LMFDB - Embedded newform 3822.2.a.bk.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3822,2,Mod(1,3822)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3822, 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("3822.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3822.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:	$30.5188236525$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{7}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 7 $ x^2 - 7
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.64575$ of defining polynomial
Character	$\chi$	$=$	3822.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.64575 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.64575 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +3.64575 q^{10} +0.645751 q^{11} +1.00000 q^{12} +1.00000 q^{13} -3.64575 q^{15} +1.00000 q^{16} -6.64575 q^{17} -1.00000 q^{18} +5.00000 q^{19} -3.64575 q^{20} -0.645751 q^{22} -2.35425 q^{23} -1.00000 q^{24} +8.29150 q^{25} -1.00000 q^{26} +1.00000 q^{27} +4.29150 q^{29} +3.64575 q^{30} +3.29150 q^{31} -1.00000 q^{32} +0.645751 q^{33} +6.64575 q^{34} +1.00000 q^{36} +5.64575 q^{37} -5.00000 q^{38} +1.00000 q^{39} +3.64575 q^{40} -2.35425 q^{41} -5.29150 q^{43} +0.645751 q^{44} -3.64575 q^{45} +2.35425 q^{46} +3.00000 q^{47} +1.00000 q^{48} -8.29150 q^{50} -6.64575 q^{51} +1.00000 q^{52} -3.00000 q^{53} -1.00000 q^{54} -2.35425 q^{55} +5.00000 q^{57} -4.29150 q^{58} -7.93725 q^{59} -3.64575 q^{60} -11.9373 q^{61} -3.29150 q^{62} +1.00000 q^{64} -3.64575 q^{65} -0.645751 q^{66} +7.58301 q^{67} -6.64575 q^{68} -2.35425 q^{69} +16.2915 q^{71} -1.00000 q^{72} -13.6458 q^{73} -5.64575 q^{74} +8.29150 q^{75} +5.00000 q^{76} -1.00000 q^{78} -10.0000 q^{79} -3.64575 q^{80} +1.00000 q^{81} +2.35425 q^{82} -13.2915 q^{83} +24.2288 q^{85} +5.29150 q^{86} +4.29150 q^{87} -0.645751 q^{88} +16.9373 q^{89} +3.64575 q^{90} -2.35425 q^{92} +3.29150 q^{93} -3.00000 q^{94} -18.2288 q^{95} -1.00000 q^{96} +0.937254 q^{97} +0.645751 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{15} + 2 q^{16} - 8 q^{17} - 2 q^{18} + 10 q^{19} - 2 q^{20} + 4 q^{22} - 10 q^{23} - 2 q^{24} + 6 q^{25} - 2 q^{26} + 2 q^{27} - 2 q^{29} + 2 q^{30} - 4 q^{31} - 2 q^{32} - 4 q^{33} + 8 q^{34} + 2 q^{36} + 6 q^{37} - 10 q^{38} + 2 q^{39} + 2 q^{40} - 10 q^{41} - 4 q^{44} - 2 q^{45} + 10 q^{46} + 6 q^{47} + 2 q^{48} - 6 q^{50} - 8 q^{51} + 2 q^{52} - 6 q^{53} - 2 q^{54} - 10 q^{55} + 10 q^{57} + 2 q^{58} - 2 q^{60} - 8 q^{61} + 4 q^{62} + 2 q^{64} - 2 q^{65} + 4 q^{66} - 6 q^{67} - 8 q^{68} - 10 q^{69} + 22 q^{71} - 2 q^{72} - 22 q^{73} - 6 q^{74} + 6 q^{75} + 10 q^{76} - 2 q^{78} - 20 q^{79} - 2 q^{80} + 2 q^{81} + 10 q^{82} - 16 q^{83} + 22 q^{85} - 2 q^{87} + 4 q^{88} + 18 q^{89} + 2 q^{90} - 10 q^{92} - 4 q^{93} - 6 q^{94} - 10 q^{95} - 2 q^{96} - 14 q^{97} - 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^15 + 2 * q^16 - 8 * q^17 - 2 * q^18 + 10 * q^19 - 2 * q^20 + 4 * q^22 - 10 * q^23 - 2 * q^24 + 6 * q^25 - 2 * q^26 + 2 * q^27 - 2 * q^29 + 2 * q^30 - 4 * q^31 - 2 * q^32 - 4 * q^33 + 8 * q^34 + 2 * q^36 + 6 * q^37 - 10 * q^38 + 2 * q^39 + 2 * q^40 - 10 * q^41 - 4 * q^44 - 2 * q^45 + 10 * q^46 + 6 * q^47 + 2 * q^48 - 6 * q^50 - 8 * q^51 + 2 * q^52 - 6 * q^53 - 2 * q^54 - 10 * q^55 + 10 * q^57 + 2 * q^58 - 2 * q^60 - 8 * q^61 + 4 * q^62 + 2 * q^64 - 2 * q^65 + 4 * q^66 - 6 * q^67 - 8 * q^68 - 10 * q^69 + 22 * q^71 - 2 * q^72 - 22 * q^73 - 6 * q^74 + 6 * q^75 + 10 * q^76 - 2 * q^78 - 20 * q^79 - 2 * q^80 + 2 * q^81 + 10 * q^82 - 16 * q^83 + 22 * q^85 - 2 * q^87 + 4 * q^88 + 18 * q^89 + 2 * q^90 - 10 * q^92 - 4 * q^93 - 6 * q^94 - 10 * q^95 - 2 * q^96 - 14 * q^97 - 4 * 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
$5$	−3.64575	−1.63043	−0.815215	−	0.579159i	$-0.803381\pi$
$5$	−3.64575	−1.63043	−0.815215	+	0.579159i	$0.803381\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.64575	1.15289
$11$	0.645751	0.194701	0.0973507	−	0.995250i	$-0.468963\pi$
$11$	0.645751	0.194701	0.0973507	+	0.995250i	$0.468963\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	−3.64575	−0.941329
$16$	1.00000	0.250000
$17$	−6.64575	−1.61183	−0.805916	−	0.592030i	$-0.798327\pi$
$17$	−6.64575	−1.61183	−0.805916	+	0.592030i	$0.798327\pi$
$18$	−1.00000	−0.235702
$19$	5.00000	1.14708	0.573539	−	0.819178i	$-0.305570\pi$
$19$	5.00000	1.14708	0.573539	+	0.819178i	$0.305570\pi$
$20$	−3.64575	−0.815215
$21$	0	0
$22$	−0.645751	−0.137675
$23$	−2.35425	−0.490895	−0.245447	−	0.969410i	$-0.578935\pi$
$23$	−2.35425	−0.490895	−0.245447	+	0.969410i	$0.578935\pi$
$24$	−1.00000	−0.204124
$25$	8.29150	1.65830
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	0	0
$29$	4.29150	0.796912	0.398456	−	0.917187i	$-0.369546\pi$
$29$	4.29150	0.796912	0.398456	+	0.917187i	$0.369546\pi$
$30$	3.64575	0.665620
$31$	3.29150	0.591171	0.295586	−	0.955316i	$-0.404485\pi$
$31$	3.29150	0.591171	0.295586	+	0.955316i	$0.404485\pi$
$32$	−1.00000	−0.176777
$33$	0.645751	0.112411
$34$	6.64575	1.13974
$35$	0	0
$36$	1.00000	0.166667
$37$	5.64575	0.928156	0.464078	−	0.885794i	$-0.346386\pi$
$37$	5.64575	0.928156	0.464078	+	0.885794i	$0.346386\pi$
$38$	−5.00000	−0.811107
$39$	1.00000	0.160128
$40$	3.64575	0.576444
$41$	−2.35425	−0.367672	−0.183836	−	0.982957i	$-0.558852\pi$
$41$	−2.35425	−0.367672	−0.183836	+	0.982957i	$0.558852\pi$
$42$	0	0
$43$	−5.29150	−0.806947	−0.403473	−	0.914991i	$-0.632197\pi$
$43$	−5.29150	−0.806947	−0.403473	+	0.914991i	$0.632197\pi$
$44$	0.645751	0.0973507
$45$	−3.64575	−0.543477
$46$	2.35425	0.347115
