LMFDB - Embedded newform 4025.2.a.y.1.12

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 14 x^{10} + 26 x^{9} + 71 x^{8} - 120 x^{7} - 162 x^{6} + 244 x^{5} + 170 x^{4} + \cdots + 17 $ x^12 - 2x^11 - 14x^10 + 26x^9 + 71x^8 - 120x^7 - 162x^6 + 244x^5 + 170x^4 - 210x^3 - 81x^2 + 58*x + 17
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$2.55311$ 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)

$f(q)$	$=$	$q+2.55311 q^{2} -0.556415 q^{3} +4.51835 q^{4} -1.42059 q^{6} -1.00000 q^{7} +6.42962 q^{8} -2.69040 q^{9} +O(q^{10})$	\(q+2.55311 q^{2} -0.556415 q^{3} +4.51835 q^{4} -1.42059 q^{6} -1.00000 q^{7} +6.42962 q^{8} -2.69040 q^{9} +2.39863 q^{11} -2.51408 q^{12} -4.84612 q^{13} -2.55311 q^{14} +7.37879 q^{16} -7.58115 q^{17} -6.86888 q^{18} -6.61505 q^{19} +0.556415 q^{21} +6.12396 q^{22} +1.00000 q^{23} -3.57753 q^{24} -12.3727 q^{26} +3.16622 q^{27} -4.51835 q^{28} -9.11387 q^{29} -6.28180 q^{31} +5.97961 q^{32} -1.33463 q^{33} -19.3555 q^{34} -12.1562 q^{36} +6.57528 q^{37} -16.8889 q^{38} +2.69645 q^{39} +1.15847 q^{41} +1.42059 q^{42} +6.33478 q^{43} +10.8379 q^{44} +2.55311 q^{46} +7.25371 q^{47} -4.10567 q^{48} +1.00000 q^{49} +4.21827 q^{51} -21.8965 q^{52} -6.06923 q^{53} +8.08371 q^{54} -6.42962 q^{56} +3.68071 q^{57} -23.2687 q^{58} -1.85447 q^{59} +2.62295 q^{61} -16.0381 q^{62} +2.69040 q^{63} +0.508984 q^{64} -3.40746 q^{66} +4.02415 q^{67} -34.2543 q^{68} -0.556415 q^{69} +8.33582 q^{71} -17.2983 q^{72} +11.6930 q^{73} +16.7874 q^{74} -29.8891 q^{76} -2.39863 q^{77} +6.88433 q^{78} -7.68708 q^{79} +6.30947 q^{81} +2.95770 q^{82} +10.3338 q^{83} +2.51408 q^{84} +16.1734 q^{86} +5.07109 q^{87} +15.4223 q^{88} -7.07788 q^{89} +4.84612 q^{91} +4.51835 q^{92} +3.49529 q^{93} +18.5195 q^{94} -3.32714 q^{96} -11.3217 q^{97} +2.55311 q^{98} -6.45328 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 8 q^{4} - 6 q^{6} - 12 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 + 8 * q^4 - 6 * q^6 - 12 * q^7 + 6 * q^8 + 8 * q^9	$ 12 q + 2 q^{2} + 8 q^{4} - 6 q^{6} - 12 q^{7} + 6 q^{8} + 8 q^{9} - 8 q^{11} - 12 q^{12} + 2 q^{13} - 2 q^{14} - 4 q^{16} - 8 q^{17} + 20 q^{18} - 26 q^{19} + 4 q^{22} + 12 q^{23} - 12 q^{24} - 22 q^{26} + 12 q^{27} - 8 q^{28} - 12 q^{29} - 50 q^{31} + 14 q^{32} + 4 q^{33} - 28 q^{34} - 18 q^{36} + 8 q^{37} - 4 q^{38} - 26 q^{39} - 4 q^{41} + 6 q^{42} + 26 q^{43} - 10 q^{44} + 2 q^{46} + 16 q^{47} - 40 q^{48} + 12 q^{49} - 32 q^{51} + 10 q^{52} - 18 q^{53} - 10 q^{54} - 6 q^{56} - 10 q^{57} - 18 q^{58} - 18 q^{59} + 8 q^{61} - 54 q^{62} - 8 q^{63} + 12 q^{64} - 2 q^{66} + 38 q^{67} - 36 q^{68} - 24 q^{71} + 18 q^{72} - 14 q^{73} + 36 q^{74} - 56 q^{76} + 8 q^{77} - 26 q^{78} - 44 q^{79} - 16 q^{81} - 44 q^{82} - 14 q^{83} + 12 q^{84} - 32 q^{86} + 16 q^{87} + 32 q^{88} - 10 q^{89} - 2 q^{91} + 8 q^{92} + 26 q^{93} + 18 q^{94} - 38 q^{96} - 4 q^{97} + 2 q^{98} - 56 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + 8 * q^4 - 6 * q^6 - 12 * q^7 + 6 * q^8 + 8 * q^9 - 8 * q^11 - 12 * q^12 + 2 * q^13 - 2 * q^14 - 4 * q^16 - 8 * q^17 + 20 * q^18 - 26 * q^19 + 4 * q^22 + 12 * q^23 - 12 * q^24 - 22 * q^26 + 12 * q^27 - 8 * q^28 - 12 * q^29 - 50 * q^31 + 14 * q^32 + 4 * q^33 - 28 * q^34 - 18 * q^36 + 8 * q^37 - 4 * q^38 - 26 * q^39 - 4 * q^41 + 6 * q^42 + 26 * q^43 - 10 * q^44 + 2 * q^46 + 16 * q^47 - 40 * q^48 + 12 * q^49 - 32 * q^51 + 10 * q^52 - 18 * q^53 - 10 * q^54 - 6 * q^56 - 10 * q^57 - 18 * q^58 - 18 * q^59 + 8 * q^61 - 54 * q^62 - 8 * q^63 + 12 * q^64 - 2 * q^66 + 38 * q^67 - 36 * q^68 - 24 * q^71 + 18 * q^72 - 14 * q^73 + 36 * q^74 - 56 * q^76 + 8 * q^77 - 26 * q^78 - 44 * q^79 - 16 * q^81 - 44 * q^82 - 14 * q^83 + 12 * q^84 - 32 * q^86 + 16 * q^87 + 32 * q^88 - 10 * q^89 - 2 * q^91 + 8 * q^92 + 26 * q^93 + 18 * q^94 - 38 * q^96 - 4 * q^97 + 2 * q^98 - 56 * 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 $

$2$	2.55311	1.80532	0.902659	−	0.430356i	$-0.141612\pi$
$2$	2.55311	1.80532	0.902659	+	0.430356i	$0.141612\pi$
$3$	−0.556415	−0.321246	−0.160623	−	0.987016i	$-0.551350\pi$
$3$	−0.556415	−0.321246	−0.160623	+	0.987016i	$0.551350\pi$
$4$	4.51835	2.25918
$5$	0	0
$5$	0	0
$6$	−1.42059	−0.579952
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	6.42962	2.27321
$9$	−2.69040	−0.896801
$10$	0	0
$11$	2.39863	0.723215	0.361607	−	0.932331i	$-0.382228\pi$
$11$	2.39863	0.723215	0.361607	+	0.932331i	$0.382228\pi$
$12$	−2.51408	−0.725752
$13$	−4.84612	−1.34407	−0.672036	−	0.740519i	$-0.734580\pi$
$13$	−4.84612	−1.34407	−0.672036	+	0.740519i	$0.734580\pi$
$14$	−2.55311	−0.682346
$15$	0	0
$16$	7.37879	1.84470
$17$	−7.58115	−1.83870	−0.919350	−	0.393441i	$-0.871285\pi$
$17$	−7.58115	−1.83870	−0.919350	+	0.393441i	$0.871285\pi$
$18$	−6.86888	−1.61901
$19$	−6.61505	−1.51760	−0.758798	−	0.651326i	$-0.774213\pi$
$19$	−6.61505	−1.51760	−0.758798	+	0.651326i	$0.774213\pi$
$20$	0	0
$21$	0.556415	0.121420
$22$	6.12396	1.30563
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−3.57753	−0.730261
$25$	0	0
$26$	−12.3727	−2.42648
$27$	3.16622	0.609340
$28$	−4.51835	−0.853888
$29$	−9.11387	−1.69240	−0.846202	−	0.532863i	$-0.821116\pi$
$29$	−9.11387	−1.69240	−0.846202	+	0.532863i	$0.821116\pi$
$30$	0	0
$31$	−6.28180	−1.12824	−0.564122	−	0.825691i	$-0.690785\pi$
$31$	−6.28180	−1.12824	−0.564122	+	0.825691i	$0.690785\pi$
$32$	5.97961	1.05706
$33$	−1.33463	−0.232330
$34$	−19.3555	−3.31944
$35$	0	0
$36$	−12.1562	−2.02603
$37$	6.57528	1.08097	0.540485	−	0.841354i	$-0.318241\pi$
$37$	6.57528	1.08097	0.540485	+	0.841354i	$0.318241\pi$
$38$	−16.8889	−2.73974
$39$	2.69645	0.431778
$40$	0	0
