LMFDB - Embedded newform 946.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [946,2,Mod(1,946)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(946, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("946.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 946 = 2 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	946.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:	$7.55384803121$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.13676.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 6x^{2} + 7x + 1 $ x^4 - x^3 - 6x^2 + 7x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.128950$ of defining polynomial
Character	$\chi$	$=$	946.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.98337 q^{3} +1.00000 q^{4} +2.64261 q^{5} -2.98337 q^{6} +1.00000 q^{8} +5.90051 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.98337 q^{3} +1.00000 q^{4} +2.64261 q^{5} -2.98337 q^{6} +1.00000 q^{8} +5.90051 q^{9} +2.64261 q^{10} -1.00000 q^{11} -2.98337 q^{12} +1.74210 q^{13} -7.88388 q^{15} +1.00000 q^{16} -0.301842 q^{17} +5.90051 q^{18} -0.384707 q^{19} +2.64261 q^{20} -1.00000 q^{22} -0.900508 q^{23} -2.98337 q^{24} +1.98337 q^{25} +1.74210 q^{26} -8.65329 q^{27} +4.98337 q^{29} -7.88388 q^{30} +8.26859 q^{31} +1.00000 q^{32} +2.98337 q^{33} -0.301842 q^{34} +5.90051 q^{36} -0.559743 q^{37} -0.384707 q^{38} -5.19733 q^{39} +2.64261 q^{40} +6.21898 q^{41} -1.00000 q^{43} -1.00000 q^{44} +15.5927 q^{45} -0.900508 q^{46} +3.66490 q^{47} -2.98337 q^{48} -7.00000 q^{49} +1.98337 q^{50} +0.900508 q^{51} +1.74210 q^{52} +11.9667 q^{53} -8.65329 q^{54} -2.64261 q^{55} +1.14772 q^{57} +4.98337 q^{58} +1.28521 q^{59} -7.88388 q^{60} +8.57043 q^{61} +8.26859 q^{62} +1.00000 q^{64} +4.60368 q^{65} +2.98337 q^{66} +12.4493 q^{67} -0.301842 q^{68} +2.68655 q^{69} -6.31253 q^{71} +5.90051 q^{72} +3.96674 q^{73} -0.559743 q^{74} -5.91714 q^{75} -0.384707 q^{76} -5.19733 q^{78} +5.15841 q^{79} +2.64261 q^{80} +8.11447 q^{81} +6.21898 q^{82} -11.7678 q^{83} -0.797650 q^{85} -1.00000 q^{86} -14.8673 q^{87} -1.00000 q^{88} +3.36306 q^{89} +15.5927 q^{90} -0.900508 q^{92} -24.6683 q^{93} +3.66490 q^{94} -1.01663 q^{95} -2.98337 q^{96} -9.47094 q^{97} -7.00000 q^{98} -5.90051 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + q^{3} + 4 q^{4} + q^{5} + q^{6} + 4 q^{8} + 11 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + q^3 + 4 * q^4 + q^5 + q^6 + 4 * q^8 + 11 * q^9	$ 4 q + 4 q^{2} + q^{3} + 4 q^{4} + q^{5} + q^{6} + 4 q^{8} + 11 q^{9} + q^{10} - 4 q^{11} + q^{12} + 10 q^{13} - 6 q^{15} + 4 q^{16} + 5 q^{17} + 11 q^{18} + 5 q^{19} + q^{20} - 4 q^{22} + 9 q^{23} + q^{24} - 5 q^{25} + 10 q^{26} + 4 q^{27} + 7 q^{29} - 6 q^{30} + q^{31} + 4 q^{32} - q^{33} + 5 q^{34} + 11 q^{36} + 7 q^{37} + 5 q^{38} - 8 q^{39} + q^{40} + 19 q^{41} - 4 q^{43} - 4 q^{44} + 14 q^{45} + 9 q^{46} - 5 q^{47} + q^{48} - 28 q^{49} - 5 q^{50} - 9 q^{51} + 10 q^{52} + 22 q^{53} + 4 q^{54} - q^{55} + 18 q^{57} + 7 q^{58} - 14 q^{59} - 6 q^{60} - 4 q^{61} + q^{62} + 4 q^{64} + 6 q^{65} - q^{66} - 8 q^{67} + 5 q^{68} - 2 q^{69} + 10 q^{71} + 11 q^{72} - 10 q^{73} + 7 q^{74} - 24 q^{75} + 5 q^{76} - 8 q^{78} + 5 q^{79} + q^{80} + 20 q^{81} + 19 q^{82} + 4 q^{83} - 22 q^{85} - 4 q^{86} - 21 q^{87} - 4 q^{88} + 14 q^{90} + 9 q^{92} - 35 q^{93} - 5 q^{94} - 17 q^{95} + q^{96} + 13 q^{97} - 28 q^{98} - 11 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + q^3 + 4 * q^4 + q^5 + q^6 + 4 * q^8 + 11 * q^9 + q^10 - 4 * q^11 + q^12 + 10 * q^13 - 6 * q^15 + 4 * q^16 + 5 * q^17 + 11 * q^18 + 5 * q^19 + q^20 - 4 * q^22 + 9 * q^23 + q^24 - 5 * q^25 + 10 * q^26 + 4 * q^27 + 7 * q^29 - 6 * q^30 + q^31 + 4 * q^32 - q^33 + 5 * q^34 + 11 * q^36 + 7 * q^37 + 5 * q^38 - 8 * q^39 + q^40 + 19 * q^41 - 4 * q^43 - 4 * q^44 + 14 * q^45 + 9 * q^46 - 5 * q^47 + q^48 - 28 * q^49 - 5 * q^50 - 9 * q^51 + 10 * q^52 + 22 * q^53 + 4 * q^54 - q^55 + 18 * q^57 + 7 * q^58 - 14 * q^59 - 6 * q^60 - 4 * q^61 + q^62 + 4 * q^64 + 6 * q^65 - q^66 - 8 * q^67 + 5 * q^68 - 2 * q^69 + 10 * q^71 + 11 * q^72 - 10 * q^73 + 7 * q^74 - 24 * q^75 + 5 * q^76 - 8 * q^78 + 5 * q^79 + q^80 + 20 * q^81 + 19 * q^82 + 4 * q^83 - 22 * q^85 - 4 * q^86 - 21 * q^87 - 4 * q^88 + 14 * q^90 + 9 * q^92 - 35 * q^93 - 5 * q^94 - 17 * q^95 + q^96 + 13 * q^97 - 28 * q^98 - 11 * 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
$3$	−2.98337	−1.72245	−0.861225	−	0.508223i	$-0.830302\pi$
$3$	−2.98337	−1.72245	−0.861225	+	0.508223i	$0.830302\pi$
$4$	1.00000	0.500000
$5$	2.64261	1.18181	0.590905	−	0.806741i	$-0.298771\pi$
$5$	2.64261	1.18181	0.590905	+	0.806741i	$0.298771\pi$
$6$	−2.98337	−1.21796
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	1.00000	0.353553
$9$	5.90051	1.96684
$10$	2.64261	0.835666
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.98337	−0.861225
$13$	1.74210	0.483171	0.241586	−	0.970379i	$-0.422332\pi$
$13$	1.74210	0.483171	0.241586	+	0.970379i	$0.422332\pi$
$14$	0	0
$15$	−7.88388	−2.03561
$16$	1.00000	0.250000
$17$	−0.301842	−0.0732075	−0.0366037	−	0.999330i	$-0.511654\pi$
$17$	−0.301842	−0.0732075	−0.0366037	+	0.999330i	$0.511654\pi$
$18$	5.90051	1.39076
$19$	−0.384707	−0.0882577	−0.0441289	−	0.999026i	$-0.514051\pi$
$19$	−0.384707	−0.0882577	−0.0441289	+	0.999026i	$0.514051\pi$
$20$	2.64261	0.590905
$21$	0	0
$22$	−1.00000	−0.213201
$23$	−0.900508	−0.187769	−0.0938844	−	0.995583i	$-0.529928\pi$
$23$	−0.900508	−0.187769	−0.0938844	+	0.995583i	$0.529928\pi$
$24$	−2.98337	−0.608978
$25$	1.98337	0.396674
$26$	1.74210	0.341654
$27$	−8.65329	−1.66533
$28$	0	0
$29$	4.98337	0.925389	0.462694	−	0.886518i	$-0.346883\pi$
$29$	4.98337	0.925389	0.462694	+	0.886518i	$0.346883\pi$
$30$	−7.88388	−1.43939
$31$	8.26859	1.48508	0.742541	−	0.669801i	$-0.233620\pi$
$31$	8.26859	1.48508	0.742541	+	0.669801i	$0.233620\pi$
$32$	1.00000	0.176777
$33$	2.98337	0.519338