$47$	3.00000	0.437595	0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000	0.437595	0.218797	+	0.975770i	$0.429787\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	−8.29150	−1.17260
$51$	−6.64575	−0.930591
$52$	1.00000	0.138675
$53$	−3.00000	−0.412082	−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000	−0.412082	−0.206041	+	0.978543i	$0.566058\pi$
$54$	−1.00000	−0.136083
$55$	−2.35425	−0.317447
$56$	0	0
$57$	5.00000	0.662266
$58$	−4.29150	−0.563502
$59$	−7.93725	−1.03334	−0.516671	−	0.856184i	$-0.672829\pi$
$59$	−7.93725	−1.03334	−0.516671	+	0.856184i	$0.672829\pi$
$60$	−3.64575	−0.470664
$61$	−11.9373	−1.52841	−0.764204	−	0.644974i	$-0.776868\pi$
$61$	−11.9373	−1.52841	−0.764204	+	0.644974i	$0.776868\pi$
$62$	−3.29150	−0.418021
$63$	0	0
$64$	1.00000	0.125000
$65$	−3.64575	−0.452200
$66$	−0.645751	−0.0794865
$67$	7.58301	0.926412	0.463206	−	0.886251i	$-0.346699\pi$
$67$	7.58301	0.926412	0.463206	+	0.886251i	$0.346699\pi$
$68$	−6.64575	−0.805916
$69$	−2.35425	−0.283418
$70$	0	0
$71$	16.2915	1.93345	0.966723	−	0.255826i	$-0.0823474\pi$
$71$	16.2915	1.93345	0.966723	+	0.255826i	$0.0823474\pi$
$72$	−1.00000	−0.117851
$73$	−13.6458	−1.59711	−0.798557	−	0.601919i	$-0.794403\pi$
$73$	−13.6458	−1.59711	−0.798557	+	0.601919i	$0.794403\pi$
$74$	−5.64575	−0.656305
$75$	8.29150	0.957420
$76$	5.00000	0.573539
$77$	0	0
$78$	−1.00000	−0.113228
$79$	−10.0000	−1.12509	−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000	−1.12509	−0.562544	+	0.826767i	$0.690177\pi$
$80$	−3.64575	−0.407607
$81$	1.00000	0.111111
$82$	2.35425	0.259983
$83$	−13.2915	−1.45893	−0.729466	−	0.684017i	$-0.760231\pi$
$83$	−13.2915	−1.45893	−0.729466	+	0.684017i	$0.760231\pi$
$84$	0	0
$85$	24.2288	2.62798
$86$	5.29150	0.570597
$87$	4.29150	0.460097
$88$	−0.645751	−0.0688373
$89$	16.9373	1.79535	0.897673	−	0.440663i	$-0.145257\pi$
$89$	16.9373	1.79535	0.897673	+	0.440663i	$0.145257\pi$
$90$	3.64575	0.384296
$91$	0	0
$92$	−2.35425	−0.245447
$93$	3.29150	0.341313
$94$	−3.00000	−0.309426
$95$	−18.2288	−1.87023
$96$	−1.00000	−0.102062
$97$	0.937254	0.0951637	0.0475819	−	0.998867i	$-0.484849\pi$
$97$	0.937254	0.0951637	0.0475819	+	0.998867i	$0.484849\pi$
$98$	0	0
$99$	0.645751	0.0649004
$100$	8.29150	0.829150
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	6.64575	0.658027
$103$	−5.29150	−0.521387	−0.260694	−	0.965422i	$-0.583951\pi$
$103$	−5.29150	−0.521387	−0.260694	+	0.965422i	$0.583951\pi$
$104$	−1.00000	−0.0980581
$105$	0	0
$106$	3.00000	0.291386
$107$	−12.0000	−1.16008	−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000	−1.16008	−0.580042	+	0.814587i	$0.696964\pi$
$108$	1.00000	0.0962250
$109$	−4.00000	−0.383131	−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000	−0.383131	−0.191565	+	0.981480i	$0.561356\pi$
$110$	2.35425	0.224469
$111$	5.64575	0.535871
$112$	0	0
$113$	15.2288	1.43260	0.716300	−	0.697792i	$-0.245834\pi$
$113$	15.2288	1.43260	0.716300	+	0.697792i	$0.245834\pi$
$114$	−5.00000	−0.468293
$115$	8.58301	0.800369
$116$	4.29150	0.398456
$117$	1.00000	0.0924500
$118$	7.93725	0.730683
$119$	0	0
$120$	3.64575	0.332810
$121$	−10.5830	−0.962091
$122$	11.9373	1.08075
$123$	−2.35425	−0.212275
$124$	3.29150	0.295586
$125$	−12.0000	−1.07331
$126$	0	0
$127$	−10.2288	−0.907655	−0.453828	−	0.891089i	$-0.649942\pi$
$127$	−10.2288	−0.907655	−0.453828	+	0.891089i	$0.649942\pi$
$128$	−1.00000	−0.0883883
$129$	−5.29150	−0.465891
$130$	3.64575	0.319754
$131$	10.9373	0.955592	0.477796	−	0.878471i	$-0.341436\pi$
$131$	10.9373	0.955592	0.477796	+	0.878471i	$0.341436\pi$
$132$	0.645751	0.0562054
$133$	0	0
$134$	−7.58301	−0.655072
$135$	−3.64575	−0.313776
$136$	6.64575	0.569868
$137$	−19.5203	−1.66773	−0.833864	−	0.551970i	$-0.813876\pi$
$137$	−19.5203	−1.66773	−0.833864	+	0.551970i	$0.813876\pi$
$138$	2.35425	0.200407
$139$	−22.2288	−1.88542	−0.942709	−	0.333615i	$-0.891731\pi$
$139$	−22.2288	−1.88542	−0.942709	+	0.333615i	$0.891731\pi$
$140$	0	0
$141$	3.00000	0.252646
$142$	−16.2915	−1.36715
$143$	0.645751	0.0540004
$144$	1.00000	0.0833333
$145$	−15.6458	−1.29931
$146$	13.6458	1.12933
$147$	0	0
$148$	5.64575	0.464078
$149$	−7.06275	−0.578603	−0.289301	−	0.957238i	$-0.593423\pi$
$149$	−7.06275	−0.578603	−0.289301	+	0.957238i	$0.593423\pi$
$150$	−8.29150	−0.676998
$151$	6.06275	0.493379	0.246690	−	0.969095i	$-0.420657\pi$
$151$	6.06275	0.493379	0.246690	+	0.969095i	$0.420657\pi$
$152$	−5.00000	−0.405554
$153$	−6.64575	−0.537277
$154$	0	0
$155$	−12.0000	−0.963863
$156$	1.00000	0.0800641
$157$	2.64575	0.211154	0.105577	−	0.994411i	$-0.466331\pi$
$157$	2.64575	0.211154	0.105577	+	0.994411i	$0.466331\pi$
$158$	10.0000	0.795557
$159$	−3.00000	−0.237915
$160$	3.64575	0.288222
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	2.41699	0.189314	0.0946568	−	0.995510i	$-0.469825\pi$
$163$	2.41699	0.189314	0.0946568	+	0.995510i	$0.469825\pi$
$164$	−2.35425	−0.183836
$165$	−2.35425	−0.183278
$166$	13.2915	1.03162
$167$	−6.87451	−0.531965	−0.265983	−	0.963978i	$-0.585696\pi$
$167$	−6.87451	−0.531965	−0.265983	+	0.963978i	$0.585696\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−24.2288	−1.85826
$171$	5.00000	0.382360
$172$	−5.29150	−0.403473
$173$	−22.2915	−1.69479	−0.847396	−	0.530962i	$-0.821831\pi$
$173$	−22.2915	−1.69479	−0.847396	+	0.530962i	$0.821831\pi$
$174$	−4.29150	−0.325338
$175$	0	0
$176$	0.645751	0.0486753
$177$	−7.93725	−0.596601
$178$	−16.9373	−1.26950
$179$	−6.00000	−0.448461	−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000	−0.448461	−0.224231	+	0.974536i	$0.571987\pi$
$180$	−3.64575	−0.271738
$181$	14.6458	1.08861	0.544305	−	0.838887i	$-0.316793\pi$
$181$	14.6458	1.08861	0.544305	+	0.838887i	$0.316793\pi$
$182$	0	0
$183$	−11.9373	−0.882427
$184$	2.35425	0.173558
