LMFDB - Embedded newform 3234.2.a.bg.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3234,2,Mod(1,3234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3234, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("3234.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3234.a (trivial)

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:	yes
Analytic conductor:	$25.8236200137$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.621.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 6x - 3 $ x^3 - 6*x - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 462)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.66908$ of defining polynomial
Character	$\chi$	$=$	3234.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.454904 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.454904 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -0.454904 q^{10} +1.00000 q^{11} -1.00000 q^{12} -0.909808 q^{13} +0.454904 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -3.88325 q^{19} -0.454904 q^{20} +1.00000 q^{22} +8.33816 q^{23} -1.00000 q^{24} -4.79306 q^{25} -0.909808 q^{26} -1.00000 q^{27} -2.79306 q^{29} +0.454904 q^{30} +9.58612 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +1.00000 q^{36} +7.88325 q^{37} -3.88325 q^{38} +0.909808 q^{39} -0.454904 q^{40} +1.79306 q^{41} +7.88325 q^{43} +1.00000 q^{44} -0.454904 q^{45} +8.33816 q^{46} -0.338158 q^{47} -1.00000 q^{48} -4.79306 q^{50} +1.00000 q^{51} -0.909808 q^{52} +0.909808 q^{53} -1.00000 q^{54} -0.454904 q^{55} +3.88325 q^{57} -2.79306 q^{58} -6.97345 q^{59} +0.454904 q^{60} +14.0410 q^{61} +9.58612 q^{62} +1.00000 q^{64} +0.413875 q^{65} -1.00000 q^{66} -3.79306 q^{67} -1.00000 q^{68} -8.33816 q^{69} -4.79306 q^{71} +1.00000 q^{72} -10.6763 q^{73} +7.88325 q^{74} +4.79306 q^{75} -3.88325 q^{76} +0.909808 q^{78} +5.36471 q^{79} -0.454904 q^{80} +1.00000 q^{81} +1.79306 q^{82} -1.97345 q^{83} +0.454904 q^{85} +7.88325 q^{86} +2.79306 q^{87} +1.00000 q^{88} +11.0902 q^{89} -0.454904 q^{90} +8.33816 q^{92} -9.58612 q^{93} -0.338158 q^{94} +1.76651 q^{95} -1.00000 q^{96} -14.5861 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^6 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{6} + 3 q^{8} + 3 q^{9} + 3 q^{11} - 3 q^{12} + 3 q^{16} - 3 q^{17} + 3 q^{18} + 3 q^{19} + 3 q^{22} + 9 q^{23} - 3 q^{24} + 3 q^{25} - 3 q^{27} + 9 q^{29} - 6 q^{31} + 3 q^{32} - 3 q^{33} - 3 q^{34} + 3 q^{36} + 9 q^{37} + 3 q^{38} - 12 q^{41} + 9 q^{43} + 3 q^{44} + 9 q^{46} + 15 q^{47} - 3 q^{48} + 3 q^{50} + 3 q^{51} - 3 q^{54} - 3 q^{57} + 9 q^{58} - 9 q^{59} + 6 q^{61} - 6 q^{62} + 3 q^{64} + 36 q^{65} - 3 q^{66} + 6 q^{67} - 3 q^{68} - 9 q^{69} + 3 q^{71} + 3 q^{72} + 9 q^{74} - 3 q^{75} + 3 q^{76} + 12 q^{79} + 3 q^{81} - 12 q^{82} + 6 q^{83} + 9 q^{86} - 9 q^{87} + 3 q^{88} + 36 q^{89} + 9 q^{92} + 6 q^{93} + 15 q^{94} - 24 q^{95} - 3 q^{96} - 9 q^{97} + 3 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^6 + 3 * q^8 + 3 * q^9 + 3 * q^11 - 3 * q^12 + 3 * q^16 - 3 * q^17 + 3 * q^18 + 3 * q^19 + 3 * q^22 + 9 * q^23 - 3 * q^24 + 3 * q^25 - 3 * q^27 + 9 * q^29 - 6 * q^31 + 3 * q^32 - 3 * q^33 - 3 * q^34 + 3 * q^36 + 9 * q^37 + 3 * q^38 - 12 * q^41 + 9 * q^43 + 3 * q^44 + 9 * q^46 + 15 * q^47 - 3 * q^48 + 3 * q^50 + 3 * q^51 - 3 * q^54 - 3 * q^57 + 9 * q^58 - 9 * q^59 + 6 * q^61 - 6 * q^62 + 3 * q^64 + 36 * q^65 - 3 * q^66 + 6 * q^67 - 3 * q^68 - 9 * q^69 + 3 * q^71 + 3 * q^72 + 9 * q^74 - 3 * q^75 + 3 * q^76 + 12 * q^79 + 3 * q^81 - 12 * q^82 + 6 * q^83 + 9 * q^86 - 9 * q^87 + 3 * q^88 + 36 * q^89 + 9 * q^92 + 6 * q^93 + 15 * q^94 - 24 * q^95 - 3 * q^96 - 9 * q^97 + 3 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−0.454904	−0.203439	−0.101720	−	0.994813i	$-0.532434\pi$
$5$	−0.454904	−0.203439	−0.101720	+	0.994813i	$0.532434\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.454904	−0.143853
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	−0.909808	−0.252335	−0.126168	−	0.992009i	$-0.540268\pi$
$13$	−0.909808	−0.252335	−0.126168	+	0.992009i	$0.540268\pi$
$14$	0	0
$15$	0.454904	0.117456
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536	−0.121268	−	0.992620i	$-0.538696\pi$
$17$	−1.00000	−0.242536	−0.121268	+	0.992620i	$0.538696\pi$
$18$	1.00000	0.235702
$19$	−3.88325	−0.890880	−0.445440	−	0.895312i	$-0.646953\pi$
$19$	−3.88325	−0.890880	−0.445440	+	0.895312i	$0.646953\pi$
$20$	−0.454904	−0.101720
$21$	0	0
$22$	1.00000	0.213201
$23$	8.33816	1.73863	0.869313	−	0.494262i	$-0.164562\pi$
$23$	8.33816	1.73863	0.869313	+	0.494262i	$0.164562\pi$
$24$	−1.00000	−0.204124
$25$	−4.79306	−0.958612
$26$	−0.909808	−0.178428
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−2.79306	−0.518659	−0.259329	−	0.965789i	$-0.583502\pi$
$29$	−2.79306	−0.518659	−0.259329	+	0.965789i	$0.583502\pi$
$30$	0.454904	0.0830537
$31$	9.58612	1.72172	0.860859	−	0.508843i	$-0.169927\pi$
$31$	9.58612	1.72172	0.860859	+	0.508843i	$0.169927\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	−1.00000	−0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	7.88325	1.29600	0.647999	−	0.761641i	$-0.275606\pi$
$37$	7.88325	1.29600	0.647999	+	0.761641i	$0.275606\pi$
$38$	−3.88325	−0.629947
$39$	0.909808	0.145686
$40$	−0.454904	−0.0719267
$41$	1.79306	0.280029	0.140015	−	0.990149i	$-0.455285\pi$
$41$	1.79306	0.280029	0.140015	+	0.990149i	$0.455285\pi$
$42$	0	0
$43$	7.88325	1.20218	0.601092	−	0.799179i	$-0.294732\pi$
$43$	7.88325	1.20218	0.601092	+	0.799179i	$0.294732\pi$
$44$	1.00000	0.150756
$45$	−0.454904	−0.0678131
$46$	8.33816	1.22939
$47$	−0.338158	−0.0493254	−0.0246627	−	0.999696i	$-0.507851\pi$
$47$	−0.338158	−0.0493254	−0.0246627	+	0.999696i	$0.507851\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	−4.79306	−0.677841