$34$	−0.301842	−0.0517655
$35$	0	0
$36$	5.90051	0.983418
$37$	−0.559743	−0.0920211	−0.0460106	−	0.998941i	$-0.514651\pi$
$37$	−0.559743	−0.0920211	−0.0460106	+	0.998941i	$0.514651\pi$
$38$	−0.384707	−0.0624076
$39$	−5.19733	−0.832239
$40$	2.64261	0.417833
$41$	6.21898	0.971241	0.485621	−	0.874170i	$-0.338594\pi$
$41$	6.21898	0.971241	0.485621	+	0.874170i	$0.338594\pi$
$42$	0	0
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−1.00000	−0.150756
$45$	15.5927	2.32443
$46$	−0.900508	−0.132773
$47$	3.66490	0.534581	0.267290	−	0.963616i	$-0.413872\pi$
$47$	3.66490	0.534581	0.267290	+	0.963616i	$0.413872\pi$
$48$	−2.98337	−0.430613
$49$	−7.00000	−1.00000
$50$	1.98337	0.280491
$51$	0.900508	0.126096
$52$	1.74210	0.241586
$53$	11.9667	1.64376	0.821879	−	0.569662i	$-0.192926\pi$
$53$	11.9667	1.64376	0.821879	+	0.569662i	$0.192926\pi$
$54$	−8.65329	−1.17756
$55$	−2.64261	−0.356329
$56$	0	0
$57$	1.14772	0.152020
$58$	4.98337	0.654349
$59$	1.28521	0.167321	0.0836603	−	0.996494i	$-0.473339\pi$
$59$	1.28521	0.167321	0.0836603	+	0.996494i	$0.473339\pi$
$60$	−7.88388	−1.01780
$61$	8.57043	1.09733	0.548665	−	0.836042i	$-0.315136\pi$
$61$	8.57043	1.09733	0.548665	+	0.836042i	$0.315136\pi$
$62$	8.26859	1.05011
$63$	0	0
$64$	1.00000	0.125000
$65$	4.60368	0.571017
$66$	2.98337	0.367228
$67$	12.4493	1.52092	0.760461	−	0.649383i	$-0.224973\pi$
$67$	12.4493	1.52092	0.760461	+	0.649383i	$0.224973\pi$
$68$	−0.301842	−0.0366037
$69$	2.68655	0.323422
$70$	0	0
$71$	−6.31253	−0.749159	−0.374580	−	0.927195i	$-0.622213\pi$
$71$	−6.31253	−0.749159	−0.374580	+	0.927195i	$0.622213\pi$
$72$	5.90051	0.695381
$73$	3.96674	0.464272	0.232136	−	0.972683i	$-0.425429\pi$
$73$	3.96674	0.464272	0.232136	+	0.972683i	$0.425429\pi$
$74$	−0.559743	−0.0650688
$75$	−5.91714	−0.683252
$76$	−0.384707	−0.0441289
$77$	0	0
$78$	−5.19733	−0.588482
$79$	5.15841	0.580366	0.290183	−	0.956971i	$-0.406284\pi$
$79$	5.15841	0.580366	0.290183	+	0.956971i	$0.406284\pi$
$80$	2.64261	0.295452
$81$	8.11447	0.901607
$82$	6.21898	0.686771
$83$	−11.7678	−1.29168	−0.645840	−	0.763473i	$-0.723493\pi$
$83$	−11.7678	−1.29168	−0.645840	+	0.763473i	$0.723493\pi$
$84$	0	0
$85$	−0.797650	−0.0865173
$86$	−1.00000	−0.107833
$87$	−14.8673	−1.59394
$88$	−1.00000	−0.106600
$89$	3.36306	0.356484	0.178242	−	0.983987i	$-0.442959\pi$
$89$	3.36306	0.356484	0.178242	+	0.983987i	$0.442959\pi$
$90$	15.5927	1.64362
$91$	0	0
$92$	−0.900508	−0.0938844
$93$	−24.6683	−2.55798
$94$	3.66490	0.378006
$95$	−1.01663	−0.104304
$96$	−2.98337	−0.304489
$97$	−9.47094	−0.961628	−0.480814	−	0.876823i	$-0.659659\pi$
$97$	−9.47094	−0.961628	−0.480814	+	0.876823i	$0.659659\pi$
$98$	−7.00000	−0.707107
$99$	−5.90051	−0.593023
$100$	1.98337	0.198337
$101$	6.42363	0.639175	0.319587	−	0.947557i	$-0.396456\pi$
$101$	6.42363	0.639175	0.319587	+	0.947557i	$0.396456\pi$
$102$	0.900508	0.0891635
$103$	−9.49415	−0.935487	−0.467743	−	0.883864i	$-0.654933\pi$
$103$	−9.49415	−0.935487	−0.467743	+	0.883864i	$0.654933\pi$
$104$	1.74210	0.170827
$105$	0	0
$106$	11.9667	1.16231
$107$	−5.87886	−0.568331	−0.284165	−	0.958775i	$-0.591716\pi$
$107$	−5.87886	−0.568331	−0.284165	+	0.958775i	$0.591716\pi$
$108$	−8.65329	−0.832663
$109$	−6.25790	−0.599398	−0.299699	−	0.954034i	$-0.596886\pi$
$109$	−6.25790	−0.599398	−0.299699	+	0.954034i	$0.596886\pi$
$110$	−2.64261	−0.251963
$111$	1.66992	0.158502
$112$	0	0
$113$	−17.1641	−1.61466	−0.807330	−	0.590100i	$-0.799088\pi$
$113$	−17.1641	−1.61466	−0.807330	+	0.590100i	$0.799088\pi$
$114$	1.14772	0.107494
$115$	−2.37969	−0.221907
$116$	4.98337	0.462694
$117$	10.2793	0.950319
$118$	1.28521	0.118314
$119$	0	0
$120$	−7.88388	−0.719696
$121$	1.00000	0.0909091
$122$	8.57043	0.775930
$123$	−18.5535	−1.67291
$124$	8.26859	0.742541
$125$	−7.97176	−0.713016
$126$	0	0
$127$	−8.69222	−0.771309	−0.385655	−	0.922643i	$-0.626024\pi$
$127$	−8.69222	−0.771309	−0.385655	+	0.922643i	$0.626024\pi$
$128$	1.00000	0.0883883
$129$	2.98337	0.262671
$130$	4.60368	0.403770
$131$	2.21396	0.193434	0.0967172	−	0.995312i	$-0.469166\pi$
$131$	2.21396	0.193434	0.0967172	+	0.995312i	$0.469166\pi$
$132$	2.98337	0.259669
$133$	0	0
$134$	12.4493	1.07545
$135$	−22.8673	−1.96810
$136$	−0.301842	−0.0258828
$137$	−2.68153	−0.229099	−0.114549	−	0.993418i	$-0.536542\pi$
$137$	−2.68153	−0.229099	−0.114549	+	0.993418i	$0.536542\pi$
$138$	2.68655	0.228694
$139$	19.8456	1.68328	0.841641	−	0.540037i	$-0.181590\pi$
$139$	19.8456	1.68328	0.841641	+	0.540037i	$0.181590\pi$
$140$	0	0
$141$	−10.9338	−0.920789
$142$	−6.31253	−0.529736
$143$	−1.74210	−0.145682
$144$	5.90051	0.491709
$145$	13.1691	1.09363
$146$	3.96674	0.328290
$147$	20.8836	1.72245
$148$	−0.559743	−0.0460106
$149$	6.01497	0.492766	0.246383	−	0.969173i	$-0.420758\pi$
$149$	6.01497	0.492766	0.246383	+	0.969173i	$0.420758\pi$
$150$	−5.91714	−0.483132
$151$	−0.847258	−0.0689489	−0.0344745	−	0.999406i	$-0.510976\pi$
$151$	−0.847258	−0.0689489	−0.0344745	+	0.999406i	$0.510976\pi$
$152$	−0.384707	−0.0312038
$153$	−1.78102	−0.143987
$154$	0	0
$155$	21.8506	1.75508
$156$	−5.19733	−0.416119
$157$	2.56476	0.204690	0.102345	−	0.994749i	$-0.467365\pi$
$157$	2.56476	0.204690	0.102345	+	0.994749i	$0.467365\pi$
$158$	5.15841	0.410381
$159$	−35.7012	−2.83129
$160$	2.64261	0.208916
$161$	0	0
$162$	8.11447	0.637533
$163$	−8.98839	−0.704025	−0.352013	−	0.935995i	$-0.614503\pi$
$163$	−8.98839	−0.704025	−0.352013	+	0.935995i	$0.614503\pi$
$164$	6.21898	0.485621
$165$	7.88388	0.613759
$166$	−11.7678	−0.913355
$167$	9.70884	0.751293	0.375646	−	0.926763i	$-0.377421\pi$
$167$	9.70884	0.751293	0.375646	+	0.926763i	$0.377421\pi$
$168$	0	0
$169$	−9.96509	−0.766545
$170$	−0.797650	−0.0611770
$171$	−2.26996	−0.173588
$172$	−1.00000	−0.0762493
$173$	−18.8830	−1.43564	−0.717822	−	0.696226i	$-0.754861\pi$
$173$	−18.8830	−1.43564	−0.717822	+	0.696226i	$0.754861\pi$