$185$	−20.5830	−1.51329
$186$	−3.29150	−0.241345
$187$	−4.29150	−0.313826
$188$	3.00000	0.218797
$189$	0	0
$190$	18.2288	1.32245
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	1.00000	0.0721688
$193$	18.9373	1.36313	0.681567	−	0.731756i	$-0.261299\pi$
$193$	18.9373	1.36313	0.681567	+	0.731756i	$0.261299\pi$
$194$	−0.937254	−0.0672909
$195$	−3.64575	−0.261078
$196$	0	0
$197$	−26.8118	−1.91026	−0.955129	−	0.296189i	$-0.904284\pi$
$197$	−26.8118	−1.91026	−0.955129	+	0.296189i	$0.904284\pi$
$198$	−0.645751	−0.0458915
$199$	−22.2288	−1.57575	−0.787877	−	0.615832i	$-0.788820\pi$
$199$	−22.2288	−1.57575	−0.787877	+	0.615832i	$0.788820\pi$
$200$	−8.29150	−0.586298
$201$	7.58301	0.534864
$202$	0	0
$203$	0	0
$204$	−6.64575	−0.465296
$205$	8.58301	0.599463
$206$	5.29150	0.368676
$207$	−2.35425	−0.163632
$208$	1.00000	0.0693375
$209$	3.22876	0.223338
$210$	0	0
$211$	−6.35425	−0.437445	−0.218722	−	0.975787i	$-0.570189\pi$
$211$	−6.35425	−0.437445	−0.218722	+	0.975787i	$0.570189\pi$
$212$	−3.00000	−0.206041
$213$	16.2915	1.11628
$214$	12.0000	0.820303
$215$	19.2915	1.31567
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	4.00000	0.270914
$219$	−13.6458	−0.922094
$220$	−2.35425	−0.158723
$221$	−6.64575	−0.447042
$222$	−5.64575	−0.378918
$223$	−20.5203	−1.37414	−0.687069	−	0.726592i	$-0.741103\pi$
$223$	−20.5203	−1.37414	−0.687069	+	0.726592i	$0.741103\pi$
$224$	0	0
$225$	8.29150	0.552767
$226$	−15.2288	−1.01300
$227$	−4.70850	−0.312514	−0.156257	−	0.987716i	$-0.549943\pi$
$227$	−4.70850	−0.312514	−0.156257	+	0.987716i	$0.549943\pi$
$228$	5.00000	0.331133
$229$	26.4575	1.74836	0.874181	−	0.485601i	$-0.161399\pi$
$229$	26.4575	1.74836	0.874181	+	0.485601i	$0.161399\pi$
$230$	−8.58301	−0.565947
$231$	0	0
$232$	−4.29150	−0.281751
$233$	0.645751	0.0423046	0.0211523	−	0.999776i	$-0.493267\pi$
$233$	0.645751	0.0423046	0.0211523	+	0.999776i	$0.493267\pi$
$234$	−1.00000	−0.0653720
$235$	−10.9373	−0.713468
$236$	−7.93725	−0.516671
$237$	−10.0000	−0.649570
$238$	0	0
$239$	3.00000	0.194054	0.0970269	−	0.995282i	$-0.469067\pi$
$239$	3.00000	0.194054	0.0970269	+	0.995282i	$0.469067\pi$
$240$	−3.64575	−0.235332
$241$	−13.8745	−0.893736	−0.446868	−	0.894600i	$-0.647461\pi$
$241$	−13.8745	−0.893736	−0.446868	+	0.894600i	$0.647461\pi$
$242$	10.5830	0.680301
$243$	1.00000	0.0641500
$244$	−11.9373	−0.764204
$245$	0	0
$246$	2.35425	0.150101
$247$	5.00000	0.318142
$248$	−3.29150	−0.209011
$249$	−13.2915	−0.842315
$250$	12.0000	0.758947
$251$	−13.2915	−0.838952	−0.419476	−	0.907766i	$-0.637786\pi$
$251$	−13.2915	−0.838952	−0.419476	+	0.907766i	$0.637786\pi$
$252$	0	0
$253$	−1.52026	−0.0955779
$254$	10.2288	0.641809
$255$	24.2288	1.51726
$256$	1.00000	0.0625000
$257$	−15.8745	−0.990225	−0.495112	−	0.868829i	$-0.664873\pi$
$257$	−15.8745	−0.990225	−0.495112	+	0.868829i	$0.664873\pi$
$258$	5.29150	0.329435
$259$	0	0
$260$	−3.64575	−0.226100
$261$	4.29150	0.265637
$262$	−10.9373	−0.675706
$263$	−3.64575	−0.224807	−0.112403	−	0.993663i	$-0.535855\pi$
$263$	−3.64575	−0.224807	−0.112403	+	0.993663i	$0.535855\pi$
$264$	−0.645751	−0.0397432
$265$	10.9373	0.671870
$266$	0	0
$267$	16.9373	1.03654
$268$	7.58301	0.463206
$269$	6.87451	0.419146	0.209573	−	0.977793i	$-0.432793\pi$
$269$	6.87451	0.419146	0.209573	+	0.977793i	$0.432793\pi$
$270$	3.64575	0.221873
$271$	−22.6458	−1.37563	−0.687816	−	0.725885i	$-0.741430\pi$
$271$	−22.6458	−1.37563	−0.687816	+	0.725885i	$0.741430\pi$
$272$	−6.64575	−0.402958
$273$	0	0
$274$	19.5203	1.17926
$275$	5.35425	0.322873
$276$	−2.35425	−0.141709
$277$	18.5203	1.11277	0.556387	−	0.830923i	$-0.312187\pi$
$277$	18.5203	1.11277	0.556387	+	0.830923i	$0.312187\pi$
$278$	22.2288	1.33319
$279$	3.29150	0.197057
$280$	0	0
$281$	−2.58301	−0.154089	−0.0770446	−	0.997028i	$-0.524548\pi$
$281$	−2.58301	−0.154089	−0.0770446	+	0.997028i	$0.524548\pi$
$282$	−3.00000	−0.178647
$283$	−11.0627	−0.657612	−0.328806	−	0.944397i	$-0.606646\pi$
$283$	−11.0627	−0.657612	−0.328806	+	0.944397i	$0.606646\pi$
$284$	16.2915	0.966723
$285$	−18.2288	−1.07978
$286$	−0.645751	−0.0381841
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	27.1660	1.59800
$290$	15.6458	0.918750
$291$	0.937254	0.0549428
$292$	−13.6458	−0.798557
$293$	7.52026	0.439338	0.219669	−	0.975574i	$-0.429502\pi$
$293$	7.52026	0.439338	0.219669	+	0.975574i	$0.429502\pi$
$294$	0	0
$295$	28.9373	1.68479
$296$	−5.64575	−0.328153
$297$	0.645751	0.0374703
$298$	7.06275	0.409134
$299$	−2.35425	−0.136150
$300$	8.29150	0.478710
$301$	0	0
$302$	−6.06275	−0.348872
$303$	0	0
$304$	5.00000	0.286770
$305$	43.5203	2.49196
$306$	6.64575	0.379912
$307$	−9.58301	−0.546931	−0.273465	−	0.961882i	$-0.588170\pi$
$307$	−9.58301	−0.546931	−0.273465	+	0.961882i	$0.588170\pi$
$308$	0	0
$309$	−5.29150	−0.301023
$310$	12.0000	0.681554
$311$	−1.06275	−0.0602628	−0.0301314	−	0.999546i	$-0.509593\pi$
$311$	−1.06275	−0.0602628	−0.0301314	+	0.999546i	$0.509593\pi$
$312$	−1.00000	−0.0566139
$313$	13.1660	0.744187	0.372093	−	0.928195i	$-0.378640\pi$
$313$	13.1660	0.744187	0.372093	+	0.928195i	$0.378640\pi$
$314$	−2.64575	−0.149308
$315$	0	0
$316$	−10.0000	−0.562544
$317$	−13.2915	−0.746525	−0.373263	−	0.927726i	$-0.621761\pi$
$317$	−13.2915	−0.746525	−0.373263	+	0.927726i	$0.621761\pi$
$318$	3.00000	0.168232
$319$	2.77124	0.155160
$320$	−3.64575	−0.203804
$321$	−12.0000	−0.669775
$322$	0	0
$323$	−33.2288	−1.84890
$324$	1.00000	0.0555556
$325$	8.29150	0.459930
$326$	−2.41699	−0.133865
$327$	−4.00000	−0.221201
$328$	2.35425	0.129992
$329$	0	0
$330$	2.35425	0.129597
$331$	11.4170	0.627535	0.313767	−	0.949500i	$-0.398409\pi$
$331$	11.4170	0.627535	0.313767	+	0.949500i	$0.398409\pi$