$51$	1.00000	0.140028
$52$	−0.909808	−0.126168
$53$	0.909808	0.124972	0.0624859	−	0.998046i	$-0.480097\pi$
$53$	0.909808	0.124972	0.0624859	+	0.998046i	$0.480097\pi$
$54$	−1.00000	−0.136083
$55$	−0.454904	−0.0613393
$56$	0	0
$57$	3.88325	0.514350
$58$	−2.79306	−0.366747
$59$	−6.97345	−0.907865	−0.453933	−	0.891036i	$-0.649979\pi$
$59$	−6.97345	−0.907865	−0.453933	+	0.891036i	$0.649979\pi$
$60$	0.454904	0.0587279
$61$	14.0410	1.79777	0.898885	−	0.438185i	$-0.144379\pi$
$61$	14.0410	1.79777	0.898885	+	0.438185i	$0.144379\pi$
$62$	9.58612	1.21744
$63$	0	0
$64$	1.00000	0.125000
$65$	0.413875	0.0513349
$66$	−1.00000	−0.123091
$67$	−3.79306	−0.463396	−0.231698	−	0.972788i	$-0.574428\pi$
$67$	−3.79306	−0.463396	−0.231698	+	0.972788i	$0.574428\pi$
$68$	−1.00000	−0.121268
$69$	−8.33816	−1.00380
$70$	0	0
$71$	−4.79306	−0.568832	−0.284416	−	0.958701i	$-0.591800\pi$
$71$	−4.79306	−0.568832	−0.284416	+	0.958701i	$0.591800\pi$
$72$	1.00000	0.117851
$73$	−10.6763	−1.24957	−0.624784	−	0.780798i	$-0.714813\pi$
$73$	−10.6763	−1.24957	−0.624784	+	0.780798i	$0.714813\pi$
$74$	7.88325	0.916410
$75$	4.79306	0.553455
$76$	−3.88325	−0.445440
$77$	0	0
$78$	0.909808	0.103015
$79$	5.36471	0.603577	0.301789	−	0.953375i	$-0.402416\pi$
$79$	5.36471	0.603577	0.301789	+	0.953375i	$0.402416\pi$
$80$	−0.454904	−0.0508598
$81$	1.00000	0.111111
$82$	1.79306	0.198011
$83$	−1.97345	−0.216614	−0.108307	−	0.994118i	$-0.534543\pi$
$83$	−1.97345	−0.216614	−0.108307	+	0.994118i	$0.534543\pi$
$84$	0	0
$85$	0.454904	0.0493413
$86$	7.88325	0.850073
$87$	2.79306	0.299448
$88$	1.00000	0.106600
$89$	11.0902	1.17556	0.587779	−	0.809022i	$-0.300002\pi$
$89$	11.0902	1.17556	0.587779	+	0.809022i	$0.300002\pi$
$90$	−0.454904	−0.0479511
$91$	0	0
$92$	8.33816	0.869313
$93$	−9.58612	−0.994035
$94$	−0.338158	−0.0348784
$95$	1.76651	0.181240
$96$	−1.00000	−0.102062
$97$	−14.5861	−1.48100	−0.740498	−	0.672058i	$-0.765410\pi$
$97$	−14.5861	−1.48100	−0.740498	+	0.672058i	$0.765410\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	−4.79306	−0.479306
$101$	8.06364	0.802362	0.401181	−	0.915999i	$-0.368600\pi$
$101$	8.06364	0.802362	0.401181	+	0.915999i	$0.368600\pi$
$102$	1.00000	0.0990148
$103$	−5.76651	−0.568191	−0.284095	−	0.958796i	$-0.591693\pi$
$103$	−5.76651	−0.568191	−0.284095	+	0.958796i	$0.591693\pi$
$104$	−0.909808	−0.0892140
$105$	0	0
$106$	0.909808	0.0883684
$107$	15.6127	1.50933	0.754667	−	0.656108i	$-0.227798\pi$
$107$	15.6127	1.50933	0.754667	+	0.656108i	$0.227798\pi$
$108$	−1.00000	−0.0962250
$109$	14.0410	1.34489	0.672443	−	0.740149i	$-0.265245\pi$
$109$	14.0410	1.34489	0.672443	+	0.740149i	$0.265245\pi$
$110$	−0.454904	−0.0433734
$111$	−7.88325	−0.748245
$112$	0	0
$113$	7.58612	0.713643	0.356821	−	0.934173i	$-0.383861\pi$
$113$	7.58612	0.713643	0.356821	+	0.934173i	$0.383861\pi$
$114$	3.88325	0.363700
$115$	−3.79306	−0.353705
$116$	−2.79306	−0.259329
$117$	−0.909808	−0.0841118
$118$	−6.97345	−0.641958
$119$	0	0
$120$	0.454904	0.0415269
$121$	1.00000	0.0909091
$122$	14.0410	1.27122
$123$	−1.79306	−0.161675
$124$	9.58612	0.860859
$125$	4.45490	0.398459
$126$	0	0
$127$	7.42835	0.659159	0.329580	−	0.944128i	$-0.393093\pi$
$127$	7.42835	0.659159	0.329580	+	0.944128i	$0.393093\pi$
$128$	1.00000	0.0883883
$129$	−7.88325	−0.694082
$130$	0.413875	0.0362993
$131$	19.4057	1.69549	0.847744	−	0.530406i	$-0.177961\pi$
$131$	19.4057	1.69549	0.847744	+	0.530406i	$0.177961\pi$
$132$	−1.00000	−0.0870388
$133$	0	0
$134$	−3.79306	−0.327671
$135$	0.454904	0.0391519
$136$	−1.00000	−0.0857493
$137$	0.909808	0.0777302	0.0388651	−	0.999244i	$-0.487626\pi$
$137$	0.909808	0.0777302	0.0388651	+	0.999244i	$0.487626\pi$
$138$	−8.33816	−0.709791
$139$	8.37919	0.710713	0.355357	−	0.934731i	$-0.384359\pi$
$139$	8.37919	0.710713	0.355357	+	0.934731i	$0.384359\pi$
$140$	0	0
$141$	0.338158	0.0284781
$142$	−4.79306	−0.402225
$143$	−0.909808	−0.0760820
$144$	1.00000	0.0833333
$145$	1.27058	0.105516
$146$	−10.6763	−0.883578
$147$	0	0
$148$	7.88325	0.647999
$149$	4.11675	0.337257	0.168628	−	0.985680i	$-0.446066\pi$
$149$	4.11675	0.337257	0.168628	+	0.985680i	$0.446066\pi$
$150$	4.79306	0.391352
$151$	−6.15777	−0.501113	−0.250556	−	0.968102i	$-0.580614\pi$
$151$	−6.15777	−0.501113	−0.250556	+	0.968102i	$0.580614\pi$
$152$	−3.88325	−0.314973
$153$	−1.00000	−0.0808452
$154$	0	0
$155$	−4.36077	−0.350265
$156$	0.909808	0.0728430
$157$	17.6498	1.40860	0.704302	−	0.709900i	$-0.251260\pi$
$157$	17.6498	1.40860	0.704302	+	0.709900i	$0.251260\pi$
$158$	5.36471	0.426794
$159$	−0.909808	−0.0721525
$160$	−0.454904	−0.0359633
$161$	0	0
$162$	1.00000	0.0785674
$163$	−11.6127	−0.909575	−0.454788	−	0.890600i	$-0.650285\pi$
$163$	−11.6127	−0.909575	−0.454788	+	0.890600i	$0.650285\pi$
$164$	1.79306	0.140015
$165$	0.454904	0.0354142
$166$	−1.97345	−0.153169
$167$	4.85670	0.375823	0.187911	−	0.982186i	$-0.439828\pi$
$167$	4.85670	0.375823	0.187911	+	0.982186i	$0.439828\pi$
$168$	0	0
$169$	−12.1722	−0.936327
$170$	0.454904	0.0348896
$171$	−3.88325	−0.296960
$172$	7.88325	0.601092
$173$	25.5861	1.94528	0.972639	−	0.232324i	$-0.0746329\pi$
$173$	25.5861	1.94528	0.972639	+	0.232324i	$0.0746329\pi$
$174$	2.79306	0.211742
$175$	0	0
$176$	1.00000	0.0753778
$177$	6.97345	0.524156
$178$	11.0902	0.831245
$179$	−15.7029	−1.17369	−0.586844	−	0.809700i	$-0.699630\pi$
$179$	−15.7029	−1.17369	−0.586844	+	0.809700i	$0.699630\pi$
$180$	−0.454904	−0.0339065
$181$	2.49593	0.185521	0.0927606	−	0.995688i	$-0.470431\pi$
$181$	2.49593	0.185521	0.0927606	+	0.995688i	$0.470431\pi$
$182$	0	0
$183$	−14.0410	−1.03794
$184$	8.33816	0.614697
$185$	−3.58612	−0.263657
$186$	−9.58612	−0.702889
$187$	−1.00000	−0.0731272
