LMFDB - Embedded newform 4025.2.a.z.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 3 x^{13} - 18 x^{12} + 58 x^{11} + 111 x^{10} - 414 x^{9} - 244 x^{8} + 1330 x^{7} - 27 x^{6} + \cdots - 9 $ x^14 - 3x^13 - 18x^12 + 58x^11 + 111x^10 - 414x^9 - 244x^8 + 1330x^7 - 27x^6 - 1853x^5 + 539x^4 + 891x^3 - 218x^2 - 133*x - 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-1.51853$ of defining polynomial
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.51853 q^{2} -0.630051 q^{3} +0.305932 q^{4} -0.956751 q^{6} -1.00000 q^{7} -2.57249 q^{8} -2.60304 q^{9} +O(q^{10})$	\(q+1.51853 q^{2} -0.630051 q^{3} +0.305932 q^{4} -0.956751 q^{6} -1.00000 q^{7} -2.57249 q^{8} -2.60304 q^{9} +4.75041 q^{11} -0.192753 q^{12} -2.10352 q^{13} -1.51853 q^{14} -4.51827 q^{16} +5.16017 q^{17} -3.95279 q^{18} +5.33686 q^{19} +0.630051 q^{21} +7.21364 q^{22} -1.00000 q^{23} +1.62080 q^{24} -3.19425 q^{26} +3.53020 q^{27} -0.305932 q^{28} -5.93659 q^{29} +1.56328 q^{31} -1.71614 q^{32} -2.99300 q^{33} +7.83587 q^{34} -0.796353 q^{36} -8.19571 q^{37} +8.10418 q^{38} +1.32532 q^{39} +6.11124 q^{41} +0.956751 q^{42} -4.23005 q^{43} +1.45330 q^{44} -1.51853 q^{46} -11.8512 q^{47} +2.84674 q^{48} +1.00000 q^{49} -3.25117 q^{51} -0.643534 q^{52} -4.68316 q^{53} +5.36071 q^{54} +2.57249 q^{56} -3.36249 q^{57} -9.01488 q^{58} -6.62464 q^{59} -13.8091 q^{61} +2.37389 q^{62} +2.60304 q^{63} +6.43052 q^{64} -4.54496 q^{66} +5.37143 q^{67} +1.57866 q^{68} +0.630051 q^{69} -1.79472 q^{71} +6.69629 q^{72} -4.69642 q^{73} -12.4454 q^{74} +1.63272 q^{76} -4.75041 q^{77} +2.01254 q^{78} -11.3675 q^{79} +5.58490 q^{81} +9.28010 q^{82} -7.39394 q^{83} +0.192753 q^{84} -6.42345 q^{86} +3.74035 q^{87} -12.2204 q^{88} -9.67563 q^{89} +2.10352 q^{91} -0.305932 q^{92} -0.984947 q^{93} -17.9963 q^{94} +1.08126 q^{96} -12.7456 q^{97} +1.51853 q^{98} -12.3655 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9}+O(q^{10}) $ 14 * q - 3 * q^2 - 4 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9	$ 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9} + 5 q^{11} - 17 q^{12} - 11 q^{13} + 3 q^{14} + 23 q^{16} - 3 q^{17} - 15 q^{18} - 2 q^{19} + 4 q^{21} - 23 q^{22} - 14 q^{23} - 12 q^{24} - 9 q^{26} - 25 q^{27} - 17 q^{28} + 7 q^{29} - 3 q^{31} - 24 q^{32} - 6 q^{33} - 14 q^{34} + 13 q^{36} - 22 q^{37} - 20 q^{38} - 10 q^{39} - 17 q^{41} + 4 q^{42} - 18 q^{43} + 28 q^{44} + 3 q^{46} - 30 q^{47} - 8 q^{48} + 14 q^{49} + 4 q^{51} - 8 q^{52} - 11 q^{53} + 20 q^{54} + 3 q^{56} - 18 q^{57} - 38 q^{58} - 22 q^{59} - 8 q^{61} + 22 q^{62} - 18 q^{63} + 29 q^{64} - 9 q^{66} - 39 q^{67} - q^{68} + 4 q^{69} - 5 q^{71} + 24 q^{72} - 18 q^{73} + 35 q^{74} - 41 q^{76} - 5 q^{77} + 22 q^{78} + 10 q^{79} + 2 q^{81} + 8 q^{82} - 24 q^{83} + 17 q^{84} - 26 q^{86} - 5 q^{87} - 58 q^{88} + 25 q^{89} + 11 q^{91} - 17 q^{92} - 47 q^{93} - 2 q^{94} - 117 q^{96} - 43 q^{97} - 3 q^{98} + 55 q^{99}+O(q^{100}) $ 14 * q - 3 * q^2 - 4 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9 + 5 * q^11 - 17 * q^12 - 11 * q^13 + 3 * q^14 + 23 * q^16 - 3 * q^17 - 15 * q^18 - 2 * q^19 + 4 * q^21 - 23 * q^22 - 14 * q^23 - 12 * q^24 - 9 * q^26 - 25 * q^27 - 17 * q^28 + 7 * q^29 - 3 * q^31 - 24 * q^32 - 6 * q^33 - 14 * q^34 + 13 * q^36 - 22 * q^37 - 20 * q^38 - 10 * q^39 - 17 * q^41 + 4 * q^42 - 18 * q^43 + 28 * q^44 + 3 * q^46 - 30 * q^47 - 8 * q^48 + 14 * q^49 + 4 * q^51 - 8 * q^52 - 11 * q^53 + 20 * q^54 + 3 * q^56 - 18 * q^57 - 38 * q^58 - 22 * q^59 - 8 * q^61 + 22 * q^62 - 18 * q^63 + 29 * q^64 - 9 * q^66 - 39 * q^67 - q^68 + 4 * q^69 - 5 * q^71 + 24 * q^72 - 18 * q^73 + 35 * q^74 - 41 * q^76 - 5 * q^77 + 22 * q^78 + 10 * q^79 + 2 * q^81 + 8 * q^82 - 24 * q^83 + 17 * q^84 - 26 * q^86 - 5 * q^87 - 58 * q^88 + 25 * q^89 + 11 * q^91 - 17 * q^92 - 47 * q^93 - 2 * q^94 - 117 * q^96 - 43 * q^97 - 3 * q^98 + 55 * 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 $

$2$	1.51853	1.07376	0.536881	−	0.843658i	$-0.319602\pi$
$2$	1.51853	1.07376	0.536881	+	0.843658i	$0.319602\pi$
$3$	−0.630051	−0.363760	−0.181880	−	0.983321i	$-0.558218\pi$
$3$	−0.630051	−0.363760	−0.181880	+	0.983321i	$0.558218\pi$
$4$	0.305932	0.152966
$5$	0	0
$5$	0	0
$6$	−0.956751	−0.390592
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.57249	−0.909513
$9$	−2.60304	−0.867679
$10$	0	0
$11$	4.75041	1.43230	0.716151	−	0.697945i	$-0.245902\pi$
$11$	4.75041	1.43230	0.716151	+	0.697945i	$0.245902\pi$
$12$	−0.192753	−0.0556430
$13$	−2.10352	−0.583410	−0.291705	−	0.956508i	$-0.594223\pi$
$13$	−2.10352	−0.583410	−0.291705	+	0.956508i	$0.594223\pi$
$14$	−1.51853	−0.405844
$15$	0	0
$16$	−4.51827	−1.12957
$17$	5.16017	1.25153	0.625763	−	0.780014i	$-0.284788\pi$
$17$	5.16017	1.25153	0.625763	+	0.780014i	$0.284788\pi$
$18$	−3.95279	−0.931681
$19$	5.33686	1.22436	0.612179	−	0.790719i	$-0.290293\pi$
$19$	5.33686	1.22436	0.612179	+	0.790719i	$0.290293\pi$
$20$	0	0
$21$	0.630051	0.137488
$22$	7.21364	1.53795
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.62080	0.330845
$25$	0	0
$26$	−3.19425	−0.626444
$27$	3.53020	0.679387
$28$	−0.305932	−0.0578158
$29$	−5.93659	−1.10240	−0.551198	−	0.834374i	$-0.685829\pi$
$29$	−5.93659	−1.10240	−0.551198	+	0.834374i	$0.685829\pi$
$30$	0	0
$31$	1.56328	0.280774	0.140387	−	0.990097i	$-0.455165\pi$
$31$	1.56328	0.280774	0.140387	+	0.990097i	$0.455165\pi$
$32$	−1.71614	−0.303374
$33$	−2.99300	−0.521014
$34$	7.83587	1.34384
$35$	0	0
$36$	−0.796353	−0.132726
$37$	−8.19571	−1.34737	−0.673683	−	0.739020i	$-0.735289\pi$
$37$	−8.19571	−1.34737	−0.673683	+	0.739020i	$0.735289\pi$
$38$	8.10418	1.31467
$39$	1.32532	0.212221
$40$	0	0
