LMFDB - Embedded newform 4025.2.a.z.1.14

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			1.14
Root			$-2.60812$ 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)

$f(q)$	$=$	$q+2.60812 q^{2} -2.93022 q^{3} +4.80228 q^{4} -7.64237 q^{6} -1.00000 q^{7} +7.30867 q^{8} +5.58621 q^{9} +O(q^{10})$	\(q+2.60812 q^{2} -2.93022 q^{3} +4.80228 q^{4} -7.64237 q^{6} -1.00000 q^{7} +7.30867 q^{8} +5.58621 q^{9} +0.264873 q^{11} -14.0717 q^{12} -1.35623 q^{13} -2.60812 q^{14} +9.45731 q^{16} -5.30702 q^{17} +14.5695 q^{18} -4.34051 q^{19} +2.93022 q^{21} +0.690820 q^{22} -1.00000 q^{23} -21.4160 q^{24} -3.53721 q^{26} -7.57817 q^{27} -4.80228 q^{28} -5.48568 q^{29} +8.13926 q^{31} +10.0484 q^{32} -0.776137 q^{33} -13.8413 q^{34} +26.8265 q^{36} -5.32439 q^{37} -11.3206 q^{38} +3.97406 q^{39} +2.17992 q^{41} +7.64237 q^{42} +2.38515 q^{43} +1.27199 q^{44} -2.60812 q^{46} -11.7321 q^{47} -27.7120 q^{48} +1.00000 q^{49} +15.5507 q^{51} -6.51300 q^{52} +8.02056 q^{53} -19.7648 q^{54} -7.30867 q^{56} +12.7187 q^{57} -14.3073 q^{58} -9.46127 q^{59} +3.95896 q^{61} +21.2281 q^{62} -5.58621 q^{63} +7.29290 q^{64} -2.02426 q^{66} -9.20059 q^{67} -25.4858 q^{68} +2.93022 q^{69} -9.36670 q^{71} +40.8277 q^{72} -6.26188 q^{73} -13.8866 q^{74} -20.8443 q^{76} -0.264873 q^{77} +10.3648 q^{78} -7.93971 q^{79} +5.44710 q^{81} +5.68549 q^{82} +2.13885 q^{83} +14.0717 q^{84} +6.22076 q^{86} +16.0743 q^{87} +1.93587 q^{88} +14.4466 q^{89} +1.35623 q^{91} -4.80228 q^{92} -23.8498 q^{93} -30.5988 q^{94} -29.4442 q^{96} -15.4112 q^{97} +2.60812 q^{98} +1.47964 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.60812	1.84422	0.922109	−	0.386931i	$-0.126465\pi$
$2$	2.60812	1.84422	0.922109	+	0.386931i	$0.126465\pi$
$3$	−2.93022	−1.69177	−0.845883	−	0.533369i	$-0.820926\pi$
$3$	−2.93022	−1.69177	−0.845883	+	0.533369i	$0.820926\pi$
$4$	4.80228	2.40114
$5$	0	0
$5$	0	0
$6$	−7.64237	−3.11998
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	7.30867	2.58400
$9$	5.58621	1.86207
$10$	0	0
$11$	0.264873	0.0798622	0.0399311	−	0.999202i	$-0.487286\pi$
$11$	0.264873	0.0798622	0.0399311	+	0.999202i	$0.487286\pi$
$12$	−14.0717	−4.06216
$13$	−1.35623	−0.376151	−0.188076	−	0.982155i	$-0.560225\pi$
$13$	−1.35623	−0.376151	−0.188076	+	0.982155i	$0.560225\pi$
$14$	−2.60812	−0.697049
$15$	0	0
$16$	9.45731	2.36433
$17$	−5.30702	−1.28714	−0.643570	−	0.765387i	$-0.722548\pi$
$17$	−5.30702	−1.28714	−0.643570	+	0.765387i	$0.722548\pi$
$18$	14.5695	3.43406
$19$	−4.34051	−0.995781	−0.497891	−	0.867240i	$-0.665892\pi$
$19$	−4.34051	−0.995781	−0.497891	+	0.867240i	$0.665892\pi$
$20$	0	0
$21$	2.93022	0.639427
$22$	0.690820	0.147283
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−21.4160	−4.37153
$25$	0	0
$26$	−3.53721	−0.693705
$27$	−7.57817	−1.45842
$28$	−4.80228	−0.907545
$29$	−5.48568	−1.01867	−0.509333	−	0.860570i	$-0.670108\pi$
$29$	−5.48568	−1.01867	−0.509333	+	0.860570i	$0.670108\pi$
$30$	0	0
$31$	8.13926	1.46185	0.730927	−	0.682456i	$-0.239088\pi$
$31$	8.13926	1.46185	0.730927	+	0.682456i	$0.239088\pi$
$32$	10.0484	1.77633
$33$	−0.776137	−0.135108
$34$	−13.8413	−2.37377
$35$	0	0
$36$	26.8265	4.47109
$37$	−5.32439	−0.875325	−0.437662	−	0.899139i	$-0.644194\pi$
$37$	−5.32439	−0.875325	−0.437662	+	0.899139i	$0.644194\pi$
$38$	−11.3206	−1.83644
$39$	3.97406	0.636360
$40$	0	0
$41$	2.17992	0.340447	0.170223	−	0.985406i	$-0.445551\pi$
$41$	2.17992	0.340447	0.170223	+	0.985406i	$0.445551\pi$
$42$	7.64237	1.17924
$43$	2.38515	0.363732	0.181866	−	0.983323i	$-0.441786\pi$
$43$	2.38515	0.363732	0.181866	+	0.983323i	$0.441786\pi$
$44$	1.27199	0.191760
$45$	0	0
$46$	−2.60812	−0.384546
$47$	−11.7321	−1.71131	−0.855655	−	0.517547i	$-0.826845\pi$
$47$	−11.7321	−1.71131	−0.855655	+	0.517547i	$0.826845\pi$
$48$	−27.7120	−3.99989
$49$	1.00000	0.142857
$50$	0	0
$51$	15.5507	2.17754
$52$	−6.51300	−0.903191
$53$	8.02056	1.10171	0.550855	−	0.834601i	$-0.314302\pi$
$53$	8.02056	1.10171	0.550855	+	0.834601i	$0.314302\pi$
$54$	−19.7648	−2.68964
$55$	0	0
$56$	−7.30867	−0.976662
$57$	12.7187	1.68463
$58$	−14.3073	−1.87864
$59$	−9.46127	−1.23175	−0.615876	−	0.787843i	$-0.711198\pi$
$59$	−9.46127	−1.23175	−0.615876	+	0.787843i	$0.711198\pi$
$60$	0	0
$61$	3.95896	0.506893	0.253447	−	0.967349i	$-0.418436\pi$
$61$	3.95896	0.506893	0.253447	+	0.967349i	$0.418436\pi$
$62$	21.2281	2.69598
$63$	−5.58621	−0.703796
$64$	7.29290	0.911613
$65$	0	0
$66$	−2.02426	−0.249169
$67$	−9.20059	−1.12403	−0.562015	−	0.827127i	$-0.689974\pi$
$67$	−9.20059	−1.12403	−0.562015	+	0.827127i	$0.689974\pi$
$68$	−25.4858	−3.09060
$69$	2.93022	0.352757
$70$	0	0
$71$	−9.36670	−1.11162	−0.555811	−	0.831308i	$-0.687592\pi$
$71$	−9.36670	−1.11162	−0.555811	+	0.831308i	$0.687592\pi$
$72$	40.8277	4.81160
$73$	−6.26188	−0.732898	−0.366449	−	0.930438i	$-0.619427\pi$
$73$	−6.26188	−0.732898	−0.366449	+	0.930438i	$0.619427\pi$
$74$	−13.8866	−1.61429
$75$	0	0
$76$	−20.8443	−2.39101
$77$	−0.264873	−0.0301851
$78$	10.3648	1.17359
$79$	−7.93971	−0.893288	−0.446644	−	0.894712i	$-0.647381\pi$