$332$	−13.2915	−0.729466
$333$	5.64575	0.309385
$334$	6.87451	0.376156
$335$	−27.6458	−1.51045
$336$	0	0
$337$	−15.5830	−0.848860	−0.424430	−	0.905461i	$-0.639526\pi$
$337$	−15.5830	−0.848860	−0.424430	+	0.905461i	$0.639526\pi$
$338$	−1.00000	−0.0543928
$339$	15.2288	0.827113
$340$	24.2288	1.31399
$341$	2.12549	0.115102
$342$	−5.00000	−0.270369
$343$	0	0
$344$	5.29150	0.285299
$345$	8.58301	0.462093
$346$	22.2915	1.19840
$347$	0.228757	0.0122803	0.00614015	−	0.999981i	$-0.498046\pi$
$347$	0.228757	0.0122803	0.00614015	+	0.999981i	$0.498046\pi$
$348$	4.29150	0.230049
$349$	18.9373	1.01369	0.506844	−	0.862038i	$-0.330812\pi$
$349$	18.9373	1.01369	0.506844	+	0.862038i	$0.330812\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	−0.645751	−0.0344187
$353$	−20.5830	−1.09552	−0.547761	−	0.836635i	$-0.684520\pi$
$353$	−20.5830	−1.09552	−0.547761	+	0.836635i	$0.684520\pi$
$354$	7.93725	0.421860
$355$	−59.3948	−3.15235
$356$	16.9373	0.897673
$357$	0	0
$358$	6.00000	0.317110
$359$	−6.00000	−0.316668	−0.158334	−	0.987386i	$-0.550612\pi$
$359$	−6.00000	−0.316668	−0.158334	+	0.987386i	$0.550612\pi$
$360$	3.64575	0.192148
$361$	6.00000	0.315789
$362$	−14.6458	−0.769764
$363$	−10.5830	−0.555464
$364$	0	0
$365$	49.7490	2.60398
$366$	11.9373	0.623970
$367$	−0.583005	−0.0304326	−0.0152163	−	0.999884i	$-0.504844\pi$
$367$	−0.583005	−0.0304326	−0.0152163	+	0.999884i	$0.504844\pi$
$368$	−2.35425	−0.122724
$369$	−2.35425	−0.122557
$370$	20.5830	1.07006
$371$	0	0
$372$	3.29150	0.170656
$373$	14.6458	0.758328	0.379164	−	0.925329i	$-0.376212\pi$
$373$	14.6458	0.758328	0.379164	+	0.925329i	$0.376212\pi$
$374$	4.29150	0.221908
$375$	−12.0000	−0.619677
$376$	−3.00000	−0.154713
$377$	4.29150	0.221024
$378$	0	0
$379$	−9.16601	−0.470826	−0.235413	−	0.971895i	$-0.575644\pi$
$379$	−9.16601	−0.470826	−0.235413	+	0.971895i	$0.575644\pi$
$380$	−18.2288	−0.935115
$381$	−10.2288	−0.524035
$382$	0	0
$383$	25.7490	1.31571	0.657857	−	0.753143i	$-0.271463\pi$
$383$	25.7490	1.31571	0.657857	+	0.753143i	$0.271463\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−18.9373	−0.963881
$387$	−5.29150	−0.268982
$388$	0.937254	0.0475819
$389$	7.70850	0.390836	0.195418	−	0.980720i	$-0.437394\pi$
$389$	7.70850	0.390836	0.195418	+	0.980720i	$0.437394\pi$
$390$	3.64575	0.184610
$391$	15.6458	0.791240
$392$	0	0
$393$	10.9373	0.551711
$394$	26.8118	1.35076
$395$	36.4575	1.83438
$396$	0.645751	0.0324502
$397$	−14.9373	−0.749679	−0.374840	−	0.927090i	$-0.622302\pi$
$397$	−14.9373	−0.749679	−0.374840	+	0.927090i	$0.622302\pi$
$398$	22.2288	1.11423
$399$	0	0
$400$	8.29150	0.414575
$401$	−18.2288	−0.910301	−0.455150	−	0.890415i	$-0.650414\pi$
$401$	−18.2288	−0.910301	−0.455150	+	0.890415i	$0.650414\pi$
$402$	−7.58301	−0.378206
$403$	3.29150	0.163961
$404$	0	0
$405$	−3.64575	−0.181159
$406$	0	0
$407$	3.64575	0.180713
$408$	6.64575	0.329014
$409$	−26.9373	−1.33196	−0.665981	−	0.745969i	$-0.731987\pi$
$409$	−26.9373	−1.33196	−0.665981	+	0.745969i	$0.731987\pi$
$410$	−8.58301	−0.423884
$411$	−19.5203	−0.962863
$412$	−5.29150	−0.260694
$413$	0	0
$414$	2.35425	0.115705
$415$	48.4575	2.37869
$416$	−1.00000	−0.0490290
$417$	−22.2288	−1.08855
$418$	−3.22876	−0.157924
$419$	30.4575	1.48795	0.743973	−	0.668209i	$-0.232939\pi$
$419$	30.4575	1.48795	0.743973	+	0.668209i	$0.232939\pi$
$420$	0	0
$421$	−24.3542	−1.18695	−0.593477	−	0.804851i	$-0.702245\pi$
$421$	−24.3542	−1.18695	−0.593477	+	0.804851i	$0.702245\pi$
$422$	6.35425	0.309320
$423$	3.00000	0.145865
$424$	3.00000	0.145693
$425$	−55.1033	−2.67290
$426$	−16.2915	−0.789326
$427$	0	0
$428$	−12.0000	−0.580042
$429$	0.645751	0.0311772
$430$	−19.2915	−0.930319
$431$	20.5830	0.991448	0.495724	−	0.868480i	$-0.334903\pi$
$431$	20.5830	0.991448	0.495724	+	0.868480i	$0.334903\pi$
$432$	1.00000	0.0481125
$433$	−33.5830	−1.61390	−0.806948	−	0.590622i	$-0.798882\pi$
$433$	−33.5830	−1.61390	−0.806948	+	0.590622i	$0.798882\pi$
$434$	0	0
$435$	−15.6458	−0.750156
$436$	−4.00000	−0.191565
$437$	−11.7712	−0.563095
$438$	13.6458	0.652019
$439$	23.6458	1.12855	0.564275	−	0.825587i	$-0.309156\pi$
$439$	23.6458	1.12855	0.564275	+	0.825587i	$0.309156\pi$
$440$	2.35425	0.112234
$441$	0	0
$442$	6.64575	0.316106
$443$	19.0627	0.905698	0.452849	−	0.891587i	$-0.350408\pi$
$443$	19.0627	0.905698	0.452849	+	0.891587i	$0.350408\pi$
$444$	5.64575	0.267935
$445$	−61.7490	−2.92718
$446$	20.5203	0.971662
$447$	−7.06275	−0.334056
$448$	0	0
$449$	12.0000	0.566315	0.283158	−	0.959073i	$-0.408618\pi$
$449$	12.0000	0.566315	0.283158	+	0.959073i	$0.408618\pi$
$450$	−8.29150	−0.390865
$451$	−1.52026	−0.0715862
$452$	15.2288	0.716300
$453$	6.06275	0.284853
$454$	4.70850	0.220981
$455$	0	0
$456$	−5.00000	−0.234146
$457$	32.2288	1.50760	0.753799	−	0.657105i	$-0.228219\pi$
$457$	32.2288	1.50760	0.753799	+	0.657105i	$0.228219\pi$
$458$	−26.4575	−1.23628
$459$	−6.64575	−0.310197
$460$	8.58301	0.400185
$461$	−36.4575	−1.69800	−0.848998	−	0.528396i	$-0.822794\pi$
$461$	−36.4575	−1.69800	−0.848998	+	0.528396i	$0.822794\pi$
$462$	0	0
$463$	25.1660	1.16956	0.584782	−	0.811191i	$-0.301180\pi$
$463$	25.1660	1.16956	0.584782	+	0.811191i	$0.301180\pi$
$464$	4.29150	0.199228
$465$	−12.0000	−0.556487
$466$	−0.645751	−0.0299139
$467$	−37.5203	−1.73623	−0.868115	−	0.496363i	$-0.834669\pi$
$467$	−37.5203	−1.73623	−0.868115	+	0.496363i	$0.834669\pi$
$468$	1.00000	0.0462250
$469$	0	0
$470$	10.9373	0.504498
$471$	2.64575	0.121910
$472$	7.93725	0.365342
$473$	−3.41699	−0.157114
$474$	10.0000	0.459315
$475$	41.4575	1.90220
$476$	0	0
$477$	−3.00000	−0.137361
$478$	−3.00000	−0.137217
$479$	−34.7490	−1.58772	−0.793862	−	0.608099i	$-0.791933\pi$