$174$	−14.8673	−1.12708
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	−3.83427	−0.288201
$178$	3.36306	0.252072
$179$	−20.4061	−1.52522	−0.762611	−	0.646857i	$-0.776083\pi$
$179$	−20.4061	−1.52522	−0.762611	+	0.646857i	$0.776083\pi$
$180$	15.5927	1.16221
$181$	−7.88890	−0.586377	−0.293189	−	0.956055i	$-0.594716\pi$
$181$	−7.88890	−0.586377	−0.293189	+	0.956055i	$0.594716\pi$
$182$	0	0
$183$	−25.5688	−1.89010
$184$	−0.900508	−0.0663863
$185$	−1.47918	−0.108751
$186$	−24.6683	−1.80877
$187$	0.301842	0.0220729
$188$	3.66490	0.267290
$189$	0	0
$190$	−1.01663	−0.0737540
$191$	1.60963	0.116469	0.0582343	−	0.998303i	$-0.481453\pi$
$191$	1.60963	0.116469	0.0582343	+	0.998303i	$0.481453\pi$
$192$	−2.98337	−0.215306
$193$	−15.1841	−1.09297	−0.546487	−	0.837468i	$-0.684035\pi$
$193$	−15.1841	−1.09297	−0.546487	+	0.837468i	$0.684035\pi$
$194$	−9.47094	−0.679974
$195$	−13.7345	−0.983548
$196$	−7.00000	−0.500000
$197$	13.5977	0.968799	0.484399	−	0.874847i	$-0.339038\pi$
$197$	13.5977	0.968799	0.484399	+	0.874847i	$0.339038\pi$
$198$	−5.90051	−0.419331
$199$	13.8267	0.980147	0.490073	−	0.871681i	$-0.336970\pi$
$199$	13.8267	0.980147	0.490073	+	0.871681i	$0.336970\pi$
$200$	1.98337	0.140246
$201$	−37.1409	−2.61971
$202$	6.42363	0.451965
$203$	0	0
$204$	0.900508	0.0630481
$205$	16.4343	1.14782
$206$	−9.49415	−0.661489
$207$	−5.31345	−0.369310
$208$	1.74210	0.120793
$209$	0.384707	0.0266107
$210$	0	0
$211$	−20.6965	−1.42481	−0.712403	−	0.701771i	$-0.752393\pi$
$211$	−20.6965	−1.42481	−0.712403	+	0.701771i	$0.752393\pi$
$212$	11.9667	0.821879
$213$	18.8326	1.29039
$214$	−5.87886	−0.401871
$215$	−2.64261	−0.180224
$216$	−8.65329	−0.588782
$217$	0	0
$218$	−6.25790	−0.423839
$219$	−11.8343	−0.799686
$220$	−2.64261	−0.178165
$221$	−0.525839	−0.0353718
$222$	1.66992	0.112078
$223$	6.82833	0.457259	0.228629	−	0.973514i	$-0.426576\pi$
$223$	6.82833	0.457259	0.228629	+	0.973514i	$0.426576\pi$
$224$	0	0
$225$	11.7029	0.780193
$226$	−17.1641	−1.14174
$227$	1.74777	0.116003	0.0580016	−	0.998316i	$-0.481527\pi$
$227$	1.74777	0.116003	0.0580016	+	0.998316i	$0.481527\pi$
$228$	1.14772	0.0760098
$229$	−17.0197	−1.12469	−0.562347	−	0.826901i	$-0.690102\pi$
$229$	−17.0197	−1.12469	−0.562347	+	0.826901i	$0.690102\pi$
$230$	−2.37969	−0.156912
$231$	0	0
$232$	4.98337	0.327174
$233$	−19.9002	−1.30371	−0.651854	−	0.758345i	$-0.726008\pi$
$233$	−19.9002	−1.30371	−0.651854	+	0.758345i	$0.726008\pi$
$234$	10.2793	0.671977
$235$	9.68489	0.631773
$236$	1.28521	0.0836603
$237$	−15.3894	−0.999652
$238$	0	0
$239$	15.9824	1.03382	0.516909	−	0.856040i	$-0.327082\pi$
$239$	15.9824	1.03382	0.516909	+	0.856040i	$0.327082\pi$
$240$	−7.88388	−0.508902
$241$	14.9651	0.963986	0.481993	−	0.876175i	$-0.339913\pi$
$241$	14.9651	0.963986	0.481993	+	0.876175i	$0.339913\pi$
$242$	1.00000	0.0642824
$243$	1.75141	0.112353
$244$	8.57043	0.548665
$245$	−18.4982	−1.18181
$246$	−18.5535	−1.18293
$247$	−0.670197	−0.0426436
$248$	8.26859	0.525056
$249$	35.1076	2.22485
$250$	−7.97176	−0.504179
$251$	13.1195	0.828095	0.414047	−	0.910255i	$-0.364115\pi$
$251$	13.1195	0.828095	0.414047	+	0.910255i	$0.364115\pi$
$252$	0	0
$253$	0.900508	0.0566144
$254$	−8.69222	−0.545398
$255$	2.37969	0.149022
$256$	1.00000	0.0625000
$257$	−5.76776	−0.359783	−0.179891	−	0.983686i	$-0.557575\pi$
$257$	−5.76776	−0.359783	−0.179891	+	0.983686i	$0.557575\pi$
$258$	2.98337	0.185737
$259$	0	0
$260$	4.60368	0.285508
$261$	29.4044	1.82009
$262$	2.21396	0.136779
$263$	−23.8456	−1.47038	−0.735191	−	0.677860i	$-0.762908\pi$
$263$	−23.8456	−1.47038	−0.735191	+	0.677860i	$0.762908\pi$
$264$	2.98337	0.183614
$265$	31.6234	1.94261
$266$	0	0
$267$	−10.0333	−0.614025
$268$	12.4493	0.760461
$269$	12.5604	0.765820	0.382910	−	0.923786i	$-0.374922\pi$
$269$	12.5604	0.765820	0.382910	+	0.923786i	$0.374922\pi$
$270$	−22.8673	−1.39166
$271$	−11.8732	−0.721245	−0.360623	−	0.932712i	$-0.617436\pi$
$271$	−11.8732	−0.721245	−0.360623	+	0.932712i	$0.617436\pi$
$272$	−0.301842	−0.0183019
$273$	0	0
$274$	−2.68153	−0.161997
$275$	−1.98337	−0.119602
$276$	2.68655	0.161711
$277$	−3.66992	−0.220504	−0.110252	−	0.993904i	$-0.535166\pi$
$277$	−3.66992	−0.220504	−0.110252	+	0.993904i	$0.535166\pi$
$278$	19.8456	1.19026
$279$	48.7889	2.92091
$280$	0	0
$281$	−2.18070	−0.130090	−0.0650449	−	0.997882i	$-0.520719\pi$
$281$	−2.18070	−0.130090	−0.0650449	+	0.997882i	$0.520719\pi$
$282$	−10.9338	−0.651096
$283$	−1.88890	−0.112283	−0.0561417	−	0.998423i	$-0.517880\pi$
$283$	−1.88890	−0.112283	−0.0561417	+	0.998423i	$0.517880\pi$
$284$	−6.31253	−0.374580
$285$	3.03298	0.179658
$286$	−1.74210	−0.103013
$287$	0	0
$288$	5.90051	0.347691
$289$	−16.9089	−0.994641
$290$	13.1691	0.773316
$291$	28.2553	1.65636
$292$	3.96674	0.232136
$293$	18.1801	1.06209	0.531045	−	0.847344i	$-0.321799\pi$
$293$	18.1801	1.06209	0.531045	+	0.847344i	$0.321799\pi$
$294$	20.8836	1.21796
$295$	3.39632	0.197741
$296$	−0.559743	−0.0325344
$297$	8.65329	0.502115
$298$	6.01497	0.348438
$299$	−1.56877	−0.0907245
$300$	−5.91714	−0.341626
$301$	0	0
$302$	−0.847258	−0.0487542
$303$	−19.1641	−1.10095
$304$	−0.384707	−0.0220644
$305$	22.6483	1.29684
$306$	−1.78102	−0.101814
$307$	−12.0000	−0.684876	−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000	−0.684876	−0.342438	+	0.939540i	$0.611253\pi$
$308$	0	0
$309$	28.3246	1.61133
$310$	21.8506	1.24103
$311$	27.4690	1.55762	0.778812	−	0.627257i	$-0.215823\pi$
$311$	27.4690	1.55762	0.778812	+	0.627257i	$0.215823\pi$
$312$	−5.19733	−0.294241
$313$	6.35007	0.358927	0.179464	−	0.983765i	$-0.442564\pi$
$313$	6.35007	0.358927	0.179464	+	0.983765i	$0.442564\pi$
$314$	2.56476	0.144738
$315$	0	0
$316$	5.15841	0.290183
$317$	12.7362	0.715334	0.357667	−	0.933849i	$-0.383572\pi$
$317$	12.7362	0.715334	0.357667	+	0.933849i	$0.383572\pi$
$318$	−35.7012	−2.00203
$319$	−4.98337	−0.279015
$320$	2.64261	0.147726
$321$	17.5388	0.978922