$41$	6.11124	0.954415	0.477208	−	0.878791i	$-0.341649\pi$
$41$	6.11124	0.954415	0.477208	+	0.878791i	$0.341649\pi$
$42$	0.956751	0.147630
$43$	−4.23005	−0.645076	−0.322538	−	0.946556i	$-0.604536\pi$
$43$	−4.23005	−0.645076	−0.322538	+	0.946556i	$0.604536\pi$
$44$	1.45330	0.219094
$45$	0	0
$46$	−1.51853	−0.223895
$47$	−11.8512	−1.72867	−0.864334	−	0.502918i	$-0.832260\pi$
$47$	−11.8512	−1.72867	−0.864334	+	0.502918i	$0.832260\pi$
$48$	2.84674	0.410892
$49$	1.00000	0.142857
$50$	0	0
$51$	−3.25117	−0.455255
$52$	−0.643534	−0.0892421
$53$	−4.68316	−0.643282	−0.321641	−	0.946862i	$-0.604234\pi$
$53$	−4.68316	−0.643282	−0.321641	+	0.946862i	$0.604234\pi$
$54$	5.36071	0.729500
$55$	0	0
$56$	2.57249	0.343764
$57$	−3.36249	−0.445373
$58$	−9.01488	−1.18371
$59$	−6.62464	−0.862455	−0.431227	−	0.902243i	$-0.641919\pi$
$59$	−6.62464	−0.862455	−0.431227	+	0.902243i	$0.641919\pi$
$60$	0	0
$61$	−13.8091	−1.76807	−0.884035	−	0.467421i	$-0.845183\pi$
$61$	−13.8091	−1.76807	−0.884035	+	0.467421i	$0.845183\pi$
$62$	2.37389	0.301484
$63$	2.60304	0.327952
$64$	6.43052	0.803816
$65$	0	0
$66$	−4.54496	−0.559446
$67$	5.37143	0.656225	0.328112	−	0.944639i	$-0.393588\pi$
$67$	5.37143	0.656225	0.328112	+	0.944639i	$0.393588\pi$
$68$	1.57866	0.191441
$69$	0.630051	0.0758492
$70$	0	0
$71$	−1.79472	−0.212994	−0.106497	−	0.994313i	$-0.533963\pi$
$71$	−1.79472	−0.212994	−0.106497	+	0.994313i	$0.533963\pi$
$72$	6.69629	0.789165
$73$	−4.69642	−0.549675	−0.274837	−	0.961491i	$-0.588624\pi$
$73$	−4.69642	−0.549675	−0.274837	+	0.961491i	$0.588624\pi$
$74$	−12.4454	−1.44675
$75$	0	0
$76$	1.63272	0.187286
$77$	−4.75041	−0.541359
$78$	2.01254	0.227875
$79$	−11.3675	−1.27895	−0.639473	−	0.768814i	$-0.720847\pi$
$79$	−11.3675	−1.27895	−0.639473	+	0.768814i	$0.720847\pi$
$80$	0	0
$81$	5.58490	0.620545
$82$	9.28010	1.02482
$83$	−7.39394	−0.811590	−0.405795	−	0.913964i	$-0.633005\pi$
$83$	−7.39394	−0.811590	−0.405795	+	0.913964i	$0.633005\pi$
$84$	0.192753	0.0210311
$85$	0	0
$86$	−6.42345	−0.692659
$87$	3.74035	0.401008
$88$	−12.2204	−1.30270
$89$	−9.67563	−1.02561	−0.512807	−	0.858504i	$-0.671394\pi$
$89$	−9.67563	−1.02561	−0.512807	+	0.858504i	$0.671394\pi$
$90$	0	0
$91$	2.10352	0.220508
$92$	−0.305932	−0.0318957
$93$	−0.984947	−0.102134
$94$	−17.9963	−1.85618
$95$	0	0
$96$	1.08126	0.110355
$97$	−12.7456	−1.29412	−0.647061	−	0.762438i	$-0.724002\pi$
$97$	−12.7456	−1.29412	−0.647061	+	0.762438i	$0.724002\pi$
$98$	1.51853	0.153395
$99$	−12.3655	−1.24278
$100$	0	0
$101$	−0.636924	−0.0633763	−0.0316881	−	0.999498i	$-0.510088\pi$
$101$	−0.636924	−0.0633763	−0.0316881	+	0.999498i	$0.510088\pi$
$102$	−4.93700	−0.488836
$103$	−6.41998	−0.632579	−0.316290	−	0.948663i	$-0.602437\pi$
$103$	−6.41998	−0.632579	−0.316290	+	0.948663i	$0.602437\pi$
$104$	5.41128	0.530619
$105$	0	0
$106$	−7.11152	−0.690732
$107$	17.3766	1.67986	0.839930	−	0.542695i	$-0.182596\pi$
$107$	17.3766	1.67986	0.839930	+	0.542695i	$0.182596\pi$
$108$	1.08000	0.103923
$109$	4.57000	0.437727	0.218863	−	0.975756i	$-0.429765\pi$
$109$	4.57000	0.437727	0.218863	+	0.975756i	$0.429765\pi$
$110$	0	0
$111$	5.16371	0.490118
$112$	4.51827	0.426936
$113$	−13.3896	−1.25959	−0.629795	−	0.776761i	$-0.716861\pi$
$113$	−13.3896	−1.25959	−0.629795	+	0.776761i	$0.716861\pi$
$114$	−5.10604	−0.478225
$115$	0	0
$116$	−1.81619	−0.168629
$117$	5.47553	0.506213
$118$	−10.0597	−0.926072
$119$	−5.16017	−0.473032
$120$	0	0
$121$	11.5664	1.05149
$122$	−20.9695	−1.89849
$123$	−3.85039	−0.347178
$124$	0.478259	0.0429489
$125$	0	0
$126$	3.95279	0.352142
$127$	10.1264	0.898576	0.449288	−	0.893387i	$-0.351678\pi$
$127$	10.1264	0.898576	0.449288	+	0.893387i	$0.351678\pi$
$128$	13.1972	1.16648
$129$	2.66515	0.234653
$130$	0	0
$131$	−16.5042	−1.44198	−0.720991	−	0.692944i	$-0.756313\pi$
$131$	−16.5042	−1.44198	−0.720991	+	0.692944i	$0.756313\pi$
$132$	−0.915656	−0.0796976
$133$	−5.33686	−0.462764
$134$	8.15668	0.704630
$135$	0	0
$136$	−13.2745	−1.13828
$137$	−4.82625	−0.412334	−0.206167	−	0.978517i	$-0.566099\pi$
$137$	−4.82625	−0.412334	−0.206167	+	0.978517i	$0.566099\pi$
$138$	0.956751	0.0814441
$139$	7.44982	0.631885	0.315943	−	0.948778i	$-0.397679\pi$
$139$	7.44982	0.631885	0.315943	+	0.948778i	$0.397679\pi$
$140$	0	0
$141$	7.46683	0.628820
$142$	−2.72533	−0.228705
$143$	−9.99256	−0.835620
$144$	11.7612	0.980102
$145$	0	0
$146$	−7.13166	−0.590220
$147$	−0.630051	−0.0519657
$148$	−2.50733	−0.206102
$149$	8.87399	0.726986	0.363493	−	0.931597i	$-0.381584\pi$
$149$	8.87399	0.726986	0.363493	+	0.931597i	$0.381584\pi$
$150$	0	0
$151$	−6.97681	−0.567765	−0.283882	−	0.958859i	$-0.591623\pi$
$151$	−6.97681	−0.567765	−0.283882	+	0.958859i	$0.591623\pi$
$152$	−13.7290	−1.11357
$153$	−13.4321	−1.08592
$154$	−7.21364	−0.581292
$155$	0	0
$156$	0.405459	0.0324627
$157$	−11.6867	−0.932697	−0.466348	−	0.884601i	$-0.654431\pi$
$157$	−11.6867	−0.932697	−0.466348	+	0.884601i	$0.654431\pi$
$158$	−17.2619	−1.37328
$159$	2.95063	0.234000
$160$	0	0
$161$	1.00000	0.0788110
$162$	8.48084	0.666318
$163$	8.27924	0.648480	0.324240	−	0.945975i	$-0.394891\pi$
$163$	8.27924	0.648480	0.324240	+	0.945975i	$0.394891\pi$
$164$	1.86963	0.145993
$165$	0	0
$166$	−11.2279	−0.871456
$167$	2.06237	0.159591	0.0797953	−	0.996811i	$-0.474573\pi$
$167$	2.06237	0.159591	0.0797953	+	0.996811i	$0.474573\pi$
$168$	−1.62080	−0.125048
$169$	−8.57522	−0.659632
$170$	0	0
$171$	−13.8920	−1.06235
$172$	−1.29411	−0.0986749
$173$	13.3560	1.01544	0.507719	−	0.861523i	$-0.330489\pi$
$173$	13.3560	1.01544	0.507719	+	0.861523i	$0.330489\pi$
$174$	5.67984	0.430587
$175$	0	0
$176$	−21.4636	−1.61788
$177$	4.17386	0.313727
$178$	−14.6927	−1.10127