$479$	−34.7490	−1.58772	−0.793862	+	0.608099i	$0.791933\pi$
$480$	3.64575	0.166405
$481$	5.64575	0.257424
$482$	13.8745	0.631967
$483$	0	0
$484$	−10.5830	−0.481046
$485$	−3.41699	−0.155158
$486$	−1.00000	−0.0453609
$487$	−23.9373	−1.08470	−0.542350	−	0.840152i	$-0.682465\pi$
$487$	−23.9373	−1.08470	−0.542350	+	0.840152i	$0.682465\pi$
$488$	11.9373	0.540374
$489$	2.41699	0.109300
$490$	0	0
$491$	11.1660	0.503915	0.251957	−	0.967738i	$-0.418926\pi$
$491$	11.1660	0.503915	0.251957	+	0.967738i	$0.418926\pi$
$492$	−2.35425	−0.106138
$493$	−28.5203	−1.28449
$494$	−5.00000	−0.224961
$495$	−2.35425	−0.105816
$496$	3.29150	0.147793
$497$	0	0
$498$	13.2915	0.595606
$499$	−29.2915	−1.31127	−0.655634	−	0.755079i	$-0.727599\pi$
$499$	−29.2915	−1.31127	−0.655634	+	0.755079i	$0.727599\pi$
$500$	−12.0000	−0.536656
$501$	−6.87451	−0.307130
$502$	13.2915	0.593229
$503$	36.4575	1.62556	0.812780	−	0.582571i	$-0.197953\pi$
$503$	36.4575	1.62556	0.812780	+	0.582571i	$0.197953\pi$
$504$	0	0
$505$	0	0
$506$	1.52026	0.0675838
$507$	1.00000	0.0444116
$508$	−10.2288	−0.453828
$509$	24.0000	1.06378	0.531891	−	0.846813i	$-0.321482\pi$
$509$	24.0000	1.06378	0.531891	+	0.846813i	$0.321482\pi$
$510$	−24.2288	−1.07287
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	5.00000	0.220755
$514$	15.8745	0.700195
$515$	19.2915	0.850085
$516$	−5.29150	−0.232945
$517$	1.93725	0.0852003
$518$	0	0
$519$	−22.2915	−0.978488
$520$	3.64575	0.159877
$521$	18.0000	0.788594	0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000	0.788594	0.394297	+	0.918983i	$0.370988\pi$
$522$	−4.29150	−0.187834
$523$	−26.7085	−1.16788	−0.583941	−	0.811796i	$-0.698490\pi$
$523$	−26.7085	−1.16788	−0.583941	+	0.811796i	$0.698490\pi$
$524$	10.9373	0.477796
$525$	0	0
$526$	3.64575	0.158962
$527$	−21.8745	−0.952869
$528$	0.645751	0.0281027
$529$	−17.4575	−0.759022
$530$	−10.9373	−0.475084
$531$	−7.93725	−0.344447
$532$	0	0
$533$	−2.35425	−0.101974
$534$	−16.9373	−0.732947
$535$	43.7490	1.89143
$536$	−7.58301	−0.327536
$537$	−6.00000	−0.258919
$538$	−6.87451	−0.296381
$539$	0	0
$540$	−3.64575	−0.156888
$541$	41.6458	1.79049	0.895245	−	0.445574i	$-0.147000\pi$
$541$	41.6458	1.79049	0.895245	+	0.445574i	$0.147000\pi$
$542$	22.6458	0.972718
$543$	14.6458	0.628509
$544$	6.64575	0.284934
$545$	14.5830	0.624667
$546$	0	0
$547$	−20.9373	−0.895212	−0.447606	−	0.894231i	$-0.647723\pi$
$547$	−20.9373	−0.895212	−0.447606	+	0.894231i	$0.647723\pi$
$548$	−19.5203	−0.833864
$549$	−11.9373	−0.509470
$550$	−5.35425	−0.228306
$551$	21.4575	0.914121
$552$	2.35425	0.100203
$553$	0	0
$554$	−18.5203	−0.786850
$555$	−20.5830	−0.873700
$556$	−22.2288	−0.942709
$557$	11.1660	0.473119	0.236560	−	0.971617i	$-0.423980\pi$
$557$	11.1660	0.473119	0.236560	+	0.971617i	$0.423980\pi$
$558$	−3.29150	−0.139340
$559$	−5.29150	−0.223807
$560$	0	0
$561$	−4.29150	−0.181187
$562$	2.58301	0.108958
$563$	−27.0405	−1.13962	−0.569811	−	0.821776i	$-0.692984\pi$
$563$	−27.0405	−1.13962	−0.569811	+	0.821776i	$0.692984\pi$
$564$	3.00000	0.126323
$565$	−55.5203	−2.33575
$566$	11.0627	0.465002
$567$	0	0
$568$	−16.2915	−0.683576
$569$	−33.2288	−1.39302	−0.696511	−	0.717546i	$-0.745265\pi$
$569$	−33.2288	−1.39302	−0.696511	+	0.717546i	$0.745265\pi$
$570$	18.2288	0.763519
$571$	−16.0000	−0.669579	−0.334790	−	0.942293i	$-0.608665\pi$
$571$	−16.0000	−0.669579	−0.334790	+	0.942293i	$0.608665\pi$
$572$	0.645751	0.0270002
$573$	0	0
$574$	0	0
$575$	−19.5203	−0.814051
$576$	1.00000	0.0416667
$577$	−12.5830	−0.523837	−0.261919	−	0.965090i	$-0.584355\pi$
$577$	−12.5830	−0.523837	−0.261919	+	0.965090i	$0.584355\pi$
$578$	−27.1660	−1.12996
$579$	18.9373	0.787005
$580$	−15.6458	−0.649654
$581$	0	0
$582$	−0.937254	−0.0388504
$583$	−1.93725	−0.0802329
$584$	13.6458	0.564665
$585$	−3.64575	−0.150733
$586$	−7.52026	−0.310659
$587$	31.9373	1.31819	0.659096	−	0.752059i	$-0.270939\pi$
$587$	31.9373	1.31819	0.659096	+	0.752059i	$0.270939\pi$
$588$	0	0
$589$	16.4575	0.678120
$590$	−28.9373	−1.19133
$591$	−26.8118	−1.10289
$592$	5.64575	0.232039
$593$	43.5203	1.78716	0.893581	−	0.448901i	$-0.148184\pi$
$593$	43.5203	1.78716	0.893581	+	0.448901i	$0.148184\pi$
$594$	−0.645751	−0.0264955
$595$	0	0
$596$	−7.06275	−0.289301
$597$	−22.2288	−0.909762
$598$	2.35425	0.0962724
$599$	−32.8118	−1.34065	−0.670326	−	0.742067i	$-0.733846\pi$
$599$	−32.8118	−1.34065	−0.670326	+	0.742067i	$0.733846\pi$
$600$	−8.29150	−0.338499
$601$	14.8745	0.606744	0.303372	−	0.952872i	$-0.401888\pi$
$601$	14.8745	0.606744	0.303372	+	0.952872i	$0.401888\pi$
$602$	0	0
$603$	7.58301	0.308804
$604$	6.06275	0.246690
$605$	38.5830	1.56862
$606$	0	0
$607$	16.8118	0.682368	0.341184	−	0.939996i	$-0.389172\pi$
$607$	16.8118	0.682368	0.341184	+	0.939996i	$0.389172\pi$
$608$	−5.00000	−0.202777
$609$	0	0
$610$	−43.5203	−1.76208
$611$	3.00000	0.121367
$612$	−6.64575	−0.268639
$613$	41.8745	1.69130	0.845648	−	0.533741i	$-0.179214\pi$
$613$	41.8745	1.69130	0.845648	+	0.533741i	$0.179214\pi$
$614$	9.58301	0.386739
$615$	8.58301	0.346100
$616$	0	0
$617$	−10.7085	−0.431108	−0.215554	−	0.976492i	$-0.569156\pi$
$617$	−10.7085	−0.431108	−0.215554	+	0.976492i	$0.569156\pi$
$618$	5.29150	0.212855
$619$	−41.7490	−1.67803	−0.839017	−	0.544105i	$-0.816869\pi$
$619$	−41.7490	−1.67803	−0.839017	+	0.544105i	$0.816869\pi$
$620$	−12.0000	−0.481932
$621$	−2.35425	−0.0944727
$622$	1.06275	0.0426122
$623$	0	0
$624$	1.00000	0.0400320
$625$	2.29150	0.0916601
$626$	−13.1660	−0.526220
$627$	3.22876	0.128944
$628$	2.64575	0.105577
$629$	−37.5203	−1.49603
$630$	0	0
$631$	14.4575	0.575545	0.287772	−	0.957699i	$-0.407085\pi$
$631$	14.4575	0.575545	0.287772	+	0.957699i	$0.407085\pi$
$632$	10.0000	0.397779