$322$	0	0
$323$	0.116121	0.00646113
$324$	8.11447	0.450804
$325$	3.45523	0.191662
$326$	−8.98839	−0.497821
$327$	18.6696	1.03243
$328$	6.21898	0.343386
$329$	0	0
$330$	7.88388	0.433993
$331$	−33.8123	−1.85849	−0.929247	−	0.369458i	$-0.879543\pi$
$331$	−33.8123	−1.85849	−0.929247	+	0.369458i	$0.879543\pi$
$332$	−11.7678	−0.645840
$333$	−3.30277	−0.180990
$334$	9.70884	0.531244
$335$	32.8986	1.79744
$336$	0	0
$337$	−29.2883	−1.59544	−0.797718	−	0.603031i	$-0.793960\pi$
$337$	−29.2883	−1.59544	−0.797718	+	0.603031i	$0.793960\pi$
$338$	−9.96509	−0.542029
$339$	51.2068	2.78117
$340$	−0.797650	−0.0432587
$341$	−8.26859	−0.447769
$342$	−2.26996	−0.122746
$343$	0	0
$344$	−1.00000	−0.0539164
$345$	7.09949	0.382224
$346$	−18.8830	−1.01515
$347$	32.8654	1.76431	0.882154	−	0.470962i	$-0.156093\pi$
$347$	32.8654	1.76431	0.882154	+	0.470962i	$0.156093\pi$
$348$	−14.8673	−0.796968
$349$	11.9518	0.639764	0.319882	−	0.947457i	$-0.396357\pi$
$349$	11.9518	0.639764	0.319882	+	0.947457i	$0.396357\pi$
$350$	0	0
$351$	−15.0749	−0.804638
$352$	−1.00000	−0.0533002
$353$	17.9335	0.954503	0.477252	−	0.878767i	$-0.341633\pi$
$353$	17.9335	0.954503	0.477252	+	0.878767i	$0.341633\pi$
$354$	−3.83427	−0.203789
$355$	−16.6815	−0.885364
$356$	3.36306	0.178242
$357$	0	0
$358$	−20.4061	−1.07849
$359$	15.1534	0.799765	0.399883	−	0.916566i	$-0.369051\pi$
$359$	15.1534	0.799765	0.399883	+	0.916566i	$0.369051\pi$
$360$	15.5927	0.821809
$361$	−18.8520	−0.992211
$362$	−7.88890	−0.414631
$363$	−2.98337	−0.156586
$364$	0	0
$365$	10.4825	0.548681
$366$	−25.5688	−1.33650
$367$	6.54542	0.341668	0.170834	−	0.985300i	$-0.445354\pi$
$367$	6.54542	0.341668	0.170834	+	0.985300i	$0.445354\pi$
$368$	−0.900508	−0.0469422
$369$	36.6951	1.91027
$370$	−1.47918	−0.0768989
$371$	0	0
$372$	−24.6683	−1.27899
$373$	−12.9551	−0.670791	−0.335396	−	0.942077i	$-0.608870\pi$
$373$	−12.9551	−0.670791	−0.335396	+	0.942077i	$0.608870\pi$
$374$	0.301842	0.0156079
$375$	23.7827	1.22814
$376$	3.66490	0.189003
$377$	8.68153	0.447122
$378$	0	0
$379$	2.31682	0.119007	0.0595034	−	0.998228i	$-0.481048\pi$
$379$	2.31682	0.119007	0.0595034	+	0.998228i	$0.481048\pi$
$380$	−1.01663	−0.0521519
$381$	25.9321	1.32854
$382$	1.60963	0.0823557
$383$	−6.90617	−0.352889	−0.176444	−	0.984311i	$-0.556460\pi$
$383$	−6.90617	−0.352889	−0.176444	+	0.984311i	$0.556460\pi$
$384$	−2.98337	−0.152245
$385$	0	0
$386$	−15.1841	−0.772849
$387$	−5.90051	−0.299940
$388$	−9.47094	−0.480814
$389$	12.2912	0.623186	0.311593	−	0.950216i	$-0.399137\pi$
$389$	12.2912	0.623186	0.311593	+	0.950216i	$0.399137\pi$
$390$	−13.7345	−0.695474
$391$	0.271811	0.0137461
$392$	−7.00000	−0.353553
$393$	−6.60506	−0.333181
$394$	13.5977	0.685044
$395$	13.6316	0.685883
$396$	−5.90051	−0.296512
$397$	−11.7232	−0.588369	−0.294185	−	0.955749i	$-0.595048\pi$
$397$	−11.7232	−0.588369	−0.294185	+	0.955749i	$0.595048\pi$
$398$	13.8267	0.693069
$399$	0	0
$400$	1.98337	0.0991686
$401$	−26.3764	−1.31717	−0.658587	−	0.752505i	$-0.728845\pi$
$401$	−26.3764	−1.31717	−0.658587	+	0.752505i	$0.728845\pi$
$402$	−37.1409	−1.85242
$403$	14.4047	0.717549
$404$	6.42363	0.319587
$405$	21.4433	1.06553
$406$	0	0
$407$	0.559743	0.0277454
$408$	0.900508	0.0445818
$409$	−27.0643	−1.33824	−0.669122	−	0.743153i	$-0.733330\pi$
$409$	−27.0643	−1.33824	−0.669122	+	0.743153i	$0.733330\pi$
$410$	16.4343	0.811633
$411$	8.00000	0.394611
$412$	−9.49415	−0.467743
$413$	0	0
$414$	−5.31345	−0.261142
$415$	−31.0976	−1.52652
$416$	1.74210	0.0854135
$417$	−59.2068	−2.89937
$418$	0.384707	0.0188166
$419$	−21.5901	−1.05475	−0.527374	−	0.849633i	$-0.676823\pi$
$419$	−21.5901	−1.05475	−0.527374	+	0.849633i	$0.676823\pi$
$420$	0	0
$421$	37.0022	1.80338	0.901688	−	0.432388i	$-0.142329\pi$
$421$	37.0022	1.80338	0.901688	+	0.432388i	$0.142329\pi$
$422$	−20.6965	−1.00749
$423$	21.6248	1.05143
$424$	11.9667	0.581156
$425$	−0.598665	−0.0290395
$426$	18.8326	0.912443
$427$	0	0
$428$	−5.87886	−0.284165
$429$	5.19733	0.250929
$430$	−2.64261	−0.127438
$431$	−28.4499	−1.37039	−0.685193	−	0.728362i	$-0.740282\pi$
$431$	−28.4499	−1.37039	−0.685193	+	0.728362i	$0.740282\pi$
$432$	−8.65329	−0.416332
$433$	−28.3495	−1.36239	−0.681195	−	0.732102i	$-0.738540\pi$
$433$	−28.3495	−1.36239	−0.681195	+	0.732102i	$0.738540\pi$
$434$	0	0
$435$	−39.2883	−1.88373
$436$	−6.25790	−0.299699
$437$	0.346431	0.0165720
$438$	−11.8343	−0.565463
$439$	−9.20802	−0.439475	−0.219737	−	0.975559i	$-0.570520\pi$
$439$	−9.20802	−0.439475	−0.219737	+	0.975559i	$0.570520\pi$
$440$	−2.64261	−0.125981
$441$	−41.3036	−1.96684
$442$	−0.525839	−0.0250116
$443$	−14.3082	−0.679805	−0.339902	−	0.940461i	$-0.610394\pi$
$443$	−14.3082	−0.679805	−0.339902	+	0.940461i	$0.610394\pi$
$444$	1.66992	0.0792509
$445$	8.88724	0.421296
$446$	6.82833	0.323331
$447$	−17.9449	−0.848765
$448$	0	0
$449$	21.3185	1.00608	0.503040	−	0.864263i	$-0.332215\pi$
$449$	21.3185	1.00608	0.503040	+	0.864263i	$0.332215\pi$
$450$	11.7029	0.551680
$451$	−6.21898	−0.292840
$452$	−17.1641	−0.807330
$453$	2.52769	0.118761
$454$	1.74777	0.0820267
$455$	0	0
$456$	1.14772	0.0537470
$457$	−31.0643	−1.45313	−0.726563	−	0.687099i	$-0.758884\pi$
$457$	−31.0643	−1.45313	−0.726563	+	0.687099i	$0.758884\pi$
$458$	−17.0197	−0.795279
$459$	2.61193	0.121914
$460$	−2.37969	−0.110953
$461$	39.6823	1.84819	0.924095	−	0.382163i	$-0.124821\pi$
$461$	39.6823	1.84819	0.924095	+	0.382163i	$0.124821\pi$
$462$	0	0
$463$	−18.0690	−0.839735	−0.419868	−	0.907585i	$-0.637924\pi$
$463$	−18.0690	−0.839735	−0.419868	+	0.907585i	$0.637924\pi$
$464$	4.98337	0.231347
$465$	−65.1885	−3.02305
$466$	−19.9002	−0.921860
$467$	6.53408	0.302361	0.151181	−	0.988506i	$-0.451692\pi$
$467$	6.53408	0.302361	0.151181	+	0.988506i	$0.451692\pi$
$468$	10.2793	0.475159
$469$	0	0
$470$	9.68489	0.446731
$471$	−7.65164	−0.352569
$472$	1.28521	0.0591568
$473$	1.00000	0.0459800