$79$	−7.93971	−0.893288	−0.446644	+	0.894712i	$0.647381\pi$
$80$	0	0
$81$	5.44710	0.605234
$82$	5.68549	0.627858
$83$	2.13885	0.234769	0.117385	−	0.993087i	$-0.462549\pi$
$83$	2.13885	0.234769	0.117385	+	0.993087i	$0.462549\pi$
$84$	14.0717	1.53535
$85$	0	0
$86$	6.22076	0.670802
$87$	16.0743	1.72334
$88$	1.93587	0.206364
$89$	14.4466	1.53134	0.765668	−	0.643235i	$-0.222408\pi$
$89$	14.4466	1.53134	0.765668	+	0.643235i	$0.222408\pi$
$90$	0	0
$91$	1.35623	0.142172
$92$	−4.80228	−0.500672
$93$	−23.8498	−2.47311
$94$	−30.5988	−3.15603
$95$	0	0
$96$	−29.4442	−3.00513
$97$	−15.4112	−1.56477	−0.782386	−	0.622794i	$-0.785998\pi$
$97$	−15.4112	−1.56477	−0.782386	+	0.622794i	$0.785998\pi$
$98$	2.60812	0.263460
$99$	1.47964	0.148709
$100$	0	0
$101$	−10.5012	−1.04491	−0.522455	−	0.852667i	$-0.674984\pi$
$101$	−10.5012	−1.04491	−0.522455	+	0.852667i	$0.674984\pi$
$102$	40.5582	4.01586
$103$	1.84958	0.182244	0.0911222	−	0.995840i	$-0.470955\pi$
$103$	1.84958	0.182244	0.0911222	+	0.995840i	$0.470955\pi$
$104$	−9.91225	−0.971976
$105$	0	0
$106$	20.9186	2.03179
$107$	6.11108	0.590781	0.295390	−	0.955377i	$-0.404550\pi$
$107$	6.11108	0.590781	0.295390	+	0.955377i	$0.404550\pi$
$108$	−36.3925	−3.50187
$109$	16.1038	1.54246	0.771232	−	0.636554i	$-0.219641\pi$
$109$	16.1038	1.54246	0.771232	+	0.636554i	$0.219641\pi$
$110$	0	0
$111$	15.6017	1.48084
$112$	−9.45731	−0.893632
$113$	17.2281	1.62068	0.810342	−	0.585957i	$-0.199281\pi$
$113$	17.2281	1.62068	0.810342	+	0.585957i	$0.199281\pi$
$114$	33.1718	3.10682
$115$	0	0
$116$	−26.3438	−2.44596
$117$	−7.57620	−0.700420
$118$	−24.6761	−2.27162
$119$	5.30702	0.486493
$120$	0	0
$121$	−10.9298	−0.993622
$122$	10.3254	0.934822
$123$	−6.38766	−0.575956
$124$	39.0870	3.51011
$125$	0	0
$126$	−14.5695	−1.29795
$127$	−15.6891	−1.39218	−0.696090	−	0.717955i	$-0.745078\pi$
$127$	−15.6891	−1.39218	−0.696090	+	0.717955i	$0.745078\pi$
$128$	−1.07615	−0.0951188
$129$	−6.98903	−0.615350
$130$	0	0
$131$	7.27872	0.635945	0.317972	−	0.948100i	$-0.396998\pi$
$131$	7.27872	0.635945	0.317972	+	0.948100i	$0.396998\pi$
$132$	−3.72722	−0.324413
$133$	4.34051	0.376370
$134$	−23.9962	−2.07296
$135$	0	0
$136$	−38.7872	−3.32598
$137$	−6.44195	−0.550373	−0.275186	−	0.961391i	$-0.588740\pi$
$137$	−6.44195	−0.550373	−0.275186	+	0.961391i	$0.588740\pi$
$138$	7.64237	0.650561
$139$	8.32746	0.706326	0.353163	−	0.935562i	$-0.385106\pi$
$139$	8.32746	0.706326	0.353163	+	0.935562i	$0.385106\pi$
$140$	0	0
$141$	34.3778	2.89513
$142$	−24.4295	−2.05007
$143$	−0.359229	−0.0300403
$144$	52.8305	4.40254
$145$	0	0
$146$	−16.3317	−1.35162
$147$	−2.93022	−0.241681
$148$	−25.5692	−2.10178
$149$	−1.46341	−0.119888	−0.0599438	−	0.998202i	$-0.519092\pi$
$149$	−1.46341	−0.119888	−0.0599438	+	0.998202i	$0.519092\pi$
$150$	0	0
$151$	−17.6024	−1.43247	−0.716233	−	0.697861i	$-0.754135\pi$
$151$	−17.6024	−1.43247	−0.716233	+	0.697861i	$0.754135\pi$
$152$	−31.7233	−2.57310
$153$	−29.6461	−2.39675
$154$	−0.690820	−0.0556678
$155$	0	0
$156$	19.0846	1.52799
$157$	−11.0479	−0.881721	−0.440861	−	0.897576i	$-0.645327\pi$
$157$	−11.0479	−0.881721	−0.440861	+	0.897576i	$0.645327\pi$
$158$	−20.7077	−1.64742
$159$	−23.5020	−1.86383
$160$	0	0
$161$	1.00000	0.0788110
$162$	14.2067	1.11618
$163$	−18.1543	−1.42196	−0.710979	−	0.703213i	$-0.751748\pi$
$163$	−18.1543	−1.42196	−0.710979	+	0.703213i	$0.751748\pi$
$164$	10.4686	0.817459
$165$	0	0
$166$	5.57837	0.432965
$167$	−11.6676	−0.902870	−0.451435	−	0.892304i	$-0.649088\pi$
$167$	−11.6676	−0.902870	−0.451435	+	0.892304i	$0.649088\pi$
$168$	21.4160	1.65228
$169$	−11.1606	−0.858510
$170$	0	0
$171$	−24.2470	−1.85421
$172$	11.4542	0.873372
$173$	−9.36349	−0.711893	−0.355946	−	0.934506i	$-0.615841\pi$
$173$	−9.36349	−0.711893	−0.355946	+	0.934506i	$0.615841\pi$
$174$	41.9236	3.17822
$175$	0	0
$176$	2.50499	0.188820
$177$	27.7236	2.08384
$178$	37.6784	2.82412
$179$	−8.69874	−0.650174	−0.325087	−	0.945684i	$-0.605394\pi$
$179$	−8.69874	−0.650174	−0.325087	+	0.945684i	$0.605394\pi$
$180$	0	0
$181$	20.3702	1.51411	0.757053	−	0.653353i	$-0.226638\pi$
$181$	20.3702	1.51411	0.757053	+	0.653353i	$0.226638\pi$
$182$	3.53721	0.262196
$183$	−11.6006	−0.857544
$184$	−7.30867	−0.538802
$185$	0	0
$186$	−62.2032	−4.56096
$187$	−1.40569	−0.102794
$188$	−56.3410	−4.10909
$189$	7.57817	0.551231
$190$	0	0
$191$	−3.73267	−0.270086	−0.135043	−	0.990840i	$-0.543117\pi$
$191$	−3.73267	−0.270086	−0.135043	+	0.990840i	$0.543117\pi$
$192$	−21.3698	−1.54223
$193$	−7.62742	−0.549034	−0.274517	−	0.961582i	$-0.588518\pi$
$193$	−7.62742	−0.549034	−0.274517	+	0.961582i	$0.588518\pi$
$194$	−40.1943	−2.88578
$195$	0	0
$196$	4.80228	0.343020
$197$	22.7710	1.62237	0.811185	−	0.584790i	$-0.198823\pi$
$197$	22.7710	1.62237	0.811185	+	0.584790i	$0.198823\pi$
$198$	3.85906	0.274252
$199$	17.4624	1.23788	0.618939	−	0.785439i	$-0.287563\pi$
$199$	17.4624	1.23788	0.618939	+	0.785439i	$0.287563\pi$
$200$	0	0
$201$	26.9598	1.90160
$202$	−27.3884	−1.92704
$203$	5.48568	0.385019
$204$	74.6790	5.22857
$205$	0	0
$206$	4.82392	0.336098
$207$	−5.58621	−0.388268