$633$	−6.35425	−0.252559
$634$	13.2915	0.527873
$635$	37.2915	1.47987
$636$	−3.00000	−0.118958
$637$	0	0
$638$	−2.77124	−0.109715
$639$	16.2915	0.644482
$640$	3.64575	0.144111
$641$	−21.4170	−0.845920	−0.422960	−	0.906148i	$-0.639009\pi$
$641$	−21.4170	−0.845920	−0.422960	+	0.906148i	$0.639009\pi$
$642$	12.0000	0.473602
$643$	−10.8745	−0.428849	−0.214424	−	0.976741i	$-0.568788\pi$
$643$	−10.8745	−0.428849	−0.214424	+	0.976741i	$0.568788\pi$
$644$	0	0
$645$	19.2915	0.759602
$646$	33.2288	1.30737
$647$	25.7490	1.01230	0.506149	−	0.862446i	$-0.331069\pi$
$647$	25.7490	1.01230	0.506149	+	0.862446i	$0.331069\pi$
$648$	−1.00000	−0.0392837
$649$	−5.12549	−0.201193
$650$	−8.29150	−0.325219
$651$	0	0
$652$	2.41699	0.0946568
$653$	12.0000	0.469596	0.234798	−	0.972044i	$-0.424557\pi$
$653$	12.0000	0.469596	0.234798	+	0.972044i	$0.424557\pi$
$654$	4.00000	0.156412
$655$	−39.8745	−1.55803
$656$	−2.35425	−0.0919180
$657$	−13.6458	−0.532371
$658$	0	0
$659$	−16.9373	−0.659782	−0.329891	−	0.944019i	$-0.607012\pi$
$659$	−16.9373	−0.659782	−0.329891	+	0.944019i	$0.607012\pi$
$660$	−2.35425	−0.0916390
$661$	15.5203	0.603668	0.301834	−	0.953360i	$-0.402401\pi$
$661$	15.5203	0.603668	0.301834	+	0.953360i	$0.402401\pi$
$662$	−11.4170	−0.443734
$663$	−6.64575	−0.258100
$664$	13.2915	0.515810
$665$	0	0
$666$	−5.64575	−0.218768
$667$	−10.1033	−0.391200
$668$	−6.87451	−0.265983
$669$	−20.5203	−0.793359
$670$	27.6458	1.06805
$671$	−7.70850	−0.297583
$672$	0	0
$673$	−6.58301	−0.253756	−0.126878	−	0.991918i	$-0.540496\pi$
$673$	−6.58301	−0.253756	−0.126878	+	0.991918i	$0.540496\pi$
$674$	15.5830	0.600235
$675$	8.29150	0.319140
$676$	1.00000	0.0384615
$677$	20.1660	0.775043	0.387521	−	0.921861i	$-0.373331\pi$
$677$	20.1660	0.775043	0.387521	+	0.921861i	$0.373331\pi$
$678$	−15.2288	−0.584857
$679$	0	0
$680$	−24.2288	−0.929130
$681$	−4.70850	−0.180430
$682$	−2.12549	−0.0813893
$683$	19.2915	0.738169	0.369084	−	0.929396i	$-0.379671\pi$
$683$	19.2915	0.738169	0.369084	+	0.929396i	$0.379671\pi$
$684$	5.00000	0.191180
$685$	71.1660	2.71911
$686$	0	0
$687$	26.4575	1.00942
$688$	−5.29150	−0.201737
$689$	−3.00000	−0.114291
$690$	−8.58301	−0.326749
$691$	−40.0405	−1.52321	−0.761607	−	0.648040i	$-0.775589\pi$
$691$	−40.0405	−1.52321	−0.761607	+	0.648040i	$0.775589\pi$
$692$	−22.2915	−0.847396
$693$	0	0
$694$	−0.228757	−0.00868348
$695$	81.0405	3.07404
$696$	−4.29150	−0.162669
$697$	15.6458	0.592625
$698$	−18.9373	−0.716786
$699$	0.645751	0.0244246
$700$	0	0
$701$	12.0000	0.453234	0.226617	−	0.973984i	$-0.427233\pi$
$701$	12.0000	0.453234	0.226617	+	0.973984i	$0.427233\pi$
$702$	−1.00000	−0.0377426
$703$	28.2288	1.06467
$704$	0.645751	0.0243377
$705$	−10.9373	−0.411921
$706$	20.5830	0.774652
$707$	0	0
$708$	−7.93725	−0.298300
$709$	6.47974	0.243352	0.121676	−	0.992570i	$-0.461173\pi$
$709$	6.47974	0.243352	0.121676	+	0.992570i	$0.461173\pi$
$710$	59.3948	2.22905
$711$	−10.0000	−0.375029
$712$	−16.9373	−0.634750
$713$	−7.74902	−0.290203
$714$	0	0
$715$	−2.35425	−0.0880439
$716$	−6.00000	−0.224231
$717$	3.00000	0.112037
$718$	6.00000	0.223918
$719$	44.5830	1.66267	0.831333	−	0.555775i	$-0.187578\pi$
$719$	44.5830	1.66267	0.831333	+	0.555775i	$0.187578\pi$
$720$	−3.64575	−0.135869
$721$	0	0
$722$	−6.00000	−0.223297
$723$	−13.8745	−0.515998
$724$	14.6458	0.544305
$725$	35.5830	1.32152
$726$	10.5830	0.392772
$727$	−16.4575	−0.610375	−0.305188	−	0.952292i	$-0.598719\pi$
$727$	−16.4575	−0.610375	−0.305188	+	0.952292i	$0.598719\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−49.7490	−1.84129
$731$	35.1660	1.30066
$732$	−11.9373	−0.441214
$733$	14.2288	0.525551	0.262776	−	0.964857i	$-0.415362\pi$
$733$	14.2288	0.525551	0.262776	+	0.964857i	$0.415362\pi$
$734$	0.583005	0.0215191
$735$	0	0
$736$	2.35425	0.0867788
$737$	4.89674	0.180374
$738$	2.35425	0.0866611
$739$	−17.2915	−0.636078	−0.318039	−	0.948078i	$-0.603024\pi$
$739$	−17.2915	−0.636078	−0.318039	+	0.948078i	$0.603024\pi$
$740$	−20.5830	−0.756646
$741$	5.00000	0.183680
$742$	0	0
$743$	−51.4575	−1.88779	−0.943897	−	0.330241i	$-0.892870\pi$
$743$	−51.4575	−1.88779	−0.943897	+	0.330241i	$0.892870\pi$
$744$	−3.29150	−0.120672
$745$	25.7490	0.943371
$746$	−14.6458	−0.536219
$747$	−13.2915	−0.486311
$748$	−4.29150	−0.156913
$749$	0	0
$750$	12.0000	0.438178
$751$	−33.1660	−1.21024	−0.605122	−	0.796132i	$-0.706876\pi$
$751$	−33.1660	−1.21024	−0.605122	+	0.796132i	$0.706876\pi$
$752$	3.00000	0.109399
$753$	−13.2915	−0.484369
$754$	−4.29150	−0.156287
$755$	−22.1033	−0.804420
$756$	0	0
$757$	26.6458	0.968456	0.484228	−	0.874942i	$-0.339100\pi$
$757$	26.6458	0.968456	0.484228	+	0.874942i	$0.339100\pi$
$758$	9.16601	0.332924
$759$	−1.52026	−0.0551819
$760$	18.2288	0.661226
$761$	7.29150	0.264317	0.132158	−	0.991229i	$-0.457809\pi$
$761$	7.29150	0.264317	0.132158	+	0.991229i	$0.457809\pi$
$762$	10.2288	0.370549
$763$	0	0
$764$	0	0
$765$	24.2288	0.875993
$766$	−25.7490	−0.930350
$767$	−7.93725	−0.286598
$768$	1.00000	0.0360844
$769$	5.64575	0.203591	0.101795	−	0.994805i	$-0.467541\pi$
$769$	5.64575	0.203591	0.101795	+	0.994805i	$0.467541\pi$
$770$	0	0
$771$	−15.8745	−0.571706
$772$	18.9373	0.681567
$773$	40.3320	1.45064	0.725321	−	0.688411i	$-0.241691\pi$
$773$	40.3320	1.45064	0.725321	+	0.688411i	$0.241691\pi$
$774$	5.29150	0.190199
$775$	27.2915	0.980340
$776$	−0.937254	−0.0336455
$777$	0	0
$778$	−7.70850	−0.276363
$779$	−11.7712	−0.421749
$780$	−3.64575	−0.130539
$781$	10.5203	0.376444
$782$	−15.6458	−0.559491
$783$	4.29150	0.153366
$784$	0	0
$785$	−9.64575	−0.344272
$786$	−10.9373	−0.390119
$787$	52.6235	1.87583	0.937913	−	0.346871i	$-0.112756\pi$
$787$	52.6235	1.87583	0.937913	+	0.346871i	$0.112756\pi$
