LMFDB - Embedded newform 950.2.b.b.799.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(799,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("950.799");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			799.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	950.799
Dual form			950.2.b.b.799.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +1.00000i q^{7} -1.00000i q^{8} +2.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +1.00000i q^{7} -1.00000i q^{8} +2.00000 q^{9} -6.00000 q^{11} -1.00000i q^{12} +5.00000i q^{13} -1.00000 q^{14} +1.00000 q^{16} -3.00000i q^{17} +2.00000i q^{18} -1.00000 q^{19} -1.00000 q^{21} -6.00000i q^{22} +3.00000i q^{23} +1.00000 q^{24} -5.00000 q^{26} +5.00000i q^{27} -1.00000i q^{28} -9.00000 q^{29} -4.00000 q^{31} +1.00000i q^{32} -6.00000i q^{33} +3.00000 q^{34} -2.00000 q^{36} -2.00000i q^{37} -1.00000i q^{38} -5.00000 q^{39} -1.00000i q^{42} +8.00000i q^{43} +6.00000 q^{44} -3.00000 q^{46} +1.00000i q^{48} +6.00000 q^{49} +3.00000 q^{51} -5.00000i q^{52} -3.00000i q^{53} -5.00000 q^{54} +1.00000 q^{56} -1.00000i q^{57} -9.00000i q^{58} -9.00000 q^{59} -10.0000 q^{61} -4.00000i q^{62} +2.00000i q^{63} -1.00000 q^{64} +6.00000 q^{66} -5.00000i q^{67} +3.00000i q^{68} -3.00000 q^{69} -6.00000 q^{71} -2.00000i q^{72} -7.00000i q^{73} +2.00000 q^{74} +1.00000 q^{76} -6.00000i q^{77} -5.00000i q^{78} +10.0000 q^{79} +1.00000 q^{81} -6.00000i q^{83} +1.00000 q^{84} -8.00000 q^{86} -9.00000i q^{87} +6.00000i q^{88} +12.0000 q^{89} -5.00000 q^{91} -3.00000i q^{92} -4.00000i q^{93} -1.00000 q^{96} +10.0000i q^{97} +6.00000i q^{98} -12.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} - 2 q^{6} + 4 q^{9}+O(q^{10}) $ 2 * q - 2 * q^4 - 2 * q^6 + 4 * q^9	$ 2 q - 2 q^{4} - 2 q^{6} + 4 q^{9} - 12 q^{11} - 2 q^{14} + 2 q^{16} - 2 q^{19} - 2 q^{21} + 2 q^{24} - 10 q^{26} - 18 q^{29} - 8 q^{31} + 6 q^{34} - 4 q^{36} - 10 q^{39} + 12 q^{44} - 6 q^{46} + 12 q^{49} + 6 q^{51} - 10 q^{54} + 2 q^{56} - 18 q^{59} - 20 q^{61} - 2 q^{64} + 12 q^{66} - 6 q^{69} - 12 q^{71} + 4 q^{74} + 2 q^{76} + 20 q^{79} + 2 q^{81} + 2 q^{84} - 16 q^{86} + 24 q^{89} - 10 q^{91} - 2 q^{96} - 24 q^{99}+O(q^{100}) $ 2 * q - 2 * q^4 - 2 * q^6 + 4 * q^9 - 12 * q^11 - 2 * q^14 + 2 * q^16 - 2 * q^19 - 2 * q^21 + 2 * q^24 - 10 * q^26 - 18 * q^29 - 8 * q^31 + 6 * q^34 - 4 * q^36 - 10 * q^39 + 12 * q^44 - 6 * q^46 + 12 * q^49 + 6 * q^51 - 10 * q^54 + 2 * q^56 - 18 * q^59 - 20 * q^61 - 2 * q^64 + 12 * q^66 - 6 * q^69 - 12 * q^71 + 4 * q^74 + 2 * q^76 + 20 * q^79 + 2 * q^81 + 2 * q^84 - 16 * q^86 + 24 * q^89 - 10 * q^91 - 2 * q^96 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$1$

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 $

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	1.00000i	0.577350i	0.957427	+	0.288675i	$0.0932147\pi$
$3$	1.00000i	0.577350i	−0.957427	+	0.288675i	$0.906785\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	1.00000i	0.377964i	0.981981	+	0.188982i	$0.0605189\pi$
$7$	1.00000i	0.377964i	−0.981981	+	0.188982i	$0.939481\pi$
$8$	− 1.00000i	− 0.353553i
$9$	2.00000	0.666667
$10$	0	0
$11$	−6.00000	−1.80907	−0.904534	−	0.426401i	$-0.859781\pi$
$11$	−6.00000	−1.80907	−0.904534	+	0.426401i	$0.859781\pi$
$12$	− 1.00000i	− 0.288675i
$13$	5.00000i	1.38675i	0.720577	+	0.693375i	$0.243877\pi$
$13$	5.00000i	1.38675i	−0.720577	+	0.693375i	$0.756123\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	− 3.00000i	− 0.727607i	−0.931476	−	0.363803i	$-0.881478\pi$
$17$	− 3.00000i	− 0.727607i	0.931476	−	0.363803i	$-0.118522\pi$
$18$	2.00000i	0.471405i
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0	0
$21$	−1.00000	−0.218218
$22$	− 6.00000i	− 1.27920i
$23$	3.00000i	0.625543i	0.949828	+	0.312772i	$0.101257\pi$
$23$	3.00000i	0.625543i	−0.949828	+	0.312772i	$0.898743\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	−5.00000	−0.980581
$27$	5.00000i	0.962250i
$28$	− 1.00000i	− 0.188982i
$29$	−9.00000	−1.67126	−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000	−1.67126	−0.835629	+	0.549294i	$0.814897\pi$
$30$	0	0
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	1.00000i	0.176777i
$33$	− 6.00000i	− 1.04447i
$34$	3.00000	0.514496
$35$	0	0
$36$	−2.00000	−0.333333
$37$	− 2.00000i	− 0.328798i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$	− 2.00000i	− 0.328798i	0.986394	−	0.164399i	$-0.0525685\pi$
$38$	− 1.00000i	− 0.162221i
$39$	−5.00000	−0.800641
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	− 1.00000i	− 0.154303i
$43$	8.00000i	1.21999i	0.792406	+	0.609994i	$0.208828\pi$
$43$	8.00000i	1.21999i	−0.792406	+	0.609994i	$0.791172\pi$
$44$	6.00000	0.904534
$45$	0	0
$46$	−3.00000	−0.442326
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	1.00000i	0.144338i
$49$	6.00000	0.857143
$50$	0	0
$51$	3.00000	0.420084
$52$	− 5.00000i	− 0.693375i
$53$	− 3.00000i	− 0.412082i	−0.978543	−	0.206041i	$-0.933942\pi$
$53$	− 3.00000i	− 0.412082i	0.978543	−	0.206041i	$-0.0660580\pi$
$54$	−5.00000	−0.680414
$55$	0	0
$56$	1.00000	0.133631
$57$	− 1.00000i	− 0.132453i
$58$	− 9.00000i	− 1.18176i
$59$	−9.00000	−1.17170	−0.585850	−	0.810419i	$-0.699239\pi$
$59$	−9.00000	−1.17170	−0.585850	+	0.810419i	$0.699239\pi$
$60$	0	0
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	− 4.00000i	− 0.508001i
$63$	2.00000i	0.251976i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	6.00000	0.738549
$67$	− 5.00000i	− 0.610847i	−0.952217	−	0.305424i	$-0.901202\pi$
$67$	− 5.00000i	− 0.610847i	0.952217	−	0.305424i	$-0.0987981\pi$
$68$	3.00000i	0.363803i