$188$	−0.338158	−0.0246627
$189$	0	0
$190$	1.76651	0.128156
$191$	9.81962	0.710523	0.355261	−	0.934767i	$-0.384392\pi$
$191$	9.81962	0.710523	0.355261	+	0.934767i	$0.384392\pi$
$192$	−1.00000	−0.0721688
$193$	6.85670	0.493556	0.246778	−	0.969072i	$-0.420628\pi$
$193$	6.85670	0.493556	0.246778	+	0.969072i	$0.420628\pi$
$194$	−14.5861	−1.04722
$195$	−0.413875	−0.0296382
$196$	0	0
$197$	23.4694	1.67212	0.836062	−	0.548635i	$-0.184852\pi$
$197$	23.4694	1.67212	0.836062	+	0.548635i	$0.184852\pi$
$198$	1.00000	0.0710669
$199$	2.23349	0.158328	0.0791640	−	0.996862i	$-0.474775\pi$
$199$	2.23349	0.158328	0.0791640	+	0.996862i	$0.474775\pi$
$200$	−4.79306	−0.338921
$201$	3.79306	0.267542
$202$	8.06364	0.567356
$203$	0	0
$204$	1.00000	0.0700140
$205$	−0.815671	−0.0569690
$206$	−5.76651	−0.401772
$207$	8.33816	0.579542
$208$	−0.909808	−0.0630838
$209$	−3.88325	−0.268610
$210$	0	0
$211$	−18.2624	−1.25724	−0.628619	−	0.777713i	$-0.716380\pi$
$211$	−18.2624	−1.25724	−0.628619	+	0.777713i	$0.716380\pi$
$212$	0.909808	0.0624859
$213$	4.79306	0.328415
$214$	15.6127	1.06726
$215$	−3.58612	−0.244572
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	14.0410	0.950978
$219$	10.6763	0.721439
$220$	−0.454904	−0.0306696
$221$	0.909808	0.0612003
$222$	−7.88325	−0.529089
$223$	−12.4959	−0.836790	−0.418395	−	0.908265i	$-0.637407\pi$
$223$	−12.4959	−0.836790	−0.418395	+	0.908265i	$0.637407\pi$
$224$	0	0
$225$	−4.79306	−0.319537
$226$	7.58612	0.504621
$227$	−9.79306	−0.649988	−0.324994	−	0.945716i	$-0.605362\pi$
$227$	−9.79306	−0.649988	−0.324994	+	0.945716i	$0.605362\pi$
$228$	3.88325	0.257175
$229$	−8.67632	−0.573347	−0.286674	−	0.958028i	$-0.592550\pi$
$229$	−8.67632	−0.573347	−0.286674	+	0.958028i	$0.592550\pi$
$230$	−3.79306	−0.250107
$231$	0	0
$232$	−2.79306	−0.183374
$233$	16.7665	1.09841	0.549205	−	0.835688i	$-0.314931\pi$
$233$	16.7665	1.09841	0.549205	+	0.835688i	$0.314931\pi$
$234$	−0.909808	−0.0594760
$235$	0.153830	0.0100347
$236$	−6.97345	−0.453933
$237$	−5.36471	−0.348476
$238$	0	0
$239$	−26.2624	−1.69878	−0.849388	−	0.527769i	$-0.823029\pi$
$239$	−26.2624	−1.69878	−0.849388	+	0.527769i	$0.823029\pi$
$240$	0.454904	0.0293639
$241$	−7.94689	−0.511904	−0.255952	−	0.966689i	$-0.582389\pi$
$241$	−7.94689	−0.511904	−0.255952	+	0.966689i	$0.582389\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	14.0410	0.898885
$245$	0	0
$246$	−1.79306	−0.114321
$247$	3.53302	0.224800
$248$	9.58612	0.608720
$249$	1.97345	0.125062
$250$	4.45490	0.281753
$251$	3.93636	0.248461	0.124230	−	0.992253i	$-0.460354\pi$
$251$	3.93636	0.248461	0.124230	+	0.992253i	$0.460354\pi$
$252$	0	0
$253$	8.33816	0.524216
$254$	7.42835	0.466096
$255$	−0.454904	−0.0284872
$256$	1.00000	0.0625000
$257$	15.0902	0.941300	0.470650	−	0.882320i	$-0.344019\pi$
$257$	15.0902	0.941300	0.470650	+	0.882320i	$0.344019\pi$
$258$	−7.88325	−0.490790
$259$	0	0
$260$	0.413875	0.0256675
$261$	−2.79306	−0.172886
$262$	19.4057	1.19889
$263$	−28.6232	−1.76498	−0.882491	−	0.470329i	$-0.844135\pi$
$263$	−28.6232	−1.76498	−0.882491	+	0.470329i	$0.844135\pi$
$264$	−1.00000	−0.0615457
$265$	−0.413875	−0.0254242
$266$	0	0
$267$	−11.0902	−0.678709
$268$	−3.79306	−0.231698
$269$	22.9508	1.39934	0.699669	−	0.714468i	$-0.253331\pi$
$269$	22.9508	1.39934	0.699669	+	0.714468i	$0.253331\pi$
$270$	0.454904	0.0276846
$271$	−9.81962	−0.596499	−0.298250	−	0.954488i	$-0.596403\pi$
$271$	−9.81962	−0.596499	−0.298250	+	0.954488i	$0.596403\pi$
$272$	−1.00000	−0.0606339
$273$	0	0
$274$	0.909808	0.0549635
$275$	−4.79306	−0.289033
$276$	−8.33816	−0.501898
$277$	10.7294	0.644669	0.322334	−	0.946626i	$-0.395532\pi$
$277$	10.7294	0.644669	0.322334	+	0.946626i	$0.395532\pi$
$278$	8.37919	0.502550
$279$	9.58612	0.573906
$280$	0	0
$281$	2.58612	0.154275	0.0771376	−	0.997020i	$-0.475422\pi$
$281$	2.58612	0.154275	0.0771376	+	0.997020i	$0.475422\pi$
$282$	0.338158	0.0201370
$283$	20.0821	1.19375	0.596877	−	0.802333i	$-0.296408\pi$
$283$	20.0821	1.19375	0.596877	+	0.802333i	$0.296408\pi$
$284$	−4.79306	−0.284416
$285$	−1.76651	−0.104639
$286$	−0.909808	−0.0537981
$287$	0	0
$288$	1.00000	0.0589256
$289$	−16.0000	−0.941176
$290$	1.27058	0.0746108
$291$	14.5861	0.855054
$292$	−10.6763	−0.624784
$293$	−10.3792	−0.606359	−0.303179	−	0.952934i	$-0.598048\pi$
$293$	−10.3792	−0.606359	−0.303179	+	0.952934i	$0.598048\pi$
$294$	0	0
$295$	3.17225	0.184695
$296$	7.88325	0.458205
$297$	−1.00000	−0.0580259
$298$	4.11675	0.238477
$299$	−7.58612	−0.438717
$300$	4.79306	0.276728
$301$	0	0
$302$	−6.15777	−0.354340
$303$	−8.06364	−0.463244
$304$	−3.88325	−0.222720
$305$	−6.38732	−0.365737
$306$	−1.00000	−0.0571662
$307$	−9.76651	−0.557404	−0.278702	−	0.960378i	$-0.589904\pi$
$307$	−9.76651	−0.557404	−0.278702	+	0.960378i	$0.589904\pi$
$308$	0	0
$309$	5.76651	0.328045
$310$	−4.36077	−0.247675
$311$	6.51854	0.369633	0.184816	−	0.982773i	$-0.440831\pi$
$311$	6.51854	0.369633	0.184816	+	0.982773i	$0.440831\pi$
$312$	0.909808	0.0515077
$313$	−30.7931	−1.74053	−0.870263	−	0.492587i	$-0.836051\pi$
$313$	−30.7931	−1.74053	−0.870263	+	0.492587i	$0.836051\pi$
$314$	17.6498	0.996034
$315$	0	0
$316$	5.36471	0.301789
$317$	−27.6272	−1.55170	−0.775848	−	0.630920i	$-0.782678\pi$
$317$	−27.6272	−1.55170	−0.775848	+	0.630920i	$0.782678\pi$
$318$	−0.909808	−0.0510195
$319$	−2.79306	−0.156381
$320$	−0.454904	−0.0254299
$321$	−15.6127	−0.871415
$322$	0	0
$323$	3.88325	0.216070
$324$	1.00000	0.0555556
$325$	4.36077	0.241892
$326$	−11.6127	−0.643167
$327$	−14.0410	−0.776471
$328$	1.79306	0.0990053
$329$	0	0
$330$	0.454904	0.0250416
$331$	−28.9653	−1.59208	−0.796039	−	0.605246i	$-0.793075\pi$
$331$	−28.9653	−1.59208	−0.796039	+	0.605246i	$0.793075\pi$
$332$	−1.97345	−0.108307