$788$	−26.8118	−0.955129
$789$	−3.64575	−0.129792
$790$	−36.4575	−1.29710
$791$	0	0
$792$	−0.645751	−0.0229458
$793$	−11.9373	−0.423904
$794$	14.9373	0.530103
$795$	10.9373	0.387904
$796$	−22.2288	−0.787877
$797$	−45.8745	−1.62496	−0.812479	−	0.582990i	$-0.801883\pi$
$797$	−45.8745	−1.62496	−0.812479	+	0.582990i	$0.801883\pi$
$798$	0	0
$799$	−19.9373	−0.705329
$800$	−8.29150	−0.293149
$801$	16.9373	0.598448
$802$	18.2288	0.643680
$803$	−8.81176	−0.310960
$804$	7.58301	0.267432
$805$	0	0
$806$	−3.29150	−0.115938
$807$	6.87451	0.241994
$808$	0	0
$809$	23.8118	0.837177	0.418588	−	0.908176i	$-0.362525\pi$
$809$	23.8118	0.837177	0.418588	+	0.908176i	$0.362525\pi$
$810$	3.64575	0.128099
$811$	38.0000	1.33436	0.667180	−	0.744896i	$-0.267501\pi$
$811$	38.0000	1.33436	0.667180	+	0.744896i	$0.267501\pi$
$812$	0	0
$813$	−22.6458	−0.794221
$814$	−3.64575	−0.127784
$815$	−8.81176	−0.308663
$816$	−6.64575	−0.232648
$817$	−26.4575	−0.925631
$818$	26.9373	0.941839
$819$	0	0
$820$	8.58301	0.299732
$821$	−5.77124	−0.201418	−0.100709	−	0.994916i	$-0.532111\pi$
$821$	−5.77124	−0.201418	−0.100709	+	0.994916i	$0.532111\pi$
$822$	19.5203	0.680847
$823$	15.5203	0.541002	0.270501	−	0.962720i	$-0.412811\pi$
$823$	15.5203	0.541002	0.270501	+	0.962720i	$0.412811\pi$
$824$	5.29150	0.184338
$825$	5.35425	0.186411
$826$	0	0
$827$	35.3542	1.22939	0.614694	−	0.788766i	$-0.289280\pi$
$827$	35.3542	1.22939	0.614694	+	0.788766i	$0.289280\pi$
$828$	−2.35425	−0.0818158
$829$	47.2288	1.64032	0.820161	−	0.572132i	$-0.193884\pi$
$829$	47.2288	1.64032	0.820161	+	0.572132i	$0.193884\pi$
$830$	−48.4575	−1.68198
$831$	18.5203	0.642461
$832$	1.00000	0.0346688
$833$	0	0
$834$	22.2288	0.769719
$835$	25.0627	0.867332
$836$	3.22876	0.111669
$837$	3.29150	0.113771
$838$	−30.4575	−1.05214
$839$	21.0000	0.725001	0.362500	−	0.931984i	$-0.381923\pi$
$839$	21.0000	0.725001	0.362500	+	0.931984i	$0.381923\pi$
$840$	0	0
$841$	−10.5830	−0.364931
$842$	24.3542	0.839303
$843$	−2.58301	−0.0889634
$844$	−6.35425	−0.218722
$845$	−3.64575	−0.125418
$846$	−3.00000	−0.103142
$847$	0	0
$848$	−3.00000	−0.103020
$849$	−11.0627	−0.379672
$850$	55.1033	1.89003
$851$	−13.2915	−0.455627
$852$	16.2915	0.558138
$853$	−20.1033	−0.688323	−0.344161	−	0.938911i	$-0.611837\pi$
$853$	−20.1033	−0.688323	−0.344161	+	0.938911i	$0.611837\pi$
$854$	0	0
$855$	−18.2288	−0.623410
$856$	12.0000	0.410152
$857$	13.9373	0.476088	0.238044	−	0.971254i	$-0.423494\pi$
$857$	13.9373	0.476088	0.238044	+	0.971254i	$0.423494\pi$
$858$	−0.645751	−0.0220456
$859$	44.4575	1.51687	0.758435	−	0.651748i	$-0.225964\pi$
$859$	44.4575	1.51687	0.758435	+	0.651748i	$0.225964\pi$
$860$	19.2915	0.657835
$861$	0	0
$862$	−20.5830	−0.701060
$863$	31.7490	1.08075	0.540375	−	0.841425i	$-0.318283\pi$
$863$	31.7490	1.08075	0.540375	+	0.841425i	$0.318283\pi$
$864$	−1.00000	−0.0340207
$865$	81.2693	2.76324
$866$	33.5830	1.14120
$867$	27.1660	0.922606
$868$	0	0
$869$	−6.45751	−0.219056
$870$	15.6458	0.530441
$871$	7.58301	0.256940
$872$	4.00000	0.135457
$873$	0.937254	0.0317212
$874$	11.7712	0.398168
$875$	0	0
$876$	−13.6458	−0.461047
$877$	−54.8118	−1.85086	−0.925431	−	0.378917i	$-0.876297\pi$
$877$	−54.8118	−1.85086	−0.925431	+	0.378917i	$0.876297\pi$
$878$	−23.6458	−0.798005
$879$	7.52026	0.253652
$880$	−2.35425	−0.0793617
$881$	−10.7085	−0.360778	−0.180389	−	0.983595i	$-0.557736\pi$
$881$	−10.7085	−0.360778	−0.180389	+	0.983595i	$0.557736\pi$
$882$	0	0
$883$	−29.0627	−0.978039	−0.489020	−	0.872273i	$-0.662645\pi$
$883$	−29.0627	−0.978039	−0.489020	+	0.872273i	$0.662645\pi$
$884$	−6.64575	−0.223521
$885$	28.9373	0.972715
$886$	−19.0627	−0.640425
$887$	20.5830	0.691110	0.345555	−	0.938399i	$-0.387691\pi$
$887$	20.5830	0.691110	0.345555	+	0.938399i	$0.387691\pi$
$888$	−5.64575	−0.189459
$889$	0	0
$890$	61.7490	2.06983
$891$	0.645751	0.0216335
$892$	−20.5203	−0.687069
$893$	15.0000	0.501956
$894$	7.06275	0.236214
$895$	21.8745	0.731184
$896$	0	0
$897$	−2.35425	−0.0786061
$898$	−12.0000	−0.400445
$899$	14.1255	0.471112
$900$	8.29150	0.276383
$901$	19.9373	0.664206
$902$	1.52026	0.0506191
$903$	0	0
$904$	−15.2288	−0.506501
$905$	−53.3948	−1.77490
$906$	−6.06275	−0.201421
$907$	−3.77124	−0.125222	−0.0626110	−	0.998038i	$-0.519943\pi$
$907$	−3.77124	−0.125222	−0.0626110	+	0.998038i	$0.519943\pi$
$908$	−4.70850	−0.156257
$909$	0	0
$910$	0	0
$911$	−37.7490	−1.25068	−0.625340	−	0.780352i	$-0.715040\pi$
$911$	−37.7490	−1.25068	−0.625340	+	0.780352i	$0.715040\pi$
$912$	5.00000	0.165567
$913$	−8.58301	−0.284056
$914$	−32.2288	−1.06603
$915$	43.5203	1.43874
$916$	26.4575	0.874181
$917$	0	0
$918$	6.64575	0.219342
$919$	47.8745	1.57923	0.789617	−	0.613600i	$-0.210279\pi$
$919$	47.8745	1.57923	0.789617	+	0.613600i	$0.210279\pi$
$920$	−8.58301	−0.282973
$921$	−9.58301	−0.315771
$922$	36.4575	1.20066
$923$	16.2915	0.536241
$924$	0	0
$925$	46.8118	1.53916
$926$	−25.1660	−0.827006
$927$	−5.29150	−0.173796
$928$	−4.29150	−0.140875
$929$	−13.7490	−0.451091	−0.225545	−	0.974233i	$-0.572416\pi$
$929$	−13.7490	−0.451091	−0.225545	+	0.974233i	$0.572416\pi$
$930$	12.0000	0.393496
$931$	0	0
$932$	0.645751	0.0211523
$933$	−1.06275	−0.0347927
$934$	37.5203	1.22770
$935$	15.6458	0.511671
$936$	−1.00000	−0.0326860
$937$	−31.4575	−1.02767	−0.513836	−	0.857888i	$-0.671776\pi$
$937$	−31.4575	−1.02767	−0.513836	+	0.857888i	$0.671776\pi$
$938$	0	0
$939$	13.1660	0.429657
$940$	−10.9373	−0.356734
$941$	−17.1660	−0.559596	−0.279798	−	0.960059i	$-0.590267\pi$
$941$	−17.1660	−0.559596	−0.279798	+	0.960059i	$0.590267\pi$
$942$	−2.64575	−0.0862032
$943$	5.54249	0.180488
$944$	−7.93725	−0.258336
$945$	0	0
$946$	3.41699	0.111096
