LMFDB - Embedded newform 2225.2.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2225,2,Mod(1,2225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2225, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2225.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2225 = 5^{2} \cdot 89 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2225.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:	$17.7667144497$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 8x^{5} + 6x^{4} + 19x^{3} - 10x^{2} - 12x + 6 $ x^7 - x^6 - 8x^5 + 6x^4 + 19x^3 - 10x^2 - 12*x + 6
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 445)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.26266$ of defining polynomial
Character	$\chi$	$=$	2225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.11962 q^{2} +3.29058 q^{3} +2.49279 q^{4} -6.97477 q^{6} +4.83304 q^{7} -1.04452 q^{8} +7.82788 q^{9} +O(q^{10})$	\(q-2.11962 q^{2} +3.29058 q^{3} +2.49279 q^{4} -6.97477 q^{6} +4.83304 q^{7} -1.04452 q^{8} +7.82788 q^{9} -2.21586 q^{11} +8.20270 q^{12} +2.26162 q^{13} -10.2442 q^{14} -2.77159 q^{16} +3.10920 q^{17} -16.5921 q^{18} -5.93952 q^{19} +15.9035 q^{21} +4.69678 q^{22} -5.79416 q^{23} -3.43708 q^{24} -4.79378 q^{26} +15.8865 q^{27} +12.0477 q^{28} +2.32757 q^{29} +4.47624 q^{31} +7.96375 q^{32} -7.29145 q^{33} -6.59033 q^{34} +19.5133 q^{36} +8.23124 q^{37} +12.5895 q^{38} +7.44204 q^{39} -0.278075 q^{41} -33.7093 q^{42} +0.176109 q^{43} -5.52366 q^{44} +12.2814 q^{46} -1.91855 q^{47} -9.12011 q^{48} +16.3583 q^{49} +10.2311 q^{51} +5.63775 q^{52} -8.65904 q^{53} -33.6734 q^{54} -5.04821 q^{56} -19.5444 q^{57} -4.93357 q^{58} +5.39666 q^{59} -9.69150 q^{61} -9.48792 q^{62} +37.8325 q^{63} -11.3370 q^{64} +15.4551 q^{66} -8.06916 q^{67} +7.75058 q^{68} -19.0661 q^{69} -5.00576 q^{71} -8.17640 q^{72} +9.18909 q^{73} -17.4471 q^{74} -14.8060 q^{76} -10.7093 q^{77} -15.7743 q^{78} -1.78949 q^{79} +28.7921 q^{81} +0.589414 q^{82} -13.8879 q^{83} +39.6440 q^{84} -0.373284 q^{86} +7.65906 q^{87} +2.31451 q^{88} +1.00000 q^{89} +10.9305 q^{91} -14.4436 q^{92} +14.7294 q^{93} +4.06660 q^{94} +26.2053 q^{96} +5.52008 q^{97} -34.6733 q^{98} -17.3455 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 4 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{6} + 16 q^{7} + 12 q^{8} + 11 q^{9}+O(q^{10}) $ 7 * q + 4 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^6 + 16 * q^7 + 12 * q^8 + 11 * q^9	$ 7 q + 4 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{6} + 16 q^{7} + 12 q^{8} + 11 q^{9} - 10 q^{11} + 11 q^{12} + 7 q^{13} + 3 q^{14} + 10 q^{16} + 13 q^{17} - 4 q^{18} - 7 q^{19} + 16 q^{21} - 2 q^{22} + 13 q^{23} + 4 q^{24} + q^{26} + 23 q^{27} + 21 q^{28} - 4 q^{29} + q^{31} + 13 q^{32} + 6 q^{33} + 10 q^{34} + 20 q^{36} + 5 q^{37} + 40 q^{38} - 13 q^{39} + 5 q^{41} - 30 q^{42} + 31 q^{43} - 21 q^{44} + 16 q^{46} + 14 q^{47} + 7 q^{48} + 19 q^{49} - q^{51} + 13 q^{53} - 17 q^{54} - q^{56} - 21 q^{57} - 17 q^{58} - 14 q^{59} + 3 q^{61} - 26 q^{62} + 54 q^{63} + 14 q^{64} + 36 q^{66} - q^{67} + 35 q^{68} + 31 q^{69} - 8 q^{71} - 53 q^{72} - 9 q^{73} - 35 q^{74} + 40 q^{76} - 42 q^{77} - 46 q^{78} + 9 q^{79} + 35 q^{81} - 29 q^{82} + 42 q^{83} + 55 q^{84} + 35 q^{86} - 6 q^{87} - 30 q^{88} + 7 q^{89} + 31 q^{91} - 19 q^{92} - 24 q^{93} + 37 q^{94} + 44 q^{96} + 7 q^{97} - 9 q^{98} + 5 q^{99}+O(q^{100}) $ 7 * q + 4 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^6 + 16 * q^7 + 12 * q^8 + 11 * q^9 - 10 * q^11 + 11 * q^12 + 7 * q^13 + 3 * q^14 + 10 * q^16 + 13 * q^17 - 4 * q^18 - 7 * q^19 + 16 * q^21 - 2 * q^22 + 13 * q^23 + 4 * q^24 + q^26 + 23 * q^27 + 21 * q^28 - 4 * q^29 + q^31 + 13 * q^32 + 6 * q^33 + 10 * q^34 + 20 * q^36 + 5 * q^37 + 40 * q^38 - 13 * q^39 + 5 * q^41 - 30 * q^42 + 31 * q^43 - 21 * q^44 + 16 * q^46 + 14 * q^47 + 7 * q^48 + 19 * q^49 - q^51 + 13 * q^53 - 17 * q^54 - q^56 - 21 * q^57 - 17 * q^58 - 14 * q^59 + 3 * q^61 - 26 * q^62 + 54 * q^63 + 14 * q^64 + 36 * q^66 - q^67 + 35 * q^68 + 31 * q^69 - 8 * q^71 - 53 * q^72 - 9 * q^73 - 35 * q^74 + 40 * q^76 - 42 * q^77 - 46 * q^78 + 9 * q^79 + 35 * q^81 - 29 * q^82 + 42 * q^83 + 55 * q^84 + 35 * q^86 - 6 * q^87 - 30 * q^88 + 7 * q^89 + 31 * q^91 - 19 * q^92 - 24 * q^93 + 37 * q^94 + 44 * q^96 + 7 * q^97 - 9 * q^98 + 5 * 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 $

$2$	−2.11962	−1.49880	−0.749399	−	0.662119i	$-0.769657\pi$
$2$	−2.11962	−1.49880	−0.749399	+	0.662119i	$0.769657\pi$
$3$	3.29058	1.89981	0.949907	−	0.312532i	$-0.101177\pi$
$3$	3.29058	1.89981	0.949907	+	0.312532i	$0.101177\pi$
$4$	2.49279	1.24639
$5$	0	0
$5$	0	0
$6$	−6.97477	−2.84744
$7$	4.83304	1.82672	0.913358	−	0.407157i	$-0.133480\pi$
$7$	4.83304	1.82672	0.913358	+	0.407157i	$0.133480\pi$
$8$	−1.04452	−0.369294
$9$	7.82788	2.60929
$10$	0	0
$11$	−2.21586	−0.668106	−0.334053	−	0.942554i	$-0.608417\pi$
$11$	−2.21586	−0.668106	−0.334053	+	0.942554i	$0.608417\pi$
$12$	8.20270	2.36792
$13$	2.26162	0.627261	0.313631	−	0.949545i	$-0.398455\pi$
$13$	2.26162	0.627261	0.313631	+	0.949545i	$0.398455\pi$
$14$	−10.2442	−2.73788
$15$	0	0
$16$	−2.77159	−0.692896
$17$	3.10920	0.754092	0.377046	−	0.926194i	$-0.376940\pi$
$17$	3.10920	0.754092	0.377046	+	0.926194i	$0.376940\pi$
$18$	−16.5921	−3.91080
$19$	−5.93952	−1.36262	−0.681309	−	0.731996i	$-0.738589\pi$
$19$	−5.93952	−1.36262	−0.681309	+	0.731996i	$0.738589\pi$
$20$	0	0
$21$	15.9035	3.47042
$22$	4.69678	1.00136
$23$	−5.79416	−1.20817	−0.604083	−	0.796921i	$-0.706460\pi$
$23$	−5.79416	−1.20817	−0.604083	+	0.796921i	$0.706460\pi$
$24$	−3.43708	−0.701590
$25$	0	0
$26$	−4.79378	−0.940138
$27$	15.8865	3.05736
$28$	12.0477	2.27681
$29$	2.32757	0.432220	0.216110	−	0.976369i	$-0.430663\pi$