$333$	7.88325	0.432000
$334$	4.85670	0.265747
$335$	1.72548	0.0942730
$336$	0	0
$337$	−9.03708	−0.492281	−0.246141	−	0.969234i	$-0.579163\pi$
$337$	−9.03708	−0.492281	−0.246141	+	0.969234i	$0.579163\pi$
$338$	−12.1722	−0.662083
$339$	−7.58612	−0.412022
$340$	0.454904	0.0246706
$341$	9.58612	0.519118
$342$	−3.88325	−0.209982
$343$	0	0
$344$	7.88325	0.425037
$345$	3.79306	0.204212
$346$	25.5861	1.37552
$347$	−21.6127	−1.16023	−0.580115	−	0.814535i	$-0.696992\pi$
$347$	−21.6127	−1.16023	−0.580115	+	0.814535i	$0.696992\pi$
$348$	2.79306	0.149724
$349$	−14.2745	−0.764098	−0.382049	−	0.924142i	$-0.624781\pi$
$349$	−14.2745	−0.764098	−0.382049	+	0.924142i	$0.624781\pi$
$350$	0	0
$351$	0.909808	0.0485620
$352$	1.00000	0.0533002
$353$	28.4959	1.51669	0.758343	−	0.651856i	$-0.226009\pi$
$353$	28.4959	1.51669	0.758343	+	0.651856i	$0.226009\pi$
$354$	6.97345	0.370634
$355$	2.18038	0.115723
$356$	11.0902	0.587779
$357$	0	0
$358$	−15.7029	−0.829922
$359$	−13.6392	−0.719851	−0.359926	−	0.932981i	$-0.617198\pi$
$359$	−13.6392	−0.719851	−0.359926	+	0.932981i	$0.617198\pi$
$360$	−0.454904	−0.0239756
$361$	−3.92034	−0.206334
$362$	2.49593	0.131183
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	4.85670	0.254211
$366$	−14.0410	−0.733936
$367$	−22.7294	−1.18647	−0.593233	−	0.805031i	$-0.702149\pi$
$367$	−22.7294	−1.18647	−0.593233	+	0.805031i	$0.702149\pi$
$368$	8.33816	0.434657
$369$	1.79306	0.0933431
$370$	−3.58612	−0.186434
$371$	0	0
$372$	−9.58612	−0.497017
$373$	10.4018	0.538585	0.269292	−	0.963058i	$-0.413210\pi$
$373$	10.4018	0.538585	0.269292	+	0.963058i	$0.413210\pi$
$374$	−1.00000	−0.0517088
$375$	−4.45490	−0.230050
$376$	−0.338158	−0.0174392
$377$	2.54115	0.130876
$378$	0	0
$379$	7.61268	0.391037	0.195519	−	0.980700i	$-0.437361\pi$
$379$	7.61268	0.391037	0.195519	+	0.980700i	$0.437361\pi$
$380$	1.76651	0.0906200
$381$	−7.42835	−0.380566
$382$	9.81962	0.502415
$383$	22.1457	1.13159	0.565796	−	0.824545i	$-0.308569\pi$
$383$	22.1457	1.13159	0.565796	+	0.824545i	$0.308569\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	6.85670	0.348997
$387$	7.88325	0.400728
$388$	−14.5861	−0.740498
$389$	−3.54510	−0.179743	−0.0898717	−	0.995953i	$-0.528646\pi$
$389$	−3.54510	−0.179743	−0.0898717	+	0.995953i	$0.528646\pi$
$390$	−0.413875	−0.0209574
$391$	−8.33816	−0.421679
$392$	0	0
$393$	−19.4057	−0.978890
$394$	23.4694	1.18237
$395$	−2.44043	−0.122791
$396$	1.00000	0.0502519
$397$	2.55957	0.128461	0.0642306	−	0.997935i	$-0.479541\pi$
$397$	2.55957	0.128461	0.0642306	+	0.997935i	$0.479541\pi$
$398$	2.23349	0.111955
$399$	0	0
$400$	−4.79306	−0.239653
$401$	10.4959	0.524142	0.262071	−	0.965049i	$-0.415595\pi$
$401$	10.4959	0.524142	0.262071	+	0.965049i	$0.415595\pi$
$402$	3.79306	0.189181
$403$	−8.72153	−0.434451
$404$	8.06364	0.401181
$405$	−0.454904	−0.0226044
$406$	0	0
$407$	7.88325	0.390758
$408$	1.00000	0.0495074
$409$	−15.8486	−0.783661	−0.391831	−	0.920037i	$-0.628158\pi$
$409$	−15.8486	−0.783661	−0.391831	+	0.920037i	$0.628158\pi$
$410$	−0.815671	−0.0402831
$411$	−0.909808	−0.0448775
$412$	−5.76651	−0.284095
$413$	0	0
$414$	8.33816	0.409798
$415$	0.897729	0.0440678
$416$	−0.909808	−0.0446070
$417$	−8.37919	−0.410331
$418$	−3.88325	−0.189936
$419$	9.52249	0.465204	0.232602	−	0.972572i	$-0.425276\pi$
$419$	9.52249	0.465204	0.232602	+	0.972572i	$0.425276\pi$
$420$	0	0
$421$	−0.530621	−0.0258609	−0.0129305	−	0.999916i	$-0.504116\pi$
$421$	−0.530621	−0.0258609	−0.0129305	+	0.999916i	$0.504116\pi$
$422$	−18.2624	−0.889002
$423$	−0.338158	−0.0164418
$424$	0.909808	0.0441842
$425$	4.79306	0.232498
$426$	4.79306	0.232225
$427$	0	0
$428$	15.6127	0.754667
$429$	0.909808	0.0439260
$430$	−3.58612	−0.172938
$431$	20.8036	1.00207	0.501037	−	0.865426i	$-0.332952\pi$
$431$	20.8036	1.00207	0.501037	+	0.865426i	$0.332952\pi$
$432$	−1.00000	−0.0481125
$433$	4.40574	0.211726	0.105863	−	0.994381i	$-0.466239\pi$
$433$	4.40574	0.211726	0.105863	+	0.994381i	$0.466239\pi$
$434$	0	0
$435$	−1.27058	−0.0609194
$436$	14.0410	0.672443
$437$	−32.3792	−1.54891
$438$	10.6763	0.510134
$439$	15.1949	0.725211	0.362606	−	0.931943i	$-0.381887\pi$
$439$	15.1949	0.725211	0.362606	+	0.931943i	$0.381887\pi$
$440$	−0.454904	−0.0216867
$441$	0	0
$442$	0.909808	0.0432752
$443$	−11.3873	−0.541028	−0.270514	−	0.962716i	$-0.587194\pi$
$443$	−11.3873	−0.541028	−0.270514	+	0.962716i	$0.587194\pi$
$444$	−7.88325	−0.374123
$445$	−5.04497	−0.239155
$446$	−12.4959	−0.591700
$447$	−4.11675	−0.194715
$448$	0	0
$449$	−24.0821	−1.13650	−0.568251	−	0.822855i	$-0.692380\pi$
$449$	−24.0821	−1.13650	−0.568251	+	0.822855i	$0.692380\pi$
$450$	−4.79306	−0.225947
$451$	1.79306	0.0844320
$452$	7.58612	0.356821
$453$	6.15777	0.289317
$454$	−9.79306	−0.459611
$455$	0	0
$456$	3.88325	0.181850
$457$	−29.5330	−1.38150	−0.690748	−	0.723095i	$-0.742719\pi$
$457$	−29.5330	−1.38150	−0.690748	+	0.723095i	$0.742719\pi$
$458$	−8.67632	−0.405418
$459$	1.00000	0.0466760
$460$	−3.79306	−0.176852
$461$	−4.14569	−0.193084	−0.0965421	−	0.995329i	$-0.530778\pi$
$461$	−4.14569	−0.193084	−0.0965421	+	0.995329i	$0.530778\pi$
$462$	0	0
$463$	−9.32368	−0.433308	−0.216654	−	0.976248i	$-0.569514\pi$
$463$	−9.32368	−0.433308	−0.216654	+	0.976248i	$0.569514\pi$
$464$	−2.79306	−0.129665
$465$	4.36077	0.202226
$466$	16.7665	0.776693
$467$	−36.5596	−1.69178	−0.845888	−	0.533361i	$-0.820929\pi$
$467$	−36.5596	−1.69178	−0.845888	+	0.533361i	$0.820929\pi$
$468$	−0.909808	−0.0420559
$469$	0	0
$470$	0.153830	0.00709563
$471$	−17.6498	−0.813258
$472$	−6.97345	−0.320979
$473$	7.88325	0.362472
$474$	−5.36471	−0.246409
$475$	18.6127	0.854008
$476$	0	0
$477$	0.909808	0.0416573
$478$	−26.2624	−1.20122
$479$	−0.729425	−0.0333283	−0.0166641	−	0.999861i	$-0.505305\pi$