$474$	−15.3894	−0.706861
$475$	−0.763016	−0.0350096
$476$	0	0
$477$	70.6099	3.23300
$478$	15.9824	0.731020
$479$	22.6972	1.03706	0.518532	−	0.855058i	$-0.326479\pi$
$479$	22.6972	1.03706	0.518532	+	0.855058i	$0.326479\pi$
$480$	−7.88388	−0.359848
$481$	−0.975127	−0.0444620
$482$	14.9651	0.681641
$483$	0	0
$484$	1.00000	0.0454545
$485$	−25.0280	−1.13646
$486$	1.75141	0.0794454
$487$	23.8424	1.08040	0.540201	−	0.841536i	$-0.318348\pi$
$487$	23.8424	1.08040	0.540201	+	0.841536i	$0.318348\pi$
$488$	8.57043	0.387965
$489$	26.8157	1.21265
$490$	−18.4982	−0.835666
$491$	−3.53745	−0.159643	−0.0798214	−	0.996809i	$-0.525435\pi$
$491$	−3.53745	−0.159643	−0.0798214	+	0.996809i	$0.525435\pi$
$492$	−18.5535	−0.836457
$493$	−1.50419	−0.0677454
$494$	−0.670197	−0.0301536
$495$	−15.5927	−0.700841
$496$	8.26859	0.371270
$497$	0	0
$498$	35.1076	1.57321
$499$	6.91686	0.309641	0.154821	−	0.987943i	$-0.450520\pi$
$499$	6.91686	0.309641	0.154821	+	0.987943i	$0.450520\pi$
$500$	−7.97176	−0.356508
$501$	−28.9651	−1.29406
$502$	13.1195	0.585551
$503$	−33.6380	−1.49985	−0.749923	−	0.661525i	$-0.769910\pi$
$503$	−33.6380	−1.49985	−0.749923	+	0.661525i	$0.769910\pi$
$504$	0	0
$505$	16.9751	0.755383
$506$	0.900508	0.0400324
$507$	29.7296	1.32034
$508$	−8.69222	−0.385655
$509$	−29.7791	−1.31994	−0.659968	−	0.751294i	$-0.729430\pi$
$509$	−29.7791	−1.31994	−0.659968	+	0.751294i	$0.729430\pi$
$510$	2.37969	0.105374
$511$	0	0
$512$	1.00000	0.0441942
$513$	3.32898	0.146978
$514$	−5.76776	−0.254405
$515$	−25.0893	−1.10557
$516$	2.98337	0.131336
$517$	−3.66490	−0.161182
$518$	0	0
$519$	56.3349	2.47283
$520$	4.60368	0.201885
$521$	−1.57338	−0.0689309	−0.0344654	−	0.999406i	$-0.510973\pi$
$521$	−1.57338	−0.0689309	−0.0344654	+	0.999406i	$0.510973\pi$
$522$	29.4044	1.28700
$523$	0.150755	0.00659205	0.00329603	−	0.999995i	$-0.498951\pi$
$523$	0.150755	0.00659205	0.00329603	+	0.999995i	$0.498951\pi$
$524$	2.21396	0.0967172
$525$	0	0
$526$	−23.8456	−1.03972
$527$	−2.49581	−0.108719
$528$	2.98337	0.129835
$529$	−22.1891	−0.964743
$530$	31.6234	1.37363
$531$	7.58342	0.329092
$532$	0	0
$533$	10.8341	0.469276
$534$	−10.0333	−0.434181
$535$	−15.5355	−0.671659
$536$	12.4493	0.537727
$537$	60.8789	2.62712
$538$	12.5604	0.541517
$539$	7.00000	0.301511
$540$	−22.8673	−0.984050
$541$	46.1349	1.98349	0.991747	−	0.128207i	$-0.0409222\pi$
$541$	46.1349	1.98349	0.991747	+	0.128207i	$0.0409222\pi$
$542$	−11.8732	−0.509997
$543$	23.5355	1.01001
$544$	−0.301842	−0.0129414
$545$	−16.5372	−0.708375
$546$	0	0
$547$	23.7577	1.01581	0.507903	−	0.861414i	$-0.330421\pi$
$547$	23.7577	1.01581	0.507903	+	0.861414i	$0.330421\pi$
$548$	−2.68153	−0.114549
$549$	50.5699	2.15827
$550$	−1.98337	−0.0845713
$551$	−1.91714	−0.0816727
$552$	2.68655	0.114347
$553$	0	0
$554$	−3.66992	−0.155920
$555$	4.41294	0.187319
$556$	19.8456	0.841641
$557$	−9.52119	−0.403426	−0.201713	−	0.979445i	$-0.564651\pi$
$557$	−9.52119	−0.403426	−0.201713	+	0.979445i	$0.564651\pi$
$558$	48.7889	2.06540
$559$	−1.74210	−0.0736830
$560$	0	0
$561$	−0.900508	−0.0380195
$562$	−2.18070	−0.0919874
$563$	36.4593	1.53658	0.768289	−	0.640103i	$-0.221109\pi$
$563$	36.4593	1.53658	0.768289	+	0.640103i	$0.221109\pi$
$564$	−10.9338	−0.460395
$565$	−45.3579	−1.90822
$566$	−1.88890	−0.0793963
$567$	0	0
$568$	−6.31253	−0.264868
$569$	−27.6567	−1.15943	−0.579714	−	0.814820i	$-0.696836\pi$
$569$	−27.6567	−1.15943	−0.579714	+	0.814820i	$0.696836\pi$
$570$	3.03298	0.127038
$571$	14.1474	0.592052	0.296026	−	0.955180i	$-0.404338\pi$
$571$	14.1474	0.592052	0.296026	+	0.955180i	$0.404338\pi$
$572$	−1.74210	−0.0728408
$573$	−4.80212	−0.200611
$574$	0	0
$575$	−1.78604	−0.0744831
$576$	5.90051	0.245854
$577$	−46.5671	−1.93861	−0.969307	−	0.245852i	$-0.920932\pi$
$577$	−46.5671	−1.93861	−0.969307	+	0.245852i	$0.920932\pi$
$578$	−16.9089	−0.703317
$579$	45.2997	1.88259
$580$	13.1691	0.546817
$581$	0	0
$582$	28.2553	1.17122
$583$	−11.9667	−0.495612
$584$	3.96674	0.164145
$585$	27.1641	1.12310
$586$	18.1801	0.751011
$587$	−24.6251	−1.01638	−0.508192	−	0.861244i	$-0.669686\pi$
$587$	−24.6251	−1.01638	−0.508192	+	0.861244i	$0.669686\pi$
$588$	20.8836	0.861225
$589$	−3.18098	−0.131070
$590$	3.39632	0.139824
$591$	−40.5671	−1.66871
$592$	−0.559743	−0.0230053
$593$	−5.40635	−0.222012	−0.111006	−	0.993820i	$-0.535407\pi$
$593$	−5.40635	−0.222012	−0.111006	+	0.993820i	$0.535407\pi$
$594$	8.65329	0.355049
$595$	0	0
$596$	6.01497	0.246383
$597$	−41.2501	−1.68825
$598$	−1.56877	−0.0641519
$599$	39.6198	1.61882	0.809410	−	0.587244i	$-0.199787\pi$
$599$	39.6198	1.61882	0.809410	+	0.587244i	$0.199787\pi$
$600$	−5.91714	−0.241566
$601$	−19.5023	−0.795514	−0.397757	−	0.917491i	$-0.630211\pi$
$601$	−19.5023	−0.795514	−0.397757	+	0.917491i	$0.630211\pi$
$602$	0	0
$603$	73.4571	2.99141
$604$	−0.847258	−0.0344745
$605$	2.64261	0.107437
$606$	−19.1641	−0.778487
$607$	−12.2649	−0.497819	−0.248909	−	0.968527i	$-0.580072\pi$
$607$	−12.2649	−0.497819	−0.248909	+	0.968527i	$0.580072\pi$
$608$	−0.384707	−0.0156019
$609$	0	0
$610$	22.6483	0.917002
$611$	6.38462	0.258294
$612$	−1.78102	−0.0719936
$613$	7.29954	0.294826	0.147413	−	0.989075i	$-0.452905\pi$
$613$	7.29954	0.294826	0.147413	+	0.989075i	$0.452905\pi$
$614$	−12.0000	−0.484281
$615$	−49.0297	−1.97707
$616$	0	0
$617$	2.83399	0.114092	0.0570462	−	0.998372i	$-0.481832\pi$
$617$	2.83399	0.114092	0.0570462	+	0.998372i	$0.481832\pi$
$618$	28.3246	1.13938
$619$	28.7429	1.15527	0.577637	−	0.816294i	$-0.303975\pi$
$619$	28.7429	1.15527	0.577637	+	0.816294i	$0.303975\pi$
$620$	21.8506	0.877542
$621$	7.79235	0.312696
$622$	27.4690	1.10141
$623$	0	0
$624$	−5.19733	−0.208060
$625$	−30.9831	−1.23932
$626$	6.35007	0.253800
$627$	−1.14772	−0.0458356
$628$	2.56476	0.102345
$629$	0.168954	0.00673664
$630$	0	0
$631$	−37.5431	−1.49457	−0.747284	−	0.664505i	$-0.768642\pi$