$69$	−3.00000	−0.361158
$70$	0	0
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	− 2.00000i	− 0.235702i
$73$	− 7.00000i	− 0.819288i	−0.912245	−	0.409644i	$-0.865653\pi$
$73$	− 7.00000i	− 0.819288i	0.912245	−	0.409644i	$-0.134347\pi$
$74$	2.00000	0.232495
$75$	0	0
$76$	1.00000	0.114708
$77$	− 6.00000i	− 0.683763i
$78$	− 5.00000i	− 0.566139i
$79$	10.0000	1.12509	0.562544	−	0.826767i	$-0.309823\pi$
$79$	10.0000	1.12509	0.562544	+	0.826767i	$0.309823\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	− 6.00000i	− 0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$	− 6.00000i	− 0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$	1.00000	0.109109
$85$	0	0
$86$	−8.00000	−0.862662
$87$	− 9.00000i	− 0.964901i
$88$	6.00000i	0.639602i
$89$	12.0000	1.27200	0.635999	−	0.771690i	$-0.280588\pi$
$89$	12.0000	1.27200	0.635999	+	0.771690i	$0.280588\pi$
$90$	0	0
$91$	−5.00000	−0.524142
$92$	− 3.00000i	− 0.312772i
$93$	− 4.00000i	− 0.414781i
$94$	0	0
$95$	0	0
$96$	−1.00000	−0.102062
$97$	10.0000i	1.01535i	0.861550	+	0.507673i	$0.169494\pi$
$97$	10.0000i	1.01535i	−0.861550	+	0.507673i	$0.830506\pi$
$98$	6.00000i	0.606092i
$99$	−12.0000	−1.20605
$100$	0	0
$101$	18.0000	1.79107	0.895533	−	0.444994i	$-0.146794\pi$
$101$	18.0000	1.79107	0.895533	+	0.444994i	$0.146794\pi$
$102$	3.00000i	0.297044i
$103$	14.0000i	1.37946i	0.724066	+	0.689730i	$0.242271\pi$
$103$	14.0000i	1.37946i	−0.724066	+	0.689730i	$0.757729\pi$
$104$	5.00000	0.490290
$105$	0	0
$106$	3.00000	0.291386
$107$	9.00000i	0.870063i	0.900415	+	0.435031i	$0.143263\pi$
$107$	9.00000i	0.870063i	−0.900415	+	0.435031i	$0.856737\pi$
$108$	− 5.00000i	− 0.481125i
$109$	−11.0000	−1.05361	−0.526804	−	0.849987i	$-0.676610\pi$
$109$	−11.0000	−1.05361	−0.526804	+	0.849987i	$0.676610\pi$
$110$	0	0
$111$	2.00000	0.189832
$112$	1.00000i	0.0944911i
$113$	6.00000i	0.564433i	0.959351	+	0.282216i	$0.0910696\pi$
$113$	6.00000i	0.564433i	−0.959351	+	0.282216i	$0.908930\pi$
$114$	1.00000	0.0936586
$115$	0	0
$116$	9.00000	0.835629
$117$	10.0000i	0.924500i
$118$	− 9.00000i	− 0.828517i
$119$	3.00000	0.275010
$120$	0	0
$121$	25.0000	2.27273
$122$	− 10.0000i	− 0.905357i
$123$	0	0
$124$	4.00000	0.359211
$125$	0	0
$126$	−2.00000	−0.178174
$127$	− 2.00000i	− 0.177471i	−0.996055	−	0.0887357i	$-0.971717\pi$
$127$	− 2.00000i	− 0.177471i	0.996055	−	0.0887357i	$-0.0282826\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−8.00000	−0.704361
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	6.00000i	0.522233i
$133$	− 1.00000i	− 0.0867110i
$134$	5.00000	0.431934
$135$	0	0
$136$	−3.00000	−0.257248
$137$	9.00000i	0.768922i	0.923141	+	0.384461i	$0.125613\pi$
$137$	9.00000i	0.768922i	−0.923141	+	0.384461i	$0.874387\pi$
$138$	− 3.00000i	− 0.255377i
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	0	0
$141$	0	0
$142$	− 6.00000i	− 0.503509i
$143$	− 30.0000i	− 2.50873i
$144$	2.00000	0.166667
$145$	0	0
$146$	7.00000	0.579324
$147$	6.00000i	0.494872i
$148$	2.00000i	0.164399i
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	−10.0000	−0.813788	−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000	−0.813788	−0.406894	+	0.913475i	$0.633388\pi$
$152$	1.00000i	0.0811107i
$153$	− 6.00000i	− 0.485071i
$154$	6.00000	0.483494
$155$	0	0
$156$	5.00000	0.400320
$157$	22.0000i	1.75579i	0.478852	+	0.877896i	$0.341053\pi$
$157$	22.0000i	1.75579i	−0.478852	+	0.877896i	$0.658947\pi$
$158$	10.0000i	0.795557i
$159$	3.00000	0.237915
$160$	0	0
$161$	−3.00000	−0.236433
$162$	1.00000i	0.0785674i
$163$	20.0000i	1.56652i	0.621694	+	0.783260i	$0.286445\pi$
$163$	20.0000i	1.56652i	−0.621694	+	0.783260i	$0.713555\pi$
$164$	0	0
$165$	0	0
$166$	6.00000	0.465690
$167$	− 12.0000i	− 0.928588i	−0.885681	−	0.464294i	$-0.846308\pi$
$167$	− 12.0000i	− 0.928588i	0.885681	−	0.464294i	$-0.153692\pi$
$168$	1.00000i	0.0771517i
$169$	−12.0000	−0.923077
$170$	0	0
$171$	−2.00000	−0.152944
$172$	− 8.00000i	− 0.609994i
$173$	6.00000i	0.456172i	0.973641	+	0.228086i	$0.0732467\pi$
$173$	6.00000i	0.456172i	−0.973641	+	0.228086i	$0.926753\pi$
$174$	9.00000	0.682288
$175$	0	0
$176$	−6.00000	−0.452267
$177$	− 9.00000i	− 0.676481i
$178$	12.0000i	0.899438i
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	− 5.00000i	− 0.370625i
$183$	− 10.0000i	− 0.739221i
$184$	3.00000	0.221163
$185$	0	0
$186$	4.00000	0.293294
$187$	18.0000i	1.31629i
$188$	0	0
$189$	−5.00000	−0.363696
$190$	0	0
$191$	3.00000	0.217072	0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000	0.217072	0.108536	+	0.994092i	$0.465384\pi$
$192$	− 1.00000i	− 0.0721688i
$193$	14.0000i	1.00774i	0.863779	+	0.503871i	$0.168091\pi$
$193$	14.0000i	1.00774i	−0.863779	+	0.503871i	$0.831909\pi$
$194$	−10.0000	−0.717958
$195$	0	0
$196$	−6.00000	−0.428571
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	− 12.0000i	− 0.852803i
$199$	−11.0000	−0.779769	−0.389885	−	0.920864i	$-0.627485\pi$
$199$	−11.0000	−0.779769	−0.389885	+	0.920864i	$0.627485\pi$
$200$	0	0
$201$	5.00000	0.352673
$202$	18.0000i	1.26648i
$203$	− 9.00000i	− 0.631676i
$204$	−3.00000	−0.210042
$205$	0	0
$206$	−14.0000	−0.975426
$207$	6.00000i	0.417029i
$208$	5.00000i	0.346688i
$209$	6.00000	0.415029
$210$	0	0
$211$	5.00000	0.344214	0.172107	−	0.985078i	$-0.444942\pi$
$211$	5.00000	0.344214	0.172107	+	0.985078i	$0.444942\pi$
$212$	3.00000i	0.206041i
$213$	− 6.00000i	− 0.411113i
$214$	−9.00000	−0.615227
$215$	0	0
$216$	5.00000	0.340207
$217$	− 4.00000i	− 0.271538i
$218$	− 11.0000i	− 0.745014i
$219$	7.00000	0.473016
$220$	0	0
$221$	15.0000	1.00901
$222$	2.00000i	0.134231i