$179$	22.3346	1.66937	0.834683	−	0.550730i	$-0.185651\pi$
$179$	22.3346	1.66937	0.834683	+	0.550730i	$0.185651\pi$
$180$	0	0
$181$	8.34328	0.620151	0.310076	−	0.950712i	$-0.399646\pi$
$181$	8.34328	0.620151	0.310076	+	0.950712i	$0.399646\pi$
$182$	3.19425	0.236774
$183$	8.70042	0.643153
$184$	2.57249	0.189647
$185$	0	0
$186$	−1.49567	−0.109668
$187$	24.5129	1.79256
$188$	−3.62565	−0.264428
$189$	−3.53020	−0.256784
$190$	0	0
$191$	9.28415	0.671778	0.335889	−	0.941902i	$-0.390963\pi$
$191$	9.28415	0.671778	0.335889	+	0.941902i	$0.390963\pi$
$192$	−4.05156	−0.292396
$193$	−5.65526	−0.407074	−0.203537	−	0.979067i	$-0.565244\pi$
$193$	−5.65526	−0.407074	−0.203537	+	0.979067i	$0.565244\pi$
$194$	−19.3546	−1.38958
$195$	0	0
$196$	0.305932	0.0218523
$197$	−27.4161	−1.95332	−0.976659	−	0.214795i	$-0.931092\pi$
$197$	−27.4161	−1.95332	−0.976659	+	0.214795i	$0.931092\pi$
$198$	−18.7774	−1.33445
$199$	23.7006	1.68009	0.840046	−	0.542515i	$-0.182528\pi$
$199$	23.7006	1.68009	0.840046	+	0.542515i	$0.182528\pi$
$200$	0	0
$201$	−3.38428	−0.238708
$202$	−0.967187	−0.0680511
$203$	5.93659	0.416667
$204$	−0.994639	−0.0696386
$205$	0	0
$206$	−9.74893	−0.679240
$207$	2.60304	0.180923
$208$	9.50425	0.659001
$209$	25.3523	1.75365
$210$	0	0
$211$	27.0437	1.86177	0.930883	−	0.365317i	$-0.119040\pi$
$211$	27.0437	1.86177	0.930883	+	0.365317i	$0.119040\pi$
$212$	−1.43273	−0.0984004
$213$	1.13076	0.0774786
$214$	26.3869	1.80377
$215$	0	0
$216$	−9.08141	−0.617911
$217$	−1.56328	−0.106122
$218$	6.93968	0.470015
$219$	2.95899	0.199950
$220$	0	0
$221$	−10.8545	−0.730153
$222$	7.84125	0.526270
$223$	−3.57241	−0.239226	−0.119613	−	0.992821i	$-0.538165\pi$
$223$	−3.57241	−0.239226	−0.119613	+	0.992821i	$0.538165\pi$
$224$	1.71614	0.114665
$225$	0	0
$226$	−20.3326	−1.35250
$227$	−0.202464	−0.0134380	−0.00671901	−	0.999977i	$-0.502139\pi$
$227$	−0.202464	−0.0134380	−0.00671901	+	0.999977i	$0.502139\pi$
$228$	−1.02870	−0.0681270
$229$	−12.7126	−0.840073	−0.420036	−	0.907507i	$-0.637983\pi$
$229$	−12.7126	−0.840073	−0.420036	+	0.907507i	$0.637983\pi$
$230$	0	0
$231$	2.99300	0.196925
$232$	15.2718	1.00264
$233$	−2.97024	−0.194587	−0.0972935	−	0.995256i	$-0.531019\pi$
$233$	−2.97024	−0.194587	−0.0972935	+	0.995256i	$0.531019\pi$
$234$	8.31475	0.543552
$235$	0	0
$236$	−2.02669	−0.131926
$237$	7.16211	0.465229
$238$	−7.83587	−0.507924
$239$	−7.00791	−0.453304	−0.226652	−	0.973976i	$-0.572778\pi$
$239$	−7.00791	−0.453304	−0.226652	+	0.973976i	$0.572778\pi$
$240$	0	0
$241$	8.64331	0.556764	0.278382	−	0.960470i	$-0.410202\pi$
$241$	8.64331	0.556764	0.278382	+	0.960470i	$0.410202\pi$
$242$	17.5639	1.12905
$243$	−14.1094	−0.905116
$244$	−4.22464	−0.270455
$245$	0	0
$246$	−5.84694	−0.372787
$247$	−11.2262	−0.714304
$248$	−4.02153	−0.255367
$249$	4.65856	0.295224
$250$	0	0
$251$	−26.0742	−1.64579	−0.822894	−	0.568196i	$-0.807642\pi$
$251$	−26.0742	−1.64579	−0.822894	+	0.568196i	$0.807642\pi$
$252$	0.796353	0.0501655
$253$	−4.75041	−0.298656
$254$	15.3773	0.964857
$255$	0	0
$256$	7.17934	0.448709
$257$	0.0970434	0.00605340	0.00302670	−	0.999995i	$-0.499037\pi$
$257$	0.0970434	0.00605340	0.00302670	+	0.999995i	$0.499037\pi$
$258$	4.04710	0.251962
$259$	8.19571	0.509256
$260$	0	0
$261$	15.4531	0.956526
$262$	−25.0622	−1.54835
$263$	−2.18380	−0.134659	−0.0673295	−	0.997731i	$-0.521448\pi$
$263$	−2.18380	−0.134659	−0.0673295	+	0.997731i	$0.521448\pi$
$264$	7.69947	0.473870
$265$	0	0
$266$	−8.10418	−0.496899
$267$	6.09614	0.373078
$268$	1.64330	0.100380
$269$	−6.35091	−0.387222	−0.193611	−	0.981078i	$-0.562020\pi$
$269$	−6.35091	−0.387222	−0.193611	+	0.981078i	$0.562020\pi$
$270$	0	0
$271$	−7.02861	−0.426957	−0.213479	−	0.976948i	$-0.568479\pi$
$271$	−7.02861	−0.426957	−0.213479	+	0.976948i	$0.568479\pi$
$272$	−23.3150	−1.41368
$273$	−1.32532	−0.0802121
$274$	−7.32880	−0.442749
$275$	0	0
$276$	0.192753	0.0116024
$277$	−9.88291	−0.593806	−0.296903	−	0.954908i	$-0.595954\pi$
$277$	−9.88291	−0.593806	−0.296903	+	0.954908i	$0.595954\pi$
$278$	11.3128	0.678495
$279$	−4.06928	−0.243621
$280$	0	0
$281$	15.0842	0.899849	0.449925	−	0.893067i	$-0.351451\pi$
$281$	15.0842	0.899849	0.449925	+	0.893067i	$0.351451\pi$
$282$	11.3386	0.675204
$283$	−16.7011	−0.992777	−0.496388	−	0.868101i	$-0.665341\pi$
$283$	−16.7011	−0.992777	−0.496388	+	0.868101i	$0.665341\pi$
$284$	−0.549062	−0.0325808
$285$	0	0
$286$	−15.1740	−0.897258
$287$	−6.11124	−0.360735
$288$	4.46718	0.263231
$289$	9.62735	0.566315
$290$	0	0
$291$	8.03039	0.470750
$292$	−1.43679	−0.0840817
$293$	−14.6468	−0.855675	−0.427838	−	0.903856i	$-0.640724\pi$
$293$	−14.6468	−0.855675	−0.427838	+	0.903856i	$0.640724\pi$
$294$	−0.956751	−0.0557989
$295$	0	0
$296$	21.0834	1.22545
$297$	16.7699	0.973088
$298$	13.4754	0.780610
$299$	2.10352	0.121649
$300$	0	0
$301$	4.23005	0.243816
$302$	−10.5945	−0.609645
$303$	0.401294	0.0230538
$304$	−24.1134	−1.38300
$305$	0	0
$306$	−20.3971	−1.16602
$307$	−10.8376	−0.618536	−0.309268	−	0.950975i	$-0.600084\pi$
$307$	−10.8376	−0.618536	−0.309268	+	0.950975i	$0.600084\pi$
$308$	−1.45330	−0.0828097
$309$	4.04491	0.230107
$310$	0	0
$311$	12.7454	0.722725	0.361362	−	0.932425i	$-0.382312\pi$
$311$	12.7454	0.722725	0.361362	+	0.932425i	$0.382312\pi$
$312$	−3.40938	−0.193018
$313$	29.0450	1.64172	0.820861	−	0.571128i	$-0.193494\pi$
$313$	29.0450	1.64172	0.820861	+	0.571128i	$0.193494\pi$
$314$	−17.7465	−1.00149
$315$	0	0
$316$	−3.47769	−0.195635
$317$	−18.9107	−1.06213	−0.531066	−	0.847330i	$-0.678208\pi$
$317$	−18.9107	−1.06213	−0.531066	+	0.847330i	$0.678208\pi$
$318$	4.48062	0.251261
$319$	−28.2012	−1.57897
$320$	0	0
$321$	−10.9481	−0.611066
$322$	1.51853	0.0846244