$479$	−0.729425	−0.0333283	−0.0166641	+	0.999861i	$0.505305\pi$
$480$	0.454904	0.0207634
$481$	−7.17225	−0.327026
$482$	−7.94689	−0.361971
$483$	0	0
$484$	1.00000	0.0454545
$485$	6.63529	0.301293
$486$	−1.00000	−0.0453609
$487$	−36.8567	−1.67014	−0.835068	−	0.550146i	$-0.814572\pi$
$487$	−36.8567	−1.67014	−0.835068	+	0.550146i	$0.814572\pi$
$488$	14.0410	0.635608
$489$	11.6127	0.525143
$490$	0	0
$491$	25.5065	1.15109	0.575545	−	0.817770i	$-0.304790\pi$
$491$	25.5065	1.15109	0.575545	+	0.817770i	$0.304790\pi$
$492$	−1.79306	−0.0808375
$493$	2.79306	0.125793
$494$	3.53302	0.158958
$495$	−0.454904	−0.0204464
$496$	9.58612	0.430430
$497$	0	0
$498$	1.97345	0.0884322
$499$	−4.12728	−0.184762	−0.0923811	−	0.995724i	$-0.529448\pi$
$499$	−4.12728	−0.184762	−0.0923811	+	0.995724i	$0.529448\pi$
$500$	4.45490	0.199229
$501$	−4.85670	−0.216981
$502$	3.93636	0.175688
$503$	6.85670	0.305725	0.152863	−	0.988247i	$-0.451151\pi$
$503$	6.85670	0.305725	0.152863	+	0.988247i	$0.451151\pi$
$504$	0	0
$505$	−3.66818	−0.163232
$506$	8.33816	0.370676
$507$	12.1722	0.540589
$508$	7.42835	0.329580
$509$	−16.4428	−0.728815	−0.364408	−	0.931240i	$-0.618729\pi$
$509$	−16.4428	−0.728815	−0.364408	+	0.931240i	$0.618729\pi$
$510$	−0.454904	−0.0201435
$511$	0	0
$512$	1.00000	0.0441942
$513$	3.88325	0.171450
$514$	15.0902	0.665600
$515$	2.62321	0.115592
$516$	−7.88325	−0.347041
$517$	−0.338158	−0.0148722
$518$	0	0
$519$	−25.5861	−1.12311
$520$	0.413875	0.0181496
$521$	5.63923	0.247059	0.123530	−	0.992341i	$-0.460579\pi$
$521$	5.63923	0.247059	0.123530	+	0.992341i	$0.460579\pi$
$522$	−2.79306	−0.122249
$523$	4.08206	0.178496	0.0892480	−	0.996009i	$-0.471554\pi$
$523$	4.08206	0.178496	0.0892480	+	0.996009i	$0.471554\pi$
$524$	19.4057	0.847744
$525$	0	0
$526$	−28.6232	−1.24803
$527$	−9.58612	−0.417578
$528$	−1.00000	−0.0435194
$529$	46.5249	2.02282
$530$	−0.413875	−0.0179776
$531$	−6.97345	−0.302622
$532$	0	0
$533$	−1.63134	−0.0706613
$534$	−11.0902	−0.479920
$535$	−7.10227	−0.307058
$536$	−3.79306	−0.163835
$537$	15.7029	0.677629
$538$	22.9508	0.989481
$539$	0	0
$540$	0.454904	0.0195760
$541$	−4.89773	−0.210570	−0.105285	−	0.994442i	$-0.533575\pi$
$541$	−4.89773	−0.210570	−0.105285	+	0.994442i	$0.533575\pi$
$542$	−9.81962	−0.421789
$543$	−2.49593	−0.107111
$544$	−1.00000	−0.0428746
$545$	−6.38732	−0.273603
$546$	0	0
$547$	21.4694	0.917964	0.458982	−	0.888445i	$-0.348214\pi$
$547$	21.4694	0.917964	0.458982	+	0.888445i	$0.348214\pi$
$548$	0.909808	0.0388651
$549$	14.0410	0.599256
$550$	−4.79306	−0.204377
$551$	10.8462	0.462062
$552$	−8.33816	−0.354896
$553$	0	0
$554$	10.7294	0.455850
$555$	3.58612	0.152223
$556$	8.37919	0.355357
$557$	−39.4694	−1.67237	−0.836186	−	0.548447i	$-0.815219\pi$
$557$	−39.4694	−1.67237	−0.836186	+	0.548447i	$0.815219\pi$
$558$	9.58612	0.405813
$559$	−7.17225	−0.303354
$560$	0	0
$561$	1.00000	0.0422200
$562$	2.58612	0.109089
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	0.338158	0.0142390
$565$	−3.45096	−0.145183
$566$	20.0821	0.844112
$567$	0	0
$568$	−4.79306	−0.201112
$569$	34.1988	1.43369	0.716844	−	0.697233i	$-0.245586\pi$
$569$	34.1988	1.43369	0.716844	+	0.697233i	$0.245586\pi$
$570$	−1.76651	−0.0739909
$571$	14.7931	0.619070	0.309535	−	0.950888i	$-0.399827\pi$
$571$	14.7931	0.619070	0.309535	+	0.950888i	$0.399827\pi$
$572$	−0.909808	−0.0380410
$573$	−9.81962	−0.410220
$574$	0	0
$575$	−39.9653	−1.66667
$576$	1.00000	0.0416667
$577$	7.19880	0.299690	0.149845	−	0.988709i	$-0.452123\pi$
$577$	7.19880	0.299690	0.149845	+	0.988709i	$0.452123\pi$
$578$	−16.0000	−0.665512
$579$	−6.85670	−0.284955
$580$	1.27058	0.0527578
$581$	0	0
$582$	14.5861	0.604614
$583$	0.909808	0.0376804
$584$	−10.6763	−0.441789
$585$	0.413875	0.0171116
$586$	−10.3792	−0.428760
$587$	44.4959	1.83654	0.918272	−	0.395951i	$-0.129585\pi$
$587$	44.4959	1.83654	0.918272	+	0.395951i	$0.129585\pi$
$588$	0	0
$589$	−37.2254	−1.53384
$590$	3.17225	0.130599
$591$	−23.4694	−0.965401
$592$	7.88325	0.324000
$593$	−17.9653	−0.737747	−0.368873	−	0.929480i	$-0.620256\pi$
$593$	−17.9653	−0.737747	−0.368873	+	0.929480i	$0.620256\pi$
$594$	−1.00000	−0.0410305
$595$	0	0
$596$	4.11675	0.168628
$597$	−2.23349	−0.0914107
$598$	−7.58612	−0.310220
$599$	−25.8075	−1.05447	−0.527234	−	0.849720i	$-0.676771\pi$
$599$	−25.8075	−1.05447	−0.527234	+	0.849720i	$0.676771\pi$
$600$	4.79306	0.195676
$601$	−10.4139	−0.424791	−0.212395	−	0.977184i	$-0.568126\pi$
$601$	−10.4139	−0.424791	−0.212395	+	0.977184i	$0.568126\pi$
$602$	0	0
$603$	−3.79306	−0.154465
$604$	−6.15777	−0.250556
$605$	−0.454904	−0.0184945
$606$	−8.06364	−0.327563
$607$	8.89773	0.361148	0.180574	−	0.983561i	$-0.442205\pi$
$607$	8.89773	0.361148	0.180574	+	0.983561i	$0.442205\pi$
$608$	−3.88325	−0.157487
$609$	0	0
$610$	−6.38732	−0.258615
$611$	0.307659	0.0124466
$612$	−1.00000	−0.0404226
$613$	−23.6272	−0.954292	−0.477146	−	0.878824i	$-0.658329\pi$
$613$	−23.6272	−0.954292	−0.477146	+	0.878824i	$0.658329\pi$
$614$	−9.76651	−0.394144
$615$	0.815671	0.0328910
$616$	0	0
$617$	−35.8486	−1.44321	−0.721604	−	0.692306i	$-0.756595\pi$
$617$	−35.8486	−1.44321	−0.721604	+	0.692306i	$0.756595\pi$
$618$	5.76651	0.231963
$619$	−27.9203	−1.12221	−0.561107	−	0.827744i	$-0.689624\pi$
$619$	−27.9203	−1.12221	−0.561107	+	0.827744i	$0.689624\pi$
$620$	−4.36077	−0.175133
$621$	−8.33816	−0.334599
$622$	6.51854	0.261370
$623$	0	0
$624$	0.909808	0.0364215
$625$	21.9388	0.877550
$626$	−30.7931	−1.23074
$627$	3.88325	0.155082
$628$	17.6498	0.704302
$629$	−7.88325	−0.314326
$630$	0	0
$631$	43.6682	1.73840	0.869201	−	0.494458i	$-0.164633\pi$
$631$	43.6682	1.73840	0.869201	+	0.494458i	$0.164633\pi$
$632$	5.36471	0.213397
$633$	18.2624	0.725867