$29$	2.32757	0.432220	0.216110	+	0.976369i	$0.430663\pi$
$30$	0	0
$31$	4.47624	0.803956	0.401978	−	0.915649i	$-0.368323\pi$
$31$	4.47624	0.803956	0.401978	+	0.915649i	$0.368323\pi$
$32$	7.96375	1.40781
$33$	−7.29145	−1.26928
$34$	−6.59033	−1.13023
$35$	0	0
$36$	19.5133	3.25221
$37$	8.23124	1.35321	0.676604	−	0.736347i	$-0.263451\pi$
$37$	8.23124	1.35321	0.676604	+	0.736347i	$0.263451\pi$
$38$	12.5895	2.04229
$39$	7.44204	1.19168
$40$	0	0
$41$	−0.278075	−0.0434281	−0.0217140	−	0.999764i	$-0.506912\pi$
$41$	−0.278075	−0.0434281	−0.0217140	+	0.999764i	$0.506912\pi$
$42$	−33.7093	−5.20146
$43$	0.176109	0.0268564	0.0134282	−	0.999910i	$-0.495726\pi$
$43$	0.176109	0.0268564	0.0134282	+	0.999910i	$0.495726\pi$
$44$	−5.52366	−0.832724
$45$	0	0
$46$	12.2814	1.81080
$47$	−1.91855	−0.279850	−0.139925	−	0.990162i	$-0.544686\pi$
$47$	−1.91855	−0.279850	−0.139925	+	0.990162i	$0.544686\pi$
$48$	−9.12011	−1.31637
$49$	16.3583	2.33689
$50$	0	0
$51$	10.2311	1.43264
$52$	5.63775	0.781815
$53$	−8.65904	−1.18941	−0.594706	−	0.803944i	$-0.702731\pi$
$53$	−8.65904	−1.18941	−0.594706	+	0.803944i	$0.702731\pi$
$54$	−33.6734	−4.58237
$55$	0	0
$56$	−5.04821	−0.674596
$57$	−19.5444	−2.58872
$58$	−4.93357	−0.647810
$59$	5.39666	0.702585	0.351292	−	0.936266i	$-0.385742\pi$
$59$	5.39666	0.702585	0.351292	+	0.936266i	$0.385742\pi$
$60$	0	0
$61$	−9.69150	−1.24087	−0.620434	−	0.784258i	$-0.713044\pi$
$61$	−9.69150	−1.24087	−0.620434	+	0.784258i	$0.713044\pi$
$62$	−9.48792	−1.20497
$63$	37.8325	4.76644
$64$	−11.3370	−1.41712
$65$	0	0
$66$	15.4551	1.90239
$67$	−8.06916	−0.985805	−0.492903	−	0.870084i	$-0.664064\pi$
$67$	−8.06916	−0.985805	−0.492903	+	0.870084i	$0.664064\pi$
$68$	7.75058	0.939896
$69$	−19.0661	−2.29529
$70$	0	0
$71$	−5.00576	−0.594075	−0.297037	−	0.954866i	$-0.595999\pi$
$71$	−5.00576	−0.594075	−0.297037	+	0.954866i	$0.595999\pi$
$72$	−8.17640	−0.963597
$73$	9.18909	1.07550	0.537751	−	0.843104i	$-0.319274\pi$
$73$	9.18909	1.07550	0.537751	+	0.843104i	$0.319274\pi$
$74$	−17.4471	−2.02818
$75$	0	0
$76$	−14.8060	−1.69836
$77$	−10.7093	−1.22044
$78$	−15.7743	−1.78609
$79$	−1.78949	−0.201333	−0.100666	−	0.994920i	$-0.532097\pi$
$79$	−1.78949	−0.201333	−0.100666	+	0.994920i	$0.532097\pi$
$80$	0	0
$81$	28.7921	3.19912
$82$	0.589414	0.0650899
$83$	−13.8879	−1.52439	−0.762197	−	0.647345i	$-0.775879\pi$
$83$	−13.8879	−1.52439	−0.762197	+	0.647345i	$0.775879\pi$
$84$	39.6440	4.32551
$85$	0	0
$86$	−0.373284	−0.0402523
$87$	7.65906	0.821137
$88$	2.31451	0.246728
$89$	1.00000	0.106000
$89$	1.00000	0.106000
$90$	0	0
$91$	10.9305	1.14583
$92$	−14.4436	−1.50585
$93$	14.7294	1.52737
$94$	4.06660	0.419438
$95$	0	0
$96$	26.2053	2.67457
$97$	5.52008	0.560479	0.280240	−	0.959930i	$-0.409586\pi$
$97$	5.52008	0.560479	0.280240	+	0.959930i	$0.409586\pi$
$98$	−34.6733	−3.50253
$99$	−17.3455	−1.74329
$100$	0	0
$101$	−12.8409	−1.27772	−0.638860	−	0.769323i	$-0.720594\pi$
$101$	−12.8409	−1.27772	−0.638860	+	0.769323i	$0.720594\pi$
$102$	−21.6860	−2.14723
$103$	11.7697	1.15970	0.579852	−	0.814722i	$-0.303110\pi$
$103$	11.7697	1.15970	0.579852	+	0.814722i	$0.303110\pi$
$104$	−2.36231	−0.231644
$105$	0	0
$106$	18.3539	1.78269
$107$	15.4620	1.49477	0.747383	−	0.664393i	$-0.231310\pi$
$107$	15.4620	1.49477	0.747383	+	0.664393i	$0.231310\pi$
$108$	39.6017	3.81068
$109$	−7.88060	−0.754824	−0.377412	−	0.926045i	$-0.623186\pi$
$109$	−7.88060	−0.754824	−0.377412	+	0.926045i	$0.623186\pi$
$110$	0	0
$111$	27.0855	2.57084
$112$	−13.3952	−1.26573
$113$	2.01004	0.189088	0.0945442	−	0.995521i	$-0.469861\pi$
$113$	2.01004	0.189088	0.0945442	+	0.995521i	$0.469861\pi$
$114$	41.4268	3.87997
$115$	0	0
$116$	5.80215	0.538716
$117$	17.7037	1.63671
$118$	−11.4389	−1.05303
$119$	15.0269	1.37751
$120$	0	0
$121$	−6.08997	−0.553634
$122$	20.5423	1.85981
$123$	−0.915028	−0.0825053
$124$	11.1583	1.00205
$125$	0	0
$126$	−80.1904	−7.14393
$127$	12.0158	1.06623	0.533113	−	0.846044i	$-0.321022\pi$
$127$	12.0158	1.06623	0.533113	+	0.846044i	$0.321022\pi$
$128$	8.10252	0.716169
$129$	0.579500	0.0510221
$130$	0	0
$131$	−20.6066	−1.80040	−0.900202	−	0.435472i	$-0.856581\pi$
$131$	−20.6066	−1.80040	−0.900202	+	0.435472i	$0.856581\pi$
$132$	−18.1760	−1.58202
$133$	−28.7059	−2.48912
$134$	17.1036	1.47752
$135$	0	0
$136$	−3.24763	−0.278482
$137$	−10.9369	−0.934400	−0.467200	−	0.884152i	$-0.654737\pi$
$137$	−10.9369	−0.934400	−0.467200	+	0.884152i	$0.654737\pi$
$138$	40.4129	3.44018
$139$	−0.432073	−0.0366479	−0.0183240	−	0.999832i	$-0.505833\pi$
$139$	−0.432073	−0.0366479	−0.0183240	+	0.999832i	$0.505833\pi$
$140$	0	0
$141$	−6.31314	−0.531663
$142$	10.6103	0.890397
$143$	−5.01144	−0.419077
$144$	−21.6957	−1.80797
$145$	0	0
$146$	−19.4774	−1.61196
$147$	53.8281	4.43966
$148$	20.5187	1.68663
$149$	−13.6417	−1.11757	−0.558785	−	0.829313i	$-0.688732\pi$
$149$	−13.6417	−1.11757	−0.558785	+	0.829313i	$0.688732\pi$
$150$	0	0
$151$	22.3825	1.82146	0.910730	−	0.413002i	$-0.135520\pi$
$151$	22.3825	1.82146	0.910730	+	0.413002i	$0.135520\pi$
$152$	6.20396	0.503207
$153$	24.3385	1.96765
$154$	22.6997	1.82919
$155$	0	0
$156$	18.5514	1.48530
$157$	−11.7366	−0.936683	−0.468342	−	0.883547i	$-0.655148\pi$
$157$	−11.7366	−0.936683	−0.468342	+	0.883547i	$0.655148\pi$
$158$	3.79303	0.301757
$159$	−28.4932	−2.25966
$160$	0	0
$161$	−28.0034	−2.20698
$162$	−61.0283	−4.79484
$163$	−1.49678	−0.117237	−0.0586184	−	0.998280i	$-0.518670\pi$
$163$	−1.49678	−0.117237	−0.0586184	+	0.998280i	$0.518670\pi$
$164$	−0.693183	−0.0541285
$165$	0	0
$166$	29.4371	2.28476
$167$	0.555849	0.0430129	0.0215064	−	0.999769i	$-0.493154\pi$
$167$	0.555849	0.0430129	0.0215064	+	0.999769i	$0.493154\pi$
$168$	−16.6115	−1.28161