$223$	26.0000i	1.74109i	0.492090	+	0.870544i	$0.336233\pi$
$223$	26.0000i	1.74109i	−0.492090	+	0.870544i	$0.663767\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	−6.00000	−0.399114
$227$	15.0000i	0.995585i	0.867296	+	0.497792i	$0.165856\pi$
$227$	15.0000i	0.995585i	−0.867296	+	0.497792i	$0.834144\pi$
$228$	1.00000i	0.0662266i
$229$	22.0000	1.45380	0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000	1.45380	0.726900	+	0.686743i	$0.240960\pi$
$230$	0	0
$231$	6.00000	0.394771
$232$	9.00000i	0.590879i
$233$	− 6.00000i	− 0.393073i	−0.980497	−	0.196537i	$-0.937031\pi$
$233$	− 6.00000i	− 0.393073i	0.980497	−	0.196537i	$-0.0629694\pi$
$234$	−10.0000	−0.653720
$235$	0	0
$236$	9.00000	0.585850
$237$	10.0000i	0.649570i
$238$	3.00000i	0.194461i
$239$	21.0000	1.35838	0.679189	−	0.733964i	$-0.262332\pi$
$239$	21.0000	1.35838	0.679189	+	0.733964i	$0.262332\pi$
$240$	0	0
$241$	8.00000	0.515325	0.257663	−	0.966235i	$-0.417048\pi$
$241$	8.00000	0.515325	0.257663	+	0.966235i	$0.417048\pi$
$242$	25.0000i	1.60706i
$243$	16.0000i	1.02640i
$244$	10.0000	0.640184
$245$	0	0
$246$	0	0
$247$	− 5.00000i	− 0.318142i
$248$	4.00000i	0.254000i
$249$	6.00000	0.380235
$250$	0	0
$251$	6.00000	0.378717	0.189358	−	0.981908i	$-0.439359\pi$
$251$	6.00000	0.378717	0.189358	+	0.981908i	$0.439359\pi$
$252$	− 2.00000i	− 0.125988i
$253$	− 18.0000i	− 1.13165i
$254$	2.00000	0.125491
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 12.0000i	− 0.748539i	−0.927320	−	0.374270i	$-0.877893\pi$
$257$	− 12.0000i	− 0.748539i	0.927320	−	0.374270i	$-0.122107\pi$
$258$	− 8.00000i	− 0.498058i
$259$	2.00000	0.124274
$260$	0	0
$261$	−18.0000	−1.11417
$262$	0	0
$263$	24.0000i	1.47990i	0.672660	+	0.739952i	$0.265152\pi$
$263$	24.0000i	1.47990i	−0.672660	+	0.739952i	$0.734848\pi$
$264$	−6.00000	−0.369274
$265$	0	0
$266$	1.00000	0.0613139
$267$	12.0000i	0.734388i
$268$	5.00000i	0.305424i
$269$	6.00000	0.365826	0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000	0.365826	0.182913	+	0.983129i	$0.441447\pi$
$270$	0	0
$271$	11.0000	0.668202	0.334101	−	0.942537i	$-0.391567\pi$
$271$	11.0000	0.668202	0.334101	+	0.942537i	$0.391567\pi$
$272$	− 3.00000i	− 0.181902i
$273$	− 5.00000i	− 0.302614i
$274$	−9.00000	−0.543710
$275$	0	0
$276$	3.00000	0.180579
$277$	− 8.00000i	− 0.480673i	−0.970690	−	0.240337i	$-0.922742\pi$
$277$	− 8.00000i	− 0.480673i	0.970690	−	0.240337i	$-0.0772579\pi$
$278$	4.00000i	0.239904i
$279$	−8.00000	−0.478947
$280$	0	0
$281$	0	0		−	1.00000i	$-0.5\pi$
$281$	0	0			1.00000i	$0.5\pi$
$282$	0	0
$283$	− 22.0000i	− 1.30776i	−0.756596	−	0.653882i	$-0.773139\pi$
$283$	− 22.0000i	− 1.30776i	0.756596	−	0.653882i	$-0.226861\pi$
$284$	6.00000	0.356034
$285$	0	0
$286$	30.0000	1.77394
$287$	0	0
$288$	2.00000i	0.117851i
$289$	8.00000	0.470588
$290$	0	0
$291$	−10.0000	−0.586210
$292$	7.00000i	0.409644i
$293$	− 21.0000i	− 1.22683i	−0.789760	−	0.613417i	$-0.789795\pi$
$293$	− 21.0000i	− 1.22683i	0.789760	−	0.613417i	$-0.210205\pi$
$294$	−6.00000	−0.349927
$295$	0	0
$296$	−2.00000	−0.116248
$297$	− 30.0000i	− 1.74078i
$298$	0	0
$299$	−15.0000	−0.867472
$300$	0	0
$301$	−8.00000	−0.461112
$302$	− 10.0000i	− 0.575435i
$303$	18.0000i	1.03407i
$304$	−1.00000	−0.0573539
$305$	0	0
$306$	6.00000	0.342997
$307$	− 20.0000i	− 1.14146i	−0.821138	−	0.570730i	$-0.806660\pi$
$307$	− 20.0000i	− 1.14146i	0.821138	−	0.570730i	$-0.193340\pi$
$308$	6.00000i	0.341882i
$309$	−14.0000	−0.796432
$310$	0	0
$311$	−21.0000	−1.19080	−0.595400	−	0.803429i	$-0.703007\pi$
$311$	−21.0000	−1.19080	−0.595400	+	0.803429i	$0.703007\pi$
$312$	5.00000i	0.283069i
$313$	− 19.0000i	− 1.07394i	−0.843600	−	0.536972i	$-0.819568\pi$
$313$	− 19.0000i	− 1.07394i	0.843600	−	0.536972i	$-0.180432\pi$
$314$	−22.0000	−1.24153
$315$	0	0
$316$	−10.0000	−0.562544
$317$	9.00000i	0.505490i	0.967533	+	0.252745i	$0.0813334\pi$
$317$	9.00000i	0.505490i	−0.967533	+	0.252745i	$0.918667\pi$
$318$	3.00000i	0.168232i
$319$	54.0000	3.02342
$320$	0	0
$321$	−9.00000	−0.502331
$322$	− 3.00000i	− 0.167183i
$323$	3.00000i	0.166924i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	−20.0000	−1.10770
$327$	− 11.0000i	− 0.608301i
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−1.00000	−0.0549650	−0.0274825	−	0.999622i	$-0.508749\pi$
$331$	−1.00000	−0.0549650	−0.0274825	+	0.999622i	$0.508749\pi$
$332$	6.00000i	0.329293i
$333$	− 4.00000i	− 0.219199i
$334$	12.0000	0.656611
$335$	0	0
$336$	−1.00000	−0.0545545
$337$	4.00000i	0.217894i	0.994048	+	0.108947i	$0.0347479\pi$
$337$	4.00000i	0.217894i	−0.994048	+	0.108947i	$0.965252\pi$
$338$	− 12.0000i	− 0.652714i
$339$	−6.00000	−0.325875
$340$	0	0
$341$	24.0000	1.29967
$342$	− 2.00000i	− 0.108148i
$343$	13.0000i	0.701934i
$344$	8.00000	0.431331
$345$	0	0
$346$	−6.00000	−0.322562
$347$	− 18.0000i	− 0.966291i	−0.875540	−	0.483145i	$-0.839494\pi$
$347$	− 18.0000i	− 0.966291i	0.875540	−	0.483145i	$-0.160506\pi$
$348$	9.00000i	0.482451i
$349$	10.0000	0.535288	0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000	0.535288	0.267644	+	0.963518i	$0.413755\pi$
$350$	0	0
$351$	−25.0000	−1.33440
$352$	− 6.00000i	− 0.319801i
$353$	− 15.0000i	− 0.798369i	−0.916871	−	0.399185i	$-0.869293\pi$
$353$	− 15.0000i	− 0.798369i	0.916871	−	0.399185i	$-0.130707\pi$
$354$	9.00000	0.478345
$355$	0	0
$356$	−12.0000	−0.635999
$357$	3.00000i	0.158777i
$358$	0	0
$359$	−21.0000	−1.10834	−0.554169	−	0.832404i	$-0.686964\pi$
$359$	−21.0000	−1.10834	−0.554169	+	0.832404i	$0.686964\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	2.00000i	0.105118i
$363$	25.0000i	1.31216i
$364$	5.00000	0.262071
$365$	0	0