$634$	−27.6272	−1.09721
$635$	−3.37919	−0.134099
$636$	−0.909808	−0.0360762
$637$	0	0
$638$	−2.79306	−0.110578
$639$	−4.79306	−0.189611
$640$	−0.454904	−0.0179817
$641$	−19.7665	−0.780730	−0.390365	−	0.920660i	$-0.627651\pi$
$641$	−19.7665	−0.780730	−0.390365	+	0.920660i	$0.627651\pi$
$642$	−15.6127	−0.616183
$643$	−24.7584	−0.976375	−0.488187	−	0.872739i	$-0.662342\pi$
$643$	−24.7584	−0.976375	−0.488187	+	0.872739i	$0.662342\pi$
$644$	0	0
$645$	3.58612	0.141204
$646$	3.88325	0.152785
$647$	−31.0781	−1.22181	−0.610903	−	0.791705i	$-0.709194\pi$
$647$	−31.0781	−1.22181	−0.610903	+	0.791705i	$0.709194\pi$
$648$	1.00000	0.0392837
$649$	−6.97345	−0.273732
$650$	4.36077	0.171043
$651$	0	0
$652$	−11.6127	−0.454788
$653$	22.7173	0.888998	0.444499	−	0.895779i	$-0.353382\pi$
$653$	22.7173	0.888998	0.444499	+	0.895779i	$0.353382\pi$
$654$	−14.0410	−0.549048
$655$	−8.82775	−0.344929
$656$	1.79306	0.0700073
$657$	−10.6763	−0.416523
$658$	0	0
$659$	43.6127	1.69891	0.849454	−	0.527662i	$-0.176931\pi$
$659$	43.6127	1.69891	0.849454	+	0.527662i	$0.176931\pi$
$660$	0.454904	0.0177071
$661$	7.93636	0.308689	0.154344	−	0.988017i	$-0.450673\pi$
$661$	7.93636	0.308689	0.154344	+	0.988017i	$0.450673\pi$
$662$	−28.9653	−1.12577
$663$	−0.909808	−0.0353340
$664$	−1.97345	−0.0765846
$665$	0	0
$666$	7.88325	0.305470
$667$	−23.2890	−0.901753
$668$	4.85670	0.187911
$669$	12.4959	0.483121
$670$	1.72548	0.0666611
$671$	14.0410	0.542048
$672$	0	0
$673$	36.9388	1.42388	0.711942	−	0.702238i	$-0.247816\pi$
$673$	36.9388	1.42388	0.711942	+	0.702238i	$0.247816\pi$
$674$	−9.03708	−0.348095
$675$	4.79306	0.184485
$676$	−12.1722	−0.468163
$677$	39.6498	1.52386	0.761932	−	0.647657i	$-0.224251\pi$
$677$	39.6498	1.52386	0.761932	+	0.647657i	$0.224251\pi$
$678$	−7.58612	−0.291343
$679$	0	0
$680$	0.454904	0.0174448
$681$	9.79306	0.375271
$682$	9.58612	0.367072
$683$	−45.5514	−1.74298	−0.871489	−	0.490416i	$-0.836845\pi$
$683$	−45.5514	−1.74298	−0.871489	+	0.490416i	$0.836845\pi$
$684$	−3.88325	−0.148480
$685$	−0.413875	−0.0158134
$686$	0	0
$687$	8.67632	0.331022
$688$	7.88325	0.300546
$689$	−0.827751	−0.0315348
$690$	3.79306	0.144399
$691$	19.1988	0.730357	0.365178	−	0.930938i	$-0.381008\pi$
$691$	19.1988	0.730357	0.365178	+	0.930938i	$0.381008\pi$
$692$	25.5861	0.972639
$693$	0	0
$694$	−21.6127	−0.820406
$695$	−3.81173	−0.144587
$696$	2.79306	0.105871
$697$	−1.79306	−0.0679171
$698$	−14.2745	−0.540299
$699$	−16.7665	−0.634168
$700$	0	0
$701$	23.2890	0.879613	0.439807	−	0.898093i	$-0.355047\pi$
$701$	23.2890	0.879613	0.439807	+	0.898093i	$0.355047\pi$
$702$	0.909808	0.0343385
$703$	−30.6127	−1.15458
$704$	1.00000	0.0376889
$705$	−0.153830	−0.00579356
$706$	28.4959	1.07246
$707$	0	0
$708$	6.97345	0.262078
$709$	−20.7931	−0.780900	−0.390450	−	0.920624i	$-0.627681\pi$
$709$	−20.7931	−0.780900	−0.390450	+	0.920624i	$0.627681\pi$
$710$	2.18038	0.0818283
$711$	5.36471	0.201192
$712$	11.0902	0.415623
$713$	79.9306	2.99343
$714$	0	0
$715$	0.413875	0.0154781
$716$	−15.7029	−0.586844
$717$	26.2624	0.980789
$718$	−13.6392	−0.509012
$719$	5.48146	0.204424	0.102212	−	0.994763i	$-0.467408\pi$
$719$	5.48146	0.204424	0.102212	+	0.994763i	$0.467408\pi$
$720$	−0.454904	−0.0169533
$721$	0	0
$722$	−3.92034	−0.145900
$723$	7.94689	0.295548
$724$	2.49593	0.0927606
$725$	13.3873	0.497193
$726$	−1.00000	−0.0371135
$727$	−25.5330	−0.946967	−0.473484	−	0.880803i	$-0.657004\pi$
$727$	−25.5330	−0.946967	−0.473484	+	0.880803i	$0.657004\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	4.85670	0.179755
$731$	−7.88325	−0.291573
$732$	−14.0410	−0.518971
$733$	−16.2214	−0.599152	−0.299576	−	0.954073i	$-0.596845\pi$
$733$	−16.2214	−0.599152	−0.299576	+	0.954073i	$0.596845\pi$
$734$	−22.7294	−0.838958
$735$	0	0
$736$	8.33816	0.307349
$737$	−3.79306	−0.139719
$738$	1.79306	0.0660035
$739$	18.7584	0.690038	0.345019	−	0.938596i	$-0.387872\pi$
$739$	18.7584	0.690038	0.345019	+	0.938596i	$0.387872\pi$
$740$	−3.58612	−0.131829
$741$	−3.53302	−0.129789
$742$	0	0
$743$	−44.6763	−1.63902	−0.819508	−	0.573068i	$-0.805753\pi$
$743$	−44.6763	−1.63902	−0.819508	+	0.573068i	$0.805753\pi$
$744$	−9.58612	−0.351444
$745$	−1.87272	−0.0686113
$746$	10.4018	0.380837
$747$	−1.97345	−0.0722046
$748$	−1.00000	−0.0365636
$749$	0	0
$750$	−4.45490	−0.162670
$751$	−2.96292	−0.108118	−0.0540592	−	0.998538i	$-0.517216\pi$
$751$	−2.96292	−0.108118	−0.0540592	+	0.998538i	$0.517216\pi$
$752$	−0.338158	−0.0123314
$753$	−3.93636	−0.143449
$754$	2.54115	0.0925433
$755$	2.80120	0.101946
$756$	0	0
$757$	26.1988	0.952212	0.476106	−	0.879388i	$-0.342048\pi$
$757$	26.1988	0.952212	0.476106	+	0.879388i	$0.342048\pi$
$758$	7.61268	0.276505
$759$	−8.33816	−0.302656
$760$	1.76651	0.0640780
$761$	−25.7931	−0.934998	−0.467499	−	0.883994i	$-0.654845\pi$
$761$	−25.7931	−0.934998	−0.467499	+	0.883994i	$0.654845\pi$
$762$	−7.42835	−0.269101
$763$	0	0
$764$	9.81962	0.355261
$765$	0.454904	0.0164471
$766$	22.1457	0.800156
$767$	6.34450	0.229087
$768$	−1.00000	−0.0360844
$769$	37.2012	1.34151	0.670755	−	0.741679i	$-0.265970\pi$
$769$	37.2012	1.34151	0.670755	+	0.741679i	$0.265970\pi$
$770$	0	0
$771$	−15.0902	−0.543460
$772$	6.85670	0.246778
$773$	40.7705	1.46641	0.733206	−	0.680007i	$-0.238023\pi$
$773$	40.7705	1.46641	0.733206	+	0.680007i	$0.238023\pi$
$774$	7.88325	0.283358
$775$	−45.9469	−1.65046
$776$	−14.5861	−0.523611
$777$	0	0
$778$	−3.54510	−0.127098
$779$	−6.96292	−0.249472
$780$	−0.413875	−0.0148191
$781$	−4.79306	−0.171509
$782$	−8.33816	−0.298172
$783$	2.79306	0.0998159
$784$	0	0
$785$	−8.02895	−0.286565
$786$	−19.4057	−0.692180
$787$	−54.5885	−1.94587	−0.972935	−	0.231078i	$-0.925775\pi$
$787$	−54.5885	−1.94587	−0.972935	+	0.231078i	$0.925775\pi$
