LMFDB - Embedded newform 3822.2.a.bi.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:	$0$
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.64575 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.64575 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.64575 q^{10} -4.64575 q^{11} -1.00000 q^{12} -1.00000 q^{13} +1.64575 q^{15} +1.00000 q^{16} +1.35425 q^{17} -1.00000 q^{18} -5.00000 q^{19} -1.64575 q^{20} +4.64575 q^{22} -7.64575 q^{23} +1.00000 q^{24} -2.29150 q^{25} +1.00000 q^{26} -1.00000 q^{27} -6.29150 q^{29} -1.64575 q^{30} +7.29150 q^{31} -1.00000 q^{32} +4.64575 q^{33} -1.35425 q^{34} +1.00000 q^{36} +0.354249 q^{37} +5.00000 q^{38} +1.00000 q^{39} +1.64575 q^{40} +7.64575 q^{41} +5.29150 q^{43} -4.64575 q^{44} -1.64575 q^{45} +7.64575 q^{46} -3.00000 q^{47} -1.00000 q^{48} +2.29150 q^{50} -1.35425 q^{51} -1.00000 q^{52} -3.00000 q^{53} +1.00000 q^{54} +7.64575 q^{55} +5.00000 q^{57} +6.29150 q^{58} -7.93725 q^{59} +1.64575 q^{60} -3.93725 q^{61} -7.29150 q^{62} +1.00000 q^{64} +1.64575 q^{65} -4.64575 q^{66} -13.5830 q^{67} +1.35425 q^{68} +7.64575 q^{69} +5.70850 q^{71} -1.00000 q^{72} +8.35425 q^{73} -0.354249 q^{74} +2.29150 q^{75} -5.00000 q^{76} -1.00000 q^{78} -10.0000 q^{79} -1.64575 q^{80} +1.00000 q^{81} -7.64575 q^{82} +2.70850 q^{83} -2.22876 q^{85} -5.29150 q^{86} +6.29150 q^{87} +4.64575 q^{88} -1.06275 q^{89} +1.64575 q^{90} -7.64575 q^{92} -7.29150 q^{93} +3.00000 q^{94} +8.22876 q^{95} +1.00000 q^{96} +14.9373 q^{97} -4.64575 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.64575	−0.736002	−0.368001	−	0.929825i	$-0.619958\pi$
$5$	−1.64575	−0.736002	−0.368001	+	0.929825i	$0.619958\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.64575	0.520432
$11$	−4.64575	−1.40075	−0.700373	−	0.713777i	$-0.746983\pi$
$11$	−4.64575	−1.40075	−0.700373	+	0.713777i	$0.746983\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	1.64575	0.424931
$16$	1.00000	0.250000
$17$	1.35425	0.328454	0.164227	−	0.986423i	$-0.447487\pi$
$17$	1.35425	0.328454	0.164227	+	0.986423i	$0.447487\pi$
$18$	−1.00000	−0.235702
$19$	−5.00000	−1.14708	−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000	−1.14708	−0.573539	+	0.819178i	$0.694430\pi$
$20$	−1.64575	−0.368001
$21$	0	0
$22$	4.64575	0.990478
$23$	−7.64575	−1.59425	−0.797125	−	0.603815i	$-0.793647\pi$
$23$	−7.64575	−1.59425	−0.797125	+	0.603815i	$0.793647\pi$
$24$	1.00000	0.204124
$25$	−2.29150	−0.458301
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−6.29150	−1.16830	−0.584151	−	0.811645i	$-0.698573\pi$
$29$	−6.29150	−1.16830	−0.584151	+	0.811645i	$0.698573\pi$
$30$	−1.64575	−0.300472
$31$	7.29150	1.30959	0.654796	−	0.755805i	$-0.272754\pi$
$31$	7.29150	1.30959	0.654796	+	0.755805i	$0.272754\pi$
$32$	−1.00000	−0.176777
$33$	4.64575	0.808721
$34$	−1.35425	−0.232252
$35$	0	0
$36$	1.00000	0.166667
$37$	0.354249	0.0582381	0.0291191	−	0.999576i	$-0.490730\pi$
$37$	0.354249	0.0582381	0.0291191	+	0.999576i	$0.490730\pi$
$38$	5.00000	0.811107
$39$	1.00000	0.160128
$40$	1.64575	0.260216
$41$	7.64575	1.19407	0.597033	−	0.802217i	$-0.296346\pi$
$41$	7.64575	1.19407	0.597033	+	0.802217i	$0.296346\pi$
$42$	0	0
$43$	5.29150	0.806947	0.403473	−	0.914991i	$-0.367803\pi$
$43$	5.29150	0.806947	0.403473	+	0.914991i	$0.367803\pi$
$44$	−4.64575	−0.700373
$45$	−1.64575	−0.245334
$46$	7.64575	1.12730
$47$	−3.00000	−0.437595	−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000	−0.437595	−0.218797	+	0.975770i	$0.570213\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	2.29150	0.324067
$51$	−1.35425	−0.189633
$52$	−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
$55$	7.64575	1.03095
$56$	0	0
$57$	5.00000	0.662266
$58$	6.29150	0.826115
$59$	−7.93725	−1.03334	−0.516671	−	0.856184i	$-0.672829\pi$
$59$	−7.93725	−1.03334	−0.516671	+	0.856184i	$0.672829\pi$
$60$	1.64575	0.212466
$61$	−3.93725	−0.504114	−0.252057	−	0.967712i	$-0.581107\pi$
$61$	−3.93725	−0.504114	−0.252057	+	0.967712i	$0.581107\pi$
$62$	−7.29150	−0.926022
$63$	0	0
$64$	1.00000	0.125000
$65$	1.64575	0.204130
$66$	−4.64575	−0.571852
$67$	−13.5830	−1.65943	−0.829714	−	0.558189i	$-0.811497\pi$
$67$	−13.5830	−1.65943	−0.829714	+	0.558189i	$0.811497\pi$
$68$	1.35425	0.164227
$69$	7.64575	0.920440
$70$	0	0
$71$	5.70850	0.677474	0.338737	−	0.940881i	$-0.390000\pi$
$71$	5.70850	0.677474	0.338737	+	0.940881i	$0.390000\pi$
$72$	−1.00000	−0.117851
$73$	8.35425	0.977791	0.488895	−	0.872342i	$-0.337400\pi$
$73$	8.35425	0.977791	0.488895	+	0.872342i	$0.337400\pi$
$74$	−0.354249	−0.0411806
$75$	2.29150	0.264600
$76$	−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	$0.690177\pi$
$80$	−1.64575	−0.184001
$81$	1.00000	0.111111
$82$	−7.64575	−0.844332
$83$	2.70850	0.297296	0.148648	−	0.988890i	$-0.452508\pi$
$83$	2.70850	0.297296	0.148648	+	0.988890i	$0.452508\pi$
$84$	0	0
$85$	−2.22876	−0.241743
$86$	−5.29150	−0.570597
$87$	6.29150	0.674520
$88$	4.64575	0.495239
$89$	−1.06275	−0.112651	−0.0563254	−	0.998412i	$-0.517938\pi$
$89$	−1.06275	−0.112651	−0.0563254	+	0.998412i	$0.517938\pi$
