a.7.2	yes	4	12.11	even	2
27.4.c.a.10.1		4	36.31	odd	6
27.4.c.a.19.1		4	4.3	odd	2
81.4.a.a.1.2		2	36.7	odd	6
81.4.a.d.1.1		2	36.11	even	6
144.4.i.c.49.2		4	9.5	odd	6
144.4.i.c.97.2		4	3.2	odd	2
225.4.e.b.76.1		4	180.59	even	6
225.4.e.b.151.1		4	60.59	even	2
225.4.k.b.49.2		8	180.167	odd	12
225.4.k.b.49.3		8	180.23	odd	12
225.4.k.b.124.2		8	60.23	odd	4
225.4.k.b.124.3		8	60.47	odd	4
432.4.i.c.145.2		4	9.4	even	3	inner
432.4.i.c.289.2		4	1.1	even	1	trivial
1296.4.a.i.1.1		2	9.7	even	3
1296.4.a.u.1.2		2	9.2	odd	6
2025.4.a.g.1.2		2	180.119	even	6
2025.4.a.n.1.1		2	180.79	odd	6

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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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	432.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(5.18614 + 8.98266i) q^{5} +(-2.55842 + 4.43132i) q^{7} +O(q^{10})\)	\(q+(5.18614 + 8.98266i) q^{5} +(-2.55842 + 4.43132i) q^{7} +(-27.9891 + 48.4786i) q^{11} +(-18.7921 - 32.5489i) q^{13} -23.6495 q^{17} -39.0516 q^{19} +(-35.5367 - 61.5513i) q^{23} +(8.70789 - 15.0825i) q^{25} +(-14.1861 + 24.5711i) q^{29} +(6.44158 + 11.1571i) q^{31} -53.0733 q^{35} -180.103 q^{37} +(-107.742 - 186.614i) q^{41} +(30.6168 - 53.0299i) q^{43} +(30.9388 - 53.5876i) q^{47} +(158.409 + 274.372i) q^{49} -492.310 q^{53} -580.622 q^{55} +(-394.815 - 683.840i) q^{59} +(-260.545 + 451.277i) q^{61} +(194.917 - 337.606i) q^{65} +(152.215 + 263.644i) q^{67} +270.391 q^{71} -925.464 q^{73} +(-143.216 - 248.057i) q^{77} +(-644.517 + 1116.34i) q^{79} +(-356.917 + 618.198i) q^{83} +(-122.649 - 212.435i) q^{85} +404.804 q^{89} +192.313 q^{91} +(-202.527 - 350.787i) q^{95} +(-37.5137 + 64.9756i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 15 q^{5} + 7 q^{7}+O(q^{10}) \) 4 * q + 15 * q^5 + 7 * q^7	\( 4 q + 15 q^{5} + 7 q^{7} - 66 q^{11} + 11 q^{13} - 198 q^{17} + 154 q^{19} - 33 q^{23} + 121 q^{25} - 51 q^{29} + 43 q^{31} + 6 q^{35} - 100 q^{37} + 132 q^{41} + 88 q^{43} - 399 q^{47} + 513 q^{49} - 108 q^{53} - 1254 q^{55} - 798 q^{59} - 439 q^{61} + 165 q^{65} + 988 q^{67} + 2736 q^{71} - 910 q^{73} - 165 q^{77} - 803 q^{79} - 813 q^{83} - 594 q^{85} + 792 q^{89} + 1562 q^{91} + 132 q^{95} - 736 q^{97}+O(q^{100}) \) 4 * q + 15 * q^5 + 7 * q^7 - 66 * q^11 + 11 * q^13 - 198 * q^17 + 154 * q^19 - 33 * q^23 + 121 * q^25 - 51 * q^29 + 43 * q^31 + 6 * q^35 - 100 * q^37 + 132 * q^41 + 88 * q^43 - 399 * q^47 + 513 * q^49 - 108 * q^53 - 1254 * q^55 - 798 * q^59 - 439 * q^61 + 165 * q^65 + 988 * q^67 + 2736 * q^71 - 910 * q^73 - 165 * q^77 - 803 * q^79 - 813 * q^83 - 594 * q^85 + 792 * q^89 + 1562 * q^91 + 132 * q^95 - 736 * q^97

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