$323$	27.5391	1.53232
$324$	1.70860	0.0949224
$325$	0	0
$326$	12.5723	0.696314
$327$	−2.87933	−0.159227
$328$	−15.7211	−0.868053
$329$	11.8512	0.653375
$330$	0	0
$331$	24.4740	1.34521	0.672606	−	0.740001i	$-0.265175\pi$
$331$	24.4740	1.34521	0.672606	+	0.740001i	$0.265175\pi$
$332$	−2.26205	−0.124146
$333$	21.3337	1.16908
$334$	3.13176	0.171362
$335$	0	0
$336$	−2.84674	−0.155302
$337$	20.9933	1.14358	0.571789	−	0.820401i	$-0.306250\pi$
$337$	20.9933	1.14358	0.571789	+	0.820401i	$0.306250\pi$
$338$	−13.0217	−0.708289
$339$	8.43615	0.458189
$340$	0	0
$341$	7.42623	0.402153
$342$	−21.0955	−1.14071
$343$	−1.00000	−0.0539949
$344$	10.8818	0.586705
$345$	0	0
$346$	20.2815	1.09034
$347$	−20.5758	−1.10457	−0.552284	−	0.833656i	$-0.686244\pi$
$347$	−20.5758	−1.10457	−0.552284	+	0.833656i	$0.686244\pi$
$348$	1.14430	0.0613407
$349$	31.9324	1.70930	0.854651	−	0.519203i	$-0.173771\pi$
$349$	31.9324	1.70930	0.854651	+	0.519203i	$0.173771\pi$
$350$	0	0
$351$	−7.42583	−0.396361
$352$	−8.15239	−0.434524
$353$	−12.9730	−0.690483	−0.345241	−	0.938514i	$-0.612203\pi$
$353$	−12.9730	−0.690483	−0.345241	+	0.938514i	$0.612203\pi$
$354$	6.33813	0.336868
$355$	0	0
$356$	−2.96009	−0.156884
$357$	3.25117	0.172070
$358$	33.9158	1.79250
$359$	−34.3005	−1.81031	−0.905157	−	0.425078i	$-0.860247\pi$
$359$	−34.3005	−1.81031	−0.905157	+	0.425078i	$0.860247\pi$
$360$	0	0
$361$	9.48204	0.499055
$362$	12.6695	0.665895
$363$	−7.28742	−0.382490
$364$	0.643534	0.0337303
$365$	0	0
$366$	13.2118	0.690594
$367$	11.7322	0.612417	0.306208	−	0.951964i	$-0.400940\pi$
$367$	11.7322	0.612417	0.306208	+	0.951964i	$0.400940\pi$
$368$	4.51827	0.235531
$369$	−15.9078	−0.828126
$370$	0	0
$371$	4.68316	0.243138
$372$	−0.301327	−0.0156231
$373$	−21.0980	−1.09241	−0.546206	−	0.837651i	$-0.683928\pi$
$373$	−21.0980	−1.09241	−0.546206	+	0.837651i	$0.683928\pi$
$374$	37.2236	1.92479
$375$	0	0
$376$	30.4870	1.57225
$377$	12.4877	0.643149
$378$	−5.36071	−0.275725
$379$	30.5644	1.56999	0.784993	−	0.619505i	$-0.212667\pi$
$379$	30.5644	1.56999	0.784993	+	0.619505i	$0.212667\pi$
$380$	0	0
$381$	−6.38017	−0.326866
$382$	14.0983	0.721330
$383$	−7.70404	−0.393658	−0.196829	−	0.980438i	$-0.563064\pi$
$383$	−7.70404	−0.393658	−0.196829	+	0.980438i	$0.563064\pi$
$384$	−8.31493	−0.424319
$385$	0	0
$386$	−8.58767	−0.437101
$387$	11.0110	0.559719
$388$	−3.89930	−0.197957
$389$	3.52083	0.178513	0.0892567	−	0.996009i	$-0.471551\pi$
$389$	3.52083	0.178513	0.0892567	+	0.996009i	$0.471551\pi$
$390$	0	0
$391$	−5.16017	−0.260961
$392$	−2.57249	−0.129930
$393$	10.3985	0.524536
$394$	−41.6322	−2.09740
$395$	0	0
$396$	−3.78300	−0.190103
$397$	−25.2507	−1.26729	−0.633647	−	0.773622i	$-0.718443\pi$
$397$	−25.2507	−1.26729	−0.633647	+	0.773622i	$0.718443\pi$
$398$	35.9901	1.80402
$399$	3.36249	0.168335
$400$	0	0
$401$	1.36125	0.0679775	0.0339887	−	0.999422i	$-0.489179\pi$
$401$	1.36125	0.0679775	0.0339887	+	0.999422i	$0.489179\pi$
$402$	−5.13912	−0.256316
$403$	−3.28839	−0.163806
$404$	−0.194856	−0.00969443
$405$	0	0
$406$	9.01488	0.447401
$407$	−38.9330	−1.92984
$408$	8.36361	0.414060
$409$	−6.15135	−0.304165	−0.152082	−	0.988368i	$-0.548598\pi$
$409$	−6.15135	−0.304165	−0.152082	+	0.988368i	$0.548598\pi$
$410$	0	0
$411$	3.04078	0.149991
$412$	−1.96408	−0.0967633
$413$	6.62464	0.325977
$414$	3.95279	0.194269
$415$	0	0
$416$	3.60994	0.176992
$417$	−4.69377	−0.229855
$418$	38.4982	1.88301
$419$	−11.6740	−0.570313	−0.285156	−	0.958481i	$-0.592046\pi$
$419$	−11.6740	−0.570313	−0.285156	+	0.958481i	$0.592046\pi$
$420$	0	0
$421$	−18.0112	−0.877811	−0.438905	−	0.898533i	$-0.644634\pi$
$421$	−18.0112	−0.877811	−0.438905	+	0.898533i	$0.644634\pi$
$422$	41.0667	1.99909
$423$	30.8490	1.49993
$424$	12.0474	0.585073
$425$	0	0
$426$	1.71710	0.0831936
$427$	13.8091	0.668268
$428$	5.31607	0.256962
$429$	6.29582	0.303965
$430$	0	0
$431$	−36.7021	−1.76788	−0.883940	−	0.467600i	$-0.845119\pi$
$431$	−36.7021	−1.76788	−0.883940	+	0.467600i	$0.845119\pi$
$432$	−15.9504	−0.767413
$433$	−14.1730	−0.681111	−0.340555	−	0.940224i	$-0.610615\pi$
$433$	−14.1730	−0.681111	−0.340555	+	0.940224i	$0.610615\pi$
$434$	−2.37389	−0.113950
$435$	0	0
$436$	1.39811	0.0669574
$437$	−5.33686	−0.255296
$438$	4.49331	0.214699
$439$	16.9922	0.810992	0.405496	−	0.914097i	$-0.367099\pi$
$439$	16.9922	0.810992	0.405496	+	0.914097i	$0.367099\pi$
$440$	0	0
$441$	−2.60304	−0.123954
$442$	−16.4829	−0.784011
$443$	24.0212	1.14128	0.570641	−	0.821200i	$-0.306695\pi$
$443$	24.0212	1.14128	0.570641	+	0.821200i	$0.306695\pi$
$444$	1.57975	0.0749715
$445$	0	0
$446$	−5.42481	−0.256872
$447$	−5.59107	−0.264448
$448$	−6.43052	−0.303814
$449$	10.7220	0.506003	0.253001	−	0.967466i	$-0.418582\pi$
$449$	10.7220	0.506003	0.253001	+	0.967466i	$0.418582\pi$
$450$	0	0
$451$	29.0309	1.36701
$452$	−4.09632	−0.192675
$453$	4.39575	0.206530
$454$	−0.307448	−0.0144292
$455$	0	0
$456$	8.64998	0.405073
$457$	−3.97460	−0.185924	−0.0929620	−	0.995670i	$-0.529633\pi$
$457$	−3.97460	−0.185924	−0.0929620	+	0.995670i	$0.529633\pi$
$458$	−19.3045	−0.902039
$459$	18.2164	0.850270
$460$	0	0
$461$	−28.6967	−1.33654	−0.668269	−	0.743920i	$-0.732964\pi$
$461$	−28.6967	−1.33654	−0.668269	+	0.743920i	$0.732964\pi$
$462$	4.54496	0.211451
$463$	0.125491	0.00583207	0.00291603	−	0.999996i	$-0.499072\pi$
$463$	0.125491	0.00583207	0.00291603	+	0.999996i	$0.499072\pi$
$464$	26.8231	1.24523
$465$	0	0
$466$	−4.51040	−0.208940
$467$	26.4731	1.22503	0.612515	−	0.790459i	$-0.290158\pi$
$467$	26.4731	1.22503	0.612515	+	0.790459i	$0.290158\pi$
$468$	1.67514	0.0774334
$469$	−5.37143	−0.248030
$470$	0	0
$471$	7.36319	0.339278
$472$	17.0418	0.784414