$90$	1.64575	0.173477
$91$	0	0
$92$	−7.64575	−0.797125
$93$	−7.29150	−0.756094
$94$	3.00000	0.309426
$95$	8.22876	0.844253
$96$	1.00000	0.102062
$97$	14.9373	1.51665	0.758324	−	0.651878i	$-0.226018\pi$
$97$	14.9373	1.51665	0.758324	+	0.651878i	$0.226018\pi$
$98$	0	0
$99$	−4.64575	−0.466916
$100$	−2.29150	−0.229150
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	1.35425	0.134091
$103$	−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	$0.561356\pi$
$110$	−7.64575	−0.728994
$111$	−0.354249	−0.0336238
$112$	0	0
$113$	−11.2288	−1.05631	−0.528156	−	0.849147i	$-0.677116\pi$
$113$	−11.2288	−1.05631	−0.528156	+	0.849147i	$0.677116\pi$
$114$	−5.00000	−0.468293
$115$	12.5830	1.17337
$116$	−6.29150	−0.584151
$117$	−1.00000	−0.0924500
$118$	7.93725	0.730683
$119$	0	0
$120$	−1.64575	−0.150236
$121$	10.5830	0.962091
$122$	3.93725	0.356462
$123$	−7.64575	−0.689394
$124$	7.29150	0.654796
$125$	12.0000	1.07331
$126$	0	0
$127$	16.2288	1.44007	0.720035	−	0.693938i	$-0.244126\pi$
$127$	16.2288	1.44007	0.720035	+	0.693938i	$0.244126\pi$
$128$	−1.00000	−0.0883883
$129$	−5.29150	−0.465891
$130$	−1.64575	−0.144342
$131$	4.93725	0.431370	0.215685	−	0.976463i	$-0.430802\pi$
$131$	4.93725	0.431370	0.215685	+	0.976463i	$0.430802\pi$
$132$	4.64575	0.404361
$133$	0	0
$134$	13.5830	1.17339
$135$	1.64575	0.141644
$136$	−1.35425	−0.116126
$137$	17.5203	1.49686	0.748428	−	0.663216i	$-0.230809\pi$
$137$	17.5203	1.49686	0.748428	+	0.663216i	$0.230809\pi$
$138$	−7.64575	−0.650850
$139$	−4.22876	−0.358678	−0.179339	−	0.983787i	$-0.557396\pi$
$139$	−4.22876	−0.358678	−0.179339	+	0.983787i	$0.557396\pi$
$140$	0	0
$141$	3.00000	0.252646
$142$	−5.70850	−0.479046
$143$	4.64575	0.388497
$144$	1.00000	0.0833333
$145$	10.3542	0.859874
$146$	−8.35425	−0.691403
$147$	0	0
$148$	0.354249	0.0291191
$149$	−22.9373	−1.87909	−0.939547	−	0.342421i	$-0.888753\pi$
$149$	−22.9373	−1.87909	−0.939547	+	0.342421i	$0.888753\pi$
$150$	−2.29150	−0.187100
$151$	21.9373	1.78523	0.892614	−	0.450821i	$-0.148869\pi$
$151$	21.9373	1.78523	0.892614	+	0.450821i	$0.148869\pi$
$152$	5.00000	0.405554
$153$	1.35425	0.109485
$154$	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
$160$	1.64575	0.130108
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	23.5830	1.84716	0.923582	−	0.383402i	$-0.125247\pi$
$163$	23.5830	1.84716	0.923582	+	0.383402i	$0.125247\pi$
$164$	7.64575	0.597033
$165$	−7.64575	−0.595221
$166$	−2.70850	−0.210220
$167$	−24.8745	−1.92485	−0.962424	−	0.271553i	$-0.912463\pi$
$167$	−24.8745	−1.92485	−0.962424	+	0.271553i	$0.912463\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	2.22876	0.170938
$171$	−5.00000	−0.382360
$172$	5.29150	0.403473
$173$	11.7085	0.890181	0.445090	−	0.895486i	$-0.353172\pi$
$173$	11.7085	0.890181	0.445090	+	0.895486i	$0.353172\pi$
$174$	−6.29150	−0.476958
$175$	0	0
$176$	−4.64575	−0.350187
$177$	7.93725	0.596601
$178$	1.06275	0.0796562
$179$	−6.00000	−0.448461	−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000	−0.448461	−0.224231	+	0.974536i	$0.571987\pi$
$180$	−1.64575	−0.122667
$181$	−9.35425	−0.695296	−0.347648	−	0.937625i	$-0.613020\pi$
$181$	−9.35425	−0.695296	−0.347648	+	0.937625i	$0.613020\pi$
$182$	0	0
$183$	3.93725	0.291050
$184$	7.64575	0.563652
$185$	−0.583005	−0.0428634
$186$	7.29150	0.534639
$187$	−6.29150	−0.460080
$188$	−3.00000	−0.218797
$189$	0	0
$190$	−8.22876	−0.596977
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	−1.00000	−0.0721688
$193$	3.06275	0.220461	0.110231	−	0.993906i	$-0.464841\pi$
$193$	3.06275	0.220461	0.110231	+	0.993906i	$0.464841\pi$
$194$	−14.9373	−1.07243
$195$	−1.64575	−0.117855
$196$	0	0
$197$	20.8118	1.48278	0.741388	−	0.671076i	$-0.234168\pi$
$197$	20.8118	1.48278	0.741388	+	0.671076i	$0.234168\pi$
$198$	4.64575	0.330159
$199$	−4.22876	−0.299769	−0.149884	−	0.988704i	$-0.547890\pi$
$199$	−4.22876	−0.299769	−0.149884	+	0.988704i	$0.547890\pi$
$200$	2.29150	0.162034
$201$	13.5830	0.958071
$202$	0	0
$203$	0	0
$204$	−1.35425	−0.0948164
$205$	−12.5830	−0.878835
$206$	5.29150	0.368676
$207$	−7.64575	−0.531416
$208$	−1.00000	−0.0693375
$209$	23.2288	1.60677
$210$	0	0
$211$	−11.6458	−0.801727	−0.400863	−	0.916138i	$-0.631290\pi$
$211$	−11.6458	−0.801727	−0.400863	+	0.916138i	$0.631290\pi$
$212$	−3.00000	−0.206041
$213$	−5.70850	−0.391140
$214$	12.0000	0.820303
$215$	−8.70850	−0.593915
$216$	1.00000	0.0680414
$217$	0	0
$218$	4.00000	0.270914
$219$	−8.35425	−0.564528
$220$	7.64575	0.515476
$221$	−1.35425	−0.0910966
$222$	0.354249	0.0237756
$223$	−16.5203	−1.10628	−0.553139	−	0.833089i	$-0.686570\pi$
$223$	−16.5203	−1.10628	−0.553139	+	0.833089i	$0.686570\pi$
$224$	0	0
$225$	−2.29150	−0.152767
$226$	11.2288	0.746926
$227$	15.2915	1.01493	0.507466	−	0.861672i	$-0.330582\pi$
$227$	15.2915	1.01493	0.507466	+	0.861672i	$0.330582\pi$
$228$	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	$0.161399\pi$
$230$	−12.5830	−0.829699
$231$	0	0
$232$	6.29150	0.413057
$233$	−4.64575	−0.304353	−0.152177	−	0.988353i	$-0.548628\pi$