$169$	−7.88506	−0.606543
$170$	0	0
$171$	−46.4939	−3.55547
$172$	0.439002	0.0334736
$173$	−14.0371	−1.06722	−0.533611	−	0.845730i	$-0.679165\pi$
$173$	−14.0371	−1.06722	−0.533611	+	0.845730i	$0.679165\pi$
$174$	−16.2343	−1.23072
$175$	0	0
$176$	6.14144	0.462929
$177$	17.7581	1.33478
$178$	−2.11962	−0.158872
$179$	9.22570	0.689561	0.344780	−	0.938683i	$-0.387953\pi$
$179$	9.22570	0.689561	0.344780	+	0.938683i	$0.387953\pi$
$180$	0	0
$181$	−10.4704	−0.778259	−0.389129	−	0.921183i	$-0.627224\pi$
$181$	−10.4704	−0.778259	−0.389129	+	0.921183i	$0.627224\pi$
$182$	−23.1685	−1.71737
$183$	−31.8906	−2.35742
$184$	6.05213	0.446169
$185$	0	0
$186$	−31.2207	−2.28921
$187$	−6.88955	−0.503814
$188$	−4.78255	−0.348803
$189$	76.7801	5.58493
$190$	0	0
$191$	−4.73905	−0.342906	−0.171453	−	0.985192i	$-0.554846\pi$
$191$	−4.73905	−0.342906	−0.171453	+	0.985192i	$0.554846\pi$
$192$	−37.3051	−2.69226
$193$	−1.48587	−0.106955	−0.0534775	−	0.998569i	$-0.517031\pi$
$193$	−1.48587	−0.106955	−0.0534775	+	0.998569i	$0.517031\pi$
$194$	−11.7005	−0.840045
$195$	0	0
$196$	40.7777	2.91269
$197$	4.51312	0.321547	0.160773	−	0.986991i	$-0.448601\pi$
$197$	4.51312	0.321547	0.160773	+	0.986991i	$0.448601\pi$
$198$	36.7658	2.61283
$199$	7.28028	0.516085	0.258043	−	0.966134i	$-0.416923\pi$
$199$	7.28028	0.516085	0.258043	+	0.966134i	$0.416923\pi$
$200$	0	0
$201$	−26.5522	−1.87285
$202$	27.2179	1.91504
$203$	11.2493	0.789543
$204$	25.5039	1.78563
$205$	0	0
$206$	−24.9473	−1.73816
$207$	−45.3560	−3.15246
$208$	−6.26828	−0.434627
$209$	13.1611	0.910374
$210$	0	0
$211$	14.0051	0.964154	0.482077	−	0.876129i	$-0.339883\pi$
$211$	14.0051	0.964154	0.482077	+	0.876129i	$0.339883\pi$
$212$	−21.5852	−1.48247
$213$	−16.4718	−1.12863
$214$	−32.7735	−2.24035
$215$	0	0
$216$	−16.5938	−1.12907
$217$	21.6338	1.46860
$218$	16.7039	1.13133
$219$	30.2374	2.04325
$220$	0	0
$221$	7.03184	0.473013
$222$	−57.4110	−3.85317
$223$	8.76611	0.587022	0.293511	−	0.955956i	$-0.405176\pi$
$223$	8.76611	0.587022	0.293511	+	0.955956i	$0.405176\pi$
$224$	38.4891	2.57166
$225$	0	0
$226$	−4.26051	−0.283405
$227$	21.8527	1.45042	0.725209	−	0.688529i	$-0.241743\pi$
$227$	21.8527	1.45042	0.725209	+	0.688529i	$0.241743\pi$
$228$	−48.7201	−3.22657
$229$	−20.0211	−1.32303	−0.661514	−	0.749932i	$-0.730086\pi$
$229$	−20.0211	−1.32303	−0.661514	+	0.749932i	$0.730086\pi$
$230$	0	0
$231$	−35.2398	−2.31861
$232$	−2.43120	−0.159616
$233$	−15.3296	−1.00428	−0.502139	−	0.864787i	$-0.667453\pi$
$233$	−15.3296	−1.00428	−0.502139	+	0.864787i	$0.667453\pi$
$234$	−37.5252	−2.45310
$235$	0	0
$236$	13.4527	0.875697
$237$	−5.88844	−0.382495
$238$	−31.8513	−2.06461
$239$	7.27188	0.470379	0.235190	−	0.971950i	$-0.424429\pi$
$239$	7.27188	0.470379	0.235190	+	0.971950i	$0.424429\pi$
$240$	0	0
$241$	4.02887	0.259522	0.129761	−	0.991545i	$-0.458579\pi$
$241$	4.02887	0.259522	0.129761	+	0.991545i	$0.458579\pi$
$242$	12.9084	0.829785
$243$	47.0831	3.02038
$244$	−24.1588	−1.54661
$245$	0	0
$246$	1.93951	0.123659
$247$	−13.4329	−0.854718
$248$	−4.67553	−0.296896
$249$	−45.6992	−2.89607
$250$	0	0
$251$	−6.99410	−0.441464	−0.220732	−	0.975335i	$-0.570845\pi$
$251$	−6.99410	−0.441464	−0.220732	+	0.975335i	$0.570845\pi$
$252$	94.3083	5.94086
$253$	12.8390	0.807183
$254$	−25.4688	−1.59806
$255$	0	0
$256$	5.49964	0.343727
$257$	19.3582	1.20753	0.603767	−	0.797161i	$-0.293666\pi$
$257$	19.3582	1.20753	0.603767	+	0.797161i	$0.293666\pi$
$258$	−1.22832	−0.0764718
$259$	39.7819	2.47193
$260$	0	0
$261$	18.2200	1.12779
$262$	43.6781	2.69844
$263$	5.73446	0.353602	0.176801	−	0.984247i	$-0.443425\pi$
$263$	5.73446	0.353602	0.176801	+	0.984247i	$0.443425\pi$
$264$	7.61608	0.468737
$265$	0	0
$266$	60.8456	3.73068
$267$	3.29058	0.201380
$268$	−20.1147	−1.22870
$269$	5.07725	0.309565	0.154783	−	0.987949i	$-0.450532\pi$
$269$	5.07725	0.309565	0.154783	+	0.987949i	$0.450532\pi$
$270$	0	0
$271$	14.8909	0.904557	0.452278	−	0.891877i	$-0.350611\pi$
$271$	14.8909	0.904557	0.452278	+	0.891877i	$0.350611\pi$
$272$	−8.61742	−0.522508
$273$	35.9677	2.17686
$274$	23.1820	1.40048
$275$	0	0
$276$	−47.5278	−2.86084
$277$	30.6930	1.84417	0.922083	−	0.386993i	$-0.126486\pi$
$277$	30.6930	1.84417	0.922083	+	0.386993i	$0.126486\pi$
$278$	0.915829	0.0549278
$279$	35.0395	2.09776
$280$	0	0
$281$	19.5982	1.16913	0.584564	−	0.811348i	$-0.301266\pi$
$281$	19.5982	1.16913	0.584564	+	0.811348i	$0.301266\pi$
$282$	13.3815	0.796855
$283$	−32.1638	−1.91194	−0.955968	−	0.293469i	$-0.905190\pi$
$283$	−32.1638	−1.91194	−0.955968	+	0.293469i	$0.905190\pi$
$284$	−12.4783	−0.740451
$285$	0	0
$286$	10.6223	0.628112
$287$	−1.34395	−0.0793308
$288$	62.3393	3.67338
$289$	−7.33286	−0.431345
$290$	0	0
$291$	18.1642	1.06481
$292$	22.9064	1.34050
$293$	22.7569	1.32947	0.664737	−	0.747077i	$-0.268543\pi$
$293$	22.7569	1.32947	0.664737	+	0.747077i	$0.268543\pi$
$294$	−114.095	−6.65416
$295$	0	0
$296$	−8.59771	−0.499732
$297$	−35.2023	−2.04264
$298$	28.9152	1.67501
$299$	−13.1042	−0.757836
$300$	0	0
$301$	0.851142	0.0490590
$302$	−47.4423	−2.73000
$303$	−42.2541	−2.42743
$304$	16.4619	0.944154
$305$	0	0
$306$	−51.5883	−2.94911
$307$	−0.883192	−0.0504064	−0.0252032	−	0.999682i	$-0.508023\pi$
$307$	−0.883192	−0.0504064	−0.0252032	+	0.999682i	$0.508023\pi$
$308$	−26.6961	−1.52115
$309$	38.7291	2.20322
$310$	0	0
$311$	−2.98323	−0.169163	−0.0845816	−	0.996417i	$-0.526955\pi$
$311$	−2.98323	−0.169163	−0.0845816	+	0.996417i	$0.526955\pi$
$312$	−7.77337	−0.440081
$313$	−6.07859	−0.343582	−0.171791	−	0.985133i	$-0.554955\pi$
$313$	−6.07859	−0.343582	−0.171791	+	0.985133i	$0.554955\pi$
$314$	24.8771	1.40390
$315$	0	0
$316$	−4.46081	−0.250940
$317$	−2.02998	−0.114015	−0.0570075	−	0.998374i	$-0.518156\pi$