$473$	−20.0945	−0.923944
$474$	10.8759	0.499546
$475$	0	0
$476$	−1.57866	−0.0723579
$477$	12.1904	0.558162
$478$	−10.6417	−0.486741
$479$	−3.46245	−0.158204	−0.0791018	−	0.996867i	$-0.525205\pi$
$479$	−3.46245	−0.158204	−0.0791018	+	0.996867i	$0.525205\pi$
$480$	0	0
$481$	17.2398	0.786067
$482$	13.1251	0.597833
$483$	−0.630051	−0.0286683
$484$	3.53854	0.160843
$485$	0	0
$486$	−21.4255	−0.971880
$487$	−18.3048	−0.829471	−0.414736	−	0.909942i	$-0.636126\pi$
$487$	−18.3048	−0.829471	−0.414736	+	0.909942i	$0.636126\pi$
$488$	35.5237	1.60808
$489$	−5.21635	−0.235891
$490$	0	0
$491$	4.92603	0.222309	0.111154	−	0.993803i	$-0.464545\pi$
$491$	4.92603	0.222309	0.111154	+	0.993803i	$0.464545\pi$
$492$	−1.17796	−0.0531066
$493$	−30.6338	−1.37968
$494$	−17.0473	−0.766993
$495$	0	0
$496$	−7.06333	−0.317153
$497$	1.79472	0.0805040
$498$	7.07416	0.317001
$499$	−27.7378	−1.24171	−0.620856	−	0.783924i	$-0.713215\pi$
$499$	−27.7378	−1.24171	−0.620856	+	0.783924i	$0.713215\pi$
$500$	0	0
$501$	−1.29940	−0.0580527
$502$	−39.5944	−1.76718
$503$	−29.5389	−1.31708	−0.658538	−	0.752547i	$-0.728825\pi$
$503$	−29.5389	−1.31708	−0.658538	+	0.752547i	$0.728825\pi$
$504$	−6.69629	−0.298276
$505$	0	0
$506$	−7.21364	−0.320685
$507$	5.40283	0.239948
$508$	3.09801	0.137452
$509$	−1.50647	−0.0667729	−0.0333865	−	0.999443i	$-0.510629\pi$
$509$	−1.50647	−0.0667729	−0.0333865	+	0.999443i	$0.510629\pi$
$510$	0	0
$511$	4.69642	0.207758
$512$	−15.4924	−0.684675
$513$	18.8402	0.831813
$514$	0.147363	0.00649992
$515$	0	0
$516$	0.815355	0.0358940
$517$	−56.2978	−2.47598
$518$	12.4454	0.546821
$519$	−8.41495	−0.369375
$520$	0	0
$521$	2.38970	0.104695	0.0523473	−	0.998629i	$-0.483330\pi$
$521$	2.38970	0.104695	0.0523473	+	0.998629i	$0.483330\pi$
$522$	23.4661	1.02708
$523$	−29.8831	−1.30670	−0.653348	−	0.757058i	$-0.726636\pi$
$523$	−29.8831	−1.30670	−0.653348	+	0.757058i	$0.726636\pi$
$524$	−5.04918	−0.220575
$525$	0	0
$526$	−3.31617	−0.144592
$527$	8.06680	0.351395
$528$	13.5232	0.588521
$529$	1.00000	0.0434783
$530$	0	0
$531$	17.2442	0.748334
$532$	−1.63272	−0.0707873
$533$	−12.8551	−0.556816
$534$	9.25717	0.400597
$535$	0	0
$536$	−13.8180	−0.596845
$537$	−14.0719	−0.607249
$538$	−9.64405	−0.415784
$539$	4.75041	0.204615
$540$	0	0
$541$	37.5786	1.61563	0.807815	−	0.589436i	$-0.200650\pi$
$541$	37.5786	1.61563	0.807815	+	0.589436i	$0.200650\pi$
$542$	−10.6731	−0.458451
$543$	−5.25669	−0.225586
$544$	−8.85559	−0.379680
$545$	0	0
$546$	−2.01254	−0.0861288
$547$	−34.7339	−1.48511	−0.742557	−	0.669783i	$-0.766387\pi$
$547$	−34.7339	−1.48511	−0.742557	+	0.669783i	$0.766387\pi$
$548$	−1.47651	−0.0630732
$549$	35.9455	1.53412
$550$	0	0
$551$	−31.6827	−1.34973
$552$	−1.62080	−0.0689859
$553$	11.3675	0.483396
$554$	−15.0075	−0.637607
$555$	0	0
$556$	2.27914	0.0966571
$557$	26.3811	1.11780	0.558901	−	0.829235i	$-0.311223\pi$
$557$	26.3811	1.11780	0.558901	+	0.829235i	$0.311223\pi$
$558$	−6.17932	−0.261591
$559$	8.89797	0.376344
$560$	0	0
$561$	−15.4444	−0.652063
$562$	22.9058	0.966224
$563$	7.22447	0.304475	0.152238	−	0.988344i	$-0.451352\pi$
$563$	7.22447	0.304475	0.152238	+	0.988344i	$0.451352\pi$
$564$	2.28435	0.0961883
$565$	0	0
$566$	−25.3611	−1.06601
$567$	−5.58490	−0.234544
$568$	4.61689	0.193720
$569$	44.0392	1.84622	0.923109	−	0.384537i	$-0.125639\pi$
$569$	44.0392	1.84622	0.923109	+	0.384537i	$0.125639\pi$
$570$	0	0
$571$	20.7826	0.869723	0.434862	−	0.900497i	$-0.356797\pi$
$571$	20.7826	0.869723	0.434862	+	0.900497i	$0.356797\pi$
$572$	−3.05705	−0.127822
$573$	−5.84949	−0.244366
$574$	−9.28010	−0.387344
$575$	0	0
$576$	−16.7389	−0.697454
$577$	−5.22799	−0.217644	−0.108822	−	0.994061i	$-0.534708\pi$
$577$	−5.22799	−0.217644	−0.108822	+	0.994061i	$0.534708\pi$
$578$	14.6194	0.608088
$579$	3.56310	0.148077
$580$	0	0
$581$	7.39394	0.306752
$582$	12.1944	0.505473
$583$	−22.2469	−0.921374
$584$	12.0815	0.499936
$585$	0	0
$586$	−22.2416	−0.918792
$587$	−43.2143	−1.78365	−0.891823	−	0.452385i	$-0.850573\pi$
$587$	−43.2143	−1.78365	−0.891823	+	0.452385i	$0.850573\pi$
$588$	−0.192753	−0.00794900
$589$	8.34301	0.343768
$590$	0	0
$591$	17.2736	0.710539
$592$	37.0304	1.52194
$593$	17.6804	0.726048	0.363024	−	0.931780i	$-0.381744\pi$
$593$	17.6804	0.726048	0.363024	+	0.931780i	$0.381744\pi$
$594$	25.4656	1.04487
$595$	0	0
$596$	2.71484	0.111204
$597$	−14.9326	−0.611151
$598$	3.19425	0.130623
$599$	22.9595	0.938101	0.469050	−	0.883171i	$-0.344596\pi$
$599$	22.9595	0.938101	0.469050	+	0.883171i	$0.344596\pi$
$600$	0	0
$601$	19.8025	0.807761	0.403880	−	0.914812i	$-0.367661\pi$
$601$	19.8025	0.807761	0.403880	+	0.914812i	$0.367661\pi$
$602$	6.42345	0.261800
$603$	−13.9820	−0.569392
$604$	−2.13443	−0.0868488
$605$	0	0
$606$	0.609377	0.0247543
$607$	−42.7901	−1.73680	−0.868399	−	0.495866i	$-0.834851\pi$
$607$	−42.7901	−1.73680	−0.868399	+	0.495866i	$0.834851\pi$
$608$	−9.15881	−0.371439
$609$	−3.74035	−0.151567
$610$	0	0
$611$	24.9291	1.00852
$612$	−4.10932	−0.166109
$613$	−2.64070	−0.106657	−0.0533284	−	0.998577i	$-0.516983\pi$
$613$	−2.64070	−0.106657	−0.0533284	+	0.998577i	$0.516983\pi$
$614$	−16.4573	−0.664161
$615$	0	0
$616$	12.2204	0.492374
$617$	−9.48598	−0.381891	−0.190946	−	0.981601i	$-0.561155\pi$
$617$	−9.48598	−0.381891	−0.190946	+	0.981601i	$0.561155\pi$
$618$	6.14232	0.247080
$619$	−16.5427	−0.664908	−0.332454	−	0.943120i	$-0.607877\pi$
$619$	−16.5427	−0.664908	−0.332454	+	0.943120i	$0.607877\pi$
$620$	0	0
$621$	−3.53020	−0.141662
$622$	19.3543	0.776035
$623$	9.67563	0.387646
$624$	−5.98816	−0.239718
$625$	0	0
$626$	44.1058	1.76282
$627$	−15.9732	−0.637909
$628$	−3.57533	−0.142671
$629$	−42.2912	−1.68626
$630$	0	0