$41$	1.15847	0.180923	0.0904614	−	0.995900i	$-0.471166\pi$
$41$	1.15847	0.180923	0.0904614	+	0.995900i	$0.471166\pi$
$42$	1.42059	0.219201
$43$	6.33478	0.966044	0.483022	−	0.875608i	$-0.339539\pi$
$43$	6.33478	0.966044	0.483022	+	0.875608i	$0.339539\pi$
$44$	10.8379	1.63387
$45$	0	0
$46$	2.55311	0.376435
$47$	7.25371	1.05806	0.529031	−	0.848602i	$-0.322556\pi$
$47$	7.25371	1.05806	0.529031	+	0.848602i	$0.322556\pi$
$48$	−4.10567	−0.592602
$49$	1.00000	0.142857
$50$	0	0
$51$	4.21827	0.590676
$52$	−21.8965	−3.03649
$53$	−6.06923	−0.833673	−0.416837	−	0.908981i	$-0.636861\pi$
$53$	−6.06923	−0.833673	−0.416837	+	0.908981i	$0.636861\pi$
$54$	8.08371	1.10005
$55$	0	0
$56$	−6.42962	−0.859194
$57$	3.68071	0.487522
$58$	−23.2687	−3.05533
$59$	−1.85447	−0.241432	−0.120716	−	0.992687i	$-0.538519\pi$
$59$	−1.85447	−0.241432	−0.120716	+	0.992687i	$0.538519\pi$
$60$	0	0
$61$	2.62295	0.335834	0.167917	−	0.985801i	$-0.446296\pi$
$61$	2.62295	0.335834	0.167917	+	0.985801i	$0.446296\pi$
$62$	−16.0381	−2.03684
$63$	2.69040	0.338959
$64$	0.508984	0.0636230
$65$	0	0
$66$	−3.40746	−0.419430
$67$	4.02415	0.491628	0.245814	−	0.969317i	$-0.420945\pi$
$67$	4.02415	0.491628	0.245814	+	0.969317i	$0.420945\pi$
$68$	−34.2543	−4.15395
$69$	−0.556415	−0.0669845
$70$	0	0
$71$	8.33582	0.989279	0.494640	−	0.869098i	$-0.335300\pi$
$71$	8.33582	0.989279	0.494640	+	0.869098i	$0.335300\pi$
$72$	−17.2983	−2.03862
$73$	11.6930	1.36856	0.684282	−	0.729218i	$-0.260116\pi$
$73$	11.6930	1.36856	0.684282	+	0.729218i	$0.260116\pi$
$74$	16.7874	1.95150
$75$	0	0
$76$	−29.8891	−3.42852
$77$	−2.39863	−0.273349
$78$	6.88433	0.779497
$79$	−7.68708	−0.864864	−0.432432	−	0.901666i	$-0.642345\pi$
$79$	−7.68708	−0.864864	−0.432432	+	0.901666i	$0.642345\pi$
$80$	0	0
$81$	6.30947	0.701052
$82$	2.95770	0.326623
$83$	10.3338	1.13428	0.567142	−	0.823620i	$-0.308049\pi$
$83$	10.3338	1.13428	0.567142	+	0.823620i	$0.308049\pi$
$84$	2.51408	0.274308
$85$	0	0
$86$	16.1734	1.74402
$87$	5.07109	0.543678
$88$	15.4223	1.64402
$89$	−7.07788	−0.750253	−0.375127	−	0.926974i	$-0.622401\pi$
$89$	−7.07788	−0.750253	−0.375127	+	0.926974i	$0.622401\pi$
$90$	0	0
$91$	4.84612	0.508011
$92$	4.51835	0.471071
$93$	3.49529	0.362444
$94$	18.5195	1.91014
$95$	0	0
$96$	−3.32714	−0.339575
$97$	−11.3217	−1.14954	−0.574772	−	0.818314i	$-0.694909\pi$
$97$	−11.3217	−1.14954	−0.574772	+	0.818314i	$0.694909\pi$
$98$	2.55311	0.257903
$99$	−6.45328	−0.648579
$100$	0	0
$101$	11.7171	1.16590	0.582948	−	0.812509i	$-0.301899\pi$
$101$	11.7171	1.16590	0.582948	+	0.812509i	$0.301899\pi$
$102$	10.7697	1.06636
$103$	8.77477	0.864604	0.432302	−	0.901729i	$-0.357701\pi$
$103$	8.77477	0.864604	0.432302	+	0.901729i	$0.357701\pi$
$104$	−31.1587	−3.05536
$105$	0	0
$106$	−15.4954	−1.50505
$107$	12.6982	1.22758	0.613788	−	0.789471i	$-0.289645\pi$
$107$	12.6982	1.22758	0.613788	+	0.789471i	$0.289645\pi$
$108$	14.3061	1.37661
$109$	−8.01851	−0.768034	−0.384017	−	0.923326i	$-0.625460\pi$
$109$	−8.01851	−0.768034	−0.384017	+	0.923326i	$0.625460\pi$
$110$	0	0
$111$	−3.65859	−0.347258
$112$	−7.37879	−0.697230
$113$	−17.0556	−1.60446	−0.802228	−	0.597018i	$-0.796352\pi$
$113$	−17.0556	−1.60446	−0.802228	+	0.597018i	$0.796352\pi$
$114$	9.39725	0.880133
$115$	0	0
$116$	−41.1797	−3.82344
$117$	13.0380	1.20536
$118$	−4.73466	−0.435861
$119$	7.58115	0.694963
$120$	0	0
$121$	−5.24657	−0.476961
$122$	6.69667	0.606288
$123$	−0.644591	−0.0581208
$124$	−28.3834	−2.54890
$125$	0	0
$126$	6.86888	0.611929
$127$	−2.21683	−0.196712	−0.0983559	−	0.995151i	$-0.531358\pi$
$127$	−2.21683	−0.196712	−0.0983559	+	0.995151i	$0.531358\pi$
$128$	−10.6597	−0.942195
$129$	−3.52476	−0.310338
$130$	0	0
$131$	−16.1099	−1.40753	−0.703766	−	0.710432i	$-0.748500\pi$
$131$	−16.1099	−1.40753	−0.703766	+	0.710432i	$0.748500\pi$
$132$	−6.03035	−0.524874
$133$	6.61505	0.573597
$134$	10.2741	0.887546
$135$	0	0
$136$	−48.7439	−4.17976
$137$	−2.60560	−0.222611	−0.111306	−	0.993786i	$-0.535503\pi$
$137$	−2.60560	−0.222611	−0.111306	+	0.993786i	$0.535503\pi$
$138$	−1.42059	−0.120928
$139$	9.73547	0.825752	0.412876	−	0.910787i	$-0.364524\pi$
$139$	9.73547	0.825752	0.412876	+	0.910787i	$0.364524\pi$
$140$	0	0
$141$	−4.03607	−0.339899
$142$	21.2822	1.78596
$143$	−11.6240	−0.972052
$144$	−19.8519	−1.65433
$145$	0	0
$146$	29.8535	2.47069
$147$	−0.556415	−0.0458923
$148$	29.7094	2.44210
$149$	8.66017	0.709469	0.354735	−	0.934967i	$-0.384571\pi$
$149$	8.66017	0.709469	0.354735	+	0.934967i	$0.384571\pi$
$150$	0	0
$151$	−19.1408	−1.55766	−0.778830	−	0.627235i	$-0.784187\pi$
$151$	−19.1408	−1.55766	−0.778830	+	0.627235i	$0.784187\pi$
$152$	−42.5322	−3.44982
$153$	20.3964	1.64895
$154$	−6.12396	−0.493483
$155$	0	0
$156$	12.1835	0.975462
$157$	−17.5640	−1.40176	−0.700879	−	0.713280i	$-0.747209\pi$
$157$	−17.5640	−1.40176	−0.700879	+	0.713280i	$0.747209\pi$
$158$	−19.6259	−1.56136
$159$	3.37701	0.267814
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	16.1088	1.26562
$163$	−11.0659	−0.866748	−0.433374	−	0.901214i	$-0.642677\pi$
$163$	−11.0659	−0.866748	−0.433374	+	0.901214i	$0.642677\pi$
$164$	5.23438	0.408737
$165$	0	0
$166$	26.3833	2.04774
$167$	18.6038	1.43961	0.719803	−	0.694178i	$-0.244232\pi$
$167$	18.6038	1.43961	0.719803	+	0.694178i	$0.244232\pi$
$168$	3.57753	0.276013
$169$	10.4849	0.806527
$170$	0	0
$171$	17.7971	1.36098
$172$	28.6227	2.18246
$173$	−9.13648	−0.694634	−0.347317	−	0.937748i	$-0.612907\pi$
$173$	−9.13648	−0.694634	−0.347317	+	0.937748i	$0.612907\pi$
$174$	12.9470	0.981513
$175$	0	0
$176$	17.6990	1.33411
$177$	1.03186	0.0775590
$178$	−18.0706	−1.35445
$179$	12.3317	0.921715	0.460858	−	0.887474i	$-0.347542\pi$