$631$	−37.5431	−1.49457	−0.747284	+	0.664505i	$0.768642\pi$
$632$	5.15841	0.205190
$633$	61.7454	2.45416
$634$	12.7362	0.505817
$635$	−22.9701	−0.911541
$636$	−35.7012	−1.41565
$637$	−12.1947	−0.483171
$638$	−4.98337	−0.197294
$639$	−37.2471	−1.47347
$640$	2.64261	0.104458
$641$	−19.5502	−0.772185	−0.386092	−	0.922460i	$-0.626175\pi$
$641$	−19.5502	−0.772185	−0.386092	+	0.922460i	$0.626175\pi$
$642$	17.5388	0.692202
$643$	−32.8207	−1.29432	−0.647162	−	0.762353i	$-0.724044\pi$
$643$	−32.8207	−1.29432	−0.647162	+	0.762353i	$0.724044\pi$
$644$	0	0
$645$	7.88388	0.310427
$646$	0.116121	0.00456871
$647$	−27.1006	−1.06543	−0.532716	−	0.846294i	$-0.678829\pi$
$647$	−27.1006	−1.06543	−0.532716	+	0.846294i	$0.678829\pi$
$648$	8.11447	0.318766
$649$	−1.28521	−0.0504491
$650$	3.45523	0.135525
$651$	0	0
$652$	−8.98839	−0.352013
$653$	−11.0919	−0.434059	−0.217030	−	0.976165i	$-0.569637\pi$
$653$	−11.0919	−0.434059	−0.217030	+	0.976165i	$0.569637\pi$
$654$	18.6696	0.730041
$655$	5.85062	0.228603
$656$	6.21898	0.242810
$657$	23.4058	0.913147
$658$	0	0
$659$	37.9994	1.48025	0.740124	−	0.672470i	$-0.234767\pi$
$659$	37.9994	1.48025	0.740124	+	0.672470i	$0.234767\pi$
$660$	7.88388	0.306880
$661$	−12.2869	−0.477904	−0.238952	−	0.971031i	$-0.576804\pi$
$661$	−12.2869	−0.477904	−0.238952	+	0.971031i	$0.576804\pi$
$662$	−33.8123	−1.31415
$663$	1.56877	0.0609261
$664$	−11.7678	−0.456678
$665$	0	0
$666$	−3.30277	−0.127980
$667$	−4.48756	−0.173759
$668$	9.70884	0.375646
$669$	−20.3714	−0.787605
$670$	32.8986	1.27098
$671$	−8.57043	−0.330858
$672$	0	0
$673$	21.7577	0.838698	0.419349	−	0.907825i	$-0.362258\pi$
$673$	21.7577	0.838698	0.419349	+	0.907825i	$0.362258\pi$
$674$	−29.2883	−1.12814
$675$	−17.1627	−0.660592
$676$	−9.96509	−0.383273
$677$	33.0330	1.26956	0.634780	−	0.772693i	$-0.281091\pi$
$677$	33.0330	1.26956	0.634780	+	0.772693i	$0.281091\pi$
$678$	51.2068	1.96659
$679$	0	0
$680$	−0.797650	−0.0305885
$681$	−5.21424	−0.199810
$682$	−8.26859	−0.316621
$683$	−32.5885	−1.24696	−0.623482	−	0.781838i	$-0.714283\pi$
$683$	−32.5885	−1.24696	−0.623482	+	0.781838i	$0.714283\pi$
$684$	−2.26996	−0.0867942
$685$	−7.08623	−0.270751
$686$	0	0
$687$	50.7761	1.93723
$688$	−1.00000	−0.0381246
$689$	20.8473	0.794217
$690$	7.09949	0.270273
$691$	9.31662	0.354421	0.177211	−	0.984173i	$-0.443293\pi$
$691$	9.31662	0.354421	0.177211	+	0.984173i	$0.443293\pi$
$692$	−18.8830	−0.717822
$693$	0	0
$694$	32.8654	1.24755
$695$	52.4441	1.98932
$696$	−14.8673	−0.563542
$697$	−1.87715	−0.0711021
$698$	11.9518	0.452381
$699$	59.3698	2.24557
$700$	0	0
$701$	22.8830	0.864277	0.432139	−	0.901807i	$-0.357759\pi$
$701$	22.8830	0.864277	0.432139	+	0.901807i	$0.357759\pi$
$702$	−15.0749	−0.568965
$703$	0.215337	0.00812158
$704$	−1.00000	−0.0376889
$705$	−28.8936	−1.08820
$706$	17.9335	0.674936
$707$	0	0
$708$	−3.83427	−0.144101
$709$	24.6996	0.927613	0.463806	−	0.885937i	$-0.346483\pi$
$709$	24.6996	0.927613	0.463806	+	0.885937i	$0.346483\pi$
$710$	−16.6815	−0.626047
$711$	30.4372	1.14149
$712$	3.36306	0.126036
$713$	−7.44592	−0.278852
$714$	0	0
$715$	−4.60368	−0.172168
$716$	−20.4061	−0.762611
$717$	−47.6816	−1.78070
$718$	15.1534	0.565519
$719$	42.3232	1.57839	0.789195	−	0.614143i	$-0.210498\pi$
$719$	42.3232	1.57839	0.789195	+	0.614143i	$0.210498\pi$
$720$	15.5927	0.581106
$721$	0	0
$722$	−18.8520	−0.701599
$723$	−44.6464	−1.66042
$724$	−7.88890	−0.293189
$725$	9.88388	0.367078
$726$	−2.98337	−0.110723
$727$	14.5661	0.540228	0.270114	−	0.962828i	$-0.412939\pi$
$727$	14.5661	0.540228	0.270114	+	0.962828i	$0.412939\pi$
$728$	0	0
$729$	−29.5685	−1.09513
$730$	10.4825	0.387976
$731$	0.301842	0.0111640
$732$	−25.5688	−0.945049
$733$	44.8790	1.65764	0.828822	−	0.559513i	$-0.189012\pi$
$733$	44.8790	1.65764	0.828822	+	0.559513i	$0.189012\pi$
$734$	6.54542	0.241596
$735$	55.1872	2.03561
$736$	−0.900508	−0.0331931
$737$	−12.4493	−0.458575
$738$	36.6951	1.35077
$739$	−32.3565	−1.19025	−0.595126	−	0.803632i	$-0.702898\pi$
$739$	−32.3565	−1.19025	−0.595126	+	0.803632i	$0.702898\pi$
$740$	−1.47918	−0.0543757
$741$	1.99945	0.0734515
$742$	0	0
$743$	47.4025	1.73903	0.869514	−	0.493908i	$-0.164432\pi$
$743$	47.4025	1.73903	0.869514	+	0.493908i	$0.164432\pi$
$744$	−24.6683	−0.904383
$745$	15.8952	0.582356
$746$	−12.9551	−0.474321
$747$	−69.4357	−2.54052
$748$	0.301842	0.0110364
$749$	0	0
$750$	23.7827	0.868423
$751$	−26.8183	−0.978613	−0.489307	−	0.872112i	$-0.662750\pi$
$751$	−26.8183	−0.978613	−0.489307	+	0.872112i	$0.662750\pi$
$752$	3.66490	0.133645
$753$	−39.1403	−1.42635
$754$	8.68153	0.316163
$755$	−2.23897	−0.0814845
$756$	0	0
$757$	−22.2164	−0.807469	−0.403734	−	0.914876i	$-0.632288\pi$
$757$	−22.2164	−0.807469	−0.403734	+	0.914876i	$0.632288\pi$
$758$	2.31682	0.0841505
$759$	−2.68655	−0.0975155
$760$	−1.01663	−0.0368770
$761$	−9.72777	−0.352631	−0.176316	−	0.984334i	$-0.556418\pi$
$761$	−9.72777	−0.352631	−0.176316	+	0.984334i	$0.556418\pi$
$762$	25.9321	0.939421
$763$	0	0
$764$	1.60963	0.0582343
$765$	−4.70654	−0.170165
$766$	−6.90617	−0.249530
$767$	2.23897	0.0808445
$768$	−2.98337	−0.107653
$769$	−20.5967	−0.742737	−0.371369	−	0.928486i	$-0.621111\pi$
$769$	−20.5967	−0.742737	−0.371369	+	0.928486i	$0.621111\pi$
$770$	0	0
$771$	17.2074	0.619708
$772$	−15.1841	−0.546487
$773$	12.7355	0.458064	0.229032	−	0.973419i	$-0.426444\pi$
$773$	12.7355	0.458064	0.229032	+	0.973419i	$0.426444\pi$
$774$	−5.90051	−0.212089
$775$	16.3997	0.589094
$776$	−9.47094	−0.339987
$777$	0	0
$778$	12.2912	0.440659
$779$	−2.39248	−0.0857195
$780$	−13.7345	−0.491774
$781$	6.31253	0.225880
$782$	0.271811	0.00971995
$783$	−43.1226	−1.54108
$784$	−7.00000	−0.250000
$785$	6.77766	0.241905
$786$	−6.60506	−0.235595
$787$	29.9515	1.06766	0.533829	−	0.845593i	$-0.320753\pi$
$787$	29.9515	1.06766	0.533829	+	0.845593i	$0.320753\pi$
$788$	13.5977	0.484399
$789$	71.1403	2.53266
$790$	13.6316	0.484992
$791$	0	0