$631$	−13.2530	−0.527595	−0.263797	−	0.964578i	$-0.584975\pi$
$631$	−13.2530	−0.527595	−0.263797	+	0.964578i	$0.584975\pi$
$632$	29.2428	1.16322
$633$	−17.0389	−0.677236
$634$	−28.7165	−1.14048
$635$	0	0
$636$	0.902694	0.0357941
$637$	−2.10352	−0.0833443
$638$	−42.8244	−1.69543
$639$	4.67171	0.184810
$640$	0	0
$641$	−2.02934	−0.0801543	−0.0400771	−	0.999197i	$-0.512760\pi$
$641$	−2.02934	−0.0801543	−0.0400771	+	0.999197i	$0.512760\pi$
$642$	−16.6251	−0.656140
$643$	−10.9340	−0.431196	−0.215598	−	0.976482i	$-0.569170\pi$
$643$	−10.9340	−0.431196	−0.215598	+	0.976482i	$0.569170\pi$
$644$	0.305932	0.0120554
$645$	0	0
$646$	41.8189	1.64534
$647$	40.8520	1.60606	0.803028	−	0.595941i	$-0.203221\pi$
$647$	40.8520	1.60606	0.803028	+	0.595941i	$0.203221\pi$
$648$	−14.3671	−0.564394
$649$	−31.4698	−1.23530
$650$	0	0
$651$	0.984947	0.0386031
$652$	2.53289	0.0991956
$653$	32.8743	1.28647	0.643235	−	0.765668i	$-0.277592\pi$
$653$	32.8743	1.28647	0.643235	+	0.765668i	$0.277592\pi$
$654$	−4.37235	−0.170973
$655$	0	0
$656$	−27.6122	−1.07808
$657$	12.2250	0.476941
$658$	17.9963	0.701570
$659$	−38.4186	−1.49658	−0.748289	−	0.663373i	$-0.769124\pi$
$659$	−38.4186	−1.49658	−0.748289	+	0.663373i	$0.769124\pi$
$660$	0	0
$661$	32.9620	1.28207	0.641036	−	0.767511i	$-0.278505\pi$
$661$	32.9620	1.28207	0.641036	+	0.767511i	$0.278505\pi$
$662$	37.1645	1.44444
$663$	6.83889	0.265600
$664$	19.0209	0.738152
$665$	0	0
$666$	32.3959	1.25532
$667$	5.93659	0.229866
$668$	0.630945	0.0244120
$669$	2.25080	0.0870209
$670$	0	0
$671$	−65.5987	−2.53241
$672$	−1.08126	−0.0417104
$673$	36.7861	1.41800	0.709001	−	0.705208i	$-0.249146\pi$
$673$	36.7861	1.41800	0.709001	+	0.705208i	$0.249146\pi$
$674$	31.8790	1.22793
$675$	0	0
$676$	−2.62344	−0.100901
$677$	20.9023	0.803341	0.401670	−	0.915784i	$-0.368430\pi$
$677$	20.9023	0.803341	0.401670	+	0.915784i	$0.368430\pi$
$678$	12.8105	0.491986
$679$	12.7456	0.489132
$680$	0	0
$681$	0.127563	0.00488822
$682$	11.2769	0.431817
$683$	3.18847	0.122004	0.0610018	−	0.998138i	$-0.480570\pi$
$683$	3.18847	0.122004	0.0610018	+	0.998138i	$0.480570\pi$
$684$	−4.25002	−0.162504
$685$	0	0
$686$	−1.51853	−0.0579777
$687$	8.00959	0.305585
$688$	19.1125	0.728657
$689$	9.85110	0.375297
$690$	0	0
$691$	28.7512	1.09375	0.546874	−	0.837215i	$-0.315818\pi$
$691$	28.7512	1.09375	0.546874	+	0.837215i	$0.315818\pi$
$692$	4.08603	0.155328
$693$	12.3655	0.469726
$694$	−31.2450	−1.18604
$695$	0	0
$696$	−9.62203	−0.364722
$697$	31.5350	1.19447
$698$	48.4903	1.83538
$699$	1.87140	0.0707830
$700$	0	0
$701$	31.7625	1.19965	0.599827	−	0.800130i	$-0.295236\pi$
$701$	31.7625	1.19965	0.599827	+	0.800130i	$0.295236\pi$
$702$	−11.2763	−0.425598
$703$	−43.7393	−1.64966
$704$	30.5476	1.15131
$705$	0	0
$706$	−19.6999	−0.741415
$707$	0.636924	0.0239540
$708$	1.27692	0.0479896
$709$	−26.9898	−1.01362	−0.506812	−	0.862057i	$-0.669176\pi$
$709$	−26.9898	−1.01362	−0.506812	+	0.862057i	$0.669176\pi$
$710$	0	0
$711$	29.5900	1.10971
$712$	24.8905	0.932810
$713$	−1.56328	−0.0585453
$714$	4.93700	0.184763
$715$	0	0
$716$	6.83288	0.255357
$717$	4.41534	0.164894
$718$	−52.0864	−1.94385
$719$	−20.3346	−0.758351	−0.379176	−	0.925325i	$-0.623792\pi$
$719$	−20.3346	−0.758351	−0.379176	+	0.925325i	$0.623792\pi$
$720$	0	0
$721$	6.41998	0.239093
$722$	14.3988	0.535866
$723$	−5.44573	−0.202529
$724$	2.55248	0.0948622
$725$	0	0
$726$	−11.0662	−0.410704
$727$	−31.5131	−1.16876	−0.584378	−	0.811481i	$-0.698661\pi$
$727$	−31.5131	−1.16876	−0.584378	+	0.811481i	$0.698661\pi$
$728$	−5.41128	−0.200555
$729$	−7.86509	−0.291300
$730$	0	0
$731$	−21.8278	−0.807329
$732$	2.66174	0.0983808
$733$	28.7198	1.06079	0.530394	−	0.847751i	$-0.322044\pi$
$733$	28.7198	1.06079	0.530394	+	0.847751i	$0.322044\pi$
$734$	17.8157	0.657590
$735$	0	0
$736$	1.71614	0.0632579
$737$	25.5165	0.939913
$738$	−24.1564	−0.889211
$739$	10.0953	0.371360	0.185680	−	0.982610i	$-0.440551\pi$
$739$	10.0953	0.371360	0.185680	+	0.982610i	$0.440551\pi$
$740$	0	0
$741$	7.07305	0.259835
$742$	7.11152	0.261072
$743$	53.1107	1.94844	0.974222	−	0.225592i	$-0.0724315\pi$
$743$	53.1107	1.94844	0.974222	+	0.225592i	$0.0724315\pi$
$744$	2.53377	0.0928924
$745$	0	0
$746$	−32.0379	−1.17299
$747$	19.2467	0.704200
$748$	7.49930	0.274202
$749$	−17.3766	−0.634927
$750$	0	0
$751$	18.0756	0.659588	0.329794	−	0.944053i	$-0.393021\pi$
$751$	18.0756	0.659588	0.329794	+	0.944053i	$0.393021\pi$
$752$	53.5467	1.95265
$753$	16.4281	0.598672
$754$	18.9629	0.690590
$755$	0	0
$756$	−1.08000	−0.0392793
$757$	−22.0833	−0.802631	−0.401316	−	0.915940i	$-0.631447\pi$
$757$	−22.0833	−0.802631	−0.401316	+	0.915940i	$0.631447\pi$
$758$	46.4129	1.68579
$759$	2.99300	0.108639
$760$	0	0
$761$	5.28024	0.191409	0.0957043	−	0.995410i	$-0.469490\pi$
$761$	5.28024	0.191409	0.0957043	+	0.995410i	$0.469490\pi$
$762$	−9.68848	−0.350977
$763$	−4.57000	−0.165445
$764$	2.84032	0.102759
$765$	0	0
$766$	−11.6988	−0.422695
$767$	13.9350	0.503165
$768$	−4.52335	−0.163222
$769$	12.6400	0.455809	0.227905	−	0.973683i	$-0.426813\pi$
$769$	12.6400	0.455809	0.227905	+	0.973683i	$0.426813\pi$
$770$	0	0
$771$	−0.0611423	−0.00220199
$772$	−1.73013	−0.0622686
$773$	51.3387	1.84653	0.923263	−	0.384168i	$-0.125512\pi$
$773$	51.3387	1.84653	0.923263	+	0.384168i	$0.125512\pi$
$774$	16.7205	0.601005
$775$	0	0
$776$	32.7880	1.17702
$777$	−5.16371	−0.185247
$778$	5.34649	0.191681
$779$	32.6148	1.16855
$780$	0	0
$781$	−8.52563	−0.305071
$782$	−7.83587	−0.280210
$783$	−20.9573	−0.748954
$784$	−4.51827	−0.161367
$785$	0	0
$786$	15.7905	0.563227
$787$	18.8984	0.673654	0.336827	−	0.941567i	$-0.390646\pi$
$787$	18.8984	0.673654	0.336827	+	0.941567i	$0.390646\pi$