$179$	12.3317	0.921715	0.460858	+	0.887474i	$0.347542\pi$
$180$	0	0
$181$	−21.4535	−1.59463	−0.797315	−	0.603564i	$-0.793747\pi$
$181$	−21.4535	−1.59463	−0.797315	+	0.603564i	$0.793747\pi$
$182$	12.3727	0.917122
$183$	−1.45945	−0.107886
$184$	6.42962	0.473998
$185$	0	0
$186$	8.92384	0.654328
$187$	−18.1844	−1.32977
$188$	32.7748	2.39035
$189$	−3.16622	−0.230309
$190$	0	0
$191$	3.59564	0.260172	0.130086	−	0.991503i	$-0.458475\pi$
$191$	3.59564	0.260172	0.130086	+	0.991503i	$0.458475\pi$
$192$	−0.283207	−0.0204387
$193$	18.2622	1.31454	0.657271	−	0.753654i	$-0.271711\pi$
$193$	18.2622	1.31454	0.657271	+	0.753654i	$0.271711\pi$
$194$	−28.9055	−2.07529
$195$	0	0
$196$	4.51835	0.322739
$197$	−14.1931	−1.01122	−0.505608	−	0.862763i	$-0.668732\pi$
$197$	−14.1931	−1.01122	−0.505608	+	0.862763i	$0.668732\pi$
$198$	−16.4759	−1.17089
$199$	4.51204	0.319850	0.159925	−	0.987129i	$-0.448875\pi$
$199$	4.51204	0.319850	0.159925	+	0.987129i	$0.448875\pi$
$200$	0	0
$201$	−2.23910	−0.157934
$202$	29.9150	2.10481
$203$	9.11387	0.639668
$204$	19.0596	1.33444
$205$	0	0
$206$	22.4029	1.56089
$207$	−2.69040	−0.186996
$208$	−35.7585	−2.47941
$209$	−15.8671	−1.09755
$210$	0	0
$211$	7.34658	0.505759	0.252880	−	0.967498i	$-0.418622\pi$
$211$	7.34658	0.505759	0.252880	+	0.967498i	$0.418622\pi$
$212$	−27.4229	−1.88341
$213$	−4.63817	−0.317802
$214$	32.4197	2.21617
$215$	0	0
$216$	20.3576	1.38516
$217$	6.28180	0.426436
$218$	−20.4721	−1.38655
$219$	−6.50616	−0.439646
$220$	0	0
$221$	36.7392	2.47134
$222$	−9.34076	−0.626911
$223$	4.90225	0.328279	0.164139	−	0.986437i	$-0.447515\pi$
$223$	4.90225	0.328279	0.164139	+	0.986437i	$0.447515\pi$
$224$	−5.97961	−0.399529
$225$	0	0
$226$	−43.5447	−2.89655
$227$	−16.9372	−1.12416	−0.562082	−	0.827082i	$-0.689999\pi$
$227$	−16.9372	−1.12416	−0.562082	+	0.827082i	$0.689999\pi$
$228$	16.6307	1.10140
$229$	−19.6566	−1.29894	−0.649472	−	0.760385i	$-0.725010\pi$
$229$	−19.6566	−1.29894	−0.649472	+	0.760385i	$0.725010\pi$
$230$	0	0
$231$	1.33463	0.0878125
$232$	−58.5987	−3.84719
$233$	−6.67050	−0.436999	−0.218499	−	0.975837i	$-0.570116\pi$
$233$	−6.67050	−0.436999	−0.218499	+	0.975837i	$0.570116\pi$
$234$	33.2874	2.17607
$235$	0	0
$236$	−8.37915	−0.545436
$237$	4.27721	0.277834
$238$	19.3555	1.25463
$239$	−0.0354864	−0.00229543	−0.00114771	−	0.999999i	$-0.500365\pi$
$239$	−0.0354864	−0.00229543	−0.00114771	+	0.999999i	$0.500365\pi$
$240$	0	0
$241$	−1.09229	−0.0703606	−0.0351803	−	0.999381i	$-0.511201\pi$
$241$	−1.09229	−0.0703606	−0.0351803	+	0.999381i	$0.511201\pi$
$242$	−13.3950	−0.861066
$243$	−13.0094	−0.834551
$244$	11.8514	0.758709
$245$	0	0
$246$	−1.64571	−0.104927
$247$	32.0573	2.03976
$248$	−40.3896	−2.56474
$249$	−5.74989	−0.364384
$250$	0	0
$251$	−23.6720	−1.49417	−0.747083	−	0.664731i	$-0.768546\pi$
$251$	−23.6720	−1.49417	−0.747083	+	0.664731i	$0.768546\pi$
$252$	12.1562	0.765767
$253$	2.39863	0.150801
$254$	−5.65980	−0.355127
$255$	0	0
$256$	−28.2334	−1.76459
$257$	−3.91454	−0.244182	−0.122091	−	0.992519i	$-0.538960\pi$
$257$	−3.91454	−0.244182	−0.122091	+	0.992519i	$0.538960\pi$
$258$	−8.99910	−0.560259
$259$	−6.57528	−0.408568
$260$	0	0
$261$	24.5200	1.51775
$262$	−41.1304	−2.54104
$263$	5.50533	0.339473	0.169737	−	0.985489i	$-0.445708\pi$
$263$	5.50533	0.339473	0.169737	+	0.985489i	$0.445708\pi$
$264$	−8.58119	−0.528136
$265$	0	0
$266$	16.8889	1.03553
$267$	3.93824	0.241016
$268$	18.1825	1.11067
$269$	−15.9298	−0.971256	−0.485628	−	0.874166i	$-0.661409\pi$
$269$	−15.9298	−0.971256	−0.485628	+	0.874166i	$0.661409\pi$
$270$	0	0
$271$	−1.10147	−0.0669098	−0.0334549	−	0.999440i	$-0.510651\pi$
$271$	−1.10147	−0.0669098	−0.0334549	+	0.999440i	$0.510651\pi$
$272$	−55.9398	−3.39185
$273$	−2.69645	−0.163197
$274$	−6.65236	−0.401884
$275$	0	0
$276$	−2.51408	−0.151330
$277$	10.8273	0.650550	0.325275	−	0.945619i	$-0.394543\pi$
$277$	10.8273	0.650550	0.325275	+	0.945619i	$0.394543\pi$
$278$	24.8557	1.49075
$279$	16.9006	1.01181
$280$	0	0
$281$	−7.30154	−0.435573	−0.217787	−	0.975996i	$-0.569884\pi$
$281$	−7.30154	−0.435573	−0.217787	+	0.975996i	$0.569884\pi$
$282$	−10.3045	−0.613625
$283$	−0.0752334	−0.00447216	−0.00223608	−	0.999997i	$-0.500712\pi$
$283$	−0.0752334	−0.00447216	−0.00223608	+	0.999997i	$0.500712\pi$
$284$	37.6641	2.23496
$285$	0	0
$286$	−29.6774	−1.75486
$287$	−1.15847	−0.0683824
$288$	−16.0875	−0.947968
$289$	40.4739	2.38082
$290$	0	0
$291$	6.29956	0.369287
$292$	52.8331	3.09182
$293$	8.45589	0.493998	0.246999	−	0.969016i	$-0.420556\pi$
$293$	8.45589	0.493998	0.246999	+	0.969016i	$0.420556\pi$
$294$	−1.42059	−0.0828503
$295$	0	0
$296$	42.2766	2.45728
$297$	7.59461	0.440684
$298$	22.1103	1.28082
$299$	−4.84612	−0.280258
$300$	0	0
$301$	−6.33478	−0.365130
$302$	−48.8686	−2.81207
$303$	−6.51958	−0.374540
$304$	−48.8111	−2.79951
$305$	0	0
$306$	52.0741	2.97688
$307$	−6.63813	−0.378858	−0.189429	−	0.981894i	$-0.560664\pi$
$307$	−6.63813	−0.378858	−0.189429	+	0.981894i	$0.560664\pi$
$308$	−10.8379	−0.617544
$309$	−4.88241	−0.277751
$310$	0	0
$311$	−8.68572	−0.492522	−0.246261	−	0.969204i	$-0.579202\pi$
$311$	−8.68572	−0.492522	−0.246261	+	0.969204i	$0.579202\pi$
$312$	17.3372	0.981523
$313$	8.46628	0.478543	0.239271	−	0.970953i	$-0.423091\pi$
$313$	8.46628	0.478543	0.239271	+	0.970953i	$0.423091\pi$
$314$	−44.8427	−2.53062
$315$	0	0
$316$	−34.7329	−1.95388
$317$	−24.7310	−1.38903	−0.694516	−	0.719477i	$-0.744382\pi$
$317$	−24.7310	−1.38903	−0.694516	+	0.719477i	$0.744382\pi$
$318$	8.62187	0.483490
$319$	−21.8608	−1.22397
$320$	0	0
$321$	−7.06544	−0.394355
$322$	−2.55311	−0.142279
$323$	50.1497	2.79040
$324$	28.5084	1.58380
$325$	0	0