$366$	10.0000	0.522708
$367$	28.0000i	1.46159i	0.682598	+	0.730794i	$0.260850\pi$
$367$	28.0000i	1.46159i	−0.682598	+	0.730794i	$0.739150\pi$
$368$	3.00000i	0.156386i
$369$	0	0
$370$	0	0
$371$	3.00000	0.155752
$372$	4.00000i	0.207390i
$373$	23.0000i	1.19089i	0.803394	+	0.595447i	$0.203025\pi$
$373$	23.0000i	1.19089i	−0.803394	+	0.595447i	$0.796975\pi$
$374$	−18.0000	−0.930758
$375$	0	0
$376$	0	0
$377$	− 45.0000i	− 2.31762i
$378$	− 5.00000i	− 0.257172i
$379$	7.00000	0.359566	0.179783	−	0.983706i	$-0.442460\pi$
$379$	7.00000	0.359566	0.179783	+	0.983706i	$0.442460\pi$
$380$	0	0
$381$	2.00000	0.102463
$382$	3.00000i	0.153493i
$383$	18.0000i	0.919757i	0.887982	+	0.459879i	$0.152107\pi$
$383$	18.0000i	0.919757i	−0.887982	+	0.459879i	$0.847893\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−14.0000	−0.712581
$387$	16.0000i	0.813326i
$388$	− 10.0000i	− 0.507673i
$389$	−18.0000	−0.912636	−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000	−0.912636	−0.456318	+	0.889817i	$0.650832\pi$
$390$	0	0
$391$	9.00000	0.455150
$392$	− 6.00000i	− 0.303046i
$393$	0	0
$394$	0	0
$395$	0	0
$396$	12.0000	0.603023
$397$	− 20.0000i	− 1.00377i	−0.864934	−	0.501886i	$-0.832640\pi$
$397$	− 20.0000i	− 1.00377i	0.864934	−	0.501886i	$-0.167360\pi$
$398$	− 11.0000i	− 0.551380i
$399$	1.00000	0.0500626
$400$	0	0
$401$	0	0		−	1.00000i	$-0.5\pi$
$401$	0	0			1.00000i	$0.5\pi$
$402$	5.00000i	0.249377i
$403$	− 20.0000i	− 0.996271i
$404$	−18.0000	−0.895533
$405$	0	0
$406$	9.00000	0.446663
$407$	12.0000i	0.594818i
$408$	− 3.00000i	− 0.148522i
$409$	−32.0000	−1.58230	−0.791149	−	0.611623i	$-0.790517\pi$
$409$	−32.0000	−1.58230	−0.791149	+	0.611623i	$0.790517\pi$
$410$	0	0
$411$	−9.00000	−0.443937
$412$	− 14.0000i	− 0.689730i
$413$	− 9.00000i	− 0.442861i
$414$	−6.00000	−0.294884
$415$	0	0
$416$	−5.00000	−0.245145
$417$	4.00000i	0.195881i
$418$	6.00000i	0.293470i
$419$	12.0000	0.586238	0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000	0.586238	0.293119	+	0.956076i	$0.405307\pi$
$420$	0	0
$421$	17.0000	0.828529	0.414265	−	0.910156i	$-0.364039\pi$
$421$	17.0000	0.828529	0.414265	+	0.910156i	$0.364039\pi$
$422$	5.00000i	0.243396i
$423$	0	0
$424$	−3.00000	−0.145693
$425$	0	0
$426$	6.00000	0.290701
$427$	− 10.0000i	− 0.483934i
$428$	− 9.00000i	− 0.435031i
$429$	30.0000	1.44841
$430$	0	0
$431$	6.00000	0.289010	0.144505	−	0.989504i	$-0.453841\pi$
$431$	6.00000	0.289010	0.144505	+	0.989504i	$0.453841\pi$
$432$	5.00000i	0.240563i
$433$	2.00000i	0.0961139i	0.998845	+	0.0480569i	$0.0153029\pi$
$433$	2.00000i	0.0961139i	−0.998845	+	0.0480569i	$0.984697\pi$
$434$	4.00000	0.192006
$435$	0	0
$436$	11.0000	0.526804
$437$	− 3.00000i	− 0.143509i
$438$	7.00000i	0.334473i
$439$	28.0000	1.33637	0.668184	−	0.743996i	$-0.267072\pi$
$439$	28.0000	1.33637	0.668184	+	0.743996i	$0.267072\pi$
$440$	0	0
$441$	12.0000	0.571429
$442$	15.0000i	0.713477i
$443$	− 18.0000i	− 0.855206i	−0.903967	−	0.427603i	$-0.859358\pi$
$443$	− 18.0000i	− 0.855206i	0.903967	−	0.427603i	$-0.140642\pi$
$444$	−2.00000	−0.0949158
$445$	0	0
$446$	−26.0000	−1.23114
$447$	0	0
$448$	− 1.00000i	− 0.0472456i
$449$	18.0000	0.849473	0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000	0.849473	0.424736	+	0.905317i	$0.360367\pi$
$450$	0	0
$451$	0	0
$452$	− 6.00000i	− 0.282216i
$453$	− 10.0000i	− 0.469841i
$454$	−15.0000	−0.703985
$455$	0	0
$456$	−1.00000	−0.0468293
$457$	− 17.0000i	− 0.795226i	−0.917553	−	0.397613i	$-0.869839\pi$
$457$	− 17.0000i	− 0.795226i	0.917553	−	0.397613i	$-0.130161\pi$
$458$	22.0000i	1.02799i
$459$	15.0000	0.700140
$460$	0	0
$461$	−12.0000	−0.558896	−0.279448	−	0.960161i	$-0.590151\pi$
$461$	−12.0000	−0.558896	−0.279448	+	0.960161i	$0.590151\pi$
$462$	6.00000i	0.279145i
$463$	− 4.00000i	− 0.185896i	−0.995671	−	0.0929479i	$-0.970371\pi$
$463$	− 4.00000i	− 0.185896i	0.995671	−	0.0929479i	$-0.0296290\pi$
$464$	−9.00000	−0.417815
$465$	0	0
$466$	6.00000	0.277945
$467$	− 18.0000i	− 0.832941i	−0.909149	−	0.416470i	$-0.863267\pi$
$467$	− 18.0000i	− 0.832941i	0.909149	−	0.416470i	$-0.136733\pi$
$468$	− 10.0000i	− 0.462250i
$469$	5.00000	0.230879
$470$	0	0
$471$	−22.0000	−1.01371
$472$	9.00000i	0.414259i
$473$	− 48.0000i	− 2.20704i
$474$	−10.0000	−0.459315
$475$	0	0
$476$	−3.00000	−0.137505
$477$	− 6.00000i	− 0.274721i
$478$	21.0000i	0.960518i
$479$	−36.0000	−1.64488	−0.822441	−	0.568850i	$-0.807388\pi$
$479$	−36.0000	−1.64488	−0.822441	+	0.568850i	$0.807388\pi$
$480$	0	0
$481$	10.0000	0.455961
$482$	8.00000i	0.364390i
$483$	− 3.00000i	− 0.136505i
$484$	−25.0000	−1.13636
$485$	0	0
$486$	−16.0000	−0.725775
$487$	− 2.00000i	− 0.0906287i	−0.998973	−	0.0453143i	$-0.985571\pi$
$487$	− 2.00000i	− 0.0906287i	0.998973	−	0.0453143i	$-0.0144289\pi$
$488$	10.0000i	0.452679i
$489$	−20.0000	−0.904431
$490$	0	0
$491$	−36.0000	−1.62466	−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000	−1.62466	−0.812329	+	0.583200i	$0.801800\pi$
$492$	0	0
$493$	27.0000i	1.21602i
$494$	5.00000	0.224961
$495$	0	0
$496$	−4.00000	−0.179605
$497$	− 6.00000i	− 0.269137i
$498$	6.00000i	0.268866i
$499$	4.00000	0.179065	0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000	0.179065	0.0895323	+	0.995984i	$0.471463\pi$
$500$	0	0
$501$	12.0000	0.536120
$502$	6.00000i	0.267793i
$503$	− 21.0000i	− 0.936344i	−0.883637	−	0.468172i	$-0.844913\pi$
$503$	− 21.0000i	− 0.936344i	0.883637	−	0.468172i	$-0.155087\pi$
$504$	2.00000	0.0890871
$505$	0	0
$506$	18.0000	0.800198
$507$	− 12.0000i	− 0.532939i
$508$	2.00000i	0.0887357i
$509$	−30.0000	−1.32973	−0.664863	−	0.746965i	$-0.731510\pi$