$788$	−8.38748	−0.298792
$789$	1.37591	0.0489836
$790$	0	0
$791$	13.3896	0.476080
$792$	31.8101	1.13032
$793$	29.0476	1.03151
$794$	−38.3439	−1.36077
$795$	0	0
$796$	7.25079	0.256997
$797$	37.4811	1.32765	0.663825	−	0.747888i	$-0.268932\pi$
$797$	37.4811	1.32765	0.663825	+	0.747888i	$0.268932\pi$
$798$	5.10604	0.180752
$799$	−61.1540	−2.16347
$800$	0	0
$801$	25.1860	0.889904
$802$	2.06710	0.0729917
$803$	−22.3099	−0.787301
$804$	−1.03536	−0.0365143
$805$	0	0
$806$	−4.99351	−0.175889
$807$	4.00140	0.140856
$808$	1.63848	0.0576415
$809$	−45.0641	−1.58437	−0.792185	−	0.610281i	$-0.791056\pi$
$809$	−45.0641	−1.58437	−0.792185	+	0.610281i	$0.791056\pi$
$810$	0	0
$811$	−38.5455	−1.35351	−0.676757	−	0.736206i	$-0.736615\pi$
$811$	−38.5455	−1.35351	−0.676757	+	0.736206i	$0.736615\pi$
$812$	1.81619	0.0637359
$813$	4.42838	0.155310
$814$	−59.1209	−2.07219
$815$	0	0
$816$	14.6897	0.514241
$817$	−22.5752	−0.789805
$818$	−9.34101	−0.326601
$819$	−5.47553	−0.191330
$820$	0	0
$821$	23.6607	0.825764	0.412882	−	0.910785i	$-0.364522\pi$
$821$	23.6607	0.825764	0.412882	+	0.910785i	$0.364522\pi$
$822$	4.61752	0.161054
$823$	23.2934	0.811958	0.405979	−	0.913882i	$-0.366931\pi$
$823$	23.2934	0.811958	0.405979	+	0.913882i	$0.366931\pi$
$824$	16.5153	0.575339
$825$	0	0
$826$	10.0597	0.350022
$827$	−7.93395	−0.275890	−0.137945	−	0.990440i	$-0.544050\pi$
$827$	−7.93395	−0.275890	−0.137945	+	0.990440i	$0.544050\pi$
$828$	0.796353	0.0276752
$829$	−38.5459	−1.33875	−0.669377	−	0.742923i	$-0.733439\pi$
$829$	−38.5459	−1.33875	−0.669377	+	0.742923i	$0.733439\pi$
$830$	0	0
$831$	6.22674	0.216003
$832$	−13.5267	−0.468954
$833$	5.16017	0.178789
$834$	−7.12762	−0.246809
$835$	0	0
$836$	7.75608	0.268250
$837$	5.51869	0.190754
$838$	−17.7273	−0.612381
$839$	−38.5038	−1.32930	−0.664649	−	0.747155i	$-0.731419\pi$
$839$	−38.5038	−1.32930	−0.664649	+	0.747155i	$0.731419\pi$
$840$	0	0
$841$	6.24306	0.215278
$842$	−27.3505	−0.942561
$843$	−9.50383	−0.327329
$844$	8.27355	0.284787
$845$	0	0
$846$	46.8451	1.61057
$847$	−11.5664	−0.397426
$848$	21.1598	0.726630
$849$	10.5225	0.361132
$850$	0	0
$851$	8.19571	0.280945
$852$	0.345937	0.0118516
$853$	−11.9837	−0.410314	−0.205157	−	0.978729i	$-0.565770\pi$
$853$	−11.9837	−0.410314	−0.205157	+	0.978729i	$0.565770\pi$
$854$	20.9695	0.717561
$855$	0	0
$856$	−44.7012	−1.52785
$857$	53.6339	1.83210	0.916050	−	0.401064i	$-0.131359\pi$
$857$	53.6339	1.83210	0.916050	+	0.401064i	$0.131359\pi$
$858$	9.56039	0.326387
$859$	−1.66008	−0.0566412	−0.0283206	−	0.999599i	$-0.509016\pi$
$859$	−1.66008	−0.0566412	−0.0283206	+	0.999599i	$0.509016\pi$
$860$	0	0
$861$	3.85039	0.131221
$862$	−55.7333	−1.89828
$863$	44.4303	1.51243	0.756213	−	0.654325i	$-0.227047\pi$
$863$	44.4303	1.51243	0.756213	+	0.654325i	$0.227047\pi$
$864$	−6.05833	−0.206109
$865$	0	0
$866$	−21.5221	−0.731351
$867$	−6.06572	−0.206003
$868$	−0.478259	−0.0162332
$869$	−54.0004	−1.83184
$870$	0	0
$871$	−11.2989	−0.382848
$872$	−11.7563	−0.398118
$873$	33.1773	1.12288
$874$	−8.10418	−0.274128
$875$	0	0
$876$	0.905250	0.0305856
$877$	25.8429	0.872654	0.436327	−	0.899788i	$-0.356279\pi$
$877$	25.8429	0.872654	0.436327	+	0.899788i	$0.356279\pi$
$878$	25.8031	0.870813
$879$	9.22823	0.311261
$880$	0	0
$881$	49.7585	1.67640	0.838202	−	0.545359i	$-0.183607\pi$
$881$	49.7585	1.67640	0.838202	+	0.545359i	$0.183607\pi$
$882$	−3.95279	−0.133097
$883$	38.8725	1.30816	0.654082	−	0.756423i	$-0.273055\pi$
$883$	38.8725	1.30816	0.654082	+	0.756423i	$0.273055\pi$
$884$	−3.32074	−0.111689
$885$	0	0
$886$	36.4769	1.22547
$887$	−48.8765	−1.64111	−0.820556	−	0.571566i	$-0.806336\pi$
$887$	−48.8765	−1.64111	−0.820556	+	0.571566i	$0.806336\pi$
$888$	−13.2836	−0.445769
$889$	−10.1264	−0.339630
$890$	0	0
$891$	26.5306	0.888808
$892$	−1.09292	−0.0365935
$893$	−63.2479	−2.11651
$894$	−8.49020	−0.283955
$895$	0	0
$896$	−13.1972	−0.440889
$897$	−1.32532	−0.0442512
$898$	16.2817	0.543327
$899$	−9.28055	−0.309524
$900$	0	0
$901$	−24.1659	−0.805083
$902$	44.0843	1.46785
$903$	−2.66515	−0.0886905
$904$	34.4447	1.14561
$905$	0	0
$906$	6.67507	0.221764
$907$	−30.9918	−1.02907	−0.514533	−	0.857471i	$-0.672035\pi$
$907$	−30.9918	−1.02907	−0.514533	+	0.857471i	$0.672035\pi$
$908$	−0.0619404	−0.00205556
$909$	1.65793	0.0549902
$910$	0	0
$911$	3.14778	0.104291	0.0521453	−	0.998640i	$-0.483394\pi$
$911$	3.14778	0.104291	0.0521453	+	0.998640i	$0.483394\pi$
$912$	15.1926	0.503079
$913$	−35.1243	−1.16244
$914$	−6.03555	−0.199638
$915$	0	0
$916$	−3.88920	−0.128503
$917$	16.5042	0.545018
$918$	27.6622	0.912988
$919$	45.0543	1.48620	0.743102	−	0.669178i	$-0.233354\pi$
$919$	45.0543	1.48620	0.743102	+	0.669178i	$0.233354\pi$
$920$	0	0
$921$	6.82826	0.224999
$922$	−43.5768	−1.43512
$923$	3.77521	0.124263
$924$	0.915656	0.0301229
$925$	0	0
$926$	0.190562	0.00626226
$927$	16.7114	0.548876
$928$	10.1880	0.334439
$929$	12.0584	0.395623	0.197812	−	0.980240i	$-0.436617\pi$
$929$	12.0584	0.395623	0.197812	+	0.980240i	$0.436617\pi$
$930$	0	0
$931$	5.33686	0.174908
$932$	−0.908694	−0.0297652
$933$	−8.03024	−0.262898
$934$	40.2002	1.31539
$935$	0	0
$936$	−14.0857	−0.460407
$937$	31.0833	1.01545	0.507724	−	0.861520i	$-0.330487\pi$
$937$	31.0833	1.01545	0.507724	+	0.861520i	$0.330487\pi$
$938$	−8.15668	−0.266325
$939$	−18.2999	−0.597193
$940$	0	0
$941$	−11.9414	−0.389277	−0.194639	−	0.980875i	$-0.562353\pi$
$941$	−11.9414	−0.389277	−0.194639	+	0.980875i	$0.562353\pi$
$942$	11.1812	0.364304
$943$	−6.11124	−0.199009
$944$	29.9319	0.974201
$945$	0	0
$946$	−30.5140	−0.992097
$947$	−11.0763	−0.359930	−0.179965	−	0.983673i	$-0.557599\pi$