$326$	−28.2524	−1.56476
$327$	4.46162	0.246728
$328$	7.44853	0.411276
$329$	−7.25371	−0.399910
$330$	0	0
$331$	−3.60235	−0.198003	−0.0990014	−	0.995087i	$-0.531565\pi$
$331$	−3.60235	−0.198003	−0.0990014	+	0.995087i	$0.531565\pi$
$332$	46.6918	2.56254
$333$	−17.6902	−0.969415
$334$	47.4975	2.59895
$335$	0	0
$336$	4.10567	0.223983
$337$	−20.7690	−1.13136	−0.565680	−	0.824625i	$-0.691386\pi$
$337$	−20.7690	−1.13136	−0.565680	+	0.824625i	$0.691386\pi$
$338$	26.7689	1.45604
$339$	9.48999	0.515425
$340$	0	0
$341$	−15.0677	−0.815963
$342$	45.4380	2.45700
$343$	−1.00000	−0.0539949
$344$	40.7302	2.19602
$345$	0	0
$346$	−23.3264	−1.25404
$347$	0.912986	0.0490116	0.0245058	−	0.999700i	$-0.492199\pi$
$347$	0.912986	0.0490116	0.0245058	+	0.999700i	$0.492199\pi$
$348$	22.9130	1.22826
$349$	16.0385	0.858519	0.429260	−	0.903181i	$-0.358775\pi$
$349$	16.0385	0.858519	0.429260	+	0.903181i	$0.358775\pi$
$350$	0	0
$351$	−15.3439	−0.818997
$352$	14.3429	0.764478
$353$	5.37419	0.286039	0.143020	−	0.989720i	$-0.454319\pi$
$353$	5.37419	0.286039	0.143020	+	0.989720i	$0.454319\pi$
$354$	2.63444	0.140019
$355$	0	0
$356$	−31.9803	−1.69495
$357$	−4.21827	−0.223254
$358$	31.4842	1.66399
$359$	15.0049	0.791931	0.395965	−	0.918265i	$-0.370410\pi$
$359$	15.0049	0.791931	0.395965	+	0.918265i	$0.370410\pi$
$360$	0	0
$361$	24.7589	1.30310
$362$	−54.7732	−2.87881
$363$	2.91927	0.153222
$364$	21.8965	1.14769
$365$	0	0
$366$	−3.72613	−0.194768
$367$	31.4760	1.64303	0.821516	−	0.570185i	$-0.193128\pi$
$367$	31.4760	1.64303	0.821516	+	0.570185i	$0.193128\pi$
$368$	7.37879	0.384646
$369$	−3.11676	−0.162252
$370$	0	0
$371$	6.06923	0.315099
$372$	15.7929	0.818826
$373$	−5.86759	−0.303812	−0.151906	−	0.988395i	$-0.548541\pi$
$373$	−5.86759	−0.303812	−0.151906	+	0.988395i	$0.548541\pi$
$374$	−46.4267	−2.40067
$375$	0	0
$376$	46.6386	2.40520
$377$	44.1669	2.27471
$378$	−8.08371	−0.415781
$379$	6.24615	0.320843	0.160422	−	0.987049i	$-0.448715\pi$
$379$	6.24615	0.320843	0.160422	+	0.987049i	$0.448715\pi$
$380$	0	0
$381$	1.23348	0.0631929
$382$	9.18006	0.469693
$383$	−17.1790	−0.877804	−0.438902	−	0.898535i	$-0.644633\pi$
$383$	−17.1790	−0.877804	−0.438902	+	0.898535i	$0.644633\pi$
$384$	5.93123	0.302677
$385$	0	0
$386$	46.6253	2.37317
$387$	−17.0431	−0.866349
$388$	−51.1554	−2.59702
$389$	−13.9602	−0.707811	−0.353906	−	0.935281i	$-0.615147\pi$
$389$	−13.9602	−0.707811	−0.353906	+	0.935281i	$0.615147\pi$
$390$	0	0
$391$	−7.58115	−0.383395
$392$	6.42962	0.324745
$393$	8.96381	0.452165
$394$	−36.2365	−1.82557
$395$	0	0
$396$	−29.1582	−1.46525
$397$	32.3964	1.62593	0.812965	−	0.582312i	$-0.197852\pi$
$397$	32.3964	1.62593	0.812965	+	0.582312i	$0.197852\pi$
$398$	11.5197	0.577432
$399$	−3.68071	−0.184266
$400$	0	0
$401$	−27.9539	−1.39595	−0.697976	−	0.716121i	$-0.745916\pi$
$401$	−27.9539	−1.39595	−0.697976	+	0.716121i	$0.745916\pi$
$402$	−5.71665	−0.285121
$403$	30.4423	1.51644
$404$	52.9420	2.63396
$405$	0	0
$406$	23.2687	1.15481
$407$	15.7717	0.781773
$408$	27.1218	1.34273
$409$	11.4146	0.564416	0.282208	−	0.959353i	$-0.408933\pi$
$409$	11.4146	0.564416	0.282208	+	0.959353i	$0.408933\pi$
$410$	0	0
$411$	1.44979	0.0715130
$412$	39.6475	1.95329
$413$	1.85447	0.0912526
$414$	−6.86888	−0.337587
$415$	0	0
$416$	−28.9779	−1.42076
$417$	−5.41696	−0.265270
$418$	−40.5103	−1.98142
$419$	−3.49523	−0.170753	−0.0853765	−	0.996349i	$-0.527209\pi$
$419$	−3.49523	−0.170753	−0.0853765	+	0.996349i	$0.527209\pi$
$420$	0	0
$421$	−14.9074	−0.726540	−0.363270	−	0.931684i	$-0.618340\pi$
$421$	−14.9074	−0.726540	−0.363270	+	0.931684i	$0.618340\pi$
$422$	18.7566	0.913057
$423$	−19.5154	−0.948871
$424$	−39.0228	−1.89512
$425$	0	0
$426$	−11.8417	−0.573735
$427$	−2.62295	−0.126933
$428$	57.3747	2.77331
$429$	6.46779	0.312268
$430$	0	0
$431$	−31.9400	−1.53850	−0.769248	−	0.638950i	$-0.779369\pi$
$431$	−31.9400	−1.53850	−0.769248	+	0.638950i	$0.779369\pi$
$432$	23.3629	1.12405
$433$	−8.72911	−0.419494	−0.209747	−	0.977756i	$-0.567264\pi$
$433$	−8.72911	−0.419494	−0.209747	+	0.977756i	$0.567264\pi$
$434$	16.0381	0.769854
$435$	0	0
$436$	−36.2305	−1.73512
$437$	−6.61505	−0.316441
$438$	−16.6109	−0.793701
$439$	−17.4679	−0.833696	−0.416848	−	0.908976i	$-0.636865\pi$
$439$	−17.4679	−0.833696	−0.416848	+	0.908976i	$0.636865\pi$
$440$	0	0
$441$	−2.69040	−0.128114
$442$	93.7990	4.46156
$443$	15.4253	0.732877	0.366439	−	0.930442i	$-0.380577\pi$
$443$	15.4253	0.732877	0.366439	+	0.930442i	$0.380577\pi$
$444$	−16.5308	−0.784516
$445$	0	0
$446$	12.5160	0.592648
$447$	−4.81865	−0.227914
$448$	−0.508984	−0.0240473
$449$	−14.0136	−0.661342	−0.330671	−	0.943746i	$-0.607275\pi$
$449$	−14.0136	−0.661342	−0.330671	+	0.943746i	$0.607275\pi$
$450$	0	0
$451$	2.77875	0.130846
$452$	−77.0631	−3.62475
$453$	10.6503	0.500393
$454$	−43.2426	−2.02947
$455$	0	0
$456$	23.6656	1.10824
$457$	35.7107	1.67048	0.835238	−	0.549888i	$-0.185330\pi$
$457$	35.7107	1.67048	0.835238	+	0.549888i	$0.185330\pi$
$458$	−50.1854	−2.34501
$459$	−24.0036	−1.12039
$460$	0	0
$461$	11.4775	0.534560	0.267280	−	0.963619i	$-0.413875\pi$
$461$	11.4775	0.534560	0.267280	+	0.963619i	$0.413875\pi$
$462$	3.40746	0.158530
$463$	−33.3987	−1.55217	−0.776084	−	0.630629i	$-0.782797\pi$
$463$	−33.3987	−1.55217	−0.776084	+	0.630629i	$0.782797\pi$
$464$	−67.2494	−3.12197
$465$	0	0
$466$	−17.0305	−0.788922
$467$	−7.56453	−0.350044	−0.175022	−	0.984564i	$-0.556000\pi$
$467$	−7.56453	−0.350044	−0.175022	+	0.984564i	$0.556000\pi$
$468$	58.9103	2.72313
$469$	−4.02415	−0.185818
$470$	0	0
$471$	9.77286	0.450310
$472$	−11.9235	−0.548826
$473$	15.1948	0.698657
$474$	10.9202	0.501580
$475$	0	0