$233$	−4.64575	−0.304353	−0.152177	+	0.988353i	$0.548628\pi$
$234$	1.00000	0.0653720
$235$	4.93725	0.322071
$236$	−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	$0.469067\pi$
$240$	1.64575	0.106233
$241$	−17.8745	−1.15140	−0.575699	−	0.817662i	$-0.695270\pi$
$241$	−17.8745	−1.15140	−0.575699	+	0.817662i	$0.695270\pi$
$242$	−10.5830	−0.680301
$243$	−1.00000	−0.0641500
$244$	−3.93725	−0.252057
$245$	0	0
$246$	7.64575	0.487475
$247$	5.00000	0.318142
$248$	−7.29150	−0.463011
$249$	−2.70850	−0.171644
$250$	−12.0000	−0.758947
$251$	2.70850	0.170959	0.0854794	−	0.996340i	$-0.472758\pi$
$251$	2.70850	0.170959	0.0854794	+	0.996340i	$0.472758\pi$
$252$	0	0
$253$	35.5203	2.23314
$254$	−16.2288	−1.01828
$255$	2.22876	0.139570
$256$	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
$260$	1.64575	0.102065
$261$	−6.29150	−0.389434
$262$	−4.93725	−0.305025
$263$	1.64575	0.101481	0.0507407	−	0.998712i	$-0.483842\pi$
$263$	1.64575	0.101481	0.0507407	+	0.998712i	$0.483842\pi$
$264$	−4.64575	−0.285926
$265$	4.93725	0.303293
$266$	0	0
$267$	1.06275	0.0650390
$268$	−13.5830	−0.829714
$269$	24.8745	1.51663	0.758313	−	0.651891i	$-0.226024\pi$
$269$	24.8745	1.51663	0.758313	+	0.651891i	$0.226024\pi$
$270$	−1.64575	−0.100157
$271$	17.3542	1.05420	0.527098	−	0.849805i	$-0.323280\pi$
$271$	17.3542	1.05420	0.527098	+	0.849805i	$0.323280\pi$
$272$	1.35425	0.0821134
$273$	0	0
$274$	−17.5203	−1.05844
$275$	10.6458	0.641963
$276$	7.64575	0.460220
$277$	−18.5203	−1.11277	−0.556387	−	0.830923i	$-0.687813\pi$
$277$	−18.5203	−1.11277	−0.556387	+	0.830923i	$0.687813\pi$
$278$	4.22876	0.253624
$279$	7.29150	0.436531
$280$	0	0
$281$	18.5830	1.10857	0.554285	−	0.832327i	$-0.312992\pi$
$281$	18.5830	1.10857	0.554285	+	0.832327i	$0.312992\pi$
$282$	−3.00000	−0.178647
$283$	26.9373	1.60125	0.800627	−	0.599163i	$-0.204500\pi$
$283$	26.9373	1.60125	0.800627	+	0.599163i	$0.204500\pi$
$284$	5.70850	0.338737
$285$	−8.22876	−0.487429
$286$	−4.64575	−0.274709
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	−15.1660	−0.892118
$290$	−10.3542	−0.608022
$291$	−14.9373	−0.875637
$292$	8.35425	0.488895
$293$	29.5203	1.72459	0.862296	−	0.506405i	$-0.169026\pi$
$293$	29.5203	1.72459	0.862296	+	0.506405i	$0.169026\pi$
$294$	0	0
$295$	13.0627	0.760542
$296$	−0.354249	−0.0205903
$297$	4.64575	0.269574
$298$	22.9373	1.32872
$299$	7.64575	0.442165
$300$	2.29150	0.132300
$301$	0	0
$302$	−21.9373	−1.26235
$303$	0	0
$304$	−5.00000	−0.286770
$305$	6.47974	0.371029
$306$	−1.35425	−0.0774172
$307$	−11.5830	−0.661077	−0.330539	−	0.943793i	$-0.607230\pi$
$307$	−11.5830	−0.661077	−0.330539	+	0.943793i	$0.607230\pi$
$308$	0	0
$309$	5.29150	0.301023
$310$	12.0000	0.681554
$311$	16.9373	0.960424	0.480212	−	0.877153i	$-0.340560\pi$
$311$	16.9373	0.960424	0.480212	+	0.877153i	$0.340560\pi$
$312$	−1.00000	−0.0566139
$313$	29.1660	1.64856	0.824280	−	0.566182i	$-0.191580\pi$
$313$	29.1660	1.64856	0.824280	+	0.566182i	$0.191580\pi$
$314$	−2.64575	−0.149308
$315$	0	0
$316$	−10.0000	−0.562544
$317$	−2.70850	−0.152124	−0.0760622	−	0.997103i	$-0.524235\pi$
$317$	−2.70850	−0.152124	−0.0760622	+	0.997103i	$0.524235\pi$
$318$	−3.00000	−0.168232
$319$	29.2288	1.63650
$320$	−1.64575	−0.0920003
$321$	12.0000	0.669775
$322$	0	0
$323$	−6.77124	−0.376762
$324$	1.00000	0.0555556
$325$	2.29150	0.127110
$326$	−23.5830	−1.30614
$327$	4.00000	0.221201
$328$	−7.64575	−0.422166
$329$	0	0
$330$	7.64575	0.420885
$331$	32.5830	1.79092	0.895462	−	0.445138i	$-0.146845\pi$
$331$	32.5830	1.79092	0.895462	+	0.445138i	$0.146845\pi$
$332$	2.70850	0.148648
$333$	0.354249	0.0194127
$334$	24.8745	1.36107
$335$	22.3542	1.22134
$336$	0	0
$337$	5.58301	0.304126	0.152063	−	0.988371i	$-0.451408\pi$
$337$	5.58301	0.304126	0.152063	+	0.988371i	$0.451408\pi$
$338$	−1.00000	−0.0543928
$339$	11.2288	0.609862
$340$	−2.22876	−0.120871
$341$	−33.8745	−1.83441
$342$	5.00000	0.270369
$343$	0	0
$344$	−5.29150	−0.285299
$345$	−12.5830	−0.677446
$346$	−11.7085	−0.629453
$347$	−26.2288	−1.40803	−0.704017	−	0.710183i	$-0.748612\pi$
$347$	−26.2288	−1.40803	−0.704017	+	0.710183i	$0.748612\pi$
$348$	6.29150	0.337260
$349$	−3.06275	−0.163945	−0.0819725	−	0.996635i	$-0.526122\pi$
$349$	−3.06275	−0.163945	−0.0819725	+	0.996635i	$0.526122\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	4.64575	0.247619
$353$	−0.583005	−0.0310302	−0.0155151	−	0.999880i	$-0.504939\pi$
$353$	−0.583005	−0.0310302	−0.0155151	+	0.999880i	$0.504939\pi$
$354$	−7.93725	−0.421860
$355$	−9.39477	−0.498622
$356$	−1.06275	−0.0563254
$357$	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	$0.550612\pi$
$360$	1.64575	0.0867387
$361$	6.00000	0.315789
$362$	9.35425	0.491648
$363$	−10.5830	−0.555464
$364$	0	0
$365$	−13.7490	−0.719656
$366$	−3.93725	−0.205804
$367$	−20.5830	−1.07442	−0.537212	−	0.843447i	$-0.680523\pi$
$367$	−20.5830	−1.07442	−0.537212	+	0.843447i	$0.680523\pi$
$368$	−7.64575	−0.398562
$369$	7.64575	0.398022
$370$	0.583005	0.0303090
$371$	0	0
$372$	−7.29150	−0.378047
$373$	9.35425	0.484345	0.242172	−	0.970233i	$-0.422140\pi$