$208$	−12.8263	−0.889345
$209$	−1.14968	−0.0795253
$210$	0	0
$211$	1.68640	0.116096	0.0580482	−	0.998314i	$-0.481512\pi$
$211$	1.68640	0.116096	0.0580482	+	0.998314i	$0.481512\pi$
$212$	38.5170	2.64536
$213$	27.4465	1.88060
$214$	15.9384	1.08953
$215$	0	0
$216$	−55.3863	−3.76856
$217$	−8.13926	−0.552529
$218$	42.0006	2.84464
$219$	18.3487	1.23989
$220$	0	0
$221$	7.19755	0.484159
$222$	40.6910	2.73100
$223$	−12.1130	−0.811149	−0.405574	−	0.914062i	$-0.632928\pi$
$223$	−12.1130	−0.811149	−0.405574	+	0.914062i	$0.632928\pi$
$224$	−10.0484	−0.671390
$225$	0	0
$226$	44.9329	2.98889
$227$	6.71571	0.445737	0.222869	−	0.974849i	$-0.428458\pi$
$227$	6.71571	0.445737	0.222869	+	0.974849i	$0.428458\pi$
$228$	61.0785	4.04503
$229$	−23.8259	−1.57446	−0.787230	−	0.616659i	$-0.788486\pi$
$229$	−23.8259	−1.57446	−0.787230	+	0.616659i	$0.788486\pi$
$230$	0	0
$231$	0.776137	0.0510661
$232$	−40.0930	−2.63224
$233$	22.2706	1.45899	0.729497	−	0.683984i	$-0.239754\pi$
$233$	22.2706	1.45899	0.729497	+	0.683984i	$0.239754\pi$
$234$	−19.7596	−1.29173
$235$	0	0
$236$	−45.4356	−2.95761
$237$	23.2651	1.51123
$238$	13.8413	0.897200
$239$	−14.9157	−0.964816	−0.482408	−	0.875947i	$-0.660238\pi$
$239$	−14.9157	−0.964816	−0.482408	+	0.875947i	$0.660238\pi$
$240$	0	0
$241$	−27.5138	−1.77232	−0.886160	−	0.463379i	$-0.846637\pi$
$241$	−27.5138	−1.77232	−0.886160	+	0.463379i	$0.846637\pi$
$242$	−28.5063	−1.83246
$243$	6.77328	0.434506
$244$	19.0120	1.21712
$245$	0	0
$246$	−16.6598	−1.06219
$247$	5.88674	0.374564
$248$	59.4871	3.77744
$249$	−6.26730	−0.397174
$250$	0	0
$251$	30.3264	1.91418	0.957092	−	0.289785i	$-0.0935838\pi$
$251$	30.3264	1.91418	0.957092	+	0.289785i	$0.0935838\pi$
$252$	−26.8265	−1.68991
$253$	−0.264873	−0.0166524
$254$	−40.9189	−2.56748
$255$	0	0
$256$	−17.3925	−1.08703
$257$	2.62064	0.163471	0.0817354	−	0.996654i	$-0.473954\pi$
$257$	2.62064	0.163471	0.0817354	+	0.996654i	$0.473954\pi$
$258$	−18.2282	−1.13484
$259$	5.32439	0.330842
$260$	0	0
$261$	−30.6442	−1.89683
$262$	18.9838	1.17282
$263$	−20.4577	−1.26148	−0.630739	−	0.775995i	$-0.717248\pi$
$263$	−20.4577	−1.26148	−0.630739	+	0.775995i	$0.717248\pi$
$264$	−5.67253	−0.349120
$265$	0	0
$266$	11.3206	0.694108
$267$	−42.3318	−2.59066
$268$	−44.1838	−2.69895
$269$	−1.01232	−0.0617225	−0.0308613	−	0.999524i	$-0.509825\pi$
$269$	−1.01232	−0.0617225	−0.0308613	+	0.999524i	$0.509825\pi$
$270$	0	0
$271$	22.0400	1.33884	0.669418	−	0.742886i	$-0.266543\pi$
$271$	22.0400	1.33884	0.669418	+	0.742886i	$0.266543\pi$
$272$	−50.1901	−3.04322
$273$	−3.97406	−0.240521
$274$	−16.8014	−1.01501
$275$	0	0
$276$	14.0717	0.847020
$277$	31.4409	1.88910	0.944550	−	0.328367i	$-0.106498\pi$
$277$	31.4409	1.88910	0.944550	+	0.328367i	$0.106498\pi$
$278$	21.7190	1.30262
$279$	45.4676	2.72207
$280$	0	0
$281$	17.4757	1.04252	0.521258	−	0.853399i	$-0.325463\pi$
$281$	17.4757	1.04252	0.521258	+	0.853399i	$0.325463\pi$
$282$	89.6614	5.33926
$283$	11.9944	0.712990	0.356495	−	0.934297i	$-0.383972\pi$
$283$	11.9944	0.712990	0.356495	+	0.934297i	$0.383972\pi$
$284$	−44.9815	−2.66916
$285$	0	0
$286$	−0.936912	−0.0554008
$287$	−2.17992	−0.128677
$288$	56.1327	3.30765
$289$	11.1644	0.656731
$290$	0	0
$291$	45.1583	2.64723
$292$	−30.0713	−1.75979
$293$	22.0872	1.29035	0.645175	−	0.764035i	$-0.276784\pi$
$293$	22.0872	1.29035	0.645175	+	0.764035i	$0.276784\pi$
$294$	−7.64237	−0.445712
$295$	0	0
$296$	−38.9142	−2.26184
$297$	−2.00725	−0.116473
$298$	−3.81676	−0.221099
$299$	1.35623	0.0784329
$300$	0	0
$301$	−2.38515	−0.137478
$302$	−45.9092	−2.64178
$303$	30.7709	1.76774
$304$	−41.0496	−2.35435
$305$	0	0
$306$	−77.3205	−4.42012
$307$	12.7263	0.726330	0.363165	−	0.931725i	$-0.381696\pi$
$307$	12.7263	0.726330	0.363165	+	0.931725i	$0.381696\pi$
$308$	−1.27199	−0.0724785
$309$	−5.41968	−0.308315
$310$	0	0
$311$	−23.2645	−1.31921	−0.659604	−	0.751613i	$-0.729276\pi$
$311$	−23.2645	−1.31921	−0.659604	+	0.751613i	$0.729276\pi$
$312$	29.0451	1.64436
$313$	9.77550	0.552544	0.276272	−	0.961079i	$-0.410901\pi$
$313$	9.77550	0.552544	0.276272	+	0.961079i	$0.410901\pi$
$314$	−28.8143	−1.62609
$315$	0	0
$316$	−38.1287	−2.14491
$317$	−12.7054	−0.713605	−0.356803	−	0.934180i	$-0.616133\pi$
$317$	−12.7054	−0.713605	−0.356803	+	0.934180i	$0.616133\pi$
$318$	−61.2961	−3.43731
$319$	−1.45301	−0.0813528
$320$	0	0
$321$	−17.9068	−0.999462
$322$	2.60812	0.145345
$323$	23.0352	1.28171
$324$	26.1585	1.45325
$325$	0	0
$326$	−47.3487	−2.62240
$327$	−47.1877	−2.60949
$328$	15.9323	0.879715
$329$	11.7321	0.646814
$330$	0	0
$331$	13.4765	0.740736	0.370368	−	0.928885i	$-0.379232\pi$
$331$	13.4765	0.740736	0.370368	+	0.928885i	$0.379232\pi$
$332$	10.2713	0.563713
$333$	−29.7432	−1.62992
$334$	−30.4306	−1.66509
$335$	0	0
$336$	27.7120	1.51182
$337$	22.6729	1.23507	0.617536	−	0.786543i	$-0.288131\pi$
$337$	22.6729	1.23507	0.617536	+	0.786543i	$0.288131\pi$
$338$	−29.1082	−1.58328
$339$	−50.4822	−2.74182
$340$	0	0
$341$	2.15587	0.116747
$342$	−63.2390	−3.41957
$343$	−1.00000	−0.0539949
$344$	17.4323	0.939886
$345$	0	0
$346$	−24.4211	−1.31289