$476$	34.2543	1.57004
$477$	16.3287	0.747639
$478$	−0.0906006	−0.00414397
$479$	8.81085	0.402578	0.201289	−	0.979532i	$-0.435487\pi$
$479$	8.81085	0.402578	0.201289	+	0.979532i	$0.435487\pi$
$480$	0	0
$481$	−31.8646	−1.45290
$482$	−2.78873	−0.127023
$483$	0.556415	0.0253178
$484$	−23.7058	−1.07754
$485$	0	0
$486$	−33.2143	−1.50663
$487$	36.3346	1.64648	0.823238	−	0.567696i	$-0.192165\pi$
$487$	36.3346	1.64648	0.823238	+	0.567696i	$0.192165\pi$
$488$	16.8646	0.763423
$489$	6.15723	0.278439
$490$	0	0
$491$	21.8649	0.986748	0.493374	−	0.869817i	$-0.335763\pi$
$491$	21.8649	0.986748	0.493374	+	0.869817i	$0.335763\pi$
$492$	−2.91249	−0.131305
$493$	69.0937	3.11182
$494$	81.8457	3.68241
$495$	0	0
$496$	−46.3521	−2.08127
$497$	−8.33582	−0.373912
$498$	−14.6801	−0.657830
$499$	39.2888	1.75881	0.879404	−	0.476075i	$-0.157941\pi$
$499$	39.2888	1.75881	0.879404	+	0.476075i	$0.157941\pi$
$500$	0	0
$501$	−10.3514	−0.462468
$502$	−60.4372	−2.69744
$503$	−23.4008	−1.04339	−0.521695	−	0.853132i	$-0.674700\pi$
$503$	−23.4008	−1.04339	−0.521695	+	0.853132i	$0.674700\pi$
$504$	17.2983	0.770526
$505$	0	0
$506$	6.12396	0.272243
$507$	−5.83393	−0.259094
$508$	−10.0164	−0.444406
$509$	3.22701	0.143035	0.0715173	−	0.997439i	$-0.477216\pi$
$509$	3.22701	0.143035	0.0715173	+	0.997439i	$0.477216\pi$
$510$	0	0
$511$	−11.6930	−0.517268
$512$	−50.7633	−2.24344
$513$	−20.9447	−0.924732
$514$	−9.99423	−0.440827
$515$	0	0
$516$	−15.9261	−0.701108
$517$	17.3990	0.765206
$518$	−16.7874	−0.737596
$519$	5.08368	0.223149
$520$	0	0
$521$	−9.22986	−0.404367	−0.202184	−	0.979348i	$-0.564804\pi$
$521$	−9.22986	−0.404367	−0.202184	+	0.979348i	$0.564804\pi$
$522$	62.6021	2.74002
$523$	12.4144	0.542845	0.271423	−	0.962460i	$-0.412506\pi$
$523$	12.4144	0.542845	0.271423	+	0.962460i	$0.412506\pi$
$524$	−72.7904	−3.17986
$525$	0	0
$526$	14.0557	0.612857
$527$	47.6233	2.07450
$528$	−9.84799	−0.428579
$529$	1.00000	0.0434783
$530$	0	0
$531$	4.98928	0.216516
$532$	29.8891	1.29586
$533$	−5.61409	−0.243173
$534$	10.0547	0.435111
$535$	0	0
$536$	25.8737	1.11758
$537$	−6.86155	−0.296098
$538$	−40.6704	−1.75343
$539$	2.39863	0.103316
$540$	0	0
$541$	31.3041	1.34587	0.672934	−	0.739702i	$-0.265034\pi$
$541$	31.3041	1.34587	0.672934	+	0.739702i	$0.265034\pi$
$542$	−2.81218	−0.120794
$543$	11.9371	0.512269
$544$	−45.3323	−1.94361
$545$	0	0
$546$	−6.88433	−0.294622
$547$	26.9245	1.15121	0.575604	−	0.817729i	$-0.304767\pi$
$547$	26.9245	1.15121	0.575604	+	0.817729i	$0.304767\pi$
$548$	−11.7730	−0.502918
$549$	−7.05679	−0.301176
$550$	0	0
$551$	60.2887	2.56838
$552$	−3.57753	−0.152270
$553$	7.68708	0.326888
$554$	27.6433	1.17445
$555$	0	0
$556$	43.9883	1.86552
$557$	−29.4637	−1.24842	−0.624209	−	0.781257i	$-0.714579\pi$
$557$	−29.4637	−1.24842	−0.624209	+	0.781257i	$0.714579\pi$
$558$	43.1490	1.82664
$559$	−30.6991	−1.29843
$560$	0	0
$561$	10.1181	0.427185
$562$	−18.6416	−0.786348
$563$	−25.0656	−1.05639	−0.528194	−	0.849124i	$-0.677131\pi$
$563$	−25.0656	−1.05639	−0.528194	+	0.849124i	$0.677131\pi$
$564$	−18.2364	−0.767890
$565$	0	0
$566$	−0.192079	−0.00807367
$567$	−6.30947	−0.264973
$568$	53.5961	2.24884
$569$	−25.7115	−1.07788	−0.538941	−	0.842343i	$-0.681175\pi$
$569$	−25.7115	−1.07788	−0.538941	+	0.842343i	$0.681175\pi$
$570$	0	0
$571$	−2.07458	−0.0868185	−0.0434092	−	0.999057i	$-0.513822\pi$
$571$	−2.07458	−0.0868185	−0.0434092	+	0.999057i	$0.513822\pi$
$572$	−52.5215	−2.19604
$573$	−2.00067	−0.0835792
$574$	−2.95770	−0.123452
$575$	0	0
$576$	−1.36937	−0.0570572
$577$	−3.01136	−0.125365	−0.0626823	−	0.998034i	$-0.519965\pi$
$577$	−3.01136	−0.125365	−0.0626823	+	0.998034i	$0.519965\pi$
$578$	103.334	4.29813
$579$	−10.1614	−0.422292
$580$	0	0
$581$	−10.3338	−0.428719
$582$	16.0834	0.666680
$583$	−14.5579	−0.602925
$584$	75.1816	3.11104
$585$	0	0
$586$	21.5888	0.891824
$587$	3.59243	0.148275	0.0741376	−	0.997248i	$-0.476380\pi$
$587$	3.59243	0.148275	0.0741376	+	0.997248i	$0.476380\pi$
$588$	−2.51408	−0.103679
$589$	41.5544	1.71222
$590$	0	0
$591$	7.89725	0.324849
$592$	48.5177	1.99406
$593$	36.4187	1.49554	0.747769	−	0.663959i	$-0.231125\pi$
$593$	36.4187	1.49554	0.747769	+	0.663959i	$0.231125\pi$
$594$	19.3898	0.795575
$595$	0	0
$596$	39.1297	1.60282
$597$	−2.51057	−0.102751
$598$	−12.3727	−0.505955
$599$	−33.1772	−1.35558	−0.677791	−	0.735254i	$-0.737063\pi$
$599$	−33.1772	−1.35558	−0.677791	+	0.735254i	$0.737063\pi$
$600$	0	0
$601$	2.77685	0.113270	0.0566351	−	0.998395i	$-0.481963\pi$
$601$	2.77685	0.113270	0.0566351	+	0.998395i	$0.481963\pi$
$602$	−16.1734	−0.659177
$603$	−10.8266	−0.440893
$604$	−86.4851	−3.51903
$605$	0	0
$606$	−16.6452	−0.676164
$607$	−19.9782	−0.810890	−0.405445	−	0.914119i	$-0.632883\pi$
$607$	−19.9782	−0.810890	−0.405445	+	0.914119i	$0.632883\pi$
$608$	−39.5554	−1.60418
$609$	−5.07109	−0.205491
$610$	0	0
$611$	−35.1523	−1.42211
$612$	92.1579	3.72526
$613$	25.3582	1.02421	0.512105	−	0.858923i	$-0.328866\pi$
$613$	25.3582	1.02421	0.512105	+	0.858923i	$0.328866\pi$
$614$	−16.9478	−0.683959
$615$	0	0
$616$	−15.4223	−0.621381
$617$	6.71196	0.270213	0.135107	−	0.990831i	$-0.456862\pi$
$617$	6.71196	0.270213	0.135107	+	0.990831i	$0.456862\pi$
$618$	−12.4653	−0.501429
$619$	−3.17312	−0.127538	−0.0637691	−	0.997965i	$-0.520312\pi$
$619$	−3.17312	−0.127538	−0.0637691	+	0.997965i	$0.520312\pi$
$620$	0	0
$621$	3.16622	0.127056
$622$	−22.1756	−0.889160
$623$	7.07788	0.283569
$624$	19.8966	0.796500
$625$	0	0
$626$	21.6153	0.863922
$627$	8.82867	0.352583
$628$	−79.3602	−3.16682
$629$	−49.8482	−1.98758
$630$	0	0
$631$	−33.4492	−1.33159	−0.665796	−	0.746134i	$-0.731908\pi$