$947$	−11.0763	−0.359930	−0.179965	+	0.983673i	$0.557599\pi$
$948$	2.19112	0.0711644
$949$	9.87900	0.320686
$950$	0	0
$951$	11.9147	0.386361
$952$	13.2745	0.430229
$953$	47.1521	1.52741	0.763703	−	0.645567i	$-0.223379\pi$
$953$	47.1521	1.52741	0.763703	+	0.645567i	$0.223379\pi$
$954$	18.5115	0.599333
$955$	0	0
$956$	−2.14395	−0.0693402
$957$	17.7682	0.574365
$958$	−5.25784	−0.169873
$959$	4.82625	0.155848
$960$	0	0
$961$	−28.5562	−0.921166
$962$	26.1791	0.844050
$963$	−45.2319	−1.45758
$964$	2.64427	0.0851662
$965$	0	0
$966$	−0.956751	−0.0307830
$967$	50.6976	1.63032	0.815162	−	0.579233i	$-0.196648\pi$
$967$	50.6976	1.63032	0.815162	+	0.579233i	$0.196648\pi$
$968$	−29.7545	−0.956344
$969$	−17.3510	−0.557395
$970$	0	0
$971$	−16.6582	−0.534588	−0.267294	−	0.963615i	$-0.586130\pi$
$971$	−16.6582	−0.534588	−0.267294	+	0.963615i	$0.586130\pi$
$972$	−4.31651	−0.138452
$973$	−7.44982	−0.238830
$974$	−27.7964	−0.890655
$975$	0	0
$976$	62.3931	1.99715
$977$	3.44021	0.110062	0.0550310	−	0.998485i	$-0.482474\pi$
$977$	3.44021	0.110062	0.0550310	+	0.998485i	$0.482474\pi$
$978$	−7.92118	−0.253291
$979$	−45.9632	−1.46899
$980$	0	0
$981$	−11.8959	−0.379806
$982$	7.48033	0.238707
$983$	31.1212	0.992611	0.496305	−	0.868148i	$-0.334690\pi$
$983$	31.1212	0.992611	0.496305	+	0.868148i	$0.334690\pi$
$984$	9.90510	0.315763
$985$	0	0
$986$	−46.5183	−1.48145
$987$	−7.46683	−0.237672
$988$	−3.43445	−0.109264
$989$	4.23005	0.134508
$990$	0	0
$991$	35.8425	1.13858	0.569288	−	0.822138i	$-0.307219\pi$
$991$	35.8425	1.13858	0.569288	+	0.822138i	$0.307219\pi$
$992$	−2.68282	−0.0851795
$993$	−15.4199	−0.489334
$994$	2.72533	0.0864422
$995$	0	0
$996$	1.42520	0.0451593
$997$	−19.7299	−0.624851	−0.312425	−	0.949942i	$-0.601141\pi$
$997$	−19.7299	−0.624851	−0.312425	+	0.949942i	$0.601141\pi$
$998$	−42.1206	−1.33330
$999$	−28.9325	−0.915383

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.z.1.11	✓	14
5.4	even	2		4025.2.a.bc.1.4	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4025.2.a.z.1.11	✓	14	1.1	even	1	trivial
4025.2.a.bc.1.4	yes	14	5.4	even	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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q+1.51853 q^{2} -0.630051 q^{3} +0.305932 q^{4} -0.956751 q^{6} -1.00000 q^{7} -2.57249 q^{8} -2.60304 q^{9} +O(q^{10})\)	\(q+1.51853 q^{2} -0.630051 q^{3} +0.305932 q^{4} -0.956751 q^{6} -1.00000 q^{7} -2.57249 q^{8} -2.60304 q^{9} +4.75041 q^{11} -0.192753 q^{12} -2.10352 q^{13} -1.51853 q^{14} -4.51827 q^{16} +5.16017 q^{17} -3.95279 q^{18} +5.33686 q^{19} +0.630051 q^{21} +7.21364 q^{22} -1.00000 q^{23} +1.62080 q^{24} -3.19425 q^{26} +3.53020 q^{27} -0.305932 q^{28} -5.93659 q^{29} +1.56328 q^{31} -1.71614 q^{32} -2.99300 q^{33} +7.83587 q^{34} -0.796353 q^{36} -8.19571 q^{37} +8.10418 q^{38} +1.32532 q^{39} +6.11124 q^{41} +0.956751 q^{42} -4.23005 q^{43} +1.45330 q^{44} -1.51853 q^{46} -11.8512 q^{47} +2.84674 q^{48} +1.00000 q^{49} -3.25117 q^{51} -0.643534 q^{52} -4.68316 q^{53} +5.36071 q^{54} +2.57249 q^{56} -3.36249 q^{57} -9.01488 q^{58} -6.62464 q^{59} -13.8091 q^{61} +2.37389 q^{62} +2.60304 q^{63} +6.43052 q^{64} -4.54496 q^{66} +5.37143 q^{67} +1.57866 q^{68} +0.630051 q^{69} -1.79472 q^{71} +6.69629 q^{72} -4.69642 q^{73} -12.4454 q^{74} +1.63272 q^{76} -4.75041 q^{77} +2.01254 q^{78} -11.3675 q^{79} +5.58490 q^{81} +9.28010 q^{82} -7.39394 q^{83} +0.192753 q^{84} -6.42345 q^{86} +3.74035 q^{87} -12.2204 q^{88} -9.67563 q^{89} +2.10352 q^{91} -0.305932 q^{92} -0.984947 q^{93} -17.9963 q^{94} +1.08126 q^{96} -12.7456 q^{97} +1.51853 q^{98} -12.3655 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9}+O(q^{10}) \) 14 * q - 3 * q^2 - 4 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9	\( 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9} + 5 q^{11} - 17 q^{12} - 11 q^{13} + 3 q^{14} + 23 q^{16} - 3 q^{17} - 15 q^{18} - 2 q^{19} + 4 q^{21} - 23 q^{22} - 14 q^{23} - 12 q^{24} - 9 q^{26} - 25 q^{27} - 17 q^{28} + 7 q^{29} - 3 q^{31} - 24 q^{32} - 6 q^{33} - 14 q^{34} + 13 q^{36} - 22 q^{37} - 20 q^{38} - 10 q^{39} - 17 q^{41} + 4 q^{42} - 18 q^{43} + 28 q^{44} + 3 q^{46} - 30 q^{47} - 8 q^{48} + 14 q^{49} + 4 q^{51} - 8 q^{52} - 11 q^{53} + 20 q^{54} + 3 q^{56} - 18 q^{57} - 38 q^{58} - 22 q^{59} - 8 q^{61} + 22 q^{62} - 18 q^{63} + 29 q^{64} - 9 q^{66} - 39 q^{67} - q^{68} + 4 q^{69} - 5 q^{71} + 24 q^{72} - 18 q^{73} + 35 q^{74} - 41 q^{76} - 5 q^{77} + 22 q^{78} + 10 q^{79} + 2 q^{81} + 8 q^{82} - 24 q^{83} + 17 q^{84} - 26 q^{86} - 5 q^{87} - 58 q^{88} + 25 q^{89} + 11 q^{91} - 17 q^{92} - 47 q^{93} - 2 q^{94} - 117 q^{96} - 43 q^{97} - 3 q^{98} + 55 q^{99}+O(q^{100}) \) 14 * q - 3 * q^2 - 4 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9 + 5 * q^11 - 17 * q^12 - 11 * q^13 + 3 * q^14 + 23 * q^16 - 3 * q^17 - 15 * q^18 - 2 * q^19 + 4 * q^21 - 23 * q^22 - 14 * q^23 - 12 * q^24 - 9 * q^26 - 25 * q^27 - 17 * q^28 + 7 * q^29 - 3 * q^31 - 24 * q^32 - 6 * q^33 - 14 * q^34 + 13 * q^36 - 22 * q^37 - 20 * q^38 - 10 * q^39 - 17 * q^41 + 4 * q^42 - 18 * q^43 + 28 * q^44 + 3 * q^46 - 30 * q^47 - 8 * q^48 + 14 * q^49 + 4 * q^51 - 8 * q^52 - 11 * q^53 + 20 * q^54 + 3 * q^56 - 18 * q^57 - 38 * q^58 - 22 * q^59 - 8 * q^61 + 22 * q^62 - 18 * q^63 + 29 * q^64 - 9 * q^66 - 39 * q^67 - q^68 + 4 * q^69 - 5 * q^71 + 24 * q^72 - 18 * q^73 + 35 * q^74 - 41 * q^76 - 5 * q^77 + 22 * q^78 + 10 * q^79 + 2 * q^81 + 8 * q^82 - 24 * q^83 + 17 * q^84 - 26 * q^86 - 5 * q^87 - 58 * q^88 + 25 * q^89 + 11 * q^91 - 17 * q^92 - 47 * q^93 - 2 * q^94 - 117 * q^96 - 43 * q^97 - 3 * q^98 + 55 * q^99

Introduction

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