$373$	9.35425	0.484345	0.242172	+	0.970233i	$0.422140\pi$
$374$	6.29150	0.325326
$375$	−12.0000	−0.619677
$376$	3.00000	0.154713
$377$	6.29150	0.324029
$378$	0	0
$379$	33.1660	1.70362	0.851812	−	0.523848i	$-0.175504\pi$
$379$	33.1660	1.70362	0.851812	+	0.523848i	$0.175504\pi$
$380$	8.22876	0.422126
$381$	−16.2288	−0.831424
$382$	0	0
$383$	37.7490	1.92888	0.964442	−	0.264293i	$-0.0851388\pi$
$383$	37.7490	1.92888	0.964442	+	0.264293i	$0.0851388\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−3.06275	−0.155890
$387$	5.29150	0.268982
$388$	14.9373	0.758324
$389$	18.2915	0.927416	0.463708	−	0.885988i	$-0.346519\pi$
$389$	18.2915	0.927416	0.463708	+	0.885988i	$0.346519\pi$
$390$	1.64575	0.0833359
$391$	−10.3542	−0.523637
$392$	0	0
$393$	−4.93725	−0.249052
$394$	−20.8118	−1.04848
$395$	16.4575	0.828067
$396$	−4.64575	−0.233458
$397$	−0.937254	−0.0470394	−0.0235197	−	0.999723i	$-0.507487\pi$
$397$	−0.937254	−0.0470394	−0.0235197	+	0.999723i	$0.507487\pi$
$398$	4.22876	0.211968
$399$	0	0
$400$	−2.29150	−0.114575
$401$	8.22876	0.410924	0.205462	−	0.978665i	$-0.434130\pi$
$401$	8.22876	0.410924	0.205462	+	0.978665i	$0.434130\pi$
$402$	−13.5830	−0.677459
$403$	−7.29150	−0.363216
$404$	0	0
$405$	−1.64575	−0.0817780
$406$	0	0
$407$	−1.64575	−0.0815769
$408$	1.35425	0.0670453
$409$	11.0627	0.547018	0.273509	−	0.961870i	$-0.411816\pi$
$409$	11.0627	0.547018	0.273509	+	0.961870i	$0.411816\pi$
$410$	12.5830	0.621430
$411$	−17.5203	−0.864211
$412$	−5.29150	−0.260694
$413$	0	0
$414$	7.64575	0.375768
$415$	−4.45751	−0.218811
$416$	1.00000	0.0490290
$417$	4.22876	0.207083
$418$	−23.2288	−1.13616
$419$	22.4575	1.09712	0.548561	−	0.836111i	$-0.315176\pi$
$419$	22.4575	1.09712	0.548561	+	0.836111i	$0.315176\pi$
$420$	0	0
$421$	−29.6458	−1.44485	−0.722423	−	0.691452i	$-0.756972\pi$
$421$	−29.6458	−1.44485	−0.722423	+	0.691452i	$0.756972\pi$
$422$	11.6458	0.566906
$423$	−3.00000	−0.145865
$424$	3.00000	0.145693
$425$	−3.10326	−0.150530
$426$	5.70850	0.276578
$427$	0	0
$428$	−12.0000	−0.580042
$429$	−4.64575	−0.224299
$430$	8.70850	0.419961
$431$	−0.583005	−0.0280824	−0.0140412	−	0.999901i	$-0.504470\pi$
$431$	−0.583005	−0.0280824	−0.0140412	+	0.999901i	$0.504470\pi$
$432$	−1.00000	−0.0481125
$433$	12.4170	0.596723	0.298361	−	0.954453i	$-0.403560\pi$
$433$	12.4170	0.596723	0.298361	+	0.954453i	$0.403560\pi$
$434$	0	0
$435$	−10.3542	−0.496448
$436$	−4.00000	−0.191565
$437$	38.2288	1.82873
$438$	8.35425	0.399181
$439$	−18.3542	−0.876000	−0.438000	−	0.898975i	$-0.644313\pi$
$439$	−18.3542	−0.876000	−0.438000	+	0.898975i	$0.644313\pi$
$440$	−7.64575	−0.364497
$441$	0	0
$442$	1.35425	0.0644150
$443$	34.9373	1.65992	0.829960	−	0.557824i	$-0.188363\pi$
$443$	34.9373	1.65992	0.829960	+	0.557824i	$0.188363\pi$
$444$	−0.354249	−0.0168119
$445$	1.74902	0.0829113
$446$	16.5203	0.782257
$447$	22.9373	1.08489
$448$	0	0
$449$	12.0000	0.566315	0.283158	−	0.959073i	$-0.408618\pi$
$449$	12.0000	0.566315	0.283158	+	0.959073i	$0.408618\pi$
$450$	2.29150	0.108022
$451$	−35.5203	−1.67258
$452$	−11.2288	−0.528156
$453$	−21.9373	−1.03070
$454$	−15.2915	−0.717666
$455$	0	0
$456$	−5.00000	−0.234146
$457$	5.77124	0.269967	0.134984	−	0.990848i	$-0.456902\pi$
$457$	5.77124	0.269967	0.134984	+	0.990848i	$0.456902\pi$
$458$	−26.4575	−1.23628
$459$	−1.35425	−0.0632109
$460$	12.5830	0.586686
$461$	−16.4575	−0.766503	−0.383251	−	0.923644i	$-0.625196\pi$
$461$	−16.4575	−0.766503	−0.383251	+	0.923644i	$0.625196\pi$
$462$	0	0
$463$	−17.1660	−0.797772	−0.398886	−	0.917000i	$-0.630603\pi$
$463$	−17.1660	−0.797772	−0.398886	+	0.917000i	$0.630603\pi$
$464$	−6.29150	−0.292076
$465$	12.0000	0.556487
$466$	4.64575	0.215210
$467$	0.479741	0.0221998	0.0110999	−	0.999938i	$-0.496467\pi$
$467$	0.479741	0.0221998	0.0110999	+	0.999938i	$0.496467\pi$
$468$	−1.00000	−0.0462250
$469$	0	0
$470$	−4.93725	−0.227739
$471$	−2.64575	−0.121910
$472$	7.93725	0.365342
$473$	−24.5830	−1.13033
$474$	−10.0000	−0.459315
$475$	11.4575	0.525707
$476$	0	0
$477$	−3.00000	−0.137361
$478$	−3.00000	−0.137217
$479$	−28.7490	−1.31358	−0.656788	−	0.754075i	$-0.728085\pi$
$479$	−28.7490	−1.31358	−0.656788	+	0.754075i	$0.728085\pi$
$480$	−1.64575	−0.0751179
$481$	−0.354249	−0.0161523
$482$	17.8745	0.814162
$483$	0	0
$484$	10.5830	0.481046
$485$	−24.5830	−1.11626
$486$	1.00000	0.0453609
$487$	−8.06275	−0.365358	−0.182679	−	0.983173i	$-0.558477\pi$
$487$	−8.06275	−0.365358	−0.182679	+	0.983173i	$0.558477\pi$
$488$	3.93725	0.178231
$489$	−23.5830	−1.06646
$490$	0	0
$491$	−31.1660	−1.40650	−0.703251	−	0.710941i	$-0.748269\pi$
$491$	−31.1660	−1.40650	−0.703251	+	0.710941i	$0.748269\pi$
$492$	−7.64575	−0.344697
$493$	−8.52026	−0.383733
$494$	−5.00000	−0.224961
$495$	7.64575	0.343651
$496$	7.29150	0.327398
$497$	0	0
$498$	2.70850	0.121371
$499$	−18.7085	−0.837507	−0.418754	−	0.908100i	$-0.637533\pi$
$499$	−18.7085	−0.837507	−0.418754	+	0.908100i	$0.637533\pi$
$500$	12.0000	0.536656
$501$	24.8745	1.11131
$502$	−2.70850	−0.120886
$503$	16.4575	0.733804	0.366902	−	0.930260i	$-0.380418\pi$