$631$	−33.4492	−1.33159	−0.665796	+	0.746134i	$0.731908\pi$
$632$	−49.4250	−1.96602
$633$	−4.08775	−0.162473
$634$	−63.1409	−2.50765
$635$	0	0
$636$	15.2585	0.605040
$637$	−4.84612	−0.192010
$638$	−55.8130	−2.20966
$639$	−22.4267	−0.887187
$640$	0	0
$641$	−39.4564	−1.55843	−0.779217	−	0.626754i	$-0.784383\pi$
$641$	−39.4564	−1.55843	−0.779217	+	0.626754i	$0.784383\pi$
$642$	−18.0388	−0.711936
$643$	−27.7986	−1.09627	−0.548134	−	0.836390i	$-0.684662\pi$
$643$	−27.7986	−1.09627	−0.548134	+	0.836390i	$0.684662\pi$
$644$	−4.51835	−0.178048
$645$	0	0
$646$	128.038	5.03757
$647$	16.8410	0.662089	0.331044	−	0.943615i	$-0.392599\pi$
$647$	16.8410	0.662089	0.331044	+	0.943615i	$0.392599\pi$
$648$	40.5675	1.59364
$649$	−4.44819	−0.174607
$650$	0	0
$651$	−3.49529	−0.136991
$652$	−49.9996	−1.95813
$653$	32.9135	1.28801	0.644003	−	0.765023i	$-0.277273\pi$
$653$	32.9135	1.28801	0.644003	+	0.765023i	$0.277273\pi$
$654$	11.3910	0.445423
$655$	0	0
$656$	8.54812	0.333748
$657$	−31.4589	−1.22733
$658$	−18.5195	−0.721965
$659$	22.5217	0.877323	0.438661	−	0.898652i	$-0.355453\pi$
$659$	22.5217	0.877323	0.438661	+	0.898652i	$0.355453\pi$
$660$	0	0
$661$	−8.57652	−0.333588	−0.166794	−	0.985992i	$-0.553342\pi$
$661$	−8.57652	−0.333588	−0.166794	+	0.985992i	$0.553342\pi$
$662$	−9.19717	−0.357458
$663$	−20.4422	−0.793910
$664$	66.4424	2.57847
$665$	0	0
$666$	−45.1649	−1.75010
$667$	−9.11387	−0.352890
$668$	84.0585	3.25232
$669$	−2.72768	−0.105458
$670$	0	0
$671$	6.29149	0.242880
$672$	3.32714	0.128347
$673$	−10.8419	−0.417924	−0.208962	−	0.977924i	$-0.567008\pi$
$673$	−10.8419	−0.417924	−0.208962	+	0.977924i	$0.567008\pi$
$674$	−53.0255	−2.04247
$675$	0	0
$676$	47.3743	1.82209
$677$	20.6441	0.793418	0.396709	−	0.917944i	$-0.370152\pi$
$677$	20.6441	0.793418	0.396709	+	0.917944i	$0.370152\pi$
$678$	24.2289	0.930507
$679$	11.3217	0.434487
$680$	0	0
$681$	9.42413	0.361134
$682$	−38.4695	−1.47307
$683$	−46.9615	−1.79693	−0.898466	−	0.439043i	$-0.855318\pi$
$683$	−46.9615	−1.79693	−0.898466	+	0.439043i	$0.855318\pi$
$684$	80.4137	3.07470
$685$	0	0
$686$	−2.55311	−0.0974780
$687$	10.9372	0.417281
$688$	46.7430	1.78206
$689$	29.4122	1.12052
$690$	0	0
$691$	−30.4754	−1.15934	−0.579670	−	0.814851i	$-0.696819\pi$
$691$	−30.4754	−1.15934	−0.579670	+	0.814851i	$0.696819\pi$
$692$	−41.2818	−1.56930
$693$	6.45328	0.245140
$694$	2.33095	0.0884816
$695$	0	0
$696$	32.6052	1.23590
$697$	−8.78255	−0.332663
$698$	40.9479	1.54990
$699$	3.71157	0.140384
$700$	0	0
$701$	−27.3481	−1.03292	−0.516461	−	0.856311i	$-0.672751\pi$
$701$	−27.3481	−1.03292	−0.516461	+	0.856311i	$0.672751\pi$
$702$	−39.1746	−1.47855
$703$	−43.4958	−1.64048
$704$	1.22087	0.0460131
$705$	0	0
$706$	13.7209	0.516392
$707$	−11.7171	−0.440667
$708$	4.66229	0.175219
$709$	−14.9685	−0.562154	−0.281077	−	0.959685i	$-0.590692\pi$
$709$	−14.9685	−0.562154	−0.281077	+	0.959685i	$0.590692\pi$
$710$	0	0
$711$	20.6813	0.775611
$712$	−45.5080	−1.70549
$713$	−6.28180	−0.235255
$714$	−10.7697	−0.403045
$715$	0	0
$716$	55.7190	2.08232
$717$	0.0197452	0.000737397 0
$718$	38.3092	1.42969
$719$	−1.84235	−0.0687082	−0.0343541	−	0.999410i	$-0.510937\pi$
$719$	−1.84235	−0.0687082	−0.0343541	+	0.999410i	$0.510937\pi$
$720$	0	0
$721$	−8.77477	−0.326790
$722$	63.2120	2.35251
$723$	0.607766	0.0226031
$724$	−96.9347	−3.60255
$725$	0	0
$726$	7.45320	0.276614
$727$	−32.0335	−1.18806	−0.594029	−	0.804444i	$-0.702463\pi$
$727$	−32.0335	−1.18806	−0.594029	+	0.804444i	$0.702463\pi$
$728$	31.1587	1.15482
$729$	−11.6898	−0.432956
$730$	0	0
$731$	−48.0249	−1.77627
$732$	−6.59430	−0.243732
$733$	12.0485	0.445023	0.222512	−	0.974930i	$-0.428574\pi$
$733$	12.0485	0.445023	0.222512	+	0.974930i	$0.428574\pi$
$734$	80.3615	2.96620
$735$	0	0
$736$	5.97961	0.220411
$737$	9.65245	0.355553
$738$	−7.95741	−0.292916
$739$	−32.2795	−1.18742	−0.593710	−	0.804679i	$-0.702337\pi$
$739$	−32.2795	−1.18742	−0.593710	+	0.804679i	$0.702337\pi$
$740$	0	0
$741$	−17.8372	−0.655264
$742$	15.4954	0.568854
$743$	−19.8043	−0.726549	−0.363275	−	0.931682i	$-0.618341\pi$
$743$	−19.8043	−0.726549	−0.363275	+	0.931682i	$0.618341\pi$
$744$	22.4734	0.823913
$745$	0	0
$746$	−14.9806	−0.548478
$747$	−27.8021	−1.01723
$748$	−82.1635	−3.00419
$749$	−12.6982	−0.463980
$750$	0	0
$751$	7.71995	0.281705	0.140852	−	0.990031i	$-0.455016\pi$
$751$	7.71995	0.281705	0.140852	+	0.990031i	$0.455016\pi$
$752$	53.5236	1.95180
$753$	13.1715	0.479995
$754$	112.763	4.10658
$755$	0	0
$756$	−14.3061	−0.520308
$757$	20.2780	0.737015	0.368508	−	0.929625i	$-0.379869\pi$
$757$	20.2780	0.737015	0.368508	+	0.929625i	$0.379869\pi$
$758$	15.9471	0.579224
$759$	−1.33463	−0.0484442
$760$	0	0
$761$	9.04465	0.327868	0.163934	−	0.986471i	$-0.447582\pi$
$761$	9.04465	0.327868	0.163934	+	0.986471i	$0.447582\pi$
$762$	3.14920	0.114083
$763$	8.01851	0.290290
$764$	16.2464	0.587774
$765$	0	0
$766$	−43.8597	−1.58472
$767$	8.98699	0.324501
$768$	15.7095	0.566867
$769$	21.9807	0.792644	0.396322	−	0.918112i	$-0.370286\pi$
$769$	21.9807	0.792644	0.396322	+	0.918112i	$0.370286\pi$
$770$	0	0
$771$	2.17811	0.0784426
$772$	82.5150	2.96978
$773$	20.5383	0.738710	0.369355	−	0.929288i	$-0.379579\pi$
$773$	20.5383	0.738710	0.369355	+	0.929288i	$0.379579\pi$
$774$	−43.5128	−1.56404
$775$	0	0
$776$	−72.7941	−2.61316
$777$	3.65859	0.131251
$778$	−35.6419	−1.27782
$779$	−7.66335	−0.274568
$780$	0	0
$781$	19.9946	0.715461
$782$	−19.3555	−0.692151
$783$	−28.8566	−1.03125
$784$	7.37879	0.263528
$785$	0	0
$786$	22.8856	0.816301
$787$	13.0703	0.465907	0.232953	−	0.972488i	$-0.425161\pi$
$787$	13.0703	0.465907	0.232953	+	0.972488i	$0.425161\pi$
$788$	−64.1294	−2.28451