$509$	−30.0000	−1.32973	−0.664863	+	0.746965i	$0.731510\pi$
$510$	0	0
$511$	7.00000	0.309662
$512$	1.00000i	0.0441942i
$513$	− 5.00000i	− 0.220755i
$514$	12.0000	0.529297
$515$	0	0
$516$	8.00000	0.352180
$517$	0	0
$518$	2.00000i	0.0878750i
$519$	−6.00000	−0.263371
$520$	0	0
$521$	−36.0000	−1.57719	−0.788594	−	0.614914i	$-0.789191\pi$
$521$	−36.0000	−1.57719	−0.788594	+	0.614914i	$0.789191\pi$
$522$	− 18.0000i	− 0.787839i
$523$	11.0000i	0.480996i	0.970650	+	0.240498i	$0.0773108\pi$
$523$	11.0000i	0.480996i	−0.970650	+	0.240498i	$0.922689\pi$
$524$	0	0
$525$	0	0
$526$	−24.0000	−1.04645
$527$	12.0000i	0.522728i
$528$	− 6.00000i	− 0.261116i
$529$	14.0000	0.608696
$530$	0	0
$531$	−18.0000	−0.781133
$532$	1.00000i	0.0433555i
$533$	0	0
$534$	−12.0000	−0.519291
$535$	0	0
$536$	−5.00000	−0.215967
$537$	0	0
$538$	6.00000i	0.258678i
$539$	−36.0000	−1.55063
$540$	0	0
$541$	2.00000	0.0859867	0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000	0.0859867	0.0429934	+	0.999075i	$0.486311\pi$
$542$	11.0000i	0.472490i
$543$	2.00000i	0.0858282i
$544$	3.00000	0.128624
$545$	0	0
$546$	5.00000	0.213980
$547$	− 44.0000i	− 1.88130i	−0.339372	−	0.940652i	$-0.610215\pi$
$547$	− 44.0000i	− 1.88130i	0.339372	−	0.940652i	$-0.389785\pi$
$548$	− 9.00000i	− 0.384461i
$549$	−20.0000	−0.853579
$550$	0	0
$551$	9.00000	0.383413
$552$	3.00000i	0.127688i
$553$	10.0000i	0.425243i
$554$	8.00000	0.339887
$555$	0	0
$556$	−4.00000	−0.169638
$557$	− 24.0000i	− 1.01691i	−0.861088	−	0.508456i	$-0.830216\pi$
$557$	− 24.0000i	− 1.01691i	0.861088	−	0.508456i	$-0.169784\pi$
$558$	− 8.00000i	− 0.338667i
$559$	−40.0000	−1.69182
$560$	0	0
$561$	−18.0000	−0.759961
$562$	0	0
$563$	− 12.0000i	− 0.505740i	−0.967500	−	0.252870i	$-0.918626\pi$
$563$	− 12.0000i	− 0.505740i	0.967500	−	0.252870i	$-0.0813744\pi$
$564$	0	0
$565$	0	0
$566$	22.0000	0.924729
$567$	1.00000i	0.0419961i
$568$	6.00000i	0.251754i
$569$	24.0000	1.00613	0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000	1.00613	0.503066	+	0.864248i	$0.332205\pi$
$570$	0	0
$571$	−4.00000	−0.167395	−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000	−0.167395	−0.0836974	+	0.996491i	$0.526673\pi$
$572$	30.0000i	1.25436i
$573$	3.00000i	0.125327i
$574$	0	0
$575$	0	0
$576$	−2.00000	−0.0833333
$577$	− 11.0000i	− 0.457936i	−0.973434	−	0.228968i	$-0.926465\pi$
$577$	− 11.0000i	− 0.457936i	0.973434	−	0.228968i	$-0.0735351\pi$
$578$	8.00000i	0.332756i
$579$	−14.0000	−0.581820
$580$	0	0
$581$	6.00000	0.248922
$582$	− 10.0000i	− 0.414513i
$583$	18.0000i	0.745484i
$584$	−7.00000	−0.289662
$585$	0	0
$586$	21.0000	0.867502
$587$	12.0000i	0.495293i	0.968850	+	0.247647i	$0.0796572\pi$
$587$	12.0000i	0.495293i	−0.968850	+	0.247647i	$0.920343\pi$
$588$	− 6.00000i	− 0.247436i
$589$	4.00000	0.164817
$590$	0	0
$591$	0	0
$592$	− 2.00000i	− 0.0821995i
$593$	− 30.0000i	− 1.23195i	−0.787765	−	0.615976i	$-0.788762\pi$
$593$	− 30.0000i	− 1.23195i	0.787765	−	0.615976i	$-0.211238\pi$
$594$	30.0000	1.23091
$595$	0	0
$596$	0	0
$597$	− 11.0000i	− 0.450200i
$598$	− 15.0000i	− 0.613396i
$599$	24.0000	0.980613	0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000	0.980613	0.490307	+	0.871550i	$0.336885\pi$
$600$	0	0
$601$	−28.0000	−1.14214	−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000	−1.14214	−0.571072	+	0.820900i	$0.693472\pi$
$602$	− 8.00000i	− 0.326056i
$603$	− 10.0000i	− 0.407231i
$604$	10.0000	0.406894
$605$	0	0
$606$	−18.0000	−0.731200
$607$	22.0000i	0.892952i	0.894795	+	0.446476i	$0.147321\pi$
$607$	22.0000i	0.892952i	−0.894795	+	0.446476i	$0.852679\pi$
$608$	− 1.00000i	− 0.0405554i
$609$	9.00000	0.364698
$610$	0	0
$611$	0	0
$612$	6.00000i	0.242536i
$613$	2.00000i	0.0807792i	0.999184	+	0.0403896i	$0.0128599\pi$
$613$	2.00000i	0.0807792i	−0.999184	+	0.0403896i	$0.987140\pi$
$614$	20.0000	0.807134
$615$	0	0
$616$	−6.00000	−0.241747
$617$	6.00000i	0.241551i	0.992680	+	0.120775i	$0.0385381\pi$
$617$	6.00000i	0.241551i	−0.992680	+	0.120775i	$0.961462\pi$
$618$	− 14.0000i	− 0.563163i
$619$	10.0000	0.401934	0.200967	−	0.979598i	$-0.435592\pi$
$619$	10.0000	0.401934	0.200967	+	0.979598i	$0.435592\pi$
$620$	0	0
$621$	−15.0000	−0.601929
$622$	− 21.0000i	− 0.842023i
$623$	12.0000i	0.480770i
$624$	−5.00000	−0.200160
$625$	0	0
$626$	19.0000	0.759393
$627$	6.00000i	0.239617i
$628$	− 22.0000i	− 0.877896i
$629$	−6.00000	−0.239236
$630$	0	0
$631$	−16.0000	−0.636950	−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000	−0.636950	−0.318475	+	0.947931i	$0.603171\pi$
$632$	− 10.0000i	− 0.397779i
$633$	5.00000i	0.198732i
$634$	−9.00000	−0.357436
$635$	0	0
$636$	−3.00000	−0.118958
$637$	30.0000i	1.18864i
$638$	54.0000i	2.13788i
$639$	−12.0000	−0.474713
$640$	0	0
$641$	6.00000	0.236986	0.118493	−	0.992955i	$-0.462194\pi$
$641$	6.00000	0.236986	0.118493	+	0.992955i	$0.462194\pi$
$642$	− 9.00000i	− 0.355202i
$643$	− 22.0000i	− 0.867595i	−0.901010	−	0.433798i	$-0.857173\pi$
$643$	− 22.0000i	− 0.867595i	0.901010	−	0.433798i	$-0.142827\pi$
$644$	3.00000	0.118217
$645$	0	0
$646$	−3.00000	−0.118033
$647$	− 27.0000i	− 1.06148i	−0.847535	−	0.530740i	$-0.821914\pi$
$647$	− 27.0000i	− 1.06148i	0.847535	−	0.530740i	$-0.178086\pi$
$648$	− 1.00000i	− 0.0392837i
$649$	54.0000	2.11969
$650$	0	0
$651$	4.00000	0.156772
$652$	− 20.0000i	− 0.783260i
$653$	24.0000i	0.939193i	0.882881	+	0.469596i	$0.155601\pi$
$653$	24.0000i	0.939193i	−0.882881	+	0.469596i	$0.844399\pi$
$654$	11.0000	0.430134
$655$	0	0
$656$	0	0
$657$	− 14.0000i	− 0.546192i
$658$	0	0
$659$	45.0000	1.75295	0.876476	−	0.481446i	$-0.159888\pi$