$788$	23.4694	0.836062
$789$	28.6232	1.01901
$790$	−2.44043	−0.0868266
$791$	0	0
$792$	1.00000	0.0355335
$793$	−12.7746	−0.453641
$794$	2.55957	0.0908358
$795$	0.413875	0.0146787
$796$	2.23349	0.0791640
$797$	16.7705	0.594040	0.297020	−	0.954871i	$-0.404007\pi$
$797$	16.7705	0.594040	0.297020	+	0.954871i	$0.404007\pi$
$798$	0	0
$799$	0.338158	0.0119632
$800$	−4.79306	−0.169460
$801$	11.0902	0.391853
$802$	10.4959	0.370624
$803$	−10.6763	−0.376759
$804$	3.79306	0.133771
$805$	0	0
$806$	−8.72153	−0.307203
$807$	−22.9508	−0.807908
$808$	8.06364	0.283678
$809$	−10.2069	−0.358857	−0.179428	−	0.983771i	$-0.557425\pi$
$809$	−10.2069	−0.358857	−0.179428	+	0.983771i	$0.557425\pi$
$810$	−0.454904	−0.0159837
$811$	28.4139	0.997746	0.498873	−	0.866675i	$-0.333747\pi$
$811$	28.4139	0.997746	0.498873	+	0.866675i	$0.333747\pi$
$812$	0	0
$813$	9.81962	0.344389
$814$	7.88325	0.276308
$815$	5.28266	0.185043
$816$	1.00000	0.0350070
$817$	−30.6127	−1.07100
$818$	−15.8486	−0.554132
$819$	0	0
$820$	−0.815671	−0.0284845
$821$	−3.40574	−0.118861	−0.0594306	−	0.998232i	$-0.518928\pi$
$821$	−3.40574	−0.118861	−0.0594306	+	0.998232i	$0.518928\pi$
$822$	−0.909808	−0.0317332
$823$	−38.0289	−1.32561	−0.662803	−	0.748794i	$-0.730633\pi$
$823$	−38.0289	−1.32561	−0.662803	+	0.748794i	$0.730633\pi$
$824$	−5.76651	−0.200886
$825$	4.79306	0.166873
$826$	0	0
$827$	−12.9653	−0.450848	−0.225424	−	0.974261i	$-0.572377\pi$
$827$	−12.9653	−0.450848	−0.225424	+	0.974261i	$0.572377\pi$
$828$	8.33816	0.289771
$829$	−51.8833	−1.80198	−0.900990	−	0.433840i	$-0.857158\pi$
$829$	−51.8833	−1.80198	−0.900990	+	0.433840i	$0.857158\pi$
$830$	0.897729	0.0311606
$831$	−10.7294	−0.372200
$832$	−0.909808	−0.0315419
$833$	0	0
$834$	−8.37919	−0.290148
$835$	−2.20933	−0.0764571
$836$	−3.88325	−0.134305
$837$	−9.58612	−0.331345
$838$	9.52249	0.328949
$839$	50.2504	1.73484	0.867418	−	0.497581i	$-0.165778\pi$
$839$	50.2504	1.73484	0.867418	+	0.497581i	$0.165778\pi$
$840$	0	0
$841$	−21.1988	−0.730993
$842$	−0.530621	−0.0182864
$843$	−2.58612	−0.0890709
$844$	−18.2624	−0.628619
$845$	5.53721	0.190486
$846$	−0.338158	−0.0116261
$847$	0	0
$848$	0.909808	0.0312429
$849$	−20.0821	−0.689214
$850$	4.79306	0.164401
$851$	65.7318	2.25326
$852$	4.79306	0.164208
$853$	−13.3647	−0.457599	−0.228800	−	0.973474i	$-0.573480\pi$
$853$	−13.3647	−0.457599	−0.228800	+	0.973474i	$0.573480\pi$
$854$	0	0
$855$	1.76651	0.0604133
$856$	15.6127	0.533630
$857$	−26.3526	−0.900189	−0.450094	−	0.892981i	$-0.648610\pi$
$857$	−26.3526	−0.900189	−0.450094	+	0.892981i	$0.648610\pi$
$858$	0.909808	0.0310603
$859$	−1.97345	−0.0673331	−0.0336666	−	0.999433i	$-0.510718\pi$
$859$	−1.97345	−0.0673331	−0.0336666	+	0.999433i	$0.510718\pi$
$860$	−3.58612	−0.122286
$861$	0	0
$862$	20.8036	0.708573
$863$	−49.8075	−1.69547	−0.847734	−	0.530421i	$-0.822034\pi$
$863$	−49.8075	−1.69547	−0.847734	+	0.530421i	$0.822034\pi$
$864$	−1.00000	−0.0340207
$865$	−11.6392	−0.395746
$866$	4.40574	0.149713
$867$	16.0000	0.543388
$868$	0	0
$869$	5.36471	0.181985
$870$	−1.27058	−0.0430765
$871$	3.45096	0.116931
$872$	14.0410	0.475489
$873$	−14.5861	−0.493666
$874$	−32.3792	−1.09524
$875$	0	0
$876$	10.6763	0.360719
$877$	−24.5370	−0.828554	−0.414277	−	0.910151i	$-0.635966\pi$
$877$	−24.5370	−0.828554	−0.414277	+	0.910151i	$0.635966\pi$
$878$	15.1949	0.512802
$879$	10.3792	0.350081
$880$	−0.454904	−0.0153348
$881$	−11.5861	−0.390346	−0.195173	−	0.980769i	$-0.562527\pi$
$881$	−11.5861	−0.390346	−0.195173	+	0.980769i	$0.562527\pi$
$882$	0	0
$883$	−44.1376	−1.48535	−0.742674	−	0.669654i	$-0.766443\pi$
$883$	−44.1376	−1.48535	−0.742674	+	0.669654i	$0.766443\pi$
$884$	0.909808	0.0306002
$885$	−3.17225	−0.106634
$886$	−11.3873	−0.382565
$887$	20.0289	0.672506	0.336253	−	0.941772i	$-0.390840\pi$
$887$	20.0289	0.672506	0.336253	+	0.941772i	$0.390840\pi$
$888$	−7.88325	−0.264545
$889$	0	0
$890$	−5.04497	−0.169108
$891$	1.00000	0.0335013
$892$	−12.4959	−0.418395
$893$	1.31315	0.0439430
$894$	−4.11675	−0.137685
$895$	7.14330	0.238774
$896$	0	0
$897$	7.58612	0.253293
$898$	−24.0821	−0.803629
$899$	−26.7746	−0.892984
$900$	−4.79306	−0.159769
$901$	−0.909808	−0.0303101
$902$	1.79306	0.0597024
$903$	0	0
$904$	7.58612	0.252311
$905$	−1.13541	−0.0377423
$906$	6.15777	0.204578
$907$	−17.9203	−0.595035	−0.297518	−	0.954716i	$-0.596159\pi$
$907$	−17.9203	−0.595035	−0.297518	+	0.954716i	$0.596159\pi$
$908$	−9.79306	−0.324994
$909$	8.06364	0.267454
$910$	0	0
$911$	13.9695	0.462830	0.231415	−	0.972855i	$-0.425664\pi$
$911$	13.9695	0.462830	0.231415	+	0.972855i	$0.425664\pi$
$912$	3.88325	0.128587
$913$	−1.97345	−0.0653115
$914$	−29.5330	−0.976865
$915$	6.38732	0.211158
$916$	−8.67632	−0.286674
$917$	0	0
$918$	1.00000	0.0330049
$919$	−42.9614	−1.41716	−0.708582	−	0.705628i	$-0.750665\pi$
$919$	−42.9614	−1.41716	−0.708582	+	0.705628i	$0.750665\pi$
$920$	−3.79306	−0.125054
$921$	9.76651	0.321817
$922$	−4.14569	−0.136531
$923$	4.36077	0.143536
$924$	0	0
$925$	−37.7849	−1.24236
$926$	−9.32368	−0.306395
$927$	−5.76651	−0.189397
$928$	−2.79306	−0.0916868
$929$	25.6682	0.842146	0.421073	−	0.907027i	$-0.361654\pi$
$929$	25.6682	0.842146	0.421073	+	0.907027i	$0.361654\pi$
$930$	4.36077	0.142995
$931$	0	0
$932$	16.7665	0.549205
$933$	−6.51854	−0.213407
$934$	−36.5596	−1.19627
$935$	0.454904	0.0148770
$936$	−0.909808	−0.0297380
$937$	−26.7584	−0.874158	−0.437079	−	0.899423i	$-0.643987\pi$
$937$	−26.7584	−0.874158	−0.437079	+	0.899423i	$0.643987\pi$
$938$	0	0
$939$	30.7931	1.00489
$940$	0.153830	0.00501737
$941$	15.6208	0.509224	0.254612	−	0.967043i	$-0.418052\pi$
$941$	15.6208	0.509224	0.254612	+	0.967043i	$0.418052\pi$
$942$	−17.6498	−0.575060
$943$	14.9508	0.486866
$944$	−6.97345	−0.226966
$945$	0	0