$789$	−3.06325	−0.109055
$790$	0	0
$791$	17.0556	0.606427
$792$	−41.4921	−1.47436
$793$	−12.7111	−0.451385
$794$	82.7115	2.93532
$795$	0	0
$796$	20.3870	0.722598
$797$	0.460080	0.0162969	0.00814843	−	0.999967i	$-0.497406\pi$
$797$	0.460080	0.0162969	0.00814843	+	0.999967i	$0.497406\pi$
$798$	−9.39725	−0.332659
$799$	−54.9915	−1.94546
$800$	0	0
$801$	19.0423	0.672828
$802$	−71.3694	−2.52014
$803$	28.0472	0.989765
$804$	−10.1170	−0.356800
$805$	0	0
$806$	77.7225	2.73766
$807$	8.86357	0.312012
$808$	75.3365	2.65033
$809$	−7.93788	−0.279081	−0.139541	−	0.990216i	$-0.544563\pi$
$809$	−7.93788	−0.279081	−0.139541	+	0.990216i	$0.544563\pi$
$810$	0	0
$811$	−39.1047	−1.37315	−0.686577	−	0.727058i	$-0.740887\pi$
$811$	−39.1047	−1.37315	−0.686577	+	0.727058i	$0.740887\pi$
$812$	41.1797	1.44512
$813$	0.612877	0.0214945
$814$	40.2668	1.41135
$815$	0	0
$816$	31.1257	1.08962
$817$	−41.9048	−1.46607
$818$	29.1427	1.01895
$819$	−13.0380	−0.455585
$820$	0	0
$821$	36.0726	1.25894	0.629471	−	0.777024i	$-0.283272\pi$
$821$	36.0726	1.25894	0.629471	+	0.777024i	$0.283272\pi$
$822$	3.70148	0.129104
$823$	−18.1192	−0.631594	−0.315797	−	0.948827i	$-0.602272\pi$
$823$	−18.1192	−0.631594	−0.315797	+	0.948827i	$0.602272\pi$
$824$	56.4184	1.96543
$825$	0	0
$826$	4.73466	0.164740
$827$	23.4452	0.815271	0.407635	−	0.913145i	$-0.366353\pi$
$827$	23.4452	0.815271	0.407635	+	0.913145i	$0.366353\pi$
$828$	−12.1562	−0.422457
$829$	6.56174	0.227899	0.113949	−	0.993487i	$-0.463650\pi$
$829$	6.56174	0.227899	0.113949	+	0.993487i	$0.463650\pi$
$830$	0	0
$831$	−6.02448	−0.208987
$832$	−2.46660	−0.0855139
$833$	−7.58115	−0.262671
$834$	−13.8301	−0.478896
$835$	0	0
$836$	−71.6929	−2.47955
$837$	−19.8896	−0.687485
$838$	−8.92368	−0.308264
$839$	38.5474	1.33080	0.665402	−	0.746485i	$-0.268260\pi$
$839$	38.5474	1.33080	0.665402	+	0.746485i	$0.268260\pi$
$840$	0	0
$841$	54.0626	1.86423
$842$	−38.0601	−1.31164
$843$	4.06268	0.139926
$844$	33.1944	1.14260
$845$	0	0
$846$	−49.8249	−1.71301
$847$	5.24657	0.180274
$848$	−44.7836	−1.53788
$849$	0.0418610	0.00143666
$850$	0	0
$851$	6.57528	0.225398
$852$	−20.9569	−0.717971
$853$	−26.3434	−0.901981	−0.450991	−	0.892529i	$-0.648929\pi$
$853$	−26.3434	−0.901981	−0.450991	+	0.892529i	$0.648929\pi$
$854$	−6.69667	−0.229155
$855$	0	0
$856$	81.6443	2.79054
$857$	37.3931	1.27732	0.638661	−	0.769488i	$-0.279489\pi$
$857$	37.3931	1.27732	0.638661	+	0.769488i	$0.279489\pi$
$858$	16.5130	0.563743
$859$	57.5901	1.96495	0.982475	−	0.186396i	$-0.0596808\pi$
$859$	57.5901	1.96495	0.982475	+	0.186396i	$0.0596808\pi$
$860$	0	0
$861$	0.644591	0.0219676
$862$	−81.5463	−2.77748
$863$	−4.83221	−0.164490	−0.0822452	−	0.996612i	$-0.526209\pi$
$863$	−4.83221	−0.164490	−0.0822452	+	0.996612i	$0.526209\pi$
$864$	18.9328	0.644106
$865$	0	0
$866$	−22.2864	−0.757321
$867$	−22.5203	−0.764829
$868$	28.3834	0.963395
$869$	−18.4385	−0.625482
$870$	0	0
$871$	−19.5015	−0.660783
$872$	−51.5560	−1.74591
$873$	30.4599	1.03091
$874$	−16.8889	−0.571276
$875$	0	0
$876$	−29.3971	−0.993237
$877$	−24.7083	−0.834340	−0.417170	−	0.908828i	$-0.636978\pi$
$877$	−24.7083	−0.834340	−0.417170	+	0.908828i	$0.636978\pi$
$878$	−44.5974	−1.50509
$879$	−4.70498	−0.158695
$880$	0	0
$881$	−12.1896	−0.410678	−0.205339	−	0.978691i	$-0.565830\pi$
$881$	−12.1896	−0.410678	−0.205339	+	0.978691i	$0.565830\pi$
$882$	−6.86888	−0.231287
$883$	31.0206	1.04393	0.521963	−	0.852968i	$-0.325200\pi$
$883$	31.0206	1.04393	0.521963	+	0.852968i	$0.325200\pi$
$884$	166.000	5.58320
$885$	0	0
$886$	39.3824	1.32308
$887$	24.7530	0.831123	0.415561	−	0.909565i	$-0.363585\pi$
$887$	24.7530	0.831123	0.415561	+	0.909565i	$0.363585\pi$
$888$	−23.5233	−0.789391
$889$	2.21683	0.0743501
$890$	0	0
$891$	15.1341	0.507011
$892$	22.1501	0.741639
$893$	−47.9836	−1.60571
$894$	−12.3025	−0.411458
$895$	0	0
$896$	10.6597	0.356116
$897$	2.69645	0.0900319
$898$	−35.7782	−1.19393
$899$	57.2515	1.90945
$900$	0	0
$901$	46.0118	1.53288
$902$	7.09443	0.236219
$903$	3.52476	0.117297
$904$	−109.661	−3.64727
$905$	0	0
$906$	27.1912	0.903368
$907$	−24.2117	−0.803937	−0.401968	−	0.915654i	$-0.631674\pi$
$907$	−24.2117	−0.803937	−0.401968	+	0.915654i	$0.631674\pi$
$908$	−76.5284	−2.53968
$909$	−31.5237	−1.04558
$910$	0	0
$911$	31.9352	1.05806	0.529030	−	0.848603i	$-0.322556\pi$
$911$	31.9352	1.05806	0.529030	+	0.848603i	$0.322556\pi$
$912$	27.1592	0.899331
$913$	24.7870	0.820330
$914$	91.1732	3.01574
$915$	0	0
$916$	−88.8154	−2.93454
$917$	16.1099	0.531997
$918$	−61.2838	−2.02267
$919$	−1.57722	−0.0520276	−0.0260138	−	0.999662i	$-0.508281\pi$
$919$	−1.57722	−0.0520276	−0.0260138	+	0.999662i	$0.508281\pi$
$920$	0	0
$921$	3.69355	0.121707
$922$	29.3033	0.965052
$923$	−40.3963	−1.32966
$924$	6.03035	0.198384
$925$	0	0
$926$	−85.2704	−2.80216
$927$	−23.6077	−0.775378
$928$	−54.4974	−1.78896
$929$	18.8607	0.618800	0.309400	−	0.950932i	$-0.399872\pi$
$929$	18.8607	0.618800	0.309400	+	0.950932i	$0.399872\pi$
$930$	0	0
$931$	−6.61505	−0.216799
$932$	−30.1397	−0.987257
$933$	4.83287	0.158221
$934$	−19.3130	−0.631942
$935$	0	0
$936$	83.8294	2.74005
$937$	−52.9837	−1.73090	−0.865451	−	0.500993i	$-0.832968\pi$
$937$	−52.9837	−1.73090	−0.865451	+	0.500993i	$0.832968\pi$
$938$	−10.2741	−0.335461
$939$	−4.71077	−0.153730
$940$	0	0
$941$	18.7258	0.610442	0.305221	−	0.952281i	$-0.401270\pi$
$941$	18.7258	0.610442	0.305221	+	0.952281i	$0.401270\pi$
$942$	24.9512	0.812953
$943$	1.15847	0.0377250
$944$	−13.6838	−0.445369
$945$	0	0
$946$	38.7939	1.26130
$947$	−20.9677	−0.681358	−0.340679	−	0.940180i	$-0.610657\pi$
$947$	−20.9677	−0.681358	−0.340679	+	0.940180i	$0.610657\pi$