$347$	6.26654	0.336405	0.168203	−	0.985752i	$-0.446204\pi$
$347$	6.26654	0.336405	0.168203	+	0.985752i	$0.446204\pi$
$348$	77.1931	4.13798
$349$	−6.12044	−0.327620	−0.163810	−	0.986492i	$-0.552378\pi$
$349$	−6.12044	−0.327620	−0.163810	+	0.986492i	$0.552378\pi$
$350$	0	0
$351$	10.2778	0.548586
$352$	2.66156	0.141862
$353$	−23.4812	−1.24978	−0.624890	−	0.780713i	$-0.714856\pi$
$353$	−23.4812	−1.24978	−0.624890	+	0.780713i	$0.714856\pi$
$354$	72.3065	3.84305
$355$	0	0
$356$	69.3766	3.67695
$357$	−15.5507	−0.823033
$358$	−22.6873	−1.19906
$359$	2.80426	0.148003	0.0740017	−	0.997258i	$-0.476423\pi$
$359$	2.80426	0.148003	0.0740017	+	0.997258i	$0.476423\pi$
$360$	0	0
$361$	−0.159974	−0.00841966
$362$	53.1279	2.79234
$363$	32.0269	1.68098
$364$	6.51300	0.341374
$365$	0	0
$366$	−30.2558	−1.58150
$367$	−17.7657	−0.927360	−0.463680	−	0.886003i	$-0.653471\pi$
$367$	−17.7657	−0.927360	−0.463680	+	0.886003i	$0.653471\pi$
$368$	−9.45731	−0.492996
$369$	12.1775	0.633935
$370$	0	0
$371$	−8.02056	−0.416407
$372$	−114.534	−5.93829
$373$	5.52592	0.286121	0.143061	−	0.989714i	$-0.454306\pi$
$373$	5.52592	0.286121	0.143061	+	0.989714i	$0.454306\pi$
$374$	−3.66619	−0.189574
$375$	0	0
$376$	−85.7464	−4.42203
$377$	7.43986	0.383172
$378$	19.7648	1.01659
$379$	7.73303	0.397219	0.198610	−	0.980079i	$-0.436357\pi$
$379$	7.73303	0.397219	0.198610	+	0.980079i	$0.436357\pi$
$380$	0	0
$381$	45.9725	2.35524
$382$	−9.73523	−0.498098
$383$	17.0498	0.871207	0.435603	−	0.900139i	$-0.356535\pi$
$383$	17.0498	0.871207	0.435603	+	0.900139i	$0.356535\pi$
$384$	3.15335	0.160919
$385$	0	0
$386$	−19.8932	−1.01254
$387$	13.3240	0.677295
$388$	−74.0089	−3.75724
$389$	2.11683	0.107327	0.0536637	−	0.998559i	$-0.482910\pi$
$389$	2.11683	0.107327	0.0536637	+	0.998559i	$0.482910\pi$
$390$	0	0
$391$	5.30702	0.268387
$392$	7.30867	0.369143
$393$	−21.3283	−1.07587
$394$	59.3896	2.99200
$395$	0	0
$396$	7.10562	0.357071
$397$	34.1749	1.71519	0.857594	−	0.514327i	$-0.171958\pi$
$397$	34.1749	1.71519	0.857594	+	0.514327i	$0.171958\pi$
$398$	45.5441	2.28292
$399$	−12.7187	−0.636730
$400$	0	0
$401$	32.2156	1.60877	0.804384	−	0.594109i	$-0.202495\pi$
$401$	32.2156	1.60877	0.804384	+	0.594109i	$0.202495\pi$
$402$	70.3143	3.50696
$403$	−11.0387	−0.549878
$404$	−50.4298	−2.50898
$405$	0	0
$406$	14.3073	0.710059
$407$	−1.41029	−0.0699054
$408$	113.655	5.62677
$409$	21.1919	1.04787	0.523936	−	0.851758i	$-0.324463\pi$
$409$	21.1919	1.04787	0.523936	+	0.851758i	$0.324463\pi$
$410$	0	0
$411$	18.8763	0.931101
$412$	8.88219	0.437594
$413$	9.46127	0.465559
$414$	−14.5695	−0.716051
$415$	0	0
$416$	−13.6280	−0.668169
$417$	−24.4013	−1.19494
$418$	−2.99851	−0.146662
$419$	−26.9739	−1.31776	−0.658880	−	0.752248i	$-0.728969\pi$
$419$	−26.9739	−1.31776	−0.658880	+	0.752248i	$0.728969\pi$
$420$	0	0
$421$	24.7065	1.20412	0.602061	−	0.798450i	$-0.294347\pi$
$421$	24.7065	1.20412	0.602061	+	0.798450i	$0.294347\pi$
$422$	4.39833	0.214107
$423$	−65.5382	−3.18658
$424$	58.6196	2.84682
$425$	0	0
$426$	71.5838	3.46824
$427$	−3.95896	−0.191588
$428$	29.3471	1.41855
$429$	1.05262	0.0508211
$430$	0	0
$431$	12.6406	0.608877	0.304438	−	0.952532i	$-0.401531\pi$
$431$	12.6406	0.608877	0.304438	+	0.952532i	$0.401531\pi$
$432$	−71.6691	−3.44818
$433$	8.38436	0.402926	0.201463	−	0.979496i	$-0.435430\pi$
$433$	8.38436	0.402926	0.201463	+	0.979496i	$0.435430\pi$
$434$	−21.2281	−1.01898
$435$	0	0
$436$	77.3349	3.70367
$437$	4.34051	0.207635
$438$	47.8556	2.28663
$439$	25.8993	1.23611	0.618054	−	0.786136i	$-0.287921\pi$
$439$	25.8993	1.23611	0.618054	+	0.786136i	$0.287921\pi$
$440$	0	0
$441$	5.58621	0.266010
$442$	18.7721	0.892895
$443$	25.6141	1.21696	0.608481	−	0.793568i	$-0.291779\pi$
$443$	25.6141	1.21696	0.608481	+	0.793568i	$0.291779\pi$
$444$	74.9235	3.55571
$445$	0	0
$446$	−31.5922	−1.49593
$447$	4.28813	0.202822
$448$	−7.29290	−0.344557
$449$	−19.1007	−0.901419	−0.450709	−	0.892671i	$-0.648829\pi$
$449$	−19.1007	−0.901419	−0.450709	+	0.892671i	$0.648829\pi$
$450$	0	0
$451$	0.577402	0.0271888
$452$	82.7341	3.89149
$453$	51.5791	2.42340
$454$	17.5154	0.822036
$455$	0	0
$456$	92.9565	4.35309
$457$	20.9317	0.979142	0.489571	−	0.871964i	$-0.337153\pi$
$457$	20.9317	0.979142	0.489571	+	0.871964i	$0.337153\pi$
$458$	−62.1408	−2.90365
$459$	40.2175	1.87719
$460$	0	0
$461$	17.7059	0.824648	0.412324	−	0.911037i	$-0.364717\pi$
$461$	17.7059	0.824648	0.412324	+	0.911037i	$0.364717\pi$
$462$	2.02426	0.0941769
$463$	6.01284	0.279440	0.139720	−	0.990191i	$-0.455380\pi$
$463$	6.01284	0.279440	0.139720	+	0.990191i	$0.455380\pi$
$464$	−51.8798	−2.40846
$465$	0	0
$466$	58.0843	2.69070
$467$	−27.0237	−1.25051	−0.625254	−	0.780422i	$-0.715004\pi$
$467$	−27.0237	−1.25051	−0.625254	+	0.780422i	$0.715004\pi$
$468$	−36.3830	−1.68180
$469$	9.20059	0.424844
$470$	0	0
$471$	32.3729	1.49167
$472$	−69.1493	−3.18285
$473$	0.631762	0.0290485
$474$	60.6782	2.78704
$475$	0	0
$476$	25.4858	1.16814
$477$	44.8045	2.05146
$478$	−38.9019	−1.77933
$479$	11.3921	0.520519	0.260259	−	0.965539i	$-0.416192\pi$
$479$	11.3921	0.520519	0.260259	+	0.965539i	$0.416192\pi$