$659$	45.0000	1.75295	0.876476	+	0.481446i	$0.159888\pi$
$660$	0	0
$661$	−13.0000	−0.505641	−0.252821	−	0.967513i	$-0.581358\pi$
$661$	−13.0000	−0.505641	−0.252821	+	0.967513i	$0.581358\pi$
$662$	− 1.00000i	− 0.0388661i
$663$	15.0000i	0.582552i
$664$	−6.00000	−0.232845
$665$	0	0
$666$	4.00000	0.154997
$667$	− 27.0000i	− 1.04544i
$668$	12.0000i	0.464294i
$669$	−26.0000	−1.00522
$670$	0	0
$671$	60.0000	2.31627
$672$	− 1.00000i	− 0.0385758i
$673$	44.0000i	1.69608i	0.529936	+	0.848038i	$0.322216\pi$
$673$	44.0000i	1.69608i	−0.529936	+	0.848038i	$0.677784\pi$
$674$	−4.00000	−0.154074
$675$	0	0
$676$	12.0000	0.461538
$677$	33.0000i	1.26829i	0.773213	+	0.634147i	$0.218648\pi$
$677$	33.0000i	1.26829i	−0.773213	+	0.634147i	$0.781352\pi$
$678$	− 6.00000i	− 0.230429i
$679$	−10.0000	−0.383765
$680$	0	0
$681$	−15.0000	−0.574801
$682$	24.0000i	0.919007i
$683$	36.0000i	1.37750i	0.724998	+	0.688751i	$0.241841\pi$
$683$	36.0000i	1.37750i	−0.724998	+	0.688751i	$0.758159\pi$
$684$	2.00000	0.0764719
$685$	0	0
$686$	−13.0000	−0.496342
$687$	22.0000i	0.839352i
$688$	8.00000i	0.304997i
$689$	15.0000	0.571454
$690$	0	0
$691$	−10.0000	−0.380418	−0.190209	−	0.981744i	$-0.560917\pi$
$691$	−10.0000	−0.380418	−0.190209	+	0.981744i	$0.560917\pi$
$692$	− 6.00000i	− 0.228086i
$693$	− 12.0000i	− 0.455842i
$694$	18.0000	0.683271
$695$	0	0
$696$	−9.00000	−0.341144
$697$	0	0
$698$	10.0000i	0.378506i
$699$	6.00000	0.226941
$700$	0	0
$701$	12.0000	0.453234	0.226617	−	0.973984i	$-0.427233\pi$
$701$	12.0000	0.453234	0.226617	+	0.973984i	$0.427233\pi$
$702$	− 25.0000i	− 0.943564i
$703$	2.00000i	0.0754314i
$704$	6.00000	0.226134
$705$	0	0
$706$	15.0000	0.564532
$707$	18.0000i	0.676960i
$708$	9.00000i	0.338241i
$709$	10.0000	0.375558	0.187779	−	0.982211i	$-0.439871\pi$
$709$	10.0000	0.375558	0.187779	+	0.982211i	$0.439871\pi$
$710$	0	0
$711$	20.0000	0.750059
$712$	− 12.0000i	− 0.449719i
$713$	− 12.0000i	− 0.449404i
$714$	−3.00000	−0.112272
$715$	0	0
$716$	0	0
$717$	21.0000i	0.784259i
$718$	− 21.0000i	− 0.783713i
$719$	−39.0000	−1.45445	−0.727227	−	0.686397i	$-0.759191\pi$
$719$	−39.0000	−1.45445	−0.727227	+	0.686397i	$0.759191\pi$
$720$	0	0
$721$	−14.0000	−0.521387
$722$	1.00000i	0.0372161i
$723$	8.00000i	0.297523i
$724$	−2.00000	−0.0743294
$725$	0	0
$726$	−25.0000	−0.927837
$727$	37.0000i	1.37225i	0.727482	+	0.686127i	$0.240691\pi$
$727$	37.0000i	1.37225i	−0.727482	+	0.686127i	$0.759309\pi$
$728$	5.00000i	0.185312i
$729$	−13.0000	−0.481481
$730$	0	0
$731$	24.0000	0.887672
$732$	10.0000i	0.369611i
$733$	32.0000i	1.18195i	0.806691	+	0.590973i	$0.201256\pi$
$733$	32.0000i	1.18195i	−0.806691	+	0.590973i	$0.798744\pi$
$734$	−28.0000	−1.03350
$735$	0	0
$736$	−3.00000	−0.110581
$737$	30.0000i	1.10506i
$738$	0	0
$739$	16.0000	0.588570	0.294285	−	0.955718i	$-0.404919\pi$
$739$	16.0000	0.588570	0.294285	+	0.955718i	$0.404919\pi$
$740$	0	0
$741$	5.00000	0.183680
$742$	3.00000i	0.110133i
$743$	− 36.0000i	− 1.32071i	−0.750953	−	0.660356i	$-0.770405\pi$
$743$	− 36.0000i	− 1.32071i	0.750953	−	0.660356i	$-0.229595\pi$
$744$	−4.00000	−0.146647
$745$	0	0
$746$	−23.0000	−0.842090
$747$	− 12.0000i	− 0.439057i
$748$	− 18.0000i	− 0.658145i
$749$	−9.00000	−0.328853
$750$	0	0
$751$	−40.0000	−1.45962	−0.729810	−	0.683650i	$-0.760392\pi$
$751$	−40.0000	−1.45962	−0.729810	+	0.683650i	$0.760392\pi$
$752$	0	0
$753$	6.00000i	0.218652i
$754$	45.0000	1.63880
$755$	0	0
$756$	5.00000	0.181848
$757$	− 2.00000i	− 0.0726912i	−0.999339	−	0.0363456i	$-0.988428\pi$
$757$	− 2.00000i	− 0.0726912i	0.999339	−	0.0363456i	$-0.0115717\pi$
$758$	7.00000i	0.254251i
$759$	18.0000	0.653359
$760$	0	0
$761$	−21.0000	−0.761249	−0.380625	−	0.924730i	$-0.624291\pi$
$761$	−21.0000	−0.761249	−0.380625	+	0.924730i	$0.624291\pi$
$762$	2.00000i	0.0724524i
$763$	− 11.0000i	− 0.398227i
$764$	−3.00000	−0.108536
$765$	0	0
$766$	−18.0000	−0.650366
$767$	− 45.0000i	− 1.62486i
$768$	1.00000i	0.0360844i
$769$	−5.00000	−0.180305	−0.0901523	−	0.995928i	$-0.528735\pi$
$769$	−5.00000	−0.180305	−0.0901523	+	0.995928i	$0.528735\pi$
$770$	0	0
$771$	12.0000	0.432169
$772$	− 14.0000i	− 0.503871i
$773$	51.0000i	1.83434i	0.398493	+	0.917171i	$0.369533\pi$
$773$	51.0000i	1.83434i	−0.398493	+	0.917171i	$0.630467\pi$
$774$	−16.0000	−0.575108
$775$	0	0
$776$	10.0000	0.358979
$777$	2.00000i	0.0717496i
$778$	− 18.0000i	− 0.645331i
$779$	0	0
$780$	0	0
$781$	36.0000	1.28818
$782$	9.00000i	0.321839i
$783$	− 45.0000i	− 1.60817i
$784$	6.00000	0.214286
$785$	0	0
$786$	0	0
$787$	31.0000i	1.10503i	0.833503	+	0.552515i	$0.186332\pi$
$787$	31.0000i	1.10503i	−0.833503	+	0.552515i	$0.813668\pi$
$788$	0	0
$789$	−24.0000	−0.854423
$790$	0	0
$791$	−6.00000	−0.213335
$792$	12.0000i	0.426401i
$793$	− 50.0000i	− 1.77555i
$794$	20.0000	0.709773
$795$	0	0
$796$	11.0000	0.389885
$797$	39.0000i	1.38145i	0.723117	+	0.690725i	$0.242709\pi$
$797$	39.0000i	1.38145i	−0.723117	+	0.690725i	$0.757291\pi$
$798$	1.00000i	0.0353996i
$799$	0	0
$800$	0	0
$801$	24.0000	0.847998
$802$	0	0
$803$	42.0000i	1.48215i
$804$	−5.00000	−0.176336
$805$	0	0
$806$	20.0000	0.704470
$807$	6.00000i	0.211210i
$808$	− 18.0000i	− 0.633238i
$809$	−9.00000	−0.316423	−0.158212	−	0.987405i	$-0.550573\pi$
$809$	−9.00000	−0.316423	−0.158212	+	0.987405i	$0.550573\pi$
$810$	0	0
$811$	11.0000	0.386262	0.193131	−	0.981173i	$-0.438136\pi$
$811$	11.0000	0.386262	0.193131	+	0.981173i	$0.438136\pi$
$812$	9.00000i	0.315838i
$813$	11.0000i	0.385787i
$814$	−12.0000	−0.420600
$815$	0	0
$816$	3.00000	0.105021
$817$	− 8.00000i	− 0.279885i
$818$	− 32.0000i	− 1.11885i
$819$	−10.0000	−0.349428