$948$	19.3259	0.627677
$949$	−56.6657	−1.83945
$950$	0	0
$951$	13.7607	0.446222
$952$	48.7439	1.57980
$953$	−26.5392	−0.859688	−0.429844	−	0.902903i	$-0.641431\pi$
$953$	−26.5392	−0.859688	−0.429844	+	0.902903i	$0.641431\pi$
$954$	41.6888	1.34973
$955$	0	0
$956$	−0.160340	−0.00518577
$957$	12.1637	0.393196
$958$	22.4950	0.726781
$959$	2.60560	0.0841391
$960$	0	0
$961$	8.46102	0.272936
$962$	−81.3537	−2.62295
$963$	−34.1631	−1.10089
$964$	−4.93535	−0.158957
$965$	0	0
$966$	1.42059	0.0457066
$967$	−6.04387	−0.194358	−0.0971789	−	0.995267i	$-0.530982\pi$
$967$	−6.04387	−0.194358	−0.0971789	+	0.995267i	$0.530982\pi$
$968$	−33.7334	−1.08423
$969$	−27.9040	−0.896407
$970$	0	0
$971$	30.7528	0.986903	0.493451	−	0.869773i	$-0.335735\pi$
$971$	30.7528	0.986903	0.493451	+	0.869773i	$0.335735\pi$
$972$	−58.7809	−1.88540
$973$	−9.73547	−0.312105
$974$	92.7660	2.97242
$975$	0	0
$976$	19.3542	0.619513
$977$	53.7823	1.72065	0.860325	−	0.509746i	$-0.170261\pi$
$977$	53.7823	1.72065	0.860325	+	0.509746i	$0.170261\pi$
$978$	15.7201	0.502672
$979$	−16.9772	−0.542594
$980$	0	0
$981$	21.5730	0.688774
$982$	55.8233	1.78139
$983$	25.6689	0.818712	0.409356	−	0.912375i	$-0.365753\pi$
$983$	25.6689	0.818712	0.409356	+	0.912375i	$0.365753\pi$
$984$	−4.14447	−0.132121
$985$	0	0
$986$	176.403	5.61783
$987$	4.03607	0.128470
$988$	144.846	4.60817
$989$	6.33478	0.201434
$990$	0	0
$991$	−38.4490	−1.22137	−0.610687	−	0.791872i	$-0.709107\pi$
$991$	−38.4490	−1.22137	−0.610687	+	0.791872i	$0.709107\pi$
$992$	−37.5627	−1.19262
$993$	2.00440	0.0636077
$994$	−21.2822	−0.675031
$995$	0	0
$996$	−25.9800	−0.823208
$997$	−21.3414	−0.675888	−0.337944	−	0.941166i	$-0.609731\pi$
$997$	−21.3414	−0.675888	−0.337944	+	0.941166i	$0.609731\pi$
$998$	100.309	3.17521
$999$	20.8188	0.658679

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.y.1.12		12
5.2	odd	4		805.2.c.b.484.24	yes	24
5.3	odd	4		805.2.c.b.484.1	✓	24
5.4	even	2		4025.2.a.x.1.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.c.b.484.1	✓	24	5.3	odd	4
805.2.c.b.484.24	yes	24	5.2	odd	4
4025.2.a.x.1.1		12	5.4	even	2
4025.2.a.y.1.12		12	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+2.55311 q^{2} -0.556415 q^{3} +4.51835 q^{4} -1.42059 q^{6} -1.00000 q^{7} +6.42962 q^{8} -2.69040 q^{9} +O(q^{10})\)	\(q+2.55311 q^{2} -0.556415 q^{3} +4.51835 q^{4} -1.42059 q^{6} -1.00000 q^{7} +6.42962 q^{8} -2.69040 q^{9} +2.39863 q^{11} -2.51408 q^{12} -4.84612 q^{13} -2.55311 q^{14} +7.37879 q^{16} -7.58115 q^{17} -6.86888 q^{18} -6.61505 q^{19} +0.556415 q^{21} +6.12396 q^{22} +1.00000 q^{23} -3.57753 q^{24} -12.3727 q^{26} +3.16622 q^{27} -4.51835 q^{28} -9.11387 q^{29} -6.28180 q^{31} +5.97961 q^{32} -1.33463 q^{33} -19.3555 q^{34} -12.1562 q^{36} +6.57528 q^{37} -16.8889 q^{38} +2.69645 q^{39} +1.15847 q^{41} +1.42059 q^{42} +6.33478 q^{43} +10.8379 q^{44} +2.55311 q^{46} +7.25371 q^{47} -4.10567 q^{48} +1.00000 q^{49} +4.21827 q^{51} -21.8965 q^{52} -6.06923 q^{53} +8.08371 q^{54} -6.42962 q^{56} +3.68071 q^{57} -23.2687 q^{58} -1.85447 q^{59} +2.62295 q^{61} -16.0381 q^{62} +2.69040 q^{63} +0.508984 q^{64} -3.40746 q^{66} +4.02415 q^{67} -34.2543 q^{68} -0.556415 q^{69} +8.33582 q^{71} -17.2983 q^{72} +11.6930 q^{73} +16.7874 q^{74} -29.8891 q^{76} -2.39863 q^{77} +6.88433 q^{78} -7.68708 q^{79} +6.30947 q^{81} +2.95770 q^{82} +10.3338 q^{83} +2.51408 q^{84} +16.1734 q^{86} +5.07109 q^{87} +15.4223 q^{88} -7.07788 q^{89} +4.84612 q^{91} +4.51835 q^{92} +3.49529 q^{93} +18.5195 q^{94} -3.32714 q^{96} -11.3217 q^{97} +2.55311 q^{98} -6.45328 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 8 q^{4} - 6 q^{6} - 12 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 + 8 * q^4 - 6 * q^6 - 12 * q^7 + 6 * q^8 + 8 * q^9	\( 12 q + 2 q^{2} + 8 q^{4} - 6 q^{6} - 12 q^{7} + 6 q^{8} + 8 q^{9} - 8 q^{11} - 12 q^{12} + 2 q^{13} - 2 q^{14} - 4 q^{16} - 8 q^{17} + 20 q^{18} - 26 q^{19} + 4 q^{22} + 12 q^{23} - 12 q^{24} - 22 q^{26} + 12 q^{27} - 8 q^{28} - 12 q^{29} - 50 q^{31} + 14 q^{32} + 4 q^{33} - 28 q^{34} - 18 q^{36} + 8 q^{37} - 4 q^{38} - 26 q^{39} - 4 q^{41} + 6 q^{42} + 26 q^{43} - 10 q^{44} + 2 q^{46} + 16 q^{47} - 40 q^{48} + 12 q^{49} - 32 q^{51} + 10 q^{52} - 18 q^{53} - 10 q^{54} - 6 q^{56} - 10 q^{57} - 18 q^{58} - 18 q^{59} + 8 q^{61} - 54 q^{62} - 8 q^{63} + 12 q^{64} - 2 q^{66} + 38 q^{67} - 36 q^{68} - 24 q^{71} + 18 q^{72} - 14 q^{73} + 36 q^{74} - 56 q^{76} + 8 q^{77} - 26 q^{78} - 44 q^{79} - 16 q^{81} - 44 q^{82} - 14 q^{83} + 12 q^{84} - 32 q^{86} + 16 q^{87} + 32 q^{88} - 10 q^{89} - 2 q^{91} + 8 q^{92} + 26 q^{93} + 18 q^{94} - 38 q^{96} - 4 q^{97} + 2 q^{98} - 56 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 8 * q^4 - 6 * q^6 - 12 * q^7 + 6 * q^8 + 8 * q^9 - 8 * q^11 - 12 * q^12 + 2 * q^13 - 2 * q^14 - 4 * q^16 - 8 * q^17 + 20 * q^18 - 26 * q^19 + 4 * q^22 + 12 * q^23 - 12 * q^24 - 22 * q^26 + 12 * q^27 - 8 * q^28 - 12 * q^29 - 50 * q^31 + 14 * q^32 + 4 * q^33 - 28 * q^34 - 18 * q^36 + 8 * q^37 - 4 * q^38 - 26 * q^39 - 4 * q^41 + 6 * q^42 + 26 * q^43 - 10 * q^44 + 2 * q^46 + 16 * q^47 - 40 * q^48 + 12 * q^49 - 32 * q^51 + 10 * q^52 - 18 * q^53 - 10 * q^54 - 6 * q^56 - 10 * q^57 - 18 * q^58 - 18 * q^59 + 8 * q^61 - 54 * q^62 - 8 * q^63 + 12 * q^64 - 2 * q^66 + 38 * q^67 - 36 * q^68 - 24 * q^71 + 18 * q^72 - 14 * q^73 + 36 * q^74 - 56 * q^76 + 8 * q^77 - 26 * q^78 - 44 * q^79 - 16 * q^81 - 44 * q^82 - 14 * q^83 + 12 * q^84 - 32 * q^86 + 16 * q^87 + 32 * q^88 - 10 * q^89 - 2 * q^91 + 8 * q^92 + 26 * q^93 + 18 * q^94 - 38 * q^96 - 4 * q^97 + 2 * q^98 - 56 * q^99

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