$317$	−2.02998	−0.114015	−0.0570075	+	0.998374i	$0.518156\pi$
$318$	60.3948	3.38677
$319$	−5.15757	−0.288769
$320$	0	0
$321$	50.8788	2.83978
$322$	59.3565	3.30781
$323$	−18.4672	−1.02754
$324$	71.7726	3.98737
$325$	0	0
$326$	3.17260	0.175714
$327$	−25.9317	−1.43403
$328$	0.290456	0.0160377
$329$	−9.27244	−0.511206
$330$	0	0
$331$	−12.3999	−0.681559	−0.340779	−	0.940143i	$-0.610691\pi$
$331$	−12.3999	−0.681559	−0.340779	+	0.940143i	$0.610691\pi$
$332$	−34.6196	−1.90000
$333$	64.4332	3.53092
$334$	−1.17819	−0.0644676
$335$	0	0
$336$	−44.0778	−2.40464
$337$	−27.1425	−1.47855	−0.739274	−	0.673405i	$-0.764831\pi$
$337$	−27.1425	−1.47855	−0.739274	+	0.673405i	$0.764831\pi$
$338$	16.7133	0.909085
$339$	6.61418	0.359233
$340$	0	0
$341$	−9.91871	−0.537128
$342$	98.5493	5.32894
$343$	45.2288	2.44213
$344$	−0.183950	−0.00991790
$345$	0	0
$346$	29.7533	1.59955
$347$	17.0635	0.916019	0.458009	−	0.888947i	$-0.348563\pi$
$347$	17.0635	0.916019	0.458009	+	0.888947i	$0.348563\pi$
$348$	19.0924	1.02346
$349$	25.3297	1.35587	0.677933	−	0.735124i	$-0.262876\pi$
$349$	25.3297	1.35587	0.677933	+	0.735124i	$0.262876\pi$
$350$	0	0
$351$	35.9293	1.91776
$352$	−17.6465	−0.940564
$353$	−15.3713	−0.818132	−0.409066	−	0.912505i	$-0.634146\pi$
$353$	−15.3713	−0.818132	−0.409066	+	0.912505i	$0.634146\pi$
$354$	−37.6404	−2.00057
$355$	0	0
$356$	2.49279	0.132117
$357$	49.4471	2.61702
$358$	−19.5550	−1.03351
$359$	−4.81197	−0.253966	−0.126983	−	0.991905i	$-0.540529\pi$
$359$	−4.81197	−0.253966	−0.126983	+	0.991905i	$0.540529\pi$
$360$	0	0
$361$	16.2779	0.856730
$362$	22.1933	1.16645
$363$	−20.0395	−1.05180
$364$	27.2474	1.42815
$365$	0	0
$366$	67.5959	3.53330
$367$	−23.4281	−1.22294	−0.611468	−	0.791269i	$-0.709421\pi$
$367$	−23.4281	−1.22294	−0.611468	+	0.791269i	$0.709421\pi$
$368$	16.0590	0.837134
$369$	−2.17674	−0.113317
$370$	0	0
$371$	−41.8495	−2.17272
$372$	36.7173	1.90370
$373$	−10.4886	−0.543078	−0.271539	−	0.962427i	$-0.587533\pi$
$373$	−10.4886	−0.543078	−0.271539	+	0.962427i	$0.587533\pi$
$374$	14.6032	0.755115
$375$	0	0
$376$	2.00397	0.103347
$377$	5.26409	0.271115
$378$	−162.745	−8.37068
$379$	−20.6495	−1.06069	−0.530347	−	0.847781i	$-0.677938\pi$
$379$	−20.6495	−1.06069	−0.530347	+	0.847781i	$0.677938\pi$
$380$	0	0
$381$	39.5388	2.02563
$382$	10.0450	0.513946
$383$	−11.8529	−0.605654	−0.302827	−	0.953046i	$-0.597930\pi$
$383$	−11.8529	−0.605654	−0.302827	+	0.953046i	$0.597930\pi$
$384$	26.6620	1.36059
$385$	0	0
$386$	3.14947	0.160304
$387$	1.37856	0.0700762
$388$	13.7604	0.698578
$389$	−11.8172	−0.599157	−0.299578	−	0.954072i	$-0.596846\pi$
$389$	−11.8172	−0.599157	−0.299578	+	0.954072i	$0.596846\pi$
$390$	0	0
$391$	−18.0152	−0.911068
$392$	−17.0866	−0.863001
$393$	−67.8075	−3.42043
$394$	−9.56610	−0.481933
$395$	0	0
$396$	−43.2386	−2.17282
$397$	−36.5070	−1.83223	−0.916116	−	0.400912i	$-0.868693\pi$
$397$	−36.5070	−1.83223	−0.916116	+	0.400912i	$0.868693\pi$
$398$	−15.4314	−0.773507
$399$	−94.4590	−4.72886
$400$	0	0
$401$	1.45221	0.0725197	0.0362599	−	0.999342i	$-0.488456\pi$
$401$	1.45221	0.0725197	0.0362599	+	0.999342i	$0.488456\pi$
$402$	56.2805	2.80702
$403$	10.1236	0.504291
$404$	−32.0097	−1.59254
$405$	0	0
$406$	−23.8441	−1.18336
$407$	−18.2393	−0.904086
$408$	−10.6866	−0.529064
$409$	32.3981	1.60198	0.800992	−	0.598674i	$-0.204306\pi$
$409$	32.3981	1.60198	0.800992	+	0.598674i	$0.204306\pi$
$410$	0	0
$411$	−35.9886	−1.77519
$412$	29.3394	1.44545
$413$	26.0822	1.28342
$414$	96.1375	4.72490
$415$	0	0
$416$	18.0110	0.883062
$417$	−1.42177	−0.0696242
$418$	−27.8966	−1.36447
$419$	−10.4032	−0.508227	−0.254114	−	0.967174i	$-0.581784\pi$
$419$	−10.4032	−0.508227	−0.254114	+	0.967174i	$0.581784\pi$
$420$	0	0
$421$	1.28300	0.0625297	0.0312648	−	0.999511i	$-0.490046\pi$
$421$	1.28300	0.0625297	0.0312648	+	0.999511i	$0.490046\pi$
$422$	−29.6856	−1.44507
$423$	−15.0182	−0.730211
$424$	9.04456	0.439243
$425$	0	0
$426$	34.9140	1.69159
$427$	−46.8394	−2.26672
$428$	38.5434	1.86307
$429$	−16.4905	−0.796169
$430$	0	0
$431$	−2.37582	−0.114439	−0.0572195	−	0.998362i	$-0.518223\pi$
$431$	−2.37582	−0.114439	−0.0572195	+	0.998362i	$0.518223\pi$
$432$	−44.0308	−2.11843
$433$	−31.3903	−1.50852	−0.754262	−	0.656574i	$-0.772005\pi$
$433$	−31.3903	−1.50852	−0.754262	+	0.656574i	$0.772005\pi$
$434$	−45.8555	−2.20113
$435$	0	0
$436$	−19.6447	−0.940808
$437$	34.4145	1.64627
$438$	−64.0917	−3.06242
$439$	−8.32745	−0.397448	−0.198724	−	0.980056i	$-0.563680\pi$
$439$	−8.32745	−0.397448	−0.198724	+	0.980056i	$0.563680\pi$
$440$	0	0
$441$	128.051	6.09764
$442$	−14.9048	−0.708950
$443$	27.1908	1.29188	0.645938	−	0.763390i	$-0.276466\pi$
$443$	27.1908	1.29188	0.645938	+	0.763390i	$0.276466\pi$
$444$	67.5184	3.20428
$445$	0	0
$446$	−18.5808	−0.879827
$447$	−44.8890	−2.12318
$448$	−54.7919	−2.58867
$449$	−20.2755	−0.956861	−0.478430	−	0.878126i	$-0.658794\pi$
$449$	−20.2755	−0.956861	−0.478430	+	0.878126i	$0.658794\pi$
$450$	0	0
$451$	0.616176	0.0290146
$452$	5.01059	0.235679
$453$	73.6512	3.46044
$454$	−46.3195	−2.17388
$455$	0	0
$456$	20.4146	0.956000
$457$	27.8204	1.30138	0.650691	−	0.759343i	$-0.274479\pi$
$457$	27.8204	1.30138	0.650691	+	0.759343i	$0.274479\pi$
$458$	42.4370	1.98295
$459$	49.3944	2.30553
$460$	0	0
$461$	3.25129	0.151428	0.0757138	−	0.997130i	$-0.475876\pi$
$461$	3.25129	0.151428	0.0757138	+	0.997130i	$0.475876\pi$
$462$	74.6951	3.47513
$463$	13.8292	0.642699	0.321349	−	0.946961i	$-0.395864\pi$
$463$	13.8292	0.642699	0.321349	+	0.946961i	$0.395864\pi$
$464$	−6.45107	−0.299483
$465$	0	0
$466$	32.4930	1.50521
$467$	19.5627	0.905253	0.452626	−	0.891700i	$-0.350487\pi$
$467$	19.5627	0.905253	0.452626	+	0.891700i	$0.350487\pi$
$468$	44.1316	2.03998
$469$	−38.9986	−1.80079