$820$	0	0
$821$	0	0		−	1.00000i	$-0.5\pi$
$821$	0	0			1.00000i	$0.5\pi$
$822$	− 9.00000i	− 0.313911i
$823$	41.0000i	1.42917i	0.699549	+	0.714585i	$0.253384\pi$
$823$	41.0000i	1.42917i	−0.699549	+	0.714585i	$0.746616\pi$
$824$	14.0000	0.487713
$825$	0	0
$826$	9.00000	0.313150
$827$	− 33.0000i	− 1.14752i	−0.819023	−	0.573761i	$-0.805484\pi$
$827$	− 33.0000i	− 1.14752i	0.819023	−	0.573761i	$-0.194516\pi$
$828$	− 6.00000i	− 0.208514i
$829$	−11.0000	−0.382046	−0.191023	−	0.981586i	$-0.561180\pi$
$829$	−11.0000	−0.382046	−0.191023	+	0.981586i	$0.561180\pi$
$830$	0	0
$831$	8.00000	0.277517
$832$	− 5.00000i	− 0.173344i
$833$	− 18.0000i	− 0.623663i
$834$	−4.00000	−0.138509
$835$	0	0
$836$	−6.00000	−0.207514
$837$	− 20.0000i	− 0.691301i
$838$	12.0000i	0.414533i
$839$	48.0000	1.65714	0.828572	−	0.559883i	$-0.189154\pi$
$839$	48.0000	1.65714	0.828572	+	0.559883i	$0.189154\pi$
$840$	0	0
$841$	52.0000	1.79310
$842$	17.0000i	0.585859i
$843$	0	0
$844$	−5.00000	−0.172107
$845$	0	0
$846$	0	0
$847$	25.0000i	0.859010i
$848$	− 3.00000i	− 0.103020i
$849$	22.0000	0.755038
$850$	0	0
$851$	6.00000	0.205677
$852$	6.00000i	0.205557i
$853$	− 46.0000i	− 1.57501i	−0.616308	−	0.787505i	$-0.711372\pi$
$853$	− 46.0000i	− 1.57501i	0.616308	−	0.787505i	$-0.288628\pi$
$854$	10.0000	0.342193
$855$	0	0
$856$	9.00000	0.307614
$857$	12.0000i	0.409912i	0.978771	+	0.204956i	$0.0657052\pi$
$857$	12.0000i	0.409912i	−0.978771	+	0.204956i	$0.934295\pi$
$858$	30.0000i	1.02418i
$859$	−14.0000	−0.477674	−0.238837	−	0.971060i	$-0.576766\pi$
$859$	−14.0000	−0.477674	−0.238837	+	0.971060i	$0.576766\pi$
$860$	0	0
$861$	0	0
$862$	6.00000i	0.204361i
$863$	− 18.0000i	− 0.612727i	−0.951915	−	0.306364i	$-0.900888\pi$
$863$	− 18.0000i	− 0.612727i	0.951915	−	0.306364i	$-0.0991123\pi$
$864$	−5.00000	−0.170103
$865$	0	0
$866$	−2.00000	−0.0679628
$867$	8.00000i	0.271694i
$868$	4.00000i	0.135769i
$869$	−60.0000	−2.03536
$870$	0	0
$871$	25.0000	0.847093
$872$	11.0000i	0.372507i
$873$	20.0000i	0.676897i
$874$	3.00000	0.101477
$875$	0	0
$876$	−7.00000	−0.236508
$877$	− 23.0000i	− 0.776655i	−0.921521	−	0.388327i	$-0.873053\pi$
$877$	− 23.0000i	− 0.776655i	0.921521	−	0.388327i	$-0.126947\pi$
$878$	28.0000i	0.944954i
$879$	21.0000	0.708312
$880$	0	0
$881$	−18.0000	−0.606435	−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000	−0.606435	−0.303218	+	0.952921i	$0.598061\pi$
$882$	12.0000i	0.404061i
$883$	− 34.0000i	− 1.14419i	−0.820187	−	0.572096i	$-0.806131\pi$
$883$	− 34.0000i	− 1.14419i	0.820187	−	0.572096i	$-0.193869\pi$
$884$	−15.0000	−0.504505
$885$	0	0
$886$	18.0000	0.604722
$887$	42.0000i	1.41022i	0.709097	+	0.705111i	$0.249103\pi$
$887$	42.0000i	1.41022i	−0.709097	+	0.705111i	$0.750897\pi$
$888$	− 2.00000i	− 0.0671156i
$889$	2.00000	0.0670778
$890$	0	0
$891$	−6.00000	−0.201008
$892$	− 26.0000i	− 0.870544i
$893$	0	0
$894$	0	0
$895$	0	0
$896$	1.00000	0.0334077
$897$	− 15.0000i	− 0.500835i
$898$	18.0000i	0.600668i
$899$	36.0000	1.20067
$900$	0	0
$901$	−9.00000	−0.299833
$902$	0	0
$903$	− 8.00000i	− 0.266223i
$904$	6.00000	0.199557
$905$	0	0
$906$	10.0000	0.332228
$907$	37.0000i	1.22856i	0.789086	+	0.614282i	$0.210554\pi$
$907$	37.0000i	1.22856i	−0.789086	+	0.614282i	$0.789446\pi$
$908$	− 15.0000i	− 0.497792i
$909$	36.0000	1.19404
$910$	0	0
$911$	48.0000	1.59031	0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000	1.59031	0.795155	+	0.606406i	$0.207389\pi$
$912$	− 1.00000i	− 0.0331133i
$913$	36.0000i	1.19143i
$914$	17.0000	0.562310
$915$	0	0
$916$	−22.0000	−0.726900
$917$	0	0
$918$	15.0000i	0.495074i
$919$	7.00000	0.230909	0.115454	−	0.993313i	$-0.463168\pi$
$919$	7.00000	0.230909	0.115454	+	0.993313i	$0.463168\pi$
$920$	0	0
$921$	20.0000	0.659022
$922$	− 12.0000i	− 0.395199i
$923$	− 30.0000i	− 0.987462i
$924$	−6.00000	−0.197386
$925$	0	0
$926$	4.00000	0.131448
$927$	28.0000i	0.919641i
$928$	− 9.00000i	− 0.295439i
$929$	−33.0000	−1.08269	−0.541347	−	0.840799i	$-0.682086\pi$
$929$	−33.0000	−1.08269	−0.541347	+	0.840799i	$0.682086\pi$
$930$	0	0
$931$	−6.00000	−0.196642
$932$	6.00000i	0.196537i
$933$	− 21.0000i	− 0.687509i
$934$	18.0000	0.588978
$935$	0	0
$936$	10.0000	0.326860
$937$	7.00000i	0.228680i	0.993442	+	0.114340i	$0.0364753\pi$
$937$	7.00000i	0.228680i	−0.993442	+	0.114340i	$0.963525\pi$
$938$	5.00000i	0.163256i
$939$	19.0000	0.620042
$940$	0	0
$941$	21.0000	0.684580	0.342290	−	0.939594i	$-0.388797\pi$
$941$	21.0000	0.684580	0.342290	+	0.939594i	$0.388797\pi$
$942$	− 22.0000i	− 0.716799i
$943$	0	0
$944$	−9.00000	−0.292925
$945$	0	0
$946$	48.0000	1.56061
$947$	48.0000i	1.55979i	0.625910	+	0.779895i	$0.284728\pi$
$947$	48.0000i	1.55979i	−0.625910	+	0.779895i	$0.715272\pi$
$948$	− 10.0000i	− 0.324785i
$949$	35.0000	1.13615
$950$	0	0
$951$	−9.00000	−0.291845
$952$	− 3.00000i	− 0.0972306i
$953$	30.0000i	0.971795i	0.874016	+	0.485898i	$0.161507\pi$
$953$	30.0000i	0.971795i	−0.874016	+	0.485898i	$0.838493\pi$
$954$	6.00000	0.194257
$955$	0	0
$956$	−21.0000	−0.679189
$957$	54.0000i	1.74557i
$958$	− 36.0000i	− 1.16311i
$959$	−9.00000	−0.290625
$960$	0	0
$961$	−15.0000	−0.483871
$962$	10.0000i	0.322413i
$963$	18.0000i	0.580042i
$964$	−8.00000	−0.257663
$965$	0	0
$966$	3.00000	0.0965234
$967$	− 32.0000i	− 1.02905i	−0.857475	−	0.514525i	$-0.827968\pi$
$967$	− 32.0000i	− 1.02905i	0.857475	−	0.514525i	$-0.172032\pi$
$968$	− 25.0000i	− 0.803530i
$969$	−3.00000	−0.0963739
$970$	0	0
$971$	12.0000	0.385098	0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000	0.385098	0.192549	+	0.981287i	$0.438325\pi$
$972$	− 16.0000i	− 0.513200i
$973$	4.00000i	0.128234i