$503$	16.4575	0.733804	0.366902	+	0.930260i	$0.380418\pi$
$504$	0	0
$505$	0	0
$506$	−35.5203	−1.57907
$507$	−1.00000	−0.0444116
$508$	16.2288	0.720035
$509$	−24.0000	−1.06378	−0.531891	−	0.846813i	$-0.678518\pi$
$509$	−24.0000	−1.06378	−0.531891	+	0.846813i	$0.678518\pi$
$510$	−2.22876	−0.0986910
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	5.00000	0.220755
$514$	15.8745	0.700195
$515$	8.70850	0.383742
$516$	−5.29150	−0.232945
$517$	13.9373	0.612960
$518$	0	0
$519$	−11.7085	−0.513946
$520$	−1.64575	−0.0721710
$521$	−18.0000	−0.788594	−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000	−0.788594	−0.394297	+	0.918983i	$0.629012\pi$
$522$	6.29150	0.275372
$523$	37.2915	1.63064	0.815322	−	0.579008i	$-0.196560\pi$
$523$	37.2915	1.63064	0.815322	+	0.579008i	$0.196560\pi$
$524$	4.93725	0.215685
$525$	0	0
$526$	−1.64575	−0.0717582
$527$	9.87451	0.430140
$528$	4.64575	0.202180
$529$	35.4575	1.54163
$530$	−4.93725	−0.214461
$531$	−7.93725	−0.344447
$532$	0	0
$533$	−7.64575	−0.331174
$534$	−1.06275	−0.0459895
$535$	19.7490	0.853824
$536$	13.5830	0.586696
$537$	6.00000	0.258919
$538$	−24.8745	−1.07242
$539$	0	0
$540$	1.64575	0.0708219
$541$	36.3542	1.56299	0.781496	−	0.623911i	$-0.214457\pi$
$541$	36.3542	1.56299	0.781496	+	0.623911i	$0.214457\pi$
$542$	−17.3542	−0.745429
$543$	9.35425	0.401429
$544$	−1.35425	−0.0580629
$545$	6.58301	0.281985
$546$	0	0
$547$	−5.06275	−0.216467	−0.108234	−	0.994125i	$-0.534519\pi$
$547$	−5.06275	−0.216467	−0.108234	+	0.994125i	$0.534519\pi$
$548$	17.5203	0.748428
$549$	−3.93725	−0.168038
$550$	−10.6458	−0.453936
$551$	31.4575	1.34014
$552$	−7.64575	−0.325425
$553$	0	0
$554$	18.5203	0.786850
$555$	0.583005	0.0247472
$556$	−4.22876	−0.179339
$557$	−31.1660	−1.32055	−0.660273	−	0.751026i	$-0.729559\pi$
$557$	−31.1660	−1.32055	−0.660273	+	0.751026i	$0.729559\pi$
$558$	−7.29150	−0.308674
$559$	−5.29150	−0.223807
$560$	0	0
$561$	6.29150	0.265627
$562$	−18.5830	−0.783877
$563$	−47.0405	−1.98252	−0.991261	−	0.131917i	$-0.957887\pi$
$563$	−47.0405	−1.98252	−0.991261	+	0.131917i	$0.957887\pi$
$564$	3.00000	0.126323
$565$	18.4797	0.777449
$566$	−26.9373	−1.13226
$567$	0	0
$568$	−5.70850	−0.239523
$569$	−6.77124	−0.283865	−0.141933	−	0.989876i	$-0.545332\pi$
$569$	−6.77124	−0.283865	−0.141933	+	0.989876i	$0.545332\pi$
$570$	8.22876	0.344665
$571$	−16.0000	−0.669579	−0.334790	−	0.942293i	$-0.608665\pi$
$571$	−16.0000	−0.669579	−0.334790	+	0.942293i	$0.608665\pi$
$572$	4.64575	0.194249
$573$	0	0
$574$	0	0
$575$	17.5203	0.730645
$576$	1.00000	0.0416667
$577$	−8.58301	−0.357315	−0.178658	−	0.983911i	$-0.557175\pi$
$577$	−8.58301	−0.357315	−0.178658	+	0.983911i	$0.557175\pi$
$578$	15.1660	0.630823
$579$	−3.06275	−0.127283
$580$	10.3542	0.429937
$581$	0	0
$582$	14.9373	0.619169
$583$	13.9373	0.577222
$584$	−8.35425	−0.345701
$585$	1.64575	0.0680434
$586$	−29.5203	−1.21947
$587$	−16.0627	−0.662980	−0.331490	−	0.943459i	$-0.607551\pi$
$587$	−16.0627	−0.662980	−0.331490	+	0.943459i	$0.607551\pi$
$588$	0	0
$589$	−36.4575	−1.50221
$590$	−13.0627	−0.537785
$591$	−20.8118	−0.856081
$592$	0.354249	0.0145595
$593$	−6.47974	−0.266091	−0.133046	−	0.991110i	$-0.542476\pi$
$593$	−6.47974	−0.266091	−0.133046	+	0.991110i	$0.542476\pi$
$594$	−4.64575	−0.190617
$595$	0	0
$596$	−22.9373	−0.939547
$597$	4.22876	0.173071
$598$	−7.64575	−0.312658
$599$	14.8118	0.605192	0.302596	−	0.953119i	$-0.402147\pi$
$599$	14.8118	0.605192	0.302596	+	0.953119i	$0.402147\pi$
$600$	−2.29150	−0.0935502
$601$	16.8745	0.688326	0.344163	−	0.938910i	$-0.388163\pi$
$601$	16.8745	0.688326	0.344163	+	0.938910i	$0.388163\pi$
$602$	0	0
$603$	−13.5830	−0.553143
$604$	21.9373	0.892614
$605$	−17.4170	−0.708102
$606$	0	0
$607$	30.8118	1.25061	0.625305	−	0.780380i	$-0.284974\pi$
$607$	30.8118	1.25061	0.625305	+	0.780380i	$0.284974\pi$
$608$	5.00000	0.202777
$609$	0	0
$610$	−6.47974	−0.262357
$611$	3.00000	0.121367
$612$	1.35425	0.0547423
$613$	10.1255	0.408965	0.204482	−	0.978870i	$-0.434449\pi$
$613$	10.1255	0.408965	0.204482	+	0.978870i	$0.434449\pi$
$614$	11.5830	0.467452
$615$	12.5830	0.507396
$616$	0	0
$617$	−21.2915	−0.857164	−0.428582	−	0.903503i	$-0.640987\pi$
$617$	−21.2915	−0.857164	−0.428582	+	0.903503i	$0.640987\pi$
$618$	−5.29150	−0.212855
$619$	−21.7490	−0.874167	−0.437083	−	0.899421i	$-0.643989\pi$
$619$	−21.7490	−0.874167	−0.437083	+	0.899421i	$0.643989\pi$
$620$	−12.0000	−0.481932
$621$	7.64575	0.306813
$622$	−16.9373	−0.679122
$623$	0	0
$624$	1.00000	0.0400320
$625$	−8.29150	−0.331660
$626$	−29.1660	−1.16571
$627$	−23.2288	−0.927667
$628$	2.64575	0.105577
$629$	0.479741	0.0191285
$630$	0	0
$631$	−38.4575	−1.53097	−0.765485	−	0.643454i	$-0.777501\pi$
$631$	−38.4575	−1.53097	−0.765485	+	0.643454i	$0.777501\pi$
$632$	10.0000	0.397779
$633$	11.6458	0.462877
$634$	2.70850	0.107568
$635$	−26.7085	−1.05989
$636$	3.00000	0.118958
$637$	0	0
$638$	−29.2288	−1.15718
$639$	5.70850	0.225825
$640$	1.64575	0.0650540
$641$	−42.5830	−1.68193	−0.840964	−	0.541091i	$-0.818011\pi$