$480$	0	0
$481$	7.22112	0.329255
$482$	−71.7593	−3.26855
$483$	−2.93022	−0.133330
$484$	−52.4881	−2.38582
$485$	0	0
$486$	17.6655	0.801324
$487$	−22.2776	−1.00949	−0.504746	−	0.863268i	$-0.668414\pi$
$487$	−22.2776	−1.00949	−0.504746	+	0.863268i	$0.668414\pi$
$488$	28.9347	1.30981
$489$	53.1963	2.40562
$490$	0	0
$491$	−19.1738	−0.865303	−0.432651	−	0.901561i	$-0.642422\pi$
$491$	−19.1738	−0.865303	−0.432651	+	0.901561i	$0.642422\pi$
$492$	−30.6753	−1.38295
$493$	29.1126	1.31117
$494$	15.3533	0.690778
$495$	0	0
$496$	76.9755	3.45630
$497$	9.36670	0.420154
$498$	−16.3459	−0.732476
$499$	−11.0242	−0.493513	−0.246756	−	0.969078i	$-0.579365\pi$
$499$	−11.0242	−0.493513	−0.246756	+	0.969078i	$0.579365\pi$
$500$	0	0
$501$	34.1888	1.52744
$502$	79.0947	3.53017
$503$	−7.67908	−0.342393	−0.171197	−	0.985237i	$-0.554763\pi$
$503$	−7.67908	−0.342393	−0.171197	+	0.985237i	$0.554763\pi$
$504$	−40.8277	−1.81861
$505$	0	0
$506$	−0.690820	−0.0307107
$507$	32.7031	1.45240
$508$	−75.3433	−3.34282
$509$	22.1019	0.979650	0.489825	−	0.871821i	$-0.337061\pi$
$509$	22.1019	0.979650	0.489825	+	0.871821i	$0.337061\pi$
$510$	0	0
$511$	6.26188	0.277009
$512$	−43.2094	−1.90961
$513$	32.8931	1.45227
$514$	6.83492	0.301476
$515$	0	0
$516$	−33.5633	−1.47754
$517$	−3.10753	−0.136669
$518$	13.8866	0.610144
$519$	27.4371	1.20436
$520$	0	0
$521$	−35.9592	−1.57540	−0.787700	−	0.616059i	$-0.788728\pi$
$521$	−35.9592	−1.57540	−0.787700	+	0.616059i	$0.788728\pi$
$522$	−79.9236	−3.49816
$523$	7.63666	0.333928	0.166964	−	0.985963i	$-0.446604\pi$
$523$	7.63666	0.333928	0.166964	+	0.985963i	$0.446604\pi$
$524$	34.9544	1.52699
$525$	0	0
$526$	−53.3562	−2.32644
$527$	−43.1952	−1.88161
$528$	−7.34017	−0.319440
$529$	1.00000	0.0434783
$530$	0	0
$531$	−52.8526	−2.29361
$532$	20.8443	0.903716
$533$	−2.95648	−0.128059
$534$	−110.406	−4.77775
$535$	0	0
$536$	−67.2440	−2.90450
$537$	25.4893	1.09994
$538$	−2.64026	−0.113830
$539$	0.264873	0.0114089
$540$	0	0
$541$	19.2373	0.827076	0.413538	−	0.910487i	$-0.364293\pi$
$541$	19.2373	0.827076	0.413538	+	0.910487i	$0.364293\pi$
$542$	57.4830	2.46911
$543$	−59.6893	−2.56151
$544$	−53.3273	−2.28639
$545$	0	0
$546$	−10.3648	−0.443574
$547$	−33.6795	−1.44003	−0.720016	−	0.693957i	$-0.755866\pi$
$547$	−33.6795	−1.44003	−0.720016	+	0.693957i	$0.755866\pi$
$548$	−30.9360	−1.32152
$549$	22.1156	0.943871
$550$	0	0
$551$	23.8106	1.01437
$552$	21.4160	0.911527
$553$	7.93971	0.337631
$554$	82.0016	3.48391
$555$	0	0
$556$	39.9908	1.69599
$557$	−23.5786	−0.999059	−0.499529	−	0.866297i	$-0.666494\pi$
$557$	−23.5786	−0.999059	−0.499529	+	0.866297i	$0.666494\pi$
$558$	118.585	5.02010
$559$	−3.23482	−0.136818
$560$	0	0
$561$	4.11897	0.173903
$562$	45.5788	1.92263
$563$	−22.3385	−0.941454	−0.470727	−	0.882279i	$-0.656008\pi$
$563$	−22.3385	−0.941454	−0.470727	+	0.882279i	$0.656008\pi$
$564$	165.092	6.95162
$565$	0	0
$566$	31.2827	1.31491
$567$	−5.44710	−0.228757
$568$	−68.4581	−2.87244
$569$	29.4980	1.23662	0.618311	−	0.785934i	$-0.287817\pi$
$569$	29.4980	1.23662	0.618311	+	0.785934i	$0.287817\pi$
$570$	0	0
$571$	−24.1885	−1.01226	−0.506129	−	0.862458i	$-0.668924\pi$
$571$	−24.1885	−1.01226	−0.506129	+	0.862458i	$0.668924\pi$
$572$	−1.72512	−0.0721308
$573$	10.9375	0.456922
$574$	−5.68549	−0.237308
$575$	0	0
$576$	40.7397	1.69749
$577$	27.7186	1.15394	0.576969	−	0.816766i	$-0.304235\pi$
$577$	27.7186	1.15394	0.576969	+	0.816766i	$0.304235\pi$
$578$	29.1181	1.21115
$579$	22.3501	0.928837
$580$	0	0
$581$	−2.13885	−0.0887344
$582$	117.778	4.88206
$583$	2.12443	0.0879849
$584$	−45.7660	−1.89381
$585$	0	0
$586$	57.6061	2.37969
$587$	3.29059	0.135817	0.0679087	−	0.997692i	$-0.478367\pi$
$587$	3.29059	0.135817	0.0679087	+	0.997692i	$0.478367\pi$
$588$	−14.0717	−0.580309
$589$	−35.3285	−1.45569
$590$	0	0
$591$	−66.7243	−2.74467
$592$	−50.3545	−2.06956
$593$	23.4862	0.964461	0.482230	−	0.876044i	$-0.339827\pi$
$593$	23.4862	0.964461	0.482230	+	0.876044i	$0.339827\pi$
$594$	−5.23515	−0.214801
$595$	0	0
$596$	−7.02772	−0.287867
$597$	−51.1688	−2.09420
$598$	3.53721	0.144647
$599$	−18.7220	−0.764960	−0.382480	−	0.923964i	$-0.624930\pi$
$599$	−18.7220	−0.764960	−0.382480	+	0.923964i	$0.624930\pi$
$600$	0	0
$601$	36.0370	1.46998	0.734990	−	0.678078i	$-0.237187\pi$
$601$	36.0370	1.46998	0.734990	+	0.678078i	$0.237187\pi$
$602$	−6.22076	−0.253539
$603$	−51.3964	−2.09302
$604$	−84.5318	−3.43955
$605$	0	0
$606$	80.2542	3.26010
$607$	42.7349	1.73456	0.867278	−	0.497824i	$-0.165868\pi$
$607$	42.7349	1.73456	0.867278	+	0.497824i	$0.165868\pi$
$608$	−43.6154	−1.76884
$609$	−16.0743	−0.651362
$610$	0	0
$611$	15.9115	0.643711
$612$	−142.369	−5.75492
$613$	−18.3640	−0.741714	−0.370857	−	0.928690i	$-0.620936\pi$
$613$	−18.3640	−0.741714	−0.370857	+	0.928690i	$0.620936\pi$
$614$	33.1918	1.33951
$615$	0	0
$616$	−1.93587	−0.0779984
$617$	−17.8720	−0.719500	−0.359750	−	0.933049i	$-0.617138\pi$
$617$	−17.8720	−0.719500	−0.359750	+	0.933049i	$0.617138\pi$
$618$	−14.1352	−0.568600
$619$	−10.9172	−0.438798	−0.219399	−	0.975635i	$-0.570410\pi$