$974$	2.00000	0.0640841
$975$	0	0
$976$	−10.0000	−0.320092
$977$	12.0000i	0.383914i	0.981403	+	0.191957i	$0.0614834\pi$
$977$	12.0000i	0.383914i	−0.981403	+	0.191957i	$0.938517\pi$
$978$	− 20.0000i	− 0.639529i
$979$	−72.0000	−2.30113
$980$	0	0
$981$	−22.0000	−0.702406
$982$	− 36.0000i	− 1.14881i
$983$	− 30.0000i	− 0.956851i	−0.878128	−	0.478426i	$-0.841208\pi$
$983$	− 30.0000i	− 0.956851i	0.878128	−	0.478426i	$-0.158792\pi$
$984$	0	0
$985$	0	0
$986$	−27.0000	−0.859855
$987$	0	0
$988$	5.00000i	0.159071i
$989$	−24.0000	−0.763156
$990$	0	0
$991$	20.0000	0.635321	0.317660	−	0.948205i	$-0.397103\pi$
$991$	20.0000	0.635321	0.317660	+	0.948205i	$0.397103\pi$
$992$	− 4.00000i	− 0.127000i
$993$	− 1.00000i	− 0.0317340i
$994$	6.00000	0.190308
$995$	0	0
$996$	−6.00000	−0.190117
$997$	− 8.00000i	− 0.253363i	−0.991943	−	0.126681i	$-0.959567\pi$
$997$	− 8.00000i	− 0.253363i	0.991943	−	0.126681i	$-0.0404325\pi$
$998$	4.00000i	0.126618i
$999$	10.0000	0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.b.b.799.2		2
5.2	odd	4		38.2.a.a.1.1	✓	1
5.3	odd	4		950.2.a.d.1.1		1
5.4	even	2	inner	950.2.b.b.799.1		2
15.2	even	4		342.2.a.e.1.1		1
15.8	even	4		8550.2.a.m.1.1		1
20.3	even	4		7600.2.a.n.1.1		1
20.7	even	4		304.2.a.c.1.1		1
35.27	even	4		1862.2.a.b.1.1		1
40.27	even	4		1216.2.a.m.1.1		1
40.37	odd	4		1216.2.a.e.1.1		1
55.32	even	4		4598.2.a.p.1.1		1
60.47	odd	4		2736.2.a.n.1.1		1
65.12	odd	4		6422.2.a.h.1.1		1
95.2	even	36		722.2.e.e.99.1		6
95.7	odd	12		722.2.c.e.429.1		2
95.12	even	12		722.2.c.c.429.1		2
95.17	odd	36		722.2.e.f.99.1		6
95.22	even	36		722.2.e.e.389.1		6
95.27	even	12		722.2.c.c.653.1		2
95.32	even	36		722.2.e.e.245.1		6
95.37	even	4		722.2.a.e.1.1		1
95.42	odd	36		722.2.e.f.415.1		6
95.47	odd	36		722.2.e.f.423.1		6
95.52	even	36		722.2.e.e.595.1		6
95.62	odd	36		722.2.e.f.595.1		6
95.67	even	36		722.2.e.e.423.1		6
95.72	even	36		722.2.e.e.415.1		6
95.82	odd	36		722.2.e.f.245.1		6
95.87	odd	12		722.2.c.e.653.1		2
95.92	odd	36		722.2.e.f.389.1		6
285.227	odd	4		6498.2.a.f.1.1		1
380.227	odd	4		5776.2.a.m.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.a.a.1.1	✓	1	5.2	odd	4
304.2.a.c.1.1		1	20.7	even	4
342.2.a.e.1.1		1	15.2	even	4
722.2.a.e.1.1		1	95.37	even	4
722.2.c.c.429.1		2	95.12	even	12
722.2.c.c.653.1		2	95.27	even	12
722.2.c.e.429.1		2	95.7	odd	12
722.2.c.e.653.1		2	95.87	odd	12
722.2.e.e.99.1		6	95.2	even	36
722.2.e.e.245.1		6	95.32	even	36
722.2.e.e.389.1		6	95.22	even	36
722.2.e.e.415.1		6	95.72	even	36
722.2.e.e.423.1		6	95.67	even	36
722.2.e.e.595.1		6	95.52	even	36
722.2.e.f.99.1		6	95.17	odd	36
722.2.e.f.245.1		6	95.82	odd	36
722.2.e.f.389.1		6	95.92	odd	36
722.2.e.f.415.1		6	95.42	odd	36
722.2.e.f.423.1		6	95.47	odd	36
722.2.e.f.595.1		6	95.62	odd	36
950.2.a.d.1.1		1	5.3	odd	4
950.2.b.b.799.1		2	5.4	even	2	inner
950.2.b.b.799.2		2	1.1	even	1	trivial
1216.2.a.e.1.1		1	40.37	odd	4
1216.2.a.m.1.1		1	40.27	even	4
1862.2.a.b.1.1		1	35.27	even	4
2736.2.a.n.1.1		1	60.47	odd	4
4598.2.a.p.1.1		1	55.32	even	4
5776.2.a.m.1.1		1	380.227	odd	4
6422.2.a.h.1.1		1	65.12	odd	4
6498.2.a.f.1.1		1	285.227	odd	4
7600.2.a.n.1.1		1	20.3	even	4
8550.2.a.m.1.1		1	15.8	even	4

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +1.00000i q^{7} -1.00000i q^{8} +2.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +1.00000i q^{7} -1.00000i q^{8} +2.00000 q^{9} -6.00000 q^{11} -1.00000i q^{12} +5.00000i q^{13} -1.00000 q^{14} +1.00000 q^{16} -3.00000i q^{17} +2.00000i q^{18} -1.00000 q^{19} -1.00000 q^{21} -6.00000i q^{22} +3.00000i q^{23} +1.00000 q^{24} -5.00000 q^{26} +5.00000i q^{27} -1.00000i q^{28} -9.00000 q^{29} -4.00000 q^{31} +1.00000i q^{32} -6.00000i q^{33} +3.00000 q^{34} -2.00000 q^{36} -2.00000i q^{37} -1.00000i q^{38} -5.00000 q^{39} -1.00000i q^{42} +8.00000i q^{43} +6.00000 q^{44} -3.00000 q^{46} +1.00000i q^{48} +6.00000 q^{49} +3.00000 q^{51} -5.00000i q^{52} -3.00000i q^{53} -5.00000 q^{54} +1.00000 q^{56} -1.00000i q^{57} -9.00000i q^{58} -9.00000 q^{59} -10.0000 q^{61} -4.00000i q^{62} +2.00000i q^{63} -1.00000 q^{64} +6.00000 q^{66} -5.00000i q^{67} +3.00000i q^{68} -3.00000 q^{69} -6.00000 q^{71} -2.00000i q^{72} -7.00000i q^{73} +2.00000 q^{74} +1.00000 q^{76} -6.00000i q^{77} -5.00000i q^{78} +10.0000 q^{79} +1.00000 q^{81} -6.00000i q^{83} +1.00000 q^{84} -8.00000 q^{86} -9.00000i q^{87} +6.00000i q^{88} +12.0000 q^{89} -5.00000 q^{91} -3.00000i q^{92} -4.00000i q^{93} -1.00000 q^{96} +10.0000i q^{97} +6.00000i q^{98} -12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} - 2 q^{6} + 4 q^{9}+O(q^{10}) \) 2 * q - 2 * q^4 - 2 * q^6 + 4 * q^9	\( 2 q - 2 q^{4} - 2 q^{6} + 4 q^{9} - 12 q^{11} - 2 q^{14} + 2 q^{16} - 2 q^{19} - 2 q^{21} + 2 q^{24} - 10 q^{26} - 18 q^{29} - 8 q^{31} + 6 q^{34} - 4 q^{36} - 10 q^{39} + 12 q^{44} - 6 q^{46} + 12 q^{49} + 6 q^{51} - 10 q^{54} + 2 q^{56} - 18 q^{59} - 20 q^{61} - 2 q^{64} + 12 q^{66} - 6 q^{69} - 12 q^{71} + 4 q^{74} + 2 q^{76} + 20 q^{79} + 2 q^{81} + 2 q^{84} - 16 q^{86} + 24 q^{89} - 10 q^{91} - 2 q^{96} - 24 q^{99}+O(q^{100}) \) 2 * q - 2 * q^4 - 2 * q^6 + 4 * q^9 - 12 * q^11 - 2 * q^14 + 2 * q^16 - 2 * q^19 - 2 * q^21 + 2 * q^24 - 10 * q^26 - 18 * q^29 - 8 * q^31 + 6 * q^34 - 4 * q^36 - 10 * q^39 + 12 * q^44 - 6 * q^46 + 12 * q^49 + 6 * q^51 - 10 * q^54 + 2 * q^56 - 18 * q^59 - 20 * q^61 - 2 * q^64 + 12 * q^66 - 6 * q^69 - 12 * q^71 + 4 * q^74 + 2 * q^76 + 20 * q^79 + 2 * q^81 + 2 * q^84 - 16 * q^86 + 24 * q^89 - 10 * q^91 - 2 * q^96 - 24 * q^99

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