$470$	0	0
$471$	−38.6202	−1.77952
$472$	−5.63692	−0.259461
$473$	−0.390233	−0.0179429
$474$	12.4812	0.573283
$475$	0	0
$476$	37.4588	1.71692
$477$	−67.7820	−3.10352
$478$	−15.4136	−0.705003
$479$	26.2070	1.19743	0.598714	−	0.800963i	$-0.295679\pi$
$479$	26.2070	1.19743	0.598714	+	0.800963i	$0.295679\pi$
$480$	0	0
$481$	18.6160	0.848815
$482$	−8.53968	−0.388972
$483$	−92.1473	−4.19285
$484$	−15.1810	−0.690046
$485$	0	0
$486$	−99.7982	−4.52694
$487$	−28.8600	−1.30777	−0.653887	−	0.756592i	$-0.726863\pi$
$487$	−28.8600	−1.30777	−0.653887	+	0.756592i	$0.726863\pi$
$488$	10.1230	0.458246
$489$	−4.92526	−0.222728
$490$	0	0
$491$	−27.5737	−1.24438	−0.622192	−	0.782865i	$-0.713758\pi$
$491$	−27.5737	−1.24438	−0.622192	+	0.782865i	$0.713758\pi$
$492$	−2.28097	−0.102834
$493$	7.23690	0.325933
$494$	28.4727	1.28105
$495$	0	0
$496$	−12.4063	−0.557058
$497$	−24.1930	−1.08521
$498$	96.8648	4.34062
$499$	32.9455	1.47484	0.737422	−	0.675432i	$-0.236043\pi$
$499$	32.9455	1.47484	0.737422	+	0.675432i	$0.236043\pi$
$500$	0	0
$501$	1.82906	0.0817165
$502$	14.8248	0.661665
$503$	25.6894	1.14543	0.572717	−	0.819753i	$-0.305890\pi$
$503$	25.6894	1.14543	0.572717	+	0.819753i	$0.305890\pi$
$504$	−39.5168	−1.76022
$505$	0	0
$506$	−27.2139	−1.20980
$507$	−25.9464	−1.15232
$508$	29.9527	1.32894
$509$	27.1811	1.20478	0.602390	−	0.798202i	$-0.294215\pi$
$509$	27.1811	1.20478	0.602390	+	0.798202i	$0.294215\pi$
$510$	0	0
$511$	44.4112	1.96464
$512$	−27.8622	−1.23135
$513$	−94.3582	−4.16602
$514$	−41.0321	−1.80985
$515$	0	0
$516$	1.44457	0.0635937
$517$	4.25124	0.186969
$518$	−84.3225	−3.70492
$519$	−46.1902	−2.02752
$520$	0	0
$521$	0.901023	0.0394745	0.0197373	−	0.999805i	$-0.493717\pi$
$521$	0.901023	0.0394745	0.0197373	+	0.999805i	$0.493717\pi$
$522$	−38.6194	−1.69033
$523$	−0.0126235	−0.000551986 0	−0.000275993	−	1.00000i	$-0.500088\pi$
$523$	−0.0126235	−0.000551986 0	−0.000275993		1.00000i	$0.500088\pi$
$524$	−51.3678	−2.24401
$525$	0	0
$526$	−12.1549	−0.529978
$527$	13.9175	0.606257
$528$	20.2089	0.879478
$529$	10.5723	0.459665
$530$	0	0
$531$	42.2444	1.83325
$532$	−71.5577	−3.10242
$533$	−0.628902	−0.0272408
$534$	−6.97477	−0.301828
$535$	0	0
$536$	8.42842	0.364052
$537$	30.3578	1.31004
$538$	−10.7618	−0.463976
$539$	−36.2476	−1.56129
$540$	0	0
$541$	9.28499	0.399193	0.199596	−	0.979878i	$-0.436037\pi$
$541$	9.28499	0.399193	0.199596	+	0.979878i	$0.436037\pi$
$542$	−31.5630	−1.35575
$543$	−34.4536	−1.47855
$544$	24.7609	1.06162
$545$	0	0
$546$	−76.2378	−3.26267
$547$	12.6475	0.540770	0.270385	−	0.962752i	$-0.412849\pi$
$547$	12.6475	0.540770	0.270385	+	0.962752i	$0.412849\pi$
$548$	−27.2633	−1.16463
$549$	−75.8639	−3.23779
$550$	0	0
$551$	−13.8247	−0.588951
$552$	19.9150	0.847638
$553$	−8.64865	−0.367778
$554$	−65.0576	−2.76403
$555$	0	0
$556$	−1.07707	−0.0456777
$557$	1.89455	0.0802747	0.0401374	−	0.999194i	$-0.487220\pi$
$557$	1.89455	0.0802747	0.0401374	+	0.999194i	$0.487220\pi$
$558$	−74.2704	−3.14411
$559$	0.398292	0.0168460
$560$	0	0
$561$	−22.6706	−0.957153
$562$	−41.5406	−1.75229
$563$	39.9171	1.68231	0.841153	−	0.540797i	$-0.181877\pi$
$563$	39.9171	1.68231	0.841153	+	0.540797i	$0.181877\pi$
$564$	−15.7373	−0.662661
$565$	0	0
$566$	68.1749	2.86561
$567$	139.153	5.84389
$568$	5.22863	0.219388
$569$	−12.8214	−0.537499	−0.268750	−	0.963210i	$-0.586610\pi$
$569$	−12.8214	−0.537499	−0.268750	+	0.963210i	$0.586610\pi$
$570$	0	0
$571$	−24.0157	−1.00503	−0.502513	−	0.864570i	$-0.667591\pi$
$571$	−24.0157	−1.00503	−0.502513	+	0.864570i	$0.667591\pi$
$572$	−12.4924	−0.522335
$573$	−15.5942	−0.651457
$574$	2.84866	0.118901
$575$	0	0
$576$	−88.7443	−3.69768
$577$	28.5046	1.18666	0.593331	−	0.804959i	$-0.297813\pi$
$577$	28.5046	1.18666	0.593331	+	0.804959i	$0.297813\pi$
$578$	15.5429	0.646499
$579$	−4.88935	−0.203195
$580$	0	0
$581$	−67.1207	−2.78464
$582$	−38.5013	−1.59593
$583$	19.1872	0.794653
$584$	−9.59820	−0.397176
$585$	0	0
$586$	−48.2361	−1.99261
$587$	2.40697	0.0993462	0.0496731	−	0.998766i	$-0.484182\pi$
$587$	2.40697	0.0993462	0.0496731	+	0.998766i	$0.484182\pi$
$588$	134.182	5.53357
$589$	−26.5867	−1.09549
$590$	0	0
$591$	14.8508	0.610879
$592$	−22.8136	−0.937633
$593$	−10.4715	−0.430013	−0.215006	−	0.976613i	$-0.568977\pi$
$593$	−10.4715	−0.430013	−0.215006	+	0.976613i	$0.568977\pi$
$594$	74.6154	3.06151
$595$	0	0
$596$	−34.0058	−1.39293
$597$	23.9563	0.980466
$598$	27.7759	1.13584
$599$	9.28858	0.379521	0.189760	−	0.981830i	$-0.439229\pi$
$599$	9.28858	0.379521	0.189760	+	0.981830i	$0.439229\pi$
$600$	0	0
$601$	−18.0877	−0.737814	−0.368907	−	0.929466i	$-0.620268\pi$
$601$	−18.0877	−0.737814	−0.368907	+	0.929466i	$0.620268\pi$
$602$	−1.80410	−0.0735295
$603$	−63.1645	−2.57226
$604$	55.7948	2.27026
$605$	0	0
$606$	89.5625	3.63823
$607$	4.08445	0.165783	0.0828914	−	0.996559i	$-0.473585\pi$
$607$	4.08445	0.165783	0.0828914	+	0.996559i	$0.473585\pi$
$608$	−47.3008	−1.91830
$609$	37.0165	1.49998
$610$	0	0
$611$	−4.33904	−0.175539
$612$	60.6706	2.45247
$613$	−20.2800	−0.819101	−0.409551	−	0.912287i	$-0.634315\pi$
$613$	−20.2800	−0.819101	−0.409551	+	0.912287i	$0.634315\pi$
$614$	1.87203	0.0755490
$615$	0	0
$616$	11.1861	0.450702
$617$	−3.23902	−0.130398	−0.0651990	−	0.997872i	$-0.520768\pi$
$617$	−3.23902	−0.130398	−0.0651990	+	0.997872i	$0.520768\pi$
$618$	−82.0910	−3.30218
$619$	2.62101	0.105347	0.0526737	−	0.998612i	$-0.483226\pi$
$619$	2.62101	0.105347	0.0526737	+	0.998612i	$0.483226\pi$
$620$	0	0
$621$	−92.0490	−3.69380
$622$	6.32330	0.253541
$623$	4.83304	0.193632
$624$	−20.6263	−0.825711
$625$	0	0
$626$	12.8843	0.514960
$627$	43.3077	1.72954
$628$	−29.2569	−1.16748
$629$	25.5926	1.02044
$630$	0	0
$631$	−4.84085	−0.192711	−0.0963557	−	0.995347i	$-0.530719\pi$