$619$	−10.9172	−0.438798	−0.219399	+	0.975635i	$0.570410\pi$
$620$	0	0
$621$	7.57817	0.304101
$622$	−60.6765	−2.43291
$623$	−14.4466	−0.578791
$624$	37.5840	1.50456
$625$	0	0
$626$	25.4957	1.01901
$627$	3.36883	0.134538
$628$	−53.0552	−2.11713
$629$	28.2566	1.12667
$630$	0	0
$631$	−27.7077	−1.10302	−0.551512	−	0.834167i	$-0.685949\pi$
$631$	−27.7077	−1.10302	−0.551512	+	0.834167i	$0.685949\pi$
$632$	−58.0287	−2.30826
$633$	−4.94153	−0.196408
$634$	−33.1371	−1.31604
$635$	0	0
$636$	−112.863	−4.47532
$637$	−1.35623	−0.0537359
$638$	−3.78962	−0.150032
$639$	−52.3243	−2.06992
$640$	0	0
$641$	20.1663	0.796520	0.398260	−	0.917273i	$-0.369614\pi$
$641$	20.1663	0.796520	0.398260	+	0.917273i	$0.369614\pi$
$642$	−46.7031	−1.84323
$643$	−9.53686	−0.376097	−0.188048	−	0.982160i	$-0.560216\pi$
$643$	−9.53686	−0.376097	−0.188048	+	0.982160i	$0.560216\pi$
$644$	4.80228	0.189236
$645$	0	0
$646$	60.0784	2.36375
$647$	−33.3441	−1.31089	−0.655446	−	0.755242i	$-0.727519\pi$
$647$	−33.3441	−1.31089	−0.655446	+	0.755242i	$0.727519\pi$
$648$	39.8111	1.56393
$649$	−2.50603	−0.0983705
$650$	0	0
$651$	23.8498	0.934749
$652$	−87.1822	−3.41432
$653$	−9.23434	−0.361368	−0.180684	−	0.983541i	$-0.557831\pi$
$653$	−9.23434	−0.361368	−0.180684	+	0.983541i	$0.557831\pi$
$654$	−123.071	−4.81246
$655$	0	0
$656$	20.6162	0.804927
$657$	−34.9802	−1.36471
$658$	30.5988	1.19287
$659$	−28.9432	−1.12747	−0.563733	−	0.825957i	$-0.690635\pi$
$659$	−28.9432	−1.12747	−0.563733	+	0.825957i	$0.690635\pi$
$660$	0	0
$661$	−18.1982	−0.707826	−0.353913	−	0.935278i	$-0.615149\pi$
$661$	−18.1982	−0.707826	−0.353913	+	0.935278i	$0.615149\pi$
$662$	35.1483	1.36608
$663$	−21.0904	−0.819084
$664$	15.6321	0.606644
$665$	0	0
$666$	−77.5737	−3.00592
$667$	5.48568	0.212406
$668$	−56.0313	−2.16792
$669$	35.4939	1.37227
$670$	0	0
$671$	1.04862	0.0404816
$672$	29.4442	1.13583
$673$	−31.2671	−1.20526	−0.602630	−	0.798021i	$-0.705880\pi$
$673$	−31.2671	−1.20526	−0.602630	+	0.798021i	$0.705880\pi$
$674$	59.1336	2.27774
$675$	0	0
$676$	−53.5965	−2.06140
$677$	4.47907	0.172145	0.0860723	−	0.996289i	$-0.472568\pi$
$677$	4.47907	0.172145	0.0860723	+	0.996289i	$0.472568\pi$
$678$	−131.664	−5.05651
$679$	15.4112	0.591428
$680$	0	0
$681$	−19.6785	−0.754083
$682$	5.62276	0.215307
$683$	41.6074	1.59206	0.796031	−	0.605256i	$-0.206929\pi$
$683$	41.6074	1.59206	0.796031	+	0.605256i	$0.206929\pi$
$684$	−116.441	−4.45223
$685$	0	0
$686$	−2.60812	−0.0995784
$687$	69.8152	2.66362
$688$	22.5571	0.859983
$689$	−10.8777	−0.414409
$690$	0	0
$691$	−43.2876	−1.64674	−0.823369	−	0.567506i	$-0.807908\pi$
$691$	−43.2876	−1.64674	−0.823369	+	0.567506i	$0.807908\pi$
$692$	−44.9661	−1.70935
$693$	−1.47964	−0.0562067
$694$	16.3439	0.620405
$695$	0	0
$696$	117.481	4.45312
$697$	−11.5689	−0.438203
$698$	−15.9628	−0.604202
$699$	−65.2578	−2.46828
$700$	0	0
$701$	−0.880648	−0.0332616	−0.0166308	−	0.999862i	$-0.505294\pi$
$701$	−0.880648	−0.0332616	−0.0166308	+	0.999862i	$0.505294\pi$
$702$	26.8056	1.01171
$703$	23.1106	0.871632
$704$	1.93169	0.0728034
$705$	0	0
$706$	−61.2418	−2.30486
$707$	10.5012	0.394939
$708$	133.137	5.00358
$709$	35.5413	1.33478	0.667392	−	0.744707i	$-0.267411\pi$
$709$	35.5413	1.33478	0.667392	+	0.744707i	$0.267411\pi$
$710$	0	0
$711$	−44.3529	−1.66336
$712$	105.585	3.95698
$713$	−8.13926	−0.304818
$714$	−40.5582	−1.51785
$715$	0	0
$716$	−41.7738	−1.56116
$717$	43.7063	1.63224
$718$	7.31385	0.272950
$719$	3.14142	0.117155	0.0585775	−	0.998283i	$-0.481344\pi$
$719$	3.14142	0.117155	0.0585775	+	0.998283i	$0.481344\pi$
$720$	0	0
$721$	−1.84958	−0.0688819
$722$	−0.417230	−0.0155277
$723$	80.6216	2.99835
$724$	97.8234	3.63558
$725$	0	0
$726$	83.5299	3.10008
$727$	8.73417	0.323932	0.161966	−	0.986796i	$-0.448216\pi$
$727$	8.73417	0.323932	0.161966	+	0.986796i	$0.448216\pi$
$728$	9.91225	0.367373
$729$	−36.1885	−1.34032
$730$	0	0
$731$	−12.6580	−0.468175
$732$	−55.7095	−2.05908
$733$	−17.9669	−0.663624	−0.331812	−	0.943346i	$-0.607660\pi$
$733$	−17.9669	−0.663624	−0.331812	+	0.943346i	$0.607660\pi$
$734$	−46.3349	−1.71025
$735$	0	0
$736$	−10.0484	−0.370391
$737$	−2.43699	−0.0897675
$738$	31.7603	1.16911
$739$	−34.9398	−1.28528	−0.642640	−	0.766168i	$-0.722161\pi$
$739$	−34.9398	−1.28528	−0.642640	+	0.766168i	$0.722161\pi$
$740$	0	0
$741$	−17.2495	−0.633675
$742$	−20.9186	−0.767945
$743$	2.60865	0.0957020	0.0478510	−	0.998854i	$-0.484763\pi$
$743$	2.60865	0.0957020	0.0478510	+	0.998854i	$0.484763\pi$
$744$	−174.311	−6.39054
$745$	0	0
$746$	14.4122	0.527670
$747$	11.9481	0.437156
$748$	−6.75049	−0.246822
$749$	−6.11108	−0.223294
$750$	0	0
$751$	−31.8082	−1.16070	−0.580350	−	0.814367i	$-0.697084\pi$
$751$	−31.8082	−1.16070	−0.580350	+	0.814367i	$0.697084\pi$
$752$	−110.955	−4.04610
$753$	−88.8630	−3.23835
$754$	19.4040	0.706653
$755$	0	0
$756$	36.3925	1.32358
$757$	46.9764	1.70739	0.853694	−	0.520776i	$-0.174357\pi$
$757$	46.9764	1.70739	0.853694	+	0.520776i	$0.174357\pi$
$758$	20.1687	0.732558
$759$	0.776137	0.0281720
$760$	0	0
$761$	13.0494	0.473041	0.236521	−	0.971626i	$-0.423993\pi$