$792$	−5.90051	−0.209665
$793$	14.9305	0.530199
$794$	−11.7232	−0.416040
$795$	−94.3444	−3.34605
$796$	13.8267	0.490073
$797$	7.49608	0.265525	0.132762	−	0.991148i	$-0.457615\pi$
$797$	7.49608	0.265525	0.132762	+	0.991148i	$0.457615\pi$
$798$	0	0
$799$	−1.10622	−0.0391353
$800$	1.98337	0.0701228
$801$	19.8438	0.701145
$802$	−26.3764	−0.931382
$803$	−3.96674	−0.139983
$804$	−37.1409	−1.30986
$805$	0	0
$806$	14.4047	0.507384
$807$	−37.4723	−1.31909
$808$	6.42363	0.225982
$809$	44.7060	1.57178	0.785889	−	0.618367i	$-0.212205\pi$
$809$	44.7060	1.57178	0.785889	+	0.618367i	$0.212205\pi$
$810$	21.4433	0.753442
$811$	−40.1073	−1.40836	−0.704179	−	0.710022i	$-0.748685\pi$
$811$	−40.1073	−1.40836	−0.704179	+	0.710022i	$0.748685\pi$
$812$	0	0
$813$	35.4222	1.24231
$814$	0.559743	0.0196190
$815$	−23.7528	−0.832024
$816$	0.900508	0.0315241
$817$	0.384707	0.0134592
$818$	−27.0643	−0.946281
$819$	0	0
$820$	16.4343	0.573911
$821$	−45.7369	−1.59623	−0.798115	−	0.602505i	$-0.794169\pi$
$821$	−45.7369	−1.59623	−0.798115	+	0.602505i	$0.794169\pi$
$822$	8.00000	0.279032
$823$	13.9967	0.487894	0.243947	−	0.969789i	$-0.421558\pi$
$823$	13.9967	0.487894	0.243947	+	0.969789i	$0.421558\pi$
$824$	−9.49415	−0.330745
$825$	5.91714	0.206008
$826$	0	0
$827$	3.07619	0.106970	0.0534848	−	0.998569i	$-0.482967\pi$
$827$	3.07619	0.106970	0.0534848	+	0.998569i	$0.482967\pi$
$828$	−5.31345	−0.184655
$829$	−14.9910	−0.520658	−0.260329	−	0.965520i	$-0.583831\pi$
$829$	−14.9910	−0.520658	−0.260329	+	0.965520i	$0.583831\pi$
$830$	−31.0976	−1.07941
$831$	10.9487	0.379808
$832$	1.74210	0.0603964
$833$	2.11290	0.0732075
$834$	−59.2068	−2.05016
$835$	25.6567	0.887885
$836$	0.384707	0.0133054
$837$	−71.5505	−2.47315
$838$	−21.5901	−0.745819
$839$	−1.43386	−0.0495024	−0.0247512	−	0.999694i	$-0.507879\pi$
$839$	−1.43386	−0.0495024	−0.0247512	+	0.999694i	$0.507879\pi$
$840$	0	0
$841$	−4.16601	−0.143655
$842$	37.0022	1.27518
$843$	6.50585	0.224073
$844$	−20.6965	−0.712403
$845$	−26.3338	−0.905911
$846$	21.6248	0.743475
$847$	0	0
$848$	11.9667	0.410940
$849$	5.63529	0.193403
$850$	−0.598665	−0.0205341
$851$	0.504052	0.0172787
$852$	18.8326	0.645195
$853$	−35.3988	−1.21203	−0.606015	−	0.795453i	$-0.707233\pi$
$853$	−35.3988	−1.21203	−0.606015	+	0.795453i	$0.707233\pi$
$854$	0	0
$855$	−5.99862	−0.205149
$856$	−5.87886	−0.200935
$857$	16.0200	0.547233	0.273616	−	0.961839i	$-0.411780\pi$
$857$	16.0200	0.547233	0.273616	+	0.961839i	$0.411780\pi$
$858$	5.19733	0.177434
$859$	0.481167	0.0164172	0.00820860	−	0.999966i	$-0.497387\pi$
$859$	0.481167	0.0164172	0.00820860	+	0.999966i	$0.497387\pi$
$860$	−2.64261	−0.0901122
$861$	0	0
$862$	−28.4499	−0.969009
$863$	−27.7070	−0.943157	−0.471579	−	0.881824i	$-0.656316\pi$
$863$	−27.7070	−0.943157	−0.471579	+	0.881824i	$0.656316\pi$
$864$	−8.65329	−0.294391
$865$	−49.9002	−1.69666
$866$	−28.3495	−0.963356
$867$	50.4455	1.71322
$868$	0	0
$869$	−5.15841	−0.174987
$870$	−39.2883	−1.33200
$871$	21.6879	0.734866
$872$	−6.25790	−0.211919
$873$	−55.8833	−1.89136
$874$	0.346431	0.0117182
$875$	0	0
$876$	−11.8343	−0.399843
$877$	27.8480	0.940362	0.470181	−	0.882570i	$-0.344189\pi$
$877$	27.8480	0.940362	0.470181	+	0.882570i	$0.344189\pi$
$878$	−9.20802	−0.310755
$879$	−54.2379	−1.82940
$880$	−2.64261	−0.0890823
$881$	27.1858	0.915912	0.457956	−	0.888975i	$-0.348582\pi$
$881$	27.1858	0.915912	0.457956	+	0.888975i	$0.348582\pi$
$882$	−41.3036	−1.39076
$883$	6.47121	0.217774	0.108887	−	0.994054i	$-0.465271\pi$
$883$	6.47121	0.217774	0.108887	+	0.994054i	$0.465271\pi$
$884$	−0.525839	−0.0176859
$885$	−10.1325	−0.340599
$886$	−14.3082	−0.480695
$887$	−17.6466	−0.592515	−0.296258	−	0.955108i	$-0.595739\pi$
$887$	−17.6466	−0.592515	−0.296258	+	0.955108i	$0.595739\pi$
$888$	1.66992	0.0560389
$889$	0	0
$890$	8.88724	0.297901
$891$	−8.11447	−0.271845
$892$	6.82833	0.228629
$893$	−1.40991	−0.0471809
$894$	−17.9449	−0.600167
$895$	−53.9252	−1.80252
$896$	0	0
$897$	4.68024	0.156269
$898$	21.3185	0.711407
$899$	41.2054	1.37428
$900$	11.7029	0.390097
$901$	−3.61207	−0.120335
$902$	−6.21898	−0.207069
$903$	0	0
$904$	−17.1641	−0.570869
$905$	−20.8473	−0.692986
$906$	2.52769	0.0839768
$907$	−35.8856	−1.19156	−0.595781	−	0.803147i	$-0.703157\pi$
$907$	−35.8856	−1.19156	−0.595781	+	0.803147i	$0.703157\pi$
$908$	1.74777	0.0580016
$909$	37.9027	1.25715
$910$	0	0
$911$	40.3193	1.33584	0.667918	−	0.744235i	$-0.267186\pi$
$911$	40.3193	1.33584	0.667918	+	0.744235i	$0.267186\pi$
$912$	1.14772	0.0380049
$913$	11.7678	0.389456
$914$	−31.0643	−1.02752
$915$	−67.5682	−2.23374
$916$	−17.0197	−0.562347
$917$	0	0
$918$	2.61193	0.0862065
$919$	42.8195	1.41249	0.706243	−	0.707970i	$-0.250389\pi$
$919$	42.8195	1.41249	0.706243	+	0.707970i	$0.250389\pi$
$920$	−2.37969	−0.0784560
$921$	35.8005	1.17967
$922$	39.6823	1.30687
$923$	−10.9971	−0.361972
$924$	0	0
$925$	−1.11018	−0.0365024
$926$	−18.0690	−0.593783
$927$	−56.0203	−1.83995
$928$	4.98337	0.163587
$929$	33.8883	1.11184	0.555920	−	0.831236i	$-0.312366\pi$
$929$	33.8883	1.11184	0.555920	+	0.831236i	$0.312366\pi$
$930$	−65.1885	−2.13762
$931$	2.69295	0.0882577
$932$	−19.9002	−0.651854
$933$	−81.9503	−2.68293
$934$	6.53408	0.213802
$935$	0.797650	0.0260860
$936$	10.2793	0.335988
$937$	35.9302	1.17379	0.586894	−	0.809664i	$-0.300351\pi$
$937$	35.9302	1.17379	0.586894	+	0.809664i	$0.300351\pi$
$938$	0	0
$939$	−18.9446	−0.618235
$940$	9.68489	0.315886
$941$	25.9692	0.846571	0.423286	−	0.905996i	$-0.360877\pi$
$941$	25.9692	0.846571	0.423286	+	0.905996i	$0.360877\pi$
$942$	−7.65164	−0.249304
$943$	−5.60024	−0.182369
$944$	1.28521	0.0418302
$945$	0	0
$946$	1.00000	0.0325128
$947$	7.10760	0.230966	0.115483	−	0.993309i	$-0.463158\pi$
$947$	7.10760	0.230966	0.115483	+	0.993309i	$0.463158\pi$
$948$	−15.3894	−0.499826
$949$	6.91046	0.224323
$950$	−0.763016	−0.0247555
$951$	−37.9967	−1.23213