$641$	−42.5830	−1.68193	−0.840964	+	0.541091i	$0.818011\pi$
$642$	−12.0000	−0.473602
$643$	−20.8745	−0.823210	−0.411605	−	0.911362i	$-0.635032\pi$
$643$	−20.8745	−0.823210	−0.411605	+	0.911362i	$0.635032\pi$
$644$	0	0
$645$	8.70850	0.342897
$646$	6.77124	0.266411
$647$	37.7490	1.48407	0.742033	−	0.670363i	$-0.233862\pi$
$647$	37.7490	1.48407	0.742033	+	0.670363i	$0.233862\pi$
$648$	−1.00000	−0.0392837
$649$	36.8745	1.44745
$650$	−2.29150	−0.0898801
$651$	0	0
$652$	23.5830	0.923582
$653$	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
$655$	−8.12549	−0.317489
$656$	7.64575	0.298516
$657$	8.35425	0.325930
$658$	0	0
$659$	−1.06275	−0.0413987	−0.0206994	−	0.999786i	$-0.506589\pi$
$659$	−1.06275	−0.0413987	−0.0206994	+	0.999786i	$0.506589\pi$
$660$	−7.64575	−0.297610
$661$	21.5203	0.837041	0.418521	−	0.908207i	$-0.362549\pi$
$661$	21.5203	0.837041	0.418521	+	0.908207i	$0.362549\pi$
$662$	−32.5830	−1.26637
$663$	1.35425	0.0525947
$664$	−2.70850	−0.105110
$665$	0	0
$666$	−0.354249	−0.0137269
$667$	48.1033	1.86257
$668$	−24.8745	−0.962424
$669$	16.5203	0.638710
$670$	−22.3542	−0.863620
$671$	18.2915	0.706136
$672$	0	0
$673$	14.5830	0.562134	0.281067	−	0.959688i	$-0.409312\pi$
$673$	14.5830	0.562134	0.281067	+	0.959688i	$0.409312\pi$
$674$	−5.58301	−0.215049
$675$	2.29150	0.0882000
$676$	1.00000	0.0384615
$677$	22.1660	0.851909	0.425954	−	0.904745i	$-0.359938\pi$
$677$	22.1660	0.851909	0.425954	+	0.904745i	$0.359938\pi$
$678$	−11.2288	−0.431238
$679$	0	0
$680$	2.22876	0.0854689
$681$	−15.2915	−0.585972
$682$	33.8745	1.29712
$683$	8.70850	0.333221	0.166611	−	0.986023i	$-0.446718\pi$
$683$	8.70850	0.333221	0.166611	+	0.986023i	$0.446718\pi$
$684$	−5.00000	−0.191180
$685$	−28.8340	−1.10169
$686$	0	0
$687$	−26.4575	−1.00942
$688$	5.29150	0.201737
$689$	3.00000	0.114291
$690$	12.5830	0.479027
$691$	−34.0405	−1.29496	−0.647481	−	0.762081i	$-0.724178\pi$
$691$	−34.0405	−1.29496	−0.647481	+	0.762081i	$0.724178\pi$
$692$	11.7085	0.445090
$693$	0	0
$694$	26.2288	0.995630
$695$	6.95948	0.263988
$696$	−6.29150	−0.238479
$697$	10.3542	0.392195
$698$	3.06275	0.115927
$699$	4.64575	0.175718
$700$	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
$703$	−1.77124	−0.0668037
$704$	−4.64575	−0.175093
$705$	−4.93725	−0.185948
$706$	0.583005	0.0219417
$707$	0	0
$708$	7.93725	0.298300
$709$	43.5203	1.63444	0.817219	−	0.576328i	$-0.195515\pi$
$709$	43.5203	1.63444	0.817219	+	0.576328i	$0.195515\pi$
$710$	9.39477	0.352579
$711$	−10.0000	−0.375029
$712$	1.06275	0.0398281
$713$	−55.7490	−2.08782
$714$	0	0
$715$	−7.64575	−0.285935
$716$	−6.00000	−0.224231
$717$	−3.00000	−0.112037
$718$	6.00000	0.223918
$719$	−23.4170	−0.873307	−0.436653	−	0.899630i	$-0.643836\pi$
$719$	−23.4170	−0.873307	−0.436653	+	0.899630i	$0.643836\pi$
$720$	−1.64575	−0.0613335
$721$	0	0
$722$	−6.00000	−0.223297
$723$	17.8745	0.664760
$724$	−9.35425	−0.347648
$725$	14.4170	0.535434
$726$	10.5830	0.392772
$727$	−36.4575	−1.35213	−0.676067	−	0.736840i	$-0.736317\pi$
$727$	−36.4575	−1.35213	−0.676067	+	0.736840i	$0.736317\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	13.7490	0.508874
$731$	7.16601	0.265044
$732$	3.93725	0.145525
$733$	12.2288	0.451679	0.225840	−	0.974164i	$-0.427487\pi$
$733$	12.2288	0.451679	0.225840	+	0.974164i	$0.427487\pi$
$734$	20.5830	0.759733
$735$	0	0
$736$	7.64575	0.281826
$737$	63.1033	2.32444
$738$	−7.64575	−0.281444
$739$	−6.70850	−0.246776	−0.123388	−	0.992359i	$-0.539376\pi$
$739$	−6.70850	−0.246776	−0.123388	+	0.992359i	$0.539376\pi$
$740$	−0.583005	−0.0214317
$741$	−5.00000	−0.183680
$742$	0	0
$743$	1.45751	0.0534710	0.0267355	−	0.999643i	$-0.491489\pi$
$743$	1.45751	0.0534710	0.0267355	+	0.999643i	$0.491489\pi$
$744$	7.29150	0.267319
$745$	37.7490	1.38302
$746$	−9.35425	−0.342483
$747$	2.70850	0.0990987
$748$	−6.29150	−0.230040
$749$	0	0
$750$	12.0000	0.438178
$751$	9.16601	0.334472	0.167236	−	0.985917i	$-0.446516\pi$
$751$	9.16601	0.334472	0.167236	+	0.985917i	$0.446516\pi$
$752$	−3.00000	−0.109399
$753$	−2.70850	−0.0987031
$754$	−6.29150	−0.229123
$755$	−36.1033	−1.31393
$756$	0	0
$757$	21.3542	0.776133	0.388067	−	0.921631i	$-0.373143\pi$
$757$	21.3542	0.776133	0.388067	+	0.921631i	$0.373143\pi$
$758$	−33.1660	−1.20464
$759$	−35.5203	−1.28930
$760$	−8.22876	−0.298488
$761$	3.29150	0.119317	0.0596584	−	0.998219i	$-0.480999\pi$
$761$	3.29150	0.119317	0.0596584	+	0.998219i	$0.480999\pi$
$762$	16.2288	0.587906
$763$	0	0
$764$	0	0
$765$	−2.22876	−0.0805809
$766$	−37.7490	−1.36393
$767$	7.93725	0.286598
$768$	−1.00000	−0.0360844
$769$	−0.354249	−0.0127745	−0.00638727	−	0.999980i	$-0.502033\pi$
$769$	−0.354249	−0.0127745	−0.00638727	+	0.999980i	$0.502033\pi$
$770$	0	0
$771$	15.8745	0.571706
$772$	3.06275	0.110231
$773$	44.3320	1.59451	0.797256	−	0.603641i	$-0.206284\pi$
$773$	44.3320	1.59451	0.797256	+	0.603641i	$0.206284\pi$
$774$	−5.29150	−0.190199
$775$	−16.7085	−0.600187
$776$	−14.9373	−0.536216
$777$	0	0
$778$	−18.2915	−0.655782
$779$	−38.2288	−1.36969
$780$	−1.64575	−0.0589273
$781$	−26.5203	−0.948969