$761$	13.0494	0.473041	0.236521	+	0.971626i	$0.423993\pi$
$762$	119.902	4.34358
$763$	−16.1038	−0.582996
$764$	−17.9253	−0.648514
$765$	0	0
$766$	44.4680	1.60669
$767$	12.8317	0.463325
$768$	50.9640	1.83900
$769$	−36.7432	−1.32499	−0.662497	−	0.749065i	$-0.730503\pi$
$769$	−36.7432	−1.32499	−0.662497	+	0.749065i	$0.730503\pi$
$770$	0	0
$771$	−7.67905	−0.276554
$772$	−36.6290	−1.31831
$773$	−46.8121	−1.68371	−0.841857	−	0.539701i	$-0.818537\pi$
$773$	−46.8121	−1.68371	−0.841857	+	0.539701i	$0.818537\pi$
$774$	34.7505	1.24908
$775$	0	0
$776$	−112.635	−4.04338
$777$	−15.6017	−0.559707
$778$	5.52094	0.197935
$779$	−9.46197	−0.339010
$780$	0	0
$781$	−2.48099	−0.0887766
$782$	13.8413	0.494965
$783$	41.5714	1.48564
$784$	9.45731	0.337761
$785$	0	0
$786$	−55.6266	−1.98414
$787$	−19.6860	−0.701731	−0.350865	−	0.936426i	$-0.614112\pi$
$787$	−19.6860	−0.701731	−0.350865	+	0.936426i	$0.614112\pi$
$788$	109.353	3.89554
$789$	59.9458	2.13413
$790$	0	0
$791$	−17.2281	−0.612561
$792$	10.8142	0.384265
$793$	−5.36927	−0.190669
$794$	89.1321	3.16318
$795$	0	0
$796$	83.8594	2.97232
$797$	47.1199	1.66907	0.834536	−	0.550953i	$-0.185736\pi$
$797$	47.1199	1.66907	0.834536	+	0.550953i	$0.185736\pi$
$798$	−33.1718	−1.17427
$799$	62.2627	2.20270
$800$	0	0
$801$	80.7017	2.85146
$802$	84.0220	2.96692
$803$	−1.65860	−0.0585308
$804$	129.468	4.56599
$805$	0	0
$806$	−28.7903	−1.01410
$807$	2.96634	0.104420
$808$	−76.7500	−2.70005
$809$	−2.15971	−0.0759314	−0.0379657	−	0.999279i	$-0.512088\pi$
$809$	−2.15971	−0.0759314	−0.0379657	+	0.999279i	$0.512088\pi$
$810$	0	0
$811$	−44.0169	−1.54564	−0.772821	−	0.634624i	$-0.781155\pi$
$811$	−44.0169	−1.54564	−0.772821	+	0.634624i	$0.781155\pi$
$812$	26.3438	0.924485
$813$	−64.5822	−2.26500
$814$	−3.67820	−0.128921
$815$	0	0
$816$	147.068	5.14842
$817$	−10.3528	−0.362198
$818$	55.2709	1.93250
$819$	7.57620	0.264734
$820$	0	0
$821$	−51.0507	−1.78168	−0.890842	−	0.454314i	$-0.849884\pi$
$821$	−51.0507	−1.78168	−0.890842	+	0.454314i	$0.849884\pi$
$822$	49.2317	1.71715
$823$	8.29379	0.289103	0.144552	−	0.989497i	$-0.453826\pi$
$823$	8.29379	0.289103	0.144552	+	0.989497i	$0.453826\pi$
$824$	13.5180	0.470921
$825$	0	0
$826$	24.6761	0.858592
$827$	18.0846	0.628864	0.314432	−	0.949280i	$-0.398186\pi$
$827$	18.0846	0.628864	0.314432	+	0.949280i	$0.398186\pi$
$828$	−26.8265	−0.932286
$829$	6.31151	0.219208	0.109604	−	0.993975i	$-0.465042\pi$
$829$	6.31151	0.219208	0.109604	+	0.993975i	$0.465042\pi$
$830$	0	0
$831$	−92.1289	−3.19591
$832$	−9.89087	−0.342904
$833$	−5.30702	−0.183877
$834$	−63.6415	−2.20372
$835$	0	0
$836$	−5.52110	−0.190951
$837$	−61.6807	−2.13200
$838$	−70.3510	−2.43024
$839$	41.6165	1.43676	0.718381	−	0.695650i	$-0.244884\pi$
$839$	41.6165	1.43676	0.718381	+	0.695650i	$0.244884\pi$
$840$	0	0
$841$	1.09268	0.0376788
$842$	64.4375	2.22066
$843$	−51.2078	−1.76369
$844$	8.09855	0.278764
$845$	0	0
$846$	−170.931	−5.87674
$847$	10.9298	0.375554
$848$	75.8530	2.60480
$849$	−35.1461	−1.20621
$850$	0	0
$851$	5.32439	0.182518
$852$	131.806	4.51559
$853$	15.8989	0.544369	0.272184	−	0.962245i	$-0.412254\pi$
$853$	15.8989	0.544369	0.272184	+	0.962245i	$0.412254\pi$
$854$	−10.3254	−0.353329
$855$	0	0
$856$	44.6639	1.52658
$857$	0.825217	0.0281889	0.0140944	−	0.999901i	$-0.495513\pi$
$857$	0.825217	0.0281889	0.0140944	+	0.999901i	$0.495513\pi$
$858$	2.74536	0.0937251
$859$	34.4117	1.17411	0.587057	−	0.809546i	$-0.300287\pi$
$859$	34.4117	1.17411	0.587057	+	0.809546i	$0.300287\pi$
$860$	0	0
$861$	6.38766	0.217691
$862$	32.9682	1.12290
$863$	−22.0592	−0.750903	−0.375451	−	0.926842i	$-0.622512\pi$
$863$	−22.0592	−0.750903	−0.375451	+	0.926842i	$0.622512\pi$
$864$	−76.1488	−2.59064
$865$	0	0
$866$	21.8674	0.743084
$867$	−32.7142	−1.11103
$868$	−39.0870	−1.32670
$869$	−2.10302	−0.0713399
$870$	0	0
$871$	12.4781	0.422805
$872$	117.697	3.98573
$873$	−86.0903	−2.91371
$874$	11.3206	0.382924
$875$	0	0
$876$	88.1156	2.97715
$877$	−50.5832	−1.70807	−0.854036	−	0.520214i	$-0.825852\pi$
$877$	−50.5832	−1.70807	−0.854036	+	0.520214i	$0.825852\pi$
$878$	67.5485	2.27965
$879$	−64.7206	−2.18297
$880$	0	0
$881$	6.44596	0.217170	0.108585	−	0.994087i	$-0.465368\pi$
$881$	6.44596	0.217170	0.108585	+	0.994087i	$0.465368\pi$
$882$	14.5695	0.490580
$883$	−13.3589	−0.449562	−0.224781	−	0.974409i	$-0.572167\pi$
$883$	−13.3589	−0.449562	−0.224781	+	0.974409i	$0.572167\pi$
$884$	34.5646	1.16253
$885$	0	0
$886$	66.8046	2.24434
$887$	−31.4608	−1.05635	−0.528175	−	0.849136i	$-0.677123\pi$
$887$	−31.4608	−1.05635	−0.528175	+	0.849136i	$0.677123\pi$
$888$	114.027	3.82651
$889$	15.6891	0.526194
$890$	0	0
$891$	1.44279	0.0483353
$892$	−58.1701	−1.94768
$893$	50.9235	1.70409
$894$	11.1840	0.374047
$895$	0	0
$896$	1.07615	0.0359515
$897$	−3.97406	−0.132690
$898$	−49.8169	−1.66241
$899$	−44.6494	−1.48914
$900$	0	0
$901$	−42.5653	−1.41805
$902$	1.50593	0.0501421
$903$	6.98903	0.232580
$904$	125.915	4.18785
$905$	0	0
$906$	134.524	4.46927
$907$	−4.75791	−0.157984	−0.0789919	−	0.996875i	$-0.525170\pi$
$907$	−4.75791	−0.157984	−0.0789919	+	0.996875i	$0.525170\pi$