$952$	0	0
$953$	−16.8127	−0.544617	−0.272309	−	0.962210i	$-0.587787\pi$
$953$	−16.8127	−0.544617	−0.272309	+	0.962210i	$0.587787\pi$
$954$	70.6099	2.28608
$955$	4.25361	0.137644
$956$	15.9824	0.516909
$957$	14.8673	0.480590
$958$	22.6972	0.733314
$959$	0	0
$960$	−7.88388	−0.254451
$961$	37.3695	1.20547
$962$	−0.975127	−0.0314394
$963$	−34.6883	−1.11781
$964$	14.9651	0.481993
$965$	−40.1255	−1.29169
$966$	0	0
$967$	−3.49042	−0.112244	−0.0561221	−	0.998424i	$-0.517874\pi$
$967$	−3.49042	−0.112244	−0.0561221	+	0.998424i	$0.517874\pi$
$968$	1.00000	0.0321412
$969$	−0.346431	−0.0111290
$970$	−25.0280	−0.803599
$971$	−31.8077	−1.02076	−0.510380	−	0.859949i	$-0.670495\pi$
$971$	−31.8077	−1.02076	−0.510380	+	0.859949i	$0.670495\pi$
$972$	1.75141	0.0561764
$973$	0	0
$974$	23.8424	0.763959
$975$	−10.3082	−0.330128
$976$	8.57043	0.274333
$977$	−3.44455	−0.110201	−0.0551004	−	0.998481i	$-0.517548\pi$
$977$	−3.44455	−0.110201	−0.0551004	+	0.998481i	$0.517548\pi$
$978$	26.8157	0.857472
$979$	−3.36306	−0.107484
$980$	−18.4982	−0.590905
$981$	−36.9248	−1.17892
$982$	−3.53745	−0.112885
$983$	8.60797	0.274552	0.137276	−	0.990533i	$-0.456165\pi$
$983$	8.60797	0.274552	0.137276	+	0.990533i	$0.456165\pi$
$984$	−18.5535	−0.591465
$985$	35.9335	1.14494
$986$	−1.50419	−0.0479032
$987$	0	0
$988$	−0.670197	−0.0213218
$989$	0.900508	0.0286345
$990$	−15.5927	−0.495569
$991$	−7.24621	−0.230183	−0.115092	−	0.993355i	$-0.536716\pi$
$991$	−7.24621	−0.230183	−0.115092	+	0.993355i	$0.536716\pi$
$992$	8.26859	0.262528
$993$	100.875	3.20117
$994$	0	0
$995$	36.5385	1.15835
$996$	35.1076	1.11243
$997$	29.8593	0.945653	0.472826	−	0.881156i	$-0.343234\pi$
$997$	29.8593	0.945653	0.472826	+	0.881156i	$0.343234\pi$
$998$	6.91686	0.218949
$999$	4.84362	0.153245

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	946.2.a.h.1.1	✓	4
3.2	odd	2		8514.2.a.ba.1.1		4
4.3	odd	2		7568.2.a.y.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
946.2.a.h.1.1	✓	4	1.1	even	1	trivial
7568.2.a.y.1.4		4	4.3	odd	2
8514.2.a.ba.1.1		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 946 = 2 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	946.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.98337 q^{3} +1.00000 q^{4} +2.64261 q^{5} -2.98337 q^{6} +1.00000 q^{8} +5.90051 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.98337 q^{3} +1.00000 q^{4} +2.64261 q^{5} -2.98337 q^{6} +1.00000 q^{8} +5.90051 q^{9} +2.64261 q^{10} -1.00000 q^{11} -2.98337 q^{12} +1.74210 q^{13} -7.88388 q^{15} +1.00000 q^{16} -0.301842 q^{17} +5.90051 q^{18} -0.384707 q^{19} +2.64261 q^{20} -1.00000 q^{22} -0.900508 q^{23} -2.98337 q^{24} +1.98337 q^{25} +1.74210 q^{26} -8.65329 q^{27} +4.98337 q^{29} -7.88388 q^{30} +8.26859 q^{31} +1.00000 q^{32} +2.98337 q^{33} -0.301842 q^{34} +5.90051 q^{36} -0.559743 q^{37} -0.384707 q^{38} -5.19733 q^{39} +2.64261 q^{40} +6.21898 q^{41} -1.00000 q^{43} -1.00000 q^{44} +15.5927 q^{45} -0.900508 q^{46} +3.66490 q^{47} -2.98337 q^{48} -7.00000 q^{49} +1.98337 q^{50} +0.900508 q^{51} +1.74210 q^{52} +11.9667 q^{53} -8.65329 q^{54} -2.64261 q^{55} +1.14772 q^{57} +4.98337 q^{58} +1.28521 q^{59} -7.88388 q^{60} +8.57043 q^{61} +8.26859 q^{62} +1.00000 q^{64} +4.60368 q^{65} +2.98337 q^{66} +12.4493 q^{67} -0.301842 q^{68} +2.68655 q^{69} -6.31253 q^{71} +5.90051 q^{72} +3.96674 q^{73} -0.559743 q^{74} -5.91714 q^{75} -0.384707 q^{76} -5.19733 q^{78} +5.15841 q^{79} +2.64261 q^{80} +8.11447 q^{81} +6.21898 q^{82} -11.7678 q^{83} -0.797650 q^{85} -1.00000 q^{86} -14.8673 q^{87} -1.00000 q^{88} +3.36306 q^{89} +15.5927 q^{90} -0.900508 q^{92} -24.6683 q^{93} +3.66490 q^{94} -1.01663 q^{95} -2.98337 q^{96} -9.47094 q^{97} -7.00000 q^{98} -5.90051 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + q^{3} + 4 q^{4} + q^{5} + q^{6} + 4 q^{8} + 11 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + q^3 + 4 * q^4 + q^5 + q^6 + 4 * q^8 + 11 * q^9	\( 4 q + 4 q^{2} + q^{3} + 4 q^{4} + q^{5} + q^{6} + 4 q^{8} + 11 q^{9} + q^{10} - 4 q^{11} + q^{12} + 10 q^{13} - 6 q^{15} + 4 q^{16} + 5 q^{17} + 11 q^{18} + 5 q^{19} + q^{20} - 4 q^{22} + 9 q^{23} + q^{24} - 5 q^{25} + 10 q^{26} + 4 q^{27} + 7 q^{29} - 6 q^{30} + q^{31} + 4 q^{32} - q^{33} + 5 q^{34} + 11 q^{36} + 7 q^{37} + 5 q^{38} - 8 q^{39} + q^{40} + 19 q^{41} - 4 q^{43} - 4 q^{44} + 14 q^{45} + 9 q^{46} - 5 q^{47} + q^{48} - 28 q^{49} - 5 q^{50} - 9 q^{51} + 10 q^{52} + 22 q^{53} + 4 q^{54} - q^{55} + 18 q^{57} + 7 q^{58} - 14 q^{59} - 6 q^{60} - 4 q^{61} + q^{62} + 4 q^{64} + 6 q^{65} - q^{66} - 8 q^{67} + 5 q^{68} - 2 q^{69} + 10 q^{71} + 11 q^{72} - 10 q^{73} + 7 q^{74} - 24 q^{75} + 5 q^{76} - 8 q^{78} + 5 q^{79} + q^{80} + 20 q^{81} + 19 q^{82} + 4 q^{83} - 22 q^{85} - 4 q^{86} - 21 q^{87} - 4 q^{88} + 14 q^{90} + 9 q^{92} - 35 q^{93} - 5 q^{94} - 17 q^{95} + q^{96} + 13 q^{97} - 28 q^{98} - 11 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + q^3 + 4 * q^4 + q^5 + q^6 + 4 * q^8 + 11 * q^9 + q^10 - 4 * q^11 + q^12 + 10 * q^13 - 6 * q^15 + 4 * q^16 + 5 * q^17 + 11 * q^18 + 5 * q^19 + q^20 - 4 * q^22 + 9 * q^23 + q^24 - 5 * q^25 + 10 * q^26 + 4 * q^27 + 7 * q^29 - 6 * q^30 + q^31 + 4 * q^32 - q^33 + 5 * q^34 + 11 * q^36 + 7 * q^37 + 5 * q^38 - 8 * q^39 + q^40 + 19 * q^41 - 4 * q^43 - 4 * q^44 + 14 * q^45 + 9 * q^46 - 5 * q^47 + q^48 - 28 * q^49 - 5 * q^50 - 9 * q^51 + 10 * q^52 + 22 * q^53 + 4 * q^54 - q^55 + 18 * q^57 + 7 * q^58 - 14 * q^59 - 6 * q^60 - 4 * q^61 + q^62 + 4 * q^64 + 6 * q^65 - q^66 - 8 * q^67 + 5 * q^68 - 2 * q^69 + 10 * q^71 + 11 * q^72 - 10 * q^73 + 7 * q^74 - 24 * q^75 + 5 * q^76 - 8 * q^78 + 5 * q^79 + q^80 + 20 * q^81 + 19 * q^82 + 4 * q^83 - 22 * q^85 - 4 * q^86 - 21 * q^87 - 4 * q^88 + 14 * q^90 + 9 * q^92 - 35 * q^93 - 5 * q^94 - 17 * q^95 + q^96 + 13 * q^97 - 28 * q^98 - 11 * q^99

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