$947$	−10.5203	−0.341862	−0.170931	−	0.985283i	$-0.554678\pi$
$947$	−10.5203	−0.341862	−0.170931	+	0.985283i	$0.554678\pi$
$948$	−10.0000	−0.324785
$949$	−13.6458	−0.442960
$950$	−41.4575	−1.34506
$951$	−13.2915	−0.431007
$952$	0	0
$953$	−25.1033	−0.813174	−0.406587	−	0.913612i	$-0.633281\pi$
$953$	−25.1033	−0.813174	−0.406587	+	0.913612i	$0.633281\pi$
$954$	3.00000	0.0971286
$955$	0	0
$956$	3.00000	0.0970269
$957$	2.77124	0.0895816
$958$	34.7490	1.12269
$959$	0	0
$960$	−3.64575	−0.117666
$961$	−20.1660	−0.650516
$962$	−5.64575	−0.182026
$963$	−12.0000	−0.386695
$964$	−13.8745	−0.446868
$965$	−69.0405	−2.22249
$966$	0	0
$967$	9.10326	0.292741	0.146371	−	0.989230i	$-0.453241\pi$
$967$	9.10326	0.292741	0.146371	+	0.989230i	$0.453241\pi$
$968$	10.5830	0.340151
$969$	−33.2288	−1.06746
$970$	3.41699	0.109713
$971$	16.9373	0.543542	0.271771	−	0.962362i	$-0.412391\pi$
$971$	16.9373	0.543542	0.271771	+	0.962362i	$0.412391\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	23.9373	0.766999
$975$	8.29150	0.265541
$976$	−11.9373	−0.382102
$977$	20.1255	0.643872	0.321936	−	0.946762i	$-0.395666\pi$
$977$	20.1255	0.643872	0.321936	+	0.946762i	$0.395666\pi$
$978$	−2.41699	−0.0772870
$979$	10.9373	0.349556
$980$	0	0
$981$	−4.00000	−0.127710
$982$	−11.1660	−0.356322
$983$	−30.0405	−0.958144	−0.479072	−	0.877776i	$-0.659027\pi$
$983$	−30.0405	−0.958144	−0.479072	+	0.877776i	$0.659027\pi$
$984$	2.35425	0.0750507
$985$	97.7490	3.11454
$986$	28.5203	0.908270
$987$	0	0
$988$	5.00000	0.159071
$989$	12.4575	0.396126
$990$	2.35425	0.0748229
$991$	5.41699	0.172077	0.0860383	−	0.996292i	$-0.472579\pi$
$991$	5.41699	0.172077	0.0860383	+	0.996292i	$0.472579\pi$
$992$	−3.29150	−0.104505
$993$	11.4170	0.362307
$994$	0	0
$995$	81.0405	2.56916
$996$	−13.2915	−0.421157
$997$	−1.22876	−0.0389151	−0.0194576	−	0.999811i	$-0.506194\pi$
$997$	−1.22876	−0.0389151	−0.0194576	+	0.999811i	$0.506194\pi$
$998$	29.2915	0.927206
$999$	5.64575	0.178624

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3822.2.a.bk.1.1		2
7.2	even	3		546.2.i.j.235.2	yes	4
7.4	even	3		546.2.i.j.79.2	✓	4
7.6	odd	2		3822.2.a.bi.1.2		2
21.2	odd	6		1638.2.j.k.235.1		4
21.11	odd	6		1638.2.j.k.1171.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.i.j.79.2	✓	4	7.4	even	3
546.2.i.j.235.2	yes	4	7.2	even	3
1638.2.j.k.235.1		4	21.2	odd	6
1638.2.j.k.1171.1		4	21.11	odd	6
3822.2.a.bi.1.2		2	7.6	odd	2
3822.2.a.bk.1.1		2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3822.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.64575 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.64575 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +3.64575 q^{10} +0.645751 q^{11} +1.00000 q^{12} +1.00000 q^{13} -3.64575 q^{15} +1.00000 q^{16} -6.64575 q^{17} -1.00000 q^{18} +5.00000 q^{19} -3.64575 q^{20} -0.645751 q^{22} -2.35425 q^{23} -1.00000 q^{24} +8.29150 q^{25} -1.00000 q^{26} +1.00000 q^{27} +4.29150 q^{29} +3.64575 q^{30} +3.29150 q^{31} -1.00000 q^{32} +0.645751 q^{33} +6.64575 q^{34} +1.00000 q^{36} +5.64575 q^{37} -5.00000 q^{38} +1.00000 q^{39} +3.64575 q^{40} -2.35425 q^{41} -5.29150 q^{43} +0.645751 q^{44} -3.64575 q^{45} +2.35425 q^{46} +3.00000 q^{47} +1.00000 q^{48} -8.29150 q^{50} -6.64575 q^{51} +1.00000 q^{52} -3.00000 q^{53} -1.00000 q^{54} -2.35425 q^{55} +5.00000 q^{57} -4.29150 q^{58} -7.93725 q^{59} -3.64575 q^{60} -11.9373 q^{61} -3.29150 q^{62} +1.00000 q^{64} -3.64575 q^{65} -0.645751 q^{66} +7.58301 q^{67} -6.64575 q^{68} -2.35425 q^{69} +16.2915 q^{71} -1.00000 q^{72} -13.6458 q^{73} -5.64575 q^{74} +8.29150 q^{75} +5.00000 q^{76} -1.00000 q^{78} -10.0000 q^{79} -3.64575 q^{80} +1.00000 q^{81} +2.35425 q^{82} -13.2915 q^{83} +24.2288 q^{85} +5.29150 q^{86} +4.29150 q^{87} -0.645751 q^{88} +16.9373 q^{89} +3.64575 q^{90} -2.35425 q^{92} +3.29150 q^{93} -3.00000 q^{94} -18.2288 q^{95} -1.00000 q^{96} +0.937254 q^{97} +0.645751 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{15} + 2 q^{16} - 8 q^{17} - 2 q^{18} + 10 q^{19} - 2 q^{20} + 4 q^{22} - 10 q^{23} - 2 q^{24} + 6 q^{25} - 2 q^{26} + 2 q^{27} - 2 q^{29} + 2 q^{30} - 4 q^{31} - 2 q^{32} - 4 q^{33} + 8 q^{34} + 2 q^{36} + 6 q^{37} - 10 q^{38} + 2 q^{39} + 2 q^{40} - 10 q^{41} - 4 q^{44} - 2 q^{45} + 10 q^{46} + 6 q^{47} + 2 q^{48} - 6 q^{50} - 8 q^{51} + 2 q^{52} - 6 q^{53} - 2 q^{54} - 10 q^{55} + 10 q^{57} + 2 q^{58} - 2 q^{60} - 8 q^{61} + 4 q^{62} + 2 q^{64} - 2 q^{65} + 4 q^{66} - 6 q^{67} - 8 q^{68} - 10 q^{69} + 22 q^{71} - 2 q^{72} - 22 q^{73} - 6 q^{74} + 6 q^{75} + 10 q^{76} - 2 q^{78} - 20 q^{79} - 2 q^{80} + 2 q^{81} + 10 q^{82} - 16 q^{83} + 22 q^{85} - 2 q^{87} + 4 q^{88} + 18 q^{89} + 2 q^{90} - 10 q^{92} - 4 q^{93} - 6 q^{94} - 10 q^{95} - 2 q^{96} - 14 q^{97} - 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^15 + 2 * q^16 - 8 * q^17 - 2 * q^18 + 10 * q^19 - 2 * q^20 + 4 * q^22 - 10 * q^23 - 2 * q^24 + 6 * q^25 - 2 * q^26 + 2 * q^27 - 2 * q^29 + 2 * q^30 - 4 * q^31 - 2 * q^32 - 4 * q^33 + 8 * q^34 + 2 * q^36 + 6 * q^37 - 10 * q^38 + 2 * q^39 + 2 * q^40 - 10 * q^41 - 4 * q^44 - 2 * q^45 + 10 * q^46 + 6 * q^47 + 2 * q^48 - 6 * q^50 - 8 * q^51 + 2 * q^52 - 6 * q^53 - 2 * q^54 - 10 * q^55 + 10 * q^57 + 2 * q^58 - 2 * q^60 - 8 * q^61 + 4 * q^62 + 2 * q^64 - 2 * q^65 + 4 * q^66 - 6 * q^67 - 8 * q^68 - 10 * q^69 + 22 * q^71 - 2 * q^72 - 22 * q^73 - 6 * q^74 + 6 * q^75 + 10 * q^76 - 2 * q^78 - 20 * q^79 - 2 * q^80 + 2 * q^81 + 10 * q^82 - 16 * q^83 + 22 * q^85 - 2 * q^87 + 4 * q^88 + 18 * q^89 + 2 * q^90 - 10 * q^92 - 4 * q^93 - 6 * q^94 - 10 * q^95 - 2 * q^96 - 14 * q^97 - 4 * q^99

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