$631$	−4.84085	−0.192711	−0.0963557	+	0.995347i	$0.530719\pi$
$632$	1.86916	0.0743511
$633$	46.0850	1.83171
$634$	4.30278	0.170885
$635$	0	0
$636$	−71.0276	−2.81643
$637$	36.9962	1.46584
$638$	10.9321	0.432806
$639$	−39.1845	−1.55012
$640$	0	0
$641$	−41.4377	−1.63669	−0.818344	−	0.574728i	$-0.805108\pi$
$641$	−41.4377	−1.63669	−0.818344	+	0.574728i	$0.805108\pi$
$642$	−107.844	−4.25625
$643$	26.2789	1.03634	0.518168	−	0.855279i	$-0.326614\pi$
$643$	26.2789	1.03634	0.518168	+	0.855279i	$0.326614\pi$
$644$	−69.8065	−2.75076
$645$	0	0
$646$	39.1434	1.54007
$647$	−32.8680	−1.29218	−0.646088	−	0.763263i	$-0.723596\pi$
$647$	−32.8680	−1.29218	−0.646088	+	0.763263i	$0.723596\pi$
$648$	−30.0740	−1.18142
$649$	−11.9582	−0.469401
$650$	0	0
$651$	71.1877	2.79007
$652$	−3.73115	−0.146123
$653$	−34.0840	−1.33381	−0.666904	−	0.745143i	$-0.732381\pi$
$653$	−34.0840	−1.33381	−0.666904	+	0.745143i	$0.732381\pi$
$654$	54.9653	2.14931
$655$	0	0
$656$	0.770710	0.0300912
$657$	71.9311	2.80630
$658$	19.6540	0.766195
$659$	−22.3303	−0.869864	−0.434932	−	0.900463i	$-0.643228\pi$
$659$	−22.3303	−0.869864	−0.434932	+	0.900463i	$0.643228\pi$
$660$	0	0
$661$	−4.90059	−0.190611	−0.0953055	−	0.995448i	$-0.530383\pi$
$661$	−4.90059	−0.190611	−0.0953055	+	0.995448i	$0.530383\pi$
$662$	26.2830	1.02152
$663$	23.1388	0.898637
$664$	14.5062	0.562950
$665$	0	0
$666$	−136.574	−5.29213
$667$	−13.4863	−0.522193
$668$	1.38561	0.0536110
$669$	28.8455	1.11523
$670$	0	0
$671$	21.4750	0.829032
$672$	126.651	4.88568
$673$	−17.8142	−0.686689	−0.343344	−	0.939210i	$-0.611560\pi$
$673$	−17.8142	−0.686689	−0.343344	+	0.939210i	$0.611560\pi$
$674$	57.5318	2.21604
$675$	0	0
$676$	−19.6558	−0.755992
$677$	2.59037	0.0995561	0.0497780	−	0.998760i	$-0.484149\pi$
$677$	2.59037	0.0995561	0.0497780	+	0.998760i	$0.484149\pi$
$678$	−14.0195	−0.538417
$679$	26.6788	1.02384
$680$	0	0
$681$	71.9081	2.75552
$682$	21.0239	0.805046
$683$	−24.9388	−0.954257	−0.477128	−	0.878834i	$-0.658322\pi$
$683$	−24.9388	−0.954257	−0.477128	+	0.878834i	$0.658322\pi$
$684$	−115.899	−4.43152
$685$	0	0
$686$	−95.8678	−3.66025
$687$	−65.8808	−2.51351
$688$	−0.488101	−0.0186087
$689$	−19.5835	−0.746072
$690$	0	0
$691$	−29.1377	−1.10845	−0.554226	−	0.832366i	$-0.686986\pi$
$691$	−29.1377	−1.10845	−0.554226	+	0.832366i	$0.686986\pi$
$692$	−34.9915	−1.33018
$693$	−83.8314	−3.18449
$694$	−36.1682	−1.37293
$695$	0	0
$696$	−8.00005	−0.303241
$697$	−0.864593	−0.0327488
$698$	−53.6893	−2.03217
$699$	−50.4433	−1.90794
$700$	0	0
$701$	−37.5559	−1.41847	−0.709233	−	0.704974i	$-0.750958\pi$
$701$	−37.5559	−1.41847	−0.709233	+	0.704974i	$0.750958\pi$
$702$	−76.1565	−2.87434
$703$	−48.8896	−1.84391
$704$	25.1211	0.946786
$705$	0	0
$706$	32.5813	1.22621
$707$	−62.0607	−2.33403
$708$	44.2672	1.66366
$709$	−16.0916	−0.604334	−0.302167	−	0.953255i	$-0.597710\pi$
$709$	−16.0916	−0.604334	−0.302167	+	0.953255i	$0.597710\pi$
$710$	0	0
$711$	−14.0079	−0.525337
$712$	−1.04452	−0.0391451
$713$	−25.9360	−0.971312
$714$	−104.809	−3.92238
$715$	0	0
$716$	22.9977	0.859464
$717$	23.9287	0.893633
$718$	10.1995	0.380644
$719$	−3.86290	−0.144062	−0.0720310	−	0.997402i	$-0.522948\pi$
$719$	−3.86290	−0.144062	−0.0720310	+	0.997402i	$0.522948\pi$
$720$	0	0
$721$	56.8834	2.11845
$722$	−34.5029	−1.28406
$723$	13.2573	0.493044
$724$	−26.1005	−0.970017
$725$	0	0
$726$	42.4761	1.57644
$727$	10.4042	0.385871	0.192935	−	0.981211i	$-0.438199\pi$
$727$	10.4042	0.385871	0.192935	+	0.981211i	$0.438199\pi$
$728$	−11.4172	−0.423148
$729$	68.5541	2.53904
$730$	0	0
$731$	0.547558	0.0202522
$732$	−79.4965	−2.93827
$733$	16.9908	0.627569	0.313784	−	0.949494i	$-0.398403\pi$
$733$	16.9908	0.627569	0.313784	+	0.949494i	$0.398403\pi$
$734$	49.6587	1.83293
$735$	0	0
$736$	−46.1432	−1.70086
$737$	17.8801	0.658623
$738$	4.61387	0.169839
$739$	10.1630	0.373854	0.186927	−	0.982374i	$-0.440147\pi$
$739$	10.1630	0.373854	0.186927	+	0.982374i	$0.440147\pi$
$740$	0	0
$741$	−44.2021	−1.62381
$742$	88.7050	3.25646
$743$	25.6666	0.941617	0.470809	−	0.882235i	$-0.343962\pi$
$743$	25.6666	0.941617	0.470809	+	0.882235i	$0.343962\pi$
$744$	−15.3852	−0.564048
$745$	0	0
$746$	22.2318	0.813964
$747$	−108.713	−3.97759
$748$	−17.1742	−0.627950
$749$	74.7284	2.73051
$750$	0	0
$751$	−1.88134	−0.0686510	−0.0343255	−	0.999411i	$-0.510928\pi$
$751$	−1.88134	−0.0686510	−0.0343255	+	0.999411i	$0.510928\pi$
$752$	5.31744	0.193907
$753$	−23.0146	−0.838699
$754$	−11.1579	−0.406346
$755$	0	0
$756$	191.397	6.96102
$757$	−11.6427	−0.423161	−0.211580	−	0.977361i	$-0.567861\pi$
$757$	−11.6427	−0.423161	−0.211580	+	0.977361i	$0.567861\pi$
$758$	43.7691	1.58977
$759$	42.2478	1.53350
$760$	0	0
$761$	20.9113	0.758035	0.379017	−	0.925390i	$-0.376262\pi$
$761$	20.9113	0.758035	0.379017	+	0.925390i	$0.376262\pi$
$762$	−83.8071	−3.03601
$763$	−38.0872	−1.37885
$764$	−11.8134	−0.427395
$765$	0	0
$766$	25.1236	0.907753
$767$	12.2052	0.440704
$768$	18.0970	0.653018
$769$	−21.0699	−0.759800	−0.379900	−	0.925028i	$-0.624042\pi$
$769$	−21.0699	−0.759800	−0.379900	+	0.925028i	$0.624042\pi$
$770$	0	0
$771$	63.6997	2.29409
$772$	−3.70395	−0.133308
$773$	−4.26541	−0.153416	−0.0767080	−	0.997054i	$-0.524441\pi$
$773$	−4.26541	−0.153416	−0.0767080	+	0.997054i	$0.524441\pi$
$774$	−2.92203	−0.105030
$775$	0	0
$776$	−5.76584	−0.206982
$777$	130.905	4.69620
$778$	25.0480	0.898015
$779$	1.65163	0.0591759
$780$	0	0
$781$	11.0921	0.396905
$782$	38.1854	1.36551
$783$	36.9770	1.32145
$784$	−45.3383	−1.61923
$785$	0	0
$786$	143.726	5.12654
$787$	−46.9571	−1.67384	−0.836920	−	0.547325i	$-0.815646\pi$
$787$	−46.9571	−1.67384	−0.836920	+	0.547325i	$0.815646\pi$
$788$	11.2503	0.400774
$789$	18.8697	0.671778