$908$	32.2507	1.07028
$909$	−58.6620	−1.94570
$910$	0	0
$911$	41.0352	1.35956	0.679779	−	0.733417i	$-0.262076\pi$
$911$	41.0352	1.35956	0.679779	+	0.733417i	$0.262076\pi$
$912$	120.284	3.98301
$913$	0.566523	0.0187492
$914$	54.5922	1.80575
$915$	0	0
$916$	−114.419	−3.78050
$917$	−7.27872	−0.240364
$918$	104.892	3.46195
$919$	−42.8738	−1.41428	−0.707139	−	0.707075i	$-0.750014\pi$
$919$	−42.8738	−1.41428	−0.707139	+	0.707075i	$0.750014\pi$
$920$	0	0
$921$	−37.2910	−1.22878
$922$	46.1792	1.52083
$923$	12.7034	0.418138
$924$	3.72722	0.122617
$925$	0	0
$926$	15.6822	0.515349
$927$	10.3321	0.339352
$928$	−55.1226	−1.80949
$929$	−21.9605	−0.720499	−0.360249	−	0.932856i	$-0.617308\pi$
$929$	−21.9605	−0.720499	−0.360249	+	0.932856i	$0.617308\pi$
$930$	0	0
$931$	−4.34051	−0.142254
$932$	106.950	3.50325
$933$	68.1701	2.23179
$934$	−70.4809	−2.30621
$935$	0	0
$936$	−55.3719	−1.80989
$937$	−10.6810	−0.348933	−0.174467	−	0.984663i	$-0.555820\pi$
$937$	−10.6810	−0.348933	−0.174467	+	0.984663i	$0.555820\pi$
$938$	23.9962	0.783504
$939$	−28.6444	−0.934775
$940$	0	0
$941$	−45.6300	−1.48749	−0.743747	−	0.668461i	$-0.766953\pi$
$941$	−45.6300	−1.48749	−0.743747	+	0.668461i	$0.766953\pi$
$942$	84.4324	2.75095
$943$	−2.17992	−0.0709880
$944$	−89.4782	−2.91227
$945$	0	0
$946$	1.64771	0.0535717
$947$	18.0066	0.585136	0.292568	−	0.956245i	$-0.405490\pi$
$947$	18.0066	0.585136	0.292568	+	0.956245i	$0.405490\pi$
$948$	111.726	3.62868
$949$	8.49257	0.275680
$950$	0	0
$951$	37.2296	1.20725
$952$	38.7872	1.25710
$953$	21.4483	0.694778	0.347389	−	0.937721i	$-0.387068\pi$
$953$	21.4483	0.694778	0.347389	+	0.937721i	$0.387068\pi$
$954$	116.856	3.78334
$955$	0	0
$956$	−71.6293	−2.31666
$957$	4.25764	0.137630
$958$	29.7120	0.959950
$959$	6.44195	0.208021
$960$	0	0
$961$	35.2475	1.13702
$962$	18.8335	0.607217
$963$	34.1378	1.10007
$964$	−132.129	−4.25559
$965$	0	0
$966$	−7.64237	−0.245889
$967$	47.1081	1.51489	0.757447	−	0.652897i	$-0.226446\pi$
$967$	47.1081	1.51489	0.757447	+	0.652897i	$0.226446\pi$
$968$	−79.8826	−2.56752
$969$	−67.4982	−2.16835
$970$	0	0
$971$	21.7571	0.698217	0.349109	−	0.937082i	$-0.386484\pi$
$971$	21.7571	0.698217	0.349109	+	0.937082i	$0.386484\pi$
$972$	32.5272	1.04331
$973$	−8.32746	−0.266966
$974$	−58.1025	−1.86172
$975$	0	0
$976$	37.4411	1.19846
$977$	7.53659	0.241117	0.120558	−	0.992706i	$-0.461531\pi$
$977$	7.53659	0.241117	0.120558	+	0.992706i	$0.461531\pi$
$978$	138.742	4.43648
$979$	3.82651	0.122296
$980$	0	0
$981$	89.9591	2.87217
$982$	−50.0076	−1.59581
$983$	38.2114	1.21875	0.609376	−	0.792881i	$-0.291420\pi$
$983$	38.2114	1.21875	0.609376	+	0.792881i	$0.291420\pi$
$984$	−46.6853	−1.48827
$985$	0	0
$986$	75.9291	2.41807
$987$	−34.3778	−1.09426
$988$	28.2698	0.899381
$989$	−2.38515	−0.0758435
$990$	0	0
$991$	8.93771	0.283916	0.141958	−	0.989873i	$-0.454660\pi$
$991$	8.93771	0.283916	0.141958	+	0.989873i	$0.454660\pi$
$992$	81.7869	2.59674
$993$	−39.4892	−1.25315
$994$	24.4295	0.774855
$995$	0	0
$996$	−30.0973	−0.953670
$997$	1.66702	0.0527949	0.0263975	−	0.999652i	$-0.491596\pi$
$997$	1.66702	0.0527949	0.0263975	+	0.999652i	$0.491596\pi$
$998$	−28.7525	−0.910145
$999$	40.3492	1.27659

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.z.1.14	✓	14
5.4	even	2		4025.2.a.bc.1.1	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4025.2.a.z.1.14	✓	14	1.1	even	1	trivial
4025.2.a.bc.1.1	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)

\(f(q)\)	\(=\)	\(q+2.60812 q^{2} -2.93022 q^{3} +4.80228 q^{4} -7.64237 q^{6} -1.00000 q^{7} +7.30867 q^{8} +5.58621 q^{9} +O(q^{10})\)	\(q+2.60812 q^{2} -2.93022 q^{3} +4.80228 q^{4} -7.64237 q^{6} -1.00000 q^{7} +7.30867 q^{8} +5.58621 q^{9} +0.264873 q^{11} -14.0717 q^{12} -1.35623 q^{13} -2.60812 q^{14} +9.45731 q^{16} -5.30702 q^{17} +14.5695 q^{18} -4.34051 q^{19} +2.93022 q^{21} +0.690820 q^{22} -1.00000 q^{23} -21.4160 q^{24} -3.53721 q^{26} -7.57817 q^{27} -4.80228 q^{28} -5.48568 q^{29} +8.13926 q^{31} +10.0484 q^{32} -0.776137 q^{33} -13.8413 q^{34} +26.8265 q^{36} -5.32439 q^{37} -11.3206 q^{38} +3.97406 q^{39} +2.17992 q^{41} +7.64237 q^{42} +2.38515 q^{43} +1.27199 q^{44} -2.60812 q^{46} -11.7321 q^{47} -27.7120 q^{48} +1.00000 q^{49} +15.5507 q^{51} -6.51300 q^{52} +8.02056 q^{53} -19.7648 q^{54} -7.30867 q^{56} +12.7187 q^{57} -14.3073 q^{58} -9.46127 q^{59} +3.95896 q^{61} +21.2281 q^{62} -5.58621 q^{63} +7.29290 q^{64} -2.02426 q^{66} -9.20059 q^{67} -25.4858 q^{68} +2.93022 q^{69} -9.36670 q^{71} +40.8277 q^{72} -6.26188 q^{73} -13.8866 q^{74} -20.8443 q^{76} -0.264873 q^{77} +10.3648 q^{78} -7.93971 q^{79} +5.44710 q^{81} +5.68549 q^{82} +2.13885 q^{83} +14.0717 q^{84} +6.22076 q^{86} +16.0743 q^{87} +1.93587 q^{88} +14.4466 q^{89} +1.35623 q^{91} -4.80228 q^{92} -23.8498 q^{93} -30.5988 q^{94} -29.4442 q^{96} -15.4112 q^{97} +2.60812 q^{98} +1.47964 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9}+O(q^{10}) \) 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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