$782$	10.3542	0.370267
$783$	6.29150	0.224840
$784$	0	0
$785$	−4.35425	−0.155410
$786$	4.93725	0.176106
$787$	42.6235	1.51936	0.759682	−	0.650294i	$-0.225354\pi$
$787$	42.6235	1.51936	0.759682	+	0.650294i	$0.225354\pi$
$788$	20.8118	0.741388
$789$	−1.64575	−0.0585903
$790$	−16.4575	−0.585532
$791$	0	0
$792$	4.64575	0.165080
$793$	3.93725	0.139816
$794$	0.937254	0.0332619
$795$	−4.93725	−0.175106
$796$	−4.22876	−0.149884
$797$	14.1255	0.500351	0.250175	−	0.968201i	$-0.419512\pi$
$797$	14.1255	0.500351	0.250175	+	0.968201i	$0.419512\pi$
$798$	0	0
$799$	−4.06275	−0.143730
$800$	2.29150	0.0810169
$801$	−1.06275	−0.0375503
$802$	−8.22876	−0.290567
$803$	−38.8118	−1.36964
$804$	13.5830	0.479036
$805$	0	0
$806$	7.29150	0.256832
$807$	−24.8745	−0.875624
$808$	0	0
$809$	−23.8118	−0.837177	−0.418588	−	0.908176i	$-0.637475\pi$
$809$	−23.8118	−0.837177	−0.418588	+	0.908176i	$0.637475\pi$
$810$	1.64575	0.0578258
$811$	−38.0000	−1.33436	−0.667180	−	0.744896i	$-0.732499\pi$
$811$	−38.0000	−1.33436	−0.667180	+	0.744896i	$0.732499\pi$
$812$	0	0
$813$	−17.3542	−0.608640
$814$	1.64575	0.0576836
$815$	−38.8118	−1.35952
$816$	−1.35425	−0.0474082
$817$	−26.4575	−0.925631
$818$	−11.0627	−0.386800
$819$	0	0
$820$	−12.5830	−0.439418
$821$	−32.2288	−1.12479	−0.562396	−	0.826868i	$-0.690120\pi$
$821$	−32.2288	−1.12479	−0.562396	+	0.826868i	$0.690120\pi$
$822$	17.5203	0.611089
$823$	−21.5203	−0.750149	−0.375075	−	0.926995i	$-0.622383\pi$
$823$	−21.5203	−0.750149	−0.375075	+	0.926995i	$0.622383\pi$
$824$	5.29150	0.184338
$825$	−10.6458	−0.370637
$826$	0	0
$827$	40.6458	1.41339	0.706696	−	0.707518i	$-0.250185\pi$
$827$	40.6458	1.41339	0.706696	+	0.707518i	$0.250185\pi$
$828$	−7.64575	−0.265708
$829$	−20.7712	−0.721415	−0.360708	−	0.932679i	$-0.617465\pi$
$829$	−20.7712	−0.721415	−0.360708	+	0.932679i	$0.617465\pi$
$830$	4.45751	0.154723
$831$	18.5203	0.642461
$832$	−1.00000	−0.0346688
$833$	0	0
$834$	−4.22876	−0.146430
$835$	40.9373	1.41669
$836$	23.2288	0.803383
$837$	−7.29150	−0.252031
$838$	−22.4575	−0.775782
$839$	−21.0000	−0.725001	−0.362500	−	0.931984i	$-0.618077\pi$
$839$	−21.0000	−0.725001	−0.362500	+	0.931984i	$0.618077\pi$
$840$	0	0
$841$	10.5830	0.364931
$842$	29.6458	1.02166
$843$	−18.5830	−0.640033
$844$	−11.6458	−0.400863
$845$	−1.64575	−0.0566156
$846$	3.00000	0.103142
$847$	0	0
$848$	−3.00000	−0.103020
$849$	−26.9373	−0.924484
$850$	3.10326	0.106441
$851$	−2.70850	−0.0928461
$852$	−5.70850	−0.195570
$853$	−38.1033	−1.30463	−0.652315	−	0.757948i	$-0.726202\pi$
$853$	−38.1033	−1.30463	−0.652315	+	0.757948i	$0.726202\pi$
$854$	0	0
$855$	8.22876	0.281418
$856$	12.0000	0.410152
$857$	1.93725	0.0661753	0.0330877	−	0.999452i	$-0.489466\pi$
$857$	1.93725	0.0661753	0.0330877	+	0.999452i	$0.489466\pi$
$858$	4.64575	0.158603
$859$	8.45751	0.288567	0.144283	−	0.989536i	$-0.453912\pi$
$859$	8.45751	0.288567	0.144283	+	0.989536i	$0.453912\pi$
$860$	−8.70850	−0.296957
$861$	0	0
$862$	0.583005	0.0198572
$863$	−31.7490	−1.08075	−0.540375	−	0.841425i	$-0.681717\pi$
$863$	−31.7490	−1.08075	−0.540375	+	0.841425i	$0.681717\pi$
$864$	1.00000	0.0340207
$865$	−19.2693	−0.655175
$866$	−12.4170	−0.421947
$867$	15.1660	0.515065
$868$	0	0
$869$	46.4575	1.57596
$870$	10.3542	0.351042
$871$	13.5830	0.460243
$872$	4.00000	0.135457
$873$	14.9373	0.505549
$874$	−38.2288	−1.29311
$875$	0	0
$876$	−8.35425	−0.282264
$877$	−7.18824	−0.242730	−0.121365	−	0.992608i	$-0.538727\pi$
$877$	−7.18824	−0.242730	−0.121365	+	0.992608i	$0.538727\pi$
$878$	18.3542	0.619426
$879$	−29.5203	−0.995694
$880$	7.64575	0.257738
$881$	21.2915	0.717329	0.358664	−	0.933467i	$-0.383232\pi$
$881$	21.2915	0.717329	0.358664	+	0.933467i	$0.383232\pi$
$882$	0	0
$883$	−44.9373	−1.51226	−0.756130	−	0.654422i	$-0.772912\pi$
$883$	−44.9373	−1.51226	−0.756130	+	0.654422i	$0.772912\pi$
$884$	−1.35425	−0.0455483
$885$	−13.0627	−0.439099
$886$	−34.9373	−1.17374
$887$	0.583005	0.0195754	0.00978770	−	0.999952i	$-0.496884\pi$
$887$	0.583005	0.0195754	0.00978770	+	0.999952i	$0.496884\pi$
$888$	0.354249	0.0118878
$889$	0	0
$890$	−1.74902	−0.0586271
$891$	−4.64575	−0.155639
$892$	−16.5203	−0.553139
$893$	15.0000	0.501956
$894$	−22.9373	−0.767137
$895$	9.87451	0.330068
$896$	0	0
$897$	−7.64575	−0.255284
$898$	−12.0000	−0.400445
$899$	−45.8745	−1.53000
$900$	−2.29150	−0.0763834
$901$	−4.06275	−0.135350
$902$	35.5203	1.18270
$903$	0	0
$904$	11.2288	0.373463
$905$	15.3948	0.511739
$906$	21.9373	0.728816
$907$	−30.2288	−1.00373	−0.501865	−	0.864946i	$-0.667352\pi$
$907$	−30.2288	−1.00373	−0.501865	+	0.864946i	$0.667352\pi$
$908$	15.2915	0.507466
$909$	0	0
$910$	0	0
$911$	25.7490	0.853103	0.426551	−	0.904463i	$-0.359728\pi$
$911$	25.7490	0.853103	0.426551	+	0.904463i	$0.359728\pi$
$912$	5.00000	0.165567
$913$	−12.5830	−0.416437
$914$	−5.77124	−0.190896
$915$	−6.47974	−0.214214
$916$	26.4575	0.874181
$917$	0	0
$918$	1.35425	0.0446969
$919$	16.1255	0.531931	0.265965	−	0.963983i	$-0.414309\pi$
$919$	16.1255	0.531931	0.265965	+	0.963983i	$0.414309\pi$
$920$	−12.5830	−0.414849