$790$	0	0
$791$	9.71458	0.345411
$792$	18.1177	0.643786
$793$	−21.9185	−0.778349
$794$	77.3809	2.74615
$795$	0	0
$796$	18.1482	0.643245
$797$	36.9401	1.30849	0.654243	−	0.756284i	$-0.272987\pi$
$797$	36.9401	1.30849	0.654243	+	0.756284i	$0.272987\pi$
$798$	200.217	7.08761
$799$	−5.96517	−0.211033
$800$	0	0
$801$	7.82788	0.276585
$802$	−3.07813	−0.108692
$803$	−20.3617	−0.718549
$804$	−66.1890	−2.33431
$805$	0	0
$806$	−21.4581	−0.755829
$807$	16.7071	0.588116
$808$	13.4126	0.471855
$809$	17.3676	0.610613	0.305306	−	0.952254i	$-0.401241\pi$
$809$	17.3676	0.610613	0.305306	+	0.952254i	$0.401241\pi$
$810$	0	0
$811$	−44.5363	−1.56388	−0.781941	−	0.623352i	$-0.785770\pi$
$811$	−44.5363	−1.56388	−0.781941	+	0.623352i	$0.785770\pi$
$812$	28.0420	0.984081
$813$	48.9996	1.71849
$814$	38.6603	1.35504
$815$	0	0
$816$	−28.3563	−0.992668
$817$	−1.04600	−0.0365950
$818$	−68.6717	−2.40105
$819$	85.5628	2.98980
$820$	0	0
$821$	−17.7581	−0.619761	−0.309880	−	0.950776i	$-0.600289\pi$
$821$	−17.7581	−0.619761	−0.309880	+	0.950776i	$0.600289\pi$
$822$	76.2821	2.66064
$823$	27.7787	0.968304	0.484152	−	0.874984i	$-0.339128\pi$
$823$	27.7787	0.968304	0.484152	+	0.874984i	$0.339128\pi$
$824$	−12.2937	−0.428272
$825$	0	0
$826$	−55.2844	−1.92359
$827$	28.8725	1.00400	0.501998	−	0.864869i	$-0.332599\pi$
$827$	28.8725	1.00400	0.501998	+	0.864869i	$0.332599\pi$
$828$	−113.063	−3.92921
$829$	41.4440	1.43941	0.719704	−	0.694281i	$-0.244277\pi$
$829$	41.4440	1.43941	0.719704	+	0.694281i	$0.244277\pi$
$830$	0	0
$831$	100.998	3.50357
$832$	−25.6399	−0.888904
$833$	50.8611	1.76223
$834$	3.01361	0.104353
$835$	0	0
$836$	32.8079	1.13468
$837$	71.1118	2.45798
$838$	22.0507	0.761730
$839$	−15.0790	−0.520583	−0.260292	−	0.965530i	$-0.583819\pi$
$839$	−15.0790	−0.520583	−0.260292	+	0.965530i	$0.583819\pi$
$840$	0	0
$841$	−23.5824	−0.813186
$842$	−2.71948	−0.0937193
$843$	64.4892	2.22113
$844$	34.9118	1.20172
$845$	0	0
$846$	31.8329	1.09444
$847$	−29.4331	−1.01133
$848$	23.9993	0.824139
$849$	−105.837	−3.63233
$850$	0	0
$851$	−47.6931	−1.63490
$852$	−41.0608	−1.40672
$853$	−36.1724	−1.23852	−0.619260	−	0.785186i	$-0.712567\pi$
$853$	−36.1724	−1.23852	−0.619260	+	0.785186i	$0.712567\pi$
$854$	99.2816	3.39735
$855$	0	0
$856$	−16.1504	−0.552009
$857$	−14.1138	−0.482117	−0.241058	−	0.970511i	$-0.577495\pi$
$857$	−14.1138	−0.482117	−0.241058	+	0.970511i	$0.577495\pi$
$858$	34.9536	1.19330
$859$	−3.04904	−0.104032	−0.0520159	−	0.998646i	$-0.516565\pi$
$859$	−3.04904	−0.104032	−0.0520159	+	0.998646i	$0.516565\pi$
$860$	0	0
$861$	−4.42237	−0.150714
$862$	5.03582	0.171521
$863$	44.3700	1.51037	0.755187	−	0.655510i	$-0.227546\pi$
$863$	44.3700	1.51037	0.755187	+	0.655510i	$0.227546\pi$
$864$	126.516	4.30417
$865$	0	0
$866$	66.5356	2.26097
$867$	−24.1293	−0.819475
$868$	53.9285	1.83045
$869$	3.96525	0.134512
$870$	0	0
$871$	−18.2494	−0.618358
$872$	8.23146	0.278752
$873$	43.2105	1.46246
$874$	−72.9457	−2.46742
$875$	0	0
$876$	75.3754	2.54670
$877$	39.0474	1.31854	0.659268	−	0.751908i	$-0.270866\pi$
$877$	39.0474	1.31854	0.659268	+	0.751908i	$0.270866\pi$
$878$	17.6510	0.595693
$879$	74.8834	2.52575
$880$	0	0
$881$	8.96712	0.302110	0.151055	−	0.988525i	$-0.451733\pi$
$881$	8.96712	0.302110	0.151055	+	0.988525i	$0.451733\pi$
$882$	−271.418	−9.13913
$883$	−6.30062	−0.212033	−0.106016	−	0.994364i	$-0.533810\pi$
$883$	−6.30062	−0.212033	−0.106016	+	0.994364i	$0.533810\pi$
$884$	17.5289	0.589560
$885$	0	0
$886$	−57.6343	−1.93626
$887$	−51.6559	−1.73443	−0.867217	−	0.497931i	$-0.834093\pi$
$887$	−51.6559	−1.73443	−0.867217	+	0.497931i	$0.834093\pi$
$888$	−28.2914	−0.949397
$889$	58.0726	1.94769
$890$	0	0
$891$	−63.7993	−2.13736
$892$	21.8520	0.731660
$893$	11.3953	0.381329
$894$	95.1476	3.18221
$895$	0	0
$896$	39.1598	1.30824
$897$	−43.1204	−1.43975
$898$	42.9764	1.43414
$899$	10.4188	0.347486
$900$	0	0
$901$	−26.9227	−0.896926
$902$	−1.30606	−0.0434870
$903$	2.80075	0.0932030
$904$	−2.09953	−0.0698292
$905$	0	0
$906$	−156.113	−5.18649
$907$	30.5492	1.01437	0.507185	−	0.861837i	$-0.330686\pi$
$907$	30.5492	1.01437	0.507185	+	0.861837i	$0.330686\pi$
$908$	54.4742	1.80779
$909$	−100.517	−3.33395
$910$	0	0
$911$	13.9379	0.461784	0.230892	−	0.972979i	$-0.425836\pi$
$911$	13.9379	0.461784	0.230892	+	0.972979i	$0.425836\pi$
$912$	54.1691	1.79372
$913$	30.7736	1.01846
$914$	−58.9686	−1.95051
$915$	0	0
$916$	−49.9082	−1.64901
$917$	−99.5923	−3.28883
$918$	−104.697	−3.45553
$919$	21.5909	0.712217	0.356108	−	0.934445i	$-0.384103\pi$
$919$	21.5909	0.712217	0.356108	+	0.934445i	$0.384103\pi$
$920$	0	0
$921$	−2.90621	−0.0957628
$922$	−6.89150	−0.226959
$923$	−11.3211	−0.372640
$924$	−87.8454	−2.88990
$925$	0	0
$926$	−29.3127	−0.963275
$927$	92.1319	3.02601
$928$	18.5362	0.608481
$929$	−34.8126	−1.14216	−0.571082	−	0.820893i	$-0.693476\pi$
$929$	−34.8126	−1.14216	−0.571082	+	0.820893i	$0.693476\pi$
$930$	0	0
$931$	−97.1601	−3.18429
$932$	−38.2135	−1.25172
$933$	−9.81653	−0.321379
$934$	−41.4654	−1.35679
$935$	0	0
$936$	−18.4919	−0.604427
$937$	−29.3529	−0.958918	−0.479459	−	0.877564i	$-0.659167\pi$
$937$	−29.3529	−0.958918	−0.479459	+	0.877564i	$0.659167\pi$
$938$	82.6622	2.69901
$939$	−20.0021	−0.652743
$940$	0	0
$941$	39.9726	1.30307	0.651534	−	0.758619i	$-0.274126\pi$
$941$	39.9726	1.30307	0.651534	+	0.758619i	$0.274126\pi$
$942$	81.8601	2.66715
$943$	1.61121	0.0524683
$944$	−14.9573	−0.486819
$945$	0	0
$946$	0.827145	0.0268928
$947$	−57.0642	−1.85434	−0.927168	−	0.374646i	$-0.877764\pi$
$947$	−57.0642	−1.85434	−0.927168	+	0.374646i	$0.877764\pi$
$948$	−14.6786	−0.476739
$949$	20.7822	0.674620
$950$	0	0
$951$	−6.67980	−0.216607
$952$	−15.6959	−0.508707
$953$	−47.9488	−1.55321	−0.776607	−	0.629985i	$-0.783061\pi$