$946$	7.88325	0.256307
$947$	19.7849	0.642924	0.321462	−	0.946923i	$-0.395826\pi$
$947$	19.7849	0.642924	0.321462	+	0.946923i	$0.395826\pi$
$948$	−5.36471	−0.174238
$949$	9.71340	0.315310
$950$	18.6127	0.603875
$951$	27.6272	0.895872
$952$	0	0
$953$	43.5065	1.40931	0.704656	−	0.709549i	$-0.251101\pi$
$953$	43.5065	1.40931	0.704656	+	0.709549i	$0.251101\pi$
$954$	0.909808	0.0294561
$955$	−4.46698	−0.144548
$956$	−26.2624	−0.849388
$957$	2.79306	0.0902869
$958$	−0.729425	−0.0235666
$959$	0	0
$960$	0.454904	0.0146820
$961$	60.8938	1.96432
$962$	−7.17225	−0.231243
$963$	15.6127	0.503112
$964$	−7.94689	−0.255952
$965$	−3.11914	−0.100409
$966$	0	0
$967$	34.5185	1.11004	0.555021	−	0.831837i	$-0.312710\pi$
$967$	34.5185	1.11004	0.555021	+	0.831837i	$0.312710\pi$
$968$	1.00000	0.0321412
$969$	−3.88325	−0.124748
$970$	6.63529	0.213046
$971$	44.9388	1.44215	0.721077	−	0.692855i	$-0.243648\pi$
$971$	44.9388	1.44215	0.721077	+	0.692855i	$0.243648\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−36.8567	−1.18096
$975$	−4.36077	−0.139656
$976$	14.0410	0.449442
$977$	32.5249	1.04056	0.520282	−	0.853995i	$-0.325827\pi$
$977$	32.5249	1.04056	0.520282	+	0.853995i	$0.325827\pi$
$978$	11.6127	0.371333
$979$	11.0902	0.354444
$980$	0	0
$981$	14.0410	0.448296
$982$	25.5065	0.813944
$983$	47.1949	1.50528	0.752641	−	0.658431i	$-0.228780\pi$
$983$	47.1949	1.50528	0.752641	+	0.658431i	$0.228780\pi$
$984$	−1.79306	−0.0571607
$985$	−10.6763	−0.340176
$986$	2.79306	0.0889492
$987$	0	0
$988$	3.53302	0.112400
$989$	65.7318	2.09015
$990$	−0.454904	−0.0144578
$991$	12.5490	0.398633	0.199317	−	0.979935i	$-0.436128\pi$
$991$	12.5490	0.398633	0.199317	+	0.979935i	$0.436128\pi$
$992$	9.58612	0.304360
$993$	28.9653	0.919186
$994$	0	0
$995$	−1.01602	−0.0322101
$996$	1.97345	0.0625310
$997$	−40.9098	−1.29563	−0.647813	−	0.761799i	$-0.724316\pi$
$997$	−40.9098	−1.29563	−0.647813	+	0.761799i	$0.724316\pi$
$998$	−4.12728	−0.130647
$999$	−7.88325	−0.249415

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3234.2.a.bg.1.2		3
3.2	odd	2		9702.2.a.du.1.2		3
7.3	odd	6		462.2.i.f.331.2	yes	6
7.5	odd	6		462.2.i.f.67.2	✓	6
7.6	odd	2		3234.2.a.bi.1.2		3
21.5	even	6		1386.2.k.w.991.2		6
21.17	even	6		1386.2.k.w.793.2		6
21.20	even	2		9702.2.a.dt.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.i.f.67.2	✓	6	7.5	odd	6
462.2.i.f.331.2	yes	6	7.3	odd	6
1386.2.k.w.793.2		6	21.17	even	6
1386.2.k.w.991.2		6	21.5	even	6
3234.2.a.bg.1.2		3	1.1	even	1	trivial
3234.2.a.bi.1.2		3	7.6	odd	2
9702.2.a.dt.1.2		3	21.20	even	2
9702.2.a.du.1.2		3	3.2	odd	2

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:	\( N \)	\(=\)	\( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3234.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.454904 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.454904 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -0.454904 q^{10} +1.00000 q^{11} -1.00000 q^{12} -0.909808 q^{13} +0.454904 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -3.88325 q^{19} -0.454904 q^{20} +1.00000 q^{22} +8.33816 q^{23} -1.00000 q^{24} -4.79306 q^{25} -0.909808 q^{26} -1.00000 q^{27} -2.79306 q^{29} +0.454904 q^{30} +9.58612 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +1.00000 q^{36} +7.88325 q^{37} -3.88325 q^{38} +0.909808 q^{39} -0.454904 q^{40} +1.79306 q^{41} +7.88325 q^{43} +1.00000 q^{44} -0.454904 q^{45} +8.33816 q^{46} -0.338158 q^{47} -1.00000 q^{48} -4.79306 q^{50} +1.00000 q^{51} -0.909808 q^{52} +0.909808 q^{53} -1.00000 q^{54} -0.454904 q^{55} +3.88325 q^{57} -2.79306 q^{58} -6.97345 q^{59} +0.454904 q^{60} +14.0410 q^{61} +9.58612 q^{62} +1.00000 q^{64} +0.413875 q^{65} -1.00000 q^{66} -3.79306 q^{67} -1.00000 q^{68} -8.33816 q^{69} -4.79306 q^{71} +1.00000 q^{72} -10.6763 q^{73} +7.88325 q^{74} +4.79306 q^{75} -3.88325 q^{76} +0.909808 q^{78} +5.36471 q^{79} -0.454904 q^{80} +1.00000 q^{81} +1.79306 q^{82} -1.97345 q^{83} +0.454904 q^{85} +7.88325 q^{86} +2.79306 q^{87} +1.00000 q^{88} +11.0902 q^{89} -0.454904 q^{90} +8.33816 q^{92} -9.58612 q^{93} -0.338158 q^{94} +1.76651 q^{95} -1.00000 q^{96} -14.5861 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^6 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{6} + 3 q^{8} + 3 q^{9} + 3 q^{11} - 3 q^{12} + 3 q^{16} - 3 q^{17} + 3 q^{18} + 3 q^{19} + 3 q^{22} + 9 q^{23} - 3 q^{24} + 3 q^{25} - 3 q^{27} + 9 q^{29} - 6 q^{31} + 3 q^{32} - 3 q^{33} - 3 q^{34} + 3 q^{36} + 9 q^{37} + 3 q^{38} - 12 q^{41} + 9 q^{43} + 3 q^{44} + 9 q^{46} + 15 q^{47} - 3 q^{48} + 3 q^{50} + 3 q^{51} - 3 q^{54} - 3 q^{57} + 9 q^{58} - 9 q^{59} + 6 q^{61} - 6 q^{62} + 3 q^{64} + 36 q^{65} - 3 q^{66} + 6 q^{67} - 3 q^{68} - 9 q^{69} + 3 q^{71} + 3 q^{72} + 9 q^{74} - 3 q^{75} + 3 q^{76} + 12 q^{79} + 3 q^{81} - 12 q^{82} + 6 q^{83} + 9 q^{86} - 9 q^{87} + 3 q^{88} + 36 q^{89} + 9 q^{92} + 6 q^{93} + 15 q^{94} - 24 q^{95} - 3 q^{96} - 9 q^{97} + 3 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^6 + 3 * q^8 + 3 * q^9 + 3 * q^11 - 3 * q^12 + 3 * q^16 - 3 * q^17 + 3 * q^18 + 3 * q^19 + 3 * q^22 + 9 * q^23 - 3 * q^24 + 3 * q^25 - 3 * q^27 + 9 * q^29 - 6 * q^31 + 3 * q^32 - 3 * q^33 - 3 * q^34 + 3 * q^36 + 9 * q^37 + 3 * q^38 - 12 * q^41 + 9 * q^43 + 3 * q^44 + 9 * q^46 + 15 * q^47 - 3 * q^48 + 3 * q^50 + 3 * q^51 - 3 * q^54 - 3 * q^57 + 9 * q^58 - 9 * q^59 + 6 * q^61 - 6 * q^62 + 3 * q^64 + 36 * q^65 - 3 * q^66 + 6 * q^67 - 3 * q^68 - 9 * q^69 + 3 * q^71 + 3 * q^72 + 9 * q^74 - 3 * q^75 + 3 * q^76 + 12 * q^79 + 3 * q^81 - 12 * q^82 + 6 * q^83 + 9 * q^86 - 9 * q^87 + 3 * q^88 + 36 * q^89 + 9 * q^92 + 6 * q^93 + 15 * q^94 - 24 * q^95 - 3 * q^96 - 9 * q^97 + 3 * q^99

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