$921$	11.5830	0.381673
$922$	16.4575	0.541999
$923$	−5.70850	−0.187897
$924$	0	0
$925$	−0.811762	−0.0266906
$926$	17.1660	0.564110
$927$	−5.29150	−0.173796
$928$	6.29150	0.206529
$929$	−49.7490	−1.63221	−0.816106	−	0.577902i	$-0.803872\pi$
$929$	−49.7490	−1.63221	−0.816106	+	0.577902i	$0.803872\pi$
$930$	−12.0000	−0.393496
$931$	0	0
$932$	−4.64575	−0.152177
$933$	−16.9373	−0.554501
$934$	−0.479741	−0.0156976
$935$	10.3542	0.338620
$936$	1.00000	0.0326860
$937$	−21.4575	−0.700986	−0.350493	−	0.936565i	$-0.613986\pi$
$937$	−21.4575	−0.700986	−0.350493	+	0.936565i	$0.613986\pi$
$938$	0	0
$939$	−29.1660	−0.951797
$940$	4.93725	0.161035
$941$	−25.1660	−0.820388	−0.410194	−	0.911998i	$-0.634539\pi$
$941$	−25.1660	−0.820388	−0.410194	+	0.911998i	$0.634539\pi$
$942$	2.64575	0.0862032
$943$	−58.4575	−1.90364
$944$	−7.93725	−0.258336
$945$	0	0
$946$	24.5830	0.799262
$947$	26.5203	0.861793	0.430896	−	0.902401i	$-0.358197\pi$
$947$	26.5203	0.861793	0.430896	+	0.902401i	$0.358197\pi$
$948$	10.0000	0.324785
$949$	−8.35425	−0.271190
$950$	−11.4575	−0.371731
$951$	2.70850	0.0878290
$952$	0	0
$953$	33.1033	1.07232	0.536160	−	0.844116i	$-0.319874\pi$
$953$	33.1033	1.07232	0.536160	+	0.844116i	$0.319874\pi$
$954$	3.00000	0.0971286
$955$	0	0
$956$	3.00000	0.0970269
$957$	−29.2288	−0.944832
$958$	28.7490	0.928839
$959$	0	0
$960$	1.64575	0.0531164
$961$	22.1660	0.715033
$962$	0.354249	0.0114214
$963$	−12.0000	−0.386695
$964$	−17.8745	−0.575699
$965$	−5.04052	−0.162260
$966$	0	0
$967$	−49.1033	−1.57905	−0.789527	−	0.613715i	$-0.789674\pi$
$967$	−49.1033	−1.57905	−0.789527	+	0.613715i	$0.789674\pi$
$968$	−10.5830	−0.340151
$969$	6.77124	0.217524
$970$	24.5830	0.789313
$971$	−1.06275	−0.0341051	−0.0170526	−	0.999855i	$-0.505428\pi$
$971$	−1.06275	−0.0341051	−0.0170526	+	0.999855i	$0.505428\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	8.06275	0.258347
$975$	−2.29150	−0.0733868
$976$	−3.93725	−0.126028
$977$	51.8745	1.65961	0.829806	−	0.558052i	$-0.188451\pi$
$977$	51.8745	1.65961	0.829806	+	0.558052i	$0.188451\pi$
$978$	23.5830	0.754101
$979$	4.93725	0.157795
$980$	0	0
$981$	−4.00000	−0.127710
$982$	31.1660	0.994547
$983$	−44.0405	−1.40467	−0.702337	−	0.711844i	$-0.747860\pi$
$983$	−44.0405	−1.40467	−0.702337	+	0.711844i	$0.747860\pi$
$984$	7.64575	0.243738
$985$	−34.2510	−1.09133
$986$	8.52026	0.271340
$987$	0	0
$988$	5.00000	0.159071
$989$	−40.4575	−1.28647
$990$	−7.64575	−0.242998
$991$	26.5830	0.844437	0.422218	−	0.906494i	$-0.361252\pi$
$991$	26.5830	0.844437	0.422218	+	0.906494i	$0.361252\pi$
$992$	−7.29150	−0.231505
$993$	−32.5830	−1.03399
$994$	0	0
$995$	6.95948	0.220630
$996$	−2.70850	−0.0858220
$997$	−25.2288	−0.799003	−0.399501	−	0.916733i	$-0.630817\pi$
$997$	−25.2288	−0.799003	−0.399501	+	0.916733i	$0.630817\pi$
$998$	18.7085	0.592207
$999$	−0.354249	−0.0112079

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3822.2.a.bi.1.1		2
7.3	odd	6		546.2.i.j.79.1	✓	4
7.5	odd	6		546.2.i.j.235.1	yes	4
7.6	odd	2		3822.2.a.bk.1.2		2
21.5	even	6		1638.2.j.k.235.2		4
21.17	even	6		1638.2.j.k.1171.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.i.j.79.1	✓	4	7.3	odd	6
546.2.i.j.235.1	yes	4	7.5	odd	6
1638.2.j.k.235.2		4	21.5	even	6
1638.2.j.k.1171.2		4	21.17	even	6
3822.2.a.bi.1.1		2	1.1	even	1	trivial
3822.2.a.bk.1.2		2	7.6	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:	\( N \)	\(=\)	\( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3822.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.64575 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.64575 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.64575 q^{10} -4.64575 q^{11} -1.00000 q^{12} -1.00000 q^{13} +1.64575 q^{15} +1.00000 q^{16} +1.35425 q^{17} -1.00000 q^{18} -5.00000 q^{19} -1.64575 q^{20} +4.64575 q^{22} -7.64575 q^{23} +1.00000 q^{24} -2.29150 q^{25} +1.00000 q^{26} -1.00000 q^{27} -6.29150 q^{29} -1.64575 q^{30} +7.29150 q^{31} -1.00000 q^{32} +4.64575 q^{33} -1.35425 q^{34} +1.00000 q^{36} +0.354249 q^{37} +5.00000 q^{38} +1.00000 q^{39} +1.64575 q^{40} +7.64575 q^{41} +5.29150 q^{43} -4.64575 q^{44} -1.64575 q^{45} +7.64575 q^{46} -3.00000 q^{47} -1.00000 q^{48} +2.29150 q^{50} -1.35425 q^{51} -1.00000 q^{52} -3.00000 q^{53} +1.00000 q^{54} +7.64575 q^{55} +5.00000 q^{57} +6.29150 q^{58} -7.93725 q^{59} +1.64575 q^{60} -3.93725 q^{61} -7.29150 q^{62} +1.00000 q^{64} +1.64575 q^{65} -4.64575 q^{66} -13.5830 q^{67} +1.35425 q^{68} +7.64575 q^{69} +5.70850 q^{71} -1.00000 q^{72} +8.35425 q^{73} -0.354249 q^{74} +2.29150 q^{75} -5.00000 q^{76} -1.00000 q^{78} -10.0000 q^{79} -1.64575 q^{80} +1.00000 q^{81} -7.64575 q^{82} +2.70850 q^{83} -2.22876 q^{85} -5.29150 q^{86} +6.29150 q^{87} +4.64575 q^{88} -1.06275 q^{89} +1.64575 q^{90} -7.64575 q^{92} -7.29150 q^{93} +3.00000 q^{94} +8.22876 q^{95} +1.00000 q^{96} +14.9373 q^{97} -4.64575 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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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