$953$	−47.9488	−1.55321	−0.776607	+	0.629985i	$0.783061\pi$
$954$	143.672	4.65155
$955$	0	0
$956$	18.1273	0.586278
$957$	−16.9714	−0.548607
$958$	−55.5488	−1.79470
$959$	−52.8583	−1.70688
$960$	0	0
$961$	−10.9633	−0.353655
$962$	−39.4587	−1.27220
$963$	121.035	3.90029
$964$	10.0431	0.323467
$965$	0	0
$966$	195.317	6.28423
$967$	22.9873	0.739222	0.369611	−	0.929187i	$-0.379491\pi$
$967$	22.9873	0.739222	0.369611	+	0.929187i	$0.379491\pi$
$968$	6.36111	0.204454
$969$	−60.7676	−1.95214
$970$	0	0
$971$	4.86938	0.156266	0.0781330	−	0.996943i	$-0.475104\pi$
$971$	4.86938	0.156266	0.0781330	+	0.996943i	$0.475104\pi$
$972$	117.368	3.76458
$973$	−2.08822	−0.0669454
$974$	61.1723	1.96009
$975$	0	0
$976$	26.8608	0.859794
$977$	−5.28623	−0.169121	−0.0845607	−	0.996418i	$-0.526949\pi$
$977$	−5.28623	−0.169121	−0.0845607	+	0.996418i	$0.526949\pi$
$978$	10.4397	0.333824
$979$	−2.21586	−0.0708191
$980$	0	0
$981$	−61.6884	−1.96956
$982$	58.4458	1.86508
$983$	−21.4830	−0.685202	−0.342601	−	0.939481i	$-0.611308\pi$
$983$	−21.4830	−0.685202	−0.342601	+	0.939481i	$0.611308\pi$
$984$	0.955767	0.0304687
$985$	0	0
$986$	−15.3395	−0.488508
$987$	−30.5117	−0.971197
$988$	−33.4855	−1.06532
$989$	−1.02040	−0.0324470
$990$	0	0
$991$	−39.9796	−1.26999	−0.634997	−	0.772514i	$-0.718999\pi$
$991$	−39.9796	−1.26999	−0.634997	+	0.772514i	$0.718999\pi$
$992$	35.6476	1.13181
$993$	−40.8027	−1.29484
$994$	51.2800	1.62650
$995$	0	0
$996$	−113.918	−3.60964
$997$	40.8157	1.29265	0.646323	−	0.763064i	$-0.276306\pi$
$997$	40.8157	1.29265	0.646323	+	0.763064i	$0.276306\pi$
$998$	−69.8320	−2.21049
$999$	130.766	4.13724

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2225.2.a.k.1.1		7
5.4	even	2		445.2.a.f.1.7	✓	7
15.14	odd	2		4005.2.a.o.1.1		7
20.19	odd	2		7120.2.a.bj.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
445.2.a.f.1.7	✓	7	5.4	even	2
2225.2.a.k.1.1		7	1.1	even	1	trivial
4005.2.a.o.1.1		7	15.14	odd	2
7120.2.a.bj.1.7		7	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2225 = 5^{2} \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2225.a (trivial)

\(f(q)\)	\(=\)	\(q-2.11962 q^{2} +3.29058 q^{3} +2.49279 q^{4} -6.97477 q^{6} +4.83304 q^{7} -1.04452 q^{8} +7.82788 q^{9} +O(q^{10})\)	\(q-2.11962 q^{2} +3.29058 q^{3} +2.49279 q^{4} -6.97477 q^{6} +4.83304 q^{7} -1.04452 q^{8} +7.82788 q^{9} -2.21586 q^{11} +8.20270 q^{12} +2.26162 q^{13} -10.2442 q^{14} -2.77159 q^{16} +3.10920 q^{17} -16.5921 q^{18} -5.93952 q^{19} +15.9035 q^{21} +4.69678 q^{22} -5.79416 q^{23} -3.43708 q^{24} -4.79378 q^{26} +15.8865 q^{27} +12.0477 q^{28} +2.32757 q^{29} +4.47624 q^{31} +7.96375 q^{32} -7.29145 q^{33} -6.59033 q^{34} +19.5133 q^{36} +8.23124 q^{37} +12.5895 q^{38} +7.44204 q^{39} -0.278075 q^{41} -33.7093 q^{42} +0.176109 q^{43} -5.52366 q^{44} +12.2814 q^{46} -1.91855 q^{47} -9.12011 q^{48} +16.3583 q^{49} +10.2311 q^{51} +5.63775 q^{52} -8.65904 q^{53} -33.6734 q^{54} -5.04821 q^{56} -19.5444 q^{57} -4.93357 q^{58} +5.39666 q^{59} -9.69150 q^{61} -9.48792 q^{62} +37.8325 q^{63} -11.3370 q^{64} +15.4551 q^{66} -8.06916 q^{67} +7.75058 q^{68} -19.0661 q^{69} -5.00576 q^{71} -8.17640 q^{72} +9.18909 q^{73} -17.4471 q^{74} -14.8060 q^{76} -10.7093 q^{77} -15.7743 q^{78} -1.78949 q^{79} +28.7921 q^{81} +0.589414 q^{82} -13.8879 q^{83} +39.6440 q^{84} -0.373284 q^{86} +7.65906 q^{87} +2.31451 q^{88} +1.00000 q^{89} +10.9305 q^{91} -14.4436 q^{92} +14.7294 q^{93} +4.06660 q^{94} +26.2053 q^{96} +5.52008 q^{97} -34.6733 q^{98} -17.3455 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 4 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{6} + 16 q^{7} + 12 q^{8} + 11 q^{9}+O(q^{10}) \) 7 * q + 4 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^6 + 16 * q^7 + 12 * q^8 + 11 * q^9	\( 7 q + 4 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{6} + 16 q^{7} + 12 q^{8} + 11 q^{9} - 10 q^{11} + 11 q^{12} + 7 q^{13} + 3 q^{14} + 10 q^{16} + 13 q^{17} - 4 q^{18} - 7 q^{19} + 16 q^{21} - 2 q^{22} + 13 q^{23} + 4 q^{24} + q^{26} + 23 q^{27} + 21 q^{28} - 4 q^{29} + q^{31} + 13 q^{32} + 6 q^{33} + 10 q^{34} + 20 q^{36} + 5 q^{37} + 40 q^{38} - 13 q^{39} + 5 q^{41} - 30 q^{42} + 31 q^{43} - 21 q^{44} + 16 q^{46} + 14 q^{47} + 7 q^{48} + 19 q^{49} - q^{51} + 13 q^{53} - 17 q^{54} - q^{56} - 21 q^{57} - 17 q^{58} - 14 q^{59} + 3 q^{61} - 26 q^{62} + 54 q^{63} + 14 q^{64} + 36 q^{66} - q^{67} + 35 q^{68} + 31 q^{69} - 8 q^{71} - 53 q^{72} - 9 q^{73} - 35 q^{74} + 40 q^{76} - 42 q^{77} - 46 q^{78} + 9 q^{79} + 35 q^{81} - 29 q^{82} + 42 q^{83} + 55 q^{84} + 35 q^{86} - 6 q^{87} - 30 q^{88} + 7 q^{89} + 31 q^{91} - 19 q^{92} - 24 q^{93} + 37 q^{94} + 44 q^{96} + 7 q^{97} - 9 q^{98} + 5 q^{99}+O(q^{100}) \) 7 * q + 4 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^6 + 16 * q^7 + 12 * q^8 + 11 * q^9 - 10 * q^11 + 11 * q^12 + 7 * q^13 + 3 * q^14 + 10 * q^16 + 13 * q^17 - 4 * q^18 - 7 * q^19 + 16 * q^21 - 2 * q^22 + 13 * q^23 + 4 * q^24 + q^26 + 23 * q^27 + 21 * q^28 - 4 * q^29 + q^31 + 13 * q^32 + 6 * q^33 + 10 * q^34 + 20 * q^36 + 5 * q^37 + 40 * q^38 - 13 * q^39 + 5 * q^41 - 30 * q^42 + 31 * q^43 - 21 * q^44 + 16 * q^46 + 14 * q^47 + 7 * q^48 + 19 * q^49 - q^51 + 13 * q^53 - 17 * q^54 - q^56 - 21 * q^57 - 17 * q^58 - 14 * q^59 + 3 * q^61 - 26 * q^62 + 54 * q^63 + 14 * q^64 + 36 * q^66 - q^67 + 35 * q^68 + 31 * q^69 - 8 * q^71 - 53 * q^72 - 9 * q^73 - 35 * q^74 + 40 * q^76 - 42 * q^77 - 46 * q^78 + 9 * q^79 + 35 * q^81 - 29 * q^82 + 42 * q^83 + 55 * q^84 + 35 * q^86 - 6 * q^87 - 30 * q^88 + 7 * q^89 + 31 * q^91 - 19 * q^92 - 24 * q^93 + 37 * q^94 + 44 * q^96 + 7 * q^97 - 9 * q^98 + 5 * q^99

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